Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,13,Mod(22,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.22");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(21.0218577974\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 3347471347 x^{18} + 50192028136 x^{17} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | multiple of \( 2^{35}\cdot 3^{11}\cdot 67 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.12 | ||
Root | \(-697.167 - 19533.2i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.13.b.c.22.11 |
$q$-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 \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 20.5558 | 0.321184 | 0.160592 | − | 0.987021i | \(-0.448660\pi\) | ||||
0.160592 | + | 0.987021i | \(0.448660\pi\) | |||||||
\(3\) | 729.723 | 1.00099 | 0.500496 | − | 0.865739i | \(-0.333151\pi\) | ||||
0.500496 | + | 0.865739i | \(0.333151\pi\) | |||||||
\(4\) | −3673.46 | −0.896841 | ||||||||
\(5\) | 19533.2i | 1.25013i | 0.780574 | + | 0.625063i | \(0.214927\pi\) | ||||
−0.780574 | + | 0.625063i | \(0.785073\pi\) | |||||||
\(6\) | 15000.0 | 0.321503 | ||||||||
\(7\) | 5514.27i | 0.0468705i | 0.999725 | + | 0.0234352i | \(0.00746035\pi\) | ||||
−0.999725 | + | 0.0234352i | \(0.992540\pi\) | |||||||
\(8\) | −159707. | −0.609235 | ||||||||
\(9\) | 1054.67 | 0.00198455 | ||||||||
\(10\) | 401520.i | 0.401520i | ||||||||
\(11\) | − | 2.84785e6i | − | 1.60754i | −0.594940 | − | 0.803770i | \(-0.702824\pi\) | ||
0.594940 | − | 0.803770i | \(-0.297176\pi\) | |||||||
\(12\) | −2.68061e6 | −0.897730 | ||||||||
\(13\) | −7.37127e6 | −1.52715 | −0.763576 | − | 0.645718i | \(-0.776558\pi\) | ||||
−0.763576 | + | 0.645718i | \(0.776558\pi\) | |||||||
\(14\) | 113350.i | 0.0150540i | ||||||||
\(15\) | 1.42538e7i | 1.25137i | ||||||||
\(16\) | 1.17636e7 | 0.701164 | ||||||||
\(17\) | − | 2.30376e7i | − | 0.954428i | −0.878787 | − | 0.477214i | \(-0.841647\pi\) | ||
0.878787 | − | 0.477214i | \(-0.158353\pi\) | |||||||
\(18\) | 21679.6 | 0.000637406 | ||||||||
\(19\) | 5.27182e7i | 1.12057i | 0.828300 | + | 0.560284i | \(0.189308\pi\) | ||||
−0.828300 | + | 0.560284i | \(0.810692\pi\) | |||||||
\(20\) | − | 7.17545e7i | − | 1.12116i | ||||||
\(21\) | 4.02389e6i | 0.0469170i | ||||||||
\(22\) | − | 5.85399e7i | − | 0.516316i | ||||||
\(23\) | −1.45182e8 | + | 2.89269e7i | −0.980723 | + | 0.195405i | ||||
\(24\) | −1.16542e8 | −0.609839 | ||||||||
\(25\) | −1.37406e8 | −0.562815 | ||||||||
\(26\) | −1.51522e8 | −0.490497 | ||||||||
\(27\) | −3.87035e8 | −0.999005 | ||||||||
\(28\) | − | 2.02564e7i | − | 0.0420354i | ||||||
\(29\) | −2.08168e8 | −0.349965 | −0.174983 | − | 0.984572i | \(-0.555987\pi\) | ||||
−0.174983 | + | 0.984572i | \(0.555987\pi\) | |||||||
\(30\) | 2.92999e8i | 0.401919i | ||||||||
\(31\) | −9.37627e8 | −1.05648 | −0.528239 | − | 0.849096i | \(-0.677147\pi\) | ||||
−0.528239 | + | 0.849096i | \(0.677147\pi\) | |||||||
\(32\) | 8.95971e8 | 0.834438 | ||||||||
\(33\) | − | 2.07814e9i | − | 1.60913i | ||||||
\(34\) | − | 4.73555e8i | − | 0.306547i | ||||||
\(35\) | −1.07711e8 | −0.0585940 | ||||||||
\(36\) | −3.87430e6 | −0.00177983 | ||||||||
\(37\) | 4.16040e9i | 1.62153i | 0.585374 | + | 0.810764i | \(0.300948\pi\) | ||||
−0.585374 | + | 0.810764i | \(0.699052\pi\) | |||||||
\(38\) | 1.08366e9i | 0.359909i | ||||||||
\(39\) | −5.37898e9 | −1.52867 | ||||||||
\(40\) | − | 3.11960e9i | − | 0.761620i | ||||||
\(41\) | −2.43189e9 | −0.511965 | −0.255982 | − | 0.966681i | \(-0.582399\pi\) | ||||
−0.255982 | + | 0.966681i | \(0.582399\pi\) | |||||||
\(42\) | 8.27141e7i | 0.0150690i | ||||||||
\(43\) | − | 1.05815e10i | − | 1.67393i | −0.547257 | − | 0.836965i | \(-0.684328\pi\) | ||
0.547257 | − | 0.836965i | \(-0.315672\pi\) | |||||||
\(44\) | 1.04615e10i | 1.44171i | ||||||||
\(45\) | 2.06011e7i | 0.00248094i | ||||||||
\(46\) | −2.98433e9 | + | 5.94616e8i | −0.314992 | + | 0.0627609i | ||||
\(47\) | 9.05702e9 | 0.840230 | 0.420115 | − | 0.907471i | \(-0.361990\pi\) | ||||
0.420115 | + | 0.907471i | \(0.361990\pi\) | |||||||
\(48\) | 8.58416e9 | 0.701860 | ||||||||
\(49\) | 1.38109e10 | 0.997803 | ||||||||
\(50\) | −2.82449e9 | −0.180767 | ||||||||
\(51\) | − | 1.68110e10i | − | 0.955374i | ||||||
\(52\) | 2.70781e10 | 1.36961 | ||||||||
\(53\) | 3.52921e10i | 1.59229i | 0.605106 | + | 0.796145i | \(0.293131\pi\) | ||||
−0.605106 | + | 0.796145i | \(0.706869\pi\) | |||||||
\(54\) | −7.95581e9 | −0.320864 | ||||||||
\(55\) | 5.56278e10 | 2.00963 | ||||||||
\(56\) | − | 8.80668e8i | − | 0.0285551i | ||||||
\(57\) | 3.84697e10i | 1.12168i | ||||||||
\(58\) | −4.27905e9 | −0.112403 | ||||||||
\(59\) | −1.98838e10 | −0.471396 | −0.235698 | − | 0.971826i | \(-0.575738\pi\) | ||||
−0.235698 | + | 0.971826i | \(0.575738\pi\) | |||||||
\(60\) | − | 5.23609e10i | − | 1.12228i | ||||||
\(61\) | 9.34986e9i | 0.181479i | 0.995875 | + | 0.0907394i | \(0.0289230\pi\) | ||||
−0.995875 | + | 0.0907394i | \(0.971077\pi\) | |||||||
\(62\) | −1.92737e10 | −0.339324 | ||||||||
\(63\) | 5.81574e6i | 9.30169e-5i | ||||||||
\(64\) | −2.97663e10 | −0.433156 | ||||||||
\(65\) | − | 1.43985e11i | − | 1.90913i | ||||||
\(66\) | − | 4.27179e10i | − | 0.516828i | ||||||
\(67\) | 1.05634e11i | 1.16777i | 0.811838 | + | 0.583883i | \(0.198467\pi\) | ||||
−0.811838 | + | 0.583883i | \(0.801533\pi\) | |||||||
\(68\) | 8.46276e10i | 0.855970i | ||||||||
\(69\) | −1.05943e11 | + | 2.11086e10i | −0.981695 | + | 0.195599i | ||||
\(70\) | −2.21409e9 | −0.0188195 | ||||||||
\(71\) | −2.74716e10 | −0.214454 | −0.107227 | − | 0.994235i | \(-0.534197\pi\) | ||||
−0.107227 | + | 0.994235i | \(0.534197\pi\) | |||||||
\(72\) | −1.68439e8 | −0.00120906 | ||||||||
\(73\) | 4.00550e10 | 0.264679 | 0.132340 | − | 0.991204i | \(-0.457751\pi\) | ||||
0.132340 | + | 0.991204i | \(0.457751\pi\) | |||||||
\(74\) | 8.55202e10i | 0.520809i | ||||||||
\(75\) | −1.00268e11 | −0.563373 | ||||||||
\(76\) | − | 1.93658e11i | − | 1.00497i | ||||||
\(77\) | 1.57038e10 | 0.0753462 | ||||||||
\(78\) | −1.10569e11 | −0.490983 | ||||||||
\(79\) | − | 1.55769e11i | − | 0.640792i | −0.947284 | − | 0.320396i | \(-0.896184\pi\) | ||
0.947284 | − | 0.320396i | \(-0.103816\pi\) | |||||||
\(80\) | 2.29781e11i | 0.876544i | ||||||||
\(81\) | −2.82989e11 | −1.00198 | ||||||||
\(82\) | −4.99893e10 | −0.164435 | ||||||||
\(83\) | − | 2.09520e11i | − | 0.640850i | −0.947274 | − | 0.320425i | \(-0.896174\pi\) | ||
0.947274 | − | 0.320425i | \(-0.103826\pi\) | |||||||
\(84\) | − | 1.47816e10i | − | 0.0420771i | ||||||
\(85\) | 4.49998e11 | 1.19316 | ||||||||
\(86\) | − | 2.17511e11i | − | 0.537639i | ||||||
\(87\) | −1.51905e11 | −0.350312 | ||||||||
\(88\) | 4.54823e11i | 0.979369i | ||||||||
\(89\) | − | 1.16097e10i | − | 0.0233604i | −0.999932 | − | 0.0116802i | \(-0.996282\pi\) | ||
0.999932 | − | 0.0116802i | \(-0.00371801\pi\) | |||||||
\(90\) | 4.23473e8i | 0.000796838i | ||||||||
\(91\) | − | 4.06471e10i | − | 0.0715783i | ||||||
\(92\) | 5.33321e11 | − | 1.06262e11i | 0.879552 | − | 0.175247i | ||||
\(93\) | −6.84208e11 | −1.05752 | ||||||||
\(94\) | 1.86174e11 | 0.269868 | ||||||||
\(95\) | −1.02976e12 | −1.40085 | ||||||||
\(96\) | 6.53810e11 | 0.835265 | ||||||||
\(97\) | 1.10100e12i | 1.32177i | 0.750487 | + | 0.660885i | \(0.229819\pi\) | ||||
−0.750487 | + | 0.660885i | \(0.770181\pi\) | |||||||
\(98\) | 2.83893e11 | 0.320478 | ||||||||
\(99\) | − | 3.00355e9i | − | 0.00319025i | ||||||
\(100\) | 5.04756e11 | 0.504756 | ||||||||
\(101\) | 6.11239e11 | 0.575815 | 0.287907 | − | 0.957658i | \(-0.407040\pi\) | ||||
0.287907 | + | 0.957658i | \(0.407040\pi\) | |||||||
\(102\) | − | 3.45564e11i | − | 0.306851i | ||||||
\(103\) | − | 1.59048e12i | − | 1.33200i | −0.745953 | − | 0.665999i | \(-0.768005\pi\) | ||
0.745953 | − | 0.665999i | \(-0.231995\pi\) | |||||||
\(104\) | 1.17725e12 | 0.930394 | ||||||||
\(105\) | −7.85995e10 | −0.0586521 | ||||||||
\(106\) | 7.25457e11i | 0.511418i | ||||||||
\(107\) | − | 2.40207e12i | − | 1.60060i | −0.599599 | − | 0.800300i | \(-0.704673\pi\) | ||
