Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,18,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(9.16110436723\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 203459x^{6} + 12362849196x^{4} + 237701205446144x^{2} + 1320400799499206656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.4 | ||
Root | \(-98.5951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.18.b.a.4.5 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 197.190i | − | 0.544666i | −0.962203 | − | 0.272333i | \(-0.912205\pi\) | ||
0.962203 | − | 0.272333i | \(-0.0877952\pi\) | |||||||
\(3\) | − | 12817.1i | − | 1.12787i | −0.825819 | − | 0.563935i | \(-0.809287\pi\) | ||
0.825819 | − | 0.563935i | \(-0.190713\pi\) | |||||||
\(4\) | 92188.0 | 0.703339 | ||||||||
\(5\) | 620811. | − | 614437.i | 0.710746 | − | 0.703449i | ||||
\(6\) | −2.52741e6 | −0.614313 | ||||||||
\(7\) | 4.49140e6i | 0.294475i | 0.989101 | + | 0.147237i | \(0.0470381\pi\) | ||||
−0.989101 | + | 0.147237i | \(0.952962\pi\) | |||||||
\(8\) | − | 4.40247e7i | − | 0.927751i | ||||||
\(9\) | −3.51381e7 | −0.272093 | ||||||||
\(10\) | −1.21161e8 | − | 1.22418e8i | −0.383145 | − | 0.387119i | ||||
\(11\) | −1.08959e9 | −1.53259 | −0.766296 | − | 0.642487i | \(-0.777903\pi\) | ||||
−0.766296 | + | 0.642487i | \(0.777903\pi\) | |||||||
\(12\) | − | 1.18158e9i | − | 0.793275i | ||||||
\(13\) | − | 2.20399e9i | − | 0.749359i | −0.927154 | − | 0.374680i | \(-0.877753\pi\) | ||
0.927154 | − | 0.374680i | \(-0.122247\pi\) | |||||||
\(14\) | 8.85659e8 | 0.160390 | ||||||||
\(15\) | −7.87531e9 | − | 7.95700e9i | −0.793399 | − | 0.801630i | ||||
\(16\) | 3.40203e9 | 0.198024 | ||||||||
\(17\) | 4.96836e10i | 1.72742i | 0.503991 | + | 0.863709i | \(0.331864\pi\) | ||||
−0.503991 | + | 0.863709i | \(0.668136\pi\) | |||||||
\(18\) | 6.92889e9i | 0.148200i | ||||||||
\(19\) | 6.53775e10 | 0.883126 | 0.441563 | − | 0.897230i | \(-0.354424\pi\) | ||||
0.441563 | + | 0.897230i | \(0.354424\pi\) | |||||||
\(20\) | 5.72314e10 | − | 5.66438e10i | 0.499895 | − | 0.494763i | ||||
\(21\) | 5.75667e10 | 0.332129 | ||||||||
\(22\) | 2.14857e11i | 0.834751i | ||||||||
\(23\) | 6.03064e10i | 0.160575i | 0.996772 | + | 0.0802873i | \(0.0255838\pi\) | ||||
−0.996772 | + | 0.0802873i | \(0.974416\pi\) | |||||||
\(24\) | −5.64269e11 | −1.04638 | ||||||||
\(25\) | 7.87347e9 | − | 7.62899e11i | 0.0103199 | − | 0.999947i | ||||
\(26\) | −4.34604e11 | −0.408151 | ||||||||
\(27\) | − | 1.20483e12i | − | 0.820986i | ||||||
\(28\) | 4.14053e11i | 0.207115i | ||||||||
\(29\) | −2.63186e10 | −0.00976967 | −0.00488483 | − | 0.999988i | \(-0.501555\pi\) | ||||
−0.00488483 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(30\) | −1.56904e12 | + | 1.55293e12i | −0.436621 | + | 0.432138i | ||||
\(31\) | 3.03326e12 | 0.638756 | 0.319378 | − | 0.947627i | \(-0.396526\pi\) | ||||
0.319378 | + | 0.947627i | \(0.396526\pi\) | |||||||
\(32\) | − | 6.44125e12i | − | 1.03561i | ||||||
\(33\) | 1.39654e13i | 1.72857i | ||||||||
\(34\) | 9.79712e12 | 0.940866 | ||||||||
\(35\) | 2.75968e12 | + | 2.78831e12i | 0.207148 | + | 0.209297i | ||||
\(36\) | −3.23931e12 | −0.191373 | ||||||||
\(37\) | 8.44655e12i | 0.395334i | 0.980269 | + | 0.197667i | \(0.0633365\pi\) | ||||
−0.980269 | + | 0.197667i | \(0.936663\pi\) | |||||||
\(38\) | − | 1.28918e13i | − | 0.481009i | ||||||
\(39\) | −2.82487e13 | −0.845181 | ||||||||
\(40\) | −2.70504e13 | − | 2.73310e13i | −0.652625 | − | 0.659395i | ||||
\(41\) | 5.70631e13 | 1.11607 | 0.558036 | − | 0.829817i | \(-0.311555\pi\) | ||||
0.558036 | + | 0.829817i | \(0.311555\pi\) | |||||||
\(42\) | − | 1.13516e13i | − | 0.180900i | ||||||
\(43\) | − | 6.40476e13i | − | 0.835644i | −0.908529 | − | 0.417822i | \(-0.862794\pi\) | ||
0.908529 | − | 0.417822i | \(-0.137206\pi\) | |||||||
\(44\) | −1.00447e14 | −1.07793 | ||||||||
\(45\) | −2.18141e13 | + | 2.15901e13i | −0.193389 | + | 0.191403i | ||||
\(46\) | 1.18918e13 | 0.0874596 | ||||||||
\(47\) | 2.44975e14i | 1.50069i | 0.661048 | + | 0.750344i | \(0.270112\pi\) | ||||
−0.661048 | + | 0.750344i | \(0.729888\pi\) | |||||||
\(48\) | − | 4.36042e13i | − | 0.223346i | ||||||
\(49\) | 2.12458e14 | 0.913285 | ||||||||
\(50\) | −1.50436e14 | − | 1.55257e12i | −0.544637 | − | 0.00562090i | ||||
\(51\) | 6.36800e14 | 1.94830 | ||||||||
\(52\) | − | 2.03181e14i | − | 0.527054i | ||||||
\(53\) | 1.01305e14i | 0.223504i | 0.993736 | + | 0.111752i | \(0.0356463\pi\) | ||||
−0.993736 | + | 0.111752i | \(0.964354\pi\) | |||||||
\(54\) | −2.37582e14 | −0.447163 | ||||||||
\(55\) | −6.76432e14 | + | 6.69487e14i | −1.08928 | + | 1.07810i | ||||
\(56\) | 1.97732e14 | 0.273199 | ||||||||
\(57\) | − | 8.37950e14i | − | 0.996052i | ||||||
\(58\) | 5.18977e12i | 0.00532121i | ||||||||
\(59\) | −1.41965e15 | −1.25875 | −0.629373 | − | 0.777103i | \(-0.716688\pi\) | ||||
−0.629373 | + | 0.777103i | \(0.716688\pi\) | |||||||
\(60\) | −7.26009e14 | − | 7.33540e14i | −0.558029 | − | 0.563817i | ||||
\(61\) | 2.31838e15 | 1.54839 | 0.774195 | − | 0.632947i | \(-0.218155\pi\) | ||||
0.774195 | + | 0.632947i | \(0.218155\pi\) | |||||||
\(62\) | − | 5.98128e14i | − | 0.347908i | ||||||
\(63\) | − | 1.57819e14i | − | 0.0801244i | ||||||
\(64\) | −8.24240e14 | −0.366036 | ||||||||
\(65\) | −1.35421e15 | − | 1.36826e15i | −0.527136 | − | 0.532604i | ||||
\(66\) | 2.75385e15 | 0.941492 | ||||||||
\(67\) | 4.06306e15i | 1.22241i | 0.791472 | + | 0.611206i | \(0.209315\pi\) | ||||
−0.791472 | + | 0.611206i | \(0.790685\pi\) | |||||||
\(68\) | 4.58023e15i | 1.21496i | ||||||||
\(69\) | 7.72954e14 | 0.181107 | ||||||||
\(70\) | 5.49827e14 | − | 5.44182e14i | 0.113997 | − | 0.112826i | ||||
\(71\) | 2.68034e15 | 0.492599 | 0.246299 | − | 0.969194i | \(-0.420785\pi\) | ||||
0.246299 | + | 0.969194i | \(0.420785\pi\) | |||||||
\(72\) | 1.54694e15i | 0.252434i | ||||||||
\(73\) | − | 6.95024e15i | − | 1.00869i | −0.863504 | − | 0.504343i | \(-0.831735\pi\) | ||
0.863504 | − | 0.504343i | \(-0.168265\pi\) | |||||||
\(74\) | 1.66558e15 | 0.215325 | ||||||||
\(75\) | −9.77816e15 | − | 1.00915e14i | −1.12781 | − | 0.0116395i | ||||
\(76\) | 6.02702e15 | 0.621137 | ||||||||
\(77\) | − | 4.89380e15i | − | 0.451310i | ||||||
\(78\) | 5.57037e15i | 0.460341i | ||||||||
\(79\) | −8.28477e15 | −0.614399 | −0.307199 | − | 0.951645i | \(-0.599392\pi\) | ||||
−0.307199 | + | 0.951645i | \(0.599392\pi\) | |||||||
\(80\) | 2.11202e15 | − | 2.09034e15i | 0.140745 | − | 0.139300i | ||||
\(81\) | −1.99802e16 | −1.19806 | ||||||||
\(82\) | − | 1.12523e16i | − | 0.607887i | ||||||
\(83\) | − | 2.66711e16i | − | 1.29980i | −0.760018 | − | 0.649902i | \(-0.774810\pi\) | ||
0.760018 | − | 0.649902i | \(-0.225190\pi\) | |||||||
\(84\) | 5.30696e15 | 0.233600 | ||||||||
\(85\) | 3.05275e16 | + | 3.08441e16i | 1.21515 | + | 1.22776i | ||||
\(86\) | −1.26296e16 | −0.455147 | ||||||||
\(87\) | 3.37328e14i | 0.0110189i | ||||||||
\(88\) | 4.79690e16i | 1.42186i | ||||||||
\(89\) | 6.55891e15 | 0.176611 | 0.0883053 | − | 0.996093i | \(-0.471855\pi\) | ||||
0.0883053 | + | 0.996093i | \(0.471855\pi\) | |||||||
\(90\) | 4.25736e15 | + | 4.30153e15i | 0.104251 | + | 0.105332i | ||||
\(91\) | 9.89897e15 | 0.220667 | ||||||||
\(92\) | 5.55953e15i | 0.112938i | ||||||||
\(93\) | − | 3.88776e16i | − | 0.720434i | ||||||
\(94\) | 4.83067e16 | 0.817373 | ||||||||
\(95\) | 4.05871e16 | − | 4.01704e16i | 0.627678 | − | 0.621234i | ||||
\(96\) | −8.25582e16 | −1.16803 | ||||||||
\(97\) | 1.11864e17i | 1.44920i | 0.689169 | + | 0.724601i | \(0.257976\pi\) | ||||
−0.689169 | + | 0.724601i | \(0.742024\pi\) | |||||||
\(98\) | − | 4.18946e16i | − | 0.497435i | ||||||
\(99\) | 3.82862e16 | 0.417007 | ||||||||
\(100\) | 7.25839e14 | − | 7.03301e16i | 0.00725839 | − | 0.703301i | ||||
\(101\) | −1.99528e17 | −1.83346 | −0.916732 | − | 0.399503i | \(-0.869183\pi\) | ||||
−0.916732 | + | 0.399503i | \(0.869183\pi\) | |||||||
\(102\) | − | 1.25571e17i | − | 1.06117i | ||||||
\(103\) | 1.36484e17i | 1.06161i | 0.847495 | + | 0.530804i | \(0.178110\pi\) | ||||
−0.847495 | + | 0.530804i | \(0.821890\pi\) | |||||||
\(104\) | −9.70298e16 | −0.695219 | ||||||||
\(105\) | 3.57380e16 | − | 3.53711e16i | 0.236060 | − | 0.233636i | ||||
\(106\) | 1.99764e16 | 0.121735 | ||||||||
\(107\) | − | 4.55554e16i | − | 0.256317i | −0.991754 | − | 0.128158i | \(-0.959093\pi\) | ||
0.991754 | − | 0.128158i | \(-0.0409066\pi\) | |||||||
\(108\) | − | 1.11071e17i | − | 0.577431i | ||||||
\(109\) | 2.16082e17 | 1.03871 | 0.519355 | − | 0.854559i | \(-0.326172\pi\) | ||||
0.519355 | + | 0.854559i | \(0.326172\pi\) | |||||||
\(110\) | 1.32016e17 | + | 1.33386e17i | 0.587205 | + | 0.593296i | ||||
