Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-19.6388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.6388 | 1.91262 | 0.956309 | − | 0.292356i | \(-0.0944393\pi\) | ||||
0.956309 | + | 0.292356i | \(0.0944393\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 340.238 | 2.65811 | ||||||||
\(5\) | 399.107 | 1.42789 | 0.713945 | − | 0.700202i | \(-0.246907\pi\) | ||||
0.713945 | + | 0.700202i | \(0.246907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1780.57 | −1.96208 | −0.981039 | − | 0.193812i | \(-0.937915\pi\) | ||||
−0.981039 | + | 0.193812i | \(0.937915\pi\) | |||||||
\(8\) | 4592.58 | 3.17133 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8636.21 | 2.73101 | ||||||||
\(11\) | 204.067 | 0.0462274 | 0.0231137 | − | 0.999733i | \(-0.492642\pi\) | ||||
0.0231137 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7466.22 | 0.942539 | 0.471269 | − | 0.881989i | \(-0.343796\pi\) | ||||
0.471269 | + | 0.881989i | \(0.343796\pi\) | |||||||
\(14\) | −38529.4 | −3.75271 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 55827.6 | 3.40744 | ||||||||
\(17\) | −2070.83 | −0.102229 | −0.0511144 | − | 0.998693i | \(-0.516277\pi\) | ||||
−0.0511144 | + | 0.998693i | \(0.516277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38611.6 | 1.29146 | 0.645729 | − | 0.763566i | \(-0.276553\pi\) | ||||
0.645729 | + | 0.763566i | \(0.276553\pi\) | |||||||
\(20\) | 135792. | 3.79549 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4415.78 | 0.0884154 | ||||||||
\(23\) | 47604.4 | 0.815831 | 0.407915 | − | 0.913020i | \(-0.366256\pi\) | ||||
0.407915 | + | 0.913020i | \(0.366256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 81161.6 | 1.03887 | ||||||||
\(26\) | 161560. | 1.80272 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −605818. | −5.21542 | ||||||||
\(29\) | −223646. | −1.70282 | −0.851408 | − | 0.524505i | \(-0.824251\pi\) | ||||
−0.851408 | + | 0.524505i | \(0.824251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 273826. | 1.65085 | 0.825427 | − | 0.564508i | \(-0.190934\pi\) | ||||
0.825427 | + | 0.564508i | \(0.190934\pi\) | |||||||
\(32\) | 620192. | 3.34581 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −44810.3 | −0.195525 | ||||||||
\(35\) | −710639. | −2.80163 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −545039. | −1.76897 | −0.884487 | − | 0.466565i | \(-0.845491\pi\) | ||||
−0.884487 | + | 0.466565i | \(0.845491\pi\) | |||||||
\(38\) | 835510. | 2.47007 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.83293e6 | 4.52832 | ||||||||
\(41\) | 521804. | 1.18240 | 0.591200 | − | 0.806525i | \(-0.298654\pi\) | ||||
0.591200 | + | 0.806525i | \(0.298654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 327902. | 0.628934 | 0.314467 | − | 0.949268i | \(-0.398174\pi\) | ||||
0.314467 | + | 0.949268i | \(0.398174\pi\) | |||||||
\(44\) | 69431.5 | 0.122878 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.03010e6 | 1.56037 | ||||||||
\(47\) | 24173.5 | 0.0339623 | 0.0169811 | − | 0.999856i | \(-0.494594\pi\) | ||||
0.0169811 | + | 0.999856i | \(0.494594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.34689e6 | 2.84975 | ||||||||
\(50\) | 1.75624e6 | 1.98696 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.54029e6 | 2.50537 | ||||||||
\(53\) | 1.06061e6 | 0.978570 | 0.489285 | − | 0.872124i | \(-0.337258\pi\) | ||||
0.489285 | + | 0.872124i | \(0.337258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 81444.8 | 0.0660076 | ||||||||
\(56\) | −8.17742e6 | −6.22240 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.83943e6 | −3.25684 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.08933e6 | 0.614475 | 0.307238 | − | 0.951633i | \(-0.400595\pi\) | ||||
0.307238 | + | 0.951633i | \(0.400595\pi\) | |||||||
\(62\) | 5.92527e6 | 3.15746 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.27428e6 | 2.99181 | ||||||||
\(65\) | 2.97982e6 | 1.34584 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55751.2 | −0.0226461 | −0.0113230 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113230 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(68\) | −704575. | −0.271735 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.53774e7 | −5.35845 | ||||||||
\(71\) | 851859. | 0.282464 | 0.141232 | − | 0.989976i | \(-0.454894\pi\) | ||||
0.141232 | + | 0.989976i | \(0.454894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.44512e6 | 1.03651 | 0.518256 | − | 0.855225i | \(-0.326581\pi\) | ||||
0.518256 | + | 0.855225i | \(0.326581\pi\) | |||||||
\(74\) | −1.17940e7 | −3.38337 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.31372e7 | 3.43284 | ||||||||
\(77\) | −363356. | −0.0907017 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.05252e6 | −1.83754 | −0.918771 | − | 0.394791i | \(-0.870817\pi\) | ||||
−0.918771 | + | 0.394791i | \(0.870817\pi\) | |||||||
\(80\) | 2.22812e7 | 4.86545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.12912e7 | 2.26148 | ||||||||
\(83\) | −2.05020e6 | −0.393571 | −0.196785 | − | 0.980447i | \(-0.563050\pi\) | ||||
−0.196785 | + | 0.980447i | \(0.563050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −826483. | −0.145971 | ||||||||
\(86\) | 7.09542e6 | 1.20291 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 937197. | 0.146602 | ||||||||
\(89\) | 1.68320e6 | 0.253087 | 0.126544 | − | 0.991961i | \(-0.459612\pi\) | ||||
0.126544 | + | 0.991961i | \(0.459612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32941e7 | −1.84933 | ||||||||
\(92\) | 1.61969e7 | 2.16857 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 523086. | 0.0649569 | ||||||||
\(95\) | 1.54102e7 | 1.84406 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.14133e7 | 1.26972 | 0.634861 | − | 0.772627i | \(-0.281058\pi\) | ||||
0.634861 | + | 0.772627i | \(0.281058\pi\) | |||||||
\(98\) | 5.07839e7 | 5.45048 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.76143e7 | 2.76143 | ||||||||
\(101\) | −7.19660e6 | −0.695029 | −0.347514 | − | 0.937675i | \(-0.612974\pi\) | ||||
−0.347514 | + | 0.937675i | \(0.612974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.77089e6 | −0.249856 | −0.124928 | − | 0.992166i | \(-0.539870\pi\) | ||||
−0.124928 | + | 0.992166i | \(0.539870\pi\) | |||||||
\(104\) | 3.42893e7 | 2.98911 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.29504e7 | 1.87163 | ||||||||
\(107\) | 937525. | 0.0739843 | 0.0369922 | − | 0.999316i | \(-0.488222\pi\) | ||||
0.0369922 | + | 0.999316i | \(0.488222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.52436e7 | −1.12744 | −0.563722 | − | 0.825965i | \(-0.690631\pi\) | ||||
−0.563722 | + | 0.825965i | \(0.690631\pi\) | |||||||
\(110\) | 1.76237e6 | 0.126247 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.94049e7 | −6.68567 | ||||||||
