Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,3,Mod(44,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.44");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.14987699641\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.6 | ||
Character | \(\chi\) | \(=\) | 189.116 |
Dual form | 189.3.j.b.44.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.513687i | 0.256844i | 0.991720 | + | 0.128422i | \(0.0409911\pi\) | ||||
−0.991720 | + | 0.128422i | \(0.959009\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.73613 | 0.934031 | ||||||||
\(5\) | 6.08350 | + | 3.51231i | 1.21670 | + | 0.702462i | 0.964210 | − | 0.265138i | \(-0.0854176\pi\) |
0.252489 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23968 | − | 6.88935i | 0.177097 | − | 0.984193i | ||||
\(8\) | 3.97395i | 0.496744i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.80423 | + | 3.12502i | −0.180423 | + | 0.312502i | ||||
\(11\) | −3.15993 | + | 1.82439i | −0.287266 | + | 0.165853i | −0.636708 | − | 0.771105i | \(-0.719704\pi\) |
0.349442 | + | 0.936958i | \(0.386371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.79085 | − | 6.56594i | −0.291604 | − | 0.505073i | 0.682585 | − | 0.730806i | \(-0.260856\pi\) |
−0.974189 | + | 0.225733i | \(0.927522\pi\) | |||||||
\(14\) | 3.53897 | + | 0.636806i | 0.252784 | + | 0.0454862i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.9031 | 0.806446 | ||||||||
\(17\) | −17.5124 | − | 10.1108i | −1.03014 | − | 0.594751i | −0.113114 | − | 0.993582i | \(-0.536083\pi\) |
−0.917024 | + | 0.398831i | \(0.869416\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.6978 | + | 23.7253i | 0.720937 | + | 1.24870i | 0.960625 | + | 0.277849i | \(0.0896216\pi\) |
−0.239688 | + | 0.970850i | \(0.577045\pi\) | |||||||
\(20\) | 22.7287 | + | 13.1224i | 1.13644 | + | 0.656121i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.937164 | − | 1.62322i | −0.0425984 | − | 0.0737825i | ||||
\(23\) | −3.42024 | − | 1.97468i | −0.148706 | − | 0.0858556i | 0.423801 | − | 0.905755i | \(-0.360696\pi\) |
−0.572507 | + | 0.819900i | \(0.694029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1726 | + | 21.0836i | 0.486905 | + | 0.843344i | ||||
\(26\) | 3.37284 | − | 1.94731i | 0.129725 | − | 0.0748966i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.63159 | − | 25.7395i | 0.165414 | − | 0.919268i | ||||
\(29\) | 23.7260 | + | 13.6982i | 0.818139 | + | 0.472353i | 0.849774 | − | 0.527147i | \(-0.176738\pi\) |
−0.0316352 | + | 0.999499i | \(0.510071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.85004 | 0.156453 | 0.0782264 | − | 0.996936i | \(-0.475074\pi\) | ||||
0.0782264 | + | 0.996936i | \(0.475074\pi\) | |||||||
\(32\) | 22.5240i | 0.703874i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.19377 | − | 8.99588i | 0.152758 | − | 0.264585i | ||||
\(35\) | 31.7391 | − | 37.5572i | 0.906832 | − | 1.07306i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.7209 | − | 32.4256i | −0.505971 | − | 0.876367i | −0.999976 | − | 0.00690796i | \(-0.997801\pi\) |
0.494006 | − | 0.869459i | \(-0.335532\pi\) | |||||||
\(38\) | −12.1874 | + | 7.03639i | −0.320721 | + | 0.185168i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.9577 | + | 24.1755i | −0.348943 | + | 0.604388i | ||||
\(41\) | −61.1213 | + | 35.2884i | −1.49076 | + | 0.860693i | −0.999944 | − | 0.0105682i | \(-0.996636\pi\) |
−0.490820 | + | 0.871261i | \(0.663303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.41887 | + | 16.3140i | −0.219043 | + | 0.379394i | −0.954516 | − | 0.298160i | \(-0.903627\pi\) |
0.735472 | + | 0.677555i | \(0.236960\pi\) | |||||||
\(44\) | −11.8059 | + | 6.81613i | −0.268316 | + | 0.154912i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.01437 | − | 1.75694i | 0.0220515 | − | 0.0381943i | ||||
\(47\) | − | 23.9730i | − | 0.510063i | −0.966933 | − | 0.255031i | \(-0.917914\pi\) | ||
0.966933 | − | 0.255031i | \(-0.0820858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.9264 | − | 17.0811i | −0.937274 | − | 0.348595i | ||||
\(50\) | −10.8304 | + | 6.25292i | −0.216608 | + | 0.125058i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.1631 | − | 24.5312i | −0.272367 | − | 0.471754i | ||||
\(53\) | −23.1126 | − | 13.3441i | −0.436087 | − | 0.251775i | 0.265850 | − | 0.964015i | \(-0.414348\pi\) |
−0.701936 | + | 0.712240i | \(0.747681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25.6312 | −0.466022 | ||||||||
\(56\) | 27.3779 | + | 4.92641i | 0.488892 | + | 0.0879717i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.03661 | + | 12.1878i | −0.121321 | + | 0.210134i | ||||
\(59\) | − | 52.8103i | − | 0.895089i | −0.894262 | − | 0.447545i | \(-0.852299\pi\) | ||
0.894262 | − | 0.447545i | \(-0.147701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −106.944 | −1.75318 | −0.876588 | − | 0.481242i | \(-0.840186\pi\) | ||||
−0.876588 | + | 0.481242i | \(0.840186\pi\) | |||||||
\(62\) | 2.49140i | 0.0401839i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 40.0422 | 0.625660 | ||||||||
\(65\) | − | 53.2585i | − | 0.819362i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.155 | 1.52471 | 0.762354 | − | 0.647161i | \(-0.224044\pi\) | ||||
0.762354 | + | 0.647161i | \(0.224044\pi\) | |||||||
\(68\) | −65.4284 | − | 37.7751i | −0.962182 | − | 0.555516i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 19.2927 | + | 16.3040i | 0.275610 | + | 0.232914i | ||||
\(71\) | − | 138.410i | − | 1.94944i | −0.223427 | − | 0.974721i | \(-0.571725\pi\) | ||
0.223427 | − | 0.974721i | \(-0.428275\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −34.7679 | + | 60.2198i | −0.476273 | + | 0.824929i | −0.999630 | − | 0.0271843i | \(-0.991346\pi\) |
0.523358 | + | 0.852113i | \(0.324679\pi\) | |||||||
\(74\) | 16.6566 | − | 9.61670i | 0.225089 | − | 0.129955i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 51.1767 | + | 88.6406i | 0.673378 | + | 1.16632i | ||||
\(77\) | 8.65155 | + | 24.0315i | 0.112358 | + | 0.312098i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.2155 | 0.293867 | 0.146933 | − | 0.989146i | \(-0.453060\pi\) | ||||
0.146933 | + | 0.989146i | \(0.453060\pi\) | |||||||
\(80\) | 78.4962 | + | 45.3198i | 0.981202 | + | 0.566497i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.1272 | − | 31.3973i | −0.221064 | − | 0.382893i | ||||
\(83\) | 25.9282 | + | 14.9697i | 0.312388 | + | 0.180357i | 0.647995 | − | 0.761645i | \(-0.275608\pi\) |
−0.335606 | + | 0.942002i | \(0.608941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −71.0243 | − | 123.018i | −0.835579 | − | 1.44727i | ||||
\(86\) | −8.38027 | − | 4.83835i | −0.0974450 | − | 0.0562599i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.25002 | − | 12.5574i | −0.0823866 | − | 0.142698i | ||||
\(89\) | −135.658 | + | 78.3225i | −1.52425 | + | 0.880028i | −0.524665 | + | 0.851309i | \(0.675809\pi\) |
−0.999588 | + | 0.0287188i | \(0.990857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49.9345 | + | 17.9769i | −0.548731 | + | 0.197548i | ||||
\(92\) | −12.7785 | − | 7.37765i | −0.138896 | − | 0.0801918i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.3146 | 0.131006 | ||||||||
\(95\) | 192.444i | 2.02572i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.93155 | − | 5.07760i | 0.0302222 | − | 0.0523464i | −0.850519 | − | 0.525945i | \(-0.823712\pi\) |
0.880741 | + | 0.473598i | \(0.157045\pi\) | |||||||
\(98\) | 8.77437 | − | 23.5918i | 0.0895344 | − | 0.240733i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 45.4784 | + | 78.7710i | 0.454784 | + | 0.787710i | ||||
\(101\) | 16.8659 | − | 9.73752i | 0.166989 | − | 0.0964111i | −0.414176 | − | 0.910197i | \(-0.635930\pi\) |
0.581165 | + | 0.813786i | \(0.302597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0458 | + | 22.5961i | −0.126659 | + | 0.219379i | −0.922380 | − | 0.386284i | \(-0.873759\pi\) |
0.795721 | + | 0.605663i | \(0.207092\pi\) | |||||||
\(104\) | 26.0927 | − | 15.0646i | 0.250892 | − | 0.144852i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.85468 | − | 11.8727i | 0.0646668 | − | 0.112006i | ||||
\(107\) | −25.2215 | + | 14.5616i | −0.235715 | + | 0.136090i | −0.613206 | − | 0.789923i | \(-0.710120\pi\) |
0.377491 | + | 0.926013i | \(0.376787\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 50.9986 | − | 88.3322i | 0.467877 | − | 0.810387i | −0.531449 | − | 0.847090i | \(-0.678352\pi\) |
0.999326 | + | 0.0367034i | \(0.0116857\pi\) | |||||||
\(110\) | − | 13.1664i | − | 0.119695i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.9957 | − | 88.8943i | 0.142819 | − | 0.793699i | ||||
\(113\) | 122.755 | − | 70.8728i | 1.08633 | − | 0.627193i | 0.153734 | − | 0.988112i | \(-0.450870\pi\) |
