Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, 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("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.7032.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 14x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.32681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32681 | −0.469098 | −0.234549 | − | 0.972104i | \(-0.575361\pi\) | ||||
−0.234549 | + | 0.972104i | \(0.575361\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.23958 | −0.779947 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.1043 | −1.30151 | −0.650754 | − | 0.759289i | \(-0.725547\pi\) | ||||
−0.650754 | + | 0.759289i | \(0.725547\pi\) | |||||||
\(8\) | 18.8932 | 0.834969 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.63404 | −0.209787 | ||||||||
\(11\) | 8.27619 | 0.226851 | 0.113426 | − | 0.993546i | \(-0.463818\pi\) | ||||
0.113426 | + | 0.993546i | \(0.463818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 87.1145 | 1.85856 | 0.929278 | − | 0.369382i | \(-0.120430\pi\) | ||||
0.929278 | + | 0.369382i | \(0.120430\pi\) | |||||||
\(14\) | 31.9818 | 0.610534 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 24.8490 | 0.388265 | ||||||||
\(17\) | 51.9166 | 0.740684 | 0.370342 | − | 0.928895i | \(-0.379240\pi\) | ||||
0.370342 | + | 0.928895i | \(0.379240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −88.5107 | −1.06872 | −0.534362 | − | 0.845256i | \(-0.679448\pi\) | ||||
−0.534362 | + | 0.845256i | \(0.679448\pi\) | |||||||
\(20\) | −31.1979 | −0.348803 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.9809 | −0.106415 | ||||||||
\(23\) | −129.245 | −1.17171 | −0.585856 | − | 0.810415i | \(-0.699242\pi\) | ||||
−0.585856 | + | 0.810415i | \(0.699242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −115.584 | −0.871844 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 150.400 | 1.01511 | ||||||||
\(29\) | −271.109 | −1.73599 | −0.867993 | − | 0.496576i | \(-0.834590\pi\) | ||||
−0.867993 | + | 0.496576i | \(0.834590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 224.547 | 1.30096 | 0.650481 | − | 0.759523i | \(-0.274568\pi\) | ||||
0.650481 | + | 0.759523i | \(0.274568\pi\) | |||||||
\(32\) | −184.115 | −1.01710 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −68.8834 | −0.347453 | ||||||||
\(35\) | −120.521 | −0.582052 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.5268 | −0.313366 | −0.156683 | − | 0.987649i | \(-0.550080\pi\) | ||||
−0.156683 | + | 0.987649i | \(0.550080\pi\) | |||||||
\(38\) | 117.437 | 0.501336 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 94.4660 | 0.373410 | ||||||||
\(41\) | 366.938 | 1.39771 | 0.698855 | − | 0.715263i | \(-0.253693\pi\) | ||||
0.698855 | + | 0.715263i | \(0.253693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −195.547 | −0.693504 | −0.346752 | − | 0.937957i | \(-0.612715\pi\) | ||||
−0.346752 | + | 0.937957i | \(0.612715\pi\) | |||||||
\(44\) | −51.6399 | −0.176932 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 171.483 | 0.549648 | ||||||||
\(47\) | −359.192 | −1.11476 | −0.557378 | − | 0.830259i | \(-0.688193\pi\) | ||||
−0.557378 | + | 0.830259i | \(0.688193\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 238.016 | 0.693923 | ||||||||
\(50\) | −33.1702 | −0.0938195 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −543.558 | −1.44958 | ||||||||
\(53\) | 29.4890 | 0.0764270 | 0.0382135 | − | 0.999270i | \(-0.487833\pi\) | ||||
0.0382135 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 41.3810 | 0.101451 | ||||||||
\(56\) | −455.407 | −1.08672 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 359.709 | 0.814347 | ||||||||
\(59\) | −858.104 | −1.89349 | −0.946743 | − | 0.321991i | \(-0.895648\pi\) | ||||
−0.946743 | + | 0.321991i | \(0.895648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −556.811 | −1.16873 | −0.584364 | − | 0.811492i | \(-0.698656\pi\) | ||||
−0.584364 | + | 0.811492i | \(0.698656\pi\) | |||||||
\(62\) | −297.931 | −0.610278 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 45.4941 | 0.0888557 | ||||||||
\(65\) | 435.573 | 0.831171 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41.8987 | −0.0763991 | −0.0381995 | − | 0.999270i | \(-0.512162\pi\) | ||||
−0.0381995 | + | 0.999270i | \(0.512162\pi\) | |||||||
\(68\) | −323.938 | −0.577695 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 159.909 | 0.273039 | ||||||||
\(71\) | −549.163 | −0.917939 | −0.458970 | − | 0.888452i | \(-0.651781\pi\) | ||||
−0.458970 | + | 0.888452i | \(0.651781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −185.505 | −0.297420 | −0.148710 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148710 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(74\) | 93.5756 | 0.146999 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 552.269 | 0.833548 | ||||||||
\(77\) | −199.492 | −0.295249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.4913 | 0.114633 | 0.0573163 | − | 0.998356i | \(-0.481746\pi\) | ||||
0.0573163 | + | 0.998356i | \(0.481746\pi\) | |||||||
\(80\) | 124.245 | 0.173637 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −486.857 | −0.655663 | ||||||||
\(83\) | −576.753 | −0.762734 | −0.381367 | − | 0.924424i | \(-0.624547\pi\) | ||||
−0.381367 | + | 0.924424i | \(0.624547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 259.583 | 0.331244 | ||||||||
\(86\) | 259.454 | 0.325321 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 156.364 | 0.189414 | ||||||||
\(89\) | 224.516 | 0.267401 | 0.133700 | − | 0.991022i | \(-0.457314\pi\) | ||||
0.133700 | + | 0.991022i | \(0.457314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2099.83 | −2.41893 | ||||||||
\(92\) | 806.433 | 0.913874 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 476.579 | 0.522930 | ||||||||
\(95\) | −442.553 | −0.477948 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −555.016 | −0.580963 | −0.290481 | − | 0.956881i | \(-0.593815\pi\) | ||||
−0.290481 | + | 0.956881i | \(0.593815\pi\) | |||||||
\(98\) | −315.801 | −0.325518 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −155.989 | −0.155989 | ||||||||
\(101\) | 227.000 | 0.223637 | 0.111818 | − | 0.993729i | \(-0.464333\pi\) | ||||
0.111818 | + | 0.993729i | \(0.464333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 383.524 | 0.366891 | 0.183446 | − | 0.983030i | \(-0.441275\pi\) | ||||
0.183446 | + | 0.983030i | \(0.441275\pi\) | |||||||
\(104\) | 1645.87 | 1.55184 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −39.1263 | −0.0358517 | ||||||||
\(107\) | −1775.32 | −1.60399 | −0.801993 | − | 0.597334i | \(-0.796227\pi\) | ||||
−0.801993 | + | 0.597334i | \(0.796227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1530.50 | 1.34491 | 0.672454 | − | 0.740139i | \(-0.265240\pi\) | ||||
