Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1064390625.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-1.86886 + 1.45788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.361 |
Dual form | 450.2.h.d.91.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −2.17787 | − | 0.506822i | −0.973974 | − | 0.226658i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.31003 | −0.873110 | −0.436555 | − | 0.899677i | \(-0.643802\pi\) | ||||
−0.436555 | + | 0.899677i | \(0.643802\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.05984 | − | 0.870094i | 0.651378 | − | 0.275148i | ||||
\(11\) | 2.77305 | − | 2.01474i | 0.836106 | − | 0.607467i | −0.0851740 | − | 0.996366i | \(-0.527145\pi\) |
0.921280 | + | 0.388899i | \(0.127145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.98689 | + | 2.89665i | 1.10576 | + | 0.803385i | 0.981991 | − | 0.188926i | \(-0.0605005\pi\) |
0.123773 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(14\) | 1.86886 | − | 1.35780i | 0.499473 | − | 0.362888i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 2.36886 | + | 7.29059i | 0.574532 | + | 1.76823i | 0.637767 | + | 0.770229i | \(0.279858\pi\) |
−0.0632354 | + | 0.997999i | \(0.520142\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | + | 3.07768i | 0.229416 | + | 0.706069i | 0.997813 | + | 0.0660962i | \(0.0210544\pi\) |
−0.768398 | + | 0.639973i | \(0.778946\pi\) | |||||||
\(20\) | −1.15502 | + | 1.91466i | −0.258270 | + | 0.428132i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.05921 | + | 3.25992i | −0.225825 | + | 0.695017i | ||||
\(23\) | 3.61803 | − | 2.62866i | 0.754412 | − | 0.548113i | −0.142779 | − | 0.989755i | \(-0.545604\pi\) |
0.897191 | + | 0.441642i | \(0.145604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.48626 | + | 2.20759i | 0.897252 | + | 0.441518i | ||||
\(26\) | −4.92807 | −0.966473 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.713839 | + | 2.19697i | −0.134903 | + | 0.415189i | ||||
\(29\) | 2.13279 | − | 6.56405i | 0.396049 | − | 1.21891i | −0.532093 | − | 0.846686i | \(-0.678594\pi\) |
0.928142 | − | 0.372227i | \(-0.121406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.09581 | + | 3.37254i | 0.196812 | + | 0.605727i | 0.999951 | + | 0.00993372i | \(0.00316205\pi\) |
−0.803138 | + | 0.595793i | \(0.796838\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.20175 | − | 4.50583i | −1.06359 | − | 0.772744i | ||||
\(35\) | 5.03096 | + | 1.17078i | 0.850387 | + | 0.197897i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.20175 | − | 2.32620i | −0.526364 | − | 0.382426i | 0.292632 | − | 0.956225i | \(-0.405469\pi\) |
−0.818996 | + | 0.573799i | \(0.805469\pi\) | |||||||
\(38\) | −2.61803 | − | 1.90211i | −0.424701 | − | 0.308563i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.190983 | − | 2.22790i | −0.0301971 | − | 0.352261i | ||||
\(41\) | −0.132788 | − | 0.0964762i | −0.0207380 | − | 0.0150670i | 0.577368 | − | 0.816484i | \(-0.304080\pi\) |
−0.598106 | + | 0.801417i | \(0.704080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.71149 | 1.02349 | 0.511746 | − | 0.859137i | \(-0.328999\pi\) | ||||
0.511746 | + | 0.859137i | \(0.328999\pi\) | |||||||
\(44\) | −1.05921 | − | 3.25992i | −0.159682 | − | 0.491451i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.38197 | + | 4.25325i | −0.203760 | + | 0.627108i | ||||
\(47\) | −1.92807 | + | 5.93398i | −0.281237 | + | 0.865560i | 0.706264 | + | 0.707949i | \(0.250379\pi\) |
−0.987501 | + | 0.157611i | \(0.949621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.66375 | −0.237678 | ||||||||
\(50\) | −4.92705 | + | 0.850981i | −0.696790 | + | 0.120347i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.98689 | − | 2.89665i | 0.552882 | − | 0.401692i | ||||
\(53\) | −3.69971 | + | 11.3865i | −0.508195 | + | 1.56406i | 0.287138 | + | 0.957889i | \(0.407296\pi\) |
−0.795333 | + | 0.606173i | \(0.792704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.06047 | + | 2.98240i | −0.952033 | + | 0.402147i | ||||
\(56\) | −0.713839 | − | 2.19697i | −0.0953908 | − | 0.293583i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.13279 | + | 6.56405i | 0.280049 | + | 0.861902i | ||||
\(59\) | 8.62715 | + | 6.26799i | 1.12316 | + | 0.816023i | 0.984685 | − | 0.174343i | \(-0.0557801\pi\) |
0.138475 | + | 0.990366i | \(0.455780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.249178 | − | 0.181038i | 0.0319040 | − | 0.0231796i | −0.571719 | − | 0.820450i | \(-0.693723\pi\) |
0.603623 | + | 0.797270i | \(0.293723\pi\) | |||||||
\(62\) | −2.86886 | − | 2.08435i | −0.364345 | − | 0.264712i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −7.21486 | − | 8.32917i | −0.894893 | − | 1.03311i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.42642 | − | 4.39008i | −0.174265 | − | 0.536333i | 0.825334 | − | 0.564645i | \(-0.190987\pi\) |
−0.999599 | + | 0.0283116i | \(0.990987\pi\) | |||||||
\(68\) | 7.66578 | 0.929612 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.75830 | + | 2.00995i | −0.568725 | + | 0.240234i | ||||
\(71\) | −0.117646 | + | 0.362077i | −0.0139620 | + | 0.0429706i | −0.957795 | − | 0.287453i | \(-0.907192\pi\) |
0.943833 | + | 0.330423i | \(0.107192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0608552 | − | 0.0442139i | 0.00712256 | − | 0.00517484i | −0.584218 | − | 0.811597i | \(-0.698599\pi\) |
0.591341 | + | 0.806422i | \(0.298599\pi\) | |||||||
\(74\) | 3.95758 | 0.460059 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | −6.40584 | + | 4.65411i | −0.730013 | + | 0.530386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.72296 | − | 14.5358i | 0.531374 | − | 1.63540i | −0.219981 | − | 0.975504i | \(-0.570600\pi\) |
0.751355 | − | 0.659898i | \(-0.229400\pi\) | |||||||
\(80\) | 1.46403 | + | 1.69015i | 0.163684 | + | 0.188964i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.164135 | 0.0181257 | ||||||||
\(83\) | −0.403806 | − | 1.24279i | −0.0443235 | − | 0.136414i | 0.926446 | − | 0.376428i | \(-0.122848\pi\) |
−0.970769 | + | 0.240014i | \(0.922848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.46403 | − | 17.0786i | −0.158797 | − | 1.85243i | ||||
\(86\) | −5.42971 | + | 3.94492i | −0.585501 | + | 0.425391i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.77305 | + | 2.01474i | 0.295608 | + | 0.214772i | ||||
\(89\) | 3.58371 | − | 2.60372i | 0.379873 | − | 0.275994i | −0.381420 | − | 0.924402i | \(-0.624565\pi\) |
0.761293 | + | 0.648408i | \(0.224565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.20985 | − | 6.69135i | −0.965454 | − | 0.701444i | ||||
\(92\) | −1.38197 | − | 4.25325i | −0.144080 | − | 0.443432i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.92807 | − | 5.93398i | −0.198865 | − | 0.612043i | ||||
\(95\) | −0.618034 | − | 7.20963i | −0.0634089 | − | 0.739692i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.31876 | + | 16.3695i | −0.540039 | + | 1.66207i | 0.192464 | + | 0.981304i | \(0.438352\pi\) |
−0.732503 | + | 0.680764i | \(0.761648\pi\) | |||||||
\(98\) | 1.34600 | − | 0.977926i | 0.135966 | − | 0.0987854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.48587 | − | 3.58451i | 0.348587 | − | 0.358451i | ||||
\(101\) | −5.70946 | −0.568112 | −0.284056 | − | 0.958808i | \(-0.591680\pi\) | ||||
−0.284056 | + | 0.958808i | \(0.591680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.36013 | − | 16.4968i | 0.528149 | − | 1.62548i | −0.229855 | − | 0.973225i | \(-0.573825\pi\) |
0.758004 | − | 0.652250i | \(-0.226175\pi\) | |||||||
\(104\) | −1.52286 | + | 4.68687i | −0.149328 | + | 0.459585i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.69971 | − | 11.3865i | −0.359348 | − | 1.10596i | ||||
\(107\) | 1.57154 | 0.151927 | 0.0759635 | − | 0.997111i | \(-0.475797\pi\) | ||||
0.0759635 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3447 | + | 7.51584i | 0.990840 | + | 0.719887i | 0.960105 | − | 0.279641i | \(-0.0902153\pi\) |
0.0307348 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(110\) | 3.95903 | − | 6.56285i | 0.377478 | − | 0.625743i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.86886 | + | 1.35780i | 0.176590 | + | 0.128300i | ||||
\(113\) | 4.08536 | + | 2.96818i | 0.384318 | + | 0.279223i | 0.763123 | − | 0.646253i | \(-0.223665\pi\) |
−0.378805 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.21188 | + | 3.89118i | −0.859012 | + | 0.362854i | ||||
\(116\) | −5.58371 | − | 4.05680i | −0.518435 | − | 0.376665i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.6637 | −0.981677 | ||||||||
\(119\) | −5.47214 | − | 16.8415i | −0.501630 | − | 1.54386i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.231449 | − | 0.712325i | 0.0210408 | − | 0.0647569i | ||||
