Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.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: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.4 | ||
Root | \(206.667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.10.b.a.16.3 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.7531 | −0.740388 | −0.370194 | − | 0.928954i | \(-0.620709\pi\) | ||||
−0.370194 | + | 0.928954i | \(0.620709\pi\) | |||||||
\(3\) | 206.667i | 1.47308i | 0.676396 | + | 0.736538i | \(0.263541\pi\) | ||||
−0.676396 | + | 0.736538i | \(0.736459\pi\) | |||||||
\(4\) | −231.335 | −0.451825 | ||||||||
\(5\) | 1946.29i | 1.39265i | 0.717726 | + | 0.696326i | \(0.245183\pi\) | ||||
−0.717726 | + | 0.696326i | \(0.754817\pi\) | |||||||
\(6\) | − | 3462.30i | − | 1.09065i | ||||||
\(7\) | 1633.30i | 0.257114i | 0.991702 | + | 0.128557i | \(0.0410345\pi\) | ||||
−0.991702 | + | 0.128557i | \(0.958966\pi\) | |||||||
\(8\) | 12453.1 | 1.07491 | ||||||||
\(9\) | −23028.2 | −1.16995 | ||||||||
\(10\) | − | 32606.3i | − | 1.03110i | ||||||
\(11\) | − | 11623.3i | − | 0.239365i | −0.992812 | − | 0.119683i | \(-0.961812\pi\) | ||
0.992812 | − | 0.119683i | \(-0.0381877\pi\) | |||||||
\(12\) | − | 47809.2i | − | 0.665573i | ||||||
\(13\) | −163541. | −1.58811 | −0.794057 | − | 0.607844i | \(-0.792035\pi\) | ||||
−0.794057 | + | 0.607844i | \(0.792035\pi\) | |||||||
\(14\) | − | 27362.8i | − | 0.190364i | ||||||
\(15\) | −402234. | −2.05148 | ||||||||
\(16\) | −90185.0 | −0.344028 | ||||||||
\(17\) | 255165. | − | 231255.i | 0.740970 | − | 0.671538i | ||||
\(18\) | 385793. | 0.866219 | ||||||||
\(19\) | 673499. | 1.18562 | 0.592810 | − | 0.805342i | \(-0.298019\pi\) | ||||
0.592810 | + | 0.805342i | \(0.298019\pi\) | |||||||
\(20\) | − | 450244.i | − | 0.629236i | ||||||
\(21\) | −337549. | −0.378748 | ||||||||
\(22\) | 194725.i | 0.177223i | ||||||||
\(23\) | 1.37499e6i | 1.02453i | 0.858828 | + | 0.512264i | \(0.171193\pi\) | ||||
−0.858828 | + | 0.512264i | \(0.828807\pi\) | |||||||
\(24\) | 2.57365e6i | 1.58343i | ||||||||
\(25\) | −1.83492e6 | −0.939480 | ||||||||
\(26\) | 2.73981e6 | 1.17582 | ||||||||
\(27\) | − | 691336.i | − | 0.250353i | ||||||
\(28\) | − | 377839.i | − | 0.116171i | ||||||
\(29\) | − | 4.32926e6i | − | 1.13664i | −0.822808 | − | 0.568320i | \(-0.807594\pi\) | ||
0.822808 | − | 0.568320i | \(-0.192406\pi\) | |||||||
\(30\) | 6.73865e6 | 1.51889 | ||||||||
\(31\) | 3.45219e6i | 0.671378i | 0.941973 | + | 0.335689i | \(0.108969\pi\) | ||||
−0.941973 | + | 0.335689i | \(0.891031\pi\) | |||||||
\(32\) | −4.86513e6 | −0.820200 | ||||||||
\(33\) | 2.40214e6 | 0.352603 | ||||||||
\(34\) | −4.27479e6 | + | 3.87423e6i | −0.548605 | + | 0.497199i | ||||
\(35\) | −3.17888e6 | −0.358070 | ||||||||
\(36\) | 5.32721e6 | 0.528614 | ||||||||
\(37\) | − | 5.81427e6i | − | 0.510020i | −0.966938 | − | 0.255010i | \(-0.917921\pi\) | ||
0.966938 | − | 0.255010i | \(-0.0820788\pi\) | |||||||
\(38\) | −1.12832e7 | −0.877819 | ||||||||
\(39\) | − | 3.37985e7i | − | 2.33941i | ||||||
\(40\) | 2.42374e7i | 1.49698i | ||||||||
\(41\) | 2.37653e7i | 1.31346i | 0.754127 | + | 0.656729i | \(0.228060\pi\) | ||||
−0.754127 | + | 0.656729i | \(0.771940\pi\) | |||||||
\(42\) | 5.65499e6 | 0.280421 | ||||||||
\(43\) | −2.46177e7 | −1.09810 | −0.549048 | − | 0.835791i | \(-0.685010\pi\) | ||||
−0.549048 | + | 0.835791i | \(0.685010\pi\) | |||||||
\(44\) | 2.68886e6i | 0.108151i | ||||||||
\(45\) | − | 4.48195e7i | − | 1.62934i | ||||||
\(46\) | − | 2.30353e7i | − | 0.758549i | ||||||
\(47\) | −3.94057e7 | −1.17793 | −0.588963 | − | 0.808160i | \(-0.700464\pi\) | ||||
−0.588963 | + | 0.808160i | \(0.700464\pi\) | |||||||
\(48\) | − | 1.86382e7i | − | 0.506780i | ||||||
\(49\) | 3.76859e7 | 0.933893 | ||||||||
\(50\) | 3.07406e7 | 0.695580 | ||||||||
\(51\) | 4.77927e7 | + | 5.27341e7i | 0.989227 | + | 1.09150i | ||||
\(52\) | 3.78327e7 | 0.717550 | ||||||||
\(53\) | −9.66929e7 | −1.68327 | −0.841634 | − | 0.540048i | \(-0.818406\pi\) | ||||
−0.841634 | + | 0.540048i | \(0.818406\pi\) | |||||||
\(54\) | 1.15820e7i | 0.185358i | ||||||||
\(55\) | 2.26222e7 | 0.333352 | ||||||||
\(56\) | 2.03397e7i | 0.276375i | ||||||||
\(57\) | 1.39190e8i | 1.74651i | ||||||||
\(58\) | 7.25285e7i | 0.841555i | ||||||||
\(59\) | 2.37253e7 | 0.254905 | 0.127453 | − | 0.991845i | \(-0.459320\pi\) | ||||
0.127453 | + | 0.991845i | \(0.459320\pi\) | |||||||
\(60\) | 9.30506e7 | 0.926912 | ||||||||
\(61\) | 4.31637e7i | 0.399149i | 0.979883 | + | 0.199574i | \(0.0639559\pi\) | ||||
−0.979883 | + | 0.199574i | \(0.936044\pi\) | |||||||
\(62\) | − | 5.78348e7i | − | 0.497080i | ||||||
\(63\) | − | 3.76120e7i | − | 0.300811i | ||||||
\(64\) | 1.27681e8 | 0.951295 | ||||||||
\(65\) | − | 3.18298e8i | − | 2.21169i | ||||||
\(66\) | −4.02432e7 | −0.261063 | ||||||||
\(67\) | 3.50040e7 | 0.212217 | 0.106109 | − | 0.994355i | \(-0.466161\pi\) | ||||
0.106109 | + | 0.994355i | \(0.466161\pi\) | |||||||
\(68\) | −5.90284e7 | + | 5.34973e7i | −0.334789 | + | 0.303418i | ||||
\(69\) | −2.84165e8 | −1.50921 | ||||||||
\(70\) | 5.32560e7 | 0.265111 | ||||||||
\(71\) | − | 2.90407e8i | − | 1.35626i | −0.734940 | − | 0.678132i | \(-0.762790\pi\) | ||
0.734940 | − | 0.678132i | \(-0.237210\pi\) | |||||||
\(72\) | −2.86773e8 | −1.25760 | ||||||||
\(73\) | 4.29259e8i | 1.76916i | 0.466392 | + | 0.884578i | \(0.345554\pi\) | ||||
−0.466392 | + | 0.884578i | \(0.654446\pi\) | |||||||
\(74\) | 9.74069e7i | 0.377613i | ||||||||
\(75\) | − | 3.79217e8i | − | 1.38392i | ||||||
\(76\) | −1.55804e8 | −0.535693 | ||||||||
\(77\) | 1.89843e7 | 0.0615440 | ||||||||
\(78\) | 5.66229e8i | 1.73207i | ||||||||
\(79\) | − | 3.78639e8i | − | 1.09371i | −0.837226 | − | 0.546856i | \(-0.815824\pi\) | ||
0.837226 | − | 0.546856i | \(-0.184176\pi\) | |||||||
\(80\) | − | 1.75526e8i | − | 0.479112i | ||||||
\(81\) | −3.10387e8 | −0.801164 | ||||||||
\(82\) | − | 3.98142e8i | − | 0.972468i | ||||||
\(83\) | 9.91655e7 | 0.229355 | 0.114678 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114678 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(84\) | 7.80868e7 | 0.171128 | ||||||||
\(85\) | 4.50089e8 | + | 4.96625e8i | 0.935219 | + | 1.03191i | ||||
\(86\) | 4.12423e8 | 0.813017 | ||||||||
\(87\) | 8.94715e8 | 1.67436 | ||||||||
\(88\) | − | 1.44746e8i | − | 0.257297i | ||||||
\(89\) | −5.39631e8 | −0.911679 | −0.455840 | − | 0.890062i | \(-0.650661\pi\) | ||||
−0.455840 | + | 0.890062i | \(0.650661\pi\) | |||||||
\(90\) | 7.50864e8i | 1.20634i | ||||||||
\(91\) | − | 2.67112e8i | − | 0.408326i | ||||||
\(92\) | − | 3.18083e8i | − | 0.462908i | ||||||
\(93\) | −7.13453e8 | −0.988991 | ||||||||
\(94\) | 6.60166e8 | 0.872123 | ||||||||
\(95\) | 1.31082e9i | 1.65116i | ||||||||
\(96\) | − | 1.00546e9i | − | 1.20822i | ||||||
\(97\) | 1.21632e9i | 1.39500i | 0.716582 | + | 0.697502i | \(0.245705\pi\) | ||||
−0.716582 | + | 0.697502i | \(0.754295\pi\) | |||||||
\(98\) | −6.31355e8 | −0.691443 | ||||||||
\(99\) | 2.67662e8i | 0.280046i | ||||||||
\(100\) | 4.24481e8 | 0.424481 | ||||||||
\(101\) | 1.24853e9 | 1.19386 | 0.596928 | − | 0.802295i | \(-0.296388\pi\) | ||||
0.596928 | + | 0.802295i | \(0.296388\pi\) | |||||||
\(102\) | −8.00675e8 | − | 8.83458e8i | −0.732412 | − | 0.808137i | ||||
\(103\) | 5.96498e7 | 0.0522206 | 0.0261103 | − | 0.999659i | \(-0.491688\pi\) | ||||
0.0261103 | + | 0.999659i | \(0.491688\pi\) | |||||||
\(104\) | −2.03660e9 | −1.70709 | ||||||||
\(105\) | − | 6.56969e8i | − | 0.527464i | ||||||
\(106\) | 1.61990e9 | 1.24627 | ||||||||
\(107\) | − | 1.08084e9i | − | 0.797143i | −0.917137 | − | 0.398572i | \(-0.869506\pi\) | ||
0.917137 | − | 0.398572i | \(-0.130494\pi\) | |||||||
\(108\) | 1.59930e8i | 0.113116i | ||||||||
\(109\) | 1.42610e9i | 0.967678i | 0.875157 | + | 0.483839i | \(0.160758\pi\) | ||||
−0.875157 | + | 0.483839i | \(0.839242\pi\) | |||||||
\(110\) | −3.78992e8 | −0.246810 | ||||||||
\(111\) | 1.20162e9 | 0.751299 | ||||||||
\(112\) | − | 1.47299e8i | − | 0.0884544i | ||||||
\(113\) | − | 4.16774e8i | − | 0.240463i | −0.992746 | − | 0.120231i | \(-0.961636\pi\) | ||
