Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 28x^{3} - 8x^{2} + 73x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.35870\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.68562 | 1.47910 | 0.739549 | − | 0.673103i | \(-0.235039\pi\) | ||||
0.739549 | + | 0.673103i | \(0.235039\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.2627 | 1.36513 | 0.682567 | − | 0.730823i | \(-0.260864\pi\) | ||||
0.682567 | + | 0.730823i | \(0.260864\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79440 | 0.150883 | 0.0754417 | − | 0.997150i | \(-0.475963\pi\) | ||||
0.0754417 | + | 0.997150i | \(0.475963\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 32.0687 | 1.18773 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.456205 | −0.0125046 | −0.00625232 | − | 0.999980i | \(-0.501990\pi\) | ||||
−0.00625232 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.618515 | 0.0131958 | 0.00659789 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659789 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 117.303 | 2.01916 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.2449 | 0.174696 | 0.0873479 | − | 0.996178i | \(-0.472161\pi\) | ||||
0.0873479 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.4767 | 0.223171 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 116.067 | 1.05224 | 0.526122 | − | 0.850409i | \(-0.323645\pi\) | ||||
0.526122 | + | 0.850409i | \(0.323645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107.949 | 0.863588 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 38.9560 | 0.277670 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −100.701 | −0.644818 | −0.322409 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322409 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 206.884 | 1.19863 | 0.599315 | − | 0.800513i | \(-0.295440\pi\) | ||||
0.599315 | + | 0.800513i | \(0.295440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.50622 | −0.0184956 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.6500 | 0.205976 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 212.785 | 0.945450 | 0.472725 | − | 0.881210i | \(-0.343270\pi\) | ||||
0.472725 | + | 0.881210i | \(0.343270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.75367 | 0.0195179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.1719 | −0.160638 | −0.0803189 | − | 0.996769i | \(-0.525594\pi\) | ||||
−0.0803189 | + | 0.996769i | \(0.525594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.2379 | −0.121424 | −0.0607120 | − | 0.998155i | \(-0.519337\pi\) | ||||
−0.0607120 | + | 0.998155i | \(0.519337\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 489.453 | 1.62141 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 393.638 | 1.22166 | 0.610829 | − | 0.791762i | \(-0.290836\pi\) | ||||
0.610829 | + | 0.791762i | \(0.290836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −335.191 | −0.977234 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 94.1097 | 0.258392 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 497.486 | 1.28934 | 0.644670 | − | 0.764461i | \(-0.276995\pi\) | ||||
0.644670 | + | 0.764461i | \(0.276995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.96291 | −0.0170705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −146.027 | −0.339328 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −82.9196 | −0.182970 | −0.0914849 | − | 0.995806i | \(-0.529161\pi\) | ||||
−0.0914849 | + | 0.995806i | \(0.529161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 655.685 | 1.37626 | 0.688130 | − | 0.725588i | \(-0.258432\pi\) | ||||
0.688130 | + | 0.725588i | \(0.258432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 89.6128 | 0.179209 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.44018 | 0.0180140 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.1809 | −0.160791 | −0.0803956 | − | 0.996763i | \(-0.525618\pi\) | ||||
−0.0803956 | + | 0.996763i | \(0.525618\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 892.045 | 1.55637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −430.377 | −0.719386 | −0.359693 | − | 0.933071i | \(-0.617119\pi\) | ||||
−0.359693 | + | 0.933071i | \(0.617119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.8355 | 0.105554 | 0.0527771 | − | 0.998606i | \(-0.483193\pi\) | ||||
0.0527771 | + | 0.998606i | \(0.483193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 829.651 | 1.27733 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.27482 | −0.00188675 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −528.469 | −0.752626 | −0.376313 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376313 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −566.454 | −0.777029 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 592.763 | 0.783906 | 0.391953 | − | 0.919985i | \(-0.371800\pi\) | ||||
0.391953 | + | 0.919985i | \(0.371800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 186.890 | 0.238483 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −773.950 | −0.953749 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1151.89 | 1.37191 | 0.685955 | − | 0.727644i | \(-0.259385\pi\) | ||||
0.685955 | + | 0.727644i | \(0.259385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72838 | 0.00199103 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1590.03 | 1.77289 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −289.990 | −0.313183 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −51.7168 | −0.0541345 | −0.0270673 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270673 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.6299 | −0.0148521 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1656.63 | −1.63209 | −0.816044 | − | 0.577990i | \(-0.803837\pi\) | ||||
−0.816044 | + | 0.577990i | \(0.803837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −157.395 | −0.150569 | −0.0752843 | − | 0.997162i | \(-0.523986\pi\) | ||||
−0.0752843 | + | 0.997162i | \(0.523986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 327.791 | 0.304659 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 943.505 | 0.852449 | 0.426225 | − | 0.904617i | \(-0.359843\pi\) | ||||
0.426225 | + | 0.904617i | \(0.359843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −978.577 | −0.859915 | −0.429957 | − | 0.902849i | \(-0.641471\pi\) | ||||
−0.429957 | + | 0.902849i | \(0.641471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1635.38 | 1.39841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −979.602 | −0.815515 | −0.407758 | − | 0.913090i | \(-0.633689\pi\) | ||||
