Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,8,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(13.4325560958\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + 193428526 x^{6} + 11160446785 x^{5} + \cdots + 1551032970660 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(7.08185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.08185 | 0.714342 | 0.357171 | − | 0.934039i | \(-0.383741\pi\) | ||||
0.357171 | + | 0.934039i | \(0.383741\pi\) | |||||||
\(3\) | −1.19690 | −0.0255938 | −0.0127969 | − | 0.999918i | \(-0.504073\pi\) | ||||
−0.0127969 | + | 0.999918i | \(0.504073\pi\) | |||||||
\(4\) | −62.6836 | −0.489716 | ||||||||
\(5\) | 164.718 | 0.589314 | 0.294657 | − | 0.955603i | \(-0.404795\pi\) | ||||
0.294657 | + | 0.955603i | \(0.404795\pi\) | |||||||
\(6\) | −9.67319 | −0.0182827 | ||||||||
\(7\) | 1314.61 | 1.44862 | 0.724308 | − | 0.689476i | \(-0.242159\pi\) | ||||
0.724308 | + | 0.689476i | \(0.242159\pi\) | |||||||
\(8\) | −1541.08 | −1.06417 | ||||||||
\(9\) | −2185.57 | −0.999345 | ||||||||
\(10\) | 1331.23 | 0.420972 | ||||||||
\(11\) | 8636.39 | 1.95640 | 0.978201 | − | 0.207662i | \(-0.0665854\pi\) | ||||
0.978201 | + | 0.207662i | \(0.0665854\pi\) | |||||||
\(12\) | 75.0263 | 0.0125337 | ||||||||
\(13\) | 8425.12 | 1.06359 | 0.531795 | − | 0.846873i | \(-0.321518\pi\) | ||||
0.531795 | + | 0.846873i | \(0.321518\pi\) | |||||||
\(14\) | 10624.5 | 1.03481 | ||||||||
\(15\) | −197.152 | −0.0150828 | ||||||||
\(16\) | −4431.25 | −0.270462 | ||||||||
\(17\) | 6309.90 | 0.311495 | 0.155748 | − | 0.987797i | \(-0.450221\pi\) | ||||
0.155748 | + | 0.987797i | \(0.450221\pi\) | |||||||
\(18\) | −17663.4 | −0.713874 | ||||||||
\(19\) | 16664.4 | 0.557382 | 0.278691 | − | 0.960381i | \(-0.410099\pi\) | ||||
0.278691 | + | 0.960381i | \(0.410099\pi\) | |||||||
\(20\) | −10325.1 | −0.288597 | ||||||||
\(21\) | −1573.46 | −0.0370756 | ||||||||
\(22\) | 69798.0 | 1.39754 | ||||||||
\(23\) | 44105.5 | 0.755867 | 0.377933 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377933 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(24\) | 1844.52 | 0.0272360 | ||||||||
\(25\) | −50992.9 | −0.652709 | ||||||||
\(26\) | 68090.6 | 0.759767 | ||||||||
\(27\) | 5233.54 | 0.0511708 | ||||||||
\(28\) | −82404.5 | −0.709411 | ||||||||
\(29\) | −23876.9 | −0.181796 | −0.0908981 | − | 0.995860i | \(-0.528974\pi\) | ||||
−0.0908981 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(30\) | −1593.35 | −0.0107743 | ||||||||
\(31\) | 27160.3 | 0.163745 | 0.0818725 | − | 0.996643i | \(-0.473910\pi\) | ||||
0.0818725 | + | 0.996643i | \(0.473910\pi\) | |||||||
\(32\) | 161445. | 0.870964 | ||||||||
\(33\) | −10336.9 | −0.0500717 | ||||||||
\(34\) | 50995.7 | 0.222514 | ||||||||
\(35\) | 216540. | 0.853690 | ||||||||
\(36\) | 136999. | 0.489395 | ||||||||
\(37\) | −114297. | −0.370961 | −0.185481 | − | 0.982648i | \(-0.559384\pi\) | ||||
−0.185481 | + | 0.982648i | \(0.559384\pi\) | |||||||
\(38\) | 134680. | 0.398161 | ||||||||
\(39\) | −10084.1 | −0.0272213 | ||||||||
\(40\) | −253844. | −0.627128 | ||||||||
\(41\) | −792610. | −1.79604 | −0.898020 | − | 0.439954i | \(-0.854995\pi\) | ||||
−0.898020 | + | 0.439954i | \(0.854995\pi\) | |||||||
\(42\) | −12716.5 | −0.0264846 | ||||||||
\(43\) | −79507.0 | −0.152499 | ||||||||
\(44\) | −541361. | −0.958081 | ||||||||
\(45\) | −360003. | −0.588928 | ||||||||
\(46\) | 356454. | 0.539947 | ||||||||
\(47\) | 490927. | 0.689722 | 0.344861 | − | 0.938654i | \(-0.387926\pi\) | ||||
0.344861 | + | 0.938654i | \(0.387926\pi\) | |||||||
\(48\) | 5303.78 | 0.00692215 | ||||||||
\(49\) | 904653. | 1.09849 | ||||||||
\(50\) | −412117. | −0.466257 | ||||||||
\(51\) | −7552.34 | −0.00797234 | ||||||||
\(52\) | −528117. | −0.520857 | ||||||||
\(53\) | −1.64370e6 | −1.51655 | −0.758275 | − | 0.651935i | \(-0.773958\pi\) | ||||
−0.758275 | + | 0.651935i | \(0.773958\pi\) | |||||||
\(54\) | 42296.7 | 0.0365534 | ||||||||
\(55\) | 1.42257e6 | 1.15293 | ||||||||
\(56\) | −2.02591e6 | −1.54157 | ||||||||
\(57\) | −19945.7 | −0.0142655 | ||||||||
\(58\) | −192970. | −0.129865 | ||||||||
\(59\) | −625984. | −0.396809 | −0.198404 | − | 0.980120i | \(-0.563576\pi\) | ||||
−0.198404 | + | 0.980120i | \(0.563576\pi\) | |||||||
\(60\) | 12358.2 | 0.00738628 | ||||||||
\(61\) | −1.22257e6 | −0.689635 | −0.344817 | − | 0.938670i | \(-0.612059\pi\) | ||||
−0.344817 | + | 0.938670i | \(0.612059\pi\) | |||||||
\(62\) | 219505. | 0.116970 | ||||||||
\(63\) | −2.87317e6 | −1.44767 | ||||||||
\(64\) | 1.87198e6 | 0.892628 | ||||||||
\(65\) | 1.38777e6 | 0.626789 | ||||||||
\(66\) | −83541.5 | −0.0357683 | ||||||||
\(67\) | 1.75201e6 | 0.711665 | 0.355833 | − | 0.934550i | \(-0.384197\pi\) | ||||
0.355833 | + | 0.934550i | \(0.384197\pi\) | |||||||
\(68\) | −395528. | −0.152544 | ||||||||
\(69\) | −52790.0 | −0.0193455 | ||||||||
\(70\) | 1.75005e6 | 0.609826 | ||||||||
\(71\) | 1.15151e6 | 0.381823 | 0.190911 | − | 0.981607i | \(-0.438856\pi\) | ||||
0.190911 | + | 0.981607i | \(0.438856\pi\) | |||||||
\(72\) | 3.36813e6 | 1.06347 | ||||||||
\(73\) | 2.26726e6 | 0.682137 | 0.341068 | − | 0.940038i | \(-0.389211\pi\) | ||||
0.341068 | + | 0.940038i | \(0.389211\pi\) | |||||||
\(74\) | −923731. | −0.264993 | ||||||||
\(75\) | 61033.5 | 0.0167053 | ||||||||
\(76\) | −1.04459e6 | −0.272959 | ||||||||
\(77\) | 1.13535e7 | 2.83407 | ||||||||
\(78\) | −81497.8 | −0.0194453 | ||||||||
\(79\) | 4.91491e6 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(80\) | −729909. | −0.159387 | ||||||||
\(81\) | 4.77357e6 | 0.998035 | ||||||||
\(82\) | −6.40576e6 | −1.28299 | ||||||||
\(83\) | −9.34319e6 | −1.79358 | −0.896792 | − | 0.442452i | \(-0.854109\pi\) | ||||
−0.896792 | + | 0.442452i | \(0.854109\pi\) | |||||||
\(84\) | 98630.2 | 0.0181565 | ||||||||
\(85\) | 1.03936e6 | 0.183569 | ||||||||
\(86\) | −642564. | −0.108936 | ||||||||
\(87\) | 28578.3 | 0.00465286 | ||||||||
\(88\) | −1.33093e7 | −2.08194 | ||||||||
\(89\) | 9.44626e6 | 1.42035 | 0.710174 | − | 0.704026i | \(-0.248616\pi\) | ||||
0.710174 | + | 0.704026i | \(0.248616\pi\) | |||||||
\(90\) | −2.90949e6 | −0.420696 | ||||||||
\(91\) | 1.10757e7 | 1.54073 | ||||||||
\(92\) | −2.76469e6 | −0.370160 | ||||||||
\(93\) | −32508.2 | −0.00419086 | ||||||||
\(94\) | 3.96760e6 | 0.492697 | ||||||||
\(95\) | 2.74494e6 | 0.328473 | ||||||||
\(96\) | −193234. | −0.0222913 | ||||||||
\(97\) | −6.08401e6 | −0.676845 | −0.338422 | − | 0.940994i | \(-0.609893\pi\) | ||||
−0.338422 | + | 0.940994i | \(0.609893\pi\) | |||||||
\(98\) | 7.31127e6 | 0.784697 | ||||||||
\(99\) | −1.88754e7 | −1.95512 | ||||||||
\(100\) | 3.19642e6 | 0.319642 | ||||||||
\(101\) | 8.43016e6 | 0.814163 | 0.407081 | − | 0.913392i | \(-0.366547\pi\) | ||||
0.407081 | + | 0.913392i | \(0.366547\pi\) | |||||||
\(102\) | −61036.9 | −0.00569498 | ||||||||
\(103\) | −1.11690e7 | −1.00712 | −0.503561 | − | 0.863959i | \(-0.667977\pi\) | ||||
−0.503561 | + | 0.863959i | \(0.667977\pi\) | |||||||
\(104\) | −1.29838e7 | −1.13184 | ||||||||
\(105\) | −259178. | −0.0218492 | ||||||||
\(106\) | −1.32841e7 | −1.08333 | ||||||||
\(107\) | 9.97447e6 | 0.787131 | 0.393565 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393565 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(108\) | −328057. | −0.0250592 | ||||||||
\(109\) | −1.68276e7 | −1.24460 | −0.622301 | − | 0.782778i | \(-0.713802\pi\) | ||||
−0.622301 | + | 0.782778i | \(0.713802\pi\) | |||||||
\(110\) | 1.14970e7 | 0.823589 | ||||||||
