Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15529.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73914\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 | ||||||||
\(3\) | −2.35292 | −1.35846 | −0.679229 | − | 0.733927i | \(-0.737686\pi\) | ||||
−0.679229 | + | 0.733927i | \(0.737686\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14999 | 0.434656 | 0.217328 | − | 0.976099i | \(-0.430266\pi\) | ||||
0.217328 | + | 0.976099i | \(0.430266\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.53622 | 0.845406 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.32830 | −0.702008 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.91376 | 1.08548 | 0.542740 | − | 0.839901i | \(-0.317387\pi\) | ||||
0.542740 | + | 0.839901i | \(0.317387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.47829 | −0.843609 | −0.421804 | − | 0.906687i | \(-0.638603\pi\) | ||||
−0.421804 | + | 0.906687i | \(0.638603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.32830 | −1.45181 | −0.725905 | − | 0.687795i | \(-0.758579\pi\) | ||||
−0.725905 | + | 0.687795i | \(0.758579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70583 | −0.590461 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.09124 | 0.210009 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.03913 | 0.935742 | 0.467871 | − | 0.883797i | \(-0.345021\pi\) | ||||
0.467871 | + | 0.883797i | \(0.345021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.11668 | 0.200562 | 0.100281 | − | 0.994959i | \(-0.468026\pi\) | ||||
0.100281 | + | 0.994959i | \(0.468026\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.47829 | 0.953647 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00582 | −0.494153 | −0.247077 | − | 0.968996i | \(-0.579470\pi\) | ||||
−0.247077 | + | 0.968996i | \(0.579470\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.20874 | −1.47458 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50291 | 0.234715 | 0.117357 | − | 0.993090i | \(-0.462558\pi\) | ||||
0.117357 | + | 0.993090i | \(0.462558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.03413 | 0.767698 | 0.383849 | − | 0.923396i | \(-0.374598\pi\) | ||||
0.383849 | + | 0.923396i | \(0.374598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.76376 | −0.403136 | −0.201568 | − | 0.979474i | \(-0.564604\pi\) | ||||
−0.201568 | + | 0.979474i | \(0.564604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.67752 | −0.811074 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.18412 | 1.14601 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.41167 | 1.29279 | 0.646396 | − | 0.763002i | \(-0.276275\pi\) | ||||
0.646396 | + | 0.763002i | \(0.276275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.8900 | 1.97222 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.90507 | −0.898963 | −0.449482 | − | 0.893290i | \(-0.648391\pi\) | ||||
−0.449482 | + | 0.893290i | \(0.648391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.95076 | 0.505843 | 0.252921 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252921 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.91663 | 0.367461 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.705834 | 0.0862313 | 0.0431157 | − | 0.999070i | \(-0.486272\pi\) | ||||
0.0431157 | + | 0.999070i | \(0.486272\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.35292 | −0.283258 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.42036 | −0.880634 | −0.440317 | − | 0.897842i | \(-0.645134\pi\) | ||||
−0.440317 | + | 0.897842i | \(0.645134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.08255 | 0.243744 | 0.121872 | − | 0.992546i | \(-0.461110\pi\) | ||||
0.121872 | + | 0.992546i | \(0.461110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.67752 | −0.305132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.6907 | −1.99036 | −0.995181 | − | 0.0980562i | \(-0.968738\pi\) | ||||
−0.995181 | + | 0.0980562i | \(0.968738\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1763 | −1.13069 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.38335 | 0.810428 | 0.405214 | − | 0.914222i | \(-0.367197\pi\) | ||||
0.405214 | + | 0.914222i | \(0.367197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.8566 | −1.27117 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.472471 | −0.0500818 | −0.0250409 | − | 0.999686i | \(-0.507972\pi\) | ||||
−0.0250409 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.50078 | 0.471810 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.62746 | −0.272455 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.82170 | 0.895707 | 0.447854 | − | 0.894107i | \(-0.352189\pi\) | ||||
0.447854 | + | 0.894107i | \(0.352189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.90507 | −0.593482 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.03413 | 0.799426 | 0.399713 | − | 0.916640i | \(-0.369110\pi\) | ||||
0.399713 | + | 0.916640i | \(0.369110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.62828 | −0.456038 | −0.228019 | − | 0.973657i | \(-0.573225\pi\) | ||||
−0.228019 | + | 0.973657i | \(0.573225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.25656 | −0.886617 | −0.443309 | − | 0.896369i | \(-0.646195\pi\) | ||||
−0.443309 | + | 0.896369i | \(0.646195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.07244 | 0.671286 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.8900 | 1.21258 | 0.606292 | − | 0.795242i | \(-0.292656\pi\) | ||||
