Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(1,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, 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("378.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{105}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 26 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.62348\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −19.8704 | −1.77726 | −0.888632 | − | 0.458620i | \(-0.848344\pi\) | ||||
−0.888632 | + | 0.458620i | \(0.848344\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −39.7409 | −1.25672 | ||||||||
\(11\) | −39.7409 | −1.08930 | −0.544651 | − | 0.838663i | \(-0.683338\pi\) | ||||
−0.544651 | + | 0.838663i | \(0.683338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 88.6113 | 1.89049 | 0.945244 | − | 0.326364i | \(-0.105824\pi\) | ||||
0.945244 | + | 0.326364i | \(0.105824\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 72.7409 | 1.03778 | 0.518890 | − | 0.854841i | \(-0.326346\pi\) | ||||
0.518890 | + | 0.854841i | \(0.326346\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.0000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −79.4817 | −0.888632 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −79.4817 | −0.770253 | ||||||||
\(23\) | 7.12957 | 0.0646356 | 0.0323178 | − | 0.999478i | \(-0.489711\pi\) | ||||
0.0323178 | + | 0.999478i | \(0.489711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 269.834 | 2.15867 | ||||||||
\(26\) | 177.223 | 1.33678 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | 257.575 | 1.64932 | 0.824662 | − | 0.565625i | \(-0.191365\pi\) | ||||
0.824662 | + | 0.565625i | \(0.191365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −48.6113 | −0.281640 | −0.140820 | − | 0.990035i | \(-0.544974\pi\) | ||||
−0.140820 | + | 0.990035i | \(0.544974\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 145.482 | 0.733821 | ||||||||
\(35\) | −139.093 | −0.671743 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −343.279 | −1.52526 | −0.762631 | − | 0.646834i | \(-0.776093\pi\) | ||||
−0.762631 | + | 0.646834i | \(0.776093\pi\) | |||||||
\(38\) | 76.0000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −158.963 | −0.628358 | ||||||||
\(41\) | 217.093 | 0.826932 | 0.413466 | − | 0.910519i | \(-0.364318\pi\) | ||||
0.413466 | + | 0.910519i | \(0.364318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 447.445 | 1.58685 | 0.793427 | − | 0.608665i | \(-0.208295\pi\) | ||||
0.793427 | + | 0.608665i | \(0.208295\pi\) | |||||||
\(44\) | −158.963 | −0.544651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2591 | 0.0457043 | ||||||||
\(47\) | 387.279 | 1.20192 | 0.600962 | − | 0.799277i | \(-0.294784\pi\) | ||||
0.600962 | + | 0.799277i | \(0.294784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 539.668 | 1.52641 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 354.445 | 0.945244 | ||||||||
\(53\) | −322.093 | −0.834771 | −0.417386 | − | 0.908729i | \(-0.637054\pi\) | ||||
−0.417386 | + | 0.908729i | \(0.637054\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 789.668 | 1.93598 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 515.149 | 1.16625 | ||||||||
\(59\) | −539.113 | −1.18960 | −0.594801 | − | 0.803873i | \(-0.702769\pi\) | ||||
−0.594801 | + | 0.803873i | \(0.702769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 303.555 | 0.637151 | 0.318576 | − | 0.947897i | \(-0.396796\pi\) | ||||
0.318576 | + | 0.947897i | \(0.396796\pi\) | |||||||
\(62\) | −97.2226 | −0.199150 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1760.74 | −3.35990 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −365.834 | −0.667070 | −0.333535 | − | 0.942738i | \(-0.608242\pi\) | ||||
−0.333535 | + | 0.942738i | \(0.608242\pi\) | |||||||
\(68\) | 290.963 | 0.518890 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −278.186 | −0.474994 | ||||||||
\(71\) | −615.389 | −1.02864 | −0.514318 | − | 0.857599i | \(-0.671955\pi\) | ||||
−0.514318 | + | 0.857599i | \(0.671955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 123.555 | 0.198096 | 0.0990480 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990480 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(74\) | −686.558 | −1.07852 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 152.000 | 0.229416 | ||||||||
\(77\) | −278.186 | −0.411717 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 399.166 | 0.568477 | 0.284239 | − | 0.958754i | \(-0.408259\pi\) | ||||
0.284239 | + | 0.958754i | \(0.408259\pi\) | |||||||
\(80\) | −317.927 | −0.444316 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 434.186 | 0.584729 | ||||||||
\(83\) | 633.133 | 0.837293 | 0.418647 | − | 0.908149i | \(-0.362505\pi\) | ||||
0.418647 | + | 0.908149i | \(0.362505\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1445.39 | −1.84441 | ||||||||
\(86\) | 894.890 | 1.12208 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −317.927 | −0.385126 | ||||||||
\(89\) | 823.541 | 0.980845 | 0.490422 | − | 0.871485i | \(-0.336843\pi\) | ||||
0.490422 | + | 0.871485i | \(0.336843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 620.279 | 0.714537 | ||||||||
\(92\) | 28.5183 | 0.0323178 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 774.558 | 0.849889 | ||||||||
\(95\) | −755.076 | −0.815465 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −607.448 | −0.635845 | −0.317923 | − | 0.948117i | \(-0.602985\pi\) | ||||
−0.317923 | + | 0.948117i | \(0.602985\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1079.34 | 1.07934 | ||||||||
\(101\) | 1064.82 | 1.04904 | 0.524521 | − | 0.851397i | \(-0.324244\pi\) | ||||
0.524521 | + | 0.851397i | \(0.324244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1494.50 | 1.42969 | 0.714844 | − | 0.699284i | \(-0.246498\pi\) | ||||
0.714844 | + | 0.699284i | \(0.246498\pi\) | |||||||
\(104\) | 708.890 | 0.668389 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −644.186 | −0.590272 | ||||||||
\(107\) | −1733.30 | −1.56602 | −0.783009 | − | 0.622010i | \(-0.786316\pi\) | ||||
−0.783009 | + | 0.622010i | \(0.786316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.0534 | −0.0290453 | −0.0145227 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145227 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(110\) | 1579.34 | 1.36894 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −242.963 | −0.202266 | −0.101133 | − | 0.994873i | \(-0.532247\pi\) | ||||
−0.101133 | + | 0.994873i | \(0.532247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −141.668 | −0.114875 | ||||||||
