Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 15x^{6} + 56x^{5} + 87x^{4} - 248x^{3} - 241x^{2} + 340x + 248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.49694\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.49694 | −1.11667 | −0.558333 | − | 0.829617i | \(-0.688559\pi\) | ||||
−0.558333 | + | 0.829617i | \(0.688559\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.08498 | 1.54398 | 0.771989 | − | 0.635636i | \(-0.219262\pi\) | ||||
0.771989 | + | 0.635636i | \(0.219262\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.35071 | −1.91481 | −0.957406 | − | 0.288746i | \(-0.906762\pi\) | ||||
−0.957406 | + | 0.288746i | \(0.906762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.31501 | −0.919420 | −0.459710 | − | 0.888069i | \(-0.652047\pi\) | ||||
−0.459710 | + | 0.888069i | \(0.652047\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.507955 | −0.123197 | −0.0615986 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615986 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.01491 | 0.628652 | 0.314326 | − | 0.949315i | \(-0.398221\pi\) | ||||
0.314326 | + | 0.949315i | \(0.398221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23472 | 0.246943 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.18318 | 0.776796 | 0.388398 | − | 0.921492i | \(-0.373029\pi\) | ||||
0.388398 | + | 0.921492i | \(0.373029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.86256 | −1.77137 | −0.885684 | − | 0.464288i | \(-0.846310\pi\) | ||||
−0.885684 | + | 0.464288i | \(0.846310\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2000 | −1.72411 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.92158 | −1.63110 | −0.815549 | − | 0.578688i | \(-0.803565\pi\) | ||||
−0.815549 | + | 0.578688i | \(0.803565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.808619 | 0.126285 | 0.0631425 | − | 0.998005i | \(-0.479888\pi\) | ||||
0.0631425 | + | 0.998005i | \(0.479888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.39678 | −0.823001 | −0.411501 | − | 0.911409i | \(-0.634995\pi\) | ||||
−0.411501 | + | 0.911409i | \(0.634995\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.49082 | 1.11667 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4997 | 1.53154 | 0.765771 | − | 0.643114i | \(-0.222358\pi\) | ||||
0.765771 | + | 0.643114i | \(0.222358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.68707 | 1.38387 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9310 | 1.50149 | 0.750744 | − | 0.660593i | \(-0.229695\pi\) | ||||
0.750744 | + | 0.660593i | \(0.229695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.8574 | 2.13820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.91423 | 0.509589 | 0.254795 | − | 0.966995i | \(-0.417992\pi\) | ||||
0.254795 | + | 0.966995i | \(0.417992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.02958 | −1.02808 | −0.514041 | − | 0.857766i | \(-0.671852\pi\) | ||||
−0.514041 | + | 0.857766i | \(0.671852\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.2549 | −1.54398 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.27740 | 1.02668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.98899 | 0.731671 | 0.365836 | − | 0.930679i | \(-0.380783\pi\) | ||||
0.365836 | + | 0.930679i | \(0.380783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8922 | 1.29267 | 0.646333 | − | 0.763055i | \(-0.276302\pi\) | ||||
0.646333 | + | 0.763055i | \(0.276302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.522948 | 0.0612064 | 0.0306032 | − | 0.999532i | \(-0.490257\pi\) | ||||
0.0306032 | + | 0.999532i | \(0.490257\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.9425 | −2.95643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.67212 | 0.293303 | 0.146651 | − | 0.989188i | \(-0.453150\pi\) | ||||
0.146651 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.26833 | 0.137570 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.13711 | 0.120533 | 0.0602665 | − | 0.998182i | \(-0.480805\pi\) | ||||
0.0602665 | + | 0.998182i | \(0.480805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5418 | −1.41956 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.49694 | −0.256181 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.68703 | −0.780499 | −0.390250 | − | 0.920709i | \(-0.627611\pi\) | ||||
−0.390250 | + | 0.920709i | \(0.627611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.0521 | 1.91481 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8526 | −1.37838 | −0.689191 | − | 0.724580i | \(-0.742034\pi\) | ||||
−0.689191 | + | 0.724580i | \(0.742034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4443 | 1.81737 | 0.908687 | − | 0.417479i | \(-0.137086\pi\) | ||||
0.908687 | + | 0.417479i | \(0.137086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.86782 | −0.180569 | −0.0902847 | − | 0.995916i | \(-0.528778\pi\) | ||||
−0.0902847 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4363 | −1.38275 | −0.691375 | − | 0.722496i | \(-0.742995\pi\) | ||||
−0.691375 | + | 0.722496i | \(0.742995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.76762 | −0.918860 | −0.459430 | − | 0.888214i | \(-0.651946\pi\) | ||||
