Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,2,Mod(17,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.m (of order \(12\), degree \(4\), 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: | \(2.15596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 233.1 | ||
Root | \(0.500000 + 0.331082i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.233 |
Dual form | 270.2.m.b.197.1 |
$q$-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 \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(217\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | + | 0.965926i | −0.183013 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −1.36868 | + | 1.76825i | −0.612091 | + | 0.790787i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.56188 | − | 0.686453i | −0.968299 | − | 0.259455i | −0.260189 | − | 0.965558i | \(-0.583785\pi\) |
−0.708109 | + | 0.706103i | \(0.750452\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.35376 | − | 1.77970i | −0.428097 | − | 0.562790i | ||||
\(11\) | −4.15512 | + | 2.39896i | −1.25282 | + | 0.723314i | −0.971668 | − | 0.236350i | \(-0.924049\pi\) |
−0.281149 | + | 0.959664i | \(0.590715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.581838 | − | 0.155903i | 0.161373 | − | 0.0432397i | −0.177228 | − | 0.984170i | \(-0.556713\pi\) |
0.338601 | + | 0.940930i | \(0.390046\pi\) | |||||||
\(14\) | 1.32613 | − | 2.29692i | 0.354422 | − | 0.613877i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −4.40865 | − | 4.40865i | −1.06926 | − | 1.06926i | −0.997416 | − | 0.0718393i | \(-0.977113\pi\) |
−0.0718393 | − | 0.997416i | \(-0.522887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19145i | 1.19100i | 0.803355 | + | 0.595501i | \(0.203046\pi\) | ||||
−0.803355 | + | 0.595501i | \(0.796954\pi\) | |||||||
\(20\) | 2.06944 | − | 0.847015i | 0.462740 | − | 0.189398i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.24179 | − | 4.63444i | −0.264751 | − | 0.988065i | ||||
\(23\) | 0.681226 | + | 2.54237i | 0.142046 | + | 0.530121i | 0.999869 | + | 0.0161770i | \(0.00514951\pi\) |
−0.857824 | + | 0.513944i | \(0.828184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.25345 | − | 4.84034i | −0.250689 | − | 0.968068i | ||||
\(26\) | 0.602363i | 0.118133i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.87542 | + | 1.87542i | 0.354422 | + | 0.354422i | ||||
\(29\) | 0.920201 | + | 1.59383i | 0.170877 | + | 0.295968i | 0.938727 | − | 0.344662i | \(-0.112007\pi\) |
−0.767850 | + | 0.640630i | \(0.778673\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.03888 | + | 3.53145i | −0.366194 | + | 0.634266i | −0.988967 | − | 0.148136i | \(-0.952673\pi\) |
0.622773 | + | 0.782402i | \(0.286006\pi\) | |||||||
\(32\) | −0.965926 | + | 0.258819i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.39948 | − | 3.11739i | 0.926002 | − | 0.534628i | ||||
\(35\) | 4.72021 | − | 3.59052i | 0.797861 | − | 0.606909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.632057 | − | 0.632057i | 0.103910 | − | 0.103910i | −0.653241 | − | 0.757150i | \(-0.726591\pi\) |
0.757150 | + | 0.653241i | \(0.226591\pi\) | |||||||
\(38\) | −5.01456 | − | 1.34365i | −0.813469 | − | 0.217968i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.282544 | + | 2.21815i | 0.0446741 | + | 0.350720i | ||||
\(41\) | 5.58550 | + | 3.22479i | 0.872309 | + | 0.503628i | 0.868115 | − | 0.496363i | \(-0.165332\pi\) |
0.00419400 | + | 0.999991i | \(0.498665\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.644420 | + | 2.40501i | −0.0982731 | + | 0.366760i | −0.997495 | − | 0.0707320i | \(-0.977466\pi\) |
0.899222 | + | 0.437492i | \(0.144133\pi\) | |||||||
\(44\) | 4.79792 | 0.723314 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.63206 | −0.388076 | ||||||||
\(47\) | 1.02538 | − | 3.82678i | 0.149568 | − | 0.558194i | −0.849942 | − | 0.526876i | \(-0.823363\pi\) |
0.999509 | − | 0.0313173i | \(-0.00997024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0298240 | + | 0.0172189i | 0.00426058 | + | 0.00245984i | ||||
\(50\) | 4.99982 | + | 0.0420344i | 0.707082 | + | 0.00594456i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.581838 | − | 0.155903i | −0.0806865 | − | 0.0216199i | ||||
\(53\) | 1.31215 | − | 1.31215i | 0.180237 | − | 0.180237i | −0.611222 | − | 0.791459i | \(-0.709322\pi\) |
0.791459 | + | 0.611222i | \(0.209322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.44505 | − | 10.6307i | 0.194850 | − | 1.43345i | ||||
\(56\) | −2.29692 | + | 1.32613i | −0.306938 | + | 0.177211i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.77769 | + | 0.476331i | −0.233422 | + | 0.0625453i | ||||
\(59\) | 0.0645473 | − | 0.111799i | 0.00840334 | − | 0.0145550i | −0.861793 | − | 0.507260i | \(-0.830658\pi\) |
0.870196 | + | 0.492705i | \(0.163992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.27251 | + | 10.8643i | 0.803113 | + | 1.39103i | 0.917558 | + | 0.397603i | \(0.130158\pi\) |
−0.114445 | + | 0.993430i | \(0.536509\pi\) | |||||||
\(62\) | −2.88341 | − | 2.88341i | −0.366194 | − | 0.366194i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.520672 | + | 1.24222i | −0.0645815 | + | 0.154078i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85782 | + | 10.6655i | 0.349138 | + | 1.30300i | 0.887703 | + | 0.460416i | \(0.152300\pi\) |
−0.538566 | + | 0.842584i | \(0.681034\pi\) | |||||||
\(68\) | 1.61368 | + | 6.02233i | 0.195687 | + | 0.730315i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.24650 | + | 5.48866i | 0.268508 | + | 0.656021i | ||||
\(71\) | 10.4203i | 1.23666i | 0.785919 | + | 0.618329i | \(0.212190\pi\) | ||||
−0.785919 | + | 0.618329i | \(0.787810\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.30021 | + | 3.30021i | 0.386261 | + | 0.386261i | 0.873351 | − | 0.487091i | \(-0.161942\pi\) |
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(74\) | 0.446932 | + | 0.774109i | 0.0519548 | + | 0.0899883i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.59573 | − | 4.49593i | 0.297750 | − | 0.515719i | ||||
\(77\) | 12.2917 | − | 3.29355i | 1.40077 | − | 0.375335i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.62792 | − | 2.09458i | 0.408173 | − | 0.235659i | −0.281832 | − | 0.959464i | \(-0.590942\pi\) |
0.690004 | + | 0.723805i | \(0.257609\pi\) | |||||||
\(80\) | −2.21569 | − | 0.301182i | −0.247722 | − | 0.0336731i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.56054 | + | 4.56054i | −0.503628 | + | 0.503628i | ||||
\(83\) | −11.1098 | − | 2.97686i | −1.21946 | − | 0.326753i | −0.408992 | − | 0.912538i | \(-0.634119\pi\) |
−0.810466 | + | 0.585785i | \(0.800786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8296 | − | 1.76160i | 1.50004 | − | 0.191072i | ||||
\(86\) | −2.15627 | − | 1.24492i | −0.232517 | − | 0.134243i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.24179 | + | 4.63444i | −0.132376 | + | 0.494033i | ||||
\(89\) | −2.04989 | −0.217288 | −0.108644 | − | 0.994081i | \(-0.534651\pi\) | ||||
−0.108644 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.59762 | −0.167476 | ||||||||
\(92\) | 0.681226 | − | 2.54237i | 0.0710228 | − | 0.265061i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.43100 | + | 1.98089i | 0.353881 | + | 0.204313i | ||||
\(95\) | −9.17981 | − | 7.10542i | −0.941829 | − | 0.729001i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.7115 | − | 4.47782i | −1.69679 | − | 0.454654i | −0.724663 | − | 0.689104i | \(-0.758004\pi\) |
−0.972128 | + | 0.234450i | \(0.924671\pi\) | |||||||
\(98\) | −0.0243512 | + | 0.0243512i | −0.00245984 | + | 0.00245984i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.33465 | + | 4.81858i | −0.133465 | + | 0.481858i | ||||
\(101\) | 10.3594 | − | 5.98097i | 1.03079 | − | 0.595129i | 0.113582 | − | 0.993529i | \(-0.463768\pi\) |
0.917212 | + | 0.398399i | \(0.130434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4055 | + | 2.78816i | −1.02529 | + | 0.274725i | −0.732004 | − | 0.681300i | \(-0.761415\pi\) |
−0.293285 | + | 0.956025i | \(0.594748\pi\) | |||||||
\(104\) | 0.301182 | − | 0.521662i | 0.0295333 | − | 0.0511532i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.927828 | + | 1.60704i | 0.0901186 | + | 0.156090i | ||||
\(107\) | −4.35367 | − | 4.35367i | −0.420885 | − | 0.420885i | 0.464623 | − | 0.885508i | \(-0.346190\pi\) |
−0.885508 | + | 0.464623i | \(0.846190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.4546i | − | 1.48028i | −0.672452 | − | 0.740141i | \(-0.734759\pi\) | ||
0.672452 | − | 0.740141i | \(-0.265241\pi\) | |||||||
\(110\) | 9.89448 | + | 4.14724i | 0.943402 | + | 0.395424i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.686453 | − | 2.56188i | −0.0648637 | − | 0.242075i | ||||
\(113\) | −1.53568 | − | 5.73124i | −0.144465 | − | 0.539150i | −0.999779 | − | 0.0210396i | \(-0.993302\pi\) |
0.855314 | − | 0.518110i | \(-0.173364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.42794 | − | 2.27510i | −0.506158 | − | 0.212155i | ||||