\(116\) | 1030.30 | 0.824662 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1078.23 | −0.841176 | ||||||||
\(119\) | 509.186 | 0.392244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 248.335 | 0.186578 | ||||||||
\(122\) | 607.110 | 0.450534 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −194.445 | −0.140820 | ||||||||
\(125\) | −2877.91 | −2.05926 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1600.06 | 1.11797 | 0.558987 | − | 0.829177i | \(-0.311190\pi\) | ||||
0.558987 | + | 0.829177i | \(0.311190\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3521.49 | −2.37581 | ||||||||
\(131\) | 2470.58 | 1.64775 | 0.823875 | − | 0.566771i | \(-0.191808\pi\) | ||||
0.823875 | + | 0.566771i | \(0.191808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 266.000 | 0.173422 | ||||||||
\(134\) | −731.668 | −0.471690 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 581.927 | 0.366910 | ||||||||
\(137\) | −241.966 | −0.150895 | −0.0754474 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754474 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 307.780 | 0.187810 | 0.0939050 | − | 0.995581i | \(-0.470065\pi\) | ||||
0.0939050 | + | 0.995581i | \(0.470065\pi\) | |||||||
\(140\) | −556.372 | −0.335872 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1230.78 | −0.727356 | ||||||||
\(143\) | −3521.49 | −2.05931 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5118.12 | −2.93129 | ||||||||
\(146\) | 247.110 | 0.140075 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1373.12 | −0.762631 | ||||||||
\(149\) | 1298.46 | 0.713922 | 0.356961 | − | 0.934119i | \(-0.383813\pi\) | ||||
0.356961 | + | 0.934119i | \(0.383813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1430.28 | −0.770823 | −0.385411 | − | 0.922745i | \(-0.625940\pi\) | ||||
−0.385411 | + | 0.922745i | \(0.625940\pi\) | |||||||
\(152\) | 304.000 | 0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −556.372 | −0.291128 | ||||||||
\(155\) | 965.927 | 0.500549 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3641.18 | −1.85094 | −0.925469 | − | 0.378822i | \(-0.876329\pi\) | ||||
−0.925469 | + | 0.378822i | \(0.876329\pi\) | |||||||
\(158\) | 798.332 | 0.401974 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −635.854 | −0.314179 | ||||||||
\(161\) | 49.9070 | 0.0244300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3298.45 | −1.58500 | −0.792498 | − | 0.609874i | \(-0.791220\pi\) | ||||
−0.792498 | + | 0.609874i | \(0.791220\pi\) | |||||||
\(164\) | 868.372 | 0.413466 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1266.27 | 0.592056 | ||||||||
\(167\) | −1402.69 | −0.649959 | −0.324980 | − | 0.945721i | \(-0.605357\pi\) | ||||
−0.324980 | + | 0.945721i | \(0.605357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5654.96 | 2.57395 | ||||||||
\(170\) | −2890.78 | −1.30419 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1789.78 | 0.793427 | ||||||||
\(173\) | −1683.01 | −0.739635 | −0.369817 | − | 0.929104i | \(-0.620580\pi\) | ||||
−0.369817 | + | 0.929104i | \(0.620580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1888.84 | 0.815901 | ||||||||
\(176\) | −635.854 | −0.272325 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1647.08 | 0.693562 | ||||||||
\(179\) | 1492.08 | 0.623035 | 0.311517 | − | 0.950240i | \(-0.399163\pi\) | ||||
0.311517 | + | 0.950240i | \(0.399163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2945.73 | 1.20969 | 0.604846 | − | 0.796343i | \(-0.293235\pi\) | ||||
0.604846 | + | 0.796343i | \(0.293235\pi\) | |||||||
\(182\) | 1240.56 | 0.505254 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 57.0366 | 0.0228521 | ||||||||
\(185\) | 6821.10 | 2.71080 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2890.78 | −1.13045 | ||||||||
\(188\) | 1549.12 | 0.600962 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1510.15 | −0.576621 | ||||||||
\(191\) | −1913.44 | −0.724879 | −0.362439 | − | 0.932007i | \(-0.618056\pi\) | ||||
−0.362439 | + | 0.932007i | \(0.618056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −59.3263 | −0.0221264 | −0.0110632 | − | 0.999939i | \(-0.503522\pi\) | ||||
−0.0110632 | + | 0.999939i | \(0.503522\pi\) | |||||||
\(194\) | −1214.90 | −0.449611 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 287.780 | 0.104079 | 0.0520394 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520394 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4014.51 | −1.43006 | −0.715028 | − | 0.699096i | \(-0.753586\pi\) | ||||
−0.715028 | + | 0.699096i | \(0.753586\pi\) | |||||||
\(200\) | 2158.67 | 0.763205 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2129.63 | 0.741785 | ||||||||
\(203\) | 1803.02 | 0.623386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4313.73 | −1.46968 | ||||||||
\(206\) | 2989.01 | 1.01094 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1417.78 | 0.472622 | ||||||||
\(209\) | −1510.15 | −0.499806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4810.30 | −1.56945 | −0.784726 | − | 0.619842i | \(-0.787197\pi\) | ||||
−0.784726 | + | 0.619842i | \(0.787197\pi\) | |||||||
\(212\) | −1288.37 | −0.417386 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3466.59 | −1.10734 | ||||||||
\(215\) | −8890.93 | −2.82026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −340.279 | −0.106450 | ||||||||
\(218\) | −66.1068 | −0.0205381 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3158.67 | 0.967989 | ||||||||
\(221\) | 6445.66 | 1.96191 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3453.12 | 1.03694 | 0.518470 | − | 0.855096i | \(-0.326502\pi\) | ||||
0.518470 | + | 0.855096i | \(0.326502\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −485.927 | −0.143024 | ||||||||
\(227\) | −158.127 | −0.0462345 | −0.0231172 | − | 0.999733i | \(-0.507359\pi\) | ||||
−0.0231172 | + | 0.999733i | \(0.507359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −612.332 | −0.176699 | −0.0883495 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883495 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(230\) | −283.335 | −0.0812286 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2060.60 | 0.583124 | ||||||||
\(233\) | 5206.39 | 1.46387 | 0.731936 | − | 0.681374i | \(-0.238617\pi\) | ||||
0.731936 | + | 0.681374i | \(0.238617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7695.40 | −2.13614 | ||||||||
\(236\) | −2156.45 | −0.594801 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1018.37 | 0.277358 | ||||||||
\(239\) | −647.854 | −0.175340 | −0.0876698 | − | 0.996150i | \(-0.527942\pi\) | ||||
