Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8025,2,Mod(1,8025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8025, 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("8025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8025 = 3 \cdot 5^{2} \cdot 107 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8025.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: | \(64.0799476221\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 1605) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17402 | −1.53727 | −0.768633 | − | 0.639690i | \(-0.779063\pi\) | ||||
−0.768633 | + | 0.639690i | \(0.779063\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.72637 | 1.36318 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.17402 | 0.887540 | ||||||||
\(7\) | 4.66914 | 1.76477 | 0.882384 | − | 0.470529i | \(-0.155937\pi\) | ||||
0.882384 | + | 0.470529i | \(0.155937\pi\) | |||||||
\(8\) | −1.57914 | −0.558311 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.06979 | 0.322553 | 0.161276 | − | 0.986909i | \(-0.448439\pi\) | ||||
0.161276 | + | 0.986909i | \(0.448439\pi\) | |||||||
\(12\) | −2.72637 | −0.787035 | ||||||||
\(13\) | −1.40276 | −0.389055 | −0.194528 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194528 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(14\) | −10.1508 | −2.71292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.01965 | −0.504913 | ||||||||
\(17\) | −4.49347 | −1.08983 | −0.544914 | − | 0.838492i | \(-0.683438\pi\) | ||||
−0.544914 | + | 0.838492i | \(0.683438\pi\) | |||||||
\(18\) | −2.17402 | −0.512422 | ||||||||
\(19\) | −3.95111 | −0.906447 | −0.453224 | − | 0.891397i | \(-0.649726\pi\) | ||||
−0.453224 | + | 0.891397i | \(0.649726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.66914 | −1.01889 | ||||||||
\(22\) | −2.32574 | −0.495849 | ||||||||
\(23\) | 7.91994 | 1.65142 | 0.825711 | − | 0.564094i | \(-0.190774\pi\) | ||||
0.825711 | + | 0.564094i | \(0.190774\pi\) | |||||||
\(24\) | 1.57914 | 0.322341 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.04963 | 0.598081 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 12.7298 | 2.40571 | ||||||||
\(29\) | 4.24151 | 0.787629 | 0.393814 | − | 0.919190i | \(-0.371155\pi\) | ||||
0.393814 | + | 0.919190i | \(0.371155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.93856 | −0.886991 | −0.443496 | − | 0.896277i | \(-0.646262\pi\) | ||||
−0.443496 | + | 0.896277i | \(0.646262\pi\) | |||||||
\(32\) | 7.54905 | 1.33450 | ||||||||
\(33\) | −1.06979 | −0.186226 | ||||||||
\(34\) | 9.76890 | 1.67535 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.72637 | 0.454395 | ||||||||
\(37\) | −4.43858 | −0.729698 | −0.364849 | − | 0.931067i | \(-0.618879\pi\) | ||||
−0.364849 | + | 0.931067i | \(0.618879\pi\) | |||||||
\(38\) | 8.58980 | 1.39345 | ||||||||
\(39\) | 1.40276 | 0.224621 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.98642 | −1.09110 | −0.545548 | − | 0.838080i | \(-0.683678\pi\) | ||||
−0.545548 | + | 0.838080i | \(0.683678\pi\) | |||||||
\(42\) | 10.1508 | 1.56630 | ||||||||
\(43\) | −1.86731 | −0.284763 | −0.142381 | − | 0.989812i | \(-0.545476\pi\) | ||||
−0.142381 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(44\) | 2.91663 | 0.439699 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.2181 | −2.53867 | ||||||||
\(47\) | 4.27804 | 0.624016 | 0.312008 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312008 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(48\) | 2.01965 | 0.291512 | ||||||||
\(49\) | 14.8009 | 2.11441 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49347 | 0.629212 | ||||||||
\(52\) | −3.82444 | −0.530354 | ||||||||
\(53\) | 9.08154 | 1.24745 | 0.623723 | − | 0.781646i | \(-0.285619\pi\) | ||||
0.623723 | + | 0.781646i | \(0.285619\pi\) | |||||||
\(54\) | 2.17402 | 0.295847 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.37323 | −0.985289 | ||||||||
\(57\) | 3.95111 | 0.523338 | ||||||||
\(58\) | −9.22113 | −1.21079 | ||||||||
\(59\) | 5.80276 | 0.755455 | 0.377728 | − | 0.925917i | \(-0.376706\pi\) | ||||
0.377728 | + | 0.925917i | \(0.376706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.50643 | −0.961100 | −0.480550 | − | 0.876967i | \(-0.659563\pi\) | ||||
−0.480550 | + | 0.876967i | \(0.659563\pi\) | |||||||
\(62\) | 10.7365 | 1.36354 | ||||||||
\(63\) | 4.66914 | 0.588256 | ||||||||
\(64\) | −12.3725 | −1.54656 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.32574 | 0.286279 | ||||||||
\(67\) | −13.0711 | −1.59689 | −0.798443 | − | 0.602070i | \(-0.794343\pi\) | ||||
−0.798443 | + | 0.602070i | \(0.794343\pi\) | |||||||
\(68\) | −12.2509 | −1.48564 | ||||||||
\(69\) | −7.91994 | −0.953448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3092 | −1.22347 | −0.611736 | − | 0.791062i | \(-0.709528\pi\) | ||||
−0.611736 | + | 0.791062i | \(0.709528\pi\) | |||||||
\(72\) | −1.57914 | −0.186104 | ||||||||
\(73\) | 7.43920 | 0.870692 | 0.435346 | − | 0.900263i | \(-0.356626\pi\) | ||||
0.435346 | + | 0.900263i | \(0.356626\pi\) | |||||||
\(74\) | 9.64957 | 1.12174 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.7722 | −1.23565 | ||||||||
\(77\) | 4.99498 | 0.569231 | ||||||||
\(78\) | −3.04963 | −0.345302 | ||||||||
\(79\) | −17.7333 | −1.99515 | −0.997575 | − | 0.0696020i | \(-0.977827\pi\) | ||||
−0.997575 | + | 0.0696020i | \(0.977827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.1886 | 1.67730 | ||||||||
\(83\) | 9.19377 | 1.00915 | 0.504574 | − | 0.863369i | \(-0.331650\pi\) | ||||
0.504574 | + | 0.863369i | \(0.331650\pi\) | |||||||
\(84\) | −12.7298 | −1.38893 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.05958 | 0.437756 | ||||||||
\(87\) | −4.24151 | −0.454738 | ||||||||
\(88\) | −1.68934 | −0.180085 | ||||||||
\(89\) | −4.28765 | −0.454490 | −0.227245 | − | 0.973838i | \(-0.572972\pi\) | ||||
−0.227245 | + | 0.973838i | \(0.572972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.54967 | −0.686592 | ||||||||
\(92\) | 21.5927 | 2.25119 | ||||||||
\(93\) | 4.93856 | 0.512105 | ||||||||
\(94\) | −9.30055 | −0.959279 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.54905 | −0.770471 | ||||||||
\(97\) | −0.655434 | −0.0665492 | −0.0332746 | − | 0.999446i | \(-0.510594\pi\) | ||||
−0.0332746 | + | 0.999446i | \(0.510594\pi\) | |||||||
\(98\) | −32.1774 | −3.25041 | ||||||||
\(99\) | 1.06979 | 0.107518 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3839 | −1.03323 | −0.516617 | − | 0.856217i | \(-0.672809\pi\) | ||||
−0.516617 | + | 0.856217i | \(0.672809\pi\) | |||||||
\(102\) | −9.76890 | −0.967266 | ||||||||
\(103\) | 9.17727 | 0.904264 | 0.452132 | − | 0.891951i | \(-0.350664\pi\) | ||||
0.452132 | + | 0.891951i | \(0.350664\pi\) | |||||||
\(104\) | 2.21515 | 0.217214 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.7435 | −1.91766 | ||||||||
\(107\) | 1.00000 | 0.0966736 | ||||||||
\(108\) | −2.72637 | −0.262345 | ||||||||
