Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(13,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("60.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.63488158616\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.37 |
Dual form | 60.3.k.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 1.77526 | − | 4.67423i | 0.355051 | − | 0.934847i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55051 | + | 2.55051i | 0.364359 | + | 0.364359i | 0.865415 | − | 0.501056i | \(-0.167055\pi\) |
−0.501056 | + | 0.865415i | \(0.667055\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.24745 | 0.749768 | 0.374884 | − | 0.927072i | \(-0.377683\pi\) | ||||
0.374884 | + | 0.927072i | \(0.377683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.2474 | + | 12.2474i | −0.942111 | + | 0.942111i | −0.998414 | − | 0.0563023i | \(-0.982069\pi\) |
0.0563023 | + | 0.998414i | \(0.482069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.55051 | − | 7.89898i | −0.236701 | − | 0.526599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.4495 | − | 12.4495i | −0.732323 | − | 0.732323i | 0.238757 | − | 0.971079i | \(-0.423260\pi\) |
−0.971079 | + | 0.238757i | \(0.923260\pi\) | |||||||
\(18\) | 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 | −0.975275 | − | 0.220994i | \(-0.929070\pi\) |
0.220994 | + | 0.975275i | \(0.429070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.6969 | − | 16.5959i | −0.747878 | − | 0.663837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.75255i | − | 0.336295i | −0.985762 | − | 0.168147i | \(-0.946222\pi\) | ||
0.985762 | − | 0.168147i | \(-0.0537785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.4949 | 0.919190 | 0.459595 | − | 0.888129i | \(-0.347995\pi\) | ||||
0.459595 | + | 0.888129i | \(0.347995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.1010 | − | 10.1010i | 0.306092 | − | 0.306092i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.4495 | − | 7.39388i | 0.469985 | − | 0.211254i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | − | 7.34847i | −0.198607 | − | 0.198607i | 0.600795 | − | 0.799403i | \(-0.294851\pi\) |
−0.799403 | + | 0.600795i | \(0.794851\pi\) | |||||||
\(38\) | 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 | −0.173270 | − | 0.984874i | \(-0.555433\pi\) |
0.984874 | + | 0.173270i | \(0.0554334\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.0227 | − | 5.32577i | −0.311616 | − | 0.118350i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22.0454 | − | 22.0454i | −0.469051 | − | 0.469051i | 0.432556 | − | 0.901607i | \(-0.357612\pi\) |
−0.901607 | + | 0.432556i | \(0.857612\pi\) | |||||||
\(48\) | 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 | −0.253312 | + | 0.967385i | \(0.581520\pi\) |
−0.967385 | + | 0.253312i | \(0.918480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.6413 | − | 38.5505i | 0.266206 | − | 0.700918i | ||||
\(56\) | 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 | ||||||||
\(65\) | 35.5051 | + | 78.9898i | 0.546232 | + | 1.21523i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.69694 | + | 4.69694i | 0.0701036 | + | 0.0701036i | 0.741289 | − | 0.671186i | \(-0.234215\pi\) |
−0.671186 | + | 0.741289i | \(0.734215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42.4949i | 0.615868i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −117.980 | −1.66168 | −0.830842 | − | 0.556508i | \(-0.812141\pi\) | ||||
−0.830842 | + | 0.556508i | \(0.812141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.1918 | − | 34.1918i | 0.468381 | − | 0.468381i | −0.433009 | − | 0.901390i | \(-0.642548\pi\) |
0.901390 | + | 0.433009i | \(0.142548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −43.2247 | + | 2.57321i | −0.576330 | + | 0.0343095i | ||||
\(76\) | 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 | −0.808999 | − | 0.587810i | \(-0.799990\pi\) |
0.587810 | + | 0.808999i | \(0.299990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −80.2929 | + | 36.0908i | −0.944622 | + | 0.424598i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.9444 | − | 11.9444i | −0.137292 | − | 0.137292i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 136.969i | − | 1.53898i | −0.638658 | − | 0.769491i | \(-0.720510\pi\) | ||
0.638658 | − | 0.769491i | \(-0.279490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −62.4745 | −0.686533 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34.8990 | − | 34.8990i | 0.375258 | − | 0.375258i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 161.237 | + | 61.2372i | 1.69723 | + | 0.644603i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94.5959 | + | 94.5959i | 0.975216 | + | 0.975216i | 0.999700 | − | 0.0244846i | \(-0.00779446\pi\) |
−0.0244846 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(98\) | 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 | −0.146126 | − | 0.989266i | \(-0.546681\pi\) |