\(113\) | 1.00374e7 | 0.654402 | 0.327201 | − | 0.944955i | \(-0.393895\pi\) | ||||
0.327201 | + | 0.944955i | \(0.393895\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.89993e7 | 1.16492 | ||||||||
\(116\) | −7.60928e7 | −4.52627 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.44416e6 | 0.249002 | ||||||||
\(119\) | 3.68726e6 | 0.200581 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94455e7 | −0.997863 | ||||||||
\(122\) | 2.35718e7 | 1.17526 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.31661e7 | 4.38816 | ||||||||
\(125\) | 1.21192e6 | 0.0554993 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.06146e6 | 0.392541 | 0.196270 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196270 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(128\) | 5.63835e7 | 2.37639 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.44799e7 | 2.57408 | ||||||||
\(131\) | −2.09570e7 | −0.814478 | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.87507e7 | −2.53394 | ||||||||
\(134\) | −1.20639e6 | −0.0433133 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.51046e6 | −0.324202 | ||||||||
\(137\) | −2.19828e7 | −0.730399 | −0.365199 | − | 0.930929i | \(-0.618999\pi\) | ||||
−0.365199 | + | 0.930929i | \(0.618999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.44663e6 | −0.203601 | −0.101801 | − | 0.994805i | \(-0.532460\pi\) | ||||
−0.101801 | + | 0.994805i | \(0.532460\pi\) | |||||||
\(140\) | −2.41786e8 | −7.44704 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.84332e7 | 0.540247 | ||||||||
\(143\) | 1.52361e6 | 0.0435711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.92586e7 | −2.43143 | ||||||||
\(146\) | 7.45484e7 | 1.98245 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.85443e8 | −4.70213 | ||||||||
\(149\) | 3.38724e7 | 0.838869 | 0.419434 | − | 0.907786i | \(-0.362228\pi\) | ||||
0.419434 | + | 0.907786i | \(0.362228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.27255e7 | −1.48260 | −0.741301 | − | 0.671172i | \(-0.765791\pi\) | ||||
−0.741301 | + | 0.671172i | \(0.765791\pi\) | |||||||
\(152\) | 1.77327e8 | 4.09565 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.86260e6 | −0.173478 | ||||||||
\(155\) | 1.09286e8 | 2.35724 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.72239e7 | 0.973898 | 0.486949 | − | 0.873430i | \(-0.338110\pi\) | ||||
0.486949 | + | 0.873430i | \(0.338110\pi\) | |||||||
\(158\) | −1.74247e8 | −3.51452 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.47523e8 | 4.77744 | ||||||||
\(161\) | −8.47631e7 | −1.60072 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.85412e7 | −0.516198 | −0.258099 | − | 0.966119i | \(-0.583096\pi\) | ||||
−0.258099 | + | 0.966119i | \(0.583096\pi\) | |||||||
\(164\) | 1.77538e8 | 3.14295 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.43639e7 | −0.752751 | ||||||||
\(167\) | 6.05397e7 | 1.00585 | 0.502924 | − | 0.864331i | \(-0.332258\pi\) | ||||
0.502924 | + | 0.864331i | \(0.332258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00401e6 | −0.111620 | ||||||||
\(170\) | −1.78841e7 | −0.279188 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.11565e8 | 1.67178 | ||||||||
\(173\) | 8.84147e7 | 1.29826 | 0.649132 | − | 0.760676i | \(-0.275132\pi\) | ||||
0.649132 | + | 0.760676i | \(0.275132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.44514e8 | −2.03834 | ||||||||
\(176\) | 1.13926e7 | 0.157517 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.64224e7 | 0.484059 | ||||||||
\(179\) | −9.25607e7 | −1.20626 | −0.603130 | − | 0.797643i | \(-0.706080\pi\) | ||||
−0.603130 | + | 0.797643i | \(0.706080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.46139e6 | 0.0935287 | 0.0467644 | − | 0.998906i | \(-0.485109\pi\) | ||||
0.0467644 | + | 0.998906i | \(0.485109\pi\) | |||||||
\(182\) | −2.87669e8 | −3.53707 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.18627e8 | 2.58727 | ||||||||
\(185\) | −2.17529e8 | −2.52590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −422589. | −0.00472577 | ||||||||
\(188\) | 8.22475e6 | 0.0902755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.33458e8 | 3.52698 | ||||||||
\(191\) | −6.59363e7 | −0.684712 | −0.342356 | − | 0.939570i | \(-0.611225\pi\) | ||||
−0.342356 | + | 0.939570i | \(0.611225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.34481e7 | 0.134651 | 0.0673257 | − | 0.997731i | \(-0.478553\pi\) | ||||
0.0673257 | + | 0.997731i | \(0.478553\pi\) | |||||||
\(194\) | 2.46969e8 | 2.42849 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.98502e8 | 7.57495 | ||||||||
\(197\) | −1.59146e7 | −0.148308 | −0.0741539 | − | 0.997247i | \(-0.523626\pi\) | ||||
−0.0741539 | + | 0.997247i | \(0.523626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.59450e7 | 0.323335 | 0.161668 | − | 0.986845i | \(-0.448313\pi\) | ||||
0.161668 | + | 0.986845i | \(0.448313\pi\) | |||||||
\(200\) | 3.72741e8 | 3.29460 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.55726e8 | −1.32932 | ||||||||
\(203\) | 3.98217e8 | 3.34105 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.08256e8 | 1.68834 | ||||||||
\(206\) | −5.99588e7 | −0.477878 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.16821e8 | 3.21165 | ||||||||
\(209\) | 7.87937e6 | 0.0597007 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.03281e8 | −1.48973 | −0.744866 | − | 0.667214i | \(-0.767486\pi\) | ||||
−0.744866 | + | 0.667214i | \(0.767486\pi\) | |||||||
\(212\) | 3.60861e8 | 2.60115 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.02869e7 | 0.141504 | ||||||||
\(215\) | 1.30868e8 | 0.898048 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.87567e8 | −3.23910 | ||||||||
\(218\) | −3.29853e8 | −2.15637 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.77106e7 | 0.175455 | ||||||||
\(221\) | −1.54613e7 | −0.0963546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.24671e8 | −0.752830 | −0.376415 | − | 0.926451i | \(-0.622843\pi\) | ||||
−0.376415 | + | 0.926451i | \(0.622843\pi\) | |||||||
\(224\) | −1.10429e9 | −6.56473 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.17196e8 | 1.25162 | ||||||||
\(227\) | 1.63994e7 | 0.0930547 | 0.0465273 | − | 0.998917i | \(-0.485185\pi\) | ||||
0.0465273 | + | 0.998917i | \(0.485185\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34148e8 | −0.738179 | −0.369089 | − | 0.929394i | \(-0.620330\pi\) | ||||
−0.369089 | + | 0.929394i | \(0.620330\pi\) | |||||||
\(230\) | 4.11122e8 | 2.22804 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.02711e9 | −5.40020 | ||||||||
\(233\) | 6.54300e7 | 0.338869 | 0.169434 | − | 0.985541i | \(-0.445806\pi\) | ||||
0.169434 | + | 0.985541i | \(0.445806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.64781e6 | 0.0484944 | ||||||||
\(236\) | 6.98778e7 | 0.346057 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.97879e7 | 0.383634 | ||||||||