0.606292 | + | 0.795242i | \(0.292656\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.92614 | 0.917672 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.57904 | −0.507185 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.53622 | −0.318850 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11668 | −0.0990894 | −0.0495447 | − | 0.998772i | \(-0.515777\pi\) | ||||
−0.0495447 | + | 0.998772i | \(0.515777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.8449 | −1.04288 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.0153 | 1.92349 | 0.961744 | − | 0.273950i | \(-0.0883303\pi\) | ||||
0.961744 | + | 0.273950i | \(0.0883303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.27749 | −0.631038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.70002 | 0.145242 | 0.0726211 | − | 0.997360i | \(-0.476864\pi\) | ||||
0.0726211 | + | 0.997360i | \(0.476864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.23624 | −0.783407 | −0.391704 | − | 0.920091i | \(-0.628114\pi\) | ||||
−0.391704 | + | 0.920091i | \(0.628114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.50291 | 0.547644 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.11238 | −0.762016 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.3587 | 1.10181 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1275 | 0.993523 | 0.496762 | − | 0.867887i | \(-0.334522\pi\) | ||||
0.496762 | + | 0.867887i | \(0.334522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0203 | −0.978200 | −0.489100 | − | 0.872228i | \(-0.662675\pi\) | ||||
−0.489100 | + | 0.872228i | \(0.662675\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.82170 | −0.713192 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.05506 | 0.563055 | 0.281527 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281527 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.1449 | −1.75620 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.14999 | 0.0906320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.82669 | 0.221404 | 0.110702 | − | 0.993854i | \(-0.464690\pi\) | ||||
0.110702 | + | 0.993854i | \(0.464690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.44997 | 0.344349 | 0.172175 | − | 0.985066i | \(-0.444921\pi\) | ||||
0.172175 | + | 0.985066i | \(0.444921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.31748 | 0.178268 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0499 | −1.22737 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.5131 | −1.63561 | −0.817806 | − | 0.575494i | \(-0.804810\pi\) | ||||
−0.817806 | + | 0.575494i | \(0.804810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.2470 | 1.22120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.19493 | 0.537775 | 0.268887 | − | 0.963172i | \(-0.413344\pi\) | ||||
0.268887 | + | 0.963172i | \(0.413344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2942 | 0.839489 | 0.419744 | − | 0.907642i | \(-0.362120\pi\) | ||||
0.419744 | + | 0.907642i | \(0.362120\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.29581 | −0.687166 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.09848 | 0.592220 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.25492 | 0.0912818 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.56904 | −0.185890 | −0.0929448 | − | 0.995671i | \(-0.529628\pi\) | ||||
−0.0929448 | + | 0.995671i | \(0.529628\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1994 | 1.02210 | 0.511049 | − | 0.859551i | \(-0.329257\pi\) | ||||
0.511049 | + | 0.859551i | \(0.329257\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.21613 | −0.442881 | −0.221440 | − | 0.975174i | \(-0.571076\pi\) | ||||
−0.221440 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2907 | 1.15482 | 0.577408 | − | 0.816456i | \(-0.304064\pi\) | ||||
0.577408 | + | 0.816456i | \(0.304064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66077 | −0.117142 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.79495 | 0.406726 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.53622 | 0.176279 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.7341 | 1.01918 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.8865 | 1.98863 | 0.994314 | − | 0.106492i | \(-0.0339620\pi\) | ||||
0.994314 | + | 0.106492i | \(0.0339620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.4595 | 1.19630 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.28417 | 0.0871754 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.90007 | −0.331116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.6132 | −0.915721 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.56166 | 0.506366 | 0.253183 | − | 0.967418i | \(-0.418523\pi\) | ||||
0.253183 | + | 0.967418i | \(0.418523\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0683 | 1.06649 | 0.533244 | − | 0.845962i | \(-0.320973\pi\) | ||||
0.533244 | + | 0.845962i | \(0.320973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4175 | 1.61355 | 0.806776 | − | 0.590857i | \(-0.201210\pi\) | ||||
0.806776 | + | 0.590857i | \(0.201210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.29998 | 0.414508 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4703 | 1.27554 | 0.637771 | − | 0.770226i | \(-0.279857\pi\) | ||||
