Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 22x^{10} + 181x^{8} - 692x^{6} + 1240x^{4} - 936x^{2} + 244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.60257\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60257 | −1.13319 | −0.566595 | − | 0.823997i | \(-0.691740\pi\) | ||||
−0.566595 | + | 0.823997i | \(0.691740\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.568238 | 0.284119 | ||||||||
\(5\) | −1.76461 | −0.789158 | −0.394579 | − | 0.918862i | \(-0.629110\pi\) | ||||
−0.394579 | + | 0.918862i | \(0.629110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.29450 | 0.811229 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.82792 | 0.894265 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.237832 | 0.0659626 | 0.0329813 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329813 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(14\) | 1.60257 | 0.428305 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.81358 | −1.20340 | ||||||||
\(17\) | 6.14292 | 1.48988 | 0.744938 | − | 0.667133i | \(-0.232479\pi\) | ||||
0.744938 | + | 0.667133i | \(0.232479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.53812 | 0.352869 | 0.176434 | − | 0.984312i | \(-0.443544\pi\) | ||||
0.176434 | + | 0.984312i | \(0.443544\pi\) | |||||||
\(20\) | −1.00272 | −0.224215 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.89707 | −0.812596 | −0.406298 | − | 0.913741i | \(-0.633181\pi\) | ||||
−0.406298 | + | 0.913741i | \(0.633181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.88615 | −0.377230 | ||||||||
\(26\) | −0.381142 | −0.0747482 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.568238 | −0.107387 | ||||||||
\(29\) | −4.45543 | −0.827352 | −0.413676 | − | 0.910424i | \(-0.635755\pi\) | ||||
−0.413676 | + | 0.910424i | \(0.635755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.52985 | 1.53201 | 0.766003 | − | 0.642837i | \(-0.222243\pi\) | ||||
0.766003 | + | 0.642837i | \(0.222243\pi\) | |||||||
\(32\) | 3.12511 | 0.552446 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.84447 | −1.68831 | ||||||||
\(35\) | 1.76461 | 0.298274 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.64448 | −0.599149 | −0.299574 | − | 0.954073i | \(-0.596845\pi\) | ||||
−0.299574 | + | 0.954073i | \(0.596845\pi\) | |||||||
\(38\) | −2.46495 | −0.399867 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.04890 | −0.640188 | ||||||||
\(41\) | −1.90659 | −0.297760 | −0.148880 | − | 0.988855i | \(-0.547567\pi\) | ||||
−0.148880 | + | 0.988855i | \(0.547567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7102 | −1.78579 | −0.892896 | − | 0.450262i | \(-0.851330\pi\) | ||||
−0.892896 | + | 0.450262i | \(0.851330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24534 | 0.920826 | ||||||||
\(47\) | 8.55604 | 1.24803 | 0.624013 | − | 0.781414i | \(-0.285501\pi\) | ||||
0.624013 | + | 0.781414i | \(0.285501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.02269 | 0.427473 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.135145 | 0.0187412 | ||||||||
\(53\) | −3.14359 | −0.431805 | −0.215903 | − | 0.976415i | \(-0.569269\pi\) | ||||
−0.215903 | + | 0.976415i | \(0.569269\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.29450 | −0.306616 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.14015 | 0.937547 | ||||||||
\(59\) | 2.56187 | 0.333527 | 0.166764 | − | 0.985997i | \(-0.446668\pi\) | ||||
0.166764 | + | 0.985997i | \(0.446668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.78951 | −0.869307 | −0.434654 | − | 0.900598i | \(-0.643129\pi\) | ||||
−0.434654 | + | 0.900598i | \(0.643129\pi\) | |||||||
\(62\) | −13.6697 | −1.73605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.61895 | 0.577369 | ||||||||
\(65\) | −0.419680 | −0.0520549 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62185 | −0.198141 | −0.0990704 | − | 0.995080i | \(-0.531587\pi\) | ||||
−0.0990704 | + | 0.995080i | \(0.531587\pi\) | |||||||
\(68\) | 3.49064 | 0.423302 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.82792 | −0.338001 | ||||||||
\(71\) | 7.37151 | 0.874837 | 0.437418 | − | 0.899258i | \(-0.355893\pi\) | ||||
0.437418 | + | 0.899258i | \(0.355893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.60387 | 0.538842 | 0.269421 | − | 0.963023i | \(-0.413168\pi\) | ||||
0.269421 | + | 0.963023i | \(0.413168\pi\) | |||||||
\(74\) | 5.84054 | 0.678949 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.874018 | 0.100257 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.2504 | −1.94082 | −0.970409 | − | 0.241468i | \(-0.922371\pi\) | ||||
−0.970409 | + | 0.241468i | \(0.922371\pi\) | |||||||
\(80\) | 8.49410 | 0.949669 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.05546 | 0.337419 | ||||||||
\(83\) | 9.16622 | 1.00612 | 0.503062 | − | 0.864250i | \(-0.332207\pi\) | ||||
0.503062 | + | 0.864250i | \(0.332207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8399 | −1.17575 | ||||||||
\(86\) | 18.7665 | 2.02364 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.14303 | 0.121161 | 0.0605807 | − | 0.998163i | \(-0.480705\pi\) | ||||
0.0605807 | + | 0.998163i | \(0.480705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.237832 | −0.0249315 | ||||||||
\(92\) | −2.21446 | −0.230874 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.7117 | −1.41425 | ||||||||
\(95\) | −2.71418 | −0.278469 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.68538 | −0.475728 | −0.237864 | − | 0.971298i | \(-0.576447\pi\) | ||||
−0.237864 | + | 0.971298i | \(0.576447\pi\) | |||||||
\(98\) | −1.60257 | −0.161884 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.07178 | −0.107178 | ||||||||
\(101\) | 18.1433 | 1.80532 | 0.902661 | − | 0.430352i | \(-0.141611\pi\) | ||||
0.902661 | + | 0.430352i | \(0.141611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.75190 | 0.468219 | 0.234110 | − | 0.972210i | \(-0.424783\pi\) | ||||
0.234110 | + | 0.972210i | \(0.424783\pi\) | |||||||
\(104\) | 0.545705 | 0.0535108 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.03783 | 0.489317 | ||||||||
\(107\) | −2.16093 | −0.208905 | −0.104452 | − | 0.994530i | \(-0.533309\pi\) | ||||
−0.104452 | + | 0.994530i | \(0.533309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.21878 | 0.404086 | 0.202043 | − | 0.979377i | \(-0.435242\pi\) | ||||
