Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.25613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.25613 | 1.30258 | 0.651288 | − | 0.758831i | \(-0.274229\pi\) | ||||
0.651288 | + | 0.758831i | \(0.274229\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.20604 | −1.88100 | −0.940498 | − | 0.339799i | \(-0.889641\pi\) | ||||
−0.940498 | + | 0.339799i | \(0.889641\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.20604 | −1.21177 | −0.605884 | − | 0.795553i | \(-0.707180\pi\) | ||||
−0.605884 | + | 0.795553i | \(0.707180\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09011 | 0.696705 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.723884 | 0.200769 | 0.100385 | − | 0.994949i | \(-0.467993\pi\) | ||||
0.100385 | + | 0.994949i | \(0.467993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.48935 | −2.45014 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.655737 | 0.159040 | 0.0795198 | − | 0.996833i | \(-0.474661\pi\) | ||||
0.0795198 | + | 0.996833i | \(0.474661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.23323 | −1.57842 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68543 | 0.559950 | 0.279975 | − | 0.960007i | \(-0.409674\pi\) | ||||
0.279975 | + | 0.960007i | \(0.409674\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.6907 | 2.53815 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.05282 | −0.395065 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.64351 | −0.490887 | −0.245443 | − | 0.969411i | \(-0.578934\pi\) | ||||
−0.245443 | + | 0.969411i | \(0.578934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.48935 | −1.70434 | −0.852169 | − | 0.523266i | \(-0.824713\pi\) | ||||
−0.852169 | + | 0.523266i | \(0.824713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.25613 | 0.392742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.4847 | 2.27933 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.20992 | 0.692107 | 0.346053 | − | 0.938215i | \(-0.387522\pi\) | ||||
0.346053 | + | 0.938215i | \(0.387522\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.63317 | 0.261517 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.04141 | 0.787336 | 0.393668 | − | 0.919253i | \(-0.371206\pi\) | ||||
0.393668 | + | 0.919253i | \(0.371206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7480 | 1.63905 | 0.819526 | − | 0.573042i | \(-0.194237\pi\) | ||||
0.819526 | + | 0.573042i | \(0.194237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.79110 | −1.31050 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.84428 | 0.706611 | 0.353306 | − | 0.935508i | \(-0.385058\pi\) | ||||
0.353306 | + | 0.935508i | \(0.385058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.27866 | 0.468380 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.47943 | 0.207161 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.80135 | 0.384795 | 0.192397 | − | 0.981317i | \(-0.438374\pi\) | ||||
0.192397 | + | 0.981317i | \(0.438374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.20604 | −0.567142 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.25613 | −0.298831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.16817 | 1.06341 | 0.531703 | − | 0.846931i | \(-0.321552\pi\) | ||||
0.531703 | + | 0.846931i | \(0.321552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.66797 | 0.213562 | 0.106781 | − | 0.994283i | \(-0.465946\pi\) | ||||
0.106781 | + | 0.994283i | \(0.465946\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.70098 | −0.844244 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.04468 | −0.377646 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.57845 | 0.192839 | 0.0964193 | − | 0.995341i | \(-0.469261\pi\) | ||||
0.0964193 | + | 0.995341i | \(0.469261\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.05867 | 0.729378 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3445 | 1.22766 | 0.613832 | − | 0.789436i | \(-0.289627\pi\) | ||||
0.613832 | + | 0.789436i | \(0.289627\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.35322 | −0.392465 | −0.196232 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196232 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.6319 | 3.30613 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.20604 | −0.365362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.4366 | 1.96177 | 0.980884 | − | 0.194591i | \(-0.0623380\pi\) | ||||
0.980884 | + | 0.194591i | \(0.0623380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9018 | −1.21131 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.13518 | −0.453895 | −0.226948 | − | 0.973907i | \(-0.572875\pi\) | ||||
−0.226948 | + | 0.973907i | \(0.572875\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.75805 | −0.299153 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.96409 | −0.639417 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.8240 | −1.67734 | −0.838668 | − | 0.544643i | \(-0.816665\pi\) | ||||
−0.838668 | + | 0.544643i | \(0.816665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.32080 | −0.243286 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.4092 | −2.22003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.20604 | 0.431530 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.57301 | 0.565853 | 0.282926 | − | 0.959142i | \(-0.408695\pi\) | ||||
0.282926 | + | 0.959142i | \(0.408695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.09011 | 0.210064 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.98882 | 0.794917 | 0.397458 | − | 0.917620i | \(-0.369892\pi\) | ||||
0.397458 | + | 0.917620i | \(0.369892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7152 | 1.44993 | 0.724964 | − | 0.688787i | \(-0.241856\pi\) | ||||
0.724964 | + | 0.688787i | \(0.241856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.4232 | 2.96900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11242 | 0.107542 | 0.0537710 | − | 0.998553i | \(-0.482876\pi\) | ||||
0.0537710 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.03175 | −0.769302 | −0.384651 | − | 0.923062i | \(-0.625678\pi\) | ||||
−0.384651 | + | 0.923062i | \(0.625678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.49812 | 0.901522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1703 | 0.956742 | 0.478371 | − | 0.878158i | \(-0.341227\pi\) | ||||
