Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.0655463357\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23724.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 4x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.52350\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 | ||||||||
\(3\) | −2.36807 | −1.36721 | −0.683604 | − | 0.729853i | \(-0.739588\pi\) | ||||
−0.683604 | + | 0.729853i | \(0.739588\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.60777 | 0.869256 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.04701 | 1.52173 | 0.760865 | − | 0.648910i | \(-0.224775\pi\) | ||||
0.760865 | + | 0.648910i | \(0.224775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36807 | 0.611434 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.60777 | 0.389941 | 0.194971 | − | 0.980809i | \(-0.437539\pi\) | ||||
0.194971 | + | 0.980809i | \(0.437539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29691 | −0.756362 | −0.378181 | − | 0.925732i | \(-0.623450\pi\) | ||||
−0.378181 | + | 0.925732i | \(0.623450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.36807 | −0.516756 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.31086 | 0.481848 | 0.240924 | − | 0.970544i | \(-0.422550\pi\) | ||||
0.240924 | + | 0.970544i | \(0.422550\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.928833 | 0.178754 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32106 | 0.245316 | 0.122658 | − | 0.992449i | \(-0.460858\pi\) | ||||
0.122658 | + | 0.992449i | \(0.460858\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.36807 | −0.784529 | −0.392265 | − | 0.919852i | \(-0.628308\pi\) | ||||
−0.392265 | + | 0.919852i | \(0.628308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.9517 | −2.08052 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6306 | 1.74766 | 0.873831 | − | 0.486229i | \(-0.161628\pi\) | ||||
0.873831 | + | 0.486229i | \(0.161628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.36807 | −0.379195 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.249898 | 0.0390274 | 0.0195137 | − | 0.999810i | \(-0.493788\pi\) | ||||
0.0195137 | + | 0.999810i | \(0.493788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.68914 | 0.562588 | 0.281294 | − | 0.959622i | \(-0.409236\pi\) | ||||
0.281294 | + | 0.959622i | \(0.409236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.60777 | −0.388743 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.21554 | −0.469034 | −0.234517 | − | 0.972112i | \(-0.575351\pi\) | ||||
−0.234517 | + | 0.972112i | \(0.575351\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.80731 | −0.533130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73615 | −0.650560 | −0.325280 | − | 0.945618i | \(-0.605458\pi\) | ||||
−0.325280 | + | 0.945618i | \(0.605458\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.04701 | −0.680538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.80731 | 1.03410 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.58361 | −0.726924 | −0.363462 | − | 0.931609i | \(-0.618405\pi\) | ||||
−0.363462 | + | 0.931609i | \(0.618405\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.142334 | −0.0182240 | −0.00911200 | − | 0.999958i | \(-0.502900\pi\) | ||||
−0.00911200 | + | 0.999958i | \(0.502900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.60777 | 0.328548 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.34391 | −0.775032 | −0.387516 | − | 0.921863i | \(-0.626667\pi\) | ||||
−0.387516 | + | 0.921863i | \(0.626667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.47229 | −0.658786 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.42528 | −0.762541 | −0.381270 | − | 0.924464i | \(-0.624513\pi\) | ||||
−0.381270 | + | 0.924464i | \(0.624513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.35787 | 0.393009 | 0.196505 | − | 0.980503i | \(-0.437041\pi\) | ||||
0.196505 | + | 0.980503i | \(0.437041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.36807 | −0.273441 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.04701 | 0.575160 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0801 | −1.24660 | −0.623302 | − | 0.781981i | \(-0.714209\pi\) | ||||
−0.623302 | + | 0.781981i | \(0.714209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0228 | −1.11365 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.73615 | −0.519859 | −0.259930 | − | 0.965628i | \(-0.583699\pi\) | ||||
−0.259930 | + | 0.965628i | \(0.583699\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.60777 | −0.174387 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.12838 | −0.335397 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.27275 | −0.770910 | −0.385455 | − | 0.922727i | \(-0.625955\pi\) | ||||
−0.385455 | + | 0.922727i | \(0.625955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.3439 | 1.07261 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.29691 | 0.338255 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52061 | 0.357464 | 0.178732 | − | 0.983898i | \(-0.442801\pi\) | ||||
0.178732 | + | 0.983898i | \(0.442801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.1614 | 1.32277 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.91863 | 0.189048 | 0.0945242 | − | 0.995523i | \(-0.469867\pi\) | ||||
0.0945242 | + | 0.995523i | \(0.469867\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.36807 | 0.231100 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6891 | 1.13003 | 0.565016 | − | 0.825080i | \(-0.308870\pi\) | ||||
0.565016 | + | 0.825080i | \(0.308870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0940 | 1.73309 | 0.866546 | − | 0.499097i | \(-0.166335\pi\) | ||||
0.866546 | + | 0.499097i | \(0.166335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −25.1741 | −2.38942 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.25675 | 0.776730 | 0.388365 | − | 0.921506i | \(-0.373040\pi\) | ||||