0.202043 | + | 0.979377i | \(0.435242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.81358 | 0.454841 | ||||||||
\(113\) | 7.53163 | 0.708516 | 0.354258 | − | 0.935148i | \(-0.384733\pi\) | ||||
0.354258 | + | 0.935148i | \(0.384733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.87682 | 0.641267 | ||||||||
\(116\) | −2.53174 | −0.235066 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.10559 | −0.377950 | ||||||||
\(119\) | −6.14292 | −0.563120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.8807 | 0.985090 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.84698 | 0.435272 | ||||||||
\(125\) | 12.1514 | 1.08685 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.86671 | 0.343115 | 0.171557 | − | 0.985174i | \(-0.445120\pi\) | ||||
0.171557 | + | 0.985174i | \(0.445120\pi\) | |||||||
\(128\) | −13.6524 | −1.20671 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.672568 | 0.0589881 | ||||||||
\(131\) | −4.55591 | −0.398052 | −0.199026 | − | 0.979994i | \(-0.563778\pi\) | ||||
−0.199026 | + | 0.979994i | \(0.563778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53812 | −0.133372 | ||||||||
\(134\) | 2.59914 | 0.224531 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.0949 | 1.20863 | ||||||||
\(137\) | −3.34382 | −0.285682 | −0.142841 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142841 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7288 | −0.910003 | −0.455002 | − | 0.890491i | \(-0.650361\pi\) | ||||
−0.455002 | + | 0.890491i | \(0.650361\pi\) | |||||||
\(140\) | 1.00272 | 0.0847451 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.8134 | −0.991356 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.86210 | 0.652912 | ||||||||
\(146\) | −7.37803 | −0.610610 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.07093 | −0.170229 | ||||||||
\(149\) | 20.4997 | 1.67940 | 0.839699 | − | 0.543052i | \(-0.182731\pi\) | ||||
0.839699 | + | 0.543052i | \(0.182731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6500 | −1.59909 | −0.799547 | − | 0.600604i | \(-0.794927\pi\) | ||||
−0.799547 | + | 0.600604i | \(0.794927\pi\) | |||||||
\(152\) | 3.52922 | 0.286258 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.0519 | −1.20899 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.0140 | 1.03863 | 0.519313 | − | 0.854584i | \(-0.326188\pi\) | ||||
0.519313 | + | 0.854584i | \(0.326188\pi\) | |||||||
\(158\) | 27.6450 | 2.19931 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.51460 | −0.435967 | ||||||||
\(161\) | 3.89707 | 0.307133 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.09731 | 0.634230 | 0.317115 | − | 0.948387i | \(-0.397286\pi\) | ||||
0.317115 | + | 0.948387i | \(0.397286\pi\) | |||||||
\(164\) | −1.08340 | −0.0845992 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6895 | −1.14013 | ||||||||
\(167\) | −4.97203 | −0.384747 | −0.192374 | − | 0.981322i | \(-0.561619\pi\) | ||||
−0.192374 | + | 0.981322i | \(0.561619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9434 | −0.995649 | ||||||||
\(170\) | 17.3717 | 1.33235 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.65419 | −0.507377 | ||||||||
\(173\) | 14.0437 | 1.06772 | 0.533861 | − | 0.845572i | \(-0.320741\pi\) | ||||
0.533861 | + | 0.845572i | \(0.320741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.88615 | 0.142580 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.83180 | −0.137299 | ||||||||
\(179\) | 19.2574 | 1.43937 | 0.719684 | − | 0.694301i | \(-0.244286\pi\) | ||||
0.719684 | + | 0.694301i | \(0.244286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.45622 | −0.405558 | −0.202779 | − | 0.979225i | \(-0.564997\pi\) | ||||
−0.202779 | + | 0.979225i | \(0.564997\pi\) | |||||||
\(182\) | 0.381142 | 0.0282522 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.94185 | −0.659202 | ||||||||
\(185\) | 6.43108 | 0.472823 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.86187 | 0.354588 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.34967 | 0.315559 | ||||||||
\(191\) | 0.336721 | 0.0243643 | 0.0121822 | − | 0.999926i | \(-0.496122\pi\) | ||||
0.0121822 | + | 0.999926i | \(0.496122\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4807 | −0.898378 | −0.449189 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449189 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(194\) | 7.50866 | 0.539090 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.568238 | 0.0405884 | ||||||||
\(197\) | −20.9906 | −1.49552 | −0.747760 | − | 0.663969i | \(-0.768871\pi\) | ||||
−0.747760 | + | 0.663969i | \(0.768871\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6504 | −1.32209 | −0.661045 | − | 0.750346i | \(-0.729887\pi\) | ||||
−0.661045 | + | 0.750346i | \(0.729887\pi\) | |||||||
\(200\) | −4.32778 | −0.306020 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −29.0759 | −2.04577 | ||||||||
\(203\) | 4.45543 | 0.312710 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.36440 | 0.234980 | ||||||||
\(206\) | −7.61527 | −0.530581 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.14482 | −0.0793791 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.1517 | 0.836558 | 0.418279 | − | 0.908319i | \(-0.362634\pi\) | ||||
0.418279 | + | 0.908319i | \(0.362634\pi\) | |||||||
\(212\) | −1.78631 | −0.122684 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.46304 | 0.236729 | ||||||||
\(215\) | 20.6640 | 1.40927 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.52985 | −0.579044 | ||||||||
\(218\) | −6.76090 | −0.457906 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46098 | 0.0982762 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0300 | 1.47524 | 0.737618 | − | 0.675219i | \(-0.235951\pi\) | ||||
0.737618 | + | 0.675219i | \(0.235951\pi\) | |||||||
\(224\) | −3.12511 | −0.208805 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0700 | −0.802883 | ||||||||
\(227\) | −0.991072 | −0.0657798 | −0.0328899 | − | 0.999459i | \(-0.510471\pi\) | ||||
−0.0328899 | + | 0.999459i | \(0.510471\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.2425 | 1.73415 | 0.867076 | − | 0.498176i | \(-0.165997\pi\) | ||||
0.867076 | + | 0.498176i | \(0.165997\pi\) | |||||||
\(230\) | −11.0206 | −0.726677 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.2230 | −0.671172 | ||||||||
\(233\) | −10.3858 | −0.680394 | −0.340197 | − | 0.940354i | \(-0.610494\pi\) | ||||