\(109\) | −15.7486 | −1.50844 | −0.754222 | − | 0.656620i | \(-0.771986\pi\) | ||||
−0.754222 | + | 0.656620i | \(0.771986\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43858 | 0.421292 | ||||||||
\(112\) | −9.43004 | −0.891055 | ||||||||
\(113\) | −12.2457 | −1.15198 | −0.575992 | − | 0.817456i | \(-0.695384\pi\) | ||||
−0.575992 | + | 0.817456i | \(0.695384\pi\) | |||||||
\(114\) | −8.58980 | −0.804509 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.5639 | 1.07368 | ||||||||
\(117\) | −1.40276 | −0.129685 | ||||||||
\(118\) | −12.6153 | −1.16134 | ||||||||
\(119\) | −20.9806 | −1.92329 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.85556 | −0.895960 | ||||||||
\(122\) | 16.3191 | 1.47747 | ||||||||
\(123\) | 6.98642 | 0.629945 | ||||||||
\(124\) | −13.4643 | −1.20913 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.1508 | −0.904306 | ||||||||
\(127\) | −0.323746 | −0.0287278 | −0.0143639 | − | 0.999897i | \(-0.504572\pi\) | ||||
−0.0143639 | + | 0.999897i | \(0.504572\pi\) | |||||||
\(128\) | 11.8000 | 1.04298 | ||||||||
\(129\) | 1.86731 | 0.164408 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.72051 | 0.849285 | 0.424642 | − | 0.905361i | \(-0.360400\pi\) | ||||
0.424642 | + | 0.905361i | \(0.360400\pi\) | |||||||
\(132\) | −2.91663 | −0.253860 | ||||||||
\(133\) | −18.4483 | −1.59967 | ||||||||
\(134\) | 28.4168 | 2.45484 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.09583 | 0.608462 | ||||||||
\(137\) | −8.40560 | −0.718139 | −0.359069 | − | 0.933311i | \(-0.616906\pi\) | ||||
−0.359069 | + | 0.933311i | \(0.616906\pi\) | |||||||
\(138\) | 17.2181 | 1.46570 | ||||||||
\(139\) | 12.2902 | 1.04244 | 0.521222 | − | 0.853421i | \(-0.325476\pi\) | ||||
0.521222 | + | 0.853421i | \(0.325476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.27804 | −0.360276 | ||||||||
\(142\) | 22.4123 | 1.88080 | ||||||||
\(143\) | −1.50065 | −0.125491 | ||||||||
\(144\) | −2.01965 | −0.168304 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.1730 | −1.33848 | ||||||||
\(147\) | −14.8009 | −1.22075 | ||||||||
\(148\) | −12.1012 | −0.994713 | ||||||||
\(149\) | 7.61585 | 0.623914 | 0.311957 | − | 0.950096i | \(-0.399015\pi\) | ||||
0.311957 | + | 0.950096i | \(0.399015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9211 | −1.13288 | −0.566440 | − | 0.824103i | \(-0.691680\pi\) | ||||
−0.566440 | + | 0.824103i | \(0.691680\pi\) | |||||||
\(152\) | 6.23936 | 0.506079 | ||||||||
\(153\) | −4.49347 | −0.363276 | ||||||||
\(154\) | −10.8592 | −0.875059 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.82444 | 0.306200 | ||||||||
\(157\) | −6.16850 | −0.492300 | −0.246150 | − | 0.969232i | \(-0.579166\pi\) | ||||
−0.246150 | + | 0.969232i | \(0.579166\pi\) | |||||||
\(158\) | 38.5525 | 3.06707 | ||||||||
\(159\) | −9.08154 | −0.720213 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.9793 | 2.91438 | ||||||||
\(162\) | −2.17402 | −0.170807 | ||||||||
\(163\) | 5.00585 | 0.392088 | 0.196044 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196044 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(164\) | −19.0476 | −1.48736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.9875 | −1.55133 | ||||||||
\(167\) | −23.9903 | −1.85642 | −0.928212 | − | 0.372051i | \(-0.878655\pi\) | ||||
−0.928212 | + | 0.372051i | \(0.878655\pi\) | |||||||
\(168\) | 7.37323 | 0.568857 | ||||||||
\(169\) | −11.0323 | −0.848636 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.95111 | −0.302149 | ||||||||
\(172\) | −5.09099 | −0.388184 | ||||||||
\(173\) | −16.1145 | −1.22516 | −0.612581 | − | 0.790408i | \(-0.709869\pi\) | ||||
−0.612581 | + | 0.790408i | \(0.709869\pi\) | |||||||
\(174\) | 9.22113 | 0.699052 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.16060 | −0.162861 | ||||||||
\(177\) | −5.80276 | −0.436162 | ||||||||
\(178\) | 9.32144 | 0.698671 | ||||||||
\(179\) | 6.42003 | 0.479855 | 0.239928 | − | 0.970791i | \(-0.422876\pi\) | ||||
0.239928 | + | 0.970791i | \(0.422876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2293 | −1.80095 | −0.900474 | − | 0.434910i | \(-0.856780\pi\) | ||||
−0.900474 | + | 0.434910i | \(0.856780\pi\) | |||||||
\(182\) | 14.2391 | 1.05547 | ||||||||
\(183\) | 7.50643 | 0.554891 | ||||||||
\(184\) | −12.5067 | −0.922006 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.7365 | −0.787240 | ||||||||
\(187\) | −4.80706 | −0.351527 | ||||||||
\(188\) | 11.6635 | 0.850649 | ||||||||
\(189\) | −4.66914 | −0.339630 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.331627 | 0.0239957 | 0.0119978 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119978 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(192\) | 12.3725 | 0.892907 | ||||||||
\(193\) | 4.10612 | 0.295565 | 0.147782 | − | 0.989020i | \(-0.452786\pi\) | ||||
0.147782 | + | 0.989020i | \(0.452786\pi\) | |||||||
\(194\) | 1.42493 | 0.102304 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.3526 | 2.88233 | ||||||||
\(197\) | 10.5051 | 0.748459 | 0.374229 | − | 0.927336i | \(-0.377907\pi\) | ||||
0.374229 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(198\) | −2.32574 | −0.165283 | ||||||||
\(199\) | 14.6229 | 1.03659 | 0.518296 | − | 0.855201i | \(-0.326566\pi\) | ||||
0.518296 | + | 0.855201i | \(0.326566\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0711 | 0.921963 | ||||||||
\(202\) | 22.5748 | 1.58835 | ||||||||
\(203\) | 19.8042 | 1.38998 | ||||||||
\(204\) | 12.2509 | 0.857732 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −19.9516 | −1.39009 | ||||||||
\(207\) | 7.91994 | 0.550474 | ||||||||
\(208\) | 2.83308 | 0.196439 | ||||||||
\(209\) | −4.22685 | −0.292377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6450 | 1.07705 | 0.538524 | − | 0.842610i | \(-0.318982\pi\) | ||||
0.538524 | + | 0.842610i | \(0.318982\pi\) | |||||||
\(212\) | 24.7596 | 1.70050 | ||||||||
\(213\) | 10.3092 | 0.706372 | ||||||||
\(214\) | −2.17402 | −0.148613 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.57914 | 0.107447 | ||||||||
\(217\) | −23.0588 | −1.56533 | ||||||||
\(218\) | 34.2378 | 2.31888 | ||||||||
\(219\) | −7.43920 | −0.502694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.30325 | 0.424003 | ||||||||
\(222\) | −9.64957 | −0.647637 | ||||||||
\(223\) | −2.53372 | −0.169671 | −0.0848353 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848353 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(224\) | 35.2476 | 2.35508 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.6225 | 1.77090 | ||||||||
\(227\) | −8.95886 | −0.594621 | −0.297310 | − | 0.954781i | \(-0.596090\pi\) | ||||
−0.297310 | + | 0.954781i | \(0.596090\pi\) | |||||||
\(228\) | 10.7722 | 0.713406 | ||||||||
\(229\) | 5.14924 | 0.340271 | 0.170136 | − | 0.985421i | \(-0.445579\pi\) | ||||
0.170136 | + | 0.985421i | \(0.445579\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.99498 | −0.328646 | ||||||||
