Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −158.048 | −1.74620 | −0.873098 | − | 0.487546i | \(-0.837892\pi\) | ||||
−0.873098 | + | 0.487546i | \(0.837892\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 16787.0 | 2.04920 | ||||||||
\(5\) | −61907.4 | −1.77189 | −0.885947 | − | 0.463787i | \(-0.846490\pi\) | ||||
−0.885947 | + | 0.463787i | \(0.846490\pi\) | |||||||
\(6\) | −115217. | −1.00817 | ||||||||
\(7\) | 140047. | 0.449921 | 0.224961 | − | 0.974368i | \(-0.427775\pi\) | ||||
0.224961 | + | 0.974368i | \(0.427775\pi\) | |||||||
\(8\) | −1.35842e6 | −1.83210 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 9.78431e6 | 3.09407 | ||||||||
\(11\) | 1.00908e7 | 1.71741 | 0.858703 | − | 0.512473i | \(-0.171271\pi\) | ||||
0.858703 | + | 0.512473i | \(0.171271\pi\) | |||||||
\(12\) | 1.22377e7 | 1.18310 | ||||||||
\(13\) | 3.21335e7 | 1.84640 | 0.923201 | − | 0.384319i | \(-0.125564\pi\) | ||||
0.923201 | + | 0.384319i | \(0.125564\pi\) | |||||||
\(14\) | −2.21341e7 | −0.785650 | ||||||||
\(15\) | −4.51305e7 | −1.02300 | ||||||||
\(16\) | 7.71760e7 | 1.15001 | ||||||||
\(17\) | −1.32468e8 | −1.33104 | −0.665522 | − | 0.746379i | \(-0.731791\pi\) | ||||
−0.665522 | + | 0.746379i | \(0.731791\pi\) | |||||||
\(18\) | −8.39929e7 | −0.582065 | ||||||||
\(19\) | 8.81457e7 | 0.429836 | 0.214918 | − | 0.976632i | \(-0.431052\pi\) | ||||
0.214918 | + | 0.976632i | \(0.431052\pi\) | |||||||
\(20\) | −1.03924e9 | −3.63096 | ||||||||
\(21\) | 1.02094e8 | 0.259762 | ||||||||
\(22\) | −1.59483e9 | −2.99893 | ||||||||
\(23\) | −9.30531e8 | −1.31069 | −0.655345 | − | 0.755330i | \(-0.727477\pi\) | ||||
−0.655345 | + | 0.755330i | \(0.727477\pi\) | |||||||
\(24\) | −9.90290e8 | −1.05777 | ||||||||
\(25\) | 2.61183e9 | 2.13961 | ||||||||
\(26\) | −5.07862e9 | −3.22418 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 2.35097e9 | 0.921977 | ||||||||
\(29\) | −2.53556e9 | −0.791565 | −0.395782 | − | 0.918344i | \(-0.629527\pi\) | ||||
−0.395782 | + | 0.918344i | \(0.629527\pi\) | |||||||
\(30\) | 7.13277e9 | 1.78636 | ||||||||
\(31\) | −1.90332e9 | −0.385177 | −0.192588 | − | 0.981280i | \(-0.561688\pi\) | ||||
−0.192588 | + | 0.981280i | \(0.561688\pi\) | |||||||
\(32\) | −1.06928e9 | −0.176042 | ||||||||
\(33\) | 7.35619e9 | 0.991545 | ||||||||
\(34\) | 2.09362e10 | 2.32426 | ||||||||
\(35\) | −8.66995e9 | −0.797213 | ||||||||
\(36\) | 8.92131e9 | 0.683066 | ||||||||
\(37\) | −5.98250e9 | −0.383329 | −0.191664 | − | 0.981461i | \(-0.561388\pi\) | ||||
−0.191664 | + | 0.981461i | \(0.561388\pi\) | |||||||
\(38\) | −1.39312e10 | −0.750577 | ||||||||
\(39\) | 2.34253e10 | 1.06602 | ||||||||
\(40\) | 8.40964e10 | 3.24629 | ||||||||
\(41\) | −3.51635e10 | −1.15611 | −0.578053 | − | 0.816000i | \(-0.696187\pi\) | ||||
−0.578053 | + | 0.816000i | \(0.696187\pi\) | |||||||
\(42\) | −1.61357e10 | −0.453595 | ||||||||
\(43\) | −5.08079e9 | −0.122571 | −0.0612853 | − | 0.998120i | \(-0.519520\pi\) | ||||
−0.0612853 | + | 0.998120i | \(0.519520\pi\) | |||||||
\(44\) | 1.69394e11 | 3.51930 | ||||||||
\(45\) | −3.29001e10 | −0.590631 | ||||||||
\(46\) | 1.47068e11 | 2.28872 | ||||||||
\(47\) | 5.23615e10 | 0.708559 | 0.354279 | − | 0.935140i | \(-0.384726\pi\) | ||||
0.354279 | + | 0.935140i | \(0.384726\pi\) | |||||||
\(48\) | 5.62613e10 | 0.663960 | ||||||||
\(49\) | −7.72759e10 | −0.797571 | ||||||||
\(50\) | −4.12793e11 | −3.73617 | ||||||||
\(51\) | −9.65690e10 | −0.768478 | ||||||||
\(52\) | 5.39426e11 | 3.78364 | ||||||||
\(53\) | 6.77282e10 | 0.419736 | 0.209868 | − | 0.977730i | \(-0.432697\pi\) | ||||
0.209868 | + | 0.977730i | \(0.432697\pi\) | |||||||
\(54\) | −6.12309e10 | −0.336055 | ||||||||
\(55\) | −6.24695e11 | −3.04306 | ||||||||
\(56\) | −1.90243e11 | −0.824302 | ||||||||
\(57\) | 6.42582e10 | 0.248166 | ||||||||
\(58\) | 4.00739e11 | 1.38223 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −7.57607e11 | −2.09634 | ||||||||
\(61\) | −3.97617e11 | −0.988146 | −0.494073 | − | 0.869421i | \(-0.664492\pi\) | ||||
−0.494073 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(62\) | 3.00815e11 | 0.672594 | ||||||||
\(63\) | 7.44267e10 | 0.149974 | ||||||||
\(64\) | −4.63229e11 | −0.842608 | ||||||||
\(65\) | −1.98930e12 | −3.27163 | ||||||||
\(66\) | −1.16263e12 | −1.73143 | ||||||||
\(67\) | 1.31939e12 | 1.78191 | 0.890957 | − | 0.454088i | \(-0.150035\pi\) | ||||
0.890957 | + | 0.454088i | \(0.150035\pi\) | |||||||
\(68\) | −2.22374e12 | −2.72757 | ||||||||
\(69\) | −6.78357e11 | −0.756727 | ||||||||
\(70\) | 1.37026e12 | 1.39209 | ||||||||
\(71\) | 2.06032e12 | 1.90878 | 0.954389 | − | 0.298566i | \(-0.0965084\pi\) | ||||
0.954389 | + | 0.298566i | \(0.0965084\pi\) | |||||||
\(72\) | −7.21921e11 | −0.610701 | ||||||||
\(73\) | −3.72820e11 | −0.288337 | −0.144168 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144168 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(74\) | 9.45519e11 | 0.669366 | ||||||||
\(75\) | 1.90402e12 | 1.23530 | ||||||||
\(76\) | 1.47970e12 | 0.880818 | ||||||||
\(77\) | 1.41319e12 | 0.772698 | ||||||||
\(78\) | −3.70231e12 | −1.86148 | ||||||||
\(79\) | −2.77004e12 | −1.28207 | −0.641034 | − | 0.767513i | \(-0.721494\pi\) | ||||
−0.641034 | + | 0.767513i | \(0.721494\pi\) | |||||||
\(80\) | −4.77777e12 | −2.03770 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 5.55751e12 | 2.01878 | ||||||||
\(83\) | 9.61094e11 | 0.322670 | 0.161335 | − | 0.986900i | \(-0.448420\pi\) | ||||
0.161335 | + | 0.986900i | \(0.448420\pi\) | |||||||
\(84\) | 1.71386e12 | 0.532304 | ||||||||
\(85\) | 8.20074e12 | 2.35847 | ||||||||
\(86\) | 8.03006e11 | 0.214032 | ||||||||
\(87\) | −1.84842e12 | −0.457010 | ||||||||
\(88\) | −1.37076e13 | −3.14646 | ||||||||
\(89\) | −1.40040e12 | −0.298687 | −0.149344 | − | 0.988785i | \(-0.547716\pi\) | ||||
−0.149344 | + | 0.988785i | \(0.547716\pi\) | |||||||
\(90\) | 5.19979e12 | 1.03136 | ||||||||
\(91\) | 4.50020e12 | 0.830735 | ||||||||
\(92\) | −1.56208e13 | −2.68586 | ||||||||
\(93\) | −1.38752e12 | −0.222382 | ||||||||
\(94\) | −8.27560e12 | −1.23728 | ||||||||
\(95\) | −5.45687e12 | −0.761623 | ||||||||
\(96\) | −7.79505e11 | −0.101638 | ||||||||
\(97\) | −1.59667e12 | −0.194625 | −0.0973127 | − | 0.995254i | \(-0.531025\pi\) | ||||
−0.0973127 | + | 0.995254i | \(0.531025\pi\) | |||||||
\(98\) | 1.22133e13 | 1.39271 | ||||||||
\(99\) | 5.36266e12 | 0.572469 | ||||||||
\(100\) | 4.38448e13 | 4.38448 | ||||||||
\(101\) | −3.16932e12 | −0.297083 | −0.148542 | − | 0.988906i | \(-0.547458\pi\) | ||||
−0.148542 | + | 0.988906i | \(0.547458\pi\) | |||||||
\(102\) | 1.52625e13 | 1.34191 | ||||||||
\(103\) | −2.30297e13 | −1.90040 | −0.950202 | − | 0.311636i | \(-0.899123\pi\) | ||||
−0.950202 | + | 0.311636i | \(0.899123\pi\) | |||||||
\(104\) | −4.36508e13 | −3.38280 | ||||||||
\(105\) | −6.32039e12 | −0.460271 | ||||||||
\(106\) | −1.07043e13 | −0.732941 | ||||||||
\(107\) | −2.30047e13 | −1.48191 | −0.740957 | − | 0.671553i | \(-0.765628\pi\) | ||||
−0.740957 | + | 0.671553i | \(0.765628\pi\) | |||||||
\(108\) | 6.50364e12 | 0.394368 | ||||||||
\(109\) | 2.44685e13 | 1.39745 | 0.698723 | − | 0.715392i | \(-0.253752\pi\) | ||||
0.698723 | + | 0.715392i | \(0.253752\pi\) | |||||||
\(110\) | 9.87315e13 | 5.31378 | ||||||||
\(111\) | −4.36124e12 | −0.221315 | ||||||||
\(112\) | 1.08083e13 | 0.517415 | ||||||||
\(113\) | 1.21901e13 | 0.550805 | 0.275402 | − | 0.961329i | \(-0.411189\pi\) | ||||
0.275402 | + | 0.961329i | \(0.411189\pi\) | |||||||
