Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(53,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 53.12 | ||
Character | \(\chi\) | \(=\) | 360.53 |
Dual form | 360.2.x.a.197.12 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.159967 | + | 1.40514i | −0.113114 | + | 0.993582i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94882 | − | 0.449551i | −0.974411 | − | 0.224775i | ||||
\(5\) | −0.215413 | − | 2.22567i | −0.0963358 | − | 0.995349i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.32063 | + | 2.32063i | −0.877115 | + | 0.877115i | −0.993235 | − | 0.116120i | \(-0.962954\pi\) |
0.116120 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(8\) | 0.943427 | − | 2.66645i | 0.333552 | − | 0.942732i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.16183 | + | 0.0533477i | 0.999858 | + | 0.0168700i | ||||
\(11\) | −5.57646 | −1.68137 | −0.840683 | − | 0.541528i | \(-0.817846\pi\) | ||||
−0.840683 | + | 0.541528i | \(0.817846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.79226 | − | 1.79226i | 0.497083 | − | 0.497083i | −0.413446 | − | 0.910529i | \(-0.635675\pi\) |
0.910529 | + | 0.413446i | \(0.135675\pi\) | |||||||
\(14\) | −2.88958 | − | 3.63203i | −0.772272 | − | 0.970700i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.59581 | + | 1.75219i | 0.898952 | + | 0.438047i | ||||
\(17\) | −5.56203 | − | 5.56203i | −1.34899 | − | 1.34899i | −0.886758 | − | 0.462233i | \(-0.847048\pi\) |
−0.462233 | − | 0.886758i | \(-0.652952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61960 | −0.600978 | −0.300489 | − | 0.953785i | \(-0.597150\pi\) | ||||
−0.300489 | + | 0.953785i | \(0.597150\pi\) | |||||||
\(20\) | −0.580749 | + | 4.43427i | −0.129859 | + | 0.991532i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.892049 | − | 7.83569i | 0.190185 | − | 1.67058i | ||||
\(23\) | 4.44948 | − | 4.44948i | 0.927781 | − | 0.927781i | −0.0697816 | − | 0.997562i | \(-0.522230\pi\) |
0.997562 | + | 0.0697816i | \(0.0222302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90719 | + | 0.958877i | −0.981439 | + | 0.191775i | ||||
\(26\) | 2.23167 | + | 2.80507i | 0.437666 | + | 0.550120i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.56573 | − | 3.47925i | 1.05182 | − | 0.657517i | ||||
\(29\) | 2.12491i | 0.394587i | 0.980345 | + | 0.197293i | \(0.0632151\pi\) | ||||
−0.980345 | + | 0.197293i | \(0.936785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.52171 | −0.812123 | −0.406061 | − | 0.913846i | \(-0.633098\pi\) | ||||
−0.406061 | + | 0.913846i | \(0.633098\pi\) | |||||||
\(32\) | −3.03728 | + | 4.77231i | −0.536919 | + | 0.843634i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.70516 | − | 6.92568i | 1.49292 | − | 1.18774i | ||||
\(35\) | 5.66484 | + | 4.66506i | 0.957534 | + | 0.788538i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02845 | + | 5.02845i | 0.826673 | + | 0.826673i | 0.987055 | − | 0.160382i | \(-0.0512727\pi\) |
−0.160382 | + | 0.987055i | \(0.551273\pi\) | |||||||
\(38\) | 0.419049 | − | 3.68090i | 0.0679788 | − | 0.597121i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.13785 | − | 1.52537i | −0.970480 | − | 0.241182i | ||||
\(41\) | 1.73215i | 0.270516i | 0.990810 | + | 0.135258i | \(0.0431863\pi\) | ||||
−0.990810 | + | 0.135258i | \(0.956814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.19790 | − | 1.19790i | 0.182678 | − | 0.182678i | −0.609844 | − | 0.792522i | \(-0.708768\pi\) |
0.792522 | + | 0.609844i | \(0.208768\pi\) | |||||||
\(44\) | 10.8675 | + | 2.50690i | 1.63834 | + | 0.377930i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.54036 | + | 6.96390i | 0.816882 | + | 1.02677i | ||||
\(47\) | 0.849681 | + | 0.849681i | 0.123939 | + | 0.123939i | 0.766355 | − | 0.642417i | \(-0.222068\pi\) |
−0.642417 | + | 0.766355i | \(0.722068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.77064i | − | 0.538663i | ||||||
\(50\) | −0.562366 | − | 7.04867i | −0.0795305 | − | 0.996832i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.29850 | + | 2.68708i | −0.596095 | + | 0.372631i | ||||
\(53\) | −4.22906 | − | 4.22906i | −0.580906 | − | 0.580906i | 0.354246 | − | 0.935152i | \(-0.384737\pi\) |
−0.935152 | + | 0.354246i | \(0.884737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20124 | + | 12.4113i | 0.161976 | + | 1.67355i | ||||
\(56\) | 3.99849 | + | 8.37718i | 0.534321 | + | 1.11945i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.98580 | − | 0.339916i | −0.392054 | − | 0.0446331i | ||||
\(59\) | 8.08999i | 1.05323i | 0.850105 | + | 0.526614i | \(0.176539\pi\) | ||||
−0.850105 | + | 0.526614i | \(0.823461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.13786i | − | 0.401762i | −0.979616 | − | 0.200881i | \(-0.935620\pi\) | ||
0.979616 | − | 0.200881i | \(-0.0643805\pi\) | |||||||
\(62\) | 0.723323 | − | 6.35362i | 0.0918622 | − | 0.806910i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.21989 | − | 5.03120i | −0.777486 | − | 0.628900i | ||||
\(65\) | −4.37505 | − | 3.60290i | −0.542658 | − | 0.446884i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.86836 | − | 1.86836i | −0.228256 | − | 0.228256i | 0.583708 | − | 0.811964i | \(-0.301601\pi\) |
−0.811964 | + | 0.583708i | \(0.801601\pi\) | |||||||
\(68\) | 8.33899 | + | 13.3398i | 1.01125 | + | 1.61769i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.46123 | + | 7.21363i | −0.891788 | + | 0.862194i | ||||
\(71\) | 6.95452i | 0.825350i | 0.910878 | + | 0.412675i | \(0.135405\pi\) | ||||
−0.910878 | + | 0.412675i | \(0.864595\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.86607 | − | 5.86607i | −0.686572 | − | 0.686572i | 0.274901 | − | 0.961473i | \(-0.411355\pi\) |
−0.961473 | + | 0.274901i | \(0.911355\pi\) | |||||||
\(74\) | −7.87005 | + | 6.26128i | −0.914875 | + | 0.727859i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.10513 | + | 1.17764i | 0.585599 | + | 0.135085i | ||||
\(77\) | 12.9409 | − | 12.9409i | 1.47475 | − | 1.47475i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.52204i | − | 0.283752i | −0.989884 | − | 0.141876i | \(-0.954687\pi\) | ||
0.989884 | − | 0.141876i | \(-0.0453134\pi\) | |||||||
\(80\) | 3.12520 | − | 8.38052i | 0.349408 | − | 0.936971i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.43390 | − | 0.277086i | −0.268780 | − | 0.0305990i | ||||
\(83\) | −0.694298 | − | 0.694298i | −0.0762091 | − | 0.0762091i | 0.667975 | − | 0.744184i | \(-0.267161\pi\) |
−0.744184 | + | 0.667975i | \(0.767161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1811 | + | 13.5774i | −1.21276 | + | 1.47267i | ||||
\(86\) | 1.49159 | + | 1.87484i | 0.160842 | + | 0.202169i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.26099 | + | 14.8693i | −0.560823 | + | 1.58508i | ||||
\(89\) | −12.1475 | −1.28763 | −0.643816 | − | 0.765180i | \(-0.722650\pi\) | ||||
−0.643816 | + | 0.765180i | \(0.722650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.31834i | 0.871999i | ||||||||
\(92\) | −10.6715 | + | 6.67097i | −1.11258 | + | 0.695497i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.32984 | + | 1.05800i | −0.137162 | + | 0.109124i | ||||
\(95\) | 0.564297 | + | 5.83036i | 0.0578957 | + | 0.598183i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.09526 | − | 4.09526i | 0.415811 | − | 0.415811i | −0.467946 | − | 0.883757i | \(-0.655006\pi\) |
0.883757 | + | 0.467946i | \(0.155006\pi\) | |||||||
\(98\) | 5.29827 | + | 0.603178i | 0.535206 | + | 0.0609301i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.99431 | + | 0.337353i | 0.999431 | + | 0.0337353i | ||||
\(101\) | −0.617937 | −0.0614871 | −0.0307435 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307435 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.59696 | − | 2.59696i | −0.255886 | − | 0.255886i | 0.567493 | − | 0.823379i | \(-0.307914\pi\) |
−0.823379 | + | 0.567493i | \(0.807914\pi\) | |||||||
\(104\) | −3.08810 | − | 6.46983i | −0.302813 | − | 0.634419i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.61892 | − | 5.26590i | 0.642886 | − | 0.511469i | ||||
\(107\) | 1.74306 | − | 1.74306i | 0.168508 | − | 0.168508i | −0.617815 | − | 0.786323i | \(-0.711982\pi\) |
0.786323 | + | 0.617815i | \(0.211982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1487 | 1.45098 | 0.725491 | − | 0.688231i | \(-0.241613\pi\) | ||||
0.725491 | + | 0.688231i | \(0.241613\pi\) | |||||||
\(110\) | −17.6318 | − | 0.297491i | −1.68113 | − | 0.0283647i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.4107 | + | 4.27836i | −1.17270 | + | 0.404267i | ||||
\(113\) | 2.41591 | − | 2.41591i | 0.227270 | − | 0.227270i | −0.584281 | − | 0.811551i | \(-0.698624\pi\) |
0.811551 | + | 0.584281i | \(0.198624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.8615 | − | 8.94459i | −1.01284 | − | 0.834087i | ||||
