Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 45x^{6} + 47x^{5} + 654x^{4} - 157x^{3} - 2898x^{2} + 96x + 2432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.03574\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0357401 | −0.0126360 | −0.00631802 | − | 0.999980i | \(-0.502011\pi\) | ||||
−0.00631802 | + | 0.999980i | \(0.502011\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.99872 | −0.999840 | ||||||||
\(5\) | −7.80970 | −0.698521 | −0.349260 | − | 0.937026i | \(-0.613567\pi\) | ||||
−0.349260 | + | 0.937026i | \(0.613567\pi\) | |||||||
\(6\) | −0.107220 | −0.00729542 | ||||||||
\(7\) | 4.90513 | 0.264852 | 0.132426 | − | 0.991193i | \(-0.457723\pi\) | ||||
0.132426 | + | 0.991193i | \(0.457723\pi\) | |||||||
\(8\) | 0.571796 | 0.0252701 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0.279120 | 0.00882654 | ||||||||
\(11\) | 37.9474 | 1.04014 | 0.520071 | − | 0.854123i | \(-0.325905\pi\) | ||||
0.520071 | + | 0.854123i | \(0.325905\pi\) | |||||||
\(12\) | −23.9962 | −0.577258 | ||||||||
\(13\) | 27.2075 | 0.580461 | 0.290231 | − | 0.956957i | \(-0.406268\pi\) | ||||
0.290231 | + | 0.956957i | \(0.406268\pi\) | |||||||
\(14\) | −0.175310 | −0.00334668 | ||||||||
\(15\) | −23.4291 | −0.403291 | ||||||||
\(16\) | 63.9693 | 0.999521 | ||||||||
\(17\) | 63.3515 | 0.903824 | 0.451912 | − | 0.892063i | \(-0.350742\pi\) | ||||
0.451912 | + | 0.892063i | \(0.350742\pi\) | |||||||
\(18\) | −0.321661 | −0.00421202 | ||||||||
\(19\) | 97.9685 | 1.18292 | 0.591461 | − | 0.806334i | \(-0.298551\pi\) | ||||
0.591461 | + | 0.806334i | \(0.298551\pi\) | |||||||
\(20\) | 62.4676 | 0.698409 | ||||||||
\(21\) | 14.7154 | 0.152912 | ||||||||
\(22\) | −1.35625 | −0.0131433 | ||||||||
\(23\) | 9.58224 | 0.0868711 | 0.0434355 | − | 0.999056i | \(-0.486170\pi\) | ||||
0.0434355 | + | 0.999056i | \(0.486170\pi\) | |||||||
\(24\) | 1.71539 | 0.0145897 | ||||||||
\(25\) | −64.0086 | −0.512069 | ||||||||
\(26\) | −0.972399 | −0.00733473 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −39.2348 | −0.264810 | ||||||||
\(29\) | 65.2932 | 0.418091 | 0.209046 | − | 0.977906i | \(-0.432964\pi\) | ||||
0.209046 | + | 0.977906i | \(0.432964\pi\) | |||||||
\(30\) | 0.837359 | 0.00509600 | ||||||||
\(31\) | −165.898 | −0.961167 | −0.480583 | − | 0.876949i | \(-0.659575\pi\) | ||||
−0.480583 | + | 0.876949i | \(0.659575\pi\) | |||||||
\(32\) | −6.86064 | −0.0379001 | ||||||||
\(33\) | 113.842 | 0.600527 | ||||||||
\(34\) | −2.26419 | −0.0114208 | ||||||||
\(35\) | −38.3076 | −0.185005 | ||||||||
\(36\) | −71.9885 | −0.333280 | ||||||||
\(37\) | 215.965 | 0.959580 | 0.479790 | − | 0.877383i | \(-0.340713\pi\) | ||||
0.479790 | + | 0.877383i | \(0.340713\pi\) | |||||||
\(38\) | −3.50141 | −0.0149475 | ||||||||
\(39\) | 81.6224 | 0.335129 | ||||||||
\(40\) | −4.46556 | −0.0176517 | ||||||||
\(41\) | 61.9926 | 0.236137 | 0.118068 | − | 0.993005i | \(-0.462330\pi\) | ||||
0.118068 | + | 0.993005i | \(0.462330\pi\) | |||||||
\(42\) | −0.525930 | −0.00193221 | ||||||||
\(43\) | 77.4402 | 0.274640 | 0.137320 | − | 0.990527i | \(-0.456151\pi\) | ||||
0.137320 | + | 0.990527i | \(0.456151\pi\) | |||||||
\(44\) | −303.531 | −1.03998 | ||||||||
\(45\) | −70.2873 | −0.232840 | ||||||||
\(46\) | −0.342470 | −0.00109771 | ||||||||
\(47\) | 189.151 | 0.587032 | 0.293516 | − | 0.955954i | \(-0.405175\pi\) | ||||
0.293516 | + | 0.955954i | \(0.405175\pi\) | |||||||
\(48\) | 191.908 | 0.577074 | ||||||||
\(49\) | −318.940 | −0.929853 | ||||||||
\(50\) | 2.28768 | 0.00647053 | ||||||||
\(51\) | 190.055 | 0.521823 | ||||||||
\(52\) | −217.625 | −0.580368 | ||||||||
\(53\) | 558.039 | 1.44627 | 0.723137 | − | 0.690704i | \(-0.242699\pi\) | ||||
0.723137 | + | 0.690704i | \(0.242699\pi\) | |||||||
\(54\) | −0.964984 | −0.00243181 | ||||||||
\(55\) | −296.358 | −0.726561 | ||||||||
\(56\) | 2.80474 | 0.00669283 | ||||||||
\(57\) | 293.906 | 0.682960 | ||||||||
\(58\) | −2.33359 | −0.00528302 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 187.403 | 0.403227 | ||||||||
\(61\) | 451.056 | 0.946752 | 0.473376 | − | 0.880861i | \(-0.343035\pi\) | ||||
0.473376 | + | 0.880861i | \(0.343035\pi\) | |||||||
\(62\) | 5.92922 | 0.0121453 | ||||||||
\(63\) | 44.1462 | 0.0882841 | ||||||||
\(64\) | −511.510 | −0.999042 | ||||||||
\(65\) | −212.482 | −0.405464 | ||||||||
\(66\) | −4.06874 | −0.00758828 | ||||||||
\(67\) | −730.287 | −1.33162 | −0.665811 | − | 0.746120i | \(-0.731914\pi\) | ||||
−0.665811 | + | 0.746120i | \(0.731914\pi\) | |||||||
\(68\) | −506.731 | −0.903679 | ||||||||
\(69\) | 28.7467 | 0.0501550 | ||||||||
\(70\) | 1.36912 | 0.00233773 | ||||||||
\(71\) | 1040.27 | 1.73883 | 0.869414 | − | 0.494084i | \(-0.164497\pi\) | ||||
0.869414 | + | 0.494084i | \(0.164497\pi\) | |||||||
\(72\) | 5.14617 | 0.00842336 | ||||||||
\(73\) | −529.757 | −0.849361 | −0.424680 | − | 0.905343i | \(-0.639613\pi\) | ||||
−0.424680 | + | 0.905343i | \(0.639613\pi\) | |||||||
\(74\) | −7.71862 | −0.0121253 | ||||||||
\(75\) | −192.026 | −0.295643 | ||||||||
\(76\) | −783.623 | −1.18273 | ||||||||
\(77\) | 186.137 | 0.275484 | ||||||||
\(78\) | −2.91720 | −0.00423471 | ||||||||
\(79\) | −1007.53 | −1.43488 | −0.717440 | − | 0.696620i | \(-0.754686\pi\) | ||||
−0.717440 | + | 0.696620i | \(0.754686\pi\) | |||||||
\(80\) | −499.581 | −0.698186 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −2.21562 | −0.00298384 | ||||||||
\(83\) | −393.059 | −0.519805 | −0.259903 | − | 0.965635i | \(-0.583690\pi\) | ||||
−0.259903 | + | 0.965635i | \(0.583690\pi\) | |||||||
\(84\) | −117.704 | −0.152888 | ||||||||
\(85\) | −494.756 | −0.631339 | ||||||||
\(86\) | −2.76772 | −0.00347036 | ||||||||
\(87\) | 195.880 | 0.241385 | ||||||||
\(88\) | 21.6982 | 0.0262845 | ||||||||
\(89\) | −50.5608 | −0.0602183 | −0.0301092 | − | 0.999547i | \(-0.509585\pi\) | ||||
−0.0301092 | + | 0.999547i | \(0.509585\pi\) | |||||||
\(90\) | 2.51208 | 0.00294218 | ||||||||
\(91\) | 133.456 | 0.153736 | ||||||||
\(92\) | −76.6457 | −0.0868572 | ||||||||
\(93\) | −497.694 | −0.554930 | ||||||||
\(94\) | −6.76028 | −0.00741776 | ||||||||
\(95\) | −765.105 | −0.826296 | ||||||||
\(96\) | −20.5819 | −0.0218816 | ||||||||
\(97\) | −1043.06 | −1.09182 | −0.545912 | − | 0.837843i | \(-0.683817\pi\) | ||||
−0.545912 | + | 0.837843i | \(0.683817\pi\) | |||||||
\(98\) | 11.3989 | 0.0117497 | ||||||||
\(99\) | 341.527 | 0.346714 | ||||||||
\(100\) | 511.987 | 0.511987 | ||||||||
\(101\) | 1481.74 | 1.45978 | 0.729892 | − | 0.683563i | \(-0.239570\pi\) | ||||
0.729892 | + | 0.683563i | \(0.239570\pi\) | |||||||
\(102\) | −6.79258 | −0.00659378 | ||||||||
\(103\) | 61.1482 | 0.0584962 | 0.0292481 | − | 0.999572i | \(-0.490689\pi\) | ||||
0.0292481 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(104\) | 15.5571 | 0.0146683 | ||||||||
\(105\) | −114.923 | −0.106813 | ||||||||
\(106\) | −19.9444 | −0.0182752 | ||||||||
\(107\) | −1057.95 | −0.955847 | −0.477923 | − | 0.878401i | \(-0.658610\pi\) | ||||
−0.477923 | + | 0.878401i | \(0.658610\pi\) | |||||||
\(108\) | −215.966 | −0.192419 | ||||||||
\(109\) | 773.766 | 0.679939 | 0.339970 | − | 0.940436i | \(-0.389583\pi\) | ||||
0.339970 | + | 0.940436i | \(0.389583\pi\) | |||||||
\(110\) | 10.5919 | 0.00918086 | ||||||||