0.672454 | + | 0.740139i | \(0.265240\pi\) | |||||||
\(110\) | −54.9046 | −0.0475904 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −598.966 | −0.505330 | ||||||||
\(113\) | −840.782 | −0.699948 | −0.349974 | − | 0.936759i | \(-0.613810\pi\) | ||||
−0.349974 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −646.224 | −0.524006 | ||||||||
\(116\) | 1691.60 | 1.35398 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1138.54 | 0.888230 | ||||||||
\(119\) | −1251.41 | −0.964007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1262.50 | −0.948538 | ||||||||
\(122\) | 738.782 | 0.548247 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1401.08 | −1.01468 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1038.45 | 0.725572 | 0.362786 | − | 0.931873i | \(-0.381826\pi\) | ||||
0.362786 | + | 0.931873i | \(0.381826\pi\) | |||||||
\(128\) | 1412.56 | 0.975422 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −577.922 | −0.389901 | ||||||||
\(131\) | −803.410 | −0.535834 | −0.267917 | − | 0.963442i | \(-0.586335\pi\) | ||||
−0.267917 | + | 0.963442i | \(0.586335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2133.49 | 1.39095 | ||||||||
\(134\) | 55.5915 | 0.0358386 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 980.871 | 0.618449 | ||||||||
\(137\) | 869.152 | 0.542019 | 0.271010 | − | 0.962577i | \(-0.412642\pi\) | ||||
0.271010 | + | 0.962577i | \(0.412642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −196.398 | −0.119844 | −0.0599218 | − | 0.998203i | \(-0.519085\pi\) | ||||
−0.0599218 | + | 0.998203i | \(0.519085\pi\) | |||||||
\(140\) | 752.002 | 0.453970 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 728.635 | 0.430603 | ||||||||
\(143\) | 720.976 | 0.421616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1355.54 | −0.776357 | ||||||||
\(146\) | 246.129 | 0.139519 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 440.057 | 0.244409 | ||||||||
\(149\) | 754.283 | 0.414720 | 0.207360 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207360 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2057.64 | 1.10893 | 0.554464 | − | 0.832208i | \(-0.312923\pi\) | ||||
0.554464 | + | 0.832208i | \(0.312923\pi\) | |||||||
\(152\) | −1672.25 | −0.892351 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 264.687 | 0.138501 | ||||||||
\(155\) | 1122.73 | 0.581808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3358.58 | −1.70729 | −0.853644 | − | 0.520857i | \(-0.825613\pi\) | ||||
−0.853644 | + | 0.520857i | \(0.825613\pi\) | |||||||
\(158\) | −106.797 | −0.0537739 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −920.577 | −0.454863 | ||||||||
\(161\) | 3115.35 | 1.52499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −710.376 | −0.341356 | −0.170678 | − | 0.985327i | \(-0.554596\pi\) | ||||
−0.170678 | + | 0.985327i | \(0.554596\pi\) | |||||||
\(164\) | −2289.54 | −1.09014 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 765.241 | 0.357797 | ||||||||
\(167\) | −1148.27 | −0.532070 | −0.266035 | − | 0.963963i | \(-0.585714\pi\) | ||||
−0.266035 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5391.94 | 2.45423 | ||||||||
\(170\) | −344.417 | −0.155386 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1220.13 | 0.540897 | ||||||||
\(173\) | −2925.29 | −1.28558 | −0.642790 | − | 0.766042i | \(-0.722223\pi\) | ||||
−0.642790 | + | 0.766042i | \(0.722223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −602.607 | −0.260302 | ||||||||
\(176\) | 205.655 | 0.0880785 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −297.890 | −0.125437 | ||||||||
\(179\) | 3422.02 | 1.42890 | 0.714452 | − | 0.699685i | \(-0.246676\pi\) | ||||
0.714452 | + | 0.699685i | \(0.246676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1151.58 | −0.472907 | −0.236454 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236454 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(182\) | 2786.07 | 1.13471 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2441.85 | −0.978344 | ||||||||
\(185\) | −352.634 | −0.140141 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 429.672 | 0.168025 | ||||||||
\(188\) | 2241.21 | 0.869451 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 587.184 | 0.224204 | ||||||||
\(191\) | 932.120 | 0.353120 | 0.176560 | − | 0.984290i | \(-0.443503\pi\) | ||||
0.176560 | + | 0.984290i | \(0.443503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4272.81 | −1.59359 | −0.796797 | − | 0.604247i | \(-0.793474\pi\) | ||||
−0.796797 | + | 0.604247i | \(0.793474\pi\) | |||||||
\(194\) | 736.400 | 0.272528 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1485.12 | −0.541224 | ||||||||
\(197\) | −1924.15 | −0.695888 | −0.347944 | − | 0.937515i | \(-0.613120\pi\) | ||||
−0.347944 | + | 0.937515i | \(0.613120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1738.84 | 0.619414 | 0.309707 | − | 0.950832i | \(-0.399769\pi\) | ||||
0.309707 | + | 0.950832i | \(0.399769\pi\) | |||||||
\(200\) | 472.330 | 0.166994 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −301.185 | −0.104907 | ||||||||
\(203\) | 6534.87 | 2.25940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1834.69 | 0.625075 | ||||||||
\(206\) | −508.864 | −0.172108 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2164.71 | 0.721613 | ||||||||
\(209\) | −732.531 | −0.242441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3202.35 | 1.04483 | 0.522414 | − | 0.852692i | \(-0.325031\pi\) | ||||
0.522414 | + | 0.852692i | \(0.325031\pi\) | |||||||
\(212\) | −183.999 | −0.0596090 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2355.51 | 0.752426 | ||||||||
\(215\) | −977.736 | −0.310144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5412.54 | −1.69321 | ||||||||
\(218\) | −2030.68 | −0.630893 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −258.200 | −0.0791265 | ||||||||
\(221\) | 4522.69 | 1.37660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1404.99 | −0.421906 | −0.210953 | − | 0.977496i | \(-0.567657\pi\) | ||||
−0.210953 | + | 0.977496i | \(0.567657\pi\) | |||||||
\(224\) | 4437.97 | 1.32377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1115.56 | 0.328344 | ||||||||
\(227\) | 6238.35 | 1.82402 | 0.912012 | − | 0.410163i | \(-0.134528\pi\) | ||||
0.912012 | + | 0.410163i | \(0.134528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6630.31 | 1.91329 | 0.956644 | − | 0.291259i | \(-0.0940742\pi\) | ||||
0.956644 | + | 0.291259i | \(0.0940742\pi\) | |||||||
\(230\) | 857.415 | 0.245810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5122.11 | −1.44949 | ||||||||
\(233\) | 2453.48 | 0.689840 | 0.344920 | − | 0.938632i | \(-0.387906\pi\) | ||||
0.344920 | + | 0.938632i | \(0.387906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1795.96 | −0.498534 | ||||||||
