Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(298,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.dl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 415.6 | ||
Root | \(-0.929293 + 0.536527i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.415 |
Dual form | 819.2.dl.e.298.6 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.929293 | + | 0.536527i | 0.657109 | + | 0.379382i | 0.791175 | − | 0.611590i | \(-0.209470\pi\) |
−0.134065 | + | 0.990972i | \(0.542803\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.424277 | − | 0.734868i | −0.212138 | − | 0.367434i | ||||
\(5\) | −0.541640 | − | 0.312716i | −0.242229 | − | 0.139851i | 0.373972 | − | 0.927440i | \(-0.377996\pi\) |
−0.616201 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34996 | + | 1.21561i | 0.888200 | + | 0.459458i | ||||
\(8\) | − | 3.05665i | − | 1.08069i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.335561 | − | 0.581209i | −0.106114 | − | 0.183795i | ||||
\(11\) | 0.613597 | − | 0.354260i | 0.185006 | − | 0.106814i | −0.404636 | − | 0.914478i | \(-0.632602\pi\) |
0.589643 | + | 0.807664i | \(0.299269\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.848553 | − | 3.50428i | 0.235346 | − | 0.971912i | ||||
\(14\) | 1.53159 | + | 2.39047i | 0.409334 | + | 0.638881i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.791426 | − | 1.37079i | 0.197856 | − | 0.342697i | ||||
\(17\) | 1.67157 | + | 2.89524i | 0.405414 | + | 0.702199i | 0.994370 | − | 0.105967i | \(-0.0337939\pi\) |
−0.588955 | + | 0.808166i | \(0.700461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.50573 | − | 2.60138i | −1.03368 | − | 0.596798i | −0.115646 | − | 0.993290i | \(-0.536894\pi\) |
−0.918038 | + | 0.396492i | \(0.870227\pi\) | |||||||
\(20\) | 0.530712i | 0.118671i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.760282 | 0.162093 | ||||||||
\(23\) | 2.21570 | − | 3.83771i | 0.462006 | − | 0.800218i | −0.537055 | − | 0.843547i | \(-0.680463\pi\) |
0.999061 | + | 0.0433296i | \(0.0137966\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.30442 | − | 3.99137i | −0.460883 | − | 0.798274i | ||||
\(26\) | 2.66870 | − | 2.80123i | 0.523374 | − | 0.549366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.103717 | − | 2.24266i | −0.0196006 | − | 0.423824i | ||||
\(29\) | 6.59711 | 1.22505 | 0.612526 | − | 0.790450i | \(-0.290153\pi\) | ||||
0.612526 | + | 0.790450i | \(0.290153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.80238 | − | 2.19530i | 0.682927 | − | 0.394288i | −0.118030 | − | 0.993010i | \(-0.537658\pi\) |
0.800957 | + | 0.598722i | \(0.204325\pi\) | |||||||
\(32\) | −3.82335 | + | 2.20741i | −0.675879 | + | 0.390219i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.58737i | 0.615228i | ||||||||
\(35\) | −0.892689 | − | 1.39329i | −0.150892 | − | 0.235509i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.366683 | − | 0.211704i | −0.0602823 | − | 0.0348040i | 0.469556 | − | 0.882903i | \(-0.344414\pi\) |
−0.529838 | + | 0.848099i | \(0.677747\pi\) | |||||||
\(38\) | −2.79143 | − | 4.83489i | −0.452829 | − | 0.784323i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.955864 | + | 1.65561i | −0.151135 | + | 0.261774i | ||||
\(41\) | − | 5.01604i | − | 0.783374i | −0.920099 | − | 0.391687i | \(-0.871892\pi\) | ||
0.920099 | − | 0.391687i | \(-0.128108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2059 | 1.70889 | 0.854445 | − | 0.519542i | \(-0.173897\pi\) | ||||
0.854445 | + | 0.519542i | \(0.173897\pi\) | |||||||
\(44\) | −0.520670 | − | 0.300609i | −0.0784939 | − | 0.0453185i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.11807 | − | 2.37757i | 0.607177 | − | 0.350554i | ||||
\(47\) | 6.99116 | + | 4.03635i | 1.01977 | + | 0.588762i | 0.914036 | − | 0.405633i | \(-0.132949\pi\) |
0.105729 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.04458 | + | 5.71326i | 0.577797 | + | 0.816180i | ||||
\(50\) | − | 4.94553i | − | 0.699404i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.93520 | + | 0.863208i | −0.407040 | + | 0.119705i | ||||
\(53\) | −0.348553 | − | 0.603712i | −0.0478774 | − | 0.0829262i | 0.841094 | − | 0.540890i | \(-0.181912\pi\) |
−0.888971 | + | 0.457964i | \(0.848579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.443132 | −0.0597519 | ||||||||
\(56\) | 3.71570 | − | 7.18300i | 0.496532 | − | 0.959869i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.13065 | + | 3.53953i | 0.804993 | + | 0.464763i | ||||
\(59\) | −8.54177 | + | 4.93159i | −1.11204 | + | 0.642039i | −0.939358 | − | 0.342938i | \(-0.888578\pi\) |
−0.172686 | + | 0.984977i | \(0.555244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.34855 | + | 4.06781i | −0.300701 | + | 0.520830i | −0.976295 | − | 0.216444i | \(-0.930554\pi\) |
0.675594 | + | 0.737274i | \(0.263887\pi\) | |||||||
\(62\) | 4.71136 | 0.598344 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.90305 | −0.987881 | ||||||||
\(65\) | −1.55545 | + | 1.63270i | −0.192930 | + | 0.202512i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.02470 | + | 5.21041i | −1.10254 | + | 0.636553i | −0.936888 | − | 0.349631i | \(-0.886307\pi\) |
−0.165655 | + | 0.986184i | \(0.552974\pi\) | |||||||
\(68\) | 1.41841 | − | 2.45676i | 0.172008 | − | 0.297926i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0820297 | − | 1.77373i | −0.00980443 | − | 0.212001i | ||||
\(71\) | − | 14.0876i | − | 1.67189i | −0.548812 | − | 0.835946i | \(-0.684920\pi\) | ||
0.548812 | − | 0.835946i | \(-0.315080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.40273 | + | 2.54191i | −0.515300 | + | 0.297509i | −0.735010 | − | 0.678057i | \(-0.762822\pi\) |
0.219710 | + | 0.975565i | \(0.429489\pi\) | |||||||
\(74\) | −0.227170 | − | 0.393471i | −0.0264080 | − | 0.0457400i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.41482i | 0.506415i | ||||||||
\(77\) | 1.87257 | − | 0.0866008i | 0.213399 | − | 0.00986908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95586 | − | 3.38766i | 0.220052 | − | 0.381141i | −0.734772 | − | 0.678315i | \(-0.762711\pi\) |
0.954823 | + | 0.297174i | \(0.0960440\pi\) | |||||||
\(80\) | −0.857336 | + | 0.494983i | −0.0958530 | + | 0.0553408i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.69124 | − | 4.66137i | 0.297198 | − | 0.514762i | ||||
\(83\) | 10.2035i | 1.11998i | 0.828499 | + | 0.559990i | \(0.189195\pi\) | ||||
−0.828499 | + | 0.559990i | \(0.810805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.09090i | − | 0.226790i | ||||||
\(86\) | 10.4136 | + | 6.01230i | 1.12293 | + | 0.648323i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.08285 | − | 1.87555i | −0.115432 | − | 0.199935i | ||||
\(89\) | −11.5866 | − | 6.68955i | −1.22818 | − | 0.709090i | −0.261532 | − | 0.965195i | \(-0.584228\pi\) |
−0.966649 | + | 0.256104i | \(0.917561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.25390 | − | 7.20338i | 0.655587 | − | 0.755120i | ||||
\(92\) | −3.76028 | −0.392036 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.33122 | + | 7.50190i | 0.446731 | + | 0.773761i | ||||
\(95\) | 1.62699 | + | 2.81802i | 0.166925 | + | 0.289123i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.202023i | 0.0205123i | 0.999947 | + | 0.0102562i | \(0.00326470\pi\) | ||||
−0.999947 | + | 0.0102562i | \(0.996735\pi\) | |||||||
\(98\) | 0.693276 | + | 7.47932i | 0.0700315 | + | 0.755526i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.95542 | + | 3.38689i | −0.195542 | + | 0.338689i | ||||
\(101\) | 8.66723 | + | 15.0121i | 0.862421 | + | 1.49376i | 0.869585 | + | 0.493783i | \(0.164386\pi\) |
−0.00716374 | + | 0.999974i | \(0.502280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.40739 | + | 9.36587i | −0.532806 | + | 0.922847i | 0.466460 | + | 0.884542i | \(0.345529\pi\) |
−0.999266 | + | 0.0383047i | \(0.987804\pi\) | |||||||
\(104\) | −10.7114 | − | 2.59373i | −1.05034 | − | 0.254336i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.748033i | − | 0.0726554i | ||||||
\(107\) | −3.05839 | + | 5.29729i | −0.295666 | + | 0.512108i | −0.975140 | − | 0.221592i | \(-0.928875\pi\) |
0.679474 | + | 0.733700i | \(0.262208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.87196 | + | 5.69958i | −0.945563 | + | 0.545921i | −0.891700 | − | 0.452628i | \(-0.850487\pi\) |
−0.0538629 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(110\) | −0.411799 | − | 0.237752i | −0.0392635 | − | 0.0226688i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.52616 | − | 2.25923i | 0.333191 | − | 0.213477i | ||||
\(113\) | 0.923456 | 0.0868714 | 0.0434357 | − | 0.999056i | \(-0.486170\pi\) | ||||
0.0434357 | + | 0.999056i | \(0.486170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.40023 | + | 1.38577i | −0.223822 | + | 0.129224i | ||||
