Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3457x^{8} + 2937456x^{4} + 12960000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Root | \(4.70903 - 4.70903i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.6.f.e.143.3 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | + | 2.82843i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 16.0000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 103.048 | + | 103.048i | 0.794866 | + | 0.794866i | 0.982281 | − | 0.187415i | \(-0.0600108\pi\) |
−0.187415 | + | 0.982281i | \(0.560011\pi\) | |||||||
\(8\) | 45.2548 | + | 45.2548i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 744.757i | − | 1.85581i | −0.372820 | − | 0.927904i | \(-0.621609\pi\) | ||
0.372820 | − | 0.927904i | \(-0.378391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −301.835 | + | 301.835i | −0.495349 | + | 0.495349i | −0.909987 | − | 0.414637i | \(-0.863908\pi\) |
0.414637 | + | 0.909987i | \(0.363908\pi\) | |||||||
\(14\) | −582.927 | −0.794866 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | −566.318 | + | 566.318i | −0.475268 | + | 0.475268i | −0.903614 | − | 0.428347i | \(-0.859096\pi\) |
0.428347 | + | 0.903614i | \(0.359096\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 282.904i | 0.179786i | 0.995951 | + | 0.0898929i | \(0.0286525\pi\) | ||||
−0.995951 | + | 0.0898929i | \(0.971348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2106.49 | + | 2106.49i | 0.927904 | + | 0.927904i | ||||
\(23\) | 3525.74 | + | 3525.74i | 1.38973 | + | 1.38973i | 0.825869 | + | 0.563861i | \(0.190685\pi\) |
0.563861 | + | 0.825869i | \(0.309315\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1707.44i | − | 0.495349i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1648.77 | − | 1648.77i | 0.397433 | − | 0.397433i | ||||
\(29\) | 6543.59 | 1.44485 | 0.722423 | − | 0.691452i | \(-0.243029\pi\) | ||||
0.722423 | + | 0.691452i | \(0.243029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6418.84 | −1.19964 | −0.599822 | − | 0.800133i | \(-0.704762\pi\) | ||||
−0.599822 | + | 0.800133i | \(0.704762\pi\) | |||||||
\(32\) | 724.077 | − | 724.077i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3203.58i | − | 0.475268i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7026.43 | − | 7026.43i | −0.843782 | − | 0.843782i | 0.145566 | − | 0.989349i | \(-0.453500\pi\) |
−0.989349 | + | 0.145566i | \(0.953500\pi\) | |||||||
\(38\) | −800.174 | − | 800.174i | −0.0898929 | − | 0.0898929i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4019.24i | − | 0.373409i | −0.982416 | − | 0.186704i | \(-0.940219\pi\) | ||
0.982416 | − | 0.186704i | \(-0.0597806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4303.95 | − | 4303.95i | 0.354974 | − | 0.354974i | −0.506983 | − | 0.861956i | \(-0.669239\pi\) |
0.861956 | + | 0.506983i | \(0.169239\pi\) | |||||||
\(44\) | −11916.1 | −0.927904 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −19944.6 | −1.38973 | ||||||||
\(47\) | 1270.82 | − | 1270.82i | 0.0839153 | − | 0.0839153i | −0.663903 | − | 0.747818i | \(-0.731101\pi\) |
0.747818 | + | 0.663903i | \(0.231101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4430.74i | 0.263624i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4829.36 | + | 4829.36i | 0.247675 | + | 0.247675i | ||||
\(53\) | 452.023 | + | 452.023i | 0.0221040 | + | 0.0221040i | 0.718072 | − | 0.695968i | \(-0.245025\pi\) |
−0.695968 | + | 0.718072i | \(0.745025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9326.83i | 0.397433i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18508.1 | + | 18508.1i | −0.722423 | + | 0.722423i | ||||
\(59\) | 13652.9 | 0.510616 | 0.255308 | − | 0.966860i | \(-0.417823\pi\) | ||||
0.255308 | + | 0.966860i | \(0.417823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27543.3 | 0.947745 | 0.473873 | − | 0.880593i | \(-0.342856\pi\) | ||||
0.473873 | + | 0.880593i | \(0.342856\pi\) | |||||||
\(62\) | 18155.2 | − | 18155.2i | 0.599822 | − | 0.599822i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24369.6 | − | 24369.6i | −0.663226 | − | 0.663226i | 0.292913 | − | 0.956139i | \(-0.405375\pi\) |
−0.956139 | + | 0.292913i | \(0.905375\pi\) | |||||||
\(68\) | 9061.09 | + | 9061.09i | 0.237634 | + | 0.237634i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17922.9i | 0.421951i | 0.977491 | + | 0.210976i | \(0.0676641\pi\) | ||||
−0.977491 | + | 0.210976i | \(0.932336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1389.99 | + | 1389.99i | −0.0305283 | + | 0.0305283i | −0.722206 | − | 0.691678i | \(-0.756872\pi\) |
0.691678 | + | 0.722206i | \(0.256872\pi\) | |||||||
\(74\) | 39747.5 | 0.843782 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4526.47 | 0.0898929 | ||||||||
\(77\) | 76745.6 | − | 76745.6i | 1.47512 | − | 1.47512i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54864.2i | 0.989056i | 0.869162 | + | 0.494528i | \(0.164659\pi\) | ||||
−0.869162 | + | 0.494528i | \(0.835341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11368.1 | + | 11368.1i | 0.186704 | + | 0.186704i | ||||
\(83\) | 19422.4 | + | 19422.4i | 0.309463 | + | 0.309463i | 0.844701 | − | 0.535238i | \(-0.179778\pi\) |
−0.535238 | + | 0.844701i | \(0.679778\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24346.8i | 0.354974i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 33703.9 | − | 33703.9i | 0.463952 | − | 0.463952i | ||||
\(89\) | 141941. | 1.89948 | 0.949739 | − | 0.313044i | \(-0.101349\pi\) | ||||
0.949739 | + | 0.313044i | \(0.101349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −62207.0 | −0.787473 | ||||||||
\(92\) | 56411.8 | − | 56411.8i | 0.694865 | − | 0.694865i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7188.87i | 0.0839153i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 121179. | + | 121179.i | 1.30767 | + | 1.30767i | 0.923089 | + | 0.384585i | \(0.125656\pi\) |
0.384585 | + | 0.923089i | \(0.374344\pi\) | |||||||
\(98\) | −12532.0 | − | 12532.0i | −0.131812 | − | 0.131812i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 89431.2i | − | 0.872339i | −0.899864 | − | 0.436170i | \(-0.856335\pi\) | ||
0.899864 | − | 0.436170i | \(-0.143665\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −34487.5 | + | 34487.5i | −0.320309 | + | 0.320309i | −0.848886 | − | 0.528577i | \(-0.822726\pi\) |
0.528577 | + | 0.848886i | \(0.322726\pi\) | |||||||
\(104\) | −27319.0 | −0.247675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2557.03 | −0.0221040 | ||||||||
\(107\) | −87052.5 | + | 87052.5i | −0.735059 | + | 0.735059i | −0.971617 | − | 0.236559i | \(-0.923980\pi\) |
0.236559 | + | 0.971617i | \(0.423980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 213367.i | 1.72013i | 0.510185 | + | 0.860065i | \(0.329577\pi\) | ||||
−0.510185 | + | 0.860065i | \(0.670423\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −26380.3 | − | 26380.3i | −0.198717 | − | 0.198717i | ||||
\(113\) | 92875.0 | + | 92875.0i | 0.684231 | + | 0.684231i | 0.960951 | − | 0.276720i | \(-0.0892473\pi\) |