−0.0876698 | + | 0.996150i | \(0.527942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6141.67 | 1.64158 | 0.820788 | − | 0.571232i | \(-0.193535\pi\) | ||||
0.820788 | + | 0.571232i | \(0.193535\pi\) | |||||||
\(242\) | 496.671 | 0.131931 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1214.22 | 0.318576 | ||||||||
\(245\) | −973.651 | −0.253895 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3367.23 | 0.867415 | ||||||||
\(248\) | −388.890 | −0.0995748 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5755.82 | −1.45612 | ||||||||
\(251\) | −4779.84 | −1.20199 | −0.600997 | − | 0.799251i | \(-0.705230\pi\) | ||||
−0.600997 | + | 0.799251i | \(0.705230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −283.335 | −0.0704077 | ||||||||
\(254\) | 3200.12 | 0.790526 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1207.85 | 0.293165 | 0.146583 | − | 0.989198i | \(-0.453173\pi\) | ||||
0.146583 | + | 0.989198i | \(0.453173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2402.95 | −0.576495 | ||||||||
\(260\) | −7042.98 | −1.67995 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4941.16 | 1.16514 | ||||||||
\(263\) | 2869.66 | 0.672817 | 0.336408 | − | 0.941716i | \(-0.390788\pi\) | ||||
0.336408 | + | 0.941716i | \(0.390788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6400.12 | 1.48361 | ||||||||
\(266\) | 532.000 | 0.122628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1463.34 | −0.333535 | ||||||||
\(269\) | 5871.69 | 1.33087 | 0.665434 | − | 0.746457i | \(-0.268247\pi\) | ||||
0.665434 | + | 0.746457i | \(0.268247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1081.96 | 0.242525 | 0.121263 | − | 0.992620i | \(-0.461306\pi\) | ||||
0.121263 | + | 0.992620i | \(0.461306\pi\) | |||||||
\(272\) | 1163.85 | 0.259445 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −483.933 | −0.106699 | ||||||||
\(275\) | −10723.4 | −2.35144 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 931.511 | 0.202054 | 0.101027 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101027 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(278\) | 615.561 | 0.132802 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1112.74 | −0.237497 | ||||||||
\(281\) | −1915.50 | −0.406652 | −0.203326 | − | 0.979111i | \(-0.565175\pi\) | ||||
−0.203326 | + | 0.979111i | \(0.565175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 126.985 | 0.0266730 | 0.0133365 | − | 0.999911i | \(-0.495755\pi\) | ||||
0.0133365 | + | 0.999911i | \(0.495755\pi\) | |||||||
\(284\) | −2461.55 | −0.514318 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7042.98 | −1.45615 | ||||||||
\(287\) | 1519.65 | 0.312551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 378.232 | 0.0769859 | ||||||||
\(290\) | −10236.2 | −2.07273 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 494.220 | 0.0990480 | ||||||||
\(293\) | −4129.14 | −0.823300 | −0.411650 | − | 0.911342i | \(-0.635047\pi\) | ||||
−0.411650 | + | 0.911342i | \(0.635047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10712.4 | 2.11424 | ||||||||
\(296\) | −2746.23 | −0.539262 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2596.93 | 0.504819 | ||||||||
\(299\) | 631.761 | 0.122193 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3132.12 | 0.599775 | ||||||||
\(302\) | −2860.55 | −0.545054 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 608.000 | 0.114708 | ||||||||
\(305\) | −6031.76 | −1.13239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1528.43 | 0.284144 | 0.142072 | − | 0.989856i | \(-0.454624\pi\) | ||||
0.142072 | + | 0.989856i | \(0.454624\pi\) | |||||||
\(308\) | −1112.74 | −0.205859 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1931.85 | 0.353942 | ||||||||
\(311\) | 8985.18 | 1.63827 | 0.819136 | − | 0.573599i | \(-0.194453\pi\) | ||||
0.819136 | + | 0.573599i | \(0.194453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9218.80 | −1.66478 | −0.832392 | − | 0.554187i | \(-0.813029\pi\) | ||||
−0.832392 | + | 0.554187i | \(0.813029\pi\) | |||||||
\(314\) | −7282.35 | −1.30881 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1596.66 | 0.284239 | ||||||||
\(317\) | 802.226 | 0.142137 | 0.0710686 | − | 0.997471i | \(-0.477359\pi\) | ||||
0.0710686 | + | 0.997471i | \(0.477359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10236.2 | −1.79661 | ||||||||
\(320\) | −1271.71 | −0.222158 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 99.8140 | 0.0172746 | ||||||||
\(323\) | 2764.15 | 0.476166 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23910.3 | 4.08094 | ||||||||
\(326\) | −6596.90 | −1.12076 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1736.74 | 0.292365 | ||||||||
\(329\) | 2710.95 | 0.454285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −953.564 | −0.158346 | −0.0791731 | − | 0.996861i | \(-0.525228\pi\) | ||||
−0.0791731 | + | 0.996861i | \(0.525228\pi\) | |||||||
\(332\) | 2532.53 | 0.418647 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2805.37 | −0.459591 | ||||||||
\(335\) | 7269.27 | 1.18556 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9659.00 | 1.56130 | 0.780652 | − | 0.624966i | \(-0.214887\pi\) | ||||
0.780652 | + | 0.624966i | \(0.214887\pi\) | |||||||
\(338\) | 11309.9 | 1.82005 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5781.57 | −0.922204 | ||||||||
\(341\) | 1931.85 | 0.306791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3579.56 | 0.561038 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3366.02 | −0.523001 | ||||||||
\(347\) | 1854.34 | 0.286876 | 0.143438 | − | 0.989659i | \(-0.454184\pi\) | ||||
0.143438 | + | 0.989659i | \(0.454184\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2643.08 | −0.405389 | −0.202695 | − | 0.979242i | \(-0.564970\pi\) | ||||
−0.202695 | + | 0.979242i | \(0.564970\pi\) | |||||||
\(350\) | 3777.67 | 0.576929 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1271.71 | −0.192563 | ||||||||
\(353\) | −3096.64 | −0.466905 | −0.233453 | − | 0.972368i | \(-0.575002\pi\) | ||||
−0.233453 | + | 0.972368i | \(0.575002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12228.0 | 1.82816 | ||||||||
\(356\) | 3294.16 | 0.490422 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2984.16 | 0.440552 | ||||||||
\(359\) | 5575.10 | 0.819617 | 0.409809 | − | 0.912172i | \(-0.365595\pi\) | ||||
0.409809 | + | 0.912172i | \(0.365595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5415.00 | −0.789474 | ||||||||
\(362\) | 5891.45 | 0.855381 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2481.12 | 0.357269 | ||||||||