\(232\) | −6.69794 | −0.439741 | ||||||||
\(233\) | −24.7439 | −1.62102 | −0.810512 | − | 0.585722i | \(-0.800811\pi\) | ||||
−0.810512 | + | 0.585722i | \(0.800811\pi\) | |||||||
\(234\) | 3.04963 | 0.199360 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.8205 | 1.02982 | ||||||||
\(237\) | 17.7333 | 1.15190 | ||||||||
\(238\) | 45.6124 | 2.95661 | ||||||||
\(239\) | −16.8319 | −1.08876 | −0.544382 | − | 0.838837i | \(-0.683236\pi\) | ||||
−0.544382 | + | 0.838837i | \(0.683236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.9791 | 1.86671 | 0.933355 | − | 0.358956i | \(-0.116867\pi\) | ||||
0.933355 | + | 0.358956i | \(0.116867\pi\) | |||||||
\(242\) | 21.4262 | 1.37733 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −20.4653 | −1.31016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.1886 | −0.968392 | ||||||||
\(247\) | 5.54246 | 0.352658 | ||||||||
\(248\) | 7.79868 | 0.495217 | ||||||||
\(249\) | −9.19377 | −0.582631 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7596 | 0.679143 | 0.339571 | − | 0.940580i | \(-0.389718\pi\) | ||||
0.339571 | + | 0.940580i | \(0.389718\pi\) | |||||||
\(252\) | 12.7298 | 0.801902 | ||||||||
\(253\) | 8.47264 | 0.532671 | ||||||||
\(254\) | 0.703830 | 0.0441623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.908379 | −0.0567737 | ||||||||
\(257\) | 22.9235 | 1.42993 | 0.714966 | − | 0.699160i | \(-0.246442\pi\) | ||||
0.714966 | + | 0.699160i | \(0.246442\pi\) | |||||||
\(258\) | −4.05958 | −0.252739 | ||||||||
\(259\) | −20.7244 | −1.28775 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.24151 | 0.262543 | ||||||||
\(262\) | −21.1326 | −1.30558 | ||||||||
\(263\) | 10.1790 | 0.627662 | 0.313831 | − | 0.949479i | \(-0.398387\pi\) | ||||
0.313831 | + | 0.949479i | \(0.398387\pi\) | |||||||
\(264\) | 1.68934 | 0.103972 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 40.1070 | 2.45912 | ||||||||
\(267\) | 4.28765 | 0.262400 | ||||||||
\(268\) | −35.6366 | −2.17685 | ||||||||
\(269\) | 14.7697 | 0.900527 | 0.450264 | − | 0.892896i | \(-0.351330\pi\) | ||||
0.450264 | + | 0.892896i | \(0.351330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.46061 | 0.331708 | 0.165854 | − | 0.986150i | \(-0.446962\pi\) | ||||
0.165854 | + | 0.986150i | \(0.446962\pi\) | |||||||
\(272\) | 9.07525 | 0.550268 | ||||||||
\(273\) | 6.54967 | 0.396404 | ||||||||
\(274\) | 18.2740 | 1.10397 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −21.5927 | −1.29973 | ||||||||
\(277\) | −10.0960 | −0.606610 | −0.303305 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303305 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(278\) | −26.7192 | −1.60251 | ||||||||
\(279\) | −4.93856 | −0.295664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6967 | 0.697769 | 0.348884 | − | 0.937166i | \(-0.386561\pi\) | ||||
0.348884 | + | 0.937166i | \(0.386561\pi\) | |||||||
\(282\) | 9.30055 | 0.553840 | ||||||||
\(283\) | 28.7888 | 1.71131 | 0.855657 | − | 0.517543i | \(-0.173153\pi\) | ||||
0.855657 | + | 0.517543i | \(0.173153\pi\) | |||||||
\(284\) | −28.1066 | −1.66782 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.26245 | 0.192913 | ||||||||
\(287\) | −32.6206 | −1.92553 | ||||||||
\(288\) | 7.54905 | 0.444832 | ||||||||
\(289\) | 3.19129 | 0.187723 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.655434 | 0.0384222 | ||||||||
\(292\) | 20.2820 | 1.18691 | ||||||||
\(293\) | −14.5644 | −0.850864 | −0.425432 | − | 0.904990i | \(-0.639878\pi\) | ||||
−0.425432 | + | 0.904990i | \(0.639878\pi\) | |||||||
\(294\) | 32.1774 | 1.87662 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.00915 | 0.407398 | ||||||||
\(297\) | −1.06979 | −0.0620753 | ||||||||
\(298\) | −16.5570 | −0.959122 | ||||||||
\(299\) | −11.1098 | −0.642494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.71875 | −0.502541 | ||||||||
\(302\) | 30.2647 | 1.74154 | ||||||||
\(303\) | 10.3839 | 0.596538 | ||||||||
\(304\) | 7.97987 | 0.457677 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.76890 | 0.558451 | ||||||||
\(307\) | 33.5191 | 1.91304 | 0.956518 | − | 0.291673i | \(-0.0942118\pi\) | ||||
0.956518 | + | 0.291673i | \(0.0942118\pi\) | |||||||
\(308\) | 13.6182 | 0.775967 | ||||||||
\(309\) | −9.17727 | −0.522077 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.5514 | −1.67571 | −0.837854 | − | 0.545894i | \(-0.816190\pi\) | ||||
−0.837854 | + | 0.545894i | \(0.816190\pi\) | |||||||
\(312\) | −2.21515 | −0.125408 | ||||||||
\(313\) | −23.8120 | −1.34593 | −0.672966 | − | 0.739673i | \(-0.734980\pi\) | ||||
−0.672966 | + | 0.739673i | \(0.734980\pi\) | |||||||
\(314\) | 13.4105 | 0.756796 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.3475 | −2.71976 | ||||||||
\(317\) | −7.58388 | −0.425953 | −0.212976 | − | 0.977057i | \(-0.568316\pi\) | ||||
−0.212976 | + | 0.977057i | \(0.568316\pi\) | |||||||
\(318\) | 19.7435 | 1.10716 | ||||||||
\(319\) | 4.53751 | 0.254052 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | −0.0558146 | ||||||||
\(322\) | −80.3938 | −4.48017 | ||||||||
\(323\) | 17.7542 | 0.987871 | ||||||||
\(324\) | 2.72637 | 0.151465 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.8828 | −0.602744 | ||||||||
\(327\) | 15.7486 | 0.870900 | ||||||||
\(328\) | 11.0325 | 0.609170 | ||||||||
\(329\) | 19.9748 | 1.10124 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.9882 | −0.823826 | −0.411913 | − | 0.911223i | \(-0.635139\pi\) | ||||
−0.411913 | + | 0.911223i | \(0.635139\pi\) | |||||||
\(332\) | 25.0656 | 1.37565 | ||||||||
\(333\) | −4.43858 | −0.243233 | ||||||||
\(334\) | 52.1554 | 2.85382 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.43004 | 0.514451 | ||||||||
\(337\) | −32.1753 | −1.75270 | −0.876351 | − | 0.481673i | \(-0.840029\pi\) | ||||
−0.876351 | + | 0.481673i | \(0.840029\pi\) | |||||||
\(338\) | 23.9844 | 1.30458 | ||||||||
\(339\) | 12.2457 | 0.665098 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.28320 | −0.286101 | ||||||||
\(342\) | 8.58980 | 0.464483 | ||||||||
\(343\) | 36.4233 | 1.96668 | ||||||||
\(344\) | 2.94875 | 0.158986 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.0332 | 1.88340 | ||||||||
\(347\) | −6.76898 | −0.363378 | −0.181689 | − | 0.983356i | \(-0.558156\pi\) | ||||
−0.181689 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(348\) | −11.5639 | −0.619891 | ||||||||
\(349\) | 7.47216 | 0.399976 | 0.199988 | − | 0.979798i | \(-0.435910\pi\) | ||||
0.199988 | + | 0.979798i | \(0.435910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.40276 | 0.0748737 | ||||||||
\(352\) | 8.07587 | 0.430445 | ||||||||
\(353\) | −1.43249 | −0.0762436 | −0.0381218 | − | 0.999273i | \(-0.512137\pi\) | ||||
−0.0381218 | + | 0.999273i | \(0.512137\pi\) | |||||||
\(354\) | 12.6153 | 0.670497 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.6897 | −0.619553 | ||||||||
\(357\) | 20.9806 | 1.11041 | ||||||||
\(358\) | −13.9573 | −0.737665 | ||||||||