−0.340197 | + | 0.940354i | \(0.610494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0981 | −0.984890 | ||||||||
\(236\) | 1.45575 | 0.0947614 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.84447 | 0.638122 | ||||||||
\(239\) | −7.75162 | −0.501411 | −0.250705 | − | 0.968063i | \(-0.580663\pi\) | ||||
−0.250705 | + | 0.968063i | \(0.580663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.25863 | 0.338738 | 0.169369 | − | 0.985553i | \(-0.445827\pi\) | ||||
0.169369 | + | 0.985553i | \(0.445827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.85805 | −0.246987 | ||||||||
\(245\) | −1.76461 | −0.112737 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.365814 | 0.0232762 | ||||||||
\(248\) | 19.5718 | 1.24281 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −19.4735 | −1.23161 | ||||||||
\(251\) | −22.0821 | −1.39381 | −0.696905 | − | 0.717164i | \(-0.745440\pi\) | ||||
−0.696905 | + | 0.717164i | \(0.745440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.19668 | −0.388814 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.6411 | 0.790068 | ||||||||
\(257\) | 19.1651 | 1.19549 | 0.597745 | − | 0.801687i | \(-0.296064\pi\) | ||||
0.597745 | + | 0.801687i | \(0.296064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.64448 | 0.226457 | ||||||||
\(260\) | −0.238478 | −0.0147898 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.30118 | 0.451068 | ||||||||
\(263\) | −20.1639 | −1.24336 | −0.621679 | − | 0.783272i | \(-0.713549\pi\) | ||||
−0.621679 | + | 0.783272i | \(0.713549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.54721 | 0.340763 | ||||||||
\(266\) | 2.46495 | 0.151136 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.921598 | −0.0562955 | ||||||||
\(269\) | −26.6866 | −1.62711 | −0.813556 | − | 0.581487i | \(-0.802471\pi\) | ||||
−0.813556 | + | 0.581487i | \(0.802471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5714 | 0.763659 | 0.381830 | − | 0.924233i | \(-0.375294\pi\) | ||||
0.381830 | + | 0.924233i | \(0.375294\pi\) | |||||||
\(272\) | −29.5694 | −1.79291 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.35871 | 0.323732 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.65785 | −0.219779 | −0.109890 | − | 0.993944i | \(-0.535050\pi\) | ||||
−0.109890 | + | 0.993944i | \(0.535050\pi\) | |||||||
\(278\) | 17.1936 | 1.03121 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.04890 | 0.241968 | ||||||||
\(281\) | −4.74032 | −0.282784 | −0.141392 | − | 0.989954i | \(-0.545158\pi\) | ||||
−0.141392 | + | 0.989954i | \(0.545158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.64873 | 0.276338 | 0.138169 | − | 0.990409i | \(-0.455878\pi\) | ||||
0.138169 | + | 0.990409i | \(0.455878\pi\) | |||||||
\(284\) | 4.18877 | 0.248558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.90659 | 0.112543 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.7355 | 1.21973 | ||||||||
\(290\) | −12.5996 | −0.739873 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.61609 | 0.153095 | ||||||||
\(293\) | −8.26249 | −0.482700 | −0.241350 | − | 0.970438i | \(-0.577590\pi\) | ||||
−0.241350 | + | 0.970438i | \(0.577590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.52071 | −0.263206 | ||||||||
\(296\) | −8.36226 | −0.486047 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −32.8522 | −1.90308 | ||||||||
\(299\) | −0.926848 | −0.0536010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7102 | 0.674966 | ||||||||
\(302\) | 31.4905 | 1.81208 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.40387 | −0.424641 | ||||||||
\(305\) | 11.9808 | 0.686020 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8463 | −1.01854 | −0.509272 | − | 0.860606i | \(-0.670085\pi\) | ||||
−0.509272 | + | 0.860606i | \(0.670085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.1217 | 1.37002 | ||||||||
\(311\) | 12.6005 | 0.714511 | 0.357256 | − | 0.934007i | \(-0.383712\pi\) | ||||
0.357256 | + | 0.934007i | \(0.383712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.7579 | −1.56897 | −0.784484 | − | 0.620149i | \(-0.787072\pi\) | ||||
−0.784484 | + | 0.620149i | \(0.787072\pi\) | |||||||
\(314\) | −20.8558 | −1.17696 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.80231 | −0.551423 | ||||||||
\(317\) | 3.05179 | 0.171406 | 0.0857028 | − | 0.996321i | \(-0.472686\pi\) | ||||
0.0857028 | + | 0.996321i | \(0.472686\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.15065 | −0.455635 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.24534 | −0.348039 | ||||||||
\(323\) | 9.44855 | 0.525731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.448586 | −0.0248831 | ||||||||
\(326\) | −12.9765 | −0.718703 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.37469 | −0.241552 | ||||||||
\(329\) | −8.55604 | −0.471710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7323 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(332\) | 5.20859 | 0.285859 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.96804 | 0.435992 | ||||||||
\(335\) | 2.86194 | 0.156364 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2682 | −0.613815 | −0.306908 | − | 0.951739i | \(-0.599294\pi\) | ||||
−0.306908 | + | 0.951739i | \(0.599294\pi\) | |||||||
\(338\) | 20.7428 | 1.12826 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.15962 | −0.334052 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −26.8691 | −1.44869 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.5060 | −1.20993 | ||||||||
\(347\) | −27.8666 | −1.49596 | −0.747980 | − | 0.663722i | \(-0.768976\pi\) | ||||
−0.747980 | + | 0.663722i | \(0.768976\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.54901 | 0.404089 | 0.202045 | − | 0.979376i | \(-0.435241\pi\) | ||||
0.202045 | + | 0.979376i | \(0.435241\pi\) | |||||||
\(350\) | −3.02269 | −0.161570 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2041 | −0.596334 | −0.298167 | − | 0.954514i | \(-0.596375\pi\) | ||||
−0.298167 | + | 0.954514i | \(0.596375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.0078 | −0.690384 | ||||||||
\(356\) | 0.649515 | 0.0344242 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.8614 | −1.63108 | ||||||||
\(359\) | 14.2242 | 0.750725 | 0.375362 | − | 0.926878i | \(-0.377518\pi\) | ||||
0.375362 | + | 0.926878i | \(0.377518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6342 | −0.875483 | ||||||||