0.599599 | − | 0.800300i | \(-0.295327\pi\) | |||||||
\(108\) | 1.42176e12 | 0.895949 | ||||||||
\(109\) | 2.14754e12i | 1.28051i | 0.768163 | + | 0.640255i | \(0.221171\pi\) | ||||
−0.768163 | + | 0.640255i | \(0.778829\pi\) | |||||||
\(110\) | 1.14347e12 | 0.645460 | ||||||||
\(111\) | 3.03594e12i | 1.62314i | ||||||||
\(112\) | 6.48675e10i | 0.0328639i | ||||||||
\(113\) | 1.15629e12i | 0.555387i | 0.960670 | + | 0.277694i | \(0.0895700\pi\) | ||||
−0.960670 | + | 0.277694i | \(0.910430\pi\) | |||||||
\(114\) | 7.90773e11i | 0.360266i | ||||||||
\(115\) | −5.65036e11 | − | 2.83587e12i | −0.244281 | − | 1.22603i | ||||
\(116\) | 7.64695e11 | 0.313863 | ||||||||
\(117\) | −7.77427e9 | −0.00303071 | ||||||||
\(118\) | −4.08726e11 | −0.151405 | ||||||||
\(119\) | 1.27035e11 | 0.0447345 | ||||||||
\(120\) | − | 2.27644e12i | − | 0.762376i | ||||||
\(121\) | −4.97185e12 | −1.58418 | ||||||||
\(122\) | 1.92194e11i | 0.0582881i | ||||||||
\(123\) | −1.77460e12 | −0.512473 | ||||||||
\(124\) | 3.44434e12 | 0.947492 | ||||||||
\(125\) | 2.08487e12i | 0.546536i | ||||||||
\(126\) | 1.19547e8i | 2.98755e-5i | ||||||||
\(127\) | −1.12667e12 | −0.268519 | −0.134259 | − | 0.990946i | \(-0.542866\pi\) | ||||
−0.134259 | + | 0.990946i | \(0.542866\pi\) | |||||||
\(128\) | −4.28176e12 | −0.973561 | ||||||||
\(129\) | − | 7.72158e12i | − | 1.67559i | ||||||
\(130\) | − | 2.95972e12i | − | 0.613183i | ||||||
\(131\) | −7.85496e12 | −1.55423 | −0.777117 | − | 0.629356i | \(-0.783319\pi\) | ||||
−0.777117 | + | 0.629356i | \(0.783319\pi\) | |||||||
\(132\) | 7.63398e12i | 1.44314i | ||||||||
\(133\) | −2.90702e11 | −0.0525216 | ||||||||
\(134\) | 2.17139e12i | 0.375068i | ||||||||
\(135\) | − | 7.56004e12i | − | 1.24888i | ||||||
\(136\) | 3.67927e12i | 0.581471i | ||||||||
\(137\) | − | 2.84998e12i | − | 0.431041i | −0.976499 | − | 0.215521i | \(-0.930855\pi\) | ||
0.976499 | − | 0.215521i | \(-0.0691449\pi\) | |||||||
\(138\) | −2.17774e12 | + | 4.33905e11i | −0.315305 | + | 0.0628232i | ||||
\(139\) | −6.37349e11 | −0.0883667 | −0.0441834 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441834 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(140\) | 3.95673e11 | 0.0525495 | ||||||||
\(141\) | 6.60912e12 | 0.841063 | ||||||||
\(142\) | −5.64700e11 | −0.0688792 | ||||||||
\(143\) | 2.09923e13i | 2.45496i | ||||||||
\(144\) | 1.24067e10 | 0.00139150 | ||||||||
\(145\) | − | 4.06618e12i | − | 0.437501i | ||||||
\(146\) | 8.23362e11 | 0.0850108 | ||||||||
\(147\) | 1.00781e13 | 0.998793 | ||||||||
\(148\) | − | 1.52830e13i | − | 1.45425i | ||||||
\(149\) | 4.29588e12i | 0.392586i | 0.980545 | + | 0.196293i | \(0.0628903\pi\) | ||||
−0.980545 | + | 0.196293i | \(0.937110\pi\) | |||||||
\(150\) | −2.06109e12 | −0.180946 | ||||||||
\(151\) | −1.61951e13 | −1.36623 | −0.683113 | − | 0.730313i | \(-0.739374\pi\) | ||||
−0.683113 | + | 0.730313i | \(0.739374\pi\) | |||||||
\(152\) | − | 8.41947e12i | − | 0.682690i | ||||||
\(153\) | − | 2.42971e10i | − | 0.00189411i | ||||||
\(154\) | 3.22804e11 | 0.0242000 | ||||||||
\(155\) | − | 1.83149e13i | − | 1.32073i | ||||||
\(156\) | 1.97595e13 | 1.37097 | ||||||||
\(157\) | − | 6.01997e11i | − | 0.0401972i | −0.999798 | − | 0.0200986i | \(-0.993602\pi\) | ||
0.999798 | − | 0.0200986i | \(-0.00639802\pi\) | |||||||
\(158\) | − | 3.20194e12i | − | 0.205812i | ||||||
\(159\) | 2.57535e13i | 1.59387i | ||||||||
\(160\) | 1.75012e13i | 1.04315i | ||||||||
\(161\) | −1.59511e11 | − | 8.00573e11i | −0.00915872 | − | 0.0459669i | ||||
\(162\) | −5.81706e12 | −0.321820 | ||||||||
\(163\) | −6.23038e12 | −0.332192 | −0.166096 | − | 0.986110i | \(-0.553116\pi\) | ||||
−0.166096 | + | 0.986110i | \(0.553116\pi\) | |||||||
\(164\) | 8.93344e12 | 0.459151 | ||||||||
\(165\) | 4.05929e13 | 2.01162 | ||||||||
\(166\) | − | 4.30684e12i | − | 0.205831i | ||||||
\(167\) | −2.87619e13 | −1.32592 | −0.662962 | − | 0.748653i | \(-0.730701\pi\) | ||||
−0.662962 | + | 0.748653i | \(0.730701\pi\) | |||||||
\(168\) | − | 6.42644e11i | − | 0.0285835i | ||||||
\(169\) | 3.10375e13 | 1.33219 | ||||||||
\(170\) | 9.25006e12 | 0.383222 | ||||||||
\(171\) | 5.56004e10i | 0.00222383i | ||||||||
\(172\) | 3.88708e13i | 1.50125i | ||||||||
\(173\) | 2.64146e13 | 0.985297 | 0.492649 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492649 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(174\) | −3.12252e12 | −0.112515 | ||||||||
\(175\) | − | 7.57693e11i | − | 0.0263794i | ||||||
\(176\) | − | 3.35010e13i | − | 1.12715i | ||||||
\(177\) | −1.45096e13 | −0.471864 | ||||||||
\(178\) | − | 2.38646e11i | − | 0.00750299i | ||||||
\(179\) | 4.74549e13 | 1.44266 | 0.721328 | − | 0.692593i | \(-0.243532\pi\) | ||||
0.721328 | + | 0.692593i | \(0.243532\pi\) | |||||||
\(180\) | − | 7.56775e10i | − | 0.00222501i | ||||||
\(181\) | − | 2.78991e13i | − | 0.793449i | −0.917938 | − | 0.396725i | \(-0.870147\pi\) | ||
0.917938 | − | 0.396725i | \(-0.129853\pi\) | |||||||
\(182\) | − | 8.35533e11i | − | 0.0229898i | ||||||
\(183\) | 6.82281e12i | 0.181659i | ||||||||
\(184\) | 2.31866e13 | − | 4.61984e12i | 0.597490 | − | 0.119047i | ||||
\(185\) | −8.12659e13 | −2.02711 | ||||||||
\(186\) | −1.40644e13 | −0.339660 | ||||||||
\(187\) | −6.56076e13 | −1.53428 | ||||||||
\(188\) | −3.32706e13 | −0.753553 | ||||||||
\(189\) | − | 2.13421e12i | − | 0.0468239i | ||||||
\(190\) | −2.11674e13 | −0.449931 | ||||||||
\(191\) | 2.72754e13i | 0.561786i | 0.959739 | + | 0.280893i | \(0.0906306\pi\) | ||||
−0.959739 | + | 0.280893i | \(0.909369\pi\) | |||||||
\(192\) | −2.17211e13 | −0.433586 | ||||||||
\(193\) | 1.93538e13 | 0.374474 | 0.187237 | − | 0.982315i | \(-0.440047\pi\) | ||||
0.187237 | + | 0.982315i | \(0.440047\pi\) | |||||||
\(194\) | 2.26318e13i | 0.424531i | ||||||||
\(195\) | − | 1.05069e14i | − | 1.91103i | ||||||
\(196\) | −5.07337e13 | −0.894871 | ||||||||
\(197\) | −5.10053e13 | −0.872606 | −0.436303 | − | 0.899800i | \(-0.643712\pi\) | ||||
−0.436303 | + | 0.899800i | \(0.643712\pi\) | |||||||
\(198\) | − | 6.17404e10i | − | 0.00102466i | ||||||
\(199\) | 3.35197e13i | 0.539736i | 0.962897 | + | 0.269868i | \(0.0869801\pi\) | ||||
−0.962897 | + | 0.269868i | \(0.913020\pi\) | |||||||
\(200\) | 2.19447e13 | 0.342887 | ||||||||
\(201\) | 7.70837e13i | 1.16892i | ||||||||
\(202\) | 1.25645e13 | 0.184942 | ||||||||
\(203\) | − | 1.14789e12i | − | 0.0164030i | ||||||
\(204\) | 6.17547e13i | 0.856819i | ||||||||
\(205\) | − | 4.75026e13i | − | 0.640021i | ||||||
\(206\) | − | 3.26935e13i | − | 0.427816i | ||||||
\(207\) | −1.53120e11 | + | 3.05084e10i | −0.00194630 | + | 0.000387791i | ||||
\(208\) | −8.67126e13 | −1.07078 | ||||||||
\(209\) | 1.50134e14 | 1.80136 | ||||||||
\(210\) | −1.61567e12 | −0.0188381 | ||||||||
\(211\) | 5.06276e13 | 0.573710 | 0.286855 | − | 0.957974i | \(-0.407390\pi\) | ||||
0.286855 | + | 0.957974i | \(0.407390\pi\) | |||||||
\(212\) | − | 1.29644e14i | − | 1.42803i | ||||||
\(213\) | −2.00467e13 | −0.214667 | ||||||||
\(214\) | − | 4.93764e13i | − | 0.514087i | ||||||
\(215\) | 2.06691e14 | 2.09262 | ||||||||
\(216\) | 6.18123e13 | 0.608629 | ||||||||
\(217\) | − | 5.17033e12i | − | 0.0495176i | ||||||
\(218\) | 4.41444e13i | 0.411279i | ||||||||
\(219\) | 2.92291e13 | 0.264942 | ||||||||
\(220\) | −2.04346e14 | −1.80232 | ||||||||
\(221\) | 1.69816e14i | 1.45756i | ||||||||
\(222\) | 6.24060e13i | 0.521325i | ||||||||
\(223\) | −1.88271e14 | −1.53092 | −0.765462 | − | 0.643481i | \(-0.777489\pi\) | ||||
−0.765462 | + | 0.643481i | \(0.777489\pi\) | |||||||
\(224\) | 4.94062e12i | 0.0391105i | ||||||||
\(225\) | −1.44918e11 | −0.00111694 | ||||||||
\(226\) | 2.37684e13i | 0.178381i | ||||||||
\(227\) | 1.26516e14i | 0.924678i | 0.886703 | + | 0.462339i | \(0.152990\pi\) | ||||
−0.886703 | + | 0.462339i | \(0.847010\pi\) | |||||||
\(228\) | − | 1.41317e14i | − | 1.00597i | ||||||
\(229\) | − | 1.27397e14i | − | 0.883379i | −0.897168 | − | 0.441689i | \(-0.854379\pi\) | ||
0.897168 | − | 0.441689i | \(-0.145621\pi\) | |||||||
\(230\) | −1.16148e13 | − | 5.82936e13i | −0.0784591 | − | 0.393780i | ||||
