Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(29.2059454528\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −0.552092 | −0.276046 | − | 0.961144i | \(-0.589024\pi\) | ||||
−0.276046 | + | 0.961144i | \(0.589024\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.56155 | −0.695194 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2462 | −0.553243 | −0.276622 | − | 0.960979i | \(-0.589215\pi\) | ||||
−0.276622 | + | 0.960979i | \(0.589215\pi\) | |||||||
\(8\) | 21.1771 | 0.935904 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.80776 | −0.246903 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −40.8769 | −0.872093 | −0.436047 | − | 0.899924i | \(-0.643622\pi\) | ||||
−0.436047 | + | 0.899924i | \(0.643622\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | 98.7083 | 1.40825 | 0.704126 | − | 0.710075i | \(-0.251339\pi\) | ||||
0.704126 | + | 0.710075i | \(0.251339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −39.6458 | −0.478704 | −0.239352 | − | 0.970933i | \(-0.576935\pi\) | ||||
−0.239352 | + | 0.970933i | \(0.576935\pi\) | |||||||
\(20\) | −27.8078 | −0.310900 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.1771 | −0.166462 | ||||||||
\(23\) | −61.6932 | −0.559301 | −0.279650 | − | 0.960102i | \(-0.590219\pi\) | ||||
−0.279650 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 63.8314 | 0.481476 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 56.9848 | 0.384612 | ||||||||
\(29\) | 149.093 | 0.954684 | 0.477342 | − | 0.878718i | \(-0.341600\pi\) | ||||
0.477342 | + | 0.878718i | \(0.341600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54.7386 | 0.317140 | 0.158570 | − | 0.987348i | \(-0.449312\pi\) | ||||
0.158570 | + | 0.987348i | \(0.449312\pi\) | |||||||
\(32\) | −187.255 | −1.03445 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −154.138 | −0.777485 | ||||||||
\(35\) | −51.2311 | −0.247418 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.8939 | 0.199473 | 0.0997367 | − | 0.995014i | \(-0.468200\pi\) | ||||
0.0997367 | + | 0.995014i | \(0.468200\pi\) | |||||||
\(38\) | 61.9091 | 0.264289 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.885 | 0.418549 | ||||||||
\(41\) | −336.479 | −1.28169 | −0.640844 | − | 0.767671i | \(-0.721415\pi\) | ||||
−0.640844 | + | 0.767671i | \(0.721415\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.36745 | −0.00839611 | −0.00419806 | − | 0.999991i | \(-0.501336\pi\) | ||||
−0.00419806 | + | 0.999991i | \(0.501336\pi\) | |||||||
\(44\) | −61.1771 | −0.209609 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 96.3371 | 0.308786 | ||||||||
\(47\) | 333.295 | 1.03439 | 0.517193 | − | 0.855869i | \(-0.326977\pi\) | ||||
0.517193 | + | 0.855869i | \(0.326977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −238.015 | −0.693922 | ||||||||
\(50\) | −39.0388 | −0.110418 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 227.339 | 0.606274 | ||||||||
\(53\) | −640.064 | −1.65886 | −0.829430 | − | 0.558610i | \(-0.811335\pi\) | ||||
−0.829430 | + | 0.558610i | \(0.811335\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −216.985 | −0.517782 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −232.816 | −0.527074 | ||||||||
\(59\) | 370.773 | 0.818144 | 0.409072 | − | 0.912502i | \(-0.365853\pi\) | ||||
0.409072 | + | 0.912502i | \(0.365853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −714.405 | −1.49951 | −0.749756 | − | 0.661715i | \(-0.769829\pi\) | ||||
−0.749756 | + | 0.661715i | \(0.769829\pi\) | |||||||
\(62\) | −85.4773 | −0.175091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | −204.384 | −0.390012 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −404.985 | −0.738459 | −0.369230 | − | 0.929338i | \(-0.620378\pi\) | ||||
−0.369230 | + | 0.929338i | \(0.620378\pi\) | |||||||
\(68\) | −548.972 | −0.979009 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 80.0000 | 0.136598 | ||||||||
\(71\) | −939.292 | −1.57005 | −0.785024 | − | 0.619465i | \(-0.787349\pi\) | ||||
−0.785024 | + | 0.619465i | \(0.787349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −362.570 | −0.581310 | −0.290655 | − | 0.956828i | \(-0.593873\pi\) | ||||
−0.290655 | + | 0.956828i | \(0.593873\pi\) | |||||||
\(74\) | −70.1042 | −0.110128 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 220.492 | 0.332792 | ||||||||
\(77\) | −112.708 | −0.166809 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 951.835 | 1.35557 | 0.677784 | − | 0.735261i | \(-0.262941\pi\) | ||||
0.677784 | + | 0.735261i | \(0.262941\pi\) | |||||||
\(80\) | 57.1165 | 0.0798227 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 525.430 | 0.707610 | ||||||||
\(83\) | −735.221 | −0.972302 | −0.486151 | − | 0.873875i | \(-0.661599\pi\) | ||||
−0.486151 | + | 0.873875i | \(0.661599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 493.542 | 0.629789 | ||||||||
\(86\) | 3.69690 | 0.00463543 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 232.948 | 0.282186 | ||||||||
\(89\) | −385.879 | −0.459585 | −0.229793 | − | 0.973240i | \(-0.573805\pi\) | ||||
−0.229793 | + | 0.973240i | \(0.573805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 418.833 | 0.482480 | ||||||||
\(92\) | 343.110 | 0.388823 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −520.458 | −0.571076 | ||||||||
\(95\) | −198.229 | −0.214083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −966.345 | −1.01152 | −0.505760 | − | 0.862674i | \(-0.668788\pi\) | ||||
−0.505760 | + | 0.862674i | \(0.668788\pi\) | |||||||
\(98\) | 371.673 | 0.383109 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −139.039 | −0.139039 | ||||||||
\(101\) | −348.600 | −0.343436 | −0.171718 | − | 0.985146i | \(-0.554932\pi\) | ||||
−0.171718 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1536.38 | −1.46975 | −0.734873 | − | 0.678204i | \(-0.762758\pi\) | ||||
−0.734873 | + | 0.678204i | \(0.762758\pi\) | |||||||
\(104\) | −865.653 | −0.816195 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 999.494 | 0.915844 | ||||||||
\(107\) | 779.180 | 0.703983 | 0.351991 | − | 0.936003i | \(-0.385505\pi\) | ||||
0.351991 | + | 0.936003i | \(0.385505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1501.79 | −1.31968 | −0.659842 | − | 0.751404i | \(-0.729377\pi\) | ||||
−0.659842 | + | 0.751404i | \(0.729377\pi\) | |||||||
\(110\) | −85.8854 | −0.0744441 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −117.045 | −0.0987478 | ||||||||
\(113\) | −170.000 | −0.141524 | −0.0707622 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707622 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −308.466 | −0.250127 | ||||||||
\(116\) | −829.187 | −0.663691 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −578.981 | −0.451691 | ||||||||
