Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(113,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bs (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 113.13 | ||
Character | \(\chi\) | \(=\) | 360.113 |
Dual form | 360.2.bs.a.137.13 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.836139 | + | 1.51686i | 0.482745 | + | 0.875761i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22494 | − | 0.222822i | −0.995023 | − | 0.0996492i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.21063 | − | 0.860287i | −1.21351 | − | 0.325158i | −0.405369 | − | 0.914153i | \(-0.632857\pi\) |
−0.808137 | + | 0.588995i | \(0.799524\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.60174 | + | 2.53662i | −0.533915 | + | 0.845538i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.57804 | + | 2.64314i | −1.38033 | + | 0.796935i | −0.992199 | − | 0.124668i | \(-0.960214\pi\) |
−0.388134 | + | 0.921603i | \(0.626880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0106047 | − | 0.00284152i | 0.00294121 | − | 0.000788095i | −0.257348 | − | 0.966319i | \(-0.582849\pi\) |
0.260289 | + | 0.965531i | \(0.416182\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52237 | − | 3.56124i | −0.393073 | − | 0.919507i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.03890 | + | 1.03890i | 0.251969 | + | 0.251969i | 0.821778 | − | 0.569808i | \(-0.192983\pi\) |
−0.569808 | + | 0.821778i | \(0.692983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41336i | 0.324246i | 0.986771 | + | 0.162123i | \(0.0518342\pi\) | ||||
−0.986771 | + | 0.162123i | \(0.948166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.37960 | − | 5.58941i | −0.301053 | − | 1.21971i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.17810 | + | 8.12879i | 0.454166 | + | 1.69497i | 0.690528 | + | 0.723305i | \(0.257378\pi\) |
−0.236363 | + | 0.971665i | \(0.575955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.90070 | + | 0.991532i | 0.980140 | + | 0.198306i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.18698 | − | 0.308662i | −0.998234 | − | 0.0594020i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.79806 | − | 6.57844i | −0.705283 | − | 1.22159i | −0.966589 | − | 0.256330i | \(-0.917487\pi\) |
0.261306 | − | 0.965256i | \(-0.415847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47022 | − | 7.74265i | 0.802875 | − | 1.39062i | −0.114841 | − | 0.993384i | \(-0.536636\pi\) |
0.917716 | − | 0.397236i | \(-0.130031\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.83715 | − | 4.73424i | −1.36427 | − | 0.824125i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.95177 | + | 2.62949i | 1.17506 | + | 0.444464i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32005 | − | 3.32005i | 0.545813 | − | 0.545813i | −0.379414 | − | 0.925227i | \(-0.623874\pi\) |
0.925227 | + | 0.379414i | \(0.123874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0131772 | + | 0.0137100i | 0.00211004 | + | 0.00219535i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0575667 | − | 0.0332362i | −0.00899041 | − | 0.00519062i | 0.495498 | − | 0.868609i | \(-0.334986\pi\) |
−0.504488 | + | 0.863418i | \(0.668319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47585 | + | 9.23998i | −0.377563 | + | 1.40908i | 0.472001 | + | 0.881598i | \(0.343532\pi\) |
−0.849564 | + | 0.527486i | \(0.823135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.12900 | − | 5.28691i | 0.615514 | − | 0.788126i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.64609 | + | 9.87536i | −0.385972 | + | 1.44047i | 0.450656 | + | 0.892698i | \(0.351190\pi\) |
−0.836628 | + | 0.547771i | \(0.815477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50590 | + | 2.02413i | 0.500843 | + | 0.289162i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.707201 | + | 2.44452i | −0.0990279 | + | 0.342302i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.88735 | + | 3.88735i | −0.533969 | + | 0.533969i | −0.921751 | − | 0.387782i | \(-0.873241\pi\) |
0.387782 | + | 0.921751i | \(0.373241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7748 | − | 4.86072i | 1.45288 | − | 0.655420i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.14387 | + | 1.18176i | −0.283962 | + | 0.156528i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.02489 | + | 1.77516i | −0.133429 | + | 0.231106i | −0.924996 | − | 0.379976i | \(-0.875932\pi\) |
0.791567 | + | 0.611082i | \(0.209266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.37933 | + | 2.38907i | 0.176605 | + | 0.305889i | 0.940716 | − | 0.339197i | \(-0.110155\pi\) |
−0.764111 | + | 0.645085i | \(0.776822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.32483 | − | 6.76619i | 0.922842 | − | 0.852459i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0242279 | + | 0.00395924i | −0.00300511 | + | 0.000491083i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.704972 | + | 2.63099i | 0.0861260 | + | 0.321427i | 0.995525 | − | 0.0944981i | \(-0.0301246\pi\) |
−0.909399 | + | 0.415925i | \(0.863458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.5091 | + | 10.1007i | −1.26514 | + | 1.21598i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.53347i | − | 0.656703i | −0.944556 | − | 0.328351i | \(-0.893507\pi\) | ||
0.944556 | − | 0.328351i | \(-0.106493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.33627 | − | 2.33627i | −0.273439 | − | 0.273439i | 0.557044 | − | 0.830483i | \(-0.311936\pi\) |
−0.830483 | + | 0.557044i | \(0.811936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.59365 | + | 8.26275i | 0.299489 | + | 0.954100i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.9723 | − | 4.54771i | 1.93417 | − | 0.518260i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.510169 | + | 0.294546i | −0.0573985 | + | 0.0331390i | −0.528425 | − | 0.848980i | \(-0.677217\pi\) |
0.471026 | + | 0.882119i | \(0.343884\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.86883 | − | 8.12601i | −0.429871 | − | 0.902891i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.39688 | − | 1.71404i | −0.702149 | − | 0.188140i | −0.109956 | − | 0.993936i | \(-0.535071\pi\) |
−0.592193 | + | 0.805796i | \(0.701738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.07999 | − | 2.54297i | −0.225607 | − | 0.275824i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.80288 | − | 11.2616i | 0.729345 | − | 1.20737i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0611 | 1.06647 | 0.533235 | − | 0.845967i | \(-0.320976\pi\) | ||||
0.533235 | + | 0.845967i | \(0.320976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0364923 | −0.00382543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.4823 | + | 0.306780i | 1.60543 | + | 0.0318116i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.314927 | − | 3.14463i | 0.0323109 | − | 0.322632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4120 | + | 4.12964i | 1.56485 | + | 0.419301i | 0.934196 | − | 0.356760i | \(-0.116118\pi\) |
0.630658 | + | 0.776061i | \(0.282785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.628236 | − | 15.8464i | 0.0631401 | − | 1.59262i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2579 | + | 5.92241i | −1.02070 | + | 0.589301i | −0.914307 | − | 0.405023i | \(-0.867264\pi\) |
−0.106393 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7082 | + | 3.13719i | −1.15364 | + | 0.309117i | −0.784423 | − | 0.620227i | \(-0.787041\pi\) |
−0.369217 | + | 0.929343i | \(0.620374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.82408 | + | 12.7435i | 0.178012 | + | 1.24364i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.81441 | + | 3.81441i | 0.368753 | + | 0.368753i | 0.867022 | − | 0.498269i | \(-0.166031\pi\) |
−0.498269 | + | 0.867022i | \(0.666031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.04526i | 0.100117i | 0.998746 | + | 0.0500587i | \(0.0159409\pi\) | ||||
−0.998746 | + | 0.0500587i | \(0.984059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.81209 | + | 2.26004i | 0.741490 | + | 0.214513i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.13774 | + | 7.97816i | 0.201102 | + | 0.750522i | 0.990602 | + | 0.136773i | \(0.0436730\pi\) |
