Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.l.1873.4 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.68316 | −0.752730 | −0.376365 | − | 0.926471i | \(-0.622826\pi\) | ||||
−0.376365 | + | 0.926471i | \(0.622826\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.960133 | + | 2.46539i | −0.362896 | + | 0.931830i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.24498 | 0.375376 | 0.187688 | − | 0.982229i | \(-0.439901\pi\) | ||||
0.187688 | + | 0.982229i | \(0.439901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.96039 | + | 3.39550i | 0.543715 | + | 0.941743i | 0.998687 | + | 0.0512366i | \(0.0163162\pi\) |
−0.454971 | + | 0.890506i | \(0.650350\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.62691 | + | 2.81788i | 0.394582 | + | 0.683437i | 0.993048 | − | 0.117712i | \(-0.0375559\pi\) |
−0.598465 | + | 0.801149i | \(0.704223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.36192 | + | 4.09097i | −0.541863 | + | 0.938534i | 0.456935 | + | 0.889500i | \(0.348947\pi\) |
−0.998797 | + | 0.0490333i | \(0.984386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.398135 | −0.0830170 | −0.0415085 | − | 0.999138i | \(-0.513216\pi\) | ||||
−0.0415085 | + | 0.999138i | \(0.513216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.16699 | −0.433397 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.19896 | − | 5.54076i | 0.594032 | − | 1.02889i | −0.399651 | − | 0.916667i | \(-0.630869\pi\) |
0.993683 | − | 0.112226i | \(-0.0357979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.289184 | + | 0.500881i | −0.0519389 | + | 0.0899608i | −0.890826 | − | 0.454345i | \(-0.849873\pi\) |
0.838887 | + | 0.544306i | \(0.183207\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61605 | − | 4.14963i | 0.273163 | − | 0.701416i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.72146 | − | 4.71371i | 0.447405 | − | 0.774928i | −0.550811 | − | 0.834630i | \(-0.685682\pi\) |
0.998216 | + | 0.0597015i | \(0.0190149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.20216 | − | 7.27836i | −0.656267 | − | 1.13669i | −0.981574 | − | 0.191080i | \(-0.938801\pi\) |
0.325307 | − | 0.945608i | \(-0.394532\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46299 | + | 4.26603i | −0.375603 | + | 0.650563i | −0.990417 | − | 0.138109i | \(-0.955898\pi\) |
0.614814 | + | 0.788672i | \(0.289231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.212595 | + | 0.368225i | 0.0310101 | + | 0.0537112i | 0.881114 | − | 0.472904i | \(-0.156794\pi\) |
−0.850104 | + | 0.526615i | \(0.823461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15629 | − | 4.73420i | −0.736613 | − | 0.676315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.466315 | + | 0.807681i | 0.0640533 | + | 0.110944i | 0.896274 | − | 0.443501i | \(-0.146264\pi\) |
−0.832220 | + | 0.554445i | \(0.812931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.09550 | −0.282557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.02527 | + | 5.23992i | −0.393856 | + | 0.682179i | −0.992954 | − | 0.118496i | \(-0.962193\pi\) |
0.599098 | + | 0.800676i | \(0.295526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.10459 | − | 8.84140i | −0.653575 | − | 1.13203i | −0.982249 | − | 0.187582i | \(-0.939935\pi\) |
0.328674 | − | 0.944444i | \(-0.393398\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.29965 | − | 5.71516i | −0.409271 | − | 0.708878i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.70976 | + | 8.15754i | −0.575389 | + | 0.996602i | 0.420611 | + | 0.907241i | \(0.361816\pi\) |
−0.995999 | + | 0.0893612i | \(0.971517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46617 | 1.00475 | 0.502375 | − | 0.864650i | \(-0.332460\pi\) | ||||
0.502375 | + | 0.864650i | \(0.332460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.82340 | + | 11.8185i | 0.798619 | + | 1.38325i | 0.920516 | + | 0.390705i | \(0.127769\pi\) |
−0.121897 | + | 0.992543i | \(0.538898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.19535 | + | 3.06936i | −0.136222 | + | 0.349786i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.76670 | − | 4.79207i | −0.311278 | − | 0.539149i | 0.667361 | − | 0.744734i | \(-0.267424\pi\) |
−0.978639 | + | 0.205585i | \(0.934090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.03669 | + | 13.9199i | −0.882141 | + | 1.52791i | −0.0331848 | + | 0.999449i | \(0.510565\pi\) |
−0.848956 | + | 0.528463i | \(0.822768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73833 | − | 4.74293i | −0.297014 | − | 0.514444i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.03776 | − | 10.4577i | 0.640001 | − | 1.10851i | −0.345431 | − | 0.938444i | \(-0.612267\pi\) |
0.985432 | − | 0.170070i | \(-0.0543993\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2535 | + | 1.57300i | −1.07486 | + | 0.164895i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.97549 | − | 6.88575i | 0.407876 | − | 0.706463i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86046 | + | 10.1506i | −0.595040 | + | 1.03064i | 0.398501 | + | 0.917168i | \(0.369530\pi\) |
−0.993541 | + | 0.113472i | \(0.963803\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.40605 | −0.537922 | −0.268961 | − | 0.963151i | \(-0.586680\pi\) | ||||
−0.268961 | + | 0.963151i | \(0.586680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.6204 | −1.44059 | −0.720294 | − | 0.693669i | \(-0.755993\pi\) | ||||
−0.720294 | + | 0.693669i | \(0.755993\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.40209 | + | 5.89259i | −0.328892 | + | 0.569658i | −0.982292 | − | 0.187354i | \(-0.940009\pi\) |
0.653400 | + | 0.757013i | \(0.273342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.37636 | + | 14.5083i | 0.802310 | + | 1.38964i | 0.918092 | + | 0.396367i | \(0.129729\pi\) |
−0.115783 | + | 0.993275i | \(0.536938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.77154 | − | 11.7287i | −0.637013 | − | 1.10334i | −0.986085 | − | 0.166243i | \(-0.946836\pi\) |