−0.407758 | + | 0.913090i | \(0.633689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1771.49 | 1.43645 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.8350 | 0.0156730 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.2172 | 0.0263587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.79 | −0.999844 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −324.117 | −0.237599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −260.251 | −0.186220 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1327.42 | 0.927473 | 0.463737 | − | 0.885973i | \(-0.346508\pi\) | ||||
0.463737 | + | 0.885973i | \(0.346508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −263.139 | −0.179598 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2034.30 | −1.35678 | −0.678388 | − | 0.734704i | \(-0.737321\pi\) | ||||
−0.678388 | + | 0.734704i | \(0.737321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −53.0936 | −0.0346150 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 594.571 | 0.379056 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1715.79 | −1.07000 | −0.535001 | − | 0.844852i | \(-0.679689\pi\) | ||||
−0.535001 | + | 0.844852i | \(0.679689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1762.30 | 1.07537 | 0.537683 | − | 0.843147i | \(-0.319300\pi\) | ||||
0.537683 | + | 0.843147i | \(0.319300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3025.35 | 1.80695 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.282170 | −0.000165009 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1536.97 | −0.880263 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2576.15 | −1.44542 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2065.65 | −1.13574 | −0.567869 | − | 0.823119i | \(-0.692232\pi\) | ||||
−0.567869 | + | 0.823119i | \(0.692232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1177.09 | −0.634372 | −0.317186 | − | 0.948363i | \(-0.602738\pi\) | ||||
−0.317186 | + | 0.948363i | \(0.602738\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 392.678 | 0.207491 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3157.61 | 1.63629 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1802.51 | 0.916279 | 0.458140 | − | 0.888880i | \(-0.348516\pi\) | ||||
0.458140 | + | 0.888880i | \(0.348516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3823.49 | 1.90706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 324.337 | 0.158766 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2084.81 | 1.00181 | 0.500904 | − | 0.865503i | \(-0.333001\pi\) | ||||
0.500904 | + | 0.865503i | \(0.333001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −53.5142 | −0.0252489 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −939.440 | −0.435306 | −0.217653 | − | 0.976026i | \(-0.569840\pi\) | ||||
−0.217653 | + | 0.976026i | \(0.569840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.62 | −0.999826 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −609.305 | −0.272484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 214.271 | 0.0941662 | 0.0470831 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470831 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 301.651 | 0.130301 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −637.288 | −0.270630 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2644.23 | −1.10413 | −0.552064 | − | 0.833802i | \(-0.686160\pi\) | ||||
−0.552064 | + | 0.833802i | \(0.686160\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1405.73 | −0.577278 | −0.288639 | − | 0.957438i | \(-0.593203\pi\) | ||||
−0.288639 | + | 0.957438i | \(0.593203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5039.34 | 2.03562 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3247.66 | 1.29066 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.58620 | −0.00218451 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 108.859 | 0.0418957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −159.777 | −0.0605292 | −0.0302646 | − | 0.999542i | \(-0.509635\pi\) | ||||
−0.0302646 | + | 0.999542i | \(0.509635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1991.99 | −0.742936 | −0.371468 | − | 0.928446i | \(-0.621145\pi\) | ||||
−0.371468 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.5536 | 0.0266445 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3947.92 | −1.42781 | −0.713904 | − | 0.700244i | \(-0.753075\pi\) | ||||
−0.713904 | + | 0.700244i | \(0.753075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5073.60 | 1.80733 | 0.903663 | − | 0.428245i | \(-0.140868\pi\) | ||||
0.903663 | + | 0.428245i | \(0.140868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −677.725 | −0.237826 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −281.399 | −0.0972924 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −643.656 | −0.219292 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3722.11 | 1.24978 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.66790 | 0.00286876 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1782.72 | 0.581646 | 0.290823 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290823 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3307.71 | −1.06404 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −522.561 | −0.165760 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 578.118 | 0.180854 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 505.986 | 0.156125 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.57366 | 0.00230525 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 602.235 | 0.180846 | 0.0904230 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904230 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3461.77 | 1.02571 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3549.26 | 1.03776 | 0.518882 | − | 0.854846i | \(-0.326348\pi\) | ||||
0.518882 | + | 0.854846i | \(0.326348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −664.711 | −0.191814 | −0.0959069 | − | 0.995390i | \(-0.530575\pi\) | ||||
−0.0959069 | + | 0.995390i | \(0.530575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.79779 | −0.00279068 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 597.040 | 0.167869 | 0.0839344 | − | 0.996471i | \(-0.473251\pi\) | ||||