\(359\) | 36.0307 | 1.90163 | 0.950814 | − | 0.309763i | \(-0.100250\pi\) | ||||
0.950814 | + | 0.309763i | \(0.100250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.38871 | −0.178353 | ||||||||
\(362\) | 52.6750 | 2.76853 | ||||||||
\(363\) | 9.85556 | 0.517283 | ||||||||
\(364\) | −17.8568 | −0.935952 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.3191 | −0.853015 | ||||||||
\(367\) | 2.94743 | 0.153855 | 0.0769273 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769273 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(368\) | −15.9955 | −0.833824 | ||||||||
\(369\) | −6.98642 | −0.363699 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.4030 | 2.20145 | ||||||||
\(372\) | 13.4643 | 0.698093 | ||||||||
\(373\) | 10.8954 | 0.564144 | 0.282072 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282072 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(374\) | 10.4506 | 0.540390 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.75563 | −0.348395 | ||||||||
\(377\) | −5.94981 | −0.306431 | ||||||||
\(378\) | 10.1508 | 0.522101 | ||||||||
\(379\) | −15.9160 | −0.817552 | −0.408776 | − | 0.912635i | \(-0.634044\pi\) | ||||
−0.408776 | + | 0.912635i | \(0.634044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.323746 | 0.0165860 | ||||||||
\(382\) | −0.720964 | −0.0368877 | ||||||||
\(383\) | −0.461954 | −0.0236048 | −0.0118024 | − | 0.999930i | \(-0.503757\pi\) | ||||
−0.0118024 | + | 0.999930i | \(0.503757\pi\) | |||||||
\(384\) | −11.8000 | −0.602164 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.92679 | −0.454361 | ||||||||
\(387\) | −1.86731 | −0.0949209 | ||||||||
\(388\) | −1.78695 | −0.0907188 | ||||||||
\(389\) | −25.6492 | −1.30046 | −0.650232 | − | 0.759736i | \(-0.725328\pi\) | ||||
−0.650232 | + | 0.759736i | \(0.725328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.5880 | −1.79976 | ||||||||
\(392\) | −23.3727 | −1.18050 | ||||||||
\(393\) | −9.72051 | −0.490335 | ||||||||
\(394\) | −22.8384 | −1.15058 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.91663 | 0.146566 | ||||||||
\(397\) | −10.3146 | −0.517677 | −0.258838 | − | 0.965921i | \(-0.583340\pi\) | ||||
−0.258838 | + | 0.965921i | \(0.583340\pi\) | |||||||
\(398\) | −31.7906 | −1.59352 | ||||||||
\(399\) | 18.4483 | 0.923570 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.89198 | 0.194356 | 0.0971781 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971781 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(402\) | −28.4168 | −1.41730 | ||||||||
\(403\) | 6.92760 | 0.345088 | ||||||||
\(404\) | −28.3103 | −1.40849 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −43.0548 | −2.13677 | ||||||||
\(407\) | −4.74834 | −0.235366 | ||||||||
\(408\) | −7.09583 | −0.351296 | ||||||||
\(409\) | −21.7781 | −1.07686 | −0.538429 | − | 0.842671i | \(-0.680982\pi\) | ||||
−0.538429 | + | 0.842671i | \(0.680982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.40560 | 0.414618 | ||||||||
\(412\) | 25.0206 | 1.23268 | ||||||||
\(413\) | 27.0939 | 1.33320 | ||||||||
\(414\) | −17.2181 | −0.846224 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.5895 | −0.519192 | ||||||||
\(417\) | −12.2902 | −0.601855 | ||||||||
\(418\) | 9.18926 | 0.449461 | ||||||||
\(419\) | −28.7891 | −1.40644 | −0.703219 | − | 0.710973i | \(-0.748255\pi\) | ||||
−0.703219 | + | 0.710973i | \(0.748255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.50443 | −0.268270 | −0.134135 | − | 0.990963i | \(-0.542826\pi\) | ||||
−0.134135 | + | 0.990963i | \(0.542826\pi\) | |||||||
\(422\) | −34.0126 | −1.65571 | ||||||||
\(423\) | 4.27804 | 0.208005 | ||||||||
\(424\) | −14.3410 | −0.696462 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.4123 | −1.08588 | ||||||||
\(427\) | −35.0486 | −1.69612 | ||||||||
\(428\) | 2.72637 | 0.131784 | ||||||||
\(429\) | 1.50065 | 0.0724522 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.9856 | −1.01084 | −0.505421 | − | 0.862873i | \(-0.668663\pi\) | ||||
−0.505421 | + | 0.862873i | \(0.668663\pi\) | |||||||
\(432\) | 2.01965 | 0.0971705 | ||||||||
\(433\) | 10.6734 | 0.512932 | 0.256466 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256466 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(434\) | 50.1304 | 2.40633 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −42.9365 | −2.05629 | ||||||||
\(437\) | −31.2926 | −1.49693 | ||||||||
\(438\) | 16.1730 | 0.772775 | ||||||||
\(439\) | 12.0803 | 0.576563 | 0.288281 | − | 0.957546i | \(-0.406916\pi\) | ||||
0.288281 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8009 | 0.704803 | ||||||||
\(442\) | −13.7034 | −0.651805 | ||||||||
\(443\) | −24.2340 | −1.15139 | −0.575696 | − | 0.817664i | \(-0.695269\pi\) | ||||
−0.575696 | + | 0.817664i | \(0.695269\pi\) | |||||||
\(444\) | 12.1012 | 0.574298 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.50837 | 0.260829 | ||||||||
\(447\) | −7.61585 | −0.360217 | ||||||||
\(448\) | −57.7689 | −2.72932 | ||||||||
\(449\) | 27.0442 | 1.27629 | 0.638147 | − | 0.769915i | \(-0.279701\pi\) | ||||
0.638147 | + | 0.769915i | \(0.279701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.47398 | −0.351936 | ||||||||
\(452\) | −33.3864 | −1.57037 | ||||||||
\(453\) | 13.9211 | 0.654068 | ||||||||
\(454\) | 19.4768 | 0.914090 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.23936 | −0.292185 | ||||||||
\(457\) | −23.8970 | −1.11786 | −0.558928 | − | 0.829216i | \(-0.688787\pi\) | ||||
−0.558928 | + | 0.829216i | \(0.688787\pi\) | |||||||
\(458\) | −11.1946 | −0.523087 | ||||||||
\(459\) | 4.49347 | 0.209737 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6001 | 0.633419 | 0.316710 | − | 0.948523i | \(-0.397422\pi\) | ||||
0.316710 | + | 0.948523i | \(0.397422\pi\) | |||||||
\(462\) | 10.8592 | 0.505216 | ||||||||
\(463\) | −6.97450 | −0.324132 | −0.162066 | − | 0.986780i | \(-0.551816\pi\) | ||||
−0.162066 | + | 0.986780i | \(0.551816\pi\) | |||||||
\(464\) | −8.56637 | −0.397684 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 53.7937 | 2.49194 | ||||||||
\(467\) | −4.66690 | −0.215959 | −0.107979 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107979 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(468\) | −3.82444 | −0.176785 | ||||||||
\(469\) | −61.0307 | −2.81813 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.16850 | 0.284230 | ||||||||
\(472\) | −9.16338 | −0.421779 | ||||||||
\(473\) | −1.99763 | −0.0918511 | ||||||||
\(474\) | −38.5525 | −1.77078 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −57.2010 | −2.62180 | ||||||||
\(477\) | 9.08154 | 0.415815 | ||||||||
\(478\) | 36.5929 | 1.67372 | ||||||||
\(479\) | 12.8530 | 0.587271 | 0.293635 | − | 0.955917i | \(-0.405135\pi\) | ||||
0.293635 | + | 0.955917i | \(0.405135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.22626 | 0.283893 | ||||||||
\(482\) | −63.0012 | −2.86963 | ||||||||
\(483\) | −36.9793 | −1.68262 | ||||||||
