Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (of order \(2\), degree \(1\), not 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: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{4081})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2041x^{2} + 1040400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-32.4414i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.6.c.q.199.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 141.648i | 1.09261i | 0.837586 | + | 0.546306i | \(0.183966\pi\) | ||||
−0.837586 | + | 0.546306i | \(0.816034\pi\) | |||||||
\(8\) | − 64.0000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −113.296 | −0.282315 | −0.141157 | − | 0.989987i | \(-0.545082\pi\) | ||||
−0.141157 | + | 0.989987i | \(0.545082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 61.7038i | − 0.101264i | −0.998717 | − | 0.0506318i | \(-0.983877\pi\) | ||||
0.998717 | − | 0.0506318i | \(-0.0161235\pi\) | |||||||
\(14\) | −566.592 | −0.772593 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1670.48i | 1.40191i | 0.713207 | + | 0.700954i | \(0.247242\pi\) | ||||
−0.713207 | + | 0.700954i | \(0.752758\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 662.241 | 0.420854 | 0.210427 | − | 0.977610i | \(-0.432515\pi\) | ||||
0.210427 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 453.185i | − 0.199627i | ||||||||
\(23\) | − 86.4812i | − 0.0340880i | −0.999855 | − | 0.0170440i | \(-0.994574\pi\) | ||||
0.999855 | − | 0.0170440i | \(-0.00542554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 246.815 | 0.0716042 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 2266.37i | − 0.546306i | ||||||||
\(29\) | −3233.30 | −0.713922 | −0.356961 | − | 0.934119i | \(-0.616187\pi\) | ||||
−0.356961 | + | 0.934119i | \(0.616187\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3812.24 | −0.712486 | −0.356243 | − | 0.934393i | \(-0.615942\pi\) | ||||
−0.356243 | + | 0.934393i | \(0.615942\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6681.92 | −0.991298 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10249.6i | 1.23084i | 0.788200 | + | 0.615419i | \(0.211013\pi\) | ||||
−0.788200 | + | 0.615419i | \(0.788987\pi\) | |||||||
\(38\) | 2648.96i | 0.297589i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13459.4 | 1.25045 | 0.625227 | − | 0.780443i | \(-0.285007\pi\) | ||||
0.625227 | + | 0.780443i | \(0.285007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4697.57i | 0.387438i | 0.981057 | + | 0.193719i | \(0.0620550\pi\) | ||||
−0.981057 | + | 0.193719i | \(0.937945\pi\) | |||||||
\(44\) | 1812.74 | 0.141157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 345.925 | 0.0241039 | ||||||||
\(47\) | − 15264.8i | − 1.00797i | −0.863713 | − | 0.503984i | \(-0.831867\pi\) | ||||
0.863713 | − | 0.503984i | \(-0.168133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3257.19 | −0.193800 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 987.260i | 0.0506318i | ||||||||
\(53\) | − 498.632i | − 0.0243832i | −0.999926 | − | 0.0121916i | \(-0.996119\pi\) | ||||
0.999926 | − | 0.0121916i | \(-0.00388080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9065.48 | 0.386296 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 12933.2i | − 0.504819i | ||||||||
\(59\) | −15294.3 | −0.572005 | −0.286002 | − | 0.958229i | \(-0.592327\pi\) | ||||
−0.286002 | + | 0.958229i | \(0.592327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31811.3 | −1.09460 | −0.547302 | − | 0.836935i | \(-0.684345\pi\) | ||||
−0.547302 | + | 0.836935i | \(0.684345\pi\) | |||||||
\(62\) | − 15249.0i | − 0.503803i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49274.9i | 1.34103i | 0.741895 | + | 0.670516i | \(0.233927\pi\) | ||||
−0.741895 | + | 0.670516i | \(0.766073\pi\) | |||||||
\(68\) | − 26727.7i | − 0.700954i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21057.7 | −0.495752 | −0.247876 | − | 0.968792i | \(-0.579733\pi\) | ||||
−0.247876 | + | 0.968792i | \(0.579733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 39447.8i | − 0.866394i | −0.901299 | − | 0.433197i | \(-0.857385\pi\) | ||||
0.901299 | − | 0.433197i | \(-0.142615\pi\) | |||||||
\(74\) | −40998.2 | −0.870333 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10595.8 | −0.210427 | ||||||||
\(77\) | − 16048.2i | − 0.308460i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −72949.3 | −1.31508 | −0.657542 | − | 0.753418i | \(-0.728404\pi\) | ||||
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 53837.8i | 0.884204i | ||||||||
\(83\) | − 100897.i | − 1.60762i | −0.594889 | − | 0.803808i | \(-0.702804\pi\) | ||||
0.594889 | − | 0.803808i | \(-0.297196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18790.3 | −0.273960 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7250.96i | 0.0998134i | ||||||||
\(89\) | −146714. | −1.96334 | −0.981671 | − | 0.190585i | \(-0.938962\pi\) | ||||
−0.981671 | + | 0.190585i | \(0.938962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8740.22 | 0.110642 | ||||||||
\(92\) | 1383.70i | 0.0170440i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 61059.2 | 0.712741 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 43544.9i | − 0.469903i | −0.972007 | − | 0.234951i | \(-0.924507\pi\) | ||||
0.972007 | − | 0.234951i | \(-0.0754931\pi\) | |||||||
\(98\) | − 13028.8i | − 0.137037i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49966.3 | 0.487386 | 0.243693 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243693 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50579.6i | 0.469766i | 0.972024 | + | 0.234883i | \(0.0754708\pi\) | ||||
−0.972024 | + | 0.234883i | \(0.924529\pi\) | |||||||
\(104\) | −3949.04 | −0.0358021 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1994.53 | 0.0172415 | ||||||||
\(107\) | − 191553.i | − 1.61744i | −0.588193 | − | 0.808721i | \(-0.700160\pi\) | ||||
0.588193 | − | 0.808721i | \(-0.299840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −71531.6 | −0.576676 | −0.288338 | − | 0.957529i | \(-0.593103\pi\) | ||||
−0.288338 | + | 0.957529i | \(0.593103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 36261.9i | 0.273153i | ||||||||