\(116\) | − | 1.84040i | − | 0.170877i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0912837 | + | 0.0912837i | 0.00840334 | + | 0.00840334i | ||||
\(119\) | 8.26810 | + | 14.3208i | 0.757935 | + | 1.31278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.01003 | − | 10.4097i | 0.546367 | − | 0.946335i | ||||
\(122\) | −12.1176 | + | 3.24689i | −1.09707 | + | 0.293960i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.53145 | − | 2.03888i | 0.317133 | − | 0.183097i | ||||
\(125\) | 10.2745 | + | 4.40844i | 0.918980 | + | 0.394303i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.51837 | − | 2.51837i | 0.223469 | − | 0.223469i | −0.586489 | − | 0.809957i | \(-0.699490\pi\) |
0.809957 | + | 0.586489i | \(0.199490\pi\) | |||||||
\(128\) | 0.965926 | + | 0.258819i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.06513 | − | 0.824441i | −0.0934182 | − | 0.0723082i | ||||
\(131\) | −11.3102 | − | 6.52997i | −0.988181 | − | 0.570526i | −0.0834508 | − | 0.996512i | \(-0.526594\pi\) |
−0.904730 | + | 0.425985i | \(0.859927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.56369 | − | 13.2999i | 0.309011 | − | 1.15325i | ||||
\(134\) | −11.0417 | −0.953862 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.23478 | −0.534628 | ||||||||
\(137\) | −0.840942 | + | 3.13844i | −0.0718465 | + | 0.268135i | −0.992500 | − | 0.122246i | \(-0.960990\pi\) |
0.920653 | + | 0.390381i | \(0.127657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0478 | − | 10.9973i | −1.61561 | − | 0.932775i | −0.988036 | − | 0.154221i | \(-0.950713\pi\) |
−0.627578 | − | 0.778554i | \(-0.715953\pi\) | |||||||
\(140\) | −5.88308 | + | 0.749378i | −0.497211 | + | 0.0633340i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.0652 | − | 2.69696i | −0.844653 | − | 0.226324i | ||||
\(143\) | −2.04360 | + | 2.04360i | −0.170895 | + | 0.170895i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.07776 | − | 0.554295i | −0.338640 | − | 0.0460317i | ||||
\(146\) | −4.04192 | + | 2.33360i | −0.334512 | + | 0.193130i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.863406 | + | 0.231349i | −0.0709715 | + | 0.0190168i | ||||
\(149\) | −6.56668 | + | 11.3738i | −0.537964 | + | 0.931780i | 0.461050 | + | 0.887374i | \(0.347473\pi\) |
−0.999014 | + | 0.0444061i | \(0.985860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.167899 | − | 0.290810i | −0.0136634 | − | 0.0236658i | 0.859113 | − | 0.511786i | \(-0.171016\pi\) |
−0.872776 | + | 0.488120i | \(0.837683\pi\) | |||||||
\(152\) | 3.67091 | + | 3.67091i | 0.297750 | + | 0.297750i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.7253i | 1.02543i | ||||||||
\(155\) | −3.45392 | − | 8.43867i | −0.277426 | − | 0.677810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.17992 | − | 4.40352i | −0.0941678 | − | 0.351439i | 0.902724 | − | 0.430220i | \(-0.141564\pi\) |
−0.996892 | + | 0.0787808i | \(0.974897\pi\) | |||||||
\(158\) | 1.08423 | + | 4.04642i | 0.0862571 | + | 0.321916i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.864382 | − | 2.06224i | 0.0683354 | − | 0.163035i | ||||
\(161\) | − | 6.98088i | − | 0.550170i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.01496 | + | 9.01496i | 0.706106 | + | 0.706106i | 0.965714 | − | 0.259608i | \(-0.0835932\pi\) |
−0.259608 | + | 0.965714i | \(0.583593\pi\) | |||||||
\(164\) | −3.22479 | − | 5.58550i | −0.251814 | − | 0.436154i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.75085 | − | 9.96076i | 0.446353 | − | 0.773105i | ||||
\(167\) | 0.00858342 | − | 0.00229992i | 0.000664205 | − | 0.000177973i | −0.258487 | − | 0.966015i | \(-0.583224\pi\) |
0.259151 | + | 0.965837i | \(0.416557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9441 | + | 6.31858i | −0.841854 | + | 0.486045i | ||||
\(170\) | −1.87780 | + | 13.8143i | −0.144021 | + | 1.05951i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.76059 | − | 1.76059i | 0.134243 | − | 0.134243i | ||||
\(173\) | 10.0291 | + | 2.68729i | 0.762500 | + | 0.204311i | 0.619056 | − | 0.785347i | \(-0.287516\pi\) |
0.143444 | + | 0.989658i | \(0.454182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.111486 | + | 13.2608i | −0.00842753 | + | 1.00242i | ||||
\(176\) | −4.15512 | − | 2.39896i | −0.313204 | − | 0.180829i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.530550 | − | 1.98004i | 0.0397664 | − | 0.148410i | ||||
\(179\) | −1.46292 | −0.109343 | −0.0546717 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546717 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.68576 | −0.645607 | −0.322804 | − | 0.946466i | \(-0.604625\pi\) | ||||
−0.322804 | + | 0.946466i | \(0.604625\pi\) | |||||||
\(182\) | 0.413494 | − | 1.54318i | 0.0306502 | − | 0.114388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.27943 | + | 1.31603i | 0.168042 | + | 0.0970189i | ||||
\(185\) | 0.252556 | + | 1.98272i | 0.0185683 | + | 0.145772i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.8947 | + | 7.74231i | 2.11299 | + | 0.566174i | ||||
\(188\) | −2.80140 | + | 2.80140i | −0.204313 | + | 0.204313i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.23922 | − | 7.02800i | 0.670284 | − | 0.509865i | ||||
\(191\) | 4.33795 | − | 2.50452i | 0.313883 | − | 0.181220i | −0.334780 | − | 0.942296i | \(-0.608662\pi\) |
0.648663 | + | 0.761076i | \(0.275329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.25355 | + | 0.871785i | −0.234195 | + | 0.0627524i | −0.374008 | − | 0.927426i | \(-0.622017\pi\) |
0.139812 | + | 0.990178i | \(0.455350\pi\) | |||||||
\(194\) | 8.65048 | − | 14.9831i | 0.621069 | − | 1.07572i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0172189 | − | 0.0298240i | −0.00122992 | − | 0.00213029i | ||||
\(197\) | 15.5027 | + | 15.5027i | 1.10452 | + | 1.10452i | 0.993858 | + | 0.110665i | \(0.0352980\pi\) |
0.110665 | + | 0.993858i | \(0.464702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4607i | 1.30864i | 0.756217 | + | 0.654321i | \(0.227045\pi\) | ||||
−0.756217 | + | 0.654321i | \(0.772955\pi\) | |||||||
\(200\) | −4.30896 | − | 2.53631i | −0.304689 | − | 0.179345i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.09598 | + | 11.5544i | 0.217832 | + | 0.812962i | ||||
\(203\) | −1.26335 | − | 4.71488i | −0.0886697 | − | 0.330920i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.3470 | + | 5.46289i | −0.932195 | + | 0.381545i | ||||
\(206\) | − | 10.7726i | − | 0.750564i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.425935 | + | 0.425935i | 0.0295333 | + | 0.0295333i | ||||
\(209\) | −12.4541 | − | 21.5711i | −0.861468 | − | 1.49211i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.654465 | − | 1.13357i | 0.0450552 | − | 0.0780380i | −0.842618 | − | 0.538511i | \(-0.818987\pi\) |
0.887674 | + | 0.460473i | \(0.152320\pi\) | |||||||
\(212\) | −1.79243 | + | 0.480279i | −0.123104 | + | 0.0329857i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.33213 | − | 3.07851i | 0.364497 | − | 0.210442i | ||||
\(215\) | −3.37066 | − | 4.43117i | −0.229877 | − | 0.302204i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.64754 | − | 7.64754i | 0.519149 | − | 0.519149i | ||||
\(218\) | 14.9280 | + | 3.99994i | 1.01105 | + | 0.270910i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.56681 | + | 8.48395i | −0.442734 | + | 0.571988i | ||||
\(221\) | −3.25245 | − | 1.87780i | −0.218783 | − | 0.126315i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.42903 | − | 20.2614i | 0.363555 | − | 1.35681i | −0.505814 | − | 0.862643i | \(-0.668808\pi\) |
0.869369 | − | 0.494163i | \(-0.164526\pi\) | |||||||
\(224\) | 2.65225 | 0.177211 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.93342 | 0.394685 | ||||||||
\(227\) | −1.54126 | + | 5.75206i | −0.102297 | + | 0.381778i | −0.998025 | − | 0.0628257i | \(-0.979989\pi\) |
0.895727 | + | 0.444604i | \(0.146655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1822 | + | 5.87872i | 0.672862 | + | 0.388477i | 0.797160 | − | 0.603768i | \(-0.206335\pi\) |
−0.124298 | + | 0.992245i | \(0.539668\pi\) | |||||||
\(230\) | 3.60244 | − | 4.65415i | 0.237538 | − | 0.306885i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.77769 | + | 0.476331i | 0.116711 | + | 0.0312727i | ||||
\(233\) | −13.4322 | + | 13.4322i | −0.879973 | + | 0.879973i | −0.993531 | − | 0.113558i | \(-0.963775\pi\) |
0.113558 | + | 0.993531i | \(0.463775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.36331 | + | 7.05077i | 0.349864 | + | 0.459941i | ||||
\(236\) | −0.111799 | + | 0.0645473i | −0.00727751 | + | 0.00420167i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.9727 | + | 4.27988i | −1.03536 | + | 0.277424i | ||||
\(239\) | 2.27943 | − | 3.94809i | 0.147444 | − | 0.255380i | −0.782838 | − | 0.622225i | \(-0.786229\pi\) |
0.930282 | + | 0.366845i | \(0.119562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.03104 | + | 13.9102i | 0.517325 | + | 0.896032i | 0.999798 | + | 0.0201215i | \(0.00640532\pi\) |
−0.482473 | + | 0.875911i | \(0.660261\pi\) | |||||||
