Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.904420 | −0.639522 | −0.319761 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319761 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.18202 | −0.591012 | ||||||||
\(5\) | −0.974726 | −0.435911 | −0.217955 | − | 0.975959i | \(-0.569939\pi\) | ||||
−0.217955 | + | 0.975959i | \(0.569939\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.87789 | 1.01749 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.881562 | 0.278774 | ||||||||
\(11\) | 1.96544 | 0.592603 | 0.296302 | − | 0.955094i | \(-0.404247\pi\) | ||||
0.296302 | + | 0.955094i | \(0.404247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74141 | 0.760330 | 0.380165 | − | 0.924919i | \(-0.375867\pi\) | ||||
0.380165 | + | 0.924919i | \(0.375867\pi\) | |||||||
\(14\) | 0.904420 | 0.241717 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.238773 | −0.0596931 | ||||||||
\(17\) | −1.83682 | −0.445495 | −0.222748 | − | 0.974876i | \(-0.571503\pi\) | ||||
−0.222748 | + | 0.974876i | \(0.571503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.02640 | 0.464889 | 0.232444 | − | 0.972610i | \(-0.425328\pi\) | ||||
0.232444 | + | 0.972610i | \(0.425328\pi\) | |||||||
\(20\) | 1.15215 | 0.257628 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.77759 | −0.378983 | ||||||||
\(23\) | −4.95844 | −1.03391 | −0.516953 | − | 0.856014i | \(-0.672934\pi\) | ||||
−0.516953 | + | 0.856014i | \(0.672934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04991 | −0.809982 | ||||||||
\(26\) | −2.47939 | −0.486248 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.18202 | 0.223381 | ||||||||
\(29\) | 5.22491 | 0.970242 | 0.485121 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485121 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.18264 | −0.212408 | −0.106204 | − | 0.994344i | \(-0.533870\pi\) | ||||
−0.106204 | + | 0.994344i | \(0.533870\pi\) | |||||||
\(32\) | −5.53982 | −0.979312 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.66126 | 0.284904 | ||||||||
\(35\) | 0.974726 | 0.164759 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.458876 | −0.0754388 | −0.0377194 | − | 0.999288i | \(-0.512009\pi\) | ||||
−0.0377194 | + | 0.999288i | \(0.512009\pi\) | |||||||
\(38\) | −1.83272 | −0.297307 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.80515 | −0.443533 | ||||||||
\(41\) | 4.63274 | 0.723512 | 0.361756 | − | 0.932273i | \(-0.382177\pi\) | ||||
0.361756 | + | 0.932273i | \(0.382177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.80048 | −1.49456 | −0.747280 | − | 0.664509i | \(-0.768641\pi\) | ||||
−0.747280 | + | 0.664509i | \(0.768641\pi\) | |||||||
\(44\) | −2.32320 | −0.350235 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.48451 | 0.661205 | ||||||||
\(47\) | −1.05030 | −0.153202 | −0.0766010 | − | 0.997062i | \(-0.524407\pi\) | ||||
−0.0766010 | + | 0.997062i | \(0.524407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.66282 | 0.518001 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.24041 | −0.449364 | ||||||||
\(53\) | 0.354557 | 0.0487021 | 0.0243511 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243511 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.91577 | −0.258322 | ||||||||
\(56\) | −2.87789 | −0.384574 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.72552 | −0.620491 | ||||||||
\(59\) | 2.99975 | 0.390534 | 0.195267 | − | 0.980750i | \(-0.437443\pi\) | ||||
0.195267 | + | 0.980750i | \(0.437443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7918 | 1.38174 | 0.690872 | − | 0.722977i | \(-0.257227\pi\) | ||||
0.690872 | + | 0.722977i | \(0.257227\pi\) | |||||||
\(62\) | 1.06960 | 0.135839 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.48787 | 0.685984 | ||||||||
\(65\) | −2.67212 | −0.331436 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3466 | −1.38621 | −0.693104 | − | 0.720837i | \(-0.743757\pi\) | ||||
−0.693104 | + | 0.720837i | \(0.743757\pi\) | |||||||
\(68\) | 2.17117 | 0.263293 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.881562 | −0.105367 | ||||||||
\(71\) | −11.1482 | −1.32305 | −0.661525 | − | 0.749923i | \(-0.730091\pi\) | ||||
−0.661525 | + | 0.749923i | \(0.730091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2419 | 1.78393 | 0.891966 | − | 0.452102i | \(-0.149326\pi\) | ||||
0.891966 | + | 0.452102i | \(0.149326\pi\) | |||||||
\(74\) | 0.415017 | 0.0482447 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.39526 | −0.274755 | ||||||||
\(77\) | −1.96544 | −0.223983 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8394 | −1.21953 | −0.609764 | − | 0.792583i | \(-0.708736\pi\) | ||||
−0.609764 | + | 0.792583i | \(0.708736\pi\) | |||||||
\(80\) | 0.232738 | 0.0260209 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.18994 | −0.462702 | ||||||||
\(83\) | 2.78288 | 0.305461 | 0.152730 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.79040 | 0.194196 | ||||||||
\(86\) | 8.86376 | 0.955804 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.65632 | 0.602966 | ||||||||
\(89\) | 5.79864 | 0.614655 | 0.307327 | − | 0.951604i | \(-0.400565\pi\) | ||||
0.307327 | + | 0.951604i | \(0.400565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74141 | −0.287378 | ||||||||
\(92\) | 5.86099 | 0.611051 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.949912 | 0.0979760 | ||||||||
\(95\) | −1.97519 | −0.202650 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0797 | 1.42957 | 0.714787 | − | 0.699343i | \(-0.246524\pi\) | ||||
0.714787 | + | 0.699343i | \(0.246524\pi\) | |||||||
\(98\) | −0.904420 | −0.0913603 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.78709 | 0.478709 | ||||||||
\(101\) | −18.6908 | −1.85980 | −0.929901 | − | 0.367809i | \(-0.880108\pi\) | ||||
−0.929901 | + | 0.367809i | \(0.880108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2067 | −1.10423 | −0.552114 | − | 0.833768i | \(-0.686179\pi\) | ||||
−0.552114 | + | 0.833768i | \(0.686179\pi\) | |||||||
\(104\) | 7.88947 | 0.773626 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.320668 | −0.0311461 | ||||||||
\(107\) | −0.851347 | −0.0823028 | −0.0411514 | − | 0.999153i | \(-0.513103\pi\) | ||||
−0.0411514 | + | 0.999153i | \(0.513103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.23394 | 0.501320 | 0.250660 | − | 0.968075i | \(-0.419352\pi\) | ||||
0.250660 | + | 0.968075i | \(0.419352\pi\) | |||||||
\(110\) | 1.73266 | 0.165203 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.238773 | 0.0225619 | ||||||||
\(113\) | 20.4549 | 1.92424 | 0.962118 | − | 0.272634i | \(-0.0878949\pi\) | ||||
