Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(199,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.da (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 244.1 | ||
Character | \(\chi\) | \(=\) | 855.244 |
Dual form | 855.2.da.b.424.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72697 | + | 2.05812i | −1.22115 | + | 1.45531i | −0.371115 | + | 0.928587i | \(0.621024\pi\) |
−0.850036 | + | 0.526724i | \(0.823420\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.906145 | − | 5.13900i | −0.453073 | − | 2.56950i | ||||
\(5\) | 1.71358 | − | 1.43654i | 0.766337 | − | 0.642439i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41018 | + | 1.39152i | −0.910961 | + | 0.525944i | −0.880740 | − | 0.473600i | \(-0.842954\pi\) |
−0.0302209 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(8\) | 7.48810 | + | 4.32326i | 2.64744 | + | 1.52850i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.00273678 | + | 6.00761i | −0.000865447 | + | 1.89977i | ||||
\(11\) | −1.19000 | + | 2.06113i | −0.358797 | + | 0.621455i | −0.987760 | − | 0.155980i | \(-0.950146\pi\) |
0.628963 | + | 0.777435i | \(0.283480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0138492 | − | 0.0380504i | 0.00384108 | − | 0.0105533i | −0.937757 | − | 0.347291i | \(-0.887101\pi\) |
0.941598 | + | 0.336738i | \(0.109324\pi\) | |||||||
\(14\) | 1.29839 | − | 7.36354i | 0.347010 | − | 1.96799i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.0223 | + | 4.37577i | −3.00558 | + | 1.09394i | ||||
\(17\) | 1.16714 | − | 1.39094i | 0.283073 | − | 0.337353i | −0.605707 | − | 0.795688i | \(-0.707109\pi\) |
0.888780 | + | 0.458335i | \(0.151554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.07652 | − | 1.54336i | 0.935219 | − | 0.354071i | ||||
\(20\) | −8.93512 | − | 7.50439i | −1.99795 | − | 1.67803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.18698 | − | 6.00867i | −0.466265 | − | 1.28105i | ||||
\(23\) | −2.50568 | + | 0.441819i | −0.522471 | + | 0.0921257i | −0.428663 | − | 0.903465i | \(-0.641015\pi\) |
−0.0938080 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.872727 | − | 4.92325i | 0.174545 | − | 0.984649i | ||||
\(26\) | 0.0543952 | + | 0.0942153i | 0.0106678 | + | 0.0184771i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.33498 | + | 11.1250i | 1.76414 | + | 2.10243i | ||||
\(29\) | 2.25845 | − | 1.89507i | 0.419384 | − | 0.351905i | −0.408545 | − | 0.912738i | \(-0.633964\pi\) |
0.827929 | + | 0.560833i | \(0.189519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.44307 | + | 2.49947i | 0.259183 | + | 0.448918i | 0.966023 | − | 0.258455i | \(-0.0832134\pi\) |
−0.706840 | + | 0.707373i | \(0.749880\pi\) | |||||||
\(32\) | 5.84176 | − | 16.0501i | 1.03269 | − | 2.83728i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.847116 | + | 4.80423i | 0.145279 | + | 0.823919i | ||||
\(35\) | −2.13107 | + | 5.84678i | −0.360217 | + | 0.988287i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.227089i | 0.0373333i | 0.999826 | + | 0.0186666i | \(0.00594212\pi\) | ||||
−0.999826 | + | 0.0186666i | \(0.994058\pi\) | |||||||
\(38\) | −3.86361 | + | 11.0553i | −0.626761 | + | 1.79341i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19.0420 | − | 3.34867i | 3.01080 | − | 0.529472i | ||||
\(41\) | 7.55269 | − | 2.74896i | 1.17953 | − | 0.429315i | 0.323496 | − | 0.946230i | \(-0.395142\pi\) |
0.856037 | + | 0.516915i | \(0.172920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.05471 | + | 0.891282i | 0.770836 | + | 0.135919i | 0.545215 | − | 0.838296i | \(-0.316448\pi\) |
0.225621 | + | 0.974215i | \(0.427559\pi\) | |||||||
\(44\) | 11.6705 | + | 4.24771i | 1.75939 | + | 0.640366i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.41791 | − | 5.92000i | 0.503944 | − | 0.872857i | ||||
\(47\) | 7.11977 | + | 8.48501i | 1.03853 | + | 1.23767i | 0.970782 | + | 0.239964i | \(0.0771355\pi\) |
0.0677434 | + | 0.997703i | \(0.478420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.372635 | − | 0.645423i | 0.0532336 | − | 0.0922032i | ||||
\(50\) | 8.62546 | + | 10.2985i | 1.21982 | + | 1.45642i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.208091 | − | 0.0366920i | −0.0288570 | − | 0.00508827i | ||||
\(53\) | 5.62767 | − | 0.992310i | 0.773020 | − | 0.136304i | 0.226794 | − | 0.973943i | \(-0.427175\pi\) |
0.546225 | + | 0.837638i | \(0.316064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.921737 | + | 5.24139i | 0.124287 | + | 0.706749i | ||||
\(56\) | −24.0635 | −3.21562 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.92088i | 1.04006i | ||||||||
\(59\) | 8.89878 | + | 7.46696i | 1.15852 | + | 0.972116i | 0.999884 | − | 0.0152208i | \(-0.00484512\pi\) |
0.158638 | + | 0.987337i | \(0.449290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.795974 | + | 4.51419i | 0.101914 | + | 0.577983i | 0.992408 | + | 0.122988i | \(0.0392477\pi\) |
−0.890494 | + | 0.454995i | \(0.849641\pi\) | |||||||
\(62\) | −7.63635 | − | 1.34649i | −0.969817 | − | 0.171005i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.1506 | + | 17.5814i | 1.26883 | + | 2.19767i | ||||
\(65\) | −0.0309291 | − | 0.0850975i | −0.00383628 | − | 0.0105550i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.11931 | − | 3.71745i | −0.381084 | − | 0.454159i | 0.541072 | − | 0.840976i | \(-0.318019\pi\) |
−0.922156 | + | 0.386818i | \(0.873574\pi\) | |||||||
\(68\) | −8.20566 | − | 4.73754i | −0.995083 | − | 0.574511i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.35309 | − | 14.4832i | −0.998386 | − | 1.73108i | ||||
\(71\) | 1.34912 | − | 7.65124i | 0.160111 | − | 0.908035i | −0.793852 | − | 0.608111i | \(-0.791928\pi\) |
0.953963 | − | 0.299924i | \(-0.0969614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.45279 | + | 3.99151i | 0.170036 | + | 0.467171i | 0.995216 | − | 0.0976997i | \(-0.0311485\pi\) |
−0.825180 | + | 0.564870i | \(0.808926\pi\) | |||||||
\(74\) | −0.467377 | − | 0.392176i | −0.0543315 | − | 0.0455896i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.6252 | − | 19.5508i | −1.33351 | − | 2.24263i | ||||
\(77\) | − | 6.62359i | − | 0.754828i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9102 | − | 3.97100i | 1.22750 | − | 0.446773i | 0.354758 | − | 0.934958i | \(-0.384563\pi\) |
0.872740 | + | 0.488185i | \(0.162341\pi\) | |||||||
\(80\) | −14.3153 | + | 24.7688i | −1.60050 | + | 2.76923i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.38558 | + | 20.2917i | −0.815601 | + | 2.24085i | ||||
\(83\) | −3.87161 | + | 2.23528i | −0.424965 | + | 0.245354i | −0.697199 | − | 0.716877i | \(-0.745571\pi\) |
0.272234 | + | 0.962231i | \(0.412237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.00184961 | − | 4.06014i | 0.000200618 | − | 0.440383i | ||||
\(86\) | −10.5637 | + | 8.86399i | −1.13911 | + | 0.955828i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.8216 | + | 10.2893i | −1.89979 | + | 1.09684i | ||||
\(89\) | −14.4648 | − | 5.26476i | −1.53327 | − | 0.558064i | −0.568849 | − | 0.822442i | \(-0.692611\pi\) |
−0.964419 | + | 0.264378i | \(0.914833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0195687 | + | 0.110980i | 0.00205136 | + | 0.0116338i | ||||
\(92\) | 4.54102 | + | 12.4764i | 0.473434 | + | 1.30075i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29.7588 | −3.06939 | ||||||||
\(95\) | 4.76837 | − | 8.50074i | 0.489224 | − | 0.872158i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.59666 | − | 4.28633i | 0.365185 | − | 0.435211i | −0.551895 | − | 0.833914i | \(-0.686095\pi\) |
0.917080 | + | 0.398703i | \(0.130540\pi\) | |||||||
\(98\) | 0.684829 | + | 1.88155i | 0.0691782 | + | 0.190066i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −26.0914 | − | 0.0237720i | −2.60914 | − | 0.00237720i | ||||
\(101\) | 11.2361 | + | 4.08961i | 1.11804 | + | 0.406932i | 0.833935 | − | 0.551863i | \(-0.186083\pi\) |
0.284101 | + | 0.958794i | \(0.408305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2058 | + | 7.04702i | 1.20267 | + | 0.694363i | 0.961149 | − | 0.276031i | \(-0.0890194\pi\) |
0.241524 | + | 0.970395i | \(0.422353\pi\) | |||||||
\(104\) | 0.268206 | − | 0.225052i | 0.0262998 | − | 0.0220681i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.67651 | + | 13.2961i | −0.745609 | + | 1.29143i | ||||
\(107\) | −10.1541 | + | 5.86249i | −0.981637 | + | 0.566748i | −0.902764 | − | 0.430137i | \(-0.858465\pi\) |
−0.0788727 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.16558 | − | 6.61032i | 0.111642 | − | 0.633154i | −0.876716 | − | 0.481008i | \(-0.840271\pi\) |
0.988358 | − | 0.152145i | \(-0.0486182\pi\) | |||||||
\(110\) | −12.3792 | − | 7.15467i | −1.18031 | − | 0.682171i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 22.8870 | − | 27.2757i | 2.16262 | − | 2.57731i | ||||
\(113\) | − | 2.46603i | − | 0.231985i | −0.993250 | − | 0.115992i | \(-0.962995\pi\) | ||
0.993250 | − | 0.115992i | \(-0.0370048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65900 | + | 4.35660i | −0.341204 | + | 0.406255i | ||||