\(231\) | 1.14594e13 | 0.0754209 | ||||||||
\(232\) | 3.32459e13 | 0.213211 | ||||||||
\(233\) | 1.50162e14 | 0.938478 | 0.469239 | − | 0.883071i | \(-0.344528\pi\) | ||||
0.469239 | + | 0.883071i | \(0.344528\pi\) | |||||||
\(234\) | −1.59806e11 | −0.000973416 | ||||||||
\(235\) | 1.76913e14i | 1.05039i | ||||||||
\(236\) | 7.30422e13 | 0.422768 | ||||||||
\(237\) | − | 1.13668e14i | − | 0.641428i | ||||||
\(238\) | 2.61131e12 | 0.0143680 | ||||||||
\(239\) | 2.59073e14 | 1.39007 | 0.695033 | − | 0.718978i | \(-0.255390\pi\) | ||||
0.695033 | + | 0.718978i | \(0.255390\pi\) | |||||||
\(240\) | 1.67676e14i | 0.877413i | ||||||||
\(241\) | − | 9.35922e13i | − | 0.477680i | −0.971059 | − | 0.238840i | \(-0.923233\pi\) | ||
0.971059 | − | 0.238840i | \(-0.0767672\pi\) | |||||||
\(242\) | −1.02200e14 | −0.508814 | ||||||||
\(243\) | −8.17202e11 | −0.00396910 | ||||||||
\(244\) | − | 3.43463e13i | − | 0.162758i | ||||||
\(245\) | 2.69771e14i | 1.24738i | ||||||||
\(246\) | −3.64784e13 | −0.164598 | ||||||||
\(247\) | − | 3.88600e14i | − | 1.71128i | ||||||
\(248\) | 1.49746e14 | 0.643643 | ||||||||
\(249\) | − | 1.52891e14i | − | 0.641485i | ||||||
\(250\) | 4.28561e13i | 0.175539i | ||||||||
\(251\) | − | 1.84432e14i | − | 0.737555i | −0.929518 | − | 0.368778i | \(-0.879776\pi\) | ||
0.929518 | − | 0.368778i | \(-0.120224\pi\) | |||||||
\(252\) | − | 2.13639e10i | − | 8.34214e-5i | ||||||
\(253\) | 8.23797e13 | + | 4.13458e14i | 0.314121 | + | 1.57655i | ||||
\(254\) | −2.31596e13 | −0.0862439 | ||||||||
\(255\) | 3.28374e14 | 1.19434 | ||||||||
\(256\) | 3.39077e13 | 0.120464 | ||||||||
\(257\) | 1.26033e14 | 0.437407 | 0.218703 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218703 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(258\) | − | 1.58723e14i | − | 0.538173i | ||||||
\(259\) | −2.29415e13 | −0.0760018 | ||||||||
\(260\) | 5.28922e14i | 1.71219i | ||||||||
\(261\) | −2.19549e11 | −0.000694525 | ||||||||
\(262\) | −1.61465e14 | −0.499195 | ||||||||
\(263\) | − | 1.67551e14i | − | 0.506306i | −0.967426 | − | 0.253153i | \(-0.918532\pi\) | ||
0.967426 | − | 0.253153i | \(-0.0814676\pi\) | |||||||
\(264\) | 3.31895e14i | 0.980340i | ||||||||
\(265\) | −6.89368e14 | −1.99056 | ||||||||
\(266\) | −5.97560e12 | −0.0168691 | ||||||||
\(267\) | − | 8.47186e12i | − | 0.0233836i | ||||||
\(268\) | − | 3.88043e14i | − | 1.04730i | ||||||
\(269\) | −4.35619e14 | −1.14972 | −0.574861 | − | 0.818251i | \(-0.694944\pi\) | ||||
−0.574861 | + | 0.818251i | \(0.694944\pi\) | |||||||
\(270\) | − | 1.55403e14i | − | 0.401121i | ||||||
\(271\) | −3.58017e14 | −0.903833 | −0.451917 | − | 0.892060i | \(-0.649260\pi\) | ||||
−0.451917 | + | 0.892060i | \(0.649260\pi\) | |||||||
\(272\) | − | 2.71004e14i | − | 0.669211i | ||||||
\(273\) | − | 2.96611e13i | − | 0.0716493i | ||||||
\(274\) | − | 5.85836e13i | − | 0.138444i | ||||||
\(275\) | 3.91312e14i | 0.904748i | ||||||||
\(276\) | 3.89176e14 | − | 7.75418e13i | 0.880424 | − | 0.175421i | ||||
\(277\) | −6.80322e14 | −1.50604 | −0.753019 | − | 0.657999i | \(-0.771403\pi\) | ||||
−0.753019 | + | 0.657999i | \(0.771403\pi\) | |||||||
\(278\) | −1.31012e13 | −0.0283820 | ||||||||
\(279\) | −9.88890e11 | −0.00209663 | ||||||||
\(280\) | 1.72023e13 | 0.0356975 | ||||||||
\(281\) | − | 8.41639e14i | − | 1.70957i | −0.518979 | − | 0.854787i | \(-0.673688\pi\) | ||
0.518979 | − | 0.854787i | \(-0.326312\pi\) | |||||||
\(282\) | 1.35856e14 | 0.270136 | ||||||||
\(283\) | − | 2.82620e14i | − | 0.550153i | −0.961422 | − | 0.275077i | \(-0.911297\pi\) | ||
0.961422 | − | 0.275077i | \(-0.0887032\pi\) | |||||||
\(284\) | 1.00916e14 | 0.192331 | ||||||||
\(285\) | −7.51436e14 | −1.40224 | ||||||||
\(286\) | 4.31513e14i | 0.788493i | ||||||||
\(287\) | − | 1.34101e13i | − | 0.0239960i | ||||||
\(288\) | 9.44955e11 | 0.00165599 | ||||||||
\(289\) | 5.18927e13 | 0.0890674 | ||||||||
\(290\) | − | 8.35835e13i | − | 0.140518i | ||||||
\(291\) | 8.03423e14i | 1.32308i | ||||||||
\(292\) | −1.47141e14 | −0.237375 | ||||||||
\(293\) | 3.31155e14i | 0.523390i | 0.965151 | + | 0.261695i | \(0.0842814\pi\) | ||||
−0.965151 | + | 0.261695i | \(0.915719\pi\) | |||||||
\(294\) | 2.07164e14 | 0.320796 | ||||||||
\(295\) | − | 3.88394e14i | − | 0.589305i | ||||||
\(296\) | − | 6.64445e14i | − | 0.987891i | ||||||
\(297\) | 1.10222e15i | 1.60594i | ||||||||
\(298\) | 8.83051e13i | 0.126092i | ||||||||
\(299\) | 1.07018e15 | − | 2.13228e14i | 1.49771 | − | 0.298413i | ||||
\(300\) | 3.68332e14 | 0.505256 | ||||||||
\(301\) | 5.83493e13 | 0.0784579 | ||||||||
\(302\) | −3.32903e14 | −0.438810 | ||||||||
\(303\) | 4.46035e14 | 0.576386 | ||||||||
\(304\) | 6.20155e14i | 0.785703i | ||||||||
\(305\) | −1.82633e14 | −0.226871 | ||||||||
\(306\) | − | 4.99445e11i | − | 0.000608358i | ||||||
\(307\) | −3.73992e14 | −0.446716 | −0.223358 | − | 0.974736i | \(-0.571702\pi\) | ||||
−0.223358 | + | 0.974736i | \(0.571702\pi\) | |||||||
\(308\) | −5.76874e13 | −0.0675735 | ||||||||
\(309\) | − | 1.16061e15i | − | 1.33332i | ||||||
\(310\) | − | 3.76477e14i | − | 0.424197i | ||||||
\(311\) | 7.83220e14 | 0.865609 | 0.432804 | − | 0.901488i | \(-0.357524\pi\) | ||||
0.432804 | + | 0.901488i | \(0.357524\pi\) | |||||||
\(312\) | 8.59063e14 | 0.931317 | ||||||||
\(313\) | 3.68279e14i | 0.391661i | 0.980638 | + | 0.195831i | \(0.0627403\pi\) | ||||
−0.980638 | + | 0.195831i | \(0.937260\pi\) | |||||||
\(314\) | − | 1.23745e13i | − | 0.0129107i | ||||||
\(315\) | −1.13600e11 | −0.000116283 | ||||||||
\(316\) | 5.72210e14i | 0.574689i | ||||||||
\(317\) | −4.24203e14 | −0.418040 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(318\) | 5.29382e14i | 0.511925i | ||||||||
\(319\) | 5.92831e14i | 0.562583i | ||||||||
\(320\) | − | 5.81431e14i | − | 0.541500i | ||||||
\(321\) | − | 1.75285e15i | − | 1.60219i | ||||||
\(322\) | −3.27887e12 | − | 1.64564e13i | −0.00294163 | − | 0.0147638i | ||||
\(323\) | 1.21450e15 | 1.06950 | ||||||||
\(324\) | 1.03955e15 | 0.898617 | ||||||||
\(325\) | 1.01286e15 | 0.859504 | ||||||||
\(326\) | −1.28070e14 | −0.106695 | ||||||||
\(327\) | 1.56711e15i | 1.28178i | ||||||||
\(328\) | 3.88390e14 | 0.311907 | ||||||||
\(329\) | 4.99428e13i | 0.0393820i | ||||||||
\(330\) | 8.34418e14 | 0.646100 | ||||||||
\(331\) | −8.59733e14 | −0.653726 | −0.326863 | − | 0.945072i | \(-0.605992\pi\) | ||||
−0.326863 | + | 0.945072i | \(0.605992\pi\) | |||||||
\(332\) | 7.69662e14i | 0.574740i | ||||||||
\(333\) | 4.38785e12i | 0.00321801i | ||||||||
\(334\) | −5.91223e14 | −0.425865 | ||||||||
\(335\) | −2.06338e15 | −1.45985 | ||||||||
\(336\) | 4.73353e13i | 0.0328965i | ||||||||
\(337\) | − | 2.81112e15i | − | 1.91911i | −0.281525 | − | 0.959554i | \(-0.590840\pi\) | ||
0.281525 | − | 0.959554i | \(-0.409160\pi\) | |||||||
\(338\) | 6.38000e14 | 0.427879 | ||||||||
\(339\) | 8.43771e14i | 0.555938i | ||||||||
\(340\) | −1.65305e15 | −1.07007 | ||||||||
\(341\) | 2.67023e15i | 1.69833i | ||||||||
\(342\) | 1.14291e12i | 0.000714258i | ||||||||
\(343\) | 1.52481e14i | 0.0936380i | ||||||||
\(344\) | 1.68995e15i | 1.01982i | ||||||||
\(345\) | −4.12320e14 | − | 2.06940e15i | −0.244523 | − | 1.22724i | ||||
\(346\) | 5.42973e14 | 0.316462 | ||||||||
\(347\) | −6.87742e13 | −0.0393957 | −0.0196979 | − | 0.999806i | \(-0.506270\pi\) | ||||
−0.0196979 | + | 0.999806i | \(0.506270\pi\) | |||||||
\(348\) | 5.58016e14 | 0.314175 | ||||||||
\(349\) | −2.44456e15 | −1.35285 | −0.676423 | − | 0.736514i | \(-0.736471\pi\) | ||||
−0.676423 | + | 0.736514i | \(0.736471\pi\) | |||||||
\(350\) | − | 1.55750e13i | − | 0.00847265i | ||||||
\(351\) | 2.85294e15 | 1.52563 | ||||||||
\(352\) | − | 2.55159e15i | − | 1.34139i | ||||||
\(353\) | −1.72335e15 | −0.890686 | −0.445343 | − | 0.895360i | \(-0.646918\pi\) | ||||
−0.445343 | + | 0.895360i | \(0.646918\pi\) | |||||||
\(354\) | −2.98257e14 | −0.151555 | ||||||||
\(355\) | − | 5.36609e14i | − | 0.268095i | ||||||
\(356\) | 4.26477e13i | 0.0209506i | ||||||||
\(357\) | 9.27006e13 | 0.0447789 | ||||||||
