Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(323,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.j (of order \(2\), degree \(1\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.9 | ||
Character | \(\chi\) | \(=\) | 504.323 |
Dual form | 504.2.j.a.323.10 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.386593 | − | 1.36035i | −0.273363 | − | 0.961911i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.70109 | + | 1.05180i | −0.850546 | + | 0.525901i | ||||
\(5\) | 3.11999 | 1.39530 | 0.697652 | − | 0.716437i | \(-0.254228\pi\) | ||||
0.697652 | + | 0.716437i | \(0.254228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.08845 | + | 1.90746i | 0.738378 | + | 0.674387i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.20617 | − | 4.24428i | −0.381424 | − | 1.34216i | ||||
\(11\) | 5.48338i | 1.65330i | 0.562716 | + | 0.826650i | \(0.309756\pi\) | ||||
−0.562716 | + | 0.826650i | \(0.690244\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.65814i | 0.459886i | 0.973204 | + | 0.229943i | \(0.0738540\pi\) | ||||
−0.973204 | + | 0.229943i | \(0.926146\pi\) | |||||||
\(14\) | 1.36035 | − | 0.386593i | 0.363568 | − | 0.103321i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.78742 | − | 3.57842i | 0.446856 | − | 0.894606i | ||||
\(17\) | 4.14743i | 1.00590i | 0.864316 | + | 0.502950i | \(0.167752\pi\) | ||||
−0.864316 | + | 0.502950i | \(0.832248\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94109 | −0.674733 | −0.337367 | − | 0.941373i | \(-0.609536\pi\) | ||||
−0.337367 | + | 0.941373i | \(0.609536\pi\) | |||||||
\(20\) | −5.30739 | + | 3.28162i | −1.18677 | + | 0.733792i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.45930 | − | 2.11984i | 1.59033 | − | 0.451951i | ||||
\(23\) | −0.388249 | −0.0809554 | −0.0404777 | − | 0.999180i | \(-0.512888\pi\) | ||||
−0.0404777 | + | 0.999180i | \(0.512888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73436 | 0.946871 | ||||||||
\(26\) | 2.25565 | − | 0.641027i | 0.442370 | − | 0.125716i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.05180 | − | 1.70109i | −0.198772 | − | 0.321476i | ||||
\(29\) | 6.81281 | 1.26511 | 0.632554 | − | 0.774516i | \(-0.282007\pi\) | ||||
0.632554 | + | 0.774516i | \(0.282007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.59877i | 0.287147i | 0.989640 | + | 0.143573i | \(0.0458593\pi\) | ||||
−0.989640 | + | 0.143573i | \(0.954141\pi\) | |||||||
\(32\) | −5.55891 | − | 1.04812i | −0.982685 | − | 0.185284i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.64195 | − | 1.60337i | 0.967586 | − | 0.274975i | ||||
\(35\) | 3.11999i | 0.527375i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.6958i | − | 1.75837i | −0.476479 | − | 0.879186i | \(-0.658087\pi\) | ||
0.476479 | − | 0.879186i | \(-0.341913\pi\) | |||||||
\(38\) | 1.13701 | + | 4.00091i | 0.184447 | + | 0.649034i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.51594 | + | 5.95125i | 1.03026 | + | 0.940975i | ||||
\(41\) | − | 4.43752i | − | 0.693025i | −0.938045 | − | 0.346512i | \(-0.887366\pi\) | ||
0.938045 | − | 0.346512i | \(-0.112634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.18690 | −0.638497 | −0.319248 | − | 0.947671i | \(-0.603430\pi\) | ||||
−0.319248 | + | 0.947671i | \(0.603430\pi\) | |||||||
\(44\) | −5.76743 | − | 9.32772i | −0.869473 | − | 1.40621i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.150094 | + | 0.528153i | 0.0221302 | + | 0.0778719i | ||||
\(47\) | 11.5212 | 1.68053 | 0.840267 | − | 0.542172i | \(-0.182398\pi\) | ||||
0.840267 | + | 0.542172i | \(0.182398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.83027 | − | 6.44037i | −0.258839 | − | 0.910806i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.74404 | − | 2.82065i | −0.241855 | − | 0.391154i | ||||
\(53\) | 7.45281 | 1.02372 | 0.511861 | − | 0.859068i | \(-0.328956\pi\) | ||||
0.511861 | + | 0.859068i | \(0.328956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.1081i | 2.30686i | ||||||||
\(56\) | −1.90746 | + | 2.08845i | −0.254895 | + | 0.279081i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.63379 | − | 9.26779i | −0.345833 | − | 1.21692i | ||||
\(59\) | − | 11.5212i | − | 1.49993i | −0.661479 | − | 0.749964i | \(-0.730071\pi\) | ||
0.661479 | − | 0.749964i | \(-0.269929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.75419i | − | 0.864786i | −0.901685 | − | 0.432393i | \(-0.857669\pi\) | ||
0.901685 | − | 0.432393i | \(-0.142331\pi\) | |||||||
\(62\) | 2.17488 | − | 0.618072i | 0.276210 | − | 0.0784953i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.723225 | + | 7.96724i | 0.0904031 | + | 0.995905i | ||||
\(65\) | 5.17340i | 0.641681i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.03553 | 0.615188 | 0.307594 | − | 0.951518i | \(-0.400476\pi\) | ||||
0.307594 | + | 0.951518i | \(0.400476\pi\) | |||||||
\(68\) | −4.36228 | − | 7.05516i | −0.529004 | − | 0.855564i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.24428 | − | 1.20617i | 0.507288 | − | 0.144165i | ||||
\(71\) | −15.2213 | −1.80644 | −0.903218 | − | 0.429182i | \(-0.858802\pi\) | ||||
−0.903218 | + | 0.429182i | \(0.858802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.4687 | −1.92751 | −0.963755 | − | 0.266789i | \(-0.914037\pi\) | ||||
−0.963755 | + | 0.266789i | \(0.914037\pi\) | |||||||
\(74\) | −14.5500 | + | 4.13491i | −1.69140 | + | 0.480673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00307 | − | 3.09345i | 0.573892 | − | 0.354843i | ||||
\(77\) | −5.48338 | −0.624889 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.01684i | 0.226912i | 0.993543 | + | 0.113456i | \(0.0361921\pi\) | ||||
−0.993543 | + | 0.113456i | \(0.963808\pi\) | |||||||
\(80\) | 5.57675 | − | 11.1647i | 0.623499 | − | 1.24825i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.03658 | + | 1.71552i | −0.666628 | + | 0.189447i | ||||
\(83\) | − | 6.21127i | − | 0.681775i | −0.940104 | − | 0.340888i | \(-0.889272\pi\) | ||
0.940104 | − | 0.340888i | \(-0.110728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9400i | 1.40354i | ||||||||
\(86\) | 1.61863 | + | 5.69564i | 0.174541 | + | 0.614177i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.4593 | + | 11.4517i | −1.11496 | + | 1.22076i | ||||
\(89\) | 5.93308i | 0.628905i | 0.949273 | + | 0.314453i | \(0.101821\pi\) | ||||
−0.949273 | + | 0.314453i | \(0.898179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.65814 | −0.173821 | ||||||||
\(92\) | 0.660446 | − | 0.408361i | 0.0688563 | − | 0.0425746i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.45400 | − | 15.6728i | −0.459396 | − | 1.61652i | ||||
\(95\) | −9.17620 | −0.941458 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1578 | 1.43751 | 0.718753 | − | 0.695265i | \(-0.244713\pi\) | ||||
0.718753 | + | 0.695265i | \(0.244713\pi\) | |||||||
\(98\) | 0.386593 | + | 1.36035i | 0.0390518 | + | 0.137416i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.05357 | + | 4.97961i | −0.805357 | + | 0.497961i | ||||
\(101\) | 13.5036 | 1.34366 | 0.671830 | − | 0.740705i | \(-0.265509\pi\) | ||||
0.671830 | + | 0.740705i | \(0.265509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2021i | 1.00524i | 0.864508 | + | 0.502620i | \(0.167630\pi\) | ||||
−0.864508 | + | 0.502620i | \(0.832370\pi\) | |||||||
\(104\) | −3.16284 | + | 3.46295i | −0.310142 | + | 0.339570i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.88121 | − | 10.1384i | −0.279847 | − | 0.984729i | ||||
\(107\) | 6.99660i | 0.676386i | 0.941077 | + | 0.338193i | \(0.109816\pi\) | ||||
−0.941077 | + | 0.338193i | \(0.890184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.53986i | − | 0.626405i | −0.949686 | − | 0.313203i | \(-0.898598\pi\) | ||
0.949686 | − | 0.313203i | \(-0.101402\pi\) | |||||||
\(110\) | 23.2730 | − | 6.61387i | 2.21899 | − | 0.630608i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.57842 | + | 1.78742i | 0.338129 | + | 0.168896i | ||||
\(113\) | 13.4345i | 1.26382i | 0.775044 | + | 0.631908i | \(0.217728\pi\) | ||||