\(116\) | −11.7852 | − | 9.88899i | −1.09423 | − | 0.918169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −30.7358 | + | 5.41956i | −2.82946 | + | 0.498911i | ||||
\(119\) | −0.877494 | + | 4.97651i | −0.0804397 | + | 0.456196i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.66782 | + | 4.62080i | 0.242529 | + | 0.420073i | ||||
\(122\) | −10.6654 | − | 6.15765i | −0.965597 | − | 0.557488i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.5372 | − | 9.68082i | 1.03607 | − | 0.869364i | ||||
\(125\) | −5.57693 | − | 9.69009i | −0.498816 | − | 0.866708i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.252761 | + | 0.694456i | −0.0224289 | + | 0.0616230i | −0.950402 | − | 0.311025i | \(-0.899328\pi\) |
0.927973 | + | 0.372648i | \(0.121550\pi\) | |||||||
\(128\) | −20.0731 | − | 3.53942i | −1.77423 | − | 0.312844i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.228554 | + | 0.0833049i | 0.0200455 | + | 0.00730632i | ||||
\(131\) | 8.35925 | + | 7.01424i | 0.730351 | + | 0.612837i | 0.930227 | − | 0.366984i | \(-0.119610\pi\) |
−0.199876 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.67754 | + | 9.39231i | −0.665727 | + | 0.814417i | ||||
\(134\) | 13.0379 | 1.12630 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.7531 | − | 5.36968i | 1.26506 | − | 0.460446i | ||||
\(137\) | −4.52066 | + | 0.797114i | −0.386226 | + | 0.0681021i | −0.363390 | − | 0.931637i | \(-0.618381\pi\) |
−0.0228361 | + | 0.999739i | \(0.507270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.37217 | − | 2.68325i | −0.625299 | − | 0.227590i | 0.00988487 | − | 0.999951i | \(-0.496853\pi\) |
−0.635184 | + | 0.772361i | \(0.719076\pi\) | |||||||
\(140\) | 31.9777 | + | 5.65355i | 2.70261 | + | 0.477813i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.4173 | + | 15.9901i | 1.12595 | + | 1.34186i | ||||
\(143\) | 0.0619465 | + | 0.0738250i | 0.00518023 | + | 0.00617355i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.14771 | − | 6.49170i | 0.0953122 | − | 0.539106i | ||||
\(146\) | −10.7239 | − | 3.90319i | −0.887518 | − | 0.323030i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.16701 | − | 0.205776i | 0.0959279 | − | 0.0169147i | ||||
\(149\) | 20.4289 | − | 7.43550i | 1.67360 | − | 0.609140i | 0.681188 | − | 0.732108i | \(-0.261463\pi\) |
0.992411 | + | 0.122968i | \(0.0392412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.68916 | 0.788493 | 0.394247 | − | 0.919005i | \(-0.371006\pi\) | ||||
0.394247 | + | 0.919005i | \(0.371006\pi\) | |||||||
\(152\) | 37.1977 | + | 6.06704i | 3.01714 | + | 0.492102i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.6322 | + | 11.4387i | 1.09851 | + | 0.921760i | ||||
\(155\) | 6.06340 | + | 2.21002i | 0.487024 | + | 0.177513i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.26744 | − | 1.28145i | −0.580005 | − | 0.102271i | −0.124054 | − | 0.992275i | \(-0.539590\pi\) |
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(158\) | −10.6688 | + | 29.3124i | −0.848767 | + | 2.33197i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.0462 | − | 35.8951i | −1.03139 | − | 2.83775i | ||||
\(161\) | 5.42434 | − | 4.55156i | 0.427498 | − | 0.358713i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.24622 | − | 2.45155i | −0.332589 | − | 0.192021i | 0.324401 | − | 0.945920i | \(-0.394837\pi\) |
−0.656990 | + | 0.753899i | \(0.728171\pi\) | |||||||
\(164\) | −20.9707 | − | 36.3224i | −1.63754 | − | 2.83630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.08568 | − | 11.8285i | 0.161880 | − | 0.918070i | ||||
\(167\) | 9.93844 | − | 1.75241i | 0.769059 | − | 0.135606i | 0.224666 | − | 0.974436i | \(-0.427871\pi\) |
0.544394 | + | 0.838830i | \(0.316760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.95732 | + | 8.35518i | 0.765948 | + | 0.642707i | ||||
\(170\) | 8.35305 | + | 7.01553i | 0.640650 | + | 0.538067i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 26.7838i | − | 2.04225i | ||||||
\(173\) | −3.13636 | + | 3.73777i | −0.238453 | + | 0.284177i | −0.871978 | − | 0.489545i | \(-0.837163\pi\) |
0.633525 | + | 0.773722i | \(0.281607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.74735 | + | 13.0803i | 0.358866 | + | 0.988778i | ||||
\(176\) | 5.28748 | − | 29.9868i | 0.398559 | − | 2.26034i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 35.8158 | − | 20.6783i | 2.68451 | − | 1.54990i | ||||
\(179\) | −11.9422 | + | 20.6845i | −0.892604 | + | 1.54604i | −0.0558613 | + | 0.998439i | \(0.517790\pi\) |
−0.836743 | + | 0.547597i | \(0.815543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.96682 | − | 1.65036i | 0.146193 | − | 0.122670i | −0.566758 | − | 0.823884i | \(-0.691803\pi\) |
0.712951 | + | 0.701214i | \(0.247358\pi\) | |||||||
\(182\) | −0.262204 | − | 0.151384i | −0.0194359 | − | 0.0112213i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.6729 | − | 7.52431i | −1.52403 | − | 0.554700i | ||||
\(185\) | 0.326222 | + | 0.389136i | 0.0239843 | + | 0.0286099i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.47803 | + | 4.06085i | 0.108084 | + | 0.296959i | ||||
\(188\) | 37.1530 | − | 44.2772i | 2.70966 | − | 3.22925i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.26074 | + | 24.4944i | 0.671845 | + | 1.77701i | ||||
\(191\) | −9.28746 | −0.672017 | −0.336008 | − | 0.941859i | \(-0.609077\pi\) | ||||
−0.336008 | + | 0.941859i | \(0.609077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.49293 | − | 23.3341i | −0.611334 | − | 1.67963i | −0.727254 | − | 0.686368i | \(-0.759204\pi\) |
0.115920 | − | 0.993259i | \(-0.463018\pi\) | |||||||
\(194\) | 2.61047 | + | 14.8047i | 0.187421 | + | 1.06292i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.65449 | − | 1.33013i | −0.261035 | − | 0.0950090i | ||||
\(197\) | −3.61406 | + | 2.08658i | −0.257491 | + | 0.148663i | −0.623190 | − | 0.782071i | \(-0.714164\pi\) |
0.365698 | + | 0.930733i | \(0.380830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.1492 | + | 14.3899i | −1.21567 | + | 1.02007i | −0.216635 | + | 0.976253i | \(0.569508\pi\) |
−0.999039 | + | 0.0438194i | \(0.986047\pi\) | |||||||
\(200\) | 27.8195 | − | 33.0927i | 1.96714 | − | 2.34001i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −27.8213 | + | 16.0627i | −1.95750 | + | 1.13016i | ||||
\(203\) | −2.80625 | + | 7.71012i | −0.196960 | + | 0.541144i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.99319 | − | 15.5603i | 0.628111 | − | 1.08678i | ||||
\(206\) | −35.5826 | + | 12.9510i | −2.47916 | + | 0.902340i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.518056i | 0.0359207i | ||||||||
\(209\) | −1.66998 | + | 10.2388i | −0.115515 | + | 0.708236i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.28817 | + | 1.08090i | 0.0886814 | + | 0.0744125i | 0.686051 | − | 0.727554i | \(-0.259343\pi\) |
−0.597369 | + | 0.801966i | \(0.703787\pi\) | |||||||
\(212\) | −10.1990 | − | 28.0214i | −0.700468 | − | 1.92452i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.47015 | − | 31.0228i | 0.373932 | − | 2.12067i | ||||
\(215\) | 9.94202 | − | 5.73399i | 0.678040 | − | 0.391055i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.95611 | − | 4.01611i | −0.472211 | − | 0.272631i | ||||
\(218\) | 11.5919 | + | 13.8147i | 0.785104 | + | 0.935650i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 26.1003 | − | 9.48627i | 1.75968 | − | 0.639564i | ||||
\(221\) | −0.0367620 | − | 0.0636737i | −0.00247288 | − | 0.00428316i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.46555 | + | 1.66903i | 0.633860 | + | 0.111767i | 0.481340 | − | 0.876534i | \(-0.340150\pi\) |
0.152520 | + | 0.988300i | \(0.451261\pi\) | |||||||
\(224\) | 8.25431 | + | 46.8125i | 0.551514 | + | 3.12779i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.07539 | + | 4.25876i | 0.337610 | + | 0.283288i | ||||
\(227\) | − | 23.4650i | − | 1.55743i | −0.627379 | − | 0.778714i | \(-0.715872\pi\) | ||
0.627379 | − | 0.778714i | \(-0.284128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.19088 | 0.0786952 | 0.0393476 | − | 0.999226i | \(-0.487472\pi\) | ||||
0.0393476 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(230\) | −2.64742 | − | 15.0544i | −0.174566 | − | 0.992656i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.1044 | − | 4.42658i | 1.64818 | − | 0.290619i | ||||
\(233\) | 22.7889 | + | 4.01831i | 1.49295 | + | 0.263248i | 0.859741 | − | 0.510730i | \(-0.170625\pi\) |
0.633212 | + | 0.773978i | \(0.281736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.3893 | + | 4.31196i | 1.59099 | + | 0.281281i | ||||
\(236\) | 30.3092 | − | 52.4970i | 1.97296 | − | 3.41727i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.72686 | − | 10.4003i | −0.565679 | − | 0.674149i | ||||
\(239\) | −4.84358 | + | 8.38932i | −0.313305 | + | 0.542660i | −0.979076 | − | 0.203496i | \(-0.934770\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8334 | − | 5.39891i | −0.955503 | − | 0.347775i | −0.183233 | − | 0.983070i | \(-0.558656\pi\) |
−0.772270 | + | 0.635295i | \(0.780879\pi\) | |||||||
\(242\) | −14.1174 | − | 2.48928i | −0.907502 | − | 0.160017i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.4772 | − | 8.18102i | 1.43895 | − | 0.523736i | ||||
