Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,4,Mod(163,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.163");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.1786532220\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.627014547.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 147 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.1 | ||
Root | \(1.01248i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.235 |
Dual form | 342.4.g.h.163.1 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −4.22121 | − | 7.31135i | −0.377556 | − | 0.653947i | 0.613150 | − | 0.789967i | \(-0.289902\pi\) |
−0.990706 | + | 0.136020i | \(0.956569\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.44242 | −0.509843 | −0.254921 | − | 0.966962i | \(-0.582050\pi\) | ||||
−0.254921 | + | 0.966962i | \(0.582050\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.44242 | − | 14.6227i | 0.266973 | − | 0.462410i | ||||
\(11\) | 47.4865 | 1.30161 | 0.650805 | − | 0.759245i | \(-0.274432\pi\) | ||||
0.650805 | + | 0.759245i | \(0.274432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −33.8272 | + | 58.5905i | −0.721692 | + | 1.25001i | 0.238630 | + | 0.971111i | \(0.423302\pi\) |
−0.960321 | + | 0.278896i | \(0.910032\pi\) | |||||||
\(14\) | −9.44242 | − | 16.3547i | −0.180257 | − | 0.312214i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −38.8052 | − | 67.2126i | −0.553626 | − | 0.958909i | −0.998009 | − | 0.0630719i | \(-0.979910\pi\) |
0.444383 | − | 0.895837i | \(-0.353423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.6901 | − | 63.0585i | 0.648281 | − | 0.761401i | ||||
\(20\) | 33.7697 | 0.377556 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 47.4865 | + | 82.2490i | 0.460189 | + | 0.797070i | ||||
\(23\) | 85.4773 | − | 148.051i | 0.774924 | − | 1.34221i | −0.159913 | − | 0.987131i | \(-0.551121\pi\) |
0.934837 | − | 0.355077i | \(-0.115545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 26.8628 | − | 46.5277i | 0.214902 | − | 0.372222i | ||||
\(26\) | −135.309 | −1.02063 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.8848 | − | 32.7095i | 0.127461 | − | 0.220768i | ||||
\(29\) | 120.061 | − | 207.952i | 0.768787 | − | 1.33158i | −0.169433 | − | 0.985542i | \(-0.554194\pi\) |
0.938221 | − | 0.346037i | \(-0.112473\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 279.104 | 1.61705 | 0.808526 | − | 0.588460i | \(-0.200265\pi\) | ||||
0.808526 | + | 0.588460i | \(0.200265\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 77.6104 | − | 134.425i | 0.391473 | − | 0.678051i | ||||
\(35\) | 39.8584 | + | 69.0368i | 0.192494 | + | 0.333410i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.0617 | −0.0891383 | −0.0445692 | − | 0.999006i | \(-0.514192\pi\) | ||||
−0.0445692 | + | 0.999006i | \(0.514192\pi\) | |||||||
\(38\) | 162.911 | + | 29.9354i | 0.695463 | + | 0.127794i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 33.7697 | + | 58.4908i | 0.133486 | + | 0.231205i | ||||
\(41\) | 35.9106 | + | 62.1990i | 0.136788 | + | 0.236923i | 0.926279 | − | 0.376839i | \(-0.122989\pi\) |
−0.789491 | + | 0.613762i | \(0.789655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −73.6589 | − | 127.581i | −0.261230 | − | 0.452463i | 0.705339 | − | 0.708870i | \(-0.250795\pi\) |
−0.966569 | + | 0.256407i | \(0.917461\pi\) | |||||||
\(44\) | −94.9729 | + | 164.498i | −0.325402 | + | 0.563614i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 341.909 | 1.09591 | ||||||||
\(47\) | −103.671 | + | 179.564i | −0.321746 | + | 0.557280i | −0.980848 | − | 0.194773i | \(-0.937603\pi\) |
0.659103 | + | 0.752053i | \(0.270936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −253.841 | −0.740061 | ||||||||
\(50\) | 107.451 | 0.303918 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −135.309 | − | 234.362i | −0.360846 | − | 0.625003i | ||||
\(53\) | −130.761 | + | 226.486i | −0.338896 | + | 0.586985i | −0.984225 | − | 0.176920i | \(-0.943387\pi\) |
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −200.450 | − | 347.190i | −0.491431 | − | 0.851184i | ||||
\(56\) | 75.5393 | 0.180257 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 480.245 | 1.08723 | ||||||||
\(59\) | −10.9909 | − | 19.0367i | −0.0242524 | − | 0.0420063i | 0.853644 | − | 0.520856i | \(-0.174387\pi\) |
−0.877897 | + | 0.478850i | \(0.841054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 326.552 | − | 565.604i | 0.685420 | − | 1.18718i | −0.287884 | − | 0.957665i | \(-0.592952\pi\) |
0.973304 | − | 0.229518i | \(-0.0737149\pi\) | |||||||
\(62\) | 279.104 | + | 483.423i | 0.571715 | + | 0.990239i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 571.167 | 1.08992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 206.898 | − | 358.357i | 0.377262 | − | 0.653438i | −0.613400 | − | 0.789772i | \(-0.710199\pi\) |
0.990663 | + | 0.136334i | \(0.0435322\pi\) | |||||||
\(68\) | 310.442 | 0.553626 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −79.7168 | + | 138.074i | −0.136114 | + | 0.235756i | ||||
\(71\) | −78.9726 | − | 136.785i | −0.132005 | − | 0.228639i | 0.792445 | − | 0.609944i | \(-0.208808\pi\) |
−0.924449 | + | 0.381305i | \(0.875475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 551.073 | + | 954.486i | 0.883537 | + | 1.53033i | 0.847382 | + | 0.530984i | \(0.178178\pi\) |
0.0361550 | + | 0.999346i | \(0.488489\pi\) | |||||||
\(74\) | −20.0617 | − | 34.7478i | −0.0315151 | − | 0.0545858i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 111.061 | + | 312.105i | 0.167626 | + | 0.471064i | ||||
\(77\) | −448.387 | −0.663616 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 208.907 | + | 361.837i | 0.297517 | + | 0.515314i | 0.975567 | − | 0.219701i | \(-0.0705083\pi\) |
−0.678050 | + | 0.735015i | \(0.737175\pi\) | |||||||
\(80\) | −67.5393 | + | 116.982i | −0.0943891 | + | 0.163487i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −71.8213 | + | 124.398i | −0.0967236 | + | 0.167530i | ||||
\(83\) | −1431.80 | −1.89350 | −0.946751 | − | 0.321967i | \(-0.895656\pi\) | ||||
−0.946751 | + | 0.321967i | \(0.895656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −327.610 | + | 567.437i | −0.418050 | + | 0.724084i | ||||
\(86\) | 147.318 | − | 255.162i | 0.184717 | − | 0.319940i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −379.892 | −0.460189 | ||||||||
\(89\) | 644.697 | − | 1116.65i | 0.767839 | − | 1.32994i | −0.170893 | − | 0.985290i | \(-0.554665\pi\) |
0.938732 | − | 0.344647i | \(-0.112001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 319.411 | − | 553.236i | 0.367949 | − | 0.637306i | ||||
\(92\) | 341.909 | + | 592.204i | 0.387462 | + | 0.671104i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −414.686 | −0.455017 | ||||||||
\(95\) | −687.680 | − | 126.363i | −0.742678 | − | 0.136470i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.3811 | − | 120.172i | −0.0726245 | − | 0.125789i | 0.827426 | − | 0.561574i | \(-0.189804\pi\) |
−0.900051 | + | 0.435785i | \(0.856471\pi\) | |||||||
\(98\) | −253.841 | − | 439.665i | −0.261651 | − | 0.453193i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 107.451 | + | 186.111i | 0.107451 | + | 0.186111i | ||||
\(101\) | −34.8153 | + | 60.3018i | −0.0342995 | + | 0.0594085i | −0.882666 | − | 0.470002i | \(-0.844253\pi\) |
0.848366 | + | 0.529410i | \(0.177587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −644.346 | −0.616401 | −0.308201 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308201 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(104\) | 270.618 | − | 468.724i | 0.255157 | − | 0.441944i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −523.046 | −0.479271 | ||||||||
\(107\) | 189.454 | 0.171171 | 0.0855853 | − | 0.996331i | \(-0.472724\pi\) | ||||
0.0855853 | + | 0.996331i | \(0.472724\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 119.576 | + | 207.112i | 0.105076 | + | 0.181998i | 0.913769 | − | 0.406233i | \(-0.133158\pi\) |
−0.808693 | + | 0.588231i | \(0.799825\pi\) | |||||||
\(110\) | 400.901 | − | 694.380i | 0.347494 | − | 0.601878i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 75.5393 | + | 130.838i | 0.0637303 | + | 0.110384i | ||||
\(113\) | −162.743 | −0.135483 | −0.0677413 | − | 0.997703i | \(-0.521579\pi\) | ||||
−0.0677413 | + | 0.997703i | \(0.521579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1443.27 | −1.17031 | ||||||||
