Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34067 | −0.947995 | −0.473997 | − | 0.880526i | \(-0.657189\pi\) | ||||
−0.473997 | + | 0.880526i | \(0.657189\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.202611 | −0.101306 | ||||||||
\(5\) | 1.16053 | 0.519004 | 0.259502 | − | 0.965743i | \(-0.416442\pi\) | ||||
0.259502 | + | 0.965743i | \(0.416442\pi\) | |||||||
\(6\) | 1.34067 | 0.547325 | ||||||||
\(7\) | −4.05917 | −1.53422 | −0.767111 | − | 0.641514i | \(-0.778307\pi\) | ||||
−0.767111 | + | 0.641514i | \(0.778307\pi\) | |||||||
\(8\) | 2.95297 | 1.04403 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.55588 | −0.492013 | ||||||||
\(11\) | 0.687421 | 0.207265 | 0.103633 | − | 0.994616i | \(-0.466953\pi\) | ||||
0.103633 | + | 0.994616i | \(0.466953\pi\) | |||||||
\(12\) | 0.202611 | 0.0584888 | ||||||||
\(13\) | −5.30961 | −1.47262 | −0.736310 | − | 0.676644i | \(-0.763434\pi\) | ||||
−0.736310 | + | 0.676644i | \(0.763434\pi\) | |||||||
\(14\) | 5.44200 | 1.45444 | ||||||||
\(15\) | −1.16053 | −0.299647 | ||||||||
\(16\) | −3.55373 | −0.888432 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.34067 | −0.315998 | ||||||||
\(19\) | 7.04145 | 1.61542 | 0.807710 | − | 0.589580i | \(-0.200707\pi\) | ||||
0.807710 | + | 0.589580i | \(0.200707\pi\) | |||||||
\(20\) | −0.235136 | −0.0525780 | ||||||||
\(21\) | 4.05917 | 0.885784 | ||||||||
\(22\) | −0.921603 | −0.196486 | ||||||||
\(23\) | 3.83710 | 0.800091 | 0.400045 | − | 0.916495i | \(-0.368994\pi\) | ||||
0.400045 | + | 0.916495i | \(0.368994\pi\) | |||||||
\(24\) | −2.95297 | −0.602772 | ||||||||
\(25\) | −3.65317 | −0.730635 | ||||||||
\(26\) | 7.11842 | 1.39604 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.822434 | 0.155425 | ||||||||
\(29\) | 5.25655 | 0.976118 | 0.488059 | − | 0.872811i | \(-0.337705\pi\) | ||||
0.488059 | + | 0.872811i | \(0.337705\pi\) | |||||||
\(30\) | 1.55588 | 0.284064 | ||||||||
\(31\) | −6.46598 | −1.16132 | −0.580662 | − | 0.814145i | \(-0.697206\pi\) | ||||
−0.580662 | + | 0.814145i | \(0.697206\pi\) | |||||||
\(32\) | −1.14157 | −0.201804 | ||||||||
\(33\) | −0.687421 | −0.119665 | ||||||||
\(34\) | 1.34067 | 0.229923 | ||||||||
\(35\) | −4.71078 | −0.796268 | ||||||||
\(36\) | −0.202611 | −0.0337685 | ||||||||
\(37\) | −10.3188 | −1.69640 | −0.848200 | − | 0.529677i | \(-0.822313\pi\) | ||||
−0.848200 | + | 0.529677i | \(0.822313\pi\) | |||||||
\(38\) | −9.44024 | −1.53141 | ||||||||
\(39\) | 5.30961 | 0.850218 | ||||||||
\(40\) | 3.42700 | 0.541857 | ||||||||
\(41\) | 7.73454 | 1.20793 | 0.603966 | − | 0.797010i | \(-0.293586\pi\) | ||||
0.603966 | + | 0.797010i | \(0.293586\pi\) | |||||||
\(42\) | −5.44200 | −0.839719 | ||||||||
\(43\) | −11.8132 | −1.80150 | −0.900749 | − | 0.434340i | \(-0.856982\pi\) | ||||
−0.900749 | + | 0.434340i | \(0.856982\pi\) | |||||||
\(44\) | −0.139279 | −0.0209971 | ||||||||
\(45\) | 1.16053 | 0.173001 | ||||||||
\(46\) | −5.14428 | −0.758482 | ||||||||
\(47\) | −7.75967 | −1.13186 | −0.565932 | − | 0.824452i | \(-0.691484\pi\) | ||||
−0.565932 | + | 0.824452i | \(0.691484\pi\) | |||||||
\(48\) | 3.55373 | 0.512936 | ||||||||
\(49\) | 9.47688 | 1.35384 | ||||||||
\(50\) | 4.89769 | 0.692638 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.07579 | 0.149185 | ||||||||
\(53\) | 11.5622 | 1.58819 | 0.794093 | − | 0.607796i | \(-0.207946\pi\) | ||||
0.794093 | + | 0.607796i | \(0.207946\pi\) | |||||||
\(54\) | 1.34067 | 0.182442 | ||||||||
\(55\) | 0.797771 | 0.107571 | ||||||||
\(56\) | −11.9866 | −1.60178 | ||||||||
\(57\) | −7.04145 | −0.932663 | ||||||||
\(58\) | −7.04729 | −0.925355 | ||||||||
\(59\) | −3.00997 | −0.391865 | −0.195933 | − | 0.980617i | \(-0.562773\pi\) | ||||
−0.195933 | + | 0.980617i | \(0.562773\pi\) | |||||||
\(60\) | 0.235136 | 0.0303559 | ||||||||
\(61\) | −11.8368 | −1.51555 | −0.757774 | − | 0.652517i | \(-0.773713\pi\) | ||||
−0.757774 | + | 0.652517i | \(0.773713\pi\) | |||||||
\(62\) | 8.66873 | 1.10093 | ||||||||
\(63\) | −4.05917 | −0.511408 | ||||||||
\(64\) | 8.63792 | 1.07974 | ||||||||
\(65\) | −6.16195 | −0.764296 | ||||||||
\(66\) | 0.921603 | 0.113441 | ||||||||
\(67\) | 11.4342 | 1.39690 | 0.698452 | − | 0.715656i | \(-0.253872\pi\) | ||||
0.698452 | + | 0.715656i | \(0.253872\pi\) | |||||||
\(68\) | 0.202611 | 0.0245702 | ||||||||
\(69\) | −3.83710 | −0.461933 | ||||||||
\(70\) | 6.31559 | 0.754858 | ||||||||
\(71\) | 4.29205 | 0.509373 | 0.254686 | − | 0.967024i | \(-0.418028\pi\) | ||||
0.254686 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(72\) | 2.95297 | 0.348011 | ||||||||
\(73\) | −2.60512 | −0.304907 | −0.152453 | − | 0.988311i | \(-0.548717\pi\) | ||||
−0.152453 | + | 0.988311i | \(0.548717\pi\) | |||||||
\(74\) | 13.8341 | 1.60818 | ||||||||
\(75\) | 3.65317 | 0.421832 | ||||||||
\(76\) | −1.42668 | −0.163651 | ||||||||
\(77\) | −2.79036 | −0.317991 | ||||||||
\(78\) | −7.11842 | −0.806002 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −4.12420 | −0.461100 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.3694 | −1.14511 | ||||||||
\(83\) | −5.07294 | −0.556828 | −0.278414 | − | 0.960461i | \(-0.589809\pi\) | ||||
−0.278414 | + | 0.960461i | \(0.589809\pi\) | |||||||
\(84\) | −0.822434 | −0.0897349 | ||||||||
\(85\) | −1.16053 | −0.125877 | ||||||||
\(86\) | 15.8376 | 1.70781 | ||||||||
\(87\) | −5.25655 | −0.563562 | ||||||||
\(88\) | 2.02993 | 0.216392 | ||||||||
\(89\) | −6.92093 | −0.733617 | −0.366809 | − | 0.930296i | \(-0.619550\pi\) | ||||
−0.366809 | + | 0.930296i | \(0.619550\pi\) | |||||||
\(90\) | −1.55588 | −0.164004 | ||||||||
\(91\) | 21.5526 | 2.25933 | ||||||||
\(92\) | −0.777440 | −0.0810537 | ||||||||
\(93\) | 6.46598 | 0.670491 | ||||||||
\(94\) | 10.4031 | 1.07300 | ||||||||
\(95\) | 8.17180 | 0.838409 | ||||||||
\(96\) | 1.14157 | 0.116511 | ||||||||
\(97\) | −7.18674 | −0.729703 | −0.364851 | − | 0.931066i | \(-0.618880\pi\) | ||||
−0.364851 | + | 0.931066i | \(0.618880\pi\) | |||||||
\(98\) | −12.7053 | −1.28343 | ||||||||
\(99\) | 0.687421 | 0.0690884 | ||||||||
\(100\) | 0.740174 | 0.0740174 | ||||||||
\(101\) | 14.3632 | 1.42919 | 0.714596 | − | 0.699537i | \(-0.246611\pi\) | ||||
0.714596 | + | 0.699537i | \(0.246611\pi\) | |||||||
\(102\) | −1.34067 | −0.132746 | ||||||||
\(103\) | 16.2362 | 1.59980 | 0.799899 | − | 0.600135i | \(-0.204886\pi\) | ||||
0.799899 | + | 0.600135i | \(0.204886\pi\) | |||||||
\(104\) | −15.6791 | −1.53746 | ||||||||
\(105\) | 4.71078 | 0.459725 | ||||||||
\(106\) | −15.5010 | −1.50559 | ||||||||
\(107\) | −17.7659 | −1.71750 | −0.858749 | − | 0.512396i | \(-0.828758\pi\) | ||||
−0.858749 | + | 0.512396i | \(0.828758\pi\) | |||||||
\(108\) | 0.202611 | 0.0194963 | ||||||||
\(109\) | −12.2214 | −1.17060 | −0.585299 | − | 0.810817i | \(-0.699023\pi\) | ||||
−0.585299 | + | 0.810817i | \(0.699023\pi\) | |||||||
\(110\) | −1.06955 | −0.101977 | ||||||||
\(111\) | 10.3188 | 0.979417 | ||||||||
\(112\) | 14.4252 | 1.36305 | ||||||||
\(113\) | 11.5125 | 1.08300 | 0.541502 | − | 0.840700i | \(-0.317856\pi\) | ||||
0.541502 | + | 0.840700i | \(0.317856\pi\) | |||||||
\(114\) | 9.44024 | 0.884160 | ||||||||