\(239\) | 1.59121e8 | 0.753936 | 0.376968 | − | 0.926226i | \(-0.376967\pi\) | ||||
0.376968 | + | 0.926226i | \(0.376967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.38094e8 | 0.635501 | 0.317750 | − | 0.948174i | \(-0.397073\pi\) | ||||
0.317750 | + | 0.948174i | \(0.397073\pi\) | |||||||
\(242\) | −4.20778e8 | −1.90853 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.70631e8 | 1.63334 | ||||||||
\(245\) | 9.36661e8 | 4.06912 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.88283e8 | 1.21725 | ||||||||
\(248\) | 1.25757e9 | 5.23541 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.62244e7 | 0.106149 | ||||||||
\(251\) | −1.39109e8 | −0.555262 | −0.277631 | − | 0.960688i | \(-0.589549\pi\) | ||||
−0.277631 | + | 0.960688i | \(0.589549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.71452e6 | 0.0377137 | ||||||||
\(254\) | 1.96079e8 | 0.750781 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.16963e8 | 1.55331 | ||||||||
\(257\) | −4.09751e8 | −1.50575 | −0.752877 | − | 0.658162i | \(-0.771334\pi\) | ||||
−0.752877 | + | 0.658162i | \(0.771334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.70480e8 | 3.47086 | ||||||||
\(260\) | 1.01385e9 | 3.57740 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.53484e8 | −1.55779 | ||||||||
\(263\) | −1.19894e8 | −0.406400 | −0.203200 | − | 0.979137i | \(-0.565134\pi\) | ||||
−0.203200 | + | 0.979137i | \(0.565134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.23299e8 | 1.39729 | ||||||||
\(266\) | −1.48768e9 | −4.84647 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.89687e7 | −0.0601958 | ||||||||
\(269\) | 2.45594e8 | 0.769282 | 0.384641 | − | 0.923066i | \(-0.374325\pi\) | ||||
0.384641 | + | 0.923066i | \(0.374325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.52445e8 | 0.770503 | 0.385252 | − | 0.922812i | \(-0.374115\pi\) | ||||
0.385252 | + | 0.922812i | \(0.374115\pi\) | |||||||
\(272\) | −1.15609e8 | −0.348339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.75681e8 | −1.39697 | ||||||||
\(275\) | 1.65624e7 | 0.0480241 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.24074e8 | 0.916147 | 0.458074 | − | 0.888914i | \(-0.348540\pi\) | ||||
0.458074 | + | 0.888914i | \(0.348540\pi\) | |||||||
\(278\) | −1.39497e8 | −0.389412 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.26367e9 | −8.88491 | ||||||||
\(281\) | 1.78256e8 | 0.479260 | 0.239630 | − | 0.970864i | \(-0.422974\pi\) | ||||
0.239630 | + | 0.970864i | \(0.422974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.64602e8 | −1.21851 | −0.609254 | − | 0.792975i | \(-0.708531\pi\) | ||||
−0.609254 | + | 0.792975i | \(0.708531\pi\) | |||||||
\(284\) | 2.89835e8 | 0.750822 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.29692e7 | 0.0833349 | ||||||||
\(287\) | −9.29110e8 | −2.31996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.06050e8 | −0.989549 | ||||||||
\(290\) | −1.93145e9 | −4.65040 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.17216e9 | 2.75517 | ||||||||
\(293\) | 7.63943e8 | 1.77429 | 0.887145 | − | 0.461492i | \(-0.152686\pi\) | ||||
0.887145 | + | 0.461492i | \(0.152686\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.19682e7 | 0.185895 | ||||||||
\(296\) | −2.50314e9 | −5.61001 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.32959e8 | 1.60444 | ||||||||
\(299\) | 3.55425e8 | 0.768952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.83853e8 | −1.23402 | ||||||||
\(302\) | −1.35731e9 | −2.83565 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.15559e9 | 4.40057 | ||||||||
\(305\) | 4.34759e8 | 0.877402 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.34126e8 | −1.05356 | −0.526780 | − | 0.850001i | \(-0.676601\pi\) | ||||
−0.526780 | + | 0.850001i | \(0.676601\pi\) | |||||||
\(308\) | −1.23628e8 | −0.241095 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.36482e9 | 4.50850 | ||||||||
\(311\) | −7.32126e8 | −1.38014 | −0.690072 | − | 0.723741i | \(-0.742421\pi\) | ||||
−0.690072 | + | 0.723741i | \(0.742421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.31534e8 | 0.979774 | 0.489887 | − | 0.871786i | \(-0.337038\pi\) | ||||
0.489887 | + | 0.871786i | \(0.337038\pi\) | |||||||
\(314\) | 1.02187e9 | 1.86270 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.73978e9 | −4.88439 | ||||||||
\(317\) | −1.07205e9 | −1.89020 | −0.945102 | − | 0.326775i | \(-0.894038\pi\) | ||||
−0.945102 | + | 0.326775i | \(0.894038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56388e7 | −0.0787167 | ||||||||
\(320\) | 2.50411e9 | 4.27197 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.83417e9 | −3.06157 | ||||||||
\(323\) | −7.99581e7 | −0.132024 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.05970e8 | 0.979174 | ||||||||
\(326\) | −6.17598e8 | −0.987289 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.39643e9 | 3.74979 | ||||||||
\(329\) | −4.30426e7 | −0.0666366 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.36057e7 | −0.0660914 | −0.0330457 | − | 0.999454i | \(-0.510521\pi\) | ||||
−0.0330457 | + | 0.999454i | \(0.510521\pi\) | |||||||
\(332\) | −6.97556e8 | −1.04615 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31001e9 | 1.92380 | ||||||||
\(335\) | −2.22507e7 | −0.0323361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.67140e8 | −0.949538 | −0.474769 | − | 0.880110i | \(-0.657468\pi\) | ||||
−0.474769 | + | 0.880110i | \(0.657468\pi\) | |||||||
\(338\) | −1.51559e8 | −0.213487 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.81201e8 | −0.388008 | ||||||||
\(341\) | 5.58790e7 | 0.0763147 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.71243e9 | −3.62935 | ||||||||
\(344\) | 1.50592e9 | 1.99456 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.91319e9 | 2.48308 | ||||||||
\(347\) | −3.15540e7 | −0.0405417 | −0.0202708 | − | 0.999795i | \(-0.506453\pi\) | ||||
−0.0202708 | + | 0.999795i | \(0.506453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.24543e8 | 0.912379 | 0.456189 | − | 0.889883i | \(-0.349214\pi\) | ||||
0.456189 | + | 0.889883i | \(0.349214\pi\) | |||||||
\(350\) | −3.12711e9 | −3.89857 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26561e8 | 0.154668 | ||||||||
\(353\) | −9.26501e8 | −1.12107 | −0.560537 | − | 0.828129i | \(-0.689405\pi\) | ||||
−0.560537 | + | 0.828129i | \(0.689405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.39983e8 | 0.403328 | ||||||||
\(356\) | 5.72688e8 | 0.672734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00290e9 | −2.30712 | ||||||||
\(359\) | 1.08624e9 | 1.23906 | 0.619532 | − | 0.784971i | \(-0.287322\pi\) | ||||
0.619532 | + | 0.784971i | \(0.287322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.96986e8 | 0.667866 | ||||||||
