Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81598 | −1.28409 | −0.642046 | − | 0.766666i | \(-0.721914\pi\) | ||||
−0.642046 | + | 0.766666i | \(0.721914\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.29778 | 0.648892 | ||||||||
\(5\) | −1.85785 | −0.830855 | −0.415427 | − | 0.909626i | \(-0.636368\pi\) | ||||
−0.415427 | + | 0.909626i | \(0.636368\pi\) | |||||||
\(6\) | −1.81598 | −0.741371 | ||||||||
\(7\) | −3.71645 | −1.40469 | −0.702344 | − | 0.711838i | \(-0.747863\pi\) | ||||
−0.702344 | + | 0.711838i | \(0.747863\pi\) | |||||||
\(8\) | 1.27521 | 0.450855 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.37381 | 1.06689 | ||||||||
\(11\) | 2.48466 | 0.749152 | 0.374576 | − | 0.927196i | \(-0.377788\pi\) | ||||
0.374576 | + | 0.927196i | \(0.377788\pi\) | |||||||
\(12\) | 1.29778 | 0.374638 | ||||||||
\(13\) | 3.08636 | 0.856001 | 0.428000 | − | 0.903779i | \(-0.359218\pi\) | ||||
0.428000 | + | 0.903779i | \(0.359218\pi\) | |||||||
\(14\) | 6.74901 | 1.80375 | ||||||||
\(15\) | −1.85785 | −0.479694 | ||||||||
\(16\) | −4.91132 | −1.22783 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.81598 | −0.428031 | ||||||||
\(19\) | 3.85995 | 0.885534 | 0.442767 | − | 0.896637i | \(-0.353997\pi\) | ||||
0.442767 | + | 0.896637i | \(0.353997\pi\) | |||||||
\(20\) | −2.41109 | −0.539135 | ||||||||
\(21\) | −3.71645 | −0.810997 | ||||||||
\(22\) | −4.51209 | −0.961980 | ||||||||
\(23\) | 9.02732 | 1.88233 | 0.941163 | − | 0.337954i | \(-0.109735\pi\) | ||||
0.941163 | + | 0.337954i | \(0.109735\pi\) | |||||||
\(24\) | 1.27521 | 0.260301 | ||||||||
\(25\) | −1.54840 | −0.309681 | ||||||||
\(26\) | −5.60476 | −1.09918 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.82316 | −0.911491 | ||||||||
\(29\) | −6.29127 | −1.16826 | −0.584129 | − | 0.811661i | \(-0.698564\pi\) | ||||
−0.584129 | + | 0.811661i | \(0.698564\pi\) | |||||||
\(30\) | 3.37381 | 0.615971 | ||||||||
\(31\) | 11.0388 | 1.98264 | 0.991318 | − | 0.131487i | \(-0.0419753\pi\) | ||||
0.991318 | + | 0.131487i | \(0.0419753\pi\) | |||||||
\(32\) | 6.36845 | 1.12579 | ||||||||
\(33\) | 2.48466 | 0.432523 | ||||||||
\(34\) | 1.81598 | 0.311438 | ||||||||
\(35\) | 6.90460 | 1.16709 | ||||||||
\(36\) | 1.29778 | 0.216297 | ||||||||
\(37\) | 6.78754 | 1.11586 | 0.557932 | − | 0.829887i | \(-0.311595\pi\) | ||||
0.557932 | + | 0.829887i | \(0.311595\pi\) | |||||||
\(38\) | −7.00960 | −1.13711 | ||||||||
\(39\) | 3.08636 | 0.494212 | ||||||||
\(40\) | −2.36914 | −0.374595 | ||||||||
\(41\) | 1.22529 | 0.191359 | 0.0956794 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956794 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(42\) | 6.74901 | 1.04139 | ||||||||
\(43\) | −1.24300 | −0.189556 | −0.0947780 | − | 0.995498i | \(-0.530214\pi\) | ||||
−0.0947780 | + | 0.995498i | \(0.530214\pi\) | |||||||
\(44\) | 3.22455 | 0.486119 | ||||||||
\(45\) | −1.85785 | −0.276952 | ||||||||
\(46\) | −16.3934 | −2.41708 | ||||||||
\(47\) | −3.57446 | −0.521389 | −0.260694 | − | 0.965421i | \(-0.583951\pi\) | ||||
−0.260694 | + | 0.965421i | \(0.583951\pi\) | |||||||
\(48\) | −4.91132 | −0.708889 | ||||||||
\(49\) | 6.81203 | 0.973147 | ||||||||
\(50\) | 2.81187 | 0.397658 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 4.00542 | 0.555452 | ||||||||
\(53\) | −10.3387 | −1.42012 | −0.710062 | − | 0.704139i | \(-0.751333\pi\) | ||||
−0.710062 | + | 0.704139i | \(0.751333\pi\) | |||||||
\(54\) | −1.81598 | −0.247124 | ||||||||
\(55\) | −4.61611 | −0.622437 | ||||||||
\(56\) | −4.73926 | −0.633310 | ||||||||
\(57\) | 3.85995 | 0.511263 | ||||||||
\(58\) | 11.4248 | 1.50015 | ||||||||
\(59\) | 14.2796 | 1.85904 | 0.929522 | − | 0.368768i | \(-0.120220\pi\) | ||||
0.929522 | + | 0.368768i | \(0.120220\pi\) | |||||||
\(60\) | −2.41109 | −0.311270 | ||||||||
\(61\) | −12.5550 | −1.60751 | −0.803754 | − | 0.594962i | \(-0.797167\pi\) | ||||
−0.803754 | + | 0.594962i | \(0.797167\pi\) | |||||||
\(62\) | −20.0463 | −2.54589 | ||||||||
\(63\) | −3.71645 | −0.468229 | ||||||||
\(64\) | −1.74233 | −0.217791 | ||||||||
\(65\) | −5.73398 | −0.711212 | ||||||||
\(66\) | −4.51209 | −0.555400 | ||||||||
\(67\) | 2.94647 | 0.359968 | 0.179984 | − | 0.983670i | \(-0.442395\pi\) | ||||
0.179984 | + | 0.983670i | \(0.442395\pi\) | |||||||
\(68\) | −1.29778 | −0.157379 | ||||||||
\(69\) | 9.02732 | 1.08676 | ||||||||
\(70\) | −12.5386 | −1.49865 | ||||||||
\(71\) | −7.48333 | −0.888107 | −0.444054 | − | 0.896000i | \(-0.646460\pi\) | ||||
−0.444054 | + | 0.896000i | \(0.646460\pi\) | |||||||
\(72\) | 1.27521 | 0.150285 | ||||||||
\(73\) | 11.4226 | 1.33692 | 0.668458 | − | 0.743750i | \(-0.266955\pi\) | ||||
0.668458 | + | 0.743750i | \(0.266955\pi\) | |||||||
\(74\) | −12.3260 | −1.43287 | ||||||||
\(75\) | −1.54840 | −0.178794 | ||||||||
\(76\) | 5.00939 | 0.574616 | ||||||||
\(77\) | −9.23411 | −1.05232 | ||||||||
\(78\) | −5.60476 | −0.634614 | ||||||||
\(79\) | −10.4893 | −1.18014 | −0.590069 | − | 0.807353i | \(-0.700899\pi\) | ||||
−0.590069 | + | 0.807353i | \(0.700899\pi\) | |||||||
\(80\) | 9.12449 | 1.02015 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.22511 | −0.245722 | ||||||||
\(83\) | 7.82837 | 0.859275 | 0.429638 | − | 0.903001i | \(-0.358641\pi\) | ||||
0.429638 | + | 0.903001i | \(0.358641\pi\) | |||||||
\(84\) | −4.82316 | −0.526249 | ||||||||
\(85\) | 1.85785 | 0.201512 | ||||||||
\(86\) | 2.25727 | 0.243407 | ||||||||
\(87\) | −6.29127 | −0.674494 | ||||||||
\(88\) | 3.16846 | 0.337759 | ||||||||
\(89\) | 6.91836 | 0.733345 | 0.366672 | − | 0.930350i | \(-0.380497\pi\) | ||||
0.366672 | + | 0.930350i | \(0.380497\pi\) | |||||||
\(90\) | 3.37381 | 0.355631 | ||||||||
\(91\) | −11.4703 | −1.20241 | ||||||||
\(92\) | 11.7155 | 1.22143 | ||||||||
\(93\) | 11.0388 | 1.14468 | ||||||||
\(94\) | 6.49115 | 0.669511 | ||||||||
\(95\) | −7.17120 | −0.735750 | ||||||||
\(96\) | 6.36845 | 0.649977 | ||||||||
\(97\) | −13.1097 | −1.33109 | −0.665545 | − | 0.746358i | \(-0.731801\pi\) | ||||
−0.665545 | + | 0.746358i | \(0.731801\pi\) | |||||||
\(98\) | −12.3705 | −1.24961 | ||||||||
\(99\) | 2.48466 | 0.249717 | ||||||||
\(100\) | −2.00949 | −0.200949 | ||||||||
\(101\) | 11.4665 | 1.14095 | 0.570477 | − | 0.821313i | \(-0.306758\pi\) | ||||
0.570477 | + | 0.821313i | \(0.306758\pi\) | |||||||
\(102\) | 1.81598 | 0.179809 | ||||||||
\(103\) | −2.82872 | −0.278722 | −0.139361 | − | 0.990242i | \(-0.544505\pi\) | ||||
−0.139361 | + | 0.990242i | \(0.544505\pi\) | |||||||
\(104\) | 3.93575 | 0.385932 | ||||||||
\(105\) | 6.90460 | 0.673820 | ||||||||
\(106\) | 18.7748 | 1.82357 | ||||||||
\(107\) | −3.78434 | −0.365846 | −0.182923 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182923 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(108\) | 1.29778 | 0.124879 | ||||||||
\(109\) | 6.68734 | 0.640531 | 0.320266 | − | 0.947328i | \(-0.396228\pi\) | ||||
0.320266 | + | 0.947328i | \(0.396228\pi\) | |||||||
\(110\) | 8.38277 | 0.799266 | ||||||||
\(111\) | 6.78754 | 0.644244 | ||||||||
\(112\) | 18.2527 | 1.72472 | ||||||||
\(113\) | 12.1005 | 1.13832 | 0.569160 | − | 0.822227i | \(-0.307269\pi\) | ||||