\(245\) | −0.288633 | − | 1.64129i | −0.0184401 | − | 0.104858i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.00226874 | − | 0.176488i | −0.000144356 | − | 0.0112297i | ||||
\(248\) | 24.9550i | 1.58465i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.5746 | + | 5.25648i | 1.87046 | + | 0.332449i | ||||
\(251\) | −0.951469 | − | 5.39605i | −0.0600562 | − | 0.340596i | 0.939944 | − | 0.341330i | \(-0.110877\pi\) |
−1.00000 | 0.000734411i | \(0.999766\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.07110 | − | 5.69030i | 0.130209 | − | 0.357746i | ||||
\(254\) | −0.992764 | − | 1.71952i | −0.0622915 | − | 0.107892i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.8468 | − | 9.10155i | 0.677926 | − | 0.568847i | ||||
\(257\) | −2.28060 | − | 2.71792i | −0.142260 | − | 0.169539i | 0.690210 | − | 0.723609i | \(-0.257518\pi\) |
−0.832470 | + | 0.554070i | \(0.813074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.315999 | − | 0.547326i | −0.0196352 | − | 0.0340092i | ||||
\(260\) | −0.409290 | + | 0.236055i | −0.0253831 | + | 0.0146395i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −28.8723 | + | 5.09097i | −1.78374 | + | 0.314521i | ||||
\(263\) | −9.01141 | − | 24.7587i | −0.555668 | − | 1.52668i | −0.825858 | − | 0.563877i | \(-0.809309\pi\) |
0.270191 | − | 0.962807i | \(-0.412913\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.21798 | − | 9.78475i | 0.504827 | − | 0.601073i | ||||
\(266\) | −6.07166 | − | 32.0215i | −0.372277 | − | 1.96337i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.2774 | + | 19.3987i | −0.994303 | + | 1.18496i | ||||
\(269\) | −21.7224 | + | 7.90629i | −1.32444 | + | 0.482055i | −0.904877 | − | 0.425673i | \(-0.860037\pi\) |
−0.419559 | + | 0.907728i | \(0.637815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.20656 | − | 18.1853i | 0.194785 | − | 1.10468i | −0.717941 | − | 0.696104i | \(-0.754915\pi\) |
0.912725 | − | 0.408574i | \(-0.133974\pi\) | |||||||
\(272\) | −7.94530 | + | 21.8295i | −0.481754 | + | 1.32361i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.16648 | − | 10.6807i | 0.372531 | − | 0.645242i | ||||
\(275\) | 9.10892 | + | 7.65745i | 0.549289 | + | 0.461761i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.9554 | − | 14.9854i | −1.55951 | − | 0.900384i | −0.997303 | − | 0.0733885i | \(-0.976619\pi\) |
−0.562208 | − | 0.826996i | \(-0.690048\pi\) | |||||||
\(278\) | 18.2540 | − | 10.5389i | 1.09480 | − | 0.632083i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −41.2348 | + | 34.5681i | −2.46425 | + | 2.06584i | ||||
\(281\) | 0.690977 | + | 3.91872i | 0.0412202 | + | 0.233771i | 0.998457 | − | 0.0555351i | \(-0.0176865\pi\) |
−0.957237 | + | 0.289306i | \(0.906575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.81678 | − | 6.93217i | 0.345772 | − | 0.412075i | −0.564930 | − | 0.825139i | \(-0.691097\pi\) |
0.910702 | + | 0.413064i | \(0.135541\pi\) | |||||||
\(284\) | −40.5423 | −2.40574 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.258920 | −0.0153103 | ||||||||
\(287\) | −14.3781 | + | 17.1352i | −0.848713 | + | 1.01146i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.37951 | + | 13.4949i | 0.139971 | + | 0.793816i | ||||
\(290\) | 11.3786 | + | 13.5731i | 0.668177 | + | 0.797039i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.1959 | − | 11.0828i | 1.12336 | − | 0.648570i | ||||
\(293\) | 2.02341 | + | 1.16822i | 0.118209 | + | 0.0682479i | 0.557939 | − | 0.829882i | \(-0.311592\pi\) |
−0.439730 | + | 0.898130i | \(0.644926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.9754 | + | 0.0118331i | 1.51234 | + | 0.000688952i | ||||
\(296\) | −0.981765 | + | 1.70047i | −0.0570640 | + | 0.0988377i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.9769 | + | 54.8860i | −1.15723 | + | 3.17946i | ||||
\(299\) | −0.0178903 | + | 0.101461i | −0.00103462 | + | 0.00586765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4230 | + | 4.88556i | −0.773687 | + | 0.281599i | ||||
\(302\) | −16.7329 | + | 19.9415i | −0.962869 | + | 1.14750i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −42.2559 | + | 36.3927i | −2.42354 | + | 2.08726i | ||||
\(305\) | 7.84876 | + | 6.59199i | 0.449419 | + | 0.377456i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.59974 | + | 7.14274i | 0.148375 | + | 0.407658i | 0.991508 | − | 0.130048i | \(-0.0415133\pi\) |
−0.843132 | + | 0.537706i | \(0.819291\pi\) | |||||||
\(308\) | −34.0387 | + | 6.00194i | −1.93953 | + | 0.341992i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.0198 | + | 8.66256i | −0.853067 | + | 0.492000i | ||||
\(311\) | −9.41207 | − | 16.3022i | −0.533709 | − | 0.924412i | −0.999225 | − | 0.0393720i | \(-0.987464\pi\) |
0.465515 | − | 0.885040i | \(-0.345869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2771 | + | 17.0147i | 0.806987 | + | 0.961729i | 0.999810 | − | 0.0195042i | \(-0.00620878\pi\) |
−0.192823 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(314\) | 15.1880 | − | 12.7443i | 0.857109 | − | 0.719200i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.2933 | − | 52.4695i | −1.70413 | − | 2.95164i | ||||
\(317\) | 1.39295 | − | 3.82711i | 0.0782360 | − | 0.214952i | −0.894408 | − | 0.447252i | \(-0.852403\pi\) |
0.972644 | + | 0.232300i | \(0.0746251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.21843 | + | 6.91009i | 0.0682193 | + | 0.386891i | ||||
\(320\) | 42.6502 | + | 15.5454i | 2.38422 | + | 0.869015i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 19.0243i | 1.06018i | ||||||||
\(323\) | 2.61115 | − | 7.47153i | 0.145288 | − | 0.415727i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.175245 | − | 0.101391i | −0.00972085 | − | 0.00562415i | ||||
\(326\) | 12.3787 | − | 4.50547i | 0.685591 | − | 0.249535i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 68.4398 | + | 12.0678i | 3.77895 | + | 0.666331i | ||||
\(329\) | −28.9669 | − | 10.5431i | −1.59700 | − | 0.581260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3939 | + | 18.0028i | −0.571301 | + | 0.989523i | 0.425132 | + | 0.905132i | \(0.360228\pi\) |
−0.996433 | + | 0.0843910i | \(0.973106\pi\) | |||||||
\(332\) | 14.9953 | + | 17.8708i | 0.822976 | + | 0.980785i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.5567 | + | 23.4809i | −0.741789 | + | 1.28482i | ||||
\(335\) | −10.6854 | − | 1.88915i | −0.583808 | − | 0.103215i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.7746 | − | 4.54476i | −1.40403 | − | 0.247569i | −0.580234 | − | 0.814450i | \(-0.697039\pi\) |
−0.823800 | + | 0.566881i | \(0.808150\pi\) | |||||||
\(338\) | −34.3920 | + | 6.06423i | −1.87068 | + | 0.329851i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.8667 | + | 3.66957i | −1.13166 | + | 0.199010i | ||||
\(341\) | −6.86899 | −0.371976 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.4071i | − | 0.939896i | ||||||
\(344\) | 33.9969 | + | 28.5268i | 1.83299 | + | 1.53806i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.27639 | − | 12.9100i | −0.122379 | − | 0.694047i | ||||
\(347\) | −20.2859 | − | 3.57695i | −1.08901 | − | 0.192021i | −0.399811 | − | 0.916598i | \(-0.630924\pi\) |
−0.689194 | + | 0.724577i | \(0.742035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5153 | − | 21.6772i | −0.669929 | − | 1.16035i | −0.977924 | − | 0.208963i | \(-0.932991\pi\) |
0.307994 | − | 0.951388i | \(-0.400342\pi\) | |||||||
\(350\) | −35.1194 | − | 12.8187i | −1.87721 | − | 0.685186i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.1297 | + | 31.1402i | 1.39272 | + | 1.65978i | ||||
\(353\) | 6.24627 | + | 3.60628i | 0.332455 | + | 0.191943i | 0.656931 | − | 0.753951i | \(-0.271854\pi\) |
−0.324475 | + | 0.945894i | \(0.605188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.67946 | − | 15.0491i | −0.460658 | − | 0.798723i | ||||
\(356\) | −13.9484 | + | 79.1054i | −0.739265 | + | 4.19258i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.9474 | − | 60.3001i | −1.15996 | − | 3.18696i | ||||
\(359\) | 12.1097 | + | 10.1613i | 0.639128 | + | 0.536292i | 0.903750 | − | 0.428060i | \(-0.140803\pi\) |
−0.264622 | + | 0.964352i | \(0.585247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2361 | − | 12.5831i | 0.749268 | − | 0.662267i | ||||
\(362\) | 6.89807i | 0.362554i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.552593 | − | 0.201127i | 0.0289637 | − | 0.0105419i | ||||
\(365\) | 8.22342 | + | 4.75279i | 0.430433 | + | 0.248772i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.903831 | + | 2.48326i | −0.0471796 | + | 0.129625i | −0.961045 | − | 0.276393i | \(-0.910861\pi\) |
0.913865 | + | 0.406018i | \(0.133083\pi\) | |||||||
\(368\) | 28.1908 | − | 16.2760i | 1.46955 | − | 0.848444i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.36426 | 0.000621494i | −0.0709248 | 3.23100e-5i | ||||||
\(371\) | −12.1829 | + | 10.2226i | −0.632502 | + | 0.530733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.33853 | − | 3.08220i | 0.276419 | − | 0.159590i | −0.355382 | − | 0.934721i | \(-0.615649\pi\) |
