Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.00299522 | 0.00211794 | 0.00105897 | − | 0.999999i | \(-0.499663\pi\) | ||||
0.00105897 | + | 0.999999i | \(0.499663\pi\) | |||||||
\(3\) | 0.0189616 | 0.0109475 | 0.00547374 | − | 0.999985i | \(-0.498258\pi\) | ||||
0.00547374 | + | 0.999985i | \(0.498258\pi\) | |||||||
\(4\) | −1.99999 | −0.999996 | ||||||||
\(5\) | 1.18959 | 0.532002 | 0.266001 | − | 0.963973i | \(-0.414298\pi\) | ||||
0.266001 | + | 0.963973i | \(0.414298\pi\) | |||||||
\(6\) | 5.67941e−5 0 | 2.31861e−5 0 | ||||||||
\(7\) | −5.08173 | −1.92071 | −0.960356 | − | 0.278775i | \(-0.910072\pi\) | ||||
−0.960356 | + | 0.278775i | \(0.910072\pi\) | |||||||
\(8\) | −0.0119809 | −0.00423587 | ||||||||
\(9\) | −2.99964 | −0.999880 | ||||||||
\(10\) | 0.00356309 | 0.00112675 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.0379230 | −0.0109474 | ||||||||
\(13\) | 1.44977 | 0.402095 | 0.201047 | − | 0.979582i | \(-0.435565\pi\) | ||||
0.201047 | + | 0.979582i | \(0.435565\pi\) | |||||||
\(14\) | −0.0152209 | −0.00406795 | ||||||||
\(15\) | 0.0225565 | 0.00582408 | ||||||||
\(16\) | 3.99995 | 0.999987 | ||||||||
\(17\) | −2.75724 | −0.668729 | −0.334364 | − | 0.942444i | \(-0.608522\pi\) | ||||
−0.334364 | + | 0.942444i | \(0.608522\pi\) | |||||||
\(18\) | −0.00898458 | −0.00211769 | ||||||||
\(19\) | −1.37486 | −0.315414 | −0.157707 | − | 0.987486i | \(-0.550410\pi\) | ||||
−0.157707 | + | 0.987486i | \(0.550410\pi\) | |||||||
\(20\) | −2.37917 | −0.531999 | ||||||||
\(21\) | −0.0963576 | −0.0210269 | ||||||||
\(22\) | 0.00299522 | 0.000638583 0 | ||||||||
\(23\) | 5.74246 | 1.19738 | 0.598692 | − | 0.800979i | \(-0.295687\pi\) | ||||
0.598692 | + | 0.800979i | \(0.295687\pi\) | |||||||
\(24\) | −0.000227176 0 | −4.63721e−5 0 | ||||||||
\(25\) | −3.58487 | −0.716974 | ||||||||
\(26\) | 0.00434239 | 0.000851613 0 | ||||||||
\(27\) | −0.113763 | −0.0218936 | ||||||||
\(28\) | 10.1634 | 1.92070 | ||||||||
\(29\) | 3.99015 | 0.740952 | 0.370476 | − | 0.928842i | \(-0.379195\pi\) | ||||
0.370476 | + | 0.928842i | \(0.379195\pi\) | |||||||
\(30\) | 6.75618e−5 0 | 1.23350e−5 0 | ||||||||
\(31\) | 9.63671 | 1.73080 | 0.865402 | − | 0.501078i | \(-0.167063\pi\) | ||||
0.865402 | + | 0.501078i | \(0.167063\pi\) | |||||||
\(32\) | 0.0359424 | 0.00635378 | ||||||||
\(33\) | 0.0189616 | 0.00330079 | ||||||||
\(34\) | −0.00825854 | −0.00141633 | ||||||||
\(35\) | −6.04518 | −1.02182 | ||||||||
\(36\) | 5.99925 | 0.999876 | ||||||||
\(37\) | −10.3333 | −1.69879 | −0.849395 | − | 0.527758i | \(-0.823033\pi\) | ||||
−0.849395 | + | 0.527758i | \(0.823033\pi\) | |||||||
\(38\) | −0.00411800 | −0.000668028 0 | ||||||||
\(39\) | 0.0274900 | 0.00440192 | ||||||||
\(40\) | −0.0142523 | −0.00225349 | ||||||||
\(41\) | 10.9906 | 1.71644 | 0.858219 | − | 0.513284i | \(-0.171571\pi\) | ||||
0.858219 | + | 0.513284i | \(0.171571\pi\) | |||||||
\(42\) | −0.000288612 0 | −4.45338e−5 0 | ||||||||
\(43\) | 8.25810 | 1.25935 | 0.629674 | − | 0.776859i | \(-0.283188\pi\) | ||||
0.629674 | + | 0.776859i | \(0.283188\pi\) | |||||||
\(44\) | −1.99999 | −0.301510 | ||||||||
\(45\) | −3.56835 | −0.531938 | ||||||||
\(46\) | 0.0171999 | 0.00253599 | ||||||||
\(47\) | −3.38103 | −0.493174 | −0.246587 | − | 0.969121i | \(-0.579309\pi\) | ||||
−0.246587 | + | 0.969121i | \(0.579309\pi\) | |||||||
\(48\) | 0.0758453 | 0.0109473 | ||||||||
\(49\) | 18.8240 | 2.68914 | ||||||||
\(50\) | −0.0107375 | −0.00151851 | ||||||||
\(51\) | −0.0522816 | −0.00732089 | ||||||||
\(52\) | −2.89953 | −0.402093 | ||||||||
\(53\) | −4.69708 | −0.645193 | −0.322597 | − | 0.946537i | \(-0.604556\pi\) | ||||
−0.322597 | + | 0.946537i | \(0.604556\pi\) | |||||||
\(54\) | −0.000340744 0 | −4.63694e−5 0 | ||||||||
\(55\) | 1.18959 | 0.160405 | ||||||||
\(56\) | 0.0608834 | 0.00813589 | ||||||||
\(57\) | −0.0260695 | −0.00345299 | ||||||||
\(58\) | 0.0119514 | 0.00156929 | ||||||||
\(59\) | −0.0799144 | −0.0104040 | −0.00520199 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520199 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(60\) | −0.0451129 | −0.00582405 | ||||||||
\(61\) | 11.2096 | 1.43524 | 0.717622 | − | 0.696433i | \(-0.245231\pi\) | ||||
0.717622 | + | 0.696433i | \(0.245231\pi\) | |||||||
\(62\) | 0.0288641 | 0.00366574 | ||||||||
\(63\) | 15.2434 | 1.92048 | ||||||||
\(64\) | −7.99978 | −0.999973 | ||||||||
\(65\) | 1.72464 | 0.213915 | ||||||||
\(66\) | 5.67941e−5 0 | 6.99087e−6 0 | ||||||||
\(67\) | −8.01596 | −0.979306 | −0.489653 | − | 0.871917i | \(-0.662877\pi\) | ||||
−0.489653 | + | 0.871917i | \(0.662877\pi\) | |||||||
\(68\) | 5.51446 | 0.668726 | ||||||||
\(69\) | 0.108886 | 0.0131083 | ||||||||
\(70\) | −0.0181067 | −0.00216416 | ||||||||
\(71\) | 0.191268 | 0.0226994 | 0.0113497 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113497 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(72\) | 0.0359383 | 0.00423536 | ||||||||
\(73\) | 7.76499 | 0.908823 | 0.454412 | − | 0.890792i | \(-0.349850\pi\) | ||||
0.454412 | + | 0.890792i | \(0.349850\pi\) | |||||||
\(74\) | −0.0309506 | −0.00359793 | ||||||||
\(75\) | −0.0679748 | −0.00784905 | ||||||||
\(76\) | 2.74970 | 0.315413 | ||||||||
\(77\) | −5.08173 | −0.579117 | ||||||||
\(78\) | 8.23386e−5 0 | 9.32301e−6 0 | ||||||||
\(79\) | 4.16667 | 0.468787 | 0.234393 | − | 0.972142i | \(-0.424690\pi\) | ||||
0.234393 | + | 0.972142i | \(0.424690\pi\) | |||||||
\(80\) | 4.75830 | 0.531995 | ||||||||
\(81\) | 8.99676 | 0.999640 | ||||||||
\(82\) | 0.0329192 | 0.00363531 | ||||||||
\(83\) | −3.16287 | −0.347171 | −0.173585 | − | 0.984819i | \(-0.555535\pi\) | ||||
−0.173585 | + | 0.984819i | \(0.555535\pi\) | |||||||
\(84\) | 0.192714 | 0.0210269 | ||||||||
\(85\) | −3.27999 | −0.355765 | ||||||||
\(86\) | 0.0247348 | 0.00266723 | ||||||||
\(87\) | 0.0756596 | 0.00811156 | ||||||||
\(88\) | −0.0119809 | −0.00127716 | ||||||||
\(89\) | −6.45631 | −0.684368 | −0.342184 | − | 0.939633i | \(-0.611167\pi\) | ||||
−0.342184 | + | 0.939633i | \(0.611167\pi\) | |||||||
\(90\) | −0.0106880 | −0.00112661 | ||||||||
\(91\) | −7.36735 | −0.772309 | ||||||||
\(92\) | −11.4849 | −1.19738 | ||||||||
\(93\) | 0.182727 | 0.0189479 | ||||||||
\(94\) | −0.0101269 | −0.00104451 | ||||||||
\(95\) | −1.63552 | −0.167801 | ||||||||
\(96\) | 0.000681525 0 | 6.95579e−5 0 | ||||||||
\(97\) | 11.8916 | 1.20741 | 0.603705 | − | 0.797208i | \(-0.293691\pi\) | ||||
0.603705 | + | 0.797208i | \(0.293691\pi\) | |||||||
\(98\) | 0.0563819 | 0.00569543 | ||||||||
\(99\) | −2.99964 | −0.301475 | ||||||||
\(100\) | 7.16971 | 0.716971 | ||||||||
\(101\) | −11.4022 | −1.13456 | −0.567280 | − | 0.823525i | \(-0.692004\pi\) | ||||
−0.567280 | + | 0.823525i | \(0.692004\pi\) | |||||||
\(102\) | −0.000156595 0 | −1.55052e−5 0 | ||||||||
\(103\) | 4.21109 | 0.414931 | 0.207465 | − | 0.978242i | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978242i | \(0.433479\pi\) | |||||||
\(104\) | −0.0173695 | −0.00170322 | ||||||||
\(105\) | −0.114626 | −0.0111864 | ||||||||
\(106\) | −0.0140688 | −0.00136648 | ||||||||
\(107\) | 5.54290 | 0.535853 | 0.267926 | − | 0.963439i | \(-0.413662\pi\) | ||||
0.267926 | + | 0.963439i | \(0.413662\pi\) | |||||||
\(108\) | 0.227524 | 0.0218935 | ||||||||
\(109\) | −1.17949 | −0.112974 | −0.0564872 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564872 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(110\) | 0.00356309 | 0.000339727 0 | ||||||||
\(111\) | −0.195936 | −0.0185975 | ||||||||