−0.789501 | + | 0.613750i | \(0.789660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.03487 | − | 18.5714i | −0.283003 | − | 1.73179i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.00977816 | + | 0.0314514i | −0.000903991 | + | 0.00290768i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.44177 | − | 4.22926i | −0.223836 | − | 0.387696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.47233 | − | 14.6745i | 0.770212 | − | 1.33405i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.00228091 | − | 0.115111i | 0.000205663 | − | 0.0103792i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6828 | − | 3.29808i | −0.955500 | − | 0.294990i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00572 | + | 2.00572i | −0.177979 | + | 0.177979i | −0.790474 | − | 0.612495i | \(-0.790166\pi\) |
0.612495 | + | 0.790474i | \(0.290166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.0859 | + | 3.97039i | −1.41629 | + | 0.349573i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.96773 | − | 1.13607i | −0.171921 | − | 0.0992587i | 0.411570 | − | 0.911378i | \(-0.364980\pi\) |
−0.583491 | + | 0.812119i | \(0.698314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.21589 | − | 4.53777i | 0.105431 | − | 0.393475i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4719 | + | 1.84253i | 0.987346 | + | 0.158580i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.58696 | − | 13.3867i | 0.306455 | − | 1.14370i | −0.625231 | − | 0.780439i | \(-0.714995\pi\) |
0.931686 | − | 0.363265i | \(-0.118338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.21060 | + | 0.698941i | 0.102682 | + | 0.0592834i | 0.550462 | − | 0.834861i | \(-0.314452\pi\) |
−0.447780 | + | 0.894144i | \(0.647785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.1921 | + | 4.24341i | −1.44783 | + | 0.357359i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0410382 | + | 0.0410382i | −0.00343179 | + | 0.00343179i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.98464 | + | 15.4829i | 0.580042 | + | 1.28579i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.138911 | + | 7.01043i | −0.0114572 | + | 0.578210i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.12858 | + | 12.3471i | −0.583996 | + | 1.01151i | 0.411003 | + | 0.911634i | \(0.365178\pi\) |
−0.995000 | + | 0.0998776i | \(0.968155\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.63051 | − | 11.4844i | −0.539583 | − | 0.934586i | −0.998926 | − | 0.0463267i | \(-0.985248\pi\) |
0.459343 | − | 0.888259i | \(-0.348085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.29932 | + | 0.971234i | −0.347580 | + | 0.0785196i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.6712 | + | 16.2308i | −0.937453 | + | 1.30369i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.83404 | + | 18.0409i | 0.385798 | + | 1.43982i | 0.836905 | + | 0.547349i | \(0.184363\pi\) |
−0.451106 | + | 0.892470i | \(0.648970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.14695 | − | 2.64621i | −0.725400 | − | 0.209858i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 27.9724i | − | 2.20453i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.256781 | − | 0.256781i | −0.0201126 | − | 0.0201126i | 0.696979 | − | 0.717092i | \(-0.254527\pi\) |
−0.717092 | + | 0.696979i | \(0.754527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.3823 | + | 12.2797i | 1.27536 | + | 0.955972i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.56639 | + | 0.955610i | −0.275975 | + | 0.0739473i | −0.394152 | − | 0.919045i | \(-0.628962\pi\) |
0.118177 | + | 0.992993i | \(0.462295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2582 | + | 6.49994i | −0.866017 | + | 0.499995i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.58514 | − | 2.26383i | −0.274163 | − | 0.173120i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.99572 | + | 2.67834i | 0.759960 | + | 0.203631i | 0.617932 | − | 0.786232i | \(-0.287971\pi\) |
0.142029 | + | 0.989863i | \(0.454638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.8814 | − | 7.39946i | −1.12492 | − | 0.559346i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.54962 | − | 0.0703355i | −0.266806 | − | 0.00528674i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.94287 | 0.294704 | 0.147352 | − | 0.989084i | \(-0.452925\pi\) | ||||
0.147352 | + | 0.989084i | \(0.452925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.9901 | −1.18854 | −0.594268 | − | 0.804267i | \(-0.702558\pi\) | ||||
−0.594268 | + | 0.804267i | \(0.702558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.47058 | + | 4.08984i | −0.182630 | + | 0.302330i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.12669 | + | 6.64713i | −0.597486 | + | 0.488707i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.50205 | − | 2.01017i | −0.548605 | − | 0.146998i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.3879 | + | 5.45329i | 1.19205 | + | 0.396668i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6180 | − | 7.86236i | 0.985364 | − | 0.568900i | 0.0814788 | − | 0.996675i | \(-0.474036\pi\) |
0.903885 | + | 0.427775i | \(0.140702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9076 | + | 5.06628i | −1.36100 | + | 0.364679i | −0.864184 | − | 0.503177i | \(-0.832164\pi\) |
−0.496817 | + | 0.867856i | \(0.665498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0262635 | − | 0.0334400i | −0.00188077 | − | 0.00239469i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.05729 | − | 5.05729i | −0.360317 | − | 0.360317i | 0.503612 | − | 0.863930i | \(-0.332004\pi\) |
−0.863930 | + | 0.503612i | \(0.832004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3561i | 1.23034i | 0.788394 | + | 0.615171i | \(0.210913\pi\) | ||||
−0.788394 | + | 0.615171i | \(0.789087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.40140 | + | 3.26922i | −0.239916 | + | 0.230593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.53485 | + | 24.3884i | 0.458657 | + | 1.71173i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.120677 | + | 0.0867755i | 0.00842842 | + | 0.00606067i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.1084 | − | 7.49523i | −1.67565 | − | 0.520954i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.73569 | − | 6.47041i | −0.258403 | − | 0.447567i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5587 | + | 23.4844i | −0.933421 | + | 1.61673i | −0.155996 | + | 0.987758i | \(0.549859\pi\) |
−0.777425 | + | 0.628975i | \(0.783475\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.39352 | − | 4.62675i | 0.575115 | − | 0.317020i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.56748 | − | 20.0067i | 0.516098 | − | 1.36445i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.0131 | + | 21.0131i | −1.42646 | + | 1.42646i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.59035 | − | 5.49724i | 0.107466 | − | 0.371469i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0139692 | + | 0.00806513i | 0.000939671 | + | 0.000542519i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.20378 | − | 11.9567i | 0.214541 | − | 0.800677i | −0.771787 | − | 0.635881i | \(-0.780637\pi\) |
0.986328 | − | 0.164796i | \(-0.0526965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.3648 | + | 10.8430i | −0.690987 | + | 0.722867i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.57784 | − | 24.5488i | 0.436586 | − | 1.62936i | −0.300655 | − | 0.953733i | \(-0.597205\pi\) |
0.737242 | − | 0.675629i | \(-0.236128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5518 | + | 6.09206i | 0.697280 | + | 0.402575i | 0.806333 | − | 0.591461i | \(-0.201449\pi\) |
−0.109054 | + | 0.994036i | \(0.534782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.0894 | + | 21.9421i | 1.38758 | + | 1.44368i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2997 | − | 14.2997i | 0.936806 | − | 0.936806i | −0.0613130 | − | 0.998119i | \(-0.519529\pi\) |
0.998119 | + | 0.0613130i | \(0.0195288\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.08785 | − | 21.3824i | 0.527593 | − | 1.39484i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.873358 | − | 0.527575i | −0.0567307 | − | 0.0342697i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7785 | − | 22.1330i | 0.826573 | − | 1.43167i | −0.0741389 | − | 0.997248i | \(-0.523621\pi\) |
