Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.210422 | −0.121487 | −0.0607437 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607437 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.28610 | −1.61999 | −0.809996 | − | 0.586435i | \(-0.800531\pi\) | ||||
−0.809996 | + | 0.586435i | \(0.800531\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.95572 | −0.985241 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.06403 | 0.320817 | 0.160409 | − | 0.987051i | \(-0.448719\pi\) | ||||
0.160409 | + | 0.987051i | \(0.448719\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.73502 | 1.86796 | 0.933980 | − | 0.357326i | \(-0.116311\pi\) | ||||
0.933980 | + | 0.357326i | \(0.116311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.210422 | −0.0543308 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.31084 | −0.317925 | −0.158962 | − | 0.987285i | \(-0.550815\pi\) | ||||
−0.158962 | + | 0.987285i | \(0.550815\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.85994 | −0.885531 | −0.442765 | − | 0.896637i | \(-0.646003\pi\) | ||||
−0.442765 | + | 0.896637i | \(0.646003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.901891 | 0.196809 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.51918 | −0.316771 | −0.158385 | − | 0.987377i | \(-0.550629\pi\) | ||||
−0.158385 | + | 0.987377i | \(0.550629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.25322 | 0.241182 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.71498 | −0.875550 | −0.437775 | − | 0.899085i | \(-0.644233\pi\) | ||||
−0.437775 | + | 0.899085i | \(0.644233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.73676 | 1.74877 | 0.874387 | − | 0.485230i | \(-0.161264\pi\) | ||||
0.874387 | + | 0.485230i | \(0.161264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.223896 | −0.0389753 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.28610 | −0.724483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0446856 | −0.00734627 | −0.00367314 | − | 0.999993i | \(-0.501169\pi\) | ||||
−0.00367314 | + | 0.999993i | \(0.501169\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41720 | −0.226934 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52783 | 0.394781 | 0.197391 | − | 0.980325i | \(-0.436753\pi\) | ||||
0.197391 | + | 0.980325i | \(0.436753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8904 | −1.81326 | −0.906632 | − | 0.421921i | \(-0.861356\pi\) | ||||
−0.906632 | + | 0.421921i | \(0.861356\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.95572 | −0.440613 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7086 | −1.70787 | −0.853936 | − | 0.520378i | \(-0.825791\pi\) | ||||
−0.853936 | + | 0.520378i | \(0.825791\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3706 | 1.62437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.275830 | 0.0386239 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1737 | 1.67219 | 0.836095 | − | 0.548585i | \(-0.184833\pi\) | ||||
0.836095 | + | 0.548585i | \(0.184833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.06403 | 0.143474 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.812218 | 0.107581 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.13146 | −0.668060 | −0.334030 | − | 0.942563i | \(-0.608409\pi\) | ||||
−0.334030 | + | 0.942563i | \(0.608409\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2531 | −1.31277 | −0.656386 | − | 0.754425i | \(-0.727916\pi\) | ||||
−0.656386 | + | 0.754425i | \(0.727916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.6685 | 1.59608 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.73502 | 0.835377 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.09659 | 0.378308 | 0.189154 | − | 0.981947i | \(-0.439425\pi\) | ||||
0.189154 | + | 0.981947i | \(0.439425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.319669 | 0.0384836 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.55846 | −0.540989 | −0.270495 | − | 0.962721i | \(-0.587187\pi\) | ||||
−0.270495 | + | 0.962721i | \(0.587187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6323 | 1.24442 | 0.622208 | − | 0.782852i | \(-0.286236\pi\) | ||||
0.622208 | + | 0.782852i | \(0.286236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.210422 | −0.0242975 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.56054 | −0.519722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.01867 | 0.339627 | 0.169814 | − | 0.985476i | \(-0.445683\pi\) | ||||
0.169814 | + | 0.985476i | \(0.445683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.60346 | 0.955940 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6498 | 1.38850 | 0.694250 | − | 0.719734i | \(-0.255736\pi\) | ||||
0.694250 | + | 0.719734i | \(0.255736\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31084 | −0.142180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.992137 | 0.106368 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1908 | 1.08023 | 0.540113 | − | 0.841593i | \(-0.318382\pi\) | ||||
0.540113 | + | 0.841593i | \(0.318382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.8670 | −3.02608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.04883 | −0.212454 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.85994 | −0.396021 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2840 | −1.45032 | −0.725162 | − | 0.688578i | \(-0.758235\pi\) | ||||
−0.725162 | + | 0.688578i | \(0.758235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.14498 | −0.316082 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.77839 | 0.674475 | 0.337237 | − | 0.941420i | \(-0.390508\pi\) | ||||
0.337237 | + | 0.941420i | \(0.390508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9190 | 1.07588 | 0.537940 | − | 0.842983i | \(-0.319203\pi\) | ||||
0.537940 | + | 0.842983i | \(0.319203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.901891 | 0.0880155 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.28967 | −0.124677 | −0.0623384 | − | 0.998055i | \(-0.519856\pi\) | ||||
−0.0623384 | + | 0.998055i | \(0.519856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3087 | −1.75365 | −0.876827 | − | 0.480805i | \(-0.840344\pi\) | ||||
−0.876827 | + | 0.480805i | \(0.840344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.00940286 | 0.000892480 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2950 | −1.06254 | −0.531272 | − | 0.847201i | \(-0.678286\pi\) | ||||