0.349072 | − | 0.937096i | \(-0.386497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.670124 | 0.0624894 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.50922 | + | 1.30541i | −0.780039 | + | 0.119667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.45002 | −0.859093 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0632 | 1.07896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5904 | −0.939748 | −0.469874 | − | 0.882734i | \(-0.655701\pi\) | ||||
−0.469874 | + | 0.882734i | \(0.655701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.3638 | −1.95394 | −0.976968 | − | 0.213387i | \(-0.931551\pi\) | ||||
−0.976968 | + | 0.213387i | \(0.931551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.81808 | − | 9.75094i | −0.677914 | − | 0.845514i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.9540 | −1.53391 | −0.766957 | − | 0.641699i | \(-0.778230\pi\) | ||||
−0.766957 | + | 0.641699i | \(0.778230\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.570825 | − | 0.988699i | −0.0484168 | − | 0.0838603i | 0.840801 | − | 0.541344i | \(-0.182084\pi\) |
−0.889218 | + | 0.457483i | \(0.848751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44065 | + | 4.22733i | 0.204098 | + | 0.353507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.38434 | + | 9.32596i | −0.447145 | + | 0.774479i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6583 | −1.44663 | −0.723313 | − | 0.690521i | \(-0.757381\pi\) | ||||
−0.723313 | + | 0.690521i | \(0.757381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2354 | 1.23984 | 0.619919 | − | 0.784666i | \(-0.287166\pi\) | ||||
0.619919 | + | 0.784666i | \(0.287166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.486741 | − | 0.843060i | 0.0390960 | − | 0.0677162i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.81439 | − | 11.8029i | 0.543847 | − | 0.941971i | −0.454831 | − | 0.890578i | \(-0.650300\pi\) |
0.998678 | − | 0.0513933i | \(-0.0163662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.382263 | − | 0.981559i | 0.0301265 | − | 0.0773577i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.04726 | − | 7.01005i | 0.317006 | − | 0.549070i | −0.662856 | − | 0.748747i | \(-0.730656\pi\) |
0.979862 | + | 0.199677i | \(0.0639893\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07739 | − | 3.59814i | −0.160753 | − | 0.278433i | 0.774386 | − | 0.632714i | \(-0.218059\pi\) |
−0.935139 | + | 0.354281i | \(0.884726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.18629 | + | 2.05471i | −0.0912529 | + | 0.158055i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.91730 | + | 11.9811i | 0.525913 | + | 0.910907i | 0.999544 | + | 0.0301845i | \(0.00960947\pi\) |
−0.473632 | + | 0.880723i | \(0.657057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.08059 | − | 5.34247i | 0.157278 | − | 0.403852i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71167 | − | 8.16084i | −0.352166 | − | 0.609970i | 0.634462 | − | 0.772954i | \(-0.281222\pi\) |
−0.986629 | + | 0.162984i | \(0.947888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32133 | 0.0982136 | 0.0491068 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491068 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.58064 | + | 7.93390i | −0.336775 | + | 0.583312i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.02546 | + | 3.50821i | 0.148117 | + | 0.256546i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.14271 | − | 14.1036i | −0.589186 | − | 1.02050i | −0.994339 | − | 0.106251i | \(-0.966115\pi\) |
0.405153 | − | 0.914249i | \(-0.367218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.28077 | + | 2.21837i | −0.0921921 | + | 0.159681i | −0.908433 | − | 0.418030i | \(-0.862721\pi\) |
0.816241 | + | 0.577711i | \(0.196054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.6916 | −1.54546 | −0.772730 | − | 0.634735i | \(-0.781109\pi\) | ||||
−0.772730 | + | 0.634735i | \(0.781109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.59684 | + | 9.69402i | 0.396750 | + | 0.687191i | 0.993323 | − | 0.115368i | \(-0.0368047\pi\) |
−0.596573 | + | 0.802559i | \(0.703471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5887 | + | 13.2065i | 0.743181 | + | 0.926917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.07289 | + | 12.2506i | 0.493992 | + | 0.855620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.94055 | + | 5.09318i | −0.203402 | + | 0.352303i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1807 | + | 24.5616i | 0.976237 | + | 1.69089i | 0.675793 | + | 0.737092i | \(0.263801\pi\) |
0.300444 | + | 0.953799i | \(0.402865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.14560 | − | 7.18039i | 0.282728 | − | 0.489699i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.957211 | − | 1.19386i | −0.0649797 | − | 0.0810446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.37875 | + | 11.0483i | −0.429081 | + | 0.743190i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6962 | − | 21.9905i | 0.850202 | − | 1.47259i | −0.0308242 | − | 0.999525i | \(-0.509813\pi\) |
0.881026 | − | 0.473068i | \(-0.156853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.62860 | 0.307211 | 0.153606 | − | 0.988132i | \(-0.450911\pi\) | ||||
0.153606 | + | 0.988132i | \(0.450911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.32592 | 0.153701 | 0.0768506 | − | 0.997043i | \(-0.475514\pi\) | ||||
0.0768506 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.37989 | − | 11.0503i | 0.417960 | − | 0.723929i | −0.577774 | − | 0.816197i | \(-0.696078\pi\) |
0.995734 | + | 0.0922683i | \(0.0294117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.357830 | − | 0.619780i | −0.0233423 | − | 0.0404300i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0492 | − | 19.1378i | −0.714714 | − | 1.23792i | −0.963070 | − | 0.269252i | \(-0.913223\pi\) |