\(113\) | − 163395.i | − 1.20377i | −0.798583 | − | 0.601885i | \(-0.794417\pi\) | ||||
0.798583 | − | 0.601885i | \(-0.205583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 51732.7 | 0.356961 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 61177.2i | − 0.404468i | ||||||||
\(119\) | −236621. | −1.53174 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −148215. | −0.920298 | ||||||||
\(122\) | − 127245.i | − 0.774002i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 60995.8 | 0.356243 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 34350.7i | − 0.188984i | −0.995526 | − | 0.0944922i | \(-0.969877\pi\) | ||||
0.995526 | − | 0.0944922i | \(-0.0301228\pi\) | |||||||
\(128\) | − 16384.0i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 349293. | 1.77833 | 0.889164 | − | 0.457588i | \(-0.151287\pi\) | ||||
0.889164 | + | 0.457588i | \(0.151287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 93805.1i | 0.459830i | ||||||||
\(134\) | −197100. | −0.948253 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 106911. | 0.495649 | ||||||||
\(137\) | − 274334.i | − 1.24876i | −0.781122 | − | 0.624379i | \(-0.785352\pi\) | ||||
0.781122 | − | 0.624379i | \(-0.214648\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 47842.2 | 0.210027 | 0.105013 | − | 0.994471i | \(-0.466511\pi\) | ||||
0.105013 | + | 0.994471i | \(0.466511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 84230.6i | − 0.350549i | ||||||||
\(143\) | 6990.80i | 0.0285882i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 157791. | 0.612633 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 163993.i | − 0.615419i | ||||||||
\(149\) | −335645. | −1.23855 | −0.619276 | − | 0.785174i | \(-0.712574\pi\) | ||||
−0.619276 | + | 0.785174i | \(0.712574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 336370. | 1.20054 | 0.600268 | − | 0.799799i | \(-0.295061\pi\) | ||||
0.600268 | + | 0.799799i | \(0.295061\pi\) | |||||||
\(152\) | − 42383.4i | − 0.148794i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 64192.8 | 0.218114 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 381573.i | − 1.23546i | −0.786391 | − | 0.617729i | \(-0.788053\pi\) | ||||
0.786391 | − | 0.617729i | \(-0.211947\pi\) | |||||||
\(158\) | − 291797.i | − 0.929905i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12249.9 | 0.0372450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 579006.i | 1.70692i | 0.521155 | + | 0.853462i | \(0.325501\pi\) | ||||
−0.521155 | + | 0.853462i | \(0.674499\pi\) | |||||||
\(164\) | −215351. | −0.625227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 403587. | 1.13676 | ||||||||
\(167\) | 128108.i | 0.355455i | 0.984080 | + | 0.177728i | \(0.0568746\pi\) | ||||
−0.984080 | + | 0.177728i | \(0.943125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 367486. | 0.989746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 75161.2i | − 0.193719i | ||||||||
\(173\) | − 487187.i | − 1.23760i | −0.785548 | − | 0.618800i | \(-0.787619\pi\) | ||||
0.785548 | − | 0.618800i | \(-0.212381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −29003.8 | −0.0705787 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 586855.i | − 1.38829i | ||||||||
\(179\) | −848235. | −1.97872 | −0.989359 | − | 0.145497i | \(-0.953522\pi\) | ||||
−0.989359 | + | 0.145497i | \(0.953522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −575423. | −1.30554 | −0.652771 | − | 0.757555i | \(-0.726394\pi\) | ||||
−0.652771 | + | 0.757555i | \(0.726394\pi\) | |||||||
\(182\) | 34960.9i | 0.0782355i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5534.79 | −0.0120519 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 189259.i | − 0.395779i | ||||||||
\(188\) | 244237.i | 0.503984i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18362.7 | −0.0364211 | −0.0182105 | − | 0.999834i | \(-0.505797\pi\) | ||||
−0.0182105 | + | 0.999834i | \(0.505797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 349513.i | 0.675414i | 0.941251 | + | 0.337707i | \(0.109651\pi\) | ||||
−0.941251 | + | 0.337707i | \(0.890349\pi\) | |||||||
\(194\) | 174180. | 0.332272 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 52115.0 | 0.0968998 | ||||||||
\(197\) | − 371791.i | − 0.682547i | −0.939964 | − | 0.341274i | \(-0.889142\pi\) | ||||
0.939964 | − | 0.341274i | \(-0.110858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −300569. | −0.538036 | −0.269018 | − | 0.963135i | \(-0.586699\pi\) | ||||
−0.269018 | + | 0.963135i | \(0.586699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 199865.i | 0.344634i | ||||||||
\(203\) | − 457990.i | − 0.780039i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −202318. | −0.332175 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 15796.2i | − 0.0253159i | ||||||||
\(209\) | −75029.4 | −0.118813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 59499.2 | 0.0920036 | 0.0460018 | − | 0.998941i | \(-0.485352\pi\) | ||||
0.0460018 | + | 0.998941i | \(0.485352\pi\) | |||||||
\(212\) | 7978.11i | 0.0121916i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 766210. | 1.14370 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 539997.i | − 0.778470i | ||||||||
\(218\) | − 286127.i | − 0.407772i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 103075. | 0.141962 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 866124.i | 1.16632i | 0.812357 | + | 0.583160i | \(0.198184\pi\) | ||||
−0.812357 | + | 0.583160i | \(0.801816\pi\) | |||||||
\(224\) | −145048. | −0.193148 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 653581. | 0.851194 | ||||||||
\(227\) | − 737058.i | − 0.949374i | −0.880155 | − | 0.474687i | \(-0.842561\pi\) | ||||
0.880155 | − | 0.474687i | \(-0.157439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −846501. | −1.06669 | −0.533346 | − | 0.845897i | \(-0.679065\pi\) | ||||
−0.533346 | + | 0.845897i | \(0.679065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 206931.i | 0.252409i | ||||||||
\(233\) | 590760.i | 0.712888i | 0.934317 | + | 0.356444i | \(0.116011\pi\) | ||||
−0.934317 | + | 0.356444i | \(0.883989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 244709. | 0.286002 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 946482.i | − 1.08310i | ||||||||
