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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.143 |
Dual form | 450.6.f.d.107.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(7\) | 52.0000 | − | 52.0000i | 0.401105 | − | 0.401105i | −0.477517 | − | 0.878622i | \(-0.658463\pi\) |
0.878622 | + | 0.477517i | \(0.158463\pi\) | |||||||
\(8\) | −45.2548 | + | 45.2548i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 124.451i | − | 0.310110i | −0.987906 | − | 0.155055i | \(-0.950445\pi\) | ||
0.987906 | − | 0.155055i | \(-0.0495555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −183.000 | − | 183.000i | −0.300326 | − | 0.300326i | 0.540815 | − | 0.841141i | \(-0.318116\pi\) |
−0.841141 | + | 0.540815i | \(0.818116\pi\) | |||||||
\(14\) | 294.156 | 0.401105 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | −350.725 | − | 350.725i | −0.294337 | − | 0.294337i | 0.544454 | − | 0.838791i | \(-0.316737\pi\) |
−0.838791 | + | 0.544454i | \(0.816737\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2108.00i | 1.33964i | 0.742526 | + | 0.669818i | \(0.233628\pi\) | ||||
−0.742526 | + | 0.669818i | \(0.766372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 352.000 | − | 352.000i | 0.155055 | − | 0.155055i | ||||
\(23\) | −1813.02 | + | 1813.02i | −0.714634 | + | 0.714634i | −0.967501 | − | 0.252867i | \(-0.918626\pi\) |
0.252867 | + | 0.967501i | \(0.418626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1035.20i | − | 0.300326i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 832.000 | + | 832.000i | 0.200553 | + | 0.200553i | ||||
\(29\) | 6998.94 | 1.54539 | 0.772694 | − | 0.634779i | \(-0.218909\pi\) | ||||
0.772694 | + | 0.634779i | \(0.218909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6784.00 | 1.26789 | 0.633945 | − | 0.773378i | \(-0.281435\pi\) | ||||
0.633945 | + | 0.773378i | \(0.281435\pi\) | |||||||
\(32\) | −724.077 | − | 724.077i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1984.00i | − | 0.294337i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3723.00 | + | 3723.00i | −0.447084 | + | 0.447084i | −0.894384 | − | 0.447300i | \(-0.852386\pi\) |
0.447300 | + | 0.894384i | \(0.352386\pi\) | |||||||
\(38\) | −5962.32 | + | 5962.32i | −0.669818 | + | 0.669818i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12208.9i | 1.13427i | 0.823624 | + | 0.567136i | \(0.191949\pi\) | ||||
−0.823624 | + | 0.567136i | \(0.808051\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3180.00 | − | 3180.00i | −0.262274 | − | 0.262274i | 0.563703 | − | 0.825978i | \(-0.309376\pi\) |
−0.825978 | + | 0.563703i | \(0.809376\pi\) | |||||||
\(44\) | 1991.21 | 0.155055 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10256.0 | −0.714634 | ||||||||
\(47\) | 7764.03 | + | 7764.03i | 0.512676 | + | 0.512676i | 0.915345 | − | 0.402670i | \(-0.131918\pi\) |
−0.402670 | + | 0.915345i | \(0.631918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11399.0i | 0.678229i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2928.00 | − | 2928.00i | 0.150163 | − | 0.150163i | ||||
\(53\) | 22856.5 | − | 22856.5i | 1.11769 | − | 1.11769i | 0.125608 | − | 0.992080i | \(-0.459912\pi\) |
0.992080 | − | 0.125608i | \(-0.0400880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4706.50i | 0.200553i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 19796.0 | + | 19796.0i | 0.772694 | + | 0.772694i | ||||
\(59\) | −35847.5 | −1.34069 | −0.670345 | − | 0.742049i | \(-0.733854\pi\) | ||||
−0.670345 | + | 0.742049i | \(0.733854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13740.0 | 0.472783 | 0.236392 | − | 0.971658i | \(-0.424035\pi\) | ||||
0.236392 | + | 0.971658i | \(0.424035\pi\) | |||||||
\(62\) | 19188.0 | + | 19188.0i | 0.633945 | + | 0.633945i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 4096.00i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34064.0 | + | 34064.0i | −0.927062 | + | 0.927062i | −0.997515 | − | 0.0704534i | \(-0.977555\pi\) |
0.0704534 | + | 0.997515i | \(0.477555\pi\) | |||||||
\(68\) | 5611.60 | − | 5611.60i | 0.147168 | − | 0.147168i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48032.3i | 1.13081i | 0.824815 | + | 0.565403i | \(0.191279\pi\) | ||||
−0.824815 | + | 0.565403i | \(0.808721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 29891.0 | + | 29891.0i | 0.656498 | + | 0.656498i | 0.954550 | − | 0.298052i | \(-0.0963368\pi\) |
−0.298052 | + | 0.954550i | \(0.596337\pi\) | |||||||
\(74\) | −21060.5 | −0.447084 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33728.0 | −0.669818 | ||||||||
\(77\) | −6471.44 | − | 6471.44i | −0.124387 | − | 0.124387i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59328.0i | 1.06953i | 0.845002 | + | 0.534764i | \(0.179599\pi\) | ||||
−0.845002 | + | 0.534764i | \(0.820401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34532.0 | + | 34532.0i | −0.567136 | + | 0.567136i | ||||
\(83\) | 38132.9 | − | 38132.9i | 0.607581 | − | 0.607581i | −0.334732 | − | 0.942313i | \(-0.608646\pi\) |
0.942313 | + | 0.334732i | \(0.108646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 17988.8i | − | 0.262274i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5632.00 | + | 5632.00i | 0.0775275 | + | 0.0775275i | ||||
\(89\) | −17045.5 | −0.228105 | −0.114053 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114053 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19032.0 | −0.240924 | ||||||||
\(92\) | −29008.3 | − | 29008.3i | −0.357317 | − | 0.357317i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 43920.0i | 0.512676i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −96093.0 | + | 96093.0i | −1.03696 | + | 1.03696i | −0.0376708 | + | 0.999290i | \(0.511994\pi\) |
−0.999290 | + | 0.0376708i | \(0.988006\pi\) | |||||||
\(98\) | −32241.2 | + | 32241.2i | −0.339115 | + | 0.339115i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36615.4i | 0.357158i | 0.983926 | + | 0.178579i | \(0.0571500\pi\) | ||||
−0.983926 | + | 0.178579i | \(0.942850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20528.0 | + | 20528.0i | 0.190657 | + | 0.190657i | 0.795980 | − | 0.605323i | \(-0.206956\pi\) |
−0.605323 | + | 0.795980i | \(0.706956\pi\) | |||||||
\(104\) | 16563.3 | 0.150163 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 129296. | 1.11769 | ||||||||
\(107\) | −52637.0 | − | 52637.0i | −0.444459 | − | 0.444459i | 0.449048 | − | 0.893507i | \(-0.351763\pi\) |
−0.893507 | + | 0.449048i | \(0.851763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 166492.i | 1.34223i | 0.741353 | + | 0.671115i | \(0.234184\pi\) | ||||
−0.741353 | + | 0.671115i | \(0.765816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13312.0 | + | 13312.0i | −0.100276 | + | 0.100276i | ||||
\(113\) | −179182. | + | 179182.i | −1.32008 | + | 1.32008i | −0.406365 | + | 0.913711i | \(0.633204\pi\) |
−0.913711 | + | 0.406365i | \(0.866796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 111983.i | 0.772694i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −101392. | − | 101392.i | −0.670345 | − | 0.670345i | ||||
