Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 20x^{3} - 33x^{2} + 17x + 40 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1248) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.04635\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 22.0884 | 1.97565 | 0.987824 | − | 0.155578i | \(-0.0497239\pi\) | ||||
0.987824 | + | 0.155578i | \(0.0497239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.570636 | 0.0308115 | 0.0154057 | − | 0.999881i | \(-0.495096\pi\) | ||||
0.0154057 | + | 0.999881i | \(0.495096\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.5147 | −0.397849 | −0.198925 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198925 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −66.2652 | −1.14064 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.8354 | 0.896460 | 0.448230 | − | 0.893918i | \(-0.352055\pi\) | ||||
0.448230 | + | 0.893918i | \(0.352055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −106.914 | −1.29093 | −0.645467 | − | 0.763788i | \(-0.723337\pi\) | ||||
−0.645467 | + | 0.763788i | \(0.723337\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71191 | −0.0177890 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −175.759 | −1.59341 | −0.796704 | − | 0.604370i | \(-0.793425\pi\) | ||||
−0.796704 | + | 0.604370i | \(0.793425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 362.898 | 2.90318 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −66.4653 | −0.425597 | −0.212798 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212798 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −53.0145 | −0.307151 | −0.153576 | − | 0.988137i | \(-0.549079\pi\) | ||||
−0.153576 | + | 0.988137i | \(0.549079\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 43.5441 | 0.229698 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6045 | 0.0608726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61.7208 | −0.274239 | −0.137119 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137119 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −244.872 | −0.932747 | −0.466373 | − | 0.884588i | \(-0.654440\pi\) | ||||
−0.466373 | + | 0.884588i | \(0.654440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.2156 | 0.227739 | 0.113870 | − | 0.993496i | \(-0.463675\pi\) | ||||
0.113870 | + | 0.993496i | \(0.463675\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 198.796 | 0.658549 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 51.2733 | 0.159127 | 0.0795636 | − | 0.996830i | \(-0.474647\pi\) | ||||
0.0795636 | + | 0.996830i | \(0.474647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.674 | −0.999051 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −188.506 | −0.517571 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −495.893 | −1.28521 | −0.642605 | − | 0.766198i | \(-0.722146\pi\) | ||||
−0.642605 | + | 0.766198i | \(0.722146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −320.606 | −0.786010 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 320.742 | 0.745321 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 322.773 | 0.712229 | 0.356115 | − | 0.934442i | \(-0.384101\pi\) | ||||
0.356115 | + | 0.934442i | \(0.384101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −499.239 | −1.04788 | −0.523942 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523942 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.13573 | 0.0102705 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 287.149 | 0.547946 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −145.751 | −0.265765 | −0.132883 | − | 0.991132i | \(-0.542423\pi\) | ||||
−0.132883 | + | 0.991132i | \(0.542423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 527.278 | 0.919954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1111.55 | −1.85799 | −0.928994 | − | 0.370094i | \(-0.879325\pi\) | ||||
−0.928994 | + | 0.370094i | \(0.879325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −592.186 | −0.949454 | −0.474727 | − | 0.880133i | \(-0.657453\pi\) | ||||
−0.474727 | + | 0.880133i | \(0.657453\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1088.69 | −1.67615 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.28261 | −0.0122583 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −124.450 | −0.177238 | −0.0886188 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886188 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −675.769 | −0.893678 | −0.446839 | − | 0.894614i | \(-0.647450\pi\) | ||||
−0.446839 | + | 0.894614i | \(0.647450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1387.93 | 1.77109 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 199.396 | 0.245718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −411.589 | −0.490206 | −0.245103 | − | 0.969497i | \(-0.578822\pi\) | ||||
−0.245103 | + | 0.969497i | \(0.578822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.41827 | 0.00854556 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 159.044 | 0.177334 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2361.56 | −2.55043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1633.14 | −1.70949 | −0.854744 | − | 0.519050i | \(-0.826286\pi\) | ||||
−0.854744 | + | 0.519050i | \(0.826286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −130.632 | −0.132616 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1695.34 | 1.67023 | 0.835114 | − | 0.550077i | \(-0.185402\pi\) | ||||
0.835114 | + | 0.550077i | \(0.185402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1055.03 | 1.00927 | 0.504637 | − | 0.863331i | \(-0.331626\pi\) | ||||
0.504637 | + | 0.863331i | \(0.331626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −37.8134 | −0.0351448 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1434.41 | 1.29598 | 0.647990 | − | 0.761649i | \(-0.275610\pi\) | ||||
0.647990 | + | 0.761649i | \(0.275610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 210.166 | 0.184681 | 0.0923406 | − | 0.995727i | \(-0.470565\pi\) | ||||
0.0923406 | + | 0.995727i | \(0.470565\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 185.163 | 0.158332 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 788.100 | 0.656090 | 0.328045 | − | 0.944662i | \(-0.393610\pi\) | ||||
