Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(11.0664835671\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.714018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.2042 | −1.80386 | −0.901932 | − | 0.431878i | \(-0.857851\pi\) | ||||
−0.901932 | + | 0.431878i | \(0.857851\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 72.1256 | 2.25393 | ||||||||
\(5\) | −55.5168 | −0.993114 | −0.496557 | − | 0.868004i | \(-0.665403\pi\) | ||||
−0.496557 | + | 0.868004i | \(0.665403\pi\) | |||||||
\(6\) | −91.8378 | −1.04146 | ||||||||
\(7\) | 2.50462 | 0.0193196 | 0.00965978 | − | 0.999953i | \(-0.496925\pi\) | ||||
0.00965978 | + | 0.999953i | \(0.496925\pi\) | |||||||
\(8\) | −409.450 | −2.26191 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 566.504 | 1.79144 | ||||||||
\(11\) | 228.550 | 0.569508 | 0.284754 | − | 0.958601i | \(-0.408088\pi\) | ||||
0.284754 | + | 0.958601i | \(0.408088\pi\) | |||||||
\(12\) | 649.131 | 1.30130 | ||||||||
\(13\) | 658.703 | 1.08101 | 0.540507 | − | 0.841339i | \(-0.318232\pi\) | ||||
0.540507 | + | 0.841339i | \(0.318232\pi\) | |||||||
\(14\) | −25.5577 | −0.0348499 | ||||||||
\(15\) | −499.651 | −0.573375 | ||||||||
\(16\) | 1870.09 | 1.82626 | ||||||||
\(17\) | −1443.81 | −1.21168 | −0.605839 | − | 0.795587i | \(-0.707162\pi\) | ||||
−0.605839 | + | 0.795587i | \(0.707162\pi\) | |||||||
\(18\) | −826.540 | −0.601288 | ||||||||
\(19\) | −982.167 | −0.624168 | −0.312084 | − | 0.950055i | \(-0.601027\pi\) | ||||
−0.312084 | + | 0.950055i | \(0.601027\pi\) | |||||||
\(20\) | −4004.18 | −2.23841 | ||||||||
\(21\) | 22.5416 | 0.0111542 | ||||||||
\(22\) | −2332.17 | −1.02731 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | −3685.05 | −1.30592 | ||||||||
\(25\) | −42.8875 | −0.0137240 | ||||||||
\(26\) | −6721.54 | −1.95000 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 180.648 | 0.0435449 | ||||||||
\(29\) | −7157.56 | −1.58041 | −0.790205 | − | 0.612842i | \(-0.790026\pi\) | ||||
−0.790205 | + | 0.612842i | \(0.790026\pi\) | |||||||
\(30\) | 5098.54 | 1.03429 | ||||||||
\(31\) | −9259.98 | −1.73064 | −0.865318 | − | 0.501223i | \(-0.832884\pi\) | ||||
−0.865318 | + | 0.501223i | \(0.832884\pi\) | |||||||
\(32\) | −5980.33 | −1.03240 | ||||||||
\(33\) | 2056.95 | 0.328805 | ||||||||
\(34\) | 14732.9 | 2.18570 | ||||||||
\(35\) | −139.049 | −0.0191865 | ||||||||
\(36\) | 5842.18 | 0.751309 | ||||||||
\(37\) | 2422.50 | 0.290911 | 0.145455 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145455 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(38\) | 10022.2 | 1.12591 | ||||||||
\(39\) | 5928.33 | 0.624124 | ||||||||
\(40\) | 22731.3 | 2.24634 | ||||||||
\(41\) | −4075.27 | −0.378614 | −0.189307 | − | 0.981918i | \(-0.560624\pi\) | ||||
−0.189307 | + | 0.981918i | \(0.560624\pi\) | |||||||
\(42\) | −230.019 | −0.0201206 | ||||||||
\(43\) | −10417.3 | −0.859178 | −0.429589 | − | 0.903024i | \(-0.641342\pi\) | ||||
−0.429589 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(44\) | 16484.3 | 1.28363 | ||||||||
\(45\) | −4496.86 | −0.331038 | ||||||||
\(46\) | −5398.02 | −0.376132 | ||||||||
\(47\) | 9358.08 | 0.617934 | 0.308967 | − | 0.951073i | \(-0.400017\pi\) | ||||
0.308967 | + | 0.951073i | \(0.400017\pi\) | |||||||
\(48\) | 16830.8 | 1.05439 | ||||||||
\(49\) | −16800.7 | −0.999627 | ||||||||
\(50\) | 437.632 | 0.0247562 | ||||||||
\(51\) | −12994.3 | −0.699563 | ||||||||
\(52\) | 47509.4 | 2.43653 | ||||||||
\(53\) | −34280.3 | −1.67631 | −0.838157 | − | 0.545428i | \(-0.816367\pi\) | ||||
−0.838157 | + | 0.545428i | \(0.816367\pi\) | |||||||
\(54\) | −7438.86 | −0.347154 | ||||||||
\(55\) | −12688.4 | −0.565586 | ||||||||
\(56\) | −1025.52 | −0.0436991 | ||||||||
\(57\) | −8839.51 | −0.360364 | ||||||||
\(58\) | 73037.2 | 2.85085 | ||||||||
\(59\) | −7268.79 | −0.271852 | −0.135926 | − | 0.990719i | \(-0.543401\pi\) | ||||
−0.135926 | + | 0.990719i | \(0.543401\pi\) | |||||||
\(60\) | −36037.6 | −1.29234 | ||||||||
\(61\) | 26611.7 | 0.915687 | 0.457844 | − | 0.889033i | \(-0.348622\pi\) | ||||
0.457844 | + | 0.889033i | \(0.348622\pi\) | |||||||
\(62\) | 94490.6 | 3.12183 | ||||||||
\(63\) | 202.874 | 0.00643985 | ||||||||
\(64\) | 1181.70 | 0.0360625 | ||||||||
\(65\) | −36569.1 | −1.07357 | ||||||||
\(66\) | −20989.5 | −0.593120 | ||||||||
\(67\) | 53450.8 | 1.45468 | 0.727339 | − | 0.686278i | \(-0.240757\pi\) | ||||
0.727339 | + | 0.686278i | \(0.240757\pi\) | |||||||
\(68\) | −104136. | −2.73103 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 1418.88 | 0.0346099 | ||||||||
\(71\) | 21673.7 | 0.510255 | 0.255128 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255128 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(72\) | −33165.4 | −0.753970 | ||||||||
\(73\) | −82856.3 | −1.81978 | −0.909889 | − | 0.414851i | \(-0.863834\pi\) | ||||
−0.909889 | + | 0.414851i | \(0.863834\pi\) | |||||||
\(74\) | −24719.7 | −0.524764 | ||||||||
\(75\) | −385.987 | −0.00792355 | ||||||||
\(76\) | −70839.4 | −1.40683 | ||||||||
\(77\) | 572.432 | 0.0110026 | ||||||||
\(78\) | −60493.9 | −1.12584 | ||||||||
\(79\) | −23960.0 | −0.431936 | −0.215968 | − | 0.976400i | \(-0.569291\pi\) | ||||
−0.215968 | + | 0.976400i | \(0.569291\pi\) | |||||||
\(80\) | −103821. | −1.81368 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 41584.9 | 0.682968 | ||||||||
\(83\) | 81187.7 | 1.29359 | 0.646793 | − | 0.762666i | \(-0.276110\pi\) | ||||
0.646793 | + | 0.762666i | \(0.276110\pi\) | |||||||
\(84\) | 1625.83 | 0.0251406 | ||||||||
\(85\) | 80155.6 | 1.20334 | ||||||||
\(86\) | 106300. | 1.54984 | ||||||||
\(87\) | −64418.0 | −0.912451 | ||||||||
\(88\) | −93579.7 | −1.28818 | ||||||||
\(89\) | 100115. | 1.33975 | 0.669876 | − | 0.742473i | \(-0.266347\pi\) | ||||
0.669876 | + | 0.742473i | \(0.266347\pi\) | |||||||
\(90\) | 45886.8 | 0.597148 | ||||||||
\(91\) | 1649.80 | 0.0208847 | ||||||||
\(92\) | 38154.5 | 0.469976 | ||||||||
\(93\) | −83339.8 | −0.999183 | ||||||||
\(94\) | −95491.7 | −1.11467 | ||||||||
\(95\) | 54526.8 | 0.619870 | ||||||||
\(96\) | −53822.9 | −0.596059 | ||||||||
\(97\) | 36122.1 | 0.389802 | 0.194901 | − | 0.980823i | \(-0.437562\pi\) | ||||
0.194901 | + | 0.980823i | \(0.437562\pi\) | |||||||
\(98\) | 171438. | 1.80319 | ||||||||
\(99\) | 18512.6 | 0.189836 | ||||||||
\(100\) | −3093.29 | −0.0309329 | ||||||||
\(101\) | −41151.8 | −0.401408 | −0.200704 | − | 0.979652i | \(-0.564323\pi\) | ||||
−0.200704 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(102\) | 132596. | 1.26192 | ||||||||
\(103\) | −172534. | −1.60244 | −0.801221 | − | 0.598369i | \(-0.795816\pi\) | ||||
−0.801221 | + | 0.598369i | \(0.795816\pi\) | |||||||
\(104\) | −269706. | −2.44516 | ||||||||
\(105\) | −1251.44 | −0.0110774 | ||||||||
\(106\) | 349803. | 3.02384 | ||||||||
\(107\) | 178228. | 1.50493 | 0.752464 | − | 0.658633i | \(-0.228865\pi\) | ||||
0.752464 | + | 0.658633i | \(0.228865\pi\) | |||||||
\(108\) | 52579.6 | 0.433768 | ||||||||
\(109\) | −138352. | −1.11537 | −0.557686 | − | 0.830052i | \(-0.688311\pi\) | ||||
−0.557686 | + | 0.830052i | \(0.688311\pi\) | |||||||
\(110\) | 129475. | 1.02024 | ||||||||
\(111\) | 21802.5 | 0.167958 | ||||||||
\(112\) | 4683.86 | 0.0352825 | ||||||||
\(113\) | −13523.5 | −0.0996307 | −0.0498153 | − | 0.998758i | \(-0.515863\pi\) | ||||