0.932597 | + | 0.360919i | \(0.117537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.8714 | − | 24.0259i | −0.120621 | − | 0.208921i | ||||
\(116\) | 88.6434 | + | 51.1783i | 0.764168 | + | 0.441192i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.1280 | 0.229898 | ||||||||
\(119\) | −91.3663 | + | 108.115i | −0.767784 | + | 0.908527i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.8432 | + | 93.2592i | −0.444985 | + | 0.770737i | ||||
\(122\) | − | 54.9356i | − | 0.450292i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.1204 | 0.146132 | ||||||||
\(125\) | − | 4.59944i | − | 0.0367955i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −39.8045 | −0.313421 | −0.156711 | − | 0.987645i | \(-0.550089\pi\) | ||||
−0.156711 | + | 0.987645i | \(0.550089\pi\) | |||||||
\(128\) | 110.665i | 0.864571i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27.3582 | 0.210448 | ||||||||
\(131\) | 60.2047 | + | 34.7592i | 0.459578 | + | 0.265337i | 0.711867 | − | 0.702315i | \(-0.247850\pi\) |
−0.252289 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 180.433 | − | 64.9573i | 1.35664 | − | 0.488401i | ||||
\(134\) | 52.4759i | 0.391611i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 40.1797 | − | 69.5932i | 0.295439 | − | 0.511715i | ||||
\(137\) | 65.6043 | − | 37.8766i | 0.478863 | − | 0.276472i | −0.241079 | − | 0.970505i | \(-0.577501\pi\) |
0.719943 | + | 0.694034i | \(0.244168\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37.4261 | + | 64.8239i | 0.269253 | + | 0.466359i | 0.968669 | − | 0.248355i | \(-0.0798900\pi\) |
−0.699416 | + | 0.714714i | \(0.746557\pi\) | |||||||
\(140\) | 118.581 | − | 140.319i | 0.847009 | − | 1.00228i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 71.0996 | 0.500702 | ||||||||
\(143\) | 23.9576 | + | 13.8319i | 0.167536 | + | 0.0967269i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 96.2248 | + | 166.666i | 0.663620 | + | 1.14942i | ||||
\(146\) | −30.9342 | − | 17.8598i | −0.211878 | − | 0.122328i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −69.9437 | − | 121.146i | −0.472592 | − | 0.818554i | ||||
\(149\) | 18.7773 | + | 10.8411i | 0.126022 | + | 0.0727591i | 0.561686 | − | 0.827351i | \(-0.310153\pi\) |
−0.435664 | + | 0.900110i | \(0.643486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 85.7533 | + | 148.529i | 0.567902 | + | 0.983636i | 0.996773 | + | 0.0802700i | \(0.0255783\pi\) |
−0.428871 | + | 0.903366i | \(0.641088\pi\) | |||||||
\(152\) | −94.2831 | + | 54.4344i | −0.620284 | + | 0.358121i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.3447 | + | 4.44419i | −0.0801603 | + | 0.0288584i | ||||
\(155\) | 29.5052 | + | 17.0348i | 0.190356 | + | 0.109902i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −80.4532 | −0.512441 | −0.256220 | − | 0.966618i | \(-0.582477\pi\) | ||||
−0.256220 | + | 0.966618i | \(0.582477\pi\) | |||||||
\(158\) | 11.9255i | 0.0754778i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −79.1112 | + | 137.025i | −0.494445 | + | 0.856403i | ||||
\(161\) | −17.8443 | + | 21.1153i | −0.110834 | + | 0.131151i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −67.6792 | − | 117.224i | −0.415210 | − | 0.719165i | 0.580240 | − | 0.814445i | \(-0.302959\pi\) |
−0.995450 | + | 0.0952804i | \(0.969625\pi\) | |||||||
\(164\) | −228.357 | + | 131.842i | −1.39242 | + | 0.803914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.68973 | + | 13.3190i | −0.0463237 | + | 0.0802349i | ||||
\(167\) | −97.2491 | + | 56.1468i | −0.582330 | + | 0.336208i | −0.762059 | − | 0.647508i | \(-0.775811\pi\) |
0.179729 | + | 0.983716i | \(0.442478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 55.7589 | − | 96.5773i | 0.329934 | − | 0.571463i | ||||
\(170\) | 63.1926 | − | 36.4843i | 0.371721 | − | 0.214613i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −35.1901 | + | 60.9510i | −0.204593 | + | 0.354366i | ||||
\(173\) | − | 182.045i | − | 1.05229i | −0.850396 | − | 0.526143i | \(-0.823638\pi\) | ||
0.850396 | − | 0.526143i | \(-0.176362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 160.342 | − | 57.7246i | 0.916243 | − | 0.329855i | ||||
\(176\) | −40.7730 | + | 23.5403i | −0.231665 | + | 0.133752i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −40.2333 | − | 69.6860i | −0.226030 | − | 0.391495i | ||||
\(179\) | 182.206 | + | 105.197i | 1.01791 | + | 0.587691i | 0.913498 | − | 0.406843i | \(-0.133370\pi\) |
0.104413 | + | 0.994534i | \(0.466704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 104.037 | 0.574791 | 0.287396 | − | 0.957812i | \(-0.407211\pi\) | ||||
0.287396 | + | 0.957812i | \(0.407211\pi\) | |||||||
\(182\) | −9.23449 | − | 25.6507i | −0.0507389 | − | 0.140938i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.84728 | − | 13.5919i | 0.0426482 | − | 0.0738689i | ||||
\(185\) | − | 263.014i | − | 1.42170i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 73.7838 | 0.394566 | ||||||||
\(188\) | − | 89.5660i | − | 0.476415i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −98.8559 | −0.520294 | ||||||||
\(191\) | − | 89.7823i | − | 0.470065i | −0.971988 | − | 0.235032i | \(-0.924480\pi\) | ||
0.971988 | − | 0.235032i | \(-0.0755196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −80.1195 | −0.415127 | −0.207564 | − | 0.978222i | \(-0.566553\pi\) | ||||
−0.207564 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(194\) | 2.60830 | + | 1.50590i | 0.0134448 | + | 0.00776238i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −171.587 | − | 63.8173i | −0.875443 | − | 0.325598i | ||||
\(197\) | 49.3712i | 0.250615i | 0.992118 | + | 0.125308i | \(0.0399918\pi\) | ||||
−0.992118 | + | 0.125308i | \(0.960008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01765 | − | 1.76262i | 0.00511381 | − | 0.00885737i | −0.863457 | − | 0.504422i | \(-0.831706\pi\) |
0.868571 | + | 0.495565i | \(0.165039\pi\) | |||||||
\(200\) | −83.7852 | + | 48.3734i | −0.418926 | + | 0.241867i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.00204 | + | 8.66379i | 0.0247626 | + | 0.0428900i | ||||
\(203\) | 123.785 | − | 146.476i | 0.609776 | − | 0.721555i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −495.775 | −2.41842 | ||||||||
\(206\) | −11.6073 | − | 6.70148i | −0.0563462 | − | 0.0325315i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −48.9138 | − | 84.7213i | −0.235163 | − | 0.407314i | ||||
\(209\) | −86.5682 | − | 49.9802i | −0.414202 | − | 0.239139i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 144.840 | + | 250.871i | 0.686446 | + | 1.18896i | 0.972980 | + | 0.230890i | \(0.0741637\pi\) |
−0.286534 | + | 0.958070i | \(0.592503\pi\) | |||||||
\(212\) | −86.3516 | − | 49.8551i | −0.407319 | − | 0.235166i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.48013 | − | 12.9560i | −0.0349539 | − | 0.0605419i | ||||
\(215\) | −114.599 | + | 66.1639i | −0.533020 | + | 0.307739i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.01248 | − | 33.4136i | 0.0277073 | − | 0.153980i | ||||
\(218\) | 45.3751 | + | 26.1973i | 0.208143 | + | 0.120171i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −95.7615 | −0.435279 | ||||||||
\(221\) | 153.314i | 0.693727i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67.9693 | − | 117.726i | 0.304795 | − | 0.527921i | −0.672421 | − | 0.740169i | \(-0.734745\pi\) |
0.977216 | + | 0.212249i | \(0.0680787\pi\) | |||||||
\(224\) | 155.176 | + | 27.9225i | 0.692748 | + | 0.124654i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 36.4065 | + | 63.0579i | 0.161091 | + | 0.279017i | ||||
\(227\) | 43.1303 | − | 24.9013i | 0.190001 | − | 0.109697i | −0.401982 | − | 0.915648i | \(-0.631678\pi\) |
0.591983 | + | 0.805950i | \(0.298345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −71.2489 | + | 123.407i | −0.311131 | + | 0.538894i | −0.978607 | − | 0.205737i | \(-0.934041\pi\) |
0.667477 | + | 0.744631i | \(0.267374\pi\) | |||||||
\(230\) | 12.3418 | − | 7.12555i | 0.0536600 | − | 0.0309806i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −54.4361 | + | 94.2861i | −0.234638 | + | 0.406405i | ||||
\(233\) | −72.6863 | + | 41.9654i | −0.311958 | + | 0.180109i | −0.647802 | − | 0.761808i | \(-0.724312\pi\) |
0.335844 | + | 0.941918i | \(0.390978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 84.2004 | − | 145.839i | 0.358300 | − | 0.620593i | ||||
\(236\) | − | 197.306i | − | 0.836041i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −55.5372 | − | 46.9337i | −0.233350 | − | 0.197201i | ||||
\(239\) | −222.986 | + | 128.741i | −0.932995 | + | 0.538665i | −0.887758 | − | 0.460311i | \(-0.847738\pi\) |