\(116\) | −2.79900 | − | 4.84801i | −0.259880 | − | 0.450126i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5837 | −0.974312 | ||||||||
\(119\) | 0.408623 | + | 8.83566i | 0.0374584 | + | 0.809963i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.24900 | + | 9.09153i | −0.477182 | + | 0.826503i | ||||
\(122\) | −4.36499 | + | 2.52013i | −0.395187 | + | 0.228162i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.22652 | − | 1.86283i | −0.289750 | − | 0.167287i | ||||
\(125\) | 6.00967i | 0.537521i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.50972 | 0.755116 | 0.377558 | − | 0.925986i | \(-0.376764\pi\) | ||||
0.377558 | + | 0.925986i | \(0.376764\pi\) | |||||||
\(128\) | 0.302447 | + | 0.174618i | 0.0267328 | + | 0.0154342i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.32146 | + | 0.682713i | −0.203606 | + | 0.0598779i | ||||
\(131\) | −3.50152 | + | 6.06482i | −0.305930 | + | 0.529885i | −0.977468 | − | 0.211084i | \(-0.932301\pi\) |
0.671538 | + | 0.740970i | \(0.265634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.42599 | − | 11.5903i | −0.643915 | − | 1.00501i | ||||
\(134\) | −11.1821 | −0.965988 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.84974 | − | 5.10940i | 0.758859 | − | 0.438128i | ||||
\(137\) | 5.38403 | − | 3.10847i | 0.459989 | − | 0.265575i | −0.252051 | − | 0.967714i | \(-0.581105\pi\) |
0.712040 | + | 0.702139i | \(0.247772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.53140 | 0.553986 | 0.276993 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276993 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(140\) | −0.645140 | + | 1.24715i | −0.0545242 | + | 0.105403i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.55839 | − | 13.0915i | 0.634286 | − | 1.09862i | ||||
\(143\) | −0.720757 | − | 2.45082i | −0.0602727 | − | 0.204948i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.57326 | − | 2.06302i | −0.296743 | − | 0.171325i | ||||
\(146\) | −5.45523 | −0.451478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.359285i | 0.0295330i | ||||||||
\(149\) | 3.20203 | + | 1.84869i | 0.262320 | + | 0.151451i | 0.625393 | − | 0.780310i | \(-0.284939\pi\) |
−0.363072 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.22425 | + | 2.43887i | −0.343764 | + | 0.198473i | −0.661935 | − | 0.749561i | \(-0.730265\pi\) |
0.318171 | + | 0.948033i | \(0.396931\pi\) | |||||||
\(152\) | −7.95152 | + | 13.7724i | −0.644954 | + | 1.11709i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.78663 | + | 0.924207i | 0.143971 | + | 0.0744747i | ||||
\(155\) | −2.74603 | −0.220566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.75984 | + | 8.24428i | 0.379876 | + | 0.657965i | 0.991044 | − | 0.133536i | \(-0.0426332\pi\) |
−0.611168 | + | 0.791501i | \(0.709300\pi\) | |||||||
\(158\) | 3.63514 | − | 2.09875i | 0.289196 | − | 0.166968i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.76117 | 0.218290 | ||||||||
\(161\) | 9.87196 | − | 6.32501i | 0.778020 | − | 0.498481i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5325 | + | 11.8544i | 1.60823 | + | 0.928511i | 0.989767 | + | 0.142696i | \(0.0455770\pi\) |
0.618461 | + | 0.785815i | \(0.287756\pi\) | |||||||
\(164\) | −3.68613 | + | 2.12819i | −0.287838 | + | 0.166184i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.47446 | + | 9.48204i | −0.424901 | + | 0.735949i | ||||
\(167\) | − | 1.13193i | − | 0.0875914i | −0.999041 | − | 0.0437957i | \(-0.986055\pi\) | ||
0.999041 | − | 0.0437957i | \(-0.0139451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5599 | − | 5.94713i | −0.889224 | − | 0.457472i | ||||
\(170\) | 1.12183 | − | 1.94306i | 0.0860402 | − | 0.149026i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.75442 | − | 8.23489i | −0.362521 | − | 0.627905i | ||||
\(173\) | −5.99458 | + | 10.3829i | −0.455760 | + | 0.789399i | −0.998732 | − | 0.0503522i | \(-0.983966\pi\) |
0.542972 | + | 0.839751i | \(0.317299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.563327 | − | 12.1808i | −0.0425835 | − | 0.920783i | ||||
\(176\) | − | 1.12148i | − | 0.0845350i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.17825 | − | 12.4331i | −0.538033 | − | 0.931900i | ||||
\(179\) | −4.73538 | − | 8.20192i | −0.353939 | − | 0.613040i | 0.632997 | − | 0.774154i | \(-0.281825\pi\) |
−0.986936 | + | 0.161114i | \(0.948491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4314 | −0.849690 | −0.424845 | − | 0.905266i | \(-0.639671\pi\) | ||||
−0.424845 | + | 0.905266i | \(0.639671\pi\) | |||||||
\(182\) | 9.67652 | − | 3.33866i | 0.717271 | − | 0.247478i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.7305 | − | 6.77264i | −0.864788 | − | 0.499285i | ||||
\(185\) | 0.132407 | + | 0.229335i | 0.00973473 | + | 0.0168611i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.05134 | + | 1.18434i | 0.150009 | + | 0.0866075i | ||||
\(188\) | − | 6.85011i | − | 0.499595i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.49169i | 0.253314i | ||||||||
\(191\) | 7.84377 | − | 13.5858i | 0.567555 | − | 0.983034i | −0.429252 | − | 0.903185i | \(-0.641223\pi\) |
0.996807 | − | 0.0798496i | \(-0.0254440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9248 | − | 11.5036i | 1.43422 | − | 0.828045i | 0.436776 | − | 0.899570i | \(-0.356120\pi\) |
0.997439 | + | 0.0715256i | \(0.0227868\pi\) | |||||||
\(194\) | −0.108391 | + | 0.187739i | −0.00778202 | + | 0.0134788i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.48248 | − | 5.39624i | 0.177320 | − | 0.385446i | ||||
\(197\) | − | 10.2035i | − | 0.726970i | −0.931600 | − | 0.363485i | \(-0.881587\pi\) | ||
0.931600 | − | 0.363485i | \(-0.118413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.96173 | + | 10.3260i | 0.422616 | + | 0.731992i | 0.996194 | − | 0.0871586i | \(-0.0277787\pi\) |
−0.573579 | + | 0.819150i | \(0.694445\pi\) | |||||||
\(200\) | −12.2002 | + | 7.04381i | −0.862687 | + | 0.498072i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.6008i | 1.30875i | ||||||||
\(203\) | 15.5029 | + | 8.01952i | 1.08809 | + | 0.562860i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.56860 | + | 2.71689i | −0.109555 | + | 0.189756i | ||||
\(206\) | −10.0501 | + | 5.80243i | −0.700223 | + | 0.404274i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.13206 | − | 3.93656i | −0.286507 | − | 0.272952i | ||||
\(209\) | −3.68627 | −0.254984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5893 | −1.07321 | −0.536606 | − | 0.843833i | \(-0.680294\pi\) | ||||
−0.536606 | + | 0.843833i | \(0.680294\pi\) | |||||||
\(212\) | −0.295766 | + | 0.512281i | −0.0203133 | + | 0.0351836i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.68428 | + | 3.28182i | −0.388570 | + | 0.224341i | ||||
\(215\) | −6.06959 | − | 3.50428i | −0.413942 | − | 0.238990i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.6041 | − | 0.536653i | 0.787734 | − | 0.0364304i | ||||
\(218\) | −12.2319 | −0.828451 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.188010 | + | 0.325643i | 0.0126757 | + | 0.0219549i | ||||
\(221\) | 11.5641 | − | 3.40087i | 0.777888 | − | 0.228767i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.76662i | − | 0.453126i | −0.973996 | − | 0.226563i | \(-0.927251\pi\) | ||
0.973996 | − | 0.226563i | \(-0.0727490\pi\) | |||||||
\(224\) | −11.6680 | + | 0.539613i | −0.779604 | + | 0.0360544i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.858161 | + | 0.495459i | 0.0570840 | + | 0.0329575i | ||||
\(227\) | −14.5704 | + | 8.41225i | −0.967074 | + | 0.558340i | −0.898343 | − | 0.439295i | \(-0.855228\pi\) |
−0.0687311 | + | 0.997635i | \(0.521895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.54855 | + | 5.51286i | 0.630986 | + | 0.364300i | 0.781134 | − | 0.624364i | \(-0.214642\pi\) |
−0.150148 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(230\) | −2.97402 | −0.196101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 20.1651i | − | 1.32390i | ||||||
\(233\) | −8.67743 | + | 15.0298i | −0.568477 | + | 0.984632i | 0.428239 | + | 0.903665i | \(0.359134\pi\) |
−0.996717 | + | 0.0809664i | \(0.974199\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.52446 | − | 4.37249i | −0.164678 | − | 0.285230i | ||||
\(236\) | 7.24814 | + | 4.18472i | 0.471814 | + | 0.272402i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.36084 | + | 8.43015i | −0.282671 | + | 0.546445i | ||||
\(239\) | − | 19.7223i | − | 1.27573i | −0.770148 | − | 0.637865i | \(-0.779818\pi\) | ||
0.770148 | − | 0.637865i | \(-0.220182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.41112 | + | 1.39206i | −0.155314 | + | 0.0896706i | −0.575643 | − | 0.817701i | \(-0.695248\pi\) |
0.420329 | + | 0.907372i | \(0.361915\pi\) | |||||||