0.388365 | + | 0.921506i | \(0.373040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.31086 | −0.215489 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.60777 | 0.241088 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.60777 | 0.147384 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.4723 | 1.31566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.591776 | −0.0533586 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.18934 | 0.460480 | 0.230240 | − | 0.973134i | \(-0.426049\pi\) | ||||
0.230240 | + | 0.973134i | \(0.426049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.73615 | −0.769175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.37827 | −0.295161 | −0.147581 | − | 0.989050i | \(-0.547149\pi\) | ||||
−0.147581 | + | 0.989050i | \(0.547149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.29691 | −0.285878 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.928833 | −0.0799412 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.84167 | 0.242781 | 0.121390 | − | 0.992605i | \(-0.461265\pi\) | ||||
0.121390 | + | 0.992605i | \(0.461265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.95168 | 0.674453 | 0.337226 | − | 0.941424i | \(-0.390511\pi\) | ||||
0.337226 | + | 0.941424i | \(0.390511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.61462 | 0.641267 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.04701 | 0.422052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32106 | −0.109708 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.36807 | −0.195315 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.09402 | −0.171548 | −0.0857742 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857742 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.64082 | 0.459043 | 0.229522 | − | 0.973304i | \(-0.426284\pi\) | ||||
0.229522 | + | 0.973304i | \(0.426284\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.19269 | 0.338959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.36807 | 0.350852 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7450 | 1.81525 | 0.907626 | − | 0.419780i | \(-0.137893\pi\) | ||||
0.907626 | + | 0.419780i | \(0.137893\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.2155 | 0.889450 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.31086 | 0.182121 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7202 | −0.917993 | −0.458997 | − | 0.888438i | \(-0.651791\pi\) | ||||
−0.458997 | + | 0.888438i | \(0.651791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.9517 | 0.930437 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.2364 | 1.25641 | 0.628203 | − | 0.778049i | \(-0.283791\pi\) | ||||
0.628203 | + | 0.778049i | \(0.283791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.59757 | −0.657472 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3872 | 1.62604 | 0.813018 | − | 0.582238i | \(-0.197823\pi\) | ||||
0.813018 | + | 0.582238i | \(0.197823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2224 | 0.993856 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.823305 | −0.0615367 | −0.0307684 | − | 0.999527i | \(-0.509795\pi\) | ||||
−0.0307684 | + | 0.999527i | \(0.509795\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3579 | 0.844224 | 0.422112 | − | 0.906544i | \(-0.361289\pi\) | ||||
0.422112 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.337057 | 0.0249160 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.6306 | −0.781579 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.11442 | 0.593385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.928833 | 0.0675627 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.4400 | −1.33427 | −0.667135 | − | 0.744937i | \(-0.732479\pi\) | ||||
−0.667135 | + | 0.744937i | \(0.732479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.93773 | 0.499388 | 0.249694 | − | 0.968325i | \(-0.419670\pi\) | ||||
0.249694 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.36807 | 0.169581 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.3668 | 1.94980 | 0.974901 | − | 0.222641i | \(-0.0714677\pi\) | ||||
0.974901 | + | 0.222641i | \(0.0714677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5663 | 0.819914 | 0.409957 | − | 0.912105i | \(-0.365544\pi\) | ||||
0.409957 | + | 0.912105i | \(0.365544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.0228 | 1.05963 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.32106 | 0.0927206 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.249898 | −0.0174536 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.02619 | 0.418849 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.6395 | −1.15098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.48625 | 0.308846 | 0.154423 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154423 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.2155 | 1.04255 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.68914 | −0.251597 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.36807 | −0.296524 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.95168 | −0.537325 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.60777 | 0.108150 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.2816 | −1.55905 | −0.779527 | − | 0.626369i | \(-0.784540\pi\) | ||||
−0.779527 | + | 0.626369i | \(0.784540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.60777 | 0.173851 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9238 | 1.18964 | 0.594821 | − | 0.803858i | \(-0.297223\pi\) | ||||
0.594821 | + | 0.803858i | \(0.297223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.9834 | −1.38662 | −0.693312 | − | 0.720638i | \(-0.743849\pi\) | ||||
−0.693312 | + | 0.720638i | \(0.743849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.9517 | −0.786363 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.35787 | −0.219981 | −0.109991 | − | 0.993933i | \(-0.535082\pi\) | ||||
−0.109991 | + | 0.993933i | \(0.535082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.21554 | 0.209758 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.2384 | 1.70437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.16853 | 0.269640 | 0.134820 | − | 0.990870i | \(-0.456954\pi\) | ||||
0.134820 | + | 0.990870i | \(0.456954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.93773 | 0.575729 | 0.287865 | − | 0.957671i | \(-0.407055\pi\) | ||||