\(239\) | 1.60375e6 | 1.81611 | 0.908054 | − | 0.418853i | \(-0.137568\pi\) | ||||
0.908054 | + | 0.418853i | \(0.137568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −347071. | −0.384925 | −0.192463 | − | 0.981304i | \(-0.561647\pi\) | ||||
−0.192463 | + | 0.981304i | \(0.561647\pi\) | |||||||
\(242\) | − 592860.i | − 0.650749i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 508981. | 0.547302 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 40862.7i | − 0.0426172i | ||||||||
\(248\) | 243983.i | 0.251902i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −536438. | −0.537446 | −0.268723 | − | 0.963217i | \(-0.586602\pi\) | ||||
−0.268723 | + | 0.963217i | \(0.586602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9797.99i | 0.00962356i | ||||||||
\(254\) | 137403. | 0.133632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 763565.i | 0.721130i | 0.932734 | + | 0.360565i | \(0.117416\pi\) | ||||
−0.932734 | + | 0.360565i | \(0.882584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.45183e6 | −1.34483 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.39717e6i | 1.25747i | ||||||||
\(263\) | 341099.i | 0.304082i | 0.988374 | + | 0.152041i | \(0.0485846\pi\) | ||||
−0.988374 | + | 0.152041i | \(0.951415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −375221. | −0.325149 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 788399.i | − 0.670516i | ||||||||
\(269\) | 750163. | 0.632084 | 0.316042 | − | 0.948745i | \(-0.397646\pi\) | ||||
0.316042 | + | 0.948745i | \(0.397646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.64462e6 | −1.36033 | −0.680163 | − | 0.733061i | \(-0.738091\pi\) | ||||
−0.680163 | + | 0.733061i | \(0.738091\pi\) | |||||||
\(272\) | 427643.i | 0.350477i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.09734e6 | 0.883005 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.04631e6i | 0.819337i | 0.912235 | + | 0.409668i | \(0.134356\pi\) | ||||
−0.912235 | + | 0.409668i | \(0.865644\pi\) | |||||||
\(278\) | 191369.i | 0.148511i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 54503.6 | 0.0411774 | 0.0205887 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205887 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 150130.i | − 0.111429i | −0.998447 | − | 0.0557147i | \(-0.982256\pi\) | ||||
0.998447 | − | 0.0557147i | \(-0.0177437\pi\) | |||||||
\(284\) | 336923. | 0.247876 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27963.2 | −0.0202149 | ||||||||
\(287\) | 1.90650e6i | 1.36626i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37065e6 | −0.965344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 631164.i | 0.433197i | ||||||||
\(293\) | 1.54001e6i | 1.04799i | 0.851723 | + | 0.523993i | \(0.175558\pi\) | ||||
−0.851723 | + | 0.523993i | \(0.824442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 655972. | 0.435167 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.34258e6i | − 0.875788i | ||||||||
\(299\) | −5336.21 | −0.00345188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −665402. | −0.423319 | ||||||||
\(302\) | 1.34548e6i | 0.848907i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 169534. | 0.105214 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 914773.i | − 0.553946i | −0.960878 | − | 0.276973i | \(-0.910669\pi\) | ||||
0.960878 | − | 0.276973i | \(-0.0893312\pi\) | |||||||
\(308\) | 256771.i | 0.154230i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.59808e6 | −0.936910 | −0.468455 | − | 0.883487i | \(-0.655189\pi\) | ||||
−0.468455 | + | 0.883487i | \(0.655189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.38412e6i | 1.37552i | 0.725938 | + | 0.687760i | \(0.241406\pi\) | ||||
−0.725938 | + | 0.687760i | \(0.758594\pi\) | |||||||
\(314\) | 1.52629e6 | 0.873601 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.16719e6 | 0.657542 | ||||||||
\(317\) | 2.00013e6i | 1.11792i | 0.829194 | + | 0.558960i | \(0.188800\pi\) | ||||
−0.829194 | + | 0.558960i | \(0.811200\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 366320. | 0.201551 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 48999.6i | 0.0263362i | ||||||||
\(323\) | 1.10626e6i | 0.589999i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.31602e6 | −1.20698 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 861404.i | − 0.442102i | ||||||||
\(329\) | 2.16223e6 | 1.10132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48362e6 | −0.744306 | −0.372153 | − | 0.928171i | \(-0.621380\pi\) | ||||
−0.372153 | + | 0.928171i | \(0.621380\pi\) | |||||||
\(332\) | 1.61435e6i | 0.803808i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −512432. | −0.251345 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.42490e6i | 1.16311i | 0.813508 | + | 0.581553i | \(0.197555\pi\) | ||||
−0.813508 | + | 0.581553i | \(0.802445\pi\) | |||||||
\(338\) | 1.46994e6i | 0.699856i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 431912. | 0.201145 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.91931e6i | 0.880864i | ||||||||
\(344\) | 300645. | 0.136980 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.94875e6 | 0.875116 | ||||||||
\(347\) | 1.26681e6i | 0.564793i | 0.959298 | + | 0.282397i | \(0.0911294\pi\) | ||||
−0.959298 | + | 0.282397i | \(0.908871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.54257e6 | −1.11740 | −0.558701 | − | 0.829369i | \(-0.688700\pi\) | ||||
−0.558701 | + | 0.829369i | \(0.688700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 116015.i | − 0.0499067i | ||||||||
\(353\) | 1.28509e6i | 0.548906i | 0.961601 | + | 0.274453i | \(0.0884967\pi\) | ||||
−0.961601 | + | 0.274453i | \(0.911503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.34742e6 | 0.981671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 3.39294e6i | − 1.39916i | ||||||||
\(359\) | 4.16251e6 | 1.70459 | 0.852294 | − | 0.523063i | \(-0.175211\pi\) | ||||
0.852294 | + | 0.523063i | \(0.175211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03754e6 | −0.822882 | ||||||||
\(362\) | − 2.30169e6i | − 0.923158i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −139844. | −0.0553209 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.13066e6i | − 0.438195i | −0.975703 | − | 0.219098i | \(-0.929689\pi\) | ||||