0.637771 | + | 0.770226i | \(0.279857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 41.6248 | 2.70382 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8602 | 0.896543 | 0.448271 | − | 0.893898i | \(-0.352040\pi\) | ||||
0.448271 | + | 0.893898i | \(0.352040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.92756 | 0.317412 | 0.158706 | − | 0.987326i | \(-0.449268\pi\) | ||||
0.158706 | + | 0.987326i | \(0.449268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.6702 | 1.32599 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.7674 | −1.57591 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.3724 | −1.10093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.51015 | 0.600275 | 0.300138 | − | 0.953896i | \(-0.402967\pi\) | ||||
0.300138 | + | 0.953896i | \(0.402967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.32830 | −0.146379 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.2355 | 1.44939 | 0.724695 | − | 0.689070i | \(-0.241981\pi\) | ||||
0.724695 | + | 0.689070i | \(0.241981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.45666 | −0.214787 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7803 | 0.791082 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0290 | 1.11172 | 0.555858 | − | 0.831277i | \(-0.312390\pi\) | ||||
0.555858 | + | 0.831277i | \(0.312390\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.11169 | 0.0680340 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.4111 | 1.67128 | 0.835641 | − | 0.549276i | \(-0.185096\pi\) | ||||
0.835641 | + | 0.549276i | \(0.185096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.24847 | −0.379568 | −0.189784 | − | 0.981826i | \(-0.560779\pi\) | ||||
−0.189784 | + | 0.981826i | \(0.560779\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.5900 | −0.640934 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.40443 | −0.0843837 | −0.0421919 | − | 0.999110i | \(-0.513434\pi\) | ||||
−0.0421919 | + | 0.999110i | \(0.513434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.83215 | 0.169556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.18994 | 0.548226 | 0.274113 | − | 0.961698i | \(-0.411616\pi\) | ||||
0.274113 | + | 0.961698i | \(0.411616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0016 | −1.07009 | −0.535043 | − | 0.844825i | \(-0.679705\pi\) | ||||
−0.535043 | + | 0.844825i | \(0.679705\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.72833 | 0.102020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.90152 | −0.288325 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.7567 | −1.21678 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.42323 | 0.492090 | 0.246045 | − | 0.969258i | \(-0.420869\pi\) | ||||
0.246045 | + | 0.969258i | \(0.420869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.54073 | −0.147428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.91376 | 0.226338 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.78921 | 0.333684 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.9036 | −1.08599 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8900 | 0.619508 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0849 | 1.02550 | 0.512750 | − | 0.858538i | \(-0.328627\pi\) | ||||
0.512750 | + | 0.858538i | \(0.328627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4915 | −1.27129 | −0.635647 | − | 0.771980i | \(-0.719267\pi\) | ||||
−0.635647 | + | 0.771980i | \(0.719267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8443 | −0.609075 | −0.304537 | − | 0.952500i | \(-0.598502\pi\) | ||||
−0.304537 | + | 0.952500i | \(0.598502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7326 | −0.656898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.0116 | 1.22476 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.7799 | 1.20443 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.17830 | −0.175226 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.20804 | 0.231295 | 0.115648 | − | 0.993290i | \(-0.463106\pi\) | ||||
0.115648 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.62341 | −0.417760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.41748 | −0.131689 | −0.0658444 | − | 0.997830i | \(-0.520974\pi\) | ||||
−0.0658444 | + | 0.997830i | \(0.520974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.3290 | −1.64724 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59996 | −0.140796 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.5790 | −0.787194 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.45154 | 0.292654 | 0.146327 | − | 0.989236i | \(-0.453255\pi\) | ||||
0.146327 | + | 0.989236i | \(0.453255\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.03119 | 0.269313 | 0.134657 | − | 0.990892i | \(-0.457007\pi\) | ||||
0.134657 | + | 0.990892i | \(0.457007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.27085 | 0.227961 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.44203 | 0.183201 | 0.0916005 | − | 0.995796i | \(-0.470802\pi\) | ||||
0.0916005 | + | 0.995796i | \(0.470802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.41167 | 0.498118 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.62985 | −0.0860201 | −0.0430100 | − | 0.999075i | \(-0.513695\pi\) | ||||
−0.0430100 | + | 0.999075i | \(0.513695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.0473 | 1.10775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.1270 | 0.688989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.1442 | −1.73012 | −0.865058 | − | 0.501672i | \(-0.832718\pi\) | ||||