\(365\) | −2455.09 | −0.352069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8400.17 | 1.19478 | 0.597391 | − | 0.801950i | \(-0.296204\pi\) | ||||
0.597391 | + | 0.801950i | \(0.296204\pi\) | |||||||
\(368\) | 114.073 | 0.0161589 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13642.2 | 1.91682 | ||||||||
\(371\) | −2254.65 | −0.315514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4612.62 | 0.640301 | 0.320151 | − | 0.947367i | \(-0.396266\pi\) | ||||
0.320151 | + | 0.947367i | \(0.396266\pi\) | |||||||
\(374\) | −5781.57 | −0.799352 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3098.23 | 0.424944 | ||||||||
\(377\) | 22824.0 | 3.11803 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 669.166 | 0.0906933 | 0.0453466 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453466 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(380\) | −3020.30 | −0.407733 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3826.88 | −0.512567 | ||||||||
\(383\) | −2190.08 | −0.292187 | −0.146094 | − | 0.989271i | \(-0.546670\pi\) | ||||
−0.146094 | + | 0.989271i | \(0.546670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5527.67 | 0.731731 | ||||||||
\(386\) | −118.653 | −0.0156457 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2429.79 | −0.317923 | ||||||||
\(389\) | 12281.9 | 1.60082 | 0.800410 | − | 0.599452i | \(-0.204615\pi\) | ||||
0.800410 | + | 0.599452i | \(0.204615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 518.611 | 0.0670775 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 575.561 | 0.0735948 | ||||||||
\(395\) | −7931.60 | −1.01033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11016.9 | −1.39275 | −0.696376 | − | 0.717677i | \(-0.745206\pi\) | ||||
−0.696376 | + | 0.717677i | \(0.745206\pi\) | |||||||
\(398\) | −8029.02 | −1.01120 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4317.34 | 0.539668 | ||||||||
\(401\) | −2428.73 | −0.302456 | −0.151228 | − | 0.988499i | \(-0.548323\pi\) | ||||
−0.151228 | + | 0.988499i | \(0.548323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4307.51 | −0.532437 | ||||||||
\(404\) | 4259.27 | 0.524521 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3606.05 | 0.440801 | ||||||||
\(407\) | 13642.2 | 1.66147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8077.01 | −0.976485 | −0.488243 | − | 0.872708i | \(-0.662362\pi\) | ||||
−0.488243 | + | 0.872708i | \(0.662362\pi\) | |||||||
\(410\) | −8627.46 | −1.03922 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5978.02 | 0.714844 | ||||||||
\(413\) | −3773.79 | −0.449627 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12580.6 | −1.48809 | ||||||||
\(416\) | 2835.56 | 0.334194 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3020.30 | −0.353416 | ||||||||
\(419\) | −10911.5 | −1.27223 | −0.636114 | − | 0.771595i | \(-0.719459\pi\) | ||||
−0.636114 | + | 0.771595i | \(0.719459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3452.68 | −0.399699 | −0.199850 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199850 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(422\) | −9620.59 | −1.10977 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2576.74 | −0.295136 | ||||||||
\(425\) | 19627.9 | 2.24022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2124.88 | 0.240821 | ||||||||
\(428\) | −6933.18 | −0.783009 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17781.9 | −1.99423 | ||||||||
\(431\) | 4418.73 | 0.493834 | 0.246917 | − | 0.969037i | \(-0.420582\pi\) | ||||
0.246917 | + | 0.969037i | \(0.420582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −517.365 | −0.0574203 | −0.0287102 | − | 0.999588i | \(-0.509140\pi\) | ||||
−0.0287102 | + | 0.999588i | \(0.509140\pi\) | |||||||
\(434\) | −680.558 | −0.0752715 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −132.214 | −0.0145227 | ||||||||
\(437\) | 270.924 | 0.0296568 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12145.5 | 1.32044 | 0.660222 | − | 0.751071i | \(-0.270462\pi\) | ||||
0.660222 | + | 0.751071i | \(0.270462\pi\) | |||||||
\(440\) | 6317.34 | 0.684471 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12891.3 | 1.38728 | ||||||||
\(443\) | −11814.7 | −1.26712 | −0.633558 | − | 0.773695i | \(-0.718406\pi\) | ||||
−0.633558 | + | 0.773695i | \(0.718406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16364.1 | −1.74322 | ||||||||
\(446\) | 6906.23 | 0.733228 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 15969.1 | 1.67846 | 0.839231 | − | 0.543775i | \(-0.183005\pi\) | ||||
0.839231 | + | 0.543775i | \(0.183005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8627.46 | −0.900779 | ||||||||
\(452\) | −971.854 | −0.101133 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −316.253 | −0.0326927 | ||||||||
\(455\) | −12325.2 | −1.26992 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12880.2 | 1.31840 | 0.659201 | − | 0.751967i | \(-0.270895\pi\) | ||||
0.659201 | + | 0.751967i | \(0.270895\pi\) | |||||||
\(458\) | −1224.66 | −0.124945 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −566.671 | −0.0574373 | ||||||||
\(461\) | −6764.57 | −0.683421 | −0.341711 | − | 0.939805i | \(-0.611006\pi\) | ||||
−0.341711 | + | 0.939805i | \(0.611006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1121.06 | 0.112527 | 0.0562636 | − | 0.998416i | \(-0.482081\pi\) | ||||
0.0562636 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(464\) | 4121.20 | 0.412331 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10412.8 | 1.03511 | ||||||||
\(467\) | −15671.4 | −1.55286 | −0.776431 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776431 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2560.84 | −0.252129 | ||||||||
\(470\) | −15390.8 | −1.51048 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4312.90 | −0.420588 | ||||||||
\(473\) | −17781.9 | −1.72856 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10253.7 | 0.990466 | ||||||||
\(476\) | 2036.74 | 0.196122 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1295.71 | −0.123984 | ||||||||
\(479\) | −11211.7 | −1.06947 | −0.534734 | − | 0.845020i | \(-0.679588\pi\) | ||||
−0.534734 | + | 0.845020i | \(0.679588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30418.4 | −2.88349 | ||||||||
\(482\) | 12283.3 | 1.16077 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 993.341 | 0.0932890 | ||||||||
\(485\) | 12070.3 | 1.13007 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5261.00 | −0.489525 | −0.244762 | − | 0.969583i | \(-0.578710\pi\) | ||||
−0.244762 | + | 0.969583i | \(0.578710\pi\) | |||||||
\(488\) | 2428.44 | 0.225267 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1947.30 | −0.179531 | ||||||||