0.989266 | + | 0.146126i | \(0.0466806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.0908 | − | 29.2020i | 0.105627 | − | 0.278115i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −96.3383 | − | 96.3383i | −0.900358 | − | 0.900358i | 0.0951092 | − | 0.995467i | \(-0.469680\pi\) |
−0.995467 | + | 0.0951092i | \(0.969680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5153i | 0.114819i | 0.998351 | + | 0.0574097i | \(0.0182841\pi\) | ||||
−0.998351 | + | 0.0574097i | \(0.981716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.0000 | −0.162162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 66.9444 | − | 66.9444i | 0.592428 | − | 0.592428i | −0.345858 | − | 0.938287i | \(-0.612412\pi\) |
0.938287 | + | 0.345858i | \(0.112412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50.2929 | + | 111.889i | 0.437329 | + | 0.972946i | ||||
\(116\) | 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 | ||||||||
\(125\) | −110.765 | + | 57.9319i | −0.886120 | + | 0.463455i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55051 | + | 2.55051i | 0.0200828 | + | 0.0200828i | 0.717077 | − | 0.696994i | \(-0.245480\pi\) |
−0.696994 | + | 0.717077i | \(0.745480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 85.4847i | − | 0.662672i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44.2474 | 0.337767 | 0.168883 | − | 0.985636i | \(-0.445984\pi\) | ||||
0.168883 | + | 0.985636i | \(0.445984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −87.9796 | + | 87.9796i | −0.661501 | + | 0.661501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.6969 | + | 10.6515i | −0.175533 | + | 0.0789002i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.3587 | − | 18.3587i | −0.134005 | − | 0.134005i | 0.636923 | − | 0.770928i | \(-0.280207\pi\) |
−0.770928 | + | 0.636923i | \(0.780207\pi\) | |||||||
\(138\) | 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 | ||||||||
\(145\) | −45.5857 | − | 17.3133i | −0.314384 | − | 0.119402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −44.0783 | − | 44.0783i | −0.299852 | − | 0.299852i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 28.2679i | − | 0.189717i | −0.995491 | − | 0.0948586i | \(-0.969760\pi\) | ||
0.995491 | − | 0.0948586i | \(-0.0302399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −61.0102 | −0.404041 | −0.202021 | − | 0.979381i | \(-0.564751\pi\) | ||||
−0.202021 | + | 0.979381i | \(0.564751\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.3485 | + | 37.3485i | −0.244108 | + | 0.244108i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.5857 | − | 133.192i | 0.326359 | − | 0.859302i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.6515 | − | 22.6515i | −0.144277 | − | 0.144277i | 0.631279 | − | 0.775556i | \(-0.282530\pi\) |
−0.775556 | + | 0.631279i | \(0.782530\pi\) | |||||||
\(158\) | 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 | −0.925267 | − | 0.379317i | \(-0.876159\pi\) |
0.379317 | + | 0.925267i | \(0.376159\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.2827 | − | 65.1464i | −0.177471 | − | 0.394827i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 171.641 | + | 171.641i | 1.02779 | + | 1.02779i | 0.999603 | + | 0.0281898i | \(0.00897427\pi\) |
0.0281898 | + | 0.999603i | \(0.491026\pi\) | |||||||
\(168\) | 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 | \(-0.763836\pi\) |
0.675713 | + | 0.737165i | \(0.263836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.35867 | − | 90.0148i | −0.0306210 | − | 0.514370i | ||||
\(176\) | 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 | ||||||||
\(185\) | −47.3939 | + | 21.3031i | −0.256183 | + | 0.115152i | ||||
\(186\) | 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 | \(-0.434983\pi\) | ||||
0.202840 | + | 0.979212i | \(0.434983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 83.5857 | − | 83.5857i | 0.433087 | − | 0.433087i | −0.456590 | − | 0.889677i | \(-0.650930\pi\) |
0.889677 | + | 0.456590i | \(0.150930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 140.227 | + | 53.2577i | 0.719113 | + | 0.273116i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −200.252 | − | 200.252i | −1.01651 | − | 1.01651i | −0.999861 | − | 0.0166464i | \(-0.994701\pi\) |
−0.0166464 | − | 0.999861i | \(-0.505299\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 132.247 | − | 348.207i | 0.645110 | − | 1.69857i | ||||
\(206\) | 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 | \(-0.335958\pi\) | ||||
0.492843 | + | 0.870118i | \(0.335958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −144.495 | + | 144.495i | −0.678380 | + | 0.678380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −101.171 | − | 225.081i | −0.470565 | − | 1.04689i | ||||
\(216\) | 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 | −0.637318 | − | 0.770601i | \(-0.719956\pi\) |
0.770601 | + | 0.637318i | \(0.219956\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −49.7878 | + | 56.0908i | −0.221279 | + | 0.249293i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 197.980 | + | 197.980i | 0.872157 | + | 0.872157i | 0.992707 | − | 0.120550i | \(-0.0384659\pi\) |