0.631801 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(374\) | −10.9102 | − | 3.97100i | −0.564154 | − | 0.205335i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.6307 | + | 94.3172i | 0.857661 | + | 4.86404i | ||||
\(377\) | −0.0408303 | − | 0.112180i | −0.00210287 | − | 0.00577758i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.156142 | −0.00802047 | −0.00401024 | − | 0.999992i | \(-0.501277\pi\) | ||||
−0.00401024 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(380\) | −48.0062 | − | 16.8018i | −2.46267 | − | 0.861912i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0391 | − | 19.1147i | 0.820634 | − | 0.977993i | ||||
\(383\) | −5.51405 | − | 15.1497i | −0.281755 | − | 0.774115i | −0.997153 | − | 0.0753983i | \(-0.975977\pi\) |
0.715399 | − | 0.698716i | \(-0.246245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.51503 | − | 11.3501i | −0.484931 | − | 0.578453i | ||||
\(386\) | 62.6915 | + | 22.8178i | 3.19091 | + | 1.16140i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.2866 | − | 14.5992i | −1.28373 | − | 0.741162i | ||||
\(389\) | 2.07987 | − | 1.74521i | 0.105453 | − | 0.0884859i | −0.588537 | − | 0.808471i | \(-0.700296\pi\) |
0.693990 | + | 0.719985i | \(0.255851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.30994 | + | 4.00093i | −0.116818 | + | 0.202336i | ||||
\(392\) | 5.58065 | − | 3.22199i | 0.281866 | − | 0.162735i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.94694 | − | 11.0416i | 0.0980854 | − | 0.556270i | ||||
\(395\) | 12.9911 | − | 22.4776i | 0.653653 | − | 1.13097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.1900 | + | 12.1440i | −0.511422 | + | 0.609488i | −0.958530 | − | 0.284991i | \(-0.908009\pi\) |
0.447109 | + | 0.894480i | \(0.352454\pi\) | |||||||
\(398\) | − | 60.1460i | − | 3.01485i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.0508 | + | 63.0077i | 0.552539 | + | 3.15039i | ||||
\(401\) | 2.54746 | + | 2.13757i | 0.127214 | + | 0.106745i | 0.704175 | − | 0.710026i | \(-0.251317\pi\) |
−0.576961 | + | 0.816772i | \(0.695761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.115091 | − | 0.0202937i | 0.00573311 | − | 0.00101090i | ||||
\(404\) | 10.8350 | − | 61.4483i | 0.539061 | − | 3.05717i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.0220 | − | 19.0907i | −0.547015 | − | 0.947457i | ||||
\(407\) | −0.468061 | − | 0.270235i | −0.0232009 | − | 0.0133951i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.73789 | + | 4.81466i | −0.283720 | + | 0.238070i | −0.773530 | − | 0.633760i | \(-0.781511\pi\) |
0.489809 | + | 0.871830i | \(0.337066\pi\) | |||||||
\(410\) | 16.4940 | + | 45.3812i | 0.814580 | + | 2.24122i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 25.1544 | − | 69.1113i | 1.23927 | − | 3.40487i | ||||
\(413\) | −31.8380 | − | 5.61391i | −1.56665 | − | 0.276242i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.42327 | + | 9.39204i | −0.168042 | + | 0.461037i | ||||
\(416\) | −0.529810 | − | 0.444563i | −0.0259761 | − | 0.0217965i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.1888 | − | 21.1192i | −0.889642 | − | 1.03297i | ||||
\(419\) | 14.4108 | 0.704012 | 0.352006 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352006 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6092 | − | 12.2327i | 1.63801 | − | 0.596187i | 0.651322 | − | 0.758802i | \(-0.274215\pi\) |
0.986690 | + | 0.162614i | \(0.0519927\pi\) | |||||||
\(422\) | −4.44926 | + | 0.784525i | −0.216587 | + | 0.0381901i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 46.4305 | + | 16.8993i | 2.25487 | + | 0.820704i | ||||
\(425\) | −5.82936 | − | 6.96003i | −0.282766 | − | 0.337611i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.20001 | − | 9.77239i | −0.396826 | − | 0.472919i | ||||
\(428\) | 39.3285 | + | 46.8698i | 1.90101 | + | 2.26554i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.36831 | + | 30.3643i | −0.258883 | + | 1.46430i | ||||
\(431\) | 9.76286 | + | 3.55339i | 0.470260 | + | 0.171161i | 0.566270 | − | 0.824220i | \(-0.308386\pi\) |
−0.0960100 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.5482 | − | 6.09178i | 1.66028 | − | 0.292752i | 0.736718 | − | 0.676200i | \(-0.236374\pi\) |
0.923563 | + | 0.383448i | \(0.125263\pi\) | |||||||
\(434\) | 20.2786 | − | 7.38081i | 0.973405 | − | 0.354290i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.0266 | −1.67747 | ||||||||
\(437\) | −9.53258 | + | 5.66825i | −0.456005 | + | 0.271149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6520 | − | 12.2945i | −0.699303 | − | 0.586785i | 0.222272 | − | 0.974985i | \(-0.428653\pi\) |
−0.921575 | + | 0.388199i | \(0.873097\pi\) | |||||||
\(440\) | −15.7578 | + | 43.2330i | −0.751225 | + | 2.06105i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.194535 | + | 0.0343018i | 0.00925309 | + | 0.00163157i | ||||
\(443\) | 7.86358 | − | 21.6050i | 0.373610 | − | 1.02649i | −0.600344 | − | 0.799742i | \(-0.704970\pi\) |
0.973954 | − | 0.226744i | \(-0.0728080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.3497 | + | 11.7576i | −1.53352 | + | 0.557365i | ||||
\(446\) | −19.7818 | + | 16.5989i | −0.936694 | + | 0.785980i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −48.9296 | − | 28.2495i | −2.31171 | − | 1.33466i | ||||
\(449\) | −7.88692 | − | 13.6605i | −0.372207 | − | 0.644681i | 0.617698 | − | 0.786415i | \(-0.288065\pi\) |
−0.989905 | + | 0.141734i | \(0.954732\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.32171 | + | 18.8384i | −0.156413 | + | 0.887063i | ||||
\(452\) | −12.6729 | + | 2.23458i | −0.596085 | + | 0.105106i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.2939 | + | 40.5234i | 2.26654 | + | 1.90186i | ||||
\(455\) | 0.192959 | + | 0.162062i | 0.00904606 | + | 0.00759757i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.6414i | 1.62046i | 0.586114 | + | 0.810229i | \(0.300657\pi\) | ||||
−0.586114 | + | 0.810229i | \(0.699343\pi\) | |||||||
\(458\) | −2.05660 | + | 2.45096i | −0.0960988 | + | 0.114526i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.7041 | + | 14.8559i | 1.19846 | + | 0.692661i | ||||
\(461\) | −4.26528 | + | 24.1896i | −0.198654 | + | 1.12662i | 0.708465 | + | 0.705746i | \(0.249388\pi\) |
−0.907119 | + | 0.420875i | \(0.861723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.67368 | + | 3.85305i | −0.310152 | + | 0.179067i | −0.646995 | − | 0.762495i | \(-0.723974\pi\) |
0.336842 | + | 0.941561i | \(0.390641\pi\) | |||||||
\(464\) | −18.8595 | + | 32.6656i | −0.875529 | + | 1.51646i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.6260 | + | 39.9629i | −2.20623 | + | 1.85125i | ||||
\(467\) | 5.64552 | + | 3.25944i | 0.261243 | + | 0.150829i | 0.624902 | − | 0.780704i | \(-0.285139\pi\) |
−0.363658 | + | 0.931532i | \(0.618472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.6910 | + | 4.61914i | 0.586015 | + | 0.213292i | ||||
\(470\) | −50.9941 | + | 42.7496i | −2.35218 | + | 1.97189i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.3534 | + | 94.3851i | 1.58124 | + | 4.34442i | ||||
\(473\) | −7.85213 | + | 9.35781i | −0.361041 | + | 0.430272i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.04064 | − | 21.4167i | −0.185397 | − | 0.982664i | ||||
\(476\) | 26.3695 | 1.20864 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.90153 | − | 24.4568i | −0.407147 | − | 1.11863i | ||||
\(479\) | 2.14887 | + | 12.1868i | 0.0981842 | + | 0.556830i | 0.993725 | + | 0.111851i | \(0.0356779\pi\) |
−0.895541 | + | 0.444979i | \(0.853211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.00864085 | + | 0.00314501i | 0.000393989 | + | 0.000143400i | ||||
\(482\) | 36.7284 | − | 21.2052i | 1.67293 | − | 0.965868i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.3289 | − | 17.8971i | 0.969495 | − | 0.813503i | ||||
\(485\) | 0.00569974 | − | 12.5117i | 0.000258812 | − | 0.568127i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.5333 | − | 19.3605i | 1.51954 | − | 0.877306i | 0.519804 | − | 0.854285i | \(-0.326005\pi\) |
0.999735 | − | 0.0230209i | \(-0.00732844\pi\) | |||||||
\(488\) | −13.5557 | + | 37.2439i | −0.613636 | + | 1.68595i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.87643 | + | 2.24041i | 0.175119 | + | 0.101212i | ||||
\(491\) | −29.5147 | + | 10.7425i | −1.33198 | + | 0.484802i | −0.907278 | − | 0.420531i | \(-0.861844\pi\) |
−0.424704 | + | 0.905332i | \(0.639622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.35319i | − | 0.241095i | ||||||
\(494\) | 0.367151 | + | 0.300120i | 0.0165189 | + | 0.0135030i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.2862 | − | 23.7349i | −1.27009 | − | 1.06573i | ||||
\(497\) | 7.39521 | + | 20.3182i | 0.331720 | + | 0.911394i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.37331 | + | 19.1310i | −0.151010 | + | 0.856422i | 0.811333 | + | 0.584584i | \(0.198742\pi\) |
−0.962343 | + | 0.271837i | \(0.912369\pi\) | |||||||
\(500\) | −44.7439 | + | 37.4405i | −2.00101 | + | 1.67439i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.7489 | + | 7.36057i | 0.569010 | + | 0.328518i | ||||