−0.0452374 | + | 0.998976i | \(0.514404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 63.9892 | + | 110.832i | 0.265515 | + | 0.459886i | 0.967698 | − | 0.252110i | \(-0.0811246\pi\) |
−0.702183 | + | 0.711996i | \(0.747791\pi\) | |||||||
\(242\) | −47.9061 | − | 27.6586i | −0.197959 | − | 0.114292i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −399.555 | −1.63752 | ||||||||
\(245\) | −219.399 | − | 265.221i | −0.895506 | − | 1.08253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 103.853 | − | 179.878i | 0.420456 | − | 0.728251i | ||||
\(248\) | 19.2738i | 0.0777170i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.36267 | 0.00945069 | ||||||||
\(251\) | 277.115i | 1.10404i | 0.833830 | + | 0.552022i | \(0.186144\pi\) | ||||
−0.833830 | + | 0.552022i | \(0.813856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.4103 | 0.0569577 | ||||||||
\(254\) | − | 20.4471i | − | 0.0805003i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 103.322 | 0.403600 | ||||||||
\(257\) | 164.899 | + | 95.2045i | 0.641630 | + | 0.370445i | 0.785242 | − | 0.619189i | \(-0.212538\pi\) |
−0.143612 | + | 0.989634i | \(0.545872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −246.599 | + | 88.7778i | −0.952120 | + | 0.342771i | ||||
\(260\) | − | 198.981i | − | 0.765310i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.8554 | + | 30.9264i | −0.0681502 | + | 0.118040i | ||||
\(263\) | 44.0020 | − | 25.4046i | 0.167308 | − | 0.0965954i | −0.414008 | − | 0.910273i | \(-0.635871\pi\) |
0.581316 | + | 0.813678i | \(0.302538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −93.7369 | − | 162.357i | −0.353724 | − | 0.612669i | ||||
\(266\) | 33.3678 | + | 92.6860i | 0.125443 | + | 0.348444i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 381.665 | 1.42412 | ||||||||
\(269\) | 15.6224 | + | 9.01962i | 0.0580760 | + | 0.0335302i | 0.528757 | − | 0.848773i | \(-0.322658\pi\) |
−0.470681 | + | 0.882304i | \(0.655992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −85.9218 | − | 148.821i | −0.317055 | − | 0.549155i | 0.662818 | − | 0.748781i | \(-0.269361\pi\) |
−0.979872 | + | 0.199626i | \(0.936027\pi\) | |||||||
\(272\) | −225.964 | − | 130.461i | −0.830751 | − | 0.479634i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.4568 | + | 33.7001i | 0.0710101 | + | 0.122993i | ||||
\(275\) | −76.9292 | − | 44.4151i | −0.279743 | − | 0.161510i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113.295 | + | 196.232i | 0.409006 | + | 0.708419i | 0.994779 | − | 0.102057i | \(-0.0325423\pi\) |
−0.585773 | + | 0.810475i | \(0.699209\pi\) | |||||||
\(278\) | −33.2992 | + | 19.2253i | −0.119781 | + | 0.0691558i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 149.251 | + | 126.130i | 0.533038 | + | 0.450463i | ||||
\(281\) | 360.913 | + | 208.373i | 1.28439 | + | 0.741541i | 0.977647 | − | 0.210252i | \(-0.0674286\pi\) |
0.306740 | + | 0.951793i | \(0.400762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −124.309 | −0.439255 | −0.219627 | − | 0.975584i | \(-0.570484\pi\) | ||||
−0.219627 | + | 0.975584i | \(0.570484\pi\) | |||||||
\(284\) | − | 517.118i | − | 1.82084i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.10530 | + | 12.3067i | −0.0248437 | + | 0.0430305i | ||||
\(287\) | 167.344 | + | 464.833i | 0.583079 | + | 1.61963i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 59.9552 | + | 103.845i | 0.207457 | + | 0.359327i | ||||
\(290\) | −85.6144 | + | 49.4295i | −0.295222 | + | 0.170446i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −129.897 | + | 224.989i | −0.444854 | + | 0.770509i | ||||
\(293\) | 362.584 | − | 209.338i | 1.23749 | − | 0.714464i | 0.268908 | − | 0.963166i | \(-0.413337\pi\) |
0.968580 | + | 0.248702i | \(0.0800039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 185.486 | − | 321.271i | 0.628766 | − | 1.08905i | ||||
\(296\) | 128.858 | − | 74.3960i | 0.435330 | − | 0.251338i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.56894 | + | 9.64568i | −0.0186877 | + | 0.0323681i | ||||
\(299\) | 29.9429i | 0.100143i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 100.716 | + | 85.1139i | 0.334605 | + | 0.282771i | ||||
\(302\) | −76.2975 | + | 44.0504i | −0.252641 | + | 0.145862i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 176.745 | + | 306.131i | 0.581397 | + | 1.00701i | ||||
\(305\) | −650.592 | − | 375.619i | −2.13309 | − | 1.23154i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 457.334 | 1.48969 | 0.744843 | − | 0.667239i | \(-0.232524\pi\) | ||||
0.744843 | + | 0.667239i | \(0.232524\pi\) | |||||||
\(308\) | 32.3233 | + | 89.7848i | 0.104946 | + | 0.291509i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.75058 | + | 15.1564i | −0.0282277 | + | 0.0488918i | ||||
\(311\) | 348.141i | 1.11942i | 0.828687 | + | 0.559712i | \(0.189088\pi\) | ||||
−0.828687 | + | 0.559712i | \(0.810912\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −135.708 | −0.433571 | −0.216785 | − | 0.976219i | \(-0.569557\pi\) | ||||
−0.216785 | + | 0.976219i | \(0.569557\pi\) | |||||||
\(314\) | − | 41.3278i | − | 0.131617i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 86.7359 | 0.274481 | ||||||||
\(317\) | 407.641i | 1.28593i | 0.765894 | + | 0.642967i | \(0.222297\pi\) | ||||
−0.765894 | + | 0.642967i | \(0.777703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −99.9634 | −0.313365 | ||||||||
\(320\) | 243.597 | + | 140.641i | 0.761240 | + | 0.439502i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.8467 | − | 9.16637i | −0.0336853 | − | 0.0284670i | ||||
\(323\) | − | 553.981i | − | 1.71511i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 92.2892 | − | 159.850i | 0.283967 | − | 0.491845i | ||||
\(326\) | 60.2164 | − | 34.7660i | 0.184713 | − | 0.106644i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −140.234 | − | 242.893i | −0.427544 | − | 0.740528i | ||||
\(329\) | −165.158 | − | 29.7187i | −0.502001 | − | 0.0903304i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 184.399 | 0.557098 | 0.278549 | − | 0.960422i | \(-0.410147\pi\) | ||||
0.278549 | + | 0.960422i | \(0.410147\pi\) | |||||||
\(332\) | 96.8711 | + | 55.9285i | 0.291780 | + | 0.168459i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.8419 | − | 49.9557i | −0.0863530 | − | 0.149568i | ||||
\(335\) | 621.462 | + | 358.801i | 1.85511 | + | 1.07105i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 121.608 | + | 210.631i | 0.360855 | + | 0.625019i | 0.988102 | − | 0.153802i | \(-0.0491516\pi\) |
−0.627247 | + | 0.778820i | \(0.715818\pi\) | |||||||
\(338\) | 49.6105 | + | 28.6426i | 0.146777 | + | 0.0847416i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −265.356 | − | 459.609i | −0.780457 | − | 1.35179i | ||||
\(341\) | −15.3258 | + | 8.84834i | −0.0449436 | + | 0.0259482i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −174.612 | + | 295.228i | −0.509073 | + | 0.860723i | ||||
\(344\) | −64.8308 | − | 37.4301i | −0.188462 | − | 0.108808i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 93.5145 | 0.270273 | ||||||||
\(347\) | 336.800i | 0.970604i | 0.874347 | + | 0.485302i | \(0.161290\pi\) | ||||
−0.874347 | + | 0.485302i | \(0.838710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 239.411 | − | 414.673i | 0.685992 | − | 1.18817i | −0.287132 | − | 0.957891i | \(-0.592702\pi\) |
0.973124 | − | 0.230282i | \(-0.0739650\pi\) | |||||||
\(350\) | 29.6524 | + | 82.3659i | 0.0847212 | + | 0.235331i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −41.0924 | − | 71.1742i | −0.116740 | − | 0.202199i | ||||
\(353\) | 184.488 | − | 106.514i | 0.522630 | − | 0.301740i | −0.215380 | − | 0.976530i | \(-0.569099\pi\) |
0.738010 | + | 0.674790i | \(0.235766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 486.140 | − | 842.019i | 1.36941 | − | 2.37188i | ||||
\(356\) | −506.837 | + | 292.623i | −1.42370 | + | 0.821973i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −54.0382 | + | 93.5970i | −0.150945 | + | 0.261444i | ||||
\(359\) | 439.984 | − | 254.025i | 1.22558 | − | 0.707590i | 0.259479 | − | 0.965749i | \(-0.416449\pi\) |
0.966103 | + | 0.258159i | \(0.0831157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −194.760 | + | 337.333i | −0.539500 | + | 0.934441i | ||||
\(362\) | 53.4426i | 0.147631i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −186.562 | + | 67.1638i | −0.512532 | + | 0.184516i | ||||
\(365\) | −423.021 | + | 244.231i | −1.15896 | + | 0.669127i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.9885 | − | 34.6211i | −0.0544646 | − | 0.0943355i | 0.837508 | − | 0.546426i | \(-0.184012\pi\) |
−0.891972 | + | 0.452090i | \(0.850679\pi\) | |||||||