\(111\) | 647.895 | 0.554014 | ||||||||
\(112\) | 313.778 | 0.264725 | ||||||||
\(113\) | 170.203 | 0.141694 | 0.0708469 | − | 0.997487i | \(-0.477430\pi\) | ||||
0.0708469 | + | 0.997487i | \(0.477430\pi\) | |||||||
\(114\) | −10.5042 | −0.00862992 | ||||||||
\(115\) | −74.8344 | −0.0606812 | ||||||||
\(116\) | −522.262 | −0.418024 | ||||||||
\(117\) | 244.867 | 0.193487 | ||||||||
\(118\) | −2.10867 | −0.00164507 | ||||||||
\(119\) | 310.748 | 0.239380 | ||||||||
\(120\) | −13.3967 | −0.0101912 | ||||||||
\(121\) | 109.005 | 0.0818971 | ||||||||
\(122\) | −16.1208 | −0.0119632 | ||||||||
\(123\) | 185.978 | 0.136334 | ||||||||
\(124\) | 1326.97 | 0.961013 | ||||||||
\(125\) | 1476.10 | 1.05621 | ||||||||
\(126\) | −1.57779 | −0.00111556 | ||||||||
\(127\) | 148.411 | 0.103695 | 0.0518477 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518477 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(128\) | 73.1666 | 0.0505240 | ||||||||
\(129\) | 232.321 | 0.158563 | ||||||||
\(130\) | 7.59414 | 0.00512346 | ||||||||
\(131\) | −514.797 | −0.343344 | −0.171672 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171672 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(132\) | −910.592 | −0.600431 | ||||||||
\(133\) | 480.549 | 0.313300 | ||||||||
\(134\) | 26.1005 | 0.0168264 | ||||||||
\(135\) | −210.862 | −0.134430 | ||||||||
\(136\) | 36.2242 | 0.0228397 | ||||||||
\(137\) | 2145.47 | 1.33795 | 0.668976 | − | 0.743284i | \(-0.266733\pi\) | ||||
0.668976 | + | 0.743284i | \(0.266733\pi\) | |||||||
\(138\) | −1.02741 | −0.000633761 0 | ||||||||
\(139\) | 951.765 | 0.580775 | 0.290387 | − | 0.956909i | \(-0.406216\pi\) | ||||
0.290387 | + | 0.956909i | \(0.406216\pi\) | |||||||
\(140\) | 306.412 | 0.184975 | ||||||||
\(141\) | 567.452 | 0.338923 | ||||||||
\(142\) | −37.1792 | −0.0219719 | ||||||||
\(143\) | 1032.45 | 0.603762 | ||||||||
\(144\) | 575.724 | 0.333174 | ||||||||
\(145\) | −509.920 | −0.292045 | ||||||||
\(146\) | 18.9336 | 0.0107326 | ||||||||
\(147\) | −956.819 | −0.536851 | ||||||||
\(148\) | −1727.45 | −0.959426 | ||||||||
\(149\) | −2363.38 | −1.29944 | −0.649718 | − | 0.760175i | \(-0.725113\pi\) | ||||
−0.649718 | + | 0.760175i | \(0.725113\pi\) | |||||||
\(150\) | 6.86303 | 0.00373576 | ||||||||
\(151\) | 2047.04 | 1.10322 | 0.551609 | − | 0.834103i | \(-0.314014\pi\) | ||||
0.551609 | + | 0.834103i | \(0.314014\pi\) | |||||||
\(152\) | 56.0181 | 0.0298925 | ||||||||
\(153\) | 570.164 | 0.301275 | ||||||||
\(154\) | −6.65256 | −0.00348103 | ||||||||
\(155\) | 1295.61 | 0.671395 | ||||||||
\(156\) | −652.875 | −0.335076 | ||||||||
\(157\) | 1779.17 | 0.904416 | 0.452208 | − | 0.891912i | \(-0.350636\pi\) | ||||
0.452208 | + | 0.891912i | \(0.350636\pi\) | |||||||
\(158\) | 36.0091 | 0.0181312 | ||||||||
\(159\) | 1674.12 | 0.835007 | ||||||||
\(160\) | 53.5796 | 0.0264740 | ||||||||
\(161\) | 47.0021 | 0.0230080 | ||||||||
\(162\) | −2.89495 | −0.00140401 | ||||||||
\(163\) | 389.908 | 0.187362 | 0.0936808 | − | 0.995602i | \(-0.470137\pi\) | ||||
0.0936808 | + | 0.995602i | \(0.470137\pi\) | |||||||
\(164\) | −495.861 | −0.236099 | ||||||||
\(165\) | −889.073 | −0.419480 | ||||||||
\(166\) | 14.0480 | 0.00656828 | ||||||||
\(167\) | −1317.81 | −0.610632 | −0.305316 | − | 0.952251i | \(-0.598762\pi\) | ||||
−0.305316 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(168\) | 8.41421 | 0.00386411 | ||||||||
\(169\) | −1456.75 | −0.663065 | ||||||||
\(170\) | 17.6827 | 0.00797763 | ||||||||
\(171\) | 881.717 | 0.394307 | ||||||||
\(172\) | −619.423 | −0.274596 | ||||||||
\(173\) | −821.841 | −0.361176 | −0.180588 | − | 0.983559i | \(-0.557800\pi\) | ||||
−0.180588 | + | 0.983559i | \(0.557800\pi\) | |||||||
\(174\) | −7.00076 | −0.00305015 | ||||||||
\(175\) | −313.971 | −0.135623 | ||||||||
\(176\) | 2427.47 | 1.03964 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 1.80705 | 0.000760921 0 | ||||||||
\(179\) | −592.023 | −0.247206 | −0.123603 | − | 0.992332i | \(-0.539445\pi\) | ||||
−0.123603 | + | 0.992332i | \(0.539445\pi\) | |||||||
\(180\) | 562.208 | 0.232803 | ||||||||
\(181\) | −812.424 | −0.333630 | −0.166815 | − | 0.985988i | \(-0.553348\pi\) | ||||
−0.166815 | + | 0.985988i | \(0.553348\pi\) | |||||||
\(182\) | −4.76974 | −0.00194262 | ||||||||
\(183\) | 1353.17 | 0.546607 | ||||||||
\(184\) | 5.47909 | 0.00219524 | ||||||||
\(185\) | −1686.62 | −0.670286 | ||||||||
\(186\) | 17.7877 | 0.00701212 | ||||||||
\(187\) | 2404.03 | 0.940106 | ||||||||
\(188\) | −1512.96 | −0.586938 | ||||||||
\(189\) | 132.439 | 0.0509708 | ||||||||
\(190\) | 27.3449 | 0.0104411 | ||||||||
\(191\) | 2821.53 | 1.06890 | 0.534448 | − | 0.845202i | \(-0.320520\pi\) | ||||
0.534448 | + | 0.845202i | \(0.320520\pi\) | |||||||
\(192\) | −1534.53 | −0.576797 | ||||||||
\(193\) | −2254.59 | −0.840875 | −0.420437 | − | 0.907322i | \(-0.638123\pi\) | ||||
−0.420437 | + | 0.907322i | \(0.638123\pi\) | |||||||
\(194\) | 37.2792 | 0.0137963 | ||||||||
\(195\) | −637.446 | −0.234095 | ||||||||
\(196\) | 2551.11 | 0.929705 | ||||||||
\(197\) | −2019.03 | −0.730203 | −0.365102 | − | 0.930968i | \(-0.618966\pi\) | ||||
−0.365102 | + | 0.930968i | \(0.618966\pi\) | |||||||
\(198\) | −12.2062 | −0.00438110 | ||||||||
\(199\) | 1504.81 | 0.536047 | 0.268024 | − | 0.963412i | \(-0.413630\pi\) | ||||
0.268024 | + | 0.963412i | \(0.413630\pi\) | |||||||
\(200\) | −36.5999 | −0.0129400 | ||||||||
\(201\) | −2190.86 | −0.768813 | ||||||||
\(202\) | −52.9574 | −0.0184459 | ||||||||
\(203\) | 320.272 | 0.110732 | ||||||||
\(204\) | −1520.19 | −0.521740 | ||||||||
\(205\) | −484.143 | −0.164946 | ||||||||
\(206\) | −2.18544 | −0.000739161 0 | ||||||||
\(207\) | 86.2401 | 0.0289570 | ||||||||
\(208\) | 1740.44 | 0.580183 | ||||||||
\(209\) | 3717.65 | 1.23041 | ||||||||
\(210\) | 4.10736 | 0.00134969 | ||||||||
\(211\) | 1789.09 | 0.583724 | 0.291862 | − | 0.956460i | \(-0.405725\pi\) | ||||
0.291862 | + | 0.956460i | \(0.405725\pi\) | |||||||
\(212\) | −4463.60 | −1.44604 | ||||||||
\(213\) | 3120.80 | 1.00391 | ||||||||
\(214\) | 37.8112 | 0.0120781 | ||||||||
\(215\) | −604.784 | −0.191842 | ||||||||
\(216\) | 15.4385 | 0.00486323 | ||||||||
\(217\) | −813.752 | −0.254567 | ||||||||
\(218\) | −27.6545 | −0.00859174 | ||||||||
\(219\) | −1589.27 | −0.490379 | ||||||||
\(220\) | 2370.48 | 0.726445 | ||||||||
\(221\) | 1723.63 | 0.524634 | ||||||||
\(222\) | −23.1559 | −0.00700054 | ||||||||
\(223\) | −1853.90 | −0.556710 | −0.278355 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278355 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(224\) | −33.6524 | −0.0100379 | ||||||||
\(225\) | −576.078 | −0.170690 | ||||||||
\(226\) | −6.08309 | −0.00179045 | ||||||||
\(227\) | 2113.71 | 0.618026 | 0.309013 | − | 0.951058i | \(-0.400001\pi\) | ||||
0.309013 | + | 0.951058i | \(0.400001\pi\) | |||||||
\(228\) | −2350.87 | −0.682851 | ||||||||
\(229\) | −993.951 | −0.286822 | −0.143411 | − | 0.989663i | \(-0.545807\pi\) | ||||
−0.143411 | + | 0.989663i | \(0.545807\pi\) | |||||||
\(230\) | 2.67459 | 0.000766771 0 | ||||||||
\(231\) | 558.411 | 0.159051 | ||||||||
\(232\) | 37.3344 | 0.0105652 | ||||||||
\(233\) | 1982.82 | 0.557505 | 0.278753 | − | 0.960363i | \(-0.410079\pi\) | ||||
0.278753 | + | 0.960363i | \(0.410079\pi\) | |||||||