\(119\) | −36475.4 | −0.236120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 145563. | 0.903832 | ||||||||
\(122\) | 38862.6 | + | 38862.6i | 0.236392 | + | 0.236392i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 108544.i | 0.633945i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 211384. | − | 211384.i | 1.16295 | − | 1.16295i | 0.179129 | − | 0.983826i | \(-0.442672\pi\) |
0.983826 | − | 0.179129i | \(-0.0573280\pi\) | |||||||
\(128\) | 11585.2 | − | 11585.2i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 169592.i | − | 0.863432i | −0.902009 | − | 0.431716i | \(-0.857908\pi\) | ||
0.902009 | − | 0.431716i | \(-0.142092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 109616. | + | 109616.i | 0.537335 | + | 0.537335i | ||||
\(134\) | −192695. | −0.927062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31744.0 | 0.147168 | ||||||||
\(137\) | −193044. | − | 193044.i | −0.878731 | − | 0.878731i | 0.114673 | − | 0.993403i | \(-0.463418\pi\) |
−0.993403 | + | 0.114673i | \(0.963418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 309604.i | 1.35916i | 0.733603 | + | 0.679578i | \(0.237837\pi\) | ||||
−0.733603 | + | 0.679578i | \(0.762163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −135856. | + | 135856.i | −0.565403 | + | 0.565403i | ||||
\(143\) | −22774.5 | + | 22774.5i | −0.0931341 | + | 0.0931341i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 169089.i | 0.656498i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −59568.0 | − | 59568.0i | −0.223542 | − | 0.223542i | ||||
\(149\) | 59078.8 | 0.218005 | 0.109002 | − | 0.994041i | \(-0.465234\pi\) | ||||
0.109002 | + | 0.994041i | \(0.465234\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 332872. | 1.18805 | 0.594025 | − | 0.804446i | \(-0.297538\pi\) | ||||
0.594025 | + | 0.804446i | \(0.297538\pi\) | |||||||
\(152\) | −95397.2 | − | 95397.2i | −0.334909 | − | 0.334909i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 36608.0i | − | 0.124387i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −319869. | + | 319869.i | −1.03567 | + | 1.03567i | −0.0363342 | + | 0.999340i | \(0.511568\pi\) |
−0.999340 | + | 0.0363342i | \(0.988432\pi\) | |||||||
\(158\) | −167805. | + | 167805.i | −0.534764 | + | 0.534764i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 188554.i | 0.573286i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 408844. | + | 408844.i | 1.20528 | + | 1.20528i | 0.972538 | + | 0.232744i | \(0.0747703\pi\) |
0.232744 | + | 0.972538i | \(0.425230\pi\) | |||||||
\(164\) | −195342. | −0.567136 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 215712. | 0.607581 | ||||||||
\(167\) | −97951.3 | − | 97951.3i | −0.271781 | − | 0.271781i | 0.558036 | − | 0.829817i | \(-0.311555\pi\) |
−0.829817 | + | 0.558036i | \(0.811555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 304315.i | − | 0.819609i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 50880.0 | − | 50880.0i | 0.131137 | − | 0.131137i | ||||
\(173\) | 171384. | − | 171384.i | 0.435367 | − | 0.435367i | −0.455082 | − | 0.890449i | \(-0.650390\pi\) |
0.890449 | + | 0.455082i | \(0.150390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 31859.4i | 0.0775275i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −48212.0 | − | 48212.0i | −0.114053 | − | 0.114053i | ||||
\(179\) | −716033. | −1.67032 | −0.835162 | − | 0.550004i | \(-0.814626\pi\) | ||||
−0.835162 | + | 0.550004i | \(0.814626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18052.0 | −0.0409571 | −0.0204785 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204785 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(182\) | −53830.6 | − | 53830.6i | −0.120462 | − | 0.120462i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 164096.i | − | 0.357317i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −43648.0 | + | 43648.0i | −0.0912768 | + | 0.0912768i | ||||
\(188\) | −124225. | + | 124225.i | −0.256338 | + | 0.256338i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 304260.i | − | 0.603477i | −0.953391 | − | 0.301739i | \(-0.902433\pi\) | ||
0.953391 | − | 0.301739i | \(-0.0975670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 132339. | + | 132339.i | 0.255738 | + | 0.255738i | 0.823318 | − | 0.567580i | \(-0.192120\pi\) |
−0.567580 | + | 0.823318i | \(0.692120\pi\) | |||||||
\(194\) | −543584. | −1.03696 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −182384. | −0.339115 | ||||||||
\(197\) | −507237. | − | 507237.i | −0.931206 | − | 0.931206i | 0.0665755 | − | 0.997781i | \(-0.478793\pi\) |
−0.997781 | + | 0.0665755i | \(0.978793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 990840.i | 1.77366i | 0.462094 | + | 0.886831i | \(0.347098\pi\) | ||||
−0.462094 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −103564. | + | 103564.i | −0.178579 | + | 0.178579i | ||||
\(203\) | 363945. | − | 363945.i | 0.619863 | − | 0.619863i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 116124.i | 0.190657i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 46848.0 | + | 46848.0i | 0.0750815 | + | 0.0750815i | ||||
\(209\) | 262342. | 0.415435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 217076. | 0.335665 | 0.167832 | − | 0.985816i | \(-0.446323\pi\) | ||||
0.167832 | + | 0.985816i | \(0.446323\pi\) | |||||||
\(212\) | 365704. | + | 365704.i | 0.558844 | + | 0.558844i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 297760.i | − | 0.444459i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 352768. | − | 352768.i | 0.508557 | − | 0.508557i | ||||
\(218\) | −470910. | + | 470910.i | −0.671115 | + | 0.671115i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 128365.i | 0.176794i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −800004. | − | 800004.i | −1.07728 | − | 1.07728i | −0.996752 | − | 0.0805314i | \(-0.974338\pi\) |
−0.0805314 | − | 0.996752i | \(-0.525662\pi\) | |||||||
\(224\) | −75304.0 | −0.100276 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.01361e6 | −1.32008 | ||||||||
\(227\) | 231286. | + | 231286.i | 0.297910 | + | 0.297910i | 0.840195 | − | 0.542285i | \(-0.182441\pi\) |
−0.542285 | + | 0.840195i | \(0.682441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 185046.i | 0.233180i | 0.993180 | + | 0.116590i | \(0.0371963\pi\) | ||||
−0.993180 | + | 0.116590i | \(0.962804\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −316736. | + | 316736.i | −0.386347 | + | 0.386347i | ||||
\(233\) | −59685.5 | + | 59685.5i | −0.0720243 | + | 0.0720243i | −0.742201 | − | 0.670177i | \(-0.766218\pi\) |
0.670177 | + | 0.742201i | \(0.266218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 573560.i | − | 0.670345i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −103168. | − | 103168.i | −0.118060 | − | 0.118060i | ||||
\(239\) | 612960. | 0.694124 | 0.347062 | − | 0.937842i | \(-0.387179\pi\) | ||||
0.347062 | + | 0.937842i | \(0.387179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.28174e6 | 1.42154 | 0.710768 | − | 0.703426i | \(-0.248347\pi\) | ||||
0.710768 | + | 0.703426i | \(0.248347\pi\) | |||||||
