Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.193 |
Dual form | 1200.3.bg.o.1057.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55051 | − | 2.55051i | 0.364359 | − | 0.364359i | −0.501056 | − | 0.865415i | \(-0.667055\pi\) |
0.865415 | + | 0.501056i | \(0.167055\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.24745 | −0.749768 | −0.374884 | − | 0.927072i | \(-0.622317\pi\) | ||||
−0.374884 | + | 0.927072i | \(0.622317\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.2474 | + | 12.2474i | 0.942111 | + | 0.942111i | 0.998414 | − | 0.0563023i | \(-0.0179311\pi\) |
−0.0563023 | + | 0.998414i | \(0.517931\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.4495 | − | 12.4495i | 0.732323 | − | 0.732323i | −0.238757 | − | 0.971079i | \(-0.576740\pi\) |
0.971079 | + | 0.238757i | \(0.0767398\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.4949i | 1.81552i | 0.419489 | + | 0.907760i | \(0.362209\pi\) | ||||
−0.419489 | + | 0.907760i | \(0.637791\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.24745 | 0.297498 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −17.3485 | − | 17.3485i | −0.754281 | − | 0.754281i | 0.220994 | − | 0.975275i | \(-0.429070\pi\) |
−0.975275 | + | 0.220994i | \(0.929070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.75255i | 0.336295i | 0.985762 | + | 0.168147i | \(0.0537785\pi\) | ||||
−0.985762 | + | 0.168147i | \(0.946222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.4949 | −0.919190 | −0.459595 | − | 0.888129i | \(-0.652005\pi\) | ||||
−0.459595 | + | 0.888129i | \(0.652005\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.1010 | − | 10.1010i | −0.306092 | − | 0.306092i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.34847 | − | 7.34847i | 0.198607 | − | 0.198607i | −0.600795 | − | 0.799403i | \(-0.705149\pi\) |
0.799403 | + | 0.600795i | \(0.205149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0000i | 0.769231i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 74.4949 | 1.81695 | 0.908474 | − | 0.417941i | \(-0.137248\pi\) | ||||
0.908474 | + | 0.417941i | \(0.137248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.8990 | + | 34.8990i | 0.811604 | + | 0.811604i | 0.984874 | − | 0.173270i | \(-0.0554334\pi\) |
−0.173270 | + | 0.984874i | \(0.555433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22.0454 | + | 22.0454i | −0.469051 | + | 0.469051i | −0.901607 | − | 0.432556i | \(-0.857612\pi\) |
0.432556 | + | 0.901607i | \(0.357612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.9898i | 0.734486i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.4949 | 0.597939 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 64.6969 | + | 64.6969i | 1.22070 | + | 1.22070i | 0.967385 | + | 0.253312i | \(0.0815201\pi\) |
0.253312 | + | 0.967385i | \(0.418480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −42.2474 | + | 42.2474i | −0.741183 | + | 0.741183i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 15.2577i | − | 0.258604i | −0.991605 | − | 0.129302i | \(-0.958726\pi\) | ||
0.991605 | − | 0.129302i | \(-0.0412737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.5051 | −0.877133 | −0.438566 | − | 0.898699i | \(-0.644514\pi\) | ||||
−0.438566 | + | 0.898699i | \(0.644514\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.65153 | + | 7.65153i | 0.121453 | + | 0.121453i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.69694 | − | 4.69694i | 0.0701036 | − | 0.0701036i | −0.671186 | − | 0.741289i | \(-0.734215\pi\) |
0.741289 | + | 0.671186i | \(0.234215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 42.4949i | − | 0.615868i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 117.980 | 1.66168 | 0.830842 | − | 0.556508i | \(-0.187859\pi\) | ||||
0.830842 | + | 0.556508i | \(0.187859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −34.1918 | − | 34.1918i | −0.468381 | − | 0.468381i | 0.433009 | − | 0.901390i | \(-0.357452\pi\) |
−0.901390 | + | 0.433009i | \(0.857452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.0352 | + | 21.0352i | −0.273184 | + | 0.273184i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.494897i | 0.00626452i | 0.999995 | + | 0.00313226i | \(0.000997032\pi\) | ||||
−0.999995 | + | 0.00313226i | \(0.999003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18.3587 | − | 18.3587i | −0.221189 | − | 0.221189i | 0.587810 | − | 0.808999i | \(-0.299990\pi\) |
−0.808999 | + | 0.587810i | \(0.799990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.9444 | + | 11.9444i | −0.137292 | + | 0.137292i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 136.969i | 1.53898i | 0.638658 | + | 0.769491i | \(0.279490\pi\) | ||||
−0.638658 | + | 0.769491i | \(0.720510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.4745 | 0.686533 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −34.8990 | − | 34.8990i | −0.375258 | − | 0.375258i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −94.5959 | + | 94.5959i | −0.975216 | + | 0.975216i | −0.999700 | − | 0.0244846i | \(-0.992206\pi\) |
0.0244846 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 24.7423i | − | 0.249923i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 70.2474 | 0.695519 | 0.347760 | − | 0.937584i | \(-0.386943\pi\) | ||||
0.347760 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 86.8434 | + | 86.8434i | 0.843139 | + | 0.843139i | 0.989266 | − | 0.146126i | \(-0.0466806\pi\) |
−0.146126 | + | 0.989266i | \(0.546681\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −96.3383 | + | 96.3383i | −0.900358 | + | 0.900358i | −0.995467 | − | 0.0951092i | \(-0.969680\pi\) |
0.0951092 | + | 0.995467i | \(0.469680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.5153i | − | 0.114819i | −0.998351 | − | 0.0574097i | \(-0.981716\pi\) | ||
0.998351 | − | 0.0574097i | \(-0.0182841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.0000 | 0.162162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −66.9444 | − | 66.9444i | −0.592428 | − | 0.592428i | 0.345858 | − | 0.938287i | \(-0.387588\pi\) |
−0.938287 | + | 0.345858i | \(0.887588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36.7423 | + | 36.7423i | −0.314037 | + | 0.314037i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 63.5051i | − | 0.533656i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.9796 | −0.437848 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 91.2372 | + | 91.2372i | 0.741766 | + | 0.741766i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55051 | − | 2.55051i | 0.0200828 | − | 0.0200828i | −0.696994 | − | 0.717077i | \(-0.745480\pi\) |