−0.459430 | + | 0.888214i | \(0.651946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.52806 | −0.701995 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.94504 | 0.919420 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.07499 | −0.190214 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.3315 | 2.66650 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.40169 | 0.840913 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.81406 | 0.338443 | 0.169221 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169221 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.45543 | 0.826125 | 0.413062 | − | 0.910703i | \(-0.364459\pi\) | ||||
0.413062 | + | 0.910703i | \(0.364459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.08498 | 0.354213 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.54392 | −0.131906 | −0.0659531 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659531 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4177 | 1.05325 | 0.526626 | − | 0.850097i | \(-0.323457\pi\) | ||||
0.526626 | + | 0.850097i | \(0.323457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.0527 | 1.76052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4451 | −0.867422 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.47555 | −0.284728 | −0.142364 | − | 0.989814i | \(-0.545470\pi\) | ||||
−0.142364 | + | 0.989814i | \(0.545470\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.06919 | 0.656662 | 0.328331 | − | 0.944563i | \(-0.393514\pi\) | ||||
0.328331 | + | 0.944563i | \(0.393514\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.52386 | 0.123197 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.6262 | 1.97803 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.40571 | 0.112188 | 0.0560939 | − | 0.998425i | \(-0.482135\pi\) | ||||
0.0560939 | + | 0.998425i | \(0.482135\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.3159 | 0.970625 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5229 | 1.52915 | 0.764574 | − | 0.644535i | \(-0.222949\pi\) | ||||
0.764574 | + | 0.644535i | \(0.222949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.18980 | 0.324217 | 0.162108 | − | 0.986773i | \(-0.448171\pi\) | ||||
0.162108 | + | 0.986773i | \(0.448171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.01068 | −0.154668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.27868 | 0.477359 | 0.238680 | − | 0.971098i | \(-0.423285\pi\) | ||||
0.238680 | + | 0.971098i | \(0.423285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.04379 | 0.381275 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.07119 | 0.603269 | 0.301635 | − | 0.953424i | \(-0.402468\pi\) | ||||
0.301635 | + | 0.953424i | \(0.402468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5445 | −1.45273 | −0.726366 | − | 0.687309i | \(-0.758792\pi\) | ||||
−0.726366 | + | 0.687309i | \(0.758792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.7736 | 1.82139 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.22587 | 0.235899 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6953 | 0.846241 | 0.423120 | − | 0.906073i | \(-0.360935\pi\) | ||||
0.423120 | + | 0.906073i | \(0.360935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.8686 | 1.21423 | 0.607114 | − | 0.794615i | \(-0.292327\pi\) | ||||
0.607114 | + | 0.794615i | \(0.292327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.2840 | −1.01770 | −0.508848 | − | 0.860856i | \(-0.669928\pi\) | ||||
−0.508848 | + | 0.860856i | \(0.669928\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.2835 | −1.57964 | −0.789819 | − | 0.613340i | \(-0.789826\pi\) | ||||
−0.789819 | + | 0.613340i | \(0.789826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.0882 | 1.19936 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.01907 | −0.141018 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.04473 | −0.628652 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.35071 | −0.439288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.30639 | −0.640678 | −0.320339 | − | 0.947303i | \(-0.603797\pi\) | ||||
−0.320339 | + | 0.947303i | \(0.603797\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4754 | 0.919018 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.2884 | −2.73495 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.68388 | 0.113270 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1136 | −1.48083 | −0.740417 | − | 0.672147i | \(-0.765372\pi\) | ||||
−0.740417 | + | 0.672147i | \(0.765372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.70415 | −0.246943 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.8498 | 0.919245 | 0.459623 | − | 0.888114i | \(-0.347985\pi\) | ||||
0.459623 | + | 0.888114i | \(0.347985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.86364 | 0.585726 | 0.292863 | − | 0.956154i | \(-0.405392\pi\) | ||||
0.292863 | + | 0.956154i | \(0.405392\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.1016 | 1.12036 | 0.560181 | − | 0.828370i | \(-0.310732\pi\) | ||||
0.560181 | + | 0.828370i | \(0.310732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.2172 | −1.71022 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.83880 | −0.507050 | −0.253525 | − | 0.967329i | \(-0.581590\pi\) | ||||