−0.865058 | + | 0.501672i | \(0.832718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.81170 | 0.198429 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8233 | 0.561920 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.988438 | 0.0511794 | 0.0255897 | − | 0.999673i | \(-0.491854\pi\) | ||||
0.0255897 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7219 | 1.01573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0116 | −1.54159 | −0.770797 | − | 0.637081i | \(-0.780142\pi\) | ||||
−0.770797 | + | 0.637081i | \(0.780142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.62746 | 0.134609 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.79920 | −0.296325 | −0.148163 | − | 0.988963i | \(-0.547336\pi\) | ||||
−0.148163 | + | 0.988963i | \(0.547336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.7677 | 0.649016 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0173782 | −0.000881108 0 | −0.000440554 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000440554 | 1.00000i | \(0.500140\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.47829 | −0.175905 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −51.8002 | −2.61298 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0414 | 0.503963 | 0.251982 | − | 0.967732i | \(-0.418918\pi\) | ||||
0.251982 | + | 0.967732i | \(0.418918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.1233 | 0.857238 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5639 | 0.677350 | 0.338675 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338675 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.37042 | 0.217706 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.99843 | 0.346899 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.9320 | 1.77672 | 0.888362 | − | 0.459143i | \(-0.151844\pi\) | ||||
0.888362 | + | 0.459143i | \(0.151844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.94077 | −0.390740 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.7321 | 1.06423 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4516 | −1.14569 | −0.572843 | − | 0.819665i | \(-0.694160\pi\) | ||||
−0.572843 | + | 0.819665i | \(0.694160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4043 | 0.945707 | 0.472853 | − | 0.881141i | \(-0.343224\pi\) | ||||
0.472853 | + | 0.881141i | \(0.343224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.00951 | −0.340814 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.54334 | 0.219868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.4407 | 1.03517 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.95076 | 0.0939647 | 0.0469824 | − | 0.998896i | \(-0.485040\pi\) | ||||
0.0469824 | + | 0.998896i | \(0.485040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.24336 | 0.203923 | 0.101961 | − | 0.994788i | \(-0.467488\pi\) | ||||
0.101961 | + | 0.994788i | \(0.467488\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.32830 | −0.302723 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.10799 | 0.148336 | 0.0741682 | − | 0.997246i | \(-0.476370\pi\) | ||||
0.0741682 | + | 0.997246i | \(0.476370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.3994 | −0.685687 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.1652 | −0.482963 | −0.241481 | − | 0.970405i | \(-0.577633\pi\) | ||||
−0.241481 | + | 0.970405i | \(0.577633\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.5350 | −1.34966 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.2659 | 0.578861 | 0.289431 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289431 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.49922 | −0.164772 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.2828 | 1.32884 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0016 | 1.02919 | 0.514597 | − | 0.857432i | \(-0.327942\pi\) | ||||
0.514597 | + | 0.857432i | \(0.327942\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.79565 | −0.177166 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.4111 | 1.46296 | 0.731479 | − | 0.681863i | \(-0.238830\pi\) | ||||
0.731479 | + | 0.681863i | \(0.238830\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4764 | 1.13751 | 0.568757 | − | 0.822506i | \(-0.307425\pi\) | ||||
0.568757 | + | 0.822506i | \(0.307425\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.5050 | 0.671213 | 0.335606 | − | 0.942002i | \(-0.391059\pi\) | ||||
0.335606 | + | 0.942002i | \(0.391059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.811703 | 0.0374809 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.6000 | −0.764886 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.7209 | −0.538930 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.8700 | 1.09293 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.8472 | −1.27237 | −0.636186 | − | 0.771536i | \(-0.719489\pi\) | ||||
−0.636186 | + | 0.771536i | \(0.719489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7640 | −0.536394 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.70583 | −0.123120 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.57547 | 0.343277 | 0.171639 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171639 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.65097 | −0.300767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.43773 | −0.335660 | −0.167830 | − | 0.985816i | \(-0.553676\pi\) | ||||