\(242\) | 8.49947 | + | 8.49947i | 0.546367 | + | 0.546367i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.5450i | − | 0.803113i | ||||||
\(245\) | −0.0712669 | + | 0.0291693i | −0.00455307 | + | 0.00186356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.809364 | + | 3.02059i | 0.0514986 | + | 0.192195i | ||||
\(248\) | 1.05540 | + | 3.93882i | 0.0670181 | + | 0.250115i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.91747 | + | 8.78343i | −0.437499 | + | 0.555513i | ||||
\(251\) | 18.9981i | 1.19915i | 0.800319 | + | 0.599574i | \(0.204663\pi\) | ||||
−0.800319 | + | 0.599574i | \(0.795337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.92963 | − | 8.92963i | −0.561401 | − | 0.561401i | ||||
\(254\) | 1.78075 | + | 3.08436i | 0.111734 | + | 0.193530i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.23709 | + | 0.867374i | −0.201924 | + | 0.0541053i | −0.358363 | − | 0.933582i | \(-0.616665\pi\) |
0.156439 | + | 0.987688i | \(0.449998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.05313 | + | 1.18538i | −0.127575 | + | 0.0736557i | ||||
\(260\) | 1.07203 | − | 0.815457i | 0.0664842 | − | 0.0505725i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.23478 | − | 9.23478i | 0.570526 | − | 0.570526i | ||||
\(263\) | 16.1748 | + | 4.33402i | 0.997380 | + | 0.267247i | 0.720347 | − | 0.693614i | \(-0.243982\pi\) |
0.277032 | + | 0.960861i | \(0.410649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.524304 | + | 4.11611i | 0.0322078 | + | 0.252851i | ||||
\(266\) | 11.9243 | + | 6.88452i | 0.731128 | + | 0.422117i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.85782 | − | 10.6655i | 0.174569 | − | 0.651500i | ||||
\(269\) | −0.535741 | −0.0326647 | −0.0163324 | − | 0.999867i | \(-0.505199\pi\) | ||||
−0.0163324 | + | 0.999867i | \(0.505199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5412 | −0.944063 | −0.472032 | − | 0.881582i | \(-0.656479\pi\) | ||||
−0.472032 | + | 0.881582i | \(0.656479\pi\) | |||||||
\(272\) | 1.61368 | − | 6.02233i | 0.0978437 | − | 0.365158i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.81385 | − | 1.62458i | −0.169991 | − | 0.0981442i | ||||
\(275\) | 16.8200 | + | 17.1052i | 1.01428 | + | 1.03148i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.7200 | + | 4.48011i | 1.00461 | + | 0.269184i | 0.723374 | − | 0.690456i | \(-0.242590\pi\) |
0.281232 | + | 0.959640i | \(0.409257\pi\) | |||||||
\(278\) | 15.5525 | − | 15.5525i | 0.932775 | − | 0.932775i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.798810 | − | 5.87657i | 0.0477380 | − | 0.351192i | ||||
\(281\) | 20.8909 | − | 12.0613i | 1.24624 | − | 0.719519i | 0.275886 | − | 0.961190i | \(-0.411029\pi\) |
0.970358 | + | 0.241671i | \(0.0776955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9876 | − | 4.28387i | 0.950365 | − | 0.254649i | 0.249848 | − | 0.968285i | \(-0.419619\pi\) |
0.700517 | + | 0.713636i | \(0.252953\pi\) | |||||||
\(284\) | 5.21013 | − | 9.02421i | 0.309164 | − | 0.535489i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.44505 | − | 2.50289i | −0.0854474 | − | 0.147999i | ||||
\(287\) | −12.0957 | − | 12.0957i | −0.713987 | − | 0.713987i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.8725i | 1.28661i | ||||||||
\(290\) | 1.59081 | − | 3.79535i | 0.0934156 | − | 0.222871i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.20796 | − | 4.50818i | −0.0706906 | − | 0.263821i | ||||
\(293\) | −4.18032 | − | 15.6012i | −0.244217 | − | 0.911431i | −0.973775 | − | 0.227512i | \(-0.926941\pi\) |
0.729558 | − | 0.683919i | \(-0.239726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.109345 | + | 0.267153i | 0.00636631 | + | 0.0155542i | ||||
\(296\) | − | 0.893864i | − | 0.0519548i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.28669 | − | 9.28669i | −0.537964 | − | 0.537964i | ||||
\(299\) | 0.792727 | + | 1.37304i | 0.0458446 | + | 0.0794052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.30185 | − | 5.71897i | 0.190315 | − | 0.329636i | ||||
\(302\) | 0.324356 | − | 0.0869109i | 0.0186646 | − | 0.00500116i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.49593 | + | 2.59573i | −0.257859 | + | 0.148875i | ||||
\(305\) | −27.7959 | − | 3.77833i | −1.59159 | − | 0.216347i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.45642 | + | 1.45642i | −0.0831222 | + | 0.0831222i | −0.747445 | − | 0.664323i | \(-0.768720\pi\) |
0.664323 | + | 0.747445i | \(0.268720\pi\) | |||||||
\(308\) | −12.2917 | − | 3.29355i | −0.700384 | − | 0.187667i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.04507 | − | 1.15215i | 0.513725 | − | 0.0654376i | ||||
\(311\) | 1.81462 | + | 1.04767i | 0.102898 | + | 0.0594081i | 0.550566 | − | 0.834792i | \(-0.314412\pi\) |
−0.447668 | + | 0.894200i | \(0.647745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.11217 | + | 19.0789i | −0.288957 | + | 1.07840i | 0.656942 | + | 0.753941i | \(0.271850\pi\) |
−0.945899 | + | 0.324461i | \(0.894817\pi\) | |||||||
\(314\) | 4.55886 | 0.257271 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.18916 | −0.235659 | ||||||||
\(317\) | −8.82217 | + | 32.9248i | −0.495503 | + | 1.84924i | 0.0316937 | + | 0.999498i | \(0.489910\pi\) |
−0.527196 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.64709 | − | 4.41505i | −0.428155 | − | 0.247195i | ||||
\(320\) | 1.76825 | + | 1.36868i | 0.0988484 | + | 0.0765114i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.74301 | + | 1.80678i | 0.375773 | + | 0.100688i | ||||
\(323\) | 22.8873 | − | 22.8873i | 1.27348 | − | 1.27348i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.48393 | − | 2.62088i | −0.0823135 | − | 0.145380i | ||||
\(326\) | −11.0410 | + | 6.37454i | −0.611506 | + | 0.353053i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.22982 | − | 1.66927i | 0.343984 | − | 0.0921703i | ||||
\(329\) | −5.25381 | + | 9.09987i | −0.289652 | + | 0.501692i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0140 | − | 20.8088i | −0.660348 | − | 1.14376i | −0.980524 | − | 0.196399i | \(-0.937075\pi\) |
0.320176 | − | 0.947358i | \(-0.396258\pi\) | |||||||
\(332\) | 8.13293 | + | 8.13293i | 0.446353 | + | 0.446353i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.00888621i | 0.000486232i | ||||||||
\(335\) | −22.7708 | − | 9.54429i | −1.24410 | − | 0.521460i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.17090 | + | 11.8340i | 0.172730 | + | 0.644637i | 0.996927 | + | 0.0783338i | \(0.0249600\pi\) |
−0.824197 | + | 0.566303i | \(0.808373\pi\) | |||||||
\(338\) | −3.27074 | − | 12.2066i | −0.177905 | − | 0.663949i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.8576 | − | 5.38923i | −0.697302 | − | 0.292272i | ||||
\(341\) | − | 19.5648i | − | 1.05949i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0634 | + | 13.0634i | 0.705357 | + | 0.705357i | ||||
\(344\) | 1.24492 | + | 2.15627i | 0.0671217 | + | 0.116258i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.19145 | + | 8.99186i | −0.279094 | + | 0.483405i | ||||
\(347\) | 17.9559 | − | 4.81127i | 0.963924 | − | 0.258283i | 0.257663 | − | 0.966235i | \(-0.417047\pi\) |
0.706260 | + | 0.707952i | \(0.250381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2305 | − | 15.7215i | 1.45761 | − | 0.841553i | 0.458720 | − | 0.888581i | \(-0.348308\pi\) |
0.998894 | + | 0.0470278i | \(0.0149749\pi\) | |||||||
\(350\) | −12.7801 | − | 3.53983i | −0.683124 | − | 0.189212i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.39264 | − | 3.39264i | 0.180829 | − | 0.180829i | ||||
\(353\) | −11.7440 | − | 3.14681i | −0.625073 | − | 0.167488i | −0.0676398 | − | 0.997710i | \(-0.521547\pi\) |
−0.557433 | + | 0.830222i | \(0.688214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.4257 | − | 14.2620i | −0.977933 | − | 0.756947i | ||||
\(356\) | 1.77526 | + | 1.02494i | 0.0940883 | + | 0.0543219i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.378631 | − | 1.41307i | 0.0200112 | − | 0.0746830i | ||||
\(359\) | 4.31606 | 0.227793 | 0.113896 | − | 0.993493i | \(-0.463667\pi\) | ||||
0.113896 | + | 0.993493i | \(0.463667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.95119 | −0.418484 | ||||||||
\(362\) | 2.24804 | − | 8.38980i | 0.118154 | − | 0.440958i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.38358 | + | 0.798810i | 0.0725192 | + | 0.0418690i | ||||
\(365\) | −10.3525 | + | 1.31869i | −0.541877 | + | 0.0690235i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2008 | − | 5.14485i | −1.00228 | − | 0.268559i | −0.279877 | − | 0.960036i | \(-0.590294\pi\) |
−0.722399 | + | 0.691477i | \(0.756960\pi\) | |||||||
\(368\) | −1.86115 | + | 1.86115i | −0.0970189 | + | 0.0970189i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.98053 | − | 0.269215i | −0.102963 | − | 0.0139958i | ||||
\(371\) | −4.26229 | + | 2.46083i | −0.221287 | + | 0.127760i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.53800 | − | 0.680056i | 0.131413 | − | 0.0352120i | −0.192513 | − | 0.981294i | \(-0.561664\pi\) |
0.323926 | + | 0.946082i | \(0.394997\pi\) | |||||||
