Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
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, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\), degree \(2\), not 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(1.90412 + 1.09935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.d.249.4 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.315621 | − | 0.182224i | 0.182224 | − | 0.105207i | −0.406113 | − | 0.913823i | \(-0.633116\pi\) |
0.588337 | + | 0.808616i | \(0.299783\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.58850 | + | 2.11581i | 0.600397 | + | 0.799702i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.43359 | + | 2.48305i | −0.477863 | + | 0.827683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.682224 | − | 1.18165i | −0.205698 | − | 0.356280i | 0.744657 | − | 0.667448i | \(-0.232613\pi\) |
−0.950355 | + | 0.311168i | \(0.899280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.63555i | 0.730971i | 0.930817 | + | 0.365485i | \(0.119097\pi\) | ||||
−0.930817 | + | 0.365485i | \(0.880903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.93264 | − | 1.11581i | 0.468735 | − | 0.270624i | −0.246975 | − | 0.969022i | \(-0.579437\pi\) |
0.715710 | + | 0.698398i | \(0.246103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.11581 | + | 5.39675i | −0.714816 | + | 1.23810i | 0.248214 | + | 0.968705i | \(0.420156\pi\) |
−0.963030 | + | 0.269393i | \(0.913177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.886917 | + | 0.378332i | 0.193541 | + | 0.0825589i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.71237 | + | 3.29804i | 1.19111 | + | 0.687688i | 0.958559 | − | 0.284896i | \(-0.0919589\pi\) |
0.232552 | + | 0.972584i | \(0.425292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13828i | 0.411512i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.50273 | −1.02183 | −0.510916 | − | 0.859631i | \(-0.670694\pi\) | ||||
−0.510916 | + | 0.859631i | \(0.670694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.25136 | − | 3.89948i | −0.404357 | − | 0.700367i | 0.589889 | − | 0.807484i | \(-0.299171\pi\) |
−0.994246 | + | 0.107117i | \(0.965838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.430649 | − | 0.248635i | −0.0749663 | − | 0.0432818i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.81289 | + | 1.04667i | 0.298037 | + | 0.172072i | 0.641561 | − | 0.767072i | \(-0.278287\pi\) |
−0.343524 | + | 0.939144i | \(0.611621\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 1.86718i | 0.284742i | 0.989813 | + | 0.142371i | \(0.0454726\pi\) | ||||
−0.989813 | + | 0.142371i | \(0.954527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.94715 | + | 3.43359i | 0.867481 | + | 0.500840i | 0.866510 | − | 0.499159i | \(-0.166358\pi\) |
0.000970685 | 1.00000i | \(0.499691\pi\) | ||||||||
\(48\) | 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 | ||||||||
\(53\) | 8.78001 | − | 5.06914i | 1.20603 | − | 0.696300i | 0.244138 | − | 0.969740i | \(-0.421495\pi\) |
0.961889 | + | 0.273440i | \(0.0881616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.27110i | 0.300815i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.817776 | − | 1.41643i | −0.106465 | − | 0.184403i | 0.807871 | − | 0.589360i | \(-0.200620\pi\) |
−0.914336 | + | 0.404956i | \(0.867287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0197391 | + | 0.0341891i | −0.00252733 | + | 0.00437747i | −0.867286 | − | 0.497810i | \(-0.834138\pi\) |
0.864759 | + | 0.502187i | \(0.167471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.53092 | + | 0.911120i | −0.948807 | + | 0.114790i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.82739 | + | 3.36445i | −0.711930 | + | 0.411033i | −0.811775 | − | 0.583970i | \(-0.801498\pi\) |
0.0998455 | + | 0.995003i | \(0.468165\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 3.46410 | − | 2.00000i | 0.405442 | − | 0.234082i | −0.283387 | − | 0.959006i | \(-0.591458\pi\) |
0.688830 | + | 0.724923i | \(0.258125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41643 | − | 3.32051i | 0.161417 | − | 0.378407i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.66248 | − | 4.61156i | 0.299553 | − | 0.518841i | −0.676481 | − | 0.736460i | \(-0.736496\pi\) |
0.976034 | + | 0.217619i | \(0.0698291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.91112 | − | 6.77426i | −0.434569 | − | 0.752695i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7738i | 1.62164i | 0.585296 | + | 0.810819i | \(0.300978\pi\) | ||||
−0.585296 | + | 0.810819i | \(0.699022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.73678 | + | 1.00273i | −0.186202 | + | 0.107504i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.433589 | − | 0.750998i | 0.0459603 | − | 0.0796056i | −0.842130 | − | 0.539274i | \(-0.818699\pi\) |
0.888090 | + | 0.459669i | \(0.152032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.57633 | + | 4.18658i | −0.584559 | + | 0.438873i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.42116 | − | 0.820506i | −0.147367 | − | 0.0850825i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.0988i | − | 1.63459i | −0.576222 | − | 0.817293i | \(-0.695474\pi\) | ||
0.576222 | − | 0.817293i | \(-0.304526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.91211 | 0.393182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.84744 | + | 13.5922i | 0.780849 | + | 1.35247i | 0.931448 | + | 0.363876i | \(0.118547\pi\) |
−0.150598 | + | 0.988595i | \(0.548120\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5787 | − | 6.68495i | −1.14088 | − | 0.658688i | −0.194233 | − | 0.980956i | \(-0.562222\pi\) |
−0.946649 | + | 0.322267i | \(0.895555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.67994 | − | 2.70196i | −0.452427 | − | 0.261209i | 0.256428 | − | 0.966563i | \(-0.417454\pi\) |