\(503\) | −2.73706 | − | 3.26190i | −0.122039 | − | 0.145441i | 0.701565 | − | 0.712605i | \(-0.252485\pi\) |
−0.823605 | + | 0.567164i | \(0.808040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1289 | − | 9.13321i | 1.11822 | − | 0.406422i | ||||
\(506\) | 8.13461 | + | 14.0896i | 0.361627 | + | 0.626357i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.79785 | + | 0.669664i | 0.168502 | + | 0.0297115i | ||||
\(509\) | −1.27413 | − | 7.22597i | −0.0564750 | − | 0.320286i | 0.943462 | − | 0.331480i | \(-0.107548\pi\) |
−0.999937 | + | 0.0111941i | \(0.996437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.05573 | − | 7.59866i | −0.400602 | − | 0.336145i | ||||
\(512\) | − | 2.72331i | − | 0.120354i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.53234 | 0.420453 | ||||||||
\(515\) | 31.0389 | − | 5.45842i | 1.36774 | − | 0.240527i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.9612 | + | 4.57767i | −1.14177 | + | 0.201326i | ||||
\(518\) | 1.67218 | + | 0.294851i | 0.0734714 | + | 0.0129550i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.136298 | − | 0.770932i | 0.00597708 | − | 0.0338076i | ||||
\(521\) | −3.98404 | + | 6.90057i | −0.174544 | + | 0.302319i | −0.940003 | − | 0.341165i | \(-0.889178\pi\) |
0.765459 | + | 0.643484i | \(0.222512\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0759 | + | 12.0080i | 0.440590 | + | 0.525075i | 0.939946 | − | 0.341322i | \(-0.110875\pi\) |
−0.499357 | + | 0.866397i | \(0.666430\pi\) | |||||||
\(524\) | 28.4715 | − | 49.3141i | 1.24378 | − | 2.15430i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 66.5187 | + | 24.2108i | 2.90035 | + | 1.05564i | ||||
\(527\) | 5.16089 | + | 0.910003i | 0.224812 | + | 0.0396404i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5297 | + | 5.65235i | −0.675204 | + | 0.245754i | ||||
\(530\) | 5.94601 | + | 33.8116i | 0.258278 | + | 1.46868i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 55.2241 | + | 30.9441i | 2.39427 | + | 1.34160i | ||||
\(533\) | − | 0.325454i | − | 0.0140970i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.97825 | + | 24.6326i | −0.388164 | + | 1.06496i | ||||
\(536\) | −7.28622 | − | 41.3222i | −0.314717 | − | 1.78485i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.2417 | − | 58.3612i | 0.915796 | − | 2.51613i | ||||
\(539\) | 0.886868 | + | 1.53610i | 0.0382001 | + | 0.0661645i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3123 | − | 18.7223i | 0.959283 | − | 0.804934i | −0.0215537 | − | 0.999768i | \(-0.506861\pi\) |
0.980836 | + | 0.194834i | \(0.0624168\pi\) | |||||||
\(542\) | 31.8899 | + | 38.0049i | 1.36979 | + | 1.63245i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.5066 | − | 26.8583i | −0.664841 | − | 1.15154i | ||||
\(545\) | −7.49865 | − | 13.0017i | −0.321207 | − | 0.556932i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2470 | + | 2.51214i | −0.609160 | + | 0.107411i | −0.469714 | − | 0.882818i | \(-0.655643\pi\) |
−0.139445 | + | 0.990230i | \(0.544532\pi\) | |||||||
\(548\) | 8.19275 | + | 22.5094i | 0.349977 | + | 0.961553i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.4908 | + | 5.52309i | −1.34277 | + | 0.235506i | ||||
\(551\) | 6.28187 | − | 11.2109i | 0.267617 | − | 0.477599i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.7699 | + | 24.7526i | −0.883226 | + | 1.05259i | ||||
\(554\) | 75.6660 | − | 27.5402i | 3.21474 | − | 1.17007i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.10898 | + | 40.3170i | −0.301488 | + | 1.70982i | ||||
\(557\) | 11.5184 | − | 31.6465i | 0.488049 | − | 1.34090i | −0.414395 | − | 0.910097i | \(-0.636007\pi\) |
0.902444 | − | 0.430807i | \(-0.141771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.103917 | − | 0.179990i | 0.00439524 | − | 0.00761278i | ||||
\(560\) | 0.0362698 | − | 79.6171i | 0.00153268 | − | 3.36443i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.25850 | − | 5.34540i | −0.390546 | − | 0.225482i | ||||
\(563\) | 21.5774 | − | 12.4577i | 0.909378 | − | 0.525030i | 0.0291473 | − | 0.999575i | \(-0.490721\pi\) |
0.880231 | + | 0.474545i | \(0.157387\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.54254 | − | 4.22575i | −0.149036 | − | 0.177779i | ||||
\(566\) | 4.22185 | + | 23.9433i | 0.177457 | + | 1.00641i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 43.1806 | − | 51.4607i | 1.81182 | − | 2.15924i | ||||
\(569\) | 19.7304 | 0.827141 | 0.413571 | − | 0.910472i | \(-0.364281\pi\) | ||||
0.413571 | + | 0.910472i | \(0.364281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8463 | −0.579452 | −0.289726 | − | 0.957110i | \(-0.593564\pi\) | ||||
−0.289726 | + | 0.957110i | \(0.593564\pi\) | |||||||
\(572\) | 0.323254 | − | 0.385239i | 0.0135159 | − | 0.0161077i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.4357 | − | 59.1838i | −0.435578 | − | 2.47028i | ||||
\(575\) | −0.0115908 | + | 12.7217i | −0.000483369 | + | 0.530530i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.0832 | + | 20.8327i | −1.50216 | + | 0.867275i | −0.502167 | + | 0.864771i | \(0.667464\pi\) |
−0.999997 | + | 0.00250405i | \(0.999203\pi\) | |||||||
\(578\) | −31.8834 | − | 18.4079i | −1.32618 | − | 0.765668i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −34.4009 | − | 0.0156714i | −1.42842 | − | 0.000650719i | ||||
\(581\) | 6.22085 | − | 10.7748i | 0.258084 | − | 0.447015i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.65162 | + | 12.7802i | −0.192650 | + | 0.529302i | ||||
\(584\) | −6.37767 | + | 36.1696i | −0.263910 | + | 1.49671i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.89869 | + | 2.14695i | −0.243673 | + | 0.0886896i | ||||
\(587\) | −10.3943 | + | 12.3875i | −0.429020 | + | 0.511286i | −0.936639 | − | 0.350296i | \(-0.886081\pi\) |
0.507619 | + | 0.861581i | \(0.330526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.74028 | + | 7.96198i | 0.401341 | + | 0.328068i | ||||
\(590\) | −44.8830 | + | 53.4400i | −1.84780 | + | 2.20009i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.993691 | − | 2.73014i | −0.0408405 | − | 0.112208i | ||||
\(593\) | −22.1249 | + | 3.90122i | −0.908562 | + | 0.160204i | −0.608350 | − | 0.793669i | \(-0.708168\pi\) |
−0.300212 | + | 0.953873i | \(0.597057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.64529 | + | 9.78822i | 0.231434 | + | 0.401278i | ||||
\(596\) | −56.7226 | − | 98.2464i | −2.32345 | − | 4.02433i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.177923 | − | 0.212041i | −0.00727582 | − | 0.00867099i | ||||
\(599\) | 1.65472 | − | 1.38847i | 0.0676099 | − | 0.0567314i | −0.608356 | − | 0.793664i | \(-0.708171\pi\) |
0.675966 | + | 0.736932i | \(0.263726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.52974 | + | 14.7739i | 0.347935 | + | 0.602641i | 0.985883 | − | 0.167439i | \(-0.0535496\pi\) |
−0.637947 | + | 0.770080i | \(0.720216\pi\) | |||||||
\(602\) | 13.1260 | − | 36.0633i | 0.534975 | − | 1.46983i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.77979 | − | 49.7927i | −0.357245 | − | 2.02603i | ||||
\(605\) | 11.2095 | + | 4.08570i | 0.455730 | + | 0.166107i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.47625i | 0.141097i | 0.997508 | + | 0.0705483i | \(0.0224749\pi\) | ||||
−0.997508 | + | 0.0705483i | \(0.977525\pi\) | |||||||
\(608\) | −0.956978 | − | 74.4446i | −0.0388106 | − | 3.01913i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.1217 | + | 4.76955i | −1.09812 | + | 0.193113i | ||||
\(611\) | 0.421462 | − | 0.153400i | 0.0170505 | − | 0.00620588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.3007 | − | 3.22691i | −0.739159 | − | 0.130334i | −0.208623 | − | 0.977996i | \(-0.566898\pi\) |
−0.530536 | + | 0.847663i | \(0.678009\pi\) | |||||||
\(614\) | −19.1903 | − | 6.98470i | −0.774457 | − | 0.281879i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6355 | − | 49.5981i | 1.15376 | − | 1.99837i | ||||
\(617\) | −12.7710 | − | 15.2199i | −0.514141 | − | 0.612729i | 0.445044 | − | 0.895509i | \(-0.353188\pi\) |
−0.959185 | + | 0.282779i | \(0.908744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.21208 | + | 7.29553i | −0.169298 | + | 0.293232i | −0.938173 | − | 0.346166i | \(-0.887483\pi\) |
0.768875 | + | 0.639399i | \(0.220817\pi\) | |||||||
\(620\) | 5.86301 | − | 33.1624i | 0.235464 | − | 1.33184i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 49.8062 | + | 8.78218i | 1.99705 | + | 0.352133i | ||||
\(623\) | 42.1888 | − | 7.43902i | 1.69026 | − | 0.298038i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4767 | − | 8.59330i | −0.939068 | − | 0.343732i | ||||
\(626\) | −59.6744 | −2.38507 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 38.5086i | 1.53666i | ||||||||
\(629\) | 0.315868 | + | 0.265045i | 0.0125945 | + | 0.0105680i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.278838 | + | 1.58137i | 0.0111004 | + | 0.0629534i | 0.989855 | − | 0.142083i | \(-0.0453799\pi\) |
−0.978754 | + | 0.205036i | \(0.934269\pi\) | |||||||
