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: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34710 | 0.952544 | 0.476272 | − | 0.879298i | \(-0.341988\pi\) | ||||
0.476272 | + | 0.879298i | \(0.341988\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.185322 | −0.0926609 | ||||||||
\(5\) | −0.124848 | −0.0558338 | −0.0279169 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279169 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.94385 | −1.04081 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.168183 | −0.0531841 | ||||||||
\(11\) | −0.0232879 | −0.00702156 | −0.00351078 | − | 0.999994i | \(-0.501118\pi\) | ||||
−0.00351078 | + | 0.999994i | \(0.501118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.81631 | −0.503755 | −0.251877 | − | 0.967759i | \(-0.581048\pi\) | ||||
−0.251877 | + | 0.967759i | \(0.581048\pi\) | |||||||
\(14\) | −1.34710 | −0.360028 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.59501 | −0.898753 | ||||||||
\(17\) | −5.85992 | −1.42124 | −0.710620 | − | 0.703576i | \(-0.751585\pi\) | ||||
−0.710620 | + | 0.703576i | \(0.751585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.33861 | −1.45418 | −0.727088 | − | 0.686544i | \(-0.759127\pi\) | ||||
−0.727088 | + | 0.686544i | \(0.759127\pi\) | |||||||
\(20\) | 0.0231371 | 0.00517361 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0313711 | −0.00668834 | ||||||||
\(23\) | −5.01952 | −1.04664 | −0.523322 | − | 0.852135i | \(-0.675307\pi\) | ||||
−0.523322 | + | 0.852135i | \(0.675307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98441 | −0.996883 | ||||||||
\(26\) | −2.44676 | −0.479849 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.185322 | 0.0350225 | ||||||||
\(29\) | 5.62396 | 1.04434 | 0.522172 | − | 0.852840i | \(-0.325122\pi\) | ||||
0.522172 | + | 0.852840i | \(0.325122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.17849 | 1.28930 | 0.644648 | − | 0.764480i | \(-0.277004\pi\) | ||||
0.644648 | + | 0.764480i | \(0.277004\pi\) | |||||||
\(32\) | 1.04485 | 0.184706 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.89390 | −1.35379 | ||||||||
\(35\) | 0.124848 | 0.0211032 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.76017 | 0.618167 | 0.309084 | − | 0.951035i | \(-0.399978\pi\) | ||||
0.309084 | + | 0.951035i | \(0.399978\pi\) | |||||||
\(38\) | −8.53874 | −1.38517 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.367534 | 0.0581122 | ||||||||
\(41\) | 1.39770 | 0.218284 | 0.109142 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109142 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00299 | 0.152954 | 0.0764771 | − | 0.997071i | \(-0.475633\pi\) | ||||
0.0764771 | + | 0.997071i | \(0.475633\pi\) | |||||||
\(44\) | 0.00431575 | 0.000650624 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.76180 | −0.996973 | ||||||||
\(47\) | 1.58115 | 0.230634 | 0.115317 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115317 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.71450 | −0.949574 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.336602 | 0.0466784 | ||||||||
\(53\) | 9.43367 | 1.29581 | 0.647907 | − | 0.761719i | \(-0.275644\pi\) | ||||
0.647907 | + | 0.761719i | \(0.275644\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.00290745 | 0.000392040 0 | ||||||||
\(56\) | 2.94385 | 0.393388 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.57604 | 0.994782 | ||||||||
\(59\) | 8.78661 | 1.14392 | 0.571960 | − | 0.820282i | \(-0.306183\pi\) | ||||
0.571960 | + | 0.820282i | \(0.306183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4912 | 1.34327 | 0.671633 | − | 0.740884i | \(-0.265593\pi\) | ||||
0.671633 | + | 0.740884i | \(0.265593\pi\) | |||||||
\(62\) | 9.67015 | 1.22811 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59755 | 1.07469 | ||||||||
\(65\) | 0.226764 | 0.0281266 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.56958 | 0.680432 | 0.340216 | − | 0.940347i | \(-0.389500\pi\) | ||||
0.340216 | + | 0.940347i | \(0.389500\pi\) | |||||||
\(68\) | 1.08597 | 0.131693 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.168183 | 0.0201017 | ||||||||
\(71\) | −9.21819 | −1.09400 | −0.546999 | − | 0.837133i | \(-0.684230\pi\) | ||||
−0.546999 | + | 0.837133i | \(0.684230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.24252 | 0.964714 | 0.482357 | − | 0.875975i | \(-0.339781\pi\) | ||||
0.482357 | + | 0.875975i | \(0.339781\pi\) | |||||||
\(74\) | 5.06532 | 0.588831 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.17468 | 0.134745 | ||||||||
\(77\) | 0.0232879 | 0.00265390 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.90911 | −0.552318 | −0.276159 | − | 0.961112i | \(-0.589062\pi\) | ||||
−0.276159 | + | 0.961112i | \(0.589062\pi\) | |||||||
\(80\) | 0.448831 | 0.0501808 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.88284 | 0.207925 | ||||||||
\(83\) | 1.62186 | 0.178022 | 0.0890112 | − | 0.996031i | \(-0.471629\pi\) | ||||
0.0890112 | + | 0.996031i | \(0.471629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.731601 | 0.0793532 | ||||||||
\(86\) | 1.35112 | 0.145695 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0685559 | 0.00730809 | ||||||||
\(89\) | 9.82593 | 1.04155 | 0.520773 | − | 0.853695i | \(-0.325644\pi\) | ||||
0.520773 | + | 0.853695i | \(0.325644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.81631 | 0.190401 | ||||||||
\(92\) | 0.930227 | 0.0969829 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.12996 | 0.219689 | ||||||||
\(95\) | 0.791364 | 0.0811923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.84997 | −0.390905 | −0.195453 | − | 0.980713i | \(-0.562618\pi\) | ||||
−0.195453 | + | 0.980713i | \(0.562618\pi\) | |||||||
\(98\) | 1.34710 | 0.136078 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.923720 | 0.0923720 | ||||||||
\(101\) | −0.486490 | −0.0484076 | −0.0242038 | − | 0.999707i | \(-0.507705\pi\) | ||||
−0.0242038 | + | 0.999707i | \(0.507705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.22701 | −0.120901 | −0.0604507 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604507 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(104\) | 5.34695 | 0.524312 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.7081 | 1.23432 | ||||||||
\(107\) | 12.9702 | 1.25388 | 0.626941 | − | 0.779067i | \(-0.284307\pi\) | ||||
0.626941 | + | 0.779067i | \(0.284307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.10456 | −0.105797 | −0.0528987 | − | 0.998600i | \(-0.516846\pi\) | ||||
−0.0528987 | + | 0.998600i | \(0.516846\pi\) | |||||||
\(110\) | 0.00391662 | 0.000373436 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.59501 | 0.339697 | ||||||||