−0.0498153 | + | 0.998758i | \(0.515863\pi\) | |||||||
\(114\) | 90200.0 | 0.650047 | ||||||||
\(115\) | −29368.4 | −0.207079 | ||||||||
\(116\) | −516243. | −3.56213 | ||||||||
\(117\) | 53355.0 | 0.360338 | ||||||||
\(118\) | 74172.1 | 0.490383 | ||||||||
\(119\) | −3616.20 | −0.0234091 | ||||||||
\(120\) | 204582. | 1.29692 | ||||||||
\(121\) | −108816. | −0.675661 | ||||||||
\(122\) | −271551. | −1.65178 | ||||||||
\(123\) | −36677.4 | −0.218593 | ||||||||
\(124\) | −667882. | −3.90073 | ||||||||
\(125\) | 175871. | 1.00674 | ||||||||
\(126\) | −2070.17 | −0.0116166 | ||||||||
\(127\) | 158567. | 0.872376 | 0.436188 | − | 0.899856i | \(-0.356328\pi\) | ||||
0.436188 | + | 0.899856i | \(0.356328\pi\) | |||||||
\(128\) | 179312. | 0.967353 | ||||||||
\(129\) | −93755.6 | −0.496047 | ||||||||
\(130\) | 373158. | 1.93658 | ||||||||
\(131\) | −383514. | −1.95255 | −0.976277 | − | 0.216526i | \(-0.930527\pi\) | ||||
−0.976277 | + | 0.216526i | \(0.930527\pi\) | |||||||
\(132\) | 148359. | 0.741103 | ||||||||
\(133\) | −2459.96 | −0.0120587 | ||||||||
\(134\) | −545422. | −2.62404 | ||||||||
\(135\) | −40471.7 | −0.191125 | ||||||||
\(136\) | 591167. | 2.74071 | ||||||||
\(137\) | −33171.1 | −0.150994 | −0.0754968 | − | 0.997146i | \(-0.524054\pi\) | ||||
−0.0754968 | + | 0.997146i | \(0.524054\pi\) | |||||||
\(138\) | −48582.2 | −0.217160 | ||||||||
\(139\) | −128488. | −0.564060 | −0.282030 | − | 0.959406i | \(-0.591008\pi\) | ||||
−0.282030 | + | 0.959406i | \(0.591008\pi\) | |||||||
\(140\) | −10029.0 | −0.0432450 | ||||||||
\(141\) | 84222.7 | 0.356764 | ||||||||
\(142\) | −221163. | −0.920431 | ||||||||
\(143\) | 150547. | 0.615646 | ||||||||
\(144\) | 151477. | 0.608752 | ||||||||
\(145\) | 397365. | 1.56953 | ||||||||
\(146\) | 845482. | 3.28263 | ||||||||
\(147\) | −151207. | −0.577135 | ||||||||
\(148\) | 174725. | 0.655692 | ||||||||
\(149\) | −184228. | −0.679814 | −0.339907 | − | 0.940459i | \(-0.610396\pi\) | ||||
−0.339907 | + | 0.940459i | \(0.610396\pi\) | |||||||
\(150\) | 3938.69 | 0.0142930 | ||||||||
\(151\) | −19798.1 | −0.0706610 | −0.0353305 | − | 0.999376i | \(-0.511248\pi\) | ||||
−0.0353305 | + | 0.999376i | \(0.511248\pi\) | |||||||
\(152\) | 402148. | 1.41181 | ||||||||
\(153\) | −116948. | −0.403893 | ||||||||
\(154\) | −5841.21 | −0.0198473 | ||||||||
\(155\) | 514084. | 1.71872 | ||||||||
\(156\) | 427585. | 1.40673 | ||||||||
\(157\) | 193317. | 0.625923 | 0.312962 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312962 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(158\) | 244493. | 0.779154 | ||||||||
\(159\) | −308523. | −0.967821 | ||||||||
\(160\) | 332008. | 1.02530 | ||||||||
\(161\) | 1324.95 | 0.00402841 | ||||||||
\(162\) | −66949.7 | −0.200429 | ||||||||
\(163\) | 106286. | 0.313334 | 0.156667 | − | 0.987651i | \(-0.449925\pi\) | ||||
0.156667 | + | 0.987651i | \(0.449925\pi\) | |||||||
\(164\) | −293931. | −0.853368 | ||||||||
\(165\) | −114195. | −0.326541 | ||||||||
\(166\) | −828456. | −2.33345 | ||||||||
\(167\) | −77715.5 | −0.215634 | −0.107817 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107817 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(168\) | −9229.66 | −0.0252297 | ||||||||
\(169\) | 62597.3 | 0.168593 | ||||||||
\(170\) | −817923. | −2.17065 | ||||||||
\(171\) | −79555.5 | −0.208056 | ||||||||
\(172\) | −751353. | −1.93652 | ||||||||
\(173\) | 218524. | 0.555115 | 0.277558 | − | 0.960709i | \(-0.410475\pi\) | ||||
0.277558 | + | 0.960709i | \(0.410475\pi\) | |||||||
\(174\) | 657334. | 1.64594 | ||||||||
\(175\) | −107.417 | −0.000265142 0 | ||||||||
\(176\) | 427408. | 1.04007 | ||||||||
\(177\) | −65419.1 | −0.156954 | ||||||||
\(178\) | −1.02159e6 | −2.41673 | ||||||||
\(179\) | −545493. | −1.27250 | −0.636248 | − | 0.771485i | \(-0.719514\pi\) | ||||
−0.636248 | + | 0.771485i | \(0.719514\pi\) | |||||||
\(180\) | −324339. | −0.746135 | ||||||||
\(181\) | 510878. | 1.15910 | 0.579549 | − | 0.814937i | \(-0.303229\pi\) | ||||
0.579549 | + | 0.814937i | \(0.303229\pi\) | |||||||
\(182\) | −16834.9 | −0.0376732 | ||||||||
\(183\) | 239505. | 0.528672 | ||||||||
\(184\) | −216599. | −0.471641 | ||||||||
\(185\) | −134490. | −0.288908 | ||||||||
\(186\) | 850416. | 1.80239 | ||||||||
\(187\) | −329982. | −0.690060 | ||||||||
\(188\) | 674957. | 1.39278 | ||||||||
\(189\) | 1825.87 | 0.00371805 | ||||||||
\(190\) | −556402. | −1.11816 | ||||||||
\(191\) | −57685.2 | −0.114415 | −0.0572073 | − | 0.998362i | \(-0.518220\pi\) | ||||
−0.0572073 | + | 0.998362i | \(0.518220\pi\) | |||||||
\(192\) | 10635.3 | 0.0208207 | ||||||||
\(193\) | −822091. | −1.58864 | −0.794322 | − | 0.607497i | \(-0.792174\pi\) | ||||
−0.794322 | + | 0.607497i | \(0.792174\pi\) | |||||||
\(194\) | −368597. | −0.703149 | ||||||||
\(195\) | −329122. | −0.619827 | ||||||||
\(196\) | −1.21176e6 | −2.25308 | ||||||||
\(197\) | 971571. | 1.78365 | 0.891824 | − | 0.452383i | \(-0.149426\pi\) | ||||
0.891824 | + | 0.452383i | \(0.149426\pi\) | |||||||
\(198\) | −188906. | −0.342438 | ||||||||
\(199\) | 806110. | 1.44298 | 0.721492 | − | 0.692423i | \(-0.243457\pi\) | ||||
0.721492 | + | 0.692423i | \(0.243457\pi\) | |||||||
\(200\) | 17560.3 | 0.0310425 | ||||||||
\(201\) | 481057. | 0.839859 | ||||||||
\(202\) | 419921. | 0.724085 | ||||||||
\(203\) | −17927.0 | −0.0305329 | ||||||||
\(204\) | −937220. | −1.57676 | ||||||||
\(205\) | 226246. | 0.376007 | ||||||||
\(206\) | 1.76057e6 | 2.89059 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | 1.23183e6 | 1.97421 | ||||||||
\(209\) | −224474. | −0.355468 | ||||||||
\(210\) | 12769.9 | 0.0199820 | ||||||||
\(211\) | −821913. | −1.27092 | −0.635462 | − | 0.772132i | \(-0.719190\pi\) | ||||
−0.635462 | + | 0.772132i | \(0.719190\pi\) | |||||||
\(212\) | −2.47249e6 | −3.77829 | ||||||||
\(213\) | 195063. | 0.294596 | ||||||||
\(214\) | −1.81867e6 | −2.71469 | ||||||||
\(215\) | 578334. | 0.853262 | ||||||||
\(216\) | −298489. | −0.435305 | ||||||||
\(217\) | −23192.8 | −0.0334351 | ||||||||
\(218\) | 1.41177e6 | 2.01198 | ||||||||
\(219\) | −745707. | −1.05065 | ||||||||
\(220\) | −915156. | −1.27479 | ||||||||
\(221\) | −951042. | −1.30984 | ||||||||
\(222\) | −222477. | −0.302973 | ||||||||
\(223\) | 511948. | 0.689388 | 0.344694 | − | 0.938715i | \(-0.387983\pi\) | ||||
0.344694 | + | 0.938715i | \(0.387983\pi\) | |||||||
\(224\) | −14978.5 | −0.0199456 | ||||||||
\(225\) | −3473.89 | −0.00457467 | ||||||||
\(226\) | 137996. | 0.179720 | ||||||||
\(227\) | −1.45074e6 | −1.86864 | −0.934321 | − | 0.356433i | \(-0.883993\pi\) | ||||
−0.934321 | + | 0.356433i | \(0.883993\pi\) | |||||||
\(228\) | −637555. | −0.812233 | ||||||||
\(229\) | 621169. | 0.782747 | 0.391373 | − | 0.920232i | \(-0.372000\pi\) | ||||
0.391373 | + | 0.920232i | \(0.372000\pi\) | |||||||
\(230\) | 299681. | 0.373542 | ||||||||
\(231\) | 5151.89 | 0.00635238 | ||||||||
\(232\) | 2.93066e6 | 3.57475 | ||||||||
\(233\) | 490334. | 0.591701 | 0.295851 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(234\) | −544445. | −0.650001 | ||||||||
\(235\) | −519530. | −0.613679 | ||||||||
\(236\) | −524266. | −0.612733 | ||||||||
\(237\) | −215640. | −0.249378 | ||||||||
\(238\) | 36900.4 | 0.0422268 | ||||||||
\(239\) | 109503. | 0.124003 | 0.0620014 | − | 0.998076i | \(-0.480252\pi\) | ||||