−0.708854 | + | 0.705355i | \(0.750788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.91385 | − | 13.7072i | −0.758009 | − | 1.31291i | −0.943864 | − | 0.330333i | \(-0.892839\pi\) |
0.185855 | − | 0.982577i | \(-0.440495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.762915 | 0.0724127 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.4238i | − | 1.73316i | −0.499036 | − | 0.866581i | \(-0.666312\pi\) | ||
0.499036 | − | 0.866581i | \(-0.333688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.54420 | − | 3.77830i | −0.605012 | − | 0.349304i | ||||
\(118\) | 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 | ||||||||
\(123\) | 2.94316 | − | 1.69923i | 0.265376 | − | 0.153215i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.32497i | 0.472515i | 0.971691 | + | 0.236257i | \(0.0759208\pi\) | ||||
−0.971691 | + | 0.236257i | \(0.924079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.340245 | + | 0.589321i | 0.0299569 | + | 0.0518868i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.11854 | + | 14.0617i | −0.709320 | + | 1.22858i | 0.255789 | + | 0.966733i | \(0.417665\pi\) |
−0.965110 | + | 0.261846i | \(0.915669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.3680 | + | 1.98026i | −1.41928 | + | 0.171710i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.81864 | − | 2.20469i | 0.326248 | − | 0.188360i | −0.327926 | − | 0.944703i | \(-0.606350\pi\) |
0.654174 | + | 0.756344i | \(0.273016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.3699 | 1.89739 | 0.948695 | − | 0.316192i | \(-0.102404\pi\) | ||||
0.948695 | + | 0.316192i | \(0.102404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.50273 | 0.210768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.11429 | − | 1.79804i | 0.260430 | − | 0.150359i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.608388 | + | 2.47753i | 0.0501790 | + | 0.204343i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.2541 | − | 19.4927i | 0.921971 | − | 1.59690i | 0.125610 | − | 0.992080i | \(-0.459911\pi\) |
0.796361 | − | 0.604822i | \(-0.206756\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.75136 | − | 11.6937i | −0.549418 | − | 0.951620i | −0.998314 | − | 0.0580365i | \(-0.981516\pi\) |
0.448896 | − | 0.893584i | \(-0.351817\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.39847i | 0.517285i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4724 | + | 7.77830i | −1.07522 | + | 0.620776i | −0.929602 | − | 0.368566i | \(-0.879849\pi\) |
−0.145613 | + | 0.989342i | \(0.546516\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 3.81391 | + | 2.20196i | 0.298729 | + | 0.172471i | 0.641872 | − | 0.766812i | \(-0.278158\pi\) |
−0.343143 | + | 0.939283i | \(0.611492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.09880i | − | 0.704087i | −0.935984 | − | 0.352043i | \(-0.885487\pi\) | ||
0.935984 | − | 0.352043i | \(-0.114513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.05387 | 0.465682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.93359 | − | 15.4734i | −0.683169 | − | 1.18328i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2863 | − | 9.98026i | −1.31425 | − | 0.758785i | −0.331457 | − | 0.943470i | \(-0.607540\pi\) |
−0.982798 | + | 0.184685i | \(0.940873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.516215 | − | 0.298037i | −0.0388011 | − | 0.0224018i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.59607 | − | 11.4247i | −0.493014 | − | 0.853925i | 0.506954 | − | 0.861973i | \(-0.330771\pi\) |
−0.999968 | + | 0.00804839i | \(0.997438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2316 | 0.760511 | 0.380255 | − | 0.924882i | \(-0.375836\pi\) | ||||
0.380255 | + | 0.924882i | \(0.375836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0143878i | 0.00106357i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.63699 | − | 1.52247i | −0.192836 | − | 0.111334i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.52420 | + | 3.39666i | −0.329087 | + | 0.247071i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00273 | + | 12.1291i | −0.506700 | + | 0.877630i | 0.493270 | + | 0.869876i | \(0.335801\pi\) |
−0.999970 | + | 0.00775353i | \(0.997532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4789 | − | 7.20469i | 0.898250 | − | 0.518605i | 0.0216183 | − | 0.999766i | \(-0.493118\pi\) |
0.876632 | + | 0.481161i | \(0.159785\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.5566i | − | 0.823373i | −0.911325 | − | 0.411687i | \(-0.864940\pi\) | ||
0.911325 | − | 0.411687i | \(-0.135060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.70469 | − | 4.68467i | −0.191731 | − | 0.332087i | 0.754093 | − | 0.656767i | \(-0.228077\pi\) |
−0.945824 | + | 0.324680i | \(0.894743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.22617 | + | 2.12378i | −0.0864871 | + | 0.149800i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.74109 | − | 11.6427i | −0.613504 | − | 0.817161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.3784 | + | 9.45606i | −1.13838 | + | 0.657241i | ||||
\(208\) | 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 | ||||||||
\(213\) | −1.97929 | + | 1.14275i | −0.135619 | + | 0.0782997i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.67427 | − | 10.9578i | 0.317310 | − | 0.743863i | ||||
\(218\) | 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 | ||||||||
\(223\) | 21.5566i | 1.44354i | 0.692135 | + | 0.721768i | \(0.256670\pi\) | ||||
−0.692135 | + | 0.721768i | \(0.743330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7593 | − | 6.21189i | 0.714120 | − | 0.412297i | −0.0984646 | − | 0.995141i | \(-0.531393\pi\) |
0.812585 | + | 0.582843i | \(0.198060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.18222 | + | 7.24382i | −0.276369 | + | 0.478685i | −0.970480 | − | 0.241183i | \(-0.922465\pi\) |
