Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.a.373.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.00000 | − | 12.1244i | −0.626099 | − | 1.08444i | −0.988327 | − | 0.152346i | \(-0.951317\pi\) |
0.362228 | − | 0.932089i | \(-0.382016\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.0548202 | + | 0.0949514i | −0.892133 | − | 0.451772i | \(-0.850792\pi\) |
0.837313 | + | 0.546724i | \(0.184125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0000 | 1.15207 | 0.576035 | − | 0.817425i | \(-0.304599\pi\) | ||||
0.576035 | + | 0.817425i | \(0.304599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 42.0000 | 0.722957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.00000 | − | 12.1244i | 0.0998676 | − | 0.172976i | −0.811762 | − | 0.583988i | \(-0.801491\pi\) |
0.911630 | + | 0.411012i | \(0.134825\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −46.0000 | − | 79.6743i | −0.555428 | − | 0.962029i | −0.997870 | − | 0.0652319i | \(-0.979221\pi\) |
0.442443 | − | 0.896797i | \(-0.354112\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 76.0000 | + | 131.636i | 0.689004 | + | 1.19339i | 0.972160 | + | 0.234316i | \(0.0752852\pi\) |
−0.283156 | + | 0.959074i | \(0.591381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.5000 | + | 61.4878i | −0.284000 | + | 0.491902i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −106.000 | −0.678748 | −0.339374 | − | 0.940651i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940651i | \(0.610215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.0000 | − | 124.708i | 0.417148 | − | 0.722521i | −0.578503 | − | 0.815680i | \(-0.696363\pi\) |
0.995651 | + | 0.0931587i | \(0.0296964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | − | 10.3923i | −0.0316505 | − | 0.0548202i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −79.0000 | − | 136.832i | −0.351014 | − | 0.607974i | 0.635413 | − | 0.772172i | \(-0.280830\pi\) |
−0.986427 | + | 0.164198i | \(0.947496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −81.0000 | + | 140.296i | −0.332574 | + | 0.576035i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −508.000 | −1.80161 | −0.900806 | − | 0.434223i | \(-0.857023\pi\) | ||||
−0.900806 | + | 0.434223i | \(0.857023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −63.0000 | + | 109.119i | −0.208700 | + | 0.361478i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 264.000 | + | 457.261i | 0.819327 | + | 1.41912i | 0.906179 | + | 0.422894i | \(0.138986\pi\) |
−0.0868522 | + | 0.996221i | \(0.527681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.0000 | + | 36.3731i | 0.0576586 | + | 0.0998676i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −303.000 | + | 524.811i | −0.785288 | + | 1.36016i | 0.143539 | + | 0.989645i | \(0.454152\pi\) |
−0.928827 | + | 0.370514i | \(0.879182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0000 | 0.137292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 182.000 | − | 315.233i | 0.401600 | − | 0.695591i | −0.592319 | − | 0.805703i | \(-0.701788\pi\) |
0.993919 | + | 0.110112i | \(0.0351210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −339.000 | − | 587.165i | −0.711549 | − | 1.23244i | −0.964275 | − | 0.264902i | \(-0.914661\pi\) |
0.252726 | − | 0.967538i | \(-0.418673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −378.000 | − | 654.715i | −0.721310 | − | 1.24935i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −422.000 | + | 730.925i | −0.769485 | + | 1.33279i | 0.168357 | + | 0.985726i | \(0.446154\pi\) |
−0.937842 | + | 0.347061i | \(0.887180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −456.000 | −0.795593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.0133722 | −0.00668609 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668609 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 211.000 | − | 365.463i | 0.338297 | − | 0.585948i | −0.645816 | − | 0.763494i | \(-0.723482\pi\) |
0.984113 | + | 0.177546i | \(0.0568158\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −106.500 | − | 184.463i | −0.163967 | − | 0.284000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −192.000 | − | 332.554i | −0.273439 | − | 0.473610i | 0.696301 | − | 0.717750i | \(-0.254828\pi\) |
−0.969740 | + | 0.244139i | \(0.921495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −548.000 | −0.724709 | −0.362354 | − | 0.932040i | \(-0.618027\pi\) | ||||
−0.362354 | + | 0.932040i | \(0.618027\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −196.000 | −0.250108 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 159.000 | − | 275.396i | 0.195938 | − | 0.339374i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −597.000 | − | 1034.03i | −0.711032 | − | 1.23154i | −0.964470 | − | 0.264192i | \(-0.914895\pi\) |
0.253438 | − | 0.967352i | \(-0.418439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 216.000 | + | 374.123i | 0.240840 | + | 0.417148i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −644.000 | + | 1115.44i | −0.695505 | + | 1.20465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1502.00 | −1.57222 | −0.786108 | − | 0.618089i | \(-0.787907\pi\) | ||||