−0.531272 | + | 0.847201i | \(0.678286\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.51918 | −0.141664 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.9069 | −1.84039 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.61838 | 0.515036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.86784 | −0.897076 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.531913 | −0.0479610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.88811 | −0.788693 | −0.394346 | − | 0.918962i | \(-0.629029\pi\) | ||||
−0.394346 | + | 0.918962i | \(0.629029\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.50200 | 0.220289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1740 | 1.58787 | 0.793937 | − | 0.608000i | \(-0.208028\pi\) | ||||
0.793937 | + | 0.608000i | \(0.208028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.5441 | 1.43455 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25322 | 0.107860 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.6208 | 1.76175 | 0.880876 | − | 0.473348i | \(-0.156955\pi\) | ||||
0.880876 | + | 0.473348i | \(0.156955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.20414 | −0.356591 | −0.178295 | − | 0.983977i | \(-0.557058\pi\) | ||||
−0.178295 | + | 0.983977i | \(0.557058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.46375 | 0.207485 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.16627 | 0.599274 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.71498 | −0.391558 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.39263 | −0.197341 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6819 | 1.03894 | 0.519469 | − | 0.854489i | \(-0.326130\pi\) | ||||
0.519469 | + | 0.854489i | \(0.326130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.80764 | −0.472619 | −0.236309 | − | 0.971678i | \(-0.575938\pi\) | ||||
−0.236309 | + | 0.971678i | \(0.575938\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.87447 | 0.313233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.73676 | 0.782075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.68576 | 0.773008 | 0.386504 | − | 0.922288i | \(-0.373683\pi\) | ||||
0.386504 | + | 0.922288i | \(0.373683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.56163 | −0.203150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.51134 | 0.513166 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5682 | 0.827766 | 0.413883 | − | 0.910330i | \(-0.364172\pi\) | ||||
0.413883 | + | 0.910330i | \(0.364172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.223896 | −0.0174303 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.95077 | 0.305720 | 0.152860 | − | 0.988248i | \(-0.451152\pi\) | ||||
0.152860 | + | 0.988248i | \(0.451152\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.3605 | 2.48927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4089 | 0.872461 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.6528 | −1.11403 | −0.557016 | − | 0.830501i | \(-0.688054\pi\) | ||||
−0.557016 | + | 0.830501i | \(0.688054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.28610 | −0.323998 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.07978 | 0.0811609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.1044 | −1.42793 | −0.713966 | − | 0.700180i | \(-0.753103\pi\) | ||||
−0.713966 | + | 0.700180i | \(0.753103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8763 | 1.32874 | 0.664368 | − | 0.747406i | \(-0.268701\pi\) | ||||
0.664368 | + | 0.747406i | \(0.268701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.15748 | 0.159485 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0446856 | −0.00328535 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39477 | −0.101996 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.37141 | −0.390713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.31803 | −0.167727 | −0.0838633 | − | 0.996477i | \(-0.526726\pi\) | ||||
−0.0838633 | + | 0.996477i | \(0.526726\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.63579 | 0.189728 | 0.0948641 | − | 0.995490i | \(-0.469758\pi\) | ||||
0.0948641 | + | 0.995490i | \(0.469758\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.41720 | −0.101488 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9127 | 0.919993 | 0.459997 | − | 0.887921i | \(-0.347851\pi\) | ||||
0.459997 | + | 0.887921i | \(0.347851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.46739 | 0.671125 | 0.335563 | − | 0.942018i | \(-0.391074\pi\) | ||||
0.335563 | + | 0.942018i | \(0.391074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.651592 | −0.0459597 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.2089 | 1.41838 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.52783 | 0.176552 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.49027 | 0.312095 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.10709 | −0.284094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0659 | 1.65677 | 0.828384 | − | 0.560161i | \(-0.189261\pi\) | ||||
0.828384 | + | 0.560161i | \(0.189261\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.959202 | 0.0657234 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.8904 | −0.810917 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41.7327 | −2.83300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.23727 | −0.151181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.82853 | −0.593871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.29356 | 0.153588 | 0.0767942 | − | 0.997047i | \(-0.475532\pi\) | ||||
0.0767942 | + | 0.997047i | \(0.475532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.95572 | −0.197048 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.91541 | 0.392619 | 0.196310 | − | 0.980542i | \(-0.437104\pi\) | ||||
0.196310 | + | 0.980542i | \(0.437104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.29024 | 0.349589 | 0.174794 | − | 0.984605i | \(-0.444074\pi\) | ||||
0.174794 | + | 0.984605i | \(0.444074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.959640 | 0.0631397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.8272 | 1.88854 | 0.944268 | − | 0.329179i | \(-0.106772\pi\) | ||||
0.944268 | + | 0.329179i | \(0.106772\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.7086 | −0.763784 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.635196 | −0.0412604 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9836 | −1.35732 | −0.678658 | − | 0.734454i | \(-0.737438\pi\) | ||||
−0.678658 | + | 0.734454i | \(0.737438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9505 | 0.769803 | 0.384901 | − | 0.922958i | \(-0.374235\pi\) | ||||
0.384901 | + | 0.922958i | \(0.374235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.57001 | −0.357317 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.3706 | 0.726442 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.9968 | −1.65414 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.66181 | −0.168685 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6227 | 1.17545 | 0.587727 | − | 0.809060i | \(-0.300023\pi\) | ||||
0.587727 | + | 0.809060i | \(0.300023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.61645 | −0.101625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.275830 | 0.0172731 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.1720 | 1.00878 | 0.504390 | − | 0.863476i | \(-0.331717\pi\) | ||||
0.504390 | + | 0.863476i | \(0.331717\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.191527 | 0.0119009 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.9362 | 0.862627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.82088 | −0.112281 | −0.0561403 | − | 0.998423i | \(-0.517879\pi\) | ||||
−0.0561403 | + | 0.998423i | \(0.517879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1737 | 0.747826 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.14438 | −0.131234 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6642 | 1.01604 | 0.508018 | − | 0.861346i | \(-0.330378\pi\) | ||||
0.508018 | + | 0.861346i | \(0.330378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5625 | 1.24908 | 0.624541 | − | 0.780992i | \(-0.285286\pi\) | ||||
0.624541 | + | 0.780992i | \(0.285286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.07426 | 0.367631 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.06403 | 0.0641635 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.7768 | 1.24836 | 0.624179 | − | 0.781282i | \(-0.285434\pi\) | ||||
0.624179 | + | 0.781282i | \(0.285434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.7792 | −1.72296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.09635 | 0.542643 | 0.271321 | − | 0.962489i | \(-0.412539\pi\) | ||||
0.271321 | + | 0.962489i | \(0.412539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.28342 | 0.373511 | 0.186755 | − | 0.982406i | \(-0.440203\pi\) | ||||
0.186755 | + | 0.982406i | \(0.440203\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.812218 | 0.0481116 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8345 | −0.639543 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2817 | −0.898924 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00568 | 0.176196 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.24930 | −0.540350 | −0.270175 | − | 0.962811i | \(-0.587082\pi\) | ||||
−0.270175 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.13146 | −0.298765 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.33346 | 0.0773753 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.2317 | −0.591715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.9633 | 2.93747 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.42632 | −0.0819402 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.2531 | −0.587090 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.4362 | 1.56587 | 0.782934 | − | 0.622104i | \(-0.213722\pi\) | ||||
0.782934 | + | 0.622104i | \(0.213722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.29760 | −0.130706 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.65992 | 0.207535 | 0.103768 | − | 0.994602i | \(-0.466910\pi\) | ||||
0.103768 | + | 0.994602i | \(0.466910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3693 | −0.642631 | −0.321316 | − | 0.946972i | \(-0.604125\pi\) | ||||
−0.321316 | + | 0.946972i | \(0.604125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.6685 | 0.713790 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.15992 | −0.289810 | −0.144905 | − | 0.989446i | \(-0.546288\pi\) | ||||
−0.144905 | + | 0.989446i | \(0.546288\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.01688 | −0.280892 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.271375 | 0.0151467 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.05976 | 0.281532 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.73502 | 0.373592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.85256 | 0.213047 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 50.1841 | 2.76674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0976 | −1.32453 | −0.662263 | − | 0.749271i | \(-0.730404\pi\) | ||||
−0.662263 | + | 0.749271i | \(0.730404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.132078 | 0.00723785 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.09659 | 0.169185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7255 | 0.584253 | 0.292126 | − | 0.956380i | \(-0.405637\pi\) | ||||
0.292126 | + | 0.956380i | \(0.405637\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.37672 | 0.129086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3602 | 0.561037 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7329 | −1.01148 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.319669 | 0.0172104 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.94536 | 0.426529 | 0.213265 | − | 0.976994i | \(-0.431590\pi\) | ||||
0.213265 | + | 0.976994i | \(0.431590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.7190 | 1.53729 | 0.768645 | − | 0.639675i | \(-0.220931\pi\) | ||||
0.768645 | + | 0.639675i | \(0.220931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.44045 | 0.450518 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.33583 | −0.230773 | −0.115387 | − | 0.993321i | \(-0.536811\pi\) | ||||
−0.115387 | + | 0.993321i | \(0.536811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.55846 | −0.241938 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.18223 | −0.0625704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1095 | −1.11412 | −0.557058 | − | 0.830474i | \(-0.688070\pi\) | ||||
−0.557058 | + | 0.830474i | \(0.688070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.10087 | −0.215835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.07641 | 0.108984 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.6323 | 0.556520 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.3726 | 1.84643 | 0.923217 | − | 0.384279i | \(-0.125550\pi\) | ||||
0.923217 | + | 0.384279i | \(0.125550\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.47157 | −0.388955 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −52.1778 | −2.70893 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.0835 | 1.60944 | 0.804720 | − | 0.593654i | \(-0.202315\pi\) | ||||
0.804720 | + | 0.593654i | \(0.202315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.210422 | −0.0108662 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.7555 | −1.63549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.44745 | 0.177084 | 0.0885419 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885419 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.87026 | 0.0958163 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.1927 | −1.59387 | −0.796935 | − | 0.604065i | \(-0.793547\pi\) | ||||
−0.796935 | + | 0.604065i | \(0.793547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.56054 | −0.232427 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 35.1446 | 1.78650 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.4197 | −1.23813 | −0.619063 | − | 0.785341i | \(-0.712487\pi\) | ||||
−0.619063 | + | 0.785341i | \(0.712487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.99140 | 0.100709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.82423 | −0.192907 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.01867 | 0.151886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5362 | −0.729550 | −0.364775 | − | 0.931096i | \(-0.618854\pi\) | ||||
−0.364775 | + | 0.931096i | \(0.618854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.48124 | −0.174280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 65.5773 | 3.26664 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.60346 | 0.427509 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0475469 | −0.00235681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9212 | 0.836697 | 0.418349 | − | 0.908287i | \(-0.362609\pi\) | ||||
0.418349 | + | 0.908287i | \(0.362609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.33907 | −0.214031 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.9939 | 1.08225 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.6498 | 0.620956 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.884646 | 0.0433213 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2221 | −0.645944 | −0.322972 | − | 0.946408i | \(-0.604682\pi\) | ||||
−0.322972 | + | 0.946408i | \(0.604682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1125 | 0.687803 | 0.343901 | − | 0.939006i | \(-0.388251\pi\) | ||||
0.343901 | + | 0.939006i | \(0.388251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.6073 | 1.68267 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.31084 | −0.0635850 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.9457 | 2.12668 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.50794 | −0.0728043 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.90094 | −0.428743 | −0.214372 | − | 0.976752i | \(-0.568770\pi\) | ||||
−0.214372 | + | 0.976752i | \(0.568770\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.01120 | −0.336937 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.992137 | 0.0475693 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.86394 | 0.280510 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.74796 | −0.417517 | −0.208759 | − | 0.977967i | \(-0.566942\pi\) | ||||
−0.208759 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.6084 | −1.60040 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.29372 | −0.0614667 | −0.0307334 | − | 0.999528i | \(-0.509784\pi\) | ||||
−0.0307334 | + | 0.999528i | \(0.509784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1908 | 0.483092 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.66855 | −0.126218 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.55203 | 0.356402 | 0.178201 | − | 0.983994i | \(-0.442972\pi\) | ||||
0.178201 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.68969 | 0.126653 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.22206 | 0.0574173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.8670 | −1.35330 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.3717 | 0.999724 | 0.499862 | − | 0.866105i | \(-0.333384\pi\) | ||||
0.499862 | + | 0.866105i | \(0.333384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.64277 | −0.0766777 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.9630 | −0.557173 | −0.278587 | − | 0.960411i | \(-0.589866\pi\) | ||||
−0.278587 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.58246 | −0.120017 | −0.0600086 | − | 0.998198i | \(-0.519113\pi\) | ||||
−0.0600086 | + | 0.998198i | \(0.519113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.04883 | −0.0950123 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.95577 | 0.229326 | 0.114663 | − | 0.993404i | \(-0.463421\pi\) | ||||
0.114663 | + | 0.993404i | \(0.463421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2723 | −0.612857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.03810 | −0.0939107 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.6517 | −0.581727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.85994 | −0.177106 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.9822 | −1.64751 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.9505 | 1.45985 | 0.729927 | − | 0.683525i | \(-0.239554\pi\) | ||||
0.729927 | + | 0.683525i | \(0.239554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.300959 | −0.0137225 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.37013 | −0.0623432 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.2840 | −0.648605 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.0593 | −1.63400 | −0.817002 | − | 0.576634i | \(-0.804366\pi\) | ||||
−0.817002 | + | 0.576634i | \(0.804366\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.22379 | −0.100563 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0659 | −0.679915 | −0.339957 | − | 0.940441i | \(-0.610413\pi\) | ||||
−0.339957 | + | 0.940441i | \(0.610413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.18057 | 0.278359 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.14498 | −0.141356 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.5380 | 0.876399 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.69725 | 0.344576 | 0.172288 | − | 0.985047i | \(-0.444884\pi\) | ||||
0.172288 | + | 0.985047i | \(0.444884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.831331 | −0.0371411 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.4430 | 1.66950 | 0.834751 | − | 0.550627i | \(-0.185611\pi\) | ||||
0.834751 | + | 0.550627i | \(0.185611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.77839 | 0.301634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.80938 | −0.302415 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.7503 | −1.49596 | −0.747979 | − | 0.663723i | \(-0.768976\pi\) | ||||
−0.747979 | + | 0.663723i | \(0.768976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.5710 | −2.01594 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.83734 | −0.213574 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.9190 | 0.481148 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4583 | −0.547915 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.08328 | 0.135341 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.4889 | −0.810013 | −0.405006 | − | 0.914314i | \(-0.632731\pi\) | ||||
−0.405006 | + | 0.914314i | \(0.632731\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0049 | −0.962206 | −0.481103 | − | 0.876664i | \(-0.659764\pi\) | ||||
−0.481103 | + | 0.876664i | \(0.659764\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.901891 | 0.0393617 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.7633 | −0.555979 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6921 | −0.899656 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.1672 | 0.658200 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0250 | 0.737435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28967 | −0.0557571 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.02000 | 0.173476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0987 | 0.521128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.47730 | 0.235487 | 0.117744 | − | 0.993044i | \(-0.462434\pi\) | ||||
0.117744 | + | 0.993044i | \(0.462434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.76158 | −0.161425 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3087 | −0.784258 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.2221 | 0.907390 | 0.453695 | − | 0.891157i | \(-0.350106\pi\) | ||||
0.453695 | + | 0.891157i | \(0.350106\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.3053 | 1.29340 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.1995 | 0.775326 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9383 | −0.550193 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.00940286 | 0.000399129 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.0557 | 1.48536 | 0.742679 | − | 0.669648i | \(-0.233555\pi\) | ||||
0.742679 | + | 0.669648i | \(0.233555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −80.0819 | −3.38711 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.293491 | 0.0123912 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.8664 | 1.46944 | 0.734722 | − | 0.678368i | \(-0.237313\pi\) | ||||
0.734722 | + | 0.678368i | \(0.237313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2950 | −0.475184 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.8753 | −1.54862 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2725 | 0.514488 | 0.257244 | − | 0.966346i | \(-0.417186\pi\) | ||||
0.257244 | + | 0.966346i | \(0.417186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.7445 | −1.74695 | −0.873477 | − | 0.486866i | \(-0.838140\pi\) | ||||
−0.873477 | + | 0.486866i | \(0.838140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.487765 | 0.0203767 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.51918 | −0.0633541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.8412 | −1.24231 | −0.621153 | − | 0.783689i | \(-0.713335\pi\) | ||||
−0.621153 | + | 0.783689i | \(0.713335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.554629 | −0.0230496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −54.2184 | −2.24936 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9532 | 0.536468 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.9069 | −0.823047 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.5901 | 1.67533 | 0.837666 | − | 0.546183i | \(-0.183920\pi\) | ||||
0.837666 | + | 0.546183i | \(0.183920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.5833 | −1.54859 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.71713 | −0.111768 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.36923 | 0.220488 | 0.110244 | − | 0.993905i | \(-0.464837\pi\) | ||||
0.110244 | + | 0.993905i | \(0.464837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.61838 | 0.230331 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.99215 | −0.0815333 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.2663 | −0.501187 | −0.250594 | − | 0.968092i | \(-0.580626\pi\) | ||||
−0.250594 | + | 0.968092i | \(0.580626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.73817 | 0.111692 | 0.0558462 | − | 0.998439i | \(-0.482214\pi\) | ||||
0.0558462 | + | 0.998439i | \(0.482214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.15266 | −0.372725 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.86784 | −0.401185 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.52229 | −0.0617880 | −0.0308940 | − | 0.999523i | \(-0.509835\pi\) | ||||
−0.0308940 | + | 0.999523i | \(0.509835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.25240 | −0.172316 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −78.8576 | −3.19024 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1669 | 1.42038 | 0.710188 | − | 0.704012i | \(-0.248610\pi\) | ||||
0.710188 | + | 0.704012i | \(0.248610\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.531913 | −0.0214488 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.5902 | 1.67436 | 0.837179 | − | 0.546929i | \(-0.184203\pi\) | ||||