0.694110 | + | 0.719868i | \(0.255798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.158021 | − | 1.30613i | −0.0103970 | − | 0.0859370i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1291 | + | 7.00273i | 0.794603 | + | 0.458764i | 0.841580 | − | 0.540132i | \(-0.181626\pi\) |
−0.0469777 | + | 0.998896i | \(0.514959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.94067i | − | 0.126060i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9605 | −1.09708 | −0.548542 | − | 0.836123i | \(-0.684817\pi\) | ||||
−0.548542 | + | 0.836123i | \(0.684817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16521 | − | 8.94641i | −0.332721 | − | 0.576289i | 0.650324 | − | 0.759657i | \(-0.274633\pi\) |
−0.983044 | + | 0.183368i | \(0.941300\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.02428 | − | 4.63282i | −0.514758 | − | 0.297196i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2234 | − | 8.21189i | −0.905014 | − | 0.522510i | ||||
\(248\) | 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 | ||||||||
\(253\) | − | 9.00000i | − | 0.565825i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6499 | + | 14.2316i | 1.53762 | + | 0.887744i | 0.998978 | + | 0.0452090i | \(0.0143954\pi\) |
0.538641 | + | 0.842535i | \(0.318938\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 24.7355 | − | 14.2810i | 1.52525 | − | 0.880606i | 0.525702 | − | 0.850669i | \(-0.323803\pi\) |
0.999552 | − | 0.0299373i | \(-0.00953075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.316041i | − | 0.0193414i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.59880 | − | 7.96536i | −0.280394 | − | 0.485657i | 0.691088 | − | 0.722771i | \(-0.257132\pi\) |
−0.971482 | + | 0.237114i | \(0.923798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.93086 | + | 3.34435i | −0.117291 | + | 0.203155i | −0.918693 | − | 0.394971i | \(-0.870754\pi\) |
0.801402 | + | 0.598126i | \(0.204088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.997115 | + | 2.33752i | −0.0603481 | + | 0.141473i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.21539 | + | 5.32051i | −0.553699 | + | 0.319678i | −0.750613 | − | 0.660743i | \(-0.770241\pi\) |
0.196914 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −5.12004 | + | 2.95606i | −0.304355 | + | 0.175719i | −0.644398 | − | 0.764691i | \(-0.722892\pi\) |
0.340043 | + | 0.940410i | \(0.389558\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.8127 | + | 19.7299i | 0.874368 | + | 1.16462i | ||||
\(288\) | 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 | ||||||||
\(293\) | 24.3250i | 1.42108i | 0.703657 | + | 0.710540i | \(0.251549\pi\) | ||||
−0.703657 | + | 0.710540i | \(0.748451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.52669 | − | 1.45879i | 0.146614 | − | 0.0846474i | ||||
\(298\) | 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 | ||||||||
\(303\) | 4.95364 | + | 2.85998i | 0.284579 | + | 0.164302i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5226i | 1.34250i | 0.741229 | + | 0.671252i | \(0.234243\pi\) | ||||
−0.741229 | + | 0.671252i | \(0.765757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.87264 | −0.277195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.40939 | + | 7.63728i | 0.250033 | + | 0.433070i | 0.963535 | − | 0.267583i | \(-0.0862251\pi\) |
−0.713501 | + | 0.700654i | \(0.752892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0808384 | + | 0.0466721i | 0.00456926 | + | 0.00263806i | 0.502283 | − | 0.864703i | \(-0.332494\pi\) |
−0.497714 | + | 0.867341i | \(0.665827\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.06764 | + | 1.77110i | 0.172296 | + | 0.0994751i | 0.583668 | − | 0.811992i | \(-0.301617\pi\) |
−0.411372 | + | 0.911468i | \(0.634950\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.75409 | + | 6.50228i | 0.210189 | + | 0.364058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.96945 | −0.109924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9067i | 0.773787i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.99556 | − | 2.88419i | −0.276255 | − | 0.159496i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.18222 | + | 18.0373i | 0.120310 | + | 0.994429i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.82497 | − | 17.0173i | 0.540029 | − | 0.935358i | −0.458872 | − | 0.888502i | \(-0.651747\pi\) |
0.998902 | − | 0.0468558i | \(-0.0149201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.19788 | + | 3.00099i | −0.284842 | + | 0.164454i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0449i | 1.25534i | 0.778480 | + | 0.627669i | \(0.215991\pi\) | ||||
−0.778480 | + | 0.627669i | \(0.784009\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | −17.3252 | + | 6.54494i | −0.935475 | + | 0.353393i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.5393 | − | 11.2810i | 1.04893 | − | 0.605597i | 0.126577 | − | 0.991957i | \(-0.459601\pi\) |
0.922348 | + | 0.386360i | \(0.126268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3250 | −0.766798 | −0.383399 | − | 0.923583i | \(-0.625247\pi\) | ||||
−0.383399 | + | 0.923583i | \(0.625247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63555 | −0.300804 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.3193 | − | 16.3502i | 1.50729 | − | 0.870232i | 0.507321 | − | 0.861757i | \(-0.330636\pi\) |
0.999964 | − | 0.00847467i | \(-0.00269760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.13624 | − | 0.258451i | 0.113062 | − | 0.0136787i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0791 | + | 22.6536i | −0.690287 | + | 1.19561i | 0.281457 | + | 0.959574i | \(0.409182\pi\) |
−0.971744 | + | 0.236038i | \(0.924151\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.91658 | − | 17.1760i | −0.521925 | − | 0.904001i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.33043i | − | 0.174802i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8512 | − | 12.6158i | 1.14062 | − | 0.658540i | 0.194040 | − | 0.980994i | \(-0.437841\pi\) |