\(114\) | −1.01558e13 | −0.433346 | ||||||||
\(115\) | 5.76068e13 | 2.32240 | ||||||||
\(116\) | −4.25645e13 | −1.62207 | ||||||||
\(117\) | 1.70771e13 | 0.615467 | ||||||||
\(118\) | −6.66653e12 | −0.227335 | ||||||||
\(119\) | −1.85517e13 | −0.598865 | ||||||||
\(120\) | 6.13063e13 | 1.87425 | ||||||||
\(121\) | 6.73015e13 | 1.94948 | ||||||||
\(122\) | 6.28424e13 | 1.72549 | ||||||||
\(123\) | −2.56342e13 | −0.667478 | ||||||||
\(124\) | −3.19510e13 | −0.789303 | ||||||||
\(125\) | −8.61208e13 | −2.01926 | ||||||||
\(126\) | −1.17630e13 | −0.261883 | ||||||||
\(127\) | 3.93074e13 | 0.831286 | 0.415643 | − | 0.909528i | \(-0.363557\pi\) | ||||
0.415643 | + | 0.909528i | \(0.363557\pi\) | |||||||
\(128\) | 8.19717e13 | 1.64740 | ||||||||
\(129\) | −3.70390e12 | −0.0707662 | ||||||||
\(130\) | 3.14404e14 | 5.71290 | ||||||||
\(131\) | −1.54608e13 | −0.267281 | −0.133641 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133641 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(132\) | 1.23489e14 | 2.03187 | ||||||||
\(133\) | 1.23445e13 | 0.193392 | ||||||||
\(134\) | −2.08526e14 | −3.11157 | ||||||||
\(135\) | −2.39842e13 | −0.341001 | ||||||||
\(136\) | 1.79947e14 | 2.43861 | ||||||||
\(137\) | 1.17132e14 | 1.51353 | 0.756765 | − | 0.653688i | \(-0.226779\pi\) | ||||
0.756765 | + | 0.653688i | \(0.226779\pi\) | |||||||
\(138\) | 1.07213e14 | 1.32139 | ||||||||
\(139\) | 8.88527e13 | 1.04490 | 0.522450 | − | 0.852670i | \(-0.325018\pi\) | ||||
0.522450 | + | 0.852670i | \(0.325018\pi\) | |||||||
\(140\) | −1.45543e14 | −1.63365 | ||||||||
\(141\) | 3.81715e13 | 0.409087 | ||||||||
\(142\) | −3.25628e14 | −3.33310 | ||||||||
\(143\) | 3.24252e14 | 3.17102 | ||||||||
\(144\) | 4.10145e13 | 0.383337 | ||||||||
\(145\) | 1.56970e14 | 1.40257 | ||||||||
\(146\) | 5.89232e13 | 0.503493 | ||||||||
\(147\) | −5.63341e13 | −0.460478 | ||||||||
\(148\) | −1.00428e14 | −0.785516 | ||||||||
\(149\) | 9.14953e13 | 0.684996 | 0.342498 | − | 0.939519i | \(-0.388727\pi\) | ||||
0.342498 | + | 0.939519i | \(0.388727\pi\) | |||||||
\(150\) | −3.00926e14 | −2.15708 | ||||||||
\(151\) | −1.45208e14 | −0.996872 | −0.498436 | − | 0.866926i | \(-0.666092\pi\) | ||||
−0.498436 | + | 0.866926i | \(0.666092\pi\) | |||||||
\(152\) | −1.19739e14 | −0.787503 | ||||||||
\(153\) | −7.03988e13 | −0.443681 | ||||||||
\(154\) | −2.23351e14 | −1.34928 | ||||||||
\(155\) | 1.17829e14 | 0.682492 | ||||||||
\(156\) | 3.93241e14 | 2.18449 | ||||||||
\(157\) | −1.15862e14 | −0.617437 | −0.308718 | − | 0.951154i | \(-0.599900\pi\) | ||||
−0.308718 | + | 0.951154i | \(0.599900\pi\) | |||||||
\(158\) | 4.37799e14 | 2.23874 | ||||||||
\(159\) | 4.93738e13 | 0.242335 | ||||||||
\(160\) | 6.61964e13 | 0.311928 | ||||||||
\(161\) | −1.30318e14 | −0.589707 | ||||||||
\(162\) | −4.46373e13 | −0.194022 | ||||||||
\(163\) | −2.91754e14 | −1.21842 | −0.609211 | − | 0.793008i | \(-0.708514\pi\) | ||||
−0.609211 | + | 0.793008i | \(0.708514\pi\) | |||||||
\(164\) | −5.90291e14 | −2.36909 | ||||||||
\(165\) | −4.55403e14 | −1.75691 | ||||||||
\(166\) | −1.51898e14 | −0.563444 | ||||||||
\(167\) | −4.20713e14 | −1.50082 | −0.750410 | − | 0.660973i | \(-0.770144\pi\) | ||||
−0.750410 | + | 0.660973i | \(0.770144\pi\) | |||||||
\(168\) | −1.38687e14 | −0.475911 | ||||||||
\(169\) | 7.29686e14 | 2.40920 | ||||||||
\(170\) | −1.29611e15 | −4.11834 | ||||||||
\(171\) | 4.68442e13 | 0.143279 | ||||||||
\(172\) | −8.52913e13 | −0.251171 | ||||||||
\(173\) | −5.29159e14 | −1.50067 | −0.750337 | − | 0.661056i | \(-0.770109\pi\) | ||||
−0.750337 | + | 0.661056i | \(0.770109\pi\) | |||||||
\(174\) | 2.92138e14 | 0.798029 | ||||||||
\(175\) | 3.65778e14 | 0.962655 | ||||||||
\(176\) | 7.78767e14 | 1.97504 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 2.21330e14 | 0.521566 | ||||||||
\(179\) | −8.18391e14 | −1.85959 | −0.929793 | − | 0.368082i | \(-0.880014\pi\) | ||||
−0.929793 | + | 0.368082i | \(0.880014\pi\) | |||||||
\(180\) | −5.52295e14 | −1.21032 | ||||||||
\(181\) | 6.63558e13 | 0.140271 | 0.0701355 | − | 0.997537i | \(-0.477657\pi\) | ||||
0.0701355 | + | 0.997537i | \(0.477657\pi\) | |||||||
\(182\) | −7.11245e14 | −1.45063 | ||||||||
\(183\) | −2.89863e14 | −0.570506 | ||||||||
\(184\) | 1.26405e15 | 2.40132 | ||||||||
\(185\) | 3.70361e14 | 0.679217 | ||||||||
\(186\) | 2.19294e14 | 0.388322 | ||||||||
\(187\) | −1.33671e15 | −2.28594 | ||||||||
\(188\) | 8.78994e14 | 1.45198 | ||||||||
\(189\) | 5.42571e13 | 0.0865874 | ||||||||
\(190\) | 8.62445e14 | 1.32994 | ||||||||
\(191\) | 6.03349e14 | 0.899190 | 0.449595 | − | 0.893232i | \(-0.351568\pi\) | ||||
0.449595 | + | 0.893232i | \(0.351568\pi\) | |||||||
\(192\) | −3.37694e14 | −0.486480 | ||||||||
\(193\) | 8.07855e14 | 1.12515 | 0.562575 | − | 0.826746i | \(-0.309811\pi\) | ||||
0.562575 | + | 0.826746i | \(0.309811\pi\) | |||||||
\(194\) | 2.52350e14 | 0.339854 | ||||||||
\(195\) | −1.45020e15 | −1.88887 | ||||||||
\(196\) | −1.29723e15 | −1.63438 | ||||||||
\(197\) | −5.05002e14 | −0.615549 | −0.307775 | − | 0.951459i | \(-0.599584\pi\) | ||||
−0.307775 | + | 0.951459i | \(0.599584\pi\) | |||||||
\(198\) | −8.47556e14 | −0.999642 | ||||||||
\(199\) | 6.88300e14 | 0.785656 | 0.392828 | − | 0.919612i | \(-0.371497\pi\) | ||||
0.392828 | + | 0.919612i | \(0.371497\pi\) | |||||||
\(200\) | −3.54796e15 | −3.91998 | ||||||||
\(201\) | 9.61835e14 | 1.02879 | ||||||||
\(202\) | 5.00904e14 | 0.518765 | ||||||||
\(203\) | −3.55097e14 | −0.356142 | ||||||||
\(204\) | −1.62111e15 | −1.57476 | ||||||||
\(205\) | 2.17688e15 | 2.04850 | ||||||||
\(206\) | 3.63978e15 | 3.31847 | ||||||||
\(207\) | −4.94522e14 | −0.436897 | ||||||||
\(208\) | 2.47993e15 | 2.12338 | ||||||||
\(209\) | 8.89460e14 | 0.738203 | ||||||||
\(210\) | 9.98922e14 | 0.803723 | ||||||||
\(211\) | 9.51142e14 | 0.742009 | 0.371005 | − | 0.928631i | \(-0.379013\pi\) | ||||
0.371005 | + | 0.928631i | \(0.379013\pi\) | |||||||
\(212\) | 1.13695e15 | 0.860122 | ||||||||
\(213\) | 1.50197e15 | 1.10203 | ||||||||
\(214\) | 3.63584e15 | 2.58771 | ||||||||
\(215\) | 3.14539e14 | 0.217182 | ||||||||
\(216\) | −5.26281e14 | −0.352588 | ||||||||
\(217\) | −2.66554e14 | −0.173299 | ||||||||
\(218\) | −3.86719e15 | −2.44021 | ||||||||
\(219\) | −2.71786e14 | −0.166471 | ||||||||
\(220\) | −1.04868e16 | −6.23583 | ||||||||
\(221\) | −4.25665e15 | −2.45764 | ||||||||
\(222\) | 6.89283e14 | 0.386459 | ||||||||
\(223\) | −1.68205e15 | −0.915919 | −0.457959 | − | 0.888973i | \(-0.651419\pi\) | ||||
−0.457959 | + | 0.888973i | \(0.651419\pi\) | |||||||
\(224\) | −1.49749e14 | −0.0792051 | ||||||||
\(225\) | 1.38803e15 | 0.713202 | ||||||||
\(226\) | −1.92662e15 | −0.961813 | ||||||||
\(227\) | −4.72938e14 | −0.229423 | −0.114711 | − | 0.993399i | \(-0.536594\pi\) | ||||
−0.114711 | + | 0.993399i | \(0.536594\pi\) | |||||||
\(228\) | 1.07870e15 | 0.508541 | ||||||||
\(229\) | −4.56797e14 | −0.209311 | −0.104656 | − | 0.994509i | \(-0.533374\pi\) | ||||
−0.104656 | + | 0.994509i | \(0.533374\pi\) | |||||||
\(230\) | −9.10461e15 | −4.05537 | ||||||||
\(231\) | 1.03021e15 | 0.446117 | ||||||||
\(232\) | 3.44436e15 | 1.45023 | ||||||||
\(233\) | −2.89061e15 | −1.18352 | −0.591760 | − | 0.806114i | \(-0.701567\pi\) | ||||
−0.591760 | + | 0.806114i | \(0.701567\pi\) | |||||||
\(234\) | −2.69899e15 | −1.07473 | ||||||||
\(235\) | −3.24156e15 | −1.25549 | ||||||||
\(236\) | 7.08086e14 | 0.266783 | ||||||||
\(237\) | −2.01936e15 | −0.740202 | ||||||||
