Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 82x^{10} + 2137x^{8} - 22488x^{6} + 89784x^{4} - 67392x^{2} + 11664 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.17158\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.90363 | −1.73370 | −0.866848 | − | 0.498573i | \(-0.833857\pi\) | ||||
−0.866848 | + | 0.498573i | \(0.833857\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0456 | 2.00570 | ||||||||
\(5\) | 5.61325 | 0.502065 | 0.251032 | − | 0.967979i | \(-0.419230\pi\) | ||||
0.251032 | + | 0.967979i | \(0.419230\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21345 | 0.173510 | 0.0867550 | − | 0.996230i | \(-0.472350\pi\) | ||||
0.0867550 | + | 0.996230i | \(0.472350\pi\) | |||||||
\(8\) | −39.4526 | −1.74357 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −27.5253 | −0.870427 | ||||||||
\(11\) | 43.6466 | 1.19636 | 0.598179 | − | 0.801362i | \(-0.295891\pi\) | ||||
0.598179 | + | 0.801362i | \(0.295891\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −15.7576 | −0.300813 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65.0962 | 1.01713 | ||||||||
\(17\) | 65.8757 | 0.939835 | 0.469918 | − | 0.882710i | \(-0.344284\pi\) | ||||
0.469918 | + | 0.882710i | \(0.344284\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.06427 | 0.0369996 | 0.0184998 | − | 0.999829i | \(-0.494111\pi\) | ||||
0.0184998 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(20\) | 90.0680 | 1.00699 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −214.027 | −2.07412 | ||||||||
\(23\) | −163.764 | −1.48466 | −0.742330 | − | 0.670034i | \(-0.766279\pi\) | ||||
−0.742330 | + | 0.670034i | \(0.766279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −93.4914 | −0.747931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 51.5617 | 0.348009 | ||||||||
\(29\) | 155.449 | 0.995382 | 0.497691 | − | 0.867354i | \(-0.334181\pi\) | ||||
0.497691 | + | 0.867354i | \(0.334181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −240.463 | −1.39318 | −0.696588 | − | 0.717471i | \(-0.745299\pi\) | ||||
−0.696588 | + | 0.717471i | \(0.745299\pi\) | |||||||
\(32\) | −3.58708 | −0.0198160 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −323.030 | −1.62939 | ||||||||
\(35\) | 18.0379 | 0.0871132 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 317.662 | 1.41144 | 0.705721 | − | 0.708490i | \(-0.250623\pi\) | ||||
0.705721 | + | 0.708490i | \(0.250623\pi\) | |||||||
\(38\) | −15.0261 | −0.0641460 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −221.457 | −0.875387 | ||||||||
\(41\) | 127.910 | 0.487224 | 0.243612 | − | 0.969873i | \(-0.421668\pi\) | ||||
0.243612 | + | 0.969873i | \(0.421668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −379.001 | −1.34412 | −0.672060 | − | 0.740497i | \(-0.734590\pi\) | ||||
−0.672060 | + | 0.740497i | \(0.734590\pi\) | |||||||
\(44\) | 700.336 | 2.39954 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 803.039 | 2.57395 | ||||||||
\(47\) | 79.4626 | 0.246613 | 0.123306 | − | 0.992369i | \(-0.460650\pi\) | ||||
0.123306 | + | 0.992369i | \(0.460650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −332.674 | −0.969894 | ||||||||
\(50\) | 458.447 | 1.29668 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −571.746 | −1.48180 | −0.740899 | − | 0.671616i | \(-0.765600\pi\) | ||||
−0.740899 | + | 0.671616i | \(0.765600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 244.999 | 0.600649 | ||||||||
\(56\) | −126.779 | −0.302528 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −762.263 | −1.72569 | ||||||||
\(59\) | −105.538 | −0.232879 | −0.116440 | − | 0.993198i | \(-0.537148\pi\) | ||||
−0.116440 | + | 0.993198i | \(0.537148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −724.638 | −1.52099 | −0.760495 | − | 0.649344i | \(-0.775043\pi\) | ||||
−0.760495 | + | 0.649344i | \(0.775043\pi\) | |||||||
\(62\) | 1179.14 | 2.41534 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −503.180 | −0.982774 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −302.222 | −0.551078 | −0.275539 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275539 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(68\) | 1057.01 | 1.88503 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −88.4512 | −0.151028 | ||||||||
\(71\) | −1003.39 | −1.67719 | −0.838594 | − | 0.544757i | \(-0.816622\pi\) | ||||
−0.838594 | + | 0.544757i | \(0.816622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −277.988 | −0.445699 | −0.222850 | − | 0.974853i | \(-0.571536\pi\) | ||||
−0.222850 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(74\) | −1557.70 | −2.44701 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 49.1681 | 0.0742101 | ||||||||
\(77\) | 140.256 | 0.207580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −959.137 | −1.36597 | −0.682983 | − | 0.730434i | \(-0.739318\pi\) | ||||
−0.682983 | + | 0.730434i | \(0.739318\pi\) | |||||||
\(80\) | 365.402 | 0.510664 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −627.224 | −0.844699 | ||||||||
\(83\) | 410.957 | 0.543475 | 0.271737 | − | 0.962371i | \(-0.412402\pi\) | ||||
0.271737 | + | 0.962371i | \(0.412402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 369.777 | 0.471858 | ||||||||
\(86\) | 1858.48 | 2.33029 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1721.97 | −2.08594 | ||||||||
\(89\) | −226.199 | −0.269405 | −0.134703 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134703 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2627.69 | −2.97778 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −389.655 | −0.427552 | ||||||||
\(95\) | 17.2005 | 0.0185762 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 888.458 | 0.929992 | 0.464996 | − | 0.885313i | \(-0.346056\pi\) | ||||
0.464996 | + | 0.885313i | \(0.346056\pi\) | |||||||
\(98\) | 1631.31 | 1.68150 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1500.12 | −1.50012 | ||||||||
\(101\) | 1860.36 | 1.83280 | 0.916400 | − | 0.400264i | \(-0.131082\pi\) | ||||
0.916400 | + | 0.400264i | \(0.131082\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 328.512 | 0.314265 | 0.157132 | − | 0.987578i | \(-0.449775\pi\) | ||||
0.157132 | + | 0.987578i | \(0.449775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2803.63 | 2.56899 | ||||||||
\(107\) | −328.774 | −0.297045 | −0.148522 | − | 0.988909i | \(-0.547452\pi\) | ||||
−0.148522 | + | 0.988909i | \(0.547452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −201.673 | −0.177218 | −0.0886092 | − | 0.996066i | \(-0.528242\pi\) | ||||