\(236\) | 5354.21 | 1.47682 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1660.38 | 0.452213 | ||||||||
\(239\) | −6949.74 | −1.88093 | −0.940463 | − | 0.339895i | \(-0.889608\pi\) | ||||
−0.940463 | + | 0.339895i | \(0.889608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6335.19 | 1.69330 | 0.846651 | − | 0.532149i | \(-0.178615\pi\) | ||||
0.846651 | + | 0.532149i | \(0.178615\pi\) | |||||||
\(242\) | 1675.10 | 0.444957 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3474.27 | 0.911546 | ||||||||
\(245\) | 1190.08 | 0.310332 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7710.57 | −1.98628 | ||||||||
\(248\) | 4242.41 | 1.08626 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −165.851 | −0.0419574 | ||||||||
\(251\) | −4022.65 | −1.01158 | −0.505792 | − | 0.862656i | \(-0.668800\pi\) | ||||
−0.505792 | + | 0.862656i | \(0.668800\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1069.65 | −0.265805 | ||||||||
\(254\) | −1377.83 | −0.340364 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2238.15 | −0.546424 | ||||||||
\(257\) | −4997.74 | −1.21304 | −0.606519 | − | 0.795069i | \(-0.707435\pi\) | ||||
−0.606519 | + | 0.795069i | \(0.707435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1700.00 | 0.407848 | ||||||||
\(260\) | −2717.79 | −0.648270 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1065.97 | 0.251359 | ||||||||
\(263\) | −3992.47 | −0.936069 | −0.468035 | − | 0.883710i | \(-0.655038\pi\) | ||||
−0.468035 | + | 0.883710i | \(0.655038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 147.445 | 0.0341792 | ||||||||
\(266\) | −2830.73 | −0.652493 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 261.430 | 0.0595872 | ||||||||
\(269\) | −2188.89 | −0.496131 | −0.248065 | − | 0.968743i | \(-0.579795\pi\) | ||||
−0.248065 | + | 0.968743i | \(0.579795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4280.26 | 0.959437 | 0.479718 | − | 0.877423i | \(-0.340739\pi\) | ||||
0.479718 | + | 0.877423i | \(0.340739\pi\) | |||||||
\(272\) | 1290.08 | 0.287582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1153.20 | −0.254260 | ||||||||
\(275\) | 206.905 | 0.0453703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3879.97 | −0.841606 | −0.420803 | − | 0.907152i | \(-0.638252\pi\) | ||||
−0.420803 | + | 0.907152i | \(0.638252\pi\) | |||||||
\(278\) | 260.583 | 0.0562184 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2277.03 | −0.485996 | ||||||||
\(281\) | −6397.43 | −1.35814 | −0.679072 | − | 0.734071i | \(-0.737618\pi\) | ||||
−0.679072 | + | 0.734071i | \(0.737618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −342.869 | −0.0720193 | −0.0360096 | − | 0.999351i | \(-0.511465\pi\) | ||||
−0.0360096 | + | 0.999351i | \(0.511465\pi\) | |||||||
\(284\) | 3426.55 | 0.715944 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −956.598 | −0.197779 | ||||||||
\(287\) | −8844.78 | −1.81913 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2217.66 | −0.451387 | ||||||||
\(290\) | 1798.55 | 0.364187 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1157.47 | 0.231972 | ||||||||
\(293\) | −7333.43 | −1.46220 | −0.731098 | − | 0.682272i | \(-0.760992\pi\) | ||||
−0.731098 | + | 0.682272i | \(0.760992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4290.52 | −0.846793 | ||||||||
\(296\) | −1332.48 | −0.261651 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1000.79 | −0.194544 | ||||||||
\(299\) | −11259.1 | −2.17769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4713.52 | 0.902601 | ||||||||
\(302\) | −2730.09 | −0.520195 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2199.40 | −0.414948 | ||||||||
\(305\) | −2784.06 | −0.522671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7965.33 | −1.48080 | −0.740399 | − | 0.672167i | \(-0.765364\pi\) | ||||
−0.740399 | + | 0.672167i | \(0.765364\pi\) | |||||||
\(308\) | 1244.74 | 0.230279 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1489.65 | −0.272925 | ||||||||
\(311\) | −2186.19 | −0.398609 | −0.199305 | − | 0.979938i | \(-0.563868\pi\) | ||||
−0.199305 | + | 0.979938i | \(0.563868\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 38.6303 | 0.00697609 | 0.00348805 | − | 0.999994i | \(-0.498890\pi\) | ||||
0.00348805 | + | 0.999994i | \(0.498890\pi\) | |||||||
\(314\) | 4456.20 | 0.800885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −502.232 | −0.0894074 | ||||||||
\(317\) | 9535.81 | 1.68954 | 0.844770 | − | 0.535129i | \(-0.179737\pi\) | ||||
0.844770 | + | 0.535129i | \(0.179737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2243.75 | −0.393811 | ||||||||
\(320\) | 227.471 | 0.0397375 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4133.47 | −0.715371 | ||||||||
\(323\) | −4595.18 | −0.791587 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2177.86 | 0.371711 | ||||||||
\(326\) | 942.533 | 0.160129 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6932.63 | 1.16704 | ||||||||
\(329\) | 8658.06 | 1.45086 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3010.58 | −0.499929 | −0.249964 | − | 0.968255i | \(-0.580419\pi\) | ||||
−0.249964 | + | 0.968255i | \(0.580419\pi\) | |||||||
\(332\) | 3598.70 | 0.594892 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1523.53 | 0.249593 | ||||||||
\(335\) | −209.493 | −0.0341667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2812.72 | 0.454655 | 0.227327 | − | 0.973818i | \(-0.427001\pi\) | ||||
0.227327 | + | 0.973818i | \(0.427001\pi\) | |||||||
\(338\) | −7154.07 | −1.15127 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1619.69 | −0.258353 | ||||||||
\(341\) | 1858.39 | 0.295125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2530.57 | 0.398361 | ||||||||
\(344\) | −3694.51 | −0.579054 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3881.30 | 0.603063 | ||||||||
\(347\) | −139.354 | −0.0215588 | −0.0107794 | − | 0.999942i | \(-0.503431\pi\) | ||||
−0.0107794 | + | 0.999942i | \(0.503431\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5210.29 | −0.799141 | −0.399571 | − | 0.916702i | \(-0.630841\pi\) | ||||
−0.399571 | + | 0.916702i | \(0.630841\pi\) | |||||||
\(350\) | 799.544 | 0.122107 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1523.77 | −0.230731 | ||||||||
\(353\) | −3410.46 | −0.514223 | −0.257112 | − | 0.966382i | \(-0.582771\pi\) | ||||
−0.257112 | + | 0.966382i | \(0.582771\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2745.82 | −0.410515 | ||||||||
\(356\) | −1400.89 | −0.208558 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4540.36 | −0.670295 | ||||||||
\(359\) | 8131.85 | 1.19549 | 0.597747 | − | 0.801685i | \(-0.296063\pi\) | ||||
0.597747 | + | 0.801685i | \(0.296063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 975.143 | 0.142170 | ||||||||