\(122\) | −0.0951775 | + | 0.292926i | −0.00861697 | + | 0.0265203i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.54610 | 0.318449 | ||||||||
\(125\) | −8.65165 | − | 7.08159i | −0.773827 | − | 0.633397i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.51076 | + | 3.27726i | −0.400265 | + | 0.290810i | −0.769649 | − | 0.638467i | \(-0.779569\pi\) |
0.369384 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.7327 | + | 2.49765i | 0.941320 | + | 0.219059i | ||||
\(131\) | −1.89856 | − | 5.84316i | −0.165878 | − | 0.510520i | 0.833222 | − | 0.552939i | \(-0.186494\pi\) |
−0.999100 | + | 0.0424190i | \(0.986494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.31003 | − | 7.10955i | −0.200305 | − | 0.616476i | ||||
\(134\) | 3.73442 | + | 2.71322i | 0.322605 | + | 0.234386i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.20175 | + | 4.50583i | −0.531795 | + | 0.386372i | ||||
\(137\) | 4.10657 | + | 2.98360i | 0.350848 | + | 0.254906i | 0.749225 | − | 0.662316i | \(-0.230426\pi\) |
−0.398377 | + | 0.917222i | \(0.630426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.80636 | + | 3.49202i | −0.407670 | + | 0.296189i | −0.772658 | − | 0.634823i | \(-0.781073\pi\) |
0.364988 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(140\) | 2.66813 | − | 4.42294i | 0.225498 | − | 0.373806i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.117646 | − | 0.362077i | −0.00987262 | − | 0.0303848i | ||||
\(143\) | 16.8918 | 1.41257 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.97175 | + | 13.2147i | −0.662018 | + | 1.09742i | ||||
\(146\) | −0.0232446 | + | 0.0715396i | −0.00192374 | + | 0.00592066i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.20175 | + | 2.32620i | −0.263182 | + | 0.191213i | ||||
\(149\) | −9.88361 | −0.809697 | −0.404848 | − | 0.914384i | \(-0.632676\pi\) | ||||
−0.404848 | + | 0.914384i | \(0.632676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.63424 | −0.214371 | −0.107186 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107186 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(152\) | −2.61803 | + | 1.90211i | −0.212351 | + | 0.154282i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.44681 | − | 7.53051i | 0.197170 | − | 0.606826i | ||||
\(155\) | −0.677245 | − | 7.90035i | −0.0543976 | − | 0.634571i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.71822 | −0.296746 | −0.148373 | − | 0.988931i | \(-0.547404\pi\) | ||||
−0.148373 | + | 0.988931i | \(0.547404\pi\) | |||||||
\(158\) | 4.72296 | + | 14.5358i | 0.375738 | + | 1.15640i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.17787 | − | 0.506822i | −0.172176 | − | 0.0400678i | ||||
\(161\) | −8.35778 | + | 6.07228i | −0.658685 | + | 0.478563i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3262 | + | 8.22899i | 0.887139 | + | 0.644545i | 0.935131 | − | 0.354303i | \(-0.115282\pi\) |
−0.0479912 | + | 0.998848i | \(0.515282\pi\) | |||||||
\(164\) | −0.132788 | + | 0.0964762i | −0.0103690 | + | 0.00753352i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.05718 | + | 0.768085i | 0.0820530 | + | 0.0596150i | ||||
\(167\) | −7.66452 | − | 23.5890i | −0.593099 | − | 1.82537i | −0.563972 | − | 0.825794i | \(-0.690727\pi\) |
−0.0291269 | − | 0.999576i | \(-0.509273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.48752 | + | 10.7335i | 0.268271 | + | 0.825652i | ||||
\(170\) | 11.2230 | + | 12.9563i | 0.860762 | + | 0.993704i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.07397 | − | 6.38301i | 0.158138 | − | 0.486700i | ||||
\(173\) | 17.2347 | − | 12.5218i | 1.31033 | − | 0.952012i | 0.310334 | − | 0.950628i | \(-0.399559\pi\) |
0.999999 | − | 0.00138481i | \(-0.000440800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.3634 | − | 5.09961i | −0.783400 | − | 0.385494i | ||||
\(176\) | −3.42768 | −0.258371 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.36886 | + | 4.21291i | −0.102600 | + | 0.315771i | ||||
\(179\) | −2.94991 | + | 9.07888i | −0.220486 | + | 0.678587i | 0.778232 | + | 0.627977i | \(0.216117\pi\) |
−0.998718 | + | 0.0506106i | \(0.983883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.222958 | − | 0.686194i | −0.0165723 | − | 0.0510044i | 0.942428 | − | 0.334408i | \(-0.108536\pi\) |
−0.959001 | + | 0.283404i | \(0.908536\pi\) | |||||||
\(182\) | 11.3840 | 0.843838 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.61803 | + | 2.62866i | 0.266725 | + | 0.193787i | ||||
\(185\) | 5.79402 | + | 6.68889i | 0.425985 | + | 0.491777i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.2576 | + | 15.4445i | 1.55451 | + | 1.12942i | ||||
\(188\) | 5.04775 | + | 3.66740i | 0.368145 | + | 0.267473i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.73771 | + | 5.46944i | 0.343710 | + | 0.396795i | ||||
\(191\) | −1.00000 | − | 0.726543i | −0.0723575 | − | 0.0525708i | 0.551018 | − | 0.834493i | \(-0.314239\pi\) |
−0.623376 | + | 0.781922i | \(0.714239\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.9529 | −1.94011 | −0.970055 | − | 0.242884i | \(-0.921907\pi\) | ||||
−0.970055 | + | 0.242884i | \(0.921907\pi\) | |||||||
\(194\) | −5.31876 | − | 16.3695i | −0.381865 | − | 1.17526i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.514126 | + | 1.58232i | −0.0367233 | + | 0.113023i | ||||
\(197\) | −7.85473 | + | 24.1744i | −0.559626 | + | 1.72235i | 0.123775 | + | 0.992310i | \(0.460500\pi\) |
−0.683402 | + | 0.730043i | \(0.739500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.7585 | 1.54242 | 0.771208 | − | 0.636583i | \(-0.219653\pi\) | ||||
0.771208 | + | 0.636583i | \(0.219653\pi\) | |||||||
\(200\) | −0.713211 | + | 4.94887i | −0.0504317 | + | 0.349938i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.61905 | − | 3.35594i | 0.324995 | − | 0.236123i | ||||
\(203\) | −4.92681 | + | 15.1632i | −0.345794 | + | 1.06425i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.240299 | + | 0.277413i | 0.0167832 | + | 0.0193754i | ||||
\(206\) | 5.36013 | + | 16.4968i | 0.373458 | + | 1.14938i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.52286 | − | 4.68687i | −0.105591 | − | 0.324976i | ||||
\(209\) | 8.97378 | + | 6.51983i | 0.620729 | + | 0.450986i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9476 | − | 13.0397i | 1.23556 | − | 0.897688i | 0.238267 | − | 0.971200i | \(-0.423421\pi\) |
0.997294 | + | 0.0735122i | \(0.0234208\pi\) | |||||||
\(212\) | 9.68598 | + | 7.03727i | 0.665236 | + | 0.483322i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.27141 | + | 0.923731i | −0.0869116 | + | 0.0631449i | ||||
\(215\) | −14.6168 | − | 3.40153i | −0.996856 | − | 0.231983i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.53135 | − | 7.79069i | −0.171839 | − | 0.528866i | ||||
\(218\) | −12.7867 | −0.866026 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.654628 | + | 7.63652i | 0.0441350 | + | 0.514854i | ||||
\(221\) | −11.6739 | + | 35.9285i | −0.785270 | + | 2.41681i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.39108 | + | 4.64339i | −0.427979 | + | 0.310945i | −0.780840 | − | 0.624731i | \(-0.785209\pi\) |
0.352861 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(224\) | −2.31003 | −0.154346 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.04978 | −0.335906 | ||||||||
\(227\) | −2.15502 | + | 1.56571i | −0.143033 | + | 0.103920i | −0.657001 | − | 0.753890i | \(-0.728175\pi\) |
0.513967 | + | 0.857810i | \(0.328175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.90685 | + | 8.94638i | −0.192090 | + | 0.591193i | 0.807908 | + | 0.589309i | \(0.200600\pi\) |
−0.999998 | + | 0.00188454i | \(0.999400\pi\) | |||||||
\(230\) | 5.16539 | − | 8.56264i | 0.340596 | − | 0.564603i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.90185 | 0.453128 | ||||||||
\(233\) | −4.56935 | − | 14.0630i | −0.299348 | − | 0.921298i | −0.981726 | − | 0.190299i | \(-0.939054\pi\) |
0.682378 | − | 0.730999i | \(-0.260946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.20656 | − | 11.9463i | 0.470104 | − | 0.779289i | ||||
\(236\) | 8.62715 | − | 6.26799i | 0.561580 | − | 0.408012i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.3262 | + | 10.4086i | 0.928632 | + | 0.674691i | ||||
\(239\) | −10.2098 | + | 7.41789i | −0.660420 | + | 0.479823i | −0.866805 | − | 0.498648i | \(-0.833830\pi\) |
0.206385 | + | 0.978471i | \(0.433830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.9247 | + | 10.1169i | 0.896969 | + | 0.651686i | 0.937686 | − | 0.347485i | \(-0.112964\pi\) |
−0.0407167 | + | 0.999171i | \(0.512964\pi\) | |||||||
\(242\) | 0.231449 | + | 0.712325i | 0.0148781 | + | 0.0457900i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0951775 | − | 0.292926i | −0.00609312 | − | 0.0187527i | ||||