0.287865 | + | 0.957671i | \(0.407055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.9483 | 1.34384 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.29691 | −0.209777 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2155 | 0.710756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9034 | 1.50877 | 0.754383 | − | 0.656434i | \(-0.227936\pi\) | ||||
0.754383 | + | 0.656434i | \(0.227936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.6629 | 0.733243 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.80731 | 0.238423 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0457 | −0.876147 | −0.438073 | − | 0.898939i | \(-0.644339\pi\) | ||||
−0.438073 | + | 0.898939i | \(0.644339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6306 | 0.660554 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.44503 | 0.213242 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.68914 | 0.104157 | 0.0520783 | − | 0.998643i | \(-0.483415\pi\) | ||||
0.0520783 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.73615 | 0.290939 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.2224 | 1.05399 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3991 | −0.634044 | −0.317022 | − | 0.948418i | \(-0.602683\pi\) | ||||
−0.317022 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7903 | −0.655461 | −0.327731 | − | 0.944771i | \(-0.606284\pi\) | ||||
−0.327731 | + | 0.944771i | \(0.606284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.36807 | −0.143322 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.04701 | 0.304346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6629 | 0.700758 | 0.350379 | − | 0.936608i | \(-0.386053\pi\) | ||||
0.350379 | + | 0.936608i | \(0.386053\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3909 | −0.681957 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.5180 | 1.76090 | 0.880448 | − | 0.474143i | \(-0.157242\pi\) | ||||
0.880448 | + | 0.474143i | \(0.157242\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.8703 | −1.65672 | −0.828359 | − | 0.560197i | \(-0.810725\pi\) | ||||
−0.828359 | + | 0.560197i | \(0.810725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.80731 | −0.462465 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.249898 | 0.0147510 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4151 | −0.847946 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.33706 | −0.488727 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.89888 | 0.403037 | 0.201519 | − | 0.979485i | \(-0.435412\pi\) | ||||
0.201519 | + | 0.979485i | \(0.435412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.58361 | 0.325090 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.68783 | 0.272015 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.31086 | 0.133641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.68914 | 0.212638 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.2084 | −0.816253 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.142334 | 0.00815002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.74325 | −0.0994923 | −0.0497461 | − | 0.998762i | \(-0.515841\pi\) | ||||
−0.0497461 | + | 0.998762i | \(0.515841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.54346 | −0.258468 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1189 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5295 | −1.21692 | −0.608460 | − | 0.793585i | \(-0.708212\pi\) | ||||
−0.608460 | + | 0.793585i | \(0.708212\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.60777 | −0.146931 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.9034 | 1.67954 | 0.839770 | − | 0.542942i | \(-0.182690\pi\) | ||||
0.839770 | + | 0.542942i | \(0.182690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.66742 | 0.373304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.6807 | −1.54499 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.30066 | −0.294937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −42.8479 | −2.36950 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.21554 | −0.177278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.93259 | −0.271120 | −0.135560 | − | 0.990769i | \(-0.543283\pi\) | ||||
−0.135560 | + | 0.990769i | \(0.543283\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.7222 | 1.51917 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.34391 | 0.346605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.24345 | −0.176682 | −0.0883410 | − | 0.996090i | \(-0.528157\pi\) | ||||
−0.0883410 | + | 0.996090i | \(0.528157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.5526 | −1.06195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.0457 | −1.19384 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.47229 | 0.294618 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.2758 | 1.35688 | 0.678439 | − | 0.734656i | \(-0.262657\pi\) | ||||
0.678439 | + | 0.734656i | \(0.262657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.62614 | 0.194103 | 0.0970513 | − | 0.995279i | \(-0.469059\pi\) | ||||
0.0970513 | + | 0.995279i | \(0.469059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.928833 | 0.0495774 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1876 | −0.808356 | −0.404178 | − | 0.914680i | \(-0.632442\pi\) | ||||
−0.404178 | + | 0.914680i | \(0.632442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.42528 | 0.341019 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.80731 | −0.201504 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.23766 | −0.0653212 | −0.0326606 | − | 0.999467i | \(-0.510398\pi\) | ||||
−0.0326606 | + | 0.999467i | \(0.510398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.13041 | −0.427916 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −34.2714 | −1.79878 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.35787 | −0.175759 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.79025 | −0.354448 | −0.177224 | − | 0.984171i | \(-0.556712\pi\) | ||||
−0.177224 | + | 0.984171i | \(0.556712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.651675 | 0.0339248 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.73615 | −0.245888 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8550 | −0.820943 | −0.410472 | − | 0.911873i | \(-0.634636\pi\) | ||||