0.248355 | − | 0.968669i | \(-0.420110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0177 | 1.28945 | 0.644726 | − | 0.764414i | \(-0.276972\pi\) | ||||
0.644726 | + | 0.764414i | \(0.276972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.67884 | + | 7.96840i | 0.554471 | + | 0.509082i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.5212 | −1.17848 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.12390 | −0.134059 | −0.0670297 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670297 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.495671 | −0.0311625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7630 | 0.796134 | 0.398067 | − | 0.917356i | \(-0.369681\pi\) | ||||
0.398067 | + | 0.917356i | \(0.369681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.00816 | + | 11.2352i | 0.559740 | + | 0.698124i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0686 | −0.682522 | −0.341261 | − | 0.939969i | \(-0.610854\pi\) | ||||
−0.341261 | + | 0.939969i | \(0.610854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.784881 | − | 1.35945i | −0.0482148 | − | 0.0835105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.77479 | + | 3.07403i | 0.108211 | + | 0.187427i | 0.915046 | − | 0.403351i | \(-0.132154\pi\) |
−0.806835 | + | 0.590777i | \(0.798821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.687666 | − | 1.19107i | 0.0417727 | − | 0.0723525i | −0.844383 | − | 0.535740i | \(-0.820033\pi\) |
0.886156 | + | 0.463387i | \(0.153366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.69786 | −0.162687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.1617 | −1.75216 | −0.876079 | − | 0.482168i | \(-0.839849\pi\) | ||||
−0.876079 | + | 0.482168i | \(0.839849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.29603 | + | 10.9050i | −0.375590 | + | 0.650540i | −0.990415 | − | 0.138123i | \(-0.955893\pi\) |
0.614826 | + | 0.788663i | \(0.289226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.73028 | + | 8.19309i | −0.281186 | + | 0.487029i | −0.971677 | − | 0.236312i | \(-0.924061\pi\) |
0.690491 | + | 0.723341i | \(0.257394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.9786 | − | 3.37178i | 1.29736 | − | 0.199030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.20636 | − | 5.55358i | 0.188609 | − | 0.326681i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.32726 | + | 14.4232i | 0.486484 | + | 0.842614i | 0.999879 | − | 0.0155376i | \(-0.00494598\pi\) |
−0.513396 | + | 0.858152i | \(0.671613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.09200 | − | 8.81960i | 0.296468 | − | 0.513497i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.780502 | − | 1.35187i | −0.0451376 | − | 0.0781806i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.15262 | − | 10.1682i | −0.469909 | − | 0.586085i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.59181 | + | 14.8815i | 0.491966 | + | 0.852110i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.55966 | 0.545599 | 0.272799 | − | 0.962071i | \(-0.412051\pi\) | ||||
0.272799 | + | 0.962071i | \(0.412051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1851 | + | 22.8373i | −0.747658 | + | 1.29498i | 0.201284 | + | 0.979533i | \(0.435488\pi\) |
−0.948943 | + | 0.315449i | \(0.897845\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.35091 | + | 11.0001i | 0.358975 | + | 0.621762i | 0.987790 | − | 0.155792i | \(-0.0497931\pi\) |
−0.628815 | + | 0.777555i | \(0.716460\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.0165768 | + | 0.0287119i | 0.000931047 | + | 0.00161262i | 0.866491 | − | 0.499193i | \(-0.166370\pi\) |
−0.865560 | + | 0.500806i | \(0.833037\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.98264 | − | 6.89813i | 0.222985 | − | 0.386221i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3705 | −0.855238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24815 | − | 7.35801i | −0.235645 | − | 0.408149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.11194 | + | 0.170584i | −0.0613031 | + | 0.00940461i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42694 | − | 4.20358i | −0.133397 | − | 0.231050i | 0.791587 | − | 0.611056i | \(-0.209255\pi\) |
−0.924984 | + | 0.380006i | \(0.875922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.92726 | − | 13.7304i | 0.433112 | − | 0.750173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.32200 | − | 7.48592i | −0.235434 | − | 0.407784i | 0.723965 | − | 0.689837i | \(-0.242318\pi\) |
−0.959399 | + | 0.282053i | \(0.908985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.360028 | + | 0.623586i | −0.0194966 | + | 0.0337691i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6224 | − | 8.16680i | 0.897524 | − | 0.440966i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6116 | − | 20.1119i | 0.623344 | − | 1.07966i | −0.365515 | − | 0.930806i | \(-0.619107\pi\) |
0.988859 | − | 0.148858i | \(-0.0475596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.76025 | + | 6.51295i | −0.201282 | + | 0.348630i | −0.948942 | − | 0.315452i | \(-0.897844\pi\) |
0.747660 | + | 0.664082i | \(0.231177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.919056 | 0.0489164 | 0.0244582 | − | 0.999701i | \(-0.492214\pi\) | ||||
0.0244582 | + | 0.999701i | \(0.492214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2499 | −0.756306 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.24300 | − | 14.2773i | 0.435049 | − | 0.753527i | −0.562251 | − | 0.826967i | \(-0.690064\pi\) |
0.997300 | + | 0.0734398i | \(0.0233977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65737 | − | 2.87066i | −0.0872302 | − | 0.151087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4848 | − | 19.8923i | −0.601144 | − | 1.04121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.6784 | 0.661808 | 0.330904 | − | 0.943664i | \(-0.392646\pi\) | ||||