−0.276720 | + | 0.960951i | \(0.589247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 104698.i | − | 0.722423i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −38616.2 | + | 38616.2i | −0.255308 | + | 0.255308i | ||||
\(119\) | −116716. | −0.755548 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −393612. | −2.44402 | ||||||||
\(122\) | −77904.2 | + | 77904.2i | −0.473873 | + | 0.473873i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 102701.i | 0.599822i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 128111. | + | 128111.i | 0.704817 | + | 0.704817i | 0.965440 | − | 0.260624i | \(-0.0839282\pi\) |
−0.260624 | + | 0.965440i | \(0.583928\pi\) | |||||||
\(128\) | −11585.2 | − | 11585.2i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 270354.i | 1.37643i | 0.725507 | + | 0.688215i | \(0.241605\pi\) | ||||
−0.725507 | + | 0.688215i | \(0.758395\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29152.7 | + | 29152.7i | −0.142906 | + | 0.142906i | ||||
\(134\) | 137855. | 0.663226 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −51257.3 | −0.237634 | ||||||||
\(137\) | 60081.8 | − | 60081.8i | 0.273490 | − | 0.273490i | −0.557013 | − | 0.830504i | \(-0.688053\pi\) |
0.830504 | + | 0.557013i | \(0.188053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 192670.i | − | 0.845819i | −0.906172 | − | 0.422910i | \(-0.861009\pi\) | ||
0.906172 | − | 0.422910i | \(-0.138991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −50693.6 | − | 50693.6i | −0.210976 | − | 0.210976i | ||||
\(143\) | 224794. | + | 224794.i | 0.919273 | + | 0.919273i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 7862.94i | − | 0.0305283i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −112423. | + | 112423.i | −0.421891 | + | 0.421891i | ||||
\(149\) | 406382. | 1.49958 | 0.749788 | − | 0.661678i | \(-0.230155\pi\) | ||||
0.749788 | + | 0.661678i | \(0.230155\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 211613. | 0.755267 | 0.377634 | − | 0.925955i | \(-0.376738\pi\) | ||||
0.377634 | + | 0.925955i | \(0.376738\pi\) | |||||||
\(152\) | −12802.8 | + | 12802.8i | −0.0449464 | + | 0.0449464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 434139.i | 1.47512i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 297822. | + | 297822.i | 0.964292 | + | 0.964292i | 0.999384 | − | 0.0350925i | \(-0.0111726\pi\) |
−0.0350925 | + | 0.999384i | \(0.511173\pi\) | |||||||
\(158\) | −155179. | − | 155179.i | −0.494528 | − | 0.494528i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 726640.i | 2.20930i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21493.5 | + | 21493.5i | −0.0633635 | + | 0.0633635i | −0.738078 | − | 0.674715i | \(-0.764267\pi\) |
0.674715 | + | 0.738078i | \(0.264267\pi\) | |||||||
\(164\) | −64307.9 | −0.186704 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −109870. | −0.309463 | ||||||||
\(167\) | 231934. | − | 231934.i | 0.643537 | − | 0.643537i | −0.307886 | − | 0.951423i | \(-0.599622\pi\) |
0.951423 | + | 0.307886i | \(0.0996216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 189084.i | 0.509258i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −68863.2 | − | 68863.2i | −0.177487 | − | 0.177487i | ||||
\(173\) | −428012. | − | 428012.i | −1.08728 | − | 1.08728i | −0.995808 | − | 0.0914698i | \(-0.970844\pi\) |
−0.0914698 | − | 0.995808i | \(-0.529156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 190658.i | 0.463952i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −401471. | + | 401471.i | −0.949739 | + | 0.949739i | ||||
\(179\) | 242661. | 0.566066 | 0.283033 | − | 0.959110i | \(-0.408659\pi\) | ||||
0.283033 | + | 0.959110i | \(0.408659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 68244.2 | 0.154835 | 0.0774176 | − | 0.996999i | \(-0.475333\pi\) | ||||
0.0774176 | + | 0.996999i | \(0.475333\pi\) | |||||||
\(182\) | 175948. | − | 175948.i | 0.393736 | − | 0.393736i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 319114.i | 0.694865i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 421769. | + | 421769.i | 0.882005 | + | 0.882005i | ||||
\(188\) | −20333.2 | − | 20333.2i | −0.0419576 | − | 0.0419576i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 105778.i | 0.209803i | 0.994483 | + | 0.104901i | \(0.0334527\pi\) | ||||
−0.994483 | + | 0.104901i | \(0.966547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27490.4 | + | 27490.4i | −0.0531236 | + | 0.0531236i | −0.733170 | − | 0.680046i | \(-0.761960\pi\) |
0.680046 | + | 0.733170i | \(0.261960\pi\) | |||||||
\(194\) | −685495. | −1.30767 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 70891.8 | 0.131812 | ||||||||
\(197\) | −178152. | + | 178152.i | −0.327059 | + | 0.327059i | −0.851467 | − | 0.524408i | \(-0.824287\pi\) |
0.524408 | + | 0.851467i | \(0.324287\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 757628.i | 1.35620i | 0.734970 | + | 0.678100i | \(0.237196\pi\) | ||||
−0.734970 | + | 0.678100i | \(0.762804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 252950. | + | 252950.i | 0.436170 | + | 0.436170i | ||||
\(203\) | 674304. | + | 674304.i | 1.14846 | + | 1.14846i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 195091.i | − | 0.320309i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 77269.8 | − | 77269.8i | 0.123837 | − | 0.123837i | ||||
\(209\) | 210695. | 0.333648 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 840932. | 1.30033 | 0.650167 | − | 0.759791i | \(-0.274699\pi\) | ||||
0.650167 | + | 0.759791i | \(0.274699\pi\) | |||||||
\(212\) | 7232.37 | − | 7232.37i | 0.0110520 | − | 0.0110520i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 492443.i | − | 0.735059i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −661448. | − | 661448.i | −0.953557 | − | 0.953557i | ||||
\(218\) | −603493. | − | 603493.i | −0.860065 | − | 0.860065i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 341870.i | − | 0.470847i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −600800. | + | 600800.i | −0.809036 | + | 0.809036i | −0.984488 | − | 0.175452i | \(-0.943861\pi\) |
0.175452 | + | 0.984488i | \(0.443861\pi\) | |||||||
\(224\) | 149229. | 0.198717 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −525381. | −0.684231 | ||||||||
\(227\) | −642116. | + | 642116.i | −0.827082 | + | 0.827082i | −0.987112 | − | 0.160030i | \(-0.948841\pi\) |
0.160030 | + | 0.987112i | \(0.448841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 217938.i | − | 0.274628i | −0.990528 | − | 0.137314i | \(-0.956153\pi\) | ||
0.990528 | − | 0.137314i | \(-0.0438469\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 296129. | + | 296129.i | 0.361211 | + | 0.361211i | ||||
\(233\) | 63784.0 | + | 63784.0i | 0.0769701 | + | 0.0769701i | 0.744544 | − | 0.667574i | \(-0.232667\pi\) |
−0.667574 | + | 0.744544i | \(0.732667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 218446.i | − | 0.255308i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 330122. | − | 330122.i | 0.377774 | − | 0.377774i | ||||
\(239\) | 772095. | 0.874331 | 0.437165 | − | 0.899381i | \(-0.355982\pi\) | ||||
0.437165 | + | 0.899381i | \(0.355982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.36558e6 | −1.51451 | −0.757257 | − | 0.653117i | \(-0.773461\pi\) | ||||
