Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 20 x^{10} + 11 x^{9} + 144 x^{8} - 29 x^{7} - 440 x^{6} + 4 x^{5} + 556 x^{4} + \cdots + 45 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 5000) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.504162\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | −3.42065 | −1.97491 | −0.987456 | − | 0.157896i | \(-0.949529\pi\) | ||||
−0.987456 | + | 0.157896i | \(0.949529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.76868 | −1.42443 | −0.712214 | − | 0.701962i | \(-0.752308\pi\) | ||||
−0.712214 | + | 0.701962i | \(0.752308\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.70082 | 2.90027 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.95163 | 1.19146 | 0.595731 | − | 0.803184i | \(-0.296863\pi\) | ||||
0.595731 | + | 0.803184i | \(0.296863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.68697 | 1.02258 | 0.511290 | − | 0.859408i | \(-0.329168\pi\) | ||||
0.511290 | + | 0.859408i | \(0.329168\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.88348 | −0.941882 | −0.470941 | − | 0.882165i | \(-0.656086\pi\) | ||||
−0.470941 | + | 0.882165i | \(0.656086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0723216 | −0.0165917 | −0.00829586 | − | 0.999966i | \(-0.502641\pi\) | ||||
−0.00829586 | + | 0.999966i | \(0.502641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.8913 | 2.81312 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.44731 | −0.301785 | −0.150892 | − | 0.988550i | \(-0.548215\pi\) | ||||
−0.150892 | + | 0.988550i | \(0.548215\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.5005 | −3.75287 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.60731 | −0.484166 | −0.242083 | − | 0.970256i | \(-0.577831\pi\) | ||||
−0.242083 | + | 0.970256i | \(0.577831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00035 | 0.179668 | 0.0898340 | − | 0.995957i | \(-0.471366\pi\) | ||||
0.0898340 | + | 0.995957i | \(0.471366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.5171 | −2.35303 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8238 | 1.94382 | 0.971908 | − | 0.235359i | \(-0.0756266\pi\) | ||||
0.971908 | + | 0.235359i | \(0.0756266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.6118 | −2.01951 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.61168 | −1.03257 | −0.516285 | − | 0.856417i | \(-0.672686\pi\) | ||||
−0.516285 | + | 0.856417i | \(0.672686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.39793 | −0.365680 | −0.182840 | − | 0.983143i | \(-0.558529\pi\) | ||||
−0.182840 | + | 0.983143i | \(0.558529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.145509 | −0.0212247 | −0.0106124 | − | 0.999944i | \(-0.503378\pi\) | ||||
−0.0106124 | + | 0.999944i | \(0.503378\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.20298 | 1.02900 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.2840 | 1.86013 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.88987 | −0.396955 | −0.198477 | − | 0.980105i | \(-0.563600\pi\) | ||||
−0.198477 | + | 0.980105i | \(0.563600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.247387 | 0.0327672 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.31862 | 0.692426 | 0.346213 | − | 0.938156i | \(-0.387467\pi\) | ||||
0.346213 | + | 0.938156i | \(0.387467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.06706 | −1.16092 | −0.580459 | − | 0.814290i | \(-0.697127\pi\) | ||||
−0.580459 | + | 0.814290i | \(0.697127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −32.7907 | −4.13123 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8524 | −1.32584 | −0.662918 | − | 0.748692i | \(-0.730682\pi\) | ||||
−0.662918 | + | 0.748692i | \(0.730682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.95073 | 0.595998 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.71253 | −1.15267 | −0.576333 | − | 0.817215i | \(-0.695517\pi\) | ||||
−0.576333 | + | 0.817215i | \(0.695517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.867634 | 0.101549 | 0.0507745 | − | 0.998710i | \(-0.483831\pi\) | ||||
0.0507745 | + | 0.998710i | \(0.483831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.8924 | −1.69715 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1995 | 1.48506 | 0.742529 | − | 0.669814i | \(-0.233626\pi\) | ||||
0.742529 | + | 0.669814i | \(0.233626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 40.6019 | 4.51132 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.55497 | 0.719501 | 0.359750 | − | 0.933049i | \(-0.382862\pi\) | ||||
0.359750 | + | 0.933049i | \(0.382862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.91870 | 0.956185 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.96887 | −0.844699 | −0.422349 | − | 0.906433i | \(-0.638794\pi\) | ||||
−0.422349 | + | 0.906433i | \(0.638794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8950 | −1.45659 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.42184 | −0.354829 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1480 | 1.13191 | 0.565955 | − | 0.824436i | \(-0.308508\pi\) | ||||
0.565955 | + | 0.824436i | \(0.308508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 34.3825 | 3.45557 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.69306 | −0.864992 | −0.432496 | − | 0.901636i | \(-0.642367\pi\) | ||||
−0.432496 | + | 0.901636i | \(0.642367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.32655 | −0.426307 | −0.213154 | − | 0.977019i | \(-0.568373\pi\) | ||||