0.837179 | + | 0.546929i | \(0.184203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.14656 | −0.247051 | −0.123525 | − | 0.992341i | \(-0.539420\pi\) | ||||
−0.123525 | + | 0.992341i | \(0.539420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.90386 | −0.0763993 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −43.6789 | −1.74996 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.864225 | 0.0345138 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0585757 | 0.00233556 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4888 | −1.09431 | −0.547156 | − | 0.837031i | \(-0.684289\pi\) | ||||
−0.547156 | + | 0.837031i | \(0.684289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.06401 | −0.201277 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.88811 | −0.352714 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 76.5814 | 3.03427 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.4735 | 0.533005 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6000 | −0.892645 | −0.446322 | − | 0.894872i | \(-0.647267\pi\) | ||||
−0.446322 | + | 0.894872i | \(0.647267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3949 | 1.31697 | 0.658483 | − | 0.752596i | \(-0.271199\pi\) | ||||
0.658483 | + | 0.752596i | \(0.271199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.50200 | 0.0985162 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.42401 | −0.291868 | −0.145934 | − | 0.989294i | \(-0.546619\pi\) | ||||
−0.145934 | + | 0.989294i | \(0.546619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.46004 | −0.214325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.78149 | 0.344174 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.6074 | −0.884697 | −0.442348 | − | 0.896843i | \(-0.645855\pi\) | ||||
−0.442348 | + | 0.896843i | \(0.645855\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1740 | 0.710119 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.4261 | −1.22605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4590 | 0.719061 | 0.359531 | − | 0.933133i | \(-0.382937\pi\) | ||||
0.359531 | + | 0.933133i | \(0.382937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3737 | −1.10361 | −0.551805 | − | 0.833973i | \(-0.686061\pi\) | ||||
−0.551805 | + | 0.833973i | \(0.686061\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.85772 | 0.0721479 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.5441 | 0.641552 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.16289 | 0.277348 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.482617 | −0.0186591 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.9096 | −0.421160 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.8614 | −1.72928 | −0.864639 | − | 0.502393i | \(-0.832453\pi\) | ||||
−0.864639 | + | 0.502393i | \(0.832453\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.25322 | 0.0482364 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.9517 | −1.65077 | −0.825383 | − | 0.564573i | \(-0.809041\pi\) | ||||
−0.825383 | + | 0.564573i | \(0.809041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 61.2227 | 2.34951 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.24473 | −0.0476983 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.12606 | −0.0813516 | −0.0406758 | − | 0.999172i | \(-0.512951\pi\) | ||||
−0.0406758 | + | 0.999172i | \(0.512951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.6208 | 0.787879 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.11318 | −0.0424706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 81.9903 | 3.12358 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9580 | −0.645112 | −0.322556 | − | 0.946550i | \(-0.604542\pi\) | ||||
−0.322556 | + | 0.946550i | \(0.604542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.4797 | 0.512051 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.20414 | −0.159472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.31358 | −0.125511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.06590 | −0.229433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1912 | 0.687073 | 0.343537 | − | 0.939139i | \(-0.388375\pi\) | ||||
0.343537 | + | 0.939139i | \(0.388375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.172484 | 0.00650535 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.46375 | 0.0927901 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.0528 | −1.09264 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6321 | −0.436854 | −0.218427 | − | 0.975853i | \(-0.570092\pi\) | ||||
−0.218427 | + | 0.975853i | \(0.570092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.92236 | −0.334615 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.7919 | −0.553960 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.16627 | 0.268003 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.41542 | 0.164897 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4081 | 0.947563 | 0.473782 | − | 0.880642i | \(-0.342889\pi\) | ||||
0.473782 | + | 0.880642i | \(0.342889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.7999 | −1.74292 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.51466 | −0.0935214 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.71498 | −0.175110 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0922 | 0.671001 | 0.335501 | − | 0.942040i | \(-0.391095\pi\) | ||||
0.335501 | + | 0.942040i | \(0.391095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.6383 | −0.912531 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5864 | 0.576482 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.3044 | 1.45174 | 0.725870 | − | 0.687832i | \(-0.241437\pi\) | ||||
0.725870 | + | 0.687832i | \(0.241437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.39263 | −0.0882536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.29487 | 0.121368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.3035 | 1.48259 | 0.741294 | − | 0.671180i | \(-0.234212\pi\) | ||||
0.741294 | + | 0.671180i | \(0.234212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.47031 | 0.200957 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7950 | 0.616150 | 0.308075 | − | 0.951362i | \(-0.400315\pi\) | ||||