0.992746 | − | 0.120231i | \(-0.0383636\pi\) | |||||||
\(114\) | − | 2.33186e9i | − | 1.29309i | ||||||
\(115\) | −2.67613e9 | −1.42681 | ||||||||
\(116\) | 1.00151e9i | 0.513563i | ||||||||
\(117\) | 3.76605e9 | 1.85802 | ||||||||
\(118\) | −3.97472e8 | −0.188729 | ||||||||
\(119\) | 3.77709e8 | + | 4.16761e8i | 0.172662 | + | 0.190514i | ||||
\(120\) | −5.00907e9 | −2.20517 | ||||||||
\(121\) | 2.22285e9 | 0.942704 | ||||||||
\(122\) | − | 7.23125e8i | − | 0.295525i | ||||||
\(123\) | −4.91150e9 | −1.93482 | ||||||||
\(124\) | − | 7.98611e8i | − | 0.303346i | ||||||
\(125\) | 2.30059e8i | 0.0842839i | ||||||||
\(126\) | 6.30116e8i | 0.222717i | ||||||||
\(127\) | 3.27631e8 | 0.111755 | 0.0558777 | − | 0.998438i | \(-0.482204\pi\) | ||||
0.0558777 | + | 0.998438i | \(0.482204\pi\) | |||||||
\(128\) | 3.51905e8 | 0.115873 | ||||||||
\(129\) | − | 5.08767e9i | − | 1.61758i | ||||||
\(130\) | 5.33247e9i | 1.63751i | ||||||||
\(131\) | 3.69810e8i | 0.109713i | 0.998494 | + | 0.0548565i | \(0.0174701\pi\) | ||||
−0.998494 | + | 0.0548565i | \(0.982530\pi\) | |||||||
\(132\) | −5.55698e8 | −0.159315 | ||||||||
\(133\) | 1.10003e9i | 0.304839i | ||||||||
\(134\) | −5.86424e8 | −0.157123 | ||||||||
\(135\) | 1.34554e9 | 0.348654 | ||||||||
\(136\) | 3.17760e9 | − | 2.87985e9i | 0.796479 | − | 0.721846i | ||||
\(137\) | 1.59553e9 | 0.386957 | 0.193478 | − | 0.981105i | \(-0.438023\pi\) | ||||
0.193478 | + | 0.981105i | \(0.438023\pi\) | |||||||
\(138\) | 4.76063e9 | 1.11740 | ||||||||
\(139\) | 6.26171e9i | 1.42274i | 0.702817 | + | 0.711371i | \(0.251925\pi\) | ||||
−0.702817 | + | 0.711371i | \(0.748075\pi\) | |||||||
\(140\) | 7.35385e8 | 0.161785 | ||||||||
\(141\) | − | 8.14384e9i | − | 1.73518i | ||||||
\(142\) | 4.86521e9i | 1.00416i | ||||||||
\(143\) | 1.90088e9i | 0.380139i | ||||||||
\(144\) | 2.07679e9 | 0.402497 | ||||||||
\(145\) | 8.42600e9 | 1.58294 | ||||||||
\(146\) | − | 7.19140e9i | − | 1.30986i | ||||||
\(147\) | 7.78843e9i | 1.37569i | ||||||||
\(148\) | 1.34504e9i | 0.230440i | ||||||||
\(149\) | −6.90664e9 | −1.14796 | −0.573982 | − | 0.818868i | \(-0.694602\pi\) | ||||
−0.573982 | + | 0.818868i | \(0.694602\pi\) | |||||||
\(150\) | 6.35305e9i | 1.02464i | ||||||||
\(151\) | −8.82900e9 | −1.38202 | −0.691012 | − | 0.722843i | \(-0.742835\pi\) | ||||
−0.691012 | + | 0.722843i | \(0.742835\pi\) | |||||||
\(152\) | 8.38717e9 | 1.27444 | ||||||||
\(153\) | −5.87598e9 | + | 5.32538e9i | −0.866899 | + | 0.785668i | ||||
\(154\) | −3.18045e8 | −0.0455665 | ||||||||
\(155\) | −6.71897e9 | −0.934996 | ||||||||
\(156\) | 7.81876e9i | 1.05701i | ||||||||
\(157\) | 6.94492e8 | 0.0912261 | 0.0456130 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456130 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(158\) | 6.34336e9i | 0.809772i | ||||||||
\(159\) | − | 1.99832e10i | − | 2.47958i | ||||||
\(160\) | − | 9.46896e9i | − | 1.14225i | ||||||
\(161\) | −2.24577e9 | −0.263420 | ||||||||
\(162\) | 5.19994e9 | 0.593172 | ||||||||
\(163\) | − | 1.05314e10i | − | 1.16854i | −0.811559 | − | 0.584270i | \(-0.801381\pi\) | ||
0.811559 | − | 0.584270i | \(-0.198619\pi\) | |||||||
\(164\) | − | 5.49774e9i | − | 0.593454i | ||||||
\(165\) | 4.67526e9i | 0.491053i | ||||||||
\(166\) | −1.66133e9 | −0.169812 | ||||||||
\(167\) | − | 1.06743e10i | − | 1.06198i | −0.847378 | − | 0.530990i | \(-0.821820\pi\) | ||
0.847378 | − | 0.530990i | \(-0.178180\pi\) | |||||||
\(168\) | −4.20355e9 | −0.407122 | ||||||||
\(169\) | 1.61412e10 | 1.52210 | ||||||||
\(170\) | −7.54038e9 | − | 8.31999e9i | −0.692425 | − | 0.764016i | ||||
\(171\) | −1.55094e10 | −1.38712 | ||||||||
\(172\) | 5.69494e9 | 0.496148 | ||||||||
\(173\) | 5.38138e9i | 0.456758i | 0.973572 | + | 0.228379i | \(0.0733425\pi\) | ||||
−0.973572 | + | 0.228379i | \(0.926657\pi\) | |||||||
\(174\) | −1.49892e10 | −1.23967 | ||||||||
\(175\) | − | 2.99698e9i | − | 0.241553i | ||||||
\(176\) | 1.04824e9i | 0.0823484i | ||||||||
\(177\) | 4.90324e9i | 0.375494i | ||||||||
\(178\) | 9.04048e9 | 0.674996 | ||||||||
\(179\) | −1.10785e10 | −0.806573 | −0.403286 | − | 0.915074i | \(-0.632132\pi\) | ||||
−0.403286 | + | 0.915074i | \(0.632132\pi\) | |||||||
\(180\) | 1.03683e10i | 0.736176i | ||||||||
\(181\) | 1.10717e10i | 0.766761i | 0.923591 | + | 0.383380i | \(0.125240\pi\) | ||||
−0.923591 | + | 0.383380i | \(0.874760\pi\) | |||||||
\(182\) | 4.47494e9i | 0.302320i | ||||||||
\(183\) | −8.92051e9 | −0.587976 | ||||||||
\(184\) | 1.71229e10i | 1.10128i | ||||||||
\(185\) | 1.13163e10 | 0.710281 | ||||||||
\(186\) | 1.19525e10 | 0.732237 | ||||||||
\(187\) | −2.68793e9 | − | 2.96584e9i | −0.160743 | − | 0.177362i | ||||
\(188\) | 9.11589e9 | 0.532217 | ||||||||
\(189\) | 1.12916e9 | 0.0643691 | ||||||||
\(190\) | − | 2.19603e10i | − | 1.22250i | ||||||
\(191\) | 1.39536e10 | 0.758642 | 0.379321 | − | 0.925265i | \(-0.376158\pi\) | ||||
0.379321 | + | 0.925265i | \(0.376158\pi\) | |||||||
\(192\) | 2.63873e10i | 1.40133i | ||||||||
\(193\) | − | 4.25693e9i | − | 0.220845i | −0.993885 | − | 0.110423i | \(-0.964780\pi\) | ||
0.993885 | − | 0.110423i | \(-0.0352205\pi\) | |||||||
\(194\) | − | 2.03771e10i | − | 1.03285i | ||||||
\(195\) | 6.57817e10 | 3.25799 | ||||||||
\(196\) | −8.71806e9 | −0.421956 | ||||||||
\(197\) | 3.75774e10i | 1.77758i | 0.458317 | + | 0.888789i | \(0.348452\pi\) | ||||
−0.458317 | + | 0.888789i | \(0.651548\pi\) | |||||||
\(198\) | − | 4.48417e9i | − | 0.207342i | ||||||
\(199\) | − | 8.68102e9i | − | 0.392403i | −0.980564 | − | 0.196201i | \(-0.937139\pi\) | ||
0.980564 | − | 0.196201i | \(-0.0628606\pi\) | |||||||
\(200\) | −2.28505e10 | −1.00986 | ||||||||
\(201\) | 7.23416e9i | 0.312612i | ||||||||
\(202\) | −2.09167e10 | −0.883916 | ||||||||
\(203\) | 7.07099e9 | 0.292246 | ||||||||
\(204\) | −1.10561e10 | − | 1.21992e10i | −0.446958 | − | 0.493170i | ||||
\(205\) | −4.62542e10 | −1.82919 | ||||||||
\(206\) | −9.99318e8 | −0.0386635 | ||||||||
\(207\) | − | 3.16635e10i | − | 1.19865i | ||||||
\(208\) | 1.47489e10 | 0.546356 | ||||||||
\(209\) | − | 7.82825e9i | − | 0.283796i | ||||||
\(210\) | 1.10062e10i | 0.390528i | ||||||||
\(211\) | 3.93859e10i | 1.36795i | 0.729507 | + | 0.683974i | \(0.239750\pi\) | ||||
−0.729507 | + | 0.683974i | \(0.760250\pi\) | |||||||
\(212\) | 2.23684e10 | 0.760543 | ||||||||
\(213\) | 6.00175e10 | 1.99788 | ||||||||
\(214\) | 1.81075e10i | 0.590195i | ||||||||
\(215\) | − | 4.79133e10i | − | 1.52927i | ||||||
\(216\) | − | 8.60930e9i | − | 0.269108i | ||||||
\(217\) | −5.63847e9 | −0.172621 | ||||||||
\(218\) | − | 2.38916e10i | − | 0.716457i | ||||||
\(219\) | −8.87135e10 | −2.60610 | ||||||||
\(220\) | −5.23330e9 | −0.150617 | ||||||||
\(221\) | −4.17299e10 | + | 3.78197e10i | −1.17674 | + | 1.06648i | ||||
\(222\) | −2.01308e10 | −0.556253 | ||||||||
\(223\) | 2.60341e9 | 0.0704971 | 0.0352486 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352486 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(224\) | − | 7.94623e9i | − | 0.210885i | ||||||
\(225\) | 4.22549e10 | 1.09915 | ||||||||
\(226\) | 6.98225e9i | 0.178036i | ||||||||
\(227\) | 6.62728e10i | 1.65660i | 0.560282 | + | 0.828302i | \(0.310693\pi\) | ||||
−0.560282 | + | 0.828302i | \(0.689307\pi\) | |||||||
\(228\) | − | 3.21994e10i | − | 0.789117i | ||||||
\(229\) | −1.37362e10 | −0.330071 | −0.165036 | − | 0.986288i | \(-0.552774\pi\) | ||||
−0.165036 | + | 0.986288i | \(0.552774\pi\) | |||||||
\(230\) | 4.48334e10 | 1.05639 | ||||||||
\(231\) | 3.92342e9i | 0.0906590i | ||||||||
\(232\) | − | 5.39129e10i | − | 1.22179i | ||||||
\(233\) | 8.93389e9i | 0.198582i | 0.995058 | + | 0.0992908i | \(0.0316574\pi\) | ||||
−0.995058 | + | 0.0992908i | \(0.968343\pi\) | |||||||
\(234\) | −6.30929e10 | −1.37565 | ||||||||
\(235\) | − | 7.66948e10i | − | 1.64044i | ||||||
\(236\) | −5.48849e9 | −0.115173 | ||||||||
\(237\) | 7.82521e10 | 1.61112 | ||||||||
\(238\) | −6.32779e9 | − | 6.98203e9i | −0.127837 | − | 0.141054i | ||||
\(239\) | 1.31552e10 | 0.260800 | 0.130400 | − | 0.991461i | \(-0.458374\pi\) | ||||