\(111\) | 136802. | 0.00949430 | ||||||||
\(112\) | −5.82536e6 | −0.391796 | ||||||||
\(113\) | −1.00006e7 | −0.652006 | −0.326003 | − | 0.945369i | \(-0.605702\pi\) | ||||
−0.326003 | + | 0.945369i | \(0.605702\pi\) | |||||||
\(114\) | −161198. | −0.0101905 | ||||||||
\(115\) | 7.26498e6 | 0.445443 | ||||||||
\(116\) | 1.49669e6 | 0.0890285 | ||||||||
\(117\) | −1.84137e7 | −1.06289 | ||||||||
\(118\) | −5.05911e6 | −0.283457 | ||||||||
\(119\) | 8.29505e6 | 0.451237 | ||||||||
\(120\) | 303826. | 0.0160506 | ||||||||
\(121\) | 5.51001e7 | 2.82751 | ||||||||
\(122\) | −9.88063e6 | −0.492635 | ||||||||
\(123\) | 948677. | 0.0459675 | ||||||||
\(124\) | −1.70250e6 | −0.0801886 | ||||||||
\(125\) | −2.12681e7 | −0.973965 | ||||||||
\(126\) | −2.32205e7 | −1.03413 | ||||||||
\(127\) | 1.37203e7 | 0.594362 | 0.297181 | − | 0.954821i | \(-0.403954\pi\) | ||||
0.297181 | + | 0.954821i | \(0.403954\pi\) | |||||||
\(128\) | −5.53594e6 | −0.233322 | ||||||||
\(129\) | 95162.2 | 0.00390302 | ||||||||
\(130\) | 1.12158e7 | 0.447741 | ||||||||
\(131\) | −2.22841e7 | −0.866054 | −0.433027 | − | 0.901381i | \(-0.642554\pi\) | ||||
−0.433027 | + | 0.901381i | \(0.642554\pi\) | |||||||
\(132\) | 647956. | 0.0245209 | ||||||||
\(133\) | 2.19072e7 | 0.807433 | ||||||||
\(134\) | 1.41595e7 | 0.508372 | ||||||||
\(135\) | 862060. | 0.0301557 | ||||||||
\(136\) | −9.72405e6 | −0.331483 | ||||||||
\(137\) | −1.65210e6 | −0.0548928 | −0.0274464 | − | 0.999623i | \(-0.508738\pi\) | ||||
−0.0274464 | + | 0.999623i | \(0.508738\pi\) | |||||||
\(138\) | −426641. | −0.0138193 | ||||||||
\(139\) | 167822. | 0.00530027 | 0.00265014 | − | 0.999996i | \(-0.499156\pi\) | ||||
0.00265014 | + | 0.999996i | \(0.499156\pi\) | |||||||
\(140\) | −1.35735e7 | −0.418066 | ||||||||
\(141\) | −587592. | −0.0176526 | ||||||||
\(142\) | 9.30630e6 | 0.272752 | ||||||||
\(143\) | 7.27626e7 | 2.08081 | ||||||||
\(144\) | 9.68480e6 | 0.270285 | ||||||||
\(145\) | −3.93296e6 | −0.107135 | ||||||||
\(146\) | 1.83237e7 | 0.487279 | ||||||||
\(147\) | −1.08278e6 | −0.0281145 | ||||||||
\(148\) | 7.16455e6 | 0.181666 | ||||||||
\(149\) | −3.24074e7 | −0.802587 | −0.401294 | − | 0.915949i | \(-0.631439\pi\) | ||||
−0.401294 | + | 0.915949i | \(0.631439\pi\) | |||||||
\(150\) | 493264. | 0.0119333 | ||||||||
\(151\) | −2.03174e7 | −0.480229 | −0.240114 | − | 0.970745i | \(-0.577185\pi\) | ||||
−0.240114 | + | 0.970745i | \(0.577185\pi\) | |||||||
\(152\) | −2.56812e7 | −0.593147 | ||||||||
\(153\) | −1.37907e7 | −0.311291 | ||||||||
\(154\) | 9.17571e7 | 2.02450 | ||||||||
\(155\) | 4.47379e6 | 0.0964973 | ||||||||
\(156\) | 632105. | 0.0133307 | ||||||||
\(157\) | −7.75567e7 | −1.59945 | −0.799725 | − | 0.600366i | \(-0.795022\pi\) | ||||
−0.799725 | + | 0.600366i | \(0.795022\pi\) | |||||||
\(158\) | 3.97216e7 | 0.801174 | ||||||||
\(159\) | 1.96735e6 | 0.0388143 | ||||||||
\(160\) | 2.65930e7 | 0.513271 | ||||||||
\(161\) | 5.79814e7 | 1.09496 | ||||||||
\(162\) | 3.85793e7 | 0.712938 | ||||||||
\(163\) | −8.55135e7 | −1.54660 | −0.773300 | − | 0.634040i | \(-0.781395\pi\) | ||||
−0.773300 | + | 0.634040i | \(0.781395\pi\) | |||||||
\(164\) | 4.96837e7 | 0.879550 | ||||||||
\(165\) | −1.70268e6 | −0.0295080 | ||||||||
\(166\) | −7.55103e7 | −1.28123 | ||||||||
\(167\) | −5.30786e7 | −0.881885 | −0.440942 | − | 0.897535i | \(-0.645356\pi\) | ||||
−0.440942 | + | 0.897535i | \(0.645356\pi\) | |||||||
\(168\) | 2.42482e6 | 0.0394546 | ||||||||
\(169\) | 8.23412e6 | 0.131224 | ||||||||
\(170\) | 8.39993e6 | 0.131131 | ||||||||
\(171\) | −3.64213e7 | −0.557017 | ||||||||
\(172\) | 4.98379e6 | 0.0746810 | ||||||||
\(173\) | 7.43872e7 | 1.09229 | 0.546144 | − | 0.837691i | \(-0.316095\pi\) | ||||
0.546144 | + | 0.837691i | \(0.316095\pi\) | |||||||
\(174\) | 230966. | 0.00332373 | ||||||||
\(175\) | −6.70357e7 | −0.945525 | ||||||||
\(176\) | −3.82700e7 | −0.529133 | ||||||||
\(177\) | 749243. | 0.0101558 | ||||||||
\(178\) | 7.63433e7 | 1.01461 | ||||||||
\(179\) | 1.45355e8 | 1.89428 | 0.947139 | − | 0.320824i | \(-0.103960\pi\) | ||||
0.947139 | + | 0.320824i | \(0.103960\pi\) | |||||||
\(180\) | 2.25663e7 | 0.288408 | ||||||||
\(181\) | −4.70208e7 | −0.589406 | −0.294703 | − | 0.955589i | \(-0.595221\pi\) | ||||
−0.294703 | + | 0.955589i | \(0.595221\pi\) | |||||||
\(182\) | 8.95125e7 | 1.10061 | ||||||||
\(183\) | 1.46330e6 | 0.0176504 | ||||||||
\(184\) | −6.79699e7 | −0.804368 | ||||||||
\(185\) | −1.88268e7 | −0.218613 | ||||||||
\(186\) | −262727. | −0.00299370 | ||||||||
\(187\) | 5.44948e7 | 0.609410 | ||||||||
\(188\) | −3.07731e7 | −0.337768 | ||||||||
\(189\) | 6.88006e6 | 0.0741269 | ||||||||
\(190\) | 2.21842e7 | 0.234642 | ||||||||
\(191\) | −6.43802e7 | −0.668552 | −0.334276 | − | 0.942475i | \(-0.608492\pi\) | ||||
−0.334276 | + | 0.942475i | \(0.608492\pi\) | |||||||
\(192\) | −2.24057e6 | −0.0228457 | ||||||||
\(193\) | −1.29604e8 | −1.29768 | −0.648842 | − | 0.760923i | \(-0.724746\pi\) | ||||
−0.648842 | + | 0.760923i | \(0.724746\pi\) | |||||||
\(194\) | −4.91701e7 | −0.483499 | ||||||||
\(195\) | −1.66103e6 | −0.0160419 | ||||||||
\(196\) | −5.67070e7 | −0.537948 | ||||||||
\(197\) | 8.33653e7 | 0.776879 | 0.388440 | − | 0.921474i | \(-0.373014\pi\) | ||||
0.388440 | + | 0.921474i | \(0.373014\pi\) | |||||||
\(198\) | −1.52548e8 | −1.39662 | ||||||||
\(199\) | −1.89130e8 | −1.70127 | −0.850636 | − | 0.525755i | \(-0.823783\pi\) | ||||
−0.850636 | + | 0.525755i | \(0.823783\pi\) | |||||||
\(200\) | 7.85840e7 | 0.694591 | ||||||||
\(201\) | −2.09699e6 | −0.0182142 | ||||||||
\(202\) | 6.81313e7 | 0.581590 | ||||||||
\(203\) | −3.13888e7 | −0.263353 | ||||||||
\(204\) | 473408. | 0.00390418 | ||||||||
\(205\) | −1.30557e8 | −1.05843 | ||||||||
\(206\) | −9.02659e7 | −0.719430 | ||||||||
\(207\) | −9.63955e7 | −0.755371 | ||||||||
\(208\) | −3.73338e7 | −0.287661 | ||||||||
\(209\) | 1.43921e8 | 1.09046 | ||||||||
\(210\) | −2.09463e6 | −0.0156078 | ||||||||
\(211\) | 1.41316e8 | 1.03563 | 0.517814 | − | 0.855493i | \(-0.326746\pi\) | ||||
0.517814 | + | 0.855493i | \(0.326746\pi\) | |||||||
\(212\) | 1.03033e8 | 0.742679 | ||||||||
\(213\) | −1.37824e6 | −0.00977229 | ||||||||
\(214\) | 8.06122e7 | 0.562280 | ||||||||
\(215\) | −1.30963e7 | −0.0898696 | ||||||||
\(216\) | −8.06529e6 | −0.0544542 | ||||||||
\(217\) | 3.57051e7 | 0.237204 | ||||||||
\(218\) | −1.35998e8 | −0.889070 | ||||||||
\(219\) | −2.71369e6 | −0.0174585 | ||||||||
\(220\) | −8.91720e7 | −0.564611 | ||||||||
\(221\) | 5.31617e7 | 0.331303 | ||||||||
\(222\) | 1.10562e6 | 0.00678218 | ||||||||
\(223\) | −1.10823e8 | −0.669211 | −0.334605 | − | 0.942358i | \(-0.608603\pi\) | ||||
−0.334605 | + | 0.942358i | \(0.608603\pi\) | |||||||
\(224\) | 2.12237e8 | 1.26169 | ||||||||
\(225\) | 1.11448e8 | 0.652281 | ||||||||
\(226\) | −8.08234e7 | −0.465755 | ||||||||
\(227\) | −1.43855e8 | −0.816269 | −0.408134 | − | 0.912922i | \(-0.633820\pi\) | ||||
−0.408134 | + | 0.912922i | \(0.633820\pi\) | |||||||
\(228\) | 1.25027e6 | 0.00698606 | ||||||||
\(229\) | −3.52277e8 | −1.93847 | −0.969236 | − | 0.246132i | \(-0.920840\pi\) | ||||
−0.969236 | + | 0.246132i | \(0.920840\pi\) | |||||||
\(230\) | 5.87145e7 | 0.318198 | ||||||||
\(231\) | −1.35890e7 | −0.0725347 | ||||||||
\(232\) | 3.67961e7 | 0.193461 | ||||||||
\(233\) | 3.78934e6 | 0.0196254 | 0.00981269 | − | 0.999952i | \(-0.496876\pi\) | ||||
0.00981269 | + | 0.999952i | \(0.496876\pi\) | |||||||
\(234\) | −1.48817e8 | −0.759269 | ||||||||