\(484\) | −26.8699 | −1.22136 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.17402 | 0.0986156 | ||||||||
\(487\) | 29.4969 | 1.33663 | 0.668315 | − | 0.743878i | \(-0.267016\pi\) | ||||
0.668315 | + | 0.743878i | \(0.267016\pi\) | |||||||
\(488\) | 11.8537 | 0.536592 | ||||||||
\(489\) | −5.00585 | −0.226372 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5562 | 0.476396 | 0.238198 | − | 0.971217i | \(-0.423443\pi\) | ||||
0.238198 | + | 0.971217i | \(0.423443\pi\) | |||||||
\(492\) | 19.0476 | 0.858730 | ||||||||
\(493\) | −19.0591 | −0.858379 | ||||||||
\(494\) | −12.0494 | −0.542129 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.97416 | 0.447853 | ||||||||
\(497\) | −48.1349 | −2.15915 | ||||||||
\(498\) | 19.9875 | 0.895659 | ||||||||
\(499\) | −1.52896 | −0.0684455 | −0.0342227 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342227 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.9903 | 1.07181 | ||||||||
\(502\) | −23.3917 | −1.04402 | ||||||||
\(503\) | −30.4842 | −1.35922 | −0.679611 | − | 0.733573i | \(-0.737851\pi\) | ||||
−0.679611 | + | 0.733573i | \(0.737851\pi\) | |||||||
\(504\) | −7.37323 | −0.328430 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.4197 | −0.818856 | ||||||||
\(507\) | 11.0323 | 0.489960 | ||||||||
\(508\) | −0.882651 | −0.0391613 | ||||||||
\(509\) | −6.59117 | −0.292148 | −0.146074 | − | 0.989274i | \(-0.546664\pi\) | ||||
−0.146074 | + | 0.989274i | \(0.546664\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.7347 | 1.53657 | ||||||||
\(512\) | −21.6251 | −0.955702 | ||||||||
\(513\) | 3.95111 | 0.174446 | ||||||||
\(514\) | −49.8363 | −2.19818 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.09099 | 0.224118 | ||||||||
\(517\) | 4.57659 | 0.201278 | ||||||||
\(518\) | 45.0552 | 1.97961 | ||||||||
\(519\) | 16.1145 | 0.707348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4192 | −1.20126 | −0.600628 | − | 0.799528i | \(-0.705083\pi\) | ||||
−0.600628 | + | 0.799528i | \(0.705083\pi\) | |||||||
\(522\) | −9.22113 | −0.403598 | ||||||||
\(523\) | 2.83442 | 0.123941 | 0.0619703 | − | 0.998078i | \(-0.480262\pi\) | ||||
0.0619703 | + | 0.998078i | \(0.480262\pi\) | |||||||
\(524\) | 26.5017 | 1.15773 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.1293 | −0.964883 | ||||||||
\(527\) | 22.1913 | 0.966667 | ||||||||
\(528\) | 2.16060 | 0.0940279 | ||||||||
\(529\) | 39.7254 | 1.72719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.80276 | 0.251818 | ||||||||
\(532\) | −50.2969 | −2.18065 | ||||||||
\(533\) | 9.80026 | 0.424496 | ||||||||
\(534\) | −9.32144 | −0.403378 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.6411 | 0.891558 | ||||||||
\(537\) | −6.42003 | −0.277045 | ||||||||
\(538\) | −32.1097 | −1.38435 | ||||||||
\(539\) | 15.8338 | 0.682009 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4034 | 1.30714 | 0.653572 | − | 0.756865i | \(-0.273270\pi\) | ||||
0.653572 | + | 0.756865i | \(0.273270\pi\) | |||||||
\(542\) | −11.8715 | −0.509924 | ||||||||
\(543\) | 24.2293 | 1.03978 | ||||||||
\(544\) | −33.9214 | −1.45437 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.2391 | −0.609379 | ||||||||
\(547\) | 42.1064 | 1.80034 | 0.900170 | − | 0.435538i | \(-0.143442\pi\) | ||||
0.900170 | + | 0.435538i | \(0.143442\pi\) | |||||||
\(548\) | −22.9168 | −0.978956 | ||||||||
\(549\) | −7.50643 | −0.320367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.7587 | −0.713944 | ||||||||
\(552\) | 12.5067 | 0.532320 | ||||||||
\(553\) | −82.7992 | −3.52098 | ||||||||
\(554\) | 21.9489 | 0.932520 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.5077 | 1.42104 | ||||||||
\(557\) | 32.5940 | 1.38105 | 0.690527 | − | 0.723307i | \(-0.257379\pi\) | ||||
0.690527 | + | 0.723307i | \(0.257379\pi\) | |||||||
\(558\) | 10.7365 | 0.454514 | ||||||||
\(559\) | 2.61939 | 0.110788 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.80706 | 0.202954 | ||||||||
\(562\) | −25.4290 | −1.07266 | ||||||||
\(563\) | 38.9190 | 1.64024 | 0.820119 | − | 0.572193i | \(-0.193907\pi\) | ||||
0.820119 | + | 0.572193i | \(0.193907\pi\) | |||||||
\(564\) | −11.6635 | −0.491123 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −62.5874 | −2.63074 | ||||||||
\(567\) | 4.66914 | 0.196085 | ||||||||
\(568\) | 16.2796 | 0.683077 | ||||||||
\(569\) | −2.39160 | −0.100261 | −0.0501305 | − | 0.998743i | \(-0.515964\pi\) | ||||
−0.0501305 | + | 0.998743i | \(0.515964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.997647 | 0.0417502 | 0.0208751 | − | 0.999782i | \(-0.493355\pi\) | ||||
0.0208751 | + | 0.999782i | \(0.493355\pi\) | |||||||
\(572\) | −4.09133 | −0.171067 | ||||||||
\(573\) | −0.331627 | −0.0138539 | ||||||||
\(574\) | 70.9178 | 2.96005 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.3725 | −0.515520 | ||||||||
\(577\) | −27.7402 | −1.15484 | −0.577420 | − | 0.816447i | \(-0.695940\pi\) | ||||
−0.577420 | + | 0.816447i | \(0.695940\pi\) | |||||||
\(578\) | −6.93794 | −0.288580 | ||||||||
\(579\) | −4.10612 | −0.170644 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.9270 | 1.78091 | ||||||||
\(582\) | −1.42493 | −0.0590651 | ||||||||
\(583\) | 9.71531 | 0.402367 | ||||||||
\(584\) | −11.7475 | −0.486117 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.6634 | 1.30800 | ||||||||
\(587\) | 9.48639 | 0.391545 | 0.195773 | − | 0.980649i | \(-0.437279\pi\) | ||||
0.195773 | + | 0.980649i | \(0.437279\pi\) | |||||||
\(588\) | −40.3526 | −1.66411 | ||||||||
\(589\) | 19.5128 | 0.804011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5051 | −0.432123 | ||||||||
\(592\) | 8.96439 | 0.368434 | ||||||||
\(593\) | 0.0132108 | 0.000542503 0 | 0.000271251 | − | 1.00000i | \(-0.499914\pi\) | ||||
0.000271251 | 1.00000i | \(0.499914\pi\) | ||||||||
\(594\) | 2.32574 | 0.0954262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.7636 | 0.850510 | ||||||||
\(597\) | −14.6229 | −0.598477 | ||||||||
\(598\) | 24.1528 | 0.987683 | ||||||||
\(599\) | −14.8054 | −0.604932 | −0.302466 | − | 0.953160i | \(-0.597810\pi\) | ||||
−0.302466 | + | 0.953160i | \(0.597810\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1577 | −0.699879 | −0.349939 | − | 0.936772i | \(-0.613798\pi\) | ||||
−0.349939 | + | 0.936772i | \(0.613798\pi\) | |||||||
\(602\) | 18.9548 | 0.772538 | ||||||||
\(603\) | −13.0711 | −0.532295 | ||||||||
\(604\) | −37.9539 | −1.54432 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.5748 | −0.917037 | ||||||||
\(607\) | 4.25499 | 0.172705 | 0.0863524 | − | 0.996265i | \(-0.472479\pi\) | ||||
0.0863524 | + | 0.996265i | \(0.472479\pi\) | |||||||
\(608\) | −29.8271 | −1.20965 | ||||||||
\(609\) | −19.8042 | −0.802507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00106 | −0.242777 | ||||||||
\(612\) | −12.2509 | −0.495212 | ||||||||
\(613\) | −29.0134 | −1.17184 | −0.585919 | − | 0.810369i | \(-0.699266\pi\) | ||||
−0.585919 | + | 0.810369i | \(0.699266\pi\) | |||||||
