Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,6,Mod(19,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("90.19");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.c (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: | \(14.4345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.19 |
Dual form | 90.6.c.b.19.2 |
$q$-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 \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 55.0000 | − | 10.0000i | 0.983870 | − | 0.178885i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 0.0308542i | −0.999881 | − | 0.0154271i | \(-0.995089\pi\) | ||
0.999881 | − | 0.0154271i | \(-0.00491080\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −40.0000 | − | 220.000i | −0.126491 | − | 0.695701i | ||||
\(11\) | 500.000 | 1.24591 | 0.622957 | − | 0.782256i | \(-0.285931\pi\) | ||||
0.622957 | + | 0.782256i | \(0.285931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 288.000i | 0.472644i | 0.971675 | + | 0.236322i | \(0.0759420\pi\) | ||||
−0.971675 | + | 0.236322i | \(0.924058\pi\) | |||||||
\(14\) | −16.0000 | −0.0218172 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − | 1516.00i | − | 1.27226i | −0.771581 | − | 0.636132i | \(-0.780534\pi\) | ||
0.771581 | − | 0.636132i | \(-0.219466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1344.00 | 0.854113 | 0.427056 | − | 0.904225i | \(-0.359551\pi\) | ||||
0.427056 | + | 0.904225i | \(0.359551\pi\) | |||||||
\(20\) | −880.000 | + | 160.000i | −0.491935 | + | 0.0894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2000.00i | − | 0.880995i | ||||||
\(23\) | − | 4100.00i | − | 1.61609i | −0.589124 | − | 0.808043i | \(-0.700527\pi\) | ||
0.589124 | − | 0.808043i | \(-0.299473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2925.00 | − | 1100.00i | 0.936000 | − | 0.352000i | ||||
\(26\) | 1152.00 | 0.334210 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 64.0000i | 0.0154271i | ||||||||
\(29\) | −2646.00 | −0.584245 | −0.292122 | − | 0.956381i | \(-0.594361\pi\) | ||||
−0.292122 | + | 0.956381i | \(0.594361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5612.00 | −1.04885 | −0.524425 | − | 0.851457i | \(-0.675720\pi\) | ||||
−0.524425 | + | 0.851457i | \(0.675720\pi\) | |||||||
\(32\) | − | 1024.00i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6064.00 | −0.899626 | ||||||||
\(35\) | −40.0000 | − | 220.000i | −0.00551937 | − | 0.0303566i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7288.00i | − | 0.875193i | −0.899171 | − | 0.437597i | \(-0.855830\pi\) | ||
0.899171 | − | 0.437597i | \(-0.144170\pi\) | |||||||
\(38\) | − | 5376.00i | − | 0.603949i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 640.000 | + | 3520.00i | 0.0632456 | + | 0.347851i | ||||
\(41\) | 18986.0 | 1.76390 | 0.881950 | − | 0.471343i | \(-0.156231\pi\) | ||||
0.881950 | + | 0.471343i | \(0.156231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2404.00i | 0.198273i | 0.995074 | + | 0.0991364i | \(0.0316080\pi\) | ||||
−0.995074 | + | 0.0991364i | \(0.968392\pi\) | |||||||
\(44\) | −8000.00 | −0.622957 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16400.0 | −1.14274 | ||||||||
\(47\) | − | 8900.00i | − | 0.587686i | −0.955854 | − | 0.293843i | \(-0.905066\pi\) | ||
0.955854 | − | 0.293843i | \(-0.0949343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16791.0 | 0.999048 | ||||||||
\(50\) | −4400.00 | − | 11700.0i | −0.248902 | − | 0.661852i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4608.00i | − | 0.236322i | ||||||
\(53\) | 39804.0i | 1.94642i | 0.229913 | + | 0.973211i | \(0.426156\pi\) | ||||
−0.229913 | + | 0.973211i | \(0.573844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27500.0 | − | 5000.00i | 1.22582 | − | 0.222876i | ||||
\(56\) | 256.000 | 0.0109086 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10584.0i | 0.413123i | ||||||||
\(59\) | −28300.0 | −1.05842 | −0.529208 | − | 0.848492i | \(-0.677511\pi\) | ||||
−0.529208 | + | 0.848492i | \(0.677511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18290.0 | 0.629345 | 0.314673 | − | 0.949200i | \(-0.398105\pi\) | ||||
0.314673 | + | 0.949200i | \(0.398105\pi\) | |||||||
\(62\) | 22448.0i | 0.741649i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 2880.00 | + | 15840.0i | 0.0845491 | + | 0.465020i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65956.0i | 1.79501i | 0.441002 | + | 0.897506i | \(0.354623\pi\) | ||||
−0.441002 | + | 0.897506i | \(0.645377\pi\) | |||||||
\(68\) | 24256.0i | 0.636132i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −880.000 | + | 160.000i | −0.0214653 | + | 0.00390279i | ||||
\(71\) | 28800.0 | 0.678026 | 0.339013 | − | 0.940782i | \(-0.389907\pi\) | ||||
0.339013 | + | 0.940782i | \(0.389907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30808.0i | 0.676638i | 0.941031 | + | 0.338319i | \(0.109858\pi\) | ||||
−0.941031 | + | 0.338319i | \(0.890142\pi\) | |||||||
\(74\) | −29152.0 | −0.618855 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21504.0 | −0.427056 | ||||||||
\(77\) | − | 2000.00i | − | 0.0384418i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −60228.0 | −1.08575 | −0.542876 | − | 0.839813i | \(-0.682665\pi\) | ||||
−0.542876 | + | 0.839813i | \(0.682665\pi\) | |||||||
\(80\) | 14080.0 | − | 2560.00i | 0.245967 | − | 0.0447214i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 75944.0i | − | 1.24727i | ||||||
\(83\) | − | 2468.00i | − | 0.0393233i | −0.999807 | − | 0.0196616i | \(-0.993741\pi\) | ||
0.999807 | − | 0.0196616i | \(-0.00625890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15160.0 | − | 83380.0i | −0.227589 | − | 1.25174i | ||||
\(86\) | 9616.00 | 0.140200 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 32000.0i | 0.440497i | ||||||||
\(89\) | 22678.0 | 0.303480 | 0.151740 | − | 0.988420i | \(-0.451512\pi\) | ||||
0.151740 | + | 0.988420i | \(0.451512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1152.00 | 0.0145831 | ||||||||
\(92\) | 65600.0i | 0.808043i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −35600.0 | −0.415557 | ||||||||
\(95\) | 73920.0 | − | 13440.0i | 0.840336 | − | 0.152788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 36968.0i | − | 0.398930i | −0.979905 | − | 0.199465i | \(-0.936080\pi\) | ||
0.979905 | − | 0.199465i | \(-0.0639204\pi\) | |||||||
\(98\) | − | 67164.0i | − | 0.706434i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −46800.0 | + | 17600.0i | −0.468000 | + | 0.176000i | ||||
\(101\) | −167918. | −1.63792 | −0.818962 | − | 0.573848i | \(-0.805450\pi\) | ||||
−0.818962 | + | 0.573848i | \(0.805450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 154364.i | 1.43368i | 0.697236 | + | 0.716841i | \(0.254413\pi\) | ||||
−0.697236 | + | 0.716841i | \(0.745587\pi\) | |||||||
\(104\) | −18432.0 | −0.167105 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 159216. | 1.37633 | ||||||||
\(107\) | − | 136788.i | − | 1.15502i | −0.816385 | − | 0.577509i | \(-0.804025\pi\) | ||
0.816385 | − | 0.577509i | \(-0.195975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53810.0 | 0.433807 | 0.216904 | − | 0.976193i | \(-0.430404\pi\) | ||||
0.216904 | + | 0.976193i | \(0.430404\pi\) | |||||||
\(110\) | −20000.0 | − | 110000.i | −0.157597 | − | 0.866784i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1024.00i | − | 0.00771356i | ||||||
\(113\) | 82692.0i | 0.609211i | 0.952479 | + | 0.304605i | \(0.0985245\pi\) | ||||