0.569160 | + | 0.822227i | \(0.307269\pi\) | |||||||
\(114\) | −7.00960 | −0.656509 | ||||||||
\(115\) | −16.7714 | −1.56394 | ||||||||
\(116\) | −8.16471 | −0.758074 | ||||||||
\(117\) | 3.08636 | 0.285334 | ||||||||
\(118\) | −25.9314 | −2.38718 | ||||||||
\(119\) | 3.71645 | 0.340687 | ||||||||
\(120\) | −2.36914 | −0.216272 | ||||||||
\(121\) | −4.82648 | −0.438771 | ||||||||
\(122\) | 22.7997 | 2.06419 | ||||||||
\(123\) | 1.22529 | 0.110481 | ||||||||
\(124\) | 14.3260 | 1.28652 | ||||||||
\(125\) | 12.1659 | 1.08815 | ||||||||
\(126\) | 6.74901 | 0.601249 | ||||||||
\(127\) | −2.22421 | −0.197367 | −0.0986835 | − | 0.995119i | \(-0.531463\pi\) | ||||
−0.0986835 | + | 0.995119i | \(0.531463\pi\) | |||||||
\(128\) | −9.57286 | −0.846129 | ||||||||
\(129\) | −1.24300 | −0.109440 | ||||||||
\(130\) | 10.4128 | 0.913262 | ||||||||
\(131\) | −5.60301 | −0.489537 | −0.244768 | − | 0.969582i | \(-0.578712\pi\) | ||||
−0.244768 | + | 0.969582i | \(0.578712\pi\) | |||||||
\(132\) | 3.22455 | 0.280661 | ||||||||
\(133\) | −14.3453 | −1.24390 | ||||||||
\(134\) | −5.35073 | −0.462232 | ||||||||
\(135\) | −1.85785 | −0.159898 | ||||||||
\(136\) | −1.27521 | −0.109348 | ||||||||
\(137\) | −11.8173 | −1.00962 | −0.504810 | − | 0.863231i | \(-0.668437\pi\) | ||||
−0.504810 | + | 0.863231i | \(0.668437\pi\) | |||||||
\(138\) | −16.3934 | −1.39550 | ||||||||
\(139\) | 7.98464 | 0.677249 | 0.338624 | − | 0.940922i | \(-0.390038\pi\) | ||||
0.338624 | + | 0.940922i | \(0.390038\pi\) | |||||||
\(140\) | 8.96069 | 0.757316 | ||||||||
\(141\) | −3.57446 | −0.301024 | ||||||||
\(142\) | 13.5896 | 1.14041 | ||||||||
\(143\) | 7.66853 | 0.641275 | ||||||||
\(144\) | −4.91132 | −0.409277 | ||||||||
\(145\) | 11.6882 | 0.970653 | ||||||||
\(146\) | −20.7432 | −1.71672 | ||||||||
\(147\) | 6.81203 | 0.561847 | ||||||||
\(148\) | 8.80876 | 0.724075 | ||||||||
\(149\) | −16.3198 | −1.33697 | −0.668484 | − | 0.743726i | \(-0.733056\pi\) | ||||
−0.668484 | + | 0.743726i | \(0.733056\pi\) | |||||||
\(150\) | 2.81187 | 0.229588 | ||||||||
\(151\) | −16.1016 | −1.31033 | −0.655164 | − | 0.755487i | \(-0.727400\pi\) | ||||
−0.655164 | + | 0.755487i | \(0.727400\pi\) | |||||||
\(152\) | 4.92225 | 0.399247 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 16.7690 | 1.35128 | ||||||||
\(155\) | −20.5085 | −1.64728 | ||||||||
\(156\) | 4.00542 | 0.320691 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 19.0484 | 1.51541 | ||||||||
\(159\) | −10.3387 | −0.819909 | ||||||||
\(160\) | −11.8316 | −0.935371 | ||||||||
\(161\) | −33.5496 | −2.64408 | ||||||||
\(162\) | −1.81598 | −0.142677 | ||||||||
\(163\) | −4.58586 | −0.359192 | −0.179596 | − | 0.983740i | \(-0.557479\pi\) | ||||
−0.179596 | + | 0.983740i | \(0.557479\pi\) | |||||||
\(164\) | 1.59017 | 0.124171 | ||||||||
\(165\) | −4.61611 | −0.359364 | ||||||||
\(166\) | −14.2162 | −1.10339 | ||||||||
\(167\) | 7.15609 | 0.553755 | 0.276877 | − | 0.960905i | \(-0.410700\pi\) | ||||
0.276877 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(168\) | −4.73926 | −0.365642 | ||||||||
\(169\) | −3.47441 | −0.267262 | ||||||||
\(170\) | −3.37381 | −0.258760 | ||||||||
\(171\) | 3.85995 | 0.295178 | ||||||||
\(172\) | −1.61315 | −0.123001 | ||||||||
\(173\) | −22.4736 | −1.70863 | −0.854317 | − | 0.519753i | \(-0.826024\pi\) | ||||
−0.854317 | + | 0.519753i | \(0.826024\pi\) | |||||||
\(174\) | 11.4248 | 0.866113 | ||||||||
\(175\) | 5.75457 | 0.435005 | ||||||||
\(176\) | −12.2030 | −0.919832 | ||||||||
\(177\) | 14.2796 | 1.07332 | ||||||||
\(178\) | −12.5636 | −0.941682 | ||||||||
\(179\) | 10.4271 | 0.779360 | 0.389680 | − | 0.920950i | \(-0.372586\pi\) | ||||
0.389680 | + | 0.920950i | \(0.372586\pi\) | |||||||
\(180\) | −2.41109 | −0.179712 | ||||||||
\(181\) | −12.4596 | −0.926114 | −0.463057 | − | 0.886328i | \(-0.653248\pi\) | ||||
−0.463057 | + | 0.886328i | \(0.653248\pi\) | |||||||
\(182\) | 20.8298 | 1.54401 | ||||||||
\(183\) | −12.5550 | −0.928095 | ||||||||
\(184\) | 11.5117 | 0.848655 | ||||||||
\(185\) | −12.6102 | −0.927121 | ||||||||
\(186\) | −20.0463 | −1.46987 | ||||||||
\(187\) | −2.48466 | −0.181696 | ||||||||
\(188\) | −4.63888 | −0.338325 | ||||||||
\(189\) | −3.71645 | −0.270332 | ||||||||
\(190\) | 13.0228 | 0.944771 | ||||||||
\(191\) | 21.2165 | 1.53517 | 0.767586 | − | 0.640946i | \(-0.221458\pi\) | ||||
0.767586 | + | 0.640946i | \(0.221458\pi\) | |||||||
\(192\) | −1.74233 | −0.125742 | ||||||||
\(193\) | −23.0429 | −1.65866 | −0.829332 | − | 0.558756i | \(-0.811279\pi\) | ||||
−0.829332 | + | 0.558756i | \(0.811279\pi\) | |||||||
\(194\) | 23.8070 | 1.70924 | ||||||||
\(195\) | −5.73398 | −0.410619 | ||||||||
\(196\) | 8.84054 | 0.631467 | ||||||||
\(197\) | 23.3293 | 1.66214 | 0.831071 | − | 0.556166i | \(-0.187728\pi\) | ||||
0.831071 | + | 0.556166i | \(0.187728\pi\) | |||||||
\(198\) | −4.51209 | −0.320660 | ||||||||
\(199\) | −0.170206 | −0.0120656 | −0.00603280 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603280 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(200\) | −1.97454 | −0.139621 | ||||||||
\(201\) | 2.94647 | 0.207828 | ||||||||
\(202\) | −20.8228 | −1.46509 | ||||||||
\(203\) | 23.3812 | 1.64104 | ||||||||
\(204\) | −1.29778 | −0.0908631 | ||||||||
\(205\) | −2.27641 | −0.158991 | ||||||||
\(206\) | 5.13690 | 0.357905 | ||||||||
\(207\) | 9.02732 | 0.627442 | ||||||||
\(208\) | −15.1581 | −1.05102 | ||||||||
\(209\) | 9.59066 | 0.663400 | ||||||||
\(210\) | −12.5386 | −0.865247 | ||||||||
\(211\) | 13.8948 | 0.956559 | 0.478280 | − | 0.878208i | \(-0.341261\pi\) | ||||
0.478280 | + | 0.878208i | \(0.341261\pi\) | |||||||
\(212\) | −13.4174 | −0.921508 | ||||||||
\(213\) | −7.48333 | −0.512749 | ||||||||
\(214\) | 6.87228 | 0.469780 | ||||||||
\(215\) | 2.30931 | 0.157493 | ||||||||
\(216\) | 1.27521 | 0.0867670 | ||||||||
\(217\) | −41.0254 | −2.78498 | ||||||||
\(218\) | −12.1441 | −0.822501 | ||||||||
\(219\) | 11.4226 | 0.771869 | ||||||||
\(220\) | −5.99072 | −0.403894 | ||||||||
\(221\) | −3.08636 | −0.207611 | ||||||||
\(222\) | −12.3260 | −0.827269 | ||||||||
\(223\) | 20.1691 | 1.35062 | 0.675310 | − | 0.737534i | \(-0.264010\pi\) | ||||
0.675310 | + | 0.737534i | \(0.264010\pi\) | |||||||
\(224\) | −23.6680 | −1.58139 | ||||||||
\(225\) | −1.54840 | −0.103227 | ||||||||
\(226\) | −21.9743 | −1.46171 | ||||||||
\(227\) | 21.7809 | 1.44565 | 0.722825 | − | 0.691031i | \(-0.242843\pi\) | ||||
0.722825 | + | 0.691031i | \(0.242843\pi\) | |||||||
\(228\) | 5.00939 | 0.331755 | ||||||||
\(229\) | −15.0518 | −0.994650 | −0.497325 | − | 0.867564i | \(-0.665684\pi\) | ||||
−0.497325 | + | 0.867564i | \(0.665684\pi\) | |||||||
\(230\) | 30.4565 | 2.00824 | ||||||||
\(231\) | −9.23411 | −0.607560 | ||||||||
\(232\) | −8.02268 | −0.526715 | ||||||||
\(233\) | 23.6200 | 1.54740 | 0.773699 | − | 0.633553i | \(-0.218404\pi\) | ||||
0.773699 | + | 0.633553i | \(0.218404\pi\) | |||||||
\(234\) | −5.60476 | −0.366395 | ||||||||
\(235\) | 6.64080 | 0.433198 | ||||||||
\(236\) | 18.5318 | 1.20632 | ||||||||
\(237\) | −10.4893 | −0.681353 | ||||||||
\(238\) | −6.74901 | −0.437473 | ||||||||