−0.786108 | + | 0.618089i | \(0.787907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 36.0000 | 0.0365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −199.000 | + | 344.678i | −0.196052 | + | 0.339572i | −0.947245 | − | 0.320511i | \(-0.896145\pi\) |
0.751193 | + | 0.660083i | \(0.229479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −580.000 | − | 1004.59i | −0.554846 | − | 0.961021i | −0.997916 | − | 0.0645337i | \(-0.979444\pi\) |
0.443070 | − | 0.896487i | \(-0.353889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −162.000 | − | 280.592i | −0.146366 | − | 0.253513i | 0.783516 | − | 0.621372i | \(-0.213424\pi\) |
−0.929882 | + | 0.367859i | \(0.880091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 469.000 | − | 812.332i | 0.412129 | − | 0.713828i | −0.582993 | − | 0.812477i | \(-0.698119\pi\) |
0.995122 | + | 0.0986487i | \(0.0314520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 474.000 | 0.405316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −622.000 | −0.517813 | −0.258906 | − | 0.965902i | \(-0.583362\pi\) | ||||
−0.258906 | + | 0.965902i | \(0.583362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1064.00 | − | 1842.90i | 0.862770 | − | 1.49436i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −243.000 | − | 420.888i | −0.192012 | − | 0.332574i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 657.500 | + | 1138.82i | 0.493989 | + | 0.855615i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 585.000 | − | 1013.25i | 0.428843 | − | 0.742778i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1200.00 | 0.838447 | 0.419224 | − | 0.907883i | \(-0.362302\pi\) | ||||
0.419224 | + | 0.907883i | \(0.362302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 762.000 | − | 1319.82i | 0.520080 | − | 0.900806i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 698.000 | + | 1208.97i | 0.465531 | + | 0.806323i | 0.999225 | − | 0.0393543i | \(-0.0125301\pi\) |
−0.533694 | + | 0.845677i | \(0.679197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −189.000 | − | 327.358i | −0.120493 | − | 0.208700i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1405.00 | + | 2433.53i | −0.876184 | + | 1.51760i | −0.0206885 | + | 0.999786i | \(0.506586\pi\) |
−0.855496 | + | 0.517810i | \(0.826747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.00244083 | 0.00122042 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00122042 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1584.00 | −0.946077 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −108.000 | + | 187.061i | −0.0631567 | + | 0.109391i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 742.000 | + | 1285.18i | 0.424964 | + | 0.736059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −687.000 | − | 1189.92i | −0.377726 | − | 0.654241i | 0.613005 | − | 0.790079i | \(-0.289961\pi\) |
−0.990731 | + | 0.135838i | \(0.956627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1052.00 | + | 1822.12i | −0.566957 | + | 0.981999i | 0.429907 | + | 0.902873i | \(0.358546\pi\) |
−0.996865 | + | 0.0791258i | \(0.974787\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −126.000 | −0.0665784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2016.00 | −1.04470 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1603.00 | + | 2776.48i | −0.814862 | + | 1.41138i | 0.0945650 | + | 0.995519i | \(0.469854\pi\) |
−0.909427 | + | 0.415864i | \(0.863479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −909.000 | − | 1574.43i | −0.453386 | − | 0.785288i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −166.000 | − | 287.520i | −0.0797676 | − | 0.138162i | 0.823382 | − | 0.567488i | \(-0.192084\pi\) |
−0.903150 | + | 0.429326i | \(0.858751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −84.0000 | + | 145.492i | −0.0396327 | + | 0.0686458i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1496.00 | 0.693197 | 0.346599 | − | 0.938014i | \(-0.387337\pi\) | ||||
0.346599 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −414.000 | + | 717.069i | −0.185143 | + | 0.320676i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1661.00 | + | 2876.94i | 0.729962 | + | 1.26433i | 0.956899 | + | 0.290422i | \(0.0937958\pi\) |
−0.226936 | + | 0.973910i | \(0.572871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 546.000 | + | 945.700i | 0.231864 | + | 0.401600i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 450.000 | − | 779.423i | 0.187903 | − | 0.325457i | −0.756648 | − | 0.653822i | \(-0.773164\pi\) |
0.944551 | + | 0.328365i | \(0.106498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1902.00 | 0.781075 | 0.390537 | − | 0.920587i | \(-0.372289\pi\) | ||||
0.390537 | + | 0.920587i | \(0.372289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2034.00 | 0.821626 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1106.00 | + | 1915.65i | −0.439539 | + | 0.761304i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.0000 | + | 48.4974i | 0.0109495 | + | 0.0189651i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2064.00 | − | 3574.95i | −0.781915 | − | 1.35432i | −0.930825 | − | 0.365466i | \(-0.880910\pi\) |
0.148910 | − | 0.988851i | \(-0.452424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 671.000 | − | 1162.21i | 0.250257 | − | 0.433458i | −0.713339 | − | 0.700819i | \(-0.752818\pi\) |