−0.120550 | + | 0.992707i | \(0.538466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.96938i | 0.0391676i | 0.999808 | + | 0.0195838i | \(0.00623412\pi\) | ||||
−0.999808 | + | 0.0195838i | \(0.993766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 51.5255 | 0.223054 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.7628 | − | 28.7628i | 0.123445 | − | 0.123445i | −0.642685 | − | 0.766130i | \(-0.722180\pi\) |
0.766130 | + | 0.642685i | \(0.222180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −142.182 | + | 63.9092i | −0.605028 | + | 0.271954i | ||||
\(236\) | 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 | ||||||||
\(245\) | −168.225 | − | 63.8911i | −0.686632 | − | 0.260780i | ||||
\(246\) | 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 | \(-0.666493\pi\) | ||||
−0.499527 | + | 0.866298i | \(0.666493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −143.081 | + | 143.081i | −0.565536 | + | 0.565536i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −54.1362 | + | 142.540i | −0.212299 | + | 0.558982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −73.8638 | − | 73.8638i | −0.287408 | − | 0.287408i | 0.548647 | − | 0.836054i | \(-0.315143\pi\) |
−0.836054 | + | 0.548647i | \(0.815143\pi\) | |||||||
\(258\) | 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 | −0.607428 | − | 0.794374i | \(-0.707799\pi\) |
0.794374 | + | 0.607428i | \(0.207799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 187.555 | + | 417.262i | 0.707755 | + | 1.57457i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −167.753 | − | 167.753i | −0.628287 | − | 0.628287i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 278.742i | 1.03622i | 0.855315 | + | 0.518108i | \(0.173364\pi\) | ||||
−0.855315 | + | 0.518108i | \(0.826636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −66.0000 | −0.243542 | −0.121771 | − | 0.992558i | \(-0.538857\pi\) | ||||
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −76.5153 | + | 76.5153i | −0.280276 | + | 0.280276i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −154.202 | − | 136.874i | −0.560735 | − | 0.497724i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 211.843 | + | 211.843i | 0.764777 | + | 0.764777i | 0.977182 | − | 0.212404i | \(-0.0681294\pi\) |
−0.212404 | + | 0.977182i | \(0.568129\pi\) | |||||||
\(278\) | 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 | −0.969314 | − | 0.245826i | \(-0.920941\pi\) |
0.245826 | + | 0.969314i | \(0.420941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 272.474 | − | 122.474i | 0.956051 | − | 0.429735i | ||||
\(286\) | 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 | 0.116545 | − | 0.993185i | \(-0.462818\pi\) |
0.993185 | − | 0.116545i | \(-0.0371819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −71.3179 | − | 27.0862i | −0.241755 | − | 0.0918177i | ||||
\(296\) | 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 | ||||||||
\(305\) | −94.9852 | + | 250.095i | −0.311427 | + | 0.819985i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 179.394 | + | 179.394i | 0.584345 | + | 0.584345i | 0.936094 | − | 0.351749i | \(-0.114413\pi\) |
−0.351749 | + | 0.936094i | \(0.614413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 212.722i | − | 0.688421i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −213.980 | −0.688037 | −0.344019 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344019 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −186.414 | + | 186.414i | −0.595573 | + | 0.595573i | −0.939131 | − | 0.343558i | \(-0.888368\pi\) |
0.343558 | + | 0.939131i | \(0.388368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.1816 | − | 49.3485i | −0.0704179 | − | 0.156662i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 57.5505 | + | 57.5505i | 0.181547 | + | 0.181547i | 0.792030 | − | 0.610482i | \(-0.209024\pi\) |
−0.610482 | + | 0.792030i | \(0.709024\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 432.247 | − | 25.7321i | 1.32999 | − | 0.0791758i | ||||
\(326\) | 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 | \(-0.604990\pi\) | ||||
−0.323887 | + | 0.946096i | \(0.604990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.0454 | + | 22.0454i | −0.0662024 | + | 0.0662024i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.2929 | − | 13.6163i | 0.0904264 | − | 0.0406458i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −94.5959 | − | 94.5959i | −0.280700 | − | 0.280700i | 0.552688 | − | 0.833388i | \(-0.313602\pi\) |
−0.833388 | + | 0.552688i | \(0.813602\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 198.631 | + | 75.4393i | 0.575742 | + | 0.218665i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 226.919 | + | 226.919i | 0.653946 | + | 0.653946i | 0.953941 | − | 0.299995i | \(-0.0969849\pi\) |
−0.299995 | + | 0.953941i | \(0.596985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.454i | 0.522791i | 0.965232 | + | 0.261396i | \(0.0841827\pi\) | ||||