\(119\) | −1011.39 | −0.779106 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1115.58 | 0.827869 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −304.432 | −0.220474 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1739.82 | −1.21562 | −0.607811 | − | 0.794082i | \(-0.707952\pi\) | ||||
−0.607811 | + | 0.794082i | \(0.707952\pi\) | |||||||
\(128\) | 1184.13 | 0.817683 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 319.157 | 0.215323 | ||||||||
\(131\) | −312.837 | −0.208647 | −0.104323 | − | 0.994543i | \(-0.533268\pi\) | ||||
−0.104323 | + | 0.994543i | \(0.533268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 406.220 | 0.264840 | ||||||||
\(134\) | 632.405 | 0.407698 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2090.35 | 1.31799 | ||||||||
\(137\) | 716.928 | 0.447090 | 0.223545 | − | 0.974694i | \(-0.428237\pi\) | ||||
0.223545 | + | 0.974694i | \(0.428237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −876.483 | −0.534837 | −0.267418 | − | 0.963581i | \(-0.586171\pi\) | ||||
−0.267418 | + | 0.963581i | \(0.586171\pi\) | |||||||
\(140\) | 284.924 | 0.172004 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1466.75 | 0.866811 | ||||||||
\(143\) | −449.646 | −0.262946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 745.464 | 0.426948 | ||||||||
\(146\) | 566.172 | 0.320937 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −249.680 | −0.138673 | ||||||||
\(149\) | 2376.36 | 1.30657 | 0.653285 | − | 0.757112i | \(-0.273390\pi\) | ||||
0.653285 | + | 0.757112i | \(0.273390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −92.8466 | −0.0500381 | −0.0250190 | − | 0.999687i | \(-0.507965\pi\) | ||||
−0.0250190 | + | 0.999687i | \(0.507965\pi\) | |||||||
\(152\) | −839.583 | −0.448021 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 176.000 | 0.0920941 | ||||||||
\(155\) | 273.693 | 0.141829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1881.24 | −0.956301 | −0.478150 | − | 0.878278i | \(-0.658693\pi\) | ||||
−0.478150 | + | 0.878278i | \(0.658693\pi\) | |||||||
\(158\) | −1486.34 | −0.748398 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −936.274 | −0.462618 | ||||||||
\(161\) | 632.121 | 0.309429 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2465.49 | −1.18474 | −0.592369 | − | 0.805667i | \(-0.701807\pi\) | ||||
−0.592369 | + | 0.805667i | \(0.701807\pi\) | |||||||
\(164\) | 1871.35 | 0.891022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1148.09 | 0.536800 | ||||||||
\(167\) | 1254.30 | 0.581200 | 0.290600 | − | 0.956845i | \(-0.406145\pi\) | ||||
0.290600 | + | 0.956845i | \(0.406145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −526.080 | −0.239454 | ||||||||
\(170\) | −770.691 | −0.347702 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.1667 | 0.00583693 | ||||||||
\(173\) | 1206.71 | 0.530314 | 0.265157 | − | 0.964205i | \(-0.414576\pi\) | ||||
0.265157 | + | 0.964205i | \(0.414576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −256.155 | −0.110649 | ||||||||
\(176\) | 125.656 | 0.0538164 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 602.570 | 0.253733 | ||||||||
\(179\) | 1442.29 | 0.602244 | 0.301122 | − | 0.953586i | \(-0.402639\pi\) | ||||
0.301122 | + | 0.953586i | \(0.402639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4261.81 | 1.75015 | 0.875076 | − | 0.483985i | \(-0.160811\pi\) | ||||
0.875076 | + | 0.483985i | \(0.160811\pi\) | |||||||
\(182\) | −654.030 | −0.266373 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1306.48 | −0.523451 | ||||||||
\(185\) | 224.470 | 0.0892072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1085.79 | 0.424604 | ||||||||
\(188\) | −1853.64 | −0.719099 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 309.545 | 0.118194 | ||||||||
\(191\) | 852.223 | 0.322852 | 0.161426 | − | 0.986885i | \(-0.448391\pi\) | ||||
0.161426 | + | 0.986885i | \(0.448391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2459.95 | −0.917468 | −0.458734 | − | 0.888574i | \(-0.651697\pi\) | ||||
−0.458734 | + | 0.888574i | \(0.651697\pi\) | |||||||
\(194\) | 1509.00 | 0.558452 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1323.73 | 0.482410 | ||||||||
\(197\) | −3477.06 | −1.25751 | −0.628756 | − | 0.777602i | \(-0.716436\pi\) | ||||
−0.628756 | + | 0.777602i | \(0.716436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3995.04 | 1.42312 | 0.711560 | − | 0.702626i | \(-0.247989\pi\) | ||||
0.711560 | + | 0.702626i | \(0.247989\pi\) | |||||||
\(200\) | 529.427 | 0.187181 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 544.358 | 0.189608 | ||||||||
\(203\) | −1527.64 | −0.528173 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1682.40 | −0.573188 | ||||||||
\(206\) | 2399.14 | 0.811436 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −466.949 | −0.155659 | ||||||||
\(209\) | −436.104 | −0.144335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1046.13 | 0.341319 | 0.170660 | − | 0.985330i | \(-0.445410\pi\) | ||||
0.170660 | + | 0.985330i | \(0.445410\pi\) | |||||||
\(212\) | 3559.75 | 1.15323 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1216.73 | −0.388664 | ||||||||
\(215\) | −11.8373 | −0.00375486 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −560.864 | −0.175456 | ||||||||
\(218\) | 2345.13 | 0.728587 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −305.885 | −0.0937400 | ||||||||
\(221\) | −4034.89 | −1.22813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −506.265 | −0.152027 | −0.0760135 | − | 0.997107i | \(-0.524219\pi\) | ||||
−0.0760135 | + | 0.997107i | \(0.524219\pi\) | |||||||
\(224\) | 1918.65 | 0.572300 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 265.464 | 0.0781345 | ||||||||
\(227\) | 4286.29 | 1.25326 | 0.626632 | − | 0.779315i | \(-0.284433\pi\) | ||||
0.626632 | + | 0.779315i | \(0.284433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5709.37 | 1.64754 | 0.823769 | − | 0.566926i | \(-0.191867\pi\) | ||||
0.823769 | + | 0.566926i | \(0.191867\pi\) | |||||||
\(230\) | 481.686 | 0.138093 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3157.35 | 0.893492 | ||||||||
\(233\) | −2946.09 | −0.828348 | −0.414174 | − | 0.910198i | \(-0.635929\pi\) | ||||
−0.414174 | + | 0.910198i | \(0.635929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1666.48 | 0.462591 | ||||||||
\(236\) | −2062.07 | −0.568769 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1579.33 | 0.430139 | ||||||||
\(239\) | 2078.89 | 0.562646 | 0.281323 | − | 0.959613i | \(-0.409227\pi\) | ||||
0.281323 | + | 0.959613i | \(0.409227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1853.37 | 0.495378 | 0.247689 | − | 0.968840i | \(-0.420329\pi\) | ||||