0.130400 | + | 0.991461i | \(0.458374\pi\) | |||||||
\(240\) | 3.62754e10 | 0.705768 | ||||||||
\(241\) | − | 3.35182e9i | − | 0.0640036i | −0.999488 | − | 0.0320018i | \(-0.989812\pi\) | ||
0.999488 | − | 0.0320018i | \(-0.0101882\pi\) | |||||||
\(242\) | −3.72395e10 | −0.697967 | ||||||||
\(243\) | − | 7.77543e10i | − | 1.43053i | ||||||
\(244\) | − | 9.98526e9i | − | 0.180346i | ||||||
\(245\) | 7.33478e10i | 1.30059i | ||||||||
\(246\) | 8.22827e10 | 1.43252 | ||||||||
\(247\) | −1.10145e11 | −1.88290 | ||||||||
\(248\) | 4.29906e10i | 0.721674i | ||||||||
\(249\) | 2.04942e10i | 0.337858i | ||||||||
\(250\) | − | 3.85420e9i | − | 0.0624028i | ||||||
\(251\) | −1.16052e9 | −0.0184553 | −0.00922766 | − | 0.999957i | \(-0.502937\pi\) | ||||
−0.00922766 | + | 0.999957i | \(0.502937\pi\) | |||||||
\(252\) | 8.70095e9i | 0.135914i | ||||||||
\(253\) | 1.59819e10 | 0.245236 | ||||||||
\(254\) | −5.48883e9 | −0.0827424 | ||||||||
\(255\) | −1.02636e11 | + | 9.30185e10i | −1.52009 | + | 1.37765i | ||||
\(256\) | −7.12680e10 | −1.03709 | ||||||||
\(257\) | 1.16697e11 | 1.66864 | 0.834319 | − | 0.551282i | \(-0.185861\pi\) | ||||
0.834319 | + | 0.551282i | \(0.185861\pi\) | |||||||
\(258\) | 8.52341e10i | 1.19764i | ||||||||
\(259\) | 9.49646e9 | 0.131133 | ||||||||
\(260\) | 7.36334e10i | 0.999298i | ||||||||
\(261\) | 9.96950e10i | 1.32981i | ||||||||
\(262\) | − | 6.19546e9i | − | 0.0812302i | ||||||
\(263\) | 1.29675e11 | 1.67130 | 0.835652 | − | 0.549259i | \(-0.185090\pi\) | ||||
0.835652 | + | 0.549259i | \(0.185090\pi\) | |||||||
\(264\) | 2.99142e10 | 0.379018 | ||||||||
\(265\) | − | 1.88193e11i | − | 2.34421i | ||||||
\(266\) | − | 1.84288e10i | − | 0.225699i | ||||||
\(267\) | − | 1.11524e11i | − | 1.34297i | ||||||
\(268\) | −8.09763e9 | −0.0958852 | ||||||||
\(269\) | − | 4.33626e10i | − | 0.504928i | −0.967606 | − | 0.252464i | \(-0.918759\pi\) | ||
0.967606 | − | 0.252464i | \(-0.0812410\pi\) | |||||||
\(270\) | −2.25419e10 | −0.258139 | ||||||||
\(271\) | 1.14864e11 | 1.29367 | 0.646834 | − | 0.762631i | \(-0.276093\pi\) | ||||
0.646834 | + | 0.762631i | \(0.276093\pi\) | |||||||
\(272\) | −2.30120e10 | + | 2.08557e10i | −0.254915 | + | 0.231028i | ||||
\(273\) | 5.52032e10 | 0.601495 | ||||||||
\(274\) | −2.67300e10 | −0.286498 | ||||||||
\(275\) | 2.13278e10i | 0.224879i | ||||||||
\(276\) | 6.57371e10 | 0.681899 | ||||||||
\(277\) | 9.76316e10i | 0.996395i | 0.867064 | + | 0.498197i | \(0.166004\pi\) | ||||
−0.867064 | + | 0.498197i | \(0.833996\pi\) | |||||||
\(278\) | − | 1.04903e11i | − | 1.05338i | ||||||
\(279\) | − | 7.94977e10i | − | 0.785481i | ||||||
\(280\) | −3.95870e10 | −0.384895 | ||||||||
\(281\) | 1.09933e11 | 1.05184 | 0.525921 | − | 0.850534i | \(-0.323721\pi\) | ||||
0.525921 | + | 0.850534i | \(0.323721\pi\) | |||||||
\(282\) | 1.36434e11i | 1.28470i | ||||||||
\(283\) | 1.55506e11i | 1.44115i | 0.693378 | + | 0.720574i | \(0.256122\pi\) | ||||
−0.693378 | + | 0.720574i | \(0.743878\pi\) | |||||||
\(284\) | 6.71812e10i | 0.612795i | ||||||||
\(285\) | −2.70904e11 | −2.43228 | ||||||||
\(286\) | − | 3.18456e10i | − | 0.281450i | ||||||
\(287\) | −3.88159e10 | −0.337708 | ||||||||
\(288\) | 1.12035e11 | 0.959595 | ||||||||
\(289\) | 1.16302e10 | − | 1.18016e11i | 0.0980726 | − | 0.995179i | ||||
\(290\) | −1.41161e11 | −1.17199 | ||||||||
\(291\) | −2.51373e11 | −2.05495 | ||||||||
\(292\) | − | 9.93024e10i | − | 0.799350i | ||||||
\(293\) | −1.34231e11 | −1.06402 | −0.532010 | − | 0.846738i | \(-0.678563\pi\) | ||||
−0.532010 | + | 0.846738i | \(0.678563\pi\) | |||||||
\(294\) | − | 1.30480e11i | − | 1.01855i | ||||||
\(295\) | 4.61764e10i | 0.354994i | ||||||||
\(296\) | − | 7.24059e10i | − | 0.548228i | ||||||
\(297\) | −8.03557e9 | −0.0599257 | ||||||||
\(298\) | 1.15707e11 | 0.849939 | ||||||||
\(299\) | − | 2.24867e11i | − | 1.62707i | ||||||
\(300\) | 8.77261e10i | 0.625292i | ||||||||
\(301\) | − | 4.02082e10i | − | 0.282336i | ||||||
\(302\) | 1.47913e11 | 1.02323 | ||||||||
\(303\) | 2.58029e11i | 1.75864i | ||||||||
\(304\) | −6.07394e10 | −0.407887 | ||||||||
\(305\) | −8.40091e10 | −0.555875 | ||||||||
\(306\) | 9.84407e10 | − | 8.92164e10i | 0.641842 | − | 0.581699i | ||||
\(307\) | −1.61753e11 | −1.03927 | −0.519637 | − | 0.854387i | \(-0.673933\pi\) | ||||
−0.519637 | + | 0.854387i | \(0.673933\pi\) | |||||||
\(308\) | −4.39172e9 | −0.0278072 | ||||||||
\(309\) | 1.23276e10i | 0.0769249i | ||||||||
\(310\) | 1.12563e11 | 0.692260 | ||||||||
\(311\) | − | 8.13115e10i | − | 0.492867i | −0.969160 | − | 0.246434i | \(-0.920741\pi\) | ||
0.969160 | − | 0.246434i | \(-0.0792587\pi\) | |||||||
\(312\) | − | 4.20897e11i | − | 2.51467i | ||||||
\(313\) | 1.35663e11i | 0.798935i | 0.916747 | + | 0.399467i | \(0.130805\pi\) | ||||
−0.916747 | + | 0.399467i | \(0.869195\pi\) | |||||||
\(314\) | −1.16349e10 | −0.0675427 | ||||||||
\(315\) | 7.32038e10 | 0.418925 | ||||||||
\(316\) | 8.75923e10i | 0.494167i | ||||||||
\(317\) | − | 1.13377e11i | − | 0.630604i | −0.948991 | − | 0.315302i | \(-0.897894\pi\) | ||
0.948991 | − | 0.315302i | \(-0.102106\pi\) | |||||||
\(318\) | 3.34780e11i | 1.83585i | ||||||||
\(319\) | −5.03201e10 | −0.272072 | ||||||||
\(320\) | 2.48504e11i | 1.32482i | ||||||||
\(321\) | 2.23375e11 | 1.17425 | ||||||||
\(322\) | 3.76236e10 | 0.195033 | ||||||||
\(323\) | 1.71853e11 | − | 1.55750e11i | 0.878509 | − | 0.796189i | ||||
\(324\) | 7.18033e10 | 0.361986 | ||||||||
\(325\) | 3.00085e11 | 1.49200 | ||||||||
\(326\) | 1.76434e11i | 0.865173i | ||||||||
\(327\) | −2.94728e11 | −1.42546 | ||||||||
\(328\) | 2.95953e11i | 1.41185i | ||||||||
\(329\) | − | 6.43613e10i | − | 0.302861i | ||||||
\(330\) | − | 7.83250e10i | − | 0.363570i | ||||||
\(331\) | 1.63912e11 | 0.750557 | 0.375279 | − | 0.926912i | \(-0.377547\pi\) | ||||
0.375279 | + | 0.926912i | \(0.377547\pi\) | |||||||
\(332\) | −2.29404e10 | −0.103629 | ||||||||
\(333\) | 1.33892e11i | 0.596699i | ||||||||
\(334\) | 1.78828e11i | 0.786277i | ||||||||
\(335\) | 6.81279e10i | 0.295545i | ||||||||
\(336\) | 3.04419e10 | 0.130300 | ||||||||
\(337\) | 1.21263e11i | 0.512146i | 0.966657 | + | 0.256073i | \(0.0824288\pi\) | ||||
−0.966657 | + | 0.256073i | \(0.917571\pi\) | |||||||
\(338\) | −2.70414e11 | −1.12695 | ||||||||
\(339\) | 8.61334e10 | 0.354220 | ||||||||
\(340\) | −1.04121e11 | − | 1.14886e11i | −0.422556 | − | 0.466245i | ||||
\(341\) | 4.01257e10 | 0.160704 | ||||||||
\(342\) | 2.59831e11 | 1.02701 | ||||||||
\(343\) | 1.27462e11i | 0.497230i | ||||||||
\(344\) | −3.06568e11 | −1.18036 | ||||||||
\(345\) | − | 5.53067e11i | − | 2.10180i | ||||||
\(346\) | − | 9.01547e10i | − | 0.338178i | ||||||
\(347\) | − | 9.25071e10i | − | 0.342525i | −0.985225 | − | 0.171263i | \(-0.945215\pi\) | ||
0.985225 | − | 0.171263i | \(-0.0547846\pi\) | |||||||
\(348\) | −2.06979e11 | −0.756517 | ||||||||
\(349\) | −1.54729e11 | −0.558285 | −0.279143 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279143 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(350\) | 5.02086e10i | 0.178843i | ||||||||
\(351\) | 1.13062e11i | 0.397588i | ||||||||
\(352\) | 5.65487e10i | 0.196327i | ||||||||
\(353\) | −7.41434e9 | −0.0254148 | −0.0127074 | − | 0.999919i | \(-0.504045\pi\) | ||||
−0.0127074 | + | 0.999919i | \(0.504045\pi\) | |||||||
\(354\) | − | 8.21443e10i | − | 0.278012i | ||||||
\(355\) | 5.65216e11 | 1.88881 | ||||||||
\(356\) | 1.24835e11 | 0.411920 | ||||||||
\(357\) | −8.61307e10 | + | 7.80599e10i | −0.280641 | + | 0.254344i | ||||
\(358\) | 1.85599e11 | 0.597177 | ||||||||
\(359\) | −3.11894e11 | −0.991019 | −0.495509 | − | 0.868603i | \(-0.665019\pi\) | ||||
−0.495509 | + | 0.868603i | \(0.665019\pi\) | |||||||
\(360\) | − | 5.58143e11i | − | 1.75140i | ||||||
\(361\) | 1.30913e11 | 0.405694 | ||||||||
\(362\) | − | 1.85485e11i | − | 0.567701i | ||||||
\(363\) | 4.59389e11i | 1.38868i | ||||||||
\(364\) | 6.17922e10i | 0.184492i | ||||||||
\(365\) | −8.35462e11 | −2.46382 | ||||||||
\(366\) | 1.49446e11 | 0.435331 | ||||||||