\(112\) | −20.3266 | −1.92069 | ||||||||
\(113\) | −14.6163 | −1.37499 | −0.687495 | − | 0.726189i | \(-0.741290\pi\) | ||||
−0.687495 | + | 0.726189i | \(0.741290\pi\) | |||||||
\(114\) | −7.80838e−5 0 | −7.31322e−6 0 | ||||||||
\(115\) | 6.83118 | 0.637011 | ||||||||
\(116\) | −7.98027 | −0.740949 | ||||||||
\(117\) | −4.34880 | −0.402047 | ||||||||
\(118\) | −0.000239361 0 | −2.20350e−5 0 | ||||||||
\(119\) | 14.0115 | 1.28444 | ||||||||
\(120\) | −0.000270247 0 | −2.46700e−5 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.0335753 | 0.00303976 | ||||||||
\(123\) | 0.208398 | 0.0187907 | ||||||||
\(124\) | −19.2733 | −1.73080 | ||||||||
\(125\) | −10.2125 | −0.913433 | ||||||||
\(126\) | 0.0456572 | 0.00406747 | ||||||||
\(127\) | 8.07328 | 0.716388 | 0.358194 | − | 0.933647i | \(-0.383393\pi\) | ||||
0.358194 | + | 0.933647i | \(0.383393\pi\) | |||||||
\(128\) | −0.0958460 | −0.00847167 | ||||||||
\(129\) | 0.156587 | 0.0137867 | ||||||||
\(130\) | 0.00516567 | 0.000453060 0 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −0.0379230 | −0.00330077 | ||||||||
\(133\) | 6.98665 | 0.605820 | ||||||||
\(134\) | −0.0240096 | −0.00207411 | ||||||||
\(135\) | −0.135331 | −0.0116475 | ||||||||
\(136\) | 0.0330341 | 0.00283265 | ||||||||
\(137\) | 10.9330 | 0.934068 | 0.467034 | − | 0.884239i | \(-0.345323\pi\) | ||||
0.467034 | + | 0.884239i | \(0.345323\pi\) | |||||||
\(138\) | 0.000326138 0 | 2.77627e−5 0 | ||||||||
\(139\) | 4.14223 | 0.351340 | 0.175670 | − | 0.984449i | \(-0.443791\pi\) | ||||
0.175670 | + | 0.984449i | \(0.443791\pi\) | |||||||
\(140\) | 12.0903 | 1.02182 | ||||||||
\(141\) | −0.0641097 | −0.00539901 | ||||||||
\(142\) | 0.000572891 0 | 4.80760e−5 0 | ||||||||
\(143\) | 1.44977 | 0.121236 | ||||||||
\(144\) | −11.9984 | −0.999867 | ||||||||
\(145\) | 4.74665 | 0.394188 | ||||||||
\(146\) | 0.0232578 | 0.00192483 | ||||||||
\(147\) | 0.356932 | 0.0294393 | ||||||||
\(148\) | 20.6666 | 1.69878 | ||||||||
\(149\) | 21.7119 | 1.77871 | 0.889354 | − | 0.457220i | \(-0.151155\pi\) | ||||
0.889354 | + | 0.457220i | \(0.151155\pi\) | |||||||
\(150\) | −0.000203599 0 | −1.66238e−5 0 | ||||||||
\(151\) | 1.61826 | 0.131692 | 0.0658460 | − | 0.997830i | \(-0.479025\pi\) | ||||
0.0658460 | + | 0.997830i | \(0.479025\pi\) | |||||||
\(152\) | 0.0164720 | 0.00133605 | ||||||||
\(153\) | 8.27073 | 0.668649 | ||||||||
\(154\) | −0.0152209 | −0.00122653 | ||||||||
\(155\) | 11.4638 | 0.920791 | ||||||||
\(156\) | −0.0549797 | −0.00440190 | ||||||||
\(157\) | −0.275367 | −0.0219766 | −0.0109883 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109883 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(158\) | 0.0124801 | 0.000992862 0 | ||||||||
\(159\) | −0.0890640 | −0.00706323 | ||||||||
\(160\) | 0.0427568 | 0.00338022 | ||||||||
\(161\) | −29.1816 | −2.29983 | ||||||||
\(162\) | 0.0269473 | 0.00211718 | ||||||||
\(163\) | 16.0544 | 1.25748 | 0.628738 | − | 0.777618i | \(-0.283572\pi\) | ||||
0.628738 | + | 0.777618i | \(0.283572\pi\) | |||||||
\(164\) | −21.9810 | −1.71643 | ||||||||
\(165\) | 0.0225565 | 0.00175602 | ||||||||
\(166\) | −0.00947350 | −0.000735286 0 | ||||||||
\(167\) | 19.0195 | 1.47177 | 0.735885 | − | 0.677107i | \(-0.236766\pi\) | ||||
0.735885 | + | 0.677107i | \(0.236766\pi\) | |||||||
\(168\) | 0.00115445 | 8.90674e−5 0 | ||||||||
\(169\) | −10.8982 | −0.838320 | ||||||||
\(170\) | −0.00982430 | −0.000753489 0 | ||||||||
\(171\) | 4.12408 | 0.315376 | ||||||||
\(172\) | −16.5161 | −1.25934 | ||||||||
\(173\) | −11.0081 | −0.836928 | −0.418464 | − | 0.908233i | \(-0.637431\pi\) | ||||
−0.418464 | + | 0.908233i | \(0.637431\pi\) | |||||||
\(174\) | 0.000226617 0 | 1.71798e−5 0 | ||||||||
\(175\) | 18.2173 | 1.37710 | ||||||||
\(176\) | 3.99995 | 0.301507 | ||||||||
\(177\) | −0.00151530 | −0.000113897 0 | ||||||||
\(178\) | −0.0193381 | −0.00144945 | ||||||||
\(179\) | 19.6848 | 1.47131 | 0.735654 | − | 0.677357i | \(-0.236875\pi\) | ||||
0.735654 | + | 0.677357i | \(0.236875\pi\) | |||||||
\(180\) | 7.13667 | 0.531936 | ||||||||
\(181\) | 18.4053 | 1.36806 | 0.684029 | − | 0.729455i | \(-0.260226\pi\) | ||||
0.684029 | + | 0.729455i | \(0.260226\pi\) | |||||||
\(182\) | −0.0220668 | −0.00163570 | ||||||||
\(183\) | 0.212552 | 0.0157123 | ||||||||
\(184\) | −0.0687995 | −0.00507197 | ||||||||
\(185\) | −12.2925 | −0.903759 | ||||||||
\(186\) | 0.000547308 0 | 4.01306e−5 0 | ||||||||
\(187\) | −2.75724 | −0.201629 | ||||||||
\(188\) | 6.76203 | 0.493172 | ||||||||
\(189\) | 0.578111 | 0.0420514 | ||||||||
\(190\) | −0.00489874 | −0.000355392 0 | ||||||||
\(191\) | −22.4339 | −1.62326 | −0.811631 | − | 0.584171i | \(-0.801420\pi\) | ||||
−0.811631 | + | 0.584171i | \(0.801420\pi\) | |||||||
\(192\) | −0.151689 | −0.0109472 | ||||||||
\(193\) | −6.70265 | −0.482467 | −0.241234 | − | 0.970467i | \(-0.577552\pi\) | ||||
−0.241234 | + | 0.970467i | \(0.577552\pi\) | |||||||
\(194\) | 0.0356180 | 0.00255722 | ||||||||
\(195\) | 0.0327019 | 0.00234183 | ||||||||
\(196\) | −37.6478 | −2.68913 | ||||||||
\(197\) | −6.95014 | −0.495177 | −0.247589 | − | 0.968865i | \(-0.579638\pi\) | ||||
−0.247589 | + | 0.968865i | \(0.579638\pi\) | |||||||
\(198\) | −0.00898458 | −0.000638506 0 | ||||||||
\(199\) | −7.57942 | −0.537291 | −0.268645 | − | 0.963239i | \(-0.586576\pi\) | ||||
−0.268645 | + | 0.963239i | \(0.586576\pi\) | |||||||
\(200\) | 0.0429498 | 0.00303701 | ||||||||
\(201\) | −0.151995 | −0.0107209 | ||||||||
\(202\) | −0.0341521 | −0.00240293 | ||||||||
\(203\) | −20.2769 | −1.42316 | ||||||||
\(204\) | 0.104563 | 0.00732086 | ||||||||
\(205\) | 13.0743 | 0.913148 | ||||||||
\(206\) | 0.0126131 | 0.000878798 0 | ||||||||
\(207\) | −17.2253 | −1.19724 | ||||||||
\(208\) | 5.79902 | 0.402089 | ||||||||
\(209\) | −1.37486 | −0.0951009 | ||||||||
\(210\) | −0.000343331 0 | −2.36921e−5 0 | ||||||||
\(211\) | 26.2317 | 1.80586 | 0.902932 | − | 0.429784i | \(-0.141410\pi\) | ||||
0.902932 | + | 0.429784i | \(0.141410\pi\) | |||||||
\(212\) | 9.39411 | 0.645190 | ||||||||
\(213\) | 0.00362675 | 0.000248501 0 | ||||||||
\(214\) | 0.0166022 | 0.00113490 | ||||||||
\(215\) | 9.82377 | 0.669976 | ||||||||
\(216\) | 0.00136297 | 9.27386e−5 0 | ||||||||
\(217\) | −48.9711 | −3.32438 | ||||||||
\(218\) | −0.00353282 | −0.000239273 0 | ||||||||
\(219\) | 0.147236 | 0.00994932 | ||||||||
\(220\) | −2.37917 | −0.160404 | ||||||||
\(221\) | −3.99737 | −0.268892 | ||||||||
\(222\) | −0.000586872 0 | −3.93883e−5 0 | ||||||||
\(223\) | −12.9697 | −0.868517 | −0.434258 | − | 0.900788i | \(-0.642990\pi\) | ||||
−0.434258 | + | 0.900788i | \(0.642990\pi\) | |||||||
\(224\) | −0.182650 | −0.0122038 | ||||||||
\(225\) | 10.7533 | 0.716888 | ||||||||
\(226\) | −0.0437792 | −0.00291215 | ||||||||
\(227\) | 28.5061 | 1.89202 | 0.946010 | − | 0.324139i | \(-0.105074\pi\) | ||||
0.946010 | + | 0.324139i | \(0.105074\pi\) | |||||||
\(228\) | 0.0521387 | 0.00345297 | ||||||||
\(229\) | −20.8825 | −1.37995 | −0.689977 | − | 0.723831i | \(-0.742379\pi\) | ||||
−0.689977 | + | 0.723831i | \(0.742379\pi\) | |||||||
\(230\) | 0.0204609 | 0.00134915 | ||||||||
\(231\) | −0.0963576 | −0.00633986 | ||||||||
\(232\) | −0.0478054 | −0.00313858 | ||||||||
\(233\) | −17.0451 | −1.11666 | −0.558330 | − | 0.829619i | \(-0.688558\pi\) | ||||
−0.558330 | + | 0.829619i | \(0.688558\pi\) | |||||||
\(234\) | −0.0130256 | −0.000851511 0 | ||||||||
\(235\) | −4.02205 | −0.262370 | ||||||||