\(115\) | 4.45307 | 0.415250 | ||||||||
\(116\) | −1.06504 | −0.0988862 | ||||||||
\(117\) | −5.30961 | −0.490873 | ||||||||
\(118\) | 4.03537 | 0.371486 | ||||||||
\(119\) | 4.05917 | 0.372104 | ||||||||
\(120\) | −3.42700 | −0.312841 | ||||||||
\(121\) | −10.5275 | −0.957041 | ||||||||
\(122\) | 15.8692 | 1.43673 | ||||||||
\(123\) | −7.73454 | −0.697400 | ||||||||
\(124\) | 1.31008 | 0.117649 | ||||||||
\(125\) | −10.0423 | −0.898206 | ||||||||
\(126\) | 5.44200 | 0.484812 | ||||||||
\(127\) | 3.35833 | 0.298004 | 0.149002 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149002 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(128\) | −9.29743 | −0.821785 | ||||||||
\(129\) | 11.8132 | 1.04010 | ||||||||
\(130\) | 8.26113 | 0.724549 | ||||||||
\(131\) | 14.5046 | 1.26727 | 0.633635 | − | 0.773632i | \(-0.281562\pi\) | ||||
0.633635 | + | 0.773632i | \(0.281562\pi\) | |||||||
\(132\) | 0.139279 | 0.0121227 | ||||||||
\(133\) | −28.5825 | −2.47841 | ||||||||
\(134\) | −15.3294 | −1.32426 | ||||||||
\(135\) | −1.16053 | −0.0998824 | ||||||||
\(136\) | −2.95297 | −0.253215 | ||||||||
\(137\) | −16.8949 | −1.44343 | −0.721716 | − | 0.692190i | \(-0.756646\pi\) | ||||
−0.721716 | + | 0.692190i | \(0.756646\pi\) | |||||||
\(138\) | 5.14428 | 0.437910 | ||||||||
\(139\) | 12.1040 | 1.02665 | 0.513326 | − | 0.858194i | \(-0.328413\pi\) | ||||
0.513326 | + | 0.858194i | \(0.328413\pi\) | |||||||
\(140\) | 0.954458 | 0.0806664 | ||||||||
\(141\) | 7.75967 | 0.653482 | ||||||||
\(142\) | −5.75421 | −0.482883 | ||||||||
\(143\) | −3.64993 | −0.305223 | ||||||||
\(144\) | −3.55373 | −0.296144 | ||||||||
\(145\) | 6.10038 | 0.506609 | ||||||||
\(146\) | 3.49260 | 0.289050 | ||||||||
\(147\) | −9.47688 | −0.781640 | ||||||||
\(148\) | 2.09070 | 0.171855 | ||||||||
\(149\) | −3.03517 | −0.248651 | −0.124326 | − | 0.992241i | \(-0.539677\pi\) | ||||
−0.124326 | + | 0.992241i | \(0.539677\pi\) | |||||||
\(150\) | −4.89769 | −0.399895 | ||||||||
\(151\) | −11.8078 | −0.960903 | −0.480452 | − | 0.877021i | \(-0.659527\pi\) | ||||
−0.480452 | + | 0.877021i | \(0.659527\pi\) | |||||||
\(152\) | 20.7932 | 1.68655 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 3.74094 | 0.301454 | ||||||||
\(155\) | −7.50395 | −0.602732 | ||||||||
\(156\) | −1.07579 | −0.0861318 | ||||||||
\(157\) | −8.10733 | −0.647036 | −0.323518 | − | 0.946222i | \(-0.604866\pi\) | ||||
−0.323518 | + | 0.946222i | \(0.604866\pi\) | |||||||
\(158\) | −1.34067 | −0.106658 | ||||||||
\(159\) | −11.5622 | −0.916940 | ||||||||
\(160\) | −1.32483 | −0.104737 | ||||||||
\(161\) | −15.5755 | −1.22752 | ||||||||
\(162\) | −1.34067 | −0.105333 | ||||||||
\(163\) | −6.17262 | −0.483477 | −0.241739 | − | 0.970341i | \(-0.577718\pi\) | ||||
−0.241739 | + | 0.970341i | \(0.577718\pi\) | |||||||
\(164\) | −1.56710 | −0.122370 | ||||||||
\(165\) | −0.797771 | −0.0621064 | ||||||||
\(166\) | 6.80113 | 0.527870 | ||||||||
\(167\) | −20.3368 | −1.57371 | −0.786854 | − | 0.617139i | \(-0.788292\pi\) | ||||
−0.786854 | + | 0.617139i | \(0.788292\pi\) | |||||||
\(168\) | 11.9866 | 0.924787 | ||||||||
\(169\) | 15.1919 | 1.16861 | ||||||||
\(170\) | 1.55588 | 0.119331 | ||||||||
\(171\) | 7.04145 | 0.538473 | ||||||||
\(172\) | 2.39349 | 0.182502 | ||||||||
\(173\) | 16.1657 | 1.22906 | 0.614528 | − | 0.788895i | \(-0.289347\pi\) | ||||
0.614528 | + | 0.788895i | \(0.289347\pi\) | |||||||
\(174\) | 7.04729 | 0.534254 | ||||||||
\(175\) | 14.8289 | 1.12096 | ||||||||
\(176\) | −2.44291 | −0.184141 | ||||||||
\(177\) | 3.00997 | 0.226243 | ||||||||
\(178\) | 9.27866 | 0.695465 | ||||||||
\(179\) | 3.23273 | 0.241625 | 0.120813 | − | 0.992675i | \(-0.461450\pi\) | ||||
0.120813 | + | 0.992675i | \(0.461450\pi\) | |||||||
\(180\) | −0.235136 | −0.0175260 | ||||||||
\(181\) | −10.3861 | −0.771996 | −0.385998 | − | 0.922500i | \(-0.626143\pi\) | ||||
−0.385998 | + | 0.922500i | \(0.626143\pi\) | |||||||
\(182\) | −28.8949 | −2.14183 | ||||||||
\(183\) | 11.8368 | 0.875002 | ||||||||
\(184\) | 11.3308 | 0.835321 | ||||||||
\(185\) | −11.9753 | −0.880438 | ||||||||
\(186\) | −8.66873 | −0.635622 | ||||||||
\(187\) | −0.687421 | −0.0502692 | ||||||||
\(188\) | 1.57220 | 0.114664 | ||||||||
\(189\) | 4.05917 | 0.295261 | ||||||||
\(190\) | −10.9557 | −0.794808 | ||||||||
\(191\) | 13.0022 | 0.940803 | 0.470401 | − | 0.882453i | \(-0.344109\pi\) | ||||
0.470401 | + | 0.882453i | \(0.344109\pi\) | |||||||
\(192\) | −8.63792 | −0.623388 | ||||||||
\(193\) | 3.38016 | 0.243309 | 0.121655 | − | 0.992572i | \(-0.461180\pi\) | ||||
0.121655 | + | 0.992572i | \(0.461180\pi\) | |||||||
\(194\) | 9.63503 | 0.691755 | ||||||||
\(195\) | 6.16195 | 0.441266 | ||||||||
\(196\) | −1.92012 | −0.137152 | ||||||||
\(197\) | −3.49753 | −0.249189 | −0.124594 | − | 0.992208i | \(-0.539763\pi\) | ||||
−0.124594 | + | 0.992208i | \(0.539763\pi\) | |||||||
\(198\) | −0.921603 | −0.0654954 | ||||||||
\(199\) | 11.2955 | 0.800715 | 0.400357 | − | 0.916359i | \(-0.368886\pi\) | ||||
0.400357 | + | 0.916359i | \(0.368886\pi\) | |||||||
\(200\) | −10.7877 | −0.762806 | ||||||||
\(201\) | −11.4342 | −0.806503 | ||||||||
\(202\) | −19.2563 | −1.35487 | ||||||||
\(203\) | −21.3373 | −1.49758 | ||||||||
\(204\) | −0.202611 | −0.0141856 | ||||||||
\(205\) | 8.97615 | 0.626922 | ||||||||
\(206\) | −21.7673 | −1.51660 | ||||||||
\(207\) | 3.83710 | 0.266697 | ||||||||
\(208\) | 18.8689 | 1.30832 | ||||||||
\(209\) | 4.84044 | 0.334820 | ||||||||
\(210\) | −6.31559 | −0.435817 | ||||||||
\(211\) | 18.1639 | 1.25046 | 0.625228 | − | 0.780442i | \(-0.285006\pi\) | ||||
0.625228 | + | 0.780442i | \(0.285006\pi\) | |||||||
\(212\) | −2.34262 | −0.160892 | ||||||||
\(213\) | −4.29205 | −0.294086 | ||||||||
\(214\) | 23.8182 | 1.62818 | ||||||||
\(215\) | −13.7096 | −0.934985 | ||||||||
\(216\) | −2.95297 | −0.200924 | ||||||||
\(217\) | 26.2465 | 1.78173 | ||||||||
\(218\) | 16.3848 | 1.10972 | ||||||||
\(219\) | 2.60512 | 0.176038 | ||||||||
\(220\) | −0.161637 | −0.0108976 | ||||||||
\(221\) | 5.30961 | 0.357163 | ||||||||
\(222\) | −13.8341 | −0.928482 | ||||||||
\(223\) | 4.09022 | 0.273901 | 0.136951 | − | 0.990578i | \(-0.456270\pi\) | ||||
0.136951 | + | 0.990578i | \(0.456270\pi\) | |||||||
\(224\) | 4.63384 | 0.309612 | ||||||||
\(225\) | −3.65317 | −0.243545 | ||||||||
\(226\) | −15.4344 | −1.02668 | ||||||||
\(227\) | 24.9126 | 1.65351 | 0.826755 | − | 0.562562i | \(-0.190184\pi\) | ||||
0.826755 | + | 0.562562i | \(0.190184\pi\) | |||||||
\(228\) | 1.42668 | 0.0944840 | ||||||||
\(229\) | 27.3467 | 1.80712 | 0.903560 | − | 0.428461i | \(-0.140944\pi\) | ||||
0.903560 | + | 0.428461i | \(0.140944\pi\) | |||||||
\(230\) | −5.97008 | −0.393655 | ||||||||
\(231\) | 2.79036 | 0.183592 | ||||||||
\(232\) | 15.5224 | 1.01910 | ||||||||
\(233\) | 12.8636 | 0.842723 | 0.421361 | − | 0.906893i | \(-0.361552\pi\) | ||||
0.421361 | + | 0.906893i | \(0.361552\pi\) | |||||||
\(234\) | 7.11842 | 0.465345 | ||||||||
\(235\) | −9.00532 | −0.587442 | ||||||||
\(236\) | 0.609854 | 0.0396981 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −5.44200 | −0.352752 | ||||||||