\(234\) | −8.75159 | −0.00244491 | ||||||||
\(235\) | −1477.21 | −0.410054 | ||||||||
\(236\) | −471.925 | −0.130168 | ||||||||
\(237\) | −3022.58 | −0.828429 | ||||||||
\(238\) | −11.1062 | −0.00302481 | ||||||||
\(239\) | −4186.15 | −1.13297 | −0.566485 | − | 0.824072i | \(-0.691697\pi\) | ||||
−0.566485 | + | 0.824072i | \(0.691697\pi\) | |||||||
\(240\) | −1498.74 | −0.403098 | ||||||||
\(241\) | 455.312 | 0.121698 | 0.0608490 | − | 0.998147i | \(-0.480619\pi\) | ||||
0.0608490 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(242\) | −3.89586 | −0.00103486 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3607.87 | −0.946600 | ||||||||
\(245\) | 2490.82 | 0.649522 | ||||||||
\(246\) | −6.64687 | −0.00172272 | ||||||||
\(247\) | 2665.48 | 0.686640 | ||||||||
\(248\) | −94.8599 | −0.0242887 | ||||||||
\(249\) | −1179.18 | −0.300110 | ||||||||
\(250\) | −52.7560 | −0.0133463 | ||||||||
\(251\) | −7160.56 | −1.80068 | −0.900340 | − | 0.435188i | \(-0.856682\pi\) | ||||
−0.900340 | + | 0.435188i | \(0.856682\pi\) | |||||||
\(252\) | −353.113 | −0.0882700 | ||||||||
\(253\) | 363.621 | 0.0903583 | ||||||||
\(254\) | −5.30421 | −0.00131030 | ||||||||
\(255\) | −1484.27 | −0.364504 | ||||||||
\(256\) | 4089.46 | 0.998404 | ||||||||
\(257\) | −813.094 | −0.197352 | −0.0986759 | − | 0.995120i | \(-0.531461\pi\) | ||||
−0.0986759 | + | 0.995120i | \(0.531461\pi\) | |||||||
\(258\) | −8.30317 | −0.00200361 | ||||||||
\(259\) | 1059.34 | 0.254147 | ||||||||
\(260\) | 1699.59 | 0.405399 | ||||||||
\(261\) | 587.639 | 0.139364 | ||||||||
\(262\) | 18.3989 | 0.00433851 | ||||||||
\(263\) | −3135.36 | −0.735112 | −0.367556 | − | 0.930001i | \(-0.619805\pi\) | ||||
−0.367556 | + | 0.930001i | \(0.619805\pi\) | |||||||
\(264\) | 65.0946 | 0.0151754 | ||||||||
\(265\) | −4358.12 | −1.01025 | ||||||||
\(266\) | −17.1749 | −0.00395887 | ||||||||
\(267\) | −151.682 | −0.0347671 | ||||||||
\(268\) | 5841.36 | 1.33141 | ||||||||
\(269\) | −4459.37 | −1.01075 | −0.505377 | − | 0.862899i | \(-0.668646\pi\) | ||||
−0.505377 | + | 0.862899i | \(0.668646\pi\) | |||||||
\(270\) | 7.53623 | 0.00169867 | ||||||||
\(271\) | 5557.17 | 1.24566 | 0.622830 | − | 0.782357i | \(-0.285983\pi\) | ||||
0.622830 | + | 0.782357i | \(0.285983\pi\) | |||||||
\(272\) | 4052.56 | 0.903391 | ||||||||
\(273\) | 400.369 | 0.0887598 | ||||||||
\(274\) | −76.6792 | −0.0169064 | ||||||||
\(275\) | −2428.96 | −0.532625 | ||||||||
\(276\) | −229.937 | −0.0501470 | ||||||||
\(277\) | −3618.46 | −0.784881 | −0.392440 | − | 0.919777i | \(-0.628369\pi\) | ||||
−0.392440 | + | 0.919777i | \(0.628369\pi\) | |||||||
\(278\) | −34.0162 | −0.00733869 | ||||||||
\(279\) | −1493.08 | −0.320389 | ||||||||
\(280\) | −21.9041 | −0.00467508 | ||||||||
\(281\) | −4971.01 | −1.05532 | −0.527661 | − | 0.849455i | \(-0.676931\pi\) | ||||
−0.527661 | + | 0.849455i | \(0.676931\pi\) | |||||||
\(282\) | −20.2808 | −0.00428264 | ||||||||
\(283\) | −4836.09 | −1.01582 | −0.507908 | − | 0.861412i | \(-0.669581\pi\) | ||||
−0.507908 | + | 0.861412i | \(0.669581\pi\) | |||||||
\(284\) | −8320.80 | −1.73855 | ||||||||
\(285\) | −2295.31 | −0.477062 | ||||||||
\(286\) | −36.9000 | −0.00762917 | ||||||||
\(287\) | 304.082 | 0.0625414 | ||||||||
\(288\) | −61.7458 | −0.0126334 | ||||||||
\(289\) | −899.584 | −0.183103 | ||||||||
\(290\) | 18.2246 | 0.00369030 | ||||||||
\(291\) | −3129.19 | −0.630365 | ||||||||
\(292\) | 4237.38 | 0.849225 | ||||||||
\(293\) | −6061.44 | −1.20858 | −0.604288 | − | 0.796766i | \(-0.706543\pi\) | ||||
−0.604288 | + | 0.796766i | \(0.706543\pi\) | |||||||
\(294\) | 34.1968 | 0.00678367 | ||||||||
\(295\) | −460.772 | −0.0909396 | ||||||||
\(296\) | 123.488 | 0.0242486 | ||||||||
\(297\) | 1024.58 | 0.200176 | ||||||||
\(298\) | 84.4677 | 0.0164197 | ||||||||
\(299\) | 260.708 | 0.0504253 | ||||||||
\(300\) | 1535.96 | 0.295596 | ||||||||
\(301\) | 379.854 | 0.0727390 | ||||||||
\(302\) | −73.1615 | −0.0139403 | ||||||||
\(303\) | 4445.21 | 0.842807 | ||||||||
\(304\) | 6266.98 | 1.18236 | ||||||||
\(305\) | −3522.61 | −0.661326 | ||||||||
\(306\) | −20.3777 | −0.00380692 | ||||||||
\(307\) | −3807.74 | −0.707880 | −0.353940 | − | 0.935268i | \(-0.615158\pi\) | ||||
−0.353940 | + | 0.935268i | \(0.615158\pi\) | |||||||
\(308\) | −1488.86 | −0.275440 | ||||||||
\(309\) | 183.445 | 0.0337728 | ||||||||
\(310\) | −46.3054 | −0.00848377 | ||||||||
\(311\) | 7633.34 | 1.39179 | 0.695896 | − | 0.718143i | \(-0.255008\pi\) | ||||
0.695896 | + | 0.718143i | \(0.255008\pi\) | |||||||
\(312\) | 46.6714 | 0.00846874 | ||||||||
\(313\) | −5921.30 | −1.06930 | −0.534651 | − | 0.845073i | \(-0.679557\pi\) | ||||
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(314\) | −63.5878 | −0.0114282 | ||||||||
\(315\) | −344.768 | −0.0616682 | ||||||||
\(316\) | 8058.92 | 1.43465 | ||||||||
\(317\) | −1748.08 | −0.309722 | −0.154861 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154861 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(318\) | −59.8332 | −0.0105512 | ||||||||
\(319\) | 2477.71 | 0.434875 | ||||||||
\(320\) | 3994.74 | 0.697852 | ||||||||
\(321\) | −3173.84 | −0.551858 | ||||||||
\(322\) | −1.67986 | −0.000290730 0 | ||||||||
\(323\) | 6206.46 | 1.06915 | ||||||||
\(324\) | −647.897 | −0.111093 | ||||||||
\(325\) | −1741.51 | −0.297236 | ||||||||
\(326\) | −13.9354 | −0.00236751 | ||||||||
\(327\) | 2321.30 | 0.392563 | ||||||||
\(328\) | 35.4471 | 0.00596720 | ||||||||
\(329\) | 927.810 | 0.155477 | ||||||||
\(330\) | 31.7756 | 0.00530057 | ||||||||
\(331\) | 10853.1 | 1.80223 | 0.901116 | − | 0.433579i | \(-0.142749\pi\) | ||||
0.901116 | + | 0.433579i | \(0.142749\pi\) | |||||||
\(332\) | 3143.97 | 0.519722 | ||||||||
\(333\) | 1943.69 | 0.319860 | ||||||||
\(334\) | 47.0989 | 0.00771597 | ||||||||
\(335\) | 5703.32 | 0.930166 | ||||||||
\(336\) | 941.334 | 0.152839 | ||||||||
\(337\) | 8975.80 | 1.45087 | 0.725435 | − | 0.688291i | \(-0.241639\pi\) | ||||
0.725435 | + | 0.688291i | \(0.241639\pi\) | |||||||
\(338\) | 52.0646 | 0.00837852 | ||||||||
\(339\) | 510.610 | 0.0818069 | ||||||||
\(340\) | 3957.42 | 0.631239 | ||||||||
\(341\) | −6295.40 | −0.999750 | ||||||||
\(342\) | −31.5127 | −0.00498249 | ||||||||
\(343\) | −3246.90 | −0.511126 | ||||||||
\(344\) | 44.2800 | 0.00694017 | ||||||||
\(345\) | −224.503 | −0.0350343 | ||||||||
\(346\) | 29.3727 | 0.00456384 | ||||||||
\(347\) | 6240.09 | 0.965377 | 0.482688 | − | 0.875792i | \(-0.339660\pi\) | ||||
0.482688 | + | 0.875792i | \(0.339660\pi\) | |||||||
\(348\) | −1566.79 | −0.241347 | ||||||||
\(349\) | −12565.4 | −1.92724 | −0.963621 | − | 0.267271i | \(-0.913878\pi\) | ||||
−0.963621 | + | 0.267271i | \(0.913878\pi\) | |||||||
\(350\) | 11.2214 | 0.00171373 | ||||||||
\(351\) | 734.602 | 0.111710 | ||||||||
\(352\) | −260.344 | −0.0394215 | ||||||||
\(353\) | 4825.08 | 0.727516 | 0.363758 | − | 0.931494i | \(-0.381494\pi\) | ||||
0.363758 | + | 0.931494i | \(0.381494\pi\) | |||||||
\(354\) | −6.32600 | −0.000949783 0 | ||||||||
\(355\) | −8124.16 | −1.21461 | ||||||||
\(356\) | 404.422 | 0.0602087 | ||||||||
\(357\) | 932.243 | 0.138206 | ||||||||
\(358\) | 21.1590 | 0.00312371 | ||||||||
\(359\) | −2919.83 | −0.429256 | −0.214628 | − | 0.976696i | \(-0.568854\pi\) | ||||