−0.952479 | + | 0.304605i | \(0.901475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −41000.0 | − | 225500.i | −0.289094 | − | 1.59002i | ||||
\(116\) | 42336.0 | 0.292122 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 113200.i | 0.748413i | ||||||||
\(119\) | −6064.00 | −0.0392547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88949.0 | 0.552303 | ||||||||
\(122\) | − | 73160.0i | − | 0.445014i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 89792.0 | 0.524425 | ||||||||
\(125\) | 149875. | − | 89750.0i | 0.857935 | − | 0.513759i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 211780.i | − | 1.16513i | −0.812783 | − | 0.582567i | \(-0.802048\pi\) | ||
0.812783 | − | 0.582567i | \(-0.197952\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 63360.0 | − | 11520.0i | 0.328819 | − | 0.0597853i | ||||
\(131\) | −169500. | −0.862962 | −0.431481 | − | 0.902122i | \(-0.642009\pi\) | ||||
−0.431481 | + | 0.902122i | \(0.642009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5376.00i | − | 0.0263530i | ||||||
\(134\) | 263824. | 1.26927 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 97024.0 | 0.449813 | ||||||||
\(137\) | − | 252036.i | − | 1.14726i | −0.819115 | − | 0.573629i | \(-0.805535\pi\) | ||
0.819115 | − | 0.573629i | \(-0.194465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −192016. | −0.842947 | −0.421474 | − | 0.906841i | \(-0.638487\pi\) | ||||
−0.421474 | + | 0.906841i | \(0.638487\pi\) | |||||||
\(140\) | 640.000 | + | 3520.00i | 0.00275969 | + | 0.0151783i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 115200.i | − | 0.479437i | ||||||
\(143\) | 144000.i | 0.588874i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −145530. | + | 26460.0i | −0.574821 | + | 0.104513i | ||||
\(146\) | 123232. | 0.478455 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 116608.i | 0.437597i | ||||||||
\(149\) | 235694. | 0.869727 | 0.434863 | − | 0.900496i | \(-0.356797\pi\) | ||||
0.434863 | + | 0.900496i | \(0.356797\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −371492. | −1.32589 | −0.662944 | − | 0.748669i | \(-0.730693\pi\) | ||||
−0.662944 | + | 0.748669i | \(0.730693\pi\) | |||||||
\(152\) | 86016.0i | 0.301975i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8000.00 | −0.0271824 | ||||||||
\(155\) | −308660. | + | 56120.0i | −1.03193 | + | 0.187624i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 264952.i | 0.857863i | 0.903337 | + | 0.428932i | \(0.141110\pi\) | ||||
−0.903337 | + | 0.428932i | \(0.858890\pi\) | |||||||
\(158\) | 240912.i | 0.767743i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10240.0 | − | 56320.0i | −0.0316228 | − | 0.173925i | ||||
\(161\) | −16400.0 | −0.0498631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 403124.i | 1.18842i | 0.804310 | + | 0.594210i | \(0.202535\pi\) | ||||
−0.804310 | + | 0.594210i | \(0.797465\pi\) | |||||||
\(164\) | −303776. | −0.881950 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9872.00 | −0.0278058 | ||||||||
\(167\) | 261900.i | 0.726682i | 0.931656 | + | 0.363341i | \(0.118364\pi\) | ||||
−0.931656 | + | 0.363341i | \(0.881636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 288349. | 0.776608 | ||||||||
\(170\) | −333520. | + | 60640.0i | −0.885115 | + | 0.160930i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 38464.0i | − | 0.0991364i | ||||||
\(173\) | 326228.i | 0.828716i | 0.910114 | + | 0.414358i | \(0.135994\pi\) | ||||
−0.910114 | + | 0.414358i | \(0.864006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4400.00 | − | 11700.0i | −0.0108607 | − | 0.0288796i | ||||
\(176\) | 128000. | 0.311479 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 90712.0i | − | 0.214593i | ||||||
\(179\) | −109516. | −0.255473 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −53146.0 | −0.120580 | −0.0602898 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602898 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(182\) | − | 4608.00i | − | 0.0103118i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 262400. | 0.571372 | ||||||||
\(185\) | −72880.0 | − | 400840.i | −0.156559 | − | 0.861076i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 758000.i | − | 1.58513i | ||||||
\(188\) | 142400.i | 0.293843i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −53760.0 | − | 295680.i | −0.108038 | − | 0.594207i | ||||
\(191\) | −232056. | −0.460267 | −0.230133 | − | 0.973159i | \(-0.573916\pi\) | ||||
−0.230133 | + | 0.973159i | \(0.573916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03067e6i | 1.99172i | 0.0909274 | + | 0.995858i | \(0.471017\pi\) | ||||
−0.0909274 | + | 0.995858i | \(0.528983\pi\) | |||||||
\(194\) | −147872. | −0.282086 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −268656. | −0.499524 | ||||||||
\(197\) | 522796.i | 0.959769i | 0.877332 | + | 0.479884i | \(0.159321\pi\) | ||||
−0.877332 | + | 0.479884i | \(0.840679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 215292. | 0.385385 | 0.192693 | − | 0.981259i | \(-0.438278\pi\) | ||||
0.192693 | + | 0.981259i | \(0.438278\pi\) | |||||||
\(200\) | 70400.0 | + | 187200.i | 0.124451 | + | 0.330926i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 671672.i | 1.15819i | ||||||||
\(203\) | 10584.0i | 0.0180264i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04423e6 | − | 189860.i | 1.73545 | − | 0.315536i | ||||
\(206\) | 617456. | 1.01377 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 73728.0i | 0.118161i | ||||||||
\(209\) | 672000. | 1.06415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.03008e6 | −1.59281 | −0.796407 | − | 0.604762i | \(-0.793268\pi\) | ||||
−0.796407 | + | 0.604762i | \(0.793268\pi\) | |||||||
\(212\) | − | 636864.i | − | 0.973211i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −547152. | −0.816721 | ||||||||
\(215\) | 24040.0 | + | 132220.i | 0.0354681 | + | 0.195075i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22448.0i | 0.0323615i | ||||||||
\(218\) | − | 215240.i | − | 0.306748i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −440000. | + | 80000.0i | −0.612909 | + | 0.111438i | ||||
\(221\) | 436608. | 0.601327 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 456020.i | − | 0.614075i | −0.951697 | − | 0.307038i | \(-0.900662\pi\) | ||
0.951697 | − | 0.307038i | \(-0.0993378\pi\) | |||||||
\(224\) | −4096.00 | −0.00545431 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 330768. | 0.430777 | ||||||||
\(227\) | 434252.i | 0.559342i | 0.960096 | + | 0.279671i | \(0.0902253\pi\) | ||||
−0.960096 | + | 0.279671i | \(0.909775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 722710. | 0.910700 | 0.455350 | − | 0.890313i | \(-0.349514\pi\) | ||||
0.455350 | + | 0.890313i | \(0.349514\pi\) | |||||||
\(230\) | −902000. | + | 164000.i | −1.12431 | + | 0.204420i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 169344.i | − | 0.206562i | ||||||
\(233\) | − | 565348.i | − | 0.682223i | −0.940023 | − | 0.341111i | \(-0.889197\pi\) | ||
0.940023 | − | 0.341111i | \(-0.110803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −89000.0 | − | 489500.i | −0.105128 | − | 0.578207i | ||||
\(236\) | 452800. | 0.529208 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24256.0i | 0.0277573i | ||||||||
\(239\) | 324904. | 0.367926 | 0.183963 | − | 0.982933i | \(-0.441107\pi\) | ||||
0.183963 | + | 0.982933i | \(0.441107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 915262. | 1.01509 | 0.507543 | − | 0.861626i | \(-0.330554\pi\) | ||||