−0.167830 | + | 0.985816i | \(0.553676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.5275 | −0.789400 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.53335 | −0.382773 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.4602 | 1.18452 | 0.592260 | − | 0.805747i | \(-0.298236\pi\) | ||||
0.592260 | + | 0.805747i | \(0.298236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.4704 | −0.467784 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9385 | 1.02278 | 0.511389 | − | 0.859350i | \(-0.329131\pi\) | ||||
0.511389 | + | 0.859350i | \(0.329131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.45285 | −0.242169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.5603 | −1.53186 | −0.765929 | − | 0.642925i | \(-0.777721\pi\) | ||||
−0.765929 | + | 0.642925i | \(0.777721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.39492 | 0.105945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.90569 | −0.304894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.43486 | 0.283005 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.6186 | 2.22191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.2202 | −0.666807 | −0.333404 | − | 0.942784i | \(-0.608197\pi\) | ||||
−0.333404 | + | 0.942784i | \(0.608197\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.0892 | 0.790985 | 0.395492 | − | 0.918469i | \(-0.370574\pi\) | ||||
0.395492 | + | 0.918469i | \(0.370574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.88414 | −0.169196 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5128 | −0.759989 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.88202 | 0.254778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.9291 | −0.730544 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.2189 | 0.569380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.1203 | 1.85389 | 0.926944 | − | 0.375200i | \(-0.122426\pi\) | ||||
0.926944 | + | 0.375200i | \(0.122426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.5742 | −1.14041 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.6045 | −1.60785 | −0.803926 | − | 0.594730i | \(-0.797259\pi\) | ||||
−0.803926 | + | 0.594730i | \(0.797259\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0200 | 0.427643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.8891 | −1.35852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.3442 | −0.865122 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.1085 | 0.597795 | 0.298898 | − | 0.954285i | \(-0.403381\pi\) | ||||
0.298898 | + | 0.954285i | \(0.403381\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.7024 | 0.833321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.0551 | −0.804505 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.5675 | 1.62543 | 0.812714 | − | 0.582663i | \(-0.197989\pi\) | ||||
0.812714 | + | 0.582663i | \(0.197989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.7026 | −0.491463 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.62316 | −0.0680464 | −0.0340232 | − | 0.999421i | \(-0.510832\pi\) | ||||
−0.0340232 | + | 0.999421i | \(0.510832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2942 | 0.430800 | 0.215400 | − | 0.976526i | \(-0.430894\pi\) | ||||
0.215400 | + | 0.976526i | \(0.430894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.04475 | 0.252523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.2278 | −1.50818 | −0.754091 | − | 0.656770i | \(-0.771922\pi\) | ||||
−0.754091 | + | 0.656770i | \(0.771922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.4101 | −1.38848 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.49079 | 0.352257 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.9131 | −0.907550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.1626 | 1.41004 | 0.705020 | − | 0.709187i | \(-0.250938\pi\) | ||||
0.705020 | + | 0.709187i | \(0.250938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.06669 | −0.291178 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.6260 | 0.601635 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.7326 | −0.810320 | −0.405160 | − | 0.914246i | \(-0.632784\pi\) | ||||
−0.405160 | + | 0.914246i | \(0.632784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.3306 | −1.56877 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5500 | 0.635357 | 0.317678 | − | 0.948199i | \(-0.397097\pi\) | ||||
0.317678 | + | 0.948199i | \(0.397097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7182 | 0.681950 | 0.340975 | − | 0.940072i | \(-0.389243\pi\) | ||||
0.340975 | + | 0.940072i | \(0.389243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.79015 | 0.0729005 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4784 | 1.07472 | 0.537362 | − | 0.843352i | \(-0.319421\pi\) | ||||
0.537362 | + | 0.843352i | \(0.319421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6350 | −0.552520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8167 | −0.437597 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1667 | −0.733748 | −0.366874 | − | 0.930271i | \(-0.619572\pi\) | ||||
−0.366874 | + | 0.930271i | \(0.619572\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.4540 | −1.74939 | −0.874695 | − | 0.484674i | \(-0.838938\pi\) | ||||
−0.874695 | + | 0.484674i | \(0.838938\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.3841 | −1.02027 | −0.510136 | − | 0.860094i | \(-0.670405\pi\) | ||||