\(235\) | 8.08647e7 | 0.406463 | ||||||||
\(236\) | 3.92390e7 | 0.194324 | ||||||||
\(237\) | −5.88267e6 | −0.0287048 | ||||||||
\(238\) | 6.70394e7 | 0.322337 | ||||||||
\(239\) | −9.27614e6 | −0.0439516 | −0.0219758 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219758 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(240\) | 873630. | 0.00407932 | ||||||||
\(241\) | 3.57012e8 | 1.64294 | 0.821472 | − | 0.570249i | \(-0.193153\pi\) | ||||
0.821472 | + | 0.570249i | \(0.193153\pi\) | |||||||
\(242\) | 4.45311e8 | 2.01981 | ||||||||
\(243\) | −1.71593e7 | −0.0767143 | ||||||||
\(244\) | 7.66351e7 | 0.337725 | ||||||||
\(245\) | 1.49013e8 | 0.647355 | ||||||||
\(246\) | 7.66707e6 | 0.0328365 | ||||||||
\(247\) | 1.40400e8 | 0.592826 | ||||||||
\(248\) | −4.18561e7 | −0.174252 | ||||||||
\(249\) | 1.11829e7 | 0.0459046 | ||||||||
\(250\) | −1.71885e8 | −0.695744 | ||||||||
\(251\) | 4.81876e8 | 1.92343 | 0.961716 | − | 0.274047i | \(-0.0883625\pi\) | ||||
0.961716 | + | 0.274047i | \(0.0883625\pi\) | |||||||
\(252\) | 1.80101e8 | 0.708946 | ||||||||
\(253\) | 3.80912e8 | 1.47878 | ||||||||
\(254\) | 1.10886e8 | 0.424577 | ||||||||
\(255\) | −1.24401e6 | −0.00469822 | ||||||||
\(256\) | −2.84354e8 | −1.05930 | ||||||||
\(257\) | −1.70067e6 | −0.00624962 | −0.00312481 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312481 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(258\) | 769087. | 0.00278809 | ||||||||
\(259\) | −1.50256e8 | −0.537380 | ||||||||
\(260\) | −8.69906e7 | −0.306948 | ||||||||
\(261\) | 5.21846e7 | 0.181677 | ||||||||
\(262\) | −1.80097e8 | −0.618658 | ||||||||
\(263\) | −3.62647e8 | −1.22925 | −0.614623 | − | 0.788821i | \(-0.710692\pi\) | ||||
−0.614623 | + | 0.788821i | \(0.710692\pi\) | |||||||
\(264\) | 1.59300e7 | 0.0532846 | ||||||||
\(265\) | −2.70747e8 | −0.893724 | ||||||||
\(266\) | 1.77051e8 | 0.576783 | ||||||||
\(267\) | −1.13063e7 | −0.0363521 | ||||||||
\(268\) | −1.09823e8 | −0.348514 | ||||||||
\(269\) | 3.91885e8 | 1.22751 | 0.613756 | − | 0.789496i | \(-0.289658\pi\) | ||||
0.613756 | + | 0.789496i | \(0.289658\pi\) | |||||||
\(270\) | 6.96704e6 | 0.0215415 | ||||||||
\(271\) | 5.27272e6 | 0.0160932 | 0.00804660 | − | 0.999968i | \(-0.497439\pi\) | ||||
0.00804660 | + | 0.999968i | \(0.497439\pi\) | |||||||
\(272\) | −2.79608e7 | −0.0842477 | ||||||||
\(273\) | −1.32566e7 | −0.0394332 | ||||||||
\(274\) | −1.33521e7 | −0.0392122 | ||||||||
\(275\) | −4.40394e8 | −1.27696 | ||||||||
\(276\) | 3.30907e6 | 0.00947380 | ||||||||
\(277\) | 5.31633e8 | 1.50291 | 0.751455 | − | 0.659784i | \(-0.229352\pi\) | ||||
0.751455 | + | 0.659784i | \(0.229352\pi\) | |||||||
\(278\) | 1.35632e6 | 0.00378620 | ||||||||
\(279\) | −5.93606e7 | −0.163638 | ||||||||
\(280\) | −3.33705e8 | −0.908468 | ||||||||
\(281\) | 5.83130e8 | 1.56781 | 0.783905 | − | 0.620881i | \(-0.213225\pi\) | ||||
0.783905 | + | 0.620881i | \(0.213225\pi\) | |||||||
\(282\) | −4.74883e6 | −0.0126100 | ||||||||
\(283\) | −2.16632e8 | −0.568159 | −0.284079 | − | 0.958801i | \(-0.591688\pi\) | ||||
−0.284079 | + | 0.958801i | \(0.591688\pi\) | |||||||
\(284\) | −7.21806e7 | −0.186985 | ||||||||
\(285\) | −3.28543e6 | −0.00840688 | ||||||||
\(286\) | 5.88057e8 | 1.48641 | ||||||||
\(287\) | −1.04197e9 | −2.60177 | ||||||||
\(288\) | −3.52849e8 | −0.870393 | ||||||||
\(289\) | −3.70524e8 | −0.902971 | ||||||||
\(290\) | −3.17856e7 | −0.0765311 | ||||||||
\(291\) | 7.28198e6 | 0.0173230 | ||||||||
\(292\) | −1.42120e8 | −0.334053 | ||||||||
\(293\) | −9.62588e7 | −0.223565 | −0.111782 | − | 0.993733i | \(-0.535656\pi\) | ||||
−0.111782 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(294\) | −8.75088e6 | −0.0200834 | ||||||||
\(295\) | −1.03111e8 | −0.233845 | ||||||||
\(296\) | 1.76140e8 | 0.394764 | ||||||||
\(297\) | 4.51989e7 | 0.100111 | ||||||||
\(298\) | −2.61912e8 | −0.573321 | ||||||||
\(299\) | 3.71594e8 | 0.803932 | ||||||||
\(300\) | −3.82580e6 | −0.00818085 | ||||||||
\(301\) | −1.04521e8 | −0.220912 | ||||||||
\(302\) | −1.64202e8 | −0.343047 | ||||||||
\(303\) | −1.00901e7 | −0.0208375 | ||||||||
\(304\) | −7.38444e7 | −0.150751 | ||||||||
\(305\) | −2.01380e8 | −0.406411 | ||||||||
\(306\) | −1.11455e8 | −0.222368 | ||||||||
\(307\) | 7.18187e8 | 1.41662 | 0.708310 | − | 0.705902i | \(-0.249458\pi\) | ||||
0.708310 | + | 0.705902i | \(0.249458\pi\) | |||||||
\(308\) | −7.11677e8 | −1.38789 | ||||||||
\(309\) | 1.33682e7 | 0.0257761 | ||||||||
\(310\) | 3.61565e7 | 0.0689320 | ||||||||
\(311\) | −1.67567e8 | −0.315883 | −0.157942 | − | 0.987448i | \(-0.550486\pi\) | ||||
−0.157942 | + | 0.987448i | \(0.550486\pi\) | |||||||
\(312\) | 1.55403e7 | 0.0289680 | ||||||||
\(313\) | 6.19823e8 | 1.14252 | 0.571258 | − | 0.820770i | \(-0.306455\pi\) | ||||
0.571258 | + | 0.820770i | \(0.306455\pi\) | |||||||
\(314\) | −6.26802e8 | −1.14255 | ||||||||
\(315\) | −4.73263e8 | −0.853131 | ||||||||
\(316\) | −3.08084e8 | −0.549244 | ||||||||
\(317\) | 2.63030e8 | 0.463765 | 0.231883 | − | 0.972744i | \(-0.425511\pi\) | ||||
0.231883 | + | 0.972744i | \(0.425511\pi\) | |||||||
\(318\) | 1.58998e7 | 0.0277266 | ||||||||
\(319\) | −2.06210e8 | −0.355666 | ||||||||
\(320\) | 3.08349e8 | 0.526038 | ||||||||
\(321\) | −1.19385e7 | −0.0201457 | ||||||||
\(322\) | 4.68598e8 | 0.782176 | ||||||||
\(323\) | 1.05151e8 | 0.173622 | ||||||||
\(324\) | −2.99225e8 | −0.488754 | ||||||||
\(325\) | −4.29621e8 | −0.694215 | ||||||||
\(326\) | −6.91108e8 | −1.10480 | ||||||||
\(327\) | 2.01410e7 | 0.0318541 | ||||||||
\(328\) | 1.22147e9 | 1.91129 | ||||||||
\(329\) | 6.45377e8 | 0.999143 | ||||||||
\(330\) | −1.37608e7 | −0.0210788 | ||||||||
\(331\) | −9.80269e8 | −1.48575 | −0.742877 | − | 0.669427i | \(-0.766540\pi\) | ||||
−0.742877 | + | 0.669427i | \(0.766540\pi\) | |||||||
\(332\) | 5.85665e8 | 0.878347 | ||||||||
\(333\) | 2.49804e8 | 0.370718 | ||||||||
\(334\) | −4.28973e8 | −0.629967 | ||||||||
\(335\) | 2.88589e8 | 0.419394 | ||||||||
\(336\) | 6.97240e6 | 0.0100275 | ||||||||
\(337\) | −6.28527e8 | −0.894580 | −0.447290 | − | 0.894389i | \(-0.647611\pi\) | ||||
−0.447290 | + | 0.894389i | \(0.647611\pi\) | |||||||
\(338\) | 6.65470e7 | 0.0937389 | ||||||||
\(339\) | 1.19697e7 | 0.0166873 | ||||||||
\(340\) | −6.51507e7 | −0.0898965 | ||||||||
\(341\) | 2.34567e8 | 0.320351 | ||||||||
\(342\) | −2.94351e8 | −0.397901 | ||||||||
\(343\) | 1.06628e8 | 0.142673 | ||||||||
\(344\) | 1.22526e8 | 0.162284 | ||||||||
\(345\) | −8.69548e6 | −0.0114006 | ||||||||
\(346\) | 6.01187e8 | 0.780267 | ||||||||
\(347\) | 1.41484e9 | 1.81783 | 0.908915 | − | 0.416982i | \(-0.136912\pi\) | ||||
0.908915 | + | 0.416982i | \(0.136912\pi\) | |||||||
\(348\) | −1.79139e6 | −0.00227858 | ||||||||
\(349\) | 1.08261e9 | 1.36327 | 0.681637 | − | 0.731691i | \(-0.261269\pi\) | ||||
0.681637 | + | 0.731691i | \(0.261269\pi\) | |||||||
\(350\) | −5.41773e8 | −0.675428 | ||||||||
\(351\) | 4.40932e7 | 0.0544248 | ||||||||
\(352\) | 1.39430e9 | 1.70395 | ||||||||
\(353\) | −1.04347e9 | −1.26261 | −0.631306 | − | 0.775533i | \(-0.717481\pi\) | ||||
−0.631306 | + | 0.775533i | \(0.717481\pi\) | |||||||
\(354\) | 6.05527e6 | 0.00725474 | ||||||||
\(355\) | 1.89674e8 | 0.225014 | ||||||||
\(356\) | −5.92126e8 | −0.695567 | ||||||||
\(357\) | −9.92838e6 | −0.0115489 | ||||||||
\(358\) | 1.17474e9 | 1.35316 | ||||||||
\(359\) | 7.36087e8 | 0.839650 | 0.419825 | − | 0.907605i | \(-0.362091\pi\) | ||||
0.419825 | + | 0.907605i | \(0.362091\pi\) | |||||||