\(111\) | 1.08260e17 | 0.445886 | ||||||||
\(112\) | 1.52799e16i | 0.0583132i | ||||||||
\(113\) | 2.03188e17i | 0.719005i | 0.933144 | + | 0.359502i | \(0.117054\pi\) | ||||
−0.933144 | + | 0.359502i | \(0.882946\pi\) | |||||||
\(114\) | −1.65236e17 | −0.542516 | ||||||||
\(115\) | 3.70545e16 | + | 3.74389e16i | 0.112956 | + | 0.114128i | ||||
\(116\) | −2.42626e15 | −0.00687139 | ||||||||
\(117\) | 7.74438e16i | 0.203895i | ||||||||
\(118\) | 2.79941e17i | 0.685597i | ||||||||
\(119\) | −2.23149e17 | −0.508681 | ||||||||
\(120\) | −3.50305e17 | + | 3.46708e17i | −0.743713 | + | 0.736077i | ||||
\(121\) | 6.81767e17 | 1.34884 | ||||||||
\(122\) | − | 4.57161e17i | − | 0.843355i | ||||||
\(123\) | − | 7.31384e17i | − | 1.25879i | ||||||
\(124\) | 2.79630e17 | 0.449262 | ||||||||
\(125\) | −4.63865e17 | − | 4.78454e17i | −0.696076 | − | 0.717968i | ||||
\(126\) | −3.11204e16 | −0.0436410 | ||||||||
\(127\) | 1.49219e17i | 0.195655i | 0.995203 | + | 0.0978277i | \(0.0311894\pi\) | ||||
−0.995203 | + | 0.0978277i | \(0.968811\pi\) | |||||||
\(128\) | − | 6.81736e17i | − | 0.836241i | ||||||
\(129\) | −8.20905e17 | −0.942498 | ||||||||
\(130\) | −2.69807e17 | + | 2.67037e17i | −0.290091 | + | 0.287113i | ||||
\(131\) | −4.10281e17 | −0.413309 | −0.206655 | − | 0.978414i | \(-0.566258\pi\) | ||||
−0.206655 | + | 0.978414i | \(0.566258\pi\) | |||||||
\(132\) | 1.28745e18i | 1.21577i | ||||||||
\(133\) | 2.93636e17i | 0.260058i | ||||||||
\(134\) | 8.01196e17 | 0.665806 | ||||||||
\(135\) | −7.40295e17 | − | 7.47975e17i | −0.577521 | − | 0.583512i | ||||
\(136\) | 2.18731e18 | 1.60261 | ||||||||
\(137\) | 6.17653e17i | 0.425226i | 0.977137 | + | 0.212613i | \(0.0681973\pi\) | ||||
−0.977137 | + | 0.212613i | \(0.931803\pi\) | |||||||
\(138\) | − | 1.52419e17i | − | 0.0986431i | ||||||
\(139\) | −1.59873e18 | −0.973080 | −0.486540 | − | 0.873658i | \(-0.661741\pi\) | ||||
−0.486540 | + | 0.873658i | \(0.661741\pi\) | |||||||
\(140\) | 2.54409e17 | + | 2.57049e17i | 0.145695 | + | 0.147207i | ||||
\(141\) | 3.13987e18 | 1.69258 | ||||||||
\(142\) | − | 5.28536e17i | − | 0.268302i | ||||||
\(143\) | 2.40145e18i | 1.14846i | ||||||||
\(144\) | −1.19541e17 | −0.0538810 | ||||||||
\(145\) | −1.63389e16 | + | 1.61711e16i | −0.00694375 | + | 0.00687246i | ||||
\(146\) | −1.37052e18 | −0.549397 | ||||||||
\(147\) | − | 2.72310e18i | − | 1.03007i | ||||||
\(148\) | 7.78671e17i | 0.278054i | ||||||||
\(149\) | 1.08941e18 | 0.367373 | 0.183687 | − | 0.982985i | \(-0.441197\pi\) | ||||
0.183687 | + | 0.982985i | \(0.441197\pi\) | |||||||
\(150\) | −1.98995e16 | + | 1.92816e18i | −0.00633965 | + | 0.614280i | ||||
\(151\) | −4.15139e18 | −1.24994 | −0.624970 | − | 0.780649i | \(-0.714889\pi\) | ||||
−0.624970 | + | 0.780649i | \(0.714889\pi\) | |||||||
\(152\) | − | 2.87822e18i | − | 0.819321i | ||||||
\(153\) | − | 1.74579e18i | − | 0.470018i | ||||||
\(154\) | −9.65009e17 | −0.245813 | ||||||||
\(155\) | 1.88308e18 | − | 1.86375e18i | 0.453993 | − | 0.449332i | ||||
\(156\) | −2.60419e18 | −0.594448 | ||||||||
\(157\) | 8.05540e16i | 0.0174157i | 0.999962 | + | 0.00870783i | \(0.00277182\pi\) | ||||
−0.999962 | + | 0.00870783i | \(0.997228\pi\) | |||||||
\(158\) | 1.63368e18i | 0.334642i | ||||||||
\(159\) | 1.29844e18 | 0.252084 | ||||||||
\(160\) | −3.95774e18 | − | 3.99880e18i | −0.728497 | − | 0.736054i | ||||
\(161\) | −2.70860e17 | −0.0472852 | ||||||||
\(162\) | 3.93991e18i | 0.652542i | ||||||||
\(163\) | − | 2.71154e18i | − | 0.426207i | −0.977030 | − | 0.213104i | \(-0.931643\pi\) | ||
0.977030 | − | 0.213104i | \(-0.0683572\pi\) | |||||||
\(164\) | 5.26053e18 | 0.784977 | ||||||||
\(165\) | 8.58088e18 | + | 8.66990e18i | 1.21596 | + | 1.22857i | ||||
\(166\) | −5.25929e18 | −0.707959 | ||||||||
\(167\) | 7.86788e18i | 1.00639i | 0.864172 | + | 0.503197i | \(0.167843\pi\) | ||||
−0.864172 | + | 0.503197i | \(0.832157\pi\) | |||||||
\(168\) | − | 2.53436e18i | − | 0.308133i | ||||||
\(169\) | 3.79286e18 | 0.438460 | ||||||||
\(170\) | 6.08216e18 | − | 6.01971e18i | 0.668717 | − | 0.661851i | ||||
\(171\) | −2.29724e18 | −0.240292 | ||||||||
\(172\) | − | 5.90443e18i | − | 0.587741i | ||||||
\(173\) | 3.01075e18i | 0.285288i | 0.989774 | + | 0.142644i | \(0.0455604\pi\) | ||||
−0.989774 | + | 0.142644i | \(0.954440\pi\) | |||||||
\(174\) | 6.65178e16 | 0.00600163 | ||||||||
\(175\) | 3.42648e18 | + | 3.53628e16i | 0.294459 | + | 0.00303895i | ||||
\(176\) | −3.70683e18 | −0.303491 | ||||||||
\(177\) | 1.81958e19i | 1.41970i | ||||||||
\(178\) | − | 1.29335e18i | − | 0.0961938i | ||||||
\(179\) | −1.11507e19 | −0.790774 | −0.395387 | − | 0.918515i | \(-0.629390\pi\) | ||||
−0.395387 | + | 0.918515i | \(0.629390\pi\) | |||||||
\(180\) | −2.01100e18 | + | 1.99035e18i | −0.136018 | + | 0.134621i | ||||
\(181\) | −1.16284e19 | −0.750332 | −0.375166 | − | 0.926958i | \(-0.622414\pi\) | ||||
−0.375166 | + | 0.926958i | \(0.622414\pi\) | |||||||
\(182\) | − | 1.95198e18i | − | 0.120190i | ||||||
\(183\) | − | 2.97149e19i | − | 1.74638i | ||||||
\(184\) | 2.65497e18 | 0.148973 | ||||||||
\(185\) | 5.18987e18 | + | 5.24371e18i | 0.278097 | + | 0.280982i | ||||
\(186\) | −7.66627e18 | −0.392396 | ||||||||
\(187\) | − | 5.41349e19i | − | 2.64743i | ||||||
\(188\) | 2.25838e19i | 1.05549i | ||||||||
\(189\) | 5.41139e18 | 0.241759 | ||||||||
\(190\) | −7.92120e18 | − | 8.00337e18i | −0.338365 | − | 0.341875i | ||||
\(191\) | 1.23347e19 | 0.503901 | 0.251951 | − | 0.967740i | \(-0.418928\pi\) | ||||
0.251951 | + | 0.967740i | \(0.418928\pi\) | |||||||
\(192\) | 1.05644e19i | 0.412842i | ||||||||
\(193\) | 4.31622e19i | 1.61386i | 0.590645 | + | 0.806931i | \(0.298873\pi\) | ||||
−0.590645 | + | 0.806931i | \(0.701127\pi\) | |||||||
\(194\) | 2.20584e19 | 0.789331 | ||||||||
\(195\) | −1.75371e19 | + | 1.73571e19i | −0.600709 | + | 0.594541i | ||||
\(196\) | 1.95861e19 | 0.642349 | ||||||||
\(197\) | 2.74515e18i | 0.0862191i | 0.999070 | + | 0.0431096i | \(0.0137265\pi\) | ||||
−0.999070 | + | 0.0431096i | \(0.986274\pi\) | |||||||
\(198\) | − | 7.54967e18i | − | 0.227130i | ||||||
\(199\) | −5.45248e19 | −1.57160 | −0.785802 | − | 0.618478i | \(-0.787750\pi\) | ||||
−0.785802 | + | 0.618478i | \(0.787750\pi\) | |||||||
\(200\) | −3.35864e19 | − | 3.46627e17i | −0.927701 | − | 0.00957430i | ||||
\(201\) | 5.20767e19 | 1.37872 | ||||||||
\(202\) | 3.93450e19i | 0.998625i | ||||||||
\(203\) | − | 1.18207e17i | − | 0.00287692i | ||||||
\(204\) | 5.87053e19 | 1.37032 | ||||||||
\(205\) | 3.54254e19 | − | 3.50617e19i | 0.793244 | − | 0.785100i | ||||
\(206\) | 2.69132e19 | 0.578222 | ||||||||
\(207\) | − | 2.11905e18i | − | 0.0436912i | ||||||
\(208\) | − | 7.49803e18i | − | 0.148391i | ||||||
\(209\) | −7.12349e19 | −1.35347 | ||||||||
\(210\) | −6.97484e18 | − | 7.04719e18i | −0.127254 | − | 0.128574i | ||||
\(211\) | 8.75529e18 | 0.153416 | 0.0767078 | − | 0.997054i | \(-0.475559\pi\) | ||||
0.0767078 | + | 0.997054i | \(0.475559\pi\) | |||||||
\(212\) | 9.33911e18i | 0.157199i | ||||||||
\(213\) | − | 3.43541e19i | − | 0.555588i | ||||||
\(214\) | −8.98307e18 | −0.139607 | ||||||||
\(215\) | −3.93532e19 | − | 3.97615e19i | −0.587833 | − | 0.593931i | ||||
\(216\) | −5.30425e19 | −0.761670 | ||||||||
\(217\) | 1.36236e19i | 0.188097i | ||||||||
\(218\) | − | 4.26093e19i | − | 0.565750i | ||||||
\(219\) | −8.90820e19 | −1.13767 | ||||||||
\(220\) | −6.23589e19 | + | 6.17187e19i | −0.766136 | + | 0.758270i | ||||
\(221\) | 1.09502e20 | 1.29446 | ||||||||
\(222\) | − | 2.13479e19i | − | 0.242859i | ||||||
\(223\) | 4.58536e19i | 0.502091i | 0.967975 | + | 0.251045i | \(0.0807743\pi\) | ||||
−0.967975 | + | 0.251045i | \(0.919226\pi\) | |||||||
\(224\) | 2.89302e19 | 0.304960 | ||||||||
\(225\) | −2.76659e17 | + | 2.68068e19i | −0.00280797 | + | 0.272078i | ||||
\(226\) | 4.00667e19 | 0.391617 | ||||||||
\(227\) | − | 4.24431e19i | − | 0.399565i | −0.979840 | − | 0.199782i | \(-0.935977\pi\) | ||
0.979840 | − | 0.199782i | \(-0.0640235\pi\) | |||||||
\(228\) | − | 7.72490e19i | − | 0.700562i | ||||||
\(229\) | 1.66894e20 | 1.45828 | 0.729138 | − | 0.684367i | \(-0.239921\pi\) | ||||
0.729138 | + | 0.684367i | \(0.239921\pi\) | |||||||
\(230\) | 7.38258e18 | − | 7.30679e18i | 0.0621615 | − | 0.0615233i | ||||
\(231\) | −6.27243e19 | −0.509019 | ||||||||
\(232\) | 1.15867e18i | 0.00906382i | ||||||||
\(233\) | 6.95294e19i | 0.524377i | 0.965017 | + | 0.262188i | \(0.0844442\pi\) | ||||
−0.965017 | + | 0.262188i | \(0.915556\pi\) | |||||||
\(234\) | 1.52712e19 | 0.111055 | ||||||||
\(235\) | 1.50522e20 | + | 1.52083e20i | 1.05566 | + | 1.06661i | ||||