−0.0886092 | + | 0.996066i | \(0.528242\pi\) | |||||||
\(110\) | −1201.39 | −1.04134 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 209.183 | 0.176482 | ||||||||
\(113\) | −289.984 | −0.241411 | −0.120705 | − | 0.992688i | \(-0.538516\pi\) | ||||
−0.120705 | + | 0.992688i | \(0.538516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −919.250 | −0.745395 | ||||||||
\(116\) | 2494.27 | 1.99644 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 517.520 | 0.403742 | ||||||||
\(119\) | 211.688 | 0.163071 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 574.026 | 0.431274 | ||||||||
\(122\) | 3553.36 | 2.63693 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3858.37 | −2.79429 | ||||||||
\(125\) | −1226.45 | −0.877574 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 752.567 | 0.525823 | 0.262911 | − | 0.964820i | \(-0.415317\pi\) | ||||
0.262911 | + | 0.964820i | \(0.415317\pi\) | |||||||
\(128\) | 2496.11 | 1.72365 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2200.41 | −1.46756 | −0.733782 | − | 0.679385i | \(-0.762247\pi\) | ||||
−0.733782 | + | 0.679385i | \(0.762247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.84689 | 0.00641980 | ||||||||
\(134\) | 1481.98 | 0.955402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2598.97 | −1.63867 | ||||||||
\(137\) | 364.076 | 0.227044 | 0.113522 | − | 0.993535i | \(-0.463787\pi\) | ||||
0.113522 | + | 0.993535i | \(0.463787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2453.59 | 1.49720 | 0.748600 | − | 0.663022i | \(-0.230727\pi\) | ||||
0.748600 | + | 0.663022i | \(0.230727\pi\) | |||||||
\(140\) | 289.429 | 0.174723 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4920.25 | 2.90773 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 872.573 | 0.499746 | ||||||||
\(146\) | 1363.15 | 0.772706 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5097.08 | 2.83093 | ||||||||
\(149\) | −65.1448 | −0.0358179 | −0.0179090 | − | 0.999840i | \(-0.505701\pi\) | ||||
−0.0179090 | + | 0.999840i | \(0.505701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 250.204 | 0.134843 | 0.0674216 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674216 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(152\) | −120.894 | −0.0645116 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −687.764 | −0.359881 | ||||||||
\(155\) | −1349.78 | −0.699464 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1768.99 | 0.899242 | 0.449621 | − | 0.893219i | \(-0.351559\pi\) | ||||
0.449621 | + | 0.893219i | \(0.351559\pi\) | |||||||
\(158\) | 4703.25 | 2.36817 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20.1352 | −0.00994890 | ||||||||
\(161\) | −526.248 | −0.257603 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2707.32 | −1.30094 | −0.650470 | − | 0.759532i | \(-0.725428\pi\) | ||||
−0.650470 | + | 0.759532i | \(0.725428\pi\) | |||||||
\(164\) | 2052.39 | 0.977226 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2015.18 | −0.942220 | ||||||||
\(167\) | 3492.29 | 1.61821 | 0.809107 | − | 0.587661i | \(-0.199951\pi\) | ||||
0.809107 | + | 0.587661i | \(0.199951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1813.25 | −0.818058 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6081.30 | −2.69590 | ||||||||
\(173\) | 3981.96 | 1.74996 | 0.874979 | − | 0.484160i | \(-0.160875\pi\) | ||||
0.874979 | + | 0.484160i | \(0.160875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −300.430 | −0.129774 | ||||||||
\(176\) | 2841.23 | 1.21685 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1109.20 | 0.467066 | ||||||||
\(179\) | −2255.05 | −0.941624 | −0.470812 | − | 0.882234i | \(-0.656039\pi\) | ||||
−0.470812 | + | 0.882234i | \(0.656039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −890.108 | −0.365532 | −0.182766 | − | 0.983156i | \(-0.558505\pi\) | ||||
−0.182766 | + | 0.983156i | \(0.558505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6460.92 | 2.58862 | ||||||||
\(185\) | 1783.12 | 0.708635 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2875.25 | 1.12438 | ||||||||
\(188\) | 1275.02 | 0.494631 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −84.3451 | −0.0322055 | ||||||||
\(191\) | −799.774 | −0.302982 | −0.151491 | − | 0.988459i | \(-0.548407\pi\) | ||||
−0.151491 | + | 0.988459i | \(0.548407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2693.40 | −1.00454 | −0.502268 | − | 0.864712i | \(-0.667501\pi\) | ||||
−0.502268 | + | 0.864712i | \(0.667501\pi\) | |||||||
\(194\) | −4356.67 | −1.61232 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5337.95 | −1.94532 | ||||||||
\(197\) | −2735.70 | −0.989395 | −0.494698 | − | 0.869065i | \(-0.664721\pi\) | ||||
−0.494698 | + | 0.869065i | \(0.664721\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1176.44 | −0.419072 | −0.209536 | − | 0.977801i | \(-0.567195\pi\) | ||||
−0.209536 | + | 0.977801i | \(0.567195\pi\) | |||||||
\(200\) | 3688.48 | 1.30407 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9122.52 | −3.17752 | ||||||||
\(203\) | 499.526 | 0.172709 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 717.992 | 0.244618 | ||||||||
\(206\) | −1610.90 | −0.544839 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 133.745 | 0.0442648 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2914.65 | −0.950961 | −0.475481 | − | 0.879726i | \(-0.657726\pi\) | ||||
−0.475481 | + | 0.879726i | \(0.657726\pi\) | |||||||
\(212\) | −9174.00 | −2.97204 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1612.19 | 0.514985 | ||||||||
\(215\) | −2127.43 | −0.674835 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −772.716 | −0.241730 | ||||||||
\(218\) | 988.932 | 0.307243 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3931.16 | 1.20472 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1481.39 | −0.444848 | −0.222424 | − | 0.974950i | \(-0.571397\pi\) | ||||
−0.222424 | + | 0.974950i | \(0.571397\pi\) | |||||||
\(224\) | −11.5269 | −0.00343827 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1421.98 | 0.418533 | ||||||||
\(227\) | −4.38339 | −0.00128166 | −0.000640828 | − | 1.00000i | \(-0.500204\pi\) | ||||
−0.000640828 | 1.00000i | \(0.500204\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4689.58 | 1.35326 | 0.676629 | − | 0.736324i | \(-0.263440\pi\) | ||||
0.676629 | + | 0.736324i | \(0.263440\pi\) | |||||||
\(230\) | 4507.66 | 1.29229 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6132.85 | −1.73552 | ||||||||
\(233\) | 4124.52 | 1.15968 | 0.579842 | − | 0.814729i | \(-0.303114\pi\) | ||||