\(245\) | 3.62343 | + | 0.843224i | 0.231492 | + | 0.0538716i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.92807 | + | 15.1670i | −0.313565 | + | 0.965055i | ||||
\(248\) | −2.86886 | + | 2.08435i | −0.182173 | + | 0.132356i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.1618 | + | 0.643811i | 0.705933 | + | 0.0407182i | ||||
\(251\) | 18.1097 | 1.14307 | 0.571536 | − | 0.820577i | \(-0.306348\pi\) | ||||
0.571536 | + | 0.820577i | \(0.306348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73694 | − | 14.5788i | 0.297809 | − | 0.916561i | ||||
\(254\) | 1.72296 | − | 5.30272i | 0.108108 | − | 0.332722i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 1.07193 | 0.0668653 | 0.0334327 | − | 0.999441i | \(-0.489356\pi\) | ||||
0.0334327 | + | 0.999441i | \(0.489356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.39614 | + | 5.37361i | 0.459574 | + | 0.333900i | ||||
\(260\) | −10.1510 | + | 4.28788i | −0.629540 | + | 0.265923i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.97049 | + | 3.61127i | 0.307078 | + | 0.223105i | ||||
\(263\) | −19.8756 | − | 14.4405i | −1.22558 | − | 0.890439i | −0.229032 | − | 0.973419i | \(-0.573556\pi\) |
−0.996551 | + | 0.0829801i | \(0.973556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.8285 | − | 22.9234i | 0.849476 | − | 1.40817i | ||||
\(266\) | 6.04775 | + | 4.39394i | 0.370811 | + | 0.269410i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.61600 | −0.281967 | ||||||||
\(269\) | 6.23670 | + | 19.1946i | 0.380258 | + | 1.17031i | 0.939862 | + | 0.341554i | \(0.110953\pi\) |
−0.559604 | + | 0.828760i | \(0.689047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.55174 | + | 4.77575i | −0.0942613 | + | 0.290106i | −0.987060 | − | 0.160349i | \(-0.948738\pi\) |
0.892799 | + | 0.450455i | \(0.148738\pi\) | |||||||
\(272\) | 2.36886 | − | 7.29059i | 0.143633 | − | 0.442057i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.07600 | −0.306652 | ||||||||
\(275\) | 16.8883 | − | 2.91689i | 1.01841 | − | 0.175895i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.50975 | − | 5.45615i | 0.451217 | − | 0.327828i | −0.338859 | − | 0.940837i | \(-0.610041\pi\) |
0.790076 | + | 0.613009i | \(0.210041\pi\) | |||||||
\(278\) | 1.83586 | − | 5.65021i | 0.110108 | − | 0.338877i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.441177 | + | 5.14652i | 0.0263654 | + | 0.307563i | ||||
\(281\) | −8.45092 | − | 26.0093i | −0.504140 | − | 1.55158i | −0.802212 | − | 0.597039i | \(-0.796344\pi\) |
0.298072 | − | 0.954543i | \(-0.403656\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.33829 | + | 13.3519i | 0.257884 | + | 0.793686i | 0.993248 | + | 0.116013i | \(0.0370115\pi\) |
−0.735363 | + | 0.677673i | \(0.762988\pi\) | |||||||
\(284\) | 0.308001 | + | 0.223776i | 0.0182765 | + | 0.0132786i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.6658 | + | 9.92877i | −0.808074 | + | 0.587100i | ||||
\(287\) | 0.306745 | + | 0.222863i | 0.0181066 | + | 0.0131552i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.7879 | + | 24.5484i | −1.98752 | + | 1.44402i | ||||
\(290\) | −1.31814 | − | 15.3766i | −0.0774036 | − | 0.902945i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.0232446 | − | 0.0715396i | −0.00136029 | − | 0.00418654i | ||||
\(293\) | 1.70695 | 0.0997210 | 0.0498605 | − | 0.998756i | \(-0.484122\pi\) | ||||
0.0498605 | + | 0.998756i | \(0.484122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.6121 | − | 18.0233i | −0.908971 | − | 1.04936i | ||||
\(296\) | 1.22296 | − | 3.76388i | 0.0710830 | − | 0.218771i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.99601 | − | 5.80944i | 0.463196 | − | 0.336532i | ||||
\(299\) | 22.0390 | 1.27455 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5038 | −0.893622 | ||||||||
\(302\) | 2.13114 | − | 1.54837i | 0.122634 | − | 0.0890985i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | − | 3.07768i | 0.0573539 | − | 0.176517i | ||||
\(305\) | −0.634432 | + | 0.267990i | −0.0363275 | + | 0.0153450i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5669 | −1.00259 | −0.501297 | − | 0.865276i | \(-0.667143\pi\) | ||||
−0.501297 | + | 0.865276i | \(0.667143\pi\) | |||||||
\(308\) | 2.44681 | + | 7.53051i | 0.139420 | + | 0.429091i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.19161 | + | 5.99344i | 0.294864 | + | 0.340405i | ||||
\(311\) | 6.78546 | − | 4.92992i | 0.384768 | − | 0.279550i | −0.378540 | − | 0.925585i | \(-0.623574\pi\) |
0.763308 | + | 0.646035i | \(0.223574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3407 | − | 14.7784i | −1.14972 | − | 0.835323i | −0.161279 | − | 0.986909i | \(-0.551562\pi\) |
−0.988444 | + | 0.151586i | \(0.951562\pi\) | |||||||
\(314\) | 3.00810 | − | 2.18551i | 0.169757 | − | 0.123336i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3649 | − | 8.98360i | −0.695578 | − | 0.505367i | ||||
\(317\) | −1.83857 | − | 5.65854i | −0.103264 | − | 0.317815i | 0.886055 | − | 0.463581i | \(-0.153436\pi\) |
−0.989319 | + | 0.145765i | \(0.953436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.31051 | − | 22.4994i | −0.409310 | − | 1.25973i | ||||
\(320\) | 2.05984 | − | 0.870094i | 0.115149 | − | 0.0486397i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.19239 | − | 9.82516i | 0.177905 | − | 0.547535i | ||||
\(323\) | −20.0693 | + | 14.5812i | −1.11668 | + | 0.811318i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.4916 | + | 21.7965i | 0.637441 | + | 1.20905i | ||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0507205 | − | 0.156102i | 0.00280057 | − | 0.00861928i | ||||
\(329\) | 4.45390 | − | 13.7077i | 0.245551 | − | 0.755729i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.47339 | + | 23.0007i | 0.410775 | + | 1.26423i | 0.915976 | + | 0.401233i | \(0.131418\pi\) |
−0.505201 | + | 0.863002i | \(0.668582\pi\) | |||||||
\(332\) | −1.30674 | −0.0717169 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0660 | + | 14.5788i | 1.09796 | + | 0.797716i | ||||
\(335\) | 0.881578 | + | 10.2840i | 0.0481657 | + | 0.561874i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.18218 | + | 6.67124i | 0.500185 | + | 0.363406i | 0.809088 | − | 0.587688i | \(-0.199962\pi\) |
−0.308903 | + | 0.951094i | \(0.599962\pi\) | |||||||
\(338\) | −9.13044 | − | 6.63365i | −0.496631 | − | 0.360823i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.6951 | − | 3.88519i | −0.905419 | − | 0.210704i | ||||
\(341\) | 9.83352 | + | 7.14447i | 0.532515 | + | 0.386895i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0135 | 1.08063 | ||||||||
\(344\) | 2.07397 | + | 6.38301i | 0.111821 | + | 0.344149i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.58308 | + | 20.2606i | −0.353909 | + | 1.08922i | ||||
\(347\) | 3.56086 | − | 10.9592i | 0.191157 | − | 0.588320i | −0.808843 | − | 0.588024i | \(-0.799906\pi\) |
1.00000 | 0.000295559i | \(-9.40792e-5\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81216 | −0.0970025 | −0.0485013 | − | 0.998823i | \(-0.515444\pi\) | ||||
−0.0485013 | + | 0.998823i | \(0.515444\pi\) | |||||||
\(350\) | 11.3817 | − | 1.96579i | 0.608375 | − | 0.105076i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.77305 | − | 2.01474i | 0.147804 | − | 0.107386i | ||||
\(353\) | 0.939338 | − | 2.89099i | 0.0499959 | − | 0.153872i | −0.922942 | − | 0.384940i | \(-0.874222\pi\) |
0.972938 | + | 0.231068i | \(0.0742221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.439726 | − | 0.728932i | 0.0233383 | − | 0.0386877i | ||||
\(356\) | −1.36886 | − | 4.21291i | −0.0725492 | − | 0.223284i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.94991 | − | 9.07888i | −0.155907 | − | 0.479834i | ||||
\(359\) | 4.93136 | + | 3.58284i | 0.260267 | + | 0.189095i | 0.710265 | − | 0.703935i | \(-0.248575\pi\) |
−0.449998 | + | 0.893030i | \(0.648575\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.89919 | − | 5.01255i | 0.363115 | − | 0.263819i | ||||
\(362\) | 0.583712 | + | 0.424091i | 0.0306792 | + | 0.0222897i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.20985 | + | 6.69135i | −0.482727 | + | 0.350722i | ||||
\(365\) | −0.154943 | + | 0.0654495i | −0.00811011 | + | 0.00342578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.14152 | − | 25.0570i | −0.424984 | − | 1.30797i | −0.903010 | − | 0.429620i | \(-0.858648\pi\) |
0.478026 | − | 0.878346i | \(-0.341352\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.61910 | − | 2.00579i | −0.448085 | − | 0.104276i | ||||
\(371\) | 8.54646 | − | 26.3033i | 0.443710 | − | 1.36560i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4742 | + | 8.33647i | −0.594110 | + | 0.431646i | −0.843783 | − | 0.536684i | \(-0.819677\pi\) |