\(360\) | 5.54792e8 | 0.626717 | ||||||||
\(361\) | −6.16168e8 | −0.689325 | ||||||||
\(362\) | −3.80015e8 | −0.421037 | ||||||||
\(363\) | −6.59495e7 | −0.0723666 | ||||||||
\(364\) | −6.94267e8 | −0.754522 | ||||||||
\(365\) | 3.73459e8 | 0.401993 | ||||||||
\(366\) | 1.18262e7 | 0.0126084 | ||||||||
\(367\) | 5.85636e8 | 0.618439 | 0.309219 | − | 0.950991i | \(-0.399932\pi\) | ||||
0.309219 | + | 0.950991i | \(0.399932\pi\) | |||||||
\(368\) | −1.95443e8 | −0.204433 | ||||||||
\(369\) | 1.73230e9 | 1.79486 | ||||||||
\(370\) | −1.52155e8 | −0.156164 | ||||||||
\(371\) | −2.16082e9 | −2.19690 | ||||||||
\(372\) | 2.03773e6 | 0.00205233 | ||||||||
\(373\) | −1.55931e9 | −1.55579 | −0.777896 | − | 0.628393i | \(-0.783713\pi\) | ||||
−0.777896 | + | 0.628393i | \(0.783713\pi\) | |||||||
\(374\) | 4.40419e8 | 0.435327 | ||||||||
\(375\) | 2.54558e7 | 0.0249274 | ||||||||
\(376\) | −7.56556e8 | −0.733979 | ||||||||
\(377\) | −2.01166e8 | −0.193357 | ||||||||
\(378\) | 5.56036e7 | 0.0529519 | ||||||||
\(379\) | −2.07398e7 | −0.0195689 | −0.00978446 | − | 0.999952i | \(-0.503115\pi\) | ||||
−0.00978446 | + | 0.999952i | \(0.503115\pi\) | |||||||
\(380\) | −1.72063e8 | −0.160859 | ||||||||
\(381\) | −1.64219e7 | −0.0152120 | ||||||||
\(382\) | −5.20311e8 | −0.477575 | ||||||||
\(383\) | 1.16713e9 | 1.06151 | 0.530755 | − | 0.847525i | \(-0.321908\pi\) | ||||
0.530755 | + | 0.847525i | \(0.321908\pi\) | |||||||
\(384\) | 6.62598e6 | 0.00597161 | ||||||||
\(385\) | 1.87013e9 | 1.67016 | ||||||||
\(386\) | −1.04744e9 | −0.926990 | ||||||||
\(387\) | 1.73768e8 | 0.152399 | ||||||||
\(388\) | 3.81368e8 | 0.331462 | ||||||||
\(389\) | −1.12210e9 | −0.966512 | −0.483256 | − | 0.875479i | \(-0.660546\pi\) | ||||
−0.483256 | + | 0.875479i | \(0.660546\pi\) | |||||||
\(390\) | −1.34242e7 | −0.0114594 | ||||||||
\(391\) | 2.78301e8 | 0.235449 | ||||||||
\(392\) | −1.39414e9 | −1.16897 | ||||||||
\(393\) | 2.66719e7 | 0.0221656 | ||||||||
\(394\) | 6.73746e8 | 0.554957 | ||||||||
\(395\) | 8.09575e8 | 0.660948 | ||||||||
\(396\) | 1.18318e9 | 0.957453 | ||||||||
\(397\) | 6.25123e8 | 0.501417 | 0.250708 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250708 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(398\) | −1.52852e9 | −1.21529 | ||||||||
\(399\) | −2.62208e7 | −0.0206653 | ||||||||
\(400\) | 2.25962e8 | 0.176533 | ||||||||
\(401\) | 6.80350e8 | 0.526899 | 0.263449 | − | 0.964673i | \(-0.415140\pi\) | ||||
0.263449 | + | 0.964673i | \(0.415140\pi\) | |||||||
\(402\) | −1.69476e7 | −0.0130112 | ||||||||
\(403\) | 2.28828e8 | 0.174158 | ||||||||
\(404\) | −5.28433e8 | −0.398708 | ||||||||
\(405\) | 7.86295e8 | 0.588156 | ||||||||
\(406\) | −2.53680e8 | −0.188124 | ||||||||
\(407\) | −9.87113e8 | −0.725749 | ||||||||
\(408\) | 1.16387e7 | 0.00848390 | ||||||||
\(409\) | 1.45254e9 | 1.04977 | 0.524887 | − | 0.851172i | \(-0.324108\pi\) | ||||
0.524887 | + | 0.851172i | \(0.324108\pi\) | |||||||
\(410\) | −1.05515e9 | −0.756082 | ||||||||
\(411\) | 1.97741e6 | 0.00140491 | ||||||||
\(412\) | 7.00111e8 | 0.493204 | ||||||||
\(413\) | −8.22925e8 | −0.574824 | ||||||||
\(414\) | −7.79054e8 | −0.539593 | ||||||||
\(415\) | −1.53899e9 | −1.05698 | ||||||||
\(416\) | 1.36019e9 | 0.926349 | ||||||||
\(417\) | −200867. | −0.000135654 0 | ||||||||
\(418\) | 1.16315e9 | 0.778963 | ||||||||
\(419\) | −2.07021e9 | −1.37488 | −0.687441 | − | 0.726240i | \(-0.741266\pi\) | ||||
−0.687441 | + | 0.726240i | \(0.741266\pi\) | |||||||
\(420\) | 1.62462e7 | 0.0106999 | ||||||||
\(421\) | −1.86742e9 | −1.21971 | −0.609853 | − | 0.792514i | \(-0.708772\pi\) | ||||
−0.609853 | + | 0.792514i | \(0.708772\pi\) | |||||||
\(422\) | 1.14210e9 | 0.739792 | ||||||||
\(423\) | −1.07295e9 | −0.689271 | ||||||||
\(424\) | 2.53307e9 | 1.61386 | ||||||||
\(425\) | −3.21760e8 | −0.203316 | ||||||||
\(426\) | −1.11387e7 | −0.00698076 | ||||||||
\(427\) | −1.60720e9 | −0.999016 | ||||||||
\(428\) | −6.25236e8 | −0.385470 | ||||||||
\(429\) | −8.70898e7 | −0.0532558 | ||||||||
\(430\) | −1.05842e8 | −0.0641976 | ||||||||
\(431\) | 1.03410e9 | 0.622144 | 0.311072 | − | 0.950386i | \(-0.399312\pi\) | ||||
0.311072 | + | 0.950386i | \(0.399312\pi\) | |||||||
\(432\) | −2.31911e7 | −0.0138398 | ||||||||
\(433\) | 1.88745e9 | 1.11730 | 0.558648 | − | 0.829405i | \(-0.311320\pi\) | ||||
0.558648 | + | 0.829405i | \(0.311320\pi\) | |||||||
\(434\) | 2.88564e8 | 0.169444 | ||||||||
\(435\) | 4.70738e6 | 0.00274199 | ||||||||
\(436\) | 1.05482e9 | 0.609501 | ||||||||
\(437\) | 7.34993e8 | 0.421307 | ||||||||
\(438\) | −2.19317e7 | −0.0124713 | ||||||||
\(439\) | −2.19197e9 | −1.23654 | −0.618270 | − | 0.785965i | \(-0.712166\pi\) | ||||
−0.618270 | + | 0.785965i | \(0.712166\pi\) | |||||||
\(440\) | −2.19229e9 | −1.22691 | ||||||||
\(441\) | −1.97718e9 | −1.09777 | ||||||||
\(442\) | 4.29645e8 | 0.236664 | ||||||||
\(443\) | −1.23285e9 | −0.673745 | −0.336873 | − | 0.941550i | \(-0.609369\pi\) | ||||
−0.336873 | + | 0.941550i | \(0.609369\pi\) | |||||||
\(444\) | −8.57527e6 | −0.00464951 | ||||||||
\(445\) | 1.55597e9 | 0.837031 | ||||||||
\(446\) | −8.95655e8 | −0.478045 | ||||||||
\(447\) | 3.87885e7 | 0.0205412 | ||||||||
\(448\) | 2.46092e9 | 1.29308 | ||||||||
\(449\) | 2.06378e9 | 1.07597 | 0.537985 | − | 0.842954i | \(-0.319186\pi\) | ||||
0.537985 | + | 0.842954i | \(0.319186\pi\) | |||||||
\(450\) | 9.00709e8 | 0.465952 | ||||||||
\(451\) | −6.84529e9 | −3.51378 | ||||||||
\(452\) | 6.26874e8 | 0.319298 | ||||||||
\(453\) | 2.43179e7 | 0.0122909 | ||||||||
\(454\) | −1.16261e9 | −0.583095 | ||||||||
\(455\) | 1.82438e9 | 0.907976 | ||||||||
\(456\) | 3.07379e7 | 0.0151809 | ||||||||
\(457\) | −3.67119e9 | −1.79928 | −0.899642 | − | 0.436628i | \(-0.856173\pi\) | ||||
−0.899642 | + | 0.436628i | \(0.856173\pi\) | |||||||
\(458\) | −2.84705e9 | −1.38473 | ||||||||
\(459\) | 3.30231e7 | 0.0159395 | ||||||||
\(460\) | −4.55395e8 | −0.218140 | ||||||||
\(461\) | 1.50027e9 | 0.713206 | 0.356603 | − | 0.934256i | \(-0.383935\pi\) | ||||
0.356603 | + | 0.934256i | \(0.383935\pi\) | |||||||
\(462\) | −1.09824e8 | −0.0518146 | ||||||||
\(463\) | 1.00012e9 | 0.468293 | 0.234147 | − | 0.972201i | \(-0.424770\pi\) | ||||
0.234147 | + | 0.972201i | \(0.424770\pi\) | |||||||
\(464\) | 1.05805e8 | 0.0491690 | ||||||||
\(465\) | −5.35470e6 | −0.00246973 | ||||||||
\(466\) | 3.06249e7 | 0.0140192 | ||||||||
\(467\) | −1.13114e9 | −0.513933 | −0.256967 | − | 0.966420i | \(-0.582723\pi\) | ||||
−0.256967 | + | 0.966420i | \(0.582723\pi\) | |||||||
\(468\) | 1.15424e9 | 0.520516 | ||||||||
\(469\) | 2.30321e9 | 1.03093 | ||||||||
\(470\) | 6.53536e8 | 0.290354 | ||||||||
\(471\) | 9.28279e7 | 0.0409360 | ||||||||
\(472\) | 9.64690e8 | 0.422271 | ||||||||
\(473\) | −6.86654e8 | −0.298348 | ||||||||
\(474\) | −4.75429e7 | −0.0205051 | ||||||||
\(475\) | −8.49768e8 | −0.363808 | ||||||||
\(476\) | −5.19964e8 | −0.220978 | ||||||||
\(477\) | 3.59242e9 | 1.51556 | ||||||||
\(478\) | −7.49684e7 | −0.0313964 | ||||||||
\(479\) | 4.27056e8 | 0.177546 | 0.0887730 | − | 0.996052i | \(-0.471705\pi\) | ||||
0.0887730 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(480\) | −3.18292e7 | −0.0131366 | ||||||||
\(481\) | −9.62965e8 | −0.394551 | ||||||||
\(482\) | 2.88532e9 | 1.17362 | ||||||||
\(483\) | −6.93982e7 | −0.0280242 | ||||||||
\(484\) | −3.45387e9 | −1.38467 | ||||||||
\(485\) | −1.00215e9 | −0.398874 | ||||||||
\(486\) | −1.38679e8 | −0.0548002 | ||||||||