\(368\) | −44.1319 | − | 25.4795i | −0.119924 | − | 0.0692379i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 135.107 | 0.365155 | ||||||||
\(371\) | −120.584 | + | 142.689i | −0.325025 | + | 0.384605i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6838 | + | 60.0741i | −0.0929860 | + | 0.161056i | −0.908766 | − | 0.417305i | \(-0.862975\pi\) |
0.815780 | + | 0.578362i | \(0.196308\pi\) | |||||||
\(374\) | 37.9018i | 0.101342i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 95.2673 | 0.253371 | ||||||||
\(377\) | − | 207.712i | − | 0.550960i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −140.172 | −0.369847 | −0.184924 | − | 0.982753i | \(-0.559204\pi\) | ||||
−0.184924 | + | 0.982753i | \(0.559204\pi\) | |||||||
\(380\) | 718.993i | 1.89209i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.1201 | 0.120733 | ||||||||
\(383\) | 453.525 | + | 261.843i | 1.18414 | + | 0.683663i | 0.956968 | − | 0.290192i | \(-0.0937193\pi\) |
0.227170 | + | 0.973855i | \(0.427053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.7744 | + | 176.583i | −0.0825310 | + | 0.458656i | ||||
\(386\) | − | 41.1564i | − | 0.106623i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.9526 | − | 18.9705i | 0.0282285 | − | 0.0488931i | ||||
\(389\) | 127.462 | − | 73.5902i | 0.327666 | − | 0.189178i | −0.327139 | − | 0.944976i | \(-0.606084\pi\) |
0.654804 | + | 0.755798i | \(0.272751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.9310 | + | 69.1626i | 0.102125 | + | 0.176886i | ||||
\(392\) | 67.8796 | − | 182.509i | 0.173162 | − | 0.465585i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.3614 | −0.0643690 | ||||||||
\(395\) | 141.231 | + | 81.5399i | 0.357547 | + | 0.206430i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 91.5634 | + | 158.592i | 0.230638 | + | 0.399477i | 0.957996 | − | 0.286781i | \(-0.0925853\pi\) |
−0.727358 | + | 0.686258i | \(0.759252\pi\) | |||||||
\(398\) | 0.905434 | + | 0.522753i | 0.00227496 | + | 0.00131345i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 157.065 | + | 272.044i | 0.392662 | + | 0.680111i | ||||
\(401\) | −531.766 | − | 307.015i | −1.32610 | − | 0.765624i | −0.341406 | − | 0.939916i | \(-0.610903\pi\) |
−0.984694 | + | 0.174291i | \(0.944237\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.3858 | − | 31.8451i | −0.0456223 | − | 0.0790201i | ||||
\(404\) | 63.0130 | − | 36.3806i | 0.155973 | − | 0.0900510i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 75.2427 | + | 63.5866i | 0.185327 | + | 0.156617i | ||||
\(407\) | 118.313 | + | 68.3083i | 0.290697 | + | 0.167834i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 477.066 | 1.16642 | 0.583210 | − | 0.812321i | \(-0.301796\pi\) | ||||
0.583210 | + | 0.812321i | \(0.301796\pi\) | |||||||
\(410\) | − | 254.673i | − | 0.621155i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −48.7409 | + | 84.4217i | −0.118303 | + | 0.204907i | ||||
\(413\) | −363.829 | − | 65.4677i | −0.880941 | − | 0.158517i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 105.156 | + | 182.136i | 0.253388 | + | 0.438881i | ||||
\(416\) | 147.891 | − | 85.3850i | 0.355508 | − | 0.205252i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.6742 | − | 44.4690i | 0.0614215 | − | 0.106385i | ||||
\(419\) | 212.402 | − | 122.630i | 0.506926 | − | 0.292674i | −0.224643 | − | 0.974441i | \(-0.572122\pi\) |
0.731569 | + | 0.681767i | \(0.238788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −247.132 | + | 428.045i | −0.587012 | + | 1.01673i | 0.407609 | + | 0.913156i | \(0.366363\pi\) |
−0.994621 | + | 0.103578i | \(0.966971\pi\) | |||||||
\(422\) | −128.869 | + | 74.4026i | −0.305377 | + | 0.176309i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 53.0287 | − | 91.8483i | 0.125068 | − | 0.216623i | ||||
\(425\) | − | 492.298i | − | 1.15835i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −132.576 | + | 736.773i | −0.310482 | + | 1.72546i | ||||
\(428\) | −94.2307 | + | 54.4041i | −0.220165 | + | 0.127112i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −33.9876 | − | 58.8682i | −0.0790409 | − | 0.136903i | ||||
\(431\) | −274.768 | − | 158.637i | −0.637513 | − | 0.368068i | 0.146143 | − | 0.989263i | \(-0.453314\pi\) |
−0.783656 | + | 0.621195i | \(0.786647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −671.335 | −1.55043 | −0.775213 | − | 0.631699i | \(-0.782358\pi\) | ||||
−0.775213 | + | 0.631699i | \(0.782358\pi\) | |||||||
\(434\) | 17.1642 | + | 3.08854i | 0.0395488 | + | 0.00711644i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 190.537 | − | 330.020i | 0.437012 | − | 0.756927i | ||||
\(437\) | − | 108.195i | − | 0.247586i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 297.955 | 0.678713 | 0.339356 | − | 0.940658i | \(-0.389791\pi\) | ||||
0.339356 | + | 0.940658i | \(0.389791\pi\) | |||||||
\(440\) | − | 101.857i | − | 0.231494i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −78.7553 | −0.178179 | ||||||||
\(443\) | − | 829.378i | − | 1.87218i | −0.351754 | − | 0.936092i | \(-0.614415\pi\) | ||
0.351754 | − | 0.936092i | \(-0.385585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1100.37 | −2.47274 | ||||||||
\(446\) | 60.4745 | + | 34.9150i | 0.135593 | + | 0.0782847i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 49.6395 | − | 275.865i | 0.110802 | − | 0.615771i | ||||
\(449\) | 190.382i | 0.424012i | 0.977268 | + | 0.212006i | \(0.0679997\pi\) | ||||
−0.977268 | + | 0.212006i | \(0.932000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 128.759 | − | 223.018i | 0.285497 | − | 0.494496i | ||||
\(452\) | 458.629 | − | 264.790i | 1.01467 | − | 0.585818i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.7915 | + | 22.1555i | 0.0281751 | + | 0.0488007i | ||||
\(455\) | −366.917 | − | 66.0234i | −0.806411 | − | 0.145106i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −279.974 | −0.612635 | −0.306318 | − | 0.951929i | \(-0.599097\pi\) | ||||
−0.306318 | + | 0.951929i | \(0.599097\pi\) | |||||||
\(458\) | −63.3925 | − | 36.5997i | −0.138411 | − | 0.0799119i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −51.8252 | − | 89.7638i | −0.112663 | − | 0.195139i | ||||
\(461\) | −132.923 | − | 76.7433i | −0.288337 | − | 0.166471i | 0.348855 | − | 0.937177i | \(-0.386571\pi\) |
−0.637192 | + | 0.770705i | \(0.719904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −251.599 | − | 435.782i | −0.543410 | − | 0.941215i | −0.998705 | − | 0.0508737i | \(-0.983799\pi\) |
0.455295 | − | 0.890341i | \(-0.349534\pi\) | |||||||
\(464\) | 306.140 | + | 176.750i | 0.659785 | + | 0.380927i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5571 | − | 37.3380i | −0.0462599 | − | 0.0801245i | ||||
\(467\) | 153.150 | − | 88.4210i | 0.327943 | − | 0.189338i | −0.326984 | − | 0.945030i | \(-0.606032\pi\) |
0.654928 | + | 0.755692i | \(0.272699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 126.640 | − | 703.785i | 0.270021 | − | 1.50061i | ||||
\(470\) | 74.9159 | + | 43.2527i | 0.159395 | + | 0.0920270i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 209.865 | 0.444630 | ||||||||
\(473\) | − | 68.7346i | − | 0.145316i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −333.476 | + | 577.598i | −0.702055 | + | 1.21600i | ||||
\(476\) | −341.356 | + | 403.930i | −0.717134 | + | 0.848593i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −66.1326 | − | 114.545i | −0.138353 | − | 0.239634i | ||||
\(479\) | −409.511 | + | 236.431i | −0.854928 | + | 0.493593i | −0.862311 | − | 0.506380i | \(-0.830983\pi\) |
0.00738248 | + | 0.999973i | \(0.497650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −141.936 | + | 245.841i | −0.295086 | + | 0.511104i | ||||
\(482\) | −56.9332 | + | 32.8704i | −0.118119 | + | 0.0681959i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −201.165 | + | 348.428i | −0.415630 | + | 0.719893i | ||||
\(485\) | 35.6682 | − | 20.5930i | 0.0735426 | − | 0.0424599i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −49.3289 | + | 85.4401i | −0.101291 | + | 0.175442i | −0.912217 | − | 0.409708i | \(-0.865631\pi\) |
0.810926 | + | 0.585149i | \(0.198964\pi\) | |||||||
\(488\) | − | 424.989i | − | 0.870879i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 136.241 | − | 112.702i | 0.278042 | − | 0.230005i | ||||
\(491\) | −807.412 | + | 466.160i | −1.64442 | + | 0.949409i | −0.665190 | + | 0.746674i | \(0.731650\pi\) |
−0.979234 | + | 0.202735i | \(0.935017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −276.999 | − | 479.777i | −0.561865 | − | 0.973178i | ||||
\(494\) | 92.4011 | + | 53.3478i | 0.187047 | + | 0.107991i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 62.5807 | 0.126171 | ||||||||