\(236\) | 0.159828 | 0.0104039 | ||||||||
\(237\) | 0.0790066 | 0.00513203 | ||||||||
\(238\) | 0.0419677 | 0.00272036 | ||||||||
\(239\) | 12.7967 | 0.827750 | 0.413875 | − | 0.910334i | \(-0.364175\pi\) | ||||
0.413875 | + | 0.910334i | \(0.364175\pi\) | |||||||
\(240\) | 0.0902250 | 0.00582400 | ||||||||
\(241\) | −3.81428 | −0.245699 | −0.122850 | − | 0.992425i | \(-0.539203\pi\) | ||||
−0.122850 | + | 0.992425i | \(0.539203\pi\) | |||||||
\(242\) | 0.00299522 | 0.000192540 0 | ||||||||
\(243\) | 0.511881 | 0.0328372 | ||||||||
\(244\) | −22.4191 | −1.43524 | ||||||||
\(245\) | 22.3928 | 1.43063 | ||||||||
\(246\) | 0.000624199 0 | 3.97975e−5 0 | ||||||||
\(247\) | −1.99323 | −0.126826 | ||||||||
\(248\) | −0.115456 | −0.00733146 | ||||||||
\(249\) | −0.0599731 | −0.00380064 | ||||||||
\(250\) | −0.0305887 | −0.00193460 | ||||||||
\(251\) | 6.39438 | 0.403609 | 0.201805 | − | 0.979426i | \(-0.435319\pi\) | ||||
0.201805 | + | 0.979426i | \(0.435319\pi\) | |||||||
\(252\) | −30.4866 | −1.92047 | ||||||||
\(253\) | 5.74246 | 0.361025 | ||||||||
\(254\) | 0.0241812 | 0.00151727 | ||||||||
\(255\) | −0.0621938 | −0.00389473 | ||||||||
\(256\) | 15.9993 | 0.999955 | ||||||||
\(257\) | 1.54303 | 0.0962516 | 0.0481258 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481258 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(258\) | 0.000469011 0 | 2.91994e−5 0 | ||||||||
\(259\) | 52.5112 | 3.26289 | ||||||||
\(260\) | −3.44926 | −0.213914 | ||||||||
\(261\) | −11.9690 | −0.740864 | ||||||||
\(262\) | −0.00299522 | −0.000185045 0 | ||||||||
\(263\) | −18.2444 | −1.12500 | −0.562498 | − | 0.826799i | \(-0.690160\pi\) | ||||
−0.562498 | + | 0.826799i | \(0.690160\pi\) | |||||||
\(264\) | −0.000227176 0 | −1.39817e−5 0 | ||||||||
\(265\) | −5.58761 | −0.343244 | ||||||||
\(266\) | 0.0209266 | 0.00128309 | ||||||||
\(267\) | −0.122422 | −0.00749209 | ||||||||
\(268\) | 16.0319 | 0.979302 | ||||||||
\(269\) | −10.9953 | −0.670396 | −0.335198 | − | 0.942148i | \(-0.608803\pi\) | ||||
−0.335198 | + | 0.942148i | \(0.608803\pi\) | |||||||
\(270\) | −0.000405347 0 | −2.46686e−5 0 | ||||||||
\(271\) | −12.4539 | −0.756520 | −0.378260 | − | 0.925699i | \(-0.623477\pi\) | ||||
−0.378260 | + | 0.925699i | \(0.623477\pi\) | |||||||
\(272\) | −11.0288 | −0.668720 | ||||||||
\(273\) | −0.139697 | −0.00845483 | ||||||||
\(274\) | 0.0327467 | 0.00197830 | ||||||||
\(275\) | −3.58487 | −0.216176 | ||||||||
\(276\) | −0.217771 | −0.0131083 | ||||||||
\(277\) | 11.2442 | 0.675601 | 0.337801 | − | 0.941218i | \(-0.390317\pi\) | ||||
0.337801 | + | 0.941218i | \(0.390317\pi\) | |||||||
\(278\) | 0.0124069 | 0.000744117 0 | ||||||||
\(279\) | −28.9067 | −1.73060 | ||||||||
\(280\) | 0.0724265 | 0.00432831 | ||||||||
\(281\) | −25.4542 | −1.51847 | −0.759237 | − | 0.650815i | \(-0.774427\pi\) | ||||
−0.759237 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(282\) | −0.000192023 0 | −1.14348e−5 0 | ||||||||
\(283\) | −19.0526 | −1.13256 | −0.566279 | − | 0.824214i | \(-0.691618\pi\) | ||||
−0.566279 | + | 0.824214i | \(0.691618\pi\) | |||||||
\(284\) | −0.382535 | −0.0226993 | ||||||||
\(285\) | −0.0310120 | −0.00183699 | ||||||||
\(286\) | 0.00434239 | 0.000256771 0 | ||||||||
\(287\) | −55.8511 | −3.29678 | ||||||||
\(288\) | −0.107814 | −0.00635302 | ||||||||
\(289\) | −9.39763 | −0.552802 | ||||||||
\(290\) | 0.0142173 | 0.000834867 0 | ||||||||
\(291\) | 0.225484 | 0.0132181 | ||||||||
\(292\) | −15.5299 | −0.908819 | ||||||||
\(293\) | 17.0748 | 0.997518 | 0.498759 | − | 0.866741i | \(-0.333789\pi\) | ||||
0.498759 | + | 0.866741i | \(0.333789\pi\) | |||||||
\(294\) | 0.00106909 | 6.23506e−5 0 | ||||||||
\(295\) | −0.0950656 | −0.00553493 | ||||||||
\(296\) | 0.123802 | 0.00719585 | ||||||||
\(297\) | −0.113763 | −0.00660118 | ||||||||
\(298\) | 0.0650319 | 0.00376720 | ||||||||
\(299\) | 8.32526 | 0.481462 | ||||||||
\(300\) | 0.135949 | 0.00784902 | ||||||||
\(301\) | −41.9654 | −2.41885 | ||||||||
\(302\) | 0.00484704 | 0.000278916 0 | ||||||||
\(303\) | −0.216204 | −0.0124206 | ||||||||
\(304\) | −5.49936 | −0.315410 | ||||||||
\(305\) | 13.3349 | 0.763552 | ||||||||
\(306\) | 0.0247727 | 0.00141616 | ||||||||
\(307\) | 20.5073 | 1.17041 | 0.585207 | − | 0.810884i | \(-0.301013\pi\) | ||||
0.585207 | + | 0.810884i | \(0.301013\pi\) | |||||||
\(308\) | 10.1634 | 0.579114 | ||||||||
\(309\) | 0.0798488 | 0.00454244 | ||||||||
\(310\) | 0.0343365 | 0.00195018 | ||||||||
\(311\) | 28.3991 | 1.61037 | 0.805183 | − | 0.593026i | \(-0.202067\pi\) | ||||
0.805183 | + | 0.593026i | \(0.202067\pi\) | |||||||
\(312\) | −0.000329354 0 | −1.86460e−5 0 | ||||||||
\(313\) | 3.47957 | 0.196677 | 0.0983385 | − | 0.995153i | \(-0.468647\pi\) | ||||
0.0983385 | + | 0.995153i | \(0.468647\pi\) | |||||||
\(314\) | −0.000824783 0 | −4.65452e−5 0 | ||||||||
\(315\) | 18.1334 | 1.02170 | ||||||||
\(316\) | −8.33330 | −0.468785 | ||||||||
\(317\) | −12.1135 | −0.680363 | −0.340182 | − | 0.940360i | \(-0.610489\pi\) | ||||
−0.340182 | + | 0.940360i | \(0.610489\pi\) | |||||||
\(318\) | −0.000266766 0 | −1.49595e−5 0 | ||||||||
\(319\) | 3.99015 | 0.223406 | ||||||||
\(320\) | −9.51648 | −0.531988 | ||||||||
\(321\) | 0.105102 | 0.00586623 | ||||||||
\(322\) | −0.0874053 | −0.00487091 | ||||||||
\(323\) | 3.79081 | 0.210926 | ||||||||
\(324\) | −17.9934 | −0.999636 | ||||||||
\(325\) | −5.19725 | −0.288292 | ||||||||
\(326\) | 0.0480864 | 0.00266326 | ||||||||
\(327\) | −0.0223649 | −0.00123678 | ||||||||
\(328\) | −0.131676 | −0.00727061 | ||||||||
\(329\) | 17.1815 | 0.947246 | ||||||||
\(330\) | 6.75618e−5 0 | 3.71916e−6 0 | ||||||||
\(331\) | 9.15508 | 0.503209 | 0.251604 | − | 0.967830i | \(-0.419042\pi\) | ||||
0.251604 | + | 0.967830i | \(0.419042\pi\) | |||||||
\(332\) | 6.32572 | 0.347169 | ||||||||
\(333\) | 30.9963 | 1.69859 | ||||||||
\(334\) | 0.0569675 | 0.00311712 | ||||||||
\(335\) | −9.53573 | −0.520993 | ||||||||
\(336\) | −0.385425 | −0.0210267 | ||||||||
\(337\) | 17.1798 | 0.935843 | 0.467921 | − | 0.883770i | \(-0.345003\pi\) | ||||
0.467921 | + | 0.883770i | \(0.345003\pi\) | |||||||
\(338\) | −0.0326424 | −0.00177551 | ||||||||
\(339\) | −0.277149 | −0.0150527 | ||||||||
\(340\) | 6.55995 | 0.355763 | ||||||||
\(341\) | 9.63671 | 0.521857 | ||||||||
\(342\) | 0.0123525 | 0.000667948 0 | ||||||||
\(343\) | −60.0862 | −3.24435 | ||||||||
\(344\) | −0.0989391 | −0.00533444 | ||||||||
\(345\) | 0.129530 | 0.00697366 | ||||||||
\(346\) | −0.0329716 | −0.00177256 | ||||||||
\(347\) | −20.5620 | −1.10383 | −0.551913 | − | 0.833902i | \(-0.686102\pi\) | ||||
−0.551913 | + | 0.833902i | \(0.686102\pi\) | |||||||
\(348\) | −0.151318 | −0.00811152 | ||||||||
\(349\) | −34.3249 | −1.83737 | −0.918684 | − | 0.394994i | \(-0.870747\pi\) | ||||
−0.918684 | + | 0.394994i | \(0.870747\pi\) | |||||||
\(350\) | 0.0545649 | 0.00291662 | ||||||||
\(351\) | −0.164930 | −0.00880332 | ||||||||
\(352\) | 0.0359424 | 0.00191574 | ||||||||
\(353\) | 29.8431 | 1.58839 | 0.794194 | − | 0.607665i | \(-0.207894\pi\) | ||||
0.794194 | + | 0.607665i | \(0.207894\pi\) | |||||||
\(354\) | −4.53867e−6 0 | −2.41227e−7 0 | ||||||||
\(355\) | 0.227531 | 0.0120761 | ||||||||
\(356\) | 12.9126 | 0.684364 | ||||||||
\(357\) | 0.265681 | 0.0140613 | ||||||||
\(358\) | 0.0589602 | 0.00311614 | ||||||||
\(359\) | 33.7829 | 1.78299 | 0.891497 | − | 0.453027i | \(-0.149656\pi\) | ||||
0.891497 | + | 0.453027i | \(0.149656\pi\) | |||||||
\(360\) | 0.0427519 | 0.00225322 | ||||||||