0.478371 | + | 0.878158i | \(0.341227\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.2950 | −1.05326 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.51300 | 0.139877 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.10232 | −0.192719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3741 | 1.02556 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.3475 | −2.89325 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6874 | 1.03709 | 0.518544 | − | 0.855051i | \(-0.326474\pi\) | ||||
0.518544 | + | 0.855051i | \(0.326474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.2488 | 2.13499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.2777 | −1.33482 | −0.667409 | − | 0.744691i | \(-0.732597\pi\) | ||||
−0.667409 | + | 0.744691i | \(0.732597\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.20604 | 0.277999 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.63422 | 0.743115 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8730 | −1.09982 | −0.549909 | − | 0.835225i | \(-0.685338\pi\) | ||||
−0.549909 | + | 0.835225i | \(0.685338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1802 | 1.11793 | 0.558965 | − | 0.829191i | \(-0.311199\pi\) | ||||
0.558965 | + | 0.829191i | \(0.311199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9293 | 0.920415 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.723884 | 0.0605342 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.1187 | 0.923356 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.39708 | 0.610101 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5422 | 1.35519 | 0.677594 | − | 0.735436i | \(-0.263023\pi\) | ||||
0.677594 | + | 0.735436i | \(0.263023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0851 | −1.30899 | −0.654495 | − | 0.756067i | \(-0.727119\pi\) | ||||
−0.654495 | + | 0.756067i | \(0.727119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.37057 | 0.110804 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.9126 | 3.20585 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3684 | 1.38615 | 0.693074 | − | 0.720866i | \(-0.256256\pi\) | ||||
0.693074 | + | 0.720866i | \(0.256256\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.32020 | 0.501224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.60958 | −0.678530 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3725 | 1.43904 | 0.719521 | − | 0.694471i | \(-0.244362\pi\) | ||||
0.719521 | + | 0.694471i | \(0.244362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.48935 | −0.738745 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.62676 | 0.203265 | 0.101632 | − | 0.994822i | \(-0.467593\pi\) | ||||
0.101632 | + | 0.994822i | \(0.467593\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4760 | −0.959692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.09011 | −0.159835 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.23475 | −0.474020 | −0.237010 | − | 0.971507i | \(-0.576167\pi\) | ||||
−0.237010 | + | 0.971507i | \(0.576167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −40.6869 | −3.07564 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.4284 | 1.38517 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.29357 | −0.320917 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.52254 | 0.336158 | 0.168079 | − | 0.985774i | \(-0.446244\pi\) | ||||
0.168079 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.76316 | 0.278181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.7071 | −1.30185 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.655737 | 0.0479523 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.58140 | 0.478727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.0370 | −1.81162 | −0.905808 | − | 0.423689i | \(-0.860735\pi\) | ||||
−0.905808 | + | 0.423689i | \(0.860735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.60176 | 0.331242 | 0.165621 | − | 0.986189i | \(-0.447037\pi\) | ||||
0.165621 | + | 0.986189i | \(0.447037\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.86919 | −0.491913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.51765 | 0.393117 | 0.196558 | − | 0.980492i | \(-0.437024\pi\) | ||||
0.196558 | + | 0.980492i | \(0.437024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.84534 | 0.697917 | 0.348959 | − | 0.937138i | \(-0.386535\pi\) | ||||
0.348959 | + | 0.937138i | \(0.386535\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.56119 | 0.251187 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.47517 | 0.594841 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.2043 | −1.48098 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.61285 | 0.390120 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3536 | 1.40120 | 0.700601 | − | 0.713553i | \(-0.252915\pi\) | ||||
0.700601 | + | 0.713553i | \(0.252915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.3385 | 1.59913 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −45.2064 | −3.08305 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.4232 | 2.06526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.56530 | −0.511215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.474677 | 0.0319303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.69489 | −0.381358 | −0.190679 | − | 0.981652i | \(-0.561069\pi\) | ||||
−0.190679 | + | 0.981652i | \(0.561069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.5251 | 1.76834 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0945 | 1.06823 | 0.534116 | − | 0.845411i | \(-0.320644\pi\) | ||||
0.534116 | + | 0.845411i | \(0.320644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1886 | 0.673280 | 0.336640 | − | 0.941633i | \(-0.390709\pi\) | ||||
0.336640 | + | 0.941633i | \(0.390709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.23323 | −0.475911 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5112 | 1.08168 | 0.540841 | − | 0.841125i | \(-0.318106\pi\) | ||||
0.540841 | + | 0.841125i | \(0.318106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.3752 | −1.32913 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39.3392 | 2.55535 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.1261 | 1.81933 | 0.909664 | − | 0.415345i | \(-0.136339\pi\) | ||||