0.507543 | + | 0.861626i | \(0.330554\pi\) | |||||||
\(242\) | − | 355796.i | − | 0.390537i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −292640. | −0.314673 | ||||||||
\(245\) | 923505. | − | 167910.i | 0.982933 | − | 0.178715i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 387072.i | 0.403691i | ||||||||
\(248\) | − | 359168.i | − | 0.370825i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −359000. | − | 599500.i | −0.363282 | − | 0.606651i | ||||
\(251\) | −1.36708e6 | −1.36965 | −0.684823 | − | 0.728709i | \(-0.740121\pi\) | ||||
−0.684823 | + | 0.728709i | \(0.740121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.05000e6i | − | 2.01350i | ||||||
\(254\) | −847120. | −0.823874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − | 892932.i | − | 0.843307i | −0.906757 | − | 0.421653i | \(-0.861450\pi\) | ||
0.906757 | − | 0.421653i | \(-0.138550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29152.0 | −0.0270034 | ||||||||
\(260\) | −46080.0 | − | 253440.i | −0.0422746 | − | 0.232510i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 678000.i | 0.610206i | ||||||||
\(263\) | − | 1.86650e6i | − | 1.66394i | −0.554818 | − | 0.831972i | \(-0.687212\pi\) | ||
0.554818 | − | 0.831972i | \(-0.312788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 398040. | + | 2.18922e6i | 0.348187 | + | 1.91503i | ||||
\(266\) | −21504.0 | −0.0186344 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 1.05530e6i | − | 0.897506i | ||||||
\(269\) | −1.37227e6 | −1.15627 | −0.578133 | − | 0.815943i | \(-0.696218\pi\) | ||||
−0.578133 | + | 0.815943i | \(0.696218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 458644. | 0.379361 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(272\) | − | 388096.i | − | 0.318066i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.00814e6 | −0.811234 | ||||||||
\(275\) | 1.46250e6 | − | 550000.i | 1.16618 | − | 0.438562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 985408.i | − | 0.771643i | −0.922573 | − | 0.385822i | \(-0.873918\pi\) | ||
0.922573 | − | 0.385822i | \(-0.126082\pi\) | |||||||
\(278\) | 768064.i | 0.596054i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14080.0 | − | 2560.00i | 0.0107327 | − | 0.00195139i | ||||
\(281\) | −165798. | −0.125260 | −0.0626302 | − | 0.998037i | \(-0.519949\pi\) | ||||
−0.0626302 | + | 0.998037i | \(0.519949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.66471e6i | 1.23558i | 0.786342 | + | 0.617792i | \(0.211972\pi\) | ||||
−0.786342 | + | 0.617792i | \(0.788028\pi\) | |||||||
\(284\) | −460800. | −0.339013 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 576000. | 0.416397 | ||||||||
\(287\) | − | 75944.0i | − | 0.0544238i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −878399. | −0.618653 | ||||||||
\(290\) | 105840. | + | 582120.i | 0.0739018 | + | 0.406460i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 492928.i | − | 0.338319i | ||||||
\(293\) | 2.55104e6i | 1.73600i | 0.496567 | + | 0.867998i | \(0.334594\pi\) | ||||
−0.496567 | + | 0.867998i | \(0.665406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.55650e6 | + | 283000.i | −1.04134 | + | 0.189335i | ||||
\(296\) | 466432. | 0.309428 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 942776.i | − | 0.614990i | ||||||
\(299\) | 1.18080e6 | 0.763833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9616.00 | 0.00611756 | ||||||||
\(302\) | 1.48597e6i | 0.937545i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 344064. | 0.213528 | ||||||||
\(305\) | 1.00595e6 | − | 182900.i | 0.619194 | − | 0.112581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 736020.i | 0.445701i | 0.974853 | + | 0.222851i | \(0.0715362\pi\) | ||||
−0.974853 | + | 0.222851i | \(0.928464\pi\) | |||||||
\(308\) | 32000.0i | 0.0192209i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 224480. | + | 1.23464e6i | 0.132670 | + | 0.729686i | ||||
\(311\) | −1.71660e6 | −1.00639 | −0.503197 | − | 0.864172i | \(-0.667843\pi\) | ||||
−0.503197 | + | 0.864172i | \(0.667843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.83851e6i | − | 1.63768i | −0.574020 | − | 0.818842i | \(-0.694617\pi\) | ||
0.574020 | − | 0.818842i | \(-0.305383\pi\) | |||||||
\(314\) | 1.05981e6 | 0.606601 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 963648. | 0.542876 | ||||||||
\(317\) | 1.27605e6i | 0.713215i | 0.934254 | + | 0.356607i | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356607i | \(0.883933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.32300e6 | −0.727919 | ||||||||
\(320\) | −225280. | + | 40960.0i | −0.122984 | + | 0.0223607i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 65600.0i | 0.0352585i | ||||||||
\(323\) | − | 2.03750e6i | − | 1.08666i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 316800. | + | 842400.i | 0.166371 | + | 0.442395i | ||||
\(326\) | 1.61250e6 | 0.840339 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.21510e6i | 0.623633i | ||||||||
\(329\) | −35600.0 | −0.0181326 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 443992. | 0.222744 | 0.111372 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(332\) | 39488.0i | 0.0196616i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.04760e6 | 0.513842 | ||||||||
\(335\) | 659560. | + | 3.62758e6i | 0.321101 | + | 1.76606i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.71326e6i | 1.30142i | 0.759328 | + | 0.650708i | \(0.225528\pi\) | ||||
−0.759328 | + | 0.650708i | \(0.774472\pi\) | |||||||
\(338\) | − | 1.15340e6i | − | 0.549145i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 242560. | + | 1.33408e6i | 0.113795 | + | 0.625871i | ||||
\(341\) | −2.80600e6 | −1.30678 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 134392.i | − | 0.0616791i | ||||||
\(344\) | −153856. | −0.0701001 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.30491e6 | 0.585991 | ||||||||
\(347\) | 1.31051e6i | 0.584273i | 0.956377 | + | 0.292137i | \(0.0943662\pi\) | ||||
−0.956377 | + | 0.292137i | \(0.905634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 298910. | 0.131364 | 0.0656821 | − | 0.997841i | \(-0.479078\pi\) | ||||
0.0656821 | + | 0.997841i | \(0.479078\pi\) | |||||||
\(350\) | −46800.0 | + | 17600.0i | −0.0204209 | + | 0.00767967i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 512000.i | − | 0.220249i | ||||||
\(353\) | 737996.i | 0.315223i | 0.987501 | + | 0.157611i | \(0.0503793\pi\) | ||||
−0.987501 | + | 0.157611i | \(0.949621\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.58400e6 | − | 288000.i | 0.667090 | − | 0.121289i | ||||
\(356\) | −362848. | −0.151740 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 438064.i | 0.180647i | ||||||||
\(359\) | −2.34074e6 | −0.958557 | −0.479278 | − | 0.877663i | \(-0.659102\pi\) | ||||
−0.479278 | + | 0.877663i | \(0.659102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −669763. | −0.270491 | ||||||||
\(362\) | 212584.i | 0.0852627i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18432.0 | −0.00729154 | ||||||||
\(365\) | 308080. | + | 1.69444e6i | 0.121041 | + | 0.665724i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 127292.i | 0.0493328i | 0.999696 | + | 0.0246664i | \(0.00785236\pi\) | ||||
−0.999696 | + | 0.0246664i | \(0.992148\pi\) | |||||||
\(368\) | − | 1.04960e6i | − | 0.404021i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.60336e6 | + | 291520.i | −0.608873 | + | 0.110704i | ||||