−0.253525 | + | 0.967329i | \(0.581590\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.6217 | 1.71486 | 0.857428 | − | 0.514604i | \(-0.172061\pi\) | ||||
0.857428 | + | 0.514604i | \(0.172061\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.1881 | −1.54532 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.31501 | −0.210929 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.1053 | −1.71087 | −0.855435 | − | 0.517911i | \(-0.826710\pi\) | ||||
−0.855435 | + | 0.517911i | \(0.826710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.1468 | −1.20375 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.93317 | −0.245345 | −0.122672 | − | 0.992447i | \(-0.539146\pi\) | ||||
−0.122672 | + | 0.992447i | \(0.539146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.5295 | −2.51838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.5495 | −0.776796 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.3410 | 1.00763 | 0.503814 | − | 0.863812i | \(-0.331930\pi\) | ||||
0.503814 | + | 0.863812i | \(0.331930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.2941 | −1.67666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4203 | 1.18408 | 0.592040 | − | 0.805909i | \(-0.298323\pi\) | ||||
0.592040 | + | 0.805909i | \(0.298323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.275233 | −0.0167192 | −0.00835960 | − | 0.999965i | \(-0.502661\pi\) | ||||
−0.00835960 | + | 0.999965i | \(0.502661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.84132 | −0.472850 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.03924 | −0.0624416 | −0.0312208 | − | 0.999513i | \(-0.509940\pi\) | ||||
−0.0312208 | + | 0.999513i | \(0.509940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.5877 | 1.77137 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.68166 | −0.279284 | −0.139642 | − | 0.990202i | \(-0.544595\pi\) | ||||
−0.139642 | + | 0.990202i | \(0.544595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4508 | 0.918456 | 0.459228 | − | 0.888319i | \(-0.348126\pi\) | ||||
0.459228 | + | 0.888319i | \(0.348126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.30319 | 0.194981 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7420 | −0.984822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.14756 | 0.0670413 | 0.0335206 | − | 0.999438i | \(-0.489328\pi\) | ||||
0.0335206 | + | 0.999438i | \(0.489328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.77360 | −0.569041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.99447 | −0.577995 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0457 | −1.27070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.0494 | 1.14802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.35748 | 0.419914 | 0.209957 | − | 0.977711i | \(-0.432668\pi\) | ||||
0.209957 | + | 0.977711i | \(0.432668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0968 | −0.912766 | −0.456383 | − | 0.889783i | \(-0.650855\pi\) | ||||
−0.456383 | + | 0.889783i | \(0.650855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1282 | 0.742050 | 0.371025 | − | 0.928623i | \(-0.379006\pi\) | ||||
0.371025 | + | 0.928623i | \(0.379006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.5999 | 1.72411 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3176 | 0.579493 | 0.289747 | − | 0.957103i | \(-0.406429\pi\) | ||||
0.289747 | + | 0.957103i | \(0.406429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.5661 | −1.48742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.507955 | −0.0282634 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.09310 | −0.227044 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.8912 | 2.36467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0219 | −1.21044 | −0.605218 | − | 0.796060i | \(-0.706914\pi\) | ||||
−0.605218 | + | 0.796060i | \(0.706914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.7648 | 1.63110 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.9541 | −0.817032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8706 | 0.918998 | 0.459499 | − | 0.888178i | \(-0.348029\pi\) | ||||
0.459499 | + | 0.888178i | \(0.348029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 62.6343 | 3.39184 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9767 | 0.592683 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.0736 | 1.18497 | 0.592485 | − | 0.805581i | \(-0.298147\pi\) | ||||
0.592485 | + | 0.805581i | \(0.298147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6558 | 0.730977 | 0.365489 | − | 0.930816i | \(-0.380902\pi\) | ||||
0.365489 | + | 0.930816i | \(0.380902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.4971 | 1.19740 | 0.598699 | − | 0.800974i | \(-0.295684\pi\) | ||||
0.598699 | + | 0.800974i | \(0.295684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.1972 | −1.44348 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.1036 | 1.06103 | 0.530515 | − | 0.847676i | \(-0.321999\pi\) | ||||