0.0620014 | + | 0.998076i | \(0.480252\pi\) | |||||||
\(240\) | −934390. | −1.04713 | ||||||||
\(241\) | 1.36171e6 | 1.51022 | 0.755111 | − | 0.655597i | \(-0.227583\pi\) | ||||
0.755111 | + | 0.655597i | \(0.227583\pi\) | |||||||
\(242\) | 1.11038e6 | 1.21880 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 1.91938e6 | 2.06389 | ||||||||
\(245\) | 932722. | 0.992744 | ||||||||
\(246\) | 374264. | 0.394312 | ||||||||
\(247\) | −646957. | −0.674735 | ||||||||
\(248\) | 3.79150e6 | 3.91455 | ||||||||
\(249\) | 730690. | 0.746852 | ||||||||
\(250\) | −1.79462e6 | −1.81603 | ||||||||
\(251\) | 8042.27 | 0.00805739 | 0.00402869 | − | 0.999992i | \(-0.498718\pi\) | ||||
0.00402869 | + | 0.999992i | \(0.498718\pi\) | |||||||
\(252\) | 14632.4 | 0.0145150 | ||||||||
\(253\) | 120903. | 0.118751 | ||||||||
\(254\) | −1.61805e6 | −1.57365 | ||||||||
\(255\) | 721400. | 0.694746 | ||||||||
\(256\) | −1.86755e6 | −1.78104 | ||||||||
\(257\) | 1.16730e6 | 1.10243 | 0.551214 | − | 0.834364i | \(-0.314165\pi\) | ||||
0.551214 | + | 0.834364i | \(0.314165\pi\) | |||||||
\(258\) | 956700. | 0.894801 | ||||||||
\(259\) | 6067.46 | 0.00562027 | ||||||||
\(260\) | −2.63757e6 | −2.41975 | ||||||||
\(261\) | −579762. | −0.526804 | ||||||||
\(262\) | 3.91345e6 | 3.52214 | ||||||||
\(263\) | −558051. | −0.497490 | −0.248745 | − | 0.968569i | \(-0.580018\pi\) | ||||
−0.248745 | + | 0.968569i | \(0.580018\pi\) | |||||||
\(264\) | −842218. | −0.743729 | ||||||||
\(265\) | 1.90313e6 | 1.66477 | ||||||||
\(266\) | 25101.9 | 0.0217522 | ||||||||
\(267\) | 901036. | 0.773506 | ||||||||
\(268\) | 3.85517e6 | 3.27874 | ||||||||
\(269\) | −1.21947e6 | −1.02752 | −0.513759 | − | 0.857935i | \(-0.671747\pi\) | ||||
−0.513759 | + | 0.857935i | \(0.671747\pi\) | |||||||
\(270\) | 412981. | 0.344763 | ||||||||
\(271\) | 1.40581e6 | 1.16280 | 0.581399 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581399 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(272\) | −2.70005e6 | −2.21283 | ||||||||
\(273\) | 14848.2 | 0.0120578 | ||||||||
\(274\) | 338484. | 0.272372 | ||||||||
\(275\) | −9801.94 | −0.00781592 | ||||||||
\(276\) | 343390. | 0.271341 | ||||||||
\(277\) | 1.87799e6 | 1.47060 | 0.735300 | − | 0.677742i | \(-0.237041\pi\) | ||||
0.735300 | + | 0.677742i | \(0.237041\pi\) | |||||||
\(278\) | 1.31112e6 | 1.01749 | ||||||||
\(279\) | −750058. | −0.576879 | ||||||||
\(280\) | 56933.4 | 0.0433982 | ||||||||
\(281\) | −2.11759e6 | −1.59984 | −0.799920 | − | 0.600106i | \(-0.795125\pi\) | ||||
−0.799920 | + | 0.600106i | \(0.795125\pi\) | |||||||
\(282\) | −859425. | −0.643555 | ||||||||
\(283\) | 1.16042e6 | 0.861288 | 0.430644 | − | 0.902522i | \(-0.358286\pi\) | ||||
0.430644 | + | 0.902522i | \(0.358286\pi\) | |||||||
\(284\) | 1.56323e6 | 1.15008 | ||||||||
\(285\) | 490741. | 0.357882 | ||||||||
\(286\) | −1.53621e6 | −1.11054 | ||||||||
\(287\) | −10207.0 | −0.00731466 | ||||||||
\(288\) | −484406. | −0.344135 | ||||||||
\(289\) | 664726. | 0.468164 | ||||||||
\(290\) | −4.05479e6 | −2.83122 | ||||||||
\(291\) | 325099. | 0.225052 | ||||||||
\(292\) | −5.97606e6 | −4.10165 | ||||||||
\(293\) | −1.27325e6 | −0.866449 | −0.433225 | − | 0.901286i | \(-0.642624\pi\) | ||||
−0.433225 | + | 0.901286i | \(0.642624\pi\) | |||||||
\(294\) | 1.54294e6 | 1.04107 | ||||||||
\(295\) | 403540. | 0.269980 | ||||||||
\(296\) | −991893. | −0.658015 | ||||||||
\(297\) | 166613. | 0.109602 | ||||||||
\(298\) | 1.87990e6 | 1.22629 | ||||||||
\(299\) | 348454. | 0.225407 | ||||||||
\(300\) | −27839.6 | −0.0178591 | ||||||||
\(301\) | −26091.4 | −0.0165990 | ||||||||
\(302\) | 202023. | 0.127463 | ||||||||
\(303\) | −370367. | −0.231753 | ||||||||
\(304\) | −1.83674e6 | −1.13989 | ||||||||
\(305\) | −1.47739e6 | −0.909382 | ||||||||
\(306\) | 1.19337e6 | 0.728568 | ||||||||
\(307\) | −2.26175e6 | −1.36961 | −0.684807 | − | 0.728724i | \(-0.740114\pi\) | ||||
−0.684807 | + | 0.728724i | \(0.740114\pi\) | |||||||
\(308\) | 41287.0 | 0.0247991 | ||||||||
\(309\) | −1.55281e6 | −0.925170 | ||||||||
\(310\) | −5.24582e6 | −3.10034 | ||||||||
\(311\) | 1.20263e6 | 0.705066 | 0.352533 | − | 0.935799i | \(-0.385320\pi\) | ||||
0.352533 | + | 0.935799i | \(0.385320\pi\) | |||||||
\(312\) | −2.42735e6 | −1.41171 | ||||||||
\(313\) | −484311. | −0.279424 | −0.139712 | − | 0.990192i | \(-0.544618\pi\) | ||||
−0.139712 | + | 0.990192i | \(0.544618\pi\) | |||||||
\(314\) | −1.97265e6 | −1.12908 | ||||||||
\(315\) | −11262.9 | −0.00639551 | ||||||||
\(316\) | −1.72813e6 | −0.973551 | ||||||||
\(317\) | 796624. | 0.445251 | 0.222626 | − | 0.974904i | \(-0.428537\pi\) | ||||
0.222626 | + | 0.974904i | \(0.428537\pi\) | |||||||
\(318\) | 3.14823e6 | 1.74582 | ||||||||
\(319\) | −1.63586e6 | −0.900056 | ||||||||
\(320\) | −65603.9 | −0.0358142 | ||||||||
\(321\) | 1.60405e6 | 0.868871 | ||||||||
\(322\) | −13520.0 | −0.00726670 | ||||||||
\(323\) | 1.41806e6 | 0.756291 | ||||||||
\(324\) | 473216. | 0.250436 | ||||||||
\(325\) | −28250.1 | −0.0148358 | ||||||||
\(326\) | −1.08456e6 | −0.565212 | ||||||||
\(327\) | −1.24517e6 | −0.643961 | ||||||||
\(328\) | 1.66862e6 | 0.856391 | ||||||||
\(329\) | 23438.5 | 0.0119382 | ||||||||
\(330\) | 1.16527e6 | 0.589036 | ||||||||
\(331\) | −262856. | −0.131871 | −0.0659353 | − | 0.997824i | \(-0.521003\pi\) | ||||
−0.0659353 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(332\) | 5.85572e6 | 2.91565 | ||||||||
\(333\) | 196223. | 0.0969703 | ||||||||
\(334\) | 793024. | 0.388974 | ||||||||
\(335\) | −2.96741e6 | −1.44466 | ||||||||
\(336\) | 42154.7 | 0.0203703 | ||||||||
\(337\) | 1.23123e6 | 0.590558 | 0.295279 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295279 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(338\) | −638755. | −0.304118 | ||||||||
\(339\) | −121712. | −0.0575218 | ||||||||
\(340\) | 5.78127e6 | 2.71223 | ||||||||
\(341\) | −2.11637e6 | −0.985611 | ||||||||
\(342\) | 811800. | 0.375305 | ||||||||
\(343\) | −84174.7 | −0.0386319 | ||||||||
\(344\) | 4.26535e6 | 1.94339 | ||||||||
\(345\) | −264315. | −0.119557 | ||||||||
\(346\) | −2.22986e6 | −1.00135 | ||||||||
\(347\) | −3.70344e6 | −1.65113 | −0.825567 | − | 0.564305i | \(-0.809144\pi\) | ||||
−0.825567 | + | 0.564305i | \(0.809144\pi\) | |||||||
\(348\) | −4.64619e6 | −2.05660 | ||||||||
\(349\) | 1.62884e6 | 0.715837 | 0.357918 | − | 0.933753i | \(-0.383487\pi\) | ||||
0.357918 | + | 0.933753i | \(0.383487\pi\) | |||||||
\(350\) | 1096.10 | 0.000478279 0 | ||||||||
\(351\) | 480195. | 0.208041 | ||||||||
\(352\) | −1.36680e6 | −0.587962 | ||||||||
\(353\) | 2.56589e6 | 1.09598 | 0.547989 | − | 0.836486i | \(-0.315394\pi\) | ||||
0.547989 | + | 0.836486i | \(0.315394\pi\) | |||||||
\(354\) | 667549. | 0.283123 | ||||||||
\(355\) | −1.20326e6 | −0.506742 | ||||||||
\(356\) | 7.22086e6 | 3.01970 | ||||||||
\(357\) | −32545.8 | −0.0135152 | ||||||||
\(358\) | 5.56631e6 | 2.29541 | ||||||||
\(359\) | −3.46895e6 | −1.42057 | −0.710284 | − | 0.703916i | \(-0.751433\pi\) | ||||
−0.710284 | + | 0.703916i | \(0.751433\pi\) | |||||||
\(360\) | 1.84124e6 | 0.748779 | ||||||||
\(361\) | −1.51145e6 | −0.610414 | ||||||||
\(362\) | −5.21310e6 | −2.09086 | ||||||||
\(363\) | −979343. | −0.390093 | ||||||||
\(364\) | 118993. | 0.0470726 | ||||||||
\(365\) | 4.59992e6 | 1.80725 | ||||||||
\(366\) | −2.44395e6 | −0.953653 | ||||||||