\(238\) | 2.93205e15 | 1.04573 | ||||||||
\(239\) | 8.89025e14 | 0.308552 | 0.154276 | − | 0.988028i | \(-0.450696\pi\) | ||||
0.154276 | + | 0.988028i | \(0.450696\pi\) | |||||||
\(240\) | −3.48299e15 | −1.17647 | ||||||||
\(241\) | −1.22768e15 | −0.403623 | −0.201811 | − | 0.979424i | \(-0.564683\pi\) | ||||
−0.201811 | + | 0.979424i | \(0.564683\pi\) | |||||||
\(242\) | −1.06368e16 | −3.40418 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −6.67480e15 | −2.02491 | ||||||||
\(245\) | 4.78395e15 | 1.41321 | ||||||||
\(246\) | 4.05142e15 | 1.16555 | ||||||||
\(247\) | 2.83243e15 | 0.793649 | ||||||||
\(248\) | 2.58551e15 | 0.705683 | ||||||||
\(249\) | 7.00637e14 | 0.186293 | ||||||||
\(250\) | 1.36112e16 | 3.52603 | ||||||||
\(251\) | 3.49950e15 | 0.883338 | 0.441669 | − | 0.897178i | \(-0.354387\pi\) | ||||
0.441669 | + | 0.897178i | \(0.354387\pi\) | |||||||
\(252\) | 1.24940e15 | 0.307326 | ||||||||
\(253\) | −9.38980e15 | −2.25099 | ||||||||
\(254\) | −6.21244e15 | −1.45159 | ||||||||
\(255\) | 5.97834e15 | 1.36166 | ||||||||
\(256\) | −9.16065e15 | −2.03407 | ||||||||
\(257\) | −6.40028e14 | −0.138559 | −0.0692794 | − | 0.997597i | \(-0.522070\pi\) | ||||
−0.0692794 | + | 0.997597i | \(0.522070\pi\) | |||||||
\(258\) | 5.85392e14 | 0.123572 | ||||||||
\(259\) | −8.37830e14 | −0.172468 | ||||||||
\(260\) | −3.33944e16 | −6.70421 | ||||||||
\(261\) | −1.34750e15 | −0.263855 | ||||||||
\(262\) | 2.44354e15 | 0.466725 | ||||||||
\(263\) | 9.02734e15 | 1.68208 | 0.841042 | − | 0.540970i | \(-0.181943\pi\) | ||||
0.841042 | + | 0.540970i | \(0.181943\pi\) | |||||||
\(264\) | −9.99281e15 | −1.81661 | ||||||||
\(265\) | −4.19288e15 | −0.743728 | ||||||||
\(266\) | −1.95102e15 | −0.337701 | ||||||||
\(267\) | −1.02089e15 | −0.172447 | ||||||||
\(268\) | 2.21486e16 | 3.65149 | ||||||||
\(269\) | 6.46851e15 | 1.04091 | 0.520457 | − | 0.853888i | \(-0.325762\pi\) | ||||
0.520457 | + | 0.853888i | \(0.325762\pi\) | |||||||
\(270\) | 3.79064e15 | 0.595454 | ||||||||
\(271\) | 5.40533e15 | 0.828937 | 0.414469 | − | 0.910064i | \(-0.363967\pi\) | ||||
0.414469 | + | 0.910064i | \(0.363967\pi\) | |||||||
\(272\) | −1.02233e16 | −1.53072 | ||||||||
\(273\) | 3.28064e15 | 0.479625 | ||||||||
\(274\) | −1.85124e16 | −2.64292 | ||||||||
\(275\) | 2.63554e16 | 3.67457 | ||||||||
\(276\) | −1.13876e16 | −1.55068 | ||||||||
\(277\) | −4.86724e15 | −0.647388 | −0.323694 | − | 0.946162i | \(-0.604925\pi\) | ||||
−0.323694 | + | 0.946162i | \(0.604925\pi\) | |||||||
\(278\) | −1.40430e16 | −1.82460 | ||||||||
\(279\) | −1.01150e15 | −0.128392 | ||||||||
\(280\) | 1.17774e16 | 1.46058 | ||||||||
\(281\) | −9.80811e15 | −1.18849 | −0.594244 | − | 0.804285i | \(-0.702548\pi\) | ||||
−0.594244 | + | 0.804285i | \(0.702548\pi\) | |||||||
\(282\) | −6.03292e15 | −0.714345 | ||||||||
\(283\) | 8.07718e15 | 0.934648 | 0.467324 | − | 0.884086i | \(-0.345218\pi\) | ||||
0.467324 | + | 0.884086i | \(0.345218\pi\) | |||||||
\(284\) | 3.45866e16 | 3.91146 | ||||||||
\(285\) | −3.97806e15 | −0.439723 | ||||||||
\(286\) | −5.12473e16 | −5.53722 | ||||||||
\(287\) | −4.92455e15 | −0.520156 | ||||||||
\(288\) | −5.68259e14 | −0.0586807 | ||||||||
\(289\) | 7.64313e15 | 0.771676 | ||||||||
\(290\) | −2.48087e16 | −2.44916 | ||||||||
\(291\) | −1.16397e15 | −0.112367 | ||||||||
\(292\) | −6.25853e15 | −0.590859 | ||||||||
\(293\) | 5.49347e15 | 0.507233 | 0.253616 | − | 0.967305i | \(-0.418380\pi\) | ||||
0.253616 | + | 0.967305i | \(0.418380\pi\) | |||||||
\(294\) | 8.90347e15 | 0.804084 | ||||||||
\(295\) | −2.61129e15 | −0.230681 | ||||||||
\(296\) | 8.12675e15 | 0.702297 | ||||||||
\(297\) | 3.90938e15 | 0.330515 | ||||||||
\(298\) | −1.44606e16 | −1.19614 | ||||||||
\(299\) | −2.99012e16 | −2.42006 | ||||||||
\(300\) | 3.19628e16 | 2.53138 | ||||||||
\(301\) | −7.11549e14 | −0.0551471 | ||||||||
\(302\) | 2.29497e16 | 1.74073 | ||||||||
\(303\) | −2.31044e15 | −0.171521 | ||||||||
\(304\) | 6.80273e15 | 0.494316 | ||||||||
\(305\) | 2.46154e16 | 1.75089 | ||||||||
\(306\) | 1.11264e16 | 0.774754 | ||||||||
\(307\) | −1.51216e16 | −1.03086 | −0.515429 | − | 0.856932i | \(-0.672368\pi\) | ||||
−0.515429 | + | 0.856932i | \(0.672368\pi\) | |||||||
\(308\) | 2.37232e16 | 1.58341 | ||||||||
\(309\) | −1.67886e16 | −1.09720 | ||||||||
\(310\) | −1.86226e16 | −1.19176 | ||||||||
\(311\) | 4.47789e15 | 0.280628 | 0.140314 | − | 0.990107i | \(-0.455189\pi\) | ||||
0.140314 | + | 0.990107i | \(0.455189\pi\) | |||||||
\(312\) | −3.18215e16 | −1.95306 | ||||||||
\(313\) | −1.50670e16 | −0.905708 | −0.452854 | − | 0.891585i | \(-0.649594\pi\) | ||||
−0.452854 | + | 0.891585i | \(0.649594\pi\) | |||||||
\(314\) | 1.83117e16 | 1.07816 | ||||||||
\(315\) | −4.60757e15 | −0.265738 | ||||||||
\(316\) | −4.65008e16 | −2.62721 | ||||||||
\(317\) | 1.49652e16 | 0.828321 | 0.414160 | − | 0.910204i | \(-0.364075\pi\) | ||||
0.414160 | + | 0.910204i | \(0.364075\pi\) | |||||||
\(318\) | −7.80341e15 | −0.423164 | ||||||||
\(319\) | −2.55858e16 | −1.35944 | ||||||||
\(320\) | 2.86773e16 | 1.49301 | ||||||||
\(321\) | −1.67705e16 | −0.855583 | ||||||||
\(322\) | 2.05965e16 | 1.02974 | ||||||||
\(323\) | −1.16765e16 | −0.572130 | ||||||||
\(324\) | 4.74115e15 | 0.227689 | ||||||||
\(325\) | 8.39270e16 | 3.95057 | ||||||||
\(326\) | 4.61110e16 | 2.12760 | ||||||||
\(327\) | 1.78375e16 | 0.806816 | ||||||||
\(328\) | 4.77669e16 | 2.11810 | ||||||||
\(329\) | 7.33307e15 | 0.318796 | ||||||||
\(330\) | 7.19753e16 | 3.06791 | ||||||||
\(331\) | −5.41429e14 | −0.0226287 | −0.0113144 | − | 0.999936i | \(-0.503602\pi\) | ||||
−0.0113144 | + | 0.999936i | \(0.503602\pi\) | |||||||
\(332\) | 1.61339e16 | 0.661214 | ||||||||
\(333\) | −3.17934e15 | −0.127776 | ||||||||
\(334\) | 6.64926e16 | 2.62072 | ||||||||
\(335\) | −8.16800e16 | −3.15736 | ||||||||
\(336\) | 7.87922e15 | 0.298730 | ||||||||
\(337\) | −5.33197e15 | −0.198287 | −0.0991434 | − | 0.995073i | \(-0.531610\pi\) | ||||
−0.0991434 | + | 0.995073i | \(0.531610\pi\) | |||||||
\(338\) | −1.15325e17 | −4.20693 | ||||||||
\(339\) | 8.88659e15 | 0.318007 | ||||||||
\(340\) | 1.37666e17 | 4.83296 | ||||||||
\(341\) | −1.92060e16 | −0.661505 | ||||||||
\(342\) | −7.40361e15 | −0.250192 | ||||||||
\(343\) | −2.43913e16 | −0.808765 | ||||||||
\(344\) | 6.90186e15 | 0.224562 | ||||||||
\(345\) | 4.19953e16 | 1.34084 | ||||||||
\(346\) | 8.36322e16 | 2.62047 | ||||||||
\(347\) | 4.11371e16 | 1.26500 | 0.632502 | − | 0.774559i | \(-0.282028\pi\) | ||||
0.632502 | + | 0.774559i | \(0.282028\pi\) | |||||||
\(348\) | −3.10295e16 | −0.936504 | ||||||||
\(349\) | −5.85757e16 | −1.73521 | −0.867606 | − | 0.497253i | \(-0.834342\pi\) | ||||
−0.867606 | + | 0.497253i | \(0.834342\pi\) | |||||||
\(350\) | −5.78104e16 | −1.68098 | ||||||||
\(351\) | 1.24492e16 | 0.355340 | ||||||||
\(352\) | −1.07899e16 | −0.302336 | ||||||||
\(353\) | −4.27597e16 | −1.17625 | −0.588124 | − | 0.808771i | \(-0.700133\pi\) | ||||
−0.588124 | + | 0.808771i | \(0.700133\pi\) | |||||||
\(354\) | −4.85990e15 | −0.131252 | ||||||||
\(355\) | −1.27549e17 | −3.38215 | ||||||||
\(356\) | −2.35085e16 | −0.612069 | ||||||||
\(357\) | −1.35242e16 | −0.345755 | ||||||||
\(358\) | 1.29345e17 | 3.24720 | ||||||||
\(359\) | 2.36312e16 | 0.582603 | 0.291301 | − | 0.956631i | \(-0.405912\pi\) | ||||
0.291301 | + | 0.956631i | \(0.405912\pi\) | |||||||
\(360\) | 4.46923e16 | 1.08210 | ||||||||
\(361\) | −3.42833e16 | −0.815241 | ||||||||
\(362\) | −1.04874e16 | −0.244941 | ||||||||