−0.775044 | + | 0.631908i | \(0.782272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.21133 | −0.112957 | ||||||||
\(116\) | −11.5892 | + | 7.16573i | −1.07603 | + | 0.665322i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.6728 | + | 4.45400i | −1.44280 | + | 0.410024i | ||||
\(119\) | −4.14743 | −0.380194 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.0674 | −1.73340 | ||||||||
\(122\) | −9.18805 | + | 2.61113i | −0.831847 | + | 0.236400i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.68159 | − | 2.71965i | −0.151011 | − | 0.244232i | ||||
\(125\) | −0.828803 | −0.0741304 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.49155i | 0.309825i | 0.987928 | + | 0.154912i | \(0.0495096\pi\) | ||||
−0.987928 | + | 0.154912i | \(0.950490\pi\) | |||||||
\(128\) | 10.5586 | − | 4.06392i | 0.933259 | − | 0.359203i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.03762 | − | 2.00000i | 0.617240 | − | 0.175412i | ||||
\(131\) | − | 9.26178i | − | 0.809205i | −0.914493 | − | 0.404603i | \(-0.867410\pi\) | ||
0.914493 | − | 0.404603i | \(-0.132590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.94109i | − | 0.255025i | ||||||
\(134\) | −1.94670 | − | 6.85008i | −0.168170 | − | 0.591757i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.91104 | + | 8.66169i | −0.678366 | + | 0.742734i | ||||
\(137\) | − | 3.67521i | − | 0.313994i | −0.987599 | − | 0.156997i | \(-0.949819\pi\) | ||
0.987599 | − | 0.156997i | \(-0.0501814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.410254 | 0.0347973 | 0.0173986 | − | 0.999849i | \(-0.494462\pi\) | ||||
0.0173986 | + | 0.999849i | \(0.494462\pi\) | |||||||
\(140\) | −3.28162 | − | 5.30739i | −0.277347 | − | 0.448557i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.88445 | + | 20.7063i | 0.493812 | + | 1.73763i | ||||
\(143\) | −9.09222 | −0.760330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.2559 | 1.76521 | ||||||||
\(146\) | 6.36667 | + | 22.4031i | 0.526909 | + | 1.85409i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2498 | + | 18.1945i | 0.924730 | + | 1.49558i | ||||
\(149\) | −2.94652 | −0.241388 | −0.120694 | − | 0.992690i | \(-0.538512\pi\) | ||||
−0.120694 | + | 0.992690i | \(0.538512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.58975i | 0.292129i | 0.989275 | + | 0.146065i | \(0.0466608\pi\) | ||||
−0.989275 | + | 0.146065i | \(0.953339\pi\) | |||||||
\(152\) | −6.14232 | − | 5.61001i | −0.498208 | − | 0.455032i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.11984 | + | 7.45930i | 0.170821 | + | 0.601087i | ||||
\(155\) | 4.98814i | 0.400657i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.7551i | − | 1.33721i | −0.743620 | − | 0.668603i | \(-0.766893\pi\) | ||
0.743620 | − | 0.668603i | \(-0.233107\pi\) | |||||||
\(158\) | 2.74360 | − | 0.779696i | 0.218269 | − | 0.0620292i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.3437 | − | 3.27013i | −1.37114 | − | 0.258527i | ||||
\(161\) | − | 0.388249i | − | 0.0305983i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6681 | −0.913917 | −0.456958 | − | 0.889488i | \(-0.651061\pi\) | ||||
−0.456958 | + | 0.889488i | \(0.651061\pi\) | |||||||
\(164\) | 4.66740 | + | 7.54863i | 0.364463 | + | 0.589449i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.44948 | + | 2.40123i | −0.655807 | + | 0.186372i | ||||
\(167\) | 17.1810 | 1.32950 | 0.664751 | − | 0.747065i | \(-0.268537\pi\) | ||||
0.664751 | + | 0.747065i | \(0.268537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2506 | 0.788505 | ||||||||
\(170\) | 17.6028 | − | 5.00250i | 1.35008 | − | 0.383674i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.12230 | − | 4.40379i | 0.543070 | − | 0.335786i | ||||
\(173\) | −18.8574 | −1.43370 | −0.716849 | − | 0.697228i | \(-0.754416\pi\) | ||||
−0.716849 | + | 0.697228i | \(0.754416\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.73436i | 0.357884i | ||||||||
\(176\) | 19.6218 | + | 9.80111i | 1.47905 | + | 0.738787i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.07105 | − | 2.29369i | 0.604951 | − | 0.171919i | ||||
\(179\) | − | 10.4376i | − | 0.780145i | −0.920784 | − | 0.390073i | \(-0.872450\pi\) | ||
0.920784 | − | 0.390073i | \(-0.127550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.463832i | 0.0344764i | 0.999851 | + | 0.0172382i | \(0.00548736\pi\) | ||||
−0.999851 | + | 0.0172382i | \(0.994513\pi\) | |||||||
\(182\) | 0.641027 | + | 2.25565i | 0.0475161 | + | 0.167200i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.810837 | − | 0.740567i | −0.0597757 | − | 0.0545953i | ||||
\(185\) | − | 33.3707i | − | 2.45346i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.7419 | −1.66305 | ||||||||
\(188\) | −19.5986 | + | 12.1180i | −1.42937 | + | 0.883795i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.54746 | + | 12.4828i | 0.257359 | + | 0.905599i | ||||
\(191\) | −3.44417 | −0.249211 | −0.124606 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124606 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8325 | −0.779740 | −0.389870 | − | 0.920870i | \(-0.627480\pi\) | ||||
−0.389870 | + | 0.920870i | \(0.627480\pi\) | |||||||
\(194\) | −5.47331 | − | 19.2595i | −0.392961 | − | 1.38275i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70109 | − | 1.05180i | 0.121507 | − | 0.0751287i | ||||
\(197\) | 3.62039 | 0.257942 | 0.128971 | − | 0.991648i | \(-0.458833\pi\) | ||||
0.128971 | + | 0.991648i | \(0.458833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.2359i | − | 1.64715i | −0.567209 | − | 0.823574i | \(-0.691977\pi\) | ||
0.567209 | − | 0.823574i | \(-0.308023\pi\) | |||||||
\(200\) | 9.88746 | + | 9.03058i | 0.699149 | + | 0.638558i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.22041 | − | 18.3696i | −0.367306 | − | 1.29248i | ||||
\(203\) | 6.81281i | 0.478166i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 13.8450i | − | 0.966980i | ||||||
\(206\) | 13.8784 | − | 3.94405i | 0.966951 | − | 0.274795i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.93354 | + | 2.96380i | 0.411417 | + | 0.205503i | ||||
\(209\) | − | 16.1271i | − | 1.11554i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.81404 | 0.400255 | 0.200128 | − | 0.979770i | \(-0.435864\pi\) | ||||
0.200128 | + | 0.979770i | \(0.435864\pi\) | |||||||
\(212\) | −12.6779 | + | 7.83888i | −0.870722 | + | 0.538377i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.51780 | − | 2.70484i | 0.650624 | − | 0.184899i | ||||
\(215\) | −13.0631 | −0.890896 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.59877 | −0.108531 | ||||||||
\(218\) | −8.89648 | + | 2.52827i | −0.602546 | + | 0.171236i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.9943 | − | 29.1024i | −1.21318 | − | 1.96209i | ||||
\(221\) | −6.87704 | −0.462599 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.60873i | − | 0.643448i | −0.946833 | − | 0.321724i | \(-0.895738\pi\) | ||
0.946833 | − | 0.321724i | \(-0.104262\pi\) | |||||||
\(224\) | 1.04812 | − | 5.55891i | 0.0700306 | − | 0.371420i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.2756 | − | 5.19370i | 1.21568 | − | 0.345480i | ||||
\(227\) | 12.9929i | 0.862370i | 0.902264 | + | 0.431185i | \(0.141904\pi\) | ||||
−0.902264 | + | 0.431185i | \(0.858096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.47738i | − | 0.0976283i | −0.998808 | − | 0.0488141i | \(-0.984456\pi\) | ||
0.998808 | − | 0.0488141i | \(-0.0155442\pi\) | |||||||
\(230\) | 0.468293 | + | 1.64783i | 0.0308783 | + | 0.108655i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.2282 | + | 12.9951i | 0.934127 | + | 0.853173i | ||||
\(233\) | − | 12.8931i | − | 0.844658i | −0.906443 | − | 0.422329i | \(-0.861213\pi\) | ||
0.906443 | − | 0.422329i | \(-0.138787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.9460 | 2.34486 | ||||||||
\(236\) | 12.1180 | + | 19.5986i | 0.788814 | + | 1.27576i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.60337 | + | 5.64195i | 0.103931 | + | 0.365713i | ||||
