Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 324.3 | ||
Root | \(0.929293 - 0.536527i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.324 |
Dual form | 637.2.r.f.116.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.134065 | − | 0.990972i | \(-0.457197\pi\) |
−0.791175 | + | 0.611590i | \(0.790530\pi\) | |||||||
\(3\) | −1.21570 | − | 2.10566i | −0.701886 | − | 1.21570i | −0.967804 | − | 0.251707i | \(-0.919008\pi\) |
0.265918 | − | 0.963996i | \(-0.414325\pi\) | |||||||
\(4\) | −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 | \(0.711329\pi\) | |||||||
\(6\) | 2.60903i | 1.06513i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.05665i | 1.08069i | ||||||||
\(9\) | −1.45586 | + | 2.52163i | −0.485288 | + | 0.840544i | ||||
\(10\) | 0.335561 | + | 0.581209i | 0.106114 | + | 0.183795i | ||||
\(11\) | −0.613597 | + | 0.354260i | −0.185006 | + | 0.106814i | −0.589643 | − | 0.807664i | \(-0.700731\pi\) |
0.404636 | + | 0.914478i | \(0.367398\pi\) | |||||||
\(12\) | −1.03159 | + | 1.78676i | −0.297794 | + | 0.515794i | ||||
\(13\) | −0.848553 | + | 3.50428i | −0.235346 | + | 0.971912i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52068i | 0.392637i | ||||||||
\(16\) | 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 | \(0.700461\pi\) | |||||||
\(18\) | 2.70585 | − | 1.56222i | 0.637775 | − | 0.368219i | ||||
\(19\) | 4.50573 | + | 2.60138i | 1.03368 | + | 0.596798i | 0.918038 | − | 0.396492i | \(-0.129773\pi\) |
0.115646 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(20\) | 0.530712i | 0.118671i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.760282 | 0.162093 | ||||||||
\(23\) | −2.21570 | + | 3.83771i | −0.462006 | + | 0.800218i | −0.999061 | − | 0.0433296i | \(-0.986203\pi\) |
0.537055 | + | 0.843547i | \(0.319537\pi\) | |||||||
\(24\) | 6.43627 | − | 3.71598i | 1.31380 | − | 0.758522i | ||||
\(25\) | −2.30442 | − | 3.99137i | −0.460883 | − | 0.798274i | ||||
\(26\) | 2.66870 | − | 2.80123i | 0.523374 | − | 0.549366i | ||||
\(27\) | −0.214623 | −0.0413042 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.59711 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(30\) | 0.815886 | − | 1.41316i | 0.148960 | − | 0.258006i | ||||
\(31\) | −3.80238 | + | 2.19530i | −0.682927 | + | 0.394288i | −0.800957 | − | 0.598722i | \(-0.795675\pi\) |
0.118030 | + | 0.993010i | \(0.462342\pi\) | |||||||
\(32\) | 3.82335 | − | 2.20741i | 0.675879 | − | 0.390219i | ||||
\(33\) | 1.49190 | + | 0.861351i | 0.259707 | + | 0.149942i | ||||
\(34\) | − | 3.58737i | − | 0.615228i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.47076 | 0.411793 | ||||||||
\(37\) | −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 | ||||
\(39\) | 8.41040 | − | 2.47340i | 1.34674 | − | 0.396060i | ||||
\(40\) | 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 | ||||
\(45\) | 1.57711 | − | 0.910544i | 0.235101 | − | 0.135736i | ||||
\(46\) | 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 | \(0.466282\pi\) | |||||||
\(48\) | −3.84855 | −0.555491 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.94553i | 0.699404i | ||||||||
\(51\) | 4.06426 | − | 7.03950i | 0.569110 | − | 0.985727i | ||||
\(52\) | 2.93520 | − | 0.863208i | 0.407040 | − | 0.119705i | ||||
\(53\) | 0.348553 | + | 0.603712i | 0.0478774 | + | 0.0829262i | 0.888971 | − | 0.457964i | \(-0.151421\pi\) |
−0.841094 | + | 0.540890i | \(0.818088\pi\) | |||||||
\(54\) | 0.199447 | + | 0.115151i | 0.0271414 | + | 0.0156701i | ||||
\(55\) | 0.443132 | 0.0597519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.6500i | − | 1.67554i | ||||||
\(58\) | 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 | \(0.555244\pi\) | |||||||
\(60\) | 1.11750 | − | 0.645188i | 0.144268 | − | 0.0832934i | ||||
\(61\) | 2.34855 | − | 4.06781i | 0.300701 | − | 0.520830i | −0.675594 | − | 0.737274i | \(-0.736113\pi\) |
0.976295 | + | 0.216444i | \(0.0694459\pi\) | |||||||
\(62\) | 4.71136 | 0.598344 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.90305 | −0.987881 | ||||||||
\(65\) | 1.55545 | − | 1.63270i | 0.192930 | − | 0.202512i | ||||
\(66\) | −0.924277 | − | 1.60089i | −0.113771 | − | 0.197056i | ||||
\(67\) | −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 | ||||
\(69\) | 10.7745 | 1.29710 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0876i | 1.67189i | 0.548812 | + | 0.835946i | \(0.315080\pi\) | ||||
−0.548812 | + | 0.835946i | \(0.684920\pi\) | |||||||
\(72\) | −7.70775 | − | 4.45007i | −0.908368 | − | 0.524446i | ||||
\(73\) | 4.40273 | − | 2.54191i | 0.515300 | − | 0.297509i | −0.219710 | − | 0.975565i | \(-0.570511\pi\) |
0.735010 | + | 0.678057i | \(0.237178\pi\) | |||||||
\(74\) | 0.227170 | + | 0.393471i | 0.0264080 | + | 0.0457400i | ||||
\(75\) | −5.60297 | + | 9.70463i | −0.646975 | + | 1.12059i | ||||
\(76\) | − | 4.41482i | − | 0.506415i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.14277 | − | 2.21390i | −1.03521 | − | 0.250675i | ||||
\(79\) | 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 | ||||
\(81\) | 4.62851 | + | 8.01682i | 0.514279 | + | 0.890757i | ||||
\(82\) | −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 | ||||
\(87\) | 8.02012 | + | 13.8913i | 0.859847 | + | 1.48930i | ||||
\(88\) | −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 | \(0.917561\pi\) | |||||||
\(90\) | −1.95413 | −0.205983 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.76028 | 0.392036 | ||||||||
\(93\) | 9.24512 | + | 5.33767i | 0.958674 | + | 0.553491i | ||||
\(94\) | −4.33122 | − | 7.50190i | −0.446731 | − | 0.773761i | ||||
\(95\) | −1.62699 | − | 2.81802i | −0.166925 | − | 0.289123i | ||||
\(96\) | −9.29610 | − | 5.36711i | −0.948780 | − | 0.547778i | ||||
\(97\) | − | 0.202023i | − | 0.0205123i | −0.999947 | − | 0.0102562i | \(-0.996735\pi\) | ||
0.999947 | − | 0.0102562i | \(-0.00326470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.06302i | − | 0.207341i | ||||||
\(100\) | −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 | \(0.502280\pi\) | |||||||
\(102\) | −7.55377 | + | 4.36117i | −0.747934 | + | 0.431820i | ||||
\(103\) | 5.40739 | − | 9.36587i | 0.532806 | − | 0.922847i | −0.466460 | − | 0.884542i | \(-0.654471\pi\) |
0.999266 | − | 0.0383047i | \(-0.0121957\pi\) | |||||||
\(104\) | −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 | −0.679474 | − | 0.733700i | \(-0.737792\pi\) |
0.975140 | + | 0.221592i | \(0.0711252\pi\) | |||||||
\(108\) | 0.0910594 | + | 0.157720i | 0.00876220 | + | 0.0151766i | ||||
\(109\) | −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 | ||||
\(111\) | 1.02948i | 0.0977137i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.923456 | −0.0868714 | −0.0434357 | − | 0.999056i | \(-0.513830\pi\) | ||||
−0.0434357 | + | 0.999056i | \(0.513830\pi\) | |||||||
\(114\) | −6.78709 | + | 11.7556i | −0.635669 | + | 1.10101i | ||||
\(115\) | 2.40023 | − | 1.38577i | 0.223822 | − | 0.129224i | ||||
\(116\) | 2.79900 | + | 4.84801i | 0.259880 | + | 0.450126i | ||||
\(117\) | −7.60112 | − | 7.24149i | −0.702723 | − | 0.669476i | ||||
\(118\) | 10.5837 | 0.974312 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.64819 | −0.424319 | ||||||||