0.909664 | + | 0.415345i | \(0.136339\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8092 | 1.21160 | 0.605802 | − | 0.795615i | \(-0.292852\pi\) | ||||
0.605802 | + | 0.795615i | \(0.292852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.4373 | −1.18276 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.7902 | −0.881021 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.723884 | −0.0460596 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.32950 | −0.591233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2974 | −1.21804 | −0.609020 | − | 0.793155i | \(-0.708437\pi\) | ||||
−0.609020 | + | 0.793155i | \(0.708437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.68543 | 0.168831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.22252 | −0.389669 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.9480 | −1.36908 | −0.684540 | − | 0.728976i | \(-0.739997\pi\) | ||||
−0.684540 | + | 0.728976i | \(0.739997\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4972 | −0.838672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.52523 | −0.342003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.31030 | 0.574098 | 0.287049 | − | 0.957916i | \(-0.407326\pi\) | ||||
0.287049 | + | 0.957916i | \(0.407326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7826 | −0.723797 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.7009 | −2.18486 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.1406 | −1.10605 | −0.553026 | − | 0.833164i | \(-0.686527\pi\) | ||||
−0.553026 | + | 0.833164i | \(0.686527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.8372 | −1.56950 | −0.784750 | − | 0.619813i | \(-0.787208\pi\) | ||||
−0.784750 | + | 0.619813i | \(0.787208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.23602 | −0.316898 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.6907 | 0.765280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9438 | −0.897886 | −0.448943 | − | 0.893560i | \(-0.648199\pi\) | ||||
−0.448943 | + | 0.893560i | \(0.648199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.8338 | −1.18742 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4663 | −1.45954 | −0.729769 | − | 0.683694i | \(-0.760372\pi\) | ||||
−0.729769 | + | 0.683694i | \(0.760372\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.68159 | −0.516067 | −0.258034 | − | 0.966136i | \(-0.583075\pi\) | ||||
−0.258034 | + | 0.966136i | \(0.583075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.48935 | 0.562101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.1629 | −0.954068 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5700 | −0.974706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5734 | 0.737067 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.2517 | −1.06628 | −0.533138 | − | 0.846028i | \(-0.678987\pi\) | ||||
−0.533138 | + | 0.846028i | \(0.678987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.3556 | −2.00026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.05282 | −0.119117 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.94394 | 0.112421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.4584 | −1.98615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.0238 | 1.03544 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.01555 | −0.401709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.22644 | −0.298289 | −0.149144 | − | 0.988815i | \(-0.547652\pi\) | ||||
−0.149144 | + | 0.988815i | \(0.547652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.1993 | 1.88864 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.53926 | 0.314103 | 0.157051 | − | 0.987590i | \(-0.449801\pi\) | ||||
0.157051 | + | 0.987590i | \(0.449801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7911 | −0.722998 | −0.361499 | − | 0.932372i | \(-0.617735\pi\) | ||||
−0.361499 | + | 0.932372i | \(0.617735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 28.1846 | 1.58802 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.2257 | −1.64148 | −0.820740 | − | 0.571301i | \(-0.806439\pi\) | ||||
−0.820740 | + | 0.571301i | \(0.806439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.64351 | −0.148008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.50977 | 0.140082 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.655737 | −0.0364862 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.18661 | 0.509582 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1207 | −1.00207 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.5309 | −0.856249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8740 | 0.872513 | 0.436256 | − | 0.899822i | \(-0.356304\pi\) | ||||
0.436256 | + | 0.899822i | \(0.356304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.79922 | 0.482194 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.63903 | −0.362729 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.93726 | 0.160003 | 0.0800014 | − | 0.996795i | \(-0.474508\pi\) | ||||
0.0800014 | + | 0.996795i | \(0.474508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.9455 | 1.24623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.48935 | −0.513877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.9307 | 0.644200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.4830 | −1.37196 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.74992 | 0.469721 | 0.234860 | − | 0.972029i | \(-0.424537\pi\) | ||||
0.234860 | + | 0.972029i | \(0.424537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4164 | −0.985807 | −0.492904 | − | 0.870084i | \(-0.664064\pi\) | ||||
−0.492904 | + | 0.870084i | \(0.664064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.48600 | −0.0793169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.9919 | −1.06406 | −0.532031 | − | 0.846725i | \(-0.678571\pi\) | ||||
−0.532031 | + | 0.846725i | \(0.678571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.5093 | −2.30923 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.74310 | −0.251031 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.29606 | −0.173960 | −0.0869798 | − | 0.996210i | \(-0.527722\pi\) | ||||
−0.0869798 | + | 0.996210i | \(0.527722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.25613 | 0.118416 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.1038 | 0.738225 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.2683 | 1.31900 | 0.659498 | − | 0.751707i | \(-0.270769\pi\) | ||||