0.247689 | + | 0.968840i | \(0.420329\pi\) | |||||||
\(242\) | −188.948 | −0.0501902 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3973.20 | 1.04245 | ||||||||
\(245\) | −1190.08 | −0.310331 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1620.60 | 0.417475 | ||||||||
\(248\) | 1159.20 | 0.296813 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −195.194 | −0.0493806 | ||||||||
\(251\) | 2358.39 | 0.593068 | 0.296534 | − | 0.955022i | \(-0.404169\pi\) | ||||
0.296534 | + | 0.955022i | \(0.404169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −678.625 | −0.168635 | ||||||||
\(254\) | 2716.82 | 0.671135 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | −5519.25 | −1.33962 | −0.669809 | − | 0.742534i | \(-0.733624\pi\) | ||||
−0.669809 | + | 0.742534i | \(0.733624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −459.993 | −0.110357 | ||||||||
\(260\) | 1136.70 | 0.271134 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 488.512 | 0.115192 | ||||||||
\(263\) | −2259.65 | −0.529795 | −0.264898 | − | 0.964277i | \(-0.585338\pi\) | ||||
−0.264898 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3200.32 | −0.741865 | ||||||||
\(266\) | −634.333 | −0.146216 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2252.34 | 0.513373 | ||||||||
\(269\) | −7039.53 | −1.59557 | −0.797783 | − | 0.602944i | \(-0.793994\pi\) | ||||
−0.797783 | + | 0.602944i | \(0.793994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5155.08 | 1.15553 | 0.577765 | − | 0.816203i | \(-0.303925\pi\) | ||||
0.577765 | + | 0.816203i | \(0.303925\pi\) | |||||||
\(272\) | 1127.57 | 0.251357 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1119.52 | −0.246835 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9074.52 | 1.96836 | 0.984179 | − | 0.177175i | \(-0.0566960\pi\) | ||||
0.984179 | + | 0.177175i | \(0.0566960\pi\) | |||||||
\(278\) | 1368.67 | 0.295279 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1084.92 | −0.231559 | ||||||||
\(281\) | 3407.79 | 0.723459 | 0.361729 | − | 0.932283i | \(-0.382186\pi\) | ||||
0.361729 | + | 0.932283i | \(0.382186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8827.73 | −1.85425 | −0.927127 | − | 0.374746i | \(-0.877730\pi\) | ||||
−0.927127 | + | 0.374746i | \(0.877730\pi\) | |||||||
\(284\) | 5223.92 | 1.09149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 702.146 | 0.145170 | ||||||||
\(287\) | 3447.64 | 0.709085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4830.33 | 0.983174 | ||||||||
\(290\) | −1164.08 | −0.235715 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2016.45 | 0.404123 | ||||||||
\(293\) | 4528.29 | 0.902886 | 0.451443 | − | 0.892300i | \(-0.350909\pi\) | ||||
0.451443 | + | 0.892300i | \(0.350909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1853.86 | 0.365885 | ||||||||
\(296\) | 950.722 | 0.186688 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3710.81 | −0.721347 | ||||||||
\(299\) | 2521.83 | 0.487762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2574 | 0.00464509 | ||||||||
\(302\) | 144.985 | 0.0276256 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −452.886 | −0.0854434 | ||||||||
\(305\) | −3572.03 | −0.670602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 568.106 | 0.105614 | 0.0528071 | − | 0.998605i | \(-0.483183\pi\) | ||||
0.0528071 | + | 0.998605i | \(0.483183\pi\) | |||||||
\(308\) | 626.833 | 0.115965 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −427.386 | −0.0783029 | ||||||||
\(311\) | 6853.59 | 1.24962 | 0.624809 | − | 0.780778i | \(-0.285177\pi\) | ||||
0.624809 | + | 0.780778i | \(0.285177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1138.92 | −0.205673 | −0.102837 | − | 0.994698i | \(-0.532792\pi\) | ||||
−0.102837 | + | 0.994698i | \(0.532792\pi\) | |||||||
\(314\) | 2937.65 | 0.527966 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5293.68 | −0.942382 | ||||||||
\(317\) | −3207.48 | −0.568297 | −0.284148 | − | 0.958780i | \(-0.591711\pi\) | ||||
−0.284148 | + | 0.958780i | \(0.591711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1640.02 | 0.287848 | ||||||||
\(320\) | 1005.11 | 0.175585 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −987.091 | −0.170834 | ||||||||
\(323\) | −3913.37 | −0.674136 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1021.92 | −0.174419 | ||||||||
\(326\) | 3850.00 | 0.654085 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7125.65 | −1.19954 | ||||||||
\(329\) | −3415.02 | −0.572267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9135.12 | −1.51695 | −0.758477 | − | 0.651700i | \(-0.774056\pi\) | ||||
−0.758477 | + | 0.651700i | \(0.774056\pi\) | |||||||
\(332\) | 4088.97 | 0.675938 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1958.65 | −0.320876 | ||||||||
\(335\) | −2024.92 | −0.330249 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3470.05 | −0.560907 | −0.280453 | − | 0.959868i | \(-0.590485\pi\) | ||||
−0.280453 | + | 0.959868i | \(0.590485\pi\) | |||||||
\(338\) | 821.501 | 0.132200 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2744.86 | −0.437826 | ||||||||
\(341\) | 602.125 | 0.0956214 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5953.20 | 0.937151 | ||||||||
\(344\) | −50.1357 | −0.00785795 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1884.34 | −0.292782 | ||||||||
\(347\) | 89.3315 | 0.0138201 | 0.00691004 | − | 0.999976i | \(-0.497800\pi\) | ||||
0.00691004 | + | 0.999976i | \(0.497800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −149.375 | −0.0229107 | −0.0114554 | − | 0.999934i | \(-0.503646\pi\) | ||||
−0.0114554 | + | 0.999934i | \(0.503646\pi\) | |||||||
\(350\) | 400.000 | 0.0610883 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2059.80 | −0.311897 | ||||||||
\(353\) | −7867.64 | −1.18627 | −0.593133 | − | 0.805104i | \(-0.702109\pi\) | ||||
−0.593133 | + | 0.805104i | \(0.702109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4696.46 | −0.702147 | ||||||||
\(356\) | 2146.09 | 0.319501 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2252.21 | −0.332494 | ||||||||
\(359\) | −4974.22 | −0.731279 | −0.365639 | − | 0.930757i | \(-0.619150\pi\) | ||||
−0.365639 | + | 0.930757i | \(0.619150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5287.21 | −0.770842 | ||||||||
\(362\) | −6655.04 | −0.966246 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2329.36 | −0.335417 | ||||||||
\(365\) | −1812.85 | −0.259970 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13266.7 | −1.88696 | −0.943479 | − | 0.331433i | \(-0.892468\pi\) | ||||
−0.943479 | + | 0.331433i | \(0.892468\pi\) | |||||||