\(242\) | −9.75571 | + | 5.63246i | −0.627121 | + | 0.362069i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.98574 | 0.255161 | ||||||||
\(245\) | −0.404077 | − | 4.35934i | −0.0258155 | − | 0.278508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9393 | + | 13.5819i | −0.823309 | + | 0.864196i | ||||
\(248\) | −6.71028 | − | 11.6226i | −0.426103 | − | 0.738033i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.22435 | + | 5.58475i | −0.203926 | + | 0.353210i | ||||
\(251\) | 23.5608 | 1.48714 | 0.743572 | − | 0.668655i | \(-0.233130\pi\) | ||||
0.743572 | + | 0.668655i | \(0.233130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.13974i | − | 0.197394i | ||||||
\(254\) | 7.90803 | + | 4.56570i | 0.496194 | + | 0.286478i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.09042 | + | 14.0130i | 0.505651 | + | 0.875814i | ||||
\(257\) | 1.71615 | − | 2.97245i | 0.107050 | − | 0.185417i | −0.807524 | − | 0.589835i | \(-0.799193\pi\) |
0.914574 | + | 0.404419i | \(0.132526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.604338 | − | 0.943239i | −0.0375517 | − | 0.0586100i | ||||
\(260\) | 1.85976 | + | 0.450337i | 0.115338 | + | 0.0279287i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50788 | + | 3.75733i | −0.402058 | + | 0.232128i | ||||
\(263\) | −10.7245 | − | 18.5754i | −0.661303 | − | 1.14541i | −0.980273 | − | 0.197646i | \(-0.936670\pi\) |
0.318970 | − | 0.947765i | \(-0.396663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.435992i | 0.0267828i | ||||||||
\(266\) | −0.682378 | − | 14.7551i | −0.0418393 | − | 0.904691i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.65794 | + | 4.42131i | 0.467783 | + | 0.270075i | ||||
\(269\) | 7.32843 | + | 12.6932i | 0.446822 | + | 0.773919i | 0.998177 | − | 0.0603517i | \(-0.0192222\pi\) |
−0.551355 | + | 0.834271i | \(0.685889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.76986 | − | 1.02183i | −0.107511 | − | 0.0620717i | 0.445280 | − | 0.895391i | \(-0.353104\pi\) |
−0.552792 | + | 0.833320i | \(0.686437\pi\) | |||||||
\(272\) | 5.29168 | 0.320856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.67112 | 0.403017 | ||||||||
\(275\) | −2.82797 | − | 1.63273i | −0.170533 | − | 0.0984572i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.71678 | − | 4.70560i | −0.163236 | − | 0.282732i | 0.772792 | − | 0.634660i | \(-0.218860\pi\) |
−0.936027 | + | 0.351927i | \(0.885526\pi\) | |||||||
\(278\) | 6.06959 | + | 3.50428i | 0.364030 | + | 0.210173i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.25881 | + | 2.72864i | −0.254513 | + | 0.163067i | ||||
\(281\) | 20.2356i | 1.20715i | 0.797305 | + | 0.603577i | \(0.206258\pi\) | ||||
−0.797305 | + | 0.603577i | \(0.793742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.867593 | + | 1.50272i | 0.0515731 | + | 0.0893272i | 0.890659 | − | 0.454671i | \(-0.150243\pi\) |
−0.839086 | + | 0.543998i | \(0.816910\pi\) | |||||||
\(284\) | −10.3525 | + | 5.97704i | −0.614310 | + | 0.354672i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.645140 | − | 2.66424i | 0.0381479 | − | 0.157540i | ||||
\(287\) | 6.09755 | − | 11.7875i | 0.359927 | − | 0.695792i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.91173 | − | 5.04326i | 0.171278 | − | 0.296662i | ||||
\(290\) | −2.21373 | − | 3.83430i | −0.129995 | − | 0.225158i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.73595 | + | 2.15695i | 0.218630 | + | 0.126226i | ||||
\(293\) | 27.2441i | 1.59162i | 0.605547 | + | 0.795810i | \(0.292954\pi\) | ||||
−0.605547 | + | 0.795810i | \(0.707046\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16875 | 0.359159 | ||||||||
\(296\) | −0.647107 | + | 1.12082i | −0.0376123 | + | 0.0651465i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.98375 | + | 3.43595i | 0.114915 | + | 0.199039i | ||||
\(299\) | −11.5683 | − | 11.0209i | −0.669009 | − | 0.637357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3335 | + | 13.6221i | 1.51784 | + | 0.785163i | ||||
\(302\) | −5.23409 | −0.301188 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.13190 | + | 4.11760i | −0.409042 | + | 0.236161i | ||||
\(305\) | 2.54414 | − | 1.46886i | 0.145677 | − | 0.0841067i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.7138i | − | 0.725612i | −0.931865 | − | 0.362806i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362806i | \(-0.118181\pi\) | |||||||
\(308\) | −0.858127 | − | 1.33935i | −0.0488963 | − | 0.0763165i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.55186 | − | 1.47332i | −0.144936 | − | 0.0836788i | ||||
\(311\) | −4.80939 | − | 8.33011i | −0.272716 | − | 0.472357i | 0.696841 | − | 0.717226i | \(-0.254588\pi\) |
−0.969556 | + | 0.244869i | \(0.921255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.51273 | − | 7.81628i | 0.255075 | − | 0.441802i | −0.709841 | − | 0.704362i | \(-0.751233\pi\) |
0.964916 | + | 0.262559i | \(0.0845666\pi\) | |||||||
\(314\) | 10.2151i | 0.576473i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.31931 | −0.186726 | ||||||||
\(317\) | 21.3269 | + | 12.3131i | 1.19784 | + | 0.691572i | 0.960073 | − | 0.279750i | \(-0.0902517\pi\) |
0.237766 | + | 0.971323i | \(0.423585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.04797 | − | 2.33709i | 0.226643 | − | 0.130852i | ||||
\(320\) | 4.28061 | + | 2.47141i | 0.239293 | + | 0.138156i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.5675 | − | 0.581209i | 0.700359 | − | 0.0323895i | ||||
\(323\) | − | 17.3935i | − | 0.967802i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.9423 | + | 4.68843i | −0.884319 | + | 0.260067i | ||||
\(326\) | 12.7205 | + | 22.0325i | 0.704521 | + | 1.22027i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.3323 | −0.846584 | ||||||||
\(329\) | 11.5223 | + | 17.9838i | 0.635244 | + | 0.991477i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4071 | − | 6.58591i | −0.626993 | − | 0.361994i | 0.152594 | − | 0.988289i | \(-0.451237\pi\) |
−0.779586 | + | 0.626295i | \(0.784571\pi\) | |||||||
\(332\) | 7.49823 | − | 4.32911i | 0.411519 | − | 0.237591i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.607311 | − | 1.05189i | 0.0332306 | − | 0.0575571i | ||||
\(335\) | 6.51752 | 0.356090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0307 | 0.927720 | 0.463860 | − | 0.885909i | \(-0.346464\pi\) | ||||
0.463860 | + | 0.885909i | \(0.346464\pi\) | |||||||
\(338\) | −7.55175 | − | 11.7288i | −0.410761 | − | 0.637965i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.53654 | + | 0.887121i | −0.0833305 | + | 0.0481109i | ||||
\(341\) | 1.55542 | − | 2.69406i | 0.0842306 | − | 0.145892i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.55948 | + | 18.3425i | 0.138199 | + | 0.990405i | ||||
\(344\) | − | 34.2527i | − | 1.84678i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.1414 | + | 6.43251i | −0.598968 | + | 0.345814i | ||||
\(347\) | 0.229959 | + | 0.398300i | 0.0123448 | + | 0.0213819i | 0.872132 | − | 0.489271i | \(-0.162737\pi\) |
−0.859787 | + | 0.510653i | \(0.829404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.87822i | 0.368183i | 0.982909 | + | 0.184091i | \(0.0589342\pi\) | ||||
−0.982909 | + | 0.184091i | \(0.941066\pi\) | |||||||
\(350\) | 6.01184 | − | 11.6218i | 0.321347 | − | 0.621210i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.56400 | + | 2.70892i | −0.0833613 | + | 0.144386i | ||||
\(353\) | −1.32784 | + | 0.766631i | −0.0706740 | + | 0.0408036i | −0.534921 | − | 0.844902i | \(-0.679658\pi\) |
0.464247 | + | 0.885706i | \(0.346325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.40542 | + | 7.63041i | −0.233815 | + | 0.404980i | ||||
\(356\) | 11.3529i | 0.601701i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 10.1626i | − | 0.537112i | ||||||
\(359\) | 23.5617 | + | 13.6034i | 1.24354 | + | 0.717959i | 0.969813 | − | 0.243848i | \(-0.0784099\pi\) |
0.273728 | + | 0.961807i | \(0.411743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.03438 | + | 6.98774i | 0.212336 | + | 0.367776i | ||||
\(362\) | −10.6231 | − | 6.13326i | −0.558339 | − | 0.322357i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.94692 | − | 1.53957i | −0.416532 | − | 0.0806952i | ||||
\(365\) | 3.17959 | 0.166427 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4907 | − | 23.3666i | −0.704208 | − | 1.21972i | −0.966977 | − | 0.254865i | \(-0.917969\pi\) |
0.262769 | − | 0.964859i | \(-0.415364\pi\) | |||||||
\(368\) | −3.50713 | − | 6.07452i | −0.182822 | − | 0.316656i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.284159i | 0.0147727i | ||||||||
\(371\) | −0.0852056 | − | 1.84240i | −0.00442365 | − | 0.0956526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.98619 | + | 3.44018i | −0.102841 | + | 0.178126i | −0.912854 | − | 0.408286i | \(-0.866127\pi\) |