0.0839344 | + | 0.996471i | \(0.473251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6007.96 | 1.66773 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4061.61 | −1.11321 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6306.26 | −1.70677 | −0.853385 | − | 0.521281i | \(-0.825454\pi\) | ||||
−0.853385 | + | 0.521281i | \(0.825454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5991.75 | −1.60150 | −0.800752 | − | 0.598995i | \(-0.795567\pi\) | ||||
−0.800752 | + | 0.598995i | \(0.795567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5405.36 | −1.42697 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5115.91 | −1.33405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.7518 | −0.00302732 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4555.75 | 1.15947 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6010.68 | 1.51152 | 0.755759 | − | 0.654850i | \(-0.227268\pi\) | ||||
0.755759 | + | 0.654850i | \(0.227268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −52.9503 | −0.0131579 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1436.36 | 0.352739 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1646.63 | −0.399664 | −0.199832 | − | 0.979830i | \(-0.564040\pi\) | ||||
−0.199832 | + | 0.979830i | \(0.564040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 594.607 | 0.142653 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3229.35 | −0.765869 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1824.24 | 0.427708 | 0.213854 | − | 0.976866i | \(-0.431398\pi\) | ||||
0.213854 | + | 0.976866i | \(0.431398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7592.96 | 1.76012 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8852.97 | 2.02919 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4156.89 | −0.942193 | −0.471097 | − | 0.882082i | \(-0.656142\pi\) | ||||
−0.471097 | + | 0.882082i | \(0.656142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −790.092 | −0.177102 | −0.0885510 | − | 0.996072i | \(-0.528224\pi\) | ||||
−0.0885510 | + | 0.996072i | \(0.528224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.2837 | 0.00294492 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −49.2467 | −0.0107989 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2474.69 | 0.536785 | 0.268393 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268393 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6634.51 | 1.42365 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5244.82 | 1.11345 | 0.556726 | − | 0.830696i | \(-0.312057\pi\) | ||||
0.556726 | + | 0.830696i | \(0.312057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4045.21 | −0.849691 | −0.424846 | − | 0.905266i | \(-0.639672\pi\) | ||||
−0.424846 | + | 0.905266i | \(0.639672\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2228.75 | −0.463228 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −117.845 | −0.0242376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4763.06 | −0.969481 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −397.476 | −0.0800702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6654.39 | 1.32680 | 0.663402 | − | 0.748264i | \(-0.269112\pi\) | ||||
0.663402 | + | 0.748264i | \(0.269112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1265.57 | −0.249778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.7719 | −0.00347216 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 71.7891 | 0.0138852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −95.6745 | −0.0183209 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12732.2 | −2.41402 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10007.5 | 1.87878 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5788.70 | 1.07615 | 0.538075 | − | 0.842897i | \(-0.319152\pi\) | ||||
0.538075 | + | 0.842897i | \(0.319152\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1209.68 | −0.222706 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7503.90 | 1.36819 | 0.684095 | − | 0.729393i | \(-0.260197\pi\) | ||||
0.684095 | + | 0.729393i | \(0.260197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10133.5 | 1.82997 | 0.914983 | − | 0.403492i | \(-0.132204\pi\) | ||||
0.914983 | + | 0.403492i | \(0.132204\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1367.73 | 0.244644 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8752.21 | 1.55070 | 0.775352 | − | 0.631529i | \(-0.217572\pi\) | ||||
0.775352 | + | 0.631529i | \(0.217572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.9404 | 0.00806322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7251.41 | 1.26086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −232.653 | −0.0400779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 66.7678 | 0.0113957 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7520.97 | −1.27190 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1099.98 | 0.184328 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6268.49 | 1.04093 | 0.520464 | − | 0.853883i | \(-0.325759\pi\) | ||||
0.520464 | + | 0.853883i | \(0.325759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6823.74 | 1.12294 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1345.87 | −0.219501 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8373.12 | −1.35345 | −0.676725 | − | 0.736236i | \(-0.736602\pi\) | ||||
−0.676725 | + | 0.736236i | \(0.736602\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7528.85 | −1.20623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −94.3818 | −0.0149885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1895.14 | −0.298332 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13615.0 | 2.12465 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3172.02 | −0.490729 | −0.245365 | − | 0.969431i | \(-0.578908\pi\) | ||||
−0.245365 | + | 0.969431i | \(0.578908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7706.05 | −1.18194 | −0.590968 | − | 0.806695i | \(-0.701254\pi\) | ||||
−0.590968 | + | 0.806695i | \(0.701254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0948 | 0.00366407 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9170.03 | −1.38264 | −0.691319 | − | 0.722550i | \(-0.742970\pi\) | ||||
−0.691319 | + | 0.722550i | \(0.742970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6568.70 | −0.982057 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 262.980 | 0.0389871 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3545.04 | −0.521171 | −0.260585 | − | 0.965451i | \(-0.583916\pi\) | ||||