\(487\) | 1.86591e9 | 0.732049 | 0.366025 | − | 0.930605i | \(-0.380719\pi\) | ||||
0.366025 | + | 0.930605i | \(0.380719\pi\) | |||||||
\(488\) | 1.88407e9 | 0.733886 | ||||||||
\(489\) | 1.02351e8 | 0.0395834 | ||||||||
\(490\) | 1.20430e9 | 0.462433 | ||||||||
\(491\) | −2.67497e9 | −1.01985 | −0.509923 | − | 0.860220i | \(-0.670326\pi\) | ||||
−0.509923 | + | 0.860220i | \(0.670326\pi\) | |||||||
\(492\) | −5.94666e7 | −0.0225110 | ||||||||
\(493\) | −1.50661e8 | −0.0566287 | ||||||||
\(494\) | 1.13469e9 | 0.423481 | ||||||||
\(495\) | −3.10913e9 | −1.15218 | ||||||||
\(496\) | −1.20354e8 | −0.0442868 | ||||||||
\(497\) | 1.51378e9 | 0.553115 | ||||||||
\(498\) | 9.03785e7 | 0.0327916 | ||||||||
\(499\) | −2.01727e9 | −0.726794 | −0.363397 | − | 0.931634i | \(-0.618383\pi\) | ||||
−0.363397 | + | 0.931634i | \(0.618383\pi\) | |||||||
\(500\) | 1.33316e9 | 0.476966 | ||||||||
\(501\) | 6.35299e7 | 0.0225708 | ||||||||
\(502\) | 3.89445e9 | 1.37399 | ||||||||
\(503\) | 2.78344e9 | 0.975201 | 0.487601 | − | 0.873067i | \(-0.337872\pi\) | ||||
0.487601 | + | 0.873067i | \(0.337872\pi\) | |||||||
\(504\) | 4.42777e9 | 1.54056 | ||||||||
\(505\) | 1.38860e9 | 0.479798 | ||||||||
\(506\) | 3.07848e9 | 1.05635 | ||||||||
\(507\) | −9.85545e6 | −0.00335852 | ||||||||
\(508\) | −8.60039e8 | −0.291068 | ||||||||
\(509\) | −6.34132e8 | −0.213141 | −0.106571 | − | 0.994305i | \(-0.533987\pi\) | ||||
−0.106571 | + | 0.994305i | \(0.533987\pi\) | |||||||
\(510\) | −1.00539e7 | −0.00335613 | ||||||||
\(511\) | 2.98056e9 | 0.988154 | ||||||||
\(512\) | −1.58950e9 | −0.523380 | ||||||||
\(513\) | 8.72140e7 | 0.0285217 | ||||||||
\(514\) | −1.37446e7 | −0.00446437 | ||||||||
\(515\) | −1.83973e9 | −0.593512 | ||||||||
\(516\) | −5.96511e6 | −0.00191137 | ||||||||
\(517\) | 4.23984e9 | 1.34937 | ||||||||
\(518\) | −1.21434e9 | −0.383873 | ||||||||
\(519\) | −8.90343e7 | −0.0279558 | ||||||||
\(520\) | −2.13866e9 | −0.667007 | ||||||||
\(521\) | −2.55557e9 | −0.791692 | −0.395846 | − | 0.918317i | \(-0.629549\pi\) | ||||
−0.395846 | + | 0.918317i | \(0.629549\pi\) | |||||||
\(522\) | 4.21748e8 | 0.129780 | ||||||||
\(523\) | 1.86691e9 | 0.570647 | 0.285323 | − | 0.958431i | \(-0.407899\pi\) | ||||
0.285323 | + | 0.958431i | \(0.407899\pi\) | |||||||
\(524\) | 1.39685e9 | 0.424120 | ||||||||
\(525\) | 8.02352e7 | 0.0241996 | ||||||||
\(526\) | −2.93086e9 | −0.878101 | ||||||||
\(527\) | 1.71379e8 | 0.0510058 | ||||||||
\(528\) | 4.58055e7 | 0.0135425 | ||||||||
\(529\) | −1.45953e9 | −0.428666 | ||||||||
\(530\) | −2.18814e9 | −0.638425 | ||||||||
\(531\) | 1.36813e9 | 0.396549 | ||||||||
\(532\) | −1.37322e9 | −0.395413 | ||||||||
\(533\) | −6.67783e9 | −1.91025 | ||||||||
\(534\) | −9.13755e7 | −0.0259678 | ||||||||
\(535\) | 1.64298e9 | 0.463867 | ||||||||
\(536\) | −2.69999e9 | −0.757330 | ||||||||
\(537\) | −1.73976e8 | −0.0484817 | ||||||||
\(538\) | 3.16716e9 | 0.876863 | ||||||||
\(539\) | 7.81294e9 | 2.14909 | ||||||||
\(540\) | −5.40371e7 | −0.0147677 | ||||||||
\(541\) | −2.51318e8 | −0.0682391 | −0.0341195 | − | 0.999418i | \(-0.510863\pi\) | ||||
−0.0341195 | + | 0.999418i | \(0.510863\pi\) | |||||||
\(542\) | 4.26134e7 | 0.0114960 | ||||||||
\(543\) | 5.62793e7 | 0.0150851 | ||||||||
\(544\) | 1.01870e9 | 0.271301 | ||||||||
\(545\) | −2.77182e9 | −0.733461 | ||||||||
\(546\) | −1.07138e8 | −0.0281688 | ||||||||
\(547\) | 1.95845e9 | 0.511631 | 0.255815 | − | 0.966726i | \(-0.417656\pi\) | ||||
0.255815 | + | 0.966726i | \(0.417656\pi\) | |||||||
\(548\) | 1.03560e8 | 0.0268819 | ||||||||
\(549\) | 2.67201e9 | 0.689183 | ||||||||
\(550\) | −3.55920e9 | −0.912186 | ||||||||
\(551\) | −3.97895e8 | −0.101330 | ||||||||
\(552\) | 8.13534e7 | 0.0205868 | ||||||||
\(553\) | 6.46118e9 | 1.62470 | ||||||||
\(554\) | 4.29658e9 | 1.07359 | ||||||||
\(555\) | 2.25338e7 | 0.00559513 | ||||||||
\(556\) | −1.05197e7 | −0.00259563 | ||||||||
\(557\) | −9.85537e7 | −0.0241646 | −0.0120823 | − | 0.999927i | \(-0.503846\pi\) | ||||
−0.0120823 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(558\) | −4.79744e8 | −0.116893 | ||||||||
\(559\) | −6.69856e8 | −0.162196 | ||||||||
\(560\) | −9.59544e8 | −0.230891 | ||||||||
\(561\) | −6.52250e7 | −0.0155971 | ||||||||
\(562\) | 4.71277e9 | 1.11995 | ||||||||
\(563\) | −8.32439e8 | −0.196595 | −0.0982976 | − | 0.995157i | \(-0.531340\pi\) | ||||
−0.0982976 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(564\) | 3.68324e7 | 0.00864477 | ||||||||
\(565\) | −1.64728e9 | −0.384236 | ||||||||
\(566\) | −1.75079e9 | −0.405859 | ||||||||
\(567\) | 6.27538e9 | 1.44577 | ||||||||
\(568\) | −1.77456e9 | −0.406323 | ||||||||
\(569\) | −4.82012e8 | −0.109689 | −0.0548447 | − | 0.998495i | \(-0.517466\pi\) | ||||
−0.0548447 | + | 0.998495i | \(0.517466\pi\) | |||||||
\(570\) | −2.65523e7 | −0.00600538 | ||||||||
\(571\) | −3.91868e9 | −0.880874 | −0.440437 | − | 0.897784i | \(-0.645176\pi\) | ||||
−0.440437 | + | 0.897784i | \(0.645176\pi\) | |||||||
\(572\) | −4.56103e9 | −1.01901 | ||||||||
\(573\) | 7.70568e7 | 0.0171108 | ||||||||
\(574\) | −8.42107e9 | −1.85856 | ||||||||
\(575\) | −2.24907e9 | −0.493361 | ||||||||
\(576\) | −4.09133e9 | −0.892043 | ||||||||
\(577\) | −6.04095e9 | −1.30915 | −0.654576 | − | 0.755996i | \(-0.727153\pi\) | ||||
−0.654576 | + | 0.755996i | \(0.727153\pi\) | |||||||
\(578\) | −2.99452e9 | −0.645030 | ||||||||
\(579\) | 1.55124e8 | 0.0332127 | ||||||||
\(580\) | 2.46532e8 | 0.0524658 | ||||||||
\(581\) | −1.22826e10 | −2.59822 | ||||||||
\(582\) | 5.88519e7 | 0.0123746 | ||||||||
\(583\) | −1.41956e10 | −2.96698 | ||||||||
\(584\) | −3.49402e9 | −0.725907 | ||||||||
\(585\) | −3.03307e9 | −0.626378 | ||||||||
\(586\) | −7.77949e8 | −0.159702 | ||||||||
\(587\) | 9.41828e9 | 1.92193 | 0.960967 | − | 0.276665i | \(-0.0892291\pi\) | ||||
0.960967 | + | 0.276665i | \(0.0892291\pi\) | |||||||
\(588\) | 6.78727e7 | 0.0137681 | ||||||||
\(589\) | 4.52611e8 | 0.0912686 | ||||||||
\(590\) | −8.33329e8 | −0.167045 | ||||||||
\(591\) | −9.97802e7 | −0.0198833 | ||||||||
\(592\) | 5.06479e8 | 0.100331 | ||||||||
\(593\) | 2.77653e9 | 0.546778 | 0.273389 | − | 0.961904i | \(-0.411855\pi\) | ||||
0.273389 | + | 0.961904i | \(0.411855\pi\) | |||||||
\(594\) | 3.65291e8 | 0.0715132 | ||||||||
\(595\) | 1.36635e9 | 0.265920 | ||||||||
\(596\) | 2.03141e9 | 0.393040 | ||||||||
\(597\) | 2.26370e8 | 0.0435420 | ||||||||
\(598\) | 3.00317e9 | 0.574282 | ||||||||
\(599\) | 2.48861e9 | 0.473110 | 0.236555 | − | 0.971618i | \(-0.423982\pi\) | ||||
0.236555 | + | 0.971618i | \(0.423982\pi\) | |||||||
\(600\) | −9.40574e7 | −0.0177772 | ||||||||
\(601\) | 9.96150e8 | 0.187182 | 0.0935910 | − | 0.995611i | \(-0.470165\pi\) | ||||
0.0935910 | + | 0.995611i | \(0.470165\pi\) | |||||||
\(602\) | −8.44720e8 | −0.157807 | ||||||||
\(603\) | −3.82914e9 | −0.711199 | ||||||||
\(604\) | 1.27357e9 | 0.235176 | ||||||||
\(605\) | 9.07599e9 | 1.66629 | ||||||||
\(606\) | −8.15466e7 | −0.0148851 | ||||||||
\(607\) | 4.07704e9 | 0.739920 | 0.369960 | − | 0.929048i | \(-0.379371\pi\) | ||||
0.369960 | + | 0.929048i | \(0.379371\pi\) | |||||||
\(608\) | 2.69039e9 | 0.485460 | ||||||||
\(609\) | 3.75693e7 | 0.00674020 | ||||||||
\(610\) | −1.62752e9 | −0.290317 | ||||||||
\(611\) | 4.13612e9 | 0.733582 | ||||||||
\(612\) | 8.64453e8 | 0.152444 | ||||||||
\(613\) | 7.37622e9 | 1.29337 | 0.646684 | − | 0.762758i | \(-0.276155\pi\) | ||||
0.646684 | + | 0.762758i | \(0.276155\pi\) | |||||||
\(614\) | 5.80428e9 | 1.01195 | ||||||||
