Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6900,2,Mod(1,6900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6900.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: | \(55.0967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6900.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.79129 | 1.43297 | 0.716486 | − | 0.697601i | \(-0.245749\pi\) | ||||
0.716486 | + | 0.697601i | \(0.245749\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79129 | −0.540094 | −0.270047 | − | 0.962847i | \(-0.587039\pi\) | ||||
−0.270047 | + | 0.962847i | \(0.587039\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.20871 | 0.612587 | 0.306293 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306293 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.58258 | −1.11144 | −0.555719 | − | 0.831370i | \(-0.687557\pi\) | ||||
−0.555719 | + | 0.831370i | \(0.687557\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.58258 | 1.28073 | 0.640365 | − | 0.768070i | \(-0.278783\pi\) | ||||
0.640365 | + | 0.768070i | \(0.278783\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.79129 | −0.827327 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.58258 | −0.293877 | −0.146938 | − | 0.989146i | \(-0.546942\pi\) | ||||
−0.146938 | + | 0.989146i | \(0.546942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79129 | 0.321725 | 0.160862 | − | 0.986977i | \(-0.448572\pi\) | ||||
0.160862 | + | 0.986977i | \(0.448572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.79129 | 0.311823 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.20871 | −0.353677 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.582576 | −0.0909830 | −0.0454915 | − | 0.998965i | \(-0.514485\pi\) | ||||
−0.0454915 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.58258 | 1.00383 | 0.501917 | − | 0.864916i | \(-0.332628\pi\) | ||||
0.501917 | + | 0.864916i | \(0.332628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | −0.0729325 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729325 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.37386 | 1.05341 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58258 | 0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.20871 | 0.578111 | 0.289056 | − | 0.957312i | \(-0.406659\pi\) | ||||
0.289056 | + | 0.957312i | \(0.406659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.58258 | −0.739430 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.79129 | −0.493584 | −0.246792 | − | 0.969069i | \(-0.579376\pi\) | ||||
−0.246792 | + | 0.969069i | \(0.579376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.37386 | −0.175905 | −0.0879526 | − | 0.996125i | \(-0.528032\pi\) | ||||
−0.0879526 | + | 0.996125i | \(0.528032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.79129 | 0.477657 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.20871 | 0.147668 | 0.0738338 | − | 0.997271i | \(-0.476477\pi\) | ||||
0.0738338 | + | 0.997271i | \(0.476477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.95644 | 1.06293 | 0.531467 | − | 0.847079i | \(-0.321641\pi\) | ||||
0.531467 | + | 0.847079i | \(0.321641\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0000 | 1.52153 | 0.760767 | − | 0.649025i | \(-0.224823\pi\) | ||||
0.760767 | + | 0.649025i | \(0.224823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.79129 | −0.773939 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.41742 | −0.159473 | −0.0797363 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797363 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | 0.109764 | 0.0548821 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548821 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.58258 | 0.169670 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.00000 | −0.529999 | −0.264999 | − | 0.964249i | \(-0.585372\pi\) | ||||
−0.264999 | + | 0.964249i | \(0.585372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.37386 | 0.877819 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.79129 | −0.185748 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.62614 | −0.469713 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.79129 | −0.180031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.62614 | −0.360814 | −0.180407 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180407 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.41742 | 0.829393 | 0.414697 | − | 0.909960i | \(-0.363888\pi\) | ||||
0.414697 | + | 0.909960i | \(0.363888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.16515 | −0.789355 | −0.394677 | − | 0.918820i | \(-0.629144\pi\) | ||||
−0.394677 | + | 0.918820i | \(0.629144\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.74773 | 0.933663 | 0.466831 | − | 0.884346i | \(-0.345395\pi\) | ||||
0.466831 | + | 0.884346i | \(0.345395\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9564 | 1.12477 | 0.562384 | − | 0.826876i | \(-0.309884\pi\) | ||||