\(362\) | 1.61456e8 | 0.178885 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.52318e9 | −4.91574 | ||||||||
\(365\) | 1.37497e9 | 1.48003 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.58587e8 | 0.906678 | 0.453339 | − | 0.891338i | \(-0.350233\pi\) | ||||
0.453339 | + | 0.891338i | \(0.350233\pi\) | |||||||
\(368\) | 2.65764e9 | 2.77990 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.70707e9 | −4.83108 | ||||||||
\(371\) | −1.88850e9 | −1.92003 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.80912e8 | −0.180504 | −0.0902518 | − | 0.995919i | \(-0.528767\pi\) | ||||
−0.0902518 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(374\) | −9.14432e6 | −0.00903859 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.11019e8 | 0.107706 | ||||||||
\(377\) | −1.66979e9 | −1.60497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.73658e9 | −1.63854 | −0.819270 | − | 0.573408i | \(-0.805621\pi\) | ||||
−0.819270 | + | 0.573408i | \(0.805621\pi\) | |||||||
\(380\) | 5.24313e9 | 4.90172 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.42678e9 | −1.30959 | ||||||||
\(383\) | −1.24471e9 | −1.13207 | −0.566035 | − | 0.824381i | \(-0.691523\pi\) | ||||
−0.566035 | + | 0.824381i | \(0.691523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.45018e8 | −0.129512 | ||||||||
\(386\) | 2.91001e8 | 0.257537 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.88322e9 | 3.37506 | ||||||||
\(389\) | 1.41664e9 | 1.22021 | 0.610106 | − | 0.792320i | \(-0.291127\pi\) | ||||
0.610106 | + | 0.792320i | \(0.291127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.85807e7 | −0.0834014 | ||||||||
\(392\) | 1.07783e10 | 9.03750 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.44373e8 | −0.283656 | ||||||||
\(395\) | −3.21382e9 | −2.62381 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.99168e9 | −1.59755 | −0.798773 | − | 0.601633i | \(-0.794517\pi\) | ||||
−0.798773 | + | 0.601633i | \(0.794517\pi\) | |||||||
\(398\) | 7.77808e8 | 0.618417 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.53105e9 | 3.53988 | ||||||||
\(401\) | 9.22799e8 | 0.714664 | 0.357332 | − | 0.933977i | \(-0.383687\pi\) | ||||
0.357332 | + | 0.933977i | \(0.383687\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.04445e9 | 1.55599 | ||||||||
\(404\) | −2.44856e9 | −1.84746 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.61694e9 | 6.39017 | ||||||||
\(407\) | −1.11225e8 | −0.0817750 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.58871e7 | −0.0259362 | −0.0129681 | − | 0.999916i | \(-0.504128\pi\) | ||||
−0.0129681 | + | 0.999916i | \(0.504128\pi\) | |||||||
\(410\) | 4.50641e9 | 3.22914 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.42763e8 | −0.664144 | ||||||||
\(413\) | −3.65692e8 | −0.255441 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.18249e8 | −0.561975 | ||||||||
\(416\) | 4.63049e9 | 3.15355 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.70500e8 | 0.114185 | ||||||||
\(419\) | 2.26805e8 | 0.150627 | 0.0753135 | − | 0.997160i | \(-0.476004\pi\) | ||||
0.0753135 | + | 0.997160i | \(0.476004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.22132e8 | 0.471660 | 0.235830 | − | 0.971794i | \(-0.424219\pi\) | ||||
0.235830 | + | 0.971794i | \(0.424219\pi\) | |||||||
\(422\) | −4.39876e9 | −2.84929 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.87096e9 | 3.10337 | ||||||||
\(425\) | −1.68072e8 | −0.106202 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.93963e9 | −1.20565 | ||||||||
\(428\) | 3.18982e8 | 0.196659 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.83183e9 | 1.71762 | ||||||||
\(431\) | −2.37550e8 | −0.142917 | −0.0714586 | − | 0.997444i | \(-0.522765\pi\) | ||||
−0.0714586 | + | 0.997444i | \(0.522765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.62934e8 | −0.155646 | −0.0778231 | − | 0.996967i | \(-0.524797\pi\) | ||||
−0.0778231 | + | 0.996967i | \(0.524797\pi\) | |||||||
\(434\) | −1.05504e10 | −6.19517 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.18645e9 | −2.99687 | ||||||||
\(437\) | 1.83809e9 | 1.05361 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.64067e8 | 0.543853 | 0.271926 | − | 0.962318i | \(-0.412339\pi\) | ||||
0.271926 | + | 0.962318i | \(0.412339\pi\) | |||||||
\(440\) | 3.74042e8 | 0.209332 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.34564e8 | −0.184290 | ||||||||
\(443\) | −2.26896e9 | −1.23998 | −0.619989 | − | 0.784611i | \(-0.712863\pi\) | ||||
−0.619989 | + | 0.784611i | \(0.712863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.71776e8 | 0.361380 | ||||||||
\(446\) | −2.69772e9 | −1.43988 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.11718e10 | −5.87016 | ||||||||
\(449\) | 6.29447e8 | 0.328168 | 0.164084 | − | 0.986446i | \(-0.447533\pi\) | ||||
0.164084 | + | 0.986446i | \(0.447533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06483e8 | 0.0546592 | ||||||||
\(452\) | 3.41509e9 | 1.73947 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.54864e8 | 0.177978 | ||||||||
\(455\) | −5.30579e9 | −2.64064 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.73973e9 | −1.34277 | −0.671383 | − | 0.741111i | \(-0.734299\pi\) | ||||
−0.671383 | + | 0.741111i | \(0.734299\pi\) | |||||||
\(458\) | −2.90281e9 | −1.41185 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.46428e9 | 3.09648 | ||||||||
\(461\) | −1.50755e9 | −0.716668 | −0.358334 | − | 0.933593i | \(-0.616655\pi\) | ||||
−0.358334 | + | 0.933593i | \(0.616655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.07432e8 | −0.331246 | −0.165623 | − | 0.986189i | \(-0.552964\pi\) | ||||
−0.165623 | + | 0.986189i | \(0.552964\pi\) | |||||||
\(464\) | −1.24856e10 | −5.80225 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.41583e9 | 0.648126 | ||||||||
\(467\) | 3.62529e9 | 1.64715 | 0.823575 | − | 0.567207i | \(-0.191976\pi\) | ||||
0.823575 | + | 0.567207i | \(0.191976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.92690e7 | 0.0444333 | ||||||||
\(470\) | 2.08767e8 | 0.0927513 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.43220e8 | 0.412873 | ||||||||
\(473\) | 6.69142e7 | 0.0290740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.13378e9 | 1.34166 | ||||||||
\(476\) | 1.25455e9 | 0.533166 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.44319e9 | 1.44199 | ||||||||
\(479\) | −1.79818e9 | −0.747580 | −0.373790 | − | 0.927513i | \(-0.621942\pi\) | ||||
−0.373790 | + | 0.927513i | \(0.621942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.06938e9 | −1.66733 | ||||||||
\(482\) | 2.98820e9 | 1.21547 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.61611e9 | −2.65243 | ||||||||
\(485\) | 4.55511e9 | 1.81302 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.58236e9 | −0.620802 | −0.310401 | − | 0.950606i | \(-0.600463\pi\) | ||||
−0.310401 | + | 0.950606i | \(0.600463\pi\) | |||||||