−0.965232 | + | 0.261396i | \(0.915817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 90.0000 | 0.256410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 263.914 | − | 263.914i | 0.747631 | − | 0.747631i | −0.226403 | − | 0.974034i | \(-0.572697\pi\) |
0.974034 | + | 0.226403i | \(0.0726965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −209.444 | + | 551.464i | −0.589983 | + | 1.55342i | ||||
\(356\) | 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 | ||||||||
\(365\) | −99.1214 | − | 220.520i | −0.271566 | − | 0.604164i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 418.964 | + | 418.964i | 1.14159 | + | 1.14159i | 0.988159 | + | 0.153431i | \(0.0490324\pi\) |
0.153431 | + | 0.988159i | \(0.450968\pi\) | |||||||
\(368\) | 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 | \(-0.569674\pi\) |
0.976140 | + | 0.217143i | \(0.0696739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −64.7071 | + | 206.611i | −0.172552 | + | 0.550962i | ||||
\(376\) | 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 | −0.557572 | + | 0.830129i | \(0.688267\pi\) |
−0.830129 | + | 0.557572i | \(0.811733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 135.666 | − | 60.9806i | 0.352380 | − | 0.158391i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −104.697 | − | 104.697i | −0.270535 | − | 0.270535i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 479.196i | 1.23187i | 0.787798 | + | 0.615934i | \(0.211221\pi\) | ||||
−0.787798 | + | 0.615934i | \(0.788779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 431.959 | 1.10475 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.1918 | − | 54.1918i | 0.137893 | − | 0.137893i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.31327 | + | 0.878569i | 0.00585637 | + | 0.00222423i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −389.267 | − | 389.267i | −0.980521 | − | 0.980521i | 0.0192929 | − | 0.999814i | \(-0.493858\pi\) |
−0.999814 | + | 0.0192929i | \(0.993858\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | −15.9773 | + | 42.0681i | −0.0394501 | + | 0.103872i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −60.6061 | − | 60.6061i | −0.148909 | − | 0.148909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 183.959i | − | 0.449778i | −0.974384 | − | 0.224889i | \(-0.927798\pi\) | ||
0.974384 | − | 0.224889i | \(-0.0722019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.9694 | −0.109415 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.9148 | − | 38.9148i | 0.0942247 | − | 0.0942247i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53.2214 | + | 118.404i | 0.128244 | + | 0.285311i | ||||
\(416\) | 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 | ||||||||
\(425\) | 26.1566 | + | 439.378i | 0.0615450 | + | 1.03383i | ||||
\(426\) | 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 | \(-0.367536\pi\) | ||||
0.404239 | + | 0.914653i | \(0.367536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 60.1010 | − | 60.1010i | 0.138801 | − | 0.138801i | −0.634292 | − | 0.773094i | \(-0.718708\pi\) |
0.773094 | + | 0.634292i | \(0.218708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −77.0352 | + | 34.6265i | −0.177092 | + | 0.0796012i | ||||
\(436\) | 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 | −0.590984 | − | 0.806684i | \(-0.701260\pi\) |
0.806684 | + | 0.590984i | \(0.201260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −640.227 | − | 243.156i | −1.43871 | − | 0.546417i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.6209 | − | 34.6209i | −0.0774517 | − | 0.0774517i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 213.423i | 0.475331i | 0.971347 | + | 0.237665i | \(0.0763821\pi\) | ||||
−0.971347 | + | 0.237665i | \(0.923618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 614.393 | 1.36229 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −74.7219 | + | 74.7219i | −0.164949 | + | 0.164949i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −110.908 | + | 292.020i | −0.243754 | + | 0.641803i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.9388 | − | 38.9388i | −0.0852052 | − | 0.0852052i | 0.663220 | − | 0.748425i | \(-0.269190\pi\) |
−0.748425 | + | 0.663220i | \(0.769190\pi\) | |||||||
\(458\) | 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 | 0.0669397 | − | 0.997757i | \(-0.478676\pi\) |
0.997757 | − | 0.0669397i | \(-0.0213235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −101.171 | − | 225.081i | −0.217573 | − | 0.484044i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 647.044 | + | 647.044i | 1.38553 | + | 1.38553i | 0.834449 | + | 0.551085i | \(0.185786\pi\) |
0.551085 | + | 0.834449i | \(0.314214\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 572.474 | − | 644.949i | 1.20521 | − | 1.35779i | ||||
\(476\) | 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 | ||||||||