\(242\) | 411714. | + | 411714.i | 0.451916 | + | 0.451916i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 219840.i | 0.236392i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 385764. | − | 385764.i | 0.402327 | − | 0.402327i | ||||
\(248\) | −307009. | + | 307009.i | −0.316973 | + | 0.316973i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 101603.i | − | 0.101794i | −0.998704 | − | 0.0508969i | \(-0.983792\pi\) | ||
0.998704 | − | 0.0508969i | \(-0.0162080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 225632. | + | 225632.i | 0.221615 | + | 0.221615i | ||||
\(254\) | 1.19577e6 | 1.16295 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −812060. | − | 812060.i | −0.766929 | − | 0.766929i | 0.210636 | − | 0.977565i | \(-0.432447\pi\) |
−0.977565 | + | 0.210636i | \(0.932447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 387192.i | 0.358655i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 479680. | − | 479680.i | 0.431716 | − | 0.431716i | ||||
\(263\) | 885657. | − | 885657.i | 0.789544 | − | 0.789544i | −0.191876 | − | 0.981419i | \(-0.561457\pi\) |
0.981419 | + | 0.191876i | \(0.0614570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 620082.i | 0.537335i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −545024. | − | 545024.i | −0.463531 | − | 0.463531i | ||||
\(269\) | 2.09847e6 | 1.76816 | 0.884080 | − | 0.467335i | \(-0.154786\pi\) | ||||
0.884080 | + | 0.467335i | \(0.154786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.52784e6 | −1.26373 | −0.631866 | − | 0.775078i | \(-0.717711\pi\) | ||||
−0.631866 | + | 0.775078i | \(0.717711\pi\) | |||||||
\(272\) | 89785.6 | + | 89785.6i | 0.0735842 | + | 0.0735842i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.09202e6i | − | 0.878731i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −808071. | + | 808071.i | −0.632776 | + | 0.632776i | −0.948763 | − | 0.315987i | \(-0.897664\pi\) |
0.315987 | + | 0.948763i | \(0.397664\pi\) | |||||||
\(278\) | −875692. | + | 875692.i | −0.679578 | + | 0.679578i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 487322.i | − | 0.368172i | −0.982910 | − | 0.184086i | \(-0.941068\pi\) | ||
0.982910 | − | 0.184086i | \(-0.0589325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 401968. | + | 401968.i | 0.298350 | + | 0.298350i | 0.840367 | − | 0.542018i | \(-0.182339\pi\) |
−0.542018 | + | 0.840367i | \(0.682339\pi\) | |||||||
\(284\) | −768518. | −0.565403 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −128832. | −0.0931341 | ||||||||
\(287\) | 634863. | + | 634863.i | 0.454962 | + | 0.454962i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.17384e6i | − | 0.826732i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −478256. | + | 478256.i | −0.328249 | + | 0.328249i | ||||
\(293\) | 1.12004e6 | − | 1.12004e6i | 0.762195 | − | 0.762195i | −0.214524 | − | 0.976719i | \(-0.568820\pi\) |
0.976719 | + | 0.214524i | \(0.0688199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 336967.i | − | 0.223542i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 167100. | + | 167100.i | 0.109002 | + | 0.109002i | ||||
\(299\) | 663566. | 0.429246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −330720. | −0.210399 | ||||||||
\(302\) | 941504. | + | 941504.i | 0.594025 | + | 0.594025i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 539648.i | − | 0.334909i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80918e6 | − | 1.80918e6i | 1.09556 | − | 1.09556i | 0.100636 | − | 0.994923i | \(-0.467912\pi\) |
0.994923 | − | 0.100636i | \(-0.0320877\pi\) | |||||||
\(308\) | 103543. | − | 103543.i | 0.0621934 | − | 0.0621934i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 170831.i | 0.100154i | 0.998745 | + | 0.0500768i | \(0.0159466\pi\) | ||||
−0.998745 | + | 0.0500768i | \(0.984053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 713409. | + | 713409.i | 0.411602 | + | 0.411602i | 0.882296 | − | 0.470694i | \(-0.155996\pi\) |
−0.470694 | + | 0.882296i | \(0.655996\pi\) | |||||||
\(314\) | −1.80945e6 | −1.03567 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −949248. | −0.534764 | ||||||||
\(317\) | 1.89874e6 | + | 1.89874e6i | 1.06125 | + | 1.06125i | 0.997998 | + | 0.0632533i | \(0.0201476\pi\) |
0.0632533 | + | 0.997998i | \(0.479852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 871024.i | − | 0.479240i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −533312. | + | 533312.i | −0.286643 | + | 0.286643i | ||||
\(323\) | 739328. | − | 739328.i | 0.394304 | − | 0.394304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.31277e6i | 1.20528i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −552512. | − | 552512.i | −0.283568 | − | 0.283568i | ||||
\(329\) | 807459. | 0.411274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.07412e6 | −1.04055 | −0.520277 | − | 0.853997i | \(-0.674171\pi\) | ||||
−0.520277 | + | 0.853997i | \(0.674171\pi\) | |||||||
\(332\) | 610126. | + | 610126.i | 0.303790 | + | 0.303790i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 554096.i | − | 0.271781i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 954609. | − | 954609.i | 0.457879 | − | 0.457879i | −0.440080 | − | 0.897959i | \(-0.645050\pi\) |
0.897959 | + | 0.440080i | \(0.145050\pi\) | |||||||
\(338\) | 860733. | − | 860733.i | 0.409804 | − | 0.409804i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 844274.i | − | 0.393186i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.46671e6 | + | 1.46671e6i | 0.673146 | + | 0.673146i | ||||
\(344\) | 287821. | 0.131137 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 969496. | 0.435367 | ||||||||
\(347\) | 803681. | + | 803681.i | 0.358311 | + | 0.358311i | 0.863190 | − | 0.504879i | \(-0.168463\pi\) |
−0.504879 | + | 0.863190i | \(0.668463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.59168e6i | − | 1.57846i | −0.614098 | − | 0.789230i | \(-0.710480\pi\) | ||
0.614098 | − | 0.789230i | \(-0.289520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −90112.0 | + | 90112.0i | −0.0387638 | + | 0.0387638i | ||||
\(353\) | 1.06648e6 | − | 1.06648e6i | 0.455529 | − | 0.455529i | −0.441655 | − | 0.897185i | \(-0.645609\pi\) |
0.897185 | + | 0.441655i | \(0.145609\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 272728.i | − | 0.114053i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.02525e6 | − | 2.02525e6i | −0.835162 | − | 0.835162i | ||||
\(359\) | 1.93336e6 | 0.791729 | 0.395865 | − | 0.918309i | \(-0.370445\pi\) | ||||
0.395865 | + | 0.918309i | \(0.370445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.96756e6 | −0.794623 | ||||||||
\(362\) | −51058.8 | − | 51058.8i | −0.0204785 | − | 0.0204785i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 304512.i | − | 0.120462i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −320192. | + | 320192.i | −0.124092 | + | 0.124092i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.642333 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(368\) | 464134. | − | 464134.i | 0.178658 | − | 0.178658i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.37708e6i | − | 0.896621i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 194975. | + | 194975.i | 0.0725616 | + | 0.0725616i | 0.742456 | − | 0.669895i | \(-0.233661\pi\) |