0.900711 | − | 0.434418i | \(-0.143046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5509 | + | 23.4709i | 0.872892 | + | 1.51189i | 0.858991 | + | 0.511990i | \(0.171092\pi\) |
0.0139008 | + | 0.999903i | \(0.495575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.09116 | − | 12.6630i | 0.583198 | − | 0.812330i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.34939 | − | 5.28477i | −0.469536 | − | 0.337631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.00401608 | + | 0.0149882i | 0.000255537 | + | 0.000953677i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.74872 | − | 11.1364i | −0.174193 | − | 0.705738i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.32014i | − | 0.525163i | −0.964910 | − | 0.262581i | \(-0.915426\pi\) | ||
0.964910 | − | 0.262581i | \(-0.0845738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.4569 | − | 31.4569i | −1.97768 | − | 1.97768i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.11817 | − | 5.28133i | 0.132645 | − | 0.330730i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.27846 | + | 0.878461i | −0.204505 | + | 0.0547969i | −0.359617 | − | 0.933100i | \(-0.617093\pi\) |
0.155112 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5157 | + | 7.80328i | −0.839823 | + | 0.484872i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.7705 | + | 0.902747i | 1.40946 | + | 0.0558786i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.54654 | − | 0.414393i | −0.0953636 | − | 0.0255526i | 0.210822 | − | 0.977525i | \(-0.432386\pi\) |
−0.306185 | + | 0.951972i | \(0.599053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.51531 | − | 7.78293i | 0.584521 | − | 0.478102i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.41244 | + | 15.2612i | 0.514833 | + | 0.933973i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5660 | 0.644220 | 0.322110 | − | 0.946702i | \(-0.395608\pi\) | ||||
0.322110 | + | 0.946702i | \(0.395608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0835748 | −0.00507681 | −0.00253840 | − | 0.999997i | \(-0.500808\pi\) | ||||
−0.00253840 | + | 0.999997i | \(0.500808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0305126 | − | 0.0553538i | −0.00184671 | − | 0.00335016i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.0564 | + | 8.41393i | −1.51096 | + | 0.507379i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1104 | − | 3.78086i | −0.847810 | − | 0.227170i | −0.191342 | − | 0.981523i | \(-0.561284\pi\) |
−0.656469 | + | 0.754353i | \(0.727951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.4800 | + | 23.7410i | 0.747156 | + | 1.42133i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4207 | + | 9.48051i | −0.979578 | + | 0.565560i | −0.902143 | − | 0.431437i | \(-0.858007\pi\) |
−0.0774356 | + | 0.996997i | \(0.524673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.52400 | − | 2.01605i | 0.447255 | − | 0.119842i | −0.0281594 | − | 0.999603i | \(-0.508965\pi\) |
0.475415 | + | 0.879762i | \(0.342298\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.03329 | − | 2.15165i | 0.298147 | − | 0.127453i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.156233 | + | 0.156233i | 0.00922214 | + | 0.00922214i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.8414i | − | 0.873023i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.62250 | + | 26.8309i | 0.388218 | + | 1.57285i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.87427 | + | 14.4590i | 0.226337 | + | 0.844703i | 0.981864 | + | 0.189585i | \(0.0607143\pi\) |
−0.755527 | + | 0.655118i | \(0.772619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.67586 | − | 3.72125i | 0.155794 | − | 0.216660i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.5620 | − | 12.2968i | 1.42523 | − | 0.713533i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0461962 | + | 0.0800142i | 0.00267160 | + | 0.00462734i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.8981 | − | 27.5363i | 0.916349 | − | 1.58716i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.5605 | − | 10.6079i | −1.00883 | − | 0.609407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.53658 | − | 5.62287i | −0.145244 | − | 0.321965i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.29999 | + | 9.29999i | −0.530779 | + | 0.530779i | −0.920804 | − | 0.390025i | \(-0.872466\pi\) |
0.390025 | + | 0.920804i | \(0.372466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5483 | − | 15.1365i | −0.827626 | − | 0.861088i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.84114 | + | 1.64033i | 0.161106 | + | 0.0930146i | 0.578385 | − | 0.815764i | \(-0.303683\pi\) |
−0.417279 | + | 0.908778i | \(0.637016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.140261 | + | 0.523461i | −0.00792802 | + | 0.0295878i | −0.969777 | − | 0.243995i | \(-0.921542\pi\) |
0.961849 | + | 0.273583i | \(0.0882087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.8050 | + | 13.4222i | −1.00320 | + | 0.756256i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.25232 | − | 4.67373i | 0.0703375 | − | 0.262503i | −0.921798 | − | 0.387670i | \(-0.873280\pi\) |
0.992136 | + | 0.125167i | \(0.0399467\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.7754 | + | 20.0776i | 1.94705 | + | 1.12413i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.59656 | + | 8.97531i | −0.144926 | + | 0.500953i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.46833 | + | 1.46833i | −0.0817001 | + | 0.0817001i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0547879 | − | 0.00341054i | 0.00303908 | − | 0.000189182i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.58551 | + | 0.873980i | −0.0876790 | + | 0.0483312i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9913 | − | 29.4298i | 0.936760 | − | 1.62252i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.54691 | + | 7.87548i | 0.249921 | + | 0.432876i | 0.963504 | − | 0.267695i | \(-0.0862620\pi\) |
−0.713583 | + | 0.700571i | \(0.752929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.10382 | + | 13.7396i | 0.170088 | + | 0.752924i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.982275 | − | 6.01087i | −0.0536674 | − | 0.328409i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.26314 | − | 15.9103i | −0.232228 | − | 0.866687i | −0.979379 | − | 0.202033i | \(-0.935245\pi\) |
0.747151 | − | 0.664655i | \(-0.231421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3143 | + | 9.91351i | −0.560197 | + | 0.538428i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.2616i | 2.55936i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.93760 | + | 6.93760i | 0.374595 | + | 0.374595i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.6327 | − | 20.1317i | 1.38002 | − | 1.08386i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.87351 | − | 2.64560i | 0.530038 | − | 0.142023i | 0.0161322 | − | 0.999870i | \(-0.494865\pi\) |
0.513906 | + | 0.857847i | \(0.328198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.7834 | − | 15.4634i | 1.43368 | − | 0.827736i | 0.436282 | − | 0.899810i | \(-0.356295\pi\) |
0.997399 | + | 0.0720741i | \(0.0229618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0558833 | + | 0.0114656i | −0.00298283 | + | 0.000611990i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.1173 | + | 4.85451i | 0.964285 | + | 0.258379i | 0.706413 | − | 0.707800i | \(-0.250312\pi\) |
0.257872 | + | 0.966179i | \(0.416979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.23298 | + | 12.3116i | −0.0654399 | + | 0.653434i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.37356 | − | 7.24008i | 0.231473 | − | 0.383185i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.2779 | −1.49245 | −0.746226 | − | 0.665693i | \(-0.768136\pi\) | ||||
−0.746226 | + | 0.665693i | \(0.768136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0024 | 0.894864 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.3432 | + | 0.581435i | 1.54012 | + | 0.0305174i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.67748 | + | 5.71862i | 0.244830 | + | 0.299326i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.8161 | + | 4.23791i | 0.825593 | + | 0.221217i | 0.646790 | − | 0.762668i | \(-0.276111\pi\) |