0.975703 | − | 0.219098i | \(-0.0703113\pi\) | |||||||
\(368\) | − 22139.2i | − 0.00852201i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 70630.3 | 0.0266413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 312371.i | 0.116251i | 0.998309 | + | 0.0581257i | \(0.0185124\pi\) | ||||
−0.998309 | + | 0.0581257i | \(0.981488\pi\) | |||||||
\(374\) | 757037. | 0.279858 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −976948. | −0.356371 | ||||||||
\(377\) | 199507.i | 0.0722943i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.19990e6 | 0.786692 | 0.393346 | − | 0.919390i | \(-0.371317\pi\) | ||||
0.393346 | + | 0.919390i | \(0.371317\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 73450.8i | − 0.0257536i | ||||||||
\(383\) | 3.93331e6i | 1.37013i | 0.728482 | + | 0.685065i | \(0.240226\pi\) | ||||
−0.728482 | + | 0.685065i | \(0.759774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.39805e6 | −0.477590 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 696719.i | 0.234951i | ||||||||
\(389\) | 4.20593e6 | 1.40925 | 0.704625 | − | 0.709580i | \(-0.251115\pi\) | ||||
0.704625 | + | 0.709580i | \(0.251115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 144465. | 0.0477883 | ||||||||
\(392\) | 208460.i | 0.0685185i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.48716e6 | 0.482634 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.39484e6i | − 0.762606i | −0.924450 | − | 0.381303i | \(-0.875475\pi\) | ||||
0.924450 | − | 0.381303i | \(-0.124525\pi\) | |||||||
\(398\) | − 1.20228e6i | − 0.380449i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.42161e6 | −1.37315 | −0.686577 | − | 0.727057i | \(-0.740888\pi\) | ||||
−0.686577 | + | 0.727057i | \(0.740888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 235230.i | 0.0721488i | ||||||||
\(404\) | −799460. | −0.243693 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.83196e6 | 0.551571 | ||||||||
\(407\) | − 1.16124e6i | − 0.347484i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.61075e6 | 0.771717 | 0.385858 | − | 0.922558i | \(-0.373905\pi\) | ||||
0.385858 | + | 0.922558i | \(0.373905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 809273.i | − 0.234883i | ||||||||
\(413\) | − 2.16641e6i | − 0.624979i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 63184.7 | 0.0179010 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 300117.i | − 0.0840138i | ||||||||
\(419\) | 1.01624e6 | 0.282789 | 0.141395 | − | 0.989953i | \(-0.454841\pi\) | ||||
0.141395 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.96915e6 | 1.64137 | 0.820687 | − | 0.571379i | \(-0.193591\pi\) | ||||
0.820687 | + | 0.571379i | \(0.193591\pi\) | |||||||
\(422\) | 237997.i | 0.0650564i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −31912.4 | −0.00862076 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.50601e6i | − 1.19598i | ||||||||
\(428\) | 3.06484e6i | 0.808721i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.97145e6 | 0.770504 | 0.385252 | − | 0.922811i | \(-0.374115\pi\) | ||||
0.385252 | + | 0.922811i | \(0.374115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.95237e6i | 1.26938i | 0.772765 | + | 0.634692i | \(0.218873\pi\) | ||||
−0.772765 | + | 0.634692i | \(0.781127\pi\) | |||||||
\(434\) | 2.15999e6 | 0.550461 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.14451e6 | 0.288338 | ||||||||
\(437\) | − 57271.3i | − 0.0143461i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.12115e6 | 0.277652 | 0.138826 | − | 0.990317i | \(-0.455667\pi\) | ||||
0.138826 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 412300.i | 0.100382i | ||||||||
\(443\) | − 2.66233e6i | − 0.644544i | −0.946647 | − | 0.322272i | \(-0.895553\pi\) | ||||
0.946647 | − | 0.322272i | \(-0.104447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.46449e6 | −0.824713 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 580191.i | − 0.136576i | ||||||||
\(449\) | −3.88781e6 | −0.910101 | −0.455050 | − | 0.890466i | \(-0.650379\pi\) | ||||
−0.455050 | + | 0.890466i | \(0.650379\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52490e6 | −0.353022 | ||||||||
\(452\) | 2.61432e6i | 0.601885i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.94823e6 | 0.671309 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.52630e6i | 0.565841i | 0.959143 | + | 0.282920i | \(0.0913032\pi\) | ||||
−0.959143 | + | 0.282920i | \(0.908697\pi\) | |||||||
\(458\) | − 3.38600e6i | − 0.754265i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.63589e6 | −1.01597 | −0.507985 | − | 0.861366i | \(-0.669610\pi\) | ||||
−0.507985 | + | 0.861366i | \(0.669610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.62380e6i | − 0.785619i | −0.919620 | − | 0.392810i | \(-0.871503\pi\) | ||||
0.919620 | − | 0.392810i | \(-0.128497\pi\) | |||||||
\(464\) | −827724. | −0.178480 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.36304e6 | −0.504088 | ||||||||
\(467\) | 3.72757e6i | 0.790922i | 0.918483 | + | 0.395461i | \(0.129415\pi\) | ||||
−0.918483 | + | 0.395461i | \(0.870585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.97970e6 | −1.46523 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 978835.i | 0.202234i | ||||||||
\(473\) | − 532217.i | − 0.109380i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.78593e6 | 0.765870 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.41500e6i | 1.28418i | ||||||||
\(479\) | −6.88374e6 | −1.37084 | −0.685418 | − | 0.728150i | \(-0.740381\pi\) | ||||
−0.685418 | + | 0.728150i | \(0.740381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 632436. | 0.124639 | ||||||||
\(482\) | − 1.38829e6i | − 0.272183i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.37144e6 | 0.460149 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.58990e6i | − 1.64122i | −0.571492 | − | 0.820608i | \(-0.693635\pi\) | ||||
0.571492 | − | 0.820608i | \(-0.306365\pi\) | |||||||
\(488\) | 2.03593e6i | 0.387001i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.46999e6 | 0.275176 | 0.137588 | − | 0.990490i | \(-0.456065\pi\) | ||||