\(368\) | −704.739 | −0.0998290 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −350.521 | −0.0492506 | ||||||||
\(371\) | 6558.23 | 0.917754 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4632.77 | −0.643099 | −0.321549 | − | 0.946893i | \(-0.604204\pi\) | ||||
−0.321549 | + | 0.946893i | \(0.604204\pi\) | |||||||
\(374\) | −1695.52 | −0.234421 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7058.22 | 0.968085 | ||||||||
\(377\) | −6094.45 | −0.832573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6503.31 | 0.881406 | 0.440703 | − | 0.897653i | \(-0.354729\pi\) | ||||
0.440703 | + | 0.897653i | \(0.354729\pi\) | |||||||
\(380\) | 1102.46 | 0.148829 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1330.79 | −0.178244 | ||||||||
\(383\) | −12734.5 | −1.69897 | −0.849484 | − | 0.527614i | \(-0.823087\pi\) | ||||
−0.849484 | + | 0.527614i | \(0.823087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −563.542 | −0.0745993 | ||||||||
\(386\) | 3841.35 | 0.506527 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5374.38 | 0.703203 | ||||||||
\(389\) | −12024.6 | −1.56728 | −0.783639 | − | 0.621216i | \(-0.786639\pi\) | ||||
−0.783639 | + | 0.621216i | \(0.786639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6089.63 | −0.787636 | ||||||||
\(392\) | −5040.47 | −0.649444 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5429.61 | 0.694263 | ||||||||
\(395\) | 4759.18 | 0.606228 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5223.65 | −0.660371 | −0.330186 | − | 0.943916i | \(-0.607111\pi\) | ||||
−0.330186 | + | 0.943916i | \(0.607111\pi\) | |||||||
\(398\) | −6238.46 | −0.785693 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 285.582 | 0.0356978 | ||||||||
\(401\) | −9648.18 | −1.20151 | −0.600757 | − | 0.799432i | \(-0.705134\pi\) | ||||
−0.600757 | + | 0.799432i | \(0.705134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2237.55 | −0.276576 | ||||||||
\(404\) | 1938.76 | 0.238755 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2385.48 | 0.291600 | ||||||||
\(407\) | 493.833 | 0.0601435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2010.47 | −0.243060 | −0.121530 | − | 0.992588i | \(-0.538780\pi\) | ||||
−0.121530 | + | 0.992588i | \(0.538780\pi\) | |||||||
\(410\) | 2627.15 | 0.316453 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8544.65 | 1.02176 | ||||||||
\(413\) | −3799.02 | −0.452633 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3676.11 | −0.434827 | ||||||||
\(416\) | 7654.39 | 0.902133 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 681.000 | 0.0796861 | ||||||||
\(419\) | −4435.27 | −0.517129 | −0.258565 | − | 0.965994i | \(-0.583250\pi\) | ||||
−0.258565 | + | 0.965994i | \(0.583250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15217.9 | 1.76170 | 0.880852 | − | 0.473392i | \(-0.156971\pi\) | ||||
0.880852 | + | 0.473392i | \(0.156971\pi\) | |||||||
\(422\) | −1633.58 | −0.188440 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13554.7 | −1.55253 | ||||||||
\(425\) | 2467.71 | 0.281650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7319.95 | 0.829595 | ||||||||
\(428\) | −4333.45 | −0.489405 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.4845 | 0.00207303 | ||||||||
\(431\) | 5622.11 | 0.628324 | 0.314162 | − | 0.949369i | \(-0.398277\pi\) | ||||
0.314162 | + | 0.949369i | \(0.398277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14306.3 | −1.58780 | −0.793898 | − | 0.608051i | \(-0.791951\pi\) | ||||
−0.793898 | + | 0.608051i | \(0.791951\pi\) | |||||||
\(434\) | 875.818 | 0.0968678 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8352.29 | 0.917436 | ||||||||
\(437\) | 2445.88 | 0.267740 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4384.20 | 0.476643 | 0.238322 | − | 0.971186i | \(-0.423403\pi\) | ||||
0.238322 | + | 0.971186i | \(0.423403\pi\) | |||||||
\(440\) | 1164.74 | 0.126197 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6300.69 | 0.678039 | ||||||||
\(443\) | 10090.0 | 1.08214 | 0.541071 | − | 0.840977i | \(-0.318019\pi\) | ||||
0.541071 | + | 0.840977i | \(0.318019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1929.39 | −0.205533 | ||||||||
\(446\) | 790.560 | 0.0839330 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2059.71 | −0.217215 | ||||||||
\(449\) | −9582.52 | −1.00719 | −0.503594 | − | 0.863941i | \(-0.667989\pi\) | ||||
−0.503594 | + | 0.863941i | \(0.667989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3701.27 | −0.386444 | ||||||||
\(452\) | 945.464 | 0.0983869 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6693.27 | −0.691918 | ||||||||
\(455\) | 2094.17 | 0.215772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9999.34 | 1.02352 | 0.511761 | − | 0.859128i | \(-0.328993\pi\) | ||||
0.511761 | + | 0.859128i | \(0.328993\pi\) | |||||||
\(458\) | −8915.49 | −0.909593 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1715.55 | 0.173887 | ||||||||
\(461\) | 11115.8 | 1.12302 | 0.561512 | − | 0.827468i | \(-0.310220\pi\) | ||||
0.561512 | + | 0.827468i | \(0.310220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1567.16 | −0.157305 | −0.0786524 | − | 0.996902i | \(-0.525062\pi\) | ||||
−0.0786524 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(464\) | 1703.13 | 0.170401 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4600.48 | 0.457325 | ||||||||
\(467\) | −12648.8 | −1.25335 | −0.626675 | − | 0.779281i | \(-0.715585\pi\) | ||||
−0.626675 | + | 0.779281i | \(0.715585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4149.56 | 0.408548 | ||||||||
\(470\) | −2602.29 | −0.255393 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7851.88 | 0.765704 | ||||||||
\(473\) | −26.0420 | −0.00253152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −991.146 | −0.0957408 | ||||||||
\(476\) | 5624.88 | 0.541630 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3246.30 | −0.310633 | ||||||||
\(479\) | 10719.2 | 1.02249 | 0.511247 | − | 0.859434i | \(-0.329184\pi\) | ||||
0.511247 | + | 0.859434i | \(0.329184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1835.12 | −0.173959 | ||||||||
\(482\) | −2894.14 | −0.273494 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −672.948 | −0.0631995 | ||||||||
\(485\) | −4831.72 | −0.452365 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7161.20 | 0.666335 | 0.333167 | − | 0.942868i | \(-0.391883\pi\) | ||||
0.333167 | + | 0.942868i | \(0.391883\pi\) | |||||||
\(488\) | −15129.0 | −1.40340 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1858.37 | 0.171331 | ||||||||
\(491\) | −14567.3 | −1.33893 | −0.669463 | − | 0.742845i | \(-0.733476\pi\) | ||||
−0.669463 | + | 0.742845i | \(0.733476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14716.7 | 1.34444 | ||||||||
