Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(37,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.d (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: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 206x^{10} + 24336x^{8} - 1510912x^{6} + 398721024x^{4} - 55297703936x^{2} + 4398046511104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{6}\cdot 5^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(10.2927 + 4.69692i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.37 |
Dual form | 72.8.d.c.37.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.2927 | + | 4.69692i | −0.909752 | + | 0.415153i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 83.8779 | − | 96.6877i | 0.655296 | − | 0.755372i | ||||
\(5\) | 316.260i | 1.13149i | 0.824581 | + | 0.565744i | \(0.191411\pi\) | ||||
−0.824581 | + | 0.565744i | \(0.808589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1193.16 | 1.31479 | 0.657393 | − | 0.753548i | \(-0.271659\pi\) | ||||
0.657393 | + | 0.753548i | \(0.271659\pi\) | |||||||
\(8\) | −409.193 | + | 1389.14i | −0.282561 | + | 0.959249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1485.45 | − | 3255.16i | −0.469740 | − | 1.02937i | ||||
\(11\) | − | 2202.76i | − | 0.498992i | −0.968376 | − | 0.249496i | \(-0.919735\pi\) | ||
0.968376 | − | 0.249496i | \(-0.0802650\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2138.97i | 0.270024i | 0.990844 | + | 0.135012i | \(0.0431073\pi\) | ||||
−0.990844 | + | 0.135012i | \(0.956893\pi\) | |||||||
\(14\) | −12280.8 | + | 5604.17i | −1.19613 | + | 0.545838i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2313.01 | − | 16219.9i | −0.141175 | − | 0.989985i | ||||
\(17\) | 29183.7 | 1.44068 | 0.720342 | − | 0.693619i | \(-0.243985\pi\) | ||||
0.720342 | + | 0.693619i | \(0.243985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 44710.6i | − | 1.49545i | −0.664006 | − | 0.747727i | \(-0.731145\pi\) | ||
0.664006 | − | 0.747727i | \(-0.268855\pi\) | |||||||
\(20\) | 30578.5 | + | 26527.2i | 0.854694 | + | 0.741459i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10346.2 | + | 22672.3i | 0.207158 | + | 0.453959i | ||||
\(23\) | −30861.6 | −0.528897 | −0.264448 | − | 0.964400i | \(-0.585190\pi\) | ||||
−0.264448 | + | 0.964400i | \(0.585190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21895.6 | −0.280263 | ||||||||
\(26\) | −10046.6 | − | 22015.7i | −0.112101 | − | 0.245655i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 100080. | − | 115364.i | 0.861574 | − | 0.993153i | ||||
\(29\) | 189611.i | 1.44368i | 0.692060 | + | 0.721840i | \(0.256703\pi\) | ||||
−0.692060 | + | 0.721840i | \(0.743297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 133272. | 0.803473 | 0.401737 | − | 0.915755i | \(-0.368407\pi\) | ||||
0.401737 | + | 0.915755i | \(0.368407\pi\) | |||||||
\(32\) | 99990.6 | + | 156082.i | 0.539429 | + | 0.842031i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −300378. | + | 137073.i | −1.31067 | + | 0.598105i | ||||
\(35\) | 377349.i | 1.48766i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 557840.i | 1.81052i | 0.424855 | + | 0.905261i | \(0.360325\pi\) | ||||
−0.424855 | + | 0.905261i | \(0.639675\pi\) | |||||||
\(38\) | 210002. | + | 460192.i | 0.620843 | + | 1.36049i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −439330. | − | 129411.i | −1.08538 | − | 0.319715i | ||||
\(41\) | −185292. | −0.419868 | −0.209934 | − | 0.977716i | \(-0.567325\pi\) | ||||
−0.209934 | + | 0.977716i | \(0.567325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 372296.i | 0.714084i | 0.934088 | + | 0.357042i | \(0.116215\pi\) | ||||
−0.934088 | + | 0.357042i | \(0.883785\pi\) | |||||||
\(44\) | −212980. | − | 184763.i | −0.376925 | − | 0.326988i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 317648. | − | 144954.i | 0.481165 | − | 0.219573i | ||||
\(47\) | 1.00993e6 | 1.41889 | 0.709444 | − | 0.704762i | \(-0.248946\pi\) | ||||
0.709444 | + | 0.704762i | \(0.248946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 600086. | 0.728664 | ||||||||
\(50\) | 225364. | − | 102842.i | 0.254970 | − | 0.116352i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 206812. | + | 179412.i | 0.203969 | + | 0.176945i | ||||
\(53\) | − | 245619.i | − | 0.226619i | −0.993560 | − | 0.113309i | \(-0.963855\pi\) | ||
0.993560 | − | 0.113309i | \(-0.0361452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 696647. | 0.564603 | ||||||||
\(56\) | −488232. | + | 1.65747e6i | −0.371508 | + | 1.26121i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −890589. | − | 1.95160e6i | −0.599348 | − | 1.31339i | ||||
\(59\) | 81380.0i | 0.0515864i | 0.999667 | + | 0.0257932i | \(0.00821115\pi\) | ||||
−0.999667 | + | 0.0257932i | \(0.991789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 775123.i | − | 0.437236i | −0.975810 | − | 0.218618i | \(-0.929845\pi\) | ||
0.975810 | − | 0.218618i | \(-0.0701549\pi\) | |||||||
\(62\) | −1.37172e6 | + | 625966.i | −0.730961 | + | 0.333564i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.76227e6 | − | 1.13685e6i | −0.840318 | − | 0.542093i | ||||
\(65\) | −676470. | −0.305528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.37188e6i | 1.77585i | 0.459986 | + | 0.887926i | \(0.347854\pi\) | ||||
−0.459986 | + | 0.887926i | \(0.652146\pi\) | |||||||
\(68\) | 2.44787e6 | − | 2.82170e6i | 0.944075 | − | 1.08825i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.77238e6 | − | 3.88392e6i | −0.617608 | − | 1.35340i | ||||
\(71\) | −2.32062e6 | −0.769484 | −0.384742 | − | 0.923024i | \(-0.625710\pi\) | ||||
−0.384742 | + | 0.923024i | \(0.625710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.44398e6 | 1.63790 | 0.818949 | − | 0.573866i | \(-0.194557\pi\) | ||||
0.818949 | + | 0.573866i | \(0.194557\pi\) | |||||||
\(74\) | −2.62013e6 | − | 5.74166e6i | −0.751644 | − | 1.64713i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.32297e6 | − | 3.75023e6i | −1.12962 | − | 0.979965i | ||||
\(77\) | − | 2.62825e6i | − | 0.656068i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.51878e6 | 0.802966 | 0.401483 | − | 0.915866i | \(-0.368495\pi\) | ||||
0.401483 | + | 0.915866i | \(0.368495\pi\) | |||||||
\(80\) | 5.12971e6 | − | 731512.i | 1.12015 | − | 0.159737i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.90715e6 | − | 870301.i | 0.381976 | − | 0.174309i | ||||
\(83\) | − | 4.53923e6i | − | 0.871383i | −0.900096 | − | 0.435691i | \(-0.856504\pi\) | ||
0.900096 | − | 0.435691i | \(-0.143496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.22964e6i | 1.63012i | ||||||||
\(86\) | −1.74865e6 | − | 3.83192e6i | −0.296454 | − | 0.649639i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.05995e6 | + | 901355.i | 0.478658 | + | 0.140996i | ||||
\(89\) | −7.05346e6 | −1.06056 | −0.530282 | − | 0.847821i | \(-0.677914\pi\) | ||||
−0.530282 | + | 0.847821i | \(0.677914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.55213e6i | 0.355024i | ||||||||
\(92\) | −2.58860e6 | + | 2.98394e6i | −0.346584 | + | 0.399514i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.03949e7 | + | 4.74355e6i | −1.29084 | + | 0.589056i | ||||
\(95\) | 1.41402e7 | 1.69209 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.75365e6 | −0.640092 | −0.320046 | − | 0.947402i | \(-0.603698\pi\) | ||||
−0.320046 | + | 0.947402i | \(0.603698\pi\) | |||||||
\(98\) | −6.17648e6 | + | 2.81856e6i | −0.662903 | + | 0.302507i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.83655e6 | + | 2.11703e6i | −0.183655 | + | 0.211703i | ||||
\(101\) | − | 1.38615e7i | − | 1.33871i | −0.742944 | − | 0.669354i | \(-0.766571\pi\) | ||
0.742944 | − | 0.669354i | \(-0.233429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.40590e6 | 0.667802 | 0.333901 | − | 0.942608i | \(-0.391635\pi\) | ||||
0.333901 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(104\) | −2.97133e6 | − | 875249.i | −0.259020 | − | 0.0762983i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.15365e6 | + | 2.52807e6i | 0.0940816 | + | 0.206167i | ||||
\(107\) | 1.83880e7i | 1.45108i | 0.688181 | + | 0.725539i | \(0.258409\pi\) | ||||
−0.688181 | + | 0.725539i | \(0.741591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.30010e7i | 0.961576i | 0.876837 | + | 0.480788i | \(0.159649\pi\) | ||||
−0.876837 | + | 0.480788i | \(0.840351\pi\) | |||||||