\(239\) | −24.8490 | −1.60735 | −0.803675 | − | 0.595068i | \(-0.797125\pi\) | ||||
−0.803675 | + | 0.595068i | \(0.797125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.8088 | 1.34041 | 0.670206 | − | 0.742175i | \(-0.266206\pi\) | ||||
0.670206 | + | 0.742175i | \(0.266206\pi\) | |||||||
\(242\) | 7.37133 | + | 25.9383i | 0.473847 | + | 1.66738i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.10408 | + | 11.4895i | 0.454792 | + | 0.735540i | ||||
\(245\) | −3.11999 | −0.199329 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.87676i | − | 0.310301i | ||||||
\(248\) | −3.04958 | + | 3.33894i | −0.193648 | + | 0.212023i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.320410 | + | 1.12746i | 0.0202645 | + | 0.0713069i | ||||
\(251\) | − | 20.1787i | − | 1.27367i | −0.771001 | − | 0.636834i | \(-0.780244\pi\) | ||
0.771001 | − | 0.636834i | \(-0.219756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.12891i | − | 0.133844i | ||||||
\(254\) | 4.74972 | − | 1.34981i | 0.298024 | − | 0.0846946i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.61024 | − | 12.7923i | −0.600640 | − | 0.799520i | ||||
\(257\) | 17.8844i | 1.11560i | 0.829976 | + | 0.557800i | \(0.188354\pi\) | ||||
−0.829976 | + | 0.557800i | \(0.811646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6958 | 0.664602 | ||||||||
\(260\) | −5.44139 | − | 8.80042i | −0.337461 | − | 0.545779i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.5992 | + | 3.58054i | −0.778384 | + | 0.221207i | ||||
\(263\) | 2.52143 | 0.155478 | 0.0777390 | − | 0.996974i | \(-0.475230\pi\) | ||||
0.0777390 | + | 0.996974i | \(0.475230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.2527 | 1.42840 | ||||||||
\(266\) | −4.00091 | + | 1.13701i | −0.245312 | + | 0.0697144i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.56590 | + | 5.29639i | −0.523246 | + | 0.323528i | ||||
\(269\) | 12.8535 | 0.783695 | 0.391847 | − | 0.920030i | \(-0.371836\pi\) | ||||
0.391847 | + | 0.920030i | \(0.371836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.7743i | − | 1.68717i | −0.536995 | − | 0.843586i | \(-0.680440\pi\) | ||
0.536995 | − | 0.843586i | \(-0.319560\pi\) | |||||||
\(272\) | 14.8413 | + | 7.41321i | 0.899884 | + | 0.449492i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.99956 | + | 1.42081i | −0.302035 | + | 0.0858344i | ||||
\(275\) | 25.9603i | 1.56546i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3940i | 1.40561i | 0.711382 | + | 0.702806i | \(0.248070\pi\) | ||||
−0.711382 | + | 0.702806i | \(0.751930\pi\) | |||||||
\(278\) | −0.158601 | − | 0.558088i | −0.00951228 | − | 0.0334719i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.95125 | + | 6.51594i | −0.355655 | + | 0.389402i | ||||
\(281\) | 29.1013i | 1.73604i | 0.496531 | + | 0.868019i | \(0.334607\pi\) | ||||
−0.496531 | + | 0.868019i | \(0.665393\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.415808 | −0.0247172 | −0.0123586 | − | 0.999924i | \(-0.503934\pi\) | ||||
−0.0123586 | + | 0.999924i | \(0.503934\pi\) | |||||||
\(284\) | 25.8928 | − | 16.0098i | 1.53646 | − | 0.950007i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.51499 | + | 12.3686i | 0.207846 | + | 0.731370i | ||||
\(287\) | 4.43752 | 0.261939 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.201184 | −0.0118343 | ||||||||
\(290\) | −8.21740 | − | 28.9155i | −0.482542 | − | 1.69797i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28.0147 | − | 17.3218i | 1.63944 | − | 1.01368i | ||||
\(293\) | 14.1198 | 0.824887 | 0.412444 | − | 0.910983i | \(-0.364675\pi\) | ||||
0.412444 | + | 0.910983i | \(0.364675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 35.9460i | − | 2.09285i | ||||||
\(296\) | 20.4017 | − | 22.3375i | 1.18582 | − | 1.29834i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.13910 | + | 4.00829i | 0.0659865 | + | 0.232194i | ||||
\(299\) | − | 0.643772i | − | 0.0372303i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.18690i | − | 0.241329i | ||||||
\(302\) | 4.88330 | − | 1.38777i | 0.281002 | − | 0.0798573i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.25698 | + | 10.5245i | −0.301509 | + | 0.603621i | ||||
\(305\) | − | 21.0730i | − | 1.20664i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.8671 | 1.93289 | 0.966447 | − | 0.256864i | \(-0.0826893\pi\) | ||||
0.966447 | + | 0.256864i | \(0.0826893\pi\) | |||||||
\(308\) | 9.32772 | − | 5.76743i | 0.531496 | − | 0.328630i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.78560 | − | 1.92838i | 0.385396 | − | 0.109525i | ||||
\(311\) | 18.2024 | 1.03216 | 0.516081 | − | 0.856540i | \(-0.327390\pi\) | ||||
0.516081 | + | 0.856540i | \(0.327390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.21910 | −0.351524 | −0.175762 | − | 0.984433i | \(-0.556239\pi\) | ||||
−0.175762 | + | 0.984433i | \(0.556239\pi\) | |||||||
\(314\) | −22.7928 | + | 6.47742i | −1.28627 | + | 0.365542i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.12131 | − | 3.43082i | −0.119333 | − | 0.192999i | ||||
\(317\) | −22.4002 | −1.25812 | −0.629059 | − | 0.777357i | \(-0.716560\pi\) | ||||
−0.629059 | + | 0.777357i | \(0.716560\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.3572i | 2.09160i | ||||||||
\(320\) | 2.25646 | + | 24.8577i | 0.126140 | + | 1.38959i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.528153 | + | 0.150094i | −0.0294328 | + | 0.00836443i | ||||
\(323\) | − | 12.1980i | − | 0.678714i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.85024i | 0.435453i | ||||||||
\(326\) | 4.51081 | + | 15.8727i | 0.249831 | + | 0.879107i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.46438 | − | 9.26754i | 0.467367 | − | 0.511714i | ||||
\(329\) | 11.5212i | 0.635182i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1097 | 1.21526 | 0.607630 | − | 0.794220i | \(-0.292120\pi\) | ||||
0.607630 | + | 0.794220i | \(0.292120\pi\) | |||||||
\(332\) | 6.53303 | + | 10.5659i | 0.358546 | + | 0.579881i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.64205 | − | 23.3721i | −0.363437 | − | 1.27886i | ||||
\(335\) | 15.7108 | 0.858374 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1994 | −1.04586 | −0.522930 | − | 0.852376i | \(-0.675161\pi\) | ||||
−0.522930 | + | 0.852376i | \(0.675161\pi\) | |||||||
\(338\) | −3.96280 | − | 13.9443i | −0.215548 | − | 0.758471i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.6103 | − | 22.0120i | −0.738121 | − | 1.19377i | ||||
\(341\) | −8.76664 | −0.474740 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −8.74412 | − | 7.98633i | −0.471452 | − | 0.430594i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.29013 | + | 25.6526i | 0.391920 | + | 1.37909i | ||||
\(347\) | − | 3.40174i | − | 0.182615i | −0.995823 | − | 0.0913076i | \(-0.970895\pi\) | ||
0.995823 | − | 0.0913076i | \(-0.0291046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.872003i | − | 0.0466773i | −0.999728 | − | 0.0233386i | \(-0.992570\pi\) | ||
0.999728 | − | 0.0233386i | \(-0.00742959\pi\) | |||||||
\(350\) | 6.44037 | − | 1.83027i | 0.344252 | − | 0.0978321i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.74725 | − | 30.4816i | 0.306329 | − | 1.62467i | ||||
\(353\) | 6.37269i | 0.339184i | 0.985514 | + | 0.169592i | \(0.0542450\pi\) | ||||
−0.985514 | + | 0.169592i | \(0.945755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −47.4903 | −2.52053 | ||||||||
\(356\) | −6.24043 | − | 10.0927i | −0.330742 | − | 0.534912i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.1988 | + | 4.03512i | −0.750430 | + | 0.213263i | ||||
\(359\) | −6.15450 | −0.324822 | −0.162411 | − | 0.986723i | \(-0.551927\pi\) | ||||
−0.162411 | + | 0.986723i | \(0.551927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3500 | −0.544735 | ||||||||
\(362\) | 0.630973 | − | 0.179314i | 0.0331632 | − | 0.00942456i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.82065 | − | 1.74404i | 0.147842 | − | 0.0914125i | ||||