\(632\) | 98.8646 | + | 17.4325i | 3.93262 | + | 0.693428i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.47106 | + | 9.47616i | 0.217284 | + | 0.376346i | ||||
\(635\) | 0.564484 | + | 1.55311i | 0.0224009 | + | 0.0616332i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0193979 | − | 0.0231175i | −0.000768573 | − | 0.000915950i | ||||
\(638\) | −16.3260 | − | 9.42582i | −0.646352 | − | 0.373172i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −39.4814 | + | 22.7706i | −1.56064 | + | 0.900087i | ||||
\(641\) | 7.96102 | − | 45.1492i | 0.314442 | − | 1.78329i | −0.260892 | − | 0.965368i | \(-0.584017\pi\) |
0.575334 | − | 0.817919i | \(-0.304872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.26834 | − | 17.2221i | −0.247199 | − | 0.679175i | −0.999786 | − | 0.0206816i | \(-0.993416\pi\) |
0.752587 | − | 0.658493i | \(-0.228806\pi\) | |||||||
\(644\) | −28.3057 | − | 23.7513i | −1.11540 | − | 0.935933i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.8679 | + | 18.2772i | 0.427593 | + | 0.719105i | ||||
\(647\) | 25.1770i | 0.989808i | 0.868948 | + | 0.494904i | \(0.164797\pi\) | ||||
−0.868948 | + | 0.494904i | \(0.835203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.9799 | + | 9.45592i | −1.01980 | + | 0.371177i | ||||
\(650\) | 0.511317 | − | 0.185577i | 0.0200555 | − | 0.00727892i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.75086 | + | 24.0428i | −0.342710 | + | 0.941588i | ||||
\(653\) | −0.604989 | + | 0.349290i | −0.0236750 | + | 0.0136688i | −0.511791 | − | 0.859110i | \(-0.671018\pi\) |
0.488116 | + | 0.872779i | \(0.337684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.4005 | + | 0.0111157i | 0.953406 | + | 0.000434326i | ||||
\(656\) | −78.7722 | + | 66.0977i | −3.07554 | + | 2.58068i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 71.7240 | − | 41.4099i | 2.79609 | − | 1.61432i | ||||
\(659\) | −19.1350 | − | 6.96458i | −0.745395 | − | 0.271301i | −0.0587281 | − | 0.998274i | \(-0.518705\pi\) |
−0.686667 | + | 0.726973i | \(0.740927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.03199 | − | 34.2091i | −0.234617 | − | 1.33058i | −0.843418 | − | 0.537258i | \(-0.819460\pi\) |
0.608801 | − | 0.793323i | \(-0.291651\pi\) | |||||||
\(662\) | −19.1019 | − | 52.4822i | −0.742418 | − | 2.03978i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.6547 | −1.50009 | ||||||||
\(665\) | 0.336313 | + | 27.1236i | 0.0130416 | + | 1.05181i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.82168 | + | 5.74626i | −0.186696 | + | 0.222496i | ||||
\(668\) | −18.0113 | − | 49.4857i | −0.696879 | − | 1.91466i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 22.3415 | − | 18.7294i | 0.863128 | − | 0.723581i | ||||
\(671\) | −10.2516 | − | 3.73126i | −0.395757 | − | 0.144044i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.1298 | + | 12.7767i | 0.853043 | + | 0.492505i | 0.861676 | − | 0.507458i | \(-0.169415\pi\) |
−0.00863342 | + | 0.999963i | \(0.502748\pi\) | |||||||
\(674\) | 53.8656 | − | 45.1986i | 2.07483 | − | 1.74099i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.9146 | − | 58.7417i | 1.30441 | − | 2.25930i | ||||
\(677\) | −32.9463 | + | 19.0216i | −1.26623 | + | 0.731058i | −0.974273 | − | 0.225373i | \(-0.927640\pi\) |
−0.291957 | + | 0.956431i | \(0.594307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.70408 | + | 15.3356i | −0.103773 | + | 0.588527i | ||||
\(680\) | 17.5669 | − | 30.3947i | 0.673658 | − | 1.16558i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.8625 | − | 14.1372i | 0.454239 | − | 0.541342i | ||||
\(683\) | 31.7070i | 1.21324i | 0.794994 | + | 0.606618i | \(0.207474\pi\) | ||||
−0.794994 | + | 0.606618i | \(0.792526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.60144 | + | 7.86001i | −0.252228 | + | 0.300316i | ||||
\(686\) | 35.8260 | + | 30.0615i | 1.36784 | + | 1.14775i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −64.6694 | + | 11.4030i | −2.46550 | + | 0.434734i | ||||
\(689\) | 0.0401810 | − | 0.227878i | 0.00153078 | − | 0.00868146i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.05528 | − | 3.55984i | −0.0781864 | − | 0.135423i | 0.824281 | − | 0.566181i | \(-0.191580\pi\) |
−0.902467 | + | 0.430758i | \(0.858246\pi\) | |||||||
\(692\) | 22.0504 | + | 12.7308i | 0.838231 | + | 0.483953i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.3949 | − | 35.5736i | 1.60929 | − | 1.35035i | ||||
\(695\) | −16.4874 | + | 5.99242i | −0.625403 | + | 0.227305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.99141 | − | 13.7138i | 0.189063 | − | 0.519447i | ||||
\(698\) | 66.2277 | + | 11.6777i | 2.50676 | + | 0.442009i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 62.9180 | − | 36.2493i | 2.37808 | − | 1.37010i | ||||
\(701\) | 3.40592 | + | 2.85791i | 0.128640 | + | 0.107942i | 0.704838 | − | 0.709369i | \(-0.251020\pi\) |
−0.576198 | + | 0.817310i | \(0.695464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.350480 | + | 0.925735i | 0.0132186 | + | 0.0349148i | ||||
\(704\) | −48.3168 | −1.82101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.2093 | + | 6.62763i | −0.685315 | + | 0.249434i | ||||
\(707\) | −32.7718 | + | 5.77855i | −1.23251 | + | 0.217325i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.15334 | + | 1.14772i | 0.118426 | + | 0.0431036i | 0.400554 | − | 0.916273i | \(-0.368818\pi\) |
−0.282127 | + | 0.959377i | \(0.591040\pi\) | |||||||
\(710\) | 45.9620 | + | 8.12593i | 1.72492 | + | 0.304961i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −85.5531 | − | 101.958i | −3.20624 | − | 3.82104i | ||||
\(713\) | −4.72019 | − | 5.62530i | −0.176772 | − | 0.210669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.212203 | + | 0.0375167i | 0.00793593 | + | 0.00140305i | ||||
\(716\) | 117.119 | + | 42.6279i | 4.37695 | + | 1.59308i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.8263 | + | 7.37510i | −1.56094 | + | 0.275236i | ||||
\(719\) | −38.6145 | + | 14.0545i | −1.44008 | + | 0.524145i | −0.939801 | − | 0.341721i | \(-0.888990\pi\) |
−0.500275 | + | 0.865866i | \(0.666768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.2242 | −1.46078 | ||||||||
\(722\) | 1.31219 | + | 51.0302i | 0.0488348 | + | 1.89915i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.2634 | − | 8.61203i | −0.381437 | − | 0.320064i | ||||
\(725\) | −7.35886 | − | 12.7728i | −0.273301 | − | 0.474369i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8832 | − | 2.09533i | −0.440723 | − | 0.0777114i | −0.0511164 | − | 0.998693i | \(-0.516278\pi\) |
−0.389607 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(728\) | −0.333261 | + | 0.915628i | −0.0123515 | + | 0.0339354i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23.9834 | + | 8.71687i | −0.887665 | + | 0.322626i | ||||
\(731\) | 7.13928 | − | 5.99056i | 0.264056 | − | 0.221569i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.8082 | − | 6.81748i | −0.436147 | − | 0.251809i | 0.265815 | − | 0.964024i | \(-0.414359\pi\) |
−0.701962 | + | 0.712215i | \(0.747692\pi\) | |||||||
\(734\) | −3.54995 | − | 6.14870i | −0.131031 | − | 0.226953i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.54634 | + | 42.7974i | −0.278162 | + | 1.57753i | ||||
\(737\) | 11.3741 | − | 2.00556i | 0.418971 | − | 0.0738759i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.2757 | − | 24.5652i | −1.07692 | − | 0.903645i | −0.0812609 | − | 0.996693i | \(-0.525895\pi\) |
−0.995662 | + | 0.0930476i | \(0.970339\pi\) | |||||||
\(740\) | 1.70417 | − | 2.02907i | 0.0626465 | − | 0.0745901i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 42.7280i | − | 1.56859i | ||||||
\(743\) | −3.90379 | + | 4.65236i | −0.143216 | + | 0.170679i | −0.832884 | − | 0.553447i | \(-0.813312\pi\) |
0.689668 | + | 0.724126i | \(0.257757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.3252 | − | 42.0882i | 0.891206 | − | 1.54199i | ||||
\(746\) | −2.87593 | + | 16.3102i | −0.105295 | + | 0.597159i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.5294 | − | 11.2753i | 0.714066 | − | 0.412266i | ||||
\(749\) | 16.3155 | − | 28.2593i | 0.596155 | − | 1.03257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.156655 | − | 0.131449i | 0.00571641 | − | 0.00479664i | −0.639925 | − | 0.768437i | \(-0.721035\pi\) |
0.645641 | + | 0.763641i | \(0.276590\pi\) | |||||||
\(752\) | −122.725 | − | 70.8551i | −4.47531 | − | 2.58382i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.301393 | + | 0.109698i | 0.0109761 | + | 0.00399497i | ||||
\(755\) | 16.6032 | − | 13.9188i | 0.604252 | − | 0.506558i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.28814 | − | 17.2765i | −0.228546 | − | 0.627926i | 0.771418 | − | 0.636328i | \(-0.219548\pi\) |
−0.999965 | + | 0.00840229i | \(0.997325\pi\) | |||||||
\(758\) | 0.269652 | − | 0.321359i | 0.00979421 | − | 0.0116723i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 72.4569 | − | 43.0395i | 2.62829 | − | 1.56121i | ||||
\(761\) | 31.4304 | 1.13935 | 0.569675 | − | 0.821870i | \(-0.307069\pi\) | ||||
0.569675 | + | 0.821870i | \(0.307069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.38912 | + | 17.5540i | 0.231302 | + | 0.635496i | ||||