\(361\) | −17.1098 | −0.900514 | ||||||||
\(362\) | 0.0551281 | 0.00289747 | ||||||||
\(363\) | 0.0189616 | 0.000995225 0 | ||||||||
\(364\) | 14.7346 | 0.772305 | ||||||||
\(365\) | 9.23717 | 0.483496 | ||||||||
\(366\) | 0.000636640 0 | 3.32777e−5 0 | ||||||||
\(367\) | 31.6426 | 1.65173 | 0.825866 | − | 0.563866i | \(-0.190687\pi\) | ||||
0.825866 | + | 0.563866i | \(0.190687\pi\) | |||||||
\(368\) | 22.9695 | 1.19737 | ||||||||
\(369\) | −32.9677 | −1.71623 | ||||||||
\(370\) | −0.0368186 | −0.00191411 | ||||||||
\(371\) | 23.8693 | 1.23923 | ||||||||
\(372\) | −0.365453 | −0.0189478 | ||||||||
\(373\) | −26.1411 | −1.35354 | −0.676768 | − | 0.736197i | \(-0.736620\pi\) | ||||
−0.676768 | + | 0.736197i | \(0.736620\pi\) | |||||||
\(374\) | −0.00825854 | −0.000427039 0 | ||||||||
\(375\) | −0.193645 | −0.00999979 | ||||||||
\(376\) | 0.0405076 | 0.00208902 | ||||||||
\(377\) | 5.78481 | 0.297933 | ||||||||
\(378\) | 0.00173157 | 8.90623e−5 0 | ||||||||
\(379\) | 0.518853 | 0.0266517 | 0.0133258 | − | 0.999911i | \(-0.495758\pi\) | ||||
0.0133258 | + | 0.999911i | \(0.495758\pi\) | |||||||
\(380\) | 3.27103 | 0.167800 | ||||||||
\(381\) | 0.153082 | 0.00784263 | ||||||||
\(382\) | −0.0671945 | −0.00343797 | ||||||||
\(383\) | 8.21048 | 0.419536 | 0.209768 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209768 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(384\) | −0.00181739 | −9.27433e−5 0 | ||||||||
\(385\) | −6.04518 | −0.308091 | ||||||||
\(386\) | −0.0200759 | −0.00102184 | ||||||||
\(387\) | −24.7713 | −1.25920 | ||||||||
\(388\) | −23.7831 | −1.20740 | ||||||||
\(389\) | −12.8195 | −0.649972 | −0.324986 | − | 0.945719i | \(-0.605360\pi\) | ||||
−0.324986 | + | 0.945719i | \(0.605360\pi\) | |||||||
\(390\) | 9.79493e−5 0 | 4.95986e−6 0 | ||||||||
\(391\) | −15.8333 | −0.800726 | ||||||||
\(392\) | −0.225527 | −0.0113908 | ||||||||
\(393\) | −0.0189616 | −0.000956485 0 | ||||||||
\(394\) | −0.0208172 | −0.00104876 | ||||||||
\(395\) | 4.95663 | 0.249395 | ||||||||
\(396\) | 5.99925 | 0.301474 | ||||||||
\(397\) | 12.3913 | 0.621904 | 0.310952 | − | 0.950426i | \(-0.399352\pi\) | ||||
0.310952 | + | 0.950426i | \(0.399352\pi\) | |||||||
\(398\) | −0.0227020 | −0.00113795 | ||||||||
\(399\) | 0.132478 | 0.00663219 | ||||||||
\(400\) | −14.3393 | −0.716964 | ||||||||
\(401\) | 26.3548 | 1.31609 | 0.658047 | − | 0.752977i | \(-0.271383\pi\) | ||||
0.658047 | + | 0.752977i | \(0.271383\pi\) | |||||||
\(402\) | −0.000455259 0 | −2.27063e−5 0 | ||||||||
\(403\) | 13.9710 | 0.695948 | ||||||||
\(404\) | 22.8043 | 1.13456 | ||||||||
\(405\) | 10.7025 | 0.531811 | ||||||||
\(406\) | −0.0607337 | −0.00301416 | ||||||||
\(407\) | −10.3333 | −0.512204 | ||||||||
\(408\) | 0.000626378 0 | 3.10104e−5 0 | ||||||||
\(409\) | 2.02187 | 0.0999749 | 0.0499875 | − | 0.998750i | \(-0.484082\pi\) | ||||
0.0499875 | + | 0.998750i | \(0.484082\pi\) | |||||||
\(410\) | 0.0391604 | 0.00193399 | ||||||||
\(411\) | 0.207307 | 0.0102257 | ||||||||
\(412\) | −8.42213 | −0.414929 | ||||||||
\(413\) | 0.406103 | 0.0199830 | ||||||||
\(414\) | −0.0515936 | −0.00253569 | ||||||||
\(415\) | −3.76253 | −0.184695 | ||||||||
\(416\) | 0.0521084 | 0.00255482 | ||||||||
\(417\) | 0.0785433 | 0.00384628 | ||||||||
\(418\) | −0.00411800 | −0.000201418 0 | ||||||||
\(419\) | 15.0937 | 0.737378 | 0.368689 | − | 0.929553i | \(-0.379807\pi\) | ||||
0.368689 | + | 0.929553i | \(0.379807\pi\) | |||||||
\(420\) | 0.229251 | 0.0111863 | ||||||||
\(421\) | 20.0115 | 0.975302 | 0.487651 | − | 0.873039i | \(-0.337854\pi\) | ||||
0.487651 | + | 0.873039i | \(0.337854\pi\) | |||||||
\(422\) | 0.0785697 | 0.00382471 | ||||||||
\(423\) | 10.1419 | 0.493115 | ||||||||
\(424\) | 0.0562750 | 0.00273296 | ||||||||
\(425\) | 9.88435 | 0.479461 | ||||||||
\(426\) | 1.08629e−5 0 | 5.26310e−7 0 | ||||||||
\(427\) | −56.9642 | −2.75669 | ||||||||
\(428\) | −11.0858 | −0.535850 | ||||||||
\(429\) | 0.0274900 | 0.00132723 | ||||||||
\(430\) | 0.0294244 | 0.00141897 | ||||||||
\(431\) | 8.60486 | 0.414481 | 0.207241 | − | 0.978290i | \(-0.433552\pi\) | ||||
0.207241 | + | 0.978290i | \(0.433552\pi\) | |||||||
\(432\) | −0.455045 | −0.0218933 | ||||||||
\(433\) | −16.6009 | −0.797788 | −0.398894 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398894 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(434\) | −0.146679 | −0.00704083 | ||||||||
\(435\) | 0.0900040 | 0.00431536 | ||||||||
\(436\) | 2.35896 | 0.112974 | ||||||||
\(437\) | −7.89506 | −0.377672 | ||||||||
\(438\) | 0.000441006 0 | 2.10721e−5 0 | ||||||||
\(439\) | 27.3932 | 1.30740 | 0.653702 | − | 0.756752i | \(-0.273215\pi\) | ||||
0.653702 | + | 0.756752i | \(0.273215\pi\) | |||||||
\(440\) | −0.0142523 | −0.000679453 0 | ||||||||
\(441\) | −56.4651 | −2.68881 | ||||||||
\(442\) | −0.0119730 | −0.000569498 0 | ||||||||
\(443\) | −22.7824 | −1.08243 | −0.541213 | − | 0.840886i | \(-0.682035\pi\) | ||||
−0.541213 | + | 0.840886i | \(0.682035\pi\) | |||||||
\(444\) | 0.391871 | 0.0185974 | ||||||||
\(445\) | −7.68038 | −0.364085 | ||||||||
\(446\) | −0.0388472 | −0.00183947 | ||||||||
\(447\) | 0.411692 | 0.0194723 | ||||||||
\(448\) | 40.6527 | 1.92066 | ||||||||
\(449\) | −12.1536 | −0.573562 | −0.286781 | − | 0.957996i | \(-0.592585\pi\) | ||||
−0.286781 | + | 0.957996i | \(0.592585\pi\) | |||||||
\(450\) | 0.0322086 | 0.00151833 | ||||||||
\(451\) | 10.9906 | 0.517526 | ||||||||
\(452\) | 29.2326 | 1.37498 | ||||||||
\(453\) | 0.0306847 | 0.00144169 | ||||||||
\(454\) | 0.0853822 | 0.00400718 | ||||||||
\(455\) | −8.76415 | −0.410870 | ||||||||
\(456\) | 0.000312335 0 | 1.46264e−5 0 | ||||||||
\(457\) | −24.8173 | −1.16090 | −0.580452 | − | 0.814294i | \(-0.697124\pi\) | ||||
−0.580452 | + | 0.814294i | \(0.697124\pi\) | |||||||
\(458\) | −0.0625476 | −0.00292266 | ||||||||
\(459\) | 0.313671 | 0.0146409 | ||||||||
\(460\) | −13.6623 | −0.637008 | ||||||||
\(461\) | 41.5814 | 1.93664 | 0.968319 | − | 0.249717i | \(-0.0803375\pi\) | ||||
0.968319 | + | 0.249717i | \(0.0803375\pi\) | |||||||
\(462\) | −0.000288612 0 | −1.34275e−5 0 | ||||||||
\(463\) | −35.4811 | −1.64895 | −0.824473 | − | 0.565902i | \(-0.808528\pi\) | ||||
−0.824473 | + | 0.565902i | \(0.808528\pi\) | |||||||
\(464\) | 15.9604 | 0.740942 | ||||||||
\(465\) | 0.217371 | 0.0100803 | ||||||||
\(466\) | −0.0510538 | −0.00236502 | ||||||||
\(467\) | 0.211806 | 0.00980123 | 0.00490062 | − | 0.999988i | \(-0.498440\pi\) | ||||
0.00490062 | + | 0.999988i | \(0.498440\pi\) | |||||||
\(468\) | 8.69756 | 0.402045 | ||||||||
\(469\) | 40.7350 | 1.88097 | ||||||||
\(470\) | −0.0120469 | −0.000555683 0 | ||||||||
\(471\) | −0.00522139 | −0.000240589 0 | ||||||||
\(472\) | 0.000957443 0 | 4.40699e−5 0 | ||||||||
\(473\) | 8.25810 | 0.379708 | ||||||||
\(474\) | 0.000236642 0 | 1.08693e−5 0 | ||||||||
\(475\) | 4.92869 | 0.226144 | ||||||||
\(476\) | −28.0230 | −1.28443 | ||||||||
\(477\) | 14.0895 | 0.645116 | ||||||||
\(478\) | 0.0383289 | 0.00175312 | ||||||||
\(479\) | 31.7167 | 1.44917 | 0.724587 | − | 0.689184i | \(-0.242031\pi\) | ||||
0.724587 | + | 0.689184i | \(0.242031\pi\) | |||||||
\(480\) | 0.000810737 0 | 3.70049e−5 0 | ||||||||
\(481\) | −14.9810 | −0.683074 | ||||||||
\(482\) | −0.0114246 | −0.000520376 0 | ||||||||
\(483\) | −0.553329 | −0.0251774 | ||||||||
\(484\) | −1.99999 | −0.0909087 | ||||||||
\(485\) | 14.1462 | 0.642344 | ||||||||
\(486\) | 0.00153320 | 6.95472e−5 0 | ||||||||