0.178803 | + | 0.983885i | \(0.442778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.176514 | − | 0.0927888i | 0.00918898 | − | 0.00483039i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.8251 | − | 9.13663i | 0.821599 | − | 0.474350i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2614 | + | 4.35722i | −0.841982 | + | 0.225608i | −0.653934 | − | 0.756551i | \(-0.726883\pi\) |
−0.188048 | + | 0.982160i | \(0.560216\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.92958 | − | 18.9620i | −0.202923 | − | 0.979195i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0589701 | − | 0.0589701i | −0.00303711 | − | 0.00303711i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.2839i | − | 1.40148i | −0.713417 | − | 0.700740i | \(-0.752853\pi\) | ||
0.713417 | − | 0.700740i | \(-0.247147\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.71947 | − | 1.36534i | −0.241786 | − | 0.0699486i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.73374 | + | 10.2025i | 0.139688 | + | 0.521321i | 0.999935 | + | 0.0114437i | \(0.00364271\pi\) |
−0.860247 | + | 0.509878i | \(0.829691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −38.7756 | + | 6.33657i | −1.97619 | + | 0.322941i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.4726 | − | 21.0803i | −0.989848 | − | 1.07157i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.16870 | + | 3.75630i | 0.109957 | + | 0.190452i | 0.915753 | − | 0.401742i | \(-0.131595\pi\) |
−0.805795 | + | 0.592194i | \(0.798262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.18215 | + | 10.7078i | −0.312645 | + | 0.541516i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0779655 | − | 3.93468i | 0.00393284 | − | 0.198478i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.20073 | − | 0.541670i | 0.0604151 | − | 0.0272544i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.18346 | + | 7.18346i | −0.360527 | + | 0.360527i | −0.864007 | − | 0.503480i | \(-0.832053\pi\) |
0.503480 | + | 0.864007i | \(0.332053\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.89983 | − | 1.94987i | 0.395486 | − | 0.0976154i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.145839 | + | 0.0842005i | 0.00728288 | + | 0.00420477i | 0.503637 | − | 0.863915i | \(-0.331995\pi\) |
−0.496354 | + | 0.868120i | \(0.665328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0254044 | − | 0.0948106i | 0.00126548 | − | 0.00472285i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.79726 | + | 18.9419i | 0.337759 | + | 0.941233i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.42400 | + | 23.9747i | −0.318426 | + | 1.18838i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.84998 | + | 2.22278i | 0.190369 | + | 0.109910i | 0.592155 | − | 0.805824i | \(-0.298277\pi\) |
−0.401786 | + | 0.915733i | \(0.631611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.3050 | − | 5.75223i | 1.14955 | − | 0.283736i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.81769 | − | 4.81769i | 0.237063 | − | 0.237063i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8507 | + | 5.23900i | 0.679906 | + | 0.257172i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0479666 | + | 2.42073i | −0.00234893 | + | 0.118544i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7355 | − | 23.7906i | 0.671024 | − | 1.16225i | −0.306590 | − | 0.951842i | \(-0.599188\pi\) |
0.977614 | − | 0.210406i | \(-0.0674785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.83154 | − | 8.36847i | −0.235475 | − | 0.407854i | 0.723936 | − | 0.689867i | \(-0.242331\pi\) |
−0.959411 | + | 0.282013i | \(0.908998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.8116 | − | 22.5299i | −1.01190 | − | 1.09544i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.06122 | + | 6.12142i | 0.196998 | + | 0.296932i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.37324 | − | 8.85704i | −0.114849 | − | 0.428622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0965630 | − | 0.0279357i | −0.00466211 | − | 0.00134875i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.32261i | 0.352718i | 0.984326 | + | 0.176359i | \(0.0564319\pi\) | ||||
−0.984326 | + | 0.176359i | \(0.943568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5489 | + | 18.5489i | 0.891403 | + | 0.891403i | 0.994655 | − | 0.103252i | \(-0.0329248\pi\) |
−0.103252 | + | 0.994655i | \(0.532925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.6453 | + | 23.5406i | −0.846029 | + | 1.12869i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.4889 | + | 3.07844i | −0.549588 | + | 0.147262i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.757943 | − | 0.437599i | 0.0361747 | − | 0.0208854i | −0.481804 | − | 0.876279i | \(-0.660018\pi\) |
0.517978 | + | 0.855394i | \(0.326685\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.7500 | + | 5.65098i | −0.511905 | + | 0.269094i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.69784 | − | 0.990833i | −0.175690 | − | 0.0470759i | 0.169902 | − | 0.985461i | \(-0.445655\pi\) |
−0.345591 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3852 | − | 2.24183i | −1.06116 | − | 0.106273i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.6893 | − | 0.489217i | −1.16776 | − | 0.0231392i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.1148 | 0.902084 | 0.451042 | − | 0.892503i | \(-0.351052\pi\) | ||||
0.451042 | + | 0.892503i | \(0.351052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.351391 | 0.0165463 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8762 | − | 19.6601i | 0.557992 | − | 0.923712i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0811931 | + | 0.00813130i | 0.00380639 | + | 0.000381201i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.3972 | + | 8.14491i | 1.42192 | + | 0.381003i | 0.886165 | − | 0.463370i | \(-0.153360\pi\) |
0.535756 | + | 0.844373i | \(0.320027\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.06806 | − | 5.70940i | −0.236557 | − | 0.266492i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1639 | + | 7.02285i | −0.566531 | + | 0.327087i | −0.755763 | − | 0.654846i | \(-0.772734\pi\) |
0.189232 | + | 0.981932i | \(0.439400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6925 | + | 7.68813i | −1.33345 | + | 0.357298i | −0.854002 | − | 0.520270i | \(-0.825831\pi\) |
−0.479452 | + | 0.877568i | \(0.659165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.3787 | − | 4.13236i | −1.59427 | − | 0.191634i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.29536 | + | 2.29536i | 0.106216 | + | 0.106216i | 0.758218 | − | 0.652001i | \(-0.226070\pi\) |
−0.652001 | + | 0.758218i | \(0.726070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.05362i | − | 0.418058i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.3236 | + | 22.4173i | −1.07470 | + | 1.03293i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.0880 | − | 48.8450i | −0.601786 | − | 2.24590i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.40139 | + | 6.92644i | −0.0643001 | + | 0.317807i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.63418 | − | 16.0873i | −0.166398 | − | 0.736585i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.90847 | + | 3.30557i | 0.0872003 | + | 0.151035i | 0.906327 | − | 0.422578i | \(-0.138875\pi\) |
−0.819126 | + | 0.573613i | \(0.805541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0257741 | − | 0.0446421i | 0.00117520 | − | 0.00203550i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 42.4302 | − | 23.3888i | 1.93064 | − | 1.06423i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.3706 | − | 12.6223i | −1.51528 | − | 0.573151i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.907013 | − | 0.907013i | 0.0411007 | − | 0.0411007i | −0.686258 | − | 0.727358i | \(-0.740748\pi\) |
0.727358 | + | 0.686258i | \(0.240748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.174797 | − | 0.604206i | 0.00790459 | − | 0.0273231i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.7642 | − | 15.4523i | −1.20785 | − | 0.697354i | −0.245563 | − | 0.969381i | \(-0.578973\pi\) |