\(494\) | −2530.65 | −0.230485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 625.295 | 0.0566060 | ||||||||
\(497\) | 9624.18 | 0.868619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4638.99 | −0.416172 | −0.208086 | − | 0.978111i | \(-0.566723\pi\) | ||||
−0.208086 | + | 0.978111i | \(0.566723\pi\) | |||||||
\(500\) | −695.194 | −0.0621801 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3682.75 | −0.327428 | ||||||||
\(503\) | 12206.3 | 1.08201 | 0.541006 | − | 0.841019i | \(-0.318044\pi\) | ||||
0.541006 | + | 0.841019i | \(0.318044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1743.00 | −0.153589 | ||||||||
\(506\) | 1059.71 | 0.0931024 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9676.09 | 0.845093 | ||||||||
\(509\) | −10018.6 | −0.872427 | −0.436214 | − | 0.899843i | \(-0.643681\pi\) | ||||
−0.436214 | + | 0.899843i | \(0.643681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3714.97 | 0.321606 | ||||||||
\(512\) | −4074.36 | −0.351686 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8618.61 | 0.739592 | ||||||||
\(515\) | −7681.89 | −0.657291 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3666.25 | 0.311879 | ||||||||
\(518\) | 718.303 | 0.0609274 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4328.27 | −0.365014 | ||||||||
\(521\) | −1054.72 | −0.0886916 | −0.0443458 | − | 0.999016i | \(-0.514120\pi\) | ||||
−0.0443458 | + | 0.999016i | \(0.514120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16234.2 | −1.35730 | −0.678652 | − | 0.734460i | \(-0.737436\pi\) | ||||
−0.678652 | + | 0.734460i | \(0.737436\pi\) | |||||||
\(524\) | 1739.86 | 0.145050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3528.57 | 0.292496 | ||||||||
\(527\) | 5403.16 | 0.446613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8360.95 | −0.687183 | ||||||||
\(530\) | 4997.47 | 0.409578 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2259.21 | −0.184115 | ||||||||
\(533\) | 13754.2 | 1.11775 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3895.90 | 0.314831 | ||||||||
\(536\) | −8576.40 | −0.691127 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10992.6 | 0.880900 | ||||||||
\(539\) | −2618.17 | −0.209225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 675.936 | 0.0537167 | 0.0268584 | − | 0.999639i | \(-0.491450\pi\) | ||||
0.0268584 | + | 0.999639i | \(0.491450\pi\) | |||||||
\(542\) | −8049.93 | −0.637960 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18483.6 | −1.45676 | ||||||||
\(545\) | −7508.96 | −0.590181 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13058.2 | 1.02071 | 0.510355 | − | 0.859964i | \(-0.329514\pi\) | ||||
0.510355 | + | 0.859964i | \(0.329514\pi\) | |||||||
\(548\) | −3987.23 | −0.310814 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −429.427 | −0.0332924 | ||||||||
\(551\) | −5910.91 | −0.457011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9752.70 | −0.749959 | ||||||||
\(554\) | −14170.3 | −1.08672 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4874.61 | 0.371815 | ||||||||
\(557\) | 6710.48 | 0.510471 | 0.255236 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255236 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 96.7741 | 0.00732219 | ||||||||
\(560\) | −585.227 | −0.0441614 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5321.45 | −0.399416 | ||||||||
\(563\) | 20820.5 | 1.55858 | 0.779288 | − | 0.626666i | \(-0.215581\pi\) | ||||
0.779288 | + | 0.626666i | \(0.215581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −850.000 | −0.0632916 | ||||||||
\(566\) | 13785.0 | 1.02372 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19891.5 | −1.46941 | ||||||||
\(569\) | −3251.08 | −0.239530 | −0.119765 | − | 0.992802i | \(-0.538214\pi\) | ||||
−0.119765 | + | 0.992802i | \(0.538214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4637.50 | −0.339883 | −0.169941 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169941 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(572\) | 2500.73 | 0.182798 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5383.67 | −0.391481 | ||||||||
\(575\) | −1542.33 | −0.111860 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14462.4 | 1.04346 | 0.521730 | − | 0.853111i | \(-0.325287\pi\) | ||||
0.521730 | + | 0.853111i | \(0.325287\pi\) | |||||||
\(578\) | −7542.82 | −0.542803 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4145.94 | −0.296812 | ||||||||
\(581\) | 7533.23 | 0.537920 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7040.71 | −0.500165 | ||||||||
\(584\) | −7678.18 | −0.544050 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7071.17 | −0.498476 | ||||||||
\(587\) | 22759.7 | 1.60033 | 0.800166 | − | 0.599779i | \(-0.204745\pi\) | ||||
0.800166 | + | 0.599779i | \(0.204745\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2170.16 | −0.151816 | ||||||||
\(590\) | −2894.91 | −0.202002 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 512.836 | 0.0356038 | ||||||||
\(593\) | 14956.4 | 1.03573 | 0.517864 | − | 0.855463i | \(-0.326727\pi\) | ||||
0.517864 | + | 0.855463i | \(0.326727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5056.93 | −0.348427 | ||||||||
\(596\) | −13216.2 | −0.908319 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3937.96 | −0.269290 | ||||||||
\(599\) | −2150.77 | −0.146708 | −0.0733539 | − | 0.997306i | \(-0.523370\pi\) | ||||
−0.0733539 | + | 0.997306i | \(0.523370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27759.8 | 1.88410 | 0.942050 | − | 0.335472i | \(-0.108896\pi\) | ||||
0.942050 | + | 0.335472i | \(0.108896\pi\) | |||||||
\(602\) | −37.8792 | −0.00256452 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 516.371 | 0.0347862 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10991.5 | −0.734974 | −0.367487 | − | 0.930029i | \(-0.619782\pi\) | ||||
−0.367487 | + | 0.930029i | \(0.619782\pi\) | |||||||
\(608\) | 7423.87 | 0.495194 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5577.91 | 0.370234 | ||||||||
\(611\) | −13624.1 | −0.902081 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10646.1 | 0.701457 | 0.350728 | − | 0.936477i | \(-0.385934\pi\) | ||||
0.350728 | + | 0.936477i | \(0.385934\pi\) | |||||||
\(614\) | −887.128 | −0.0583088 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2386.83 | −0.156117 | ||||||||
\(617\) | −7199.92 | −0.469786 | −0.234893 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234893 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12186.9 | 0.791332 | 0.395666 | − | 0.918395i | \(-0.370514\pi\) | ||||
0.395666 | + | 0.918395i | \(0.370514\pi\) | |||||||
