Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9814581.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 66x^{2} + 271x - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.60967\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −1.29416 | −0.115753 | −0.0578764 | − | 0.998324i | \(-0.518433\pi\) | ||||
−0.0578764 | + | 0.998324i | \(0.518433\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −2.58831 | −0.0818496 | ||||||||
\(11\) | −49.0162 | −1.34354 | −0.671770 | − | 0.740760i | \(-0.734466\pi\) | ||||
−0.671770 | + | 0.740760i | \(0.734466\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 82.4110 | 1.75821 | 0.879104 | − | 0.476631i | \(-0.158142\pi\) | ||||
0.879104 | + | 0.476631i | \(0.158142\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 3.88247 | 0.0668299 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −90.3504 | −1.28901 | −0.644506 | − | 0.764600i | \(-0.722937\pi\) | ||||
−0.644506 | + | 0.764600i | \(0.722937\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −80.5815 | −0.972982 | −0.486491 | − | 0.873685i | \(-0.661723\pi\) | ||||
−0.486491 | + | 0.873685i | \(0.661723\pi\) | |||||||
\(20\) | −5.17663 | −0.0578764 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −98.0324 | −0.950027 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −123.325 | −0.986601 | ||||||||
\(26\) | 164.822 | 1.24324 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −141.887 | −0.908545 | −0.454272 | − | 0.890863i | \(-0.650101\pi\) | ||||
−0.454272 | + | 0.890863i | \(0.650101\pi\) | |||||||
\(30\) | 7.76494 | 0.0472559 | ||||||||
\(31\) | 94.3956 | 0.546902 | 0.273451 | − | 0.961886i | \(-0.411835\pi\) | ||||
0.273451 | + | 0.961886i | \(0.411835\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 147.049 | 0.775693 | ||||||||
\(34\) | −180.701 | −0.911469 | ||||||||
\(35\) | −9.05909 | −0.0437505 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 445.105 | 1.97770 | 0.988848 | − | 0.148927i | \(-0.0475819\pi\) | ||||
0.988848 | + | 0.148927i | \(0.0475819\pi\) | |||||||
\(38\) | −161.163 | −0.688002 | ||||||||
\(39\) | −247.233 | −1.01510 | ||||||||
\(40\) | −10.3533 | −0.0409248 | ||||||||
\(41\) | 37.5069 | 0.142868 | 0.0714340 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714340 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 256.931 | 0.911199 | 0.455600 | − | 0.890185i | \(-0.349425\pi\) | ||||
0.455600 | + | 0.890185i | \(0.349425\pi\) | |||||||
\(44\) | −196.065 | −0.671770 | ||||||||
\(45\) | −11.6474 | −0.0385843 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −156.166 | −0.484662 | −0.242331 | − | 0.970194i | \(-0.577912\pi\) | ||||
−0.242331 | + | 0.970194i | \(0.577912\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −246.650 | −0.697632 | ||||||||
\(51\) | 271.051 | 0.744211 | ||||||||
\(52\) | 329.644 | 0.879104 | ||||||||
\(53\) | −518.418 | −1.34359 | −0.671794 | − | 0.740738i | \(-0.734476\pi\) | ||||
−0.671794 | + | 0.740738i | \(0.734476\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 63.4346 | 0.155519 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 241.745 | 0.561752 | ||||||||
\(58\) | −283.774 | −0.642438 | ||||||||
\(59\) | −628.541 | −1.38693 | −0.693467 | − | 0.720489i | \(-0.743918\pi\) | ||||
−0.693467 | + | 0.720489i | \(0.743918\pi\) | |||||||
\(60\) | 15.5299 | 0.0334150 | ||||||||
\(61\) | −396.834 | −0.832941 | −0.416470 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416470 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(62\) | 188.791 | 0.386718 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −106.653 | −0.203518 | ||||||||
\(66\) | 294.097 | 0.548498 | ||||||||
\(67\) | −927.524 | −1.69127 | −0.845635 | − | 0.533762i | \(-0.820778\pi\) | ||||
−0.845635 | + | 0.533762i | \(0.820778\pi\) | |||||||
\(68\) | −361.402 | −0.644506 | ||||||||
\(69\) | −69.0000 | −0.120386 | ||||||||
\(70\) | −18.1182 | −0.0309363 | ||||||||
\(71\) | −857.272 | −1.43295 | −0.716475 | − | 0.697612i | \(-0.754246\pi\) | ||||
−0.716475 | + | 0.697612i | \(0.754246\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −114.015 | −0.182801 | −0.0914007 | − | 0.995814i | \(-0.529134\pi\) | ||||
−0.0914007 | + | 0.995814i | \(0.529134\pi\) | |||||||
\(74\) | 890.209 | 1.39844 | ||||||||
\(75\) | 369.975 | 0.569615 | ||||||||
\(76\) | −322.326 | −0.486491 | ||||||||
\(77\) | −343.113 | −0.507811 | ||||||||
\(78\) | −494.466 | −0.717785 | ||||||||
\(79\) | 305.602 | 0.435227 | 0.217614 | − | 0.976035i | \(-0.430173\pi\) | ||||
0.217614 | + | 0.976035i | \(0.430173\pi\) | |||||||
\(80\) | −20.7065 | −0.0289382 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 75.0138 | 0.101023 | ||||||||
\(83\) | −1234.53 | −1.63262 | −0.816308 | − | 0.577617i | \(-0.803983\pi\) | ||||
−0.816308 | + | 0.577617i | \(0.803983\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | 116.928 | 0.149207 | ||||||||
\(86\) | 513.861 | 0.644315 | ||||||||
\(87\) | 425.662 | 0.524548 | ||||||||
\(88\) | −392.130 | −0.475013 | ||||||||
\(89\) | 827.954 | 0.986100 | 0.493050 | − | 0.870001i | \(-0.335882\pi\) | ||||
0.493050 | + | 0.870001i | \(0.335882\pi\) | |||||||
\(90\) | −23.2948 | −0.0272832 | ||||||||
\(91\) | 576.877 | 0.664540 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −283.187 | −0.315754 | ||||||||
\(94\) | −312.332 | −0.342708 | ||||||||
\(95\) | 104.285 | 0.112625 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −1343.90 | −1.40673 | −0.703363 | − | 0.710831i | \(-0.748319\pi\) | ||||
−0.703363 | + | 0.710831i | \(0.748319\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −441.146 | −0.447847 | ||||||||
\(100\) | −493.301 | −0.493301 | ||||||||
\(101\) | 1380.26 | 1.35981 | 0.679906 | − | 0.733299i | \(-0.262020\pi\) | ||||
0.679906 | + | 0.733299i | \(0.262020\pi\) | |||||||
\(102\) | 542.102 | 0.526237 | ||||||||
\(103\) | −1848.11 | −1.76796 | −0.883981 | − | 0.467523i | \(-0.845147\pi\) | ||||
−0.883981 | + | 0.467523i | \(0.845147\pi\) | |||||||
\(104\) | 659.288 | 0.621620 | ||||||||
\(105\) | 27.1773 | 0.0252593 | ||||||||
\(106\) | −1036.84 | −0.950060 | ||||||||
\(107\) | 1595.43 | 1.44145 | 0.720727 | − | 0.693219i | \(-0.243808\pi\) | ||||
0.720727 | + | 0.693219i | \(0.243808\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −140.344 | −0.123326 | −0.0616631 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616631 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(110\) | 126.869 | 0.109968 | ||||||||
\(111\) | −1335.31 | −1.14182 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −1226.94 | −1.02142 | −0.510711 | − | 0.859753i | \(-0.670618\pi\) | ||||
−0.510711 | + | 0.859753i | \(0.670618\pi\) | |||||||
\(114\) | 483.489 | 0.397218 | ||||||||
\(115\) | −29.7656 | −0.0241361 | ||||||||
\(116\) | −567.549 | −0.454272 | ||||||||
\(117\) | 741.699 | 0.586069 | ||||||||
\(118\) | −1257.08 | −0.980710 | ||||||||
\(119\) | −632.453 | −0.487200 | ||||||||
\(120\) | 31.0598 | 0.0236280 | ||||||||
\(121\) | 1071.59 | 0.805101 | ||||||||
\(122\) | −793.668 | −0.588978 | ||||||||