0.562384 | + | 0.826876i | \(0.309884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.20871 | 0.204196 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.3739 | −1.59266 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.79129 | −0.708299 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.582576 | 0.0525291 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.58258 | −0.579563 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.16515 | 0.713393 | 0.356696 | − | 0.934220i | \(-0.383903\pi\) | ||||
0.356696 | + | 0.934220i | \(0.383903\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.1652 | 1.83525 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9564 | −1.09895 | −0.549475 | − | 0.835510i | \(-0.685172\pi\) | ||||
−0.549475 | + | 0.835510i | \(0.685172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.95644 | −0.330854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.37386 | −0.608186 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5826 | −1.03080 | −0.515402 | − | 0.856948i | \(-0.672358\pi\) | ||||
−0.515402 | + | 0.856948i | \(0.672358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.582576 | −0.0474093 | −0.0237047 | − | 0.999719i | \(-0.507546\pi\) | ||||
−0.0237047 | + | 0.999719i | \(0.507546\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.58258 | −0.370479 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.16515 | 0.252607 | 0.126303 | − | 0.991992i | \(-0.459689\pi\) | ||||
0.126303 | + | 0.991992i | \(0.459689\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.20871 | −0.333773 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.79129 | −0.298795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7477 | −0.920153 | −0.460077 | − | 0.887879i | \(-0.652178\pi\) | ||||
−0.460077 | + | 0.887879i | \(0.652178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.1216 | 1.78920 | 0.894601 | − | 0.446865i | \(-0.147460\pi\) | ||||
0.894601 | + | 0.446865i | \(0.147460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.12159 | −0.624738 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.58258 | 0.426910 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.626136 | 0.0476043 | 0.0238021 | − | 0.999717i | \(-0.492423\pi\) | ||||
0.0238021 | + | 0.999717i | \(0.492423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79129 | 0.284971 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.53901 | 0.638236 | 0.319118 | − | 0.947715i | \(-0.396613\pi\) | ||||
0.319118 | + | 0.947715i | \(0.396613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7477 | −1.24485 | −0.622424 | − | 0.782680i | \(-0.713852\pi\) | ||||
−0.622424 | + | 0.782680i | \(0.713852\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.37386 | 0.101559 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.20871 | 0.600280 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.79129 | −0.275776 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.16515 | −0.156665 | −0.0783324 | − | 0.996927i | \(-0.524960\pi\) | ||||
−0.0783324 | + | 0.996927i | \(0.524960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1652 | 1.45152 | 0.725760 | − | 0.687948i | \(-0.241488\pi\) | ||||
0.725760 | + | 0.687948i | \(0.241488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7477 | 1.47821 | 0.739107 | − | 0.673588i | \(-0.235248\pi\) | ||||
0.739107 | + | 0.673588i | \(0.235248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.58258 | −0.537515 | −0.268757 | − | 0.963208i | \(-0.586613\pi\) | ||||
−0.268757 | + | 0.963208i | \(0.586613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.20871 | −0.0852560 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | −0.421117 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.74773 | −0.464533 | −0.232266 | − | 0.972652i | \(-0.574614\pi\) | ||||
−0.232266 | + | 0.972652i | \(0.574614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.95644 | −0.613685 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.79129 | 0.461023 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.0000 | −0.878459 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1216 | −0.680852 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62614 | −0.108894 | −0.0544471 | − | 0.998517i | \(-0.517340\pi\) | ||||
−0.0544471 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.582576 | −0.0386669 | −0.0193335 | − | 0.999813i | \(-0.506154\pi\) | ||||
−0.0193335 | + | 0.999813i | \(0.506154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.79129 | 0.446834 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.7913 | 1.16555 | 0.582773 | − | 0.812635i | \(-0.301968\pi\) | ||||
0.582773 | + | 0.812635i | \(0.301968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.41742 | 0.0920716 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.5826 | −1.78417 | −0.892084 | − | 0.451869i | \(-0.850757\pi\) | ||||
−0.892084 | + | 0.451869i | \(0.850757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3739 | 1.05473 | 0.527367 | − | 0.849638i | \(-0.323179\pi\) | ||||
0.527367 | + | 0.849638i | \(0.323179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3303 | 0.784558 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.00000 | −0.0633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.2087 | 1.27556 | 0.637781 | − | 0.770218i | \(-0.279852\pi\) | ||||