\(358\) | 9.75473e14 | 0.463358 | ||||||||
\(359\) | − | 2.86070e15i | − | 1.33630i | −0.744025 | − | 0.668151i | \(-0.767086\pi\) | ||
0.744025 | − | 0.668151i | \(-0.232914\pi\) | |||||||
\(360\) | − | 3.29015e12i | − | 0.00151148i | ||||||
\(361\) | −5.65889e14 | −0.255675 | ||||||||
\(362\) | − | 5.73488e14i | − | 0.254843i | ||||||
\(363\) | −3.62807e15 | −1.58575 | ||||||||
\(364\) | 1.49316e14i | 0.0641944i | ||||||||
\(365\) | 7.82404e14i | 0.330882i | ||||||||
\(366\) | 1.40248e14i | 0.0583459i | ||||||||
\(367\) | 2.70015e15i | 1.10508i | 0.833488 | + | 0.552538i | \(0.186340\pi\) | ||||
−0.833488 | + | 0.552538i | \(0.813660\pi\) | |||||||
\(368\) | −1.70786e15 | + | 3.40284e14i | −0.687648 | + | 0.137011i | ||||
\(369\) | −2.56484e12 | −0.00101602 | ||||||||
\(370\) | −1.67048e15 | −0.651076 | ||||||||
\(371\) | −1.94610e14 | −0.0746314 | ||||||||
\(372\) | 2.51341e15 | 0.948432 | ||||||||
\(373\) | 1.55815e15i | 0.578569i | 0.957243 | + | 0.289285i | \(0.0934174\pi\) | ||||
−0.957243 | + | 0.289285i | \(0.906583\pi\) | |||||||
\(374\) | −1.34862e15 | −0.492786 | ||||||||
\(375\) | 1.52138e15i | 0.547078i | ||||||||
\(376\) | −1.44647e15 | −0.511897 | ||||||||
\(377\) | 1.53446e15 | 0.534450 | ||||||||
\(378\) | − | 4.38704e13i | − | 0.0150391i | ||||||
\(379\) | − | 1.15321e15i | − | 0.389109i | −0.980892 | − | 0.194555i | \(-0.937674\pi\) | ||
0.980892 | − | 0.194555i | \(-0.0623261\pi\) | |||||||
\(380\) | 3.78276e15 | 1.25634 | ||||||||
\(381\) | −8.22158e14 | −0.268785 | ||||||||
\(382\) | 5.60667e14i | 0.180437i | ||||||||
\(383\) | − | 2.36350e15i | − | 0.748794i | −0.927268 | − | 0.374397i | \(-0.877850\pi\) | ||
0.927268 | − | 0.374397i | \(-0.122150\pi\) | |||||||
\(384\) | −3.12450e15 | −0.974526 | ||||||||
\(385\) | 3.06746e14i | 0.0941922i | ||||||||
\(386\) | 3.97832e14 | 0.120275 | ||||||||
\(387\) | − | 1.11600e13i | − | 0.00332200i | ||||||
\(388\) | − | 4.04447e15i | − | 1.18542i | ||||||
\(389\) | 9.73213e14i | 0.280873i | 0.990090 | + | 0.140437i | \(0.0448506\pi\) | ||||
−0.990090 | + | 0.140437i | \(0.955149\pi\) | |||||||
\(390\) | − | 2.15977e15i | − | 0.613791i | ||||||
\(391\) | 6.66406e14 | + | 3.34464e15i | 0.186500 | + | 0.936029i | ||||
\(392\) | −2.20570e15 | −0.607897 | ||||||||
\(393\) | −5.73195e15 | −1.55578 | ||||||||
\(394\) | −1.04845e15 | −0.280267 | ||||||||
\(395\) | 3.04266e15 | 0.801071 | ||||||||
\(396\) | 1.10334e13i | 0.00286114i | ||||||||
\(397\) | 7.32666e15 | 1.87138 | 0.935692 | − | 0.352818i | \(-0.114776\pi\) | ||||
0.935692 | + | 0.352818i | \(0.114776\pi\) | |||||||
\(398\) | 6.89024e14i | 0.173355i | ||||||||
\(399\) | −2.12132e14 | −0.0525737 | ||||||||
\(400\) | −1.61639e15 | −0.394626 | ||||||||
\(401\) | 1.40000e15i | 0.336715i | 0.985726 | + | 0.168357i | \(0.0538463\pi\) | ||||
−0.985726 | + | 0.168357i | \(0.946154\pi\) | |||||||
\(402\) | 1.58451e15i | 0.375440i | ||||||||
\(403\) | 6.91150e15 | 1.61340 | ||||||||
\(404\) | −2.24536e15 | −0.516414 | ||||||||
\(405\) | − | 5.52768e15i | − | 1.25260i | ||||||
\(406\) | − | 2.35958e13i | − | 0.00526840i | ||||||
\(407\) | 1.18482e16 | 2.60667 | ||||||||
\(408\) | 2.68485e15i | 0.582047i | ||||||||
\(409\) | 1.86884e15 | 0.399238 | 0.199619 | − | 0.979874i | \(-0.436030\pi\) | ||||
0.199619 | + | 0.979874i | \(0.436030\pi\) | |||||||
\(410\) | − | 9.76452e14i | − | 0.205564i | ||||||
\(411\) | − | 2.07970e15i | − | 0.431469i | ||||||
\(412\) | 5.84255e15i | 1.19459i | ||||||||
\(413\) | − | 1.09644e14i | − | 0.0220946i | ||||||
\(414\) | −3.14749e12 | + | 6.27125e11i | −0.000625119 | + | 0.000124552i | ||||
\(415\) | 4.09259e15 | 0.801143 | ||||||||
\(416\) | −6.60444e15 | −1.27431 | ||||||||
\(417\) | −4.65089e14 | −0.0884544 | ||||||||
\(418\) | 3.08611e15 | 0.578568 | ||||||||
\(419\) | − | 3.82847e15i | − | 0.707523i | −0.935336 | − | 0.353762i | \(-0.884902\pi\) | ||
0.935336 | − | 0.353762i | \(-0.115098\pi\) | |||||||
\(420\) | 2.88732e14 | 0.0526016 | ||||||||
\(421\) | 7.95700e15i | 1.42908i | 0.699594 | + | 0.714540i | \(0.253364\pi\) | ||||
−0.699594 | + | 0.714540i | \(0.746636\pi\) | |||||||
\(422\) | 1.04069e15 | 0.184266 | ||||||||
\(423\) | 9.55219e12 | 0.00166748 | ||||||||
\(424\) | − | 5.63641e15i | − | 0.970079i | ||||||
\(425\) | 3.16550e15i | 0.537166i | ||||||||
\(426\) | −4.12075e14 | −0.0689475 | ||||||||
\(427\) | −5.15576e13 | −0.00850600 | ||||||||
\(428\) | 8.82391e15i | 1.43548i | ||||||||
\(429\) | 1.53186e16i | 2.45739i | ||||||||
\(430\) | 4.24870e15 | 0.672117 | ||||||||
\(431\) | − | 8.78299e15i | − | 1.37018i | −0.728457 | − | 0.685092i | \(-0.759762\pi\) | ||
0.728457 | − | 0.685092i | \(-0.240238\pi\) | |||||||
\(432\) | −4.55292e15 | −0.700467 | ||||||||
\(433\) | − | 6.57765e15i | − | 0.998029i | −0.866594 | − | 0.499014i | \(-0.833695\pi\) | ||
0.866594 | − | 0.499014i | \(-0.166305\pi\) | |||||||
\(434\) | − | 1.06280e14i | − | 0.0159043i | ||||||
\(435\) | − | 2.96719e15i | − | 0.437935i | ||||||
\(436\) | − | 7.88891e15i | − | 1.14841i | ||||||
\(437\) | −1.52497e15 | − | 7.65374e15i | −0.218965 | − | 1.09897i | ||||
\(438\) | 6.00826e14 | 0.0850951 | ||||||||
\(439\) | −4.74277e15 | −0.662590 | −0.331295 | − | 0.943527i | \(-0.607485\pi\) | ||||
−0.331295 | + | 0.943527i | \(0.607485\pi\) | |||||||
\(440\) | −8.88416e15 | −1.22433 | ||||||||
\(441\) | 1.45660e13 | 0.00198019 | ||||||||
\(442\) | 3.49070e15i | 0.468144i | ||||||||
\(443\) | −7.59767e15 | −1.00521 | −0.502607 | − | 0.864515i | \(-0.667626\pi\) | ||||
−0.502607 | + | 0.864515i | \(0.667626\pi\) | |||||||
\(444\) | − | 1.11524e16i | − | 1.45569i | ||||||
\(445\) | 2.26775e14 | 0.0292035 | ||||||||
\(446\) | −3.87005e15 | −0.491708 | ||||||||
\(447\) | 3.13480e15i | 0.392975i | ||||||||
\(448\) | − | 1.64139e14i | − | 0.0203022i | ||||||
\(449\) | 1.43574e16 | 1.75226 | 0.876129 | − | 0.482076i | \(-0.160117\pi\) | ||||
0.876129 | + | 0.482076i | \(0.160117\pi\) | |||||||
\(450\) | −2.97891e12 | −0.000358742 | ||||||||
\(451\) | 6.92566e15i | 0.823004i | ||||||||
\(452\) | − | 4.24758e15i | − | 0.498094i | ||||||
\(453\) | −1.18179e16 | −1.36758 | ||||||||
\(454\) | 2.60064e15i | 0.296992i | ||||||||
\(455\) | 7.93969e14 | 0.0894819 | ||||||||
\(456\) | − | 6.14388e15i | − | 0.683367i | ||||||
\(457\) | 9.08837e15i | 0.997674i | 0.866696 | + | 0.498837i | \(0.166239\pi\) | ||||
−0.866696 | + | 0.498837i | \(0.833761\pi\) | |||||||
\(458\) | − | 2.61875e15i | − | 0.283727i | ||||||
\(459\) | 8.91635e15i | 0.953478i | ||||||||
\(460\) | 2.07564e15 | + | 1.04175e16i | 0.219081 | + | 1.09955i | ||||
\(461\) | 3.88514e15 | 0.404763 | 0.202381 | − | 0.979307i | \(-0.435132\pi\) | ||||
0.202381 | + | 0.979307i | \(0.435132\pi\) | |||||||
\(462\) | 2.35558e14 | 0.0242240 | ||||||||
\(463\) | 4.99994e15 | 0.507550 | 0.253775 | − | 0.967263i | \(-0.418328\pi\) | ||||
0.253775 | + | 0.967263i | \(0.418328\pi\) | |||||||
\(464\) | −2.44880e15 | −0.245383 | ||||||||
\(465\) | − | 1.33648e16i | − | 1.32204i | ||||||
\(466\) | 3.08669e15 | 0.301424 | ||||||||
\(467\) | 3.88089e15i | 0.374136i | 0.982347 | + | 0.187068i | \(0.0598985\pi\) | ||||
−0.982347 | + | 0.187068i | \(0.940101\pi\) | |||||||
\(468\) | 2.85585e13 | 0.00271807 | ||||||||
\(469\) | −5.82495e14 | −0.0547337 | ||||||||
\(470\) | 3.63658e15i | 0.337370i | ||||||||
\(471\) | − | 4.39291e14i | − | 0.0402371i | ||||||
\(472\) | 3.17558e15 | 0.287191 | ||||||||
\(473\) | −3.01346e16 | −2.69091 | ||||||||
\(474\) | − | 2.33653e15i | − | 0.206016i | ||||||
\(475\) | − | 7.24379e15i | − | 0.630673i | ||||||
\(476\) | −4.66659e14 | −0.0401197 | ||||||||
\(477\) | 3.72216e13i | 0.00315998i | ||||||||
\(478\) | 5.32545e15 | 0.446467 | ||||||||
\(479\) | 1.12520e16i | 0.931569i | 0.884898 | + | 0.465784i | \(0.154228\pi\) | ||||
−0.884898 | + | 0.465784i | \(0.845772\pi\) | |||||||
\(480\) | 1.27710e16i | 1.04419i | ||||||||
\(481\) | − | 3.06674e16i | − | 2.47632i | ||||||
\(482\) | − | 1.92386e15i | − | 0.153423i | ||||||
\(483\) | −1.16399e14 | − | 5.84197e14i | −0.00916780 | − | 0.0460125i | ||||