\(239\) | 15.3534 | 0.993127 | 0.496563 | − | 0.868000i | \(-0.334595\pi\) | ||||
0.496563 | + | 0.868000i | \(0.334595\pi\) | |||||||
\(240\) | 9.12449 | 0.588983 | ||||||||
\(241\) | −0.0257356 | −0.00165777 | −0.000828887 | − | 1.00000i | \(-0.500264\pi\) | ||||
−0.000828887 | 1.00000i | \(0.500264\pi\) | ||||||||
\(242\) | 8.76479 | 0.563422 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −16.2937 | −1.04310 | ||||||||
\(245\) | −12.6557 | −0.808544 | ||||||||
\(246\) | −2.22511 | −0.141868 | ||||||||
\(247\) | 11.9132 | 0.758018 | ||||||||
\(248\) | 14.0768 | 0.893881 | ||||||||
\(249\) | 7.82837 | 0.496103 | ||||||||
\(250\) | −22.0931 | −1.39729 | ||||||||
\(251\) | 0.618199 | 0.0390204 | 0.0195102 | − | 0.999810i | \(-0.493789\pi\) | ||||
0.0195102 | + | 0.999810i | \(0.493789\pi\) | |||||||
\(252\) | −4.82316 | −0.303830 | ||||||||
\(253\) | 22.4298 | 1.41015 | ||||||||
\(254\) | 4.03913 | 0.253437 | ||||||||
\(255\) | 1.85785 | 0.116343 | ||||||||
\(256\) | 20.8688 | 1.30430 | ||||||||
\(257\) | 6.60186 | 0.411813 | 0.205906 | − | 0.978572i | \(-0.433986\pi\) | ||||
0.205906 | + | 0.978572i | \(0.433986\pi\) | |||||||
\(258\) | 2.25727 | 0.140531 | ||||||||
\(259\) | −25.2256 | −1.56744 | ||||||||
\(260\) | −7.44147 | −0.461500 | ||||||||
\(261\) | −6.29127 | −0.389420 | ||||||||
\(262\) | 10.1749 | 0.628610 | ||||||||
\(263\) | 12.7120 | 0.783854 | 0.391927 | − | 0.919996i | \(-0.371809\pi\) | ||||
0.391927 | + | 0.919996i | \(0.371809\pi\) | |||||||
\(264\) | 3.16846 | 0.195005 | ||||||||
\(265\) | 19.2077 | 1.17992 | ||||||||
\(266\) | 26.0509 | 1.59728 | ||||||||
\(267\) | 6.91836 | 0.423397 | ||||||||
\(268\) | 3.82388 | 0.233581 | ||||||||
\(269\) | 3.93410 | 0.239867 | 0.119933 | − | 0.992782i | \(-0.461732\pi\) | ||||
0.119933 | + | 0.992782i | \(0.461732\pi\) | |||||||
\(270\) | 3.37381 | 0.205324 | ||||||||
\(271\) | −4.94157 | −0.300179 | −0.150089 | − | 0.988672i | \(-0.547956\pi\) | ||||
−0.150089 | + | 0.988672i | \(0.547956\pi\) | |||||||
\(272\) | 4.91132 | 0.297793 | ||||||||
\(273\) | −11.4703 | −0.694214 | ||||||||
\(274\) | 21.4600 | 1.29644 | ||||||||
\(275\) | −3.84725 | −0.231998 | ||||||||
\(276\) | 11.7155 | 0.705191 | ||||||||
\(277\) | −28.9275 | −1.73809 | −0.869043 | − | 0.494736i | \(-0.835265\pi\) | ||||
−0.869043 | + | 0.494736i | \(0.835265\pi\) | |||||||
\(278\) | −14.5000 | −0.869650 | ||||||||
\(279\) | 11.0388 | 0.660879 | ||||||||
\(280\) | 8.80482 | 0.526188 | ||||||||
\(281\) | −8.54227 | −0.509589 | −0.254795 | − | 0.966995i | \(-0.582008\pi\) | ||||
−0.254795 | + | 0.966995i | \(0.582008\pi\) | |||||||
\(282\) | 6.49115 | 0.386542 | ||||||||
\(283\) | −15.5300 | −0.923165 | −0.461583 | − | 0.887097i | \(-0.652718\pi\) | ||||
−0.461583 | + | 0.887097i | \(0.652718\pi\) | |||||||
\(284\) | −9.71174 | −0.576286 | ||||||||
\(285\) | −7.17120 | −0.424786 | ||||||||
\(286\) | −13.9259 | −0.823456 | ||||||||
\(287\) | −4.55375 | −0.268799 | ||||||||
\(288\) | 6.36845 | 0.375264 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −21.2256 | −1.24641 | ||||||||
\(291\) | −13.1097 | −0.768505 | ||||||||
\(292\) | 14.8241 | 0.867514 | ||||||||
\(293\) | −9.19833 | −0.537372 | −0.268686 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268686 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(294\) | −12.3705 | −0.721463 | ||||||||
\(295\) | −26.5293 | −1.54459 | ||||||||
\(296\) | 8.65553 | 0.503093 | ||||||||
\(297\) | 2.48466 | 0.144174 | ||||||||
\(298\) | 29.6364 | 1.71679 | ||||||||
\(299\) | 27.8615 | 1.61127 | ||||||||
\(300\) | −2.00949 | −0.116018 | ||||||||
\(301\) | 4.61956 | 0.266267 | ||||||||
\(302\) | 29.2402 | 1.68258 | ||||||||
\(303\) | 11.4665 | 0.658730 | ||||||||
\(304\) | −18.9575 | −1.08729 | ||||||||
\(305\) | 23.3253 | 1.33561 | ||||||||
\(306\) | 1.81598 | 0.103813 | ||||||||
\(307\) | 10.6143 | 0.605791 | 0.302895 | − | 0.953024i | \(-0.402047\pi\) | ||||
0.302895 | + | 0.953024i | \(0.402047\pi\) | |||||||
\(308\) | −11.9839 | −0.682845 | ||||||||
\(309\) | −2.82872 | −0.160920 | ||||||||
\(310\) | 37.2430 | 2.11526 | ||||||||
\(311\) | 29.2727 | 1.65990 | 0.829950 | − | 0.557837i | \(-0.188369\pi\) | ||||
0.829950 | + | 0.557837i | \(0.188369\pi\) | |||||||
\(312\) | 3.93575 | 0.222818 | ||||||||
\(313\) | 24.2953 | 1.37325 | 0.686624 | − | 0.727012i | \(-0.259092\pi\) | ||||
0.686624 | + | 0.727012i | \(0.259092\pi\) | |||||||
\(314\) | 1.81598 | 0.102482 | ||||||||
\(315\) | 6.90460 | 0.389030 | ||||||||
\(316\) | −13.6128 | −0.765782 | ||||||||
\(317\) | −10.0946 | −0.566972 | −0.283486 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283486 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(318\) | 18.7748 | 1.05284 | ||||||||
\(319\) | −15.6316 | −0.875204 | ||||||||
\(320\) | 3.23698 | 0.180953 | ||||||||
\(321\) | −3.78434 | −0.211221 | ||||||||
\(322\) | 60.9254 | 3.39524 | ||||||||
\(323\) | −3.85995 | −0.214774 | ||||||||
\(324\) | 1.29778 | 0.0720991 | ||||||||
\(325\) | −4.77892 | −0.265087 | ||||||||
\(326\) | 8.32782 | 0.461235 | ||||||||
\(327\) | 6.68734 | 0.369811 | ||||||||
\(328\) | 1.56251 | 0.0862750 | ||||||||
\(329\) | 13.2843 | 0.732388 | ||||||||
\(330\) | 8.38277 | 0.461456 | ||||||||
\(331\) | −8.02086 | −0.440866 | −0.220433 | − | 0.975402i | \(-0.570747\pi\) | ||||
−0.220433 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(332\) | 10.1595 | 0.557577 | ||||||||
\(333\) | 6.78754 | 0.371955 | ||||||||
\(334\) | −12.9953 | −0.711072 | ||||||||
\(335\) | −5.47409 | −0.299081 | ||||||||
\(336\) | 18.2527 | 0.995767 | ||||||||
\(337\) | −17.1477 | −0.934092 | −0.467046 | − | 0.884233i | \(-0.654682\pi\) | ||||
−0.467046 | + | 0.884233i | \(0.654682\pi\) | |||||||
\(338\) | 6.30946 | 0.343189 | ||||||||
\(339\) | 12.1005 | 0.657209 | ||||||||
\(340\) | 2.41109 | 0.130759 | ||||||||
\(341\) | 27.4278 | 1.48530 | ||||||||
\(342\) | −7.00960 | −0.379036 | ||||||||
\(343\) | 0.698588 | 0.0377202 | ||||||||
\(344\) | −1.58509 | −0.0854622 | ||||||||
\(345\) | −16.7714 | −0.902940 | ||||||||
\(346\) | 40.8116 | 2.19404 | ||||||||
\(347\) | −18.5049 | −0.993396 | −0.496698 | − | 0.867924i | \(-0.665454\pi\) | ||||
−0.496698 | + | 0.867924i | \(0.665454\pi\) | |||||||
\(348\) | −8.16471 | −0.437674 | ||||||||
\(349\) | 0.565183 | 0.0302535 | 0.0151268 | − | 0.999886i | \(-0.495185\pi\) | ||||
0.0151268 | + | 0.999886i | \(0.495185\pi\) | |||||||
\(350\) | −10.4502 | −0.558586 | ||||||||
\(351\) | 3.08636 | 0.164737 | ||||||||
\(352\) | 15.8234 | 0.843391 | ||||||||
\(353\) | 5.77035 | 0.307125 | 0.153562 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153562 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(354\) | −25.9314 | −1.37824 | ||||||||
\(355\) | 13.9029 | 0.737888 | ||||||||
\(356\) | 8.97854 | 0.475862 | ||||||||
\(357\) | 3.71645 | 0.196696 | ||||||||
\(358\) | −18.9355 | −1.00077 | ||||||||
\(359\) | −7.28091 | −0.384272 | −0.192136 | − | 0.981368i | \(-0.561541\pi\) | ||||
−0.192136 | + | 0.981368i | \(0.561541\pi\) | |||||||
\(360\) | −2.36914 | −0.124865 | ||||||||
\(361\) | −4.10076 | −0.215829 | ||||||||