0.637781 | + | 0.770218i | \(0.279852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.79129 | 0.112617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.20871 | 0.324911 | 0.162455 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162455 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3739 | 0.706737 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.58258 | −0.0979590 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.53901 | −0.218225 | −0.109113 | − | 0.994029i | \(-0.534801\pi\) | ||||
−0.109113 | + | 0.994029i | \(0.534801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00000 | 0.305995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.747727 | −0.0455897 | −0.0227949 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227949 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1652 | 0.617489 | 0.308744 | − | 0.951145i | \(-0.400091\pi\) | ||||
0.308744 | + | 0.951145i | \(0.400091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.37386 | −0.506809 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.791288 | −0.0475439 | −0.0237719 | − | 0.999717i | \(-0.507568\pi\) | ||||
−0.0237719 | + | 0.999717i | \(0.507568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.79129 | 0.107242 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1652 | 0.725712 | 0.362856 | − | 0.931845i | \(-0.381802\pi\) | ||||
0.362856 | + | 0.931845i | \(0.381802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.58258 | −0.153518 | −0.0767591 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767591 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.20871 | −0.130376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | 0.235294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.62614 | 0.271189 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1652 | 0.827537 | 0.413768 | − | 0.910382i | \(-0.364212\pi\) | ||||
0.413768 | + | 0.910382i | \(0.364212\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.79129 | 0.103941 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.20871 | −0.127733 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.9564 | 1.43847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.62614 | 0.208316 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.3303 | −1.38860 | −0.694302 | − | 0.719684i | \(-0.744287\pi\) | ||||
−0.694302 | + | 0.719684i | \(0.744287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.41742 | −0.478851 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.16515 | −0.122774 | −0.0613872 | − | 0.998114i | \(-0.519552\pi\) | ||||
−0.0613872 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.5826 | 1.38949 | 0.694745 | − | 0.719256i | \(-0.255517\pi\) | ||||
0.694745 | + | 0.719256i | \(0.255517\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.7913 | 1.89791 | 0.948954 | − | 0.315415i | \(-0.102144\pi\) | ||||
0.948954 | + | 0.315415i | \(0.102144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.83485 | 0.158721 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.16515 | 0.455734 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.5826 | −1.42345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.74773 | −0.539051 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.79129 | −0.209020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.53901 | −0.414382 | −0.207191 | − | 0.978301i | \(-0.566432\pi\) | ||||
−0.207191 | + | 0.978301i | \(0.566432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | 0.164399 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9129 | −0.812356 | −0.406178 | − | 0.913794i | \(-0.633139\pi\) | ||||
−0.406178 | + | 0.913794i | \(0.633139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9564 | −0.649385 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.20871 | −0.173762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.41742 | 0.0765337 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00000 | −0.107366 | −0.0536828 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536828 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5826 | −0.780587 | −0.390294 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390294 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.20871 | −0.117892 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.95644 | 0.370254 | 0.185127 | − | 0.982715i | \(-0.440730\pi\) | ||||
0.185127 | + | 0.982715i | \(0.440730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.3739 | 0.919522 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.74773 | 0.303353 | 0.151677 | − | 0.988430i | \(-0.451533\pi\) | ||||
0.151677 | + | 0.988430i | \(0.451533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1652 | 0.640271 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.79129 | 0.408937 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.9129 | −1.40484 | −0.702420 | − | 0.711762i | \(-0.747897\pi\) | ||||
−0.702420 | + | 0.711762i | \(0.747897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.582576 | −0.0303277 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.9564 | 0.828417 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1652 | 0.629888 | 0.314944 | − | 0.949110i | \(-0.398014\pi\) | ||||