−0.260585 | + | 0.965451i | \(0.583916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10228.0 | −1.47887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1004.82 | 0.144096 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10096.4 | −1.43604 | −0.718021 | − | 0.696021i | \(-0.754952\pi\) | ||||
−0.718021 | + | 0.696021i | \(0.754952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1352.40 | −0.190794 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1390.18 | 0.194540 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8445.91 | 1.17242 | 0.586210 | − | 0.810159i | \(-0.300619\pi\) | ||||
0.586210 | + | 0.810159i | \(0.300619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2000.19 | −0.275438 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −62.2852 | −0.00850888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4057.60 | −0.549933 | −0.274967 | − | 0.961454i | \(-0.588667\pi\) | ||||
−0.274967 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10202.0 | 1.37182 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1348.64 | −0.179927 | −0.0899637 | − | 0.995945i | \(-0.528675\pi\) | ||||
−0.0899637 | + | 0.995945i | \(0.528675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.4572 | −0.00257566 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1097.96 | −0.144219 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1764.98 | −0.230047 | −0.115024 | − | 0.993363i | \(-0.536694\pi\) | ||||
−0.115024 | + | 0.993363i | \(0.536694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1421.23 | 0.183823 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15634.9 | −2.00680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8065.85 | −1.02743 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1813.78 | −0.229297 | −0.114648 | − | 0.993406i | \(-0.536574\pi\) | ||||
−0.114648 | + | 0.993406i | \(0.536574\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −408.057 | −0.0511990 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1987.91 | 0.247560 | 0.123780 | − | 0.992310i | \(-0.460498\pi\) | ||||
0.123780 | + | 0.992310i | \(0.460498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 127.961 | 0.0158169 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8645.59 | −1.06075 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −97.0737 | −0.0118225 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9369.41 | −1.13273 | −0.566366 | − | 0.824154i | \(-0.691651\pi\) | ||||
−0.566366 | + | 0.824154i | \(0.691651\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13186.9 | −1.58264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −231.711 | −0.0276071 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9047.14 | 1.07014 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13544.3 | 1.59057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3469.26 | 0.404497 | 0.202249 | − | 0.979334i | \(-0.435175\pi\) | ||||
0.202249 | + | 0.979334i | \(0.435175\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6978.44 | 0.807858 | 0.403929 | − | 0.914790i | \(-0.367644\pi\) | ||||
0.403929 | + | 0.914790i | \(0.367644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12623.4 | 1.45100 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1321.82 | 0.150865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1832.25 | 0.207655 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.16865 | −0.000244064 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 141.266 | 0.0157878 | 0.00789391 | − | 0.999969i | \(-0.497487\pi\) | ||||
0.00789391 | + | 0.999969i | \(0.497487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4320.19 | 0.479480 | 0.239740 | − | 0.970837i | \(-0.422938\pi\) | ||||
0.239740 | + | 0.970837i | \(0.422938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11812.5 | −1.30199 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2205.27 | −0.241401 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14353.3 | 1.56047 | 0.780234 | − | 0.625488i | \(-0.215100\pi\) | ||||
0.780234 | + | 0.625488i | \(0.215100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10749.1 | −1.16069 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10320.9 | −1.10691 | −0.553453 | − | 0.832881i | \(-0.686690\pi\) | ||||
−0.553453 | + | 0.832881i | \(0.686690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17580.9 | 1.87284 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15875.8 | −1.67987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15853.2 | −1.66628 | −0.833140 | − | 0.553062i | \(-0.813459\pi\) | ||||
−0.833140 | + | 0.553062i | \(0.813459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.2391 | 0.00200872 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9046.65 | −0.938298 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.3797 | 0.00271802 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6963.89 | 0.712816 | 0.356408 | − | 0.934330i | \(-0.384001\pi\) | ||||
0.356408 | + | 0.934330i | \(0.384001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 477.012 | 0.0485077 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9994.12 | −1.00970 | −0.504851 | − | 0.863207i | \(-0.668453\pi\) | ||||
−0.504851 | + | 0.863207i | \(0.668453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3474.18 | −0.348723 | −0.174362 | − | 0.984682i | \(-0.555786\pi\) | ||||
−0.174362 | + | 0.984682i | \(0.555786\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24268.1 | 2.42023 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6248.92 | 0.619199 | 0.309599 | − | 0.950867i | \(-0.399805\pi\) | ||||
0.309599 | + | 0.950867i | \(0.399805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −246.413 | −0.0242607 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13853.4 | 1.35527 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.6195 | 0.00151836 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2051.02 | −0.198121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15953.7 | 1.53139 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6277.23 | −0.598777 | −0.299388 | − | 0.954131i | \(-0.596783\pi\) | ||||
−0.299388 | + | 0.954131i | \(0.596783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 131.611 | 0.0124760 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2492.73 | 0.234831 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −789.336 | −0.0739008 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7311.96 | −0.680363 | −0.340181 | − | 0.940360i | \(-0.610488\pi\) | ||||