0.328045 | + | 0.944662i | \(0.393610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3882.25 | −3.14801 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.8561 | 0.0276212 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1120.32 | −0.841716 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 734.617 | 0.538522 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5254.78 | 3.76002 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1668.08 | −1.16550 | −0.582750 | − | 0.812652i | \(-0.698023\pi\) | ||||
−0.582750 | + | 0.812652i | \(0.698023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −192.647 | −0.131485 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2635.33 | 1.75763 | 0.878817 | − | 0.477159i | \(-0.158333\pi\) | ||||
0.878817 | + | 0.477159i | \(0.158333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −61.0090 | −0.0397756 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −596.387 | −0.380214 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1228.31 | −0.765997 | −0.382999 | − | 0.923749i | \(-0.625109\pi\) | ||||
−0.382999 | + | 0.923749i | \(0.625109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1363.03 | −0.831734 | −0.415867 | − | 0.909426i | \(-0.636522\pi\) | ||||
−0.415867 | + | 0.909426i | \(0.636522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −153.820 | −0.0918722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −188.691 | −0.110344 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1468.11 | −0.840829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1028.02 | 0.576802 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 298.498 | 0.164120 | 0.0820600 | − | 0.996627i | \(-0.473850\pi\) | ||||
0.0820600 | + | 0.996627i | \(0.473850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3297.44 | 1.77710 | 0.888550 | − | 0.458781i | \(-0.151714\pi\) | ||||
0.888550 | + | 0.458781i | \(0.151714\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 565.518 | 0.298820 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1171.01 | −0.606823 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1969.65 | −1.00124 | −0.500620 | − | 0.865667i | \(-0.666895\pi\) | ||||
−0.500620 | + | 0.865667i | \(0.666895\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1487.68 | 0.742016 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −100.295 | −0.0490952 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2046.76 | 0.983525 | 0.491762 | − | 0.870729i | \(-0.336353\pi\) | ||||
0.491762 | + | 0.870729i | \(0.336353\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 961.819 | 0.453803 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2873.01 | −1.33126 | −0.665628 | − | 0.746283i | \(-0.731836\pi\) | ||||
−0.665628 | + | 0.746283i | \(0.731836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −962.226 | −0.430311 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 534.246 | 0.234786 | 0.117393 | − | 0.993086i | \(-0.462546\pi\) | ||||
0.117393 | + | 0.993086i | \(0.462546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 207.083 | 0.0894513 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −968.320 | −0.411206 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3504.15 | −1.46320 | −0.731599 | − | 0.681735i | \(-0.761226\pi\) | ||||
−0.731599 | + | 0.681735i | \(0.761226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4027.89 | 1.65409 | 0.827047 | − | 0.562133i | \(-0.190019\pi\) | ||||
0.827047 | + | 0.562133i | \(0.190019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1497.72 | 0.604996 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1363.32 | −0.541800 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −912.036 | −0.356656 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4072 | −0.00592967 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1516.47 | 0.574493 | 0.287247 | − | 0.957857i | \(-0.407260\pi\) | ||||
0.287247 | + | 0.957857i | \(0.407260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 429.841 | 0.160314 | 0.0801571 | − | 0.996782i | \(-0.474458\pi\) | ||||
0.0801571 | + | 0.996782i | \(0.474458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −861.448 | −0.316357 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −630.616 | −0.228069 | −0.114034 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114034 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4222.79 | 1.50425 | 0.752124 | − | 0.659021i | \(-0.229029\pi\) | ||||
0.752124 | + | 0.659021i | \(0.229029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 437.252 | 0.153440 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37.9275 | −0.0131133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5408.84 | −1.84278 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1581.84 | −0.531136 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1551.82 | 0.513597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1464.08 | −0.477686 | −0.238843 | − | 0.971058i | \(-0.576768\pi\) | ||||
−0.238843 | + | 0.971058i | \(0.576768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3334.66 | 1.07271 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1418.42 | 0.449933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.2520 | −0.00946379 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1776.56 | 0.548167 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 816.860 | 0.248633 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5488.41 | −1.64812 | −0.824061 | − | 0.566501i | \(-0.808297\pi\) | ||||
−0.824061 | + | 0.566501i | \(0.808297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3266.08 | 0.967727 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1538.34 | −0.449793 | −0.224896 | − | 0.974383i | \(-0.572204\pi\) | ||||
−0.224896 | + | 0.974383i | \(0.572204\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2544.64 | −0.734300 | −0.367150 | − | 0.930162i | \(-0.619666\pi\) | ||||
−0.367150 | + | 0.930162i | \(0.619666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.8478 | 0.00707735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 588.474 | 0.165460 | 0.0827301 | − | 0.996572i | \(-0.473636\pi\) | ||||
0.0827301 | + | 0.996572i | \(0.473636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1132.55 | 0.314379 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 373.351 | 0.102328 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −655.416 | −0.177386 | −0.0886932 | − | 0.996059i | \(-0.528269\pi\) | ||||