\(236\) | −1.30875e20 | −0.885326 | ||||||||
\(237\) | 1.06187e20i | 0.692962i | ||||||||
\(238\) | 4.40027e19i | 0.277061i | ||||||||
\(239\) | −4.98454e19 | −0.302861 | −0.151430 | − | 0.988468i | \(-0.548388\pi\) | ||||
−0.151430 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(240\) | −2.67921e19 | − | 2.70700e19i | −0.157112 | − | 0.158742i | ||||
\(241\) | −2.34973e19 | −0.133007 | −0.0665033 | − | 0.997786i | \(-0.521184\pi\) | ||||
−0.0665033 | + | 0.997786i | \(0.521184\pi\) | |||||||
\(242\) | − | 1.34438e20i | − | 0.734668i | ||||||
\(243\) | 1.00496e20i | 0.530269i | ||||||||
\(244\) | 2.13727e20 | 1.08904 | ||||||||
\(245\) | 1.31896e20 | − | 1.30542e20i | 0.649113 | − | 0.642449i | ||||
\(246\) | −1.44222e20 | −0.685618 | ||||||||
\(247\) | − | 1.44091e20i | − | 0.661779i | ||||||
\(248\) | − | 1.33538e20i | − | 0.592606i | ||||||
\(249\) | −3.41847e20 | −1.46601 | ||||||||
\(250\) | −9.43464e19 | + | 9.14697e19i | −0.391053 | + | 0.379129i | ||||
\(251\) | −1.73046e20 | −0.693322 | −0.346661 | − | 0.937990i | \(-0.612685\pi\) | ||||
−0.346661 | + | 0.937990i | \(0.612685\pi\) | |||||||
\(252\) | − | 1.45490e19i | − | 0.0563546i | ||||||
\(253\) | − | 6.57095e19i | − | 0.246096i | ||||||
\(254\) | 2.94245e19 | 0.106567 | ||||||||
\(255\) | 3.95333e20 | − | 3.91274e20i | 1.38475 | − | 1.37053i | ||||
\(256\) | −2.42466e20 | −0.821508 | ||||||||
\(257\) | 4.12299e20i | 1.35139i | 0.737181 | + | 0.675695i | \(0.236156\pi\) | ||||
−0.737181 | + | 0.675695i | \(0.763844\pi\) | |||||||
\(258\) | 1.61875e20i | 0.513347i | ||||||||
\(259\) | −3.79368e19 | −0.116416 | ||||||||
\(260\) | −1.24842e20 | − | 1.26137e20i | −0.370755 | − | 0.374601i | ||||
\(261\) | 9.24785e17 | 0.00265825 | ||||||||
\(262\) | 8.09033e19i | 0.225116i | ||||||||
\(263\) | − | 2.09492e20i | − | 0.564343i | −0.959364 | − | 0.282171i | \(-0.908945\pi\) | ||
0.959364 | − | 0.282171i | \(-0.0910546\pi\) | |||||||
\(264\) | 6.14824e20 | 1.60368 | ||||||||
\(265\) | 6.22456e19 | + | 6.28913e19i | 0.157224 | + | 0.158855i | ||||
\(266\) | 5.79022e19 | 0.141645 | ||||||||
\(267\) | − | 8.40663e19i | − | 0.199194i | ||||||
\(268\) | 3.74566e20i | 0.859770i | ||||||||
\(269\) | −1.23146e20 | −0.273859 | −0.136930 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136930 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(270\) | −1.47493e20 | + | 1.45979e20i | −0.317819 | + | 0.314556i | ||||
\(271\) | 1.71222e20 | 0.357536 | 0.178768 | − | 0.983891i | \(-0.442789\pi\) | ||||
0.178768 | + | 0.983891i | \(0.442789\pi\) | |||||||
\(272\) | 1.69025e20i | 0.342071i | ||||||||
\(273\) | − | 1.26876e20i | − | 0.248884i | ||||||
\(274\) | 1.21795e20 | 0.231606 | ||||||||
\(275\) | −8.57888e18 | + | 8.31250e20i | −0.0158162 | + | 1.53251i | ||||
\(276\) | 7.12571e19 | 0.127380 | ||||||||
\(277\) | − | 4.23825e20i | − | 0.734698i | −0.930083 | − | 0.367349i | \(-0.880266\pi\) | ||
0.930083 | − | 0.367349i | \(-0.119734\pi\) | |||||||
\(278\) | 3.15253e20i | 0.530004i | ||||||||
\(279\) | −1.06583e20 | −0.173801 | ||||||||
\(280\) | 1.22754e20 | − | 1.21494e20i | 0.194175 | − | 0.192182i | ||||
\(281\) | −3.64626e20 | −0.559556 | −0.279778 | − | 0.960065i | \(-0.590261\pi\) | ||||
−0.279778 | + | 0.960065i | \(0.590261\pi\) | |||||||
\(282\) | − | 6.19152e20i | − | 0.921892i | ||||||
\(283\) | − | 5.68589e20i | − | 0.821511i | −0.911745 | − | 0.410756i | \(-0.865265\pi\) | ||
0.911745 | − | 0.410756i | \(-0.134735\pi\) | |||||||
\(284\) | 2.47095e20 | 0.346464 | ||||||||
\(285\) | −5.14868e20 | − | 5.20209e20i | −0.700671 | − | 0.707940i | ||||
\(286\) | 4.73542e20 | 0.625529 | ||||||||
\(287\) | 2.56293e20i | 0.328655i | ||||||||
\(288\) | 2.26333e20i | 0.281781i | ||||||||
\(289\) | −1.64122e21 | −1.98397 | ||||||||
\(290\) | 3.18879e18 | + | 3.22187e18i | 0.00374320 | + | 0.00378203i | ||||
\(291\) | 1.43377e21 | 1.63451 | ||||||||
\(292\) | − | 6.40729e20i | − | 0.709448i | ||||||
\(293\) | − | 1.46631e21i | − | 1.57707i | −0.614991 | − | 0.788534i | \(-0.710841\pi\) | ||
0.614991 | − | 0.788534i | \(-0.289159\pi\) | |||||||
\(294\) | −5.36968e20 | −0.561043 | ||||||||
\(295\) | −8.81333e20 | + | 8.72284e20i | −0.894649 | + | 0.885464i | ||||
\(296\) | 3.71857e20 | 0.366772 | ||||||||
\(297\) | 1.31278e21i | 1.25824i | ||||||||
\(298\) | − | 2.14821e20i | − | 0.200096i | ||||||
\(299\) | 1.32914e20 | 0.120328 | ||||||||
\(300\) | −9.01429e20 | − | 9.30316e18i | −0.793233 | − | 0.00818653i | ||||
\(301\) | 2.87663e20 | 0.246076 | ||||||||
\(302\) | 8.18613e20i | 0.680800i | ||||||||
\(303\) | 2.55737e21i | 2.06791i | ||||||||
\(304\) | 2.22416e20 | 0.174880 | ||||||||
\(305\) | 1.43927e21 | − | 1.42450e21i | 1.10051 | − | 1.08921i | ||||
\(306\) | −3.44252e20 | −0.256003 | ||||||||
\(307\) | − | 1.00902e21i | − | 0.729833i | −0.931040 | − | 0.364916i | \(-0.881098\pi\) | ||
0.931040 | − | 0.364916i | \(-0.118902\pi\) | |||||||
\(308\) | − | 4.51149e20i | − | 0.317424i | ||||||
\(309\) | 1.74933e21 | 1.19736 | ||||||||
\(310\) | −3.67512e20 | − | 3.71325e20i | −0.244736 | − | 0.247275i | ||||
\(311\) | 1.79361e21 | 1.16216 | 0.581078 | − | 0.813848i | \(-0.302631\pi\) | ||||
0.581078 | + | 0.813848i | \(0.302631\pi\) | |||||||
\(312\) | 1.24364e21i | 0.784117i | ||||||||
\(313\) | − | 6.24766e20i | − | 0.383345i | −0.981459 | − | 0.191673i | \(-0.938609\pi\) | ||
0.981459 | − | 0.191673i | \(-0.0613912\pi\) | |||||||
\(314\) | 1.58845e19 | 0.00948572 | ||||||||
\(315\) | −9.69699e19 | − | 9.79758e19i | −0.0563634 | − | 0.0569481i | ||||
\(316\) | −7.63757e20 | −0.432130 | ||||||||
\(317\) | 3.52085e20i | 0.193930i | 0.995288 | + | 0.0969648i | \(0.0309134\pi\) | ||||
−0.995288 | + | 0.0969648i | \(0.969087\pi\) | |||||||
\(318\) | − | 2.56039e20i | − | 0.137302i | ||||||
\(319\) | 2.86766e19 | 0.0149729 | ||||||||
\(320\) | −5.11697e20 | + | 5.06444e20i | −0.260159 | + | 0.257488i | ||||
\(321\) | −5.83888e20 | −0.289092 | ||||||||
\(322\) | 5.34109e19i | 0.0257546i | ||||||||
\(323\) | 3.24819e21i | 1.52553i | ||||||||
\(324\) | −1.84194e21 | −0.842641 | ||||||||
\(325\) | −1.68142e21 | − | 1.73530e19i | −0.749320 | − | 0.00773332i | ||||
\(326\) | −5.34689e20 | −0.232141 | ||||||||
\(327\) | − | 2.76955e21i | − | 1.17153i | ||||||
\(328\) | − | 2.51218e21i | − | 1.03544i | ||||||
\(329\) | −1.10028e21 | −0.441914 | ||||||||
\(330\) | 1.70962e21 | − | 1.69207e21i | 0.669161 | − | 0.662291i | ||||
\(331\) | −2.87953e21 | −1.09846 | −0.549229 | − | 0.835672i | \(-0.685079\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685079\pi\) | |||||||
\(332\) | − | 2.45876e21i | − | 0.914202i | ||||||
\(333\) | − | 2.96795e20i | − | 0.107568i | ||||||
\(334\) | 1.55147e21 | 0.548148 | ||||||||
\(335\) | 2.49650e21 | + | 2.52239e21i | 0.859904 | + | 0.868824i | ||||
\(336\) | 1.95844e20 | 0.0657697 | ||||||||
\(337\) | − | 6.69424e20i | − | 0.219203i | −0.993976 | − | 0.109602i | \(-0.965042\pi\) | ||
0.993976 | − | 0.109602i | \(-0.0349575\pi\) | |||||||
\(338\) | − | 7.47916e20i | − | 0.238814i | ||||||
\(339\) | 2.60428e21 | 0.810944 | ||||||||
\(340\) | 2.81427e21 | + | 2.84346e21i | 0.854662 | + | 0.863528i | ||||
\(341\) | −3.30502e21 | −0.978952 | ||||||||
\(342\) | 4.52993e20i | 0.130879i | ||||||||
\(343\) | 1.99907e21i | 0.563414i | ||||||||
\(344\) | −2.81968e21 | −0.775269 | ||||||||
\(345\) | 4.79858e20 | − | 4.74932e20i | 0.128721 | − | 0.127400i | ||||
\(346\) | 5.93691e20 | 0.155387 | ||||||||
\(347\) | 8.92234e20i | 0.227865i | 0.993488 | + | 0.113933i | \(0.0363448\pi\) | ||||
−0.993488 | + | 0.113933i | \(0.963655\pi\) | |||||||
\(348\) | 3.10976e19i | 0.00775004i | ||||||||
\(349\) | 2.36533e21 | 0.575274 | 0.287637 | − | 0.957739i | \(-0.407130\pi\) | ||||
0.287637 | + | 0.957739i | \(0.407130\pi\) | |||||||
\(350\) | 6.97321e18 | − | 6.75668e20i | 0.00165521 | − | 0.160382i | ||||
\(351\) | −2.65544e21 | −0.615213 | ||||||||
\(352\) | 7.01835e21i | 1.58717i | ||||||||
\(353\) | − | 2.51330e21i | − | 0.554829i | −0.960750 | − | 0.277414i | \(-0.910523\pi\) | ||
0.960750 | − | 0.277414i | \(-0.0894774\pi\) | |||||||
\(354\) | 3.58803e21 | 0.773265 | ||||||||
\(355\) | 1.66398e21 | − | 1.64690e21i | 0.350113 | − | 0.346518i | ||||
\(356\) | 6.04653e20 | 0.124217 | ||||||||
\(357\) | 2.86012e21i | 0.573726i | ||||||||
\(358\) | 2.19881e21i | 0.430708i | ||||||||
\(359\) | 2.10167e21 | 0.402033 | 0.201017 | − | 0.979588i | \(-0.435576\pi\) | ||||
0.201017 | + | 0.979588i | \(0.435576\pi\) | |||||||
\(360\) | 9.50499e20 | + | 9.60360e20i | 0.177574 | + | 0.179417i | ||||
\(361\) | −1.20617e21 | −0.220089 | ||||||||
\(362\) | 2.29301e21i | 0.408680i | ||||||||