−0.757257 | + | 0.653117i | \(0.773461\pi\) | |||||||
\(242\) | 1.11330e6 | − | 1.11330e6i | 1.22201 | − | 1.22201i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 440693.i | − | 0.473873i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −85390.4 | − | 85390.4i | −0.0890568 | − | 0.0890568i | ||||
\(248\) | −290484. | − | 290484.i | −0.299911 | − | 0.299911i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 782791.i | − | 0.784263i | −0.919909 | − | 0.392131i | \(-0.871738\pi\) | ||
0.919909 | − | 0.392131i | \(-0.128262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.62582e6 | − | 2.62582e6i | 2.57907 | − | 2.57907i | ||||
\(254\) | −724704. | −0.704817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.31783e6 | + | 1.31783e6i | −1.24459 | + | 1.24459i | −0.286510 | + | 0.958077i | \(0.592495\pi\) |
−0.958077 | + | 0.286510i | \(0.907505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.44812e6i | − | 1.34139i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −764676. | − | 764676.i | −0.688215 | − | 0.688215i | ||||
\(263\) | 1.26266e6 | + | 1.26266e6i | 1.12563 | + | 1.12563i | 0.990879 | + | 0.134752i | \(0.0430239\pi\) |
0.134752 | + | 0.990879i | \(0.456976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 164912.i | − | 0.142906i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −389913. | + | 389913.i | −0.331613 | + | 0.331613i | ||||
\(269\) | 323403. | 0.272498 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17418e6 | 0.971203 | 0.485602 | − | 0.874180i | \(-0.338601\pi\) | ||||
0.485602 | + | 0.874180i | \(0.338601\pi\) | |||||||
\(272\) | 144977. | − | 144977.i | 0.118817 | − | 0.118817i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 339874.i | 0.273490i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 182207. | + | 182207.i | 0.142681 | + | 0.142681i | 0.774839 | − | 0.632158i | \(-0.217831\pi\) |
−0.632158 | + | 0.774839i | \(0.717831\pi\) | |||||||
\(278\) | 544954. | + | 544954.i | 0.422910 | + | 0.422910i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 464741.i | − | 0.351111i | −0.984469 | − | 0.175556i | \(-0.943828\pi\) | ||
0.984469 | − | 0.175556i | \(-0.0561722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −72230.5 | + | 72230.5i | −0.0536110 | + | 0.0536110i | −0.733404 | − | 0.679793i | \(-0.762070\pi\) |
0.679793 | + | 0.733404i | \(0.262070\pi\) | |||||||
\(284\) | 286766. | 0.210976 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.27163e6 | −0.919273 | ||||||||
\(287\) | 414174. | − | 414174.i | 0.296810 | − | 0.296810i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 778424.i | 0.548241i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22239.8 | + | 22239.8i | 0.0152642 | + | 0.0152642i | ||||
\(293\) | −430913. | − | 430913.i | −0.293238 | − | 0.293238i | 0.545120 | − | 0.838358i | \(-0.316484\pi\) |
−0.838358 | + | 0.545120i | \(0.816484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 635960.i | − | 0.421891i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.14942e6 | + | 1.14942e6i | −0.749788 | + | 0.749788i | ||||
\(299\) | −2.12839e6 | −1.37680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 887026. | 0.564313 | ||||||||
\(302\) | −598533. | + | 598533.i | −0.377634 | + | 0.377634i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 72423.5i | − | 0.0449464i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −520866. | − | 520866.i | −0.315414 | − | 0.315414i | 0.531589 | − | 0.847002i | \(-0.321595\pi\) |
−0.847002 | + | 0.531589i | \(0.821595\pi\) | |||||||
\(308\) | −1.22793e6 | − | 1.22793e6i | −0.737559 | − | 0.737559i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.65179e6i | − | 0.968396i | −0.874958 | − | 0.484198i | \(-0.839111\pi\) | ||
0.874958 | − | 0.484198i | \(-0.160889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −808852. | + | 808852.i | −0.466668 | + | 0.466668i | −0.900833 | − | 0.434165i | \(-0.857043\pi\) |
0.434165 | + | 0.900833i | \(0.357043\pi\) | |||||||
\(314\) | −1.68474e6 | −0.964292 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 877827. | 0.494528 | ||||||||
\(317\) | 1.04885e6 | − | 1.04885e6i | 0.586227 | − | 0.586227i | −0.350381 | − | 0.936607i | \(-0.613948\pi\) |
0.936607 | + | 0.350381i | \(0.113948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.87339e6i | − | 2.68135i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.05525e6 | − | 2.05525e6i | −1.10465 | − | 1.10465i | ||||
\(323\) | −160214. | − | 160214.i | −0.0854464 | − | 0.0854464i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 121586.i | − | 0.0633635i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 181890. | − | 181890.i | 0.0933522 | − | 0.0933522i | ||||
\(329\) | 261912. | 0.133403 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 772673. | 0.387637 | 0.193819 | − | 0.981037i | \(-0.437913\pi\) | ||||
0.193819 | + | 0.981037i | \(0.437913\pi\) | |||||||
\(332\) | 310759. | − | 310759.i | 0.154731 | − | 0.154731i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31202e6i | 0.643537i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −485089. | − | 485089.i | −0.232673 | − | 0.232673i | 0.581134 | − | 0.813808i | \(-0.302609\pi\) |
−0.813808 | + | 0.581134i | \(0.802609\pi\) | |||||||
\(338\) | −534810. | − | 534810.i | −0.254629 | − | 0.254629i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.78048e6i | 2.22631i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.27535e6 | − | 1.27535e6i | 0.585320 | − | 0.585320i | ||||
\(344\) | 389549. | 0.177487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.42120e6 | 1.08728 | ||||||||
\(347\) | 1.31517e6 | − | 1.31517e6i | 0.586352 | − | 0.586352i | −0.350289 | − | 0.936642i | \(-0.613917\pi\) |
0.936642 | + | 0.350289i | \(0.113917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.36535e6i | − | 1.91847i | −0.282604 | − | 0.959237i | \(-0.591198\pi\) | ||
0.282604 | − | 0.959237i | \(-0.408802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −539262. | − | 539262.i | −0.231976 | − | 0.231976i | ||||
\(353\) | 1.99522e6 | + | 1.99522e6i | 0.852223 | + | 0.852223i | 0.990407 | − | 0.138184i | \(-0.0441265\pi\) |
−0.138184 | + | 0.990407i | \(0.544127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 2.27106e6i | − | 0.949739i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −686348. | + | 686348.i | −0.283033 | + | 0.283033i | ||||
\(359\) | 1.45280e6 | 0.594934 | 0.297467 | − | 0.954732i | \(-0.403858\pi\) | ||||
0.297467 | + | 0.954732i | \(0.403858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.39606e6 | 0.967677 | ||||||||
\(362\) | −193024. | + | 193024.i | −0.0774176 | + | 0.0774176i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 995312.i | 0.393736i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.63291e6 | − | 2.63291e6i | −1.02040 | − | 1.02040i | −0.999787 | − | 0.0206148i | \(-0.993438\pi\) |
−0.0206148 | − | 0.999787i | \(-0.506562\pi\) | |||||||