\(123\) | −112.521 | −0.0824849 | ||||||||
\(124\) | 377.582 | 0.273451 | ||||||||
\(125\) | 321.372 | 0.229955 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | −929.972 | −0.649777 | −0.324889 | − | 0.945752i | \(-0.605327\pi\) | ||||
−0.324889 | + | 0.945752i | \(0.605327\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −770.792 | −0.526081 | ||||||||
\(130\) | −213.305 | −0.143909 | ||||||||
\(131\) | −1804.26 | −1.20335 | −0.601675 | − | 0.798741i | \(-0.705500\pi\) | ||||
−0.601675 | + | 0.798741i | \(0.705500\pi\) | |||||||
\(132\) | 588.195 | 0.387847 | ||||||||
\(133\) | −564.071 | −0.367753 | ||||||||
\(134\) | −1855.05 | −1.19591 | ||||||||
\(135\) | 34.9422 | 0.0222766 | ||||||||
\(136\) | −722.803 | −0.455734 | ||||||||
\(137\) | 691.762 | 0.431396 | 0.215698 | − | 0.976460i | \(-0.430797\pi\) | ||||
0.215698 | + | 0.976460i | \(0.430797\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | 1907.71 | 1.16410 | 0.582050 | − | 0.813153i | \(-0.302251\pi\) | ||||
0.582050 | + | 0.813153i | \(0.302251\pi\) | |||||||
\(140\) | −36.2364 | −0.0218752 | ||||||||
\(141\) | 468.497 | 0.279820 | ||||||||
\(142\) | −1714.54 | −1.01325 | ||||||||
\(143\) | −4039.47 | −2.36222 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 183.624 | 0.105167 | ||||||||
\(146\) | −228.031 | −0.129260 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 1780.42 | 0.988848 | ||||||||
\(149\) | 77.3801 | 0.0425451 | 0.0212726 | − | 0.999774i | \(-0.493228\pi\) | ||||
0.0212726 | + | 0.999774i | \(0.493228\pi\) | |||||||
\(150\) | 739.951 | 0.402778 | ||||||||
\(151\) | 1693.51 | 0.912686 | 0.456343 | − | 0.889804i | \(-0.349159\pi\) | ||||
0.456343 | + | 0.889804i | \(0.349159\pi\) | |||||||
\(152\) | −644.652 | −0.344001 | ||||||||
\(153\) | −813.154 | −0.429670 | ||||||||
\(154\) | −686.227 | −0.359076 | ||||||||
\(155\) | −122.163 | −0.0633054 | ||||||||
\(156\) | −988.932 | −0.507551 | ||||||||
\(157\) | −2761.74 | −1.40389 | −0.701946 | − | 0.712230i | \(-0.747685\pi\) | ||||
−0.701946 | + | 0.712230i | \(0.747685\pi\) | |||||||
\(158\) | 611.204 | 0.307752 | ||||||||
\(159\) | 1555.25 | 0.775721 | ||||||||
\(160\) | −41.4130 | −0.0204624 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −3382.22 | −1.62525 | −0.812626 | − | 0.582786i | \(-0.801963\pi\) | ||||
−0.812626 | + | 0.582786i | \(0.801963\pi\) | |||||||
\(164\) | 150.028 | 0.0714340 | ||||||||
\(165\) | −190.304 | −0.0897887 | ||||||||
\(166\) | −2469.06 | −1.15443 | ||||||||
\(167\) | −997.598 | −0.462254 | −0.231127 | − | 0.972924i | \(-0.574241\pi\) | ||||
−0.231127 | + | 0.972924i | \(0.574241\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | 4594.57 | 2.09129 | ||||||||
\(170\) | 233.855 | 0.105505 | ||||||||
\(171\) | −725.234 | −0.324327 | ||||||||
\(172\) | 1027.72 | 0.455600 | ||||||||
\(173\) | −420.461 | −0.184781 | −0.0923903 | − | 0.995723i | \(-0.529451\pi\) | ||||
−0.0923903 | + | 0.995723i | \(0.529451\pi\) | |||||||
\(174\) | 851.323 | 0.370912 | ||||||||
\(175\) | −863.276 | −0.372900 | ||||||||
\(176\) | −784.259 | −0.335885 | ||||||||
\(177\) | 1885.62 | 0.800747 | ||||||||
\(178\) | 1655.91 | 0.697278 | ||||||||
\(179\) | −531.844 | −0.222078 | −0.111039 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111039 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(180\) | −46.5896 | −0.0192921 | ||||||||
\(181\) | −497.521 | −0.204312 | −0.102156 | − | 0.994768i | \(-0.532574\pi\) | ||||
−0.102156 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(182\) | 1153.75 | 0.469901 | ||||||||
\(183\) | 1190.50 | 0.480899 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −576.035 | −0.228924 | ||||||||
\(186\) | −566.374 | −0.223272 | ||||||||
\(187\) | 4428.63 | 1.73184 | ||||||||
\(188\) | −624.663 | −0.242331 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 208.570 | 0.0796382 | ||||||||
\(191\) | 1079.54 | 0.408967 | 0.204484 | − | 0.978870i | \(-0.434448\pi\) | ||||
0.204484 | + | 0.978870i | \(0.434448\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −1761.70 | −0.657048 | −0.328524 | − | 0.944496i | \(-0.606551\pi\) | ||||
−0.328524 | + | 0.944496i | \(0.606551\pi\) | |||||||
\(194\) | −2687.80 | −0.994706 | ||||||||
\(195\) | 319.958 | 0.117501 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 2747.60 | 0.993698 | 0.496849 | − | 0.867837i | \(-0.334490\pi\) | ||||
0.496849 | + | 0.867837i | \(0.334490\pi\) | |||||||
\(198\) | −882.292 | −0.316676 | ||||||||
\(199\) | −1910.52 | −0.680569 | −0.340284 | − | 0.940323i | \(-0.610523\pi\) | ||||
−0.340284 | + | 0.940323i | \(0.610523\pi\) | |||||||
\(200\) | −986.601 | −0.348816 | ||||||||
\(201\) | 2782.57 | 0.976455 | ||||||||
\(202\) | 2760.52 | 0.961533 | ||||||||
\(203\) | −993.211 | −0.343398 | ||||||||
\(204\) | 1084.20 | 0.372106 | ||||||||
\(205\) | −48.5398 | −0.0165374 | ||||||||
\(206\) | −3696.23 | −1.25014 | ||||||||
\(207\) | 207.000 | 0.0695048 | ||||||||
\(208\) | 1318.58 | 0.439552 | ||||||||
\(209\) | 3949.80 | 1.30724 | ||||||||
\(210\) | 54.3546 | 0.0178611 | ||||||||
\(211\) | 2578.90 | 0.841416 | 0.420708 | − | 0.907196i | \(-0.361782\pi\) | ||||
0.420708 | + | 0.907196i | \(0.361782\pi\) | |||||||
\(212\) | −2073.67 | −0.671794 | ||||||||
\(213\) | 2571.82 | 0.827315 | ||||||||
\(214\) | 3190.85 | 1.01926 | ||||||||
\(215\) | −332.508 | −0.105474 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 660.769 | 0.206709 | ||||||||
\(218\) | −280.689 | −0.0872047 | ||||||||
\(219\) | 342.046 | 0.105540 | ||||||||
\(220\) | 253.739 | 0.0777593 | ||||||||
\(221\) | −7445.87 | −2.26635 | ||||||||
\(222\) | −2670.63 | −0.807391 | ||||||||
\(223\) | 394.705 | 0.118526 | 0.0592632 | − | 0.998242i | \(-0.481125\pi\) | ||||
0.0592632 | + | 0.998242i | \(0.481125\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −1109.93 | −0.328867 | ||||||||
\(226\) | −2453.88 | −0.722254 | ||||||||
\(227\) | −1497.44 | −0.437836 | −0.218918 | − | 0.975743i | \(-0.570253\pi\) | ||||
−0.218918 | + | 0.975743i | \(0.570253\pi\) | |||||||
\(228\) | 966.978 | 0.280876 | ||||||||
\(229\) | −3152.77 | −0.909787 | −0.454893 | − | 0.890546i | \(-0.650323\pi\) | ||||
−0.454893 | + | 0.890546i | \(0.650323\pi\) | |||||||
\(230\) | −59.5312 | −0.0170668 | ||||||||
\(231\) | 1029.34 | 0.293185 | ||||||||
\(232\) | −1135.10 | −0.321219 | ||||||||
\(233\) | 5529.90 | 1.55483 | 0.777416 | − | 0.628987i | \(-0.216530\pi\) | ||||
0.777416 | + | 0.628987i | \(0.216530\pi\) | |||||||
\(234\) | 1483.40 | 0.414413 | ||||||||
\(235\) | 202.103 | 0.0561010 | ||||||||
\(236\) | −2514.16 | −0.693467 | ||||||||
\(237\) | −916.807 | −0.251278 | ||||||||
\(238\) | −1264.91 | −0.344503 | ||||||||
\(239\) | 5043.44 | 1.36499 | 0.682496 | − | 0.730889i | \(-0.260894\pi\) | ||||
0.682496 | + | 0.730889i | \(0.260894\pi\) | |||||||
\(240\) | 62.1195 | 0.0167075 | ||||||||
\(241\) | −986.086 | −0.263566 | −0.131783 | − | 0.991279i | \(-0.542070\pi\) | ||||
−0.131783 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(242\) | 2143.18 | 0.569292 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1587.34 | −0.416470 | ||||||||