\(239\) | 9.75104 | 0.630742 | 0.315371 | − | 0.948968i | \(-0.397871\pi\) | ||||
0.315371 | + | 0.948968i | \(0.397871\pi\) | |||||||
\(240\) | 4.12420 | 0.266216 | ||||||||
\(241\) | −3.15488 | −0.203224 | −0.101612 | − | 0.994824i | \(-0.532400\pi\) | ||||
−0.101612 | + | 0.994824i | \(0.532400\pi\) | |||||||
\(242\) | 14.1138 | 0.907270 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.39827 | 0.153534 | ||||||||
\(245\) | 10.9982 | 0.702648 | ||||||||
\(246\) | 10.3694 | 0.661132 | ||||||||
\(247\) | −37.3873 | −2.37890 | ||||||||
\(248\) | −19.0938 | −1.21246 | ||||||||
\(249\) | 5.07294 | 0.321485 | ||||||||
\(250\) | 13.4633 | 0.851495 | ||||||||
\(251\) | 6.60429 | 0.416859 | 0.208430 | − | 0.978037i | \(-0.433165\pi\) | ||||
0.208430 | + | 0.978037i | \(0.433165\pi\) | |||||||
\(252\) | 0.822434 | 0.0518085 | ||||||||
\(253\) | 2.63770 | 0.165831 | ||||||||
\(254\) | −4.50241 | −0.282506 | ||||||||
\(255\) | 1.16053 | 0.0726751 | ||||||||
\(256\) | −4.81108 | −0.300692 | ||||||||
\(257\) | −13.9554 | −0.870514 | −0.435257 | − | 0.900306i | \(-0.643343\pi\) | ||||
−0.435257 | + | 0.900306i | \(0.643343\pi\) | |||||||
\(258\) | −15.8376 | −0.986005 | ||||||||
\(259\) | 41.8858 | 2.60265 | ||||||||
\(260\) | 1.24848 | 0.0774275 | ||||||||
\(261\) | 5.25655 | 0.325373 | ||||||||
\(262\) | −19.4458 | −1.20137 | ||||||||
\(263\) | 25.7056 | 1.58508 | 0.792538 | − | 0.609823i | \(-0.208759\pi\) | ||||
0.792538 | + | 0.609823i | \(0.208759\pi\) | |||||||
\(264\) | −2.02993 | −0.124934 | ||||||||
\(265\) | 13.4182 | 0.824275 | ||||||||
\(266\) | 38.3196 | 2.34952 | ||||||||
\(267\) | 6.92093 | 0.423554 | ||||||||
\(268\) | −2.31669 | −0.141514 | ||||||||
\(269\) | 15.0361 | 0.916767 | 0.458383 | − | 0.888755i | \(-0.348429\pi\) | ||||
0.458383 | + | 0.888755i | \(0.348429\pi\) | |||||||
\(270\) | 1.55588 | 0.0946880 | ||||||||
\(271\) | 11.8915 | 0.722357 | 0.361178 | − | 0.932497i | \(-0.382375\pi\) | ||||
0.361178 | + | 0.932497i | \(0.382375\pi\) | |||||||
\(272\) | 3.55373 | 0.215476 | ||||||||
\(273\) | −21.5526 | −1.30442 | ||||||||
\(274\) | 22.6505 | 1.36837 | ||||||||
\(275\) | −2.51127 | −0.151435 | ||||||||
\(276\) | 0.777440 | 0.0467964 | ||||||||
\(277\) | 30.7994 | 1.85056 | 0.925278 | − | 0.379289i | \(-0.123831\pi\) | ||||
0.925278 | + | 0.379289i | \(0.123831\pi\) | |||||||
\(278\) | −16.2275 | −0.973261 | ||||||||
\(279\) | −6.46598 | −0.387108 | ||||||||
\(280\) | −13.9108 | −0.831329 | ||||||||
\(281\) | 9.74076 | 0.581085 | 0.290543 | − | 0.956862i | \(-0.406164\pi\) | ||||
0.290543 | + | 0.956862i | \(0.406164\pi\) | |||||||
\(282\) | −10.4031 | −0.619498 | ||||||||
\(283\) | 26.2209 | 1.55867 | 0.779335 | − | 0.626607i | \(-0.215557\pi\) | ||||
0.779335 | + | 0.626607i | \(0.215557\pi\) | |||||||
\(284\) | −0.869617 | −0.0516023 | ||||||||
\(285\) | −8.17180 | −0.484056 | ||||||||
\(286\) | 4.89335 | 0.289350 | ||||||||
\(287\) | −31.3958 | −1.85324 | ||||||||
\(288\) | −1.14157 | −0.0672678 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.17858 | −0.480263 | ||||||||
\(291\) | 7.18674 | 0.421294 | ||||||||
\(292\) | 0.527827 | 0.0308888 | ||||||||
\(293\) | −25.6696 | −1.49963 | −0.749816 | − | 0.661647i | \(-0.769858\pi\) | ||||
−0.749816 | + | 0.661647i | \(0.769858\pi\) | |||||||
\(294\) | 12.7053 | 0.740990 | ||||||||
\(295\) | −3.49316 | −0.203380 | ||||||||
\(296\) | −30.4711 | −1.77110 | ||||||||
\(297\) | −0.687421 | −0.0398882 | ||||||||
\(298\) | 4.06916 | 0.235720 | ||||||||
\(299\) | −20.3735 | −1.17823 | ||||||||
\(300\) | −0.740174 | −0.0427340 | ||||||||
\(301\) | 47.9519 | 2.76390 | ||||||||
\(302\) | 15.8303 | 0.910931 | ||||||||
\(303\) | −14.3632 | −0.825144 | ||||||||
\(304\) | −25.0234 | −1.43519 | ||||||||
\(305\) | −13.7370 | −0.786576 | ||||||||
\(306\) | 1.34067 | 0.0766408 | ||||||||
\(307\) | 15.0301 | 0.857811 | 0.428906 | − | 0.903349i | \(-0.358899\pi\) | ||||
0.428906 | + | 0.903349i | \(0.358899\pi\) | |||||||
\(308\) | 0.565358 | 0.0322143 | ||||||||
\(309\) | −16.2362 | −0.923644 | ||||||||
\(310\) | 10.0603 | 0.571387 | ||||||||
\(311\) | −23.4034 | −1.32709 | −0.663543 | − | 0.748138i | \(-0.730948\pi\) | ||||
−0.663543 | + | 0.748138i | \(0.730948\pi\) | |||||||
\(312\) | 15.6791 | 0.887655 | ||||||||
\(313\) | −5.99411 | −0.338807 | −0.169404 | − | 0.985547i | \(-0.554184\pi\) | ||||
−0.169404 | + | 0.985547i | \(0.554184\pi\) | |||||||
\(314\) | 10.8692 | 0.613387 | ||||||||
\(315\) | −4.71078 | −0.265423 | ||||||||
\(316\) | −0.202611 | −0.0113978 | ||||||||
\(317\) | 2.48476 | 0.139558 | 0.0697789 | − | 0.997562i | \(-0.477771\pi\) | ||||
0.0697789 | + | 0.997562i | \(0.477771\pi\) | |||||||
\(318\) | 15.5010 | 0.869254 | ||||||||
\(319\) | 3.61346 | 0.202315 | ||||||||
\(320\) | 10.0246 | 0.560390 | ||||||||
\(321\) | 17.7659 | 0.991598 | ||||||||
\(322\) | 20.8815 | 1.16368 | ||||||||
\(323\) | −7.04145 | −0.391797 | ||||||||
\(324\) | −0.202611 | −0.0112562 | ||||||||
\(325\) | 19.3969 | 1.07595 | ||||||||
\(326\) | 8.27544 | 0.458334 | ||||||||
\(327\) | 12.2214 | 0.675845 | ||||||||
\(328\) | 22.8399 | 1.26112 | ||||||||
\(329\) | 31.4978 | 1.73653 | ||||||||
\(330\) | 1.06955 | 0.0588766 | ||||||||
\(331\) | −13.2932 | −0.730660 | −0.365330 | − | 0.930878i | \(-0.619044\pi\) | ||||
−0.365330 | + | 0.930878i | \(0.619044\pi\) | |||||||
\(332\) | 1.02783 | 0.0564098 | ||||||||
\(333\) | −10.3188 | −0.565466 | ||||||||
\(334\) | 27.2649 | 1.49187 | ||||||||
\(335\) | 13.2697 | 0.724999 | ||||||||
\(336\) | −14.4252 | −0.786958 | ||||||||
\(337\) | −16.1094 | −0.877535 | −0.438768 | − | 0.898601i | \(-0.644585\pi\) | ||||
−0.438768 | + | 0.898601i | \(0.644585\pi\) | |||||||
\(338\) | −20.3673 | −1.10784 | ||||||||
\(339\) | −11.5125 | −0.625273 | ||||||||
\(340\) | 0.235136 | 0.0127520 | ||||||||
\(341\) | −4.44485 | −0.240702 | ||||||||
\(342\) | −9.44024 | −0.510470 | ||||||||
\(343\) | −10.0541 | −0.542869 | ||||||||
\(344\) | −34.8840 | −1.88082 | ||||||||
\(345\) | −4.45307 | −0.239745 | ||||||||
\(346\) | −21.6728 | −1.16514 | ||||||||
\(347\) | 8.63515 | 0.463559 | 0.231780 | − | 0.972768i | \(-0.425545\pi\) | ||||
0.231780 | + | 0.972768i | \(0.425545\pi\) | |||||||
\(348\) | 1.06504 | 0.0570920 | ||||||||
\(349\) | −19.7336 | −1.05631 | −0.528157 | − | 0.849147i | \(-0.677117\pi\) | ||||
−0.528157 | + | 0.849147i | \(0.677117\pi\) | |||||||
\(350\) | −19.8806 | −1.06266 | ||||||||
\(351\) | 5.30961 | 0.283406 | ||||||||
\(352\) | −0.784741 | −0.0418268 | ||||||||
\(353\) | 20.0675 | 1.06809 | 0.534043 | − | 0.845457i | \(-0.320672\pi\) | ||||
0.534043 | + | 0.845457i | \(0.320672\pi\) | |||||||
\(354\) | −4.03537 | −0.214478 | ||||||||
\(355\) | 4.98105 | 0.264366 | ||||||||
\(356\) | 1.40226 | 0.0743195 | ||||||||
\(357\) | −4.05917 | −0.214834 | ||||||||
\(358\) | −4.33401 | −0.229060 | ||||||||
\(359\) | 0.383076 | 0.0202180 | 0.0101090 | − | 0.999949i | \(-0.496782\pi\) | ||||
0.0101090 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(360\) | 3.42700 | 0.180619 | ||||||||
\(361\) | 30.5820 | 1.60958 | ||||||||
\(362\) | 13.9244 | 0.731848 | ||||||||
\(363\) | 10.5275 | 0.552548 | ||||||||