0.249673 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(374\) | −26.2758 | −1.35869 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.23936 | −0.321770 | ||||||||
\(377\) | 27.5169 | − | 19.9922i | 1.41719 | − | 1.02965i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.82663 | − | 30.2432i | 0.504760 | − | 1.55349i | −0.296414 | − | 0.955060i | \(-0.595791\pi\) |
0.801174 | − | 0.598432i | \(-0.204209\pi\) | |||||||
\(380\) | −7.04775 | − | 1.64011i | −0.361542 | − | 0.0841360i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.23607 | 0.0632427 | ||||||||
\(383\) | −7.16336 | − | 22.0466i | −0.366031 | − | 1.12653i | −0.949333 | − | 0.314271i | \(-0.898240\pi\) |
0.583303 | − | 0.812255i | \(-0.301760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3099 | − | 6.88945i | 0.831230 | − | 0.351119i | ||||
\(386\) | 21.8053 | − | 15.8425i | 1.10986 | − | 0.806362i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.9247 | + | 10.1169i | 0.706920 | + | 0.513607i | ||||
\(389\) | −10.3323 | + | 7.50683i | −0.523866 | + | 0.380611i | −0.818058 | − | 0.575135i | \(-0.804949\pi\) |
0.294192 | + | 0.955746i | \(0.404949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.7350 | + | 20.1507i | 1.40262 | + | 1.01906i | ||||
\(392\) | −0.514126 | − | 1.58232i | −0.0259673 | − | 0.0799191i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.85473 | − | 24.1744i | −0.395716 | − | 1.21789i | ||||
\(395\) | −17.6531 | + | 29.2634i | −0.888222 | + | 1.47240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.21110 | − | 16.0381i | 0.261538 | − | 0.804931i | −0.730933 | − | 0.682449i | \(-0.760915\pi\) |
0.992471 | − | 0.122481i | \(-0.0390852\pi\) | |||||||
\(398\) | −17.6030 | + | 12.7893i | −0.882357 | + | 0.641070i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.33187 | − | 4.42294i | −0.116594 | − | 0.221147i | ||||
\(401\) | −2.02027 | −0.100887 | −0.0504437 | − | 0.998727i | \(-0.516064\pi\) | ||||
−0.0504437 | + | 0.998727i | \(0.516064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.40020 | + | 16.6201i | −0.269003 | + | 0.827907i | ||||
\(404\) | −1.76432 | + | 5.43002i | −0.0877782 | + | 0.270154i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.92681 | − | 15.1632i | −0.244514 | − | 0.752535i | ||||
\(407\) | −13.5653 | −0.672407 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.07827 | − | 2.23649i | −0.152211 | − | 0.110587i | 0.509073 | − | 0.860723i | \(-0.329988\pi\) |
−0.661284 | + | 0.750136i | \(0.729988\pi\) | |||||||
\(410\) | −0.357465 | − | 0.0831873i | −0.0176540 | − | 0.00410833i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0330 | − | 10.1956i | −0.691356 | − | 0.502299i | ||||
\(413\) | −19.9290 | − | 14.4793i | −0.980642 | − | 0.712478i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.249566 | + | 2.91129i | 0.0122507 | + | 0.142910i | ||||
\(416\) | 3.98689 | + | 2.89665i | 0.195473 | + | 0.142020i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0922 | −0.542537 | ||||||||
\(419\) | 2.33265 | + | 7.17916i | 0.113957 | + | 0.350725i | 0.991728 | − | 0.128356i | \(-0.0409700\pi\) |
−0.877771 | + | 0.479081i | \(0.840970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.73955 | − | 14.5868i | 0.230992 | − | 0.710919i | −0.766636 | − | 0.642082i | \(-0.778071\pi\) |
0.997628 | − | 0.0688374i | \(-0.0219290\pi\) | |||||||
\(422\) | −6.85536 | + | 21.0986i | −0.333714 | + | 1.02706i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.9725 | −0.581437 | ||||||||
\(425\) | −5.46732 | + | 37.9370i | −0.265204 | + | 1.84021i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.575609 | + | 0.418205i | −0.0278557 | + | 0.0202383i | ||||
\(428\) | 0.485634 | − | 1.49463i | 0.0234740 | − | 0.0722456i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.8246 | − | 5.83963i | 0.666681 | − | 0.281612i | ||||
\(431\) | −2.89981 | − | 8.92471i | −0.139679 | − | 0.429888i | 0.856609 | − | 0.515966i | \(-0.172567\pi\) |
−0.996288 | + | 0.0860773i | \(0.972567\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.34803 | − | 28.7703i | −0.449238 | − | 1.38261i | −0.877769 | − | 0.479085i | \(-0.840969\pi\) |
0.428531 | − | 0.903527i | \(-0.359031\pi\) | |||||||
\(434\) | 6.62715 | + | 4.81491i | 0.318114 | + | 0.231123i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3447 | − | 7.51584i | 0.495420 | − | 0.359944i | ||||
\(437\) | 11.7082 | + | 8.50651i | 0.560079 | + | 0.406921i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8108 | + | 22.3853i | −1.47052 | + | 1.06839i | −0.490055 | + | 0.871691i | \(0.663023\pi\) |
−0.980463 | + | 0.196703i | \(0.936977\pi\) | |||||||
\(440\) | −5.01824 | − | 5.79329i | −0.239235 | − | 0.276184i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.6739 | − | 35.9285i | −0.555270 | − | 1.70895i | ||||
\(443\) | 1.53797 | 0.0730713 | 0.0365356 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365356 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.12449 | + | 3.85426i | −0.432542 | + | 0.182710i | ||||
\(446\) | 2.44118 | − | 7.51317i | 0.115593 | − | 0.355759i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.86886 | − | 1.35780i | 0.0882951 | − | 0.0641502i | ||||
\(449\) | −14.0449 | −0.662822 | −0.331411 | − | 0.943487i | \(-0.607525\pi\) | ||||
−0.331411 | + | 0.943487i | \(0.607525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.562602 | −0.0264919 | ||||||||
\(452\) | 4.08536 | − | 2.96818i | 0.192159 | − | 0.139612i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.823143 | − | 2.53337i | 0.0386320 | − | 0.118897i | ||||
\(455\) | 16.6666 | + | 19.2407i | 0.781340 | + | 0.902016i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5748 | 0.681782 | 0.340891 | − | 0.940103i | \(-0.389271\pi\) | ||||
0.340891 | + | 0.940103i | \(0.389271\pi\) | |||||||
\(458\) | −2.90685 | − | 8.94638i | −0.135828 | − | 0.418037i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.854102 | + | 9.96346i | 0.0398227 | + | 0.464549i | ||||
\(461\) | 14.6187 | − | 10.6211i | 0.680862 | − | 0.494675i | −0.192781 | − | 0.981242i | \(-0.561751\pi\) |
0.873644 | + | 0.486566i | \(0.161751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6322 | − | 12.0840i | −0.772964 | − | 0.561591i | 0.129895 | − | 0.991528i | \(-0.458536\pi\) |
−0.902859 | + | 0.429936i | \(0.858536\pi\) | |||||||
\(464\) | −5.58371 | + | 4.05680i | −0.259217 | + | 0.188332i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.9627 | + | 8.69141i | 0.554161 | + | 0.402622i | ||||
\(467\) | −7.78691 | − | 23.9656i | −0.360335 | − | 1.10900i | −0.952851 | − | 0.303439i | \(-0.901865\pi\) |
0.592516 | − | 0.805559i | \(-0.298135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.29508 | + | 10.1412i | 0.152153 | + | 0.468278i | ||||
\(470\) | 1.19161 | + | 13.9006i | 0.0549649 | + | 0.641189i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.29528 | + | 10.1418i | −0.151678 | + | 0.466815i | ||||
\(473\) | 18.6113 | − | 13.5219i | 0.855749 | − | 0.621738i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.30800 | + | 16.0149i | −0.105898 | + | 0.734813i | ||||
\(476\) | −17.7082 | −0.811654 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.89981 | − | 12.0024i | 0.178373 | − | 0.548977i | ||||
\(479\) | −0.809645 | + | 2.49183i | −0.0369936 | + | 0.113855i | −0.967848 | − | 0.251536i | \(-0.919064\pi\) |
0.930854 | + | 0.365390i | \(0.119064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.02682 | − | 18.5486i | −0.274799 | − | 0.845745i | ||||
\(482\) | −17.2119 | −0.783980 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.605940 | − | 0.440241i | −0.0275427 | − | 0.0200110i | ||||
\(485\) | 19.8800 | − | 32.9550i | 0.902705 | − | 1.49641i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3452 | − | 14.7817i | −0.921930 | − | 0.669821i | 0.0220737 | − | 0.999756i | \(-0.492973\pi\) |
−0.944004 | + | 0.329935i | \(0.892973\pi\) | |||||||
\(488\) | 0.249178 | + | 0.181038i | 0.0112798 | + | 0.00819522i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.42705 | + | 1.44762i | −0.154818 | + | 0.0653966i | ||||
\(491\) | 25.5824 | + | 18.5867i | 1.15452 | + | 0.838805i | 0.989075 | − | 0.147414i | \(-0.0470950\pi\) |
0.165442 | + | 0.986220i | \(0.447095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.9080 | 2.38286 | ||||||||
\(494\) | −4.92807 | − | 15.1670i | −0.221724 | − | 0.682397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.09581 | − | 3.37254i | 0.0492031 | − | 0.151432i | ||||
\(497\) | 0.271766 | − | 0.836409i | 0.0121904 | − | 0.0375181i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6266 | −1.28150 | −0.640752 | − | 0.767748i | \(-0.721377\pi\) | ||||
−0.640752 | + | 0.767748i | \(0.721377\pi\) | |||||||