0.530515 | + | 0.847676i | \(0.321999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.30577 | −0.0683471 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.85917 | −0.462445 | −0.231222 | − | 0.972901i | \(-0.574273\pi\) | ||||
−0.231222 | + | 0.972901i | \(0.574273\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.42586 | −0.126285 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44.6529 | 2.31827 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.74466 | 0.504559 | 0.252280 | − | 0.967654i | \(-0.418820\pi\) | ||||
0.252280 | + | 0.967654i | \(0.418820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.8673 | −0.714202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5084 | 0.642513 | 0.321256 | − | 0.946992i | \(-0.395895\pi\) | ||||
0.321256 | + | 0.946992i | \(0.395895\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.3826 | −0.734917 | −0.367459 | − | 0.930040i | \(-0.619772\pi\) | ||||
−0.367459 | + | 0.930040i | \(0.619772\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 64.7770 | 3.30134 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.1903 | 0.823001 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.3344 | −1.79152 | −0.895762 | − | 0.444533i | \(-0.853370\pi\) | ||||
−0.895762 | + | 0.444533i | \(0.853370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53144 | −0.0774482 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.49694 | −0.125635 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.2423 | 1.26687 | 0.633436 | − | 0.773795i | \(-0.281644\pi\) | ||||
0.633436 | + | 0.773795i | \(0.281644\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.7168 | −0.784858 | −0.392429 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392429 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.6945 | 1.62863 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.4725 | −1.11667 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 63.0091 | 3.12325 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.0241 | −1.63294 | −0.816468 | − | 0.577390i | \(-0.804071\pi\) | ||||
−0.816468 | + | 0.577390i | \(0.804071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.9896 | 0.786795 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.67212 | −0.327521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6339 | 0.910326 | 0.455163 | − | 0.890408i | \(-0.349581\pi\) | ||||
0.455163 | + | 0.890408i | \(0.349581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6986 | 1.78858 | 0.894289 | − | 0.447489i | \(-0.147682\pi\) | ||||
0.894289 | + | 0.447489i | \(0.147682\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.4992 | −1.53154 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.627180 | −0.0304227 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.8007 | −1.58734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0376 | 0.724336 | 0.362168 | − | 0.932113i | \(-0.382037\pi\) | ||||
0.362168 | + | 0.932113i | \(0.382037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3826 | −0.691183 | −0.345591 | − | 0.938385i | \(-0.612322\pi\) | ||||
−0.345591 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.01491 | 0.144223 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.78244 | −0.180526 | −0.0902629 | − | 0.995918i | \(-0.528771\pi\) | ||||
−0.0902629 | + | 0.995918i | \(0.528771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.0612 | −1.38387 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.93406 | −0.376958 | −0.188479 | − | 0.982077i | \(-0.560356\pi\) | ||||
−0.188479 | + | 0.982077i | \(0.560356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.83929 | −0.134595 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.2329 | −1.47397 | −0.736987 | − | 0.675907i | \(-0.763752\pi\) | ||||
−0.736987 | + | 0.675907i | \(0.763752\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.13530 | −0.241812 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.8130 | 1.58518 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1402 | 0.474337 | 0.237168 | − | 0.971469i | \(-0.423781\pi\) | ||||
0.237168 | + | 0.971469i | \(0.423781\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6407 | −0.495587 | −0.247793 | − | 0.968813i | \(-0.579705\pi\) | ||||
−0.247793 | + | 0.968813i | \(0.579705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.36515 | −0.435235 | −0.217618 | − | 0.976034i | \(-0.569829\pi\) | ||||
−0.217618 | + | 0.976034i | \(0.569829\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2947 | 0.754029 | 0.377015 | − | 0.926207i | \(-0.376951\pi\) | ||||
0.377015 | + | 0.926207i | \(0.376951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.4649 | 1.12968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.2734 | 1.57589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.23472 | 0.0566526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.7930 | −1.50149 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.19942 | 0.100494 | 0.0502470 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502470 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.8902 | 1.49966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.1941 | 0.871557 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0675 | 0.682772 | 0.341386 | − | 0.939923i | \(-0.389104\pi\) | ||||