\(620\) | −1522.16 | −0.0985990 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10702.2 | −0.689905 | ||||||||
\(623\) | 3953.80 | 0.254262 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 1778.49 | 0.113551 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10462.6 | 0.664814 | ||||||||
\(629\) | 4431.40 | 0.280909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7370.64 | 0.465009 | 0.232505 | − | 0.972595i | \(-0.425308\pi\) | ||||
0.232505 | + | 0.972595i | \(0.425308\pi\) | |||||||
\(632\) | 20157.1 | 1.26868 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5008.65 | 0.313752 | ||||||||
\(635\) | −8699.09 | −0.543642 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9729.32 | 0.605164 | ||||||||
\(638\) | −2560.98 | −0.158919 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5920.66 | 0.365679 | ||||||||
\(641\) | 25014.9 | 1.54139 | 0.770693 | − | 0.637207i | \(-0.219910\pi\) | ||||
0.770693 | + | 0.637207i | \(0.219910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21668.2 | −1.32894 | −0.664472 | − | 0.747313i | \(-0.731343\pi\) | ||||
−0.664472 | + | 0.747313i | \(0.731343\pi\) | |||||||
\(644\) | −3515.58 | −0.215113 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6110.94 | 0.372185 | ||||||||
\(647\) | 27625.3 | 1.67861 | 0.839305 | − | 0.543661i | \(-0.182962\pi\) | ||||
0.839305 | + | 0.543661i | \(0.182962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4078.50 | 0.246680 | ||||||||
\(650\) | 1595.79 | 0.0962952 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13712.0 | 0.823623 | ||||||||
\(653\) | 14314.0 | 0.857810 | 0.428905 | − | 0.903350i | \(-0.358899\pi\) | ||||
0.428905 | + | 0.903350i | \(0.358899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1564.19 | −0.0933096 | ||||||||
\(656\) | −3843.70 | −0.228767 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5332.73 | 0.315944 | ||||||||
\(659\) | 28327.8 | 1.67450 | 0.837249 | − | 0.546822i | \(-0.184163\pi\) | ||||
0.837249 | + | 0.546822i | \(0.184163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32190.9 | −1.89422 | −0.947112 | − | 0.320905i | \(-0.896013\pi\) | ||||
−0.947112 | + | 0.320905i | \(0.896013\pi\) | |||||||
\(662\) | 14265.0 | 0.837498 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15569.8 | −0.909981 | ||||||||
\(665\) | 2031.10 | 0.118440 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9198.01 | −0.533955 | ||||||||
\(668\) | −6975.84 | −0.404047 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3162.03 | 0.182328 | ||||||||
\(671\) | −7858.46 | −0.452120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6207.38 | −0.355538 | −0.177769 | − | 0.984072i | \(-0.556888\pi\) | ||||
−0.177769 | + | 0.984072i | \(0.556888\pi\) | |||||||
\(674\) | 5418.66 | 0.309672 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2925.82 | 0.166467 | ||||||||
\(677\) | −28831.1 | −1.63674 | −0.818368 | − | 0.574695i | \(-0.805121\pi\) | ||||
−0.818368 | + | 0.574695i | \(0.805121\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9901.37 | 0.559617 | ||||||||
\(680\) | 10451.8 | 0.589422 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −940.250 | −0.0527918 | ||||||||
\(683\) | −3193.10 | −0.178888 | −0.0894441 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894441 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3584.64 | 0.199945 | ||||||||
\(686\) | −9296.24 | −0.517394 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.0441 | −0.00149861 | ||||||||
\(689\) | 26163.8 | 1.44668 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7682.49 | 0.422946 | 0.211473 | − | 0.977384i | \(-0.432174\pi\) | ||||
0.211473 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(692\) | −6711.17 | −0.368671 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −139.496 | −0.00762996 | ||||||||
\(695\) | −4382.41 | −0.239186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33213.3 | −1.80494 | ||||||||
\(698\) | 233.256 | 0.0126488 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1424.62 | 0.0769223 | ||||||||
\(701\) | −26551.6 | −1.43058 | −0.715292 | − | 0.698825i | \(-0.753707\pi\) | ||||
−0.715292 | + | 0.698825i | \(0.753707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1779.86 | −0.0954887 | ||||||||
\(704\) | 2211.24 | 0.118380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12285.7 | 0.654928 | ||||||||
\(707\) | 3571.83 | 0.190004 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16304.6 | −0.863655 | −0.431828 | − | 0.901956i | \(-0.642131\pi\) | ||||
−0.431828 | + | 0.901956i | \(0.642131\pi\) | |||||||
\(710\) | 7333.77 | 0.387650 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8171.79 | −0.430127 | ||||||||
\(713\) | −3377.00 | −0.177377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2248.23 | −0.117593 | ||||||||
\(716\) | −8021.36 | −0.418676 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7767.50 | 0.403733 | ||||||||
\(719\) | 3973.62 | 0.206107 | 0.103053 | − | 0.994676i | \(-0.467139\pi\) | ||||
0.103053 | + | 0.994676i | \(0.467139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15742.1 | 0.813128 | ||||||||
\(722\) | 8256.25 | 0.425576 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23702.3 | −1.21670 | ||||||||
\(725\) | 3727.32 | 0.190937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10780.4 | −0.549961 | −0.274980 | − | 0.961450i | \(-0.588671\pi\) | ||||
−0.274980 | + | 0.961450i | \(0.588671\pi\) | |||||||
\(728\) | 8869.67 | 0.451555 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2830.86 | 0.143527 | ||||||||
\(731\) | −233.687 | −0.0118238 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9211.46 | −0.464165 | −0.232083 | − | 0.972696i | \(-0.574554\pi\) | ||||
−0.232083 | + | 0.972696i | \(0.574554\pi\) | |||||||
\(734\) | 20716.6 | 1.04177 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11552.3 | 0.578566 | ||||||||
\(737\) | −4454.83 | −0.222654 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11084.7 | 0.551768 | 0.275884 | − | 0.961191i | \(-0.411029\pi\) | ||||
0.275884 | + | 0.961191i | \(0.411029\pi\) | |||||||
\(740\) | −1248.40 | −0.0620163 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10241.0 | −0.506685 | ||||||||
\(743\) | 27420.4 | 1.35391 | 0.676955 | − | 0.736024i | \(-0.263299\pi\) | ||||
0.676955 | + | 0.736024i | \(0.263299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11881.8 | 0.584316 | ||||||||
\(746\) | 7234.32 | 0.355050 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6038.69 | −0.295182 | ||||||||
\(749\) | −7983.64 | −0.389474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11290.8 | −0.548614 | −0.274307 | − | 0.961642i | \(-0.588448\pi\) | ||||
−0.274307 | + | 0.961642i | \(0.588448\pi\) | |||||||