\(488\) | 5.00283e9 | 1.94871 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.02682e10 | 7.78268 | ||||||||
\(491\) | 2.99676e8 | 0.114253 | 0.0571264 | − | 0.998367i | \(-0.481806\pi\) | ||||
0.0571264 | + | 0.998367i | \(0.481806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.63132e8 | 0.174077 | ||||||||
\(494\) | 6.23810e9 | 2.32814 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.52870e10 | 5.62520 | ||||||||
\(497\) | −1.51680e9 | −0.554217 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.35009e9 | 0.486419 | 0.243210 | − | 0.969974i | \(-0.421800\pi\) | ||||
0.243210 | + | 0.969974i | \(0.421800\pi\) | |||||||
\(500\) | 4.12340e8 | 0.147523 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.01016e9 | −1.06200 | ||||||||
\(503\) | −1.94191e9 | −0.680365 | −0.340183 | − | 0.940359i | \(-0.610489\pi\) | ||||
−0.340183 | + | 0.940359i | \(0.610489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.87222e9 | −0.992424 | ||||||||
\(506\) | 2.10211e8 | 0.0721320 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.08305e9 | 1.04342 | ||||||||
\(509\) | 1.85092e9 | 0.622120 | 0.311060 | − | 0.950390i | \(-0.399316\pi\) | ||||
0.311060 | + | 0.950390i | \(0.399316\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.13429e9 | −2.03372 | ||||||||
\(512\) | 1.80551e9 | 0.594504 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.86652e9 | −2.87993 | ||||||||
\(515\) | −1.10588e9 | −0.356766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.93302e6 | 0.00156999 | ||||||||
\(518\) | 2.10000e10 | 6.63844 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.36851e10 | 4.26811 | ||||||||
\(521\) | −2.35474e9 | −0.729475 | −0.364738 | − | 0.931110i | \(-0.618841\pi\) | ||||
−0.364738 | + | 0.931110i | \(0.618841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.86850e9 | 0.571133 | 0.285566 | − | 0.958359i | \(-0.407818\pi\) | ||||
0.285566 | + | 0.958359i | \(0.407818\pi\) | |||||||
\(524\) | −7.13037e9 | −2.16497 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.59437e9 | −0.777288 | ||||||||
\(527\) | −5.67047e8 | −0.168765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.13864e9 | −0.334420 | ||||||||
\(530\) | 9.15968e9 | 2.67248 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.33916e10 | −6.73550 | ||||||||
\(533\) | 3.89591e9 | 1.11446 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.74173e8 | 0.105641 | ||||||||
\(536\) | −2.56042e8 | −0.0718183 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.31437e9 | 1.47134 | ||||||||
\(539\) | 4.78924e8 | 0.131736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58014e8 | −0.0429046 | −0.0214523 | − | 0.999770i | \(-0.506829\pi\) | ||||
−0.0214523 | + | 0.999770i | \(0.506829\pi\) | |||||||
\(542\) | 5.46261e9 | 1.47368 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.28431e9 | −0.342038 | ||||||||
\(545\) | −6.08383e9 | −1.60986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.19427e8 | −0.109572 | −0.0547862 | − | 0.998498i | \(-0.517448\pi\) | ||||
−0.0547862 | + | 0.998498i | \(0.517448\pi\) | |||||||
\(548\) | −7.47937e9 | −1.94148 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.58391e8 | 0.0918519 | ||||||||
\(551\) | −8.63532e9 | −2.19912 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.43381e10 | 3.60540 | ||||||||
\(554\) | 7.01258e9 | 1.75224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.19339e9 | −0.541195 | ||||||||
\(557\) | 7.37086e9 | 1.80728 | 0.903639 | − | 0.428295i | \(-0.140886\pi\) | ||||
0.903639 | + | 0.428295i | \(0.140886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44819e9 | 0.592795 | ||||||||
\(560\) | −3.96732e10 | −9.54640 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.85724e9 | 0.916642 | ||||||||
\(563\) | 5.40369e9 | 1.27618 | 0.638089 | − | 0.769963i | \(-0.279725\pi\) | ||||
0.638089 | + | 0.769963i | \(0.279725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00598e9 | 0.934414 | ||||||||
\(566\) | −1.00534e10 | −2.33054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.91224e9 | 0.895789 | ||||||||
\(569\) | 2.39098e9 | 0.544104 | 0.272052 | − | 0.962283i | \(-0.412298\pi\) | ||||
0.272052 | + | 0.962283i | \(0.412298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.97857e9 | −1.11912 | −0.559562 | − | 0.828789i | \(-0.689031\pi\) | ||||
−0.559562 | + | 0.828789i | \(0.689031\pi\) | |||||||
\(572\) | 5.18391e8 | 0.115817 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.01048e10 | −4.43720 | ||||||||
\(575\) | 3.86365e9 | 0.847541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.57830e9 | 0.775464 | 0.387732 | − | 0.921772i | \(-0.373259\pi\) | ||||
0.387732 | + | 0.921772i | \(0.373259\pi\) | |||||||
\(578\) | −8.78645e9 | −1.89263 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.03692e10 | −6.46302 | ||||||||
\(581\) | 3.65053e9 | 0.772216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.16437e8 | 0.0452367 | ||||||||
\(584\) | 1.58220e10 | 3.28713 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.65308e10 | 3.39354 | ||||||||
\(587\) | 2.26324e9 | 0.461845 | 0.230923 | − | 0.972972i | \(-0.425826\pi\) | ||||
0.230923 | + | 0.972972i | \(0.425826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05729e10 | 2.13201 | ||||||||
\(590\) | 1.77370e9 | 0.355547 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.04282e10 | −6.02768 | ||||||||
\(593\) | −2.71803e9 | −0.535257 | −0.267628 | − | 0.963522i | \(-0.586240\pi\) | ||||
−0.267628 | + | 0.963522i | \(0.586240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.47161e9 | 0.286407 | ||||||||
\(596\) | 1.15247e10 | 2.22981 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.69099e9 | 1.47071 | ||||||||
\(599\) | −5.48589e9 | −1.04293 | −0.521463 | − | 0.853274i | \(-0.674614\pi\) | ||||
−0.521463 | + | 0.853274i | \(0.674614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.20845e9 | 0.978695 | 0.489348 | − | 0.872089i | \(-0.337235\pi\) | ||||
0.489348 | + | 0.872089i | \(0.337235\pi\) | |||||||
\(602\) | −1.26339e10 | −2.36020 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.13416e10 | −3.94092 | ||||||||
\(605\) | −7.76085e9 | −1.42484 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.43683e9 | −1.53115 | −0.765577 | − | 0.643345i | \(-0.777546\pi\) | ||||
−0.765577 | + | 0.643345i | \(0.777546\pi\) | |||||||
\(608\) | 2.39466e10 | 4.32097 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.40766e9 | 1.67814 | ||||||||
\(611\) | 1.80485e8 | 0.0320108 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.65621e9 | −1.16712 | −0.583560 | − | 0.812070i | \(-0.698341\pi\) | ||||
−0.583560 | + | 0.812070i | \(0.698341\pi\) | |||||||
\(614\) | −1.15579e10 | −2.01506 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.66874e9 | −0.287645 | ||||||||