−0.0886932 | + | 0.996059i | \(0.528269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −603.681 | −0.161355 | −0.0806774 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806774 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7569.13 | −1.97377 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1389.88 | −0.358041 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2027.31 | 0.515965 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6332.16 | 1.59236 | 0.796180 | − | 0.605060i | \(-0.206851\pi\) | ||||
0.796180 | + | 0.605060i | \(0.206851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2551.09 | 0.633936 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4163.80 | −1.02254 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2114.90 | 0.513323 | 0.256662 | − | 0.966501i | \(-0.417377\pi\) | ||||
0.256662 | + | 0.966501i | \(0.417377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.2202 | −0.00844971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −598.188 | −0.141866 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3186.29 | 0.747054 | 0.373527 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373527 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10953.5 | −2.53912 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1234.77 | 0.283020 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2056.40 | 0.466100 | 0.233050 | − | 0.972465i | \(-0.425129\pi\) | ||||
0.233050 | + | 0.972465i | \(0.425129\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −399.938 | −0.0896476 | −0.0448238 | − | 0.998995i | \(-0.514273\pi\) | ||||
−0.0448238 | + | 0.998995i | \(0.514273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.2548 | −0.00493378 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5267.35 | −1.15503 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4470.24 | 0.969643 | 0.484821 | − | 0.874613i | \(-0.338885\pi\) | ||||
0.484821 | + | 0.874613i | \(0.338885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −477.131 | −0.102384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −401.796 | −0.0852993 | −0.0426497 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426497 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3914.77 | 0.822292 | 0.411146 | − | 0.911569i | \(-0.365129\pi\) | ||||
0.411146 | + | 0.911569i | \(0.365129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7084.68 | 1.47249 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −139.733 | −0.0287393 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −964.717 | −0.196360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4899.42 | 0.986973 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 433.936 | 0.0865216 | 0.0432608 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432608 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7129.55 | 1.40711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 391.897 | 0.0765661 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2284.87 | −0.441932 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.6438 | 0.00701699 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5086.03 | −0.964306 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11027.4 | −2.07025 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4680.64 | −0.870157 | −0.435078 | − | 0.900393i | \(-0.643279\pi\) | ||||
−0.435078 | + | 0.900393i | \(0.643279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3165.09 | −0.582705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −670.394 | −0.122233 | −0.0611167 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611167 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2198.73 | 0.397060 | 0.198530 | − | 0.980095i | \(-0.436383\pi\) | ||||
0.198530 | + | 0.980095i | \(0.436383\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 113.440 | 0.0202909 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7510.62 | 1.33072 | 0.665360 | − | 0.746523i | \(-0.268278\pi\) | ||||
0.665360 | + | 0.746523i | \(0.268278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 964.724 | 0.169323 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4303.24 | −0.748235 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6717.98 | −1.15727 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4717.67 | 0.805198 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −630.498 | −0.106626 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.2584 | 0.00490295 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8426.86 | −1.39934 | −0.699671 | − | 0.714465i | \(-0.746670\pi\) | ||||
−0.699671 | + | 0.714465i | \(0.746670\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −555.488 | −0.0914130 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3219.40 | −0.525058 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9064.12 | −1.46515 | −0.732573 | − | 0.680689i | \(-0.761681\pi\) | ||||
−0.732573 | + | 0.680689i | \(0.761681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2364.30 | −0.378794 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 769.489 | 0.122200 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −391.271 | −0.0615937 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11646.7 | 1.81751 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4496.43 | 0.695622 | 0.347811 | − | 0.937565i | \(-0.386925\pi\) | ||||
0.347811 | + | 0.937565i | \(0.386925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9397.56 | −1.44137 | −0.720687 | − | 0.693260i | \(-0.756174\pi\) | ||||
−0.720687 | + | 0.693260i | \(0.756174\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8189.26 | −1.23476 | −0.617380 | − | 0.786665i | \(-0.711806\pi\) | ||||
−0.617380 | + | 0.786665i | \(0.711806\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24552.5 | −3.67073 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −107.568 | −0.0159471 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4176.24 | −0.613965 | −0.306983 | − | 0.951715i | \(-0.599319\pi\) | ||||
−0.306983 | + | 0.951715i | \(0.599319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4571.60 | 0.666511 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3360.97 | 0.485965 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13080.4 | −1.87579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5272.91 | −0.749983 | −0.374991 | − | 0.927028i | \(-0.622354\pi\) | ||||