−0.213154 | + | 0.977019i | \(0.568373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.42272 | −0.910929 | −0.455464 | − | 0.890254i | \(-0.650527\pi\) | ||||
−0.455464 | + | 0.890254i | \(0.650527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.18249 | 0.592175 | 0.296088 | − | 0.955161i | \(-0.404318\pi\) | ||||
0.296088 | + | 0.955161i | \(0.404318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −40.4450 | −3.83887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2323 | 1.05665 | 0.528325 | − | 0.849042i | \(-0.322820\pi\) | ||||
0.528325 | + | 0.849042i | \(0.322820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.0797 | 2.96576 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.6356 | 1.34164 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.61539 | 0.419581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.6162 | 2.03924 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.29067 | 0.380736 | 0.190368 | − | 0.981713i | \(-0.439032\pi\) | ||||
0.190368 | + | 0.981713i | \(0.439032\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.20246 | 0.722186 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.71954 | −0.587089 | −0.293544 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293544 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.272557 | 0.0236337 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1950 | 1.12733 | 0.563663 | − | 0.826005i | \(-0.309392\pi\) | ||||
0.563663 | + | 0.826005i | \(0.309392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.82978 | 0.579295 | 0.289647 | − | 0.957133i | \(-0.406462\pi\) | ||||
0.289647 | + | 0.957133i | \(0.406462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.497737 | 0.0419170 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.5695 | 1.21837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −24.6388 | −2.03218 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2053 | −1.40951 | −0.704757 | − | 0.709448i | \(-0.748944\pi\) | ||||
−0.704757 | + | 0.709448i | \(0.748944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.18246 | 0.665879 | 0.332939 | − | 0.942948i | \(-0.391960\pi\) | ||||
0.332939 | + | 0.942948i | \(0.391960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.7895 | −2.73172 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3674 | −1.22645 | −0.613227 | − | 0.789907i | \(-0.710129\pi\) | ||||
−0.613227 | + | 0.789907i | \(0.710129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.88524 | 0.783951 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.45445 | 0.429871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4103 | 1.67698 | 0.838491 | − | 0.544916i | \(-0.183438\pi\) | ||||
0.838491 | + | 0.544916i | \(0.183438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.3260 | 1.65025 | 0.825126 | − | 0.564949i | \(-0.191104\pi\) | ||||
0.825126 | + | 0.564949i | \(0.191104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.593724 | 0.0456710 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.629258 | −0.0481205 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0299212 | 0.00227487 | 0.00113743 | − | 0.999999i | \(-0.499638\pi\) | ||||
0.00113743 | + | 0.999999i | \(0.499638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.1931 | −1.36748 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8591 | 1.03588 | 0.517938 | − | 0.855418i | \(-0.326700\pi\) | ||||
0.517938 | + | 0.855418i | \(0.326700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.18118 | 0.533773 | 0.266887 | − | 0.963728i | \(-0.414005\pi\) | ||||
0.266887 | + | 0.963728i | \(0.414005\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.0152 | 2.29271 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3461 | −1.12222 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 73.4913 | 5.34570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.82214 | −0.204203 | −0.102102 | − | 0.994774i | \(-0.532557\pi\) | ||||
−0.102102 | + | 0.994774i | \(0.532557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9234 | 1.29015 | 0.645076 | − | 0.764118i | \(-0.276826\pi\) | ||||
0.645076 | + | 0.764118i | \(0.276826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.4954 | −1.03275 | −0.516377 | − | 0.856361i | \(-0.672720\pi\) | ||||
−0.516377 | + | 0.856361i | \(0.672720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.880104 | −0.0623889 | −0.0311945 | − | 0.999513i | \(-0.509931\pi\) | ||||
−0.0311945 | + | 0.999513i | \(0.509931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.1223 | 2.61841 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.82614 | 0.689660 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.5928 | −0.875259 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.285788 | −0.0197684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9932 | 0.894486 | 0.447243 | − | 0.894412i | \(-0.352406\pi\) | ||||
0.447243 | + | 0.894412i | \(0.352406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 33.2231 | 2.27641 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.77000 | −0.255924 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.96787 | −0.200550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3183 | −0.963150 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6759 | 1.38456 | 0.692281 | − | 0.721628i | \(-0.256606\pi\) | ||||
0.692281 | + | 0.721628i | \(0.256606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6103 | −0.836973 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.69149 | 0.310022 | 0.155011 | − | 0.987913i | \(-0.450459\pi\) | ||||