\(110\) | −7.17035e6 | + | 3.27210e6i | −0.513649 | + | 0.234397i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.75978e6 | − | 1.93529e7i | −0.185615 | − | 1.30162i | ||||
\(113\) | −2.57409e7 | −1.67822 | −0.839112 | − | 0.543959i | \(-0.816925\pi\) | ||||
−0.839112 | + | 0.543959i | \(0.816925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.76030e6i | − | 0.598440i | ||||||
\(116\) | 1.83331e7 | + | 1.59042e7i | 1.09052 | + | 0.946037i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −382235. | − | 837617.i | −0.0214163 | − | 0.0469308i | ||||
\(119\) | 3.48208e7 | 1.89419 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.46350e7 | 0.751007 | ||||||||
\(122\) | 3.64069e6 | + | 7.97808e6i | 0.181520 | + | 0.397776i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.11785e7 | − | 1.28857e7i | 0.526513 | − | 0.606921i | ||||
\(125\) | 1.77831e7i | 0.814373i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.01595e7 | −0.440109 | −0.220054 | − | 0.975488i | \(-0.570623\pi\) | ||||
−0.220054 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(128\) | 2.34782e7 | + | 3.42397e6i | 0.989533 | + | 0.144310i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.96268e6 | − | 3.17733e6i | 0.277955 | − | 0.126841i | ||||
\(131\) | 2.50477e7i | 0.973462i | 0.873552 | + | 0.486731i | \(0.161811\pi\) | ||||
−0.873552 | + | 0.486731i | \(0.838189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.33469e7i | − | 1.96620i | ||||||
\(134\) | −2.05344e7 | − | 4.49983e7i | −0.737251 | − | 1.61558i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.19417e7 | + | 4.05403e7i | −0.407082 | + | 1.38198i | ||||
\(137\) | −2.23725e7 | −0.743348 | −0.371674 | − | 0.928363i | \(-0.621216\pi\) | ||||
−0.371674 | + | 0.928363i | \(0.621216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.36116e7i | − | 0.429889i | −0.976626 | − | 0.214944i | \(-0.931043\pi\) | ||
0.976626 | − | 0.214944i | \(-0.0689570\pi\) | |||||||
\(140\) | 3.64850e7 | + | 3.16512e7i | 1.12374 | + | 0.974860i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.38854e7 | − | 1.08998e7i | 0.700040 | − | 0.319454i | ||||
\(143\) | 4.71164e6 | 0.134740 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.99665e7 | −1.63351 | ||||||||
\(146\) | −5.60331e7 | + | 2.55700e7i | −1.49008 | + | 0.679978i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.39363e7 | + | 4.67905e7i | 1.36762 | + | 1.18643i | ||||
\(149\) | − | 1.07544e7i | − | 0.266339i | −0.991093 | − | 0.133169i | \(-0.957485\pi\) | ||
0.991093 | − | 0.133169i | \(-0.0425154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.91328e7 | −1.16132 | −0.580660 | − | 0.814146i | \(-0.697205\pi\) | ||||
−0.580660 | + | 0.814146i | \(0.697205\pi\) | |||||||
\(152\) | 6.21094e7 | + | 1.82953e7i | 1.43451 | + | 0.422558i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.23447e7 | + | 2.70517e7i | 0.272369 | + | 0.596859i | ||||
\(155\) | 4.21485e7i | 0.909120i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.83533e7i | − | 0.584729i | −0.956307 | − | 0.292365i | \(-0.905558\pi\) | ||
0.956307 | − | 0.292365i | \(-0.0944421\pi\) | |||||||
\(158\) | −3.62176e7 | + | 1.65274e7i | −0.730500 | + | 0.333354i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.93626e7 | + | 3.16231e7i | −0.952747 | + | 0.610357i | ||||
\(161\) | −3.68228e7 | −0.695386 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.43798e7i | 0.260073i | 0.991509 | + | 0.130037i | \(0.0415095\pi\) | ||||
−0.991509 | + | 0.130037i | \(0.958490\pi\) | |||||||
\(164\) | −1.55419e7 | + | 1.79154e7i | −0.275138 | + | 0.317157i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.13204e7 | + | 4.67208e7i | 0.361757 | + | 0.792742i | ||||
\(167\) | 1.16629e8 | 1.93775 | 0.968876 | − | 0.247547i | \(-0.0796245\pi\) | ||||
0.968876 | + | 0.247547i | \(0.0796245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.81733e7 | 0.927087 | ||||||||
\(170\) | −4.33509e7 | − | 9.49976e7i | −0.676748 | − | 1.48300i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.59965e7 | + | 3.12274e7i | 0.539399 | + | 0.467936i | ||||
\(173\) | − | 1.20656e8i | − | 1.77169i | −0.463985 | − | 0.885843i | \(-0.653581\pi\) | ||
0.463985 | − | 0.885843i | \(-0.346419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.61249e7 | −0.368486 | ||||||||
\(176\) | −3.57286e7 | + | 5.09501e6i | −0.493995 | + | 0.0704450i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.25989e7 | − | 3.31295e7i | 0.964851 | − | 0.440297i | ||||
\(179\) | − | 1.08890e8i | − | 1.41907i | −0.704670 | − | 0.709535i | \(-0.748905\pi\) | ||
0.704670 | − | 0.709535i | \(-0.251095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.29863e7i | 0.162784i | 0.996682 | + | 0.0813918i | \(0.0259365\pi\) | ||||
−0.996682 | + | 0.0813918i | \(0.974063\pi\) | |||||||
\(182\) | −1.19871e7 | − | 2.62682e7i | −0.147389 | − | 0.322983i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.26283e7 | − | 4.28711e7i | 0.149446 | − | 0.507344i | ||||
\(185\) | −1.76423e8 | −2.04858 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.42848e7i | − | 0.718890i | ||||||
\(188\) | 8.47106e7 | − | 9.76476e7i | 0.929791 | − | 1.07179i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.45540e8 | + | 6.64154e7i | −1.53938 | + | 0.702475i | ||||
\(191\) | 9.02408e7 | 0.937101 | 0.468550 | − | 0.883437i | \(-0.344776\pi\) | ||||
0.468550 | + | 0.883437i | \(0.344776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84834e8 | −1.85068 | −0.925340 | − | 0.379138i | \(-0.876221\pi\) | ||||
−0.925340 | + | 0.379138i | \(0.876221\pi\) | |||||||
\(194\) | 5.92204e7 | − | 2.70244e7i | 0.582325 | − | 0.265736i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.03339e7 | − | 5.80209e7i | 0.477490 | − | 0.550412i | ||||
\(197\) | − | 5.92205e7i | − | 0.551874i | −0.961176 | − | 0.275937i | \(-0.911012\pi\) | ||
0.961176 | − | 0.275937i | \(-0.0889881\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.52395e7 | 0.316988 | 0.158494 | − | 0.987360i | \(-0.449336\pi\) | ||||
0.158494 | + | 0.987360i | \(0.449336\pi\) | |||||||
\(200\) | 8.95950e6 | − | 3.04160e7i | 0.0791915 | − | 0.268842i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.51064e7 | + | 1.42672e8i | 0.555769 | + | 1.21789i | ||||
\(203\) | 2.26236e8i | 1.89813i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 5.86004e7i | − | 0.475075i | ||||||
\(206\) | −7.62265e7 | + | 3.47849e7i | −0.607534 | + | 0.277240i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46938e7 | − | 4.94744e6i | 0.267319 | − | 0.0381205i | ||||
\(209\) | −9.84870e7 | −0.746220 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.14798e8i | − | 1.57413i | −0.616869 | − | 0.787066i | \(-0.711599\pi\) | ||
0.616869 | − | 0.787066i | \(-0.288401\pi\) | |||||||
\(212\) | −2.37483e7 | − | 2.06020e7i | −0.171182 | − | 0.148502i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.63669e7 | − | 1.89261e8i | −0.602419 | − | 1.32012i | ||||
\(215\) | −1.17743e8 | −0.807977 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.59014e8 | 1.05640 | ||||||||
\(218\) | −6.10646e7 | − | 1.33815e8i | −0.399201 | − | 0.874795i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.84333e7 | − | 6.73572e7i | 0.369982 | − | 0.426486i | ||||
\(221\) | 6.24229e7i | 0.389019i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.82914e7 | 0.472767 | 0.236383 | − | 0.971660i | \(-0.424038\pi\) | ||||
0.236383 | + | 0.971660i | \(0.424038\pi\) | |||||||
\(224\) | 1.19305e8 | + | 1.86231e8i | 0.709234 | + | 1.10709i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.64943e8 | − | 1.20903e8i | 1.52677 | − | 0.696720i | ||||
\(227\) | − | 2.67847e8i | − | 1.51983i | −0.650021 | − | 0.759917i | \(-0.725240\pi\) | ||
0.650021 | − | 0.759917i | \(-0.274760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.73358e8i | 1.50421i | 0.659045 | + | 0.752104i | \(0.270961\pi\) | ||||
−0.659045 | + | 0.752104i | \(0.729039\pi\) | |||||||
\(230\) | 4.58433e7 | + | 1.00459e8i | 0.248444 | + | 0.544432i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.63397e8 | − | 7.75875e7i | −1.38485 | − | 0.407928i | ||||
\(233\) | 3.26079e8 | 1.68879 | 0.844397 | − | 0.535718i | \(-0.179959\pi\) | ||||
0.844397 | + | 0.535718i | \(0.179959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.19400e8i | 1.60545i | ||||||||
