Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.242500 | −0.171474 | −0.0857368 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857368 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94119 | −0.970597 | ||||||||
\(5\) | 2.79671 | 1.25073 | 0.625364 | − | 0.780333i | \(-0.284950\pi\) | ||||
0.625364 | + | 0.780333i | \(0.284950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.955741 | 0.337905 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.678204 | −0.214467 | ||||||||
\(11\) | 4.59836 | 1.38646 | 0.693229 | − | 0.720718i | \(-0.256188\pi\) | ||||
0.693229 | + | 0.720718i | \(0.256188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.92098 | −1.36483 | −0.682417 | − | 0.730963i | \(-0.739071\pi\) | ||||
−0.682417 | + | 0.730963i | \(0.739071\pi\) | |||||||
\(14\) | 0.242500 | 0.0648109 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.65062 | 0.912655 | ||||||||
\(17\) | −2.21339 | −0.536826 | −0.268413 | − | 0.963304i | \(-0.586499\pi\) | ||||
−0.268413 | + | 0.963304i | \(0.586499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.299740 | 0.0687650 | 0.0343825 | − | 0.999409i | \(-0.489054\pi\) | ||||
0.0343825 | + | 0.999409i | \(0.489054\pi\) | |||||||
\(20\) | −5.42896 | −1.21395 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.11510 | −0.237741 | ||||||||
\(23\) | −2.16929 | −0.452329 | −0.226165 | − | 0.974089i | \(-0.572619\pi\) | ||||
−0.226165 | + | 0.974089i | \(0.572619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.82161 | 0.564321 | ||||||||
\(26\) | 1.19334 | 0.234033 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.94119 | 0.366851 | ||||||||
\(29\) | −5.57762 | −1.03574 | −0.517869 | − | 0.855460i | \(-0.673274\pi\) | ||||
−0.517869 | + | 0.855460i | \(0.673274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00125 | 1.07786 | 0.538928 | − | 0.842352i | \(-0.318829\pi\) | ||||
0.538928 | + | 0.842352i | \(0.318829\pi\) | |||||||
\(32\) | −2.79676 | −0.494402 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.536748 | 0.0920515 | ||||||||
\(35\) | −2.79671 | −0.472731 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.81952 | 1.44992 | 0.724960 | − | 0.688791i | \(-0.241858\pi\) | ||||
0.724960 | + | 0.688791i | \(0.241858\pi\) | |||||||
\(38\) | −0.0726869 | −0.0117914 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.67293 | 0.422628 | ||||||||
\(41\) | −10.5020 | −1.64014 | −0.820071 | − | 0.572262i | \(-0.806066\pi\) | ||||
−0.820071 | + | 0.572262i | \(0.806066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.69985 | −1.02172 | −0.510859 | − | 0.859665i | \(-0.670673\pi\) | ||||
−0.510859 | + | 0.859665i | \(0.670673\pi\) | |||||||
\(44\) | −8.92631 | −1.34569 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.526055 | 0.0775625 | ||||||||
\(47\) | 7.58321 | 1.10613 | 0.553063 | − | 0.833140i | \(-0.313459\pi\) | ||||
0.553063 | + | 0.833140i | \(0.313459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.684241 | −0.0967662 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.55257 | 1.32470 | ||||||||
\(53\) | −1.04200 | −0.143130 | −0.0715649 | − | 0.997436i | \(-0.522799\pi\) | ||||
−0.0715649 | + | 0.997436i | \(0.522799\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.8603 | 1.73408 | ||||||||
\(56\) | −0.955741 | −0.127716 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.35257 | 0.177602 | ||||||||
\(59\) | −5.65706 | −0.736487 | −0.368243 | − | 0.929729i | \(-0.620041\pi\) | ||||
−0.368243 | + | 0.929729i | \(0.620041\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.161967 | 0.0207378 | 0.0103689 | − | 0.999946i | \(-0.496699\pi\) | ||||
0.0103689 | + | 0.999946i | \(0.496699\pi\) | |||||||
\(62\) | −1.45530 | −0.184824 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.62302 | −0.827878 | ||||||||
\(65\) | −13.7626 | −1.70704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.60257 | 0.317954 | 0.158977 | − | 0.987282i | \(-0.449180\pi\) | ||||
0.158977 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(68\) | 4.29662 | 0.521041 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.678204 | 0.0810609 | ||||||||
\(71\) | −2.49985 | −0.296678 | −0.148339 | − | 0.988937i | \(-0.547393\pi\) | ||||
−0.148339 | + | 0.988937i | \(0.547393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.94931 | −0.696314 | −0.348157 | − | 0.937436i | \(-0.613192\pi\) | ||||
−0.348157 | + | 0.937436i | \(0.613192\pi\) | |||||||
\(74\) | −2.13874 | −0.248623 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.581853 | −0.0667431 | ||||||||
\(77\) | −4.59836 | −0.524032 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1275 | −1.47696 | −0.738482 | − | 0.674273i | \(-0.764457\pi\) | ||||
−0.738482 | + | 0.674273i | \(0.764457\pi\) | |||||||
\(80\) | 10.2097 | 1.14148 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.54675 | 0.281241 | ||||||||
\(83\) | −9.40919 | −1.03279 | −0.516396 | − | 0.856350i | \(-0.672727\pi\) | ||||
−0.516396 | + | 0.856350i | \(0.672727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.19022 | −0.671423 | ||||||||
\(86\) | 1.62472 | 0.175198 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.39484 | 0.468492 | ||||||||
\(89\) | 9.33298 | 0.989294 | 0.494647 | − | 0.869094i | \(-0.335297\pi\) | ||||
0.494647 | + | 0.869094i | \(0.335297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.92098 | 0.515859 | ||||||||
\(92\) | 4.21102 | 0.439029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.83893 | −0.189671 | ||||||||
\(95\) | 0.838286 | 0.0860063 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8534 | −1.20353 | −0.601767 | − | 0.798672i | \(-0.705536\pi\) | ||||
−0.601767 | + | 0.798672i | \(0.705536\pi\) | |||||||
\(98\) | −0.242500 | −0.0244962 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.47729 | −0.547729 | ||||||||
\(101\) | −5.46441 | −0.543729 | −0.271864 | − | 0.962336i | \(-0.587640\pi\) | ||||
−0.271864 | + | 0.962336i | \(0.587640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.754962 | 0.0743886 | 0.0371943 | − | 0.999308i | \(-0.488158\pi\) | ||||
0.0371943 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(104\) | −4.70318 | −0.461185 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.252685 | 0.0245430 | ||||||||
\(107\) | 10.6424 | 1.02884 | 0.514419 | − | 0.857539i | \(-0.328008\pi\) | ||||
0.514419 | + | 0.857539i | \(0.328008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.61161 | 0.633277 | 0.316639 | − | 0.948546i | \(-0.397446\pi\) | ||||
0.316639 | + | 0.948546i | \(0.397446\pi\) | |||||||
\(110\) | −3.11863 | −0.297349 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.65062 | −0.344951 | ||||||||
\(113\) | −3.73009 | −0.350897 | −0.175449 | − | 0.984489i | \(-0.556138\pi\) | ||||
−0.175449 | + | 0.984489i | \(0.556138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.06690 | −0.565741 | ||||||||
\(116\) | 10.8272 | 1.00528 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.37184 | 0.126288 | ||||||||
\(119\) | 2.21339 | 0.202901 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1449 | 0.922265 | ||||||||
\(122\) | −0.0392771 | −0.00355598 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.6496 | −1.04616 | ||||||||
\(125\) | −6.09234 | −0.544916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 7.19960 | 0.636361 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.33743 | 0.292712 | ||||||||
\(131\) | 4.24308 | 0.370720 | 0.185360 | − | 0.982671i | \(-0.440655\pi\) | ||||
0.185360 | + | 0.982671i | \(0.440655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.299740 | −0.0259907 | ||||||||
\(134\) | −0.631124 | −0.0545208 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.11543 | −0.181396 | ||||||||
\(137\) | −6.12330 | −0.523148 | −0.261574 | − | 0.965183i | \(-0.584242\pi\) | ||||
−0.261574 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.79278 | −0.491337 | −0.245668 | − | 0.969354i | \(-0.579007\pi\) | ||||
−0.245668 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(140\) | 5.42896 | 0.458831 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.606215 | 0.0508725 | ||||||||
\(143\) | −22.6284 | −1.89228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.5990 | −1.29543 | ||||||||
\(146\) | 1.44271 | 0.119399 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.1204 | −1.40729 | ||||||||
\(149\) | −8.83924 | −0.724139 | −0.362070 | − | 0.932151i | \(-0.617930\pi\) | ||||
−0.362070 | + | 0.932151i | \(0.617930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.09628 | −0.658866 | −0.329433 | − | 0.944179i | \(-0.606858\pi\) | ||||
−0.329433 | + | 0.944179i | \(0.606858\pi\) | |||||||
\(152\) | 0.286473 | 0.0232361 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.11510 | 0.0898576 | ||||||||
\(155\) | 16.7838 | 1.34811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0956181 | −0.00763116 | −0.00381558 | − | 0.999993i | \(-0.501215\pi\) | ||||
−0.00381558 | + | 0.999993i | \(0.501215\pi\) | |||||||
\(158\) | 3.18344 | 0.253260 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.82173 | −0.618362 | ||||||||
\(161\) | 2.16929 | 0.170964 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4482 | 1.21000 | 0.604998 | − | 0.796227i | \(-0.293174\pi\) | ||||
0.604998 | + | 0.796227i | \(0.293174\pi\) | |||||||
\(164\) | 20.3865 | 1.59192 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.28173 | 0.177097 | ||||||||
\(167\) | 15.5614 | 1.20418 | 0.602089 | − | 0.798429i | \(-0.294335\pi\) | ||||
0.602089 | + | 0.798429i | \(0.294335\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.2160 | 0.862772 | ||||||||
\(170\) | 1.50113 | 0.115131 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.0057 | 0.991676 | ||||||||
\(173\) | 3.17589 | 0.241459 | 0.120729 | − | 0.992685i | \(-0.461477\pi\) | ||||
0.120729 | + | 0.992685i | \(0.461477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82161 | −0.213293 | ||||||||
\(176\) | 16.7869 | 1.26536 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.26325 | −0.169638 | ||||||||
\(179\) | −0.645010 | −0.0482103 | −0.0241051 | − | 0.999709i | \(-0.507674\pi\) | ||||
−0.0241051 | + | 0.999709i | \(0.507674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.26616 | 0.0941132 | 0.0470566 | − | 0.998892i | \(-0.485016\pi\) | ||||
0.0470566 | + | 0.998892i | \(0.485016\pi\) | |||||||
\(182\) | −1.19334 | −0.0884562 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.07328 | −0.152845 | ||||||||
\(185\) | 24.6657 | 1.81346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.1780 | −0.744286 | ||||||||
\(188\) | −14.7205 | −1.07360 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.203285 | −0.0147478 | ||||||||
\(191\) | 18.1421 | 1.31272 | 0.656359 | − | 0.754449i | \(-0.272096\pi\) | ||||
0.656359 | + | 0.754449i | \(0.272096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8712 | 1.50234 | 0.751170 | − | 0.660109i | \(-0.229490\pi\) | ||||
0.751170 | + | 0.660109i | \(0.229490\pi\) | |||||||
\(194\) | 2.87446 | 0.206374 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.94119 | −0.138657 | ||||||||
\(197\) | −14.1011 | −1.00466 | −0.502331 | − | 0.864676i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864676i | \(0.667524\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2186 | −1.50415 | −0.752073 | − | 0.659080i | \(-0.770946\pi\) | ||||
−0.752073 | + | 0.659080i | \(0.770946\pi\) | |||||||
\(200\) | 2.69672 | 0.190687 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.32512 | 0.0932352 | ||||||||
\(203\) | 5.57762 | 0.391472 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.3712 | −2.05137 | ||||||||
\(206\) | −0.183079 | −0.0127557 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.9646 | −1.24562 | ||||||||
\(209\) | 1.37831 | 0.0953397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.78981 | −0.123215 | −0.0616077 | − | 0.998100i | \(-0.519623\pi\) | ||||
−0.0616077 | + | 0.998100i | \(0.519623\pi\) | |||||||
\(212\) | 2.02272 | 0.138921 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.58078 | −0.176419 | ||||||||
\(215\) | −18.7376 | −1.27789 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00125 | −0.407391 | ||||||||
\(218\) | −1.60332 | −0.108590 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24.9643 | −1.68309 | ||||||||
\(221\) | 10.8920 | 0.732678 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.33108 | −0.156101 | −0.0780504 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780504 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(224\) | 2.79676 | 0.186866 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.904548 | 0.0601696 | ||||||||
\(227\) | −17.3413 | −1.15098 | −0.575490 | − | 0.817809i | \(-0.695189\pi\) | ||||
−0.575490 | + | 0.817809i | \(0.695189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1731 | −0.738342 | −0.369171 | − | 0.929361i | \(-0.620358\pi\) | ||||
−0.369171 | + | 0.929361i | \(0.620358\pi\) | |||||||
\(230\) | 1.47122 | 0.0970097 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.33076 | −0.349981 | ||||||||
\(233\) | −12.6112 | −0.826189 | −0.413094 | − | 0.910688i | \(-0.635552\pi\) | ||||
−0.413094 | + | 0.910688i | \(0.635552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.2081 | 1.38346 | ||||||||
\(236\) | 10.9815 | 0.714832 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.536748 | −0.0347922 | ||||||||
\(239\) | 6.93025 | 0.448280 | 0.224140 | − | 0.974557i | \(-0.428043\pi\) | ||||
0.224140 | + | 0.974557i | \(0.428043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.07372 | −0.584489 | −0.292245 | − | 0.956344i | \(-0.594402\pi\) | ||||
−0.292245 | + | 0.956344i | \(0.594402\pi\) | |||||||
\(242\) | −2.46015 | −0.158144 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.314410 | −0.0201280 | ||||||||
\(245\) | 2.79671 | 0.178675 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47501 | −0.0938528 | ||||||||
\(248\) | 5.73564 | 0.364213 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.47739 | 0.0934387 | ||||||||
\(251\) | −17.1122 | −1.08011 | −0.540057 | − | 0.841628i | \(-0.681597\pi\) | ||||
−0.540057 | + | 0.841628i | \(0.681597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.97520 | −0.627135 | ||||||||
\(254\) | 0.242500 | 0.0152158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5001 | 0.718759 | ||||||||
\(257\) | −9.41351 | −0.587199 | −0.293599 | − | 0.955929i | \(-0.594853\pi\) | ||||
−0.293599 | + | 0.955929i | \(0.594853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.81952 | −0.548018 | ||||||||
\(260\) | 26.7158 | 1.65684 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.02895 | −0.0635686 | ||||||||
\(263\) | 6.64471 | 0.409730 | 0.204865 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204865 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.91418 | −0.179016 | ||||||||
\(266\) | 0.0726869 | 0.00445672 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.05209 | −0.308605 | ||||||||
\(269\) | 16.0652 | 0.979514 | 0.489757 | − | 0.871859i | \(-0.337085\pi\) | ||||
0.489757 | + | 0.871859i | \(0.337085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.0605 | 1.76530 | 0.882651 | − | 0.470030i | \(-0.155757\pi\) | ||||
0.882651 | + | 0.470030i | \(0.155757\pi\) | |||||||
\(272\) | −8.08024 | −0.489937 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.48490 | 0.0897062 | ||||||||
\(275\) | 12.9748 | 0.782408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0489 | 0.723950 | 0.361975 | − | 0.932188i | \(-0.382103\pi\) | ||||
0.361975 | + | 0.932188i | \(0.382103\pi\) | |||||||
\(278\) | 1.40475 | 0.0842513 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.67293 | −0.159738 | ||||||||
\(281\) | −0.729114 | −0.0434953 | −0.0217476 | − | 0.999763i | \(-0.506923\pi\) | ||||
−0.0217476 | + | 0.999763i | \(0.506923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.70007 | 0.338834 | 0.169417 | − | 0.985544i | \(-0.445811\pi\) | ||||
0.169417 | + | 0.985544i | \(0.445811\pi\) | |||||||
\(284\) | 4.85270 | 0.287955 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.48740 | 0.324477 | ||||||||
\(287\) | 10.5020 | 0.619915 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1009 | −0.711818 | ||||||||
\(290\) | 3.78276 | 0.222131 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.5488 | 0.675840 | ||||||||
\(293\) | −16.3296 | −0.953983 | −0.476991 | − | 0.878908i | \(-0.658273\pi\) | ||||
−0.476991 | + | 0.878908i | \(0.658273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.8212 | −0.921145 | ||||||||
\(296\) | 8.42918 | 0.489936 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.14352 | 0.124171 | ||||||||
\(299\) | 10.6751 | 0.617354 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.69985 | 0.386173 | ||||||||
\(302\) | 1.96335 | 0.112978 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.09424 | 0.0627587 | ||||||||
\(305\) | 0.452976 | 0.0259373 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.16022 | 0.180363 | 0.0901816 | − | 0.995925i | \(-0.471255\pi\) | ||||
0.0901816 | + | 0.995925i | \(0.471255\pi\) | |||||||
\(308\) | 8.92631 | 0.508624 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.07007 | −0.231165 | ||||||||
\(311\) | −27.0887 | −1.53606 | −0.768029 | − | 0.640415i | \(-0.778763\pi\) | ||||
−0.768029 | + | 0.640415i | \(0.778763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.0755 | −1.02169 | −0.510844 | − | 0.859673i | \(-0.670667\pi\) | ||||
−0.510844 | + | 0.859673i | \(0.670667\pi\) | |||||||
\(314\) | 0.0231874 | 0.00130854 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.4831 | 1.43354 | ||||||||
\(317\) | −14.8515 | −0.834142 | −0.417071 | − | 0.908874i | \(-0.636943\pi\) | ||||
−0.417071 | + | 0.908874i | \(0.636943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.6479 | −1.43601 | ||||||||
\(320\) | −18.5227 | −1.03545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.526055 | −0.0293159 | ||||||||
\(323\) | −0.663440 | −0.0369148 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.8851 | −0.770205 | ||||||||
\(326\) | −3.74620 | −0.207483 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.0372 | −0.554213 | ||||||||
\(329\) | −7.58321 | −0.418076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7585 | −1.63568 | −0.817839 | − | 0.575447i | \(-0.804828\pi\) | ||||
−0.817839 | + | 0.575447i | \(0.804828\pi\) | |||||||
\(332\) | 18.2651 | 1.00243 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.77365 | −0.206485 | ||||||||
\(335\) | 7.27864 | 0.397675 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3368 | 0.944397 | 0.472198 | − | 0.881492i | \(-0.343461\pi\) | ||||
0.472198 | + | 0.881492i | \(0.343461\pi\) | |||||||
\(338\) | −2.71989 | −0.147943 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.0164 | 0.651681 | ||||||||
\(341\) | 27.5959 | 1.49440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.40332 | −0.345244 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.770156 | −0.0414038 | ||||||||
\(347\) | 13.4672 | 0.722959 | 0.361479 | − | 0.932380i | \(-0.382272\pi\) | ||||
0.361479 | + | 0.932380i | \(0.382272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6140 | −0.889328 | −0.444664 | − | 0.895697i | \(-0.646677\pi\) | ||||
−0.444664 | + | 0.895697i | \(0.646677\pi\) | |||||||
\(350\) | 0.684241 | 0.0365742 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.8605 | −0.685467 | ||||||||
\(353\) | 0.705030 | 0.0375249 | 0.0187625 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187625 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.99137 | −0.371064 | ||||||||
\(356\) | −18.1171 | −0.960205 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.156415 | 0.00826679 | ||||||||
\(359\) | −6.08609 | −0.321211 | −0.160606 | − | 0.987019i | \(-0.551345\pi\) | ||||
−0.160606 | + | 0.987019i | \(0.551345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9102 | −0.995271 | ||||||||
\(362\) | −0.307045 | −0.0161379 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.55257 | −0.500691 | ||||||||
\(365\) | −16.6385 | −0.870900 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.822218 | 0.0429194 | 0.0214597 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214597 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(368\) | −7.91927 | −0.412821 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.98143 | −0.310960 | ||||||||
\(371\) | 1.04200 | 0.0540980 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.32058 | −0.171933 | −0.0859665 | − | 0.996298i | \(-0.527398\pi\) | ||||
−0.0859665 | + | 0.996298i | \(0.527398\pi\) | |||||||
\(374\) | 2.46816 | 0.127625 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.24759 | 0.373766 | ||||||||
\(377\) | 27.4473 | 1.41361 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.11526 | 0.416853 | 0.208426 | − | 0.978038i | \(-0.433166\pi\) | ||||
0.208426 | + | 0.978038i | \(0.433166\pi\) | |||||||
\(380\) | −1.62727 | −0.0834774 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.39947 | −0.225096 | ||||||||
\(383\) | 6.77315 | 0.346092 | 0.173046 | − | 0.984914i | \(-0.444639\pi\) | ||||
0.173046 | + | 0.984914i | \(0.444639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.8603 | −0.655421 | ||||||||
\(386\) | −5.06127 | −0.257612 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.0098 | 1.16815 | ||||||||
\(389\) | −8.89791 | −0.451142 | −0.225571 | − | 0.974227i | \(-0.572425\pi\) | ||||
−0.225571 | + | 0.974227i | \(0.572425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.80149 | 0.242822 | ||||||||
\(392\) | 0.955741 | 0.0482722 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.41952 | 0.172273 | ||||||||
\(395\) | −36.7140 | −1.84728 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.55375 | 0.328923 | 0.164462 | − | 0.986383i | \(-0.447411\pi\) | ||||
0.164462 | + | 0.986383i | \(0.447411\pi\) | |||||||
\(398\) | 5.14551 | 0.257921 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.3006 | 0.515031 | ||||||||
\(401\) | −2.19709 | −0.109717 | −0.0548586 | − | 0.998494i | \(-0.517471\pi\) | ||||
−0.0548586 | + | 0.998494i | \(0.517471\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.5320 | −1.47109 | ||||||||
\(404\) | 10.6075 | 0.527742 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.35257 | −0.0671271 | ||||||||
\(407\) | 40.5553 | 2.01025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.3816 | −1.89785 | −0.948923 | − | 0.315507i | \(-0.897825\pi\) | ||||
−0.948923 | + | 0.315507i | \(0.897825\pi\) | |||||||
\(410\) | 7.12252 | 0.351756 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.46553 | −0.0722014 | ||||||||
\(413\) | 5.65706 | 0.278366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.3148 | −1.29174 | ||||||||
\(416\) | 13.7628 | 0.674776 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.334241 | −0.0163482 | ||||||||
\(419\) | −22.1140 | −1.08034 | −0.540169 | − | 0.841556i | \(-0.681640\pi\) | ||||
−0.540169 | + | 0.841556i | \(0.681640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8139 | 1.11188 | 0.555940 | − | 0.831223i | \(-0.312359\pi\) | ||||
0.555940 | + | 0.831223i | \(0.312359\pi\) | |||||||
\(422\) | 0.434029 | 0.0211282 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.995882 | −0.0483643 | ||||||||
\(425\) | −6.24531 | −0.302942 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.161967 | −0.00783815 | ||||||||
\(428\) | −20.6589 | −0.998587 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.54387 | 0.219125 | ||||||||
\(431\) | −31.7123 | −1.52753 | −0.763764 | − | 0.645495i | \(-0.776651\pi\) | ||||
−0.763764 | + | 0.645495i | \(0.776651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3802 | 1.45998 | 0.729988 | − | 0.683459i | \(-0.239525\pi\) | ||||
0.729988 | + | 0.683459i | \(0.239525\pi\) | |||||||
\(434\) | 1.45530 | 0.0698569 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8344 | −0.614657 | ||||||||
\(437\) | −0.650224 | −0.0311044 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.8747 | −1.33038 | −0.665192 | − | 0.746672i | \(-0.731650\pi\) | ||||
−0.665192 | + | 0.746672i | \(0.731650\pi\) | |||||||
\(440\) | 12.2911 | 0.585956 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.64132 | −0.125635 | ||||||||
\(443\) | −33.6373 | −1.59816 | −0.799078 | − | 0.601227i | \(-0.794679\pi\) | ||||
−0.799078 | + | 0.601227i | \(0.794679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.1017 | 1.23734 | ||||||||
\(446\) | 0.565289 | 0.0267672 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.62302 | 0.312908 | ||||||||
\(449\) | 2.86855 | 0.135375 | 0.0676876 | − | 0.997707i | \(-0.478438\pi\) | ||||
0.0676876 | + | 0.997707i | \(0.478438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.2921 | −2.27399 | ||||||||
\(452\) | 7.24082 | 0.340580 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.20526 | 0.197363 | ||||||||
\(455\) | 13.7626 | 0.645199 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.3334 | −1.27860 | −0.639301 | − | 0.768957i | \(-0.720776\pi\) | ||||
−0.639301 | + | 0.768957i | \(0.720776\pi\) | |||||||
\(458\) | 2.70949 | 0.126606 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.7770 | 0.549106 | ||||||||
\(461\) | −3.54928 | −0.165306 | −0.0826531 | − | 0.996578i | \(-0.526339\pi\) | ||||
−0.0826531 | + | 0.996578i | \(0.526339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.7780 | −1.24448 | −0.622239 | − | 0.782828i | \(-0.713777\pi\) | ||||
−0.622239 | + | 0.782828i | \(0.713777\pi\) | |||||||
\(464\) | −20.3618 | −0.945271 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.05823 | 0.141670 | ||||||||
\(467\) | 13.4294 | 0.621438 | 0.310719 | − | 0.950502i | \(-0.399430\pi\) | ||||
0.310719 | + | 0.950502i | \(0.399430\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.60257 | −0.120175 | ||||||||
\(470\) | −5.14297 | −0.237227 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.40668 | −0.248863 | ||||||||
\(473\) | −30.8083 | −1.41657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.845747 | 0.0388055 | ||||||||
\(476\) | −4.29662 | −0.196935 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.68059 | −0.0768683 | ||||||||
\(479\) | 24.0582 | 1.09925 | 0.549624 | − | 0.835412i | \(-0.314771\pi\) | ||||
0.549624 | + | 0.835412i | \(0.314771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.4007 | −1.97890 | ||||||||
\(482\) | 2.20038 | 0.100225 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.6932 | −0.895147 | ||||||||
\(485\) | −33.1507 | −1.50529 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.40323 | 0.0635864 | 0.0317932 | − | 0.999494i | \(-0.489878\pi\) | ||||
0.0317932 | + | 0.999494i | \(0.489878\pi\) | |||||||
\(488\) | 0.154799 | 0.00700741 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.678204 | −0.0306381 | ||||||||
\(491\) | −18.9765 | −0.856398 | −0.428199 | − | 0.903684i | \(-0.640852\pi\) | ||||
−0.428199 | + | 0.903684i | \(0.640852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.3454 | 0.556011 | ||||||||
\(494\) | 0.357691 | 0.0160933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.9083 | 0.983711 | ||||||||
\(497\) | 2.49985 | 0.112134 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.91564 | −0.175288 | −0.0876441 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876441 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(500\) | 11.8264 | 0.528893 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.14972 | 0.185211 | ||||||||
\(503\) | 4.39051 | 0.195763 | 0.0978815 | − | 0.995198i | \(-0.468793\pi\) | ||||
0.0978815 | + | 0.995198i | \(0.468793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2824 | −0.680057 | ||||||||
\(506\) | 2.41899 | 0.107537 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.94119 | 0.0861265 | ||||||||
\(509\) | 3.77299 | 0.167235 | 0.0836175 | − | 0.996498i | \(-0.473353\pi\) | ||||
0.0836175 | + | 0.996498i | \(0.473353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.94931 | 0.263182 | ||||||||
\(512\) | −17.1880 | −0.759609 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.28278 | 0.100689 | ||||||||
\(515\) | 2.11141 | 0.0930400 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.8703 | 1.53360 | ||||||||
\(518\) | 2.13874 | 0.0939707 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.1534 | −0.576817 | ||||||||
\(521\) | −40.5257 | −1.77546 | −0.887731 | − | 0.460362i | \(-0.847719\pi\) | ||||
−0.887731 | + | 0.460362i | \(0.847719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.15256 | 0.0503979 | 0.0251990 | − | 0.999682i | \(-0.491978\pi\) | ||||
0.0251990 | + | 0.999682i | \(0.491978\pi\) | |||||||
\(524\) | −8.23664 | −0.359819 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.61134 | −0.0702580 | ||||||||
\(527\) | −13.2831 | −0.578621 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2942 | −0.795398 | ||||||||
\(530\) | 0.706689 | 0.0306966 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.581853 | 0.0252265 | ||||||||
\(533\) | 51.6803 | 2.23852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.7637 | 1.28680 | ||||||||
\(536\) | 2.48738 | 0.107438 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.89582 | −0.167961 | ||||||||
\(539\) | 4.59836 | 0.198065 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.7874 | 1.02270 | 0.511349 | − | 0.859373i | \(-0.329146\pi\) | ||||
0.511349 | + | 0.859373i | \(0.329146\pi\) | |||||||
\(542\) | −7.04719 | −0.302703 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.19031 | 0.265408 | ||||||||
\(545\) | 18.4908 | 0.792058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2951 | −0.482945 | −0.241473 | − | 0.970408i | \(-0.577630\pi\) | ||||
−0.241473 | + | 0.970408i | \(0.577630\pi\) | |||||||
\(548\) | 11.8865 | 0.507766 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.14638 | −0.134162 | ||||||||
\(551\) | −1.67183 | −0.0712225 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1275 | 0.558240 | ||||||||
\(554\) | −2.92187 | −0.124138 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.2449 | 0.476890 | ||||||||
\(557\) | 13.6757 | 0.579459 | 0.289730 | − | 0.957109i | \(-0.406435\pi\) | ||||
0.289730 | + | 0.957109i | \(0.406435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9698 | 1.39448 | ||||||||
\(560\) | −10.2097 | −0.431440 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.176810 | 0.00745829 | ||||||||
\(563\) | 23.5207 | 0.991278 | 0.495639 | − | 0.868529i | \(-0.334934\pi\) | ||||
0.495639 | + | 0.868529i | \(0.334934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4320 | −0.438877 | ||||||||
\(566\) | −1.38227 | −0.0581011 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.38921 | −0.100249 | ||||||||
\(569\) | −4.30680 | −0.180550 | −0.0902752 | − | 0.995917i | \(-0.528775\pi\) | ||||
−0.0902752 | + | 0.995917i | \(0.528775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.3440 | −0.725822 | −0.362911 | − | 0.931824i | \(-0.618217\pi\) | ||||
−0.362911 | + | 0.931824i | \(0.618217\pi\) | |||||||
\(572\) | 43.9262 | 1.83665 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.54675 | −0.106299 | ||||||||
\(575\) | −6.12090 | −0.255259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.97581 | −0.123885 | −0.0619423 | − | 0.998080i | \(-0.519729\pi\) | ||||
−0.0619423 | + | 0.998080i | \(0.519729\pi\) | |||||||
\(578\) | 2.93447 | 0.122058 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.2807 | 1.25734 | ||||||||
\(581\) | 9.40919 | 0.390359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79149 | −0.198443 | ||||||||
\(584\) | −5.68600 | −0.235288 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.95992 | 0.163583 | ||||||||
\(587\) | 35.0446 | 1.44645 | 0.723224 | − | 0.690614i | \(-0.242660\pi\) | ||||
0.723224 | + | 0.690614i | \(0.242660\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.79881 | 0.0741187 | ||||||||
\(590\) | 3.83664 | 0.157952 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32.1967 | 1.32328 | ||||||||
\(593\) | 13.3444 | 0.547988 | 0.273994 | − | 0.961731i | \(-0.411655\pi\) | ||||
0.273994 | + | 0.961731i | \(0.411655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.19022 | 0.253774 | ||||||||
\(596\) | 17.1587 | 0.702847 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.58870 | −0.105860 | ||||||||
\(599\) | 25.1804 | 1.02884 | 0.514421 | − | 0.857538i | \(-0.328007\pi\) | ||||
0.514421 | + | 0.857538i | \(0.328007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.7897 | −1.29673 | −0.648364 | − | 0.761331i | \(-0.724546\pi\) | ||||
−0.648364 | + | 0.761331i | \(0.724546\pi\) | |||||||
\(602\) | −1.62472 | −0.0662185 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.7164 | 0.639493 | ||||||||
\(605\) | 28.3724 | 1.15350 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.3805 | −1.11134 | −0.555669 | − | 0.831403i | \(-0.687538\pi\) | ||||
−0.555669 | + | 0.831403i | \(0.687538\pi\) | |||||||
\(608\) | −0.838299 | −0.0339975 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.109847 | −0.00444757 | ||||||||
\(611\) | −37.3168 | −1.50968 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.9879 | −1.93821 | −0.969107 | − | 0.246642i | \(-0.920673\pi\) | ||||
−0.969107 | + | 0.246642i | \(0.920673\pi\) | |||||||
\(614\) | −0.766355 | −0.0309276 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.39484 | −0.177073 | ||||||||
\(617\) | 23.4031 | 0.942174 | 0.471087 | − | 0.882087i | \(-0.343862\pi\) | ||||
0.471087 | + | 0.882087i | \(0.343862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.26112 | −0.131076 | −0.0655378 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655378 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(620\) | −32.5806 | −1.30847 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.56902 | 0.263394 | ||||||||
\(623\) | −9.33298 | −0.373918 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1466 | −1.24586 | ||||||||
\(626\) | 4.38332 | 0.175193 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.185613 | 0.00740678 | ||||||||
\(629\) | −19.5210 | −0.778355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.8046 | −0.788407 | −0.394203 | − | 0.919023i | \(-0.628979\pi\) | ||||
−0.394203 | + | 0.919023i | \(0.628979\pi\) | |||||||
\(632\) | −12.5465 | −0.499074 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.60149 | 0.143033 | ||||||||
\(635\) | −2.79671 | −0.110984 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.92098 | −0.194976 | ||||||||
\(638\) | 6.21962 | 0.246237 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.1352 | 0.795915 | ||||||||
\(641\) | 45.0976 | 1.78125 | 0.890624 | − | 0.454741i | \(-0.150268\pi\) | ||||
0.890624 | + | 0.454741i | \(0.150268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.19892 | 0.244461 | 0.122231 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122231 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(644\) | −4.21102 | −0.165937 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.160885 | 0.00632992 | ||||||||
\(647\) | 12.8151 | 0.503815 | 0.251907 | − | 0.967751i | \(-0.418942\pi\) | ||||
0.251907 | + | 0.967751i | \(0.418942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0132 | −1.02111 | ||||||||
\(650\) | 3.36713 | 0.132070 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.9880 | −1.17442 | ||||||||
\(653\) | 6.35355 | 0.248633 | 0.124317 | − | 0.992243i | \(-0.460326\pi\) | ||||
0.124317 | + | 0.992243i | \(0.460326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8667 | 0.463669 | ||||||||
\(656\) | −38.3389 | −1.49688 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.83893 | 0.0716890 | ||||||||
\(659\) | −29.5580 | −1.15141 | −0.575707 | − | 0.817656i | \(-0.695273\pi\) | ||||
−0.575707 | + | 0.817656i | \(0.695273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8995 | −1.20185 | −0.600926 | − | 0.799305i | \(-0.705201\pi\) | ||||
−0.600926 | + | 0.799305i | \(0.705201\pi\) | |||||||
\(662\) | 7.21646 | 0.280476 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.99275 | −0.348986 | ||||||||
\(665\) | −0.838286 | −0.0325073 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0995 | 0.468494 | ||||||||
\(668\) | −30.2077 | −1.16877 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.76507 | −0.0681907 | ||||||||
\(671\) | 0.744784 | 0.0287521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1773 | 1.43308 | 0.716540 | − | 0.697546i | \(-0.245725\pi\) | ||||
0.716540 | + | 0.697546i | \(0.245725\pi\) | |||||||
\(674\) | −4.20418 | −0.161939 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.7725 | −0.837404 | ||||||||
\(677\) | 0.0588742 | 0.00226272 | 0.00113136 | − | 0.999999i | \(-0.499640\pi\) | ||||
0.00113136 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8534 | 0.454893 | ||||||||
\(680\) | −5.91624 | −0.226878 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.69202 | −0.256251 | ||||||||
\(683\) | 7.13511 | 0.273018 | 0.136509 | − | 0.990639i | \(-0.456412\pi\) | ||||
0.136509 | + | 0.990639i | \(0.456412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.1251 | −0.654317 | ||||||||
\(686\) | 0.242500 | 0.00925871 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.4586 | −0.932476 | ||||||||
\(689\) | 5.12766 | 0.195348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8916 | −0.908878 | −0.454439 | − | 0.890778i | \(-0.650160\pi\) | ||||
−0.454439 | + | 0.890778i | \(0.650160\pi\) | |||||||
\(692\) | −6.16503 | −0.234359 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.26581 | −0.123968 | ||||||||
\(695\) | −16.2007 | −0.614529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2451 | 0.880470 | ||||||||
\(698\) | 4.02891 | 0.152496 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.47729 | 0.207022 | ||||||||
\(701\) | 42.6818 | 1.61207 | 0.806034 | − | 0.591869i | \(-0.201610\pi\) | ||||
0.806034 | + | 0.591869i | \(0.201610\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.64356 | 0.0997037 | ||||||||
\(704\) | −30.4551 | −1.14782 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.170970 | −0.00643454 | ||||||||
\(707\) | 5.46441 | 0.205510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4112 | −1.10456 | −0.552280 | − | 0.833658i | \(-0.686242\pi\) | ||||
−0.552280 | + | 0.833658i | \(0.686242\pi\) | |||||||
\(710\) | 1.69541 | 0.0636276 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.91991 | 0.334288 | ||||||||
\(713\) | −13.0185 | −0.487546 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63.2852 | −2.36673 | ||||||||
\(716\) | 1.25209 | 0.0467927 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.47588 | 0.0550793 | ||||||||
\(719\) | 48.1805 | 1.79683 | 0.898416 | − | 0.439146i | \(-0.144719\pi\) | ||||
0.898416 | + | 0.439146i | \(0.144719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.754962 | −0.0281163 | ||||||||
\(722\) | 4.58572 | 0.170663 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.45787 | −0.0913459 | ||||||||
\(725\) | −15.7378 | −0.584489 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1964 | 1.52789 | 0.763944 | − | 0.645282i | \(-0.223260\pi\) | ||||
0.763944 | + | 0.645282i | \(0.223260\pi\) | |||||||
\(728\) | 4.70318 | 0.174311 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.03485 | 0.149336 | ||||||||
\(731\) | 14.8294 | 0.548484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.8699 | −1.91586 | −0.957929 | − | 0.287004i | \(-0.907341\pi\) | ||||
−0.957929 | + | 0.287004i | \(0.907341\pi\) | |||||||
\(734\) | −0.199388 | −0.00735955 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.06699 | 0.223632 | ||||||||
\(737\) | 11.9675 | 0.440830 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.1518 | 0.925222 | 0.462611 | − | 0.886561i | \(-0.346913\pi\) | ||||
0.462611 | + | 0.886561i | \(0.346913\pi\) | |||||||
\(740\) | −47.8808 | −1.76013 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.252685 | −0.00927637 | ||||||||
\(743\) | −39.8449 | −1.46177 | −0.730884 | − | 0.682502i | \(-0.760892\pi\) | ||||
−0.730884 | + | 0.682502i | \(0.760892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.7208 | −0.905701 | ||||||||
\(746\) | 0.805242 | 0.0294820 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.7574 | 0.722402 | ||||||||
\(749\) | −10.6424 | −0.388864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6188 | 0.496958 | 0.248479 | − | 0.968637i | \(-0.420069\pi\) | ||||
0.248479 | + | 0.968637i | \(0.420069\pi\) | |||||||
\(752\) | 27.6834 | 1.00951 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.65599 | −0.242397 | ||||||||
\(755\) | −22.6430 | −0.824062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3375 | 1.35705 | 0.678527 | − | 0.734576i | \(-0.262619\pi\) | ||||
0.678527 | + | 0.734576i | \(0.262619\pi\) | |||||||
\(758\) | −1.96795 | −0.0714793 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.801184 | 0.0290620 | ||||||||
\(761\) | −7.96910 | −0.288880 | −0.144440 | − | 0.989514i | \(-0.546138\pi\) | ||||
−0.144440 | + | 0.989514i | \(0.546138\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.61161 | −0.239356 | ||||||||
\(764\) | −35.2174 | −1.27412 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.64249 | −0.0593456 | ||||||||
\(767\) | 27.8383 | 1.00518 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.8938 | 1.18618 | 0.593091 | − | 0.805136i | \(-0.297908\pi\) | ||||
0.593091 | + | 0.805136i | \(0.297908\pi\) | |||||||
\(770\) | 3.11863 | 0.112387 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −40.5150 | −1.45817 | ||||||||
\(773\) | −3.09221 | −0.111219 | −0.0556095 | − | 0.998453i | \(-0.517710\pi\) | ||||
−0.0556095 | + | 0.998453i | \(0.517710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.9332 | 0.608257 | ||||||||
\(776\) | −11.3288 | −0.406681 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.15775 | 0.0773590 | ||||||||
\(779\) | −3.14787 | −0.112784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4952 | −0.411332 | ||||||||
\(782\) | −1.16436 | −0.0416376 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.65062 | 0.130379 | ||||||||
\(785\) | −0.267416 | −0.00954450 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1780 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(788\) | 27.3730 | 0.975121 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.90316 | 0.316760 | ||||||||
\(791\) | 3.73009 | 0.132627 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.797038 | −0.0283036 | ||||||||
\(794\) | −1.58929 | −0.0564017 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.1894 | 1.45992 | ||||||||
\(797\) | −12.4294 | −0.440273 | −0.220136 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220136 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.7846 | −0.593797 | ||||||||
\(800\) | −7.89135 | −0.279001 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.532794 | 0.0188136 | ||||||||
\(803\) | −27.3571 | −0.965410 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.06690 | 0.213830 | ||||||||
\(806\) | 7.16153 | 0.252254 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.22256 | −0.183729 | ||||||||
\(809\) | −38.2936 | −1.34633 | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
−0.673165 | + | 0.739492i | \(0.735066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.5810 | −1.53034 | −0.765168 | − | 0.643830i | \(-0.777344\pi\) | ||||
−0.765168 | + | 0.643830i | \(0.777344\pi\) | |||||||
\(812\) | −10.8272 | −0.379962 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.83468 | −0.344705 | ||||||||
\(815\) | 43.2042 | 1.51338 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00821 | −0.0702584 | ||||||||
\(818\) | 9.30754 | 0.325431 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 57.0151 | 1.99105 | ||||||||
\(821\) | 34.7141 | 1.21153 | 0.605765 | − | 0.795644i | \(-0.292867\pi\) | ||||
0.605765 | + | 0.795644i | \(0.292867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.6184 | −1.06729 | −0.533645 | − | 0.845708i | \(-0.679178\pi\) | ||||
−0.533645 | + | 0.845708i | \(0.679178\pi\) | |||||||
\(824\) | 0.721548 | 0.0251363 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.37184 | −0.0477324 | ||||||||
\(827\) | −48.9512 | −1.70220 | −0.851099 | − | 0.525005i | \(-0.824064\pi\) | ||||
−0.851099 | + | 0.525005i | \(0.824064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52359 | −0.122379 | −0.0611897 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611897 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(830\) | 6.38135 | 0.221500 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.5918 | 1.12992 | ||||||||
\(833\) | −2.21339 | −0.0766894 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.5208 | 1.50610 | ||||||||
\(836\) | −2.67557 | −0.0925364 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.36265 | 0.185250 | ||||||||
\(839\) | −11.5384 | −0.398349 | −0.199175 | − | 0.979964i | \(-0.563826\pi\) | ||||
−0.199175 | + | 0.979964i | \(0.563826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.10982 | 0.0727525 | ||||||||
\(842\) | −5.53237 | −0.190658 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.47436 | 0.119592 | ||||||||
\(845\) | 31.3680 | 1.07909 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.1449 | −0.348583 | ||||||||
\(848\) | −3.80395 | −0.130628 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.51449 | 0.0519466 | ||||||||
\(851\) | −19.1321 | −0.655841 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.47685 | 0.187524 | 0.0937618 | − | 0.995595i | \(-0.470111\pi\) | ||||
0.0937618 | + | 0.995595i | \(0.470111\pi\) | |||||||
\(854\) | 0.0392771 | 0.00134404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1714 | 0.347650 | ||||||||
\(857\) | −9.38512 | −0.320590 | −0.160295 | − | 0.987069i | \(-0.551244\pi\) | ||||
−0.160295 | + | 0.987069i | \(0.551244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.15150 | −0.278126 | −0.139063 | − | 0.990284i | \(-0.544409\pi\) | ||||
−0.139063 | + | 0.990284i | \(0.544409\pi\) | |||||||
\(860\) | 36.3732 | 1.24032 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.69025 | 0.261931 | ||||||||
\(863\) | −17.5317 | −0.596784 | −0.298392 | − | 0.954443i | \(-0.596450\pi\) | ||||
−0.298392 | + | 0.954443i | \(0.596450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.88207 | 0.301999 | ||||||||
\(866\) | −7.36720 | −0.250348 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.6496 | 0.395413 | ||||||||
\(869\) | −60.3652 | −2.04775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.8072 | −0.433955 | ||||||||
\(872\) | 6.31898 | 0.213988 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.157679 | 0.00533359 | ||||||||
\(875\) | 6.09234 | 0.205959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.2611 | 0.853008 | 0.426504 | − | 0.904486i | \(-0.359745\pi\) | ||||
0.426504 | + | 0.904486i | \(0.359745\pi\) | |||||||
\(878\) | 6.75961 | 0.228126 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 46.9480 | 1.58262 | ||||||||
\(881\) | −8.27215 | −0.278696 | −0.139348 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139348 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8500 | 1.81220 | 0.906099 | − | 0.423066i | \(-0.139046\pi\) | ||||
0.906099 | + | 0.423066i | \(0.139046\pi\) | |||||||
\(884\) | −21.1436 | −0.711135 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.15706 | 0.274042 | ||||||||
\(887\) | −26.0125 | −0.873414 | −0.436707 | − | 0.899604i | \(-0.643855\pi\) | ||||
−0.436707 | + | 0.899604i | \(0.643855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −6.32966 | −0.212171 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.52508 | 0.151511 | ||||||||
\(893\) | 2.27299 | 0.0760627 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.80391 | −0.0602980 | ||||||||
\(896\) | −7.19960 | −0.240522 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.695624 | −0.0232133 | ||||||||
\(899\) | −33.4727 | −1.11638 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.30635 | 0.0768357 | ||||||||
\(902\) | 11.7109 | 0.389929 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.56500 | −0.118570 | ||||||||
\(905\) | 3.54110 | 0.117710 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.7207 | 1.45172 | 0.725861 | − | 0.687842i | \(-0.241442\pi\) | ||||
0.725861 | + | 0.687842i | \(0.241442\pi\) | |||||||
\(908\) | 33.6628 | 1.11714 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.33743 | −0.110635 | ||||||||
\(911\) | −56.2800 | −1.86464 | −0.932320 | − | 0.361634i | \(-0.882219\pi\) | ||||
−0.932320 | + | 0.361634i | \(0.882219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.2669 | −1.43192 | ||||||||
\(914\) | 6.62836 | 0.219247 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.6892 | 0.716633 | ||||||||
\(917\) | −4.24308 | −0.140119 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.1675 | −1.62189 | −0.810943 | − | 0.585125i | \(-0.801045\pi\) | ||||
−0.810943 | + | 0.585125i | \(0.801045\pi\) | |||||||
\(920\) | −5.79838 | −0.191167 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.860701 | 0.0283457 | ||||||||
\(923\) | 12.3017 | 0.404916 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.8852 | 0.818221 | ||||||||
\(926\) | 6.49367 | 0.213395 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.5992 | 0.512070 | ||||||||
\(929\) | 18.0024 | 0.590640 | 0.295320 | − | 0.955398i | \(-0.404574\pi\) | ||||
0.295320 | + | 0.955398i | \(0.404574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.299740 | 0.00982357 | ||||||||
\(932\) | 24.4808 | 0.801896 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.25663 | −0.106560 | ||||||||
\(935\) | −28.4648 | −0.930900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.11724 | 0.199842 | 0.0999208 | − | 0.994995i | \(-0.468141\pi\) | ||||
0.0999208 | + | 0.994995i | \(0.468141\pi\) | |||||||
\(938\) | 0.631124 | 0.0206069 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −41.1690 | −1.34278 | ||||||||
\(941\) | −39.7665 | −1.29635 | −0.648175 | − | 0.761492i | \(-0.724467\pi\) | ||||
−0.648175 | + | 0.761492i | \(0.724467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.7820 | 0.741884 | ||||||||
\(944\) | −20.6518 | −0.672158 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.47103 | 0.242904 | ||||||||
\(947\) | −17.0699 | −0.554698 | −0.277349 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277349 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.2764 | 0.950353 | ||||||||
\(950\) | −0.205094 | −0.00665413 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.11543 | 0.0685614 | ||||||||
\(953\) | −14.4999 | −0.469698 | −0.234849 | − | 0.972032i | \(-0.575460\pi\) | ||||
−0.234849 | + | 0.972032i | \(0.575460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.7383 | 1.64185 | ||||||||
\(956\) | −13.4529 | −0.435099 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.83412 | −0.188492 | ||||||||
\(959\) | 6.12330 | 0.197732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.01499 | 0.161774 | ||||||||
\(962\) | 10.5247 | 0.339329 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.6138 | 0.567304 | ||||||||
\(965\) | 58.3707 | 1.87902 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.8725 | −0.639056 | −0.319528 | − | 0.947577i | \(-0.603524\pi\) | ||||
−0.319528 | + | 0.947577i | \(0.603524\pi\) | |||||||
\(968\) | 9.69591 | 0.311638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.03905 | 0.258118 | ||||||||
\(971\) | 16.7784 | 0.538446 | 0.269223 | − | 0.963078i | \(-0.413233\pi\) | ||||
0.269223 | + | 0.963078i | \(0.413233\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.79278 | 0.185708 | ||||||||
\(974\) | −0.340284 | −0.0109034 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.591281 | 0.0189264 | ||||||||
\(977\) | 58.6614 | 1.87675 | 0.938373 | − | 0.345625i | \(-0.112333\pi\) | ||||
0.938373 | + | 0.345625i | \(0.112333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.9164 | 1.37161 | ||||||||
\(980\) | −5.42896 | −0.173422 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.60181 | 0.146850 | ||||||||
\(983\) | 4.99877 | 0.159436 | 0.0797181 | − | 0.996817i | \(-0.474598\pi\) | ||||
0.0797181 | + | 0.996817i | \(0.474598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.4367 | −1.25656 | ||||||||
\(986\) | −2.99377 | −0.0953412 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.86328 | 0.0910932 | ||||||||
\(989\) | 14.5340 | 0.462153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.62682 | −0.0516775 | −0.0258388 | − | 0.999666i | \(-0.508226\pi\) | ||||
−0.0258388 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(992\) | −16.7840 | −0.532894 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.606215 | −0.0192280 | ||||||||
\(995\) | −59.3423 | −1.88128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.8421 | 1.10346 | 0.551730 | − | 0.834023i | \(-0.313968\pi\) | ||||
0.551730 | + | 0.834023i | \(0.313968\pi\) | |||||||
\(998\) | 0.949544 | 0.0300573 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.z.1.15 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.18 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.15 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.18 | yes | 32 | 3.2 | odd | 2 | inner |