0.810013 | + | 0.586412i | \(0.199460\pi\) | |||||||
\(374\) | 1.27086 | + | 2.20120i | 0.0657147 | + | 0.113821i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.3377 | − | 21.3695i | 0.636269 | − | 1.10205i | ||||
\(377\) | 5.59800 | − | 23.1181i | 0.288311 | − | 1.19064i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.4059i | − | 0.585884i | −0.956130 | − | 0.292942i | \(-0.905366\pi\) | ||
0.956130 | − | 0.292942i | \(-0.0946343\pi\) | |||||||
\(380\) | 1.38058 | − | 2.39124i | 0.0708225 | − | 0.122668i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.5783 | − | 8.41680i | 0.745892 | − | 0.430641i | ||||
\(383\) | −20.6044 | − | 11.8960i | −1.05284 | − | 0.607856i | −0.129395 | − | 0.991593i | \(-0.541304\pi\) |
−0.923442 | + | 0.383737i | \(0.874637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04134 | − | 0.538676i | −0.0530716 | − | 0.0274535i | ||||
\(386\) | 24.6879 | 1.25658 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.148460 | − | 0.0857137i | 0.00753694 | − | 0.00435145i | ||||
\(389\) | 14.2055 | + | 24.6046i | 0.720247 | + | 1.24751i | 0.960901 | + | 0.276894i | \(0.0893051\pi\) |
−0.240653 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8148 | 0.749216 | ||||||||
\(392\) | 17.4635 | − | 12.3629i | 0.882038 | − | 0.624420i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.47446 | − | 9.48204i | 0.275799 | − | 0.477698i | ||||
\(395\) | −2.11875 | + | 1.22326i | −0.106606 | + | 0.0615489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.53825 | − | 4.92956i | −0.428522 | − | 0.247408i | 0.270195 | − | 0.962806i | \(-0.412912\pi\) |
−0.698717 | + | 0.715398i | \(0.746245\pi\) | |||||||
\(398\) | 12.7945i | 0.641332i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.29510 | −0.364755 | ||||||||
\(401\) | −10.9287 | − | 6.30971i | −0.545756 | − | 0.315092i | 0.201653 | − | 0.979457i | \(-0.435369\pi\) |
−0.747408 | + | 0.664365i | \(0.768702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.46643 | − | 15.1874i | −0.222489 | − | 0.756539i | ||||
\(404\) | 7.35460 | − | 12.7385i | 0.365905 | − | 0.633766i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.1041 | + | 15.7702i | 0.501456 | + | 0.782663i | ||||
\(407\) | −0.299994 | −0.0148701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.6381 | + | 9.02867i | −0.773255 | + | 0.446439i | −0.834035 | − | 0.551712i | \(-0.813975\pi\) |
0.0607793 | + | 0.998151i | \(0.480641\pi\) | |||||||
\(410\) | −2.91537 | + | 1.68319i | −0.143980 | + | 0.0831268i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.17691 | 0.452114 | ||||||||
\(413\) | −26.0677 | + | 1.20555i | −1.28271 | + | 0.0593214i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.19080 | − | 5.52663i | 0.156630 | − | 0.271291i | ||||
\(416\) | 4.49107 | + | 15.2712i | 0.220193 | + | 0.748731i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.42562 | − | 1.97778i | −0.167553 | − | 0.0967366i | ||||
\(419\) | −14.2805 | −0.697647 | −0.348823 | − | 0.937188i | \(-0.613419\pi\) | ||||
−0.348823 | + | 0.937188i | \(0.613419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.27439i | 0.208321i | 0.994561 | + | 0.104160i | \(0.0332155\pi\) | ||||
−0.994561 | + | 0.104160i | \(0.966784\pi\) | |||||||
\(422\) | −14.4870 | − | 8.36410i | −0.705218 | − | 0.407158i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.84534 | + | 1.06541i | −0.0896175 | + | 0.0517407i | ||||
\(425\) | 7.70398 | − | 13.3437i | 0.373698 | − | 0.647263i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.4639 | + | 6.70425i | −0.506382 | + | 0.324441i | ||||
\(428\) | 5.19042 | 0.250888 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.76028 | − | 6.51300i | −0.181337 | − | 0.314085i | ||||
\(431\) | −12.6498 | + | 7.30335i | −0.609318 | + | 0.351790i | −0.772698 | − | 0.634773i | \(-0.781094\pi\) |
0.163381 | + | 0.986563i | \(0.447760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0099 | 1.34607 | 0.673035 | − | 0.739611i | \(-0.264991\pi\) | ||||
0.673035 | + | 0.739611i | \(0.264991\pi\) | |||||||
\(434\) | 11.0715 | + | 5.72718i | 0.531449 | + | 0.274914i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.37688 | + | 4.83640i | 0.401180 | + | 0.231621i | ||||
\(437\) | −19.9667 | + | 11.5278i | −0.955137 | + | 0.551448i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.53872 | − | 14.7895i | 0.407531 | − | 0.705864i | −0.587082 | − | 0.809528i | \(-0.699723\pi\) |
0.994612 | + | 0.103664i | \(0.0330566\pi\) | |||||||
\(440\) | 1.35450i | 0.0645733i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.5711 | + | 3.04407i | 0.597947 | + | 0.144792i | ||||
\(443\) | 6.90783 | − | 11.9647i | 0.328201 | − | 0.568461i | −0.653954 | − | 0.756534i | \(-0.726891\pi\) |
0.982155 | + | 0.188073i | \(0.0602243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.18386 | + | 7.24665i | 0.198334 | + | 0.343524i | ||||
\(446\) | 3.63048 | − | 6.28817i | 0.171908 | − | 0.297754i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.5718 | − | 9.60703i | −0.877436 | − | 0.453890i | ||||
\(449\) | 32.6410i | 1.54042i | 0.637789 | + | 0.770211i | \(0.279849\pi\) | ||||
−0.637789 | + | 0.770211i | \(0.720151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.77698 | − | 3.07783i | −0.0836749 | − | 0.144929i | ||||
\(452\) | −0.391801 | − | 0.678619i | −0.0184287 | − | 0.0319195i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0536 | −0.847298 | ||||||||
\(455\) | −5.63997 | + | 1.94595i | −0.264406 | + | 0.0912274i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.74559 | + | 1.58517i | 0.128433 | + | 0.0741511i | 0.562840 | − | 0.826566i | \(-0.309709\pi\) |
−0.434407 | + | 0.900717i | \(0.643042\pi\) | |||||||
\(458\) | 5.91560 | + | 10.2461i | 0.276418 | + | 0.478769i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.03672 | + | 1.17590i | 0.0949625 | + | 0.0548266i | ||||
\(461\) | 0.202023i | 0.00940915i | 0.999989 | + | 0.00470458i | \(0.00149752\pi\) | ||||
−0.999989 | + | 0.00470458i | \(0.998502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2121i | 0.799912i | 0.916534 | + | 0.399956i | \(0.130975\pi\) | ||||
−0.916534 | + | 0.399956i | \(0.869025\pi\) | |||||||
\(464\) | 5.22112 | − | 9.04325i | 0.242384 | − | 0.419822i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.1277 | + | 9.31136i | −0.747103 | + | 0.431340i | ||||
\(467\) | 0.0955845 | − | 0.165557i | 0.00442312 | − | 0.00766108i | −0.863805 | − | 0.503826i | \(-0.831925\pi\) |
0.868228 | + | 0.496165i | \(0.165259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.5415 | + | 1.27371i | −1.27175 | + | 0.0588146i | ||||
\(470\) | − | 5.41777i | − | 0.249903i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.0742 | + | 26.1092i | 0.693845 | + | 1.20177i | ||||
\(473\) | 6.87593 | − | 3.96982i | 0.316156 | − | 0.182533i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.9787i | 1.10022i | ||||||||
\(476\) | 6.31968 | − | 4.04905i | 0.289662 | − | 0.185588i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5816 | − | 18.3278i | 0.483989 | − | 0.838294i | ||||
\(479\) | 18.6009 | − | 10.7392i | 0.849897 | − | 0.490688i | −0.0107189 | − | 0.999943i | \(-0.503412\pi\) |
0.860616 | + | 0.509254i | \(0.170079\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05302 | + | 1.10532i | −0.0480136 | + | 0.0503981i | ||||
\(482\) | −2.98752 | −0.136078 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.90811 | 0.404914 | ||||||||
\(485\) | 0.0631758 | − | 0.109424i | 0.00286867 | − | 0.00496868i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4964 | − | 9.52422i | 0.747525 | − | 0.431584i | −0.0772740 | − | 0.997010i | \(-0.524622\pi\) |
0.824799 | + | 0.565426i | \(0.191288\pi\) | |||||||
\(488\) | 12.4339 | + | 7.17871i | 0.562856 | + | 0.324965i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.96340 | − | 4.26790i | 0.0886973 | − | 0.192804i | ||||
\(491\) | 35.7559 | 1.61364 | 0.806821 | − | 0.590796i | \(-0.201186\pi\) | ||||
0.806821 | + | 0.590796i | \(0.201186\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0275 | + | 19.1002i | 0.496654 | + | 0.860230i | ||||
\(494\) | −19.3115 | + | 5.67927i | −0.868864 | + | 0.255522i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.94968i | − | 0.312050i | ||||||
\(497\) | 17.1251 | − | 33.1053i | 0.768164 | − | 1.48497i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3192 | − | 8.84457i | −0.685784 | − | 0.395937i | 0.116247 | − | 0.993220i | \(-0.462914\pi\) |
−0.802031 | + | 0.597283i | \(0.796247\pi\) | |||||||
\(500\) | 4.41632 | − | 2.54976i | 0.197504 | − | 0.114029i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.8949 | + | 12.6410i | 0.977217 | + | 0.564196i | ||||