0.330904 | + | 0.943664i | \(0.392646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.43897 | + | 0.374167i | −0.126625 | + | 0.0194258i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6821 | 1.17443 | 0.587217 | − | 0.809430i | \(-0.300224\pi\) | ||||
0.587217 | + | 0.809430i | \(0.300224\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.0849 | 1.29194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0925 | −0.980717 | −0.490358 | − | 0.871521i | \(-0.663134\pi\) | ||||
−0.490358 | + | 0.871521i | \(0.663134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.07925 | −0.310635 | −0.155318 | − | 0.987865i | \(-0.549640\pi\) | ||||
−0.155318 | + | 0.987865i | \(0.549640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01195 | − | 5.16621i | 0.102539 | − | 0.263295i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.631562 | 0.0320214 | 0.0160107 | − | 0.999872i | \(-0.494903\pi\) | ||||
0.0160107 | + | 0.999872i | \(0.494903\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.647728 | − | 1.12190i | −0.0327570 | − | 0.0567368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.65679 | + | 8.06579i | 0.234308 | + | 0.405834i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1830 | + | 31.4939i | −0.912578 | + | 1.58063i | −0.102170 | + | 0.994767i | \(0.532579\pi\) |
−0.810408 | + | 0.585865i | \(0.800755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.6137 | 1.57871 | 0.789357 | − | 0.613934i | \(-0.210414\pi\) | ||||
0.789357 | + | 0.613934i | \(0.210414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.26765 | −0.112960 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.38816 | − | 5.86847i | 0.167945 | − | 0.290889i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0906 | + | 17.4774i | −0.498948 | + | 0.864203i | −0.999999 | − | 0.00121422i | \(-0.999614\pi\) |
0.501051 | + | 0.865418i | \(0.332947\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0138 | − | 12.4895i | −0.492746 | − | 0.614567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5270 | − | 23.4294i | 0.664014 | − | 1.15011i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.4159 | − | 21.5049i | −0.606555 | − | 1.05058i | −0.991804 | − | 0.127772i | \(-0.959217\pi\) |
0.385248 | − | 0.922813i | \(-0.374116\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.71841 | + | 9.90458i | −0.278698 | + | 0.482720i | −0.971062 | − | 0.238829i | \(-0.923236\pi\) |
0.692363 | + | 0.721549i | \(0.256570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.52548 | − | 6.10631i | −0.171011 | − | 0.296200i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.6986 | − | 4.09587i | 1.29203 | − | 0.198213i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.80157 | + | 4.85246i | 0.134947 | + | 0.233735i | 0.925577 | − | 0.378559i | \(-0.123580\pi\) |
−0.790630 | + | 0.612294i | \(0.790247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.22555 | −0.203067 | −0.101534 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101534 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.940366 | − | 1.62876i | 0.0449838 | − | 0.0779142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7316 | − | 30.7120i | −0.846281 | − | 1.46580i | −0.884504 | − | 0.466532i | \(-0.845503\pi\) |
0.0382233 | − | 0.999269i | \(-0.487830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4658 | + | 19.8593i | 0.544755 | + | 0.943543i | 0.998622 | + | 0.0524740i | \(0.0167107\pi\) |
−0.453867 | + | 0.891069i | \(0.649956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1625 | + | 17.6019i | −0.481748 | + | 0.834412i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4850 | −0.966747 | −0.483373 | − | 0.875414i | \(-0.660589\pi\) | ||||
−0.483373 | + | 0.875414i | \(0.660589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.23161 | − | 9.06141i | −0.246347 | − | 0.426685i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.2582 | − | 2.64761i | 0.809076 | − | 0.124122i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.72677 | − | 13.3832i | −0.361443 | − | 0.626038i | 0.626755 | − | 0.779216i | \(-0.284383\pi\) |
−0.988199 | + | 0.153178i | \(0.951049\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0815 | + | 24.3898i | −0.655839 | + | 1.13595i | 0.325844 | + | 0.945424i | \(0.394352\pi\) |
−0.981683 | + | 0.190523i | \(0.938982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3193 | + | 26.5338i | 0.711948 | + | 1.23313i | 0.964125 | + | 0.265449i | \(0.0855202\pi\) |
−0.252177 | + | 0.967681i | \(0.581146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.61798 | + | 11.4627i | −0.306244 | + | 0.530429i | −0.977537 | − | 0.210762i | \(-0.932406\pi\) |
0.671294 | + | 0.741191i | \(0.265739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5895 | − | 19.4437i | −0.719857 | − | 0.897827i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.06638 | + | 5.31112i | −0.140992 | + | 0.244206i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.11826 | − | 8.86508i | 0.234842 | − | 0.406758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0872 | 0.643658 | 0.321829 | − | 0.946798i | \(-0.395702\pi\) | ||||
0.321829 | + | 0.946798i | \(0.395702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.3405 | 0.973044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.86407 | − | 17.0851i | 0.447904 | − | 0.775793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.45654 | − | 5.98690i | −0.156631 | − | 0.271292i | 0.777021 | − | 0.629475i | \(-0.216730\pi\) |
−0.933652 | + | 0.358183i | \(0.883397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3481 | − | 26.5837i | −0.692651 | − | 1.19971i | −0.970966 | − | 0.239217i | \(-0.923109\pi\) |
0.278315 | − | 0.960490i | \(-0.410224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.8176 | 0.937578 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.12865 | + | 20.8724i | −0.364620 | + | 0.936256i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0371 | 0.986518 | 0.493259 | − | 0.869882i | \(-0.335805\pi\) | ||||