0.962118 | + | 0.272634i | \(0.0878949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.83312 | 0.450690 | ||||||||
\(116\) | −6.17597 | −0.573424 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.71304 | −0.249755 | ||||||||
\(119\) | 1.83682 | 0.168381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.13704 | −0.648822 | ||||||||
\(122\) | −9.76030 | −0.883656 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.39790 | 0.125536 | ||||||||
\(125\) | 8.82118 | 0.788990 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 6.11630 | 0.540610 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.41672 | 0.211961 | ||||||||
\(131\) | 4.73386 | 0.413600 | 0.206800 | − | 0.978383i | \(-0.433695\pi\) | ||||
0.206800 | + | 0.978383i | \(0.433695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.02640 | −0.175712 | ||||||||
\(134\) | 10.2621 | 0.886511 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.28617 | −0.453285 | ||||||||
\(137\) | −2.27099 | −0.194024 | −0.0970118 | − | 0.995283i | \(-0.530928\pi\) | ||||
−0.0970118 | + | 0.995283i | \(0.530928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.52891 | −0.129680 | −0.0648402 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648402 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(140\) | −1.15215 | −0.0973743 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0827 | 0.846120 | ||||||||
\(143\) | 5.38808 | 0.450574 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.09286 | −0.422939 | ||||||||
\(146\) | −13.7851 | −1.14086 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.542402 | 0.0445852 | ||||||||
\(149\) | 3.83317 | 0.314025 | 0.157013 | − | 0.987597i | \(-0.449814\pi\) | ||||
0.157013 | + | 0.987597i | \(0.449814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1993 | −1.15553 | −0.577763 | − | 0.816205i | \(-0.696074\pi\) | ||||
−0.577763 | + | 0.816205i | \(0.696074\pi\) | |||||||
\(152\) | 5.83176 | 0.473018 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.77759 | 0.143242 | ||||||||
\(155\) | 1.15275 | 0.0925908 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.23858 | 0.418084 | 0.209042 | − | 0.977907i | \(-0.432965\pi\) | ||||
0.209042 | + | 0.977907i | \(0.432965\pi\) | |||||||
\(158\) | 9.80338 | 0.779915 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.39981 | 0.426892 | ||||||||
\(161\) | 4.95844 | 0.390780 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56149 | 0.278957 | 0.139479 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139479 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(164\) | −5.47601 | −0.427604 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.51689 | −0.195349 | ||||||||
\(167\) | 15.4593 | 1.19628 | 0.598140 | − | 0.801392i | \(-0.295907\pi\) | ||||
0.598140 | + | 0.801392i | \(0.295907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.48467 | −0.421898 | ||||||||
\(170\) | −1.61927 | −0.124193 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.5844 | 0.883303 | ||||||||
\(173\) | 13.8233 | 1.05097 | 0.525484 | − | 0.850804i | \(-0.323884\pi\) | ||||
0.525484 | + | 0.850804i | \(0.323884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.04991 | 0.306144 | ||||||||
\(176\) | −0.469294 | −0.0353743 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.24441 | −0.393085 | ||||||||
\(179\) | 24.2437 | 1.81206 | 0.906028 | − | 0.423218i | \(-0.139099\pi\) | ||||
0.906028 | + | 0.423218i | \(0.139099\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.1972 | −1.42692 | −0.713460 | − | 0.700696i | \(-0.752873\pi\) | ||||
−0.713460 | + | 0.700696i | \(0.752873\pi\) | |||||||
\(182\) | 2.47939 | 0.183784 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.2698 | −1.05199 | ||||||||
\(185\) | 0.447278 | 0.0328846 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.61017 | −0.264002 | ||||||||
\(188\) | 1.24148 | 0.0905442 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.78640 | 0.129599 | ||||||||
\(191\) | −7.51446 | −0.543727 | −0.271864 | − | 0.962336i | \(-0.587640\pi\) | ||||
−0.271864 | + | 0.962336i | \(0.587640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.90984 | −0.353418 | −0.176709 | − | 0.984263i | \(-0.556545\pi\) | ||||
−0.176709 | + | 0.984263i | \(0.556545\pi\) | |||||||
\(194\) | −12.7339 | −0.914243 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.18202 | −0.0844303 | ||||||||
\(197\) | 23.6073 | 1.68195 | 0.840975 | − | 0.541074i | \(-0.181982\pi\) | ||||
0.840975 | + | 0.541074i | \(0.181982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.60082 | −0.467920 | −0.233960 | − | 0.972246i | \(-0.575168\pi\) | ||||
−0.233960 | + | 0.972246i | \(0.575168\pi\) | |||||||
\(200\) | −11.6552 | −0.824146 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.9043 | 1.18938 | ||||||||
\(203\) | −5.22491 | −0.366717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.51565 | −0.315387 | ||||||||
\(206\) | 10.1356 | 0.706178 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.654573 | −0.0453865 | ||||||||
\(209\) | 3.98278 | 0.275495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9501 | −1.09805 | −0.549024 | − | 0.835806i | \(-0.685001\pi\) | ||||
−0.549024 | + | 0.835806i | \(0.685001\pi\) | |||||||
\(212\) | −0.419094 | −0.0287835 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.769976 | 0.0526345 | ||||||||
\(215\) | 9.55278 | 0.651494 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.18264 | 0.0802826 | ||||||||
\(218\) | −4.73368 | −0.320605 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.26448 | 0.152671 | ||||||||
\(221\) | −5.03549 | −0.338724 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.7130 | 0.717399 | 0.358699 | − | 0.933453i | \(-0.383220\pi\) | ||||
0.358699 | + | 0.933453i | \(0.383220\pi\) | |||||||
\(224\) | 5.53982 | 0.370145 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.4998 | −1.23059 | ||||||||
\(227\) | −3.94057 | −0.261545 | −0.130772 | − | 0.991412i | \(-0.541746\pi\) | ||||
−0.130772 | + | 0.991412i | \(0.541746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.2625 | −1.20682 | −0.603409 | − | 0.797432i | \(-0.706191\pi\) | ||||
−0.603409 | + | 0.797432i | \(0.706191\pi\) | |||||||
\(230\) | −4.37117 | −0.288226 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.0367 | 0.987208 | ||||||||
\(233\) | 8.66383 | 0.567587 | 0.283793 | − | 0.958885i | \(-0.408407\pi\) | ||||
0.283793 | + | 0.958885i | \(0.408407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02375 | 0.0667823 | ||||||||
\(236\) | −3.54578 | −0.230810 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.66126 | −0.107684 | ||||||||