\(116\) | 480.245 | + | 831.809i | 0.384394 | + | 0.665789i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21.9817 | − | 38.0735i | 0.0171490 | − | 0.0297030i | ||||
\(119\) | 366.415 | + | 634.649i | 0.282262 | + | 0.488893i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 923.965 | 0.694188 | ||||||||
\(122\) | 1306.21 | 0.969331 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −558.209 | + | 966.846i | −0.404263 | + | 0.700204i | ||||
\(125\) | −1508.88 | −1.07966 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 48.6891 | − | 84.3320i | 0.0340194 | − | 0.0589233i | −0.848514 | − | 0.529172i | \(-0.822503\pi\) |
0.882534 | + | 0.470249i | \(0.155836\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 571.167 | + | 989.291i | 0.385344 | + | 0.667435i | ||||
\(131\) | 189.699 | + | 328.568i | 0.126520 | + | 0.219138i | 0.922326 | − | 0.386413i | \(-0.126286\pi\) |
−0.795806 | + | 0.605551i | \(0.792953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −506.964 | + | 595.425i | −0.330521 | + | 0.388195i | ||||
\(134\) | 827.591 | 0.533530 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 310.442 | + | 537.701i | 0.195736 | + | 0.339026i | ||||
\(137\) | 1206.84 | − | 2090.31i | 0.752609 | − | 1.30356i | −0.193945 | − | 0.981012i | \(-0.562128\pi\) |
0.946554 | − | 0.322545i | \(-0.104538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1554.52 | − | 2692.51i | 0.948582 | − | 1.64299i | 0.200166 | − | 0.979762i | \(-0.435852\pi\) |
0.748416 | − | 0.663230i | \(-0.230815\pi\) | |||||||
\(140\) | −318.867 | −0.192494 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 157.945 | − | 273.569i | 0.0933414 | − | 0.161672i | ||||
\(143\) | −1606.34 | + | 2782.26i | −0.939361 | + | 1.62702i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2027.22 | −1.16104 | ||||||||
\(146\) | −1102.15 | + | 1908.97i | −0.624755 | + | 1.08211i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 40.1233 | − | 69.4956i | 0.0222846 | − | 0.0385980i | ||||
\(149\) | −1459.55 | − | 2528.02i | −0.802491 | − | 1.38995i | −0.917972 | − | 0.396645i | \(-0.870174\pi\) |
0.115481 | − | 0.993310i | \(-0.463159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1915.72 | −1.03244 | −0.516221 | − | 0.856455i | \(-0.672662\pi\) | ||||
−0.516221 | + | 0.856455i | \(0.672662\pi\) | |||||||
\(152\) | −429.520 | + | 504.468i | −0.229202 | + | 0.269196i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −448.387 | − | 776.629i | −0.234624 | − | 0.406380i | ||||
\(155\) | −1178.16 | − | 2040.63i | −0.610529 | − | 1.05747i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1268.34 | + | 2196.84i | 0.644744 | + | 1.11673i | 0.984361 | + | 0.176166i | \(0.0563694\pi\) |
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(158\) | −417.813 | + | 723.673i | −0.210376 | + | 0.364382i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −270.157 | −0.133486 | ||||||||
\(161\) | −807.113 | + | 1397.96i | −0.395089 | + | 0.684315i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1731.52 | −0.832044 | −0.416022 | − | 0.909355i | \(-0.636576\pi\) | ||||
−0.416022 | + | 0.909355i | \(0.636576\pi\) | |||||||
\(164\) | −287.285 | −0.136788 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1431.80 | − | 2479.95i | −0.669454 | − | 1.15953i | ||||
\(167\) | −715.062 | + | 1238.52i | −0.331336 | + | 0.573891i | −0.982774 | − | 0.184811i | \(-0.940833\pi\) |
0.651438 | + | 0.758702i | \(0.274166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1190.07 | − | 2061.25i | −0.541677 | − | 0.938213i | ||||
\(170\) | −1310.44 | −0.591212 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 589.271 | 0.261230 | ||||||||
\(173\) | 146.662 | + | 254.027i | 0.0644539 | + | 0.111638i | 0.896452 | − | 0.443142i | \(-0.146136\pi\) |
−0.831998 | + | 0.554779i | \(0.812803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −253.650 | + | 439.334i | −0.109566 | + | 0.189775i | ||||
\(176\) | −379.892 | − | 657.992i | −0.162701 | − | 0.281807i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2578.79 | 1.08589 | ||||||||
\(179\) | 3843.52 | 1.60490 | 0.802452 | − | 0.596716i | \(-0.203528\pi\) | ||||
0.802452 | + | 0.596716i | \(0.203528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −884.639 | + | 1532.24i | −0.363286 | + | 0.629229i | −0.988499 | − | 0.151224i | \(-0.951678\pi\) |
0.625214 | + | 0.780454i | \(0.285012\pi\) | |||||||
\(182\) | 1277.64 | 0.520359 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −683.819 | + | 1184.41i | −0.273977 | + | 0.474542i | ||||
\(185\) | 84.6845 | + | 146.678i | 0.0336547 | + | 0.0582917i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1842.72 | − | 3191.69i | −0.720606 | − | 1.24813i | ||||
\(188\) | −414.686 | − | 718.257i | −0.160873 | − | 0.278640i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −468.812 | − | 1317.46i | −0.179006 | − | 0.503045i | ||||
\(191\) | 504.006 | 0.190935 | 0.0954676 | − | 0.995433i | \(-0.469565\pi\) | ||||
0.0954676 | + | 0.995433i | \(0.469565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1083.79 | + | 1877.19i | 0.404213 | + | 0.700118i | 0.994230 | − | 0.107273i | \(-0.0342120\pi\) |
−0.590016 | + | 0.807391i | \(0.700879\pi\) | |||||||
\(194\) | 138.762 | − | 240.343i | 0.0513533 | − | 0.0889465i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 507.682 | − | 879.330i | 0.185015 | − | 0.320456i | ||||
\(197\) | −2111.10 | −0.763501 | −0.381750 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381750 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1069.30 | + | 1852.08i | −0.380907 | + | 0.659750i | −0.991192 | − | 0.132432i | \(-0.957722\pi\) |
0.610285 | + | 0.792182i | \(0.291055\pi\) | |||||||
\(200\) | −214.902 | + | 372.222i | −0.0759795 | + | 0.131600i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −139.261 | −0.0485068 | ||||||||
\(203\) | −1133.67 | + | 1963.57i | −0.391961 | + | 0.678896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 303.172 | − | 525.110i | 0.103290 | − | 0.178904i | ||||
\(206\) | −644.346 | − | 1116.04i | −0.217931 | − | 0.377467i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1082.47 | 0.360846 | ||||||||
\(209\) | 2549.55 | − | 2994.43i | 0.843809 | − | 0.991047i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 487.977 | + | 845.200i | 0.159212 | + | 0.275763i | 0.934585 | − | 0.355741i | \(-0.115771\pi\) |
−0.775373 | + | 0.631504i | \(0.782438\pi\) | |||||||
\(212\) | −523.046 | − | 905.942i | −0.169448 | − | 0.293492i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 189.454 | + | 328.145i | 0.0605179 | + | 0.104820i | ||||
\(215\) | −621.859 | + | 1077.09i | −0.197258 | + | 0.341661i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2635.42 | −0.824442 | ||||||||
\(218\) | −239.152 | + | 414.224i | −0.0743002 | + | 0.128692i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1603.60 | 0.491431 | ||||||||
\(221\) | 5250.70 | 1.59819 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1787.73 | + | 3096.43i | 0.536839 | + | 0.929832i | 0.999072 | + | 0.0430737i | \(0.0137150\pi\) |
−0.462233 | + | 0.886758i | \(0.652952\pi\) | |||||||
\(224\) | −151.079 | + | 261.676i | −0.0450641 | + | 0.0780534i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −162.743 | − | 281.878i | −0.0479003 | − | 0.0829658i | ||||
\(227\) | 86.5237 | 0.0252986 | 0.0126493 | − | 0.999920i | \(-0.495973\pi\) | ||||
0.0126493 | + | 0.999920i | \(0.495973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3928.05 | −1.13351 | −0.566753 | − | 0.823888i | \(-0.691801\pi\) | ||||
−0.566753 | + | 0.823888i | \(0.691801\pi\) | |||||||
\(230\) | −1443.27 | − | 2499.82i | −0.413767 | − | 0.716666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −960.491 | + | 1663.62i | −0.271807 | + | 0.470784i | ||||
\(233\) | 510.013 | + | 883.368i | 0.143399 | + | 0.248375i | 0.928775 | − | 0.370645i | \(-0.120863\pi\) |
−0.785375 | + | 0.619020i | \(0.787530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1750.48 | 0.485908 | ||||||||
\(236\) | 87.9270 | 0.0242524 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −732.830 | + | 1269.30i | −0.199590 | + | 0.345699i | ||||
\(239\) | −264.681 | −0.0716351 | −0.0358175 | − | 0.999358i | \(-0.511404\pi\) | ||||