\(491\) | 8754.40 | 0.804645 | 0.402322 | − | 0.915498i | \(-0.368203\pi\) | ||||
0.402322 | + | 0.915498i | \(0.368203\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18736.2 | 1.71164 | ||||||||
\(494\) | 6734.46 | 0.613355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −777.780 | −0.0704100 | ||||||||
\(497\) | −4307.72 | −0.388788 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18969.8 | −1.70181 | −0.850905 | − | 0.525319i | \(-0.823946\pi\) | ||||
−0.850905 | + | 0.525319i | \(0.823946\pi\) | |||||||
\(500\) | −11511.6 | −1.02963 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9559.67 | −0.849938 | ||||||||
\(503\) | −3563.27 | −0.315862 | −0.157931 | − | 0.987450i | \(-0.550482\pi\) | ||||
−0.157931 | + | 0.987450i | \(0.550482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21158.4 | −1.86443 | ||||||||
\(506\) | −566.671 | −0.0497857 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6400.25 | 0.558987 | ||||||||
\(509\) | 722.492 | 0.0629153 | 0.0314577 | − | 0.999505i | \(-0.489985\pi\) | ||||
0.0314577 | + | 0.999505i | \(0.489985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 864.884 | 0.0748732 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2415.70 | 0.207299 | ||||||||
\(515\) | −29696.4 | −2.54094 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15390.8 | −1.30926 | ||||||||
\(518\) | −4805.91 | −0.407644 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14086.0 | −1.18790 | ||||||||
\(521\) | 10687.6 | 0.898721 | 0.449361 | − | 0.893350i | \(-0.351652\pi\) | ||||
0.449361 | + | 0.893350i | \(0.351652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4810.42 | −0.402189 | −0.201095 | − | 0.979572i | \(-0.564450\pi\) | ||||
−0.201095 | + | 0.979572i | \(0.564450\pi\) | |||||||
\(524\) | 9882.31 | 0.823875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5739.32 | 0.475753 | ||||||||
\(527\) | −3536.03 | −0.292280 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12116.2 | −0.995822 | ||||||||
\(530\) | 12800.2 | 1.04907 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1064.00 | 0.0867110 | ||||||||
\(533\) | 19236.9 | 1.56331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34441.3 | 2.78323 | ||||||||
\(536\) | −2926.67 | −0.235845 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11743.4 | 0.941065 | ||||||||
\(539\) | −1947.30 | −0.155615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8090.06 | −0.642918 | −0.321459 | − | 0.946923i | \(-0.604173\pi\) | ||||
−0.321459 | + | 0.946923i | \(0.604173\pi\) | |||||||
\(542\) | 2163.92 | 0.171491 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2327.71 | 0.183455 | ||||||||
\(545\) | 656.785 | 0.0516212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11831.9 | −0.924852 | −0.462426 | − | 0.886658i | \(-0.653021\pi\) | ||||
−0.462426 | + | 0.886658i | \(0.653021\pi\) | |||||||
\(548\) | −967.866 | −0.0754474 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21446.9 | −1.66272 | ||||||||
\(551\) | 9787.84 | 0.756762 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2794.16 | 0.214864 | ||||||||
\(554\) | 1863.02 | 0.142874 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1231.12 | 0.0939050 | ||||||||
\(557\) | 15783.2 | 1.20064 | 0.600321 | − | 0.799759i | \(-0.295040\pi\) | ||||
0.600321 | + | 0.799759i | \(0.295040\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39648.7 | 2.99993 | ||||||||
\(560\) | −2225.49 | −0.167936 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3831.00 | −0.287546 | ||||||||
\(563\) | −4353.81 | −0.325917 | −0.162958 | − | 0.986633i | \(-0.552104\pi\) | ||||
−0.162958 | + | 0.986633i | \(0.552104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4827.79 | 0.359481 | ||||||||
\(566\) | 253.970 | 0.0188607 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4923.11 | −0.363678 | ||||||||
\(569\) | −16526.4 | −1.21761 | −0.608806 | − | 0.793319i | \(-0.708351\pi\) | ||||
−0.608806 | + | 0.793319i | \(0.708351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24307.8 | −1.78152 | −0.890761 | − | 0.454471i | \(-0.849828\pi\) | ||||
−0.890761 | + | 0.454471i | \(0.849828\pi\) | |||||||
\(572\) | −14086.0 | −1.02966 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3039.30 | 0.221007 | ||||||||
\(575\) | 1923.80 | 0.139527 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5474.80 | −0.395007 | −0.197503 | − | 0.980302i | \(-0.563283\pi\) | ||||
−0.197503 | + | 0.980302i | \(0.563283\pi\) | |||||||
\(578\) | 756.463 | 0.0544372 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20472.5 | −1.46564 | ||||||||
\(581\) | 4431.93 | 0.316467 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12800.2 | 0.909318 | ||||||||
\(584\) | 988.439 | 0.0700375 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8258.28 | −0.582161 | ||||||||
\(587\) | −12868.2 | −0.904818 | −0.452409 | − | 0.891811i | \(-0.649435\pi\) | ||||
−0.452409 | + | 0.891811i | \(0.649435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1847.23 | −0.129225 | ||||||||
\(590\) | 21424.8 | 1.49499 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5492.46 | −0.381316 | ||||||||
\(593\) | −16734.6 | −1.15886 | −0.579432 | − | 0.815020i | \(-0.696726\pi\) | ||||
−0.579432 | + | 0.815020i | \(0.696726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10117.7 | −0.697121 | ||||||||
\(596\) | 5193.86 | 0.356961 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1263.52 | 0.0864034 | ||||||||
\(599\) | −7640.15 | −0.521149 | −0.260574 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260574 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6068.66 | −0.411890 | −0.205945 | − | 0.978564i | \(-0.566027\pi\) | ||||
−0.205945 | + | 0.978564i | \(0.566027\pi\) | |||||||
\(602\) | 6264.23 | 0.424105 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5721.10 | −0.385411 | ||||||||
\(605\) | −4934.53 | −0.331599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11318.1 | 0.756814 | 0.378407 | − | 0.925639i | \(-0.376472\pi\) | ||||
0.378407 | + | 0.925639i | \(0.376472\pi\) | |||||||
\(608\) | 1216.00 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12063.5 | −0.800718 | ||||||||
\(611\) | 34317.3 | 2.27222 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16973.1 | 1.11833 | 0.559167 | − | 0.829055i | \(-0.311121\pi\) | ||||
0.559167 | + | 0.829055i | \(0.311121\pi\) | |||||||
\(614\) | 3056.87 | 0.200920 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2225.49 | −0.145564 | ||||||||
\(617\) | 13351.7 | 0.871182 | 0.435591 | − | 0.900145i | \(-0.356539\pi\) | ||||