\(368\) | −902589. | − | 902589.i | −0.347433 | − | 0.347433i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 93160.0i | 0.0351394i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.50759e6 | − | 1.50759e6i | 0.561061 | − | 0.561061i | −0.368548 | − | 0.929609i | \(-0.620145\pi\) |
0.929609 | + | 0.368548i | \(0.120145\pi\) | |||||||
\(374\) | −2.38589e6 | −0.882005 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 115022. | 0.0419576 | ||||||||
\(377\) | −1.97509e6 | + | 1.97509e6i | −0.715703 | + | 0.715703i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 773746.i | − | 0.276694i | −0.990384 | − | 0.138347i | \(-0.955821\pi\) | ||
0.990384 | − | 0.138347i | \(-0.0441790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −299185. | − | 299185.i | −0.104901 | − | 0.104901i | ||||
\(383\) | −2.82130e6 | − | 2.82130e6i | −0.982772 | − | 0.982772i | 0.0170818 | − | 0.999854i | \(-0.494562\pi\) |
−0.999854 | + | 0.0170818i | \(0.994562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 155509.i | − | 0.0531236i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.93887e6 | − | 1.93887e6i | 0.653837 | − | 0.653837i | ||||
\(389\) | −2.37203e6 | −0.794778 | −0.397389 | − | 0.917650i | \(-0.630084\pi\) | ||||
−0.397389 | + | 0.917650i | \(0.630084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.99338e6 | −1.32099 | ||||||||
\(392\) | −200512. | + | 200512.i | −0.0659061 | + | 0.0659061i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 1.00778e6i | − | 0.327059i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.98940e6 | + | 1.98940e6i | 0.633498 | + | 0.633498i | 0.948944 | − | 0.315446i | \(-0.102154\pi\) |
−0.315446 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(398\) | −2.14290e6 | − | 2.14290e6i | −0.678100 | − | 0.678100i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 868678.i | − | 0.269773i | −0.990861 | − | 0.134886i | \(-0.956933\pi\) | ||
0.990861 | − | 0.134886i | \(-0.0430669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.93743e6 | − | 1.93743e6i | 0.594243 | − | 0.594243i | ||||
\(404\) | −1.43090e6 | −0.436170 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.81444e6 | −1.14846 | ||||||||
\(407\) | −5.23298e6 | + | 5.23298e6i | −1.56590 | + | 1.56590i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.60852e6i | 0.475464i | 0.971331 | + | 0.237732i | \(0.0764040\pi\) | ||||
−0.971331 | + | 0.237732i | \(0.923596\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 551800. | + | 551800.i | 0.160154 | + | 0.160154i | ||||
\(413\) | 1.40690e6 | + | 1.40690e6i | 0.405871 | + | 0.405871i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 437104.i | 0.123837i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −595935. | + | 595935.i | −0.166824 | + | 0.166824i | ||||
\(419\) | −386112. | −0.107443 | −0.0537215 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537215 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.36712e6 | 1.47583 | 0.737915 | − | 0.674894i | \(-0.235811\pi\) | ||||
0.737915 | + | 0.674894i | \(0.235811\pi\) | |||||||
\(422\) | −2.37852e6 | + | 2.37852e6i | −0.650167 | + | 0.650167i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 40912.4i | 0.0110520i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.83828e6 | + | 2.83828e6i | 0.753330 | + | 0.753330i | ||||
\(428\) | 1.39284e6 | + | 1.39284e6i | 0.367529 | + | 0.367529i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.40932e6i | − | 0.884046i | −0.897004 | − | 0.442023i | \(-0.854261\pi\) | ||
0.897004 | − | 0.442023i | \(-0.145739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.74187e6 | + | 2.74187e6i | −0.702792 | + | 0.702792i | −0.965009 | − | 0.262217i | \(-0.915546\pi\) |
0.262217 | + | 0.965009i | \(0.415546\pi\) | |||||||
\(434\) | 3.74172e6 | 0.953557 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.41387e6 | 0.860065 | ||||||||
\(437\) | −997446. | + | 997446.i | −0.249854 | + | 0.249854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.42105e6i | 1.59017i | 0.606495 | + | 0.795087i | \(0.292575\pi\) | ||||
−0.606495 | + | 0.795087i | \(0.707425\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 966953. | + | 966953.i | 0.235424 | + | 0.235424i | ||||
\(443\) | 2.88801e6 | + | 2.88801e6i | 0.699180 | + | 0.699180i | 0.964234 | − | 0.265054i | \(-0.0853898\pi\) |
−0.265054 | + | 0.964234i | \(0.585390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 3.39864e6i | − | 0.809036i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −422084. | + | 422084.i | −0.0993583 | + | 0.0993583i | ||||
\(449\) | −2.70977e6 | −0.634332 | −0.317166 | − | 0.948370i | \(-0.602731\pi\) | ||||
−0.317166 | + | 0.948370i | \(0.602731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.99336e6 | −0.692974 | ||||||||
\(452\) | 1.48600e6 | − | 1.48600e6i | 0.342116 | − | 0.342116i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.63235e6i | − | 0.827082i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.63241e6 | + | 2.63241e6i | 0.589607 | + | 0.589607i | 0.937525 | − | 0.347918i | \(-0.113111\pi\) |
−0.347918 | + | 0.937525i | \(0.613111\pi\) | |||||||
\(458\) | 616422. | + | 616422.i | 0.137314 | + | 0.137314i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.96571e6i | − | 1.08825i | −0.839004 | − | 0.544126i | \(-0.816861\pi\) | ||
0.839004 | − | 0.544126i | \(-0.183139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 851371. | − | 851371.i | 0.184572 | − | 0.184572i | −0.608773 | − | 0.793345i | \(-0.708338\pi\) |
0.793345 | + | 0.608773i | \(0.208338\pi\) | |||||||
\(464\) | −1.67516e6 | −0.361211 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −360817. | −0.0769701 | ||||||||
\(467\) | 2.86333e6 | − | 2.86333e6i | 0.607546 | − | 0.607546i | −0.334758 | − | 0.942304i | \(-0.608654\pi\) |
0.942304 | + | 0.334758i | \(0.108654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.02247e6i | − | 1.05435i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 617859. | + | 617859.i | 0.127654 | + | 0.127654i | ||||
\(473\) | −3.20540e6 | − | 3.20540e6i | −0.658763 | − | 0.658763i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.86745e6i | 0.377774i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.18381e6 | + | 2.18381e6i | −0.437165 | + | 0.437165i | ||||
\(479\) | 3.88850e6 | 0.774361 | 0.387180 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387180 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.24165e6 | 0.835934 | ||||||||
\(482\) | 3.86243e6 | − | 3.86243e6i | 0.757257 | − | 0.757257i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.29779e6i | 1.22201i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.14170e6 | − | 2.14170e6i | −0.409200 | − | 0.409200i | 0.472259 | − | 0.881460i | \(-0.343439\pi\) |
−0.881460 | + | 0.472259i | \(0.843439\pi\) | |||||||
\(488\) | 1.24647e6 | + | 1.24647e6i | 0.236936 | + | 0.236936i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.55003e6i | 1.41334i | 0.707546 | + | 0.706668i | \(0.249802\pi\) | ||||
−0.707546 | + | 0.706668i | \(0.750198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.70576e6 | + | 3.70576e6i | −0.686688 | + | 0.686688i | ||||
\(494\) | 483041. | 0.0890568 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.64322e6 | 0.299911 | ||||||||