\(364\) | −4.36680 | −0.228883 | ||||||||
\(365\) | −3.02332 | −0.158248 | ||||||||
\(366\) | −15.8692 | −0.829498 | ||||||||
\(367\) | 29.8216 | 1.55667 | 0.778337 | − | 0.627846i | \(-0.216063\pi\) | ||||
0.778337 | + | 0.627846i | \(0.216063\pi\) | |||||||
\(368\) | −13.6360 | −0.710826 | ||||||||
\(369\) | 7.73454 | 0.402644 | ||||||||
\(370\) | 16.0548 | 0.834651 | ||||||||
\(371\) | −46.9328 | −2.43663 | ||||||||
\(372\) | −1.31008 | −0.0679245 | ||||||||
\(373\) | −3.20080 | −0.165731 | −0.0828655 | − | 0.996561i | \(-0.526407\pi\) | ||||
−0.0828655 | + | 0.996561i | \(0.526407\pi\) | |||||||
\(374\) | 0.921603 | 0.0476549 | ||||||||
\(375\) | 10.0423 | 0.518580 | ||||||||
\(376\) | −22.9141 | −1.18170 | ||||||||
\(377\) | −27.9102 | −1.43745 | ||||||||
\(378\) | −5.44200 | −0.279906 | ||||||||
\(379\) | −7.99675 | −0.410765 | −0.205383 | − | 0.978682i | \(-0.565844\pi\) | ||||
−0.205383 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(380\) | −1.65570 | −0.0849356 | ||||||||
\(381\) | −3.35833 | −0.172053 | ||||||||
\(382\) | −17.4316 | −0.891876 | ||||||||
\(383\) | 35.3913 | 1.80841 | 0.904205 | − | 0.427099i | \(-0.140464\pi\) | ||||
0.904205 | + | 0.427099i | \(0.140464\pi\) | |||||||
\(384\) | 9.29743 | 0.474458 | ||||||||
\(385\) | −3.23829 | −0.165039 | ||||||||
\(386\) | −4.53167 | −0.230656 | ||||||||
\(387\) | −11.8132 | −0.600499 | ||||||||
\(388\) | 1.45611 | 0.0739230 | ||||||||
\(389\) | 7.34691 | 0.372503 | 0.186252 | − | 0.982502i | \(-0.440366\pi\) | ||||
0.186252 | + | 0.982502i | \(0.440366\pi\) | |||||||
\(390\) | −8.26113 | −0.418318 | ||||||||
\(391\) | −3.83710 | −0.194051 | ||||||||
\(392\) | 27.9849 | 1.41345 | ||||||||
\(393\) | −14.5046 | −0.731658 | ||||||||
\(394\) | 4.68903 | 0.236230 | ||||||||
\(395\) | 1.16053 | 0.0583925 | ||||||||
\(396\) | −0.139279 | −0.00699904 | ||||||||
\(397\) | 3.24085 | 0.162653 | 0.0813267 | − | 0.996687i | \(-0.474084\pi\) | ||||
0.0813267 | + | 0.996687i | \(0.474084\pi\) | |||||||
\(398\) | −15.1435 | −0.759073 | ||||||||
\(399\) | 28.5825 | 1.43091 | ||||||||
\(400\) | 12.9824 | 0.649119 | ||||||||
\(401\) | 12.8012 | 0.639263 | 0.319632 | − | 0.947542i | \(-0.396441\pi\) | ||||
0.319632 | + | 0.947542i | \(0.396441\pi\) | |||||||
\(402\) | 15.3294 | 0.764561 | ||||||||
\(403\) | 34.3318 | 1.71019 | ||||||||
\(404\) | −2.91015 | −0.144785 | ||||||||
\(405\) | 1.16053 | 0.0576671 | ||||||||
\(406\) | 28.6062 | 1.41970 | ||||||||
\(407\) | −7.09335 | −0.351605 | ||||||||
\(408\) | 2.95297 | 0.146194 | ||||||||
\(409\) | 27.0191 | 1.33601 | 0.668004 | − | 0.744158i | \(-0.267149\pi\) | ||||
0.668004 | + | 0.744158i | \(0.267149\pi\) | |||||||
\(410\) | −12.0340 | −0.594319 | ||||||||
\(411\) | 16.8949 | 0.833365 | ||||||||
\(412\) | −3.28963 | −0.162069 | ||||||||
\(413\) | 12.2180 | 0.601208 | ||||||||
\(414\) | −5.14428 | −0.252827 | ||||||||
\(415\) | −5.88729 | −0.288996 | ||||||||
\(416\) | 6.06130 | 0.297180 | ||||||||
\(417\) | −12.1040 | −0.592738 | ||||||||
\(418\) | −6.48942 | −0.317408 | ||||||||
\(419\) | 11.2668 | 0.550420 | 0.275210 | − | 0.961384i | \(-0.411253\pi\) | ||||
0.275210 | + | 0.961384i | \(0.411253\pi\) | |||||||
\(420\) | −0.954458 | −0.0465728 | ||||||||
\(421\) | −18.5205 | −0.902633 | −0.451317 | − | 0.892364i | \(-0.649046\pi\) | ||||
−0.451317 | + | 0.892364i | \(0.649046\pi\) | |||||||
\(422\) | −24.3518 | −1.18543 | ||||||||
\(423\) | −7.75967 | −0.377288 | ||||||||
\(424\) | 34.1427 | 1.65812 | ||||||||
\(425\) | 3.65317 | 0.177205 | ||||||||
\(426\) | 5.75421 | 0.278792 | ||||||||
\(427\) | 48.0477 | 2.32519 | ||||||||
\(428\) | 3.59958 | 0.173992 | ||||||||
\(429\) | 3.64993 | 0.176221 | ||||||||
\(430\) | 18.3800 | 0.886361 | ||||||||
\(431\) | 3.19388 | 0.153844 | 0.0769219 | − | 0.997037i | \(-0.475491\pi\) | ||||
0.0769219 | + | 0.997037i | \(0.475491\pi\) | |||||||
\(432\) | 3.55373 | 0.170979 | ||||||||
\(433\) | 28.2453 | 1.35738 | 0.678692 | − | 0.734423i | \(-0.262547\pi\) | ||||
0.678692 | + | 0.734423i | \(0.262547\pi\) | |||||||
\(434\) | −35.1879 | −1.68907 | ||||||||
\(435\) | −6.10038 | −0.292491 | ||||||||
\(436\) | 2.47619 | 0.118588 | ||||||||
\(437\) | 27.0188 | 1.29248 | ||||||||
\(438\) | −3.49260 | −0.166883 | ||||||||
\(439\) | −18.6279 | −0.889061 | −0.444530 | − | 0.895764i | \(-0.646629\pi\) | ||||
−0.444530 | + | 0.895764i | \(0.646629\pi\) | |||||||
\(440\) | 2.35579 | 0.112308 | ||||||||
\(441\) | 9.47688 | 0.451280 | ||||||||
\(442\) | −7.11842 | −0.338589 | ||||||||
\(443\) | −19.3894 | −0.921220 | −0.460610 | − | 0.887603i | \(-0.652369\pi\) | ||||
−0.460610 | + | 0.887603i | \(0.652369\pi\) | |||||||
\(444\) | −2.09070 | −0.0992204 | ||||||||
\(445\) | −8.03194 | −0.380750 | ||||||||
\(446\) | −5.48362 | −0.259657 | ||||||||
\(447\) | 3.03517 | 0.143559 | ||||||||
\(448\) | −35.0628 | −1.65656 | ||||||||
\(449\) | −4.85756 | −0.229243 | −0.114621 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114621 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(450\) | 4.89769 | 0.230879 | ||||||||
\(451\) | 5.31688 | 0.250362 | ||||||||
\(452\) | −2.33256 | −0.109714 | ||||||||
\(453\) | 11.8078 | 0.554778 | ||||||||
\(454\) | −33.3996 | −1.56752 | ||||||||
\(455\) | 25.0124 | 1.17260 | ||||||||
\(456\) | −20.7932 | −0.973730 | ||||||||
\(457\) | 40.2164 | 1.88124 | 0.940622 | − | 0.339457i | \(-0.110243\pi\) | ||||
0.940622 | + | 0.339457i | \(0.110243\pi\) | |||||||
\(458\) | −36.6628 | −1.71314 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.902241 | −0.0420672 | ||||||||
\(461\) | −7.02805 | −0.327329 | −0.163665 | − | 0.986516i | \(-0.552331\pi\) | ||||
−0.163665 | + | 0.986516i | \(0.552331\pi\) | |||||||
\(462\) | −3.74094 | −0.174044 | ||||||||
\(463\) | −3.27707 | −0.152298 | −0.0761492 | − | 0.997096i | \(-0.524263\pi\) | ||||
−0.0761492 | + | 0.997096i | \(0.524263\pi\) | |||||||
\(464\) | −18.6804 | −0.867214 | ||||||||
\(465\) | 7.50395 | 0.347987 | ||||||||
\(466\) | −17.2458 | −0.798897 | ||||||||
\(467\) | 25.2454 | 1.16822 | 0.584108 | − | 0.811676i | \(-0.301444\pi\) | ||||
0.584108 | + | 0.811676i | \(0.301444\pi\) | |||||||
\(468\) | 1.07579 | 0.0497282 | ||||||||
\(469\) | −46.4132 | −2.14316 | ||||||||
\(470\) | 12.0731 | 0.556892 | ||||||||
\(471\) | 8.10733 | 0.373566 | ||||||||
\(472\) | −8.88836 | −0.409120 | ||||||||
\(473\) | −8.12065 | −0.373388 | ||||||||
\(474\) | 1.34067 | 0.0615789 | ||||||||
\(475\) | −25.7236 | −1.18028 | ||||||||
\(476\) | −0.822434 | −0.0376962 | ||||||||
\(477\) | 11.5622 | 0.529395 | ||||||||
\(478\) | −13.0729 | −0.597941 | ||||||||
\(479\) | 29.0095 | 1.32548 | 0.662740 | − | 0.748850i | \(-0.269394\pi\) | ||||
0.662740 | + | 0.748850i | \(0.269394\pi\) | |||||||
\(480\) | 1.32483 | 0.0604698 | ||||||||
\(481\) | 54.7888 | 2.49815 | ||||||||
\(482\) | 4.22964 | 0.192655 | ||||||||
\(483\) | 15.5755 | 0.708708 | ||||||||
\(484\) | 2.13298 | 0.0969536 | ||||||||
\(485\) | −8.34042 | −0.378719 | ||||||||
\(486\) | 1.34067 | 0.0608139 | ||||||||
\(487\) | 27.0840 | 1.22729 | 0.613647 | − | 0.789581i | \(-0.289702\pi\) | ||||
0.613647 | + | 0.789581i | \(0.289702\pi\) | |||||||