\(113\) | −19.9356 | −1.87538 | −0.937691 | − | 0.347472i | \(-0.887040\pi\) | ||||
−0.937691 | + | 0.347472i | \(0.887040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.626679 | 0.0584381 | ||||||||
\(116\) | −1.04224 | −0.0967697 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.8364 | 1.08963 | ||||||||
\(119\) | 5.85992 | 0.537178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9995 | −0.999951 | ||||||||
\(122\) | 14.1328 | 1.27952 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.33033 | −0.119467 | ||||||||
\(125\) | 1.24654 | 0.111494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 9.49205 | 0.838986 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.305473 | 0.0267918 | ||||||||
\(131\) | 2.17649 | 0.190161 | 0.0950805 | − | 0.995470i | \(-0.469689\pi\) | ||||
0.0950805 | + | 0.995470i | \(0.469689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.33861 | 0.549627 | ||||||||
\(134\) | 7.50278 | 0.648141 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.2507 | 1.47924 | ||||||||
\(137\) | −14.1303 | −1.20724 | −0.603618 | − | 0.797274i | \(-0.706275\pi\) | ||||
−0.603618 | + | 0.797274i | \(0.706275\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7203 | 0.994105 | 0.497052 | − | 0.867721i | \(-0.334416\pi\) | ||||
0.497052 | + | 0.867721i | \(0.334416\pi\) | |||||||
\(140\) | −0.0231371 | −0.00195544 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.4178 | −1.04208 | ||||||||
\(143\) | 0.0422981 | 0.00353714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.702141 | −0.0583097 | ||||||||
\(146\) | 11.1035 | 0.918932 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.696840 | −0.0572799 | ||||||||
\(149\) | −16.5132 | −1.35281 | −0.676407 | − | 0.736528i | \(-0.736464\pi\) | ||||
−0.676407 | + | 0.736528i | \(0.736464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.59928 | −0.781178 | −0.390589 | − | 0.920565i | \(-0.627729\pi\) | ||||
−0.390589 | + | 0.920565i | \(0.627729\pi\) | |||||||
\(152\) | 18.6599 | 1.51352 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0313711 | 0.00252795 | ||||||||
\(155\) | −0.896222 | −0.0719863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.16452 | −0.731408 | −0.365704 | − | 0.930731i | \(-0.619172\pi\) | ||||
−0.365704 | + | 0.930731i | \(0.619172\pi\) | |||||||
\(158\) | −6.61306 | −0.526107 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.130448 | −0.0103128 | ||||||||
\(161\) | 5.01952 | 0.395594 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0298 | 1.33388 | 0.666939 | − | 0.745112i | \(-0.267604\pi\) | ||||
0.666939 | + | 0.745112i | \(0.267604\pi\) | |||||||
\(164\) | −0.259024 | −0.0202264 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.18481 | 0.169574 | ||||||||
\(167\) | −10.5430 | −0.815845 | −0.407923 | − | 0.913016i | \(-0.633747\pi\) | ||||
−0.407923 | + | 0.913016i | \(0.633747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.70100 | −0.746231 | ||||||||
\(170\) | 0.985539 | 0.0755874 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.185875 | −0.0141729 | ||||||||
\(173\) | 3.46156 | 0.263178 | 0.131589 | − | 0.991304i | \(-0.457992\pi\) | ||||
0.131589 | + | 0.991304i | \(0.457992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.98441 | 0.376786 | ||||||||
\(176\) | 0.0837202 | 0.00631065 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.2365 | 0.992118 | ||||||||
\(179\) | 5.32899 | 0.398308 | 0.199154 | − | 0.979968i | \(-0.436181\pi\) | ||||
0.199154 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2408 | −1.43016 | −0.715078 | − | 0.699045i | \(-0.753609\pi\) | ||||
−0.715078 | + | 0.699045i | \(0.753609\pi\) | |||||||
\(182\) | 2.44676 | 0.181366 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.7767 | 1.08935 | ||||||||
\(185\) | −0.469450 | −0.0345146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.136465 | 0.00997932 | ||||||||
\(188\) | −0.293021 | −0.0213708 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.06605 | 0.0773392 | ||||||||
\(191\) | 20.7182 | 1.49911 | 0.749557 | − | 0.661939i | \(-0.230266\pi\) | ||||
0.749557 | + | 0.661939i | \(0.230266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.9852 | 1.87045 | 0.935227 | − | 0.354050i | \(-0.115196\pi\) | ||||
0.935227 | + | 0.354050i | \(0.115196\pi\) | |||||||
\(194\) | −5.18629 | −0.372354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.185322 | −0.0132373 | ||||||||
\(197\) | 24.2925 | 1.73077 | 0.865386 | − | 0.501105i | \(-0.167073\pi\) | ||||
0.865386 | + | 0.501105i | \(0.167073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9908 | 1.55889 | 0.779443 | − | 0.626473i | \(-0.215502\pi\) | ||||
0.779443 | + | 0.626473i | \(0.215502\pi\) | |||||||
\(200\) | 14.6733 | 1.03756 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.655351 | −0.0461104 | ||||||||
\(203\) | −5.62396 | −0.394725 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.174501 | −0.0121876 | ||||||||
\(206\) | −1.65291 | −0.115164 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.52967 | 0.452751 | ||||||||
\(209\) | 0.147613 | 0.0102106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.17029 | 0.562466 | 0.281233 | − | 0.959640i | \(-0.409257\pi\) | ||||
0.281233 | + | 0.959640i | \(0.409257\pi\) | |||||||
\(212\) | −1.74826 | −0.120071 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.4722 | 1.19438 | ||||||||
\(215\) | −0.125221 | −0.00854001 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.17849 | −0.487308 | ||||||||
\(218\) | −1.48795 | −0.100777 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.000538813 0 | −3.63268e−5 0 | ||||||||
\(221\) | 10.6435 | 0.715957 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4912 | −1.23826 | −0.619131 | − | 0.785288i | \(-0.712515\pi\) | ||||
−0.619131 | + | 0.785288i | \(0.712515\pi\) | |||||||
\(224\) | −1.04485 | −0.0698121 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −26.8552 | −1.78638 | ||||||||
\(227\) | 5.25708 | 0.348925 | 0.174462 | − | 0.984664i | \(-0.444181\pi\) | ||||
0.174462 | + | 0.984664i | \(0.444181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.22204 | 0.345082 | 0.172541 | − | 0.985002i | \(-0.444802\pi\) | ||||
0.172541 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(230\) | 0.844199 | 0.0556648 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.5561 | −1.08696 | ||||||||
\(233\) | −8.58212 | −0.562234 | −0.281117 | − | 0.959674i | \(-0.590705\pi\) | ||||
−0.281117 | + | 0.959674i | \(0.590705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.197404 | −0.0128772 | ||||||||
\(236\) | −1.62835 | −0.105997 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.89390 | 0.511686 | ||||||||