\(485\) | 610.095 | − | 274.232i | 1.25793 | − | 0.565426i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6209 | − | 34.6209i | −0.0710902 | − | 0.0710902i | 0.670668 | − | 0.741758i | \(-0.266008\pi\) |
−0.741758 | + | 0.670668i | \(0.766008\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 217.980i | 0.445766i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −155.217 | −0.316124 | −0.158062 | − | 0.987429i | \(-0.550525\pi\) | ||||
−0.158062 | + | 0.987429i | \(0.550525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −121.414 | + | 121.414i | −0.246276 | + | 0.246276i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −115.652 | − | 43.9240i | −0.233639 | − | 0.0887353i | ||||
\(496\) | 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 | −0.0480545 | + | 0.998845i | \(0.515302\pi\) |
−0.998845 | + | 0.0480545i | \(0.984698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 124.707 | − | 328.353i | 0.246945 | − | 0.650204i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −160.442 | − | 160.442i | −0.316453 | − | 0.316453i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 115.773i | − | 0.227452i | −0.993512 | − | 0.113726i | \(-0.963721\pi\) | ||
0.993512 | − | 0.113726i | \(-0.0362786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 174.413 | 0.341318 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 126.742 | − | 126.742i | 0.247061 | − | 0.247061i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −251.757 | − | 560.095i | −0.488849 | − | 1.08756i | ||||
\(516\) | 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 | −0.611845 | − | 0.790978i | \(-0.709572\pi\) |
0.790978 | + | 0.611845i | \(0.209572\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −116.808 | − | 103.682i | −0.222492 | − | 0.197490i | ||||
\(526\) | 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 | ||||||||
\(535\) | −621.333 | + | 279.283i | −1.16137 | + | 0.522024i | ||||
\(536\) | 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 | ||||||||
\(545\) | 58.4995 | + | 22.2179i | 0.107339 | + | 0.0407667i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 164.647 | + | 164.647i | 0.301000 | + | 0.301000i | 0.841405 | − | 0.540405i | \(-0.181729\pi\) |
−0.540405 | + | 0.841405i | \(0.681729\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | −31.9546 | + | 84.1362i | −0.0575758 | + | 0.151597i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 139.040 | + | 139.040i | 0.249623 | + | 0.249623i | 0.820816 | − | 0.571193i | \(-0.193519\pi\) |
−0.571193 | + | 0.820816i | \(0.693519\pi\) | |||||||
\(558\) | 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 | −0.594596 | + | 0.804024i | \(0.702688\pi\) |
−0.804024 | + | 0.594596i | \(0.797312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −194.070 | − | 431.757i | −0.343487 | − | 0.764172i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.9546 | − | 22.9546i | −0.0404843 | − | 0.0404843i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.92856i | 0.00866180i | 0.999991 | + | 0.00433090i | \(0.00137857\pi\) | ||||
−0.999991 | + | 0.00433090i | \(0.998621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 205.505 | 0.359904 | 0.179952 | − | 0.983675i | \(-0.442406\pi\) | ||||
0.179952 | + | 0.983675i | \(0.442406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 94.8990 | − | 94.8990i | 0.165618 | − | 0.165618i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 612.277 | − | 36.4495i | 1.06483 | − | 0.0633904i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 689.999 | + | 689.999i | 1.19584 | + | 1.19584i | 0.975401 | + | 0.220438i | \(0.0707486\pi\) |
0.220438 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(578\) | 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 | ||||||||
\(585\) | 236.969 | − | 106.515i | 0.405076 | − | 0.182077i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −672.347 | − | 672.347i | −1.14540 | − | 1.14540i | −0.987447 | − | 0.157949i | \(-0.949512\pi\) |
−0.157949 | − | 0.987447i | \(-0.550488\pi\) | |||||||
\(588\) | 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 | \(-0.615224\pi\) |
0.935195 | + | 0.354133i | \(0.115224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −296.838 | − | 112.738i | −0.498887 | − | 0.189475i | ||||
\(596\) | 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 | ||||||||
\(605\) | −94.0523 | + | 247.639i | −0.155458 | + | 0.409321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −362.803 | − | 362.803i | −0.597698 | − | 0.597698i | 0.342002 | − | 0.939699i | \(-0.388895\pi\) |
−0.939699 | + | 0.342002i | \(0.888895\pi\) | |||||||
\(608\) | 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 | −0.197398 | + | 0.980323i | \(0.563249\pi\) |
−0.980323 | + | 0.197398i | \(0.936751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −264.495 | − | 588.434i | −0.430073 | − | 0.956803i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 72.9036 | + | 72.9036i | 0.118158 | + | 0.118158i | 0.763713 | − | 0.645555i | \(-0.223374\pi\) |
−0.645555 | + | 0.763713i | \(0.723374\pi\) | |||||||