\(371\) | 159216. | 0.0600554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.03870e6i | − | 1.50303i | −0.659713 | − | 0.751517i | \(-0.729322\pi\) | ||
0.659713 | − | 0.751517i | \(-0.270678\pi\) | |||||||
\(374\) | −3.03200e6 | −1.12086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 569600. | 0.207778 | ||||||||
\(377\) | − | 762048.i | − | 0.276140i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.01214e6 | −0.361944 | −0.180972 | − | 0.983488i | \(-0.557924\pi\) | ||||
−0.180972 | + | 0.983488i | \(0.557924\pi\) | |||||||
\(380\) | −1.18272e6 | + | 215040.i | −0.420168 | + | 0.0763942i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 928224.i | 0.325458i | ||||||||
\(383\) | − | 2.37610e6i | − | 0.827690i | −0.910347 | − | 0.413845i | \(-0.864186\pi\) | ||
0.910347 | − | 0.413845i | \(-0.135814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20000.0 | − | 110000.i | −0.00687667 | − | 0.0378217i | ||||
\(386\) | 4.12269e6 | 1.40836 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 591488.i | 0.199465i | ||||||||
\(389\) | 1.42497e6 | 0.477456 | 0.238728 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238728 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.21560e6 | −2.05609 | ||||||||
\(392\) | 1.07462e6i | 0.353217i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.09118e6 | 0.678659 | ||||||||
\(395\) | −3.31254e6 | + | 602280.i | −1.06824 | + | 0.194225i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.69345e6i | 0.539257i | 0.962964 | + | 0.269628i | \(0.0869009\pi\) | ||||
−0.962964 | + | 0.269628i | \(0.913099\pi\) | |||||||
\(398\) | − | 861168.i | − | 0.272509i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 748800. | − | 281600.i | 0.234000 | − | 0.0880000i | ||||
\(401\) | 2.84501e6 | 0.883532 | 0.441766 | − | 0.897130i | \(-0.354352\pi\) | ||||
0.441766 | + | 0.897130i | \(0.354352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.61626e6i | − | 0.495733i | ||||||
\(404\) | 2.68669e6 | 0.818962 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 42336.0 | 0.0127466 | ||||||||
\(407\) | − | 3.64400e6i | − | 1.09042i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.89069e6 | 0.558873 | 0.279436 | − | 0.960164i | \(-0.409852\pi\) | ||||
0.279436 | + | 0.960164i | \(0.409852\pi\) | |||||||
\(410\) | −759440. | − | 4.17692e6i | −0.223118 | − | 1.22715i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.46982e6i | − | 0.716841i | ||||||
\(413\) | 113200.i | 0.0326566i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24680.0 | − | 135740.i | −0.00703437 | − | 0.0386890i | ||||
\(416\) | 294912. | 0.0835524 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 2.68800e6i | − | 0.752469i | ||||||
\(419\) | 4.60930e6 | 1.28263 | 0.641313 | − | 0.767280i | \(-0.278390\pi\) | ||||
0.641313 | + | 0.767280i | \(0.278390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04151e6 | −1.66127 | −0.830635 | − | 0.556817i | \(-0.812022\pi\) | ||||
−0.830635 | + | 0.556817i | \(0.812022\pi\) | |||||||
\(422\) | 4.12032e6i | 1.12629i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.54746e6 | −0.688164 | ||||||||
\(425\) | −1.66760e6 | − | 4.43430e6i | −0.447837 | − | 1.19084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 73160.0i | − | 0.0194180i | ||||||
\(428\) | 2.18861e6i | 0.577509i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 528880. | − | 96160.0i | 0.137939 | − | 0.0250798i | ||||
\(431\) | 3800.00 | 0.000985350 | 0.000492675 | − | 1.00000i | \(-0.499843\pi\) | ||||
0.000492675 | 1.00000i | \(0.499843\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 250736.i | − | 0.0642683i | −0.999484 | − | 0.0321342i | \(-0.989770\pi\) | ||
0.999484 | − | 0.0321342i | \(-0.0102304\pi\) | |||||||
\(434\) | 89792.0 | 0.0228830 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −860960. | −0.216904 | ||||||||
\(437\) | − | 5.51040e6i | − | 1.38032i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.58873e6 | 0.888750 | 0.444375 | − | 0.895841i | \(-0.353426\pi\) | ||||
0.444375 | + | 0.895841i | \(0.353426\pi\) | |||||||
\(440\) | 320000. | + | 1.76000e6i | 0.0787986 | + | 0.433392i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.74643e6i | − | 0.425203i | ||||||
\(443\) | − | 1.41479e6i | − | 0.342517i | −0.985226 | − | 0.171258i | \(-0.945217\pi\) | ||
0.985226 | − | 0.171258i | \(-0.0547833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.24729e6 | − | 226780.i | 0.298585 | − | 0.0542881i | ||||
\(446\) | −1.82408e6 | −0.434217 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16384.0i | 0.00385678i | ||||||||
\(449\) | −829806. | −0.194250 | −0.0971249 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971249 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.49300e6 | 2.19767 | ||||||||
\(452\) | − | 1.32307e6i | − | 0.304605i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.73701e6 | 0.395514 | ||||||||
\(455\) | 63360.0 | − | 11520.0i | 0.0143478 | − | 0.00260870i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.68198e6i | 1.04867i | 0.851512 | + | 0.524335i | \(0.175686\pi\) | ||||
−0.851512 | + | 0.524335i | \(0.824314\pi\) | |||||||
\(458\) | − | 2.89084e6i | − | 0.643962i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 656000. | + | 3.60800e6i | 0.144547 | + | 0.795009i | ||||
\(461\) | 141930. | 0.0311044 | 0.0155522 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155522 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 727476.i | − | 0.157713i | −0.996886 | − | 0.0788563i | \(-0.974873\pi\) | ||
0.996886 | − | 0.0788563i | \(-0.0251268\pi\) | |||||||
\(464\) | −677376. | −0.146061 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.26139e6 | −0.482404 | ||||||||
\(467\) | 4.47640e6i | 0.949809i | 0.880037 | + | 0.474905i | \(0.157517\pi\) | ||||
−0.880037 | + | 0.474905i | \(0.842483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 263824. | 0.0553837 | ||||||||
\(470\) | −1.95800e6 | + | 356000.i | −0.408854 | + | 0.0743371i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 1.81120e6i | − | 0.374207i | ||||||
\(473\) | 1.20200e6i | 0.247031i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.93120e6 | − | 1.47840e6i | 0.799450 | − | 0.300648i | ||||
\(476\) | 97024.0 | 0.0196274 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 1.29962e6i | − | 0.260163i | ||||||
\(479\) | −1.32718e6 | −0.264297 | −0.132149 | − | 0.991230i | \(-0.542188\pi\) | ||||
−0.132149 | + | 0.991230i | \(0.542188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.09894e6 | 0.413655 | ||||||||
\(482\) | − | 3.66105e6i | − | 0.717774i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.42318e6 | −0.276152 | ||||||||
\(485\) | −369680. | − | 2.03324e6i | −0.0713628 | − | 0.392495i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.11647e6i | − | 0.786507i | −0.919430 | − | 0.393253i | \(-0.871350\pi\) | ||
0.919430 | − | 0.393253i | \(-0.128650\pi\) | |||||||
\(488\) | 1.17056e6i | 0.222507i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −671640. | − | 3.69402e6i | −0.126371 | − | 0.695039i | ||||
\(491\) | 6.12316e6 | 1.14623 | 0.573115 | − | 0.819475i | \(-0.305735\pi\) | ||||
0.573115 | + | 0.819475i | \(0.305735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.01134e6i | 0.743313i | ||||||||
\(494\) | 1.54829e6 | 0.285453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.43667e6 | −0.262213 | ||||||||
\(497\) | − | 115200.i | − | 0.0209200i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.90490e6 | 1.42117 | 0.710584 | − | 0.703613i | \(-0.248431\pi\) | ||||