\(121\) | −5.24900 | + | 9.09153i | −0.477182 | + | 0.826503i | ||||
\(122\) | −4.36499 | + | 2.52013i | −0.395187 | + | 0.228162i | ||||
\(123\) | −10.5621 | + | 6.09801i | −0.952349 | + | 0.549839i | ||||
\(124\) | 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 | ||||
\(129\) | −13.6231 | − | 23.5959i | −1.19945 | − | 2.07750i | ||||
\(130\) | −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 | \(0.265634\pi\) | |||||||
\(132\) | − | 1.46180i | − | 0.127234i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1821 | 0.965988 | ||||||||
\(135\) | 0.116248 | + | 0.0671160i | 0.0100051 | + | 0.00577642i | ||||
\(136\) | −8.84974 | + | 5.10940i | −0.758859 | + | 0.438128i | ||||
\(137\) | −5.38403 | + | 3.10847i | −0.459989 | + | 0.265575i | −0.712040 | − | 0.702139i | \(-0.752228\pi\) |
0.252051 | + | 0.967714i | \(0.418895\pi\) | |||||||
\(138\) | −10.0127 | − | 5.78084i | −0.852338 | − | 0.492097i | ||||
\(139\) | −6.53140 | −0.553986 | −0.276993 | − | 0.960872i | \(-0.589338\pi\) | ||||
−0.276993 | + | 0.960872i | \(0.589338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 19.6280i | − | 1.65297i | ||||||
\(142\) | 7.55839 | − | 13.0915i | 0.634286 | − | 1.09862i | ||||
\(143\) | −0.720757 | − | 2.45082i | −0.0602727 | − | 0.204948i | ||||
\(144\) | 2.30442 | + | 3.99137i | 0.192035 | + | 0.332614i | ||||
\(145\) | 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 | 0.363072 | − | 0.931761i | \(-0.381728\pi\) |
−0.625393 | + | 0.780310i | \(0.715061\pi\) | |||||||
\(150\) | 10.4136 | − | 6.01230i | 0.850267 | − | 0.490902i | ||||
\(151\) | −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 | ||||
\(153\) | −9.73430 | −0.786971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74603 | 0.220566 | ||||||||
\(156\) | −5.38595 | − | 5.13113i | −0.431221 | − | 0.410819i | ||||
\(157\) | −4.75984 | − | 8.24428i | −0.379876 | − | 0.657965i | 0.611168 | − | 0.791501i | \(-0.290700\pi\) |
−0.991044 | + | 0.133536i | \(0.957367\pi\) | |||||||
\(158\) | −3.63514 | + | 2.09875i | −0.289196 | + | 0.166968i | ||||
\(159\) | 0.847473 | − | 1.46787i | 0.0672090 | − | 0.116409i | ||||
\(160\) | −2.76117 | −0.218290 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 9.93329i | − | 0.780433i | ||||||
\(163\) | 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 | ||||
\(165\) | −0.538716 | − | 0.933084i | −0.0419390 | − | 0.0726405i | ||||
\(166\) | 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 | ||||
\(171\) | −13.1195 | + | 7.57452i | −1.00327 | + | 0.579238i | ||||
\(172\) | −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 | \(0.317299\pi\) | |||||||
\(174\) | − | 17.2121i | − | 1.30484i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.12148i | 0.0845350i | ||||||||
\(177\) | 20.7685 | + | 11.9907i | 1.56106 | + | 0.901276i | ||||
\(178\) | 7.17825 | + | 12.4331i | 0.538033 | + | 0.931900i | ||||
\(179\) | 4.73538 | + | 8.20192i | 0.353939 | + | 0.613040i | 0.986936 | − | 0.161114i | \(-0.0515088\pi\) |
−0.632997 | + | 0.774154i | \(0.718175\pi\) | |||||||
\(180\) | −1.33826 | − | 0.772645i | −0.0997480 | − | 0.0575896i | ||||
\(181\) | 11.4314 | 0.849690 | 0.424845 | − | 0.905266i | \(-0.360329\pi\) | ||||
0.424845 | + | 0.905266i | \(0.360329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4206 | −0.844233 | ||||||||
\(184\) | −11.7305 | − | 6.77264i | −0.864788 | − | 0.499285i | ||||
\(185\) | 0.132407 | + | 0.229335i | 0.00973473 | + | 0.0168611i | ||||
\(186\) | −5.72761 | − | 9.92052i | −0.419969 | − | 0.727408i | ||||
\(187\) | −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 | \(0.358777\pi\) |
−0.996807 | + | 0.0798496i | \(0.974556\pi\) | |||||||
\(192\) | 9.60776 | + | 16.6411i | 0.693380 | + | 1.20097i | ||||
\(193\) | 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 | ||||
\(195\) | −5.32888 | − | 1.29038i | −0.381609 | − | 0.0924057i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2035i | 0.726970i | 0.931600 | + | 0.363485i | \(0.118413\pi\) | ||||
−0.931600 | + | 0.363485i | \(0.881587\pi\) | |||||||
\(198\) | −1.10687 | + | 1.91715i | −0.0786616 | + | 0.136246i | ||||
\(199\) | −5.96173 | − | 10.3260i | −0.422616 | − | 0.731992i | 0.573579 | − | 0.819150i | \(-0.305555\pi\) |
−0.996194 | + | 0.0871586i | \(0.972221\pi\) | |||||||
\(200\) | 12.2002 | − | 7.04381i | 0.862687 | − | 0.498072i | ||||
\(201\) | 21.9427 | + | 12.6686i | 1.54772 | + | 0.893576i | ||||
\(202\) | − | 18.6008i | − | 1.30875i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.89747 | −0.482920 | ||||||||
\(205\) | −1.56860 | + | 2.71689i | −0.109555 | + | 0.189756i | ||||
\(206\) | −10.0501 | + | 5.80243i | −0.700223 | + | 0.404274i | ||||
\(207\) | −6.45152 | − | 11.1744i | −0.448412 | − | 0.776672i | ||||
\(208\) | 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 | ||||
\(213\) | 29.6637 | − | 17.1263i | 2.03252 | − | 1.17348i | ||||
\(214\) | −5.68428 | + | 3.28182i | −0.388570 | + | 0.224341i | ||||
\(215\) | −6.06959 | − | 3.50428i | −0.413942 | − | 0.238990i | ||||
\(216\) | − | 0.656028i | − | 0.0446370i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.2319 | 0.828451 | ||||||||
\(219\) | −10.7048 | − | 6.18042i | −0.723364 | − | 0.417634i | ||||
\(220\) | −0.188010 | − | 0.325643i | −0.0126757 | − | 0.0219549i | ||||
\(221\) | −11.5641 | + | 3.40087i | −0.777888 | + | 0.228767i | ||||
\(222\) | 0.552343 | − | 0.956687i | 0.0370709 | − | 0.0642086i | ||||
\(223\) | 6.76662i | 0.453126i | 0.973996 | + | 0.226563i | \(0.0727490\pi\) | ||||
−0.973996 | + | 0.226563i | \(0.927251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.4197 | 0.894645 | ||||||||
\(226\) | 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 | \(0.521895\pi\) | |||||||
\(228\) | −9.29610 | + | 5.36711i | −0.615650 | + | 0.355445i | ||||
\(229\) | −9.54855 | − | 5.51286i | −0.630986 | − | 0.364300i | 0.150148 | − | 0.988664i | \(-0.452025\pi\) |
−0.781134 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(230\) | −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 | \(-0.640866\pi\) |
0.996717 | − | 0.0809664i | \(-0.0258006\pi\) | |||||||
\(234\) | 3.17840 | + | 10.8077i | 0.207779 | + | 0.706520i | ||||
\(235\) | −2.52446 | − | 4.37249i | −0.164678 | − | 0.285230i | ||||
\(236\) | 7.24814 | + | 4.18472i | 0.471814 | + | 0.272402i | ||||
\(237\) | −9.51100 | −0.617806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.7223i | 1.27573i | 0.770148 | + | 0.637865i | \(0.220182\pi\) | ||||
−0.770148 | + | 0.637865i | \(0.779818\pi\) | |||||||
\(240\) | 2.08453 | + | 1.20350i | 0.134556 | + | 0.0776858i | ||||
\(241\) | 2.41112 | − | 1.39206i | 0.155314 | − | 0.0896706i | −0.420329 | − | 0.907372i | \(-0.638085\pi\) |
0.575643 | + | 0.817701i | \(0.304752\pi\) | |||||||
\(242\) | 9.75571 | − | 5.63246i | 0.627121 | − | 0.362069i | ||||
\(243\) | 10.9318 | − | 18.9345i | 0.701278 | − | 1.21465i | ||||
\(244\) | −3.98574 | −0.255161 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.0870 | 0.834397 | ||||||||
\(247\) | −12.9393 | + | 13.5819i | −0.823309 | + | 0.864196i | ||||
\(248\) | −6.71028 | − | 11.6226i | −0.426103 | − | 0.738033i | ||||