−0.374991 | + | 0.927028i | \(0.622354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2203.85 | −0.310916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −282.975 | −0.0395992 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9751.86 | −1.35371 | −0.676853 | − | 0.736118i | \(-0.736657\pi\) | ||||
−0.676853 | + | 0.736118i | \(0.736657\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15764.4 | −2.17085 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −864.049 | −0.118039 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12570.3 | 1.70368 | 0.851839 | − | 0.523803i | \(-0.175487\pi\) | ||||
0.851839 | + | 0.523803i | \(0.175487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5004.25 | 0.672901 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10564.7 | −1.40948 | −0.704741 | − | 0.709464i | \(-0.748937\pi\) | ||||
−0.704741 | + | 0.709464i | \(0.748937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −182.950 | −0.0242181 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 577.941 | 0.0759131 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9376.03 | 1.22207 | 0.611033 | − | 0.791605i | \(-0.290754\pi\) | ||||
0.611033 | + | 0.791605i | \(0.290754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11043.9 | −1.42843 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7906.00 | −1.01477 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2748.91 | −0.350159 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3449.75 | 0.436116 | 0.218058 | − | 0.975936i | \(-0.430028\pi\) | ||||
0.218058 | + | 0.975936i | \(0.430028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 183.027 | 0.0229644 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6580.34 | 0.819467 | 0.409734 | − | 0.912205i | \(-0.365622\pi\) | ||||
0.409734 | + | 0.912205i | \(0.365622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −689.189 | −0.0851885 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1789.16 | 0.219516 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 895.859 | 0.109106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6394.78 | −0.773109 | −0.386554 | − | 0.922267i | \(-0.626335\pi\) | ||||
−0.386554 | + | 0.922267i | \(0.626335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3684.93 | 0.442249 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 184.186 | 0.0219448 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14926.7 | −1.76559 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4089.10 | 0.480202 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8951.92 | −1.04375 | −0.521873 | − | 0.853023i | \(-0.674767\pi\) | ||||
−0.521873 | + | 0.853023i | \(0.674767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 414.532 | 0.0479883 | 0.0239941 | − | 0.999712i | \(-0.492362\pi\) | ||||
0.0239941 | + | 0.999712i | \(0.492362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 461.460 | 0.0530424 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22802.8 | 2.60259 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −284.884 | −0.0322869 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 566.073 | 0.0637069 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −945.412 | −0.105659 | −0.0528293 | − | 0.998604i | \(-0.516824\pi\) | ||||
−0.0528293 | + | 0.998604i | \(0.516824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6691.85 | 0.742702 | 0.371351 | − | 0.928493i | \(-0.378895\pi\) | ||||
0.371351 | + | 0.928493i | \(0.378895\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4404.34 | 0.485453 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18791.1 | 2.05698 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 799.787 | 0.0869516 | 0.0434758 | − | 0.999054i | \(-0.486157\pi\) | ||||
0.0434758 | + | 0.999054i | \(0.486157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3084.07 | −0.333017 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4856.67 | −0.520874 | −0.260437 | − | 0.965491i | \(-0.583867\pi\) | ||||
−0.260437 | + | 0.965491i | \(0.583867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9091.34 | −0.968474 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −895.493 | −0.0947548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16801.4 | −1.76594 | −0.882969 | − | 0.469431i | \(-0.844459\pi\) | ||||
−0.882969 | + | 0.469431i | \(0.844459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3554.24 | 0.371093 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9892.32 | −1.02601 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 163.858 | 0.0168830 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3603.14 | −0.368814 | −0.184407 | − | 0.982850i | \(-0.559036\pi\) | ||||
−0.184407 | + | 0.982850i | \(0.559036\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1696.55 | −0.172524 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7442.82 | −0.751946 | −0.375973 | − | 0.926631i | \(-0.622691\pi\) | ||||
−0.375973 | + | 0.926631i | \(0.622691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1873.49 | −0.188053 | −0.0940265 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940265 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3513.02 | 0.350349 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8925.09 | −0.884377 | −0.442188 | − | 0.896922i | \(-0.645798\pi\) | ||||
−0.442188 | + | 0.896922i | \(0.645798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −83.1706 | −0.00818862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5908.94 | 0.578067 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −932.070 | −0.0906060 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38798.8 | −3.74782 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4463.04 | −0.428403 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2863.80 | −0.273174 | −0.136587 | − | 0.990628i | \(-0.543613\pi\) | ||||
−0.136587 | + | 0.990628i | \(0.543613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −802.371 | −0.0760602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 300.884 | 0.0283452 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36073.5 | −3.37734 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2976.01 | 0.276911 | 0.138456 | − | 0.990369i | \(-0.455786\pi\) | ||||
0.138456 | + | 0.990369i | \(0.455786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6140.28 | −0.567838 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14753.6 | −1.35605 | −0.678027 | − | 0.735037i | \(-0.737165\pi\) | ||||