−0.510136 | + | 0.860094i | \(0.670405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.09124 | 0.0437900 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.543338 | −0.0217684 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.6682 | −1.38452 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.4551 | 0.416872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.2646 | −1.72234 | −0.861169 | − | 0.508319i | \(-0.830267\pi\) | ||||
−0.861169 | + | 0.508319i | \(0.830267\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −67.9675 | −2.70146 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.2204 | −0.880405 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.8196 | −0.744494 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.6508 | 0.815659 | 0.407830 | − | 0.913058i | \(-0.366286\pi\) | ||||
0.407830 | + | 0.913058i | \(0.366286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.2357 | 1.58674 | 0.793371 | − | 0.608739i | \(-0.208324\pi\) | ||||
0.793371 | + | 0.608739i | \(0.208324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.11511 | 0.161782 | 0.0808909 | − | 0.996723i | \(-0.474223\pi\) | ||||
0.0808909 | + | 0.996723i | \(0.474223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0770 | 0.631079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.02155 | −0.118424 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.74914 | 0.264114 | 0.132057 | − | 0.991242i | \(-0.457842\pi\) | ||||
0.132057 | + | 0.991242i | \(0.457842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.28180 | 0.206063 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.7500 | 0.613531 | 0.306766 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306766 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.51590 | 0.292334 | 0.146167 | − | 0.989260i | \(-0.453306\pi\) | ||||
0.146167 | + | 0.989260i | \(0.453306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.0307 | 1.24397 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.03913 | 0.195116 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7920 | −0.687877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.19854 | −0.355106 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.14630 | 0.275470 | 0.137735 | − | 0.990469i | \(-0.456018\pi\) | ||||
0.137735 | + | 0.990469i | \(0.456018\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.568102 | −0.0218339 | −0.0109170 | − | 0.999940i | \(-0.503475\pi\) | ||||
−0.0109170 | + | 0.999940i | \(0.503475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1449 | 0.389324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.8073 | −1.44878 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.52671 | 0.173210 | 0.0866048 | − | 0.996243i | \(-0.472398\pi\) | ||||
0.0866048 | + | 0.996243i | \(0.472398\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −57.4523 | −2.19194 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.8350 | 1.40330 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0499 | −0.572527 | −0.286263 | − | 0.958151i | \(-0.592413\pi\) | ||||
−0.286263 | + | 0.958151i | \(0.592413\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.79077 | −0.257960 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.22755 | −0.198007 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.8120 | −1.73277 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.3696 | −1.29812 | −0.649062 | − | 0.760736i | \(-0.724838\pi\) | ||||
−0.649062 | + | 0.760736i | \(0.724838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.0217 | 0.717417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.23918 | 0.347475 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.1391 | −1.13190 | −0.565949 | − | 0.824440i | \(-0.691490\pi\) | ||||
−0.565949 | + | 0.824440i | \(0.691490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.8675 | −1.68266 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.11668 | 0.0418200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.6119 | −1.21792 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.6015 | 0.507252 | 0.253626 | − | 0.967302i | \(-0.418377\pi\) | ||||
0.253626 | + | 0.967302i | \(0.418377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.32248 | −0.198220 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.5941 | −0.431191 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.3146 | 1.16139 | 0.580697 | − | 0.814120i | \(-0.302780\pi\) | ||||
0.580697 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1064 | −0.670607 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5102 | −0.647636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.76985 | 0.176178 | 0.0880892 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880892 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64339 | −0.0605351 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.65160 | 0.0975405 | 0.0487703 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487703 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 58.2756 | 2.14081 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.8225 | 1.31420 | 0.657099 | − | 0.753804i | \(-0.271783\pi\) | ||||
0.657099 | + | 0.753804i | \(0.271783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.7258 | 0.685141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.1834 | −0.809485 | −0.404742 | − | 0.914431i | \(-0.632639\pi\) | ||||