−0.0358175 | + | 0.999358i | \(0.511404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 86.1935 | − | 149.292i | 0.0230382 | − | 0.0399034i | −0.854276 | − | 0.519819i | \(-0.825999\pi\) |
0.877315 | + | 0.479916i | \(0.159333\pi\) | |||||||
\(242\) | 923.965 | + | 1600.35i | 0.245433 | + | 0.425102i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1306.21 | + | 2262.42i | 0.342710 | + | 0.593592i | ||||
\(245\) | 1071.51 | + | 1855.92i | 0.279415 | + | 0.483960i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1878.44 | + | 5278.82i | 0.483897 | + | 1.35985i | ||||
\(248\) | −2232.84 | −0.571715 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1508.88 | − | 2613.45i | −0.381719 | − | 0.661156i | ||||
\(251\) | −2442.43 | + | 4230.42i | −0.614203 | + | 1.06383i | 0.376321 | + | 0.926490i | \(0.377189\pi\) |
−0.990524 | + | 0.137342i | \(0.956144\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4059.02 | − | 7030.42i | 1.00865 | − | 1.74703i | ||||
\(254\) | 194.757 | 0.0481107 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2011.32 | − | 3483.71i | 0.488181 | − | 0.845555i | −0.511726 | − | 0.859149i | \(-0.670994\pi\) |
0.999908 | + | 0.0135936i | \(0.00432710\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 189.431 | 0.0454465 | ||||||||
\(260\) | −1142.33 | + | 1978.58i | −0.272479 | + | 0.471948i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −379.398 | + | 657.136i | −0.0894629 | + | 0.154954i | ||||
\(263\) | −3571.06 | − | 6185.26i | −0.837266 | − | 1.45019i | −0.892172 | − | 0.451695i | \(-0.850819\pi\) |
0.0549063 | − | 0.998492i | \(-0.482514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2207.89 | 0.511809 | ||||||||
\(266\) | −1538.27 | − | 282.662i | −0.354577 | − | 0.0651546i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 827.591 | + | 1433.43i | 0.188631 | + | 0.326719i | ||||
\(269\) | 2540.63 | + | 4400.50i | 0.575855 | + | 0.997410i | 0.995948 | + | 0.0899291i | \(0.0286640\pi\) |
−0.420093 | + | 0.907481i | \(0.638003\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1486.90 | + | 2575.39i | 0.333295 | + | 0.577284i | 0.983156 | − | 0.182770i | \(-0.0585062\pi\) |
−0.649861 | + | 0.760053i | \(0.725173\pi\) | |||||||
\(272\) | −620.884 | + | 1075.40i | −0.138407 | + | 0.239727i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4827.37 | 1.06435 | ||||||||
\(275\) | 1275.62 | − | 2209.44i | 0.279719 | − | 0.484488i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7778.48 | 1.68723 | 0.843617 | − | 0.536946i | \(-0.180422\pi\) | ||||
0.843617 | + | 0.536946i | \(0.180422\pi\) | |||||||
\(278\) | 6218.09 | 1.34150 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −318.867 | − | 552.294i | −0.0680570 | − | 0.117878i | ||||
\(281\) | 1110.34 | − | 1923.16i | 0.235720 | − | 0.408279i | −0.723762 | − | 0.690050i | \(-0.757589\pi\) |
0.959482 | + | 0.281771i | \(0.0909219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3808.17 | + | 6595.95i | 0.799902 | + | 1.38547i | 0.919679 | + | 0.392671i | \(0.128449\pi\) |
−0.119777 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(284\) | 631.781 | 0.132005 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6425.35 | −1.32846 | ||||||||
\(287\) | −339.083 | − | 587.309i | −0.0697402 | − | 0.120794i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −555.190 | + | 961.618i | −0.113004 | + | 0.195729i | ||||
\(290\) | −2027.22 | − | 3511.24i | −0.410490 | − | 0.710990i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4408.58 | −0.883537 | ||||||||
\(293\) | 9036.61 | 1.80179 | 0.900894 | − | 0.434038i | \(-0.142912\pi\) | ||||
0.900894 | + | 0.434038i | \(0.142912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −92.7895 | + | 160.716i | −0.0183133 | + | 0.0317195i | ||||
\(296\) | 160.493 | 0.0315151 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2919.10 | − | 5056.03i | 0.567447 | − | 0.982846i | ||||
\(299\) | 5782.93 | + | 10016.3i | 1.11851 | + | 1.93732i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 695.518 | + | 1204.67i | 0.133186 | + | 0.230685i | ||||
\(302\) | −1915.72 | − | 3318.12i | −0.365023 | − | 0.632239i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1303.29 | − | 239.483i | −0.245883 | − | 0.0451819i | ||||
\(305\) | −5513.77 | −1.03514 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3898.58 | − | 6752.55i | −0.724769 | − | 1.25534i | −0.959069 | − | 0.283172i | \(-0.908613\pi\) |
0.234300 | − | 0.972164i | \(-0.424720\pi\) | |||||||
\(308\) | 896.774 | − | 1553.26i | 0.165904 | − | 0.287354i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2356.32 | − | 4081.26i | 0.431709 | − | 0.747742i | ||||
\(311\) | −2737.49 | −0.499128 | −0.249564 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249564 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3823.08 | − | 6621.76i | 0.690393 | − | 1.19580i | −0.281316 | − | 0.959615i | \(-0.590771\pi\) |
0.971709 | − | 0.236181i | \(-0.0758957\pi\) | |||||||
\(314\) | −2536.69 | + | 4393.67i | −0.455903 | + | 0.789647i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1671.25 | −0.297517 | ||||||||
\(317\) | −3210.19 | + | 5560.22i | −0.568777 | + | 0.985152i | 0.427910 | + | 0.903821i | \(0.359250\pi\) |
−0.996687 | + | 0.0813300i | \(0.974083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5701.29 | − | 9874.92i | 1.00066 | − | 1.73320i | ||||
\(320\) | −270.157 | − | 467.926i | −0.0471945 | − | 0.0817433i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3228.45 | −0.558741 | ||||||||
\(323\) | −6321.78 | − | 1161.65i | −1.08902 | − | 0.200111i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1817.39 | + | 3147.81i | 0.310187 | + | 0.537259i | ||||
\(326\) | −1731.52 | − | 2999.08i | −0.294172 | − | 0.509521i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −287.285 | − | 497.592i | −0.0483618 | − | 0.0837651i | ||||
\(329\) | 978.909 | − | 1695.52i | 0.164040 | − | 0.284125i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4594.77 | −0.762996 | −0.381498 | − | 0.924370i | \(-0.624592\pi\) | ||||
−0.381498 | + | 0.924370i | \(0.624592\pi\) | |||||||
\(332\) | 2863.60 | − | 4959.91i | 0.473375 | − | 0.819910i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2860.25 | −0.468580 | ||||||||
\(335\) | −3493.43 | −0.569751 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3305.63 | − | 5725.53i | −0.534331 | − | 0.925488i | −0.999195 | − | 0.0401060i | \(-0.987230\pi\) |
0.464865 | − | 0.885382i | \(-0.346103\pi\) | |||||||
\(338\) | 2380.13 | − | 4122.51i | 0.383024 | − | 0.663417i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1310.44 | − | 2269.75i | −0.209025 | − | 0.362042i | ||||
\(341\) | 13253.7 | 2.10477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5635.62 | 0.887157 | ||||||||
\(344\) | 589.271 | + | 1020.65i | 0.0923586 | + | 0.159970i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −293.325 | + | 508.053i | −0.0455758 | + | 0.0789396i | ||||
\(347\) | −1249.31 | − | 2163.88i | −0.193276 | − | 0.334764i | 0.753058 | − | 0.657954i | \(-0.228578\pi\) |
−0.946334 | + | 0.323190i | \(0.895245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10330.5 | 1.58447 | 0.792235 | − | 0.610216i | \(-0.208917\pi\) | ||||
0.792235 | + | 0.610216i | \(0.208917\pi\) | |||||||
\(350\) | −1014.60 | −0.154950 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 759.784 | − | 1315.98i | 0.115047 | − | 0.199268i | ||||
\(353\) | −2608.83 | −0.393354 | −0.196677 | − | 0.980468i | \(-0.563015\pi\) | ||||
−0.196677 | + | 0.980468i | \(0.563015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −666.720 | + | 1154.79i | −0.0996783 | + | 0.172648i | ||||
\(356\) | 2578.79 | + | 4466.59i | 0.383920 | + | 0.664968i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3843.52 | + | 6657.16i | 0.567419 | + | 0.982799i | ||||
\(359\) | 2075.16 | + | 3594.29i | 0.305078 | + | 0.528410i | 0.977279 | − | 0.211958i | \(-0.0679842\pi\) |
−0.672201 | + | 0.740369i | \(0.734651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1093.76 | − | 6771.23i | −0.159463 | − | 0.987204i | ||||
\(362\) | −3538.56 | −0.513764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1277.64 | + | 2212.94i | 0.183975 | + | 0.318653i | ||||
\(365\) | 4652.38 | − | 8058.17i | 0.667170 | − | 1.15557i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3685.24 | − | 6383.02i | 0.524163 | − | 0.907878i | −0.475441 | − | 0.879748i | \(-0.657711\pi\) |