\(484\) | 1.82639e16 | 1.42076 | ||||||||
\(485\) | −2.15060e16 | −1.65238 | ||||||||
\(486\) | −1.67982e13 | −0.00127481 | ||||||||
\(487\) | 4.99647e15 | 0.374533 | 0.187266 | − | 0.982309i | \(-0.440037\pi\) | ||||
0.187266 | + | 0.982309i | \(0.440037\pi\) | |||||||
\(488\) | − | 1.49324e15i | − | 0.110563i | ||||||
\(489\) | −4.54645e15 | −0.332521 | ||||||||
\(490\) | 5.54535e15i | 0.400638i | ||||||||
\(491\) | 3.60546e15 | 0.257319 | 0.128660 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128660 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(492\) | 6.51894e15 | 0.459606 | ||||||||
\(493\) | 4.79567e15i | 0.334017i | ||||||||
\(494\) | − | 7.98797e15i | − | 0.549635i | ||||||
\(495\) | 5.86691e13 | 0.00398821 | ||||||||
\(496\) | −1.10299e16 | −0.740764 | ||||||||
\(497\) | − | 1.51486e14i | − | 0.0100516i | ||||||
\(498\) | − | 3.14280e15i | − | 0.206035i | ||||||
\(499\) | −1.23847e16 | −0.802202 | −0.401101 | − | 0.916034i | \(-0.631372\pi\) | ||||
−0.401101 | + | 0.916034i | \(0.631372\pi\) | |||||||
\(500\) | − | 7.65869e15i | − | 0.490156i | ||||||
\(501\) | −2.09882e16 | −1.32724 | ||||||||
\(502\) | − | 3.79115e15i | − | 0.236891i | ||||||
\(503\) | 5.45188e15i | 0.336619i | 0.985734 | + | 0.168309i | \(0.0538308\pi\) | ||||
−0.985734 | + | 0.168309i | \(0.946169\pi\) | |||||||
\(504\) | − | 9.28817e11i | − | 5.66692e-5i | ||||||
\(505\) | 1.19395e16i | 0.719841i | ||||||||
\(506\) | 1.69338e15 | + | 8.49894e15i | 0.100891 | + | 0.506363i | ||||
\(507\) | 2.26488e16 | 1.33351 | ||||||||
\(508\) | 4.13878e15 | 0.240819 | ||||||||
\(509\) | −1.70661e16 | −0.981358 | −0.490679 | − | 0.871340i | \(-0.663251\pi\) | ||||
−0.490679 | + | 0.871340i | \(0.663251\pi\) | |||||||
\(510\) | 6.74998e15 | 0.383602 | ||||||||
\(511\) | 2.20874e14i | 0.0124056i | ||||||||
\(512\) | 1.82351e16 | 1.01225 | ||||||||
\(513\) | − | 2.04038e16i | − | 1.11945i | ||||||
\(514\) | 2.59071e15 | 0.140488 | ||||||||
\(515\) | 3.10671e16 | 1.66517 | ||||||||
\(516\) | 2.83649e16i | 1.50274i | ||||||||
\(517\) | − | 2.57931e16i | − | 1.35070i | ||||||
\(518\) | −4.71581e14 | −0.0244106 | ||||||||
\(519\) | 1.92753e16 | 0.986275 | ||||||||
\(520\) | 2.29954e16i | 1.16311i | ||||||||
\(521\) | 3.27861e16i | 1.63932i | 0.572852 | + | 0.819659i | \(0.305837\pi\) | ||||
−0.572852 | + | 0.819659i | \(0.694163\pi\) | |||||||
\(522\) | −4.51299e12 | −0.000223070 | ||||||||
\(523\) | 1.02947e16i | 0.503041i | 0.967852 | + | 0.251520i | \(0.0809305\pi\) | ||||
−0.967852 | + | 0.251520i | \(0.919069\pi\) | |||||||
\(524\) | 2.88549e16 | 1.39390 | ||||||||
\(525\) | − | 5.52906e14i | − | 0.0264056i | ||||||
\(526\) | − | 3.44415e15i | − | 0.162617i | ||||||
\(527\) | 2.16007e16i | 1.00833i | ||||||||
\(528\) | − | 2.44464e16i | − | 1.12827i | ||||||
\(529\) | 2.02411e16 | − | 8.39935e15i | 0.923634 | − | 0.383276i | ||||
\(530\) | −1.41705e16 | −0.639337 | ||||||||
\(531\) | −2.09708e13 | −0.000935511 | ||||||||
\(532\) | 1.06788e15 | 0.0471035 | ||||||||
\(533\) | 1.79261e16 | 0.781848 | ||||||||
\(534\) | − | 1.74146e14i | − | 0.00751043i | ||||||
\(535\) | 4.69202e16 | 2.00095 | ||||||||
\(536\) | − | 1.68705e16i | − | 0.711443i | ||||||
\(537\) | 3.46289e16 | 1.44409 | ||||||||
\(538\) | −8.95448e15 | −0.369272 | ||||||||
\(539\) | − | 3.93314e16i | − | 1.60401i | ||||||
\(540\) | 2.77715e16i | 1.12005i | ||||||||
\(541\) | −4.53166e16 | −1.80748 | −0.903741 | − | 0.428079i | \(-0.859191\pi\) | ||||
−0.903741 | + | 0.428079i | \(0.859191\pi\) | |||||||
\(542\) | −7.35932e15 | −0.290297 | ||||||||
\(543\) | − | 2.03586e16i | − | 0.794236i | ||||||
\(544\) | − | 2.06410e16i | − | 0.796411i | ||||||
\(545\) | −4.19484e16 | −1.60080 | ||||||||
\(546\) | − | 6.09708e14i | − | 0.0230126i | ||||||
\(547\) | −1.47231e16 | −0.549637 | −0.274818 | − | 0.961496i | \(-0.588618\pi\) | ||||
−0.274818 | + | 0.961496i | \(0.588618\pi\) | |||||||
\(548\) | 1.04693e16i | 0.386575i | ||||||||
\(549\) | 9.86104e12i | 0.000360154i | ||||||||
\(550\) | 8.04373e15i | 0.290590i | ||||||||
\(551\) | − | 1.09742e16i | − | 0.392160i | ||||||
\(552\) | 1.69198e16 | − | 3.37120e15i | 0.598083 | − | 0.119166i | ||||
\(553\) | 8.58950e14 | 0.0300343 | ||||||||
\(554\) | −1.39845e16 | −0.483715 | ||||||||
\(555\) | −5.93016e16 | −2.02912 | ||||||||
\(556\) | 2.34128e15 | 0.0792509 | ||||||||
\(557\) | 1.48773e16i | 0.498188i | 0.968479 | + | 0.249094i | \(0.0801328\pi\) | ||||
−0.968479 | + | 0.249094i | \(0.919867\pi\) | |||||||
\(558\) | −2.03274e13 | −0.000673405 | ||||||||
\(559\) | 7.79992e16i | 2.55634i | ||||||||
\(560\) | −1.26707e15 | −0.0410840 | ||||||||
\(561\) | −4.78754e16 | −1.53580 | ||||||||
\(562\) | − | 1.73005e16i | − | 0.549088i | ||||||
\(563\) | 2.49578e16i | 0.783709i | 0.920027 | + | 0.391855i | \(0.128166\pi\) | ||||
−0.920027 | + | 0.391855i | \(0.871834\pi\) | |||||||
\(564\) | −2.42783e16 | −0.754300 | ||||||||
\(565\) | −2.25861e16 | −0.694304 | ||||||||
\(566\) | − | 5.80947e15i | − | 0.176700i | ||||||
\(567\) | − | 1.56048e15i | − | 0.0469633i | ||||||
\(568\) | 4.38742e15 | 0.130653 | ||||||||
\(569\) | − | 1.63399e16i | − | 0.481478i | −0.970590 | − | 0.240739i | \(-0.922610\pi\) | ||
0.970590 | − | 0.240739i | \(-0.0773898\pi\) | |||||||
\(570\) | −1.54464e16 | −0.450378 | ||||||||
\(571\) | − | 3.45158e16i | − | 0.995868i | −0.867215 | − | 0.497934i | \(-0.834092\pi\) | ||
0.867215 | − | 0.497934i | \(-0.165908\pi\) | |||||||
\(572\) | − | 7.71144e16i | − | 2.20171i | ||||||
\(573\) | 1.99035e16i | 0.562343i | ||||||||
\(574\) | − | 2.75654e14i | − | 0.00770714i | ||||||
\(575\) | 1.99489e16 | − | 3.97474e15i | 0.551966 | − | 0.109977i | ||||
\(576\) | −3.13937e13 | −0.000859621 | ||||||||
\(577\) | −1.46857e16 | −0.397961 | −0.198981 | − | 0.980003i | \(-0.563763\pi\) | ||||
−0.198981 | + | 0.980003i | \(0.563763\pi\) | |||||||
\(578\) | 1.06669e15 | 0.0286070 | ||||||||
\(579\) | 1.41229e16 | 0.374846 | ||||||||
\(580\) | 1.49370e16i | 0.392369i | ||||||||
\(581\) | 1.15535e15 | 0.0300369 | ||||||||
\(582\) | 1.65150e16i | 0.424952i | ||||||||
\(583\) | 1.00507e17 | 2.55967 | ||||||||
\(584\) | −6.39708e15 | −0.161252 | ||||||||
\(585\) | − | 1.51857e14i | − | 0.00378877i | ||||||
\(586\) | 6.80714e15i | 0.168104i | ||||||||
\(587\) | −4.11858e16 | −1.00674 | −0.503372 | − | 0.864070i | \(-0.667907\pi\) | ||||
−0.503372 | + | 0.864070i | \(0.667907\pi\) | |||||||
\(588\) | −3.70216e16 | −0.895758 | ||||||||
\(589\) | − | 4.94300e16i | − | 1.18386i | ||||||
\(590\) | − | 7.98373e15i | − | 0.189275i | ||||||
\(591\) | −3.72198e16 | −0.873472 | ||||||||
\(592\) | 4.89412e16i | 1.13696i | ||||||||
\(593\) | 6.12005e15 | 0.140743 | 0.0703715 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703715 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(594\) | 2.26570e16i | 0.515802i | ||||||||
\(595\) | 2.48141e15i | 0.0559238i | ||||||||
\(596\) | − | 1.57807e16i | − | 0.352087i | ||||||
\(597\) | 2.44601e16i | 0.540272i | ||||||||
\(598\) | 2.19983e16 | − | 4.38307e15i | 0.481041 | − | 0.0958454i | ||||
\(599\) | 4.85506e16 | 1.05107 | 0.525537 | − | 0.850771i | \(-0.323864\pi\) | ||||
0.525537 | + | 0.850771i | \(0.323864\pi\) | |||||||
\(600\) | 1.60136e16 | 0.343227 | ||||||||
\(601\) | −5.47790e16 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697423\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697423\pi\) | |||||||
\(602\) | 1.19941e15 | 0.0251994 | ||||||||
\(603\) | 1.11409e14i | 0.00231749i | ||||||||
\(604\) | 5.94921e16 | 1.22529 | ||||||||
\(605\) | − | 9.71162e16i | − | 1.98043i | ||||||
\(606\) | 9.16860e15 | 0.185126 | ||||||||
\(607\) | 1.51959e16 | 0.303804 | 0.151902 | − | 0.988396i | \(-0.451460\pi\) | ||||
0.151902 | + | 0.988396i | \(0.451460\pi\) | |||||||
\(608\) | 4.72339e16i | 0.935045i | ||||||||
\(609\) | − | 8.37643e14i | − | 0.0164193i | ||||||
\(610\) | −3.75416e15 | −0.0728675 | ||||||||
\(611\) | −6.67617e16 | −1.28316 | ||||||||
\(612\) | 8.92544e13i | 0.00169872i | ||||||||