\(362\) | 22.6264 | 1.18922 | ||||||||
\(363\) | −4.82648 | −0.253324 | ||||||||
\(364\) | −14.8860 | −0.780237 | ||||||||
\(365\) | −21.2215 | −1.11078 | ||||||||
\(366\) | 22.7997 | 1.19176 | ||||||||
\(367\) | 14.3613 | 0.749653 | 0.374826 | − | 0.927095i | \(-0.377702\pi\) | ||||
0.374826 | + | 0.927095i | \(0.377702\pi\) | |||||||
\(368\) | −44.3361 | −2.31118 | ||||||||
\(369\) | 1.22529 | 0.0637862 | ||||||||
\(370\) | 22.8999 | 1.19051 | ||||||||
\(371\) | 38.4232 | 1.99483 | ||||||||
\(372\) | 14.3260 | 0.742771 | ||||||||
\(373\) | 19.2163 | 0.994981 | 0.497491 | − | 0.867469i | \(-0.334255\pi\) | ||||
0.497491 | + | 0.867469i | \(0.334255\pi\) | |||||||
\(374\) | 4.51209 | 0.233315 | ||||||||
\(375\) | 12.1659 | 0.628246 | ||||||||
\(376\) | −4.55819 | −0.235071 | ||||||||
\(377\) | −19.4171 | −1.00003 | ||||||||
\(378\) | 6.74901 | 0.347131 | ||||||||
\(379\) | 22.4576 | 1.15357 | 0.576784 | − | 0.816897i | \(-0.304308\pi\) | ||||
0.576784 | + | 0.816897i | \(0.304308\pi\) | |||||||
\(380\) | −9.30668 | −0.477423 | ||||||||
\(381\) | −2.22421 | −0.113950 | ||||||||
\(382\) | −38.5287 | −1.97130 | ||||||||
\(383\) | 25.4733 | 1.30162 | 0.650812 | − | 0.759239i | \(-0.274429\pi\) | ||||
0.650812 | + | 0.759239i | \(0.274429\pi\) | |||||||
\(384\) | −9.57286 | −0.488513 | ||||||||
\(385\) | 17.1556 | 0.874329 | ||||||||
\(386\) | 41.8454 | 2.12988 | ||||||||
\(387\) | −1.24300 | −0.0631853 | ||||||||
\(388\) | −17.0136 | −0.863733 | ||||||||
\(389\) | 30.2037 | 1.53139 | 0.765694 | − | 0.643205i | \(-0.222395\pi\) | ||||
0.765694 | + | 0.643205i | \(0.222395\pi\) | |||||||
\(390\) | 10.4128 | 0.527272 | ||||||||
\(391\) | −9.02732 | −0.456531 | ||||||||
\(392\) | 8.68676 | 0.438748 | ||||||||
\(393\) | −5.60301 | −0.282634 | ||||||||
\(394\) | −42.3655 | −2.13434 | ||||||||
\(395\) | 19.4875 | 0.980523 | ||||||||
\(396\) | 3.22455 | 0.162040 | ||||||||
\(397\) | 32.0423 | 1.60816 | 0.804078 | − | 0.594524i | \(-0.202659\pi\) | ||||
0.804078 | + | 0.594524i | \(0.202659\pi\) | |||||||
\(398\) | 0.309091 | 0.0154933 | ||||||||
\(399\) | −14.3453 | −0.718165 | ||||||||
\(400\) | 7.60471 | 0.380236 | ||||||||
\(401\) | −25.7052 | −1.28366 | −0.641829 | − | 0.766848i | \(-0.721824\pi\) | ||||
−0.641829 | + | 0.766848i | \(0.721824\pi\) | |||||||
\(402\) | −5.35073 | −0.266870 | ||||||||
\(403\) | 34.0698 | 1.69714 | ||||||||
\(404\) | 14.8810 | 0.740356 | ||||||||
\(405\) | −1.85785 | −0.0923172 | ||||||||
\(406\) | −42.4598 | −2.10724 | ||||||||
\(407\) | 16.8647 | 0.835952 | ||||||||
\(408\) | −1.27521 | −0.0631323 | ||||||||
\(409\) | 16.6542 | 0.823496 | 0.411748 | − | 0.911298i | \(-0.364918\pi\) | ||||
0.411748 | + | 0.911298i | \(0.364918\pi\) | |||||||
\(410\) | 4.13391 | 0.204159 | ||||||||
\(411\) | −11.8173 | −0.582904 | ||||||||
\(412\) | −3.67107 | −0.180861 | ||||||||
\(413\) | −53.0694 | −2.61137 | ||||||||
\(414\) | −16.3934 | −0.805693 | ||||||||
\(415\) | −14.5439 | −0.713933 | ||||||||
\(416\) | 19.6553 | 0.963680 | ||||||||
\(417\) | 7.98464 | 0.391010 | ||||||||
\(418\) | −17.4165 | −0.851866 | ||||||||
\(419\) | 13.2840 | 0.648966 | 0.324483 | − | 0.945892i | \(-0.394810\pi\) | ||||
0.324483 | + | 0.945892i | \(0.394810\pi\) | |||||||
\(420\) | 8.96069 | 0.437237 | ||||||||
\(421\) | 4.41988 | 0.215412 | 0.107706 | − | 0.994183i | \(-0.465650\pi\) | ||||
0.107706 | + | 0.994183i | \(0.465650\pi\) | |||||||
\(422\) | −25.2327 | −1.22831 | ||||||||
\(423\) | −3.57446 | −0.173796 | ||||||||
\(424\) | −13.1840 | −0.640270 | ||||||||
\(425\) | 1.54840 | 0.0751086 | ||||||||
\(426\) | 13.5896 | 0.658417 | ||||||||
\(427\) | 46.6602 | 2.25805 | ||||||||
\(428\) | −4.91125 | −0.237394 | ||||||||
\(429\) | 7.66853 | 0.370240 | ||||||||
\(430\) | −4.19366 | −0.202236 | ||||||||
\(431\) | 21.6388 | 1.04231 | 0.521153 | − | 0.853463i | \(-0.325502\pi\) | ||||
0.521153 | + | 0.853463i | \(0.325502\pi\) | |||||||
\(432\) | −4.91132 | −0.236296 | ||||||||
\(433\) | −8.20028 | −0.394080 | −0.197040 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197040 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(434\) | 74.5013 | 3.57617 | ||||||||
\(435\) | 11.6882 | 0.560407 | ||||||||
\(436\) | 8.67873 | 0.415636 | ||||||||
\(437\) | 34.8450 | 1.66686 | ||||||||
\(438\) | −20.7432 | −0.991150 | ||||||||
\(439\) | 6.45795 | 0.308221 | 0.154111 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154111 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(440\) | −5.88651 | −0.280628 | ||||||||
\(441\) | 6.81203 | 0.324382 | ||||||||
\(442\) | 5.60476 | 0.266591 | ||||||||
\(443\) | 23.9380 | 1.13733 | 0.568663 | − | 0.822570i | \(-0.307461\pi\) | ||||
0.568663 | + | 0.822570i | \(0.307461\pi\) | |||||||
\(444\) | 8.80876 | 0.418045 | ||||||||
\(445\) | −12.8533 | −0.609303 | ||||||||
\(446\) | −36.6266 | −1.73432 | ||||||||
\(447\) | −16.3198 | −0.771899 | ||||||||
\(448\) | 6.47529 | 0.305929 | ||||||||
\(449\) | −13.0183 | −0.614372 | −0.307186 | − | 0.951650i | \(-0.599387\pi\) | ||||
−0.307186 | + | 0.951650i | \(0.599387\pi\) | |||||||
\(450\) | 2.81187 | 0.132553 | ||||||||
\(451\) | 3.04443 | 0.143357 | ||||||||
\(452\) | 15.7038 | 0.738647 | ||||||||
\(453\) | −16.1016 | −0.756518 | ||||||||
\(454\) | −39.5537 | −1.85635 | ||||||||
\(455\) | 21.3101 | 0.999031 | ||||||||
\(456\) | 4.92225 | 0.230505 | ||||||||
\(457\) | 11.7973 | 0.551856 | 0.275928 | − | 0.961178i | \(-0.411015\pi\) | ||||
0.275928 | + | 0.961178i | \(0.411015\pi\) | |||||||
\(458\) | 27.3337 | 1.27722 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −21.7656 | −1.01483 | ||||||||
\(461\) | −19.6307 | −0.914291 | −0.457146 | − | 0.889392i | \(-0.651128\pi\) | ||||
−0.457146 | + | 0.889392i | \(0.651128\pi\) | |||||||
\(462\) | 16.7690 | 0.780163 | ||||||||
\(463\) | −17.5000 | −0.813293 | −0.406646 | − | 0.913586i | \(-0.633302\pi\) | ||||
−0.406646 | + | 0.913586i | \(0.633302\pi\) | |||||||
\(464\) | 30.8984 | 1.43442 | ||||||||
\(465\) | −20.5085 | −0.951059 | ||||||||
\(466\) | −42.8935 | −1.98700 | ||||||||
\(467\) | 25.6935 | 1.18896 | 0.594478 | − | 0.804112i | \(-0.297359\pi\) | ||||
0.594478 | + | 0.804112i | \(0.297359\pi\) | |||||||
\(468\) | 4.00542 | 0.185151 | ||||||||
\(469\) | −10.9504 | −0.505643 | ||||||||
\(470\) | −12.0596 | −0.556266 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 18.2095 | 0.838158 | ||||||||
\(473\) | −3.08843 | −0.142006 | ||||||||
\(474\) | 19.0484 | 0.874920 | ||||||||
\(475\) | −5.97677 | −0.274233 | ||||||||
\(476\) | 4.82316 | 0.221069 | ||||||||
\(477\) | −10.3387 | −0.473375 | ||||||||
\(478\) | −27.8814 | −1.27527 | ||||||||
\(479\) | 41.8153 | 1.91059 | 0.955294 | − | 0.295658i | \(-0.0955388\pi\) | ||||
0.955294 | + | 0.295658i | \(0.0955388\pi\) | |||||||
\(480\) | −11.8316 | −0.540036 | ||||||||
\(481\) | 20.9487 | 0.955181 | ||||||||
\(482\) | 0.0467353 | 0.00212873 | ||||||||
\(483\) | −33.5496 | −1.52656 | ||||||||
\(484\) | −6.26373 | −0.284715 | ||||||||
\(485\) | 24.3558 | 1.10594 | ||||||||
\(486\) | −1.81598 | −0.0823745 | ||||||||
\(487\) | −28.3163 | −1.28313 | −0.641566 | − | 0.767067i | \(-0.721715\pi\) | ||||