−0.340181 | + | 0.940360i | \(0.610488\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16023.0 | 1.48177 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17240.0 | 1.58458 | 0.792289 | − | 0.610145i | \(-0.208889\pi\) | ||||
0.792289 | + | 0.610145i | \(0.208889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1233.08 | −0.112647 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −223.291 | −0.0202751 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1202.65 | −0.108543 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 843.857 | 0.0757039 | 0.0378519 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378519 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7220.18 | −0.643860 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18235.7 | −1.61648 | −0.808242 | − | 0.588850i | \(-0.799581\pi\) | ||||
−0.808242 | + | 0.588850i | \(0.799581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25284.6 | −2.22802 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16882.4 | −1.47884 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4978.87 | 0.433565 | 0.216783 | − | 0.976220i | \(-0.430444\pi\) | ||||
0.216783 | + | 0.976220i | \(0.430444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 183.971 | 0.0159264 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −740.163 | −0.0637018 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2402.26 | −0.205546 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −179.580 | −0.0152764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1646.81 | 0.139281 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9413.57 | −0.791585 | −0.395793 | − | 0.918340i | \(-0.629530\pi\) | ||||
−0.395793 | + | 0.918340i | \(0.629530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18142.6 | 1.51687 | 0.758434 | − | 0.651750i | \(-0.225965\pi\) | ||||
0.758434 | + | 0.651750i | \(0.225965\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2318.38 | 0.192728 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2533.28 | 0.209396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1304.52 | 0.107218 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2659.12 | −0.217319 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0840 | −0.00211974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14400.4 | 1.16371 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20322.5 | −1.63311 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 152.916 | 0.0122200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7901.85 | −0.627961 | −0.313981 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313981 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10803.9 | −0.853850 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14935.7 | −1.17390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12821.6 | 1.00222 | 0.501109 | − | 0.865384i | \(-0.332926\pi\) | ||||
0.501109 | + | 0.865384i | \(0.332926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21026.9 | 1.63462 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1913.32 | 0.147931 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1476.76 | −0.113559 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24960.3 | 1.90902 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14141.8 | −1.07577 | −0.537886 | − | 0.843017i | \(-0.680777\pi\) | ||||
−0.537886 | + | 0.843017i | \(0.680777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.1767 | −0.00160229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.9334 | −0.00323110 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20912.4 | −1.56546 | −0.782729 | − | 0.622363i | \(-0.786173\pi\) | ||||
−0.782729 | + | 0.622363i | \(0.786173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14951.3 | −1.11329 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1582.90 | −0.117241 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20364.1 | −1.50036 | −0.750181 | − | 0.661232i | \(-0.770034\pi\) | ||||
−0.750181 | + | 0.661232i | \(0.770034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14151.3 | −1.03715 | −0.518575 | − | 0.855032i | \(-0.673537\pi\) | ||||
−0.518575 | + | 0.855032i | \(0.673537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1227.99 | −0.0895285 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12529.2 | 0.908706 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22908.6 | −1.65285 | −0.826427 | − | 0.563044i | \(-0.809630\pi\) | ||||
−0.826427 | + | 0.563044i | \(0.809630\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15309.7 | −1.09887 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1656.42 | 0.118278 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −226.956 | −0.0161227 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 302.734 | 0.0213958 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22949.0 | 1.61364 | 0.806819 | − | 0.590798i | \(-0.201187\pi\) | ||||
0.806819 | + | 0.590798i | \(0.201187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3930.80 | −0.274985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30342.2 | −2.11187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17528.1 | −1.21381 | −0.606907 | − | 0.794773i | \(-0.707590\pi\) | ||||
−0.606907 | + | 0.794773i | \(0.707590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 522.245 | 0.0359831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38993.7 | 2.67321 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8232.99 | −0.561587 | −0.280794 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280794 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25516.6 | −1.73185 | −0.865927 | − | 0.500170i | \(-0.833271\pi\) | ||||
−0.865927 | + | 0.500170i | \(0.833271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2827.85 | −0.190976 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20311.4 | −1.36492 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28319.1 | −1.89363 | −0.946816 | − | 0.321775i | \(-0.895721\pi\) | ||||
−0.946816 | + | 0.321775i | \(0.895721\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2162.73 | −0.143905 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 243.471 | 0.0161207 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22313.5 | 1.47020 | 0.735100 | − | 0.677959i | \(-0.237135\pi\) | ||||
0.735100 | + | 0.677959i | \(0.237135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4946.89 | −0.324354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4432.54 | 0.289218 | 0.144609 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144609 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24084.8 | −1.56390 | −0.781948 | − | 0.623344i | \(-0.785774\pi\) | ||||