0.341386 | + | 0.939923i | \(0.389104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.8717 | −1.93477 | −0.967386 | − | 0.253306i | \(-0.918482\pi\) | ||||
−0.967386 | + | 0.253306i | \(0.918482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.12486 | −0.0956990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −47.5721 | −2.13820 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 44.4944 | 1.99585 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.649143 | 0.0290596 | 0.0145298 | − | 0.999894i | \(-0.495375\pi\) | ||||
0.0145298 | + | 0.999894i | \(0.495375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.7477 | 1.37097 | 0.685485 | − | 0.728086i | \(-0.259590\pi\) | ||||
0.685485 | + | 0.728086i | \(0.259590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.5890 | 1.53919 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.8935 | −1.32501 | −0.662504 | − | 0.749059i | \(-0.730506\pi\) | ||||
−0.662504 | + | 0.749059i | \(0.730506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.13623 | 0.0945013 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −46.0544 | −2.02940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −66.6807 | −2.93261 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1825 | 0.752778 | 0.376389 | − | 0.926462i | \(-0.377166\pi\) | ||||
0.376389 | + | 0.926462i | \(0.377166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.53100 | 0.198127 | 0.0990634 | − | 0.995081i | \(-0.468415\pi\) | ||||
0.0990634 | + | 0.995081i | \(0.468415\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.00974 | 0.218227 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.9103 | −0.604796 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.7427 | −0.509589 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.68058 | −0.116109 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.66385 | 0.201636 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −61.5198 | −2.64985 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3847 | −0.575452 | −0.287726 | − | 0.957713i | \(-0.592899\pi\) | ||||
−0.287726 | + | 0.957713i | \(0.592899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.0467 | 1.54407 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.8240 | −0.890370 | −0.445185 | − | 0.895439i | \(-0.646862\pi\) | ||||
−0.445185 | + | 0.895439i | \(0.646862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.0887 | 1.02808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.18318 | 0.178209 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.08498 | 0.173711 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50324 | 0.190809 | 0.0954043 | − | 0.995439i | \(-0.469586\pi\) | ||||
0.0954043 | + | 0.995439i | \(0.469586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.8904 | 0.756684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.8178 | 1.67812 | 0.839060 | − | 0.544039i | \(-0.183106\pi\) | ||||
0.839060 | + | 0.544039i | \(0.183106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.3892 | 1.02606 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.7648 | 1.54398 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.5776 | 1.40765 | 0.703824 | − | 0.710375i | \(-0.251474\pi\) | ||||
0.703824 | + | 0.710375i | \(0.251474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.4471 | −0.520897 | −0.260448 | − | 0.965488i | \(-0.583870\pi\) | ||||
−0.260448 | + | 0.965488i | \(0.583870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.72256 | 0.155241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.5869 | 1.93944 | 0.969718 | − | 0.244226i | \(-0.0785338\pi\) | ||||
0.969718 | + | 0.244226i | \(0.0785338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9155 | 0.452853 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −69.4196 | −2.87507 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.8322 | −1.02668 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.6035 | 1.01549 | 0.507747 | − | 0.861506i | \(-0.330479\pi\) | ||||
0.507747 | + | 0.861506i | \(0.330479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.86256 | −0.406380 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4433 | −0.510983 | −0.255492 | − | 0.966811i | \(-0.582237\pi\) | ||||
−0.255492 | + | 0.966811i | \(0.582237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.18112 | 0.212405 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.5515 | 1.41174 | 0.705868 | − | 0.708343i | \(-0.250557\pi\) | ||||
0.705868 | + | 0.708343i | \(0.250557\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0978 | 0.860598 | 0.430299 | − | 0.902686i | \(-0.358408\pi\) | ||||
0.430299 | + | 0.902686i | \(0.358408\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.9670 | −0.731671 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −73.2391 | −2.97759 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.07158 | 0.205849 | 0.102925 | − | 0.994689i | \(-0.467180\pi\) | ||||
0.102925 | + | 0.994689i | \(0.467180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.8067 | −1.40813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.0490 | 1.17328 | 0.586639 | − | 0.809848i | \(-0.300451\pi\) | ||||