\(503\) | −11.3305 | −0.505203 | −0.252601 | − | 0.967570i | \(-0.581286\pi\) | ||||
−0.252601 | + | 0.967570i | \(0.581286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.8415i | − | 0.482441i | ||||||
\(506\) | 1.68456 | − | 2.91774i | 0.0748878 | − | 0.129709i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.61048 | − | 6.25353i | −0.160189 | − | 0.277455i | ||||
\(509\) | −16.7588 | − | 9.67569i | −0.742821 | − | 0.428868i | 0.0802734 | − | 0.996773i | \(-0.474421\pi\) |
−0.823094 | + | 0.567905i | \(0.807754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4362 | + | 0.621384i | −0.594382 | + | 0.0274884i | ||||
\(512\) | 16.6645i | 0.736472i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.18961 | − | 1.84152i | 0.140687 | − | 0.0812259i | ||||
\(515\) | 5.85772 | − | 3.38195i | 0.258122 | − | 0.149027i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.71967 | 0.251551 | ||||||||
\(518\) | −0.0555330 | − | 1.20079i | −0.00243998 | − | 0.0527597i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.99060 | + | 4.75448i | 0.218852 | + | 0.208498i | ||||
\(521\) | −3.85550 | − | 6.67791i | −0.168912 | − | 0.292565i | 0.769125 | − | 0.639098i | \(-0.220692\pi\) |
−0.938038 | + | 0.346533i | \(0.887359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5251 | − | 30.3543i | 0.766317 | − | 1.32730i | −0.173230 | − | 0.984881i | \(-0.555420\pi\) |
0.939547 | − | 0.342419i | \(-0.111246\pi\) | |||||||
\(524\) | 5.94246 | 0.259597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 23.0160i | − | 1.00355i | ||||||
\(527\) | 12.7119 | + | 7.33919i | 0.553737 | + | 0.319700i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.68133 | + | 2.91214i | 0.0731011 | + | 0.126615i | ||||
\(530\) | −0.233922 | + | 0.405165i | −0.0101609 | + | 0.0175992i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.36671 | + | 10.3746i | −0.232676 | + | 0.449797i | ||||
\(533\) | −17.5776 | − | 4.25637i | −0.761370 | − | 0.184364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.31309 | − | 1.91282i | 0.143238 | − | 0.0826982i | ||||
\(536\) | 15.9264 | + | 27.5854i | 0.687917 | + | 1.19151i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.7276i | 0.678066i | ||||||||
\(539\) | 4.50573 | + | 2.07281i | 0.194075 | + | 0.0892821i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5079 | + | 6.06674i | 0.451770 | + | 0.260829i | 0.708577 | − | 0.705633i | \(-0.249337\pi\) |
−0.256807 | + | 0.966463i | \(0.582671\pi\) | |||||||
\(542\) | −1.09648 | − | 1.89916i | −0.0470978 | − | 0.0815758i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.7820 | − | 7.37967i | −0.548022 | − | 0.316401i | ||||
\(545\) | 7.12940 | 0.305390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12546 | −0.219149 | −0.109575 | − | 0.993979i | \(-0.534949\pi\) | ||||
−0.109575 | + | 0.993979i | \(0.534949\pi\) | |||||||
\(548\) | −4.56864 | − | 2.63770i | −0.195162 | − | 0.112677i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.75201 | − | 3.03457i | −0.0747058 | − | 0.129394i | ||||
\(551\) | −29.7248 | − | 17.1616i | −1.26632 | − | 0.731109i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71427 | − | 5.58327i | 0.370568 | − | 0.237425i | ||||
\(554\) | − | 5.83051i | − | 0.247715i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.77112 | − | 4.79972i | −0.117522 | − | 0.203554i | ||||
\(557\) | 32.5267 | − | 18.7793i | 1.37820 | − | 0.795705i | 0.386258 | − | 0.922391i | \(-0.373767\pi\) |
0.991943 | + | 0.126686i | \(0.0404341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.50884 | − | 39.2687i | 0.402181 | − | 1.66089i | ||||
\(560\) | −2.61641 | + | 0.121001i | −0.110563 | + | 0.00511323i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8569 | + | 18.8048i | −0.457973 | + | 0.793232i | ||||
\(563\) | −14.3504 | − | 24.8557i | −0.604799 | − | 1.04754i | −0.992083 | − | 0.125583i | \(-0.959920\pi\) |
0.387284 | − | 0.921960i | \(-0.373413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.500180 | − | 0.288779i | −0.0210428 | − | 0.0121490i | ||||
\(566\) | 1.86195i | 0.0782636i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.0610 | −1.80680 | ||||||||
\(569\) | −8.97417 | + | 15.5437i | −0.376217 | + | 0.651627i | −0.990508 | − | 0.137452i | \(-0.956109\pi\) |
0.614291 | + | 0.789079i | \(0.289442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.91370 | + | 15.4390i | 0.373027 | + | 0.646101i | 0.990030 | − | 0.140860i | \(-0.0449867\pi\) |
−0.617003 | + | 0.786961i | \(0.711653\pi\) | |||||||
\(572\) | −1.49523 | + | 1.56949i | −0.0625188 | + | 0.0656236i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9907 | − | 7.68250i | 0.500483 | − | 0.320662i | ||||
\(575\) | −20.4236 | −0.851724 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.6282 | − | 16.5285i | 1.19181 | − | 0.688091i | 0.233092 | − | 0.972455i | \(-0.425116\pi\) |
0.958717 | + | 0.284363i | \(0.0917822\pi\) | |||||||
\(578\) | 5.41170 | − | 3.12445i | 0.225097 | − | 0.129960i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.50117i | 0.145378i | ||||||||
\(581\) | −12.4035 | + | 23.9778i | −0.514584 | + | 0.994766i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.427742 | − | 0.246957i | −0.0177153 | − | 0.0102279i | ||||
\(584\) | 7.76975 | + | 13.4576i | 0.321515 | + | 0.556880i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6172 | + | 25.3178i | −0.603832 | + | 1.04587i | ||||
\(587\) | − | 14.7295i | − | 0.607953i | −0.952680 | − | 0.303976i | \(-0.901686\pi\) | ||
0.952680 | − | 0.303976i | \(-0.0983144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8433 | −0.941241 | ||||||||
\(590\) | 5.73258 | + | 3.30970i | 0.236006 | + | 0.136258i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.580404 | + | 0.335097i | −0.0238545 | + | 0.0137724i | ||||
\(593\) | 7.97598 | + | 4.60494i | 0.327534 | + | 0.189102i | 0.654746 | − | 0.755849i | \(-0.272776\pi\) |
−0.327212 | + | 0.944951i | \(0.606109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.54172 | − | 4.91353i | 0.104201 | − | 0.201435i | ||||
\(596\) | − | 3.13743i | − | 0.128514i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.83726 | − | 16.4484i | −0.197810 | − | 0.672624i | ||||
\(599\) | −5.28727 | − | 9.15782i | −0.216032 | − | 0.374178i | 0.737559 | − | 0.675282i | \(-0.235978\pi\) |
−0.953591 | + | 0.301104i | \(0.902645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.08916 | 0.166800 | 0.0834001 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0834001 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(602\) | 17.1629 | + | 26.7875i | 0.699507 | + | 1.09178i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.58450 | + | 2.06951i | 0.145851 | + | 0.0842072i | ||||
\(605\) | 5.68613 | − | 3.28289i | 0.231174 | − | 0.133469i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.80353 | + | 3.12380i | −0.0732030 | + | 0.126791i | −0.900303 | − | 0.435263i | \(-0.856655\pi\) |
0.827100 | + | 0.562054i | \(0.189989\pi\) | |||||||
\(608\) | 22.9693 | 0.931527 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.15233 | 0.127634 | ||||||||
\(611\) | 20.0768 | − | 21.0739i | 0.812222 | − | 0.852559i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.3285 | + | 19.2422i | −1.34613 | + | 0.777186i | −0.987698 | − | 0.156371i | \(-0.950020\pi\) |
−0.358428 | + | 0.933557i | \(0.616687\pi\) | |||||||
\(614\) | 6.82128 | − | 11.8148i | 0.275284 | − | 0.476806i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.264709 | − | 5.72379i | −0.0106654 | − | 0.230618i | ||||
\(617\) | 3.09503i | 0.124601i | 0.998057 | + | 0.0623007i | \(0.0198438\pi\) | ||||
−0.998057 | + | 0.0623007i | \(0.980156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6255 | + | 6.13462i | −0.427074 | + | 0.246571i | −0.698099 | − | 0.716001i | \(-0.745971\pi\) |
0.271025 | + | 0.962572i | \(0.412637\pi\) | |||||||
\(620\) | 1.16507 | + | 2.01797i | 0.0467905 | + | 0.0810435i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.3215i | − | 0.413854i | ||||||
\(623\) | −19.0962 | − | 29.8050i | −0.765073 | − | 1.19411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.64277 | + | 16.7018i | −0.385711 | + | 0.668071i | ||||
\(626\) | 8.38730 | − | 4.84241i | 0.335224 | − | 0.193542i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.03897 | − | 6.99571i | 0.161173 | − | 0.279159i | ||||
\(629\) | − | 1.41551i | − | 0.0564402i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.31780i | 0.211698i | 0.994382 | + | 0.105849i | \(0.0337561\pi\) | ||||
−0.994382 | + | 0.105849i | \(0.966244\pi\) | |||||||
\(632\) | −10.3549 | − | 5.97840i | −0.411896 | − | 0.237808i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.2126 | + | 22.8849i | 0.524740 | + | 0.908877i | ||||