0.579842 | + | 0.814729i | \(0.303114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 446.044 | 0.123816 | ||||||||
\(236\) | −1693.42 | −0.467086 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1038.04 | −0.282715 | ||||||||
\(239\) | −3455.41 | −0.935196 | −0.467598 | − | 0.883941i | \(-0.654880\pi\) | ||||
−0.467598 | + | 0.883941i | \(0.654880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4109.67 | 1.09845 | 0.549226 | − | 0.835674i | \(-0.314923\pi\) | ||||
0.549226 | + | 0.835674i | \(0.314923\pi\) | |||||||
\(242\) | −2814.81 | −0.747698 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11627.2 | −3.05065 | ||||||||
\(245\) | −1867.38 | −0.486950 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9486.89 | 2.42911 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6014.05 | 1.52145 | ||||||||
\(251\) | 5032.21 | 1.26546 | 0.632730 | − | 0.774372i | \(-0.281934\pi\) | ||||
0.632730 | + | 0.774372i | \(0.281934\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7147.75 | −1.77619 | ||||||||
\(254\) | −3690.31 | −0.911617 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8214.54 | −2.00550 | ||||||||
\(257\) | 5633.97 | 1.36746 | 0.683731 | − | 0.729735i | \(-0.260356\pi\) | ||||
0.683731 | + | 0.729735i | \(0.260356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1020.79 | 0.244899 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10790.0 | 2.54431 | ||||||||
\(263\) | −5112.62 | −1.19870 | −0.599350 | − | 0.800487i | \(-0.704574\pi\) | ||||
−0.599350 | + | 0.800487i | \(0.704574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3209.35 | −0.743959 | ||||||||
\(266\) | −48.2855 | −0.0111300 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4849.32 | −1.10530 | ||||||||
\(269\) | −6562.49 | −1.48744 | −0.743721 | − | 0.668490i | \(-0.766941\pi\) | ||||
−0.743721 | + | 0.668490i | \(0.766941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8161.31 | 1.82939 | 0.914694 | − | 0.404146i | \(-0.132431\pi\) | ||||
0.914694 | + | 0.404146i | \(0.132431\pi\) | |||||||
\(272\) | 4288.26 | 0.955934 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1785.29 | −0.393626 | ||||||||
\(275\) | −4080.58 | −0.894794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2726.57 | 0.591421 | 0.295710 | − | 0.955278i | \(-0.404444\pi\) | ||||
0.295710 | + | 0.955278i | \(0.404444\pi\) | |||||||
\(278\) | −12031.5 | −2.59569 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −711.642 | −0.151888 | ||||||||
\(281\) | −1216.67 | −0.258294 | −0.129147 | − | 0.991625i | \(-0.541224\pi\) | ||||
−0.129147 | + | 0.991625i | \(0.541224\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3248.32 | −0.682306 | −0.341153 | − | 0.940008i | \(-0.610817\pi\) | ||||
−0.341153 | + | 0.940008i | \(0.610817\pi\) | |||||||
\(284\) | −16100.0 | −3.36393 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 411.033 | 0.0845383 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −573.393 | −0.116709 | ||||||||
\(290\) | −4278.77 | −0.866408 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4460.48 | −0.893938 | ||||||||
\(293\) | −9222.59 | −1.83887 | −0.919435 | − | 0.393241i | \(-0.871354\pi\) | ||||
−0.919435 | + | 0.393241i | \(0.871354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −592.412 | −0.116920 | ||||||||
\(296\) | −12532.6 | −2.46095 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 319.446 | 0.0620974 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1217.90 | −0.233218 | ||||||||
\(302\) | −1226.91 | −0.233777 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 199.473 | 0.0376334 | ||||||||
\(305\) | −4067.58 | −0.763635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2993.33 | −0.556477 | −0.278238 | − | 0.960512i | \(-0.589751\pi\) | ||||
−0.278238 | + | 0.960512i | \(0.589751\pi\) | |||||||
\(308\) | 2250.49 | 0.416343 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6618.82 | 1.21266 | ||||||||
\(311\) | −7261.04 | −1.32391 | −0.661955 | − | 0.749544i | \(-0.730273\pi\) | ||||
−0.661955 | + | 0.749544i | \(0.730273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3903.02 | −0.704829 | −0.352415 | − | 0.935844i | \(-0.614639\pi\) | ||||
−0.352415 | + | 0.935844i | \(0.614639\pi\) | |||||||
\(314\) | −8674.49 | −1.55901 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15389.9 | −2.73972 | ||||||||
\(317\) | −4592.24 | −0.813646 | −0.406823 | − | 0.913507i | \(-0.633363\pi\) | ||||
−0.406823 | + | 0.913507i | \(0.633363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6784.81 | 1.19083 | ||||||||
\(320\) | −2824.48 | −0.493416 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2580.52 | 0.446606 | ||||||||
\(323\) | 201.861 | 0.0347735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13275.7 | 2.25543 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5046.39 | −0.849512 | ||||||||
\(329\) | 255.349 | 0.0427898 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5115.67 | 0.849495 | 0.424747 | − | 0.905312i | \(-0.360363\pi\) | ||||
0.424747 | + | 0.905312i | \(0.360363\pi\) | |||||||
\(332\) | 6594.05 | 1.09005 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17124.9 | −2.80549 | ||||||||
\(335\) | −1696.45 | −0.276677 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6808.37 | −1.10052 | −0.550260 | − | 0.834993i | \(-0.685471\pi\) | ||||
−0.550260 | + | 0.834993i | \(0.685471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5933.29 | 0.946405 | ||||||||
\(341\) | −10495.4 | −1.66674 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2171.24 | −0.341796 | ||||||||
\(344\) | 14952.6 | 2.34357 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19526.1 | −3.03389 | ||||||||
\(347\) | 10918.2 | 1.68910 | 0.844551 | − | 0.535475i | \(-0.179867\pi\) | ||||
0.844551 | + | 0.535475i | \(0.179867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10239.2 | −1.57047 | −0.785234 | − | 0.619199i | \(-0.787457\pi\) | ||||
−0.785234 | + | 0.619199i | \(0.787457\pi\) | |||||||
\(350\) | 1473.20 | 0.224988 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −156.564 | −0.0237070 | ||||||||
\(353\) | −864.031 | −0.130277 | −0.0651384 | − | 0.997876i | \(-0.520749\pi\) | ||||
−0.0651384 | + | 0.997876i | \(0.520749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5632.27 | −0.842057 | ||||||||
\(356\) | −3629.50 | −0.540346 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11058.0 | 1.63249 | ||||||||
\(359\) | −11430.0 | −1.68036 | −0.840182 | − | 0.542305i | \(-0.817552\pi\) | ||||