\(362\) | 8.74398 | 0.459574 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.135145 | −0.00708352 | ||||||||
\(365\) | −8.12403 | −0.425231 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3499 | −0.853455 | −0.426728 | − | 0.904380i | \(-0.640334\pi\) | ||||
−0.426728 | + | 0.904380i | \(0.640334\pi\) | |||||||
\(368\) | 18.7589 | 0.977875 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.3063 | −0.535798 | ||||||||
\(371\) | 3.14359 | 0.163207 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6303 | −1.17175 | −0.585877 | − | 0.810400i | \(-0.699250\pi\) | ||||
−0.585877 | + | 0.810400i | \(0.699250\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.6319 | 1.01244 | ||||||||
\(377\) | −1.05964 | −0.0545743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.82350 | 0.0936671 | 0.0468335 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468335 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(380\) | −1.54230 | −0.0791184 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.539620 | −0.0276094 | ||||||||
\(383\) | 11.1434 | 0.569404 | 0.284702 | − | 0.958616i | \(-0.408105\pi\) | ||||
0.284702 | + | 0.958616i | \(0.408105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0012 | 1.01803 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.66241 | −0.135163 | ||||||||
\(389\) | 28.6576 | 1.45300 | 0.726499 | − | 0.687168i | \(-0.241146\pi\) | ||||
0.726499 | + | 0.687168i | \(0.241146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.9394 | −1.21067 | ||||||||
\(392\) | 2.29450 | 0.115890 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 33.6390 | 1.69471 | ||||||||
\(395\) | 30.4402 | 1.53161 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.37451 | −0.470493 | −0.235247 | − | 0.971936i | \(-0.575590\pi\) | ||||
−0.235247 | + | 0.971936i | \(0.575590\pi\) | |||||||
\(398\) | 29.8886 | 1.49818 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.07914 | 0.453957 | ||||||||
\(401\) | −17.1824 | −0.858048 | −0.429024 | − | 0.903293i | \(-0.641142\pi\) | ||||
−0.429024 | + | 0.903293i | \(0.641142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.02867 | 0.101055 | ||||||||
\(404\) | 10.3097 | 0.512926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.14015 | −0.354360 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.548440 | 0.0271186 | 0.0135593 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135593 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(410\) | −5.39169 | −0.266276 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.70021 | 0.133030 | ||||||||
\(413\) | −2.56187 | −0.126061 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.1748 | −0.793990 | ||||||||
\(416\) | 0.743249 | 0.0364408 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.31528 | −0.259668 | −0.129834 | − | 0.991536i | \(-0.541444\pi\) | ||||
−0.129834 | + | 0.991536i | \(0.541444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.52820 | 0.464376 | 0.232188 | − | 0.972671i | \(-0.425412\pi\) | ||||
0.232188 | + | 0.972671i | \(0.425412\pi\) | |||||||
\(422\) | −19.4740 | −0.947978 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.21298 | −0.350293 | ||||||||
\(425\) | −11.5865 | −0.562026 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.78951 | 0.328567 | ||||||||
\(428\) | −1.22792 | −0.0593537 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −33.1155 | −1.59697 | ||||||||
\(431\) | −35.6144 | −1.71548 | −0.857742 | − | 0.514081i | \(-0.828133\pi\) | ||||
−0.857742 | + | 0.514081i | \(0.828133\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.15006 | 0.0552682 | 0.0276341 | − | 0.999618i | \(-0.491203\pi\) | ||||
0.0276341 | + | 0.999618i | \(0.491203\pi\) | |||||||
\(434\) | 13.6697 | 0.656167 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.39727 | 0.114808 | ||||||||
\(437\) | −5.99417 | −0.286740 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.3954 | −1.59388 | −0.796938 | − | 0.604061i | \(-0.793548\pi\) | ||||
−0.796938 | + | 0.604061i | \(0.793548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.34133 | −0.111366 | ||||||||
\(443\) | 20.8554 | 0.990871 | 0.495435 | − | 0.868645i | \(-0.335009\pi\) | ||||
0.495435 | + | 0.868645i | \(0.335009\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.01701 | −0.0956155 | ||||||||
\(446\) | −35.3046 | −1.67172 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.61895 | −0.218225 | ||||||||
\(449\) | −32.8374 | −1.54969 | −0.774846 | − | 0.632150i | \(-0.782173\pi\) | ||||
−0.774846 | + | 0.632150i | \(0.782173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.27975 | 0.201303 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.58826 | 0.0745410 | ||||||||
\(455\) | 0.419680 | 0.0196749 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9232 | −1.07230 | −0.536151 | − | 0.844122i | \(-0.680122\pi\) | ||||
−0.536151 | + | 0.844122i | \(0.680122\pi\) | |||||||
\(458\) | −42.0555 | −1.96512 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.90767 | 0.182196 | ||||||||
\(461\) | −19.5054 | −0.908455 | −0.454228 | − | 0.890886i | \(-0.650085\pi\) | ||||
−0.454228 | + | 0.890886i | \(0.650085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.22668 | −0.289378 | −0.144689 | − | 0.989477i | \(-0.546218\pi\) | ||||
−0.144689 | + | 0.989477i | \(0.546218\pi\) | |||||||
\(464\) | 21.4466 | 0.995632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.6439 | 0.771016 | ||||||||
\(467\) | 5.20609 | 0.240909 | 0.120455 | − | 0.992719i | \(-0.461565\pi\) | ||||
0.120455 | + | 0.992719i | \(0.461565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.62185 | 0.0748902 | ||||||||
\(470\) | 24.1958 | 1.11607 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.87822 | 0.270567 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.90113 | −0.133113 | ||||||||
\(476\) | −3.49064 | −0.159993 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.4225 | 0.568193 | ||||||||
\(479\) | 25.9938 | 1.18769 | 0.593844 | − | 0.804580i | \(-0.297609\pi\) | ||||
0.593844 | + | 0.804580i | \(0.297609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.866772 | −0.0395214 | ||||||||
\(482\) | −8.42733 | −0.383855 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.26787 | 0.375424 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.1070 | 1.68148 | 0.840739 | − | 0.541441i | \(-0.182121\pi\) | ||||