\(236\) | 7.86844e6 | + | 6.82598e6i | 0.0389670 | + | 0.0338044i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.58399e8 | + | 1.63550e8i | −1.72325 | + | 0.786380i | ||||
\(239\) | 8.21057e7 | 0.389028 | 0.194514 | − | 0.980900i | \(-0.437687\pi\) | ||||
0.194514 | + | 0.980900i | \(0.437687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.42032e8 | 0.653622 | 0.326811 | − | 0.945090i | \(-0.394026\pi\) | ||||
0.326811 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(242\) | −1.50633e8 | + | 6.87394e7i | −0.683230 | + | 0.311783i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.49448e7 | − | 6.50157e7i | −0.330276 | − | 0.286519i | ||||
\(245\) | 1.89783e8i | 0.824473i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.56345e7 | 0.403808 | ||||||||
\(248\) | −5.45337e7 | + | 1.85133e8i | −0.227030 | + | 0.770731i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.35260e7 | − | 1.83036e8i | −0.338089 | − | 0.740877i | ||||
\(251\) | 2.23144e8i | 0.890690i | 0.895359 | + | 0.445345i | \(0.146919\pi\) | ||||
−0.895359 | + | 0.445345i | \(0.853081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.79808e7i | 0.263915i | ||||||||
\(254\) | 1.04568e8 | − | 4.77184e7i | 0.400390 | − | 0.182712i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.57735e8 | + | 7.50335e7i | −0.960139 | + | 0.279521i | ||||
\(257\) | 2.58377e8 | 0.949484 | 0.474742 | − | 0.880125i | \(-0.342541\pi\) | ||||
0.474742 | + | 0.880125i | \(0.342541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.65592e8i | 2.38045i | ||||||||
\(260\) | −5.67409e7 | + | 6.54063e7i | −0.200212 | + | 0.230788i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.17647e8 | − | 2.57808e8i | −0.404136 | − | 0.885608i | ||||
\(263\) | −2.71648e8 | −0.920793 | −0.460396 | − | 0.887714i | \(-0.652293\pi\) | ||||
−0.460396 | + | 0.887714i | \(0.652293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.76795e7 | 0.256416 | ||||||||
\(266\) | 2.50566e8 | + | 5.49082e8i | 0.816275 | + | 1.78876i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.22707e8 | + | 3.66704e8i | 1.34143 | + | 1.16371i | ||||
\(269\) | 1.66488e8i | 0.521494i | 0.965407 | + | 0.260747i | \(0.0839689\pi\) | ||||
−0.965407 | + | 0.260747i | \(0.916031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.36637e7 | 0.133269 | 0.0666344 | − | 0.997777i | \(-0.478774\pi\) | ||||
0.0666344 | + | 0.997777i | \(0.478774\pi\) | |||||||
\(272\) | −6.75020e7 | − | 4.73357e8i | −0.203388 | − | 1.42626i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.30272e8 | − | 1.05082e8i | 0.676262 | − | 0.308603i | ||||
\(275\) | 4.82308e7i | 0.139849i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.76808e8i | − | 0.782528i | −0.920278 | − | 0.391264i | \(-0.872038\pi\) | ||
0.920278 | − | 0.391264i | \(-0.127962\pi\) | |||||||
\(278\) | 6.39324e7 | + | 1.40099e8i | 0.178470 | + | 0.391092i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.24191e8 | − | 1.54408e8i | −1.42704 | − | 0.420356i | ||||
\(281\) | −1.48932e8 | −0.400421 | −0.200211 | − | 0.979753i | \(-0.564163\pi\) | ||||
−0.200211 | + | 0.979753i | \(0.564163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.28883e8i | − | 0.600290i | −0.953894 | − | 0.300145i | \(-0.902965\pi\) | ||
0.953894 | − | 0.300145i | \(-0.0970351\pi\) | |||||||
\(284\) | −1.94649e8 | + | 2.24375e8i | −0.504240 | + | 0.581247i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.84953e7 | + | 2.21302e7i | −0.122580 | + | 0.0559376i | ||||
\(287\) | −2.21083e8 | −0.552037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.41349e8 | 1.07557 | ||||||||
\(290\) | 6.17215e8 | − | 2.81658e8i | 1.48608 | − | 0.678155i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.56630e8 | − | 5.26366e8i | 1.07331 | − | 1.23722i | ||||
\(293\) | 2.99647e8i | 0.695942i | 0.937505 | + | 0.347971i | \(0.113129\pi\) | ||||
−0.937505 | + | 0.347971i | \(0.886871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.57373e7 | −0.0583694 | ||||||||
\(296\) | −7.74919e8 | − | 2.28264e8i | −1.73674 | − | 0.511584i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.05126e7 | + | 1.10691e8i | 0.110571 | + | 0.242302i | ||||
\(299\) | − | 6.60119e7i | − | 0.142815i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.44209e8i | 0.938868i | ||||||||
\(302\) | 5.05707e8 | − | 2.30773e8i | 1.05651 | − | 0.482125i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.25202e8 | + | 1.03416e8i | −1.48048 | + | 0.211120i | ||||
\(305\) | 2.45141e8 | 0.494727 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.47105e8i | − | 0.684662i | −0.939579 | − | 0.342331i | \(-0.888784\pi\) | ||
0.939579 | − | 0.342331i | \(-0.111216\pi\) | |||||||
\(308\) | −2.54119e8 | − | 2.20452e8i | −0.495576 | − | 0.429919i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.97968e8 | − | 4.33820e8i | −0.377424 | − | 0.827073i | ||||
\(311\) | −2.88699e8 | −0.544231 | −0.272115 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272115 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.29567e8 | −0.976149 | −0.488074 | − | 0.872802i | \(-0.662300\pi\) | ||||
−0.488074 | + | 0.872802i | \(0.662300\pi\) | |||||||
\(314\) | 1.33173e8 | + | 2.91831e8i | 0.242752 | + | 0.531958i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.95148e8 | − | 3.40223e8i | 0.526180 | − | 0.606538i | ||||
\(317\) | − | 4.77983e8i | − | 0.842763i | −0.906884 | − | 0.421381i | \(-0.861545\pi\) | ||
0.906884 | − | 0.421381i | \(-0.138455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.17669e8 | 0.720385 | ||||||||
\(320\) | 3.59541e8 | − | 5.57338e8i | 0.613372 | − | 0.950809i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.79005e8 | − | 1.72954e8i | 0.632629 | − | 0.288692i | ||||
\(323\) | − | 1.30482e9i | − | 2.15448i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.68338e7i | − | 0.0756777i | ||||||
\(326\) | −6.75407e7 | − | 1.48006e8i | −0.107970 | − | 0.236602i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.58200e7 | − | 2.57397e8i | 0.118638 | − | 0.402758i | ||||
\(329\) | 1.20501e9 | 1.86553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.00324e8i | − | 0.455189i | −0.973756 | − | 0.227595i | \(-0.926914\pi\) | ||
0.973756 | − | 0.227595i | \(-0.0730861\pi\) | |||||||
\(332\) | −4.38888e8 | − | 3.80741e8i | −0.658218 | − | 0.571014i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.20042e9 | + | 5.47796e8i | −1.76287 | + | 0.804464i | ||||
\(335\) | −1.38265e9 | −2.00935 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.42727e8 | −0.203143 | −0.101572 | − | 0.994828i | \(-0.532387\pi\) | ||||
−0.101572 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(338\) | −5.98759e8 | + | 2.73236e8i | −0.843419 | + | 0.384883i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.92392e8 | + | 7.74163e8i | 1.23134 | + | 1.06821i | ||||
\(341\) | − | 2.93566e8i | − | 0.400927i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.66620e8 | −0.356749 | ||||||||
\(344\) | −5.17172e8 | − | 1.52341e8i | −0.684984 | − | 0.201772i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.66711e8 | + | 1.24187e9i | 0.735521 | + | 1.61179i | ||||
\(347\) | − | 3.44497e8i | − | 0.442621i | −0.975203 | − | 0.221310i | \(-0.928967\pi\) | ||
0.975203 | − | 0.221310i | \(-0.0710334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.86434e7i | − | 0.0612541i | −0.999531 | − | 0.0306271i | \(-0.990250\pi\) | ||
0.999531 | − | 0.0306271i | \(-0.00975042\pi\) | |||||||
\(350\) | 2.68895e8 | − | 1.22707e8i | 0.335231 | − | 0.152978i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.43812e8 | − | 2.20256e8i | 0.420167 | − | 0.269171i | ||||
\(353\) | 9.56323e8 | 1.15716 | 0.578580 | − | 0.815626i | \(-0.303607\pi\) | ||||
0.578580 | + | 0.815626i | \(0.303607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.33920e8i | − | 0.870662i | ||||||
\(356\) | −5.91629e8 | + | 6.81983e8i | −0.694984 | + | 0.801121i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.11449e8 | + | 1.12077e9i | 0.589131 | + | 1.29100i | ||||
\(359\) | −3.16193e8 | −0.360679 | −0.180340 | − | 0.983604i | \(-0.557720\pi\) | ||||
−0.180340 | + | 0.983604i | \(0.557720\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.10517e9 | −1.23638 | ||||||||