\(239\) | 3.60516 | 0.233198 | 0.116599 | − | 0.993179i | \(-0.462801\pi\) | ||||
0.116599 | + | 0.993179i | \(0.462801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.19669 | −0.399164 | −0.199582 | − | 0.979881i | \(-0.563958\pi\) | ||||
−0.199582 | + | 0.979881i | \(0.563958\pi\) | |||||||
\(242\) | 6.45488 | 0.414936 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.7561 | −0.816628 | ||||||||
\(245\) | −0.974726 | −0.0622729 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.55520 | 0.353469 | ||||||||
\(248\) | −3.40350 | −0.216122 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.97805 | −0.504576 | ||||||||
\(251\) | 0.903566 | 0.0570326 | 0.0285163 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285163 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.74552 | −0.612696 | ||||||||
\(254\) | 0.904420 | 0.0567484 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.5075 | −1.03172 | ||||||||
\(257\) | −8.84869 | −0.551966 | −0.275983 | − | 0.961162i | \(-0.589003\pi\) | ||||
−0.275983 | + | 0.961162i | \(0.589003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.458876 | 0.0285132 | ||||||||
\(260\) | 3.15851 | 0.195883 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.28140 | −0.264506 | ||||||||
\(263\) | 1.87830 | 0.115821 | 0.0579104 | − | 0.998322i | \(-0.481556\pi\) | ||||
0.0579104 | + | 0.998322i | \(0.481556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.345595 | −0.0212298 | ||||||||
\(266\) | 1.83272 | 0.112371 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.4120 | 0.819266 | ||||||||
\(269\) | −27.5980 | −1.68268 | −0.841339 | − | 0.540507i | \(-0.818232\pi\) | ||||
−0.841339 | + | 0.540507i | \(0.818232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.69809 | −0.103151 | −0.0515757 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515757 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(272\) | 0.438583 | 0.0265930 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.05393 | 0.124082 | ||||||||
\(275\) | −7.95986 | −0.479998 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.81718 | −0.469689 | −0.234844 | − | 0.972033i | \(-0.575458\pi\) | ||||
−0.234844 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(278\) | 1.38278 | 0.0829334 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.80515 | 0.167640 | ||||||||
\(281\) | 27.2136 | 1.62343 | 0.811713 | − | 0.584056i | \(-0.198535\pi\) | ||||
0.811713 | + | 0.584056i | \(0.198535\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2507 | −1.67933 | −0.839663 | − | 0.543107i | \(-0.817248\pi\) | ||||
−0.839663 | + | 0.543107i | \(0.817248\pi\) | |||||||
\(284\) | 13.1775 | 0.781939 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.87309 | −0.288152 | ||||||||
\(287\) | −4.63274 | −0.273462 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6261 | −0.801534 | ||||||||
\(290\) | 4.60608 | 0.270478 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.0163 | −1.05433 | ||||||||
\(293\) | −28.5553 | −1.66822 | −0.834108 | − | 0.551601i | \(-0.814017\pi\) | ||||
−0.834108 | + | 0.551601i | \(0.814017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.92393 | −0.170238 | ||||||||
\(296\) | −1.32059 | −0.0767579 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.46679 | −0.200826 | ||||||||
\(299\) | −13.5931 | −0.786110 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.80048 | 0.564891 | ||||||||
\(302\) | 12.8422 | 0.738984 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.483850 | −0.0277507 | ||||||||
\(305\) | −10.5190 | −0.602317 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.6944 | 1.58060 | 0.790301 | − | 0.612719i | \(-0.209924\pi\) | ||||
0.790301 | + | 0.612719i | \(0.209924\pi\) | |||||||
\(308\) | 2.32320 | 0.132377 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.04257 | −0.0592139 | ||||||||
\(311\) | 9.66622 | 0.548121 | 0.274061 | − | 0.961712i | \(-0.411633\pi\) | ||||
0.274061 | + | 0.961712i | \(0.411633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.52701 | 0.312405 | 0.156203 | − | 0.987725i | \(-0.450075\pi\) | ||||
0.156203 | + | 0.987725i | \(0.450075\pi\) | |||||||
\(314\) | −4.73788 | −0.267374 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.8124 | 0.720756 | ||||||||
\(317\) | 11.9503 | 0.671193 | 0.335597 | − | 0.942006i | \(-0.391062\pi\) | ||||
0.335597 | + | 0.942006i | \(0.391062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.2693 | 0.574968 | ||||||||
\(320\) | −5.34917 | −0.299028 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.48451 | −0.249912 | ||||||||
\(323\) | −3.72215 | −0.207106 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.1025 | −0.615854 | ||||||||
\(326\) | −3.22108 | −0.178399 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.3325 | 0.736164 | ||||||||
\(329\) | 1.05030 | 0.0579049 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3085 | −0.841432 | −0.420716 | − | 0.907192i | \(-0.638221\pi\) | ||||
−0.420716 | + | 0.907192i | \(0.638221\pi\) | |||||||
\(332\) | −3.28943 | −0.180531 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.9817 | −0.765047 | ||||||||
\(335\) | 11.0598 | 0.604263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.6748 | −1.34412 | −0.672062 | − | 0.740495i | \(-0.734591\pi\) | ||||
−0.672062 | + | 0.740495i | \(0.734591\pi\) | |||||||
\(338\) | 4.96045 | 0.269813 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.11629 | −0.114772 | ||||||||
\(341\) | −2.32440 | −0.125874 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −28.2047 | −1.52069 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.5021 | −0.672117 | ||||||||
\(347\) | 16.4238 | 0.881674 | 0.440837 | − | 0.897587i | \(-0.354682\pi\) | ||||
0.440837 | + | 0.897587i | \(0.354682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5558 | −0.779156 | −0.389578 | − | 0.920994i | \(-0.627379\pi\) | ||||
−0.389578 | + | 0.920994i | \(0.627379\pi\) | |||||||
\(350\) | −3.66282 | −0.195786 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.8882 | −0.580343 | ||||||||
\(353\) | −6.68260 | −0.355679 | −0.177839 | − | 0.984060i | \(-0.556911\pi\) | ||||
−0.177839 | + | 0.984060i | \(0.556911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8665 | 0.576732 | ||||||||
\(356\) | −6.85413 | −0.363268 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.9265 | −1.15885 | ||||||||
\(359\) | −31.4312 | −1.65888 | −0.829439 | − | 0.558598i | \(-0.811340\pi\) | ||||
−0.829439 | + | 0.558598i | \(0.811340\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8937 | −0.783878 | ||||||||