−0.410472 | + | 0.911873i | \(0.634636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.36807 | 0.122287 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.32106 | 0.0680383 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.40488 | 0.123530 | 0.0617652 | − | 0.998091i | \(-0.480327\pi\) | ||||
0.0617652 | + | 0.998091i | \(0.480327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2887 | −0.629571 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.7818 | 1.57288 | 0.786439 | − | 0.617667i | \(-0.211922\pi\) | ||||
0.786439 | + | 0.617667i | \(0.211922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.04701 | −0.257219 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.62042 | 0.489033 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.8233 | 0.954379 | 0.477190 | − | 0.878800i | \(-0.341655\pi\) | ||||
0.477190 | + | 0.878800i | \(0.341655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.71533 | 0.187892 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0801 | 0.557498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.5459 | −1.78400 | −0.891999 | − | 0.452038i | \(-0.850697\pi\) | ||||
−0.891999 | + | 0.452038i | \(0.850697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.80731 | 0.390854 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5180 | 0.874807 | 0.437403 | − | 0.899265i | \(-0.355898\pi\) | ||||
0.437403 | + | 0.899265i | \(0.355898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.36807 | −0.217589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0228 | 0.498039 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.6528 | 2.65947 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.2333 | 1.74218 | 0.871088 | − | 0.491127i | \(-0.163415\pi\) | ||||
0.871088 | + | 0.491127i | \(0.163415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.72929 | −0.331931 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.58361 | −0.274751 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.73615 | 0.232488 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.8302 | −0.922117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.58051 | 0.0772129 | 0.0386064 | − | 0.999254i | \(-0.487708\pi\) | ||||
0.0386064 | + | 0.999254i | \(0.487708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9521 | −0.923668 | −0.461834 | − | 0.886966i | \(-0.652808\pi\) | ||||
−0.461834 | + | 0.886966i | \(0.652808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.38538 | −0.407711 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.60777 | 0.0779882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.142334 | −0.00688803 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.9517 | −0.577033 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3566 | −0.787868 | −0.393934 | − | 0.919139i | \(-0.628886\pi\) | ||||
−0.393934 | + | 0.919139i | \(0.628886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0801 | 0.916929 | 0.458465 | − | 0.888713i | \(-0.348400\pi\) | ||||
0.458465 | + | 0.888713i | \(0.348400\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.12838 | 0.149994 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.61870 | −0.364452 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.4244 | −1.35662 | −0.678311 | − | 0.734775i | \(-0.737288\pi\) | ||||
−0.678311 | + | 0.734775i | \(0.737288\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.60777 | 0.124179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.8493 | −0.848044 | −0.424022 | − | 0.905652i | \(-0.639382\pi\) | ||||
−0.424022 | + | 0.905652i | \(0.639382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.27275 | 0.344761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.95878 | 0.234542 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.21554 | 0.434908 | 0.217454 | − | 0.976071i | \(-0.430225\pi\) | ||||
0.217454 | + | 0.976071i | \(0.430225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.26124 | 0.0593892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.3579 | −0.627608 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.55741 | 0.0728528 | 0.0364264 | − | 0.999336i | \(-0.488403\pi\) | ||||
0.0364264 | + | 0.999336i | \(0.488403\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.49335 | 0.0697035 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8878 | 1.29886 | 0.649432 | − | 0.760420i | \(-0.275007\pi\) | ||||
0.649432 | + | 0.760420i | \(0.275007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7913 | 0.501515 | 0.250758 | − | 0.968050i | \(-0.419320\pi\) | ||||
0.250758 | + | 0.968050i | \(0.419320\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.3439 | −0.479688 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.69599 | 0.356128 | 0.178064 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178064 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.34391 | −0.292935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.8619 | −2.48183 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6191 | 0.856107 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.29691 | −0.151272 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3508 | −0.565503 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.0488 | 0.916053 | 0.458027 | − | 0.888939i | \(-0.348556\pi\) | ||||
0.458027 | + | 0.888939i | \(0.348556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6306 | 0.484714 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.47229 | −0.248998 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.52061 | −0.159863 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.26868 | 0.148118 | 0.0740589 | − | 0.997254i | \(-0.476405\pi\) | ||||
0.0740589 | + | 0.997254i | \(0.476405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.7542 | 1.25509 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3761 | 1.64163 | 0.820814 | − | 0.571195i | \(-0.193520\pi\) | ||||