\(615\) | 1.56265e8 | 0.0270893 | ||||||||
\(616\) | −1.74966e10 | −3.01593 | ||||||||
\(617\) | −3.57832e9 | −0.613312 | −0.306656 | − | 0.951820i | \(-0.599210\pi\) | ||||
−0.306656 | + | 0.951820i | \(0.599210\pi\) | |||||||
\(618\) | 1.08040e8 | 0.0184129 | ||||||||
\(619\) | −2.12273e9 | −0.359731 | −0.179865 | − | 0.983691i | \(-0.557566\pi\) | ||||
−0.179865 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(620\) | −2.80434e8 | −0.0472563 | ||||||||
\(621\) | 2.30828e8 | 0.0386783 | ||||||||
\(622\) | −1.35425e9 | −0.225649 | ||||||||
\(623\) | 1.24181e10 | 2.05754 | ||||||||
\(624\) | 4.46850e7 | 0.00736233 | ||||||||
\(625\) | 4.80577e8 | 0.0787377 | ||||||||
\(626\) | 5.00932e9 | 0.816147 | ||||||||
\(627\) | −1.72259e8 | −0.0279091 | ||||||||
\(628\) | 4.86154e9 | 0.783277 | ||||||||
\(629\) | −7.21203e8 | −0.115553 | ||||||||
\(630\) | −3.82484e9 | −0.609427 | ||||||||
\(631\) | −1.03343e10 | −1.63749 | −0.818744 | − | 0.574159i | \(-0.805329\pi\) | ||||
−0.818744 | + | 0.574159i | \(0.805329\pi\) | |||||||
\(632\) | −7.57425e9 | −1.19352 | ||||||||
\(633\) | −1.69142e8 | −0.0265056 | ||||||||
\(634\) | 2.12577e9 | 0.331287 | ||||||||
\(635\) | 2.25999e9 | 0.350266 | ||||||||
\(636\) | −1.23321e8 | −0.0190080 | ||||||||
\(637\) | 7.62181e9 | 1.16834 | ||||||||
\(638\) | −1.66656e9 | −0.254067 | ||||||||
\(639\) | −2.51669e9 | −0.381573 | ||||||||
\(640\) | −9.11871e8 | −0.137500 | ||||||||
\(641\) | 4.06584e9 | 0.609744 | 0.304872 | − | 0.952393i | \(-0.401386\pi\) | ||||
0.304872 | + | 0.952393i | \(0.401386\pi\) | |||||||
\(642\) | −9.64850e7 | −0.0143909 | ||||||||
\(643\) | 1.27525e10 | 1.89172 | 0.945860 | − | 0.324574i | \(-0.105221\pi\) | ||||
0.945860 | + | 0.324574i | \(0.105221\pi\) | |||||||
\(644\) | −3.63449e9 | −0.536220 | ||||||||
\(645\) | 1.56750e7 | 0.00230010 | ||||||||
\(646\) | 8.49815e8 | 0.124025 | ||||||||
\(647\) | 6.06984e9 | 0.881074 | 0.440537 | − | 0.897734i | \(-0.354788\pi\) | ||||
0.440537 | + | 0.897734i | \(0.354788\pi\) | |||||||
\(648\) | −7.35644e9 | −1.06208 | ||||||||
\(649\) | −5.40625e9 | −0.776318 | ||||||||
\(650\) | −3.47213e9 | −0.495907 | ||||||||
\(651\) | −4.27356e7 | −0.00607094 | ||||||||
\(652\) | 5.36030e9 | 0.757395 | ||||||||
\(653\) | 8.96474e9 | 1.25992 | 0.629958 | − | 0.776629i | \(-0.283072\pi\) | ||||
0.629958 | + | 0.776629i | \(0.283072\pi\) | |||||||
\(654\) | 1.62777e8 | 0.0227547 | ||||||||
\(655\) | −3.67059e9 | −0.510378 | ||||||||
\(656\) | 3.51226e9 | 0.485761 | ||||||||
\(657\) | −4.95525e9 | −0.681690 | ||||||||
\(658\) | 5.21584e9 | 0.713730 | ||||||||
\(659\) | 7.66829e9 | 1.04376 | 0.521879 | − | 0.853020i | \(-0.325231\pi\) | ||||
0.521879 | + | 0.853020i | \(0.325231\pi\) | |||||||
\(660\) | 1.06730e8 | 0.0144505 | ||||||||
\(661\) | 9.45702e9 | 1.27365 | 0.636824 | − | 0.771010i | \(-0.280248\pi\) | ||||
0.636824 | + | 0.771010i | \(0.280248\pi\) | |||||||
\(662\) | −7.92239e9 | −1.06134 | ||||||||
\(663\) | −6.36294e7 | −0.00847931 | ||||||||
\(664\) | 1.43986e10 | 1.90867 | ||||||||
\(665\) | 3.60852e9 | 0.475832 | ||||||||
\(666\) | 2.01888e9 | 0.264819 | ||||||||
\(667\) | −1.05310e9 | −0.137414 | ||||||||
\(668\) | 3.32716e9 | 0.431873 | ||||||||
\(669\) | 1.32644e8 | 0.0171276 | ||||||||
\(670\) | 2.33233e9 | 0.299591 | ||||||||
\(671\) | −1.05586e10 | −1.34920 | ||||||||
\(672\) | −2.54027e8 | −0.0322915 | ||||||||
\(673\) | 7.72168e9 | 0.976470 | 0.488235 | − | 0.872712i | \(-0.337641\pi\) | ||||
0.488235 | + | 0.872712i | \(0.337641\pi\) | |||||||
\(674\) | −5.07966e9 | −0.639036 | ||||||||
\(675\) | −2.66873e8 | −0.0333996 | ||||||||
\(676\) | −5.16145e8 | −0.0642626 | ||||||||
\(677\) | −3.61144e9 | −0.447321 | −0.223661 | − | 0.974667i | \(-0.571801\pi\) | ||||
−0.223661 | + | 0.974667i | \(0.571801\pi\) | |||||||
\(678\) | 9.67377e7 | 0.0119204 | ||||||||
\(679\) | −7.99810e9 | −0.980489 | ||||||||
\(680\) | −1.60173e9 | −0.195347 | ||||||||
\(681\) | 1.72180e8 | 0.0208914 | ||||||||
\(682\) | 1.89573e9 | 0.228840 | ||||||||
\(683\) | 1.07988e10 | 1.29689 | 0.648444 | − | 0.761262i | \(-0.275420\pi\) | ||||
0.648444 | + | 0.761262i | \(0.275420\pi\) | |||||||
\(684\) | 2.28302e9 | 0.272780 | ||||||||
\(685\) | −2.72132e8 | −0.0323491 | ||||||||
\(686\) | 8.61751e8 | 0.101917 | ||||||||
\(687\) | 4.21641e8 | 0.0496129 | ||||||||
\(688\) | 3.52316e8 | 0.0412451 | ||||||||
\(689\) | −1.38484e10 | −1.61299 | ||||||||
\(690\) | −7.02756e7 | −0.00814390 | ||||||||
\(691\) | 3.51258e9 | 0.404998 | 0.202499 | − | 0.979282i | \(-0.435094\pi\) | ||||
0.202499 | + | 0.979282i | \(0.435094\pi\) | |||||||
\(692\) | −4.66286e9 | −0.534911 | ||||||||
\(693\) | −2.48138e10 | −2.83222 | ||||||||
\(694\) | 1.14345e10 | 1.29855 | ||||||||
\(695\) | 2.76434e7 | 0.00312353 | ||||||||
\(696\) | −4.40414e7 | −0.00495141 | ||||||||
\(697\) | −5.00129e9 | −0.559458 | ||||||||
\(698\) | 8.74949e9 | 0.973843 | ||||||||
\(699\) | −4.53547e6 | −0.000502288 0 | ||||||||
\(700\) | 4.20204e9 | 0.463039 | ||||||||
\(701\) | −2.46256e9 | −0.270006 | −0.135003 | − | 0.990845i | \(-0.543104\pi\) | ||||
−0.135003 | + | 0.990845i | \(0.543104\pi\) | |||||||
\(702\) | 3.56355e8 | 0.0388779 | ||||||||
\(703\) | −1.90469e9 | −0.206767 | ||||||||
\(704\) | 1.61671e10 | 1.74634 | ||||||||
\(705\) | −9.67871e7 | −0.0104029 | ||||||||
\(706\) | −8.43320e9 | −0.901937 | ||||||||
\(707\) | 1.10824e10 | 1.17941 | ||||||||
\(708\) | −4.69653e7 | −0.00497348 | ||||||||
\(709\) | −1.34920e10 | −1.42172 | −0.710859 | − | 0.703335i | \(-0.751693\pi\) | ||||
−0.710859 | + | 0.703335i | \(0.751693\pi\) | |||||||
\(710\) | 1.53292e9 | 0.160737 | ||||||||
\(711\) | −1.07419e10 | −1.12082 | ||||||||
\(712\) | −1.45574e10 | −1.51149 | ||||||||
\(713\) | 1.19792e9 | 0.123769 | ||||||||
\(714\) | −8.02397e7 | −0.00824984 | ||||||||
\(715\) | 1.19853e10 | 1.22625 | ||||||||
\(716\) | −9.11137e9 | −0.927658 | ||||||||
\(717\) | 1.11026e7 | 0.00112489 | ||||||||
\(718\) | 5.94894e9 | 0.599797 | ||||||||
\(719\) | 7.00395e9 | 0.702736 | 0.351368 | − | 0.936237i | \(-0.385717\pi\) | ||||
0.351368 | + | 0.936237i | \(0.385717\pi\) | |||||||
\(720\) | 1.59526e9 | 0.159283 | ||||||||
\(721\) | −1.46828e10 | −1.45893 | ||||||||
\(722\) | −4.97978e9 | −0.492414 | ||||||||
\(723\) | −4.27308e8 | −0.0420492 | ||||||||
\(724\) | 2.94743e9 | 0.288642 | ||||||||
\(725\) | 1.21755e9 | 0.118660 | ||||||||
\(726\) | −5.32994e8 | −0.0516945 | ||||||||
\(727\) | 8.00714e9 | 0.772871 | 0.386436 | − | 0.922316i | \(-0.373706\pi\) | ||||
0.386436 | + | 0.922316i | \(0.373706\pi\) | |||||||
\(728\) | −1.70686e10 | −1.63960 | ||||||||
\(729\) | −1.04193e10 | −0.996072 | ||||||||
\(730\) | 3.01824e9 | 0.287160 | ||||||||
\(731\) | −5.01681e8 | −0.0475026 | ||||||||
\(732\) | −9.17248e7 | −0.00864367 | ||||||||
\(733\) | 9.27809e9 | 0.870151 | 0.435075 | − | 0.900394i | \(-0.356722\pi\) | ||||
0.435075 | + | 0.900394i | \(0.356722\pi\) | |||||||
\(734\) | 4.73303e9 | 0.441777 | ||||||||
\(735\) | −1.78354e8 | −0.0165683 | ||||||||
\(736\) | 7.12062e9 | 0.658332 | ||||||||
\(737\) | 1.51311e10 | 1.39230 | ||||||||
\(738\) | 1.40002e10 | 1.28215 | ||||||||
\(739\) | −1.50075e10 | −1.36789 | −0.683947 | − | 0.729532i | \(-0.739738\pi\) | ||||
−0.683947 | + | 0.729532i | \(0.739738\pi\) | |||||||
\(740\) | 1.18013e9 | 0.107058 | ||||||||
\(741\) | −1.68045e8 | −0.0151727 | ||||||||
\(742\) | −1.74634e10 | −1.56934 | ||||||||