−0.669895 | + | 0.742456i | \(0.733661\pi\) | |||||||
\(374\) | −246910. | −0.0912768 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −702720. | −0.256338 | ||||||||
\(377\) | −1.28081e6 | − | 1.28081e6i | −0.464120 | − | 0.464120i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.13974e6i | − | 0.407575i | −0.979015 | − | 0.203788i | \(-0.934675\pi\) | ||
0.979015 | − | 0.203788i | \(-0.0653252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 860576. | − | 860576.i | 0.301739 | − | 0.301739i | ||||
\(383\) | 893780. | − | 893780.i | 0.311339 | − | 0.311339i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) |
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 748622.i | 0.255738i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.53749e6 | − | 1.53749e6i | −0.518480 | − | 0.518480i | ||||
\(389\) | 537776. | 0.180189 | 0.0900943 | − | 0.995933i | \(-0.471283\pi\) | ||||
0.0900943 | + | 0.995933i | \(0.471283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.27174e6 | 0.420686 | ||||||||
\(392\) | −515860. | − | 515860.i | −0.169557 | − | 0.169557i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 2.86937e6i | − | 0.931206i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.68409e6 | − | 2.68409e6i | 0.854713 | − | 0.854713i | −0.135996 | − | 0.990709i | \(-0.543424\pi\) |
0.990709 | + | 0.135996i | \(0.0434235\pi\) | |||||||
\(398\) | −2.80252e6 | + | 2.80252e6i | −0.886831 | + | 0.886831i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.27600e6i | − | 1.32794i | −0.747761 | − | 0.663968i | \(-0.768871\pi\) | ||
0.747761 | − | 0.663968i | \(-0.231129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.24147e6 | − | 1.24147e6i | −0.380780 | − | 0.380780i | ||||
\(404\) | −585846. | −0.178579 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.05878e6 | 0.619863 | ||||||||
\(407\) | 463330. | + | 463330.i | 0.138645 | + | 0.138645i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.75446e6i | 0.814193i | 0.913385 | + | 0.407097i | \(0.133459\pi\) | ||||
−0.913385 | + | 0.407097i | \(0.866541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −328448. | + | 328448.i | −0.0953287 | + | 0.0953287i | ||||
\(413\) | −1.86407e6 | + | 1.86407e6i | −0.537758 | + | 0.537758i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 265012.i | 0.0750815i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 742016. | + | 742016.i | 0.207717 | + | 0.207717i | ||||
\(419\) | 5.76471e6 | 1.60414 | 0.802071 | − | 0.597229i | \(-0.203732\pi\) | ||||
0.802071 | + | 0.597229i | \(0.203732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −256330. | −0.0704846 | −0.0352423 | − | 0.999379i | \(-0.511220\pi\) | ||||
−0.0352423 | + | 0.999379i | \(0.511220\pi\) | |||||||
\(422\) | 613984. | + | 613984.i | 0.167832 | + | 0.167832i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.06874e6i | 0.558844i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 714480. | − | 714480.i | 0.189636 | − | 0.189636i | ||||
\(428\) | 842192. | − | 842192.i | 0.222230 | − | 0.222230i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.57507e6i | 0.667723i | 0.942622 | + | 0.333862i | \(0.108352\pi\) | ||||
−0.942622 | + | 0.333862i | \(0.891648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.45903e6 | − | 2.45903e6i | −0.630295 | − | 0.630295i | 0.317847 | − | 0.948142i | \(-0.397040\pi\) |
−0.948142 | + | 0.317847i | \(0.897040\pi\) | |||||||
\(434\) | 1.99556e6 | 0.508557 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.66387e6 | −0.671115 | ||||||||
\(437\) | −3.82185e6 | − | 3.82185e6i | −0.957348 | − | 0.957348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 282472.i | 0.0699542i | 0.999388 | + | 0.0349771i | \(0.0111358\pi\) | ||||
−0.999388 | + | 0.0349771i | \(0.988864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −363072. | + | 363072.i | −0.0883969 | + | 0.0883969i | ||||
\(443\) | −2.56554e6 | + | 2.56554e6i | −0.621112 | + | 0.621112i | −0.945816 | − | 0.324704i | \(-0.894735\pi\) |
0.324704 | + | 0.945816i | \(0.394735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 4.52551e6i | − | 1.07728i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −212992. | − | 212992.i | −0.0501381 | − | 0.0501381i | ||||
\(449\) | −3.48771e6 | −0.816440 | −0.408220 | − | 0.912884i | \(-0.633850\pi\) | ||||
−0.408220 | + | 0.912884i | \(0.633850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.51941e6 | 0.351749 | ||||||||
\(452\) | −2.86692e6 | − | 2.86692e6i | −0.660038 | − | 0.660038i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.30835e6i | 0.297910i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.53370e6 | − | 2.53370e6i | 0.567497 | − | 0.567497i | −0.363929 | − | 0.931427i | \(-0.618565\pi\) |
0.931427 | + | 0.363929i | \(0.118565\pi\) | |||||||
\(458\) | −523389. | + | 523389.i | −0.116590 | + | 0.116590i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.97168e6i | − | 0.870406i | −0.900332 | − | 0.435203i | \(-0.856677\pi\) | ||
0.900332 | − | 0.435203i | \(-0.143323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00226e6 | − | 2.00226e6i | −0.434077 | − | 0.434077i | 0.455935 | − | 0.890013i | \(-0.349305\pi\) |
−0.890013 | + | 0.455935i | \(0.849305\pi\) | |||||||
\(464\) | −1.79173e6 | −0.386347 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −337632. | −0.0720243 | ||||||||
\(467\) | −2.66700e6 | − | 2.66700e6i | −0.565889 | − | 0.565889i | 0.365085 | − | 0.930974i | \(-0.381040\pi\) |
−0.930974 | + | 0.365085i | \(0.881040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.54266e6i | 0.743698i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.62227e6 | − | 1.62227e6i | 0.335173 | − | 0.335173i | ||||
\(473\) | −395754. | + | 395754.i | −0.0813340 | + | 0.0813340i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 583606.i | − | 0.118060i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.73371e6 | + | 1.73371e6i | 0.347062 | + | 0.347062i | ||||
\(479\) | −6.79230e6 | −1.35263 | −0.676314 | − | 0.736614i | \(-0.736424\pi\) | ||||
−0.676314 | + | 0.736614i | \(0.736424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36262e6 | 0.268542 | ||||||||
\(482\) | 3.62531e6 | + | 3.62531e6i | 0.710768 | + | 0.710768i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.32901e6i | 0.451916i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.81905e6 | + | 6.81905e6i | −1.30287 | + | 1.30287i | −0.376423 | + | 0.926448i | \(0.622846\pi\) |
−0.926448 | + | 0.376423i | \(0.877154\pi\) | |||||||
\(488\) | −621801. | + | 621801.i | −0.118196 | + | 0.118196i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.09964e6i | 0.393043i | 0.980499 | + | 0.196522i | \(0.0629646\pi\) | ||||
−0.980499 | + | 0.196522i | \(0.937035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.45470e6 | − | 2.45470e6i | −0.454864 | − | 0.454864i | ||||
\(494\) | 2.18221e6 | 0.402327 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.73670e6 | −0.316973 | ||||||||