−0.214628 | + | 0.976696i | \(0.568854\pi\) | |||||||
\(360\) | −40.1900 | −0.00588389 | ||||||||
\(361\) | 2738.83 | 0.399305 | ||||||||
\(362\) | 29.0362 | 0.00421576 | ||||||||
\(363\) | 327.015 | 0.0472833 | ||||||||
\(364\) | −1067.48 | −0.153712 | ||||||||
\(365\) | 4137.24 | 0.593296 | ||||||||
\(366\) | −48.3624 | −0.00690695 | ||||||||
\(367\) | −9268.74 | −1.31832 | −0.659161 | − | 0.752002i | \(-0.729088\pi\) | ||||
−0.659161 | + | 0.752002i | \(0.729088\pi\) | |||||||
\(368\) | 612.969 | 0.0868295 | ||||||||
\(369\) | 557.933 | 0.0787123 | ||||||||
\(370\) | 60.2801 | 0.00846977 | ||||||||
\(371\) | 2737.26 | 0.383049 | ||||||||
\(372\) | 3980.92 | 0.554841 | ||||||||
\(373\) | 6510.93 | 0.903816 | 0.451908 | − | 0.892065i | \(-0.350744\pi\) | ||||
0.451908 | + | 0.892065i | \(0.350744\pi\) | |||||||
\(374\) | −85.9202 | −0.0118792 | ||||||||
\(375\) | 4428.30 | 0.609804 | ||||||||
\(376\) | 108.156 | 0.0148343 | ||||||||
\(377\) | 1776.46 | 0.242686 | ||||||||
\(378\) | −4.73337 | −0.000644070 0 | ||||||||
\(379\) | −2068.45 | −0.280341 | −0.140171 | − | 0.990127i | \(-0.544765\pi\) | ||||
−0.140171 | + | 0.990127i | \(0.544765\pi\) | |||||||
\(380\) | 6119.86 | 0.826164 | ||||||||
\(381\) | 445.232 | 0.0598685 | ||||||||
\(382\) | −100.842 | −0.0135066 | ||||||||
\(383\) | 12258.5 | 1.63545 | 0.817727 | − | 0.575606i | \(-0.195234\pi\) | ||||
0.817727 | + | 0.575606i | \(0.195234\pi\) | |||||||
\(384\) | 219.500 | 0.0291700 | ||||||||
\(385\) | −1453.67 | −0.192431 | ||||||||
\(386\) | 80.5793 | 0.0106253 | ||||||||
\(387\) | 696.962 | 0.0915466 | ||||||||
\(388\) | 8343.16 | 1.09165 | ||||||||
\(389\) | −4389.85 | −0.572171 | −0.286085 | − | 0.958204i | \(-0.592354\pi\) | ||||
−0.286085 | + | 0.958204i | \(0.592354\pi\) | |||||||
\(390\) | 22.7824 | 0.00295803 | ||||||||
\(391\) | 607.049 | 0.0785161 | ||||||||
\(392\) | −182.369 | −0.0234975 | ||||||||
\(393\) | −1544.39 | −0.198230 | ||||||||
\(394\) | 72.1604 | 0.00922688 | ||||||||
\(395\) | 7868.48 | 1.00229 | ||||||||
\(396\) | −2731.78 | −0.346659 | ||||||||
\(397\) | 4517.53 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(398\) | −53.7822 | −0.00677352 | ||||||||
\(399\) | 1441.65 | 0.180884 | ||||||||
\(400\) | −4094.59 | −0.511824 | ||||||||
\(401\) | −4353.84 | −0.542195 | −0.271098 | − | 0.962552i | \(-0.587387\pi\) | ||||
−0.271098 | + | 0.962552i | \(0.587387\pi\) | |||||||
\(402\) | 78.3016 | 0.00971475 | ||||||||
\(403\) | −4513.66 | −0.557920 | ||||||||
\(404\) | −11852.0 | −1.45955 | ||||||||
\(405\) | −632.586 | −0.0776134 | ||||||||
\(406\) | −11.4466 | −0.00139922 | ||||||||
\(407\) | 8195.31 | 0.998100 | ||||||||
\(408\) | 108.673 | 0.0131865 | ||||||||
\(409\) | −12382.7 | −1.49702 | −0.748512 | − | 0.663121i | \(-0.769231\pi\) | ||||
−0.748512 | + | 0.663121i | \(0.769231\pi\) | |||||||
\(410\) | 17.3033 | 0.00208427 | ||||||||
\(411\) | 6436.40 | 0.772467 | ||||||||
\(412\) | −489.107 | −0.0584869 | ||||||||
\(413\) | 289.403 | 0.0344808 | ||||||||
\(414\) | −3.08223 | −0.000365902 0 | ||||||||
\(415\) | 3069.67 | 0.363095 | ||||||||
\(416\) | −186.661 | −0.0219995 | ||||||||
\(417\) | 2855.30 | 0.335310 | ||||||||
\(418\) | −132.869 | −0.0155475 | ||||||||
\(419\) | 2273.01 | 0.265020 | 0.132510 | − | 0.991182i | \(-0.457696\pi\) | ||||
0.132510 | + | 0.991182i | \(0.457696\pi\) | |||||||
\(420\) | 919.236 | 0.106795 | ||||||||
\(421\) | −11870.2 | −1.37415 | −0.687076 | − | 0.726586i | \(-0.741106\pi\) | ||||
−0.687076 | + | 0.726586i | \(0.741106\pi\) | |||||||
\(422\) | −63.9422 | −0.00737597 | ||||||||
\(423\) | 1702.36 | 0.195677 | ||||||||
\(424\) | 319.085 | 0.0365475 | ||||||||
\(425\) | −4055.04 | −0.462820 | ||||||||
\(426\) | −111.538 | −0.0126855 | ||||||||
\(427\) | 2212.49 | 0.250749 | ||||||||
\(428\) | 8462.23 | 0.955694 | ||||||||
\(429\) | 3097.36 | 0.348582 | ||||||||
\(430\) | 21.6151 | 0.00242412 | ||||||||
\(431\) | −15025.7 | −1.67926 | −0.839629 | − | 0.543160i | \(-0.817228\pi\) | ||||
−0.839629 | + | 0.543160i | \(0.817228\pi\) | |||||||
\(432\) | 1727.17 | 0.192358 | ||||||||
\(433\) | −16251.4 | −1.80368 | −0.901838 | − | 0.432074i | \(-0.857782\pi\) | ||||
−0.901838 | + | 0.432074i | \(0.857782\pi\) | |||||||
\(434\) | 29.0836 | 0.00321672 | ||||||||
\(435\) | −1529.76 | −0.168612 | ||||||||
\(436\) | −6189.14 | −0.679831 | ||||||||
\(437\) | 938.758 | 0.102762 | ||||||||
\(438\) | 56.8007 | 0.00619645 | ||||||||
\(439\) | 2884.92 | 0.313644 | 0.156822 | − | 0.987627i | \(-0.449875\pi\) | ||||
0.156822 | + | 0.987627i | \(0.449875\pi\) | |||||||
\(440\) | −169.456 | −0.0183603 | ||||||||
\(441\) | −2870.46 | −0.309951 | ||||||||
\(442\) | −61.6029 | −0.00662930 | ||||||||
\(443\) | 9495.38 | 1.01837 | 0.509187 | − | 0.860656i | \(-0.329946\pi\) | ||||
0.509187 | + | 0.860656i | \(0.329946\pi\) | |||||||
\(444\) | −5182.34 | −0.553925 | ||||||||
\(445\) | 394.864 | 0.0420637 | ||||||||
\(446\) | 66.2586 | 0.00703461 | ||||||||
\(447\) | −7090.15 | −0.750230 | ||||||||
\(448\) | −2509.02 | −0.264599 | ||||||||
\(449\) | 8540.14 | 0.897626 | 0.448813 | − | 0.893626i | \(-0.351847\pi\) | ||||
0.448813 | + | 0.893626i | \(0.351847\pi\) | |||||||
\(450\) | 20.5891 | 0.00215684 | ||||||||
\(451\) | 2352.46 | 0.245616 | ||||||||
\(452\) | −1361.41 | −0.141671 | ||||||||
\(453\) | 6141.12 | 0.636943 | ||||||||
\(454\) | −75.5443 | −0.00780940 | ||||||||
\(455\) | −1042.25 | −0.107388 | ||||||||
\(456\) | 168.054 | 0.0172585 | ||||||||
\(457\) | −7167.88 | −0.733696 | −0.366848 | − | 0.930281i | \(-0.619563\pi\) | ||||
−0.366848 | + | 0.930281i | \(0.619563\pi\) | |||||||
\(458\) | 35.5239 | 0.00362429 | ||||||||
\(459\) | 1710.49 | 0.173941 | ||||||||
\(460\) | 598.579 | 0.0606715 | ||||||||
\(461\) | −5091.59 | −0.514401 | −0.257200 | − | 0.966358i | \(-0.582800\pi\) | ||||
−0.257200 | + | 0.966358i | \(0.582800\pi\) | |||||||
\(462\) | −19.9577 | −0.00200977 | ||||||||
\(463\) | 9870.55 | 0.990764 | 0.495382 | − | 0.868675i | \(-0.335028\pi\) | ||||
0.495382 | + | 0.868675i | \(0.335028\pi\) | |||||||
\(464\) | 4176.76 | 0.417891 | ||||||||
\(465\) | 3886.84 | 0.387630 | ||||||||
\(466\) | −70.8662 | −0.00704466 | ||||||||
\(467\) | −16600.2 | −1.64489 | −0.822446 | − | 0.568844i | \(-0.807391\pi\) | ||||
−0.822446 | + | 0.568844i | \(0.807391\pi\) | |||||||
\(468\) | −1958.62 | −0.193456 | ||||||||
\(469\) | −3582.15 | −0.352683 | ||||||||
\(470\) | 52.7957 | 0.00518146 | ||||||||
\(471\) | 5337.52 | 0.522165 | ||||||||
\(472\) | 33.7360 | 0.00328988 | ||||||||
\(473\) | 2938.65 | 0.285665 | ||||||||
\(474\) | 108.027 | 0.0104681 | ||||||||
\(475\) | −6270.83 | −0.605738 | ||||||||
\(476\) | −2485.58 | −0.239341 | ||||||||
\(477\) | 5022.35 | 0.482092 | ||||||||
\(478\) | 149.614 | 0.0143163 | ||||||||
\(479\) | 11476.4 | 1.09472 | 0.547360 | − | 0.836897i | \(-0.315633\pi\) | ||||
0.547360 | + | 0.836897i | \(0.315633\pi\) | |||||||
\(480\) | 160.739 | 0.0152848 | ||||||||
\(481\) | 5875.86 | 0.556999 | ||||||||
\(482\) | −16.2729 | −0.00153778 | ||||||||
\(483\) | 141.006 | 0.0132837 | ||||||||
\(484\) | −871.901 | −0.0818840 | ||||||||
\(485\) | 8146.00 | 0.762661 | ||||||||
\(486\) | −8.68485 | −0.000810603 0 | ||||||||