\(362\) | 1527.93 | 0.221840 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13102.1 | 1.88663 | ||||||||
\(365\) | −927.523 | −0.133010 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 132.151 | 0.0187963 | 0.00939816 | − | 0.999956i | \(-0.497008\pi\) | ||||
0.00939816 | + | 0.999956i | \(0.497008\pi\) | |||||||
\(368\) | −3211.60 | −0.454935 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 467.878 | 0.0657400 | ||||||||
\(371\) | −710.812 | −0.0994703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9348.88 | 1.29777 | 0.648883 | − | 0.760888i | \(-0.275236\pi\) | ||||
0.648883 | + | 0.760888i | \(0.275236\pi\) | |||||||
\(374\) | −570.092 | −0.0788203 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6786.29 | −0.930787 | ||||||||
\(377\) | −23617.5 | −3.22643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6164.17 | 0.835441 | 0.417720 | − | 0.908576i | \(-0.362829\pi\) | ||||
0.417720 | + | 0.908576i | \(0.362829\pi\) | |||||||
\(380\) | 2761.35 | 0.372774 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1236.75 | −0.165648 | ||||||||
\(383\) | −2601.27 | −0.347047 | −0.173523 | − | 0.984830i | \(-0.555515\pi\) | ||||
−0.173523 | + | 0.984830i | \(0.555515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −997.458 | −0.132039 | ||||||||
\(386\) | 5669.20 | 0.747552 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3463.07 | 0.453120 | ||||||||
\(389\) | −4250.57 | −0.554017 | −0.277008 | − | 0.960867i | \(-0.589343\pi\) | ||||
−0.277008 | + | 0.960867i | \(0.589343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6709.95 | −0.867869 | ||||||||
\(392\) | 4496.88 | 0.579405 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2552.98 | 0.326440 | ||||||||
\(395\) | 402.456 | 0.0512653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6088.35 | −0.769687 | −0.384843 | − | 0.922982i | \(-0.625745\pi\) | ||||
−0.384843 | + | 0.922982i | \(0.625745\pi\) | |||||||
\(398\) | −2307.11 | −0.290566 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 621.224 | 0.0776530 | ||||||||
\(401\) | −7725.79 | −0.962114 | −0.481057 | − | 0.876689i | \(-0.659747\pi\) | ||||
−0.481057 | + | 0.876689i | \(0.659747\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19561.3 | 2.41791 | ||||||||
\(404\) | −1416.38 | −0.174425 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8670.53 | −1.05988 | ||||||||
\(407\) | −583.693 | −0.0710875 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16321.1 | 1.97318 | 0.986588 | − | 0.163232i | \(-0.0521920\pi\) | ||||
0.986588 | + | 0.163232i | \(0.0521920\pi\) | |||||||
\(410\) | −2434.28 | −0.293221 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2393.03 | −0.286156 | ||||||||
\(413\) | 20684.0 | 2.46439 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2883.77 | −0.341105 | ||||||||
\(416\) | −16039.1 | −1.89034 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 971.929 | 0.113729 | ||||||||
\(419\) | −1152.46 | −0.134370 | −0.0671851 | − | 0.997741i | \(-0.521402\pi\) | ||||
−0.0671851 | + | 0.997741i | \(0.521402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3531.23 | −0.408792 | −0.204396 | − | 0.978888i | \(-0.565523\pi\) | ||||
−0.204396 | + | 0.978888i | \(0.565523\pi\) | |||||||
\(422\) | −4248.91 | −0.490127 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 557.142 | 0.0638142 | ||||||||
\(425\) | 1297.92 | 0.148137 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13421.5 | 1.52111 | ||||||||
\(428\) | 11077.2 | 1.25102 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1297.27 | 0.145488 | ||||||||
\(431\) | −10230.6 | −1.14337 | −0.571683 | − | 0.820475i | \(-0.693709\pi\) | ||||
−0.571683 | + | 0.820475i | \(0.693709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7311.31 | −0.811453 | −0.405726 | − | 0.913995i | \(-0.632981\pi\) | ||||
−0.405726 | + | 0.913995i | \(0.632981\pi\) | |||||||
\(434\) | 7181.40 | 0.794282 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9549.65 | −1.04896 | ||||||||
\(437\) | 11439.5 | 1.25224 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7053.18 | 0.766811 | 0.383405 | − | 0.923580i | \(-0.374751\pi\) | ||||
0.383405 | + | 0.923580i | \(0.374751\pi\) | |||||||
\(440\) | 781.818 | 0.0847085 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6000.75 | −0.645761 | ||||||||
\(443\) | 167.790 | 0.0179954 | 0.00899770 | − | 0.999960i | \(-0.497136\pi\) | ||||
0.00899770 | + | 0.999960i | \(0.497136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1122.58 | 0.119585 | ||||||||
\(446\) | 1864.15 | 0.197915 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1096.60 | −0.115646 | ||||||||
\(449\) | −3949.94 | −0.415165 | −0.207582 | − | 0.978218i | \(-0.566560\pi\) | ||||
−0.207582 | + | 0.978218i | \(0.566560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3036.85 | 0.317072 | ||||||||
\(452\) | 5246.13 | 0.545922 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8277.09 | −0.855646 | ||||||||
\(455\) | −10499.2 | −1.08178 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7447.60 | −0.762328 | −0.381164 | − | 0.924507i | \(-0.624477\pi\) | ||||
−0.381164 | + | 0.924507i | \(0.624477\pi\) | |||||||
\(458\) | −8797.15 | −0.897519 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4032.16 | 0.408697 | ||||||||
\(461\) | −10887.6 | −1.09997 | −0.549987 | − | 0.835173i | \(-0.685367\pi\) | ||||
−0.549987 | + | 0.835173i | \(0.685367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3171.27 | −0.318318 | −0.159159 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159159 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(464\) | −6736.77 | −0.674023 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3255.29 | −0.323602 | ||||||||
\(467\) | 16348.5 | 1.61996 | 0.809978 | − | 0.586461i | \(-0.199479\pi\) | ||||
0.809978 | + | 0.586461i | \(0.199479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1009.94 | 0.0994340 | ||||||||
\(470\) | 2382.90 | 0.233861 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16212.3 | −1.58100 | ||||||||
\(473\) | −1618.39 | −0.157322 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2212.77 | −0.213745 | ||||||||
\(476\) | 7808.29 | 0.751874 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9220.98 | 0.882338 | ||||||||
\(479\) | −9413.69 | −0.897959 | −0.448980 | − | 0.893542i | \(-0.648212\pi\) | ||||
−0.448980 | + | 0.893542i | \(0.648212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6143.91 | −0.582408 | ||||||||
\(482\) | −8405.59 | −0.794324 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7877.50 | 0.739810 | ||||||||
\(485\) | −2775.08 | −0.259814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13482.3 | 1.25450 | 0.627250 | − | 0.778818i | \(-0.284180\pi\) | ||||