0.435591 | + | 0.900145i | \(0.356539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7258.04 | −0.471284 | −0.235642 | − | 0.971840i | \(-0.575719\pi\) | ||||
−0.235642 | + | 0.971840i | \(0.575719\pi\) | |||||||
\(620\) | 3863.71 | 0.250275 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17970.4 | 1.15843 | ||||||||
\(623\) | 5764.79 | 0.370724 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23456.1 | 1.50119 | ||||||||
\(626\) | −18437.6 | −1.17718 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14564.7 | −0.925469 | ||||||||
\(629\) | −24970.4 | −1.58289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9332.14 | −0.588758 | −0.294379 | − | 0.955689i | \(-0.595113\pi\) | ||||
−0.294379 | + | 0.955689i | \(0.595113\pi\) | |||||||
\(632\) | 3193.33 | 0.200987 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1604.45 | 0.100506 | ||||||||
\(635\) | −31793.9 | −1.98693 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4341.95 | 0.270070 | ||||||||
\(638\) | −20472.5 | −1.27040 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2543.41 | −0.157090 | ||||||||
\(641\) | −9908.84 | −0.610571 | −0.305285 | − | 0.952261i | \(-0.598752\pi\) | ||||
−0.305285 | + | 0.952261i | \(0.598752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7468.14 | −0.458032 | −0.229016 | − | 0.973423i | \(-0.573551\pi\) | ||||
−0.229016 | + | 0.973423i | \(0.573551\pi\) | |||||||
\(644\) | 199.628 | 0.0122150 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5528.30 | 0.336700 | ||||||||
\(647\) | 4863.05 | 0.295496 | 0.147748 | − | 0.989025i | \(-0.452798\pi\) | ||||
0.147748 | + | 0.989025i | \(0.452798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21424.8 | 1.29584 | ||||||||
\(650\) | 47820.6 | 2.88566 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13193.8 | −0.792498 | ||||||||
\(653\) | 1144.48 | 0.0685863 | 0.0342931 | − | 0.999412i | \(-0.489082\pi\) | ||||
0.0342931 | + | 0.999412i | \(0.489082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49091.4 | −2.92849 | ||||||||
\(656\) | 3473.49 | 0.206733 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5421.91 | 0.321228 | ||||||||
\(659\) | −20783.3 | −1.22853 | −0.614267 | − | 0.789098i | \(-0.710548\pi\) | ||||
−0.614267 | + | 0.789098i | \(0.710548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6071.70 | 0.357280 | 0.178640 | − | 0.983915i | \(-0.442830\pi\) | ||||
0.178640 | + | 0.983915i | \(0.442830\pi\) | |||||||
\(662\) | −1907.13 | −0.111968 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5065.06 | 0.296028 | ||||||||
\(665\) | −5285.53 | −0.308217 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1836.40 | 0.106605 | ||||||||
\(668\) | −5610.75 | −0.324980 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14538.5 | 0.838318 | ||||||||
\(671\) | −12063.5 | −0.694050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25493.0 | −1.46015 | −0.730077 | − | 0.683365i | \(-0.760516\pi\) | ||||
−0.730077 | + | 0.683365i | \(0.760516\pi\) | |||||||
\(674\) | 19318.0 | 1.10401 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22619.8 | 1.28697 | ||||||||
\(677\) | −14911.3 | −0.846511 | −0.423256 | − | 0.906010i | \(-0.639113\pi\) | ||||
−0.423256 | + | 0.906010i | \(0.639113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4252.14 | −0.240327 | ||||||||
\(680\) | −11563.1 | −0.652097 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3863.71 | 0.216934 | ||||||||
\(683\) | 7005.90 | 0.392494 | 0.196247 | − | 0.980555i | \(-0.437125\pi\) | ||||
0.196247 | + | 0.980555i | \(0.437125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4807.98 | 0.268180 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7159.12 | 0.396714 | ||||||||
\(689\) | −28541.1 | −1.57813 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2772.02 | 0.152609 | 0.0763045 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763045 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(692\) | −6732.04 | −0.369817 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3708.68 | 0.202852 | ||||||||
\(695\) | −6115.73 | −0.333788 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15791.5 | 0.858173 | ||||||||
\(698\) | −5286.16 | −0.286654 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7555.35 | 0.407950 | ||||||||
\(701\) | −9933.72 | −0.535223 | −0.267612 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267612 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13044.6 | −0.699838 | ||||||||
\(704\) | −2543.41 | −0.136163 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6193.28 | −0.330152 | ||||||||
\(707\) | 7453.72 | 0.396501 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13314.4 | −0.705266 | −0.352633 | − | 0.935762i | \(-0.614714\pi\) | ||||
−0.352633 | + | 0.935762i | \(0.614714\pi\) | |||||||
\(710\) | 24456.1 | 1.29270 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6588.33 | 0.346781 | ||||||||
\(713\) | −346.578 | −0.0182040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 69973.5 | 3.65994 | ||||||||
\(716\) | 5968.32 | 0.311517 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11150.2 | 0.579557 | ||||||||
\(719\) | −17436.0 | −0.904386 | −0.452193 | − | 0.891920i | \(-0.649358\pi\) | ||||
−0.452193 | + | 0.891920i | \(0.649358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10461.5 | 0.540371 | ||||||||
\(722\) | −10830.0 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11782.9 | 0.604846 | ||||||||
\(725\) | 69502.4 | 3.56035 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5380.39 | 0.274481 | 0.137240 | − | 0.990538i | \(-0.456177\pi\) | ||||
0.137240 | + | 0.990538i | \(0.456177\pi\) | |||||||
\(728\) | 4962.23 | 0.252627 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4910.18 | −0.248950 | ||||||||
\(731\) | 32547.5 | 1.64680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37200.7 | −1.87454 | −0.937271 | − | 0.348600i | \(-0.886657\pi\) | ||||
−0.937271 | + | 0.348600i | \(0.886657\pi\) | |||||||
\(734\) | 16800.3 | 0.844839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 228.146 | 0.0114261 | ||||||||
\(737\) | 14538.5 | 0.726641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17236.5 | 0.857988 | 0.428994 | − | 0.903307i | \(-0.358868\pi\) | ||||
0.428994 | + | 0.903307i | \(0.358868\pi\) | |||||||
\(740\) | 27284.4 | 1.35540 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4509.30 | −0.223102 | ||||||||
\(743\) | −16450.2 | −0.812246 | −0.406123 | − | 0.913818i | \(-0.633120\pi\) | ||||
−0.406123 | + | 0.913818i | \(0.633120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25801.1 | −1.26883 | ||||||||