0.155011 | + | 0.987913i | \(0.450459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 50.9418 | 3.35173 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.09367 | −0.0716486 | −0.0358243 | − | 0.999358i | \(-0.511406\pi\) | ||||
−0.0358243 | + | 0.999358i | \(0.511406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −45.1508 | −2.93286 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1664 | 1.36914 | 0.684569 | − | 0.728948i | \(-0.259990\pi\) | ||||
0.684569 | + | 0.728948i | \(0.259990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.18632 | −0.398496 | −0.199248 | − | 0.979949i | \(-0.563850\pi\) | ||||
−0.199248 | + | 0.979949i | \(0.563850\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −80.3832 | −5.15658 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.266647 | −0.0169664 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.4222 | −1.42095 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.9447 | −1.51138 | −0.755689 | − | 0.654930i | \(-0.772698\pi\) | ||||
−0.755689 | + | 0.654930i | \(0.772698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.71923 | −0.359565 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1167 | 1.06771 | 0.533854 | − | 0.845576i | \(-0.320743\pi\) | ||||
0.533854 | + | 0.845576i | \(0.320743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.5601 | −2.76883 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.6858 | −1.40421 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6070 | 1.08569 | 0.542847 | − | 0.839832i | \(-0.317346\pi\) | ||||
0.542847 | + | 0.839832i | \(0.317346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.2587 | 1.66821 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.0019 | 1.76827 | 0.884137 | − | 0.467227i | \(-0.154747\pi\) | ||||
0.884137 | + | 0.467227i | \(0.154747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.68477 | −0.527562 | −0.263781 | − | 0.964583i | \(-0.584970\pi\) | ||||
−0.263781 | + | 0.964583i | \(0.584970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 47.5299 | 2.87664 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0902 | 0.786516 | 0.393258 | − | 0.919428i | \(-0.371348\pi\) | ||||
0.393258 | + | 0.919428i | \(0.371348\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.70387 | 0.521087 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.17892 | −0.547569 | −0.273784 | − | 0.961791i | \(-0.588275\pi\) | ||||
−0.273784 | + | 0.961791i | \(0.588275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9124 | −1.06478 | −0.532390 | − | 0.846499i | \(-0.678706\pi\) | ||||
−0.532390 | + | 0.846499i | \(0.678706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.9173 | 1.47082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.91859 | −0.112858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −38.1334 | −2.23542 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.7875 | −1.27284 | −0.636420 | − | 0.771343i | \(-0.719586\pi\) | ||||
−0.636420 | + | 0.771343i | \(0.719586\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −77.0588 | −4.47141 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.33618 | −0.308599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.03703 | 0.520886 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.7359 | 1.70828 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.30372 | −0.530991 | −0.265496 | − | 0.964112i | \(-0.585536\pi\) | ||||
−0.265496 | + | 0.964112i | \(0.585536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7996 | 0.841919 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.6490 | −1.39771 | −0.698857 | − | 0.715261i | \(-0.746308\pi\) | ||||
−0.698857 | + | 0.715261i | \(0.746308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.8619 | −1.57485 | −0.787424 | − | 0.616411i | \(-0.788586\pi\) | ||||
−0.787424 | + | 0.616411i | \(0.788586\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.4157 | −1.53982 | −0.769910 | − | 0.638153i | \(-0.779699\pi\) | ||||
−0.769910 | + | 0.638153i | \(0.779699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3031 | −0.576865 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 32.2318 | 1.79900 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.280859 | 0.0156274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.1481 | −1.16949 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.548379 | 0.0302331 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3477 | −0.623724 | −0.311862 | − | 0.950127i | \(-0.600953\pi\) | ||||
−0.311862 | + | 0.950127i | \(0.600953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 102.877 | 5.63760 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8690 | 0.701017 | 0.350508 | − | 0.936560i | \(-0.386009\pi\) | ||||
0.350508 | + | 0.936560i | \(0.386009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −38.4219 | −2.08679 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.95301 | 0.214068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.764965 | −0.0413042 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4978 | −0.831966 | −0.415983 | − | 0.909372i | \(-0.636563\pi\) | ||||
−0.415983 | + | 0.909372i | \(0.636563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0522 | 0.698668 | 0.349334 | − | 0.936998i | \(-0.386408\pi\) | ||||
0.349334 | + | 0.936998i | \(0.386408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −71.8977 | −3.83762 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.9684 | −0.849914 | −0.424957 | − | 0.905214i | \(-0.639711\pi\) | ||||