0.840739 | + | 0.541441i | \(0.182121\pi\) | |||||||
\(488\) | −15.5785 | −0.705207 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.82792 | 0.127752 | ||||||||
\(491\) | 27.7241 | 1.25117 | 0.625585 | − | 0.780156i | \(-0.284860\pi\) | ||||
0.625585 | + | 0.780156i | \(0.284860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.3693 | −1.23265 | ||||||||
\(494\) | −0.586243 | −0.0263763 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −41.0591 | −1.84361 | ||||||||
\(497\) | −7.37151 | −0.330657 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9850 | −0.849885 | −0.424942 | − | 0.905220i | \(-0.639706\pi\) | ||||
−0.424942 | + | 0.905220i | \(0.639706\pi\) | |||||||
\(500\) | 6.90487 | 0.308795 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 35.3881 | 1.57945 | ||||||||
\(503\) | −23.2430 | −1.03635 | −0.518177 | − | 0.855273i | \(-0.673389\pi\) | ||||
−0.518177 | + | 0.855273i | \(0.673389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0158 | −1.42468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.19721 | 0.0974853 | ||||||||
\(509\) | −28.8227 | −1.27754 | −0.638771 | − | 0.769397i | \(-0.720557\pi\) | ||||
−0.638771 | + | 0.769397i | \(0.720557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.60387 | −0.203663 | ||||||||
\(512\) | 7.04659 | 0.311418 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.7135 | −1.35472 | ||||||||
\(515\) | −8.38526 | −0.369499 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.84054 | −0.256619 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.962957 | −0.0422285 | ||||||||
\(521\) | −41.2984 | −1.80931 | −0.904657 | − | 0.426140i | \(-0.859873\pi\) | ||||
−0.904657 | + | 0.426140i | \(0.859873\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.0083 | −0.918629 | −0.459315 | − | 0.888274i | \(-0.651905\pi\) | ||||
−0.459315 | + | 0.888274i | \(0.651905\pi\) | |||||||
\(524\) | −2.58884 | −0.113094 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.3141 | 1.40896 | ||||||||
\(527\) | 52.3982 | 2.28250 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.81281 | −0.339687 | ||||||||
\(530\) | −8.88981 | −0.386149 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.874018 | −0.0378935 | ||||||||
\(533\) | −0.453449 | −0.0196410 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.81319 | 0.164859 | ||||||||
\(536\) | −3.72134 | −0.160738 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.7672 | 1.84383 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00282 | −0.301075 | −0.150537 | − | 0.988604i | \(-0.548100\pi\) | ||||
−0.150537 | + | 0.988604i | \(0.548100\pi\) | |||||||
\(542\) | −20.1466 | −0.865371 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.1973 | 0.823076 | ||||||||
\(545\) | −7.44450 | −0.318887 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6735 | 0.670149 | 0.335075 | − | 0.942192i | \(-0.391238\pi\) | ||||
0.335075 | + | 0.942192i | \(0.391238\pi\) | |||||||
\(548\) | −1.90008 | −0.0811676 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.85299 | −0.291947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2504 | 0.733560 | ||||||||
\(554\) | 5.86197 | 0.249051 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.09650 | −0.258549 | ||||||||
\(557\) | 43.2989 | 1.83463 | 0.917317 | − | 0.398157i | \(-0.130350\pi\) | ||||
0.917317 | + | 0.398157i | \(0.130350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.78506 | −0.117796 | ||||||||
\(560\) | −8.49410 | −0.358941 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.59671 | 0.320448 | ||||||||
\(563\) | 10.3329 | 0.435482 | 0.217741 | − | 0.976007i | \(-0.430131\pi\) | ||||
0.217741 | + | 0.976007i | \(0.430131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2904 | −0.559131 | ||||||||
\(566\) | −7.44992 | −0.313144 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.9139 | 0.709693 | ||||||||
\(569\) | 21.1095 | 0.884957 | 0.442479 | − | 0.896779i | \(-0.354099\pi\) | ||||
0.442479 | + | 0.896779i | \(0.354099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8603 | 1.45886 | 0.729430 | − | 0.684056i | \(-0.239786\pi\) | ||||
0.729430 | + | 0.684056i | \(0.239786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.05546 | −0.127532 | ||||||||
\(575\) | 7.35047 | 0.306536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5157 | 0.562668 | 0.281334 | − | 0.959610i | \(-0.409223\pi\) | ||||
0.281334 | + | 0.959610i | \(0.409223\pi\) | |||||||
\(578\) | −33.2301 | −1.38219 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.46754 | 0.185504 | ||||||||
\(581\) | −9.16622 | −0.380279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.5636 | 0.437124 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2412 | 0.546990 | ||||||||
\(587\) | 2.25845 | 0.0932161 | 0.0466081 | − | 0.998913i | \(-0.485159\pi\) | ||||
0.0466081 | + | 0.998913i | \(0.485159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1199 | 0.540597 | ||||||||
\(590\) | 7.24476 | 0.298262 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.5430 | 0.721013 | ||||||||
\(593\) | 30.2674 | 1.24293 | 0.621467 | − | 0.783440i | \(-0.286537\pi\) | ||||
0.621467 | + | 0.783440i | \(0.286537\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8399 | 0.444391 | ||||||||
\(596\) | 11.6487 | 0.477149 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.48534 | 0.0607401 | ||||||||
\(599\) | −21.3459 | −0.872169 | −0.436084 | − | 0.899906i | \(-0.643635\pi\) | ||||
−0.436084 | + | 0.899906i | \(0.643635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.9786 | −1.79392 | −0.896962 | − | 0.442108i | \(-0.854231\pi\) | ||||
−0.896962 | + | 0.442108i | \(0.854231\pi\) | |||||||
\(602\) | −18.7665 | −0.764865 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.1659 | −0.454333 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7123 | −0.759507 | −0.379753 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379753 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(608\) | 4.80679 | 0.194941 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.2001 | −0.777391 | ||||||||
\(611\) | 2.03490 | 0.0823231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.9777 | 1.08962 | 0.544810 | − | 0.838560i | \(-0.316602\pi\) | ||||
0.544810 | + | 0.838560i | \(0.316602\pi\) | |||||||