0.659498 | + | 0.751707i | \(0.270769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.5371 | 0.548541 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.98122 | −0.466282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.25095 | −0.271884 | −0.135942 | − | 0.990717i | \(-0.543406\pi\) | ||||
−0.135942 | + | 0.990717i | \(0.543406\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −72.9801 | −3.76868 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.91359 | −0.0985550 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3964 | 1.25316 | 0.626580 | − | 0.779357i | \(-0.284454\pi\) | ||||
0.626580 | + | 0.779357i | \(0.284454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.3682 | 1.35089 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5585 | −1.51037 | −0.755184 | − | 0.655512i | \(-0.772453\pi\) | ||||
−0.755184 | + | 0.655512i | \(0.772453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4847 | 0.687244 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.4645 | 1.14194 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.0958 | 1.67803 | 0.839013 | − | 0.544112i | \(-0.183133\pi\) | ||||
0.839013 | + | 0.544112i | \(0.183133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.76093 | 0.0890543 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.4684 | −1.73870 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −73.3389 | −3.69008 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55966 | −0.0782769 | −0.0391385 | − | 0.999234i | \(-0.512461\pi\) | ||||
−0.0391385 | + | 0.999234i | \(0.512461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.23323 | 0.362114 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.9881 | 0.898282 | 0.449141 | − | 0.893461i | \(-0.351730\pi\) | ||||
0.449141 | + | 0.893461i | \(0.351730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.86919 | −0.342179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 45.8532 | 2.27846 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.20992 | 0.208678 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8247 | 1.57363 | 0.786816 | − | 0.617188i | \(-0.211728\pi\) | ||||
0.786816 | + | 0.617188i | \(0.211728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.0432 | −1.43260 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.1874 | −1.28860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.3927 | 0.853775 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.7362 | 1.45619 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0175 | 1.07563 | 0.537814 | − | 0.843064i | \(-0.319250\pi\) | ||||
0.537814 | + | 0.843064i | \(0.319250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5466 | −0.855171 | −0.427585 | − | 0.903975i | \(-0.640636\pi\) | ||||
−0.427585 | + | 0.903975i | \(0.640636\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.1251 | 0.492300 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.32178 | 0.403666 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.34758 | −0.258788 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.63317 | 0.0788504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.854799 | −0.0411742 | −0.0205871 | − | 0.999788i | \(-0.506554\pi\) | ||||
−0.0205871 | + | 0.999788i | \(0.506554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.0259 | −0.818214 | −0.409107 | − | 0.912486i | \(-0.634160\pi\) | ||||
−0.409107 | + | 0.912486i | \(0.634160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.0852 | 1.20274 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.68543 | −0.128461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.81936 | −0.134561 | −0.0672804 | − | 0.997734i | \(-0.521432\pi\) | ||||
−0.0672804 | + | 0.997734i | \(0.521432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.85278 | 0.326323 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.4356 | 0.923414 | 0.461707 | − | 0.887033i | \(-0.347237\pi\) | ||||
0.461707 | + | 0.887033i | \(0.347237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 66.5561 | 3.15506 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 37.3213 | 1.76524 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7032 | 0.646693 | 0.323347 | − | 0.946281i | \(-0.395192\pi\) | ||||
0.323347 | + | 0.946281i | \(0.395192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.04141 | 0.237391 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36.2901 | −1.70506 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.76135 | 0.457619 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2586 | −0.526653 | −0.263326 | − | 0.964707i | \(-0.584820\pi\) | ||||
−0.263326 | + | 0.964707i | \(0.584820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.34611 | −0.0628310 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5115 | 0.815594 | 0.407797 | − | 0.913073i | \(-0.366297\pi\) | ||||
0.407797 | + | 0.913073i | \(0.366297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4636 | 0.951022 | 0.475511 | − | 0.879710i | \(-0.342263\pi\) | ||||
0.475511 | + | 0.879710i | \(0.342263\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 90.0479 | 4.17587 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.1897 | 0.517796 | 0.258898 | − | 0.965905i | \(-0.416641\pi\) | ||||
0.258898 | + | 0.965905i | \(0.416641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.06057 | −0.233676 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.1853 | 1.80556 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7480 | 0.494193 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6907 | −0.582291 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.85514 | 0.268088 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.8664 | −1.77585 | −0.887926 | − | 0.459986i | \(-0.847855\pi\) | ||||
−0.887926 | + | 0.459986i | \(0.847855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.04749 | 0.138954 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.4243 | −0.883837 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.4403 | −1.06437 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6592 | 1.07210 | 0.536050 | − | 0.844186i | \(-0.319916\pi\) | ||||