\(613\) | − | 2.14547e16i | − | 0.404353i | −0.979349 | − | 0.202176i | \(-0.935199\pi\) | ||
0.979349 | − | 0.202176i | \(-0.0648014\pi\) | |||||||
\(614\) | −7.68769e15 | −0.143478 | ||||||||
\(615\) | − | 3.46637e16i | − | 0.640655i | ||||||
\(616\) | −2.50802e15 | −0.0459035 | ||||||||
\(617\) | 7.31022e16i | 1.32501i | 0.749057 | + | 0.662506i | \(0.230507\pi\) | ||||
−0.749057 | + | 0.662506i | \(0.769493\pi\) | |||||||
\(618\) | − | 2.38572e16i | − | 0.428241i | ||||||
\(619\) | 1.01544e17i | 1.80514i | 0.430539 | + | 0.902572i | \(0.358323\pi\) | ||||
−0.430539 | + | 0.902572i | \(0.641677\pi\) | |||||||
\(620\) | 6.72790e16i | 1.18448i | ||||||||
\(621\) | 5.61906e16 | − | 1.11957e16i | 0.979747 | − | 0.195210i | ||||
\(622\) | 1.60997e16 | 0.278020 | ||||||||
\(623\) | 6.40189e13 | 0.00109491 | ||||||||
\(624\) | −6.32761e16 | −1.07185 | ||||||||
\(625\) | −7.42706e16 | −1.24605 | ||||||||
\(626\) | 7.57026e15i | 0.125795i | ||||||||
\(627\) | 1.09556e17 | 1.80315 | ||||||||
\(628\) | 2.21141e15i | 0.0360505i | ||||||||
\(629\) | 9.58454e16 | 1.54763 | ||||||||
\(630\) | −2.33514e12 | −3.73482e−5 | ||||||||
\(631\) | − | 9.47729e16i | − | 1.50144i | −0.660621 | − | 0.750720i | \(-0.729707\pi\) | ||
0.660621 | − | 0.750720i | \(-0.270293\pi\) | |||||||
\(632\) | 2.48774e16i | 0.390393i | ||||||||
\(633\) | 3.69441e16 | 0.574279 | ||||||||
\(634\) | −8.71982e15 | −0.134268 | ||||||||
\(635\) | − | 2.20075e16i | − | 0.335682i | ||||||
\(636\) | − | 9.46043e16i | − | 1.42945i | ||||||
\(637\) | −1.01804e17 | −1.52380 | ||||||||
\(638\) | 1.21861e16i | 0.180693i | ||||||||
\(639\) | −2.89736e13 | −0.000425595 | ||||||||
\(640\) | − | 8.36366e16i | − | 1.21707i | ||||||
\(641\) | 1.20517e17i | 1.73739i | 0.495344 | + | 0.868697i | \(0.335042\pi\) | ||||
−0.495344 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(642\) | − | 3.60311e16i | − | 0.514597i | ||||||
\(643\) | 3.08086e16i | 0.435920i | 0.975958 | + | 0.217960i | \(0.0699402\pi\) | ||||
−0.975958 | + | 0.217960i | \(0.930060\pi\) | |||||||
\(644\) | 5.85957e14 | + | 2.94087e15i | 0.00821392 | + | 0.0412250i | ||||
\(645\) | 1.50827e17 | 2.09470 | ||||||||
\(646\) | 2.49650e16 | 0.343507 | ||||||||
\(647\) | 1.60873e16 | 0.219310 | 0.109655 | − | 0.993970i | \(-0.465025\pi\) | ||||
0.109655 | + | 0.993970i | \(0.465025\pi\) | |||||||
\(648\) | 4.51954e16 | 0.610442 | ||||||||
\(649\) | 5.66260e16i | 0.757788i | ||||||||
\(650\) | 2.08201e16 | 0.276059 | ||||||||
\(651\) | − | 3.77291e15i | − | 0.0495667i | ||||||
\(652\) | 2.28871e16 | 0.297923 | ||||||||
\(653\) | 5.79193e16 | 0.747040 | 0.373520 | − | 0.927622i | \(-0.378151\pi\) | ||||
0.373520 | + | 0.927622i | \(0.378151\pi\) | |||||||
\(654\) | 3.22132e16i | 0.411687i | ||||||||
\(655\) | − | 1.53433e17i | − | 1.94299i | ||||||
\(656\) | −2.86077e16 | −0.358972 | ||||||||
\(657\) | 4.22449e13 | 0.000525270 | ||||||||
\(658\) | 1.02661e15i | 0.0126489i | ||||||||
\(659\) | 3.13243e15i | 0.0382445i | 0.999817 | + | 0.0191223i | \(0.00608717\pi\) | ||||
−0.999817 | + | 0.0191223i | \(0.993913\pi\) | |||||||
\(660\) | −1.49116e17 | −1.80410 | ||||||||
\(661\) | 4.36627e16i | 0.523482i | 0.965138 | + | 0.261741i | \(0.0842966\pi\) | ||||
−0.965138 | + | 0.261741i | \(0.915703\pi\) | |||||||
\(662\) | −1.76725e16 | −0.209966 | ||||||||
\(663\) | 1.23919e17i | 1.45900i | ||||||||
\(664\) | 3.34618e16i | 0.390428i | ||||||||
\(665\) | − | 5.67834e15i | − | 0.0656586i | ||||||
\(666\) | 9.01957e13i | 0.00103357i | ||||||||
\(667\) | 3.02222e16 | − | 6.02165e15i | 0.343219 | − | 0.0683849i | ||||
\(668\) | 1.05656e17 | 1.18914 | ||||||||
\(669\) | −1.37385e17 | −1.53244 | ||||||||
\(670\) | −4.24143e16 | −0.468882 | ||||||||
\(671\) | 2.66270e16 | 0.291734 | ||||||||
\(672\) | 3.60528e15i | 0.0391493i | ||||||||
\(673\) | 1.97947e15 | 0.0213039 | 0.0106519 | − | 0.999943i | \(-0.496609\pi\) | ||||
0.0106519 | + | 0.999943i | \(0.496609\pi\) | |||||||
\(674\) | − | 5.77847e16i | − | 0.616387i | ||||||
\(675\) | 5.31810e16 | 0.562255 | ||||||||
\(676\) | −1.14015e17 | −1.19476 | ||||||||
\(677\) | 5.52494e16i | 0.573846i | 0.957954 | + | 0.286923i | \(0.0926324\pi\) | ||||
−0.957954 | + | 0.286923i | \(0.907368\pi\) | |||||||
\(678\) | 1.73444e16i | 0.178558i | ||||||||
\(679\) | −6.07119e15 | −0.0619520 | ||||||||
\(680\) | −7.18679e16 | −0.726912 | ||||||||
\(681\) | 9.23217e16i | 0.925595i | ||||||||
\(682\) | 5.48886e16i | 0.545476i | ||||||||
\(683\) | −8.11803e15 | −0.0799699 | −0.0399849 | − | 0.999200i | \(-0.512731\pi\) | ||||
−0.0399849 | + | 0.999200i | \(0.512731\pi\) | |||||||
\(684\) | − | 2.04246e14i | − | 0.00199442i | ||||||
\(685\) | 5.56693e16 | 0.538856 | ||||||||
\(686\) | 3.13437e15i | 0.0300750i | ||||||||
\(687\) | − | 9.29647e16i | − | 0.884255i | ||||||
\(688\) | − | 1.24477e17i | − | 1.17370i | ||||||
\(689\) | − | 2.60148e17i | − | 2.43167i | ||||||
\(690\) | −8.47555e15 | − | 4.25382e16i | −0.0785369 | − | 0.394171i | ||||
\(691\) | −1.04730e17 | −0.962063 | −0.481032 | − | 0.876703i | \(-0.659738\pi\) | ||||
−0.481032 | + | 0.876703i | \(0.659738\pi\) | |||||||
\(692\) | −9.70330e16 | −0.883655 | ||||||||
\(693\) | 1.65624e13 | 0.000149528 | ||||||||
\(694\) | −1.41371e15 | −0.0126533 | ||||||||
\(695\) | − | 1.24495e16i | − | 0.110470i | ||||||
\(696\) | 2.42603e16 | 0.213423 | ||||||||
\(697\) | 5.60248e16i | 0.488634i | ||||||||
\(698\) | −5.02498e16 | −0.434512 | ||||||||
\(699\) | 1.09577e17 | 0.939409 | ||||||||
\(700\) | 2.78336e15i | 0.0236581i | ||||||||
\(701\) | 4.92437e16i | 0.414995i | 0.978236 | + | 0.207498i | \(0.0665319\pi\) | ||||
−0.978236 | + | 0.207498i | \(0.933468\pi\) | |||||||
\(702\) | 5.86444e16 | 0.490009 | ||||||||
\(703\) | −2.19328e17 | −1.81703 | ||||||||
\(704\) | 8.47700e16i | 0.696316i | ||||||||
\(705\) | 1.29097e17i | 1.05144i | ||||||||
\(706\) | −3.54248e16 | −0.286074 | ||||||||
\(707\) | 3.37053e15i | 0.0269887i | ||||||||
\(708\) | 5.33006e16 | 0.423187 | ||||||||
\(709\) | − | 7.44193e16i | − | 0.585879i | −0.956131 | − | 0.292940i | \(-0.905367\pi\) | ||
0.956131 | − | 0.292940i | \(-0.0946335\pi\) | |||||||
\(710\) | − | 1.10304e16i | − | 0.0861077i | ||||||
\(711\) | − | 1.64285e14i | − | 0.00127169i | ||||||
\(712\) | 1.85415e15i | 0.0142320i | ||||||||
\(713\) | 1.36127e17 | − | 2.71227e16i | 1.03611 | − | 0.206441i | ||||
\(714\) | 1.90553e15 | 0.0143823 | ||||||||
\(715\) | −4.10047e17 | −3.06900 | ||||||||
\(716\) | −1.74324e17 | −1.29383 | ||||||||
\(717\) | 1.89052e17 | 1.39144 | ||||||||
\(718\) | − | 5.88038e16i | − | 0.429199i | ||||||
\(719\) | 2.09057e17 | 1.51318 | 0.756591 | − | 0.653889i | \(-0.226864\pi\) | ||||
0.756591 | + | 0.653889i | \(0.226864\pi\) | |||||||
\(720\) | 2.42343e14i | 0.00173955i | ||||||||
\(721\) | 8.77030e15 | 0.0624314 | ||||||||
\(722\) | −1.16323e16 | −0.0821187 | ||||||||
\(723\) | − | 6.82964e16i | − | 0.478154i | ||||||
\(724\) | 1.02486e17i | 0.711598i | ||||||||
\(725\) | 2.86035e16 | 0.196966 | ||||||||
\(726\) | −7.45778e16 | −0.509319 | ||||||||
\(727\) | − | 9.98224e16i | − | 0.676117i | −0.941125 | − | 0.338058i | \(-0.890230\pi\) | ||
0.941125 | − | 0.338058i | \(-0.109770\pi\) | |||||||
\(728\) | 6.49164e15i | 0.0436080i | ||||||||
\(729\) | 1.49796e17 | 0.998008 | ||||||||
\(730\) | 1.60829e16i | 0.106274i | ||||||||
\(731\) | −2.43772e17 | −1.59764 | ||||||||
\(732\) | − | 2.50633e16i | − | 0.162919i | ||||||
\(733\) | 7.93088e16i | 0.511326i | 0.966766 | + | 0.255663i | \(0.0822937\pi\) | ||||
−0.966766 | + | 0.255663i | \(0.917706\pi\) | |||||||
\(734\) | 5.55037e16i | 0.354932i | ||||||||
\(735\) | 1.96858e17i | 1.24862i | ||||||||
\(736\) | −1.30079e17 | + | 2.59177e16i | −0.818352 | + | 0.163053i | ||||
\(737\) | 3.00831e17 | 1.87723 | ||||||||
\(738\) | −5.27223e13 | −0.000326330 | ||||||||
\(739\) | −2.14675e17 | −1.31800 | −0.658998 | − | 0.752144i | \(-0.729020\pi\) | ||||
−0.658998 | + | 0.752144i | \(0.729020\pi\) | |||||||
\(740\) | 2.98527e17 | 1.81800 | ||||||||
\(741\) | − | 2.83570e17i | − | 1.71298i | ||||||
\(742\) | −4.00036e15 | −0.0239704 | ||||||||