\(365\) | −51.3821 | −2.68946 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1419i | 0.738201i | 0.929389 | + | 0.369101i | \(0.120334\pi\) | ||||
−0.929389 | + | 0.369101i | \(0.879666\pi\) | |||||||
\(368\) | −0.693965 | + | 1.38932i | −0.0361754 | + | 0.0724232i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −45.3958 | + | 12.9009i | −2.36001 | + | 0.670685i | ||||
\(371\) | 7.45281i | 0.386930i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.8957i | 1.59972i | 0.600186 | + | 0.799860i | \(0.295093\pi\) | ||||
−0.600186 | + | 0.799860i | \(0.704907\pi\) | |||||||
\(374\) | 8.79187 | + | 30.9369i | 0.454617 | + | 1.59971i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.0613 | + | 21.9761i | 1.24087 | + | 1.13333i | ||||
\(377\) | 11.2966i | 0.581806i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3446 | −1.40460 | −0.702300 | − | 0.711881i | \(-0.747843\pi\) | ||||
−0.702300 | + | 0.711881i | \(0.747843\pi\) | |||||||
\(380\) | 15.6095 | − | 9.65155i | 0.800753 | − | 0.495114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.33149 | + | 4.68526i | 0.0681250 | + | 0.239719i | ||||
\(383\) | 8.62880 | 0.440911 | 0.220456 | − | 0.975397i | \(-0.429246\pi\) | ||||
0.220456 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1081 | −0.871909 | ||||||||
\(386\) | 4.18777 | + | 14.7360i | 0.213152 | + | 0.750040i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.0837 | + | 14.8912i | −1.22266 | + | 0.755986i | ||||
\(389\) | 7.11018 | 0.360501 | 0.180250 | − | 0.983621i | \(-0.442309\pi\) | ||||
0.180250 | + | 0.983621i | \(0.442309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.61023i | − | 0.0814330i | ||||||
\(392\) | −2.08845 | − | 1.90746i | −0.105483 | − | 0.0963411i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.39962 | − | 4.92499i | −0.0705118 | − | 0.248118i | ||||
\(395\) | 6.29252i | 0.316611i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0677i | 0.706038i | 0.935616 | + | 0.353019i | \(0.114845\pi\) | ||||
−0.935616 | + | 0.353019i | \(0.885155\pi\) | |||||||
\(398\) | −31.6089 | + | 8.98283i | −1.58441 | + | 0.450269i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.46230 | − | 16.9415i | 0.423115 | − | 0.847077i | ||||
\(401\) | − | 5.92345i | − | 0.295803i | −0.989002 | − | 0.147902i | \(-0.952748\pi\) | ||
0.989002 | − | 0.147902i | \(-0.0472519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.65098 | −0.132055 | ||||||||
\(404\) | −22.9709 | + | 14.2031i | −1.14284 | + | 0.706632i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.26779 | − | 2.63379i | 0.459953 | − | 0.130713i | ||||
\(407\) | 58.6489 | 2.90712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6481 | −1.16933 | −0.584663 | − | 0.811276i | \(-0.698773\pi\) | ||||
−0.584663 | + | 0.811276i | \(0.698773\pi\) | |||||||
\(410\) | −18.8341 | + | 5.35240i | −0.930149 | + | 0.264336i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.7306 | − | 17.3546i | −0.528657 | − | 0.855002i | ||||
\(413\) | 11.5212 | 0.566919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 19.3791i | − | 0.951283i | ||||||
\(416\) | 1.73794 | − | 9.21746i | 0.0852094 | − | 0.451923i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.9385 | + | 6.23464i | −1.07305 | + | 0.304946i | ||||
\(419\) | − | 24.0507i | − | 1.17495i | −0.809241 | − | 0.587477i | \(-0.800121\pi\) | ||
0.809241 | − | 0.587477i | \(-0.199879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.2740i | − | 0.841881i | −0.907088 | − | 0.420941i | \(-0.861700\pi\) | ||
0.907088 | − | 0.420941i | \(-0.138300\pi\) | |||||||
\(422\) | −2.24767 | − | 7.90912i | −0.109415 | − | 0.385010i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.5648 | + | 14.2159i | 0.755893 | + | 0.690385i | ||||
\(425\) | 19.6354i | 0.952458i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.75419 | 0.326858 | ||||||||
\(428\) | −7.35904 | − | 11.9018i | −0.355712 | − | 0.575298i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.05011 | + | 17.7704i | 0.243538 | + | 0.856963i | ||||
\(431\) | 10.2315 | 0.492836 | 0.246418 | − | 0.969164i | \(-0.420746\pi\) | ||||
0.246418 | + | 0.969164i | \(0.420746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5332 | −0.506192 | −0.253096 | − | 0.967441i | \(-0.581449\pi\) | ||||
−0.253096 | + | 0.967441i | \(0.581449\pi\) | |||||||
\(434\) | 0.618072 | + | 2.17488i | 0.0296684 | + | 0.104397i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.87864 | + | 11.1249i | 0.329427 | + | 0.532786i | ||||
\(437\) | 1.14188 | 0.0546233 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17.3145i | − | 0.826374i | −0.910646 | − | 0.413187i | \(-0.864416\pi\) | ||
0.910646 | − | 0.413187i | \(-0.135584\pi\) | |||||||
\(440\) | −32.6329 | + | 35.7294i | −1.55571 | + | 1.70333i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.65862 | + | 9.35516i | 0.126457 | + | 0.444980i | ||||
\(443\) | 3.09962i | 0.147267i | 0.997285 | + | 0.0736336i | \(0.0234595\pi\) | ||||
−0.997285 | + | 0.0736336i | \(0.976540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.5112i | 0.877513i | ||||||||
\(446\) | −13.0712 | + | 3.71467i | −0.618940 | + | 0.175895i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.96724 | + | 0.723225i | −0.376417 | + | 0.0341692i | ||||
\(449\) | 5.06298i | 0.238937i | 0.992838 | + | 0.119468i | \(0.0381190\pi\) | ||||
−0.992838 | + | 0.119468i | \(0.961881\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.3326 | 1.14578 | ||||||||
\(452\) | −14.1305 | − | 22.8534i | −0.664642 | − | 1.07493i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.6749 | − | 5.02297i | 0.829523 | − | 0.235740i | ||||
\(455\) | −5.17340 | −0.242533 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.6475 | −1.66752 | −0.833760 | − | 0.552127i | \(-0.813816\pi\) | ||||
−0.833760 | + | 0.552127i | \(0.813816\pi\) | |||||||
\(458\) | −2.00976 | + | 0.571147i | −0.0939097 | + | 0.0266879i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.06059 | − | 1.27408i | 0.0960754 | − | 0.0594044i | ||||
\(461\) | −15.3638 | −0.715563 | −0.357782 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0189i | 0.883884i | 0.897044 | + | 0.441942i | \(0.145710\pi\) | ||||
−0.897044 | + | 0.441942i | \(0.854290\pi\) | |||||||
\(464\) | 12.1774 | − | 24.3791i | 0.565321 | − | 1.13177i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5392 | + | 4.98440i | −0.812486 | + | 0.230898i | ||||
\(467\) | − | 16.4557i | − | 0.761477i | −0.924683 | − | 0.380739i | \(-0.875670\pi\) | ||
0.924683 | − | 0.380739i | \(-0.124330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.03553i | 0.232519i | ||||||||
\(470\) | −13.8965 | − | 48.8990i | −0.640996 | − | 2.25554i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.9761 | − | 24.0613i | 1.01153 | − | 1.10751i | ||||
\(473\) | − | 22.9584i | − | 1.05563i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.9242 | −0.638886 | ||||||||
\(476\) | 7.05516 | − | 4.36228i | 0.323373 | − | 0.199945i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.60647 | + | 33.8033i | 0.439390 | + | 1.54613i | ||||
\(479\) | 27.7577 | 1.26828 | 0.634141 | − | 0.773218i | \(-0.281354\pi\) | ||||
0.634141 | + | 0.773218i | \(0.281354\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.7351 | 0.808651 | ||||||||
\(482\) | −8.04453 | − | 28.3072i | −0.366418 | − | 1.28936i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 32.4354 | − | 20.0552i | 1.47434 | − | 0.911598i | ||||
\(485\) | 44.1722 | 2.00576 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.5490i | − | 0.795221i | −0.917554 | − | 0.397611i | \(-0.869839\pi\) | ||
0.917554 | − | 0.397611i | \(-0.130161\pi\) | |||||||
\(488\) | 12.8833 | − | 14.1058i | 0.583201 | − | 0.638539i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.20617 | + | 4.24428i | 0.0544891 | + | 0.191737i | ||||
\(491\) | 11.6865i | 0.527406i | 0.964604 | + | 0.263703i | \(0.0849439\pi\) | ||||