\(614\) | −72.8712 | −2.94084 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.88778 | −0.317808 | ||||||||
\(617\) | −16.9082 | −0.680697 | −0.340349 | − | 0.940299i | \(-0.610545\pi\) | ||||
−0.340349 | + | 0.940299i | \(0.610545\pi\) | |||||||
\(618\) | 19.9516 | 0.802571 | ||||||||
\(619\) | 14.0463 | 0.564570 | 0.282285 | − | 0.959331i | \(-0.408908\pi\) | ||||
0.282285 | + | 0.959331i | \(0.408908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.91994 | −0.317816 | ||||||||
\(622\) | 64.2455 | 2.57601 | ||||||||
\(623\) | −20.0196 | −0.802069 | ||||||||
\(624\) | −2.83308 | −0.113414 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 51.7677 | 2.06905 | ||||||||
\(627\) | 4.22685 | 0.168804 | ||||||||
\(628\) | −16.8176 | −0.671096 | ||||||||
\(629\) | 19.9446 | 0.795245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.29572 | −0.0913910 | −0.0456955 | − | 0.998955i | \(-0.514550\pi\) | ||||
−0.0456955 | + | 0.998955i | \(0.514550\pi\) | |||||||
\(632\) | 28.0033 | 1.11391 | ||||||||
\(633\) | −15.6450 | −0.621834 | ||||||||
\(634\) | 16.4875 | 0.654803 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.7596 | −0.981783 | ||||||||
\(637\) | −20.7620 | −0.822622 | ||||||||
\(638\) | −9.86464 | −0.390545 | ||||||||
\(639\) | −10.3092 | −0.407824 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.1115 | −1.18933 | −0.594666 | − | 0.803973i | \(-0.702716\pi\) | ||||
−0.594666 | + | 0.803973i | \(0.702716\pi\) | |||||||
\(642\) | 2.17402 | 0.0858018 | ||||||||
\(643\) | −7.51571 | −0.296391 | −0.148195 | − | 0.988958i | \(-0.547346\pi\) | ||||
−0.148195 | + | 0.988958i | \(0.547346\pi\) | |||||||
\(644\) | 100.819 | 3.97283 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.5980 | −1.51862 | ||||||||
\(647\) | 28.6328 | 1.12567 | 0.562836 | − | 0.826568i | \(-0.309710\pi\) | ||||
0.562836 | + | 0.826568i | \(0.309710\pi\) | |||||||
\(648\) | −1.57914 | −0.0620345 | ||||||||
\(649\) | 6.20772 | 0.243674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.0588 | 0.903746 | ||||||||
\(652\) | 13.6478 | 0.534489 | ||||||||
\(653\) | 47.2548 | 1.84922 | 0.924612 | − | 0.380910i | \(-0.124389\pi\) | ||||
0.924612 | + | 0.380910i | \(0.124389\pi\) | |||||||
\(654\) | −34.2378 | −1.33880 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.1101 | 0.550908 | ||||||||
\(657\) | 7.43920 | 0.290231 | ||||||||
\(658\) | −43.4256 | −1.69291 | ||||||||
\(659\) | −32.5178 | −1.26672 | −0.633358 | − | 0.773859i | \(-0.718324\pi\) | ||||
−0.633358 | + | 0.773859i | \(0.718324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.48645 | −0.0967118 | −0.0483559 | − | 0.998830i | \(-0.515398\pi\) | ||||
−0.0483559 | + | 0.998830i | \(0.515398\pi\) | |||||||
\(662\) | 32.5847 | 1.26644 | ||||||||
\(663\) | −6.30325 | −0.244798 | ||||||||
\(664\) | −14.5183 | −0.563418 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.64957 | 0.373913 | ||||||||
\(667\) | 33.5925 | 1.30071 | ||||||||
\(668\) | −65.4064 | −2.53065 | ||||||||
\(669\) | 2.53372 | 0.0979594 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.03028 | −0.310006 | ||||||||
\(672\) | −35.2476 | −1.35970 | ||||||||
\(673\) | −13.9616 | −0.538180 | −0.269090 | − | 0.963115i | \(-0.586723\pi\) | ||||
−0.269090 | + | 0.963115i | \(0.586723\pi\) | |||||||
\(674\) | 69.9499 | 2.69437 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.0780 | −1.15685 | ||||||||
\(677\) | 22.4345 | 0.862228 | 0.431114 | − | 0.902298i | \(-0.358121\pi\) | ||||
0.431114 | + | 0.902298i | \(0.358121\pi\) | |||||||
\(678\) | −26.6225 | −1.02243 | ||||||||
\(679\) | −3.06031 | −0.117444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.95886 | 0.343304 | ||||||||
\(682\) | 11.4858 | 0.439814 | ||||||||
\(683\) | −3.22700 | −0.123478 | −0.0617390 | − | 0.998092i | \(-0.519665\pi\) | ||||
−0.0617390 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(684\) | −10.7722 | −0.411885 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −79.1851 | −3.02330 | ||||||||
\(687\) | −5.14924 | −0.196456 | ||||||||
\(688\) | 3.77133 | 0.143780 | ||||||||
\(689\) | −12.7392 | −0.485325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6815 | 0.558511 | 0.279255 | − | 0.960217i | \(-0.409912\pi\) | ||||
0.279255 | + | 0.960217i | \(0.409912\pi\) | |||||||
\(692\) | −43.9340 | −1.67012 | ||||||||
\(693\) | 4.99498 | 0.189744 | ||||||||
\(694\) | 14.7159 | 0.558608 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.69794 | 0.253885 | ||||||||
\(697\) | 31.3933 | 1.18911 | ||||||||
\(698\) | −16.2446 | −0.614869 | ||||||||
\(699\) | 24.7439 | 0.935899 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9415 | 0.639870 | 0.319935 | − | 0.947440i | \(-0.396339\pi\) | ||||
0.319935 | + | 0.947440i | \(0.396339\pi\) | |||||||
\(702\) | −3.04963 | −0.115101 | ||||||||
\(703\) | 17.5373 | 0.661433 | ||||||||
\(704\) | −13.2359 | −0.498848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.11426 | 0.117207 | ||||||||
\(707\) | −48.4837 | −1.82342 | ||||||||
\(708\) | −15.8205 | −0.594570 | ||||||||
\(709\) | 42.6493 | 1.60173 | 0.800863 | − | 0.598847i | \(-0.204374\pi\) | ||||
0.800863 | + | 0.598847i | \(0.204374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7333 | −0.665050 | ||||||||
\(712\) | 6.77080 | 0.253746 | ||||||||
\(713\) | −39.1131 | −1.46480 | ||||||||
\(714\) | −45.6124 | −1.70700 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.5034 | 0.654131 | ||||||||
\(717\) | 16.8319 | 0.628599 | ||||||||
\(718\) | −78.3315 | −2.92331 | ||||||||
\(719\) | 37.5010 | 1.39855 | 0.699276 | − | 0.714852i | \(-0.253506\pi\) | ||||
0.699276 | + | 0.714852i | \(0.253506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.8500 | 1.59582 | ||||||||
\(722\) | 7.36713 | 0.274176 | ||||||||
\(723\) | −28.9791 | −1.07775 | ||||||||
\(724\) | −66.0579 | −2.45502 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.4262 | −0.795200 | ||||||||
\(727\) | 2.99876 | 0.111218 | 0.0556090 | − | 0.998453i | \(-0.482290\pi\) | ||||
0.0556090 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(728\) | 10.3429 | 0.383332 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.39073 | 0.310342 | ||||||||
\(732\) | 20.4653 | 0.756419 | ||||||||
\(733\) | −28.1441 | −1.03953 | −0.519763 | − | 0.854310i | \(-0.673980\pi\) | ||||
−0.519763 | + | 0.854310i | \(0.673980\pi\) | |||||||
\(734\) | −6.40778 | −0.236515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 59.7880 | 2.20381 | ||||||||
\(737\) | −13.9833 | −0.515080 | ||||||||
\(738\) | 15.1886 | 0.559101 | ||||||||
\(739\) | −11.3139 | −0.416189 | −0.208095 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208095 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.54246 | −0.203607 | ||||||||
\(742\) | −92.1850 | −3.38422 | ||||||||