−0.424957 | + | 0.905214i | \(0.639711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −50.0632 | −2.64963 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.3026 | −1.81042 | −0.905212 | − | 0.424961i | \(-0.860288\pi\) | ||||
−0.905212 | + | 0.424961i | \(0.860288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9948 | −0.999725 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.7876 | −0.828635 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.938953 | 0.0490130 | 0.0245065 | − | 0.999700i | \(-0.492199\pi\) | ||||
0.0245065 | + | 0.999700i | \(0.492199\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −57.5271 | −2.99474 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8910 | 0.565434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.9345 | −1.75706 | −0.878530 | − | 0.477688i | \(-0.841475\pi\) | ||||
−0.878530 | + | 0.477688i | \(0.841475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.61308 | −0.495099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.13651 | −0.366578 | −0.183289 | − | 0.983059i | \(-0.558674\pi\) | ||||
−0.183289 | + | 0.983059i | \(0.558674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6769 | −0.751919 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.2628 | 0.575505 | 0.287752 | − | 0.957705i | \(-0.407092\pi\) | ||||
0.287752 | + | 0.957705i | \(0.407092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.8639 | −1.06057 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0850 | 0.562033 | 0.281017 | − | 0.959703i | \(-0.409328\pi\) | ||||
0.281017 | + | 0.959703i | \(0.409328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62060 | 0.284246 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.9852 | 1.15945 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6762 | 1.23846 | 0.619231 | − | 0.785209i | \(-0.287444\pi\) | ||||
0.619231 | + | 0.785209i | \(0.287444\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.932322 | −0.0466745 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.07442 | −0.253404 | −0.126702 | − | 0.991941i | \(-0.540439\pi\) | ||||
−0.126702 | + | 0.991941i | \(0.540439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.68826 | 0.183725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.7232 | 2.31598 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.39890 | −0.0691713 | −0.0345856 | − | 0.999402i | \(-0.511011\pi\) | ||||
−0.0345856 | + | 0.999402i | \(0.511011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.1355 | −2.22637 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.0442 | −0.986311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.3623 | −1.14406 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0710 | 0.589709 | 0.294854 | − | 0.955542i | \(-0.404729\pi\) | ||||
0.294854 | + | 0.955542i | \(0.404729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.5353 | −1.43946 | −0.719731 | − | 0.694253i | \(-0.755735\pi\) | ||||
−0.719731 | + | 0.694253i | \(0.755735\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.26605 | −0.0615576 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.1709 | 1.65364 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −49.8372 | −2.40616 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.267267 | −0.0128738 | −0.00643689 | − | 0.999979i | \(-0.502049\pi\) | ||||
−0.00643689 | + | 0.999979i | \(0.502049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.1641 | −0.632628 | −0.316314 | − | 0.948655i | \(-0.602445\pi\) | ||||
−0.316314 | + | 0.948655i | \(0.602445\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.104672 | 0.00500713 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.21345 | 0.296552 | 0.148276 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148276 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.6719 | 2.98437 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.60370 | 0.171217 | 0.0856085 | − | 0.996329i | \(-0.472717\pi\) | ||||
0.0856085 | + | 0.996329i | \(0.472717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 58.8533 | 2.78367 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4541 | 1.01248 | 0.506241 | − | 0.862392i | \(-0.331035\pi\) | ||||
0.506241 | + | 0.862392i | \(0.331035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.1269 | −1.23027 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.9893 | −1.31505 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.5872 | −1.29048 | −0.645238 | − | 0.763981i | \(-0.723242\pi\) | ||||
−0.645238 | + | 0.763981i | \(0.723242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 75.7298 | 3.53477 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4464 | 0.533113 | 0.266557 | − | 0.963819i | \(-0.414114\pi\) | ||||
0.266557 | + | 0.963819i | \(0.414114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.536092 | −0.0249143 | −0.0124571 | − | 0.999922i | \(-0.503965\pi\) | ||||
−0.0124571 | + | 0.999922i | \(0.503965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.96429 | −0.322269 | −0.161134 | − | 0.986932i | \(-0.551515\pi\) | ||||
−0.161134 | + | 0.986932i | \(0.551515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.8994 | 1.88856 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 52.5665 | 2.42214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.47572 | −0.435694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.1443 | −1.15128 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0542 | 0.642155 | 0.321077 | − | 0.947053i | \(-0.395955\pi\) | ||||