\(362\) | 17.3624 | 0.912547 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.24041 | 0.169844 | ||||||||
\(365\) | −14.8567 | −0.777635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.1243 | −1.72907 | −0.864537 | − | 0.502570i | \(-0.832388\pi\) | ||||
−0.864537 | + | 0.502570i | \(0.832388\pi\) | |||||||
\(368\) | 1.18394 | 0.0617171 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.404528 | −0.0210304 | ||||||||
\(371\) | −0.354557 | −0.0184077 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3474 | −0.742883 | −0.371441 | − | 0.928456i | \(-0.621136\pi\) | ||||
−0.371441 | + | 0.928456i | \(0.621136\pi\) | |||||||
\(374\) | 3.26511 | 0.168835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.02264 | −0.155881 | ||||||||
\(377\) | 14.3236 | 0.737704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7475 | 0.552061 | 0.276031 | − | 0.961149i | \(-0.410981\pi\) | ||||
0.276031 | + | 0.961149i | \(0.410981\pi\) | |||||||
\(380\) | 2.33472 | 0.119769 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.79623 | 0.347725 | ||||||||
\(383\) | −15.3578 | −0.784746 | −0.392373 | − | 0.919806i | \(-0.628346\pi\) | ||||
−0.392373 | + | 0.919806i | \(0.628346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.91577 | 0.0976365 | ||||||||
\(386\) | 4.44056 | 0.226019 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.6425 | −0.844895 | ||||||||
\(389\) | −26.9989 | −1.36890 | −0.684449 | − | 0.729061i | \(-0.739957\pi\) | ||||
−0.684449 | + | 0.729061i | \(0.739957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.10778 | 0.460600 | ||||||||
\(392\) | 2.87789 | 0.145355 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.3509 | −1.07564 | ||||||||
\(395\) | 10.5654 | 0.531605 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.42370 | 0.472962 | 0.236481 | − | 0.971636i | \(-0.424006\pi\) | ||||
0.236481 | + | 0.971636i | \(0.424006\pi\) | |||||||
\(398\) | 5.96992 | 0.299245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.967007 | 0.0483504 | ||||||||
\(401\) | 27.0326 | 1.34994 | 0.674972 | − | 0.737843i | \(-0.264155\pi\) | ||||
0.674972 | + | 0.737843i | \(0.264155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.24209 | −0.161500 | ||||||||
\(404\) | 22.0929 | 1.09917 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.72552 | 0.234523 | ||||||||
\(407\) | −0.901894 | −0.0447052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.53002 | −0.0756546 | −0.0378273 | − | 0.999284i | \(-0.512044\pi\) | ||||
−0.0378273 | + | 0.999284i | \(0.512044\pi\) | |||||||
\(410\) | 4.08405 | 0.201697 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.2466 | 0.652612 | ||||||||
\(413\) | −2.99975 | −0.147608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.71254 | −0.133153 | ||||||||
\(416\) | −15.1869 | −0.744600 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.60211 | −0.176185 | ||||||||
\(419\) | −24.5561 | −1.19964 | −0.599821 | − | 0.800134i | \(-0.704761\pi\) | ||||
−0.599821 | + | 0.800134i | \(0.704761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0319 | −0.830082 | −0.415041 | − | 0.909803i | \(-0.636233\pi\) | ||||
−0.415041 | + | 0.909803i | \(0.636233\pi\) | |||||||
\(422\) | 14.4256 | 0.702226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.02037 | 0.0495538 | ||||||||
\(425\) | 7.43897 | 0.360843 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7918 | −0.522250 | ||||||||
\(428\) | 1.00631 | 0.0486420 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.63973 | −0.416645 | ||||||||
\(431\) | −19.1165 | −0.920807 | −0.460404 | − | 0.887710i | \(-0.652295\pi\) | ||||
−0.460404 | + | 0.887710i | \(0.652295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.3990 | −0.980314 | −0.490157 | − | 0.871634i | \(-0.663061\pi\) | ||||
−0.490157 | + | 0.871634i | \(0.663061\pi\) | |||||||
\(434\) | −1.06960 | −0.0513425 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.18664 | −0.296286 | ||||||||
\(437\) | −10.0478 | −0.480651 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7152 | 1.22732 | 0.613661 | − | 0.789570i | \(-0.289696\pi\) | ||||
0.613661 | + | 0.789570i | \(0.289696\pi\) | |||||||
\(440\) | −5.51336 | −0.262839 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.55420 | 0.216621 | ||||||||
\(443\) | 1.86722 | 0.0887145 | 0.0443572 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443572 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.65209 | −0.267935 | ||||||||
\(446\) | −9.68910 | −0.458792 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.48787 | −0.259278 | ||||||||
\(449\) | −31.0418 | −1.46495 | −0.732477 | − | 0.680792i | \(-0.761636\pi\) | ||||
−0.732477 | + | 0.680792i | \(0.761636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.10538 | 0.428756 | ||||||||
\(452\) | −24.1782 | −1.13725 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.56393 | 0.167264 | ||||||||
\(455\) | 2.67212 | 0.125271 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.64753 | −0.310958 | −0.155479 | − | 0.987839i | \(-0.549692\pi\) | ||||
−0.155479 | + | 0.987839i | \(0.549692\pi\) | |||||||
\(458\) | 16.5170 | 0.771787 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.71286 | −0.266363 | ||||||||
\(461\) | −39.1504 | −1.82342 | −0.911709 | − | 0.410837i | \(-0.865237\pi\) | ||||
−0.911709 | + | 0.410837i | \(0.865237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.32152 | 0.154364 | 0.0771821 | − | 0.997017i | \(-0.475408\pi\) | ||||
0.0771821 | + | 0.997017i | \(0.475408\pi\) | |||||||
\(464\) | −1.24757 | −0.0579168 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.83575 | −0.362984 | ||||||||
\(467\) | 4.67881 | 0.216509 | 0.108255 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108255 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3466 | 0.523938 | ||||||||
\(470\) | −0.925904 | −0.0427088 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.63294 | 0.397363 | ||||||||
\(473\) | −19.2623 | −0.885681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.20675 | −0.376552 | ||||||||
\(476\) | −2.17117 | −0.0995154 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.26058 | −0.149135 | ||||||||
\(479\) | 13.8988 | 0.635054 | 0.317527 | − | 0.948249i | \(-0.397148\pi\) | ||||
0.317527 | + | 0.948249i | \(0.397148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25797 | −0.0573584 | ||||||||
\(482\) | 5.60442 | 0.255274 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.43615 | 0.383461 | ||||||||
\(485\) | −13.7238 | −0.623166 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.1874 | 1.82106 | 0.910532 | − | 0.413439i | \(-0.135673\pi\) | ||||