\(362\) | −6.09957e7 | − | 1.33664e8i | −0.0675801 | − | 0.148093i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.46759e8 | + | 2.14067e8i | 0.268175 | + | 0.232646i | ||||
\(365\) | 1.72172e9i | 1.85326i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.18396e9 | −1.25028 | −0.625138 | − | 0.780514i | \(-0.714957\pi\) | ||||
−0.625138 | + | 0.780514i | \(0.714957\pi\) | |||||||
\(368\) | 7.13830e7 | + | 5.00572e8i | 0.0746668 | + | 0.523600i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.81586e9 | − | 8.28644e8i | 1.86370 | − | 0.850475i | ||||
\(371\) | − | 2.93062e8i | − | 0.297956i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.53550e8i | − | 0.652076i | −0.945357 | − | 0.326038i | \(-0.894286\pi\) | ||
0.945357 | − | 0.326038i | \(-0.105714\pi\) | |||||||
\(374\) | 3.01941e8 | + | 6.61662e8i | 0.298450 | + | 0.654012i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.13255e8 | + | 1.40293e9i | −0.400923 | + | 1.36107i | ||||
\(377\) | −4.05572e8 | −0.389828 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.25264e8i | 0.212547i | 0.994337 | + | 0.106273i | \(0.0338919\pi\) | ||||
−0.994337 | + | 0.106273i | \(0.966108\pi\) | |||||||
\(380\) | 1.18605e9 | − | 1.36718e9i | 1.10882 | − | 1.27816i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.28819e8 | + | 4.23854e8i | −0.852529 | + | 0.389040i | ||||
\(383\) | −7.88929e8 | −0.717534 | −0.358767 | − | 0.933427i | \(-0.616803\pi\) | ||||
−0.358767 | + | 0.933427i | \(0.616803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.31211e8 | 0.742333 | ||||||||
\(386\) | 1.90243e9 | − | 8.68151e8i | 1.68366 | − | 0.768316i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.82604e8 | + | 5.56307e8i | −0.419450 | + | 0.483508i | ||||
\(389\) | − | 5.49026e8i | − | 0.472900i | −0.971644 | − | 0.236450i | \(-0.924016\pi\) | ||
0.971644 | − | 0.236450i | \(-0.0759840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00655e8 | −0.761974 | ||||||||
\(392\) | −2.45551e8 | + | 8.33604e8i | −0.205892 | + | 0.698970i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.78154e8 | + | 6.09536e8i | 0.229112 | + | 0.502068i | ||||
\(395\) | 1.11285e9i | 0.908546i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.35509e9i | − | 1.08693i | −0.839431 | − | 0.543466i | \(-0.817112\pi\) | ||
0.839431 | − | 0.543466i | \(-0.182888\pi\) | |||||||
\(398\) | −3.62708e8 | + | 1.65517e8i | −0.288381 | + | 0.131599i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.06445e7 | + | 3.55144e8i | 0.0395660 | + | 0.277456i | ||||
\(401\) | −1.38484e8 | −0.107249 | −0.0536244 | − | 0.998561i | \(-0.517077\pi\) | ||||
−0.0536244 | + | 0.998561i | \(0.517077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.85063e8i | 0.216957i | ||||||||
\(404\) | −1.34024e9 | − | 1.16267e9i | −1.01122 | − | 0.877250i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.06261e9 | − | 2.32857e9i | −0.788015 | − | 1.72683i | ||||
\(407\) | 1.22879e9 | 0.903436 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.35047e9 | −0.976010 | −0.488005 | − | 0.872841i | \(-0.662275\pi\) | ||||
−0.488005 | + | 0.872841i | \(0.662275\pi\) | |||||||
\(410\) | 2.75242e8 | + | 6.03155e8i | 0.197229 | + | 0.432200i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.21191e8 | − | 7.16059e8i | 0.437608 | − | 0.504439i | ||||
\(413\) | 9.70993e7i | 0.0678252i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.43558e9 | 0.985958 | ||||||||
\(416\) | −3.33854e8 | + | 2.13876e8i | −0.227368 | + | 0.145659i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.01369e9 | − | 4.62586e8i | 0.678875 | − | 0.309796i | ||||
\(419\) | 2.80534e9i | 1.86310i | 0.363612 | + | 0.931550i | \(0.381543\pi\) | ||||
−0.363612 | + | 0.931550i | \(0.618457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.48841e8i | − | 0.293160i | −0.989199 | − | 0.146580i | \(-0.953173\pi\) | ||
0.989199 | − | 0.146580i | \(-0.0468266\pi\) | |||||||
\(422\) | 1.00889e9 | + | 2.21084e9i | 0.653506 | + | 1.43207i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.41199e8 | + | 1.00505e8i | 0.217384 | + | 0.0640338i | ||||
\(425\) | −6.38993e8 | −0.403771 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.24845e8i | − | 0.574872i | ||||||
\(428\) | 1.77789e9 | + | 1.54234e9i | 1.09610 | + | 0.950885i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.21188e9 | − | 5.53027e8i | 0.735058 | − | 0.335434i | ||||
\(431\) | 2.67589e9 | 1.60990 | 0.804949 | − | 0.593344i | \(-0.202192\pi\) | ||||
0.804949 | + | 0.593344i | \(0.202192\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.68907e9 | 0.999860 | 0.499930 | − | 0.866066i | \(-0.333359\pi\) | ||||
0.499930 | + | 0.866066i | \(0.333359\pi\) | |||||||
\(434\) | −1.63668e9 | + | 7.46877e8i | −0.961058 | + | 0.438566i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.25703e9 | + | 1.09049e9i | 0.726348 | + | 0.630117i | ||||
\(437\) | 1.37984e9i | 0.790941i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.19152e8 | −0.518515 | −0.259258 | − | 0.965808i | \(-0.583478\pi\) | ||||
−0.259258 | + | 0.965808i | \(0.583478\pi\) | |||||||
\(440\) | −2.85063e8 | + | 9.67741e8i | −0.159535 | + | 0.541595i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.93195e8 | − | 6.42498e8i | −0.161503 | − | 0.353911i | ||||
\(443\) | − | 2.83982e9i | − | 1.55195i | −0.630764 | − | 0.775975i | \(-0.717258\pi\) | ||
0.630764 | − | 0.775975i | \(-0.282742\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.23073e9i | − | 1.20002i | ||||||
\(446\) | −8.05827e8 | + | 3.67728e8i | −0.430100 | + | 0.196271i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.10267e9 | − | 1.35645e9i | −1.10484 | − | 0.712737i | ||||
\(449\) | −1.24346e9 | −0.648291 | −0.324145 | − | 0.946007i | \(-0.605077\pi\) | ||||
−0.324145 | + | 0.946007i | \(0.605077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.08154e8i | 0.209511i | ||||||||
\(452\) | −2.15909e9 | + | 2.48883e9i | −1.09973 | + | 1.26768i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.25805e9 | + | 2.75686e9i | 0.630963 | + | 1.38267i | ||||
\(455\) | −8.07136e8 | −0.401705 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.93504e8 | −0.0948384 | −0.0474192 | − | 0.998875i | \(-0.515100\pi\) | ||||
−0.0474192 | + | 0.998875i | \(0.515100\pi\) | |||||||
\(458\) | −1.28394e9 | − | 2.81358e9i | −0.624476 | − | 1.36845i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.43700e8 | − | 8.18673e8i | −0.452045 | − | 0.392155i | ||||
\(461\) | − | 1.97565e9i | − | 0.939197i | −0.882880 | − | 0.469599i | \(-0.844399\pi\) | ||
0.882880 | − | 0.469599i | \(-0.155601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.13506e9 | −0.531478 | −0.265739 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265739 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(464\) | 3.07548e9 | − | 4.38572e8i | 1.42922 | − | 0.203811i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.35622e9 | + | 1.53157e9i | −1.53638 | + | 0.701108i | ||||
\(467\) | 2.02735e9i | 0.921127i | 0.887627 | + | 0.460564i | \(0.152353\pi\) | ||||
−0.887627 | + | 0.460564i | \(0.847647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.21635e9i | 2.33487i | ||||||||
\(470\) | −1.50020e9 | − | 3.28748e9i | −0.666509 | − | 1.46056i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.13048e8 | − | 3.33001e7i | −0.0494843 | − | 0.0145763i | ||||
\(473\) | 8.20081e8 | 0.356322 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.78964e8i | 0.419121i | ||||||||
\(476\) | 2.92069e9 | − | 3.36674e9i | 1.24126 | − | 1.43082i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.45086e8 | + | 3.85644e8i | −0.353919 | + | 0.161506i | ||||
\(479\) | 1.67866e9 | 0.697893 | 0.348947 | − | 0.937143i | \(-0.386539\pi\) | ||||
0.348947 | + | 0.937143i | \(0.386539\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.19320e9 | −0.488884 | ||||||||
\(482\) | −1.46189e9 | + | 6.67113e8i | −0.594634 | + | 0.271353i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.22755e9 | − | 1.41502e9i | 0.492132 | − | 0.567290i | ||||
\(485\) | − | 1.81965e9i | − | 0.724256i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.64775e9 | 1.43111 | 0.715556 | − | 0.698555i | \(-0.246173\pi\) | ||||
0.715556 | + | 0.698555i | \(0.246173\pi\) | |||||||
\(488\) | 1.07676e9 | + | 3.17174e8i | 0.419418 | + | 0.123546i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.91397e8 | − | 1.95338e9i | −0.342283 | − | 0.750066i | ||||