−0.964604 | + | 0.263703i | \(0.915056\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.2557i | 1.27257i | ||||||||
\(494\) | −6.63408 | + | 1.88532i | −0.298482 | + | 0.0848246i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.72106 | + | 2.85767i | 0.256883 | + | 0.128313i | ||||
\(497\) | − | 15.2213i | − | 0.682769i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8124 | 0.573562 | 0.286781 | − | 0.957996i | \(-0.407415\pi\) | ||||
0.286781 | + | 0.957996i | \(0.407415\pi\) | |||||||
\(500\) | 1.40987 | − | 0.871738i | 0.0630513 | − | 0.0389853i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.4500 | + | 7.80094i | −1.22515 | + | 0.348173i | ||||
\(503\) | −24.4646 | −1.09082 | −0.545410 | − | 0.838169i | \(-0.683626\pi\) | ||||
−0.545410 | + | 0.838169i | \(0.683626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.1312 | 1.87481 | ||||||||
\(506\) | −2.89606 | + | 0.823023i | −0.128746 | + | 0.0365879i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.67242 | − | 5.93944i | −0.162937 | − | 0.263520i | ||||
\(509\) | −13.8535 | −0.614046 | −0.307023 | − | 0.951702i | \(-0.599333\pi\) | ||||
−0.307023 | + | 0.951702i | \(0.599333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.4687i | − | 0.728530i | ||||||
\(512\) | −13.6867 | + | 18.0187i | −0.604874 | + | 0.796321i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.3290 | − | 6.91399i | 1.07311 | − | 0.304963i | ||||
\(515\) | 31.8304i | 1.40261i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.1749i | 2.77843i | ||||||||
\(518\) | −4.13491 | − | 14.5500i | −0.181677 | − | 0.639288i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.86802 | + | 10.8044i | −0.432741 | + | 0.473803i | ||||
\(521\) | − | 11.9375i | − | 0.522990i | −0.965205 | − | 0.261495i | \(-0.915785\pi\) | ||
0.965205 | − | 0.261495i | \(-0.0842155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.4656 | −0.632535 | −0.316267 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(524\) | 9.74156 | + | 15.7551i | 0.425562 | + | 0.688266i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.974768 | − | 3.43002i | −0.0425019 | − | 0.149556i | ||||
\(527\) | −6.63077 | −0.288841 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8493 | −0.993446 | ||||||||
\(530\) | −8.98934 | − | 31.6318i | −0.390472 | − | 1.37400i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.09345 | + | 5.00307i | 0.134118 | + | 0.216911i | ||||
\(533\) | 7.35805 | 0.318713 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.8293i | 0.943764i | ||||||||
\(536\) | 10.5164 | + | 9.60506i | 0.454241 | + | 0.414875i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.96909 | − | 17.4853i | −0.214233 | − | 0.753844i | ||||
\(539\) | − | 5.48338i | − | 0.236186i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.4119i | − | 0.963563i | −0.876292 | − | 0.481781i | \(-0.839990\pi\) | ||
0.876292 | − | 0.481781i | \(-0.160010\pi\) | |||||||
\(542\) | −37.7828 | + | 10.7374i | −1.62291 | + | 0.461210i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.34702 | − | 23.0552i | 0.186377 | − | 0.988483i | ||||
\(545\) | − | 20.4043i | − | 0.874025i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.7026 | −1.52653 | −0.763266 | − | 0.646084i | \(-0.776406\pi\) | ||||
−0.763266 | + | 0.646084i | \(0.776406\pi\) | |||||||
\(548\) | 3.86560 | + | 6.25187i | 0.165130 | + | 0.267067i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 35.3150 | − | 10.0361i | 1.50584 | − | 0.427939i | ||||
\(551\) | −20.0371 | −0.853610 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.01684 | −0.0857646 | ||||||||
\(554\) | 31.8240 | − | 9.04398i | 1.35207 | − | 0.384242i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.697879 | + | 0.431506i | −0.0295967 | + | 0.0182999i | ||||
\(557\) | 6.50159 | 0.275481 | 0.137741 | − | 0.990468i | \(-0.456016\pi\) | ||||
0.137741 | + | 0.990468i | \(0.456016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.94248i | − | 0.293636i | ||||||
\(560\) | 11.1647 | + | 5.57675i | 0.471793 | + | 0.235661i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 39.5879 | − | 11.2504i | 1.66991 | − | 0.474568i | ||||
\(563\) | 10.2444i | 0.431750i | 0.976421 | + | 0.215875i | \(0.0692603\pi\) | ||||
−0.976421 | + | 0.215875i | \(0.930740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41.9157i | 1.76341i | ||||||||
\(566\) | 0.160749 | + | 0.565643i | 0.00675676 | + | 0.0237758i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.7889 | − | 29.0340i | −1.33383 | − | 1.21824i | ||||
\(569\) | 8.12955i | 0.340808i | 0.985374 | + | 0.170404i | \(0.0545073\pi\) | ||||
−0.985374 | + | 0.170404i | \(0.945493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4322 | 0.520273 | 0.260136 | − | 0.965572i | \(-0.416232\pi\) | ||||
0.260136 | + | 0.965572i | \(0.416232\pi\) | |||||||
\(572\) | 15.4667 | − | 9.56322i | 0.646695 | − | 0.399858i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.71552 | − | 6.03658i | −0.0716043 | − | 0.251962i | ||||
\(575\) | −1.83811 | −0.0766544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.73519 | −0.363651 | −0.181825 | − | 0.983331i | \(-0.558201\pi\) | ||||
−0.181825 | + | 0.983331i | \(0.558201\pi\) | |||||||
\(578\) | 0.0777762 | + | 0.273680i | 0.00323506 | + | 0.0113836i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −36.1583 | + | 22.3570i | −1.50139 | + | 0.928325i | ||||
\(581\) | 6.21127 | 0.257687 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.8665i | 1.69252i | ||||||||
\(584\) | −34.3939 | − | 31.4132i | −1.42323 | − | 1.29989i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.45862 | − | 19.2078i | −0.225493 | − | 0.793468i | ||||
\(587\) | − | 1.73075i | − | 0.0714356i | −0.999362 | − | 0.0357178i | \(-0.988628\pi\) | ||
0.999362 | − | 0.0357178i | \(-0.0113718\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.70212i | − | 0.193748i | ||||||
\(590\) | −48.8990 | + | 13.8965i | −2.01314 | + | 0.572108i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −38.2740 | − | 19.1179i | −1.57305 | − | 0.785739i | ||||
\(593\) | 44.7702i | 1.83849i | 0.393683 | + | 0.919246i | \(0.371201\pi\) | ||||
−0.393683 | + | 0.919246i | \(0.628799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.9400 | −0.530486 | ||||||||
\(596\) | 5.01229 | − | 3.09915i | 0.205311 | − | 0.126946i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.875753 | + | 0.248878i | −0.0358122 | + | 0.0101774i | ||||
\(599\) | 30.6963 | 1.25422 | 0.627109 | − | 0.778932i | \(-0.284238\pi\) | ||||
0.627109 | + | 0.778932i | \(0.284238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2391 | 0.947942 | 0.473971 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473971 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(602\) | −5.69564 | + | 1.61863i | −0.232137 | + | 0.0659704i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.77570 | − | 6.10649i | −0.153631 | − | 0.248469i | ||||
\(605\) | −59.4902 | −2.41862 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.7110i | − | 1.08417i | −0.840325 | − | 0.542084i | \(-0.817636\pi\) | ||
0.840325 | − | 0.542084i | \(-0.182364\pi\) | |||||||
\(608\) | 16.3493 | + | 3.08263i | 0.663051 | + | 0.125017i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.6667 | + | 8.14669i | −1.16068 | + | 0.329850i | ||||
\(611\) | 19.1037i | 0.772855i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.9292i | − | 1.00688i | −0.864030 | − | 0.503440i | \(-0.832067\pi\) | ||
0.864030 | − | 0.503440i | \(-0.167933\pi\) | |||||||
\(614\) | −13.0928 | − | 46.0710i | −0.528381 | − | 1.85927i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.4517 | − | 10.4593i | −0.461404 | − | 0.421417i | ||||
\(617\) | − | 4.95198i | − | 0.199359i | −0.995020 | − | 0.0996796i | \(-0.968218\pi\) | ||
0.995020 | − | 0.0996796i | \(-0.0317818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.0773 | 1.89220 | 0.946099 | − | 0.323879i | \(-0.104987\pi\) | ||||
0.946099 | + | 0.323879i | \(0.104987\pi\) | |||||||