\(239\) | 8.10547 | 0.524300 | 0.262150 | − | 0.965027i | \(-0.415569\pi\) | ||||
0.262150 | + | 0.965027i | \(0.415569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0876 | −1.61603 | −0.808017 | − | 0.589160i | \(-0.799459\pi\) | ||||
−0.808017 | + | 0.589160i | \(0.799459\pi\) | |||||||
\(242\) | −14.8174 | −0.952497 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.94426 | −0.124468 | ||||||||
\(245\) | −0.124848 | −0.00797626 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5129 | 0.732549 | ||||||||
\(248\) | −21.1324 | −1.34191 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.67921 | 0.106202 | ||||||||
\(251\) | 0.464425 | 0.0293143 | 0.0146571 | − | 0.999893i | \(-0.495334\pi\) | ||||
0.0146571 | + | 0.999893i | \(0.495334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.116894 | 0.00734907 | ||||||||
\(254\) | 1.34710 | 0.0845246 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.40835 | −0.275522 | ||||||||
\(257\) | 6.25568 | 0.390219 | 0.195109 | − | 0.980781i | \(-0.437494\pi\) | ||||
0.195109 | + | 0.980781i | \(0.437494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.76017 | −0.233645 | ||||||||
\(260\) | −0.0420242 | −0.00260623 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.93195 | 0.181137 | ||||||||
\(263\) | −29.6611 | −1.82898 | −0.914492 | − | 0.404604i | \(-0.867409\pi\) | ||||
−0.914492 | + | 0.404604i | \(0.867409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17778 | −0.0723503 | ||||||||
\(266\) | 8.53874 | 0.523544 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.03216 | −0.0630494 | ||||||||
\(269\) | −15.2324 | −0.928733 | −0.464366 | − | 0.885643i | \(-0.653718\pi\) | ||||
−0.464366 | + | 0.885643i | \(0.653718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3142 | −1.23400 | −0.617000 | − | 0.786963i | \(-0.711652\pi\) | ||||
−0.617000 | + | 0.786963i | \(0.711652\pi\) | |||||||
\(272\) | 21.0665 | 1.27734 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.0350 | −1.14995 | ||||||||
\(275\) | 0.116076 | 0.00699967 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.0157 | 1.50305 | 0.751523 | − | 0.659707i | \(-0.229319\pi\) | ||||
0.751523 | + | 0.659707i | \(0.229319\pi\) | |||||||
\(278\) | 15.7884 | 0.946928 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.367534 | −0.0219644 | ||||||||
\(281\) | 20.2609 | 1.20867 | 0.604333 | − | 0.796732i | \(-0.293440\pi\) | ||||
0.604333 | + | 0.796732i | \(0.293440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.30742 | 0.256050 | 0.128025 | − | 0.991771i | \(-0.459136\pi\) | ||||
0.128025 | + | 0.991771i | \(0.459136\pi\) | |||||||
\(284\) | 1.70833 | 0.101371 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0569798 | 0.00336928 | ||||||||
\(287\) | −1.39770 | −0.0825037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.3387 | 1.01992 | ||||||||
\(290\) | −0.945855 | −0.0555425 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.52752 | −0.0893912 | ||||||||
\(293\) | −4.11421 | −0.240355 | −0.120177 | − | 0.992752i | \(-0.538346\pi\) | ||||
−0.120177 | + | 0.992752i | \(0.538346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.09699 | −0.0638694 | ||||||||
\(296\) | −11.0694 | −0.643393 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.2449 | −1.28861 | ||||||||
\(299\) | 9.11703 | 0.527252 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00299 | −0.0578112 | ||||||||
\(302\) | −12.9312 | −0.744106 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 22.7874 | 1.30695 | ||||||||
\(305\) | −1.30981 | −0.0749997 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.6296 | 0.834956 | 0.417478 | − | 0.908687i | \(-0.362914\pi\) | ||||
0.417478 | + | 0.908687i | \(0.362914\pi\) | |||||||
\(308\) | −0.00431575 | −0.000245913 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.20730 | −0.0685701 | ||||||||
\(311\) | −14.6918 | −0.833096 | −0.416548 | − | 0.909114i | \(-0.636760\pi\) | ||||
−0.416548 | + | 0.909114i | \(0.636760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.7208 | 1.79297 | 0.896483 | − | 0.443079i | \(-0.146114\pi\) | ||||
0.896483 | + | 0.443079i | \(0.146114\pi\) | |||||||
\(314\) | −12.3455 | −0.696698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.909764 | 0.0511782 | ||||||||
\(317\) | −10.6694 | −0.599251 | −0.299626 | − | 0.954057i | \(-0.596862\pi\) | ||||
−0.299626 | + | 0.954057i | \(0.596862\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.130970 | −0.00733292 | ||||||||
\(320\) | −1.07339 | −0.0600042 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.76180 | 0.376820 | ||||||||
\(323\) | 37.1438 | 2.06673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.05326 | 0.502185 | ||||||||
\(326\) | 22.9409 | 1.27058 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.11462 | −0.227192 | ||||||||
\(329\) | −1.58115 | −0.0871715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.9750 | 1.75750 | 0.878752 | − | 0.477278i | \(-0.158377\pi\) | ||||
0.878752 | + | 0.477278i | \(0.158377\pi\) | |||||||
\(332\) | −0.300566 | −0.0164957 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.2025 | −0.777128 | ||||||||
\(335\) | −0.695352 | −0.0379911 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7774 | −1.13182 | −0.565908 | − | 0.824468i | \(-0.691474\pi\) | ||||
−0.565908 | + | 0.824468i | \(0.691474\pi\) | |||||||
\(338\) | −13.0682 | −0.710817 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.135581 | −0.00735294 | ||||||||
\(341\) | −0.167172 | −0.00905286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.95264 | −0.159196 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.66307 | 0.250688 | ||||||||
\(347\) | −1.89823 | −0.101903 | −0.0509513 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509513 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6543 | 1.64089 | 0.820443 | − | 0.571729i | \(-0.193727\pi\) | ||||
0.820443 | + | 0.571729i | \(0.193727\pi\) | |||||||
\(350\) | 6.71450 | 0.358905 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0243324 | −0.00129692 | ||||||||
\(353\) | −26.7737 | −1.42502 | −0.712510 | − | 0.701662i | \(-0.752442\pi\) | ||||
−0.712510 | + | 0.701662i | \(0.752442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.15087 | 0.0610821 | ||||||||
\(356\) | −1.82096 | −0.0965106 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.17869 | 0.379405 | ||||||||
\(359\) | 20.6079 | 1.08764 | 0.543821 | − | 0.839201i | \(-0.316977\pi\) | ||||
0.543821 | + | 0.839201i | \(0.316977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.1780 | 1.11463 | ||||||||
\(362\) | −25.9193 | −1.36229 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.336602 | −0.0176428 | ||||||||