\(374\) | −14.9570 | + | 25.9063i | −0.773408 | + | 1.33958i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.98089 | − | 3.43100i | −0.102157 | − | 0.176940i | ||||
\(377\) | 0.783892 | + | 0.783892i | 0.0403725 | + | 0.0403725i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.03124i | 0.155705i | 0.996965 | + | 0.0778523i | \(0.0248063\pi\) | ||||
−0.996965 | + | 0.0778523i | \(0.975194\pi\) | |||||||
\(380\) | 4.39724 | + | 10.7434i | 0.225574 | + | 0.551124i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.29643 | + | 4.83835i | 0.0663313 | + | 0.247552i | ||||
\(383\) | 6.14717 | + | 22.9416i | 0.314106 | + | 1.17226i | 0.924819 | + | 0.380407i | \(0.124216\pi\) |
−0.610713 | + | 0.791852i | \(0.709117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9995 | + | 26.2426i | −0.560588 | + | 1.33745i | ||||
\(386\) | − | 3.36832i | − | 0.171443i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.2336 | + | 12.2336i | 0.621069 | + | 0.621069i | ||||
\(389\) | −3.33254 | − | 5.77213i | −0.168966 | − | 0.292659i | 0.769090 | − | 0.639140i | \(-0.220710\pi\) |
−0.938057 | + | 0.346482i | \(0.887376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.20515 | − | 14.2117i | 0.414952 | − | 0.718718i | ||||
\(392\) | 0.0332644 | − | 0.00891317i | 0.00168011 | − | 0.000450183i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.9869 | + | 10.9621i | −0.956545 | + | 0.552261i | ||||
\(395\) | −1.26170 | + | 9.28189i | −0.0634829 | + | 0.467022i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2242 | + | 13.2242i | −0.663703 | + | 0.663703i | −0.956251 | − | 0.292548i | \(-0.905497\pi\) |
0.292548 | + | 0.956251i | \(0.405497\pi\) | |||||||
\(398\) | −17.8316 | − | 4.77797i | −0.893819 | − | 0.239498i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.56513 | − | 3.50569i | 0.178257 | − | 0.175284i | ||||
\(401\) | −4.66934 | − | 2.69585i | −0.233176 | − | 0.134624i | 0.378860 | − | 0.925454i | \(-0.376316\pi\) |
−0.612036 | + | 0.790830i | \(0.709649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.635736 | + | 2.37260i | −0.0316683 | + | 0.118188i | ||||
\(404\) | −11.9619 | −0.595129 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.88121 | 0.242250 | ||||||||
\(407\) | −1.10999 | + | 4.14256i | −0.0550204 | + | 0.205339i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.43574 | − | 4.29303i | −0.367674 | − | 0.212277i | 0.304768 | − | 0.952427i | \(-0.401421\pi\) |
−0.672442 | + | 0.740150i | \(0.734754\pi\) | |||||||
\(410\) | −1.82229 | − | 14.3061i | −0.0899965 | − | 0.706528i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.4055 | + | 2.78816i | 0.512644 | + | 0.137363i | ||||
\(413\) | −0.242107 | + | 0.242107i | −0.0119133 | + | 0.0119133i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.4696 | − | 15.5706i | 1.00481 | − | 0.764329i | ||||
\(416\) | −0.521662 | + | 0.301182i | −0.0255766 | + | 0.0147666i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.0595 | − | 6.44672i | 1.17679 | − | 0.315319i | ||||
\(419\) | −7.72749 | + | 13.3844i | −0.377512 | + | 0.653871i | −0.990700 | − | 0.136067i | \(-0.956554\pi\) |
0.613187 | + | 0.789938i | \(0.289887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.45129 | + | 16.3701i | 0.460628 | + | 0.797831i | 0.998992 | − | 0.0448812i | \(-0.0142909\pi\) |
−0.538364 | + | 0.842712i | \(0.680958\pi\) | |||||||
\(422\) | 0.925553 | + | 0.925553i | 0.0450552 | + | 0.0450552i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 1.85566i | − | 0.0901186i | ||||||
\(425\) | −15.8134 | + | 26.8654i | −0.767060 | + | 1.30316i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.61157 | − | 32.1388i | −0.416743 | − | 1.55531i | ||||
\(428\) | 1.59355 | + | 5.94722i | 0.0770273 | + | 0.287470i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.15258 | − | 2.10894i | 0.248479 | − | 0.101702i | ||||
\(431\) | − | 3.91428i | − | 0.188544i | −0.995546 | − | 0.0942720i | \(-0.969948\pi\) | ||
0.995546 | − | 0.0942720i | \(-0.0300523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.2049 | − | 27.2049i | −1.30738 | − | 1.30738i | −0.923297 | − | 0.384086i | \(-0.874517\pi\) |
−0.384086 | − | 0.923297i | \(-0.625483\pi\) | |||||||
\(434\) | 5.40762 | + | 9.36628i | 0.259574 | + | 0.449596i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.72730 | + | 13.3841i | −0.370070 | + | 0.640981i | ||||
\(437\) | −13.1986 | + | 3.53656i | −0.631375 | + | 0.169176i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2725 | + | 7.66286i | −0.633460 | + | 0.365728i | −0.782091 | − | 0.623164i | \(-0.785847\pi\) |
0.148631 | + | 0.988893i | \(0.452513\pi\) | |||||||
\(440\) | −6.49525 | − | 8.53886i | −0.309649 | − | 0.407074i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.65561 | − | 2.65561i | 0.126315 | − | 0.126315i | ||||
\(443\) | 26.8719 | + | 7.20031i | 1.27672 | + | 0.342097i | 0.832603 | − | 0.553870i | \(-0.186850\pi\) |
0.444120 | + | 0.895967i | \(0.353516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.80563 | − | 3.62472i | 0.133000 | − | 0.171828i | ||||
\(446\) | 18.1659 | + | 10.4881i | 0.860180 | + | 0.496625i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.686453 | + | 2.56188i | −0.0324319 | + | 0.121037i | ||||
\(449\) | 24.3627 | 1.14975 | 0.574874 | − | 0.818242i | \(-0.305051\pi\) | ||||
0.574874 | + | 0.818242i | \(0.305051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.9446 | −1.45712 | ||||||||
\(452\) | −1.53568 | + | 5.73124i | −0.0722324 | + | 0.269575i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.15716 | − | 2.97749i | −0.242037 | − | 0.139740i | ||||
\(455\) | 2.18662 | − | 2.82500i | 0.102511 | − | 0.132438i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6705 | − | 3.39506i | −0.592702 | − | 0.158814i | −0.0500141 | − | 0.998749i | \(-0.515927\pi\) |
−0.542688 | + | 0.839935i | \(0.682593\pi\) | |||||||
\(458\) | −8.31377 | + | 8.31377i | −0.388477 | + | 0.388477i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.56318 | + | 4.68427i | 0.166134 | + | 0.218405i | ||||
\(461\) | −34.7684 | + | 20.0736i | −1.61933 | + | 0.934919i | −0.632233 | + | 0.774778i | \(0.717861\pi\) |
−0.987094 | + | 0.160141i | \(0.948805\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5688 | + | 3.09986i | −0.537649 | + | 0.144063i | −0.517418 | − | 0.855733i | \(-0.673107\pi\) |
−0.0202307 | + | 0.999795i | \(0.506440\pi\) | |||||||
\(464\) | −0.920201 | + | 1.59383i | −0.0427192 | + | 0.0739919i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.49800 | − | 16.4510i | −0.439986 | − | 0.762079i | ||||
\(467\) | −8.63124 | − | 8.63124i | −0.399406 | − | 0.399406i | 0.478617 | − | 0.878024i | \(-0.341138\pi\) |
−0.878024 | + | 0.478617i | \(0.841138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 29.2855i | − | 1.35228i | ||||||
\(470\) | −8.19864 | + | 3.35568i | −0.378175 | + | 0.154786i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0334121 | − | 0.124696i | −0.00153792 | − | 0.00573959i | ||||
\(473\) | −3.09188 | − | 11.5390i | −0.142165 | − | 0.530565i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.1284 | − | 6.50721i | 1.15297 | − | 0.298571i | ||||
\(476\) | − | 16.5362i | − | 0.757935i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.22360 | + | 3.22360i | 0.147444 | + | 0.147444i | ||||
\(479\) | −5.13488 | − | 8.89388i | −0.234619 | − | 0.406372i | 0.724543 | − | 0.689230i | \(-0.242051\pi\) |
−0.959162 | + | 0.282858i | \(0.908718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.269215 | − | 0.466295i | 0.0122752 | − | 0.0212612i | ||||
\(482\) | −15.5148 | + | 4.15717i | −0.706678 | + | 0.189354i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.4097 | + | 6.01003i | −0.473167 | + | 0.273183i | ||||
\(485\) | 30.7905 | − | 23.4214i | 1.39812 | − | 1.06351i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5218 | − | 17.5218i | 0.793987 | − | 0.793987i | −0.188153 | − | 0.982140i | \(-0.560250\pi\) |
0.982140 | + | 0.188153i | \(0.0602500\pi\) | |||||||
\(488\) | 12.1176 | + | 3.24689i | 0.548536 | + | 0.146980i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.00973020 | − | 0.0763881i | −0.000439566 | − | 0.00345086i | ||||
\(491\) | 7.70100 | + | 4.44617i | 0.347541 | + | 0.200653i | 0.663602 | − | 0.748086i | \(-0.269027\pi\) |
−0.316061 | + | 0.948739i | \(0.602360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.96982 | − | 11.0835i | 0.133754 | − | 0.499176i | ||||
\(494\) | −3.12714 | −0.140697 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.07776 | −0.183097 | ||||||||
\(497\) | 7.15302 | − | 26.6954i | 0.320857 | − | 1.19745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.4186 | + | 14.6754i | 1.13789 | + | 0.656963i | 0.945908 | − | 0.324435i | \(-0.105174\pi\) |
0.191985 | + | 0.981398i | \(0.438507\pi\) | |||||||
\(500\) | −6.69377 | − | 8.95508i | −0.299354 | − | 0.400483i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.3507 | − | 4.91707i | −0.819034 | − | 0.219459i | ||||