\(497\) | 2.49768e6 | + | 2.49768e6i | 0.453572 | + | 0.453572i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.39057e6i | − | 0.609567i | −0.952422 | − | 0.304784i | \(-0.901416\pi\) | ||
0.952422 | − | 0.304784i | \(-0.0985841\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 287376. | − | 287376.i | 0.0508969 | − | 0.0508969i | ||||
\(503\) | 1.45919e6 | − | 1.45919e6i | 0.257153 | − | 0.257153i | −0.566742 | − | 0.823895i | \(-0.691796\pi\) |
0.823895 | + | 0.566742i | \(0.191796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.27637e6i | 0.221615i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.38214e6 | + | 3.38214e6i | 0.581477 | + | 0.581477i | ||||
\(509\) | −7.03058e6 | −1.20281 | −0.601405 | − | 0.798944i | \(-0.705392\pi\) | ||||
−0.601405 | + | 0.798944i | \(0.705392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.10866e6 | 0.526649 | ||||||||
\(512\) | 185364. | + | 185364.i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 4.59370e6i | − | 0.766929i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 966240. | − | 966240.i | 0.158986 | − | 0.158986i | ||||
\(518\) | −1.09514e6 | + | 1.09514e6i | −0.179328 | + | 0.179328i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.98178e6i | 1.44967i | 0.688924 | + | 0.724834i | \(0.258083\pi\) | ||||
−0.688924 | + | 0.724834i | \(0.741917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.11278e6 | + | 6.11278e6i | 0.977202 | + | 0.977202i | 0.999746 | − | 0.0225440i | \(-0.00717660\pi\) |
−0.0225440 | + | 0.999746i | \(0.507177\pi\) | |||||||
\(524\) | 2.71348e6 | 0.431716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.01003e6 | 0.789544 | ||||||||
\(527\) | −2.37932e6 | − | 2.37932e6i | −0.373187 | − | 0.373187i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 137753.i | − | 0.0214024i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.75386e6 | + | 1.75386e6i | −0.268667 | + | 0.268667i | ||||
\(533\) | 2.23423e6 | − | 2.23423e6i | 0.340651 | − | 0.340651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.08312e6i | − | 0.463531i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.93536e6 | + | 5.93536e6i | 0.884080 | + | 0.884080i | ||||
\(539\) | 1.41861e6 | 0.210326 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.23123e7 | 1.80861 | 0.904307 | − | 0.426883i | \(-0.140389\pi\) | ||||
0.904307 | + | 0.426883i | \(0.140389\pi\) | |||||||
\(542\) | −4.32138e6 | − | 4.32138e6i | −0.631866 | − | 0.631866i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 507904.i | 0.0735842i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.04163e6 | + | 6.04163e6i | −0.863348 | + | 0.863348i | −0.991725 | − | 0.128378i | \(-0.959023\pi\) |
0.128378 | + | 0.991725i | \(0.459023\pi\) | |||||||
\(548\) | 3.08871e6 | − | 3.08871e6i | 0.439365 | − | 0.439365i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.47538e7i | 2.07026i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.08506e6 | + | 3.08506e6i | 0.428993 | + | 0.428993i | ||||
\(554\) | −4.57114e6 | −0.632776 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.95366e6 | −0.679578 | ||||||||
\(557\) | 1.67984e6 | + | 1.67984e6i | 0.229419 | + | 0.229419i | 0.812450 | − | 0.583031i | \(-0.198133\pi\) |
−0.583031 | + | 0.812450i | \(0.698133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.16388e6i | 0.157536i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.37836e6 | − | 1.37836e6i | 0.184086 | − | 0.184086i | ||||
\(563\) | −1.54549e6 | + | 1.54549e6i | −0.205492 | + | 0.205492i | −0.802348 | − | 0.596856i | \(-0.796416\pi\) |
0.596856 | + | 0.802348i | \(0.296416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.27387e6i | 0.298350i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.17370e6 | − | 2.17370e6i | −0.282701 | − | 0.282701i | ||||
\(569\) | −1.07876e7 | −1.39683 | −0.698414 | − | 0.715694i | \(-0.746111\pi\) | ||||
−0.698414 | + | 0.715694i | \(0.746111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00501e6 | −0.642414 | −0.321207 | − | 0.947009i | \(-0.604088\pi\) | ||||
−0.321207 | + | 0.947009i | \(0.604088\pi\) | |||||||
\(572\) | −364392. | − | 364392.i | −0.0465670 | − | 0.0465670i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.59133e6i | 0.454962i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.63956e6 | + | 3.63956e6i | −0.455103 | + | 0.455103i | −0.897044 | − | 0.441941i | \(-0.854290\pi\) |
0.441941 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(578\) | 3.32012e6 | − | 3.32012e6i | 0.413366 | − | 0.413366i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.96582e6i | − | 0.487408i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.84451e6 | − | 2.84451e6i | −0.346606 | − | 0.346606i | ||||
\(584\) | −2.70542e6 | −0.328249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.33593e6 | 0.762195 | ||||||||
\(587\) | 7.09648e6 | + | 7.09648e6i | 0.850056 | + | 0.850056i | 0.990140 | − | 0.140084i | \(-0.0447371\pi\) |
−0.140084 | + | 0.990140i | \(0.544737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.43007e7i | 1.69851i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 953088. | − | 953088.i | 0.111771 | − | 0.111771i | ||||
\(593\) | −5.45083e6 | + | 5.45083e6i | −0.636540 | + | 0.636540i | −0.949700 | − | 0.313160i | \(-0.898612\pi\) |
0.313160 | + | 0.949700i | \(0.398612\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 945260.i | 0.109002i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.87685e6 | + | 1.87685e6i | 0.214623 | + | 0.214623i | ||||
\(599\) | 305261. | 0.0347619 | 0.0173810 | − | 0.999849i | \(-0.494467\pi\) | ||||
0.0173810 | + | 0.999849i | \(0.494467\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.67187e6 | −1.09226 | −0.546128 | − | 0.837702i | \(-0.683899\pi\) | ||||
−0.546128 | + | 0.837702i | \(0.683899\pi\) | |||||||
\(602\) | −935417. | − | 935417.i | −0.105200 | − | 0.105200i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.32595e6i | 0.594025i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.87772e6 | + | 3.87772e6i | −0.427173 | + | 0.427173i | −0.887664 | − | 0.460491i | \(-0.847673\pi\) |
0.460491 | + | 0.887664i | \(0.347673\pi\) | |||||||
\(608\) | 1.52636e6 | − | 1.52636e6i | 0.167454 | − | 0.167454i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.84164e6i | − | 0.307940i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.14632e6 | − | 2.14632e6i | −0.230698 | − | 0.230698i | 0.582286 | − | 0.812984i | \(-0.302158\pi\) |
−0.812984 | + | 0.582286i | \(0.802158\pi\) | |||||||
\(614\) | 1.02343e7 | 1.09556 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 585728. | 0.0621934 | ||||||||
\(617\) | −2.19835e6 | − | 2.19835e6i | −0.232479 | − | 0.232479i | 0.581248 | − | 0.813727i | \(-0.302565\pi\) |
−0.813727 | + | 0.581248i | \(0.802565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.24533e6i | 0.235534i | 0.993041 | + | 0.117767i | \(0.0375736\pi\) | ||||
−0.993041 | + | 0.117767i | \(0.962426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −483184. | + | 483184.i | −0.0500768 | + | 0.0500768i | ||||
\(623\) | −886367. | + | 886367.i | −0.0914942 | + | 0.0914942i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.03565e6i | 0.411602i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.11790e6 | − | 5.11790e6i | −0.517837 | − | 0.517837i | ||||