\(487\) | 0.619605 | 0.0280770 | 0.0140385 | − | 0.999901i | \(-0.495531\pi\) | ||||
0.0140385 | + | 0.999901i | \(0.495531\pi\) | |||||||
\(488\) | −0.134301 | −0.00607951 | ||||||||
\(489\) | 0.304416 | 0.0137662 | ||||||||
\(490\) | 0.0670715 | 0.00302998 | ||||||||
\(491\) | 6.89709 | 0.311261 | 0.155631 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155631 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(492\) | −0.416795 | −0.0187906 | ||||||||
\(493\) | −11.0018 | −0.495496 | ||||||||
\(494\) | −0.00597017 | −0.000268611 0 | ||||||||
\(495\) | −3.56835 | −0.160385 | ||||||||
\(496\) | 38.5463 | 1.73078 | ||||||||
\(497\) | −0.971974 | −0.0435990 | ||||||||
\(498\) | −0.000179633 0 | −8.04953e−6 0 | ||||||||
\(499\) | 3.02506 | 0.135420 | 0.0677100 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677100 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(500\) | 20.4249 | 0.913429 | ||||||||
\(501\) | 0.360639 | 0.0161122 | ||||||||
\(502\) | 0.0191526 | 0.000854821 0 | ||||||||
\(503\) | 28.9167 | 1.28933 | 0.644665 | − | 0.764465i | \(-0.276997\pi\) | ||||
0.644665 | + | 0.764465i | \(0.276997\pi\) | |||||||
\(504\) | −0.182628 | −0.00813492 | ||||||||
\(505\) | −13.5640 | −0.603588 | ||||||||
\(506\) | 0.0171999 | 0.000764630 0 | ||||||||
\(507\) | −0.206646 | −0.00917748 | ||||||||
\(508\) | −16.1465 | −0.716384 | ||||||||
\(509\) | −10.1134 | −0.448270 | −0.224135 | − | 0.974558i | \(-0.571956\pi\) | ||||
−0.224135 | + | 0.974558i | \(0.571956\pi\) | |||||||
\(510\) | −0.000186284 0 | −8.24880e−6 0 | ||||||||
\(511\) | −39.4596 | −1.74559 | ||||||||
\(512\) | 0.239613 | 0.0105895 | ||||||||
\(513\) | 0.156407 | 0.00690556 | ||||||||
\(514\) | 0.00462172 | 0.000203855 0 | ||||||||
\(515\) | 5.00947 | 0.220744 | ||||||||
\(516\) | −0.313172 | −0.0137866 | ||||||||
\(517\) | −3.38103 | −0.148698 | ||||||||
\(518\) | 0.157283 | 0.00691060 | ||||||||
\(519\) | −0.208730 | −0.00916225 | ||||||||
\(520\) | −0.0206627 | −0.000906117 0 | ||||||||
\(521\) | −2.06817 | −0.0906082 | −0.0453041 | − | 0.998973i | \(-0.514426\pi\) | ||||
−0.0453041 | + | 0.998973i | \(0.514426\pi\) | |||||||
\(522\) | −0.0358498 | −0.00156910 | ||||||||
\(523\) | −0.356664 | −0.0155958 | −0.00779791 | − | 0.999970i | \(-0.502482\pi\) | ||||
−0.00779791 | + | 0.999970i | \(0.502482\pi\) | |||||||
\(524\) | 1.99999 | 0.0873700 | ||||||||
\(525\) | 0.345429 | 0.0150758 | ||||||||
\(526\) | −0.0546459 | −0.00238267 | ||||||||
\(527\) | −26.5707 | −1.15744 | ||||||||
\(528\) | 0.0758453 | 0.00330074 | ||||||||
\(529\) | 9.97580 | 0.433731 | ||||||||
\(530\) | −0.0167361 | −0.000726970 0 | ||||||||
\(531\) | 0.239715 | 0.0104027 | ||||||||
\(532\) | −13.9732 | −0.605817 | ||||||||
\(533\) | 15.9338 | 0.690171 | ||||||||
\(534\) | −0.000366680 0 | −1.58678e−5 0 | ||||||||
\(535\) | 6.59379 | 0.285075 | ||||||||
\(536\) | 0.0960381 | 0.00414821 | ||||||||
\(537\) | 0.373254 | 0.0161071 | ||||||||
\(538\) | −0.0329334 | −0.00141986 | ||||||||
\(539\) | 18.8240 | 0.810805 | ||||||||
\(540\) | 0.270661 | 0.0116474 | ||||||||
\(541\) | −1.16142 | −0.0499334 | −0.0249667 | − | 0.999688i | \(-0.507948\pi\) | ||||
−0.0249667 | + | 0.999688i | \(0.507948\pi\) | |||||||
\(542\) | −0.0373021 | −0.00160226 | ||||||||
\(543\) | 0.348994 | 0.0149768 | ||||||||
\(544\) | −0.0991019 | −0.00424896 | ||||||||
\(545\) | −1.40311 | −0.0601026 | ||||||||
\(546\) | −0.000418422 0 | −1.79068e−5 0 | ||||||||
\(547\) | 24.9514 | 1.06684 | 0.533421 | − | 0.845850i | \(-0.320906\pi\) | ||||
0.533421 | + | 0.845850i | \(0.320906\pi\) | |||||||
\(548\) | −21.8659 | −0.934064 | ||||||||
\(549\) | −33.6248 | −1.43507 | ||||||||
\(550\) | −0.0107375 | −0.000457847 0 | ||||||||
\(551\) | −5.48589 | −0.233707 | ||||||||
\(552\) | −0.00130455 | −5.55252e−5 0 | ||||||||
\(553\) | −21.1739 | −0.900405 | ||||||||
\(554\) | 0.0336790 | 0.00143088 | ||||||||
\(555\) | −0.233084 | −0.00989388 | ||||||||
\(556\) | −8.28443 | −0.351338 | ||||||||
\(557\) | 14.9826 | 0.634834 | 0.317417 | − | 0.948286i | \(-0.397185\pi\) | ||||
0.317417 | + | 0.948286i | \(0.397185\pi\) | |||||||
\(558\) | −0.0865818 | −0.00366530 | ||||||||
\(559\) | 11.9724 | 0.506378 | ||||||||
\(560\) | −24.1804 | −1.02181 | ||||||||
\(561\) | −0.0522816 | −0.00220733 | ||||||||
\(562\) | −0.0762411 | −0.00321604 | ||||||||
\(563\) | −11.4564 | −0.482829 | −0.241414 | − | 0.970422i | \(-0.577611\pi\) | ||||
−0.241414 | + | 0.970422i | \(0.577611\pi\) | |||||||
\(564\) | 0.128219 | 0.00539899 | ||||||||
\(565\) | −17.3875 | −0.731497 | ||||||||
\(566\) | −0.0570666 | −0.00239869 | ||||||||
\(567\) | −45.7191 | −1.92002 | ||||||||
\(568\) | −0.00229156 | −9.61517e−5 0 | ||||||||
\(569\) | −33.4609 | −1.40275 | −0.701376 | − | 0.712791i | \(-0.747431\pi\) | ||||
−0.701376 | + | 0.712791i | \(0.747431\pi\) | |||||||
\(570\) | −9.28879e−5 0 | −3.89065e−6 0 | ||||||||
\(571\) | −33.9850 | −1.42223 | −0.711114 | − | 0.703077i | \(-0.751809\pi\) | ||||
−0.711114 | + | 0.703077i | \(0.751809\pi\) | |||||||
\(572\) | −2.89953 | −0.121236 | ||||||||
\(573\) | −0.425382 | −0.0177706 | ||||||||
\(574\) | −0.167286 | −0.00698239 | ||||||||
\(575\) | −20.5860 | −0.858494 | ||||||||
\(576\) | 23.9965 | 0.999853 | ||||||||
\(577\) | 9.63029 | 0.400914 | 0.200457 | − | 0.979702i | \(-0.435757\pi\) | ||||
0.200457 | + | 0.979702i | \(0.435757\pi\) | |||||||
\(578\) | −0.0281480 | −0.00117080 | ||||||||
\(579\) | −0.127093 | −0.00528180 | ||||||||
\(580\) | −9.49326 | −0.394186 | ||||||||
\(581\) | 16.0729 | 0.666815 | ||||||||
\(582\) | 0.000675373 0 | 2.79951e−5 0 | ||||||||
\(583\) | −4.69708 | −0.194533 | ||||||||
\(584\) | −0.0930312 | −0.00384966 | ||||||||
\(585\) | −5.17330 | −0.213890 | ||||||||
\(586\) | 0.0511427 | 0.00211268 | ||||||||
\(587\) | 35.3558 | 1.45929 | 0.729645 | − | 0.683826i | \(-0.239685\pi\) | ||||
0.729645 | + | 0.683826i | \(0.239685\pi\) | |||||||
\(588\) | −0.713861 | −0.0294391 | ||||||||
\(589\) | −13.2491 | −0.545920 | ||||||||
\(590\) | −0.000284742 0 | −1.17227e−5 0 | ||||||||
\(591\) | −0.131786 | −0.00542094 | ||||||||
\(592\) | −41.3328 | −1.69877 | ||||||||
\(593\) | 6.38899 | 0.262364 | 0.131182 | − | 0.991358i | \(-0.458123\pi\) | ||||
0.131182 | + | 0.991358i | \(0.458123\pi\) | |||||||
\(594\) | −0.000340744 0 | −1.39809e−5 0 | ||||||||
\(595\) | 16.6680 | 0.683322 | ||||||||
\(596\) | −43.4236 | −1.77870 | ||||||||
\(597\) | −0.143718 | −0.00588198 | ||||||||
\(598\) | 0.0249360 | 0.00101971 | ||||||||
\(599\) | −29.0366 | −1.18640 | −0.593201 | − | 0.805054i | \(-0.702136\pi\) | ||||
−0.593201 | + | 0.805054i | \(0.702136\pi\) | |||||||
\(600\) | 0.000814396 0 | 3.32476e−5 0 | ||||||||
\(601\) | 24.5758 | 1.00247 | 0.501235 | − | 0.865311i | \(-0.332879\pi\) | ||||
0.501235 | + | 0.865311i | \(0.332879\pi\) | |||||||
\(602\) | −0.125696 | −0.00512297 | ||||||||
\(603\) | 24.0450 | 0.979189 | ||||||||
\(604\) | −3.23650 | −0.131691 | ||||||||
\(605\) | 1.18959 | 0.0483638 | ||||||||
\(606\) | −0.000647577 0 | −2.63060e−5 0 | ||||||||
\(607\) | 19.8870 | 0.807187 | 0.403594 | − | 0.914938i | \(-0.367761\pi\) | ||||
0.403594 | + | 0.914938i | \(0.367761\pi\) | |||||||
\(608\) | −0.0494157 | −0.00200407 | ||||||||
\(609\) | −0.384481 | −0.0155800 | ||||||||
\(610\) | 0.0399409 | 0.00161716 | ||||||||
\(611\) | −4.90173 | −0.198303 | ||||||||
\(612\) | −16.5414 | −0.668646 | ||||||||
\(613\) | 8.05506 | 0.325341 | 0.162670 | − | 0.986680i | \(-0.447989\pi\) | ||||