\(503\) | −10.0766 | + | 10.0766i | −0.449293 | + | 0.449293i | −0.895120 | − | 0.445826i | \(-0.852910\pi\) |
0.445826 | + | 0.895120i | \(0.352910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.60272 | + | 26.5040i | −0.160319 | + | 1.17941i | ||||
\(506\) | 10.9365 | − | 6.31420i | 0.486188 | − | 0.280701i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.44015 | + | 0.921786i | −0.152632 | + | 0.0408976i | ||||
\(509\) | 15.0024 | − | 25.9849i | 0.664970 | − | 1.15176i | −0.314323 | − | 0.949316i | \(-0.601777\pi\) |
0.979293 | − | 0.202446i | \(-0.0648892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.18930 | − | 10.7202i | −0.273799 | − | 0.474233i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.35128i | − | 0.147819i | ||||||
\(515\) | 9.31166 | − | 22.2157i | 0.410321 | − | 0.978943i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.91971 | + | 18.3606i | 0.216369 | + | 0.807499i | ||||
\(518\) | −0.613596 | − | 2.28997i | −0.0269598 | − | 0.100615i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.510211 | + | 1.24655i | 0.0223742 | + | 0.0546649i | ||||
\(521\) | − | 6.40485i | − | 0.280602i | −0.990109 | − | 0.140301i | \(-0.955193\pi\) | ||
0.990109 | − | 0.140301i | \(-0.0448070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0596 | + | 16.0596i | 0.702237 | + | 0.702237i | 0.964890 | − | 0.262653i | \(-0.0845974\pi\) |
−0.262653 | + | 0.964890i | \(0.584597\pi\) | |||||||
\(524\) | 6.52997 | + | 11.3102i | 0.285263 | + | 0.494090i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.37268 | + | 14.5019i | −0.365066 | + | 0.632313i | ||||
\(527\) | 24.5576 | − | 6.58020i | 1.06975 | − | 0.286638i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.9190 | − | 8.03614i | 0.605174 | − | 0.349397i | ||||
\(530\) | −4.11156 | − | 0.558889i | −0.178595 | − | 0.0242766i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.73618 | + | 9.73618i | −0.422117 | + | 0.422117i | ||||
\(533\) | 3.75261 | + | 1.00551i | 0.162544 | + | 0.0435535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6572 | − | 1.73963i | 0.590450 | − | 0.0752107i | ||||
\(536\) | 9.56244 | + | 5.52087i | 0.413034 | + | 0.238465i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.138660 | − | 0.517486i | 0.00597806 | − | 0.0223104i | ||||
\(539\) | −0.165230 | −0.00711696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.6389 | 1.91917 | 0.959587 | − | 0.281412i | \(-0.0908026\pi\) | ||||
0.959587 | + | 0.281412i | \(0.0908026\pi\) | |||||||
\(542\) | 4.02237 | − | 15.0117i | 0.172776 | − | 0.644807i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.39948 | + | 3.11739i | 0.231501 | + | 0.133657i | ||||
\(545\) | 27.3276 | + | 21.1523i | 1.17059 | + | 0.906067i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.15053 | + | 1.38008i | 0.220221 | + | 0.0590080i | 0.367242 | − | 0.930125i | \(-0.380302\pi\) |
−0.147022 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(548\) | 2.29750 | − | 2.29750i | 0.0981442 | − | 0.0981442i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.8757 | + | 11.8197i | −0.890144 | + | 0.503995i | ||||
\(551\) | −8.27432 | + | 4.77718i | −0.352498 | + | 0.203515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7321 | + | 2.87566i | −0.456376 | + | 0.122286i | ||||
\(554\) | −8.65490 | + | 14.9907i | −0.367712 | + | 0.636895i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.9973 | + | 19.0478i | 0.466388 | + | 0.807807i | ||||
\(557\) | −4.10329 | − | 4.10329i | −0.173862 | − | 0.173862i | 0.614812 | − | 0.788674i | \(-0.289232\pi\) |
−0.788674 | + | 0.614812i | \(0.789232\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.49979i | 0.0634344i | ||||||||
\(560\) | 5.46959 | + | 2.29256i | 0.231132 | + | 0.0968783i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.24341 | + | 23.3007i | 0.263362 | + | 0.982882i | ||||
\(563\) | −1.53547 | − | 5.73047i | −0.0647125 | − | 0.241510i | 0.925992 | − | 0.377544i | \(-0.123231\pi\) |
−0.990704 | + | 0.136033i | \(0.956565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2361 | + | 5.12874i | 0.514778 | + | 0.215768i | ||||
\(566\) | 16.5516i | 0.695715i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.36824 | + | 7.36824i | 0.309164 | + | 0.309164i | ||||
\(569\) | −17.6714 | − | 30.6077i | −0.740822 | − | 1.28314i | −0.952122 | − | 0.305720i | \(-0.901103\pi\) |
0.211300 | − | 0.977421i | \(-0.432230\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50529 | − | 2.60725i | 0.0629946 | − | 0.109110i | −0.832808 | − | 0.553562i | \(-0.813268\pi\) |
0.895803 | + | 0.444452i | \(0.146602\pi\) | |||||||
\(572\) | 2.79162 | − | 0.748011i | 0.116723 | − | 0.0312759i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.8142 | − | 8.55296i | 0.618331 | − | 0.356993i | ||||
\(575\) | 11.4521 | − | 6.48410i | 0.477584 | − | 0.270405i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5350 | + | 11.5350i | −0.480208 | + | 0.480208i | −0.905198 | − | 0.424990i | \(-0.860278\pi\) |
0.424990 | + | 0.905198i | \(0.360278\pi\) | |||||||
\(578\) | −21.1272 | − | 5.66101i | −0.878774 | − | 0.235467i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.25430 | + | 2.51891i | 0.135127 | + | 0.104592i | ||||
\(581\) | 26.4185 | + | 15.2527i | 1.09602 | + | 0.632789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.30434 | + | 8.59992i | −0.0954361 | + | 0.356172i | ||||
\(584\) | 4.66721 | 0.193130 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.1515 | 0.667214 | ||||||||
\(587\) | 2.95165 | − | 11.0157i | 0.121828 | − | 0.454666i | −0.877879 | − | 0.478882i | \(-0.841042\pi\) |
0.999707 | + | 0.0242156i | \(0.00770882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3333 | − | 10.5848i | −0.755412 | − | 0.436137i | ||||
\(590\) | −0.286351 | + | 0.0364749i | −0.0117889 | + | 0.00150165i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.863406 | + | 0.231349i | 0.0354858 | + | 0.00950838i | ||||
\(593\) | −23.4664 | + | 23.4664i | −0.963651 | + | 0.963651i | −0.999362 | − | 0.0357109i | \(-0.988630\pi\) |
0.0357109 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.6391 | − | 4.98040i | −1.50206 | − | 0.204177i | ||||
\(596\) | 11.3738 | − | 6.56668i | 0.465890 | − | 0.268982i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.53143 | + | 0.410346i | −0.0626249 | + | 0.0167803i | ||||
\(599\) | 17.2683 | − | 29.9097i | 0.705566 | − | 1.22208i | −0.260922 | − | 0.965360i | \(-0.584026\pi\) |
0.966487 | − | 0.256715i | \(-0.0826403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.57759 | − | 2.73247i | −0.0643513 | − | 0.111460i | 0.832055 | − | 0.554694i | \(-0.187164\pi\) |
−0.896406 | + | 0.443234i | \(0.853831\pi\) | |||||||
\(602\) | 4.66952 | + | 4.66952i | 0.190315 | + | 0.190315i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.335798i | 0.0136634i | ||||||||
\(605\) | 10.1812 | + | 24.8748i | 0.413924 | + | 1.01130i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.32070 | + | 4.92890i | 0.0536054 | + | 0.200058i | 0.987535 | − | 0.157399i | \(-0.0503107\pi\) |
−0.933930 | + | 0.357456i | \(0.883644\pi\) | |||||||
\(608\) | −1.34365 | − | 5.01456i | −0.0544921 | − | 0.203367i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.8437 | − | 25.8709i | 0.439048 | − | 1.04748i | ||||
\(611\) | − | 2.38643i | − | 0.0965446i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.09622 | − | 9.09622i | −0.367393 | − | 0.367393i | 0.499133 | − | 0.866525i | \(-0.333652\pi\) |
−0.866525 | + | 0.499133i | \(0.833652\pi\) | |||||||
\(614\) | −1.02984 | − | 1.78374i | −0.0415611 | − | 0.0719859i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.36265 | − | 11.0204i | 0.256358 | − | 0.444026i | ||||
\(617\) | −23.2998 | + | 6.24315i | −0.938013 | + | 0.251340i | −0.695268 | − | 0.718751i | \(-0.744714\pi\) |
−0.242745 | + | 0.970090i | \(0.578048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9280 | − | 15.5469i | 1.08233 | − | 0.624883i | 0.150806 | − | 0.988563i | \(-0.451813\pi\) |
0.931524 | + | 0.363680i | \(0.118480\pi\) | |||||||
\(620\) | −1.22815 | + | 9.03506i | −0.0493236 | + | 0.362857i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.48163 | + | 1.48163i | −0.0594081 | + | 0.0594081i | ||||
\(623\) | 5.25156 | + | 1.40715i | 0.210399 | + | 0.0563764i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.8577 | + | 12.1342i | −0.874310 | + | 0.485369i | ||||
\(626\) | −17.1057 | − | 9.87595i | −0.683679 | − | 0.394723i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.17992 | + | 4.40352i | −0.0470839 | + | 0.175719i | ||||
\(629\) | −5.57304 | −0.222212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1604 | 1.83762 | 0.918809 | − | 0.394703i | \(-0.129153\pi\) | ||||
0.918809 | + | 0.394703i | \(0.129153\pi\) | |||||||
\(632\) | 1.08423 | − | 4.04642i | 0.0431285 | − | 0.160958i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.5196 | − | 17.0431i | −1.17237 | − | 0.676869i | ||||