\(497\) | −1.84692e6 | + | 1.84692e6i | −0.335395 | + | 0.335395i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 521365.i | 0.0937326i | 0.998901 | + | 0.0468663i | \(0.0149235\pi\) | ||||
−0.998901 | + | 0.0468663i | \(0.985077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.21407e6 | + | 2.21407e6i | 0.392131 | + | 0.392131i | ||||
\(503\) | −5.01780e6 | − | 5.01780e6i | −0.884287 | − | 0.884287i | 0.109680 | − | 0.993967i | \(-0.465017\pi\) |
−0.993967 | + | 0.109680i | \(0.965017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.48539e7i | 2.57907i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.04977e6 | − | 2.04977e6i | 0.352408 | − | 0.352408i | ||||
\(509\) | 284518. | 0.0486761 | 0.0243380 | − | 0.999704i | \(-0.492252\pi\) | ||||
0.0243380 | + | 0.999704i | \(0.492252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −286470. | −0.0485319 | ||||||||
\(512\) | −185364. | + | 185364.i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 7.45475e6i | − | 1.24459i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −946455. | − | 946455.i | −0.155731 | − | 0.155731i | ||||
\(518\) | 4.09590e6 | + | 4.09590e6i | 0.670694 | + | 0.670694i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00835e6i | 0.485550i | 0.970083 | + | 0.242775i | \(0.0780576\pi\) | ||||
−0.970083 | + | 0.242775i | \(0.921942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 395738. | − | 395738.i | 0.0632635 | − | 0.0632635i | −0.674767 | − | 0.738031i | \(-0.735756\pi\) |
0.738031 | + | 0.674767i | \(0.235756\pi\) | |||||||
\(524\) | 4.32566e6 | 0.688215 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.14267e6 | −1.12563 | ||||||||
\(527\) | 3.63511e6 | − | 3.63511e6i | 0.570152 | − | 0.570152i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.84253e7i | 2.86270i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 466443. | + | 466443.i | 0.0714528 | + | 0.0714528i | ||||
\(533\) | 1.21315e6 | + | 1.21315e6i | 0.184968 | + | 0.184968i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.20568e6i | − | 0.331613i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −914721. | + | 914721.i | −0.136249 | + | 0.136249i | ||||
\(539\) | 3.29982e6 | 0.489236 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.89254e6 | −0.278004 | −0.139002 | − | 0.990292i | \(-0.544389\pi\) | ||||
−0.139002 | + | 0.990292i | \(0.544389\pi\) | |||||||
\(542\) | −3.32107e6 | + | 3.32107e6i | −0.485602 | + | 0.485602i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 820116.i | 0.118817i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.48168e6 | − | 5.48168e6i | −0.783331 | − | 0.783331i | 0.197060 | − | 0.980391i | \(-0.436861\pi\) |
−0.980391 | + | 0.197060i | \(0.936861\pi\) | |||||||
\(548\) | −961310. | − | 961310.i | −0.136745 | − | 0.136745i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.85121e6i | 0.259763i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.65364e6 | + | 5.65364e6i | −0.786168 | + | 0.786168i | ||||
\(554\) | −1.03072e6 | −0.142681 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.08272e6 | −0.422910 | ||||||||
\(557\) | 881422. | − | 881422.i | 0.120378 | − | 0.120378i | −0.644352 | − | 0.764729i | \(-0.722873\pi\) |
0.764729 | + | 0.644352i | \(0.222873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.59817e6i | 0.351672i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.31449e6 | + | 1.31449e6i | 0.175556 | + | 0.175556i | ||||
\(563\) | −4.65833e6 | − | 4.65833e6i | −0.619382 | − | 0.619382i | 0.325991 | − | 0.945373i | \(-0.394302\pi\) |
−0.945373 | + | 0.325991i | \(0.894302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 408597.i | − | 0.0536110i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −811097. | + | 811097.i | −0.105488 | + | 0.105488i | ||||
\(569\) | −5.23579e6 | −0.677957 | −0.338978 | − | 0.940794i | \(-0.610081\pi\) | ||||
−0.338978 | + | 0.940794i | \(0.610081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.08355e7 | −1.39078 | −0.695392 | − | 0.718630i | \(-0.744769\pi\) | ||||
−0.695392 | + | 0.718630i | \(0.744769\pi\) | |||||||
\(572\) | 3.59670e6 | − | 3.59670e6i | 0.459636 | − | 0.459636i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.34292e6i | 0.296810i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.55499e6 | + | 3.55499e6i | 0.444528 | + | 0.444528i | 0.893530 | − | 0.449003i | \(-0.148221\pi\) |
−0.449003 | + | 0.893530i | \(0.648221\pi\) | |||||||
\(578\) | −2.20172e6 | − | 2.20172e6i | −0.274121 | − | 0.274121i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00288e6i | 0.491963i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 336647. | − | 336647.i | 0.0410208 | − | 0.0410208i | ||||
\(584\) | −125807. | −0.0152642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.43761e6 | 0.293238 | ||||||||
\(587\) | 9.52451e6 | − | 9.52451e6i | 1.14090 | − | 1.14090i | 0.152614 | − | 0.988286i | \(-0.451231\pi\) |
0.988286 | − | 0.152614i | \(-0.0487690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.81592e6i | − | 0.215679i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.79877e6 | + | 1.79877e6i | 0.210946 | + | 0.210946i | ||||
\(593\) | 6.05271e6 | + | 6.05271e6i | 0.706827 | + | 0.706827i | 0.965867 | − | 0.259040i | \(-0.0834061\pi\) |
−0.259040 | + | 0.965867i | \(0.583406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.50211e6i | − | 0.749788i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.01998e6 | − | 6.01998e6i | 0.688402 | − | 0.688402i | ||||
\(599\) | 1.13352e7 | 1.29081 | 0.645407 | − | 0.763838i | \(-0.276688\pi\) | ||||
0.645407 | + | 0.763838i | \(0.276688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33968e7 | −1.51292 | −0.756459 | − | 0.654041i | \(-0.773072\pi\) | ||||
−0.756459 | + | 0.654041i | \(0.773072\pi\) | |||||||
\(602\) | −2.50889e6 | + | 2.50889e6i | −0.282157 | + | 0.282157i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3.38581e6i | − | 0.377634i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.22734e6 | − | 1.22734e6i | −0.135205 | − | 0.135205i | 0.636265 | − | 0.771470i | \(-0.280478\pi\) |
−0.771470 | + | 0.636265i | \(0.780478\pi\) | |||||||
\(608\) | 204844. | + | 204844.i | 0.0224732 | + | 0.0224732i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 767159.i | 0.0831347i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.42422e6 | + | 8.42422e6i | −0.905479 | + | 0.905479i | −0.995903 | − | 0.0904240i | \(-0.971178\pi\) |
0.0904240 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(614\) | 2.94646e6 | 0.315414 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.94622e6 | 0.737559 | ||||||||
\(617\) | 608492. | − | 608492.i | 0.0643491 | − | 0.0643491i | −0.674200 | − | 0.738549i | \(-0.735511\pi\) |
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.53768e6i | 0.476001i | 0.971265 | + | 0.238000i | \(0.0764920\pi\) | ||||
−0.971265 | + | 0.238000i | \(0.923508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.67196e6 | + | 4.67196e6i | 0.484198 | + | 0.484198i | ||||
\(623\) | 1.46268e7 | + | 1.46268e7i | 1.50983 | + | 1.50983i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 4.57556e6i | − | 0.466668i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.76516e6 | − | 4.76516e6i | 0.482146 | − | 0.482146i | ||||