0.321077 | + | 0.947053i | \(0.395955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.5939 | 1.98771 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.6578 | −0.848957 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.44305 | 0.0653910 | 0.0326955 | − | 0.999465i | \(-0.489591\pi\) | ||||
0.0326955 | + | 0.999465i | \(0.489591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −73.2370 | −3.31189 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.7195 | 1.38635 | 0.693175 | − | 0.720769i | \(-0.256211\pi\) | ||||
0.693175 | + | 0.720769i | \(0.256211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1255 | 0.456027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.6035 | 1.64189 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8449 | −0.485484 | −0.242742 | − | 0.970091i | \(-0.578047\pi\) | ||||
−0.242742 | + | 0.970091i | \(0.578047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.9486 | −3.25910 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6255 | −0.785882 | −0.392941 | − | 0.919564i | \(-0.628542\pi\) | ||||
−0.392941 | + | 0.919564i | \(0.628542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.03092 | −0.0901963 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.01417 | 0.266573 | 0.133287 | − | 0.991078i | \(-0.457447\pi\) | ||||
0.133287 | + | 0.991078i | \(0.457447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.26984 | −0.144649 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.41031 | 0.0622666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.575000 | −0.0252885 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.102350 | −0.00449266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.5378 | −0.636913 | −0.318457 | − | 0.947937i | \(-0.603165\pi\) | ||||
−0.318457 | + | 0.947937i | \(0.603165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7324 | −0.644204 | −0.322102 | − | 0.946705i | \(-0.604389\pi\) | ||||
−0.322102 | + | 0.946705i | \(0.604389\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.88484 | −0.169226 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9053 | −0.908926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 46.2764 | 2.00823 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.3770 | −1.05589 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −47.4070 | −2.04576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.4635 | 1.22601 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4953 | −0.537216 | −0.268608 | − | 0.963250i | \(-0.586564\pi\) | ||||
−0.268608 | + | 0.963250i | \(0.586564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.5643 | −1.05415 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1367 | −0.775471 | −0.387736 | − | 0.921771i | \(-0.626743\pi\) | ||||
−0.387736 | + | 0.921771i | \(0.626743\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −78.8909 | −3.36698 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.188565 | 0.00803315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.7447 | −2.11536 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.0780 | 1.52867 | 0.764336 | − | 0.644818i | \(-0.223067\pi\) | ||||
0.764336 | + | 0.644818i | \(0.223067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.84108 | −0.373938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.4935 | 2.21628 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.7068 | −1.08341 | −0.541705 | − | 0.840568i | \(-0.682221\pi\) | ||||
−0.541705 | + | 0.840568i | \(0.682221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −153.016 | −6.42605 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.8438 | 0.622286 | 0.311143 | − | 0.950363i | \(-0.399288\pi\) | ||||
0.311143 | + | 0.950363i | \(0.399288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5775 | 1.53072 | 0.765361 | − | 0.643601i | \(-0.222561\pi\) | ||||
0.765361 | + | 0.643601i | \(0.222561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.65356 | 0.403283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.8315 | −1.20027 | −0.600135 | − | 0.799899i | \(-0.704886\pi\) | ||||
−0.600135 | + | 0.799899i | \(0.704886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −61.3095 | −2.54794 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.7036 | −1.02488 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.4197 | −0.472956 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.5572 | −1.05486 | −0.527430 | − | 0.849598i | \(-0.676844\pi\) | ||||
−0.527430 | + | 0.849598i | \(0.676844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0723469 | −0.00298100 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.5836 | 2.03960 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7017 | 1.13757 | 0.568786 | − | 0.822486i | \(-0.307413\pi\) | ||||
0.568786 | + | 0.822486i | \(0.307413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.01053 | 0.123213 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.7768 | 0.440328 | 0.220164 | − | 0.975463i | \(-0.429341\pi\) | ||||
0.220164 | + | 0.975463i | \(0.429341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.56300 | 0.390083 | 0.195041 | − | 0.980795i | \(-0.437516\pi\) | ||||
0.195041 | + | 0.980795i | \(0.437516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −94.4251 | −3.84529 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.6290 | −1.44614 | −0.723069 | − | 0.690776i | \(-0.757269\pi\) | ||||
−0.723069 | + | 0.690776i | \(0.757269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.6118 | −1.36202 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.536489 | −0.0217040 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7107 | −0.796108 | −0.398054 | − | 0.917362i | \(-0.630314\pi\) | ||||