0.910532 | + | 0.413439i | \(0.135673\pi\) | |||||||
\(488\) | 31.0575 | 1.40591 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.881562 | 0.0398249 | ||||||||
\(491\) | −19.5893 | −0.884052 | −0.442026 | − | 0.897002i | \(-0.645740\pi\) | ||||
−0.442026 | + | 0.897002i | \(0.645740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.59724 | −0.432238 | ||||||||
\(494\) | −5.02424 | −0.226051 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.282381 | 0.0126793 | ||||||||
\(497\) | 11.1482 | 0.500066 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0588 | −0.539826 | −0.269913 | − | 0.962885i | \(-0.586995\pi\) | ||||
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(500\) | −10.4268 | −0.466303 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.817203 | −0.0364736 | ||||||||
\(503\) | 16.7958 | 0.748889 | 0.374444 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374444 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.2184 | 0.810707 | ||||||||
\(506\) | 8.81405 | 0.391832 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.18202 | 0.0524438 | ||||||||
\(509\) | 3.01771 | 0.133758 | 0.0668789 | − | 0.997761i | \(-0.478696\pi\) | ||||
0.0668789 | + | 0.997761i | \(0.478696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.2419 | −0.674263 | ||||||||
\(512\) | 2.69708 | 0.119195 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.00294 | 0.352994 | ||||||||
\(515\) | 10.9235 | 0.481345 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.06430 | −0.0907880 | ||||||||
\(518\) | −0.415017 | −0.0182348 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.69007 | −0.337232 | ||||||||
\(521\) | −39.2726 | −1.72056 | −0.860281 | − | 0.509819i | \(-0.829712\pi\) | ||||
−0.860281 | + | 0.509819i | \(0.829712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.32811 | −0.364163 | −0.182081 | − | 0.983283i | \(-0.558283\pi\) | ||||
−0.182081 | + | 0.983283i | \(0.558283\pi\) | |||||||
\(524\) | −5.59554 | −0.244442 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.69877 | −0.0740700 | ||||||||
\(527\) | 2.17230 | 0.0946267 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.58611 | 0.0689615 | ||||||||
\(530\) | 0.312564 | 0.0135769 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.39526 | 0.103848 | ||||||||
\(533\) | 12.7002 | 0.550108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.829830 | 0.0358767 | ||||||||
\(536\) | −32.6542 | −1.41045 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.9602 | 1.07611 | ||||||||
\(539\) | 1.96544 | 0.0846576 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.5876 | 1.10010 | 0.550048 | − | 0.835133i | \(-0.314609\pi\) | ||||
0.550048 | + | 0.835133i | \(0.314609\pi\) | |||||||
\(542\) | 1.53579 | 0.0659676 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.1757 | 0.436279 | ||||||||
\(545\) | −5.10165 | −0.218531 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.33215 | −0.399014 | −0.199507 | − | 0.979896i | \(-0.563934\pi\) | ||||
−0.199507 | + | 0.979896i | \(0.563934\pi\) | |||||||
\(548\) | 2.68436 | 0.114670 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.19906 | 0.306969 | ||||||||
\(551\) | 10.5878 | 0.451055 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8394 | 0.460939 | ||||||||
\(554\) | 7.07001 | 0.300376 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.80721 | 0.0766426 | ||||||||
\(557\) | 29.0421 | 1.23055 | 0.615276 | − | 0.788312i | \(-0.289045\pi\) | ||||
0.615276 | + | 0.788312i | \(0.289045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.8671 | −1.13636 | ||||||||
\(560\) | −0.232738 | −0.00983496 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.6125 | −1.03822 | ||||||||
\(563\) | −42.9533 | −1.81027 | −0.905134 | − | 0.425127i | \(-0.860229\pi\) | ||||
−0.905134 | + | 0.425127i | \(0.860229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.9379 | −0.838795 | ||||||||
\(566\) | 25.5505 | 1.07397 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.0833 | −1.34619 | ||||||||
\(569\) | 17.8917 | 0.750060 | 0.375030 | − | 0.927013i | \(-0.377632\pi\) | ||||
0.375030 | + | 0.927013i | \(0.377632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4317 | 0.687646 | 0.343823 | − | 0.939035i | \(-0.388278\pi\) | ||||
0.343823 | + | 0.939035i | \(0.388278\pi\) | |||||||
\(572\) | −6.36884 | −0.266295 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.18994 | 0.174885 | ||||||||
\(575\) | 20.0812 | 0.837445 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.9708 | −1.87216 | −0.936079 | − | 0.351789i | \(-0.885574\pi\) | ||||
−0.936079 | + | 0.351789i | \(0.885574\pi\) | |||||||
\(578\) | 12.3237 | 0.512598 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.01988 | 0.249962 | ||||||||
\(581\) | −2.78288 | −0.115453 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.696861 | 0.0288610 | ||||||||
\(584\) | 43.8646 | 1.81513 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8260 | 1.06686 | ||||||||
\(587\) | 6.71570 | 0.277186 | 0.138593 | − | 0.990349i | \(-0.455742\pi\) | ||||
0.138593 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.39650 | −0.0987461 | ||||||||
\(590\) | 2.64446 | 0.108871 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.109567 | 0.00450318 | ||||||||
\(593\) | 16.3420 | 0.671085 | 0.335543 | − | 0.942025i | \(-0.391080\pi\) | ||||
0.335543 | + | 0.942025i | \(0.391080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.79040 | −0.0733992 | ||||||||
\(596\) | −4.53089 | −0.185593 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.2939 | 0.502735 | ||||||||
\(599\) | 18.6301 | 0.761207 | 0.380603 | − | 0.924738i | \(-0.375716\pi\) | ||||
0.380603 | + | 0.924738i | \(0.375716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0537 | 0.777217 | 0.388608 | − | 0.921403i | \(-0.372956\pi\) | ||||
0.388608 | + | 0.921403i | \(0.372956\pi\) | |||||||
\(602\) | −8.86376 | −0.361260 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.7839 | 0.682929 | ||||||||
\(605\) | 6.95665 | 0.282828 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.4627 | −1.84527 | −0.922636 | − | 0.385672i | \(-0.873970\pi\) | ||||
−0.922636 | + | 0.385672i | \(0.873970\pi\) | |||||||
\(608\) | −11.2259 | −0.455271 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.51361 | 0.385195 | ||||||||
\(611\) | −2.87930 | −0.116484 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.9261 | 1.69338 | 0.846689 | − | 0.532088i | \(-0.178592\pi\) | ||||
0.846689 | + | 0.532088i | \(0.178592\pi\) | |||||||
\(614\) | −25.0474 | −1.01083 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.65632 | −0.227900 | ||||||||