0.493259 | + | 0.869882i | \(0.335805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9653 | 1.73737 | 0.868687 | − | 0.495361i | \(-0.164964\pi\) | ||||
0.868687 | + | 0.495361i | \(0.164964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.09922 | 0.404910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2941 | 1.25412 | 0.627058 | − | 0.778973i | \(-0.284259\pi\) | ||||
0.627058 | + | 0.778973i | \(0.284259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.6885 | + | 5.47503i | −1.57877 | + | 0.242201i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6084 | 1.08437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.264676 | + | 0.458433i | 0.0116405 | + | 0.0201619i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.98150 | + | 10.3603i | 0.262054 | + | 0.453892i | 0.966788 | − | 0.255581i | \(-0.0822667\pi\) |
−0.704733 | + | 0.709472i | \(0.748933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.15056 | − | 5.45693i | 0.137764 | − | 0.238615i | −0.788886 | − | 0.614540i | \(-0.789342\pi\) |
0.926650 | + | 0.375925i | \(0.122675\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.88190 | −0.0819767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8415 | −0.993108 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.4758 | − | 28.5369i | 0.713645 | − | 1.23607i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.72625 | − | 9.91815i | 0.247567 | − | 0.428799i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.41948 | − | 5.89399i | −0.276507 | − | 0.253872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.88191 | − | 17.1160i | 0.424857 | − | 0.735873i | −0.571550 | − | 0.820567i | \(-0.693658\pi\) |
0.996407 | + | 0.0846937i | \(0.0269912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0987 | − | 24.4197i | −0.603923 | − | 1.04602i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6125 | + | 37.4340i | −0.924085 | + | 1.60056i | −0.131059 | + | 0.991375i | \(0.541838\pi\) |
−0.793026 | + | 0.609188i | \(0.791496\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.1114 | + | 26.1737i | 0.643767 | + | 1.11504i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4707 | − | 2.21997i | 0.615357 | − | 0.0944029i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0838 | + | 24.3938i | 0.596748 | + | 1.03360i | 0.993298 | + | 0.115584i | \(0.0368740\pi\) |
−0.396550 | + | 0.918013i | \(0.629793\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3137 | −0.816884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.8472 | + | 22.2520i | −0.541445 | + | 0.937810i | 0.457377 | + | 0.889273i | \(0.348789\pi\) |
−0.998821 | + | 0.0485366i | \(0.984544\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3976 | + | 19.7411i | 0.479499 | + | 0.830516i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.7441 | + | 30.7336i | 0.743870 | + | 1.28842i | 0.950721 | + | 0.310048i | \(0.100345\pi\) |
−0.206851 | + | 0.978373i | \(0.566321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8412 | − | 18.7775i | 0.453689 | − | 0.785813i | −0.544923 | − | 0.838486i | \(-0.683441\pi\) |
0.998612 | + | 0.0526737i | \(0.0167743\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.862754 | 0.0359793 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.60727 | − | 13.1762i | −0.316695 | − | 0.548531i | 0.663102 | − | 0.748529i | \(-0.269240\pi\) |
−0.979796 | + | 0.199998i | \(0.935906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.6018 | − | 33.1786i | −1.10363 | − | 1.37648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.580553 | + | 1.00555i | 0.0240440 | + | 0.0416455i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1924 | + | 33.2423i | −0.792157 | + | 1.37206i | 0.132472 | + | 0.991187i | \(0.457708\pi\) |
−0.924629 | + | 0.380869i | \(0.875625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.36606 | − | 2.36608i | −0.0562875 | − | 0.0974928i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.25559 | − | 16.0311i | 0.380081 | − | 0.658320i | −0.610992 | − | 0.791637i | \(-0.709229\pi\) |
0.991074 | + | 0.133316i | \(0.0425626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.3223 | − | 2.19721i | 0.587159 | − | 0.0900770i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.8413 | − | 18.7776i | 0.442962 | − | 0.767233i | −0.554946 | − | 0.831887i | \(-0.687261\pi\) |
0.997908 | + | 0.0646536i | \(0.0205942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.95776 | − | 6.85505i | 0.161441 | − | 0.279623i | −0.773945 | − | 0.633253i | \(-0.781719\pi\) |
0.935386 | + | 0.353630i | \(0.115053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.9059 | 0.646665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.9247 | −1.45814 | −0.729068 | − | 0.684441i | \(-0.760046\pi\) | ||||
−0.729068 | + | 0.684441i | \(0.760046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.833539 | + | 1.44373i | −0.0337214 | + | 0.0584072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.60252 | − | 2.77565i | −0.0647253 | − | 0.112108i | 0.831847 | − | 0.555005i | \(-0.187284\pi\) |
−0.896572 | + | 0.442898i | \(0.853950\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9357 | − | 27.6015i | −0.641549 | − | 1.11120i | −0.985087 | − | 0.172056i | \(-0.944959\pi\) |
0.343538 | − | 0.939139i | \(-0.388374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.9726 | 0.842959 | 0.421480 | − | 0.906838i | \(-0.361511\pi\) | ||||
0.421480 | + | 0.906838i | \(0.361511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.9853 | + | 24.9262i | 0.800692 | + | 0.998647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.46924 | −0.378769 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.7102 | 0.706153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4435 | −1.05270 | −0.526349 | − | 0.850268i | \(-0.676440\pi\) | ||||