\(629\) | 2.61150e6 | 0.263186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32882e7 | 1.32860 | 0.664300 | − | 0.747466i | \(-0.268730\pi\) | ||||
0.664300 | + | 0.747466i | \(0.268730\pi\) | |||||||
\(632\) | −2.68488e6 | − | 2.68488e6i | −0.267382 | − | 0.267382i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.07409e7i | 1.06125i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.08602e6 | − | 2.08602e6i | 0.203690 | − | 0.203690i | ||||
\(638\) | 2.46363e6 | − | 2.46363e6i | 0.239620 | − | 0.239620i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 241509.i | 0.0232161i | 0.999933 | + | 0.0116080i | \(0.00369504\pi\) | ||||
−0.999933 | + | 0.0116080i | \(0.996305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.31899e7 | + | 1.31899e7i | 1.25810 | + | 1.25810i | 0.951999 | + | 0.306101i | \(0.0990245\pi\) |
0.306101 | + | 0.951999i | \(0.400976\pi\) | |||||||
\(644\) | −3.01687e6 | −0.286643 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.18227e6 | 0.394304 | ||||||||
\(647\) | 2.08840e6 | + | 2.08840e6i | 0.196134 | + | 0.196134i | 0.798340 | − | 0.602206i | \(-0.205712\pi\) |
−0.602206 | + | 0.798340i | \(0.705712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.46125e6i | 0.415762i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.54150e6 | + | 6.54150e6i | −0.602641 | + | 0.602641i | ||||
\(653\) | −9.34448e6 | + | 9.34448e6i | −0.857575 | + | 0.857575i | −0.991052 | − | 0.133477i | \(-0.957386\pi\) |
0.133477 | + | 0.991052i | \(0.457386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3.12548e6i | − | 0.283568i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.28384e6 | + | 2.28384e6i | 0.205637 | + | 0.205637i | ||||
\(659\) | 1.69591e6 | 0.152121 | 0.0760604 | − | 0.997103i | \(-0.475766\pi\) | ||||
0.0760604 | + | 0.997103i | \(0.475766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.77243e6 | −0.691915 | −0.345958 | − | 0.938250i | \(-0.612446\pi\) | ||||
−0.345958 | + | 0.938250i | \(0.612446\pi\) | |||||||
\(662\) | −5.86651e6 | − | 5.86651e6i | −0.520277 | − | 0.520277i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.45139e6i | 0.303790i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.26892e7 | + | 1.26892e7i | −1.10439 | + | 1.10439i | ||||
\(668\) | 1.56722e6 | − | 1.56722e6i | 0.135890 | − | 0.135890i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.70995e6i | − | 0.146615i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.04638e7 | − | 1.04638e7i | −0.890540 | − | 0.890540i | 0.104033 | − | 0.994574i | \(-0.466825\pi\) |
−0.994574 | + | 0.104033i | \(0.966825\pi\) | |||||||
\(674\) | 5.40008e6 | 0.457879 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.86904e6 | 0.409804 | ||||||||
\(677\) | −2.25257e6 | − | 2.25257e6i | −0.188889 | − | 0.188889i | 0.606327 | − | 0.795216i | \(-0.292642\pi\) |
−0.795216 | + | 0.606327i | \(0.792642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.99367e6i | 0.831861i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.38797e6 | − | 2.38797e6i | 0.196593 | − | 0.196593i | ||||
\(683\) | −9.66190e6 | + | 9.66190e6i | −0.792521 | + | 0.792521i | −0.981903 | − | 0.189382i | \(-0.939351\pi\) |
0.189382 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.29698e6i | 0.673146i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 814080. | + | 814080.i | 0.0655686 | + | 0.0655686i | ||||
\(689\) | −8.36549e6 | −0.671341 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.36923e7 | −1.88761 | −0.943803 | − | 0.330508i | \(-0.892780\pi\) | ||||
−0.943803 | + | 0.330508i | \(0.892780\pi\) | |||||||
\(692\) | 2.74215e6 | + | 2.74215e6i | 0.217684 | + | 0.217684i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.54630e6i | 0.358311i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.28197e6 | − | 4.28197e6i | 0.333858 | − | 0.333858i | ||||
\(698\) | 1.01588e7 | − | 1.01588e7i | 0.789230 | − | 0.789230i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.35032e6i | 0.411230i | 0.978633 | + | 0.205615i | \(0.0659194\pi\) | ||||
−0.978633 | + | 0.205615i | \(0.934081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.84808e6 | − | 7.84808e6i | −0.598929 | − | 0.598929i | ||||
\(704\) | −509750. | −0.0387638 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.03293e6 | 0.455529 | ||||||||
\(707\) | 1.90400e6 | + | 1.90400e6i | 0.143258 | + | 0.143258i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.20669e7i | − | 0.901532i | −0.892642 | − | 0.450766i | \(-0.851151\pi\) | ||
0.892642 | − | 0.450766i | \(-0.148849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 771392. | − | 771392.i | 0.0570263 | − | 0.0570263i | ||||
\(713\) | −1.22995e7 | + | 1.22995e7i | −0.906077 | + | 0.906077i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.14565e7i | − | 0.835162i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.46837e6 | + | 5.46837e6i | 0.395865 | + | 0.395865i | ||||
\(719\) | 6.03607e6 | 0.435444 | 0.217722 | − | 0.976011i | \(-0.430137\pi\) | ||||
0.217722 | + | 0.976011i | \(0.430137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.13491e6 | 0.152947 | ||||||||
\(722\) | −5.56511e6 | − | 5.56511e6i | −0.397311 | − | 0.397311i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 288832.i | − | 0.0204785i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.79026e6 | + | 7.79026e6i | −0.546658 | + | 0.546658i | −0.925473 | − | 0.378815i | \(-0.876332\pi\) |
0.378815 | + | 0.925473i | \(0.376332\pi\) | |||||||
\(728\) | 861290. | − | 861290.i | 0.0602311 | − | 0.0602311i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.23061e6i | 0.154394i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.98675e6 | + | 1.98675e6i | 0.136579 | + | 0.136579i | 0.772091 | − | 0.635512i | \(-0.219211\pi\) |
−0.635512 | + | 0.772091i | \(0.719211\pi\) | |||||||
\(734\) | −1.81128e6 | −0.124092 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.62554e6 | 0.178658 | ||||||||
\(737\) | 4.23929e6 | + | 4.23929e6i | 0.287491 | + | 0.287491i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.35338e7i | − | 0.911608i | −0.890080 | − | 0.455804i | \(-0.849352\pi\) | ||
0.890080 | − | 0.455804i | \(-0.150648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.72339e6 | − | 6.72339e6i | 0.448310 | − | 0.448310i | ||||
\(743\) | 1.97667e7 | − | 1.97667e7i | 1.31360 | − | 1.31360i | 0.394856 | − | 0.918743i | \(-0.370794\pi\) |
0.918743 | − | 0.394856i | \(-0.129206\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.10295e6i | 0.0725616i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −698368. | − | 698368.i | −0.0456384 | − | 0.0456384i | ||||
\(749\) | −5.47425e6 | −0.356550 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.12214e7 | 0.726016 | 0.363008 | − | 0.931786i | \(-0.381750\pi\) | ||||
0.363008 | + | 0.931786i | \(0.381750\pi\) | |||||||
\(752\) | −1.98759e6 | − | 1.98759e6i | −0.128169 | − | 0.128169i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 7.24534e6i | − | 0.464120i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.20785e6 | − | 3.20785e6i | 0.203458 | − | 0.203458i | −0.598022 | − | 0.801480i | \(-0.704046\pi\) |