\(367\) | − | 3.42287e11i | − | 0.984902i | −0.870340 | − | 0.492451i | \(-0.836101\pi\) | ||
0.870340 | − | 0.492451i | \(-0.163899\pi\) | |||||||
\(368\) | − | 1.24003e11i | − | 0.352467i | ||||||
\(369\) | − | 5.47272e11i | − | 1.53668i | ||||||
\(370\) | −1.89582e11 | −0.525883 | ||||||||
\(371\) | − | 1.57929e11i | − | 0.432791i | ||||||
\(372\) | 1.65046e11 | 0.446851 | ||||||||
\(373\) | 2.39957e11 | 0.641866 | 0.320933 | − | 0.947102i | \(-0.396004\pi\) | ||||
0.320933 | + | 0.947102i | \(0.396004\pi\) | |||||||
\(374\) | 4.50312e10 | + | 4.96870e10i | 0.119012 | + | 0.131317i | ||||
\(375\) | −4.75456e10 | −0.124157 | ||||||||
\(376\) | −4.90724e11 | −1.26617 | ||||||||
\(377\) | 7.08012e11i | 1.80511i | ||||||||
\(378\) | −1.89169e10 | −0.0476581 | ||||||||
\(379\) | 7.31981e11i | 1.82231i | 0.412060 | + | 0.911157i | \(0.364809\pi\) | ||||
−0.412060 | + | 0.911157i | \(0.635191\pi\) | |||||||
\(380\) | − | 3.03239e11i | − | 0.746034i | ||||||
\(381\) | 6.77105e10i | 0.164624i | ||||||||
\(382\) | −2.33766e11 | −0.561689 | ||||||||
\(383\) | −3.51103e10 | −0.0833758 | −0.0416879 | − | 0.999131i | \(-0.513274\pi\) | ||||
−0.0416879 | + | 0.999131i | \(0.513274\pi\) | |||||||
\(384\) | 7.27271e10i | 0.170689i | ||||||||
\(385\) | 3.69489e10i | 0.0857094i | ||||||||
\(386\) | 7.13166e10i | 0.163511i | ||||||||
\(387\) | 5.66902e11 | 1.28472 | ||||||||
\(388\) | − | 2.81377e11i | − | 0.630299i | ||||||
\(389\) | −4.06726e10 | −0.0900593 | −0.0450297 | − | 0.998986i | \(-0.514338\pi\) | ||||
−0.0450297 | + | 0.998986i | \(0.514338\pi\) | |||||||
\(390\) | −1.10205e12 | −2.41217 | ||||||||
\(391\) | 3.17973e11 | + | 3.50849e11i | 0.688010 | + | 0.759145i | ||||
\(392\) | 4.69308e11 | 1.00385 | ||||||||
\(393\) | −7.64275e10 | −0.161616 | ||||||||
\(394\) | − | 6.29537e11i | − | 1.31610i | ||||||
\(395\) | 7.36941e11 | 1.52316 | ||||||||
\(396\) | − | 6.19196e10i | − | 0.126532i | ||||||
\(397\) | 8.82945e11i | 1.78392i | 0.452110 | + | 0.891962i | \(0.350672\pi\) | ||||
−0.452110 | + | 0.891962i | \(0.649328\pi\) | |||||||
\(398\) | 1.45434e11i | 0.290530i | ||||||||
\(399\) | −2.27339e11 | −0.449051 | ||||||||
\(400\) | 1.65482e11 | 0.323208 | ||||||||
\(401\) | − | 5.06461e11i | − | 0.978130i | −0.872247 | − | 0.489065i | \(-0.837338\pi\) | ||
0.872247 | − | 0.489065i | \(-0.162662\pi\) | |||||||
\(402\) | − | 1.21194e11i | − | 0.231454i | ||||||
\(403\) | − | 5.64575e11i | − | 1.06622i | ||||||
\(404\) | −2.88827e11 | −0.539414 | ||||||||
\(405\) | − | 6.04104e11i | − | 1.11574i | ||||||
\(406\) | −1.18461e11 | −0.216375 | ||||||||
\(407\) | −6.75807e10 | −0.122081 | ||||||||
\(408\) | 5.95169e11 | + | 6.56705e11i | 1.06333 | + | 1.17327i | ||||
\(409\) | 5.97268e11 | 1.05539 | 0.527697 | − | 0.849433i | \(-0.323056\pi\) | ||||
0.527697 | + | 0.849433i | \(0.323056\pi\) | |||||||
\(410\) | 7.74900e11 | 1.35431 | ||||||||
\(411\) | 3.29743e11i | 0.570016i | ||||||||
\(412\) | −1.37991e10 | −0.0235946 | ||||||||
\(413\) | 3.87506e10i | 0.0655396i | ||||||||
\(414\) | 5.30461e11i | 0.887466i | ||||||||
\(415\) | 1.93005e11i | 0.319412i | ||||||||
\(416\) | 7.95648e11 | 1.30257 | ||||||||
\(417\) | −1.29409e12 | −2.09581 | ||||||||
\(418\) | 1.31147e11i | 0.210119i | ||||||||
\(419\) | − | 6.76816e11i | − | 1.07277i | −0.843972 | − | 0.536386i | \(-0.819789\pi\) | ||
0.843972 | − | 0.536386i | \(-0.180211\pi\) | |||||||
\(420\) | 1.51980e11i | 0.238322i | ||||||||
\(421\) | 4.95533e11 | 0.768782 | 0.384391 | − | 0.923170i | \(-0.374411\pi\) | ||||
0.384391 | + | 0.923170i | \(0.374411\pi\) | |||||||
\(422\) | − | 6.59834e11i | − | 1.01281i | ||||||
\(423\) | 9.07440e11 | 1.37812 | ||||||||
\(424\) | −1.20413e12 | −1.80937 | ||||||||
\(425\) | −4.68207e11 | + | 4.24334e11i | −0.696126 | + | 0.630897i | ||||
\(426\) | −1.00548e12 | −1.47921 | ||||||||
\(427\) | −7.04994e10 | −0.102627 | ||||||||
\(428\) | 2.50037e11i | 0.360169i | ||||||||
\(429\) | −3.92849e11 | −0.559973 | ||||||||
\(430\) | 8.02695e11i | 1.13225i | ||||||||
\(431\) | − | 1.02852e11i | − | 0.143571i | −0.997420 | − | 0.0717854i | \(-0.977130\pi\) | ||
0.997420 | − | 0.0717854i | \(-0.0228697\pi\) | |||||||
\(432\) | 6.23481e10i | 0.0861284i | ||||||||
\(433\) | −2.70612e10 | −0.0369957 | −0.0184978 | − | 0.999829i | \(-0.505888\pi\) | ||||
−0.0184978 | + | 0.999829i | \(0.505888\pi\) | |||||||
\(434\) | 9.44617e10 | 0.127806 | ||||||||
\(435\) | 1.74138e12i | 2.33180i | ||||||||
\(436\) | − | 3.29906e11i | − | 0.437222i | ||||||
\(437\) | 9.26053e11i | 1.21470i | ||||||||
\(438\) | 1.48622e12 | 1.92953 | ||||||||
\(439\) | − | 5.59050e11i | − | 0.718390i | −0.933263 | − | 0.359195i | \(-0.883051\pi\) | ||
0.933263 | − | 0.359195i | \(-0.116949\pi\) | |||||||
\(440\) | 2.81718e11 | 0.358325 | ||||||||
\(441\) | −8.67838e11 | −1.09261 | ||||||||
\(442\) | 6.99104e11 | − | 6.33595e11i | 0.871247 | − | 0.789608i | ||||
\(443\) | 4.39616e11 | 0.542321 | 0.271161 | − | 0.962534i | \(-0.412593\pi\) | ||||
0.271161 | + | 0.962534i | \(0.412593\pi\) | |||||||
\(444\) | −2.77976e11 | −0.339456 | ||||||||
\(445\) | − | 1.05028e12i | − | 1.26965i | ||||||
\(446\) | −4.36152e10 | −0.0521952 | ||||||||
\(447\) | − | 1.42737e12i | − | 1.69104i | ||||||
\(448\) | 2.08541e11i | 0.244591i | ||||||||
\(449\) | − | 3.20262e11i | − | 0.371874i | −0.982562 | − | 0.185937i | \(-0.940468\pi\) | ||
0.982562 | − | 0.185937i | \(-0.0595321\pi\) | |||||||
\(450\) | −7.07899e11 | −0.813795 | ||||||||
\(451\) | 2.76230e11 | 0.314396 | ||||||||
\(452\) | 9.64143e10i | 0.108647i | ||||||||
\(453\) | − | 1.82466e12i | − | 2.03583i | ||||||
\(454\) | − | 1.11027e12i | − | 1.22653i | ||||||
\(455\) | 5.19877e11 | 0.568656 | ||||||||
\(456\) | 1.73335e12i | 1.87735i | ||||||||
\(457\) | −1.12742e12 | −1.20910 | −0.604550 | − | 0.796567i | \(-0.706647\pi\) | ||||
−0.604550 | + | 0.796567i | \(0.706647\pi\) | |||||||
\(458\) | 2.30124e11 | 0.244381 | ||||||||
\(459\) | −1.59875e11 | − | 1.76405e11i | −0.168121 | − | 0.185504i | ||||
\(460\) | 6.19081e11 | 0.644670 | ||||||||
\(461\) | −1.06579e12 | −1.09905 | −0.549523 | − | 0.835478i | \(-0.685191\pi\) | ||||
−0.549523 | + | 0.835478i | \(0.685191\pi\) | |||||||
\(462\) | − | 6.57294e10i | − | 0.0671229i | ||||||
\(463\) | 2.47213e11 | 0.250010 | 0.125005 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125005 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(464\) | 3.90434e11i | 0.391036i | ||||||||
\(465\) | − | 1.38859e12i | − | 1.37732i | ||||||
\(466\) | − | 1.49670e11i | − | 0.147027i | ||||||
\(467\) | −1.64486e12 | −1.60030 | −0.800151 | − | 0.599799i | \(-0.795247\pi\) | ||||
−0.800151 | + | 0.599799i | \(0.795247\pi\) | |||||||
\(468\) | −8.71218e11 | −0.839499 | ||||||||
\(469\) | 5.71721e10i | 0.0545640i | ||||||||
\(470\) | 1.28487e12i | 1.21456i | ||||||||
\(471\) | 1.43528e11i | 0.134383i | ||||||||
\(472\) | 2.95455e11 | 0.274001 | ||||||||
\(473\) | 2.86138e11i | 0.262846i | ||||||||
\(474\) | −1.31096e12 | −1.19286 | ||||||||
\(475\) | −1.23582e12 | −1.11387 | ||||||||
\(476\) | −8.73772e10 | − | 9.64113e10i | −0.0780130 | − | 0.0860789i | ||||
\(477\) | 2.22666e12 | 1.96934 | ||||||||
\(478\) | −2.20390e11 | −0.193093 | ||||||||
\(479\) | − | 5.67060e11i | − | 0.492175i | −0.969248 | − | 0.246087i | \(-0.920855\pi\) | ||
0.969248 | − | 0.246087i | \(-0.0791450\pi\) | |||||||
\(480\) | 1.95692e12 | 1.68263 | ||||||||
\(481\) | 9.50872e11i | 0.809970i | ||||||||
\(482\) | 5.61533e10i | 0.0473875i | ||||||||
\(483\) | − | 4.64127e11i | − | 0.388038i | ||||||
\(484\) | −5.14222e11 | −0.425938 | ||||||||
\(485\) | −2.36732e12 | −1.94276 | ||||||||
\(486\) | 1.30262e12i | 1.05915i | ||||||||
\(487\) | 2.01812e12i | 1.62580i | 0.582402 | + | 0.812901i | \(0.302113\pi\) | ||||
−0.582402 | + | 0.812901i | \(0.697887\pi\) | |||||||
\(488\) | 5.37524e11i | 0.429051i | ||||||||
\(489\) | 2.17650e12 | 1.72135 | ||||||||
\(490\) | − | 1.22880e12i | − | 0.962939i | ||||||
\(491\) | 1.15865e12 | 0.899672 | 0.449836 | − | 0.893111i | \(-0.351482\pi\) | ||||
0.449836 | + | 0.893111i | \(0.351482\pi\) | |||||||