−0.526349 | + | 0.850268i | \(0.676440\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.8253 | 0.707377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.96663 | − | 26.7891i | 0.236407 | − | 1.06142i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.9618 | 1.10443 | 0.552213 | − | 0.833703i | \(-0.313783\pi\) | ||||
0.552213 | + | 0.833703i | \(0.313783\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.12936 | + | 10.6164i | 0.241718 | + | 0.418669i | 0.961204 | − | 0.275839i | \(-0.0889556\pi\) |
−0.719485 | + | 0.694508i | \(0.755622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.49923 | + | 7.79290i | 0.176883 | + | 0.306371i | 0.940811 | − | 0.338931i | \(-0.110065\pi\) |
−0.763928 | + | 0.645301i | \(0.776732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.76640 | + | 6.52360i | −0.147844 | + | 0.256074i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.7901 | 0.891844 | 0.445922 | − | 0.895072i | \(-0.352876\pi\) | ||||
0.445922 | + | 0.895072i | \(0.352876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.6418 | 1.47079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3311 | + | 33.4824i | −0.753033 | + | 1.30429i | 0.193314 | + | 0.981137i | \(0.438076\pi\) |
−0.946347 | + | 0.323154i | \(0.895257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.75399 | − | 9.96621i | 0.223804 | − | 0.387641i | −0.732156 | − | 0.681137i | \(-0.761486\pi\) |
0.955960 | + | 0.293497i | \(0.0948190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.1590 | + | 16.4124i | 0.510286 | + | 0.636444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.27362 | + | 2.20597i | −0.0493147 | + | 0.0854156i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35511 | − | 11.0074i | −0.245336 | − | 0.424935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6642 | + | 18.4709i | −0.411075 | + | 0.712002i | −0.995008 | − | 0.0997997i | \(-0.968180\pi\) |
0.583933 | + | 0.811802i | \(0.301513\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.8799 | + | 24.0407i | 0.533449 | + | 0.923961i | 0.999237 | + | 0.0390641i | \(0.0124377\pi\) |
−0.465788 | + | 0.884896i | \(0.654229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.3984 | − | 24.1943i | −0.744443 | − | 0.928491i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.66854 | − | 15.0143i | −0.331692 | − | 0.574508i | 0.651151 | − | 0.758948i | \(-0.274286\pi\) |
−0.982844 | + | 0.184440i | \(0.940953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.2194 | 1.15462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.82832 | + | 3.16675i | −0.0696535 | + | 0.120643i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8023 | + | 34.2986i | 0.753315 | + | 1.30478i | 0.946207 | + | 0.323560i | \(0.104880\pi\) |
−0.192892 | + | 0.981220i | \(0.561787\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.960788 | + | 1.66413i | 0.0364448 | + | 0.0631242i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6730 | − | 23.6824i | 0.517903 | − | 0.897035i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.28469 | −0.275139 | −0.137570 | − | 0.990492i | \(-0.543929\pi\) | ||||
−0.137570 | + | 0.990492i | \(0.543929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8558 | + | 22.2668i | 0.484864 | + | 0.839809i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.19052 | − | 13.3280i | 0.195210 | − | 0.501251i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.00541 | − | 10.4017i | −0.225538 | − | 0.390643i | 0.730943 | − | 0.682439i | \(-0.239081\pi\) |
−0.956481 | + | 0.291796i | \(0.905747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.115134 | − | 0.199418i | 0.00431181 | − | 0.00746827i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.10800 | − | 7.11526i | −0.153630 | − | 0.266096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.15819 | + | 3.73809i | −0.0804868 | + | 0.139407i | −0.903459 | − | 0.428674i | \(-0.858981\pi\) |
0.822972 | + | 0.568081i | \(0.192314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0375 | − | 36.0449i | 0.522783 | − | 1.34238i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.93210 | + | 12.0067i | −0.257452 | + | 0.445919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.2483 | + | 17.7506i | −0.380090 | + | 0.658334i | −0.991075 | − | 0.133308i | \(-0.957440\pi\) |
0.610985 | + | 0.791642i | \(0.290774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0282 | −0.592825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3322 | 0.935666 | 0.467833 | − | 0.883817i | \(-0.345035\pi\) | ||||
0.467833 | + | 0.883817i | \(0.345035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.86356 | + | 10.1560i | −0.215987 | + | 0.374100i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.63391 | + | 11.4903i | 0.244032 | + | 0.422676i | 0.961859 | − | 0.273545i | \(-0.0881964\pi\) |
−0.717827 | + | 0.696222i | \(0.754863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6116 | + | 39.1644i | 0.829538 | + | 1.43680i | 0.898401 | + | 0.439176i | \(0.144730\pi\) |
−0.0688624 | + | 0.997626i | \(0.521937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.7217 | 1.08892 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2611 | − | 14.0451i | −0.411471 | − | 0.513199i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3797 | 1.03559 | 0.517795 | − | 0.855505i | \(-0.326753\pi\) | ||||
0.517795 | + | 0.855505i | \(0.326753\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.6435 | −0.933263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.08483 | 0.184811 | 0.0924056 | − | 0.995721i | \(-0.470544\pi\) | ||||
0.0924056 | + | 0.995721i | \(0.470544\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7225 | −1.36744 | −0.683720 | − | 0.729745i | \(-0.739639\pi\) | ||||