\(249\) | 21.4851 | − | 12.4044i | 1.36156 | − | 0.786098i | ||||
\(250\) | 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 | ||||
\(255\) | −4.40273 | + | 2.54191i | −0.275709 | + | 0.159181i | ||||
\(256\) | 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 | \(0.132526\pi\) | |||||||
\(258\) | 29.2367i | 1.82019i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.85976 | − | 0.450337i | −0.115338 | − | 0.0279287i | ||||
\(261\) | 9.60450 | − | 16.6355i | 0.594503 | − | 1.02971i | ||||
\(262\) | 6.50788 | − | 3.75733i | 0.402058 | − | 0.232128i | ||||
\(263\) | 10.7245 | + | 18.5754i | 0.661303 | + | 1.14541i | 0.980273 | + | 0.197646i | \(0.0633298\pi\) |
−0.318970 | + | 0.947765i | \(0.603337\pi\) | |||||||
\(264\) | −2.63285 | + | 4.56023i | −0.162041 | + | 0.280663i | ||||
\(265\) | − | 0.435992i | − | 0.0267828i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.5300i | 1.99080i | ||||||||
\(268\) | 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 | \(0.685889\pi\) | |||||||
\(270\) | −0.0720191 | − | 0.124741i | −0.00438294 | − | 0.00759148i | ||||
\(271\) | 1.76986 | + | 1.02183i | 0.107511 | + | 0.0620717i | 0.552792 | − | 0.833320i | \(-0.313563\pi\) |
−0.445280 | + | 0.895391i | \(0.646896\pi\) | |||||||
\(272\) | 5.29168 | 0.320856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.67112 | 0.403017 | ||||||||
\(275\) | 2.82797 | + | 1.63273i | 0.170533 | + | 0.0984572i | ||||
\(276\) | −4.57138 | − | 7.91787i | −0.275165 | − | 0.476600i | ||||
\(277\) | −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 | ||||
\(279\) | − | 12.7843i | − | 0.765373i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.2356i | − | 1.20715i | −0.797305 | − | 0.603577i | \(-0.793742\pi\) | ||
0.797305 | − | 0.603577i | \(-0.206258\pi\) | |||||||
\(282\) | −10.5310 | + | 18.2401i | −0.627109 | + | 1.08618i | ||||
\(283\) | −0.867593 | − | 1.50272i | −0.0515731 | − | 0.0893272i | 0.839086 | − | 0.543998i | \(-0.183090\pi\) |
−0.890659 | + | 0.454671i | \(0.849757\pi\) | |||||||
\(284\) | 10.3525 | − | 5.97704i | 0.614310 | − | 0.354672i | ||||
\(285\) | −3.95586 | + | 6.85176i | −0.234325 | + | 0.405863i | ||||
\(286\) | −0.645140 | + | 2.66424i | −0.0381479 | + | 0.157540i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.8548i | 0.757474i | ||||||||
\(289\) | 2.91173 | − | 5.04326i | 0.171278 | − | 0.296662i | ||||
\(290\) | −2.21373 | − | 3.83430i | −0.129995 | − | 0.225158i | ||||
\(291\) | −0.425392 | + | 0.245600i | −0.0249369 | + | 0.0143973i | ||||
\(292\) | −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 | ||||
\(297\) | 0.131692 | − | 0.0760324i | 0.00764154 | − | 0.00441185i | ||||
\(298\) | 1.98375 | + | 3.43595i | 0.114915 | + | 0.199039i | ||||
\(299\) | −11.5683 | − | 11.0209i | −0.669009 | − | 0.637357i | ||||
\(300\) | 9.50884 | 0.548993 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.23409 | 0.301188 | ||||||||
\(303\) | 21.0735 | − | 36.5004i | 1.21064 | − | 2.09690i | ||||
\(304\) | 7.13190 | − | 4.11760i | 0.409042 | − | 0.236161i | ||||
\(305\) | −2.54414 | + | 1.46886i | −0.145677 | + | 0.0841067i | ||||
\(306\) | 9.04601 | + | 5.22272i | 0.517126 | + | 0.298563i | ||||
\(307\) | 12.7138i | 0.725612i | 0.931865 | + | 0.362806i | \(0.118181\pi\) | ||||
−0.931865 | + | 0.362806i | \(0.881819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.2951 | −1.49588 | ||||||||
\(310\) | −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 | \(0.921255\pi\) | |||||||
\(312\) | 7.56031 | + | 25.7077i | 0.428018 | + | 1.45541i | ||||
\(313\) | −4.51273 | + | 7.81628i | −0.255075 | + | 0.441802i | −0.964916 | − | 0.262559i | \(-0.915433\pi\) |
0.709841 | + | 0.704362i | \(0.248767\pi\) | |||||||
\(314\) | 10.2151i | 0.576473i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.31931 | −0.186726 | ||||||||
\(317\) | −21.3269 | − | 12.3131i | −1.19784 | − | 0.691572i | −0.237766 | − | 0.971323i | \(-0.576415\pi\) |
−0.960073 | + | 0.279750i | \(0.909748\pi\) | |||||||
\(318\) | −1.57510 | + | 0.909386i | −0.0883273 | + | 0.0509958i | ||||
\(319\) | 4.04797 | − | 2.33709i | 0.226643 | − | 0.130852i | ||||
\(320\) | 4.28061 | + | 2.47141i | 0.239293 | + | 0.138156i | ||||
\(321\) | −14.8724 | −0.830095 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.3935i | 0.967802i | ||||||||
\(324\) | 3.92754 | − | 6.80269i | 0.218196 | − | 0.377927i | ||||
\(325\) | 15.9423 | − | 4.68843i | 0.884319 | − | 0.260067i | ||||
\(326\) | −12.7205 | − | 22.0325i | −0.704521 | − | 1.22027i | ||||
\(327\) | 24.0027 | + | 13.8580i | 1.32735 | + | 0.766348i | ||||
\(328\) | 15.3323 | 0.846584 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.15614i | 0.0636436i | ||||||||
\(331\) | −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 | ||||
\(333\) | 1.06768 | − | 0.616426i | 0.0585085 | − | 0.0337799i | ||||
\(334\) | −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 | ||||
\(339\) | 1.12265 | + | 1.94448i | 0.0609738 | + | 0.105610i | ||||
\(340\) | −1.53654 | + | 0.887121i | −0.0833305 | + | 0.0481109i | ||||
\(341\) | 1.55542 | − | 2.69406i | 0.0842306 | − | 0.145892i | ||||
\(342\) | 16.2558 | 0.879010 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 34.2527i | 1.84678i | ||||||||
\(345\) | −5.83592 | − | 3.36937i | −0.314195 | − | 0.181401i | ||||
\(346\) | 11.1414 | − | 6.43251i | 0.598968 | − | 0.345814i | ||||
\(347\) | −0.229959 | − | 0.398300i | −0.0123448 | − | 0.0213819i | 0.859787 | − | 0.510653i | \(-0.170596\pi\) |
−0.872132 | + | 0.489271i | \(0.837263\pi\) | |||||||
\(348\) | 6.80550 | − | 11.7875i | 0.364813 | − | 0.631875i | ||||
\(349\) | − | 6.87822i | − | 0.368183i | −0.982909 | − | 0.184091i | \(-0.941066\pi\) | ||
0.982909 | − | 0.184091i | \(-0.0589342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.182119 | − | 0.752098i | 0.00972078 | − | 0.0401440i | ||||
\(352\) | −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 | \(0.346325\pi\) | |||||||
\(354\) | −12.8667 | − | 22.2857i | −0.683856 | − | 1.18447i | ||||
\(355\) | 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 | −0.273728 | − | 0.961807i | \(-0.588257\pi\) |
−0.969813 | + | 0.243848i | \(0.921590\pi\) | |||||||
\(360\) | 2.78322 | + | 4.82068i | 0.146688 | + | 0.254072i | ||||
\(361\) | 4.03438 | + | 6.98774i | 0.212336 | + | 0.367776i | ||||
\(362\) | −10.6231 | − | 6.13326i | −0.558339 | − | 0.322357i | ||||
\(363\) | 25.5249 | 1.33971 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.17959 | −0.166427 | ||||||||
\(366\) | 10.6131 | + | 6.12745i | 0.554753 | + | 0.320287i | ||||
\(367\) | 13.4907 | + | 23.3666i | 0.704208 | + | 1.21972i | 0.966977 | + | 0.254865i | \(0.0820311\pi\) |
−0.262769 | + | 0.964859i | \(0.584636\pi\) | |||||||
\(368\) | 3.50713 | + | 6.07452i | 0.182822 | + | 0.316656i | ||||
\(369\) | 12.6486 | + | 7.30267i | 0.658460 | + | 0.380162i | ||||
\(370\) | − | 0.284159i | − | 0.0147727i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 9.05859i | − | 0.469666i | ||||||
\(373\) | −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 | ||||
\(375\) | 12.6543 | − | 7.30597i | 0.653466 | − | 0.377279i | ||||