\(491\) | − | 2.01669e9i | − | 0.768870i | −0.923152 | − | 0.384435i | \(-0.874396\pi\) | ||
0.923152 | − | 0.384435i | \(-0.125604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.53355e9i | 2.07989i | ||||||||
\(494\) | −9.84334e8 | + | 4.49188e8i | −0.367365 | + | 0.167642i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.08258e8 | − | 2.16165e9i | −0.113430 | − | 0.795426i | ||||
\(497\) | −2.76887e9 | −1.01171 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.19631e9i | 0.431014i | 0.976502 | + | 0.215507i | \(0.0691404\pi\) | ||||
−0.976502 | + | 0.215507i | \(0.930860\pi\) | |||||||
\(500\) | 1.71941e9 | + | 1.49161e9i | 0.615155 | + | 0.533655i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.04809e9 | − | 2.29674e9i | −0.369773 | − | 0.810307i | ||||
\(503\) | −1.62416e9 | −0.569038 | −0.284519 | − | 0.958670i | \(-0.591834\pi\) | ||||
−0.284519 | + | 0.958670i | \(0.591834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.38385e9 | 1.51473 | ||||||||
\(506\) | −3.19301e8 | − | 6.99704e8i | −0.109565 | − | 0.240097i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.52159e8 | + | 9.82300e8i | −0.288401 | + | 0.332446i | ||||
\(509\) | − | 2.38008e9i | − | 0.799981i | −0.916519 | − | 0.399990i | \(-0.869013\pi\) | ||
0.916519 | − | 0.399990i | \(-0.130987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.49554e9 | 2.15349 | ||||||||
\(512\) | 2.30036e9 | − | 1.98286e9i | 0.757444 | − | 0.652900i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.65939e9 | + | 1.21358e9i | −0.863795 | + | 0.394181i | ||||
\(515\) | 2.34219e9i | 0.755609i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.22463e9i | − | 0.708014i | ||||||
\(518\) | −3.12623e9 | − | 6.85072e9i | −0.988251 | − | 2.16562i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.76806e8 | − | 9.39712e8i | 0.0863305 | − | 0.293078i | ||||
\(521\) | −5.54589e9 | −1.71806 | −0.859032 | − | 0.511922i | \(-0.828934\pi\) | ||||
−0.859032 | + | 0.511922i | \(0.828934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.10271e9i | 0.948386i | 0.880421 | + | 0.474193i | \(0.157260\pi\) | ||||
−0.880421 | + | 0.474193i | \(0.842740\pi\) | |||||||
\(524\) | 2.42181e9 | + | 2.10095e9i | 0.735326 | + | 0.637905i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.79598e9 | − | 1.27591e9i | 0.837692 | − | 0.382270i | ||||
\(527\) | 3.88935e9 | 1.15755 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.45239e9 | −0.720268 | ||||||||
\(530\) | −7.99529e8 | + | 3.64854e8i | −0.233275 | + | 0.106452i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.15799e9 | − | 4.47462e9i | −1.48522 | − | 1.28845i | ||||
\(533\) | − | 3.96333e8i | − | 0.113374i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.81539e9 | −1.64188 | ||||||||
\(536\) | −6.07317e9 | − | 1.78894e9i | −1.70349 | − | 0.501787i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.81980e8 | − | 1.71360e9i | −0.216500 | − | 0.474430i | ||||
\(539\) | − | 1.32185e9i | − | 0.363597i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.26721e9i | 0.887128i | 0.896243 | + | 0.443564i | \(0.146286\pi\) | ||||
−0.896243 | + | 0.443564i | \(0.853714\pi\) | |||||||
\(542\) | −4.49416e8 | + | 2.05085e8i | −0.121241 | + | 0.0553269i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.91809e9 | + | 4.55505e9i | 0.777147 | + | 1.21310i | ||||
\(545\) | −4.11169e9 | −1.08801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.58100e9i | − | 1.19675i | −0.801214 | − | 0.598377i | \(-0.795812\pi\) | ||
0.801214 | − | 0.598377i | \(-0.204188\pi\) | |||||||
\(548\) | −1.87656e9 | + | 2.16314e9i | −0.487113 | + | 0.561504i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.26536e8 | − | 4.96423e8i | −0.0580588 | − | 0.127228i | ||||
\(551\) | 8.47763e9 | 2.15896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.19846e9 | 1.05573 | ||||||||
\(554\) | 1.30015e9 | + | 2.84910e9i | 0.324869 | + | 0.711906i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.31607e9 | − | 1.14171e9i | −0.324726 | − | 0.281704i | ||||
\(557\) | − | 1.65111e9i | − | 0.404838i | −0.979299 | − | 0.202419i | \(-0.935120\pi\) | ||
0.979299 | − | 0.202419i | \(-0.0648804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.96329e8 | −0.192820 | ||||||||
\(560\) | 6.12056e9 | − | 8.72810e8i | 1.47276 | − | 0.210020i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.53291e9 | − | 6.99524e8i | 0.364284 | − | 0.166236i | ||||
\(563\) | 2.19386e9i | 0.518118i | 0.965861 | + | 0.259059i | \(0.0834125\pi\) | ||||
−0.965861 | + | 0.259059i | \(0.916588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.14084e9i | − | 1.89889i | ||||||
\(566\) | 1.07505e9 | + | 2.35582e9i | 0.249212 | + | 0.546115i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.49580e8 | − | 3.22367e9i | 0.217426 | − | 0.738127i | ||||
\(569\) | −1.95566e9 | −0.445041 | −0.222520 | − | 0.974928i | \(-0.571428\pi\) | ||||
−0.222520 | + | 0.974928i | \(0.571428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.49759e9i | 0.336640i | 0.985732 | + | 0.168320i | \(0.0538342\pi\) | ||||
−0.985732 | + | 0.168320i | \(0.946166\pi\) | |||||||
\(572\) | 3.95202e8 | − | 4.55557e8i | 0.0882944 | − | 0.101779i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.27553e9 | − | 1.03841e9i | 0.502216 | − | 0.229180i | ||||
\(575\) | 6.75732e8 | 0.148230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.22656e8 | −0.113266 | −0.0566332 | − | 0.998395i | \(-0.518037\pi\) | ||||
−0.0566332 | + | 0.998395i | \(0.518037\pi\) | |||||||
\(578\) | −4.54266e9 | + | 2.07298e9i | −0.978504 | + | 0.446527i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.02986e9 | + | 5.79802e9i | −1.07043 | + | 1.23390i | ||||
\(581\) | − | 5.41603e9i | − | 1.14568i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.41041e8 | −0.113081 | ||||||||
\(584\) | −2.22764e9 | + | 7.56246e9i | −0.462807 | + | 1.57115i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40742e9 | − | 3.08416e9i | −0.288922 | − | 0.633134i | ||||
\(587\) | 4.68092e9i | 0.955208i | 0.878575 | + | 0.477604i | \(0.158495\pi\) | ||||
−0.878575 | + | 0.477604i | \(0.841505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.95865e9i | − | 1.20156i | ||||||
\(590\) | 2.64905e8 | − | 1.20886e8i | 0.0531017 | − | 0.0242322i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.04812e9 | − | 1.29029e9i | 1.79239 | − | 0.255600i | ||||
\(593\) | 6.28546e9 | 1.23779 | 0.618893 | − | 0.785475i | \(-0.287581\pi\) | ||||
0.618893 | + | 0.785475i | \(0.287581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.10124e10i | 2.14325i | ||||||||
\(596\) | −1.03982e9 | − | 9.02057e8i | −0.201185 | − | 0.174531i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.10053e8 | + | 6.79438e8i | 0.0592900 | + | 0.129926i | ||||
\(599\) | 3.47628e9 | 0.660877 | 0.330438 | − | 0.943828i | \(-0.392803\pi\) | ||||
0.330438 | + | 0.943828i | \(0.392803\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.06456e9 | 0.200037 | 0.100018 | − | 0.994986i | \(-0.468110\pi\) | ||||
0.100018 | + | 0.994986i | \(0.468110\pi\) | |||||||
\(602\) | −2.08641e9 | − | 4.57209e9i | −0.389774 | − | 0.854136i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.12115e9 | + | 4.75053e9i | −0.761008 | + | 0.877229i | ||||
\(605\) | 4.62847e9i | 0.849755i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.59754e9 | 0.652898 | 0.326449 | − | 0.945215i | \(-0.394148\pi\) | ||||
0.326449 | + | 0.945215i | \(0.394148\pi\) | |||||||
\(608\) | 6.97853e9 | − | 4.47064e9i | 1.25922 | − | 0.806692i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.52315e9 | + | 1.15141e9i | −0.450079 | + | 0.205387i | ||||
\(611\) | 2.16020e9i | 0.383133i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.53170e9i | 1.32063i | 0.750988 | + | 0.660315i | \(0.229577\pi\) | ||||
−0.750988 | + | 0.660315i | \(0.770423\pi\) | |||||||
\(614\) | 1.63032e9 | + | 3.57263e9i | 0.284239 | + | 0.622872i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.65101e9 | + | 1.07546e9i | 0.629333 | + | 0.185380i | ||||
\(617\) | −2.41576e9 | −0.414053 | −0.207026 | − | 0.978335i | \(-0.566379\pi\) | ||||
−0.207026 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.34652e9i | − | 1.41445i | −0.706988 | − | 0.707226i | \(-0.749946\pi\) | ||