0.820814 | + | 0.571195i | \(0.193520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.12397 | 0.0956586 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.1614 | −0.591562 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.42528 | −0.288213 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.68914 | 0.165148 | 0.0825742 | − | 0.996585i | \(-0.473686\pi\) | ||||
0.0825742 | + | 0.996585i | \(0.473686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.4489 | −1.71777 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50600 | 0.245500 | 0.122750 | − | 0.992438i | \(-0.460829\pi\) | ||||
0.122750 | + | 0.992438i | \(0.460829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.36807 | −0.105170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.59447 | 0.114998 | 0.0574988 | − | 0.998346i | \(-0.481687\pi\) | ||||
0.0574988 | + | 0.998346i | \(0.481687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.35787 | 0.148543 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.06227 | −0.135203 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.91863 | −0.0845450 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2288 | −0.713744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −50.6464 | −2.22313 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.83278 | −0.124106 | −0.0620532 | − | 0.998073i | \(-0.519765\pi\) | ||||
−0.0620532 | + | 0.998073i | \(0.519765\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.12021 | 0.355072 | 0.177536 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.36807 | −0.103351 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.02285 | −0.305920 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6599 | −0.767822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.5608 | −0.631883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.249898 | 0.0108243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6891 | −0.505365 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.94965 | 0.0841335 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.04701 | 0.217390 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.5251 | −1.05442 | −0.527208 | − | 0.849736i | \(-0.676761\pi\) | ||||
−0.527208 | + | 0.849736i | \(0.676761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.8963 | −1.15423 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0940 | −0.775062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2168 | 0.607868 | 0.303934 | − | 0.952693i | \(-0.401700\pi\) | ||||
0.303934 | + | 0.952693i | \(0.401700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.371174 | −0.0158413 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.35543 | −0.185547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0801 | −0.471172 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.1741 | 1.06858 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.10349 | −0.173871 | −0.0869353 | − | 0.996214i | \(-0.527707\pi\) | ||||
−0.0869353 | + | 0.996214i | \(0.527707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.68914 | 0.156034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.2155 | −0.811281 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0446 | −0.507621 | −0.253810 | − | 0.967254i | \(-0.581684\pi\) | ||||
−0.253810 | + | 0.967254i | \(0.581684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.25675 | −0.347364 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.0228 | −0.420920 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.17204 | −0.384512 | −0.192256 | − | 0.981345i | \(-0.561580\pi\) | ||||
−0.192256 | + | 0.981345i | \(0.561580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.9565 | 0.500364 | 0.250182 | − | 0.968199i | \(-0.419510\pi\) | ||||
0.250182 | + | 0.968199i | \(0.419510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.6672 | 1.82422 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.31086 | 0.0963696 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.5459 | −1.47980 | −0.739898 | − | 0.672719i | \(-0.765126\pi\) | ||||
−0.739898 | + | 0.672719i | \(0.765126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.4290 | −0.682768 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.73615 | −0.196488 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.9034 | −0.989976 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.60777 | −0.107818 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.4373 | −1.25628 | −0.628140 | − | 0.778100i | \(-0.716184\pi\) | ||||
−0.628140 | + | 0.778100i | \(0.716184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.4011 | 0.593388 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −64.8065 | −2.66578 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9197 | −0.489483 | −0.244742 | − | 0.969588i | \(-0.578703\pi\) | ||||
−0.244742 | + | 0.969588i | \(0.578703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.60777 | −0.0659121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.3899 | −1.12099 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.7011 | 1.05012 | 0.525060 | − | 0.851065i | \(-0.324043\pi\) | ||||
0.525060 | + | 0.851065i | \(0.324043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3712 | −0.830958 | −0.415479 | − | 0.909603i | \(-0.636386\pi\) | ||||
−0.415479 | + | 0.909603i | \(0.636386\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.5435 | −0.673702 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.4723 | −0.588382 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.6746 | 1.81329 | 0.906643 | − | 0.421899i | \(-0.138636\pi\) | ||||
0.906643 | + | 0.421899i | \(0.138636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.12838 | −0.126768 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.21554 | −0.130087 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.43369 | 0.0982959 | 0.0491480 | − | 0.998792i | \(-0.484349\pi\) | ||||
0.0491480 | + | 0.998792i | \(0.484349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.591776 | 0.0238627 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.9102 | 1.44569 | 0.722846 | − | 0.691010i | \(-0.242834\pi\) | ||||
0.722846 | + | 0.691010i | \(0.242834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1677 | 1.33312 | 0.666561 | − | 0.745450i | \(-0.267765\pi\) | ||||