−0.962290 | + | 0.272026i | \(0.912306\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.88852 | − | 10.7801i | 0.130092 | − | 0.485512i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.92871 | + | 35.1172i | −0.221529 | + | 1.57840i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.76038 | + | 17.7660i | −0.213532 | + | 0.796912i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.6894 | + | 20.0280i | 1.55291 | + | 0.896574i | 0.997903 | + | 0.0647306i | \(0.0206188\pi\) |
0.555010 | + | 0.831844i | \(0.312715\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.43152 | − | 4.61069i | −0.197986 | − | 0.205991i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8659 | + | 13.8659i | −0.618248 | + | 0.618248i | −0.945082 | − | 0.326834i | \(-0.894018\pi\) |
0.326834 | + | 0.945082i | \(0.394018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.1429 | − | 10.8913i | 1.07434 | − | 0.484656i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.2730 | − | 11.6423i | −0.855942 | − | 0.517054i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0026 | + | 25.9852i | −0.664978 | + | 1.15178i | 0.314313 | + | 0.949319i | \(0.398226\pi\) |
−0.979291 | + | 0.202457i | \(0.935108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.49104 | + | 9.51076i | 0.242909 | + | 0.420731i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.436249 | − | 7.33105i | 0.0192609 | − | 0.323674i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.7490 | − | 4.37122i | 1.17870 | − | 0.192619i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.9880 | − | 52.2038i | −0.615190 | − | 2.29592i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.29513 | + | 17.4016i | 0.188535 | + | 0.763845i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0626i | 0.922769i | 0.887200 | + | 0.461384i | \(0.152647\pi\) | ||||
−0.887200 | + | 0.461384i | \(0.847353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.7483 | + | 20.7483i | 0.907258 | + | 0.907258i | 0.996050 | − | 0.0887920i | \(-0.0283006\pi\) |
−0.0887920 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.21892 | − | 28.7599i | −0.0531981 | − | 1.25519i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6879 | − | 3.39971i | 0.552693 | − | 0.148094i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.4145 | + | 23.9107i | −1.80063 | + | 1.03960i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.86129 | − | 5.44310i | −0.124169 | − | 0.236210i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.000704918 | 0 | 0.000188882i | −3.05334e−5 | 0 | 8.18140e-6i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.63689 | − | 9.33676i | −0.330172 | − | 0.403664i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.29678 | + | 5.98078i | 0.142267 | + | 0.258090i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.4002 | −0.921774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6900 | 0.502590 | 0.251295 | − | 0.967911i | \(-0.419144\pi\) | ||||
0.251295 | + | 0.967911i | \(0.419144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.3700 | − | 24.2548i | −0.573760 | − | 1.04087i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.232907 | − | 2.32563i | 0.00997663 | − | 0.0996192i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4949 | + | 2.81211i | 0.448731 | + | 0.120237i | 0.476105 | − | 0.879388i | \(-0.342048\pi\) |
−0.0273747 | + | 0.999625i | \(0.508715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.26948 | − | 0.327847i | −0.352933 | − | 0.0139922i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.29768 | − | 5.36802i | 0.396095 | − | 0.228685i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.89136 | − | 0.506789i | 0.0804288 | − | 0.0215508i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.8778 | − | 6.76915i | −0.716424 | − | 0.287334i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.1366 | + | 20.1366i | 0.853213 | + | 0.853213i | 0.990528 | − | 0.137314i | \(-0.0438470\pi\) |
−0.137314 | + | 0.990528i | \(0.543847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.105022i | 0.00444197i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.22361 | − | 13.0604i | −0.136101 | − | 0.551409i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.103875 | − | 0.387669i | −0.00437783 | − | 0.0163383i | 0.963702 | − | 0.266979i | \(-0.0860254\pi\) |
−0.968080 | + | 0.250641i | \(0.919359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.97863 | − | 18.2273i | −0.125312 | − | 0.766826i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.43071 | + | 29.4180i | 0.228068 | + | 1.23544i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.1817 | + | 29.7596i | 0.720295 | + | 1.24759i | 0.960882 | + | 0.276959i | \(0.0893267\pi\) |
−0.240587 | + | 0.970628i | \(0.577340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3967 | − | 31.8640i | 0.769878 | − | 1.33347i | −0.167751 | − | 0.985829i | \(-0.553650\pi\) |
0.937629 | − | 0.347638i | \(-0.113016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.3127 | + | 14.0826i | 0.973900 | + | 0.588310i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.61427 | + | 41.9964i | 0.109023 | + | 1.75137i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.4388 | + | 27.4388i | −1.14229 | + | 1.14229i | −0.154262 | + | 0.988030i | \(0.549300\pi\) |
−0.988030 | + | 0.154262i | \(0.950700\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.4942 | − | 24.4441i | −0.976387 | − | 1.01586i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.0635 | + | 11.0063i | 0.790886 | + | 0.456619i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.52168 | − | 28.0713i | 0.311516 | − | 1.16259i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0287639 | − | 0.0677986i | 0.00118924 | − | 0.00280313i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.19051 | − | 4.44305i | 0.0491377 | − | 0.183384i | −0.936995 | − | 0.349342i | \(-0.886405\pi\) |
0.986133 | + | 0.165958i | \(0.0530717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9431 | + | 6.31801i | 0.450903 | + | 0.260329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.44262 | − | 11.8998i | 0.141610 | − | 0.489493i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.2955 | + | 29.2955i | −1.20302 | + | 1.20302i | −0.229782 | + | 0.973242i | \(0.573801\pi\) |
−0.973242 | + | 0.229782i | \(0.926199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.49040 | + | 9.95393i | 0.184089 | + | 0.408071i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.3268 | + | 14.5121i | −1.07749 | + | 0.593941i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0523 | + | 22.6072i | −0.533301 | + | 0.923704i | 0.465943 | + | 0.884815i | \(0.345715\pi\) |
−0.999244 | + | 0.0388889i | \(0.987618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2193 | + | 17.7004i | 0.416855 | + | 0.722014i | 0.995621 | − | 0.0934795i | \(-0.0297990\pi\) |
−0.578766 | + | 0.815494i | \(0.696466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.80299 | − | 2.42593i | −0.317762 | − | 0.0987915i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.1202 | + | 30.7620i | −0.899315 | + | 1.25065i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.47319 | + | 12.9621i | 0.140973 | + | 0.526117i | 0.999902 | + | 0.0140223i | \(0.00446357\pi\) |
−0.858929 | + | 0.512094i | \(0.828870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.5298 | + | 30.3046i | −1.27765 | + | 1.22800i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.112244i | 0.00454091i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.02234 | + | 1.02234i | 0.0412919 | + | 0.0412919i | 0.727451 | − | 0.686159i | \(-0.240705\pi\) |
−0.686159 | + | 0.727451i | \(0.740705\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0307242 | + | 0.255606i | −0.00123892 | + | 0.0103070i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.3812 | + | 7.33677i | −1.10233 | + | 0.295367i | −0.763712 | − | 0.645558i | \(-0.776625\pi\) |
−0.338615 | + | 0.940925i | \(0.609958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8445 | + | 6.83845i | −0.476073 | + | 0.274861i | −0.718778 | − | 0.695239i | \(-0.755298\pi\) |
0.242706 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.78872 | − | 42.8361i | −0.352679 | − | 1.71896i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.3024 | − | 8.65540i | −1.29417 | − | 0.346771i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0337 | + | 9.71841i | 0.921349 | + | 0.388736i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.69116 | − | 11.0767i | 0.267219 | − | 0.442360i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.89838 | 0.275056 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5918 | −0.819746 | −0.409873 | − | 0.912143i | \(-0.634427\pi\) | ||||