0.314944 | + | 0.949110i | \(0.398014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.49545 | −0.180025 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1652 | 0.984448 | 0.492224 | − | 0.870469i | \(-0.336184\pi\) | ||||
0.492224 | + | 0.870469i | \(0.336184\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.7913 | 1.82885 | 0.914425 | − | 0.404756i | \(-0.132644\pi\) | ||||
0.914425 | + | 0.404756i | \(0.132644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.58258 | 0.334611 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.626136 | −0.0317464 | −0.0158732 | − | 0.999874i | \(-0.505053\pi\) | ||||
−0.0158732 | + | 0.999874i | \(0.505053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.58258 | 0.231751 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.16515 | −0.411877 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3303 | 0.518463 | 0.259232 | − | 0.965815i | \(-0.416531\pi\) | ||||
0.259232 | + | 0.965815i | \(0.416531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.1652 | −1.05958 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3739 | 1.46686 | 0.733430 | − | 0.679765i | \(-0.237918\pi\) | ||||
0.733430 | + | 0.679765i | \(0.237918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.95644 | 0.197084 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.37386 | −0.266373 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.7477 | 1.61927 | 0.809635 | − | 0.586933i | \(-0.199665\pi\) | ||||
0.809635 | + | 0.586933i | \(0.199665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.3739 | −0.707292 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.9564 | 0.634480 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.12159 | 0.347912 | 0.173956 | − | 0.984753i | \(-0.444345\pi\) | ||||
0.173956 | + | 0.984753i | \(0.444345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.53901 | 0.464903 | 0.232452 | − | 0.972608i | \(-0.425325\pi\) | ||||
0.232452 | + | 0.972608i | \(0.425325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.20871 | −0.252067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.95644 | 0.191019 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.7477 | −1.14389 | −0.571944 | − | 0.820293i | \(-0.693811\pi\) | ||||
−0.571944 | + | 0.820293i | \(0.693811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0000 | 0.913082 | 0.456541 | − | 0.889702i | \(-0.349088\pi\) | ||||
0.456541 | + | 0.889702i | \(0.349088\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.58258 | −0.267051 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.33030 | −0.445311 | −0.222656 | − | 0.974897i | \(-0.571473\pi\) | ||||
−0.222656 | + | 0.974897i | \(0.571473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.37386 | 0.351136 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4955 | 1.30635 | 0.653174 | − | 0.757208i | \(-0.273437\pi\) | ||||
0.653174 | + | 0.757208i | \(0.273437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.5826 | 0.595135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.2867 | 1.38213 | 0.691063 | − | 0.722794i | \(-0.257143\pi\) | ||||
0.691063 | + | 0.722794i | \(0.257143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04356 | 0.0491394 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.582576 | 0.0273718 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.58258 | 0.213896 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.3739 | −1.27493 | −0.637464 | − | 0.770480i | \(-0.720017\pi\) | ||||
−0.637464 | + | 0.770480i | \(0.720017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.12159 | −0.0985987 | −0.0492993 | − | 0.998784i | \(-0.515699\pi\) | ||||
−0.0492993 | + | 0.998784i | \(0.515699\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.41742 | −0.296963 | −0.148481 | − | 0.988915i | \(-0.547439\pi\) | ||||
−0.148481 | + | 0.988915i | \(0.547439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.58258 | 0.211604 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.16515 | −0.145842 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.7913 | −0.542164 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.20871 | 0.192704 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.58258 | −0.0723097 | −0.0361549 | − | 0.999346i | \(-0.511511\pi\) | ||||
−0.0361549 | + | 0.999346i | \(0.511511\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.62614 | 0.302126 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.79129 | 0.172510 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.74773 | 0.396397 | 0.198199 | − | 0.980162i | \(-0.436491\pi\) | ||||
0.198199 | + | 0.980162i | \(0.436491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.7477 | 0.531251 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.1216 | 1.53989 | 0.769943 | − | 0.638113i | \(-0.220285\pi\) | ||||
0.769943 | + | 0.638113i | \(0.220285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.25227 | 0.326626 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.9564 | 1.52315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.8348 | 0.798397 | 0.399199 | − | 0.916864i | \(-0.369288\pi\) | ||||