\(363\) | − | 8.73829e21i | − | 1.52132i | ||||||
\(364\) | 9.12566e20 | 0.155204 | ||||||||
\(365\) | −4.27049e21 | − | 4.31479e21i | −0.709558 | − | 0.716919i | ||||
\(366\) | −5.85948e21 | −0.951196 | ||||||||
\(367\) | − | 7.00996e21i | − | 1.11187i | −0.831226 | − | 0.555935i | \(-0.812360\pi\) | ||
0.831226 | − | 0.555935i | \(-0.187640\pi\) | |||||||
\(368\) | 2.05165e20i | 0.0317977i | ||||||||
\(369\) | −2.00509e21 | −0.303675 | ||||||||
\(370\) | 1.03401e21 | − | 1.02339e21i | 0.153042 | − | 0.151470i | ||||
\(371\) | −4.55001e20 | −0.0658164 | ||||||||
\(372\) | − | 3.58405e21i | − | 0.506709i | ||||||
\(373\) | 5.69623e21i | 0.787158i | 0.919291 | + | 0.393579i | \(0.128763\pi\) | ||||
−0.919291 | + | 0.393579i | \(0.871237\pi\) | |||||||
\(374\) | −1.06749e22 | −1.44196 | ||||||||
\(375\) | −6.13239e21 | + | 5.94541e21i | −0.809775 | + | 0.785084i | ||||
\(376\) | 1.07850e22 | 1.39226 | ||||||||
\(377\) | 5.80058e19i | 0.00732099i | ||||||||
\(378\) | − | 1.06707e21i | − | 0.131678i | ||||||
\(379\) | 4.63351e21 | 0.559083 | 0.279542 | − | 0.960134i | \(-0.409817\pi\) | ||||
0.279542 | + | 0.960134i | \(0.409817\pi\) | |||||||
\(380\) | 3.74164e21 | − | 3.70323e21i | 0.441470 | − | 0.436938i | ||||
\(381\) | 1.91255e21 | 0.220674 | ||||||||
\(382\) | − | 2.43228e21i | − | 0.274458i | ||||||
\(383\) | 8.22870e20i | 0.0908117i | 0.998969 | + | 0.0454058i | \(0.0144581\pi\) | ||||
−0.998969 | + | 0.0454058i | \(0.985542\pi\) | |||||||
\(384\) | −8.73788e21 | −0.943171 | ||||||||
\(385\) | −3.00693e21 | − | 3.03812e21i | −0.317473 | − | 0.320767i | ||||
\(386\) | 8.51117e21 | 0.879016 | ||||||||
\(387\) | 2.25051e21i | 0.227373i | ||||||||
\(388\) | 1.03125e22i | 1.01928i | ||||||||
\(389\) | 6.11949e21 | 0.591757 | 0.295879 | − | 0.955226i | \(-0.404388\pi\) | ||||
0.295879 | + | 0.955226i | \(0.404388\pi\) | |||||||
\(390\) | 3.42264e21 | + | 3.45815e21i | 0.323826 | + | 0.327186i | ||||
\(391\) | −2.99624e21 | −0.277379 | ||||||||
\(392\) | − | 9.35339e21i | − | 0.847301i | ||||||
\(393\) | 5.25861e21i | 0.466159i | ||||||||
\(394\) | 5.41317e20 | 0.0469606 | ||||||||
\(395\) | −5.14328e21 | + | 5.09047e21i | −0.436681 | + | 0.432198i | ||||
\(396\) | 3.52953e21 | 0.293297 | ||||||||
\(397\) | 1.23524e22i | 1.00469i | 0.864668 | + | 0.502344i | \(0.167529\pi\) | ||||
−0.864668 | + | 0.502344i | \(0.832471\pi\) | |||||||
\(398\) | 1.07518e22i | 0.855999i | ||||||||
\(399\) | 3.76357e21 | 0.293312 | ||||||||
\(400\) | 2.67858e19 | − | 2.59541e21i | 0.00204359 | − | 0.198014i | ||||
\(401\) | 2.56078e22 | 1.91269 | 0.956346 | − | 0.292237i | \(-0.0943996\pi\) | ||||
0.956346 | + | 0.292237i | \(0.0943996\pi\) | |||||||
\(402\) | − | 1.02690e22i | − | 0.750943i | ||||||
\(403\) | − | 6.68525e21i | − | 0.478657i | ||||||
\(404\) | −1.83941e22 | −1.28955 | ||||||||
\(405\) | −1.24040e22 | + | 1.22766e22i | −0.851515 | + | 0.842772i | ||||
\(406\) | −2.33093e19 | −0.00156696 | ||||||||
\(407\) | − | 9.20330e21i | − | 0.605887i | ||||||
\(408\) | − | 2.80349e22i | − | 1.80754i | ||||||
\(409\) | 1.54083e22 | 0.972986 | 0.486493 | − | 0.873684i | \(-0.338276\pi\) | ||||
0.486493 | + | 0.873684i | \(0.338276\pi\) | |||||||
\(410\) | −6.91382e21 | − | 6.98554e21i | −0.427617 | − | 0.432053i | ||||
\(411\) | 7.91652e21 | 0.479600 | ||||||||
\(412\) | 1.25822e22i | 0.746670i | ||||||||
\(413\) | − | 6.37620e21i | − | 0.370669i | ||||||
\(414\) | −4.17856e20 | −0.0237971 | ||||||||
\(415\) | −1.63877e22 | − | 1.65577e22i | −0.914345 | − | 0.923830i | ||||
\(416\) | −1.41964e22 | −0.776043 | ||||||||
\(417\) | 2.04911e22i | 1.09751i | ||||||||
\(418\) | 1.40468e22i | 0.737190i | ||||||||
\(419\) | −2.60959e22 | −1.34200 | −0.671001 | − | 0.741456i | \(-0.734136\pi\) | ||||
−0.671001 | + | 0.741456i | \(0.734136\pi\) | |||||||
\(420\) | 3.29462e21 | − | 3.26079e21i | 0.166030 | − | 0.164325i | ||||
\(421\) | −2.31572e22 | −1.14364 | −0.571818 | − | 0.820380i | \(-0.693762\pi\) | ||||
−0.571818 | + | 0.820380i | \(0.693762\pi\) | |||||||
\(422\) | − | 1.72646e21i | − | 0.0835603i | ||||||
\(423\) | − | 8.60796e21i | − | 0.408326i | ||||||
\(424\) | 4.45992e21 | 0.207356 | ||||||||
\(425\) | 3.79036e22 | + | 3.91182e20i | 1.72733 | + | 0.0178268i | ||||
\(426\) | −6.77430e21 | −0.302610 | ||||||||
\(427\) | 1.04127e22i | 0.455962i | ||||||||
\(428\) | − | 4.19966e21i | − | 0.180278i | ||||||
\(429\) | 3.07796e22 | 1.29532 | ||||||||
\(430\) | −7.84057e21 | + | 7.76007e21i | −0.323494 | + | 0.320172i | ||||
\(431\) | 6.11457e20 | 0.0247348 | 0.0123674 | − | 0.999924i | \(-0.496063\pi\) | ||||
0.0123674 | + | 0.999924i | \(0.496063\pi\) | |||||||
\(432\) | − | 4.09889e21i | − | 0.162575i | ||||||
\(433\) | − | 3.10026e22i | − | 1.20573i | −0.797842 | − | 0.602867i | \(-0.794025\pi\) | ||
0.797842 | − | 0.602867i | \(-0.205975\pi\) | |||||||
\(434\) | 2.68643e21 | 0.102450 | ||||||||
\(435\) | 2.07267e20 | + | 2.09417e20i | 0.00775125 | + | 0.00783166i | ||||
\(436\) | 1.99202e22 | 0.730565 | ||||||||
\(437\) | 3.94268e21i | 0.141808i | ||||||||
\(438\) | 1.75661e22i | 0.619649i | ||||||||
\(439\) | −1.11795e22 | −0.386787 | −0.193394 | − | 0.981121i | \(-0.561949\pi\) | ||||
−0.193394 | + | 0.981121i | \(0.561949\pi\) | |||||||
\(440\) | 2.94739e22 | + | 2.97797e22i | 1.00021 | + | 1.01058i | ||||
\(441\) | −7.46536e21 | −0.248498 | ||||||||
\(442\) | − | 2.15927e22i | − | 0.705047i | ||||||
\(443\) | 4.87194e22i | 1.56052i | 0.625454 | + | 0.780261i | \(0.284914\pi\) | ||||
−0.625454 | + | 0.780261i | \(0.715086\pi\) | |||||||
\(444\) | 9.98030e21 | 0.313609 | ||||||||
\(445\) | 4.07185e21 | − | 4.03004e21i | 0.125525 | − | 0.124237i | ||||
\(446\) | 9.04188e21 | 0.273472 | ||||||||
\(447\) | − | 1.39631e22i | − | 0.414349i | ||||||
\(448\) | − | 3.70199e21i | − | 0.107788i | ||||||
\(449\) | −8.32387e21 | −0.237811 | −0.118905 | − | 0.992906i | \(-0.537938\pi\) | ||||
−0.118905 | + | 0.992906i | \(0.537938\pi\) | |||||||
\(450\) | 5.28604e21 | + | 5.45543e19i | 0.148192 | + | 0.00152941i | ||||
\(451\) | −6.21756e22 | −1.71048 | ||||||||
\(452\) | 1.87315e22i | 0.505704i | ||||||||
\(453\) | 5.32088e22i | 1.40977i | ||||||||
\(454\) | −8.36936e21 | −0.217629 | ||||||||
\(455\) | 6.14539e21 | − | 6.08229e21i | 0.156838 | − | 0.155228i | ||||
\(456\) | −3.68905e22 | −0.924088 | ||||||||
\(457\) | − | 6.51348e22i | − | 1.60149i | −0.599002 | − | 0.800747i | \(-0.704436\pi\) | ||
0.599002 | − | 0.800747i | \(-0.295564\pi\) | |||||||
\(458\) | − | 3.29099e22i | − | 0.794273i | ||||||
\(459\) | 5.98605e22 | 1.41818 | ||||||||
\(460\) | 3.41598e21 | + | 3.45142e21i | 0.0794464 | + | 0.0802705i | ||||
\(461\) | −3.15500e22 | −0.720346 | −0.360173 | − | 0.932886i | \(-0.617282\pi\) | ||||
−0.360173 | + | 0.932886i | \(0.617282\pi\) | |||||||
\(462\) | 1.23686e22i | 0.277245i | ||||||||
\(463\) | − | 7.28815e22i | − | 1.60391i | −0.597388 | − | 0.801953i | \(-0.703795\pi\) | ||
0.597388 | − | 0.801953i | \(-0.296205\pi\) | |||||||
\(464\) | −8.95368e19 | −0.00193463 | ||||||||
\(465\) | −2.38878e22 | − | 2.41356e22i | −0.506788 | − | 0.512045i | ||||
\(466\) | 1.37105e22 | 0.285610 | ||||||||
\(467\) | − | 2.24397e22i | − | 0.459011i | −0.973307 | − | 0.229506i | \(-0.926289\pi\) | ||
0.973307 | − | 0.229506i | \(-0.0737109\pi\) | |||||||
\(468\) | 7.13939e21i | 0.143407i | ||||||||
\(469\) | −1.82488e22 | −0.359969 | ||||||||
\(470\) | 2.99893e22 | − | 2.96814e22i | 0.580945 | − | 0.574980i | ||||
\(471\) | 1.03247e21 | 0.0196426 | ||||||||
\(472\) | 6.24995e22i | 1.16780i | ||||||||
\(473\) | 6.97859e22i | 1.28070i | ||||||||
\(474\) | 2.09390e22 | 0.377433 | ||||||||
\(475\) | 5.14747e20 | − | 4.98764e22i | 0.00911378 | − | 0.883079i | ||||
\(476\) | −2.05716e22 | −0.357775 | ||||||||
\(477\) | − | 3.55966e21i | − | 0.0608139i | ||||||
\(478\) | 9.82902e21i | 0.164958i | ||||||||
\(479\) | −6.47401e22 | −1.06739 | −0.533693 | − | 0.845678i | \(-0.679196\pi\) | ||||
−0.533693 | + | 0.845678i | \(0.679196\pi\) | |||||||
\(480\) | −5.12531e22 | + | 5.07268e22i | −0.830174 | + | 0.821651i | ||||
\(481\) | 1.86161e22 | 0.296248 | ||||||||
\(482\) | 4.63344e21i | 0.0724442i | ||||||||
\(483\) | 3.47164e21i | 0.0533316i | ||||||||
\(484\) | 6.28508e22 | 0.948692 | ||||||||
\(485\) | 6.87331e22 | + | 6.94461e22i | 1.01944 | + | 1.03001i | ||||
\(486\) | 1.98169e22 | 0.288820 | ||||||||
\(487\) | 1.32206e23i | 1.89346i | 0.322030 | + | 0.946730i | \(0.395635\pi\) | ||||
−0.322030 | + | 0.946730i | \(0.604365\pi\) | |||||||
\(488\) | − | 1.02066e23i | − | 1.43652i | ||||||
\(489\) | −3.47541e22 | −0.480707 | ||||||||