\(116\) | 0.955257 | − | 4.14108i | 0.0886934 | − | 0.384489i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.3675 | − | 1.29413i | −1.04647 | − | 0.119134i | ||||
\(119\) | 25.8148 | 2.36644 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.0969 | 1.82699 | ||||||||
\(122\) | 4.40913 | + | 0.501954i | 0.399184 | + | 0.0454448i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.81200 | + | 2.03274i | 0.791341 | + | 0.182545i | ||||
\(125\) | 3.19122 | + | 10.7152i | 0.285431 | + | 0.958399i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.40304 | + | 1.40304i | −0.124500 | + | 0.124500i | −0.766611 | − | 0.642112i | \(-0.778059\pi\) |
0.642112 | + | 0.766611i | \(0.278059\pi\) | |||||||
\(128\) | 8.06450 | − | 7.93497i | 0.712808 | − | 0.701359i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.76243 | − | 5.57120i | 0.505398 | − | 0.488627i | ||||
\(131\) | −7.14182 | −0.623984 | −0.311992 | − | 0.950085i | \(-0.600996\pi\) | ||||
−0.311992 | + | 0.950085i | \(0.600996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07912 | − | 6.07912i | 0.527127 | − | 0.527127i | ||||
\(134\) | 2.92417 | − | 2.32642i | 0.252610 | − | 0.200972i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.0783 | + | 9.58350i | −1.72170 | + | 0.821778i | ||||
\(137\) | 6.58546 | + | 6.58546i | 0.562634 | + | 0.562634i | 0.930055 | − | 0.367421i | \(-0.119759\pi\) |
−0.367421 | + | 0.930055i | \(0.619759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.1568 | −1.28558 | −0.642791 | − | 0.766042i | \(-0.722224\pi\) | ||||
−0.642791 | + | 0.766042i | \(0.722224\pi\) | |||||||
\(140\) | −8.94259 | − | 11.6380i | −0.755787 | − | 0.983590i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.77206 | − | 1.11249i | −0.820053 | − | 0.0933583i | ||||
\(143\) | −9.99446 | + | 9.99446i | −0.835779 | + | 0.835779i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.72935 | − | 0.457735i | 0.392751 | − | 0.0380128i | ||||
\(146\) | 9.18101 | − | 7.30426i | 0.759826 | − | 0.604505i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.53901 | − | 12.0601i | −0.619703 | − | 0.991334i | ||||
\(149\) | 5.51376i | 0.451705i | 0.974162 | + | 0.225852i | \(0.0725167\pi\) | ||||
−0.974162 | + | 0.225852i | \(0.927483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7042 | 1.19661 | 0.598307 | − | 0.801267i | \(-0.295840\pi\) | ||||
0.598307 | + | 0.801267i | \(0.295840\pi\) | |||||||
\(152\) | −2.47140 | + | 6.98503i | −0.200457 | + | 0.566561i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.1136 | + | 20.2539i | 1.29847 | + | 1.63210i | ||||
\(155\) | 0.974036 | + | 10.0638i | 0.0782365 | + | 0.808345i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3534 | − | 11.3534i | −0.906103 | − | 0.906103i | 0.0898521 | − | 0.995955i | \(-0.471361\pi\) |
−0.995955 | + | 0.0898521i | \(0.971361\pi\) | |||||||
\(158\) | 3.54381 | + | 0.403443i | 0.281931 | + | 0.0320962i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.2759 | + | 5.73195i | 0.891434 | + | 0.453150i | ||||
\(161\) | 20.6512i | 1.62754i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7245 | − | 11.7245i | 0.918331 | − | 0.918331i | −0.0785768 | − | 0.996908i | \(-0.525038\pi\) |
0.996908 | + | 0.0785768i | \(0.0250376\pi\) | |||||||
\(164\) | 0.778688 | − | 3.37564i | 0.0608053 | − | 0.263594i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.08665 | − | 0.864519i | 0.0843402 | − | 0.0670997i | ||||
\(167\) | −7.91997 | − | 7.91997i | −0.612865 | − | 0.612865i | 0.330826 | − | 0.943692i | \(-0.392673\pi\) |
−0.943692 | + | 0.330826i | \(0.892673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.57562i | 0.505817i | ||||||||
\(170\) | −17.2895 | − | 17.8829i | −1.32604 | − | 1.37156i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.87301 | + | 1.79598i | −0.219065 | + | 0.136942i | ||||
\(173\) | −7.22597 | − | 7.22597i | −0.549380 | − | 0.549380i | 0.376881 | − | 0.926262i | \(-0.376996\pi\) |
−0.926262 | + | 0.376881i | \(0.876996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.16258 | − | 13.6130i | 0.692626 | − | 1.02904i | ||||
\(176\) | −20.0519 | − | 9.77101i | −1.51147 | − | 0.736517i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.94320 | − | 17.0689i | 0.145649 | − | 1.27937i | ||||
\(179\) | − | 13.7942i | − | 1.03103i | −0.856880 | − | 0.515515i | \(-0.827601\pi\) | ||
0.856880 | − | 0.515515i | \(-0.172399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.3310i | − | 1.36254i | −0.732034 | − | 0.681268i | \(-0.761429\pi\) | ||
0.732034 | − | 0.681268i | \(-0.238571\pi\) | |||||||
\(182\) | −11.6884 | − | 1.33066i | −0.866402 | − | 0.0986349i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.66655 | − | 16.0621i | −0.565185 | − | 1.18411i | ||||
\(185\) | 10.1085 | − | 12.2749i | 0.743190 | − | 0.902466i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.0165 | + | 31.0165i | 2.26815 | + | 2.26815i | ||||
\(188\) | −1.27390 | − | 2.03785i | −0.0929088 | − | 0.148626i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.28273 | − | 0.139750i | −0.600892 | − | 0.0101385i | ||||
\(191\) | − | 12.2206i | − | 0.884251i | −0.896953 | − | 0.442125i | \(-0.854225\pi\) | ||
0.896953 | − | 0.442125i | \(-0.145775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67882 | − | 1.67882i | −0.120844 | − | 0.120844i | 0.644099 | − | 0.764943i | \(-0.277233\pi\) |
−0.764943 | + | 0.644099i | \(0.777233\pi\) | |||||||
\(194\) | 5.09930 | + | 6.40951i | 0.366108 | + | 0.460176i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.69509 | + | 7.34831i | −0.121078 | + | 0.524879i | ||||
\(197\) | 4.43727 | − | 4.43727i | 0.316143 | − | 0.316143i | −0.531141 | − | 0.847283i | \(-0.678237\pi\) |
0.847283 | + | 0.531141i | \(0.178237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.2067i | − | 1.14886i | −0.818553 | − | 0.574432i | \(-0.805223\pi\) | ||
0.818553 | − | 0.574432i | \(-0.194777\pi\) | |||||||
\(200\) | −2.07278 | + | 13.9894i | −0.146568 | + | 0.989201i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0988495 | − | 0.868287i | 0.00695503 | − | 0.0610924i | ||||
\(203\) | −4.93114 | − | 4.93114i | −0.346098 | − | 0.346098i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.85518 | − | 0.373128i | 0.269258 | − | 0.0260604i | ||||
\(206\) | 4.06451 | − | 3.23366i | 0.283188 | − | 0.225300i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.58499 | − | 3.30424i | 0.664600 | − | 0.229108i | ||||
\(209\) | 14.6081 | 1.01046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.6302i | − | 1.55793i | −0.627068 | − | 0.778964i | \(-0.715745\pi\) | ||
0.627068 | − | 0.778964i | \(-0.284255\pi\) | |||||||
\(212\) | 6.34050 | + | 10.1429i | 0.435467 | + | 0.696614i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.17041 | + | 2.72807i | 0.148366 | + | 0.186487i | ||||
\(215\) | −2.92417 | − | 2.40808i | −0.199427 | − | 0.164230i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4932 | − | 10.4932i | 0.712325 | − | 0.712325i | ||||
\(218\) | −2.42329 | + | 21.2860i | −0.164126 | + | 1.44167i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.23852 | − | 24.7275i | 0.218341 | − | 1.66713i | ||||
\(221\) | −19.9372 | −1.34112 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8423 | + | 10.8423i | 0.726057 | + | 0.726057i | 0.969832 | − | 0.243775i | \(-0.0783859\pi\) |
−0.243775 | + | 0.969832i | \(0.578386\pi\) | |||||||
\(224\) | −4.02638 | − | 18.1232i | −0.269024 | − | 1.21090i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00822 | + | 3.78115i | 0.200104 | + | 0.251518i | ||||
\(227\) | 12.6177 | − | 12.6177i | 0.837465 | − | 0.837465i | −0.151059 | − | 0.988525i | \(-0.548268\pi\) |
0.988525 | + | 0.151059i | \(0.0482685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.594060 | −0.0392566 | −0.0196283 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196283 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(230\) | 14.3059 | − | 13.8311i | 0.943300 | − | 0.911997i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.66597 | + | 2.00470i | 0.371989 | + | 0.131615i | ||||
\(233\) | −5.12779 | + | 5.12779i | −0.335933 | + | 0.335933i | −0.854834 | − | 0.518901i | \(-0.826341\pi\) |
0.518901 | + | 0.854834i | \(0.326341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.70807 | − | 2.07414i | 0.111423 | − | 0.135302i | ||||
\(236\) | 3.63686 | − | 15.7659i | 0.236740 | − | 1.02628i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.12952 | + | 36.2734i | −0.267677 | + | 2.35126i | ||||
\(239\) | −11.1582 | −0.721763 | −0.360881 | − | 0.932612i | \(-0.617524\pi\) | ||||
−0.360881 | + | 0.932612i | \(0.617524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.9706 | −1.28642 | −0.643209 | − | 0.765691i | \(-0.722397\pi\) | ||||