\(617\) | −26.3445 | −1.06059 | −0.530295 | − | 0.847813i | \(-0.677919\pi\) | ||||
−0.530295 | + | 0.847813i | \(0.677919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.1455 | 0.608748 | 0.304374 | − | 0.952553i | \(-0.401553\pi\) | ||||
0.304374 | + | 0.952553i | \(0.401553\pi\) | |||||||
\(620\) | −1.36257 | −0.0547223 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.74233 | −0.350536 | ||||||||
\(623\) | −5.79864 | −0.232318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6513 | 0.466053 | ||||||||
\(626\) | −4.99874 | −0.199790 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.19213 | −0.247093 | ||||||||
\(629\) | 0.842875 | 0.0336076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.6323 | 1.49812 | 0.749060 | − | 0.662502i | \(-0.230506\pi\) | ||||
0.749060 | + | 0.662502i | \(0.230506\pi\) | |||||||
\(632\) | −31.1946 | −1.24085 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.8081 | −0.429243 | ||||||||
\(635\) | 0.974726 | 0.0386808 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.74141 | 0.108619 | ||||||||
\(638\) | −9.28773 | −0.367705 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.96172 | −0.235657 | ||||||||
\(641\) | 16.6216 | 0.656513 | 0.328256 | − | 0.944589i | \(-0.393539\pi\) | ||||
0.328256 | + | 0.944589i | \(0.393539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.1067 | −1.54222 | −0.771109 | − | 0.636703i | \(-0.780298\pi\) | ||||
−0.771109 | + | 0.636703i | \(0.780298\pi\) | |||||||
\(644\) | −5.86099 | −0.230955 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.36639 | 0.132449 | ||||||||
\(647\) | −42.9546 | −1.68872 | −0.844360 | − | 0.535776i | \(-0.820019\pi\) | ||||
−0.844360 | + | 0.535776i | \(0.820019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.89584 | 0.231432 | ||||||||
\(650\) | 10.0413 | 0.393852 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.20976 | −0.164867 | ||||||||
\(653\) | −23.8090 | −0.931719 | −0.465859 | − | 0.884859i | \(-0.654255\pi\) | ||||
−0.465859 | + | 0.884859i | \(0.654255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.61422 | −0.180292 | ||||||||
\(656\) | −1.10617 | −0.0431887 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.949912 | −0.0370314 | ||||||||
\(659\) | 30.9550 | 1.20583 | 0.602917 | − | 0.797804i | \(-0.294005\pi\) | ||||
0.602917 | + | 0.797804i | \(0.294005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.0899 | −1.13147 | −0.565733 | − | 0.824588i | \(-0.691407\pi\) | ||||
−0.565733 | + | 0.824588i | \(0.691407\pi\) | |||||||
\(662\) | 13.8453 | 0.538114 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00881 | 0.310802 | ||||||||
\(665\) | 1.97519 | 0.0765945 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.9074 | −1.00314 | ||||||||
\(668\) | −18.2733 | −0.707015 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0027 | −0.386439 | ||||||||
\(671\) | 21.2106 | 0.818826 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.04793 | −0.117489 | −0.0587446 | − | 0.998273i | \(-0.518710\pi\) | ||||
−0.0587446 | + | 0.998273i | \(0.518710\pi\) | |||||||
\(674\) | 22.3164 | 0.859597 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.48301 | 0.249347 | ||||||||
\(677\) | −29.7290 | −1.14258 | −0.571289 | − | 0.820749i | \(-0.693556\pi\) | ||||
−0.571289 | + | 0.820749i | \(0.693556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.0797 | −0.540328 | ||||||||
\(680\) | 5.15257 | 0.197592 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.10224 | 0.0804989 | ||||||||
\(683\) | −28.7088 | −1.09851 | −0.549256 | − | 0.835654i | \(-0.685089\pi\) | ||||
−0.549256 | + | 0.835654i | \(0.685089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.21359 | 0.0845770 | ||||||||
\(686\) | 0.904420 | 0.0345309 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.34009 | 0.0892149 | ||||||||
\(689\) | 0.971985 | 0.0370297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.9473 | −1.40554 | −0.702772 | − | 0.711416i | \(-0.748054\pi\) | ||||
−0.702772 | + | 0.711416i | \(0.748054\pi\) | |||||||
\(692\) | −16.3395 | −0.621134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.8540 | −0.563850 | ||||||||
\(695\) | 1.49027 | 0.0565290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.50953 | −0.322321 | ||||||||
\(698\) | 13.1646 | 0.498287 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.78709 | −0.180935 | ||||||||
\(701\) | −3.28373 | −0.124025 | −0.0620123 | − | 0.998075i | \(-0.519752\pi\) | ||||
−0.0620123 | + | 0.998075i | \(0.519752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.929868 | −0.0350707 | ||||||||
\(704\) | 10.7861 | 0.406516 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.04388 | 0.227464 | ||||||||
\(707\) | 18.6908 | 0.702939 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0439 | 0.489874 | 0.244937 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244937 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(710\) | −9.82784 | −0.368832 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.6878 | 0.625403 | ||||||||
\(713\) | 5.86403 | 0.219610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.25190 | −0.196410 | ||||||||
\(716\) | −28.6566 | −1.07095 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.4271 | 1.06089 | ||||||||
\(719\) | −22.6400 | −0.844329 | −0.422165 | − | 0.906519i | \(-0.638730\pi\) | ||||
−0.422165 | + | 0.906519i | \(0.638730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2067 | 0.417359 | ||||||||
\(722\) | 13.4702 | 0.501307 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.6916 | 0.843327 | ||||||||
\(725\) | −21.1604 | −0.785878 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.0887 | −0.485435 | −0.242717 | − | 0.970097i | \(-0.578039\pi\) | ||||
−0.242717 | + | 0.970097i | \(0.578039\pi\) | |||||||
\(728\) | −7.88947 | −0.292403 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.4367 | 0.497315 | ||||||||
\(731\) | 18.0018 | 0.665819 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.28284 | 0.0473828 | 0.0236914 | − | 0.999719i | \(-0.492458\pi\) | ||||
0.0236914 | + | 0.999719i | \(0.492458\pi\) | |||||||
\(734\) | 29.9583 | 1.10578 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.4689 | 1.01252 | ||||||||
\(737\) | −22.3011 | −0.821471 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5084 | −0.938341 | −0.469171 | − | 0.883108i | \(-0.655447\pi\) | ||||
−0.469171 | + | 0.883108i | \(0.655447\pi\) | |||||||
\(740\) | −0.528693 | −0.0194352 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.320668 | 0.0117721 | ||||||||
\(743\) | 7.17039 | 0.263056 | 0.131528 | − | 0.991312i | \(-0.458012\pi\) | ||||