\(500\) | −9.40850 | + | 6.03988i | −0.420761 | + | 0.270112i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.6510 | + | 10.6446i | −0.653907 | + | 0.475091i | ||||
\(503\) | −1.48960 | + | 4.58451i | −0.0664178 | + | 0.204413i | −0.978758 | − | 0.205021i | \(-0.934274\pi\) |
0.912340 | + | 0.409434i | \(0.134274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4345 | + | 2.89368i | 0.553327 | + | 0.128767i | ||||
\(506\) | 4.73694 | + | 14.5788i | 0.210582 | + | 0.648106i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.72296 | + | 5.30272i | 0.0764439 | + | 0.235270i | ||||
\(509\) | −10.8604 | − | 7.89057i | −0.481380 | − | 0.349743i | 0.320479 | − | 0.947255i | \(-0.396156\pi\) |
−0.801860 | + | 0.597512i | \(0.796156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.140578 | + | 0.102136i | −0.00621878 | + | 0.00451821i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.867212 | + | 0.630066i | −0.0382511 | + | 0.0277910i | ||||
\(515\) | −20.0346 | + | 33.2112i | −0.882830 | + | 1.46346i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.60880 | + | 20.3398i | 0.290654 | + | 0.894543i | ||||
\(518\) | −9.14213 | −0.401682 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.69200 | − | 9.43559i | 0.249611 | − | 0.413778i | ||||
\(521\) | 1.15710 | − | 3.56117i | 0.0506933 | − | 0.156018i | −0.922505 | − | 0.385985i | \(-0.873862\pi\) |
0.973198 | + | 0.229967i | \(0.0738618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5938 | − | 7.69688i | 0.463237 | − | 0.336561i | −0.331563 | − | 0.943433i | \(-0.607576\pi\) |
0.794800 | + | 0.606872i | \(0.207576\pi\) | |||||||
\(524\) | −6.14387 | −0.268396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.5676 | 1.07120 | ||||||||
\(527\) | −21.9920 | + | 15.9781i | −0.957987 | + | 0.696019i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.927051 | + | 2.85317i | −0.0403066 | + | 0.124051i | ||||
\(530\) | 2.28655 | + | 26.6736i | 0.0993213 | + | 1.15863i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.47542 | −0.324101 | ||||||||
\(533\) | −0.249954 | − | 0.769280i | −0.0108267 | − | 0.0333212i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.42262 | − | 0.796494i | −0.147973 | − | 0.0344354i | ||||
\(536\) | 3.73442 | − | 2.71322i | 0.161303 | − | 0.117193i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.3279 | − | 11.8629i | −0.703945 | − | 0.511446i | ||||
\(539\) | −4.61365 | + | 3.35202i | −0.198724 | + | 0.144382i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0349 | − | 12.3766i | −0.732390 | − | 0.532112i | 0.157929 | − | 0.987450i | \(-0.449518\pi\) |
−0.890319 | + | 0.455338i | \(0.849518\pi\) | |||||||
\(542\) | −1.55174 | − | 4.77575i | −0.0666528 | − | 0.205136i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.36886 | + | 7.29059i | 0.101564 | + | 0.312581i | ||||
\(545\) | −18.7202 | − | 21.6115i | −0.801884 | − | 0.925733i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.24608 | + | 13.0681i | −0.181549 | + | 0.558752i | −0.999872 | − | 0.0160078i | \(-0.994904\pi\) |
0.818322 | + | 0.574759i | \(0.194904\pi\) | |||||||
\(548\) | 4.10657 | − | 2.98360i | 0.175424 | − | 0.127453i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.9485 | + | 12.2865i | −0.509484 | + | 0.523900i | ||||
\(551\) | 22.3348 | 0.951496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9102 | + | 33.5781i | −0.463948 | + | 1.42789i | ||||
\(554\) | −2.86847 | + | 8.82824i | −0.121870 | + | 0.375076i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.83586 | + | 5.65021i | 0.0778580 | + | 0.239622i | ||||
\(557\) | 16.0148 | 0.678569 | 0.339284 | − | 0.940684i | \(-0.389815\pi\) | ||||
0.339284 | + | 0.940684i | \(0.389815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.7580 | + | 19.4408i | 1.13174 | + | 0.822259i | ||||
\(560\) | −3.38197 | − | 3.90430i | −0.142914 | − | 0.164987i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.1248 | + | 16.0746i | 0.933279 | + | 0.678067i | ||||
\(563\) | 24.9328 | + | 18.1147i | 1.05079 | + | 0.763445i | 0.972363 | − | 0.233474i | \(-0.0750094\pi\) |
0.0784295 | + | 0.996920i | \(0.475009\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.39304 | − | 8.53488i | −0.311028 | − | 0.359065i | ||||
\(566\) | −11.3578 | − | 8.25191i | −0.477403 | − | 0.346854i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.380710 | −0.0159742 | ||||||||
\(569\) | 11.0326 | + | 33.9549i | 0.462511 | + | 1.42346i | 0.862086 | + | 0.506762i | \(0.169158\pi\) |
−0.399576 | + | 0.916700i | \(0.630842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.21188 | − | 28.3513i | 0.385505 | − | 1.18646i | −0.550608 | − | 0.834764i | \(-0.685604\pi\) |
0.936113 | − | 0.351699i | \(-0.114396\pi\) | |||||||
\(572\) | 5.21986 | − | 16.0651i | 0.218253 | − | 0.671715i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.379157 | −0.0158257 | ||||||||
\(575\) | 22.0344 | − | 3.80570i | 0.918900 | − | 0.158709i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6772 | − | 8.48402i | 0.486130 | − | 0.353194i | −0.317564 | − | 0.948237i | \(-0.602865\pi\) |
0.803694 | + | 0.595043i | \(0.202865\pi\) | |||||||
\(578\) | 12.9058 | − | 39.7201i | 0.536812 | − | 1.65214i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1045 | + | 11.6652i | 0.419568 | + | 0.484369i | ||||
\(581\) | 0.932806 | + | 2.87088i | 0.0386993 | + | 0.119104i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6814 | + | 39.0294i | 0.525211 | + | 1.61643i | ||||
\(584\) | 0.0608552 | + | 0.0442139i | 0.00251821 | + | 0.00182958i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.38095 | + | 1.00332i | −0.0570465 | + | 0.0414467i | ||||
\(587\) | 8.65134 | + | 6.28557i | 0.357079 | + | 0.259433i | 0.751833 | − | 0.659354i | \(-0.229170\pi\) |
−0.394754 | + | 0.918787i | \(0.629170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.28381 | + | 6.74509i | −0.382533 | + | 0.277926i | ||||
\(590\) | 23.2243 | + | 5.40463i | 0.956129 | + | 0.222505i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.22296 | + | 3.76388i | 0.0502633 | + | 0.154694i | ||||
\(593\) | −1.89856 | −0.0779645 | −0.0389822 | − | 0.999240i | \(-0.512412\pi\) | ||||
−0.0389822 | + | 0.999240i | \(0.512412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.38197 | + | 39.4521i | 0.138647 | + | 1.61738i | ||||
\(596\) | −3.05420 | + | 9.39987i | −0.125105 | + | 0.385034i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.8299 | + | 12.9542i | −0.729119 | + | 0.529736i | ||||
\(599\) | 8.35410 | 0.341339 | 0.170670 | − | 0.985328i | \(-0.445407\pi\) | ||||
0.170670 | + | 0.985328i | \(0.445407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.38816 | 0.0974149 | 0.0487075 | − | 0.998813i | \(-0.484490\pi\) | ||||
0.0487075 | + | 0.998813i | \(0.484490\pi\) | |||||||
\(602\) | 12.5428 | − | 9.11289i | 0.511207 | − | 0.371414i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.814025 | + | 2.50531i | −0.0331222 | + | 0.101940i | ||||
\(605\) | −0.865088 | + | 1.43405i | −0.0351708 | + | 0.0583025i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3129 | −0.662122 | −0.331061 | − | 0.943609i | \(-0.607407\pi\) | ||||
−0.331061 | + | 0.943609i | \(0.607407\pi\) | |||||||
\(608\) | 1.00000 | + | 3.07768i | 0.0405554 | + | 0.124817i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.355746 | − | 0.589718i | 0.0144037 | − | 0.0238770i | ||||
\(611\) | −24.8756 | + | 18.0732i | −1.00636 | + | 0.731163i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.4823 | − | 8.34236i | −0.463765 | − | 0.336945i | 0.331242 | − | 0.943546i | \(-0.392532\pi\) |
−0.795006 | + | 0.606601i | \(0.792532\pi\) | |||||||
\(614\) | 14.2119 | − | 10.3255i | 0.573545 | − | 0.416705i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.40584 | − | 4.65411i | −0.258099 | − | 0.187520i | ||||
\(617\) | −9.01449 | − | 27.7437i | −0.362910 | − | 1.11692i | −0.951280 | − | 0.308329i | \(-0.900230\pi\) |
0.588370 | − | 0.808592i | \(-0.299770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.16617 | − | 25.1329i | −0.328226 | − | 1.01018i | −0.969963 | − | 0.243251i | \(-0.921786\pi\) |
0.641737 | − | 0.766924i | \(-0.278214\pi\) | |||||||
\(620\) | −7.72296 | − | 1.79724i | −0.310161 | − | 0.0721790i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.59181 | + | 7.97678i | −0.103922 | + | 0.319840i | ||||
\(623\) | −8.27849 | + | 6.01468i | −0.331671 | + | 0.240973i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.2531 | + | 19.8077i | 0.610124 | + | 0.792306i | ||||
\(626\) | 25.1425 | 1.00489 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.14899 | + | 3.53624i | −0.0458498 | + | 0.141111i | ||||