\(635\) | −4.60921 | − | 2.66113i | −0.182911 | − | 0.105604i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.4529 | − | 9.32532i | 0.929238 | − | 0.369483i | ||||
\(638\) | 5.01566 | 0.198572 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.109212 | − | 0.189160i | −0.00431697 | − | 0.00747721i | ||||
\(641\) | −6.09521 | − | 10.5572i | −0.240746 | − | 0.416985i | 0.720181 | − | 0.693787i | \(-0.244059\pi\) |
−0.960927 | + | 0.276801i | \(0.910726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.9733i | − | 0.748235i | −0.927381 | − | 0.374117i | \(-0.877946\pi\) | ||
0.927381 | − | 0.374117i | \(-0.122054\pi\) | |||||||
\(644\) | −8.83649 | − | 4.57104i | −0.348207 | − | 0.180124i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.33211 | − | 16.1637i | 0.367167 | − | 0.635952i | ||||
\(647\) | −9.85587 | − | 17.0709i | −0.387474 | − | 0.671125i | 0.604635 | − | 0.796503i | \(-0.293319\pi\) |
−0.992109 | + | 0.125378i | \(0.959986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.49414 | + | 6.05202i | −0.137157 | + | 0.237563i | ||||
\(650\) | −17.3305 | − | 4.19655i | −0.679759 | − | 0.164602i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 20.1182i | − | 0.787891i | ||||||
\(653\) | −10.1986 | + | 17.6645i | −0.399103 | + | 0.691267i | −0.993616 | − | 0.112819i | \(-0.964012\pi\) |
0.594512 | + | 0.804087i | \(0.297345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79313 | − | 2.18996i | 0.148210 | − | 0.0855690i | ||||
\(656\) | −6.87593 | − | 3.96982i | −0.268460 | − | 0.154996i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.05879 | + | 22.8942i | 0.0412759 | + | 0.892509i | ||||
\(659\) | −32.6628 | −1.27236 | −0.636181 | − | 0.771540i | \(-0.719487\pi\) | ||||
−0.636181 | + | 0.771540i | \(0.719487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.43242 | − | 4.86846i | 0.327983 | − | 0.189361i | −0.326962 | − | 0.945037i | \(-0.606025\pi\) |
0.654945 | + | 0.755676i | \(0.272692\pi\) | |||||||
\(662\) | −7.06704 | − | 12.2405i | −0.274668 | − | 0.475740i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.1886 | 1.21035 | ||||||||
\(665\) | 0.397725 | + | 8.60002i | 0.0154231 | + | 0.333494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6172 | − | 25.3178i | 0.565981 | − | 0.980308i | ||||
\(668\) | −0.831819 | + | 0.480251i | −0.0321841 | + | 0.0185815i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.05668 | + | 3.49683i | 0.233990 | + | 0.135094i | ||||
\(671\) | 3.32800i | 0.128476i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4512 | −1.52073 | −0.760367 | − | 0.649494i | \(-0.774981\pi\) | ||||
−0.760367 | + | 0.649494i | \(0.774981\pi\) | |||||||
\(674\) | 15.8265 | + | 9.13742i | 0.609613 | + | 0.351960i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.534242 | + | 11.0182i | 0.0205478 | + | 0.423779i | ||||
\(677\) | −24.3169 | + | 42.1182i | −0.934576 | + | 1.61873i | −0.159187 | + | 0.987248i | \(0.550887\pi\) |
−0.775389 | + | 0.631484i | \(0.782446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.245582 | + | 0.474745i | −0.00942455 | + | 0.0182191i | ||||
\(680\) | −6.39117 | −0.245090 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.89088 | − | 1.66905i | 0.110697 | − | 0.0639112i | ||||
\(683\) | 4.94304 | − | 2.85387i | 0.189140 | − | 0.109200i | −0.402440 | − | 0.915446i | \(-0.631838\pi\) |
0.591580 | + | 0.806246i | \(0.298504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.88828 | −0.148563 | ||||||||
\(686\) | −7.46278 | + | 18.4188i | −0.284930 | + | 0.703234i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.86867 | − | 15.3610i | 0.338115 | − | 0.585632i | ||||
\(689\) | −2.41134 | + | 0.709145i | −0.0918647 | + | 0.0270163i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1766 | + | 20.8866i | 1.37622 | + | 0.794563i | 0.991703 | − | 0.128553i | \(-0.0410333\pi\) |
0.384521 | + | 0.923116i | \(0.374367\pi\) | |||||||
\(692\) | 10.1734 | 0.386736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.493517i | 0.0187336i | ||||||||
\(695\) | −3.53767 | − | 2.04247i | −0.134191 | − | 0.0774754i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5226 | − | 8.38464i | 0.550084 | − | 0.317591i | ||||
\(698\) | −3.69035 | + | 6.39188i | −0.139682 | + | 0.241936i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.71229 | + | 5.58200i | −0.329294 | + | 0.210980i | ||||
\(701\) | −22.4361 | −0.847399 | −0.423700 | − | 0.905803i | \(-0.639269\pi\) | ||||
−0.423700 | + | 0.905803i | \(0.639269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10145 | + | 1.90776i | 0.0415419 | + | 0.0719527i | ||||
\(704\) | −4.84929 | + | 2.79974i | −0.182764 | + | 0.105519i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.64527 | −0.0619207 | ||||||||
\(707\) | 2.11875 | + | 45.8137i | 0.0796837 | + | 1.72300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.8955 | − | 14.3734i | −0.934969 | − | 0.539804i | −0.0465891 | − | 0.998914i | \(-0.514835\pi\) |
−0.888380 | + | 0.459110i | \(0.848168\pi\) | |||||||
\(710\) | −8.18785 | + | 4.72726i | −0.307285 | + | 0.177411i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.4476 | + | 35.4163i | −0.766307 | + | 1.32728i | ||||
\(713\) | − | 19.4566i | − | 0.728654i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.376021 | + | 1.55286i | −0.0140624 | + | 0.0580735i | ||||
\(716\) | −4.01822 | + | 6.95976i | −0.150168 | + | 0.260098i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.5972 | + | 25.2830i | 0.544762 | + | 0.943555i | ||||
\(719\) | 2.10450 | − | 3.64509i | 0.0784844 | − | 0.135939i | −0.824112 | − | 0.566427i | \(-0.808325\pi\) |
0.902596 | + | 0.430488i | \(0.141659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0924 | + | 15.4361i | −0.897247 | + | 0.574870i | ||||
\(722\) | 8.65821i | 0.322225i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.85008 | + | 8.40058i | 0.180252 | + | 0.312205i | ||||
\(725\) | −15.2025 | − | 26.3315i | −0.564606 | − | 0.977927i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.4680 | −1.61214 | −0.806070 | − | 0.591820i | \(-0.798409\pi\) | ||||
−0.806070 | + | 0.591820i | \(0.798409\pi\) | |||||||
\(728\) | −22.0183 | − | 19.1160i | −0.816051 | − | 0.708486i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.95477 | + | 1.70594i | 0.109361 | + | 0.0631396i | ||||
\(731\) | 18.7315 | + | 32.4439i | 0.692809 | + | 1.19998i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.87581 | + | 4.54710i | 0.290900 | + | 0.167951i | 0.638348 | − | 0.769748i | \(-0.279618\pi\) |
−0.347448 | + | 0.937699i | \(0.612952\pi\) | |||||||
\(734\) | − | 28.9525i | − | 1.06866i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5639i | 0.721133i | ||||||||
\(737\) | −3.69169 | + | 6.39419i | −0.135985 | + | 0.235533i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.32135 | − | 4.80433i | 0.306106 | − | 0.176730i | −0.339077 | − | 0.940759i | \(-0.610115\pi\) |
0.645183 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(740\) | 0.112354 | − | 0.194603i | 0.00413022 | − | 0.00715375i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.909317 | − | 1.75784i | 0.0333821 | − | 0.0645325i | ||||
\(743\) | 32.1771i | 1.18046i | 0.807234 | + | 0.590231i | \(0.200964\pi\) | ||||
−0.807234 | + | 0.590231i | \(0.799036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.15623 | − | 2.00265i | −0.0423610 | − | 0.0733714i | ||||
\(746\) | −3.69150 | + | 2.13129i | −0.135155 | + | 0.0780320i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 2.00995i | − | 0.0734911i | ||||||
\(749\) | −13.6265 | + | 8.73058i | −0.497903 | + | 0.319008i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.89892 | − | 6.75313i | 0.142274 | − | 0.246425i | −0.786079 | − | 0.618126i | \(-0.787892\pi\) |
0.928352 | + | 0.371701i | \(0.121225\pi\) | |||||||
\(752\) | 11.0660 | − | 6.38894i | 0.403534 | − | 0.232981i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.6057 | − | 18.4800i | 0.641161 | − | 0.673002i | ||||
\(755\) | 3.05070 | 0.111026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.9970 | 0.654110 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(758\) | 6.11960 | − | 10.5995i | 0.222274 | − | 0.384990i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.61373 | − | 4.97314i | 0.312453 | − | 0.180395i | ||||
\(761\) | 35.2290 | + | 20.3395i | 1.27705 | + | 0.737306i | 0.976305 | − | 0.216398i | \(-0.0694309\pi\) |
0.300746 | + | 0.953704i | \(0.402764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.1271 | + | 1.39329i | −1.09068 | + | 0.0504406i | ||||
\(764\) | −13.3117 | −0.481601 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.7650 | − | 22.1097i | −0.461220 | − | 0.798856i | ||||