−0.641566 | + | 0.767067i | \(0.721715\pi\) | |||||||
\(488\) | −16.0103 | −0.724752 | ||||||||
\(489\) | −4.58586 | −0.207380 | ||||||||
\(490\) | 22.9825 | 1.03824 | ||||||||
\(491\) | −22.4161 | −1.01163 | −0.505813 | − | 0.862643i | \(-0.668807\pi\) | ||||
−0.505813 | + | 0.862643i | \(0.668807\pi\) | |||||||
\(492\) | 1.59017 | 0.0716903 | ||||||||
\(493\) | 6.29127 | 0.283344 | ||||||||
\(494\) | −21.6341 | −0.973365 | ||||||||
\(495\) | −4.61611 | −0.207479 | ||||||||
\(496\) | −54.2154 | −2.43434 | ||||||||
\(497\) | 27.8114 | 1.24751 | ||||||||
\(498\) | −14.2162 | −0.637042 | ||||||||
\(499\) | 6.39303 | 0.286191 | 0.143096 | − | 0.989709i | \(-0.454294\pi\) | ||||
0.143096 | + | 0.989709i | \(0.454294\pi\) | |||||||
\(500\) | 15.7888 | 0.706095 | ||||||||
\(501\) | 7.15609 | 0.319710 | ||||||||
\(502\) | −1.12264 | −0.0501057 | ||||||||
\(503\) | −16.8300 | −0.750413 | −0.375207 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375207 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(504\) | −4.73926 | −0.211103 | ||||||||
\(505\) | −21.3029 | −0.947967 | ||||||||
\(506\) | −40.7320 | −1.81076 | ||||||||
\(507\) | −3.47441 | −0.154304 | ||||||||
\(508\) | −2.88655 | −0.128070 | ||||||||
\(509\) | −39.3748 | −1.74526 | −0.872629 | − | 0.488384i | \(-0.837587\pi\) | ||||
−0.872629 | + | 0.488384i | \(0.837587\pi\) | |||||||
\(510\) | −3.37381 | −0.149395 | ||||||||
\(511\) | −42.4516 | −1.87795 | ||||||||
\(512\) | −18.7516 | −0.828711 | ||||||||
\(513\) | 3.85995 | 0.170421 | ||||||||
\(514\) | −11.9889 | −0.528806 | ||||||||
\(515\) | 5.25533 | 0.231578 | ||||||||
\(516\) | −1.61315 | −0.0710149 | ||||||||
\(517\) | −8.88131 | −0.390600 | ||||||||
\(518\) | 45.8091 | 2.01274 | ||||||||
\(519\) | −22.4736 | −0.986480 | ||||||||
\(520\) | −7.31202 | −0.320653 | ||||||||
\(521\) | −4.16490 | −0.182467 | −0.0912337 | − | 0.995830i | \(-0.529081\pi\) | ||||
−0.0912337 | + | 0.995830i | \(0.529081\pi\) | |||||||
\(522\) | 11.4248 | 0.500050 | ||||||||
\(523\) | −13.4591 | −0.588526 | −0.294263 | − | 0.955724i | \(-0.595074\pi\) | ||||
−0.294263 | + | 0.955724i | \(0.595074\pi\) | |||||||
\(524\) | −7.27149 | −0.317657 | ||||||||
\(525\) | 5.75457 | 0.251150 | ||||||||
\(526\) | −23.0847 | −1.00654 | ||||||||
\(527\) | −11.0388 | −0.480860 | ||||||||
\(528\) | −12.2030 | −0.531066 | ||||||||
\(529\) | 58.4924 | 2.54315 | ||||||||
\(530\) | −34.8807 | −1.51512 | ||||||||
\(531\) | 14.2796 | 0.619681 | ||||||||
\(532\) | −18.6172 | −0.807156 | ||||||||
\(533\) | 3.78169 | 0.163803 | ||||||||
\(534\) | −12.5636 | −0.543680 | ||||||||
\(535\) | 7.03072 | 0.303965 | ||||||||
\(536\) | 3.75736 | 0.162293 | ||||||||
\(537\) | 10.4271 | 0.449964 | ||||||||
\(538\) | −7.14426 | −0.308011 | ||||||||
\(539\) | 16.9256 | 0.729035 | ||||||||
\(540\) | −2.41109 | −0.103757 | ||||||||
\(541\) | −17.4282 | −0.749297 | −0.374648 | − | 0.927167i | \(-0.622237\pi\) | ||||
−0.374648 | + | 0.927167i | \(0.622237\pi\) | |||||||
\(542\) | 8.97379 | 0.385457 | ||||||||
\(543\) | −12.4596 | −0.534692 | ||||||||
\(544\) | −6.36845 | −0.273045 | ||||||||
\(545\) | −12.4241 | −0.532188 | ||||||||
\(546\) | 20.8298 | 0.891435 | ||||||||
\(547\) | 3.60373 | 0.154084 | 0.0770421 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770421 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(548\) | −15.3363 | −0.655134 | ||||||||
\(549\) | −12.5550 | −0.535836 | ||||||||
\(550\) | 6.98653 | 0.297907 | ||||||||
\(551\) | −24.2840 | −1.03453 | ||||||||
\(552\) | 11.5117 | 0.489971 | ||||||||
\(553\) | 38.9830 | 1.65772 | ||||||||
\(554\) | 52.5318 | 2.23186 | ||||||||
\(555\) | −12.6102 | −0.535273 | ||||||||
\(556\) | 10.3623 | 0.439461 | ||||||||
\(557\) | −4.98862 | −0.211375 | −0.105687 | − | 0.994399i | \(-0.533704\pi\) | ||||
−0.105687 | + | 0.994399i | \(0.533704\pi\) | |||||||
\(558\) | −20.0463 | −0.848629 | ||||||||
\(559\) | −3.83635 | −0.162260 | ||||||||
\(560\) | −33.9107 | −1.43299 | ||||||||
\(561\) | −2.48466 | −0.104902 | ||||||||
\(562\) | 15.5126 | 0.654359 | ||||||||
\(563\) | −12.9858 | −0.547287 | −0.273644 | − | 0.961831i | \(-0.588229\pi\) | ||||
−0.273644 | + | 0.961831i | \(0.588229\pi\) | |||||||
\(564\) | −4.63888 | −0.195332 | ||||||||
\(565\) | −22.4809 | −0.945778 | ||||||||
\(566\) | 28.2023 | 1.18543 | ||||||||
\(567\) | −3.71645 | −0.156076 | ||||||||
\(568\) | −9.54281 | −0.400407 | ||||||||
\(569\) | 30.7135 | 1.28758 | 0.643789 | − | 0.765203i | \(-0.277361\pi\) | ||||
0.643789 | + | 0.765203i | \(0.277361\pi\) | |||||||
\(570\) | 13.0228 | 0.545464 | ||||||||
\(571\) | −0.927566 | −0.0388174 | −0.0194087 | − | 0.999812i | \(-0.506178\pi\) | ||||
−0.0194087 | + | 0.999812i | \(0.506178\pi\) | |||||||
\(572\) | 9.95210 | 0.416118 | ||||||||
\(573\) | 21.2165 | 0.886332 | ||||||||
\(574\) | 8.26952 | 0.345163 | ||||||||
\(575\) | −13.9779 | −0.582920 | ||||||||
\(576\) | −1.74233 | −0.0725971 | ||||||||
\(577\) | 34.1100 | 1.42002 | 0.710009 | − | 0.704192i | \(-0.248691\pi\) | ||||
0.710009 | + | 0.704192i | \(0.248691\pi\) | |||||||
\(578\) | −1.81598 | −0.0755348 | ||||||||
\(579\) | −23.0429 | −0.957630 | ||||||||
\(580\) | 15.1688 | 0.629849 | ||||||||
\(581\) | −29.0938 | −1.20701 | ||||||||
\(582\) | 23.8070 | 0.986831 | ||||||||
\(583\) | −25.6880 | −1.06389 | ||||||||
\(584\) | 14.5662 | 0.602755 | ||||||||
\(585\) | −5.73398 | −0.237071 | ||||||||
\(586\) | 16.7040 | 0.690035 | ||||||||
\(587\) | 19.4587 | 0.803146 | 0.401573 | − | 0.915827i | \(-0.368464\pi\) | ||||
0.401573 | + | 0.915827i | \(0.368464\pi\) | |||||||
\(588\) | 8.84054 | 0.364578 | ||||||||
\(589\) | 42.6094 | 1.75569 | ||||||||
\(590\) | 48.1767 | 1.98340 | ||||||||
\(591\) | 23.3293 | 0.959639 | ||||||||
\(592\) | −33.3358 | −1.37009 | ||||||||
\(593\) | −7.19389 | −0.295417 | −0.147709 | − | 0.989031i | \(-0.547190\pi\) | ||||
−0.147709 | + | 0.989031i | \(0.547190\pi\) | |||||||
\(594\) | −4.51209 | −0.185133 | ||||||||
\(595\) | −6.90460 | −0.283061 | ||||||||
\(596\) | −21.1796 | −0.867548 | ||||||||
\(597\) | −0.170206 | −0.00696607 | ||||||||
\(598\) | −50.5959 | −2.06902 | ||||||||
\(599\) | −28.4340 | −1.16178 | −0.580892 | − | 0.813981i | \(-0.697296\pi\) | ||||
−0.580892 | + | 0.813981i | \(0.697296\pi\) | |||||||
\(600\) | −1.97454 | −0.0806102 | ||||||||
\(601\) | 23.0662 | 0.940891 | 0.470446 | − | 0.882429i | \(-0.344093\pi\) | ||||
0.470446 | + | 0.882429i | \(0.344093\pi\) | |||||||
\(602\) | −8.38903 | −0.341911 | ||||||||
\(603\) | 2.94647 | 0.119989 | ||||||||
\(604\) | −20.8964 | −0.850262 | ||||||||
\(605\) | 8.96686 | 0.364555 | ||||||||
\(606\) | −20.8228 | −0.845870 | ||||||||
\(607\) | −42.6536 | −1.73126 | −0.865628 | − | 0.500688i | \(-0.833080\pi\) | ||||
−0.865628 | + | 0.500688i | \(0.833080\pi\) | |||||||
\(608\) | 24.5819 | 0.996928 | ||||||||
\(609\) | 23.3812 | 0.947454 | ||||||||
\(610\) | −42.3584 | −1.71504 | ||||||||
\(611\) | −11.0321 | −0.446309 | ||||||||
\(612\) | −1.29778 | −0.0524598 | ||||||||
\(613\) | 9.72973 | 0.392980 | 0.196490 | − | 0.980506i | \(-0.437046\pi\) | ||||
0.196490 | + | 0.980506i | \(0.437046\pi\) | |||||||