0.137588 | + | 0.990490i | \(0.456065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.40116e6i | − 1.00085i | ||||||||
\(494\) | 163451. | 0.0301349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −975934. | −0.178121 | ||||||||
\(497\) | − 2.98278e6i | − 0.541664i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.13043e6 | 0.562798 | 0.281399 | − | 0.959591i | \(-0.409202\pi\) | ||||
0.281399 | + | 0.959591i | \(0.409202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2.14575e6i | − 0.380032i | ||||||||
\(503\) | − 2.29993e6i | − 0.405317i | −0.979249 | − | 0.202658i | \(-0.935042\pi\) | ||||
0.979249 | − | 0.202658i | \(-0.0649581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −39192.0 | −0.00680488 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 549611.i | 0.0944922i | ||||||||
\(509\) | −5.16574e6 | −0.883767 | −0.441884 | − | 0.897072i | \(-0.645690\pi\) | ||||
−0.441884 | + | 0.897072i | \(0.645690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.58770e6 | 0.946632 | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.05426e6 | −0.509916 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72945e6i | 0.284564i | ||||||||
\(518\) | − 5.80732e6i | − 0.950936i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.12853e7 | 1.82146 | 0.910729 | − | 0.413004i | \(-0.135520\pi\) | ||||
0.910729 | + | 0.413004i | \(0.135520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.86022e6i | 0.776966i | 0.921456 | + | 0.388483i | \(0.127001\pi\) | ||||
−0.921456 | + | 0.388483i | \(0.872999\pi\) | |||||||
\(524\) | −5.58869e6 | −0.889164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.36440e6 | −0.215019 | ||||||||
\(527\) | − 6.36828e6i | − 0.998839i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.42886e6 | 0.998838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 1.50088e6i | − 0.229915i | ||||||||
\(533\) | − 830498.i | − 0.126625i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.15360e6 | 0.474126 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00065e6i | 0.446951i | ||||||||
\(539\) | 369027. | 0.0547125 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.23864e6 | −0.769530 | −0.384765 | − | 0.923015i | \(-0.625717\pi\) | ||||
−0.384765 | + | 0.923015i | \(0.625717\pi\) | |||||||
\(542\) | − 6.57849e6i | − 0.961896i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.71057e6 | −0.247825 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.88586e6i | 0.412389i | 0.978511 | + | 0.206194i | \(0.0661079\pi\) | ||||
−0.978511 | + | 0.206194i | \(0.933892\pi\) | |||||||
\(548\) | 4.38934e6i | 0.624379i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.14122e6 | −0.300457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.03331e7i | − 1.43688i | ||||||||
\(554\) | −4.18525e6 | −0.579359 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −765476. | −0.105013 | ||||||||
\(557\) | − 3.27936e6i | − 0.447869i | −0.974604 | − | 0.223935i | \(-0.928110\pi\) | ||||
0.974604 | − | 0.223935i | \(-0.0718902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 289858. | 0.0392334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 218014.i | 0.0291168i | ||||||||
\(563\) | − 664023.i | − 0.0882901i | −0.999025 | − | 0.0441451i | \(-0.985944\pi\) | ||||
0.999025 | − | 0.0441451i | \(-0.0140564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 600518. | 0.0787925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.34769e6i | 0.175275i | ||||||||
\(569\) | −3.00851e6 | −0.389557 | −0.194778 | − | 0.980847i | \(-0.562399\pi\) | ||||
−0.194778 | + | 0.980847i | \(0.562399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.07571e7 | 1.38072 | 0.690359 | − | 0.723467i | \(-0.257453\pi\) | ||||
0.690359 | + | 0.723467i | \(0.257453\pi\) | |||||||
\(572\) | − 111853.i | − 0.0142941i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.62602e6 | −0.966091 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.53859e7i | 1.92390i | 0.273220 | + | 0.961952i | \(0.411911\pi\) | ||||
−0.273220 | + | 0.961952i | \(0.588089\pi\) | |||||||
\(578\) | − 5.48260e6i | − 0.682601i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.42918e7 | 1.75650 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56493.1i | 0.00688374i | ||||||||
\(584\) | −2.52466e6 | −0.306316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.16005e6 | −0.741038 | ||||||||
\(587\) | − 1.16896e7i | − 1.40025i | −0.714020 | − | 0.700125i | \(-0.753128\pi\) | ||||
0.714020 | − | 0.700125i | \(-0.246872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.52462e6 | −0.299853 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.62389e6i | 0.307709i | ||||||||
\(593\) | − 2.29301e6i | − 0.267774i | −0.990997 | − | 0.133887i | \(-0.957254\pi\) | ||||
0.990997 | − | 0.133887i | \(-0.0427459\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.37031e6 | 0.619276 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 21344.9i | − 0.00244084i | ||||||||
\(599\) | −1.58740e7 | −1.80767 | −0.903834 | − | 0.427884i | \(-0.859259\pi\) | ||||
−0.903834 | + | 0.427884i | \(0.859259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.16506e7 | −1.31571 | −0.657855 | − | 0.753144i | \(-0.728536\pi\) | ||||
−0.657855 | + | 0.753144i | \(0.728536\pi\) | |||||||
\(602\) | − 2.66161e6i | − 0.299332i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.38193e6 | −0.600268 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.40797e6i | 1.03639i | 0.855262 | + | 0.518196i | \(0.173396\pi\) | ||||
−0.855262 | + | 0.518196i | \(0.826604\pi\) | |||||||
\(608\) | 678134.i | 0.0743972i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −941896. | −0.102070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 9.30509e6i | − 1.00016i | −0.865979 | − | 0.500080i | \(-0.833304\pi\) | ||||
0.865979 | − | 0.500080i | \(-0.166696\pi\) | |||||||
\(614\) | 3.65909e6 | 0.391699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.02708e6 | −0.109057 | ||||||||
\(617\) | 268346.i | 0.0283780i | 0.999899 | + | 0.0141890i | \(0.00451665\pi\) | ||||
−0.999899 | + | 0.0141890i | \(0.995483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.97678e6 | 0.836760 | 0.418380 | − | 0.908272i | \(-0.362598\pi\) | ||||