\(629\) | 7.95839e6 | 0.802045 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.73983e6 | 0.473903 | 0.236952 | − | 0.971521i | \(-0.423852\pi\) | ||||
0.236952 | + | 0.971521i | \(0.423852\pi\) | |||||||
\(632\) | −2.48287e6 | + | 2.48287e6i | −0.247264 | + | 0.247264i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.93320e6i | 0.586227i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.33735e6 | − | 1.33735e6i | −0.130586 | − | 0.130586i | ||||
\(638\) | 1.37840e7 | + | 1.37840e7i | 1.34068 | + | 1.34068i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.51535e6i | − | 0.818573i | −0.912406 | − | 0.409287i | \(-0.865778\pi\) | ||
0.912406 | − | 0.409287i | \(-0.134222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83215e6 | − | 6.83215e6i | 0.651673 | − | 0.651673i | −0.301722 | − | 0.953396i | \(-0.597562\pi\) |
0.953396 | + | 0.301722i | \(0.0975616\pi\) | |||||||
\(644\) | 1.16262e7 | 1.10465 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 906306. | 0.0854464 | ||||||||
\(647\) | 7.55983e6 | − | 7.55983e6i | 0.709989 | − | 0.709989i | −0.256544 | − | 0.966533i | \(-0.582584\pi\) |
0.966533 | + | 0.256544i | \(0.0825839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.01681e7i | − | 0.947605i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 343897. | + | 343897.i | 0.0316817 | + | 0.0316817i | ||||
\(653\) | −8.56784e6 | − | 8.56784e6i | −0.786300 | − | 0.786300i | 0.194586 | − | 0.980886i | \(-0.437664\pi\) |
−0.980886 | + | 0.194586i | \(0.937664\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.02893e6i | 0.0933522i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −740798. | + | 740798.i | −0.0667014 | + | 0.0667014i | ||||
\(659\) | −1.85670e6 | −0.166544 | −0.0832718 | − | 0.996527i | \(-0.526537\pi\) | ||||
−0.0832718 | + | 0.996527i | \(0.526537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.58327e6 | 0.229967 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(662\) | −2.18545e6 | + | 2.18545e6i | −0.193819 | + | 0.193819i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.75792e6i | 0.154731i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.30710e7 | + | 2.30710e7i | 2.00795 | + | 2.00795i | ||||
\(668\) | −3.71095e6 | − | 3.71095e6i | −0.321769 | − | 0.321769i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.05131e7i | − | 1.75883i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.77133e6 | + | 4.77133e6i | −0.406071 | + | 0.406071i | −0.880366 | − | 0.474295i | \(-0.842703\pi\) |
0.474295 | + | 0.880366i | \(0.342703\pi\) | |||||||
\(674\) | 2.74408e6 | 0.232673 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.02534e6 | 0.254629 | ||||||||
\(677\) | 1.24737e7 | − | 1.24737e7i | 1.04598 | − | 1.04598i | 0.0470935 | − | 0.998890i | \(-0.485004\pi\) |
0.998890 | − | 0.0470935i | \(-0.0149959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.49746e7i | 2.07885i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.35212e7 | − | 1.35212e7i | −1.11315 | − | 1.11315i | ||||
\(683\) | 2.99944e6 | + | 2.99944e6i | 0.246030 | + | 0.246030i | 0.819339 | − | 0.573309i | \(-0.194341\pi\) |
−0.573309 | + | 0.819339i | \(0.694341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.21446e6i | 0.585320i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.10181e6 | + | 1.10181e6i | −0.0887434 | + | 0.0887434i | ||||
\(689\) | −272873. | −0.0218984 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.35493e7 | −1.87622 | −0.938108 | − | 0.346343i | \(-0.887423\pi\) | ||||
−0.938108 | + | 0.346343i | \(0.887423\pi\) | |||||||
\(692\) | −6.84819e6 | + | 6.84819e6i | −0.543639 | + | 0.543639i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.43973e6i | 0.586352i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.27617e6 | + | 2.27617e6i | 0.177469 | + | 0.177469i | ||||
\(698\) | 1.23471e7 | + | 1.23471e7i | 0.959237 | + | 0.959237i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.55909e6i | 0.196694i | 0.995152 | + | 0.0983469i | \(0.0313555\pi\) | ||||
−0.995152 | + | 0.0983469i | \(0.968645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.98781e6 | − | 1.98781e6i | 0.151700 | − | 0.151700i | ||||
\(704\) | 3.05052e6 | 0.231976 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.12866e7 | −0.852223 | ||||||||
\(707\) | 9.21569e6 | − | 9.21569e6i | 0.693393 | − | 0.693393i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.92286e6i | 0.218369i | 0.994021 | + | 0.109185i | \(0.0348240\pi\) | ||||
−0.994021 | + | 0.109185i | \(0.965176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.42353e6 | + | 6.42353e6i | 0.474869 | + | 0.474869i | ||||
\(713\) | −2.26312e7 | − | 2.26312e7i | −1.66718 | − | 1.66718i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 3.88257e6i | − | 0.283033i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.10913e6 | + | 4.10913e6i | −0.297467 | + | 0.297467i | ||||
\(719\) | −1.94781e7 | −1.40516 | −0.702578 | − | 0.711606i | \(-0.747968\pi\) | ||||
−0.702578 | + | 0.711606i | \(0.747968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.10773e6 | −0.509205 | ||||||||
\(722\) | −6.77709e6 | + | 6.77709e6i | −0.483839 | + | 0.483839i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1.09191e6i | − | 0.0774176i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.36184e7 | − | 1.36184e7i | −0.955630 | − | 0.955630i | 0.0434265 | − | 0.999057i | \(-0.486173\pi\) |
−0.999057 | + | 0.0434265i | \(0.986173\pi\) | |||||||
\(728\) | −2.81517e6 | − | 2.81517e6i | −0.196868 | − | 0.196868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87481e6i | 0.337415i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.32962e7 | − | 1.32962e7i | 0.914044 | − | 0.914044i | −0.0825431 | − | 0.996587i | \(-0.526304\pi\) |
0.996587 | + | 0.0825431i | \(0.0263042\pi\) | |||||||
\(734\) | 1.48940e7 | 1.02040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.10582e6 | 0.347433 | ||||||||
\(737\) | −1.81494e7 | + | 1.81494e7i | −1.23082 | + | 1.23082i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.64692e7i | − | 1.10933i | −0.832073 | − | 0.554666i | \(-0.812846\pi\) | ||
0.832073 | − | 0.554666i | \(-0.187154\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −263496. | − | 263496.i | −0.0175697 | − | 0.0175697i | ||||
\(743\) | −6.90258e6 | − | 6.90258e6i | −0.458711 | − | 0.458711i | 0.439521 | − | 0.898232i | \(-0.355148\pi\) |
−0.898232 | + | 0.439521i | \(0.855148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.52819e6i | 0.561061i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.74831e6 | − | 6.74831e6i | 0.441003 | − | 0.441003i | ||||
\(749\) | −1.79412e7 | −1.16855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.31540e7 | 1.49805 | 0.749023 | − | 0.662544i | \(-0.230523\pi\) | ||||
0.749023 | + | 0.662544i | \(0.230523\pi\) | |||||||
\(752\) | −325331. | + | 325331.i | −0.0209788 | + | 0.0209788i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1.11728e7i | − | 0.715703i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.12366e7 | − | 1.12366e7i | −0.712682 | − | 0.712682i | 0.254414 | − | 0.967096i | \(-0.418118\pi\) |