0.399199 | + | 0.916864i | \(0.369288\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.1216 | −1.03300 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4955 | 0.557145 | 0.278572 | − | 0.960415i | \(-0.410139\pi\) | ||||
0.278572 | + | 0.960415i | \(0.410139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.12159 | 0.360693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.956439 | 0.0423934 | 0.0211967 | − | 0.999775i | \(-0.493252\pi\) | ||||
0.0211967 | + | 0.999775i | \(0.493252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.2867 | 2.18032 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.58258 | −0.246477 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.79129 | 0.0787807 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.626136 | −0.0274843 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.74773 | −0.208002 | −0.104001 | − | 0.994577i | \(-0.533164\pi\) | ||||
−0.104001 | + | 0.994577i | \(0.533164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | −0.306089 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.20871 | −0.357577 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.79129 | −0.164528 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.28674 | −0.0557350 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.53901 | −0.368486 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2087 | −0.568940 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9129 | 0.684148 | 0.342074 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342074 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.7477 | 0.718714 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4955 | 0.448753 | 0.224377 | − | 0.974503i | \(-0.427965\pi\) | ||||
0.224377 | + | 0.974503i | \(0.427965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.37386 | −0.0586351 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.83485 | −0.376377 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.37386 | −0.228520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.2432 | −1.62042 | −0.810208 | − | 0.586143i | \(-0.800646\pi\) | ||||
−0.810208 | + | 0.586143i | \(0.800646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5390 | 0.614935 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.20871 | −0.346572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.3739 | 1.19582 | 0.597908 | − | 0.801565i | \(-0.295999\pi\) | ||||
0.597908 | + | 0.801565i | \(0.295999\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.79129 | 0.159219 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.4174 | 1.06555 | 0.532777 | − | 0.846256i | \(-0.321148\pi\) | ||||
0.532777 | + | 0.846256i | \(0.321148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0780 | −1.00763 | −0.503817 | − | 0.863810i | \(-0.668071\pi\) | ||||
−0.503817 | + | 0.863810i | \(0.668071\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.16515 | 0.0904505 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.1216 | −1.58702 | −0.793511 | − | 0.608556i | \(-0.791749\pi\) | ||||
−0.793511 | + | 0.608556i | \(0.791749\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.1652 | −0.838035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.79129 | 0.157289 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.53901 | −0.312234 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.9564 | 0.823690 | 0.411845 | − | 0.911254i | \(-0.364884\pi\) | ||||
0.411845 | + | 0.911254i | \(0.364884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.7477 | −0.853447 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4955 | 1.00591 | 0.502954 | − | 0.864313i | \(-0.332247\pi\) | ||||
0.502954 | + | 0.864313i | \(0.332247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.58258 | 0.310334 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.5826 | −1.82159 | −0.910797 | − | 0.412854i | \(-0.864532\pi\) | ||||
−0.910797 | + | 0.412854i | \(0.864532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.3303 | 1.64511 | 0.822554 | − | 0.568687i | \(-0.192549\pi\) | ||||
0.822554 | + | 0.568687i | \(0.192549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.20871 | 0.0492226 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.9564 | −1.45943 | −0.729713 | − | 0.683753i | \(-0.760347\pi\) | ||||
−0.729713 | + | 0.683753i | \(0.760347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.20871 | −0.0893549 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.53901 | −0.0621602 | −0.0310801 | − | 0.999517i | \(-0.509895\pi\) | ||||
−0.0310801 | + | 0.999517i | \(0.509895\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.2867 | 1.01801 | 0.509003 | − | 0.860765i | \(-0.330014\pi\) | ||||
0.509003 | + | 0.860765i | \(0.330014\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7913 | 0.473932 | 0.236966 | − | 0.971518i | \(-0.423847\pi\) | ||||
0.236966 | + | 0.971518i | \(0.423847\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9564 | −0.759474 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0000 | 0.399362 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7477 | −0.548158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.3739 | 1.60726 | 0.803629 | − | 0.595131i | \(-0.202900\pi\) | ||||