\(245\) | −63.4137 | −0.0165361 | ||||||||
\(246\) | −225.041 | −0.0583257 | ||||||||
\(247\) | −6640.80 | −1.71070 | ||||||||
\(248\) | 755.165 | 0.193359 | ||||||||
\(249\) | 3703.59 | 0.942591 | ||||||||
\(250\) | 642.743 | 0.162603 | ||||||||
\(251\) | −2918.07 | −0.733812 | −0.366906 | − | 0.930258i | \(-0.619583\pi\) | ||||
−0.366906 | + | 0.930258i | \(0.619583\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | −1127.37 | −0.280148 | ||||||||
\(254\) | −1859.94 | −0.459462 | ||||||||
\(255\) | −350.783 | −0.0861445 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2482.59 | −0.602567 | −0.301284 | − | 0.953535i | \(-0.597415\pi\) | ||||
−0.301284 | + | 0.953535i | \(0.597415\pi\) | |||||||
\(258\) | −1541.58 | −0.371995 | ||||||||
\(259\) | 3115.73 | 0.747499 | ||||||||
\(260\) | −426.611 | −0.101759 | ||||||||
\(261\) | −1276.98 | −0.302848 | ||||||||
\(262\) | −3608.52 | −0.850897 | ||||||||
\(263\) | 5568.78 | 1.30565 | 0.652825 | − | 0.757509i | \(-0.273584\pi\) | ||||
0.652825 | + | 0.757509i | \(0.273584\pi\) | |||||||
\(264\) | 1176.39 | 0.274249 | ||||||||
\(265\) | 670.914 | 0.155524 | ||||||||
\(266\) | −1128.14 | −0.260040 | ||||||||
\(267\) | −2483.86 | −0.569325 | ||||||||
\(268\) | −3710.10 | −0.845635 | ||||||||
\(269\) | −2665.62 | −0.604186 | −0.302093 | − | 0.953278i | \(-0.597685\pi\) | ||||
−0.302093 | + | 0.953278i | \(0.597685\pi\) | |||||||
\(270\) | 69.8844 | 0.0157520 | ||||||||
\(271\) | −3635.18 | −0.814840 | −0.407420 | − | 0.913241i | \(-0.633572\pi\) | ||||
−0.407420 | + | 0.913241i | \(0.633572\pi\) | |||||||
\(272\) | −1445.61 | −0.322253 | ||||||||
\(273\) | −1730.63 | −0.383672 | ||||||||
\(274\) | 1383.52 | 0.305043 | ||||||||
\(275\) | 6044.93 | 1.32554 | ||||||||
\(276\) | −276.000 | −0.0601929 | ||||||||
\(277\) | −3729.83 | −0.809038 | −0.404519 | − | 0.914529i | \(-0.632561\pi\) | ||||
−0.404519 | + | 0.914529i | \(0.632561\pi\) | |||||||
\(278\) | 3815.42 | 0.823143 | ||||||||
\(279\) | 849.560 | 0.182301 | ||||||||
\(280\) | −72.4728 | −0.0154681 | ||||||||
\(281\) | 2095.46 | 0.444856 | 0.222428 | − | 0.974949i | \(-0.428602\pi\) | ||||
0.222428 | + | 0.974949i | \(0.428602\pi\) | |||||||
\(282\) | 936.995 | 0.197863 | ||||||||
\(283\) | 8578.79 | 1.80197 | 0.900983 | − | 0.433854i | \(-0.142847\pi\) | ||||
0.900983 | + | 0.433854i | \(0.142847\pi\) | |||||||
\(284\) | −3429.09 | −0.716475 | ||||||||
\(285\) | −312.855 | −0.0650244 | ||||||||
\(286\) | −8078.95 | −1.67034 | ||||||||
\(287\) | 262.548 | 0.0539991 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 3250.20 | 0.661550 | ||||||||
\(290\) | 367.248 | 0.0743640 | ||||||||
\(291\) | 4031.70 | 0.812174 | ||||||||
\(292\) | −456.062 | −0.0914007 | ||||||||
\(293\) | −3816.23 | −0.760911 | −0.380455 | − | 0.924799i | \(-0.624233\pi\) | ||||
−0.380455 | + | 0.924799i | \(0.624233\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | 813.430 | 0.160542 | ||||||||
\(296\) | 3560.84 | 0.699221 | ||||||||
\(297\) | 1323.44 | 0.258564 | ||||||||
\(298\) | 154.760 | 0.0300839 | ||||||||
\(299\) | 1895.45 | 0.366612 | ||||||||
\(300\) | 1479.90 | 0.284807 | ||||||||
\(301\) | 1798.51 | 0.344401 | ||||||||
\(302\) | 3387.01 | 0.645366 | ||||||||
\(303\) | −4140.78 | −0.785088 | ||||||||
\(304\) | −1289.30 | −0.243246 | ||||||||
\(305\) | 513.565 | 0.0964153 | ||||||||
\(306\) | −1626.31 | −0.303823 | ||||||||
\(307\) | 6176.53 | 1.14825 | 0.574125 | − | 0.818767i | \(-0.305342\pi\) | ||||
0.574125 | + | 0.818767i | \(0.305342\pi\) | |||||||
\(308\) | −1372.45 | −0.253905 | ||||||||
\(309\) | 5544.34 | 1.02073 | ||||||||
\(310\) | −244.325 | −0.0447637 | ||||||||
\(311\) | 1969.82 | 0.359159 | 0.179579 | − | 0.983743i | \(-0.442526\pi\) | ||||
0.179579 | + | 0.983743i | \(0.442526\pi\) | |||||||
\(312\) | −1977.86 | −0.358893 | ||||||||
\(313\) | 2657.30 | 0.479870 | 0.239935 | − | 0.970789i | \(-0.422874\pi\) | ||||
0.239935 | + | 0.970789i | \(0.422874\pi\) | |||||||
\(314\) | −5523.49 | −0.992702 | ||||||||
\(315\) | −81.5318 | −0.0145835 | ||||||||
\(316\) | 1222.41 | 0.217614 | ||||||||
\(317\) | 3309.95 | 0.586453 | 0.293226 | − | 0.956043i | \(-0.405271\pi\) | ||||
0.293226 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(318\) | 3110.51 | 0.548518 | ||||||||
\(319\) | 6954.77 | 1.22067 | ||||||||
\(320\) | −82.8260 | −0.0144691 | ||||||||
\(321\) | −4786.28 | −0.832224 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 7280.57 | 1.25419 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −10163.3 | −1.73465 | ||||||||
\(326\) | −6764.44 | −1.14923 | ||||||||
\(327\) | 421.033 | 0.0712024 | ||||||||
\(328\) | 300.055 | 0.0505115 | ||||||||
\(329\) | −1093.16 | −0.183185 | ||||||||
\(330\) | −380.608 | −0.0634902 | ||||||||
\(331\) | 10329.2 | 1.71524 | 0.857620 | − | 0.514284i | \(-0.171942\pi\) | ||||
0.857620 | + | 0.514284i | \(0.171942\pi\) | |||||||
\(332\) | −4938.11 | −0.816308 | ||||||||
\(333\) | 4005.94 | 0.659232 | ||||||||
\(334\) | −1995.20 | −0.326863 | ||||||||
\(335\) | 1200.36 | 0.195769 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 8882.04 | 1.43571 | 0.717857 | − | 0.696191i | \(-0.245123\pi\) | ||||
0.717857 | + | 0.696191i | \(0.245123\pi\) | |||||||
\(338\) | 9189.14 | 1.47877 | ||||||||
\(339\) | 3680.81 | 0.589718 | ||||||||
\(340\) | 467.710 | 0.0746034 | ||||||||
\(341\) | −4626.91 | −0.734784 | ||||||||
\(342\) | −1450.47 | −0.229334 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 2055.45 | 0.322158 | ||||||||
\(345\) | 89.2968 | 0.0139350 | ||||||||
\(346\) | −840.921 | −0.130660 | ||||||||
\(347\) | 6600.40 | 1.02112 | 0.510560 | − | 0.859842i | \(-0.329438\pi\) | ||||
0.510560 | + | 0.859842i | \(0.329438\pi\) | |||||||
\(348\) | 1702.65 | 0.262274 | ||||||||
\(349\) | 9416.49 | 1.44428 | 0.722139 | − | 0.691748i | \(-0.243159\pi\) | ||||
0.722139 | + | 0.691748i | \(0.243159\pi\) | |||||||
\(350\) | −1726.55 | −0.263680 | ||||||||
\(351\) | −2225.10 | −0.338367 | ||||||||
\(352\) | −1568.52 | −0.237507 | ||||||||
\(353\) | 12937.9 | 1.95075 | 0.975374 | − | 0.220555i | \(-0.0707869\pi\) | ||||
0.975374 | + | 0.220555i | \(0.0707869\pi\) | |||||||
\(354\) | 3771.25 | 0.566213 | ||||||||
\(355\) | 1109.44 | 0.165868 | ||||||||
\(356\) | 3311.81 | 0.493050 | ||||||||
\(357\) | 1897.36 | 0.281285 | ||||||||
\(358\) | −1063.69 | −0.157033 | ||||||||
\(359\) | 4687.95 | 0.689193 | 0.344597 | − | 0.938751i | \(-0.388016\pi\) | ||||
0.344597 | + | 0.938751i | \(0.388016\pi\) | |||||||
\(360\) | −93.1793 | −0.0136416 | ||||||||
\(361\) | −365.621 | −0.0533052 | ||||||||
\(362\) | −995.042 | −0.144470 | ||||||||
\(363\) | −3214.77 | −0.464825 | ||||||||
\(364\) | 2307.51 | 0.332270 | ||||||||
\(365\) | 147.554 | 0.0211598 | ||||||||
\(366\) | 2381.00 | 0.340047 | ||||||||
\(367\) | −10802.7 | −1.53650 | −0.768251 | − | 0.640149i | \(-0.778873\pi\) | ||||
−0.768251 | + | 0.640149i | \(0.778873\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 337.562 | 0.0476227 | ||||||||