\(614\) | 28.6000 | 1.15420 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.1127 | −1.17203 | −0.586016 | − | 0.810300i | \(-0.699304\pi\) | ||||
−0.586016 | + | 0.810300i | \(0.699304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.41996 | 0.378620 | 0.189310 | − | 0.981917i | \(-0.439375\pi\) | ||||
0.189310 | + | 0.981917i | \(0.439375\pi\) | |||||||
\(620\) | −8.55303 | −0.343498 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.1933 | −0.809677 | ||||||||
\(623\) | −1.14303 | −0.0457947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0117 | −0.480467 | ||||||||
\(626\) | 44.4840 | 1.77794 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.39502 | 0.295093 | ||||||||
\(629\) | −22.3877 | −0.892657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.99811 | −0.0795436 | −0.0397718 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397718 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(632\) | −39.5810 | −1.57445 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.89071 | −0.194235 | ||||||||
\(635\) | −6.82323 | −0.270772 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.237832 | 0.00942323 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.0912 | 0.952288 | ||||||||
\(641\) | −45.5981 | −1.80102 | −0.900508 | − | 0.434840i | \(-0.856805\pi\) | ||||
−0.900508 | + | 0.434840i | \(0.856805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0073 | −0.710140 | −0.355070 | − | 0.934840i | \(-0.615543\pi\) | ||||
−0.355070 | + | 0.934840i | \(0.615543\pi\) | |||||||
\(644\) | 2.21446 | 0.0872621 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.1420 | −0.595753 | ||||||||
\(647\) | 47.3237 | 1.86049 | 0.930243 | − | 0.366944i | \(-0.119596\pi\) | ||||
0.930243 | + | 0.366944i | \(0.119596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.718892 | 0.0281973 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.60119 | 0.180197 | ||||||||
\(653\) | −5.87593 | −0.229943 | −0.114972 | − | 0.993369i | \(-0.536678\pi\) | ||||
−0.114972 | + | 0.993369i | \(0.536678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.03941 | 0.314126 | ||||||||
\(656\) | 9.17755 | 0.358323 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.7117 | 0.534537 | ||||||||
\(659\) | −40.3862 | −1.57322 | −0.786612 | − | 0.617448i | \(-0.788167\pi\) | ||||
−0.786612 | + | 0.617448i | \(0.788167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.8932 | 0.890442 | 0.445221 | − | 0.895421i | \(-0.353125\pi\) | ||||
0.445221 | + | 0.895421i | \(0.353125\pi\) | |||||||
\(662\) | −36.4301 | −1.41590 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.0319 | 0.816197 | ||||||||
\(665\) | 2.71418 | 0.105251 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.3631 | 0.672303 | ||||||||
\(668\) | −2.82530 | −0.109314 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.58646 | −0.177190 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1286 | −0.621712 | −0.310856 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310856 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(674\) | 18.0580 | 0.695569 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.35495 | −0.282883 | ||||||||
\(677\) | 27.0862 | 1.04101 | 0.520504 | − | 0.853859i | \(-0.325744\pi\) | ||||
0.520504 | + | 0.853859i | \(0.325744\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.68538 | 0.179808 | ||||||||
\(680\) | −24.8721 | −0.953801 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7408 | −0.793623 | −0.396811 | − | 0.917900i | \(-0.629883\pi\) | ||||
−0.396811 | + | 0.917900i | \(0.629883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.90054 | 0.225448 | ||||||||
\(686\) | 1.60257 | 0.0611865 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 56.3681 | 2.14901 | ||||||||
\(689\) | −0.747645 | −0.0284830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8328 | −0.640348 | −0.320174 | − | 0.947359i | \(-0.603741\pi\) | ||||
−0.320174 | + | 0.947359i | \(0.603741\pi\) | |||||||
\(692\) | 7.98015 | 0.303360 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.6583 | 1.69521 | ||||||||
\(695\) | 18.9321 | 0.718136 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.7121 | −0.443626 | ||||||||
\(698\) | −12.0978 | −0.457910 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.07178 | 0.0405095 | ||||||||
\(701\) | −39.9602 | −1.50928 | −0.754638 | − | 0.656141i | \(-0.772188\pi\) | ||||
−0.754638 | + | 0.656141i | \(0.772188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.60565 | −0.211421 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9554 | 0.675760 | ||||||||
\(707\) | −18.1433 | −0.682348 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.60837 | −0.0979595 | −0.0489797 | − | 0.998800i | \(-0.515597\pi\) | ||||
−0.0489797 | + | 0.998800i | \(0.515597\pi\) | |||||||
\(710\) | 20.8460 | 0.782336 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.62270 | 0.0982897 | ||||||||
\(713\) | −33.2415 | −1.24490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.9428 | 0.408952 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.7953 | −0.850714 | ||||||||
\(719\) | −38.7626 | −1.44560 | −0.722800 | − | 0.691057i | \(-0.757145\pi\) | ||||
−0.722800 | + | 0.691057i | \(0.757145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.75190 | −0.176970 | ||||||||
\(722\) | 26.6575 | 0.992089 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.10043 | −0.115227 | ||||||||
\(725\) | 8.40361 | 0.312102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.3510 | −1.90450 | −0.952251 | − | 0.305317i | \(-0.901238\pi\) | ||||
−0.952251 | + | 0.305317i | \(0.901238\pi\) | |||||||
\(728\) | −0.545705 | −0.0202252 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0193 | 0.481868 | ||||||||
\(731\) | −71.9350 | −2.66061 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.8445 | −1.80411 | −0.902057 | − | 0.431617i | \(-0.857943\pi\) | ||||
−0.902057 | + | 0.431617i | \(0.857943\pi\) | |||||||
\(734\) | 26.2018 | 0.967127 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.1788 | −0.448916 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0365 | −0.553127 | −0.276563 | − | 0.960996i | \(-0.589196\pi\) | ||||
−0.276563 | + | 0.960996i | \(0.589196\pi\) | |||||||
\(740\) | 3.65438 | 0.134338 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.03783 | −0.184945 | ||||||||
\(743\) | −45.1304 | −1.65567 | −0.827836 | − | 0.560970i | \(-0.810428\pi\) | ||||