−0.409873 | + | 0.912143i | \(0.634427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.9596 | − | 0.930501i | −1.86648 | − | 0.0369841i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.90953 | − | 4.01569i | 0.194829 | − | 0.159358i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0429306 | + | 0.0115032i | 0.00170097 | + | 0.000455774i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0363 | + | 8.86321i | 0.555267 | + | 0.350623i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.83627 | + | 5.67897i | −0.388509 | + | 0.224306i | −0.681514 | − | 0.731805i | \(-0.738678\pi\) |
0.293005 | + | 0.956111i | \(0.405345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3604 | − | 5.72351i | 0.842373 | − | 0.225713i | 0.188269 | − | 0.982118i | \(-0.439712\pi\) |
0.654104 | + | 0.756404i | \(0.273046\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.6749 | − | 5.24957i | 1.44407 | − | 0.206701i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0725336 | + | 0.0725336i | 0.00285159 | + | 0.00285159i | 0.708531 | − | 0.705680i | \(-0.249358\pi\) |
−0.705680 | + | 0.708531i | \(0.749358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.8357i | − | 0.425337i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −49.4439 | − | 14.3041i | −1.93786 | − | 0.560623i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.275111 | − | 1.02673i | −0.0107659 | − | 0.0401790i | 0.960334 | − | 0.278853i | \(-0.0899541\pi\) |
−0.971100 | + | 0.238674i | \(0.923287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.12493 | + | 2.96614i | 0.161174 | + | 0.115896i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.66831 | − | 2.18411i | 0.377197 | − | 0.0852102i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1407 | − | 33.1526i | −0.745615 | − | 1.29144i | −0.949907 | − | 0.312533i | \(-0.898823\pi\) |
0.204292 | − | 0.978910i | \(-0.434511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.12766 | − | 3.68521i | 0.0827562 | − | 0.143338i | −0.821677 | − | 0.569954i | \(-0.806961\pi\) |
0.904433 | + | 0.426616i | \(0.140294\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.000553489 | 0.0279329i | −2.14957e−5 | 0.00108483i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.71640 | + | 9.82533i | −0.144116 | + | 0.381010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.2022 | − | 45.2022i | 1.75024 | − | 1.75024i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8154 | − | 5.13774i | 0.804770 | − | 0.198636i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.6293 | − | 7.29150i | −0.487547 | − | 0.281485i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.02542 | − | 11.2910i | 0.116621 | − | 0.435237i | −0.882782 | − | 0.469783i | \(-0.844332\pi\) |
0.999403 | + | 0.0345464i | \(0.0109986\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.1138 | − | 6.65572i | −0.966629 | − | 0.256179i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.06941 | − | 11.4552i | 0.117967 | − | 0.440258i | −0.881525 | − | 0.472138i | \(-0.843483\pi\) |
0.999492 | + | 0.0318792i | \(0.0101492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.9297 | − | 26.5175i | −1.76262 | − | 1.01765i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.7372 | − | 10.5485i | 1.63769 | − | 0.404221i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0019 | − | 13.0019i | 0.497505 | − | 0.497505i | −0.413156 | − | 0.910660i | \(-0.635573\pi\) |
0.910660 | + | 0.413156i | \(0.135573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9636 | + | 28.9854i | −0.418898 | + | 1.10747i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.418083 | + | 21.0994i | −0.0159509 | + | 0.804991i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0301782 | + | 0.0522702i | −0.00114970 | + | 0.00199133i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.55175 | − | 14.8121i | −0.325324 | − | 0.563478i | 0.656254 | − | 0.754540i | \(-0.272140\pi\) |
−0.981578 | + | 0.191062i | \(0.938807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.6495 | + | 50.3364i | −0.594474 | + | 1.91212i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.53778 | − | 1.82485i | −0.0962633 | − | 0.0692205i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0252769 | − | 0.0943347i | −0.000957431 | − | 0.00357318i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.6473 | + | 9.73415i | 1.27266 | + | 0.368180i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.2554i | 0.576189i | 0.957602 | + | 0.288094i | \(0.0930217\pi\) | ||||
−0.957602 | + | 0.288094i | \(0.906978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.69242 | + | 4.69242i | 0.176978 | + | 0.176978i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.1968 | − | 5.61055i | 1.47624 | − | 0.211305i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.0294 | − | 10.1899i | 1.43024 | − | 0.383232i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6295 | + | 6.13692i | −0.399198 | + | 0.230477i | −0.686138 | − | 0.727472i | \(-0.740695\pi\) |
0.286940 | + | 0.957949i | \(0.407362\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0700095 | − | 1.76589i | 0.00262556 | − | 0.0662261i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 72.6749 | + | 19.4732i | 2.72170 | + | 0.729277i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.100452 | − | 0.0821633i | 0.00375668 | − | 0.00307273i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.2573 | + | 0.876956i | 1.65282 | + | 0.0327505i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.5290 | 1.28771 | 0.643857 | − | 0.765146i | \(-0.277333\pi\) | ||||
0.643857 | + | 0.765146i | \(0.277333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.2895 | 1.50046 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.2717 | + | 40.1798i | −0.902673 | + | 1.49430i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0904 | − | 36.0049i | −0.449028 | − | 1.33719i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.0060 | + | 13.3991i | 1.85462 | + | 0.496944i | 0.999760 | − | 0.0219129i | \(-0.00697566\pi\) |
0.854861 | + | 0.518857i | \(0.173642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8095 | + | 3.20205i | 0.992943 | + | 0.118594i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.1715 | + | 7.02723i | −0.450180 | + | 0.259912i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1801 | − | 4.33544i | 0.597625 | − | 0.160133i | 0.0526892 | − | 0.998611i | \(-0.483221\pi\) |
0.544936 | + | 0.838478i | \(0.316554\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.87115 | − | 15.5668i | 0.0690184 | − | 0.574191i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.1815 | − | 10.1815i | −0.375039 | − | 0.375039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.6951i | − | 0.761283i | −0.924723 | − | 0.380642i | \(-0.875703\pi\) | ||
0.924723 | − | 0.380642i | \(-0.124297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0193770 | + | 0.0186241i | −0.000711834 | + | 0.000684172i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.9451 | − | 48.3118i | −0.474910 | − | 1.77239i | −0.621738 | − | 0.783225i | \(-0.713573\pi\) |
0.146828 | − | 0.989162i | \(-0.453094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6119 | − | 25.8831i | 0.681886 | − | 0.948282i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.5940 | − | 13.4810i | 0.533967 | − | 0.493243i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.96519 | − | 15.5282i | −0.327581 | − | 0.567387i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0420 | + | 17.3933i | −0.366438 | + | 0.634690i | −0.989006 | − | 0.147876i | \(-0.952756\pi\) |
0.622568 | + | 0.782566i | \(0.286090\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.6205 | − | 6.95679i | 0.459917 | − | 0.253520i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1935 | + | 27.0295i | 0.443767 | + | 0.983703i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.40854 | + | 8.40854i | −0.305614 | + | 0.305614i | −0.843205 | − | 0.537592i | \(-0.819334\pi\) |