0.706988 | − | 0.707226i | \(-0.250054\pi\) | |||||||
\(620\) | 4.07524e9 | + | 3.53533e9i | 0.686724 | + | 0.595742i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.97148e9 | − | 1.35599e9i | 0.495115 | − | 0.225939i | ||||
\(623\) | −8.41590e9 | −1.39442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.33469e9 | −1.20172 | ||||||||
\(626\) | 5.45066e9 | − | 2.48734e9i | 0.888053 | − | 0.405251i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.74141e9 | − | 2.37821e9i | −0.441688 | − | 0.383171i | ||||
\(629\) | 1.62798e10i | 2.60839i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.01432e9 | −0.794528 | −0.397264 | − | 0.917704i | \(-0.630040\pi\) | ||||
−0.397264 | + | 0.917704i | \(0.630040\pi\) | |||||||
\(632\) | −1.43986e9 | + | 4.88808e9i | −0.226887 | + | 0.770245i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.24505e9 | + | 4.91972e9i | 0.349875 | + | 0.766705i | ||||
\(635\) | − | 3.21305e9i | − | 0.497977i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.28356e9i | 0.196757i | ||||||||
\(638\) | −4.29892e9 | + | 1.96176e9i | −0.655371 | + | 0.299070i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.08287e9 | + | 7.42522e9i | −0.163285 | + | 1.11964i | ||||
\(641\) | −2.31712e9 | −0.347493 | −0.173747 | − | 0.984790i | \(-0.555587\pi\) | ||||
−0.173747 | + | 0.984790i | \(0.555587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.61604e9i | − | 0.981431i | −0.871320 | − | 0.490716i | \(-0.836735\pi\) | ||
0.871320 | − | 0.490716i | \(-0.163265\pi\) | |||||||
\(644\) | −3.08862e9 | + | 3.56031e9i | −0.455684 | + | 0.525276i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.12864e9 | + | 1.34301e10i | 0.894438 | + | 1.96004i | ||||
\(647\) | −7.71651e9 | −1.12010 | −0.560049 | − | 0.828460i | \(-0.689218\pi\) | ||||
−0.560049 | + | 0.828460i | \(0.689218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.79261e8 | 0.0257412 | ||||||||
\(650\) | 2.19975e8 | + | 4.82045e8i | 0.0314178 | + | 0.0688479i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.39035e9 | + | 1.20615e9i | 0.196452 | + | 0.170425i | ||||
\(653\) | − | 4.65540e8i | − | 0.0654275i | −0.999465 | − | 0.0327138i | \(-0.989585\pi\) | ||
0.999465 | − | 0.0327138i | \(-0.0104150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.92160e9 | −1.10146 | ||||||||
\(656\) | 4.28581e8 | + | 3.00542e9i | 0.0592747 | + | 0.415663i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.24027e10 | + | 5.65981e9i | −1.69717 | + | 0.774482i | ||||
\(659\) | 6.54492e9i | 0.890851i | 0.895319 | + | 0.445426i | \(0.146948\pi\) | ||||
−0.895319 | + | 0.445426i | \(0.853052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.92056e9i | − | 0.393333i | −0.980470 | − | 0.196666i | \(-0.936988\pi\) | ||
0.980470 | − | 0.196666i | \(-0.0630116\pi\) | |||||||
\(662\) | 1.41060e9 | + | 3.09113e9i | 0.188973 | + | 0.414109i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.30563e9 | + | 1.85742e9i | 0.835873 | + | 0.246219i | ||||
\(665\) | 1.68715e10 | 2.22473 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.85170e9i | − | 0.763558i | ||||||
\(668\) | 9.78257e9 | − | 1.12766e10i | 1.26980 | − | 1.46372i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.42312e10 | − | 6.49421e9i | 1.82801 | − | 0.834190i | ||||
\(671\) | −1.70741e9 | −0.218177 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.21338e9 | −1.16511 | −0.582554 | − | 0.812792i | \(-0.697947\pi\) | ||||
−0.582554 | + | 0.812792i | \(0.697947\pi\) | |||||||
\(674\) | 1.46904e9 | − | 6.70379e8i | 0.184810 | − | 0.0843355i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.87946e9 | − | 5.62464e9i | 0.607516 | − | 0.700296i | ||||
\(677\) | − | 9.01623e9i | − | 1.11677i | −0.829581 | − | 0.558386i | \(-0.811421\pi\) | ||
0.829581 | − | 0.558386i | \(-0.188579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.86502e9 | −0.841585 | ||||||||
\(680\) | −1.28213e10 | − | 3.77670e9i | −1.56369 | − | 0.460608i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.37886e9 | + | 3.02157e9i | 0.166446 | + | 0.364744i | ||||
\(683\) | − | 1.23626e10i | − | 1.48470i | −0.670012 | − | 0.742350i | \(-0.733711\pi\) | ||
0.670012 | − | 0.742350i | \(-0.266289\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.07553e9i | − | 0.841089i | ||||||
\(686\) | 2.74423e9 | − | 1.25229e9i | 0.324553 | − | 0.148106i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.03861e9 | − | 8.61123e8i | 0.706932 | − | 0.100811i | ||||
\(689\) | 5.25370e8 | 0.0611925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.32041e10i | − | 1.52243i | −0.648500 | − | 0.761214i | \(-0.724603\pi\) | ||
0.648500 | − | 0.761214i | \(-0.275397\pi\) | |||||||
\(692\) | −1.16659e10 | − | 1.01204e10i | −1.33828 | − | 1.16098i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.61807e9 | + | 3.54579e9i | 0.183755 | + | 0.402675i | ||||
\(695\) | 4.30480e9 | 0.486414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.40750e9 | −0.604897 | ||||||||
\(698\) | 2.28474e8 | + | 5.00671e8i | 0.0254298 | + | 0.0557260i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.19130e9 | + | 2.52595e9i | −0.241467 | + | 0.278344i | ||||
\(701\) | − | 8.01688e9i | − | 0.879007i | −0.898241 | − | 0.439504i | \(-0.855154\pi\) | ||
0.898241 | − | 0.439504i | \(-0.144846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.49414e10 | 2.70755 | ||||||||
\(704\) | −2.50422e9 | + | 3.88188e9i | −0.270500 | + | 0.419312i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.84312e9 | + | 4.49178e9i | −1.05273 | + | 0.480398i | ||||
\(707\) | − | 1.65390e10i | − | 1.76012i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.49980e8i | 0.0158042i | 0.999969 | + | 0.00790209i | \(0.00251534\pi\) | ||||
−0.999969 | + | 0.00790209i | \(0.997485\pi\) | |||||||
\(710\) | 3.44716e9 | + | 7.55399e9i | 0.361458 | + | 0.792086i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.88622e9 | − | 9.79825e9i | 0.299675 | − | 1.01735i | ||||
\(713\) | −4.11297e9 | −0.424954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.49010e9i | 0.152456i | ||||||||
\(716\) | −1.05284e10 | − | 9.13349e9i | −1.07193 | − | 0.929911i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.25447e9 | − | 1.48513e9i | 0.328129 | − | 0.149737i | ||||
\(719\) | −4.43085e9 | −0.444565 | −0.222283 | − | 0.974982i | \(-0.571351\pi\) | ||||
−0.222283 | + | 0.974982i | \(0.571351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.83642e9 | 0.878017 | ||||||||
\(722\) | 1.13751e10 | − | 5.19089e9i | 1.12480 | − | 0.513289i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.25562e9 | + | 1.08926e9i | 0.122962 | + | 0.106671i | ||||
\(725\) | − | 4.15164e9i | − | 0.404610i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.33493e10 | −1.28851 | −0.644255 | − | 0.764811i | \(-0.722832\pi\) | ||||
−0.644255 | + | 0.764811i | \(0.722832\pi\) | |||||||
\(728\) | −3.54526e9 | − | 1.04431e9i | −0.340556 | − | 0.100316i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.08676e9 | − | 1.77210e10i | −0.769387 | − | 1.68601i | ||||
\(731\) | 1.08650e10i | 1.02877i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.28787e9i | − | 0.683497i | −0.939791 | − | 0.341749i | \(-0.888981\pi\) | ||
0.939791 | − | 0.341749i | \(-0.111019\pi\) | |||||||
\(734\) | 1.21861e10 | − | 5.56097e9i | 1.13744 | − | 0.519056i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.08587e9 | − | 4.81694e9i | −0.285302 | − | 0.445348i | ||||
\(737\) | 9.63023e9 | 0.886136 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.20806e9i | 0.839291i | 0.907688 | + | 0.419646i | \(0.137846\pi\) | ||||
−0.907688 | + | 0.419646i | \(0.862154\pi\) | |||||||
\(740\) | −1.47980e10 | + | 1.70579e10i | −1.34243 | + | 1.54744i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.37649e9 | + | 3.01639e9i | 0.123697 | + | 0.271066i | ||||
\(743\) | −1.72064e10 | −1.53896 | −0.769481 | − | 0.638669i | \(-0.779485\pi\) | ||||
−0.769481 | + | 0.638669i | \(0.779485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.40119e9 | 0.301359 | ||||||||
\(746\) | 3.06967e9 | + | 6.72677e9i | 0.270711 | + | 0.593227i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.21555e9 | − | 5.39207e9i | −0.543030 | − | 0.471086i | ||||
\(749\) | 2.19398e10i | 1.90786i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.62266e9 | −0.829001 | −0.414501 | − | 0.910049i | \(-0.636044\pi\) | ||||