\(363\) | 4.90628e16 | 1.12554 | ||||||||
\(364\) | 7.55449e16 | 1.70234 | ||||||||
\(365\) | 2.30803e16 | 0.510902 | ||||||||
\(366\) | 4.58121e16 | 0.996215 | ||||||||
\(367\) | −8.56988e15 | −0.183082 | −0.0915409 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915409 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(368\) | −7.18147e16 | −1.50731 | ||||||||
\(369\) | −1.86873e16 | −0.385368 | ||||||||
\(370\) | −5.85346e16 | −1.18605 | ||||||||
\(371\) | 9.48513e15 | 0.188848 | ||||||||
\(372\) | −2.32923e16 | −0.455704 | ||||||||
\(373\) | −5.52818e16 | −1.06286 | −0.531429 | − | 0.847103i | \(-0.678345\pi\) | ||||
−0.531429 | + | 0.847103i | \(0.678345\pi\) | |||||||
\(374\) | 2.11263e17 | 3.99170 | ||||||||
\(375\) | −6.27820e16 | −1.16582 | ||||||||
\(376\) | −7.11290e16 | −1.29815 | ||||||||
\(377\) | −8.14763e16 | −1.46155 | ||||||||
\(378\) | −8.57520e15 | −0.151198 | ||||||||
\(379\) | 5.37567e16 | 0.931704 | 0.465852 | − | 0.884863i | \(-0.345748\pi\) | ||||
0.465852 | + | 0.884863i | \(0.345748\pi\) | |||||||
\(380\) | −9.16046e16 | −1.56072 | ||||||||
\(381\) | 2.86551e16 | 0.479943 | ||||||||
\(382\) | −9.53578e16 | −1.57016 | ||||||||
\(383\) | −5.59865e16 | −0.906340 | −0.453170 | − | 0.891424i | \(-0.649707\pi\) | ||||
−0.453170 | + | 0.891424i | \(0.649707\pi\) | |||||||
\(384\) | 5.97574e16 | 0.951127 | ||||||||
\(385\) | −8.74867e16 | −1.36914 | ||||||||
\(386\) | −1.27679e17 | −1.96473 | ||||||||
\(387\) | −2.70014e15 | −0.0408569 | ||||||||
\(388\) | −2.68034e16 | −0.398826 | ||||||||
\(389\) | −7.95592e16 | −1.16417 | −0.582087 | − | 0.813126i | \(-0.697764\pi\) | ||||
−0.582087 | + | 0.813126i | \(0.697764\pi\) | |||||||
\(390\) | 2.29201e17 | 3.29834 | ||||||||
\(391\) | 1.23265e17 | 1.74459 | ||||||||
\(392\) | 1.04973e17 | 1.46123 | ||||||||
\(393\) | −1.12709e16 | −0.154315 | ||||||||
\(394\) | 7.98143e16 | 1.07487 | ||||||||
\(395\) | 1.71486e17 | 2.27169 | ||||||||
\(396\) | 9.00232e16 | 1.17310 | ||||||||
\(397\) | −5.81774e16 | −0.745789 | −0.372895 | − | 0.927874i | \(-0.621635\pi\) | ||||
−0.372895 | + | 0.927874i | \(0.621635\pi\) | |||||||
\(398\) | −1.08784e17 | −1.37191 | ||||||||
\(399\) | 8.99916e15 | 0.111655 | ||||||||
\(400\) | 2.01570e17 | 2.46057 | ||||||||
\(401\) | −5.08924e16 | −0.611244 | −0.305622 | − | 0.952153i | \(-0.598864\pi\) | ||||
−0.305622 | + | 0.952153i | \(0.598864\pi\) | |||||||
\(402\) | −1.52016e17 | −1.79647 | ||||||||
\(403\) | −6.11602e16 | −0.711191 | ||||||||
\(404\) | −5.32035e16 | −0.608782 | ||||||||
\(405\) | −1.74845e16 | −0.196877 | ||||||||
\(406\) | 5.61222e16 | 0.621893 | ||||||||
\(407\) | −6.03681e16 | −0.658331 | ||||||||
\(408\) | 1.31181e17 | 1.40793 | ||||||||
\(409\) | 8.10710e16 | 0.856375 | 0.428187 | − | 0.903690i | \(-0.359152\pi\) | ||||
0.428187 | + | 0.903690i | \(0.359152\pi\) | |||||||
\(410\) | −3.44051e17 | −3.57707 | ||||||||
\(411\) | 8.53890e16 | 0.873836 | ||||||||
\(412\) | −3.86600e17 | −3.89430 | ||||||||
\(413\) | 5.90726e15 | 0.0585748 | ||||||||
\(414\) | 7.81580e16 | 0.762907 | ||||||||
\(415\) | −5.94988e16 | −0.571736 | ||||||||
\(416\) | −3.43597e16 | −0.325044 | ||||||||
\(417\) | 6.47736e16 | 0.603273 | ||||||||
\(418\) | −1.40577e17 | −1.28905 | ||||||||
\(419\) | −1.51656e17 | −1.36920 | −0.684600 | − | 0.728919i | \(-0.740023\pi\) | ||||
−0.684600 | + | 0.728919i | \(0.740023\pi\) | |||||||
\(420\) | −1.06101e17 | −0.943186 | ||||||||
\(421\) | −1.00481e17 | −0.879531 | −0.439765 | − | 0.898113i | \(-0.644938\pi\) | ||||
−0.439765 | + | 0.898113i | \(0.644938\pi\) | |||||||
\(422\) | −1.50326e17 | −1.29569 | ||||||||
\(423\) | 2.78270e16 | 0.236186 | ||||||||
\(424\) | −9.20035e16 | −0.769000 | ||||||||
\(425\) | −3.45983e17 | −2.84791 | ||||||||
\(426\) | −2.37383e17 | −1.92437 | ||||||||
\(427\) | −5.56851e16 | −0.444588 | ||||||||
\(428\) | −3.86181e17 | −3.03673 | ||||||||
\(429\) | 2.36380e17 | 1.83079 | ||||||||
\(430\) | −4.97120e16 | −0.379242 | ||||||||
\(431\) | −1.90697e17 | −1.43298 | −0.716491 | − | 0.697596i | \(-0.754253\pi\) | ||||
−0.716491 | + | 0.697596i | \(0.754253\pi\) | |||||||
\(432\) | 2.98996e16 | 0.221320 | ||||||||
\(433\) | 1.32349e17 | 0.965047 | 0.482524 | − | 0.875883i | \(-0.339720\pi\) | ||||
0.482524 | + | 0.875883i | \(0.339720\pi\) | |||||||
\(434\) | 4.21282e16 | 0.302614 | ||||||||
\(435\) | 1.14431e17 | 0.809773 | ||||||||
\(436\) | 4.10753e17 | 2.86364 | ||||||||
\(437\) | −8.20223e16 | −0.563381 | ||||||||
\(438\) | 4.29550e16 | 0.290692 | ||||||||
\(439\) | −8.19240e16 | −0.546250 | −0.273125 | − | 0.961978i | \(-0.588057\pi\) | ||||
−0.273125 | + | 0.961978i | \(0.588057\pi\) | |||||||
\(440\) | 8.48600e17 | 5.57520 | ||||||||
\(441\) | −4.10676e16 | −0.265857 | ||||||||
\(442\) | 6.72753e17 | 4.29152 | ||||||||
\(443\) | −6.69174e16 | −0.420644 | −0.210322 | − | 0.977632i | \(-0.567451\pi\) | ||||
−0.210322 | + | 0.977632i | \(0.567451\pi\) | |||||||
\(444\) | −7.32122e16 | −0.453518 | ||||||||
\(445\) | 8.66951e16 | 0.529242 | ||||||||
\(446\) | 2.65844e17 | 1.59937 | ||||||||
\(447\) | 6.67001e16 | 0.395483 | ||||||||
\(448\) | −6.48738e16 | −0.379107 | ||||||||
\(449\) | 2.47874e17 | 1.42768 | 0.713838 | − | 0.700311i | \(-0.246955\pi\) | ||||
0.713838 | + | 0.700311i | \(0.246955\pi\) | |||||||
\(450\) | −2.19375e17 | −1.24539 | ||||||||
\(451\) | −3.54828e17 | −1.98550 | ||||||||
\(452\) | 2.04636e17 | 1.12871 | ||||||||
\(453\) | −1.05856e17 | −0.575545 | ||||||||
\(454\) | 7.47467e16 | 0.400617 | ||||||||
\(455\) | −2.78596e17 | −1.47197 | ||||||||
\(456\) | −8.72897e16 | −0.454665 | ||||||||
\(457\) | −4.08041e16 | −0.209531 | −0.104765 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104765 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(458\) | 7.21956e16 | 0.365498 | ||||||||
\(459\) | −5.13207e16 | −0.256159 | ||||||||
\(460\) | 9.67046e17 | 4.75906 | ||||||||
\(461\) | −2.20725e17 | −1.07102 | −0.535508 | − | 0.844530i | \(-0.679880\pi\) | ||||
−0.535508 | + | 0.844530i | \(0.679880\pi\) | |||||||
\(462\) | −1.62823e17 | −0.779008 | ||||||||
\(463\) | 2.05707e17 | 0.970447 | 0.485224 | − | 0.874390i | \(-0.338738\pi\) | ||||
0.485224 | + | 0.874390i | \(0.338738\pi\) | |||||||
\(464\) | −1.95684e17 | −0.910309 | ||||||||
\(465\) | 8.58976e16 | 0.394037 | ||||||||
\(466\) | 4.56853e17 | 2.06666 | ||||||||
\(467\) | −2.62262e17 | −1.16997 | −0.584987 | − | 0.811043i | \(-0.698900\pi\) | ||||
−0.584987 | + | 0.811043i | \(0.698900\pi\) | |||||||
\(468\) | 2.86673e17 | 1.26121 | ||||||||
\(469\) | 1.84776e17 | 0.801721 | ||||||||
\(470\) | 5.12321e17 | 2.19233 | ||||||||
\(471\) | −8.44632e16 | −0.356477 | ||||||||
\(472\) | −5.72990e16 | −0.238519 | ||||||||
\(473\) | −5.12692e16 | −0.210503 | ||||||||
\(474\) | 3.19155e17 | 1.29254 | ||||||||
\(475\) | 2.30221e17 | 0.919680 | ||||||||
\(476\) | −3.11428e17 | −1.22719 | ||||||||
\(477\) | 3.59935e16 | 0.139912 | ||||||||
\(478\) | −1.40508e17 | −0.538791 | ||||||||
\(479\) | −1.65029e17 | −0.624281 | −0.312140 | − | 0.950036i | \(-0.601046\pi\) | ||||
−0.312140 | + | 0.950036i | \(0.601046\pi\) | |||||||
\(480\) | 4.82571e16 | 0.180092 | ||||||||
\(481\) | −1.92238e17 | −0.707778 | ||||||||
\(482\) | 1.94032e17 | 0.704804 | ||||||||
\(483\) | −9.50019e16 | −0.340468 | ||||||||
\(484\) | 1.12979e18 | 3.99488 | ||||||||
\(485\) | 9.88458e16 | 0.344855 | ||||||||
\(486\) | −3.25406e16 | −0.112018 | ||||||||
\(487\) | 4.36977e17 | 1.48430 | 0.742148 | − | 0.670236i | \(-0.233807\pi\) | ||||