\(629\) | 9.37493 | − | 28.8531i | 0.373803 | − | 1.15045i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.06192 | + | 3.26825i | 0.0422743 | + | 0.130107i | 0.969966 | − | 0.243240i | \(-0.0782102\pi\) |
−0.927692 | + | 0.373347i | \(0.878210\pi\) | |||||||
\(632\) | 15.2838 | 0.607957 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.81344 | + | 3.49717i | 0.191166 | + | 0.138890i | ||||
\(635\) | 11.4849 | − | 4.85130i | 0.455763 | − | 0.192518i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.63318 | − | 4.81928i | −0.262816 | − | 0.190947i | ||||
\(638\) | 19.1392 | + | 13.9054i | 0.757727 | + | 0.550521i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.15502 | + | 1.91466i | −0.0456560 | + | 0.0756837i | ||||
\(641\) | −7.17071 | − | 5.20983i | −0.283226 | − | 0.205776i | 0.437097 | − | 0.899414i | \(-0.356007\pi\) |
−0.720323 | + | 0.693638i | \(0.756007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9508 | −0.431859 | −0.215930 | − | 0.976409i | \(-0.569278\pi\) | ||||
−0.215930 | + | 0.976409i | \(0.569278\pi\) | |||||||
\(644\) | 3.19239 | + | 9.82516i | 0.125798 | + | 0.387165i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.66578 | − | 23.5928i | 0.301606 | − | 0.928248i | ||||
\(647\) | 11.2381 | − | 34.5873i | 0.441815 | − | 1.35977i | −0.444124 | − | 0.895966i | \(-0.646485\pi\) |
0.885939 | − | 0.463802i | \(-0.153515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.5519 | 1.43479 | ||||||||
\(650\) | −22.1086 | − | 10.8792i | −0.867171 | − | 0.426715i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.3262 | − | 8.22899i | 0.443570 | − | 0.322272i | ||||
\(653\) | −3.58386 | + | 11.0300i | −0.140247 | + | 0.431637i | −0.996369 | − | 0.0851371i | \(-0.972867\pi\) |
0.856122 | + | 0.516774i | \(0.172867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.17337 | + | 13.6879i | 0.0458475 | + | 0.534831i | ||||
\(656\) | 0.0507205 | + | 0.156102i | 0.00198030 | + | 0.00609475i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.45390 | + | 13.7077i | 0.173631 | + | 0.534381i | ||||
\(659\) | −39.1957 | − | 28.4774i | −1.52685 | − | 1.10932i | −0.957959 | − | 0.286907i | \(-0.907373\pi\) |
−0.568890 | − | 0.822414i | \(-0.692627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.33751 | + | 0.971757i | −0.0520231 | + | 0.0377970i | −0.613493 | − | 0.789700i | \(-0.710236\pi\) |
0.561470 | + | 0.827497i | \(0.310236\pi\) | |||||||
\(662\) | −19.5656 | − | 14.2152i | −0.760438 | − | 0.552491i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.05718 | − | 0.768085i | 0.0410265 | − | 0.0298075i | ||||
\(665\) | 1.42768 | + | 16.6545i | 0.0553630 | + | 0.645833i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.53812 | − | 29.3553i | −0.369317 | − | 1.13664i | ||||
\(668\) | −24.8029 | −0.959654 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.75798 | − | 7.80173i | −0.261084 | − | 0.301407i | ||||
\(671\) | 0.326238 | − | 1.00406i | 0.0125943 | − | 0.0387612i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.79971 | − | 5.66682i | 0.300657 | − | 0.218440i | −0.427220 | − | 0.904147i | \(-0.640507\pi\) |
0.727877 | + | 0.685708i | \(0.240507\pi\) | |||||||
\(674\) | −11.3498 | −0.437178 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.2858 | 0.434071 | ||||||||
\(677\) | −7.61063 | + | 5.52945i | −0.292500 | + | 0.212514i | −0.724351 | − | 0.689431i | \(-0.757861\pi\) |
0.431851 | + | 0.901945i | \(0.357861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2865 | − | 37.8140i | 0.471513 | − | 1.45117i | ||||
\(680\) | 15.7903 | − | 6.66995i | 0.605529 | − | 0.255781i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.1549 | −0.465435 | ||||||||
\(683\) | 3.20637 | + | 9.86818i | 0.122688 | + | 0.377595i | 0.993473 | − | 0.114069i | \(-0.0363886\pi\) |
−0.870785 | + | 0.491665i | \(0.836389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.43143 | − | 8.57920i | −0.283940 | − | 0.327794i | ||||
\(686\) | −16.1913 | + | 11.7637i | −0.618187 | + | 0.449139i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.42971 | − | 3.94492i | −0.207006 | − | 0.150399i | ||||
\(689\) | −47.7331 | + | 34.6802i | −1.81849 | + | 1.32121i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.19568 | − | 2.32179i | −0.121569 | − | 0.0883252i | 0.525339 | − | 0.850893i | \(-0.323938\pi\) |
−0.646908 | + | 0.762568i | \(0.723938\pi\) | |||||||
\(692\) | −6.58308 | − | 20.2606i | −0.250251 | − | 0.770194i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.56086 | + | 10.9592i | 0.135168 | + | 0.416005i | ||||
\(695\) | 12.2375 | − | 5.16921i | 0.464194 | − | 0.196079i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.388812 | − | 1.19664i | 0.0147273 | − | 0.0453260i | ||||
\(698\) | 1.46607 | − | 1.06516i | 0.0554914 | − | 0.0403169i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.05248 | + | 8.28033i | −0.304355 | + | 0.312967i | ||||
\(701\) | 14.6454 | 0.553148 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.95758 | − | 12.1802i | 0.149263 | − | 0.459384i | ||||
\(704\) | −1.05921 | + | 3.25992i | −0.0399205 | + | 0.122863i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.939338 | + | 2.89099i | 0.0353525 | + | 0.108804i | ||||
\(707\) | 13.1890 | 0.496025 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.2889 | + | 27.0920i | 1.40042 | + | 1.01746i | 0.994630 | + | 0.103493i | \(0.0330020\pi\) |
0.405785 | + | 0.913968i | \(0.366998\pi\) | |||||||
\(710\) | 0.0727091 | + | 0.848183i | 0.00272873 | + | 0.0318317i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.58371 | + | 2.60372i | 0.134305 | + | 0.0975785i | ||||
\(713\) | 12.8299 | + | 9.32148i | 0.480484 | + | 0.349092i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.7883 | − | 8.56116i | −1.37580 | − | 0.320169i | ||||
\(716\) | 7.72296 | + | 5.61106i | 0.288620 | + | 0.209695i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.09549 | −0.227482 | ||||||||
\(719\) | −7.22238 | − | 22.2282i | −0.269349 | − | 0.828971i | −0.990659 | − | 0.136359i | \(-0.956460\pi\) |
0.721310 | − | 0.692612i | \(-0.243540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3821 | + | 38.1081i | −0.461132 | + | 1.41922i | ||||
\(722\) | −2.63525 | + | 8.11048i | −0.0980740 | + | 0.301841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.721507 | −0.0268146 | ||||||||
\(725\) | 24.0590 | − | 24.7397i | 0.893528 | − | 0.918810i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.97049 | − | 5.06436i | 0.258521 | − | 0.187827i | −0.450974 | − | 0.892537i | \(-0.648923\pi\) |
0.709495 | + | 0.704711i | \(0.248923\pi\) | |||||||
\(728\) | 3.51785 | − | 10.8268i | 0.130380 | − | 0.401269i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0868817 | − | 0.144023i | 0.00321564 | − | 0.00533054i | ||||
\(731\) | 15.8986 | + | 48.9307i | 0.588029 | + | 1.80977i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.61959 | − | 14.2176i | −0.170628 | − | 0.525140i | 0.828779 | − | 0.559577i | \(-0.189036\pi\) |
−0.999407 | + | 0.0344367i | \(0.989036\pi\) | |||||||
\(734\) | 21.3148 | + | 15.4861i | 0.786743 | + | 0.571602i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.61803 | − | 2.62866i | 0.133363 | − | 0.0968935i | ||||
\(737\) | −12.8004 | − | 9.30004i | −0.471509 | − | 0.342571i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0484 | − | 24.0110i | 1.21570 | − | 0.883261i | 0.219968 | − | 0.975507i | \(-0.429405\pi\) |
0.995736 | + | 0.0922465i | \(0.0294048\pi\) | |||||||
\(740\) | 8.15197 | − | 3.44346i | 0.299672 | − | 0.126584i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.54646 | + | 26.3033i | 0.313750 | + | 0.965625i | ||||
\(743\) | −13.6476 | −0.500683 | −0.250342 | − | 0.968158i | \(-0.580543\pi\) | ||||
−0.250342 | + | 0.968158i | \(0.580543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.5252 | + | 5.00924i | 0.788624 | + | 0.183524i | ||||
\(746\) | 4.38274 | − | 13.4887i | 0.160464 | − | 0.493856i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.2576 | − | 15.4445i | 0.777255 | − | 0.564709i | ||||
\(749\) | −3.63032 | −0.132649 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.3014 | 1.50711 | 0.753555 | − | 0.657385i | \(-0.228337\pi\) | ||||
0.753555 | + | 0.657385i | \(0.228337\pi\) | |||||||
\(752\) | 5.04775 | − | 3.66740i | 0.184072 | − | 0.133736i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.5105 | + | 32.3481i | −0.382771 | + | 1.17805i | ||||
\(755\) | 5.73704 | + | 1.33509i | 0.208792 | + | 0.0485889i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1132 | 0.658337 | 0.329169 | − | 0.944271i | \(-0.393232\pi\) | ||||
0.329169 | + | 0.944271i | \(0.393232\pi\) | |||||||