0.627250 | + | 0.778818i | \(0.284180\pi\) | |||||||
\(488\) | −10519.9 | −0.975852 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1579.01 | −0.145576 | ||||||||
\(491\) | 9219.74 | 0.847416 | 0.423708 | − | 0.905799i | \(-0.360728\pi\) | ||||
0.423708 | + | 0.905799i | \(0.360728\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14075.0 | −1.28582 | ||||||||
\(494\) | 10230.4 | 0.931760 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5579.76 | 0.505118 | ||||||||
\(497\) | 13237.2 | 1.19471 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 104.346 | 0.00936108 | 0.00468054 | − | 0.999989i | \(-0.498510\pi\) | ||||
0.00468054 | + | 0.999989i | \(0.498510\pi\) | |||||||
\(500\) | −779.947 | −0.0697606 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5337.29 | 0.474531 | ||||||||
\(503\) | −490.652 | −0.0434933 | −0.0217466 | − | 0.999764i | \(-0.506923\pi\) | ||||
−0.0217466 | + | 0.999764i | \(0.506923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1135.00 | 0.100013 | ||||||||
\(506\) | 1419.23 | 0.124688 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6479.50 | −0.565908 | ||||||||
\(509\) | 3412.81 | 0.297191 | 0.148595 | − | 0.988898i | \(-0.452525\pi\) | ||||
0.148595 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4471.45 | 0.387095 | ||||||||
\(512\) | −8330.89 | −0.719095 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6631.05 | 0.569033 | ||||||||
\(515\) | 1917.62 | 0.164079 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2972.74 | −0.252884 | ||||||||
\(518\) | −2255.57 | −0.191321 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8229.36 | 0.694002 | ||||||||
\(521\) | 3486.31 | 0.293163 | 0.146582 | − | 0.989199i | \(-0.453173\pi\) | ||||
0.146582 | + | 0.989199i | \(0.453173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14465.6 | 1.20943 | 0.604717 | − | 0.796440i | \(-0.293286\pi\) | ||||
0.604717 | + | 0.796440i | \(0.293286\pi\) | |||||||
\(524\) | 5012.94 | 0.417923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5297.24 | 0.439108 | ||||||||
\(527\) | 11657.7 | 0.963602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4537.21 | 0.372911 | ||||||||
\(530\) | −195.632 | −0.0160334 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13312.1 | −1.08487 | ||||||||
\(533\) | 31965.6 | 2.59772 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8876.59 | −0.717324 | ||||||||
\(536\) | −791.600 | −0.0637909 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2904.24 | 0.232734 | ||||||||
\(539\) | 1969.86 | 0.157417 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6602.78 | 0.524724 | 0.262362 | − | 0.964970i | \(-0.415499\pi\) | ||||
0.262362 | + | 0.964970i | \(0.415499\pi\) | |||||||
\(542\) | −5679.09 | −0.450070 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9558.65 | −0.753353 | ||||||||
\(545\) | 7652.48 | 0.601461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6358.56 | 0.497024 | 0.248512 | − | 0.968629i | \(-0.420058\pi\) | ||||
0.248512 | + | 0.968629i | \(0.420058\pi\) | |||||||
\(548\) | −5423.14 | −0.422746 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −274.523 | −0.0212831 | ||||||||
\(551\) | 23996.0 | 1.85529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1940.18 | −0.149195 | ||||||||
\(554\) | 5147.98 | 0.394795 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1225.44 | 0.0934717 | ||||||||
\(557\) | 20782.3 | 1.58092 | 0.790461 | − | 0.612513i | \(-0.209841\pi\) | ||||
0.790461 | + | 0.612513i | \(0.209841\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17035.0 | −1.28892 | ||||||||
\(560\) | −2994.83 | −0.225991 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8488.17 | 0.637103 | ||||||||
\(563\) | −16470.0 | −1.23291 | −0.616453 | − | 0.787392i | \(-0.711431\pi\) | ||||
−0.616453 | + | 0.787392i | \(0.711431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4203.91 | −0.313026 | ||||||||
\(566\) | 454.922 | 0.0337841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10375.4 | −0.766451 | ||||||||
\(569\) | −5425.39 | −0.399726 | −0.199863 | − | 0.979824i | \(-0.564050\pi\) | ||||
−0.199863 | + | 0.979824i | \(0.564050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14689.7 | −1.07661 | −0.538306 | − | 0.842749i | \(-0.680936\pi\) | ||||
−0.538306 | + | 0.842749i | \(0.680936\pi\) | |||||||
\(572\) | −4498.59 | −0.328838 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11735.3 | 0.853350 | ||||||||
\(575\) | −3231.12 | −0.234343 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17933.1 | −1.29387 | −0.646935 | − | 0.762545i | \(-0.723949\pi\) | ||||
−0.646935 | + | 0.762545i | \(0.723949\pi\) | |||||||
\(578\) | 2942.41 | 0.211745 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8458.02 | 0.605517 | ||||||||
\(581\) | 13902.2 | 0.992704 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 244.057 | 0.0173376 | ||||||||
\(584\) | −3504.78 | −0.248337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9730.06 | 0.685913 | ||||||||
\(587\) | −4801.16 | −0.337589 | −0.168795 | − | 0.985651i | \(-0.553987\pi\) | ||||
−0.168795 | + | 0.985651i | \(0.553987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19874.8 | −1.39037 | ||||||||
\(590\) | 5692.70 | 0.397228 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1752.52 | −0.121669 | ||||||||
\(593\) | 16803.8 | 1.16366 | 0.581830 | − | 0.813311i | \(-0.302337\pi\) | ||||
0.581830 | + | 0.813311i | \(0.302337\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6257.06 | −0.431117 | ||||||||
\(596\) | −4706.41 | −0.323460 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14938.7 | 1.02155 | ||||||||
\(599\) | 17220.2 | 1.17462 | 0.587310 | − | 0.809362i | \(-0.300187\pi\) | ||||
0.587310 | + | 0.809362i | \(0.300187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21536.7 | 1.46173 | 0.730865 | − | 0.682522i | \(-0.239117\pi\) | ||||
0.730865 | + | 0.682522i | \(0.239117\pi\) | |||||||
\(602\) | −6253.94 | −0.423408 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12838.8 | −0.864905 | ||||||||
\(605\) | −6312.52 | −0.424199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24050.9 | −1.60823 | −0.804117 | − | 0.594472i | \(-0.797361\pi\) | ||||
−0.804117 | + | 0.594472i | \(0.797361\pi\) | |||||||
\(608\) | 16296.2 | 1.08700 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3693.91 | 0.245184 | ||||||||
\(611\) | −31290.8 | −2.07184 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3554.49 | −0.234200 | −0.117100 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117100 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(614\) | 10568.5 | 0.694639 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3769.03 | −0.246524 | ||||||||