\(764\) | 8.41578 | + | 47.7283i | 0.304472 | + | 1.72675i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.7026 | + | 14.8145i | 1.47064 | + | 0.535270i | ||||
\(767\) | 0.407363 | − | 0.235191i | 0.0147090 | − | 0.00849225i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.5419 | − | 13.8803i | 0.596516 | − | 0.500537i | −0.293807 | − | 0.955865i | \(-0.594922\pi\) |
0.890324 | + | 0.455328i | \(0.150478\pi\) | |||||||
\(770\) | 39.7920 | + | 0.0181273i | 1.43400 | + | 0.000653264i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −112.218 | + | 64.7893i | −4.03883 | + | 2.33182i | ||||
\(773\) | −12.6854 | + | 34.8529i | −0.456263 | + | 1.25357i | 0.471983 | + | 0.881607i | \(0.343538\pi\) |
−0.928247 | + | 0.371965i | \(0.878684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.5649 | − | 4.92323i | 0.487266 | − | 0.176848i | ||||
\(776\) | 45.4630 | − | 16.5472i | 1.63203 | − | 0.594009i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.29454i | 0.261522i | ||||||||
\(779\) | 26.5461 | − | 22.8627i | 0.951113 | − | 0.819141i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1648 | + | 11.8857i | 0.506856 | + | 0.425302i | ||||
\(782\) | −4.24520 | − | 11.6636i | −0.151808 | − | 0.417089i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.65572 | + | 9.39005i | −0.0591328 | + | 0.335359i | ||||
\(785\) | −14.2942 | + | 8.24408i | −0.510182 | + | 0.294244i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.73479 | − | 1.00158i | −0.0618385 | − | 0.0357025i | 0.468762 | − | 0.883325i | \(-0.344700\pi\) |
−0.530600 | + | 0.847622i | \(0.678034\pi\) | |||||||
\(788\) | 13.9978 | + | 16.6819i | 0.498652 | + | 0.594270i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.8264 | + | 65.5554i | 0.847705 | + | 2.33236i | ||||
\(791\) | 3.43152 | + | 5.94357i | 0.122011 | + | 0.211329i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.182791 | + | 0.0322309i | 0.00649108 | + | 0.00114455i | ||||
\(794\) | −7.39595 | − | 41.9445i | −0.262472 | − | 1.48856i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 89.4894 | + | 75.0905i | 3.17187 | + | 2.66151i | ||||
\(797\) | − | 12.8587i | − | 0.455480i | −0.973722 | − | 0.227740i | \(-0.926866\pi\) | ||
0.973722 | − | 0.227740i | \(-0.0731336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.1119 | 0.711509 | ||||||||
\(800\) | −73.9203 | − | 42.7678i | −2.61348 | − | 1.51207i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.79877 | + | 1.55146i | −0.310695 | + | 0.0547840i | ||||
\(803\) | −9.95584 | − | 1.75548i | −0.351334 | − | 0.0619496i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.75657 | − | 15.5917i | 0.0971562 | − | 0.549536i | ||||
\(806\) | −0.156992 | + | 0.271918i | −0.00552981 | + | 0.00957792i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 66.4567 | + | 79.2001i | 2.33794 | + | 2.78625i | ||||
\(809\) | −10.5986 | + | 18.3573i | −0.372627 | + | 0.645410i | −0.989969 | − | 0.141286i | \(-0.954876\pi\) |
0.617341 | + | 0.786695i | \(0.288210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.40909 | + | 3.06066i | 0.295283 | + | 0.107474i | 0.485414 | − | 0.874284i | \(-0.338669\pi\) |
−0.190131 | + | 0.981759i | \(0.560891\pi\) | |||||||
\(812\) | 42.1652 | + | 7.43486i | 1.47971 | + | 0.260912i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.36450 | − | 0.496639i | 0.0478258 | − | 0.0174072i | ||||
\(815\) | −10.7980 | + | 1.89890i | −0.378237 | + | 0.0665157i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.9812 | − | 4.16789i | 0.769025 | − | 0.145816i | ||||
\(818\) | − | 20.1240i | − | 0.703621i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −88.1135 | − | 32.1161i | −3.07706 | − | 1.12154i | ||||
\(821\) | 0.600509 | + | 3.40566i | 0.0209579 | + | 0.118858i | 0.993492 | − | 0.113903i | \(-0.0363352\pi\) |
−0.972534 | + | 0.232761i | \(0.925224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.20022 | + | 17.0350i | −0.216126 | + | 0.593801i | −0.999619 | − | 0.0275992i | \(-0.991214\pi\) |
0.783493 | + | 0.621401i | \(0.213436\pi\) | |||||||
\(824\) | 60.9321 | + | 105.538i | 2.12267 | + | 3.67657i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 66.5374 | − | 55.8315i | 2.31513 | − | 1.94263i | ||||
\(827\) | 18.8909 | + | 22.5132i | 0.656899 | + | 0.782862i | 0.986937 | − | 0.161105i | \(-0.0515059\pi\) |
−0.330038 | + | 0.943968i | \(0.607061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.73389 | − | 3.00318i | −0.0602204 | − | 0.104305i | 0.834343 | − | 0.551245i | \(-0.185847\pi\) |
−0.894564 | + | 0.446940i | \(0.852514\pi\) | |||||||
\(830\) | −13.4181 | − | 23.2653i | −0.465748 | − | 0.807549i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.809558 | − | 0.142747i | 0.0280664 | − | 0.00494886i | ||||
\(833\) | −0.462829 | − | 1.27161i | −0.0160361 | − | 0.0440588i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.5129 | − | 17.2798i | 0.502240 | − | 0.597993i | ||||
\(836\) | 54.1307 | − | 0.695845i | 1.87215 | − | 0.0240663i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.8869 | + | 29.6591i | −0.859705 | + | 1.02456i | ||||
\(839\) | −37.4283 | + | 13.6228i | −1.29217 | + | 0.470311i | −0.894438 | − | 0.447192i | \(-0.852424\pi\) |
−0.397730 | + | 0.917503i | \(0.630202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.52647 | + | 19.9996i | −0.121602 | + | 0.689641i | ||||
\(842\) | −32.8655 | + | 90.2973i | −1.13262 | + | 3.11185i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.38750 | − | 7.59938i | 0.151024 | − | 0.261581i | ||||
\(845\) | 29.0652 | + | 0.0132407i | 0.999874 | + | 0.000455495i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8598 | − | 7.42463i | −0.441869 | − | 0.255113i | ||||
\(848\) | −63.3156 | + | 36.5553i | −2.17427 | + | 1.25531i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.3917 | + | 0.0222234i | 0.836629 | + | 0.000762257i | ||||
\(851\) | −0.100332 | − | 0.569014i | −0.00343935 | − | 0.0195055i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2917 | − | 12.2652i | 0.352383 | − | 0.419953i | −0.560513 | − | 0.828145i | \(-0.689396\pi\) |
0.912896 | + | 0.408192i | \(0.133841\pi\) | |||||||
\(854\) | 34.2739 | 1.17283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −101.380 | −3.46510 | ||||||||
\(857\) | −10.4417 | + | 12.4439i | −0.356680 | + | 0.425075i | −0.914310 | − | 0.405015i | \(-0.867266\pi\) |
0.557630 | + | 0.830090i | \(0.311711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.76555 | + | 55.3832i | 0.333196 | + | 1.88965i | 0.444360 | + | 0.895849i | \(0.353431\pi\) |
−0.111163 | + | 0.993802i | \(0.535458\pi\) | |||||||
\(860\) | −38.4759 | − | 45.8962i | −1.31202 | − | 1.56505i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.1734 | + | 13.9565i | −0.823351 | + | 0.475362i | ||||
\(863\) | 12.2619 | + | 7.07944i | 0.417402 | + | 0.240987i | 0.693965 | − | 0.720009i | \(-0.255862\pi\) |
−0.276563 | + | 0.960996i | \(0.589196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.00497030 | + | 10.9105i | −0.000168995 | + | 0.370967i | ||||
\(866\) | −47.1260 | + | 81.6247i | −1.60141 | + | 2.77372i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.3356 | + | 39.3866i | −0.486581 | + | 1.33687i | ||||
\(869\) | −4.79838 | + | 27.2129i | −0.162774 | + | 0.923136i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.184651 | + | 0.0672073i | −0.00625665 | + | 0.00227723i | ||||
\(872\) | 37.3061 | − | 44.4596i | 1.26334 | − | 1.50559i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.79653 | − | 29.4081i | 0.162245 | − | 0.994744i | ||||
\(875\) | 26.9253 | + | 15.5944i | 0.910242 | + | 0.527188i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.19162 | + | 6.02143i | 0.0740058 | + | 0.203329i | 0.971180 | − | 0.238348i | \(-0.0766059\pi\) |
−0.897174 | + | 0.441677i | \(0.854384\pi\) | |||||||
\(878\) | 50.6072 | − | 8.92342i | 1.70791 | − | 0.301151i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −34.0166 | − | 58.9804i | −1.14670 | − | 1.98823i | ||||
\(881\) | −5.80585 | − | 10.0560i | −0.195604 | − | 0.338796i | 0.751494 | − | 0.659740i | \(-0.229333\pi\) |
−0.947098 | + | 0.320943i | \(0.896000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9859 | − | 20.2430i | −0.571620 | − | 0.681231i | 0.400342 | − | 0.916366i | \(-0.368891\pi\) |
−0.971963 | + | 0.235135i | \(0.924447\pi\) | |||||||
\(884\) | −0.293908 | + | 0.246618i | −0.00988518 | + | 0.00829465i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.8856 | + | 53.4954i | 1.03762 | + | 1.79721i | ||||
\(887\) | 13.3596 | − | 36.7051i | 0.448570 | − | 1.23244i | −0.485149 | − | 0.874431i | \(-0.661235\pi\) |
0.933720 | − | 0.358005i | \(-0.116543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.357147 | − | 2.02548i | −0.0119783 | − | 0.0679325i | ||||
\(890\) | 31.6682 | − | 86.8846i | 1.06152 | − | 2.91238i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 50.1559i | − | 1.67934i | ||||||
\(893\) | 42.1193 | + | 23.6010i | 1.40947 | + | 0.789777i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.25011 | + | 52.6001i | 0.309197 | + | 1.75823i | ||||