\(743\) | −4.78783 | −0.175649 | −0.0878243 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878243 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(744\) | −7.79868 | −0.285913 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.6869 | −0.867239 | ||||||||
\(747\) | 9.19377 | 0.336382 | ||||||||
\(748\) | −13.1058 | −0.479196 | ||||||||
\(749\) | 4.66914 | 0.170607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2184 | −0.482346 | −0.241173 | − | 0.970482i | \(-0.577532\pi\) | ||||
−0.241173 | + | 0.970482i | \(0.577532\pi\) | |||||||
\(752\) | −8.64015 | −0.315074 | ||||||||
\(753\) | −10.7596 | −0.392103 | ||||||||
\(754\) | 12.9350 | 0.471066 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.7298 | −0.462978 | ||||||||
\(757\) | −5.23924 | −0.190424 | −0.0952118 | − | 0.995457i | \(-0.530353\pi\) | ||||
−0.0952118 | + | 0.995457i | \(0.530353\pi\) | |||||||
\(758\) | 34.6018 | 1.25679 | ||||||||
\(759\) | −8.47264 | −0.307537 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.3080 | −0.989914 | −0.494957 | − | 0.868917i | \(-0.664816\pi\) | ||||
−0.494957 | + | 0.868917i | \(0.664816\pi\) | |||||||
\(762\) | −0.703830 | −0.0254971 | ||||||||
\(763\) | −73.5325 | −2.66205 | ||||||||
\(764\) | 0.904137 | 0.0327105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00430 | 0.0362868 | ||||||||
\(767\) | −8.13987 | −0.293914 | ||||||||
\(768\) | 0.908379 | 0.0327783 | ||||||||
\(769\) | 24.8465 | 0.895987 | 0.447993 | − | 0.894037i | \(-0.352139\pi\) | ||||
0.447993 | + | 0.894037i | \(0.352139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.9235 | −0.825571 | ||||||||
\(772\) | 11.1948 | 0.402909 | ||||||||
\(773\) | 28.9230 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(774\) | 4.05958 | 0.145919 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.03502 | 0.0371551 | ||||||||
\(777\) | 20.7244 | 0.743482 | ||||||||
\(778\) | 55.7618 | 1.99916 | ||||||||
\(779\) | 27.6041 | 0.989021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0286 | −0.394634 | ||||||||
\(782\) | 77.3691 | 2.76671 | ||||||||
\(783\) | −4.24151 | −0.151579 | ||||||||
\(784\) | −29.8926 | −1.06759 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.1326 | 0.753775 | ||||||||
\(787\) | 30.8669 | 1.10029 | 0.550144 | − | 0.835070i | \(-0.314573\pi\) | ||||
0.550144 | + | 0.835070i | \(0.314573\pi\) | |||||||
\(788\) | 28.6408 | 1.02029 | ||||||||
\(789\) | −10.1790 | −0.362381 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −57.1771 | −2.03298 | ||||||||
\(792\) | −1.68934 | −0.0600282 | ||||||||
\(793\) | 10.5297 | 0.373921 | ||||||||
\(794\) | 22.4242 | 0.795806 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.8675 | 1.41307 | ||||||||
\(797\) | −15.1196 | −0.535565 | −0.267783 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267783 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(798\) | −40.1070 | −1.41977 | ||||||||
\(799\) | −19.2233 | −0.680070 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.28765 | −0.151497 | ||||||||
\(802\) | −8.46125 | −0.298777 | ||||||||
\(803\) | 7.95835 | 0.280844 | ||||||||
\(804\) | 35.6366 | 1.25680 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.0608 | −0.530492 | ||||||||
\(807\) | −14.7697 | −0.519920 | ||||||||
\(808\) | 16.3976 | 0.576865 | ||||||||
\(809\) | −41.6969 | −1.46598 | −0.732992 | − | 0.680237i | \(-0.761877\pi\) | ||||
−0.732992 | + | 0.680237i | \(0.761877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.467700 | −0.0164232 | −0.00821158 | − | 0.999966i | \(-0.502614\pi\) | ||||
−0.00821158 | + | 0.999966i | \(0.502614\pi\) | |||||||
\(812\) | 53.9936 | 1.89480 | ||||||||
\(813\) | −5.46061 | −0.191512 | ||||||||
\(814\) | 10.3230 | 0.361820 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.07525 | −0.317697 | ||||||||
\(817\) | 7.37797 | 0.258123 | ||||||||
\(818\) | 47.3461 | 1.65542 | ||||||||
\(819\) | −6.54967 | −0.228864 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3299 | 0.849118 | 0.424559 | − | 0.905400i | \(-0.360429\pi\) | ||||
0.424559 | + | 0.905400i | \(0.360429\pi\) | |||||||
\(822\) | −18.2740 | −0.637377 | ||||||||
\(823\) | −44.3480 | −1.54588 | −0.772938 | − | 0.634482i | \(-0.781213\pi\) | ||||
−0.772938 | + | 0.634482i | \(0.781213\pi\) | |||||||
\(824\) | −14.4922 | −0.504860 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.9027 | −2.04949 | ||||||||
\(827\) | −14.9028 | −0.518221 | −0.259110 | − | 0.965848i | \(-0.583429\pi\) | ||||
−0.259110 | + | 0.965848i | \(0.583429\pi\) | |||||||
\(828\) | 21.5927 | 0.750397 | ||||||||
\(829\) | −27.7741 | −0.964634 | −0.482317 | − | 0.875997i | \(-0.660205\pi\) | ||||
−0.482317 | + | 0.875997i | \(0.660205\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0960 | 0.350226 | ||||||||
\(832\) | 17.3556 | 0.601697 | ||||||||
\(833\) | −66.5073 | −2.30434 | ||||||||
\(834\) | 26.7192 | 0.925211 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.5239 | −0.398564 | ||||||||
\(837\) | 4.93856 | 0.170702 | ||||||||
\(838\) | 62.5881 | 2.16207 | ||||||||
\(839\) | 30.5184 | 1.05361 | 0.526807 | − | 0.849985i | \(-0.323389\pi\) | ||||
0.526807 | + | 0.849985i | \(0.323389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0096 | −0.379641 | ||||||||
\(842\) | 11.9668 | 0.412402 | ||||||||
\(843\) | −11.6967 | −0.402857 | ||||||||
\(844\) | 42.6541 | 1.46821 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.30055 | −0.319760 | ||||||||
\(847\) | −46.0170 | −1.58116 | ||||||||
\(848\) | −18.3416 | −0.629851 | ||||||||
\(849\) | −28.7888 | −0.988028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.1533 | −1.20504 | ||||||||
\(852\) | 28.1066 | 0.962915 | ||||||||
\(853\) | −45.3475 | −1.55267 | −0.776334 | − | 0.630321i | \(-0.782923\pi\) | ||||
−0.776334 | + | 0.630321i | \(0.782923\pi\) | |||||||
\(854\) | 76.1964 | 2.60739 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.57914 | −0.0539739 | ||||||||
\(857\) | 43.9763 | 1.50220 | 0.751100 | − | 0.660188i | \(-0.229523\pi\) | ||||
0.751100 | + | 0.660188i | \(0.229523\pi\) | |||||||
\(858\) | −3.26245 | −0.111378 | ||||||||
\(859\) | −23.2635 | −0.793739 | −0.396870 | − | 0.917875i | \(-0.629903\pi\) | ||||
−0.396870 | + | 0.917875i | \(0.629903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.6206 | 1.11171 | ||||||||
\(862\) | 45.6232 | 1.55393 | ||||||||
\(863\) | −35.3225 | −1.20239 | −0.601197 | − | 0.799101i | \(-0.705309\pi\) | ||||
−0.601197 | + | 0.799101i | \(0.705309\pi\) | |||||||
\(864\) | −7.54905 | −0.256824 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.2042 | −0.788512 | ||||||||
\(867\) | −3.19129 | −0.108382 | ||||||||
\(868\) | −62.8668 | −2.13384 | ||||||||
\(869\) | −18.9708 | −0.643541 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3356 | 0.621277 | ||||||||
\(872\) | 24.8693 | 0.842180 | ||||||||
\(873\) | −0.655434 | −0.0221831 | ||||||||
\(874\) | 68.0307 | 2.30117 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.2820 | −0.685265 | ||||||||
\(877\) | −47.1264 | −1.59135 | −0.795673 | − | 0.605726i | \(-0.792883\pi\) | ||||