\(743\) | 2.52291e9 | 0.225653 | 0.112827 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112827 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(744\) | 5.00977e7 | 0.00445977 | ||||||||
\(745\) | −5.33809e9 | −0.472976 | ||||||||
\(746\) | −1.26021e10 | −1.11137 | ||||||||
\(747\) | 2.04202e10 | 1.79241 | ||||||||
\(748\) | −3.41593e9 | −0.298438 | ||||||||
\(749\) | 1.31125e10 | 1.14025 | ||||||||
\(750\) | 2.05730e8 | 0.0178067 | ||||||||
\(751\) | −9.71269e9 | −0.836758 | −0.418379 | − | 0.908273i | \(-0.637402\pi\) | ||||
−0.418379 | + | 0.908273i | \(0.637402\pi\) | |||||||
\(752\) | −2.17542e9 | −0.186544 | ||||||||
\(753\) | −5.76758e8 | −0.0492279 | ||||||||
\(754\) | −1.62579e9 | −0.138123 | ||||||||
\(755\) | −3.34664e9 | −0.283006 | ||||||||
\(756\) | −4.31267e8 | −0.0363011 | ||||||||
\(757\) | −1.39407e10 | −1.16802 | −0.584008 | − | 0.811748i | \(-0.698516\pi\) | ||||
−0.584008 | + | 0.811748i | \(0.698516\pi\) | |||||||
\(758\) | −1.67616e8 | −0.0139789 | ||||||||
\(759\) | −4.55915e8 | −0.0378475 | ||||||||
\(760\) | −4.23016e9 | −0.349550 | ||||||||
\(761\) | 9.33520e9 | 0.767852 | 0.383926 | − | 0.923364i | \(-0.374572\pi\) | ||||
0.383926 | + | 0.923364i | \(0.374572\pi\) | |||||||
\(762\) | −1.32719e8 | −0.0108665 | ||||||||
\(763\) | −2.21217e10 | −1.80295 | ||||||||
\(764\) | 4.03558e9 | 0.327401 | ||||||||
\(765\) | −2.27158e9 | −0.183448 | ||||||||
\(766\) | 9.43258e9 | 0.758281 | ||||||||
\(767\) | −5.27399e9 | −0.422042 | ||||||||
\(768\) | 3.40344e8 | 0.0271115 | ||||||||
\(769\) | −1.02873e10 | −0.815754 | −0.407877 | − | 0.913037i | \(-0.633731\pi\) | ||||
−0.407877 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(770\) | 1.51141e10 | 1.19307 | ||||||||
\(771\) | 2.03554e6 | 0.000159952 0 | ||||||||
\(772\) | 8.12408e9 | 0.635497 | ||||||||
\(773\) | −6.15947e9 | −0.479640 | −0.239820 | − | 0.970817i | \(-0.577088\pi\) | ||||
−0.239820 | + | 0.970817i | \(0.577088\pi\) | |||||||
\(774\) | 1.40437e9 | 0.108865 | ||||||||
\(775\) | −1.38498e9 | −0.106878 | ||||||||
\(776\) | 9.37594e9 | 0.720275 | ||||||||
\(777\) | 1.79842e8 | 0.0137536 | ||||||||
\(778\) | −9.06863e9 | −0.690420 | ||||||||
\(779\) | −1.32084e10 | −1.00108 | ||||||||
\(780\) | 1.04119e8 | 0.00785597 | ||||||||
\(781\) | 9.94486e9 | 0.746999 | ||||||||
\(782\) | 2.24919e9 | 0.168191 | ||||||||
\(783\) | −1.24961e8 | −0.00930266 | ||||||||
\(784\) | −4.00875e9 | −0.297100 | ||||||||
\(785\) | −1.27750e10 | −0.942579 | ||||||||
\(786\) | 2.15558e8 | 0.0158338 | ||||||||
\(787\) | 6.80084e9 | 0.497337 | 0.248669 | − | 0.968589i | \(-0.420007\pi\) | ||||
0.248669 | + | 0.968589i | \(0.420007\pi\) | |||||||
\(788\) | −5.22564e9 | −0.380450 | ||||||||
\(789\) | 4.34053e8 | 0.0314611 | ||||||||
\(790\) | 6.54287e9 | 0.472143 | ||||||||
\(791\) | −1.31469e10 | −0.944506 | ||||||||
\(792\) | 2.90885e10 | 2.08057 | ||||||||
\(793\) | −1.03003e10 | −0.733489 | ||||||||
\(794\) | 5.05215e9 | 0.358183 | ||||||||
\(795\) | 3.24058e8 | 0.0228738 | ||||||||
\(796\) | 1.18553e10 | 0.833140 | ||||||||
\(797\) | −1.73727e10 | −1.21552 | −0.607762 | − | 0.794119i | \(-0.707933\pi\) | ||||
−0.607762 | + | 0.794119i | \(0.707933\pi\) | |||||||
\(798\) | −2.11913e8 | −0.0147621 | ||||||||
\(799\) | 3.09770e9 | 0.214845 | ||||||||
\(800\) | −8.23255e9 | −0.568486 | ||||||||
\(801\) | −2.06454e10 | −1.41942 | ||||||||
\(802\) | 5.49849e9 | 0.376386 | ||||||||
\(803\) | 1.95810e10 | 1.33453 | ||||||||
\(804\) | 1.31447e8 | 0.00891979 | ||||||||
\(805\) | 9.55061e9 | 0.645276 | ||||||||
\(806\) | 1.84936e9 | 0.124408 | ||||||||
\(807\) | −4.69048e8 | −0.0314167 | ||||||||
\(808\) | −1.29915e10 | −0.866404 | ||||||||
\(809\) | 9.63683e9 | 0.639903 | 0.319952 | − | 0.947434i | \(-0.396333\pi\) | ||||
0.319952 | + | 0.947434i | \(0.396333\pi\) | |||||||
\(810\) | 6.35472e9 | 0.420145 | ||||||||
\(811\) | 9.66741e9 | 0.636410 | 0.318205 | − | 0.948022i | \(-0.396920\pi\) | ||||
0.318205 | + | 0.948022i | \(0.396920\pi\) | |||||||
\(812\) | 1.96756e9 | 0.128968 | ||||||||
\(813\) | −6.31094e6 | −0.000411886 0 | ||||||||
\(814\) | −7.97770e9 | −0.518433 | ||||||||
\(815\) | −1.40856e10 | −0.911433 | ||||||||
\(816\) | 3.34663e7 | 0.00215622 | ||||||||
\(817\) | −1.32494e9 | −0.0850000 | ||||||||
\(818\) | 1.17392e10 | 0.749897 | ||||||||
\(819\) | −2.42068e10 | −1.53972 | ||||||||
\(820\) | 8.18381e9 | 0.518331 | ||||||||
\(821\) | 4.33448e9 | 0.273361 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(822\) | 1.59811e7 | 0.00100359 | ||||||||
\(823\) | 7.05830e9 | 0.441368 | 0.220684 | − | 0.975345i | \(-0.429171\pi\) | ||||
0.220684 | + | 0.975345i | \(0.429171\pi\) | |||||||
\(824\) | 1.72122e10 | 1.07175 | ||||||||
\(825\) | 5.27109e8 | 0.0326823 | ||||||||
\(826\) | −6.65076e9 | −0.410621 | ||||||||
\(827\) | 1.97938e10 | 1.21691 | 0.608457 | − | 0.793587i | \(-0.291789\pi\) | ||||
0.608457 | + | 0.793587i | \(0.291789\pi\) | |||||||
\(828\) | 6.04242e9 | 0.369917 | ||||||||
\(829\) | 1.55516e10 | 0.948055 | 0.474027 | − | 0.880510i | \(-0.342800\pi\) | ||||
0.474027 | + | 0.880510i | \(0.342800\pi\) | |||||||
\(830\) | −1.24379e10 | −0.755048 | ||||||||
\(831\) | −6.36313e8 | −0.0384652 | ||||||||
\(832\) | 1.57716e10 | 0.949390 | ||||||||
\(833\) | 5.70827e9 | 0.342174 | ||||||||
\(834\) | −1.62338e6 | −9.69033e−5 0 | ||||||||
\(835\) | −8.74302e9 | −0.519707 | ||||||||
\(836\) | −9.02147e9 | −0.534017 | ||||||||
\(837\) | 1.42144e8 | 0.00837897 | ||||||||
\(838\) | −1.67311e10 | −0.982135 | ||||||||
\(839\) | −4.02189e9 | −0.235106 | −0.117553 | − | 0.993067i | \(-0.537505\pi\) | ||||
−0.117553 | + | 0.993067i | \(0.537505\pi\) | |||||||
\(840\) | 3.99413e8 | 0.0232511 | ||||||||
\(841\) | −1.66798e10 | −0.966950 | ||||||||
\(842\) | −1.50922e10 | −0.871287 | ||||||||
\(843\) | −6.97950e8 | −0.0401262 | ||||||||
\(844\) | −8.85822e9 | −0.507163 | ||||||||
\(845\) | 1.35631e9 | 0.0773323 | ||||||||
\(846\) | −8.67146e9 | −0.492375 | ||||||||
\(847\) | 7.24351e10 | 4.09597 | ||||||||
\(848\) | 7.28365e9 | 0.410170 | ||||||||
\(849\) | 2.59287e8 | 0.0145413 | ||||||||
\(850\) | −2.60042e9 | −0.145237 | ||||||||
\(851\) | −5.04112e9 | −0.280397 | ||||||||
\(852\) | 8.63932e7 | 0.00478565 | ||||||||
\(853\) | −7.65536e9 | −0.422322 | −0.211161 | − | 0.977451i | \(-0.567725\pi\) | ||||
−0.211161 | + | 0.977451i | \(0.567725\pi\) | |||||||
\(854\) | −1.29892e10 | −0.713639 | ||||||||
\(855\) | −5.99925e9 | −0.328258 | ||||||||
\(856\) | −1.53714e10 | −0.837638 | ||||||||
\(857\) | −1.60019e10 | −0.868437 | −0.434218 | − | 0.900808i | \(-0.642975\pi\) | ||||
−0.434218 | + | 0.900808i | \(0.642975\pi\) | |||||||
\(858\) | −7.03847e8 | −0.0380428 | ||||||||
\(859\) | −9.96999e9 | −0.536684 | −0.268342 | − | 0.963324i | \(-0.586476\pi\) | ||||
−0.268342 | + | 0.963324i | \(0.586476\pi\) | |||||||
\(860\) | 8.20921e8 | 0.0440106 | ||||||||
\(861\) | 1.24714e9 | 0.0665892 | ||||||||
\(862\) | 8.35742e9 | 0.444423 | ||||||||
\(863\) | 2.21580e10 | 1.17353 | 0.586763 | − | 0.809759i | \(-0.300402\pi\) | ||||
0.586763 | + | 0.809759i | \(0.300402\pi\) | |||||||
\(864\) | 8.44930e8 | 0.0445679 | ||||||||
\(865\) | 1.22529e10 | 0.643701 | ||||||||
\(866\) | 1.52541e10 | 0.798131 | ||||||||
\(867\) | 4.43481e8 | 0.0231104 | ||||||||
\(868\) | −2.23813e9 | −0.116162 | ||||||||
\(869\) | 4.24471e10 | 2.19421 | ||||||||
\(870\) | 3.80443e7 | 0.00195872 | ||||||||
\(871\) | 1.47609e10 | 0.756920 | ||||||||
\(872\) | 2.59327e10 | 1.32446 | ||||||||
\(873\) | 1.32970e10 | 0.676402 | ||||||||
\(874\) | 5.94011e9 | 0.300957 | ||||||||