−0.398054 | + | 0.917362i | \(0.630314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1501 | −1.25406 | −0.627028 | − | 0.778997i | \(-0.715729\pi\) | ||||
−0.627028 | + | 0.778997i | \(0.715729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1321 | −0.527824 | −0.263912 | − | 0.964547i | \(-0.585013\pi\) | ||||
−0.263912 | + | 0.964547i | \(0.585013\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.2233 | 1.13256 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0322 | 1.20321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.977581 | 0.0390408 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.9174 | −1.83085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.4286 | −1.41039 | −0.705196 | − | 0.709012i | \(-0.749141\pi\) | ||||
−0.705196 | + | 0.709012i | \(0.749141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.4450 | −1.76653 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.5571 | 1.05223 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84.5070 | −3.34305 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2806 | 0.485053 | 0.242527 | − | 0.970145i | \(-0.422024\pi\) | ||||
0.242527 | + | 0.970145i | \(0.422024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.6669 | 1.72205 | 0.861027 | − | 0.508560i | \(-0.169822\pi\) | ||||
0.861027 | + | 0.508560i | \(0.169822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.1816 | −1.69765 | −0.848823 | − | 0.528678i | \(-0.822688\pi\) | ||||
−0.848823 | + | 0.528678i | \(0.822688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.0172 | 0.824999 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8958 | 0.505428 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.02161 | 0.196511 | 0.0982554 | − | 0.995161i | \(-0.468674\pi\) | ||||
0.0982554 | + | 0.995161i | \(0.468674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.54914 | 0.294520 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.17693 | 0.0458466 | 0.0229233 | − | 0.999737i | \(-0.492703\pi\) | ||||
0.0229233 | + | 0.999737i | \(0.492703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.6608 | −0.764717 | −0.382359 | − | 0.924014i | \(-0.624888\pi\) | ||||
−0.382359 | + | 0.924014i | \(0.624888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.9777 | 1.90214 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.77359 | 0.146114 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −70.7251 | −2.73439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.8297 | −1.38319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.8685 | 1.84520 | 0.922598 | − | 0.385762i | \(-0.126061\pi\) | ||||
0.922598 | + | 0.385762i | \(0.126061\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0777 | 0.464183 | 0.232092 | − | 0.972694i | \(-0.425443\pi\) | ||||
0.232092 | + | 0.972694i | \(0.425443\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.0133 | −1.61232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.1353 | 1.65295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.39442 | −0.129884 | −0.0649420 | − | 0.997889i | \(-0.520686\pi\) | ||||
−0.0649420 | + | 0.997889i | \(0.520686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.0479 | −0.612267 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.6549 | −0.405918 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5857 | 0.516824 | 0.258412 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258412 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −129.577 | −4.92221 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.6763 | 0.972560 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.74105 | 0.141500 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.8052 | −1.76781 | −0.883903 | − | 0.467670i | \(-0.845094\pi\) | ||||
−0.883903 | + | 0.467670i | \(0.845094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.855114 | −0.0322513 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.7614 | 1.23212 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.09300 | 0.341495 | 0.170747 | − | 0.985315i | \(-0.445382\pi\) | ||||
0.170747 | + | 0.985315i | \(0.445382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 114.846 | 4.30708 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.44782 | −0.0542211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −72.4026 | −2.70393 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.5875 | 1.58825 | 0.794123 | − | 0.607757i | \(-0.207931\pi\) | ||||
0.794123 | + | 0.607757i | \(0.207931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.3054 | 0.607244 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.1612 | 0.786995 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.2124 | 1.41722 | 0.708610 | − | 0.705600i | \(-0.249323\pi\) | ||||
0.708610 | + | 0.705600i | \(0.249323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 153.157 | 5.67247 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.31230 | 0.344428 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.3999 | −1.15978 | −0.579891 | − | 0.814694i | \(-0.696905\pi\) | ||||
−0.579891 | + | 0.814694i | \(0.696905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.8848 | −1.57968 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.2745 | −1.15045 | −0.575226 | − | 0.817994i | \(-0.695086\pi\) | ||||