\(617\) | −9747.42 | −0.636007 | −0.318003 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318003 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20765.2 | −1.34834 | −0.674171 | − | 0.738576i | \(-0.735499\pi\) | ||||
−0.674171 | + | 0.738576i | \(0.735499\pi\) | |||||||
\(620\) | −7005.39 | −0.453779 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2900.66 | 0.186987 | ||||||||
\(623\) | −5411.80 | −0.348024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −51.2551 | −0.00327247 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20956.2 | 1.33159 | ||||||||
\(629\) | −3661.51 | −0.232105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23740.6 | 1.49778 | 0.748890 | − | 0.662694i | \(-0.230587\pi\) | ||||
0.748890 | + | 0.662694i | \(0.230587\pi\) | |||||||
\(632\) | 1520.74 | 0.0957147 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12652.2 | −0.792560 | ||||||||
\(635\) | 5192.25 | 0.324486 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20734.6 | 1.28970 | ||||||||
\(638\) | 2977.02 | 0.184736 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7062.81 | 0.436222 | ||||||||
\(641\) | 26108.7 | 1.60879 | 0.804394 | − | 0.594097i | \(-0.202490\pi\) | ||||
0.804394 | + | 0.594097i | \(0.202490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24017.9 | −1.47305 | −0.736526 | − | 0.676409i | \(-0.763535\pi\) | ||||
−0.736526 | + | 0.676409i | \(0.763535\pi\) | |||||||
\(644\) | −19438.5 | −1.18941 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6096.92 | 0.371331 | ||||||||
\(647\) | 18588.3 | 1.12949 | 0.564747 | − | 0.825264i | \(-0.308974\pi\) | ||||
0.564747 | + | 0.825264i | \(0.308974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7101.83 | −0.429540 | ||||||||
\(650\) | −2889.61 | −0.174369 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4432.45 | 0.266239 | ||||||||
\(653\) | 12171.9 | 0.729441 | 0.364721 | − | 0.931117i | \(-0.381165\pi\) | ||||
0.364721 | + | 0.931117i | \(0.381165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4017.05 | −0.239632 | ||||||||
\(656\) | 9118.04 | 0.542682 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11487.6 | −0.680597 | ||||||||
\(659\) | 8589.64 | 0.507746 | 0.253873 | − | 0.967238i | \(-0.418295\pi\) | ||||
0.253873 | + | 0.967238i | \(0.418295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24995.3 | 1.47081 | 0.735405 | − | 0.677628i | \(-0.236992\pi\) | ||||
0.735405 | + | 0.677628i | \(0.236992\pi\) | |||||||
\(662\) | 3994.46 | 0.234515 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10896.7 | −0.636859 | ||||||||
\(665\) | 10667.4 | 0.622053 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35039.4 | 2.03408 | ||||||||
\(668\) | 7164.71 | 0.414987 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 277.958 | 0.0160275 | ||||||||
\(671\) | −4608.28 | −0.265127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2540.17 | −0.145492 | −0.0727461 | − | 0.997350i | \(-0.523176\pi\) | ||||
−0.0727461 | + | 0.997350i | \(0.523176\pi\) | |||||||
\(674\) | −3731.94 | −0.213277 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33643.4 | −1.91417 | ||||||||
\(677\) | 4197.79 | 0.238307 | 0.119154 | − | 0.992876i | \(-0.461982\pi\) | ||||
0.119154 | + | 0.992876i | \(0.461982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13378.3 | 0.756128 | ||||||||
\(680\) | 4904.36 | 0.276579 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2465.73 | −0.138442 | ||||||||
\(683\) | 8523.02 | 0.477488 | 0.238744 | − | 0.971083i | \(-0.423264\pi\) | ||||
0.238744 | + | 0.971083i | \(0.423264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4345.76 | 0.242398 | ||||||||
\(686\) | −3357.58 | −0.186870 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4859.15 | −0.269263 | ||||||||
\(689\) | 2568.92 | 0.142044 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20292.0 | −1.11714 | −0.558571 | − | 0.829457i | \(-0.688650\pi\) | ||||
−0.558571 | + | 0.829457i | \(0.688650\pi\) | |||||||
\(692\) | 18252.6 | 1.00269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 184.896 | 0.0101132 | ||||||||
\(695\) | −981.990 | −0.0535957 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19050.2 | 1.03526 | ||||||||
\(698\) | 6913.05 | 0.374875 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3760.01 | 0.203022 | ||||||||
\(701\) | 11223.6 | 0.604721 | 0.302361 | − | 0.953194i | \(-0.402225\pi\) | ||||
0.302361 | + | 0.953194i | \(0.402225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6242.38 | 0.334901 | ||||||||
\(704\) | 376.518 | 0.0201570 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4525.03 | 0.241221 | ||||||||
\(707\) | −5471.66 | −0.291065 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19931.0 | −1.05575 | −0.527873 | − | 0.849324i | \(-0.677010\pi\) | ||||
−0.527873 | + | 0.849324i | \(0.677010\pi\) | |||||||
\(710\) | 3643.17 | 0.192572 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4241.83 | 0.223271 | ||||||||
\(713\) | −29021.5 | −1.52435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3604.88 | 0.188552 | ||||||||
\(716\) | −21352.0 | −1.11447 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10789.4 | −0.560804 | ||||||||
\(719\) | 3186.13 | 0.165261 | 0.0826305 | − | 0.996580i | \(-0.473668\pi\) | ||||
0.0826305 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9244.58 | −0.477512 | ||||||||
\(722\) | −1293.83 | −0.0666916 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7185.37 | 0.368843 | ||||||||
\(725\) | −6777.71 | −0.347197 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23088.2 | −1.17785 | −0.588923 | − | 0.808189i | \(-0.700448\pi\) | ||||
−0.588923 | + | 0.808189i | \(0.700448\pi\) | |||||||
\(728\) | −39672.5 | −2.01973 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1230.65 | 0.0623949 | ||||||||
\(731\) | −10152.2 | −0.513667 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29801.4 | −1.50169 | −0.750846 | − | 0.660477i | \(-0.770354\pi\) | ||||
−0.750846 | + | 0.660477i | \(0.770354\pi\) | |||||||
\(734\) | −175.340 | −0.00881731 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23796.0 | 1.19175 | ||||||||
\(737\) | −346.761 | −0.0173312 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39741.5 | 1.97823 | 0.989117 | − | 0.147134i | \(-0.0470047\pi\) | ||||
0.989117 | + | 0.147134i | \(0.0470047\pi\) | |||||||
\(740\) | 2200.29 | 0.109303 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 943.111 | 0.0466613 | ||||||||
\(743\) | −9713.53 | −0.479616 | −0.239808 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239808 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3771.42 | 0.185468 | ||||||||
\(746\) | −12404.2 | −0.608779 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2680.97 | −0.131051 | ||||||||