\(376\) | −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 | ||||
\(381\) | −10.3453 | − | 17.9186i | −0.530005 | − | 0.917996i | ||||
\(382\) | 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 | \(0.874637\pi\) | |||||||
\(384\) | 0.849134i | 0.0433322i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.6879 | −1.25658 | ||||||||
\(387\) | −16.3143 | + | 28.2573i | −0.829304 | + | 1.43640i | ||||
\(388\) | −0.148460 | + | 0.0857137i | −0.00753694 | + | 0.00435145i | ||||
\(389\) | −14.2055 | − | 24.6046i | −0.720247 | − | 1.24751i | −0.960901 | − | 0.276894i | \(-0.910695\pi\) |
0.240653 | − | 0.970611i | \(-0.422638\pi\) | |||||||
\(390\) | 4.25977 | + | 4.05823i | 0.215702 | + | 0.205496i | ||||
\(391\) | −14.8148 | −0.749216 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0272 | 0.858911 | ||||||||
\(394\) | 5.47446 | − | 9.48204i | 0.275799 | − | 0.477698i | ||||
\(395\) | −2.11875 | + | 1.22326i | −0.106606 | + | 0.0615489i | ||||
\(396\) | −1.51605 | + | 0.875291i | −0.0761843 | + | 0.0439850i | ||||
\(397\) | 8.53825 | + | 4.92956i | 0.428522 | + | 0.247408i | 0.698717 | − | 0.715398i | \(-0.253755\pi\) |
−0.270195 | + | 0.962806i | \(0.587088\pi\) | |||||||
\(398\) | 12.7945i | 0.641332i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.29510 | −0.364755 | ||||||||
\(401\) | 10.9287 | + | 6.30971i | 0.545756 | + | 0.315092i | 0.747408 | − | 0.664365i | \(-0.231298\pi\) |
−0.201653 | + | 0.979457i | \(0.564631\pi\) | |||||||
\(402\) | −13.5941 | − | 23.5457i | −0.678013 | − | 1.17435i | ||||
\(403\) | −4.46643 | − | 15.1874i | −0.222489 | − | 0.756539i | ||||
\(404\) | 7.35460 | − | 12.7385i | 0.365905 | − | 0.633766i | ||||
\(405\) | − | 5.78964i | − | 0.287689i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.299994 | 0.0148701 | ||||||||
\(408\) | 21.5173 | + | 12.4230i | 1.06527 | + | 0.615031i | ||||
\(409\) | 15.6381 | − | 9.02867i | 0.773255 | − | 0.446439i | −0.0607793 | − | 0.998151i | \(-0.519359\pi\) |
0.834035 | + | 0.551712i | \(0.186025\pi\) | |||||||
\(410\) | 2.91537 | − | 1.68319i | 0.143980 | − | 0.0831268i | ||||
\(411\) | 13.0908 | + | 7.55795i | 0.645720 | + | 0.372806i | ||||
\(412\) | −9.17691 | −0.452114 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.8457i | 0.680478i | ||||||||
\(415\) | 3.19080 | − | 5.52663i | 0.156630 | − | 0.271291i | ||||
\(416\) | 4.49107 | + | 15.2712i | 0.220193 | + | 0.748731i | ||||
\(417\) | 7.94024 | + | 13.7529i | 0.388835 | + | 0.673483i | ||||
\(418\) | 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 | ||||
\(423\) | −20.3564 | + | 11.7527i | −0.989760 | + | 0.571438i | ||||
\(424\) | −1.84534 | + | 1.06541i | −0.0896175 | + | 0.0517407i | ||||
\(425\) | 7.70398 | − | 13.3437i | 0.373698 | − | 0.647263i | ||||
\(426\) | −36.7550 | −1.78079 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.19042 | −0.250888 | ||||||||
\(429\) | −4.28437 | + | 4.49714i | −0.206851 | + | 0.217124i | ||||
\(430\) | 3.76028 | + | 6.51300i | 0.181337 | + | 0.314085i | ||||
\(431\) | 12.6498 | − | 7.30335i | 0.609318 | − | 0.351790i | −0.163381 | − | 0.986563i | \(-0.552240\pi\) |
0.772698 | + | 0.634773i | \(0.218906\pi\) | |||||||
\(432\) | −0.169858 | + | 0.294203i | −0.00817230 | + | 0.0141548i | ||||
\(433\) | −28.0099 | −1.34607 | −0.673035 | − | 0.739611i | \(-0.735009\pi\) | ||||
−0.673035 | + | 0.739611i | \(0.735009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.0321i | − | 0.481001i | ||||||
\(436\) | 8.37688 | + | 4.83640i | 0.401180 | + | 0.231621i | ||||
\(437\) | −19.9667 | + | 11.5278i | −0.955137 | + | 0.551448i | ||||
\(438\) | 6.63193 | + | 11.4868i | 0.316886 | + | 0.548863i | ||||
\(439\) | −8.53872 | + | 14.7895i | −0.407531 | + | 0.705864i | −0.994612 | − | 0.103664i | \(-0.966943\pi\) |
0.587082 | + | 0.809528i | \(0.300277\pi\) | |||||||
\(440\) | 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 | −0.982155 | − | 0.188073i | \(-0.939776\pi\) |
0.653954 | + | 0.756534i | \(0.273109\pi\) | |||||||
\(444\) | 0.756531 | − | 0.436783i | 0.0359034 | − | 0.0207288i | ||||
\(445\) | 4.18386 | + | 7.24665i | 0.198334 | + | 0.343524i | ||||
\(446\) | 3.63048 | − | 6.28817i | 0.171908 | − | 0.297754i | ||||
\(447\) | 8.98984i | 0.425205i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.6410i | − | 1.54042i | −0.637789 | − | 0.770211i | \(-0.720151\pi\) | ||
0.637789 | − | 0.770211i | \(-0.279849\pi\) | |||||||
\(450\) | −12.4708 | − | 7.20003i | −0.587880 | − | 0.339412i | ||||
\(451\) | 1.77698 | + | 3.07783i | 0.0836749 | + | 0.144929i | ||||
\(452\) | 0.391801 | + | 0.678619i | 0.0184287 | + | 0.0319195i | ||||
\(453\) | 10.2709 | + | 5.92988i | 0.482567 | + | 0.278610i | ||||
\(454\) | 18.0536 | 0.847298 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6667 | 1.81074 | ||||||||
\(457\) | 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 | ||||
\(459\) | −0.358756 | − | 0.621384i | −0.0167453 | − | 0.0290037i | ||||
\(460\) | −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 | ||||
\(465\) | −3.33835 | − | 5.78219i | −0.154812 | − | 0.268143i | ||||
\(466\) | −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 | \(0.165259\pi\) | |||||||
\(468\) | −2.09657 | + | 8.65821i | −0.0969139 | + | 0.400226i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.41777i | 0.249903i | ||||||||
\(471\) | −11.5731 | + | 20.0452i | −0.533260 | + | 0.923633i | ||||
\(472\) | −15.0742 | − | 26.1092i | −0.693845 | − | 1.20177i | ||||
\(473\) | −6.87593 | + | 3.96982i | −0.316156 | + | 0.182533i | ||||
\(474\) | 8.83850 | + | 5.10291i | 0.405966 | + | 0.234384i | ||||
\(475\) | − | 23.9787i | − | 1.10022i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.02978 | −0.0929374 | ||||||||
\(478\) | 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 | \(0.170079\pi\) | |||||||
\(480\) | 3.35676 | + | 5.81408i | 0.153214 | + | 0.265375i | ||||
\(481\) | 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 | ||||
\(486\) | −20.3178 | + | 11.7305i | −0.921633 | + | 0.532105i | ||||
\(487\) | 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 | ||||
\(489\) | − | 57.6458i | − | 2.60684i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.7559 | −1.61364 | −0.806821 | − | 0.590796i | \(-0.798814\pi\) | ||||
−0.806821 | + | 0.590796i | \(0.798814\pi\) | |||||||
\(492\) | 8.96247 | + | 5.17448i | 0.404059 | + | 0.233284i | ||||
\(493\) | −11.0275 | − | 19.1002i | −0.496654 | − | 0.860230i | ||||
\(494\) | 19.3115 | − | 5.67927i | 0.868864 | − | 0.255522i | ||||
\(495\) | −0.645140 | + | 1.11741i | −0.0289969 | + | 0.0502240i | ||||
\(496\) | 6.94968i | 0.312050i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.6213 | −1.19293 | ||||||||
\(499\) | −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 | ||||
\(501\) | −2.38346 | + | 1.37609i | −0.106485 | + | 0.0614792i | ||||
\(502\) | −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 | ||||
\(507\) | 1.53079 | + | 31.5712i | 0.0679849 | + | 1.40212i | ||||
\(508\) | −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 | \(0.807754\pi\) | |||||||
\(510\) | 5.45523 | 0.241562 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 16.6645i | − | 0.736472i | ||||||