−0.781948 | + | 0.623344i | \(0.785774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4521.50 | 0.292176 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3218.84 | 0.206998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17465.7 | −1.11780 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 66.6182 | 0.00424318 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2605.53 | 0.165166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16357.1 | −1.03196 | −0.515979 | − | 0.856601i | \(-0.672572\pi\) | ||||
−0.515979 | + | 0.856601i | \(0.672572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13701.3 | 0.860311 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20259.9 | 1.26612 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −207.321 | −0.0128954 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13801.6 | −0.854436 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9044.36 | 0.557302 | 0.278651 | − | 0.960392i | \(-0.410113\pi\) | ||||
0.278651 | + | 0.960392i | \(0.410113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0941 | −0.000987073 0 | −0.000493537 | − | 1.00000i | \(-0.500157\pi\) | ||||
−0.000493537 | 1.00000i | \(0.500157\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4016.21 | −0.245175 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5673.50 | 0.344743 | 0.172371 | − | 0.985032i | \(-0.444857\pi\) | ||||
0.172371 | + | 0.985032i | \(0.444857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.8284 | 0.00228797 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4443.19 | 0.267500 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24349.4 | −1.45921 | −0.729605 | − | 0.683869i | \(-0.760296\pi\) | ||||
−0.729605 | + | 0.683869i | \(0.760296\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31048.8 | −1.85218 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2111.26 | 0.125370 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19990.2 | −1.18165 | −0.590825 | − | 0.806800i | \(-0.701198\pi\) | ||||
−0.590825 | + | 0.806800i | \(0.701198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7138.48 | −0.420052 | −0.210026 | − | 0.977696i | \(-0.567355\pi\) | ||||
−0.210026 | + | 0.977696i | \(0.567355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 58.2083 | 0.00340969 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −810.349 | −0.0472541 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11688.1 | −0.678506 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4628.55 | 0.267489 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −299.127 | −0.0172096 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 331.701 | 0.0189987 | 0.00949936 | − | 0.999955i | \(-0.496976\pi\) | ||||
0.00949936 | + | 0.999955i | \(0.496976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4205.24 | 0.239792 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23542.7 | 1.33651 | 0.668257 | − | 0.743930i | \(-0.267041\pi\) | ||||
0.668257 | + | 0.743930i | \(0.267041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −144.518 | −0.00816801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27278.2 | 1.53495 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20417.1 | −1.14383 | −0.571917 | − | 0.820312i | \(-0.693800\pi\) | ||||
−0.571917 | + | 0.820312i | \(0.693800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26187.6 | −1.46069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5108.71 | −0.283711 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 307.703 | 0.0170138 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15846.0 | −0.872372 | −0.436186 | − | 0.899857i | \(-0.643671\pi\) | ||||
−0.436186 | + | 0.899857i | \(0.643671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.8818 | −0.00224094 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26897.3 | 1.46802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −516.392 | −0.0280627 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4588.62 | 0.248294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16511.6 | 0.889636 | 0.444818 | − | 0.895621i | \(-0.353268\pi\) | ||||
0.444818 | + | 0.895621i | \(0.353268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4042.92 | −0.216901 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46174.8 | 2.46673 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4629.29 | −0.246255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5585.31 | −0.295854 | −0.147927 | − | 0.988998i | \(-0.547260\pi\) | ||||
−0.147927 | + | 0.988998i | \(0.547260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16947.3 | −0.893916 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24012.4 | 1.26125 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.30666 | −0.000225259 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48467.5 | −2.52448 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19604.0 | 1.01684 | 0.508418 | − | 0.861110i | \(-0.330230\pi\) | ||||
0.508418 | + | 0.861110i | \(0.330230\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −439.824 | −0.0227183 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46050.3 | −2.36878 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10870.5 | −0.556857 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19691.4 | 1.00456 | 0.502279 | − | 0.864706i | \(-0.332495\pi\) | ||||
0.502279 | + | 0.864706i | \(0.332495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26249.2 | −1.33360 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −419.240 | −0.0212123 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20622.2 | 1.03915 | 0.519576 | − | 0.854424i | \(-0.326090\pi\) | ||||
0.519576 | + | 0.854424i | \(0.326090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −39318.9 | −1.97320 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.2286 | 0.00201064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29541.2 | −1.47049 | −0.735243 | − | 0.677804i | \(-0.762932\pi\) | ||||
−0.735243 | + | 0.677804i | \(0.762932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −90.3197 | −0.00447770 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10131.7 | 0.500263 | 0.250132 | − | 0.968212i | \(-0.419526\pi\) | ||||