0.963597 | + | 0.267361i | \(0.0861515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2268.00 | 0.832897 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3506.00 | −1.26798 | −0.633990 | − | 0.773341i | \(-0.718584\pi\) | ||||
−0.633990 | + | 0.773341i | \(0.718584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −340.000 | + | 588.897i | −0.121115 | + | 0.209778i | −0.920208 | − | 0.391430i | \(-0.871980\pi\) |
0.799092 | + | 0.601208i | \(0.205314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1266.00 | − | 2192.78i | −0.444262 | − | 0.769485i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2730.00 | + | 4728.50i | 0.930105 | + | 1.61099i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 684.000 | − | 1184.72i | 0.229668 | − | 0.397797i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 368.000 | 0.121795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5372.00 | 1.75272 | 0.876360 | − | 0.481657i | \(-0.159965\pi\) | ||||
0.876360 | + | 0.481657i | \(0.159965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | − | 20.7846i | 0.00386022 | − | 0.00668609i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3556.00 | + | 6159.17i | 1.12799 | + | 1.95373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 633.000 | + | 1096.39i | 0.195316 | + | 0.338297i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 378.000 | − | 654.715i | 0.115054 | − | 0.199280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1072.00 | −0.321912 | −0.160956 | − | 0.986962i | \(-0.551458\pi\) | ||||
−0.160956 | + | 0.986962i | \(0.551458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 639.000 | 0.189333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1434.00 | − | 2483.76i | 0.419286 | − | 0.726225i | −0.576582 | − | 0.817039i | \(-0.695614\pi\) |
0.995868 | + | 0.0908148i | \(0.0289471\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2399.00 | − | 4155.19i | −0.692272 | − | 1.19905i | −0.971092 | − | 0.238707i | \(-0.923276\pi\) |
0.278819 | − | 0.960344i | \(-0.410057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2563.00 | + | 4439.25i | 0.720634 | + | 1.24817i | 0.960746 | + | 0.277429i | \(0.0894825\pi\) |
−0.240112 | + | 0.970745i | \(0.577184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3696.00 | − | 6401.66i | 1.02596 | − | 1.77701i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1152.00 | 0.315740 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −528.000 | −0.142902 | −0.0714508 | − | 0.997444i | \(-0.522763\pi\) | ||||
−0.0714508 | + | 0.997444i | \(0.522763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 407.000 | − | 704.945i | 0.108785 | − | 0.188421i | −0.806493 | − | 0.591243i | \(-0.798637\pi\) |
0.915278 | + | 0.402822i | \(0.131971\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2484.00 | − | 4302.41i | −0.639891 | − | 1.10832i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 822.000 | − | 1423.75i | 0.209205 | − | 0.362354i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1932.00 | −0.485844 | −0.242922 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242922 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −608.000 | −0.151086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 294.000 | − | 509.223i | 0.0722000 | − | 0.125054i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1647.00 | + | 2852.69i | 0.399755 | + | 0.692396i | 0.993695 | − | 0.112113i | \(-0.0357619\pi\) |
−0.593940 | + | 0.804509i | \(0.702429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 477.000 | + | 826.188i | 0.113125 | + | 0.195938i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3540.00 | − | 6131.46i | 0.829984 | − | 1.43757i | −0.0680662 | − | 0.997681i | \(-0.521683\pi\) |
0.898050 | − | 0.439893i | \(-0.144984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8484.00 | 1.96667 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3582.00 | 0.821029 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3907.00 | + | 6767.12i | −0.885554 | + | 1.53382i | −0.0404764 | + | 0.999180i | \(0.512888\pi\) |
−0.845078 | + | 0.534644i | \(0.820446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1584.00 | − | 2743.57i | −0.355060 | − | 0.614981i | 0.632069 | − | 0.774912i | \(-0.282206\pi\) |
−0.987128 | + | 0.159931i | \(0.948873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −142.000 | − | 245.951i | −0.0311379 | − | 0.0539324i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3929.00 | − | 6805.23i | 0.852241 | − | 1.47612i | −0.0269403 | − | 0.999637i | \(-0.508576\pi\) |
0.879181 | − | 0.476488i | \(-0.158090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1296.00 | −0.278099 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6730.00 | 1.42875 | 0.714374 | − | 0.699764i | \(-0.246712\pi\) | ||||
0.714374 | + | 0.699764i | \(0.246712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1510.00 | − | 2615.40i | 0.317174 | − | 0.549361i | −0.662723 | − | 0.748864i | \(-0.730599\pi\) |
0.979897 | + | 0.199503i | \(0.0639328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1932.00 | − | 3346.32i | −0.401550 | − | 0.695505i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2358.50 | + | 4085.04i | 0.480053 | + | 0.831476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2253.00 | − | 3902.31i | 0.453860 | − | 0.786108i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6834.00 | −1.36262 | −0.681308 | − | 0.731997i | \(-0.738589\pi\) | ||||