\(492\) | 1.13620e12 | 0.874202 | ||||||||
\(493\) | −1.00116e12 | − | 1.10468e12i | −0.763297 | − | 0.842216i | ||||
\(494\) | 1.84526e12 | 1.39408 | ||||||||
\(495\) | −5.20949e11 | −0.390006 | ||||||||
\(496\) | − | 3.11336e11i | − | 0.230973i | ||||||
\(497\) | 4.74322e11 | 0.348714 | ||||||||
\(498\) | − | 3.43341e11i | − | 0.250146i | ||||||
\(499\) | − | 2.89972e11i | − | 0.209365i | −0.994506 | − | 0.104682i | \(-0.966617\pi\) | ||
0.994506 | − | 0.104682i | \(-0.0333826\pi\) | |||||||
\(500\) | − | 5.32206e10i | − | 0.0380816i | ||||||
\(501\) | 2.20603e12 | 1.56438 | ||||||||
\(502\) | 1.94423e10 | 0.0136641 | ||||||||
\(503\) | 3.27029e11i | 0.227788i | 0.993493 | + | 0.113894i | \(0.0363324\pi\) | ||||
−0.993493 | + | 0.113894i | \(0.963668\pi\) | |||||||
\(504\) | − | 4.68387e11i | − | 0.323346i | ||||||
\(505\) | 2.43000e12i | 1.66262i | ||||||||
\(506\) | −2.67745e11 | −0.181570 | ||||||||
\(507\) | 3.33584e12i | 2.24218i | ||||||||
\(508\) | −7.57924e10 | −0.0504939 | ||||||||
\(509\) | 5.42106e11 | 0.357976 | 0.178988 | − | 0.983851i | \(-0.442718\pi\) | ||||
0.178988 | + | 0.983851i | \(0.442718\pi\) | |||||||
\(510\) | 1.71947e12 | − | 1.55835e12i | 1.12545 | − | 1.01999i | ||||
\(511\) | −7.01109e11 | −0.454875 | ||||||||
\(512\) | 1.01378e12 | 0.651973 | ||||||||
\(513\) | − | 4.65614e11i | − | 0.296823i | ||||||
\(514\) | −1.95504e12 | −1.23544 | ||||||||
\(515\) | 1.16096e11i | 0.0727251i | ||||||||
\(516\) | 1.17695e12i | 0.730863i | ||||||||
\(517\) | 4.58022e11i | 0.281954i | ||||||||
\(518\) | −1.59095e11 | −0.0970895 | ||||||||
\(519\) | −1.11215e12 | −0.672839 | ||||||||
\(520\) | − | 3.96381e12i | − | 2.37738i | ||||||
\(521\) | 7.31594e11i | 0.435011i | 0.976059 | + | 0.217506i | \(0.0697920\pi\) | ||||
−0.976059 | + | 0.217506i | \(0.930208\pi\) | |||||||
\(522\) | − | 1.67020e12i | − | 0.984579i | ||||||
\(523\) | −6.27765e11 | −0.366893 | −0.183447 | − | 0.983030i | \(-0.558725\pi\) | ||||
−0.183447 | + | 0.983030i | \(0.558725\pi\) | |||||||
\(524\) | − | 8.55499e10i | − | 0.0495711i | ||||||
\(525\) | 6.19376e11 | 0.355826 | ||||||||
\(526\) | −2.17245e12 | −1.23741 | ||||||||
\(527\) | 7.98336e11 | + | 8.80878e11i | 0.450856 | + | 0.497471i | ||||
\(528\) | −2.16637e11 | −0.121305 | ||||||||
\(529\) | −8.94434e10 | −0.0496590 | ||||||||
\(530\) | 3.15280e12i | 1.73562i | ||||||||
\(531\) | −5.46351e11 | −0.298227 | ||||||||
\(532\) | − | 2.54474e11i | − | 0.137734i | ||||||
\(533\) | − | 3.88660e12i | − | 2.08592i | ||||||
\(534\) | 1.86837e12i | 0.994321i | ||||||||
\(535\) | 2.10364e12 | 1.11014 | ||||||||
\(536\) | 4.35909e11 | 0.228115 | ||||||||
\(537\) | − | 2.28957e12i | − | 1.18814i | ||||||
\(538\) | 7.26456e11i | 0.373843i | ||||||||
\(539\) | − | 4.38033e11i | − | 0.223541i | ||||||
\(540\) | −3.11270e11 | −0.157531 | ||||||||
\(541\) | − | 9.88955e11i | − | 0.496351i | −0.968715 | − | 0.248176i | \(-0.920169\pi\) | ||
0.968715 | − | 0.248176i | \(-0.0798310\pi\) | |||||||
\(542\) | −1.92433e12 | −0.957816 | ||||||||
\(543\) | −2.28815e12 | −1.12950 | ||||||||
\(544\) | −1.24141e12 | + | 1.12509e12i | −0.607743 | + | 0.550796i | ||||
\(545\) | −2.77561e12 | −1.34764 | ||||||||
\(546\) | −9.24822e11 | −0.445340 | ||||||||
\(547\) | 1.80571e12i | 0.862394i | 0.902258 | + | 0.431197i | \(0.141909\pi\) | ||||
−0.902258 | + | 0.431197i | \(0.858091\pi\) | |||||||
\(548\) | −3.69101e11 | −0.174837 | ||||||||
\(549\) | − | 9.93982e11i | − | 0.466985i | ||||||
\(550\) | − | 3.57305e11i | − | 0.166497i | ||||||
\(551\) | − | 2.91575e12i | − | 1.34762i | ||||||
\(552\) | −3.53874e12 | −1.62227 | ||||||||
\(553\) | 6.18432e11 | 0.281209 | ||||||||
\(554\) | − | 1.63563e12i | − | 0.737719i | ||||||
\(555\) | 2.33869e12i | 1.04630i | ||||||||
\(556\) | − | 1.44855e12i | − | 0.642831i | ||||||
\(557\) | 3.45273e12 | 1.51990 | 0.759949 | − | 0.649982i | \(-0.225224\pi\) | ||||
0.759949 | + | 0.649982i | \(0.225224\pi\) | |||||||
\(558\) | 1.33183e12i | 0.581560i | ||||||||
\(559\) | 4.02601e12 | 1.74390 | ||||||||
\(560\) | 2.86687e11 | 0.123186 | ||||||||
\(561\) | 6.12942e11 | − | 5.55507e11i | 0.261268 | − | 0.236786i | ||||
\(562\) | −1.84172e12 | −0.778771 | ||||||||
\(563\) | 6.22962e11 | 0.261321 | 0.130660 | − | 0.991427i | \(-0.458290\pi\) | ||||
0.130660 | + | 0.991427i | \(0.458290\pi\) | |||||||
\(564\) | 1.88395e12i | 0.783996i | ||||||||
\(565\) | 8.11163e11 | 0.334881 | ||||||||
\(566\) | − | 2.60521e12i | − | 1.06701i | ||||||
\(567\) | − | 5.06956e11i | − | 0.205990i | ||||||
\(568\) | − | 3.61648e12i | − | 1.45787i | ||||||
\(569\) | −6.19292e11 | −0.247680 | −0.123840 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123840 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(570\) | 4.53847e12 | 1.80083 | ||||||||
\(571\) | − | 7.93244e11i | − | 0.312280i | −0.987735 | − | 0.156140i | \(-0.950095\pi\) | ||
0.987735 | − | 0.156140i | \(-0.0499051\pi\) | |||||||
\(572\) | − | 4.39739e11i | − | 0.171756i | ||||||
\(573\) | 2.88375e12i | 1.11754i | ||||||||
\(574\) | 6.50286e11 | 0.250035 | ||||||||
\(575\) | − | 2.52300e12i | − | 0.962524i | ||||||
\(576\) | −2.94025e12 | −1.11297 | ||||||||
\(577\) | 1.65552e12 | 0.621790 | 0.310895 | − | 0.950444i | \(-0.399371\pi\) | ||||
0.310895 | + | 0.950444i | \(0.399371\pi\) | |||||||
\(578\) | −1.94842e11 | + | 1.97713e12i | −0.0726118 | + | 0.736819i | ||||
\(579\) | 8.79765e11 | 0.325322 | ||||||||
\(580\) | −1.94923e12 | −0.715214 | ||||||||
\(581\) | 1.61967e11i | 0.0589704i | ||||||||
\(582\) | 4.21128e12 | 1.52146 | ||||||||
\(583\) | 1.12389e12i | 0.402916i | ||||||||
\(584\) | 5.34562e12i | 1.90169i | ||||||||
\(585\) | 7.32983e12i | 2.58757i | ||||||||
\(586\) | 2.24879e12 | 0.787788 | ||||||||
\(587\) | −1.55182e12 | −0.539473 | −0.269736 | − | 0.962934i | \(-0.586937\pi\) | ||||
−0.269736 | + | 0.962934i | \(0.586937\pi\) | |||||||
\(588\) | − | 1.80173e12i | − | 0.621574i | ||||||
\(589\) | 2.32505e12i | 0.795999i | ||||||||
\(590\) | − | 7.73596e11i | − | 0.262833i | ||||||
\(591\) | −7.76600e12 | −2.61851 | ||||||||
\(592\) | 5.24360e11i | 0.175461i | ||||||||
\(593\) | −6.74726e10 | −0.0224069 | −0.0112034 | − | 0.999937i | \(-0.503566\pi\) | ||||
−0.0112034 | + | 0.999937i | \(0.503566\pi\) | |||||||
\(594\) | 1.34621e11 | 0.0443682 | ||||||||
\(595\) | −8.11138e11 | + | 7.35132e11i | −0.265319 | + | 0.240458i | ||||
\(596\) | 1.59774e12 | 0.518680 | ||||||||
\(597\) | 1.79408e12 | 0.578039 | ||||||||
\(598\) | 3.76722e12i | 1.20466i | ||||||||
\(599\) | −2.69514e12 | −0.855384 | −0.427692 | − | 0.903925i | \(-0.640673\pi\) | ||||
−0.427692 | + | 0.903925i | \(0.640673\pi\) | |||||||
\(600\) | − | 4.72245e12i | − | 1.48760i | ||||||
\(601\) | − | 2.33770e11i | − | 0.0730893i | −0.999332 | − | 0.0365447i | \(-0.988365\pi\) | ||
0.999332 | − | 0.0365447i | \(-0.0116351\pi\) | |||||||
\(602\) | 6.73611e11i | 0.209038i | ||||||||
\(603\) | −8.06078e11 | −0.248284 | ||||||||
\(604\) | 2.04245e12 | 0.624433 | ||||||||
\(605\) | 4.32631e12i | 1.31286i | ||||||||
\(606\) | − | 4.32278e12i | − | 1.30208i | ||||||
\(607\) | − | 4.93542e12i | − | 1.47562i | −0.675008 | − | 0.737811i | \(-0.735860\pi\) | ||
0.675008 | − | 0.737811i | \(-0.264140\pi\) | |||||||
\(608\) | −3.27666e12 | −0.972445 | ||||||||
\(609\) | 1.46134e12i | 0.430500i | ||||||||
\(610\) | 1.40741e12 | 0.411563 | ||||||||
\(611\) | 6.44444e12 | 1.87068 | ||||||||
\(612\) | 1.35932e12 | − | 1.23194e12i | 0.391687 | − | 0.354985i | ||||
\(613\) | 9.23540e11 | 0.264170 | 0.132085 | − | 0.991238i | \(-0.457833\pi\) | ||||
0.132085 | + | 0.991238i | \(0.457833\pi\) | |||||||
\(614\) | 2.70986e12 | 0.769467 | ||||||||
\(615\) | − | 9.55921e12i | − | 2.69453i | ||||||
\(616\) | 2.36414e11 | 0.0661546 | ||||||||
\(617\) | 6.93577e12i | 1.92669i | 0.268268 | + | 0.963344i | \(0.413549\pi\) | ||||
−0.268268 | + | 0.963344i | \(0.586451\pi\) | |||||||
\(618\) | − | 2.06526e11i | − | 0.0569543i | ||||||
\(619\) | − | 4.16055e12i | − | 1.13905i | −0.821974 | − | 0.569525i | \(-0.807127\pi\) | ||