−0.683720 | + | 0.729745i | \(0.739639\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.8110 | + | 6.72111i | −1.58606 | + | 0.243321i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.7229 | −0.856583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8729 | + | 20.5644i | 0.428147 | + | 0.741572i | 0.996709 | − | 0.0810688i | \(-0.0258333\pi\) |
−0.568562 | + | 0.822641i | \(0.692500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.5347 | − | 33.8351i | −0.702614 | − | 1.21696i | −0.967546 | − | 0.252696i | \(-0.918683\pi\) |
0.264932 | − | 0.964267i | \(-0.414650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.626657 | − | 1.08540i | 0.0225102 | − | 0.0389888i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.7008 | 1.42243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5402 | 0.377159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4697 | + | 19.8661i | −0.409370 | + | 0.709050i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.90458 | − | 3.29882i | 0.0678908 | − | 0.117590i | −0.830082 | − | 0.557642i | \(-0.811706\pi\) |
0.897973 | + | 0.440051i | \(0.145040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.4173 | − | 5.43342i | 1.25929 | − | 0.193190i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0140 | − | 34.6653i | 0.710718 | − | 1.23100i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.8239 | + | 18.7476i | 0.383404 | + | 0.664075i | 0.991546 | − | 0.129753i | \(-0.0414184\pi\) |
−0.608143 | + | 0.793828i | \(0.708085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.691743 | + | 1.19813i | −0.0244721 | + | 0.0423870i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.49500 | + | 14.7138i | 0.299782 | + | 0.519238i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.643408 | + | 1.65212i | −0.0226771 | + | 0.0582294i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5128 | + | 32.0652i | 0.650877 | + | 1.12735i | 0.982910 | + | 0.184084i | \(0.0589319\pi\) |
−0.332034 | + | 0.943268i | \(0.607735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.37416 | −0.188712 | −0.0943561 | − | 0.995539i | \(-0.530079\pi\) | ||||
−0.0943561 | + | 0.995539i | \(0.530079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.81216 | + | 11.7990i | −0.238620 | + | 0.413301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6348 | − | 20.1521i | −0.407050 | − | 0.705032i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.11119 | + | 1.92464i | 0.0387809 | + | 0.0671706i | 0.884764 | − | 0.466039i | \(-0.154319\pi\) |
−0.845983 | + | 0.533209i | \(0.820986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5537 | − | 32.1359i | 0.646740 | − | 1.12019i | −0.337157 | − | 0.941449i | \(-0.609465\pi\) |
0.983897 | − | 0.178738i | \(-0.0572015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4790 | 0.677351 | 0.338676 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.137129 | + | 0.237514i | 0.00476267 | + | 0.00824919i | 0.868397 | − | 0.495870i | \(-0.165151\pi\) |
−0.863634 | + | 0.504119i | \(0.831817\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.95163 | − | 22.2319i | 0.171564 | − | 0.770290i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.49657 | + | 6.05623i | 0.121004 | + | 0.209585i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0711 | − | 36.4962i | 0.727455 | − | 1.25999i | −0.230501 | − | 0.973072i | \(-0.574036\pi\) |
0.957956 | − | 0.286917i | \(-0.0926303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.96666 | − | 10.3346i | −0.205747 | − | 0.356364i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.99671 | − | 3.45840i | 0.0686888 | − | 0.118973i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.07328 | − | 23.2980i | 0.311762 | − | 0.800528i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.08351 | + | 1.87669i | −0.0371422 | + | 0.0643322i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3086 | − | 38.6397i | 0.763833 | − | 1.32300i | −0.177029 | − | 0.984206i | \(-0.556649\pi\) |
0.940862 | − | 0.338791i | \(-0.110018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.33227 | 0.250466 | 0.125233 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125233 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.70146 | 0.0921725 | 0.0460863 | − | 0.998937i | \(-0.485325\pi\) | ||||
0.0460863 | + | 0.998937i | \(0.485325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.40188 | − | 12.8204i | 0.251963 | − | 0.436413i | −0.712103 | − | 0.702075i | \(-0.752257\pi\) |
0.964066 | + | 0.265662i | \(0.0855905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6429 | − | 20.1661i | −0.395870 | − | 0.685668i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.44449 | − | 5.96603i | −0.116846 | − | 0.202384i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.9319 | −1.25139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.5822 | + | 29.7404i | −0.391551 | + | 1.00541i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0961 | −0.374690 | −0.187345 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187345 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0536 | −0.507168 | −0.253584 | − | 0.967313i | \(-0.581609\pi\) | ||||
−0.253584 | + | 0.967313i | \(0.581609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.39418 | −0.0805704 | −0.0402852 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402852 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.93394 | −0.165666 | −0.0828328 | − | 0.996563i | \(-0.526397\pi\) | ||||
−0.0828328 | + | 0.996563i | \(0.526397\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1682 | − | 26.1095i | 0.341031 | − | 0.875685i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.00853 | −0.0672130 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.93047 | + | 13.7360i | 0.265086 | + | 0.459143i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.85017 | + | 3.20459i | 0.0617067 | + | 0.106879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51730 | + | 2.62804i | −0.0505486 | + | 0.0875527i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.22400 | −0.0739284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.39631 | 0.112773 | 0.0563863 | − | 0.998409i | \(-0.482042\pi\) | ||||