\(758\) | 9.82663 | + | 30.2432i | 0.356919 | + | 1.09848i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.66578 | − | 2.81568i | 0.241793 | − | 0.102136i | ||||
\(761\) | −7.95941 | + | 5.78285i | −0.288529 | + | 0.209628i | −0.722629 | − | 0.691236i | \(-0.757066\pi\) |
0.434100 | + | 0.900865i | \(0.357066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.8965 | − | 17.3618i | −0.865112 | − | 0.628541i | ||||
\(764\) | −1.00000 | + | 0.726543i | −0.0361787 | + | 0.0262854i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.7539 | + | 13.6255i | 0.677607 | + | 0.492310i | ||||
\(767\) | 16.2394 | + | 49.9796i | 0.586369 | + | 1.80466i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8687 | − | 51.9166i | −0.608302 | − | 1.87216i | −0.472262 | − | 0.881458i | \(-0.656562\pi\) |
−0.136040 | − | 0.990703i | \(-0.543438\pi\) | |||||||
\(770\) | −9.14548 | + | 15.1604i | −0.329580 | + | 0.546343i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.32890 | + | 25.6337i | −0.299764 | + | 0.922578i | ||||
\(773\) | −25.9764 | + | 18.8729i | −0.934305 | + | 0.678812i | −0.947043 | − | 0.321107i | \(-0.895945\pi\) |
0.0127381 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.52912 | + | 17.5492i | −0.0908487 | + | 0.630386i | ||||
\(776\) | −17.2119 | −0.617870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.94657 | − | 12.1463i | 0.141491 | − | 0.435466i | ||||
\(779\) | 0.164135 | − | 0.505156i | 0.00588075 | − | 0.0180991i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.403252 | + | 1.24108i | 0.0144295 | + | 0.0444094i | ||||
\(782\) | −34.2824 | −1.22594 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.34600 | + | 0.977926i | 0.0480714 | + | 0.0349259i | ||||
\(785\) | 8.09781 | + | 1.88448i | 0.289023 | + | 0.0672599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.1703 | + | 31.3651i | 1.53886 | + | 1.11804i | 0.951048 | + | 0.309044i | \(0.100009\pi\) |
0.587808 | + | 0.809000i | \(0.299991\pi\) | |||||||
\(788\) | 20.5640 | + | 14.9406i | 0.732560 | + | 0.532236i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.91895 | − | 34.0508i | −0.103852 | − | 1.21147i | ||||
\(791\) | −9.43731 | − | 6.85661i | −0.335552 | − | 0.243793i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.51785 | 0.0539004 | ||||||||
\(794\) | 5.21110 | + | 16.0381i | 0.184935 | + | 0.569172i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.72373 | − | 20.6935i | 0.238316 | − | 0.733463i | ||||
\(797\) | −3.52634 | + | 10.8530i | −0.124909 | + | 0.384431i | −0.993885 | − | 0.110424i | \(-0.964779\pi\) |
0.868975 | + | 0.494856i | \(0.164779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.8295 | −1.69209 | ||||||||
\(800\) | 4.48626 | + | 2.20759i | 0.158613 | + | 0.0780501i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.63443 | − | 1.18748i | 0.0577138 | − | 0.0419315i | ||||
\(803\) | 0.0796751 | − | 0.245215i | 0.00281167 | − | 0.00865344i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.2797 | − | 8.98875i | 0.750013 | − | 0.316812i | ||||
\(806\) | −5.40020 | − | 16.6201i | −0.190214 | − | 0.585419i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.76432 | − | 5.43002i | −0.0620686 | − | 0.191027i | ||||
\(809\) | 22.9630 | + | 16.6836i | 0.807337 | + | 0.586564i | 0.913057 | − | 0.407831i | \(-0.133715\pi\) |
−0.105721 | + | 0.994396i | \(0.533715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0027 | + | 23.2513i | −1.12377 | + | 0.816463i | −0.984776 | − | 0.173831i | \(-0.944386\pi\) |
−0.138990 | + | 0.990294i | \(0.544386\pi\) | |||||||
\(812\) | 12.8986 | + | 9.37135i | 0.452651 | + | 0.328870i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.9746 | − | 7.97348i | 0.384658 | − | 0.279470i | ||||
\(815\) | −20.4965 | − | 23.6621i | −0.717960 | − | 0.828847i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.71149 | + | 20.6558i | 0.234805 | + | 0.722657i | ||||
\(818\) | 3.80495 | 0.133037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.338092 | − | 0.142813i | 0.0118067 | − | 0.00498724i | ||||
\(821\) | 7.65811 | − | 23.5692i | 0.267270 | − | 0.822572i | −0.723892 | − | 0.689913i | \(-0.757649\pi\) |
0.991162 | − | 0.132659i | \(-0.0423514\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.39437 | + | 3.91924i | −0.188036 | + | 0.136616i | −0.677821 | − | 0.735227i | \(-0.737075\pi\) |
0.489785 | + | 0.871843i | \(0.337075\pi\) | |||||||
\(824\) | 17.3457 | 0.604267 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.6336 | 0.857113 | ||||||||
\(827\) | 8.30060 | − | 6.03074i | 0.288640 | − | 0.209709i | −0.434037 | − | 0.900895i | \(-0.642911\pi\) |
0.722677 | + | 0.691186i | \(0.242911\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0307 | + | 40.1043i | −0.452575 | + | 1.39288i | 0.421385 | + | 0.906882i | \(0.361544\pi\) |
−0.873959 | + | 0.485999i | \(0.838456\pi\) | |||||||
\(830\) | −1.91312 | − | 2.20859i | −0.0664053 | − | 0.0766614i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.92807 | −0.170850 | ||||||||
\(833\) | −3.94118 | − | 12.1297i | −0.136554 | − | 0.420269i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73694 | + | 55.2583i | 0.163928 | + | 1.91229i | ||||
\(836\) | 8.97378 | − | 6.51983i | 0.310365 | − | 0.225493i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.10696 | − | 4.43696i | −0.210961 | − | 0.153272i | ||||
\(839\) | −37.9625 | + | 27.5814i | −1.31061 | + | 0.952215i | −0.310613 | + | 0.950537i | \(0.600534\pi\) |
−0.999999 | + | 0.00167835i | \(0.999466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0764 | − | 10.9537i | −0.519877 | − | 0.377713i | ||||
\(842\) | 4.73955 | + | 14.5868i | 0.163336 | + | 0.502696i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.85536 | − | 21.0986i | −0.235971 | − | 0.726245i | ||||
\(845\) | −2.15540 | − | 25.1437i | −0.0741482 | − | 0.864970i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.534654 | + | 1.64550i | −0.0183709 | + | 0.0565399i | ||||
\(848\) | 9.68598 | − | 7.03727i | 0.332618 | − | 0.241661i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.8756 | − | 33.9053i | −0.613129 | − | 1.16294i | ||||
\(851\) | −17.6988 | −0.606708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.49257 | + | 7.67135i | −0.0853440 | + | 0.262662i | −0.984617 | − | 0.174726i | \(-0.944096\pi\) |
0.899273 | + | 0.437388i | \(0.144096\pi\) | |||||||
\(854\) | 0.219863 | − | 0.676669i | 0.00752356 | − | 0.0231551i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.485634 | + | 1.49463i | 0.0165986 | + | 0.0510853i | ||||
\(857\) | −15.1446 | −0.517331 | −0.258666 | − | 0.965967i | \(-0.583283\pi\) | ||||
−0.258666 | + | 0.965967i | \(0.583283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.55268 | − | 5.48734i | −0.257694 | − | 0.187226i | 0.451436 | − | 0.892304i | \(-0.350912\pi\) |
−0.709130 | + | 0.705078i | \(0.750912\pi\) | |||||||
\(860\) | −7.75188 | + | 12.8502i | −0.264337 | + | 0.438190i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.59181 | + | 5.51578i | 0.258578 | + | 0.187868i | ||||
\(863\) | −6.85207 | − | 4.97832i | −0.233247 | − | 0.169464i | 0.465022 | − | 0.885299i | \(-0.346046\pi\) |
−0.698270 | + | 0.715835i | \(0.746046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.8814 | + | 18.5359i | −1.49201 | + | 0.630239i | ||||
\(866\) | 24.4735 | + | 17.7810i | 0.831642 | + | 0.604223i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.19161 | −0.278041 | ||||||||
\(869\) | −16.1888 | − | 49.8240i | −0.549167 | − | 1.69016i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.02951 | − | 21.6346i | 0.238186 | − | 0.733061i | ||||
\(872\) | −3.95131 | + | 12.1609i | −0.133808 | + | 0.411820i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.4721 | −0.489527 | ||||||||
\(875\) | 19.9856 | + | 16.3587i | 0.675637 | + | 0.553025i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8678 | − | 11.5287i | 0.535819 | − | 0.389295i | −0.286711 | − | 0.958017i | \(-0.592562\pi\) |
0.822530 | + | 0.568722i | \(0.192562\pi\) | |||||||
\(878\) | 11.7687 | − | 36.2202i | 0.397173 | − | 1.22237i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.46505 | + | 1.73722i | 0.251647 | + | 0.0585618i | ||||
\(881\) | 0.663267 | + | 2.04133i | 0.0223460 | + | 0.0687740i | 0.961608 | − | 0.274428i | \(-0.0884885\pi\) |
−0.939262 | + | 0.343202i | \(0.888488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.291020 | − | 0.895667i | −0.00979360 | − | 0.0301416i | 0.946040 | − | 0.324049i | \(-0.105044\pi\) |
−0.955834 | + | 0.293907i | \(0.905044\pi\) | |||||||
\(884\) | 30.5626 | + | 22.2050i | 1.02793 | + | 0.746836i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.24425 | + | 0.903997i | −0.0418012 | + | 0.0303704i | ||||
\(887\) | −26.5838 | − | 19.3143i | −0.892598 | − | 0.648510i | 0.0439563 | − | 0.999033i | \(-0.486004\pi\) |