\(767\) | 10.0335 | + | 34.1174i | 0.362290 | + | 1.23191i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.3098i | 1.41755i | 0.705435 | + | 0.708774i | \(0.250752\pi\) | ||||
−0.705435 | + | 0.708774i | \(0.749248\pi\) | |||||||
\(770\) | −0.678695 | − | 1.05929i | −0.0244585 | − | 0.0381743i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.9072 | − | 9.76138i | −0.608504 | − | 0.351320i | ||||
\(773\) | −11.6685 | + | 6.73679i | −0.419685 | + | 0.242306i | −0.694943 | − | 0.719065i | \(-0.744570\pi\) |
0.275257 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5245 | − | 10.1178i | −0.629500 | − | 0.363442i | ||||
\(776\) | 0.617515 | 0.0221675 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.4866i | 1.09300i | ||||||||
\(779\) | −13.0486 | + | 22.6009i | −0.467516 | + | 0.809761i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.99068 | − | 8.64412i | −0.178581 | − | 0.309311i | ||||
\(782\) | 13.7673 | + | 7.94854i | 0.492316 | + | 0.284239i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.0327 | − | 1.02264i | 0.394024 | − | 0.0365230i | ||||
\(785\) | − | 5.95391i | − | 0.212504i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.4930 | + | 19.9145i | −1.22954 | + | 0.709877i | −0.966934 | − | 0.255026i | \(-0.917916\pi\) |
−0.262608 | + | 0.964903i | \(0.584583\pi\) | |||||||
\(788\) | −7.49823 | + | 4.32911i | −0.267114 | + | 0.154218i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.62525 | −0.0934022 | ||||||||
\(791\) | 2.17008 | + | 1.12256i | 0.0771592 | + | 0.0399137i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2619 | + | 11.6817i | 0.435432 | + | 0.414831i | ||||
\(794\) | −5.28969 | − | 9.16201i | −0.187724 | − | 0.325148i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.05884 | − | 8.76217i | 0.179306 | − | 0.310567i | ||||
\(797\) | −21.2530 | −0.752821 | −0.376410 | − | 0.926453i | \(-0.622842\pi\) | ||||
−0.376410 | + | 0.926453i | \(0.622842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.9881i | 0.954770i | ||||||||
\(800\) | 17.6212 | + | 10.1736i | 0.623003 | + | 0.359691i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.77067 | − | 11.7271i | −0.239081 | − | 0.414100i | ||||
\(803\) | −1.80100 | + | 3.11942i | −0.0635559 | + | 0.110082i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.32498 | + | 0.338759i | −0.258172 | + | 0.0119397i | ||||
\(806\) | 3.99784 | − | 16.5099i | 0.140818 | − | 0.581537i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.8867 | − | 26.4927i | 1.61429 | − | 0.932010i | ||||
\(809\) | 10.7088 | + | 18.5481i | 0.376500 | + | 0.652117i | 0.990550 | − | 0.137150i | \(-0.0437942\pi\) |
−0.614050 | + | 0.789267i | \(0.710461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.0116i | − | 0.386669i | −0.981133 | − | 0.193335i | \(-0.938070\pi\) | ||
0.981133 | − | 0.193335i | \(-0.0619303\pi\) | |||||||
\(812\) | −0.684230 | − | 14.7951i | −0.0240118 | − | 0.519206i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.278782 | − | 0.160955i | −0.00977131 | − | 0.00564147i | ||||
\(815\) | −7.41414 | − | 12.8417i | −0.259706 | − | 0.449824i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50.4909 | − | 29.1509i | −1.76645 | − | 1.01986i | ||||
\(818\) | −19.3765 | −0.677484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.66207 | 0.0929636 | ||||||||
\(821\) | −33.4879 | − | 19.3342i | −1.16873 | − | 0.674769i | −0.215353 | − | 0.976536i | \(-0.569090\pi\) |
−0.953382 | + | 0.301767i | \(0.902424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.2283 | − | 17.7160i | −0.356537 | − | 0.617540i | 0.630843 | − | 0.775911i | \(-0.282709\pi\) |
−0.987380 | + | 0.158371i | \(0.949376\pi\) | |||||||
\(824\) | 28.6282 | + | 16.5285i | 0.997312 | + | 0.575798i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.8713 | − | 12.8657i | −0.865384 | − | 0.447655i | ||||
\(827\) | 27.3451i | 0.950881i | 0.879748 | + | 0.475440i | \(0.157711\pi\) | ||||
−0.879748 | + | 0.475440i | \(0.842289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5043 | − | 21.6581i | −0.434292 | − | 0.752217i | 0.562945 | − | 0.826494i | \(-0.309668\pi\) |
−0.997238 | + | 0.0742776i | \(0.976335\pi\) | |||||||
\(830\) | 5.93037 | − | 3.42390i | 0.205846 | − | 0.118845i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.70616 | + | 27.6945i | −0.232494 | + | 0.960133i | ||||
\(833\) | −9.78048 | + | 21.2601i | −0.338873 | + | 0.736620i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.353972 | + | 0.613098i | −0.0122497 | + | 0.0212171i | ||||
\(836\) | 1.56400 | + | 2.70892i | 0.0540920 | + | 0.0936900i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.2707 | − | 7.66187i | −0.458430 | − | 0.264675i | ||||
\(839\) | 8.76981i | 0.302768i | 0.988475 | + | 0.151384i | \(0.0483729\pi\) | ||||
−0.988475 | + | 0.151384i | \(0.951627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5218 | 0.500753 | ||||||||
\(842\) | −2.29333 | + | 3.97216i | −0.0790332 | + | 0.136890i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.61418 | + | 11.4561i | 0.227669 | + | 0.394335i | ||||
\(845\) | 4.40155 | + | 6.83617i | 0.151418 | + | 0.235171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.3867 | + | 14.9840i | −0.803576 | + | 0.514855i | ||||
\(848\) | −1.10342 | −0.0378914 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.3185 | − | 8.26679i | 0.491120 | − | 0.283549i | ||||
\(851\) | −1.62492 | + | 0.938148i | −0.0557015 | + | 0.0321593i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.8232i | − | 0.678734i | −0.940654 | − | 0.339367i | \(-0.889787\pi\) | ||
0.940654 | − | 0.339367i | \(-0.110213\pi\) | |||||||
\(854\) | −13.3210 | + | 0.616058i | −0.455836 | + | 0.0210811i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.1920 | + | 9.34845i | 0.553431 | + | 0.319523i | ||||
\(857\) | 1.33518 | + | 2.31261i | 0.0456090 | + | 0.0789972i | 0.887929 | − | 0.459981i | \(-0.152144\pi\) |
−0.842320 | + | 0.538978i | \(0.818810\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4798 | − | 33.7401i | 0.664644 | − | 1.15120i | −0.314738 | − | 0.949179i | \(-0.601917\pi\) |
0.979382 | − | 0.202018i | \(-0.0647500\pi\) | |||||||
\(860\) | 5.94713i | 0.202795i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.6738 | −0.533851 | ||||||||
\(863\) | −21.4754 | − | 12.3988i | −0.731030 | − | 0.422060i | 0.0877689 | − | 0.996141i | \(-0.472026\pi\) |
−0.818799 | + | 0.574081i | \(0.805360\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.49381 | − | 3.74920i | 0.220796 | − | 0.127477i | ||||
\(866\) | 26.0294 | + | 15.0281i | 0.884514 | + | 0.510675i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.31770 | − | 8.29976i | −0.180494 | − | 0.281712i | ||||
\(869\) | − | 2.77154i | − | 0.0940181i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6008 | + | 36.0464i | 0.359194 | + | 1.22138i | ||||
\(872\) | 17.4216 | + | 30.1752i | 0.589971 | + | 1.02186i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.7399 | −0.836839 | ||||||||
\(875\) | −7.30542 | + | 14.1225i | −0.246968 | + | 0.477426i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.71335 | − | 0.989201i | −0.0578556 | − | 0.0334029i | 0.470793 | − | 0.882244i | \(-0.343968\pi\) |
−0.528649 | + | 0.848841i | \(0.677301\pi\) | |||||||
\(878\) | 15.8699 | − | 9.16251i | 0.535584 | − | 0.309220i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.350706 | + | 0.607440i | −0.0118223 | + | 0.0204768i | ||||
\(881\) | 17.1466 | 0.577683 | 0.288841 | − | 0.957377i | \(-0.406730\pi\) | ||||
0.288841 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.2168 | 0.343822 | 0.171911 | − | 0.985112i | \(-0.445006\pi\) | ||||
0.171911 | + | 0.985112i | \(0.445006\pi\) | |||||||
\(884\) | −7.40558 | − | 7.05521i | −0.249077 | − | 0.237292i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.8388 | − | 7.41248i | 0.431328 | − | 0.249027i | ||||
\(887\) | 25.4965 | − | 44.1613i | 0.856090 | − | 1.48279i | −0.0195395 | − | 0.999809i | \(-0.506220\pi\) |
0.875630 | − | 0.482983i | \(-0.160447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.9975 | + | 10.3445i | 0.670694 | + | 0.346944i | ||||
\(890\) | 8.97901i | 0.300977i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.97258 | + | 2.87092i | −0.166494 | + | 0.0961255i | ||||
\(893\) | −21.0002 | − | 36.3733i | −0.702743 | − | 1.21719i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.92331i | 0.197995i | ||||||||
\(896\) | 0.498470 | + | 0.778003i | 0.0166527 | + | 0.0259913i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.5128 | + | 30.3330i | −0.584409 | + | 1.01223i | ||||
\(899\) | 25.0847 | − | 14.4827i | 0.836621 | − | 0.483024i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16526 | − | 2.01829i | 0.0388204 | − | 0.0672389i | ||||