0.0563863 | + | 0.998409i | \(0.482042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.65142 | − | 8.05649i | 0.154108 | − | 0.266924i | −0.778626 | − | 0.627489i | \(-0.784083\pi\) |
0.932734 | + | 0.360565i | \(0.117416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0055 | + | 17.3301i | −0.331134 | + | 0.573541i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4722 | − | 55.1355i | 0.709076 | − | 1.82073i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.92656 | + | 15.4613i | −0.294460 | + | 0.510020i | −0.974859 | − | 0.222822i | \(-0.928473\pi\) |
0.680399 | + | 0.732842i | \(0.261806\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5970 | + | 28.7469i | 0.546298 | + | 0.946216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.89737 | + | 10.2145i | −0.193904 | + | 0.335852i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6430 | − | 40.9510i | −0.775703 | − | 1.34356i | −0.934398 | − | 0.356230i | \(-0.884062\pi\) |
0.158695 | − | 0.987328i | \(-0.449271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.5463 | − | 9.91242i | 1.03389 | − | 0.324866i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.40917 | − | 5.90486i | −0.111492 | − | 0.193110i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2493 | 0.694183 | 0.347092 | − | 0.937831i | \(-0.387169\pi\) | ||||
0.347092 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0405 | + | 52.0316i | −0.979292 | + | 1.69618i | −0.314315 | + | 0.949319i | \(0.601775\pi\) |
−0.664977 | + | 0.746864i | \(0.731559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.67303 | + | 2.89777i | 0.0544813 | + | 0.0943644i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.83468 | − | 3.17775i | −0.0596189 | − | 0.103263i | 0.834675 | − | 0.550742i | \(-0.185655\pi\) |
−0.894294 | + | 0.447479i | \(0.852322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.7531 | + | 46.3377i | −0.868442 | + | 1.50419i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.837421 | −0.0271267 | −0.0135634 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135634 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7055 | + | 23.7385i | 0.443498 | + | 0.768161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.2382 | − | 44.2636i | 0.556651 | − | 1.42935i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3327 | + | 26.5571i | 0.494605 | + | 0.856680i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.15574 | − | 3.73386i | 0.0693958 | − | 0.120197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8856 | − | 37.9070i | −0.703795 | − | 1.21901i | −0.967125 | − | 0.254302i | \(-0.918154\pi\) |
0.263330 | − | 0.964706i | \(-0.415179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3059 | + | 35.1709i | −0.651648 | + | 1.12869i | 0.331075 | + | 0.943605i | \(0.392589\pi\) |
−0.982723 | + | 0.185083i | \(0.940745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.98560 | − | 0.458025i | 0.0957138 | − | 0.0146836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.7479 | − | 49.7929i | 0.919728 | − | 1.59302i | 0.119901 | − | 0.992786i | \(-0.461742\pi\) |
0.799827 | − | 0.600230i | \(-0.204924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.51689 | − | 13.0196i | 0.240241 | − | 0.416109i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4594 | −0.429289 | −0.214644 | − | 0.976692i | \(-0.568859\pi\) | ||||
−0.214644 | + | 0.976692i | \(0.568859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.5103 | 1.16331 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.980604 | − | 1.69846i | 0.0311814 | − | 0.0540078i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7821 | + | 30.7995i | 0.564867 | + | 0.978379i | 0.997062 | + | 0.0765983i | \(0.0244059\pi\) |
−0.432195 | + | 0.901780i | \(0.642261\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.42036 | − | 16.3165i | −0.298645 | − | 0.517269i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7289 | 1.03653 | 0.518267 | − | 0.855219i | \(-0.326577\pi\) | ||||
0.518267 | + | 0.855219i | \(0.326577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3024.2.t.l.289.4 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.961.6 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.289.4 | 22 | |||
7.4 | even | 3 | 3024.2.q.k.2881.8 | 22 | |||
9.4 | even | 3 | 3024.2.q.k.2305.8 | 22 | |||
9.5 | odd | 6 | 1008.2.q.k.625.11 | 22 | |||
12.11 | even | 2 | 504.2.t.d.457.6 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.k.529.11 | 22 | |||
28.11 | odd | 6 | 1512.2.q.c.1369.8 | 22 | |||
36.23 | even | 6 | 504.2.q.d.121.1 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.c.793.8 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.l.1873.4 | 22 | ||
63.32 | odd | 6 | 1008.2.t.k.193.6 | 22 | |||
84.11 | even | 6 | 504.2.q.d.25.1 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.d.361.4 | 22 | |||
252.95 | even | 6 | 504.2.t.d.193.6 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.1 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.d.121.1 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.193.6 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.d.457.6 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.k.529.11 | 22 | 21.11 | odd | 6 | |||
1008.2.q.k.625.11 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.193.6 | 22 | 63.32 | odd | 6 | |||
1008.2.t.k.961.6 | 22 | 3.2 | odd | 2 | |||
1512.2.q.c.793.8 | 22 | 36.31 | odd | 6 | |||
1512.2.q.c.1369.8 | 22 | 28.11 | odd | 6 | |||
1512.2.t.d.289.4 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.361.4 | 22 | 252.67 | odd | 6 | |||
3024.2.q.k.2305.8 | 22 | 9.4 | even | 3 | |||
3024.2.q.k.2881.8 | 22 | 7.4 | even | 3 | |||
3024.2.t.l.289.4 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.1873.4 | 22 | 63.4 | even | 3 | inner |