0.418380 | + | 0.908272i | \(0.362598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 6.39233e6i | − 0.662496i | ||||||||
\(623\) | − 2.07817e7i | − 2.14517i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.53647e6 | −0.972640 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.10516e6i | 0.617729i | ||||||||
\(629\) | −1.71217e7 | −1.72552 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.94679e6 | 0.294629 | 0.147314 | − | 0.989090i | \(-0.452937\pi\) | ||||
0.147314 | + | 0.989090i | \(0.452937\pi\) | |||||||
\(632\) | 4.66876e6i | 0.464952i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.00053e6 | −0.790489 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 200981.i | 0.0196248i | ||||||||
\(638\) | 1.46528e6i | 0.142518i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.28989e7 | −1.23996 | −0.619981 | − | 0.784617i | \(-0.712860\pi\) | ||||
−0.619981 | + | 0.784617i | \(0.712860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 9.20262e6i | − 0.877777i | −0.898542 | − | 0.438889i | \(-0.855372\pi\) | ||||
0.898542 | − | 0.438889i | \(-0.144628\pi\) | |||||||
\(644\) | −195998. | −0.0186225 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.42504e6 | −0.417192 | ||||||||
\(647\) | − 177907.i | − 0.0167083i | −0.999965 | − | 0.00835417i | \(-0.997341\pi\) | ||||
0.999965 | − | 0.00835417i | \(-0.00265925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.73279e6 | 0.161485 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 9.26410e6i | − 0.853462i | ||||||||
\(653\) | − 1.11867e7i | − 1.02664i | −0.858197 | − | 0.513321i | \(-0.828415\pi\) | ||||
0.858197 | − | 0.513321i | \(-0.171585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.44562e6 | 0.312613 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.64893e6i | 0.778749i | ||||||||
\(659\) | 2.34591e6 | 0.210425 | 0.105213 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105213 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.73844e6 | −0.332803 | −0.166401 | − | 0.986058i | \(-0.553215\pi\) | ||||
−0.166401 | + | 0.986058i | \(0.553215\pi\) | |||||||
\(662\) | − 5.93446e6i | − 0.526304i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.45740e6 | −0.568378 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 279619.i | 0.0243362i | ||||||||
\(668\) | − 2.04973e6i | − 0.177728i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.60410e6 | 0.309023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 6.11773e6i | − 0.520658i | −0.965520 | − | 0.260329i | \(-0.916169\pi\) | ||||
0.965520 | − | 0.260329i | \(-0.0838310\pi\) | |||||||
\(674\) | −9.69961e6 | −0.822440 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.87977e6 | −0.494873 | ||||||||
\(677\) | − 6.50221e6i | − 0.545242i | −0.962121 | − | 0.272621i | \(-0.912109\pi\) | ||||
0.962121 | − | 0.272621i | \(-0.0878905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.16805e6 | 0.513421 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.72765e6i | 0.142231i | ||||||||
\(683\) | 1.37285e7i | 1.12609i | 0.826427 | + | 0.563044i | \(0.190370\pi\) | ||||
−0.826427 | + | 0.563044i | \(0.809630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.67722e6 | −0.622865 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.20258e6i | 0.0968595i | ||||||||
\(689\) | −30767.5 | −0.00246913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.36316e7 | 1.08606 | 0.543028 | − | 0.839715i | \(-0.317278\pi\) | ||||
0.543028 | + | 0.839715i | \(0.317278\pi\) | |||||||
\(692\) | 7.79499e6i | 0.618800i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.06726e6 | −0.399369 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.24837e7i | 1.75302i | ||||||||
\(698\) | − 1.01703e7i | − 0.790123i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.08567e6 | −0.160306 | −0.0801531 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801531 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.78767e6i | 0.518003i | ||||||||
\(704\) | 464061. | 0.0352894 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.14037e6 | −0.388135 | ||||||||
\(707\) | 7.07763e6i | 0.532524i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.23349e7 | −0.921554 | −0.460777 | − | 0.887516i | \(-0.652429\pi\) | ||||
−0.460777 | + | 0.887516i | \(0.652429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.38968e6i | 0.694146i | ||||||||
\(713\) | 329687.i | 0.0242872i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.35718e7 | 0.989359 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.66500e7i | 1.20533i | ||||||||
\(719\) | −2.83517e6 | −0.204530 | −0.102265 | − | 0.994757i | \(-0.532609\pi\) | ||||
−0.102265 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.16450e6 | −0.513272 | ||||||||
\(722\) | − 8.15015e6i | − 0.581865i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.20677e6 | 0.652771 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.19423e7i | − 0.838017i | −0.907982 | − | 0.419009i | \(-0.862378\pi\) | ||||
0.907982 | − | 0.419009i | \(-0.137622\pi\) | |||||||
\(728\) | − 559374.i | − 0.0391178i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.84721e6 | −0.543152 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.50999e7i | − 1.72549i | −0.505642 | − | 0.862744i | \(-0.668744\pi\) | ||||
0.505642 | − | 0.862744i | \(-0.331256\pi\) | |||||||
\(734\) | 4.52265e6 | 0.309851 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 88556.7 | 0.00602597 | ||||||||
\(737\) | − 5.58267e6i | − 0.378593i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.66189e6 | 0.111942 | 0.0559708 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559708 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 282521.i | 0.0188383i | ||||||||
\(743\) | − 988158.i | − 0.0656681i | −0.999461 | − | 0.0328340i | \(-0.989547\pi\) | ||||
0.999461 | − | 0.0328340i | \(-0.0104533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.24948e6 | −0.0822022 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.02815e6i | 0.197890i | ||||||||
\(749\) | 2.71331e7 | 1.76724 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.42260e7 | 1.56741 | 0.783704 | − | 0.621135i | \(-0.213328\pi\) | ||||
0.783704 | + | 0.621135i | \(0.213328\pi\) | |||||||