0.821974 | − | 0.569525i | \(-0.192873\pi\) | |||||||
\(620\) | 1.55433e12 | 0.422455 | ||||||||
\(621\) | 9.50579e11 | 0.256493 | ||||||||
\(622\) | 1.36222e12i | 0.364913i | ||||||||
\(623\) | − | 8.81381e11i | − | 0.234405i | ||||||
\(624\) | 3.04812e12i | 0.804824i | ||||||||
\(625\) | −4.03159e12 | −1.05686 | ||||||||
\(626\) | − | 2.27277e12i | − | 0.591522i | ||||||
\(627\) | 1.61784e12 | 0.418053 | ||||||||
\(628\) | −1.60660e11 | −0.0412183 | ||||||||
\(629\) | −1.34458e12 | − | 1.48360e12i | −0.342498 | − | 0.377910i | ||||
\(630\) | −1.22639e12 | −0.310167 | ||||||||
\(631\) | 6.87945e12 | 1.72751 | 0.863757 | − | 0.503909i | \(-0.168105\pi\) | ||||
0.863757 | + | 0.503909i | \(0.168105\pi\) | |||||||
\(632\) | − | 4.71524e12i | − | 1.17565i | ||||||
\(633\) | −8.13975e12 | −2.01509 | ||||||||
\(634\) | 1.89941e12i | 0.466892i | ||||||||
\(635\) | 6.37665e11i | 0.155636i | ||||||||
\(636\) | 4.62281e12i | 1.12034i | ||||||||
\(637\) | −6.16319e12 | −1.48313 | ||||||||
\(638\) | 8.43017e11 | 0.201439 | ||||||||
\(639\) | 6.68754e12i | 1.58677i | ||||||||
\(640\) | 6.84909e11i | 0.161370i | ||||||||
\(641\) | 3.56709e11i | 0.0834550i | 0.999129 | + | 0.0417275i | \(0.0132861\pi\) | ||||
−0.999129 | + | 0.0417275i | \(0.986714\pi\) | |||||||
\(642\) | −3.74221e12 | −0.869402 | ||||||||
\(643\) | 6.44704e11i | 0.148734i | 0.997231 | + | 0.0743672i | \(0.0236937\pi\) | ||||
−0.997231 | + | 0.0743672i | \(0.976306\pi\) | |||||||
\(644\) | 5.19525e11 | 0.119020 | ||||||||
\(645\) | 9.90208e12 | 2.25272 | ||||||||
\(646\) | −2.87907e12 | + | 2.60929e12i | −0.650437 | + | 0.589489i | ||||
\(647\) | −6.40320e12 | −1.43657 | −0.718287 | − | 0.695747i | \(-0.755073\pi\) | ||||
−0.718287 | + | 0.695747i | \(0.755073\pi\) | |||||||
\(648\) | −3.86530e12 | −0.861183 | ||||||||
\(649\) | − | 2.75766e11i | − | 0.0610153i | ||||||
\(650\) | −5.02734e12 | −1.10466 | ||||||||
\(651\) | − | 1.16528e12i | − | 0.254283i | ||||||
\(652\) | 2.43629e12i | 0.527976i | ||||||||
\(653\) | − | 2.26464e12i | − | 0.487404i | −0.969850 | − | 0.243702i | \(-0.921638\pi\) | ||
0.969850 | − | 0.243702i | \(-0.0783619\pi\) | |||||||
\(654\) | 4.93759e12 | 1.05540 | ||||||||
\(655\) | −7.19758e11 | −0.152792 | ||||||||
\(656\) | − | 2.14327e12i | − | 0.451867i | ||||||
\(657\) | − | 9.88504e12i | − | 2.06983i | ||||||
\(658\) | 1.07825e12i | 0.224235i | ||||||||
\(659\) | 5.66256e12 | 1.16958 | 0.584788 | − | 0.811186i | \(-0.301178\pi\) | ||||
0.584788 | + | 0.811186i | \(0.301178\pi\) | |||||||
\(660\) | − | 1.08155e12i | − | 0.221870i | ||||||
\(661\) | 3.57090e12 | 0.727563 | 0.363782 | − | 0.931484i | \(-0.381485\pi\) | ||||
0.363782 | + | 0.931484i | \(0.381485\pi\) | |||||||
\(662\) | −2.74602e12 | −0.555704 | ||||||||
\(663\) | −7.81607e12 | − | 8.62418e12i | −1.57100 | − | 1.73343i | ||||
\(664\) | 1.23492e12 | 0.246537 | ||||||||
\(665\) | −2.14097e12 | −0.424535 | ||||||||
\(666\) | − | 2.24310e12i | − | 0.441789i | ||||||
\(667\) | 5.95269e12 | 1.16452 | ||||||||
\(668\) | 2.46934e12i | 0.479829i | ||||||||
\(669\) | 5.38039e11i | 0.103848i | ||||||||
\(670\) | − | 1.14135e12i | − | 0.218818i | ||||||
\(671\) | 5.01703e11 | 0.0955422 | ||||||||
\(672\) | 1.64222e12 | 0.310649 | ||||||||
\(673\) | 7.77167e12i | 1.46031i | 0.683279 | + | 0.730157i | \(0.260553\pi\) | ||||
−0.683279 | + | 0.730157i | \(0.739447\pi\) | |||||||
\(674\) | − | 2.03153e12i | − | 0.379187i | ||||||
\(675\) | 1.26855e12i | 0.235201i | ||||||||
\(676\) | −3.73401e12 | −0.687726 | ||||||||
\(677\) | − | 7.80583e12i | − | 1.42814i | −0.700076 | − | 0.714069i | \(-0.746850\pi\) | ||
0.700076 | − | 0.714069i | \(-0.253150\pi\) | |||||||
\(678\) | −1.44300e12 | −0.262260 | ||||||||
\(679\) | −1.98662e12 | −0.358675 | ||||||||
\(680\) | 5.60502e12 | + | 6.18454e12i | 1.00528 | + | 1.10922i | ||||
\(681\) | −1.36964e13 | −2.44030 | ||||||||
\(682\) | −6.72229e11 | −0.118984 | ||||||||
\(683\) | − | 1.18413e12i | − | 0.208212i | −0.994566 | − | 0.104106i | \(-0.966802\pi\) | ||
0.994566 | − | 0.104106i | \(-0.0331981\pi\) | |||||||
\(684\) | 3.58787e12 | 0.626735 | ||||||||
\(685\) | 3.10536e12i | 0.538896i | ||||||||
\(686\) | − | 2.13538e12i | − | 0.368143i | ||||||
\(687\) | − | 2.83882e12i | − | 0.486220i | ||||||
\(688\) | 2.22015e12 | 0.377776 | ||||||||
\(689\) | 1.58133e13 | 2.67322 | ||||||||
\(690\) | 9.26557e12i | 1.55615i | ||||||||
\(691\) | − | 1.71186e12i | − | 0.285639i | −0.989749 | − | 0.142820i | \(-0.954383\pi\) | ||
0.989749 | − | 0.142820i | \(-0.0456169\pi\) | |||||||
\(692\) | − | 1.24490e12i | − | 0.206375i | ||||||
\(693\) | −4.37173e11 | −0.0720036 | ||||||||
\(694\) | 1.54978e12i | 0.253601i | ||||||||
\(695\) | −1.21871e13 | −1.98138 | ||||||||
\(696\) | 1.11420e13 | 1.79979 | ||||||||
\(697\) | 5.49584e12 | + | 6.06407e12i | 0.882037 | + | 0.973233i | ||||
\(698\) | 2.59218e12 | 0.413348 | ||||||||
\(699\) | −1.84634e12 | −0.292526 | ||||||||
\(700\) | 6.93305e11i | 0.109140i | ||||||||
\(701\) | −3.61533e12 | −0.565480 | −0.282740 | − | 0.959197i | \(-0.591243\pi\) | ||||
−0.282740 | + | 0.959197i | \(0.591243\pi\) | |||||||
\(702\) | − | 1.89413e12i | − | 0.294370i | ||||||
\(703\) | − | 3.91590e12i | − | 0.604690i | ||||||
\(704\) | − | 1.48406e12i | − | 0.227707i | ||||||
\(705\) | 1.58503e13 | 2.41650 | ||||||||
\(706\) | 1.24213e11 | 0.0188168 | ||||||||
\(707\) | 2.03922e12i | 0.306957i | ||||||||
\(708\) | − | 1.13429e12i | − | 0.169658i | ||||||
\(709\) | 4.40149e12i | 0.654172i | 0.944995 | + | 0.327086i | \(0.106067\pi\) | ||||
−0.944995 | + | 0.327086i | \(0.893933\pi\) | |||||||
\(710\) | −9.46911e12 | −1.39845 | ||||||||
\(711\) | 8.71936e12i | 1.27959i | ||||||||
\(712\) | −6.72010e12 | −0.979977 | ||||||||
\(713\) | −4.74673e12 | −0.687846 | ||||||||
\(714\) | 1.44295e12 | − | 1.30774e12i | 0.207783 | − | 0.188313i | ||||
\(715\) | −3.69966e12 | −0.529401 | ||||||||
\(716\) | 2.56285e12 | 0.364430 | ||||||||
\(717\) | 2.71875e12i | 0.384178i | ||||||||
\(718\) | 5.22518e12 | 0.733739 | ||||||||
\(719\) | 6.79671e12i | 0.948459i | 0.880401 | + | 0.474230i | \(0.157273\pi\) | ||||
−0.880401 | + | 0.474230i | \(0.842727\pi\) | |||||||
\(720\) | 4.04205e12i | 0.560538i | ||||||||
\(721\) | 9.74262e10i | 0.0134266i | ||||||||
\(722\) | −2.19319e12 | −0.300371 | ||||||||
\(723\) | 6.92710e11 | 0.0942821 | ||||||||
\(724\) | − | 2.56126e12i | − | 0.346442i | ||||||
\(725\) | 7.94386e12i | 1.06785i | ||||||||
\(726\) | − | 7.69617e12i | − | 1.02816i | ||||||
\(727\) | −2.72583e10 | −0.00361904 | −0.00180952 | − | 0.999998i | \(-0.500576\pi\) | ||||
−0.00180952 | + | 0.999998i | \(0.500576\pi\) | |||||||
\(728\) | − | 3.32638e12i | − | 0.438915i | ||||||
\(729\) | 9.95988e12 | 1.30611 | ||||||||
\(730\) | 1.39966e13 | 1.82418 | ||||||||
\(731\) | −6.28158e12 | + | 5.69297e12i | −0.813656 | + | 0.737413i | ||||
\(732\) | 2.06362e12 | 0.265663 | ||||||||
\(733\) | 3.31700e12 | 0.424403 | 0.212201 | − | 0.977226i | \(-0.431937\pi\) | ||||
0.212201 | + | 0.977226i | \(0.431937\pi\) | |||||||
\(734\) | 5.73436e12i | 0.729210i | ||||||||
\(735\) | −1.51585e13 | −1.91586 | ||||||||
\(736\) | − | 6.68950e12i | − | 0.840318i | ||||||
\(737\) | − | 4.06860e11i | − | 0.0507974i | ||||||
\(738\) | 9.16848e12i | 1.13774i | ||||||||
\(739\) | 7.15630e12 | 0.882650 | 0.441325 | − | 0.897347i | \(-0.354509\pi\) | ||||
0.441325 | + | 0.897347i | \(0.354509\pi\) | |||||||
\(740\) | −2.61784e12 | −0.320923 | ||||||||
\(741\) | − | 2.27632e13i | − | 2.77365i | ||||||
\(742\) | 2.64579e12i | 0.320434i | ||||||||
\(743\) | − | 9.58156e12i | − | 1.15342i | −0.816950 | − | 0.576709i | \(-0.804337\pi\) | ||
0.816950 | − | 0.576709i | \(-0.195663\pi\) | |||||||
\(744\) | −8.88473e12 | −1.06308 | ||||||||
\(745\) | − | 1.34423e13i | − | 1.59872i | ||||||
\(746\) | −4.02002e12 | −0.475230 | ||||||||
\(747\) | −2.28360e12 | −0.268335 | ||||||||
\(748\) | 6.21812e11 | + | 6.86103e11i | 0.0726277 | + | 0.0801368i | ||||
\(749\) | 1.76535e12 | 0.204956 | ||||||||
\(750\) | 7.96535e11 | 0.0919240 | ||||||||
\(751\) | 1.53884e13i | 1.76528i | 0.470047 | + | 0.882641i | \(0.344237\pi\) | ||||