0.946585 | + | 0.322454i | \(0.104508\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 4.93191 | + | 2.84744i | 0.255365 | + | 0.147435i | 0.622218 | − | 0.782844i | \(-0.286232\pi\) |
−0.366854 | + | 0.930279i | \(0.619565\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 14.5027i | − | 0.746929i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9660 | −0.768751 | −0.384375 | − | 0.923177i | \(-0.625583\pi\) | ||||
−0.384375 | + | 0.923177i | \(0.625583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.970337 | + | 1.68067i | 0.0497119 | + | 0.0861035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.1983 | + | 12.2388i | 1.08318 | + | 0.625374i | 0.931753 | − | 0.363094i | \(-0.118280\pi\) |
0.151428 | + | 0.988468i | \(0.451613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.63629 | − | 2.67676i | −0.235676 | − | 0.136068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6230 | − | 27.0598i | −0.792118 | − | 1.37199i | −0.924653 | − | 0.380810i | \(-0.875645\pi\) |
0.132535 | − | 0.991178i | \(-0.457688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.7200 | 0.744421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.91757i | 0.298502i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.981053 | − | 0.566411i | −0.0492376 | − | 0.0284274i | 0.475179 | − | 0.879889i | \(-0.342383\pi\) |
−0.524417 | + | 0.851462i | \(0.675717\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.80523 | + | 3.60765i | −0.240562 | + | 0.180608i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.91112 | − | 3.31016i | 0.0954368 | − | 0.165301i | −0.814354 | − | 0.580368i | \(-0.802909\pi\) |
0.909791 | + | 0.415067i | \(0.136242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2773 | − | 5.93359i | 0.511948 | − | 0.295573i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.85626i | − | 0.141580i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8304 | + | 29.1512i | 0.832211 | + | 1.44143i | 0.896281 | + | 0.443487i | \(0.146259\pi\) |
−0.0640699 | + | 0.997945i | \(0.520408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.803496 | − | 1.39170i | 0.0396335 | − | 0.0686473i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.69786 | − | 3.98026i | 0.0835463 | − | 0.195856i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.06042 | − | 4.07633i | 0.345750 | − | 0.199619i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.497270 | 0.0242933 | 0.0121466 | − | 0.999926i | \(-0.496134\pi\) | ||||
0.0121466 | + | 0.999926i | \(0.496134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28003 | −0.0623850 | −0.0311925 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311925 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.0515 | + | 9.84471i | −0.829074 | + | 0.478666i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.103693 | + | 0.0125452i | −0.00501808 | + | 0.000607106i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.655291 | − | 1.13500i | 0.0316377 | − | 0.0547982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.14548 | + | 8.91222i | 0.247849 | + | 0.429287i | 0.962929 | − | 0.269756i | \(-0.0869430\pi\) |
−0.715080 | + | 0.699043i | \(0.753610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8870i | 1.43628i | 0.695899 | + | 0.718139i | \(0.255006\pi\) | ||||
−0.695899 | + | 0.718139i | \(0.744994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.5973 | + | 20.5521i | −1.70285 | + | 0.983142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.52420 | + | 4.37205i | −0.120474 | + | 0.208666i | −0.919955 | − | 0.392025i | \(-0.871775\pi\) |
0.799481 | + | 0.600692i | \(0.205108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8906 | − | 14.4867i | −0.661459 | − | 0.689843i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.1964 | + | 5.88692i | 0.484447 | + | 0.279696i | 0.722268 | − | 0.691613i | \(-0.243100\pi\) |
−0.237821 | + | 0.971309i | \(0.576433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 8.20307i | − | 0.387992i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3843 | 0.537258 | 0.268629 | − | 0.963244i | \(-0.413429\pi\) | ||||
0.268629 | + | 0.963244i | \(0.413429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36172 | − | 11.0188i | −0.299562 | − | 0.518856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.26175 | − | 2.46052i | −0.200234 | − | 0.115605i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.2607 | + | 18.6257i | 1.50909 | + | 0.871275i | 0.999944 | + | 0.0105968i | \(0.00337314\pi\) |
0.509149 | + | 0.860678i | \(0.329960\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 31.2031i | − | 1.45013i | −0.688681 | − | 0.725065i | \(-0.741810\pi\) | ||
0.688681 | − | 0.725065i | \(-0.258190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2539 | + | 9.38419i | 0.752140 | + | 0.434248i | 0.826467 | − | 0.562986i | \(-0.190347\pi\) |
−0.0743264 | + | 0.997234i | \(0.523681\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 2.20634 | − | 1.27383i | 0.101448 | − | 0.0585709i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.0683i | 1.33094i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.357254 | − | 0.618782i | −0.0163234 | − | 0.0282729i | 0.857748 | − | 0.514070i | \(-0.171863\pi\) |
−0.874072 | + | 0.485797i | \(0.838529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.75856 | + | 4.77796i | −0.125779 | + | 0.217856i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.81864 | + | 5.08626i | 0.173754 | + | 0.231433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4582 | + | 8.34744i | −0.655163 | + | 0.378259i | −0.790432 | − | 0.612550i | \(-0.790144\pi\) |
0.135268 | + | 0.990809i | \(0.456810\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −10.6348 | + | 6.14002i | −0.478968 | + | 0.276532i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.96166 | − | 13.2685i | −0.446841 | − | 0.595173i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.23436 | − | 12.5303i | 0.323854 | − | 0.560932i | −0.657426 | − | 0.753519i | \(-0.728355\pi\) |