0.710584 | + | 0.703613i | \(0.248431\pi\) | |||||||
\(500\) | −2.39800e6 | + | 1.43600e6i | −0.428967 | + | 0.256879i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.46830e6i | 0.968486i | ||||||||
\(503\) | 3.97628e6i | 0.700741i | 0.936611 | + | 0.350370i | \(0.113944\pi\) | ||||
−0.936611 | + | 0.350370i | \(0.886056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.23549e6 | + | 1.67918e6i | −1.61150 | + | 0.293001i | ||||
\(506\) | −8.20000e6 | −1.42376 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.38848e6i | 0.582567i | ||||||||
\(509\) | 781914. | 0.133772 | 0.0668859 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668859 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 123232. | 0.0208772 | ||||||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.57173e6 | −0.596308 | ||||||||
\(515\) | 1.54364e6 | + | 8.49002e6i | 0.256465 | + | 1.41056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.45000e6i | − | 0.732207i | ||||||
\(518\) | 116608.i | 0.0190943i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.01376e6 | + | 184320.i | −0.164409 | + | 0.0298926i | ||||
\(521\) | −5.82694e6 | −0.940472 | −0.470236 | − | 0.882541i | \(-0.655831\pi\) | ||||
−0.470236 | + | 0.882541i | \(0.655831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.78938e6i | 1.56495i | 0.622681 | + | 0.782476i | \(0.286043\pi\) | ||||
−0.622681 | + | 0.782476i | \(0.713957\pi\) | |||||||
\(524\) | 2.71200e6 | 0.431481 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.46600e6 | −1.17659 | ||||||||
\(527\) | 8.50779e6i | 1.33441i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.03737e7 | −1.61173 | ||||||||
\(530\) | 8.75688e6 | − | 1.59216e6i | 1.35413 | − | 0.246205i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 86016.0i | 0.0131765i | ||||||||
\(533\) | 5.46797e6i | 0.833696i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.36788e6 | − | 7.52334e6i | −0.206616 | − | 1.13639i | ||||
\(536\) | −4.22118e6 | −0.634633 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.48906e6i | 0.817603i | ||||||||
\(539\) | 8.39550e6 | 1.24473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.76059e6 | 0.699307 | 0.349653 | − | 0.936879i | \(-0.386299\pi\) | ||||
0.349653 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(542\) | − | 1.83458e6i | − | 0.268249i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.55238e6 | −0.224906 | ||||||||
\(545\) | 2.95955e6 | − | 538100.i | 0.426810 | − | 0.0776018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.16595e6i | − | 0.166614i | −0.996524 | − | 0.0833069i | \(-0.973452\pi\) | ||
0.996524 | − | 0.0833069i | \(-0.0265482\pi\) | |||||||
\(548\) | 4.03258e6i | 0.573629i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.20000e6 | − | 5.85000e6i | −0.310110 | − | 0.824611i | ||||
\(551\) | −3.55622e6 | −0.499011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 240912.i | 0.0335001i | ||||||||
\(554\) | −3.94163e6 | −0.545634 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.07226e6 | 0.421474 | ||||||||
\(557\) | 1.61293e6i | 0.220282i | 0.993916 | + | 0.110141i | \(0.0351302\pi\) | ||||
−0.993916 | + | 0.110141i | \(0.964870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −692352. | −0.0937125 | ||||||||
\(560\) | −10240.0 | − | 56320.0i | −0.00137984 | − | 0.00758914i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 663192.i | 0.0885724i | ||||||||
\(563\) | 3.40603e6i | 0.452874i | 0.974026 | + | 0.226437i | \(0.0727077\pi\) | ||||
−0.974026 | + | 0.226437i | \(0.927292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 826920. | + | 4.54806e6i | 0.108979 | + | 0.599384i | ||||
\(566\) | 6.65883e6 | 0.873689 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.84320e6i | 0.239719i | ||||||||
\(569\) | −1.44009e7 | −1.86470 | −0.932350 | − | 0.361557i | \(-0.882245\pi\) | ||||
−0.932350 | + | 0.361557i | \(0.882245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74772e6 | 0.609389 | 0.304695 | − | 0.952450i | \(-0.401446\pi\) | ||||
0.304695 | + | 0.952450i | \(0.401446\pi\) | |||||||
\(572\) | − | 2.30400e6i | − | 0.294437i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −303776. | −0.0384834 | ||||||||
\(575\) | −4.51000e6 | − | 1.19925e7i | −0.568862 | − | 1.51266i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.09094e7i | − | 1.36415i | −0.731283 | − | 0.682074i | \(-0.761078\pi\) | ||
0.731283 | − | 0.682074i | \(-0.238922\pi\) | |||||||
\(578\) | 3.51360e6i | 0.437454i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.32848e6 | − | 423360.i | 0.287410 | − | 0.0522564i | ||||
\(581\) | −9872.00 | −0.00121329 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.99020e7i | 2.42508i | ||||||||
\(584\) | −1.97171e6 | −0.239228 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.02042e7 | 1.22754 | ||||||||
\(587\) | − | 8.53223e6i | − | 1.02204i | −0.859569 | − | 0.511019i | \(-0.829268\pi\) | ||
0.859569 | − | 0.511019i | \(-0.170732\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.54253e6 | −0.895836 | ||||||||
\(590\) | 1.13200e6 | + | 6.22600e6i | 0.133880 | + | 0.736341i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.86573e6i | − | 0.218798i | ||||||
\(593\) | − | 4.63182e6i | − | 0.540897i | −0.962734 | − | 0.270449i | \(-0.912828\pi\) | ||
0.962734 | − | 0.270449i | \(-0.0871721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −333520. | + | 60640.0i | −0.0386215 | + | 0.00702210i | ||||
\(596\) | −3.77110e6 | −0.434863 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 4.72320e6i | − | 0.540111i | ||||||
\(599\) | 6.27598e6 | 0.714684 | 0.357342 | − | 0.933974i | \(-0.383683\pi\) | ||||
0.357342 | + | 0.933974i | \(0.383683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.71988e6 | 0.871815 | 0.435907 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435907 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(602\) | − | 38464.0i | − | 0.00432577i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.94387e6 | 0.662944 | ||||||||
\(605\) | 4.89220e6 | − | 889490.i | 0.543395 | − | 0.0987990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.06160e6i | − | 0.667753i | −0.942617 | − | 0.333876i | \(-0.891643\pi\) | ||
0.942617 | − | 0.333876i | \(-0.108357\pi\) | |||||||
\(608\) | − | 1.37626e6i | − | 0.150987i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −731600. | − | 4.02380e6i | −0.0796066 | − | 0.437836i | ||||
\(611\) | 2.56320e6 | 0.277766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66489e6i | 0.393921i | 0.980411 | + | 0.196961i | \(0.0631071\pi\) | ||||
−0.980411 | + | 0.196961i | \(0.936893\pi\) | |||||||
\(614\) | 2.94408e6 | 0.315158 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 128000. | 0.0135912 | ||||||||
\(617\) | 9.32522e6i | 0.986157i | 0.869985 | + | 0.493079i | \(0.164129\pi\) | ||||
−0.869985 | + | 0.493079i | \(0.835871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.40162e6 | 0.776426 | 0.388213 | − | 0.921570i | \(-0.373093\pi\) | ||||
0.388213 | + | 0.921570i | \(0.373093\pi\) | |||||||
\(620\) | 4.93856e6 | − | 897920.i | 0.515966 | − | 0.0938120i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.86640e6i | 0.711628i | ||||||||
\(623\) | − | 90712.0i | − | 0.00936364i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.34562e6 | − | 6.43500e6i | 0.752192 | − | 0.658944i | ||||
\(626\) | −1.13540e7 | −1.15802 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4.23923e6i | − | 0.428932i | ||||||