\(513\) | −0.967032 | − | 0.558316i | −0.0426955 | − | 0.0246502i | ||||
\(514\) | −3.18961 | + | 1.84152i | −0.140687 | + | 0.0812259i | ||||
\(515\) | −5.85772 | + | 3.38195i | −0.258122 | + | 0.149027i | ||||
\(516\) | −11.5599 | + | 20.0224i | −0.508897 | + | 0.881435i | ||||
\(517\) | −5.71967 | −0.251551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.1505 | 1.27957 | ||||||||
\(520\) | 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 | \(0.887359\pi\) | |||||||
\(522\) | −17.8508 | + | 10.3062i | −0.781307 | + | 0.451088i | ||||
\(523\) | −17.5251 | + | 30.3543i | −0.766317 | + | 1.32730i | 0.173230 | + | 0.984881i | \(0.444580\pi\) |
−0.939547 | + | 0.342419i | \(0.888754\pi\) | |||||||
\(524\) | 5.94246 | 0.259597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 23.0160i | − | 1.00355i | ||||||
\(527\) | −12.7119 | − | 7.33919i | −0.553737 | − | 0.319700i | ||||
\(528\) | 2.36146 | − | 1.36339i | 0.102769 | − | 0.0593339i | ||||
\(529\) | 1.68133 | + | 2.91214i | 0.0731011 | + | 0.126615i | ||||
\(530\) | −0.233922 | + | 0.405165i | −0.0101609 | + | 0.0175992i | ||||
\(531\) | − | 28.7189i | − | 1.24630i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.5776 | + | 4.25637i | 0.761370 | + | 0.184364i | ||||
\(534\) | 17.4532 | − | 30.2299i | 0.755275 | − | 1.30818i | ||||
\(535\) | −3.31309 | + | 1.91282i | −0.143238 | + | 0.0826982i | ||||
\(536\) | −15.9264 | − | 27.5854i | −0.687917 | − | 1.19151i | ||||
\(537\) | 11.5136 | − | 19.9422i | 0.496849 | − | 0.860568i | ||||
\(538\) | − | 15.7276i | − | 0.678066i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 0.113903i | − | 0.00490160i | ||||||
\(541\) | 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 | ||||
\(543\) | −13.8972 | − | 24.0706i | −0.596385 | − | 1.03297i | ||||
\(544\) | 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 | ||||
\(549\) | 6.83835 | + | 11.8444i | 0.291854 | + | 0.505505i | ||||
\(550\) | −1.75201 | − | 3.03457i | −0.0747058 | − | 0.129394i | ||||
\(551\) | −29.7248 | − | 17.1616i | −1.26632 | − | 0.731109i | ||||
\(552\) | 32.9340i | 1.40177i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.83051i | 0.247715i | ||||||||
\(555\) | 0.321934 | − | 0.557606i | 0.0136653 | − | 0.0236691i | ||||
\(556\) | 2.77112 | + | 4.79972i | 0.117522 | + | 0.203554i | ||||
\(557\) | −32.5267 | + | 18.7793i | −1.37820 | + | 0.795705i | −0.991943 | − | 0.126686i | \(-0.959566\pi\) |
−0.386258 | + | 0.922391i | \(0.626233\pi\) | |||||||
\(558\) | −6.85911 | + | 11.8803i | −0.290369 | + | 0.502934i | ||||
\(559\) | −9.50884 | + | 39.2687i | −0.402181 | + | 1.66089i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.75922i | 0.243154i | ||||||||
\(562\) | −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 | \(-0.373413\pi\) | |||||||
\(564\) | −14.4240 | + | 8.32769i | −0.607359 | + | 0.350659i | ||||
\(565\) | 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 | −0.614291 | − | 0.789079i | \(-0.710558\pi\) |
0.990508 | + | 0.137452i | \(0.0438914\pi\) | |||||||
\(570\) | 7.35231 | − | 4.24486i | 0.307955 | − | 0.177798i | ||||
\(571\) | 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 | ||||
\(573\) | 38.1428 | 1.59344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4236 | 0.851724 | ||||||||
\(576\) | 11.5058 | − | 19.9286i | 0.479407 | − | 0.830357i | ||||
\(577\) | −28.6282 | + | 16.5285i | −1.19181 | + | 0.688091i | −0.958717 | − | 0.284363i | \(-0.908218\pi\) |
−0.233092 | + | 0.972455i | \(0.574884\pi\) | |||||||
\(578\) | −5.41170 | + | 3.12445i | −0.225097 | + | 0.129960i | ||||
\(579\) | −48.4451 | − | 27.9698i | −2.01331 | − | 1.16239i | ||||
\(580\) | − | 3.50117i | − | 0.145378i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.527085 | 0.0218484 | ||||||||
\(583\) | −0.427742 | − | 0.246957i | −0.0177153 | − | 0.0102279i | ||||
\(584\) | 7.76975 | + | 13.4576i | 0.321515 | + | 0.556880i | ||||
\(585\) | 1.85254 | + | 6.29927i | 0.0765930 | + | 0.260443i | ||||
\(586\) | 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 | ||||
\(591\) | 21.4851 | − | 12.4044i | 0.883779 | − | 0.510250i | ||||
\(592\) | −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 | \(0.606109\pi\) | |||||||
\(594\) | −0.163174 | −0.00669510 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.13743i | 0.128514i | ||||||||
\(597\) | −14.4954 | + | 25.1067i | −0.593256 | + | 1.02755i | ||||
\(598\) | 4.83726 | + | 16.4484i | 0.197810 | + | 0.672624i | ||||
\(599\) | 5.28727 | + | 9.15782i | 0.216032 | + | 0.374178i | 0.953591 | − | 0.301104i | \(-0.0973551\pi\) |
−0.737559 | + | 0.675282i | \(0.764022\pi\) | |||||||
\(600\) | −29.6637 | − | 17.1263i | −1.21102 | − | 0.699180i | ||||
\(601\) | −4.08916 | −0.166800 | −0.0834001 | − | 0.996516i | \(-0.526578\pi\) | ||||
−0.0834001 | + | 0.996516i | \(0.526578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 30.3426i | − | 1.23565i | ||||||
\(604\) | 3.58450 | + | 2.06951i | 0.145851 | + | 0.0842072i | ||||
\(605\) | 5.68613 | − | 3.28289i | 0.231174 | − | 0.133469i | ||||
\(606\) | −39.1670 | + | 22.6131i | −1.59105 | + | 0.918593i | ||||
\(607\) | 1.80353 | − | 3.12380i | 0.0732030 | − | 0.126791i | −0.827100 | − | 0.562054i | \(-0.810011\pi\) |
0.900303 | + | 0.435263i | \(0.143345\pi\) | |||||||
\(608\) | 22.9693 | 0.931527 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.15233 | 0.127634 | ||||||||
\(611\) | −20.0768 | + | 21.0739i | −0.812222 | + | 0.852559i | ||||
\(612\) | 4.13003 | + | 7.15343i | 0.166947 | + | 0.289160i | ||||
\(613\) | −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 | ||||
\(615\) | 7.62778 | 0.307582 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.09503i | − | 0.124601i | −0.998057 | − | 0.0623007i | \(-0.980156\pi\) | ||
0.998057 | − | 0.0623007i | \(-0.0198438\pi\) | |||||||
\(618\) | 24.4359 | + | 14.1080i | 0.982954 | + | 0.567509i | ||||
\(619\) | 10.6255 | − | 6.13462i | 0.427074 | − | 0.246571i | −0.271025 | − | 0.962572i | \(-0.587363\pi\) |
0.698099 | + | 0.716001i | \(0.254029\pi\) | |||||||
\(620\) | −1.16507 | − | 2.01797i | −0.0467905 | − | 0.0810435i | ||||
\(621\) | 0.475540 | − | 0.823660i | 0.0190828 | − | 0.0330523i | ||||
\(622\) | 10.3215i | 0.413854i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.26570 | − | 13.4864i | 0.130733 | − | 0.539888i | ||||
\(625\) | −9.64277 | + | 16.7018i | −0.385711 | + | 0.668071i | ||||
\(626\) | 8.38730 | − | 4.84241i | 0.335224 | − | 0.193542i | ||||
\(627\) | 4.48140 | + | 7.76202i | 0.178970 | + | 0.309985i | ||||
\(628\) | −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 | ||||
\(633\) | 18.9520 | + | 32.8258i | 0.753273 | + | 1.30471i | ||||
\(634\) | 13.2126 | + | 22.8849i | 0.524740 | + | 0.908877i | ||||
\(635\) | −4.60921 | − | 2.66113i | −0.182911 | − | 0.105604i | ||||
\(636\) | −1.43825 | −0.0570304 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.01566 | −0.198572 | ||||||||
\(639\) | −35.5238 | − | 20.5097i | −1.40530 | − | 0.811349i | ||||
\(640\) | 0.109212 | + | 0.189160i | 0.00431697 | + | 0.00747721i | ||||