−0.643209 | + | 0.765691i | \(0.722397\pi\) | |||||||
\(242\) | −3.21484 | + | 28.2389i | −0.206658 | + | 1.81527i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.41063 | + | 6.11513i | −0.0903062 | + | 0.391481i | ||||
\(245\) | −8.39219 | + | 0.812247i | −0.536158 | + | 0.0518925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.69500 | + | 4.69500i | −0.298736 | + | 0.298736i | ||||
\(248\) | −4.26590 | + | 12.0569i | −0.270885 | + | 0.765614i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.5669 | + | 2.77002i | −0.984534 | + | 0.175191i | ||||
\(251\) | −20.4134 | −1.28848 | −0.644240 | − | 0.764823i | \(-0.722826\pi\) | ||||
−0.644240 | + | 0.764823i | \(0.722826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8123 | + | 24.8123i | −1.55994 | + | 1.55994i | ||||
\(254\) | −1.74703 | − | 2.19591i | −0.109618 | − | 0.137783i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.85967 | + | 12.6011i | 0.616230 | + | 0.787567i | ||||
\(257\) | 13.9742 | + | 13.9742i | 0.871688 | + | 0.871688i | 0.992656 | − | 0.120968i | \(-0.0385999\pi\) |
−0.120968 | + | 0.992656i | \(0.538600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.3384 | −1.45017 | ||||||||
\(260\) | 6.90650 | + | 8.98821i | 0.428323 | + | 0.557425i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.14246 | − | 10.0352i | 0.0705811 | − | 0.619979i | ||||
\(263\) | −10.4243 | + | 10.4243i | −0.642788 | + | 0.642788i | −0.951240 | − | 0.308452i | \(-0.900189\pi\) |
0.308452 | + | 0.951240i | \(0.400189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.50148 | + | 10.3235i | −0.522242 | + | 0.634166i | ||||
\(266\) | 7.56954 | + | 9.51446i | 0.464119 | + | 0.583369i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.80117 | + | 4.48101i | 0.171109 | + | 0.273721i | ||||
\(269\) | 29.5007i | 1.79869i | 0.437241 | + | 0.899345i | \(0.355956\pi\) | ||||
−0.437241 | + | 0.899345i | \(0.644044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3447 | −1.17511 | −0.587554 | − | 0.809185i | \(-0.699909\pi\) | ||||
−0.587554 | + | 0.809185i | \(0.699909\pi\) | |||||||
\(272\) | −10.2543 | − | 29.7457i | −0.621757 | − | 1.80360i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3069 | + | 8.20002i | −0.622664 | + | 0.495381i | ||||
\(275\) | 27.3648 | − | 5.34714i | 1.65016 | − | 0.322445i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44346 | + | 1.44346i | 0.0867293 | + | 0.0867293i | 0.749140 | − | 0.662411i | \(-0.230467\pi\) |
−0.662411 | + | 0.749140i | \(0.730467\pi\) | |||||||
\(278\) | 2.42458 | − | 21.2974i | 0.145417 | − | 1.27733i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.7835 | − | 10.7039i | 1.06277 | − | 0.639679i | ||||
\(281\) | − | 23.9276i | − | 1.42740i | −0.700450 | − | 0.713702i | \(-0.747017\pi\) | ||
0.700450 | − | 0.713702i | \(-0.252983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.90740 | − | 7.90740i | 0.470046 | − | 0.470046i | −0.431883 | − | 0.901930i | \(-0.642151\pi\) |
0.901930 | + | 0.431883i | \(0.142151\pi\) | |||||||
\(284\) | 3.12641 | − | 13.5531i | 0.185518 | − | 0.804229i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.4448 | − | 15.6424i | −0.735877 | − | 0.924953i | ||||
\(287\) | −4.01967 | − | 4.01967i | −0.237274 | − | 0.237274i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.8725i | 2.63956i | ||||||||
\(290\) | −0.113359 | + | 6.71861i | −0.00665669 | + | 0.394530i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.79483 | + | 14.0690i | 0.514678 | + | 0.823327i | ||||
\(293\) | 5.38544 | + | 5.38544i | 0.314621 | + | 0.314621i | 0.846697 | − | 0.532076i | \(-0.178588\pi\) |
−0.532076 | + | 0.846697i | \(0.678588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.0056 | − | 1.74269i | 1.04833 | − | 0.101463i | ||||
\(296\) | 18.1521 | − | 8.66413i | 1.05507 | − | 0.503592i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.74758 | − | 0.882018i | −0.448806 | − | 0.0510940i | ||||
\(299\) | − | 15.9492i | − | 0.922368i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.55977i | 0.320460i | ||||||||
\(302\) | −2.35219 | + | 20.6615i | −0.135353 | + | 1.18893i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.41958 | − | 4.59003i | −0.540250 | − | 0.263257i | ||||
\(305\) | −6.98384 | + | 0.675938i | −0.399893 | + | 0.0387041i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.116076 | + | 0.116076i | 0.00662479 | + | 0.00662479i | 0.710411 | − | 0.703787i | \(-0.248509\pi\) |
−0.703787 | + | 0.710411i | \(0.748509\pi\) | |||||||
\(308\) | −31.0371 | + | 19.4019i | −1.76850 | + | 1.10553i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.2969 | − | 0.241223i | −0.812007 | − | 0.0137005i | ||||
\(311\) | 1.42835i | 0.0809944i | 0.999180 | + | 0.0404972i | \(0.0128942\pi\) | ||||
−0.999180 | + | 0.0404972i | \(0.987106\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.59396 | − | 6.59396i | −0.372712 | − | 0.372712i | 0.495752 | − | 0.868464i | \(-0.334893\pi\) |
−0.868464 | + | 0.495752i | \(0.834893\pi\) | |||||||
\(314\) | 17.7693 | − | 14.1370i | 1.00278 | − | 0.797795i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.13379 | + | 4.91500i | −0.0637804 | + | 0.276491i | ||||
\(317\) | 11.2572 | − | 11.2572i | 0.632269 | − | 0.632269i | −0.316367 | − | 0.948637i | \(-0.602463\pi\) |
0.948637 | + | 0.316367i | \(0.102463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.8495i | − | 0.663444i | ||||||
\(320\) | −9.85793 | + | 14.9272i | −0.551075 | + | 0.834456i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −29.0178 | − | 3.30351i | −1.61710 | − | 0.184097i | ||||
\(323\) | 14.5703 | + | 14.5703i | 0.810714 | + | 0.810714i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07640 | + | 10.5135i | −0.392528 | + | 0.583185i | ||||
\(326\) | 14.5990 | + | 18.3500i | 0.808562 | + | 1.01631i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.61868 | + | 1.63415i | 0.255024 | + | 0.0902311i | ||||
\(329\) | −3.94359 | −0.217417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.0445i | 1.92622i | 0.269113 | + | 0.963109i | \(0.413270\pi\) | ||||
−0.269113 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(332\) | 1.04094 | + | 1.66518i | 0.0571290 | + | 0.0913888i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.3956 | − | 9.86171i | 0.678256 | − | 0.539609i | ||||
\(335\) | −3.75587 | + | 4.56081i | −0.205205 | + | 0.249184i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.94865 | − | 1.94865i | 0.106150 | − | 0.106150i | −0.652037 | − | 0.758187i | \(-0.726085\pi\) |
0.758187 | + | 0.652037i | \(0.226085\pi\) | |||||||
\(338\) | −9.23965 | − | 1.05188i | −0.502570 | − | 0.0572148i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 27.8937 | − | 21.4334i | 1.51275 | − | 1.16239i | ||||
\(341\) | 25.2151 | 1.36548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.49415 | − | 7.49415i | −0.404646 | − | 0.404646i | ||||
\(344\) | −2.06401 | − | 4.32427i | −0.111284 | − | 0.233149i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.3094 | − | 8.99756i | 0.607997 | − | 0.483712i | ||||
\(347\) | −18.0347 | + | 18.0347i | −0.968151 | + | 0.968151i | −0.999508 | − | 0.0313569i | \(-0.990017\pi\) |
0.0313569 | + | 0.999508i | \(0.490017\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.54696 | 0.0828069 | 0.0414035 | − | 0.999143i | \(-0.486817\pi\) | ||||
0.0414035 | + | 0.999143i | \(0.486817\pi\) | |||||||
\(350\) | 17.6624 | + | 15.0523i | 0.944095 | + | 0.804580i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9372 | − | 26.6126i | 0.902758 | − | 1.41846i | ||||
\(353\) | 13.4669 | − | 13.4669i | 0.716770 | − | 0.716770i | −0.251172 | − | 0.967942i | \(-0.580816\pi\) |
0.967942 | + | 0.251172i | \(0.0808161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4785 | − | 1.49810i | 0.821511 | − | 0.0795107i | ||||
\(356\) | 23.6733 | + | 5.46092i | 1.25468 | + | 0.289428i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.3828 | + | 2.20662i | 1.02441 | + | 0.116624i | ||||
\(359\) | −32.2230 | −1.70067 | −0.850334 | − | 0.526244i | \(-0.823600\pi\) | ||||
−0.850334 | + | 0.526244i | \(0.823600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1377 | −0.638826 | ||||||||
\(362\) | 25.7576 | + | 2.93236i | 1.35379 | + | 0.154121i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.73951 | − | 16.2109i | 0.196004 | − | 0.849685i | ||||
\(365\) | −11.7923 | + | 14.3196i | −0.617237 | + | 0.749520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.07186 | + | 7.07186i | −0.369148 | + | 0.369148i | −0.867167 | − | 0.498018i | \(-0.834061\pi\) |
0.498018 | + | 0.867167i | \(0.334061\pi\) | |||||||
\(368\) | 23.7958 | − | 8.20315i | 1.24044 | − | 0.427619i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.6308 | + | 16.1674i | 0.812609 | + | 0.840501i | ||||