\(367\) | 1.64135e6 | 0.636115 | 0.318058 | − | 0.948071i | \(-0.396969\pi\) | ||||
0.318058 | + | 0.948071i | \(0.396969\pi\) | |||||||
\(368\) | 989275. | 0.380801 | ||||||||
\(369\) | −330097. | −0.126205 | ||||||||
\(370\) | 1.37236e6 | 0.521151 | ||||||||
\(371\) | −85859.4 | −0.0323857 | ||||||||
\(372\) | −6.01094e6 | −2.25208 | ||||||||
\(373\) | 1.58607e6 | 0.590268 | 0.295134 | − | 0.955456i | \(-0.404636\pi\) | ||||
0.295134 | + | 0.955456i | \(0.404636\pi\) | |||||||
\(374\) | 3.36721e6 | 1.24477 | ||||||||
\(375\) | 1.58284e6 | 0.581244 | ||||||||
\(376\) | −3.83166e6 | −1.39771 | ||||||||
\(377\) | −4.71471e6 | −1.70845 | ||||||||
\(378\) | −18631.5 | −0.00670686 | ||||||||
\(379\) | −966030. | −0.345456 | −0.172728 | − | 0.984970i | \(-0.555258\pi\) | ||||
−0.172728 | + | 0.984970i | \(0.555258\pi\) | |||||||
\(380\) | 3.93278e6 | 1.39714 | ||||||||
\(381\) | 1.42710e6 | 0.503667 | ||||||||
\(382\) | 588631. | 0.206388 | ||||||||
\(383\) | −3.10322e6 | −1.08097 | −0.540487 | − | 0.841352i | \(-0.681760\pi\) | ||||
−0.540487 | + | 0.841352i | \(0.681760\pi\) | |||||||
\(384\) | 1.61381e6 | 0.558501 | ||||||||
\(385\) | −31779.6 | −0.0109269 | ||||||||
\(386\) | 8.38878e6 | 2.86570 | ||||||||
\(387\) | −843800. | −0.286393 | ||||||||
\(388\) | 2.60533e6 | 0.878584 | ||||||||
\(389\) | 624568. | 0.209269 | 0.104635 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(390\) | 3.35842e6 | 1.11808 | ||||||||
\(391\) | −763775. | −0.252652 | ||||||||
\(392\) | 6.87905e6 | 2.26107 | ||||||||
\(393\) | −3.45163e6 | −1.12731 | ||||||||
\(394\) | −9.91410e6 | −3.21746 | ||||||||
\(395\) | 1.33018e6 | 0.428962 | ||||||||
\(396\) | 1.33523e6 | 0.427876 | ||||||||
\(397\) | 2.80814e6 | 0.894216 | 0.447108 | − | 0.894480i | \(-0.352454\pi\) | ||||
0.447108 | + | 0.894480i | \(0.352454\pi\) | |||||||
\(398\) | −8.22570e6 | −2.60295 | ||||||||
\(399\) | −22139.6 | −0.00696207 | ||||||||
\(400\) | −80203.3 | −0.0250635 | ||||||||
\(401\) | 3.81287e6 | 1.18411 | 0.592053 | − | 0.805899i | \(-0.298318\pi\) | ||||
0.592053 | + | 0.805899i | \(0.298318\pi\) | |||||||
\(402\) | −4.90880e6 | −1.51499 | ||||||||
\(403\) | −6.09958e6 | −1.87084 | ||||||||
\(404\) | −2.96810e6 | −0.904743 | ||||||||
\(405\) | −364246. | −0.110346 | ||||||||
\(406\) | 182931. | 0.0550771 | ||||||||
\(407\) | 553663. | 0.165676 | ||||||||
\(408\) | 5.32050e6 | 1.58235 | ||||||||
\(409\) | −3.86268e6 | −1.14178 | −0.570888 | − | 0.821028i | \(-0.693401\pi\) | ||||
−0.570888 | + | 0.821028i | \(0.693401\pi\) | |||||||
\(410\) | −2.30866e6 | −0.678266 | ||||||||
\(411\) | −298540. | −0.0871762 | ||||||||
\(412\) | −1.24441e7 | −3.61178 | ||||||||
\(413\) | −18205.6 | −0.00525206 | ||||||||
\(414\) | −437240. | −0.125377 | ||||||||
\(415\) | −4.50728e6 | −1.28468 | ||||||||
\(416\) | −3.93926e6 | −1.11604 | ||||||||
\(417\) | −1.15639e6 | −0.325660 | ||||||||
\(418\) | 2.29058e6 | 0.641217 | ||||||||
\(419\) | −4.00521e6 | −1.11453 | −0.557263 | − | 0.830336i | \(-0.688149\pi\) | ||||
−0.557263 | + | 0.830336i | \(0.688149\pi\) | |||||||
\(420\) | −90260.7 | −0.0249675 | ||||||||
\(421\) | 4.89697e6 | 1.34655 | 0.673275 | − | 0.739392i | \(-0.264887\pi\) | ||||
0.673275 | + | 0.739392i | \(0.264887\pi\) | |||||||
\(422\) | 8.38696e6 | 2.29257 | ||||||||
\(423\) | 758005. | 0.205978 | ||||||||
\(424\) | 1.40361e7 | 3.79168 | ||||||||
\(425\) | 61921.3 | 0.0166291 | ||||||||
\(426\) | −1.99047e6 | −0.531411 | ||||||||
\(427\) | 66652.2 | 0.0176907 | ||||||||
\(428\) | 1.28548e7 | 3.39200 | ||||||||
\(429\) | 1.35492e6 | 0.355443 | ||||||||
\(430\) | −5.90143e6 | −1.53917 | ||||||||
\(431\) | 1.81874e6 | 0.471605 | 0.235803 | − | 0.971801i | \(-0.424228\pi\) | ||||
0.235803 | + | 0.971801i | \(0.424228\pi\) | |||||||
\(432\) | 1.36329e6 | 0.351463 | ||||||||
\(433\) | 545672. | 0.139866 | 0.0699330 | − | 0.997552i | \(-0.477721\pi\) | ||||
0.0699330 | + | 0.997552i | \(0.477721\pi\) | |||||||
\(434\) | 236663. | 0.0603124 | ||||||||
\(435\) | 3.57628e6 | 0.906168 | ||||||||
\(436\) | −9.97874e6 | −2.51397 | ||||||||
\(437\) | −519566. | −0.130148 | ||||||||
\(438\) | 7.60934e6 | 1.89523 | ||||||||
\(439\) | 2.81114e6 | 0.696179 | 0.348090 | − | 0.937461i | \(-0.386830\pi\) | ||||
0.348090 | + | 0.937461i | \(0.386830\pi\) | |||||||
\(440\) | 5.19525e6 | 1.27931 | ||||||||
\(441\) | −1.36086e6 | −0.333209 | ||||||||
\(442\) | 9.70462e6 | 2.36278 | ||||||||
\(443\) | −2.81428e6 | −0.681332 | −0.340666 | − | 0.940184i | \(-0.610652\pi\) | ||||
−0.340666 | + | 0.940184i | \(0.610652\pi\) | |||||||
\(444\) | 1.57252e6 | 0.378564 | ||||||||
\(445\) | −5.55807e6 | −1.33053 | ||||||||
\(446\) | −5.22402e6 | −1.24356 | ||||||||
\(447\) | −1.65805e6 | −0.392491 | ||||||||
\(448\) | 2959.70 | 0.000696712 0 | ||||||||
\(449\) | 4.00644e6 | 0.937871 | 0.468936 | − | 0.883232i | \(-0.344638\pi\) | ||||
0.468936 | + | 0.883232i | \(0.344638\pi\) | |||||||
\(450\) | 35448.2 | 0.00825207 | ||||||||
\(451\) | −931403. | −0.215624 | ||||||||
\(452\) | −975391. | −0.224560 | ||||||||
\(453\) | −178182. | −0.0407962 | ||||||||
\(454\) | 1.48037e7 | 3.37078 | ||||||||
\(455\) | −91591.8 | −0.0207409 | ||||||||
\(456\) | 3.61933e6 | 0.815110 | ||||||||
\(457\) | −5.43801e6 | −1.21801 | −0.609003 | − | 0.793168i | \(-0.708430\pi\) | ||||
−0.609003 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(458\) | −6.33853e6 | −1.41197 | ||||||||
\(459\) | −1.05254e6 | −0.233188 | ||||||||
\(460\) | −2.11821e6 | −0.466740 | ||||||||
\(461\) | 2.50966e6 | 0.550001 | 0.275000 | − | 0.961444i | \(-0.411322\pi\) | ||||
0.275000 | + | 0.961444i | \(0.411322\pi\) | |||||||
\(462\) | −52570.9 | −0.0114588 | ||||||||
\(463\) | 108662. | 0.0235573 | 0.0117787 | − | 0.999931i | \(-0.496251\pi\) | ||||
0.0117787 | + | 0.999931i | \(0.496251\pi\) | |||||||
\(464\) | −1.33852e7 | −2.88623 | ||||||||
\(465\) | 4.62676e6 | 0.992303 | ||||||||
\(466\) | −5.00347e6 | −1.06735 | ||||||||
\(467\) | 3.09125e6 | 0.655906 | 0.327953 | − | 0.944694i | \(-0.393641\pi\) | ||||
0.327953 | + | 0.944694i | \(0.393641\pi\) | |||||||
\(468\) | 3.84826e6 | 0.812176 | ||||||||
\(469\) | 133874. | 0.0281037 | ||||||||
\(470\) | 5.30139e6 | 1.10699 | ||||||||
\(471\) | 1.73985e6 | 0.361377 | ||||||||
\(472\) | 2.97620e6 | 0.614904 | ||||||||
\(473\) | −2.38087e6 | −0.489309 | ||||||||
\(474\) | 2.20043e6 | 0.449845 | ||||||||
\(475\) | 42122.7 | 0.00856608 | ||||||||
\(476\) | −260820. | −0.0527624 | ||||||||
\(477\) | −2.77671e6 | −0.558772 | ||||||||
\(478\) | −1.11739e6 | −0.223684 | ||||||||
\(479\) | −7.74743e6 | −1.54283 | −0.771417 | − | 0.636330i | \(-0.780452\pi\) | ||||
−0.771417 | + | 0.636330i | \(0.780452\pi\) | |||||||
\(480\) | 2.98808e6 | 0.591955 | ||||||||
\(481\) | 1.59571e6 | 0.314479 | ||||||||
\(482\) | −1.38951e7 | −2.72424 | ||||||||
\(483\) | 11924.5 | 0.00232580 | ||||||||
\(484\) | −7.84841e6 | −1.52289 | ||||||||
\(485\) | −2.00538e6 | −0.387118 | ||||||||
\(486\) | −602548. | −0.115718 | ||||||||
\(487\) | 6.60929e6 | 1.26279 | 0.631397 | − | 0.775460i | \(-0.282482\pi\) | ||||
0.631397 | + | 0.775460i | \(0.282482\pi\) | |||||||
\(488\) | −1.08961e7 | −2.07120 | ||||||||
\(489\) | 956575. | 0.180903 | ||||||||
\(490\) | −9.51768e6 | −1.79077 | ||||||||
\(491\) | 1.68453e6 | 0.315337 | 0.157669 | − | 0.987492i | \(-0.449602\pi\) | ||||