\(488\) | −34.9537 | −1.58228 | ||||||||
\(489\) | 6.17262 | 0.279136 | ||||||||
\(490\) | −14.7449 | −0.666107 | ||||||||
\(491\) | 31.1323 | 1.40498 | 0.702491 | − | 0.711693i | \(-0.252071\pi\) | ||||
0.702491 | + | 0.711693i | \(0.252071\pi\) | |||||||
\(492\) | 1.56710 | 0.0706505 | ||||||||
\(493\) | −5.25655 | −0.236743 | ||||||||
\(494\) | 50.1240 | 2.25518 | ||||||||
\(495\) | 0.797771 | 0.0358572 | ||||||||
\(496\) | 22.9783 | 1.03176 | ||||||||
\(497\) | −17.4222 | −0.781491 | ||||||||
\(498\) | −6.80113 | −0.304766 | ||||||||
\(499\) | −38.9804 | −1.74500 | −0.872501 | − | 0.488613i | \(-0.837503\pi\) | ||||
−0.872501 | + | 0.488613i | \(0.837503\pi\) | |||||||
\(500\) | 2.03467 | 0.0909934 | ||||||||
\(501\) | 20.3368 | 0.908581 | ||||||||
\(502\) | −8.85416 | −0.395181 | ||||||||
\(503\) | −5.89255 | −0.262736 | −0.131368 | − | 0.991334i | \(-0.541937\pi\) | ||||
−0.131368 | + | 0.991334i | \(0.541937\pi\) | |||||||
\(504\) | −11.9866 | −0.533926 | ||||||||
\(505\) | 16.6689 | 0.741756 | ||||||||
\(506\) | −3.53628 | −0.157207 | ||||||||
\(507\) | −15.1919 | −0.674697 | ||||||||
\(508\) | −0.680436 | −0.0301895 | ||||||||
\(509\) | −8.30520 | −0.368122 | −0.184061 | − | 0.982915i | \(-0.558924\pi\) | ||||
−0.184061 | + | 0.982915i | \(0.558924\pi\) | |||||||
\(510\) | −1.55588 | −0.0688956 | ||||||||
\(511\) | 10.5746 | 0.467795 | ||||||||
\(512\) | 25.0449 | 1.10684 | ||||||||
\(513\) | −7.04145 | −0.310888 | ||||||||
\(514\) | 18.7096 | 0.825243 | ||||||||
\(515\) | 18.8425 | 0.830302 | ||||||||
\(516\) | −2.39349 | −0.105367 | ||||||||
\(517\) | −5.33416 | −0.234596 | ||||||||
\(518\) | −56.1549 | −2.46730 | ||||||||
\(519\) | −16.1657 | −0.709596 | ||||||||
\(520\) | −18.1960 | −0.797949 | ||||||||
\(521\) | −36.7470 | −1.60992 | −0.804958 | − | 0.593332i | \(-0.797812\pi\) | ||||
−0.804958 | + | 0.593332i | \(0.797812\pi\) | |||||||
\(522\) | −7.04729 | −0.308452 | ||||||||
\(523\) | −32.8646 | −1.43707 | −0.718534 | − | 0.695492i | \(-0.755186\pi\) | ||||
−0.718534 | + | 0.695492i | \(0.755186\pi\) | |||||||
\(524\) | −2.93879 | −0.128382 | ||||||||
\(525\) | −14.8289 | −0.647185 | ||||||||
\(526\) | −34.4627 | −1.50264 | ||||||||
\(527\) | 6.46598 | 0.281662 | ||||||||
\(528\) | 2.44291 | 0.106314 | ||||||||
\(529\) | −8.27665 | −0.359854 | ||||||||
\(530\) | −17.9894 | −0.781408 | ||||||||
\(531\) | −3.00997 | −0.130622 | ||||||||
\(532\) | 5.79113 | 0.251077 | ||||||||
\(533\) | −41.0674 | −1.77883 | ||||||||
\(534\) | −9.27866 | −0.401527 | ||||||||
\(535\) | −20.6179 | −0.891389 | ||||||||
\(536\) | 33.7647 | 1.45841 | ||||||||
\(537\) | −3.23273 | −0.139502 | ||||||||
\(538\) | −20.1584 | −0.869090 | ||||||||
\(539\) | 6.51460 | 0.280604 | ||||||||
\(540\) | 0.235136 | 0.0101186 | ||||||||
\(541\) | −1.61268 | −0.0693346 | −0.0346673 | − | 0.999399i | \(-0.511037\pi\) | ||||
−0.0346673 | + | 0.999399i | \(0.511037\pi\) | |||||||
\(542\) | −15.9425 | −0.684790 | ||||||||
\(543\) | 10.3861 | 0.445712 | ||||||||
\(544\) | 1.14157 | 0.0489445 | ||||||||
\(545\) | −14.1833 | −0.607545 | ||||||||
\(546\) | 28.8949 | 1.23659 | ||||||||
\(547\) | −29.1427 | −1.24605 | −0.623025 | − | 0.782202i | \(-0.714097\pi\) | ||||
−0.623025 | + | 0.782202i | \(0.714097\pi\) | |||||||
\(548\) | 3.42310 | 0.146228 | ||||||||
\(549\) | −11.8368 | −0.505183 | ||||||||
\(550\) | 3.36677 | 0.143560 | ||||||||
\(551\) | 37.0138 | 1.57684 | ||||||||
\(552\) | −11.3308 | −0.482273 | ||||||||
\(553\) | −4.05917 | −0.172614 | ||||||||
\(554\) | −41.2917 | −1.75432 | ||||||||
\(555\) | 11.9753 | 0.508321 | ||||||||
\(556\) | −2.45242 | −0.104006 | ||||||||
\(557\) | 25.6246 | 1.08575 | 0.542874 | − | 0.839814i | \(-0.317336\pi\) | ||||
0.542874 | + | 0.839814i | \(0.317336\pi\) | |||||||
\(558\) | 8.66873 | 0.366976 | ||||||||
\(559\) | 62.7235 | 2.65292 | ||||||||
\(560\) | 16.7408 | 0.707430 | ||||||||
\(561\) | 0.687421 | 0.0290229 | ||||||||
\(562\) | −13.0591 | −0.550866 | ||||||||
\(563\) | 18.2169 | 0.767749 | 0.383874 | − | 0.923385i | \(-0.374590\pi\) | ||||
0.383874 | + | 0.923385i | \(0.374590\pi\) | |||||||
\(564\) | −1.57220 | −0.0662014 | ||||||||
\(565\) | 13.3606 | 0.562083 | ||||||||
\(566\) | −35.1535 | −1.47761 | ||||||||
\(567\) | −4.05917 | −0.170469 | ||||||||
\(568\) | 12.6743 | 0.531801 | ||||||||
\(569\) | 14.7930 | 0.620154 | 0.310077 | − | 0.950711i | \(-0.399645\pi\) | ||||
0.310077 | + | 0.950711i | \(0.399645\pi\) | |||||||
\(570\) | 10.9557 | 0.458883 | ||||||||
\(571\) | −0.378441 | −0.0158372 | −0.00791862 | − | 0.999969i | \(-0.502521\pi\) | ||||
−0.00791862 | + | 0.999969i | \(0.502521\pi\) | |||||||
\(572\) | 0.739518 | 0.0309208 | ||||||||
\(573\) | −13.0022 | −0.543173 | ||||||||
\(574\) | 42.0914 | 1.75686 | ||||||||
\(575\) | −14.0176 | −0.584574 | ||||||||
\(576\) | 8.63792 | 0.359913 | ||||||||
\(577\) | 14.4007 | 0.599509 | 0.299754 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299754 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(578\) | −1.34067 | −0.0557644 | ||||||||
\(579\) | −3.38016 | −0.140475 | ||||||||
\(580\) | −1.23601 | −0.0513223 | ||||||||
\(581\) | 20.5919 | 0.854298 | ||||||||
\(582\) | −9.63503 | −0.399385 | ||||||||
\(583\) | 7.94808 | 0.329176 | ||||||||
\(584\) | −7.69285 | −0.318332 | ||||||||
\(585\) | −6.16195 | −0.254765 | ||||||||
\(586\) | 34.4143 | 1.42164 | ||||||||
\(587\) | 23.9942 | 0.990347 | 0.495173 | − | 0.868794i | \(-0.335105\pi\) | ||||
0.495173 | + | 0.868794i | \(0.335105\pi\) | |||||||
\(588\) | 1.92012 | 0.0791845 | ||||||||
\(589\) | −45.5299 | −1.87603 | ||||||||
\(590\) | 4.68316 | 0.192803 | ||||||||
\(591\) | 3.49753 | 0.143869 | ||||||||
\(592\) | 36.6702 | 1.50713 | ||||||||
\(593\) | −24.4590 | −1.00441 | −0.502205 | − | 0.864748i | \(-0.667478\pi\) | ||||
−0.502205 | + | 0.864748i | \(0.667478\pi\) | |||||||
\(594\) | 0.921603 | 0.0378138 | ||||||||
\(595\) | 4.71078 | 0.193123 | ||||||||
\(596\) | 0.614960 | 0.0251897 | ||||||||
\(597\) | −11.2955 | −0.462293 | ||||||||
\(598\) | 27.3141 | 1.11696 | ||||||||
\(599\) | 43.5632 | 1.77995 | 0.889973 | − | 0.456013i | \(-0.150723\pi\) | ||||
0.889973 | + | 0.456013i | \(0.150723\pi\) | |||||||
\(600\) | 10.7877 | 0.440406 | ||||||||
\(601\) | 16.2585 | 0.663197 | 0.331598 | − | 0.943421i | \(-0.392412\pi\) | ||||
0.331598 | + | 0.943421i | \(0.392412\pi\) | |||||||
\(602\) | −64.2875 | −2.62016 | ||||||||
\(603\) | 11.4342 | 0.465635 | ||||||||
\(604\) | 2.39239 | 0.0973449 | ||||||||
\(605\) | −12.2174 | −0.496708 | ||||||||
\(606\) | 19.2563 | 0.782233 | ||||||||
\(607\) | −17.9372 | −0.728047 | −0.364023 | − | 0.931390i | \(-0.618597\pi\) | ||||
−0.364023 | + | 0.931390i | \(0.618597\pi\) | |||||||
\(608\) | −8.03833 | −0.325997 | ||||||||
\(609\) | 21.3373 | 0.864629 | ||||||||
\(610\) | 18.4167 | 0.745670 | ||||||||
\(611\) | 41.2008 | 1.66681 | ||||||||
\(612\) | 0.202611 | 0.00819007 | ||||||||
\(613\) | −33.0964 | −1.33675 | −0.668374 | − | 0.743825i | \(-0.733010\pi\) | ||||
−0.668374 | + | 0.743825i | \(0.733010\pi\) | |||||||
\(614\) | −20.1503 | −0.813201 | ||||||||
\(615\) | −8.97615 | −0.361953 | ||||||||