0.537592 | + | 0.843205i | \(0.319334\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.4135 | − | 74.0182i | 0.777260 | − | 2.68669i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.59644 | − | 5.54051i | −0.347871 | − | 0.200843i | 0.315876 | − | 0.948800i | \(-0.397702\pi\) |
−0.663747 | + | 0.747957i | \(0.731035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.899221 | − | 3.35594i | 0.0325540 | − | 0.121493i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.78214 | − | 1.20295i | 0.353674 | − | 0.0434928i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.00582448 | + | 0.0217372i | −0.000210310 | + | 0.000784886i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.4335 | − | 17.5708i | −1.09746 | − | 0.633618i | −0.161907 | − | 0.986806i | \(-0.551764\pi\) |
−0.935553 | + | 0.353188i | \(0.885098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.07375 | − | 4.23846i | −0.146713 | − | 0.152644i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.2350 | + | 26.2350i | −0.943606 | + | 0.943606i | −0.998493 | − | 0.0548870i | \(-0.982520\pi\) |
0.0548870 | + | 0.998493i | \(0.482520\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.5843 | − | 33.5120i | 1.06270 | − | 1.20379i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.1375 | − | 13.9768i | −0.830052 | − | 0.501415i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0469745 | − | 0.0813623i | 0.00168304 | − | 0.00291511i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6257 | + | 25.3325i | 0.523350 | + | 0.906468i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6700 | + | 35.2945i | 0.631473 | + | 1.26132i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.73553 | − | 41.2170i | −0.240401 | − | 1.47110i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.04748 | − | 11.3733i | −0.108631 | − | 0.405416i | 0.890101 | − | 0.455764i | \(-0.150634\pi\) |
−0.998732 | + | 0.0503475i | \(0.983967\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.664542 | − | 2.69237i | −0.0236583 | − | 0.0958511i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 27.4540i | − | 0.976153i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0214159 | + | 0.0214159i | 0.000760502 | + | 0.000760502i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.7618 | + | 7.92581i | 0.700877 | + | 0.281099i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.29699 | + | 0.347528i | −0.0459419 | + | 0.0123101i | −0.281717 | − | 0.959498i | \(-0.590904\pi\) |
0.235775 | + | 0.971808i | \(0.424237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.0085 | + | 7.51045i | −0.460207 | + | 0.265701i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.1152 | + | 25.5210i | −0.569404 | + | 0.901742i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8706 | + | 4.52046i | 0.595351 | + | 0.159524i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.23287 | + | 62.2368i | −0.219680 | + | 2.19356i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.83463 | + | 16.0272i | 0.310994 | + | 0.564182i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.2154 | 0.956842 | 0.478421 | − | 0.878131i | \(-0.341209\pi\) | ||||
0.478421 | + | 0.878131i | \(0.341209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.3129 | −1.94230 | −0.971150 | − | 0.238471i | \(-0.923354\pi\) | ||||
−0.971150 | + | 0.238471i | \(0.923354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0698802 | − | 0.126772i | −0.00245080 | − | 0.00444607i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.514105 | + | 0.628539i | 0.0180083 | + | 0.0220167i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.0594 | − | 3.49925i | −0.456890 | − | 0.122423i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0584513 | − | 0.0925669i | 0.00204245 | − | 0.00323455i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.8123 | − | 20.6762i | 1.24986 | − | 0.721605i | 0.278776 | − | 0.960356i | \(-0.410071\pi\) |
0.971081 | + | 0.238751i | \(0.0767378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.4930 | + | 5.49108i | −0.714341 | + | 0.191407i | −0.597645 | − | 0.801761i | \(-0.703897\pi\) |
−0.116696 | + | 0.993168i | \(0.537230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −33.7134 | − | 30.9719i | −1.17375 | − | 1.07830i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.1508 | − | 18.1508i | −0.631166 | − | 0.631166i | 0.317195 | − | 0.948360i | \(-0.397259\pi\) |
−0.948360 | + | 0.317195i | \(0.897259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.0466i | − | 0.904637i | −0.891856 | − | 0.452319i | \(-0.850597\pi\) | ||
0.891856 | − | 0.452319i | \(-0.149403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.06318 | − | 24.5648i | −0.210330 | − | 0.852145i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.53940 | + | 5.74513i | 0.0533372 | + | 0.199057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.14792 | − | 1.33150i | 0.281970 | − | 0.0460786i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.5768 | + | 38.7811i | −0.884063 | + | 1.34047i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.2213 | + | 40.2205i | 0.801690 | + | 1.38857i | 0.918503 | + | 0.395413i | \(0.129399\pi\) |
−0.116814 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3506 | + | 24.8560i | −0.494848 | + | 0.857102i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.1106 | − | 16.9810i | −0.968182 | − | 0.584855i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.4972 | − | 11.9534i | 0.911531 | − | 0.411209i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.8258 | + | 39.8258i | −1.36843 | + | 1.36843i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.34918 | + | 9.72718i | 0.320863 | + | 0.333836i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.2194 | + | 19.7566i | 1.17303 | + | 0.677247i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3189 | + | 38.5107i | −0.353313 | + | 1.31858i | 0.529281 | + | 0.848446i | \(0.322462\pi\) |
−0.882594 | + | 0.470136i | \(0.844205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.47228 | + | 5.83574i | 0.255547 | + | 0.199578i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.45183 | − | 35.2747i | 0.322868 | − | 1.20496i | −0.593569 | − | 0.804783i | \(-0.702282\pi\) |
0.916438 | − | 0.400178i | \(-0.131052\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.5506 | + | 19.3705i | 1.14473 | + | 0.660912i | 0.947598 | − | 0.319465i | \(-0.103503\pi\) |
0.197135 | + | 0.980376i | \(0.436836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.106352 | + | 0.367617i | −0.00362445 | + | 0.0125283i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.5234 | + | 13.5234i | −0.460341 | + | 0.460341i | −0.898767 | − | 0.438426i | \(-0.855536\pi\) |
0.438426 | + | 0.898767i | \(0.355536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.6431 | − | 8.18642i | −0.735886 | − | 0.278347i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5123 | − | 12.4095i | 0.764559 | − | 0.421447i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.55705 | − | 2.69689i | 0.0528193 | − | 0.0914858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0149520 | + | 0.0258976i | 0.000506630 | + | 0.000877508i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.1614 | + | 32.4798i | −1.19003 | + | 1.09927i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.4613 | + | 19.7792i | 1.06359 | + | 0.668660i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.135609 | + | 0.506099i | 0.00457918 | + | 0.0170898i | 0.968178 | − | 0.250264i | \(-0.0805174\pi\) |
−0.963598 | + | 0.267354i | \(0.913851\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.6929 | + | 17.9665i | −0.630494 | + | 0.605993i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39.0309i | − | 1.31499i | −0.753461 | − | 0.657493i | \(-0.771617\pi\) | ||
0.753461 | − | 0.657493i | \(-0.228383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.5869 | + | 19.5869i | 0.659151 | + | 0.659151i | 0.955179 | − | 0.296028i | \(-0.0956621\pi\) |
−0.296028 | + | 0.955179i | \(0.595662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.88201 | + | 0.947427i | 0.264951 | + | 0.0318474i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.58895 | + | 1.49755i | −0.187658 | + | 0.0502829i | −0.351424 | − | 0.936216i | \(-0.614303\pi\) |