−0.470047 | + | 0.882641i | \(0.655763\pi\) | |||||||
\(752\) | 3.55380e12 | 0.405240 | ||||||||
\(753\) | − | 2.39841e11i | − | 0.0271861i | ||||||
\(754\) | − | 1.18614e13i | − | 1.33648i | ||||||
\(755\) | − | 1.71838e13i | − | 1.92468i | ||||||
\(756\) | −2.61214e11 | −0.0290836 | ||||||||
\(757\) | −1.07153e13 | −1.18597 | −0.592983 | − | 0.805215i | \(-0.702050\pi\) | ||||
−0.592983 | + | 0.805215i | \(0.702050\pi\) | |||||||
\(758\) | − | 1.22629e13i | − | 1.34922i | ||||||
\(759\) | 3.30292e12i | 0.361252i | ||||||||
\(760\) | 1.63239e13i | 1.77485i | ||||||||
\(761\) | −2.41871e12 | −0.261428 | −0.130714 | − | 0.991420i | \(-0.541727\pi\) | ||||
−0.130714 | + | 0.991420i | \(0.541727\pi\) | |||||||
\(762\) | − | 1.13436e12i | − | 0.121886i | ||||||
\(763\) | −2.32925e12 | −0.248803 | ||||||||
\(764\) | −3.22795e12 | −0.342774 | ||||||||
\(765\) | −1.03647e13 | − | 1.14364e13i | −1.09416 | − | 1.20729i | ||||
\(766\) | 5.88206e11 | 0.0617305 | ||||||||
\(767\) | −3.88007e12 | −0.404818 | ||||||||
\(768\) | − | 1.47287e13i | − | 1.52771i | ||||||
\(769\) | 1.04607e13 | 1.07868 | 0.539339 | − | 0.842089i | \(-0.318674\pi\) | ||||
0.539339 | + | 0.842089i | \(0.318674\pi\) | |||||||
\(770\) | − | 6.19008e11i | − | 0.0634582i | ||||||
\(771\) | 2.41175e13i | 2.45803i | ||||||||
\(772\) | 9.84774e11i | 0.0997835i | ||||||||
\(773\) | 6.75781e12 | 0.680767 | 0.340383 | − | 0.940287i | \(-0.389443\pi\) | ||||
0.340383 | + | 0.940287i | \(0.389443\pi\) | |||||||
\(774\) | −9.49734e12 | −0.951191 | ||||||||
\(775\) | − | 6.33450e12i | − | 0.630746i | ||||||
\(776\) | 1.51470e13i | 1.49951i | ||||||||
\(777\) | 1.96260e12i | 0.193169i | ||||||||
\(778\) | 6.81391e11 | 0.0666789 | ||||||||
\(779\) | 1.60059e13i | 1.55726i | ||||||||
\(780\) | −1.52176e13 | −1.47204 | ||||||||
\(781\) | −3.37547e12 | −0.324642 | ||||||||
\(782\) | −5.32703e12 | − | 5.87780e12i | −0.509395 | − | 0.562062i | ||||
\(783\) | −2.99297e12 | −0.284561 | ||||||||
\(784\) | −3.39870e12 | −0.321286 | ||||||||
\(785\) | 1.35168e12i | 0.127046i | ||||||||
\(786\) | 1.28040e12 | 0.119658 | ||||||||
\(787\) | − | 1.52232e13i | − | 1.41456i | −0.706935 | − | 0.707279i | \(-0.749922\pi\) | ||
0.706935 | − | 0.707279i | \(-0.250078\pi\) | |||||||
\(788\) | − | 8.69295e12i | − | 0.803155i | ||||||
\(789\) | 2.67995e13i | 2.46196i | ||||||||
\(790\) | −1.23460e13 | −1.12773 | ||||||||
\(791\) | 6.80718e11 | 0.0618263 | ||||||||
\(792\) | 3.33324e12i | 0.301025i | ||||||||
\(793\) | − | 7.05904e12i | − | 0.633893i | ||||||
\(794\) | − | 1.47920e13i | − | 1.32080i | ||||||
\(795\) | 3.88932e13 | 3.45319 | ||||||||
\(796\) | 2.00822e12i | 0.177298i | ||||||||
\(797\) | 1.41512e13 | 1.24231 | 0.621155 | − | 0.783688i | \(-0.286664\pi\) | ||||
0.621155 | + | 0.783688i | \(0.286664\pi\) | |||||||
\(798\) | 3.80863e12 | 0.332472 | ||||||||
\(799\) | −1.00549e13 | + | 9.11275e12i | −0.872808 | + | 0.791023i | ||||
\(800\) | 8.92713e12 | 0.770561 | ||||||||
\(801\) | 1.24267e13 | 1.06662 | ||||||||
\(802\) | 8.48478e12i | 0.724196i | ||||||||
\(803\) | 4.98938e12 | 0.423474 | ||||||||
\(804\) | − | 1.67351e12i | − | 0.141246i | ||||||
\(805\) | − | 4.37093e12i | − | 0.366853i | ||||||
\(806\) | 9.45836e12i | 0.789420i | ||||||||
\(807\) | 8.96161e12 | 0.743798 | ||||||||
\(808\) | 1.55481e13 | 1.28329 | ||||||||
\(809\) | − | 1.28851e13i | − | 1.05760i | −0.848748 | − | 0.528798i | \(-0.822643\pi\) | ||
0.848748 | − | 0.528798i | \(-0.177357\pi\) | |||||||
\(810\) | 1.01206e13i | 0.826083i | ||||||||
\(811\) | − | 4.50010e12i | − | 0.365282i | −0.983180 | − | 0.182641i | \(-0.941535\pi\) | ||
0.983180 | − | 0.182641i | \(-0.0584646\pi\) | |||||||
\(812\) | −1.63577e12 | −0.132044 | ||||||||
\(813\) | 2.37386e13i | 1.90567i | ||||||||
\(814\) | 1.13218e12 | 0.0903873 | ||||||||
\(815\) | 2.04972e13 | 1.62737 | ||||||||
\(816\) | −4.31018e12 | − | 4.75582e12i | −0.340322 | − | 0.375509i | ||||
\(817\) | −1.65800e13 | −1.30192 | ||||||||
\(818\) | −1.00061e13 | −0.781401 | ||||||||
\(819\) | 6.15110e12i | 0.477722i | ||||||||
\(820\) | 1.07002e13 | 0.826474 | ||||||||
\(821\) | − | 7.07667e12i | − | 0.543606i | −0.962353 | − | 0.271803i | \(-0.912380\pi\) | ||
0.962353 | − | 0.271803i | \(-0.0876200\pi\) | |||||||
\(822\) | − | 5.52421e12i | − | 0.422033i | ||||||
\(823\) | − | 2.16722e13i | − | 1.64666i | −0.567563 | − | 0.823330i | \(-0.692114\pi\) | ||
0.567563 | − | 0.823330i | \(-0.307886\pi\) | |||||||
\(824\) | 7.42827e11 | 0.0561326 | ||||||||
\(825\) | −4.40774e12 | −0.331263 | ||||||||
\(826\) | − | 6.49192e11i | − | 0.0485247i | ||||||
\(827\) | 9.53709e12i | 0.708992i | 0.935058 | + | 0.354496i | \(0.115347\pi\) | ||||
−0.935058 | + | 0.354496i | \(0.884653\pi\) | |||||||
\(828\) | 7.32486e12i | 0.541580i | ||||||||
\(829\) | −1.85810e13 | −1.36639 | −0.683194 | − | 0.730237i | \(-0.739410\pi\) | ||||
−0.683194 | + | 0.730237i | \(0.739410\pi\) | |||||||
\(830\) | − | 3.23342e12i | − | 0.236489i | ||||||
\(831\) | −2.01772e13 | −1.46776 | ||||||||
\(832\) | −2.08810e13 | −1.51076 | ||||||||
\(833\) | 9.61612e12 | − | 8.71506e12i | 0.691986 | − | 0.627145i | ||||
\(834\) | 2.16799e13 | 1.55171 | ||||||||
\(835\) | 2.07753e13 | 1.47897 | ||||||||
\(836\) | 1.81094e12i | 0.128226i | ||||||||
\(837\) | 2.38662e12 | 0.168081 | ||||||||
\(838\) | 1.13388e13i | 0.794268i | ||||||||
\(839\) | 1.59920e12i | 0.111422i | 0.998447 | + | 0.0557112i | \(0.0177426\pi\) | ||||
−0.998447 | + | 0.0557112i | \(0.982257\pi\) | |||||||
\(840\) | − | 8.18133e12i | − | 0.566979i | ||||||
\(841\) | −4.23537e12 | −0.291951 | ||||||||
\(842\) | −8.30170e12 | −0.569197 | ||||||||
\(843\) | 2.27195e13i | 1.54944i | ||||||||
\(844\) | − | 9.11132e12i | − | 0.618073i | ||||||
\(845\) | 3.14154e13i | 2.11976i | ||||||||
\(846\) | −1.52024e13 | −1.02034 | ||||||||
\(847\) | 3.63058e12i | 0.242382i | ||||||||
\(848\) | 8.72025e12 | 0.579092 | ||||||||
\(849\) | −3.21380e13 | −2.12292 | ||||||||
\(850\) | 7.84391e12 | − | 7.10891e12i | 0.515403 | − | 0.467108i | ||||
\(851\) | 7.99456e12 | 0.522530 | ||||||||
\(852\) | −1.38841e13 | −0.902693 | ||||||||
\(853\) | 3.66406e10i | 0.00236969i | 0.999999 | + | 0.00118485i | \(0.000377148\pi\) | ||||
−0.999999 | + | 0.00118485i | \(0.999623\pi\) | |||||||
\(854\) | 1.18108e12 | 0.0759835 | ||||||||
\(855\) | − | 3.01859e13i | − | 1.93177i | ||||||
\(856\) | − | 1.34599e13i | − | 0.856860i | ||||||
\(857\) | 1.12995e13i | 0.715559i | 0.933806 | + | 0.357779i | \(0.116466\pi\) | ||||
−0.933806 | + | 0.357779i | \(0.883534\pi\) | |||||||
\(858\) | 6.58142e12 | 0.414598 | ||||||||
\(859\) | −1.13307e13 | −0.710049 | −0.355025 | − | 0.934857i | \(-0.615528\pi\) | ||||
−0.355025 | + | 0.934857i | \(0.615528\pi\) | |||||||
\(860\) | 1.10840e13i | 0.690961i | ||||||||
\(861\) | − | 8.02196e12i | − | 0.497470i | ||||||
\(862\) | 1.72309e12i | 0.106298i | ||||||||
\(863\) | 5.46870e12 | 0.335610 | 0.167805 | − | 0.985820i | \(-0.446332\pi\) | ||||
0.167805 | + | 0.985820i | \(0.446332\pi\) | |||||||
\(864\) | 3.36344e12i | 0.205339i | ||||||||
\(865\) | −1.04737e13 | −0.636105 | ||||||||
\(866\) | 4.53358e11 | 0.0273912 | ||||||||
\(867\) | 2.43900e13 | + | 2.40358e12i | 1.46597 | + | 0.144468i | ||||
\(868\) | 1.30437e12 | 0.0779944 | ||||||||
\(869\) | −4.40102e12 | −0.261797 | ||||||||
\(870\) | − | 2.91734e13i | − | 1.72643i | ||||||
\(871\) | −5.72459e12 | −0.337025 | ||||||||
\(872\) | 1.77594e13i | 1.04017i | ||||||||
\(873\) | − | 2.80097e13i | − | 1.63209i | ||||||
\(874\) | − | 1.55142e13i | − | 0.899351i | ||||||
\(875\) | −3.75756e11 | −0.0216705 | ||||||||
\(876\) | 2.05225e13 | 1.17750 | ||||||||
\(877\) | − | 2.29940e12i | − | 0.131255i | −0.997844 | − | 0.0656275i | \(-0.979095\pi\) | ||
0.997844 | − | 0.0656275i | \(-0.0209049\pi\) | |||||||
\(878\) | 9.36580e12i | 0.531887i | ||||||||
\(879\) | − | 2.77412e13i | − | 1.56738i | ||||||
\(880\) | −2.04019e12 | −0.114683 | ||||||||
\(881\) | − | 1.11997e13i | − | 0.626348i | −0.949696 | − | 0.313174i | \(-0.898608\pi\) | ||