\(365\) | −1.02906 | −0.0538637 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.09130 | 0.317963 | 0.158982 | − | 0.987282i | \(-0.449179\pi\) | ||||
0.158982 | + | 0.987282i | \(0.449179\pi\) | |||||||
\(368\) | 18.0453 | 0.940674 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.632396 | −0.0328767 | ||||||||
\(371\) | −9.43367 | −0.489772 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.81287 | −0.300979 | −0.150490 | − | 0.988612i | \(-0.548085\pi\) | ||||
−0.150490 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(374\) | 0.183832 | 0.00950573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.65466 | −0.240046 | ||||||||
\(377\) | −10.2149 | −0.526093 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8302 | −1.63501 | −0.817504 | − | 0.575922i | \(-0.804643\pi\) | ||||
−0.817504 | + | 0.575922i | \(0.804643\pi\) | |||||||
\(380\) | −0.146657 | −0.00752334 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 27.9095 | 1.42797 | ||||||||
\(383\) | 29.5476 | 1.50981 | 0.754906 | − | 0.655833i | \(-0.227683\pi\) | ||||
0.754906 | + | 0.655833i | \(0.227683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.00290745 | −0.000148177 0 | ||||||||
\(386\) | 35.0046 | 1.78169 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.713483 | 0.0362216 | ||||||||
\(389\) | 25.8440 | 1.31034 | 0.655171 | − | 0.755480i | \(-0.272596\pi\) | ||||
0.655171 | + | 0.755480i | \(0.272596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.4140 | 1.48753 | ||||||||
\(392\) | −2.94385 | −0.148687 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.7245 | 1.64864 | ||||||||
\(395\) | 0.612893 | 0.0308380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4251 | 0.974920 | 0.487460 | − | 0.873145i | \(-0.337924\pi\) | ||||
0.487460 | + | 0.873145i | \(0.337924\pi\) | |||||||
\(398\) | 29.6238 | 1.48491 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.9190 | 0.895951 | ||||||||
\(401\) | −39.6369 | −1.97937 | −0.989686 | − | 0.143254i | \(-0.954243\pi\) | ||||
−0.989686 | + | 0.143254i | \(0.954243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0384 | −0.649489 | ||||||||
\(404\) | 0.0901572 | 0.00448549 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.57604 | −0.375992 | ||||||||
\(407\) | −0.0875663 | −0.00434050 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.7310 | 1.76678 | 0.883392 | − | 0.468635i | \(-0.155254\pi\) | ||||
0.883392 | + | 0.468635i | \(0.155254\pi\) | |||||||
\(410\) | −0.235070 | −0.0116093 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.227392 | 0.0112028 | ||||||||
\(413\) | −8.78661 | −0.432361 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.202487 | −0.00993967 | ||||||||
\(416\) | −1.89778 | −0.0930463 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.198849 | 0.00972603 | ||||||||
\(419\) | 36.2048 | 1.76872 | 0.884360 | − | 0.466805i | \(-0.154595\pi\) | ||||
0.884360 | + | 0.466805i | \(0.154595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.08095 | −0.0526824 | −0.0263412 | − | 0.999653i | \(-0.508386\pi\) | ||||
−0.0263412 | + | 0.999653i | \(0.508386\pi\) | |||||||
\(422\) | 11.0062 | 0.535773 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27.7713 | −1.34869 | ||||||||
\(425\) | 29.2083 | 1.41681 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.4912 | −0.507707 | ||||||||
\(428\) | −2.40367 | −0.116186 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.168685 | −0.00813473 | ||||||||
\(431\) | −29.0605 | −1.39980 | −0.699898 | − | 0.714243i | \(-0.746771\pi\) | ||||
−0.699898 | + | 0.714243i | \(0.746771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0990 | 1.11007 | 0.555033 | − | 0.831828i | \(-0.312706\pi\) | ||||
0.555033 | + | 0.831828i | \(0.312706\pi\) | |||||||
\(434\) | −9.67015 | −0.464182 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.204698 | 0.00980327 | ||||||||
\(437\) | 31.8168 | 1.52200 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.62374 | 0.268407 | 0.134203 | − | 0.990954i | \(-0.457152\pi\) | ||||
0.134203 | + | 0.990954i | \(0.457152\pi\) | |||||||
\(440\) | −0.00855909 | −0.000408038 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.3378 | 0.681980 | ||||||||
\(443\) | −19.9387 | −0.947315 | −0.473658 | − | 0.880709i | \(-0.657067\pi\) | ||||
−0.473658 | + | 0.880709i | \(0.657067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.22675 | −0.0581535 | ||||||||
\(446\) | −24.9095 | −1.17950 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.59755 | −0.406196 | ||||||||
\(449\) | 33.6204 | 1.58664 | 0.793322 | − | 0.608802i | \(-0.208350\pi\) | ||||
0.793322 | + | 0.608802i | \(0.208350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0325495 | −0.00153270 | ||||||||
\(452\) | 3.69449 | 0.173774 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.08181 | 0.332366 | ||||||||
\(455\) | −0.226764 | −0.0106308 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.43769 | 0.160808 | 0.0804042 | − | 0.996762i | \(-0.474379\pi\) | ||||
0.0804042 | + | 0.996762i | \(0.474379\pi\) | |||||||
\(458\) | 7.03461 | 0.328706 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.116137 | −0.00541492 | ||||||||
\(461\) | 34.0720 | 1.58689 | 0.793445 | − | 0.608642i | \(-0.208285\pi\) | ||||
0.793445 | + | 0.608642i | \(0.208285\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.1909 | 1.58898 | 0.794492 | − | 0.607274i | \(-0.207737\pi\) | ||||
0.794492 | + | 0.607274i | \(0.207737\pi\) | |||||||
\(464\) | −20.2182 | −0.938607 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5610 | −0.535552 | ||||||||
\(467\) | 4.91008 | 0.227211 | 0.113606 | − | 0.993526i | \(-0.463760\pi\) | ||||
0.113606 | + | 0.993526i | \(0.463760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.56958 | −0.257179 | ||||||||
\(470\) | −0.265922 | −0.0122661 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.8664 | −1.19060 | ||||||||
\(473\) | −0.0233574 | −0.00107398 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.5943 | 1.44964 | ||||||||
\(476\) | −1.08597 | −0.0497754 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.9189 | 0.499418 | ||||||||
\(479\) | −34.0644 | −1.55644 | −0.778222 | − | 0.627989i | \(-0.783878\pi\) | ||||
−0.778222 | + | 0.627989i | \(0.783878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.82964 | −0.311405 | ||||||||
\(482\) | −33.7955 | −1.53934 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.03844 | 0.0926563 | ||||||||
\(485\) | 0.480662 | 0.0218257 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0362 | −0.817298 | −0.408649 | − | 0.912692i | \(-0.634000\pi\) | ||||
−0.408649 | + | 0.912692i | \(0.634000\pi\) | |||||||