\(752\) | 3807.33 | 0.184626 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9516.81 | 0.459657 | ||||||||
\(755\) | −464.233 | −0.0223777 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3739.19 | 0.179528 | 0.0897642 | − | 0.995963i | \(-0.471389\pi\) | ||||
0.0897642 | + | 0.995963i | \(0.471389\pi\) | |||||||
\(758\) | −10155.3 | −0.486617 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4197.92 | −0.200361 | ||||||||
\(761\) | 15621.1 | 0.744107 | 0.372053 | − | 0.928211i | \(-0.378654\pi\) | ||||
0.372053 | + | 0.928211i | \(0.378654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15387.7 | 0.730106 | ||||||||
\(764\) | −4739.69 | −0.224445 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19885.7 | 0.937987 | ||||||||
\(767\) | −15156.0 | −0.713498 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40241.7 | 1.88706 | 0.943531 | − | 0.331284i | \(-0.107482\pi\) | ||||
0.943531 | + | 0.331284i | \(0.107482\pi\) | |||||||
\(770\) | 880.000 | 0.0411857 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13681.2 | 0.637818 | ||||||||
\(773\) | −22821.4 | −1.06187 | −0.530936 | − | 0.847412i | \(-0.678160\pi\) | ||||
−0.530936 | + | 0.847412i | \(0.678160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1368.47 | 0.0634281 | ||||||||
\(776\) | −20464.4 | −0.946685 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18777.0 | 0.865282 | ||||||||
\(779\) | 13340.0 | 0.613549 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10332.2 | −0.473387 | ||||||||
\(782\) | 9509.28 | 0.434848 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2718.92 | −0.123857 | ||||||||
\(785\) | −9406.19 | −0.427671 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29454.3 | −1.33410 | −0.667048 | − | 0.745015i | \(-0.732442\pi\) | ||||
−0.667048 | + | 0.745015i | \(0.732442\pi\) | |||||||
\(788\) | 19337.8 | 0.874216 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7431.70 | −0.334694 | ||||||||
\(791\) | 1741.86 | 0.0782974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29202.7 | 1.30771 | ||||||||
\(794\) | 8157.00 | 0.364586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22218.6 | −0.989344 | ||||||||
\(797\) | 27440.3 | 1.21955 | 0.609777 | − | 0.792573i | \(-0.291259\pi\) | ||||
0.609777 | + | 0.792573i | \(0.291259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32899.0 | 1.45668 | ||||||||
\(800\) | −4681.37 | −0.206889 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15066.1 | 0.663346 | ||||||||
\(803\) | −3988.27 | −0.175272 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3160.61 | 0.138381 | ||||||||
\(806\) | 3494.05 | 0.152695 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7382.34 | −0.321423 | ||||||||
\(809\) | 5060.18 | 0.219909 | 0.109954 | − | 0.993937i | \(-0.464930\pi\) | ||||
0.109954 | + | 0.993937i | \(0.464930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30480.1 | 1.31973 | 0.659865 | − | 0.751384i | \(-0.270613\pi\) | ||||
0.659865 | + | 0.751384i | \(0.270613\pi\) | |||||||
\(812\) | 8496.03 | 0.367183 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −771.146 | −0.0332048 | ||||||||
\(815\) | −12327.5 | −0.529831 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 93.8596 | 0.00401925 | ||||||||
\(818\) | 3139.46 | 0.134192 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9356.73 | 0.398477 | ||||||||
\(821\) | −37909.0 | −1.61149 | −0.805745 | − | 0.592263i | \(-0.798235\pi\) | ||||
−0.805745 | + | 0.592263i | \(0.798235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23636.0 | 1.00109 | 0.500546 | − | 0.865710i | \(-0.333133\pi\) | ||||
0.500546 | + | 0.865710i | \(0.333133\pi\) | |||||||
\(824\) | −32536.0 | −1.37554 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5932.36 | 0.249895 | ||||||||
\(827\) | 42634.3 | 1.79267 | 0.896336 | − | 0.443376i | \(-0.146219\pi\) | ||||
0.896336 | + | 0.443376i | \(0.146219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45152.5 | −1.89169 | −0.945845 | − | 0.324619i | \(-0.894764\pi\) | ||||
−0.945845 | + | 0.324619i | \(0.894764\pi\) | |||||||
\(830\) | 5740.44 | 0.240064 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8217.15 | −0.342402 | ||||||||
\(833\) | −23494.1 | −0.977217 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6271.49 | 0.259921 | ||||||||
\(836\) | 2425.42 | 0.100341 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6925.91 | 0.285503 | ||||||||
\(839\) | −30431.5 | −1.25222 | −0.626110 | − | 0.779734i | \(-0.715354\pi\) | ||||
−0.626110 | + | 0.779734i | \(0.715354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2160.34 | −0.0885784 | ||||||||
\(842\) | −23763.6 | −0.972623 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5818.09 | −0.237283 | ||||||||
\(845\) | −2630.40 | −0.107087 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1239.79 | −0.0502949 | ||||||||
\(848\) | −7311.64 | −0.296088 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3853.46 | −0.155497 | ||||||||
\(851\) | −2769.65 | −0.111566 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10367.2 | 0.416139 | 0.208070 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208070 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(854\) | −11430.5 | −0.458013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16500.8 | 0.658860 | ||||||||
\(857\) | −12947.1 | −0.516063 | −0.258032 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258032 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20383.5 | −0.809636 | −0.404818 | − | 0.914397i | \(-0.632665\pi\) | ||||
−0.404818 | + | 0.914397i | \(0.632665\pi\) | |||||||
\(860\) | 65.8335 | 0.00261035 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8779.22 | −0.346893 | ||||||||
\(863\) | −9056.42 | −0.357224 | −0.178612 | − | 0.983920i | \(-0.557161\pi\) | ||||
−0.178612 | + | 0.983920i | \(0.557161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6033.54 | 0.237164 | ||||||||
\(866\) | 22340.0 | 0.876610 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3119.27 | 0.121976 | ||||||||
\(869\) | 10470.2 | 0.408719 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16554.5 | 0.644005 | ||||||||
\(872\) | −31803.6 | −1.23510 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3819.37 | −0.147817 | ||||||||
\(875\) | −1280.78 | −0.0494836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2867.88 | −0.110424 | −0.0552118 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552118 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(878\) | −6846.16 | −0.263151 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 628.281 | 0.0240674 | ||||||||