0.666561 | + | 0.745450i | \(0.267765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.14641 | 0.0861323 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.27275 | −0.291376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 39.4036 | 1.57363 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.0916 | 0.681486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.8452 | −1.26774 | −0.633868 | − | 0.773441i | \(-0.718534\pi\) | ||||
−0.633868 | + | 0.773441i | \(0.718534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6238 | −0.422257 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.18934 | −0.205933 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.7556 | −0.662843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.5619 | −0.970137 | −0.485068 | − | 0.874476i | \(-0.661205\pi\) | ||||
−0.485068 | + | 0.874476i | \(0.661205\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9521 | −0.905142 | −0.452571 | − | 0.891728i | \(-0.649493\pi\) | ||||
−0.452571 | + | 0.891728i | \(0.649493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.73615 | 0.343985 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.4138 | −0.881176 | −0.440588 | − | 0.897709i | \(-0.645230\pi\) | ||||
−0.440588 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.1805 | −1.10618 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.3439 | 0.405410 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.7539 | −0.968696 | −0.484348 | − | 0.874875i | \(-0.660943\pi\) | ||||
−0.484348 | + | 0.874875i | \(0.660943\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.37827 | 0.132000 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.75655 | 0.341626 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1329 | −0.550538 | −0.275269 | − | 0.961367i | \(-0.588767\pi\) | ||||
−0.275269 | + | 0.961367i | \(0.588767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4145 | 0.755136 | 0.377568 | − | 0.925982i | \(-0.376760\pi\) | ||||
0.377568 | + | 0.925982i | \(0.376760\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.80731 | −0.147864 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.29691 | 0.127849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.05280 | 0.118205 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.1326 | 2.13155 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.718361 | −0.0277320 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.9211 | 1.92432 | 0.962159 | − | 0.272487i | \(-0.0878462\pi\) | ||||
0.962159 | + | 0.272487i | \(0.0878462\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.928833 | 0.0357508 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1880 | 0.699023 | 0.349511 | − | 0.936932i | \(-0.386348\pi\) | ||||
0.349511 | + | 0.936932i | \(0.386348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52061 | 0.135109 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.4448 | −1.62649 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.9879 | 1.91273 | 0.956367 | − | 0.292168i | \(-0.0943766\pi\) | ||||
0.956367 | + | 0.292168i | \(0.0943766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.84167 | −0.108575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.6903 | 1.89580 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.73615 | −0.180433 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.75386 | −0.371054 | −0.185527 | − | 0.982639i | \(-0.559399\pi\) | ||||
−0.185527 | + | 0.982639i | \(0.559399\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.1614 | 0.499961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.95168 | −0.301624 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.401777 | 0.0152184 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.95168 | 0.300760 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.10756 | −0.306218 | −0.153109 | − | 0.988209i | \(-0.548929\pi\) | ||||
−0.153109 | + | 0.988209i | \(0.548929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.0481 | −1.32187 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.61462 | −0.286783 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.13523 | 0.192858 | 0.0964289 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964289 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.8942 | −1.08362 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.0940 | −0.378024 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.04701 | −0.188747 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.87138 | −0.368653 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.9034 | 1.18979 | 0.594897 | − | 0.803802i | \(-0.297193\pi\) | ||||
0.594897 | + | 0.803802i | \(0.297193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.91863 | 0.0714536 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.1652 | −0.787142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32106 | 0.0490631 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.3402 | −0.976902 | −0.488451 | − | 0.872591i | \(-0.662438\pi\) | ||||
−0.488451 | + | 0.872591i | \(0.662438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.5386 | −0.723653 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.93128 | 0.219376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.89929 | 0.217895 | 0.108948 | − | 0.994047i | \(-0.465252\pi\) | ||||
0.108948 | + | 0.994047i | \(0.465252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.36807 | 0.0873477 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.0178 | −1.17939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.8697 | 0.583775 | 0.291887 | − | 0.956453i | \(-0.405717\pi\) | ||||
0.291887 | + | 0.956453i | \(0.405717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.80731 | 0.286809 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.55945 | 0.350702 | 0.175351 | − | 0.984506i | \(-0.443894\pi\) | ||||
0.175351 | + | 0.984506i | \(0.443894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.09402 | 0.0767188 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.3508 | −0.451891 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6891 | 0.427112 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.7863 | −0.722011 | −0.361005 | − | 0.932564i | \(-0.617566\pi\) | ||||