0.157669 | + | 0.987492i | \(0.449602\pi\) | |||||||
\(492\) | −2.64538e6 | −0.492692 | ||||||||
\(493\) | 1.03341e7 | 1.91495 | ||||||||
\(494\) | 6.60168e6 | 1.21713 | ||||||||
\(495\) | −1.02776e6 | −0.188529 | ||||||||
\(496\) | −1.73170e7 | −3.16058 | ||||||||
\(497\) | 54284.5 | 0.00985791 | ||||||||
\(498\) | −7.45610e6 | −1.34722 | ||||||||
\(499\) | 6.29003e6 | 1.13084 | 0.565420 | − | 0.824803i | \(-0.308714\pi\) | ||||
0.565420 | + | 0.824803i | \(0.308714\pi\) | |||||||
\(500\) | 1.26848e7 | 2.26913 | ||||||||
\(501\) | −699440. | −0.124496 | ||||||||
\(502\) | −82064.9 | −0.0145344 | ||||||||
\(503\) | 3.68350e6 | 0.649143 | 0.324572 | − | 0.945861i | \(-0.394780\pi\) | ||||
0.324572 | + | 0.945861i | \(0.394780\pi\) | |||||||
\(504\) | −83066.9 | −0.0145664 | ||||||||
\(505\) | 2.28462e6 | 0.398644 | ||||||||
\(506\) | −1.23372e6 | −0.214210 | ||||||||
\(507\) | 563376. | 0.0973371 | ||||||||
\(508\) | 1.14367e7 | 1.96627 | ||||||||
\(509\) | 3.33612e6 | 0.570752 | 0.285376 | − | 0.958416i | \(-0.407882\pi\) | ||||
0.285376 | + | 0.958416i | \(0.407882\pi\) | |||||||
\(510\) | −7.36131e6 | −1.25323 | ||||||||
\(511\) | −207524. | −0.0351573 | ||||||||
\(512\) | 1.33189e7 | 2.24539 | ||||||||
\(513\) | −716000. | −0.120121 | ||||||||
\(514\) | −1.19114e7 | −1.98863 | ||||||||
\(515\) | 9.57854e6 | 1.59141 | ||||||||
\(516\) | −6.76218e6 | −1.11805 | ||||||||
\(517\) | 2.13879e6 | 0.351918 | ||||||||
\(518\) | −61913.5 | −0.0101382 | ||||||||
\(519\) | 1.96671e6 | 0.320496 | ||||||||
\(520\) | 1.49732e7 | 2.42832 | ||||||||
\(521\) | −987399. | −0.159367 | −0.0796835 | − | 0.996820i | \(-0.525391\pi\) | ||||
−0.0796835 | + | 0.996820i | \(0.525391\pi\) | |||||||
\(522\) | 5.91601e6 | 0.950282 | ||||||||
\(523\) | 6.57834e6 | 1.05163 | 0.525814 | − | 0.850600i | \(-0.323761\pi\) | ||||
0.525814 | + | 0.850600i | \(0.323761\pi\) | |||||||
\(524\) | −2.76612e7 | −4.40091 | ||||||||
\(525\) | −966.753 | −0.000153080 0 | ||||||||
\(526\) | 5.69446e6 | 0.897404 | ||||||||
\(527\) | 1.33696e7 | 2.09697 | ||||||||
\(528\) | 3.84667e6 | 0.600483 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −1.94200e7 | −3.00302 | ||||||||
\(531\) | −588772. | −0.0906172 | ||||||||
\(532\) | −177426. | −0.0271793 | ||||||||
\(533\) | −2.68439e6 | −0.409287 | ||||||||
\(534\) | −9.19435e6 | −1.39530 | ||||||||
\(535\) | −9.89463e6 | −1.49457 | ||||||||
\(536\) | −2.18854e7 | −3.29035 | ||||||||
\(537\) | −4.90943e6 | −0.734676 | ||||||||
\(538\) | 1.24437e7 | 1.85350 | ||||||||
\(539\) | −3.83981e6 | −0.569295 | ||||||||
\(540\) | −2.91905e6 | −0.430781 | ||||||||
\(541\) | −6.47470e6 | −0.951101 | −0.475551 | − | 0.879688i | \(-0.657751\pi\) | ||||
−0.475551 | + | 0.879688i | \(0.657751\pi\) | |||||||
\(542\) | −1.43452e7 | −2.09753 | ||||||||
\(543\) | 4.59790e6 | 0.669206 | ||||||||
\(544\) | 8.63445e6 | 1.25094 | ||||||||
\(545\) | 7.68087e6 | 1.10769 | ||||||||
\(546\) | −151514. | −0.0217506 | ||||||||
\(547\) | −495799. | −0.0708496 | −0.0354248 | − | 0.999372i | \(-0.511278\pi\) | ||||
−0.0354248 | + | 0.999372i | \(0.511278\pi\) | |||||||
\(548\) | −2.39249e6 | −0.340328 | ||||||||
\(549\) | 2.15554e6 | 0.305229 | ||||||||
\(550\) | 100021. | 0.0140989 | ||||||||
\(551\) | 7.02992e6 | 0.986442 | ||||||||
\(552\) | −1.94939e6 | −0.272302 | ||||||||
\(553\) | −60010.8 | −0.00834481 | ||||||||
\(554\) | −1.91634e7 | −2.65276 | ||||||||
\(555\) | −1.21041e6 | −0.166801 | ||||||||
\(556\) | −9.26727e6 | −1.27135 | ||||||||
\(557\) | 3.94887e6 | 0.539306 | 0.269653 | − | 0.962958i | \(-0.413091\pi\) | ||||
0.269653 | + | 0.962958i | \(0.413091\pi\) | |||||||
\(558\) | 7.65374e6 | 1.04061 | ||||||||
\(559\) | −6.86190e6 | −0.928784 | ||||||||
\(560\) | −260033. | −0.0350395 | ||||||||
\(561\) | −2.96984e6 | −0.398406 | ||||||||
\(562\) | 2.16083e7 | 2.88590 | ||||||||
\(563\) | −2.70237e6 | −0.359314 | −0.179657 | − | 0.983729i | \(-0.557499\pi\) | ||||
−0.179657 | + | 0.983729i | \(0.557499\pi\) | |||||||
\(564\) | 6.07462e6 | 0.804120 | ||||||||
\(565\) | 750781. | 0.0989447 | ||||||||
\(566\) | −1.18411e7 | −1.55365 | ||||||||
\(567\) | 16432.8 | 0.00214662 | ||||||||
\(568\) | −8.87430e6 | −1.15415 | ||||||||
\(569\) | 1.33108e7 | 1.72355 | 0.861773 | − | 0.507294i | \(-0.169354\pi\) | ||||
0.861773 | + | 0.507294i | \(0.169354\pi\) | |||||||
\(570\) | −5.00762e6 | −0.645571 | ||||||||
\(571\) | −1.10053e7 | −1.41257 | −0.706286 | − | 0.707926i | \(-0.749631\pi\) | ||||
−0.706286 | + | 0.707926i | \(0.749631\pi\) | |||||||
\(572\) | 1.08583e7 | 1.38762 | ||||||||
\(573\) | −519167. | −0.0660572 | ||||||||
\(574\) | 104154. | 0.0131947 | ||||||||
\(575\) | −22687.5 | −0.00286165 | ||||||||
\(576\) | 95717.3 | 0.0120208 | ||||||||
\(577\) | −480544. | −0.0600888 | −0.0300444 | − | 0.999549i | \(-0.509565\pi\) | ||||
−0.0300444 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(578\) | −6.78300e6 | −0.844505 | ||||||||
\(579\) | −7.39882e6 | −0.917204 | ||||||||
\(580\) | 2.86602e7 | 3.53760 | ||||||||
\(581\) | 203345. | 0.0249915 | ||||||||
\(582\) | −3.31737e6 | −0.405963 | ||||||||
\(583\) | −7.83477e6 | −0.954674 | ||||||||
\(584\) | 3.39255e7 | 4.11618 | ||||||||
\(585\) | −2.96210e6 | −0.357857 | ||||||||
\(586\) | 1.29924e7 | 1.56296 | ||||||||
\(587\) | 9.12805e6 | 1.09341 | 0.546705 | − | 0.837325i | \(-0.315882\pi\) | ||||
0.546705 | + | 0.837325i | \(0.315882\pi\) | |||||||
\(588\) | −1.09059e7 | −1.30082 | ||||||||
\(589\) | 9.09485e6 | 1.08021 | ||||||||
\(590\) | −4.11780e6 | −0.487007 | ||||||||
\(591\) | 8.74414e6 | 1.02979 | ||||||||
\(592\) | 4.53029e6 | 0.531278 | ||||||||
\(593\) | −2.66114e6 | −0.310765 | −0.155382 | − | 0.987854i | \(-0.549661\pi\) | ||||
−0.155382 | + | 0.987854i | \(0.549661\pi\) | |||||||
\(594\) | −1.70015e6 | −0.197707 | ||||||||
\(595\) | 200760. | 0.0232479 | ||||||||
\(596\) | −1.32876e7 | −1.53225 | ||||||||
\(597\) | 7.25499e6 | 0.833107 | ||||||||
\(598\) | −3.55569e6 | −0.406604 | ||||||||
\(599\) | 6.44915e6 | 0.734405 | 0.367202 | − | 0.930141i | \(-0.380316\pi\) | ||||
0.367202 | + | 0.930141i | \(0.380316\pi\) | |||||||
\(600\) | 158042. | 0.0179224 | ||||||||
\(601\) | −1.48491e6 | −0.167693 | −0.0838463 | − | 0.996479i | \(-0.526720\pi\) | ||||
−0.0838463 | + | 0.996479i | \(0.526720\pi\) | |||||||
\(602\) | 266241. | 0.0299423 | ||||||||
\(603\) | 4.32951e6 | 0.484893 | ||||||||
\(604\) | −1.42795e6 | −0.159265 | ||||||||
\(605\) | 6.04111e6 | 0.671009 | ||||||||
\(606\) | 3.77929e6 | 0.418051 | ||||||||
\(607\) | −6.56656e6 | −0.723379 | −0.361690 | − | 0.932299i | \(-0.617800\pi\) | ||||
−0.361690 | + | 0.932299i | \(0.617800\pi\) | |||||||
\(608\) | 5.87368e6 | 0.644394 | ||||||||
\(609\) | −161343. | −0.0176281 | ||||||||
\(610\) | 1.50756e7 | 1.64040 | ||||||||
\(611\) | 6.16420e6 | 0.667996 | ||||||||
\(612\) | −8.43498e6 | −0.910344 | ||||||||
\(613\) | −9.33817e6 | −1.00372 | −0.501858 | − | 0.864950i | \(-0.667350\pi\) | ||||
−0.501858 | + | 0.864950i | \(0.667350\pi\) | |||||||
\(614\) | 2.30793e7 | 2.47060 | ||||||||
\(615\) | 2.03621e6 | 0.217088 | ||||||||
\(616\) | −234382. | −0.0248870 | ||||||||
\(617\) | 7.56128e6 | 0.799617 | 0.399809 | − | 0.916599i | \(-0.369077\pi\) | ||||
0.399809 | + | 0.916599i | \(0.369077\pi\) | |||||||
\(618\) | 1.58452e7 | 1.66888 | ||||||||