0.308075 | + | 0.951362i | \(0.400315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6819 | 0.464627 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.3894 | −1.36801 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.52763 | 0.201975 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9908 | 1.02140 | 0.510699 | − | 0.859759i | \(-0.329387\pi\) | ||||
0.510699 | + | 0.859759i | \(0.329387\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.91863 | −0.142803 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.80764 | −0.211362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0791012 | 0.00287498 | 0.00143749 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00143749 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.340138 | 0.0123462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.7965 | 1.04387 | 0.521936 | − | 0.852985i | \(-0.325210\pi\) | ||||
0.521936 | + | 0.852985i | \(0.325210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 78.4728 | 2.84091 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.87447 | 0.140082 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.5605 | −1.24791 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3883 | −1.16795 | −0.583976 | − | 0.811771i | \(-0.698504\pi\) | ||||
−0.583976 | + | 0.811771i | \(0.698504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.40295 | −0.122554 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9188 | 1.07611 | 0.538053 | − | 0.842911i | \(-0.319160\pi\) | ||||
0.538053 | + | 0.842911i | \(0.319160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.73676 | 0.349755 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0403016 | −0.00144581 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.75728 | −0.349591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.85034 | −0.173559 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.90889 | −0.211167 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.68576 | 0.345700 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5332 | 1.26662 | 0.633312 | − | 0.773897i | \(-0.281695\pi\) | ||||
0.633312 | + | 0.773897i | \(0.281695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.383155 | 0.0136407 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.4115 | 1.72131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −69.0547 | −2.45220 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.56163 | −0.0908515 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.6009 | 1.11936 | 0.559681 | − | 0.828708i | \(-0.310924\pi\) | ||||
0.559681 | + | 0.828708i | \(0.310924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3481 | 0.542975 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.1213 | −1.06428 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3131 | 0.399230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.51134 | 0.229495 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.50653 | −0.123436 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.23228 | 0.148799 | 0.0743995 | − | 0.997229i | \(-0.476296\pi\) | ||||
0.0743995 | + | 0.997229i | \(0.476296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.2699 | −0.817118 | −0.408559 | − | 0.912732i | \(-0.633969\pi\) | ||||
−0.408559 | + | 0.912732i | \(0.633969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.32681 | −0.151748 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5682 | 0.370188 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.8961 | 1.60570 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 85.3227 | 2.98142 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2926 | 0.533715 | 0.266858 | − | 0.963736i | \(-0.414015\pi\) | ||||
0.266858 | + | 0.963736i | \(0.414015\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.16187 | 0.0753581 | 0.0376790 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376790 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.223896 | −0.00779506 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.3349 | −1.40258 | −0.701291 | − | 0.712875i | \(-0.747393\pi\) | ||||
−0.701291 | + | 0.712875i | \(0.747393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.2799 | −1.22532 | −0.612661 | − | 0.790346i | \(-0.709901\pi\) | ||||
−0.612661 | + | 0.790346i | \(0.709901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.37191 | −0.151660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.9050 | −0.516429 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.95077 | 0.136722 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2023 | 0.421772 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.98484 | −0.344715 | −0.172358 | − | 0.985034i | \(-0.555138\pi\) | ||||
−0.172358 | + | 0.985034i | \(0.555138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.76898 | −0.233413 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.91408 | −0.0659243 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.3605 | 1.11324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.2945 | 1.45326 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.32217 | −0.0453769 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0678855 | 0.00232708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.1348 | −1.71658 | −0.858292 | − | 0.513162i | \(-0.828474\pi\) | ||||
−0.858292 | + | 0.513162i | \(0.828474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4089 | 0.390176 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.4240 | 1.21006 | 0.605030 | − | 0.796203i | \(-0.293161\pi\) | ||||
0.605030 | + | 0.796203i | \(0.293161\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.6681 | 1.18286 | 0.591429 | − | 0.806357i | \(-0.298564\pi\) | ||||
0.591429 | + | 0.806357i | \(0.298564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.27983 | 0.0776964 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.09376 | 0.241474 | 0.120737 | − | 0.992685i | \(-0.461474\pi\) | ||||
0.120737 | + | 0.992685i | \(0.461474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6528 | −0.498211 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.21561 | 0.109208 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.21196 | 0.108958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.8556 | 0.706665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.2196 | 1.42892 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.28610 | −0.144897 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.8887 | 1.24564 | 0.622822 | − | 0.782363i | \(-0.285986\pi\) | ||||