\(620\) | −5.24654 | − | 8.48528i | −0.210706 | − | 0.340777i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.03692 | − | 24.7616i | −0.282155 | − | 0.992848i | ||||
\(623\) | −5.93308 | −0.237704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.2576 | −1.05031 | ||||||||
\(626\) | 2.40426 | + | 8.46014i | 0.0960936 | + | 0.338135i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.6231 | + | 28.5020i | 0.703238 | + | 1.13735i | ||||
\(629\) | 44.3599 | 1.76875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.73191i | − | 0.387421i | −0.981059 | − | 0.193711i | \(-0.937948\pi\) | ||
0.981059 | − | 0.193711i | \(-0.0620523\pi\) | |||||||
\(632\) | −3.84703 | + | 4.21206i | −0.153027 | + | 0.167547i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.65975 | + | 30.4720i | 0.343923 | + | 1.21020i | ||||
\(635\) | 10.8936i | 0.432300i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.65814i | − | 0.0656980i | ||||||
\(638\) | 50.8188 | − | 14.4420i | 2.01194 | − | 0.571766i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32.9428 | − | 12.6794i | 1.30218 | − | 0.501197i | ||||
\(641\) | − | 43.9546i | − | 1.73610i | −0.496474 | − | 0.868051i | \(-0.665372\pi\) | ||
0.496474 | − | 0.868051i | \(-0.334628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6029 | −1.20686 | −0.603429 | − | 0.797416i | \(-0.706199\pi\) | ||||
−0.603429 | + | 0.797416i | \(0.706199\pi\) | |||||||
\(644\) | 0.408361 | + | 0.660446i | 0.0160917 | + | 0.0260252i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.5935 | + | 4.71566i | −0.652863 | + | 0.185535i | ||||
\(647\) | −19.5958 | −0.770391 | −0.385195 | − | 0.922835i | \(-0.625866\pi\) | ||||
−0.385195 | + | 0.922835i | \(0.625866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 63.1749 | 2.47983 | ||||||||
\(650\) | 10.6791 | − | 3.03485i | 0.418867 | − | 0.119037i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.8485 | − | 12.2725i | 0.777328 | − | 0.480630i | ||||
\(653\) | −7.43907 | −0.291113 | −0.145557 | − | 0.989350i | \(-0.546497\pi\) | ||||
−0.145557 | + | 0.989350i | \(0.546497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 28.8967i | − | 1.12909i | ||||||
\(656\) | −15.8793 | − | 7.93173i | −0.619984 | − | 0.309682i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.6728 | − | 4.45400i | 0.610989 | − | 0.173635i | ||||
\(659\) | 28.4918i | 1.10988i | 0.831889 | + | 0.554942i | \(0.187260\pi\) | ||||
−0.831889 | + | 0.554942i | \(0.812740\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 7.08125i | − | 0.275429i | −0.990472 | − | 0.137714i | \(-0.956024\pi\) | ||
0.990472 | − | 0.137714i | \(-0.0439756\pi\) | |||||||
\(662\) | −8.54746 | − | 30.0769i | −0.332207 | − | 1.16897i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.8477 | − | 12.9719i | 0.459781 | − | 0.503407i | ||||
\(665\) | − | 9.17620i | − | 0.355838i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.64506 | −0.102417 | ||||||||
\(668\) | −29.2264 | + | 18.0710i | −1.13080 | + | 0.699187i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.07370 | − | 21.3722i | −0.234648 | − | 0.825680i | ||||
\(671\) | 37.0358 | 1.42975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7718 | −0.762145 | −0.381073 | − | 0.924545i | \(-0.624445\pi\) | ||||
−0.381073 | + | 0.924545i | \(0.624445\pi\) | |||||||
\(674\) | 7.42237 | + | 26.1179i | 0.285899 | + | 1.00602i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.4371 | + | 10.7816i | −0.670659 | + | 0.414676i | ||||
\(677\) | 19.0768 | 0.733183 | 0.366591 | − | 0.930382i | \(-0.380525\pi\) | ||||
0.366591 | + | 0.930382i | \(0.380525\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1578i | 0.543326i | ||||||||
\(680\) | −24.6824 | + | 27.0244i | −0.946527 | + | 1.03634i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.38912 | + | 11.9257i | 0.129776 | + | 0.456658i | ||||
\(683\) | 10.5466i | 0.403555i | 0.979431 | + | 0.201778i | \(0.0646718\pi\) | ||||
−0.979431 | + | 0.201778i | \(0.935328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.4666i | − | 0.438117i | ||||||
\(686\) | −1.36035 | + | 0.386593i | −0.0519383 | + | 0.0147602i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.48377 | + | 14.9825i | −0.285316 | + | 0.571203i | ||||
\(689\) | 12.3578i | 0.470796i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2552 | 1.11292 | 0.556461 | − | 0.830874i | \(-0.312159\pi\) | ||||
0.556461 | + | 0.830874i | \(0.312159\pi\) | |||||||
\(692\) | 32.0781 | − | 19.8342i | 1.21943 | − | 0.753984i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.62755 | + | 1.31509i | −0.175660 | + | 0.0499202i | ||||
\(695\) | 1.27999 | 0.0485527 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.4043 | 0.697114 | ||||||||
\(698\) | −1.18623 | + | 0.337111i | −0.0448994 | + | 0.0127598i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.97961 | − | 8.05357i | −0.188212 | − | 0.304396i | ||||
\(701\) | −13.5828 | −0.513016 | −0.256508 | − | 0.966542i | \(-0.582572\pi\) | ||||
−0.256508 | + | 0.966542i | \(0.582572\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.4572i | 1.18643i | ||||||||
\(704\) | −43.6874 | + | 3.96571i | −1.64653 | + | 0.149463i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.66908 | − | 2.46364i | 0.326265 | − | 0.0927203i | ||||
\(707\) | 13.5036i | 0.507856i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.52460i | 0.245036i | 0.992466 | + | 0.122518i | \(0.0390970\pi\) | ||||
−0.992466 | + | 0.122518i | \(0.960903\pi\) | |||||||
\(710\) | 18.3594 | + | 64.6034i | 0.689018 | + | 2.42452i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.3171 | + | 12.3909i | −0.424126 | + | 0.464369i | ||||
\(713\) | − | 0.620719i | − | 0.0232461i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.3677 | −1.06089 | ||||||||
\(716\) | 10.9783 | + | 17.7554i | 0.410279 | + | 0.663549i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.37929 | + | 8.37225i | 0.0887942 | + | 0.312450i | ||||
\(719\) | 1.06415 | 0.0396860 | 0.0198430 | − | 0.999803i | \(-0.493683\pi\) | ||||
0.0198430 | + | 0.999803i | \(0.493683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2021 | −0.379945 | ||||||||
\(722\) | 4.00122 | + | 14.0795i | 0.148910 | + | 0.523986i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.487860 | − | 0.789021i | −0.0181312 | − | 0.0293237i | ||||
\(725\) | 32.2543 | 1.19789 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.07254i | 0.0397781i | 0.999802 | + | 0.0198891i | \(0.00633130\pi\) | ||||
−0.999802 | + | 0.0198891i | \(0.993669\pi\) | |||||||
\(728\) | −3.46295 | − | 3.16284i | −0.128345 | − | 0.117222i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.8640 | + | 69.8975i | 0.735198 | + | 2.58702i | ||||
\(731\) | − | 17.3649i | − | 0.642264i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.5340i | − | 0.462952i | −0.972841 | − | 0.231476i | \(-0.925644\pi\) | ||
0.972841 | − | 0.231476i | \(-0.0743555\pi\) | |||||||
\(734\) | 19.2379 | − | 5.46716i | 0.710084 | − | 0.201797i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.15824 | + | 0.406932i | 0.0795537 | + | 0.0149997i | ||||
\(737\) | 27.6117i | 1.01709i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3506 | 0.417537 | 0.208768 | − | 0.977965i | \(-0.433055\pi\) | ||||
0.208768 | + | 0.977965i | \(0.433055\pi\) | |||||||
\(740\) | 35.0994 | + | 56.7666i | 1.29028 | + | 2.08678i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.1384 | − | 2.88121i | 0.372193 | − | 0.105772i | ||||
\(743\) | 34.5495 | 1.26750 | 0.633750 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.19311 | −0.336809 | ||||||||
\(746\) | 42.0289 | − | 11.9441i | 1.53879 | − | 0.437304i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 38.6861 | − | 23.9200i | 1.41450 | − | 0.874602i | ||||
\(749\) | −6.99660 | −0.255650 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.8163i | − | 1.63537i | −0.575667 | − | 0.817684i | \(-0.695257\pi\) | ||
0.575667 | − | 0.817684i | \(-0.304743\pi\) | |||||||