\(488\) | −30.8846 | −1.39808 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.168183 | −0.00759773 | ||||||||
\(491\) | −16.9027 | −0.762807 | −0.381403 | − | 0.924409i | \(-0.624559\pi\) | ||||
−0.381403 | + | 0.924409i | \(0.624559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.9560 | −1.48426 | ||||||||
\(494\) | 15.5090 | 0.697785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.8068 | −1.15876 | ||||||||
\(497\) | 9.21819 | 0.413492 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.6444 | −1.37183 | −0.685916 | − | 0.727681i | \(-0.740598\pi\) | ||||
−0.685916 | + | 0.727681i | \(0.740598\pi\) | |||||||
\(500\) | −0.231010 | −0.0103311 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.625627 | 0.0279231 | ||||||||
\(503\) | −6.83573 | −0.304790 | −0.152395 | − | 0.988320i | \(-0.548699\pi\) | ||||
−0.152395 | + | 0.988320i | \(0.548699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0607375 | 0.00270278 | ||||||||
\(506\) | 0.157468 | 0.00700031 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.185322 | −0.00822232 | ||||||||
\(509\) | 29.0466 | 1.28747 | 0.643735 | − | 0.765249i | \(-0.277384\pi\) | ||||
0.643735 | + | 0.765249i | \(0.277384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.24252 | −0.364628 | ||||||||
\(512\) | −24.9226 | −1.10143 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.42703 | 0.371700 | ||||||||
\(515\) | 0.153191 | 0.00675038 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0368216 | −0.00161941 | ||||||||
\(518\) | −5.06532 | −0.222557 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.667557 | −0.0292743 | ||||||||
\(521\) | 0.707723 | 0.0310059 | 0.0155030 | − | 0.999880i | \(-0.495065\pi\) | ||||
0.0155030 | + | 0.999880i | \(0.495065\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.0484 | 1.53256 | 0.766280 | − | 0.642507i | \(-0.222106\pi\) | ||||
0.766280 | + | 0.642507i | \(0.222106\pi\) | |||||||
\(524\) | −0.403351 | −0.0176205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.9565 | −1.74219 | ||||||||
\(527\) | −42.0654 | −1.83240 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.19563 | 0.0954622 | ||||||||
\(530\) | −1.58658 | −0.0689168 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.17468 | −0.0509289 | ||||||||
\(533\) | −2.53867 | −0.109962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.61931 | −0.0700090 | ||||||||
\(536\) | −16.3960 | −0.708199 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.5195 | −0.884658 | ||||||||
\(539\) | −0.0232879 | −0.00100308 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.6213 | 0.886577 | 0.443289 | − | 0.896379i | \(-0.353812\pi\) | ||||
0.443289 | + | 0.896379i | \(0.353812\pi\) | |||||||
\(542\) | −27.3653 | −1.17544 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.12275 | −0.262511 | ||||||||
\(545\) | 0.137902 | 0.00590707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7235 | 1.14261 | 0.571306 | − | 0.820737i | \(-0.306437\pi\) | ||||
0.571306 | + | 0.820737i | \(0.306437\pi\) | |||||||
\(548\) | 2.61866 | 0.111864 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.156366 | 0.00666749 | ||||||||
\(551\) | −35.6481 | −1.51866 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.90911 | 0.208756 | ||||||||
\(554\) | 33.6986 | 1.43172 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.17203 | −0.0921146 | ||||||||
\(557\) | −30.1554 | −1.27773 | −0.638863 | − | 0.769321i | \(-0.720595\pi\) | ||||
−0.638863 | + | 0.769321i | \(0.720595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.82174 | −0.0770514 | ||||||||
\(560\) | −0.448831 | −0.0189666 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.2935 | 1.15131 | ||||||||
\(563\) | −38.3423 | −1.61593 | −0.807967 | − | 0.589227i | \(-0.799432\pi\) | ||||
−0.807967 | + | 0.589227i | \(0.799432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.48892 | 0.104710 | ||||||||
\(566\) | 5.80253 | 0.243898 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.1369 | 1.13864 | ||||||||
\(569\) | 12.3771 | 0.518875 | 0.259437 | − | 0.965760i | \(-0.416463\pi\) | ||||
0.259437 | + | 0.965760i | \(0.416463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8770 | 1.33401 | 0.667006 | − | 0.745052i | \(-0.267576\pi\) | ||||
0.667006 | + | 0.745052i | \(0.267576\pi\) | |||||||
\(572\) | −0.00783876 | −0.000327755 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.88284 | −0.0785884 | ||||||||
\(575\) | 25.0194 | 1.04338 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.83358 | 0.326116 | 0.163058 | − | 0.986616i | \(-0.447864\pi\) | ||||
0.163058 | + | 0.986616i | \(0.447864\pi\) | |||||||
\(578\) | 23.3569 | 0.971520 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.130122 | 0.00540302 | ||||||||
\(581\) | −1.62186 | −0.0672862 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.219690 | −0.00909864 | ||||||||
\(584\) | −24.2647 | −1.00408 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.54225 | −0.228948 | ||||||||
\(587\) | −42.9733 | −1.77370 | −0.886849 | − | 0.462060i | \(-0.847111\pi\) | ||||
−0.886849 | + | 0.462060i | \(0.847111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.5017 | −1.87486 | ||||||||
\(590\) | −1.47776 | −0.0608384 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.5178 | −0.555580 | ||||||||
\(593\) | −20.2941 | −0.833379 | −0.416689 | − | 0.909049i | \(-0.636810\pi\) | ||||
−0.416689 | + | 0.909049i | \(0.636810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.731601 | −0.0299927 | ||||||||
\(596\) | 3.06025 | 0.125353 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.2816 | 0.502230 | ||||||||
\(599\) | −35.2549 | −1.44048 | −0.720239 | − | 0.693727i | \(-0.755968\pi\) | ||||
−0.720239 | + | 0.693727i | \(0.755968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.68415 | 0.109489 | 0.0547443 | − | 0.998500i | \(-0.482566\pi\) | ||||
0.0547443 | + | 0.998500i | \(0.482566\pi\) | |||||||
\(602\) | −1.35112 | −0.0550677 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.77895 | 0.0723846 | ||||||||
\(605\) | 1.37326 | 0.0558311 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.9417 | 1.78354 | 0.891768 | − | 0.452492i | \(-0.149465\pi\) | ||||
0.891768 | + | 0.452492i | \(0.149465\pi\) | |||||||
\(608\) | −6.62291 | −0.268595 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.76445 | −0.0714405 | ||||||||
\(611\) | −2.87186 | −0.116183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.4561 | −1.87634 | −0.938171 | − | 0.346171i | \(-0.887482\pi\) | ||||
−0.938171 | + | 0.346171i | \(0.887482\pi\) | |||||||
\(614\) | 19.7075 | 0.795332 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0685559 | −0.00276220 | ||||||||