−0.678027 | + | 0.735037i | \(0.737165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4176.37 | −0.381530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2885.46 | −0.262003 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −634.293 | −0.0572474 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16239.3 | 1.45685 | 0.728426 | − | 0.685124i | \(-0.240252\pi\) | ||||
0.728426 | + | 0.685124i | \(0.240252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8619.02 | 0.768601 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1975.94 | 0.175155 | 0.0875774 | − | 0.996158i | \(-0.472087\pi\) | ||||
0.0875774 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37447.4 | 3.29978 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18898.0 | −1.64565 | −0.822827 | − | 0.568292i | \(-0.807605\pi\) | ||||
−0.822827 | + | 0.568292i | \(0.807605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −337.923 | −0.0292541 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2886.68 | 0.248440 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23304.0 | 1.99397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −744.216 | −0.0633087 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1602.74 | −0.135554 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19031.4 | 1.60035 | 0.800175 | − | 0.599767i | \(-0.204740\pi\) | ||||
0.800175 | + | 0.599767i | \(0.204740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20162.4 | −1.68574 | −0.842870 | − | 0.538117i | \(-0.819136\pi\) | ||||
−0.842870 | + | 0.538117i | \(0.819136\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −621.248 | −0.0516447 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3331.19 | −0.275349 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18724.4 | 1.53895 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2904.96 | 0.237410 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3183.34 | −0.258697 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31683.9 | 2.56040 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10512.4 | 0.844778 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4973.81 | 0.397472 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1067.93 | −0.0848688 | −0.0424344 | − | 0.999099i | \(-0.513511\pi\) | ||||
−0.0424344 | + | 0.999099i | \(0.513511\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12083.7 | −0.954992 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4642.23 | 0.364865 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18158.4 | −1.41938 | −0.709688 | − | 0.704516i | \(-0.751164\pi\) | ||||
−0.709688 | + | 0.704516i | \(0.751164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4493.15 | −0.349295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7106.07 | 0.549417 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −71.0159 | −0.00546095 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4089.95 | 0.312808 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21903.8 | −1.66624 | −0.833120 | − | 0.553092i | \(-0.813448\pi\) | ||||
−0.833120 | + | 0.553092i | \(0.813448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 834.803 | 0.0631635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2736.11 | 0.205915 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6633.07 | 0.496538 | 0.248269 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248269 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17407.9 | 1.29620 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 46.2216 | 0.00342350 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14739.5 | −1.08596 | −0.542981 | − | 0.839745i | \(-0.682704\pi\) | ||||
−0.542981 | + | 0.839745i | \(0.682704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22073.0 | −1.61774 | −0.808868 | − | 0.587990i | \(-0.799920\pi\) | ||||
−0.808868 | + | 0.587990i | \(0.799920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4549.42 | −0.331684 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −63782.7 | −4.62595 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9921.43 | 0.715831 | 0.357915 | − | 0.933754i | \(-0.383488\pi\) | ||||
0.357915 | + | 0.933754i | \(0.383488\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1289.52 | −0.0925574 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −385.618 | −0.0275355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7197.73 | 0.511320 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2584.34 | 0.182649 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22175.4 | 1.55924 | 0.779622 | − | 0.626250i | \(-0.215411\pi\) | ||||
0.779622 | + | 0.626250i | \(0.215411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5668.00 | 0.396512 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1891.85 | 0.131676 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19410.7 | −1.34419 | −0.672093 | − | 0.740467i | \(-0.734605\pi\) | ||||
−0.672093 | + | 0.740467i | \(0.734605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 792.005 | 0.0545698 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12668.4 | −0.868478 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23121.5 | −1.57716 | −0.788582 | − | 0.614930i | \(-0.789184\pi\) | ||||
−0.788582 | + | 0.614930i | \(0.789184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11376.1 | −0.772117 | −0.386059 | − | 0.922474i | \(-0.626164\pi\) | ||||
−0.386059 | + | 0.922474i | \(0.626164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1311.76 | −0.0885884 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24746.2 | −1.66293 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10687.2 | 0.714628 | 0.357314 | − | 0.933984i | \(-0.383693\pi\) | ||||
0.357314 | + | 0.933984i | \(0.383693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 113.783 | 0.00757094 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 666.553 | 0.0441340 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23589.4 | 1.55427 | 0.777135 | − | 0.629334i | \(-0.216672\pi\) | ||||
0.777135 | + | 0.629334i | \(0.216672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16226.5 | 1.06393 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14195.7 | −0.926249 | −0.463124 | − | 0.886293i | \(-0.653272\pi\) | ||||
−0.463124 | + | 0.886293i | \(0.653272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11206.6 | −0.727678 | −0.363839 | − | 0.931462i | \(-0.618534\pi\) | ||||