\(752\) | 20.5932 | − | 41.2276i | 0.750957 | − | 1.50342i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.3673 | − | 4.36720i | 0.559645 | − | 0.159044i | ||||
\(755\) | 11.2000i | 0.407609i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9597i | 0.434683i | 0.976096 | + | 0.217342i | \(0.0697386\pi\) | ||||
−0.976096 | + | 0.217342i | \(0.930261\pi\) | |||||||
\(758\) | 10.5713 | + | 37.1982i | 0.383965 | + | 1.35110i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.1640 | − | 17.5032i | −0.695151 | − | 0.634907i | ||||
\(761\) | 35.3858i | 1.28273i | 0.767234 | + | 0.641367i | \(0.221632\pi\) | ||||
−0.767234 | + | 0.641367i | \(0.778368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.53986 | 0.236759 | ||||||||
\(764\) | 5.85884 | − | 3.62258i | 0.211965 | − | 0.131060i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.33584 | − | 11.7382i | −0.120529 | − | 0.424117i | ||||
\(767\) | 19.1037 | 0.689796 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.89574 | −0.320789 | −0.160394 | − | 0.987053i | \(-0.551277\pi\) | ||||
−0.160394 | + | 0.987053i | \(0.551277\pi\) | |||||||
\(770\) | 6.61387 | + | 23.2730i | 0.238348 | + | 0.838699i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.4271 | − | 11.3936i | 0.663204 | − | 0.410066i | ||||
\(773\) | −1.97112 | −0.0708962 | −0.0354481 | − | 0.999372i | \(-0.511286\pi\) | ||||
−0.0354481 | + | 0.999372i | \(0.511286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.56913i | 0.271891i | ||||||||
\(776\) | 29.5678 | + | 27.0054i | 1.06142 | + | 0.969436i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.74875 | − | 9.67232i | −0.0985474 | − | 0.346770i | ||||
\(779\) | 13.0512i | 0.467607i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 83.4641i | − | 2.98658i | ||||||
\(782\) | −2.19048 | + | 0.622506i | −0.0783313 | + | 0.0222608i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.78742 | + | 3.57842i | −0.0638365 | + | 0.127801i | ||||
\(785\) | − | 52.2759i | − | 1.86581i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.69609 | −0.0604590 | −0.0302295 | − | 0.999543i | \(-0.509624\pi\) | ||||
−0.0302295 | + | 0.999543i | \(0.509624\pi\) | |||||||
\(788\) | −6.15862 | + | 3.80794i | −0.219392 | + | 0.135652i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.56001 | − | 2.43264i | 0.304552 | − | 0.0865496i | ||||
\(791\) | −13.4345 | −0.477677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1994 | 0.397703 | ||||||||
\(794\) | 19.1370 | − | 5.43848i | 0.679146 | − | 0.193004i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.4395 | + | 39.5263i | 0.866237 | + | 1.40097i | ||||
\(797\) | 22.4897 | 0.796628 | 0.398314 | − | 0.917249i | \(-0.369596\pi\) | ||||
0.398314 | + | 0.917249i | \(0.369596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.7832i | 1.69045i | ||||||||
\(800\) | −26.3178 | − | 4.96219i | −0.930476 | − | 0.175440i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.05795 | + | 2.28997i | −0.284536 | + | 0.0808615i | ||||
\(803\) | − | 90.3038i | − | 3.18675i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.21133i | − | 0.0426939i | ||||||
\(806\) | 1.02485 | + | 3.60626i | 0.0360989 | + | 0.127025i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.2016 | + | 25.7575i | 0.992128 | + | 0.906147i | ||||
\(809\) | 36.3829i | 1.27915i | 0.768727 | + | 0.639577i | \(0.220890\pi\) | ||||
−0.768727 | + | 0.639577i | \(0.779110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.67771 | −0.234486 | −0.117243 | − | 0.993103i | \(-0.537406\pi\) | ||||
−0.117243 | + | 0.993103i | \(0.537406\pi\) | |||||||
\(812\) | −7.16573 | − | 11.5892i | −0.251468 | − | 0.406702i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.6733 | − | 79.7829i | −0.794697 | − | 2.79639i | ||||
\(815\) | −36.4044 | −1.27519 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3141 | 0.430815 | ||||||||
\(818\) | 9.14221 | + | 32.1697i | 0.319650 | + | 1.12479i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.5623 | + | 23.5517i | 0.508536 | + | 0.822461i | ||||
\(821\) | −20.3477 | −0.710139 | −0.355070 | − | 0.934840i | \(-0.615543\pi\) | ||||
−0.355070 | + | 0.934840i | \(0.615543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.441780i | 0.0153995i | 0.999970 | + | 0.00769974i | \(0.00245093\pi\) | ||||
−0.999970 | + | 0.00769974i | \(0.997549\pi\) | |||||||
\(824\) | −19.4600 | + | 21.3065i | −0.677921 | + | 0.742246i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.45400 | − | 15.6728i | −0.154975 | − | 0.545326i | ||||
\(827\) | − | 32.9989i | − | 1.14749i | −0.819035 | − | 0.573743i | \(-0.805491\pi\) | ||
0.819035 | − | 0.573743i | \(-0.194509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.2694i | − | 1.19023i | −0.803642 | − | 0.595113i | \(-0.797107\pi\) | ||
0.803642 | − | 0.595113i | \(-0.202893\pi\) | |||||||
\(830\) | −26.3623 | + | 7.49183i | −0.915050 | + | 0.260045i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.2108 | + | 1.19921i | −0.458003 | + | 0.0415751i | ||||
\(833\) | − | 4.14743i | − | 0.143700i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53.6045 | 1.85506 | ||||||||
\(836\) | 16.9626 | + | 27.4337i | 0.586662 | + | 0.948815i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.7173 | + | 9.29785i | −1.13020 | + | 0.321189i | ||||
\(839\) | −54.5494 | −1.88325 | −0.941626 | − | 0.336660i | \(-0.890703\pi\) | ||||
−0.941626 | + | 0.336660i | \(0.890703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.4144 | 0.600497 | ||||||||
\(842\) | −23.4986 | + | 6.67800i | −0.809815 | + | 0.230139i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.89022 | + | 6.11522i | −0.340435 | + | 0.210495i | ||||
\(845\) | 31.9817 | 1.10020 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.0674i | − | 0.655164i | ||||||
\(848\) | 13.3213 | − | 26.6693i | 0.457456 | − | 0.915828i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.7110 | − | 7.59092i | 0.916180 | − | 0.260366i | ||||
\(851\) | 4.15261i | 0.142350i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37.3044i | − | 1.27728i | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||
0.769506 | − | 0.638639i | \(-0.220502\pi\) | |||||||
\(854\) | −2.61113 | − | 9.18805i | −0.0893509 | − | 0.314409i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.3457 | + | 14.6120i | −0.456147 | + | 0.499429i | ||||
\(857\) | 27.8499i | 0.951333i | 0.879626 | + | 0.475667i | \(0.157793\pi\) | ||||
−0.879626 | + | 0.475667i | \(0.842207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.7277 | −1.59433 | −0.797164 | − | 0.603763i | \(-0.793667\pi\) | ||||
−0.797164 | + | 0.603763i | \(0.793667\pi\) | |||||||
\(860\) | 22.2215 | − | 13.7398i | 0.757748 | − | 0.468523i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.95545 | − | 13.9185i | −0.134723 | − | 0.474065i | ||||
\(863\) | −21.6286 | −0.736247 | −0.368123 | − | 0.929777i | \(-0.620000\pi\) | ||||
−0.368123 | + | 0.929777i | \(0.620000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.8348 | −2.00044 | ||||||||
\(866\) | 4.07205 | + | 14.3288i | 0.138374 | + | 0.486912i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.71965 | − | 1.68159i | 0.0923108 | − | 0.0570768i | ||||
\(869\) | −11.0591 | −0.375153 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.34964i | 0.282917i | ||||||||
\(872\) | 12.4745 | − | 13.6582i | 0.422440 | − | 0.462524i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.441442 | − | 1.55335i | −0.0149320 | − | 0.0525428i | ||||
\(875\) | − | 0.828803i | − | 0.0280187i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7567i | 0.768438i | 0.923242 | + | 0.384219i | \(0.125529\pi\) | ||||
−0.923242 | + | 0.384219i | \(0.874471\pi\) | |||||||
\(878\) | −23.5537 | + | 6.69365i | −0.794898 | + | 0.225900i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 61.2200 | + | 30.5794i | 2.06373 | + | 1.03083i | ||||
\(881\) | 18.6695i | 0.628992i | 0.949259 | + | 0.314496i | \(0.101835\pi\) | ||||