0.803629 | + | 0.595131i | \(0.202900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.74773 | 0.268198 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.2867 | 0.645304 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.95644 | 0.354311 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.04356 | −0.278204 | −0.139102 | − | 0.990278i | \(-0.544422\pi\) | ||||
−0.139102 | + | 0.990278i | \(0.544422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.46099 | −0.0576156 | −0.0288078 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288078 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.79129 | 0.266581 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.79129 | −0.266172 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.1652 | −0.397793 | −0.198897 | − | 0.980020i | \(-0.563736\pi\) | ||||
−0.198897 | + | 0.980020i | \(0.563736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0000 | 0.507178 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.4519 | −1.92637 | −0.963186 | − | 0.268835i | \(-0.913361\pi\) | ||||
−0.963186 | + | 0.268835i | \(0.913361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1216 | −0.471475 | −0.235738 | − | 0.971817i | \(-0.575751\pi\) | ||||
−0.235738 | + | 0.971817i | \(0.575751\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.1216 | 0.393090 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.58258 | 0.0612776 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.62614 | 0.0628701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.46099 | 0.0950053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4955 | 0.520212 | 0.260106 | − | 0.965580i | \(-0.416243\pi\) | ||||
0.260106 | + | 0.965580i | \(0.416243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.5390 | 1.36588 | 0.682938 | − | 0.730477i | \(-0.260702\pi\) | ||||
0.682938 | + | 0.730477i | \(0.260702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5390 | −0.673086 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.582576 | 0.0223243 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.9129 | −1.87160 | −0.935800 | − | 0.352532i | \(-0.885321\pi\) | ||||
−0.935800 | + | 0.352532i | \(0.885321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.00000 | −0.0381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.29583 | 0.354143 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1652 | 0.538868 | 0.269434 | − | 0.963019i | \(-0.413163\pi\) | ||||
0.269434 | + | 0.963019i | \(0.413163\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.79129 | −0.257980 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.66970 | 0.101122 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.7913 | −0.672928 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1652 | 0.459471 | 0.229736 | − | 0.973253i | \(-0.426214\pi\) | ||||
0.229736 | + | 0.973253i | \(0.426214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7477 | 0.631652 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.7477 | −0.517036 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2523 | 0.647923 | 0.323961 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323961 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41742 | −0.0531576 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.79129 | −0.0670843 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.5826 | 1.03009 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.5826 | 0.693013 | 0.346507 | − | 0.938048i | \(-0.387368\pi\) | ||||
0.346507 | + | 0.938048i | \(0.387368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.9129 | 1.18850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.3739 | −0.608951 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0000 | 0.815935 | 0.407967 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407967 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1652 | −1.11570 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4955 | 0.904760 | 0.452380 | − | 0.891825i | \(-0.350575\pi\) | ||||
0.452380 | + | 0.891825i | \(0.350575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.16515 | −0.0797544 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9564 | 0.697324 | 0.348662 | − | 0.937249i | \(-0.386636\pi\) | ||||
0.348662 | + | 0.937249i | \(0.386636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.3303 | −0.452965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4519 | 1.15386 | 0.576929 | − | 0.816794i | \(-0.304251\pi\) | ||||
0.576929 | + | 0.816794i | \(0.304251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.00000 | 0.0365881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.9564 | −1.13112 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.1216 | 1.53704 | 0.768519 | − | 0.639827i | \(-0.220994\pi\) | ||||
0.768519 | + | 0.639827i | \(0.220994\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.2087 | −0.736446 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.0345 | −1.96392 | −0.981958 | − | 0.189099i | \(-0.939443\pi\) | ||||