\(490\) | −2.57416e22 | − | 2.60086e22i | −0.349920 | − | 0.353550i | ||||
\(491\) | 1.24365e23 | 1.66151 | 0.830757 | − | 0.556636i | \(-0.187908\pi\) | ||||
0.830757 | + | 0.556636i | \(0.187908\pi\) | |||||||
\(492\) | − | 6.74248e22i | − | 0.885353i | ||||||
\(493\) | − | 1.30760e21i | − | 0.0168763i | ||||||
\(494\) | −2.84133e22 | −0.360448 | ||||||||
\(495\) | 2.37685e22 | − | 2.35245e22i | 0.296386 | − | 0.293343i | ||||
\(496\) | 1.03192e22 | 0.126489 | ||||||||
\(497\) | 1.20384e22i | 0.145058i | ||||||||
\(498\) | 6.74088e22i | 0.798486i | ||||||||
\(499\) | 1.71668e22 | 0.199910 | 0.0999550 | − | 0.994992i | \(-0.468130\pi\) | ||||
0.0999550 | + | 0.994992i | \(0.468130\pi\) | |||||||
\(500\) | −4.27628e22 | − | 4.41077e22i | −0.489578 | − | 0.504975i | ||||
\(501\) | 1.00844e23 | 1.13508 | ||||||||
\(502\) | 3.41230e22i | 0.377629i | ||||||||
\(503\) | − | 6.39694e22i | − | 0.696057i | −0.937484 | − | 0.348028i | \(-0.886851\pi\) | ||
0.937484 | − | 0.348028i | \(-0.113149\pi\) | |||||||
\(504\) | −6.94793e21 | −0.0743355 | ||||||||
\(505\) | −1.23869e23 | + | 1.22597e23i | −1.30313 | + | 1.28975i | ||||
\(506\) | −1.29573e22 | −0.134040 | ||||||||
\(507\) | − | 4.86136e22i | − | 0.494527i | ||||||
\(508\) | 1.37562e22i | 0.137612i | ||||||||
\(509\) | −1.87713e23 | −1.84669 | −0.923346 | − | 0.383970i | \(-0.874557\pi\) | ||||
−0.923346 | + | 0.383970i | \(0.874557\pi\) | |||||||
\(510\) | −7.71553e22 | − | 7.79557e22i | −0.746482 | − | 0.754226i | ||||
\(511\) | 3.12163e22 | 0.297032 | ||||||||
\(512\) | − | 4.15445e22i | − | 0.388793i | ||||||
\(513\) | − | 7.87691e22i | − | 0.725034i | ||||||
\(514\) | 8.13013e22 | 0.736057 | ||||||||
\(515\) | 8.38606e22 | + | 8.47306e22i | 0.746787 | + | 0.754534i | ||||
\(516\) | −7.56777e22 | −0.662896 | ||||||||
\(517\) | − | 2.66923e23i | − | 2.29994i | ||||||
\(518\) | 7.48076e21i | 0.0634078i | ||||||||
\(519\) | 3.85891e22 | 0.321768 | ||||||||
\(520\) | −6.02372e22 | + | 5.96187e22i | −0.494124 | + | 0.489051i | ||||
\(521\) | 2.51826e22 | 0.203226 | 0.101613 | − | 0.994824i | \(-0.467600\pi\) | ||||
0.101613 | + | 0.994824i | \(0.467600\pi\) | |||||||
\(522\) | − | 1.82359e20i | − | 0.00144786i | ||||||
\(523\) | 1.41643e23i | 1.10645i | 0.833033 | + | 0.553223i | \(0.186602\pi\) | ||||
−0.833033 | + | 0.553223i | \(0.813398\pi\) | |||||||
\(524\) | −3.78230e22 | −0.290696 | ||||||||
\(525\) | 4.53249e20 | − | 4.39176e22i | 0.00342754 | − | 0.332112i | ||||
\(526\) | −4.13097e22 | −0.307378 | ||||||||
\(527\) | 1.50703e23i | 1.10340i | ||||||||
\(528\) | 4.75109e22i | 0.342298i | ||||||||
\(529\) | 1.37413e23 | 0.974216 | ||||||||
\(530\) | 1.24015e22 | − | 1.22742e22i | 0.0865229 | − | 0.0856345i | ||||
\(531\) | 4.98837e22 | 0.342496 | ||||||||
\(532\) | 2.70697e22i | 0.182909i | ||||||||
\(533\) | − | 1.25766e23i | − | 0.836340i | ||||||
\(534\) | −1.65771e22 | −0.108494 | ||||||||
\(535\) | −2.79909e22 | − | 2.82813e22i | −0.180306 | − | 0.182176i | ||||
\(536\) | 1.78875e23 | 1.13409 | ||||||||
\(537\) | 1.42920e23i | 0.891891i | ||||||||
\(538\) | 2.42833e22i | 0.149162i | ||||||||
\(539\) | −2.31493e23 | −1.39969 | ||||||||
\(540\) | −6.82464e22 | − | 6.89543e22i | −0.406193 | − | 0.410407i | ||||
\(541\) | 4.04123e22 | 0.236776 | 0.118388 | − | 0.992967i | \(-0.462227\pi\) | ||||
0.118388 | + | 0.992967i | \(0.462227\pi\) | |||||||
\(542\) | − | 3.37632e22i | − | 0.194738i | ||||||
\(543\) | 1.49043e23i | 0.846278i | ||||||||
\(544\) | 3.20025e23 | 1.78893 | ||||||||
\(545\) | 1.34146e23 | − | 1.32769e23i | 0.738259 | − | 0.730679i | ||||
\(546\) | −2.50187e22 | −0.135559 | ||||||||
\(547\) | 2.57609e23i | 1.37426i | 0.726535 | + | 0.687130i | \(0.241130\pi\) | ||||
−0.726535 | + | 0.687130i | \(0.758870\pi\) | |||||||
\(548\) | 5.69402e22i | 0.299078i | ||||||||
\(549\) | −8.14633e22 | −0.421305 | ||||||||
\(550\) | 1.63914e23 | + | 1.69167e21i | 0.834707 | + | 0.00861456i | ||||
\(551\) | −1.72064e21 | −0.00862785 | ||||||||
\(552\) | − | 3.40291e22i | − | 0.168023i | ||||||
\(553\) | − | 3.72102e22i | − | 0.180925i | ||||||
\(554\) | −8.35742e22 | −0.400165 | ||||||||
\(555\) | 6.72092e22 | − | 6.65191e22i | 0.316912 | − | 0.313658i | ||||
\(556\) | −1.47383e23 | −0.684405 | ||||||||
\(557\) | − | 2.94142e23i | − | 1.34520i | −0.740004 | − | 0.672602i | \(-0.765176\pi\) | ||
0.740004 | − | 0.672602i | \(-0.234824\pi\) | |||||||
\(558\) | 2.10171e22i | 0.0946633i | ||||||||
\(559\) | −1.41160e23 | −0.626198 | ||||||||
\(560\) | 9.38852e21 | + | 9.48592e21i | 0.0410203 | + | 0.0414459i | ||||
\(561\) | −6.93853e23 | −2.98596 | ||||||||
\(562\) | 7.19007e22i | 0.304771i | ||||||||
\(563\) | − | 2.02557e23i | − | 0.845719i | −0.906195 | − | 0.422859i | \(-0.861026\pi\) | ||
0.906195 | − | 0.422859i | \(-0.138974\pi\) | |||||||
\(564\) | 2.89459e23 | 1.19046 | ||||||||
\(565\) | 1.24846e23 | + | 1.26141e23i | 0.505783 | + | 0.511030i | ||||
\(566\) | −1.12120e23 | −0.447449 | ||||||||
\(567\) | − | 8.97391e22i | − | 0.352798i | ||||||
\(568\) | − | 1.18001e23i | − | 0.457009i | ||||||
\(569\) | −1.65130e23 | −0.630045 | −0.315022 | − | 0.949084i | \(-0.602012\pi\) | ||||
−0.315022 | + | 0.949084i | \(0.602012\pi\) | |||||||
\(570\) | −1.02580e23 | + | 1.01527e23i | −0.385591 | + | 0.381632i | ||||
\(571\) | 9.39406e22 | 0.347894 | 0.173947 | − | 0.984755i | \(-0.444348\pi\) | ||||
0.173947 | + | 0.984755i | \(0.444348\pi\) | |||||||
\(572\) | 2.21385e23i | 0.807759i | ||||||||
\(573\) | − | 1.58095e23i | − | 0.568336i | ||||||
\(574\) | 5.05384e22 | 0.179007 | ||||||||
\(575\) | 4.60077e22 | + | 4.74821e20i | 0.160566 | + | 0.00165712i | ||||
\(576\) | 2.89622e22 | 0.0995957 | ||||||||
\(577\) | − | 3.22752e23i | − | 1.09364i | −0.837250 | − | 0.546820i | \(-0.815838\pi\) | ||
0.837250 | − | 0.546820i | \(-0.184162\pi\) | |||||||
\(578\) | 3.23633e23i | 1.08060i | ||||||||
\(579\) | 5.53215e23 | 1.82023 | ||||||||
\(580\) | −1.50625e21 | + | 1.49078e21i | −0.00488381 | + | 0.00483367i | ||||
\(581\) | 1.19791e23 | 0.382759 | ||||||||
\(582\) | − | 2.82725e23i | − | 0.890263i | ||||||
\(583\) | − | 1.10381e23i | − | 0.342541i | ||||||
\(584\) | −3.05982e23 | −0.935809 | ||||||||
\(585\) | 4.75844e22 | + | 4.80780e22i | 0.143430 | + | 0.144918i | ||||
\(586\) | −2.89141e23 | −0.858975 | ||||||||
\(587\) | 1.54906e23i | 0.453570i | 0.973945 | + | 0.226785i | \(0.0728215\pi\) | ||||
−0.973945 | + | 0.226785i | \(0.927178\pi\) | |||||||
\(588\) | − | 2.51037e23i | − | 0.724486i | ||||||
\(589\) | 1.98307e23 | 0.564102 | ||||||||
\(590\) | 1.72006e23 | + | 1.73790e23i | 0.482282 | + | 0.487285i | ||||
\(591\) | 3.51849e22 | 0.0972440 | ||||||||
\(592\) | 2.87354e22i | 0.0782859i | ||||||||
\(593\) | 6.15543e23i | 1.65308i | 0.562879 | + | 0.826539i | \(0.309694\pi\) | ||||
−0.562879 | + | 0.826539i | \(0.690306\pi\) | |||||||
\(594\) | 2.58867e23 | 0.685319 | ||||||||
\(595\) | −1.38533e23 | + | 1.37111e23i | −0.361543 | + | 0.357831i | ||||
\(596\) | 1.00430e23 | 0.258388 | ||||||||
\(597\) | 6.98851e23i | 1.77257i | ||||||||
\(598\) | − | 2.62094e22i | − | 0.0655387i | ||||||
\(599\) | −2.44389e23 | −0.602496 | −0.301248 | − | 0.953546i | \(-0.597403\pi\) | ||||
−0.301248 | + | 0.953546i | \(0.597403\pi\) | |||||||
\(600\) | −4.44275e21 | + | 4.30480e23i | −0.0107986 | + | 1.04633i | ||||
\(601\) | −2.29017e23 | −0.548825 | −0.274413 | − | 0.961612i | \(-0.588483\pi\) | ||||
−0.274413 | + | 0.961612i | \(0.588483\pi\) | |||||||
\(602\) | − | 5.67244e22i | − | 0.134029i | ||||||
\(603\) | − | 1.42768e23i | − | 0.332609i | ||||||
\(604\) | −3.82708e23 | −0.879131 | ||||||||
\(605\) | 4.23249e23 | − | 4.18903e23i | 0.958683 | − | 0.948840i | ||||
\(606\) | 5.04289e23 | 1.12632 | ||||||||
\(607\) | − | 5.08927e23i | − | 1.12086i | −0.828202 | − | 0.560430i | \(-0.810636\pi\) | ||
0.828202 | − | 0.560430i | \(-0.189364\pi\) | |||||||
\(608\) | − | 4.21113e23i | − | 0.914572i | ||||||
\(609\) | −1.51507e21 | −0.00324479 | ||||||||
\(610\) | −2.80897e23 | − | 2.83811e23i | −0.593257 | − | 0.599412i | ||||
\(611\) | 5.39922e23 | 1.12455 | ||||||||
\(612\) | − | 1.60941e23i | − | 0.330582i | ||||||
\(613\) | 3.80505e23i | 0.770808i | 0.922748 | + | 0.385404i | \(0.125938\pi\) | ||||
−0.922748 | + | 0.385404i | \(0.874062\pi\) | |||||||
\(614\) | −1.98969e23 | −0.397515 | ||||||||
\(615\) | −4.49389e23 | − | 4.54051e23i | −0.885491 | − | 0.894677i | ||||
\(616\) | −2.15448e23 | −0.418703 | ||||||||
\(617\) | 3.08703e23i | 0.591721i | 0.955231 | + | 0.295860i | \(0.0956063\pi\) | ||||
−0.955231 | + | 0.295860i | \(0.904394\pi\) | |||||||
\(618\) | − | 3.44950e23i | − | 0.652160i | ||||||