−0.414501 | + | 0.910049i | \(0.636044\pi\) | |||||||
\(752\) | −2.33597e9 | − | 1.63809e10i | −0.200311 | − | 1.40468i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.17441e9 | − | 1.90494e9i | 0.354647 | − | 0.161838i | ||||
\(755\) | − | 1.55387e10i | − | 1.31402i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.06615e10i | 0.893269i | 0.894716 | + | 0.446635i | \(0.147378\pi\) | ||||
−0.894716 | + | 0.446635i | \(0.852622\pi\) | |||||||
\(758\) | −1.05805e9 | − | 2.31857e9i | −0.0882394 | − | 0.193365i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.78606e9 | + | 1.96427e10i | −0.478119 | + | 1.62313i | ||||
\(761\) | 9.85241e8 | 0.0810394 | 0.0405197 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405197 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.55122e10i | 1.26427i | ||||||||
\(764\) | 7.56921e9 | − | 8.72518e9i | 0.614078 | − | 0.707860i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.12018e9 | − | 3.70554e9i | 0.652777 | − | 0.297886i | ||||
\(767\) | −1.74069e8 | −0.0139296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.77074e9 | 0.299009 | 0.149505 | − | 0.988761i | \(-0.452232\pi\) | ||||
0.149505 | + | 0.988761i | \(0.452232\pi\) | |||||||
\(770\) | −8.55537e9 | + | 3.90413e9i | −0.675338 | + | 0.308182i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.55035e10 | + | 1.78712e10i | −1.21274 | + | 1.39795i | ||||
\(773\) | − | 5.93783e9i | − | 0.462381i | −0.972909 | − | 0.231190i | \(-0.925738\pi\) | ||
0.972909 | − | 0.231190i | \(-0.0742620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.91805e9 | −0.225184 | ||||||||
\(776\) | 2.35435e9 | − | 7.99264e9i | 0.180865 | − | 0.614008i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.57873e9 | + | 5.65094e9i | 0.196326 | + | 0.430222i | ||||
\(779\) | 8.28452e9i | 0.627894i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.11178e9i | 0.383967i | ||||||||
\(782\) | 9.27014e9 | − | 4.23031e9i | 0.693207 | − | 0.316336i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.38800e9 | − | 9.73334e9i | −0.102869 | − | 0.721366i | ||||
\(785\) | 8.96702e9 | 0.661614 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.44036e9i | − | 0.251589i | −0.992056 | − | 0.125795i | \(-0.959852\pi\) | ||
0.992056 | − | 0.125795i | \(-0.0401480\pi\) | |||||||
\(788\) | −5.72589e9 | − | 4.96729e9i | −0.416870 | − | 0.361641i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.22697e9 | − | 1.14542e10i | −0.377186 | − | 0.826551i | ||||
\(791\) | −3.07130e10 | −2.20651 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.65796e9 | 0.118064 | ||||||||
\(794\) | 6.36476e9 | + | 1.39475e10i | 0.451243 | + | 0.988838i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.95581e9 | − | 3.40722e9i | 0.207721 | − | 0.239444i | ||||
\(797\) | 1.01695e9i | 0.0711537i | 0.999367 | + | 0.0355769i | \(0.0113269\pi\) | ||||
−0.999367 | + | 0.0355769i | \(0.988673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.94734e10 | 2.04417 | ||||||||
\(800\) | −2.18935e9 | − | 3.41750e9i | −0.151182 | − | 0.235990i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.42536e9 | − | 6.50446e8i | 0.0975699 | − | 0.0445247i | ||||
\(803\) | − | 1.19918e10i | − | 0.817298i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.16456e10i | − | 0.786821i | ||||||
\(806\) | −1.33892e9 | − | 2.93406e9i | −0.0900703 | − | 0.197377i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.92556e10 | + | 5.67203e9i | 1.28415 | + | 0.378267i | ||||
\(809\) | 2.54544e10 | 1.69022 | 0.845108 | − | 0.534595i | \(-0.179536\pi\) | ||||
0.845108 | + | 0.534595i | \(0.179536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.46755e10i | 0.966096i | 0.875594 | + | 0.483048i | \(0.160470\pi\) | ||||
−0.875594 | + | 0.483048i | \(0.839530\pi\) | |||||||
\(812\) | 2.18743e10 | + | 1.89762e10i | 1.43380 | + | 1.24384i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.26475e10 | + | 5.77153e9i | −0.821903 | + | 0.375064i | ||||
\(815\) | −4.54775e9 | −0.294270 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.66456e10 | 1.06788 | ||||||||
\(818\) | 1.39000e10 | − | 6.34306e9i | 0.887927 | − | 0.405194i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.66594e9 | − | 4.91528e9i | −0.358859 | − | 0.311315i | ||||
\(821\) | 2.29026e10i | 1.44439i | 0.691691 | + | 0.722193i | \(0.256866\pi\) | ||||
−0.691691 | + | 0.722193i | \(0.743134\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.16697e10 | −0.729729 | −0.364864 | − | 0.931061i | \(-0.618885\pi\) | ||||
−0.364864 | + | 0.931061i | \(0.618885\pi\) | |||||||
\(824\) | −3.03044e9 | + | 1.02878e10i | −0.188695 | + | 0.640589i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.56068e8 | − | 9.99410e8i | −0.0281578 | − | 0.0617040i | ||||
\(827\) | 1.59065e10i | 0.977928i | 0.872304 | + | 0.488964i | \(0.162625\pi\) | ||||
−0.872304 | + | 0.488964i | \(0.837375\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.22501e10i | 1.35641i | 0.734873 | + | 0.678205i | \(0.237242\pi\) | ||||
−0.734873 | + | 0.678205i | \(0.762758\pi\) | |||||||
\(830\) | −1.47759e10 | + | 6.74280e9i | −0.896977 | + | 0.409324i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.43169e9 | − | 3.76945e9i | 0.146378 | − | 0.226906i | ||||
\(833\) | 1.75127e10 | 1.04977 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.68851e10i | 2.19254i | ||||||||
\(836\) | −8.26088e9 | + | 9.52248e9i | −0.488995 | + | 0.563674i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.31765e10 | − | 2.88744e10i | −0.773472 | − | 1.69496i | ||||
\(839\) | 1.74931e10 | 1.02258 | 0.511292 | − | 0.859407i | \(-0.329167\pi\) | ||||
0.511292 | + | 0.859407i | \(0.329167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.87025e10 | −1.08421 | ||||||||
\(842\) | 2.10817e9 | + | 4.61977e9i | 0.121706 | + | 0.266703i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.07683e10 | − | 1.80168e10i | −1.18906 | − | 1.03152i | ||||
\(845\) | 1.83979e10i | 1.04899i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.74619e10 | 0.987414 | ||||||||
\(848\) | −3.98392e9 | + | 5.68118e8i | −0.224349 | + | 0.0319929i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.57694e9 | − | 3.00130e9i | 0.367331 | − | 0.167627i | ||||
\(851\) | − | 1.72158e10i | − | 0.957580i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.33580e9i | 0.294359i | 0.989110 | + | 0.147180i | \(0.0470195\pi\) | ||||
−0.989110 | + | 0.147180i | \(0.952980\pi\) | |||||||
\(854\) | 4.34392e9 | + | 9.51912e9i | 0.238660 | + | 0.522991i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.55435e10 | − | 7.52422e9i | −1.39195 | − | 0.410019i | ||||
\(857\) | −1.18390e10 | −0.642516 | −0.321258 | − | 0.946992i | \(-0.604106\pi\) | ||||
−0.321258 | + | 0.946992i | \(0.604106\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3.05240e10i | − | 1.64310i | −0.570133 | − | 0.821552i | \(-0.693109\pi\) | ||
0.570133 | − | 0.821552i | \(-0.306891\pi\) | |||||||
\(860\) | −9.87599e9 | + | 1.13843e10i | −0.529464 | + | 0.610323i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.75421e10 | + | 1.25685e10i | −1.46461 | + | 0.668354i | ||||
\(863\) | 2.15426e9 | 0.114093 | 0.0570466 | − | 0.998372i | \(-0.481832\pi\) | ||||
0.0570466 | + | 0.998372i | \(0.481832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.81586e10 | 2.00464 | ||||||||
\(866\) | −1.73850e10 | + | 7.93342e9i | −0.909625 | + | 0.415095i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.33378e10 | − | 1.53747e10i | 0.692252 | − | 0.797972i | ||||
\(869\) | − | 7.75104e9i | − | 0.400674i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.35131e9 | −0.479522 | ||||||||
\(872\) | −1.80602e10 | − | 5.31991e9i | −0.922391 | − | 0.271704i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.48101e9 | − | 1.42022e10i | −0.328362 | − | 0.719560i | ||||
\(875\) | 2.12181e10i | 1.07073i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.98515e10i | 0.993789i | 0.867811 | + | 0.496894i | \(0.165526\pi\) | ||||
−0.867811 | + | 0.496894i | \(0.834474\pi\) | |||||||
\(878\) | 9.46053e9 | − | 4.31719e9i | 0.471720 | − | 0.215263i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.61135e9 | − | 1.12996e10i | −0.0797077 | − | 0.558949i | ||||
\(881\) | −1.81176e10 | −0.892659 | −0.446330 | − | 0.894869i | \(-0.647269\pi\) | ||||