−0.575226 | + | 0.817994i | \(0.695086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.912106 | 0.0335071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.79596 | −0.286006 | −0.143003 | − | 0.989722i | \(-0.545676\pi\) | ||||
−0.143003 | + | 0.989722i | \(0.545676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 57.0336 | 2.08675 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.5113 | 1.29755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.39100 | 0.123739 | 0.0618696 | − | 0.998084i | \(-0.480294\pi\) | ||||
0.0618696 | + | 0.998084i | \(0.480294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 81.9065 | 2.98484 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.6809 | 1.26050 | 0.630250 | − | 0.776392i | \(-0.282952\pi\) | ||||
0.630250 | + | 0.776392i | \(0.282952\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.5635 | 0.710109 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5014 | 0.489426 | 0.244713 | − | 0.969596i | \(-0.421306\pi\) | ||||
0.244713 | + | 0.969596i | \(0.421306\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.2999 | −0.843511 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.6096 | 0.708061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8933 | −0.681310 | −0.340655 | − | 0.940188i | \(-0.610649\pi\) | ||||
−0.340655 | + | 0.940188i | \(0.610649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.5501 | −2.10863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.7892 | −0.388060 | −0.194030 | − | 0.980996i | \(-0.562156\pi\) | ||||
−0.194030 | + | 0.980996i | \(0.562156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 152.424 | 5.46819 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.478167 | 0.0171321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.3803 | −1.37336 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.8440 | 1.81701 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.5898 | −1.23299 | −0.616496 | − | 0.787358i | \(-0.711448\pi\) | ||||
−0.616496 | + | 0.787358i | \(0.711448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −60.2273 | −2.14415 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.3312 | −1.50512 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.4299 | −1.18713 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.51613 | 0.230813 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.565083 | 0.0199912 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −69.3358 | −2.44986 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.42857 | 0.120992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −99.2051 | −3.49219 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.6137 | 0.619264 | 0.309632 | − | 0.950856i | \(-0.399794\pi\) | ||||
0.309632 | + | 0.950856i | \(0.399794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.33225 | 0.327700 | 0.163850 | − | 0.986485i | \(-0.447609\pi\) | ||||
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.7075 | 1.04189 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.173422 | 0.00606726 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −120.898 | −4.22452 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2652 | 0.462959 | 0.231480 | − | 0.972840i | \(-0.425643\pi\) | ||||
0.231480 | + | 0.972840i | \(0.425643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.8504 | 1.42396 | 0.711978 | − | 0.702202i | \(-0.247800\pi\) | ||||
0.711978 | + | 0.702202i | \(0.247800\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.10663 | −0.281895 | −0.140948 | − | 0.990017i | \(-0.545015\pi\) | ||||
−0.140948 | + | 0.990017i | \(0.545015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.9061 | −1.31653 | −0.658267 | − | 0.752784i | \(-0.728710\pi\) | ||||
−0.658267 | + | 0.752784i | \(0.728710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.7771 | −1.55330 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.9726 | −0.969194 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.5073 | −0.674272 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.714266 | 0.0246592 | 0.0123296 | − | 0.999924i | \(-0.496075\pi\) | ||||
0.0123296 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2019 | −0.765583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.3979 | 1.08140 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.3939 | −0.597663 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 61.2718 | 2.10284 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1127 | −0.586615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.11289 | 0.243541 | 0.121770 | − | 0.992558i | \(-0.461143\pi\) | ||||
0.121770 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.7346 | 0.674120 | 0.337060 | − | 0.941483i | \(-0.390567\pi\) | ||||
0.337060 | + | 0.941483i | \(0.390567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.4365 | −1.51615 | −0.758077 | − | 0.652165i | \(-0.773861\pi\) | ||||
−0.758077 | + | 0.652165i | \(0.773861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85.2334 | −2.90475 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.6482 | 0.362469 | 0.181235 | − | 0.983440i | \(-0.441991\pi\) | ||||
0.181235 | + | 0.983440i | \(0.441991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.56282 | 0.222885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.1595 | 1.76939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.0125 | −1.35577 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 96.9969 | 3.28285 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.2559 | −1.05544 | −0.527718 | − | 0.849420i | \(-0.676952\pi\) | ||||