\(635\) | 1.00628 | + | 7.89994i | 0.0399331 | + | 0.313500i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0200372 | + | 0.00536896i | 0.000793905 | + | 0.000212726i | ||||
\(638\) | 6.24383 | − | 6.24383i | 0.247195 | − | 0.247195i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.77970 | + | 1.35376i | −0.0703487 | + | 0.0535122i | ||||
\(641\) | 3.41084 | − | 1.96925i | 0.134720 | − | 0.0777808i | −0.431125 | − | 0.902292i | \(-0.641883\pi\) |
0.565845 | + | 0.824511i | \(0.308550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9917 | + | 8.03625i | −1.18276 | + | 0.316919i | −0.796019 | − | 0.605271i | \(-0.793065\pi\) |
−0.386737 | + | 0.922190i | \(0.626398\pi\) | |||||||
\(644\) | −3.49044 | + | 6.04562i | −0.137543 | + | 0.238231i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.1838 | + | 28.0311i | 0.636742 | + | 1.10287i | ||||
\(647\) | 18.0986 | + | 18.0986i | 0.711531 | + | 0.711531i | 0.966855 | − | 0.255325i | \(-0.0821824\pi\) |
−0.255325 | + | 0.966855i | \(0.582182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.619386i | 0.0243130i | ||||||||
\(650\) | 2.91564 | − | 0.755031i | 0.114361 | − | 0.0296147i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.29971 | − | 12.3147i | −0.129226 | − | 0.482280i | ||||
\(653\) | −3.63685 | − | 13.5729i | −0.142321 | − | 0.531148i | −0.999860 | − | 0.0167299i | \(-0.994674\pi\) |
0.857539 | − | 0.514419i | \(-0.171992\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0267 | − | 11.0620i | 1.05602 | − | 0.432227i | ||||
\(656\) | 6.44958i | 0.251814i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.43002 | − | 7.43002i | −0.289652 | − | 0.289652i | ||||
\(659\) | 18.2709 | + | 31.6462i | 0.711734 | + | 1.23276i | 0.964206 | + | 0.265155i | \(0.0854233\pi\) |
−0.252471 | + | 0.967604i | \(0.581243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.9365 | + | 31.0670i | −0.697650 | + | 1.20836i | 0.271629 | + | 0.962402i | \(0.412438\pi\) |
−0.969279 | + | 0.245963i | \(0.920896\pi\) | |||||||
\(662\) | 23.2092 | − | 6.21890i | 0.902053 | − | 0.241704i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.96076 | + | 5.75085i | −0.386553 | + | 0.223176i | ||||
\(665\) | 18.6400 | + | 24.5047i | 0.722829 | + | 0.950253i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.42525 | + | 3.42525i | −0.132626 | + | 0.132626i | ||||
\(668\) | −0.00858342 | − | 0.00229992i | −0.000332102 | − | 8.89866e-5i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.1126 | − | 19.5246i | 0.583850 | − | 0.754302i | ||||
\(671\) | −52.1261 | − | 30.0950i | −2.01231 | − | 1.16181i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.49200 | + | 24.2285i | −0.250248 | + | 0.933939i | 0.720424 | + | 0.693534i | \(0.243947\pi\) |
−0.970673 | + | 0.240406i | \(0.922720\pi\) | |||||||
\(674\) | −12.2514 | −0.471907 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.6372 | 0.486045 | ||||||||
\(677\) | −1.40152 | + | 5.23054i | −0.0538647 | + | 0.201026i | −0.987614 | − | 0.156901i | \(-0.949850\pi\) |
0.933750 | + | 0.357927i | \(0.116516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.7389 | + | 22.9433i | 1.52504 | + | 0.880481i | ||||
\(680\) | 8.53340 | − | 11.0247i | 0.327241 | − | 0.422777i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.8981 | + | 5.06374i | 0.723647 | + | 0.193901i | ||||
\(683\) | −14.3302 | + | 14.3302i | −0.548331 | + | 0.548331i | −0.925958 | − | 0.377627i | \(-0.876740\pi\) |
0.377627 | + | 0.925958i | \(0.376740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.39858 | − | 5.78251i | −0.168061 | − | 0.220938i | ||||
\(686\) | −15.9993 | + | 9.23721i | −0.610857 | + | 0.352678i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.40501 | + | 0.644420i | −0.0916900 | + | 0.0245683i | ||||
\(689\) | 0.558889 | − | 0.968025i | 0.0212920 | − | 0.0368788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.85991 | − | 10.1497i | −0.222921 | − | 0.386111i | 0.732772 | − | 0.680474i | \(-0.238226\pi\) |
−0.955694 | + | 0.294363i | \(0.904893\pi\) | |||||||
\(692\) | −7.34182 | − | 7.34182i | −0.279094 | − | 0.279094i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5893i | 0.705641i | ||||||||
\(695\) | 45.5162 | − | 18.6297i | 1.72653 | − | 0.706664i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.4076 | − | 38.8415i | −0.394214 | − | 1.47123i | ||||
\(698\) | 8.13805 | + | 30.3716i | 0.308030 | + | 1.14958i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.72694 | − | 11.4284i | 0.254255 | − | 0.431954i | ||||
\(701\) | 30.7235i | 1.16041i | 0.814471 | + | 0.580205i | \(0.197028\pi\) | ||||
−0.814471 | + | 0.580205i | \(0.802972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.28129 | + | 3.28129i | 0.123756 | + | 0.123756i | ||||
\(704\) | 2.39896 | + | 4.15512i | 0.0904143 | + | 0.156602i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.07917 | − | 10.5294i | 0.228792 | − | 0.396280i | ||||
\(707\) | −30.6451 | + | 8.21132i | −1.15253 | + | 0.308818i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.4879 | + | 15.8701i | −1.03233 | + | 0.596015i | −0.917651 | − | 0.397387i | \(-0.869917\pi\) |
−0.114678 | + | 0.993403i | \(0.536584\pi\) | |||||||
\(710\) | 18.5449 | − | 14.1066i | 0.695979 | − | 0.529410i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.44949 | + | 1.44949i | −0.0543219 | + | 0.0543219i | ||||
\(713\) | −10.3672 | − | 2.77788i | −0.388254 | − | 0.104032i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.816579 | − | 6.41065i | −0.0305383 | − | 0.239745i | ||||
\(716\) | 1.26692 | + | 0.731458i | 0.0473471 | + | 0.0273359i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.11708 | + | 4.16899i | −0.0416890 | + | 0.155585i | ||||
\(719\) | 7.79879 | 0.290846 | 0.145423 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145423 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.5717 | 1.06407 | ||||||||
\(722\) | 2.05792 | − | 7.68026i | 0.0765878 | − | 0.285830i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.52209 | + | 4.34288i | 0.279556 | + | 0.161402i | ||||
\(725\) | 6.56127 | − | 6.45187i | 0.243680 | − | 0.239616i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.7863 | − | 11.4645i | −1.58685 | − | 0.425196i | −0.645815 | − | 0.763494i | \(-0.723482\pi\) |
−0.941039 | + | 0.338297i | \(0.890149\pi\) | |||||||
\(728\) | −1.12969 | + | 1.12969i | −0.0418690 | + | 0.0418690i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.40568 | − | 10.3411i | 0.0520265 | − | 0.382741i | ||||
\(731\) | 13.4439 | − | 7.76182i | 0.497239 | − | 0.287081i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.9304 | − | 7.21598i | 0.994697 | − | 0.266528i | 0.275475 | − | 0.961308i | \(-0.411165\pi\) |
0.719222 | + | 0.694780i | \(0.244498\pi\) | |||||||
\(734\) | 9.93909 | − | 17.2150i | 0.366858 | − | 0.635418i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.31603 | − | 2.27943i | −0.0485095 | − | 0.0840208i | ||||
\(737\) | −37.4607 | − | 37.4607i | −1.37988 | − | 1.37988i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 10.8068i | − | 0.397536i | −0.980047 | − | 0.198768i | \(-0.936306\pi\) | ||
0.980047 | − | 0.198768i | \(-0.0636941\pi\) | |||||||
\(740\) | 0.772640 | − | 1.84336i | 0.0284028 | − | 0.0677634i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.27382 | − | 4.75396i | −0.0467634 | − | 0.174523i | ||||
\(743\) | 5.75762 | + | 21.4877i | 0.211227 | + | 0.788309i | 0.987461 | + | 0.157864i | \(0.0504608\pi\) |
−0.776234 | + | 0.630445i | \(0.782873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.1242 | − | 27.1787i | −0.407558 | − | 0.995749i | ||||
\(746\) | 2.62754i | 0.0962009i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.1524 | − | 21.1524i | −0.773408 | − | 0.773408i | ||||
\(749\) | 8.16498 | + | 14.1422i | 0.298342 | + | 0.516743i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6235 | + | 35.7209i | −0.752561 | + | 1.30347i | 0.194017 | + | 0.980998i | \(0.437848\pi\) |
−0.946578 | + | 0.322476i | \(0.895485\pi\) | |||||||
\(752\) | 3.82678 | − | 1.02538i | 0.139548 | − | 0.0373919i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.960067 | + | 0.554295i | −0.0349636 | + | 0.0201862i | ||||
\(755\) | 0.744025 | + | 0.101136i | 0.0270778 | + | 0.00368072i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.5246 | + | 20.5246i | −0.745978 | + | 0.745978i | −0.973721 | − | 0.227743i | \(-0.926865\pi\) |
0.227743 | + | 0.973721i | \(0.426865\pi\) | |||||||
\(758\) | −2.92796 | − | 0.784544i | −0.106348 | − | 0.0284959i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.5154 | + | 1.46681i | −0.417707 | + | 0.0532069i | ||||
\(761\) | −39.8188 | − | 22.9894i | −1.44343 | − | 0.833365i | −0.445353 | − | 0.895355i | \(-0.646922\pi\) |
−0.998077 | + | 0.0619904i | \(0.980255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6089 | + | 39.5928i | −0.384066 | + | 1.43335i | ||||
\(764\) | −5.00903 | −0.181220 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.7508 | −0.858153 | ||||||||