\(641\) | 6.09521 | + | 10.5572i | 0.240746 | + | 0.416985i | 0.960927 | − | 0.276801i | \(-0.0892744\pi\) |
−0.720181 | + | 0.693787i | \(0.755941\pi\) | |||||||
\(642\) | 13.8208 | + | 7.97944i | 0.545463 | + | 0.314923i | ||||
\(643\) | 18.9733i | 0.748235i | 0.927381 | + | 0.374117i | \(0.122054\pi\) | ||||
−0.927381 | + | 0.374117i | \(0.877946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0406i | 0.670974i | ||||||||
\(646\) | 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 | \(0.959986\pi\) | |||||||
\(648\) | −24.5046 | + | 14.1478i | −0.962633 | + | 0.555776i | ||||
\(649\) | 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 | −0.594512 | − | 0.804087i | \(-0.702655\pi\) |
0.993616 | + | 0.112819i | \(0.0359882\pi\) | |||||||
\(654\) | −14.8704 | − | 25.7563i | −0.581478 | − | 1.00715i | ||||
\(655\) | 3.79313 | − | 2.18996i | 0.148210 | − | 0.0855690i | ||||
\(656\) | −6.87593 | − | 3.96982i | −0.268460 | − | 0.154996i | ||||
\(657\) | 14.8027i | 0.577510i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6628 | 1.27236 | 0.636181 | − | 0.771540i | \(-0.280513\pi\) | ||||
0.636181 | + | 0.771540i | \(0.280513\pi\) | |||||||
\(660\) | −0.457129 | + | 0.791771i | −0.0177937 | + | 0.0308196i | ||||
\(661\) | −8.43242 | + | 4.86846i | −0.327983 | + | 0.189361i | −0.654945 | − | 0.755676i | \(-0.727308\pi\) |
0.326962 | + | 0.945037i | \(0.393975\pi\) | |||||||
\(662\) | 7.06704 | + | 12.2405i | 0.274668 | + | 0.475740i | ||||
\(663\) | 21.2196 | + | 20.2157i | 0.824101 | + | 0.785111i | ||||
\(664\) | −31.1886 | −1.21035 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.32292 | −0.0512620 | ||||||||
\(667\) | 14.6172 | − | 25.3178i | 0.565981 | − | 0.980308i | ||||
\(668\) | −0.831819 | + | 0.480251i | −0.0321841 | + | 0.0185815i | ||||
\(669\) | 14.2482 | − | 8.22620i | 0.550867 | − | 0.318043i | ||||
\(670\) | −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 | ||||
\(675\) | 0.494581 | + | 0.856639i | 0.0190364 | + | 0.0329720i | ||||
\(676\) | 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 | \(0.782446\pi\) | |||||||
\(678\) | − | 2.40932i | − | 0.0925296i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.39117 | 0.245090 | ||||||||
\(681\) | 35.4266 | + | 20.4536i | 1.35755 | + | 0.783783i | ||||
\(682\) | −2.89088 | + | 1.66905i | −0.110697 | + | 0.0639112i | ||||
\(683\) | −4.94304 | + | 2.85387i | −0.189140 | + | 0.109200i | −0.591580 | − | 0.806246i | \(-0.701496\pi\) |
0.402440 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(684\) | 11.1326 | + | 6.42738i | 0.425664 | + | 0.245757i | ||||
\(685\) | 3.88828 | 0.148563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8080i | 1.02279i | ||||||||
\(688\) | 8.86867 | − | 15.3610i | 0.338115 | − | 0.585632i | ||||
\(689\) | −2.41134 | + | 0.709145i | −0.0918647 | + | 0.0270163i | ||||
\(690\) | 3.61552 | + | 6.26226i | 0.137640 | + | 0.238400i | ||||
\(691\) | −36.1766 | − | 20.8866i | −1.37622 | − | 0.794563i | −0.384521 | − | 0.923116i | \(-0.625633\pi\) |
−0.991703 | + | 0.128553i | \(0.958967\pi\) | |||||||
\(692\) | 10.1734 | 0.386736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.493517i | 0.0187336i | ||||||||
\(695\) | 3.53767 | + | 2.04247i | 0.134191 | + | 0.0774754i | ||||
\(696\) | −42.4608 | + | 24.5147i | −1.60947 | + | 0.929228i | ||||
\(697\) | 14.5226 | − | 8.38464i | 0.550084 | − | 0.317591i | ||||
\(698\) | −3.69035 | + | 6.39188i | −0.139682 | + | 0.241936i | ||||
\(699\) | −42.1967 | −1.59603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4361 | 0.847399 | 0.423700 | − | 0.905803i | \(-0.360731\pi\) | ||||
0.423700 | + | 0.905803i | \(0.360731\pi\) | |||||||
\(702\) | −0.572763 | + | 0.601207i | −0.0216175 | + | 0.0226911i | ||||
\(703\) | −1.10145 | − | 1.90776i | −0.0415419 | − | 0.0719527i | ||||
\(704\) | 4.84929 | − | 2.79974i | 0.182764 | − | 0.105519i | ||||
\(705\) | −6.13798 | + | 10.6313i | −0.231170 | + | 0.400398i | ||||
\(706\) | 1.64527 | 0.0619207 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 20.3495i | − | 0.764780i | ||||||
\(709\) | −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 | ||||
\(711\) | 5.69495 | + | 9.86394i | 0.213577 | + | 0.369927i | ||||
\(712\) | 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 | ||||
\(717\) | 41.5284 | − | 23.9765i | 1.55091 | − | 0.895417i | ||||
\(718\) | 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 | \(0.141659\pi\) | |||||||
\(720\) | − | 2.88251i | − | 0.107425i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 8.65821i | − | 0.322225i | ||||||
\(723\) | −5.86242 | − | 3.38467i | −0.218026 | − | 0.125877i | ||||
\(724\) | −4.85008 | − | 8.40058i | −0.180252 | − | 0.312205i | ||||
\(725\) | 15.2025 | + | 26.3315i | 0.564606 | + | 0.977927i | ||||
\(726\) | −23.7201 | − | 13.6948i | −0.880335 | − | 0.508262i | ||||
\(727\) | 43.4680 | 1.61214 | 0.806070 | − | 0.591820i | \(-0.201591\pi\) | ||||
0.806070 | + | 0.591820i | \(0.201591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3884 | −0.940312 | ||||||||
\(730\) | 2.95477 | + | 1.70594i | 0.109361 | + | 0.0631396i | ||||
\(731\) | 18.7315 | + | 32.4439i | 0.692809 | + | 1.19998i | ||||
\(732\) | 4.84548 | + | 8.39261i | 0.179094 | + | 0.310200i | ||||
\(733\) | −7.87581 | − | 4.54710i | −0.290900 | − | 0.167951i | 0.347448 | − | 0.937699i | \(-0.387048\pi\) |
−0.638348 | + | 0.769748i | \(0.720382\pi\) | |||||||
\(734\) | − | 28.9525i | − | 1.06866i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5639i | 0.721133i | ||||||||
\(737\) | 3.69169 | − | 6.39419i | 0.135985 | − | 0.235533i | ||||
\(738\) | −7.83617 | − | 13.5726i | −0.288453 | − | 0.499616i | ||||
\(739\) | 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 | ||||
\(741\) | 44.3292 | + | 10.7342i | 1.62847 | + | 0.394331i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.1771i | − | 1.18046i | −0.807234 | − | 0.590231i | \(-0.799036\pi\) | ||
0.807234 | − | 0.590231i | \(-0.200964\pi\) | |||||||
\(744\) | −16.3154 | + | 28.2591i | −0.598152 | + | 1.03603i | ||||
\(745\) | 1.15623 | + | 2.00265i | 0.0423610 | + | 0.0733714i | ||||
\(746\) | 3.69150 | − | 2.13129i | 0.135155 | − | 0.0780320i | ||||
\(747\) | −25.7295 | − | 14.8549i | −0.941392 | − | 0.543513i | ||||
\(748\) | 2.00995i | 0.0734911i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.6794 | −0.572531 | ||||||||
\(751\) | 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 | ||||
\(753\) | −28.6429 | − | 49.6110i | −1.04381 | − | 1.80793i | ||||
\(754\) | −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 | ||||
\(759\) | −6.61123 | + | 3.81699i | −0.239972 | + | 0.138548i | ||||
\(760\) | 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 | \(0.402764\pi\) | |||||||
\(762\) | 22.2021i | 0.804299i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.3117 | 0.481601 | ||||||||
\(765\) | 5.27248 | + | 3.04407i | 0.190627 | + | 0.110059i | ||||
\(766\) | 12.7650 | + | 22.1097i | 0.461220 | + | 0.798856i | ||||
\(767\) | −10.0335 | − | 34.1174i | −0.362290 | − | 1.23191i | ||||
\(768\) | 19.6711 | − | 34.0713i | 0.709819 | − | 1.22944i | ||||
\(769\) | − | 39.3098i | − | 1.41755i | −0.705435 | − | 0.708774i | \(-0.749248\pi\) | ||