0.162670 | + | 0.986680i | \(0.447989\pi\) | |||||||
\(614\) | 0.0614239 | 0.00247887 | ||||||||
\(615\) | 0.247909 | 0.00999666 | ||||||||
\(616\) | 0.0608834 | 0.00245306 | ||||||||
\(617\) | −15.1000 | −0.607904 | −0.303952 | − | 0.952687i | \(-0.598306\pi\) | ||||
−0.303952 | + | 0.952687i | \(0.598306\pi\) | |||||||
\(618\) | 0.000239165 0 | 9.62062e−6 0 | ||||||||
\(619\) | −17.3259 | −0.696387 | −0.348193 | − | 0.937423i | \(-0.613205\pi\) | ||||
−0.348193 | + | 0.937423i | \(0.613205\pi\) | |||||||
\(620\) | −22.9274 | −0.920787 | ||||||||
\(621\) | −0.653277 | −0.0262151 | ||||||||
\(622\) | 0.0850616 | 0.00341066 | ||||||||
\(623\) | 32.8092 | 1.31447 | ||||||||
\(624\) | 0.109959 | 0.00440186 | ||||||||
\(625\) | 5.77565 | 0.231026 | ||||||||
\(626\) | 0.0104221 | 0.000416550 0 | ||||||||
\(627\) | −0.0260695 | −0.00104111 | ||||||||
\(628\) | 0.550731 | 0.0219765 | ||||||||
\(629\) | 28.4915 | 1.13603 | ||||||||
\(630\) | 0.0543135 | 0.00216390 | ||||||||
\(631\) | 19.6945 | 0.784027 | 0.392013 | − | 0.919960i | \(-0.371779\pi\) | ||||
0.392013 | + | 0.919960i | \(0.371779\pi\) | |||||||
\(632\) | −0.0499202 | −0.00198572 | ||||||||
\(633\) | 0.497394 | 0.0197696 | ||||||||
\(634\) | −0.0362827 | −0.00144097 | ||||||||
\(635\) | 9.60391 | 0.381120 | ||||||||
\(636\) | 0.178127 | 0.00706320 | ||||||||
\(637\) | 27.2905 | 1.08129 | ||||||||
\(638\) | 0.0119514 | 0.000473160 0 | ||||||||
\(639\) | −0.573737 | −0.0226967 | ||||||||
\(640\) | −0.114018 | −0.00450694 | ||||||||
\(641\) | 44.3028 | 1.74985 | 0.874927 | − | 0.484255i | \(-0.160909\pi\) | ||||
0.874927 | + | 0.484255i | \(0.160909\pi\) | |||||||
\(642\) | 0.000314804 0 | 1.24243e−5 0 | ||||||||
\(643\) | 3.75270 | 0.147992 | 0.0739960 | − | 0.997259i | \(-0.476425\pi\) | ||||
0.0739960 | + | 0.997259i | \(0.476425\pi\) | |||||||
\(644\) | 58.3629 | 2.29982 | ||||||||
\(645\) | 0.186274 | 0.00733454 | ||||||||
\(646\) | 0.0113543 | 0.000446730 0 | ||||||||
\(647\) | 35.5688 | 1.39835 | 0.699177 | − | 0.714949i | \(-0.253550\pi\) | ||||
0.699177 | + | 0.714949i | \(0.253550\pi\) | |||||||
\(648\) | −0.107789 | −0.00423435 | ||||||||
\(649\) | −0.0799144 | −0.00313692 | ||||||||
\(650\) | −0.0155669 | −0.000610584 0 | ||||||||
\(651\) | −0.928570 | −0.0363935 | ||||||||
\(652\) | −32.1086 | −1.25747 | ||||||||
\(653\) | 28.5458 | 1.11708 | 0.558542 | − | 0.829476i | \(-0.311361\pi\) | ||||
0.558542 | + | 0.829476i | \(0.311361\pi\) | |||||||
\(654\) | −6.69879e−5 0 | −2.61944e−6 0 | ||||||||
\(655\) | −1.18959 | −0.0464812 | ||||||||
\(656\) | 43.9617 | 1.71641 | ||||||||
\(657\) | −23.2922 | −0.908714 | ||||||||
\(658\) | 0.0514623 | 0.00200621 | ||||||||
\(659\) | 21.5539 | 0.839621 | 0.419810 | − | 0.907612i | \(-0.362097\pi\) | ||||
0.419810 | + | 0.907612i | \(0.362097\pi\) | |||||||
\(660\) | −0.0451129 | −0.00175602 | ||||||||
\(661\) | −9.53127 | −0.370723 | −0.185362 | − | 0.982670i | \(-0.559346\pi\) | ||||
−0.185362 | + | 0.982670i | \(0.559346\pi\) | |||||||
\(662\) | 0.0274215 | 0.00106577 | ||||||||
\(663\) | −0.0757965 | −0.00294369 | ||||||||
\(664\) | 0.0378939 | 0.00147057 | ||||||||
\(665\) | 8.31127 | 0.322297 | ||||||||
\(666\) | 0.0928407 | 0.00359750 | ||||||||
\(667\) | 22.9133 | 0.887205 | ||||||||
\(668\) | −38.0387 | −1.47176 | ||||||||
\(669\) | −0.245926 | −0.00950806 | ||||||||
\(670\) | −0.0285616 | −0.00110343 | ||||||||
\(671\) | 11.2096 | 0.432742 | ||||||||
\(672\) | −0.00346333 | −0.000133601 0 | ||||||||
\(673\) | 41.3552 | 1.59412 | 0.797062 | − | 0.603897i | \(-0.206386\pi\) | ||||
0.797062 | + | 0.603897i | \(0.206386\pi\) | |||||||
\(674\) | 0.0514573 | 0.00198206 | ||||||||
\(675\) | 0.407824 | 0.0156972 | ||||||||
\(676\) | 21.7962 | 0.838316 | ||||||||
\(677\) | 0.584026 | 0.0224459 | 0.0112230 | − | 0.999937i | \(-0.496428\pi\) | ||||
0.0112230 | + | 0.999937i | \(0.496428\pi\) | |||||||
\(678\) | −0.000830122 0 | −3.18807e−5 0 | ||||||||
\(679\) | −60.4299 | −2.31909 | ||||||||
\(680\) | 0.0392971 | 0.00150697 | ||||||||
\(681\) | 0.540521 | 0.0207128 | ||||||||
\(682\) | 0.0288641 | 0.00110526 | ||||||||
\(683\) | −9.41515 | −0.360261 | −0.180130 | − | 0.983643i | \(-0.557652\pi\) | ||||
−0.180130 | + | 0.983643i | \(0.557652\pi\) | |||||||
\(684\) | −8.24812 | −0.315375 | ||||||||
\(685\) | 13.0058 | 0.496926 | ||||||||
\(686\) | −0.179971 | −0.00687133 | ||||||||
\(687\) | −0.395965 | −0.0151070 | ||||||||
\(688\) | 33.0320 | 1.25933 | ||||||||
\(689\) | −6.80970 | −0.259429 | ||||||||
\(690\) | 0.000387971 0 | 1.47698e−5 0 | ||||||||
\(691\) | −47.0630 | −1.79036 | −0.895180 | − | 0.445705i | \(-0.852953\pi\) | ||||
−0.895180 | + | 0.445705i | \(0.852953\pi\) | |||||||
\(692\) | 22.0160 | 0.836924 | ||||||||
\(693\) | 15.2434 | 0.579047 | ||||||||
\(694\) | −0.0615877 | −0.00233784 | ||||||||
\(695\) | 4.92757 | 0.186913 | ||||||||
\(696\) | −0.000906466 0 | −3.43595e−5 0 | ||||||||
\(697\) | −30.3036 | −1.14783 | ||||||||
\(698\) | −0.102811 | −0.00389143 | ||||||||
\(699\) | −0.323202 | −0.0122246 | ||||||||
\(700\) | −36.4345 | −1.37709 | ||||||||
\(701\) | −0.559212 | −0.0211211 | −0.0105606 | − | 0.999944i | \(-0.503362\pi\) | ||||
−0.0105606 | + | 0.999944i | \(0.503362\pi\) | |||||||
\(702\) | −0.000494002 0 | −1.86449e−5 0 | ||||||||
\(703\) | 14.2069 | 0.535822 | ||||||||
\(704\) | −7.99978 | −0.301503 | ||||||||
\(705\) | −0.0762644 | −0.00287228 | ||||||||
\(706\) | 0.0893866 | 0.00336411 | ||||||||
\(707\) | 57.9428 | 2.17916 | ||||||||
\(708\) | 0.00303059 | 0.000113897 0 | ||||||||
\(709\) | 23.2314 | 0.872472 | 0.436236 | − | 0.899832i | \(-0.356311\pi\) | ||||
0.436236 | + | 0.899832i | \(0.356311\pi\) | |||||||
\(710\) | 0.000681507 0 | 2.55765e−5 0 | ||||||||
\(711\) | −12.4985 | −0.468730 | ||||||||
\(712\) | 0.0773521 | 0.00289889 | ||||||||
\(713\) | 55.3384 | 2.07244 | ||||||||
\(714\) | 0.000795773 0 | 2.97811e−5 0 | ||||||||
\(715\) | 1.72464 | 0.0644979 | ||||||||
\(716\) | −39.3694 | −1.47130 | ||||||||
\(717\) | 0.242646 | 0.00906177 | ||||||||
\(718\) | 0.101187 | 0.00377627 | ||||||||
\(719\) | 50.2931 | 1.87561 | 0.937807 | − | 0.347156i | \(-0.112853\pi\) | ||||
0.937807 | + | 0.347156i | \(0.112853\pi\) | |||||||
\(720\) | −14.2732 | −0.531931 | ||||||||
\(721\) | −21.3996 | −0.796962 | ||||||||
\(722\) | −0.0512475 | −0.00190723 | ||||||||
\(723\) | −0.0723247 | −0.00268978 | ||||||||
\(724\) | −36.8105 | −1.36805 | ||||||||
\(725\) | −14.3042 | −0.531244 | ||||||||
\(726\) | 5.67941e−5 0 | 2.10783e−6 0 | ||||||||
\(727\) | 9.22301 | 0.342063 | 0.171031 | − | 0.985266i | \(-0.445290\pi\) | ||||
0.171031 | + | 0.985266i | \(0.445290\pi\) | |||||||
\(728\) | 0.0882672 | 0.00327140 | ||||||||
\(729\) | −26.9806 | −0.999281 | ||||||||
\(730\) | 0.0276674 | 0.00102401 | ||||||||
\(731\) | −22.7696 | −0.842163 | ||||||||
\(732\) | −0.425102 | −0.0157122 | ||||||||
\(733\) | 39.1288 | 1.44526 | 0.722628 | − | 0.691237i | \(-0.242934\pi\) | ||||
0.722628 | + | 0.691237i | \(0.242934\pi\) | |||||||
\(734\) | 0.0947767 | 0.00349827 | ||||||||
\(735\) | 0.424604 | 0.0156617 | ||||||||
\(736\) | 0.206398 | 0.00760792 | ||||||||
\(737\) | −8.01596 | −0.295272 | ||||||||
\(738\) | −0.0987456 | −0.00363488 | ||||||||
\(739\) | 25.5896 | 0.941328 | 0.470664 | − | 0.882312i | \(-0.344014\pi\) | ||||
0.470664 | + | 0.882312i | \(0.344014\pi\) | |||||||
\(740\) | 24.5848 | 0.903755 | ||||||||
\(741\) | −0.0377948 | −0.00138843 | ||||||||
\(742\) | 0.0714937 | 0.00262462 | ||||||||