\(767\) | 0.0201262 | − | 0.0751122i | 0.000726717 | − | 0.00271214i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.6702 | + | 15.3980i | 0.961752 | + | 0.555268i | 0.896712 | − | 0.442615i | \(-0.145949\pi\) |
0.0650399 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(770\) | −22.5016 | − | 17.4168i | −0.810900 | − | 0.627659i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.25355 | + | 0.871785i | 0.117098 | + | 0.0313762i | ||||
\(773\) | −29.6376 | + | 29.6376i | −1.06599 | + | 1.06599i | −0.0683287 | + | 0.997663i | \(0.521767\pi\) |
−0.997663 | + | 0.0683287i | \(0.978233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6490 | + | 5.44239i | 0.705814 | + | 0.195496i | ||||
\(776\) | −14.9831 | + | 8.65048i | −0.537861 | + | 0.310534i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.43797 | − | 1.72505i | 0.230813 | − | 0.0618460i | ||||
\(779\) | −16.7414 | + | 28.9969i | −0.599821 | + | 1.03892i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9978 | − | 43.2975i | −0.894492 | − | 1.54931i | ||||
\(782\) | 11.6038 | + | 11.6038i | 0.414952 | + | 0.414952i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0344378i | 0.00122992i | ||||||||
\(785\) | 9.40147 | + | 3.94060i | 0.335553 | + | 0.140646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.98316 | − | 26.0615i | −0.248923 | − | 0.928993i | −0.971371 | − | 0.237568i | \(-0.923650\pi\) |
0.722448 | − | 0.691425i | \(-0.243017\pi\) | |||||||
\(788\) | −5.67439 | − | 21.1771i | −0.202142 | − | 0.754403i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.63906 | − | 3.62104i | −0.307364 | − | 0.128831i | ||||
\(791\) | 15.7369i | 0.559540i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.34337 | + | 5.34337i | 0.189749 | + | 0.189749i | ||||
\(794\) | −9.35091 | − | 16.1963i | −0.331852 | − | 0.574784i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.23033 | − | 15.9874i | 0.327161 | − | 0.566659i | ||||
\(797\) | −6.28188 | + | 1.68322i | −0.222515 | + | 0.0596228i | −0.368354 | − | 0.929686i | \(-0.620079\pi\) |
0.145839 | + | 0.989308i | \(0.453412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.3915 | + | 12.3504i | −0.756778 | + | 0.436926i | ||||
\(800\) | 2.46351 | + | 4.35099i | 0.0870982 | + | 0.153831i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.81250 | − | 3.81250i | 0.134624 | − | 0.134624i | ||||
\(803\) | −21.6299 | − | 5.79571i | −0.763302 | − | 0.204526i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.3440 | + | 9.55456i | 0.435068 | + | 0.336754i | ||||
\(806\) | −2.12721 | − | 1.22815i | −0.0749279 | − | 0.0432596i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.09598 | − | 11.5544i | 0.108916 | − | 0.406481i | ||||
\(809\) | 5.79431 | 0.203717 | 0.101859 | − | 0.994799i | \(-0.467521\pi\) | ||||
0.101859 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90498 | 0.0668929 | 0.0334465 | − | 0.999441i | \(-0.489352\pi\) | ||||
0.0334465 | + | 0.999441i | \(0.489352\pi\) | |||||||
\(812\) | −1.26335 | + | 4.71488i | −0.0443349 | + | 0.165460i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.71411 | − | 2.14434i | −0.130180 | − | 0.0751592i | ||||
\(815\) | −28.2793 | + | 3.60218i | −0.990581 | + | 0.126179i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.4855 | − | 3.34547i | −0.436812 | − | 0.117043i | ||||
\(818\) | 6.07126 | − | 6.07126i | 0.212277 | − | 0.212277i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.2903 | + | 1.94250i | 0.499038 | + | 0.0678349i | ||||
\(821\) | 33.4503 | − | 19.3125i | 1.16742 | − | 0.674012i | 0.214351 | − | 0.976757i | \(-0.431236\pi\) |
0.953072 | + | 0.302745i | \(0.0979030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6711 | − | 5.53879i | 0.720548 | − | 0.193070i | 0.120132 | − | 0.992758i | \(-0.461668\pi\) |
0.600416 | + | 0.799688i | \(0.295002\pi\) | |||||||
\(824\) | −5.38631 | + | 9.32936i | −0.187641 | + | 0.325004i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.171196 | − | 0.296520i | −0.00595666 | − | 0.0103172i | ||||
\(827\) | −23.1603 | − | 23.1603i | −0.805364 | − | 0.805364i | 0.178564 | − | 0.983928i | \(-0.442855\pi\) |
−0.983928 | + | 0.178564i | \(0.942855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.1116i | − | 1.18475i | −0.805664 | − | 0.592373i | \(-0.798191\pi\) | ||
0.805664 | − | 0.592373i | \(-0.201809\pi\) | |||||||
\(830\) | 9.74211 | + | 23.8020i | 0.338154 | + | 0.826181i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.155903 | − | 0.581838i | −0.00540497 | − | 0.0201716i | ||||
\(833\) | −0.0555716 | − | 0.207396i | −0.00192544 | − | 0.00718585i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.00768108 | + | 0.0183255i | −0.000265815 | + | 0.000634180i | ||||
\(836\) | 24.9082i | 0.861468i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.9283 | − | 10.9283i | −0.377512 | − | 0.377512i | ||||
\(839\) | −18.8058 | − | 32.5726i | −0.649249 | − | 1.12453i | −0.983303 | − | 0.181978i | \(-0.941750\pi\) |
0.334054 | − | 0.942554i | \(-0.391583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8065 | − | 22.1814i | 0.441602 | − | 0.764877i | ||||
\(842\) | −18.2585 | + | 4.89235i | −0.629229 | + | 0.168602i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.13357 | + | 0.654465i | −0.0390190 | + | 0.0225276i | ||||
\(845\) | 3.80608 | − | 28.0000i | 0.130933 | − | 0.963231i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5427 | + | 22.5427i | −0.774577 | + | 0.774577i | ||||
\(848\) | 1.79243 | + | 0.480279i | 0.0615521 | + | 0.0164928i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.8572 | − | 22.2278i | −0.749695 | − | 0.762407i | ||||
\(851\) | 2.03750 | + | 1.17635i | 0.0698445 | + | 0.0403248i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.98742 | + | 7.41714i | −0.0680478 | + | 0.253958i | −0.991567 | − | 0.129594i | \(-0.958633\pi\) |
0.923519 | + | 0.383552i | \(0.125299\pi\) | |||||||
\(854\) | 33.2726 | 1.13856 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.15702 | −0.210442 | ||||||||
\(857\) | −1.87635 | + | 7.00264i | −0.0640949 | + | 0.239206i | −0.990540 | − | 0.137224i | \(-0.956182\pi\) |
0.926445 | + | 0.376430i | \(0.122848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.50446 | − | 0.868601i | −0.0513316 | − | 0.0296363i | 0.474115 | − | 0.880463i | \(-0.342768\pi\) |
−0.525446 | + | 0.850827i | \(0.676102\pi\) | |||||||
\(860\) | 0.703491 | + | 5.52284i | 0.0239888 | + | 0.188327i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.78090 | + | 1.01309i | 0.128778 | + | 0.0345060i | ||||
\(863\) | 36.4612 | − | 36.4612i | 1.24115 | − | 1.24115i | 0.281630 | − | 0.959523i | \(-0.409125\pi\) |
0.959523 | − | 0.281630i | \(-0.0908751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.4784 | + | 14.0560i | −0.628286 | + | 0.477918i | ||||
\(866\) | 33.3190 | − | 19.2368i | 1.13223 | − | 0.653692i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.4467 | + | 2.79919i | −0.354585 | + | 0.0950108i | ||||
\(869\) | −10.0496 | + | 17.4065i | −0.340911 | + | 0.590474i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.32557 | + | 5.76006i | 0.112683 | + | 0.195172i | ||||
\(872\) | −10.9280 | − | 10.9280i | −0.370070 | − | 0.370070i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 13.6642i | − | 0.462199i | ||||||
\(875\) | −23.2959 | − | 18.3469i | −0.787544 | − | 0.620237i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.68194 | + | 10.0092i | 0.0905628 | + | 0.337985i | 0.996309 | − | 0.0858347i | \(-0.0273557\pi\) |
−0.905747 | + | 0.423820i | \(0.860689\pi\) | |||||||
\(878\) | −3.96659 | − | 14.8035i | −0.133866 | − | 0.499594i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.92900 | − | 4.06391i | 0.334706 | − | 0.136994i | ||||
\(881\) | − | 1.17719i | − | 0.0396604i | −0.999803 | − | 0.0198302i | \(-0.993687\pi\) | ||
0.999803 | − | 0.0198302i | \(-0.00631257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.1929 | − | 22.1929i | −0.746850 | − | 0.746850i | 0.227036 | − | 0.973886i | \(-0.427097\pi\) |
−0.973886 | + | 0.227036i | \(0.927097\pi\) | |||||||
\(884\) | 1.87780 | + | 3.25245i | 0.0631573 | + | 0.109392i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.9099 | + | 24.0927i | −0.467313 | + | 0.809410i | ||||
\(887\) | −8.80492 | + | 2.35927i | −0.295640 | + | 0.0792166i | −0.403590 | − | 0.914940i | \(-0.632238\pi\) |
0.107950 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.18049 | + | 4.72301i | −0.274365 | + | 0.158405i | ||||
\(890\) | 2.77506 | + | 3.64818i | 0.0930203 | + | 0.122287i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.8324 | + | 14.8324i | −0.496625 | + | 0.496625i | ||||
\(893\) | 19.8666 | + | 5.32323i | 0.664809 | + | 0.178135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00226 | − | 2.58681i | 0.0669281 | − | 0.0864674i | ||||
\(896\) | −2.29692 | − | 1.32613i | −0.0767346 | − | 0.0443028i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.30553 | + | 23.5326i | −0.210418 | + | 0.785292i | ||||