\(619\) | −2.71878e22 | −0.0506995 | −0.0253497 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253497 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(620\) | 1.73597e23 | − | 1.71815e23i | 0.319311 | − | 0.316032i | ||||
\(621\) | 7.26593e22 | 0.131829 | ||||||||
\(622\) | − | 3.53682e23i | − | 0.632987i | ||||||
\(623\) | 2.94587e22i | 0.0520074i | ||||||||
\(624\) | −9.61031e22 | −0.167366 | ||||||||
\(625\) | −5.81953e23 | − | 1.20133e22i | −0.999787 | − | 0.0206387i | ||||
\(626\) | −1.23198e23 | −0.208795 | ||||||||
\(627\) | 9.13025e23i | 1.52654i | ||||||||
\(628\) | 7.42611e21i | 0.0122491i | ||||||||
\(629\) | −4.19655e23 | −0.682907 | ||||||||
\(630\) | −1.93199e22 | + | 1.91215e22i | −0.0310177 | + | 0.0306992i | ||||
\(631\) | 1.08541e22 | 0.0171927 | 0.00859636 | − | 0.999963i | \(-0.497264\pi\) | ||||
0.00859636 | + | 0.999963i | \(0.497264\pi\) | |||||||
\(632\) | 3.64734e23i | 0.570009i | ||||||||
\(633\) | − | 1.12217e23i | − | 0.173033i | ||||||
\(634\) | 6.94278e22 | 0.105627 | ||||||||
\(635\) | 9.16855e22 | + | 9.26367e22i | 0.137634 | + | 0.139061i | ||||
\(636\) | 1.19700e23 | 0.177301 | ||||||||
\(637\) | − | 4.68254e23i | − | 0.684379i | ||||||
\(638\) | − | 5.65474e21i | − | 0.00815524i | ||||||
\(639\) | −9.41819e22 | −0.134032 | ||||||||
\(640\) | −4.18884e23 | − | 4.23229e23i | −0.588252 | − | 0.594355i | ||||
\(641\) | 1.29824e24 | 1.79913 | 0.899563 | − | 0.436792i | \(-0.143885\pi\) | ||||
0.899563 | + | 0.436792i | \(0.143885\pi\) | |||||||
\(642\) | 1.15137e23i | 0.157459i | ||||||||
\(643\) | 9.64078e23i | 1.30113i | 0.759453 | + | 0.650563i | \(0.225467\pi\) | ||||
−0.759453 | + | 0.650563i | \(0.774533\pi\) | |||||||
\(644\) | −2.49701e22 | −0.0332575 | ||||||||
\(645\) | −5.09627e23 | + | 5.04395e23i | −0.669877 | + | 0.662999i | ||||
\(646\) | 6.40511e23 | 0.830903 | ||||||||
\(647\) | − | 1.43576e24i | − | 1.83821i | −0.394017 | − | 0.919103i | \(-0.628915\pi\) | ||
0.394017 | − | 0.919103i | \(-0.371085\pi\) | |||||||
\(648\) | 8.79624e23i | 1.11150i | ||||||||
\(649\) | 1.54684e24 | 1.92915 | ||||||||
\(650\) | −3.42184e21 | + | 3.31559e23i | −0.00421208 | + | 0.408129i | ||||
\(651\) | 1.74615e23 | 0.212149 | ||||||||
\(652\) | − | 2.49971e23i | − | 0.299768i | ||||||
\(653\) | − | 4.34101e23i | − | 0.513841i | −0.966433 | − | 0.256920i | \(-0.917292\pi\) | ||
0.966433 | − | 0.256920i | \(-0.0827078\pi\) | |||||||
\(654\) | −5.46128e23 | −0.638093 | ||||||||
\(655\) | −2.54707e23 | + | 2.52092e23i | −0.293758 | + | 0.290742i | ||||
\(656\) | 1.94131e23 | 0.221010 | ||||||||
\(657\) | 2.44218e23i | 0.274456i | ||||||||
\(658\) | 2.16964e23i | 0.240696i | ||||||||
\(659\) | −2.96685e22 | −0.0324915 | −0.0162457 | − | 0.999868i | \(-0.505171\pi\) | ||||
−0.0162457 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(660\) | 7.91055e23 | + | 7.99261e23i | 0.855230 | + | 0.864102i | ||||
\(661\) | −3.46155e23 | −0.369453 | −0.184726 | − | 0.982790i | \(-0.559140\pi\) | ||||
−0.184726 | + | 0.982790i | \(0.559140\pi\) | |||||||
\(662\) | 5.67815e23i | 0.598293i | ||||||||
\(663\) | − | 1.40350e24i | − | 1.45998i | ||||||
\(664\) | −1.17419e24 | −1.20589 | ||||||||
\(665\) | 1.80421e23 | + | 1.82293e23i | 0.182938 | + | 0.184835i | ||||
\(666\) | −5.85252e22 | −0.0585884 | ||||||||
\(667\) | − | 1.58718e21i | − | 0.00156876i | ||||||
\(668\) | 7.25325e23i | 0.707836i | ||||||||
\(669\) | 5.87711e23 | 0.566294 | ||||||||
\(670\) | 4.97391e23 | − | 4.92284e23i | 0.473219 | − | 0.468360i | ||||
\(671\) | −2.52609e24 | −2.37305 | ||||||||
\(672\) | − | 3.70802e23i | − | 0.343956i | ||||||
\(673\) | − | 1.41988e24i | − | 1.30054i | −0.759703 | − | 0.650270i | \(-0.774656\pi\) | ||
0.759703 | − | 0.650270i | \(-0.225344\pi\) | |||||||
\(674\) | −1.32004e23 | −0.119393 | ||||||||
\(675\) | −9.19167e23 | − | 9.48622e21i | −0.820942 | − | 0.00847250i | ||||
\(676\) | 3.49657e23 | 0.308386 | ||||||||
\(677\) | 8.46838e23i | 0.737559i | 0.929517 | + | 0.368779i | \(0.120224\pi\) | ||||
−0.929517 | + | 0.368779i | \(0.879776\pi\) | |||||||
\(678\) | − | 5.13539e23i | − | 0.441694i | ||||||
\(679\) | −5.02423e23 | −0.426753 | ||||||||
\(680\) | 1.35790e24 | − | 1.34396e24i | 1.13905 | − | 1.12736i | ||||
\(681\) | −5.43997e23 | −0.450657 | ||||||||
\(682\) | 6.51717e23i | 0.533202i | ||||||||
\(683\) | 3.07314e23i | 0.248317i | 0.992262 | + | 0.124159i | \(0.0396232\pi\) | ||||
−0.992262 | + | 0.124159i | \(0.960377\pi\) | |||||||
\(684\) | −2.11778e23 | −0.169007 | ||||||||
\(685\) | 3.79509e23 | + | 3.83446e23i | 0.299124 | + | 0.302227i | ||||
\(686\) | 3.94197e23 | 0.306872 | ||||||||
\(687\) | − | 2.13910e24i | − | 1.64475i | ||||||
\(688\) | − | 2.17892e23i | − | 0.165478i | ||||||
\(689\) | 2.23275e23 | 0.167485 | ||||||||
\(690\) | −9.36519e22 | − | 9.46234e22i | −0.0693904 | − | 0.0701102i | ||||
\(691\) | 2.97612e23 | 0.217815 | 0.108907 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108907 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(692\) | 2.77555e23i | 0.200654i | ||||||||
\(693\) | 1.71959e23i | 0.122798i | ||||||||
\(694\) | 1.75940e23 | 0.124111 | ||||||||
\(695\) | −9.92507e23 | + | 9.82317e23i | −0.691613 | + | 0.684512i | ||||
\(696\) | 1.48508e22 | 0.0102228 | ||||||||
\(697\) | 2.83510e24i | 1.92792i | ||||||||
\(698\) | − | 4.66419e23i | − | 0.313332i | ||||||
\(699\) | 8.91166e23 | 0.591429 | ||||||||
\(700\) | 3.15880e23 | + | 3.26003e21i | 0.207104 | + | 0.00213741i | ||||
\(701\) | −2.35616e24 | −1.52617 | −0.763084 | − | 0.646299i | \(-0.776316\pi\) | ||||
−0.763084 | + | 0.646299i | \(0.776316\pi\) | |||||||
\(702\) | 5.23626e23i | 0.335086i | ||||||||
\(703\) | 5.52214e23i | 0.349130i | ||||||||
\(704\) | 8.98087e23 | 0.560984 | ||||||||
\(705\) | 1.94927e24 | − | 1.92925e24i | 1.20300 | − | 1.19064i | ||||
\(706\) | −4.95597e23 | −0.302196 | ||||||||
\(707\) | − | 8.96159e23i | − | 0.539909i | ||||||
\(708\) | 1.67743e24i | 0.998533i | ||||||||
\(709\) | 2.77907e24 | 1.63458 | 0.817289 | − | 0.576227i | \(-0.195476\pi\) | ||||
0.817289 | + | 0.576227i | \(0.195476\pi\) | |||||||
\(710\) | −3.24752e23 | − | 3.28121e23i | −0.188737 | − | 0.190694i | ||||
\(711\) | 2.91111e23 | 0.167173 | ||||||||
\(712\) | − | 2.88754e23i | − | 0.163851i | ||||||
\(713\) | 1.82925e23i | 0.102568i | ||||||||
\(714\) | 5.63988e23 | 0.312489 | ||||||||
\(715\) | 1.47554e24 | + | 1.49085e24i | 0.807885 | + | 0.816265i | ||||
\(716\) | −1.02796e24 | −0.556182 | ||||||||
\(717\) | 6.38874e23i | 0.341588i | ||||||||
\(718\) | − | 4.14429e23i | − | 0.218974i | ||||||
\(719\) | −9.31893e23 | −0.486598 | −0.243299 | − | 0.969951i | \(-0.578230\pi\) | ||||
−0.243299 | + | 0.969951i | \(0.578230\pi\) | |||||||
\(720\) | −7.42124e22 | + | 7.34504e22i | −0.0382957 | + | 0.0379025i | ||||
\(721\) | −6.13002e23 | −0.312617 | ||||||||
\(722\) | 2.37845e23i | 0.119875i | ||||||||
\(723\) | 3.01167e23i | 0.150014i | ||||||||
\(724\) | −1.07200e24 | −0.527738 | ||||||||
\(725\) | −2.07219e20 | + | 2.00784e22i | −0.000100822 | + | 0.00976915i | ||||
\(726\) | −1.72310e24 | −0.828610 | ||||||||
\(727\) | − | 7.77376e23i | − | 0.369478i | −0.982788 | − | 0.184739i | \(-0.940856\pi\) | ||
0.982788 | − | 0.184739i | \(-0.0591440\pi\) | |||||||
\(728\) | − | 4.35799e23i | − | 0.204724i | ||||||
\(729\) | −1.29218e24 | −0.599983 | ||||||||
\(730\) | −8.50834e23 | + | 8.42098e23i | −0.390482 | + | 0.386472i | ||||
\(731\) | 3.18212e24 | 1.44351 | ||||||||
\(732\) | − | 2.73936e24i | − | 1.22830i | ||||||
\(733\) | 2.62599e24i | 1.16388i | 0.813230 | + | 0.581942i | \(0.197707\pi\) | ||||
−0.813230 | + | 0.581942i | \(0.802293\pi\) | |||||||
\(734\) | −1.38230e24 | −0.605598 | ||||||||
\(735\) | −1.67317e24 | − | 1.69053e24i | −0.724599 | − | 0.732116i | ||||
\(736\) | 3.88449e23 | 0.166292 | ||||||||
\(737\) | − | 4.42708e24i | − | 1.87346i | ||||||
\(738\) | 3.95384e23i | 0.165402i | ||||||||
\(739\) | 5.55636e23 | 0.229780 | 0.114890 | − | 0.993378i | \(-0.463348\pi\) | ||||
0.114890 | + | 0.993378i | \(0.463348\pi\) | |||||||
\(740\) | 4.78444e23 | + | 4.83407e23i | 0.195597 | + | 0.197626i | ||||
\(741\) | −1.84683e24 | −0.746401 | ||||||||
\(742\) | 8.97217e22i | 0.0358479i | ||||||||
\(743\) | − | 5.15655e23i | − | 0.203683i | −0.994801 | − | 0.101841i | \(-0.967527\pi\) | ||
0.994801 | − | 0.101841i | \(-0.0324734\pi\) | |||||||
\(744\) | −1.71157e24 | −0.668383 | ||||||||
\(745\) | 6.76317e23 | − | 6.69373e23i | 0.261109 | − | 0.258428i | ||||
\(746\) | 1.12324e24 | 0.428739 | ||||||||
\(747\) | 9.37173e23i | 0.353667i | ||||||||
\(748\) | − | 4.99059e24i | − | 1.86204i | ||||||
\(749\) | 2.04607e23 | 0.0754788 | ||||||||