−0.361005 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −56.6049 | −2.06280 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.64082 | −0.205290 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.64923 | 0.278016 | 0.139008 | − | 0.990291i | \(-0.455609\pi\) | ||||
0.139008 | + | 0.990291i | \(0.455609\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.6187 | −1.00250 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.55701 | −0.310191 | −0.155096 | − | 0.987899i | \(-0.549569\pi\) | ||||
−0.155096 | + | 0.987899i | \(0.549569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0940 | 0.655047 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.19269 | −0.151587 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.58361 | −0.201612 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4626 | −1.53124 | −0.765620 | − | 0.643293i | \(-0.777568\pi\) | ||||
−0.765620 | + | 0.643293i | \(0.777568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.2612 | 1.19787 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.7290 | −0.925409 | −0.462705 | − | 0.886512i | \(-0.653121\pi\) | ||||
−0.462705 | + | 0.886512i | \(0.653121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.36807 | −0.156906 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.1741 | −0.903115 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.823889 | −0.0295189 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.4285 | −1.16038 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.22705 | 0.0438511 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.7450 | −0.811805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.9038 | 1.10160 | 0.550800 | − | 0.834637i | \(-0.314323\pi\) | ||||
0.550800 | + | 0.834637i | \(0.314323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.00000 | −0.142404 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.25675 | 0.293576 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.142334 | −0.00505443 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.2155 | −0.397774 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.2585 | 1.81567 | 0.907835 | − | 0.419327i | \(-0.137734\pi\) | ||||
0.907835 | + | 0.419327i | \(0.137734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.16984 | −0.182896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.9656 | −0.670118 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9472 | 0.598054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.31086 | −0.0814472 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.6258 | 0.866869 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.9701 | −0.702112 | −0.351056 | − | 0.936354i | \(-0.614177\pi\) | ||||
−0.351056 | + | 0.936354i | \(0.614177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.8218 | 0.731151 | 0.365575 | − | 0.930782i | \(-0.380872\pi\) | ||||
0.365575 | + | 0.930782i | \(0.380872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5521 | 0.896151 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7202 | 0.410539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.1627 | −0.425520 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.60777 | 0.0911228 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7641 | −0.515269 | −0.257635 | − | 0.966242i | \(-0.582943\pi\) | ||||
−0.257635 | + | 0.966242i | \(0.582943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.81107 | 0.341992 | 0.170996 | − | 0.985272i | \(-0.445301\pi\) | ||||
0.170996 | + | 0.985272i | \(0.445301\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.9517 | −0.416104 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.3344 | −0.915738 | −0.457869 | − | 0.889020i | \(-0.651387\pi\) | ||||
−0.457869 | + | 0.889020i | \(0.651387\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0453 | −0.453082 | −0.226541 | − | 0.974002i | \(-0.572742\pi\) | ||||
−0.226541 | + | 0.974002i | \(0.572742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.6187 | −0.958082 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.60777 | 0.0557059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.2364 | −0.561882 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.05721 | −0.140238 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.0719 | −1.45248 | −0.726242 | − | 0.687440i | \(-0.758735\pi\) | ||||
−0.726242 | + | 0.687440i | \(0.758735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2548 | −0.939820 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −69.9007 | −2.40751 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.4723 | 0.497274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 65.9989 | 2.26508 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5659 | 0.842108 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.4444 | 1.69294 | 0.846472 | − | 0.532434i | \(-0.178722\pi\) | ||||
0.846472 | + | 0.532434i | \(0.178722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.59757 | 0.294031 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.9194 | −1.12450 | −0.562252 | − | 0.826966i | \(-0.690065\pi\) | ||||
−0.562252 | + | 0.826966i | \(0.690065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.6599 | −0.773146 | −0.386573 | − | 0.922259i | \(-0.626341\pi\) | ||||
−0.386573 | + | 0.922259i | \(0.626341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.591776 | −0.0201677 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.3967 | 0.592191 | 0.296095 | − | 0.955158i | \(-0.404315\pi\) | ||||
0.296095 | + | 0.955158i | \(0.404315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3872 | −0.727185 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.1360 | 1.15932 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55.9211 | −1.89700 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.34391 | −0.214955 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.18093 | 0.310727 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.8029 | −0.702464 | −0.351232 | − | 0.936288i | \(-0.614237\pi\) | ||||