−0.363839 | + | 0.931462i | \(0.618534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4745.51 | 0.306651 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −234.867 | −0.0151040 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 70707.6 | 4.52529 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4655.47 | −0.296526 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3878.25 | −0.245844 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2757.97 | −0.173999 | −0.0869993 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0869993 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4392.25 | 0.275792 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36845.3 | −2.30262 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4454.77 | −0.277087 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10004.0 | −0.619329 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11974.7 | −0.737869 | −0.368934 | − | 0.929455i | \(-0.620277\pi\) | ||||
−0.368934 | + | 0.929455i | \(0.620277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16145.5 | 0.990227 | 0.495114 | − | 0.868828i | \(-0.335126\pi\) | ||||
0.495114 | + | 0.868828i | \(0.335126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4255.26 | −0.259769 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21437.9 | 1.30264 | 0.651322 | − | 0.758802i | \(-0.274215\pi\) | ||||
0.651322 | + | 0.758802i | \(0.274215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4684.96 | −0.283360 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 90.7561 | 0.00546392 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17735.5 | 1.06286 | 0.531428 | − | 0.847104i | \(-0.321656\pi\) | ||||
0.531428 | + | 0.847104i | \(0.321656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58210.3 | 3.47246 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5329.67 | −0.316485 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21518.8 | 1.27201 | 0.636004 | − | 0.771686i | \(-0.280586\pi\) | ||||
0.636004 | + | 0.771686i | \(0.280586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30544.1 | 1.79732 | 0.898660 | − | 0.438646i | \(-0.144542\pi\) | ||||
0.898660 | + | 0.438646i | \(0.144542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2450.58 | −0.143548 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1347.59 | −0.0785825 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11681.9 | 0.678149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16465.2 | 0.951543 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7246.29 | 0.416900 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6938.35 | 0.397405 | 0.198703 | − | 0.980060i | \(-0.436327\pi\) | ||||
0.198703 | + | 0.980060i | \(0.436327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9798.24 | −0.558718 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8394.43 | −0.476550 | −0.238275 | − | 0.971198i | \(-0.576582\pi\) | ||||
−0.238275 | + | 0.971198i | \(0.576582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −931.930 | −0.0526718 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4615.01 | 0.259688 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18375.5 | 1.02946 | 0.514729 | − | 0.857353i | \(-0.327892\pi\) | ||||
0.514729 | + | 0.857353i | \(0.327892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27131.4 | −1.51334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7633.93 | 0.423948 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6446.61 | −0.356453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11058.8 | 0.608824 | 0.304412 | − | 0.952541i | \(-0.401540\pi\) | ||||
0.304412 | + | 0.952541i | \(0.401540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −74.5435 | −0.00408611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30107.2 | −1.64321 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15386.6 | −0.836170 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1765.42 | −0.0955284 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7955.43 | −0.428634 | −0.214317 | − | 0.976764i | \(-0.568753\pi\) | ||||
−0.214317 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6598.82 | 0.354024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3397.64 | −0.181507 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 967.425 | 0.0514622 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12814.7 | 0.678794 | 0.339397 | − | 0.940643i | \(-0.389777\pi\) | ||||
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1120.05 | −0.0590792 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9317.81 | 0.489417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4167.88 | −0.218000 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1966.25 | 0.102414 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2221.14 | −0.115208 | −0.0576039 | − | 0.998340i | \(-0.518346\pi\) | ||||
−0.0576039 | + | 0.998340i | \(0.518346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 602.039 | 0.0310972 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1811.04 | 0.0931582 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24120.1 | −1.23558 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17320.1 | 0.883587 | 0.441794 | − | 0.897117i | \(-0.354342\pi\) | ||||
0.441794 | + | 0.897117i | \(0.354342\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4035.01 | 0.204159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28448.3 | 1.43351 | 0.716755 | − | 0.697325i | \(-0.245626\pi\) | ||||
0.716755 | + | 0.697325i | \(0.245626\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22707.4 | 1.13956 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2115.52 | 0.105735 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19610.1 | 0.976141 | 0.488070 | − | 0.872804i | \(-0.337701\pi\) | ||||
0.488070 | + | 0.872804i | \(0.337701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4169.65 | 0.206715 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36346.5 | 1.79465 | 0.897325 | − | 0.441370i | \(-0.145507\pi\) | ||||
0.897325 | + | 0.441370i | \(0.145507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6593.34 | 0.324243 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6081.92 | −0.297893 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 818.528 | 0.0399311 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30350.0 | 1.47468 | 0.737342 | − | 0.675520i | \(-0.236081\pi\) | ||||