0.536050 | + | 0.844186i | \(0.319916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.4506 | 1.87446 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.74101 | −0.259088 | −0.129544 | − | 0.991574i | \(-0.541351\pi\) | ||||
−0.129544 | + | 0.991574i | \(0.541351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.73345 | −0.0780704 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.79110 | −0.395130 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.1648 | −1.48764 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.85986 | 0.217557 | 0.108779 | − | 0.994066i | \(-0.465306\pi\) | ||||
0.108779 | + | 0.994066i | \(0.465306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.92630 | 0.264768 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.08324 | −0.226650 | −0.113325 | − | 0.993558i | \(-0.536150\pi\) | ||||
−0.113325 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.6012 | −1.49524 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.1474 | −1.25007 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.2272 | 1.56142 | 0.780708 | − | 0.624896i | \(-0.214859\pi\) | ||||
0.780708 | + | 0.624896i | \(0.214859\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.7505 | 0.475576 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.05282 | 0.0906341 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −61.8925 | −2.72731 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.84428 | 0.213051 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0664 | −0.617447 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2922 | −0.582344 | −0.291172 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291172 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0749 | 1.27136 | 0.635679 | − | 0.771954i | \(-0.280720\pi\) | ||||
0.635679 | + | 0.771954i | \(0.280720\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −91.7949 | −4.00626 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.22252 | −0.271057 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7885 | −0.686456 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.0724 | 0.740880 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.64939 | 0.158073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.67889 | −0.202286 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.68685 | −0.418018 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.27866 | 0.141222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8688 | 1.11219 | 0.556093 | − | 0.831120i | \(-0.312300\pi\) | ||||
0.556093 | + | 0.831120i | \(0.312300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2034 | 0.437871 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.7818 | 1.44705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5966 | −0.453076 | −0.226538 | − | 0.974002i | \(-0.572741\pi\) | ||||
−0.226538 | + | 0.974002i | \(0.572741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.48626 | 0.148790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.64351 | 0.112617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.9023 | −2.37721 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −39.9494 | −1.69576 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.0565 | 1.95148 | 0.975738 | − | 0.218939i | \(-0.0702597\pi\) | ||||
0.975738 | + | 0.218939i | \(0.0702597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.78029 | 0.329071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.47943 | 0.0624615 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.4009 | 1.57626 | 0.788129 | − | 0.615510i | \(-0.211050\pi\) | ||||
0.788129 | + | 0.615510i | \(0.211050\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.7767 | −1.79963 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.9514 | 1.46782 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.67373 | 0.279777 | 0.139889 | − | 0.990167i | \(-0.455326\pi\) | ||||
0.139889 | + | 0.990167i | \(0.455326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.1302 | 1.17721 | 0.588606 | − | 0.808420i | \(-0.299677\pi\) | ||||
0.588606 | + | 0.808420i | \(0.299677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −56.4867 | −2.35977 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.0800 | 1.42124 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1279 | 0.879567 | 0.439784 | − | 0.898104i | \(-0.355055\pi\) | ||||
0.439784 | + | 0.898104i | \(0.355055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.3822 | 0.431468 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2575 | 0.550015 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.80135 | 0.116020 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.36373 | −0.263108 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.6634 | −0.852869 | −0.426435 | − | 0.904518i | \(-0.640231\pi\) | ||||
−0.426435 | + | 0.904518i | \(0.640231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.48935 | 0.391002 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.4485 | 0.512064 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.59734 | −0.311985 | −0.155993 | − | 0.987758i | \(-0.549858\pi\) | ||||
−0.155993 | + | 0.987758i | \(0.549858\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.84242 | 0.362504 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.2123 | 0.909091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.9894 | −1.38877 | −0.694385 | − | 0.719604i | \(-0.744323\pi\) | ||||
−0.694385 | + | 0.719604i | \(0.744323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0050 | 0.897602 | 0.448801 | − | 0.893632i | \(-0.351851\pi\) | ||||
0.448801 | + | 0.893632i | \(0.351851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.29915 | 0.134352 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.20604 | −0.171000 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9767 | 0.486120 | 0.243060 | − | 0.970011i | \(-0.421849\pi\) | ||||
0.243060 | + | 0.970011i | \(0.421849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1211 | 0.774825 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.50670 | 0.141866 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7909 | 0.799345 | 0.399673 | − | 0.916658i | \(-0.369124\pi\) | ||||
0.399673 | + | 0.916658i | \(0.369124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.8397 | −1.92908 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1026 | −1.25214 | −0.626072 | − | 0.779765i | \(-0.715338\pi\) | ||||