0.586639 | + | 0.809848i | \(0.300451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.5495 | 1.75324 | 0.876619 | − | 0.481185i | \(-0.159793\pi\) | ||||
0.876619 | + | 0.481185i | \(0.159793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.92370 | 0.197900 | 0.0989502 | − | 0.995092i | \(-0.468452\pi\) | ||||
0.0989502 | + | 0.995092i | \(0.468452\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.64506 | 0.186100 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6491 | −1.18596 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.03972 | 0.200947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.1776 | 1.04211 | 0.521057 | − | 0.853522i | \(-0.325538\pi\) | ||||
0.521057 | + | 0.853522i | \(0.325538\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.52347 | −0.377927 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.1128 | −1.27236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.6766 | −1.29267 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.8659 | 0.705662 | 0.352831 | − | 0.935687i | \(-0.385219\pi\) | ||||
0.352831 | + | 0.935687i | \(0.385219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.7348 | 1.01488 | 0.507440 | − | 0.861687i | \(-0.330592\pi\) | ||||
0.507440 | + | 0.861687i | \(0.330592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.7509 | 1.56277 | 0.781384 | − | 0.624050i | \(-0.214514\pi\) | ||||
0.781384 | + | 0.624050i | \(0.214514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.8581 | −0.975767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.7376 | 0.420197 | 0.210098 | − | 0.977680i | \(-0.432622\pi\) | ||||
0.210098 | + | 0.977680i | \(0.432622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.6097 | −0.922506 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.56884 | −0.0612064 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.5265 | −0.799599 | −0.399800 | − | 0.916603i | \(-0.630920\pi\) | ||||
−0.399800 | + | 0.916603i | \(0.630920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.06218 | 0.0413139 | 0.0206569 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206569 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.2000 | −0.395537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.6119 | 0.488335 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.9935 | 1.96858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.4033 | −1.24906 | −0.624528 | − | 0.781003i | \(-0.714709\pi\) | ||||
−0.624528 | + | 0.781003i | \(0.714709\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7933 | 0.606985 | 0.303493 | − | 0.952834i | \(-0.401847\pi\) | ||||
0.303493 | + | 0.952834i | \(0.401847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.4014 | −1.20507 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.8814 | 0.454630 | 0.227315 | − | 0.973821i | \(-0.427005\pi\) | ||||
0.227315 | + | 0.973821i | \(0.427005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.85509 | 0.147295 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.2364 | −1.38050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6715 | 0.634215 | 0.317107 | − | 0.948390i | \(-0.397288\pi\) | ||||
0.317107 | + | 0.948390i | \(0.397288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 77.8276 | 2.95643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.0062 | −1.17613 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.410742 | −0.0155580 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.2071 | 1.14090 | 0.570452 | − | 0.821331i | \(-0.306768\pi\) | ||||
0.570452 | + | 0.821331i | \(0.306768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.92158 | −0.374200 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −56.5874 | −2.12819 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.2327 | −0.759856 | −0.379928 | − | 0.925016i | \(-0.624051\pi\) | ||||
−0.379928 | + | 0.925016i | \(0.624051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.7348 | −1.11358 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.5674 | −1.96591 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.53276 | 0.169043 | 0.0845217 | − | 0.996422i | \(-0.473064\pi\) | ||||
0.0845217 | + | 0.996422i | \(0.473064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 75.3447 | 2.80598 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.16503 | 0.191824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.68674 | 0.247997 | 0.123999 | − | 0.992282i | \(-0.460428\pi\) | ||||
0.123999 | + | 0.992282i | \(0.460428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.74132 | 0.101391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.5459 | −0.611137 | −0.305569 | − | 0.952170i | \(-0.598847\pi\) | ||||
−0.305569 | + | 0.952170i | \(0.598847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.0343 | −1.40101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.1937 | −1.07391 | −0.536954 | − | 0.843611i | \(-0.680425\pi\) | ||||
−0.536954 | + | 0.843611i | \(0.680425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0213 | −1.46824 | −0.734120 | − | 0.679019i | \(-0.762405\pi\) | ||||
