Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | 2.22675 | 1.28561 | 0.642806 | − | 0.766029i | \(-0.277770\pi\) | ||||
0.642806 | + | 0.766029i | \(0.277770\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.90847 | −1.74792 | −0.873960 | − | 0.485998i | \(-0.838456\pi\) | ||||
−0.873960 | + | 0.485998i | \(0.838456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.127234 | 0.0480898 | 0.0240449 | − | 0.999711i | \(-0.492346\pi\) | ||||
0.0240449 | + | 0.999711i | \(0.492346\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.95840 | 0.652799 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.34859 | −0.406616 | −0.203308 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203308 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.48851 | −0.412837 | −0.206419 | − | 0.978464i | \(-0.566181\pi\) | ||||
−0.206419 | + | 0.978464i | \(0.566181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.70316 | −2.24715 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.12665 | 0.273254 | 0.136627 | − | 0.990623i | \(-0.456374\pi\) | ||||
0.136627 | + | 0.990623i | \(0.456374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.57046 | 0.819120 | 0.409560 | − | 0.912283i | \(-0.365682\pi\) | ||||
0.409560 | + | 0.912283i | \(0.365682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.283317 | 0.0618249 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.17751 | 1.28810 | 0.644050 | − | 0.764983i | \(-0.277253\pi\) | ||||
0.644050 | + | 0.764983i | \(0.277253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.2761 | 2.05522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.31939 | −0.446366 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0940486 | −0.0174644 | −0.00873220 | − | 0.999962i | \(-0.502780\pi\) | ||||
−0.00873220 | + | 0.999962i | \(0.502780\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35429 | −0.243238 | −0.121619 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121619 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00297 | −0.522751 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.497289 | −0.0840571 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.38774 | 0.392542 | 0.196271 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196271 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.31452 | −0.530749 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.91105 | 1.54785 | 0.773923 | − | 0.633280i | \(-0.218292\pi\) | ||||
0.773923 | + | 0.633280i | \(0.218292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.37943 | −0.362860 | −0.181430 | − | 0.983404i | \(-0.558073\pi\) | ||||
−0.181430 | + | 0.983404i | \(0.558073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.65433 | −1.14104 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.8539 | −1.87493 | −0.937467 | − | 0.348074i | \(-0.886836\pi\) | ||||
−0.937467 | + | 0.348074i | \(0.886836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98381 | −0.997687 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.50877 | 0.351298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.100296 | 0.0137767 | 0.00688835 | − | 0.999976i | \(-0.497807\pi\) | ||||
0.00688835 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.27093 | 0.710732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.95051 | 1.05307 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4855 | −1.36510 | −0.682549 | − | 0.730840i | \(-0.739129\pi\) | ||||
−0.682549 | + | 0.730840i | \(0.739129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.89059 | −1.13832 | −0.569162 | − | 0.822226i | \(-0.692732\pi\) | ||||
−0.569162 | + | 0.822226i | \(0.692732\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.249174 | 0.0313930 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.81778 | 0.721606 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.58516 | −0.682336 | −0.341168 | − | 0.940002i | \(-0.610823\pi\) | ||||
−0.341168 | + | 0.940002i | \(0.610823\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.7557 | 1.65600 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.40758 | 1.11647 | 0.558237 | − | 0.829681i | \(-0.311478\pi\) | ||||
0.558237 | + | 0.829681i | \(0.311478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.22594 | 0.494609 | 0.247304 | − | 0.968938i | \(-0.420455\pi\) | ||||
0.247304 | + | 0.968938i | \(0.420455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.8823 | 2.64222 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.171587 | −0.0195541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2627 | −1.37967 | −0.689833 | − | 0.723969i | \(-0.742316\pi\) | ||||
−0.689833 | + | 0.723969i | \(0.742316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0399 | −1.22665 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.492027 | 0.0540069 | 0.0270035 | − | 0.999635i | \(-0.491403\pi\) | ||||
0.0270035 | + | 0.999635i | \(0.491403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.40349 | −0.477625 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.209422 | −0.0224524 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.78902 | 0.931634 | 0.465817 | − | 0.884881i | \(-0.345760\pi\) | ||||
0.465817 | + | 0.884881i | \(0.345760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.189388 | −0.0198533 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.01567 | −0.312710 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.9550 | −1.43176 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6955 | 1.89824 | 0.949122 | − | 0.314908i | \(-0.101974\pi\) | ||||
0.949122 | + | 0.314908i | \(0.101974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.64108 | −0.265439 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.41811 | −0.340115 | −0.170057 | − | 0.985434i | \(-0.554395\pi\) | ||||
−0.170057 | + | 0.985434i | \(0.554395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0306739 | −0.00302239 | −0.00151119 | − | 0.999999i | \(-0.500481\pi\) | ||||
−0.00151119 | + | 0.999999i | \(0.500481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.10734 | −0.108065 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.7393 | 1.61825 | 0.809126 | − | 0.587635i | \(-0.199941\pi\) | ||||
0.809126 | + | 0.587635i | \(0.199941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.73233 | −0.644840 | −0.322420 | − | 0.946597i | \(-0.604496\pi\) | ||||