−0.681308 | + | 0.731997i | \(0.738589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5096.00 | −1.00576 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −54.0000 | + | 93.5307i | −0.0105502 | + | 0.0182734i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4104.00 | + | 7108.34i | 0.793781 | + | 1.37487i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −597.000 | − | 1034.03i | −0.113191 | − | 0.196052i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4746.00 | + | 8220.31i | −0.891001 | + | 1.54326i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2332.00 | 0.433532 | 0.216766 | − | 0.976224i | \(-0.430449\pi\) | ||||
0.216766 | + | 0.976224i | \(0.430449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3480.00 | 0.640681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4420.00 | + | 7655.66i | −0.805901 | + | 1.39586i | 0.109780 | + | 0.993956i | \(0.464985\pi\) |
−0.915681 | + | 0.401906i | \(0.868348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 523.000 | + | 905.863i | 0.0944464 | + | 0.163586i | 0.909377 | − | 0.415972i | \(-0.136559\pi\) |
−0.814931 | + | 0.579558i | \(0.803225\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3771.00 | − | 6531.56i | −0.668140 | − | 1.15725i | −0.978424 | − | 0.206609i | \(-0.933757\pi\) |
0.310283 | − | 0.950644i | \(-0.399576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 212.000 | − | 367.195i | 0.0372092 | − | 0.0644482i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 972.000 | 0.169009 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1288.00 | −0.221877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1917.00 | + | 3320.34i | −0.327188 | + | 0.566706i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1407.00 | + | 2437.00i | 0.237943 | + | 0.412129i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1378.00 | − | 2386.77i | −0.228827 | − | 0.396340i | 0.728634 | − | 0.684904i | \(-0.240156\pi\) |
−0.957461 | + | 0.288564i | \(0.906822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −711.000 | + | 1231.49i | −0.117005 | + | 0.202658i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11816.0 | 1.92710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3954.00 | 0.639134 | 0.319567 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319567 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 933.000 | − | 1616.00i | 0.149480 | − | 0.258906i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 288.000 | + | 498.831i | 0.0457363 | + | 0.0792176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3192.00 | + | 5528.71i | 0.498120 | + | 0.862770i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3450.00 | + | 5975.58i | −0.533734 | + | 0.924454i | 0.465489 | + | 0.885053i | \(0.345878\pi\) |
−0.999223 | + | 0.0394010i | \(0.987455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2426.00 | −0.372094 | −0.186047 | − | 0.982541i | \(-0.559568\pi\) | ||||
−0.186047 | + | 0.982541i | \(0.559568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1458.00 | 0.221716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 735.000 | − | 1273.06i | 0.110822 | − | 0.191949i | −0.805280 | − | 0.592895i | \(-0.797985\pi\) |
0.916102 | + | 0.400946i | \(0.131318\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 56.0000 | + | 96.9948i | 0.00837231 | + | 0.0145013i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3436.00 | − | 5951.33i | −0.505140 | − | 0.874928i | −0.999982 | − | 0.00594499i | \(-0.998108\pi\) |
0.494843 | − | 0.868983i | \(-0.335226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −802.500 | + | 1389.97i | −0.117000 | + | 0.202649i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3945.00 | −0.570410 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5908.00 | −0.847230 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3536.00 | − | 6124.53i | 0.502937 | − | 0.871112i | −0.497058 | − | 0.867717i | \(-0.665586\pi\) |
0.999994 | − | 0.00339411i | \(-0.00108038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1755.00 | + | 3039.75i | 0.247593 | + | 0.428843i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 409.000 | + | 708.409i | 0.0567754 | + | 0.0983378i | 0.893016 | − | 0.450025i | \(-0.148585\pi\) |
−0.836241 | + | 0.548362i | \(0.815251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1134.00 | − | 1964.15i | 0.156159 | − | 0.270475i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5724.00 | −0.781966 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5132.00 | −0.695549 | −0.347775 | − | 0.937578i | \(-0.613063\pi\) | ||||
−0.347775 | + | 0.937578i | \(0.613063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1800.00 | + | 3117.69i | −0.242039 | + | 0.419224i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4288.00 | + | 7427.03i | 0.572080 | + | 0.990871i | 0.996352 | + | 0.0853367i | \(0.0271966\pi\) |
−0.424272 | + | 0.905535i | \(0.639470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2286.00 | + | 3959.47i | 0.300269 | + | 0.520080i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1865.00 | − | 3230.27i | 0.243083 | − | 0.421032i | −0.718508 | − | 0.695519i | \(-0.755175\pi\) |