\(497\) | −953.558 | − | 171.584i | −1.91863 | − | 0.345240i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −237.862 | + | 411.989i | −0.476677 | + | 0.825629i | −0.999643 | − | 0.0267249i | \(-0.991492\pi\) |
0.522966 | + | 0.852354i | \(0.324826\pi\) | |||||||
\(500\) | − | 17.1841i | − | 0.0343681i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −142.351 | −0.283567 | ||||||||
\(503\) | − | 779.244i | − | 1.54919i | −0.632456 | − | 0.774596i | \(-0.717953\pi\) | ||
0.632456 | − | 0.774596i | \(-0.282047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 136.805 | 0.270900 | ||||||||
\(506\) | 7.40239i | 0.0146292i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −148.715 | −0.292745 | ||||||||
\(509\) | 368.995 | + | 213.040i | 0.724942 | + | 0.418545i | 0.816569 | − | 0.577248i | \(-0.195873\pi\) |
−0.0916270 | + | 0.995793i | \(0.529207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 371.775 | + | 314.182i | 0.727543 | + | 0.614837i | ||||
\(512\) | 495.735i | 0.968233i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −48.9053 | + | 84.7065i | −0.0951466 | + | 0.164799i | ||||
\(515\) | −158.729 | + | 91.6420i | −0.308211 | + | 0.177946i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.7359 | + | 75.7528i | 0.0845956 | + | 0.146524i | ||||
\(518\) | −45.6040 | − | 126.675i | −0.0880386 | − | 0.244546i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 211.647 | 0.407013 | ||||||||
\(521\) | 418.449 | + | 241.592i | 0.803166 | + | 0.463708i | 0.844577 | − | 0.535434i | \(-0.179852\pi\) |
−0.0414112 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −107.843 | − | 186.789i | −0.206200 | − | 0.357149i | 0.744314 | − | 0.667829i | \(-0.232776\pi\) |
−0.950514 | + | 0.310680i | \(0.899443\pi\) | |||||||
\(524\) | 224.932 | + | 129.865i | 0.429260 | + | 0.247833i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.0500 | + | 22.6033i | 0.0248099 | + | 0.0429720i | ||||
\(527\) | −84.9356 | − | 49.0376i | −0.161168 | − | 0.0930505i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −256.701 | − | 444.620i | −0.485258 | − | 0.840491i | ||||
\(530\) | 83.4008 | − | 48.1515i | 0.157360 | − | 0.0908519i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 674.119 | − | 242.689i | 1.26714 | − | 0.456182i | ||||
\(533\) | 463.404 | + | 267.546i | 0.869425 | + | 0.501963i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −204.580 | −0.382392 | ||||||||
\(536\) | 405.960i | 0.757389i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.63327 | + | 8.02505i | −0.00861202 | + | 0.0149165i | ||||
\(539\) | 176.287 | − | 29.8123i | 0.327063 | − | 0.0553103i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −436.156 | − | 755.444i | −0.806203 | − | 1.39638i | −0.915476 | − | 0.402372i | \(-0.868186\pi\) |
0.109273 | − | 0.994012i | \(-0.465148\pi\) | |||||||
\(542\) | 76.4474 | − | 44.1369i | 0.141047 | − | 0.0814335i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 227.735 | − | 394.448i | 0.418630 | − | 0.725088i | ||||
\(545\) | 620.500 | − | 358.246i | 1.13853 | − | 0.657331i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −151.008 | + | 261.554i | −0.276067 | + | 0.478161i | −0.970404 | − | 0.241489i | \(-0.922364\pi\) |
0.694337 | + | 0.719650i | \(0.255698\pi\) | |||||||
\(548\) | 245.106 | − | 141.512i | 0.447273 | − | 0.258233i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22.8155 | − | 39.5176i | 0.0414827 | − | 0.0718501i | ||||
\(551\) | 750.543i | 1.36215i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.7797 | − | 159.940i | 0.0520428 | − | 0.289222i | ||||
\(554\) | −100.802 | + | 58.1980i | −0.181953 | + | 0.105051i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 139.829 | + | 242.190i | 0.251490 | + | 0.435594i | ||||
\(557\) | −35.2462 | − | 20.3494i | −0.0632787 | − | 0.0365340i | 0.468027 | − | 0.883714i | \(-0.344965\pi\) |
−0.531306 | + | 0.847180i | \(0.678298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 142.822 | 0.255496 | ||||||||
\(560\) | 409.534 | − | 484.606i | 0.731311 | − | 0.865368i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −107.039 | + | 185.396i | −0.190460 | + | 0.329887i | ||||
\(563\) | − | 557.671i | − | 0.990534i | −0.868741 | − | 0.495267i | \(-0.835070\pi\) | ||
0.868741 | − | 0.495267i | \(-0.164930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 995.709 | 1.76232 | ||||||||
\(566\) | − | 63.8560i | − | 0.112820i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 550.036 | 0.968373 | ||||||||
\(569\) | − | 371.333i | − | 0.652606i | −0.945265 | − | 0.326303i | \(-0.894197\pi\) | ||
0.945265 | − | 0.326303i | \(-0.105803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 404.280 | 0.708021 | 0.354011 | − | 0.935241i | \(-0.384818\pi\) | ||||
0.354011 | + | 0.935241i | \(0.384818\pi\) | |||||||
\(572\) | 89.5087 | + | 51.6779i | 0.156484 | + | 0.0903460i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −238.779 | + | 85.9623i | −0.415991 | + | 0.149760i | ||||
\(575\) | − | 96.1481i | − | 0.167214i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −416.462 | + | 721.333i | −0.721770 | + | 1.25014i | 0.238519 | + | 0.971138i | \(0.423338\pi\) |
−0.960290 | + | 0.279005i | \(0.909995\pi\) | |||||||
\(578\) | −53.3441 | + | 30.7982i | −0.0922908 | + | 0.0532841i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 359.508 | + | 622.686i | 0.619841 | + | 1.07360i | ||||
\(581\) | 135.274 | − | 160.071i | 0.232830 | − | 0.275510i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 97.3789 | 0.167031 | ||||||||
\(584\) | −239.311 | − | 138.166i | −0.409778 | − | 0.236586i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 107.534 | + | 186.255i | 0.183506 | + | 0.317841i | ||||
\(587\) | −464.128 | − | 267.964i | −0.790677 | − | 0.456498i | 0.0495236 | − | 0.998773i | \(-0.484230\pi\) |
−0.840201 | + | 0.542275i | \(0.817563\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.4349 | + | 115.069i | 0.112793 | + | 0.195363i | ||||
\(590\) | 165.033 | + | 95.2818i | 0.279717 | + | 0.161495i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −241.558 | − | 418.391i | −0.408038 | − | 0.706742i | ||||
\(593\) | −522.472 | + | 301.649i | −0.881065 | + | 0.508683i | −0.871010 | − | 0.491266i | \(-0.836534\pi\) |
−0.0100559 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −935.559 | + | 336.809i | −1.57237 | + | 0.566066i | ||||
\(596\) | 70.1545 | + | 40.5037i | 0.117709 | + | 0.0679592i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.3813 | −0.0257212 | ||||||||
\(599\) | − | 795.128i | − | 1.32742i | −0.747988 | − | 0.663712i | \(-0.768980\pi\) | ||
0.747988 | − | 0.663712i | \(-0.231020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 284.164 | − | 492.186i | 0.472818 | − | 0.818945i | −0.526698 | − | 0.850053i | \(-0.676570\pi\) |
0.999516 | + | 0.0311074i | \(0.00990340\pi\) | |||||||
\(602\) | −43.7220 | + | 51.7367i | −0.0726278 | + | 0.0859413i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 320.385 | + | 554.923i | 0.530439 | + | 0.918747i | ||||
\(605\) | −655.110 | + | 378.228i | −1.08283 | + | 0.625170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 119.087 | − | 206.265i | 0.196190 | − | 0.339811i | −0.751100 | − | 0.660188i | \(-0.770476\pi\) |
0.947290 | + | 0.320378i | \(0.103810\pi\) | |||||||
\(608\) | −534.388 | + | 308.529i | −0.878927 | + | 0.507449i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 192.951 | − | 334.201i | 0.316313 | − | 0.547870i | ||||
\(611\) | −157.405 | + | 90.8779i | −0.257619 | + | 0.148736i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −352.492 | + | 610.534i | −0.575028 | + | 0.995977i | 0.421011 | + | 0.907056i | \(0.361675\pi\) |
−0.996039 | + | 0.0889215i | \(0.971658\pi\) | |||||||
\(614\) | 234.927i | 0.382617i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −95.5001 | + | 34.3808i | −0.155033 | + | 0.0558130i | ||||
\(617\) | 722.505 | − | 417.138i | 1.17100 | − | 0.676075i | 0.217082 | − | 0.976153i | \(-0.430346\pi\) |
0.953915 | + | 0.300078i | \(0.0970128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −67.3116 | − | 116.587i | −0.108743 | − | 0.188348i | 0.806519 | − | 0.591209i | \(-0.201349\pi\) |
−0.915261 | + | 0.402861i | \(0.868016\pi\) | |||||||
\(620\) | 110.235 | + | 63.6443i | 0.177799 | + | 0.102652i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −178.835 | −0.287517 | ||||||||
\(623\) | 371.418 | + | 1031.69i | 0.596177 | + | 1.65601i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 320.470 | − | 555.071i | 0.512752 | − | 0.888113i | ||||