\(617\) | −1.08431e10 | −1.85846 | −0.929231 | − | 0.369498i | \(-0.879530\pi\) | ||||
−0.929231 | + | 0.369498i | \(0.879530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.05882e10 | −1.79434 | −0.897172 | − | 0.441681i | \(-0.854382\pi\) | ||||
−0.897172 | + | 0.441681i | \(0.854382\pi\) | |||||||
\(620\) | 3.71833e10 | 6.26580 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.58423e10 | −2.63969 | ||||||||
\(623\) | −2.99705e9 | −0.496576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.85706e9 | −0.959621 | ||||||||
\(626\) | 1.15018e10 | 1.87394 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.60674e10 | 2.58873 | ||||||||
\(629\) | 1.12868e9 | 0.180840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.06740e9 | 1.43675 | 0.718373 | − | 0.695658i | \(-0.244887\pi\) | ||||
0.718373 | + | 0.695658i | \(0.244887\pi\) | |||||||
\(632\) | −3.69819e10 | −5.82746 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.31980e10 | −3.61524 | ||||||||
\(635\) | 3.61649e9 | 0.560505 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.75224e10 | 2.68600 | ||||||||
\(638\) | −9.87569e8 | −0.150555 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.25030e10 | 3.39322 | ||||||||
\(641\) | 6.94011e9 | 1.04079 | 0.520395 | − | 0.853926i | \(-0.325785\pi\) | ||||
0.520395 | + | 0.853926i | \(0.325785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.50631e9 | −0.668471 | −0.334235 | − | 0.942490i | \(-0.608478\pi\) | ||||
−0.334235 | + | 0.942490i | \(0.608478\pi\) | |||||||
\(644\) | −2.88396e10 | −4.25490 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.73020e9 | −0.252512 | ||||||||
\(647\) | −5.05823e9 | −0.734233 | −0.367116 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367116 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.19112e7 | 0.00601829 | ||||||||
\(650\) | 1.31125e10 | 1.87279 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.71082e9 | −1.37211 | ||||||||
\(653\) | 3.31489e9 | 0.465879 | 0.232940 | − | 0.972491i | \(-0.425166\pi\) | ||||
0.232940 | + | 0.972491i | \(0.425166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.36409e9 | −1.16298 | ||||||||
\(656\) | 2.91311e10 | 4.02896 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.31391e8 | −0.127450 | ||||||||
\(659\) | 9.88658e9 | 1.34570 | 0.672849 | − | 0.739780i | \(-0.265071\pi\) | ||||
0.672849 | + | 0.739780i | \(0.265071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76683e9 | −0.237952 | −0.118976 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118976 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(662\) | −9.43576e8 | −0.126408 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.41571e9 | −1.24814 | ||||||||
\(665\) | −2.74389e10 | −3.61819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.06465e10 | −1.38921 | ||||||||
\(668\) | 2.05979e10 | 2.67366 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.81479e8 | −0.0618466 | ||||||||
\(671\) | 2.22296e8 | 0.0284056 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.78145e9 | −1.11049 | −0.555244 | − | 0.831688i | \(-0.687375\pi\) | ||||
−0.555244 | + | 0.831688i | \(0.687375\pi\) | |||||||
\(674\) | −1.44361e10 | −1.81610 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.38303e9 | −0.296699 | ||||||||
\(677\) | −1.26024e9 | −0.156096 | −0.0780482 | − | 0.996950i | \(-0.524869\pi\) | ||||
−0.0780482 | + | 0.996950i | \(0.524869\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.03221e10 | −2.49129 | ||||||||
\(680\) | −3.79569e9 | −0.462924 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.20915e9 | 0.145961 | ||||||||
\(683\) | −1.20509e10 | −1.44726 | −0.723630 | − | 0.690188i | \(-0.757528\pi\) | ||||
−0.723630 | + | 0.690188i | \(0.757528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.77348e9 | −1.04293 | ||||||||
\(686\) | −5.86937e10 | −6.94156 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.83060e10 | 2.14306 | ||||||||
\(689\) | 7.91878e9 | 0.922340 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.63179e9 | −0.188144 | −0.0940720 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940720 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(692\) | 3.00820e10 | 3.45093 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.82792e8 | −0.0775408 | ||||||||
\(695\) | −2.57290e9 | −0.290720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08057e9 | −0.120875 | ||||||||
\(698\) | 1.56782e10 | 1.74503 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.91692e10 | −5.41813 | ||||||||
\(701\) | 4.92646e9 | 0.540159 | 0.270080 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270080 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.10448e10 | −2.28456 | ||||||||
\(704\) | 1.28038e9 | 0.138304 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.00484e10 | −2.14419 | ||||||||
\(707\) | 1.28141e10 | 1.36370 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.23998e10 | 1.30663 | 0.653315 | − | 0.757087i | \(-0.273378\pi\) | ||||
0.653315 | + | 0.757087i | \(0.273378\pi\) | |||||||
\(710\) | 7.35683e9 | 0.771413 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.73022e9 | 0.802624 | ||||||||
\(713\) | 1.30353e10 | 1.34682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.08085e8 | 0.0622147 | ||||||||
\(716\) | −3.14927e10 | −3.20637 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.35049e10 | 2.36986 | ||||||||
\(719\) | 7.30887e9 | 0.733329 | 0.366665 | − | 0.930353i | \(-0.380500\pi\) | ||||
0.366665 | + | 0.930353i | \(0.380500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.93377e9 | 0.490236 | ||||||||
\(722\) | 1.29181e10 | 1.27737 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.53865e9 | 0.248610 | ||||||||
\(725\) | −1.81514e10 | −1.76900 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04087e9 | −0.100467 | −0.0502337 | − | 0.998737i | \(-0.515997\pi\) | ||||
−0.0502337 | + | 0.998737i | \(0.515997\pi\) | |||||||
\(728\) | −6.10545e10 | −5.86486 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.97528e10 | 2.83073 | ||||||||
\(731\) | −6.79030e8 | −0.0642951 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.03455e10 | 0.970262 | 0.485131 | − | 0.874441i | \(-0.338772\pi\) | ||||
0.485131 | + | 0.874441i | \(0.338772\pi\) | |||||||
\(734\) | 1.85788e10 | 1.73413 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.95239e10 | 2.72961 | ||||||||
\(737\) | −1.13770e7 | −0.00104687 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.36230e9 | −0.762203 | −0.381101 | − | 0.924533i | \(-0.624455\pi\) | ||||
−0.381101 | + | 0.924533i | \(0.624455\pi\) | |||||||
\(740\) | −7.40117e10 | −6.71412 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.08649e10 | −3.67228 | ||||||||
\(743\) | 1.24177e10 | 1.11066 | 0.555330 | − | 0.831630i | \(-0.312592\pi\) | ||||