−0.351232 | + | 0.936288i | \(0.614237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.3371 | −0.551035 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4515 | 0.756409 | 0.378205 | − | 0.925722i | \(-0.376542\pi\) | ||||
0.378205 | + | 0.925722i | \(0.376542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.5309 | −0.758224 | −0.379112 | − | 0.925351i | \(-0.623771\pi\) | ||||
−0.379112 | + | 0.925351i | \(0.623771\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.2224 | −0.444466 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 58.7162 | 1.97150 | 0.985749 | − | 0.168223i | \(-0.0538030\pi\) | ||||
0.985749 | + | 0.168223i | \(0.0538030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.18934 | 0.174045 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −50.5854 | −1.69467 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6013 | 0.354760 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.823305 | 0.0275201 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.47229 | −0.182714 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.77051 | −0.192457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.61462 | −0.253680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.73615 | −0.290721 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3579 | −0.377548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5264 | 0.913999 | 0.457000 | − | 0.889467i | \(-0.348924\pi\) | ||||
0.457000 | + | 0.889467i | \(0.348924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.6466 | 0.518965 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.9559 | −0.661169 | −0.330585 | − | 0.943776i | \(-0.607246\pi\) | ||||
−0.330585 | + | 0.943776i | \(0.607246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.9034 | −0.791086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.337057 | −0.0111428 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.37827 | −0.111560 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.92646 | −0.195496 | −0.0977479 | − | 0.995211i | \(-0.531164\pi\) | ||||
−0.0977479 | + | 0.995211i | \(0.531164\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.12813 | 0.136027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.42528 | −0.211491 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6306 | 0.349533 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.00335 | 0.164331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.213745 | 0.00701275 | 0.00350637 | − | 0.999994i | \(-0.498884\pi\) | ||||
0.00350637 | + | 0.999994i | \(0.498884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.29691 | −0.108052 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.3304 | −0.862017 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.11442 | −0.265370 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6992 | 0.839555 | 0.419778 | − | 0.907627i | \(-0.362108\pi\) | ||||
0.419778 | + | 0.907627i | \(0.362108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50.9834 | 1.66378 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5257 | −0.538724 | −0.269362 | − | 0.963039i | \(-0.586813\pi\) | ||||
−0.269362 | + | 0.963039i | \(0.586813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.577479 | 0.0188053 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.928833 | −0.0302149 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.26320 | −0.0410485 | −0.0205243 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205243 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.35787 | 0.109001 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −70.8133 | −2.29628 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.7238 | 1.86986 | 0.934929 | − | 0.354836i | \(-0.115463\pi\) | ||||
0.934929 | + | 0.354836i | \(0.115463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.4400 | 0.596703 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.7889 | −0.510384 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.84167 | 0.0917624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.9199 | −0.384514 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.4826 | 0.982287 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.93773 | −0.223333 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3184 | −0.428292 | −0.214146 | − | 0.976802i | \(-0.568697\pi\) | ||||
−0.214146 | + | 0.976802i | \(0.568697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.5524 | 0.403240 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1747 | −0.743712 | −0.371856 | − | 0.928290i | \(-0.621279\pi\) | ||||
−0.371856 | + | 0.928290i | \(0.621279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.95168 | 0.254919 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.36807 | −0.0758390 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.1537 | −0.548795 | −0.274397 | − | 0.961616i | \(-0.588478\pi\) | ||||
−0.274397 | + | 0.961616i | \(0.588478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.7056 | −1.17312 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.1850 | 1.50650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.0156 | 1.56335 | 0.781677 | − | 0.623683i | \(-0.214365\pi\) | ||||
0.781677 | + | 0.623683i | \(0.214365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.3668 | −0.871978 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.61462 | 0.242376 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.52509 | 0.271082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7683 | 0.723259 | 0.361629 | − | 0.932322i | \(-0.382221\pi\) | ||||
0.361629 | + | 0.932322i | \(0.382221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.6807 | 0.370677 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.5663 | −0.366677 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4796 | −1.15532 | −0.577660 | − | 0.816278i | \(-0.696034\pi\) | ||||
−0.577660 | + | 0.816278i | \(0.696034\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.87407 | 0.312402 |
(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 | 3640.2.a.w.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 7280.2.a.bs.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.w.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7280.2.a.bs.1.4 | 4 | 4.3 | odd | 2 |