\(896\) | 53.3048 | − | 19.4014i | 1.78079 | − | 0.648154i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.7355 | + | 7.35910i | 1.39273 | + | 0.245576i | ||||
\(899\) | 7.99576 | + | 2.91022i | 0.266674 | + | 0.0970613i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.18803 | − | 8.98593i | 0.172838 | − | 0.299365i | ||||
\(902\) | −33.0351 | − | 39.3697i | −1.09995 | − | 1.31087i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6613 | − | 18.4659i | 0.354589 | − | 0.614166i | ||||
\(905\) | 0.999508 | − | 5.65343i | 0.0332248 | − | 0.187926i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.4681 | + | 9.95684i | 1.87499 | + | 0.330612i | 0.990672 | − | 0.136270i | \(-0.0435115\pi\) |
0.884320 | + | 0.466882i | \(0.154623\pi\) | |||||||
\(908\) | −120.587 | + | 21.2627i | −4.00182 | + | 0.705628i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.666777 | + | 0.117258i | −0.0221034 | + | 0.00388705i | ||||
\(911\) | −22.2118 | −0.735909 | −0.367954 | − | 0.929844i | \(-0.619942\pi\) | ||||
−0.367954 | + | 0.929844i | \(0.619942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.6399i | − | 0.352129i | ||||||
\(914\) | −71.2962 | − | 59.8247i | −2.35827 | − | 1.97882i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.07911 | − | 6.11991i | −0.0356546 | − | 0.202208i | ||||
\(917\) | −29.9077 | − | 5.27354i | −0.987640 | − | 0.174148i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0265 | + | 41.6150i | 0.792560 | + | 1.37275i | 0.924377 | + | 0.381480i | \(0.124585\pi\) |
−0.131817 | + | 0.991274i | \(0.542081\pi\) | |||||||
\(920\) | −46.2336 | + | 16.8038i | −1.52428 | + | 0.554006i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −42.4191 | − | 50.5531i | −1.39700 | − | 1.66488i | ||||
\(923\) | −0.272449 | − | 0.157298i | −0.00896776 | − | 0.00517754i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.11802 | + | 0.198187i | 0.0367602 | + | 0.00651635i | ||||
\(926\) | 3.59519 | − | 20.3893i | 0.118145 | − | 0.670035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.2227 | − | 47.3189i | −0.565362 | − | 1.55332i | ||||
\(929\) | 6.24472 | + | 5.23994i | 0.204883 | + | 0.171917i | 0.739455 | − | 0.673205i | \(-0.235083\pi\) |
−0.534573 | + | 0.845122i | \(0.679528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.522937 | − | 3.20619i | 0.0171386 | − | 0.105079i | ||||
\(932\) | − | 120.754i | − | 3.95542i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.4579 | + | 5.99020i | −0.538521 | + | 0.196005i | ||||
\(935\) | 8.36628 | + | 4.83536i | 0.273607 | + | 0.158133i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0229 | + | 33.0325i | −0.392770 | + | 1.07913i | 0.572962 | + | 0.819582i | \(0.305794\pi\) |
−0.965731 | + | 0.259544i | \(0.916428\pi\) | |||||||
\(938\) | −31.4237 | + | 18.1425i | −1.02602 | + | 0.592372i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0588775 | − | 129.244i | 0.00192037 | − | 4.21548i | ||||
\(941\) | 11.4837 | − | 9.63598i | 0.374358 | − | 0.314124i | −0.436124 | − | 0.899886i | \(-0.643649\pi\) |
0.810483 | + | 0.585762i | \(0.199205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.7101 | + | 10.2249i | −0.576720 | + | 0.332970i | ||||
\(944\) | −139.658 | − | 50.8313i | −4.54547 | − | 1.65442i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.69911 | − | 32.3213i | −0.185294 | − | 1.05086i | ||||
\(947\) | 11.2823 | + | 30.9978i | 0.366625 | + | 1.00729i | 0.976636 | + | 0.214901i | \(0.0689430\pi\) |
−0.610011 | + | 0.792393i | \(0.708835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.171999 | 0.00558331 | ||||||||
\(950\) | 51.0561 | + | 28.6698i | 1.65648 | + | 0.930170i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28.0855 | + | 33.4710i | −0.910256 | + | 1.08480i | ||||
\(953\) | 9.90142 | + | 27.2039i | 0.320739 | + | 0.881222i | 0.990360 | + | 0.138519i | \(0.0442342\pi\) |
−0.669621 | + | 0.742703i | \(0.733544\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.9148 | + | 13.3418i | −0.514991 | + | 0.431729i | ||||
\(956\) | 47.5017 | + | 17.2892i | 1.53632 | + | 0.559173i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.7930 | − | 16.6236i | −0.930259 | − | 0.537085i | ||||
\(959\) | 9.78639 | − | 8.21176i | 0.316019 | − | 0.265171i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3351 | − | 19.6330i | 0.365648 | − | 0.633322i | ||||
\(962\) | −0.0213953 | + | 0.0123526i | −0.000689812 | + | 0.000398263i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.3038 | + | 81.1210i | −0.460695 | + | 2.61273i | ||||
\(965\) | −48.0736 | − | 27.7845i | −1.54755 | − | 0.894416i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.4472 | + | 25.5597i | −0.689694 | + | 0.821945i | −0.991319 | − | 0.131481i | \(-0.958027\pi\) |
0.301625 | + | 0.953427i | \(0.402471\pi\) | |||||||
\(968\) | 46.1347i | 1.48283i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.7408 | + | 21.6190i | 0.826486 | + | 0.694146i | ||||
\(971\) | 5.21562 | + | 4.37643i | 0.167377 | + | 0.140446i | 0.722629 | − | 0.691236i | \(-0.242934\pi\) |
−0.555252 | + | 0.831682i | \(0.687378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.5020 | − | 3.79138i | 0.689323 | − | 0.121546i | ||||
\(974\) | −18.0648 | + | 102.451i | −0.578833 | + | 3.28273i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.3225 | − | 50.7881i | −0.938591 | − | 1.62569i | ||||
\(977\) | −0.0579657 | − | 0.0334665i | −0.00185449 | − | 0.00107069i | 0.499072 | − | 0.866560i | \(-0.333674\pi\) |
−0.500927 | + | 0.865490i | \(0.667007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.0644 | − | 23.5489i | 0.896944 | − | 0.752625i | ||||
\(980\) | −8.17304 | + | 2.97053i | −0.261078 | + | 0.0948901i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.8617 | − | 79.2969i | 0.921014 | − | 2.53046i | ||||
\(983\) | 49.5418 | + | 8.73556i | 1.58014 | + | 0.278621i | 0.893733 | − | 0.448599i | \(-0.148077\pi\) |
0.686405 | + | 0.727220i | \(0.259188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.19555 | + | 8.76726i | −0.101819 | + | 0.279348i | ||||
\(986\) | 11.0175 | + | 9.24478i | 0.350869 | + | 0.294414i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.904916 | + | 0.171583i | −0.0287892 | + | 0.00545877i | ||||
\(989\) | −13.0593 | −0.415261 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.99186 | + | 1.45292i | −0.126806 | + | 0.0461534i | −0.404644 | − | 0.914475i | \(-0.632604\pi\) |
0.277838 | + | 0.960628i | \(0.410382\pi\) | |||||||
\(992\) | 48.5468 | − | 8.56011i | 1.54136 | − | 0.271784i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −54.5885 | − | 19.8686i | −1.73144 | − | 0.630194i | ||||
\(995\) | −8.71497 | + | 49.2937i | −0.276283 | + | 1.56272i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5816 | + | 35.2540i | 0.936858 | + | 1.11650i | 0.993004 | + | 0.118082i | \(0.0376744\pi\) |
−0.0561457 | + | 0.998423i | \(0.517881\pi\) | |||||||
\(998\) | −33.5483 | − | 39.9813i | −1.06195 | − | 1.26559i | ||||
\(999\) | 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 | 855.2.da.b.244.1 | 48 | ||
3.2 | odd | 2 | 95.2.p.a.54.8 | yes | 48 | ||
5.4 | even | 2 | inner | 855.2.da.b.244.8 | 48 | ||
15.2 | even | 4 | 475.2.l.f.301.8 | 48 | |||
15.8 | even | 4 | 475.2.l.f.301.1 | 48 | |||
15.14 | odd | 2 | 95.2.p.a.54.1 | yes | 48 | ||
19.6 | even | 9 | inner | 855.2.da.b.424.8 | 48 | ||
57.5 | odd | 18 | 1805.2.b.k.1084.1 | 24 | |||
57.14 | even | 18 | 1805.2.b.l.1084.24 | 24 | |||
57.44 | odd | 18 | 95.2.p.a.44.1 | ✓ | 48 | ||
95.44 | even | 18 | inner | 855.2.da.b.424.1 | 48 | ||
285.14 | even | 18 | 1805.2.b.l.1084.1 | 24 | |||
285.44 | odd | 18 | 95.2.p.a.44.8 | yes | 48 | ||
285.62 | even | 36 | 9025.2.a.cu.1.24 | 24 | |||
285.119 | odd | 18 | 1805.2.b.k.1084.24 | 24 | |||
285.128 | odd | 36 | 9025.2.a.ct.1.24 | 24 | |||
285.158 | even | 36 | 475.2.l.f.101.1 | 48 | |||
285.233 | even | 36 | 9025.2.a.cu.1.1 | 24 | |||
285.242 | odd | 36 | 9025.2.a.ct.1.1 | 24 | |||
285.272 | even | 36 | 475.2.l.f.101.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.1 | ✓ | 48 | 57.44 | odd | 18 | ||
95.2.p.a.44.8 | yes | 48 | 285.44 | odd | 18 | ||
95.2.p.a.54.1 | yes | 48 | 15.14 | odd | 2 | ||
95.2.p.a.54.8 | yes | 48 | 3.2 | odd | 2 | ||
475.2.l.f.101.1 | 48 | 285.158 | even | 36 | |||
475.2.l.f.101.8 | 48 | 285.272 | even | 36 | |||
475.2.l.f.301.1 | 48 | 15.8 | even | 4 | |||
475.2.l.f.301.8 | 48 | 15.2 | even | 4 | |||
855.2.da.b.244.1 | 48 | 1.1 | even | 1 | trivial | ||
855.2.da.b.244.8 | 48 | 5.4 | even | 2 | inner | ||
855.2.da.b.424.1 | 48 | 95.44 | even | 18 | inner | ||
855.2.da.b.424.8 | 48 | 19.6 | even | 9 | inner | ||
1805.2.b.k.1084.1 | 24 | 57.5 | odd | 18 | |||
1805.2.b.k.1084.24 | 24 | 285.119 | odd | 18 | |||
1805.2.b.l.1084.1 | 24 | 285.14 | even | 18 | |||
1805.2.b.l.1084.24 | 24 | 57.14 | even | 18 | |||
9025.2.a.ct.1.1 | 24 | 285.242 | odd | 36 | |||
9025.2.a.ct.1.24 | 24 | 285.128 | odd | 36 | |||
9025.2.a.cu.1.1 | 24 | 285.233 | even | 36 | |||
9025.2.a.cu.1.24 | 24 | 285.62 | even | 36 |