\(617\) | −4.73332 | −0.190556 | −0.0952781 | − | 0.995451i | \(-0.530374\pi\) | ||||
−0.0952781 | + | 0.995451i | \(0.530374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0979 | −0.647030 | −0.323515 | − | 0.946223i | \(-0.604865\pi\) | ||||
−0.323515 | + | 0.946223i | \(0.604865\pi\) | |||||||
\(620\) | 0.166089 | 0.00667031 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.7913 | −0.793561 | ||||||||
\(623\) | −9.82593 | −0.393668 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7664 | 0.990657 | ||||||||
\(626\) | 42.7311 | 1.70788 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.69838 | 0.0677729 | ||||||||
\(629\) | −22.0343 | −0.878564 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.43050 | 0.0967567 | 0.0483783 | − | 0.998829i | \(-0.484595\pi\) | ||||
0.0483783 | + | 0.998829i | \(0.484595\pi\) | |||||||
\(632\) | 14.4517 | 0.574856 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.3727 | −0.570813 | ||||||||
\(635\) | −0.124848 | −0.00495445 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.81631 | −0.0719650 | ||||||||
\(638\) | −0.176430 | −0.00698492 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.18507 | −0.0468438 | ||||||||
\(641\) | −11.4361 | −0.451699 | −0.225849 | − | 0.974162i | \(-0.572516\pi\) | ||||
−0.225849 | + | 0.974162i | \(0.572516\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.3693 | −0.408927 | −0.204464 | − | 0.978874i | \(-0.565545\pi\) | ||||
−0.204464 | + | 0.978874i | \(0.565545\pi\) | |||||||
\(644\) | −0.930227 | −0.0366561 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50.0364 | 1.96865 | ||||||||
\(647\) | −45.9780 | −1.80758 | −0.903791 | − | 0.427975i | \(-0.859227\pi\) | ||||
−0.903791 | + | 0.427975i | \(0.859227\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.204621 | −0.00803209 | ||||||||
\(650\) | 12.1956 | 0.478353 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.15600 | −0.123598 | ||||||||
\(653\) | 1.83975 | 0.0719950 | 0.0359975 | − | 0.999352i | \(-0.488539\pi\) | ||||
0.0359975 | + | 0.999352i | \(0.488539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.271731 | −0.0106174 | ||||||||
\(656\) | −5.02475 | −0.196184 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.12996 | −0.0830347 | ||||||||
\(659\) | 29.7649 | 1.15948 | 0.579738 | − | 0.814803i | \(-0.303155\pi\) | ||||
0.579738 | + | 0.814803i | \(0.303155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0666 | 0.702710 | 0.351355 | − | 0.936242i | \(-0.385721\pi\) | ||||
0.351355 | + | 0.936242i | \(0.385721\pi\) | |||||||
\(662\) | 43.0735 | 1.67410 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.77451 | −0.185287 | ||||||||
\(665\) | −0.791364 | −0.0306878 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.2296 | −1.09305 | ||||||||
\(668\) | 1.95386 | 0.0755969 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.936708 | −0.0361882 | ||||||||
\(671\) | −0.244319 | −0.00943183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6827 | 0.604525 | 0.302262 | − | 0.953225i | \(-0.402258\pi\) | ||||
0.302262 | + | 0.953225i | \(0.402258\pi\) | |||||||
\(674\) | −27.9892 | −1.07810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.79781 | 0.0691464 | ||||||||
\(677\) | 28.5923 | 1.09889 | 0.549445 | − | 0.835530i | \(-0.314839\pi\) | ||||
0.549445 | + | 0.835530i | \(0.314839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.84997 | 0.147748 | ||||||||
\(680\) | −2.15372 | −0.0825914 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.225197 | −0.00862325 | ||||||||
\(683\) | −3.63560 | −0.139112 | −0.0695561 | − | 0.997578i | \(-0.522158\pi\) | ||||
−0.0695561 | + | 0.997578i | \(0.522158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.76415 | 0.0674046 | ||||||||
\(686\) | −1.34710 | −0.0514325 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.60575 | −0.137468 | ||||||||
\(689\) | −17.1345 | −0.652773 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.1042 | 1.79193 | 0.895965 | − | 0.444125i | \(-0.146485\pi\) | ||||
0.895965 | + | 0.444125i | \(0.146485\pi\) | |||||||
\(692\) | −0.641503 | −0.0243863 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.55711 | −0.0970666 | ||||||||
\(695\) | −1.46326 | −0.0555047 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.19042 | −0.310234 | ||||||||
\(698\) | 41.2944 | 1.56301 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.923720 | −0.0349133 | ||||||||
\(701\) | −31.6487 | −1.19535 | −0.597677 | − | 0.801737i | \(-0.703909\pi\) | ||||
−0.597677 | + | 0.801737i | \(0.703909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.8342 | −0.898925 | ||||||||
\(704\) | −0.200219 | −0.00754602 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.0668 | −1.35739 | ||||||||
\(707\) | 0.486490 | 0.0182964 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4600 | 0.693280 | 0.346640 | − | 0.937998i | \(-0.387323\pi\) | ||||
0.346640 | + | 0.937998i | \(0.387323\pi\) | |||||||
\(710\) | 1.55034 | 0.0581834 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.9260 | −1.08405 | ||||||||
\(713\) | −36.0326 | −1.34943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.00528084 | −0.000197492 0 | ||||||||
\(716\) | −0.987578 | −0.0369075 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.7609 | 1.03603 | ||||||||
\(719\) | 18.6752 | 0.696469 | 0.348235 | − | 0.937407i | \(-0.386781\pi\) | ||||
0.348235 | + | 0.937407i | \(0.386781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.22701 | 0.0456964 | ||||||||
\(722\) | 28.5289 | 1.06173 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.56573 | 0.132519 | ||||||||
\(725\) | −28.0321 | −1.04109 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.1626 | 0.970315 | 0.485158 | − | 0.874427i | \(-0.338762\pi\) | ||||
0.485158 | + | 0.874427i | \(0.338762\pi\) | |||||||
\(728\) | −5.34695 | −0.198171 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.38625 | −0.0513075 | ||||||||
\(731\) | −5.87743 | −0.217384 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5201 | −1.16422 | −0.582111 | − | 0.813109i | \(-0.697773\pi\) | ||||
−0.582111 | + | 0.813109i | \(0.697773\pi\) | |||||||
\(734\) | 8.20559 | 0.302874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.24466 | −0.193321 | ||||||||
\(737\) | −0.129704 | −0.00477769 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.78068 | 0.359788 | 0.179894 | − | 0.983686i | \(-0.442425\pi\) | ||||
0.179894 | + | 0.983686i | \(0.442425\pi\) | |||||||
\(740\) | 0.0869993 | 0.00319816 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.7081 | −0.466529 | ||||||||
\(743\) | 10.6755 | 0.391645 | 0.195823 | − | 0.980639i | \(-0.437262\pi\) | ||||