\(370\) | −1152.07 | −0.161874 | ||||||||
\(371\) | −3628.92 | −0.507829 | ||||||||
\(372\) | −1132.75 | −0.157877 | ||||||||
\(373\) | 6855.89 | 0.951701 | 0.475850 | − | 0.879526i | \(-0.342140\pi\) | ||||
0.475850 | + | 0.879526i | \(0.342140\pi\) | |||||||
\(374\) | 8857.27 | 1.22459 | ||||||||
\(375\) | −964.115 | −0.132764 | ||||||||
\(376\) | −1249.33 | −0.171354 | ||||||||
\(377\) | −11693.1 | −1.59741 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | 7348.38 | 0.995939 | 0.497969 | − | 0.867195i | \(-0.334079\pi\) | ||||
0.497969 | + | 0.867195i | \(0.334079\pi\) | |||||||
\(380\) | 417.140 | 0.0563127 | ||||||||
\(381\) | 2789.92 | 0.375149 | ||||||||
\(382\) | 2159.08 | 0.289184 | ||||||||
\(383\) | −9917.48 | −1.32313 | −0.661566 | − | 0.749887i | \(-0.730108\pi\) | ||||
−0.661566 | + | 0.749887i | \(0.730108\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 444.042 | 0.0587805 | ||||||||
\(386\) | −3523.41 | −0.464603 | ||||||||
\(387\) | 2312.38 | 0.303733 | ||||||||
\(388\) | −5375.60 | −0.703363 | ||||||||
\(389\) | −4781.41 | −0.623205 | −0.311603 | − | 0.950212i | \(-0.600866\pi\) | ||||
−0.311603 | + | 0.950212i | \(0.600866\pi\) | |||||||
\(390\) | 639.916 | 0.0830857 | ||||||||
\(391\) | −2078.06 | −0.268777 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 5412.78 | 0.694755 | ||||||||
\(394\) | 5495.20 | 0.702650 | ||||||||
\(395\) | −395.497 | −0.0503788 | ||||||||
\(396\) | −1764.58 | −0.223923 | ||||||||
\(397\) | 5412.61 | 0.684260 | 0.342130 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342130 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(398\) | −3821.04 | −0.481235 | ||||||||
\(399\) | 1692.21 | 0.212322 | ||||||||
\(400\) | −1973.20 | −0.246650 | ||||||||
\(401\) | −1971.06 | −0.245462 | −0.122731 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122731 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(402\) | 5565.14 | 0.690458 | ||||||||
\(403\) | 7779.23 | 0.961566 | ||||||||
\(404\) | 5521.04 | 0.679906 | ||||||||
\(405\) | −104.827 | −0.0128614 | ||||||||
\(406\) | −1986.42 | −0.242819 | ||||||||
\(407\) | −21817.3 | −2.65711 | ||||||||
\(408\) | 2168.41 | 0.263118 | ||||||||
\(409\) | −648.731 | −0.0784295 | −0.0392148 | − | 0.999231i | \(-0.512486\pi\) | ||||
−0.0392148 | + | 0.999231i | \(0.512486\pi\) | |||||||
\(410\) | −97.0795 | −0.0116937 | ||||||||
\(411\) | −2075.29 | −0.249067 | ||||||||
\(412\) | −7392.46 | −0.883981 | ||||||||
\(413\) | −4399.79 | −0.524212 | ||||||||
\(414\) | 414.000 | 0.0491473 | ||||||||
\(415\) | 1597.67 | 0.188980 | ||||||||
\(416\) | 2637.15 | 0.310810 | ||||||||
\(417\) | −5723.13 | −0.672094 | ||||||||
\(418\) | 7899.60 | 0.924359 | ||||||||
\(419\) | −13307.1 | −1.55154 | −0.775772 | − | 0.631014i | \(-0.782639\pi\) | ||||
−0.775772 | + | 0.631014i | \(0.782639\pi\) | |||||||
\(420\) | 108.709 | 0.0126297 | ||||||||
\(421\) | 9403.07 | 1.08855 | 0.544273 | − | 0.838908i | \(-0.316806\pi\) | ||||
0.544273 | + | 0.838908i | \(0.316806\pi\) | |||||||
\(422\) | 5157.80 | 0.594971 | ||||||||
\(423\) | −1405.49 | −0.161554 | ||||||||
\(424\) | −4147.34 | −0.475030 | ||||||||
\(425\) | 11142.5 | 1.27174 | ||||||||
\(426\) | 5143.63 | 0.585000 | ||||||||
\(427\) | −2777.84 | −0.314822 | ||||||||
\(428\) | 6381.70 | 0.720727 | ||||||||
\(429\) | 12118.4 | 1.36383 | ||||||||
\(430\) | −665.017 | −0.0745813 | ||||||||
\(431\) | −3874.55 | −0.433018 | −0.216509 | − | 0.976281i | \(-0.569467\pi\) | ||||
−0.216509 | + | 0.976281i | \(0.569467\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −9234.70 | −1.02492 | −0.512461 | − | 0.858711i | \(-0.671266\pi\) | ||||
−0.512461 | + | 0.858711i | \(0.671266\pi\) | |||||||
\(434\) | 1321.54 | 0.146166 | ||||||||
\(435\) | −550.873 | −0.0607180 | ||||||||
\(436\) | −561.377 | −0.0616631 | ||||||||
\(437\) | −1853.37 | −0.202881 | ||||||||
\(438\) | 684.093 | 0.0746283 | ||||||||
\(439\) | −17639.5 | −1.91774 | −0.958872 | − | 0.283841i | \(-0.908391\pi\) | ||||
−0.958872 | + | 0.283841i | \(0.908391\pi\) | |||||||
\(440\) | 507.477 | 0.0549841 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −14891.7 | −1.60255 | ||||||||
\(443\) | −17240.4 | −1.84902 | −0.924511 | − | 0.381155i | \(-0.875526\pi\) | ||||
−0.924511 | + | 0.381155i | \(0.875526\pi\) | |||||||
\(444\) | −5341.26 | −0.570912 | ||||||||
\(445\) | −1071.50 | −0.114144 | ||||||||
\(446\) | 789.410 | 0.0838109 | ||||||||
\(447\) | −232.140 | −0.0245634 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −9081.43 | −0.954519 | −0.477260 | − | 0.878762i | \(-0.658370\pi\) | ||||
−0.477260 | + | 0.878762i | \(0.658370\pi\) | |||||||
\(450\) | −2219.85 | −0.232544 | ||||||||
\(451\) | −1838.45 | −0.191949 | ||||||||
\(452\) | −4907.75 | −0.510711 | ||||||||
\(453\) | −5080.52 | −0.526939 | ||||||||
\(454\) | −2994.89 | −0.309597 | ||||||||
\(455\) | −746.569 | −0.0769224 | ||||||||
\(456\) | 1933.96 | 0.198609 | ||||||||
\(457\) | 1078.59 | 0.110403 | 0.0552017 | − | 0.998475i | \(-0.482420\pi\) | ||||
0.0552017 | + | 0.998475i | \(0.482420\pi\) | |||||||
\(458\) | −6305.55 | −0.643316 | ||||||||
\(459\) | 2439.46 | 0.248070 | ||||||||
\(460\) | −119.062 | −0.0120681 | ||||||||
\(461\) | 8684.43 | 0.877384 | 0.438692 | − | 0.898637i | \(-0.355442\pi\) | ||||
0.438692 | + | 0.898637i | \(0.355442\pi\) | |||||||
\(462\) | 2058.68 | 0.207313 | ||||||||
\(463\) | −18900.9 | −1.89719 | −0.948597 | − | 0.316488i | \(-0.897496\pi\) | ||||
−0.948597 | + | 0.316488i | \(0.897496\pi\) | |||||||
\(464\) | −2270.20 | −0.227136 | ||||||||
\(465\) | 366.488 | 0.0365494 | ||||||||
\(466\) | 11059.8 | 1.09943 | ||||||||
\(467\) | 809.992 | 0.0802612 | 0.0401306 | − | 0.999194i | \(-0.487223\pi\) | ||||
0.0401306 | + | 0.999194i | \(0.487223\pi\) | |||||||
\(468\) | 2966.80 | 0.293035 | ||||||||
\(469\) | −6492.67 | −0.639240 | ||||||||
\(470\) | 404.206 | 0.0396694 | ||||||||
\(471\) | 8285.23 | 0.810538 | ||||||||
\(472\) | −5028.33 | −0.490355 | ||||||||
\(473\) | −12593.8 | −1.22423 | ||||||||
\(474\) | −1833.61 | −0.177681 | ||||||||
\(475\) | 9937.73 | 0.959946 | ||||||||
\(476\) | −2529.81 | −0.243600 | ||||||||
\(477\) | −4665.76 | −0.447863 | ||||||||
\(478\) | 10086.9 | 0.965195 | ||||||||
\(479\) | −7613.75 | −0.726266 | −0.363133 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363133 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(480\) | 124.239 | 0.0118140 | ||||||||
\(481\) | 36681.5 | 3.47720 | ||||||||
\(482\) | −1972.17 | −0.186369 | ||||||||
\(483\) | −483.000 | −0.0455016 | ||||||||
\(484\) | 4286.36 | 0.402550 | ||||||||
\(485\) | 1739.22 | 0.162833 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 7458.06 | 0.693957 | 0.346978 | − | 0.937873i | \(-0.387208\pi\) | ||||
0.346978 | + | 0.937873i | \(0.387208\pi\) | |||||||
\(488\) | −3174.67 | −0.294489 | ||||||||
\(489\) | 10146.7 | 0.938339 | ||||||||
\(490\) | −126.827 | −0.0116928 | ||||||||
\(491\) | 1914.55 | 0.175972 | 0.0879862 | − | 0.996122i | \(-0.471957\pi\) | ||||
0.0879862 | + | 0.996122i | \(0.471957\pi\) | |||||||