\(371\) | 19.6282 | 1.01904 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.32291 | − | 5.32291i | 0.275610 | − | 0.275610i | −0.555744 | − | 0.831354i | \(-0.687566\pi\) |
0.831354 | + | 0.555744i | \(0.187566\pi\) | |||||||
\(374\) | −48.5440 | + | 38.6208i | −2.51015 | + | 1.99703i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06724 | − | 1.46402i | 0.158181 | − | 0.0755010i | ||||
\(377\) | 3.80839 | + | 3.80839i | 0.196142 | + | 0.196142i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7611 | 1.01506 | 0.507529 | − | 0.861635i | \(-0.330559\pi\) | ||||
0.507529 | + | 0.861635i | \(0.330559\pi\) | |||||||
\(380\) | 1.52133 | − | 11.6160i | 0.0780426 | − | 0.595889i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.1716 | + | 1.95489i | 0.878575 | + | 0.100021i | ||||
\(383\) | 13.2191 | − | 13.2191i | 0.675466 | − | 0.675466i | −0.283505 | − | 0.958971i | \(-0.591497\pi\) |
0.958971 | + | 0.283505i | \(0.0914972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.5898 | − | 26.0145i | −1.60996 | − | 1.32582i | ||||
\(386\) | 2.62753 | − | 2.09041i | 0.133738 | − | 0.106399i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.82197 | + | 6.13991i | −0.498635 | + | 0.311707i | ||||
\(389\) | 27.1107i | 1.37457i | 0.726389 | + | 0.687284i | \(0.241197\pi\) | ||||
−0.726389 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49.4963 | −2.50314 | ||||||||
\(392\) | −10.0542 | − | 3.55733i | −0.507815 | − | 0.179672i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.52516 | + | 6.94479i | 0.278354 | + | 0.349874i | ||||
\(395\) | −5.61322 | + | 0.543281i | −0.282432 | + | 0.0273354i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.68567 | − | 8.68567i | −0.435921 | − | 0.435921i | 0.454715 | − | 0.890637i | \(-0.349741\pi\) |
−0.890637 | + | 0.454715i | \(0.849741\pi\) | |||||||
\(398\) | 22.7727 | + | 2.59254i | 1.14149 | + | 0.129952i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.3255 | − | 5.15039i | −0.966273 | − | 0.257519i | ||||
\(401\) | 3.09967i | 0.154790i | 0.997000 | + | 0.0773951i | \(0.0246603\pi\) | ||||
−0.997000 | + | 0.0773951i | \(0.975340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.10407 | + | 8.10407i | −0.403692 | + | 0.403692i | ||||
\(404\) | 1.20425 | + | 0.277794i | 0.0599136 | + | 0.0138208i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.71774 | − | 6.14011i | 0.383025 | − | 0.304728i | ||||
\(407\) | −28.0410 | − | 28.0410i | −1.38994 | − | 1.38994i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1083i | 0.697610i | 0.937195 | + | 0.348805i | \(0.113412\pi\) | ||||
−0.937195 | + | 0.348805i | \(0.886588\pi\) | |||||||
\(410\) | −0.0924061 | + | 5.47675i | −0.00456361 | + | 0.270477i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.89354 | + | 6.22847i | 0.191821 | + | 0.306855i | ||||
\(413\) | −18.7739 | − | 18.7739i | −0.923802 | − | 0.923802i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.39571 | + | 1.69484i | −0.0685129 | + | 0.0831963i | ||||
\(416\) | 3.10963 | + | 13.9968i | 0.152462 | + | 0.686250i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.33681 | + | 20.5264i | −0.114297 | + | 1.00398i | ||||
\(419\) | − | 30.4747i | − | 1.48878i | −0.667743 | − | 0.744392i | \(-0.732739\pi\) | ||
0.667743 | − | 0.744392i | \(-0.267261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.0605i | − | 1.85496i | −0.373878 | − | 0.927478i | \(-0.621972\pi\) | ||
0.373878 | − | 0.927478i | \(-0.378028\pi\) | |||||||
\(422\) | 31.7986 | + | 3.62008i | 1.54793 | + | 0.176223i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.2664 | + | 7.28675i | −0.741401 | + | 0.353876i | ||||
\(425\) | 32.6273 | + | 21.9607i | 1.58266 | + | 1.06525i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.28181 | + | 7.28181i | 0.352392 | + | 0.352392i | ||||
\(428\) | −4.18051 | + | 2.61332i | −0.202073 | + | 0.126320i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.85146 | − | 3.72365i | 0.185734 | − | 0.179570i | ||||
\(431\) | − | 30.0050i | − | 1.44529i | −0.691220 | − | 0.722644i | \(-0.742927\pi\) | ||
0.691220 | − | 0.722644i | \(-0.257073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6496 | + | 20.6496i | 0.992355 | + | 0.992355i | 0.999971 | − | 0.00761624i | \(-0.00242435\pi\) |
−0.00761624 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(434\) | 13.0658 | + | 16.4230i | 0.627180 | + | 0.788327i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −29.5221 | − | 6.81011i | −1.41385 | − | 0.326145i | ||||
\(437\) | −11.6559 | + | 11.6559i | −0.557576 | + | 0.557576i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.227040i | − | 0.0108360i | −0.999985 | − | 0.00541802i | \(-0.998275\pi\) | ||
0.999985 | − | 0.00541802i | \(-0.00172462\pi\) | |||||||
\(440\) | 34.2275 | + | 8.50615i | 1.63173 | + | 0.405515i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.18929 | − | 28.0145i | 0.151699 | − | 1.33251i | ||||
\(443\) | −16.3406 | − | 16.3406i | −0.776364 | − | 0.776364i | 0.202846 | − | 0.979211i | \(-0.434981\pi\) |
−0.979211 | + | 0.202846i | \(0.934981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.61673 | + | 27.0363i | 0.124045 | + | 1.28164i | ||||
\(446\) | −16.9694 | + | 13.5006i | −0.803524 | + | 0.639270i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 26.1096 | − | 2.75851i | 1.23356 | − | 0.130327i | ||||
\(449\) | −21.4698 | −1.01322 | −0.506611 | − | 0.862175i | \(-0.669102\pi\) | ||||
−0.506611 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.65925i | − | 0.454836i | ||||||
\(452\) | −5.79425 | + | 3.62210i | −0.272539 | + | 0.170369i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.7112 | + | 19.7480i | 0.737362 | + | 0.926819i | ||||
\(455\) | 18.5139 | − | 1.79188i | 0.867943 | − | 0.0840047i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.4509 | + | 19.4509i | −0.909876 | + | 0.909876i | −0.996262 | − | 0.0863855i | \(-0.972468\pi\) |
0.0863855 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(458\) | 0.0950299 | − | 0.834736i | 0.00444046 | − | 0.0390046i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.1462 | + | 22.3142i | 0.799444 | + | 1.04041i | ||||
\(461\) | 19.2557 | 0.896828 | 0.448414 | − | 0.893826i | \(-0.351989\pi\) | ||||
0.448414 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6135 | + | 10.6135i | 0.493250 | + | 0.493250i | 0.909329 | − | 0.416079i | \(-0.136596\pi\) |
−0.416079 | + | 0.909329i | \(0.636596\pi\) | |||||||
\(464\) | −3.72325 | + | 7.64078i | −0.172847 | + | 0.354714i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.38497 | − | 8.02552i | −0.295778 | − | 0.371775i | ||||
\(467\) | 1.94796 | − | 1.94796i | 0.0901407 | − | 0.0901407i | −0.660599 | − | 0.750739i | \(-0.729697\pi\) |
0.750739 | + | 0.660599i | \(0.229697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.67152 | 0.400414 | ||||||||
\(470\) | 2.64122 | + | 2.73187i | 0.121830 | + | 0.126012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.5715 | + | 7.63232i | 0.992911 | + | 0.351306i | ||||
\(473\) | −6.68004 | + | 6.68004i | −0.307149 | + | 0.307149i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.8549 | − | 2.51188i | 0.589823 | − | 0.115253i | ||||
\(476\) | −50.3085 | − | 11.6051i | −2.30589 | − | 0.531918i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.78494 | − | 15.6788i | 0.0816412 | − | 0.717131i | ||||
\(479\) | 19.9363 | 0.910911 | 0.455456 | − | 0.890258i | \(-0.349476\pi\) | ||||
0.455456 | + | 0.890258i | \(0.349476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0246 | 0.821850 | ||||||||
\(482\) | 3.19463 | − | 28.0614i | 0.145511 | − | 1.27816i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.1653 | − | 9.03458i | −1.78024 | − | 0.410663i | ||||
\(485\) | −9.99687 | − | 8.23252i | −0.453935 | − | 0.373820i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5407 | − | 18.5407i | 0.840161 | − | 0.840161i | −0.148719 | − | 0.988880i | \(-0.547515\pi\) |
0.988880 | + | 0.148719i | \(0.0475149\pi\) | |||||||
\(488\) | −8.36695 | − | 2.96034i | −0.378754 | − | 0.134009i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.201155 | − | 11.9221i | 0.00908726 | − | 0.538586i | ||||
\(491\) | 1.08218 | 0.0488379 | 0.0244189 | − | 0.999702i | \(-0.492226\pi\) | ||||
0.0244189 | + | 0.999702i | \(0.492226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8188 | − | 11.8188i | 0.532294 | − | 0.532294i | ||||
\(494\) | −5.84608 | − | 7.34817i | −0.263028 | − | 0.330610i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.2592 | − | 7.92288i | −0.730059 | − | 0.355748i | ||||
\(497\) | −16.1389 | − | 16.1389i | −0.723927 | − | 0.723927i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6371 | −0.744779 | −0.372390 | − | 0.928076i | \(-0.621461\pi\) | ||||