\(750\) | 1.17238e24 | + | 1.20925e24i | 0.427609 | + | 0.441057i | ||||
\(751\) | 3.82210e24 | 1.37836 | 0.689180 | − | 0.724590i | \(-0.257971\pi\) | ||||
0.689180 | + | 0.724590i | \(0.257971\pi\) | |||||||
\(752\) | 8.33414e23i | 0.297173i | ||||||||
\(753\) | 2.21795e24i | 0.781978i | ||||||||
\(754\) | 1.14382e22 | 0.00398750 | ||||||||
\(755\) | −2.57723e24 | + | 2.55077e24i | −0.888390 | + | 0.879269i | ||||
\(756\) | 4.98865e23 | 0.170039 | ||||||||
\(757\) | 3.94460e24i | 1.32950i | 0.747067 | + | 0.664749i | \(0.231462\pi\) | ||||
−0.747067 | + | 0.664749i | \(0.768538\pi\) | |||||||
\(758\) | − | 9.13682e23i | − | 0.304514i | ||||||
\(759\) | −8.42206e23 | −0.277564 | ||||||||
\(760\) | −1.76849e24 | − | 1.78683e24i | −0.576350 | − | 0.582329i | ||||
\(761\) | −3.70043e23 | −0.119257 | −0.0596284 | − | 0.998221i | \(-0.518992\pi\) | ||||
−0.0596284 | + | 0.998221i | \(0.518992\pi\) | |||||||
\(762\) | − | 3.77137e23i | − | 0.120194i | ||||||
\(763\) | 9.70512e23i | 0.305874i | ||||||||
\(764\) | 1.13711e24 | 0.354413 | ||||||||
\(765\) | −1.07268e24 | − | 1.08380e24i | −0.330633 | − | 0.334063i | ||||
\(766\) | 1.62262e23 | 0.0494620 | ||||||||
\(767\) | 3.12888e24i | 0.943254i | ||||||||
\(768\) | 3.10772e24i | 0.926555i | ||||||||
\(769\) | −1.11643e24 | −0.329197 | −0.164599 | − | 0.986361i | \(-0.552633\pi\) | ||||
−0.164599 | + | 0.986361i | \(0.552633\pi\) | |||||||
\(770\) | −5.99088e23 | + | 5.92937e23i | −0.174711 | + | 0.172917i | ||||
\(771\) | 5.28448e24 | 1.52419 | ||||||||
\(772\) | 3.97904e24i | 1.13509i | ||||||||
\(773\) | − | 4.91642e24i | − | 1.38715i | −0.720385 | − | 0.693574i | \(-0.756035\pi\) | ||
0.720385 | − | 0.693574i | \(-0.243965\pi\) | |||||||
\(774\) | 4.43779e23 | 0.123842 | ||||||||
\(775\) | 2.38822e22 | − | 2.31407e24i | 0.00659190 | − | 0.638722i | ||||
\(776\) | 4.92476e24 | 1.34450 | ||||||||
\(777\) | 4.86240e23i | 0.131302i | ||||||||
\(778\) | − | 1.20670e24i | − | 0.322310i | ||||||
\(779\) | 3.73064e24 | 0.985633 | ||||||||
\(780\) | −1.61671e24 | + | 1.60011e24i | −0.422502 | + | 0.418164i | ||||
\(781\) | −2.92048e24 | −0.754953 | ||||||||
\(782\) | 5.90829e23i | 0.151079i | ||||||||
\(783\) | 3.17096e22i | 0.00802076i | ||||||||
\(784\) | 7.22789e23 | 0.180853 | ||||||||
\(785\) | 4.94953e22 | + | 5.00088e22i | 0.0122510 | + | 0.0123781i | ||||
\(786\) | 1.03695e24 | 0.253901 | ||||||||
\(787\) | − | 3.08300e24i | − | 0.746772i | −0.927676 | − | 0.373386i | \(-0.878197\pi\) | ||
0.927676 | − | 0.373386i | \(-0.121803\pi\) | |||||||
\(788\) | 2.53070e23i | 0.0606412i | ||||||||
\(789\) | −2.68508e24 | −0.636505 | ||||||||
\(790\) | 1.00379e24 | + | 1.01420e24i | 0.235404 | + | 0.237846i | ||||
\(791\) | −9.12598e23 | −0.211729 | ||||||||
\(792\) | − | 1.68554e24i | − | 0.386879i | ||||||
\(793\) | − | 5.10967e24i | − | 1.16030i | ||||||
\(794\) | 2.43577e24 | 0.547220 | ||||||||
\(795\) | 8.06084e23 | − | 7.97808e23i | 0.179168 | − | 0.177328i | ||||
\(796\) | −5.02654e24 | −1.10537 | ||||||||
\(797\) | − | 2.52033e24i | − | 0.548356i | −0.961679 | − | 0.274178i | \(-0.911594\pi\) | ||
0.961679 | − | 0.274178i | \(-0.0884057\pi\) | |||||||
\(798\) | − | 7.42138e23i | − | 0.159757i | ||||||
\(799\) | −1.21712e25 | −2.59231 | ||||||||
\(800\) | −4.91402e24 | − | 5.07150e22i | −1.03555 | − | 0.0106874i | ||||
\(801\) | −2.30468e23 | −0.0480545 | ||||||||
\(802\) | − | 5.04961e24i | − | 1.04178i | ||||||
\(803\) | 7.57294e24i | 1.54590i | ||||||||
\(804\) | 4.80085e24 | 0.969709 | ||||||||
\(805\) | −1.68153e23 | + | 1.66426e23i | −0.0336077 | + | 0.0332627i | ||||
\(806\) | −1.31827e24 | −0.260709 | ||||||||
\(807\) | 1.57838e24i | 0.308878i | ||||||||
\(808\) | 8.78416e24i | 1.70100i | ||||||||
\(809\) | −1.85576e24 | −0.355598 | −0.177799 | − | 0.984067i | \(-0.556898\pi\) | ||||
−0.177799 | + | 0.984067i | \(0.556898\pi\) | |||||||
\(810\) | 2.42082e24 | + | 2.44594e24i | 0.459030 | + | 0.463791i | ||||
\(811\) | 6.23069e24 | 1.16912 | 0.584560 | − | 0.811351i | \(-0.301267\pi\) | ||||
0.584560 | + | 0.811351i | \(0.301267\pi\) | |||||||
\(812\) | − | 1.08973e22i | − | 0.00202345i | ||||||
\(813\) | − | 2.19457e24i | − | 0.403254i | ||||||
\(814\) | −1.81480e24 | −0.330006 | ||||||||
\(815\) | −1.66607e24 | − | 1.68335e24i | −0.299815 | − | 0.302925i | ||||
\(816\) | 2.16642e24 | 0.385812 | ||||||||
\(817\) | − | 4.18727e24i | − | 0.737979i | ||||||
\(818\) | − | 3.03837e24i | − | 0.529953i | ||||||
\(819\) | −3.47831e23 | −0.0600420 | ||||||||
\(820\) | 3.26580e24 | − | 3.23227e24i | 0.557919 | − | 0.552191i | ||||
\(821\) | −3.16422e24 | −0.534995 | −0.267498 | − | 0.963559i | \(-0.586197\pi\) | ||||
−0.267498 | + | 0.963559i | \(0.586197\pi\) | |||||||
\(822\) | − | 1.56106e24i | − | 0.261222i | ||||||
\(823\) | − | 6.98168e24i | − | 1.15628i | −0.815939 | − | 0.578138i | \(-0.803780\pi\) | ||
0.815939 | − | 0.578138i | \(-0.196220\pi\) | |||||||
\(824\) | 6.00865e24 | 0.984908 | ||||||||
\(825\) | 1.06542e25 | + | 1.09956e23i | 1.72847 | + | 0.0178386i | ||||
\(826\) | −1.25732e24 | −0.201891 | ||||||||
\(827\) | 5.87487e24i | 0.933688i | 0.884340 | + | 0.466844i | \(0.154609\pi\) | ||||
−0.884340 | + | 0.466844i | \(0.845391\pi\) | |||||||
\(828\) | − | 1.95351e23i | − | 0.0307297i | ||||||
\(829\) | 1.14242e24 | 0.177873 | 0.0889366 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889366 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(830\) | −3.26502e24 | + | 3.23150e24i | −0.503179 | + | 0.498013i | ||||
\(831\) | −5.43221e24 | −0.828644 | ||||||||
\(832\) | 1.81661e24i | 0.274293i | ||||||||
\(833\) | 1.05557e25i | 1.57762i | ||||||||
\(834\) | 4.04063e24 | 0.597776 | ||||||||
\(835\) | 4.83432e24 | + | 4.88447e24i | 0.707946 | + | 0.715290i | ||||
\(836\) | −6.56700e24 | −0.951950 | ||||||||
\(837\) | − | 3.65457e24i | − | 0.524409i | ||||||
\(838\) | 5.14586e24i | 0.730943i | ||||||||
\(839\) | 1.17074e25 | 1.64621 | 0.823105 | − | 0.567889i | \(-0.192240\pi\) | ||||
0.823105 | + | 0.567889i | \(0.192240\pi\) | |||||||
\(840\) | −1.55720e24 | − | 1.57336e24i | −0.216756 | − | 0.219005i | ||||
\(841\) | −7.25646e24 | −0.999905 | ||||||||
\(842\) | 4.56637e24i | 0.622900i | ||||||||
\(843\) | 4.67345e24i | 0.631107i | ||||||||
\(844\) | 8.07133e23 | 0.107903 | ||||||||
\(845\) | 2.35465e24 | − | 2.33048e24i | 0.311634 | − | 0.308434i | ||||
\(846\) | −1.69740e24 | −0.222401 | ||||||||
\(847\) | 3.06209e24i | 0.397199i | ||||||||
\(848\) | 3.44643e23i | 0.0442593i | ||||||||
\(849\) | −7.28766e24 | −0.926559 | ||||||||
\(850\) | 7.71373e22 | − | 7.47421e24i | 0.00970965 | − | 0.940816i | ||||
\(851\) | −5.09381e23 | −0.0634807 | ||||||||
\(852\) | − | 3.16704e24i | − | 0.390766i | ||||||
\(853\) | − | 1.03109e25i | − | 1.25959i | −0.776763 | − | 0.629793i | \(-0.783140\pi\) | ||
0.776763 | − | 0.629793i | \(-0.216860\pi\) | |||||||
\(854\) | 2.05329e24 | 0.248347 | ||||||||
\(855\) | −1.42615e24 | + | 1.41151e24i | −0.170787 | + | 0.169033i | ||||
\(856\) | −2.00556e24 | −0.237798 | ||||||||
\(857\) | − | 1.60769e23i | − | 0.0188740i | −0.999955 | − | 0.00943701i | \(-0.996996\pi\) | ||
0.999955 | − | 0.00943701i | \(-0.00300394\pi\) | |||||||
\(858\) | − | 6.06944e24i | − | 0.705516i | ||||||
\(859\) | −1.64738e24 | −0.189605 | −0.0948027 | − | 0.995496i | \(-0.530222\pi\) | ||||
−0.0948027 | + | 0.995496i | \(0.530222\pi\) | |||||||
\(860\) | −3.62790e24 | − | 3.66553e24i | −0.413446 | − | 0.417734i | ||||
\(861\) | 3.28493e24 | 0.370681 | ||||||||
\(862\) | − | 1.20573e23i | − | 0.0134722i | ||||||
\(863\) | − | 1.49755e25i | − | 1.65687i | −0.560086 | − | 0.828434i | \(-0.689232\pi\) | ||
0.560086 | − | 0.828434i | \(-0.310768\pi\) | |||||||
\(864\) | −7.76064e24 | −0.850219 | ||||||||
\(865\) | 1.84992e24 | + | 1.86911e24i | 0.200685 | + | 0.202767i | ||||
\(866\) | −6.11342e24 | −0.656723 | ||||||||
\(867\) | 2.10357e25i | 2.23766i | ||||||||
\(868\) | 1.25593e24i | 0.132296i | ||||||||
\(869\) | 9.02703e24 | 0.941623 | ||||||||
\(870\) | 4.12950e22 | − | 4.08710e22i | 0.00426564 | − | 0.00422184i | ||||
\(871\) | 8.95493e24 | 0.916026 | ||||||||
\(872\) | − | 9.51296e24i | − | 0.963664i | ||||||
\(873\) | − | 3.93067e24i | − | 0.394317i | ||||||
\(874\) | 7.77458e23 | 0.0772378 | ||||||||
\(875\) | 2.14893e24 | − | 2.08340e24i | 0.211423 | − | 0.204977i | ||||
\(876\) | −8.21230e24 | −0.800165 | ||||||||
\(877\) | − | 1.81287e24i | − | 0.174932i | −0.996167 | − | 0.0874662i | \(-0.972123\pi\) | ||
0.996167 | − | 0.0874662i | \(-0.0278770\pi\) | |||||||
\(878\) | 2.20448e24i | 0.210670i | ||||||||
\(879\) | −1.87938e25 | −1.77873 | ||||||||