−0.734120 | + | 0.679019i | \(0.762405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.67824 | 0.317946 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.01635 | −0.293303 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.63003 | −0.278795 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.7899 | −1.56143 | −0.780714 | − | 0.624889i | \(-0.785144\pi\) | ||||
−0.780714 | + | 0.624889i | \(0.785144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.1483 | −0.733272 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4786 | −0.998728 | −0.499364 | − | 0.866392i | \(-0.666433\pi\) | ||||
−0.499364 | + | 0.866392i | \(0.666433\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.8375 | −1.58911 | −0.794554 | − | 0.607194i | \(-0.792295\pi\) | ||||
−0.794554 | + | 0.607194i | \(0.792295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58.9721 | −2.13493 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.80500 | −0.137570 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9757 | −0.468526 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1742 | 0.402953 | 0.201477 | − | 0.979493i | \(-0.435426\pi\) | ||||
0.201477 | + | 0.979493i | \(0.435426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.44411 | −0.159843 | −0.0799217 | − | 0.996801i | \(-0.525467\pi\) | ||||
−0.0799217 | + | 0.996801i | \(0.525467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.1775 | −0.437427 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.808619 | 0.0289718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −69.1732 | −2.47521 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.50997 | −0.125276 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.75749 | 0.276525 | 0.138262 | − | 0.990396i | \(-0.455848\pi\) | ||||
0.138262 | + | 0.990396i | \(0.455848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.9005 | −1.41870 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.6182 | 0.945239 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.9100 | −0.669827 | −0.334914 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334914 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.33338 | −0.188682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.41132 | −0.120533 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.32109 | −0.117199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.7520 | −1.08386 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.4443 | 1.28131 | 0.640656 | − | 0.767828i | \(-0.278663\pi\) | ||||
0.640656 | + | 0.767828i | \(0.278663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8752 | 0.627683 | 0.313842 | − | 0.949475i | \(-0.398384\pi\) | ||||
0.313842 | + | 0.949475i | \(0.398384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −48.7474 | −1.70755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.39678 | −0.188809 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 40.6253 | 1.41956 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8018 | 1.28439 | 0.642196 | − | 0.766541i | \(-0.278024\pi\) | ||||
0.642196 | + | 0.766541i | \(0.278024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.9718 | 1.42819 | 0.714094 | − | 0.700049i | \(-0.246839\pi\) | ||||
0.714094 | + | 0.700049i | \(0.246839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7841 | −0.792280 | −0.396140 | − | 0.918190i | \(-0.629650\pi\) | ||||
−0.396140 | + | 0.918190i | \(0.629650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7852 | −0.826094 | −0.413047 | − | 0.910710i | \(-0.635536\pi\) | ||||
−0.413047 | + | 0.910710i | \(0.635536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.92060 | −0.170489 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.4617 | −0.362042 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.31748 | −0.252627 | −0.126314 | − | 0.991990i | \(-0.540315\pi\) | ||||
−0.126314 | + | 0.991990i | \(0.540315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5010 | −0.396588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.02055 | 0.172712 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 119.819 | 4.11702 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.9127 | −1.02539 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.0182 | 1.33596 | 0.667978 | − | 0.744181i | \(-0.267160\pi\) | ||||
0.667978 | + | 0.744181i | \(0.267160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.49082 | 0.256181 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.8249 | −1.66783 | −0.833913 | − | 0.551896i | \(-0.813905\pi\) | ||||
−0.833913 | + | 0.551896i | \(0.813905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.3762 | −1.82117 | −0.910585 | − | 0.413321i | \(-0.864369\pi\) | ||||
−0.910585 | + | 0.413321i | \(0.864369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8660 | 1.35705 | 0.678527 | − | 0.734576i | \(-0.262619\pi\) | ||||
0.678527 | + | 0.734576i | \(0.262619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.6775 | −0.533051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.35071 | −0.215433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.8536 | −0.672713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.0611 | 0.780499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.4057 | 1.29835 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.76924 | 0.329884 | 0.164942 | − | 0.986303i | \(-0.447256\pi\) | ||||