−0.372390 | + | 0.928076i | \(0.621461\pi\) | |||||||
\(500\) | −1.40207 | − | 22.3167i | −0.0627026 | − | 0.998032i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.26546 | − | 28.6836i | 0.145745 | − | 1.28021i | ||||
\(503\) | −23.0316 | + | 23.0316i | −1.02693 | + | 1.02693i | −0.0273024 | + | 0.999627i | \(0.508692\pi\) |
−0.999627 | + | 0.0273024i | \(0.991308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.133112 | + | 1.37532i | 0.00592341 | + | 0.0612011i | ||||
\(506\) | −30.8956 | − | 38.8339i | −1.37348 | − | 1.72638i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.36501 | − | 2.10354i | 0.149298 | − | 0.0933294i | ||||
\(509\) | − | 25.0494i | − | 1.11030i | −0.831751 | − | 0.555148i | \(-0.812662\pi\) | ||
0.831751 | − | 0.555148i | \(-0.187338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2260 | 1.20441 | ||||||||
\(512\) | −19.2834 | + | 11.8384i | −0.852216 | + | 0.523190i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.8711 | + | 17.4003i | −0.964694 | + | 0.767494i | ||||
\(515\) | −5.22055 | + | 6.33939i | −0.230045 | + | 0.279347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.73821 | − | 4.73821i | −0.208386 | − | 0.208386i | ||||
\(518\) | 3.73336 | − | 32.7936i | 0.164035 | − | 1.44087i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.7345 | + | 8.26677i | −0.602297 | + | 0.362522i | ||||
\(521\) | 12.1278i | 0.531327i | 0.964066 | + | 0.265663i | \(0.0855909\pi\) | ||||
−0.964066 | + | 0.265663i | \(0.914409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8272 | + | 15.8272i | −0.692077 | + | 0.692077i | −0.962689 | − | 0.270611i | \(-0.912774\pi\) |
0.270611 | + | 0.962689i | \(0.412774\pi\) | |||||||
\(524\) | 13.9181 | + | 3.21061i | 0.608017 | + | 0.140256i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.9800 | − | 16.3151i | −0.565954 | − | 0.711371i | ||||
\(527\) | 25.1499 | + | 25.1499i | 1.09555 | + | 1.09555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.5957i | − | 0.721554i | ||||||
\(530\) | −13.1459 | − | 13.5972i | −0.571023 | − | 0.590623i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.5800 | + | 9.11425i | −0.632123 | + | 0.395153i | ||||
\(533\) | 3.10446 | + | 3.10446i | 0.134469 | + | 0.134469i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.25496 | − | 3.50400i | −0.183958 | − | 0.151491i | ||||
\(536\) | −6.74453 | + | 3.21922i | −0.291319 | + | 0.139049i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.4525 | − | 4.71913i | −1.78715 | − | 0.203456i | ||||
\(539\) | 21.0268i | 0.905690i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.09722i | 0.391120i | 0.980692 | + | 0.195560i | \(0.0626524\pi\) | ||||
−0.980692 | + | 0.195560i | \(0.937348\pi\) | |||||||
\(542\) | 3.09452 | − | 27.1820i | 0.132921 | − | 1.16757i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 43.4372 | − | 9.65033i | 1.86235 | − | 0.413755i | ||||
\(545\) | −3.26323 | − | 33.7160i | −0.139782 | − | 1.44423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5935 | − | 28.5935i | −1.22257 | − | 1.22257i | −0.966715 | − | 0.255856i | \(-0.917643\pi\) |
−0.255856 | − | 0.966715i | \(-0.582357\pi\) | |||||||
\(548\) | −9.87338 | − | 15.7944i | −0.421770 | − | 0.674703i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.13601 | + | 39.3066i | 0.133720 | + | 1.67604i | ||||
\(551\) | − | 5.56643i | − | 0.237138i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.85272 | + | 5.85272i | 0.248883 | + | 0.248883i | ||||
\(554\) | −2.25917 | + | 1.79736i | −0.0959829 | + | 0.0763624i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.5379 | + | 6.81375i | 1.25268 | + | 0.288967i | ||||
\(557\) | −27.5733 | + | 27.5733i | −1.16832 | + | 1.16832i | −0.185716 | + | 0.982604i | \(0.559460\pi\) |
−0.982604 | + | 0.185716i | \(0.940540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.29389i | − | 0.181612i | ||||||
\(560\) | 12.1956 | + | 26.7005i | 0.515360 | + | 1.12830i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.6216 | + | 3.82763i | 1.41824 | + | 0.161459i | ||||
\(563\) | −10.6071 | − | 10.6071i | −0.447036 | − | 0.447036i | 0.447332 | − | 0.894368i | \(-0.352374\pi\) |
−0.894368 | + | 0.447332i | \(0.852374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.89743 | − | 4.85659i | −0.248107 | − | 0.204318i | ||||
\(566\) | 9.84606 | + | 12.3759i | 0.413861 | + | 0.520198i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.5439 | + | 6.56108i | 0.778083 | + | 0.275297i | ||||
\(569\) | −13.8127 | −0.579060 | −0.289530 | − | 0.957169i | \(-0.593499\pi\) | ||||
−0.289530 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2118i | 1.13878i | 0.822068 | + | 0.569390i | \(0.192821\pi\) | ||||
−0.822068 | + | 0.569390i | \(0.807179\pi\) | |||||||
\(572\) | 23.9704 | − | 14.9844i | 1.00225 | − | 0.626529i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.29120 | − | 5.00517i | 0.262590 | − | 0.208912i | ||||
\(575\) | −17.5680 | + | 26.1010i | −0.732634 | + | 1.08849i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7851 | − | 23.7851i | 0.990188 | − | 0.990188i | −0.00976420 | − | 0.999952i | \(-0.503108\pi\) |
0.999952 | + | 0.00976420i | \(0.00310809\pi\) | |||||||
\(578\) | −63.0520 | − | 7.17811i | −2.62262 | − | 0.298570i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.42244 | − | 1.23404i | −0.391245 | − | 0.0512407i | ||||
\(581\) | 3.22241 | 0.133688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.5832 | + | 23.5832i | 0.976715 | + | 0.976715i | ||||
\(584\) | −21.1758 | + | 10.1074i | −0.876260 | + | 0.418246i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.42877 | + | 6.70579i | −0.348189 | + | 0.277014i | ||||
\(587\) | −20.8981 | + | 20.8981i | −0.862557 | + | 0.862557i | −0.991635 | − | 0.129077i | \(-0.958798\pi\) |
0.129077 | + | 0.991635i | \(0.458798\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8451 | 0.488068 | ||||||||
\(590\) | −0.431583 | + | 25.5792i | −0.0177680 | + | 1.05308i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.27056 | + | 26.8922i | 0.381018 | + | 1.10526i | ||||
\(593\) | 15.5965 | − | 15.5965i | 0.640471 | − | 0.640471i | −0.310200 | − | 0.950671i | \(-0.600396\pi\) |
0.950671 | + | 0.310200i | \(0.100396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.56086 | − | 57.4553i | −0.227973 | − | 2.35544i | ||||
\(596\) | 2.47871 | − | 10.7453i | 0.101532 | − | 0.440146i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22.4109 | + | 2.55135i | 0.916448 | + | 0.104332i | ||||
\(599\) | 17.7577 | 0.725558 | 0.362779 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362779 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.1083 | 0.412325 | 0.206163 | − | 0.978518i | \(-0.433902\pi\) | ||||
0.206163 | + | 0.978518i | \(0.433902\pi\) | |||||||
\(602\) | −7.81223 | − | 0.889378i | −0.318403 | − | 0.0362484i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −28.6560 | − | 6.61031i | −1.16599 | − | 0.268970i | ||||
\(605\) | −4.32914 | − | 44.7290i | −0.176005 | − | 1.81849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9642 | + | 15.9642i | −0.647966 | + | 0.647966i | −0.952501 | − | 0.304535i | \(-0.901499\pi\) |
0.304535 | + | 0.952501i | \(0.401499\pi\) | |||||||
\(608\) | 7.95645 | − | 12.5016i | 0.322677 | − | 0.507005i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.167398 | − | 9.92138i | 0.00677774 | − | 0.401705i | ||||
\(611\) | 3.04570 | 0.123216 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9357 | + | 16.9357i | −0.684026 | + | 0.684026i | −0.960905 | − | 0.276878i | \(-0.910700\pi\) |
0.276878 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(614\) | −0.181671 | + | 0.144534i | −0.00733163 | + | 0.00583292i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.2974 | − | 46.7150i | −0.898389 | − | 1.88220i | ||||
\(617\) | 8.84335 | + | 8.84335i | 0.356020 | + | 0.356020i | 0.862344 | − | 0.506324i | \(-0.168996\pi\) |
−0.506324 | + | 0.862344i | \(0.668996\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.27180 | −0.292278 | −0.146139 | − | 0.989264i | \(-0.546685\pi\) | ||||
−0.146139 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(620\) | 2.62597 | − | 20.0505i | 0.105462 | − | 0.805246i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.00703 | − | 0.228489i | −0.0804746 | − | 0.00916157i | ||||
\(623\) | 28.1898 | − | 28.1898i | 1.12940 | − | 1.12940i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1611 | − | 9.41079i | 0.926444 | − | 0.376432i | ||||
\(626\) | 10.3202 | − | 8.21060i | 0.412479 | − | 0.328161i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.0219 | + | 27.2298i | 0.679247 | + | 1.08659i | ||||