−0.446330 | + | 0.894869i | \(0.647269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.44143e10i | − | 1.19339i | −0.802469 | − | 0.596693i | \(-0.796481\pi\) | ||
0.802469 | − | 0.596693i | \(-0.203519\pi\) | |||||||
\(884\) | 6.03552e9 | + | 5.23590e9i | 0.293854 | + | 0.254923i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.33384e10 | + | 2.92293e10i | 0.644297 | + | 1.41189i | ||||
\(887\) | 8.86049e9 | 0.426310 | 0.213155 | − | 0.977018i | \(-0.431626\pi\) | ||||
0.213155 | + | 0.977018i | \(0.431626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21219e10 | −0.578649 | ||||||||
\(890\) | 1.04776e10 | + | 2.29601e10i | 0.498190 | + | 1.09172i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.56691e9 | − | 7.56981e9i | 0.309802 | − | 0.357115i | ||||
\(893\) | − | 4.51545e10i | − | 2.12188i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.44377e10 | 1.60566 | ||||||||
\(896\) | 2.80132e10 | + | 4.08535e9i | 1.30102 | + | 0.189737i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.27985e10 | − | 5.84043e9i | 0.589783 | − | 0.269140i | ||||
\(899\) | 2.52698e10i | 1.15996i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.16807e9i | − | 0.326487i | ||||||
\(902\) | −1.91707e9 | − | 4.20100e9i | −0.0869791 | − | 0.190603i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.05330e10 | − | 3.57578e10i | 0.474201 | − | 1.60983i | ||||
\(905\) | −4.10706e9 | −0.184188 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.38413e9i | 0.106097i | 0.998592 | + | 0.0530487i | \(0.0168939\pi\) | ||||
−0.998592 | + | 0.0530487i | \(0.983106\pi\) | |||||||
\(908\) | −2.58975e10 | − | 2.24664e10i | −1.14804 | − | 0.995940i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.30758e9 | − | 3.79105e9i | 0.365452 | − | 0.166769i | ||||
\(911\) | 1.97036e10 | 0.863440 | 0.431720 | − | 0.902008i | \(-0.357907\pi\) | ||||
0.431720 | + | 0.902008i | \(0.357907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.99886e9 | −0.434813 | ||||||||
\(914\) | 1.99168e9 | − | 9.08875e8i | 0.0862794 | − | 0.0393724i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.64303e10 | + | 2.29287e10i | 1.13624 | + | 0.985701i | ||||
\(917\) | 2.98859e10i | 1.27989i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.34466e10 | −0.996496 | −0.498248 | − | 0.867035i | \(-0.666023\pi\) | ||||
−0.498248 | + | 0.867035i | \(0.666023\pi\) | |||||||
\(920\) | 1.35584e10 | + | 3.99384e9i | 0.574053 | + | 0.169096i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.27947e9 | + | 2.03347e10i | 0.389911 | + | 0.854436i | ||||
\(923\) | − | 4.96373e9i | − | 0.207779i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.22142e10i | − | 0.507423i | ||||||
\(926\) | 1.16828e10 | − | 5.33129e9i | 0.483513 | − | 0.220645i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.95949e10 | + | 1.89593e10i | −1.21562 | + | 0.778763i | ||||
\(929\) | −2.93528e10 | −1.20114 | −0.600571 | − | 0.799572i | \(-0.705060\pi\) | ||||
−0.600571 | + | 0.799572i | \(0.705060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.68302e10i | − | 1.08968i | ||||||
\(932\) | 2.73508e10 | − | 3.15278e10i | 1.10666 | − | 1.27567i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.52230e9 | − | 2.08668e10i | −0.382409 | − | 0.837997i | ||||
\(935\) | 2.03307e10 | 0.813415 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54313e10 | −1.00991 | −0.504953 | − | 0.863147i | \(-0.668490\pi\) | ||||
−0.504953 | + | 0.863147i | \(0.668490\pi\) | |||||||
\(938\) | −2.45008e10 | − | 5.36902e10i | −0.969327 | − | 2.12415i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.08821e10 | + | 2.67906e10i | 1.21271 | + | 1.05205i | ||||
\(941\) | 3.53014e8i | 0.0138111i | 0.999976 | + | 0.00690556i | \(0.00219812\pi\) | ||||
−0.999976 | + | 0.00690556i | \(0.997802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.71840e9 | 0.222067 | ||||||||
\(944\) | 1.31998e9 | − | 1.88232e8i | 0.0510698 | − | 0.00728270i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.44082e9 | + | 3.85186e9i | −0.324165 | + | 0.147928i | ||||
\(947\) | − | 1.56019e10i | − | 0.596968i | −0.954415 | − | 0.298484i | \(-0.903519\pi\) | ||
0.954415 | − | 0.298484i | \(-0.0964810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.16445e10i | 0.442271i | ||||||||
\(950\) | −4.59812e9 | − | 1.00761e10i | −0.173999 | − | 0.381296i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.42484e10 | + | 4.83710e10i | −0.535226 | + | 1.81700i | ||||
\(953\) | −4.43492e10 | −1.65982 | −0.829909 | − | 0.557898i | \(-0.811608\pi\) | ||||
−0.829909 | + | 0.557898i | \(0.811608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.85396e10i | 1.06032i | ||||||||
\(956\) | 6.88685e9 | − | 7.93860e9i | 0.254928 | − | 0.293861i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.72779e10 | + | 7.88455e9i | −0.634910 | + | 0.289733i | ||||
\(959\) | −2.66939e10 | −0.977344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.75131e9 | −0.354431 | ||||||||
\(962\) | 1.22812e10 | − | 5.60437e9i | 0.444763 | − | 0.202962i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.19133e10 | − | 1.37327e10i | 0.428316 | − | 0.493728i | ||||
\(965\) | − | 5.84557e10i | − | 2.09402i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.48087e10 | −1.23793 | −0.618964 | − | 0.785419i | \(-0.712447\pi\) | ||||
−0.618964 | + | 0.785419i | \(0.712447\pi\) | |||||||
\(968\) | −5.98853e9 | + | 2.03301e10i | −0.212205 | + | 0.720403i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.54676e9 | + | 1.87291e10i | 0.300677 | + | 0.658893i | ||||
\(971\) | − | 2.46548e10i | − | 0.864239i | −0.901816 | − | 0.432119i | \(-0.857766\pi\) | ||
0.901816 | − | 0.432119i | \(-0.142234\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.62408e10i | − | 0.565212i | ||||||
\(974\) | −3.75451e10 | + | 1.71332e10i | −1.30196 | + | 0.594131i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.25724e10 | + | 1.79286e9i | −0.432857 | + | 0.0617267i | ||||
\(977\) | 6.03006e9 | 0.206867 | 0.103433 | − | 0.994636i | \(-0.467017\pi\) | ||||
0.103433 | + | 0.994636i | \(0.467017\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.55371e10i | 0.529214i | ||||||||
\(980\) | 1.83497e10 | + | 1.59186e10i | 0.622784 | + | 0.540274i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.47221e9 | + | 2.07571e10i | 0.319199 | + | 0.699481i | ||||
\(983\) | 4.42805e10 | 1.48688 | 0.743439 | − | 0.668803i | \(-0.233193\pi\) | ||||
0.743439 | + | 0.668803i | \(0.233193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.87291e10 | 0.624438 | ||||||||
\(986\) | −2.59907e10 | − | 5.69550e10i | −0.863472 | − | 1.89218i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.02162e9 | − | 9.24668e9i | 0.264614 | − | 0.305026i | ||||
\(989\) | − | 1.14897e10i | − | 0.377677i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23756e10 | 0.403932 | 0.201966 | − | 0.979392i | \(-0.435267\pi\) | ||||
0.201966 | + | 0.979392i | \(0.435267\pi\) | |||||||
\(992\) | 1.33259e10 | + | 2.08013e10i | 0.433417 | + | 0.676549i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.84990e10 | − | 1.30052e10i | 0.920403 | − | 0.420013i | ||||
\(995\) | 1.11448e10i | 0.358668i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.41900e10i | − | 0.453470i | −0.973957 | − | 0.226735i | \(-0.927195\pi\) | ||
0.973957 | − | 0.226735i | \(-0.0728051\pi\) | |||||||
\(998\) | −5.61897e9 | − | 1.23132e10i | −0.178937 | − | 0.392116i | ||||
\(999\) | 0 | 0 |
(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 | 72.8.d.c.37.4 | yes | 12 | |
3.2 | odd | 2 | inner | 72.8.d.c.37.9 | yes | 12 | |
4.3 | odd | 2 | 288.8.d.c.145.12 | 12 | |||
8.3 | odd | 2 | 288.8.d.c.145.1 | 12 | |||
8.5 | even | 2 | inner | 72.8.d.c.37.3 | ✓ | 12 | |
12.11 | even | 2 | 288.8.d.c.145.2 | 12 | |||
24.5 | odd | 2 | inner | 72.8.d.c.37.10 | yes | 12 | |
24.11 | even | 2 | 288.8.d.c.145.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.d.c.37.3 | ✓ | 12 | 8.5 | even | 2 | inner | |
72.8.d.c.37.4 | yes | 12 | 1.1 | even | 1 | trivial | |
72.8.d.c.37.9 | yes | 12 | 3.2 | odd | 2 | inner | |
72.8.d.c.37.10 | yes | 12 | 24.5 | odd | 2 | inner | |
288.8.d.c.145.1 | 12 | 8.3 | odd | 2 | |||
288.8.d.c.145.2 | 12 | 12.11 | even | 2 | |||
288.8.d.c.145.11 | 12 | 24.11 | even | 2 | |||
288.8.d.c.145.12 | 12 | 4.3 | odd | 2 |