\(902\) | − | 3.81360i | − | 0.126979i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.82268i | − | 0.0938811i | ||||||
\(905\) | 6.19170 | + | 3.57478i | 0.205819 | + | 0.118830i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.89269 | − | 5.01028i | −0.0960501 | − | 0.166364i | 0.813996 | − | 0.580870i | \(-0.197288\pi\) |
−0.910046 | + | 0.414506i | \(0.863954\pi\) | |||||||
\(908\) | 12.3638 | + | 7.13824i | 0.410307 | + | 0.236891i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.28524 | − | 1.21765i | −0.208354 | − | 0.0403646i | ||||
\(911\) | 1.70706 | 0.0565573 | 0.0282787 | − | 0.999600i | \(-0.490997\pi\) | ||||
0.0282787 | + | 0.999600i | \(0.490997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.61470 | + | 6.26084i | 0.119629 | + | 0.207204i | ||||
\(914\) | 1.70097 | + | 2.94617i | 0.0562632 | + | 0.0974507i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 9.35590i | − | 0.309128i | ||||||
\(917\) | −15.6009 | + | 9.99556i | −0.515187 | + | 0.330082i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6025 | + | 32.2205i | −0.613640 | + | 1.06286i | 0.376982 | + | 0.926221i | \(0.376962\pi\) |
−0.990622 | + | 0.136634i | \(0.956371\pi\) | |||||||
\(920\) | 4.23582 | + | 7.33666i | 0.139651 | + | 0.241882i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.108391 | + | 0.187739i | −0.00356967 | + | 0.00618284i | ||||
\(923\) | −49.3669 | − | 11.9541i | −1.62493 | − | 0.393474i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.95142i | 0.0641623i | ||||||||
\(926\) | −9.23474 | + | 15.9950i | −0.303472 | + | 0.525630i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.2230 | + | 14.5625i | −0.827987 | + | 0.478038i | ||||
\(929\) | −17.2379 | − | 9.95229i | −0.565556 | − | 0.326524i | 0.189816 | − | 0.981820i | \(-0.439211\pi\) |
−0.755373 | + | 0.655296i | \(0.772544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.36139 | − | 36.2639i | −0.110165 | − | 1.18850i | ||||
\(932\) | 14.7265 | 0.482383 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.177652 | − | 0.102567i | 0.00581295 | − | 0.00335611i | ||||
\(935\) | −0.740724 | − | 1.28297i | −0.0242243 | − | 0.0419577i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.16949 | 0.234217 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(938\) | −26.2775 | − | 13.5931i | −0.857990 | − | 0.443831i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.14214 | + | 3.71029i | −0.0698688 | + | 0.121016i | ||||
\(941\) | 2.65066 | − | 1.53036i | 0.0864091 | − | 0.0498883i | −0.456173 | − | 0.889891i | \(-0.650780\pi\) |
0.542582 | + | 0.840003i | \(0.317447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.2501 | − | 11.1140i | −0.626869 | − | 0.361923i | ||||
\(944\) | 15.6120i | 0.508126i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.51968 | 0.276999 | ||||||||
\(947\) | −38.2832 | − | 22.1028i | −1.24404 | − | 0.718244i | −0.274122 | − | 0.961695i | \(-0.588387\pi\) |
−0.969913 | + | 0.243451i | \(0.921721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.17163 | + | 17.5853i | 0.167878 | + | 0.570844i | ||||
\(950\) | −12.8652 | + | 22.2832i | −0.417403 | + | 0.722963i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 27.0075 | − | 1.24902i | 0.875320 | − | 0.0404810i | ||||
\(953\) | −13.7002 | −0.443791 | −0.221896 | − | 0.975070i | \(-0.571224\pi\) | ||||
−0.221896 | + | 0.975070i | \(0.571224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.49700 | + | 4.90574i | −0.274956 | + | 0.158746i | ||||
\(956\) | −14.4933 | + | 8.36771i | −0.468747 | + | 0.270631i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.0476 | 0.744634 | ||||||||
\(959\) | 16.4309 | − | 0.759882i | 0.530582 | − | 0.0245379i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.86129 | + | 10.1520i | −0.189074 | + | 0.327485i | ||||
\(962\) | −1.57160 | + | 0.462187i | −0.0506703 | + | 0.0149015i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.04597 | + | 1.18124i | 0.0658961 | + | 0.0380451i | ||||
\(965\) | −14.3894 | −0.463211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.9429i | 1.41311i | 0.707659 | + | 0.706554i | \(0.249751\pi\) | ||||
−0.707659 | + | 0.706554i | \(0.750249\pi\) | |||||||
\(968\) | 27.7897 | + | 16.0444i | 0.893194 | + | 0.515686i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.117418 | − | 0.0677912i | 0.00377006 | − | 0.00217664i | ||||
\(971\) | −10.6585 | + | 18.4611i | −0.342049 | + | 0.592446i | −0.984813 | − | 0.173618i | \(-0.944454\pi\) |
0.642764 | + | 0.766064i | \(0.277788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3485 | + | 7.93965i | 0.492050 | + | 0.254533i | ||||
\(974\) | 20.4400 | 0.654941 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.71741 | + | 6.43874i | 0.118991 | + | 0.206099i | ||||
\(977\) | −14.2432 | + | 8.22330i | −0.455679 | + | 0.263087i | −0.710226 | − | 0.703974i | \(-0.751407\pi\) |
0.254547 | + | 0.967061i | \(0.418074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.47937 | −0.302962 | ||||||||
\(980\) | −3.03210 | + | 2.14651i | −0.0968568 | + | 0.0685677i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.2277 | + | 19.1840i | 1.06034 | + | 0.612187i | ||||
\(983\) | −10.1415 | + | 5.85521i | −0.323464 | + | 0.186752i | −0.652936 | − | 0.757413i | \(-0.726463\pi\) |
0.329471 | + | 0.944166i | \(0.393129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.19080 | + | 5.52663i | −0.101667 | + | 0.176093i | ||||
\(986\) | 23.6662i | 0.753687i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.4708 | + | 3.74621i | 0.492190 | + | 0.119183i | ||||
\(989\) | 24.8290 | − | 43.0051i | 0.789517 | − | 1.36748i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.6873 | + | 27.1713i | 0.498325 | + | 0.863124i | 0.999998 | − | 0.00193305i | \(-0.000615311\pi\) |
−0.501673 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(992\) | −9.69187 | + | 16.7868i | −0.307717 | + | 0.532982i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.6761 | − | 21.5764i | 1.06814 | − | 0.684362i | ||||
\(995\) | − | 7.45731i | − | 0.236413i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.34855 | + | 4.06781i | 0.0743794 | + | 0.128829i | 0.900816 | − | 0.434201i | \(-0.142969\pi\) |
−0.826437 | + | 0.563029i | \(0.809636\pi\) | |||||||
\(998\) | −9.49071 | − | 16.4384i | −0.300423 | − | 0.520348i | ||||
\(999\) | 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 | 819.2.dl.e.415.6 | 16 | ||
3.2 | odd | 2 | 91.2.r.a.51.3 | yes | 16 | ||
7.4 | even | 3 | inner | 819.2.dl.e.298.3 | 16 | ||
13.12 | even | 2 | inner | 819.2.dl.e.415.3 | 16 | ||
21.2 | odd | 6 | 637.2.c.f.246.6 | 8 | |||
21.5 | even | 6 | 637.2.c.e.246.6 | 8 | |||
21.11 | odd | 6 | 91.2.r.a.25.6 | yes | 16 | ||
21.17 | even | 6 | 637.2.r.f.116.6 | 16 | |||
21.20 | even | 2 | 637.2.r.f.324.3 | 16 | |||
39.5 | even | 4 | 1183.2.e.i.170.3 | 16 | |||
39.8 | even | 4 | 1183.2.e.i.170.6 | 16 | |||
39.38 | odd | 2 | 91.2.r.a.51.6 | yes | 16 | ||
91.25 | even | 6 | inner | 819.2.dl.e.298.6 | 16 | ||
273.5 | odd | 12 | 8281.2.a.cj.1.6 | 8 | |||
273.38 | even | 6 | 637.2.r.f.116.3 | 16 | |||
273.44 | even | 12 | 8281.2.a.ck.1.6 | 8 | |||
273.47 | odd | 12 | 8281.2.a.cj.1.3 | 8 | |||
273.86 | even | 12 | 8281.2.a.ck.1.3 | 8 | |||
273.116 | odd | 6 | 91.2.r.a.25.3 | ✓ | 16 | ||
273.194 | even | 6 | 637.2.c.e.246.3 | 8 | |||
273.200 | even | 12 | 1183.2.e.i.508.3 | 16 | |||
273.233 | odd | 6 | 637.2.c.f.246.3 | 8 | |||
273.242 | even | 12 | 1183.2.e.i.508.6 | 16 | |||
273.272 | even | 2 | 637.2.r.f.324.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.3 | ✓ | 16 | 273.116 | odd | 6 | ||
91.2.r.a.25.6 | yes | 16 | 21.11 | odd | 6 | ||
91.2.r.a.51.3 | yes | 16 | 3.2 | odd | 2 | ||
91.2.r.a.51.6 | yes | 16 | 39.38 | odd | 2 | ||
637.2.c.e.246.3 | 8 | 273.194 | even | 6 | |||
637.2.c.e.246.6 | 8 | 21.5 | even | 6 | |||
637.2.c.f.246.3 | 8 | 273.233 | odd | 6 | |||
637.2.c.f.246.6 | 8 | 21.2 | odd | 6 | |||
637.2.r.f.116.3 | 16 | 273.38 | even | 6 | |||
637.2.r.f.116.6 | 16 | 21.17 | even | 6 | |||
637.2.r.f.324.3 | 16 | 21.20 | even | 2 | |||
637.2.r.f.324.6 | 16 | 273.272 | even | 2 | |||
819.2.dl.e.298.3 | 16 | 7.4 | even | 3 | inner | ||
819.2.dl.e.298.6 | 16 | 91.25 | even | 6 | inner | ||
819.2.dl.e.415.3 | 16 | 13.12 | even | 2 | inner | ||
819.2.dl.e.415.6 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.170.3 | 16 | 39.5 | even | 4 | |||
1183.2.e.i.170.6 | 16 | 39.8 | even | 4 | |||
1183.2.e.i.508.3 | 16 | 273.200 | even | 12 | |||
1183.2.e.i.508.6 | 16 | 273.242 | even | 12 | |||
8281.2.a.cj.1.3 | 8 | 273.47 | odd | 12 | |||
8281.2.a.cj.1.6 | 8 | 273.5 | odd | 12 | |||
8281.2.a.ck.1.3 | 8 | 273.86 | even | 12 | |||
8281.2.a.ck.1.6 | 8 | 273.44 | even | 12 |