\(880\) | −2.30124e24 | + | 2.27762e24i | −0.215705 | + | 0.213490i | ||||
\(881\) | −1.37084e25 | −1.27260 | −0.636299 | − | 0.771442i | \(-0.719536\pi\) | ||||
−0.636299 | + | 0.771442i | \(0.719536\pi\) | |||||||
\(882\) | 1.47210e24i | 0.135348i | ||||||||
\(883\) | 7.88163e24i | 0.717712i | 0.933393 | + | 0.358856i | \(0.116833\pi\) | ||||
−0.933393 | + | 0.358856i | \(0.883167\pi\) | |||||||
\(884\) | 1.00948e25 | 0.910442 | ||||||||
\(885\) | 1.11802e25 | + | 1.12961e25i | 0.998689 | + | 1.00905i | ||||
\(886\) | 9.60698e24 | 0.849964 | ||||||||
\(887\) | − | 2.04571e25i | − | 1.79264i | −0.443410 | − | 0.896319i | \(-0.646231\pi\) | ||
0.443410 | − | 0.896319i | \(-0.353769\pi\) | |||||||
\(888\) | − | 4.76613e24i | − | 0.413671i | ||||||
\(889\) | −6.70200e23 | −0.0576155 | ||||||||
\(890\) | −7.94684e23 | − | 8.02928e23i | −0.0676674 | − | 0.0683694i | ||||
\(891\) | 2.17703e25 | 1.83614 | ||||||||
\(892\) | 4.22715e24i | 0.353140i | ||||||||
\(893\) | 1.60159e25i | 1.32530i | ||||||||
\(894\) | −2.75338e24 | −0.225682 | ||||||||
\(895\) | −6.92250e24 | + | 6.85142e24i | −0.562040 | + | 0.556269i | ||||
\(896\) | 3.06194e24 | 0.246252 | ||||||||
\(897\) | − | 1.70358e24i | − | 0.135715i | ||||||
\(898\) | 1.64138e24i | 0.129527i | ||||||||
\(899\) | −7.98310e22 | −0.00624043 | ||||||||
\(900\) | −2.55046e22 | + | 2.47127e24i | −0.00197496 | + | 0.191363i | ||||
\(901\) | −5.03320e24 | −0.386085 | ||||||||
\(902\) | 1.22604e25i | 0.931643i | ||||||||
\(903\) | − | 3.68701e24i | − | 0.277542i | ||||||
\(904\) | 8.94530e24 | 0.667057 | ||||||||
\(905\) | −7.21906e24 | + | 7.14494e24i | −0.533296 | + | 0.527820i | ||||
\(906\) | 1.04922e25 | 0.767854 | ||||||||
\(907\) | − | 1.09711e25i | − | 0.795407i | −0.917514 | − | 0.397704i | \(-0.869807\pi\) | ||
0.917514 | − | 0.397704i | \(-0.130193\pi\) | |||||||
\(908\) | − | 3.91274e24i | − | 0.281029i | ||||||
\(909\) | 7.01103e24 | 0.498872 | ||||||||
\(910\) | −1.19937e24 | − | 1.21181e24i | −0.0845475 | − | 0.0854246i | ||||
\(911\) | 1.51157e25 | 1.05566 | 0.527829 | − | 0.849350i | \(-0.323006\pi\) | ||||
0.527829 | + | 0.849350i | \(0.323006\pi\) | |||||||
\(912\) | − | 2.85074e24i | − | 0.197243i | ||||||
\(913\) | 2.90607e25i | 1.99207i | ||||||||
\(914\) | −1.28439e25 | −0.872280 | ||||||||
\(915\) | −1.82579e25 | − | 1.84473e25i | −1.22849 | − | 1.24124i | ||||
\(916\) | 1.53857e25 | 1.02566 | ||||||||
\(917\) | − | 1.84273e24i | − | 0.121709i | ||||||
\(918\) | − | 1.18039e25i | − | 0.772437i | ||||||
\(919\) | −1.47234e25 | −0.954612 | −0.477306 | − | 0.878737i | \(-0.658387\pi\) | ||||
−0.477306 | + | 0.878737i | \(0.658387\pi\) | |||||||
\(920\) | 1.64824e24 | − | 1.63131e24i | 0.105882 | − | 0.104795i | ||||
\(921\) | −1.29327e25 | −0.823157 | ||||||||
\(922\) | 6.22134e24i | 0.392348i | ||||||||
\(923\) | − | 5.90742e24i | − | 0.369133i | ||||||
\(924\) | −5.78243e24 | −0.358013 | ||||||||
\(925\) | 6.44386e24 | + | 6.65036e22i | 0.395313 | + | 0.00407981i | ||||
\(926\) | −1.43715e25 | −0.873593 | ||||||||
\(927\) | − | 4.79578e24i | − | 0.288856i | ||||||
\(928\) | 1.69525e23i | 0.0101175i | ||||||||
\(929\) | 2.22221e25 | 1.31417 | 0.657084 | − | 0.753817i | \(-0.271790\pi\) | ||||
0.657084 | + | 0.753817i | \(0.271790\pi\) | |||||||
\(930\) | −4.75931e24 | + | 4.71044e24i | −0.278894 | + | 0.276030i | ||||
\(931\) | 1.38900e25 | 0.806545 | ||||||||
\(932\) | 6.40978e24i | 0.368815i | ||||||||
\(933\) | − | 2.29889e25i | − | 1.31076i | ||||||
\(934\) | −4.42489e24 | −0.250008 | ||||||||
\(935\) | −3.32625e25 | − | 3.36076e25i | −1.86233 | − | 1.88165i | ||||
\(936\) | 3.40944e24 | 0.189164 | ||||||||
\(937\) | − | 8.73364e24i | − | 0.480185i | −0.970750 | − | 0.240093i | \(-0.922822\pi\) | ||
0.970750 | − | 0.240093i | \(-0.0771778\pi\) | |||||||
\(938\) | 3.59849e24i | 0.196063i | ||||||||
\(939\) | −8.00769e24 | −0.432364 | ||||||||
\(940\) | 1.38763e25 | + | 1.40203e25i | 0.742484 | + | 0.750187i | ||||
\(941\) | −2.19322e23 | −0.0116298 | −0.00581489 | − | 0.999983i | \(-0.501851\pi\) | ||||
−0.00581489 | + | 0.999983i | \(0.501851\pi\) | |||||||
\(942\) | − | 2.03593e23i | − | 0.0106987i | ||||||
\(943\) | 3.44127e24i | 0.179213i | ||||||||
\(944\) | −4.82969e24 | −0.249263 | ||||||||
\(945\) | 3.35945e24 | − | 3.32496e24i | 0.171830 | − | 0.170065i | ||||
\(946\) | 1.37611e25 | 0.697555 | ||||||||
\(947\) | 2.00026e25i | 1.00487i | 0.864614 | + | 0.502436i | \(0.167563\pi\) | ||||
−0.864614 | + | 0.502436i | \(0.832437\pi\) | |||||||
\(948\) | 9.78915e24i | 0.487387i | ||||||||
\(949\) | −1.53182e25 | −0.755868 | ||||||||
\(950\) | −9.83514e24 | − | 1.01503e23i | −0.480983 | − | 0.00496397i | ||||
\(951\) | 4.51272e24 | 0.218728 | ||||||||
\(952\) | 9.82405e24i | 0.471929i | ||||||||
\(953\) | 4.30467e24i | 0.204951i | 0.994736 | + | 0.102475i | \(0.0326763\pi\) | ||||
−0.994736 | + | 0.102475i | \(0.967324\pi\) | |||||||
\(954\) | −7.01931e23 | −0.0331233 | ||||||||
\(955\) | 7.65753e24 | − | 7.57891e24i | 0.358146 | − | 0.354469i | ||||
\(956\) | −4.59515e24 | −0.213014 | ||||||||
\(957\) | − | 3.67551e23i | − | 0.0168875i | ||||||
\(958\) | 1.27661e25i | 0.581369i | ||||||||
\(959\) | −2.77412e24 | −0.125218 | ||||||||
\(960\) | 6.49114e24 | + | 6.55848e24i | 0.290413 | + | 0.293425i | ||||
\(961\) | −1.33495e25 | −0.591991 | ||||||||
\(962\) | − | 3.67091e24i | − | 0.161356i | ||||||
\(963\) | 1.60073e24i | 0.0697420i | ||||||||
\(964\) | −2.16617e24 | −0.0935487 | ||||||||
\(965\) | 2.65205e25 | + | 2.67956e25i | 1.13527 | + | 1.14705i | ||||
\(966\) | 6.84574e23 | 0.0290479 | ||||||||
\(967\) | − | 3.71481e24i | − | 0.156247i | −0.996944 | − | 0.0781234i | \(-0.975107\pi\) | ||
0.996944 | − | 0.0781234i | \(-0.0248928\pi\) | |||||||
\(968\) | − | 3.00146e25i | − | 1.25139i | ||||||
\(969\) | 4.16324e25 | 1.72060 | ||||||||
\(970\) | 1.36941e25 | − | 1.35535e25i | 0.561014 | − | 0.555254i | ||||
\(971\) | −8.87377e24 | −0.360367 | −0.180183 | − | 0.983633i | \(-0.557669\pi\) | ||||
−0.180183 | + | 0.983633i | \(0.557669\pi\) | |||||||
\(972\) | 9.26455e24i | 0.372959i | ||||||||
\(973\) | − | 7.18051e24i | − | 0.286547i | ||||||
\(974\) | 2.60698e25 | 1.03130 | ||||||||
\(975\) | −2.22415e23 | + | 2.15509e25i | −0.00872219 | + | 0.845136i | ||||
\(976\) | 7.88719e24 | 0.306619 | ||||||||
\(977\) | 4.31141e24i | 0.166156i | 0.996543 | + | 0.0830780i | \(0.0264751\pi\) | ||||
−0.996543 | + | 0.0830780i | \(0.973525\pi\) | |||||||
\(978\) | 6.85316e24i | 0.261825i | ||||||||
\(979\) | −7.14655e24 | −0.270672 | ||||||||
\(980\) | 1.21593e25 | − | 1.20344e25i | 0.456547 | − | 0.451859i | ||||
\(981\) | −7.59272e24 | −0.282625 | ||||||||
\(982\) | − | 2.45235e25i | − | 0.904970i | ||||||
\(983\) | 1.30001e25i | 0.475598i | 0.971314 | + | 0.237799i | \(0.0764260\pi\) | ||||
−0.971314 | + | 0.237799i | \(0.923574\pi\) | |||||||
\(984\) | −3.21989e25 | −1.16784 | ||||||||
\(985\) | 1.68672e24 | + | 1.70422e24i | 0.0606507 | + | 0.0612799i | ||||
\(986\) | −2.57846e23 | −0.00919194 | ||||||||
\(987\) | 1.41024e25i | 0.498422i | ||||||||
\(988\) | − | 1.32835e25i | − | 0.465455i | ||||||
\(989\) | 3.86248e24 | 0.134183 | ||||||||
\(990\) | −4.63880e24 | − | 4.68692e24i | −0.159774 | − | 0.161432i | ||||
\(991\) | −3.28849e25 | −1.12298 | −0.561488 | − | 0.827485i | \(-0.689771\pi\) | ||||
−0.561488 | + | 0.827485i | \(0.689771\pi\) | |||||||
\(992\) | − | 1.95380e25i | − | 0.661500i | ||||||
\(993\) | 3.69072e25i | 1.23892i | ||||||||
\(994\) | 2.37386e24 | 0.0790081 | ||||||||
\(995\) | −3.38496e25 | + | 3.35021e25i | −1.11701 | + | 1.10554i | ||||
\(996\) | −3.15142e25 | −1.03110 | ||||||||
\(997\) | − | 1.26903e25i | − | 0.411685i | −0.978585 | − | 0.205842i | \(-0.934007\pi\) | ||
0.978585 | − | 0.205842i | \(-0.0659934\pi\) | |||||||
\(998\) | − | 3.38512e24i | − | 0.108884i | ||||||
\(999\) | 1.01767e25 | 0.324564 |
(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 | 5.18.b.a.4.4 | ✓ | 8 | |
3.2 | odd | 2 | 45.18.b.b.19.5 | 8 | |||
4.3 | odd | 2 | 80.18.c.b.49.7 | 8 | |||
5.2 | odd | 4 | 25.18.a.f.1.5 | 8 | |||
5.3 | odd | 4 | 25.18.a.f.1.4 | 8 | |||
5.4 | even | 2 | inner | 5.18.b.a.4.5 | yes | 8 | |
15.14 | odd | 2 | 45.18.b.b.19.4 | 8 | |||
20.19 | odd | 2 | 80.18.c.b.49.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.18.b.a.4.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5.18.b.a.4.5 | yes | 8 | 5.4 | even | 2 | inner | |
25.18.a.f.1.4 | 8 | 5.3 | odd | 4 | |||
25.18.a.f.1.5 | 8 | 5.2 | odd | 4 | |||
45.18.b.b.19.4 | 8 | 15.14 | odd | 2 | |||
45.18.b.b.19.5 | 8 | 3.2 | odd | 2 | |||
80.18.c.b.49.2 | 8 | 20.19 | odd | 2 | |||
80.18.c.b.49.7 | 8 | 4.3 | odd | 2 |