0.737342 | + | 0.675520i | \(0.236081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18996.5 | −0.919349 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 72835.2 | 3.51092 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19424.8 | 0.932635 | 0.466318 | − | 0.884617i | \(-0.345580\pi\) | ||||
0.466318 | + | 0.884617i | \(0.345580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7653.28 | −0.366003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4640.01 | −0.221025 | −0.110513 | − | 0.993875i | \(-0.535249\pi\) | ||||
−0.110513 | + | 0.993875i | \(0.535249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 119.928 | 0.00569030 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12491.4 | 0.590363 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4196.06 | 0.197537 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34544.3 | 1.61990 | 0.809949 | − | 0.586501i | \(-0.199495\pi\) | ||||
0.809949 | + | 0.586501i | \(0.199495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6344.71 | −0.296367 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9123.70 | 0.424523 | 0.212262 | − | 0.977213i | \(-0.431917\pi\) | ||||
0.212262 | + | 0.977213i | \(0.431917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19238.9 | −0.891716 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 105.660 | 0.00487844 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26180.3 | 1.20411 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16133.9 | 0.739199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1794.56 | 0.0819061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43506.3 | −1.97810 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13224.2 | 0.598974 | 0.299487 | − | 0.954100i | \(-0.403185\pi\) | ||||
0.299487 | + | 0.954100i | \(0.403185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9558.87 | −0.431312 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 449.719 | 0.0202151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6490.10 | −0.290631 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 32860.5 | 1.46596 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14713.4 | 0.653922 | 0.326961 | − | 0.945038i | \(-0.393975\pi\) | ||||
0.326961 | + | 0.945038i | \(0.393975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3221.78 | 0.142651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3704.30 | −0.163402 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8595.39 | 0.377740 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2215.35 | −0.0969949 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6169.20 | −0.269103 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2335.80 | 0.101511 | 0.0507555 | − | 0.998711i | \(-0.483837\pi\) | ||||
0.0507555 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26446.9 | 1.14510 | 0.572550 | − | 0.819870i | \(-0.305954\pi\) | ||||
0.572550 | + | 0.819870i | \(0.305954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1199.81 | 0.0517581 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45209.7 | 1.94310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6865.55 | −0.293997 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 66.7645 | 0.00284852 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30682.1 | −1.30428 | −0.652140 | − | 0.758098i | \(-0.726129\pi\) | ||||
−0.652140 | + | 0.758098i | \(0.726129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10242.8 | −0.433829 | −0.216914 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216914 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15802.0 | 0.666856 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35864.5 | −1.50802 | −0.754008 | − | 0.656865i | \(-0.771882\pi\) | ||||
−0.754008 | + | 0.656865i | \(0.771882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3633.70 | 0.152236 | 0.0761179 | − | 0.997099i | \(-0.475747\pi\) | ||||
0.0761179 | + | 0.997099i | \(0.475747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13410.7 | −0.559823 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21532.1 | −0.895609 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −63460.1 | −2.63009 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1431.39 | 0.0591113 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22098.2 | −0.909312 | −0.454656 | − | 0.890667i | \(-0.650238\pi\) | ||||
−0.454656 | + | 0.890667i | \(0.650238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19971.4 | −0.818867 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1205.39 | 0.0492476 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3732.94 | 0.151973 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −639.298 | −0.0259345 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11744.3 | −0.474751 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10848.0 | 0.436975 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8946.55 | −0.359114 | −0.179557 | − | 0.983748i | \(-0.557466\pi\) | ||||
−0.179557 | + | 0.983748i | \(0.557466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21254.0 | −0.850144 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22867.5 | −0.911479 | −0.455740 | − | 0.890113i | \(-0.650625\pi\) | ||||
−0.455740 | + | 0.890113i | \(0.650625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31281.5 | −1.24250 | −0.621252 | − | 0.783611i | \(-0.713375\pi\) | ||||
−0.621252 | + | 0.783611i | \(0.713375\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 419.199 | 0.0165926 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23071.5 | 0.910040 | 0.455020 | − | 0.890481i | \(-0.349632\pi\) | ||||
0.455020 | + | 0.890481i | \(0.349632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11800.6 | 0.463854 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2894.15 | 0.113369 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1806.36 | 0.0705138 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1894.76 | −0.0737100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14698.3 | −0.569829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2998.57 | 0.115852 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26100.7 | 1.00497 | 0.502485 | − | 0.864586i | \(-0.332419\pi\) | ||||