0.705435 | − | 0.708774i | \(-0.250752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.34529 | −0.300548 | ||||||||
\(772\) | −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 | \(0.411237\pi\) | |||||||
\(774\) | 30.3216 | − | 17.5062i | 1.08989 | − | 0.629247i | ||||
\(775\) | 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 | ||||
\(780\) | 1.31266 | + | 4.46350i | 0.0470008 | + | 0.159819i | ||||
\(781\) | −4.99068 | − | 8.64412i | −0.178581 | − | 0.309311i | ||||
\(782\) | 13.7673 | + | 7.94854i | 0.492316 | + | 0.284239i | ||||
\(783\) | 1.41589 | 0.0505998 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.95391i | 0.212504i | ||||||||
\(786\) | −15.8233 | − | 9.13558i | −0.564398 | − | 0.325855i | ||||
\(787\) | 34.4930 | − | 19.9145i | 1.22954 | − | 0.709877i | 0.262608 | − | 0.964903i | \(-0.415417\pi\) |
0.966934 | + | 0.255026i | \(0.0820839\pi\) | |||||||
\(788\) | 7.49823 | − | 4.32911i | 0.267114 | − | 0.154218i | ||||
\(789\) | 26.0757 | − | 45.1644i | 0.928319 | − | 1.60790i | ||||
\(790\) | 2.62525 | 0.0934022 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.30594 | 0.224072 | ||||||||
\(793\) | 12.2619 | + | 11.6817i | 0.435432 | + | 0.414831i | ||||
\(794\) | −5.28969 | − | 9.16201i | −0.187724 | − | 0.325148i | ||||
\(795\) | −0.918051 | + | 0.530037i | −0.0325599 | + | 0.0187985i | ||||
\(796\) | −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 | ||||
\(801\) | 33.7371 | − | 19.4781i | 1.19204 | − | 0.688226i | ||||
\(802\) | −6.77067 | − | 11.7271i | −0.239081 | − | 0.414100i | ||||
\(803\) | −1.80100 | + | 3.11942i | −0.0635559 | + | 0.110082i | ||||
\(804\) | − | 21.5000i | − | 0.758246i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.99784 | + | 16.5099i | −0.140818 | + | 0.581537i | ||||
\(807\) | 17.8184 | − | 30.8624i | 0.627237 | − | 1.08641i | ||||
\(808\) | −45.8867 | + | 26.4927i | −1.61429 | + | 0.932010i | ||||
\(809\) | −10.7088 | − | 18.5481i | −0.376500 | − | 0.652117i | 0.614050 | − | 0.789267i | \(-0.289539\pi\) |
−0.990550 | + | 0.137150i | \(0.956206\pi\) | |||||||
\(810\) | −3.10630 | + | 5.38027i | −0.109144 | + | 0.189043i | ||||
\(811\) | 11.0116i | 0.386669i | 0.981133 | + | 0.193335i | \(0.0619303\pi\) | ||||
−0.981133 | + | 0.193335i | \(0.938070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.96896i | − | 0.174269i | ||||||
\(814\) | −0.278782 | − | 0.160955i | −0.00977131 | − | 0.00564147i | ||||
\(815\) | −7.41414 | − | 12.8417i | −0.259706 | − | 0.449824i | ||||
\(816\) | −6.43311 | − | 11.1425i | −0.225204 | − | 0.390065i | ||||
\(817\) | 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 | 0.953382 | − | 0.301767i | \(-0.0975764\pi\) |
0.215353 | + | 0.976536i | \(0.430910\pi\) | |||||||
\(822\) | −8.11010 | − | 14.0471i | −0.282872 | − | 0.489949i | ||||
\(823\) | −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 | ||||
\(825\) | − | 7.93965i | − | 0.276423i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.3451i | − | 0.950881i | −0.879748 | − | 0.475440i | \(-0.842289\pi\) | ||
0.879748 | − | 0.475440i | \(-0.157711\pi\) | |||||||
\(828\) | −5.47446 | + | 9.48204i | −0.190251 | + | 0.329524i | ||||
\(829\) | 12.5043 | + | 21.6581i | 0.434292 | + | 0.752217i | 0.997238 | − | 0.0742776i | \(-0.0236651\pi\) |
−0.562945 | + | 0.826494i | \(0.690332\pi\) | |||||||
\(830\) | −5.93037 | + | 3.42390i | −0.205846 | + | 0.118845i | ||||
\(831\) | −6.60560 | + | 11.4412i | −0.229146 | + | 0.396892i | ||||
\(832\) | 6.70616 | − | 27.6945i | 0.232494 | − | 0.960133i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 17.0406i | − | 0.590069i | ||||||
\(835\) | −0.353972 | + | 0.613098i | −0.0122497 | + | 0.0212171i | ||||
\(836\) | 1.56400 | + | 2.70892i | 0.0540920 | + | 0.0936900i | ||||
\(837\) | 0.816077 | − | 0.471162i | 0.0282077 | − | 0.0162857i | ||||
\(838\) | 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 | ||||
\(843\) | −42.6092 | + | 24.6004i | −1.46754 | + | 0.847284i | ||||
\(844\) | 6.61418 | + | 11.4561i | 0.227669 | + | 0.394335i | ||||
\(845\) | 4.40155 | + | 6.83617i | 0.151418 | + | 0.235171i | ||||
\(846\) | 25.2227 | 0.867174 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.10342 | 0.0378914 | ||||||||
\(849\) | −2.10947 | + | 3.65371i | −0.0723968 | + | 0.125395i | ||||
\(850\) | −14.3185 | + | 8.26679i | −0.491120 | + | 0.283549i | ||||
\(851\) | 1.62492 | − | 0.938148i | 0.0557015 | − | 0.0321593i | ||||
\(852\) | −25.1712 | − | 14.5326i | −0.862352 | − | 0.497879i | ||||
\(853\) | 19.8232i | 0.678734i | 0.940654 | + | 0.339367i | \(0.110213\pi\) | ||||
−0.940654 | + | 0.339367i | \(0.889787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.47469 | 0.324028 | ||||||||
\(856\) | 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 | \(0.818810\pi\) | |||||||
\(858\) | 6.39427 | − | 1.88048i | 0.218297 | − | 0.0641984i | ||||
\(859\) | −19.4798 | + | 33.7401i | −0.664644 | + | 1.15120i | 0.314738 | + | 0.949179i | \(0.398083\pi\) |
−0.979382 | + | 0.202018i | \(0.935250\pi\) | |||||||
\(860\) | 5.94713i | 0.202795i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.6738 | −0.533851 | ||||||||
\(863\) | 21.4754 | + | 12.3988i | 0.731030 | + | 0.422060i | 0.818799 | − | 0.574081i | \(-0.194640\pi\) |
−0.0877689 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(864\) | −0.820578 | + | 0.473761i | −0.0279166 | + | 0.0161177i | ||||
\(865\) | 6.49381 | − | 3.74920i | 0.220796 | − | 0.127477i | ||||
\(866\) | 26.0294 | + | 15.0281i | 0.884514 | + | 0.510675i | ||||
\(867\) | −14.1592 | −0.480871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.77154i | 0.0940181i | ||||||||
\(870\) | −5.38249 | + | 9.32274i | −0.182483 | + | 0.316070i | ||||
\(871\) | −10.6008 | − | 36.0464i | −0.359194 | − | 1.22138i | ||||
\(872\) | −17.4216 | − | 30.1752i | −0.589971 | − | 1.02186i | ||||
\(873\) | 0.509428 | + | 0.294118i | 0.0172415 | + | 0.00995439i | ||||
\(874\) | 24.7399 | 0.836839 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.4888i | 0.354385i | ||||||||
\(877\) | −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 | ||||
\(879\) | 57.3668 | − | 33.1208i | 1.93494 | − | 1.11714i | ||||
\(880\) | 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 | ||||
\(885\) | −7.49936 | − | 12.9893i | −0.252088 | − | 0.436630i | ||||
\(886\) | 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 | \(-0.160447\pi\) | |||||||
\(888\) | −3.14676 | −0.105598 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 8.97901i | − | 0.300977i | ||||||
\(891\) | −5.68008 | − | 3.27940i | −0.190290 | − | 0.109864i | ||||
\(892\) | 4.97258 | − | 2.87092i | 0.166494 | − | 0.0961255i | ||||
\(893\) | 21.0002 | + | 36.3733i | 0.702743 | + | 1.21719i | ||||
\(894\) | 4.82329 | − | 8.35419i | 0.161315 | − | 0.279406i | ||||
\(895\) | − | 5.92331i | − | 0.197995i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.14277 | + | 37.7570i | −0.305268 | + | 1.26067i | ||||
\(898\) | −17.5128 | + | 30.3330i | −0.584409 | + | 1.01223i | ||||
\(899\) | 25.0847 | − | 14.4827i | 0.836621 | − | 0.483024i | ||||
\(900\) | −5.69365 | − | 9.86170i | −0.189788 | − | 0.328723i | ||||