\(629\) | − | 55.9369i | − | 2.23035i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2389 | −0.527031 | −0.263515 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263515 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(632\) | −6.72489 | − | 2.37936i | −0.267502 | − | 0.0946459i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0172 | + | 17.6187i | 0.556693 | + | 0.699730i | ||||
\(635\) | 3.42494 | + | 2.82047i | 0.135914 | + | 0.111927i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.75796 | − | 6.75796i | −0.267760 | − | 0.267760i | ||||
\(638\) | 16.6502 | + | 1.89553i | 0.659186 | + | 0.0750446i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.3978 | − | 16.2396i | −0.766766 | − | 0.641927i | ||||
\(641\) | 16.7648i | 0.662171i | 0.943601 | + | 0.331086i | \(0.107415\pi\) | ||||
−0.943601 | + | 0.331086i | \(0.892585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.3834 | − | 35.3834i | 1.39538 | − | 1.39538i | 0.582690 | − | 0.812695i | \(-0.302000\pi\) |
0.812695 | − | 0.582690i | \(-0.198000\pi\) | |||||||
\(644\) | 9.28376 | − | 40.2455i | 0.365831 | − | 1.58589i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8041 | + | 18.1425i | −0.897214 | + | 0.713808i | ||||
\(647\) | 23.0431 | + | 23.0431i | 0.905919 | + | 0.905919i | 0.995940 | − | 0.0900206i | \(-0.0286933\pi\) |
−0.0900206 | + | 0.995940i | \(0.528693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 45.1135i | − | 1.77086i | ||||||
\(650\) | −13.6409 | − | 11.6251i | −0.535042 | − | 0.455975i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.1196 | + | 17.5781i | −1.10125 | + | 0.688413i | ||||
\(653\) | 31.6390 | + | 31.6390i | 1.23813 | + | 1.23813i | 0.960765 | + | 0.277365i | \(0.0894612\pi\) |
0.277365 | + | 0.960765i | \(0.410539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.53844 | + | 15.8953i | 0.0601120 | + | 0.621082i | ||||
\(656\) | −3.03505 | + | 6.22847i | −0.118499 | + | 0.243181i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.630844 | − | 5.54128i | 0.0245928 | − | 0.216022i | ||||
\(659\) | 20.2093i | 0.787242i | 0.919273 | + | 0.393621i | \(0.128778\pi\) | ||||
−0.919273 | + | 0.393621i | \(0.871222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1882i | 1.71872i | 0.511369 | + | 0.859361i | \(0.329139\pi\) | ||||
−0.511369 | + | 0.859361i | \(0.670861\pi\) | |||||||
\(662\) | −49.2423 | − | 5.60595i | −1.91386 | − | 0.217882i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.50633 | + | 1.19629i | −0.0972644 | + | 0.0464250i | ||||
\(665\) | −14.8396 | − | 12.2206i | −0.575456 | − | 0.473894i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.45476 | + | 9.45476i | 0.366090 | + | 0.366090i | ||||
\(668\) | 11.8742 | + | 18.9950i | 0.459426 | + | 0.734940i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.80775 | − | 6.00709i | −0.224373 | − | 0.232074i | ||||
\(671\) | 17.4982i | 0.675509i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.8238 | − | 23.8238i | −0.918340 | − | 0.918340i | 0.0785687 | − | 0.996909i | \(-0.474965\pi\) |
−0.996909 | + | 0.0785687i | \(0.974965\pi\) | |||||||
\(674\) | 2.42640 | + | 3.04984i | 0.0934615 | + | 0.117475i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.95607 | − | 12.8147i | 0.113695 | − | 0.492873i | ||||
\(677\) | 5.72866 | − | 5.72866i | 0.220170 | − | 0.220170i | −0.588400 | − | 0.808570i | \(-0.700242\pi\) |
0.808570 | + | 0.588400i | \(0.200242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.0072i | 0.729429i | ||||||||
\(680\) | 25.6548 | + | 42.6231i | 0.983817 | + | 1.63452i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.03358 | + | 35.4307i | −0.154454 | + | 1.35671i | ||||
\(683\) | 33.0998 | + | 33.0998i | 1.26653 | + | 1.26653i | 0.947869 | + | 0.318659i | \(0.103232\pi\) |
0.318659 | + | 0.947869i | \(0.396768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2384 | − | 16.0756i | 0.505815 | − | 0.614219i | ||||
\(686\) | 11.7291 | − | 9.33149i | 0.447820 | − | 0.356278i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.40637 | − | 2.20847i | 0.244240 | − | 0.0841972i | ||||
\(689\) | −15.1591 | −0.577517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.570988i | 0.0217214i | 0.999941 | + | 0.0108607i | \(0.00345714\pi\) | ||||
−0.999941 | + | 0.0108607i | \(0.996543\pi\) | |||||||
\(692\) | 10.8337 | + | 17.3306i | 0.411835 | + | 0.658809i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.4562 | − | 28.2261i | −0.852427 | − | 1.07145i | ||||
\(695\) | 3.26498 | + | 33.7340i | 0.123848 | + | 1.27960i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.63426 | − | 9.63426i | 0.364924 | − | 0.364924i | ||||
\(698\) | −0.247462 | + | 2.17369i | −0.00936659 | + | 0.0822755i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.9760 | + | 22.4102i | −0.906206 | + | 0.847026i | ||||
\(701\) | 25.9738 | 0.981018 | 0.490509 | − | 0.871436i | \(-0.336811\pi\) | ||||
0.490509 | + | 0.871436i | \(0.336811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.1725 | − | 13.1725i | −0.496812 | − | 0.496812i | ||||
\(704\) | 34.6850 | + | 28.0563i | 1.30724 | + | 1.05741i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.7686 | + | 21.0771i | 0.631093 | + | 0.793246i | ||||
\(707\) | 1.43400 | − | 1.43400i | 0.0539313 | − | 0.0539313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.8807 | 1.34753 | 0.673764 | − | 0.738947i | \(-0.264677\pi\) | ||||
0.673764 | + | 0.738947i | \(0.264677\pi\) | |||||||
\(710\) | −0.371008 | + | 21.9890i | −0.0139237 | + | 0.825232i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4603 | + | 32.3907i | −0.429492 | + | 1.21389i | ||||
\(713\) | −20.1192 | + | 20.1192i | −0.753472 | + | 0.753472i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3973 | + | 20.0914i | 0.912407 | + | 0.751376i | ||||
\(716\) | −6.20121 | + | 26.8825i | −0.231750 | + | 1.00465i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.15462 | − | 45.2778i | 0.192369 | − | 1.68975i | ||||
\(719\) | 24.2588 | 0.904699 | 0.452350 | − | 0.891841i | \(-0.350586\pi\) | ||||
0.452350 | + | 0.891841i | \(0.350586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0532 | 0.448883 | ||||||||
\(722\) | 1.94163 | − | 17.0551i | 0.0722599 | − | 0.634726i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.24073 | + | 35.7239i | −0.306264 | + | 1.32767i | ||||
\(725\) | −2.03753 | − | 10.4274i | −0.0756720 | − | 0.387263i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7764 | − | 23.7764i | 0.881819 | − | 0.881819i | −0.111900 | − | 0.993719i | \(-0.535694\pi\) |
0.993719 | + | 0.111900i | \(0.0356936\pi\) | |||||||
\(728\) | 22.1804 | + | 7.84775i | 0.822061 | + | 0.290857i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.2346 | − | 18.8604i | −0.674892 | − | 0.698057i | ||||
\(731\) | −13.3255 | −0.492862 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.58667 | − | 1.58667i | 0.0586051 | − | 0.0586051i | −0.677197 | − | 0.735802i | \(-0.736805\pi\) |
0.735802 | + | 0.677197i | \(0.236805\pi\) | |||||||
\(734\) | −8.80567 | − | 11.0682i | −0.325023 | − | 0.408535i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.72001 | + | 34.7486i | 0.284563 | + | 1.28085i | ||||
\(737\) | 10.4188 | + | 10.4188i | 0.383782 | + | 0.383782i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6836 | −0.944786 | −0.472393 | − | 0.881388i | \(-0.656610\pi\) | ||||
−0.472393 | + | 0.881388i | \(0.656610\pi\) | |||||||
\(740\) | −25.2178 | + | 19.3772i | −0.927024 | + | 0.712322i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.13985 | + | 27.5802i | −0.115268 | + | 1.01250i | ||||
\(743\) | 0.375129 | − | 0.375129i | 0.0137622 | − | 0.0137622i | −0.700192 | − | 0.713954i | \(-0.746902\pi\) |
0.713954 | + | 0.700192i | \(0.246902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2718 | − | 1.18774i | 0.449604 | − | 0.0435153i | ||||
\(746\) | 6.62793 | + | 8.33091i | 0.242666 | + | 0.305016i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −46.5021 | − | 74.3890i | −1.70028 | − | 2.71993i | ||||
\(749\) | 8.09000i | 0.295602i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.4813 | 1.84209 | 0.921045 | − | 0.389457i | \(-0.127337\pi\) | ||||
0.921045 | + | 0.389457i | \(0.127337\pi\) | |||||||
\(752\) | 1.56649 | + | 4.54409i | 0.0571240 | + | 0.165706i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.96053 | + | 4.74210i | −0.217070 | + | 0.172697i | ||||
\(755\) | −3.16749 | − | 32.7268i | −0.115277 | − | 1.19105i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.30248 | − | 7.30248i | −0.265413 | − | 0.265413i | 0.561836 | − | 0.827249i | \(-0.310095\pi\) |
−0.827249 | + | 0.561836i | \(0.810095\pi\) | |||||||
\(758\) | −3.16112 | + | 27.7670i | −0.114817 | + | 1.00854i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.0787 | + | 3.99585i | 0.583237 | + | 0.144945i | ||||