0.801480 | + | 0.598022i | \(0.204046\pi\) | |||||||
\(758\) | 3.22367e6 | − | 3.22367e6i | 0.203788 | − | 0.203788i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 522228.i | − | 0.0326888i | −0.999866 | − | 0.0163444i | \(-0.994797\pi\) | ||
0.999866 | − | 0.0163444i | \(-0.00520281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.65758e6 | + | 8.65758e6i | 0.538376 | + | 0.538376i | ||||
\(764\) | 4.86815e6 | 0.301739 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.05598e6 | 0.311339 | ||||||||
\(767\) | 6.56009e6 | + | 6.56009e6i | 0.402644 | + | 0.402644i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.13153e7i | − | 1.29980i | −0.760020 | − | 0.649899i | \(-0.774811\pi\) | ||
0.760020 | − | 0.649899i | \(-0.225189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.11742e6 | + | 2.11742e6i | −0.127869 | + | 0.127869i | ||||
\(773\) | 1.24996e6 | − | 1.24996e6i | 0.0752397 | − | 0.0752397i | −0.668486 | − | 0.743725i | \(-0.733057\pi\) |
0.743725 | + | 0.668486i | \(0.233057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 8.69735e6i | − | 0.518480i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.52106e6 | + | 1.52106e6i | 0.0900943 | + | 0.0900943i | ||||
\(779\) | −2.57364e7 | −1.51951 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.97766e6 | 0.350674 | ||||||||
\(782\) | 3.59704e6 | + | 3.59704e6i | 0.210343 | + | 0.210343i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 2.91814e6i | − | 0.169557i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.01615e7 | − | 2.01615e7i | 1.16034 | − | 1.16034i | 0.175943 | − | 0.984400i | \(-0.443703\pi\) |
0.984400 | − | 0.175943i | \(-0.0562974\pi\) | |||||||
\(788\) | 8.11580e6 | − | 8.11580e6i | 0.465603 | − | 0.465603i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.86350e7i | 1.05898i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51442e6 | − | 2.51442e6i | −0.141989 | − | 0.141989i | ||||
\(794\) | 1.51835e7 | 0.854713 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.58534e7 | −0.886831 | ||||||||
\(797\) | −3.94436e6 | − | 3.94436e6i | −0.219954 | − | 0.219954i | 0.588525 | − | 0.808479i | \(-0.299709\pi\) |
−0.808479 | + | 0.588525i | \(0.799709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.44608e6i | − | 0.301798i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.20944e7 | − | 1.20944e7i | 0.663968 | − | 0.663968i | ||||
\(803\) | 3.71996e6 | − | 3.71996e6i | 0.203587 | − | 0.203587i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 7.02283e6i | − | 0.380780i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.65702e6 | − | 1.65702e6i | −0.0892895 | − | 0.0892895i | ||||
\(809\) | 1.08001e6 | 0.0580171 | 0.0290085 | − | 0.999579i | \(-0.490765\pi\) | ||||
0.0290085 | + | 0.999579i | \(0.490765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.61743e7 | −1.39740 | −0.698702 | − | 0.715412i | \(-0.746239\pi\) | ||||
−0.698702 | + | 0.715412i | \(0.746239\pi\) | |||||||
\(812\) | 5.82312e6 | + | 5.82312e6i | 0.309931 | + | 0.309931i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.62099e6i | 0.138645i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.70344e6 | − | 6.70344e6i | 0.351352 | − | 0.351352i | ||||
\(818\) | −7.79078e6 | + | 7.79078e6i | −0.407097 | + | 0.407097i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.81466e7i | − | 0.939589i | −0.882776 | − | 0.469795i | \(-0.844328\pi\) | ||
0.882776 | − | 0.469795i | \(-0.155672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.63046e7 | − | 1.63046e7i | −0.839095 | − | 0.839095i | 0.149645 | − | 0.988740i | \(-0.452187\pi\) |
−0.988740 | + | 0.149645i | \(0.952187\pi\) | |||||||
\(824\) | −1.85798e6 | −0.0953287 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.05448e7 | −0.537758 | ||||||||
\(827\) | 1.89659e7 | + | 1.89659e7i | 0.964295 | + | 0.964295i | 0.999384 | − | 0.0350892i | \(-0.0111715\pi\) |
−0.0350892 | + | 0.999384i | \(0.511172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.48454e7i | − | 0.750251i | −0.926974 | − | 0.375126i | \(-0.877600\pi\) | ||
0.926974 | − | 0.375126i | \(-0.122400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −749568. | + | 749568.i | −0.0375407 | + | 0.0375407i | ||||
\(833\) | 3.99791e6 | − | 3.99791e6i | 0.199628 | − | 0.199628i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.19748e6i | 0.207717i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.63051e7 | + | 1.63051e7i | 0.802071 | + | 0.802071i | ||||
\(839\) | 958537. | 0.0470115 | 0.0235057 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235057 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.84741e7 | 1.38822 | ||||||||
\(842\) | −725011. | − | 725011.i | −0.0352423 | − | 0.0352423i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.47322e6i | 0.167832i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.56928e6 | − | 7.56928e6i | 0.362532 | − | 0.362532i | ||||
\(848\) | −5.85127e6 | + | 5.85127e6i | −0.279422 | + | 0.279422i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.34998e7i | − | 0.639002i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.97155e7 | − | 1.97155e7i | −0.927757 | − | 0.927757i | 0.0698035 | − | 0.997561i | \(-0.477763\pi\) |
−0.997561 | + | 0.0698035i | \(0.977763\pi\) | |||||||
\(854\) | 4.04171e6 | 0.189636 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.76416e6 | 0.222230 | ||||||||
\(857\) | −2.65954e7 | − | 2.65954e7i | −1.23696 | − | 1.23696i | −0.961239 | − | 0.275717i | \(-0.911085\pi\) |
−0.275717 | − | 0.961239i | \(-0.588915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.29136e6i | − | 0.337152i | −0.985689 | − | 0.168576i | \(-0.946083\pi\) | ||
0.985689 | − | 0.168576i | \(-0.0539169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.28341e6 | + | 7.28341e6i | −0.333862 | + | 0.333862i | ||||
\(863\) | −1.33811e7 | + | 1.33811e7i | −0.611597 | + | 0.611597i | −0.943362 | − | 0.331765i | \(-0.892356\pi\) |
0.331765 | + | 0.943362i | \(0.392356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.39104e7i | − | 0.630295i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.64429e6 | + | 5.64429e6i | 0.254279 | + | 0.254279i | ||||
\(869\) | 7.38342e6 | 0.331671 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.24674e7 | 0.556841 | ||||||||
\(872\) | −7.53457e6 | − | 7.53457e6i | −0.335558 | − | 0.335558i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.16196e7i | − | 0.957348i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.21873e7 | + | 1.21873e7i | −0.535066 | + | 0.535066i | −0.922076 | − | 0.387009i | \(-0.873508\pi\) |
0.387009 | + | 0.922076i | \(0.373508\pi\) | |||||||
\(878\) | −798951. | + | 798951.i | −0.0349771 | + | 0.0349771i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.93700e7i | − | 0.840794i | −0.907340 | − | 0.420397i | \(-0.861891\pi\) | ||
0.907340 | − | 0.420397i | \(-0.138109\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.04008e6 | − | 3.04008e6i | −0.131215 | − | 0.131215i | 0.638449 | − | 0.769664i | \(-0.279576\pi\) |