0.502485 | + | 0.864586i | \(0.332419\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1301.81 | −0.0499533 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48698.2 | 1.86230 | 0.931148 | − | 0.364642i | \(-0.118809\pi\) | ||||
0.931148 | + | 0.364642i | \(0.118809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −870.968 | −0.0331941 | −0.0165971 | − | 0.999862i | \(-0.505283\pi\) | ||||
−0.0165971 | + | 0.999862i | \(0.505283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21388.7 | −0.812398 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33022.5 | −1.25004 | −0.625022 | − | 0.780608i | \(-0.714910\pi\) | ||||
−0.625022 | + | 0.780608i | \(0.714910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −951.869 | −0.0359107 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1175.69 | −0.0442055 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5481.83 | −0.205423 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −77401.1 | −2.89076 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6854.62 | 0.255149 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3523.63 | 0.130723 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31159.6 | −1.15214 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −109.931 | −0.00405126 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 88969.8 | 3.26791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42835.0 | −1.56815 | −0.784076 | − | 0.620665i | \(-0.786863\pi\) | ||||
−0.784076 | + | 0.620665i | \(0.786863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15258.1 | 0.556742 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5584.98 | −0.203116 | −0.101558 | − | 0.994830i | \(-0.532383\pi\) | ||||
−0.101558 | + | 0.994830i | \(0.532383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9808.57 | 0.355549 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33082.2 | 1.19526 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1503.82 | 0.0541553 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50229.1 | 1.80294 | 0.901472 | − | 0.432838i | \(-0.142488\pi\) | ||||
0.901472 | + | 0.432838i | \(0.142488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14041.9 | 0.502385 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14450.2 | −0.515313 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22398.4 | −0.796166 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9495.28 | 0.336425 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13286.2 | −0.469222 | −0.234611 | − | 0.972089i | \(-0.575382\pi\) | ||||
−0.234611 | + | 0.972089i | \(0.575382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36636.7 | 1.28971 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2011.18 | 0.0705714 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20145.4 | −0.704626 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1627.36 | −0.0567380 | −0.0283690 | − | 0.999598i | \(-0.509031\pi\) | ||||
−0.0283690 | + | 0.999598i | \(0.509031\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6596.20 | −0.229243 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44267.2 | 1.53355 | 0.766774 | − | 0.641917i | \(-0.221861\pi\) | ||||
0.766774 | + | 0.641917i | \(0.221861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43038.6 | 1.48625 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −340.320 | −0.0117149 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47433.9 | −1.62766 | −0.813830 | − | 0.581103i | \(-0.802621\pi\) | ||||
−0.813830 | + | 0.581103i | \(0.802621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7698.42 | −0.263331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22531.8 | −0.768292 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38935.8 | −1.32346 | −0.661728 | − | 0.749744i | \(-0.730177\pi\) | ||||
−0.661728 | + | 0.749744i | \(0.730177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33496.5 | 1.13500 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2894.17 | −0.0977589 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −700.918 | −0.0236015 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26980.5 | −0.905658 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12909.7 | 0.431994 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9494.50 | 0.316724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18350.7 | −0.610257 | −0.305129 | − | 0.952311i | \(-0.598699\pi\) | ||||
−0.305129 | + | 0.952311i | \(0.598699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20153.9 | 0.668150 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3679.77 | −0.121616 | −0.0608082 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608082 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −777.796 | −0.0256269 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14153.0 | −0.464881 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16462.8 | −0.539092 | −0.269546 | − | 0.962988i | \(-0.586874\pi\) | ||||
−0.269546 | + | 0.962988i | \(0.586874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5974.08 | 0.195028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1891.49 | 0.0615604 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38116.1 | 1.23674 | 0.618370 | − | 0.785887i | \(-0.287793\pi\) | ||||
0.618370 | + | 0.785887i | \(0.287793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13929.3 | −0.450583 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −87.7753 | −0.00283072 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11286.5 | −0.362882 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8909.11 | 0.285577 | 0.142789 | − | 0.989753i | \(-0.454393\pi\) | ||||
0.142789 | + | 0.989753i | \(0.454393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25280.6 | 0.807910 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 93274.7 | 2.97186 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36786.4 | 1.16854 | 0.584271 | − | 0.811559i | \(-0.301381\pi\) | ||||
0.584271 | + | 0.811559i | \(0.301381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1666.46 | 0.0527773 |
(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 | 2496.4.a.ca.1.5 | 5 | ||
4.3 | odd | 2 | 2496.4.a.cf.1.5 | 5 | |||
8.3 | odd | 2 | 1248.4.a.g.1.1 | ✓ | 5 | ||
8.5 | even | 2 | 1248.4.a.l.1.1 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.4.a.g.1.1 | ✓ | 5 | 8.3 | odd | 2 | ||
1248.4.a.l.1.1 | yes | 5 | 8.5 | even | 2 | ||
2496.4.a.ca.1.5 | 5 | 1.1 | even | 1 | trivial | ||
2496.4.a.cf.1.5 | 5 | 4.3 | odd | 2 |