\(743\) | 2.85783e17i | 1.69865i | 0.527873 | + | 0.849323i | \(0.322990\pi\) | ||||
−0.527873 | + | 0.849323i | \(0.677010\pi\) | |||||||
\(744\) | 1.09273e17 | 0.644281 | ||||||||
\(745\) | −8.39123e16 | −0.490781 | ||||||||
\(746\) | 3.20289e16i | 0.185827i | ||||||||
\(747\) | − | 2.20975e14i | − | 0.00127180i | ||||||
\(748\) | 2.41007e17 | 1.37601 | ||||||||
\(749\) | 1.32457e16 | 0.0750209 | ||||||||
\(750\) | 3.12731e16i | 0.175713i | ||||||||
\(751\) | 6.85590e16i | 0.382142i | 0.981576 | + | 0.191071i | \(0.0611961\pi\) | ||||
−0.981576 | + | 0.191071i | \(0.938804\pi\) | |||||||
\(752\) | 1.06543e17 | 0.589139 | ||||||||
\(753\) | − | 1.34584e17i | − | 0.738287i | ||||||
\(754\) | 3.15420e16 | 0.171657 | ||||||||
\(755\) | − | 3.16343e17i | − | 1.70795i | ||||||
\(756\) | 7.83995e15i | 0.0419936i | ||||||||
\(757\) | − | 3.28827e17i | − | 1.74740i | −0.486467 | − | 0.873699i | \(-0.661715\pi\) | ||
0.486467 | − | 0.873699i | \(-0.338285\pi\) | |||||||
\(758\) | − | 2.37050e16i | − | 0.124976i | ||||||
\(759\) | 6.01144e16 | + | 3.01710e17i | 0.314433 | + | 1.57811i | ||||
\(760\) | 1.64459e17 | 0.853448 | ||||||||
\(761\) | −3.36910e17 | −1.73462 | −0.867312 | − | 0.497765i | \(-0.834154\pi\) | ||||
−0.867312 | + | 0.497765i | \(0.834154\pi\) | |||||||
\(762\) | −1.69001e16 | −0.0863295 | ||||||||
\(763\) | −1.18421e16 | −0.0600181 | ||||||||
\(764\) | − | 1.00195e17i | − | 0.503833i | ||||||
\(765\) | 4.74600e14 | 0.00236788 | ||||||||
\(766\) | − | 4.85835e16i | − | 0.240501i | ||||||
\(767\) | 1.46568e17 | 0.719894 | ||||||||
\(768\) | 2.47432e16 | 0.120584 | ||||||||
\(769\) | 2.17668e17i | 1.05253i | 0.850320 | + | 0.526267i | \(0.176409\pi\) | ||||
−0.850320 | + | 0.526267i | \(0.823591\pi\) | |||||||
\(770\) | 6.30541e15i | 0.0302530i | ||||||||
\(771\) | 9.19692e16 | 0.437841 | ||||||||
\(772\) | −7.10954e16 | −0.335844 | ||||||||
\(773\) | 9.78596e16i | 0.458698i | 0.973344 | + | 0.229349i | \(0.0736596\pi\) | ||||
−0.973344 | + | 0.229349i | \(0.926340\pi\) | |||||||
\(774\) | − | 2.29403e14i | − | 0.00106697i | ||||||
\(775\) | 1.28836e17 | 0.594601 | ||||||||
\(776\) | − | 1.75837e17i | − | 0.805268i | ||||||
\(777\) | −1.67410e16 | −0.0760771 | ||||||||
\(778\) | 2.00052e16i | 0.0902120i | ||||||||
\(779\) | − | 1.28205e17i | − | 0.573692i | ||||||
\(780\) | 3.85966e17i | 1.71389i | ||||||||
\(781\) | 7.82352e16i | 0.344743i | ||||||||
\(782\) | 1.36985e16 | + | 6.87517e16i | 0.0599008 | + | 0.300638i | ||||
\(783\) | 8.05682e16 | 0.349617 | ||||||||
\(784\) | 1.62465e17 | 0.699624 | ||||||||
\(785\) | 1.17589e16 | 0.0502516 | ||||||||
\(786\) | −1.17825e17 | −0.499690 | ||||||||
\(787\) | 4.32755e17i | 1.82135i | 0.413120 | + | 0.910676i | \(0.364439\pi\) | ||||
−0.413120 | + | 0.910676i | \(0.635561\pi\) | |||||||
\(788\) | 1.87366e17 | 0.782589 | ||||||||
\(789\) | − | 1.22266e17i | − | 0.506808i | ||||||
\(790\) | 6.25443e16 | 0.257291 | ||||||||
\(791\) | −6.37609e15 | −0.0260313 | ||||||||
\(792\) | 4.79689e14i | 0.00194361i | ||||||||
\(793\) | − | 6.89203e16i | − | 0.277146i | ||||||
\(794\) | 1.50605e17 | 0.601059 | ||||||||
\(795\) | −5.03048e17 | −1.99254 | ||||||||
\(796\) | − | 1.23133e17i | − | 0.484058i | ||||||
\(797\) | 1.54274e17i | 0.601924i | 0.953636 | + | 0.300962i | \(0.0973078\pi\) | ||||
−0.953636 | + | 0.300962i | \(0.902692\pi\) | |||||||
\(798\) | −4.36054e15 | −0.0168858 | ||||||||
\(799\) | − | 2.08652e17i | − | 0.801939i | ||||||
\(800\) | −1.23112e17 | −0.469634 | ||||||||
\(801\) | − | 1.22444e13i | − | 4.63600e-5i | ||||||
\(802\) | 2.87781e16i | 0.108147i | ||||||||
\(803\) | − | 1.14071e17i | − | 0.425482i | ||||||
\(804\) | − | 2.83164e17i | − | 1.04834i | ||||||
\(805\) | 1.56378e16 | − | 3.11576e15i | 0.0574645 | − | 0.0114496i | ||||
\(806\) | 1.42071e17 | 0.518198 | ||||||||
\(807\) | −3.17881e17 | −1.15086 | ||||||||
\(808\) | −9.76193e16 | −0.350806 | ||||||||
\(809\) | −1.52845e17 | −0.545204 | −0.272602 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272602 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(810\) | − | 1.13626e17i | − | 0.402316i | ||||||
\(811\) | 2.10280e17 | 0.739048 | 0.369524 | − | 0.929221i | \(-0.379521\pi\) | ||||
0.369524 | + | 0.929221i | \(0.379521\pi\) | |||||||
\(812\) | 4.21673e15i | 0.0147109i | ||||||||
\(813\) | −2.61253e17 | −0.904730 | ||||||||
\(814\) | 2.43549e17 | 0.837220 | ||||||||
\(815\) | − | 1.21699e17i | − | 0.415282i | ||||||
\(816\) | − | 1.97758e17i | − | 0.669875i | ||||||
\(817\) | 5.57838e17 | 1.87575 | ||||||||
\(818\) | 3.84154e16 | 0.128229 | ||||||||
\(819\) | − | 4.28694e13i | − | 0.000142051i | ||||||
\(820\) | 1.74499e17i | 0.573997i | ||||||||
\(821\) | −1.96166e17 | −0.640568 | −0.320284 | − | 0.947322i | \(-0.603778\pi\) | ||||
−0.320284 | + | 0.947322i | \(0.603778\pi\) | |||||||
\(822\) | − | 4.27498e16i | − | 0.138581i | ||||||
\(823\) | −5.43712e17 | −1.74973 | −0.874863 | − | 0.484370i | \(-0.839049\pi\) | ||||
−0.874863 | + | 0.484370i | \(0.839049\pi\) | |||||||
\(824\) | 2.54010e17i | 0.811500i | ||||||||
\(825\) | 2.85550e17i | 0.905645i | ||||||||
\(826\) | − | 2.25382e15i | − | 0.00709643i | ||||||
\(827\) | 1.48485e17i | 0.464142i | 0.972699 | + | 0.232071i | \(0.0745501\pi\) | ||||
−0.972699 | + | 0.232071i | \(0.925450\pi\) | |||||||
\(828\) | 5.62479e14 | − | 1.12072e14i | 0.00174552 | − | 0.000347787i | ||||
\(829\) | 1.60037e17 | 0.493053 | 0.246527 | − | 0.969136i | \(-0.420711\pi\) | ||||
0.246527 | + | 0.969136i | \(0.420711\pi\) | |||||||
\(830\) | 8.41264e16 | 0.257314 | ||||||||
\(831\) | −4.96447e17 | −1.50753 | ||||||||
\(832\) | 2.19415e17 | 0.661495 | ||||||||
\(833\) | − | 3.18169e17i | − | 0.952331i | ||||||
\(834\) | −9.56026e15 | −0.0284101 | ||||||||
\(835\) | − | 5.61812e17i | − | 1.65757i | ||||||
\(836\) | −5.51510e17 | −1.61553 | ||||||||
\(837\) | 3.62895e17 | 1.05543 | ||||||||
\(838\) | − | 7.86971e16i | − | 0.227245i | ||||||
\(839\) | 4.61878e17i | 1.32420i | 0.749413 | + | 0.662102i | \(0.230336\pi\) | ||||
−0.749413 | + | 0.662102i | \(0.769664\pi\) | |||||||
\(840\) | 1.25529e16 | 0.0357329 | ||||||||
\(841\) | −3.10481e17 | −0.877524 | ||||||||
\(842\) | 1.63562e17i | 0.458998i | ||||||||
\(843\) | − | 6.14163e17i | − | 1.71127i | ||||||
\(844\) | −1.85978e17 | −0.514527 | ||||||||
\(845\) | 6.06263e17i | 1.66541i | ||||||||
\(846\) | 1.96353e14 | 0.000535568 | ||||||||
\(847\) | − | 2.74161e16i | − | 0.0742514i | ||||||
\(848\) | 4.15162e17i | 1.11646i | ||||||||
\(849\) | − | 2.06234e17i | − | 0.550699i | ||||||
\(850\) | 6.50693e16i | 0.172529i | ||||||||
\(851\) | −1.20347e17 | − | 6.04015e17i | −0.316854 | − | 1.59027i | ||||
\(852\) | 7.36407e16 | 0.192522 | ||||||||
\(853\) | −5.60063e17 | −1.45393 | −0.726963 | − | 0.686676i | \(-0.759069\pi\) | ||||
−0.726963 | + | 0.686676i | \(0.759069\pi\) | |||||||
\(854\) | −1.05981e15 | −0.00273199 | ||||||||
\(855\) | −1.08605e15 | −0.00278006 | ||||||||
\(856\) | 3.83628e17i | 0.975142i | ||||||||
\(857\) | 2.48605e17 | 0.627516 | 0.313758 | − | 0.949503i | \(-0.398412\pi\) | ||||
0.313758 | + | 0.949503i | \(0.398412\pi\) | |||||||
\(858\) | 3.14885e17i | 0.789275i | ||||||||
\(859\) | 6.30957e17 | 1.57051 | 0.785256 | − | 0.619172i | \(-0.212531\pi\) | ||||
0.785256 | + | 0.619172i | \(0.212531\pi\) | |||||||
\(860\) | −7.59271e17 | −1.87675 | ||||||||
\(861\) | − | 9.78564e15i | − | 0.0240198i | ||||||
\(862\) | − | 1.80541e17i | − | 0.440081i | ||||||
\(863\) | −1.27577e17 | −0.308820 | −0.154410 | − | 0.988007i | \(-0.549348\pi\) | ||||
−0.154410 | + | 0.988007i | \(0.549348\pi\) | |||||||
\(864\) | −3.46772e17 | −0.833608 | ||||||||
\(865\) | 5.15962e17i | 1.23175i | ||||||||
\(866\) | − | 1.35209e17i | − | 0.320551i | ||||||
\(867\) | 3.78673e16 | 0.0891558 | ||||||||
\(868\) | 1.89930e16i | 0.0444094i | ||||||||
\(869\) | −4.43606e17 | −1.03010 | ||||||||
\(870\) | − | 6.09928e16i | − | 0.140658i | ||||||
\(871\) | − | 7.78658e17i | − | 1.78335i | ||||||
\(872\) | − | 3.42978e17i | − | 0.780131i | ||||||
\(873\) | 1.16119e15i | 0.00262312i | ||||||||