−0.769664 | + | 0.638449i | \(0.779576\pi\) | |||||||
\(884\) | −2.05385e6 | −0.0883969 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.45129e7 | −0.621112 | ||||||||
\(887\) | −1.74129e6 | − | 1.74129e6i | −0.0743125 | − | 0.0743125i | 0.668974 | − | 0.743286i | \(-0.266734\pi\) |
−0.743286 | + | 0.668974i | \(0.766734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.19839e7i | − | 0.932934i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.28001e7 | − | 1.28001e7i | 0.538642 | − | 0.538642i | ||||
\(893\) | −1.63666e7 | + | 1.63666e7i | −0.686798 | + | 0.686798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.20486e6i | − | 0.0501381i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.86472e6 | − | 9.86472e6i | −0.408220 | − | 0.408220i | ||||
\(899\) | 4.74808e7 | 1.95938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.60327e7 | −0.657953 | ||||||||
\(902\) | 4.29753e6 | + | 4.29753e6i | 0.175875 | + | 0.175875i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.62177e7i | − | 0.660038i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.57742e6 | − | 9.57742e6i | 0.386572 | − | 0.386572i | −0.486891 | − | 0.873463i | \(-0.661869\pi\) |
0.873463 | + | 0.486891i | \(0.161869\pi\) | |||||||
\(908\) | −3.70058e6 | + | 3.70058e6i | −0.148955 | + | 0.148955i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.24413e7i | 1.29510i | 0.762024 | + | 0.647549i | \(0.224206\pi\) | ||||
−0.762024 | + | 0.647549i | \(0.775794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.74566e6 | − | 4.74566e6i | −0.188417 | − | 0.188417i | ||||
\(914\) | 1.43327e7 | 0.567497 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.96074e6 | −0.116590 | ||||||||
\(917\) | −8.81881e6 | − | 8.81881e6i | −0.346327 | − | 0.346327i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.54533e7i | 1.38474i | 0.721543 | + | 0.692370i | \(0.243433\pi\) | ||||
−0.721543 | + | 0.692370i | \(0.756567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.12336e7 | − | 1.12336e7i | 0.435203 | − | 0.435203i | ||||
\(923\) | 8.78992e6 | − | 8.78992e6i | 0.339610 | − | 0.339610i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1.13265e7i | − | 0.434077i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.06778e6 | − | 5.06778e6i | −0.193173 | − | 0.193173i | ||||
\(929\) | 3.41147e7 | 1.29689 | 0.648443 | − | 0.761263i | \(-0.275420\pi\) | ||||
0.648443 | + | 0.761263i | \(0.275420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.40291e7 | −0.908580 | ||||||||
\(932\) | −954968. | − | 954968.i | −0.0360121 | − | 0.0360121i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 1.50868e7i | − | 0.565889i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.40765e7 | − | 1.40765e7i | 0.523778 | − | 0.523778i | −0.394933 | − | 0.918710i | \(-0.629232\pi\) |
0.918710 | + | 0.394933i | \(0.129232\pi\) | |||||||
\(938\) | −1.00201e7 | + | 1.00201e7i | −0.371849 | + | 0.371849i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.32932e7i | − | 1.59384i | −0.604083 | − | 0.796922i | \(-0.706460\pi\) | ||
0.604083 | − | 0.796922i | \(-0.293540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.21350e7 | − | 2.21350e7i | −0.810589 | − | 0.810589i | ||||
\(944\) | 9.17696e6 | 0.335173 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.23872e6 | −0.0813340 | ||||||||
\(947\) | 3.43867e7 | + | 3.43867e7i | 1.24599 | + | 1.24599i | 0.957474 | + | 0.288521i | \(0.0931636\pi\) |
0.288521 | + | 0.957474i | \(0.406836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.09401e7i | − | 0.394327i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.65069e6 | − | 1.65069e6i | 0.0590300 | − | 0.0590300i | ||||
\(953\) | 2.36832e6 | − | 2.36832e6i | 0.0844712 | − | 0.0844712i | −0.663609 | − | 0.748080i | \(-0.730976\pi\) |
0.748080 | + | 0.663609i | \(0.230976\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.80736e6i | 0.347062i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.92115e7 | − | 1.92115e7i | −0.676314 | − | 0.676314i | ||||
\(959\) | −2.00766e7 | −0.704927 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.73935e7 | 0.607545 | ||||||||
\(962\) | 3.85407e6 | + | 3.85407e6i | 0.134271 | + | 0.134271i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.05079e7i | 0.710768i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.30394e6 | + | 6.30394e6i | −0.216793 | + | 0.216793i | −0.807146 | − | 0.590352i | \(-0.798989\pi\) |
0.590352 | + | 0.807146i | \(0.298989\pi\) | |||||||
\(968\) | −6.58743e6 | + | 6.58743e6i | −0.225958 | + | 0.225958i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.12139e6i | − | 0.106243i | −0.998588 | − | 0.0531215i | \(-0.983083\pi\) | ||
0.998588 | − | 0.0531215i | \(-0.0169170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.60994e7 | + | 1.60994e7i | 0.545165 | + | 0.545165i | ||||
\(974\) | −3.85744e7 | −1.30287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.51744e6 | −0.118196 | ||||||||
\(977\) | −3.00825e7 | − | 3.00825e7i | −1.00827 | − | 1.00827i | −0.999966 | − | 0.00830587i | \(-0.997356\pi\) |
−0.00830587 | − | 0.999966i | \(-0.502644\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.12133e6i | 0.0707377i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.93867e6 | + | 5.93867e6i | −0.196522 | + | 0.196522i | ||||
\(983\) | 3.86947e7 | − | 3.86947e7i | 1.27723 | − | 1.27723i | 0.335013 | − | 0.942213i | \(-0.391259\pi\) |
0.942213 | − | 0.335013i | \(-0.108741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1.38859e7i | − | 0.454864i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.17222e6 | + | 6.17222e6i | 0.201164 | + | 0.201164i | ||||
\(989\) | 1.15308e7 | 0.374860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.81781e7 | −1.55835 | −0.779176 | − | 0.626805i | \(-0.784362\pi\) | ||||
−0.779176 | + | 0.626805i | \(0.784362\pi\) | |||||||
\(992\) | −4.91214e6 | − | 4.91214e6i | −0.158486 | − | 0.158486i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.41290e7i | 0.453572i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.12659e6 | − | 9.12659e6i | 0.290784 | − | 0.290784i | −0.546606 | − | 0.837390i | \(-0.684080\pi\) |
0.837390 | + | 0.546606i | \(0.184080\pi\) | |||||||
\(998\) | 9.58999e6 | − | 9.58999e6i | 0.304784 | − | 0.304784i | ||||
\(999\) | 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.d.143.2 | 4 | ||
3.2 | odd | 2 | inner | 450.6.f.d.143.1 | 4 | ||
5.2 | odd | 4 | inner | 450.6.f.d.107.1 | 4 | ||
5.3 | odd | 4 | 90.6.f.a.17.2 | yes | 4 | ||
5.4 | even | 2 | 90.6.f.a.53.1 | yes | 4 | ||
15.2 | even | 4 | inner | 450.6.f.d.107.2 | 4 | ||
15.8 | even | 4 | 90.6.f.a.17.1 | ✓ | 4 | ||
15.14 | odd | 2 | 90.6.f.a.53.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.6.f.a.17.1 | ✓ | 4 | 15.8 | even | 4 | ||
90.6.f.a.17.2 | yes | 4 | 5.3 | odd | 4 | ||
90.6.f.a.53.1 | yes | 4 | 5.4 | even | 2 | ||
90.6.f.a.53.2 | yes | 4 | 15.14 | odd | 2 | ||
450.6.f.d.107.1 | 4 | 5.2 | odd | 4 | inner | ||
450.6.f.d.107.2 | 4 | 15.2 | even | 4 | inner | ||
450.6.f.d.143.1 | 4 | 3.2 | odd | 2 | inner | ||
450.6.f.d.143.2 | 4 | 1.1 | even | 1 | trivial |