−0.840182 | + | 0.542305i | \(0.817552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6849.61 | −0.998631 | ||||||||
\(362\) | 4364.76 | 0.633720 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1560.42 | −0.223770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9212.03 | 1.31026 | 0.655128 | − | 0.755518i | \(-0.272615\pi\) | ||||
0.655128 | + | 0.755518i | \(0.272615\pi\) | |||||||
\(368\) | −10660.4 | −1.51009 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8743.75 | −1.22856 | ||||||||
\(371\) | −1837.28 | −0.257107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1118.13 | −0.155213 | −0.0776065 | − | 0.996984i | \(-0.524728\pi\) | ||||
−0.0776065 | + | 0.996984i | \(0.524728\pi\) | |||||||
\(374\) | −14099.2 | −1.94933 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3135.00 | −0.429988 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8067.99 | −1.09347 | −0.546735 | − | 0.837306i | \(-0.684129\pi\) | ||||
−0.546735 | + | 0.837306i | \(0.684129\pi\) | |||||||
\(380\) | 275.993 | 0.0372583 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3921.79 | 0.525279 | ||||||||
\(383\) | 2023.73 | 0.269995 | 0.134997 | − | 0.990846i | \(-0.456897\pi\) | ||||
0.134997 | + | 0.990846i | \(0.456897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 787.293 | 0.104219 | ||||||||
\(386\) | 13207.5 | 1.74156 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14255.8 | 1.86528 | ||||||||
\(389\) | −9697.21 | −1.26393 | −0.631964 | − | 0.774998i | \(-0.717751\pi\) | ||||
−0.631964 | + | 0.774998i | \(0.717751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10788.1 | −1.39534 | ||||||||
\(392\) | 13124.8 | 1.69108 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13414.9 | 1.71531 | ||||||||
\(395\) | −5383.88 | −0.685803 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3396.25 | −0.429353 | −0.214676 | − | 0.976685i | \(-0.568870\pi\) | ||||
−0.214676 | + | 0.976685i | \(0.568870\pi\) | |||||||
\(398\) | 5768.80 | 0.726543 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6085.94 | −0.760742 | ||||||||
\(401\) | 6649.91 | 0.828131 | 0.414066 | − | 0.910247i | \(-0.364108\pi\) | ||||
0.414066 | + | 0.910247i | \(0.364108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 29850.6 | 3.67604 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2449.49 | −0.299424 | ||||||||
\(407\) | 13864.9 | 1.68859 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2515.44 | 0.304109 | 0.152055 | − | 0.988372i | \(-0.451411\pi\) | ||||
0.152055 | + | 0.988372i | \(0.451411\pi\) | |||||||
\(410\) | −3520.77 | −0.424093 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5271.17 | 0.630320 | ||||||||
\(413\) | −339.141 | −0.0404069 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2306.81 | 0.272860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −655.837 | −0.0767417 | ||||||||
\(419\) | 11907.4 | 1.38835 | 0.694173 | − | 0.719808i | \(-0.255770\pi\) | ||||
0.694173 | + | 0.719808i | \(0.255770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2382.88 | −0.275854 | −0.137927 | − | 0.990442i | \(-0.544044\pi\) | ||||
−0.137927 | + | 0.990442i | \(0.544044\pi\) | |||||||
\(422\) | 14292.4 | 1.64868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22556.9 | 2.58363 | ||||||||
\(425\) | −6158.81 | −0.702932 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2328.59 | −0.263907 | ||||||||
\(428\) | −5275.37 | −0.595782 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10432.1 | 1.16996 | ||||||||
\(431\) | 286.545 | 0.0320241 | 0.0160121 | − | 0.999872i | \(-0.494903\pi\) | ||||
0.0160121 | + | 0.999872i | \(0.494903\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −848.354 | −0.0941555 | −0.0470777 | − | 0.998891i | \(-0.514991\pi\) | ||||
−0.0470777 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(434\) | 3789.11 | 0.419086 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3235.97 | −0.355447 | ||||||||
\(437\) | −501.818 | −0.0549318 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 69.6932 | 0.00757694 | 0.00378847 | − | 0.999993i | \(-0.498794\pi\) | ||||
0.00378847 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(440\) | −9665.87 | −1.04728 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7331.02 | −0.786247 | −0.393123 | − | 0.919486i | \(-0.628605\pi\) | ||||
−0.393123 | + | 0.919486i | \(0.628605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1269.71 | −0.135259 | ||||||||
\(446\) | 7264.18 | 0.771231 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1616.94 | −0.170521 | ||||||||
\(449\) | −14213.2 | −1.49390 | −0.746950 | − | 0.664880i | \(-0.768483\pi\) | ||||
−0.746950 | + | 0.664880i | \(0.768483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5582.84 | 0.582895 | ||||||||
\(452\) | −4652.97 | −0.484197 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.4945 | 0.00222200 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5903.20 | 0.604246 | 0.302123 | − | 0.953269i | \(-0.402305\pi\) | ||||
0.302123 | + | 0.953269i | \(0.402305\pi\) | |||||||
\(458\) | −22996.0 | −2.34614 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14749.9 | −1.49504 | ||||||||
\(461\) | 563.806 | 0.0569610 | 0.0284805 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284805 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17543.8 | 1.76097 | 0.880487 | − | 0.474070i | \(-0.157216\pi\) | ||||
0.880487 | + | 0.474070i | \(0.157216\pi\) | |||||||
\(464\) | 10119.1 | 1.01243 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20225.1 | −2.01054 | ||||||||
\(467\) | −9125.81 | −0.904266 | −0.452133 | − | 0.891951i | \(-0.649337\pi\) | ||||
−0.452133 | + | 0.891951i | \(0.649337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −971.174 | −0.0956176 | ||||||||
\(470\) | −2187.23 | −0.214659 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4163.75 | 0.406043 | ||||||||
\(473\) | −16542.1 | −1.60805 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −286.483 | −0.0276732 | ||||||||
\(476\) | 3396.66 | 0.327071 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16944.0 | 1.62134 | ||||||||
\(479\) | 4970.15 | 0.474096 | 0.237048 | − | 0.971498i | \(-0.423820\pi\) | ||||
0.237048 | + | 0.971498i | \(0.423820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −20152.3 | −1.90438 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9210.59 | 0.865006 | ||||||||
\(485\) | 4987.14 | 0.466916 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5716.80 | 0.531936 | 0.265968 | − | 0.963982i | \(-0.414308\pi\) | ||||
0.265968 | + | 0.963982i | \(0.414308\pi\) | |||||||