0.717077 | + | 0.696994i | \(0.245480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 85.4847i | 0.662672i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −44.2474 | −0.337767 | −0.168883 | − | 0.985636i | \(-0.554016\pi\) | ||||
−0.168883 | + | 0.985636i | \(0.554016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.9796 | + | 87.9796i | 0.661501 | + | 0.661501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3587 | − | 18.3587i | 0.134005 | − | 0.134005i | −0.636923 | − | 0.770928i | \(-0.719793\pi\) |
0.770928 | + | 0.636923i | \(0.219793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 219.980i | 1.58259i | 0.611437 | + | 0.791293i | \(0.290592\pi\) | ||||
−0.611437 | + | 0.791293i | \(0.709408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −54.0000 | −0.382979 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −101.010 | − | 101.010i | −0.706365 | − | 0.706365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −44.0783 | + | 44.0783i | −0.299852 | + | 0.299852i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.2679i | 0.189717i | 0.995491 | + | 0.0948586i | \(0.0302399\pi\) | ||||
−0.995491 | + | 0.0948586i | \(0.969760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 61.0102 | 0.404041 | 0.202021 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202021 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 37.3485 | + | 37.3485i | 0.244108 | + | 0.244108i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.6515 | − | 22.6515i | 0.144277 | − | 0.144277i | −0.631279 | − | 0.775556i | \(-0.717470\pi\) |
0.775556 | + | 0.631279i | \(0.217470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 158.474i | 0.996695i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −88.4949 | −0.549658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −88.9898 | − | 88.9898i | −0.545950 | − | 0.545950i | 0.379317 | − | 0.925267i | \(-0.376159\pi\) |
−0.925267 | + | 0.379317i | \(0.876159\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 171.641 | − | 171.641i | 1.02779 | − | 1.02779i | 0.0281898 | − | 0.999603i | \(-0.491026\pi\) |
0.999603 | − | 0.0281898i | \(-0.00897427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131.000i | 0.775148i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −103.485 | −0.605174 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6311 | + | 10.6311i | 0.0614516 | + | 0.0614516i | 0.737165 | − | 0.675713i | \(-0.236164\pi\) |
−0.675713 | + | 0.737165i | \(0.736164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.6867 | − | 18.6867i | 0.105575 | − | 0.105575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 100.247i | 0.560042i | 0.959994 | + | 0.280021i | \(0.0903414\pi\) | ||||
−0.959994 | + | 0.280021i | \(0.909659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 259.444 | 1.43339 | 0.716696 | − | 0.697386i | \(-0.245654\pi\) | ||||
0.716696 | + | 0.697386i | \(0.245654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −65.5301 | − | 65.5301i | −0.358088 | − | 0.358088i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −102.677 | + | 102.677i | −0.549072 | + | 0.549072i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.7423i | 0.0991659i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −77.4847 | −0.405679 | −0.202840 | − | 0.979212i | \(-0.565017\pi\) | ||||
−0.202840 | + | 0.979212i | \(0.565017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −83.5857 | − | 83.5857i | −0.433087 | − | 0.433087i | 0.456590 | − | 0.889677i | \(-0.349070\pi\) |
−0.889677 | + | 0.456590i | \(0.849070\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 200.252 | − | 200.252i | 1.01651 | − | 1.01651i | 0.0166464 | − | 0.999861i | \(-0.494701\pi\) |
0.999861 | − | 0.0166464i | \(-0.00529894\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 162.990i | − | 0.819044i | −0.912300 | − | 0.409522i | \(-0.865695\pi\) | ||
0.912300 | − | 0.409522i | \(-0.134305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.5051 | 0.0572393 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.8740 | + | 24.8740i | 0.122532 | + | 0.122532i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 52.0454 | − | 52.0454i | 0.251427 | − | 0.251427i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 284.495i | − | 1.36122i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −207.980 | −0.985685 | −0.492843 | − | 0.870118i | \(-0.664042\pi\) | ||||
−0.492843 | + | 0.870118i | \(0.664042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 144.495 | + | 144.495i | 0.678380 | + | 0.678380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −72.6765 | + | 72.6765i | −0.334915 | + | 0.334915i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 83.7526i | − | 0.382432i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 304.949 | 1.37986 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.7219 | + | 29.7219i | 0.133282 | + | 0.133282i | 0.770601 | − | 0.637318i | \(-0.219956\pi\) |
−0.637318 | + | 0.770601i | \(0.719956\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 197.980 | − | 197.980i | 0.872157 | − | 0.872157i | −0.120550 | − | 0.992707i | \(-0.538466\pi\) |
0.992707 | + | 0.120550i | \(0.0384659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.96938i | − | 0.0391676i | −0.999808 | − | 0.0195838i | \(-0.993766\pi\) | ||
0.999808 | − | 0.0195838i | \(-0.00623412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −51.5255 | −0.223054 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.7628 | − | 28.7628i | −0.123445 | − | 0.123445i | 0.642685 | − | 0.766130i | \(-0.277820\pi\) |
−0.766130 | + | 0.642685i | \(0.777820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.606123 | + | 0.606123i | −0.00255748 | + | 0.00255748i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 242.969i | 1.01661i | 0.861178 | + | 0.508304i | \(0.169727\pi\) | ||||
−0.861178 | + | 0.508304i | \(0.830273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −32.0000 | −0.132780 | −0.0663900 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663900 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −422.474 | + | 422.474i | −1.71042 | + | 1.71042i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 44.9694i | − | 0.180600i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 250.763 | 0.999055 | 0.499527 | − | 0.866298i | \(-0.333507\pi\) | ||||