0.555330 | + | 0.831630i | \(0.312592\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.35187e10 | 1.19781 | ||||||||
\(746\) | −3.91472e9 | −0.345235 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.43781e8 | −0.0125616 | ||||||||
\(749\) | −1.66933e9 | −0.145163 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.11718e9 | −0.354699 | −0.177349 | − | 0.984148i | \(-0.556752\pi\) | ||||
−0.177349 | + | 0.984148i | \(0.556752\pi\) | |||||||
\(752\) | 1.34955e9 | 0.115725 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.61322e10 | −3.06970 | ||||||||
\(755\) | −2.50342e10 | −2.11699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.02287e9 | 0.588409 | 0.294204 | − | 0.955743i | \(-0.404945\pi\) | ||||
0.294204 | + | 0.955743i | \(0.404945\pi\) | |||||||
\(758\) | −3.75775e10 | −3.13390 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.07725e10 | 5.84813 | ||||||||
\(761\) | 3.65462e9 | 0.300605 | 0.150302 | − | 0.988640i | \(-0.451975\pi\) | ||||
0.150302 | + | 0.988640i | \(0.451975\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.71423e10 | 2.21213 | ||||||||
\(764\) | −2.24340e10 | −1.82004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.69341e10 | −2.16522 | ||||||||
\(767\) | 1.53341e9 | 0.122708 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.51627e10 | 1.20236 | 0.601179 | − | 0.799114i | \(-0.294698\pi\) | ||||
0.601179 | + | 0.799114i | \(0.294698\pi\) | |||||||
\(770\) | −3.13802e9 | −0.247707 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.57556e9 | 0.357918 | ||||||||
\(773\) | −1.27681e10 | −0.994253 | −0.497126 | − | 0.867678i | \(-0.665612\pi\) | ||||
−0.497126 | + | 0.867678i | \(0.665612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22242e10 | 1.71502 | ||||||||
\(776\) | 5.24163e10 | 4.02671 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.06543e10 | 2.33380 | ||||||||
\(779\) | 2.01477e10 | 1.52702 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73837e8 | 0.0130576 | ||||||||
\(782\) | −2.13317e9 | −0.159515 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.31021e11 | 9.71036 | ||||||||
\(785\) | 1.88474e10 | 1.39062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.81227e9 | −0.278787 | −0.139394 | − | 0.990237i | \(-0.544515\pi\) | ||||
−0.139394 | + | 0.990237i | \(0.544515\pi\) | |||||||
\(788\) | −5.41476e9 | −0.394219 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.95433e10 | −5.01834 | ||||||||
\(791\) | −1.78722e10 | −1.28399 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.13317e9 | 0.579167 | ||||||||
\(794\) | −4.30976e10 | −3.05550 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.22299e10 | 0.859461 | ||||||||
\(797\) | 9.63179e9 | 0.673911 | 0.336956 | − | 0.941521i | \(-0.390603\pi\) | ||||
0.336956 | + | 0.941521i | \(0.390603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.00592e7 | −0.00347192 | ||||||||
\(800\) | 5.03357e10 | 3.47585 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.99683e10 | 1.36688 | ||||||||
\(803\) | 7.03037e8 | 0.0479153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.38296e10 | −2.28566 | ||||||||
\(806\) | 4.42394e10 | 2.97603 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.30510e10 | −2.20417 | ||||||||
\(809\) | −1.38532e9 | −0.0919878 | −0.0459939 | − | 0.998942i | \(-0.514645\pi\) | ||||
−0.0459939 | + | 0.998942i | \(0.514645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.41931e10 | 0.934339 | 0.467170 | − | 0.884168i | \(-0.345274\pi\) | ||||
0.467170 | + | 0.884168i | \(0.345274\pi\) | |||||||
\(812\) | 1.35489e11 | 8.88090 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.40677e9 | −0.156404 | ||||||||
\(815\) | −1.13910e10 | −0.737073 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.26608e10 | 0.812242 | ||||||||
\(818\) | −7.76554e8 | −0.0496061 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.08566e10 | 4.48778 | ||||||||
\(821\) | 1.94897e10 | 1.22915 | 0.614573 | − | 0.788860i | \(-0.289328\pi\) | ||||
0.614573 | + | 0.788860i | \(0.289328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94309e9 | 0.496696 | 0.248348 | − | 0.968671i | \(-0.420112\pi\) | ||||
0.248348 | + | 0.968671i | \(0.420112\pi\) | |||||||
\(824\) | −1.27255e10 | −0.792376 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.91314e9 | −0.488561 | ||||||||
\(827\) | −1.74454e10 | −1.07254 | −0.536268 | − | 0.844048i | \(-0.680166\pi\) | ||||
−0.536268 | + | 0.844048i | \(0.680166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.55780e10 | 1.55929 | 0.779644 | − | 0.626223i | \(-0.215400\pi\) | ||||
0.779644 | + | 0.626223i | \(0.215400\pi\) | |||||||
\(830\) | −1.77059e10 | −1.07484 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.68452e10 | 2.81990 | ||||||||
\(833\) | −4.86001e9 | −0.291326 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.41618e10 | 1.43624 | ||||||||
\(836\) | 2.68086e9 | 0.158691 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.90778e9 | 0.288092 | ||||||||
\(839\) | 7.34489e9 | 0.429357 | 0.214678 | − | 0.976685i | \(-0.431130\pi\) | ||||
0.214678 | + | 0.976685i | \(0.431130\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.27675e10 | 1.89958 | ||||||||
\(842\) | 1.56261e10 | 0.902106 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.91639e10 | −3.95987 | ||||||||
\(845\) | −2.79535e9 | −0.159382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46241e10 | 1.95788 | ||||||||
\(848\) | 5.92115e10 | 3.33442 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.63687e9 | −0.203124 | ||||||||
\(851\) | −2.59463e10 | −1.44318 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.22700e10 | −1.78023 | −0.890116 | − | 0.455734i | \(-0.849377\pi\) | ||||
−0.890116 | + | 0.455734i | \(0.849377\pi\) | |||||||
\(854\) | −4.19712e10 | −2.30594 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.30566e9 | 0.234629 | ||||||||
\(857\) | 7.06953e9 | 0.383670 | 0.191835 | − | 0.981427i | \(-0.438556\pi\) | ||||
0.191835 | + | 0.981427i | \(0.438556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.05380e10 | −1.10556 | −0.552779 | − | 0.833328i | \(-0.686432\pi\) | ||||
−0.552779 | + | 0.833328i | \(0.686432\pi\) | |||||||
\(860\) | 4.45264e10 | 2.38711 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.14030e9 | −0.273346 | ||||||||
\(863\) | 3.50261e10 | 1.85504 | 0.927520 | − | 0.373773i | \(-0.121936\pi\) | ||||
0.927520 | + | 0.373773i | \(0.121936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.52869e10 | 1.85378 | ||||||||
\(866\) | −5.68957e9 | −0.297692 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.65889e11 | −8.60990 | ||||||||
\(869\) | −1.64326e9 | −0.0849447 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.16251e8 | −0.0213448 | ||||||||
\(872\) | −7.00075e10 | −3.57550 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.97740e10 | 2.01516 | ||||||||