−0.404742 | + | 0.914431i | \(0.632639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.3766 | −0.815448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.9318 | −0.760780 | −0.380390 | − | 0.924826i | \(-0.624210\pi\) | ||||
−0.380390 | + | 0.924826i | \(0.624210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.47829 | 0.198849 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.5641 | −1.86920 | −0.934599 | − | 0.355703i | \(-0.884241\pi\) | ||||
−0.934599 | + | 0.355703i | \(0.884241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6450 | −0.385373 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.0247 | −0.975807 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.913079 | −0.0329265 | −0.0164632 | − | 0.999864i | \(-0.505241\pi\) | ||||
−0.0164632 | + | 0.999864i | \(0.505241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −54.6712 | −1.96893 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.4709 | 0.772255 | 0.386127 | − | 0.922445i | \(-0.373813\pi\) | ||||
0.386127 | + | 0.922445i | \(0.373813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.13324 | 0.291778 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.51085 | −0.340761 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2768 | 0.618212 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.49890 | 0.196515 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.0446 | 1.81954 | 0.909771 | − | 0.415111i | \(-0.136257\pi\) | ||||
0.909771 | + | 0.415111i | \(0.136257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.4208 | −1.51022 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.8233 | 0.527057 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4623 | 0.549082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.2250 | −1.77906 | −0.889531 | − | 0.456876i | \(-0.848968\pi\) | ||||
−0.889531 | + | 0.456876i | \(0.848968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.61317 | 0.340089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.19829 | −0.0423395 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.84880 | −0.171110 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −64.4960 | −2.27036 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.5218 | −1.35435 | −0.677177 | − | 0.735820i | \(-0.736797\pi\) | ||||
−0.677177 | + | 0.735820i | \(0.736797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0912 | 1.47802 | 0.739011 | − | 0.673694i | \(-0.235293\pi\) | ||||
0.739011 | + | 0.673694i | \(0.235293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7021 | 0.515627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.8575 | −1.11455 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.4150 | 0.398871 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.4146 | −0.677575 | −0.338788 | − | 0.940863i | \(-0.610017\pi\) | ||||
−0.338788 | + | 0.940863i | \(0.610017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0646 | −0.769122 | −0.384561 | − | 0.923099i | \(-0.625647\pi\) | ||||
−0.384561 | + | 0.923099i | \(0.625647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.3792 | −1.40412 | −0.702061 | − | 0.712117i | \(-0.747737\pi\) | ||||
−0.702061 | + | 0.712117i | \(0.747737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5682 | −0.714362 | −0.357181 | − | 0.934035i | \(-0.616262\pi\) | ||||
−0.357181 | + | 0.934035i | \(0.616262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.30450 | 0.114632 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.7480 | 0.684229 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.21857 | 0.0421199 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2414 | −1.04405 | −0.522025 | − | 0.852930i | \(-0.674823\pi\) | ||||
−0.522025 | + | 0.852930i | \(0.674823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.60721 | −0.124386 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.6232 | −0.744741 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.41584 | −0.220451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 42.3564 | 1.45367 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00582 | −0.103038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0590 | 1.09768 | 0.548839 | − | 0.835928i | \(-0.315070\pi\) | ||||
0.548839 | + | 0.835928i | \(0.315070\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.6012 | 1.83098 | 0.915491 | − | 0.402338i | \(-0.131802\pi\) | ||||
0.915491 | + | 0.402338i | \(0.131802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.33677 | 0.113849 | 0.0569246 | − | 0.998378i | \(-0.481871\pi\) | ||||
0.0569246 | + | 0.998378i | \(0.481871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.06662 | −0.138590 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.5226 | 1.82193 | 0.910966 | − | 0.412482i | \(-0.135338\pi\) | ||||
0.910966 | + | 0.412482i | \(0.135338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.5329 | 0.391677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.1892 | 1.39725 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.76246 | 0.0936024 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.3737 | 0.757236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.2457 | −1.73044 | −0.865222 | − | 0.501389i | \(-0.832823\pi\) | ||||
−0.865222 | + | 0.501389i | \(0.832823\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.8192 | −0.668484 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.3392 | −1.35906 | −0.679532 | − | 0.733646i | \(-0.737817\pi\) | ||||