0.164942 | + | 0.986303i | \(0.447256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6011 | −0.795143 | −0.397571 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397571 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.9877 | −1.41300 | −0.706500 | − | 0.707714i | \(-0.749727\pi\) | ||||
−0.706500 | + | 0.707714i | \(0.749727\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.94041 | −0.199459 | −0.0997297 | − | 0.995015i | \(-0.531798\pi\) | ||||
−0.0997297 | + | 0.995015i | \(0.531798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.5803 | 0.522548 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −57.1564 | −1.91481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.4997 | 0.351360 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.1533 | −0.673650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.2568 | −1.37599 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.55245 | −0.184979 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.8015 | 1.62222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5655 | −0.450435 | −0.225217 | − | 0.974309i | \(-0.572309\pi\) | ||||
−0.225217 | + | 0.974309i | \(0.572309\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.5577 | 1.37838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.33021 | −0.0440719 | −0.0220359 | − | 0.999757i | \(-0.507015\pi\) | ||||
−0.0220359 | + | 0.999757i | \(0.507015\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9698 | −0.561619 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.6253 | 1.27552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3273 | 0.604560 | 0.302280 | − | 0.953219i | \(-0.402252\pi\) | ||||
0.302280 | + | 0.953219i | \(0.402252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.1078 | −1.18850 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.2503 | −0.402789 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55.3330 | −1.81737 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.23053 | −0.270035 | −0.135017 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135017 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.68707 | 0.317481 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.05482 | −0.263421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.9085 | −0.911732 | −0.455866 | − | 0.890048i | \(-0.650670\pi\) | ||||
−0.455866 | + | 0.890048i | \(0.650670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.93387 | −0.291236 | −0.145618 | − | 0.989341i | \(-0.546517\pi\) | ||||
−0.145618 | + | 0.989341i | \(0.546517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.43791 | 0.0793894 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6474 | −0.670951 | −0.335476 | − | 0.942049i | \(-0.608897\pi\) | ||||
−0.335476 | + | 0.942049i | \(0.608897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.73358 | −0.0562744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.3712 | −1.63168 | −0.815841 | − | 0.578276i | \(-0.803726\pi\) | ||||
−0.815841 | + | 0.578276i | \(0.803726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.2024 | −0.944968 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.30690 | −0.203660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.2702 | 2.13775 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.60347 | 0.180569 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.1199 | −1.35589 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.8709 | −1.73237 | −0.866186 | − | 0.499722i | \(-0.833436\pi\) | ||||
−0.866186 | + | 0.499722i | \(0.833436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.1904 | −0.872580 | −0.436290 | − | 0.899806i | \(-0.643708\pi\) | ||||
−0.436290 | + | 0.899806i | \(0.643708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.7259 | 1.62620 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.6281 | 1.36379 | 0.681897 | − | 0.731448i | \(-0.261155\pi\) | ||||
0.681897 | + | 0.731448i | \(0.261155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.22143 | −0.230798 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.3090 | 1.38275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.33641 | −0.202100 | −0.101050 | − | 0.994881i | \(-0.532220\pi\) | ||||
−0.101050 | + | 0.994881i | \(0.532220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.6664 | 1.13643 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2708 | −0.517382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.49187 | −0.0473907 | −0.0236954 | − | 0.999719i | \(-0.507543\pi\) | ||||
−0.0236954 | + | 0.999719i | \(0.507543\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.6407 | 1.76393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.9745 | −1.39268 | −0.696342 | − | 0.717710i | \(-0.745190\pi\) | ||||
−0.696342 | + | 0.717710i | \(0.745190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6004.2.a.d.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.d.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |