Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(401,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.i (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.2 | ||
Root | \(1.09935 + 1.90412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.501 |
Dual form | 700.2.i.d.401.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.182224 | + | 0.315621i | −0.105207 | + | 0.182224i | −0.913823 | − | 0.406113i | \(-0.866884\pi\) |
0.808616 | + | 0.588337i | \(0.200217\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.11581 | − | 1.58850i | −0.799702 | − | 0.600397i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.43359 | + | 2.48305i | 0.477863 | + | 0.827683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.682224 | + | 1.18165i | −0.205698 | + | 0.356280i | −0.950355 | − | 0.311168i | \(-0.899280\pi\) |
0.744657 | + | 0.667448i | \(0.232613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.63555 | 0.730971 | 0.365485 | − | 0.930817i | \(-0.380903\pi\) | ||||
0.365485 | + | 0.930817i | \(0.380903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11581 | − | 1.93264i | 0.270624 | − | 0.468735i | −0.698398 | − | 0.715710i | \(-0.746103\pi\) |
0.969022 | + | 0.246975i | \(0.0794365\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11581 | + | 5.39675i | 0.714816 | + | 1.23810i | 0.963030 | + | 0.269393i | \(0.0868231\pi\) |
−0.248214 | + | 0.968705i | \(0.579844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.886917 | − | 0.378332i | 0.193541 | − | 0.0825589i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.29804 | + | 5.71237i | 0.687688 | + | 1.19111i | 0.972584 | + | 0.232552i | \(0.0747077\pi\) |
−0.284896 | + | 0.958559i | \(0.591959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.13828 | −0.411512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.50273 | 1.02183 | 0.510916 | − | 0.859631i | \(-0.329306\pi\) | ||||
0.510916 | + | 0.859631i | \(0.329306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.25136 | + | 3.89948i | −0.404357 | + | 0.700367i | −0.994246 | − | 0.107117i | \(-0.965838\pi\) |
0.589889 | + | 0.807484i | \(0.299171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.248635 | − | 0.430649i | −0.0432818 | − | 0.0749663i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.04667 | − | 1.81289i | −0.172072 | − | 0.298037i | 0.767072 | − | 0.641561i | \(-0.221713\pi\) |
−0.939144 | + | 0.343524i | \(0.888379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.480261 | + | 0.831836i | −0.0769033 | + | 0.133200i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.32497 | 1.45632 | 0.728158 | − | 0.685410i | \(-0.240377\pi\) | ||||
0.728158 | + | 0.685410i | \(0.240377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86718 | 0.284742 | 0.142371 | − | 0.989813i | \(-0.454527\pi\) | ||||
0.142371 | + | 0.989813i | \(0.454527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.43359 | − | 5.94715i | −0.500840 | − | 0.867481i | −1.00000 | 0.000970685i | \(-0.999691\pi\) | |
0.499159 | − | 0.866510i | \(-0.333642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.95333 | + | 6.72194i | 0.279047 | + | 0.960277i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.406656 | + | 0.704349i | 0.0569432 | + | 0.0986285i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.06914 | + | 8.78001i | −0.696300 | + | 1.20603i | 0.273440 | + | 0.961889i | \(0.411838\pi\) |
−0.969740 | + | 0.244138i | \(0.921495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.27110 | −0.300815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.817776 | − | 1.41643i | 0.106465 | − | 0.184403i | −0.807871 | − | 0.589360i | \(-0.799380\pi\) |
0.914336 | + | 0.404956i | \(0.132713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0197391 | − | 0.0341891i | −0.00252733 | − | 0.00437747i | 0.864759 | − | 0.502187i | \(-0.167471\pi\) |
−0.867286 | + | 0.497810i | \(0.834138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.911120 | − | 7.53092i | 0.114790 | − | 0.948807i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.36445 | + | 5.82739i | −0.411033 | + | 0.711930i | −0.995003 | − | 0.0998455i | \(-0.968165\pi\) |
0.583970 | + | 0.811775i | \(0.301498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40393 | −0.289399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.27110 | −0.744243 | −0.372122 | − | 0.928184i | \(-0.621370\pi\) | ||||
−0.372122 | + | 0.928184i | \(0.621370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | + | 3.46410i | −0.234082 | + | 0.405442i | −0.959006 | − | 0.283387i | \(-0.908542\pi\) |
0.724923 | + | 0.688830i | \(0.241875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.32051 | − | 1.41643i | 0.378407 | − | 0.161417i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.66248 | − | 4.61156i | −0.299553 | − | 0.518841i | 0.676481 | − | 0.736460i | \(-0.263504\pi\) |
−0.976034 | + | 0.217619i | \(0.930171\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.91112 | + | 6.77426i | −0.434569 | + | 0.752695i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7738 | 1.62164 | 0.810819 | − | 0.585296i | \(-0.199022\pi\) | ||||
0.810819 | + | 0.585296i | \(0.199022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00273 | + | 1.73678i | −0.107504 | + | 0.186202i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.433589 | − | 0.750998i | −0.0459603 | − | 0.0796056i | 0.842130 | − | 0.539274i | \(-0.181301\pi\) |
−0.888090 | + | 0.459669i | \(0.847968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.57633 | − | 4.18658i | −0.584559 | − | 0.438873i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.820506 | − | 1.42116i | −0.0850825 | − | 0.147367i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0988 | 1.63459 | 0.817293 | − | 0.576222i | \(-0.195474\pi\) | ||||
0.817293 | + | 0.576222i | \(0.195474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.91211 | −0.393182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.84744 | − | 13.5922i | 0.780849 | − | 1.35247i | −0.150598 | − | 0.988595i | \(-0.548120\pi\) |
0.931448 | − | 0.363876i | \(-0.118547\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.68495 | − | 11.5787i | −0.658688 | − | 1.14088i | −0.980956 | − | 0.194233i | \(-0.937778\pi\) |
0.322267 | − | 0.946649i | \(-0.395555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.70196 | + | 4.67994i | 0.261209 | + | 0.452427i | 0.966563 | − | 0.256428i | \(-0.0825456\pi\) |
−0.705355 | + | 0.708854i | \(0.749212\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.91385 | − | 13.7072i | 0.758009 | − | 1.31291i | −0.185855 | − | 0.982577i | \(-0.559505\pi\) |
0.943864 | − | 0.330333i | \(-0.107161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.762915 | 0.0724127 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4238 | −1.73316 | −0.866581 | − | 0.499036i | \(-0.833688\pi\) | ||||
−0.866581 | + | 0.499036i | \(0.833688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.77830 | + | 6.54420i | 0.349304 | + | 0.605012i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.43086 | + | 2.31664i | −0.497846 | + | 0.212366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.56914 | + | 7.91398i | 0.415376 | + | 0.719453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.69923 | + | 2.94316i | −0.153215 | + | 0.265376i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.32497 | −0.472515 | −0.236257 | − | 0.971691i | \(-0.575921\pi\) | ||||
−0.236257 | + | 0.971691i | \(0.575921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.340245 | + | 0.589321i | −0.0299569 | + | 0.0518868i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.11854 | − | 14.0617i | −0.709320 | − | 1.22858i | −0.965110 | − | 0.261846i | \(-0.915669\pi\) |
0.255789 | − | 0.966733i | \(-0.417665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.98026 | − | 16.3680i | 0.171710 | − | 1.41928i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.20469 | − | 3.81864i | 0.188360 | − | 0.326248i | −0.756344 | − | 0.654174i | \(-0.773016\pi\) |
0.944703 | + | 0.327926i | \(0.106350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.3699 | −1.89739 | −0.948695 | − | 0.316192i | \(-0.897596\pi\) | ||||
−0.948695 | + | 0.316192i | \(0.897596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.50273 | 0.210768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.79804 | + | 3.11429i | −0.150359 | + | 0.260430i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.47753 | − | 0.608388i | −0.204343 | − | 0.0501790i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.2541 | − | 19.4927i | −0.921971 | − | 1.59690i | −0.796361 | − | 0.604822i | \(-0.793244\pi\) |
−0.125610 | − | 0.992080i | \(-0.540089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.75136 | + | 11.6937i | −0.549418 | + | 0.951620i | 0.448896 | + | 0.893584i | \(0.351817\pi\) |
−0.998314 | + | 0.0580365i | \(0.981516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.39847 | 0.517285 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.77830 | + | 13.4724i | −0.620776 | + | 1.07522i | 0.368566 | + | 0.929602i | \(0.379849\pi\) |
−0.989342 | + | 0.145613i | \(0.953484\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.84744 | − | 3.19986i | −0.146511 | − | 0.253765i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.09607 | − | 17.3252i | 0.165194 | − | 1.36542i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.20196 | + | 3.81391i | 0.172471 | + | 0.298729i | 0.939283 | − | 0.343143i | \(-0.111492\pi\) |
−0.766812 | + | 0.641872i | \(0.778158\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.09880 | 0.704087 | 0.352043 | − | 0.935984i | \(-0.385487\pi\) | ||||
0.352043 | + | 0.935984i | \(0.385487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.05387 | −0.465682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.93359 | + | 15.4734i | −0.683169 | + | 1.18328i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.98026 | − | 17.2863i | −0.758785 | − | 1.31425i | −0.943470 | − | 0.331457i | \(-0.892460\pi\) |
0.184685 | − | 0.982798i | \(-0.440873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.298037 | + | 0.516215i | 0.0224018 | + | 0.0388011i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.59607 | − | 11.4247i | 0.493014 | − | 0.853925i | −0.506954 | − | 0.861973i | \(-0.669229\pi\) |
0.999968 | + | 0.00804839i | \(0.00256191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2316 | 0.760511 | 0.380255 | − | 0.924882i | \(-0.375836\pi\) | ||||
0.380255 | + | 0.924882i | \(0.375836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0143878 | 0.00106357 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.52247 | + | 2.63699i | 0.111334 | + | 0.192836i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.52420 | + | 3.39666i | 0.329087 | + | 0.247071i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00273 | − | 12.1291i | −0.506700 | − | 0.877630i | −0.999970 | − | 0.00775353i | \(-0.997532\pi\) |
0.493270 | − | 0.869876i | \(-0.335801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.20469 | + | 12.4789i | −0.518605 | + | 0.898250i | 0.481161 | + | 0.876632i | \(0.340215\pi\) |
−0.999766 | + | 0.0216183i | \(0.993118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5566 | 0.823373 | 0.411687 | − | 0.911325i | \(-0.364940\pi\) | ||||
0.411687 | + | 0.911325i | \(0.364940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.70469 | − | 4.68467i | 0.191731 | − | 0.332087i | −0.754093 | − | 0.656767i | \(-0.771923\pi\) |
0.945824 | + | 0.324680i | \(0.105257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.22617 | − | 2.12378i | −0.0864871 | − | 0.149800i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.6427 | − | 8.74109i | −0.817161 | − | 0.613504i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.45606 | + | 16.3784i | −0.657241 | + | 1.13838i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.50273 | −0.588146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9660 | −0.754929 | −0.377465 | − | 0.926024i | \(-0.623204\pi\) | ||||
−0.377465 | + | 0.926024i | \(0.623204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.14275 | − | 1.97929i | 0.0782997 | − | 0.135619i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9578 | − | 4.67427i | 0.743863 | − | 0.317310i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.728896 | − | 1.26249i | −0.0492542 | − | 0.0853108i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.94078 | − | 5.09359i | 0.197818 | − | 0.342632i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.5566 | 1.44354 | 0.721768 | − | 0.692135i | \(-0.243330\pi\) | ||||
0.721768 | + | 0.692135i | \(0.243330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.21189 | − | 10.7593i | 0.412297 | − | 0.714120i | −0.582843 | − | 0.812585i | \(-0.698060\pi\) |
0.995141 | + | 0.0984646i | \(0.0313931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.18222 | + | 7.24382i | 0.276369 | + | 0.478685i | 0.970480 | − | 0.241183i | \(-0.0775354\pi\) |
−0.694110 | + | 0.719868i | \(0.744202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.158021 | + | 1.30613i | −0.0103970 | + | 0.0859370i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00273 | + | 12.1291i | 0.458764 | + | 0.794603i | 0.998896 | − | 0.0469777i | \(-0.0149590\pi\) |
−0.540132 | + | 0.841580i | \(0.681626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.94067 | 0.126060 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9605 | 1.09708 | 0.548542 | − | 0.836123i | \(-0.315183\pi\) | ||||
0.548542 | + | 0.836123i | \(0.315183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16521 | + | 8.94641i | −0.332721 | + | 0.576289i | −0.983044 | − | 0.183368i | \(-0.941300\pi\) |
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.63282 | − | 8.02428i | −0.297196 | − | 0.514758i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.21189 | + | 14.2234i | 0.522510 | + | 0.905014i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.69215 | + | 4.66294i | −0.170608 | + | 0.295502i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5082 | 1.23135 | 0.615673 | − | 0.788002i | \(-0.288884\pi\) | ||||
0.615673 | + | 0.788002i | \(0.288884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.2316 | − | 24.6499i | −0.887744 | − | 1.53762i | −0.842535 | − | 0.538641i | \(-0.818938\pi\) |
−0.0452090 | − | 0.998978i | \(-0.514395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.665214 | + | 5.49837i | −0.0413344 | + | 0.341652i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.88865 | + | 13.6635i | 0.488295 | + | 0.845752i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.2810 | + | 24.7355i | −0.880606 | + | 1.52525i | −0.0299373 | + | 0.999552i | \(0.509531\pi\) |
−0.850669 | + | 0.525702i | \(0.823803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.316041 | 0.0193414 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.59880 | − | 7.96536i | 0.280394 | − | 0.485657i | −0.691088 | − | 0.722771i | \(-0.742868\pi\) |
0.971482 | + | 0.237114i | \(0.0762016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.93086 | − | 3.34435i | −0.117291 | − | 0.203155i | 0.801402 | − | 0.598126i | \(-0.204088\pi\) |
−0.918693 | + | 0.394971i | \(0.870754\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.33752 | − | 0.997115i | 0.141473 | − | 0.0603481i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.32051 | + | 9.21539i | −0.319678 | + | 0.553699i | −0.980421 | − | 0.196914i | \(-0.936908\pi\) |
0.660743 | + | 0.750613i | \(0.270241\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9101 | −0.772909 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73436 | 0.103463 | 0.0517315 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517315 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.95606 | − | 5.12004i | 0.175719 | − | 0.304355i | −0.764691 | − | 0.644398i | \(-0.777108\pi\) |
0.940410 | + | 0.340043i | \(0.110442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.7299 | − | 14.8127i | −1.16462 | − | 0.874368i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.00992 | + | 10.4095i | 0.353525 | + | 0.612323i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.93359 | + | 5.08112i | −0.171970 | + | 0.297861i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.3250 | 1.42108 | 0.710540 | − | 0.703657i | \(-0.248451\pi\) | ||||
0.710540 | + | 0.703657i | \(0.248451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.45879 | − | 2.52669i | 0.0846474 | − | 0.146614i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.69215 | + | 15.0552i | 0.502680 | + | 0.870667i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.95060 | − | 2.96601i | −0.227709 | − | 0.170958i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.85998 | + | 4.95364i | 0.164302 | + | 0.284579i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.5226 | −1.34250 | −0.671252 | − | 0.741229i | \(-0.734243\pi\) | ||||
−0.671252 | + | 0.741229i | \(0.734243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.87264 | 0.277195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.40939 | − | 7.63728i | 0.250033 | − | 0.433070i | −0.713501 | − | 0.700654i | \(-0.752892\pi\) |
0.963535 | + | 0.267583i | \(0.0862251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0466721 | + | 0.0808384i | 0.00263806 | + | 0.00456926i | 0.867341 | − | 0.497714i | \(-0.165827\pi\) |
−0.864703 | + | 0.502283i | \(0.832494\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.77110 | − | 3.06764i | −0.0994751 | − | 0.172296i | 0.811992 | − | 0.583668i | \(-0.198383\pi\) |
−0.911468 | + | 0.411372i | \(0.865050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.75409 | + | 6.50228i | −0.210189 | + | 0.364058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.96945 | −0.109924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9067 | 0.773787 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.88419 | + | 4.99556i | 0.159496 | + | 0.276255i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.18222 | + | 18.0373i | −0.120310 | + | 0.994429i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.82497 | + | 17.0173i | 0.540029 | + | 0.935358i | 0.998902 | + | 0.0468558i | \(0.0149201\pi\) |
−0.458872 | + | 0.888502i | \(0.651747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00099 | − | 5.19788i | 0.164454 | − | 0.284842i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0449 | −1.25534 | −0.627669 | − | 0.778480i | \(-0.715991\pi\) | ||||
−0.627669 | + | 0.778480i | \(0.715991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.35725 | − | 5.81493i | 0.182341 | − | 0.315824i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.07187 | − | 5.32064i | −0.166351 | − | 0.288129i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.54494 | − | 17.3252i | 0.353393 | − | 0.935475i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2810 | − | 19.5393i | 0.605597 | − | 1.04893i | −0.386360 | − | 0.922348i | \(-0.626268\pi\) |
0.991957 | − | 0.126577i | \(-0.0403991\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3250 | 0.766798 | 0.383399 | − | 0.923583i | \(-0.374753\pi\) | ||||
0.383399 | + | 0.923583i | \(0.374753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63555 | −0.300804 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.3502 | + | 28.3193i | −0.870232 | + | 1.50729i | −0.00847467 | + | 0.999964i | \(0.502698\pi\) |
−0.861757 | + | 0.507321i | \(0.830636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.258451 | − | 2.13624i | 0.0136787 | − | 0.113062i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.0791 | + | 22.6536i | 0.690287 | + | 1.19561i | 0.971744 | + | 0.236038i | \(0.0758489\pi\) |
−0.281457 | + | 0.959574i | \(0.590818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.91658 | + | 17.1760i | −0.521925 | + | 0.904001i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.33043 | −0.174802 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.6158 | − | 21.8512i | 0.658540 | − | 1.14062i | −0.322454 | − | 0.946585i | \(-0.604508\pi\) |
0.980994 | − | 0.194040i | \(-0.0621590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.3682 | + | 23.1544i | 0.695919 | + | 1.20537i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.6724 | − | 10.5245i | 1.28093 | − | 0.546406i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.84744 | + | 4.93191i | 0.147435 | + | 0.255365i | 0.930279 | − | 0.366854i | \(-0.119565\pi\) |
−0.782844 | + | 0.622218i | \(0.786232\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.5027 | 0.746929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9660 | 0.768751 | 0.384375 | − | 0.923177i | \(-0.374417\pi\) | ||||
0.384375 | + | 0.923177i | \(0.374417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.970337 | − | 1.68067i | 0.0497119 | − | 0.0861035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2388 | + | 21.1983i | 0.625374 | + | 1.08318i | 0.988468 | + | 0.151428i | \(0.0483871\pi\) |
−0.363094 | + | 0.931753i | \(0.618280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.67676 | + | 4.63629i | 0.136068 | + | 0.235676i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6230 | − | 27.0598i | 0.792118 | − | 1.37199i | −0.132535 | − | 0.991178i | \(-0.542312\pi\) |
0.924653 | − | 0.380810i | \(-0.124355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.7200 | 0.744421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.91757 | 0.298502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.566411 | + | 0.981053i | 0.0284274 | + | 0.0492376i | 0.879889 | − | 0.475179i | \(-0.157617\pi\) |
−0.851462 | + | 0.524417i | \(0.824283\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.80523 | + | 3.60765i | 0.240562 | + | 0.180608i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.91112 | + | 3.31016i | 0.0954368 | + | 0.165301i | 0.909791 | − | 0.415067i | \(-0.136242\pi\) |
−0.814354 | + | 0.580368i | \(0.802909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.93359 | + | 10.2773i | −0.295573 | + | 0.511948i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85626 | 0.141580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8304 | + | 29.1512i | −0.832211 | + | 1.44143i | 0.0640699 | + | 0.997945i | \(0.479592\pi\) |
−0.896281 | + | 0.443487i | \(0.853741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.803496 | + | 1.39170i | 0.0396335 | + | 0.0686473i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.98026 | + | 1.69786i | −0.195856 | + | 0.0835463i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.07633 | − | 7.06042i | 0.199619 | − | 0.345750i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.497270 | −0.0242933 | −0.0121466 | − | 0.999926i | \(-0.503866\pi\) | ||||
−0.0121466 | + | 0.999926i | \(0.503866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28003 | −0.0623850 | −0.0311925 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311925 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.84471 | − | 17.0515i | 0.478666 | − | 0.829074i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0125452 | + | 0.103693i | −0.000607106 | + | 0.00501808i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.655291 | − | 1.13500i | −0.0316377 | − | 0.0547982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.14548 | − | 8.91222i | 0.247849 | − | 0.429287i | −0.715080 | − | 0.699043i | \(-0.753610\pi\) |
0.962929 | + | 0.269756i | \(0.0869430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8870 | 1.43628 | 0.718139 | − | 0.695899i | \(-0.244994\pi\) | ||||
0.718139 | + | 0.695899i | \(0.244994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.5521 | + | 35.5973i | −0.983142 | + | 1.70285i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.52420 | + | 4.37205i | 0.120474 | + | 0.208666i | 0.919955 | − | 0.392025i | \(-0.128225\pi\) |
−0.799481 | + | 0.600692i | \(0.794892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8906 | + | 14.4867i | −0.661459 | + | 0.689843i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.88692 | + | 10.1964i | 0.279696 | + | 0.484447i | 0.971309 | − | 0.237821i | \(-0.0764330\pi\) |
−0.691613 | + | 0.722268i | \(0.743100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.20307 | 0.387992 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.3843 | −0.537258 | −0.268629 | − | 0.963244i | \(-0.586571\pi\) | ||||
−0.268629 | + | 0.963244i | \(0.586571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36172 | + | 11.0188i | −0.299562 | + | 0.518856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.46052 | − | 4.26175i | −0.115605 | − | 0.200234i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6257 | − | 32.2607i | −0.871275 | − | 1.50909i | −0.860678 | − | 0.509149i | \(-0.829960\pi\) |
−0.0105968 | − | 0.999944i | \(-0.503373\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.38592 | + | 4.13254i | −0.111365 | + | 0.192890i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0449 | −0.700713 | −0.350356 | − | 0.936616i | \(-0.613939\pi\) | ||||
−0.350356 | + | 0.936616i | \(0.613939\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.2031 | −1.45013 | −0.725065 | − | 0.688681i | \(-0.758190\pi\) | ||||
−0.725065 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.38419 | − | 16.2539i | −0.434248 | − | 0.752140i | 0.562986 | − | 0.826467i | \(-0.309653\pi\) |
−0.997234 | + | 0.0743264i | \(0.976319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3754 | − | 6.98525i | 0.756144 | − | 0.322549i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.83479 | − | 4.90999i | −0.130620 | − | 0.226241i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.27383 | + | 2.20634i | −0.0585709 | + | 0.101448i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.0683 | −1.33094 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.357254 | − | 0.618782i | 0.0163234 | − | 0.0282729i | −0.857748 | − | 0.514070i | \(-0.828137\pi\) |
0.874072 | + | 0.485797i | \(0.161471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.75856 | − | 4.77796i | −0.125779 | − | 0.217856i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.08626 | + | 3.81864i | 0.231433 | + | 0.173754i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.34744 | + | 14.4582i | −0.378259 | + | 0.655163i | −0.990809 | − | 0.135268i | \(-0.956810\pi\) |
0.612550 | + | 0.790432i | \(0.290144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.60500 | −0.0725807 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.19761 | 0.279694 | 0.139847 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139847 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.14002 | − | 10.6348i | 0.276532 | − | 0.478968i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2685 | + | 9.96166i | 0.595173 | + | 0.446841i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.23436 | − | 12.5303i | −0.323854 | − | 0.560932i | 0.657426 | − | 0.753519i | \(-0.271645\pi\) |
−0.981280 | + | 0.192588i | \(0.938312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.65802 | + | 2.87178i | −0.0740749 | + | 0.128301i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.6949 | −1.36862 | −0.684308 | − | 0.729193i | \(-0.739896\pi\) | ||||
−0.684308 | + | 0.729193i | \(0.739896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.10316 | − | 1.91073i | 0.0489930 | − | 0.0848585i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.2371 | − | 38.5158i | −0.985641 | − | 1.70718i | −0.639051 | − | 0.769165i | \(-0.720673\pi\) |
−0.346591 | − | 0.938016i | \(-0.612661\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.73436 | − | 4.15239i | 0.430623 | − | 0.183691i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.66248 | − | 11.5398i | −0.294156 | − | 0.509493i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.36991 | 0.412088 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.27457 | 0.319318 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.32497 | − | 10.9552i | 0.277102 | − | 0.479955i | −0.693561 | − | 0.720398i | \(-0.743959\pi\) |
0.970663 | + | 0.240443i | \(0.0772927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.13555 | − | 8.89504i | −0.224562 | − | 0.388953i | 0.731626 | − | 0.681706i | \(-0.238762\pi\) |
−0.956188 | + | 0.292753i | \(0.905428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.02420 | + | 8.70218i | 0.218858 | + | 0.379073i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2541 | + | 17.7606i | −0.445830 | + | 0.772201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.68942 | 0.203503 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5764 | 1.06452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.40393 | + | 4.16372i | 0.103737 | + | 0.179678i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.27557 | − | 2.27773i | −0.399527 | − | 0.0981087i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06914 | + | 1.85181i | 0.0459660 | + | 0.0796154i | 0.888093 | − | 0.459664i | \(-0.152030\pi\) |
−0.842127 | + | 0.539279i | \(0.818697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.86445 | + | 3.22932i | −0.0800111 | + | 0.138583i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0198 | 1.36907 | 0.684535 | − | 0.728980i | \(-0.260005\pi\) | ||||
0.684535 | + | 0.728980i | \(0.260005\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0565955 | − | 0.0980263i | 0.00241544 | − | 0.00418366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.1455 | + | 29.6968i | 0.730422 | + | 1.26513i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.69215 | + | 13.9866i | −0.0719574 | + | 0.594769i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.16521 | + | 7.21436i | −0.176486 | + | 0.305682i | −0.940674 | − | 0.339310i | \(-0.889806\pi\) |
0.764189 | + | 0.644993i | \(0.223140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92104 | 0.208138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10972 | −0.0468525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.73163 | + | 16.8557i | −0.410139 | + | 0.710382i | −0.994905 | − | 0.100821i | \(-0.967853\pi\) |
0.584766 | + | 0.811202i | \(0.301187\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0361 | − | 8.12024i | 0.799442 | − | 0.341018i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.44624 | − | 16.3614i | −0.396007 | − | 0.685904i | 0.597222 | − | 0.802076i | \(-0.296271\pi\) |
−0.993229 | + | 0.116172i | \(0.962938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.31505 | − | 16.1341i | 0.389823 | − | 0.675192i | −0.602603 | − | 0.798041i | \(-0.705870\pi\) |
0.992425 | + | 0.122849i | \(0.0392030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.10426 | 0.213234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.29630 | + | 16.1017i | −0.387010 | + | 0.670321i | −0.992046 | − | 0.125877i | \(-0.959825\pi\) |
0.605036 | + | 0.796198i | \(0.293159\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.62574 | − | 4.54791i | −0.109122 | − | 0.189005i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.2587 | − | 23.4683i | −1.29683 | − | 0.973627i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.91658 | − | 11.9799i | −0.286455 | − | 0.496155i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1383 | −0.418452 | −0.209226 | − | 0.977867i | \(-0.567094\pi\) | ||||
−0.209226 | + | 0.977867i | \(0.567094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.0593 | −1.15616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.10589 | + | 3.64751i | −0.0866247 | + | 0.150038i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.50273 | − | 14.7272i | −0.349165 | − | 0.604772i | 0.636936 | − | 0.770917i | \(-0.280201\pi\) |
−0.986101 | + | 0.166145i | \(0.946868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.985720 | + | 1.70732i | 0.0403428 | + | 0.0698758i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.09334 | − | 7.08988i | 0.167250 | − | 0.289685i | −0.770202 | − | 0.637800i | \(-0.779845\pi\) |
0.937452 | + | 0.348115i | \(0.113178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3359 | −1.44138 | −0.720690 | − | 0.693257i | \(-0.756175\pi\) | ||||
−0.720690 | + | 0.693257i | \(0.756175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.2929 | −0.785669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1158 | + | 24.4493i | 0.572943 | + | 0.992367i | 0.996262 | + | 0.0863858i | \(0.0275318\pi\) |
−0.423319 | + | 0.905981i | \(0.639135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.88046 | − | 2.08186i | 0.197766 | − | 0.0843613i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.04940 | − | 15.6740i | −0.366100 | − | 0.634103i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5791 | − | 26.9837i | 0.629232 | − | 1.08986i | −0.358474 | − | 0.933540i | \(-0.616703\pi\) |
0.987706 | − | 0.156323i | \(-0.0499640\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1527 | 1.57623 | 0.788114 | − | 0.615530i | \(-0.211058\pi\) | ||||
0.788114 | + | 0.615530i | \(0.211058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6921 | − | 34.1078i | 0.791494 | − | 1.37091i | −0.133547 | − | 0.991042i | \(-0.542637\pi\) |
0.925042 | − | 0.379866i | \(-0.124030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.05213 | − | 12.2146i | −0.282992 | − | 0.490157i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.275568 | + | 2.27773i | −0.0110404 | + | 0.0912552i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54940 | − | 2.68364i | 0.0618771 | − | 0.107174i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.67156 | −0.186267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7003 | 0.903686 | 0.451843 | − | 0.892097i | \(-0.350767\pi\) | ||||
0.451843 | + | 0.892097i | \(0.350767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.99827 | − | 3.46110i | 0.0794239 | − | 0.137566i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.14810 | + | 17.7160i | 0.203975 | + | 0.701935i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.99018 | − | 15.5715i | −0.355646 | − | 0.615997i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.20643 | + | 7.28575i | −0.166144 | + | 0.287770i | −0.937061 | − | 0.349166i | \(-0.886465\pi\) |
0.770917 | + | 0.636936i | \(0.219798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.7398 | −1.17282 | −0.586412 | − | 0.810013i | \(-0.699460\pi\) | ||||
−0.586412 | + | 0.810013i | \(0.699460\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.8430 | − | 18.7806i | 0.426281 | − | 0.738341i | −0.570258 | − | 0.821466i | \(-0.693157\pi\) |
0.996539 | + | 0.0831249i | \(0.0264900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.11581 | + | 1.93264i | 0.0437995 | + | 0.0758629i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.521474 | + | 4.31028i | −0.0204382 | + | 0.168933i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0351 | − | 26.0416i | −0.588370 | − | 1.01909i | −0.994446 | − | 0.105247i | \(-0.966437\pi\) |
0.406076 | − | 0.913839i | \(-0.366897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.4687 | −0.447437 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.37537 | 0.0925311 | 0.0462656 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462656 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.23163 | − | 12.5255i | 0.281278 | − | 0.487187i | −0.690422 | − | 0.723407i | \(-0.742575\pi\) |
0.971700 | + | 0.236220i | \(0.0759085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.07176 | + | 1.85635i | 0.0416238 | + | 0.0720946i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1482 | + | 31.4336i | 0.702701 | + | 1.21711i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.92813 | + | 6.80372i | −0.151870 | + | 0.263047i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0538660 | 0.00207947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.99653 | 0.346791 | 0.173395 | − | 0.984852i | \(-0.444526\pi\) | ||||
0.173395 | + | 0.984852i | \(0.444526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.74591 | − | 6.48810i | −0.143967 | − | 0.249358i | 0.785020 | − | 0.619470i | \(-0.212653\pi\) |
−0.928987 | + | 0.370112i | \(0.879319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.0621 | − | 25.5730i | −1.30718 | − | 0.981400i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.26391 | + | 3.92121i | 0.0867532 | + | 0.150261i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.1625 | − | 36.6545i | 0.809760 | − | 1.40255i | −0.103270 | − | 0.994653i | \(-0.532931\pi\) |
0.913030 | − | 0.407892i | \(-0.133736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.04841 | −0.116304 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3600 | + | 23.1402i | −0.508975 | + | 0.881570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3232 | − | 24.8086i | −0.544882 | − | 0.943763i | −0.998614 | − | 0.0526247i | \(-0.983241\pi\) |
0.453733 | − | 0.891138i | \(-0.350092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.27730 | + | 6.21440i | 0.314429 | + | 0.236066i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4049 | − | 18.0219i | 0.394114 | − | 0.682626i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.10426 | −0.193061 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4292 | −0.771601 | −0.385801 | − | 0.922582i | \(-0.626075\pi\) | ||||
−0.385801 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.52247 | − | 11.2972i | 0.246000 | − | 0.426084i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.1949 | + | 16.2928i | −1.43647 | + | 0.612754i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.4138 | − | 24.9655i | −0.541323 | − | 0.937600i | −0.998828 | − | 0.0483927i | \(-0.984590\pi\) |
0.457505 | − | 0.889207i | \(-0.348743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.63382 | − | 13.2222i | 0.286291 | − | 0.495870i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.7003 | −1.11229 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.09061 | + | 5.35310i | −0.115421 | + | 0.199915i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6553 | − | 27.1158i | −0.583844 | − | 1.01125i | −0.995018 | − | 0.0996906i | \(-0.968215\pi\) |
0.411175 | − | 0.911557i | \(-0.365119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.24864 | + | 35.1174i | −0.158227 | + | 1.30784i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.88245 | − | 3.26050i | −0.0700092 | − | 0.121259i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.17230 | −0.303094 | −0.151547 | − | 0.988450i | \(-0.548425\pi\) | ||||
−0.151547 | + | 0.988450i | \(0.548425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0899 | −0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08342 | − | 3.60859i | 0.0770581 | − | 0.133469i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7092 | + | 18.5488i | 0.395552 | + | 0.685116i | 0.993171 | − | 0.116664i | \(-0.0372201\pi\) |
−0.597620 | + | 0.801780i | \(0.703887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.59061 | − | 7.95118i | −0.169097 | − | 0.292885i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.17503 | + | 3.76726i | −0.0800098 | + | 0.138581i | −0.903254 | − | 0.429107i | \(-0.858828\pi\) |
0.823244 | + | 0.567688i | \(0.192162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.98561 | −0.219887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53328 | 0.239683 | 0.119841 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119841 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.1796 | + | 36.6841i | 0.774921 | + | 1.34220i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.71724 | − | 14.1939i | 0.0627465 | − | 0.518635i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2415 | − | 29.8632i | −0.629153 | − | 1.08973i | −0.987722 | − | 0.156222i | \(-0.950069\pi\) |
0.358569 | − | 0.933503i | \(-0.383265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.55486 | + | 6.15720i | −0.129546 | + | 0.224381i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2425 | −1.60802 | −0.804011 | − | 0.594614i | \(-0.797305\pi\) | ||||
−0.804011 | + | 0.594614i | \(0.797305\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.64002 | − | 2.84059i | 0.0595288 | − | 0.103107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.9094 | + | 20.6277i | 0.431715 | + | 0.747752i | 0.997021 | − | 0.0771290i | \(-0.0245753\pi\) |
−0.565306 | + | 0.824881i | \(0.691242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.5181 | + | 16.4307i | −1.39445 | + | 0.594831i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.15529 | − | 3.73307i | 0.0778230 | − | 0.134793i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.158128 | −0.00570225 | −0.00285113 | − | 0.999996i | \(-0.500908\pi\) | ||||
−0.00285113 | + | 0.999996i | \(0.500908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3734 | 0.373588 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.89957 | − | 15.4145i | 0.320095 | − | 0.554421i | −0.660412 | − | 0.750903i | \(-0.729618\pi\) |
0.980507 | + | 0.196482i | \(0.0629517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.61419 | − | 1.21189i | −0.0579086 | − | 0.0434764i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.0549 | + | 50.3245i | 1.04100 | + | 1.80306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.27830 | − | 7.41023i | 0.153090 | − | 0.265159i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.7664 | −0.420496 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7613 | − | 35.9596i | 0.740060 | − | 1.28182i | −0.212407 | − | 0.977181i | \(-0.568130\pi\) |
0.952467 | − | 0.304640i | \(-0.0985363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.20469 | − | 9.01479i | −0.185292 | − | 0.320935i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.9813 | + | 29.2662i | 1.38601 | + | 1.04059i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0520234 | − | 0.0901072i | −0.00184741 | − | 0.00319980i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0933 | 0.888852 | 0.444426 | − | 0.895816i | \(-0.353408\pi\) | ||||
0.444426 | + | 0.895816i | \(0.353408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.3250 | −0.542158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.24318 | − | 2.15324i | 0.0439255 | − | 0.0760811i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.72890 | − | 4.72659i | −0.0963007 | − | 0.166798i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.67602 | + | 2.90296i | 0.0589989 | + | 0.102189i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.34744 | + | 10.9941i | −0.223164 | + | 0.386531i | −0.955767 | − | 0.294125i | \(-0.904972\pi\) |
0.732603 | + | 0.680656i | \(0.238305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.9749 | 0.631184 | 0.315592 | − | 0.948895i | \(-0.397797\pi\) | ||||
0.315592 | + | 0.948895i | \(0.397797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.40740 | 0.0493595 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.81778 | + | 10.0767i | 0.203538 | + | 0.352539i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.40130 | − | 19.8481i | 0.0839084 | − | 0.693550i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0341 | − | 17.3796i | −0.350193 | − | 0.606553i | 0.636090 | − | 0.771615i | \(-0.280551\pi\) |
−0.986283 | + | 0.165062i | \(0.947217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.30523 | − | 9.18893i | 0.184929 | − | 0.320306i | −0.758624 | − | 0.651529i | \(-0.774128\pi\) |
0.943553 | + | 0.331223i | \(0.107461\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.7793 | 1.20939 | 0.604697 | − | 0.796455i | \(-0.293294\pi\) | ||||
0.604697 | + | 0.796455i | \(0.293294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1141 | − | 22.7142i | 0.455471 | − | 0.788898i | −0.543244 | − | 0.839575i | \(-0.682804\pi\) |
0.998715 | + | 0.0506761i | \(0.0161376\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.93905 | − | 3.35853i | −0.0672648 | − | 0.116506i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.1707 | + | 3.72534i | 0.525633 | + | 0.129075i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.81405 | − | 8.33818i | 0.166398 | − | 0.288210i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.9210 | 1.17108 | 0.585542 | − | 0.810642i | \(-0.300882\pi\) | ||||
0.585542 | + | 0.810642i | \(0.300882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28003 | 0.0441391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.316041 | + | 0.547399i | −0.0108850 | + | 0.0188534i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.90393 | − | 24.0026i | 0.0997801 | − | 0.824739i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.07733 | + | 1.86599i | 0.0369738 | + | 0.0640406i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.90393 | − | 11.9580i | 0.236664 | − | 0.409913i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −57.6698 | −1.97458 | −0.987288 | − | 0.158942i | \(-0.949192\pi\) | ||||
−0.987288 | + | 0.158942i | \(0.949192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.7020 | + | 30.6607i | −0.604688 | + | 1.04735i | 0.387413 | + | 0.921906i | \(0.373369\pi\) |
−0.992101 | + | 0.125443i | \(0.959965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.72170 | + | 11.6423i | 0.229342 | + | 0.397231i | 0.957613 | − | 0.288057i | \(-0.0930094\pi\) |
−0.728272 | + | 0.685289i | \(0.759676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.27047 | − | 3.52794i | 0.281857 | − | 0.120232i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.53239 | + | 6.11828i | 0.120244 | + | 0.208269i | 0.919864 | − | 0.392238i | \(-0.128299\pi\) |
−0.799620 | + | 0.600507i | \(0.794966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.38061 | −0.148773 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.26564 | 0.246470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.86718 | + | 15.3584i | −0.300453 | + | 0.520400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.0791 | + | 39.9741i | 0.781108 | + | 1.35292i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.50273 | − | 12.9951i | −0.253349 | − | 0.438814i | 0.711097 | − | 0.703094i | \(-0.248199\pi\) |
−0.964446 | + | 0.264281i | \(0.914865\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.43259 | + | 7.67748i | −0.149508 | + | 0.258955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3699 | −1.32641 | −0.663203 | − | 0.748440i | \(-0.730803\pi\) | ||||
−0.663203 | + | 0.748440i | \(0.730803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.2229 | 1.95936 | 0.979679 | − | 0.200574i | \(-0.0642808\pi\) | ||||
0.979679 | + | 0.200574i | \(0.0642808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6230 | − | 21.8637i | −0.423839 | − | 0.734111i | 0.572472 | − | 0.819924i | \(-0.305984\pi\) |