\(488\) | 28588.8 | 2.65196 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9156.95 | 0.844222 | ||||||||
\(491\) | 6044.21 | 0.555543 | 0.277771 | − | 0.960647i | \(-0.410404\pi\) | ||||
0.277771 | + | 0.960647i | \(0.410404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10240.3 | 0.935496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15653.2 | −1.41704 | ||||||||
\(497\) | −3224.34 | −0.291009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1101.16 | −0.0987870 | −0.0493935 | − | 0.998779i | \(-0.515729\pi\) | ||||
−0.0493935 | + | 0.998779i | \(0.515729\pi\) | |||||||
\(500\) | −19679.1 | −1.76015 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24676.1 | −2.19392 | ||||||||
\(503\) | 1341.97 | 0.118957 | 0.0594787 | − | 0.998230i | \(-0.481056\pi\) | ||||
0.0594787 | + | 0.998230i | \(0.481056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10442.7 | 0.920184 | ||||||||
\(506\) | 35049.9 | 3.07937 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12075.4 | 1.05464 | ||||||||
\(509\) | −13473.6 | −1.17329 | −0.586647 | − | 0.809843i | \(-0.699553\pi\) | ||||
−0.586647 | + | 0.809843i | \(0.699553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −893.300 | −0.0773332 | ||||||||
\(512\) | 20312.2 | 1.75328 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27626.9 | −2.37076 | ||||||||
\(515\) | 1844.02 | 0.157781 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3468.27 | 0.295038 | ||||||||
\(518\) | −5005.58 | −0.424581 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10374.9 | −0.872423 | −0.436211 | − | 0.899844i | \(-0.643680\pi\) | ||||
−0.436211 | + | 0.899844i | \(0.643680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22295.4 | −1.86407 | −0.932037 | − | 0.362364i | \(-0.881970\pi\) | ||||
−0.932037 | + | 0.362364i | \(0.881970\pi\) | |||||||
\(524\) | −35306.9 | −2.94349 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25070.4 | 2.07818 | ||||||||
\(527\) | −15840.7 | −1.30936 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14651.7 | 1.20422 | ||||||||
\(530\) | 15737.5 | 1.28980 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 157.999 | 0.0128762 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1845.49 | −0.149136 | ||||||||
\(536\) | 11923.4 | 0.960846 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32180.0 | 2.57877 | ||||||||
\(539\) | −14520.1 | −1.16034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10201.9 | 0.810747 | 0.405373 | − | 0.914151i | \(-0.367141\pi\) | ||||
0.405373 | + | 0.914151i | \(0.367141\pi\) | |||||||
\(542\) | −40020.1 | −3.17160 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −236.301 | −0.0186238 | ||||||||
\(545\) | −1132.04 | −0.0889751 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9312.12 | −0.727893 | −0.363947 | − | 0.931420i | \(-0.618571\pi\) | ||||
−0.363947 | + | 0.931420i | \(0.618571\pi\) | |||||||
\(548\) | 5841.81 | 0.455383 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20009.7 | 1.55130 | ||||||||
\(551\) | 476.337 | 0.0368288 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3082.14 | −0.237009 | ||||||||
\(554\) | −13370.1 | −1.02534 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39369.3 | 3.00293 | ||||||||
\(557\) | −144.324 | −0.0109788 | −0.00548940 | − | 0.999985i | \(-0.501747\pi\) | ||||
−0.00548940 | + | 0.999985i | \(0.501747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1174.20 | 0.0886054 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5966.11 | 0.447802 | ||||||||
\(563\) | 14667.0 | 1.09794 | 0.548968 | − | 0.835843i | \(-0.315021\pi\) | ||||
0.548968 | + | 0.835843i | \(0.315021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1627.75 | −0.121204 | ||||||||
\(566\) | 15928.6 | 1.18291 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 39586.3 | 2.92430 | ||||||||
\(569\) | 18754.1 | 1.38174 | 0.690871 | − | 0.722978i | \(-0.257227\pi\) | ||||
0.690871 | + | 0.722978i | \(0.257227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13886.4 | −1.01773 | −0.508867 | − | 0.860845i | \(-0.669935\pi\) | ||||
−0.508867 | + | 0.860845i | \(0.669935\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2015.55 | −0.146564 | ||||||||
\(575\) | 15310.5 | 1.11042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9338.81 | 0.673795 | 0.336898 | − | 0.941541i | \(-0.390622\pi\) | ||||
0.336898 | + | 0.941541i | \(0.390622\pi\) | |||||||
\(578\) | 2811.71 | 0.202338 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14000.9 | 1.00234 | ||||||||
\(581\) | 1320.59 | 0.0942983 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24954.8 | −1.77276 | ||||||||
\(584\) | 10967.3 | 0.777110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45224.1 | 3.18804 | ||||||||
\(587\) | 3724.13 | 0.261859 | 0.130930 | − | 0.991392i | \(-0.458204\pi\) | ||||
0.130930 | + | 0.991392i | \(0.458204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −736.845 | −0.0515470 | ||||||||
\(590\) | 2904.97 | 0.202704 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20678.6 | 1.43562 | ||||||||
\(593\) | 19910.2 | 1.37877 | 0.689387 | − | 0.724393i | \(-0.257880\pi\) | ||||
0.689387 | + | 0.724393i | \(0.257880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1188.26 | 0.0818721 | ||||||||
\(596\) | −1045.29 | −0.0718400 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14756.0 | −1.00653 | −0.503265 | − | 0.864132i | \(-0.667868\pi\) | ||||
−0.503265 | + | 0.864132i | \(0.667868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7939.05 | −0.538837 | −0.269418 | − | 0.963023i | \(-0.586831\pi\) | ||||
−0.269418 | + | 0.963023i | \(0.586831\pi\) | |||||||
\(602\) | 5972.14 | 0.404329 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4014.67 | 0.270455 | ||||||||
\(605\) | 3222.15 | 0.216528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2563.88 | −0.171441 | −0.0857205 | − | 0.996319i | \(-0.527319\pi\) | ||||
−0.0857205 | + | 0.996319i | \(0.527319\pi\) | |||||||
\(608\) | −10.9918 | −0.000733184 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19945.9 | 1.32391 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17593.4 | −1.15920 | −0.579602 | − | 0.814900i | \(-0.696792\pi\) | ||||
−0.579602 | + | 0.814900i | \(0.696792\pi\) | |||||||
\(614\) | 14678.2 | 0.964761 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5533.47 | −0.361932 | ||||||||
\(617\) | −24479.7 | −1.59727 | −0.798635 | − | 0.601816i | \(-0.794444\pi\) | ||||