\(875\) | −2.15790e9 | −0.108894 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.05838e10 | 1.03045 | 0.515225 | − | 0.857055i | \(-0.327708\pi\) | ||||
0.515225 | + | 0.857055i | \(0.327708\pi\) | |||||||
\(878\) | 2.08613e10 | 1.04018 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.54686e9 | 0.224917 | ||||||||
\(881\) | −3.80144e9 | −0.187298 | −0.0936488 | − | 0.995605i | \(-0.529853\pi\) | ||||
−0.0936488 | + | 0.995605i | \(0.529853\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.46327e10 | −1.20406 | −0.602032 | − | 0.798472i | \(-0.705642\pi\) | ||||
−0.602032 | + | 0.798472i | \(0.705642\pi\) | |||||||
\(884\) | −5.26052e9 | −0.256121 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.90976e10 | −2.37161 | ||||||||
\(887\) | 2.28817e10 | 1.10092 | 0.550461 | − | 0.834861i | \(-0.314452\pi\) | ||||
0.550461 | + | 0.834861i | \(0.314452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.61346e10 | −0.770196 | ||||||||
\(890\) | 1.45364e10 | 0.691183 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.24177e10 | −2.00111 | ||||||||
\(893\) | 9.33378e8 | 0.0438609 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.69416e10 | −1.72241 | ||||||||
\(896\) | −1.00395e11 | −4.66265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.36205e10 | 0.627661 | ||||||||
\(899\) | −6.12400e10 | −2.81110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.19635e9 | −0.100038 | ||||||||
\(902\) | 2.30417e9 | 0.104542 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.60974e10 | 2.07533 | ||||||||
\(905\) | 2.97790e9 | 0.133549 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.43988e10 | 1.08578 | 0.542892 | − | 0.839802i | \(-0.317329\pi\) | ||||
0.542892 | + | 0.839802i | \(0.317329\pi\) | |||||||
\(908\) | 5.57971e9 | 0.247350 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.14811e11 | −5.05055 | ||||||||
\(911\) | −7.15550e9 | −0.313563 | −0.156782 | − | 0.987633i | \(-0.550112\pi\) | ||||
−0.156782 | + | 0.987633i | \(0.550112\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.18379e8 | −0.0181937 | ||||||||
\(914\) | −5.92844e10 | −2.56820 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.56424e10 | −1.96216 | ||||||||
\(917\) | 3.73154e10 | 1.59807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.31022e10 | −1.40687 | −0.703433 | − | 0.710761i | \(-0.748351\pi\) | ||||
−0.703433 | + | 0.710761i | \(0.748351\pi\) | |||||||
\(920\) | 8.72558e10 | 3.69434 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.26216e10 | −1.37071 | ||||||||
\(923\) | 6.36017e9 | 0.266234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.42362e10 | −1.83773 | ||||||||
\(926\) | −1.53080e10 | −0.633548 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.38703e11 | −5.69729 | ||||||||
\(929\) | −4.50956e10 | −1.84535 | −0.922676 | − | 0.385577i | \(-0.874003\pi\) | ||||
−0.922676 | + | 0.385577i | \(0.874003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.06172e10 | 3.68033 | ||||||||
\(932\) | 2.22618e10 | 0.900750 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.84469e10 | 3.15037 | ||||||||
\(935\) | −1.68658e8 | −0.00674787 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.71853e10 | 1.07956 | 0.539779 | − | 0.841807i | \(-0.318508\pi\) | ||||
0.539779 | + | 0.841807i | \(0.318508\pi\) | |||||||
\(938\) | 2.14806e9 | 0.0849840 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.28256e9 | 0.128903 | ||||||||
\(941\) | 4.59907e10 | 1.79931 | 0.899655 | − | 0.436601i | \(-0.143818\pi\) | ||||
0.899655 | + | 0.436601i | \(0.143818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.48402e10 | 0.964638 | ||||||||
\(944\) | 1.14658e10 | 0.443611 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.44794e9 | 0.0556074 | ||||||||
\(947\) | −4.47468e10 | −1.71213 | −0.856065 | − | 0.516868i | \(-0.827098\pi\) | ||||
−0.856065 | + | 0.516868i | \(0.827098\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.57221e10 | 0.976954 | ||||||||
\(950\) | 6.78113e10 | 2.56608 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.69340e10 | 0.636109 | ||||||||
\(953\) | 6.72893e9 | 0.251838 | 0.125919 | − | 0.992041i | \(-0.459812\pi\) | ||||
0.125919 | + | 0.992041i | \(0.459812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.63156e10 | −0.977692 | ||||||||
\(956\) | 5.41390e10 | 2.00405 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.89104e10 | −1.42984 | ||||||||
\(959\) | 3.91419e10 | 1.43310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.74681e10 | 1.72532 | ||||||||
\(962\) | −8.80566e10 | −3.18896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.69849e10 | 1.68923 | ||||||||
\(965\) | 5.36724e9 | 0.192267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.86690e9 | −0.0663941 | −0.0331970 | − | 0.999449i | \(-0.510569\pi\) | ||||
−0.0331970 | + | 0.999449i | \(0.510569\pi\) | |||||||
\(968\) | −8.93052e10 | −3.16456 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.85672e10 | 3.46762 | ||||||||
\(971\) | −2.50323e10 | −0.877471 | −0.438735 | − | 0.898616i | \(-0.644573\pi\) | ||||
−0.438735 | + | 0.898616i | \(0.644573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.14787e10 | 0.399482 | ||||||||
\(974\) | −3.42403e10 | −1.18736 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.08145e10 | 2.09379 | ||||||||
\(977\) | −3.21353e10 | −1.10243 | −0.551216 | − | 0.834363i | \(-0.685836\pi\) | ||||
−0.551216 | + | 0.834363i | \(0.685836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.43486e8 | 0.0116996 | ||||||||
\(980\) | 3.18688e11 | 10.8162 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.48464e9 | 0.218522 | ||||||||
\(983\) | 2.52657e10 | 0.848387 | 0.424194 | − | 0.905572i | \(-0.360558\pi\) | ||||
0.424194 | + | 0.905572i | \(0.360558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.35163e9 | −0.211767 | ||||||||
\(986\) | 1.00216e10 | 0.332942 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.80849e10 | 3.23559 | ||||||||
\(989\) | 1.56096e10 | 0.513104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.79422e10 | −1.89120 | −0.945600 | − | 0.325331i | \(-0.894524\pi\) | ||||
−0.945600 | + | 0.325331i | \(0.894524\pi\) | |||||||
\(992\) | 1.69825e11 | 5.52344 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.28217e10 | −1.06001 | ||||||||
\(995\) | 1.43459e10 | 0.461687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.76882e10 | −1.52398 | −0.761988 | − | 0.647591i | \(-0.775777\pi\) | ||||
−0.761988 | + | 0.647591i | \(0.775777\pi\) | |||||||
\(998\) | 2.92143e10 | 0.930334 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.8.a.d.1.16 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.2 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.2 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.16 | 17 | 1.1 | even | 1 | trivial |