\(743\) | 5.17117 | 0.189712 | 0.0948560 | − | 0.995491i | \(-0.469761\pi\) | ||||
0.0948560 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(744\) | −0.00218923 | −8.02610e−5 0 | ||||||||
\(745\) | 25.8283 | 0.946275 | ||||||||
\(746\) | −0.0782984 | −0.00286671 | ||||||||
\(747\) | 9.48749 | 0.347129 | ||||||||
\(748\) | 5.51446 | 0.201628 | ||||||||
\(749\) | −28.1675 | −1.02922 | ||||||||
\(750\) | −0.000580009 0 | −2.11790e−5 0 | ||||||||
\(751\) | 24.4918 | 0.893717 | 0.446859 | − | 0.894605i | \(-0.352543\pi\) | ||||
0.446859 | + | 0.894605i | \(0.352543\pi\) | |||||||
\(752\) | −13.5239 | −0.493168 | ||||||||
\(753\) | 0.121247 | 0.00441850 | ||||||||
\(754\) | 0.0173268 | 0.000631005 0 | ||||||||
\(755\) | 1.92507 | 0.0700604 | ||||||||
\(756\) | −1.15622 | −0.0420512 | ||||||||
\(757\) | 16.0775 | 0.584348 | 0.292174 | − | 0.956365i | \(-0.405621\pi\) | ||||
0.292174 | + | 0.956365i | \(0.405621\pi\) | |||||||
\(758\) | 0.00155408 | 5.64467e−5 0 | ||||||||
\(759\) | 0.108886 | 0.00395231 | ||||||||
\(760\) | 0.0195949 | 0.000710783 0 | ||||||||
\(761\) | −44.7046 | −1.62054 | −0.810270 | − | 0.586057i | \(-0.800680\pi\) | ||||
−0.810270 | + | 0.586057i | \(0.800680\pi\) | |||||||
\(762\) | 0.000458515 0 | 1.66102e−5 0 | ||||||||
\(763\) | 5.99383 | 0.216991 | ||||||||
\(764\) | 44.8676 | 1.62325 | ||||||||
\(765\) | 9.83879 | 0.355722 | ||||||||
\(766\) | 0.0245922 | 0.000888552 0 | ||||||||
\(767\) | −0.115858 | −0.00418338 | ||||||||
\(768\) | 0.303372 | 0.0109470 | ||||||||
\(769\) | 19.2399 | 0.693810 | 0.346905 | − | 0.937900i | \(-0.387233\pi\) | ||||
0.346905 | + | 0.937900i | \(0.387233\pi\) | |||||||
\(770\) | −0.0181067 | −0.000652519 0 | ||||||||
\(771\) | 0.0292583 | 0.00105371 | ||||||||
\(772\) | 13.4052 | 0.482465 | ||||||||
\(773\) | −31.3007 | −1.12581 | −0.562905 | − | 0.826522i | \(-0.690316\pi\) | ||||
−0.562905 | + | 0.826522i | \(0.690316\pi\) | |||||||
\(774\) | −0.0741956 | −0.00266691 | ||||||||
\(775\) | −34.5464 | −1.24094 | ||||||||
\(776\) | −0.142472 | −0.00511443 | ||||||||
\(777\) | 0.995695 | 0.0357204 | ||||||||
\(778\) | −0.0383971 | −0.00137660 | ||||||||
\(779\) | −15.1105 | −0.541389 | ||||||||
\(780\) | −0.0654035 | −0.00234182 | ||||||||
\(781\) | 0.191268 | 0.00684412 | ||||||||
\(782\) | −0.0474243 | −0.00169589 | ||||||||
\(783\) | −0.453930 | −0.0162221 | ||||||||
\(784\) | 75.2948 | 2.68910 | ||||||||
\(785\) | −0.327574 | −0.0116916 | ||||||||
\(786\) | −5.67941e−5 0 | −2.02578e−6 0 | ||||||||
\(787\) | −26.5054 | −0.944815 | −0.472408 | − | 0.881380i | \(-0.656615\pi\) | ||||
−0.472408 | + | 0.881380i | \(0.656615\pi\) | |||||||
\(788\) | 13.9002 | 0.495175 | ||||||||
\(789\) | −0.345942 | −0.0123159 | ||||||||
\(790\) | 0.0148462 | 0.000528205 0 | ||||||||
\(791\) | 74.2763 | 2.64096 | ||||||||
\(792\) | 0.0359383 | 0.00127701 | ||||||||
\(793\) | 16.2514 | 0.577104 | ||||||||
\(794\) | 0.0371148 | 0.00131715 | ||||||||
\(795\) | −0.105950 | −0.00375765 | ||||||||
\(796\) | 15.1588 | 0.537289 | ||||||||
\(797\) | −3.61420 | −0.128021 | −0.0640107 | − | 0.997949i | \(-0.520389\pi\) | ||||
−0.0640107 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(798\) | 0.000396801 0 | 1.40466e−5 0 | ||||||||
\(799\) | 9.32232 | 0.329800 | ||||||||
\(800\) | −0.128849 | −0.00455550 | ||||||||
\(801\) | 19.3666 | 0.684286 | ||||||||
\(802\) | 0.0789383 | 0.00278741 | ||||||||
\(803\) | 7.76499 | 0.274020 | ||||||||
\(804\) | 0.303989 | 0.0107209 | ||||||||
\(805\) | −34.7142 | −1.22352 | ||||||||
\(806\) | 0.0418464 | 0.00147398 | ||||||||
\(807\) | −0.208489 | −0.00733915 | ||||||||
\(808\) | 0.136608 | 0.00480585 | ||||||||
\(809\) | 0.279492 | 0.00982643 | 0.00491321 | − | 0.999988i | \(-0.498436\pi\) | ||||
0.00491321 | + | 0.999988i | \(0.498436\pi\) | |||||||
\(810\) | 0.0320563 | 0.00112634 | ||||||||
\(811\) | 38.4355 | 1.34965 | 0.674827 | − | 0.737976i | \(-0.264218\pi\) | ||||
0.674827 | + | 0.737976i | \(0.264218\pi\) | |||||||
\(812\) | 40.5535 | 1.42315 | ||||||||
\(813\) | −0.236145 | −0.00828198 | ||||||||
\(814\) | −0.0309506 | −0.00108482 | ||||||||
\(815\) | 19.0982 | 0.668979 | ||||||||
\(816\) | −0.209124 | −0.00732079 | ||||||||
\(817\) | −11.3537 | −0.397216 | ||||||||
\(818\) | 0.00605594 | 0.000211741 0 | ||||||||
\(819\) | 22.0994 | 0.772216 | ||||||||
\(820\) | −26.1485 | −0.913144 | ||||||||
\(821\) | 13.9153 | 0.485648 | 0.242824 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242824 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(822\) | 0.000620929 0 | 2.16574e−5 0 | ||||||||
\(823\) | 33.9007 | 1.18171 | 0.590853 | − | 0.806779i | \(-0.298791\pi\) | ||||
0.590853 | + | 0.806779i | \(0.298791\pi\) | |||||||
\(824\) | −0.0504524 | −0.00175759 | ||||||||
\(825\) | −0.0679748 | −0.00236658 | ||||||||
\(826\) | 0.00121637 | 4.23229e−5 0 | ||||||||
\(827\) | −28.9494 | −1.00667 | −0.503335 | − | 0.864092i | \(-0.667894\pi\) | ||||
−0.503335 | + | 0.864092i | \(0.667894\pi\) | |||||||
\(828\) | 34.4505 | 1.19724 | ||||||||
\(829\) | 17.9277 | 0.622653 | 0.311327 | − | 0.950303i | \(-0.399227\pi\) | ||||
0.311327 | + | 0.950303i | \(0.399227\pi\) | |||||||
\(830\) | −0.0112696 | −0.000391174 0 | ||||||||
\(831\) | 0.213209 | 0.00739613 | ||||||||
\(832\) | −11.5979 | −0.402084 | ||||||||
\(833\) | −51.9022 | −1.79830 | ||||||||
\(834\) | 0.000235254 0 | 8.14620e−6 0 | ||||||||
\(835\) | 22.6254 | 0.782984 | ||||||||
\(836\) | 2.74970 | 0.0951005 | ||||||||
\(837\) | −1.09630 | −0.0378936 | ||||||||
\(838\) | 0.0452091 | 0.00156172 | ||||||||
\(839\) | 17.0945 | 0.590167 | 0.295084 | − | 0.955471i | \(-0.404652\pi\) | ||||
0.295084 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(840\) | 0.00137332 | 4.73840e−5 0 | ||||||||
\(841\) | −13.0787 | −0.450990 | ||||||||
\(842\) | 0.0599389 | 0.00206563 | ||||||||
\(843\) | −0.482653 | −0.0166234 | ||||||||
\(844\) | −52.4631 | −1.80586 | ||||||||
\(845\) | −12.9644 | −0.445988 | ||||||||
\(846\) | 0.0303772 | 0.00104439 | ||||||||
\(847\) | −5.08173 | −0.174610 | ||||||||
\(848\) | −18.7881 | −0.645185 | ||||||||
\(849\) | −0.361267 | −0.0123986 | ||||||||
\(850\) | 0.0296058 | 0.00101547 | ||||||||
\(851\) | −59.3387 | −2.03410 | ||||||||
\(852\) | −0.00725347 | −0.000248500 0 | ||||||||
\(853\) | 28.8473 | 0.987713 | 0.493856 | − | 0.869543i | \(-0.335587\pi\) | ||||
0.493856 | + | 0.869543i | \(0.335587\pi\) | |||||||
\(854\) | −0.170620 | −0.00583851 | ||||||||
\(855\) | 4.90597 | 0.167781 | ||||||||
\(856\) | −0.0664087 | −0.00226980 | ||||||||
\(857\) | 19.5075 | 0.666365 | 0.333183 | − | 0.942862i | \(-0.391877\pi\) | ||||
0.333183 | + | 0.942862i | \(0.391877\pi\) | |||||||
\(858\) | 8.23386e−5 0 | 2.81099e−6 0 | ||||||||
\(859\) | −37.1112 | −1.26622 | −0.633109 | − | 0.774063i | \(-0.718221\pi\) | ||||
−0.633109 | + | 0.774063i | \(0.718221\pi\) | |||||||
\(860\) | −19.6475 | −0.669973 | ||||||||
\(861\) | −1.05902 | −0.0360915 | ||||||||
\(862\) | 0.0257734 | 0.000877847 0 | ||||||||
\(863\) | 17.4095 | 0.592625 | 0.296313 | − | 0.955091i | \(-0.404243\pi\) | ||||
0.296313 | + | 0.955091i | \(0.404243\pi\) | |||||||
\(864\) | −0.00408891 | −0.000139107 0 | ||||||||
\(865\) | −13.0951 | −0.445247 | ||||||||
\(866\) | −0.0497233 | −0.00168967 | ||||||||
\(867\) | −0.178194 | −0.00605178 | ||||||||
\(868\) | 97.9419 | 3.32436 | ||||||||
\(869\) | 4.16667 | 0.141345 | ||||||||
\(870\) | 0.000269582 0 | 9.13968e−6 0 | ||||||||
\(871\) | −11.6213 | −0.393774 | ||||||||