−0.322420 | + | 0.946597i | \(0.604496\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.31689 | 0.504657 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0582 | −1.04027 | −0.520134 | − | 0.854085i | \(-0.674118\pi\) | ||||
−0.520134 | + | 0.854085i | \(0.674118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.1446 | −2.25150 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.91508 | −0.269500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.143348 | 0.0131407 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.18130 | −0.834663 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.0694 | 1.98993 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.6215 | −1.84444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.72214 | −0.152815 | −0.0764076 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764076 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.29839 | −0.466497 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9999 | 1.31055 | 0.655273 | − | 0.755393i | \(-0.272554\pi\) | ||||
0.655273 | + | 0.755393i | \(0.272554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.454283 | 0.0393913 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.06525 | 0.780212 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.23865 | −0.362132 | −0.181066 | − | 0.983471i | \(-0.557955\pi\) | ||||
−0.181066 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.2272 | −1.71565 | −0.857824 | − | 0.513944i | \(-0.828184\pi\) | ||||
−0.857824 | + | 0.513944i | \(0.828184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.6224 | −2.41044 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00739 | 0.167866 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.367586 | 0.0305264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.5512 | −1.28264 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.4272 | −1.67346 | −0.836732 | − | 0.547612i | \(-0.815537\pi\) | ||||
−0.836732 | + | 0.547612i | \(0.815537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.9022 | −1.70100 | −0.850500 | − | 0.525975i | \(-0.823701\pi\) | ||||
−0.850500 | + | 0.525975i | \(0.823701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.20643 | 0.178380 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.29321 | 0.425161 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.56927 | −0.364667 | −0.182334 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182334 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.223333 | 0.0177115 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.785988 | 0.0619445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.31476 | −0.572936 | −0.286468 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286468 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.7370 | 0.913726 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.9467 | 1.15661 | 0.578303 | − | 0.815822i | \(-0.303715\pi\) | ||||
0.578303 | + | 0.815822i | \(0.303715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7844 | −0.829565 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.99238 | 0.534721 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2864 | −1.39029 | −0.695145 | − | 0.718870i | \(-0.744660\pi\) | ||||
−0.695145 | + | 0.718870i | \(0.744660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.30747 | 0.0988353 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.3486 | −1.75499 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6387 | 1.09415 | 0.547075 | − | 0.837084i | \(-0.315741\pi\) | ||||
0.547075 | + | 0.837084i | \(0.315741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6879 | −1.38906 | −0.694531 | − | 0.719463i | \(-0.744388\pi\) | ||||
−0.694531 | + | 0.719463i | \(0.744388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.7971 | −1.46344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.33240 | −0.686132 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.51940 | −0.111109 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.295104 | −0.0214657 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.95144 | −0.575346 | −0.287673 | − | 0.957729i | \(-0.592882\pi\) | ||||
−0.287673 | + | 0.957729i | \(0.592882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.37180 | −0.530634 | −0.265317 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265317 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.9547 | 0.927706 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7159 | −0.905969 | −0.452984 | − | 0.891519i | \(-0.649641\pi\) | ||||
−0.452984 | + | 0.891519i | \(0.649641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.41792 | −0.242290 | −0.121145 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121145 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4367 | −0.877220 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0119662 | −0.000839860 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38.7370 | −2.70551 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.0980 | 0.840870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.81510 | −0.333067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1230 | 1.04111 | 0.520555 | − | 0.853828i | \(-0.325725\pi\) | ||||
0.520555 | + | 0.853828i | \(0.325725\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.9483 | 1.43535 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.29993 | 0.634250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.172312 | −0.0116973 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.41009 | 0.635875 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.67703 | −0.112809 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.0583 | −1.87892 | −0.939461 | − | 0.342657i | \(-0.888673\pi\) | ||||
−0.939461 | + | 0.342657i | \(0.888673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.1247 | 1.34165 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.52803 | −0.300536 | −0.150268 | − | 0.988645i | \(-0.548014\pi\) | ||||
−0.150268 | + | 0.988645i | \(0.548014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.88767 | 0.322986 | 0.161493 | − | 0.986874i | \(-0.448369\pi\) | ||||
0.161493 | + | 0.986874i | \(0.448369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.382080 | −0.0251390 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8902 | 0.713442 | 0.356721 | − | 0.934211i | \(-0.383895\pi\) | ||||
0.356721 | + | 0.934211i | \(0.383895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 50.2390 | 3.27723 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.3060 | −1.77371 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.468879 | 0.0303293 | 0.0151646 | − | 0.999885i | \(-0.495173\pi\) | ||||
0.0151646 | + | 0.999885i | \(0.495173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.11565 | 0.458359 | 0.229180 | − | 0.973384i | \(-0.426396\pi\) | ||||
0.229180 | + | 0.973384i | \(0.426396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.6248 | −1.13063 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.2960 | 1.74388 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.31465 | −0.338163 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.09562 | 0.0694320 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4814 | −1.04030 | −0.520150 | − | 0.854075i | \(-0.674124\pi\) | ||||
−0.520150 | + | 0.854075i | \(0.674124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.33095 | −0.523762 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.80545 | −0.614041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7437 | −1.16920 | −0.584599 | − | 0.811322i | \(-0.698748\pi\) | ||||
−0.584599 | + | 0.811322i | \(0.698748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.303801 | 0.0188773 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.184185 | −0.0114007 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.45247 | 0.212888 | 0.106444 | − | 0.994319i | \(-0.466053\pi\) | ||||
0.106444 | + | 0.994319i | \(0.466053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.392003 | −0.0240806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.5709 | 1.19772 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.54448 | 0.520966 | 0.260483 | − | 0.965478i | \(-0.416118\pi\) | ||||
0.260483 | + | 0.965478i | \(0.416118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7868 | 0.776743 | 0.388372 | − | 0.921503i | \(-0.373038\pi\) | ||||
0.388372 | + | 0.921503i | \(0.373038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.421719 | −0.0255236 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.8583 | −0.835687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4273 | 1.58786 | 0.793932 | − | 0.608006i | \(-0.208030\pi\) | ||||
0.793932 | + | 0.608006i | \(0.208030\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.65224 | −0.158786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.28222 | −0.374766 | −0.187383 | − | 0.982287i | \(-0.560001\pi\) | ||||
−0.187383 | + | 0.982287i | \(0.560001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.1857 | −1.67547 | −0.837734 | − | 0.546078i | \(-0.816120\pi\) | ||||
−0.837734 | + | 0.546078i | \(0.816120\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.0743 | −1.84068 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.26102 | 0.0744356 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7307 | −0.925332 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.6302 | 2.44041 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.2689 | −1.47622 | −0.738112 | − | 0.674678i | \(-0.764282\pi\) | ||||
−0.738112 | + | 0.674678i | \(0.764282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.9823 | 2.38608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.12791 | 0.181500 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.19526 | −0.531776 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.302744 | −0.0174499 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.61126 | −0.437255 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.7486 | 1.98970 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.65104 | −0.379595 | −0.189798 | − | 0.981823i | \(-0.560783\pi\) | ||||
−0.189798 | + | 0.981823i | \(0.560783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0683029 | −0.00388562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.2914 | 1.09391 | 0.546957 | − | 0.837161i | \(-0.315786\pi\) | ||||
0.546957 | + | 0.837161i | \(0.315786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9686 | 0.676507 | 0.338253 | − | 0.941055i | \(-0.390164\pi\) | ||||
0.338253 | + | 0.941055i | \(0.390164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.973888 | −0.0548724 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.53040 | −0.198287 | −0.0991435 | − | 0.995073i | \(-0.531610\pi\) | ||||
−0.0991435 | + | 0.995073i | \(0.531610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.126833 | 0.00710131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 37.2742 | 2.08045 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.02267 | 0.223827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.2961 | −0.848472 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.9912 | −0.829014 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.63545 | −0.0901652 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.15944 | 0.173659 | 0.0868293 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868293 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.67614 | 0.256251 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.8294 | 1.19267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.86571 | −0.156105 | −0.0780525 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780525 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.6238 | −1.33738 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.82639 | 0.0989046 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.77921 | −0.0960684 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −53.7639 | −2.89455 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.87206 | 0.100497 | 0.0502486 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502486 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.1333 | −1.02418 | −0.512091 | − | 0.858931i | \(-0.671129\pi\) | ||||
−0.512091 | + | 0.858931i | \(0.671129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.45242 | 0.184277 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9121 | 0.953365 | 0.476683 | − | 0.879075i | \(-0.341839\pi\) | ||||
0.476683 | + | 0.879075i | \(0.341839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.7692 | −1.95151 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.319200 | 0.0168939 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.6237 | −0.982920 | −0.491460 | − | 0.870900i | \(-0.663537\pi\) | ||||
−0.491460 | + | 0.870900i | \(0.663537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.25180 | −0.329042 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.4444 | −1.07305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.5169 | −0.864536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1199 | −0.737051 | −0.368526 | − | 0.929618i | \(-0.620137\pi\) | ||||
−0.368526 | + | 0.929618i | \(0.620137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.4098 | 1.01043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0127610 | 0.000662519 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.4991 | −0.906071 | −0.453035 | − | 0.891493i | \(-0.649659\pi\) | ||||
−0.453035 | + | 0.891493i | \(0.649659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −45.9189 | −2.37124 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.139992 | 0.00720995 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.86167 | −0.0956278 | −0.0478139 | − | 0.998856i | \(-0.515225\pi\) | ||||
−0.0478139 | + | 0.998856i | \(0.515225\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.83477 | −0.196461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.59670 | 0.337075 | 0.168538 | − | 0.985695i | \(-0.446096\pi\) | ||||
0.168538 | + | 0.985695i | \(0.446096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.670640 | 0.0341790 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.65987 | −0.236875 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.58169 | −0.0801950 | −0.0400975 | − | 0.999196i | \(-0.512767\pi\) | ||||
−0.0400975 | + | 0.999196i | \(0.512767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.95992 | 0.351978 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.4009 | 1.68485 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.9285 | 2.41154 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3966 | 1.27462 | 0.637309 | − | 0.770608i | \(-0.280047\pi\) | ||||
0.637309 | + | 0.770608i | \(0.280047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.01157 | 0.0506420 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.54246 | −0.376652 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.01587 | 0.100418 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 43.1490 | 2.14409 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.22009 | −0.159614 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.76455 | −0.235592 | −0.117796 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117796 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.43840 | −0.465562 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.33411 | −0.0656473 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.92307 | −0.0943998 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −45.0408 | −2.20566 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.6082 | 0.664806 | 0.332403 | − | 0.943137i | \(-0.392141\pi\) | ||||
0.332403 | + | 0.943137i | \(0.392141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8645 | −0.626978 | −0.313489 | − | 0.949592i | \(-0.601498\pi\) | ||||
−0.313489 | + | 0.949592i | \(0.601498\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.1730 | −1.22395 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.5776 | 0.561597 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13118 | −0.0547418 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.46994 | 0.215811 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4285 | 1.46569 | 0.732844 | − | 0.680397i | \(-0.238193\pi\) | ||||
0.732844 | + | 0.680397i | \(0.238193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.49495 | 0.408241 | 0.204121 | − | 0.978946i | \(-0.434567\pi\) | ||||
0.204121 | + | 0.978946i | \(0.434567\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.818521 | 0.0392451 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.0566 | 1.05511 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8520 | 0.756576 | 0.378288 | − | 0.925688i | \(-0.376513\pi\) | ||||
0.378288 | + | 0.925688i | \(0.376513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.6771 | −0.651289 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.52175 | 0.262346 | 0.131173 | − | 0.991359i | \(-0.458126\pi\) | ||||
0.131173 | + | 0.991359i | \(0.458126\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.3516 | −1.62842 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.4863 | −2.15143 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.5859 | 1.49063 | 0.745314 | − | 0.666713i | \(-0.232299\pi\) | ||||
0.745314 | + | 0.666713i | \(0.232299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.3660 | −0.629379 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.5440 | −2.18683 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.740217 | 0.0347019 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.14835 | 0.381164 | 0.190582 | − | 0.981671i | \(-0.438963\pi\) | ||||
0.190582 | + | 0.981671i | \(0.438963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.61314 | −0.121971 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2099 | −0.941269 | −0.470634 | − | 0.882328i | \(-0.655975\pi\) | ||||
−0.470634 | + | 0.882328i | \(0.655975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.03697 | 0.0481922 | 0.0240961 | − | 0.999710i | \(-0.492329\pi\) | ||||
0.0240961 | + | 0.999710i | \(0.492329\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.7866 | 0.546592 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.734354 | 0.0339819 | 0.0169909 | − | 0.999856i | \(-0.494591\pi\) | ||||
0.0169909 | + | 0.999856i | \(0.494591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.710621 | −0.0328134 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.1746 | −0.468821 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.20889 | 0.147545 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.6905 | 1.68347 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.196419 | 0.00899341 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.1901 | 1.33373 | 0.666865 | − | 0.745179i | \(-0.267636\pi\) | ||||
0.666865 | + | 0.745179i | \(0.267636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.55416 | −0.162056 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.75019 | 0.0796366 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −73.0709 | −3.31798 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.1353 | −1.36556 | −0.682781 | − | 0.730623i | \(-0.739230\pi\) | ||||
−0.682781 | + | 0.730623i | \(0.739230\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2881 | −0.736574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.5021 | −1.33141 | −0.665706 | − | 0.746214i | \(-0.731870\pi\) | ||||
−0.665706 | + | 0.746214i | \(0.731870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.105960 | −0.00477221 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3226 | 0.463965 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.19696 | 0.0536910 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.49945 | 0.246189 | 0.123095 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123095 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.2824 | 1.48695 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3596 | 0.594493 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0140 | −1.06650 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.6106 | 1.53409 | 0.767043 | − | 0.641595i | \(-0.221727\pi\) | ||||
0.767043 | + | 0.641595i | \(0.221727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.537682 | 0.0237856 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.28128 | −0.365628 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.119888 | 0.00528289 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3347 | 0.762379 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.7192 | −1.78737 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6347 | −0.947834 | −0.473917 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473917 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.56540 | −0.418266 | −0.209133 | − | 0.977887i | \(-0.567064\pi\) | ||||
−0.209133 | + | 0.977887i | \(0.567064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.91140 | 0.127064 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.52582 | −0.0664657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1617 | 0.659203 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.5348 | −0.891134 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7527 | −0.639009 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −65.4251 | −2.82857 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.5967 | 1.40665 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.41832 | 0.405676 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.05411 | −0.303280 | −0.151640 | − | 0.988436i | \(-0.548455\pi\) | ||||
−0.151640 | + | 0.988436i | \(0.548455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.6132 | −1.78579 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.3131 | 1.12713 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00855 | 0.171393 | 0.0856966 | − | 0.996321i | \(-0.472688\pi\) | ||||
0.0856966 | + | 0.996321i | \(0.472688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.4113 | −0.743096 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.335797 | −0.0143054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.56023 | −0.0663479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.7809 | −0.882099 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.1913 | 0.940275 | 0.470137 | − | 0.882593i | \(-0.344204\pi\) | ||||
0.470137 | + | 0.882593i | \(0.344204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.54180 | 0.149802 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.38331 | −0.142844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.2816 | −1.52909 | −0.764545 | − | 0.644571i | \(-0.777036\pi\) | ||||
−0.764545 | + | 0.644571i | \(0.777036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.2206 | 1.81830 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.40464 | −0.0589895 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.9315 | −1.08710 | −0.543552 | − | 0.839376i | \(-0.682921\pi\) | ||||
−0.543552 | + | 0.839376i | \(0.682921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.84904 | 0.202926 | 0.101463 | − | 0.994839i | \(-0.467648\pi\) | ||||
0.101463 | + | 0.994839i | \(0.467648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.7058 | −0.739672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 63.4808 | 2.64733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.13047 | −0.0470620 | −0.0235310 | − | 0.999723i | \(-0.507491\pi\) | ||||
−0.0235310 | + | 0.999723i | \(0.507491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.4151 | −0.682189 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0626024 | 0.00259718 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.135258 | −0.00560183 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.3935 | 0.471064 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.5250 | −0.682060 | −0.341030 | − | 0.940052i | \(-0.610776\pi\) | ||||
−0.341030 | + | 0.940052i | \(0.610776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.83545 | −0.199241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3150 | −1.16472 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.9678 | −1.39489 | −0.697445 | − | 0.716638i | \(-0.745680\pi\) | ||||
−0.697445 | + | 0.716638i | \(0.745680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.560272 | −0.0229689 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.61083 | −0.311491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.4333 | 1.12089 | 0.560447 | − | 0.828190i | \(-0.310629\pi\) | ||||
0.560447 | + | 0.828190i | \(0.310629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8279 | 0.645634 | 0.322817 | − | 0.946461i | \(-0.395370\pi\) | ||||
0.322817 | + | 0.946461i | \(0.395370\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9380 | −0.445428 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.8848 | 1.45892 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.3952 | 1.63959 | 0.819794 | − | 0.572658i | \(-0.194088\pi\) | ||||
0.819794 | + | 0.572658i | \(0.194088\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0266456 | −0.00107973 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.1331 | 0.774043 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.20436 | 0.331371 | 0.165686 | − | 0.986179i | \(-0.447016\pi\) | ||||
0.165686 | + | 0.986179i | \(0.447016\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −86.2575 | −3.47824 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.6643 | 0.630623 | 0.315311 | − | 0.948988i | \(-0.397891\pi\) | ||||
0.315311 | + | 0.948988i | \(0.397891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8251 | −0.475290 | −0.237645 | − | 0.971352i | \(-0.576375\pi\) | ||||
−0.237645 | + | 0.971352i | \(0.576375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.3280 | −0.574965 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.11826 | 0.0448021 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.2179 | 1.16872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.7220 | −0.428196 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.69015 | 0.107263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.3728 | −0.572170 | −0.286085 | − | 0.958204i | \(-0.592354\pi\) | ||||
−0.286085 | + | 0.958204i | \(0.592354\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.6751 | 1.33846 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.73093 | 0.267109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.3954 | 0.411882 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.4238 | 0.728833 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.9593 | −1.77579 | −0.887893 | − | 0.460051i | \(-0.847831\pi\) | ||||
−0.887893 | + | 0.460051i | \(0.847831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.1775 | 1.30839 | 0.654196 | − | 0.756325i | \(-0.273007\pi\) | ||||
0.654196 | + | 0.756325i | \(0.273007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.7086 | 0.815400 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.17050 | 0.124645 | 0.0623226 | − | 0.998056i | \(-0.480149\pi\) | ||||
0.0623226 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1407 | 0.555071 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.383694 | −0.0150382 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.08500 | 0.355524 | 0.177762 | − | 0.984074i | \(-0.443114\pi\) | ||||
0.177762 | + | 0.984074i | \(0.443114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −58.6265 | −2.29073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.27606 | 0.322880 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0644937 | 0.00251232 | 0.00125616 | − | 0.999999i | \(-0.499600\pi\) | ||||
0.00125616 | + | 0.999999i | \(0.499600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7167 | 0.883576 | 0.441788 | − | 0.897120i | \(-0.354344\pi\) | ||||
0.441788 | + | 0.897120i | \(0.354344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.73432 | −0.145029 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.77555 | −0.0688529 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.580987 | −0.0224959 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −62.4786 | −2.41556 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9898 | 0.462861 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.3698 | −1.17067 | −0.585335 | − | 0.810792i | \(-0.699037\pi\) | ||||
−0.585335 | + | 0.810792i | \(0.699037\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.8343 | −0.917382 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.1454 | −0.389921 | −0.194960 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194960 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.37870 | 0.0912862 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0828 | −0.386372 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.3406 | 0.586993 | 0.293497 | − | 0.955960i | \(-0.405181\pi\) | ||||
0.293497 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5666 | 0.632978 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.8836 | 0.415235 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.149291 | −0.00568753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.81419 | −0.183140 | −0.0915702 | − | 0.995799i | \(-0.529189\pi\) | ||||
−0.0915702 | + | 0.995799i | \(0.529189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.336034 | −0.0127649 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 79.0573 | 2.99881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1663 | 0.422955 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.2498 | 0.917210 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8248 | −0.635465 | −0.317733 | − | 0.948180i | \(-0.602921\pi\) | ||||
−0.317733 | + | 0.948180i | \(0.602921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.52533 | 0.321539 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 111.870 | 4.21325 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.434899 | −0.0163560 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8837 | 0.972084 | 0.486042 | − | 0.873936i | \(-0.338440\pi\) | ||||
0.486042 | + | 0.873936i | \(0.338440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0153 | −0.900644 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.36616 | −0.313315 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.84581 | −0.293417 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.04407 | 0.0389917 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.4115 | 1.50709 | 0.753547 | − | 0.657394i | \(-0.228341\pi\) | ||||
0.753547 | + | 0.657394i | \(0.228341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.00390275 | −0.000145346 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.8447 | 0.589272 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.966455 | −0.0358932 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7913 | 0.882369 | 0.441185 | − | 0.897416i | \(-0.354558\pi\) | ||||
0.441185 | + | 0.897416i | \(0.354558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.12639 | −0.226903 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.68080 | −0.0991528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.2965 | 0.971282 | 0.485641 | − | 0.874158i | \(-0.338586\pi\) | ||||
0.485641 | + | 0.874158i | \(0.338586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 60.7812 | 2.24195 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.53212 | 0.277449 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.1782 | 0.999766 | 0.499883 | − | 0.866093i | \(-0.333376\pi\) | ||||
0.499883 | + | 0.866093i | \(0.333376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.8344 | −0.434747 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.3208 | 1.29580 | 0.647898 | − | 0.761727i | \(-0.275648\pi\) | ||||