0.742148 | + | 0.670236i | \(0.233807\pi\) | |||||||
\(488\) | 5.40132e17 | 1.81038 | ||||||||
\(489\) | −2.12689e17 | −0.703456 | ||||||||
\(490\) | −7.56091e17 | −2.46774 | ||||||||
\(491\) | 4.17143e17 | 1.34356 | 0.671778 | − | 0.740753i | \(-0.265531\pi\) | ||||
0.671778 | + | 0.740753i | \(0.265531\pi\) | |||||||
\(492\) | −4.30322e17 | −1.36779 | ||||||||
\(493\) | 3.35880e17 | 1.05361 | ||||||||
\(494\) | −4.47658e17 | −1.38587 | ||||||||
\(495\) | −3.31989e17 | −1.01435 | ||||||||
\(496\) | −1.46890e17 | −0.442958 | ||||||||
\(497\) | 2.88542e17 | 0.858800 | ||||||||
\(498\) | −1.10734e17 | −0.325305 | ||||||||
\(499\) | −2.22151e17 | −0.644160 | −0.322080 | − | 0.946712i | \(-0.604382\pi\) | ||||
−0.322080 | + | 0.946712i | \(0.604382\pi\) | |||||||
\(500\) | −1.44571e18 | −4.13787 | ||||||||
\(501\) | −3.06700e17 | −0.866499 | ||||||||
\(502\) | −5.53087e17 | −1.54248 | ||||||||
\(503\) | −8.43217e16 | −0.232139 | −0.116069 | − | 0.993241i | \(-0.537029\pi\) | ||||
−0.116069 | + | 0.993241i | \(0.537029\pi\) | |||||||
\(504\) | −1.01103e17 | −0.274767 | ||||||||
\(505\) | 1.96205e17 | 0.526400 | ||||||||
\(506\) | 1.48403e18 | 3.93066 | ||||||||
\(507\) | 5.31941e17 | 1.39095 | ||||||||
\(508\) | 6.59855e17 | 1.70347 | ||||||||
\(509\) | −5.29643e17 | −1.34995 | −0.674975 | − | 0.737841i | \(-0.735846\pi\) | ||||
−0.674975 | + | 0.737841i | \(0.735846\pi\) | |||||||
\(510\) | −9.44861e17 | −2.37773 | ||||||||
\(511\) | −5.22123e16 | −0.129729 | ||||||||
\(512\) | 7.76307e17 | 1.90449 | ||||||||
\(513\) | 3.41494e16 | 0.0827219 | ||||||||
\(514\) | 1.01155e17 | 0.241951 | ||||||||
\(515\) | 1.42571e18 | 3.36731 | ||||||||
\(516\) | −6.21774e16 | −0.145014 | ||||||||
\(517\) | 5.28369e17 | 1.21688 | ||||||||
\(518\) | 1.32417e17 | 0.301162 | ||||||||
\(519\) | −3.85757e17 | −0.866414 | ||||||||
\(520\) | 2.70231e18 | 5.99396 | ||||||||
\(521\) | −6.49432e17 | −1.42262 | −0.711309 | − | 0.702879i | \(-0.751897\pi\) | ||||
−0.711309 | + | 0.702879i | \(0.751897\pi\) | |||||||
\(522\) | 2.12969e17 | 0.460742 | ||||||||
\(523\) | −2.49874e17 | −0.533899 | −0.266950 | − | 0.963710i | \(-0.586016\pi\) | ||||
−0.266950 | + | 0.963710i | \(0.586016\pi\) | |||||||
\(524\) | −2.59541e17 | −0.547712 | ||||||||
\(525\) | 2.66652e17 | 0.555789 | ||||||||
\(526\) | −1.42675e18 | −2.93725 | ||||||||
\(527\) | 2.52128e17 | 0.512687 | ||||||||
\(528\) | 5.67721e17 | 1.14029 | ||||||||
\(529\) | 3.61852e17 | 0.717908 | ||||||||
\(530\) | 6.62674e17 | 1.29869 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 2.07228e17 | 0.396299 | ||||||||
\(533\) | −1.12993e18 | −2.13463 | ||||||||
\(534\) | 1.61349e17 | 0.301127 | ||||||||
\(535\) | 1.42416e18 | 2.62579 | ||||||||
\(536\) | −1.79229e18 | −3.26465 | ||||||||
\(537\) | −5.96607e17 | −1.07363 | ||||||||
\(538\) | −1.02233e18 | −1.81764 | ||||||||
\(539\) | −7.79775e17 | −1.36975 | ||||||||
\(540\) | −4.02623e17 | −0.698778 | ||||||||
\(541\) | −4.65768e17 | −0.798707 | −0.399353 | − | 0.916797i | \(-0.630765\pi\) | ||||
−0.399353 | + | 0.916797i | \(0.630765\pi\) | |||||||
\(542\) | −8.54299e17 | −1.44749 | ||||||||
\(543\) | 4.83734e16 | 0.0809855 | ||||||||
\(544\) | 1.41645e17 | 0.234320 | ||||||||
\(545\) | −1.51478e18 | −2.47613 | ||||||||
\(546\) | −5.18498e17 | −0.837519 | ||||||||
\(547\) | −4.11476e17 | −0.656791 | −0.328395 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328395 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(548\) | 1.96629e18 | 3.10152 | ||||||||
\(549\) | −2.11310e17 | −0.329382 | ||||||||
\(550\) | −4.16541e18 | −6.41652 | ||||||||
\(551\) | −2.23498e17 | −0.340243 | ||||||||
\(552\) | 9.21496e17 | 1.38640 | ||||||||
\(553\) | −3.87936e17 | −0.576829 | ||||||||
\(554\) | 7.69256e17 | 1.13047 | ||||||||
\(555\) | 2.69993e17 | 0.392146 | ||||||||
\(556\) | 1.49157e18 | 2.14121 | ||||||||
\(557\) | 7.85547e17 | 1.11459 | 0.557293 | − | 0.830316i | \(-0.311840\pi\) | ||||
0.557293 | + | 0.830316i | \(0.311840\pi\) | |||||||
\(558\) | 1.59865e17 | 0.224198 | ||||||||
\(559\) | −1.63263e17 | −0.226314 | ||||||||
\(560\) | −6.69112e17 | −0.916804 | ||||||||
\(561\) | −9.74458e17 | −1.31979 | ||||||||
\(562\) | 1.55015e18 | 2.07533 | ||||||||
\(563\) | 2.41367e17 | 0.319429 | 0.159714 | − | 0.987163i | \(-0.448943\pi\) | ||||
0.159714 | + | 0.987163i | \(0.448943\pi\) | |||||||
\(564\) | 6.40786e17 | 0.838299 | ||||||||
\(565\) | −7.54658e17 | −0.975967 | ||||||||
\(566\) | −1.27658e18 | −1.63208 | ||||||||
\(567\) | 3.95534e16 | 0.0499912 | ||||||||
\(568\) | −2.79878e18 | −3.49708 | ||||||||
\(569\) | −4.00958e17 | −0.495300 | −0.247650 | − | 0.968850i | \(-0.579658\pi\) | ||||
−0.247650 | + | 0.968850i | \(0.579658\pi\) | |||||||
\(570\) | 6.28722e17 | 0.767843 | ||||||||
\(571\) | 1.48605e18 | 1.79432 | 0.897159 | − | 0.441708i | \(-0.145627\pi\) | ||||
0.897159 | + | 0.441708i | \(0.145627\pi\) | |||||||
\(572\) | 5.44323e18 | 6.49805 | ||||||||
\(573\) | 4.39841e17 | 0.519148 | ||||||||
\(574\) | 7.78312e17 | 0.908294 | ||||||||
\(575\) | −2.43038e18 | −2.80436 | ||||||||
\(576\) | −2.46179e17 | −0.280869 | ||||||||
\(577\) | −9.51633e16 | −0.107356 | −0.0536780 | − | 0.998558i | \(-0.517094\pi\) | ||||
−0.0536780 | + | 0.998558i | \(0.517094\pi\) | |||||||
\(578\) | −1.20798e18 | −1.34750 | ||||||||
\(579\) | 5.88926e17 | 0.649606 | ||||||||
\(580\) | 2.63506e18 | 2.87414 | ||||||||
\(581\) | 1.34598e17 | 0.145176 | ||||||||
\(582\) | 1.83963e17 | 0.196215 | ||||||||
\(583\) | 6.83431e17 | 0.720857 | ||||||||
\(584\) | 5.06447e17 | 0.528263 | ||||||||
\(585\) | −1.05720e18 | −1.09054 | ||||||||
\(586\) | −8.68229e17 | −0.885727 | ||||||||
\(587\) | 1.44895e18 | 1.46186 | 0.730931 | − | 0.682452i | \(-0.239086\pi\) | ||||
0.730931 | + | 0.682452i | \(0.239086\pi\) | |||||||
\(588\) | −9.45682e17 | −0.943610 | ||||||||
\(589\) | −1.67769e17 | −0.165563 | ||||||||
\(590\) | 4.12708e17 | 0.402814 | ||||||||
\(591\) | −3.68146e17 | −0.355387 | ||||||||
\(592\) | −4.61705e17 | −0.440832 | ||||||||
\(593\) | 3.21407e17 | 0.303529 | 0.151764 | − | 0.988417i | \(-0.451504\pi\) | ||||
0.151764 | + | 0.988417i | \(0.451504\pi\) | |||||||
\(594\) | −6.17868e17 | −0.577144 | ||||||||
\(595\) | 1.14849e18 | 1.06112 | ||||||||
\(596\) | 1.53593e18 | 1.40369 | ||||||||
\(597\) | 5.01771e17 | 0.453599 | ||||||||
\(598\) | 4.72581e18 | 4.22590 | ||||||||
\(599\) | 1.09580e18 | 0.969299 | 0.484650 | − | 0.874708i | \(-0.338947\pi\) | ||||
0.484650 | + | 0.874708i | \(0.338947\pi\) | |||||||
\(600\) | −2.58646e18 | −2.26320 | ||||||||
\(601\) | 1.71695e18 | 1.48619 | 0.743094 | − | 0.669187i | \(-0.233358\pi\) | ||||
0.743094 | + | 0.669187i | \(0.233358\pi\) | |||||||
\(602\) | 1.12459e17 | 0.0962976 | ||||||||
\(603\) | 7.01177e17 | 0.593971 | ||||||||
\(604\) | −2.43761e18 | −2.04279 | ||||||||
\(605\) | −4.16646e18 | −3.45428 | ||||||||
\(606\) | 3.65159e17 | 0.299509 | ||||||||
\(607\) | −2.14384e18 | −1.73966 | −0.869831 | − | 0.493349i | \(-0.835772\pi\) | ||||
−0.869831 | + | 0.493349i | \(0.835772\pi\) | |||||||
\(608\) | −9.42524e16 | −0.0756692 | ||||||||
\(609\) | −2.58866e17 | −0.205619 | ||||||||
\(610\) | −3.89041e18 | −3.05739 | ||||||||
\(611\) | 1.68256e18 | 1.30828 | ||||||||
\(612\) | −1.18179e18 | −0.909190 | ||||||||
\(613\) | −9.02440e17 | −0.686950 | −0.343475 | − | 0.939162i | \(-0.611604\pi\) | ||||
−0.343475 | + | 0.939162i | \(0.611604\pi\) | |||||||
\(614\) | 2.38994e18 | 1.80008 | ||||||||
\(615\) | 1.58695e18 | 1.18270 | ||||||||