\(626\) | − | 69.7113i | − | 0.111360i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −300.583 | −0.478636 | ||||||||
\(629\) | 757.131i | 1.20371i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 951.730 | 1.50829 | 0.754144 | − | 0.656709i | \(-0.228052\pi\) | ||||
0.754144 | + | 0.656709i | \(0.228052\pi\) | |||||||
\(632\) | 92.2571i | 0.145976i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −209.400 | −0.330284 | ||||||||
\(635\) | −242.151 | − | 139.806i | −0.381340 | − | 0.220166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 61.9462 | + | 366.302i | 0.0972468 | + | 0.575043i | ||||
\(638\) | − | 51.3500i | − | 0.0804858i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −388.690 | + | 673.231i | −0.607328 | + | 1.05192i | ||||
\(641\) | 30.1499 | − | 17.4071i | 0.0470358 | − | 0.0271561i | −0.476298 | − | 0.879284i | \(-0.658022\pi\) |
0.523333 | + | 0.852128i | \(0.324688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −504.419 | − | 873.680i | −0.784478 | − | 1.35876i | −0.929311 | − | 0.369299i | \(-0.879598\pi\) |
0.144833 | − | 0.989456i | \(-0.453736\pi\) | |||||||
\(644\) | −66.6684 | + | 78.8895i | −0.103522 | + | 0.122499i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 284.573 | 0.440516 | ||||||||
\(647\) | 762.764 | + | 440.382i | 1.17892 | + | 0.680653i | 0.955766 | − | 0.294129i | \(-0.0950297\pi\) |
0.223159 | + | 0.974782i | \(0.428363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 96.3463 | + | 166.877i | 0.148453 | + | 0.257129i | ||||
\(650\) | 82.1127 | + | 47.4078i | 0.126327 | + | 0.0729350i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −252.858 | − | 437.963i | −0.387819 | − | 0.671722i | ||||
\(653\) | 680.639 | + | 392.967i | 1.04233 | + | 0.601788i | 0.920491 | − | 0.390763i | \(-0.127789\pi\) |
0.121835 | + | 0.992550i | \(0.461122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 244.170 | + | 422.915i | 0.372778 | + | 0.645671i | ||||
\(656\) | −788.657 | + | 455.331i | −1.20222 | + | 0.694102i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.2661 | − | 84.8397i | 0.0232008 | − | 0.128936i | ||||
\(659\) | −692.308 | − | 399.704i | −1.05054 | − | 0.606531i | −0.127741 | − | 0.991808i | \(-0.540773\pi\) |
−0.922801 | + | 0.385276i | \(0.874106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 327.723 | 0.495798 | 0.247899 | − | 0.968786i | \(-0.420260\pi\) | ||||
0.247899 | + | 0.968786i | \(0.420260\pi\) | |||||||
\(662\) | 94.7237i | 0.143087i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.4887 | + | 103.037i | −0.0895914 | + | 0.155177i | ||||
\(665\) | 1325.81 | + | 238.568i | 1.99370 | + | 0.358749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.0992 | − | 93.7026i | −0.0811083 | − | 0.140484i | ||||
\(668\) | −363.335 | + | 209.772i | −0.543915 | + | 0.314029i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −184.312 | + | 319.237i | −0.275092 | + | 0.476473i | ||||
\(671\) | 337.935 | − | 195.107i | 0.503628 | − | 0.290770i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 287.229 | − | 497.495i | 0.426789 | − | 0.739221i | −0.569796 | − | 0.821786i | \(-0.692978\pi\) |
0.996586 | + | 0.0825652i | \(0.0263113\pi\) | |||||||
\(674\) | −108.199 | + | 62.4685i | −0.160532 | + | 0.0926833i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 208.322 | − | 360.825i | 0.308169 | − | 0.533764i | ||||
\(677\) | − | 224.951i | − | 0.332276i | −0.986102 | − | 0.166138i | \(-0.946870\pi\) | ||
0.986102 | − | 0.166138i | \(-0.0531298\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.3472 | − | 26.4911i | −0.0461667 | − | 0.0390148i | ||||
\(680\) | 488.866 | − | 282.247i | 0.718920 | − | 0.415069i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.54528 | − | 7.87266i | −0.00666464 | − | 0.0115435i | ||||
\(683\) | −322.171 | − | 186.006i | −0.471700 | − | 0.272336i | 0.245251 | − | 0.969460i | \(-0.421130\pi\) |
−0.716951 | + | 0.697123i | \(0.754463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 532.138 | 0.776844 | ||||||||
\(686\) | −151.655 | − | 89.6960i | −0.221071 | − | 0.130752i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −121.533 | + | 210.501i | −0.176647 | + | 0.305961i | ||||
\(689\) | 202.341i | 0.293674i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −973.332 | −1.40858 | −0.704292 | − | 0.709910i | \(-0.748735\pi\) | ||||
−0.704292 | + | 0.709910i | \(0.748735\pi\) | |||||||
\(692\) | − | 680.145i | − | 0.982868i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −173.010 | −0.249294 | ||||||||
\(695\) | 525.808i | 0.756558i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1427.17 | 2.04759 | ||||||||
\(698\) | 213.012 | + | 122.983i | 0.305175 | + | 0.176193i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 599.060 | − | 215.666i | 0.855799 | − | 0.308095i | ||||
\(701\) | 495.876i | 0.707384i | 0.935362 | + | 0.353692i | \(0.115074\pi\) | ||||
−0.935362 | + | 0.353692i | \(0.884926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 512.871 | − | 888.318i | 0.729546 | − | 1.26361i | ||||
\(704\) | −126.531 | + | 73.0525i | −0.179731 | + | 0.103768i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.7151 | + | 94.7693i | 0.0775001 | + | 0.134234i | ||||
\(707\) | −46.1770 | − | 128.266i | −0.0653140 | − | 0.181423i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 98.0951 | 0.138357 | 0.0691785 | − | 0.997604i | \(-0.477962\pi\) | ||||
0.0691785 | + | 0.997604i | \(0.477962\pi\) | |||||||
\(710\) | 432.534 | + | 249.724i | 0.609203 | + | 0.351724i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −311.250 | − | 539.100i | −0.437148 | − | 0.757163i | ||||
\(713\) | −16.5883 | − | 9.57727i | −0.0232655 | − | 0.0134324i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 97.1641 | + | 168.293i | 0.135894 | + | 0.235375i | ||||
\(716\) | 680.745 | + | 393.028i | 0.950761 | + | 0.548922i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 130.489 | + | 226.014i | 0.181740 | + | 0.314783i | ||||
\(719\) | 256.458 | − | 148.066i | 0.356687 | − | 0.205933i | −0.310939 | − | 0.950430i | \(-0.600644\pi\) |
0.667627 | + | 0.744496i | \(0.267310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 139.500 | + | 117.889i | 0.193481 | + | 0.163508i | ||||
\(722\) | −173.284 | − | 100.046i | −0.240005 | − | 0.138567i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 388.696 | 0.536873 | ||||||||
\(725\) | 666.973i | 0.919963i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.9897 | − | 22.4988i | 0.0178675 | − | 0.0309475i | −0.856953 | − | 0.515394i | \(-0.827646\pi\) |
0.874821 | + | 0.484446i | \(0.160979\pi\) | |||||||
\(728\) | −71.4391 | − | 198.437i | −0.0981307 | − | 0.272579i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −125.459 | − | 217.301i | −0.171861 | − | 0.297672i | ||||
\(731\) | 329.893 | − | 190.464i | 0.451290 | − | 0.260553i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −337.765 | + | 585.026i | −0.460798 | + | 0.798125i | −0.999001 | − | 0.0446898i | \(-0.985770\pi\) |
0.538203 | + | 0.842815i | \(0.319103\pi\) | |||||||
\(734\) | 17.7844 | − | 10.2678i | 0.0242295 | − | 0.0139889i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.4776 | − | 77.0375i | 0.0604316 | − | 0.104671i | ||||
\(737\) | −322.804 | + | 186.371i | −0.437997 | + | 0.252878i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.89120 | − | 15.4000i | 0.0120314 | − | 0.0208390i | −0.859947 | − | 0.510383i | \(-0.829504\pi\) |
0.871978 | + | 0.489544i | \(0.162837\pi\) | |||||||
\(740\) | − | 982.655i | − | 1.32791i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −73.2973 | − | 61.9426i | −0.0987834 | − | 0.0834805i | ||||
\(743\) | 748.369 | − | 432.071i | 1.00723 | − | 0.581522i | 0.0968479 | − | 0.995299i | \(-0.469124\pi\) |
0.910378 | + | 0.413777i | \(0.135791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 76.1546 | + | 131.904i | 0.102221 | + | 0.177052i | ||||
\(746\) | −30.8593 | − | 17.8166i | −0.0413663 | − | 0.0238829i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 275.665 | 0.368537 | ||||||||
\(749\) | 69.0538 | + | 191.812i | 0.0921947 | + | 0.256090i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −258.812 | + | 448.276i | −0.344623 | + | 0.596905i | −0.985285 | − | 0.170918i | \(-0.945327\pi\) |
0.640662 | + | 0.767823i | \(0.278660\pi\) | |||||||
\(752\) | − | 309.326i | − | 0.411338i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 106.699 | 0.141511 | ||||||||
\(755\) | 1204.77i | 1.59572i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −314.752 | −0.415789 | −0.207895 | − | 0.978151i | \(-0.566661\pi\) | ||||
−0.207895 | + | 0.978151i | \(0.566661\pi\) | |||||||