0.961591 | + | 0.274487i | \(0.0885080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2128.00 | 0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4188.00 | −0.537549 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2688.00 | + | 4655.75i | −0.342400 | + | 0.593054i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3339.00 | − | 5783.32i | −0.422115 | − | 0.731124i | 0.574031 | − | 0.818833i | \(-0.305379\pi\) |
−0.996146 | + | 0.0877090i | \(0.972045\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1527.00 | + | 2644.84i | 0.190161 | + | 0.329369i | 0.945304 | − | 0.326192i | \(-0.105766\pi\) |
−0.755142 | + | 0.655561i | \(0.772432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3888.00 | − | 6734.21i | 0.480583 | − | 0.832395i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1134.00 | 0.139133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 632.000 | 0.0769707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −133.000 | + | 230.363i | −0.0160793 | + | 0.0278501i | −0.873953 | − | 0.486010i | \(-0.838452\pi\) |
0.857874 | + | 0.513860i | \(0.171785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4215.00 | − | 7300.59i | −0.505865 | − | 0.876184i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3836.00 | + | 6644.15i | 0.453739 | + | 0.785900i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | + | 10.3923i | −0.000704607 | + | 0.00122042i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8844.00 | 1.03116 | 0.515582 | − | 0.856840i | \(-0.327576\pi\) | ||||
0.515582 | + | 0.856840i | \(0.327576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4482.00 | −0.518858 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2376.00 | − | 4115.35i | 0.273109 | − | 0.473039i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 497.000 | + | 860.829i | 0.0567248 | + | 0.0982502i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −324.000 | − | 561.184i | −0.0364636 | − | 0.0631567i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4968.00 | + | 8604.83i | −0.555221 | + | 0.961671i | 0.442666 | + | 0.896687i | \(0.354033\pi\) |
−0.997886 | + | 0.0649838i | \(0.979300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11758.0 | −1.30497 | −0.652487 | − | 0.757800i | \(-0.726274\pi\) | ||||
−0.652487 | + | 0.757800i | \(0.726274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4452.00 | −0.490706 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6992.00 | − | 12110.5i | 0.765384 | − | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2052.00 | + | 3554.17i | 0.223090 | + | 0.386404i | 0.955745 | − | 0.294197i | \(-0.0950522\pi\) |
−0.732655 | + | 0.680601i | \(0.761719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4874.00 | − | 8442.02i | −0.522733 | − | 0.905400i | −0.999650 | − | 0.0264519i | \(-0.991579\pi\) |
0.476917 | − | 0.878948i | \(-0.341754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8358.00 | + | 14476.5i | −0.890353 | + | 1.54214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4122.00 | 0.436161 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −478.000 | −0.0502410 | −0.0251205 | − | 0.999684i | \(-0.507997\pi\) | ||||
−0.0251205 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 780.000 | − | 1351.00i | 0.0814385 | − | 0.141056i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3156.00 | − | 5466.35i | −0.327333 | − | 0.566957i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5587.00 | + | 9676.97i | 0.571879 | + | 0.990524i | 0.996373 | + | 0.0850931i | \(0.0271188\pi\) |
−0.424494 | + | 0.905431i | \(0.639548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 189.000 | − | 327.358i | 0.0192195 | − | 0.0332892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11674.0 | −1.17942 | −0.589710 | − | 0.807615i | \(-0.700758\pi\) | ||||
−0.589710 | + | 0.807615i | \(0.700758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10528.0 | 1.05676 | 0.528378 | − | 0.849009i | \(-0.322801\pi\) | ||||
0.528378 | + | 0.849009i | \(0.322801\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3024.00 | − | 5237.72i | 0.301580 | − | 0.522352i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8302.00 | − | 14379.5i | −0.822635 | − | 1.42485i | −0.903713 | − | 0.428139i | \(-0.859170\pi\) |
0.0810777 | − | 0.996708i | \(-0.474164\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4809.00 | − | 8329.43i | −0.470461 | − | 0.814862i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1016.00 | − | 1759.76i | 0.0987648 | − | 0.171066i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6532.00 | 0.630966 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5454.00 | 0.523525 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4288.00 | − | 7427.03i | 0.409027 | − | 0.708455i | −0.585754 | − | 0.810489i | \(-0.699202\pi\) |
0.994781 | + | 0.102034i | \(0.0325350\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4266.00 | − | 7388.93i | −0.404393 | − | 0.700429i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10514.0 | + | 18210.8i | 0.984363 | + | 1.70497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4852.00 | + | 8403.91i | −0.451468 | + | 0.781966i | −0.998478 | − | 0.0551605i | \(-0.982433\pi\) |