\(492\) | −450.083 | −0.0412425 | ||||||||
\(493\) | 12819.6 | 1.17112 | ||||||||
\(494\) | −13281.6 | −1.20965 | ||||||||
\(495\) | 570.912 | 0.0518395 | ||||||||
\(496\) | 1510.33 | 0.136725 | ||||||||
\(497\) | −6000.91 | −0.541605 | ||||||||
\(498\) | 7407.17 | 0.666513 | ||||||||
\(499\) | 1798.53 | 0.161349 | 0.0806745 | − | 0.996740i | \(-0.474293\pi\) | ||||
0.0806745 | + | 0.996740i | \(0.474293\pi\) | |||||||
\(500\) | 1285.49 | 0.114977 | ||||||||
\(501\) | 2992.80 | 0.266883 | ||||||||
\(502\) | −5836.13 | −0.518883 | ||||||||
\(503\) | 8417.12 | 0.746125 | 0.373062 | − | 0.927806i | \(-0.378308\pi\) | ||||
0.373062 | + | 0.927806i | \(0.378308\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −1786.27 | −0.157402 | ||||||||
\(506\) | −2254.75 | −0.198094 | ||||||||
\(507\) | −13783.7 | −1.20741 | ||||||||
\(508\) | −3719.89 | −0.324889 | ||||||||
\(509\) | 9022.57 | 0.785695 | 0.392847 | − | 0.919604i | \(-0.371490\pi\) | ||||
0.392847 | + | 0.919604i | \(0.371490\pi\) | |||||||
\(510\) | −701.565 | −0.0609134 | ||||||||
\(511\) | −798.108 | −0.0690924 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 2175.70 | 0.187251 | ||||||||
\(514\) | −4965.18 | −0.426079 | ||||||||
\(515\) | 2391.75 | 0.204647 | ||||||||
\(516\) | −3083.17 | −0.263041 | ||||||||
\(517\) | 7654.66 | 0.651163 | ||||||||
\(518\) | 6231.47 | 0.528562 | ||||||||
\(519\) | 1261.38 | 0.106683 | ||||||||
\(520\) | −853.222 | −0.0719543 | ||||||||
\(521\) | 17253.7 | 1.45086 | 0.725432 | − | 0.688294i | \(-0.241640\pi\) | ||||
0.725432 | + | 0.688294i | \(0.241640\pi\) | |||||||
\(522\) | −2553.97 | −0.214146 | ||||||||
\(523\) | 14252.3 | 1.19160 | 0.595801 | − | 0.803132i | \(-0.296835\pi\) | ||||
0.595801 | + | 0.803132i | \(0.296835\pi\) | |||||||
\(524\) | −7217.04 | −0.601675 | ||||||||
\(525\) | 2589.83 | 0.215294 | ||||||||
\(526\) | 11137.6 | 0.923234 | ||||||||
\(527\) | −8528.68 | −0.704962 | ||||||||
\(528\) | 2352.78 | 0.193923 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 1341.83 | 0.109972 | ||||||||
\(531\) | −5656.87 | −0.462311 | ||||||||
\(532\) | −2256.28 | −0.183876 | ||||||||
\(533\) | 3090.98 | 0.251192 | ||||||||
\(534\) | −4967.72 | −0.402574 | ||||||||
\(535\) | −2064.73 | −0.166852 | ||||||||
\(536\) | −7420.19 | −0.597954 | ||||||||
\(537\) | 1595.53 | 0.128217 | ||||||||
\(538\) | −5331.25 | −0.427224 | ||||||||
\(539\) | −2401.79 | −0.191934 | ||||||||
\(540\) | 139.769 | 0.0111383 | ||||||||
\(541\) | 2539.10 | 0.201783 | 0.100892 | − | 0.994897i | \(-0.467831\pi\) | ||||
0.100892 | + | 0.994897i | \(0.467831\pi\) | |||||||
\(542\) | −7270.37 | −0.576179 | ||||||||
\(543\) | 1492.56 | 0.117960 | ||||||||
\(544\) | −2891.21 | −0.227867 | ||||||||
\(545\) | 181.627 | 0.0142753 | ||||||||
\(546\) | −3461.26 | −0.271297 | ||||||||
\(547\) | −6632.90 | −0.518468 | −0.259234 | − | 0.965815i | \(-0.583470\pi\) | ||||
−0.259234 | + | 0.965815i | \(0.583470\pi\) | |||||||
\(548\) | 2767.05 | 0.215698 | ||||||||
\(549\) | −3571.51 | −0.277647 | ||||||||
\(550\) | 12089.9 | 0.937297 | ||||||||
\(551\) | 11433.5 | 0.883998 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | 2139.22 | 0.164500 | ||||||||
\(554\) | −7459.66 | −0.572077 | ||||||||
\(555\) | 1728.11 | 0.132169 | ||||||||
\(556\) | 7630.85 | 0.582050 | ||||||||
\(557\) | 15215.9 | 1.15749 | 0.578743 | − | 0.815510i | \(-0.303544\pi\) | ||||
0.578743 | + | 0.815510i | \(0.303544\pi\) | |||||||
\(558\) | 1699.12 | 0.128906 | ||||||||
\(559\) | 21173.9 | 1.60208 | ||||||||
\(560\) | −144.946 | −0.0109376 | ||||||||
\(561\) | −13285.9 | −0.999878 | ||||||||
\(562\) | 4190.91 | 0.314560 | ||||||||
\(563\) | −5321.43 | −0.398351 | −0.199176 | − | 0.979964i | \(-0.563826\pi\) | ||||
−0.199176 | + | 0.979964i | \(0.563826\pi\) | |||||||
\(564\) | 1873.99 | 0.139910 | ||||||||
\(565\) | 1587.85 | 0.118232 | ||||||||
\(566\) | 17157.6 | 1.27418 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −6858.18 | −0.506625 | ||||||||
\(569\) | −6120.97 | −0.450974 | −0.225487 | − | 0.974246i | \(-0.572397\pi\) | ||||
−0.225487 | + | 0.974246i | \(0.572397\pi\) | |||||||
\(570\) | −625.710 | −0.0459792 | ||||||||
\(571\) | −26413.3 | −1.93584 | −0.967918 | − | 0.251267i | \(-0.919153\pi\) | ||||
−0.967918 | + | 0.251267i | \(0.919153\pi\) | |||||||
\(572\) | −16157.9 | −1.18111 | ||||||||
\(573\) | −3238.62 | −0.236117 | ||||||||
\(574\) | 525.096 | 0.0381831 | ||||||||
\(575\) | −2836.48 | −0.205721 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 23548.2 | 1.69901 | 0.849503 | − | 0.527584i | \(-0.176902\pi\) | ||||
0.849503 | + | 0.527584i | \(0.176902\pi\) | |||||||
\(578\) | 6500.39 | 0.467787 | ||||||||
\(579\) | 5285.11 | 0.379347 | ||||||||
\(580\) | 734.497 | 0.0525833 | ||||||||
\(581\) | −8641.70 | −0.617071 | ||||||||
\(582\) | 8063.40 | 0.574294 | ||||||||
\(583\) | 25410.9 | 1.80516 | ||||||||
\(584\) | −912.123 | −0.0646300 | ||||||||
\(585\) | −959.874 | −0.0678392 | ||||||||
\(586\) | −7632.47 | −0.538045 | ||||||||
\(587\) | 11780.0 | 0.828298 | 0.414149 | − | 0.910209i | \(-0.364079\pi\) | ||||
0.414149 | + | 0.910209i | \(0.364079\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | −7606.54 | −0.532126 | ||||||||
\(590\) | 1626.86 | 0.113520 | ||||||||
\(591\) | −8242.80 | −0.573712 | ||||||||
\(592\) | 7121.68 | 0.494424 | ||||||||
\(593\) | −6475.79 | −0.448447 | −0.224223 | − | 0.974538i | \(-0.571985\pi\) | ||||
−0.224223 | + | 0.974538i | \(0.571985\pi\) | |||||||
\(594\) | 2646.88 | 0.182833 | ||||||||
\(595\) | 818.493 | 0.0563948 | ||||||||
\(596\) | 309.520 | 0.0212726 | ||||||||
\(597\) | 5731.56 | 0.392926 | ||||||||
\(598\) | 3790.91 | 0.259234 | ||||||||
\(599\) | −969.373 | −0.0661227 | −0.0330613 | − | 0.999453i | \(-0.510526\pi\) | ||||
−0.0330613 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(600\) | 2959.80 | 0.201389 | ||||||||
\(601\) | −317.461 | −0.0215466 | −0.0107733 | − | 0.999942i | \(-0.503429\pi\) | ||||
−0.0107733 | + | 0.999942i | \(0.503429\pi\) | |||||||
\(602\) | 3597.03 | 0.243528 | ||||||||
\(603\) | −8347.72 | −0.563757 | ||||||||
\(604\) | 6774.02 | 0.456343 | ||||||||
\(605\) | −1386.80 | −0.0931927 | ||||||||
\(606\) | −8281.57 | −0.555141 | ||||||||
\(607\) | 7255.36 | 0.485150 | 0.242575 | − | 0.970133i | \(-0.422008\pi\) | ||||
0.242575 | + | 0.970133i | \(0.422008\pi\) | |||||||
\(608\) | −2578.61 | −0.172001 | ||||||||
\(609\) | 2979.63 | 0.198261 | ||||||||
\(610\) | 1027.13 | 0.0681759 | ||||||||
\(611\) | −12869.8 | −0.852137 | ||||||||
\(612\) | −3252.61 | −0.214835 | ||||||||
\(613\) | 17804.6 | 1.17312 | 0.586560 | − | 0.809906i | \(-0.300482\pi\) | ||||
0.586560 | + | 0.809906i | \(0.300482\pi\) | |||||||
\(614\) | 12353.1 | 0.811936 | ||||||||
\(615\) | 145.619 | 0.00954787 | ||||||||
\(616\) | −2744.91 | −0.179538 | ||||||||
\(617\) | −29001.0 | −1.89228 | −0.946139 | − | 0.323760i | \(-0.895053\pi\) | ||||
−0.946139 | + | 0.323760i | \(0.895053\pi\) | |||||||
\(618\) | 11088.7 | 0.721767 | ||||||||
\(619\) | −6442.18 | −0.418309 | −0.209154 | − | 0.977883i | \(-0.567071\pi\) | ||||