\(874\) | −3.13470e16 | − | 1.57328e17i | −0.0703279 | − | 0.352971i | ||||
\(875\) | −1.14965e16 | −0.0256164 | ||||||||
\(876\) | −1.07372e17 | −0.237611 | ||||||||
\(877\) | 8.76560e17 | 1.92657 | 0.963283 | − | 0.268487i | \(-0.0865235\pi\) | ||||
0.963283 | + | 0.268487i | \(0.0865235\pi\) | |||||||
\(878\) | −9.74913e16 | −0.212813 | ||||||||
\(879\) | 2.41651e17i | 0.523909i | ||||||||
\(880\) | 6.54382e17 | 1.40908 | ||||||||
\(881\) | 3.28530e17i | 0.702619i | 0.936259 | + | 0.351309i | \(0.114264\pi\) | ||||
−0.936259 | + | 0.351309i | \(0.885736\pi\) | |||||||
\(882\) | 2.99414e14 | 0.000636006 | ||||||||
\(883\) | −1.91747e17 | −0.404542 | −0.202271 | − | 0.979330i | \(-0.564832\pi\) | ||||
−0.202271 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(884\) | − | 6.23813e17i | − | 1.30720i | ||||||
\(885\) | − | 2.83420e17i | − | 0.589889i | ||||||
\(886\) | −1.56176e17 | −0.322858 | ||||||||
\(887\) | 8.25413e17 | 1.69484 | 0.847421 | − | 0.530921i | \(-0.178154\pi\) | ||||
0.847421 | + | 0.530921i | \(0.178154\pi\) | |||||||
\(888\) | − | 4.84861e17i | − | 0.988871i | ||||||
\(889\) | − | 6.21276e15i | − | 0.0125856i | ||||||
\(890\) | 4.66153e15 | 0.00937969 | ||||||||
\(891\) | 8.05911e17i | 1.61072i | ||||||||
\(892\) | 6.91605e17 | 1.37300 | ||||||||
\(893\) | 4.77469e17i | 0.941536i | ||||||||
\(894\) | 6.44383e16i | 0.126217i | ||||||||
\(895\) | 9.26947e17i | 1.80350i | ||||||||
\(896\) | − | 2.36108e16i | − | 0.0456313i | ||||||
\(897\) | 7.80933e17 | − | 1.55598e17i | 1.49920 | − | 0.298709i | ||||
\(898\) | 2.95128e17 | 0.562797 | ||||||||
\(899\) | 1.95184e17 | 0.369730 | ||||||||
\(900\) | 5.32352e14 | 0.00100171 | ||||||||
\(901\) | 8.13044e17 | 1.51973 | ||||||||
\(902\) | 1.42362e17i | 0.264336i | ||||||||
\(903\) | 4.25788e16 | 0.0785357 | ||||||||
\(904\) | − | 1.84668e17i | − | 0.338361i | ||||||
\(905\) | 5.44960e17 | 0.991912 | ||||||||
\(906\) | −2.42927e17 | −0.439245 | ||||||||
\(907\) | 9.39102e17i | 1.68682i | 0.537270 | + | 0.843410i | \(0.319456\pi\) | ||||
−0.537270 | + | 0.843410i | \(0.680544\pi\) | |||||||
\(908\) | − | 4.64752e17i | − | 0.829289i | ||||||
\(909\) | 6.44657e14 | 0.00114273 | ||||||||
\(910\) | 1.63207e16 | 0.0287402 | ||||||||
\(911\) | − | 1.05184e18i | − | 1.84009i | −0.391811 | − | 0.920046i | \(-0.628151\pi\) | ||
0.391811 | − | 0.920046i | \(-0.371849\pi\) | |||||||
\(912\) | 4.52541e17i | 0.786482i | ||||||||
\(913\) | −5.96681e17 | −1.03019 | ||||||||
\(914\) | 1.86818e17i | 0.320437i | ||||||||
\(915\) | −1.33271e17 | −0.227096 | ||||||||
\(916\) | 4.67988e17i | 0.792250i | ||||||||
\(917\) | − | 4.33144e16i | − | 0.0728477i | ||||||
\(918\) | 1.83282e17i | 0.306242i | ||||||||
\(919\) | − | 3.36581e16i | − | 0.0558723i | −0.999610 | − | 0.0279361i | \(-0.991106\pi\) | ||
0.999610 | − | 0.0279361i | \(-0.00889350\pi\) | |||||||
\(920\) | 9.02404e16 | + | 4.52910e17i | 0.148824 | + | 0.746938i | ||||
\(921\) | −2.72910e17 | −0.447159 | ||||||||
\(922\) | 7.98620e16 | 0.130003 | ||||||||
\(923\) | 2.02501e17 | 0.327504 | ||||||||
\(924\) | −4.20958e16 | −0.0676405 | ||||||||
\(925\) | − | 5.71663e17i | − | 0.912620i | ||||||
\(926\) | 1.02778e17 | 0.163017 | ||||||||
\(927\) | − | 1.67743e15i | − | 0.00264342i | ||||||
\(928\) | −1.86512e17 | −0.292024 | ||||||||
\(929\) | −8.45250e17 | −1.31489 | −0.657447 | − | 0.753501i | \(-0.728364\pi\) | ||||
−0.657447 | + | 0.753501i | \(0.728364\pi\) | |||||||
\(930\) | − | 2.74724e17i | − | 0.424618i | ||||||
\(931\) | 7.28084e17i | 1.11811i | ||||||||
\(932\) | −5.51613e17 | −0.841665 | ||||||||
\(933\) | 5.71534e17 | 0.866467 | ||||||||
\(934\) | 7.97746e16i | 0.120167i | ||||||||
\(935\) | − | 1.28153e18i | − | 1.91804i | ||||||
\(936\) | 1.24161e15 | 0.00184642 | ||||||||
\(937\) | − | 9.46842e17i | − | 1.39907i | −0.714598 | − | 0.699536i | \(-0.753390\pi\) | ||
0.714598 | − | 0.699536i | \(-0.246610\pi\) | |||||||
\(938\) | −1.19736e16 | −0.0175796 | ||||||||
\(939\) | 2.68742e17i | 0.392050i | ||||||||
\(940\) | − | 6.49882e17i | − | 0.942036i | ||||||
\(941\) | 3.16182e17i | 0.455406i | 0.973731 | + | 0.227703i | \(0.0731216\pi\) | ||||
−0.973731 | + | 0.227703i | \(0.926878\pi\) | |||||||
\(942\) | − | 9.02997e15i | − | 0.0129235i | ||||||
\(943\) | 3.53067e17 | − | 7.03470e16i | 0.502096 | − | 0.100040i | ||||
\(944\) | −2.33904e17 | −0.330526 | ||||||||
\(945\) | 4.16881e16 | 0.0585357 | ||||||||
\(946\) | −6.19440e17 | −0.864276 | ||||||||
\(947\) | −2.66774e17 | −0.369865 | −0.184933 | − | 0.982751i | \(-0.559207\pi\) | ||||
−0.184933 | + | 0.982751i | \(0.559207\pi\) | |||||||
\(948\) | 4.17555e17i | 0.575259i | ||||||||
\(949\) | −2.95256e17 | −0.404205 | ||||||||
\(950\) | − | 1.48902e17i | − | 0.202562i | ||||||
\(951\) | −3.09551e17 | −0.418455 | ||||||||
\(952\) | −2.02885e16 | −0.0272538 | ||||||||
\(953\) | − | 1.03336e17i | − | 0.137941i | −0.997619 | − | 0.0689705i | \(-0.978029\pi\) | ||
0.997619 | − | 0.0689705i | \(-0.0219714\pi\) | |||||||
\(954\) | 7.65119e14i | 0.00101494i | ||||||||
\(955\) | −5.32776e17 | −0.702303 | ||||||||
\(956\) | −9.51696e17 | −1.24667 | ||||||||
\(957\) | 4.32602e17i | 0.563141i | ||||||||
\(958\) | 2.31293e17i | 0.299205i | ||||||||
\(959\) | 1.57156e16 | 0.0202031 | ||||||||
\(960\) | − | 4.24284e17i | − | 0.542037i | ||||||
\(961\) | 9.14823e16 | 0.116144 | ||||||||
\(962\) | − | 6.30392e17i | − | 0.795354i | ||||||
\(963\) | − | 2.53340e15i | − | 0.00317648i | ||||||
\(964\) | 3.43807e17i | 0.428403i | ||||||||
\(965\) | 3.78042e17i | 0.468140i | ||||||||
\(966\) | −2.39267e15 | − | 1.20086e16i | −0.00294455 | − | 0.0147785i | ||||
\(967\) | −1.21116e18 | −1.48130 | −0.740651 | − | 0.671890i | \(-0.765483\pi\) | ||||
−0.740651 | + | 0.671890i | \(0.765483\pi\) | |||||||
\(968\) | 7.94040e17 | 0.965140 | ||||||||
\(969\) | 8.86247e17 | 1.07056 | ||||||||
\(970\) | −4.42073e17 | −0.530718 | ||||||||
\(971\) | 1.05891e18i | 1.26340i | 0.775211 | + | 0.631702i | \(0.217643\pi\) | ||||
−0.775211 | + | 0.631702i | \(0.782357\pi\) | |||||||
\(972\) | 3.00196e15 | 0.00355965 | ||||||||
\(973\) | − | 3.51451e15i | − | 0.00414179i | ||||||
\(974\) | 1.02706e17 | 0.120294 | ||||||||
\(975\) | 7.39105e17 | 0.860356 | ||||||||
\(976\) | 1.09988e17i | 0.127247i | ||||||||
\(977\) | 4.62067e16i | 0.0531298i | 0.999647 | + | 0.0265649i | \(0.00845686\pi\) | ||||
−0.999647 | + | 0.0265649i | \(0.991543\pi\) | |||||||
\(978\) | −9.34558e16 | −0.106801 | ||||||||
\(979\) | −3.30627e16 | −0.0375528 | ||||||||
\(980\) | − | 9.90993e17i | − | 1.11870i | ||||||
\(981\) | 2.26495e15i | 0.00254124i | ||||||||
\(982\) | 7.41130e16 | 0.0826467 | ||||||||
\(983\) | − | 5.45708e17i | − | 0.604838i | −0.953175 | − | 0.302419i | \(-0.902206\pi\) | ||
0.953175 | − | 0.302419i | \(-0.0977942\pi\) | |||||||
\(984\) | 2.83417e17 | 0.312216 | ||||||||
\(985\) | − | 9.96299e17i | − | 1.09087i | ||||||
\(986\) | 9.85788e16i | 0.107281i | ||||||||
\(987\) | 3.64444e16i | 0.0394210i | ||||||||
\(988\) | 1.42751e18i | 1.53474i | ||||||||
\(989\) | 3.06091e17 | + | 1.53625e18i | 0.327094 | + | 1.64166i | ||||
\(990\) | 1.20599e15 | 0.00128095 | ||||||||
\(991\) | 1.71753e18 | 1.81327 | 0.906637 | − | 0.421911i | \(-0.138641\pi\) | ||||
0.906637 | + | 0.421911i | \(0.138641\pi\) | |||||||
\(992\) | −8.40087e17 | −0.881564 | ||||||||
\(993\) | −6.27367e17 | −0.654374 | ||||||||
\(994\) | − | 3.11391e15i | − | 0.00322840i | ||||||
\(995\) | −6.54748e17 | −0.674739 | ||||||||
\(996\) | 5.61640e17i | 0.575310i | ||||||||
\(997\) | 1.31549e18 | 1.33942 | 0.669712 | − | 0.742621i | \(-0.266418\pi\) | ||||
0.669712 | + | 0.742621i | \(0.266418\pi\) | |||||||
\(998\) | −2.54578e17 | −0.257654 | ||||||||
\(999\) | − | 1.61022e18i | − | 1.61991i |
(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 | 23.13.b.c.22.12 | yes | 20 | |
23.22 | odd | 2 | inner | 23.13.b.c.22.11 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.13.b.c.22.11 | ✓ | 20 | 23.22 | odd | 2 | inner | |
23.13.b.c.22.12 | yes | 20 | 1.1 | even | 1 | trivial |