\(618\) | 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 | ||||||||
\(625\) | 74.1510 | + | 620.586i | 0.118642 | + | 0.992937i | ||||
\(626\) | 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 | \(-0.521818\pi\) | ||||
−0.0684894 | + | 0.997652i | \(0.521818\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 254.722 | − | 254.722i | 0.402404 | − | 0.402404i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.4495 | − | 7.39388i | 0.0259047 | − | 0.0116439i | ||||
\(636\) | 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 | 0.220670 | − | 0.975349i | \(-0.429176\pi\) |
0.975349 | − | 0.220670i | \(-0.0708243\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −399.576 | − | 151.757i | −0.619497 | − | 0.235282i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −602.854 | − | 602.854i | −0.931767 | − | 0.931767i | 0.0660489 | − | 0.997816i | \(-0.478961\pi\) |
−0.997816 | + | 0.0660489i | \(0.978961\pi\) | |||||||
\(648\) | 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 | \(-0.776186\pi\) |
0.646611 | + | 0.762820i | \(0.276186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 78.5505 | − | 206.823i | 0.119924 | − | 0.315760i | ||||
\(656\) | 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 | ||||||||
\(665\) | 255.051 | + | 567.423i | 0.383535 | + | 0.853268i | ||||
\(666\) | 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 | 0.0588084 | − | 0.998269i | \(-0.481270\pi\) |
0.998269 | − | 0.0588084i | \(-0.0187301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.71964 | + | 129.674i | 0.0114365 | + | 0.192110i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 351.943 | + | 351.943i | 0.519857 | + | 0.519857i | 0.917528 | − | 0.397671i | \(-0.130181\pi\) |
−0.397671 | + | 0.917528i | \(0.630181\pi\) | |||||||
\(678\) | 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 | −0.473764 | − | 0.880652i | \(-0.657105\pi\) |
0.880652 | + | 0.473764i | \(0.157105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −118.404 | + | 53.2214i | −0.172853 | + | 0.0776955i | ||||
\(686\) | 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 | \(-0.792080\pi\) | ||||
−0.794143 | + | 0.607731i | \(0.792080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 63.1056 | − | 63.1056i | 0.0910615 | − | 0.0910615i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1028.24 | + | 390.520i | 1.47948 | + | 0.561899i | ||||
\(696\) | 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 | ||||||||
\(705\) | −95.8638 | + | 252.409i | −0.135977 | + | 0.358026i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 179.167 | + | 179.167i | 0.253418 | + | 0.253418i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 368.061i | − | 0.519127i | −0.965726 | − | 0.259564i | \(-0.916421\pi\) | ||
0.965726 | − | 0.259564i | \(-0.0835787\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.48469 | 0.00208817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −494.343 | + | 494.343i | −0.693328 | + | 0.693328i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 292.827 | + | 651.464i | 0.409548 | + | 0.911139i | ||||
\(716\) | 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 | ||||||||
\(725\) | −161.853 | + | 182.343i | −0.223245 | + | 0.251507i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 837.297 | + | 837.297i | 1.15172 | + | 1.15172i | 0.986209 | + | 0.165507i | \(0.0529261\pi\) |
0.165507 | + | 0.986209i | \(0.447074\pi\) | |||||||
\(728\) | 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 | \(-0.759159\pi\) |
0.686471 | + | 0.727157i | \(0.259159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −284.283 | + | 127.782i | −0.386779 | + | 0.173853i | ||||
\(736\) | 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 | −0.661452 | − | 0.749988i | \(-0.730059\pi\) |
0.749988 | + | 0.661452i | \(0.230059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −132.131 | − | 50.1827i | −0.177357 | − | 0.0673593i | ||||
\(746\) | 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 | \(-0.691545\pi\) | ||||
−0.566092 | + | 0.824342i | \(0.691545\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −307.120 | + | 307.120i | −0.407862 | + | 0.407862i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −108.309 | + | 285.176i | −0.143455 | + | 0.377717i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 145.832 | + | 145.832i | 0.192645 | + | 0.192645i | 0.796838 | − | 0.604193i | \(-0.206504\pi\) |
−0.604193 | + | 0.796838i | \(0.706504\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 108.272 | + | 240.879i | 0.141533 | + | 0.314874i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 186.867 | + | 186.867i | 0.243634 | + | 0.243634i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 559.031i | − | 0.726958i | −0.931602 | − | 0.363479i | \(-0.881589\pi\) | ||
0.931602 | − | 0.363479i | \(-0.118411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −180.929 | −0.234667 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −348.965 | + | 348.965i | −0.451442 | + | 0.451442i | −0.895833 | − | 0.444391i | \(-0.853420\pi\) |