\(616\) | −8.23984 | −0.331993 | ||||||||
\(617\) | 38.5578 | 1.55228 | 0.776140 | − | 0.630561i | \(-0.217175\pi\) | ||||
0.776140 | + | 0.630561i | \(0.217175\pi\) | |||||||
\(618\) | 21.7673 | 0.875610 | ||||||||
\(619\) | 26.6029 | 1.06926 | 0.534631 | − | 0.845086i | \(-0.320451\pi\) | ||||
0.534631 | + | 0.845086i | \(0.320451\pi\) | |||||||
\(620\) | 1.52038 | 0.0610601 | ||||||||
\(621\) | −3.83710 | −0.153978 | ||||||||
\(622\) | 31.3762 | 1.25807 | ||||||||
\(623\) | 28.0932 | 1.12553 | ||||||||
\(624\) | −18.8689 | −0.755360 | ||||||||
\(625\) | 6.61155 | 0.264462 | ||||||||
\(626\) | 8.03611 | 0.321187 | ||||||||
\(627\) | −4.84044 | −0.193309 | ||||||||
\(628\) | 1.64264 | 0.0655483 | ||||||||
\(629\) | 10.3188 | 0.411437 | ||||||||
\(630\) | 6.31559 | 0.251619 | ||||||||
\(631\) | −36.5603 | −1.45544 | −0.727720 | − | 0.685874i | \(-0.759420\pi\) | ||||
−0.727720 | + | 0.685874i | \(0.759420\pi\) | |||||||
\(632\) | 2.95297 | 0.117463 | ||||||||
\(633\) | −18.1639 | −0.721951 | ||||||||
\(634\) | −3.33123 | −0.132300 | ||||||||
\(635\) | 3.89744 | 0.154665 | ||||||||
\(636\) | 2.34262 | 0.0928911 | ||||||||
\(637\) | −50.3185 | −1.99369 | ||||||||
\(638\) | −4.84445 | −0.191794 | ||||||||
\(639\) | 4.29205 | 0.169791 | ||||||||
\(640\) | −10.7899 | −0.426510 | ||||||||
\(641\) | 29.8352 | 1.17842 | 0.589210 | − | 0.807980i | \(-0.299439\pi\) | ||||
0.589210 | + | 0.807980i | \(0.299439\pi\) | |||||||
\(642\) | −23.8182 | −0.940030 | ||||||||
\(643\) | 15.3169 | 0.604040 | 0.302020 | − | 0.953302i | \(-0.402339\pi\) | ||||
0.302020 | + | 0.953302i | \(0.402339\pi\) | |||||||
\(644\) | 3.15576 | 0.124354 | ||||||||
\(645\) | 13.7096 | 0.539814 | ||||||||
\(646\) | 9.44024 | 0.371421 | ||||||||
\(647\) | 29.3369 | 1.15335 | 0.576676 | − | 0.816973i | \(-0.304349\pi\) | ||||
0.576676 | + | 0.816973i | \(0.304349\pi\) | |||||||
\(648\) | 2.95297 | 0.116004 | ||||||||
\(649\) | −2.06912 | −0.0812200 | ||||||||
\(650\) | −26.0048 | −1.01999 | ||||||||
\(651\) | −26.2465 | −1.02868 | ||||||||
\(652\) | 1.25064 | 0.0489790 | ||||||||
\(653\) | −3.36570 | −0.131710 | −0.0658550 | − | 0.997829i | \(-0.520977\pi\) | ||||
−0.0658550 | + | 0.997829i | \(0.520977\pi\) | |||||||
\(654\) | −16.3848 | −0.640698 | ||||||||
\(655\) | 16.8330 | 0.657718 | ||||||||
\(656\) | −27.4864 | −1.07317 | ||||||||
\(657\) | −2.60512 | −0.101636 | ||||||||
\(658\) | −42.2281 | −1.64622 | ||||||||
\(659\) | −18.9760 | −0.739199 | −0.369599 | − | 0.929191i | \(-0.620505\pi\) | ||||
−0.369599 | + | 0.929191i | \(0.620505\pi\) | |||||||
\(660\) | 0.161637 | 0.00629173 | ||||||||
\(661\) | −20.1214 | −0.782632 | −0.391316 | − | 0.920256i | \(-0.627980\pi\) | ||||
−0.391316 | + | 0.920256i | \(0.627980\pi\) | |||||||
\(662\) | 17.8218 | 0.692662 | ||||||||
\(663\) | −5.30961 | −0.206208 | ||||||||
\(664\) | −14.9802 | −0.581346 | ||||||||
\(665\) | −33.1708 | −1.28631 | ||||||||
\(666\) | 13.8341 | 0.536059 | ||||||||
\(667\) | 20.1699 | 0.780983 | ||||||||
\(668\) | 4.12046 | 0.159426 | ||||||||
\(669\) | −4.09022 | −0.158137 | ||||||||
\(670\) | −17.7902 | −0.687296 | ||||||||
\(671\) | −8.13687 | −0.314120 | ||||||||
\(672\) | −4.63384 | −0.178754 | ||||||||
\(673\) | −24.6487 | −0.950138 | −0.475069 | − | 0.879949i | \(-0.657577\pi\) | ||||
−0.475069 | + | 0.879949i | \(0.657577\pi\) | |||||||
\(674\) | 21.5974 | 0.831899 | ||||||||
\(675\) | 3.65317 | 0.140611 | ||||||||
\(676\) | −3.07806 | −0.118387 | ||||||||
\(677\) | −9.69623 | −0.372656 | −0.186328 | − | 0.982488i | \(-0.559659\pi\) | ||||
−0.186328 | + | 0.982488i | \(0.559659\pi\) | |||||||
\(678\) | 15.4344 | 0.592755 | ||||||||
\(679\) | 29.1722 | 1.11953 | ||||||||
\(680\) | −3.42700 | −0.131420 | ||||||||
\(681\) | −24.9126 | −0.954654 | ||||||||
\(682\) | 5.95906 | 0.228184 | ||||||||
\(683\) | 26.7129 | 1.02214 | 0.511070 | − | 0.859539i | \(-0.329249\pi\) | ||||
0.511070 | + | 0.859539i | \(0.329249\pi\) | |||||||
\(684\) | −1.42668 | −0.0545504 | ||||||||
\(685\) | −19.6070 | −0.749147 | ||||||||
\(686\) | 13.4792 | 0.514637 | ||||||||
\(687\) | −27.3467 | −1.04334 | ||||||||
\(688\) | 41.9809 | 1.60051 | ||||||||
\(689\) | −61.3906 | −2.33879 | ||||||||
\(690\) | 5.97008 | 0.227277 | ||||||||
\(691\) | −33.3456 | −1.26853 | −0.634263 | − | 0.773117i | \(-0.718696\pi\) | ||||
−0.634263 | + | 0.773117i | \(0.718696\pi\) | |||||||
\(692\) | −3.27535 | −0.124510 | ||||||||
\(693\) | −2.79036 | −0.105997 | ||||||||
\(694\) | −11.5769 | −0.439452 | ||||||||
\(695\) | 14.0471 | 0.532837 | ||||||||
\(696\) | −15.5224 | −0.588377 | ||||||||
\(697\) | −7.73454 | −0.292967 | ||||||||
\(698\) | 26.4561 | 1.00138 | ||||||||
\(699\) | −12.8636 | −0.486546 | ||||||||
\(700\) | −3.00449 | −0.113559 | ||||||||
\(701\) | −13.9025 | −0.525091 | −0.262546 | − | 0.964920i | \(-0.584562\pi\) | ||||
−0.262546 | + | 0.964920i | \(0.584562\pi\) | |||||||
\(702\) | −7.11842 | −0.268667 | ||||||||
\(703\) | −72.6593 | −2.74040 | ||||||||
\(704\) | 5.93789 | 0.223793 | ||||||||
\(705\) | 9.00532 | 0.339160 | ||||||||
\(706\) | −26.9039 | −1.01254 | ||||||||
\(707\) | −58.3027 | −2.19270 | ||||||||
\(708\) | −0.609854 | −0.0229197 | ||||||||
\(709\) | −42.8187 | −1.60809 | −0.804045 | − | 0.594568i | \(-0.797323\pi\) | ||||
−0.804045 | + | 0.594568i | \(0.797323\pi\) | |||||||
\(710\) | −6.67793 | −0.250618 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −20.4373 | −0.765920 | ||||||||
\(713\) | −24.8106 | −0.929165 | ||||||||
\(714\) | 5.44200 | 0.203662 | ||||||||
\(715\) | −4.23585 | −0.158412 | ||||||||
\(716\) | −0.654987 | −0.0244780 | ||||||||
\(717\) | −9.75104 | −0.364159 | ||||||||
\(718\) | −0.513578 | −0.0191666 | ||||||||
\(719\) | 13.6744 | 0.509970 | 0.254985 | − | 0.966945i | \(-0.417929\pi\) | ||||
0.254985 | + | 0.966945i | \(0.417929\pi\) | |||||||
\(720\) | −4.12420 | −0.153700 | ||||||||
\(721\) | −65.9054 | −2.45445 | ||||||||
\(722\) | −41.0003 | −1.52587 | ||||||||
\(723\) | 3.15488 | 0.117331 | ||||||||
\(724\) | 2.10435 | 0.0782075 | ||||||||
\(725\) | −19.2031 | −0.713185 | ||||||||
\(726\) | −14.1138 | −0.523813 | ||||||||
\(727\) | 30.0101 | 1.11301 | 0.556506 | − | 0.830843i | \(-0.312142\pi\) | ||||
0.556506 | + | 0.830843i | \(0.312142\pi\) | |||||||
\(728\) | 63.6442 | 2.35881 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.05327 | 0.150018 | ||||||||
\(731\) | 11.8132 | 0.436927 | ||||||||
\(732\) | −2.39827 | −0.0886426 | ||||||||
\(733\) | −15.6798 | −0.579145 | −0.289573 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(734\) | −39.9808 | −1.47572 | ||||||||
\(735\) | −10.9982 | −0.405674 | ||||||||
\(736\) | −4.38033 | −0.161461 | ||||||||
\(737\) | 7.86008 | 0.289530 | ||||||||
\(738\) | −10.3694 | −0.381705 | ||||||||
\(739\) | 18.9572 | 0.697353 | 0.348676 | − | 0.937243i | \(-0.386631\pi\) | ||||
0.348676 | + | 0.937243i | \(0.386631\pi\) | |||||||
\(740\) | 2.42632 | 0.0891933 | ||||||||
\(741\) | 37.3873 | 1.37346 | ||||||||
\(742\) | 62.9213 | 2.30991 | ||||||||
\(743\) | −35.7120 | −1.31015 | −0.655074 | − | 0.755565i | \(-0.727362\pi\) | ||||
−0.655074 | + | 0.755565i | \(0.727362\pi\) | |||||||