\(746\) | 9225.24 | 0.452761 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11563.1 | −0.565227 | ||||||||
\(749\) | −12133.1 | −0.591900 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29439.6 | −1.43045 | −0.715223 | − | 0.698897i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698897i | \(0.753675\pi\) | |||||||
\(752\) | 6196.46 | 0.300481 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 45648.0 | 2.20478 | ||||||||
\(755\) | 28420.2 | 1.36996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12924.0 | 0.620518 | 0.310259 | − | 0.950652i | \(-0.399584\pi\) | ||||
0.310259 | + | 0.950652i | \(0.399584\pi\) | |||||||
\(758\) | 1338.33 | 0.0641298 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6040.61 | −0.288310 | ||||||||
\(761\) | −12513.7 | −0.596087 | −0.298043 | − | 0.954552i | \(-0.596334\pi\) | ||||
−0.298043 | + | 0.954552i | \(0.596334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −231.374 | −0.0109781 | ||||||||
\(764\) | −7653.77 | −0.362439 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4380.16 | −0.206608 | ||||||||
\(767\) | −47771.5 | −2.24893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12823.8 | −0.601351 | −0.300675 | − | 0.953727i | \(-0.597212\pi\) | ||||
−0.300675 | + | 0.953727i | \(0.597212\pi\) | |||||||
\(770\) | 11055.3 | 0.517412 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −237.305 | −0.0110632 | ||||||||
\(773\) | −8348.45 | −0.388451 | −0.194226 | − | 0.980957i | \(-0.562219\pi\) | ||||
−0.194226 | + | 0.980957i | \(0.562219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13117.0 | −0.607968 | ||||||||
\(776\) | −4859.59 | −0.224805 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24563.9 | 1.13195 | ||||||||
\(779\) | 8249.53 | 0.379423 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24456.1 | 1.12050 | ||||||||
\(782\) | 1037.22 | 0.0474310 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 72351.7 | 3.28961 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23593.9 | −1.06865 | −0.534327 | − | 0.845278i | \(-0.679435\pi\) | ||||
−0.534327 | + | 0.845278i | \(0.679435\pi\) | |||||||
\(788\) | 1151.12 | 0.0520394 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15863.2 | −0.714415 | ||||||||
\(791\) | −1700.74 | −0.0764494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26898.4 | 1.20453 | ||||||||
\(794\) | −22033.8 | −0.984825 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16058.0 | −0.715028 | ||||||||
\(797\) | 25753.3 | 1.14458 | 0.572289 | − | 0.820052i | \(-0.306055\pi\) | ||||
0.572289 | + | 0.820052i | \(0.306055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28171.0 | 1.24733 | ||||||||
\(800\) | 8634.68 | 0.381603 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4857.46 | −0.213869 | ||||||||
\(803\) | −4910.18 | −0.215786 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −991.674 | −0.0434185 | ||||||||
\(806\) | −8615.02 | −0.376490 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8518.54 | 0.370892 | ||||||||
\(809\) | 15768.2 | 0.685266 | 0.342633 | − | 0.939469i | \(-0.388681\pi\) | ||||
0.342633 | + | 0.939469i | \(0.388681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18577.0 | −0.804351 | −0.402175 | − | 0.915563i | \(-0.631746\pi\) | ||||
−0.402175 | + | 0.915563i | \(0.631746\pi\) | |||||||
\(812\) | 7212.09 | 0.311693 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27284.4 | 1.17484 | ||||||||
\(815\) | 65541.6 | 2.81696 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17002.9 | 0.728099 | ||||||||
\(818\) | −16154.0 | −0.690479 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17254.9 | −0.734839 | ||||||||
\(821\) | 25406.7 | 1.08002 | 0.540012 | − | 0.841657i | \(-0.318420\pi\) | ||||
0.540012 | + | 0.841657i | \(0.318420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43664.6 | 1.84940 | 0.924698 | − | 0.380702i | \(-0.124318\pi\) | ||||
0.924698 | + | 0.380702i | \(0.124318\pi\) | |||||||
\(824\) | 11956.0 | 0.505471 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7547.58 | −0.317934 | ||||||||
\(827\) | −23206.4 | −0.975773 | −0.487887 | − | 0.872907i | \(-0.662232\pi\) | ||||
−0.487887 | + | 0.872907i | \(0.662232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10247.3 | 0.429316 | 0.214658 | − | 0.976689i | \(-0.431136\pi\) | ||||
0.214658 | + | 0.976689i | \(0.431136\pi\) | |||||||
\(830\) | −25161.2 | −1.05224 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5671.12 | 0.236311 | ||||||||
\(833\) | 3564.30 | 0.148254 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27872.0 | 1.15515 | ||||||||
\(836\) | −6040.61 | −0.249903 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21823.1 | −0.899600 | ||||||||
\(839\) | 12322.0 | 0.507035 | 0.253518 | − | 0.967331i | \(-0.418412\pi\) | ||||
0.253518 | + | 0.967331i | \(0.418412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41955.7 | 1.72027 | ||||||||
\(842\) | −6905.37 | −0.282630 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19241.2 | −0.784726 | ||||||||
\(845\) | −112366. | −4.57458 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1738.35 | 0.0705199 | ||||||||
\(848\) | −5153.49 | −0.208693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 39255.9 | 1.58408 | ||||||||
\(851\) | −2447.43 | −0.0985863 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38665.8 | 1.55204 | 0.776020 | − | 0.630708i | \(-0.217235\pi\) | ||||
0.776020 | + | 0.630708i | \(0.217235\pi\) | |||||||
\(854\) | 4249.77 | 0.170286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13866.4 | −0.553671 | ||||||||
\(857\) | −6516.94 | −0.259760 | −0.129880 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129880 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45946.7 | 1.82501 | 0.912504 | − | 0.409068i | \(-0.134146\pi\) | ||||
0.912504 | + | 0.409068i | \(0.134146\pi\) | |||||||
\(860\) | −35563.7 | −1.41013 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8837.45 | 0.349193 | ||||||||
\(863\) | −25825.2 | −1.01866 | −0.509328 | − | 0.860573i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860573i | \(0.670106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33442.1 | 1.31453 | ||||||||
\(866\) | −1034.73 | −0.0406023 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1361.12 | −0.0532250 | ||||||||
\(869\) | −15863.2 | −0.619243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32417.0 | −1.26109 | ||||||||
\(872\) | −264.427 | −0.0102691 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 541.848 | 0.0209706 | ||||||||