0.547009 | + | 0.837127i | \(0.315766\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 996.000 | 0.0921077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4092.00 | −0.376109 | −0.188054 | − | 0.982159i | \(-0.560218\pi\) | ||||
−0.188054 | + | 0.982159i | \(0.560218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −742.000 | + | 1285.18i | −0.0677850 | + | 0.117407i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −252.000 | − | 436.477i | −0.0228819 | − | 0.0396327i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8942.00 | − | 15488.0i | −0.802202 | − | 1.38945i | −0.918164 | − | 0.396201i | \(-0.870328\pi\) |
0.115961 | − | 0.993254i | \(-0.463005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2244.00 | + | 3886.72i | −0.200109 | + | 0.346599i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7704.00 | −0.682911 | −0.341456 | − | 0.939898i | \(-0.610920\pi\) | ||||
−0.341456 | + | 0.939898i | \(0.610920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5572.00 | 0.490992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1078.50 | + | 1868.02i | −0.0944731 | + | 0.163632i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7179.00 | − | 12434.4i | −0.625154 | − | 1.08280i | −0.988511 | − | 0.151149i | \(-0.951703\pi\) |
0.363357 | − | 0.931650i | \(-0.381631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1242.00 | − | 2151.21i | −0.106892 | − | 0.185143i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8120.00 | + | 14064.3i | −0.694777 | + | 1.20339i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2112.00 | −0.179663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9966.00 | −0.842888 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2541.00 | + | 4401.14i | −0.213672 | + | 0.370091i | −0.952861 | − | 0.303407i | \(-0.901876\pi\) |
0.739189 | + | 0.673498i | \(0.235209\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 878.000 | + | 1520.74i | 0.0734078 | + | 0.127146i | 0.900393 | − | 0.435078i | \(-0.143279\pi\) |
−0.826985 | + | 0.562224i | \(0.809946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1008.00 | − | 1745.91i | −0.0833191 | − | 0.144313i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5468.50 | + | 9471.72i | −0.449453 | + | 0.778476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3276.00 | −0.267733 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21060.0 | −1.71146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2268.00 | + | 3928.29i | −0.183279 | + | 0.317448i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1350.00 | + | 2338.27i | 0.108486 | + | 0.187903i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8115.00 | − | 14055.6i | −0.644900 | − | 1.11700i | −0.984325 | − | 0.176367i | \(-0.943566\pi\) |
0.339424 | − | 0.940633i | \(-0.389768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2853.00 | + | 4941.54i | −0.225477 | + | 0.390537i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13132.0 | −1.03213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17676.0 | 1.38167 | 0.690833 | − | 0.723014i | \(-0.257244\pi\) | ||||
0.690833 | + | 0.723014i | \(0.257244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3051.00 | + | 5284.49i | −0.237183 | + | 0.410813i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4876.00 | + | 8445.48i | 0.376996 | + | 0.652976i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3318.00 | − | 5746.94i | −0.253768 | − | 0.439539i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6125.00 | − | 10608.8i | 0.465933 | − | 0.807019i | −0.533310 | − | 0.845920i | \(-0.679052\pi\) |
0.999243 | + | 0.0389004i | \(0.0123855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27432.0 | −2.07558 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −168.000 | −0.0126434 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5026.00 | − | 8705.29i | 0.376236 | − | 0.651659i | −0.614276 | − | 0.789092i | \(-0.710552\pi\) |
0.990511 | + | 0.137432i | \(0.0438850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4354.00 | + | 7541.35i | 0.324202 | + | 0.561534i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12837.0 | − | 22234.3i | −0.945791 | − | 1.63816i | −0.754160 | − | 0.656691i | \(-0.771956\pi\) |
−0.191631 | − | 0.981467i | \(-0.561378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1866.00 | + | 3232.01i | −0.136759 | + | 0.236874i | −0.926268 | − | 0.376865i | \(-0.877002\pi\) |
0.789509 | + | 0.613739i | \(0.210335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12384.0 | 0.902878 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10792.0 | −0.782709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 607.000 | − | 1051.35i | 0.0437950 | − | 0.0758552i | −0.843297 | − | 0.537448i | \(-0.819388\pi\) |
0.887092 | + | 0.461593i | \(0.152722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2013.00 | + | 3486.62i | 0.144486 | + | 0.250257i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1212.00 | − | 2099.25i | −0.0860993 | − | 0.149128i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3402.00 | + | 5892.44i | −0.240437 | + | 0.416448i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7108.00 | 0.499793 | 0.249897 | − | 0.968273i | \(-0.419603\pi\) | ||||