\(744\) | 19.0938 | 0.700014 | ||||||||
\(745\) | −3.52240 | −0.129051 | ||||||||
\(746\) | 4.29121 | 0.157112 | ||||||||
\(747\) | −5.07294 | −0.185609 | ||||||||
\(748\) | 0.139279 | 0.00509255 | ||||||||
\(749\) | 72.1150 | 2.63503 | ||||||||
\(750\) | −13.4633 | −0.491611 | ||||||||
\(751\) | −16.8921 | −0.616402 | −0.308201 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308201 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(752\) | 27.5757 | 1.00558 | ||||||||
\(753\) | −6.60429 | −0.240674 | ||||||||
\(754\) | 37.4183 | 1.36270 | ||||||||
\(755\) | −13.7033 | −0.498713 | ||||||||
\(756\) | −0.822434 | −0.0299116 | ||||||||
\(757\) | −7.57701 | −0.275391 | −0.137696 | − | 0.990475i | \(-0.543970\pi\) | ||||
−0.137696 | + | 0.990475i | \(0.543970\pi\) | |||||||
\(758\) | 10.7210 | 0.389403 | ||||||||
\(759\) | −2.63770 | −0.0957426 | ||||||||
\(760\) | 24.1311 | 0.875326 | ||||||||
\(761\) | −0.126198 | −0.00457466 | −0.00228733 | − | 0.999997i | \(-0.500728\pi\) | ||||
−0.00228733 | + | 0.999997i | \(0.500728\pi\) | |||||||
\(762\) | 4.50241 | 0.163105 | ||||||||
\(763\) | 49.6088 | 1.79596 | ||||||||
\(764\) | −2.63438 | −0.0953086 | ||||||||
\(765\) | −1.16053 | −0.0419590 | ||||||||
\(766\) | −47.4479 | −1.71436 | ||||||||
\(767\) | 15.9818 | 0.577069 | ||||||||
\(768\) | 4.81108 | 0.173605 | ||||||||
\(769\) | −12.5225 | −0.451572 | −0.225786 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225786 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(770\) | 4.34147 | 0.156456 | ||||||||
\(771\) | 13.9554 | 0.502592 | ||||||||
\(772\) | −0.684858 | −0.0246486 | ||||||||
\(773\) | −21.5135 | −0.773786 | −0.386893 | − | 0.922125i | \(-0.626452\pi\) | ||||
−0.386893 | + | 0.922125i | \(0.626452\pi\) | |||||||
\(774\) | 15.8376 | 0.569270 | ||||||||
\(775\) | 23.6213 | 0.848504 | ||||||||
\(776\) | −21.2222 | −0.761833 | ||||||||
\(777\) | −41.8858 | −1.50264 | ||||||||
\(778\) | −9.84976 | −0.353131 | ||||||||
\(779\) | 54.4624 | 1.95132 | ||||||||
\(780\) | −1.24848 | −0.0447028 | ||||||||
\(781\) | 2.95044 | 0.105575 | ||||||||
\(782\) | 5.14428 | 0.183959 | ||||||||
\(783\) | −5.25655 | −0.187854 | ||||||||
\(784\) | −33.6782 | −1.20279 | ||||||||
\(785\) | −9.40879 | −0.335814 | ||||||||
\(786\) | 19.4458 | 0.693609 | ||||||||
\(787\) | 38.3753 | 1.36793 | 0.683966 | − | 0.729514i | \(-0.260254\pi\) | ||||
0.683966 | + | 0.729514i | \(0.260254\pi\) | |||||||
\(788\) | 0.708639 | 0.0252442 | ||||||||
\(789\) | −25.7056 | −0.915144 | ||||||||
\(790\) | −1.55588 | −0.0553558 | ||||||||
\(791\) | −46.7312 | −1.66157 | ||||||||
\(792\) | 2.02993 | 0.0721305 | ||||||||
\(793\) | 62.8488 | 2.23183 | ||||||||
\(794\) | −4.34490 | −0.154195 | ||||||||
\(795\) | −13.4182 | −0.475895 | ||||||||
\(796\) | −2.28859 | −0.0811169 | ||||||||
\(797\) | 4.11999 | 0.145938 | 0.0729688 | − | 0.997334i | \(-0.476753\pi\) | ||||
0.0729688 | + | 0.997334i | \(0.476753\pi\) | |||||||
\(798\) | −38.3196 | −1.35650 | ||||||||
\(799\) | 7.75967 | 0.274517 | ||||||||
\(800\) | 4.17036 | 0.147445 | ||||||||
\(801\) | −6.92093 | −0.244539 | ||||||||
\(802\) | −17.1622 | −0.606018 | ||||||||
\(803\) | −1.79082 | −0.0631965 | ||||||||
\(804\) | 2.31669 | 0.0817033 | ||||||||
\(805\) | −18.0758 | −0.637087 | ||||||||
\(806\) | −46.0275 | −1.62125 | ||||||||
\(807\) | −15.0361 | −0.529296 | ||||||||
\(808\) | 42.4141 | 1.49212 | ||||||||
\(809\) | 23.4514 | 0.824506 | 0.412253 | − | 0.911069i | \(-0.364742\pi\) | ||||
0.412253 | + | 0.911069i | \(0.364742\pi\) | |||||||
\(810\) | −1.55588 | −0.0546681 | ||||||||
\(811\) | 40.7618 | 1.43134 | 0.715670 | − | 0.698439i | \(-0.246121\pi\) | ||||
0.715670 | + | 0.698439i | \(0.246121\pi\) | |||||||
\(812\) | 4.32317 | 0.151713 | ||||||||
\(813\) | −11.8915 | −0.417053 | ||||||||
\(814\) | 9.50983 | 0.333319 | ||||||||
\(815\) | −7.16351 | −0.250927 | ||||||||
\(816\) | −3.55373 | −0.124405 | ||||||||
\(817\) | −83.1822 | −2.91018 | ||||||||
\(818\) | −36.2236 | −1.26653 | ||||||||
\(819\) | 21.5526 | 0.753109 | ||||||||
\(820\) | −1.81867 | −0.0635107 | ||||||||
\(821\) | 1.43536 | 0.0500944 | 0.0250472 | − | 0.999686i | \(-0.492026\pi\) | ||||
0.0250472 | + | 0.999686i | \(0.492026\pi\) | |||||||
\(822\) | −22.6505 | −0.790026 | ||||||||
\(823\) | 16.6844 | 0.581581 | 0.290790 | − | 0.956787i | \(-0.406082\pi\) | ||||
0.290790 | + | 0.956787i | \(0.406082\pi\) | |||||||
\(824\) | 47.9449 | 1.67024 | ||||||||
\(825\) | 2.51127 | 0.0874311 | ||||||||
\(826\) | −16.3803 | −0.569943 | ||||||||
\(827\) | 40.9466 | 1.42385 | 0.711926 | − | 0.702255i | \(-0.247823\pi\) | ||||
0.711926 | + | 0.702255i | \(0.247823\pi\) | |||||||
\(828\) | −0.777440 | −0.0270179 | ||||||||
\(829\) | −27.7083 | −0.962349 | −0.481174 | − | 0.876625i | \(-0.659790\pi\) | ||||
−0.481174 | + | 0.876625i | \(0.659790\pi\) | |||||||
\(830\) | 7.89290 | 0.273967 | ||||||||
\(831\) | −30.7994 | −1.06842 | ||||||||
\(832\) | −45.8640 | −1.59005 | ||||||||
\(833\) | −9.47688 | −0.328354 | ||||||||
\(834\) | 16.2275 | 0.561912 | ||||||||
\(835\) | −23.6014 | −0.816761 | ||||||||
\(836\) | −0.980727 | −0.0339192 | ||||||||
\(837\) | 6.46598 | 0.223497 | ||||||||
\(838\) | −15.1051 | −0.521796 | ||||||||
\(839\) | −29.8701 | −1.03123 | −0.515616 | − | 0.856820i | \(-0.672437\pi\) | ||||
−0.515616 | + | 0.856820i | \(0.672437\pi\) | |||||||
\(840\) | 13.9108 | 0.479968 | ||||||||
\(841\) | −1.36864 | −0.0471945 | ||||||||
\(842\) | 24.8298 | 0.855692 | ||||||||
\(843\) | −9.74076 | −0.335490 | ||||||||
\(844\) | −3.68021 | −0.126678 | ||||||||
\(845\) | 17.6307 | 0.606513 | ||||||||
\(846\) | 10.4031 | 0.357667 | ||||||||
\(847\) | 42.7327 | 1.46831 | ||||||||
\(848\) | −41.0888 | −1.41099 | ||||||||
\(849\) | −26.2209 | −0.899899 | ||||||||
\(850\) | −4.89769 | −0.167989 | ||||||||
\(851\) | −39.5943 | −1.35727 | ||||||||
\(852\) | 0.869617 | 0.0297926 | ||||||||
\(853\) | −0.862347 | −0.0295262 | −0.0147631 | − | 0.999891i | \(-0.504699\pi\) | ||||
−0.0147631 | + | 0.999891i | \(0.504699\pi\) | |||||||
\(854\) | −64.4159 | −2.20427 | ||||||||
\(855\) | 8.17180 | 0.279470 | ||||||||
\(856\) | −52.4623 | −1.79312 | ||||||||
\(857\) | 40.0791 | 1.36908 | 0.684539 | − | 0.728977i | \(-0.260004\pi\) | ||||
0.684539 | + | 0.728977i | \(0.260004\pi\) | |||||||
\(858\) | −4.89335 | −0.167056 | ||||||||
\(859\) | 14.4423 | 0.492764 | 0.246382 | − | 0.969173i | \(-0.420758\pi\) | ||||
0.246382 | + | 0.969173i | \(0.420758\pi\) | |||||||
\(860\) | 2.77771 | 0.0947192 | ||||||||
\(861\) | 31.3958 | 1.06997 | ||||||||
\(862\) | −4.28193 | −0.145843 | ||||||||
\(863\) | 44.0445 | 1.49929 | 0.749646 | − | 0.661840i | \(-0.230224\pi\) | ||||
0.749646 | + | 0.661840i | \(0.230224\pi\) | |||||||
\(864\) | 1.14157 | 0.0388371 | ||||||||
\(865\) | 18.7608 | 0.637885 | ||||||||
\(866\) | −37.8676 | −1.28679 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −5.31784 | −0.180499 | ||||||||
\(869\) | 0.687421 | 0.0233192 | ||||||||
\(870\) | 8.17858 | 0.277280 | ||||||||
\(871\) | −60.7109 | −2.05711 | ||||||||
\(872\) | −36.0894 | −1.22214 | ||||||||
\(873\) | −7.18674 | −0.243234 | ||||||||