\(487\) | 15808.1 | 1.47091 | 0.735455 | − | 0.677574i | \(-0.236969\pi\) | ||||
0.735455 | + | 0.677574i | \(0.236969\pi\) | |||||||
\(488\) | 257.912 | 0.0239245 | ||||||||
\(489\) | 1169.72 | 0.108173 | ||||||||
\(490\) | −89.0223 | −0.00820739 | ||||||||
\(491\) | 279.729 | 0.0257108 | 0.0128554 | − | 0.999917i | \(-0.495908\pi\) | ||||
0.0128554 | + | 0.999917i | \(0.495908\pi\) | |||||||
\(492\) | −1487.58 | −0.136312 | ||||||||
\(493\) | 4136.42 | 0.377881 | ||||||||
\(494\) | −95.2645 | −0.00867642 | ||||||||
\(495\) | −2667.22 | −0.242187 | ||||||||
\(496\) | −10612.4 | −0.960706 | ||||||||
\(497\) | 5102.64 | 0.460533 | ||||||||
\(498\) | 42.1440 | 0.00379220 | ||||||||
\(499\) | −11541.3 | −1.03539 | −0.517695 | − | 0.855565i | \(-0.673210\pi\) | ||||
−0.517695 | + | 0.855565i | \(0.673210\pi\) | |||||||
\(500\) | −11806.9 | −1.05604 | ||||||||
\(501\) | −3953.44 | −0.352549 | ||||||||
\(502\) | 255.919 | 0.0227535 | ||||||||
\(503\) | −6614.84 | −0.586364 | −0.293182 | − | 0.956057i | \(-0.594714\pi\) | ||||
−0.293182 | + | 0.956057i | \(0.594714\pi\) | |||||||
\(504\) | 25.2426 | 0.00223094 | ||||||||
\(505\) | −11571.9 | −1.01969 | ||||||||
\(506\) | −12.9959 | −0.00114177 | ||||||||
\(507\) | −4370.26 | −0.382821 | ||||||||
\(508\) | −1187.09 | −0.103679 | ||||||||
\(509\) | 4802.47 | 0.418204 | 0.209102 | − | 0.977894i | \(-0.432946\pi\) | ||||
0.209102 | + | 0.977894i | \(0.432946\pi\) | |||||||
\(510\) | 53.0480 | 0.00460589 | ||||||||
\(511\) | −2598.53 | −0.224955 | ||||||||
\(512\) | −731.491 | −0.0631399 | ||||||||
\(513\) | 2645.15 | 0.227653 | ||||||||
\(514\) | 29.0601 | 0.00249375 | ||||||||
\(515\) | −477.549 | −0.0408608 | ||||||||
\(516\) | −1858.27 | −0.158538 | ||||||||
\(517\) | 7177.78 | 0.610597 | ||||||||
\(518\) | −37.8609 | −0.00321141 | ||||||||
\(519\) | −2465.52 | −0.208525 | ||||||||
\(520\) | −121.497 | −0.0102461 | ||||||||
\(521\) | −13950.7 | −1.17311 | −0.586557 | − | 0.809908i | \(-0.699517\pi\) | ||||
−0.586557 | + | 0.809908i | \(0.699517\pi\) | |||||||
\(522\) | −21.0023 | −0.00176101 | ||||||||
\(523\) | −4290.15 | −0.358690 | −0.179345 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179345 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(524\) | 4117.72 | 0.343289 | ||||||||
\(525\) | −941.912 | −0.0783017 | ||||||||
\(526\) | 112.058 | 0.00928891 | ||||||||
\(527\) | −10509.9 | −0.868725 | ||||||||
\(528\) | 7282.41 | 0.600239 | ||||||||
\(529\) | −12075.2 | −0.992453 | ||||||||
\(530\) | 155.760 | 0.0127656 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | −3843.77 | −0.313250 | ||||||||
\(533\) | 1686.66 | 0.137068 | ||||||||
\(534\) | 5.42115 | 0.000439318 0 | ||||||||
\(535\) | 8262.25 | 0.667679 | ||||||||
\(536\) | −417.575 | −0.0336502 | ||||||||
\(537\) | −1776.07 | −0.142724 | ||||||||
\(538\) | 159.378 | 0.0127719 | ||||||||
\(539\) | −12102.9 | −0.967180 | ||||||||
\(540\) | 1686.63 | 0.134409 | ||||||||
\(541\) | −11817.9 | −0.939173 | −0.469586 | − | 0.882887i | \(-0.655597\pi\) | ||||
−0.469586 | + | 0.882887i | \(0.655597\pi\) | |||||||
\(542\) | −198.614 | −0.0157402 | ||||||||
\(543\) | −2437.27 | −0.192621 | ||||||||
\(544\) | −434.632 | −0.0342550 | ||||||||
\(545\) | −6042.88 | −0.474952 | ||||||||
\(546\) | −14.3092 | −0.00112157 | ||||||||
\(547\) | 9698.77 | 0.758116 | 0.379058 | − | 0.925373i | \(-0.376248\pi\) | ||||
0.379058 | + | 0.925373i | \(0.376248\pi\) | |||||||
\(548\) | −17161.0 | −1.33774 | ||||||||
\(549\) | 4059.51 | 0.315584 | ||||||||
\(550\) | 86.8114 | 0.00673027 | ||||||||
\(551\) | 6396.68 | 0.494569 | ||||||||
\(552\) | 16.4373 | 0.00126742 | ||||||||
\(553\) | −4942.05 | −0.380031 | ||||||||
\(554\) | 129.324 | 0.00991779 | ||||||||
\(555\) | −5059.87 | −0.386990 | ||||||||
\(556\) | −7612.90 | −0.580682 | ||||||||
\(557\) | −12145.8 | −0.923939 | −0.461970 | − | 0.886896i | \(-0.652857\pi\) | ||||
−0.461970 | + | 0.886896i | \(0.652857\pi\) | |||||||
\(558\) | 53.3630 | 0.00404845 | ||||||||
\(559\) | 2106.95 | 0.159418 | ||||||||
\(560\) | −2450.51 | −0.184916 | ||||||||
\(561\) | 7212.08 | 0.542770 | ||||||||
\(562\) | 177.664 | 0.0133351 | ||||||||
\(563\) | 18085.9 | 1.35387 | 0.676935 | − | 0.736043i | \(-0.263308\pi\) | ||||
0.676935 | + | 0.736043i | \(0.263308\pi\) | |||||||
\(564\) | −4538.89 | −0.338869 | ||||||||
\(565\) | −1329.24 | −0.0989760 | ||||||||
\(566\) | 172.842 | 0.0128359 | ||||||||
\(567\) | 397.316 | 0.0294280 | ||||||||
\(568\) | 594.820 | 0.0439403 | ||||||||
\(569\) | 8313.29 | 0.612498 | 0.306249 | − | 0.951952i | \(-0.400926\pi\) | ||||
0.306249 | + | 0.951952i | \(0.400926\pi\) | |||||||
\(570\) | 82.0348 | 0.00602818 | ||||||||
\(571\) | −10880.3 | −0.797418 | −0.398709 | − | 0.917078i | \(-0.630542\pi\) | ||||
−0.398709 | + | 0.917078i | \(0.630542\pi\) | |||||||
\(572\) | −8258.30 | −0.603666 | ||||||||
\(573\) | 8464.60 | 0.617127 | ||||||||
\(574\) | −10.8679 | −0.000790276 0 | ||||||||
\(575\) | −613.346 | −0.0444840 | ||||||||
\(576\) | −4603.59 | −0.333014 | ||||||||
\(577\) | 680.956 | 0.0491310 | 0.0245655 | − | 0.999698i | \(-0.492180\pi\) | ||||
0.0245655 | + | 0.999698i | \(0.492180\pi\) | |||||||
\(578\) | 32.1512 | 0.00231369 | ||||||||
\(579\) | −6763.76 | −0.485479 | ||||||||
\(580\) | 4078.71 | 0.291999 | ||||||||
\(581\) | −1928.01 | −0.137672 | ||||||||
\(582\) | 111.837 | 0.00796532 | ||||||||
\(583\) | 21176.1 | 1.50433 | ||||||||
\(584\) | −302.913 | −0.0214634 | ||||||||
\(585\) | −1912.34 | −0.135155 | ||||||||
\(586\) | 216.637 | 0.0152716 | ||||||||
\(587\) | −2603.48 | −0.183062 | −0.0915309 | − | 0.995802i | \(-0.529176\pi\) | ||||
−0.0915309 | + | 0.995802i | \(0.529176\pi\) | |||||||
\(588\) | 7653.33 | 0.536765 | ||||||||
\(589\) | −16252.8 | −1.13699 | ||||||||
\(590\) | 16.4681 | 0.00114912 | ||||||||
\(591\) | −6057.09 | −0.421583 | ||||||||
\(592\) | 13815.1 | 0.959120 | ||||||||
\(593\) | 25521.8 | 1.76737 | 0.883687 | − | 0.468078i | \(-0.155054\pi\) | ||||
0.883687 | + | 0.468078i | \(0.155054\pi\) | |||||||
\(594\) | −36.6186 | −0.00252943 | ||||||||
\(595\) | −2426.84 | −0.167212 | ||||||||
\(596\) | 18904.1 | 1.29923 | ||||||||
\(597\) | 4514.44 | 0.309487 | ||||||||
\(598\) | −9.31775 | −0.000637176 0 | ||||||||
\(599\) | −2552.55 | −0.174114 | −0.0870570 | − | 0.996203i | \(-0.527746\pi\) | ||||
−0.0870570 | + | 0.996203i | \(0.527746\pi\) | |||||||
\(600\) | −109.800 | −0.00747092 | ||||||||
\(601\) | 18890.3 | 1.28211 | 0.641057 | − | 0.767493i | \(-0.278496\pi\) | ||||
0.641057 | + | 0.767493i | \(0.278496\pi\) | |||||||
\(602\) | −13.5760 | −0.000919133 0 | ||||||||
\(603\) | −6572.58 | −0.443874 | ||||||||
\(604\) | −16373.7 | −1.10304 | ||||||||
\(605\) | −851.297 | −0.0572068 | ||||||||
\(606\) | −158.872 | −0.0106497 | ||||||||
\(607\) | 8916.27 | 0.596211 | 0.298106 | − | 0.954533i | \(-0.403645\pi\) | ||||
0.298106 | + | 0.954533i | \(0.403645\pi\) | |||||||
\(608\) | −672.127 | −0.0448328 | ||||||||
\(609\) | 960.815 | 0.0639314 | ||||||||
\(610\) | 125.899 | 0.00835654 | ||||||||
\(611\) | 5146.31 | 0.340749 | ||||||||
\(612\) | −4560.58 | −0.301226 | ||||||||
\(613\) | 7796.34 | 0.513689 | 0.256844 | − | 0.966453i | \(-0.417317\pi\) | ||||
0.256844 | + | 0.966453i | \(0.417317\pi\) | |||||||
\(614\) | 136.089 | 0.00894481 | ||||||||