\(752\) | − 3.90779e6i | − 0.251992i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −798026. | −0.0511198 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 8.03239e6i | − 0.509454i | −0.967013 | − | 0.254727i | \(-0.918014\pi\) | ||||
0.967013 | − | 0.254727i | \(-0.0819857\pi\) | |||||||
\(758\) | 8.79960e6i | 0.556275i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.44956e6 | 0.528899 | 0.264449 | − | 0.964400i | \(-0.414810\pi\) | ||||
0.264449 | + | 0.964400i | \(0.414810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.01323e7i | − 0.630083i | ||||||||
\(764\) | 293803. | 0.0182105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.57333e7 | −0.968828 | ||||||||
\(767\) | 943716.i | 0.0579232i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.68674e7 | 1.02857 | 0.514285 | − | 0.857620i | \(-0.328057\pi\) | ||||
0.514285 | + | 0.857620i | \(0.328057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 5.59220e6i | − 0.337707i | ||||||||
\(773\) | 2.37205e7i | 1.42782i | 0.700236 | + | 0.713912i | \(0.253078\pi\) | ||||
−0.700236 | + | 0.713912i | \(0.746922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.78687e6 | −0.166136 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.68237e7i | 0.996490i | ||||||||
\(779\) | 8.91339e6 | 0.526259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.38575e6 | 0.139958 | ||||||||
\(782\) | 577861.i | 0.0337914i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −833840. | −0.0484499 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.21145e7i | − 1.27274i | −0.771384 | − | 0.636370i | \(-0.780435\pi\) | ||||
0.771384 | − | 0.636370i | \(-0.219565\pi\) | |||||||
\(788\) | 5.94865e6i | 0.341274i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.31446e7 | 1.31525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.96288e6i | 0.110844i | ||||||||
\(794\) | 9.57936e6 | 0.539244 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.80910e6 | 0.269018 | ||||||||
\(797\) | 1.86780e6i | 0.104156i | 0.998643 | + | 0.0520779i | \(0.0165844\pi\) | ||||
−0.998643 | + | 0.0520779i | \(0.983416\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.54996e7 | 1.41308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1.76864e7i | − 0.970967i | ||||||||
\(803\) | 4.46928e6i | 0.244596i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −940918. | −0.0510169 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 3.19784e6i | − 0.172317i | ||||||||
\(809\) | −203197. | −0.0109156 | −0.00545778 | − | 0.999985i | \(-0.501737\pi\) | ||||
−0.00545778 | + | 0.999985i | \(0.501737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.27341e7 | 1.21374 | 0.606870 | − | 0.794801i | \(-0.292425\pi\) | ||||
0.606870 | + | 0.794801i | \(0.292425\pi\) | |||||||
\(812\) | 7.32785e6i | 0.390019i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.64494e6 | 0.245708 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.11092e6i | 0.163055i | ||||||||
\(818\) | 1.04430e7i | 0.545686i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.56056e7 | −1.32579 | −0.662897 | − | 0.748710i | \(-0.730673\pi\) | ||||
−0.662897 | + | 0.748710i | \(0.730673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.10878e6i | 0.365844i | 0.983127 | + | 0.182922i | \(0.0585555\pi\) | ||||
−0.983127 | + | 0.182922i | \(0.941444\pi\) | |||||||
\(824\) | 3.23709e6 | 0.166087 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.66563e6 | 0.441927 | ||||||||
\(827\) | 2.69334e7i | 1.36939i | 0.728830 | + | 0.684695i | \(0.240065\pi\) | ||||
−0.728830 | + | 0.684695i | \(0.759935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.89570e7 | −1.46341 | −0.731707 | − | 0.681619i | \(-0.761276\pi\) | ||||
−0.731707 | + | 0.681619i | \(0.761276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 252739.i | 0.0126579i | ||||||||
\(833\) | − 5.44107e6i | − 0.271689i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.20047e6 | 0.0594067 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.06498e6i | 0.199962i | ||||||||
\(839\) | 1.95591e7 | 0.959279 | 0.479639 | − | 0.877466i | \(-0.340767\pi\) | ||||
0.479639 | + | 0.877466i | \(0.340767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00569e7 | −0.490316 | ||||||||
\(842\) | 2.38766e7i | 1.16063i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −951987. | −0.0460018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.09944e7i | − 1.00553i | ||||||||
\(848\) | − 127650.i | − 0.00609580i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 886393. | 0.0419568 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.74251e7i | − 0.819981i | −0.912090 | − | 0.409990i | \(-0.865532\pi\) | ||||
0.912090 | − | 0.409990i | \(-0.134468\pi\) | |||||||
\(854\) | 1.80241e7 | 0.845684 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.22594e7 | −0.571852 | ||||||||
\(857\) | 2.03324e7i | 0.945663i | 0.881153 | + | 0.472831i | \(0.156768\pi\) | ||||
−0.881153 | + | 0.472831i | \(0.843232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.19607e7 | 0.553061 | 0.276530 | − | 0.961005i | \(-0.410815\pi\) | ||||
0.276530 | + | 0.961005i | \(0.410815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.18858e7i | 0.544829i | ||||||||
\(863\) | 3.87101e7i | 1.76928i | 0.466274 | + | 0.884640i | \(0.345596\pi\) | ||||
−0.466274 | + | 0.884640i | \(0.654404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.98095e7 | −0.897590 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.63995e6i | 0.389235i | ||||||||
\(869\) | 8.26488e6 | 0.371268 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.04045e6 | 0.135798 | ||||||||
\(872\) | 4.57802e6i | 0.203886i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 229085. | 0.0101442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.76410e7i | 1.65258i | 0.563247 | + | 0.826289i | \(0.309552\pi\) | ||||
−0.563247 | + | 0.826289i | \(0.690448\pi\) | |||||||
\(878\) | 4.48459e6i | 0.196330i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.92452e6 | −0.126945 | −0.0634723 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634723 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90249e7i | 1.68438i | 0.539181 | + | 0.842190i | \(0.318734\pi\) | ||||