−0.981958 | + | 0.189099i | \(0.939443\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.79129 | −0.0650196 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3303 | 0.700723 | 0.350361 | − | 0.936615i | \(-0.386059\pi\) | ||||
0.350361 | + | 0.936615i | \(0.386059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.9564 | 1.33791 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.37386 | −0.302363 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.9564 | −1.87360 | −0.936799 | − | 0.349869i | \(-0.886226\pi\) | ||||
−0.936799 | + | 0.349869i | \(0.886226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20871 | −0.187587 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.3303 | −1.81026 | −0.905128 | − | 0.425140i | \(-0.860225\pi\) | ||||
−0.905128 | + | 0.425140i | \(0.860225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.3739 | −0.408035 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.25227 | −0.116525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0436 | −0.574084 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.58258 | 0.0565566 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.4955 | −1.30092 | −0.650461 | − | 0.759539i | \(-0.725424\pi\) | ||||
−0.650461 | + | 0.759539i | \(0.725424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.53901 | 0.125992 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.3303 | 1.61176 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.03447 | −0.107757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.5826 | −1.01245 | −0.506223 | − | 0.862402i | \(-0.668959\pi\) | ||||
−0.506223 | + | 0.862402i | \(0.668959\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.58258 | 0.162120 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | −0.176666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.2867 | −0.821771 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.747727 | 0.0263212 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0780 | 1.76065 | 0.880325 | − | 0.474371i | \(-0.157325\pi\) | ||||
0.880325 | + | 0.474371i | \(0.157325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.4955 | −1.00061 | −0.500305 | − | 0.865849i | \(-0.666779\pi\) | ||||
−0.500305 | + | 0.865849i | \(0.666779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1652 | −0.356507 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.7477 | 1.28564 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.37386 | 0.292606 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.4955 | −0.785097 | −0.392548 | − | 0.919731i | \(-0.628406\pi\) | ||||
−0.392548 | + | 0.919731i | \(0.628406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.4519 | −0.852339 | −0.426170 | − | 0.904643i | \(-0.640137\pi\) | ||||
−0.426170 | + | 0.904643i | \(0.640137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.4174 | −0.605663 | −0.302832 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302832 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0780 | −0.593144 | −0.296572 | − | 0.955010i | \(-0.595844\pi\) | ||||
−0.296572 | + | 0.955010i | \(0.595844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.791288 | 0.0274495 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.7913 | −1.17080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.79129 | −0.0619160 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.7042 | −0.921930 | −0.460965 | − | 0.887418i | \(-0.652497\pi\) | ||||
−0.460965 | + | 0.887418i | \(0.652497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4955 | −0.913636 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1652 | −0.418990 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.5390 | −1.01497 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.58258 | 0.0886338 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | −0.102839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.956439 | 0.0326713 | 0.0163357 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163357 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.704166 | 0.0240258 | 0.0120129 | − | 0.999928i | \(-0.496176\pi\) | ||||
0.0120129 | + | 0.999928i | \(0.496176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.20871 | 0.0752727 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.6606 | −0.941578 | −0.470789 | − | 0.882246i | \(-0.656031\pi\) | ||||
−0.470789 | + | 0.882246i | \(0.656031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.00000 | −0.135847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.53901 | 0.0861302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.66970 | 0.0904592 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.62614 | −0.156571 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.79129 | 0.0604875 | 0.0302437 | − | 0.999543i | \(-0.490372\pi\) | ||||
0.0302437 | + | 0.999543i | \(0.490372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.1652 | −0.477779 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.8693 | −1.41061 | −0.705307 | − | 0.708902i | \(-0.749191\pi\) | ||||
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1652 | −0.981485 | −0.490743 | − | 0.871305i | \(-0.663275\pi\) | ||||