0.981280 | + | 0.192588i | \(0.0616879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.65802 | − | 2.87178i | −0.0740749 | − | 0.128301i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.6949i | − | 1.36862i | −0.729193 | − | 0.684308i | \(-0.760104\pi\) | ||
0.729193 | − | 0.684308i | \(-0.239896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.91073 | − | 1.10316i | 0.0848585 | − | 0.0489930i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.2371 | − | 38.5158i | 0.985641 | − | 1.70718i | 0.346591 | − | 0.938016i | \(-0.387339\pi\) |
0.639051 | − | 0.769165i | \(-0.279327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.73436 | + | 4.15239i | 0.430623 | + | 0.183691i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.5398 | − | 6.66248i | −0.509493 | − | 0.294156i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.36991i | − | 0.412088i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.27457 | −0.319318 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.32497 | + | 10.9552i | 0.277102 | + | 0.479955i | 0.970663 | − | 0.240443i | \(-0.0772927\pi\) |
−0.693561 | + | 0.720398i | \(0.743959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.89504 | − | 5.13555i | −0.388953 | − | 0.224562i | 0.292753 | − | 0.956188i | \(-0.405428\pi\) |
−0.681706 | + | 0.731626i | \(0.738762\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.70218 | − | 5.02420i | −0.379073 | − | 0.218858i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2541 | + | 17.7606i | 0.445830 | + | 0.772201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.68942 | 0.203503 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5764i | 1.06452i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.16372 | − | 2.40393i | −0.179678 | − | 0.103737i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.27557 | − | 2.27773i | 0.399527 | − | 0.0981087i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06914 | − | 1.85181i | 0.0459660 | − | 0.0796154i | −0.842127 | − | 0.539279i | \(-0.818697\pi\) |
0.888093 | + | 0.459664i | \(0.152030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.22932 | − | 1.86445i | 0.138583 | − | 0.0800111i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.0198i | − | 1.36907i | −0.728980 | − | 0.684535i | \(-0.760005\pi\) | ||
0.728980 | − | 0.684535i | \(-0.239995\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 13.9866 | − | 1.69215i | 0.594769 | − | 0.0719574i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.21436 | + | 4.16521i | −0.305682 | + | 0.176486i | −0.644993 | − | 0.764189i | \(-0.723140\pi\) |
0.339310 | + | 0.940674i | \(0.389806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.92104 | −0.208138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10972 | −0.0468525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.8557 | − | 9.73163i | 0.710382 | − | 0.410139i | −0.100821 | − | 0.994905i | \(-0.532147\pi\) |
0.811202 | + | 0.584766i | \(0.198813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.12024 | − | 19.0361i | 0.341018 | − | 0.799442i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.44624 | − | 16.3614i | 0.396007 | − | 0.685904i | −0.597222 | − | 0.802076i | \(-0.703729\pi\) |
0.993229 | + | 0.116172i | \(0.0370622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.31505 | + | 16.1341i | 0.389823 | + | 0.675192i | 0.992425 | − | 0.122849i | \(-0.0392030\pi\) |
−0.602603 | + | 0.798041i | \(0.705870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.10426i | 0.213234i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.1017 | + | 9.29630i | −0.670321 | + | 0.387010i | −0.796198 | − | 0.605036i | \(-0.793159\pi\) |
0.125877 | + | 0.992046i | \(0.459825\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −11.9799 | − | 6.91658i | −0.496155 | − | 0.286455i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1383i | 0.418452i | 0.977867 | + | 0.209226i | \(0.0670944\pi\) | ||||
−0.977867 | + | 0.209226i | \(0.932906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0593 | 1.15616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.10589 | − | 3.64751i | −0.0866247 | − | 0.150038i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7272 | − | 8.50273i | −0.604772 | − | 0.349165i | 0.166145 | − | 0.986101i | \(-0.446868\pi\) |
−0.770917 | + | 0.636936i | \(0.780201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.70732 | − | 0.985720i | −0.0698758 | − | 0.0403428i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.09334 | − | 7.08988i | −0.167250 | − | 0.289685i | 0.770202 | − | 0.637800i | \(-0.220155\pi\) |
−0.937452 | + | 0.348115i | \(0.886822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3359 | −1.44138 | −0.720690 | − | 0.693257i | \(-0.756175\pi\) | ||||
−0.720690 | + | 0.693257i | \(0.756175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 19.2929i | − | 0.785669i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.4493 | − | 14.1158i | −0.992367 | − | 0.572943i | −0.0863858 | − | 0.996262i | \(-0.527532\pi\) |
−0.905981 | + | 0.423319i | \(0.860865\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −26.9837 | + | 15.5791i | −1.08986 | + | 0.629232i | −0.933540 | − | 0.358474i | \(-0.883297\pi\) |
−0.156323 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.1527i | − | 1.57623i | −0.615530 | − | 0.788114i | \(-0.711058\pi\) | ||
0.615530 | − | 0.788114i | \(-0.288942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6921 | − | 34.1078i | −0.791494 | − | 1.37091i | −0.925042 | − | 0.379866i | \(-0.875970\pi\) |
0.133547 | − | 0.991042i | \(-0.457363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.05213 | + | 12.2146i | −0.282992 | + | 0.490157i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.27773 | − | 0.275568i | 0.0912552 | − | 0.0110404i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.68364 | − | 1.54940i | 0.107174 | − | 0.0618771i | ||||