0.999604 | − | 0.0281300i | \(-0.00895523\pi\) | |||||||
\(368\) | −2735.27 | −0.387462 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −169.369 | + | 293.356i | −0.0237975 | + | 0.0412185i | ||||
\(371\) | 1234.70 | − | 2138.57i | 0.172783 | − | 0.299270i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13166.5 | 1.82772 | 0.913858 | − | 0.406035i | \(-0.133089\pi\) | ||||
0.913858 | + | 0.406035i | \(0.133089\pi\) | |||||||
\(374\) | 3685.45 | − | 6383.38i | 0.509545 | − | 0.882558i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 829.372 | − | 1436.51i | 0.113754 | − | 0.197028i | ||||
\(377\) | 8122.69 | + | 14068.9i | 1.10965 | + | 1.92198i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14284.2 | −1.93596 | −0.967978 | − | 0.251034i | \(-0.919230\pi\) | ||||
−0.967978 | + | 0.251034i | \(0.919230\pi\) | |||||||
\(380\) | 1813.10 | − | 2129.47i | 0.244763 | − | 0.287472i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 504.006 | + | 872.965i | 0.0675058 | + | 0.116923i | ||||
\(383\) | −4729.31 | − | 8191.40i | −0.630957 | − | 1.09285i | −0.987357 | − | 0.158515i | \(-0.949329\pi\) |
0.356400 | − | 0.934334i | \(-0.384004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1892.73 | + | 3278.31i | 0.250552 | + | 0.433970i | ||||
\(386\) | −2167.59 | + | 3754.37i | −0.285822 | + | 0.495058i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 555.048 | 0.0726245 | ||||||||
\(389\) | −3550.48 | + | 6149.61i | −0.462767 | + | 0.801536i | −0.999098 | − | 0.0424717i | \(-0.986477\pi\) |
0.536330 | + | 0.844008i | \(0.319810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13267.9 | −1.71607 | ||||||||
\(392\) | 2030.73 | 0.261651 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2111.10 | − | 3656.53i | −0.269938 | − | 0.467547i | ||||
\(395\) | 1763.68 | − | 3054.78i | 0.224659 | − | 0.389120i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −958.081 | − | 1659.44i | −0.121120 | − | 0.209786i | 0.799090 | − | 0.601212i | \(-0.205315\pi\) |
−0.920210 | + | 0.391426i | \(0.871982\pi\) | |||||||
\(398\) | −4277.19 | −0.538684 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −859.610 | −0.107451 | ||||||||
\(401\) | −2784.34 | − | 4822.63i | −0.346742 | − | 0.600575i | 0.638927 | − | 0.769268i | \(-0.279379\pi\) |
−0.985669 | + | 0.168693i | \(0.946045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9441.34 | + | 16352.9i | −1.16701 | + | 2.02133i | ||||
\(404\) | −139.261 | − | 241.207i | −0.0171498 | − | 0.0297042i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4534.68 | −0.554316 | ||||||||
\(407\) | −952.658 | −0.116023 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.3567 | + | 62.9716i | −0.00439541 | + | 0.00761307i | −0.868215 | − | 0.496189i | \(-0.834732\pi\) |
0.863819 | + | 0.503802i | \(0.168066\pi\) | |||||||
\(410\) | 1212.69 | 0.146074 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1288.69 | − | 2232.08i | 0.154100 | − | 0.266910i | ||||
\(413\) | 103.780 | + | 179.753i | 0.0123649 | + | 0.0214166i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6043.93 | + | 10468.4i | 0.714904 | + | 1.23825i | ||||
\(416\) | 1082.47 | + | 1874.90i | 0.127578 | + | 0.220972i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7736.05 | + | 1421.53i | 0.905222 | + | 0.166337i | ||||
\(419\) | −340.170 | −0.0396620 | −0.0198310 | − | 0.999803i | \(-0.506313\pi\) | ||||
−0.0198310 | + | 0.999803i | \(0.506313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −738.497 | − | 1279.11i | −0.0854920 | − | 0.148077i | 0.820109 | − | 0.572208i | \(-0.193913\pi\) |
−0.905601 | + | 0.424131i | \(0.860580\pi\) | |||||||
\(422\) | −975.953 | + | 1690.40i | −0.112580 | + | 0.194994i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1046.09 | − | 1811.88i | 0.119818 | − | 0.207530i | ||||
\(425\) | −4169.67 | −0.475903 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3083.44 | + | 5340.67i | −0.349457 | + | 0.605276i | ||||
\(428\) | −378.909 | + | 656.289i | −0.0427926 | + | 0.0741190i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2487.44 | −0.278965 | ||||||||
\(431\) | −6139.52 | + | 10634.0i | −0.686149 | + | 1.18844i | 0.286925 | + | 0.957953i | \(0.407367\pi\) |
−0.973074 | + | 0.230492i | \(0.925966\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3105.77 | + | 5379.35i | −0.344697 | + | 0.597032i | −0.985299 | − | 0.170841i | \(-0.945352\pi\) |
0.640602 | + | 0.767873i | \(0.278685\pi\) | |||||||
\(434\) | −2635.42 | − | 4564.68i | −0.291484 | − | 0.504866i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −956.609 | −0.105076 | ||||||||
\(437\) | −4746.60 | − | 13338.9i | −0.519590 | − | 1.46016i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6734.49 | + | 11664.5i | 0.732164 | + | 1.26814i | 0.955957 | + | 0.293508i | \(0.0948228\pi\) |
−0.223793 | + | 0.974637i | \(0.571844\pi\) | |||||||
\(440\) | 1603.60 | + | 2777.52i | 0.173747 | + | 0.300939i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5250.70 | + | 9094.47i | 0.565046 | + | 0.978688i | ||||
\(443\) | 3705.54 | − | 6418.19i | 0.397417 | − | 0.688346i | −0.595989 | − | 0.802992i | \(-0.703240\pi\) |
0.993406 | + | 0.114646i | \(0.0365733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10885.6 | −1.15961 | ||||||||
\(446\) | −3575.45 | + | 6192.87i | −0.379602 | + | 0.657491i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −604.315 | −0.0637303 | ||||||||
\(449\) | 3345.93 | 0.351680 | 0.175840 | − | 0.984419i | \(-0.443736\pi\) | ||||
0.175840 | + | 0.984419i | \(0.443736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1705.27 | + | 2953.61i | 0.178044 | + | 0.308382i | ||||
\(452\) | 325.485 | − | 563.757i | 0.0338706 | − | 0.0586657i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 86.5237 | + | 149.864i | 0.00894441 | + | 0.0154922i | ||||
\(455\) | −5393.20 | −0.555686 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −542.238 | −0.0555029 | −0.0277515 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277515 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(458\) | −3928.05 | − | 6803.59i | −0.400755 | − | 0.694128i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2886.54 | − | 4999.64i | 0.292578 | − | 0.506759i | ||||
\(461\) | 1911.72 | + | 3311.19i | 0.193140 | + | 0.334528i | 0.946289 | − | 0.323322i | \(-0.104800\pi\) |
−0.753149 | + | 0.657850i | \(0.771466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3750.37 | −0.376445 | −0.188223 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188223 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(464\) | −3841.96 | −0.384394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1020.03 | + | 1766.74i | −0.101399 | + | 0.175628i | ||||
\(467\) | 2981.61 | 0.295444 | 0.147722 | − | 0.989029i | \(-0.452806\pi\) | ||||
0.147722 | + | 0.989029i | \(0.452806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1953.61 | + | 3383.76i | −0.192344 | + | 0.333150i | ||||
\(470\) | 1750.48 | + | 3031.91i | 0.171795 | + | 0.297557i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 87.9270 | + | 152.294i | 0.00857451 | + | 0.0148515i | ||||
\(473\) | −3497.80 | − | 6058.37i | −0.340019 | − | 0.588930i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1491.71 | − | 4192.01i | −0.144093 | − | 0.404931i | ||||
\(476\) | −2931.32 | −0.282262 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −264.681 | − | 458.441i | −0.0253268 | − | 0.0438674i | ||||
\(479\) | 7677.92 | − | 13298.6i | 0.732387 | − | 1.26853i | −0.223474 | − | 0.974710i | \(-0.571740\pi\) |
0.955860 | − | 0.293821i | \(-0.0949270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 678.631 | − | 1175.42i | 0.0643304 | − | 0.111423i | ||||
\(482\) | 344.774 | 0.0325810 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1847.93 | + | 3200.71i | −0.173547 | + | 0.300592i | ||||
\(485\) | −585.744 | + | 1014.54i | −0.0548397 | + | 0.0949851i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 439.463 | 0.0408911 | 0.0204455 | − | 0.999791i | \(-0.493492\pi\) | ||||
0.0204455 | + | 0.999791i | \(0.493492\pi\) | |||||||
\(488\) | −2612.41 | + | 4524.83i | −0.242333 | + | 0.419733i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2143.03 | + | 3711.84i | −0.197576 | + | 0.342212i | ||||
\(491\) | 9882.91 | + | 17117.7i | 0.908370 | + | 1.57334i | 0.816329 | + | 0.577587i | \(0.196006\pi\) |