\(629\) | −1.10486e7 | −1.11348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 160052. | 0.0160025 | 0.00800125 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800125 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(632\) | − | 3.85459e6i | − | 0.383871i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.10421e6 | 0.504319 | ||||||||
\(635\) | −2.11780e6 | − | 1.16479e7i | −0.208425 | − | 1.14634i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.83581e6i | 0.472194i | ||||||||
\(638\) | 5.29200e6i | 0.514717i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 163840. | + | 901120.i | 0.0158114 | + | 0.0869626i | ||||
\(641\) | 1.69565e7 | 1.63002 | 0.815008 | − | 0.579450i | \(-0.196732\pi\) | ||||
0.815008 | + | 0.579450i | \(0.196732\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.10128e7i | − | 1.05044i | −0.850967 | − | 0.525219i | \(-0.823984\pi\) | ||
0.850967 | − | 0.525219i | \(-0.176016\pi\) | |||||||
\(644\) | 262400. | 0.0249315 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.15002e6 | −0.768382 | ||||||||
\(647\) | − | 3.33848e6i | − | 0.313537i | −0.987635 | − | 0.156768i | \(-0.949892\pi\) | ||
0.987635 | − | 0.156768i | \(-0.0501076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.41500e7 | −1.31870 | ||||||||
\(650\) | 3.36960e6 | − | 1.26720e6i | 0.312820 | − | 0.117642i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.44998e6i | − | 0.594210i | ||||||
\(653\) | − | 4.76181e6i | − | 0.437008i | −0.975836 | − | 0.218504i | \(-0.929882\pi\) | ||
0.975836 | − | 0.218504i | \(-0.0701177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.32250e6 | + | 1.69500e6i | −0.849042 | + | 0.154371i | ||||
\(656\) | 4.86042e6 | 0.440975 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 142400.i | 0.0128217i | ||||||||
\(659\) | 798188. | 0.0715965 | 0.0357982 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357982 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54048e7 | −1.37136 | −0.685682 | − | 0.727901i | \(-0.740496\pi\) | ||||
−0.685682 | + | 0.727901i | \(0.740496\pi\) | |||||||
\(662\) | − | 1.77597e6i | − | 0.157503i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 157952. | 0.0139029 | ||||||||
\(665\) | −53760.0 | − | 295680.i | −0.00471417 | − | 0.0259279i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08486e7i | 0.944189i | ||||||||
\(668\) | − | 4.19040e6i | − | 0.363341i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.45103e7 | − | 2.63824e6i | 1.24879 | − | 0.227053i | ||||
\(671\) | 9.14500e6 | 0.784111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 976704.i | 0.0831238i | 0.999136 | + | 0.0415619i | \(0.0132334\pi\) | ||||
−0.999136 | + | 0.0415619i | \(0.986767\pi\) | |||||||
\(674\) | 1.08530e7 | 0.920240 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.61358e6 | −0.388304 | ||||||||
\(677\) | − | 1.93885e7i | − | 1.62582i | −0.582388 | − | 0.812911i | \(-0.697881\pi\) | ||
0.582388 | − | 0.812911i | \(-0.302119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −147872. | −0.0123087 | ||||||||
\(680\) | 5.33632e6 | − | 970240.i | 0.442557 | − | 0.0804650i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.12240e7i | 0.924031i | ||||||||
\(683\) | − | 5.25573e6i | − | 0.431103i | −0.976492 | − | 0.215552i | \(-0.930845\pi\) | ||
0.976492 | − | 0.215552i | \(-0.0691550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.52036e6 | − | 1.38620e7i | −0.205228 | − | 1.12875i | ||||
\(686\) | −537568. | −0.0436137 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 615424.i | 0.0495682i | ||||||||
\(689\) | −1.14636e7 | −0.919965 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.45034e6 | −0.434238 | −0.217119 | − | 0.976145i | \(-0.569666\pi\) | ||||
−0.217119 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(692\) | − | 5.21965e6i | − | 0.414358i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.24203e6 | 0.413144 | ||||||||
\(695\) | −1.05609e7 | + | 1.92016e6i | −0.829350 | + | 0.150791i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.87828e7i | − | 2.24414i | ||||||
\(698\) | − | 1.19564e6i | − | 0.0928885i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 70400.0 | + | 187200.i | 0.00543035 | + | 0.0144398i | ||||
\(701\) | 4.43961e6 | 0.341232 | 0.170616 | − | 0.985338i | \(-0.445424\pi\) | ||||
0.170616 | + | 0.985338i | \(0.445424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.79507e6i | − | 0.747514i | ||||||
\(704\) | −2.04800e6 | −0.155739 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.95198e6 | 0.222896 | ||||||||
\(707\) | 671672.i | 0.0505369i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.55918e6 | −0.340621 | −0.170310 | − | 0.985390i | \(-0.554477\pi\) | ||||
−0.170310 | + | 0.985390i | \(0.554477\pi\) | |||||||
\(710\) | −1.15200e6 | − | 6.33600e6i | −0.0857643 | − | 0.471704i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.45139e6i | 0.107296i | ||||||||
\(713\) | 2.30092e7i | 1.69503i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.44000e6 | + | 7.92000e6i | 0.105341 | + | 0.579375i | ||||
\(716\) | 1.75226e6 | 0.127736 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.36298e6i | 0.677802i | ||||||||
\(719\) | −2.06630e7 | −1.49063 | −0.745317 | − | 0.666710i | \(-0.767702\pi\) | ||||
−0.745317 | + | 0.666710i | \(0.767702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 617456. | 0.0442352 | ||||||||
\(722\) | 2.67905e6i | 0.191266i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 850336. | 0.0602898 | ||||||||
\(725\) | −7.73955e6 | + | 2.91060e6i | −0.546853 | + | 0.205654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.48161e6i | 0.384656i | 0.981331 | + | 0.192328i | \(0.0616037\pi\) | ||||
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(728\) | 73728.0i | 0.00515589i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.77776e6 | − | 1.23232e6i | 0.470738 | − | 0.0855887i | ||||
\(731\) | 3.64446e6 | 0.252255 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.55579e6i | 0.588166i | 0.955780 | + | 0.294083i | \(0.0950143\pi\) | ||||
−0.955780 | + | 0.294083i | \(0.904986\pi\) | |||||||
\(734\) | 509168. | 0.0348836 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.19840e6 | −0.285686 | ||||||||
\(737\) | 3.29780e7i | 2.23643i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.29119e6 | 0.356404 | 0.178202 | − | 0.983994i | \(-0.442972\pi\) | ||||
0.178202 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(740\) | 1.16608e6 | + | 6.41344e6i | 0.0782797 | + | 0.430538i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 636864.i | − | 0.0424656i | ||||||
\(743\) | − | 2.36432e6i | − | 0.157121i | −0.996909 | − | 0.0785606i | \(-0.974968\pi\) | ||
0.996909 | − | 0.0785606i | \(-0.0250324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.29632e7 | − | 2.35694e6i | 0.855698 | − | 0.155581i | ||||
\(746\) | −1.61548e7 | −1.06281 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.21280e7i | 0.792566i | ||||||||
\(749\) | −547152. | −0.0356372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.79694e6 | −0.569157 | −0.284578 | − | 0.958653i | \(-0.591854\pi\) | ||||
−0.284578 | + | 0.958653i | \(0.591854\pi\) | |||||||
\(752\) | − | 2.27840e6i | − | 0.146922i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.04819e6 | −0.195260 | ||||||||
\(755\) | −2.04321e7 | + | 3.71492e6i | −1.30450 | + | 0.237182i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.95808e7i | 1.87616i | 0.346421 | + | 0.938079i | \(0.387397\pi\) | ||||