0.249897 | + | 0.968273i | \(0.419603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13248.0 | −0.926782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5259.00 | − | 9108.86i | 0.366034 | − | 0.633990i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3081.00 | − | 5336.45i | −0.213358 | − | 0.369548i | 0.739405 | − | 0.673261i | \(-0.235107\pi\) |
−0.952763 | + | 0.303713i | \(0.901774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1020.00 | − | 1766.69i | −0.0699260 | − | 0.121115i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1236.00 | + | 2140.81i | −0.0843098 | + | 0.146029i | −0.905097 | − | 0.425205i | \(-0.860202\pi\) |
0.820787 | + | 0.571234i | \(0.193535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13750.0 | −0.933235 | −0.466617 | − | 0.884459i | \(-0.654528\pi\) | ||||
−0.466617 | + | 0.884459i | \(0.654528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7596.00 | 0.512990 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9205.00 | − | 15943.5i | 0.618573 | − | 1.07140i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5688.00 | + | 9851.90i | 0.380344 | + | 0.658775i | 0.991111 | − | 0.133035i | \(-0.0424723\pi\) |
−0.610767 | + | 0.791810i | \(0.709139\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14256.0 | + | 24692.1i | 0.943921 | + | 1.63492i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10191.0 | + | 17651.3i | −0.671469 | + | 1.16302i | 0.306018 | + | 0.952026i | \(0.401003\pi\) |
−0.977488 | + | 0.210993i | \(0.932330\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16380.0 | −1.07399 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21178.0 | 1.38184 | 0.690919 | − | 0.722932i | \(-0.257206\pi\) | ||||
0.690919 | + | 0.722932i | \(0.257206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2350.00 | − | 4070.32i | 0.152592 | − | 0.264297i | −0.779588 | − | 0.626293i | \(-0.784571\pi\) |
0.932180 | + | 0.361996i | \(0.117905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2052.00 | + | 3554.17i | 0.132599 | + | 0.229668i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9729.50 | + | 16852.0i | 0.622688 | + | 1.07853i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −552.000 | + | 956.092i | −0.0351591 | + | 0.0608973i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2212.00 | −0.140220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21736.0 | −1.37131 | −0.685655 | − | 0.727927i | \(-0.740484\pi\) | ||||
−0.685655 | + | 0.727927i | \(0.740484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8058.00 | + | 13956.9i | −0.505966 | + | 0.876360i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8400.00 | − | 14549.2i | −0.524951 | − | 0.909242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.0000 | + | 62.3538i | 0.00222870 | + | 0.00386022i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6511.00 | − | 11277.4i | 0.401200 | − | 0.694898i | −0.592671 | − | 0.805444i | \(-0.701927\pi\) |
0.993871 | + | 0.110546i | \(0.0352600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3308.00 | 0.202885 | 0.101442 | − | 0.994841i | \(-0.467654\pi\) | ||||
0.101442 | + | 0.994841i | \(0.467654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21336.0 | −1.30249 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6900.00 | − | 11951.2i | 0.419269 | − | 0.726195i | −0.576597 | − | 0.817029i | \(-0.695620\pi\) |
0.995866 | + | 0.0908335i | \(0.0289531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 728.000 | + | 1260.93i | 0.0440316 | + | 0.0762649i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1341.00 | + | 2322.68i | 0.0803635 | + | 0.139194i | 0.903406 | − | 0.428786i | \(-0.141059\pi\) |
−0.823043 | + | 0.567980i | \(0.807725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9772.00 | − | 16925.6i | 0.582937 | − | 1.00968i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3798.00 | −0.225531 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23836.0 | 1.40898 | 0.704491 | − | 0.709713i | \(-0.251175\pi\) | ||||
0.704491 | + | 0.709713i | \(0.251175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5641.00 | − | 9770.50i | 0.331936 | − | 0.574929i | −0.650956 | − | 0.759116i | \(-0.725632\pi\) |
0.982891 | + | 0.184186i | \(0.0589650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1134.00 | + | 1964.15i | 0.0664267 | + | 0.115054i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8056.00 | − | 13953.4i | −0.467661 | − | 0.810012i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1608.00 | − | 2785.14i | 0.0929281 | − | 0.160956i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2712.00 | 0.156029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13726.0 | −0.786179 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −958.500 | + | 1660.17i | −0.0546558 | + | 0.0946667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2487.00 | − | 4307.61i | −0.141186 | − | 0.244542i | 0.786757 | − | 0.617263i | \(-0.211758\pi\) |
−0.927944 | + | 0.372721i | \(0.878425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4302.00 | + | 7451.28i | 0.242075 | + | 0.419286i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4494.00 | − | 7783.84i | 0.251769 | − | 0.436076i | −0.712244 | − | 0.701932i | \(-0.752321\pi\) |