−0.936554 | + | 0.350523i | \(0.886004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4200 | − | 7.57058i | 0.349476 | − | 0.253909i | ||||
\(890\) | 5.11639 | − | 8.48141i | 0.171502 | − | 0.284297i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.44118 | + | 7.51317i | 0.0817367 | + | 0.251560i | ||||
\(893\) | −20.1910 | −0.675665 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0259 | − | 18.2776i | 0.368555 | − | 0.610952i | ||||
\(896\) | −0.713839 | + | 2.19697i | −0.0238477 | + | 0.0733957i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.3626 | − | 8.25541i | 0.379175 | − | 0.275486i | ||||
\(899\) | 24.4746 | 0.816275 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −91.7787 | −3.05759 | ||||||||
\(902\) | 0.455155 | − | 0.330689i | 0.0151550 | − | 0.0110108i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.56047 | + | 4.80262i | −0.0519004 | + | 0.159733i | ||||
\(905\) | 0.137796 | + | 1.60744i | 0.00458048 | + | 0.0534332i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.8128 | −1.82003 | −0.910014 | − | 0.414577i | \(-0.863930\pi\) | ||||
−0.910014 | + | 0.414577i | \(0.863930\pi\) | |||||||
\(908\) | 0.823143 | + | 2.53337i | 0.0273170 | + | 0.0840730i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.7929 | − | 5.76967i | −0.821877 | − | 0.191263i | ||||
\(911\) | 10.0457 | − | 7.29864i | 0.332829 | − | 0.241815i | −0.408801 | − | 0.912624i | \(-0.634053\pi\) |
0.741630 | + | 0.670809i | \(0.234053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.62367 | − | 2.63275i | −0.119926 | − | 0.0871313i | ||||
\(914\) | −11.7913 | + | 8.56687i | −0.390021 | + | 0.283367i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.61024 | + | 5.52917i | 0.251450 | + | 0.182689i | ||||
\(917\) | 4.38573 | + | 13.4979i | 0.144830 | + | 0.445740i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1076 | + | 31.1081i | 0.333420 | + | 1.02616i | 0.967495 | + | 0.252890i | \(0.0813810\pi\) |
−0.634075 | + | 0.773271i | \(0.718619\pi\) | |||||||
\(920\) | −6.54736 | − | 7.55858i | −0.215860 | − | 0.249199i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.58386 | + | 17.1854i | −0.183895 | + | 0.565969i | ||||
\(923\) | −1.51785 | + | 1.10278i | −0.0499606 | + | 0.0362985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.22856 | − | 17.5041i | −0.303433 | − | 0.575531i | ||||
\(926\) | 20.5585 | 0.675595 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.13279 | − | 6.56405i | 0.0700122 | − | 0.215475i | ||||
\(929\) | 11.6232 | − | 35.7724i | 0.381344 | − | 1.17365i | −0.557755 | − | 0.830006i | \(-0.688337\pi\) |
0.939098 | − | 0.343649i | \(-0.111663\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.66375 | − | 5.12049i | −0.0545271 | − | 0.167817i | ||||
\(932\) | −14.7867 | −0.484355 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.3864 | + | 14.8116i | 0.667063 | + | 0.484650i | ||||
\(935\) | −38.4687 | − | 44.4101i | −1.25806 | − | 1.45237i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.7311 | − | 15.7885i | −0.709923 | − | 0.515789i | 0.173226 | − | 0.984882i | \(-0.444581\pi\) |
−0.883149 | + | 0.469093i | \(0.844581\pi\) | |||||||
\(938\) | −8.62664 | − | 6.26762i | −0.281670 | − | 0.204645i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.13463 | − | 10.5454i | −0.297939 | − | 0.343955i | ||||
\(941\) | −34.6644 | − | 25.1852i | −1.13003 | − | 0.821014i | −0.144330 | − | 0.989530i | \(-0.546103\pi\) |
−0.985699 | + | 0.168516i | \(0.946103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.734034 | −0.0239035 | ||||||||
\(944\) | −3.29528 | − | 10.1418i | −0.107252 | − | 0.330088i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.10889 | + | 21.8789i | −0.231130 | + | 0.711345i | ||||
\(947\) | −10.4191 | + | 32.0668i | −0.338577 | + | 1.04203i | 0.626357 | + | 0.779537i | \(0.284545\pi\) |
−0.964933 | + | 0.262495i | \(0.915455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.370695 | 0.0120333 | ||||||||
\(950\) | −7.54610 | − | 14.3129i | −0.244828 | − | 0.464373i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.3262 | − | 10.4086i | 0.464316 | − | 0.337345i | ||||
\(953\) | 4.02931 | − | 12.4010i | 0.130522 | − | 0.401706i | −0.864344 | − | 0.502900i | \(-0.832266\pi\) |
0.994867 | + | 0.101194i | \(0.0322663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.80964 | + | 2.08914i | 0.0585587 | + | 0.0676030i | ||||
\(956\) | 3.89981 | + | 12.0024i | 0.126129 | + | 0.388185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.809645 | − | 2.49183i | −0.0261584 | − | 0.0805074i | ||||
\(959\) | −9.48631 | − | 6.89221i | −0.306329 | − | 0.222561i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9063 | − | 10.8300i | 0.480848 | − | 0.349356i | ||||
\(962\) | 15.7784 | + | 11.4637i | 0.508717 | + | 0.369604i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.9247 | − | 10.1169i | 0.448485 | − | 0.325843i | ||||
\(965\) | 58.7000 | + | 13.6603i | 1.88962 | + | 0.439741i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.53843 | − | 20.1232i | −0.210262 | − | 0.647119i | −0.999456 | − | 0.0329758i | \(-0.989502\pi\) |
0.789194 | − | 0.614144i | \(-0.210498\pi\) | |||||||
\(968\) | 0.748983 | 0.0240732 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.28718 | + | 38.3463i | 0.105545 | + | 1.23123i | ||||
\(971\) | −1.55251 | + | 4.77814i | −0.0498225 | + | 0.153338i | −0.972872 | − | 0.231342i | \(-0.925688\pi\) |
0.923050 | + | 0.384680i | \(0.125688\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1028 | − | 8.06669i | 0.355941 | − | 0.258606i | ||||
\(974\) | 25.1481 | 0.805796 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.308001 | −0.00985887 | ||||||||
\(977\) | 49.4746 | − | 35.9454i | 1.58283 | − | 1.15000i | 0.669477 | − | 0.742833i | \(-0.266518\pi\) |
0.913356 | − | 0.407162i | \(-0.133482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.69200 | − | 14.4405i | 0.149957 | − | 0.461520i | ||||
\(980\) | 1.92166 | − | 3.18552i | 0.0613850 | − | 0.101758i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.6216 | −1.00908 | ||||||||
\(983\) | 9.94678 | + | 30.6131i | 0.317253 | + | 0.976405i | 0.974817 | + | 0.223006i | \(0.0715870\pi\) |
−0.657564 | + | 0.753399i | \(0.728413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3587 | − | 48.6678i | 0.935447 | − | 1.55068i | ||||
\(986\) | −42.8035 | + | 31.0986i | −1.36314 | + | 0.990380i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.9018 | + | 9.37374i | 0.410462 | + | 0.298218i | ||||
\(989\) | 24.2824 | − | 17.6422i | 0.772136 | − | 0.560989i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8588 | − | 16.6079i | −0.726135 | − | 0.527568i | 0.162203 | − | 0.986757i | \(-0.448140\pi\) |
−0.888338 | + | 0.459189i | \(0.848140\pi\) | |||||||
\(992\) | 1.09581 | + | 3.37254i | 0.0347919 | + | 0.107078i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.271766 | + | 0.836409i | 0.00861989 | + | 0.0265293i | ||||
\(995\) | −47.3872 | − | 11.0277i | −1.50227 | − | 0.349601i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.06317 | − | 3.27211i | 0.0336711 | − | 0.103629i | −0.932808 | − | 0.360372i | \(-0.882650\pi\) |
0.966480 | + | 0.256744i | \(0.0826496\pi\) | |||||||
\(998\) | 23.1594 | − | 16.8263i | 0.733099 | − | 0.532628i | ||||
\(999\) | 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 | 450.2.h.d.361.1 | 8 | ||
3.2 | odd | 2 | 150.2.g.c.61.2 | ✓ | 8 | ||
15.2 | even | 4 | 750.2.h.e.199.3 | 16 | |||
15.8 | even | 4 | 750.2.h.e.199.2 | 16 | |||
15.14 | odd | 2 | 750.2.g.d.301.2 | 8 | |||
25.16 | even | 5 | inner | 450.2.h.d.91.1 | 8 | ||
75.29 | odd | 10 | 3750.2.a.q.1.3 | 4 | |||
75.38 | even | 20 | 750.2.h.e.49.4 | 16 | |||
75.41 | odd | 10 | 150.2.g.c.91.2 | yes | 8 | ||
75.47 | even | 20 | 3750.2.c.h.1249.2 | 8 | |||
75.53 | even | 20 | 3750.2.c.h.1249.7 | 8 | |||
75.59 | odd | 10 | 750.2.g.d.451.2 | 8 | |||
75.62 | even | 20 | 750.2.h.e.49.1 | 16 | |||
75.71 | odd | 10 | 3750.2.a.l.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.c.61.2 | ✓ | 8 | 3.2 | odd | 2 | ||
150.2.g.c.91.2 | yes | 8 | 75.41 | odd | 10 | ||
450.2.h.d.91.1 | 8 | 25.16 | even | 5 | inner | ||
450.2.h.d.361.1 | 8 | 1.1 | even | 1 | trivial | ||
750.2.g.d.301.2 | 8 | 15.14 | odd | 2 | |||
750.2.g.d.451.2 | 8 | 75.59 | odd | 10 | |||
750.2.h.e.49.1 | 16 | 75.62 | even | 20 | |||
750.2.h.e.49.4 | 16 | 75.38 | even | 20 | |||
750.2.h.e.199.2 | 16 | 15.8 | even | 4 | |||
750.2.h.e.199.3 | 16 | 15.2 | even | 4 | |||
3750.2.a.l.1.2 | 4 | 75.71 | odd | 10 | |||
3750.2.a.q.1.3 | 4 | 75.29 | odd | 10 | |||
3750.2.c.h.1249.2 | 8 | 75.47 | even | 20 | |||
3750.2.c.h.1249.7 | 8 | 75.53 | even | 20 |