\(761\) | − | 13.1137i | − | 0.475371i | −0.971342 | − | 0.237685i | \(-0.923611\pi\) | ||
0.971342 | − | 0.237685i | \(-0.0763887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.1545 | + | 35.1545i | −1.27268 | + | 1.27268i | ||||
\(764\) | −5.49377 | + | 23.8157i | −0.198758 | + | 0.861623i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.4601 | + | 20.6893i | 0.594726 | + | 0.747535i | ||||
\(767\) | 14.4994 | + | 14.4994i | 0.523541 | + | 0.523541i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1276i | 0.581577i | 0.956787 | + | 0.290788i | \(0.0939175\pi\) | ||||
−0.956787 | + | 0.290788i | \(0.906082\pi\) | |||||||
\(770\) | 41.6073 | − | 40.2265i | 1.49942 | − | 1.44966i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.51700 | + | 4.02643i | 0.0905889 | + | 0.144914i | ||||
\(773\) | 7.60986 | + | 7.60986i | 0.273708 | + | 0.273708i | 0.830591 | − | 0.556883i | \(-0.188003\pi\) |
−0.556883 | + | 0.830591i | \(0.688003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.1889 | − | 4.33576i | 0.797049 | − | 0.155745i | ||||
\(776\) | −7.05622 | − | 14.7834i | −0.253304 | − | 0.530693i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.0943 | − | 4.33682i | −1.36575 | − | 0.155482i | ||||
\(779\) | − | 4.53753i | − | 0.162574i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 38.7816i | − | 1.38771i | ||||||
\(782\) | 7.91777 | − | 69.5491i | 0.283139 | − | 2.48707i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.60687 | − | 13.5585i | 0.235960 | − | 0.484232i | ||||
\(785\) | −22.8233 | + | 27.7147i | −0.814598 | + | 0.989179i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1198 | − | 24.1198i | −0.859779 | − | 0.859779i | 0.131533 | − | 0.991312i | \(-0.458010\pi\) |
−0.991312 | + | 0.131533i | \(0.958010\pi\) | |||||||
\(788\) | −10.6422 | + | 6.65267i | −0.379114 | + | 0.236992i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.134545 | − | 7.97426i | 0.00478690 | − | 0.283711i | ||||
\(791\) | 11.2129i | 0.398683i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.62386 | − | 5.62386i | −0.199709 | − | 0.199709i | ||||
\(794\) | 13.5940 | − | 10.8151i | 0.482432 | − | 0.383815i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.28574 | + | 31.5840i | −0.258236 | + | 1.11946i | ||||
\(797\) | 9.34128 | − | 9.34128i | 0.330885 | − | 0.330885i | −0.522037 | − | 0.852923i | \(-0.674828\pi\) |
0.852923 | + | 0.522037i | \(0.174828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.45191i | − | 0.334385i | ||||||
\(800\) | 10.3284 | − | 26.3310i | 0.365165 | − | 0.930943i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.35547 | − | 0.495845i | −0.153797 | − | 0.0175089i | ||||
\(803\) | 32.7119 | + | 32.7119i | 1.15438 | + | 1.15438i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.9627 | − | 4.44854i | 1.61997 | − | 0.156791i | ||||
\(806\) | −10.0909 | − | 12.6837i | −0.355438 | − | 0.446765i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.582979 | + | 1.64770i | −0.0205091 | + | 0.0579658i | ||||
\(809\) | 8.47429 | 0.297940 | 0.148970 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148970 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.25683i | − | 0.0792481i | −0.999215 | − | 0.0396240i | \(-0.987384\pi\) | ||
0.999215 | − | 0.0396240i | \(-0.0126160\pi\) | |||||||
\(812\) | 7.39311 | + | 11.8267i | 0.259447 | + | 0.415036i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 43.8870 | − | 34.9158i | 1.53824 | − | 1.22380i | ||||
\(815\) | −28.6204 | − | 23.5692i | −1.00253 | − | 0.825592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.13802 | + | 3.13802i | −0.109785 | + | 0.109785i | ||||
\(818\) | −19.8241 | − | 2.25686i | −0.693132 | − | 0.0789092i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.68080 | − | 1.00594i | −0.268225 | − | 0.0351290i | ||||
\(821\) | −25.8885 | −0.903515 | −0.451757 | − | 0.892141i | \(-0.649203\pi\) | ||||
−0.451757 | + | 0.892141i | \(0.649203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.4100 | − | 32.4100i | −1.12974 | − | 1.12974i | −0.990219 | − | 0.139522i | \(-0.955443\pi\) |
−0.139522 | − | 0.990219i | \(-0.544557\pi\) | |||||||
\(824\) | −9.37470 | + | 4.47461i | −0.326583 | + | 0.155881i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.3831 | − | 23.3767i | 1.02237 | − | 0.813378i | ||||
\(827\) | −18.2295 | + | 18.2295i | −0.633901 | + | 0.633901i | −0.949044 | − | 0.315143i | \(-0.897947\pi\) |
0.315143 | + | 0.949044i | \(0.397947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3355 | −0.497894 | −0.248947 | − | 0.968517i | \(-0.580085\pi\) | ||||
−0.248947 | + | 0.968517i | \(0.580085\pi\) | |||||||
\(830\) | −2.15821 | − | 2.23229i | −0.0749126 | − | 0.0774839i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.1649 | + | 2.13044i | −0.699091 | + | 0.0738597i | ||||
\(833\) | −20.9724 | + | 20.9724i | −0.726652 | + | 0.726652i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.9211 | + | 19.3333i | −0.550974 | + | 0.669056i | ||||
\(836\) | −28.4686 | − | 6.56708i | −0.984606 | − | 0.227127i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42.8211 | + | 4.87493i | 1.47923 | + | 0.168402i | ||||
\(839\) | 29.2314 | 1.00918 | 0.504590 | − | 0.863359i | \(-0.331644\pi\) | ||||
0.504590 | + | 0.863359i | \(0.331644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.4847 | 0.844301 | ||||||||
\(842\) | 53.4802 | + | 6.08842i | 1.84305 | + | 0.209821i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.1734 | + | 44.1022i | −0.350184 | + | 1.51806i | ||||
\(845\) | 14.6351 | − | 1.41648i | 0.503464 | − | 0.0487283i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.6375 | + | 46.6375i | −1.60248 | + | 1.60248i | ||||
\(848\) | −7.79678 | − | 22.6170i | −0.267742 | − | 0.776671i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −36.0770 | + | 42.3328i | −1.23743 | + | 1.45200i | ||||
\(851\) | 44.7480 | 1.53394 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2054 | + | 28.2054i | −0.965735 | + | 0.965735i | −0.999432 | − | 0.0336967i | \(-0.989272\pi\) |
0.0336967 | + | 0.999432i | \(0.489272\pi\) | |||||||
\(854\) | −11.3968 | + | 9.06710i | −0.389990 | + | 0.310270i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00333 | − | 6.29224i | −0.102652 | − | 0.215064i | ||||
\(857\) | −12.8982 | − | 12.8982i | −0.440593 | − | 0.440593i | 0.451619 | − | 0.892211i | \(-0.350847\pi\) |
−0.892211 | + | 0.451619i | \(0.850847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2270 | 0.485421 | 0.242710 | − | 0.970099i | \(-0.421964\pi\) | ||||
0.242710 | + | 0.970099i | \(0.421964\pi\) | |||||||
\(860\) | 4.61613 | + | 6.00749i | 0.157409 | + | 0.204854i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.1611 | + | 4.79980i | 1.43601 | + | 0.163482i | ||||
\(863\) | 3.78453 | − | 3.78453i | 0.128827 | − | 0.128827i | −0.639753 | − | 0.768580i | \(-0.720964\pi\) |
0.768580 | + | 0.639753i | \(0.220964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5260 | + | 17.6392i | −0.493900 | + | 0.599750i | ||||
\(866\) | −32.3187 | + | 25.7122i | −1.09823 | + | 0.873737i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −25.1666 | + | 15.7322i | −0.854210 | + | 0.533984i | ||||
\(869\) | 14.0641i | 0.477090i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.69716 | −0.226924 | ||||||||
\(872\) | 14.2917 | − | 40.3932i | 0.483978 | − | 1.36789i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.5135 | − | 18.2426i | −0.490928 | − | 0.617066i | ||||
\(875\) | −32.2717 | − | 17.4604i | −1.09098 | − | 0.590271i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4253 | + | 18.4253i | 0.622177 | + | 0.622177i | 0.946088 | − | 0.323910i | \(-0.104998\pi\) |
−0.323910 | + | 0.946088i | \(0.604998\pi\) | |||||||
\(878\) | 0.319023 | + | 0.0363189i | 0.0107665 | + | 0.00122571i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.4276 | + | 46.7336i | −0.587483 | + | 1.57539i | ||||
\(881\) | − | 2.06935i | − | 0.0697181i | −0.999392 | − | 0.0348591i | \(-0.988902\pi\) | ||
0.999392 | − | 0.0348591i | \(-0.0110982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.3458 | + | 37.3458i | −1.25679 | + | 1.25679i | −0.304170 | + | 0.952618i | \(0.598379\pi\) |
−0.952618 | + | 0.304170i | \(0.901621\pi\) | |||||||
\(884\) | 38.8541 | + | 8.96279i | 1.30680 | + | 0.301451i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.5747 | − | 20.3468i | 0.859199 | − | 0.683564i | ||||
\(887\) | −20.7113 | − | 20.7113i | −0.695418 | − | 0.695418i | 0.268001 | − | 0.963419i | \(-0.413637\pi\) |
−0.963419 | + | 0.268001i | \(0.913637\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.51188i | − | 0.218401i | ||||||