0.444391 | + | 0.895833i | \(0.353420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −532.767 | − | 472.899i | −0.687442 | − | 0.610192i | ||||
\(776\) | 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 | ||||||||
\(785\) | −146.091 | + | 65.6663i | −0.186103 | + | 0.0836514i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −821.414 | − | 821.414i | −1.04373 | − | 1.04373i | −0.998999 | − | 0.0447293i | \(-0.985757\pi\) |
−0.0447293 | − | 0.998999i | \(-0.514243\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | 740.747 | + | 281.333i | 0.931757 | + | 0.353878i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −649.065 | − | 649.065i | −0.814385 | − | 0.814385i | 0.170903 | − | 0.985288i | \(-0.445332\pi\) |
−0.985288 | + | 0.170903i | \(0.945332\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | −157.101 | + | 413.646i | −0.195157 | + | 0.513846i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 341.388 | + | 341.388i | 0.423034 | + | 0.423034i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 909.918i | − | 1.12474i | −0.826884 | − | 0.562372i | \(-0.809889\pi\) | ||
0.826884 | − | 0.562372i | \(-0.190111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −652.929 | −0.805091 | −0.402545 | − | 0.915400i | \(-0.631874\pi\) | ||||
−0.402545 | + | 0.915400i | \(0.631874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −80.8332 | + | 80.8332i | −0.0994258 | + | 0.0994258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 257.980 | + | 573.939i | 0.316539 | + | 0.704219i | ||||
\(816\) | 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 | −0.474558 | − | 0.880224i | \(-0.657392\pi\) |
0.880224 | + | 0.474558i | \(0.157392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −356.494 | + | 21.2225i | −0.432114 | + | 0.0257242i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 481.162 | + | 481.162i | 0.581817 | + | 0.581817i | 0.935402 | − | 0.353586i | \(-0.115038\pi\) |
−0.353586 | + | 0.935402i | \(0.615038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1296.35i | − | 1.56375i | −0.623433 | − | 0.781877i | \(-0.714262\pi\) | ||
0.623433 | − | 0.781877i | \(-0.285738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 518.908 | 0.624438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −448.055 | + | 448.055i | −0.537881 | + | 0.537881i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1107.00 | − | 497.585i | 1.32575 | − | 0.595910i | ||||
\(836\) | 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 | ||||||||
\(845\) | −612.325 | − | 232.558i | −0.724645 | − | 0.275217i | ||||
\(846\) | 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 | \(-0.669966\pi\) |
0.860797 | + | 0.508948i | \(0.169966\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 183.712 | − | 483.712i | 0.214868 | − | 0.565745i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 879.823 | + | 879.823i | 1.02663 | + | 1.02663i | 0.999636 | + | 0.0269957i | \(0.00859403\pi\) |
0.0269957 | + | 0.999636i | \(0.491406\pi\) | |||||||
\(858\) | 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 | −0.578683 | − | 0.815552i | \(-0.696433\pi\) |
0.815552 | + | 0.578683i | \(0.196433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.8194 | + | 68.5653i | 0.0356294 | + | 0.0792662i | ||||
\(866\) | 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 | ||||||||
\(875\) | −430.263 | − | 134.752i | −0.491729 | − | 0.154002i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −570.025 | − | 570.025i | −0.649971 | − | 0.649971i | 0.303014 | − | 0.952986i | \(-0.402007\pi\) |
−0.952986 | + | 0.303014i | \(0.902007\pi\) | |||||||
\(878\) | 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 | −0.984274 | − | 0.176651i | \(-0.943474\pi\) |
0.176651 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −120.520 | + | 54.1725i | −0.136181 | + | 0.0612118i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 343.510 | + | 343.510i | 0.387271 | + | 0.387271i | 0.873713 | − | 0.486442i | \(-0.161705\pi\) |
−0.486442 | + | 0.873713i | \(0.661705\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 468.580 | + | 177.965i | 0.523553 | + | 0.198843i | ||||
\(896\) | 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 | ||||||||
\(905\) | 460.579 | − | 1212.70i | 0.508927 | − | 1.34000i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −918.938 | − | 918.938i | −1.01316 | − | 1.01316i | −0.999912 | − | 0.0132496i | \(-0.995782\pi\) |
−0.0132496 | − | 0.999912i | \(-0.504218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 210.742i | − | 0.231840i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 788.454 | 0.865482 | 0.432741 | − | 0.901518i | \(-0.357546\pi\) | ||||
0.432741 | + | 0.901518i | \(0.357546\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −151.412 | + | 151.412i | −0.165840 | + | 0.165840i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 189.970 | + | 422.636i | 0.207618 | + | 0.461897i | ||||