\(875\) | −2.79592e10 | −1.41090 | ||||||||
\(876\) | 1.70104e8 | 0.00854969 | ||||||||
\(877\) | −8.03090e9 | −0.402037 | −0.201018 | − | 0.979587i | \(-0.564425\pi\) | ||||
−0.201018 | + | 0.979587i | \(0.564425\pi\) | |||||||
\(878\) | −1.77152e10 | −0.883313 | ||||||||
\(879\) | 1.15212e8 | 0.00572187 | ||||||||
\(880\) | −6.30378e9 | −0.311825 | ||||||||
\(881\) | 1.58502e10 | 0.780944 | 0.390472 | − | 0.920615i | \(-0.372312\pi\) | ||||
0.390472 | + | 0.920615i | \(0.372312\pi\) | |||||||
\(882\) | −1.59793e10 | −0.784183 | ||||||||
\(883\) | −1.53480e10 | −0.750222 | −0.375111 | − | 0.926980i | \(-0.622395\pi\) | ||||
−0.375111 | + | 0.926980i | \(0.622395\pi\) | |||||||
\(884\) | −3.33237e9 | −0.162245 | ||||||||
\(885\) | 1.23414e8 | 0.00598498 | ||||||||
\(886\) | −9.96368e9 | −0.481284 | ||||||||
\(887\) | 6.55736e9 | 0.315498 | 0.157749 | − | 0.987479i | \(-0.449576\pi\) | ||||
0.157749 | + | 0.987479i | \(0.449576\pi\) | |||||||
\(888\) | −2.10823e8 | −0.0101035 | ||||||||
\(889\) | 1.80368e10 | 0.861002 | ||||||||
\(890\) | 1.25751e10 | 0.597926 | ||||||||
\(891\) | 4.12264e10 | 1.95256 | ||||||||
\(892\) | 6.94679e9 | 0.327723 | ||||||||
\(893\) | 8.18102e9 | 0.384439 | ||||||||
\(894\) | 3.13483e8 | 0.0146735 | ||||||||
\(895\) | 2.39426e10 | 1.11632 | ||||||||
\(896\) | −7.27760e9 | −0.337995 | ||||||||
\(897\) | −4.44762e8 | −0.0205757 | ||||||||
\(898\) | 1.66791e10 | 0.768611 | ||||||||
\(899\) | −6.48503e8 | −0.0297682 | ||||||||
\(900\) | −6.98599e9 | −0.319433 | ||||||||
\(901\) | −1.03716e10 | −0.472398 | ||||||||
\(902\) | −5.53226e10 | −2.51004 | ||||||||
\(903\) | 1.25101e8 | 0.00565397 | ||||||||
\(904\) | 1.54117e10 | 0.693842 | ||||||||
\(905\) | −7.74518e9 | −0.347345 | ||||||||
\(906\) | 1.96534e8 | 0.00877988 | ||||||||
\(907\) | −3.93411e10 | −1.75074 | −0.875368 | − | 0.483457i | \(-0.839381\pi\) | ||||
−0.875368 | + | 0.483457i | \(0.839381\pi\) | |||||||
\(908\) | 9.01733e9 | 0.399740 | ||||||||
\(909\) | −1.84247e10 | −0.813629 | ||||||||
\(910\) | 1.47443e10 | 0.648605 | ||||||||
\(911\) | 3.45238e10 | 1.51288 | 0.756440 | − | 0.654064i | \(-0.226937\pi\) | ||||
0.756440 | + | 0.654064i | \(0.226937\pi\) | |||||||
\(912\) | 8.83845e7 | 0.00385829 | ||||||||
\(913\) | −8.06914e10 | −3.50897 | ||||||||
\(914\) | −2.96700e10 | −1.28530 | ||||||||
\(915\) | 2.41032e8 | 0.0104016 | ||||||||
\(916\) | 2.20820e10 | 0.949301 | ||||||||
\(917\) | −2.92948e10 | −1.25458 | ||||||||
\(918\) | 2.66888e8 | 0.0113862 | ||||||||
\(919\) | −9.91457e9 | −0.421376 | −0.210688 | − | 0.977553i | \(-0.567570\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567570\pi\) | |||||||
\(920\) | −1.11959e10 | −0.474025 | ||||||||
\(921\) | −8.59600e8 | −0.0362567 | ||||||||
\(922\) | 1.21249e10 | 0.509473 | ||||||||
\(923\) | 9.70157e9 | 0.406103 | ||||||||
\(924\) | 8.51809e8 | 0.0355214 | ||||||||
\(925\) | 5.82833e9 | 0.242130 | ||||||||
\(926\) | 8.08281e9 | 0.334521 | ||||||||
\(927\) | 2.44105e10 | 1.00646 | ||||||||
\(928\) | −3.85481e9 | −0.158338 | ||||||||
\(929\) | −4.62667e10 | −1.89327 | −0.946636 | − | 0.322304i | \(-0.895543\pi\) | ||||
−0.946636 | + | 0.322304i | \(0.895543\pi\) | |||||||
\(930\) | −4.32759e7 | −0.00176423 | ||||||||
\(931\) | 1.50755e10 | 0.612278 | ||||||||
\(932\) | −2.37530e8 | −0.00961086 | ||||||||
\(933\) | 2.00561e8 | 0.00808465 | ||||||||
\(934\) | −9.14169e9 | −0.367124 | ||||||||
\(935\) | 8.97629e9 | 0.359134 | ||||||||
\(936\) | 2.83769e10 | 1.13110 | ||||||||
\(937\) | −2.62108e10 | −1.04086 | −0.520430 | − | 0.853904i | \(-0.674228\pi\) | ||||
−0.520430 | + | 0.853904i | \(0.674228\pi\) | |||||||
\(938\) | 1.86142e10 | 0.736436 | ||||||||
\(939\) | −7.41868e8 | −0.0292413 | ||||||||
\(940\) | −5.06889e9 | −0.199052 | ||||||||
\(941\) | 2.90508e10 | 1.13657 | 0.568283 | − | 0.822833i | \(-0.307608\pi\) | ||||
0.568283 | + | 0.822833i | \(0.307608\pi\) | |||||||
\(942\) | 7.50222e8 | 0.0292423 | ||||||||
\(943\) | −3.49584e10 | −1.35757 | ||||||||
\(944\) | 2.77390e9 | 0.107322 | ||||||||
\(945\) | 1.13327e9 | 0.0436840 | ||||||||
\(946\) | −5.54943e9 | −0.213123 | ||||||||
\(947\) | 6.74455e9 | 0.258064 | 0.129032 | − | 0.991640i | \(-0.458813\pi\) | ||||
0.129032 | + | 0.991640i | \(0.458813\pi\) | |||||||
\(948\) | 3.68747e8 | 0.0140572 | ||||||||
\(949\) | 1.91019e10 | 0.725514 | ||||||||
\(950\) | −6.86770e9 | −0.259883 | ||||||||
\(951\) | −3.14822e8 | −0.0118695 | ||||||||
\(952\) | −1.27833e10 | −0.480191 | ||||||||
\(953\) | 1.83022e10 | 0.684981 | 0.342490 | − | 0.939521i | \(-0.388730\pi\) | ||||
0.342490 | + | 0.939521i | \(0.388730\pi\) | |||||||
\(954\) | 2.90334e10 | 1.08263 | ||||||||
\(955\) | −1.06046e10 | −0.393987 | ||||||||
\(956\) | 5.81462e8 | 0.0215238 | ||||||||
\(957\) | 2.46814e8 | 0.00910285 | ||||||||
\(958\) | 3.45141e9 | 0.126828 | ||||||||
\(959\) | −2.17187e9 | −0.0795186 | ||||||||
\(960\) | −3.69064e8 | −0.0134633 | ||||||||
\(961\) | −2.67749e10 | −0.973188 | ||||||||
\(962\) | −7.78254e9 | −0.281844 | ||||||||
\(963\) | −2.17999e10 | −0.786615 | ||||||||
\(964\) | −2.23788e10 | −0.804576 | ||||||||
\(965\) | −2.13482e10 | −0.764744 | ||||||||
\(966\) | −5.60866e8 | −0.0200188 | ||||||||
\(967\) | −2.88943e9 | −0.102759 | −0.0513795 | − | 0.998679i | \(-0.516362\pi\) | ||||
−0.0513795 | + | 0.998679i | \(0.516362\pi\) | |||||||
\(968\) | −8.49135e10 | −3.00894 | ||||||||
\(969\) | −1.25856e8 | −0.00444364 | ||||||||
\(970\) | −8.09922e9 | −0.284933 | ||||||||
\(971\) | −5.32082e10 | −1.86514 | −0.932569 | − | 0.360991i | \(-0.882438\pi\) | ||||
−0.932569 | + | 0.360991i | \(0.882438\pi\) | |||||||
\(972\) | 1.07560e9 | 0.0375682 | ||||||||
\(973\) | 2.20621e8 | 0.00767806 | ||||||||
\(974\) | 1.50800e10 | 0.522933 | ||||||||
\(975\) | 5.14215e8 | 0.0177676 | ||||||||
\(976\) | 5.41751e9 | 0.186520 | ||||||||
\(977\) | −1.19053e10 | −0.408423 | −0.204211 | − | 0.978927i | \(-0.565463\pi\) | ||||
−0.204211 | + | 0.978927i | \(0.565463\pi\) | |||||||
\(978\) | 8.27189e8 | 0.0282760 | ||||||||
\(979\) | 8.15816e10 | 2.77877 | ||||||||
\(980\) | −9.34067e9 | −0.317020 | ||||||||
\(981\) | 3.67779e10 | 1.24379 | ||||||||
\(982\) | −2.16187e10 | −0.728518 | ||||||||
\(983\) | −4.93240e10 | −1.65623 | −0.828116 | − | 0.560557i | \(-0.810587\pi\) | ||||
−0.828116 | + | 0.560557i | \(0.810587\pi\) | |||||||
\(984\) | −1.46199e9 | −0.0489170 | ||||||||
\(985\) | 1.37318e10 | 0.457826 | ||||||||
\(986\) | −1.21762e9 | −0.0404522 | ||||||||
\(987\) | −7.72453e8 | −0.0255719 | ||||||||
\(988\) | −8.80078e9 | −0.290317 | ||||||||
\(989\) | −3.50669e9 | −0.115269 | ||||||||
\(990\) | −2.51275e10 | −0.823050 | ||||||||
\(991\) | 3.40025e10 | 1.10982 | 0.554911 | − | 0.831910i | \(-0.312752\pi\) | ||||
0.554911 | + | 0.831910i | \(0.312752\pi\) | |||||||
\(992\) | 4.38489e9 | 0.142616 | ||||||||
\(993\) | 1.17329e9 | 0.0380261 | ||||||||
\(994\) | 1.22341e10 | 0.395113 | ||||||||
\(995\) | −3.11531e10 | −1.00258 | ||||||||
\(996\) | −7.00984e8 | −0.0224802 | ||||||||
\(997\) | −4.30970e10 | −1.37725 | −0.688627 | − | 0.725116i | \(-0.741786\pi\) | ||||
−0.688627 | + | 0.725116i | \(0.741786\pi\) | |||||||
\(998\) | −1.63033e10 | −0.519179 | ||||||||
\(999\) | −5.98177e8 | −0.0189824 |
(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 | 43.8.a.b.1.9 | ✓ | 13 | |
3.2 | odd | 2 | 387.8.a.d.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.b.1.9 | ✓ | 13 | 1.1 | even | 1 | trivial | |
387.8.a.d.1.5 | 13 | 3.2 | odd | 2 |