\(619\) | 1.16180e7 | 1.21872 | 0.609359 | − | 0.792895i | \(-0.291427\pi\) | ||||
0.609359 | + | 0.792895i | \(0.291427\pi\) | |||||||
\(620\) | 3.70786e7 | 3.87387 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | −1.22718e7 | −1.27184 | ||||||||
\(623\) | 250751. | 0.0258834 | ||||||||
\(624\) | 1.10865e7 | 1.13981 | ||||||||
\(625\) | −9.62976e6 | −0.986088 | ||||||||
\(626\) | 4.94201e6 | 0.504043 | ||||||||
\(627\) | −2.02027e6 | −0.205230 | ||||||||
\(628\) | 1.39431e7 | 1.41078 | ||||||||
\(629\) | −3.49763e6 | −0.352491 | ||||||||
\(630\) | 114929. | 0.0115366 | ||||||||
\(631\) | −8.43872e6 | −0.843730 | −0.421865 | − | 0.906659i | \(-0.638624\pi\) | ||||
−0.421865 | + | 0.906659i | \(0.638624\pi\) | |||||||
\(632\) | 9.81042e6 | 0.977001 | ||||||||
\(633\) | −7.39722e6 | −0.733768 | ||||||||
\(634\) | −8.12891e6 | −0.803173 | ||||||||
\(635\) | −8.80313e6 | −0.866369 | ||||||||
\(636\) | −2.22524e7 | −2.18140 | ||||||||
\(637\) | −1.10667e7 | −1.08061 | ||||||||
\(638\) | 1.66926e7 | 1.62358 | ||||||||
\(639\) | 1.75557e6 | 0.170085 | ||||||||
\(640\) | −9.95483e6 | −0.960692 | ||||||||
\(641\) | 1.32010e7 | 1.26900 | 0.634500 | − | 0.772923i | \(-0.281206\pi\) | ||||
0.634500 | + | 0.772923i | \(0.281206\pi\) | |||||||
\(642\) | −1.63680e7 | −1.56733 | ||||||||
\(643\) | −1.57321e7 | −1.50058 | −0.750290 | − | 0.661109i | \(-0.770086\pi\) | ||||
−0.750290 | + | 0.661109i | \(0.770086\pi\) | |||||||
\(644\) | 95562.5 | 0.00907973 | ||||||||
\(645\) | 5.20501e6 | 0.492631 | ||||||||
\(646\) | −1.44702e7 | −1.36425 | ||||||||
\(647\) | −6.22066e6 | −0.584219 | −0.292109 | − | 0.956385i | \(-0.594357\pi\) | ||||
−0.292109 | + | 0.956385i | \(0.594357\pi\) | |||||||
\(648\) | −2.68640e6 | −0.251323 | ||||||||
\(649\) | −1.66128e6 | −0.154822 | ||||||||
\(650\) | 288270. | 0.0267618 | ||||||||
\(651\) | −208735. | −0.0193038 | ||||||||
\(652\) | 7.66595e6 | 0.706231 | ||||||||
\(653\) | −1.57628e7 | −1.44660 | −0.723302 | − | 0.690532i | \(-0.757376\pi\) | ||||
−0.723302 | + | 0.690532i | \(0.757376\pi\) | |||||||
\(654\) | 1.27060e7 | 1.16162 | ||||||||
\(655\) | 2.12915e7 | 1.93911 | ||||||||
\(656\) | −7.62110e6 | −0.691446 | ||||||||
\(657\) | −6.71136e6 | −0.606593 | ||||||||
\(658\) | −239171. | −0.0215349 | ||||||||
\(659\) | −5.77008e6 | −0.517569 | −0.258784 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258784 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(660\) | −8.23640e6 | −0.736000 | ||||||||
\(661\) | −1.48192e7 | −1.31924 | −0.659618 | − | 0.751601i | \(-0.729282\pi\) | ||||
−0.659618 | + | 0.751601i | \(0.729282\pi\) | |||||||
\(662\) | 2.68223e6 | 0.237877 | ||||||||
\(663\) | −8.55938e6 | −0.756238 | ||||||||
\(664\) | −3.32423e7 | −2.92598 | ||||||||
\(665\) | 136569. | 0.0119756 | ||||||||
\(666\) | −2.00230e6 | −0.174921 | ||||||||
\(667\) | −3.78635e6 | −0.329538 | ||||||||
\(668\) | −5.60528e6 | −0.486022 | ||||||||
\(669\) | 4.60753e6 | 0.398018 | ||||||||
\(670\) | 3.02801e7 | 2.60597 | ||||||||
\(671\) | 6.08209e6 | 0.521491 | ||||||||
\(672\) | −134806. | −0.0115156 | ||||||||
\(673\) | −1.74615e7 | −1.48609 | −0.743045 | − | 0.669242i | \(-0.766619\pi\) | ||||
−0.743045 | + | 0.669242i | \(0.766619\pi\) | |||||||
\(674\) | −1.25637e7 | −1.06529 | ||||||||
\(675\) | −31265.0 | −0.00264118 | ||||||||
\(676\) | 4.51487e6 | 0.379995 | ||||||||
\(677\) | −2.10975e7 | −1.76913 | −0.884564 | − | 0.466418i | \(-0.845544\pi\) | ||||
−0.884564 | + | 0.466418i | \(0.845544\pi\) | |||||||
\(678\) | 1.24197e6 | 0.103762 | ||||||||
\(679\) | 90472.2 | 0.00753080 | ||||||||
\(680\) | −3.28197e7 | −2.72184 | ||||||||
\(681\) | −1.30567e7 | −1.07886 | ||||||||
\(682\) | 2.15958e7 | 1.77791 | ||||||||
\(683\) | −1.43654e7 | −1.17833 | −0.589163 | − | 0.808014i | \(-0.700542\pi\) | ||||
−0.589163 | + | 0.808014i | \(0.700542\pi\) | |||||||
\(684\) | −5.73799e6 | −0.468943 | ||||||||
\(685\) | 1.84155e6 | 0.149954 | ||||||||
\(686\) | 858935. | 0.0696867 | ||||||||
\(687\) | 5.59052e6 | 0.451919 | ||||||||
\(688\) | −1.94812e7 | −1.56908 | ||||||||
\(689\) | −2.25806e7 | −1.81212 | ||||||||
\(690\) | 2.69713e6 | 0.215664 | ||||||||
\(691\) | 1.64154e7 | 1.30785 | 0.653923 | − | 0.756561i | \(-0.273122\pi\) | ||||
0.653923 | + | 0.756561i | \(0.273122\pi\) | |||||||
\(692\) | 1.57612e7 | 1.25119 | ||||||||
\(693\) | 46367.0 | 0.00366755 | ||||||||
\(694\) | 3.77907e7 | 2.97842 | ||||||||
\(695\) | 7.13324e6 | 0.560176 | ||||||||
\(696\) | 2.63759e7 | 2.06388 | ||||||||
\(697\) | 5.88391e6 | 0.458758 | ||||||||
\(698\) | −1.66210e7 | −1.29127 | ||||||||
\(699\) | 4.41301e6 | 0.341619 | ||||||||
\(700\) | −7747.52 | −0.000597609 0 | ||||||||
\(701\) | −1.07940e7 | −0.829635 | −0.414818 | − | 0.909905i | \(-0.636155\pi\) | ||||
−0.414818 | + | 0.909905i | \(0.636155\pi\) | |||||||
\(702\) | −4.90000e6 | −0.375278 | ||||||||
\(703\) | −2.37930e6 | −0.181577 | ||||||||
\(704\) | 270077. | 0.0205379 | ||||||||
\(705\) | −4.67577e6 | −0.354308 | ||||||||
\(706\) | −2.61829e7 | −1.97700 | ||||||||
\(707\) | −103070. | −0.00775502 | ||||||||
\(708\) | −4.71839e6 | −0.353762 | ||||||||
\(709\) | 2.44390e7 | 1.82586 | 0.912930 | − | 0.408115i | \(-0.133814\pi\) | ||||
0.912930 | + | 0.408115i | \(0.133814\pi\) | |||||||
\(710\) | 1.22783e7 | 0.914093 | ||||||||
\(711\) | −1.94076e6 | −0.143979 | ||||||||
\(712\) | −4.09921e7 | −3.03040 | ||||||||
\(713\) | −4.89853e6 | −0.360863 | ||||||||
\(714\) | 332103. | 0.0243797 | ||||||||
\(715\) | −8.35787e6 | −0.611407 | ||||||||
\(716\) | −3.93440e7 | −2.86811 | ||||||||
\(717\) | 985527. | 0.0715930 | ||||||||
\(718\) | 3.53978e7 | 2.56251 | ||||||||
\(719\) | −6.41280e6 | −0.462621 | −0.231310 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231310 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(720\) | −8.40951e6 | −0.604560 | ||||||||
\(721\) | −432133. | −0.0309585 | ||||||||
\(722\) | 1.54231e7 | 1.10110 | ||||||||
\(723\) | 1.22554e7 | 0.871928 | ||||||||
\(724\) | 3.68474e7 | 2.61252 | ||||||||
\(725\) | 306970. | 0.0216896 | ||||||||
\(726\) | 9.99341e6 | 0.703675 | ||||||||
\(727\) | −1.58788e7 | −1.11424 | −0.557122 | − | 0.830431i | \(-0.688095\pi\) | ||||
−0.557122 | + | 0.830431i | \(0.688095\pi\) | |||||||
\(728\) | −675512. | −0.0472394 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −4.69385e7 | −3.26003 | ||||||||
\(731\) | 1.50406e7 | 1.04105 | ||||||||
\(732\) | 1.72744e7 | 1.19159 | ||||||||
\(733\) | 2.52517e7 | 1.73592 | 0.867962 | − | 0.496631i | \(-0.165430\pi\) | ||||
0.867962 | + | 0.496631i | \(0.165430\pi\) | |||||||
\(734\) | −1.67487e7 | −1.14747 | ||||||||
\(735\) | 8.39450e6 | 0.573161 | ||||||||
\(736\) | −3.16359e6 | −0.215271 | ||||||||
\(737\) | 1.22162e7 | 0.828450 | ||||||||
\(738\) | 3.36837e6 | 0.227656 | ||||||||
\(739\) | −1.56260e7 | −1.05253 | −0.526267 | − | 0.850319i | \(-0.676409\pi\) | ||||
−0.526267 | + | 0.850319i | \(0.676409\pi\) | |||||||
\(740\) | −9.70015e6 | −0.651177 | ||||||||
\(741\) | −5.82261e6 | −0.389558 | ||||||||
\(742\) | 876126. | 0.0584193 | ||||||||
\(743\) | 1.42696e7 | 0.948284 | 0.474142 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474142 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(744\) | 3.41235e7 | 2.26006 | ||||||||
\(745\) | 1.02278e7 | 0.675133 | ||||||||
\(746\) | −1.61845e7 | −1.06476 | ||||||||