−0.949259 | + | 0.314496i | \(0.898165\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.60315 | 0.222214 | 0.111107 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111107 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(884\) | 11.6985 | − | 7.23328i | 0.393462 | − | 0.243282i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.21655 | − | 1.19829i | 0.141658 | − | 0.0402574i | ||||
\(887\) | 24.9136 | 0.836515 | 0.418258 | − | 0.908328i | \(-0.362641\pi\) | ||||
0.418258 | + | 0.908328i | \(0.362641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.49155 | −0.117103 | ||||||||
\(890\) | 25.1816 | − | 7.15629i | 0.844090 | − | 0.239879i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.1065 | + | 16.3453i | 0.338390 | + | 0.547282i | ||||
\(893\) | −33.8848 | −1.13391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.5653i | − | 1.08854i | ||||||
\(896\) | 4.06392 | + | 10.5586i | 0.135766 | + | 0.352739i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.88742 | − | 1.95731i | 0.229836 | − | 0.0653164i | ||||
\(899\) | 10.8921i | 0.363272i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.9100i | 1.02976i | ||||||||
\(902\) | −9.40683 | − | 33.1008i | −0.313213 | − | 1.10214i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.6258 | + | 28.0573i | −0.852301 | + | 0.933173i | ||||
\(905\) | 1.44715i | 0.0481050i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.0223 | 1.12969 | 0.564847 | − | 0.825196i | \(-0.308935\pi\) | ||||
0.564847 | + | 0.825196i | \(0.308935\pi\) | |||||||
\(908\) | −13.6660 | − | 22.1021i | −0.453521 | − | 0.733485i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.00000 | + | 7.03762i | 0.0662994 | + | 0.233295i | ||||
\(911\) | −20.9906 | −0.695449 | −0.347725 | − | 0.937597i | \(-0.613046\pi\) | ||||
−0.347725 | + | 0.937597i | \(0.613046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.0587 | 1.12718 | ||||||||
\(914\) | 13.7811 | + | 48.4930i | 0.455838 | + | 1.60401i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.55392 | + | 2.51316i | 0.0513428 | + | 0.0830373i | ||||
\(917\) | 9.26178 | 0.305851 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0942i | 1.85038i | 0.379507 | + | 0.925189i | \(0.376094\pi\) | ||||
−0.379507 | + | 0.925189i | \(0.623906\pi\) | |||||||
\(920\) | −2.52980 | − | 2.31056i | −0.0834052 | − | 0.0761770i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.93954 | + | 20.9001i | 0.195608 | + | 0.688308i | ||||
\(923\) | − | 25.2391i | − | 0.830755i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 50.6376i | − | 1.66495i | ||||||
\(926\) | 25.8723 | − | 7.35259i | 0.850218 | − | 0.241621i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37.8718 | − | 7.14066i | −1.24320 | − | 0.234404i | ||||
\(929\) | − | 21.7754i | − | 0.714427i | −0.934023 | − | 0.357213i | \(-0.883727\pi\) | ||
0.934023 | − | 0.357213i | \(-0.116273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.94109 | 0.0963905 | ||||||||
\(932\) | 13.5610 | + | 21.9324i | 0.444207 | + | 0.718420i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.3854 | + | 6.36165i | −0.732473 | + | 0.208159i | ||||
\(935\) | −70.9547 | −2.32047 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.58652 | −0.247841 | −0.123920 | − | 0.992292i | \(-0.539547\pi\) | ||||
−0.123920 | + | 0.992292i | \(0.539547\pi\) | |||||||
\(938\) | 6.85008 | − | 1.94670i | 0.223663 | − | 0.0635621i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −61.1474 | + | 37.8080i | −1.99441 | + | 1.23316i | ||||
\(941\) | −17.7633 | −0.579065 | −0.289533 | − | 0.957168i | \(-0.593500\pi\) | ||||
−0.289533 | + | 0.957168i | \(0.593500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.72286i | 0.0561041i | ||||||||
\(944\) | −41.2276 | − | 20.5932i | −1.34184 | − | 0.670252i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.2313 | + | 8.87555i | −1.01542 | + | 0.288569i | ||||
\(947\) | − | 12.7864i | − | 0.415501i | −0.978182 | − | 0.207751i | \(-0.933386\pi\) | ||
0.978182 | − | 0.207751i | \(-0.0666143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 27.3074i | − | 0.886435i | ||||||
\(950\) | 5.38300 | + | 18.9417i | 0.174648 | + | 0.614551i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.66169 | − | 7.91104i | −0.280727 | − | 0.256398i | ||||
\(953\) | 13.9943i | 0.453319i | 0.973974 | + | 0.226659i | \(0.0727804\pi\) | ||||
−0.973974 | + | 0.226659i | \(0.927220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7458 | −0.347725 | ||||||||
\(956\) | 42.2705 | − | 26.1363i | 1.36712 | − | 0.845308i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.7309 | − | 37.7601i | −0.346701 | − | 1.21997i | ||||
\(959\) | 3.67521 | 0.118679 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4439 | 0.917547 | ||||||||
\(962\) | −6.85627 | − | 24.1259i | −0.221055 | − | 0.777850i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −35.3976 | + | 21.8867i | −1.14008 | + | 0.704924i | ||||
\(965\) | −33.7973 | −1.08797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.1180i | − | 1.61169i | −0.592129 | − | 0.805843i | \(-0.701712\pi\) | ||
0.592129 | − | 0.805843i | \(-0.298288\pi\) | |||||||
\(968\) | −39.8213 | − | 36.3703i | −1.27990 | − | 1.16898i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.0767 | − | 60.0896i | −0.548299 | − | 1.92936i | ||||
\(971\) | − | 12.0972i | − | 0.388217i | −0.980980 | − | 0.194108i | \(-0.937819\pi\) | ||
0.980980 | − | 0.194108i | \(-0.0621813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.410254i | 0.0131521i | ||||||||
\(974\) | −23.8727 | + | 6.78433i | −0.764932 | + | 0.217384i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.1694 | − | 12.0726i | −0.773643 | − | 0.386435i | ||||
\(977\) | 6.37204i | 0.203860i | 0.994792 | + | 0.101930i | \(0.0325017\pi\) | ||||
−0.994792 | + | 0.101930i | \(0.967498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.5333 | −1.03977 | ||||||||
\(980\) | 5.30739 | − | 3.28162i | 0.169538 | − | 0.104827i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.8977 | − | 4.51794i | 0.507318 | − | 0.144173i | ||||
\(983\) | 0.298981 | 0.00953601 | 0.00476801 | − | 0.999989i | \(-0.498482\pi\) | ||||
0.00476801 | + | 0.999989i | \(0.498482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.2956 | 0.359908 | ||||||||
\(986\) | 38.4375 | − | 10.9235i | 1.22410 | − | 0.347874i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.12939 | + | 8.29581i | 0.163187 | + | 0.263925i | ||||
\(989\) | 1.62556 | 0.0516898 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.43504i | − | 0.109118i | −0.998511 | − | 0.0545588i | \(-0.982625\pi\) | ||
0.998511 | − | 0.0545588i | \(-0.0173752\pi\) | |||||||
\(992\) | 1.67570 | − | 8.88739i | 0.0532036 | − | 0.282175i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.7063 | + | 5.88445i | −0.656763 | + | 0.186643i | ||||
\(995\) | − | 72.4958i | − | 2.29827i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.9672i | 1.48747i | 0.668477 | + | 0.743733i | \(0.266946\pi\) | ||||
−0.668477 | + | 0.743733i | \(0.733054\pi\) | |||||||
\(998\) | −4.95319 | − | 17.4293i | −0.156790 | − | 0.551716i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.j.a.323.9 | ✓ | 24 | |
3.2 | odd | 2 | inner | 504.2.j.a.323.16 | yes | 24 | |
4.3 | odd | 2 | 2016.2.j.a.1583.22 | 24 | |||
8.3 | odd | 2 | inner | 504.2.j.a.323.15 | yes | 24 | |
8.5 | even | 2 | 2016.2.j.a.1583.4 | 24 | |||
12.11 | even | 2 | 2016.2.j.a.1583.3 | 24 | |||
24.5 | odd | 2 | 2016.2.j.a.1583.21 | 24 | |||
24.11 | even | 2 | inner | 504.2.j.a.323.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.j.a.323.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
504.2.j.a.323.10 | yes | 24 | 24.11 | even | 2 | inner | |
504.2.j.a.323.15 | yes | 24 | 8.3 | odd | 2 | inner | |
504.2.j.a.323.16 | yes | 24 | 3.2 | odd | 2 | inner | |
2016.2.j.a.1583.3 | 24 | 12.11 | even | 2 | |||
2016.2.j.a.1583.4 | 24 | 8.5 | even | 2 | |||
2016.2.j.a.1583.21 | 24 | 24.5 | odd | 2 | |||
2016.2.j.a.1583.22 | 24 | 4.3 | odd | 2 |