−0.967096 | + | 0.254414i | \(0.918118\pi\) | |||||||
\(758\) | 2.18848e6 | + | 2.18848e6i | 0.138347 | + | 0.138347i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 321915.i | 0.0201502i | 0.999949 | + | 0.0100751i | \(0.00320706\pi\) | ||||
−0.999949 | + | 0.0100751i | \(0.996793\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.19870e7 | + | 2.19870e7i | −1.36727 | + | 1.36727i | ||||
\(764\) | 1.69245e6 | 0.104901 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.59597e7 | 0.982772 | ||||||||
\(767\) | −4.12092e6 | + | 4.12092e6i | −0.252933 | + | 0.252933i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.20479e7i | − | 0.734678i | −0.930087 | − | 0.367339i | \(-0.880269\pi\) | ||
0.930087 | − | 0.367339i | \(-0.119731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 439846. | + | 439846.i | 0.0265618 | + | 0.0265618i | ||||
\(773\) | −5.01112e6 | − | 5.01112e6i | −0.301638 | − | 0.301638i | 0.540017 | − | 0.841654i | \(-0.318418\pi\) |
−0.841654 | + | 0.540017i | \(0.818418\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.09679e7i | 0.653837i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.70911e6 | − | 6.70911e6i | 0.397389 | − | 0.397389i | ||||
\(779\) | 1.13706e6 | 0.0671336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33482e7 | 0.783060 | ||||||||
\(782\) | 1.12950e7 | − | 1.12950e7i | 0.660494 | − | 0.660494i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.13427e6i | − | 0.0659061i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.08074e6 | − | 4.08074e6i | −0.234856 | − | 0.234856i | 0.579860 | − | 0.814716i | \(-0.303107\pi\) |
−0.814716 | + | 0.579860i | \(0.803107\pi\) | |||||||
\(788\) | 2.85044e6 | + | 2.85044e6i | 0.163530 | + | 0.163530i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.91412e7i | 1.08774i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.31354e6 | + | 8.31354e6i | −0.469465 | + | 0.469465i | ||||
\(794\) | −1.12537e7 | −0.633498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.21221e7 | 0.678100 | ||||||||
\(797\) | −8.30424e6 | + | 8.30424e6i | −0.463078 | + | 0.463078i | −0.899663 | − | 0.436585i | \(-0.856188\pi\) |
0.436585 | + | 0.899663i | \(0.356188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.43938e6i | 0.0797644i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.45699e6 | + | 2.45699e6i | 0.134886 | + | 0.134886i | ||||
\(803\) | 1.03520e6 | + | 1.03520e6i | 0.0566547 | + | 0.0566547i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.09598e7i | 0.594243i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.04719e6 | − | 4.04719e6i | 0.218085 | − | 0.218085i | ||||
\(809\) | −2.89113e7 | −1.55309 | −0.776545 | − | 0.630062i | \(-0.783029\pi\) | ||||
−0.776545 | + | 0.630062i | \(0.783029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.75545e6 | −0.200498 | −0.100249 | − | 0.994962i | \(-0.531964\pi\) | ||||
−0.100249 | + | 0.994962i | \(0.531964\pi\) | |||||||
\(812\) | 1.07889e7 | − | 1.07889e7i | 0.574229 | − | 0.574229i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2.96022e7i | − | 1.56590i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.21761e6 | + | 1.21761e6i | 0.0638192 | + | 0.0638192i | ||||
\(818\) | −4.54957e6 | − | 4.54957e6i | −0.237732 | − | 0.237732i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.14204e7i | 1.62687i | 0.581654 | + | 0.813436i | \(0.302406\pi\) | ||||
−0.581654 | + | 0.813436i | \(0.697594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.21173e6 | − | 1.21173e6i | 0.0623600 | − | 0.0623600i | −0.675239 | − | 0.737599i | \(-0.735960\pi\) |
0.737599 | + | 0.675239i | \(0.235960\pi\) | |||||||
\(824\) | −3.12145e6 | −0.160154 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.95864e6 | −0.405871 | ||||||||
\(827\) | 2.86118e6 | − | 2.86118e6i | 0.145473 | − | 0.145473i | −0.630619 | − | 0.776092i | \(-0.717199\pi\) |
0.776092 | + | 0.630619i | \(0.217199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.07617e7i | 1.04925i | 0.851335 | + | 0.524623i | \(0.175794\pi\) | ||||
−0.851335 | + | 0.524623i | \(0.824206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.23632e6 | − | 1.23632e6i | −0.0619187 | − | 0.0619187i | ||||
\(833\) | −2.50921e6 | − | 2.50921e6i | −0.125292 | − | 0.125292i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 3.37112e6i | − | 0.166824i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.09209e6 | − | 1.09209e6i | 0.0537215 | − | 0.0537215i | ||||
\(839\) | 1.24202e7 | 0.609147 | 0.304574 | − | 0.952489i | \(-0.401486\pi\) | ||||
0.304574 | + | 0.952489i | \(0.401486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.23075e7 | 1.08758 | ||||||||
\(842\) | −1.51805e7 | + | 1.51805e7i | −0.737915 | + | 0.737915i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 1.34549e7i | − | 0.650167i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.05609e7 | − | 4.05609e7i | −1.94267 | − | 1.94267i | ||||
\(848\) | −115718. | − | 115718.i | −0.00552600 | − | 0.00552600i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.95467e7i | − | 2.34526i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.42853e7 | + | 1.42853e7i | −0.672227 | + | 0.672227i | −0.958229 | − | 0.286002i | \(-0.907673\pi\) |
0.286002 | + | 0.958229i | \(0.407673\pi\) | |||||||
\(854\) | −1.60557e7 | −0.753330 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.87910e6 | −0.367529 | ||||||||
\(857\) | −1.41765e7 | + | 1.41765e7i | −0.659350 | + | 0.659350i | −0.955226 | − | 0.295876i | \(-0.904388\pi\) |
0.295876 | + | 0.955226i | \(0.404388\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.81052e7i | − | 1.29958i | −0.760112 | − | 0.649792i | \(-0.774856\pi\) | ||
0.760112 | − | 0.649792i | \(-0.225144\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.64302e6 | + | 9.64302e6i | 0.442023 | + | 0.442023i | ||||
\(863\) | 1.39692e6 | + | 1.39692e6i | 0.0638475 | + | 0.0638475i | 0.738310 | − | 0.674462i | \(-0.235624\pi\) |
−0.674462 | + | 0.738310i | \(0.735624\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.55103e7i | − | 0.702792i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.05832e7 | + | 1.05832e7i | −0.476778 | + | 0.476778i | ||||
\(869\) | 4.08605e7 | 1.83550 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.47112e7 | 0.657057 | ||||||||
\(872\) | −9.65589e6 | + | 9.65589e6i | −0.430032 | + | 0.430032i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 5.64241e6i | − | 0.249854i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.50455e7 | + | 2.50455e7i | 1.09959 | + | 1.09959i | 0.994458 | + | 0.105131i | \(0.0335263\pi\) |
0.105131 | + | 0.994458i | \(0.466474\pi\) | |||||||
\(878\) | −1.81615e7 | − | 1.81615e7i | −0.795087 | − | 0.795087i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 947233.i | − | 0.0411166i | −0.999789 | − | 0.0205583i | \(-0.993456\pi\) | ||
0.999789 | − | 0.0205583i | \(-0.00654437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.11113e7 | − | 2.11113e7i | 0.911199 | − | 0.911199i | −0.0851672 | − | 0.996367i | \(-0.527142\pi\) |