0.0920410 | + | 0.995755i | \(0.470661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18636.0 | −1.70248 | ||||||||
\(494\) | −7264.75 | + | 8532.39i | −0.661653 | + | 0.777106i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2232.84 | − | 3867.38i | −0.202132 | − | 0.350102i | ||||
\(497\) | 745.692 | + | 1291.58i | 0.0673016 | + | 0.116570i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4079.86 | − | 7066.53i | −0.366011 | − | 0.633950i | 0.622926 | − | 0.782280i | \(-0.285944\pi\) |
−0.988938 | + | 0.148330i | \(0.952610\pi\) | |||||||
\(500\) | 3017.75 | − | 5226.90i | 0.269916 | − | 0.467508i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9769.73 | −0.868614 | ||||||||
\(503\) | −9837.15 | + | 17038.4i | −0.872002 | + | 1.51035i | −0.0120790 | + | 0.999927i | \(0.503845\pi\) |
−0.859923 | + | 0.510424i | \(0.829488\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 587.850 | 0.0518000 | ||||||||
\(506\) | 16236.1 | 1.42645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 194.757 | + | 337.328i | 0.0170097 | + | 0.0294616i | ||||
\(509\) | −3427.87 | + | 5937.25i | −0.298502 | + | 0.517021i | −0.975794 | − | 0.218694i | \(-0.929820\pi\) |
0.677291 | + | 0.735715i | \(0.263154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5203.46 | − | 9012.65i | −0.450465 | − | 0.780228i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8045.28 | 0.690393 | ||||||||
\(515\) | 2719.92 | + | 4711.04i | 0.232726 | + | 0.403093i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4922.99 | + | 8526.87i | −0.418787 | + | 0.725361i | ||||
\(518\) | 189.431 | + | 328.103i | 0.0160678 | + | 0.0278302i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4569.34 | −0.385344 | ||||||||
\(521\) | 12666.6 | 1.06513 | 0.532567 | − | 0.846388i | \(-0.321227\pi\) | ||||
0.532567 | + | 0.846388i | \(0.321227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2358.62 | + | 4085.24i | −0.197199 | + | 0.341559i | −0.947619 | − | 0.319402i | \(-0.896518\pi\) |
0.750420 | + | 0.660961i | \(0.229851\pi\) | |||||||
\(524\) | −1517.59 | −0.126520 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7142.12 | − | 12370.5i | 0.592036 | − | 1.02544i | ||||
\(527\) | −10830.7 | − | 18759.3i | −0.895243 | − | 1.55061i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8529.25 | − | 14773.1i | −0.701015 | − | 1.21419i | ||||
\(530\) | 2207.89 | + | 3824.17i | 0.180952 | + | 0.313418i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1048.68 | − | 2947.02i | −0.0854629 | − | 0.240169i | ||||
\(533\) | −4859.03 | −0.394874 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −799.726 | − | 1385.17i | −0.0646265 | − | 0.111936i | ||||
\(536\) | −1655.18 | + | 2866.86i | −0.133382 | + | 0.231025i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5081.26 | + | 8801.00i | −0.407191 | + | 0.705275i | ||||
\(539\) | −12054.0 | −0.963270 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5870.58 | + | 10168.1i | −0.466536 | + | 0.808064i | −0.999269 | − | 0.0382192i | \(-0.987831\pi\) |
0.532733 | + | 0.846283i | \(0.321165\pi\) | |||||||
\(542\) | −2973.80 | + | 5150.78i | −0.235675 | + | 0.408201i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2483.53 | −0.195736 | ||||||||
\(545\) | 1009.51 | − | 1748.53i | 0.0793445 | − | 0.137429i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11131.1 | − | 19279.6i | 0.870073 | − | 1.50701i | 0.00815327 | − | 0.999967i | \(-0.497405\pi\) |
0.861920 | − | 0.507044i | \(-0.169262\pi\) | |||||||
\(548\) | 4827.37 | + | 8361.24i | 0.376305 | + | 0.651779i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5102.48 | 0.395583 | ||||||||
\(551\) | −6667.07 | − | 18735.9i | −0.515475 | − | 1.44859i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1972.58 | − | 3416.61i | −0.151687 | − | 0.262729i | ||||
\(554\) | 7778.48 | + | 13472.7i | 0.596527 | + | 1.03322i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6218.09 | + | 10770.0i | 0.474291 | + | 0.821496i | ||||
\(557\) | −9813.87 | + | 16998.1i | −0.746548 | + | 1.29306i | 0.202920 | + | 0.979195i | \(0.434957\pi\) |
−0.949468 | + | 0.313864i | \(0.898377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9966.71 | 0.754109 | ||||||||
\(560\) | 637.734 | − | 1104.59i | 0.0481236 | − | 0.0833525i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4441.36 | 0.333358 | ||||||||
\(563\) | −9810.37 | −0.734384 | −0.367192 | − | 0.930145i | \(-0.619681\pi\) | ||||
−0.367192 | + | 0.930145i | \(0.619681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 686.970 | + | 1189.87i | 0.0511523 | + | 0.0885984i | ||||
\(566\) | −7616.34 | + | 13191.9i | −0.565616 | + | 0.979676i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 631.781 | + | 1094.28i | 0.0466707 | + | 0.0808360i | ||||
\(569\) | −2528.37 | −0.186282 | −0.0931412 | − | 0.995653i | \(-0.529691\pi\) | ||||
−0.0931412 | + | 0.995653i | \(0.529691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21892.0 | −1.60447 | −0.802233 | − | 0.597011i | \(-0.796355\pi\) | ||||
−0.802233 | + | 0.597011i | \(0.796355\pi\) | |||||||
\(572\) | −6425.35 | − | 11129.0i | −0.469680 | − | 0.813510i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 678.166 | − | 1174.62i | 0.0493138 | − | 0.0854140i | ||||
\(575\) | −4592.32 | − | 7954.14i | −0.333066 | − | 0.576888i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4002.61 | −0.288788 | −0.144394 | − | 0.989520i | \(-0.546123\pi\) | ||||
−0.144394 | + | 0.989520i | \(0.546123\pi\) | |||||||
\(578\) | −2220.76 | −0.159812 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4054.43 | − | 7022.48i | 0.290261 | − | 0.502746i | ||||
\(581\) | 13519.7 | 0.965388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6209.40 | + | 10755.0i | −0.441110 | + | 0.764025i | ||||
\(584\) | −4408.58 | − | 7635.89i | −0.312377 | − | 0.541054i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9036.61 | + | 15651.9i | 0.637029 | + | 1.10337i | ||||
\(587\) | 12259.2 | + | 21233.6i | 0.861998 | + | 1.49302i | 0.869997 | + | 0.493056i | \(0.164120\pi\) |
−0.00799928 | + | 0.999968i | \(0.502546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14985.1 | − | 17599.9i | 1.04831 | − | 1.23123i | ||||
\(590\) | −371.158 | −0.0258989 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 160.493 | + | 277.983i | 0.0111423 | + | 0.0192990i | ||||
\(593\) | −8849.35 | + | 15327.5i | −0.612815 | + | 1.06143i | 0.377948 | + | 0.925827i | \(0.376630\pi\) |
−0.990764 | + | 0.135600i | \(0.956704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3093.43 | − | 5357.97i | 0.213140 | − | 0.369169i | ||||
\(596\) | 11676.4 | 0.802491 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11565.9 | + | 20032.6i | −0.790908 | + | 1.36989i | ||||
\(599\) | 1804.00 | − | 3124.63i | 0.123054 | − | 0.213137i | −0.797916 | − | 0.602768i | \(-0.794064\pi\) |
0.920971 | + | 0.389632i | \(0.127398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23195.0 | 1.57429 | 0.787143 | − | 0.616771i | \(-0.211559\pi\) | ||||
0.787143 | + | 0.616771i | \(0.211559\pi\) | |||||||
\(602\) | −1391.04 | + | 2409.34i | −0.0941767 | + | 0.163119i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3831.43 | − | 6636.23i | 0.258110 | − | 0.447060i | ||||
\(605\) | −3900.25 | − | 6755.43i | −0.262095 | − | 0.453962i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3485.49 | −0.233067 | −0.116534 | − | 0.993187i | \(-0.537178\pi\) | ||||
−0.116534 | + | 0.993187i | \(0.537178\pi\) | |||||||
\(608\) | −888.488 | − | 2496.84i | −0.0592647 | − | 0.166546i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5513.77 | − | 9550.13i | −0.365977 | − | 0.633891i | ||||
\(611\) | −7013.84 | − | 12148.3i | −0.464402 | − | 0.804368i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5476.62 | + | 9485.79i | 0.360846 | + | 0.625004i | 0.988100 | − | 0.153811i | \(-0.0491546\pi\) |
−0.627254 | + | 0.778815i | \(0.715821\pi\) | |||||||
\(614\) | 7797.17 | − | 13505.1i | 0.512489 | − | 0.887657i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3587.10 | 0.234624 | ||||||||
\(617\) | 3504.76 | − | 6070.42i | 0.228681 | − | 0.396088i | −0.728736 | − | 0.684794i | \(-0.759892\pi\) |
0.957418 | + | 0.288707i | \(0.0932253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24225.1 | 1.57301 | 0.786503 | − | 0.617587i | \(-0.211890\pi\) | ||||