\(872\) | 0.0141313 | 0.000478545 0 | ||||||||
\(873\) | −35.6705 | −1.20726 | ||||||||
\(874\) | −0.0236474 | −0.000799887 0 | ||||||||
\(875\) | 51.8971 | 1.75444 | ||||||||
\(876\) | −0.294472 | −0.00994927 | ||||||||
\(877\) | 26.1956 | 0.884564 | 0.442282 | − | 0.896876i | \(-0.354169\pi\) | ||||
0.442282 | + | 0.896876i | \(0.354169\pi\) | |||||||
\(878\) | 0.0820485 | 0.00276900 | ||||||||
\(879\) | 0.323764 | 0.0109203 | ||||||||
\(880\) | 4.75830 | 0.160402 | ||||||||
\(881\) | −31.1244 | −1.04861 | −0.524304 | − | 0.851531i | \(-0.675675\pi\) | ||||
−0.524304 | + | 0.851531i | \(0.675675\pi\) | |||||||
\(882\) | −0.169125 | −0.00569475 | ||||||||
\(883\) | −56.8533 | −1.91326 | −0.956632 | − | 0.291298i | \(-0.905913\pi\) | ||||
−0.956632 | + | 0.291298i | \(0.905913\pi\) | |||||||
\(884\) | 7.99471 | 0.268891 | ||||||||
\(885\) | −0.00180259 | −6.05935e−5 0 | ||||||||
\(886\) | −0.0682384 | −0.00229251 | ||||||||
\(887\) | 48.5098 | 1.62880 | 0.814401 | − | 0.580303i | \(-0.197066\pi\) | ||||
0.814401 | + | 0.580303i | \(0.197066\pi\) | |||||||
\(888\) | 0.00234748 | 7.87764e−5 0 | ||||||||
\(889\) | −41.0262 | −1.37597 | ||||||||
\(890\) | −0.0230044 | −0.000771110 0 | ||||||||
\(891\) | 8.99676 | 0.301403 | ||||||||
\(892\) | 25.9393 | 0.868513 | ||||||||
\(893\) | 4.64844 | 0.155554 | ||||||||
\(894\) | 0.00123311 | 4.12413e−5 0 | ||||||||
\(895\) | 23.4169 | 0.782739 | ||||||||
\(896\) | 0.487063 | 0.0162716 | ||||||||
\(897\) | 0.157860 | 0.00527080 | ||||||||
\(898\) | −0.0364026 | −0.00121477 | ||||||||
\(899\) | 38.4519 | 1.28244 | ||||||||
\(900\) | −21.5065 | −0.716885 | ||||||||
\(901\) | 12.9510 | 0.431459 | ||||||||
\(902\) | 0.0329192 | 0.00109609 | ||||||||
\(903\) | −0.795731 | −0.0264803 | ||||||||
\(904\) | 0.175116 | 0.00582428 | ||||||||
\(905\) | 21.8949 | 0.727810 | ||||||||
\(906\) | 9.19075e−5 0 | 3.05342e−6 0 | ||||||||
\(907\) | 31.0095 | 1.02965 | 0.514827 | − | 0.857294i | \(-0.327856\pi\) | ||||
0.514827 | + | 0.857294i | \(0.327856\pi\) | |||||||
\(908\) | −57.0120 | −1.89201 | ||||||||
\(909\) | 34.2025 | 1.13442 | ||||||||
\(910\) | −0.0262506 | −0.000870197 0 | ||||||||
\(911\) | 23.1207 | 0.766023 | 0.383012 | − | 0.923743i | \(-0.374887\pi\) | ||||
0.383012 | + | 0.923743i | \(0.374887\pi\) | |||||||
\(912\) | −0.104276 | −0.00345294 | ||||||||
\(913\) | −3.16287 | −0.104676 | ||||||||
\(914\) | −0.0743333 | −0.00245873 | ||||||||
\(915\) | 0.252850 | 0.00835897 | ||||||||
\(916\) | 41.7648 | 1.37995 | ||||||||
\(917\) | 5.08173 | 0.167813 | ||||||||
\(918\) | 0.000939513 0 | 3.10086e−5 0 | ||||||||
\(919\) | 8.22841 | 0.271430 | 0.135715 | − | 0.990748i | \(-0.456667\pi\) | ||||
0.135715 | + | 0.990748i | \(0.456667\pi\) | |||||||
\(920\) | −0.0818434 | −0.00269830 | ||||||||
\(921\) | 0.388851 | 0.0128131 | ||||||||
\(922\) | 0.124545 | 0.00410168 | ||||||||
\(923\) | 0.277296 | 0.00912731 | ||||||||
\(924\) | 0.192714 | 0.00633984 | ||||||||
\(925\) | 37.0437 | 1.21799 | ||||||||
\(926\) | −0.106274 | −0.00349237 | ||||||||
\(927\) | −12.6317 | −0.414881 | ||||||||
\(928\) | 0.143416 | 0.00470785 | ||||||||
\(929\) | 10.1397 | 0.332672 | 0.166336 | − | 0.986069i | \(-0.446806\pi\) | ||||
0.166336 | + | 0.986069i | \(0.446806\pi\) | |||||||
\(930\) | 0.000651074 0 | 2.13495e−5 0 | ||||||||
\(931\) | −25.8803 | −0.848191 | ||||||||
\(932\) | 34.0900 | 1.11666 | ||||||||
\(933\) | 0.538492 | 0.0176294 | ||||||||
\(934\) | 0.000634407 0 | 2.07584e−5 0 | ||||||||
\(935\) | −3.27999 | −0.107267 | ||||||||
\(936\) | 0.0521023 | 0.00170302 | ||||||||
\(937\) | −3.15591 | −0.103099 | −0.0515495 | − | 0.998670i | \(-0.516416\pi\) | ||||
−0.0515495 | + | 0.998670i | \(0.516416\pi\) | |||||||
\(938\) | 0.122010 | 0.00398377 | ||||||||
\(939\) | 0.0659781 | 0.00215312 | ||||||||
\(940\) | 8.04406 | 0.262368 | ||||||||
\(941\) | −5.53094 | −0.180304 | −0.0901518 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901518 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(942\) | −1.56392e−5 0 | −5.09553e−7 0 | ||||||||
\(943\) | 63.1128 | 2.05524 | ||||||||
\(944\) | −0.319653 | −0.0104038 | ||||||||
\(945\) | 0.687716 | 0.0223714 | ||||||||
\(946\) | 0.0247348 | 0.000804199 0 | ||||||||
\(947\) | −8.85200 | −0.287651 | −0.143826 | − | 0.989603i | \(-0.545940\pi\) | ||||
−0.143826 | + | 0.989603i | \(0.545940\pi\) | |||||||
\(948\) | −0.158012 | −0.00513201 | ||||||||
\(949\) | 11.2575 | 0.365433 | ||||||||
\(950\) | 0.0147625 | 0.000478959 0 | ||||||||
\(951\) | −0.229691 | −0.00744826 | ||||||||
\(952\) | −0.167870 | −0.00544071 | ||||||||
\(953\) | −45.3098 | −1.46773 | −0.733864 | − | 0.679297i | \(-0.762285\pi\) | ||||
−0.733864 | + | 0.679297i | \(0.762285\pi\) | |||||||
\(954\) | 0.0422013 | 0.00136632 | ||||||||
\(955\) | −26.6872 | −0.863578 | ||||||||
\(956\) | −25.5933 | −0.827746 | ||||||||
\(957\) | 0.0756596 | 0.00244573 | ||||||||
\(958\) | 0.0949985 | 0.00306926 | ||||||||
\(959\) | −55.5585 | −1.79408 | ||||||||
\(960\) | −0.180448 | −0.00582392 | ||||||||
\(961\) | 61.8662 | 1.99568 | ||||||||
\(962\) | −0.0448714 | −0.00144671 | ||||||||
\(963\) | −16.6267 | −0.535788 | ||||||||
\(964\) | 7.62852 | 0.245698 | ||||||||
\(965\) | −7.97342 | −0.256674 | ||||||||
\(966\) | −0.00165734 | −5.33241e−5 0 | ||||||||
\(967\) | −26.1589 | −0.841213 | −0.420607 | − | 0.907243i | \(-0.638183\pi\) | ||||
−0.420607 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(968\) | −0.0119809 | −0.000385079 0 | ||||||||
\(969\) | 0.0718798 | 0.00230911 | ||||||||
\(970\) | 0.0423708 | 0.00136045 | ||||||||
\(971\) | −45.4184 | −1.45755 | −0.728773 | − | 0.684756i | \(-0.759909\pi\) | ||||
−0.728773 | + | 0.684756i | \(0.759909\pi\) | |||||||
\(972\) | −1.02376 | −0.0328370 | ||||||||
\(973\) | −21.0497 | −0.674823 | ||||||||
\(974\) | 0.00185585 | 5.94654e−5 0 | ||||||||
\(975\) | −0.0985481 | −0.00315606 | ||||||||
\(976\) | 44.8378 | 1.43522 | ||||||||
\(977\) | −46.7563 | −1.49587 | −0.747933 | − | 0.663774i | \(-0.768954\pi\) | ||||
−0.747933 | + | 0.663774i | \(0.768954\pi\) | |||||||
\(978\) | 0.000911793 0 | 2.91559e−5 0 | ||||||||
\(979\) | −6.45631 | −0.206345 | ||||||||
\(980\) | −44.7855 | −1.43062 | ||||||||
\(981\) | 3.53804 | 0.112961 | ||||||||
\(982\) | 0.0206583 | 0.000659233 0 | ||||||||
\(983\) | −51.1595 | −1.63173 | −0.815867 | − | 0.578240i | \(-0.803740\pi\) | ||||
−0.815867 | + | 0.578240i | \(0.803740\pi\) | |||||||
\(984\) | −0.00249679 | −7.95948e−5 0 | ||||||||
\(985\) | −8.26784 | −0.263435 | ||||||||
\(986\) | −0.0329528 | −0.00104943 | ||||||||
\(987\) | 0.325788 | 0.0103699 | ||||||||
\(988\) | 3.98645 | 0.126826 | ||||||||
\(989\) | 47.4218 | 1.50793 | ||||||||
\(990\) | −0.0106880 | −0.000339687 0 | ||||||||
\(991\) | −37.4569 | −1.18986 | −0.594929 | − | 0.803778i | \(-0.702820\pi\) | ||||
−0.594929 | + | 0.803778i | \(0.702820\pi\) | |||||||
\(992\) | 0.346367 | 0.0109972 | ||||||||
\(993\) | 0.173595 | 0.00550886 | ||||||||
\(994\) | −0.00291128 | −9.23401e−5 0 | ||||||||
\(995\) | −9.01642 | −0.285840 | ||||||||
\(996\) | 0.119946 | 0.00380062 | ||||||||
\(997\) | −19.5364 | −0.618726 | −0.309363 | − | 0.950944i | \(-0.600116\pi\) | ||||
−0.309363 | + | 0.950944i | \(0.600116\pi\) | |||||||
\(998\) | 0.00906071 | 0.000286812 0 | ||||||||
\(999\) | 1.17555 | 0.0371927 |
(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 | 1441.2.a.e.1.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.e.1.13 | ✓ | 28 | 1.1 | even | 1 | trivial |