−0.626072 | + | 0.779765i | \(0.715338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.4469 | 0.580671 | 0.290335 | − | 0.956925i | \(-0.406233\pi\) | ||||
0.290335 | + | 0.956925i | \(0.406233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.51269 | −0.221217 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.7322 | 2.03254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 72.6010 | 2.90404 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.25613 | −0.0901011 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.76060 | 0.110072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.05580 | 0.161459 | 0.0807295 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807295 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.9204 | 1.82517 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −49.1575 | −1.95076 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.37337 | 0.0940363 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.6212 | 0.855320 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.8261 | −1.29655 | −0.648277 | − | 0.761405i | \(-0.724510\pi\) | ||||
−0.648277 | + | 0.761405i | \(0.724510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0138 | −0.868139 | −0.434070 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434070 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −101.991 | −4.01591 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.5626 | −1.67331 | −0.836654 | − | 0.547731i | \(-0.815492\pi\) | ||||
−0.836654 | + | 0.547731i | \(0.815492\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.16817 | 0.320629 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 68.6387 | 2.69016 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.0860 | −1.45129 | −0.725645 | − | 0.688070i | \(-0.758458\pi\) | ||||
−0.725645 | + | 0.688070i | \(0.758458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.2585 | 2.51079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.00862 | −0.273432 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0772 | 1.28850 | 0.644252 | − | 0.764814i | \(-0.277169\pi\) | ||||
0.644252 | + | 0.764814i | \(0.277169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.6789 | 1.46554 | 0.732770 | − | 0.680477i | \(-0.238227\pi\) | ||||
0.732770 | + | 0.680477i | \(0.238227\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.07093 | 0.0415916 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.4847 | −0.522914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.09894 | −0.274872 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8484 | −0.496748 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.66797 | 0.0643914 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.0065 | −1.42650 | −0.713248 | − | 0.700912i | \(-0.752777\pi\) | ||||
−0.713248 | + | 0.700912i | \(0.752777\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.0518 | −1.00273 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.1551 | −0.889923 | −0.444961 | − | 0.895550i | \(-0.646783\pi\) | ||||
−0.444961 | + | 0.895550i | \(0.646783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8672 | −0.685682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.3114 | 1.39145 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.10245 | 0.271768 | 0.135884 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135884 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.1445 | 2.06875 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.9867 | 0.876999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.02785 | 0.0772549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.3153 | −0.582622 | −0.291311 | − | 0.956628i | \(-0.594091\pi\) | ||||
−0.291311 | + | 0.956628i | \(0.594091\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.70098 | −0.254549 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −55.4364 | −2.10282 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.30584 | 0.125218 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.2513 | 1.40897 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0180 | 1.20930 | 0.604651 | − | 0.796490i | \(-0.293312\pi\) | ||||
0.604651 | + | 0.796490i | \(0.293312\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.20992 | −0.158780 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −45.9691 | −1.73130 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.6124 | −0.963254 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.61140 | −0.360964 | −0.180482 | − | 0.983578i | \(-0.557766\pi\) | ||||
−0.180482 | + | 0.983578i | \(0.557766\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.4445 | 1.36677 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.4830 | −0.954345 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.04468 | −0.113865 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63.4562 | 2.36981 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.3795 | 0.685440 | 0.342720 | − | 0.939438i | \(-0.388652\pi\) | ||||
0.342720 | + | 0.939438i | \(0.388652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.1773 | −1.75698 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.4359 | 1.57821 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.5480 | −1.24594 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6194 | 0.430941 | 0.215471 | − | 0.976510i | \(-0.430871\pi\) | ||||
0.215471 | + | 0.976510i | \(0.430871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.89168 | −0.329322 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.04785 | 0.260674 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.4420 | −0.865850 | −0.432925 | − | 0.901430i | \(-0.642519\pi\) | ||||
−0.432925 | + | 0.901430i | \(0.642519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.1124 | −1.14760 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57845 | 0.0581430 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0970 | −0.518567 | −0.259284 | − | 0.965801i | \(-0.583486\pi\) | ||||
−0.259284 | + | 0.965801i | \(0.583486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.63317 | −0.0599962 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.6727 | 1.45545 | 0.727725 | − | 0.685869i | \(-0.240578\pi\) | ||||