\(616\) | −1.91970e18 | −1.41566 | ||||||||
\(617\) | −6.39972e17 | −0.466989 | −0.233495 | − | 0.972358i | \(-0.575016\pi\) | ||||
−0.233495 | + | 0.972358i | \(0.575016\pi\) | |||||||
\(618\) | 2.65340e18 | 1.91592 | ||||||||
\(619\) | −1.18087e18 | −0.843749 | −0.421874 | − | 0.906654i | \(-0.638628\pi\) | ||||
−0.421874 | + | 0.906654i | \(0.638628\pi\) | |||||||
\(620\) | 1.97801e18 | 1.39856 | ||||||||
\(621\) | −3.60507e17 | −0.252242 | ||||||||
\(622\) | −7.07720e17 | −0.490031 | ||||||||
\(623\) | −1.96122e17 | −0.134386 | ||||||||
\(624\) | 1.80787e18 | 1.22594 | ||||||||
\(625\) | 2.14325e18 | 1.43831 | ||||||||
\(626\) | 2.38130e18 | 1.58154 | ||||||||
\(627\) | 6.48416e17 | 0.426201 | ||||||||
\(628\) | −1.94497e18 | −1.26525 | ||||||||
\(629\) | 7.92488e17 | 0.510227 | ||||||||
\(630\) | 7.28214e17 | 0.464030 | ||||||||
\(631\) | 2.10267e17 | 0.132611 | 0.0663057 | − | 0.997799i | \(-0.478879\pi\) | ||||
0.0663057 | + | 0.997799i | \(0.478879\pi\) | |||||||
\(632\) | 3.76289e18 | 2.34888 | ||||||||
\(633\) | 6.93382e17 | 0.428399 | ||||||||
\(634\) | −2.36522e18 | −1.44641 | ||||||||
\(635\) | −2.43342e18 | −1.47295 | ||||||||
\(636\) | 8.28840e17 | 0.496592 | ||||||||
\(637\) | −2.48314e18 | −1.47264 | ||||||||
\(638\) | 4.04377e18 | 2.37384 | ||||||||
\(639\) | 1.09494e18 | 0.636259 | ||||||||
\(640\) | −5.07466e18 | −2.91902 | ||||||||
\(641\) | 3.17673e17 | 0.180885 | 0.0904425 | − | 0.995902i | \(-0.471172\pi\) | ||||
0.0904425 | + | 0.995902i | \(0.471172\pi\) | |||||||
\(642\) | 2.65053e18 | 1.49401 | ||||||||
\(643\) | −1.20752e18 | −0.673788 | −0.336894 | − | 0.941543i | \(-0.609376\pi\) | ||||
−0.336894 | + | 0.941543i | \(0.609376\pi\) | |||||||
\(644\) | −2.18765e18 | −1.20843 | ||||||||
\(645\) | 2.29299e17 | 0.125390 | ||||||||
\(646\) | 1.84544e18 | 0.999051 | ||||||||
\(647\) | 2.76485e18 | 1.48181 | 0.740906 | − | 0.671609i | \(-0.234396\pi\) | ||||
0.740906 | + | 0.671609i | \(0.234396\pi\) | |||||||
\(648\) | −3.83659e17 | −0.203567 | ||||||||
\(649\) | 4.25635e17 | 0.223587 | ||||||||
\(650\) | −1.32645e19 | −6.89847 | ||||||||
\(651\) | −1.94318e17 | −0.100054 | ||||||||
\(652\) | −4.89768e18 | −2.49679 | ||||||||
\(653\) | −7.10471e17 | −0.358600 | −0.179300 | − | 0.983794i | \(-0.557383\pi\) | ||||
−0.179300 | + | 0.983794i | \(0.557383\pi\) | |||||||
\(654\) | −2.81918e18 | −1.40886 | ||||||||
\(655\) | 9.57137e17 | 0.473594 | ||||||||
\(656\) | −2.71378e18 | −1.32953 | ||||||||
\(657\) | −1.98132e17 | −0.0961123 | ||||||||
\(658\) | −1.15897e18 | −0.556679 | ||||||||
\(659\) | 3.31791e18 | 1.57801 | 0.789004 | − | 0.614387i | \(-0.210597\pi\) | ||||
0.789004 | + | 0.614387i | \(0.210597\pi\) | |||||||
\(660\) | −7.64486e18 | −3.60026 | ||||||||
\(661\) | 1.90290e18 | 0.887372 | 0.443686 | − | 0.896182i | \(-0.353671\pi\) | ||||
0.443686 | + | 0.896182i | \(0.353671\pi\) | |||||||
\(662\) | 8.55716e16 | 0.0395142 | ||||||||
\(663\) | −3.10310e18 | −1.41892 | ||||||||
\(664\) | −1.30557e18 | −0.591164 | ||||||||
\(665\) | −7.64218e17 | −0.342670 | ||||||||
\(666\) | 5.02487e17 | 0.223122 | ||||||||
\(667\) | 2.35941e18 | 1.03750 | ||||||||
\(668\) | −7.06251e18 | −3.07548 | ||||||||
\(669\) | −1.22621e18 | −0.528806 | ||||||||
\(670\) | 1.29093e19 | 5.51337 | ||||||||
\(671\) | −4.01227e18 | −1.69705 | ||||||||
\(672\) | −1.09167e17 | −0.0457291 | ||||||||
\(673\) | 1.91544e18 | 0.794639 | 0.397319 | − | 0.917680i | \(-0.369941\pi\) | ||||
0.397319 | + | 0.917680i | \(0.369941\pi\) | |||||||
\(674\) | 8.42705e17 | 0.346247 | ||||||||
\(675\) | 1.01187e18 | 0.411768 | ||||||||
\(676\) | 1.22493e19 | 4.93692 | ||||||||
\(677\) | −3.03037e18 | −1.20968 | −0.604838 | − | 0.796348i | \(-0.706762\pi\) | ||||
−0.604838 | + | 0.796348i | \(0.706762\pi\) | |||||||
\(678\) | −1.40450e18 | −0.555303 | ||||||||
\(679\) | −2.23609e17 | −0.0875661 | ||||||||
\(680\) | −1.11401e19 | −4.32095 | ||||||||
\(681\) | −3.44772e17 | −0.132457 | ||||||||
\(682\) | 3.03546e18 | 1.15512 | ||||||||
\(683\) | 2.04409e18 | 0.770487 | 0.385243 | − | 0.922815i | \(-0.374117\pi\) | ||||
0.385243 | + | 0.922815i | \(0.374117\pi\) | |||||||
\(684\) | 7.86375e17 | 0.293606 | ||||||||
\(685\) | −7.25132e18 | −2.68181 | ||||||||
\(686\) | 3.85498e18 | 1.41226 | ||||||||
\(687\) | −3.33005e17 | −0.120846 | ||||||||
\(688\) | −3.92115e17 | −0.140958 | ||||||||
\(689\) | 2.17634e18 | 0.775001 | ||||||||
\(690\) | −6.63726e18 | −2.34137 | ||||||||
\(691\) | −6.90384e17 | −0.241259 | −0.120629 | − | 0.992698i | \(-0.538491\pi\) | ||||
−0.120629 | + | 0.992698i | \(0.538491\pi\) | |||||||
\(692\) | −8.88300e18 | −3.07518 | ||||||||
\(693\) | 7.51025e17 | 0.257566 | ||||||||
\(694\) | −6.50162e18 | −2.20894 | ||||||||
\(695\) | −5.50064e18 | −1.85145 | ||||||||
\(696\) | 2.51094e18 | 0.837289 | ||||||||
\(697\) | 4.65803e18 | 1.53883 | ||||||||
\(698\) | 9.25775e18 | 3.03002 | ||||||||
\(699\) | −2.10725e18 | −0.683306 | ||||||||
\(700\) | 6.14033e18 | 1.97267 | ||||||||
\(701\) | −1.85185e18 | −0.589438 | −0.294719 | − | 0.955584i | \(-0.595226\pi\) | ||||
−0.294719 | + | 0.955584i | \(0.595226\pi\) | |||||||
\(702\) | −1.96756e18 | −0.620493 | ||||||||
\(703\) | −5.27331e17 | −0.164768 | ||||||||
\(704\) | −4.67435e18 | −1.44710 | ||||||||
\(705\) | −2.36310e18 | −0.724858 | ||||||||
\(706\) | 6.75806e18 | 2.05396 | ||||||||
\(707\) | −4.43854e17 | −0.133664 | ||||||||
\(708\) | 5.16194e17 | 0.154027 | ||||||||
\(709\) | −3.29092e18 | −0.973008 | −0.486504 | − | 0.873678i | \(-0.661728\pi\) | ||||
−0.486504 | + | 0.873678i | \(0.661728\pi\) | |||||||
\(710\) | 2.01588e19 | 5.90590 | ||||||||
\(711\) | −1.47212e18 | −0.427356 | ||||||||
\(712\) | 1.90233e18 | 0.547226 | ||||||||
\(713\) | 1.77110e18 | 0.504847 | ||||||||
\(714\) | 2.13747e18 | 0.603755 | ||||||||
\(715\) | −2.00736e19 | −5.61871 | ||||||||
\(716\) | −1.37384e19 | −3.81066 | ||||||||
\(717\) | 6.48099e17 | 0.178142 | ||||||||
\(718\) | −3.73486e18 | −1.01734 | ||||||||
\(719\) | 1.50005e18 | 0.404918 | 0.202459 | − | 0.979291i | \(-0.435107\pi\) | ||||
0.202459 | + | 0.979291i | \(0.435107\pi\) | |||||||
\(720\) | −2.53910e18 | −0.679233 | ||||||||
\(721\) | −3.22524e18 | −0.855032 | ||||||||
\(722\) | 5.41840e18 | 1.42357 | ||||||||
\(723\) | −8.94982e17 | −0.233032 | ||||||||
\(724\) | 1.11392e18 | 0.287443 | ||||||||
\(725\) | −6.62243e18 | −1.69364 | ||||||||
\(726\) | −7.75425e18 | −1.96540 | ||||||||
\(727\) | 2.81316e18 | 0.706678 | 0.353339 | − | 0.935495i | \(-0.385046\pi\) | ||||
0.353339 | + | 0.935495i | \(0.385046\pi\) | |||||||
\(728\) | −6.11317e18 | −1.52199 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −3.64779e18 | −0.892135 | ||||||||
\(731\) | 6.73041e17 | 0.163147 | ||||||||
\(732\) | −4.86593e18 | −1.16908 | ||||||||
\(733\) | 2.45741e18 | 0.585197 | 0.292598 | − | 0.956235i | \(-0.405480\pi\) | ||||
0.292598 | + | 0.956235i | \(0.405480\pi\) | |||||||
\(734\) | 1.35445e18 | 0.319697 | ||||||||
\(735\) | 3.48750e18 | 0.815918 | ||||||||
\(736\) | 9.94998e17 | 0.230737 | ||||||||
\(737\) | 1.33137e19 | 3.06027 | ||||||||
\(738\) | 2.95349e18 | 0.672928 | ||||||||
\(739\) | −9.83537e17 | −0.222127 | −0.111064 | − | 0.993813i | \(-0.535426\pi\) | ||||
−0.111064 | + | 0.993813i | \(0.535426\pi\) | |||||||
\(740\) | 6.21726e18 | 1.39185 | ||||||||
\(741\) | 2.06484e18 | 0.458214 | ||||||||
\(742\) | −1.49910e18 | −0.329766 | ||||||||
\(743\) | 2.68518e18 | 0.585527 | 0.292763 | − | 0.956185i | \(-0.405425\pi\) | ||||