\(901\) | −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 | ||||
\(906\) | −6.36309 | − | 11.0212i | −0.211400 | − | 0.366155i | ||||
\(907\) | −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 | ||||
\(909\) | −50.4732 | −1.67409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.70706 | −0.0565573 | −0.0282787 | − | 0.999600i | \(-0.509003\pi\) | ||||
−0.0282787 | + | 0.999600i | \(0.509003\pi\) | |||||||
\(912\) | −17.3405 | − | 10.0116i | −0.574202 | − | 0.331516i | ||||
\(913\) | −3.61470 | − | 6.26084i | −0.119629 | − | 0.207204i | ||||
\(914\) | −1.70097 | − | 2.94617i | −0.0562632 | − | 0.0974507i | ||||
\(915\) | 6.18583 | + | 3.57139i | 0.204497 | + | 0.118067i | ||||
\(916\) | 9.35590i | 0.309128i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.769931i | 0.0254115i | ||||||||
\(919\) | −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 | ||||
\(921\) | 26.7708 | − | 15.4561i | 0.882128 | − | 0.509297i | ||||
\(922\) | 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 | ||||
\(927\) | 15.7449 | + | 27.2709i | 0.517129 | + | 0.895693i | ||||
\(928\) | −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 | \(0.772544\pi\) | |||||||
\(930\) | 7.16447i | 0.234932i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.7265 | −0.482383 | ||||||||
\(933\) | −11.6936 | + | 20.2539i | −0.382831 | + | 0.663082i | ||||
\(934\) | −0.177652 | + | 0.102567i | −0.00581295 | + | 0.00335611i | ||||
\(935\) | 0.740724 | + | 1.28297i | 0.0242243 | + | 0.0419577i | ||||
\(936\) | 22.1347 | − | 23.2340i | 0.723496 | − | 0.759426i | ||||
\(937\) | −7.16949 | −0.234217 | −0.117109 | − | 0.993119i | \(-0.537363\pi\) | ||||
−0.117109 | + | 0.993119i | \(0.537363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9446 | 0.716134 | ||||||||
\(940\) | −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 | \(0.317447\pi\) | |||||||
\(942\) | 21.5096 | − | 12.4186i | 0.700820 | − | 0.404619i | ||||
\(943\) | 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 | 0.969913 | − | 0.243451i | \(-0.0782794\pi\) |
0.274122 | + | 0.961695i | \(0.411613\pi\) | |||||||
\(948\) | 4.03529 | + | 6.98933i | 0.131060 | + | 0.227003i | ||||
\(949\) | 5.17163 | + | 17.5853i | 0.167878 | + | 0.570844i | ||||
\(950\) | −12.8652 | + | 22.2832i | −0.417403 | + | 0.722963i | ||||
\(951\) | 59.8762i | 1.94162i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7002 | 0.443791 | 0.221896 | − | 0.975070i | \(-0.428776\pi\) | ||||
0.221896 | + | 0.975070i | \(0.428776\pi\) | |||||||
\(954\) | 1.88626 | + | 1.08903i | 0.0610700 | + | 0.0352588i | ||||
\(955\) | 8.49700 | − | 4.90574i | 0.274956 | − | 0.158746i | ||||
\(956\) | 14.4933 | − | 8.36771i | 0.468747 | − | 0.270631i | ||||
\(957\) | −9.84225 | − | 5.68242i | −0.318155 | − | 0.183687i | ||||
\(958\) | −23.0476 | −0.744634 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 12.0180i | − | 0.387879i | ||||||
\(961\) | −5.86129 | + | 10.1520i | −0.189074 | + | 0.327485i | ||||
\(962\) | −1.57160 | + | 0.462187i | −0.0506703 | + | 0.0149015i | ||||
\(963\) | 8.90521 | + | 15.4243i | 0.286966 | + | 0.497040i | ||||
\(964\) | −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 | ||||
\(969\) | 36.6248 | − | 21.1454i | 1.17656 | − | 0.679287i | ||||
\(970\) | 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 | \(0.277788\pi\) | |||||||
\(972\) | −18.5525 | −0.595072 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.4400 | −0.654941 | ||||||||
\(975\) | −29.2533 | − | 27.8693i | −0.936855 | − | 0.892531i | ||||
\(976\) | −3.71741 | − | 6.43874i | −0.118991 | − | 0.206099i | ||||
\(977\) | 14.2432 | − | 8.22330i | 0.455679 | − | 0.263087i | −0.254547 | − | 0.967061i | \(-0.581926\pi\) |
0.710226 | + | 0.703974i | \(0.248593\pi\) | |||||||
\(978\) | −30.9286 | + | 53.5699i | −0.988987 | + | 1.71298i | ||||
\(979\) | 9.47937 | 0.302962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 33.1913i | − | 1.05972i | ||||||
\(982\) | 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 | \(0.393129\pi\) | |||||||
\(984\) | −18.6395 | − | 32.2846i | −0.594206 | − | 1.02919i | ||||
\(985\) | 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 | ||||
\(990\) | 1.19905 | − | 0.692270i | 0.0381082 | − | 0.0220018i | ||||
\(991\) | 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 | ||||
\(993\) | 32.0260i | 1.01632i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.45731i | 0.236413i | ||||||||
\(996\) | −18.2312 | − | 10.5258i | −0.577679 | − | 0.333523i | ||||
\(997\) | −2.34855 | − | 4.06781i | −0.0743794 | − | 0.128829i | 0.826437 | − | 0.563029i | \(-0.190364\pi\) |
−0.900816 | + | 0.434201i | \(0.857031\pi\) | |||||||
\(998\) | 9.49071 | + | 16.4384i | 0.300423 | + | 0.520348i | ||||
\(999\) | 0.0786985 | + | 0.0454366i | 0.00248991 | + | 0.00143755i |
(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 | 637.2.r.f.324.3 | 16 | ||
7.2 | even | 3 | 637.2.c.e.246.6 | 8 | |||
7.3 | odd | 6 | 91.2.r.a.25.6 | yes | 16 | ||
7.4 | even | 3 | inner | 637.2.r.f.116.6 | 16 | ||
7.5 | odd | 6 | 637.2.c.f.246.6 | 8 | |||
7.6 | odd | 2 | 91.2.r.a.51.3 | yes | 16 | ||
13.12 | even | 2 | inner | 637.2.r.f.324.6 | 16 | ||
21.17 | even | 6 | 819.2.dl.e.298.3 | 16 | |||
21.20 | even | 2 | 819.2.dl.e.415.6 | 16 | |||
91.5 | even | 12 | 8281.2.a.ck.1.6 | 8 | |||
91.12 | odd | 6 | 637.2.c.f.246.3 | 8 | |||
91.25 | even | 6 | inner | 637.2.r.f.116.3 | 16 | ||
91.31 | even | 12 | 1183.2.e.i.508.3 | 16 | |||
91.34 | even | 4 | 1183.2.e.i.170.6 | 16 | |||
91.38 | odd | 6 | 91.2.r.a.25.3 | ✓ | 16 | ||
91.44 | odd | 12 | 8281.2.a.cj.1.6 | 8 | |||
91.47 | even | 12 | 8281.2.a.ck.1.3 | 8 | |||
91.51 | even | 6 | 637.2.c.e.246.3 | 8 | |||
91.73 | even | 12 | 1183.2.e.i.508.6 | 16 | |||
91.83 | even | 4 | 1183.2.e.i.170.3 | 16 | |||
91.86 | odd | 12 | 8281.2.a.cj.1.3 | 8 | |||
91.90 | odd | 2 | 91.2.r.a.51.6 | yes | 16 | ||
273.38 | even | 6 | 819.2.dl.e.298.6 | 16 | |||
273.272 | even | 2 | 819.2.dl.e.415.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.3 | ✓ | 16 | 91.38 | odd | 6 | ||
91.2.r.a.25.6 | yes | 16 | 7.3 | odd | 6 | ||
91.2.r.a.51.3 | yes | 16 | 7.6 | odd | 2 | ||
91.2.r.a.51.6 | yes | 16 | 91.90 | odd | 2 | ||
637.2.c.e.246.3 | 8 | 91.51 | even | 6 | |||
637.2.c.e.246.6 | 8 | 7.2 | even | 3 | |||
637.2.c.f.246.3 | 8 | 91.12 | odd | 6 | |||
637.2.c.f.246.6 | 8 | 7.5 | odd | 6 | |||
637.2.r.f.116.3 | 16 | 91.25 | even | 6 | inner | ||
637.2.r.f.116.6 | 16 | 7.4 | even | 3 | inner | ||
637.2.r.f.324.3 | 16 | 1.1 | even | 1 | trivial | ||
637.2.r.f.324.6 | 16 | 13.12 | even | 2 | inner | ||
819.2.dl.e.298.3 | 16 | 21.17 | even | 6 | |||
819.2.dl.e.298.6 | 16 | 273.38 | even | 6 | |||
819.2.dl.e.415.3 | 16 | 273.272 | even | 2 | |||
819.2.dl.e.415.6 | 16 | 21.20 | even | 2 | |||
1183.2.e.i.170.3 | 16 | 91.83 | even | 4 | |||
1183.2.e.i.170.6 | 16 | 91.34 | even | 4 | |||
1183.2.e.i.508.3 | 16 | 91.31 | even | 12 | |||
1183.2.e.i.508.6 | 16 | 91.73 | even | 12 | |||
8281.2.a.cj.1.3 | 8 | 91.86 | odd | 12 | |||
8281.2.a.cj.1.6 | 8 | 91.44 | odd | 12 | |||
8281.2.a.ck.1.3 | 8 | 91.47 | even | 12 | |||
8281.2.a.ck.1.6 | 8 | 91.5 | even | 12 |