0.786503 | + | 0.617587i | \(0.211890\pi\) | |||||||
\(620\) | 9425.26 | 0.610529 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2737.49 | − | 4741.47i | −0.176468 | − | 0.305652i | ||||
\(623\) | −6087.49 | + | 10543.8i | −0.391477 | + | 0.678058i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3011.43 | + | 5215.95i | 0.192731 | + | 0.333821i | ||||
\(626\) | 15292.3 | 0.976363 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10146.7 | −0.644744 | ||||||||
\(629\) | 778.497 | + | 1348.40i | 0.0493493 | + | 0.0854755i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7452.24 | + | 12907.7i | −0.470157 | + | 0.814336i | −0.999418 | − | 0.0341235i | \(-0.989136\pi\) |
0.529261 | + | 0.848459i | \(0.322469\pi\) | |||||||
\(632\) | −1671.25 | − | 2894.69i | −0.105188 | − | 0.182191i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12840.8 | −0.804373 | ||||||||
\(635\) | −822.108 | −0.0513769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8586.74 | − | 14872.7i | 0.534095 | − | 0.925081i | ||||
\(638\) | 22805.2 | 1.41515 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 540.315 | − | 935.852i | 0.0333716 | − | 0.0578013i | ||||
\(641\) | −8374.53 | − | 14505.1i | −0.516028 | − | 0.893787i | −0.999827 | − | 0.0186079i | \(-0.994077\pi\) |
0.483799 | − | 0.875179i | \(-0.339257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3554.81 | + | 6157.10i | 0.218022 | + | 0.377624i | 0.954203 | − | 0.299160i | \(-0.0967064\pi\) |
−0.736181 | + | 0.676784i | \(0.763373\pi\) | |||||||
\(644\) | −3228.45 | − | 5591.84i | −0.197545 | − | 0.342157i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4309.75 | − | 12111.3i | −0.262484 | − | 0.737636i | ||||
\(647\) | −6637.82 | −0.403338 | −0.201669 | − | 0.979454i | \(-0.564637\pi\) | ||||
−0.201669 | + | 0.979454i | \(0.564637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −521.918 | − | 903.988i | −0.0315671 | − | 0.0546759i | ||||
\(650\) | −3634.78 | + | 6295.62i | −0.219335 | + | 0.379899i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3463.04 | − | 5998.16i | 0.208011 | − | 0.360285i | ||||
\(653\) | 18762.0 | 1.12437 | 0.562184 | − | 0.827012i | \(-0.309961\pi\) | ||||
0.562184 | + | 0.827012i | \(0.309961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1601.52 | − | 2773.91i | 0.0955365 | − | 0.165474i | ||||
\(656\) | 574.570 | − | 995.185i | 0.0341969 | − | 0.0592308i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3915.64 | 0.231987 | ||||||||
\(659\) | 3078.28 | − | 5331.74i | 0.181962 | − | 0.315167i | −0.760587 | − | 0.649236i | \(-0.775089\pi\) |
0.942549 | + | 0.334069i | \(0.108422\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13082.6 | + | 22659.7i | −0.769824 | + | 1.33337i | 0.167835 | + | 0.985815i | \(0.446322\pi\) |
−0.937658 | + | 0.347558i | \(0.887011\pi\) | |||||||
\(662\) | −4594.77 | − | 7958.38i | −0.269760 | − | 0.467238i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11454.4 | 0.669454 | ||||||||
\(665\) | 6493.36 | + | 1193.18i | 0.378649 | + | 0.0695780i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20525.1 | − | 35550.4i | −1.19150 | − | 2.06375i | ||||
\(668\) | −2860.25 | − | 4954.09i | −0.165668 | − | 0.286946i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3493.43 | − | 6050.80i | −0.201437 | − | 0.348900i | ||||
\(671\) | 15506.8 | − | 26858.5i | 0.892150 | − | 1.54525i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31028.8 | 1.77723 | 0.888613 | − | 0.458657i | \(-0.151669\pi\) | ||||
0.888613 | + | 0.458657i | \(0.151669\pi\) | |||||||
\(674\) | 6611.27 | − | 11451.1i | 0.377829 | − | 0.654419i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9520.52 | 0.541677 | ||||||||
\(677\) | 4341.55 | 0.246469 | 0.123234 | − | 0.992378i | \(-0.460673\pi\) | ||||
0.123234 | + | 0.992378i | \(0.460673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 655.125 | + | 1134.71i | 0.0370271 | + | 0.0641328i | ||||
\(680\) | 2620.88 | − | 4539.49i | 0.147803 | − | 0.256002i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13253.7 | + | 22956.1i | 0.744149 | + | 1.28890i | ||||
\(683\) | −16457.2 | −0.921986 | −0.460993 | − | 0.887404i | \(-0.652507\pi\) | ||||
−0.460993 | + | 0.887404i | \(0.652507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20377.3 | −1.13661 | ||||||||
\(686\) | 5635.62 | + | 9761.18i | 0.313657 | + | 0.543270i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1178.54 | + | 2041.30i | −0.0653074 | + | 0.113116i | ||||
\(689\) | −8846.60 | − | 15322.8i | −0.489156 | − | 0.847244i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2522.21 | 0.138856 | 0.0694280 | − | 0.997587i | \(-0.477883\pi\) | ||||
0.0694280 | + | 0.997587i | \(0.477883\pi\) | |||||||
\(692\) | −1173.30 | −0.0644539 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2498.63 | − | 4327.75i | 0.136667 | − | 0.236714i | ||||
\(695\) | −26247.8 | −1.43257 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2787.04 | − | 4827.29i | 0.151459 | − | 0.262334i | ||||
\(698\) | 10330.5 | + | 17893.0i | 0.560195 | + | 0.970286i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1014.60 | − | 1757.34i | −0.0547832 | − | 0.0948873i | ||||
\(701\) | 2009.91 | + | 3481.27i | 0.108293 | + | 0.187569i | 0.915079 | − | 0.403275i | \(-0.132128\pi\) |
−0.806786 | + | 0.590844i | \(0.798795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1077.11 | + | 1265.06i | −0.0577867 | + | 0.0678700i | ||||
\(704\) | 3039.13 | 0.162701 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2608.83 | − | 4518.62i | −0.139072 | − | 0.240879i | ||||
\(707\) | 328.740 | − | 569.395i | 0.0174874 | − | 0.0302890i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5026.45 | − | 8706.07i | 0.266252 | − | 0.461161i | −0.701639 | − | 0.712533i | \(-0.747548\pi\) |
0.967891 | + | 0.251371i | \(0.0808814\pi\) | |||||||
\(710\) | −2666.88 | −0.140966 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5157.57 | + | 8933.18i | −0.271472 | + | 0.470204i | ||||
\(713\) | 23857.1 | − | 41321.7i | 1.25309 | − | 2.17042i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27122.7 | 1.41865 | ||||||||
\(716\) | −7687.03 | + | 13314.3i | −0.401226 | + | 0.694944i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4150.33 | + | 7188.58i | −0.215723 | + | 0.373643i | ||||
\(719\) | 5215.18 | + | 9032.95i | 0.270505 | + | 0.468529i | 0.968991 | − | 0.247095i | \(-0.0794759\pi\) |
−0.698486 | + | 0.715624i | \(0.746143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6084.18 | 0.314268 | ||||||||
\(722\) | 10634.4 | − | 8665.67i | 0.548158 | − | 0.446680i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3538.56 | − | 6128.96i | −0.181643 | − | 0.314615i | ||||
\(725\) | −6450.37 | − | 11172.4i | −0.330429 | − | 0.572319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10846.7 | + | 18787.1i | 0.553346 | + | 0.958424i | 0.998030 | + | 0.0627365i | \(0.0199828\pi\) |
−0.444684 | + | 0.895688i | \(0.646684\pi\) | |||||||
\(728\) | −2555.29 | + | 4425.89i | −0.130090 | + | 0.225322i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18609.5 | 0.943520 | ||||||||
\(731\) | −5716.70 | + | 9901.61i | −0.289247 | + | 0.500991i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3382.86 | −0.170462 | −0.0852310 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852310 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(734\) | 14741.0 | 0.741279 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2735.27 | − | 4737.64i | −0.136989 | − | 0.237271i | ||||
\(737\) | 9824.84 | − | 17017.1i | 0.491048 | − | 0.850521i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4008.94 | − | 6943.69i | −0.199555 | − | 0.345640i | 0.748829 | − | 0.662763i | \(-0.230616\pi\) |
−0.948384 | + | 0.317123i | \(0.897283\pi\) | |||||||
\(740\) | −677.476 | −0.0336547 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4938.82 | 0.244353 | ||||||||
\(743\) | 4678.96 | + | 8104.19i | 0.231029 | + | 0.400153i | 0.958111 | − | 0.286397i | \(-0.0924576\pi\) |
−0.727082 | + | 0.686550i | \(0.759124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12322.1 | + | 21342.6i | −0.605971 | + | 1.04957i | ||||
\(746\) | 13166.5 | + | 22805.1i | 0.646195 | + | 1.11924i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14741.8 | 0.720606 | ||||||||