0.195823 | + | 0.980639i | \(0.437262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.06164 | 0.0755328 | ||||||||
\(746\) | −7.83052 | −0.286696 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0252899 | −0.000924692 0 | ||||||||
\(749\) | −12.9702 | −0.473923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4434 | −0.381085 | −0.190543 | − | 0.981679i | \(-0.561025\pi\) | ||||
−0.190543 | + | 0.981679i | \(0.561025\pi\) | |||||||
\(752\) | −5.68425 | −0.207283 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.7605 | −0.501127 | ||||||||
\(755\) | 1.19845 | 0.0436161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.1218 | −1.49460 | −0.747298 | − | 0.664489i | \(-0.768649\pi\) | ||||
−0.747298 | + | 0.664489i | \(0.768649\pi\) | |||||||
\(758\) | −42.8785 | −1.55742 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.32965 | −0.0845055 | ||||||||
\(761\) | −22.5152 | −0.816176 | −0.408088 | − | 0.912943i | \(-0.633804\pi\) | ||||
−0.408088 | + | 0.912943i | \(0.633804\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10456 | 0.0399876 | ||||||||
\(764\) | −3.83953 | −0.138909 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.8036 | 1.43816 | ||||||||
\(767\) | −15.9592 | −0.576255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2486 | 0.585940 | 0.292970 | − | 0.956122i | \(-0.405356\pi\) | ||||
0.292970 | + | 0.956122i | \(0.405356\pi\) | |||||||
\(770\) | −0.00391662 | −0.000141145 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.81562 | −0.173318 | ||||||||
\(773\) | 43.5565 | 1.56662 | 0.783308 | − | 0.621633i | \(-0.213531\pi\) | ||||
0.783308 | + | 0.621633i | \(0.213531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.7806 | −1.28528 | ||||||||
\(776\) | 11.3337 | 0.406857 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.8144 | 1.24816 | ||||||||
\(779\) | −8.85949 | −0.317424 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.214672 | 0.00768157 | ||||||||
\(782\) | 39.6236 | 1.41694 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.59501 | −0.128393 | ||||||||
\(785\) | 1.14417 | 0.0408373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.6810 | 0.523323 | 0.261661 | − | 0.965160i | \(-0.415730\pi\) | ||||
0.261661 | + | 0.965160i | \(0.415730\pi\) | |||||||
\(788\) | −4.50194 | −0.160375 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.825628 | 0.0293745 | ||||||||
\(791\) | 19.9356 | 0.708827 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.0554 | −0.676677 | ||||||||
\(794\) | 26.1676 | 0.928654 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.07537 | −0.144448 | ||||||||
\(797\) | 13.6198 | 0.482437 | 0.241219 | − | 0.970471i | \(-0.422453\pi\) | ||||
0.241219 | + | 0.970471i | \(0.422453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.26541 | −0.327786 | ||||||||
\(800\) | −5.20798 | −0.184130 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −53.3949 | −1.88544 | ||||||||
\(803\) | −0.191951 | −0.00677380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.626679 | −0.0220875 | ||||||||
\(806\) | −17.5640 | −0.618667 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.43215 | 0.0503830 | ||||||||
\(809\) | −52.6461 | −1.85094 | −0.925469 | − | 0.378824i | \(-0.876329\pi\) | ||||
−0.925469 | + | 0.378824i | \(0.876329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.7302 | 1.11420 | 0.557099 | − | 0.830446i | \(-0.311914\pi\) | ||||
0.557099 | + | 0.830446i | \(0.311914\pi\) | |||||||
\(812\) | 1.04224 | 0.0365755 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.117961 | −0.00413451 | ||||||||
\(815\) | −2.12614 | −0.0744756 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.35754 | −0.222422 | ||||||||
\(818\) | 48.1332 | 1.68294 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0323387 | 0.00112932 | ||||||||
\(821\) | −33.7481 | −1.17782 | −0.588908 | − | 0.808200i | \(-0.700442\pi\) | ||||
−0.588908 | + | 0.808200i | \(0.700442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4138 | −0.432717 | −0.216359 | − | 0.976314i | \(-0.569418\pi\) | ||||
−0.216359 | + | 0.976314i | \(0.569418\pi\) | |||||||
\(824\) | 3.61214 | 0.125835 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.8364 | −0.411842 | ||||||||
\(827\) | −13.4423 | −0.467435 | −0.233718 | − | 0.972304i | \(-0.575089\pi\) | ||||
−0.233718 | + | 0.972304i | \(0.575089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1533 | 0.422101 | 0.211051 | − | 0.977475i | \(-0.432312\pi\) | ||||
0.211051 | + | 0.977475i | \(0.432312\pi\) | |||||||
\(830\) | −0.272770 | −0.00946797 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.6158 | −0.541382 | ||||||||
\(833\) | −5.85992 | −0.203034 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.31628 | 0.0455518 | ||||||||
\(836\) | −0.0273558 | −0.000946122 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 48.7715 | 1.68478 | ||||||||
\(839\) | 33.4257 | 1.15398 | 0.576991 | − | 0.816750i | \(-0.304227\pi\) | ||||
0.576991 | + | 0.816750i | \(0.304227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.62894 | 0.0906529 | ||||||||
\(842\) | −1.45615 | −0.0501823 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.51413 | −0.0521186 | ||||||||
\(845\) | 1.21115 | 0.0416649 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9995 | 0.377946 | ||||||||
\(848\) | −33.9142 | −1.16462 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 39.3465 | 1.34957 | ||||||||
\(851\) | −18.8742 | −0.647001 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.0658 | −1.47454 | −0.737272 | − | 0.675596i | \(-0.763886\pi\) | ||||
−0.737272 | + | 0.675596i | \(0.763886\pi\) | |||||||
\(854\) | −14.1328 | −0.483613 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38.1824 | −1.30505 | ||||||||
\(857\) | −15.2431 | −0.520694 | −0.260347 | − | 0.965515i | \(-0.583837\pi\) | ||||
−0.260347 | + | 0.965515i | \(0.583837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5085 | 1.48449 | 0.742246 | − | 0.670127i | \(-0.233761\pi\) | ||||
0.742246 | + | 0.670127i | \(0.233761\pi\) | |||||||
\(860\) | 0.0232062 | 0.000791325 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.1474 | −1.33337 | ||||||||
\(863\) | −37.0693 | −1.26185 | −0.630927 | − | 0.775842i | \(-0.717325\pi\) | ||||
−0.630927 | + | 0.775842i | \(0.717325\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.432170 | −0.0146942 | ||||||||
\(866\) | 31.1166 | 1.05739 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.33033 | 0.0451544 | ||||||||
\(869\) | 0.114323 | 0.00387813 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1161 | −0.342771 | ||||||||