−0.490743 | + | 0.871305i | \(0.663275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.37386 | 0.314744 | 0.157372 | − | 0.987539i | \(-0.449698\pi\) | ||||
0.157372 | + | 0.987539i | \(0.449698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.7477 | 0.762934 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.79129 | −0.0600104 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.58258 | −0.186814 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.20871 | 0.0737468 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.83485 | −0.0945475 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.2867 | −0.642535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.9564 | −0.830498 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.2432 | −1.73471 | −0.867353 | − | 0.497693i | \(-0.834181\pi\) | ||||
−0.867353 | + | 0.497693i | \(0.834181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.62614 | −0.120271 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.0000 | −1.22586 | −0.612932 | − | 0.790135i | \(-0.710010\pi\) | ||||
−0.612932 | + | 0.790135i | \(0.710010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.79129 | −0.0592830 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.9564 | 1.02227 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.9129 | 0.854787 | 0.427393 | − | 0.904066i | \(-0.359432\pi\) | ||||
0.427393 | + | 0.904066i | \(0.359432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.3303 | 0.801711 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.7822 | 0.651139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.41742 | 0.276464 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.2867 | −0.435924 | −0.217962 | − | 0.975957i | \(-0.569941\pi\) | ||||
−0.217962 | + | 0.975957i | \(0.569941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.1652 | 1.34913 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.16515 | 0.0708839 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0780 | 1.21129 | 0.605643 | − | 0.795736i | \(-0.292916\pi\) | ||||
0.605643 | + | 0.795736i | \(0.292916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.5826 | −0.802222 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.8693 | 0.712919 | 0.356460 | − | 0.934311i | \(-0.383984\pi\) | ||||
0.356460 | + | 0.934311i | \(0.383984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.582576 | 0.0189713 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.79129 | −0.155696 | −0.0778480 | − | 0.996965i | \(-0.524805\pi\) | ||||
−0.0778480 | + | 0.996965i | \(0.524805\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.7133 | 0.932072 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.7913 | −1.09576 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.0000 | −0.356325 | −0.178162 | − | 0.984001i | \(-0.557015\pi\) | ||||
−0.178162 | + | 0.984001i | \(0.557015\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.83485 | −0.0916376 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.58258 | −0.244854 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.7913 | −0.896493 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.16515 | −0.263118 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.3303 | −1.20046 | −0.600231 | − | 0.799827i | \(-0.704925\pi\) | ||||
−0.600231 | + | 0.799827i | \(0.704925\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.5826 | 0.821831 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9129 | −0.639035 | −0.319517 | − | 0.947580i | \(-0.603521\pi\) | ||||
−0.319517 | + | 0.947580i | \(0.603521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.1216 | −1.57477 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.7477 | 1.23965 | 0.619825 | − | 0.784740i | \(-0.287204\pi\) | ||||
0.619825 | + | 0.784740i | \(0.287204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.95644 | 0.286249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.74773 | 0.311221 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0345 | 1.14932 | 0.574661 | − | 0.818392i | \(-0.305134\pi\) | ||||
0.574661 | + | 0.818392i | \(0.305134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.79129 | 0.120678 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.58258 | −0.209314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0780 | −1.30489 | −0.652443 | − | 0.757838i | \(-0.726256\pi\) | ||||
−0.652443 | + | 0.757838i | \(0.726256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.53901 | 0.239243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.6261 | −1.03328 | −0.516640 | − | 0.856203i | \(-0.672817\pi\) | ||||
−0.516640 | + | 0.856203i | \(0.672817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.00000 | −0.0949158 |
(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 | 6900.2.a.o.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 6900.2.f.n.6349.4 | 4 | |||
5.3 | odd | 4 | 6900.2.f.n.6349.1 | 4 | |||
5.4 | even | 2 | 6900.2.a.q.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6900.2.a.o.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6900.2.a.q.1.1 | yes | 2 | 5.4 | even | 2 | ||
6900.2.f.n.6349.1 | 4 | 5.3 | odd | 4 | |||
6900.2.f.n.6349.4 | 4 | 5.2 | odd | 4 |