0.499527 | + | 0.866298i | \(0.333507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 143.081 | + | 143.081i | 0.565536 | + | 0.565536i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 73.8638 | − | 73.8638i | 0.287408 | − | 0.287408i | −0.548647 | − | 0.836054i | \(-0.684857\pi\) |
0.836054 | + | 0.548647i | \(0.184857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 37.4847i | − | 0.144729i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.2577 | −0.112098 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 49.1668 | + | 49.1668i | 0.186946 | + | 0.186946i | 0.794374 | − | 0.607428i | \(-0.207799\pi\) |
−0.607428 | + | 0.794374i | \(0.707799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −167.753 | + | 167.753i | −0.628287 | + | 0.628287i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 278.742i | − | 1.03622i | −0.855315 | − | 0.518108i | \(-0.826636\pi\) | ||
0.855315 | − | 0.518108i | \(-0.173364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 66.0000 | 0.243542 | 0.121771 | − | 0.992558i | \(-0.461143\pi\) | ||||
0.121771 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 76.5153 | + | 76.5153i | 0.280276 | + | 0.280276i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −211.843 | + | 211.843i | −0.764777 | + | 0.764777i | −0.977182 | − | 0.212404i | \(-0.931871\pi\) |
0.212404 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 85.4847i | − | 0.306397i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −312.434 | −1.11186 | −0.555932 | − | 0.831228i | \(-0.687638\pi\) | ||||
−0.555932 | + | 0.831228i | \(0.687638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −204.747 | − | 204.747i | −0.723487 | − | 0.723487i | 0.245826 | − | 0.969314i | \(-0.420941\pi\) |
−0.969314 | + | 0.245826i | \(0.920941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 190.000 | − | 190.000i | 0.662021 | − | 0.662021i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 20.9796i | − | 0.0725937i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −231.712 | −0.796260 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −325.151 | − | 325.151i | −1.10973 | − | 1.10973i | −0.993185 | − | 0.116545i | \(-0.962818\pi\) |
−0.116545 | − | 0.993185i | \(-0.537182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 30.3031 | − | 30.3031i | 0.102031 | − | 0.102031i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 424.949i | − | 1.42123i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 178.020 | 0.591430 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 86.0352 | + | 86.0352i | 0.283945 | + | 0.283945i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 179.394 | − | 179.394i | 0.584345 | − | 0.584345i | −0.351749 | − | 0.936094i | \(-0.614413\pi\) |
0.936094 | + | 0.351749i | \(0.114413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 212.722i | 0.688421i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 213.980 | 0.688037 | 0.344019 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344019 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 186.414 | + | 186.414i | 0.595573 | + | 0.595573i | 0.939131 | − | 0.343558i | \(-0.111632\pi\) |
−0.343558 | + | 0.939131i | \(0.611632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −57.5505 | + | 57.5505i | −0.181547 | + | 0.181547i | −0.792030 | − | 0.610482i | \(-0.790976\pi\) |
0.610482 | + | 0.792030i | \(0.290976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 80.4337i | − | 0.252143i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −235.980 | −0.735139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 429.444 | + | 429.444i | 1.32955 | + | 1.32955i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.3281 | − | 15.3281i | 0.0468748 | − | 0.0468748i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 112.454i | 0.341806i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 214.413 | 0.647774 | 0.323887 | − | 0.946096i | \(-0.395010\pi\) | ||||
0.323887 | + | 0.946096i | \(0.395010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.0454 | + | 22.0454i | 0.0662024 | + | 0.0662024i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 94.5959 | − | 94.5959i | 0.280700 | − | 0.280700i | −0.552688 | − | 0.833388i | \(-0.686398\pi\) |
0.833388 | + | 0.552688i | \(0.186398\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 163.980i | − | 0.483716i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 235.010 | 0.689179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 216.767 | + | 216.767i | 0.631975 | + | 0.631975i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 226.919 | − | 226.919i | 0.653946 | − | 0.653946i | −0.299995 | − | 0.953941i | \(-0.596985\pi\) |
0.953941 | + | 0.299995i | \(0.0969849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 182.454i | − | 0.522791i | −0.965232 | − | 0.261396i | \(-0.915817\pi\) | ||
0.965232 | − | 0.261396i | \(-0.0841827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −90.0000 | −0.256410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −263.914 | − | 263.914i | −0.747631 | − | 0.747631i | 0.226403 | − | 0.974034i | \(-0.427303\pi\) |
−0.974034 | + | 0.226403i | \(0.927303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 77.7775 | − | 77.7775i | 0.217864 | − | 0.217864i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 285.485i | − | 0.795222i | −0.917554 | − | 0.397611i | \(-0.869839\pi\) | ||
0.917554 | − | 0.397611i | \(-0.130161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −828.898 | −2.29612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −64.8865 | − | 64.8865i | −0.178751 | − | 0.178751i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 418.964 | − | 418.964i | 1.14159 | − | 1.14159i | 0.153431 | − | 0.988159i | \(-0.450968\pi\) |
0.988159 | − | 0.153431i | \(-0.0490324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 223.485i | 0.605650i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 330.020 | 0.889543 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −283.106 | − | 283.106i | −0.758996 | − | 0.758996i | 0.217143 | − | 0.976140i | \(-0.430326\pi\) |
−0.976140 | + | 0.217143i | \(0.930326\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −119.444 | + | 119.444i | −0.316827 | + | 0.316827i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 194.000i | − | 0.511873i | −0.966694 | − | 0.255937i | \(-0.917616\pi\) | ||