\(749\) | 42792.7 | 2.08760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2509.28 | −0.121924 | −0.0609619 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609619 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(752\) | −8925.55 | −0.432821 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 31335.9 | 1.51351 | ||||||||
\(755\) | 10288.2 | 0.495927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9705.73 | 0.465998 | 0.232999 | − | 0.972477i | \(-0.425146\pi\) | ||||
0.232999 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(758\) | −8178.67 | −0.391903 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8361.25 | −0.399072 | ||||||||
\(761\) | 7778.44 | 0.370523 | 0.185262 | − | 0.982689i | \(-0.440687\pi\) | ||||
0.185262 | + | 0.982689i | \(0.440687\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36891.5 | −1.75041 | ||||||||
\(764\) | −5816.04 | −0.275415 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3451.39 | 0.162799 | ||||||||
\(767\) | −74753.3 | −3.51915 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1387.90 | 0.0650833 | 0.0325416 | − | 0.999470i | \(-0.489640\pi\) | ||||
0.0325416 | + | 0.999470i | \(0.489640\pi\) | |||||||
\(770\) | 1323.44 | 0.0619393 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26660.5 | 1.24292 | ||||||||
\(773\) | −20692.0 | −0.962796 | −0.481398 | − | 0.876502i | \(-0.659871\pi\) | ||||
−0.481398 | + | 0.876502i | \(0.659871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5613.67 | 0.260192 | ||||||||
\(776\) | −10486.0 | −0.485086 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5639.70 | 0.259888 | ||||||||
\(779\) | −32478.0 | −1.49377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4544.98 | −0.208236 | ||||||||
\(782\) | 8902.82 | 0.407115 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5914.45 | 0.269426 | ||||||||
\(785\) | −16792.9 | −0.763523 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33896.8 | 1.53531 | 0.767655 | − | 0.640863i | \(-0.221423\pi\) | ||||
0.767655 | + | 0.640863i | \(0.221423\pi\) | |||||||
\(788\) | 12005.9 | 0.542756 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −533.983 | −0.0240484 | ||||||||
\(791\) | 20266.4 | 0.910988 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48506.4 | −2.17215 | ||||||||
\(794\) | 8078.08 | 0.361058 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10849.7 | −0.483110 | ||||||||
\(797\) | 11954.5 | 0.531307 | 0.265653 | − | 0.964069i | \(-0.414412\pi\) | ||||
0.265653 | + | 0.964069i | \(0.414412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18648.0 | −0.825682 | ||||||||
\(800\) | −4602.89 | −0.203421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10250.7 | 0.451325 | ||||||||
\(803\) | −1535.27 | −0.0674702 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15576.8 | 0.681998 | ||||||||
\(806\) | −25954.1 | −1.13424 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4288.75 | 0.186730 | ||||||||
\(809\) | −27377.3 | −1.18978 | −0.594891 | − | 0.803807i | \(-0.702805\pi\) | ||||
−0.594891 | + | 0.803807i | \(0.702805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −713.034 | −0.0308730 | −0.0154365 | − | 0.999881i | \(-0.504914\pi\) | ||||
−0.0154365 | + | 0.999881i | \(0.504914\pi\) | |||||||
\(812\) | −40774.9 | −1.76221 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 774.449 | 0.0333470 | ||||||||
\(815\) | −3551.88 | −0.152659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17308.0 | 0.741164 | ||||||||
\(818\) | −21655.0 | −0.925612 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11447.7 | −0.487526 | ||||||||
\(821\) | −6384.12 | −0.271385 | −0.135693 | − | 0.990751i | \(-0.543326\pi\) | ||||
−0.135693 | + | 0.990751i | \(0.543326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19636.3 | 0.831686 | 0.415843 | − | 0.909436i | \(-0.363487\pi\) | ||||
0.415843 | + | 0.909436i | \(0.363487\pi\) | |||||||
\(824\) | 7246.00 | 0.306343 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27443.7 | −1.15604 | ||||||||
\(827\) | −43578.4 | −1.83237 | −0.916185 | − | 0.400756i | \(-0.868747\pi\) | ||||
−0.916185 | + | 0.400756i | \(0.868747\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20418.8 | −0.855458 | −0.427729 | − | 0.903907i | \(-0.640686\pi\) | ||||
−0.427729 | + | 0.903907i | \(0.640686\pi\) | |||||||
\(830\) | 3826.21 | 0.160012 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3963.20 | 0.165143 | ||||||||
\(833\) | 12357.0 | 0.513978 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5741.34 | −0.237949 | ||||||||
\(836\) | 4570.69 | 0.189092 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1529.09 | 0.0630328 | ||||||||
\(839\) | 10962.0 | 0.451073 | 0.225536 | − | 0.974235i | \(-0.427587\pi\) | ||||
0.225536 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49110.9 | 2.01365 | ||||||||
\(842\) | 4685.26 | 0.191763 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19981.3 | −0.814911 | ||||||||
\(845\) | 26959.7 | 1.09756 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30431.8 | 1.23453 | ||||||||
\(848\) | 732.772 | 0.0296739 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1722.09 | −0.0694907 | ||||||||
\(851\) | 9115.22 | 0.367175 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5246.41 | −0.210590 | −0.105295 | − | 0.994441i | \(-0.533579\pi\) | ||||
−0.105295 | + | 0.994441i | \(0.533579\pi\) | |||||||
\(854\) | −17807.8 | −0.713548 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33541.4 | −1.33928 | ||||||||
\(857\) | 27283.1 | 1.08748 | 0.543741 | − | 0.839253i | \(-0.317007\pi\) | ||||
0.543741 | + | 0.839253i | \(0.317007\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3581.05 | 0.142240 | 0.0711198 | − | 0.997468i | \(-0.477343\pi\) | ||||
0.0711198 | + | 0.997468i | \(0.477343\pi\) | |||||||
\(860\) | 6100.66 | 0.241896 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13574.0 | 0.536350 | ||||||||
\(863\) | 41710.9 | 1.64526 | 0.822629 | − | 0.568579i | \(-0.192507\pi\) | ||||
0.822629 | + | 0.568579i | \(0.192507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14626.4 | −0.574929 | ||||||||
\(866\) | 9700.71 | 0.380651 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33771.9 | 1.32062 | ||||||||
\(869\) | 666.161 | 0.0260046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3649.98 | −0.141992 | ||||||||
\(872\) | 28916.0 | 1.12296 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15178.1 | −0.587422 | ||||||||
\(875\) | −3013.03 | −0.116410 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21533.6 | 0.829119 | 0.414560 | − | 0.910022i | \(-0.363936\pi\) | ||||
0.414560 | + | 0.910022i | \(0.363936\pi\) | |||||||
\(878\) | −9358.22 | −0.359709 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1028.27 | 0.0393899 | ||||||||
\(881\) | 30919.1 | 1.18240 | 0.591199 | − | 0.806526i | \(-0.298655\pi\) | ||||