\(614\) | −19.2754 | −0.777891 | ||||||||
\(615\) | −2.27641 | −0.0917937 | ||||||||
\(616\) | −11.7754 | −0.474446 | ||||||||
\(617\) | 17.2724 | 0.695359 | 0.347680 | − | 0.937613i | \(-0.386970\pi\) | ||||
0.347680 | + | 0.937613i | \(0.386970\pi\) | |||||||
\(618\) | 5.13690 | 0.206636 | ||||||||
\(619\) | −0.976399 | −0.0392448 | −0.0196224 | − | 0.999807i | \(-0.506246\pi\) | ||||
−0.0196224 | + | 0.999807i | \(0.506246\pi\) | |||||||
\(620\) | −26.6156 | −1.06891 | ||||||||
\(621\) | 9.02732 | 0.362254 | ||||||||
\(622\) | −53.1586 | −2.13147 | ||||||||
\(623\) | −25.7118 | −1.03012 | ||||||||
\(624\) | −15.1581 | −0.606809 | ||||||||
\(625\) | −14.8604 | −0.594417 | ||||||||
\(626\) | −44.1197 | −1.76338 | ||||||||
\(627\) | 9.59066 | 0.383014 | ||||||||
\(628\) | −1.29778 | −0.0517872 | ||||||||
\(629\) | −6.78754 | −0.270637 | ||||||||
\(630\) | −12.5386 | −0.499551 | ||||||||
\(631\) | −7.08981 | −0.282241 | −0.141121 | − | 0.989992i | \(-0.545071\pi\) | ||||
−0.141121 | + | 0.989992i | \(0.545071\pi\) | |||||||
\(632\) | −13.3760 | −0.532071 | ||||||||
\(633\) | 13.8948 | 0.552270 | ||||||||
\(634\) | 18.3317 | 0.728044 | ||||||||
\(635\) | 4.13225 | 0.163983 | ||||||||
\(636\) | −13.4174 | −0.532033 | ||||||||
\(637\) | 21.0243 | 0.833015 | ||||||||
\(638\) | 28.3867 | 1.12384 | ||||||||
\(639\) | −7.48333 | −0.296036 | ||||||||
\(640\) | 17.7849 | 0.703011 | ||||||||
\(641\) | 9.48668 | 0.374701 | 0.187351 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187351 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(642\) | 6.87228 | 0.271227 | ||||||||
\(643\) | 6.57351 | 0.259234 | 0.129617 | − | 0.991564i | \(-0.458625\pi\) | ||||
0.129617 | + | 0.991564i | \(0.458625\pi\) | |||||||
\(644\) | −43.5402 | −1.71572 | ||||||||
\(645\) | 2.30931 | 0.0909289 | ||||||||
\(646\) | 7.00960 | 0.275789 | ||||||||
\(647\) | 0.447485 | 0.0175925 | 0.00879623 | − | 0.999961i | \(-0.497200\pi\) | ||||
0.00879623 | + | 0.999961i | \(0.497200\pi\) | |||||||
\(648\) | 1.27521 | 0.0500950 | ||||||||
\(649\) | 35.4799 | 1.39271 | ||||||||
\(650\) | 8.67843 | 0.340396 | ||||||||
\(651\) | −41.0254 | −1.60791 | ||||||||
\(652\) | −5.95145 | −0.233077 | ||||||||
\(653\) | 26.4545 | 1.03525 | 0.517623 | − | 0.855609i | \(-0.326817\pi\) | ||||
0.517623 | + | 0.855609i | \(0.326817\pi\) | |||||||
\(654\) | −12.1441 | −0.474871 | ||||||||
\(655\) | 10.4095 | 0.406734 | ||||||||
\(656\) | −6.01782 | −0.234956 | ||||||||
\(657\) | 11.4226 | 0.445639 | ||||||||
\(658\) | −24.1241 | −0.940454 | ||||||||
\(659\) | −36.1578 | −1.40851 | −0.704253 | − | 0.709949i | \(-0.748718\pi\) | ||||
−0.704253 | + | 0.709949i | \(0.748718\pi\) | |||||||
\(660\) | −5.99072 | −0.233188 | ||||||||
\(661\) | 24.9296 | 0.969649 | 0.484824 | − | 0.874612i | \(-0.338884\pi\) | ||||
0.484824 | + | 0.874612i | \(0.338884\pi\) | |||||||
\(662\) | 14.5657 | 0.566113 | ||||||||
\(663\) | −3.08636 | −0.119864 | ||||||||
\(664\) | 9.98281 | 0.387408 | ||||||||
\(665\) | 26.6515 | 1.03350 | ||||||||
\(666\) | −12.3260 | −0.477624 | ||||||||
\(667\) | −56.7932 | −2.19904 | ||||||||
\(668\) | 9.28706 | 0.359327 | ||||||||
\(669\) | 20.1691 | 0.779781 | ||||||||
\(670\) | 9.94083 | 0.384048 | ||||||||
\(671\) | −31.1950 | −1.20427 | ||||||||
\(672\) | −23.6680 | −0.913015 | ||||||||
\(673\) | −8.70737 | −0.335644 | −0.167822 | − | 0.985817i | \(-0.553673\pi\) | ||||
−0.167822 | + | 0.985817i | \(0.553673\pi\) | |||||||
\(674\) | 31.1398 | 1.19946 | ||||||||
\(675\) | −1.54840 | −0.0595981 | ||||||||
\(676\) | −4.50904 | −0.173424 | ||||||||
\(677\) | 50.9749 | 1.95912 | 0.979562 | − | 0.201143i | \(-0.0644656\pi\) | ||||
0.979562 | + | 0.201143i | \(0.0644656\pi\) | |||||||
\(678\) | −21.9743 | −0.843917 | ||||||||
\(679\) | 48.7216 | 1.86976 | ||||||||
\(680\) | 2.36914 | 0.0908526 | ||||||||
\(681\) | 21.7809 | 0.834646 | ||||||||
\(682\) | −49.8083 | −1.90726 | ||||||||
\(683\) | 35.9882 | 1.37705 | 0.688525 | − | 0.725213i | \(-0.258259\pi\) | ||||
0.688525 | + | 0.725213i | \(0.258259\pi\) | |||||||
\(684\) | 5.00939 | 0.191539 | ||||||||
\(685\) | 21.9547 | 0.838847 | ||||||||
\(686\) | −1.26862 | −0.0484362 | ||||||||
\(687\) | −15.0518 | −0.574261 | ||||||||
\(688\) | 6.10478 | 0.232743 | ||||||||
\(689\) | −31.9088 | −1.21563 | ||||||||
\(690\) | 30.4565 | 1.15946 | ||||||||
\(691\) | −27.2666 | −1.03727 | −0.518636 | − | 0.854995i | \(-0.673560\pi\) | ||||
−0.518636 | + | 0.854995i | \(0.673560\pi\) | |||||||
\(692\) | −29.1658 | −1.10872 | ||||||||
\(693\) | −9.23411 | −0.350775 | ||||||||
\(694\) | 33.6046 | 1.27561 | ||||||||
\(695\) | −14.8342 | −0.562695 | ||||||||
\(696\) | −8.02268 | −0.304099 | ||||||||
\(697\) | −1.22529 | −0.0464113 | ||||||||
\(698\) | −1.02636 | −0.0388483 | ||||||||
\(699\) | 23.6200 | 0.893391 | ||||||||
\(700\) | 7.46819 | 0.282271 | ||||||||
\(701\) | 15.8638 | 0.599168 | 0.299584 | − | 0.954070i | \(-0.403152\pi\) | ||||
0.299584 | + | 0.954070i | \(0.403152\pi\) | |||||||
\(702\) | −5.60476 | −0.211538 | ||||||||
\(703\) | 26.1996 | 0.988136 | ||||||||
\(704\) | −4.32909 | −0.163159 | ||||||||
\(705\) | 6.64080 | 0.250107 | ||||||||
\(706\) | −10.4788 | −0.394376 | ||||||||
\(707\) | −42.6145 | −1.60268 | ||||||||
\(708\) | 18.5318 | 0.696468 | ||||||||
\(709\) | −35.9392 | −1.34973 | −0.674863 | − | 0.737943i | \(-0.735797\pi\) | ||||
−0.674863 | + | 0.737943i | \(0.735797\pi\) | |||||||
\(710\) | −25.2474 | −0.947516 | ||||||||
\(711\) | −10.4893 | −0.393379 | ||||||||
\(712\) | 8.82236 | 0.330632 | ||||||||
\(713\) | 99.6512 | 3.73197 | ||||||||
\(714\) | −6.74901 | −0.252575 | ||||||||
\(715\) | −14.2470 | −0.532806 | ||||||||
\(716\) | 13.5322 | 0.505721 | ||||||||
\(717\) | 15.3534 | 0.573382 | ||||||||
\(718\) | 13.2220 | 0.493440 | ||||||||
\(719\) | 7.28974 | 0.271862 | 0.135931 | − | 0.990718i | \(-0.456598\pi\) | ||||
0.135931 | + | 0.990718i | \(0.456598\pi\) | |||||||
\(720\) | 9.12449 | 0.340050 | ||||||||
\(721\) | 10.5128 | 0.391517 | ||||||||
\(722\) | 7.44689 | 0.277145 | ||||||||
\(723\) | −0.0257356 | −0.000957116 0 | ||||||||
\(724\) | −16.1699 | −0.600948 | ||||||||
\(725\) | 9.74142 | 0.361787 | ||||||||
\(726\) | 8.76479 | 0.325292 | ||||||||
\(727\) | 15.5564 | 0.576956 | 0.288478 | − | 0.957487i | \(-0.406851\pi\) | ||||
0.288478 | + | 0.957487i | \(0.406851\pi\) | |||||||
\(728\) | −14.6270 | −0.542114 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 38.5378 | 1.42635 | ||||||||
\(731\) | 1.24300 | 0.0459741 | ||||||||
\(732\) | −16.2937 | −0.602234 | ||||||||
\(733\) | −2.94807 | −0.108890 | −0.0544448 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544448 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(734\) | −26.0798 | −0.962623 | ||||||||
\(735\) | −12.6557 | −0.466813 | ||||||||
\(736\) | 57.4900 | 2.11911 | ||||||||
\(737\) | 7.32096 | 0.269671 | ||||||||
\(738\) | −2.22511 | −0.0819074 | ||||||||
\(739\) | 23.6089 | 0.868468 | 0.434234 | − | 0.900800i | \(-0.357019\pi\) | ||||
0.434234 | + | 0.900800i | \(0.357019\pi\) | |||||||
\(740\) | −16.3653 | −0.601601 | ||||||||
\(741\) | 11.9132 | 0.437642 | ||||||||