0.292763 | + | 0.956185i | \(0.405425\pi\) | |||||||
\(744\) | 1.88484e18 | 0.407426 | ||||||||
\(745\) | −5.66424e18 | −1.21374 | ||||||||
\(746\) | 8.73716e18 | 1.85596 | ||||||||
\(747\) | 5.10765e17 | 0.107557 | ||||||||
\(748\) | −2.24393e19 | −4.68435 | ||||||||
\(749\) | −3.22174e18 | −0.666744 | ||||||||
\(750\) | 9.92255e18 | 2.03575 | ||||||||
\(751\) | −4.88293e17 | −0.0993164 | −0.0496582 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496582 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(752\) | 4.04105e18 | 0.814851 | ||||||||
\(753\) | 2.55114e18 | 0.509995 | ||||||||
\(754\) | 1.28771e19 | 2.55214 | ||||||||
\(755\) | 8.98944e18 | 1.76635 | ||||||||
\(756\) | 9.10815e17 | 0.177435 | ||||||||
\(757\) | −8.86885e18 | −1.71295 | −0.856474 | − | 0.516190i | \(-0.827350\pi\) | ||||
−0.856474 | + | 0.516190i | \(0.827350\pi\) | |||||||
\(758\) | −8.49611e18 | −1.62694 | ||||||||
\(759\) | −6.84517e18 | −1.29961 | ||||||||
\(760\) | 7.41273e18 | 1.39537 | ||||||||
\(761\) | 2.82019e18 | 0.526355 | 0.263177 | − | 0.964747i | \(-0.415230\pi\) | ||||
0.263177 | + | 0.964747i | \(0.415230\pi\) | |||||||
\(762\) | −4.52887e18 | −0.838075 | ||||||||
\(763\) | 3.42674e18 | 0.628741 | ||||||||
\(764\) | 1.01284e19 | 1.84262 | ||||||||
\(765\) | 4.35821e18 | 0.786156 | ||||||||
\(766\) | 8.84853e18 | 1.58265 | ||||||||
\(767\) | 1.35541e18 | 0.240381 | ||||||||
\(768\) | −6.67812e18 | −1.17437 | ||||||||
\(769\) | −1.02421e19 | −1.78594 | −0.892969 | − | 0.450119i | \(-0.851382\pi\) | ||||
−0.892969 | + | 0.450119i | \(0.851382\pi\) | |||||||
\(770\) | 1.38271e19 | 2.39078 | ||||||||
\(771\) | −4.66581e17 | −0.0799969 | ||||||||
\(772\) | 1.35615e19 | 2.30566 | ||||||||
\(773\) | −4.56115e18 | −0.768967 | −0.384483 | − | 0.923132i | \(-0.625620\pi\) | ||||
−0.384483 | + | 0.923132i | \(0.625620\pi\) | |||||||
\(774\) | 4.26750e17 | 0.0713440 | ||||||||
\(775\) | −4.97113e18 | −0.824127 | ||||||||
\(776\) | 2.16895e18 | 0.356574 | ||||||||
\(777\) | −6.10778e17 | −0.0995743 | ||||||||
\(778\) | 1.25741e19 | 2.03287 | ||||||||
\(779\) | −3.09951e18 | −0.496935 | ||||||||
\(780\) | −2.43445e19 | −3.87068 | ||||||||
\(781\) | 2.07903e19 | 3.27815 | ||||||||
\(782\) | −1.94818e19 | −3.04639 | ||||||||
\(783\) | −9.82327e17 | −0.152337 | ||||||||
\(784\) | −5.96384e18 | −0.917216 | ||||||||
\(785\) | 7.17270e18 | 1.09403 | ||||||||
\(786\) | 1.78134e18 | 0.269464 | ||||||||
\(787\) | −7.63075e18 | −1.14481 | −0.572403 | − | 0.819973i | \(-0.693989\pi\) | ||||
−0.572403 | + | 0.819973i | \(0.693989\pi\) | |||||||
\(788\) | −8.47748e18 | −1.26138 | ||||||||
\(789\) | 6.58093e18 | 0.971151 | ||||||||
\(790\) | −2.71030e19 | −3.96681 | ||||||||
\(791\) | 1.70719e18 | 0.247819 | ||||||||
\(792\) | −7.28476e18 | −1.04882 | ||||||||
\(793\) | −1.27768e19 | −1.82451 | ||||||||
\(794\) | 9.19480e18 | 1.30229 | ||||||||
\(795\) | −3.05661e18 | −0.429391 | ||||||||
\(796\) | 1.15545e19 | 1.60996 | ||||||||
\(797\) | −3.81807e18 | −0.527673 | −0.263836 | − | 0.964567i | \(-0.584988\pi\) | ||||
−0.263836 | + | 0.964567i | \(0.584988\pi\) | |||||||
\(798\) | −1.42230e18 | −0.194971 | ||||||||
\(799\) | −6.93621e18 | −0.943122 | ||||||||
\(800\) | −2.79277e18 | −0.376661 | ||||||||
\(801\) | −7.44230e17 | −0.0995625 | ||||||||
\(802\) | 8.04342e18 | 1.06735 | ||||||||
\(803\) | −3.76205e18 | −0.495192 | ||||||||
\(804\) | 1.61463e19 | 2.10819 | ||||||||
\(805\) | 8.06766e18 | 1.04490 | ||||||||
\(806\) | 9.66622e18 | 1.24188 | ||||||||
\(807\) | 4.71554e18 | 0.600971 | ||||||||
\(808\) | 4.30528e18 | 0.544287 | ||||||||
\(809\) | 5.86792e18 | 0.735900 | 0.367950 | − | 0.929846i | \(-0.380060\pi\) | ||||
0.367950 | + | 0.929846i | \(0.380060\pi\) | |||||||
\(810\) | 2.76338e18 | 0.343786 | ||||||||
\(811\) | 8.51285e18 | 1.05061 | 0.525303 | − | 0.850915i | \(-0.323952\pi\) | ||||
0.525303 | + | 0.850915i | \(0.323952\pi\) | |||||||
\(812\) | −5.96102e18 | −0.729805 | ||||||||
\(813\) | 3.94048e18 | 0.478587 | ||||||||
\(814\) | 9.54104e18 | 1.14957 | ||||||||
\(815\) | 1.80617e19 | 2.15891 | ||||||||
\(816\) | −7.45281e18 | −0.883759 | ||||||||
\(817\) | −4.47849e17 | −0.0526852 | ||||||||
\(818\) | −1.28131e19 | −1.49540 | ||||||||
\(819\) | 2.39159e18 | 0.276912 | ||||||||
\(820\) | 3.65434e19 | 4.19777 | ||||||||
\(821\) | −1.10664e19 | −1.26118 | −0.630589 | − | 0.776117i | \(-0.717186\pi\) | ||||
−0.630589 | + | 0.776117i | \(0.717186\pi\) | |||||||
\(822\) | −1.34955e19 | −1.52589 | ||||||||
\(823\) | −1.39327e19 | −1.56292 | −0.781459 | − | 0.623956i | \(-0.785524\pi\) | ||||
−0.781459 | + | 0.623956i | \(0.785524\pi\) | |||||||
\(824\) | 3.12840e19 | 3.48173 | ||||||||
\(825\) | 1.92131e19 | 2.12152 | ||||||||
\(826\) | −9.33627e17 | −0.102283 | ||||||||
\(827\) | 7.46655e18 | 0.811585 | 0.405793 | − | 0.913965i | \(-0.366996\pi\) | ||||
0.405793 | + | 0.913965i | \(0.366996\pi\) | |||||||
\(828\) | −8.30156e18 | −0.895287 | ||||||||
\(829\) | −6.49135e18 | −0.694593 | −0.347297 | − | 0.937755i | \(-0.612900\pi\) | ||||
−0.347297 | + | 0.937755i | \(0.612900\pi\) | |||||||
\(830\) | 9.40364e18 | 0.998363 | ||||||||
\(831\) | −3.54822e18 | −0.373770 | ||||||||
\(832\) | −1.48852e19 | −1.55579 | ||||||||
\(833\) | 1.02366e19 | 1.06160 | ||||||||
\(834\) | −1.02373e19 | −1.05343 | ||||||||
\(835\) | 2.60452e19 | 2.65929 | ||||||||
\(836\) | 1.49314e19 | 1.51272 | ||||||||
\(837\) | −7.37384e17 | −0.0741273 | ||||||||
\(838\) | 2.39688e19 | 2.39089 | ||||||||
\(839\) | −1.24046e19 | −1.22780 | −0.613902 | − | 0.789382i | \(-0.710401\pi\) | ||||
−0.613902 | + | 0.789382i | \(0.710401\pi\) | |||||||
\(840\) | 8.58576e18 | 0.843264 | ||||||||
\(841\) | −3.83158e18 | −0.373425 | ||||||||
\(842\) | 1.58808e19 | 1.53583 | ||||||||
\(843\) | −7.15012e18 | −0.686173 | ||||||||
\(844\) | 1.59668e19 | 1.52052 | ||||||||
\(845\) | −4.51730e19 | −4.26884 | ||||||||
\(846\) | −4.39800e18 | −0.412427 | ||||||||
\(847\) | 9.42537e18 | 0.877114 | ||||||||
\(848\) | 5.22699e18 | 0.482701 | ||||||||
\(849\) | 5.88827e18 | 0.539619 | ||||||||
\(850\) | 5.46817e19 | 4.97301 | ||||||||
\(851\) | 5.56690e18 | 0.502425 | ||||||||
\(852\) | 2.52137e19 | 2.25828 | ||||||||
\(853\) | 7.66178e18 | 0.681022 | 0.340511 | − | 0.940241i | \(-0.389400\pi\) | ||||
0.340511 | + | 0.940241i | \(0.389400\pi\) | |||||||
\(854\) | 8.80088e18 | 0.776337 | ||||||||
\(855\) | −2.90000e18 | −0.253874 | ||||||||
\(856\) | 3.12501e19 | 2.71502 | ||||||||
\(857\) | −2.80801e17 | −0.0242116 | −0.0121058 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121058 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(858\) | −3.73593e19 | −3.19692 | ||||||||
\(859\) | −5.71016e18 | −0.484945 | −0.242473 | − | 0.970158i | \(-0.577958\pi\) | ||||
−0.242473 | + | 0.970158i | \(0.577958\pi\) | |||||||
\(860\) | 5.28017e18 | 0.445049 | ||||||||
\(861\) | −3.58999e18 | −0.300312 | ||||||||
\(862\) | 3.01391e19 | 2.50227 | ||||||||
\(863\) | −1.12092e19 | −0.923643 | −0.461821 | − | 0.886973i | \(-0.652804\pi\) | ||||
−0.461821 | + | 0.886973i | \(0.652804\pi\) | |||||||
\(864\) | −4.14261e17 | −0.0338793 | ||||||||
\(865\) | 3.27589e19 | 2.65903 | ||||||||
\(866\) | −2.09174e19 | −1.68516 | ||||||||
\(867\) | 5.57184e18 | 0.445528 | ||||||||
\(868\) | −4.47464e18 | −0.355124 | ||||||||
\(869\) | −2.79520e19 | −2.20183 | ||||||||
\(870\) | −1.80855e19 | −1.41402 | ||||||||
\(871\) | 4.23966e19 | 3.29013 | ||||||||
\(872\) | −3.32386e19 | −2.56027 | ||||||||