0.727725 | + | 0.685869i | \(0.240578\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −69.5770 | −2.54910 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.64300 | −0.316231 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.56647 | −0.130316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.16229 | 0.188375 | 0.0941874 | − | 0.995554i | \(-0.469975\pi\) | ||||
0.0941874 | + | 0.995554i | \(0.469975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −43.5374 | −1.58659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.6546 | 2.46220 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3285 | 1.02962 | 0.514809 | − | 0.857305i | \(-0.327863\pi\) | ||||
0.514809 | + | 0.857305i | \(0.327863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.05867 | 0.219916 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.0318 | −1.12490 | −0.562451 | − | 0.826831i | \(-0.690141\pi\) | ||||
−0.562451 | + | 0.826831i | \(0.690141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.7501 | 0.932215 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.76465 | −0.208421 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.91281 | 0.213499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6414 | 1.46557 | 0.732783 | − | 0.680462i | \(-0.238221\pi\) | ||||
0.732783 | + | 0.680462i | \(0.238221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.5175 | −1.78333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.817958 | −0.0294199 | −0.0147099 | − | 0.999892i | \(-0.504682\pi\) | ||||
−0.0147099 | + | 0.999892i | \(0.504682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −120.427 | −4.32586 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.4513 | −1.09243 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.04141 | −0.180627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.3445 | 0.370155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.42663 | 0.193932 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −73.0521 | −2.60734 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2343 | 0.400459 | 0.200229 | − | 0.979749i | \(-0.435831\pi\) | ||||
0.200229 | + | 0.979749i | \(0.435831\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0052 | 0.747806 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.6063 | −1.15935 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.20742 | 0.0428767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.5830 | −0.942801 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.03810 | 0.143037 | 0.0715184 | − | 0.997439i | \(-0.477216\pi\) | ||||
0.0715184 | + | 0.997439i | \(0.477216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.17658 | 0.112379 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.0739 | −1.16861 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.35322 | −0.118333 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.2122 | 1.27631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.9275 | −1.44072 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.1270 | 1.65690 | 0.828448 | − | 0.560066i | \(-0.189224\pi\) | ||||
0.828448 | + | 0.560066i | \(0.189224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.6251 | 1.32119 | 0.660597 | − | 0.750740i | \(-0.270303\pi\) | ||||
0.660597 | + | 0.750740i | \(0.270303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −58.2921 | −2.04439 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −77.2752 | −2.70683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7480 | −0.376024 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.85073 | −0.169498 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.5948 | −1.90537 | −0.952685 | − | 0.303959i | \(-0.901691\pi\) | ||||
−0.952685 | + | 0.303959i | \(0.901691\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.10600 | 0.177984 | 0.0889920 | − | 0.996032i | \(-0.471635\pi\) | ||||
0.0889920 | + | 0.996032i | \(0.471635\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.6319 | 0.996835 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.9650 | 0.763798 | 0.381899 | − | 0.924204i | \(-0.375270\pi\) | ||||
0.381899 | + | 0.924204i | \(0.375270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3940 | 1.05563 | 0.527813 | − | 0.849360i | \(-0.323012\pi\) | ||||
0.527813 | + | 0.849360i | \(0.323012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.7151 | −1.16957 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.14994 | 0.0744910 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0482 | −0.382340 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.4799 | 0.673324 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.38580 | 0.185938 | 0.0929692 | − | 0.995669i | \(-0.470364\pi\) | ||||
0.0929692 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0119 | −0.759030 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −55.1991 | −1.90116 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.4745 | 1.80518 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.20604 | −0.110161 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.5868 | −0.672217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3054 | 0.387545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.1015 | 1.23609 | 0.618046 | − | 0.786142i | \(-0.287925\pi\) | ||||
0.618046 | + | 0.786142i | \(0.287925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.79110 | 0.300649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.5886 | −1.24984 | −0.624922 | − | 0.780687i | \(-0.714869\pi\) | ||||
−0.624922 | + | 0.780687i | \(0.714869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7813 | 0.743168 | 0.371584 | − | 0.928399i | \(-0.378815\pi\) | ||||
0.371584 | + | 0.928399i | \(0.378815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.4656 | −1.24275 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.9178 | −1.59710 | −0.798550 | − | 0.601929i | \(-0.794399\pi\) | ||||
−0.798550 | + | 0.601929i | \(0.794399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.2236 | 0.891629 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.3841 | −1.26963 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4366 | 0.591496 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.14262 | 0.0387161 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6482 | 0.394233 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 103.707 | 3.50594 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.9565 | −1.41677 | −0.708385 | − | 0.705827i | \(-0.750576\pi\) | ||||