−0.209154 | + | 0.977883i | \(0.567071\pi\) | |||||||
\(620\) | −488.651 | −0.0316527 | ||||||||
\(621\) | −621.000 | −0.0401286 | ||||||||
\(622\) | 3939.64 | 0.253964 | ||||||||
\(623\) | 5795.68 | 0.372711 | ||||||||
\(624\) | −3955.73 | −0.253775 | ||||||||
\(625\) | 14999.7 | 0.959983 | ||||||||
\(626\) | 5314.59 | 0.339319 | ||||||||
\(627\) | −11849.4 | −0.754736 | ||||||||
\(628\) | −11047.0 | −0.701946 | ||||||||
\(629\) | −40215.4 | −2.54927 | ||||||||
\(630\) | −163.064 | −0.0103121 | ||||||||
\(631\) | −21326.5 | −1.34547 | −0.672737 | − | 0.739882i | \(-0.734881\pi\) | ||||
−0.672737 | + | 0.739882i | \(0.734881\pi\) | |||||||
\(632\) | 2444.82 | 0.153876 | ||||||||
\(633\) | −7736.70 | −0.485792 | ||||||||
\(634\) | 6619.91 | 0.414685 | ||||||||
\(635\) | 1203.53 | 0.0752136 | ||||||||
\(636\) | 6221.01 | 0.387860 | ||||||||
\(637\) | 4038.14 | 0.251172 | ||||||||
\(638\) | 13909.5 | 0.863141 | ||||||||
\(639\) | −7715.45 | −0.477650 | ||||||||
\(640\) | −165.652 | −0.0102312 | ||||||||
\(641\) | 26218.6 | 1.61556 | 0.807780 | − | 0.589484i | \(-0.200669\pi\) | ||||
0.807780 | + | 0.589484i | \(0.200669\pi\) | |||||||
\(642\) | −9572.55 | −0.588471 | ||||||||
\(643\) | −3049.87 | −0.187053 | −0.0935264 | − | 0.995617i | \(-0.529814\pi\) | ||||
−0.0935264 | + | 0.995617i | \(0.529814\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | 997.525 | 0.0608954 | ||||||||
\(646\) | 14561.1 | 0.886843 | ||||||||
\(647\) | −23702.8 | −1.44027 | −0.720135 | − | 0.693834i | \(-0.755920\pi\) | ||||
−0.720135 | + | 0.693834i | \(0.755920\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 30808.7 | 1.86340 | ||||||||
\(650\) | −20326.7 | −1.22658 | ||||||||
\(651\) | −1982.31 | −0.119344 | ||||||||
\(652\) | −13528.9 | −0.812626 | ||||||||
\(653\) | −11241.5 | −0.673681 | −0.336840 | − | 0.941562i | \(-0.609358\pi\) | ||||
−0.336840 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(654\) | 842.066 | 0.0503477 | ||||||||
\(655\) | 2334.99 | 0.139291 | ||||||||
\(656\) | 600.110 | 0.0357170 | ||||||||
\(657\) | −1026.14 | −0.0609338 | ||||||||
\(658\) | −2186.32 | −0.129531 | ||||||||
\(659\) | −119.895 | −0.00708715 | −0.00354357 | − | 0.999994i | \(-0.501128\pi\) | ||||
−0.00354357 | + | 0.999994i | \(0.501128\pi\) | |||||||
\(660\) | −761.216 | −0.0448944 | ||||||||
\(661\) | −291.504 | −0.0171531 | −0.00857653 | − | 0.999963i | \(-0.502730\pi\) | ||||
−0.00857653 | + | 0.999963i | \(0.502730\pi\) | |||||||
\(662\) | 20658.4 | 1.21286 | ||||||||
\(663\) | 22337.6 | 1.30848 | ||||||||
\(664\) | −9876.23 | −0.577217 | ||||||||
\(665\) | 729.995 | 0.0425684 | ||||||||
\(666\) | 8011.89 | 0.466148 | ||||||||
\(667\) | −3263.41 | −0.189445 | ||||||||
\(668\) | −3990.39 | −0.231127 | ||||||||
\(669\) | −1184.11 | −0.0684313 | ||||||||
\(670\) | 2400.72 | 0.138430 | ||||||||
\(671\) | 19451.3 | 1.11909 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | −620.282 | −0.0355277 | −0.0177638 | − | 0.999842i | \(-0.505655\pi\) | ||||
−0.0177638 | + | 0.999842i | \(0.505655\pi\) | |||||||
\(674\) | 17764.1 | 1.01520 | ||||||||
\(675\) | 3329.78 | 0.189872 | ||||||||
\(676\) | 18378.3 | 1.04565 | ||||||||
\(677\) | 11632.0 | 0.660344 | 0.330172 | − | 0.943921i | \(-0.392893\pi\) | ||||
0.330172 | + | 0.943921i | \(0.392893\pi\) | |||||||
\(678\) | 7361.63 | 0.416993 | ||||||||
\(679\) | −9407.30 | −0.531692 | ||||||||
\(680\) | 935.420 | 0.0527525 | ||||||||
\(681\) | 4492.33 | 0.252785 | ||||||||
\(682\) | −9253.83 | −0.519571 | ||||||||
\(683\) | −7993.51 | −0.447823 | −0.223912 | − | 0.974609i | \(-0.571883\pi\) | ||||
−0.223912 | + | 0.974609i | \(0.571883\pi\) | |||||||
\(684\) | −2900.93 | −0.162164 | ||||||||
\(685\) | −895.249 | −0.0499353 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 9458.32 | 0.525266 | ||||||||
\(688\) | 4110.89 | 0.227800 | ||||||||
\(689\) | −42723.3 | −2.36231 | ||||||||
\(690\) | 178.594 | 0.00985354 | ||||||||
\(691\) | −12692.5 | −0.698761 | −0.349381 | − | 0.936981i | \(-0.613608\pi\) | ||||
−0.349381 | + | 0.936981i | \(0.613608\pi\) | |||||||
\(692\) | −1681.84 | −0.0923903 | ||||||||
\(693\) | −3088.02 | −0.169270 | ||||||||
\(694\) | 13200.8 | 0.722040 | ||||||||
\(695\) | −2468.88 | −0.134748 | ||||||||
\(696\) | 3405.29 | 0.185456 | ||||||||
\(697\) | −3388.76 | −0.184159 | ||||||||
\(698\) | 18833.0 | 1.02126 | ||||||||
\(699\) | −16589.7 | −0.897683 | ||||||||
\(700\) | −3453.10 | −0.186450 | ||||||||
\(701\) | 12675.6 | 0.682953 | 0.341477 | − | 0.939890i | \(-0.389073\pi\) | ||||
0.341477 | + | 0.939890i | \(0.389073\pi\) | |||||||
\(702\) | −4450.19 | −0.239262 | ||||||||
\(703\) | −35867.2 | −1.92426 | ||||||||
\(704\) | −3137.04 | −0.167943 | ||||||||
\(705\) | −606.309 | −0.0323900 | ||||||||
\(706\) | 25875.8 | 1.37939 | ||||||||
\(707\) | 9661.83 | 0.513961 | ||||||||
\(708\) | 7542.49 | 0.400373 | ||||||||
\(709\) | 36203.0 | 1.91768 | 0.958838 | − | 0.283953i | \(-0.0916460\pi\) | ||||
0.958838 | + | 0.283953i | \(0.0916460\pi\) | |||||||
\(710\) | 2218.89 | 0.117287 | ||||||||
\(711\) | 2750.42 | 0.145076 | ||||||||
\(712\) | 6623.63 | 0.348639 | ||||||||
\(713\) | 2171.10 | 0.114037 | ||||||||
\(714\) | 3794.72 | 0.198899 | ||||||||
\(715\) | 5227.71 | 0.273434 | ||||||||
\(716\) | −2127.38 | −0.111039 | ||||||||
\(717\) | −15130.3 | −0.788079 | ||||||||
\(718\) | 9375.89 | 0.487333 | ||||||||
\(719\) | −5039.30 | −0.261383 | −0.130691 | − | 0.991423i | \(-0.541720\pi\) | ||||
−0.130691 | + | 0.991423i | \(0.541720\pi\) | |||||||
\(720\) | −186.359 | −0.00964607 | ||||||||
\(721\) | −12936.8 | −0.668227 | ||||||||
\(722\) | −731.241 | −0.0376925 | ||||||||
\(723\) | 2958.26 | 0.152170 | ||||||||
\(724\) | −1990.08 | −0.102156 | ||||||||
\(725\) | 17498.3 | 0.896371 | ||||||||
\(726\) | −6429.53 | −0.328681 | ||||||||
\(727\) | 8312.00 | 0.424037 | 0.212019 | − | 0.977266i | \(-0.431996\pi\) | ||||
0.212019 | + | 0.977266i | \(0.431996\pi\) | |||||||
\(728\) | 4615.02 | 0.234950 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 295.108 | 0.0149622 | ||||||||
\(731\) | −23213.8 | −1.17455 | ||||||||
\(732\) | 4762.01 | 0.240449 | ||||||||
\(733\) | −34034.7 | −1.71501 | −0.857504 | − | 0.514478i | \(-0.827986\pi\) | ||||
−0.857504 | + | 0.514478i | \(0.827986\pi\) | |||||||
\(734\) | −21605.4 | −1.08647 | ||||||||
\(735\) | 190.241 | 0.00954713 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 45463.7 | 2.27229 | ||||||||
\(738\) | 675.124 | 0.0336743 | ||||||||
\(739\) | 10630.7 | 0.529170 | 0.264585 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264585 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(740\) | −2304.14 | −0.114462 | ||||||||
\(741\) | 19922.4 | 0.987676 | ||||||||
\(742\) | −7257.85 | −0.359089 | ||||||||
\(743\) | −15072.4 | −0.744216 | −0.372108 | − | 0.928189i | \(-0.621365\pi\) | ||||
−0.372108 | + | 0.928189i | \(0.621365\pi\) | |||||||
\(744\) | −2265.49 | −0.111636 | ||||||||
\(745\) | −100.142 | −0.00492472 | ||||||||
\(746\) | 13711.8 | 0.672954 | ||||||||