\(872\) | 3.25164 | 0.110115 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 42.8604 | 1.44978 | ||||||||
\(875\) | −1.24654 | −0.0421406 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.61667 | 0.122126 | 0.0610631 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610631 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(878\) | 7.57575 | 0.255669 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0104523 | −0.000352348 0 | ||||||||
\(881\) | −12.9935 | −0.437764 | −0.218882 | − | 0.975751i | \(-0.570241\pi\) | ||||
−0.218882 | + | 0.975751i | \(0.570241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0994 | 1.45041 | 0.725205 | − | 0.688533i | \(-0.241745\pi\) | ||||
0.725205 | + | 0.688533i | \(0.241745\pi\) | |||||||
\(884\) | −1.97246 | −0.0663411 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.8594 | −0.902359 | ||||||||
\(887\) | −22.1654 | −0.744241 | −0.372121 | − | 0.928184i | \(-0.621369\pi\) | ||||
−0.372121 | + | 0.928184i | \(0.621369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −1.65255 | −0.0553938 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.42682 | 0.114738 | ||||||||
\(893\) | −10.0223 | −0.335383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.665315 | −0.0222390 | ||||||||
\(896\) | −9.49205 | −0.317107 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.2900 | 1.51135 | ||||||||
\(899\) | 40.3716 | 1.34647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55.2806 | −1.84166 | ||||||||
\(902\) | −0.0438474 | −0.00145996 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 58.6873 | 1.95191 | ||||||||
\(905\) | 2.40218 | 0.0798511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.0794 | −1.66286 | −0.831430 | − | 0.555629i | \(-0.812477\pi\) | ||||
−0.831430 | + | 0.555629i | \(0.812477\pi\) | |||||||
\(908\) | −0.974251 | −0.0323317 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.305473 | −0.0101263 | ||||||||
\(911\) | 6.00788 | 0.199050 | 0.0995249 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995249 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0377697 | −0.00125000 | ||||||||
\(914\) | 4.63091 | 0.153177 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.967757 | −0.0319756 | ||||||||
\(917\) | −2.17649 | −0.0718741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3917 | 0.573701 | 0.286850 | − | 0.957975i | \(-0.407392\pi\) | ||||
0.286850 | + | 0.957975i | \(0.407392\pi\) | |||||||
\(920\) | −1.84485 | −0.0608228 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 45.8984 | 1.51158 | ||||||||
\(923\) | 16.7431 | 0.551107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.7422 | −0.616240 | ||||||||
\(926\) | 46.0585 | 1.51358 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.87621 | 0.192896 | ||||||||
\(929\) | 3.52532 | 0.115662 | 0.0578311 | − | 0.998326i | \(-0.481582\pi\) | ||||
0.0578311 | + | 0.998326i | \(0.481582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.33861 | −0.207740 | ||||||||
\(932\) | 1.59045 | 0.0520970 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.61436 | 0.216429 | ||||||||
\(935\) | −0.0170374 | −0.000557183 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.1948 | −1.73780 | −0.868899 | − | 0.494989i | \(-0.835172\pi\) | ||||
−0.868899 | + | 0.494989i | \(0.835172\pi\) | |||||||
\(938\) | −7.50278 | −0.244974 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0365832 | 0.00119321 | ||||||||
\(941\) | 17.0900 | 0.557117 | 0.278559 | − | 0.960419i | \(-0.410143\pi\) | ||||
0.278559 | + | 0.960419i | \(0.410143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.01580 | −0.228466 | ||||||||
\(944\) | −31.5880 | −1.02810 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0314648 | −0.00102301 | ||||||||
\(947\) | 32.8715 | 1.06818 | 0.534090 | − | 0.845428i | \(-0.320655\pi\) | ||||
0.534090 | + | 0.845428i | \(0.320655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9710 | −0.485980 | ||||||||
\(950\) | 42.5606 | 1.38085 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.2507 | −0.559099 | ||||||||
\(953\) | 48.2051 | 1.56152 | 0.780758 | − | 0.624833i | \(-0.214833\pi\) | ||||
0.780758 | + | 0.624833i | \(0.214833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.58663 | −0.0837013 | ||||||||
\(956\) | −1.50212 | −0.0485820 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.8882 | −1.48258 | ||||||||
\(959\) | 14.1303 | 0.456292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.5308 | 0.662283 | ||||||||
\(962\) | −9.20021 | −0.296627 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.64927 | 0.149743 | ||||||||
\(965\) | −3.24420 | −0.104435 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7810 | 1.69732 | 0.848661 | − | 0.528937i | \(-0.177409\pi\) | ||||
0.848661 | + | 0.528937i | \(0.177409\pi\) | |||||||
\(968\) | 32.3807 | 1.04076 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.647499 | 0.0207900 | ||||||||
\(971\) | −15.9585 | −0.512133 | −0.256066 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256066 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7203 | −0.375736 | ||||||||
\(974\) | −24.2965 | −0.778511 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.7162 | −1.20727 | ||||||||
\(977\) | 3.79640 | 0.121457 | 0.0607287 | − | 0.998154i | \(-0.480658\pi\) | ||||
0.0607287 | + | 0.998154i | \(0.480658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.228825 | −0.00731328 | ||||||||
\(980\) | 0.0231371 | 0.000739087 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.7696 | −0.726607 | ||||||||
\(983\) | −9.99776 | −0.318879 | −0.159440 | − | 0.987208i | \(-0.550969\pi\) | ||||
−0.159440 | + | 0.987208i | \(0.550969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.03288 | −0.0966356 | ||||||||
\(986\) | −44.3950 | −1.41382 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.13359 | −0.0678786 | ||||||||
\(989\) | −5.03452 | −0.160088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7568 | 0.627595 | 0.313798 | − | 0.949490i | \(-0.398399\pi\) | ||||
0.313798 | + | 0.949490i | \(0.398399\pi\) | |||||||
\(992\) | 7.50047 | 0.238140 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.4178 | 0.393870 | ||||||||
\(995\) | −2.74551 | −0.0870386 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.9981 | 1.10840 | 0.554201 | − | 0.832383i | \(-0.313024\pi\) | ||||
0.554201 | + | 0.832383i | \(0.313024\pi\) | |||||||
\(998\) | −41.2811 | −1.30673 | ||||||||
\(999\) | 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.y.1.20 | yes | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.9 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.9 | ✓ | 28 | 3.2 | odd | 2 | inner | |
8001.2.a.y.1.20 | yes | 28 | 1.1 | even | 1 | trivial |