\(875\) | −20145.4 | −0.778329 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36784.9 | 1.41635 | 0.708174 | − | 0.706038i | \(-0.249519\pi\) | ||||
0.708174 | + | 0.706038i | \(0.249519\pi\) | |||||||
\(878\) | 24291.1 | 0.933695 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12634.7 | 0.483994 | ||||||||
\(881\) | −41594.5 | −1.59064 | −0.795321 | − | 0.606189i | \(-0.792698\pi\) | ||||
−0.795321 | + | 0.606189i | \(0.792698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22923.9 | −0.873670 | −0.436835 | − | 0.899542i | \(-0.643901\pi\) | ||||
−0.436835 | + | 0.899542i | \(0.643901\pi\) | |||||||
\(884\) | 25782.6 | 0.980955 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23629.4 | −0.895986 | ||||||||
\(887\) | 2603.19 | 0.0985418 | 0.0492709 | − | 0.998785i | \(-0.484310\pi\) | ||||
0.0492709 | + | 0.998785i | \(0.484310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11200.4 | 0.422554 | ||||||||
\(890\) | −32728.2 | −1.23264 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13812.5 | 0.518470 | ||||||||
\(893\) | 14716.6 | 0.551481 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29648.2 | −1.10730 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31938.3 | 1.18685 | ||||||||
\(899\) | −12521.0 | −0.464516 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23429.3 | −0.866308 | ||||||||
\(902\) | −17254.9 | −0.636947 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1943.71 | −0.0715119 | ||||||||
\(905\) | −58532.9 | −2.14994 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29167.9 | 1.06781 | 0.533905 | − | 0.845544i | \(-0.320724\pi\) | ||||
0.533905 | + | 0.845544i | \(0.320724\pi\) | |||||||
\(908\) | −632.506 | −0.0231172 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24650.4 | −0.897971 | ||||||||
\(911\) | 9798.14 | 0.356341 | 0.178171 | − | 0.984000i | \(-0.442982\pi\) | ||||
0.178171 | + | 0.984000i | \(0.442982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25161.2 | −0.912065 | ||||||||
\(914\) | 25760.4 | 0.932251 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2449.33 | −0.0883495 | ||||||||
\(917\) | 17294.0 | 0.622791 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49986.6 | −1.79424 | −0.897120 | − | 0.441786i | \(-0.854345\pi\) | ||||
−0.897120 | + | 0.441786i | \(0.854345\pi\) | |||||||
\(920\) | −1133.34 | −0.0406143 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13529.1 | −0.483252 | ||||||||
\(923\) | −54530.4 | −1.94463 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −92628.3 | −3.29254 | ||||||||
\(926\) | 2242.12 | 0.0795687 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8242.39 | 0.291562 | ||||||||
\(929\) | 50651.4 | 1.78883 | 0.894413 | − | 0.447242i | \(-0.147594\pi\) | ||||
0.894413 | + | 0.447242i | \(0.147594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1862.00 | 0.0655474 | ||||||||
\(932\) | 20825.6 | 0.731936 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31342.8 | −1.09804 | ||||||||
\(935\) | 57441.1 | 2.00912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29457.1 | 1.02702 | 0.513511 | − | 0.858083i | \(-0.328344\pi\) | ||||
0.513511 | + | 0.858083i | \(0.328344\pi\) | |||||||
\(938\) | −5121.67 | −0.178282 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30781.6 | −1.06807 | ||||||||
\(941\) | −12285.0 | −0.425590 | −0.212795 | − | 0.977097i | \(-0.568257\pi\) | ||||
−0.212795 | + | 0.977097i | \(0.568257\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1547.78 | 0.0534493 | ||||||||
\(944\) | −8625.80 | −0.297400 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35563.7 | −1.22228 | ||||||||
\(947\) | −10735.0 | −0.368363 | −0.184182 | − | 0.982892i | \(-0.558963\pi\) | ||||
−0.184182 | + | 0.982892i | \(0.558963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10948.4 | 0.374498 | ||||||||
\(950\) | 20507.4 | 0.700365 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4073.49 | 0.138679 | ||||||||
\(953\) | 101.551 | 0.00345178 | 0.00172589 | − | 0.999999i | \(-0.499451\pi\) | ||||
0.00172589 | + | 0.999999i | \(0.499451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38020.9 | 1.28830 | ||||||||
\(956\) | −2591.41 | −0.0876698 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22423.4 | −0.756228 | ||||||||
\(959\) | −1693.76 | −0.0570329 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27427.9 | −0.920679 | ||||||||
\(962\) | −60836.8 | −2.03894 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24566.7 | 0.820788 | ||||||||
\(965\) | 1178.84 | 0.0393245 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5751.74 | 0.191276 | 0.0956378 | − | 0.995416i | \(-0.469511\pi\) | ||||
0.0956378 | + | 0.995416i | \(0.469511\pi\) | |||||||
\(968\) | 1986.68 | 0.0659653 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24140.5 | 0.799077 | ||||||||
\(971\) | 1143.79 | 0.0378024 | 0.0189012 | − | 0.999821i | \(-0.493983\pi\) | ||||
0.0189012 | + | 0.999821i | \(0.493983\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2154.46 | 0.0709855 | ||||||||
\(974\) | −10522.0 | −0.346146 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4856.88 | 0.159288 | ||||||||
\(977\) | −16323.6 | −0.534532 | −0.267266 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267266 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32728.2 | −1.06844 | ||||||||
\(980\) | −3894.60 | −0.126947 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17508.8 | 0.568970 | ||||||||
\(983\) | −19016.4 | −0.617017 | −0.308509 | − | 0.951222i | \(-0.599830\pi\) | ||||
−0.308509 | + | 0.951222i | \(0.599830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5718.32 | −0.184975 | ||||||||
\(986\) | 37472.4 | 1.21031 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13468.9 | 0.433708 | ||||||||
\(989\) | 3190.09 | 0.102567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53795.4 | −1.72439 | −0.862193 | − | 0.506580i | \(-0.830909\pi\) | ||||
−0.862193 | + | 0.506580i | \(0.830909\pi\) | |||||||
\(992\) | −1555.56 | −0.0497874 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8615.44 | −0.274915 | ||||||||
\(995\) | 79770.0 | 2.54159 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29029.7 | 0.922145 | 0.461073 | − | 0.887362i | \(-0.347465\pi\) | ||||
0.461073 | + | 0.887362i | \(0.347465\pi\) | |||||||
\(998\) | −37939.5 | −1.20336 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.4.a.p.1.1 | yes | 2 | |
3.2 | odd | 2 | 378.4.a.o.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.a.o.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
378.4.a.p.1.1 | yes | 2 | 1.1 | even | 1 | trivial |