−0.539181 | + | 0.842190i | \(0.681266\pi\) | |||||||
\(884\) | −1.64920e6 | −0.0709811 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.06493e7 | 0.455761 | ||||||||
\(887\) | 1.16063e7i | 0.495318i | 0.968847 | + | 0.247659i | \(0.0796613\pi\) | ||||
−0.968847 | + | 0.247659i | \(0.920339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.86571e6 | 0.206487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 1.38580e7i | − 0.583160i | ||||||||
\(893\) | − 1.01090e7i | − 0.424208i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.32076e6 | 0.0965741 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1.55513e7i | − 0.643538i | ||||||||
\(899\) | 1.23261e7 | 0.508659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 832955. | 0.0341830 | ||||||||
\(902\) | − 6.09962e6i | − 0.249624i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.04573e7 | −0.425597 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.80327e7i | − 1.53511i | −0.640984 | − | 0.767554i | \(-0.721473\pi\) | ||||
0.640984 | − | 0.767554i | \(-0.278527\pi\) | |||||||
\(908\) | 1.17929e7i | 0.474687i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.76995e7 | −1.90422 | −0.952112 | − | 0.305748i | \(-0.901093\pi\) | ||||
−0.952112 | + | 0.305748i | \(0.901093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14312e7i | 0.453854i | ||||||||
\(914\) | −1.01052e7 | −0.400110 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.35440e7 | 0.533346 | ||||||||
\(917\) | 4.94767e7i | 1.94302i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.06445e7 | 1.19692 | 0.598459 | − | 0.801154i | \(-0.295780\pi\) | ||||
0.598459 | + | 0.801154i | \(0.295780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 1.85436e7i | − 0.718400i | ||||||||
\(923\) | 1.29934e6i | 0.0502016i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.44952e7 | 0.555517 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 3.31090e6i | − 0.126205i | ||||||||
\(929\) | 4.20442e7 | 1.59833 | 0.799165 | − | 0.601112i | \(-0.205275\pi\) | ||||
0.799165 | + | 0.601112i | \(0.205275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.15704e6 | −0.0815614 | ||||||||
\(932\) | − 9.45216e6i | − 0.356444i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.49103e7 | −0.559267 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.09921e7i | 0.781101i | 0.920582 | + | 0.390551i | \(0.127715\pi\) | ||||
−0.920582 | + | 0.390551i | \(0.872285\pi\) | |||||||
\(938\) | − 2.79188e7i | − 1.03607i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.06080e7 | −0.390536 | −0.195268 | − | 0.980750i | \(-0.562558\pi\) | ||||
−0.195268 | + | 0.980750i | \(0.562558\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.16399e6i | − 0.0426255i | ||||||||
\(944\) | −3.91534e6 | −0.143001 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.12887e6 | 0.0773430 | ||||||||
\(947\) | − 2.66948e7i | − 0.967280i | −0.875267 | − | 0.483640i | \(-0.839314\pi\) | ||||
0.875267 | − | 0.483640i | \(-0.160686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.43408e6 | −0.0877341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.51437e7i | 0.541552i | ||||||||
\(953\) | 2.68015e7i | 0.955932i | 0.878378 | + | 0.477966i | \(0.158626\pi\) | ||||
−0.878378 | + | 0.477966i | \(0.841374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.56600e7 | −0.908054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 2.75350e7i | − 0.969328i | ||||||||
\(959\) | 3.88589e7 | 1.36441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40960e7 | −0.492364 | ||||||||
\(962\) | 2.52974e6i | 0.0881331i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.55314e6 | 0.192463 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.43270e7i | − 1.18051i | −0.807217 | − | 0.590255i | \(-0.799027\pi\) | ||||
0.807217 | − | 0.590255i | \(-0.200973\pi\) | |||||||
\(968\) | 9.48576e6i | 0.325375i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.43606e7 | 0.488791 | 0.244396 | − | 0.969676i | \(-0.421410\pi\) | ||||
0.244396 | + | 0.969676i | \(0.421410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.77676e6i | 0.229477i | ||||||||
\(974\) | 3.43596e7 | 1.16051 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.14370e6 | −0.273651 | ||||||||
\(977\) | − 1.16248e7i | − 0.389627i | −0.980840 | − | 0.194813i | \(-0.937590\pi\) | ||||
0.980840 | − | 0.194813i | \(-0.0624102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.66221e7 | 0.554280 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.87996e6i | 0.194579i | ||||||||
\(983\) | 3.11250e6i | 0.102737i | 0.998680 | + | 0.0513683i | \(0.0163582\pi\) | ||||
−0.998680 | + | 0.0513683i | \(0.983642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.16046e7 | 0.707709 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 653804.i | 0.0213086i | ||||||||
\(989\) | 406251. | 0.0132070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.33325e7 | −0.754704 | −0.377352 | − | 0.926070i | \(-0.623165\pi\) | ||||
−0.377352 | + | 0.926070i | \(0.623165\pi\) | |||||||
\(992\) | − 3.90373e6i | − 0.125951i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.19311e7 | 0.383014 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.35497e7i | 1.70616i | 0.521782 | + | 0.853079i | \(0.325267\pi\) | ||||
−0.521782 | + | 0.853079i | \(0.674733\pi\) | |||||||
\(998\) | 1.25217e7i | 0.397958i | ||||||||
\(999\) | 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.c.q.199.4 | 4 | ||
3.2 | odd | 2 | 450.6.c.p.199.2 | 4 | |||
5.2 | odd | 4 | 450.6.a.ba.1.1 | yes | 2 | ||
5.3 | odd | 4 | 450.6.a.bd.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 450.6.c.q.199.1 | 4 | ||
15.2 | even | 4 | 450.6.a.bf.1.1 | yes | 2 | ||
15.8 | even | 4 | 450.6.a.y.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 450.6.c.p.199.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.a.y.1.2 | ✓ | 2 | 15.8 | even | 4 | ||
450.6.a.ba.1.1 | yes | 2 | 5.2 | odd | 4 | ||
450.6.a.bd.1.2 | yes | 2 | 5.3 | odd | 4 | ||
450.6.a.bf.1.1 | yes | 2 | 15.2 | even | 4 | ||
450.6.c.p.199.2 | 4 | 3.2 | odd | 2 | |||
450.6.c.p.199.3 | 4 | 15.14 | odd | 2 | |||
450.6.c.q.199.1 | 4 | 5.4 | even | 2 | inner | ||
450.6.c.q.199.4 | 4 | 1.1 | even | 1 | trivial |