\(615\) | −1452.43 | −0.0952319 | ||||||||
\(616\) | 106.432 | 0.00696150 | ||||||||
\(617\) | −27806.2 | −1.81432 | −0.907161 | − | 0.420784i | \(-0.861755\pi\) | ||||
−0.907161 | + | 0.420784i | \(0.861755\pi\) | |||||||
\(618\) | −6.55633 | −0.000426755 0 | ||||||||
\(619\) | 11643.6 | 0.756050 | 0.378025 | − | 0.925795i | \(-0.376603\pi\) | ||||
0.378025 | + | 0.925795i | \(0.376603\pi\) | |||||||
\(620\) | −10363.3 | −0.671287 | ||||||||
\(621\) | 258.720 | 0.0167183 | ||||||||
\(622\) | −272.817 | −0.0175867 | ||||||||
\(623\) | −248.007 | −0.0159490 | ||||||||
\(624\) | 5221.33 | 0.334969 | ||||||||
\(625\) | −3526.82 | −0.225716 | ||||||||
\(626\) | 211.628 | 0.0135118 | ||||||||
\(627\) | 11153.0 | 0.710376 | ||||||||
\(628\) | −14231.1 | −0.904272 | ||||||||
\(629\) | 13681.7 | 0.867291 | ||||||||
\(630\) | 12.3221 | 0.000779243 0 | ||||||||
\(631\) | −2815.28 | −0.177614 | −0.0888070 | − | 0.996049i | \(-0.528305\pi\) | ||||
−0.0888070 | + | 0.996049i | \(0.528305\pi\) | |||||||
\(632\) | −576.100 | −0.0362595 | ||||||||
\(633\) | 5367.26 | 0.337013 | ||||||||
\(634\) | 62.4765 | 0.00391366 | ||||||||
\(635\) | −1159.04 | −0.0724333 | ||||||||
\(636\) | −13390.8 | −0.834874 | ||||||||
\(637\) | −8677.54 | −0.539744 | ||||||||
\(638\) | −88.5536 | −0.00549509 | ||||||||
\(639\) | 9362.39 | 0.579609 | ||||||||
\(640\) | −571.409 | −0.0352921 | ||||||||
\(641\) | 19548.3 | 1.20454 | 0.602271 | − | 0.798292i | \(-0.294263\pi\) | ||||
0.602271 | + | 0.798292i | \(0.294263\pi\) | |||||||
\(642\) | 113.434 | 0.00697331 | ||||||||
\(643\) | 20675.9 | 1.26808 | 0.634041 | − | 0.773300i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773300i | \(0.281395\pi\) | |||||||
\(644\) | −375.957 | −0.0230043 | ||||||||
\(645\) | −1814.35 | −0.110760 | ||||||||
\(646\) | −221.820 | −0.0135099 | ||||||||
\(647\) | 19267.9 | 1.17078 | 0.585392 | − | 0.810750i | \(-0.300941\pi\) | ||||
0.585392 | + | 0.810750i | \(0.300941\pi\) | |||||||
\(648\) | 46.3155 | 0.00280779 | ||||||||
\(649\) | 2238.90 | 0.135415 | ||||||||
\(650\) | 62.2419 | 0.00375589 | ||||||||
\(651\) | −2441.25 | −0.146974 | ||||||||
\(652\) | −3118.76 | −0.187332 | ||||||||
\(653\) | 17386.3 | 1.04193 | 0.520963 | − | 0.853579i | \(-0.325573\pi\) | ||||
0.520963 | + | 0.853579i | \(0.325573\pi\) | |||||||
\(654\) | −82.9635 | −0.00496045 | ||||||||
\(655\) | 4020.41 | 0.239833 | ||||||||
\(656\) | 3965.62 | 0.236024 | ||||||||
\(657\) | −4767.81 | −0.283120 | ||||||||
\(658\) | −33.1600 | −0.00196461 | ||||||||
\(659\) | −15986.9 | −0.945007 | −0.472504 | − | 0.881329i | \(-0.656650\pi\) | ||||
−0.472504 | + | 0.881329i | \(0.656650\pi\) | |||||||
\(660\) | 7111.45 | 0.419413 | ||||||||
\(661\) | 14387.2 | 0.846592 | 0.423296 | − | 0.905991i | \(-0.360873\pi\) | ||||
0.423296 | + | 0.905991i | \(0.360873\pi\) | |||||||
\(662\) | −387.890 | −0.0227731 | ||||||||
\(663\) | 5170.90 | 0.302898 | ||||||||
\(664\) | −224.750 | −0.0131355 | ||||||||
\(665\) | −3752.94 | −0.218846 | ||||||||
\(666\) | −69.4676 | −0.00404176 | ||||||||
\(667\) | 625.655 | 0.0363200 | ||||||||
\(668\) | 10540.8 | 0.610535 | ||||||||
\(669\) | −5561.70 | −0.321417 | ||||||||
\(670\) | −203.837 | −0.0117536 | ||||||||
\(671\) | 17116.4 | 0.984757 | ||||||||
\(672\) | −100.957 | −0.00579539 | ||||||||
\(673\) | −21373.2 | −1.22418 | −0.612092 | − | 0.790787i | \(-0.709672\pi\) | ||||
−0.612092 | + | 0.790787i | \(0.709672\pi\) | |||||||
\(674\) | −320.796 | −0.0183333 | ||||||||
\(675\) | −1728.23 | −0.0985477 | ||||||||
\(676\) | 11652.2 | 0.662959 | ||||||||
\(677\) | 13150.7 | 0.746564 | 0.373282 | − | 0.927718i | \(-0.378232\pi\) | ||||
0.373282 | + | 0.927718i | \(0.378232\pi\) | |||||||
\(678\) | −18.2493 | −0.00103372 | ||||||||
\(679\) | −5116.36 | −0.289172 | ||||||||
\(680\) | −282.900 | −0.0159540 | ||||||||
\(681\) | 6341.13 | 0.356817 | ||||||||
\(682\) | 224.998 | 0.0126329 | ||||||||
\(683\) | 14825.3 | 0.830563 | 0.415282 | − | 0.909693i | \(-0.363683\pi\) | ||||
0.415282 | + | 0.909693i | \(0.363683\pi\) | |||||||
\(684\) | −7052.61 | −0.394244 | ||||||||
\(685\) | −16755.4 | −0.934587 | ||||||||
\(686\) | 116.045 | 0.00645861 | ||||||||
\(687\) | −2981.85 | −0.165596 | ||||||||
\(688\) | 4953.80 | 0.274508 | ||||||||
\(689\) | 15182.8 | 0.839506 | ||||||||
\(690\) | 8.02377 | 0.000442695 0 | ||||||||
\(691\) | −7056.59 | −0.388488 | −0.194244 | − | 0.980953i | \(-0.562225\pi\) | ||||
−0.194244 | + | 0.980953i | \(0.562225\pi\) | |||||||
\(692\) | 6573.68 | 0.361118 | ||||||||
\(693\) | 1675.23 | 0.0918280 | ||||||||
\(694\) | −223.022 | −0.0121985 | ||||||||
\(695\) | −7433.00 | −0.405683 | ||||||||
\(696\) | 112.003 | 0.00609982 | ||||||||
\(697\) | 3927.32 | 0.213426 | ||||||||
\(698\) | 449.087 | 0.0243527 | ||||||||
\(699\) | 5948.46 | 0.321876 | ||||||||
\(700\) | 2511.36 | 0.135601 | ||||||||
\(701\) | −15864.1 | −0.854751 | −0.427376 | − | 0.904074i | \(-0.640562\pi\) | ||||
−0.427376 | + | 0.904074i | \(0.640562\pi\) | |||||||
\(702\) | −26.2548 | −0.00141157 | ||||||||
\(703\) | 21157.8 | 1.13511 | ||||||||
\(704\) | −19410.5 | −1.03915 | ||||||||
\(705\) | −4431.63 | −0.236745 | ||||||||
\(706\) | −172.449 | −0.00919292 | ||||||||
\(707\) | 7268.11 | 0.386627 | ||||||||
\(708\) | −1415.77 | −0.0751526 | ||||||||
\(709\) | −9641.46 | −0.510709 | −0.255354 | − | 0.966848i | \(-0.582192\pi\) | ||||
−0.255354 | + | 0.966848i | \(0.582192\pi\) | |||||||
\(710\) | 290.359 | 0.0153478 | ||||||||
\(711\) | −9067.74 | −0.478294 | ||||||||
\(712\) | −28.9105 | −0.00152172 | ||||||||
\(713\) | −1589.67 | −0.0834976 | ||||||||
\(714\) | −33.3185 | −0.00174638 | ||||||||
\(715\) | −8063.14 | −0.421741 | ||||||||
\(716\) | 4735.43 | 0.247167 | ||||||||
\(717\) | −12558.5 | −0.654121 | ||||||||
\(718\) | 104.355 | 0.00542409 | ||||||||
\(719\) | −31356.7 | −1.62644 | −0.813218 | − | 0.581959i | \(-0.802286\pi\) | ||||
−0.813218 | + | 0.581959i | \(0.802286\pi\) | |||||||
\(720\) | −4496.23 | −0.232729 | ||||||||
\(721\) | 299.940 | 0.0154929 | ||||||||
\(722\) | −97.8863 | −0.00504564 | ||||||||
\(723\) | 1365.94 | 0.0702623 | ||||||||
\(724\) | 6498.36 | 0.333577 | ||||||||
\(725\) | −4179.33 | −0.214092 | ||||||||
\(726\) | −11.6876 | −0.000597474 0 | ||||||||
\(727\) | 25527.1 | 1.30227 | 0.651133 | − | 0.758964i | \(-0.274294\pi\) | ||||
0.651133 | + | 0.758964i | \(0.274294\pi\) | |||||||
\(728\) | 76.3098 | 0.00388493 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −147.865 | −0.00749691 | ||||||||
\(731\) | 4905.95 | 0.248226 | ||||||||
\(732\) | −10823.6 | −0.546520 | ||||||||
\(733\) | 32735.8 | 1.64956 | 0.824779 | − | 0.565456i | \(-0.191300\pi\) | ||||
0.824779 | + | 0.565456i | \(0.191300\pi\) | |||||||
\(734\) | 331.266 | 0.0166584 | ||||||||
\(735\) | 7472.47 | 0.375002 | ||||||||
\(736\) | −65.7403 | −0.00329242 | ||||||||
\(737\) | −27712.5 | −1.38508 | ||||||||
\(738\) | −19.9406 | −0.000994612 0 | ||||||||
\(739\) | 26530.4 | 1.32062 | 0.660308 | − | 0.750995i | \(-0.270426\pi\) | ||||
0.660308 | + | 0.750995i | \(0.270426\pi\) | |||||||
\(740\) | 13490.8 | 0.670179 | ||||||||
\(741\) | 7996.43 | 0.396432 | ||||||||
\(742\) | −97.8299 | −0.00484023 | ||||||||
\(743\) | −25269.1 | −1.24769 | −0.623845 | − | 0.781548i | \(-0.714430\pi\) | ||||