0.966694 | − | 0.255937i | \(-0.0823839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.24745 | 0.0163975 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −531.489 | − | 531.489i | −1.38770 | − | 1.38770i | −0.830129 | − | 0.557572i | \(-0.811733\pi\) |
−0.557572 | − | 0.830129i | \(-0.688267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −104.697 | + | 104.697i | −0.270535 | + | 0.270535i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 479.196i | − | 1.23187i | −0.787798 | − | 0.615934i | \(-0.788779\pi\) | ||
0.787798 | − | 0.615934i | \(-0.211221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −431.959 | −1.10475 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −54.1918 | − | 54.1918i | −0.137893 | − | 0.137893i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 389.267 | − | 389.267i | 0.980521 | − | 0.980521i | −0.0192929 | − | 0.999814i | \(-0.506142\pi\) |
0.999814 | + | 0.0192929i | \(0.00614150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 215.505i | 0.540113i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −603.898 | −1.50598 | −0.752990 | − | 0.658032i | \(-0.771389\pi\) | ||||
−0.752990 | + | 0.658032i | \(0.771389\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −348.990 | − | 348.990i | −0.865980 | − | 0.865980i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −60.6061 | + | 60.6061i | −0.148909 | + | 0.148909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 183.959i | 0.449778i | 0.974384 | + | 0.224889i | \(0.0722019\pi\) | ||||
−0.974384 | + | 0.224889i | \(0.927798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.9694 | 0.109415 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −38.9148 | − | 38.9148i | −0.0942247 | − | 0.0942247i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −269.419 | + | 269.419i | −0.646088 | + | 0.646088i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 197.814i | 0.472109i | 0.971740 | + | 0.236055i | \(0.0758544\pi\) | ||||
−0.971740 | + | 0.236055i | \(0.924146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −114.041 | −0.270881 | −0.135440 | − | 0.990785i | \(-0.543245\pi\) | ||||
−0.135440 | + | 0.990785i | \(0.543245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −66.1362 | − | 66.1362i | −0.156350 | − | 0.156350i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −136.465 | + | 136.465i | −0.319591 | + | 0.319591i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 247.423i | − | 0.576745i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −348.454 | −0.808478 | −0.404239 | − | 0.914653i | \(-0.632464\pi\) | ||||
−0.404239 | + | 0.914653i | \(0.632464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −60.1010 | − | 60.1010i | −0.138801 | − | 0.138801i | 0.634292 | − | 0.773094i | \(-0.281292\pi\) |
−0.773094 | + | 0.634292i | \(0.781292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 598.434 | − | 598.434i | 1.36941 | − | 1.36941i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 556.929i | − | 1.26863i | −0.773075 | − | 0.634315i | \(-0.781282\pi\) | ||
0.773075 | − | 0.634315i | \(-0.218718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −107.969 | −0.244829 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 95.5551 | + | 95.5551i | 0.215700 | + | 0.215700i | 0.806684 | − | 0.590984i | \(-0.201260\pi\) |
−0.590984 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.6209 | + | 34.6209i | −0.0774517 | + | 0.0774517i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 213.423i | − | 0.475331i | −0.971347 | − | 0.237665i | \(-0.923618\pi\) | ||
0.971347 | − | 0.237665i | \(-0.0763821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −614.393 | −1.36229 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 74.7219 | + | 74.7219i | 0.164949 | + | 0.164949i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.9388 | − | 38.9388i | 0.0852052 | − | 0.0852052i | −0.663220 | − | 0.748425i | \(-0.730810\pi\) |
0.748425 | + | 0.663220i | \(0.230810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 91.4847i | 0.199313i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 509.712 | 1.10567 | 0.552833 | − | 0.833292i | \(-0.313547\pi\) | ||||
0.552833 | + | 0.833292i | \(0.313547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 492.955 | + | 492.955i | 1.06470 | + | 1.06470i | 0.997757 | + | 0.0669397i | \(0.0213235\pi\) |
0.0669397 | + | 0.997757i | \(0.478676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 647.044 | − | 647.044i | 1.38553 | − | 1.38553i | 0.551085 | − | 0.834449i | \(-0.314214\pi\) |
0.834449 | − | 0.551085i | \(-0.185786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 23.9592i | − | 0.0510857i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55.4847 | 0.117802 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −287.828 | − | 287.828i | −0.608515 | − | 0.608515i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −194.091 | + | 194.091i | −0.406899 | + | 0.406899i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 198.969i | − | 0.415385i | −0.978194 | − | 0.207692i | \(-0.933405\pi\) | ||
0.978194 | − | 0.207692i | \(-0.0665953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 180.000 | 0.374220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −108.384 | − | 108.384i | −0.224397 | − | 0.224397i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6209 | + | 34.6209i | −0.0710902 | + | 0.0710902i | −0.741758 | − | 0.670668i | \(-0.766008\pi\) |
0.670668 | + | 0.741758i | \(0.266008\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 217.980i | − | 0.445766i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 155.217 | 0.316124 | 0.158062 | − | 0.987429i | \(-0.449475\pi\) | ||||
0.158062 | + | 0.987429i | \(0.449475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 121.414 | + | 121.414i | 0.246276 | + | 0.246276i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 300.908 | − | 300.908i | 0.605449 | − | 0.605449i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 547.444i | 1.09708i | 0.836124 | + | 0.548541i | \(0.184817\pi\) | ||||
−0.836124 | + | 0.548541i | \(0.815183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 420.434 | 0.839189 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −526.590 | − | 526.590i | −1.04690 | − | 1.04690i | −0.998845 | − | 0.0480545i | \(-0.984698\pi\) |