−0.798635 | + | 0.601816i | \(0.794444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2927.43 | −0.190086 | −0.0950431 | − | 0.995473i | \(-0.530299\pi\) | ||||
−0.0950431 | + | 0.995473i | \(0.530299\pi\) | |||||||
\(620\) | −21658.0 | −1.40291 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35605.5 | 2.29526 | ||||||||
\(623\) | −726.879 | −0.0467445 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4802.06 | 0.307332 | ||||||||
\(626\) | 19138.9 | 1.22196 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28384.5 | 1.80361 | ||||||||
\(629\) | 20926.2 | 1.32652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10183.0 | −0.642439 | −0.321220 | − | 0.947005i | \(-0.604093\pi\) | ||||
−0.321220 | + | 0.947005i | \(0.604093\pi\) | |||||||
\(632\) | 37840.4 | 2.38166 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22518.6 | 1.41061 | ||||||||
\(635\) | 4224.35 | 0.263997 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −33270.2 | −2.06454 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14011.3 | 0.865382 | ||||||||
\(641\) | 17103.4 | 1.05389 | 0.526946 | − | 0.849899i | \(-0.323337\pi\) | ||||
0.526946 | + | 0.849899i | \(0.323337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21733.9 | −1.33297 | −0.666485 | − | 0.745518i | \(-0.732202\pi\) | ||||
−0.666485 | + | 0.745518i | \(0.732202\pi\) | |||||||
\(644\) | −8443.96 | −0.516675 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −989.853 | −0.0602867 | ||||||||
\(647\) | 22302.3 | 1.35517 | 0.677584 | − | 0.735446i | \(-0.263027\pi\) | ||||
0.677584 | + | 0.735446i | \(0.263027\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4606.38 | −0.278607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43440.5 | −2.60930 | ||||||||
\(653\) | −6977.15 | −0.418127 | −0.209063 | − | 0.977902i | \(-0.567042\pi\) | ||||
−0.209063 | + | 0.977902i | \(0.567042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12351.5 | −0.736812 | ||||||||
\(656\) | 8326.47 | 0.495570 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1252.14 | −0.0741845 | ||||||||
\(659\) | −10026.2 | −0.592662 | −0.296331 | − | 0.955085i | \(-0.595763\pi\) | ||||
−0.296331 | + | 0.955085i | \(0.595763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4710.64 | −0.277190 | −0.138595 | − | 0.990349i | \(-0.544259\pi\) | ||||
−0.138595 | + | 0.990349i | \(0.544259\pi\) | |||||||
\(662\) | −25085.4 | −1.47277 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16213.3 | −0.947589 | ||||||||
\(665\) | 55.2731 | 0.00322316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25456.9 | −1.47780 | ||||||||
\(668\) | 56035.9 | 3.24565 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8318.75 | 0.479674 | ||||||||
\(671\) | −31628.0 | −1.81965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14727.2 | −0.843523 | −0.421762 | − | 0.906707i | \(-0.638588\pi\) | ||||
−0.421762 | + | 0.906707i | \(0.638588\pi\) | |||||||
\(674\) | 33385.7 | 1.90797 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2118.31 | −0.120256 | −0.0601279 | − | 0.998191i | \(-0.519151\pi\) | ||||
−0.0601279 | + | 0.998191i | \(0.519151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2855.02 | 0.161363 | ||||||||
\(680\) | −14588.7 | −0.822720 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 51465.6 | 2.88962 | ||||||||
\(683\) | −7070.72 | −0.396125 | −0.198063 | − | 0.980189i | \(-0.563465\pi\) | ||||
−0.198063 | + | 0.980189i | \(0.563465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2043.65 | 0.113991 | ||||||||
\(686\) | 10647.0 | 0.592571 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24671.6 | −1.36714 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15584.0 | 0.857947 | 0.428974 | − | 0.903317i | \(-0.358875\pi\) | ||||
0.428974 | + | 0.903317i | \(0.358875\pi\) | |||||||
\(692\) | 63892.9 | 3.50989 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53538.7 | −2.92839 | ||||||||
\(695\) | 13772.6 | 0.751691 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8426.17 | 0.457911 | ||||||||
\(698\) | 50209.4 | 2.72271 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4820.57 | −0.260287 | ||||||||
\(701\) | −13190.6 | −0.710703 | −0.355352 | − | 0.934733i | \(-0.615639\pi\) | ||||
−0.355352 | + | 0.934733i | \(0.615639\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 973.404 | 0.0522228 | ||||||||
\(704\) | −21962.1 | −1.17575 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4236.89 | 0.225860 | ||||||||
\(707\) | 5978.17 | 0.318009 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31565.9 | 1.67205 | 0.836025 | − | 0.548692i | \(-0.184874\pi\) | ||||
0.836025 | + | 0.548692i | \(0.184874\pi\) | |||||||
\(710\) | 27618.6 | 1.45987 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8924.14 | 0.469728 | ||||||||
\(713\) | 39379.2 | 2.06839 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −36183.7 | −1.88861 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 56048.3 | 2.91324 | ||||||||
\(719\) | −15535.3 | −0.805800 | −0.402900 | − | 0.915244i | \(-0.631998\pi\) | ||||
−0.402900 | + | 0.915244i | \(0.631998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1055.66 | 0.0545281 | ||||||||
\(722\) | 33588.0 | 1.73132 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14282.3 | −0.733146 | ||||||||
\(725\) | −14533.1 | −0.744477 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27639.6 | −1.41004 | −0.705018 | − | 0.709189i | \(-0.749061\pi\) | ||||
−0.705018 | + | 0.709189i | \(0.749061\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7651.71 | 0.387949 | ||||||||
\(731\) | −24967.0 | −1.26325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1318.97 | −0.0664629 | −0.0332314 | − | 0.999448i | \(-0.510580\pi\) | ||||
−0.0332314 | + | 0.999448i | \(0.510580\pi\) | |||||||
\(734\) | −45172.4 | −2.27158 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 587.434 | 0.0294200 | ||||||||
\(737\) | −13190.9 | −0.659287 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2970.75 | −0.147876 | −0.0739382 | − | 0.997263i | \(-0.523557\pi\) | ||||
−0.0739382 | + | 0.997263i | \(0.523557\pi\) | |||||||
\(740\) | 28611.2 | 1.42131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9009.32 | 0.445745 | ||||||||
\(743\) | 28792.6 | 1.42167 | 0.710833 | − | 0.703361i | \(-0.248318\pi\) | ||||
0.710833 | + | 0.703361i | \(0.248318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −365.675 | −0.0179829 | ||||||||
\(746\) | 5482.88 | 0.269092 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 46135.1 | 2.25517 | ||||||||