−0.795673 | + | 0.605726i | \(0.792883\pi\) | |||||||
\(878\) | −26.2629 | −0.886329 | ||||||||
\(879\) | 14.5644 | 0.491246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.42768 | −0.317627 | −0.158813 | − | 0.987309i | \(-0.550767\pi\) | ||||
−0.158813 | + | 0.987309i | \(0.550767\pi\) | |||||||
\(882\) | −32.1774 | −1.08347 | ||||||||
\(883\) | −41.6432 | −1.40140 | −0.700702 | − | 0.713454i | \(-0.747130\pi\) | ||||
−0.700702 | + | 0.713454i | \(0.747130\pi\) | |||||||
\(884\) | 17.1850 | 0.577994 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.6852 | 1.76999 | ||||||||
\(887\) | −7.55968 | −0.253829 | −0.126915 | − | 0.991914i | \(-0.540507\pi\) | ||||
−0.126915 | + | 0.991914i | \(0.540507\pi\) | |||||||
\(888\) | −7.00915 | −0.235212 | ||||||||
\(889\) | −1.51161 | −0.0506979 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.06979 | 0.0358392 | ||||||||
\(892\) | −6.90786 | −0.231292 | ||||||||
\(893\) | −16.9030 | −0.565638 | ||||||||
\(894\) | 16.5570 | 0.553749 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 55.0956 | 1.84062 | ||||||||
\(897\) | 11.1098 | 0.370944 | ||||||||
\(898\) | −58.7946 | −1.96200 | ||||||||
\(899\) | −20.9469 | −0.698620 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.8077 | −1.35950 | ||||||||
\(902\) | 16.2486 | 0.541019 | ||||||||
\(903\) | 8.71875 | 0.290142 | ||||||||
\(904\) | 19.3378 | 0.643164 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −30.2647 | −1.00548 | ||||||||
\(907\) | −33.1097 | −1.09939 | −0.549694 | − | 0.835366i | \(-0.685256\pi\) | ||||
−0.549694 | + | 0.835366i | \(0.685256\pi\) | |||||||
\(908\) | −24.4252 | −0.810577 | ||||||||
\(909\) | −10.3839 | −0.344411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.52490 | −0.315574 | −0.157787 | − | 0.987473i | \(-0.550436\pi\) | ||||
−0.157787 | + | 0.987473i | \(0.550436\pi\) | |||||||
\(912\) | −7.97987 | −0.264240 | ||||||||
\(913\) | 9.83537 | 0.325503 | ||||||||
\(914\) | 51.9527 | 1.71844 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0387 | 0.463852 | ||||||||
\(917\) | 45.3864 | 1.49879 | ||||||||
\(918\) | −9.76890 | −0.322422 | ||||||||
\(919\) | −41.6086 | −1.37254 | −0.686270 | − | 0.727347i | \(-0.740753\pi\) | ||||
−0.686270 | + | 0.727347i | \(0.740753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.5191 | −1.10449 | ||||||||
\(922\) | −29.5669 | −0.973733 | ||||||||
\(923\) | 14.4613 | 0.475998 | ||||||||
\(924\) | −13.6182 | −0.448005 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.1627 | 0.498277 | ||||||||
\(927\) | 9.17727 | 0.301421 | ||||||||
\(928\) | 32.0194 | 1.05109 | ||||||||
\(929\) | 32.7382 | 1.07411 | 0.537053 | − | 0.843549i | \(-0.319538\pi\) | ||||
0.537053 | + | 0.843549i | \(0.319538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.4799 | −1.91660 | ||||||||
\(932\) | −67.4609 | −2.20975 | ||||||||
\(933\) | 29.5514 | 0.967471 | ||||||||
\(934\) | 10.1459 | 0.331986 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.21515 | 0.0724045 | ||||||||
\(937\) | 32.8854 | 1.07432 | 0.537159 | − | 0.843481i | \(-0.319497\pi\) | ||||
0.537159 | + | 0.843481i | \(0.319497\pi\) | |||||||
\(938\) | 132.682 | 4.33222 | ||||||||
\(939\) | 23.8120 | 0.777074 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.8895 | 0.909171 | 0.454586 | − | 0.890703i | \(-0.349787\pi\) | ||||
0.454586 | + | 0.890703i | \(0.349787\pi\) | |||||||
\(942\) | −13.4105 | −0.436936 | ||||||||
\(943\) | −55.3320 | −1.80186 | ||||||||
\(944\) | −11.7196 | −0.381439 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.34289 | 0.141199 | ||||||||
\(947\) | −44.7638 | −1.45463 | −0.727313 | − | 0.686306i | \(-0.759231\pi\) | ||||
−0.727313 | + | 0.686306i | \(0.759231\pi\) | |||||||
\(948\) | 48.3475 | 1.57025 | ||||||||
\(949\) | −10.4354 | −0.338747 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.58388 | 0.245924 | ||||||||
\(952\) | 33.1314 | 1.07379 | ||||||||
\(953\) | −6.42945 | −0.208270 | −0.104135 | − | 0.994563i | \(-0.533207\pi\) | ||||
−0.104135 | + | 0.994563i | \(0.533207\pi\) | |||||||
\(954\) | −19.7435 | −0.639218 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −45.8899 | −1.48419 | ||||||||
\(957\) | −4.53751 | −0.146677 | ||||||||
\(958\) | −27.9428 | −0.902791 | ||||||||
\(959\) | −39.2469 | −1.26735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.61065 | −0.213247 | ||||||||
\(962\) | −13.5360 | −0.436419 | ||||||||
\(963\) | 1.00000 | 0.0322245 | ||||||||
\(964\) | 79.0078 | 2.54467 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 80.3938 | 2.58663 | ||||||||
\(967\) | −25.3891 | −0.816459 | −0.408230 | − | 0.912879i | \(-0.633854\pi\) | ||||
−0.408230 | + | 0.912879i | \(0.633854\pi\) | |||||||
\(968\) | 15.5633 | 0.500224 | ||||||||
\(969\) | −17.7542 | −0.570348 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.5128 | 0.594103 | 0.297052 | − | 0.954861i | \(-0.403997\pi\) | ||||
0.297052 | + | 0.954861i | \(0.403997\pi\) | |||||||
\(972\) | −2.72637 | −0.0874483 | ||||||||
\(973\) | 57.3848 | 1.83967 | ||||||||
\(974\) | −64.1268 | −2.05476 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.1604 | 0.485272 | ||||||||
\(977\) | −43.2939 | −1.38509 | −0.692547 | − | 0.721373i | \(-0.743511\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743511\pi\) | |||||||
\(978\) | 10.8828 | 0.347994 | ||||||||
\(979\) | −4.58687 | −0.146597 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.7486 | −0.502815 | ||||||||
\(982\) | −22.9495 | −0.732347 | ||||||||
\(983\) | −6.81791 | −0.217458 | −0.108729 | − | 0.994071i | \(-0.534678\pi\) | ||||
−0.108729 | + | 0.994071i | \(0.534678\pi\) | |||||||
\(984\) | −11.0325 | −0.351705 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 41.4349 | 1.31956 | ||||||||
\(987\) | −19.9748 | −0.635804 | ||||||||
\(988\) | 15.1108 | 0.480738 | ||||||||
\(989\) | −14.7890 | −0.470263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9100 | −0.378333 | −0.189166 | − | 0.981945i | \(-0.560579\pi\) | ||||
−0.189166 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(992\) | −37.2814 | −1.18369 | ||||||||
\(993\) | 14.9882 | 0.475636 | ||||||||
\(994\) | 104.646 | 3.31918 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.0656 | −0.794234 | ||||||||
\(997\) | 35.9891 | 1.13978 | 0.569892 | − | 0.821719i | \(-0.306985\pi\) | ||||
0.569892 | + | 0.821719i | \(0.306985\pi\) | |||||||
\(998\) | 3.32398 | 0.105219 | ||||||||
\(999\) | 4.43858 | 0.140431 |
(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 | 8025.2.a.bp.1.3 | 22 | ||
5.2 | odd | 4 | 1605.2.b.d.964.6 | ✓ | 44 | ||
5.3 | odd | 4 | 1605.2.b.d.964.39 | yes | 44 | ||
5.4 | even | 2 | 8025.2.a.bo.1.20 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1605.2.b.d.964.6 | ✓ | 44 | 5.2 | odd | 4 | ||
1605.2.b.d.964.39 | yes | 44 | 5.3 | odd | 4 | ||
8025.2.a.bo.1.20 | 22 | 5.4 | even | 2 | |||
8025.2.a.bp.1.3 | 22 | 1.1 | even | 1 | trivial |