−0.0480545 | − | 0.998845i | \(-0.515302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −160.442 | + | 160.442i | −0.316453 | + | 0.316453i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 115.773i | 0.227452i | 0.993512 | + | 0.113726i | \(0.0362786\pi\) | ||||
−0.993512 | + | 0.113726i | \(0.963721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −174.413 | −0.341318 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −126.742 | − | 126.742i | −0.247061 | − | 0.247061i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 181.818 | − | 181.818i | 0.351680 | − | 0.351680i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.0408i | 0.0501750i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 791.444 | 1.51909 | 0.759543 | − | 0.650457i | \(-0.225423\pi\) | ||||
0.759543 | + | 0.650457i | \(0.225423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 93.6867 | + | 93.6867i | 0.179133 | + | 0.179133i | 0.790978 | − | 0.611845i | \(-0.209572\pi\) |
−0.611845 | + | 0.790978i | \(0.709572\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −354.747 | + | 354.747i | −0.673144 | + | 0.673144i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 72.9388i | 0.137880i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 45.7730 | 0.0862014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 912.372 | + | 912.372i | 1.71177 | + | 1.71177i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −122.778 | + | 122.778i | −0.228636 | + | 0.228636i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 296.824i | − | 0.550694i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −359.526 | −0.664557 | −0.332279 | − | 0.943181i | \(-0.607817\pi\) | ||||
−0.332279 | + | 0.943181i | \(0.607817\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 317.753 | + | 317.753i | 0.585180 | + | 0.585180i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 164.647 | − | 164.647i | 0.301000 | − | 0.301000i | −0.540405 | − | 0.841405i | \(-0.681729\pi\) |
0.841405 | + | 0.540405i | \(0.181729\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 160.515i | − | 0.292378i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −336.413 | −0.610550 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.26224 | + | 1.26224i | 0.00228253 | + | 0.00228253i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −139.040 | + | 139.040i | −0.249623 | + | 0.249623i | −0.820816 | − | 0.571193i | \(-0.806481\pi\) |
0.571193 | + | 0.820816i | \(0.306481\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 854.847i | 1.52924i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −251.505 | −0.448316 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −787.423 | − | 787.423i | −1.39862 | − | 1.39862i | −0.804024 | − | 0.594596i | \(-0.797312\pi\) |
−0.594596 | − | 0.804024i | \(-0.702688\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.9546 | + | 22.9546i | −0.0404843 | + | 0.0404843i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.92856i | − | 0.00866180i | −0.999991 | − | 0.00433090i | \(-0.998621\pi\) | ||
0.999991 | − | 0.00433090i | \(-0.00137857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −205.505 | −0.359904 | −0.179952 | − | 0.983675i | \(-0.557594\pi\) | ||||
−0.179952 | + | 0.983675i | \(0.557594\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −94.8990 | − | 94.8990i | −0.165618 | − | 0.165618i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −689.999 | + | 689.999i | −1.19584 | + | 1.19584i | −0.220438 | + | 0.975401i | \(0.570749\pi\) |
−0.975401 | + | 0.220438i | \(0.929251\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 204.742i | − | 0.353614i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −93.6480 | −0.161184 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −533.585 | − | 533.585i | −0.915240 | − | 0.915240i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −672.347 | + | 672.347i | −1.14540 | + | 1.14540i | −0.157949 | + | 0.987447i | \(0.550488\pi\) |
−0.987447 | + | 0.157949i | \(0.949512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 982.929i | − | 1.66881i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 490.515 | 0.829975 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −344.570 | − | 344.570i | −0.581062 | − | 0.581062i | 0.354133 | − | 0.935195i | \(-0.384776\pi\) |
−0.935195 | + | 0.354133i | \(0.884776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 199.621 | − | 199.621i | 0.334373 | − | 0.334373i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 739.464i | − | 1.23450i | −0.786768 | − | 0.617249i | \(-0.788247\pi\) | ||
0.786768 | − | 0.617249i | \(-0.211753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −642.908 | −1.06973 | −0.534865 | − | 0.844937i | \(-0.679638\pi\) | ||||
−0.534865 | + | 0.844937i | \(0.679638\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0908 | + | 14.0908i | 0.0233679 | + | 0.0233679i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −362.803 | + | 362.803i | −0.597698 | + | 0.597698i | −0.939699 | − | 0.342002i | \(-0.888895\pi\) |
0.342002 | + | 0.939699i | \(0.388895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 60.9286i | 0.100047i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −540.000 | −0.883797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 721.943 | + | 721.943i | 1.17772 | + | 1.17772i | 0.980323 | + | 0.197398i | \(0.0632492\pi\) |
0.197398 | + | 0.980323i | \(0.436751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −72.9036 | + | 72.9036i | −0.118158 | + | 0.118158i | −0.763713 | − | 0.645555i | \(-0.776626\pi\) |
0.645555 | + | 0.763713i | \(0.276626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 228.061i | − | 0.368435i | −0.982886 | − | 0.184217i | \(-0.941025\pi\) | ||
0.982886 | − | 0.184217i | \(-0.0589751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 127.485 | 0.205289 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 349.342 | + | 349.342i | 0.560741 | + | 0.560741i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 348.434 | − | 348.434i | 0.555716 | − | 0.555716i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 182.969i | − | 0.290889i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 86.4337 | 0.136979 | 0.0684894 | − | 0.997652i | \(-0.478182\pi\) | ||||