\(747\) | 6.57621e6 | 0.431195 | ||||||||
\(748\) | −2.38002e7 | −1.55534 | ||||||||
\(749\) | 446393. | 0.0290746 | ||||||||
\(750\) | −1.61516e7 | −1.04848 | ||||||||
\(751\) | 2.22359e7 | 1.43865 | 0.719323 | − | 0.694676i | \(-0.244452\pi\) | ||||
0.719323 | + | 0.694676i | \(0.244452\pi\) | |||||||
\(752\) | 1.75004e7 | 1.12851 | ||||||||
\(753\) | 72380.4 | 0.00465193 | ||||||||
\(754\) | 4.81098e7 | 3.08181 | ||||||||
\(755\) | 1.09912e6 | 0.0701745 | ||||||||
\(756\) | 131692. | 0.00838021 | ||||||||
\(757\) | −1.09113e7 | −0.692048 | −0.346024 | − | 0.938226i | \(-0.612468\pi\) | ||||
−0.346024 | + | 0.938226i | \(0.612468\pi\) | |||||||
\(758\) | 9.85756e6 | 0.623155 | ||||||||
\(759\) | 1.08813e6 | 0.0685607 | ||||||||
\(760\) | −2.23260e7 | −1.40209 | ||||||||
\(761\) | 2.42444e6 | 0.151758 | 0.0758788 | − | 0.997117i | \(-0.475824\pi\) | ||||
0.0758788 | + | 0.997117i | \(0.475824\pi\) | |||||||
\(762\) | −1.45624e7 | −0.908546 | ||||||||
\(763\) | −346520. | −0.0215485 | ||||||||
\(764\) | −4.16058e6 | −0.257882 | ||||||||
\(765\) | 6.49260e6 | 0.401112 | ||||||||
\(766\) | 3.16659e7 | 1.94993 | ||||||||
\(767\) | −4.78798e6 | −0.293876 | ||||||||
\(768\) | −1.68080e7 | −1.02828 | ||||||||
\(769\) | 2.00363e6 | 0.122181 | 0.0610903 | − | 0.998132i | \(-0.480542\pi\) | ||||
0.0610903 | + | 0.998132i | \(0.480542\pi\) | |||||||
\(770\) | 324285. | 0.0197106 | ||||||||
\(771\) | 1.05057e7 | 0.636487 | ||||||||
\(772\) | −5.92938e7 | −3.58069 | ||||||||
\(773\) | 3.91181e6 | 0.235466 | 0.117733 | − | 0.993045i | \(-0.462437\pi\) | ||||
0.117733 | + | 0.993045i | \(0.462437\pi\) | |||||||
\(774\) | 8.61030e6 | 0.516614 | ||||||||
\(775\) | 397137. | 0.0237512 | ||||||||
\(776\) | −1.47902e7 | −0.881697 | ||||||||
\(777\) | 54607.1 | 0.00324487 | ||||||||
\(778\) | −6.37322e6 | −0.377494 | ||||||||
\(779\) | 4.00260e6 | 0.236319 | ||||||||
\(780\) | −2.37381e7 | −1.39704 | ||||||||
\(781\) | 4.95353e6 | 0.290594 | ||||||||
\(782\) | 7.79371e6 | 0.455751 | ||||||||
\(783\) | −5.21786e6 | −0.304150 | ||||||||
\(784\) | −3.14188e7 | −1.82557 | ||||||||
\(785\) | −1.07323e7 | −0.621614 | ||||||||
\(786\) | 3.52211e7 | 2.03351 | ||||||||
\(787\) | −2.37516e7 | −1.36696 | −0.683479 | − | 0.729970i | \(-0.739534\pi\) | ||||
−0.683479 | + | 0.729970i | \(0.739534\pi\) | |||||||
\(788\) | 7.00752e7 | 4.02021 | ||||||||
\(789\) | −5.02246e6 | −0.287226 | ||||||||
\(790\) | −1.35734e7 | −0.773789 | ||||||||
\(791\) | −33871.3 | −0.00192482 | ||||||||
\(792\) | −7.57996e6 | −0.429392 | ||||||||
\(793\) | 1.75292e7 | 0.989872 | ||||||||
\(794\) | −2.86548e7 | −1.61304 | ||||||||
\(795\) | 1.71282e7 | 0.961157 | ||||||||
\(796\) | 5.81412e7 | 3.25238 | ||||||||
\(797\) | −2.50486e7 | −1.39681 | −0.698405 | − | 0.715703i | \(-0.746106\pi\) | ||||
−0.698405 | + | 0.715703i | \(0.746106\pi\) | |||||||
\(798\) | 225917. | 0.0125586 | ||||||||
\(799\) | −1.35113e7 | −0.748737 | ||||||||
\(800\) | 256481. | 0.0141687 | ||||||||
\(801\) | 8.10932e6 | 0.446584 | ||||||||
\(802\) | −3.89072e7 | −2.13597 | ||||||||
\(803\) | −1.89368e7 | −1.03638 | ||||||||
\(804\) | 3.46965e7 | 1.89298 | ||||||||
\(805\) | −73556.7 | −0.00400067 | ||||||||
\(806\) | 6.22413e7 | 3.37475 | ||||||||
\(807\) | −1.09752e7 | −0.593237 | ||||||||
\(808\) | 1.68496e7 | 0.907949 | ||||||||
\(809\) | −2.26709e7 | −1.21786 | −0.608931 | − | 0.793223i | \(-0.708402\pi\) | ||||
−0.608931 | + | 0.793223i | \(0.708402\pi\) | |||||||
\(810\) | 3.71683e6 | 0.199049 | ||||||||
\(811\) | −1.66885e7 | −0.890974 | −0.445487 | − | 0.895288i | \(-0.646969\pi\) | ||||
−0.445487 | + | 0.895288i | \(0.646969\pi\) | |||||||
\(812\) | −1.29300e6 | −0.0688188 | ||||||||
\(813\) | 1.26523e7 | 0.671342 | ||||||||
\(814\) | −5.64969e6 | −0.298857 | ||||||||
\(815\) | −5.90066e6 | −0.311176 | ||||||||
\(816\) | −2.43004e7 | −1.27758 | ||||||||
\(817\) | 1.02315e7 | 0.536272 | ||||||||
\(818\) | 3.94156e7 | 2.05961 | ||||||||
\(819\) | 133634. | 0.00696158 | ||||||||
\(820\) | 1.63181e7 | 0.847492 | ||||||||
\(821\) | −2.41094e7 | −1.24833 | −0.624164 | − | 0.781293i | \(-0.714560\pi\) | ||||
−0.624164 | + | 0.781293i | \(0.714560\pi\) | |||||||
\(822\) | 3.04636e6 | 0.157254 | ||||||||
\(823\) | −9.03070e6 | −0.464753 | −0.232376 | − | 0.972626i | \(-0.574650\pi\) | ||||
−0.232376 | + | 0.972626i | \(0.574650\pi\) | |||||||
\(824\) | 7.06441e7 | 3.62458 | ||||||||
\(825\) | −88217.4 | −0.00451252 | ||||||||
\(826\) | 185773. | 0.00947399 | ||||||||
\(827\) | 1.22307e7 | 0.621852 | 0.310926 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310926 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(828\) | 3.09051e6 | 0.156659 | ||||||||
\(829\) | 2.01683e7 | 1.01925 | 0.509627 | − | 0.860395i | \(-0.329783\pi\) | ||||
0.509627 | + | 0.860395i | \(0.329783\pi\) | |||||||
\(830\) | 4.59932e7 | 2.31739 | ||||||||
\(831\) | 1.69019e7 | 0.849051 | ||||||||
\(832\) | 778387. | 0.0389841 | ||||||||
\(833\) | 2.42570e7 | 1.21123 | ||||||||
\(834\) | 1.18000e7 | 0.587447 | ||||||||
\(835\) | 4.31452e6 | 0.214149 | ||||||||
\(836\) | −1.61904e7 | −0.801199 | ||||||||
\(837\) | −6.75053e6 | −0.333061 | ||||||||
\(838\) | 4.08700e7 | 2.01045 | ||||||||
\(839\) | 1.80995e7 | 0.887690 | 0.443845 | − | 0.896103i | \(-0.353614\pi\) | ||||
0.443845 | + | 0.896103i | \(0.353614\pi\) | |||||||
\(840\) | 512401. | 0.0250560 | ||||||||
\(841\) | 3.07195e7 | 1.49770 | ||||||||
\(842\) | −4.99697e7 | −2.42899 | ||||||||
\(843\) | −1.90583e7 | −0.923668 | ||||||||
\(844\) | −5.92810e7 | −2.86457 | ||||||||
\(845\) | −3.47520e6 | −0.167432 | ||||||||
\(846\) | −7.73483e6 | −0.371556 | ||||||||
\(847\) | −272543. | −0.0130535 | ||||||||
\(848\) | −6.41072e7 | −3.06138 | ||||||||
\(849\) | 1.04438e7 | 0.497265 | ||||||||
\(850\) | −631857. | −0.0299966 | ||||||||
\(851\) | 1.28150e6 | 0.0606591 | ||||||||
\(852\) | 1.40691e7 | 0.663998 | ||||||||
\(853\) | −1.82781e7 | −0.860121 | −0.430060 | − | 0.902800i | \(-0.641508\pi\) | ||||
−0.430060 | + | 0.902800i | \(0.641508\pi\) | |||||||
\(854\) | −680132. | −0.0319116 | ||||||||
\(855\) | 4.41667e6 | 0.206623 | ||||||||
\(856\) | −7.29753e7 | −3.40402 | ||||||||
\(857\) | −1.47267e7 | −0.684940 | −0.342470 | − | 0.939529i | \(-0.611264\pi\) | ||||
−0.342470 | + | 0.939529i | \(0.611264\pi\) | |||||||
\(858\) | −1.38259e7 | −0.641172 | ||||||||
\(859\) | −1.82990e7 | −0.846142 | −0.423071 | − | 0.906096i | \(-0.639048\pi\) | ||||
−0.423071 | + | 0.906096i | \(0.639048\pi\) | |||||||
\(860\) | 4.17127e7 | 1.92319 | ||||||||
\(861\) | −91863.1 | −0.00422312 | ||||||||
\(862\) | −1.85588e7 | −0.850712 | ||||||||
\(863\) | −3.92569e6 | −0.179427 | −0.0897137 | − | 0.995968i | \(-0.528595\pi\) | ||||
−0.0897137 | + | 0.995968i | \(0.528595\pi\) | |||||||
\(864\) | −4.35966e6 | −0.198686 | ||||||||
\(865\) | −1.21317e7 | −0.551293 | ||||||||
\(866\) | −5.56814e6 | −0.252299 | ||||||||
\(867\) | 5.98254e6 | 0.270295 | ||||||||
\(868\) | −1.67279e6 | −0.0753603 | ||||||||
\(869\) | −5.47606e6 | −0.245991 | ||||||||
\(870\) | −3.64931e7 | −1.63460 | ||||||||
\(871\) | 3.52082e7 | 1.57253 | ||||||||
\(872\) | 5.66483e7 | 2.52287 | ||||||||
\(873\) | 2.92589e6 | 0.129934 | ||||||||
\(874\) | 5.30176e6 | 0.234769 | ||||||||
\(875\) | 440490. | 0.0194499 | ||||||||
\(876\) | −5.37846e7 | −2.36809 | ||||||||