−0.996311 | + | 0.0858133i | \(0.972651\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2666 | + | 8.45872i | 0.377871 | + | 0.283696i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.33652 | − | 9.24312i | −0.178780 | − | 0.309656i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.3968 | − | 37.0604i | 0.716018 | − | 1.24018i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.33567 | −0.211542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.3887 | + | 21.4578i | −0.413185 | + | 0.715657i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3124 | + | 19.5937i | 0.376872 | + | 0.652761i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.65603 | − | 0.706414i | 0.0551093 | − | 0.0235080i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5933 | + | 23.5444i | −0.451360 | + | 0.781778i | −0.998471 | − | 0.0552822i | \(-0.982394\pi\) |
0.547111 | + | 0.837060i | \(0.315727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0000 | 1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.7882 | −1.35137 | −0.675687 | − | 0.737189i | \(-0.736153\pi\) | ||||
−0.675687 | + | 0.737189i | \(0.736153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0791 | + | 17.4575i | −0.333568 | + | 0.577757i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.15976 | + | 42.6483i | −0.170390 | + | 1.40837i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.5369 | + | 40.7670i | 0.776409 | + | 1.34478i | 0.933999 | + | 0.357276i | \(0.116294\pi\) |
−0.157590 | + | 0.987505i | \(0.550372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.28638 | − | 7.42423i | 0.141241 | − | 0.244637i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.5278 | −0.544020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.1669 | − | 33.1981i | 0.629525 | − | 1.09037i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.99554 | − | 15.5807i | −0.295134 | − | 0.511187i | 0.679882 | − | 0.733321i | \(-0.262031\pi\) |
−0.975016 | + | 0.222134i | \(0.928698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.1904 | + | 31.4859i | −0.989451 | + | 1.03191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.60699 | + | 2.78339i | 0.0526106 | + | 0.0911242i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.7003 | −1.23162 | −0.615808 | − | 0.787896i | \(-0.711170\pi\) | ||||
−0.615808 | + | 0.787896i | \(0.711170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.0340191 | −0.00111017 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.41658 | + | 4.18564i | −0.0787782 | + | 0.136448i | −0.902723 | − | 0.430222i | \(-0.858435\pi\) |
0.823945 | + | 0.566670i | \(0.191769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.7541 | + | 53.2677i | 1.00149 | + | 1.73463i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.41831 | − | 2.45659i | −0.0460890 | − | 0.0798285i | 0.842061 | − | 0.539383i | \(-0.181342\pi\) |
−0.888150 | + | 0.459554i | \(0.848009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.27110 | + | 9.12982i | −0.171107 | + | 0.296366i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.29095 | 0.0418619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7991 | −0.576571 | −0.288285 | − | 0.957545i | \(-0.593085\pi\) | ||||
−0.288285 | + | 0.957545i | \(0.593085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.36817 | − | 2.36974i | −0.0442267 | − | 0.0766029i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.7306 | + | 4.57737i | −0.346510 | + | 0.147811i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.36271 | + | 9.28849i | 0.172991 | + | 0.299629i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.74701 | + | 13.4182i | −0.249644 | + | 0.432396i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1581 | 0.487453 | 0.243726 | − | 0.969844i | \(-0.421630\pi\) | ||||
0.243726 | + | 0.969844i | \(0.421630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.53413 | + | 4.38924i | −0.0814079 | + | 0.141003i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.6921 | + | 41.0360i | 0.760317 | + | 1.31691i | 0.942687 | + | 0.333678i | \(0.108290\pi\) |
−0.182370 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3305 | + | 35.5346i | 1.51735 | + | 1.13919i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.8600 | − | 20.5421i | 0.379434 | − | 0.657200i | −0.611546 | − | 0.791209i | \(-0.709452\pi\) |
0.990980 | + | 0.134009i | \(0.0427852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.18322 | 0.0378158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.3808 | 1.44890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.2272 | − | 29.8383i | 0.549461 | − | 0.951695i | −0.448850 | − | 0.893607i | \(-0.648166\pi\) |
0.998311 | − | 0.0580876i | \(-0.0185003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.29531 | − | 3.97559i | −0.168551 | − | 0.126544i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.15802 | + | 10.6660i | 0.195814 | + | 0.339159i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.8304 | − | 36.0794i | 0.661700 | − | 1.14610i | −0.318468 | − | 0.947934i | \(-0.603168\pi\) |
0.980169 | − | 0.198165i | \(-0.0634982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.16138 | −0.227260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3941 | − | 21.4672i | 0.392525 | − | 0.679874i | −0.600256 | − | 0.799808i | \(-0.704935\pi\) |
0.992782 | + | 0.119934i | \(0.0382682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.23808 | + | 3.87647i | 0.0708097 | + | 0.122646i |
(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 | 700.2.i.d.501.2 | yes | 6 | |
5.2 | odd | 4 | 700.2.r.d.249.4 | 12 | |||
5.3 | odd | 4 | 700.2.r.d.249.3 | 12 | |||
5.4 | even | 2 | 700.2.i.e.501.2 | yes | 6 | ||
7.2 | even | 3 | inner | 700.2.i.d.401.2 | ✓ | 6 | |
7.3 | odd | 6 | 4900.2.a.bb.1.2 | 3 | |||
7.4 | even | 3 | 4900.2.a.bc.1.2 | 3 | |||
35.2 | odd | 12 | 700.2.r.d.149.3 | 12 | |||
35.3 | even | 12 | 4900.2.e.s.2549.3 | 6 | |||
35.4 | even | 6 | 4900.2.a.ba.1.2 | 3 | |||
35.9 | even | 6 | 700.2.i.e.401.2 | yes | 6 | ||
35.17 | even | 12 | 4900.2.e.s.2549.4 | 6 | |||
35.18 | odd | 12 | 4900.2.e.t.2549.4 | 6 | |||
35.23 | odd | 12 | 700.2.r.d.149.4 | 12 | |||
35.24 | odd | 6 | 4900.2.a.bd.1.2 | 3 | |||
35.32 | odd | 12 | 4900.2.e.t.2549.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.2 | ✓ | 6 | 7.2 | even | 3 | inner | |
700.2.i.d.501.2 | yes | 6 | 1.1 | even | 1 | trivial | |
700.2.i.e.401.2 | yes | 6 | 35.9 | even | 6 | ||
700.2.i.e.501.2 | yes | 6 | 5.4 | even | 2 | ||
700.2.r.d.149.3 | 12 | 35.2 | odd | 12 | |||
700.2.r.d.149.4 | 12 | 35.23 | odd | 12 | |||
700.2.r.d.249.3 | 12 | 5.3 | odd | 4 | |||
700.2.r.d.249.4 | 12 | 5.2 | odd | 4 | |||
4900.2.a.ba.1.2 | 3 | 35.4 | even | 6 | |||
4900.2.a.bb.1.2 | 3 | 7.3 | odd | 6 | |||
4900.2.a.bc.1.2 | 3 | 7.4 | even | 3 | |||
4900.2.a.bd.1.2 | 3 | 35.24 | odd | 6 | |||
4900.2.e.s.2549.3 | 6 | 35.3 | even | 12 | |||
4900.2.e.s.2549.4 | 6 | 35.17 | even | 12 | |||
4900.2.e.t.2549.3 | 6 | 35.32 | odd | 12 | |||
4900.2.e.t.2549.4 | 6 | 35.18 | odd | 12 |