−0.827836 | + | 0.560970i | \(0.810428\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.1739 | −1.32531 | ||||||||
\(746\) | 36.2668 | 1.32782 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.16093 | 0.0789585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.78179 | 0.247471 | 0.123736 | − | 0.992315i | \(-0.460513\pi\) | ||||
0.123736 | + | 0.992315i | \(0.460513\pi\) | |||||||
\(752\) | −41.1852 | −1.50187 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.69815 | 0.0618431 | ||||||||
\(755\) | 34.6746 | 1.26194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.9448 | 1.81528 | 0.907638 | − | 0.419754i | \(-0.137884\pi\) | ||||
0.907638 | + | 0.419754i | \(0.137884\pi\) | |||||||
\(758\) | −2.92230 | −0.106143 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.22770 | −0.225902 | ||||||||
\(761\) | −28.2853 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.21878 | −0.152730 | ||||||||
\(764\) | 0.191338 | 0.00692236 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.8582 | −0.645242 | ||||||||
\(767\) | 0.609294 | 0.0220003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.9422 | 1.87308 | 0.936542 | − | 0.350555i | \(-0.114007\pi\) | ||||
0.936542 | + | 0.350555i | \(0.114007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.09198 | −0.255246 | ||||||||
\(773\) | 4.11535 | 0.148019 | 0.0740095 | − | 0.997258i | \(-0.476420\pi\) | ||||
0.0740095 | + | 0.997258i | \(0.476420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0886 | −0.577919 | ||||||||
\(776\) | −10.7506 | −0.385924 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.9258 | −1.64652 | ||||||||
\(779\) | −2.93257 | −0.105070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 38.3646 | 1.37192 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.81358 | −0.171914 | ||||||||
\(785\) | −22.9646 | −0.819640 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.444368 | −0.0158400 | −0.00792001 | − | 0.999969i | \(-0.502521\pi\) | ||||
−0.00792001 | + | 0.999969i | \(0.502521\pi\) | |||||||
\(788\) | −11.9277 | −0.424906 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −48.7826 | −1.73561 | ||||||||
\(791\) | −7.53163 | −0.267794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.61476 | −0.0573418 | ||||||||
\(794\) | 15.0233 | 0.533158 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.5978 | −0.375631 | ||||||||
\(797\) | 16.0300 | 0.567810 | 0.283905 | − | 0.958852i | \(-0.408370\pi\) | ||||
0.283905 | + | 0.958852i | \(0.408370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.5591 | 1.85941 | ||||||||
\(800\) | −5.89442 | −0.208399 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27.5360 | 0.972331 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.87682 | −0.242376 | ||||||||
\(806\) | −3.25109 | −0.114515 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 41.6298 | 1.46453 | ||||||||
\(809\) | −24.1194 | −0.847993 | −0.423997 | − | 0.905664i | \(-0.639373\pi\) | ||||
−0.423997 | + | 0.905664i | \(0.639373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6041 | 1.03954 | 0.519769 | − | 0.854307i | \(-0.326018\pi\) | ||||
0.519769 | + | 0.854307i | \(0.326018\pi\) | |||||||
\(812\) | 2.53174 | 0.0888468 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.2886 | −0.500507 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0117 | −0.630151 | ||||||||
\(818\) | −0.878914 | −0.0307305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91178 | 0.0667621 | ||||||||
\(821\) | 44.3006 | 1.54610 | 0.773051 | − | 0.634344i | \(-0.218730\pi\) | ||||
0.773051 | + | 0.634344i | \(0.218730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1312 | 0.841162 | 0.420581 | − | 0.907255i | \(-0.361826\pi\) | ||||
0.420581 | + | 0.907255i | \(0.361826\pi\) | |||||||
\(824\) | 10.9033 | 0.379833 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.10559 | 0.142852 | ||||||||
\(827\) | −30.3326 | −1.05477 | −0.527383 | − | 0.849627i | \(-0.676827\pi\) | ||||
−0.527383 | + | 0.849627i | \(0.676827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.1560 | −1.60306 | −0.801532 | − | 0.597951i | \(-0.795982\pi\) | ||||
−0.801532 | + | 0.597951i | \(0.795982\pi\) | |||||||
\(830\) | 25.9213 | 0.899741 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.09853 | 0.0380848 | ||||||||
\(833\) | 6.14292 | 0.212840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.77370 | 0.303626 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.51812 | 0.294253 | ||||||||
\(839\) | −39.3482 | −1.35845 | −0.679226 | − | 0.733930i | \(-0.737684\pi\) | ||||
−0.679226 | + | 0.733930i | \(0.737684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.14915 | −0.315488 | ||||||||
\(842\) | −15.2696 | −0.526226 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.90505 | 0.237682 | ||||||||
\(845\) | 22.8401 | 0.785724 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.1319 | 0.519633 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.5682 | 0.636882 | ||||||||
\(851\) | 14.2028 | 0.486866 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.9953 | −0.444950 | −0.222475 | − | 0.974938i | \(-0.571414\pi\) | ||||
−0.222475 | + | 0.974938i | \(0.571414\pi\) | |||||||
\(854\) | −10.8807 | −0.372329 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.95825 | −0.169470 | ||||||||
\(857\) | 29.0953 | 0.993877 | 0.496939 | − | 0.867786i | \(-0.334457\pi\) | ||||
0.496939 | + | 0.867786i | \(0.334457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.4404 | 0.799775 | 0.399888 | − | 0.916564i | \(-0.369049\pi\) | ||||
0.399888 | + | 0.916564i | \(0.369049\pi\) | |||||||
\(860\) | 11.7421 | 0.400401 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 57.0746 | 1.94397 | ||||||||
\(863\) | −30.9751 | −1.05441 | −0.527203 | − | 0.849740i | \(-0.676759\pi\) | ||||
−0.527203 | + | 0.849740i | \(0.676759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.7816 | −0.842601 | ||||||||
\(866\) | −1.84305 | −0.0626294 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.84698 | −0.164517 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.385728 | −0.0130699 | ||||||||
\(872\) | 9.68000 | 0.327806 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.60609 | 0.324931 | ||||||||
\(875\) | −12.1514 | −0.410791 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.4618 | −1.53514 | −0.767568 | − | 0.640967i | \(-0.778533\pi\) | ||||