0.250132 | + | 0.968212i | \(0.419526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31527.4 | −1.55043 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19009.1 | 0.931068 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2636.53 | 0.128620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31366.0 | 1.52405 | 0.762025 | − | 0.647547i | \(-0.224205\pi\) | ||||
0.762025 | + | 0.647547i | \(0.224205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46195.8 | 2.23568 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17965.5 | −0.866002 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2836.37 | 0.136182 | 0.0680909 | − | 0.997679i | \(-0.478309\pi\) | ||||
0.0680909 | + | 0.997679i | \(0.478309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −406.956 | −0.0194619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33195.4 | 1.58125 | 0.790626 | − | 0.612300i | \(-0.209755\pi\) | ||||
0.790626 | + | 0.612300i | \(0.209755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2734.54 | −0.129747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5993.31 | 0.283253 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −51.2870 | −0.00241443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −378.413 | −0.0177450 | −0.00887252 | − | 0.999961i | \(-0.502824\pi\) | ||||
−0.00887252 | + | 0.999961i | \(0.502824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12655.3 | −0.591142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9764.06 | −0.454319 | −0.227160 | − | 0.973858i | \(-0.572944\pi\) | ||||
−0.227160 | + | 0.973858i | \(0.572944\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22332.9 | 1.03512 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4569.92 | 0.210997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 801.267 | 0.0368528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 196.341 | 0.00899567 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3922.91 | −0.179046 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27511.1 | 1.25084 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11958.2 | 0.541631 | 0.270816 | − | 0.962631i | \(-0.412707\pi\) | ||||
0.270816 | + | 0.962631i | \(0.412707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14020.4 | 0.632622 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2737.40 | −0.123048 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 405.551 | 0.0181608 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 58356.6 | 2.60339 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14502.1 | −0.644529 | −0.322264 | − | 0.946650i | \(-0.604444\pi\) | ||||
−0.322264 | + | 0.946650i | \(0.604444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4820.06 | 0.213419 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36939.5 | 1.62946 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.0345 | −0.00131992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4950.25 | 0.216737 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31948.3 | −1.39360 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23743.3 | −1.03185 | −0.515926 | − | 0.856633i | \(-0.672552\pi\) | ||||
−0.515926 | + | 0.856633i | \(0.672552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1788.53 | −0.0774398 | −0.0387199 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387199 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6072.34 | −0.261951 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31819.7 | 1.36760 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 650.520 | 0.0278566 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 55.4269 | 0.00236480 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16960.6 | −0.720987 | −0.360493 | − | 0.932762i | \(-0.617392\pi\) | ||||
−0.360493 | + | 0.932762i | \(0.617392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9066.84 | 0.384022 | 0.192011 | − | 0.981393i | \(-0.438499\pi\) | ||||
0.192011 | + | 0.981393i | \(0.438499\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −378.491 | −0.0159726 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31217.7 | 1.31263 | 0.656315 | − | 0.754487i | \(-0.272114\pi\) | ||||
0.656315 | + | 0.754487i | \(0.272114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33513.6 | 1.40407 | 0.702035 | − | 0.712142i | \(-0.252275\pi\) | ||||
0.702035 | + | 0.712142i | \(0.252275\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19019.5 | 0.793958 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4104.39 | −0.170719 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14338.3 | −0.594250 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8059.38 | 0.332823 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46369.9 | 1.90807 | 0.954033 | − | 0.299703i | \(-0.0968875\pi\) | ||||
0.954033 | + | 0.299703i | \(0.0968875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14248.3 | −0.584210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 40309.7 | 1.64690 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33526.2 | −1.36490 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3718.77 | −0.150860 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31089.9 | −1.25678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24697.3 | 0.994844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 217.304 | 0.00872257 | 0.00436129 | − | 0.999990i | \(-0.498612\pi\) | ||||
0.00436129 | + | 0.999990i | \(0.498612\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9299.61 | −0.371977 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27096.2 | 1.08003 | 0.540016 | − | 0.841654i | \(-0.318418\pi\) | ||||
0.540016 | + | 0.841654i | \(0.318418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11922.6 | −0.473565 | −0.236783 | − | 0.971563i | \(-0.576093\pi\) | ||||
−0.236783 | + | 0.971563i | \(0.576093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −905.714 | −0.0358498 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7376.00 | 0.290941 | 0.145471 | − | 0.989363i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989363i | \(0.453530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3270.35 | 0.128549 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36607.1 | −1.43396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 241.091 | 0.00941132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.5412 | −0.00212177 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1658.49 | −0.0642971 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −727.245 | −0.0280976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50755.4 | 1.95426 | 0.977131 | − | 0.212637i | \(-0.0682052\pi\) | ||||