0.163766 | + | 0.986499i | \(0.447636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.16514 | − | 4.71414i | 0.273850 | − | 0.158107i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.1899 | + | 26.9754i | 1.31291 | + | 0.903710i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.9574 | − | 3.73987i | −0.467066 | − | 0.125150i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.77263 | − | 0.878559i | −0.293237 | − | 0.0293670i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0827441 | + | 0.136976i | −0.00276274 | + | 0.00457350i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −67.9127 | −2.26502 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.07711 | −0.269088 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 55.0617 | + | 1.09104i | 1.83234 | + | 0.0363077i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.5770 | + | 3.56296i | 1.18262 | + | 0.118437i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.1814 | − | 7.55119i | −0.935749 | − | 0.250733i | −0.241444 | − | 0.970415i | \(-0.577621\pi\) |
−0.694304 | + | 0.719682i | \(0.744288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.40767 | − | 35.5065i | 0.0466896 | − | 1.17768i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.5362 | − | 19.9395i | 1.14424 | − | 0.660625i | 0.196759 | − | 0.980452i | \(-0.436958\pi\) |
0.947476 | + | 0.319827i | \(0.103625\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8156 | − | 9.06087i | 1.11913 | − | 0.299871i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.40819 | − | 8.54915i | 0.211848 | − | 0.282626i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.34031 | + | 5.34031i | 0.176353 | + | 0.176353i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.3053i | 1.46150i | 0.682647 | + | 0.730748i | \(0.260829\pi\) | ||||
−0.682647 | + | 0.730748i | \(0.739171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.8829 | − | 6.33073i | −0.721066 | − | 0.208605i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0157235 | − | 0.0586808i | −0.000517544 | − | 0.00193150i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.5625 | − | 12.9786i | 0.643212 | − | 0.426735i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.7956 | − | 34.7241i | 0.354575 | − | 1.14049i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.80245 | + | 3.12193i | 0.0591363 | + | 0.102427i | 0.894078 | − | 0.447911i | \(-0.147832\pi\) |
−0.834942 | + | 0.550339i | \(0.814499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.86082 | + | 4.95509i | −0.0937597 | + | 0.162396i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.112572 | + | 5.68116i | −0.00368544 | + | 0.185993i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.2437 | + | 6.14413i | 0.531226 | + | 0.200934i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.9740 | − | 24.9740i | 0.815864 | − | 0.815864i | −0.169642 | − | 0.985506i | \(-0.554261\pi\) |
0.985506 | + | 0.169642i | \(0.0542612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.911296 | + | 0.224930i | −0.0297390 | + | 0.00734030i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.4239 | − | 7.17294i | −0.405008 | − | 0.233831i | 0.283635 | − | 0.958932i | \(-0.408460\pi\) |
−0.688642 | + | 0.725101i | \(0.741793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.144784 | − | 0.540340i | 0.00471480 | − | 0.0175959i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35.2471 | − | 15.7848i | −1.14659 | − | 0.513481i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.0396 | + | 48.6646i | −0.423731 | + | 1.58139i | 0.342947 | + | 0.939355i | \(0.388575\pi\) |
−0.766678 | + | 0.642031i | \(0.778092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0314139 | − | 0.0181368i | −0.00101974 | − | 0.000588747i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.13653 | − | 2.00829i | 0.263845 | − | 0.0651232i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.98422 | + | 5.98422i | −0.193848 | + | 0.193848i | −0.797356 | − | 0.603509i | \(-0.793769\pi\) |
0.603509 | + | 0.797356i | \(0.293769\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.0511 | + | 14.4589i | −1.03715 | + | 0.467878i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.37788 | + | 69.5372i | −0.0445404 | + | 2.24782i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.0328 | + | 39.8940i | −0.743769 | + | 1.28825i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4657 | − | 42.3758i | −0.789216 | − | 1.36696i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7854 | + | 3.56598i | −0.508677 | + | 0.114912i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.1972 | − | 7.05912i | 1.39057 | − | 0.227241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.16303 | − | 26.7328i | −0.230347 | − | 0.859669i | −0.980191 | − | 0.198054i | \(-0.936538\pi\) |
0.749844 | − | 0.661615i | \(-0.230129\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.45498 | − | 0.999527i | −0.110990 | − | 0.0321094i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 19.9390i | − | 0.639874i | −0.947439 | − | 0.319937i | \(-0.896338\pi\) | ||
0.947439 | − | 0.319937i | \(-0.103662\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.28551 | − | 3.28551i | −0.105329 | − | 0.105329i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0509836 | + | 0.0802540i | 0.00163278 | + | 0.00257018i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.6454 | + | 4.19216i | −0.500540 | + | 0.134119i | −0.500250 | − | 0.865881i | \(-0.666759\pi\) |
−0.000289240 | 1.00000i | \(0.500092\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.0600 | + | 26.5927i | −1.47208 | + | 0.849908i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.65142 | − | 1.67423i | −0.0846532 | − | 0.0534542i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.0008 | − | 10.1823i | −1.21204 | − | 0.324764i | −0.404476 | − | 0.914549i | \(-0.632546\pi\) |
−0.807561 | + | 0.589784i | \(0.799213\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1253 | + | 12.3790i | 0.322618 | + | 0.394429i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 58.8480 | + | 1.16607i | 1.87315 | + | 0.0371164i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −80.5025 | −2.55983 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0496 | −1.08162 | −0.540810 | − | 0.841145i | \(-0.681882\pi\) | ||||
−0.540810 | + | 0.841145i | \(0.681882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.14417 | + | 13.4820i | −0.258448 | + | 0.427840i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.86733 | − | 38.6163i | 0.122603 | − | 1.22422i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.80419 | + | 1.82318i | 0.215491 | + | 0.0577406i | 0.364949 | − | 0.931027i | \(-0.381086\pi\) |
−0.149458 | + | 0.988768i | \(0.547753\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.2458 | + | 16.1963i | −0.577272 | + | 0.512427i |
(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 | 360.2.bs.a.113.13 | ✓ | 72 | |
3.2 | odd | 2 | 1080.2.bt.a.233.18 | 72 | |||
4.3 | odd | 2 | 720.2.cu.e.113.6 | 72 | |||
5.2 | odd | 4 | inner | 360.2.bs.a.257.15 | yes | 72 | |
9.2 | odd | 6 | inner | 360.2.bs.a.353.15 | yes | 72 | |
9.7 | even | 3 | 1080.2.bt.a.953.12 | 72 | |||
15.2 | even | 4 | 1080.2.bt.a.17.12 | 72 | |||
20.7 | even | 4 | 720.2.cu.e.257.4 | 72 | |||
36.11 | even | 6 | 720.2.cu.e.353.4 | 72 | |||
45.2 | even | 12 | inner | 360.2.bs.a.137.13 | yes | 72 | |
45.7 | odd | 12 | 1080.2.bt.a.737.18 | 72 | |||
180.47 | odd | 12 | 720.2.cu.e.497.6 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bs.a.113.13 | ✓ | 72 | 1.1 | even | 1 | trivial | |
360.2.bs.a.137.13 | yes | 72 | 45.2 | even | 12 | inner | |
360.2.bs.a.257.15 | yes | 72 | 5.2 | odd | 4 | inner | |
360.2.bs.a.353.15 | yes | 72 | 9.2 | odd | 6 | inner | |
720.2.cu.e.113.6 | 72 | 4.3 | odd | 2 | |||
720.2.cu.e.257.4 | 72 | 20.7 | even | 4 | |||
720.2.cu.e.353.4 | 72 | 36.11 | even | 6 | |||
720.2.cu.e.497.6 | 72 | 180.47 | odd | 12 | |||
1080.2.bt.a.17.12 | 72 | 15.2 | even | 4 | |||
1080.2.bt.a.233.18 | 72 | 3.2 | odd | 2 | |||
1080.2.bt.a.737.18 | 72 | 45.7 | odd | 12 | |||
1080.2.bt.a.953.12 | 72 | 9.7 | even | 3 |