\(874\) | −36.2232 | −1.22527 | ||||||||
\(875\) | 40.7632 | 1.37805 | ||||||||
\(876\) | −0.527827 | −0.0178336 | ||||||||
\(877\) | −19.0013 | −0.641630 | −0.320815 | − | 0.947142i | \(-0.603957\pi\) | ||||
−0.320815 | + | 0.947142i | \(0.603957\pi\) | |||||||
\(878\) | 24.9738 | 0.842825 | ||||||||
\(879\) | 25.6696 | 0.865813 | ||||||||
\(880\) | −2.83506 | −0.0955699 | ||||||||
\(881\) | −35.1472 | −1.18414 | −0.592070 | − | 0.805886i | \(-0.701689\pi\) | ||||
−0.592070 | + | 0.805886i | \(0.701689\pi\) | |||||||
\(882\) | −12.7053 | −0.427811 | ||||||||
\(883\) | −7.42449 | −0.249854 | −0.124927 | − | 0.992166i | \(-0.539870\pi\) | ||||
−0.124927 | + | 0.992166i | \(0.539870\pi\) | |||||||
\(884\) | −1.07579 | −0.0361826 | ||||||||
\(885\) | 3.49316 | 0.117421 | ||||||||
\(886\) | 25.9948 | 0.873312 | ||||||||
\(887\) | −49.0405 | −1.64662 | −0.823309 | − | 0.567593i | \(-0.807875\pi\) | ||||
−0.823309 | + | 0.567593i | \(0.807875\pi\) | |||||||
\(888\) | 30.4711 | 1.02254 | ||||||||
\(889\) | −13.6320 | −0.457204 | ||||||||
\(890\) | 10.7682 | 0.360949 | ||||||||
\(891\) | 0.687421 | 0.0230295 | ||||||||
\(892\) | −0.828724 | −0.0277477 | ||||||||
\(893\) | −54.6393 | −1.82844 | ||||||||
\(894\) | −4.06916 | −0.136093 | ||||||||
\(895\) | 3.75167 | 0.125405 | ||||||||
\(896\) | 37.7399 | 1.26080 | ||||||||
\(897\) | 20.3735 | 0.680251 | ||||||||
\(898\) | 6.51238 | 0.217321 | ||||||||
\(899\) | −33.9888 | −1.13359 | ||||||||
\(900\) | 0.740174 | 0.0246725 | ||||||||
\(901\) | −11.5622 | −0.385192 | ||||||||
\(902\) | −7.12817 | −0.237342 | ||||||||
\(903\) | −47.9519 | −1.59574 | ||||||||
\(904\) | 33.9960 | 1.13069 | ||||||||
\(905\) | −12.0534 | −0.400669 | ||||||||
\(906\) | −15.8303 | −0.525926 | ||||||||
\(907\) | −27.6460 | −0.917970 | −0.458985 | − | 0.888444i | \(-0.651787\pi\) | ||||
−0.458985 | + | 0.888444i | \(0.651787\pi\) | |||||||
\(908\) | −5.04758 | −0.167510 | ||||||||
\(909\) | 14.3632 | 0.476397 | ||||||||
\(910\) | −33.5333 | −1.11162 | ||||||||
\(911\) | −33.8793 | −1.12247 | −0.561236 | − | 0.827656i | \(-0.689674\pi\) | ||||
−0.561236 | + | 0.827656i | \(0.689674\pi\) | |||||||
\(912\) | 25.0234 | 0.828607 | ||||||||
\(913\) | −3.48725 | −0.115411 | ||||||||
\(914\) | −53.9168 | −1.78341 | ||||||||
\(915\) | 13.7370 | 0.454130 | ||||||||
\(916\) | −5.54075 | −0.183071 | ||||||||
\(917\) | −58.8765 | −1.94427 | ||||||||
\(918\) | −1.34067 | −0.0442486 | ||||||||
\(919\) | 0.763246 | 0.0251772 | 0.0125886 | − | 0.999921i | \(-0.495993\pi\) | ||||
0.0125886 | + | 0.999921i | \(0.495993\pi\) | |||||||
\(920\) | 13.1498 | 0.433535 | ||||||||
\(921\) | −15.0301 | −0.495258 | ||||||||
\(922\) | 9.42228 | 0.310306 | ||||||||
\(923\) | −22.7891 | −0.750112 | ||||||||
\(924\) | −0.565358 | −0.0185989 | ||||||||
\(925\) | 37.6964 | 1.23945 | ||||||||
\(926\) | 4.39346 | 0.144378 | ||||||||
\(927\) | 16.2362 | 0.533266 | ||||||||
\(928\) | −6.00074 | −0.196984 | ||||||||
\(929\) | −36.2828 | −1.19040 | −0.595199 | − | 0.803578i | \(-0.702927\pi\) | ||||
−0.595199 | + | 0.803578i | \(0.702927\pi\) | |||||||
\(930\) | −10.0603 | −0.329890 | ||||||||
\(931\) | 66.7310 | 2.18702 | ||||||||
\(932\) | −2.60631 | −0.0853725 | ||||||||
\(933\) | 23.4034 | 0.766193 | ||||||||
\(934\) | −33.8456 | −1.10746 | ||||||||
\(935\) | −0.797771 | −0.0260899 | ||||||||
\(936\) | −15.6791 | −0.512488 | ||||||||
\(937\) | 20.3153 | 0.663672 | 0.331836 | − | 0.943337i | \(-0.392332\pi\) | ||||
0.331836 | + | 0.943337i | \(0.392332\pi\) | |||||||
\(938\) | 62.2247 | 2.03171 | ||||||||
\(939\) | 5.99411 | 0.195610 | ||||||||
\(940\) | 1.82458 | 0.0595112 | ||||||||
\(941\) | 2.62083 | 0.0854366 | 0.0427183 | − | 0.999087i | \(-0.486398\pi\) | ||||
0.0427183 | + | 0.999087i | \(0.486398\pi\) | |||||||
\(942\) | −10.8692 | −0.354139 | ||||||||
\(943\) | 29.6782 | 0.966456 | ||||||||
\(944\) | 10.6966 | 0.348145 | ||||||||
\(945\) | 4.71078 | 0.153242 | ||||||||
\(946\) | 10.8871 | 0.353970 | ||||||||
\(947\) | −27.0615 | −0.879381 | −0.439690 | − | 0.898149i | \(-0.644912\pi\) | ||||
−0.439690 | + | 0.898149i | \(0.644912\pi\) | |||||||
\(948\) | 0.202611 | 0.00658051 | ||||||||
\(949\) | 13.8322 | 0.449012 | ||||||||
\(950\) | 34.4868 | 1.11890 | ||||||||
\(951\) | −2.48476 | −0.0805737 | ||||||||
\(952\) | 11.9866 | 0.388488 | ||||||||
\(953\) | −45.7337 | −1.48146 | −0.740730 | − | 0.671803i | \(-0.765520\pi\) | ||||
−0.740730 | + | 0.671803i | \(0.765520\pi\) | |||||||
\(954\) | −15.5010 | −0.501864 | ||||||||
\(955\) | 15.0894 | 0.488280 | ||||||||
\(956\) | −1.97567 | −0.0638977 | ||||||||
\(957\) | −3.61346 | −0.116807 | ||||||||
\(958\) | −38.8921 | −1.25655 | ||||||||
\(959\) | 68.5794 | 2.21455 | ||||||||
\(960\) | −10.0246 | −0.323541 | ||||||||
\(961\) | 10.8089 | 0.348674 | ||||||||
\(962\) | −73.4535 | −2.36824 | ||||||||
\(963\) | −17.7659 | −0.572500 | ||||||||
\(964\) | 0.639214 | 0.0205877 | ||||||||
\(965\) | 3.92277 | 0.126279 | ||||||||
\(966\) | −20.8815 | −0.671851 | ||||||||
\(967\) | 52.2890 | 1.68150 | 0.840751 | − | 0.541423i | \(-0.182114\pi\) | ||||
0.840751 | + | 0.541423i | \(0.182114\pi\) | |||||||
\(968\) | −31.0872 | −0.999182 | ||||||||
\(969\) | 7.04145 | 0.226204 | ||||||||
\(970\) | 11.1817 | 0.359023 | ||||||||
\(971\) | 43.9402 | 1.41011 | 0.705055 | − | 0.709153i | \(-0.250922\pi\) | ||||
0.705055 | + | 0.709153i | \(0.250922\pi\) | |||||||
\(972\) | 0.202611 | 0.00649876 | ||||||||
\(973\) | −49.1324 | −1.57511 | ||||||||
\(974\) | −36.3106 | −1.16347 | ||||||||
\(975\) | −19.3969 | −0.621199 | ||||||||
\(976\) | 42.0648 | 1.34646 | ||||||||
\(977\) | 1.90620 | 0.0609848 | 0.0304924 | − | 0.999535i | \(-0.490292\pi\) | ||||
0.0304924 | + | 0.999535i | \(0.490292\pi\) | |||||||
\(978\) | −8.27544 | −0.264619 | ||||||||
\(979\) | −4.75759 | −0.152053 | ||||||||
\(980\) | −2.22836 | −0.0711822 | ||||||||
\(981\) | −12.2214 | −0.390199 | ||||||||
\(982\) | −41.7381 | −1.33192 | ||||||||
\(983\) | 5.52324 | 0.176164 | 0.0880819 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880819 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(984\) | −22.8399 | −0.728108 | ||||||||
\(985\) | −4.05898 | −0.129330 | ||||||||
\(986\) | 7.04729 | 0.224431 | ||||||||
\(987\) | −31.4978 | −1.00259 | ||||||||
\(988\) | 7.57509 | 0.240996 | ||||||||
\(989\) | −45.3285 | −1.44136 | ||||||||
\(990\) | −1.06955 | −0.0339924 | ||||||||
\(991\) | −0.489112 | −0.0155372 | −0.00776858 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00776858 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(992\) | 7.38139 | 0.234359 | ||||||||
\(993\) | 13.2932 | 0.421847 | ||||||||
\(994\) | 23.3573 | 0.740850 | ||||||||
\(995\) | 13.1087 | 0.415574 | ||||||||
\(996\) | −1.02783 | −0.0325682 | ||||||||
\(997\) | −29.4566 | −0.932900 | −0.466450 | − | 0.884547i | \(-0.654467\pi\) | ||||
−0.466450 | + | 0.884547i | \(0.654467\pi\) | |||||||
\(998\) | 52.2597 | 1.65425 | ||||||||
\(999\) | 10.3188 | 0.326472 |
(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 | 4029.2.a.l.1.11 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.11 | ✓ | 32 | 1.1 | even | 1 | trivial |