0.131528 | + | 0.991312i | \(0.458012\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.73629 | −0.136887 | ||||||||
\(746\) | 12.9761 | 0.475090 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.26731 | 0.156028 | ||||||||
\(749\) | 0.851347 | 0.0311076 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.47503 | −0.126805 | −0.0634027 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634027 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(752\) | 0.250783 | 0.00914510 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.9546 | −0.471778 | ||||||||
\(755\) | 13.8405 | 0.503706 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2740 | 0.882254 | 0.441127 | − | 0.897445i | \(-0.354579\pi\) | ||||
0.441127 | + | 0.897445i | \(0.354579\pi\) | |||||||
\(758\) | −9.72025 | −0.353055 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.68437 | −0.206194 | ||||||||
\(761\) | −18.2719 | −0.662355 | −0.331178 | − | 0.943568i | \(-0.607446\pi\) | ||||
−0.331178 | + | 0.943568i | \(0.607446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.23394 | −0.189481 | ||||||||
\(764\) | 8.88227 | 0.321349 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.8899 | 0.501862 | ||||||||
\(767\) | 8.22355 | 0.296935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0830 | 0.363601 | 0.181801 | − | 0.983335i | \(-0.441807\pi\) | ||||
0.181801 | + | 0.983335i | \(0.441807\pi\) | |||||||
\(770\) | −1.73266 | −0.0624407 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.80355 | 0.208874 | ||||||||
\(773\) | 17.1958 | 0.618490 | 0.309245 | − | 0.950982i | \(-0.399924\pi\) | ||||
0.309245 | + | 0.950982i | \(0.399924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.78957 | 0.172047 | ||||||||
\(776\) | 40.5197 | 1.45457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.4183 | 0.875440 | ||||||||
\(779\) | 9.38780 | 0.336353 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.9112 | −0.784044 | ||||||||
\(782\) | −8.23726 | −0.294564 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.238773 | −0.00852759 | ||||||||
\(785\) | −5.10618 | −0.182247 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.09963 | 0.217428 | 0.108714 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108714 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(788\) | −27.9044 | −0.994053 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.55561 | −0.339973 | ||||||||
\(791\) | −20.4549 | −0.727293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.5847 | 1.05058 | ||||||||
\(794\) | −8.52299 | −0.302470 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.80233 | 0.276546 | ||||||||
\(797\) | 12.7977 | 0.453318 | 0.226659 | − | 0.973974i | \(-0.427220\pi\) | ||||
0.226659 | + | 0.973974i | \(0.427220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92922 | 0.0682507 | ||||||||
\(800\) | 22.4358 | 0.793225 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.4489 | −0.863319 | ||||||||
\(803\) | 29.9571 | 1.05716 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.83312 | −0.170345 | ||||||||
\(806\) | 2.93222 | 0.103283 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −53.7900 | −1.89232 | ||||||||
\(809\) | −8.95423 | −0.314814 | −0.157407 | − | 0.987534i | \(-0.550313\pi\) | ||||
−0.157407 | + | 0.987534i | \(0.550313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.49580 | −0.0525247 | −0.0262623 | − | 0.999655i | \(-0.508361\pi\) | ||||
−0.0262623 | + | 0.999655i | \(0.508361\pi\) | |||||||
\(812\) | 6.17597 | 0.216734 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.815692 | 0.0285900 | ||||||||
\(815\) | −3.47147 | −0.121600 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.8597 | −0.694804 | ||||||||
\(818\) | 1.38378 | 0.0483828 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.33761 | 0.186397 | ||||||||
\(821\) | −53.6744 | −1.87325 | −0.936625 | − | 0.350334i | \(-0.886068\pi\) | ||||
−0.936625 | + | 0.350334i | \(0.886068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.21268 | −0.321134 | −0.160567 | − | 0.987025i | \(-0.551332\pi\) | ||||
−0.160567 | + | 0.987025i | \(0.551332\pi\) | |||||||
\(824\) | −32.2516 | −1.12354 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.71304 | 0.0943986 | ||||||||
\(827\) | 47.7919 | 1.66189 | 0.830944 | − | 0.556356i | \(-0.187801\pi\) | ||||
0.830944 | + | 0.556356i | \(0.187801\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.8026 | 0.444654 | 0.222327 | − | 0.974972i | \(-0.428635\pi\) | ||||
0.222327 | + | 0.974972i | \(0.428635\pi\) | |||||||
\(830\) | 2.45328 | 0.0851546 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.0445 | 0.521575 | ||||||||
\(833\) | −1.83682 | −0.0636422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0686 | −0.521471 | ||||||||
\(836\) | −4.70774 | −0.162821 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.2090 | 0.767197 | ||||||||
\(839\) | 26.8790 | 0.927965 | 0.463982 | − | 0.885844i | \(-0.346420\pi\) | ||||
0.463982 | + | 0.885844i | \(0.346420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.70029 | −0.0586307 | ||||||||
\(842\) | 15.4040 | 0.530856 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.8534 | 0.648960 | ||||||||
\(845\) | 5.34605 | 0.183910 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.13704 | 0.245232 | ||||||||
\(848\) | −0.0846584 | −0.00290718 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.72796 | −0.230767 | ||||||||
\(851\) | 2.27531 | 0.0779966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.36355 | −0.0466870 | −0.0233435 | − | 0.999728i | \(-0.507431\pi\) | ||||
−0.0233435 | + | 0.999728i | \(0.507431\pi\) | |||||||
\(854\) | 9.76030 | 0.333991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.45008 | −0.0837421 | ||||||||
\(857\) | 25.6174 | 0.875075 | 0.437537 | − | 0.899200i | \(-0.355851\pi\) | ||||
0.437537 | + | 0.899200i | \(0.355851\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.9662 | −0.885956 | −0.442978 | − | 0.896532i | \(-0.646078\pi\) | ||||
−0.442978 | + | 0.896532i | \(0.646078\pi\) | |||||||
\(860\) | −11.2916 | −0.385041 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.2893 | 0.588876 | ||||||||
\(863\) | −28.3650 | −0.965554 | −0.482777 | − | 0.875743i | \(-0.660372\pi\) | ||||
−0.482777 | + | 0.875743i | \(0.660372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4739 | −0.458128 | ||||||||
\(866\) | 18.4493 | 0.626932 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.39790 | −0.0474480 | ||||||||
\(869\) | −21.3042 | −0.722696 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.1057 | −1.05398 | ||||||||