0.622822 | + | 0.782363i | \(0.285986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.94626 | 0.0656457 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.6947 | 1.67426 | 0.837128 | − | 0.547007i | \(-0.184233\pi\) | ||||
0.837128 | + | 0.547007i | \(0.184233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.1640 | −1.14971 | −0.574856 | − | 0.818255i | \(-0.694942\pi\) | ||||
−0.574856 | + | 0.818255i | \(0.694942\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.07978 | 0.0362962 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.1595 | −0.542584 | −0.271292 | − | 0.962497i | \(-0.587451\pi\) | ||||
−0.271292 | + | 0.962497i | \(0.587451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.0953 | 1.27768 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.15435 | 0.306682 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.1944 | 1.51237 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.1044 | −0.638591 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.15298 | 0.0718859 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.9086 | −1.53114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.9578 | −0.531631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.7238 | −0.356866 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8763 | 0.594229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.46670 | 0.148314 | 0.0741572 | − | 0.997247i | \(-0.476373\pi\) | ||||
0.0741572 | + | 0.997247i | \(0.476373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.0350 | −0.664520 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5461 | −1.14456 | −0.572282 | − | 0.820057i | \(-0.693942\pi\) | ||||
−0.572282 | + | 0.820057i | \(0.693942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.4598 | 0.445455 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.15748 | 0.0713240 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −77.8957 | −2.57234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.7790 | 0.421541 | 0.210771 | − | 0.977536i | \(-0.432403\pi\) | ||||
0.210771 | + | 0.977536i | \(0.432403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.77320 | −0.190233 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.7013 | −1.01055 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0446856 | −0.00146925 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.2735 | −1.06000 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.2231 | 1.09002 | 0.545008 | − | 0.838431i | \(-0.316527\pi\) | ||||
0.545008 | + | 0.838431i | \(0.316527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.8899 | −1.43843 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.770130 | −0.0252129 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39477 | −0.0456139 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.1637 | −1.05074 | −0.525372 | − | 0.850873i | \(-0.676074\pi\) | ||||
−0.525372 | + | 0.850873i | \(0.676074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.39236 | 0.0780716 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.2577 | 1.70355 | 0.851776 | − | 0.523906i | \(-0.175526\pi\) | ||||
0.851776 | + | 0.523906i | \(0.175526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.84023 | −0.125055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.37141 | −0.174732 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.4123 | −0.955770 | −0.477885 | − | 0.878422i | \(-0.658596\pi\) | ||||
−0.477885 | + | 0.878422i | \(0.658596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.6088 | 2.32452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.08576 | 0.0352083 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.7473 | −1.80583 | −0.902916 | − | 0.429817i | \(-0.858578\pi\) | ||||
−0.902916 | + | 0.429817i | \(0.858578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.31803 | −0.0750096 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.05566 | 0.0341248 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −88.3826 | −2.85402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.8045 | 2.05821 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.81190 | 0.122837 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.63579 | 0.0848490 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.22188 | −0.135767 | −0.0678833 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678833 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.06469 | −0.0342026 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.5336 | −1.10824 | −0.554118 | − | 0.832438i | \(-0.686944\pi\) | ||||
−0.554118 | + | 0.832438i | \(0.686944\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0194 | 0.577674 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.41720 | −0.0453867 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.83114 | −0.314526 | −0.157263 | − | 0.987557i | \(-0.550267\pi\) | ||||
−0.157263 | + | 0.987557i | \(0.550267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.8434 | 0.346555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.1154 | 1.72777 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.2066 | 1.79271 | 0.896356 | − | 0.443334i | \(-0.146204\pi\) | ||||
0.896356 | + | 0.443334i | \(0.146204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.9127 | 0.411434 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.5599 | −0.336124 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0636 | 0.574389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.8279 | −1.74166 | −0.870832 | − | 0.491580i | \(-0.836420\pi\) | ||||
−0.870832 | + | 0.491580i | \(0.836420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.07069 | 0.160913 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.46739 | 0.300136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.51470 | 0.269663 | 0.134832 | − | 0.990869i | \(-0.456951\pi\) | ||||
0.134832 | + | 0.990869i | \(0.456951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0560008 | −0.00177179 |
(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 | 8020.2.a.f.1.17 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.f.1.17 | ✓ | 37 | 1.1 | even | 1 | trivial |