\(916\) | 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 | ||||||||
\(925\) | 15.4393 | + | 259.348i | 0.0166911 | + | 0.280377i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −260.530 | − | 260.530i | −0.281046 | − | 0.281046i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1021.51i | 1.09957i | 0.835305 | + | 0.549787i | \(0.185291\pi\) | ||||
−0.835305 | + | 0.549787i | \(0.814709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1241.46 | 1.33347 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −262.070 | + | 262.070i | −0.280890 | + | 0.280890i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −662.211 | + | 297.657i | −0.708247 | + | 0.318350i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −370.555 | − | 370.555i | −0.395470 | − | 0.395470i | 0.481162 | − | 0.876632i | \(-0.340215\pi\) |
−0.876632 | + | 0.481162i | \(0.840215\pi\) | |||||||
\(938\) | 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 | ||||||||
\(945\) | −87.6061 | − | 33.2724i | −0.0927049 | − | 0.0352089i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −644.545 | − | 644.545i | −0.680618 | − | 0.680618i | 0.279522 | − | 0.960139i | \(-0.409824\pi\) |
−0.960139 | + | 0.279522i | \(0.909824\pi\) | |||||||
\(948\) | 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 | \(-0.861283\pi\) |
0.422128 | + | 0.906536i | \(0.361283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 137.555 | − | 362.182i | 0.144037 | − | 0.379248i | ||||
\(956\) | 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 | ||||||||
\(965\) | −242.313 | − | 539.085i | −0.251102 | − | 0.558638i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 462.196 | + | 462.196i | 0.477969 | + | 0.477969i | 0.904482 | − | 0.426512i | \(-0.140258\pi\) |
−0.426512 | + | 0.904482i | \(0.640258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1051.92i | − | 1.08557i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −198.390 | −0.204315 | −0.102158 | − | 0.994768i | \(-0.532575\pi\) | ||||
−0.102158 | + | 0.994768i | \(0.532575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −561.060 | + | 561.060i | −0.576629 | + | 0.576629i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 497.878 | − | 560.908i | 0.510644 | − | 0.575290i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 543.206 | + | 543.206i | 0.555993 | + | 0.555993i | 0.928164 | − | 0.372171i | \(-0.121386\pi\) |
−0.372171 | + | 0.928164i | \(0.621386\pi\) | |||||||
\(978\) | 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 | −0.851424 | − | 0.524478i | \(-0.824260\pi\) |
0.524478 | + | 0.851424i | \(0.324260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1291.52 | + | 580.527i | −1.31119 | + | 0.589367i | ||||
\(986\) | 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 | \(-0.784231\pi\) | ||||
−0.778918 | + | 0.627125i | \(0.784231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −262.602 | + | 262.602i | −0.264453 | + | 0.264453i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −761.853 | − | 289.348i | −0.765681 | − | 0.290802i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 800.429 | + | 800.429i | 0.802838 | + | 0.802838i | 0.983538 | − | 0.180701i | \(-0.0578365\pi\) |
−0.180701 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(998\) | 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 | 60.3.k.a.37.2 | yes | 4 | |
3.2 | odd | 2 | 180.3.l.b.37.2 | 4 | |||
4.3 | odd | 2 | 240.3.bg.d.97.1 | 4 | |||
5.2 | odd | 4 | 300.3.k.a.193.1 | 4 | |||
5.3 | odd | 4 | inner | 60.3.k.a.13.2 | ✓ | 4 | |
5.4 | even | 2 | 300.3.k.a.157.1 | 4 | |||
8.3 | odd | 2 | 960.3.bg.a.577.2 | 4 | |||
8.5 | even | 2 | 960.3.bg.b.577.1 | 4 | |||
12.11 | even | 2 | 720.3.bh.f.577.2 | 4 | |||
15.2 | even | 4 | 900.3.l.b.793.2 | 4 | |||
15.8 | even | 4 | 180.3.l.b.73.2 | 4 | |||
15.14 | odd | 2 | 900.3.l.b.757.2 | 4 | |||
20.3 | even | 4 | 240.3.bg.d.193.1 | 4 | |||
20.7 | even | 4 | 1200.3.bg.o.193.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.o.1057.2 | 4 | |||
40.3 | even | 4 | 960.3.bg.a.193.2 | 4 | |||
40.13 | odd | 4 | 960.3.bg.b.193.1 | 4 | |||
60.23 | odd | 4 | 720.3.bh.f.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.k.a.13.2 | ✓ | 4 | 5.3 | odd | 4 | inner | |
60.3.k.a.37.2 | yes | 4 | 1.1 | even | 1 | trivial | |
180.3.l.b.37.2 | 4 | 3.2 | odd | 2 | |||
180.3.l.b.73.2 | 4 | 15.8 | even | 4 | |||
240.3.bg.d.97.1 | 4 | 4.3 | odd | 2 | |||
240.3.bg.d.193.1 | 4 | 20.3 | even | 4 | |||
300.3.k.a.157.1 | 4 | 5.4 | even | 2 | |||
300.3.k.a.193.1 | 4 | 5.2 | odd | 4 | |||
720.3.bh.f.433.2 | 4 | 60.23 | odd | 4 | |||
720.3.bh.f.577.2 | 4 | 12.11 | even | 2 | |||
900.3.l.b.757.2 | 4 | 15.14 | odd | 2 | |||
900.3.l.b.793.2 | 4 | 15.2 | even | 4 | |||
960.3.bg.a.193.2 | 4 | 40.3 | even | 4 | |||
960.3.bg.a.577.2 | 4 | 8.3 | odd | 2 | |||
960.3.bg.b.193.1 | 4 | 40.13 | odd | 4 | |||
960.3.bg.b.577.1 | 4 | 8.5 | even | 2 | |||
1200.3.bg.o.193.2 | 4 | 20.7 | even | 4 | |||
1200.3.bg.o.1057.2 | 4 | 20.19 | odd | 2 |