−0.346421 | + | 0.938079i | \(0.612603\pi\) | |||||||
\(758\) | 4.04854e6i | 0.255933i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 860160. | + | 4.73088e6i | 0.0540188 | + | 0.297104i | ||||
\(761\) | 1.26296e7 | 0.790549 | 0.395274 | − | 0.918563i | \(-0.370649\pi\) | ||||
0.395274 | + | 0.918563i | \(0.370649\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 215240.i | − | 0.0133848i | ||||||
\(764\) | 3.71290e6 | 0.230133 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.50440e6 | −0.585265 | ||||||||
\(767\) | − | 8.15040e6i | − | 0.500254i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.32186e7 | 1.41586 | 0.707929 | − | 0.706283i | \(-0.249630\pi\) | ||||
0.707929 | + | 0.706283i | \(0.249630\pi\) | |||||||
\(770\) | −440000. | + | 80000.0i | −0.0267440 | + | 0.00486254i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 1.64908e7i | − | 0.995858i | ||||||
\(773\) | − | 1.73201e7i | − | 1.04256i | −0.853386 | − | 0.521280i | \(-0.825455\pi\) | ||
0.853386 | − | 0.521280i | \(-0.174545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64151e7 | + | 6.17320e6i | −0.981724 | + | 0.369195i | ||||
\(776\) | 2.36595e6 | 0.141043 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.69990e6i | − | 0.337612i | ||||||
\(779\) | 2.55172e7 | 1.50657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.44000e7 | 0.844763 | ||||||||
\(782\) | 2.48624e7i | 1.45387i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.29850e6 | 0.249762 | ||||||||
\(785\) | 2.64952e6 | + | 1.45724e7i | 0.153459 | + | 0.844026i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 556676.i | 0.0320380i | 0.999872 | + | 0.0160190i | \(0.00509923\pi\) | ||||
−0.999872 | + | 0.0160190i | \(0.994901\pi\) | |||||||
\(788\) | − | 8.36474e6i | − | 0.479884i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.40912e6 | + | 1.32502e7i | 0.137338 | + | 0.755359i | ||||
\(791\) | 330768. | 0.0187967 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.26752e6i | 0.297456i | ||||||||
\(794\) | 6.77379e6 | 0.381312 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.44467e6 | −0.192693 | ||||||||
\(797\) | − | 3.00562e6i | − | 0.167606i | −0.996482 | − | 0.0838028i | \(-0.973293\pi\) | ||
0.996482 | − | 0.0838028i | \(-0.0267066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.34924e7 | −0.747691 | ||||||||
\(800\) | −1.12640e6 | − | 2.99520e6i | −0.0622254 | − | 0.165463i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.13800e7i | − | 0.624751i | ||||||
\(803\) | 1.54040e7i | 0.843033i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −902000. | + | 164000.i | −0.0490588 | + | 0.00891978i | ||||
\(806\) | −6.46502e6 | −0.350536 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 1.07468e7i | − | 0.579094i | ||||||
\(809\) | 2.23153e6 | 0.119876 | 0.0599378 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599378 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.24862e7 | 1.20051 | 0.600253 | − | 0.799810i | \(-0.295067\pi\) | ||||
0.600253 | + | 0.799810i | \(0.295067\pi\) | |||||||
\(812\) | − | 169344.i | − | 0.00901322i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.45760e7 | −0.771041 | ||||||||
\(815\) | 4.03124e6 | + | 2.21718e7i | 0.212591 | + | 1.16925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.23098e6i | 0.169347i | ||||||||
\(818\) | − | 7.56278e6i | − | 0.395183i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.67077e7 | + | 3.03776e6i | −0.867724 | + | 0.157768i | ||||
\(821\) | 1.65921e7 | 0.859098 | 0.429549 | − | 0.903044i | \(-0.358673\pi\) | ||||
0.429549 | + | 0.903044i | \(0.358673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.47544e7i | − | 0.759316i | −0.925127 | − | 0.379658i | \(-0.876042\pi\) | ||
0.925127 | − | 0.379658i | \(-0.123958\pi\) | |||||||
\(824\) | −9.87930e6 | −0.506883 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 452800. | 0.0230917 | ||||||||
\(827\) | 3.39475e6i | 0.172601i | 0.996269 | + | 0.0863006i | \(0.0275045\pi\) | ||||
−0.996269 | + | 0.0863006i | \(0.972495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 509442. | 0.0257459 | 0.0128730 | − | 0.999917i | \(-0.495902\pi\) | ||||
0.0128730 | + | 0.999917i | \(0.495902\pi\) | |||||||
\(830\) | −542960. | + | 98720.0i | −0.0273573 | + | 0.00497405i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.17965e6i | − | 0.0590805i | ||||||
\(833\) | − | 2.54552e7i | − | 1.27105i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.61900e6 | + | 1.44045e7i | 0.129993 | + | 0.714960i | ||||
\(836\) | −1.07520e7 | −0.532076 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 1.84372e7i | − | 0.906953i | ||||||
\(839\) | 4.00609e7 | 1.96479 | 0.982394 | − | 0.186819i | \(-0.0598178\pi\) | ||||
0.982394 | + | 0.186819i | \(0.0598178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.35098e7 | −0.658658 | ||||||||
\(842\) | 2.41660e7i | 1.17470i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.64813e7 | 0.796407 | ||||||||
\(845\) | 1.58592e7 | − | 2.88349e6i | 0.764081 | − | 0.138924i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 355796.i | − | 0.0170409i | ||||||
\(848\) | 1.01898e7i | 0.486606i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.77372e7 | + | 6.67040e6i | −0.842050 | + | 0.316668i | ||||
\(851\) | −2.98808e7 | −1.41439 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.67506e6i | − | 0.455283i | −0.973745 | − | 0.227641i | \(-0.926899\pi\) | ||
0.973745 | − | 0.227641i | \(-0.0731014\pi\) | |||||||
\(854\) | −292640. | −0.0137306 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.75443e6 | 0.408360 | ||||||||
\(857\) | − | 3.27535e7i | − | 1.52337i | −0.647946 | − | 0.761686i | \(-0.724372\pi\) | ||
0.647946 | − | 0.761686i | \(-0.275628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.17420e7 | 1.00535 | 0.502675 | − | 0.864476i | \(-0.332349\pi\) | ||||
0.502675 | + | 0.864476i | \(0.332349\pi\) | |||||||
\(860\) | −384640. | − | 2.11552e6i | −0.0177341 | − | 0.0975374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 15200.0i | − | 0.000696748i | ||||||
\(863\) | 2.08744e7i | 0.954087i | 0.878880 | + | 0.477043i | \(0.158292\pi\) | ||||
−0.878880 | + | 0.477043i | \(0.841708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.26228e6 | + | 1.79425e7i | 0.148245 | + | 0.815349i | ||||
\(866\) | −1.00294e6 | −0.0454446 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 359168.i | − | 0.0161807i | ||||||
\(869\) | −3.01140e7 | −1.35275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.89953e7 | −0.848401 | ||||||||
\(872\) | 3.44384e6i | 0.153374i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.20416e7 | −0.976033 | ||||||||
\(875\) | −359000. | − | 599500.i | −0.0158516 | − | 0.0264709i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.96804e7i | 1.74212i | 0.491181 | + | 0.871058i | \(0.336566\pi\) | ||||
−0.491181 | + | 0.871058i | \(0.663434\pi\) | |||||||
\(878\) | − | 1.43549e7i | − | 0.628441i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.04000e6 | − | 1.28000e6i | 0.306454 | − | 0.0557190i | ||||
\(881\) | −2.60742e7 | −1.13180 | −0.565902 | − | 0.824472i | \(-0.691472\pi\) | ||||
−0.565902 | + | 0.824472i | \(0.691472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.10486e7i | − | 1.77172i | −0.463949 | − | 0.885862i | \(-0.653568\pi\) | ||
0.463949 | − | 0.885862i | \(-0.346432\pi\) | |||||||
\(884\) | −6.98573e6 | −0.300664 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.65915e6 | −0.242196 | ||||||||