0.0684894 | + | 0.997652i | \(0.478182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −254.722 | − | 254.722i | −0.402404 | − | 0.402404i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −440.783 | + | 440.783i | −0.691967 | + | 0.691967i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 353.939i | 0.553895i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 340.061 | 0.530517 | 0.265258 | − | 0.964177i | \(-0.414543\pi\) | ||||
0.265258 | + | 0.964177i | \(0.414543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 769.040 | + | 769.040i | 1.19602 | + | 1.19602i | 0.975349 | + | 0.220670i | \(0.0708243\pi\) |
0.220670 | + | 0.975349i | \(0.429176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −602.854 | + | 602.854i | −0.931767 | + | 0.931767i | −0.997816 | − | 0.0660489i | \(-0.978961\pi\) |
0.0660489 | + | 0.997816i | \(0.478961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 125.837i | 0.193893i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −178.020 | −0.273457 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 75.8842 | + | 75.8842i | 0.116209 | + | 0.116209i | 0.762820 | − | 0.646611i | \(-0.223814\pi\) |
−0.646611 | + | 0.762820i | \(0.723814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 102.576 | − | 102.576i | 0.156127 | − | 0.156127i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 61.1964i | − | 0.0928626i | −0.998921 | − | 0.0464313i | \(-0.985215\pi\) | ||
0.998921 | − | 0.0464313i | \(-0.0147849\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1158.45 | 1.75258 | 0.876289 | − | 0.481786i | \(-0.160012\pi\) | ||||
0.876289 | + | 0.481786i | \(0.160012\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 373.485 | + | 373.485i | 0.563325 | + | 0.563325i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 169.192 | − | 169.192i | 0.253661 | − | 0.253661i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 72.8036i | 0.108824i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 441.281 | 0.657646 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −711.413 | − | 711.413i | −1.05708 | − | 1.05708i | −0.998269 | − | 0.0588084i | \(-0.981270\pi\) |
−0.0588084 | − | 0.998269i | \(-0.518730\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −351.943 | + | 351.943i | −0.519857 | + | 0.519857i | −0.917528 | − | 0.397671i | \(-0.869819\pi\) |
0.397671 | + | 0.917528i | \(0.369819\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 482.536i | 0.710656i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 484.949 | 0.712113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 277.905 | + | 277.905i | 0.406888 | + | 0.406888i | 0.880652 | − | 0.473764i | \(-0.157105\pi\) |
−0.473764 | + | 0.880652i | \(0.657105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9852 | − | 10.9852i | 0.0159901 | − | 0.0159901i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1584.74i | 2.30007i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1097.51 | 1.58829 | 0.794143 | − | 0.607731i | \(-0.207920\pi\) | ||||
0.794143 | + | 0.607731i | \(0.207920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −63.1056 | − | 63.1056i | −0.0910615 | − | 0.0910615i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 927.423 | − | 927.423i | 1.33059 | − | 1.33059i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 70.4541i | − | 0.100793i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −354.783 | −0.506110 | −0.253055 | − | 0.967452i | \(-0.581435\pi\) | ||||
−0.253055 | + | 0.967452i | \(0.581435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 253.485 | + | 253.485i | 0.360576 | + | 0.360576i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 179.167 | − | 179.167i | 0.253418 | − | 0.253418i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 368.061i | 0.519127i | 0.965726 | + | 0.259564i | \(0.0835787\pi\) | ||||
−0.965726 | + | 0.259564i | \(0.916421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48469 | −0.00208817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 494.343 | + | 494.343i | 0.693328 | + | 0.693328i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −297.576 | + | 297.576i | −0.415029 | + | 0.415029i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 382.969i | 0.532642i | 0.963884 | + | 0.266321i | \(0.0858081\pi\) | ||||
−0.963884 | + | 0.266321i | \(0.914192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 442.990 | 0.614410 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.1918 | − | 39.1918i | −0.0542072 | − | 0.0542072i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 837.297 | − | 837.297i | 1.15172 | − | 1.15172i | 0.165507 | − | 0.986209i | \(-0.447074\pi\) |
0.986209 | − | 0.165507i | \(-0.0529261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 868.949 | 1.18871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.8230 | + | 29.8230i | 0.0406862 | + | 0.0406862i | 0.727157 | − | 0.686471i | \(-0.240841\pi\) |
−0.686471 | + | 0.727157i | \(0.740841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.7378 | + | 38.7378i | −0.0525614 | + | 0.0525614i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1183.28i | − | 1.60119i | −0.599205 | − | 0.800596i | \(-0.704516\pi\) | ||
0.599205 | − | 0.800596i | \(-0.295484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1034.85 | −1.39655 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 65.7821 | + | 65.7821i | 0.0885358 | + | 0.0885358i | 0.749988 | − | 0.661452i | \(-0.230059\pi\) |
−0.661452 | + | 0.749988i | \(0.730059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 55.0760 | − | 55.0760i | 0.0737296 | − | 0.0737296i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 491.423i | 0.656106i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 850.270 | 1.13218 | 0.566092 | − | 0.824342i | \(-0.308455\pi\) | ||||
0.566092 | + | 0.824342i | \(0.308455\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 307.120 | + | 307.120i | 0.407862 | + | 0.407862i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −145.832 | + | 145.832i | −0.192645 | + | 0.192645i | −0.796838 | − | 0.604193i | \(-0.793496\pi\) |
0.604193 | + | 0.796838i | \(0.293496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 350.474i | 0.461758i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 157.505 | 0.206971 | 0.103486 | − | 0.994631i | \(-0.467000\pi\) | ||||
0.103486 | + | 0.994631i | \(0.467000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.9204 | − | 31.9204i | −0.0418354 | − | 0.0418354i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 186.867 | − | 186.867i | 0.243634 | − | 0.243634i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 559.031i | 0.726958i | 0.931602 | + | 0.363479i | \(0.118411\pi\) | ||||