\(628\) | 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 | ||||||||
\(633\) | −3.46110 | + | 1.99827i | −0.137566 | + | 0.0794239i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.7160 | − | 5.14810i | −0.701935 | − | 0.203975i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.99018 | − | 15.5715i | 0.355646 | − | 0.615997i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.20643 | − | 7.28575i | −0.166144 | − | 0.287770i | 0.770917 | − | 0.636936i | \(-0.219798\pi\) |
−0.937061 | + | 0.349166i | \(0.886465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.7398i | − | 1.17282i | −0.810013 | − | 0.586412i | \(-0.800540\pi\) | ||
0.810013 | − | 0.586412i | \(-0.199460\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7806 | − | 10.8430i | 0.738341 | − | 0.426281i | −0.0831249 | − | 0.996539i | \(-0.526490\pi\) |
0.821466 | + | 0.570258i | \(0.193157\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −26.0416 | − | 15.0351i | −1.01909 | − | 0.588370i | −0.105247 | − | 0.994446i | \(-0.533563\pi\) |
−0.913839 | + | 0.406076i | \(0.866897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.4687i | 0.447437i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.37537 | −0.0925311 | −0.0462656 | − | 0.998929i | \(-0.514732\pi\) | ||||
−0.0462656 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.23163 | + | 12.5255i | 0.281278 | + | 0.487187i | 0.971700 | − | 0.236220i | \(-0.0759085\pi\) |
−0.690422 | + | 0.723407i | \(0.742575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.85635 | + | 1.07176i | 0.0720946 | + | 0.0416238i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.4336 | − | 18.1482i | −1.21711 | − | 0.702701i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.92813 | + | 6.80372i | 0.151870 | + | 0.263047i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0538660 | 0.00207947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.99653i | 0.346791i | 0.984852 | + | 0.173395i | \(0.0554738\pi\) | ||||
−0.984852 | + | 0.173395i | \(0.944526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.48810 | + | 3.74591i | 0.249358 | + | 0.143967i | 0.619470 | − | 0.785020i | \(-0.287347\pi\) |
−0.370112 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −36.6545 | + | 21.1625i | −1.40255 | + | 0.809760i | −0.994653 | − | 0.103270i | \(-0.967069\pi\) |
−0.407892 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.04841i | 0.116304i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.3600 | + | 23.1402i | 0.508975 | + | 0.881570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3232 | + | 24.8086i | −0.544882 | + | 0.943763i | 0.453733 | + | 0.891138i | \(0.350092\pi\) |
−0.998614 | + | 0.0526247i | \(0.983241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.21440 | + | 8.27730i | 0.236066 | + | 0.314429i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0219 | − | 10.4049i | 0.682626 | − | 0.394114i | ||||
\(698\) | 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 | ||||||||
\(703\) | −11.2972 | + | 6.52247i | −0.426084 | + | 0.246000i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.2928 | + | 38.1949i | −0.612754 | + | 1.43647i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4138 | − | 24.9655i | 0.541323 | − | 0.937600i | −0.457505 | − | 0.889207i | \(-0.651257\pi\) |
0.998828 | − | 0.0483927i | \(-0.0154099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.63382 | + | 13.2222i | 0.286291 | + | 0.495870i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 29.7003i | − | 1.11229i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.35310 | + | 3.09061i | −0.199915 | + | 0.115421i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.6553 | − | 27.1158i | 0.583844 | − | 1.01125i | −0.411175 | − | 0.911557i | \(-0.634881\pi\) |
0.995018 | − | 0.0996906i | \(-0.0317853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.24864 | − | 35.1174i | −0.158227 | − | 1.30784i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.26050 | − | 1.88245i | −0.121259 | − | 0.0700092i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.17230i | 0.303094i | 0.988450 | + | 0.151547i | \(0.0484255\pi\) | ||||
−0.988450 | + | 0.151547i | \(0.951575\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0899 | 0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08342 | + | 3.60859i | 0.0770581 | + | 0.133469i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.5488 | + | 10.7092i | 0.685116 | + | 0.395552i | 0.801780 | − | 0.597620i | \(-0.203887\pi\) |
−0.116664 | + | 0.993171i | \(0.537220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.95118 | + | 4.59061i | 0.292885 | + | 0.169097i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.17503 | + | 3.76726i | 0.0800098 | + | 0.138581i | 0.903254 | − | 0.429107i | \(-0.141172\pi\) |
−0.823244 | + | 0.567688i | \(0.807838\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.98561 | −0.219887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53328i | 0.239683i | 0.992793 | + | 0.119841i | \(0.0382386\pi\) | ||||
−0.992793 | + | 0.119841i | \(0.961761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.6841 | − | 21.1796i | −1.34220 | − | 0.774921i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71724 | − | 14.1939i | −0.0627465 | − | 0.518635i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2415 | + | 29.8632i | −0.629153 | + | 1.08973i | 0.358569 | + | 0.933503i | \(0.383265\pi\) |
−0.987722 | + | 0.156222i | \(0.950069\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.15720 | − | 3.55486i | 0.224381 | − | 0.129546i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2425i | 1.60802i | 0.594614 | + | 0.804011i | \(0.297305\pi\) | ||||
−0.594614 | + | 0.804011i | \(0.702695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.64002 | − | 2.84059i | −0.0595288 | − | 0.103107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.9094 | − | 20.6277i | 0.431715 | − | 0.747752i | −0.565306 | − | 0.824881i | \(-0.691242\pi\) |