−0.527718 | + | 0.849420i | \(0.676952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 74.5274 | 2.51375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.0482 | −0.978660 | −0.489330 | − | 0.872099i | \(-0.662759\pi\) | ||||
−0.489330 | + | 0.872099i | \(0.662759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.5789 | 1.39924 | 0.699621 | − | 0.714514i | \(-0.253352\pi\) | ||||
0.699621 | + | 0.714514i | \(0.253352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.9565 | −0.837956 | −0.418978 | − | 0.907996i | \(-0.637612\pi\) | ||||
−0.418978 | + | 0.907996i | \(0.637612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1702 | −0.542331 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 160.444 | 5.37506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0105235 | 0.000352155 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.2532 | 0.609456 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.60823 | −0.0869892 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2228 | 0.373885 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.9125 | −1.02870 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.59802 | 0.318697 | 0.159349 | − | 0.987222i | \(-0.449061\pi\) | ||||
0.159349 | + | 0.987222i | \(0.449061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −75.6368 | −2.50871 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.9442 | 1.29028 | 0.645140 | − | 0.764064i | \(-0.276799\pi\) | ||||
0.645140 | + | 0.764064i | \(0.276799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9028 | 0.857258 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.3238 | 0.836266 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.1466 | −0.631589 | −0.315795 | − | 0.948828i | \(-0.602271\pi\) | ||||
−0.315795 | + | 0.948828i | \(0.602271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.8247 | 1.04866 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.8098 | −1.17869 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.6445 | −1.23641 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.8092 | 0.781153 | 0.390577 | − | 0.920570i | \(-0.372276\pi\) | ||||
0.390577 | + | 0.920570i | \(0.372276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.520931 | −0.0170728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 84.3154 | 2.76036 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.05650 | −0.197857 | −0.0989286 | − | 0.995095i | \(-0.531542\pi\) | ||||
−0.0989286 | + | 0.995095i | \(0.531542\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 95.3058 | 3.11019 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.8615 | 1.56024 | 0.780120 | − | 0.625630i | \(-0.215158\pi\) | ||||
0.780120 | + | 0.625630i | \(0.215158\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.56914 | 0.311614 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.9826 | −0.909314 | −0.454657 | − | 0.890667i | \(-0.650238\pi\) | ||||
−0.454657 | + | 0.890667i | \(0.650238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.19894 | 0.103842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 93.7795 | 3.04101 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.4714 | −1.21382 | −0.606908 | − | 0.794772i | \(-0.707590\pi\) | ||||
−0.606908 | + | 0.794772i | \(0.707590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.2434 | 1.13926 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.7278 | −1.60579 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9993 | −0.967719 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81.9854 | −2.64194 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3063 | 0.588692 | 0.294346 | − | 0.955699i | \(-0.404898\pi\) | ||||
0.294346 | + | 0.955699i | \(0.404898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.960721 | −0.0308628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.8309 | −0.443855 | −0.221928 | − | 0.975063i | \(-0.571235\pi\) | ||||
−0.221928 | + | 0.975063i | \(0.571235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.7393 | −0.825164 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.13957 | −0.196422 | −0.0982111 | − | 0.995166i | \(-0.531312\pi\) | ||||
−0.0982111 | + | 0.995166i | \(0.531312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.4900 | −1.00643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 53.7928 | 1.71747 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.7555 | −1.71453 | −0.857267 | − | 0.514872i | \(-0.827840\pi\) | ||||
−0.857267 | + | 0.514872i | \(0.827840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.87581 | −0.0597077 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.47054 | 0.110357 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.0570 | 1.62188 | 0.810939 | − | 0.585130i | \(-0.198957\pi\) | ||||
0.810939 | + | 0.585130i | \(0.198957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.8163 | 1.23180 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.4203 | −1.75518 | −0.877589 | − | 0.479413i | \(-0.840850\pi\) | ||||
−0.877589 | + | 0.479413i | \(0.840850\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −230.570 | −7.29490 |
(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 | 10000.2.a.bo.1.1 | 12 | ||
4.3 | odd | 2 | 5000.2.a.p.1.12 | yes | 12 | ||
5.4 | even | 2 | 10000.2.a.bp.1.12 | 12 | |||
20.19 | odd | 2 | 5000.2.a.o.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5000.2.a.o.1.1 | ✓ | 12 | 20.19 | odd | 2 | ||
5000.2.a.p.1.12 | yes | 12 | 4.3 | odd | 2 | ||
10000.2.a.bo.1.1 | 12 | 1.1 | even | 1 | trivial | ||
10000.2.a.bp.1.12 | 12 | 5.4 | even | 2 |