0.977131 | + | 0.212637i | \(0.0682052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51143.0 | 1.96247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28803.5 | 1.10149 | 0.550746 | − | 0.834673i | \(-0.314343\pi\) | ||||
0.550746 | + | 0.834673i | \(0.314343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51864.4 | −1.97664 | −0.988322 | − | 0.152381i | \(-0.951306\pi\) | ||||
−0.988322 | + | 0.152381i | \(0.951306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9726.71 | −0.369446 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14211.4 | −0.537962 | −0.268981 | − | 0.963145i | \(-0.586687\pi\) | ||||
−0.268981 | + | 0.963145i | \(0.586687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3709.33 | 0.139940 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 258.419 | 0.00971647 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7479.12 | −0.280268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40357.9 | −1.50728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 551.743 | 0.0205375 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20833.5 | −0.772899 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6091.68 | 0.225242 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −735.317 | −0.0270984 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21455.2 | −0.788061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2766.42 | 0.101276 | 0.0506381 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506381 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −53126.0 | −1.93848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1282.52 | 0.0466430 | 0.0233215 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233215 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −270.422 | −0.00980247 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 76913.7 | 2.77889 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5684.65 | −0.204715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31183.4 | 1.11931 | 0.559655 | − | 0.828725i | \(-0.310934\pi\) | ||||
0.559655 | + | 0.828725i | \(0.310934\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44489.7 | 1.59173 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −266.195 | −0.00949286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22969.8 | 0.816479 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5047.44 | −0.178835 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35037.3 | 1.23739 | 0.618696 | − | 0.785630i | \(-0.287661\pi\) | ||||
0.618696 | + | 0.785630i | \(0.287661\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6368.64 | 0.224193 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57672.1 | 2.02369 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −85.2602 | −0.00298214 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12969.3 | 0.452175 | 0.226087 | − | 0.974107i | \(-0.427407\pi\) | ||||
0.226087 | + | 0.974107i | \(0.427407\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 77882.2 | 2.70670 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11958.5 | −0.414279 | −0.207140 | − | 0.978311i | \(-0.566415\pi\) | ||||
−0.207140 | + | 0.978311i | \(0.566415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4894.76 | −0.169030 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1661.47 | 0.0571933 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39481.6 | 1.35478 | 0.677392 | − | 0.735622i | \(-0.263110\pi\) | ||||
0.677392 | + | 0.735622i | \(0.263110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.7202 | 0.00139287 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 67266.1 | 2.29364 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31129.5 | 1.05811 | 0.529057 | − | 0.848586i | \(-0.322546\pi\) | ||||
0.529057 | + | 0.848586i | \(0.322546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2438.62 | −0.0826303 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 353.080 | 0.0119263 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4794.62 | −0.161446 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13010.2 | 0.436715 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30257.0 | 1.01248 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30403.1 | −1.01421 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25627.5 | −0.852250 | −0.426125 | − | 0.904664i | \(-0.640122\pi\) | ||||
−0.426125 | + | 0.904664i | \(0.640122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1788.08 | −0.0592792 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18600.8 | 0.614756 | 0.307378 | − | 0.951587i | \(-0.400548\pi\) | ||||
0.307378 | + | 0.951587i | \(0.400548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4924.56 | 0.162255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 513.151 | 0.0168554 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14081.2 | 0.461103 | 0.230552 | − | 0.973060i | \(-0.425947\pi\) | ||||
0.230552 | + | 0.973060i | \(0.425947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −525.498 | −0.0171552 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31381.7 | −1.02135 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13359.2 | 0.433462 | 0.216731 | − | 0.976231i | \(-0.430460\pi\) | ||||
0.216731 | + | 0.976231i | \(0.430460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60255.8 | −1.94915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8454.04 | 0.272639 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3973.89 | −0.127768 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52748.2 | −1.69082 | −0.845409 | − | 0.534119i | \(-0.820643\pi\) | ||||
−0.845409 | + | 0.534119i | \(0.820643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48177.2 | 1.53963 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77436.5 | 2.46724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6334.73 | 0.201226 | 0.100613 | − | 0.994926i | \(-0.467920\pi\) | ||||
0.100613 | + | 0.994926i | \(0.467920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8289.24 | 0.262523 |
(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 | 1216.4.a.bd.1.5 | 5 | ||
4.3 | odd | 2 | 1216.4.a.y.1.1 | 5 | |||
8.3 | odd | 2 | 608.4.a.h.1.5 | yes | 5 | ||
8.5 | even | 2 | 608.4.a.e.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.e.1.1 | ✓ | 5 | 8.5 | even | 2 | ||
608.4.a.h.1.5 | yes | 5 | 8.3 | odd | 2 | ||
1216.4.a.y.1.1 | 5 | 4.3 | odd | 2 | |||
1216.4.a.bd.1.5 | 5 | 1.1 | even | 1 | trivial |