\(899\) | −7.50472 | −0.250296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.5696 | −0.385439 | ||||||||
\(902\) | 8.00905 | − | 29.8902i | 0.266672 | − | 0.995234i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.13849 | − | 2.96671i | −0.170904 | − | 0.0986713i | ||||
\(905\) | 11.8880 | − | 15.3586i | 0.395170 | − | 0.510538i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.35203 | + | 1.96997i | 0.244120 | + | 0.0654118i | 0.378804 | − | 0.925477i | \(-0.376335\pi\) |
−0.134684 | + | 0.990889i | \(0.543002\pi\) | |||||||
\(908\) | 4.21080 | − | 4.21080i | 0.139740 | − | 0.139740i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.16280 | + | 2.84328i | 0.0716960 | + | 0.0942538i | ||||
\(911\) | −39.2522 | + | 22.6623i | −1.30048 | + | 0.750835i | −0.980487 | − | 0.196583i | \(-0.937015\pi\) |
−0.319997 | + | 0.947418i | \(0.603682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.3039 | − | 14.2827i | 1.76410 | − | 0.472690i | ||||
\(914\) | 6.55874 | − | 11.3601i | 0.216944 | − | 0.375758i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.87872 | − | 10.1822i | −0.194238 | − | 0.336431i | ||||
\(917\) | 24.4930 | + | 24.4930i | 0.808829 | + | 0.808829i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19.9726i | − | 0.658836i | −0.944184 | − | 0.329418i | \(-0.893148\pi\) | ||
0.944184 | − | 0.329418i | \(-0.106852\pi\) | |||||||
\(920\) | −5.44687 | + | 2.22939i | −0.179578 | + | 0.0735009i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.3908 | − | 38.7791i | −0.342204 | − | 1.27712i | ||||
\(923\) | 1.62455 | + | 6.06291i | 0.0534728 | + | 0.199563i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.85162 | − | 2.26712i | −0.126640 | − | 0.0745424i | ||||
\(926\) | − | 11.9769i | − | 0.393586i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.30136 | − | 1.30136i | −0.0427192 | − | 0.0427192i | ||||
\(929\) | 24.8920 | + | 43.1142i | 0.816681 | + | 1.41453i | 0.908115 | + | 0.418721i | \(0.137522\pi\) |
−0.0914341 | + | 0.995811i | \(0.529145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0893912 | + | 0.154830i | −0.00292968 | + | 0.00507435i | ||||
\(932\) | 18.3487 | − | 4.91653i | 0.601033 | − | 0.161046i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.5711 | − | 6.10321i | 0.345896 | − | 0.199703i | ||||
\(935\) | −53.2379 | + | 40.4964i | −1.74106 | + | 1.32438i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6750 | − | 28.6750i | 0.936771 | − | 0.936771i | −0.0613453 | − | 0.998117i | \(-0.519539\pi\) |
0.998117 | + | 0.0613453i | \(0.0195391\pi\) | |||||||
\(938\) | 28.2876 | + | 7.57964i | 0.923623 | + | 0.247484i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.11938 | − | 8.78780i | −0.0365100 | − | 0.286626i | ||||
\(941\) | 42.4585 | + | 24.5134i | 1.38411 | + | 0.799115i | 0.992643 | − | 0.121078i | \(-0.0386353\pi\) |
0.391464 | + | 0.920193i | \(0.371969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.39363 | + | 16.3972i | −0.143076 | + | 0.533967i | ||||
\(944\) | 0.129095 | 0.00420167 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.9461 | 0.388401 | ||||||||
\(947\) | −11.6667 | + | 43.5407i | −0.379117 | + | 1.41488i | 0.468119 | + | 0.883665i | \(0.344932\pi\) |
−0.847236 | + | 0.531217i | \(0.821735\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.43470 | + | 1.40568i | 0.0790339 | + | 0.0456302i | ||||
\(950\) | −0.218220 | + | 25.9564i | −0.00707998 | + | 0.842135i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.9727 | + | 4.27988i | 0.517679 | + | 0.138712i | ||||
\(953\) | 2.71971 | − | 2.71971i | 0.0881001 | − | 0.0881001i | −0.661683 | − | 0.749783i | \(-0.730158\pi\) |
0.749783 | + | 0.661683i | \(0.230158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50863 | + | 11.0985i | −0.0488181 | + | 0.359138i | ||||
\(956\) | −3.94809 | + | 2.27943i | −0.127690 | + | 0.0737220i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.91983 | − | 2.65801i | 0.320495 | − | 0.0858764i | ||||
\(959\) | 4.30878 | − | 7.46303i | 0.139138 | − | 0.240994i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.18593 | + | 12.4464i | 0.231804 | + | 0.401497i | ||||
\(962\) | 0.380728 | + | 0.380728i | 0.0122752 | + | 0.0122752i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 16.0621i | − | 0.517325i | ||||||
\(965\) | 2.91151 | − | 6.94629i | 0.0937250 | − | 0.223609i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.10886 | + | 30.2627i | 0.260763 | + | 0.973182i | 0.964793 | + | 0.263011i | \(0.0847157\pi\) |
−0.704029 | + | 0.710171i | \(0.748618\pi\) | |||||||
\(968\) | −3.11102 | − | 11.6105i | −0.0999920 | − | 0.373175i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.6542 | + | 35.8032i | 0.470517 | + | 1.14957i | ||||
\(971\) | 31.9680i | 1.02590i | 0.858418 | + | 0.512951i | \(0.171448\pi\) | ||||
−0.858418 | + | 0.512951i | \(0.828552\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.2491 | + | 41.2491i | 1.32238 | + | 1.32238i | ||||
\(974\) | 12.3898 | + | 21.4597i | 0.396993 | + | 0.687613i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.27251 | + | 10.8643i | −0.200778 | + | 0.347758i | ||||
\(977\) | 8.45932 | − | 2.26667i | 0.270638 | − | 0.0725171i | −0.120948 | − | 0.992659i | \(-0.538593\pi\) |
0.391585 | + | 0.920142i | \(0.371927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.51754 | − | 4.91760i | 0.272222 | − | 0.157167i | ||||
\(980\) | 0.0763036 | + | 0.0103720i | 0.00243743 | + | 0.000331323i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.28784 | + | 6.28784i | −0.200653 | + | 0.200653i | ||||
\(983\) | −40.7397 | − | 10.9162i | −1.29940 | − | 0.348172i | −0.458174 | − | 0.888863i | \(-0.651496\pi\) |
−0.841222 | + | 0.540691i | \(0.818163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.6309 | + | 6.19454i | −1.54951 | + | 0.197374i | ||||
\(986\) | 9.93720 | + | 5.73725i | 0.316465 | + | 0.182711i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.809364 | − | 3.02059i | 0.0257493 | − | 0.0960977i | ||||
\(989\) | −6.55342 | −0.208387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9120 | −0.441929 | −0.220964 | − | 0.975282i | \(-0.570920\pi\) | ||||
−0.220964 | + | 0.975282i | \(0.570920\pi\) | |||||||
\(992\) | 1.05540 | − | 3.93882i | 0.0335091 | − | 0.125058i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.9345 | + | 13.8186i | 0.759156 | + | 0.438299i | ||||
\(995\) | −32.6432 | − | 25.2667i | −1.03486 | − | 0.801008i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.2374 | + | 7.83414i | 0.925958 | + | 0.248110i | 0.690130 | − | 0.723685i | \(-0.257553\pi\) |
0.235828 | + | 0.971795i | \(0.424220\pi\) | |||||||
\(998\) | −20.7542 | + | 20.7542i | −0.656963 | + | 0.656963i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 270.2.m.b.233.1 | 16 | ||
3.2 | odd | 2 | 90.2.l.b.23.3 | ✓ | 16 | ||
5.2 | odd | 4 | inner | 270.2.m.b.17.1 | 16 | ||
5.3 | odd | 4 | 1350.2.q.h.557.3 | 16 | |||
5.4 | even | 2 | 1350.2.q.h.1043.4 | 16 | |||
9.2 | odd | 6 | inner | 270.2.m.b.143.1 | 16 | ||
9.4 | even | 3 | 810.2.f.c.323.4 | 16 | |||
9.5 | odd | 6 | 810.2.f.c.323.5 | 16 | |||
9.7 | even | 3 | 90.2.l.b.83.3 | yes | 16 | ||
12.11 | even | 2 | 720.2.cu.b.113.4 | 16 | |||
15.2 | even | 4 | 90.2.l.b.77.3 | yes | 16 | ||
15.8 | even | 4 | 450.2.p.h.257.2 | 16 | |||
15.14 | odd | 2 | 450.2.p.h.293.2 | 16 | |||
36.7 | odd | 6 | 720.2.cu.b.353.3 | 16 | |||
45.2 | even | 12 | inner | 270.2.m.b.197.1 | 16 | ||
45.7 | odd | 12 | 90.2.l.b.47.3 | yes | 16 | ||
45.22 | odd | 12 | 810.2.f.c.647.5 | 16 | |||
45.29 | odd | 6 | 1350.2.q.h.143.3 | 16 | |||
45.32 | even | 12 | 810.2.f.c.647.4 | 16 | |||
45.34 | even | 6 | 450.2.p.h.443.2 | 16 | |||
45.38 | even | 12 | 1350.2.q.h.1007.4 | 16 | |||
45.43 | odd | 12 | 450.2.p.h.407.2 | 16 | |||
60.47 | odd | 4 | 720.2.cu.b.257.3 | 16 | |||
180.7 | even | 12 | 720.2.cu.b.497.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.b.23.3 | ✓ | 16 | 3.2 | odd | 2 | ||
90.2.l.b.47.3 | yes | 16 | 45.7 | odd | 12 | ||
90.2.l.b.77.3 | yes | 16 | 15.2 | even | 4 | ||
90.2.l.b.83.3 | yes | 16 | 9.7 | even | 3 | ||
270.2.m.b.17.1 | 16 | 5.2 | odd | 4 | inner | ||
270.2.m.b.143.1 | 16 | 9.2 | odd | 6 | inner | ||
270.2.m.b.197.1 | 16 | 45.2 | even | 12 | inner | ||
270.2.m.b.233.1 | 16 | 1.1 | even | 1 | trivial | ||
450.2.p.h.257.2 | 16 | 15.8 | even | 4 | |||
450.2.p.h.293.2 | 16 | 15.14 | odd | 2 | |||
450.2.p.h.407.2 | 16 | 45.43 | odd | 12 | |||
450.2.p.h.443.2 | 16 | 45.34 | even | 6 | |||
720.2.cu.b.113.4 | 16 | 12.11 | even | 2 | |||
720.2.cu.b.257.3 | 16 | 60.47 | odd | 4 | |||
720.2.cu.b.353.3 | 16 | 36.7 | odd | 6 | |||
720.2.cu.b.497.4 | 16 | 180.7 | even | 12 | |||
810.2.f.c.323.4 | 16 | 9.4 | even | 3 | |||
810.2.f.c.323.5 | 16 | 9.5 | odd | 6 | |||
810.2.f.c.647.4 | 16 | 45.32 | even | 12 | |||
810.2.f.c.647.5 | 16 | 45.22 | odd | 12 | |||
1350.2.q.h.143.3 | 16 | 45.29 | odd | 6 | |||
1350.2.q.h.557.3 | 16 | 5.3 | odd | 4 | |||
1350.2.q.h.1007.4 | 16 | 45.38 | even | 12 | |||
1350.2.q.h.1043.4 | 16 | 5.4 | even | 2 |