−0.767568 | + | 0.640967i | \(0.778533\pi\) | |||||||
\(878\) | 53.5186 | 1.80616 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.3625 | 1.62937 | 0.814687 | − | 0.579901i | \(-0.196909\pi\) | ||||
0.814687 | + | 0.579901i | \(0.196909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.9195 | −0.468428 | −0.234214 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234214 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(884\) | 0.830184 | 0.0279221 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.4223 | −1.12284 | ||||||||
\(887\) | −13.9089 | −0.467015 | −0.233508 | − | 0.972355i | \(-0.575020\pi\) | ||||
−0.233508 | + | 0.972355i | \(0.575020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.86671 | −0.129685 | ||||||||
\(890\) | 3.23241 | 0.108350 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.5183 | 0.419142 | ||||||||
\(893\) | 13.1602 | 0.440390 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.9819 | −1.13589 | ||||||||
\(896\) | 13.6524 | 0.456095 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52.6243 | 1.75609 | ||||||||
\(899\) | −38.0041 | −1.26751 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.3108 | −0.643337 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.2813 | 0.574769 | ||||||||
\(905\) | 9.62810 | 0.320049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.8698 | 1.55629 | 0.778144 | − | 0.628086i | \(-0.216162\pi\) | ||||
0.778144 | + | 0.628086i | \(0.216162\pi\) | |||||||
\(908\) | −0.563165 | −0.0186893 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.672568 | −0.0222954 | ||||||||
\(911\) | 17.2331 | 0.570957 | 0.285478 | − | 0.958385i | \(-0.407848\pi\) | ||||
0.285478 | + | 0.958385i | \(0.407848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.7361 | 1.21512 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.9120 | 0.492705 | ||||||||
\(917\) | 4.55591 | 0.150450 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0621 | 0.661786 | 0.330893 | − | 0.943668i | \(-0.392650\pi\) | ||||
0.330893 | + | 0.943668i | \(0.392650\pi\) | |||||||
\(920\) | 15.7789 | 0.520214 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.2587 | 1.02945 | ||||||||
\(923\) | 1.75318 | 0.0577066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.87403 | 0.226017 | ||||||||
\(926\) | 9.97870 | 0.327921 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.9237 | −0.457068 | ||||||||
\(929\) | −49.7071 | −1.63084 | −0.815419 | − | 0.578871i | \(-0.803493\pi\) | ||||
−0.815419 | + | 0.578871i | \(0.803493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.53812 | 0.0504099 | ||||||||
\(932\) | −5.90158 | −0.193313 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.34314 | −0.272996 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.9723 | −1.33851 | −0.669254 | − | 0.743034i | \(-0.733386\pi\) | ||||
−0.669254 | + | 0.743034i | \(0.733386\pi\) | |||||||
\(938\) | −2.59914 | −0.0848648 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.57930 | −0.279826 | ||||||||
\(941\) | 57.7002 | 1.88097 | 0.940486 | − | 0.339832i | \(-0.110370\pi\) | ||||
0.940486 | + | 0.339832i | \(0.110370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.43014 | 0.241959 | ||||||||
\(944\) | −12.3318 | −0.401365 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.9921 | 0.909621 | 0.454811 | − | 0.890588i | \(-0.349707\pi\) | ||||
0.454811 | + | 0.890588i | \(0.349707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.09495 | 0.0355434 | ||||||||
\(950\) | 4.64926 | 0.150842 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.0949 | −0.456820 | ||||||||
\(953\) | −14.9272 | −0.483538 | −0.241769 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241769 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.594182 | −0.0192273 | ||||||||
\(956\) | −4.40476 | −0.142460 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −41.6570 | −1.34588 | ||||||||
\(959\) | 3.34382 | 0.107978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.7583 | 1.34704 | ||||||||
\(962\) | 1.38907 | 0.0447853 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.98815 | 0.0962419 | ||||||||
\(965\) | 22.0235 | 0.708962 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.7409 | −1.31014 | −0.655070 | − | 0.755568i | \(-0.727361\pi\) | ||||
−0.655070 | + | 0.755568i | \(0.727361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.2499 | −0.425427 | ||||||||
\(971\) | −32.4367 | −1.04094 | −0.520471 | − | 0.853879i | \(-0.674244\pi\) | ||||
−0.520471 | + | 0.853879i | \(0.674244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.7288 | 0.343949 | ||||||||
\(974\) | −59.4666 | −1.90543 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.6818 | 1.04612 | ||||||||
\(977\) | −43.6622 | −1.39688 | −0.698438 | − | 0.715670i | \(-0.746121\pi\) | ||||
−0.698438 | + | 0.715670i | \(0.746121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00272 | −0.0320307 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −44.4298 | −1.41781 | ||||||||
\(983\) | −46.6583 | −1.48817 | −0.744085 | − | 0.668085i | \(-0.767114\pi\) | ||||
−0.744085 | + | 0.668085i | \(0.767114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.0403 | 1.18020 | ||||||||
\(986\) | 43.8613 | 1.39683 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.207869 | 0.00661320 | ||||||||
\(989\) | 45.6356 | 1.45113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.0760 | 0.733033 | 0.366516 | − | 0.930412i | \(-0.380550\pi\) | ||||
0.366516 | + | 0.930412i | \(0.380550\pi\) | |||||||
\(992\) | 26.6567 | 0.846351 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.8134 | 0.374697 | ||||||||
\(995\) | 32.9106 | 1.04334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.4136 | −0.931538 | −0.465769 | − | 0.884906i | \(-0.654222\pi\) | ||||
−0.465769 | + | 0.884906i | \(0.654222\pi\) | |||||||
\(998\) | 30.4248 | 0.963081 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7623.2.a.cz.1.4 | ✓ | 12 | |
3.2 | odd | 2 | inner | 7623.2.a.cz.1.9 | yes | 12 | |
11.10 | odd | 2 | 7623.2.a.da.1.9 | yes | 12 | ||
33.32 | even | 2 | 7623.2.a.da.1.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cz.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
7623.2.a.cz.1.9 | yes | 12 | 3.2 | odd | 2 | inner | |
7623.2.a.da.1.4 | yes | 12 | 33.32 | even | 2 | ||
7623.2.a.da.1.9 | yes | 12 | 11.10 | odd | 2 |