\(742\) | −69.7757 | −2.56155 | ||||||||
\(743\) | 43.8295 | 1.60795 | 0.803974 | − | 0.594665i | \(-0.202715\pi\) | ||||
0.803974 | + | 0.594665i | \(0.202715\pi\) | |||||||
\(744\) | 14.0768 | 0.516082 | ||||||||
\(745\) | 30.3197 | 1.11083 | ||||||||
\(746\) | −34.8964 | −1.27765 | ||||||||
\(747\) | 7.82837 | 0.286425 | ||||||||
\(748\) | −3.22455 | −0.117901 | ||||||||
\(749\) | 14.0643 | 0.513899 | ||||||||
\(750\) | −22.0931 | −0.806726 | ||||||||
\(751\) | 18.5276 | 0.676083 | 0.338042 | − | 0.941131i | \(-0.390236\pi\) | ||||
0.338042 | + | 0.941131i | \(0.390236\pi\) | |||||||
\(752\) | 17.5553 | 0.640177 | ||||||||
\(753\) | 0.618199 | 0.0225284 | ||||||||
\(754\) | 35.2610 | 1.28413 | ||||||||
\(755\) | 29.9143 | 1.08869 | ||||||||
\(756\) | −4.82316 | −0.175416 | ||||||||
\(757\) | 34.9084 | 1.26877 | 0.634385 | − | 0.773018i | \(-0.281254\pi\) | ||||
0.634385 | + | 0.773018i | \(0.281254\pi\) | |||||||
\(758\) | −40.7825 | −1.48129 | ||||||||
\(759\) | 22.4298 | 0.814150 | ||||||||
\(760\) | −9.14479 | −0.331716 | ||||||||
\(761\) | −33.7526 | −1.22353 | −0.611766 | − | 0.791039i | \(-0.709541\pi\) | ||||
−0.611766 | + | 0.791039i | \(0.709541\pi\) | |||||||
\(762\) | 4.03913 | 0.146322 | ||||||||
\(763\) | −24.8532 | −0.899746 | ||||||||
\(764\) | 27.5344 | 0.996161 | ||||||||
\(765\) | 1.85785 | 0.0671706 | ||||||||
\(766\) | −46.2590 | −1.67140 | ||||||||
\(767\) | 44.0719 | 1.59134 | ||||||||
\(768\) | 20.8688 | 0.753038 | ||||||||
\(769\) | −40.4986 | −1.46042 | −0.730208 | − | 0.683224i | \(-0.760577\pi\) | ||||
−0.730208 | + | 0.683224i | \(0.760577\pi\) | |||||||
\(770\) | −31.1542 | −1.12272 | ||||||||
\(771\) | 6.60186 | 0.237760 | ||||||||
\(772\) | −29.9047 | −1.07629 | ||||||||
\(773\) | −33.4501 | −1.20312 | −0.601559 | − | 0.798829i | \(-0.705453\pi\) | ||||
−0.601559 | + | 0.798829i | \(0.705453\pi\) | |||||||
\(774\) | 2.25727 | 0.0811358 | ||||||||
\(775\) | −17.0926 | −0.613984 | ||||||||
\(776\) | −16.7176 | −0.600128 | ||||||||
\(777\) | −25.2256 | −0.904962 | ||||||||
\(778\) | −54.8493 | −1.96644 | ||||||||
\(779\) | 4.72958 | 0.169455 | ||||||||
\(780\) | −7.44147 | −0.266447 | ||||||||
\(781\) | −18.5935 | −0.665328 | ||||||||
\(782\) | 16.3934 | 0.586228 | ||||||||
\(783\) | −6.29127 | −0.224831 | ||||||||
\(784\) | −33.4561 | −1.19486 | ||||||||
\(785\) | 1.85785 | 0.0663094 | ||||||||
\(786\) | 10.1749 | 0.362928 | ||||||||
\(787\) | 12.7648 | 0.455015 | 0.227508 | − | 0.973776i | \(-0.426942\pi\) | ||||
0.227508 | + | 0.973776i | \(0.426942\pi\) | |||||||
\(788\) | 30.2764 | 1.07855 | ||||||||
\(789\) | 12.7120 | 0.452558 | ||||||||
\(790\) | −35.3889 | −1.25908 | ||||||||
\(791\) | −44.9710 | −1.59898 | ||||||||
\(792\) | 3.16846 | 0.112586 | ||||||||
\(793\) | −38.7493 | −1.37603 | ||||||||
\(794\) | −58.1882 | −2.06502 | ||||||||
\(795\) | 19.2077 | 0.681225 | ||||||||
\(796\) | −0.220891 | −0.00782927 | ||||||||
\(797\) | 0.465613 | 0.0164929 | 0.00824644 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824644 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(798\) | 26.0509 | 0.922190 | ||||||||
\(799\) | 3.57446 | 0.126455 | ||||||||
\(800\) | −9.86093 | −0.348636 | ||||||||
\(801\) | 6.91836 | 0.244448 | ||||||||
\(802\) | 46.6802 | 1.64833 | ||||||||
\(803\) | 28.3813 | 1.00155 | ||||||||
\(804\) | 3.82388 | 0.134858 | ||||||||
\(805\) | 62.3300 | 2.19685 | ||||||||
\(806\) | −61.8701 | −2.17928 | ||||||||
\(807\) | 3.93410 | 0.138487 | ||||||||
\(808\) | 14.6221 | 0.514405 | ||||||||
\(809\) | 10.2849 | 0.361598 | 0.180799 | − | 0.983520i | \(-0.442132\pi\) | ||||
0.180799 | + | 0.983520i | \(0.442132\pi\) | |||||||
\(810\) | 3.37381 | 0.118544 | ||||||||
\(811\) | 17.8319 | 0.626164 | 0.313082 | − | 0.949726i | \(-0.398639\pi\) | ||||
0.313082 | + | 0.949726i | \(0.398639\pi\) | |||||||
\(812\) | 30.3438 | 1.06486 | ||||||||
\(813\) | −4.94157 | −0.173308 | ||||||||
\(814\) | −30.6260 | −1.07344 | ||||||||
\(815\) | 8.51982 | 0.298436 | ||||||||
\(816\) | 4.91132 | 0.171931 | ||||||||
\(817\) | −4.79793 | −0.167858 | ||||||||
\(818\) | −30.2436 | −1.05744 | ||||||||
\(819\) | −11.4703 | −0.400805 | ||||||||
\(820\) | −2.95429 | −0.103168 | ||||||||
\(821\) | 24.4931 | 0.854814 | 0.427407 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(822\) | 21.4600 | 0.748502 | ||||||||
\(823\) | 5.88425 | 0.205112 | 0.102556 | − | 0.994727i | \(-0.467298\pi\) | ||||
0.102556 | + | 0.994727i | \(0.467298\pi\) | |||||||
\(824\) | −3.60721 | −0.125663 | ||||||||
\(825\) | −3.84725 | −0.133944 | ||||||||
\(826\) | 96.3730 | 3.35324 | ||||||||
\(827\) | 48.3976 | 1.68295 | 0.841474 | − | 0.540298i | \(-0.181688\pi\) | ||||
0.841474 | + | 0.540298i | \(0.181688\pi\) | |||||||
\(828\) | 11.7155 | 0.407142 | ||||||||
\(829\) | −27.4652 | −0.953906 | −0.476953 | − | 0.878929i | \(-0.658259\pi\) | ||||
−0.476953 | + | 0.878929i | \(0.658259\pi\) | |||||||
\(830\) | 26.4115 | 0.916756 | ||||||||
\(831\) | −28.9275 | −1.00348 | ||||||||
\(832\) | −5.37745 | −0.186429 | ||||||||
\(833\) | −6.81203 | −0.236023 | ||||||||
\(834\) | −14.5000 | −0.502092 | ||||||||
\(835\) | −13.2949 | −0.460089 | ||||||||
\(836\) | 12.4466 | 0.430475 | ||||||||
\(837\) | 11.0388 | 0.381558 | ||||||||
\(838\) | −24.1235 | −0.833332 | ||||||||
\(839\) | −8.25758 | −0.285083 | −0.142542 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142542 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(840\) | 8.80482 | 0.303795 | ||||||||
\(841\) | 10.5800 | 0.364828 | ||||||||
\(842\) | −8.02641 | −0.276609 | ||||||||
\(843\) | −8.54227 | −0.294211 | ||||||||
\(844\) | 18.0325 | 0.620704 | ||||||||
\(845\) | 6.45492 | 0.222056 | ||||||||
\(846\) | 6.49115 | 0.223170 | ||||||||
\(847\) | 17.9374 | 0.616336 | ||||||||
\(848\) | 50.7765 | 1.74367 | ||||||||
\(849\) | −15.5300 | −0.532990 | ||||||||
\(850\) | −2.81187 | −0.0964463 | ||||||||
\(851\) | 61.2732 | 2.10042 | ||||||||
\(852\) | −9.71174 | −0.332719 | ||||||||
\(853\) | −29.7508 | −1.01865 | −0.509323 | − | 0.860575i | \(-0.670104\pi\) | ||||
−0.509323 | + | 0.860575i | \(0.670104\pi\) | |||||||
\(854\) | −84.7340 | −2.89954 | ||||||||
\(855\) | −7.17120 | −0.245250 | ||||||||
\(856\) | −4.82582 | −0.164943 | ||||||||
\(857\) | 6.37210 | 0.217667 | 0.108833 | − | 0.994060i | \(-0.465289\pi\) | ||||
0.108833 | + | 0.994060i | \(0.465289\pi\) | |||||||
\(858\) | −13.9259 | −0.475423 | ||||||||
\(859\) | 26.8962 | 0.917686 | 0.458843 | − | 0.888517i | \(-0.348264\pi\) | ||||
0.458843 | + | 0.888517i | \(0.348264\pi\) | |||||||
\(860\) | 2.99698 | 0.102196 | ||||||||
\(861\) | −4.55375 | −0.155191 | ||||||||
\(862\) | −39.2957 | −1.33842 | ||||||||
\(863\) | −50.1947 | −1.70865 | −0.854324 | − | 0.519741i | \(-0.826028\pi\) | ||||
−0.854324 | + | 0.519741i | \(0.826028\pi\) | |||||||
\(864\) | 6.36845 | 0.216659 | ||||||||
\(865\) | 41.7525 | 1.41963 | ||||||||
\(866\) | 14.8915 | 0.506035 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −53.2421 | −1.80715 | ||||||||
\(869\) | −26.0623 | −0.884103 | ||||||||
\(870\) | −21.2256 | −0.719614 | ||||||||
\(871\) | 9.09385 | 0.308133 | ||||||||