\(747\) | −11110.8 | −0.544205 | ||||||||
\(748\) | 17714.5 | 0.865919 | ||||||||
\(749\) | 11168.0 | 0.544819 | ||||||||
\(750\) | −1928.23 | −0.0938786 | ||||||||
\(751\) | −23636.4 | −1.14848 | −0.574238 | − | 0.818689i | \(-0.694701\pi\) | ||||
−0.574238 | + | 0.818689i | \(0.694701\pi\) | |||||||
\(752\) | −2498.65 | −0.121166 | ||||||||
\(753\) | 8754.20 | 0.423666 | ||||||||
\(754\) | −23386.1 | −1.12954 | ||||||||
\(755\) | −2191.66 | −0.105646 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 31193.3 | 1.49768 | 0.748838 | − | 0.662753i | \(-0.230612\pi\) | ||||
0.748838 | + | 0.662753i | \(0.230612\pi\) | |||||||
\(758\) | 14696.8 | 0.704235 | ||||||||
\(759\) | 3382.12 | 0.161743 | ||||||||
\(760\) | 834.281 | 0.0398191 | ||||||||
\(761\) | 19915.8 | 0.948680 | 0.474340 | − | 0.880342i | \(-0.342687\pi\) | ||||
0.474340 | + | 0.880342i | \(0.342687\pi\) | |||||||
\(762\) | 5579.83 | 0.265270 | ||||||||
\(763\) | −982.410 | −0.0466129 | ||||||||
\(764\) | 4318.16 | 0.204484 | ||||||||
\(765\) | 1052.35 | 0.0497356 | ||||||||
\(766\) | −19835.0 | −0.935596 | ||||||||
\(767\) | −51798.7 | −2.43852 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −36684.1 | −1.72024 | −0.860119 | − | 0.510093i | \(-0.829611\pi\) | ||||
−0.860119 | + | 0.510093i | \(0.829611\pi\) | |||||||
\(770\) | 888.085 | 0.0415641 | ||||||||
\(771\) | 7447.77 | 0.347892 | ||||||||
\(772\) | −7046.82 | −0.328524 | ||||||||
\(773\) | 18762.4 | 0.873008 | 0.436504 | − | 0.899702i | \(-0.356217\pi\) | ||||
0.436504 | + | 0.899702i | \(0.356217\pi\) | |||||||
\(774\) | 4624.75 | 0.214772 | ||||||||
\(775\) | −11641.4 | −0.539574 | ||||||||
\(776\) | −10751.2 | −0.497353 | ||||||||
\(777\) | −9347.20 | −0.431569 | ||||||||
\(778\) | −9562.81 | −0.440673 | ||||||||
\(779\) | −3022.36 | −0.139008 | ||||||||
\(780\) | 1279.83 | 0.0587504 | ||||||||
\(781\) | 42020.2 | 1.92523 | ||||||||
\(782\) | −4156.12 | −0.190054 | ||||||||
\(783\) | 3830.95 | 0.174849 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 3574.13 | 0.162505 | ||||||||
\(786\) | 10825.6 | 0.491266 | ||||||||
\(787\) | 8865.12 | 0.401534 | 0.200767 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200767 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(788\) | 10990.4 | 0.496849 | ||||||||
\(789\) | −16706.3 | −0.753817 | ||||||||
\(790\) | −790.994 | −0.0356232 | ||||||||
\(791\) | −8588.56 | −0.386061 | ||||||||
\(792\) | −3529.17 | −0.158338 | ||||||||
\(793\) | −32703.5 | −1.46448 | ||||||||
\(794\) | 10825.2 | 0.483845 | ||||||||
\(795\) | −2012.74 | −0.0897919 | ||||||||
\(796\) | −7642.08 | −0.340284 | ||||||||
\(797\) | −7271.07 | −0.323155 | −0.161578 | − | 0.986860i | \(-0.551658\pi\) | ||||
−0.161578 | + | 0.986860i | \(0.551658\pi\) | |||||||
\(798\) | 3384.42 | 0.150134 | ||||||||
\(799\) | 14109.6 | 0.624735 | ||||||||
\(800\) | −3946.41 | −0.174408 | ||||||||
\(801\) | 7451.58 | 0.328700 | ||||||||
\(802\) | −3942.12 | −0.173568 | ||||||||
\(803\) | 5588.60 | 0.245601 | ||||||||
\(804\) | 11130.3 | 0.488228 | ||||||||
\(805\) | −208.359 | −0.00912260 | ||||||||
\(806\) | 15558.5 | 0.679930 | ||||||||
\(807\) | 7996.87 | 0.348827 | ||||||||
\(808\) | 11042.1 | 0.480766 | ||||||||
\(809\) | 4495.05 | 0.195349 | 0.0976746 | − | 0.995218i | \(-0.468860\pi\) | ||||
0.0976746 | + | 0.995218i | \(0.468860\pi\) | |||||||
\(810\) | −209.653 | −0.00909440 | ||||||||
\(811\) | 20649.3 | 0.894073 | 0.447037 | − | 0.894516i | \(-0.352479\pi\) | ||||
0.447037 | + | 0.894516i | \(0.352479\pi\) | |||||||
\(812\) | −3972.84 | −0.171699 | ||||||||
\(813\) | 10905.6 | 0.470448 | ||||||||
\(814\) | −43634.7 | −1.87886 | ||||||||
\(815\) | 4377.12 | 0.188127 | ||||||||
\(816\) | 4336.82 | 0.186053 | ||||||||
\(817\) | −20703.9 | −0.886581 | ||||||||
\(818\) | −1297.46 | −0.0554580 | ||||||||
\(819\) | 5191.89 | 0.221513 | ||||||||
\(820\) | −194.159 | −0.00826869 | ||||||||
\(821\) | −31424.8 | −1.33585 | −0.667926 | − | 0.744228i | \(-0.732818\pi\) | ||||
−0.667926 | + | 0.744228i | \(0.732818\pi\) | |||||||
\(822\) | −4150.57 | −0.176117 | ||||||||
\(823\) | 11977.4 | 0.507299 | 0.253650 | − | 0.967296i | \(-0.418369\pi\) | ||||
0.253650 | + | 0.967296i | \(0.418369\pi\) | |||||||
\(824\) | −14784.9 | −0.625069 | ||||||||
\(825\) | −18134.8 | −0.765300 | ||||||||
\(826\) | −8799.58 | −0.370674 | ||||||||
\(827\) | −21289.6 | −0.895180 | −0.447590 | − | 0.894239i | \(-0.647718\pi\) | ||||
−0.447590 | + | 0.894239i | \(0.647718\pi\) | |||||||
\(828\) | 828.000 | 0.0347524 | ||||||||
\(829\) | −3264.10 | −0.136751 | −0.0683757 | − | 0.997660i | \(-0.521782\pi\) | ||||
−0.0683757 | + | 0.997660i | \(0.521782\pi\) | |||||||
\(830\) | 3195.35 | 0.133629 | ||||||||
\(831\) | 11189.5 | 0.467099 | ||||||||
\(832\) | 5274.30 | 0.219776 | ||||||||
\(833\) | −4427.17 | −0.184144 | ||||||||
\(834\) | −11446.3 | −0.475242 | ||||||||
\(835\) | 1291.05 | 0.0535073 | ||||||||
\(836\) | 15799.2 | 0.653621 | ||||||||
\(837\) | −2548.68 | −0.105251 | ||||||||
\(838\) | −26614.3 | −1.09711 | ||||||||
\(839\) | −43345.5 | −1.78361 | −0.891807 | − | 0.452416i | \(-0.850562\pi\) | ||||
−0.891807 | + | 0.452416i | \(0.850562\pi\) | |||||||
\(840\) | 217.418 | 0.00893053 | ||||||||
\(841\) | −4257.02 | −0.174547 | ||||||||
\(842\) | 18806.1 | 0.769718 | ||||||||
\(843\) | −6286.37 | −0.256837 | ||||||||
\(844\) | 10315.6 | 0.420708 | ||||||||
\(845\) | −5946.09 | −0.242073 | ||||||||
\(846\) | −2810.98 | −0.114236 | ||||||||
\(847\) | 7501.12 | 0.304299 | ||||||||
\(848\) | −8294.69 | −0.335897 | ||||||||
\(849\) | −25736.4 | −1.04037 | ||||||||
\(850\) | 22285.0 | 0.899256 | ||||||||
\(851\) | 10237.4 | 0.412378 | ||||||||
\(852\) | 10287.3 | 0.413657 | ||||||||
\(853\) | 1295.84 | 0.0520148 | 0.0260074 | − | 0.999662i | \(-0.491721\pi\) | ||||
0.0260074 | + | 0.999662i | \(0.491721\pi\) | |||||||
\(854\) | −5555.68 | −0.222613 | ||||||||
\(855\) | 938.566 | 0.0375418 | ||||||||
\(856\) | 12763.4 | 0.509631 | ||||||||
\(857\) | −35943.9 | −1.43270 | −0.716348 | − | 0.697743i | \(-0.754188\pi\) | ||||
−0.716348 | + | 0.697743i | \(0.754188\pi\) | |||||||
\(858\) | 24236.8 | 0.964373 | ||||||||
\(859\) | 14368.5 | 0.570718 | 0.285359 | − | 0.958421i | \(-0.407887\pi\) | ||||
0.285359 | + | 0.958421i | \(0.407887\pi\) | |||||||
\(860\) | −1330.03 | −0.0527370 | ||||||||
\(861\) | −787.645 | −0.0311764 | ||||||||
\(862\) | −7749.10 | −0.306190 | ||||||||
\(863\) | −56.2780 | −0.00221984 | −0.00110992 | − | 0.999999i | \(-0.500353\pi\) | ||||
−0.00110992 | + | 0.999999i | \(0.500353\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 544.142 | 0.0213889 | ||||||||
\(866\) | −18469.4 | −0.724729 | ||||||||
\(867\) | −9750.59 | −0.381946 | ||||||||
\(868\) | 2643.08 | 0.103355 | ||||||||
\(869\) | −14979.5 | −0.584745 | ||||||||
\(870\) | −1101.75 | −0.0429341 | ||||||||
\(871\) | −76438.2 | −2.97360 | ||||||||
\(872\) | −1122.75 | −0.0436024 | ||||||||
\(873\) | −12095.1 | −0.468909 | ||||||||
\(874\) | −3706.75 | −0.143458 | ||||||||
\(875\) | 2249.60 | 0.0869147 | ||||||||