0.964013 | + | 0.265855i | \(0.0856544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39340.0 | 2.19431 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14394.0 | 0.799367 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16362.0 | + | 28339.8i | −0.904706 | + | 1.56700i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5086.00 | − | 8809.21i | −0.280001 | − | 0.484976i | 0.691384 | − | 0.722488i | \(-0.257001\pi\) |
−0.971385 | + | 0.237512i | \(0.923668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.0000 | − | 48.4974i | −0.00152820 | − | 0.00264692i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2730.00 | + | 4728.50i | −0.148359 | + | 0.256965i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15378.0 | −0.832116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27446.0 | 1.47877 | 0.739387 | − | 0.673280i | \(-0.235115\pi\) | ||||
0.739387 | + | 0.673280i | \(0.235115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7268.00 | + | 12588.5i | −0.389926 | + | 0.675371i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11088.0 | + | 19205.0i | 0.592338 | + | 1.02596i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1999.00 | − | 3462.37i | −0.105887 | − | 0.183402i | 0.808213 | − | 0.588890i | \(-0.200435\pi\) |
−0.914100 | + | 0.405488i | \(0.867102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1728.00 | + | 2992.98i | −0.0911464 | + | 0.157870i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21888.0 | 1.14967 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3024.00 | 0.158169 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 792.000 | − | 1371.78i | 0.0412521 | − | 0.0714508i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12936.0 | − | 22405.8i | −0.670976 | − | 1.16216i | −0.977628 | − | 0.210342i | \(-0.932542\pi\) |
0.306652 | − | 0.951822i | \(-0.400791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1221.00 | + | 2114.83i | 0.0628070 | + | 0.108785i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3763.00 | − | 6517.71i | 0.192765 | − | 0.333878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12088.0 | 0.616670 | 0.308335 | − | 0.951278i | \(-0.400228\pi\) | ||||
0.308335 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3556.00 | + | 6159.17i | −0.179923 | + | 0.311635i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3987.00 | − | 6905.69i | −0.200905 | − | 0.347977i | 0.747915 | − | 0.663794i | \(-0.231055\pi\) |
−0.948820 | + | 0.315817i | \(0.897722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1688.00 | − | 2923.70i | −0.0843667 | − | 0.146127i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15882.0 | − | 27508.4i | 0.790567 | − | 1.36930i | −0.135050 | − | 0.990839i | \(-0.543119\pi\) |
0.925616 | − | 0.378463i | \(-0.123547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14904.0 | 0.738883 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 888.000 | 0.0438460 | 0.0219230 | − | 0.999760i | \(-0.493021\pi\) | ||||
0.0219230 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9618.00 | + | 16658.9i | −0.472988 | + | 0.819240i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2466.00 | + | 4271.24i | 0.120785 | + | 0.209205i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17328.0 | + | 30013.0i | 0.841954 | + | 1.45831i | 0.888240 | + | 0.459379i | \(0.151928\pi\) |
−0.0462858 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2898.00 | − | 5019.48i | 0.140251 | − | 0.242922i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29456.0 | 1.41989 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22866.0 | −1.09786 | −0.548929 | − | 0.835869i | \(-0.684964\pi\) | ||||
−0.548929 | + | 0.835869i | \(0.684964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 912.000 | − | 1579.63i | 0.0436146 | − | 0.0755428i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11285.0 | − | 19546.2i | −0.537557 | − | 0.931076i | −0.999035 | − | 0.0439244i | \(-0.986014\pi\) |
0.461478 | − | 0.887152i | \(-0.347319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 882.000 | + | 1527.67i | 0.0416847 | + | 0.0722000i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9828.00 | − | 17022.6i | 0.462671 | − | 0.801369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1790.00 | −0.0839389 | −0.0419695 | − | 0.999119i | \(-0.513363\pi\) | ||||
−0.0419695 | + | 0.999119i | \(0.513363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9882.00 | −0.461597 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1495.00 | + | 2589.42i | −0.0695620 | + | 0.120485i | −0.898709 | − | 0.438546i | \(-0.855493\pi\) |
0.829147 | + | 0.559031i | \(0.188827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5112.00 | + | 8854.24i | 0.236940 | + | 0.410392i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17940.0 | + | 31073.0i | 0.825118 | + | 1.42915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.000733067 | − | 0.00126971i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2862.00 | −0.130625 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44884.0 | 2.04074 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15378.0 | − | 26635.5i | 0.696527 | − | 1.20642i | −0.273137 | − | 0.961975i | \(-0.588061\pi\) |
0.969663 | − | 0.244444i | \(-0.0786056\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10620.0 | + | 18394.4i | 0.479191 | + | 0.829984i | ||||
\(790\) |