−0.708385 | + | 0.705827i | \(0.750576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.1782 | −1.38891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.6747 | −0.763931 | −0.381965 | − | 0.924177i | \(-0.624753\pi\) | ||||
−0.381965 | + | 0.924177i | \(0.624753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.7680 | −1.77578 | −0.887892 | − | 0.460052i | \(-0.847831\pi\) | ||||
−0.887892 | + | 0.460052i | \(0.847831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −77.5107 | −2.60549 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.4618 | 1.56004 | 0.780018 | − | 0.625758i | \(-0.215210\pi\) | ||||
0.780018 | + | 0.625758i | \(0.215210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.4701 | −1.25671 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9018 | −0.365223 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.84428 | −0.162108 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0589 | 0.603643 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.38577 | 0.146437 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.0852 | 0.836637 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.83695 | 0.0611976 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −77.7426 | −2.58711 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.0220 | −0.632312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.1762 | 1.33403 | 0.667014 | − | 0.745045i | \(-0.267572\pi\) | ||||
0.667014 | + | 0.745045i | \(0.267572\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.6975 | 0.553823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.8397 | 1.15429 | 0.577145 | − | 0.816642i | \(-0.304167\pi\) | ||||
0.577145 | + | 0.816642i | \(0.304167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.13518 | −0.136855 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.8280 | −0.523257 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.9808 | 1.61749 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.3172 | −1.26397 | −0.631983 | − | 0.774982i | \(-0.717759\pi\) | ||||
−0.631983 | + | 0.774982i | \(0.717759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7915 | −0.388544 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.48821 | 0.246477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.4270 | 1.75667 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.7564 | 1.01017 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.20133 | 0.105032 | 0.0525161 | − | 0.998620i | \(-0.483276\pi\) | ||||
0.0525161 | + | 0.998620i | \(0.483276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.27866 | −0.107454 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.4973 | 0.409143 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.75805 | −0.0901980 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.8123 | −1.26794 | −0.633972 | − | 0.773356i | \(-0.718576\pi\) | ||||
−0.633972 | + | 0.773356i | \(0.718576\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.8585 | −0.941761 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2516 | 1.50776 | 0.753879 | − | 0.657013i | \(-0.228180\pi\) | ||||
0.753879 | + | 0.657013i | \(0.228180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5383 | 0.440869 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27.6816 | −0.900483 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.01420 | 0.227931 | 0.113965 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113965 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.42734 | −0.0787949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.9370 | −2.13815 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.8853 | 0.449788 | 0.224894 | − | 0.974383i | \(-0.427796\pi\) | ||||
0.224894 | + | 0.974383i | \(0.427796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 105.307 | 3.40764 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.96409 | −0.192792 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.2714 | 1.33272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.0479 | 1.90477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.32509 | 0.0749250 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.3552 | −0.623065 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.4880 | 1.10906 | 0.554529 | − | 0.832164i | \(-0.312898\pi\) | ||||
0.554529 | + | 0.832164i | \(0.312898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.47943 | −0.0475260 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.98878 | −0.288464 | −0.144232 | − | 0.989544i | \(-0.546071\pi\) | ||||
−0.144232 | + | 0.989544i | \(0.546071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.2562 | −1.35467 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.7262 | 0.663769 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.8473 | −1.59476 | −0.797378 | − | 0.603480i | \(-0.793780\pi\) | ||||
−0.797378 | + | 0.603480i | \(0.793780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.8240 | −0.505736 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.7873 | −0.535977 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.4740 | 1.22713 | 0.613565 | − | 0.789644i | \(-0.289735\pi\) | ||||
0.613565 | + | 0.789644i | \(0.289735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2074 | −0.739451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.0398 | −1.11533 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.8629 | 0.917788 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0741 | −0.828271 | −0.414135 | − | 0.910215i | \(-0.635916\pi\) | ||||
−0.414135 | + | 0.910215i | \(0.635916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.8137 | 1.13651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.4098 | −1.31278 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.2926 | 1.62445 | 0.812227 | − | 0.583341i | \(-0.198255\pi\) | ||||
0.812227 | + | 0.583341i | \(0.198255\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.64220 | −0.273427 |
(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 | 3344.2.a.z.1.5 | 6 | ||
4.3 | odd | 2 | 1672.2.a.i.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.2 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.z.1.5 | 6 | 1.1 | even | 1 | trivial |