\(876\) | 1368.19 | 0.0527702 | ||||||||
\(877\) | 3184.12 | 0.122600 | 0.0612999 | − | 0.998119i | \(-0.480475\pi\) | ||||
0.0612999 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(878\) | −35279.1 | −1.35605 | ||||||||
\(879\) | 11448.7 | 0.439312 | ||||||||
\(880\) | 1014.95 | 0.0388797 | ||||||||
\(881\) | 33026.3 | 1.26298 | 0.631490 | − | 0.775384i | \(-0.282444\pi\) | ||||
0.631490 | + | 0.775384i | \(0.282444\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 19095.2 | 0.727751 | 0.363875 | − | 0.931448i | \(-0.381453\pi\) | ||||
0.363875 | + | 0.931448i | \(0.381453\pi\) | |||||||
\(884\) | −29783.5 | −1.13317 | ||||||||
\(885\) | −2440.29 | −0.0926887 | ||||||||
\(886\) | −34480.8 | −1.30746 | ||||||||
\(887\) | 38429.8 | 1.45473 | 0.727366 | − | 0.686250i | \(-0.240744\pi\) | ||||
0.727366 | + | 0.686250i | \(0.240744\pi\) | |||||||
\(888\) | −10682.5 | −0.403696 | ||||||||
\(889\) | −6509.81 | −0.245593 | ||||||||
\(890\) | −2143.00 | −0.0807119 | ||||||||
\(891\) | −3970.31 | −0.149282 | ||||||||
\(892\) | 1578.82 | 0.0592632 | ||||||||
\(893\) | 12584.1 | 0.471568 | ||||||||
\(894\) | −464.281 | −0.0173690 | ||||||||
\(895\) | 688.290 | 0.0257061 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | −5686.36 | −0.211663 | ||||||||
\(898\) | −18162.9 | −0.674947 | ||||||||
\(899\) | −13393.5 | −0.496885 | ||||||||
\(900\) | −4439.71 | −0.164434 | ||||||||
\(901\) | 46839.3 | 1.73190 | ||||||||
\(902\) | −3676.89 | −0.135728 | ||||||||
\(903\) | −5395.54 | −0.198840 | ||||||||
\(904\) | −9815.50 | −0.361127 | ||||||||
\(905\) | 643.870 | 0.0236497 | ||||||||
\(906\) | −10161.0 | −0.372602 | ||||||||
\(907\) | 461.488 | 0.0168946 | 0.00844732 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844732 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(908\) | −5989.77 | −0.218918 | ||||||||
\(909\) | 12422.3 | 0.453271 | ||||||||
\(910\) | −1493.14 | −0.0543923 | ||||||||
\(911\) | −11511.9 | −0.418667 | −0.209333 | − | 0.977844i | \(-0.567129\pi\) | ||||
−0.209333 | + | 0.977844i | \(0.567129\pi\) | |||||||
\(912\) | 3867.91 | 0.140438 | ||||||||
\(913\) | 60511.9 | 2.19349 | ||||||||
\(914\) | 2157.18 | 0.0780669 | ||||||||
\(915\) | −1540.70 | −0.0556654 | ||||||||
\(916\) | −12611.1 | −0.454893 | ||||||||
\(917\) | −12629.8 | −0.454824 | ||||||||
\(918\) | 4878.92 | 0.175412 | ||||||||
\(919\) | −30932.9 | −1.11032 | −0.555159 | − | 0.831744i | \(-0.687343\pi\) | ||||
−0.555159 | + | 0.831744i | \(0.687343\pi\) | |||||||
\(920\) | −238.125 | −0.00853341 | ||||||||
\(921\) | −18529.6 | −0.662943 | ||||||||
\(922\) | 17368.9 | 0.620404 | ||||||||
\(923\) | −70648.7 | −2.51942 | ||||||||
\(924\) | 4117.36 | 0.146592 | ||||||||
\(925\) | −54892.6 | −1.95120 | ||||||||
\(926\) | −37801.9 | −1.34152 | ||||||||
\(927\) | −16633.0 | −0.589321 | ||||||||
\(928\) | −4540.39 | −0.160610 | ||||||||
\(929\) | −37586.9 | −1.32743 | −0.663717 | − | 0.747984i | \(-0.731022\pi\) | ||||
−0.663717 | + | 0.747984i | \(0.731022\pi\) | |||||||
\(930\) | 732.976 | 0.0258443 | ||||||||
\(931\) | −3948.49 | −0.138997 | ||||||||
\(932\) | 22119.6 | 0.777416 | ||||||||
\(933\) | −5909.46 | −0.207360 | ||||||||
\(934\) | 1619.98 | 0.0567532 | ||||||||
\(935\) | −5731.35 | −0.200465 | ||||||||
\(936\) | 5933.59 | 0.207207 | ||||||||
\(937\) | −22224.0 | −0.774843 | −0.387421 | − | 0.921903i | \(-0.626634\pi\) | ||||
−0.387421 | + | 0.921903i | \(0.626634\pi\) | |||||||
\(938\) | −12985.3 | −0.452011 | ||||||||
\(939\) | −7971.89 | −0.277053 | ||||||||
\(940\) | 808.412 | 0.0280505 | ||||||||
\(941\) | −52898.1 | −1.83255 | −0.916275 | − | 0.400549i | \(-0.868819\pi\) | ||||
−0.916275 | + | 0.400549i | \(0.868819\pi\) | |||||||
\(942\) | 16570.5 | 0.573137 | ||||||||
\(943\) | 862.658 | 0.0297901 | ||||||||
\(944\) | −10056.7 | −0.346733 | ||||||||
\(945\) | 244.596 | 0.00841978 | ||||||||
\(946\) | −25187.5 | −0.865663 | ||||||||
\(947\) | −1594.40 | −0.0547107 | −0.0273554 | − | 0.999626i | \(-0.508709\pi\) | ||||
−0.0273554 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(948\) | −3667.23 | −0.125639 | ||||||||
\(949\) | −9396.12 | −0.321403 | ||||||||
\(950\) | 19875.5 | 0.678784 | ||||||||
\(951\) | −9929.86 | −0.338589 | ||||||||
\(952\) | −5059.62 | −0.172251 | ||||||||
\(953\) | −16262.4 | −0.552769 | −0.276385 | − | 0.961047i | \(-0.589136\pi\) | ||||
−0.276385 | + | 0.961047i | \(0.589136\pi\) | |||||||
\(954\) | −9331.52 | −0.316687 | ||||||||
\(955\) | −1397.09 | −0.0473391 | ||||||||
\(956\) | 20173.8 | 0.682496 | ||||||||
\(957\) | −20864.3 | −0.704752 | ||||||||
\(958\) | −15227.5 | −0.513548 | ||||||||
\(959\) | 4842.34 | 0.163052 | ||||||||
\(960\) | 248.478 | 0.00835374 | ||||||||
\(961\) | −20880.5 | −0.700899 | ||||||||
\(962\) | 73363.0 | 2.45875 | ||||||||
\(963\) | 14358.8 | 0.480485 | ||||||||
\(964\) | −3944.34 | −0.131783 | ||||||||
\(965\) | 2279.92 | 0.0760552 | ||||||||
\(966\) | −966.000 | −0.0321745 | ||||||||
\(967\) | −12443.3 | −0.413806 | −0.206903 | − | 0.978361i | \(-0.566339\pi\) | ||||
−0.206903 | + | 0.978361i | \(0.566339\pi\) | |||||||
\(968\) | 8572.71 | 0.284646 | ||||||||
\(969\) | −21841.7 | −0.724104 | ||||||||
\(970\) | 3478.43 | 0.115140 | ||||||||
\(971\) | 22843.1 | 0.754963 | 0.377481 | − | 0.926017i | \(-0.376790\pi\) | ||||
0.377481 | + | 0.926017i | \(0.376790\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 13354.0 | 0.439989 | ||||||||
\(974\) | 14916.1 | 0.490701 | ||||||||
\(975\) | 30490.0 | 1.00150 | ||||||||
\(976\) | −6349.34 | −0.208235 | ||||||||
\(977\) | −7472.82 | −0.244705 | −0.122352 | − | 0.992487i | \(-0.539044\pi\) | ||||
−0.122352 | + | 0.992487i | \(0.539044\pi\) | |||||||
\(978\) | 20293.3 | 0.663506 | ||||||||
\(979\) | −40583.2 | −1.32487 | ||||||||
\(980\) | −253.655 | −0.00826806 | ||||||||
\(981\) | −1263.10 | −0.0411087 | ||||||||
\(982\) | 3829.10 | 0.124431 | ||||||||
\(983\) | 6369.09 | 0.206655 | 0.103328 | − | 0.994647i | \(-0.467051\pi\) | ||||
0.103328 | + | 0.994647i | \(0.467051\pi\) | |||||||
\(984\) | −900.165 | −0.0291628 | ||||||||
\(985\) | −3555.83 | −0.115023 | ||||||||
\(986\) | 25639.1 | 0.828110 | ||||||||
\(987\) | 3279.48 | 0.105762 | ||||||||
\(988\) | −26563.2 | −0.855352 | ||||||||
\(989\) | 5909.41 | 0.189998 | ||||||||
\(990\) | 1141.82 | 0.0366561 | ||||||||
\(991\) | 48476.3 | 1.55389 | 0.776943 | − | 0.629571i | \(-0.216769\pi\) | ||||
0.776943 | + | 0.629571i | \(0.216769\pi\) | |||||||
\(992\) | 3020.66 | 0.0966795 | ||||||||
\(993\) | −30987.6 | −0.990294 | ||||||||
\(994\) | −12001.8 | −0.382972 | ||||||||
\(995\) | 2472.51 | 0.0787778 | ||||||||
\(996\) | 14814.3 | 0.471296 | ||||||||
\(997\) | 10534.0 | 0.334619 | 0.167310 | − | 0.985904i | \(-0.446492\pi\) | ||||
0.167310 | + | 0.985904i | \(0.446492\pi\) | |||||||
\(998\) | 3597.06 | 0.114091 | ||||||||
\(999\) | −12017.8 | −0.380608 |
(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 | 966.4.a.k.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.k.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |