Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(1,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, 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("560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56155 | 0.470826 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.438447 | 0.121603 | 0.0608017 | − | 0.998150i | \(-0.480634\pi\) | ||||
0.0608017 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.438447 | −0.106339 | −0.0531695 | − | 0.998586i | \(-0.516932\pi\) | ||||
−0.0531695 | + | 0.998586i | \(0.516932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.12311 | 1.63415 | 0.817076 | − | 0.576530i | \(-0.195593\pi\) | ||||
0.817076 | + | 0.576530i | \(0.195593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | −0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.12311 | −0.651213 | −0.325606 | − | 0.945505i | \(-0.605568\pi\) | ||||
−0.325606 | + | 0.945505i | \(0.605568\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.68466 | 1.24131 | 0.620655 | − | 0.784084i | \(-0.286867\pi\) | ||||
0.620655 | + | 0.784084i | \(0.286867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.43845 | −0.424479 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.684658 | −0.109633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.12311 | 0.800095 | 0.400047 | − | 0.916494i | \(-0.368994\pi\) | ||||
0.400047 | + | 0.916494i | \(0.368994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.876894 | −0.133725 | −0.0668626 | − | 0.997762i | \(-0.521299\pi\) | ||||
−0.0668626 | + | 0.997762i | \(0.521299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.68466 | 1.26679 | 0.633394 | − | 0.773830i | \(-0.281661\pi\) | ||||
0.633394 | + | 0.773830i | \(0.281661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.684658 | 0.0958714 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.12311 | −0.703713 | −0.351856 | − | 0.936054i | \(-0.614449\pi\) | ||||
−0.351856 | + | 0.936054i | \(0.614449\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56155 | 0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.1231 | −1.47329 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.3693 | 1.96784 | 0.983920 | − | 0.178611i | \(-0.0571605\pi\) | ||||
0.983920 | + | 0.178611i | \(0.0571605\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.438447 | 0.0543827 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2462 | −1.25177 | −0.625887 | − | 0.779914i | \(-0.715263\pi\) | ||||
−0.625887 | + | 0.779914i | \(0.715263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.87689 | 0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2462 | −1.43331 | −0.716655 | − | 0.697428i | \(-0.754328\pi\) | ||||
−0.716655 | + | 0.697428i | \(0.754328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56155 | 0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.43845 | 0.274347 | 0.137173 | − | 0.990547i | \(-0.456198\pi\) | ||||
0.137173 | + | 0.990547i | \(0.456198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.438447 | −0.0475563 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4384 | −1.11912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.12311 | −0.119049 | −0.0595245 | − | 0.998227i | \(-0.518958\pi\) | ||||
−0.0595245 | + | 0.998227i | \(0.518958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.438447 | 0.0459618 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.12311 | 0.730815 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.80776 | 0.589689 | 0.294845 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294845 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.876894 | −0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2462 | −1.61656 | −0.808279 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808279 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.56155 | −0.547996 | −0.273998 | − | 0.961730i | \(-0.588346\pi\) | ||||
−0.273998 | + | 0.961730i | \(0.588346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.56155 | −0.152392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3693 | −1.29246 | −0.646230 | − | 0.763142i | \(-0.723655\pi\) | ||||
−0.646230 | + | 0.763142i | \(0.723655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.31534 | 0.509117 | 0.254559 | − | 0.967057i | \(-0.418070\pi\) | ||||
0.254559 | + | 0.967057i | \(0.418070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.36932 | −0.889296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12311 | −0.291231 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.246211 | −0.0227622 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.438447 | −0.0401924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | −0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.24621 | 0.554262 | 0.277131 | − | 0.960832i | \(-0.410616\pi\) | ||||
0.277131 | + | 0.960832i | \(0.410616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.36932 | 0.120562 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.876894 | 0.0766146 | 0.0383073 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383073 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.12311 | 0.617652 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.1231 | −1.46293 | −0.731463 | − | 0.681881i | \(-0.761162\pi\) | ||||
−0.731463 | + | 0.681881i | \(0.761162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1231 | 1.28273 | 0.641363 | − | 0.767238i | \(-0.278369\pi\) | ||||
0.641363 | + | 0.767238i | \(0.278369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5616 | −1.14209 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.684658 | 0.0572540 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.68466 | 0.555131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.56155 | −0.128795 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2462 | 1.00325 | 0.501624 | − | 0.865086i | \(-0.332736\pi\) | ||||
0.501624 | + | 0.865086i | \(0.332736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.93087 | 0.564026 | 0.282013 | − | 0.959411i | \(-0.408998\pi\) | ||||
0.282013 | + | 0.959411i | \(0.408998\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.246211 | 0.0199050 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2462 | 1.61582 | 0.807912 | − | 0.589303i | \(-0.200598\pi\) | ||||
0.807912 | + | 0.589303i | \(0.200598\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.12311 | −0.246135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.12311 | 0.557925 | 0.278962 | − | 0.960302i | \(-0.410010\pi\) | ||||
0.278962 | + | 0.960302i | \(0.410010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.43845 | −0.189833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.93087 | 0.536327 | 0.268163 | − | 0.963373i | \(-0.413583\pi\) | ||||
0.268163 | + | 0.963373i | \(0.413583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8078 | −0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.43845 | −0.337449 | −0.168724 | − | 0.985663i | \(-0.553965\pi\) | ||||
−0.168724 | + | 0.985663i | \(0.553965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.24621 | −0.469494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6155 | −1.30935 | −0.654676 | − | 0.755910i | \(-0.727195\pi\) | ||||
−0.654676 | + | 0.755910i | \(0.727195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0000 | −1.77413 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.684658 | −0.0500672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.56155 | 0.404543 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5616 | 0.981280 | 0.490640 | − | 0.871363i | \(-0.336763\pi\) | ||||
0.490640 | + | 0.871363i | \(0.336763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3693 | 1.39423 | 0.697117 | − | 0.716957i | \(-0.254466\pi\) | ||||
0.697117 | + | 0.716957i | \(0.254466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.684658 | −0.0490294 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.12311 | 0.0800180 | 0.0400090 | − | 0.999199i | \(-0.487261\pi\) | ||||
0.0400090 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.75379 | 0.124323 | 0.0621614 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621614 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.68466 | 0.469171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.12311 | 0.357813 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.75379 | 0.121897 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1231 | 0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0540 | −0.967516 | −0.483758 | − | 0.875202i | \(-0.660728\pi\) | ||||
−0.483758 | + | 0.875202i | \(0.660728\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4924 | 0.855967 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.876894 | −0.0598037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.1231 | 1.29222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.192236 | −0.0129312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.43845 | 0.163291 | 0.0816453 | − | 0.996661i | \(-0.473983\pi\) | ||||
0.0816453 | + | 0.996661i | \(0.473983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3153 | −0.751026 | −0.375513 | − | 0.926817i | \(-0.622533\pi\) | ||||
−0.375513 | + | 0.926817i | \(0.622533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8769 | 0.718765 | 0.359383 | − | 0.933190i | \(-0.382987\pi\) | ||||
0.359383 | + | 0.933190i | \(0.382987\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.12311 | 0.335626 | 0.167813 | − | 0.985819i | \(-0.446330\pi\) | ||||
0.167813 | + | 0.985819i | \(0.446330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.68466 | 0.566525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.80776 | −0.247341 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8078 | −1.28126 | −0.640629 | − | 0.767851i | \(-0.721326\pi\) | ||||
−0.640629 | + | 0.767851i | \(0.721326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.24621 | −0.273523 | −0.136761 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136761 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12311 | 0.198718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.24621 | 0.395838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.87689 | 0.560305 | 0.280152 | − | 0.959956i | \(-0.409615\pi\) | ||||
0.280152 | + | 0.959956i | \(0.409615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.87689 | −0.306608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.684658 | 0.0428750 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4924 | −0.654499 | −0.327250 | − | 0.944938i | \(-0.606122\pi\) | ||||
−0.327250 | + | 0.944938i | \(0.606122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.75379 | −0.232354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8769 | 0.794023 | 0.397012 | − | 0.917814i | \(-0.370047\pi\) | ||||
0.397012 | + | 0.917814i | \(0.370047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.12311 | −0.314710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.75379 | 0.107330 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7386 | −1.26446 | −0.632228 | − | 0.774782i | \(-0.717860\pi\) | ||||
−0.632228 | + | 0.774782i | \(0.717860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.684658 | −0.0414374 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.56155 | 0.0941652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.246211 | −0.0147934 | −0.00739670 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739670 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4384 | 0.742016 | 0.371008 | − | 0.928630i | \(-0.379012\pi\) | ||||
0.371008 | + | 0.928630i | \(0.379012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3153 | 0.672627 | 0.336314 | − | 0.941750i | \(-0.390820\pi\) | ||||
0.336314 | + | 0.941750i | \(0.390820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1231 | −0.658876 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.12311 | 0.302407 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8078 | −0.988692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.06913 | −0.531642 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.68466 | −0.156839 | −0.0784197 | − | 0.996920i | \(-0.524987\pi\) | ||||
−0.0784197 | + | 0.996920i | \(0.524987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.68466 | 0.503935 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.36932 | −0.0791896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.876894 | −0.0505434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.3693 | 1.45743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3693 | 0.880045 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.3153 | 1.10238 | 0.551192 | − | 0.834378i | \(-0.314173\pi\) | ||||
0.551192 | + | 0.834378i | \(0.314173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.68466 | 0.494053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.6155 | −1.79275 | −0.896376 | − | 0.443294i | \(-0.853810\pi\) | ||||
−0.896376 | + | 0.443294i | \(0.853810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.3002 | −1.26048 | −0.630241 | − | 0.776400i | \(-0.717044\pi\) | ||||
−0.630241 | + | 0.776400i | \(0.717044\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.561553 | −0.0316399 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4924 | 0.589313 | 0.294657 | − | 0.955603i | \(-0.404795\pi\) | ||||
0.294657 | + | 0.955603i | \(0.404795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4384 | 0.584441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.8769 | 1.16523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.12311 | −0.173774 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.438447 | 0.0243207 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.30019 | −0.459001 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.68466 | 0.478801 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.36932 | −0.184637 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50758 | −0.0821230 | −0.0410615 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410615 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8617 | 1.18737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.87689 | 0.262563 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.12311 | −0.382388 | −0.191194 | − | 0.981552i | \(-0.561236\pi\) | ||||
−0.191194 | + | 0.981552i | \(0.561236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4924 | 0.561646 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.43845 | 0.130155 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.80776 | 0.309116 | 0.154558 | − | 0.987984i | \(-0.450605\pi\) | ||||
0.154558 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.684658 | 0.0362360 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3693 | 0.701707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.2462 | −0.640996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.68466 | 0.453335 | 0.226668 | − | 0.973972i | \(-0.427217\pi\) | ||||
0.226668 | + | 0.973972i | \(0.427217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.87689 | −0.149765 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.12311 | −0.265978 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.63068 | 0.239768 | 0.119884 | − | 0.992788i | \(-0.461748\pi\) | ||||
0.119884 | + | 0.992788i | \(0.461748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.93087 | 0.150947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4924 | 0.847159 | 0.423579 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.75379 | −0.499702 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.24621 | −0.319166 | −0.159583 | − | 0.987184i | \(-0.551015\pi\) | ||||
−0.159583 | + | 0.987184i | \(0.551015\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56155 | 0.0795841 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.492423 | 0.0250312 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.9309 | −1.26405 | −0.632023 | − | 0.774950i | \(-0.717775\pi\) | ||||
−0.632023 | + | 0.774950i | \(0.717775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.36932 | 0.0692493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36932 | −0.0690729 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.43845 | 0.122692 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.5616 | 1.38327 | 0.691637 | − | 0.722245i | \(-0.256890\pi\) | ||||
0.691637 | + | 0.722245i | \(0.256890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1231 | −0.556852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5616 | 1.57611 | 0.788054 | − | 0.615606i | \(-0.211089\pi\) | ||||
0.788054 | + | 0.615606i | \(0.211089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.36932 | 0.464420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.49242 | 0.321030 | 0.160515 | − | 0.987033i | \(-0.448685\pi\) | ||||
0.160515 | + | 0.987033i | \(0.448685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.7386 | 1.31892 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.6155 | −1.15646 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.2462 | −1.28221 | −0.641106 | − | 0.767453i | \(-0.721524\pi\) | ||||
−0.641106 | + | 0.767453i | \(0.721524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68466 | −0.130842 | −0.0654211 | − | 0.997858i | \(-0.520839\pi\) | ||||
−0.0654211 | + | 0.997858i | \(0.520839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.87689 | −0.237123 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.438447 | −0.0212678 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.3693 | 0.743773 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.06913 | −0.0516181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8078 | 0.954106 | 0.477053 | − | 0.878874i | \(-0.341705\pi\) | ||||
0.477053 | + | 0.878874i | \(0.341705\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.24621 | 0.396288 | 0.198144 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198144 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4384 | −0.500485 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.2462 | −1.06418 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.36932 | −0.447173 | −0.223587 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223587 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.561553 | −0.0267406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.63068 | 0.124988 | 0.0624938 | − | 0.998045i | \(-0.480095\pi\) | ||||
0.0624938 | + | 0.998045i | \(0.480095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.12311 | −0.0532403 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.1231 | −0.904492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.80776 | −0.0853137 | −0.0426568 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426568 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8229 | −0.508505 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.438447 | 0.0205547 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.1231 | −0.800985 | −0.400493 | − | 0.916300i | \(-0.631161\pi\) | ||||
−0.400493 | + | 0.916300i | \(0.631161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.43845 | −0.113817 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.1231 | −0.611204 | −0.305602 | − | 0.952159i | \(-0.598858\pi\) | ||||
−0.305602 | + | 0.952159i | \(0.598858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4924 | −0.580572 | −0.290286 | − | 0.956940i | \(-0.593750\pi\) | ||||
−0.290286 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4384 | −1.03833 | −0.519164 | − | 0.854675i | \(-0.673757\pi\) | ||||
−0.519164 | + | 0.854675i | \(0.673757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2462 | −0.473126 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.6155 | −1.45677 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.36932 | −0.0629613 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.12311 | 0.326831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.87689 | 0.131724 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.87689 | −0.222831 | −0.111415 | − | 0.993774i | \(-0.535538\pi\) | ||||
−0.111415 | + | 0.993774i | \(0.535538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.63068 | 0.119949 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.87689 | 0.221906 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.80776 | 0.263717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.12311 | 0.141521 | 0.0707607 | − | 0.997493i | \(-0.477457\pi\) | ||||
0.0707607 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.1231 | −0.503004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.1771 | 1.85830 | 0.929148 | − | 0.369708i | \(-0.120542\pi\) | ||||
0.929148 | + | 0.369708i | \(0.120542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93087 | −0.132000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.876894 | −0.0394135 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1771 | −1.84334 | −0.921670 | − | 0.387976i | \(-0.873174\pi\) | ||||
−0.921670 | + | 0.387976i | \(0.873174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8229 | −0.483532 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.9309 | −1.73584 | −0.867921 | − | 0.496703i | \(-0.834544\pi\) | ||||
−0.867921 | + | 0.496703i | \(0.834544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2462 | −0.722947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0000 | 0.888231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.7538 | −0.520978 | −0.260489 | − | 0.965477i | \(-0.583884\pi\) | ||||
−0.260489 | + | 0.965477i | \(0.583884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2462 | −0.541740 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.6155 | 1.74907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.56155 | −0.245071 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5616 | 0.596436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.93087 | 0.304231 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.4924 | −1.77061 | −0.885305 | − | 0.465011i | \(-0.846050\pi\) | ||||
−0.885305 | + | 0.465011i | \(0.846050\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.56155 | −0.0681518 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2462 | −0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24621 | −0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.24621 | 0.0972942 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.3693 | −0.578006 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.2311 | 1.34772 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.56155 | 0.0672608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.8078 | −1.62548 | −0.812741 | − | 0.582625i | \(-0.802026\pi\) | ||||
−0.812741 | + | 0.582625i | \(0.802026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.5076 | 1.18046 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.31534 | 0.227684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24621 | 0.0960411 | 0.0480205 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480205 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.63068 | −0.368349 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.6155 | 2.02849 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.43845 | 0.103693 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.36932 | −0.397705 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1231 | −0.556044 | −0.278022 | − | 0.960575i | \(-0.589679\pi\) | ||||
−0.278022 | + | 0.960575i | \(0.589679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.384472 | −0.0162614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06913 | 0.0451387 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.0000 | 1.18006 | 0.590030 | − | 0.807382i | \(-0.299116\pi\) | ||||
0.590030 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | −0.588984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | −0.293972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.9848 | −1.29895 | −0.649476 | − | 0.760382i | \(-0.725012\pi\) | ||||
−0.649476 | + | 0.760382i | \(0.725012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4924 | −1.69456 | −0.847278 | − | 0.531150i | \(-0.821760\pi\) | ||||
−0.847278 | + | 0.531150i | \(0.821760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.1771 | −0.884685 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.12311 | −0.130243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.0540 | −1.00138 | −0.500690 | − | 0.865627i | \(-0.666920\pi\) | ||||
−0.500690 | + | 0.865627i | \(0.666920\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.2462 | −1.25699 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.246211 | −0.0101796 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.2462 | 1.08330 | 0.541649 | − | 0.840605i | \(-0.317800\pi\) | ||||
0.541649 | + | 0.840605i | \(0.317800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.75379 | −0.0721412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.5616 | −1.13182 | −0.565909 | − | 0.824468i | \(-0.691475\pi\) | ||||
−0.565909 | + | 0.824468i | \(0.691475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.438447 | −0.0179746 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.73863 | −0.112085 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8078 | 0.482452 | 0.241226 | − | 0.970469i | \(-0.422450\pi\) | ||||
0.241226 | + | 0.970469i | \(0.422450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.49242 | 0.264831 | 0.132416 | − | 0.991194i | \(-0.457727\pi\) | ||||
0.132416 | + | 0.991194i | \(0.457727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.75379 | 0.234312 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.56155 | −0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.0540 | 1.70692 | 0.853459 | − | 0.521160i | \(-0.174500\pi\) | ||||
0.853459 | + | 0.521160i | \(0.174500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.4384 | −0.422987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.80776 | 0.154046 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.7386 | 1.64542 | 0.822709 | − | 0.568463i | \(-0.192462\pi\) | ||||
0.822709 | + | 0.568463i | \(0.192462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2462 | 1.29818 | 0.649092 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649092 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.1080 | −1.29053 | −0.645264 | − | 0.763960i | \(-0.723253\pi\) | ||||
−0.645264 | + | 0.763960i | \(0.723253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.3693 | −0.697007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.12311 | −0.0449963 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.3693 | −0.693664 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.63068 | −0.104892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8078 | 0.470060 | 0.235030 | − | 0.971988i | \(-0.424481\pi\) | ||||
0.235030 | + | 0.971988i | \(0.424481\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.9460 | 0.872276 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.24621 | 0.247873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.438447 | 0.0173719 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.49242 | 0.177717 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.56155 | −0.0615816 | −0.0307908 | − | 0.999526i | \(-0.509803\pi\) | ||||
−0.0307908 | + | 0.999526i | \(0.509803\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.36932 | 0.0539168 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.4924 | −1.43467 | −0.717333 | − | 0.696731i | \(-0.754637\pi\) | ||||
−0.717333 | + | 0.696731i | \(0.754637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.24621 | 0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.2311 | −1.30043 | −0.650216 | − | 0.759750i | \(-0.725322\pi\) | ||||
−0.650216 | + | 0.759750i | \(0.725322\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.876894 | 0.0342631 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.87689 | 0.268293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.17708 | −0.357488 | −0.178744 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178744 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.12311 | −0.199266 | −0.0996329 | − | 0.995024i | \(-0.531767\pi\) | ||||
−0.0996329 | + | 0.995024i | \(0.531767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.300187 | 0.0116583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.12311 | 0.276222 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.8769 | −0.808357 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.80776 | −0.147217 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8617 | 1.22818 | 0.614090 | − | 0.789236i | \(-0.289523\pi\) | ||||
0.614090 | + | 0.789236i | \(0.289523\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.93087 | 0.189509 | 0.0947544 | − | 0.995501i | \(-0.469793\pi\) | ||||
0.0947544 | + | 0.995501i | \(0.469793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.80776 | 0.222882 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6695 | 0.677097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.73863 | 0.257847 | 0.128923 | − | 0.991655i | \(-0.458848\pi\) | ||||
0.128923 | + | 0.991655i | \(0.458848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.1231 | −0.654240 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.9848 | −0.648012 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.24621 | −0.0855738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.4924 | 0.931736 | 0.465868 | − | 0.884854i | \(-0.345742\pi\) | ||||
0.465868 | + | 0.884854i | \(0.345742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.876894 | −0.0333105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.1231 | 0.573652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.24621 | −0.0850813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.9309 | 1.09270 | 0.546352 | − | 0.837556i | \(-0.316016\pi\) | ||||
0.546352 | + | 0.837556i | \(0.316016\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.7386 | 1.61192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.5616 | −0.510758 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.2462 | −0.611002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.1771 | 1.02066 | 0.510328 | − | 0.859980i | \(-0.329524\pi\) | ||||
0.510328 | + | 0.859980i | \(0.329524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.36932 | −0.0513534 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.684658 | 0.0256048 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.9309 | 1.15513 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.38447 | −0.312688 | −0.156344 | − | 0.987703i | \(-0.549971\pi\) | ||||
−0.156344 | + | 0.987703i | \(0.549971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.56155 | −0.207123 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.63068 | 0.246598 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.68466 | 0.248262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.4924 | −1.94684 | −0.973418 | − | 0.229035i | \(-0.926443\pi\) | ||||
−0.973418 | + | 0.229035i | \(0.926443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.384472 | 0.0142202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.68466 | 0.246903 | 0.123452 | − | 0.992351i | \(-0.460604\pi\) | ||||
0.123452 | + | 0.992351i | \(0.460604\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.56155 | −0.0575987 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.9309 | −1.28495 | −0.642476 | − | 0.766305i | \(-0.722093\pi\) | ||||
−0.642476 | + | 0.766305i | \(0.722093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.87689 | −0.179157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.9848 | 1.21010 | 0.605048 | − | 0.796189i | \(-0.293154\pi\) | ||||
0.605048 | + | 0.796189i | \(0.293154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2462 | 0.448666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.24621 | 0.0821846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.3693 | −0.488504 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0691 | −0.622861 | −0.311431 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311431 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.8617 | −0.505150 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.93087 | 0.252240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3693 | 1.43090 | 0.715451 | − | 0.698663i | \(-0.246221\pi\) | ||||
0.715451 | + | 0.698663i | \(0.246221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.61553 | 0.276426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.2462 | 1.74892 | 0.874462 | − | 0.485094i | \(-0.161215\pi\) | ||||
0.874462 | + | 0.485094i | \(0.161215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31534 | 0.192428 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.246211 | 0.00890179 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.75379 | 0.0633256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4924 | −1.53232 | −0.766158 | − | 0.642652i | \(-0.777834\pi\) | ||||
−0.766158 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3845 | 0.590072 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.9309 | 1.32831 | 0.664156 | − | 0.747594i | \(-0.268791\pi\) | ||||
0.664156 | + | 0.747594i | \(0.268791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.36932 | −0.336122 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.4924 | 1.30748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4924 | −0.447014 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.1771 | 1.32860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.2462 | 0.722618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.1771 | 1.75297 | 0.876487 | − | 0.481426i | \(-0.159881\pi\) | ||||
0.876487 | + | 0.481426i | \(0.159881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.1080 | −0.715862 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.73863 | 0.239296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.00000 | 0.283731 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0540 | 0.852036 | 0.426018 | − | 0.904715i | \(-0.359916\pi\) | ||||
0.426018 | + | 0.904715i | \(0.359916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.80776 | −0.134709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.630683 | 0.0222841 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.1231 | −0.674840 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.12311 | −0.110075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.3845 | 1.13999 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5464 | 0.581740 | 0.290870 | − | 0.956763i | \(-0.406055\pi\) | ||||
0.290870 | + | 0.956763i | \(0.406055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.6155 | −0.688794 | −0.344397 | − | 0.938824i | \(-0.611917\pi\) | ||||
−0.344397 | + | 0.938824i | \(0.611917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.9848 | −0.876257 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.12311 | 0.249512 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.24621 | −0.218527 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.246211 | −0.00860332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4233 | −0.747678 | −0.373839 | − | 0.927494i | \(-0.621959\pi\) | ||||
−0.373839 | + | 0.927494i | \(0.621959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.4924 | 1.27205 | 0.636023 | − | 0.771670i | \(-0.280578\pi\) | ||||
0.636023 | + | 0.771670i | \(0.280578\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.43845 | −0.0848958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.36932 | 0.186709 | 0.0933547 | − | 0.995633i | \(-0.470241\pi\) | ||||
0.0933547 | + | 0.995633i | \(0.470241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.8769 | 1.21132 | 0.605662 | − | 0.795722i | \(-0.292908\pi\) | ||||
0.605662 | + | 0.795722i | \(0.292908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.384472 | 0.0133372 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.438447 | −0.0151913 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.93087 | 0.239853 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.8769 | 0.996941 | 0.498471 | − | 0.866907i | \(-0.333895\pi\) | ||||
0.498471 | + | 0.866907i | \(0.333895\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.4233 | −0.668974 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.8078 | −0.440600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.56155 | −0.294178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6695 | −0.606416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7386 | −0.642352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.26137 | −0.248624 | −0.124312 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124312 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7538 | −0.538139 | −0.269070 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269070 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4924 | 0.562714 | 0.281357 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281357 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.7538 | 0.876669 | 0.438335 | − | 0.898812i | \(-0.355569\pi\) | ||||
0.438335 | + | 0.898812i | \(0.355569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.43845 | −0.150912 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.2462 | 0.891368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.80776 | 0.129170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.49242 | −0.152220 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.26137 | −0.110381 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.2462 | −1.35902 | −0.679509 | − | 0.733667i | \(-0.737807\pi\) | ||||
−0.679509 | + | 0.733667i | \(0.737807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.19224 | 0.141401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.8617 | −0.399632 | −0.199816 | − | 0.979833i | \(-0.564034\pi\) | ||||
−0.199816 | + | 0.979833i | \(0.564034\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.49242 | 0.285793 | 0.142896 | − | 0.989738i | \(-0.454358\pi\) | ||||
0.142896 | + | 0.989738i | \(0.454358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.24621 | −0.209964 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.4924 | −0.688068 | −0.344034 | − | 0.938957i | \(-0.611794\pi\) | ||||
−0.344034 | + | 0.938957i | \(0.611794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.24621 | 0.209491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9309 | −0.366198 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.8617 | 2.07012 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.13826 | 0.0713944 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.24621 | 0.0748321 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.36932 | 0.0455680 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.6155 | −0.585560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.1080 | 0.800491 | 0.400246 | − | 0.916408i | \(-0.368925\pi\) | ||||
0.400246 | + | 0.916408i | \(0.368925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.12311 | 0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4924 | 0.943996 | 0.471998 | − | 0.881600i | \(-0.343533\pi\) | ||||
0.471998 | + | 0.881600i | \(0.343533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.24621 | −0.206719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.0000 | −0.793416 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.876894 | 0.0289576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.3002 | −1.32938 | −0.664690 | − | 0.747119i | \(-0.731436\pi\) | ||||
−0.664690 | + | 0.747119i | \(0.731436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.1619 | −0.993869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.50758 | −0.115453 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.12311 | 0.102576 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.1080 | 0.725338 | 0.362669 | − | 0.931918i | \(-0.381866\pi\) | ||||
0.362669 | + | 0.931918i | \(0.381866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.12311 | 0.233450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 49.3693 | 1.61628 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.684658 | −0.0223907 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.6695 | −1.81864 | −0.909322 | − | 0.416094i | \(-0.863399\pi\) | ||||
−0.909322 | + | 0.416094i | \(0.863399\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.8229 | 1.13640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.8617 | 1.42985 | 0.714926 | − | 0.699200i | \(-0.246460\pi\) | ||||
0.714926 | + | 0.699200i | \(0.246460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.56155 | 0.180917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.00000 | −0.129983 | −0.0649913 | − | 0.997886i | \(-0.520702\pi\) | ||||
−0.0649913 | + | 0.997886i | \(0.520702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.36932 | −0.174295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3845 | −0.531303 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.1231 | −1.07296 | −0.536481 | − | 0.843912i | \(-0.680247\pi\) | ||||
−0.536481 | + | 0.843912i | \(0.680247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.5616 | 0.438842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.3002 | −0.526910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1231 | −0.552934 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.50758 | 0.241928 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3693 | 0.623520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1231 | 1.12948 | 0.564741 | − | 0.825268i | \(-0.308976\pi\) | ||||
0.564741 | + | 0.825268i | \(0.308976\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.87689 | 0.156668 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4773 | −1.58780 | −0.793901 | − | 0.608048i | \(-0.791953\pi\) | ||||
−0.793901 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.1231 | 0.484825 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.684658 | −0.0219266 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.2311 | 1.06316 | 0.531578 | − | 0.847009i | \(-0.321599\pi\) | ||||
0.531578 | + | 0.847009i | \(0.321599\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.75379 | −0.0560513 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.98485 | −0.0952988 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.4233 | −1.64015 | −0.820074 | − | 0.572257i | \(-0.806068\pi\) | ||||
−0.820074 | + | 0.572257i | \(0.806068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12311 | 0.0357851 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5616 | −0.431669 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.73863 | 0.0870835 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.4924 | −0.396835 | −0.198417 | − | 0.980118i | \(-0.563580\pi\) | ||||
−0.198417 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7386 | 0.594653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.75379 | 0.0555988 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.68466 | −0.0850240 | −0.0425120 | − | 0.999096i | \(-0.513536\pi\) | ||||
−0.0425120 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.3693 | 1.05576 |
(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 | 560.2.a.i.1.1 | 2 | ||
3.2 | odd | 2 | 5040.2.a.bt.1.1 | 2 | |||
4.3 | odd | 2 | 35.2.a.b.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 2800.2.g.t.449.3 | 4 | |||
5.3 | odd | 4 | 2800.2.g.t.449.2 | 4 | |||
5.4 | even | 2 | 2800.2.a.bi.1.2 | 2 | |||
7.6 | odd | 2 | 3920.2.a.bs.1.2 | 2 | |||
8.3 | odd | 2 | 2240.2.a.bh.1.1 | 2 | |||
8.5 | even | 2 | 2240.2.a.bd.1.2 | 2 | |||
12.11 | even | 2 | 315.2.a.e.1.2 | 2 | |||
20.3 | even | 4 | 175.2.b.b.99.4 | 4 | |||
20.7 | even | 4 | 175.2.b.b.99.1 | 4 | |||
20.19 | odd | 2 | 175.2.a.f.1.2 | 2 | |||
28.3 | even | 6 | 245.2.e.h.226.2 | 4 | |||
28.11 | odd | 6 | 245.2.e.i.226.2 | 4 | |||
28.19 | even | 6 | 245.2.e.h.116.2 | 4 | |||
28.23 | odd | 6 | 245.2.e.i.116.2 | 4 | |||
28.27 | even | 2 | 245.2.a.d.1.1 | 2 | |||
44.43 | even | 2 | 4235.2.a.m.1.2 | 2 | |||
52.51 | odd | 2 | 5915.2.a.l.1.2 | 2 | |||
60.23 | odd | 4 | 1575.2.d.e.1324.1 | 4 | |||
60.47 | odd | 4 | 1575.2.d.e.1324.4 | 4 | |||
60.59 | even | 2 | 1575.2.a.p.1.1 | 2 | |||
84.83 | odd | 2 | 2205.2.a.x.1.2 | 2 | |||
140.27 | odd | 4 | 1225.2.b.f.99.1 | 4 | |||
140.83 | odd | 4 | 1225.2.b.f.99.4 | 4 | |||
140.139 | even | 2 | 1225.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
175.2.a.f.1.2 | 2 | 20.19 | odd | 2 | |||
175.2.b.b.99.1 | 4 | 20.7 | even | 4 | |||
175.2.b.b.99.4 | 4 | 20.3 | even | 4 | |||
245.2.a.d.1.1 | 2 | 28.27 | even | 2 | |||
245.2.e.h.116.2 | 4 | 28.19 | even | 6 | |||
245.2.e.h.226.2 | 4 | 28.3 | even | 6 | |||
245.2.e.i.116.2 | 4 | 28.23 | odd | 6 | |||
245.2.e.i.226.2 | 4 | 28.11 | odd | 6 | |||
315.2.a.e.1.2 | 2 | 12.11 | even | 2 | |||
560.2.a.i.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1225.2.a.s.1.2 | 2 | 140.139 | even | 2 | |||
1225.2.b.f.99.1 | 4 | 140.27 | odd | 4 | |||
1225.2.b.f.99.4 | 4 | 140.83 | odd | 4 | |||
1575.2.a.p.1.1 | 2 | 60.59 | even | 2 | |||
1575.2.d.e.1324.1 | 4 | 60.23 | odd | 4 | |||
1575.2.d.e.1324.4 | 4 | 60.47 | odd | 4 | |||
2205.2.a.x.1.2 | 2 | 84.83 | odd | 2 | |||
2240.2.a.bd.1.2 | 2 | 8.5 | even | 2 | |||
2240.2.a.bh.1.1 | 2 | 8.3 | odd | 2 | |||
2800.2.a.bi.1.2 | 2 | 5.4 | even | 2 | |||
2800.2.g.t.449.2 | 4 | 5.3 | odd | 4 | |||
2800.2.g.t.449.3 | 4 | 5.2 | odd | 4 | |||
3920.2.a.bs.1.2 | 2 | 7.6 | odd | 2 | |||
4235.2.a.m.1.2 | 2 | 44.43 | even | 2 | |||
5040.2.a.bt.1.1 | 2 | 3.2 | odd | 2 | |||
5915.2.a.l.1.2 | 2 | 52.51 | odd | 2 |