\(758\) | − | 72.0046i | − | 0.0949929i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −764.761 | −1.00626 | ||||||||
\(761\) | −511.702 | − | 295.431i | −0.672408 | − | 0.388215i | 0.124581 | − | 0.992209i | \(-0.460241\pi\) |
−0.796988 | + | 0.603995i | \(0.793575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −545.330 | − | 460.851i | −0.714718 | − | 0.603998i | ||||
\(764\) | − | 335.438i | − | 0.439055i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −134.505 | + | 232.970i | −0.175594 | + | 0.304139i | ||||
\(767\) | −346.749 | + | 200.196i | −0.452085 | + | 0.261011i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −292.620 | − | 506.833i | −0.380521 | − | 0.659081i | 0.610616 | − | 0.791927i | \(-0.290922\pi\) |
−0.991137 | + | 0.132846i | \(0.957589\pi\) | |||||||
\(770\) | −90.7082 | − | 16.3221i | −0.117803 | − | 0.0211976i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −299.337 | −0.387742 | ||||||||
\(773\) | −856.704 | − | 494.618i | −1.10828 | − | 0.639869i | −0.169900 | − | 0.985461i | \(-0.554345\pi\) |
−0.938385 | + | 0.345593i | \(0.887678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 59.0377 | + | 102.256i | 0.0761777 | + | 0.131944i | ||||
\(776\) | 20.1781 | + | 11.6498i | 0.0260027 | + | 0.0150127i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.8024 | + | 65.4756i | 0.0485892 | + | 0.0841589i | ||||
\(779\) | −1674.46 | − | 966.747i | −2.14949 | − | 1.24101i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 252.514 | + | 437.367i | 0.323321 | + | 0.560009i | ||||
\(782\) | −35.5279 | + | 20.5121i | −0.0454322 | + | 0.0262303i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −592.594 | − | 220.400i | −0.755860 | − | 0.281123i | ||||
\(785\) | −489.437 | − | 282.576i | −0.623486 | − | 0.359970i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1228.57 | −1.56109 | −0.780543 | − | 0.625102i | \(-0.785057\pi\) | ||||
−0.780543 | + | 0.625102i | \(0.785057\pi\) | |||||||
\(788\) | 184.457i | 0.234083i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −41.8860 | + | 72.5487i | −0.0530203 | + | 0.0918338i | ||||
\(791\) | −336.091 | − | 933.565i | −0.424894 | − | 1.18023i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 405.408 | + | 702.187i | 0.511233 | + | 0.885481i | ||||
\(794\) | −81.4669 | + | 47.0349i | −0.102603 | + | 0.0592380i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.80206 | − | 6.58536i | 0.00477645 | − | 0.00827306i | ||||
\(797\) | −631.278 | + | 364.468i | −0.792068 | + | 0.457300i | −0.840690 | − | 0.541517i | \(-0.817850\pi\) |
0.0486223 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −242.385 | + | 419.823i | −0.303360 | + | 0.525436i | ||||
\(800\) | −474.886 | + | 274.176i | −0.593608 | + | 0.342720i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 157.710 | − | 273.162i | 0.196646 | − | 0.340601i | ||||
\(803\) | − | 253.720i | − | 0.315966i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −182.719 | + | 65.7804i | −0.226980 | + | 0.0817148i | ||||
\(806\) | 16.3584 | − | 9.44454i | 0.0202958 | − | 0.0117178i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 38.6964 | + | 67.0241i | 0.0478916 | + | 0.0829507i | ||||
\(809\) | 1007.55 | + | 581.707i | 1.24542 | + | 0.719044i | 0.970193 | − | 0.242335i | \(-0.0779131\pi\) |
0.275229 | + | 0.961379i | \(0.411246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −224.013 | −0.276219 | −0.138109 | − | 0.990417i | \(-0.544103\pi\) | ||||
−0.138109 | + | 0.990417i | \(0.544103\pi\) | |||||||
\(812\) | 462.475 | − | 547.251i | 0.569550 | − | 0.673955i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.0891 | + | 60.7762i | −0.0431070 | + | 0.0746636i | ||||
\(815\) | − | 950.841i | − | 1.16668i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −516.071 | −0.631666 | ||||||||
\(818\) | 245.063i | 0.299588i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1852.28 | −2.25888 | ||||||||
\(821\) | − | 1342.79i | − | 1.63556i | −0.575534 | − | 0.817778i | \(-0.695206\pi\) | ||
0.575534 | − | 0.817778i | \(-0.304794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1330.16 | 1.61623 | 0.808115 | − | 0.589024i | \(-0.200488\pi\) | ||||
0.808115 | + | 0.589024i | \(0.200488\pi\) | |||||||
\(824\) | −89.7956 | − | 51.8435i | −0.108975 | − | 0.0629169i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.6299 | − | 186.894i | 0.0407142 | − | 0.226264i | ||||
\(827\) | − | 863.204i | − | 1.04378i | −0.853014 | − | 0.521889i | \(-0.825228\pi\) | ||
0.853014 | − | 0.521889i | \(-0.174772\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 288.804 | − | 500.224i | 0.348377 | − | 0.603406i | −0.637585 | − | 0.770380i | \(-0.720066\pi\) |
0.985961 | + | 0.166974i | \(0.0533997\pi\) | |||||||
\(830\) | −93.5609 | + | 54.0174i | −0.112724 | + | 0.0650812i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −151.794 | − | 262.915i | −0.182445 | − | 0.316004i | ||||
\(833\) | 631.576 | + | 763.482i | 0.758195 | + | 0.916545i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −788.820 | −0.944694 | ||||||||
\(836\) | −323.429 | − | 186.732i | −0.386877 | − | 0.223364i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 62.9937 | + | 109.108i | 0.0751715 | + | 0.130201i | ||||
\(839\) | 264.845 | + | 152.908i | 0.315667 | + | 0.182251i | 0.649460 | − | 0.760396i | \(-0.274995\pi\) |
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −45.2169 | − | 78.3179i | −0.0537656 | − | 0.0931248i | ||||
\(842\) | −219.881 | − | 126.949i | −0.261142 | − | 0.150770i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 541.141 | + | 937.284i | 0.641162 | + | 1.11053i | ||||
\(845\) | 678.418 | − | 391.685i | 0.802862 | − | 0.463533i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 575.748 | + | 486.556i | 0.679749 | + | 0.574447i | ||||
\(848\) | −298.225 | − | 172.180i | −0.351680 | − | 0.203043i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 252.887 | 0.297514 | ||||||||
\(851\) | 147.871i | 0.173762i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0979 | + | 72.9157i | −0.0493528 | + | 0.0854815i | −0.889646 | − | 0.456650i | \(-0.849049\pi\) |
0.840294 | + | 0.542131i | \(0.182383\pi\) | |||||||
\(854\) | −378.471 | − | 68.1025i | −0.443175 | − | 0.0797453i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −57.8672 | − | 100.229i | −0.0676019 | − | 0.117090i | ||||
\(857\) | 205.440 | − | 118.611i | 0.239720 | − | 0.138402i | −0.375328 | − | 0.926892i | \(-0.622470\pi\) |
0.615048 | + | 0.788490i | \(0.289137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −581.096 | + | 1006.49i | −0.676479 | + | 1.17170i | 0.299555 | + | 0.954079i | \(0.403162\pi\) |
−0.976034 | + | 0.217617i | \(0.930172\pi\) | |||||||
\(860\) | −428.157 | + | 247.197i | −0.497857 | + | 0.287438i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 81.4900 | − | 141.145i | 0.0945360 | − | 0.163741i | ||||
\(863\) | −582.552 | + | 336.337i | −0.675032 | + | 0.389730i | −0.797980 | − | 0.602683i | \(-0.794098\pi\) |
0.122949 | + | 0.992413i | \(0.460765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 639.400 | − | 1107.47i | 0.739191 | − | 1.28032i | ||||
\(866\) | − | 344.856i | − | 0.398217i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.4634 | − | 124.838i | 0.0258795 | − | 0.143822i | ||||
\(869\) | −73.3592 | + | 42.3540i | −0.0844180 | + | 0.0487387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −387.256 | − | 670.747i | −0.444611 | − | 0.770088i | ||||
\(872\) | 351.028 | + | 202.666i | 0.402555 | + | 0.232415i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 55.5784 | 0.0635909 | ||||||||
\(875\) | −31.6872 | − | 5.70182i | −0.0362139 | − | 0.00651636i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 375.664 | − | 650.670i | 0.428352 | − | 0.741927i | −0.568375 | − | 0.822769i | \(-0.692428\pi\) |
0.996727 | + | 0.0808428i | \(0.0257612\pi\) | |||||||
\(878\) | 153.056i | 0.174323i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −330.723 | −0.375822 | ||||||||
\(881\) | 696.005i | 0.790017i | 0.918677 | + | 0.395009i | \(0.129258\pi\) | ||||
−0.918677 | + | 0.395009i | \(0.870742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1217.46 | −1.37878 | −0.689390 | − | 0.724390i | \(-0.742121\pi\) | ||||
−0.689390 | + | 0.724390i | \(0.742121\pi\) | |||||||
\(884\) | 572.799i | 0.647962i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 426.041 | 0.480859 | ||||||||
\(887\) | −504.732 | − | 291.407i | −0.569033 | − | 0.328531i | 0.187730 | − | 0.982221i | \(-0.439887\pi\) |
−0.756763 | + | 0.653689i | \(0.773220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.3447 | + | 274.227i | −0.0555059 | + | 0.308467i | ||||