−0.679532 | + | 0.733646i | \(0.737817\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3763 | 0.988592 | 0.494296 | − | 0.869294i | \(-0.335426\pi\) | ||||
0.494296 | + | 0.869294i | \(0.335426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.1776 | −1.91984 | −0.959919 | − | 0.280278i | \(-0.909573\pi\) | ||||
−0.959919 | + | 0.280278i | \(0.909573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.28417 | −0.0430698 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.6933 | 0.793756 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.4899 | 0.585278 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.20874 | −0.307471 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.62710 | 0.187674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7365 | −1.09061 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.6215 | −0.453296 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.8357 | 1.55515 | 0.777576 | − | 0.628789i | \(-0.216449\pi\) | ||||
0.777576 | + | 0.628789i | \(0.216449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.3763 | 0.675839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.7225 | −0.554042 | −0.277021 | − | 0.960864i | \(-0.589347\pi\) | ||||
−0.277021 | + | 0.960864i | \(0.589347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1906 | −0.568927 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.3174 | 0.836055 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.7915 | −0.949743 | −0.474872 | − | 0.880055i | \(-0.657505\pi\) | ||||
−0.474872 | + | 0.880055i | \(0.657505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.0415 | −0.955911 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7383 | −0.385537 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.1756 | −0.694750 | −0.347375 | − | 0.937726i | \(-0.612927\pi\) | ||||
−0.347375 | + | 0.937726i | \(0.612927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.9290 | 1.17753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.5522 | −1.39310 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5408 | −0.965056 | −0.482528 | − | 0.875881i | \(-0.660281\pi\) | ||||
−0.482528 | + | 0.875881i | \(0.660281\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.9206 | 1.72700 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.20314 | 0.0718203 | 0.0359101 | − | 0.999355i | \(-0.488567\pi\) | ||||
0.0359101 | + | 0.999355i | \(0.488567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.50291 | 0.0489414 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.5548 | 0.797922 | 0.398961 | − | 0.916968i | \(-0.369371\pi\) | ||||
0.398961 | + | 0.916968i | \(0.369371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.15060 | 0.264580 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.5157 | 0.827402 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.5697 | −1.24940 | −0.624698 | − | 0.780866i | \(-0.714778\pi\) | ||||
−0.624698 | + | 0.780866i | \(0.714778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.6058 | 0.892368 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.95501 | 0.0631304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7530 | −0.959775 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.85650 | −0.156175 | −0.0780873 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780873 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −51.7915 | −1.66378 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4384 | −0.334985 | −0.167492 | − | 0.985873i | \(-0.553567\pi\) | ||||
−0.167492 | + | 0.985873i | \(0.553567\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6216 | −0.340513 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.9985 | 1.27967 | 0.639833 | − | 0.768514i | \(-0.279004\pi\) | ||||
0.639833 | + | 0.768514i | \(0.279004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.10005 | 0.0351578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.4766 | −0.749552 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.68073 | 0.308767 | 0.154384 | − | 0.988011i | \(-0.450661\pi\) | ||||
0.154384 | + | 0.988011i | \(0.450661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.47829 | 0.238037 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.03413 | 0.160076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.6733 | −1.16497 | −0.582484 | − | 0.812842i | \(-0.697919\pi\) | ||||
−0.582484 | + | 0.812842i | \(0.697919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.90118 | −0.314204 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.2901 | −1.46602 | −0.733010 | − | 0.680217i | \(-0.761885\pi\) | ||||
−0.733010 | + | 0.680217i | \(0.761885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.28007 | −0.103777 |
(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 | 4600.2.a.ba.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 9200.2.a.cp.1.4 | 4 | |||
5.2 | odd | 4 | 4600.2.e.t.4049.7 | 8 | |||
5.3 | odd | 4 | 4600.2.e.t.4049.2 | 8 | |||
5.4 | even | 2 | 4600.2.a.bb.1.4 | yes | 4 | ||
20.19 | odd | 2 | 9200.2.a.cn.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.ba.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4600.2.a.bb.1.4 | yes | 4 | 5.4 | even | 2 | ||
4600.2.e.t.4049.2 | 8 | 5.3 | odd | 4 | |||
4600.2.e.t.4049.7 | 8 | 5.2 | odd | 4 | |||
9200.2.a.cn.1.1 | 4 | 20.19 | odd | 2 | |||
9200.2.a.cp.1.4 | 4 | 4.3 | odd | 2 |