0.647898 | + | 0.761727i | \(0.275648\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 79.8392 | 2.92508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.963583 | 0.0352557 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.12981 | 0.0778215 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.11785 | 0.186753 | 0.0933765 | − | 0.995631i | \(-0.470234\pi\) | ||||
0.0933765 | + | 0.995631i | \(0.470234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.7000 | −1.33742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 81.6957 | 2.97321 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49682 | −0.236131 | −0.118065 | − | 0.993006i | \(-0.537669\pi\) | ||||
−0.118065 | + | 0.993006i | \(0.537669\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.5509 | −0.673355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.0920 | 1.27208 | 0.636041 | − | 0.771655i | \(-0.280571\pi\) | ||||
0.636041 | + | 0.771655i | \(0.280571\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.856579 | −0.0310102 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.62377 | −0.311793 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.6077 | 0.563563 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6939 | −1.07079 | −0.535395 | − | 0.844602i | \(-0.679837\pi\) | ||||
−0.535395 | + | 0.844602i | \(0.679837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.7374 | −1.50314 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.6109 | −0.813258 | −0.406629 | − | 0.913593i | \(-0.633296\pi\) | ||||
−0.406629 | + | 0.913593i | \(0.633296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.9169 | −0.499909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.676487 | 0.0242688 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.3870 | 1.26787 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6870 | −0.453977 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.218135 | 0.00779552 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.8588 | 0.637409 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.9375 | 1.56620 | 0.783101 | − | 0.621895i | \(-0.213637\pi\) | ||||
0.783101 | + | 0.621895i | \(0.213637\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.68777 | 0.273692 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.40698 | −0.0500263 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.2337 | 0.469942 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.872891 | −0.0309583 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.7524 | 1.65605 | 0.828027 | − | 0.560688i | \(-0.189463\pi\) | ||||
0.828027 | + | 0.560688i | \(0.189463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4819 | −0.512332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.2124 | 0.608170 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.69907 | −0.201116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.07201 | −0.108274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.0264 | 0.669760 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3923 | 0.470848 | 0.235424 | − | 0.971893i | \(-0.424352\pi\) | ||||
0.235424 | + | 0.971893i | \(0.424352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3858 | 0.470037 | 0.235019 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235019 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.4730 | 0.998591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.5895 | 1.00145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.49567 | −0.297226 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.370897 | −0.0129602 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.23562 | 0.147824 | 0.0739122 | − | 0.997265i | \(-0.476452\pi\) | ||||
0.0739122 | + | 0.997265i | \(0.476452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3570 | −0.465597 | −0.232799 | − | 0.972525i | \(-0.574788\pi\) | ||||
−0.232799 | + | 0.972525i | \(0.574788\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.8589 | −1.07437 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.13307 | −0.143721 | −0.0718604 | − | 0.997415i | \(-0.522894\pi\) | ||||
−0.0718604 | + | 0.997415i | \(0.522894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.2050 | −1.04906 | −0.524532 | − | 0.851391i | \(-0.675760\pi\) | ||||
−0.524532 | + | 0.851391i | \(0.675760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.8469 | 2.04138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.86834 | −0.272622 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58.4185 | −2.02166 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.14113 | 0.108573 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.3993 | −1.18760 | −0.593798 | − | 0.804614i | \(-0.702372\pi\) | ||||
−0.593798 | + | 0.804614i | \(0.702372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9912 | −0.999695 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9889 | −0.481804 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.1503 | 1.45001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16817 | −0.0401388 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −62.7625 | −2.15400 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.7503 | 0.505633 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.70737 | −0.332374 | −0.166187 | − | 0.986094i | \(-0.553146\pi\) | ||||
−0.166187 | + | 0.986094i | \(0.553146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.3295 | −0.934648 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.7710 | −1.18775 | −0.593877 | − | 0.804556i | \(-0.702404\pi\) | ||||
−0.593877 | + | 0.804556i | \(0.702404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.5064 | 0.904387 | 0.452194 | − | 0.891920i | \(-0.350642\pi\) | ||||
0.452194 | + | 0.891920i | \(0.350642\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.80797 | 0.0956954 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.76135 | 0.264199 | 0.132100 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132100 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.4718 | 2.43011 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.0282 | −1.18962 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.5374 | 0.560994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.31355 | 0.281694 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.6133 | 1.23917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.62375 | −0.0886990 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4061 | 1.12804 | 0.564021 | − | 0.825760i | \(-0.309254\pi\) | ||||