\(877\) | −3.49463e7 | −1.53427 | −0.767135 | − | 0.641486i | \(-0.778318\pi\) | ||||
−0.767135 | + | 0.641486i | \(0.778318\pi\) | |||||||
\(878\) | −2.86854e7 | −1.25581 | ||||||||
\(879\) | −1.14592e7 | −0.500245 | ||||||||
\(880\) | −2.37283e7 | −1.03290 | ||||||||
\(881\) | −3.45541e7 | −1.49989 | −0.749945 | − | 0.661501i | \(-0.769920\pi\) | ||||
−0.749945 | + | 0.661501i | \(0.769920\pi\) | |||||||
\(882\) | 1.38865e7 | 0.601064 | ||||||||
\(883\) | 2.29538e6 | 0.0990722 | 0.0495361 | − | 0.998772i | \(-0.484226\pi\) | ||||
0.0495361 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(884\) | −6.85945e7 | −2.95229 | ||||||||
\(885\) | 3.63186e6 | 0.155873 | ||||||||
\(886\) | 2.87175e7 | 1.22903 | ||||||||
\(887\) | 2.48902e7 | 1.06223 | 0.531116 | − | 0.847299i | \(-0.321773\pi\) | ||||
0.531116 | + | 0.847299i | \(0.321773\pi\) | |||||||
\(888\) | −8.92704e6 | −0.379905 | ||||||||
\(889\) | 397151. | 0.0168539 | ||||||||
\(890\) | 5.67156e7 | 2.40009 | ||||||||
\(891\) | 1.49952e6 | 0.0632786 | ||||||||
\(892\) | 3.69246e7 | 1.55383 | ||||||||
\(893\) | −9.19120e6 | −0.385695 | ||||||||
\(894\) | 1.69191e7 | 0.708000 | ||||||||
\(895\) | 3.02840e7 | 1.26373 | ||||||||
\(896\) | 449109. | 0.0186888 | ||||||||
\(897\) | 3.13609e6 | 0.130139 | ||||||||
\(898\) | −4.08826e7 | −1.69179 | ||||||||
\(899\) | 6.62789e7 | 2.73512 | ||||||||
\(900\) | −250556. | −0.0103110 | ||||||||
\(901\) | 4.94943e7 | 2.03115 | ||||||||
\(902\) | 9.50422e6 | 0.388956 | ||||||||
\(903\) | −234822. | −0.00958341 | ||||||||
\(904\) | 5.53719e6 | 0.225356 | ||||||||
\(905\) | −2.83623e7 | −1.15112 | ||||||||
\(906\) | 1.81821e6 | 0.0735908 | ||||||||
\(907\) | −1.12581e7 | −0.454411 | −0.227205 | − | 0.973847i | \(-0.572959\pi\) | ||||
−0.227205 | + | 0.973847i | \(0.572959\pi\) | |||||||
\(908\) | −1.04636e8 | −4.21178 | ||||||||
\(909\) | −3.33330e6 | −0.133803 | ||||||||
\(910\) | 934621. | 0.0374138 | ||||||||
\(911\) | −2.07869e7 | −0.829837 | −0.414919 | − | 0.909859i | \(-0.636190\pi\) | ||||
−0.414919 | + | 0.909859i | \(0.636190\pi\) | |||||||
\(912\) | −1.65306e7 | −0.658116 | ||||||||
\(913\) | 1.85555e7 | 0.736707 | ||||||||
\(914\) | 5.54905e7 | 2.19712 | ||||||||
\(915\) | −1.32965e7 | −0.525032 | ||||||||
\(916\) | 4.48022e7 | 1.76425 | ||||||||
\(917\) | −960558. | −0.0377225 | ||||||||
\(918\) | 1.07403e7 | 0.420639 | ||||||||
\(919\) | −1.17836e7 | −0.460244 | −0.230122 | − | 0.973162i | \(-0.573913\pi\) | ||||
−0.230122 | + | 0.973162i | \(0.573913\pi\) | |||||||
\(920\) | 1.20249e7 | 0.468394 | ||||||||
\(921\) | −2.03557e7 | −0.790747 | ||||||||
\(922\) | −2.56091e7 | −0.992126 | ||||||||
\(923\) | 1.42766e7 | 0.551594 | ||||||||
\(924\) | 371583. | 0.0143178 | ||||||||
\(925\) | −103895. | −0.00399246 | ||||||||
\(926\) | −1.10881e6 | −0.0424942 | ||||||||
\(927\) | −1.39753e7 | −0.534147 | ||||||||
\(928\) | 4.28045e7 | 1.63162 | ||||||||
\(929\) | −2.82219e7 | −1.07287 | −0.536435 | − | 0.843942i | \(-0.680229\pi\) | ||||
−0.536435 | + | 0.843942i | \(0.680229\pi\) | |||||||
\(930\) | −4.72123e7 | −1.78998 | ||||||||
\(931\) | 1.65011e7 | 0.623935 | ||||||||
\(932\) | 3.53657e7 | 1.33365 | ||||||||
\(933\) | 1.08236e7 | 0.407070 | ||||||||
\(934\) | −3.15437e7 | −1.18316 | ||||||||
\(935\) | 1.83196e7 | 0.685308 | ||||||||
\(936\) | −2.18462e7 | −0.815053 | ||||||||
\(937\) | 1.34325e7 | 0.499814 | 0.249907 | − | 0.968270i | \(-0.419600\pi\) | ||||
0.249907 | + | 0.968270i | \(0.419600\pi\) | |||||||
\(938\) | −1.36608e6 | −0.0506953 | ||||||||
\(939\) | −4.35880e6 | −0.161325 | ||||||||
\(940\) | −3.74715e7 | −1.38319 | ||||||||
\(941\) | 4.06264e7 | 1.49566 | 0.747832 | − | 0.663888i | \(-0.231095\pi\) | ||||
0.747832 | + | 0.663888i | \(0.231095\pi\) | |||||||
\(942\) | −1.77538e7 | −0.651875 | ||||||||
\(943\) | −2.15582e6 | −0.0789465 | ||||||||
\(944\) | −1.35933e7 | −0.496470 | ||||||||
\(945\) | −101366. | −0.00369245 | ||||||||
\(946\) | 2.42949e7 | 0.882646 | ||||||||
\(947\) | −3.34341e7 | −1.21148 | −0.605738 | − | 0.795664i | \(-0.707122\pi\) | ||||
−0.605738 | + | 0.795664i | \(0.707122\pi\) | |||||||
\(948\) | −1.55532e7 | −0.562080 | ||||||||
\(949\) | −5.45778e7 | −1.96721 | ||||||||
\(950\) | −429828. | −0.0154520 | ||||||||
\(951\) | 7.16962e6 | 0.257066 | ||||||||
\(952\) | 1.48065e6 | 0.0529493 | ||||||||
\(953\) | −8.95158e6 | −0.319277 | −0.159638 | − | 0.987176i | \(-0.551033\pi\) | ||||
−0.159638 | + | 0.987176i | \(0.551033\pi\) | |||||||
\(954\) | 2.83341e7 | 1.00795 | ||||||||
\(955\) | 3.20250e6 | 0.113627 | ||||||||
\(956\) | 7.89797e6 | 0.279493 | ||||||||
\(957\) | −1.47227e7 | −0.519648 | ||||||||
\(958\) | 7.90563e7 | 2.78306 | ||||||||
\(959\) | −83081.1 | −0.00291713 | ||||||||
\(960\) | −590435. | −0.0206773 | ||||||||
\(961\) | 5.71181e7 | 1.99510 | ||||||||
\(962\) | −1.62830e7 | −0.567277 | ||||||||
\(963\) | 1.44365e7 | 0.501643 | ||||||||
\(964\) | 9.82140e7 | 3.40393 | ||||||||
\(965\) | 4.56399e7 | 1.57771 | ||||||||
\(966\) | −121680. | −0.00419543 | ||||||||
\(967\) | −2.94663e7 | −1.01335 | −0.506675 | − | 0.862137i | \(-0.669126\pi\) | ||||
−0.506675 | + | 0.862137i | \(0.669126\pi\) | |||||||
\(968\) | 4.45546e7 | 1.52829 | ||||||||
\(969\) | 1.27626e7 | 0.436645 | ||||||||
\(970\) | 2.04633e7 | 0.698307 | ||||||||
\(971\) | −3.03617e7 | −1.03342 | −0.516712 | − | 0.856159i | \(-0.672844\pi\) | ||||
−0.516712 | + | 0.856159i | \(0.672844\pi\) | |||||||
\(972\) | 4.25895e6 | 0.144589 | ||||||||
\(973\) | −321814. | −0.0108974 | ||||||||
\(974\) | −6.74425e7 | −2.27791 | ||||||||
\(975\) | −254251. | −0.00856548 | ||||||||
\(976\) | 4.97661e7 | 1.67228 | ||||||||
\(977\) | 3.77587e6 | 0.126555 | 0.0632777 | − | 0.997996i | \(-0.479845\pi\) | ||||
0.0632777 | + | 0.997996i | \(0.479845\pi\) | |||||||
\(978\) | −9.76107e6 | −0.326325 | ||||||||
\(979\) | 2.28813e7 | 0.762999 | ||||||||
\(980\) | 6.72732e7 | 2.23757 | ||||||||
\(981\) | −1.12065e7 | −0.371791 | ||||||||
\(982\) | −1.71893e7 | −0.568826 | ||||||||
\(983\) | 1.74788e7 | 0.576938 | 0.288469 | − | 0.957489i | \(-0.406854\pi\) | ||||
0.288469 | + | 0.957489i | \(0.406854\pi\) | |||||||
\(984\) | 1.50176e7 | 0.494438 | ||||||||
\(985\) | −5.39385e7 | −1.77137 | ||||||||
\(986\) | −1.05452e8 | −3.45431 | ||||||||
\(987\) | 210946. | 0.00689253 | ||||||||
\(988\) | −4.66622e7 | −1.52080 | ||||||||
\(989\) | −5.51074e6 | −0.179151 | ||||||||
\(990\) | 1.04874e7 | 0.340080 | ||||||||
\(991\) | 4.83380e7 | 1.56352 | 0.781762 | − | 0.623576i | \(-0.214321\pi\) | ||||
0.781762 | + | 0.623576i | \(0.214321\pi\) | |||||||
\(992\) | 5.53777e7 | 1.78672 | ||||||||
\(993\) | −2.36570e6 | −0.0761355 | ||||||||
\(994\) | −553930. | −0.0177823 | ||||||||
\(995\) | −4.47526e7 | −1.43305 | ||||||||
\(996\) | 5.27014e7 | 1.68335 | ||||||||
\(997\) | −1.74335e7 | −0.555452 | −0.277726 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277726 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(998\) | −6.41847e7 | −2.03988 | ||||||||
\(999\) | 1.76601e6 | 0.0559858 |
(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 | 69.6.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 207.6.a.c.1.3 | 3 | |||
4.3 | odd | 2 | 1104.6.a.i.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
207.6.a.c.1.3 | 3 | 3.2 | odd | 2 | |||
1104.6.a.i.1.2 | 3 | 4.3 | odd | 2 |