0.997021 | + | 0.0771290i | \(0.0245753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.4307 | − | 38.5181i | 0.594831 | − | 1.39445i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.73307 | − | 2.15529i | 0.134793 | − | 0.0778230i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.158128 | 0.00570225 | 0.00285113 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285113 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3734 | 0.373588 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.4145 | + | 8.89957i | −0.554421 | + | 0.320095i | −0.750903 | − | 0.660412i | \(-0.770382\pi\) |
0.196482 | + | 0.980507i | \(0.437048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.21189 | + | 1.61419i | 0.0434764 | + | 0.0579086i | ||||
\(778\) | 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 | ||||||||
\(783\) | − | 11.7664i | − | 0.420496i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.9596 | − | 20.7613i | 1.28182 | − | 0.740060i | 0.304640 | − | 0.952467i | \(-0.401464\pi\) |
0.977181 | + | 0.212407i | \(0.0681304\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −0.0901072 | − | 0.0520234i | −0.00319980 | − | 0.00184741i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.0933i | − | 0.888852i | −0.895816 | − | 0.444426i | \(-0.853408\pi\) | ||
0.895816 | − | 0.444426i | \(-0.146592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3250 | 0.542158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.24318 | + | 2.15324i | 0.0439255 | + | 0.0760811i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.72659 | − | 2.72890i | −0.166798 | − | 0.0963007i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.90296 | − | 1.67602i | −0.102189 | − | 0.0589989i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.34744 | + | 10.9941i | 0.223164 | + | 0.386531i | 0.955767 | − | 0.294125i | \(-0.0950281\pi\) |
−0.732603 | + | 0.680656i | \(0.761695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.9749 | 0.631184 | 0.315592 | − | 0.948895i | \(-0.397797\pi\) | ||||
0.315592 | + | 0.948895i | \(0.397797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.40740i | 0.0493595i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0767 | − | 5.81778i | −0.352539 | − | 0.203538i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.40130 | − | 19.8481i | −0.0839084 | − | 0.693550i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0341 | + | 17.3796i | −0.350193 | + | 0.606553i | −0.986283 | − | 0.165062i | \(-0.947217\pi\) |
0.636090 | + | 0.771615i | \(0.280551\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.18893 | + | 5.30523i | −0.320306 | + | 0.184929i | −0.651529 | − | 0.758624i | \(-0.725872\pi\) |
0.331223 | + | 0.943553i | \(0.392539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.7793i | − | 1.20939i | −0.796455 | − | 0.604697i | \(-0.793294\pi\) | ||
0.796455 | − | 0.604697i | \(-0.206706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.1141 | − | 22.7142i | −0.455471 | − | 0.788898i | 0.543244 | − | 0.839575i | \(-0.317196\pi\) |
−0.998715 | + | 0.0506761i | \(0.983862\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.93905 | + | 3.35853i | −0.0672648 | + | 0.116506i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.72534 | + | 15.1707i | 0.129075 | + | 0.525633i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.33818 | − | 4.81405i | 0.288210 | − | 0.166398i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.9210 | −1.17108 | −0.585542 | − | 0.810642i | \(-0.699118\pi\) | ||||
−0.585542 | + | 0.810642i | \(0.699118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28003 | 0.0441391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.547399 | − | 0.316041i | 0.0188534 | − | 0.0108850i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.0026 | − | 2.90393i | 0.824739 | − | 0.0997801i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 57.6698i | − | 1.97458i | −0.158942 | − | 0.987288i | \(-0.550808\pi\) | ||
0.158942 | − | 0.987288i | \(-0.449192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.6607 | + | 17.7020i | −1.04735 | + | 0.604688i | −0.921906 | − | 0.387413i | \(-0.873369\pi\) |
−0.125443 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.72170 | + | 11.6423i | −0.229342 | + | 0.397231i | −0.957613 | − | 0.288057i | \(-0.906991\pi\) |
0.728272 | + | 0.685289i | \(0.240324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.27047 | + | 3.52794i | 0.281857 | + | 0.120232i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.11828 | + | 3.53239i | 0.208269 | + | 0.120244i | 0.600507 | − | 0.799620i | \(-0.294966\pi\) |
−0.392238 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.38061i | 0.148773i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.26564 | −0.246470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.86718 | − | 15.3584i | −0.300453 | − | 0.520400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.9741 | + | 23.0791i | 1.35292 | + | 0.781108i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.9951 | + | 7.50273i | 0.438814 | + | 0.253349i | 0.703094 | − | 0.711097i | \(-0.251801\pi\) |
−0.264281 | + | 0.964446i | \(0.585135\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 58.2229i | 1.95936i | 0.200574 | + | 0.979679i | \(0.435719\pi\) | ||||
−0.200574 | + | 0.979679i | \(0.564281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.8637 | + | 12.6230i | 0.734111 | + | 0.423839i | 0.819924 | − | 0.572472i | \(-0.194016\pi\) |
−0.0858133 | + | 0.996311i | \(0.527349\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −37.0604 | + | 21.3968i | −1.24018 | + | 0.716018i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.33567i | 0.211542i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −0.706414 | + | 1.65603i | −0.0235080 | + | 0.0551093i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.5444 | + | 13.5933i | −0.781778 | + | 0.451360i | −0.837060 | − | 0.547111i | \(-0.815727\pi\) |