−0.931602 | + | 0.363479i | \(0.881589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 180.929 | 0.234667 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 348.965 | + | 348.965i | 0.451442 | + | 0.451442i | 0.895833 | − | 0.444391i | \(-0.146580\pi\) |
−0.444391 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.9092 | − | 45.9092i | 0.0590852 | − | 0.0590852i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2569.69i | 3.29871i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −973.031 | −1.24588 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.8332 | − | 35.8332i | −0.0457639 | − | 0.0457639i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −821.414 | + | 821.414i | −1.04373 | + | 1.04373i | −0.0447293 | + | 0.998999i | \(0.514243\pi\) |
−0.998999 | + | 0.0447293i | \(0.985757\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 120.434i | 0.152641i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −341.485 | −0.431713 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −655.301 | − | 655.301i | −0.826357 | − | 0.826357i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 649.065 | − | 649.065i | 0.814385 | − | 0.814385i | −0.170903 | − | 0.985288i | \(-0.554668\pi\) |
0.985288 | + | 0.170903i | \(0.0546685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 548.908i | 0.686994i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −410.908 | −0.512994 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 281.995 | + | 281.995i | 0.351177 | + | 0.351177i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 341.388 | − | 341.388i | 0.423034 | − | 0.423034i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 909.918i | 1.12474i | 0.826884 | + | 0.562372i | \(0.190111\pi\) | ||||
−0.826884 | + | 0.562372i | \(0.809889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 652.929 | 0.805091 | 0.402545 | − | 0.915400i | \(-0.368126\pi\) | ||||
0.402545 | + | 0.915400i | \(0.368126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 80.8332 | + | 80.8332i | 0.0994258 | + | 0.0994258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1203.84 | + | 1203.84i | −1.47348 | + | 1.47348i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 187.423i | 0.228844i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −808.064 | −0.984243 | −0.492122 | − | 0.870526i | \(-0.663778\pi\) | ||||
−0.492122 | + | 0.870526i | \(0.663778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 333.863 | + | 333.863i | 0.405666 | + | 0.405666i | 0.880224 | − | 0.474558i | \(-0.157392\pi\) |
−0.474558 | + | 0.880224i | \(0.657392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 481.162 | − | 481.162i | 0.581817 | − | 0.581817i | −0.353586 | − | 0.935402i | \(-0.615038\pi\) |
0.935402 | + | 0.353586i | \(0.115038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1296.35i | 1.56375i | 0.623433 | + | 0.781877i | \(0.285738\pi\) | ||||
−0.623433 | + | 0.781877i | \(0.714262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −518.908 | −0.624438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 448.055 | + | 448.055i | 0.537881 | + | 0.537881i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 104.697 | − | 104.697i | 0.125086 | − | 0.125086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 978.515i | − | 1.16629i | −0.812369 | − | 0.583144i | \(-0.801822\pi\) | ||
0.812369 | − | 0.583144i | \(-0.198178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 745.888 | 0.886906 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −382.652 | − | 382.652i | −0.453916 | − | 0.453916i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −135.125 | + | 135.125i | −0.159534 | + | 0.159534i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 501.526i | − | 0.590725i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −254.969 | −0.299611 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −300.127 | − | 300.127i | −0.351849 | − | 0.351849i | 0.508948 | − | 0.860797i | \(-0.330034\pi\) |
−0.860797 | + | 0.508948i | \(0.830034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −879.823 | + | 879.823i | −1.02663 | + | 1.02663i | −0.0269957 | + | 0.999636i | \(0.508594\pi\) |
−0.999636 | + | 0.0269957i | \(0.991406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 128.888i | − | 0.150044i | −0.997182 | − | 0.0750220i | \(-0.976097\pi\) | ||
0.997182 | − | 0.0750220i | \(-0.0239027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 465.403 | 0.540538 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 204.418 | + | 204.418i | 0.236869 | + | 0.236869i | 0.815552 | − | 0.578683i | \(-0.196433\pi\) |
−0.578683 | + | 0.815552i | \(0.696433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.6946 | − | 25.6946i | 0.0296363 | − | 0.0296363i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.08164i | − | 0.00469694i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 115.051 | 0.132091 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −283.788 | − | 283.788i | −0.325072 | − | 0.325072i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 570.025 | − | 570.025i | 0.649971 | − | 0.649971i | −0.303014 | − | 0.952986i | \(-0.597993\pi\) |
0.952986 | + | 0.303014i | \(0.0979931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 796.454i | − | 0.906091i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1235.86 | −1.40279 | −0.701395 | − | 0.712773i | \(-0.747439\pi\) | ||||
−0.701395 | + | 0.712773i | \(0.747439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −713.131 | − | 713.131i | −0.807622 | − | 0.807622i | 0.176651 | − | 0.984274i | \(-0.443474\pi\) |
−0.984274 | + | 0.176651i | \(0.943474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 343.510 | − | 343.510i | 0.387271 | − | 0.387271i | −0.486442 | − | 0.873713i | \(-0.661705\pi\) |
0.873713 | + | 0.486442i | \(0.161705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.0102i | − | 0.0146347i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 74.2270 | 0.0833076 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −760.454 | − | 760.454i | −0.851572 | − | 0.851572i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 520.454 | − | 520.454i | 0.580216 | − | 0.580216i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 277.898i | − | 0.309119i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1610.89 | 1.78789 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 218.030 | + | 218.030i | 0.241450 | + | 0.241450i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −918.938 | + | 918.938i | −1.01316 | + | 1.01316i | −0.0132496 | + | 0.999912i | \(0.504218\pi\) |