\(890\) | −38.4083 | − | 0.648041i | −1.28745 | − | 0.0217224i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.2556 | − | 26.0040i | −0.544278 | − | 0.870677i | ||||
\(893\) | −2.22583 | − | 2.22583i | −0.0744844 | − | 0.0744844i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.7014 | + | 2.97147i | −1.02623 | + | 0.0993251i | ||||
\(896\) | −0.300591 | + | 37.1289i | −0.0100420 | + | 1.24039i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.43446 | − | 30.1680i | 0.114609 | − | 1.00672i | ||||
\(899\) | − | 9.60824i | − | 0.320453i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.0443i | 1.56727i | ||||||||
\(902\) | 13.5726 | + | 1.54516i | 0.451917 | + | 0.0514482i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.16266 | − | 8.72113i | −0.138448 | − | 0.290061i | ||||
\(905\) | −40.7988 | + | 3.94875i | −1.35620 | + | 0.131261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.5449 | − | 10.5449i | −0.350139 | − | 0.350139i | 0.510022 | − | 0.860161i | \(-0.329637\pi\) |
−0.860161 | + | 0.510022i | \(0.829637\pi\) | |||||||
\(908\) | −30.2619 | + | 18.9173i | −1.00428 | + | 0.627794i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.443764 | + | 26.3011i | −0.0147106 | + | 0.871874i | ||||
\(911\) | 26.8997i | 0.891226i | 0.895226 | + | 0.445613i | \(0.147014\pi\) | ||||
−0.895226 | + | 0.445613i | \(0.852986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.87172 | + | 3.87172i | 0.128135 | + | 0.128135i | ||||
\(914\) | −24.2197 | − | 30.4427i | −0.801117 | − | 1.00696i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.15772 | + | 0.267060i | 0.0382520 | + | 0.00882392i | ||||
\(917\) | 16.5735 | − | 16.5735i | 0.547306 | − | 0.547306i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3696i | 1.00180i | 0.865505 | + | 0.500900i | \(0.166998\pi\) | ||||
−0.865505 | + | 0.500900i | \(0.833002\pi\) | |||||||
\(920\) | −34.0973 | + | 20.5232i | −1.12416 | + | 0.676629i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.08028 | + | 27.0569i | −0.101443 | + | 0.891072i | ||||
\(923\) | 12.4643 | + | 12.4643i | 0.410267 | + | 0.410267i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.4973 | − | 19.8539i | −0.969864 | − | 0.652793i | ||||
\(926\) | −16.6112 | + | 13.2156i | −0.545878 | + | 0.434291i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.1408 | − | 6.45395i | −0.332886 | − | 0.211861i | ||||
\(929\) | 31.6162 | 1.03729 | 0.518646 | − | 0.854989i | \(-0.326436\pi\) | ||||
0.518646 | + | 0.854989i | \(0.326436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.87758i | 0.323724i | ||||||||
\(932\) | 12.2983 | − | 7.68794i | 0.402846 | − | 0.251827i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.42554 | + | 3.04876i | 0.0793660 | + | 0.0997583i | ||||
\(935\) | 62.3510 | − | 75.7137i | 2.03910 | − | 2.47610i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.51188 | + | 3.51188i | −0.114728 | + | 0.114728i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.647412 | + | 0.762140i | \(0.275851\pi\) | |||||||
\(938\) | −1.38716 | + | 12.1847i | −0.0452923 | + | 0.397844i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.26116 | + | 3.27426i | −0.138984 | + | 0.106795i | ||||
\(941\) | 24.7342 | 0.806312 | 0.403156 | − | 0.915131i | \(-0.367913\pi\) | ||||
0.403156 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.70715 | + | 7.70715i | 0.250979 | + | 0.250979i | ||||
\(944\) | −14.1752 | + | 29.0901i | −0.461363 | + | 0.946801i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.31779 | − | 10.4550i | −0.270435 | − | 0.339920i | ||||
\(947\) | −23.0920 | + | 23.0920i | −0.750389 | + | 0.750389i | −0.974552 | − | 0.224163i | \(-0.928035\pi\) |
0.224163 | + | 0.974552i | \(0.428035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0270 | −0.682566 | ||||||||
\(950\) | 1.47317 | + | 18.4647i | 0.0477961 | + | 0.599074i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.3544 | − | 68.8339i | 0.789332 | − | 2.23092i | ||||
\(953\) | 32.1149 | − | 32.1149i | 1.04030 | − | 1.04030i | 0.0411513 | − | 0.999153i | \(-0.486897\pi\) |
0.999153 | − | 0.0411513i | \(-0.0131026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.1990 | + | 2.63248i | −0.880138 | + | 0.0851850i | ||||
\(956\) | 21.7453 | + | 5.01617i | 0.703293 | + | 0.162235i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.18914 | + | 28.0132i | −0.103037 | + | 0.905065i | ||||
\(959\) | −30.5648 | −0.986990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5542 | −0.340457 | ||||||||
\(962\) | −2.88334 | + | 25.3270i | −0.0929625 | + | 0.816575i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 38.9191 | + | 8.97779i | 1.25350 | + | 0.289155i | ||||
\(965\) | −3.37485 | + | 4.09813i | −0.108640 | + | 0.131924i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3972 | + | 29.3972i | −0.945349 | + | 0.945349i | −0.998582 | − | 0.0532327i | \(-0.983047\pi\) |
0.0532327 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(968\) | 18.9600 | − | 53.5874i | 0.609397 | − | 1.72236i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.1670 | − | 12.7300i | 0.422767 | − | 0.408737i | ||||
\(971\) | −40.7956 | −1.30919 | −0.654596 | − | 0.755979i | \(-0.727161\pi\) | ||||
−0.654596 | + | 0.755979i | \(0.727161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.1733 | − | 35.1733i | 1.12760 | − | 1.12760i | ||||
\(974\) | 23.0864 | + | 29.0182i | 0.739735 | + | 0.929802i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.49813 | − | 11.2831i | 0.175991 | − | 0.361165i | ||||
\(977\) | −8.32380 | − | 8.32380i | −0.266302 | − | 0.266302i | 0.561306 | − | 0.827608i | \(-0.310299\pi\) |
−0.827608 | + | 0.561306i | \(0.810299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 67.7400 | 2.16498 | ||||||||
\(980\) | 16.7200 | + | 2.18979i | 0.534102 | + | 0.0699504i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.173112 | + | 1.52061i | −0.00552423 | + | 0.0485245i | ||||
\(983\) | −16.0382 | + | 16.0382i | −0.511539 | + | 0.511539i | −0.914998 | − | 0.403458i | \(-0.867808\pi\) |
0.403458 | + | 0.914998i | \(0.367808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8317 | − | 8.92005i | −0.345128 | − | 0.284216i | ||||
\(986\) | 14.7165 | + | 18.4977i | 0.468668 | + | 0.589087i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.2604 | − | 7.03908i | 0.358240 | − | 0.223943i | ||||
\(989\) | − | 10.6601i | − | 0.338970i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7160 | 0.753362 | 0.376681 | − | 0.926343i | \(-0.377065\pi\) | ||||
0.376681 | + | 0.926343i | \(0.377065\pi\) | |||||||
\(992\) | 13.7337 | − | 21.5790i | 0.436044 | − | 0.685134i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.2590 | − | 20.0956i | 0.801167 | − | 0.637395i | ||||
\(995\) | −36.0708 | + | 3.49114i | −1.14352 | + | 0.110677i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.4793 | − | 22.4793i | −0.711926 | − | 0.711926i | 0.255012 | − | 0.966938i | \(-0.417921\pi\) |
−0.966938 | + | 0.255012i | \(0.917921\pi\) | |||||||
\(998\) | 2.66139 | − | 23.3774i | 0.0842447 | − | 0.739999i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 360.2.x.a.53.12 | yes | 48 | |
3.2 | odd | 2 | inner | 360.2.x.a.53.13 | yes | 48 | |
4.3 | odd | 2 | 1440.2.bj.a.593.12 | 48 | |||
5.2 | odd | 4 | inner | 360.2.x.a.197.1 | yes | 48 | |
8.3 | odd | 2 | 1440.2.bj.a.593.13 | 48 | |||
8.5 | even | 2 | inner | 360.2.x.a.53.24 | yes | 48 | |
12.11 | even | 2 | 1440.2.bj.a.593.14 | 48 | |||
15.2 | even | 4 | inner | 360.2.x.a.197.24 | yes | 48 | |
20.7 | even | 4 | 1440.2.bj.a.17.11 | 48 | |||
24.5 | odd | 2 | inner | 360.2.x.a.53.1 | ✓ | 48 | |
24.11 | even | 2 | 1440.2.bj.a.593.11 | 48 | |||
40.27 | even | 4 | 1440.2.bj.a.17.14 | 48 | |||
40.37 | odd | 4 | inner | 360.2.x.a.197.13 | yes | 48 | |
60.47 | odd | 4 | 1440.2.bj.a.17.13 | 48 | |||
120.77 | even | 4 | inner | 360.2.x.a.197.12 | yes | 48 | |
120.107 | odd | 4 | 1440.2.bj.a.17.12 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.1 | ✓ | 48 | 24.5 | odd | 2 | inner | |
360.2.x.a.53.12 | yes | 48 | 1.1 | even | 1 | trivial | |
360.2.x.a.53.13 | yes | 48 | 3.2 | odd | 2 | inner | |
360.2.x.a.53.24 | yes | 48 | 8.5 | even | 2 | inner | |
360.2.x.a.197.1 | yes | 48 | 5.2 | odd | 4 | inner | |
360.2.x.a.197.12 | yes | 48 | 120.77 | even | 4 | inner | |
360.2.x.a.197.13 | yes | 48 | 40.37 | odd | 4 | inner | |
360.2.x.a.197.24 | yes | 48 | 15.2 | even | 4 | inner | |
1440.2.bj.a.17.11 | 48 | 20.7 | even | 4 | |||
1440.2.bj.a.17.12 | 48 | 120.107 | odd | 4 | |||
1440.2.bj.a.17.13 | 48 | 60.47 | odd | 4 | |||
1440.2.bj.a.17.14 | 48 | 40.27 | even | 4 | |||
1440.2.bj.a.593.11 | 48 | 24.11 | even | 2 | |||
1440.2.bj.a.593.12 | 48 | 4.3 | odd | 2 | |||
1440.2.bj.a.593.13 | 48 | 8.3 | odd | 2 | |||
1440.2.bj.a.593.14 | 48 | 12.11 | even | 2 |