−0.623845 | + | 0.781548i | \(0.714430\pi\) | |||||||
\(744\) | −284.580 | −0.0140231 | ||||||||
\(745\) | 18457.3 | 0.907683 | ||||||||
\(746\) | −232.702 | −0.0114207 | ||||||||
\(747\) | −3537.53 | −0.173268 | ||||||||
\(748\) | −19229.1 | −0.939956 | ||||||||
\(749\) | −5189.37 | −0.253158 | ||||||||
\(750\) | −158.268 | −0.00770551 | ||||||||
\(751\) | 34954.2 | 1.69840 | 0.849199 | − | 0.528072i | \(-0.177085\pi\) | ||||
0.849199 | + | 0.528072i | \(0.177085\pi\) | |||||||
\(752\) | 12099.9 | 0.586750 | ||||||||
\(753\) | −21481.7 | −1.03962 | ||||||||
\(754\) | −63.4910 | −0.00306659 | ||||||||
\(755\) | −15986.8 | −0.770620 | ||||||||
\(756\) | −1059.34 | −0.0509627 | ||||||||
\(757\) | 38062.0 | 1.82746 | 0.913730 | − | 0.406322i | \(-0.133189\pi\) | ||||
0.913730 | + | 0.406322i | \(0.133189\pi\) | |||||||
\(758\) | 73.9268 | 0.00354241 | ||||||||
\(759\) | 1090.86 | 0.0521684 | ||||||||
\(760\) | −437.484 | −0.0208806 | ||||||||
\(761\) | −6796.71 | −0.323759 | −0.161879 | − | 0.986811i | \(-0.551756\pi\) | ||||
−0.161879 | + | 0.986811i | \(0.551756\pi\) | |||||||
\(762\) | −15.9126 | −0.000756501 0 | ||||||||
\(763\) | 3795.43 | 0.180083 | ||||||||
\(764\) | −22568.7 | −1.06872 | ||||||||
\(765\) | −4452.81 | −0.210446 | ||||||||
\(766\) | −438.120 | −0.0206657 | ||||||||
\(767\) | 1605.24 | 0.0755696 | ||||||||
\(768\) | 12268.4 | 0.576429 | ||||||||
\(769\) | −34493.8 | −1.61753 | −0.808763 | − | 0.588135i | \(-0.799862\pi\) | ||||
−0.808763 | + | 0.588135i | \(0.799862\pi\) | |||||||
\(770\) | 51.9545 | 0.00243157 | ||||||||
\(771\) | −2439.28 | −0.113941 | ||||||||
\(772\) | 18033.8 | 0.840740 | ||||||||
\(773\) | 17764.5 | 0.826576 | 0.413288 | − | 0.910600i | \(-0.364380\pi\) | ||||
0.413288 | + | 0.910600i | \(0.364380\pi\) | |||||||
\(774\) | −24.9095 | −0.00115679 | ||||||||
\(775\) | 10618.9 | 0.492184 | ||||||||
\(776\) | −596.419 | −0.0275905 | ||||||||
\(777\) | 3178.01 | 0.146732 | ||||||||
\(778\) | 156.894 | 0.00722997 | ||||||||
\(779\) | 6073.32 | 0.279332 | ||||||||
\(780\) | 5098.76 | 0.234057 | ||||||||
\(781\) | 39475.4 | 1.80863 | ||||||||
\(782\) | −21.6960 | −0.000992133 0 | ||||||||
\(783\) | 1762.92 | 0.0804617 | ||||||||
\(784\) | −20402.4 | −0.929408 | ||||||||
\(785\) | −13894.8 | −0.631753 | ||||||||
\(786\) | 55.1967 | 0.00250484 | ||||||||
\(787\) | 15912.1 | 0.720717 | 0.360359 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360359 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(788\) | 16149.7 | 0.730086 | ||||||||
\(789\) | −9406.08 | −0.424417 | ||||||||
\(790\) | −281.220 | −0.0126650 | ||||||||
\(791\) | 834.870 | 0.0375279 | ||||||||
\(792\) | 195.284 | 0.00876150 | ||||||||
\(793\) | 12272.1 | 0.549552 | ||||||||
\(794\) | −161.457 | −0.00721650 | ||||||||
\(795\) | −13074.4 | −0.583270 | ||||||||
\(796\) | −12036.6 | −0.535961 | ||||||||
\(797\) | −11535.5 | −0.512685 | −0.256343 | − | 0.966586i | \(-0.582517\pi\) | ||||
−0.256343 | + | 0.966586i | \(0.582517\pi\) | |||||||
\(798\) | −51.5246 | −0.00228565 | ||||||||
\(799\) | 11983.0 | 0.530573 | ||||||||
\(800\) | 439.140 | 0.0194074 | ||||||||
\(801\) | −455.047 | −0.0200728 | ||||||||
\(802\) | 155.607 | 0.00685120 | ||||||||
\(803\) | −20102.9 | −0.883456 | ||||||||
\(804\) | 17524.1 | 0.768690 | ||||||||
\(805\) | −367.072 | −0.0160716 | ||||||||
\(806\) | 161.319 | 0.00704990 | ||||||||
\(807\) | −13378.1 | −0.583559 | ||||||||
\(808\) | 847.251 | 0.0368888 | ||||||||
\(809\) | −43528.4 | −1.89169 | −0.945846 | − | 0.324616i | \(-0.894765\pi\) | ||||
−0.945846 | + | 0.324616i | \(0.894765\pi\) | |||||||
\(810\) | 22.6087 | 0.000980726 0 | ||||||||
\(811\) | −7310.19 | −0.316517 | −0.158259 | − | 0.987398i | \(-0.550588\pi\) | ||||
−0.158259 | + | 0.987398i | \(0.550588\pi\) | |||||||
\(812\) | −2561.77 | −0.110715 | ||||||||
\(813\) | 16671.5 | 0.719182 | ||||||||
\(814\) | −292.902 | −0.0126120 | ||||||||
\(815\) | −3045.06 | −0.130876 | ||||||||
\(816\) | 12157.7 | 0.521573 | ||||||||
\(817\) | 7586.70 | 0.324878 | ||||||||
\(818\) | 442.558 | 0.0189165 | ||||||||
\(819\) | 1201.11 | 0.0512455 | ||||||||
\(820\) | 3872.53 | 0.164920 | ||||||||
\(821\) | 14986.7 | 0.637076 | 0.318538 | − | 0.947910i | \(-0.396808\pi\) | ||||
0.318538 | + | 0.947910i | \(0.396808\pi\) | |||||||
\(822\) | −230.038 | −0.00976093 | ||||||||
\(823\) | −25042.3 | −1.06066 | −0.530328 | − | 0.847792i | \(-0.677931\pi\) | ||||
−0.530328 | + | 0.847792i | \(0.677931\pi\) | |||||||
\(824\) | 34.9643 | 0.00147820 | ||||||||
\(825\) | −7286.88 | −0.307511 | ||||||||
\(826\) | −10.3433 | −0.000435701 0 | ||||||||
\(827\) | −31526.4 | −1.32561 | −0.662806 | − | 0.748791i | \(-0.730635\pi\) | ||||
−0.662806 | + | 0.748791i | \(0.730635\pi\) | |||||||
\(828\) | −689.811 | −0.0289524 | ||||||||
\(829\) | −27719.8 | −1.16134 | −0.580668 | − | 0.814141i | \(-0.697208\pi\) | ||||
−0.580668 | + | 0.814141i | \(0.697208\pi\) | |||||||
\(830\) | −109.711 | −0.00458808 | ||||||||
\(831\) | −10855.4 | −0.453151 | ||||||||
\(832\) | −13916.9 | −0.579905 | ||||||||
\(833\) | −20205.3 | −0.840423 | ||||||||
\(834\) | −102.049 | −0.00423700 | ||||||||
\(835\) | 10291.7 | 0.426539 | ||||||||
\(836\) | −29736.5 | −1.23021 | ||||||||
\(837\) | −4479.25 | −0.184977 | ||||||||
\(838\) | −81.2375 | −0.00334881 | ||||||||
\(839\) | 29512.0 | 1.21438 | 0.607192 | − | 0.794555i | \(-0.292296\pi\) | ||||
0.607192 | + | 0.794555i | \(0.292296\pi\) | |||||||
\(840\) | −65.7124 | −0.00269916 | ||||||||
\(841\) | −20125.8 | −0.825200 | ||||||||
\(842\) | 424.242 | 0.0173638 | ||||||||
\(843\) | −14913.0 | −0.609290 | ||||||||
\(844\) | −14310.4 | −0.583631 | ||||||||
\(845\) | 11376.8 | 0.463165 | ||||||||
\(846\) | −60.8425 | −0.00247259 | ||||||||
\(847\) | 534.684 | 0.0216906 | ||||||||
\(848\) | 35697.4 | 1.44558 | ||||||||
\(849\) | −14508.3 | −0.586481 | ||||||||
\(850\) | 144.928 | 0.00584821 | ||||||||
\(851\) | 2069.43 | 0.0833597 | ||||||||
\(852\) | −24962.4 | −1.00375 | ||||||||
\(853\) | −26933.2 | −1.08109 | −0.540547 | − | 0.841314i | \(-0.681783\pi\) | ||||
−0.540547 | + | 0.841314i | \(0.681783\pi\) | |||||||
\(854\) | −79.0747 | −0.00316848 | ||||||||
\(855\) | −6885.94 | −0.275432 | ||||||||
\(856\) | −604.931 | −0.0241543 | ||||||||
\(857\) | 26634.2 | 1.06162 | 0.530809 | − | 0.847491i | \(-0.321888\pi\) | ||||
0.530809 | + | 0.847491i | \(0.321888\pi\) | |||||||
\(858\) | −110.700 | −0.00440470 | ||||||||
\(859\) | −6411.56 | −0.254668 | −0.127334 | − | 0.991860i | \(-0.540642\pi\) | ||||
−0.127334 | + | 0.991860i | \(0.540642\pi\) | |||||||
\(860\) | 4837.50 | 0.191811 | ||||||||
\(861\) | 912.245 | 0.0361083 | ||||||||
\(862\) | 537.019 | 0.0212192 | ||||||||
\(863\) | −20915.9 | −0.825011 | −0.412505 | − | 0.910955i | \(-0.635346\pi\) | ||||
−0.412505 | + | 0.910955i | \(0.635346\pi\) | |||||||
\(864\) | −185.237 | −0.00729387 | ||||||||
\(865\) | 6418.33 | 0.252289 | ||||||||
\(866\) | 580.827 | 0.0227913 | ||||||||
\(867\) | −2698.75 | −0.105714 | ||||||||
\(868\) | 6508.97 | 0.254526 | ||||||||
\(869\) | −38233.0 | −1.49248 | ||||||||
\(870\) | 54.6739 | 0.00213059 | ||||||||
\(871\) | −19869.3 | −0.772955 | ||||||||
\(872\) | 442.437 | 0.0171821 | ||||||||
\(873\) | −9387.56 | −0.363941 | ||||||||