0.0552822 | + | 0.998471i | \(0.482394\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 17.4575 | − | 10.0791i | 0.577757 | − | 0.333568i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.6483 | + | 5.15976i | −1.40837 | + | 0.170390i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5369 | + | 40.7670i | −0.776409 | + | 1.34478i | 0.157590 | + | 0.987505i | \(0.449628\pi\) |
−0.933999 | + | 0.357276i | \(0.883706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.28638 | + | 7.42423i | 0.141241 | + | 0.244637i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 16.5278i | − | 0.544020i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.1981 | − | 19.1669i | 1.09037 | − | 0.629525i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.99554 | − | 15.5807i | 0.295134 | − | 0.511187i | −0.679882 | − | 0.733321i | \(-0.737969\pi\) |
0.975016 | + | 0.222134i | \(0.0713024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.1904 | − | 31.4859i | −0.989451 | − | 1.03191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.78339 | + | 1.60699i | 0.0911242 | + | 0.0526106i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.7003i | 1.23162i | 0.787896 | + | 0.615808i | \(0.211170\pi\) | ||||
−0.787896 | + | 0.615808i | \(0.788830\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0340191 | 0.00111017 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.41658 | − | 4.18564i | −0.0787782 | − | 0.136448i | 0.823945 | − | 0.566670i | \(-0.191769\pi\) |
−0.902723 | + | 0.430222i | \(0.858435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.2677 | + | 30.7541i | 1.73463 | + | 1.00149i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.45659 | + | 1.41831i | 0.0798285 | + | 0.0460890i | 0.539383 | − | 0.842061i | \(-0.318658\pi\) |
−0.459554 | + | 0.888150i | \(0.651991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.27110 | + | 9.12982i | 0.171107 | + | 0.296366i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.29095 | 0.0418619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.7991i | − | 0.576571i | −0.957545 | − | 0.288285i | \(-0.906915\pi\) | ||
0.957545 | − | 0.288285i | \(-0.0930852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.36974 | + | 1.36817i | 0.0766029 | + | 0.0442267i | ||||
\(958\) | 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 | ||||||||
\(963\) | 13.4182 | − | 7.74701i | 0.432396 | − | 0.249644i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.1581i | − | 0.487453i | −0.969844 | − | 0.243726i | \(-0.921630\pi\) | ||
0.969844 | − | 0.243726i | \(-0.0783698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.53413 | + | 4.38924i | 0.0814079 | + | 0.141003i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.6921 | − | 41.0360i | 0.760317 | − | 1.31691i | −0.182370 | − | 0.983230i | \(-0.558377\pi\) |
0.942687 | − | 0.333678i | \(-0.108290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.5346 | + | 47.3305i | 1.13919 | + | 1.51735i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5421 | − | 11.8600i | 0.657200 | − | 0.379434i | −0.134009 | − | 0.990980i | \(-0.542785\pi\) |
0.791209 | + | 0.611546i | \(0.209452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.18322 | −0.0378158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.3808 | 1.44890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.8383 | + | 17.2272i | −0.951695 | + | 0.549461i | −0.893607 | − | 0.448850i | \(-0.851834\pi\) |
−0.0580876 | + | 0.998311i | \(0.518500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.97559 | + | 5.29531i | 0.126544 | + | 0.168551i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.15802 | + | 10.6660i | −0.195814 | + | 0.339159i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.8304 | + | 36.0794i | 0.661700 | + | 1.14610i | 0.980169 | + | 0.198165i | \(0.0634982\pi\) |
−0.318468 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.16138i | − | 0.227260i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.4672 | − | 12.3941i | 0.679874 | − | 0.392525i | −0.119934 | − | 0.992782i | \(-0.538268\pi\) |
0.799808 | + | 0.600256i | \(0.204935\pi\) | |||||||
\(998\) | 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.r.d.149.4 | 12 | ||
5.2 | odd | 4 | 700.2.i.d.401.2 | ✓ | 6 | ||
5.3 | odd | 4 | 700.2.i.e.401.2 | yes | 6 | ||
5.4 | even | 2 | inner | 700.2.r.d.149.3 | 12 | ||
7.2 | even | 3 | 4900.2.e.t.2549.4 | 6 | |||
7.4 | even | 3 | inner | 700.2.r.d.249.3 | 12 | ||
7.5 | odd | 6 | 4900.2.e.s.2549.3 | 6 | |||
35.2 | odd | 12 | 4900.2.a.bc.1.2 | 3 | |||
35.4 | even | 6 | inner | 700.2.r.d.249.4 | 12 | ||
35.9 | even | 6 | 4900.2.e.t.2549.3 | 6 | |||
35.12 | even | 12 | 4900.2.a.bb.1.2 | 3 | |||
35.18 | odd | 12 | 700.2.i.e.501.2 | yes | 6 | ||
35.19 | odd | 6 | 4900.2.e.s.2549.4 | 6 | |||
35.23 | odd | 12 | 4900.2.a.ba.1.2 | 3 | |||
35.32 | odd | 12 | 700.2.i.d.501.2 | yes | 6 | ||
35.33 | even | 12 | 4900.2.a.bd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.2 | ✓ | 6 | 5.2 | odd | 4 | ||
700.2.i.d.501.2 | yes | 6 | 35.32 | odd | 12 | ||
700.2.i.e.401.2 | yes | 6 | 5.3 | odd | 4 | ||
700.2.i.e.501.2 | yes | 6 | 35.18 | odd | 12 | ||
700.2.r.d.149.3 | 12 | 5.4 | even | 2 | inner | ||
700.2.r.d.149.4 | 12 | 1.1 | even | 1 | trivial | ||
700.2.r.d.249.3 | 12 | 7.4 | even | 3 | inner | ||
700.2.r.d.249.4 | 12 | 35.4 | even | 6 | inner | ||
4900.2.a.ba.1.2 | 3 | 35.23 | odd | 12 | |||
4900.2.a.bb.1.2 | 3 | 35.12 | even | 12 | |||
4900.2.a.bc.1.2 | 3 | 35.2 | odd | 12 | |||
4900.2.a.bd.1.2 | 3 | 35.33 | even | 12 | |||
4900.2.e.s.2549.3 | 6 | 7.5 | odd | 6 | |||
4900.2.e.s.2549.4 | 6 | 35.19 | odd | 6 | |||
4900.2.e.t.2549.3 | 6 | 35.9 | even | 6 | |||
4900.2.e.t.2549.4 | 6 | 7.2 | even | 3 |