0.996367 | + | 0.0851672i | \(0.0271425\pi\) | |||||||
\(884\) | −5.46991e6 | −0.235424 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.63370e7 | −0.699180 | ||||||||
\(887\) | −1.07682e7 | + | 1.07682e7i | −0.459553 | + | 0.459553i | −0.898509 | − | 0.438956i | \(-0.855348\pi\) |
0.438956 | + | 0.898509i | \(0.355348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.64031e7i | 1.12047i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.61281e6 | + | 9.61281e6i | 0.404518 | + | 0.404518i | ||||
\(893\) | 359522. | + | 359522.i | 0.0150868 | + | 0.0150868i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.38767e6i | − | 0.0993583i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.66439e6 | − | 7.66439e6i | 0.317166 | − | 0.317166i | ||||
\(899\) | −4.20023e7 | −1.73330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −511978. | −0.0210106 | ||||||||
\(902\) | 8.46649e6 | − | 8.46649e6i | 0.346487 | − | 0.346487i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.40609e6i | 0.342116i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 678139. | + | 678139.i | 0.0273716 | + | 0.0273716i | 0.720660 | − | 0.693289i | \(-0.243839\pi\) |
−0.693289 | + | 0.720660i | \(0.743839\pi\) | |||||||
\(908\) | 1.02739e7 | + | 1.02739e7i | 0.413541 | + | 0.413541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.26770e7i | − | 1.70372i | −0.523771 | − | 0.851859i | \(-0.675475\pi\) | ||
0.523771 | − | 0.851859i | \(-0.324525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.44650e7 | − | 1.44650e7i | 0.574303 | − | 0.574303i | ||||
\(914\) | −1.48911e7 | −0.589607 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.48701e6 | −0.137314 | ||||||||
\(917\) | −2.78594e7 | + | 2.78594e7i | −1.09408 | + | 1.09408i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.12124e7i | − | 0.828516i | −0.910159 | − | 0.414258i | \(-0.864041\pi\) | ||
0.910159 | − | 0.414258i | \(-0.135959\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.40452e7 | + | 1.40452e7i | 0.544126 | + | 0.544126i | ||||
\(923\) | −5.40976e6 | − | 5.40976e6i | −0.209013 | − | 0.209013i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.81608e6i | 0.184572i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.73807e6 | − | 4.73807e6i | 0.180606 | − | 0.180606i | ||||
\(929\) | −4.17745e7 | −1.58808 | −0.794040 | − | 0.607866i | \(-0.792026\pi\) | ||||
−0.794040 | + | 0.607866i | \(0.792026\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.25347e6 | −0.0473959 | ||||||||
\(932\) | 1.02054e6 | − | 1.02054e6i | 0.0384851 | − | 0.0384851i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.61975e7i | 0.607546i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.35181e6 | + | 9.35181e6i | 0.347974 | + | 0.347974i | 0.859354 | − | 0.511380i | \(-0.170866\pi\) |
−0.511380 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(938\) | 1.42057e7 | + | 1.42057e7i | 0.527176 | + | 0.527176i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.12220e7i | − | 0.781291i | −0.920541 | − | 0.390646i | \(-0.872252\pi\) | ||
0.920541 | − | 0.390646i | \(-0.127748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.41708e7 | − | 1.41708e7i | 0.518938 | − | 0.518938i | ||||
\(944\) | −3.49514e6 | −0.127654 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.81325e7 | 0.658763 | ||||||||
\(947\) | −1.14035e6 | + | 1.14035e6i | −0.0413202 | + | 0.0413202i | −0.727465 | − | 0.686145i | \(-0.759302\pi\) |
0.686145 | + | 0.727465i | \(0.259302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 839093.i | − | 0.0302444i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.28195e6 | − | 5.28195e6i | −0.188887 | − | 0.188887i | ||||
\(953\) | −1.20675e7 | − | 1.20675e7i | −0.430413 | − | 0.430413i | 0.458356 | − | 0.888769i | \(-0.348439\pi\) |
−0.888769 | + | 0.458356i | \(0.848439\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.23535e7i | − | 0.437165i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.09983e7 | + | 1.09983e7i | −0.387180 | + | 0.387180i | ||||
\(959\) | 1.23826e7 | 0.434776 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.25724e7 | 0.439147 | ||||||||
\(962\) | −1.19972e7 | + | 1.19972e7i | −0.417967 | + | 0.417967i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.18492e7i | 0.757257i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.02688e7 | − | 3.02688e7i | −1.04095 | − | 1.04095i | −0.999125 | − | 0.0418240i | \(-0.986683\pi\) |
−0.0418240 | − | 0.999125i | \(-0.513317\pi\) | |||||||
\(968\) | −1.78128e7 | − | 1.78128e7i | −0.611005 | − | 0.611005i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67488e7i | 0.570079i | 0.958516 | + | 0.285039i | \(0.0920067\pi\) | ||||
−0.958516 | + | 0.285039i | \(0.907993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.98543e7 | − | 1.98543e7i | 0.672313 | − | 0.672313i | ||||
\(974\) | 1.21153e7 | 0.409200 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.05109e6 | −0.236936 | ||||||||
\(977\) | 2.50120e7 | − | 2.50120e7i | 0.838326 | − | 0.838326i | −0.150313 | − | 0.988639i | \(-0.548028\pi\) |
0.988639 | + | 0.150313i | \(0.0480280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.05712e8i | − | 3.52506i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.13547e7 | − | 2.13547e7i | −0.706668 | − | 0.706668i | ||||
\(983\) | 2.18441e7 | + | 2.18441e7i | 0.721024 | + | 0.721024i | 0.968814 | − | 0.247790i | \(-0.0797042\pi\) |
−0.247790 | + | 0.968814i | \(0.579704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2.09629e7i | − | 0.686688i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.36625e6 | + | 1.36625e6i | −0.0445284 | + | 0.0445284i | ||||
\(989\) | 3.03492e7 | 0.986636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.39866e6 | 0.0775863 | 0.0387931 | − | 0.999247i | \(-0.487649\pi\) | ||||
0.0387931 | + | 0.999247i | \(0.487649\pi\) | |||||||
\(992\) | −4.64774e6 | + | 4.64774e6i | −0.149956 | + | 0.149956i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1.04477e7i | − | 0.335395i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.02022e7 | + | 1.02022e7i | 0.325055 | + | 0.325055i | 0.850702 | − | 0.525648i | \(-0.176177\pi\) |
−0.525648 | + | 0.850702i | \(0.676177\pi\) | |||||||
\(998\) | −1.47464e6 | − | 1.47464e6i | −0.0468663 | − | 0.0468663i | ||||
\(999\) | 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 | 450.6.f.e.107.3 | 12 | ||
3.2 | odd | 2 | inner | 450.6.f.e.107.6 | 12 | ||
5.2 | odd | 4 | 90.6.f.c.53.2 | yes | 12 | ||
5.3 | odd | 4 | inner | 450.6.f.e.143.6 | 12 | ||
5.4 | even | 2 | 90.6.f.c.17.5 | yes | 12 | ||
15.2 | even | 4 | 90.6.f.c.53.5 | yes | 12 | ||
15.8 | even | 4 | inner | 450.6.f.e.143.3 | 12 | ||
15.14 | odd | 2 | 90.6.f.c.17.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.6.f.c.17.2 | ✓ | 12 | 15.14 | odd | 2 | ||
90.6.f.c.17.5 | yes | 12 | 5.4 | even | 2 | ||
90.6.f.c.53.2 | yes | 12 | 5.2 | odd | 4 | ||
90.6.f.c.53.5 | yes | 12 | 15.2 | even | 4 | ||
450.6.f.e.107.3 | 12 | 1.1 | even | 1 | trivial | ||
450.6.f.e.107.6 | 12 | 3.2 | odd | 2 | inner | ||
450.6.f.e.143.3 | 12 | 15.8 | even | 4 | inner | ||
450.6.f.e.143.6 | 12 | 5.3 | odd | 4 | inner |