0.591199 | + | 0.806526i | \(0.298655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5341.72 | 0.203582 | 0.101791 | − | 0.994806i | \(-0.467543\pi\) | ||||
0.101791 | + | 0.994806i | \(0.467543\pi\) | |||||||
\(884\) | −28219.7 | −1.07368 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −222.626 | −0.00844160 | ||||||||
\(887\) | 11210.3 | 0.424358 | 0.212179 | − | 0.977231i | \(-0.431944\pi\) | ||||
0.212179 | + | 0.977231i | \(0.431944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25031.1 | −0.944337 | ||||||||
\(890\) | −1489.45 | −0.0560972 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8766.54 | 0.329064 | ||||||||
\(893\) | 31792.3 | 1.19137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17110.1 | 0.639025 | ||||||||
\(896\) | −34048.8 | −1.26952 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5240.81 | 0.194753 | ||||||||
\(899\) | −60876.6 | −2.25845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1530.97 | 0.0566083 | ||||||||
\(902\) | −4029.32 | −0.148738 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15885.1 | −0.584435 | ||||||||
\(905\) | −5757.90 | −0.211491 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20690.8 | 0.757473 | 0.378737 | − | 0.925505i | \(-0.376359\pi\) | ||||
0.378737 | + | 0.925505i | \(0.376359\pi\) | |||||||
\(908\) | −38924.6 | −1.42264 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13930.4 | 0.507459 | ||||||||
\(911\) | 19471.6 | 0.708147 | 0.354073 | − | 0.935218i | \(-0.384796\pi\) | ||||
0.354073 | + | 0.935218i | \(0.384796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4773.32 | −0.173027 | ||||||||
\(914\) | 9881.53 | 0.357606 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41370.3 | −1.49226 | ||||||||
\(917\) | 19365.6 | 0.697393 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30002.0 | −1.07690 | −0.538452 | − | 0.842656i | \(-0.680991\pi\) | ||||
−0.538452 | + | 0.842656i | \(0.680991\pi\) | |||||||
\(920\) | −12209.2 | −0.437529 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14445.8 | 0.515996 | ||||||||
\(923\) | −47840.1 | −1.70604 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1763.17 | −0.0626732 | ||||||||
\(926\) | 4207.66 | 0.149322 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49915.3 | 1.76568 | ||||||||
\(929\) | 22262.8 | 0.786241 | 0.393121 | − | 0.919487i | \(-0.371395\pi\) | ||||
0.393121 | + | 0.919487i | \(0.371395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21066.9 | −0.741612 | ||||||||
\(932\) | −15308.7 | −0.538039 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21691.4 | −0.759917 | ||||||||
\(935\) | 2148.36 | 0.0751432 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23361.5 | 0.814500 | 0.407250 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407250 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(938\) | −1339.99 | −0.0466443 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11206.0 | 0.388830 | ||||||||
\(941\) | 39330.9 | 1.36254 | 0.681271 | − | 0.732031i | \(-0.261428\pi\) | ||||
0.681271 | + | 0.732031i | \(0.261428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47424.8 | −1.63771 | ||||||||
\(944\) | −21323.0 | −0.735175 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2147.29 | 0.0737995 | ||||||||
\(947\) | −26869.9 | −0.922021 | −0.461011 | − | 0.887395i | \(-0.652513\pi\) | ||||
−0.461011 | + | 0.887395i | \(0.652513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16160.1 | −0.552772 | ||||||||
\(950\) | 2935.92 | 0.100267 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23643.2 | −0.804916 | ||||||||
\(953\) | 16422.6 | 0.558218 | 0.279109 | − | 0.960259i | \(-0.409961\pi\) | ||||
0.279109 | + | 0.960259i | \(0.409961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4660.60 | 0.157920 | ||||||||
\(956\) | 43363.5 | 1.46702 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12490.2 | 0.421231 | ||||||||
\(959\) | −20950.3 | −0.705442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20630.3 | 0.692500 | ||||||||
\(962\) | 8151.79 | 0.273206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −39528.9 | −1.32069 | ||||||||
\(965\) | −21364.1 | −0.712677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10304.4 | 0.342677 | 0.171339 | − | 0.985212i | \(-0.445191\pi\) | ||||
0.171339 | + | 0.985212i | \(0.445191\pi\) | |||||||
\(968\) | −23852.7 | −0.792000 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3682.00 | 0.121878 | ||||||||
\(971\) | −44153.1 | −1.45926 | −0.729630 | − | 0.683842i | \(-0.760308\pi\) | ||||
−0.729630 | + | 0.683842i | \(0.760308\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4734.03 | 0.155977 | ||||||||
\(974\) | −17888.4 | −0.588483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13836.2 | −0.453776 | ||||||||
\(977\) | 16115.6 | 0.527722 | 0.263861 | − | 0.964561i | \(-0.415004\pi\) | ||||
0.263861 | + | 0.964561i | \(0.415004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1858.14 | 0.0606602 | ||||||||
\(980\) | −7425.59 | −0.242043 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12232.8 | −0.397521 | ||||||||
\(983\) | 38748.6 | 1.25726 | 0.628630 | − | 0.777704i | \(-0.283616\pi\) | ||||
0.628630 | + | 0.777704i | \(0.283616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9620.75 | −0.311211 | ||||||||
\(986\) | 18674.9 | 0.603174 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48110.7 | 1.54920 | ||||||||
\(989\) | 25273.5 | 0.812587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42906.4 | −1.37534 | −0.687672 | − | 0.726022i | \(-0.741367\pi\) | ||||
−0.687672 | + | 0.726022i | \(0.741367\pi\) | |||||||
\(992\) | −41342.5 | −1.32321 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17563.2 | −0.560434 | ||||||||
\(995\) | 8694.22 | 0.277010 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19395.3 | −0.616104 | −0.308052 | − | 0.951369i | \(-0.599677\pi\) | ||||
−0.308052 | + | 0.951369i | \(0.599677\pi\) | |||||||
\(998\) | −138.447 | −0.00439126 | ||||||||
\(999\) | 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 | 405.4.a.g.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 405.4.a.i.1.2 | yes | 3 | ||
5.4 | even | 2 | 2025.4.a.r.1.2 | 3 | |||
9.2 | odd | 6 | 405.4.e.s.271.2 | 6 | |||
9.4 | even | 3 | 405.4.e.u.136.2 | 6 | |||
9.5 | odd | 6 | 405.4.e.s.136.2 | 6 | |||
9.7 | even | 3 | 405.4.e.u.271.2 | 6 | |||
15.14 | odd | 2 | 2025.4.a.p.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.g.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
405.4.a.i.1.2 | yes | 3 | 3.2 | odd | 2 | ||
405.4.e.s.136.2 | 6 | 9.5 | odd | 6 | |||
405.4.e.s.271.2 | 6 | 9.2 | odd | 6 | |||
405.4.e.u.136.2 | 6 | 9.4 | even | 3 | |||
405.4.e.u.271.2 | 6 | 9.7 | even | 3 | |||
2025.4.a.p.1.2 | 3 | 15.14 | odd | 2 | |||
2025.4.a.r.1.2 | 3 | 5.4 | even | 2 |