\(887\) | − | 1.37553e7i | − | 0.587031i | −0.955954 | − | 0.293515i | \(-0.905175\pi\) | ||
0.955954 | − | 0.293515i | \(-0.0948252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −847120. | −0.0359493 | ||||||||
\(890\) | −907120. | − | 4.98916e6i | −0.0383875 | − | 0.211131i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.29632e6i | 0.307038i | ||||||||
\(893\) | − | 1.19616e7i | − | 0.501950i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.02338e6 | + | 1.09516e6i | −0.251352 | + | 0.0457004i | ||||
\(896\) | 65536.0 | 0.00272716 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.31922e6i | 0.137355i | ||||||||
\(899\) | 1.48494e7 | 0.612785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.03429e7 | 2.47636 | ||||||||
\(902\) | − | 3.79720e7i | − | 1.55399i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.29229e6 | −0.215388 | ||||||||
\(905\) | −2.92303e6 | + | 531460.i | −0.118635 | + | 0.0215699i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.86936e6i | − | 0.236904i | −0.992960 | − | 0.118452i | \(-0.962207\pi\) | ||
0.992960 | − | 0.118452i | \(-0.0377932\pi\) | |||||||
\(908\) | − | 6.94803e6i | − | 0.279671i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −46080.0 | − | 253440.i | −0.00184463 | − | 0.0101455i | ||||
\(911\) | −4.63982e7 | −1.85227 | −0.926137 | − | 0.377188i | \(-0.876891\pi\) | ||||
−0.926137 | + | 0.377188i | \(0.876891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.23400e6i | − | 0.0489935i | ||||||
\(914\) | 1.87279e7 | 0.741521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.15634e7 | −0.455350 | ||||||||
\(917\) | 678000.i | 0.0266260i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.27859e7 | −0.889975 | −0.444988 | − | 0.895537i | \(-0.646792\pi\) | ||||
−0.444988 | + | 0.895537i | \(0.646792\pi\) | |||||||
\(920\) | 1.44320e7 | − | 2.62400e6i | 0.562156 | − | 0.102210i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 567720.i | − | 0.0219941i | ||||||
\(923\) | 8.29440e6i | 0.320465i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.01680e6 | − | 2.13174e7i | −0.308068 | − | 0.819181i | ||||
\(926\) | −2.90990e6 | −0.111520 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.70950e6i | 0.103281i | ||||||||
\(929\) | 2.70352e7 | 1.02775 | 0.513877 | − | 0.857864i | \(-0.328209\pi\) | ||||
0.513877 | + | 0.857864i | \(0.328209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.25671e7 | 0.853300 | ||||||||
\(932\) | 9.04557e6i | 0.341111i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.79056e7 | 0.671616 | ||||||||
\(935\) | −7.58000e6 | − | 4.16900e7i | −0.283557 | − | 1.55956i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.86149e7i | − | 1.06474i | −0.846512 | − | 0.532370i | \(-0.821301\pi\) | ||
0.846512 | − | 0.532370i | \(-0.178699\pi\) | |||||||
\(938\) | − | 1.05530e6i | − | 0.0391622i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.42400e6 | + | 7.83200e6i | 0.0525642 | + | 0.289103i | ||||
\(941\) | 3.67892e7 | 1.35440 | 0.677200 | − | 0.735799i | \(-0.263193\pi\) | ||||
0.677200 | + | 0.735799i | \(0.263193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.78426e7i | − | 2.85061i | ||||||
\(944\) | −7.24480e6 | −0.264604 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.80800e6 | 0.174677 | ||||||||
\(947\) | − | 7.96828e6i | − | 0.288728i | −0.989525 | − | 0.144364i | \(-0.953886\pi\) | ||
0.989525 | − | 0.144364i | \(-0.0461137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.87270e6 | −0.319809 | ||||||||
\(950\) | −5.91360e6 | − | 1.57248e7i | −0.212590 | − | 0.565296i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 388096.i | − | 0.0138786i | ||||||
\(953\) | − | 4.82202e7i | − | 1.71987i | −0.510400 | − | 0.859937i | \(-0.670503\pi\) | ||
0.510400 | − | 0.859937i | \(-0.329497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.27631e7 | + | 2.32056e6i | −0.452842 | + | 0.0823350i | ||||
\(956\) | −5.19846e6 | −0.183963 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.30874e6i | 0.186886i | ||||||||
\(959\) | −1.00814e6 | −0.0353978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86539e6 | 0.100087 | ||||||||
\(962\) | − | 8.39578e6i | − | 0.292498i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.46442e7 | −0.507543 | ||||||||
\(965\) | 1.03067e7 | + | 5.66870e7i | 0.356289 | + | 1.95959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.83510e7i | 1.66280i | 0.555678 | + | 0.831398i | \(0.312459\pi\) | ||||
−0.555678 | + | 0.831398i | \(0.687541\pi\) | |||||||
\(968\) | 5.69274e6i | 0.195269i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.13296e6 | + | 1.47872e6i | −0.277536 | + | 0.0504611i | ||||
\(971\) | 4.05515e7 | 1.38025 | 0.690127 | − | 0.723688i | \(-0.257555\pi\) | ||||
0.690127 | + | 0.723688i | \(0.257555\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 768064.i | 0.0260085i | ||||||||
\(974\) | −1.64659e7 | −0.556144 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.68224e6 | 0.157336 | ||||||||
\(977\) | 4.34929e7i | 1.45775i | 0.684648 | + | 0.728874i | \(0.259956\pi\) | ||||
−0.684648 | + | 0.728874i | \(0.740044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.13390e7 | 0.378110 | ||||||||
\(980\) | −1.47761e7 | + | 2.68656e6i | −0.491467 | + | 0.0893576i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 2.44926e7i | − | 0.810507i | ||||||
\(983\) | − | 3.34896e6i | − | 0.110542i | −0.998471 | − | 0.0552709i | \(-0.982398\pi\) | ||
0.998471 | − | 0.0552709i | \(-0.0176022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.22796e6 | + | 2.87538e7i | 0.171689 | + | 0.944288i | ||||
\(986\) | 1.60453e7 | 0.525602 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 6.19315e6i | − | 0.201846i | ||||||
\(989\) | 9.85640e6 | 0.320426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.55726e7 | −1.79753 | −0.898766 | − | 0.438429i | \(-0.855535\pi\) | ||||
−0.898766 | + | 0.438429i | \(0.855535\pi\) | |||||||
\(992\) | 5.74669e6i | 0.185412i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −460800. | −0.0147927 | ||||||||
\(995\) | 1.18411e7 | − | 2.15292e6i | 0.379169 | − | 0.0689398i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.27342e7i | − | 0.405726i | −0.979207 | − | 0.202863i | \(-0.934975\pi\) | ||
0.979207 | − | 0.202863i | \(-0.0650247\pi\) | |||||||
\(998\) | − | 3.16196e7i | − | 1.00492i | ||||||
\(999\) | 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 | 90.6.c.b.19.1 | 2 | ||
3.2 | odd | 2 | 30.6.c.a.19.2 | yes | 2 | ||
4.3 | odd | 2 | 720.6.f.g.289.1 | 2 | |||
5.2 | odd | 4 | 450.6.a.s.1.1 | 1 | |||
5.3 | odd | 4 | 450.6.a.f.1.1 | 1 | |||
5.4 | even | 2 | inner | 90.6.c.b.19.2 | 2 | ||
12.11 | even | 2 | 240.6.f.a.49.1 | 2 | |||
15.2 | even | 4 | 150.6.a.f.1.1 | 1 | |||
15.8 | even | 4 | 150.6.a.j.1.1 | 1 | |||
15.14 | odd | 2 | 30.6.c.a.19.1 | ✓ | 2 | ||
20.19 | odd | 2 | 720.6.f.g.289.2 | 2 | |||
60.59 | even | 2 | 240.6.f.a.49.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.a.19.1 | ✓ | 2 | 15.14 | odd | 2 | ||
30.6.c.a.19.2 | yes | 2 | 3.2 | odd | 2 | ||
90.6.c.b.19.1 | 2 | 1.1 | even | 1 | trivial | ||
90.6.c.b.19.2 | 2 | 5.4 | even | 2 | inner | ||
150.6.a.f.1.1 | 1 | 15.2 | even | 4 | |||
150.6.a.j.1.1 | 1 | 15.8 | even | 4 | |||
240.6.f.a.49.1 | 2 | 12.11 | even | 2 | |||
240.6.f.a.49.2 | 2 | 60.59 | even | 2 | |||
450.6.a.f.1.1 | 1 | 5.3 | odd | 4 | |||
450.6.a.s.1.1 | 1 | 5.2 | odd | 4 | |||
720.6.f.g.289.1 | 2 | 4.3 | odd | 2 | |||
720.6.f.g.289.2 | 2 | 20.19 | odd | 2 |