\(874\) | −33.5513 | −0.00129850 | ||||||||
\(875\) | 7240.47 | 0.279740 | ||||||||
\(876\) | 12712.1 | 0.490300 | ||||||||
\(877\) | −14800.0 | −0.569852 | −0.284926 | − | 0.958549i | \(-0.591969\pi\) | ||||
−0.284926 | + | 0.958549i | \(0.591969\pi\) | |||||||
\(878\) | −103.107 | −0.00396322 | ||||||||
\(879\) | −18184.3 | −0.697772 | ||||||||
\(880\) | −18957.8 | −0.726213 | ||||||||
\(881\) | 25932.2 | 0.991690 | 0.495845 | − | 0.868411i | \(-0.334858\pi\) | ||||
0.495845 | + | 0.868411i | \(0.334858\pi\) | |||||||
\(882\) | 102.591 | 0.00391656 | ||||||||
\(883\) | 20302.7 | 0.773772 | 0.386886 | − | 0.922128i | \(-0.373551\pi\) | ||||
0.386886 | + | 0.922128i | \(0.373551\pi\) | |||||||
\(884\) | −13786.9 | −0.524551 | ||||||||
\(885\) | −1382.32 | −0.0525040 | ||||||||
\(886\) | −339.366 | −0.0128682 | ||||||||
\(887\) | −39704.8 | −1.50299 | −0.751497 | − | 0.659736i | \(-0.770668\pi\) | ||||
−0.751497 | + | 0.659736i | \(0.770668\pi\) | |||||||
\(888\) | 370.464 | 0.0140000 | ||||||||
\(889\) | 727.973 | 0.0274639 | ||||||||
\(890\) | −14.1125 | −0.000531519 0 | ||||||||
\(891\) | 3073.74 | 0.115571 | ||||||||
\(892\) | 14828.8 | 0.556621 | ||||||||
\(893\) | 18530.8 | 0.694413 | ||||||||
\(894\) | 253.403 | 0.00947994 | ||||||||
\(895\) | 4623.52 | 0.172678 | ||||||||
\(896\) | 358.892 | 0.0133814 | ||||||||
\(897\) | 782.125 | 0.0291130 | ||||||||
\(898\) | −305.226 | −0.0113424 | ||||||||
\(899\) | −10832.0 | −0.401855 | ||||||||
\(900\) | 4607.88 | 0.170662 | ||||||||
\(901\) | 35352.6 | 1.30718 | ||||||||
\(902\) | −84.0771 | −0.00310362 | ||||||||
\(903\) | 1139.56 | 0.0419959 | ||||||||
\(904\) | 97.3217 | 0.00358061 | ||||||||
\(905\) | 6344.79 | 0.233047 | ||||||||
\(906\) | −219.485 | −0.00804844 | ||||||||
\(907\) | −23723.8 | −0.868507 | −0.434254 | − | 0.900791i | \(-0.642988\pi\) | ||||
−0.434254 | + | 0.900791i | \(0.642988\pi\) | |||||||
\(908\) | −16907.0 | −0.617927 | ||||||||
\(909\) | 13335.6 | 0.486595 | ||||||||
\(910\) | 37.2503 | 0.00135696 | ||||||||
\(911\) | −23515.4 | −0.855212 | −0.427606 | − | 0.903965i | \(-0.640643\pi\) | ||||
−0.427606 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(912\) | 18800.9 | 0.682633 | ||||||||
\(913\) | −14915.6 | −0.540672 | ||||||||
\(914\) | 256.181 | 0.00927102 | ||||||||
\(915\) | −10567.8 | −0.381816 | ||||||||
\(916\) | 7950.34 | 0.286776 | ||||||||
\(917\) | −2525.15 | −0.0909353 | ||||||||
\(918\) | −61.1332 | −0.00219793 | ||||||||
\(919\) | 4610.25 | 0.165482 | 0.0827411 | − | 0.996571i | \(-0.473633\pi\) | ||||
0.0827411 | + | 0.996571i | \(0.473633\pi\) | |||||||
\(920\) | −42.7900 | −0.00153342 | ||||||||
\(921\) | −11423.2 | −0.408695 | ||||||||
\(922\) | 181.974 | 0.00649999 | ||||||||
\(923\) | 28303.0 | 1.00932 | ||||||||
\(924\) | −4466.57 | −0.159025 | ||||||||
\(925\) | −13823.6 | −0.491371 | ||||||||
\(926\) | −352.775 | −0.0125193 | ||||||||
\(927\) | 550.334 | 0.0194987 | ||||||||
\(928\) | −447.954 | −0.0158457 | ||||||||
\(929\) | 34994.2 | 1.23587 | 0.617935 | − | 0.786229i | \(-0.287969\pi\) | ||||
0.617935 | + | 0.786229i | \(0.287969\pi\) | |||||||
\(930\) | −138.916 | −0.00489811 | ||||||||
\(931\) | −31246.1 | −1.09994 | ||||||||
\(932\) | −15860.0 | −0.557416 | ||||||||
\(933\) | 22900.0 | 0.803551 | ||||||||
\(934\) | 593.292 | 0.0207849 | ||||||||
\(935\) | −18774.7 | −0.656683 | ||||||||
\(936\) | 140.014 | 0.00488943 | ||||||||
\(937\) | 50967.1 | 1.77697 | 0.888485 | − | 0.458905i | \(-0.151758\pi\) | ||||
0.888485 | + | 0.458905i | \(0.151758\pi\) | |||||||
\(938\) | 128.027 | 0.00445652 | ||||||||
\(939\) | −17763.9 | −0.617362 | ||||||||
\(940\) | 11815.8 | 0.409988 | ||||||||
\(941\) | −34297.5 | −1.18817 | −0.594084 | − | 0.804403i | \(-0.702485\pi\) | ||||
−0.594084 | + | 0.804403i | \(0.702485\pi\) | |||||||
\(942\) | −190.764 | −0.00659810 | ||||||||
\(943\) | 594.027 | 0.0205135 | ||||||||
\(944\) | 3774.19 | 0.130127 | ||||||||
\(945\) | −1034.31 | −0.0356042 | ||||||||
\(946\) | −105.028 | −0.00360967 | ||||||||
\(947\) | 15651.4 | 0.537066 | 0.268533 | − | 0.963270i | \(-0.413461\pi\) | ||||
0.268533 | + | 0.963270i | \(0.413461\pi\) | |||||||
\(948\) | 24176.8 | 0.828297 | ||||||||
\(949\) | −14413.3 | −0.493021 | ||||||||
\(950\) | 224.120 | 0.00765413 | ||||||||
\(951\) | −5244.23 | −0.178818 | ||||||||
\(952\) | 177.684 | 0.00604914 | ||||||||
\(953\) | 44875.1 | 1.52534 | 0.762669 | − | 0.646789i | \(-0.223889\pi\) | ||||
0.762669 | + | 0.646789i | \(0.223889\pi\) | |||||||
\(954\) | −179.500 | −0.00609173 | ||||||||
\(955\) | −22035.3 | −0.746645 | ||||||||
\(956\) | 33483.9 | 1.13279 | ||||||||
\(957\) | 7433.12 | 0.251075 | ||||||||
\(958\) | −410.169 | −0.0138329 | ||||||||
\(959\) | 10523.8 | 0.354360 | ||||||||
\(960\) | 11984.2 | 0.402905 | ||||||||
\(961\) | −2268.85 | −0.0761589 | ||||||||
\(962\) | −210.004 | −0.00703826 | ||||||||
\(963\) | −9521.53 | −0.318616 | ||||||||
\(964\) | −3641.91 | −0.121679 | ||||||||
\(965\) | 17607.7 | 0.587368 | ||||||||
\(966\) | −5.03959 | −0.000167853 0 | ||||||||
\(967\) | −53906.6 | −1.79268 | −0.896338 | − | 0.443371i | \(-0.853783\pi\) | ||||
−0.896338 | + | 0.443371i | \(0.853783\pi\) | |||||||
\(968\) | 62.3287 | 0.00206955 | ||||||||
\(969\) | 18619.4 | 0.617276 | ||||||||
\(970\) | −291.139 | −0.00963702 | ||||||||
\(971\) | −15575.1 | −0.514755 | −0.257378 | − | 0.966311i | \(-0.582858\pi\) | ||||
−0.257378 | + | 0.966311i | \(0.582858\pi\) | |||||||
\(972\) | −1943.69 | −0.0641398 | ||||||||
\(973\) | 4668.53 | 0.153819 | ||||||||
\(974\) | −564.983 | −0.0185865 | ||||||||
\(975\) | −5224.54 | −0.171609 | ||||||||
\(976\) | 28853.8 | 0.946298 | ||||||||
\(977\) | −20898.7 | −0.684348 | −0.342174 | − | 0.939637i | \(-0.611163\pi\) | ||||
−0.342174 | + | 0.939637i | \(0.611163\pi\) | |||||||
\(978\) | −41.8061 | −0.00136688 | ||||||||
\(979\) | −1918.65 | −0.0626357 | ||||||||
\(980\) | −19923.4 | −0.649418 | ||||||||
\(981\) | 6963.90 | 0.226646 | ||||||||
\(982\) | −9.99756 | −0.000324883 0 | ||||||||
\(983\) | 54689.4 | 1.77449 | 0.887243 | − | 0.461303i | \(-0.152618\pi\) | ||||
0.887243 | + | 0.461303i | \(0.152618\pi\) | |||||||
\(984\) | 106.341 | 0.00344516 | ||||||||
\(985\) | 15768.0 | 0.510062 | ||||||||
\(986\) | −147.836 | −0.00477492 | ||||||||
\(987\) | 2783.43 | 0.0897645 | ||||||||
\(988\) | −21320.4 | −0.686531 | ||||||||
\(989\) | 742.050 | 0.0238583 | ||||||||
\(990\) | 95.3268 | 0.00306029 | ||||||||
\(991\) | −14912.4 | −0.478011 | −0.239005 | − | 0.971018i | \(-0.576821\pi\) | ||||
−0.239005 | + | 0.971018i | \(0.576821\pi\) | |||||||
\(992\) | 1138.17 | 0.0364283 | ||||||||
\(993\) | 32559.2 | 1.04052 | ||||||||
\(994\) | −182.369 | −0.00581931 | ||||||||
\(995\) | −11752.1 | −0.374440 | ||||||||
\(996\) | 9431.91 | 0.300062 | ||||||||
\(997\) | 20492.3 | 0.650951 | 0.325475 | − | 0.945550i | \(-0.394476\pi\) | ||||
0.325475 | + | 0.945550i | \(0.394476\pi\) | |||||||
\(998\) | 412.488 | 0.0130832 | ||||||||
\(999\) | 5831.06 | 0.184671 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.4.a.d.1.4 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.e.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.d.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.e.1.5 | 8 | 3.2 | odd | 2 |