\(890\) | − | 565.246i | − | 0.635108i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 253.942 | − | 439.840i | 0.284688 | − | 0.493094i | ||||
\(893\) | 568.765 | − | 328.377i | 0.636915 | − | 0.367723i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 738.967 | + | 1279.93i | 0.825661 | + | 1.43009i | ||||
\(896\) | 762.411 | + | 137.189i | 0.850905 | + | 0.153113i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −97.7966 | −0.108905 | ||||||||
\(899\) | 115.072 | + | 66.4370i | 0.128000 | + | 0.0739010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 269.837 | + | 467.372i | 0.299487 | + | 0.518726i | ||||
\(902\) | 114.561 | + | 66.1421i | 0.127008 | + | 0.0733282i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 281.645 | + | 487.824i | 0.311554 | + | 0.539628i | ||||
\(905\) | 632.910 | + | 365.411i | 0.699348 | + | 0.403769i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −99.5801 | − | 172.478i | −0.109791 | − | 0.190163i | 0.805895 | − | 0.592059i | \(-0.201685\pi\) |
−0.915685 | + | 0.401896i | \(0.868351\pi\) | |||||||
\(908\) | 161.140 | − | 93.0344i | 0.177467 | − | 0.102461i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 33.9154 | − | 188.481i | 0.0372696 | − | 0.207122i | ||||
\(911\) | 351.011 | + | 202.656i | 0.385303 | + | 0.222455i | 0.680123 | − | 0.733098i | \(-0.261926\pi\) |
−0.294820 | + | 0.955553i | \(0.595260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −109.242 | −0.119651 | ||||||||
\(914\) | − | 143.819i | − | 0.157351i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −266.195 | + | 461.063i | −0.290606 | + | 0.503344i | ||||
\(917\) | 314.103 | − | 371.681i | 0.342533 | − | 0.405323i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 471.303 | + | 816.321i | 0.512843 | + | 0.888271i | 0.999889 | + | 0.0148944i | \(0.00474119\pi\) |
−0.487046 | + | 0.873377i | \(0.661925\pi\) | |||||||
\(920\) | 95.4778 | − | 55.1241i | 0.103780 | − | 0.0599175i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.4221 | − | 68.2811i | 0.0427571 | − | 0.0740576i | ||||
\(923\) | −908.795 | + | 524.693i | −0.984609 | + | 0.568465i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 455.765 | − | 789.408i | 0.492719 | − | 0.853414i | ||||
\(926\) | 223.856 | − | 129.243i | 0.241745 | − | 0.139572i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −308.539 | + | 534.405i | −0.332477 | + | 0.575867i | ||||
\(929\) | 1385.69i | 1.49160i | 0.666171 | + | 0.745799i | \(0.267932\pi\) | ||||
−0.666171 | + | 0.745799i | \(0.732068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −223.836 | − | 1323.59i | −0.240425 | − | 1.42169i | ||||
\(932\) | −271.565 | + | 156.788i | −0.291379 | + | 0.168228i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.4207 | + | 78.6710i | 0.0486303 | + | 0.0842302i | ||||
\(935\) | 448.863 | + | 259.151i | 0.480068 | + | 0.277167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −93.8449 | −0.100155 | −0.0500773 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500773 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(938\) | 361.525 | + | 65.0532i | 0.385421 | + | 0.0693531i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 314.583 | − | 544.874i | 0.334663 | − | 0.579653i | ||||
\(941\) | 533.954i | 0.567433i | 0.958908 | + | 0.283716i | \(0.0915674\pi\) | ||||
−0.958908 | + | 0.283716i | \(0.908433\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 278.733 | 0.295581 | ||||||||
\(944\) | − | 681.418i | − | 0.721841i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3081 | 0.0373236 | ||||||||
\(947\) | 1539.94i | 1.62612i | 0.582180 | + | 0.813060i | \(0.302200\pi\) | ||||
−0.582180 | + | 0.813060i | \(0.697800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 527.200 | 0.555532 | ||||||||
\(950\) | −296.705 | − | 171.303i | −0.312321 | − | 0.180318i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −429.643 | − | 363.085i | −0.451305 | − | 0.381392i | ||||
\(953\) | 923.067i | 0.968591i | 0.874905 | + | 0.484295i | \(0.160924\pi\) | ||||
−0.874905 | + | 0.484295i | \(0.839076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 315.343 | − | 546.191i | 0.330202 | − | 0.571927i | ||||
\(956\) | −833.103 | + | 480.992i | −0.871446 | + | 0.503130i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −121.452 | − | 210.360i | −0.126776 | − | 0.219583i | ||||
\(959\) | −179.618 | − | 498.926i | −0.187297 | − | 0.520256i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −937.477 | −0.975522 | ||||||||
\(962\) | −126.285 | − | 72.9109i | −0.131274 | − | 0.0757910i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 239.072 | + | 414.084i | 0.248000 | + | 0.429548i | ||||
\(965\) | −487.407 | − | 281.404i | −0.505085 | − | 0.291611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −580.540 | − | 1005.53i | −0.600352 | − | 1.03984i | −0.992768 | − | 0.120052i | \(-0.961694\pi\) |
0.392416 | − | 0.919788i | \(-0.371639\pi\) | |||||||
\(968\) | −370.607 | − | 213.970i | −0.382859 | − | 0.221044i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.5784 | + | 18.3223i | 0.0109055 | + | 0.0188890i | ||||
\(971\) | 751.650 | − | 433.966i | 0.774099 | − | 0.446926i | −0.0602357 | − | 0.998184i | \(-0.519185\pi\) |
0.834335 | + | 0.551258i | \(0.185852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 492.991 | − | 177.481i | 0.506671 | − | 0.182406i | ||||
\(974\) | −43.8895 | − | 25.3396i | −0.0450611 | − | 0.0260160i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1379.91 | −1.41384 | ||||||||
\(977\) | 1600.75i | 1.63844i | 0.573483 | + | 0.819218i | \(0.305592\pi\) | ||||
−0.573483 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 285.781 | − | 494.987i | 0.291911 | − | 0.505605i | ||||
\(980\) | −819.702 | − | 990.898i | −0.836430 | − | 1.01112i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −239.460 | − | 414.757i | −0.243850 | − | 0.422360i | ||||
\(983\) | 1180.61 | − | 681.625i | 1.20103 | − | 0.693413i | 0.240243 | − | 0.970713i | \(-0.422773\pi\) |
0.960783 | + | 0.277300i | \(0.0894397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −173.407 | + | 300.350i | −0.176048 | + | 0.304924i | ||||
\(986\) | 246.455 | − | 142.291i | 0.249955 | − | 0.144311i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 388.006 | − | 672.047i | 0.392719 | − | 0.680209i | ||||
\(989\) | 64.4296 | − | 37.1985i | 0.0651463 | − | 0.0376122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −470.682 | + | 815.244i | −0.474956 | + | 0.822648i | −0.999589 | − | 0.0286806i | \(-0.990869\pi\) |
0.524632 | + | 0.851329i | \(0.324203\pi\) | |||||||
\(992\) | 109.242i | 0.110123i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 88.1406 | − | 489.831i | 0.0886726 | − | 0.492787i | ||||
\(995\) | 12.3817 | − | 7.14858i | 0.0124439 | − | 0.00718450i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 673.246 | + | 1166.10i | 0.675272 | + | 1.16961i | 0.976389 | + | 0.216019i | \(0.0693072\pi\) |
−0.301117 | + | 0.953587i | \(0.597359\pi\) | |||||||
\(998\) | −211.633 | − | 122.187i | −0.212058 | − | 0.122431i | ||||
\(999\) | 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 | 189.3.j.b.116.6 | 22 | ||
3.2 | odd | 2 | 63.3.j.b.11.6 | ✓ | 22 | ||
7.2 | even | 3 | 189.3.n.b.170.6 | 22 | |||
9.4 | even | 3 | 63.3.n.b.32.6 | yes | 22 | ||
9.5 | odd | 6 | 189.3.n.b.179.6 | 22 | |||
21.2 | odd | 6 | 63.3.n.b.2.6 | yes | 22 | ||
21.5 | even | 6 | 441.3.n.f.128.6 | 22 | |||
21.11 | odd | 6 | 441.3.r.g.344.6 | 22 | |||
21.17 | even | 6 | 441.3.r.f.344.6 | 22 | |||
21.20 | even | 2 | 441.3.j.f.263.6 | 22 | |||
63.4 | even | 3 | 441.3.r.g.50.6 | 22 | |||
63.13 | odd | 6 | 441.3.n.f.410.6 | 22 | |||
63.23 | odd | 6 | inner | 189.3.j.b.44.6 | 22 | ||
63.31 | odd | 6 | 441.3.r.f.50.6 | 22 | |||
63.40 | odd | 6 | 441.3.j.f.275.6 | 22 | |||
63.58 | even | 3 | 63.3.j.b.23.6 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.j.b.11.6 | ✓ | 22 | 3.2 | odd | 2 | ||
63.3.j.b.23.6 | yes | 22 | 63.58 | even | 3 | ||
63.3.n.b.2.6 | yes | 22 | 21.2 | odd | 6 | ||
63.3.n.b.32.6 | yes | 22 | 9.4 | even | 3 | ||
189.3.j.b.44.6 | 22 | 63.23 | odd | 6 | inner | ||
189.3.j.b.116.6 | 22 | 1.1 | even | 1 | trivial | ||
189.3.n.b.170.6 | 22 | 7.2 | even | 3 | |||
189.3.n.b.179.6 | 22 | 9.5 | odd | 6 | |||
441.3.j.f.263.6 | 22 | 21.20 | even | 2 | |||
441.3.j.f.275.6 | 22 | 63.40 | odd | 6 | |||
441.3.n.f.128.6 | 22 | 21.5 | even | 6 | |||
441.3.n.f.410.6 | 22 | 63.13 | odd | 6 | |||
441.3.r.f.50.6 | 22 | 63.31 | odd | 6 | |||
441.3.r.f.344.6 | 22 | 21.17 | even | 6 | |||
441.3.r.g.50.6 | 22 | 63.4 | even | 3 | |||
441.3.r.g.344.6 | 22 | 21.11 | odd | 6 |