\(881\) | 11862.5 | 0.453640 | 0.226820 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226820 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33463.8 | 1.27537 | 0.637683 | − | 0.770299i | \(-0.279893\pi\) | ||||
0.637683 | + | 0.770299i | \(0.279893\pi\) | |||||||
\(884\) | 22440.3 | 0.853787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15756.0 | −0.597442 | ||||||||
\(887\) | −2420.75 | −0.0916357 | −0.0458178 | − | 0.998950i | \(-0.514589\pi\) | ||||
−0.0458178 | + | 0.998950i | \(0.514589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17826.5 | 0.672534 | ||||||||
\(890\) | 3012.85 | 0.113473 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2815.62 | 0.105688 | ||||||||
\(893\) | −13213.8 | −0.495165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7211.44 | 0.269332 | ||||||||
\(896\) | −12132.9 | −0.452378 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14963.6 | 0.556060 | ||||||||
\(899\) | 8161.14 | 0.302769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63179.7 | −2.33609 | ||||||||
\(902\) | 5779.73 | 0.213352 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3600.10 | −0.132453 | ||||||||
\(905\) | 21309.0 | 0.782692 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38154.1 | −1.39679 | −0.698393 | − | 0.715714i | \(-0.746101\pi\) | ||||
−0.698393 | + | 0.715714i | \(0.746101\pi\) | |||||||
\(908\) | −23838.4 | −0.871262 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3270.15 | −0.119126 | ||||||||
\(911\) | 35758.0 | 1.30045 | 0.650227 | − | 0.759740i | \(-0.274674\pi\) | ||||
0.650227 | + | 0.759740i | \(0.274674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8087.44 | −0.293160 | ||||||||
\(914\) | −15614.5 | −0.565079 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31753.0 | −1.14536 | ||||||||
\(917\) | 3205.39 | 0.115432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17387.5 | 0.624115 | 0.312058 | − | 0.950063i | \(-0.398982\pi\) | ||||
0.312058 | + | 0.950063i | \(0.398982\pi\) | |||||||
\(920\) | −6532.41 | −0.234095 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17357.9 | −0.620013 | ||||||||
\(923\) | 38395.3 | 1.36923 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1122.35 | 0.0398947 | ||||||||
\(926\) | 2447.20 | 0.0868467 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27918.3 | −0.987569 | ||||||||
\(929\) | −6955.93 | −0.245658 | −0.122829 | − | 0.992428i | \(-0.539197\pi\) | ||||
−0.122829 | + | 0.992428i | \(0.539197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9436.31 | 0.332183 | ||||||||
\(932\) | 16384.9 | 0.575863 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19751.7 | 0.691965 | ||||||||
\(935\) | 5428.96 | 0.189889 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16074.5 | −0.560438 | −0.280219 | − | 0.959936i | \(-0.590407\pi\) | ||||
−0.280219 | + | 0.959936i | \(0.590407\pi\) | |||||||
\(938\) | −6479.76 | −0.225556 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9268.20 | −0.321591 | ||||||||
\(941\) | 687.126 | 0.0238041 | 0.0119021 | − | 0.999929i | \(-0.496211\pi\) | ||||
0.0119021 | + | 0.999929i | \(0.496211\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20758.5 | 0.716849 | ||||||||
\(944\) | 4235.44 | 0.146030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.6659 | 0.00139763 | ||||||||
\(947\) | −35352.0 | −1.21308 | −0.606540 | − | 0.795053i | \(-0.707443\pi\) | ||||
−0.606540 | + | 0.795053i | \(0.707443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14820.7 | 0.506956 | ||||||||
\(950\) | 1547.73 | 0.0528578 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21418.2 | −0.729168 | ||||||||
\(953\) | 19390.7 | 0.659103 | 0.329552 | − | 0.944138i | \(-0.393102\pi\) | ||||
0.329552 | + | 0.944138i | \(0.393102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4261.12 | 0.144384 | ||||||||
\(956\) | −11561.9 | −0.391148 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16738.7 | −0.564511 | ||||||||
\(959\) | −7345.80 | −0.247349 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26794.7 | −0.899422 | ||||||||
\(962\) | 2865.64 | 0.0960416 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10307.6 | −0.344384 | ||||||||
\(965\) | −12299.8 | −0.410304 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28643.6 | 0.952551 | 0.476275 | − | 0.879296i | \(-0.341987\pi\) | ||||
0.476275 | + | 0.879296i | \(0.341987\pi\) | |||||||
\(968\) | 2562.43 | 0.0850821 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7544.99 | 0.249747 | ||||||||
\(971\) | 19574.8 | 0.646946 | 0.323473 | − | 0.946237i | \(-0.395149\pi\) | ||||
0.323473 | + | 0.946237i | \(0.395149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8980.63 | 0.295895 | ||||||||
\(974\) | −11182.6 | −0.367878 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8160.86 | −0.267646 | ||||||||
\(977\) | −50095.5 | −1.64043 | −0.820213 | − | 0.572058i | \(-0.806145\pi\) | ||||
−0.820213 | + | 0.572058i | \(0.806145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4244.67 | −0.138570 | ||||||||
\(980\) | 6618.67 | 0.215740 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22747.6 | 0.739211 | ||||||||
\(983\) | −14445.4 | −0.468706 | −0.234353 | − | 0.972152i | \(-0.575297\pi\) | ||||
−0.234353 | + | 0.972152i | \(0.575297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17385.3 | −0.562377 | ||||||||
\(986\) | −22980.9 | −0.742253 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9013.05 | −0.290226 | ||||||||
\(989\) | 146.056 | 0.00469595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29120.1 | 0.933430 | 0.466715 | − | 0.884408i | \(-0.345437\pi\) | ||||
0.466715 | + | 0.884408i | \(0.345437\pi\) | |||||||
\(992\) | −10250.1 | −0.328064 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15028.7 | −0.479558 | ||||||||
\(995\) | 19975.2 | 0.636438 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9137.45 | −0.290257 | −0.145128 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145128 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(998\) | 7244.03 | 0.229765 | ||||||||
\(999\) | 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 | 495.4.a.d.1.1 | 2 | ||
3.2 | odd | 2 | 165.4.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 2475.4.a.n.1.2 | 2 | |||
15.2 | even | 4 | 825.4.c.j.199.3 | 4 | |||
15.8 | even | 4 | 825.4.c.j.199.2 | 4 | |||
15.14 | odd | 2 | 825.4.a.m.1.1 | 2 | |||
33.32 | even | 2 | 1815.4.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.c.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
495.4.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
825.4.a.m.1.1 | 2 | 15.14 | odd | 2 | |||
825.4.c.j.199.2 | 4 | 15.8 | even | 4 | |||
825.4.c.j.199.3 | 4 | 15.2 | even | 4 | |||
1815.4.a.n.1.1 | 2 | 33.32 | even | 2 | |||
2475.4.a.n.1.2 | 2 | 5.4 | even | 2 |