\(749\) | −1788.91 | −0.0872700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6483.64 | − | 11230.0i | 0.315035 | − | 0.545657i | −0.664410 | − | 0.747368i | \(-0.731317\pi\) |
0.979445 | + | 0.201712i | \(0.0646504\pi\) | |||||||
\(752\) | 3317.49 | 0.160873 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16245.4 | + | 28137.8i | −0.784644 | + | 1.35904i | ||||
\(755\) | 8086.63 | + | 14006.5i | 0.389805 | + | 0.675162i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13890.7 | − | 24059.4i | −0.666931 | − | 1.15516i | −0.978758 | − | 0.205019i | \(-0.934274\pi\) |
0.311827 | − | 0.950139i | \(-0.399059\pi\) | |||||||
\(758\) | −14284.2 | − | 24740.9i | −0.684464 | − | 1.18553i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5501.44 | + | 1010.91i | 0.262576 | + | 0.0482493i | ||||
\(761\) | −26066.1 | −1.24165 | −0.620825 | − | 0.783949i | \(-0.713202\pi\) | ||||
−0.620825 | + | 0.783949i | \(0.713202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1129.09 | − | 1955.64i | −0.0535724 | − | 0.0927901i | ||||
\(764\) | −1008.01 | + | 1745.93i | −0.0477338 | + | 0.0826774i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9458.62 | − | 16382.8i | 0.446154 | − | 0.772761i | ||||
\(767\) | 1487.16 | 0.0700109 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18417.7 | − | 31900.4i | 0.863665 | − | 1.49591i | −0.00470099 | − | 0.999989i | \(-0.501496\pi\) |
0.868366 | − | 0.495923i | \(-0.165170\pi\) | |||||||
\(770\) | −3785.47 | + | 6556.63i | −0.177167 | + | 0.306863i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8670.35 | −0.404213 | ||||||||
\(773\) | 5604.20 | − | 9706.76i | 0.260762 | − | 0.451653i | −0.705683 | − | 0.708528i | \(-0.749360\pi\) |
0.966445 | + | 0.256875i | \(0.0826929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7497.53 | − | 12986.1i | 0.347509 | − | 0.601903i | ||||
\(776\) | 555.048 | + | 961.372i | 0.0256766 | + | 0.0444733i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14201.9 | −0.654452 | ||||||||
\(779\) | 5850.22 | + | 1075.00i | 0.269071 | + | 0.0494426i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3750.13 | − | 6495.42i | −0.171819 | − | 0.297598i | ||||
\(782\) | −13267.9 | − | 22980.6i | −0.606724 | − | 1.05088i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2030.73 | + | 3517.32i | 0.0925076 | + | 0.160228i | ||||
\(785\) | 10707.9 | − | 18546.6i | 0.486854 | − | 0.843257i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25466.9 | −1.15349 | −0.576745 | − | 0.816924i | \(-0.695677\pi\) | ||||
−0.576745 | + | 0.816924i | \(0.695677\pi\) | |||||||
\(788\) | 4222.20 | − | 7313.07i | 0.190875 | − | 0.330606i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7054.70 | 0.317715 | ||||||||
\(791\) | 1536.68 | 0.0690748 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22092.7 | + | 38265.7i | 0.989324 | + | 1.71356i | ||||
\(794\) | 1916.16 | − | 3318.89i | 0.0856449 | − | 0.148341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4277.19 | − | 7408.31i | −0.190453 | − | 0.329875i | ||||
\(797\) | −31745.4 | −1.41089 | −0.705446 | − | 0.708764i | \(-0.749253\pi\) | ||||
−0.705446 | + | 0.708764i | \(0.749253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16092.0 | 0.712507 | ||||||||
\(800\) | −859.610 | − | 1488.89i | −0.0379897 | − | 0.0658002i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5568.69 | − | 9645.25i | 0.245184 | − | 0.424670i | ||||
\(803\) | 26168.5 | + | 45325.2i | 1.15002 | + | 1.99189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13628.0 | 0.596674 | ||||||||
\(806\) | −37765.3 | −1.65041 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 278.522 | − | 482.415i | 0.0121267 | − | 0.0210041i | ||||
\(809\) | 14106.2 | 0.613040 | 0.306520 | − | 0.951864i | \(-0.400835\pi\) | ||||
0.306520 | + | 0.951864i | \(0.400835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21337.7 | + | 36958.0i | −0.923882 | + | 1.60021i | −0.130532 | + | 0.991444i | \(0.541669\pi\) |
−0.793350 | + | 0.608766i | \(0.791665\pi\) | |||||||
\(812\) | −4534.68 | − | 7854.29i | −0.195980 | − | 0.339448i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −952.658 | − | 1650.05i | −0.0410204 | − | 0.0710495i | ||||
\(815\) | 7309.11 | + | 12659.7i | 0.314143 | + | 0.544112i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11999.8 | − | 2205.01i | −0.513856 | − | 0.0944228i | ||||
\(818\) | −145.427 | −0.00621604 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1212.69 | + | 2100.44i | 0.0516451 | + | 0.0894519i | ||||
\(821\) | −9719.65 | + | 16834.9i | −0.413177 | + | 0.715643i | −0.995235 | − | 0.0975038i | \(-0.968914\pi\) |
0.582058 | + | 0.813147i | \(0.302248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12511.7 | − | 21670.9i | 0.529928 | − | 0.917863i | −0.469462 | − | 0.882953i | \(-0.655552\pi\) |
0.999390 | − | 0.0349103i | \(-0.0111145\pi\) | |||||||
\(824\) | 5154.77 | 0.217931 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −207.561 | + | 359.506i | −0.00874330 | + | 0.0151438i | ||||
\(827\) | −16772.9 | + | 29051.5i | −0.705260 | + | 1.22155i | 0.261338 | + | 0.965247i | \(0.415836\pi\) |
−0.966598 | + | 0.256298i | \(0.917497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5555.52 | 0.232752 | 0.116376 | − | 0.993205i | \(-0.462872\pi\) | ||||
0.116376 | + | 0.993205i | \(0.462872\pi\) | |||||||
\(830\) | −12087.9 | + | 20936.8i | −0.505513 | + | 0.875575i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2164.94 | + | 3749.79i | −0.0902114 | + | 0.156251i | ||||
\(833\) | 9850.35 | + | 17061.3i | 0.409717 | + | 0.709651i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12073.7 | 0.500392 | ||||||||
\(836\) | 5273.90 | + | 14820.8i | 0.218184 | + | 0.613142i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −340.170 | − | 589.192i | −0.0140227 | − | 0.0242879i | ||||
\(839\) | 20491.2 | + | 35491.8i | 0.843188 | + | 1.46044i | 0.887185 | + | 0.461413i | \(0.152657\pi\) |
−0.0439970 | + | 0.999032i | \(0.514009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16635.0 | − | 28812.6i | −0.682068 | − | 1.18138i | ||||
\(842\) | 1476.99 | − | 2558.23i | 0.0604520 | − | 0.104706i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3903.81 | −0.159212 | ||||||||
\(845\) | −10047.0 | + | 17402.0i | −0.409028 | + | 0.708456i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8724.46 | −0.353927 | ||||||||
\(848\) | 4184.37 | 0.169448 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4169.67 | − | 7222.08i | −0.168257 | − | 0.291430i | ||||
\(851\) | −1714.82 | + | 2970.15i | −0.0690754 | + | 0.119642i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15804.6 | + | 27374.4i | 0.634397 | + | 1.09881i | 0.986643 | + | 0.162900i | \(0.0520849\pi\) |
−0.352245 | + | 0.935908i | \(0.614582\pi\) | |||||||
\(854\) | −12333.7 | −0.494206 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1515.63 | −0.0605179 | ||||||||
\(857\) | 10481.8 | + | 18155.1i | 0.417798 | + | 0.723647i | 0.995718 | − | 0.0924465i | \(-0.0294687\pi\) |
−0.577920 | + | 0.816094i | \(0.696135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1948.32 | + | 3374.59i | −0.0773875 | + | 0.134039i | −0.902122 | − | 0.431481i | \(-0.857991\pi\) |
0.824735 | + | 0.565520i | \(0.191325\pi\) | |||||||
\(860\) | −2487.44 | − | 4308.37i | −0.0986289 | − | 0.170830i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24558.1 | −0.970361 | ||||||||
\(863\) | −2630.83 | −0.103771 | −0.0518856 | − | 0.998653i | \(-0.516523\pi\) | ||||
−0.0518856 | + | 0.998653i | \(0.516523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1238.18 | − | 2144.60i | 0.0486700 | − | 0.0842989i | ||||
\(866\) | −12423.1 | −0.487475 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5270.84 | − | 9129.36i | 0.206111 | − | 0.356994i | ||||
\(869\) | 9920.23 | + | 17182.3i | 0.387251 | + | 0.670738i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13997.6 | + | 24244.5i | 0.544534 | + | 0.943161i | ||||
\(872\) | −956.609 | − | 1656.90i | −0.0371501 | − | 0.0643458i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18357.1 | − | 21560.3i | 0.710457 | − | 0.834426i | ||||
\(875\) | 14247.4 | 0.550459 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18288.7 | + | 31676.9i | 0.704178 | + | 1.21967i | 0.966987 | + | 0.254825i | \(0.0820178\pi\) |
−0.262809 | + | 0.964848i | \(0.584649\pi\) | |||||||