0.564021 | + | 0.825760i | \(0.309254\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −56.2674 | −1.89785 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.5473 | 1.53453 | 0.767263 | − | 0.641332i | \(-0.221618\pi\) | ||||
0.767263 | + | 0.641332i | \(0.221618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.05533 | −0.271084 | −0.135542 | − | 0.990772i | \(-0.543278\pi\) | ||||
−0.135542 | + | 0.990772i | \(0.543278\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 91.2571 | 3.06757 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.8462 | 1.27075 | 0.635376 | − | 0.772203i | \(-0.280845\pi\) | ||||
0.635376 | + | 0.772203i | \(0.280845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.219114 | −0.00734886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.8883 | 0.498777 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.8944 | −1.53580 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.2150 | −1.91249 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.4755 | −0.683657 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.127369 | 0.00424801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.112999 | 0.00376453 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.674134 | −0.0224338 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 73.0411 | 2.42797 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.311482 | 0.0103426 | 0.00517129 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517129 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.69401 | −0.222026 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8928 | −1.42110 | −0.710551 | − | 0.703646i | \(-0.751554\pi\) | ||||
−0.710551 | + | 0.703646i | \(0.751554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.663544 | −0.0219601 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 77.3762 | 2.55798 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.90849 | 0.0630239 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.2516 | −1.32778 | −0.663889 | − | 0.747831i | \(-0.731095\pi\) | ||||
−0.663889 | + | 0.747831i | \(0.731095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.8102 | −0.488012 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.0032 | −0.460922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.5367 | 0.806761 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0600716 | −0.00197301 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.7060 | 0.482489 | 0.241244 | − | 0.970464i | \(-0.422444\pi\) | ||||
0.241244 | + | 0.970464i | \(0.422444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.9354 | −0.817226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.9570 | 1.40635 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.93851 | 0.194210 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.2273 | 0.856807 | 0.428404 | − | 0.903587i | \(-0.359076\pi\) | ||||
0.428404 | + | 0.903587i | \(0.359076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.6511 | 0.869725 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.2435 | −1.67049 | −0.835246 | − | 0.549877i | \(-0.814675\pi\) | ||||
−0.835246 | + | 0.549877i | \(0.814675\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.2257 | 1.99378 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.15340 | 0.0375203 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.3479 | −1.01867 | −0.509334 | − | 0.860569i | \(-0.670108\pi\) | ||||
−0.509334 | + | 0.860569i | \(0.670108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.29034 | −0.204193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.86130 | −0.254920 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.4399 | −0.921260 | −0.460630 | − | 0.887592i | \(-0.652377\pi\) | ||||
−0.460630 | + | 0.887592i | \(0.652377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.0779 | 1.00566 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.282426 | 0.00912953 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.539299 | −0.0174149 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1659 | −0.940835 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.7822 | 1.05639 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.8124 | 0.927505 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0183 | −0.482956 | −0.241478 | − | 0.970406i | \(-0.577632\pi\) | ||||
−0.241478 | + | 0.970406i | \(0.577632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.95747 | 0.287755 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.87993 | 0.156604 | 0.0783022 | − | 0.996930i | \(-0.475050\pi\) | ||||
0.0783022 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.57358 | −0.0825052 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.0604 | −1.09081 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.3517 | 1.51492 | 0.757458 | − | 0.652884i | \(-0.226441\pi\) | ||||
0.757458 | + | 0.652884i | \(0.226441\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.8528 | −0.378818 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1846 | −0.420951 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.7138 | 0.533087 | 0.266543 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266543 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.6996 | 1.58356 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.64173 | −0.115918 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6990 | −0.467400 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3986 | 0.711516 | 0.355758 | − | 0.934578i | \(-0.384223\pi\) | ||||
0.355758 | + | 0.934578i | \(0.384223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.03527 | 0.223258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.3588 | 0.423503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.8835 | −1.67484 | −0.837418 | − | 0.546563i | \(-0.815936\pi\) | ||||
−0.837418 | + | 0.546563i | \(0.815936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.53809 | −0.175217 |
(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 | 8048.2.a.v.1.24 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.5 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.5 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.24 | 28 | 1.1 | even | 1 | trivial |