−0.999912 | + | 0.0132496i | \(0.995782\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 210.742i | 0.231840i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −788.454 | −0.865482 | −0.432741 | − | 0.901518i | \(-0.642454\pi\) | ||||
−0.432741 | + | 0.901518i | \(0.642454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 151.412 | + | 151.412i | 0.165840 | + | 0.165840i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −112.854 | + | 112.854i | −0.123068 | + | 0.123068i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1644.33i | 1.78926i | 0.446806 | + | 0.894631i | \(0.352561\pi\) | ||||
−0.446806 | + | 0.894631i | \(0.647439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 439.423 | 0.477116 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1444.95 | + | 1444.95i | 1.56549 | + | 1.56549i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −260.530 | + | 260.530i | −0.281046 | + | 0.281046i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1021.51i | − | 1.09957i | −0.835305 | − | 0.549787i | \(-0.814709\pi\) | ||
0.835305 | − | 0.549787i | \(-0.185291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1241.46 | −1.33347 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 262.070 | + | 262.070i | 0.280890 | + | 0.280890i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 370.555 | − | 370.555i | 0.395470 | − | 0.395470i | −0.481162 | − | 0.876632i | \(-0.659785\pi\) |
0.876632 | + | 0.481162i | \(0.159785\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 456.620i | 0.486283i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1524.06 | 1.61962 | 0.809811 | − | 0.586691i | \(-0.199570\pi\) | ||||
0.809811 | + | 0.586691i | \(0.199570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1292.37 | − | 1292.37i | −1.37049 | − | 1.37049i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −644.545 | + | 644.545i | −0.680618 | + | 0.680618i | −0.960139 | − | 0.279522i | \(-0.909824\pi\) |
0.279522 | + | 0.960139i | \(0.409824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 837.526i | − | 0.882535i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −140.969 | −0.148233 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 461.641 | + | 461.641i | 0.484409 | + | 0.484409i | 0.906536 | − | 0.422128i | \(-0.138717\pi\) |
−0.422128 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 98.5107 | − | 98.5107i | 0.102937 | − | 0.102937i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 93.6480i | − | 0.0976517i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −149.041 | −0.155089 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −289.015 | − | 289.015i | −0.300119 | − | 0.300119i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 462.196 | − | 462.196i | 0.477969 | − | 0.477969i | −0.426512 | − | 0.904482i | \(-0.640258\pi\) |
0.904482 | + | 0.426512i | \(0.140258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1051.92i | 1.08557i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 198.390 | 0.204315 | 0.102158 | − | 0.994768i | \(-0.467425\pi\) | ||||
0.102158 | + | 0.994768i | \(0.467425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 561.060 | + | 561.060i | 0.576629 | + | 0.576629i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −543.206 | + | 543.206i | −0.555993 | + | 0.555993i | −0.928164 | − | 0.372171i | \(-0.878614\pi\) |
0.372171 | + | 0.928164i | \(0.378614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1129.65i | − | 1.15388i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.5459 | 0.0382731 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −321.387 | − | 321.387i | −0.326945 | − | 0.326945i | 0.524478 | − | 0.851424i | \(-0.324260\pi\) |
−0.851424 | + | 0.524478i | \(0.824260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −137.728 | + | 137.728i | −0.139542 | + | 0.139542i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1210.89i | − | 1.22436i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1543.82 | 1.55784 | 0.778918 | − | 0.627125i | \(-0.215769\pi\) | ||||
0.778918 | + | 0.627125i | \(0.215769\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 262.602 | + | 262.602i | 0.264453 | + | 0.264453i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −800.429 | + | 800.429i | −0.802838 | + | 0.802838i | −0.983538 | − | 0.180701i | \(-0.942164\pi\) |
0.180701 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.0000i | 0.0540541i |
(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 | 1200.3.bg.o.193.2 | 4 | ||
4.3 | odd | 2 | 300.3.k.a.193.1 | 4 | |||
5.2 | odd | 4 | inner | 1200.3.bg.o.1057.2 | 4 | ||
5.3 | odd | 4 | 240.3.bg.d.97.1 | 4 | |||
5.4 | even | 2 | 240.3.bg.d.193.1 | 4 | |||
12.11 | even | 2 | 900.3.l.b.793.2 | 4 | |||
15.8 | even | 4 | 720.3.bh.f.577.2 | 4 | |||
15.14 | odd | 2 | 720.3.bh.f.433.2 | 4 | |||
20.3 | even | 4 | 60.3.k.a.37.2 | yes | 4 | ||
20.7 | even | 4 | 300.3.k.a.157.1 | 4 | |||
20.19 | odd | 2 | 60.3.k.a.13.2 | ✓ | 4 | ||
40.3 | even | 4 | 960.3.bg.b.577.1 | 4 | |||
40.13 | odd | 4 | 960.3.bg.a.577.2 | 4 | |||
40.19 | odd | 2 | 960.3.bg.b.193.1 | 4 | |||
40.29 | even | 2 | 960.3.bg.a.193.2 | 4 | |||
60.23 | odd | 4 | 180.3.l.b.37.2 | 4 | |||
60.47 | odd | 4 | 900.3.l.b.757.2 | 4 | |||
60.59 | even | 2 | 180.3.l.b.73.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.k.a.13.2 | ✓ | 4 | 20.19 | odd | 2 | ||
60.3.k.a.37.2 | yes | 4 | 20.3 | even | 4 | ||
180.3.l.b.37.2 | 4 | 60.23 | odd | 4 | |||
180.3.l.b.73.2 | 4 | 60.59 | even | 2 | |||
240.3.bg.d.97.1 | 4 | 5.3 | odd | 4 | |||
240.3.bg.d.193.1 | 4 | 5.4 | even | 2 | |||
300.3.k.a.157.1 | 4 | 20.7 | even | 4 | |||
300.3.k.a.193.1 | 4 | 4.3 | odd | 2 | |||
720.3.bh.f.433.2 | 4 | 15.14 | odd | 2 | |||
720.3.bh.f.577.2 | 4 | 15.8 | even | 4 | |||
900.3.l.b.757.2 | 4 | 60.47 | odd | 4 | |||
900.3.l.b.793.2 | 4 | 12.11 | even | 2 | |||
960.3.bg.a.193.2 | 4 | 40.29 | even | 2 | |||
960.3.bg.a.577.2 | 4 | 40.13 | odd | 4 | |||
960.3.bg.b.193.1 | 4 | 40.19 | odd | 2 | |||
960.3.bg.b.577.1 | 4 | 40.3 | even | 4 | |||
1200.3.bg.o.193.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.o.1057.2 | 4 | 5.2 | odd | 4 | inner |