\(749\) | −1056.50 | −0.0515402 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7839.45 | −0.380913 | −0.190456 | − | 0.981696i | \(-0.560997\pi\) | ||||
−0.190456 | + | 0.981696i | \(0.560997\pi\) | |||||||
\(752\) | 5172.71 | 0.250837 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1404.46 | 0.0677000 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3192.42 | −0.153277 | −0.0766383 | − | 0.997059i | \(-0.524419\pi\) | ||||
−0.0766383 | + | 0.997059i | \(0.524419\pi\) | |||||||
\(758\) | 39562.5 | 1.89574 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −678.606 | −0.0323890 | ||||||||
\(761\) | 25421.9 | 1.21096 | 0.605481 | − | 0.795860i | \(-0.292981\pi\) | ||||
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −648.067 | −0.0307492 | ||||||||
\(764\) | −12832.8 | −0.607691 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9923.64 | −0.468089 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33930.6 | −1.59112 | −0.795559 | − | 0.605876i | \(-0.792823\pi\) | ||||
−0.795559 | + | 0.605876i | \(0.792823\pi\) | |||||||
\(770\) | −3860.60 | −0.180683 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43217.2 | −2.01480 | ||||||||
\(773\) | 40596.9 | 1.88897 | 0.944483 | − | 0.328560i | \(-0.106563\pi\) | ||||
0.944483 | + | 0.328560i | \(0.106563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22481.2 | 1.04200 | ||||||||
\(776\) | −35052.0 | −1.62151 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47551.5 | 2.19127 | ||||||||
\(779\) | 391.952 | 0.0180271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43794.5 | −2.00652 | ||||||||
\(782\) | 52900.7 | 2.41909 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21655.8 | −0.986507 | ||||||||
\(785\) | 9929.81 | 0.451478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39046.2 | 1.76855 | 0.884274 | − | 0.466969i | \(-0.154654\pi\) | ||||
0.884274 | + | 0.466969i | \(0.154654\pi\) | |||||||
\(788\) | −43896.0 | −1.98443 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26400.5 | 1.18897 | ||||||||
\(791\) | −931.850 | −0.0418872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 16654.0 | 0.744367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18876.6 | −0.840532 | ||||||||
\(797\) | 8074.79 | 0.358876 | 0.179438 | − | 0.983769i | \(-0.442572\pi\) | ||||
0.179438 | + | 0.983769i | \(0.442572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5234.65 | 0.231776 | ||||||||
\(800\) | 335.361 | 0.0148210 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32608.7 | −1.43573 | ||||||||
\(803\) | −12133.2 | −0.533216 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2953.96 | −0.129334 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −73396.1 | −3.19562 | ||||||||
\(809\) | 30128.0 | 1.30933 | 0.654663 | − | 0.755921i | \(-0.272811\pi\) | ||||
0.654663 | + | 0.755921i | \(0.272811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −707.812 | −0.0306469 | −0.0153235 | − | 0.999883i | \(-0.504878\pi\) | ||||
−0.0153235 | + | 0.999883i | \(0.504878\pi\) | |||||||
\(812\) | 8015.20 | 0.346402 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −67988.2 | −2.92750 | ||||||||
\(815\) | −15196.9 | −0.653156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1161.36 | −0.0497319 | ||||||||
\(818\) | −12334.8 | −0.527233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11520.6 | 0.490630 | ||||||||
\(821\) | −15620.3 | −0.664009 | −0.332004 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332004 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32710.1 | 1.38542 | 0.692710 | − | 0.721216i | \(-0.256417\pi\) | ||||
0.692710 | + | 0.721216i | \(0.256417\pi\) | |||||||
\(824\) | −12960.7 | −0.547944 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1663.02 | 0.0700532 | ||||||||
\(827\) | 28246.1 | 1.18768 | 0.593842 | − | 0.804582i | \(-0.297611\pi\) | ||||
0.593842 | + | 0.804582i | \(0.297611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14099.2 | −0.590694 | −0.295347 | − | 0.955390i | \(-0.595435\pi\) | ||||
−0.295347 | + | 0.955390i | \(0.595435\pi\) | |||||||
\(830\) | −11311.7 | −0.473055 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21915.1 | −0.911541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19603.1 | 0.812449 | ||||||||
\(836\) | 2146.02 | 0.0887819 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −58389.7 | −2.40697 | ||||||||
\(839\) | −11485.3 | −0.472605 | −0.236302 | − | 0.971680i | \(-0.575936\pi\) | ||||
−0.236302 | + | 0.971680i | \(0.575936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −224.714 | −0.00921373 | ||||||||
\(842\) | 11684.8 | 0.478247 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −46767.3 | −1.90734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1844.60 | 0.0748304 | ||||||||
\(848\) | −37218.5 | −1.50718 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30200.5 | 1.21867 | ||||||||
\(851\) | −52021.7 | −2.09551 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11836.8 | 0.475128 | 0.237564 | − | 0.971372i | \(-0.423651\pi\) | ||||
0.237564 | + | 0.971372i | \(0.423651\pi\) | |||||||
\(854\) | 11418.5 | 0.457534 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12971.0 | 0.517920 | ||||||||
\(857\) | 31156.2 | 1.24186 | 0.620931 | − | 0.783865i | \(-0.286755\pi\) | ||||
0.620931 | + | 0.783865i | \(0.286755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1584.88 | −0.0629515 | −0.0314758 | − | 0.999505i | \(-0.510021\pi\) | ||||
−0.0314758 | + | 0.999505i | \(0.510021\pi\) | |||||||
\(860\) | −34135.9 | −1.35352 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1405.11 | −0.0555200 | ||||||||
\(863\) | −19884.8 | −0.784340 | −0.392170 | − | 0.919893i | \(-0.628276\pi\) | ||||
−0.392170 | + | 0.919893i | \(0.628276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22351.8 | 0.878592 | ||||||||
\(866\) | 4160.02 | 0.163237 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12398.7 | −0.484837 | ||||||||
\(869\) | −41863.1 | −1.63419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7956.54 | 0.308994 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2460.73 | 0.0952351 | ||||||||
\(875\) | −3941.13 | −0.152268 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5483.43 | −0.211132 | −0.105566 | − | 0.994412i | \(-0.533665\pi\) | ||||
−0.105566 | + | 0.994412i | \(0.533665\pi\) | |||||||
\(878\) | −341.750 | −0.0131361 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15948.5 | 0.610938 | ||||||||
\(881\) | 6581.12 | 0.251672 | 0.125836 | − | 0.992051i | \(-0.459839\pi\) | ||||