\(878\) | −13469.0 | + | 23329.0i | −0.517718 | + | 0.896714i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3207.20 | + | 5555.04i | −0.122858 | + | 0.212796i | ||||
\(881\) | −6389.06 | −0.244328 | −0.122164 | − | 0.992510i | \(-0.538983\pi\) | ||||
−0.122164 | + | 0.992510i | \(0.538983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8868.92 | − | 15361.4i | 0.338010 | − | 0.585451i | −0.646048 | − | 0.763297i | \(-0.723580\pi\) |
0.984058 | + | 0.177846i | \(0.0569129\pi\) | |||||||
\(884\) | −10501.4 | + | 18188.9i | −0.399548 | + | 0.692037i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14822.2 | 0.562033 | ||||||||
\(887\) | 14810.5 | − | 25652.6i | 0.560641 | − | 0.971058i | −0.436800 | − | 0.899559i | \(-0.643888\pi\) |
0.997441 | − | 0.0714994i | \(-0.0227784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −459.743 | + | 796.298i | −0.0173445 | + | 0.0300416i | ||||
\(890\) | −10885.6 | − | 18854.4i | −0.409984 | − | 0.710114i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14301.8 | −0.536839 | ||||||||
\(893\) | 5756.93 | + | 16178.2i | 0.215732 | + | 0.606251i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16224.3 | − | 28101.3i | −0.605942 | − | 1.04952i | ||||
\(896\) | −604.315 | − | 1046.70i | −0.0225321 | − | 0.0390267i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3345.93 | + | 5795.33i | 0.124338 | + | 0.215359i | ||||
\(899\) | 33509.7 | − | 58040.4i | 1.24317 | − | 2.15323i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20296.9 | 0.750486 | ||||||||
\(902\) | −3410.54 | + | 5907.23i | −0.125896 | + | 0.218059i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1301.94 | 0.0479003 | ||||||||
\(905\) | 14937.0 | 0.548643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7176.13 | − | 12429.4i | −0.262712 | − | 0.455030i | 0.704250 | − | 0.709952i | \(-0.251283\pi\) |
−0.966962 | + | 0.254922i | \(0.917950\pi\) | |||||||
\(908\) | −173.047 | + | 299.727i | −0.00632465 | + | 0.0109546i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5393.20 | − | 9341.30i | −0.196465 | − | 0.340287i | ||||
\(911\) | −50.5532 | −0.00183853 | −0.000919266 | − | 1.00000i | \(-0.500293\pi\) | ||||
−0.000919266 | 1.00000i | \(0.500293\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67991.2 | −2.46460 | ||||||||
\(914\) | −542.238 | − | 939.184i | −0.0196232 | − | 0.0339885i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7856.10 | − | 13607.2i | 0.283377 | − | 0.490823i | ||||
\(917\) | −1791.22 | − | 3102.48i | −0.0645051 | − | 0.111726i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38362.9 | −1.37701 | −0.688507 | − | 0.725230i | \(-0.741734\pi\) | ||||
−0.688507 | + | 0.725230i | \(0.741734\pi\) | |||||||
\(920\) | 11546.2 | 0.413767 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3823.43 | + | 6622.38i | −0.136571 | + | 0.236547i | ||||
\(923\) | 10685.7 | 0.381066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −538.913 | + | 933.424i | −0.0191560 | + | 0.0331792i | ||||
\(926\) | −3750.37 | − | 6495.82i | −0.133094 | − | 0.230525i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3841.96 | − | 6654.48i | −0.135904 | − | 0.235392i | ||||
\(929\) | −19043.5 | − | 32984.3i | −0.672548 | − | 1.16489i | −0.977179 | − | 0.212417i | \(-0.931867\pi\) |
0.304631 | − | 0.952470i | \(-0.401467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13628.7 | + | 16006.8i | −0.479767 | + | 0.563483i | ||||
\(932\) | −4080.10 | −0.143399 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2981.61 | + | 5164.30i | 0.104455 | + | 0.180922i | ||||
\(935\) | −15557.0 | + | 26945.6i | −0.544138 | + | 0.942475i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22120.0 | + | 38313.0i | −0.771217 | + | 1.33579i | 0.165680 | + | 0.986180i | \(0.447018\pi\) |
−0.936897 | + | 0.349607i | \(0.886315\pi\) | |||||||
\(938\) | −7814.46 | −0.272016 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3500.95 | + | 6063.83i | −0.121477 | + | 0.210404i | ||||
\(941\) | 12104.5 | − | 20965.7i | 0.419338 | − | 0.726314i | −0.576535 | − | 0.817072i | \(-0.695596\pi\) |
0.995873 | + | 0.0907581i | \(0.0289290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12278.2 | 0.424001 | ||||||||
\(944\) | −175.854 | + | 304.588i | −0.00606309 | + | 0.0105016i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6995.60 | − | 12116.7i | 0.240430 | − | 0.416437i | ||||
\(947\) | −10262.4 | − | 17774.9i | −0.352146 | − | 0.609935i | 0.634479 | − | 0.772940i | \(-0.281215\pi\) |
−0.986625 | + | 0.163005i | \(0.947881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −74565.1 | −2.55056 | ||||||||
\(950\) | 5769.06 | − | 6775.72i | 0.197024 | − | 0.231403i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2931.32 | − | 5077.20i | −0.0997948 | − | 0.172850i | ||||
\(953\) | −2455.68 | − | 4253.36i | −0.0834703 | − | 0.144575i | 0.821268 | − | 0.570543i | \(-0.193267\pi\) |
−0.904738 | + | 0.425968i | \(0.859934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2127.52 | − | 3684.96i | −0.0720888 | − | 0.124861i | ||||
\(956\) | 529.362 | − | 916.882i | 0.0179088 | − | 0.0310189i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30711.7 | 1.03575 | ||||||||
\(959\) | −11395.5 | + | 19737.6i | −0.383712 | + | 0.664609i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48108.3 | 1.61486 | ||||||||
\(962\) | 2714.52 | 0.0909769 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 344.774 | + | 597.166i | 0.0115191 | + | 0.0199517i | ||||
\(965\) | 9149.84 | − | 15848.0i | 0.305227 | − | 0.528668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20197.3 | + | 34982.8i | 0.671668 | + | 1.16336i | 0.977431 | + | 0.211255i | \(0.0677551\pi\) |
−0.305763 | + | 0.952108i | \(0.598912\pi\) | |||||||
\(968\) | −7391.72 | −0.245433 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2342.98 | −0.0775550 | ||||||||
\(971\) | −13395.9 | − | 23202.4i | −0.442735 | − | 0.766840i | 0.555156 | − | 0.831746i | \(-0.312659\pi\) |
−0.997891 | + | 0.0649061i | \(0.979325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14678.4 | + | 25423.8i | −0.483627 | + | 0.837667i | ||||
\(974\) | 439.463 | + | 761.172i | 0.0144572 | + | 0.0250406i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10449.7 | −0.342710 | ||||||||
\(977\) | 8122.31 | 0.265973 | 0.132987 | − | 0.991118i | \(-0.457543\pi\) | ||||
0.132987 | + | 0.991118i | \(0.457543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30614.4 | − | 53025.6i | 0.999427 | − | 1.73106i | ||||
\(980\) | −8572.12 | −0.279415 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19765.8 | + | 34235.4i | −0.642314 | + | 1.11252i | ||||
\(983\) | −16459.0 | − | 28507.9i | −0.534041 | − | 0.924986i | −0.999209 | − | 0.0397634i | \(-0.987340\pi\) |
0.465168 | − | 0.885222i | \(-0.345994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8911.39 | + | 15435.0i | 0.288265 | + | 0.499289i | ||||
\(986\) | −18636.0 | − | 32278.6i | −0.601919 | − | 1.04255i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22043.3 | − | 4050.52i | −0.709808 | − | 0.130430i | ||||
\(989\) | −25184.7 | −0.809733 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15885.1 | + | 27513.7i | 0.509189 | + | 0.881941i | 0.999943 | + | 0.0106428i | \(0.00338777\pi\) |
−0.490755 | + | 0.871298i | \(0.663279\pi\) | |||||||
\(992\) | 4465.67 | − | 7734.77i | 0.142929 | − | 0.247560i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1491.38 | + | 2583.15i | −0.0475894 | + | 0.0824272i | ||||
\(995\) | 18054.9 | 0.575255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7753.26 | + | 13429.0i | −0.246287 | + | 0.426582i | −0.962493 | − | 0.271308i | \(-0.912544\pi\) |
0.716206 | + | 0.697889i | \(0.245877\pi\) | |||||||
\(998\) | 8159.72 | − | 14133.1i | 0.258809 | − | 0.448271i | ||||
\(999\) | 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 | 342.4.g.h.235.1 | 6 | ||
3.2 | odd | 2 | 114.4.e.d.7.3 | ✓ | 6 | ||
19.11 | even | 3 | inner | 342.4.g.h.163.1 | 6 | ||
57.11 | odd | 6 | 114.4.e.d.49.3 | yes | 6 | ||
57.26 | odd | 6 | 2166.4.a.u.1.1 | 3 | |||
57.50 | even | 6 | 2166.4.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.d.7.3 | ✓ | 6 | 3.2 | odd | 2 | ||
114.4.e.d.49.3 | yes | 6 | 57.11 | odd | 6 | ||
342.4.g.h.163.1 | 6 | 19.11 | even | 3 | inner | ||
342.4.g.h.235.1 | 6 | 1.1 | even | 1 | trivial | ||
2166.4.a.t.1.1 | 3 | 57.50 | even | 6 | |||
2166.4.a.u.1.1 | 3 | 57.26 | odd | 6 |