0.949696 | − | 0.313174i | \(-0.101392\pi\) | |||||||
\(882\) | 1.45390e13 | 0.808955 | ||||||||
\(883\) | −3.12943e13 | −1.73238 | −0.866188 | − | 0.499718i | \(-0.833437\pi\) | ||||
−0.866188 | + | 0.499718i | \(0.833437\pi\) | |||||||
\(884\) | 9.65357e12 | − | 8.74900e12i | 0.531683 | − | 0.481862i | ||||
\(885\) | −9.54313e12 | −0.522933 | ||||||||
\(886\) | −7.36491e12 | −0.401528 | ||||||||
\(887\) | 1.69578e13i | 0.919840i | 0.887960 | + | 0.459920i | \(0.152122\pi\) | ||||
−0.887960 | + | 0.459920i | \(0.847878\pi\) | |||||||
\(888\) | 1.49639e13 | 0.807582 | ||||||||
\(889\) | 5.35121e11i | 0.0287338i | ||||||||
\(890\) | 1.75954e13i | 0.940035i | ||||||||
\(891\) | 3.60771e12i | 0.191771i | ||||||||
\(892\) | −6.02260e11 | −0.0318524 | ||||||||
\(893\) | −2.65397e13 | −1.39657 | ||||||||
\(894\) | 2.39129e13i | 1.25203i | ||||||||
\(895\) | − | 2.15620e13i | − | 1.12328i | ||||||
\(896\) | 5.74767e11i | 0.0297924i | ||||||||
\(897\) | 4.64726e13 | 2.39679 | ||||||||
\(898\) | 5.36536e12i | 0.275331i | ||||||||
\(899\) | 1.49454e13 | 0.763115 | ||||||||
\(900\) | −9.77502e12 | −0.496622 | ||||||||
\(901\) | −2.46726e13 | + | 2.23607e13i | −1.24725 | + | 1.13038i | ||||
\(902\) | −4.62770e12 | −0.232775 | ||||||||
\(903\) | 8.30970e12 | 0.415902 | ||||||||
\(904\) | − | 5.19014e12i | − | 0.258477i | ||||||
\(905\) | −2.15487e13 | −1.06783 | ||||||||
\(906\) | 3.05687e13i | 1.50730i | ||||||||
\(907\) | 1.21182e13i | 0.594575i | 0.954788 | + | 0.297288i | \(0.0960820\pi\) | ||||
−0.954788 | + | 0.297288i | \(0.903918\pi\) | |||||||
\(908\) | − | 1.53312e13i | − | 0.748496i | ||||||
\(909\) | −2.87513e13 | −1.39675 | ||||||||
\(910\) | −8.70954e12 | −0.421026 | ||||||||
\(911\) | − | 1.52506e13i | − | 0.733594i | −0.930301 | − | 0.366797i | \(-0.880454\pi\) | ||
0.930301 | − | 0.366797i | \(-0.119546\pi\) | |||||||
\(912\) | − | 1.25528e13i | − | 0.600848i | ||||||
\(913\) | − | 1.15263e12i | − | 0.0548997i | ||||||
\(914\) | 1.88877e13 | 0.895203 | ||||||||
\(915\) | − | 1.73619e13i | − | 0.818846i | ||||||
\(916\) | 3.17767e12 | 0.149135 | ||||||||
\(917\) | −6.04012e11 | −0.0282087 | ||||||||
\(918\) | 2.67839e12 | + | 2.95532e12i | 0.124475 | + | 0.137345i | ||||
\(919\) | −3.47751e12 | −0.160823 | −0.0804116 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804116 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(920\) | −3.33262e13 | −1.53370 | ||||||||
\(921\) | − | 3.34290e13i | − | 1.53093i | ||||||
\(922\) | 1.78552e13 | 0.813721 | ||||||||
\(923\) | 4.74935e13i | 2.15390i | ||||||||
\(924\) | − | 9.07623e11i | − | 0.0409621i | ||||||
\(925\) | 1.06687e13i | 0.479154i | ||||||||
\(926\) | −4.14158e12 | −0.185104 | ||||||||
\(927\) | −1.37363e12 | −0.0610956 | ||||||||
\(928\) | 2.10624e13i | 0.932272i | ||||||||
\(929\) | − | 1.36859e13i | − | 0.602841i | −0.953491 | − | 0.301421i | \(-0.902539\pi\) | ||
0.953491 | − | 0.301421i | \(-0.0974609\pi\) | |||||||
\(930\) | 2.32631e13i | 1.01975i | ||||||||
\(931\) | 2.53814e13 | 1.10724 | ||||||||
\(932\) | − | 2.06672e12i | − | 0.0897242i | ||||||
\(933\) | 1.68044e13 | 0.726031 | ||||||||
\(934\) | 2.75564e13 | 1.18484 | ||||||||
\(935\) | 5.77240e12 | − | 5.23150e12i | 0.247004 | − | 0.223859i | ||||
\(936\) | 4.68991e13 | 1.99721 | ||||||||
\(937\) | 2.71915e13 | 1.15241 | 0.576203 | − | 0.817307i | \(-0.304534\pi\) | ||||
0.576203 | + | 0.817307i | \(0.304534\pi\) | |||||||
\(938\) | − | 9.57808e11i | − | 0.0403985i | ||||||
\(939\) | −2.80370e13 | −1.17689 | ||||||||
\(940\) | 1.77422e13i | 0.741193i | ||||||||
\(941\) | 1.67036e13i | 0.694476i | 0.937777 | + | 0.347238i | \(0.112880\pi\) | ||||
−0.937777 | + | 0.347238i | \(0.887120\pi\) | |||||||
\(942\) | − | 2.40454e12i | − | 0.0994955i | ||||||
\(943\) | −3.26770e13 | −1.34568 | ||||||||
\(944\) | −2.13967e12 | −0.0876946 | ||||||||
\(945\) | 2.19767e12i | 0.0896438i | ||||||||
\(946\) | − | 4.79370e12i | − | 0.194608i | ||||||
\(947\) | − | 2.14351e13i | − | 0.866067i | −0.901378 | − | 0.433033i | \(-0.857443\pi\) | ||
0.901378 | − | 0.433033i | \(-0.142557\pi\) | |||||||
\(948\) | −1.81024e13 | −0.727946 | ||||||||
\(949\) | − | 7.02014e13i | − | 2.80962i | ||||||
\(950\) | 2.07037e13 | 0.824693 | ||||||||
\(951\) | 2.34312e13 | 0.928927 | ||||||||
\(952\) | 4.70366e12 | + | 5.18998e12i | 0.185597 | + | 0.204786i | ||||
\(953\) | −9.22579e12 | −0.362314 | −0.181157 | − | 0.983454i | \(-0.557984\pi\) | ||||
−0.181157 | + | 0.983454i | \(0.557984\pi\) | |||||||
\(954\) | −3.73034e13 | −1.45808 | ||||||||
\(955\) | 2.71578e13i | 1.05652i | ||||||||
\(956\) | −3.04326e12 | −0.117836 | ||||||||
\(957\) | − | 1.03995e13i | − | 0.400782i | ||||||
\(958\) | 9.50000e12i | 0.364400i | ||||||||
\(959\) | 2.60598e12i | 0.0994919i | ||||||||
\(960\) | −5.13574e13 | −1.95156 | ||||||||
\(961\) | 1.45220e13 | 0.549251 | ||||||||
\(962\) | − | 1.59300e13i | − | 0.599692i | ||||||
\(963\) | 2.48899e13i | 0.932619i | ||||||||
\(964\) | 7.75392e11i | 0.0289184i | ||||||||
\(965\) | 8.28521e12 | 0.307561 | ||||||||
\(966\) | 7.77555e12i | 0.287299i | ||||||||
\(967\) | 5.20219e13 | 1.91323 | 0.956614 | − | 0.291359i | \(-0.0941073\pi\) | ||||
0.956614 | + | 0.291359i | \(0.0941073\pi\) | |||||||
\(968\) | 2.76814e13 | 1.01333 | ||||||||
\(969\) | 3.21883e13 | + | 3.55163e13i | 1.17285 | + | 1.29411i | ||||
\(970\) | 3.96598e13 | 1.43839 | ||||||||
\(971\) | 8.53408e12 | 0.308085 | 0.154042 | − | 0.988064i | \(-0.450771\pi\) | ||||
0.154042 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(972\) | 1.79873e13i | 0.646349i | ||||||||
\(973\) | −1.02273e13 | −0.365807 | ||||||||
\(974\) | − | 3.38098e13i | − | 1.20372i | ||||||
\(975\) | 6.20176e13i | 2.19783i | ||||||||
\(976\) | − | 3.89272e12i | − | 0.137318i | ||||||
\(977\) | 1.09077e13 | 0.383008 | 0.191504 | − | 0.981492i | \(-0.438663\pi\) | ||||
0.191504 | + | 0.981492i | \(0.438663\pi\) | |||||||
\(978\) | −3.64630e13 | −1.27447 | ||||||||
\(979\) | 6.27227e12i | 0.218224i | ||||||||
\(980\) | − | 1.69679e13i | − | 0.587638i | ||||||
\(981\) | − | 3.28405e13i | − | 1.13214i | ||||||
\(982\) | −1.94109e13 | −0.666106 | ||||||||
\(983\) | − | 3.83440e12i | − | 0.130981i | −0.997853 | − | 0.0654903i | \(-0.979139\pi\) | ||
0.997853 | − | 0.0654903i | \(-0.0208611\pi\) | |||||||
\(984\) | −6.11636e13 | −2.07977 | ||||||||
\(985\) | −7.31365e13 | −2.47555 | ||||||||
\(986\) | 1.67726e13 | + | 1.85067e13i | 0.565136 | + | 0.623567i | ||||
\(987\) | 1.33014e13 | 0.446137 | ||||||||
\(988\) | 2.54803e13 | 0.850742 | ||||||||
\(989\) | − | 3.38491e13i | − | 1.12503i | ||||||
\(990\) | 8.72749e12 | 0.288756 | ||||||||
\(991\) | − | 3.67907e13i | − | 1.21173i | −0.795566 | − | 0.605867i | \(-0.792827\pi\) | ||
0.795566 | − | 0.605867i | \(-0.207173\pi\) | |||||||
\(992\) | − | 1.67954e13i | − | 0.550664i | ||||||
\(993\) | 3.38751e13i | 1.10563i | ||||||||
\(994\) | −7.94636e12 | −0.258184 | ||||||||
\(995\) | 1.68958e13 | 0.546480 | ||||||||
\(996\) | − | 4.74102e12i | − | 0.152653i | ||||||
\(997\) | 2.49866e13i | 0.800901i | 0.916318 | + | 0.400451i | \(0.131146\pi\) | ||||
−0.916318 | + | 0.400451i | \(0.868854\pi\) | |||||||
\(998\) | 4.85792e12i | 0.155011i | ||||||||
\(999\) | −4.01961e12 | −0.127685 |
(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 | 17.10.b.a.16.4 | yes | 12 | |
3.2 | odd | 2 | 153.10.d.b.118.9 | 12 | |||
4.3 | odd | 2 | 272.10.b.c.33.2 | 12 | |||
17.4 | even | 4 | 289.10.a.c.1.10 | 12 | |||
17.13 | even | 4 | 289.10.a.c.1.9 | 12 | |||
17.16 | even | 2 | inner | 17.10.b.a.16.3 | ✓ | 12 | |
51.50 | odd | 2 | 153.10.d.b.118.10 | 12 | |||
68.67 | odd | 2 | 272.10.b.c.33.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.b.a.16.3 | ✓ | 12 | 17.16 | even | 2 | inner | |
17.10.b.a.16.4 | yes | 12 | 1.1 | even | 1 | trivial | |
153.10.d.b.118.9 | 12 | 3.2 | odd | 2 | |||
153.10.d.b.118.10 | 12 | 51.50 | odd | 2 | |||
272.10.b.c.33.2 | 12 | 4.3 | odd | 2 | |||
272.10.b.c.33.11 | 12 | 68.67 | odd | 2 | |||
289.10.a.c.1.9 | 12 | 17.13 | even | 4 | |||
289.10.a.c.1.10 | 12 | 17.4 | even | 4 |