0.125836 | + | 0.992051i | \(0.459839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6942.60 | 0.264595 | 0.132297 | − | 0.991210i | \(-0.457765\pi\) | ||||
0.132297 | + | 0.991210i | \(0.457765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35948.6 | 1.36311 | ||||||||
\(887\) | −6562.68 | −0.248425 | −0.124213 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124213 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2418.34 | 0.0912355 | ||||||||
\(890\) | 6226.20 | 0.234498 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23769.7 | −0.892231 | ||||||||
\(893\) | 243.495 | 0.00912458 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12658.2 | −0.472756 | ||||||||
\(896\) | 8021.11 | 0.299070 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 69696.2 | 2.58997 | ||||||||
\(899\) | −37379.7 | −1.38674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37664.1 | −1.39265 | ||||||||
\(902\) | −27376.2 | −1.01056 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11440.6 | 0.420918 | ||||||||
\(905\) | −4996.40 | −0.183521 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1652.33 | −0.0604902 | −0.0302451 | − | 0.999543i | \(-0.509629\pi\) | ||||
−0.0302451 | + | 0.999543i | \(0.509629\pi\) | |||||||
\(908\) | −70.3341 | −0.00257061 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 506.240 | 0.0184110 | 0.00920552 | − | 0.999958i | \(-0.497070\pi\) | ||||
0.00920552 | + | 0.999958i | \(0.497070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17936.9 | 0.650191 | ||||||||
\(914\) | −28947.1 | −1.04758 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 75247.1 | 2.71423 | ||||||||
\(917\) | −7070.91 | −0.254637 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2469.29 | −0.0886336 | −0.0443168 | − | 0.999018i | \(-0.514111\pi\) | ||||
−0.0443168 | + | 0.999018i | \(0.514111\pi\) | |||||||
\(920\) | 36266.8 | 1.29965 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2764.69 | −0.0987531 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29698.7 | −1.05566 | ||||||||
\(926\) | −86028.5 | −3.05299 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −557.606 | −0.0197245 | ||||||||
\(929\) | 41645.7 | 1.47078 | 0.735388 | − | 0.677646i | \(-0.237000\pi\) | ||||
0.735388 | + | 0.677646i | \(0.237000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1019.40 | −0.0358857 | ||||||||
\(932\) | 66180.3 | 2.32597 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44749.6 | 1.56772 | ||||||||
\(935\) | 16139.5 | 0.564512 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33891.2 | −1.18162 | −0.590810 | − | 0.806811i | \(-0.701192\pi\) | ||||
−0.590810 | + | 0.806811i | \(0.701192\pi\) | |||||||
\(938\) | 4762.28 | 0.165772 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7157.03 | 0.248337 | ||||||||
\(941\) | −28351.3 | −0.982173 | −0.491087 | − | 0.871111i | \(-0.663400\pi\) | ||||
−0.491087 | + | 0.871111i | \(0.663400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20947.1 | −0.723363 | ||||||||
\(944\) | −6870.13 | −0.236868 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 81116.5 | 2.78787 | ||||||||
\(947\) | −3732.71 | −0.128085 | −0.0640427 | − | 0.997947i | \(-0.520399\pi\) | ||||
−0.0640427 | + | 0.997947i | \(0.520399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1404.81 | 0.0479768 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8351.65 | −0.284326 | ||||||||
\(953\) | −9652.09 | −0.328082 | −0.164041 | − | 0.986454i | \(-0.552453\pi\) | ||||
−0.164041 | + | 0.986454i | \(0.552453\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4489.33 | −0.152117 | ||||||||
\(956\) | −55444.1 | −1.87572 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24371.8 | −0.821938 | ||||||||
\(959\) | 1169.94 | 0.0393945 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28031.5 | 0.940939 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 65942.1 | 2.20316 | ||||||||
\(965\) | −15118.8 | −0.504342 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36196.6 | −1.20373 | −0.601864 | − | 0.798598i | \(-0.705575\pi\) | ||||
−0.601864 | + | 0.798598i | \(0.705575\pi\) | |||||||
\(968\) | −22646.8 | −0.751959 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24455.1 | −0.809490 | ||||||||
\(971\) | 5250.98 | 0.173545 | 0.0867723 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867723 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7884.48 | 0.259779 | ||||||||
\(974\) | −28033.1 | −0.922215 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47171.2 | −1.54704 | ||||||||
\(977\) | 23174.8 | 0.758881 | 0.379440 | − | 0.925216i | \(-0.376117\pi\) | ||||
0.379440 | + | 0.925216i | \(0.376117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9872.82 | −0.322305 | ||||||||
\(980\) | −29963.2 | −0.976674 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29638.6 | −0.963142 | ||||||||
\(983\) | 33285.5 | 1.08000 | 0.540001 | − | 0.841664i | \(-0.318424\pi\) | ||||
0.540001 | + | 0.841664i | \(0.318424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15356.2 | −0.496740 | ||||||||
\(986\) | −50214.6 | −1.62186 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62066.8 | 1.99556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15535.4 | −0.497979 | −0.248990 | − | 0.968506i | \(-0.580098\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580098\pi\) | |||||||
\(992\) | 862.559 | 0.0276071 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15811.0 | 0.504520 | ||||||||
\(995\) | −6603.63 | −0.210401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26302.4 | 0.835511 | 0.417756 | − | 0.908559i | \(-0.362817\pi\) | ||||
0.417756 | + | 0.908559i | \(0.362817\pi\) | |||||||
\(998\) | 5399.69 | 0.171267 | ||||||||
\(999\) | 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 | 1521.4.a.bl.1.2 | 12 | ||
3.2 | odd | 2 | inner | 1521.4.a.bl.1.12 | 12 | ||
13.2 | odd | 12 | 117.4.q.f.82.1 | yes | 12 | ||
13.7 | odd | 12 | 117.4.q.f.10.1 | ✓ | 12 | ||
13.12 | even | 2 | inner | 1521.4.a.bl.1.11 | 12 | ||
39.2 | even | 12 | 117.4.q.f.82.6 | yes | 12 | ||
39.20 | even | 12 | 117.4.q.f.10.6 | yes | 12 | ||
39.38 | odd | 2 | inner | 1521.4.a.bl.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.q.f.10.1 | ✓ | 12 | 13.7 | odd | 12 | ||
117.4.q.f.10.6 | yes | 12 | 39.20 | even | 12 | ||
117.4.q.f.82.1 | yes | 12 | 13.2 | odd | 12 | ||
117.4.q.f.82.6 | yes | 12 | 39.2 | even | 12 | ||
1521.4.a.bl.1.1 | 12 | 39.38 | odd | 2 | inner | ||
1521.4.a.bl.1.2 | 12 | 1.1 | even | 1 | trivial | ||
1521.4.a.bl.1.11 | 12 | 13.12 | even | 2 | inner | ||
1521.4.a.bl.1.12 | 12 | 3.2 | odd | 2 | inner |