\(873\) | −8.48537e17 | −0.0648751 | ||||||||
\(874\) | 1.29634e19 | 0.983774 | ||||||||
\(875\) | −1.20610e19 | −0.908509 | ||||||||
\(876\) | −4.56247e18 | −0.341133 | ||||||||
\(877\) | −8.32918e18 | −0.618166 | −0.309083 | − | 0.951035i | \(-0.600022\pi\) | ||||
−0.309083 | + | 0.951035i | \(0.600022\pi\) | |||||||
\(878\) | 1.29479e19 | 0.953860 | ||||||||
\(879\) | 4.00474e18 | 0.292851 | ||||||||
\(880\) | −4.82115e19 | −3.49956 | ||||||||
\(881\) | 1.31768e19 | 0.949441 | 0.474720 | − | 0.880137i | \(-0.342549\pi\) | ||||
0.474720 | + | 0.880137i | \(0.342549\pi\) | |||||||
\(882\) | 6.49063e18 | 0.464238 | ||||||||
\(883\) | −1.76135e19 | −1.25055 | −0.625273 | − | 0.780406i | \(-0.715013\pi\) | ||||
−0.625273 | + | 0.780406i | \(0.715013\pi\) | |||||||
\(884\) | −7.14565e19 | −5.03619 | ||||||||
\(885\) | −1.90363e18 | −0.133184 | ||||||||
\(886\) | 1.05761e19 | 0.734527 | ||||||||
\(887\) | −3.24303e18 | −0.223587 | −0.111794 | − | 0.993731i | \(-0.535660\pi\) | ||||
−0.111794 | + | 0.993731i | \(0.535660\pi\) | |||||||
\(888\) | 5.92440e18 | 0.405472 | ||||||||
\(889\) | 5.50489e18 | 0.374013 | ||||||||
\(890\) | −1.37019e19 | −0.924160 | ||||||||
\(891\) | 2.84994e18 | 0.190823 | ||||||||
\(892\) | −2.82366e19 | −1.87690 | ||||||||
\(893\) | 4.61544e18 | 0.304564 | ||||||||
\(894\) | −1.05418e19 | −0.690590 | ||||||||
\(895\) | 5.06645e19 | 3.29499 | ||||||||
\(896\) | 1.14799e19 | 0.741200 | ||||||||
\(897\) | −2.17980e19 | −1.39722 | ||||||||
\(898\) | −3.91758e19 | −2.49300 | ||||||||
\(899\) | 4.82597e18 | 0.304892 | ||||||||
\(900\) | 2.33009e19 | 1.46149 | ||||||||
\(901\) | −8.97180e18 | −0.558687 | ||||||||
\(902\) | 5.60797e19 | 3.46707 | ||||||||
\(903\) | −5.18719e17 | −0.0318392 | ||||||||
\(904\) | −1.65593e19 | −1.00913 | ||||||||
\(905\) | −4.10792e18 | −0.248545 | ||||||||
\(906\) | 1.67303e19 | 1.00501 | ||||||||
\(907\) | −2.96509e19 | −1.76844 | −0.884220 | − | 0.467071i | \(-0.845309\pi\) | ||||
−0.884220 | + | 0.467071i | \(0.845309\pi\) | |||||||
\(908\) | −7.93922e18 | −0.470132 | ||||||||
\(909\) | −1.68431e18 | −0.0990277 | ||||||||
\(910\) | 4.40313e19 | 2.57035 | ||||||||
\(911\) | 1.95371e19 | 1.13238 | 0.566188 | − | 0.824276i | \(-0.308417\pi\) | ||||
0.566188 | + | 0.824276i | \(0.308417\pi\) | |||||||
\(912\) | 4.95919e18 | 0.285394 | ||||||||
\(913\) | 9.69820e18 | 0.554155 | ||||||||
\(914\) | 6.44898e18 | 0.365882 | ||||||||
\(915\) | 1.79447e19 | 1.01088 | ||||||||
\(916\) | −7.66825e18 | −0.428920 | ||||||||
\(917\) | −2.16524e18 | −0.120255 | ||||||||
\(918\) | 8.11111e18 | 0.447304 | ||||||||
\(919\) | 7.82954e18 | 0.428731 | 0.214366 | − | 0.976753i | \(-0.431232\pi\) | ||||
0.214366 | + | 0.976753i | \(0.431232\pi\) | |||||||
\(920\) | −7.82543e19 | −4.25488 | ||||||||
\(921\) | −1.10237e19 | −0.595167 | ||||||||
\(922\) | 3.48851e19 | 1.87020 | ||||||||
\(923\) | 6.62053e19 | 3.52437 | ||||||||
\(924\) | 1.72942e19 | 0.914182 | ||||||||
\(925\) | −1.56252e19 | −0.820173 | ||||||||
\(926\) | −3.25114e19 | −1.69459 | ||||||||
\(927\) | −1.22389e19 | −0.633468 | ||||||||
\(928\) | 2.71122e18 | 0.139349 | ||||||||
\(929\) | −3.21185e19 | −1.63928 | −0.819641 | − | 0.572878i | \(-0.805827\pi\) | ||||
−0.819641 | + | 0.572878i | \(0.805827\pi\) | |||||||
\(930\) | −1.35759e19 | −0.688066 | ||||||||
\(931\) | −6.81153e18 | −0.342824 | ||||||||
\(932\) | −4.85247e19 | −2.42527 | ||||||||
\(933\) | 3.26438e18 | 0.162021 | ||||||||
\(934\) | 4.14499e19 | 2.04300 | ||||||||
\(935\) | 8.27520e19 | 4.05045 | ||||||||
\(936\) | −2.31978e19 | −1.12760 | ||||||||
\(937\) | −3.54137e19 | −1.70948 | −0.854739 | − | 0.519058i | \(-0.826283\pi\) | ||||
−0.854739 | + | 0.519058i | \(0.826283\pi\) | |||||||
\(938\) | −2.92035e19 | −1.39996 | ||||||||
\(939\) | −1.09838e19 | −0.522911 | ||||||||
\(940\) | −5.44162e19 | −2.57275 | ||||||||
\(941\) | 3.06493e19 | 1.43909 | 0.719545 | − | 0.694446i | \(-0.244351\pi\) | ||||
0.719545 | + | 0.694446i | \(0.244351\pi\) | |||||||
\(942\) | 1.33492e19 | 0.622479 | ||||||||
\(943\) | 3.27208e19 | 1.51530 | ||||||||
\(944\) | 3.25532e18 | 0.149719 | ||||||||
\(945\) | −3.35892e18 | −0.153424 | ||||||||
\(946\) | 8.10297e18 | 0.367580 | ||||||||
\(947\) | −1.06457e18 | −0.0479622 | −0.0239811 | − | 0.999712i | \(-0.507634\pi\) | ||||
−0.0239811 | + | 0.999712i | \(0.507634\pi\) | |||||||
\(948\) | −3.38991e19 | −1.51682 | ||||||||
\(949\) | −1.19800e19 | −0.532386 | ||||||||
\(950\) | −3.63859e19 | −1.60594 | ||||||||
\(951\) | 1.09097e19 | 0.478231 | ||||||||
\(952\) | 2.52011e19 | 1.09718 | ||||||||
\(953\) | −3.39355e19 | −1.46740 | −0.733702 | − | 0.679471i | \(-0.762209\pi\) | ||||
−0.733702 | + | 0.679471i | \(0.762209\pi\) | |||||||
\(954\) | −5.68869e18 | −0.244314 | ||||||||
\(955\) | −3.73518e19 | −1.59327 | ||||||||
\(956\) | 1.49241e19 | 0.632283 | ||||||||
\(957\) | −1.86520e19 | −0.784872 | ||||||||
\(958\) | 2.60825e19 | 1.09012 | ||||||||
\(959\) | 1.64039e19 | 0.680969 | ||||||||
\(960\) | 2.09057e19 | 0.861991 | ||||||||
\(961\) | −2.07949e19 | −0.851639 | ||||||||
\(962\) | 3.03828e19 | 1.23592 | ||||||||
\(963\) | −1.22257e19 | −0.493971 | ||||||||
\(964\) | −2.06092e19 | −0.827103 | ||||||||
\(965\) | −5.00122e19 | −1.99365 | ||||||||
\(966\) | 1.50148e19 | 0.594523 | ||||||||
\(967\) | −7.03476e18 | −0.276680 | −0.138340 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138340 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(968\) | −9.14238e19 | −3.57166 | ||||||||
\(969\) | −8.51214e18 | −0.330319 | ||||||||
\(970\) | −1.56223e19 | −0.602185 | ||||||||
\(971\) | 4.79224e19 | 1.83491 | 0.917453 | − | 0.397844i | \(-0.130241\pi\) | ||||
0.917453 | + | 0.397844i | \(0.130241\pi\) | |||||||
\(972\) | 3.45630e18 | 0.131456 | ||||||||
\(973\) | 1.24436e19 | 0.470123 | ||||||||
\(974\) | −6.90631e19 | −2.59187 | ||||||||
\(975\) | 6.11828e19 | 2.28086 | ||||||||
\(976\) | −3.06865e19 | −1.13638 | ||||||||
\(977\) | −4.27332e19 | −1.57199 | −0.785997 | − | 0.618230i | \(-0.787850\pi\) | ||||
−0.785997 | + | 0.618230i | \(0.787850\pi\) | |||||||
\(978\) | 3.36149e19 | 1.22837 | ||||||||
\(979\) | −1.41311e19 | −0.512968 | ||||||||
\(980\) | 8.03083e19 | 2.89595 | ||||||||
\(981\) | 1.30036e19 | 0.465816 | ||||||||
\(982\) | −6.59285e19 | −2.34611 | ||||||||
\(983\) | −1.24401e19 | −0.439771 | −0.219885 | − | 0.975526i | \(-0.570568\pi\) | ||||
−0.219885 | + | 0.975526i | \(0.570568\pi\) | |||||||
\(984\) | 3.48221e19 | 1.22289 | ||||||||
\(985\) | 3.12634e19 | 1.09069 | ||||||||
\(986\) | −5.30849e19 | −1.83980 | ||||||||
\(987\) | 5.34581e18 | 0.184057 | ||||||||
\(988\) | 4.75480e19 | 1.62634 | ||||||||
\(989\) | 4.72783e18 | 0.160652 | ||||||||
\(990\) | 5.24700e19 | 1.77126 | ||||||||
\(991\) | 1.82236e19 | 0.611159 | 0.305580 | − | 0.952167i | \(-0.401150\pi\) | ||||
0.305580 | + | 0.952167i | \(0.401150\pi\) | |||||||
\(992\) | 2.03518e18 | 0.0678073 | ||||||||
\(993\) | −3.94702e17 | −0.0130647 | ||||||||
\(994\) | −4.56033e19 | −1.49963 | ||||||||
\(995\) | −4.26109e19 | −1.39210 | ||||||||
\(996\) | 1.17616e19 | 0.381752 | ||||||||
\(997\) | 4.36946e18 | 0.140899 | 0.0704497 | − | 0.997515i | \(-0.477557\pi\) | ||||
0.0704497 | + | 0.997515i | \(0.477557\pi\) | |||||||
\(998\) | 3.51104e19 | 1.12483 | ||||||||
\(999\) | −2.31774e18 | −0.0737716 |
(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 | 177.14.a.a.1.2 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.2 | ✓ | 30 | 1.1 | even | 1 | trivial |