\(872\) | 15.0627 | 0.510087 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.08744 | 0.307387 | ||||||||
\(875\) | −8.82118 | −0.298210 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1836 | 0.411411 | 0.205705 | − | 0.978614i | \(-0.434051\pi\) | ||||
0.205705 | + | 0.978614i | \(0.434051\pi\) | |||||||
\(878\) | −23.2574 | −0.784899 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.457432 | 0.0154200 | ||||||||
\(881\) | 14.3304 | 0.482804 | 0.241402 | − | 0.970425i | \(-0.422393\pi\) | ||||
0.241402 | + | 0.970425i | \(0.422393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.3214 | −1.72710 | −0.863552 | − | 0.504260i | \(-0.831765\pi\) | ||||
−0.863552 | + | 0.504260i | \(0.831765\pi\) | |||||||
\(884\) | 5.95207 | 0.200190 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.68876 | −0.0567348 | ||||||||
\(887\) | 24.4353 | 0.820458 | 0.410229 | − | 0.911982i | \(-0.365449\pi\) | ||||
0.410229 | + | 0.911982i | \(0.365449\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 5.11186 | 0.171350 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6631 | −0.423991 | ||||||||
\(893\) | −2.12833 | −0.0712219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.6309 | −0.789894 | ||||||||
\(896\) | −6.11630 | −0.204331 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.0748 | 0.936869 | ||||||||
\(899\) | −6.17917 | −0.206087 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.651258 | −0.0216966 | ||||||||
\(902\) | −8.23509 | −0.274199 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 58.8669 | 1.95788 | ||||||||
\(905\) | 18.7120 | 0.622010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.7487 | 0.954584 | 0.477292 | − | 0.878745i | \(-0.341618\pi\) | ||||
0.477292 | + | 0.878745i | \(0.341618\pi\) | |||||||
\(908\) | 4.65785 | 0.154576 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.41672 | −0.0801136 | ||||||||
\(911\) | −27.4863 | −0.910662 | −0.455331 | − | 0.890322i | \(-0.650479\pi\) | ||||
−0.455331 | + | 0.890322i | \(0.650479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.46959 | 0.181017 | ||||||||
\(914\) | 6.01216 | 0.198865 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.5867 | 0.713244 | ||||||||
\(917\) | −4.73386 | −0.156326 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.9691 | −0.526771 | −0.263385 | − | 0.964691i | \(-0.584839\pi\) | ||||
−0.263385 | + | 0.964691i | \(0.584839\pi\) | |||||||
\(920\) | 13.9092 | 0.458572 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35.4085 | 1.16612 | ||||||||
\(923\) | −30.5618 | −1.00596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.85841 | 0.0611040 | ||||||||
\(926\) | −3.00405 | −0.0987193 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.9451 | −0.950169 | ||||||||
\(929\) | 12.7716 | 0.419023 | 0.209511 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209511 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.02640 | 0.0664127 | ||||||||
\(932\) | −10.2409 | −0.335450 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.23161 | −0.138462 | ||||||||
\(935\) | 3.51893 | 0.115081 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.7627 | 1.72368 | 0.861842 | − | 0.507178i | \(-0.169311\pi\) | ||||
0.861842 | + | 0.507178i | \(0.169311\pi\) | |||||||
\(938\) | −10.2621 | −0.335069 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.21010 | −0.0394692 | ||||||||
\(941\) | −51.2315 | −1.67010 | −0.835049 | − | 0.550176i | \(-0.814561\pi\) | ||||
−0.835049 | + | 0.550176i | \(0.814561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.9712 | −0.748044 | ||||||||
\(944\) | −0.716258 | −0.0233122 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.4212 | 0.566412 | ||||||||
\(947\) | −2.89717 | −0.0941455 | −0.0470727 | − | 0.998891i | \(-0.514989\pi\) | ||||
−0.0470727 | + | 0.998891i | \(0.514989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.7844 | 1.35638 | ||||||||
\(950\) | 7.42236 | 0.240813 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.28617 | 0.171326 | ||||||||
\(953\) | 50.7174 | 1.64290 | 0.821448 | − | 0.570283i | \(-0.193166\pi\) | ||||
0.821448 | + | 0.570283i | \(0.193166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.32454 | 0.237016 | ||||||||
\(956\) | −4.26138 | −0.137823 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.5704 | −0.406131 | ||||||||
\(959\) | 2.27099 | 0.0733341 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6014 | −0.954883 | ||||||||
\(962\) | 1.13773 | 0.0366819 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.32464 | 0.235911 | ||||||||
\(965\) | 4.78575 | 0.154059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.226419 | 0.00728114 | 0.00364057 | − | 0.999993i | \(-0.498841\pi\) | ||||
0.00364057 | + | 0.999993i | \(0.498841\pi\) | |||||||
\(968\) | −20.5396 | −0.660167 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.4121 | 0.398528 | ||||||||
\(971\) | −18.1946 | −0.583894 | −0.291947 | − | 0.956435i | \(-0.594303\pi\) | ||||
−0.291947 | + | 0.956435i | \(0.594303\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52891 | 0.0490146 | ||||||||
\(974\) | −36.3463 | −1.16461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.57678 | −0.0824807 | ||||||||
\(977\) | −35.6302 | −1.13991 | −0.569956 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569956 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3969 | 0.364246 | ||||||||
\(980\) | 1.15215 | 0.0368040 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.7170 | 0.565371 | ||||||||
\(983\) | 30.5746 | 0.975179 | 0.487589 | − | 0.873073i | \(-0.337876\pi\) | ||||
0.487589 | + | 0.873073i | \(0.337876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.0106 | −0.733180 | ||||||||
\(986\) | 8.67994 | 0.276426 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.56638 | −0.208904 | ||||||||
\(989\) | 48.5951 | 1.54523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5461 | 0.938561 | 0.469281 | − | 0.883049i | \(-0.344513\pi\) | ||||
0.469281 | + | 0.883049i | \(0.344513\pi\) | |||||||
\(992\) | 6.55160 | 0.208014 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.0827 | −0.319803 | ||||||||
\(995\) | 6.43399 | 0.203971 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.43799 | −0.235563 | −0.117782 | − | 0.993040i | \(-0.537578\pi\) | ||||
−0.117782 | + | 0.993040i | \(0.537578\pi\) | |||||||
\(998\) | 10.9062 | 0.345230 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.z.1.13 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.20 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.20 | yes | 32 | 3.2 | odd | 2 | inner |