\(872\) | 8.52776 | 0.288786 | ||||||||
\(873\) | −13.1097 | −0.443696 | ||||||||
\(874\) | −63.2779 | −2.14041 | ||||||||
\(875\) | −45.2141 | −1.52852 | ||||||||
\(876\) | 14.8241 | 0.500860 | ||||||||
\(877\) | −43.3499 | −1.46382 | −0.731911 | − | 0.681401i | \(-0.761371\pi\) | ||||
−0.731911 | + | 0.681401i | \(0.761371\pi\) | |||||||
\(878\) | −11.7275 | −0.395784 | ||||||||
\(879\) | −9.19833 | −0.310252 | ||||||||
\(880\) | 22.6712 | 0.764247 | ||||||||
\(881\) | −32.3313 | −1.08927 | −0.544635 | − | 0.838673i | \(-0.683332\pi\) | ||||
−0.544635 | + | 0.838673i | \(0.683332\pi\) | |||||||
\(882\) | −12.3705 | −0.416537 | ||||||||
\(883\) | 23.2876 | 0.783691 | 0.391845 | − | 0.920031i | \(-0.371837\pi\) | ||||
0.391845 | + | 0.920031i | \(0.371837\pi\) | |||||||
\(884\) | −4.00542 | −0.134717 | ||||||||
\(885\) | −26.5293 | −0.891772 | ||||||||
\(886\) | −43.4708 | −1.46043 | ||||||||
\(887\) | 18.2004 | 0.611111 | 0.305556 | − | 0.952174i | \(-0.401158\pi\) | ||||
0.305556 | + | 0.952174i | \(0.401158\pi\) | |||||||
\(888\) | 8.65553 | 0.290461 | ||||||||
\(889\) | 8.26619 | 0.277239 | ||||||||
\(890\) | 23.3413 | 0.782401 | ||||||||
\(891\) | 2.48466 | 0.0832391 | ||||||||
\(892\) | 26.1751 | 0.876407 | ||||||||
\(893\) | −13.7973 | −0.461708 | ||||||||
\(894\) | 29.6364 | 0.991189 | ||||||||
\(895\) | −19.3720 | −0.647535 | ||||||||
\(896\) | 35.5771 | 1.18855 | ||||||||
\(897\) | 27.8615 | 0.930269 | ||||||||
\(898\) | 23.6410 | 0.788910 | ||||||||
\(899\) | −69.4483 | −2.31623 | ||||||||
\(900\) | −2.00949 | −0.0669831 | ||||||||
\(901\) | 10.3387 | 0.344431 | ||||||||
\(902\) | −5.52863 | −0.184083 | ||||||||
\(903\) | 4.61956 | 0.153729 | ||||||||
\(904\) | 15.4307 | 0.513217 | ||||||||
\(905\) | 23.1480 | 0.769466 | ||||||||
\(906\) | 29.2402 | 0.971439 | ||||||||
\(907\) | −10.0335 | −0.333157 | −0.166579 | − | 0.986028i | \(-0.553272\pi\) | ||||
−0.166579 | + | 0.986028i | \(0.553272\pi\) | |||||||
\(908\) | 28.2669 | 0.938071 | ||||||||
\(909\) | 11.4665 | 0.380318 | ||||||||
\(910\) | −38.6987 | −1.28285 | ||||||||
\(911\) | 9.04286 | 0.299603 | 0.149802 | − | 0.988716i | \(-0.452136\pi\) | ||||
0.149802 | + | 0.988716i | \(0.452136\pi\) | |||||||
\(912\) | −18.9575 | −0.627745 | ||||||||
\(913\) | 19.4508 | 0.643728 | ||||||||
\(914\) | −21.4237 | −0.708634 | ||||||||
\(915\) | 23.3253 | 0.771112 | ||||||||
\(916\) | −19.5340 | −0.645421 | ||||||||
\(917\) | 20.8233 | 0.687646 | ||||||||
\(918\) | 1.81598 | 0.0599363 | ||||||||
\(919\) | 9.36364 | 0.308878 | 0.154439 | − | 0.988002i | \(-0.450643\pi\) | ||||
0.154439 | + | 0.988002i | \(0.450643\pi\) | |||||||
\(920\) | −21.3870 | −0.705109 | ||||||||
\(921\) | 10.6143 | 0.349753 | ||||||||
\(922\) | 35.6489 | 1.17403 | ||||||||
\(923\) | −23.0962 | −0.760221 | ||||||||
\(924\) | −11.9839 | −0.394241 | ||||||||
\(925\) | −10.5098 | −0.345561 | ||||||||
\(926\) | 31.7796 | 1.04434 | ||||||||
\(927\) | −2.82872 | −0.0929074 | ||||||||
\(928\) | −40.0656 | −1.31522 | ||||||||
\(929\) | −18.2661 | −0.599290 | −0.299645 | − | 0.954051i | \(-0.596868\pi\) | ||||
−0.299645 | + | 0.954051i | \(0.596868\pi\) | |||||||
\(930\) | 37.2430 | 1.22125 | ||||||||
\(931\) | 26.2941 | 0.861755 | ||||||||
\(932\) | 30.6537 | 1.00410 | ||||||||
\(933\) | 29.2727 | 0.958344 | ||||||||
\(934\) | −46.6590 | −1.52673 | ||||||||
\(935\) | 4.61611 | 0.150963 | ||||||||
\(936\) | 3.93575 | 0.128644 | ||||||||
\(937\) | 54.1527 | 1.76909 | 0.884546 | − | 0.466452i | \(-0.154468\pi\) | ||||
0.884546 | + | 0.466452i | \(0.154468\pi\) | |||||||
\(938\) | 19.8857 | 0.649292 | ||||||||
\(939\) | 24.2953 | 0.792846 | ||||||||
\(940\) | 8.61833 | 0.281099 | ||||||||
\(941\) | −40.3776 | −1.31627 | −0.658136 | − | 0.752899i | \(-0.728655\pi\) | ||||
−0.658136 | + | 0.752899i | \(0.728655\pi\) | |||||||
\(942\) | 1.81598 | 0.0591678 | ||||||||
\(943\) | 11.0611 | 0.360199 | ||||||||
\(944\) | −70.1317 | −2.28259 | ||||||||
\(945\) | 6.90460 | 0.224607 | ||||||||
\(946\) | 5.60853 | 0.182349 | ||||||||
\(947\) | −8.88176 | −0.288618 | −0.144309 | − | 0.989533i | \(-0.546096\pi\) | ||||
−0.144309 | + | 0.989533i | \(0.546096\pi\) | |||||||
\(948\) | −13.6128 | −0.442125 | ||||||||
\(949\) | 35.2542 | 1.14440 | ||||||||
\(950\) | 10.8537 | 0.352140 | ||||||||
\(951\) | −10.0946 | −0.327341 | ||||||||
\(952\) | 4.73926 | 0.153600 | ||||||||
\(953\) | −21.9433 | −0.710812 | −0.355406 | − | 0.934712i | \(-0.615657\pi\) | ||||
−0.355406 | + | 0.934712i | \(0.615657\pi\) | |||||||
\(954\) | 18.7748 | 0.607857 | ||||||||
\(955\) | −39.4170 | −1.27550 | ||||||||
\(956\) | 19.9254 | 0.644432 | ||||||||
\(957\) | −15.6316 | −0.505299 | ||||||||
\(958\) | −75.9357 | −2.45337 | ||||||||
\(959\) | 43.9184 | 1.41820 | ||||||||
\(960\) | 3.23698 | 0.104473 | ||||||||
\(961\) | 90.8562 | 2.93084 | ||||||||
\(962\) | −38.0425 | −1.22654 | ||||||||
\(963\) | −3.78434 | −0.121949 | ||||||||
\(964\) | −0.0333992 | −0.00107572 | ||||||||
\(965\) | 42.8102 | 1.37811 | ||||||||
\(966\) | 60.9254 | 1.96024 | ||||||||
\(967\) | 9.73403 | 0.313025 | 0.156513 | − | 0.987676i | \(-0.449975\pi\) | ||||
0.156513 | + | 0.987676i | \(0.449975\pi\) | |||||||
\(968\) | −6.15477 | −0.197822 | ||||||||
\(969\) | −3.85995 | −0.124000 | ||||||||
\(970\) | −44.2297 | −1.42013 | ||||||||
\(971\) | 34.2720 | 1.09984 | 0.549920 | − | 0.835218i | \(-0.314658\pi\) | ||||
0.549920 | + | 0.835218i | \(0.314658\pi\) | |||||||
\(972\) | 1.29778 | 0.0416265 | ||||||||
\(973\) | −29.6746 | −0.951323 | ||||||||
\(974\) | 51.4218 | 1.64766 | ||||||||
\(975\) | −4.77892 | −0.153048 | ||||||||
\(976\) | 61.6619 | 1.97375 | ||||||||
\(977\) | −4.82773 | −0.154453 | −0.0772264 | − | 0.997014i | \(-0.524606\pi\) | ||||
−0.0772264 | + | 0.997014i | \(0.524606\pi\) | |||||||
\(978\) | 8.32782 | 0.266294 | ||||||||
\(979\) | 17.1898 | 0.549387 | ||||||||
\(980\) | −16.4244 | −0.524658 | ||||||||
\(981\) | 6.68734 | 0.213510 | ||||||||
\(982\) | 40.7072 | 1.29902 | ||||||||
\(983\) | 39.0588 | 1.24578 | 0.622891 | − | 0.782309i | \(-0.285958\pi\) | ||||
0.622891 | + | 0.782309i | \(0.285958\pi\) | |||||||
\(984\) | 1.56251 | 0.0498109 | ||||||||
\(985\) | −43.3423 | −1.38100 | ||||||||
\(986\) | −11.4248 | −0.363840 | ||||||||
\(987\) | 13.2843 | 0.422845 | ||||||||
\(988\) | 15.4608 | 0.491872 | ||||||||
\(989\) | −11.2210 | −0.356806 | ||||||||
\(990\) | 8.38277 | 0.266422 | ||||||||
\(991\) | −34.8477 | −1.10697 | −0.553487 | − | 0.832858i | \(-0.686703\pi\) | ||||
−0.553487 | + | 0.832858i | \(0.686703\pi\) | |||||||
\(992\) | 70.3003 | 2.23204 | ||||||||
\(993\) | −8.02086 | −0.254534 | ||||||||
\(994\) | −50.5050 | −1.60192 | ||||||||
\(995\) | 0.316217 | 0.0100248 | ||||||||
\(996\) | 10.1595 | 0.321917 | ||||||||
\(997\) | 2.66730 | 0.0844742 | 0.0422371 | − | 0.999108i | \(-0.486552\pi\) | ||||
0.0422371 | + | 0.999108i | \(0.486552\pi\) | |||||||
\(998\) | −11.6096 | −0.367496 | ||||||||
\(999\) | 6.78754 | 0.214748 |
(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 | 8007.2.a.h.1.11 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.h.1.11 | ✓ | 56 | 1.1 | even | 1 | trivial |