Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1009,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.t (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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.4 | ||
Root | \(0.432320 - 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1009 |
Dual form | 5040.2.t.y.1009.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.432320 | + | 2.19388i | −0.193340 | + | 0.981132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.626198 | −0.188806 | −0.0944029 | − | 0.995534i | \(-0.530094\pi\) | ||||
−0.0944029 | + | 0.995534i | \(0.530094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.49084i | − | 1.52288i | −0.648233 | − | 0.761442i | \(-0.724492\pi\) | ||
0.648233 | − | 0.761442i | \(-0.275508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.896916i | − | 0.217534i | −0.994067 | − | 0.108767i | \(-0.965310\pi\) | ||
0.994067 | − | 0.108767i | \(-0.0346903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38776 | 1.46545 | 0.732726 | − | 0.680524i | \(-0.238248\pi\) | ||||
0.732726 | + | 0.680524i | \(0.238248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.72928i | 0.777609i | 0.921320 | + | 0.388805i | \(0.127112\pi\) | ||||
−0.921320 | + | 0.388805i | \(0.872888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | − | 1.89692i | −0.925240 | − | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.87859 | −1.46302 | −0.731509 | − | 0.681832i | \(-0.761184\pi\) | ||||
−0.731509 | + | 0.681832i | \(0.761184\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52311 | −1.35119 | −0.675596 | − | 0.737272i | \(-0.736113\pi\) | ||||
−0.675596 | + | 0.737272i | \(0.736113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.19388 | + | 0.432320i | 0.370833 | + | 0.0730755i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.72928 | −1.20711 | −0.603556 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603556 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.72928i | 0.263713i | 0.991269 | + | 0.131856i | \(0.0420938\pi\) | ||||
−0.991269 | + | 0.131856i | \(0.957906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.87859i | 0.857481i | 0.903428 | + | 0.428741i | \(0.141043\pi\) | ||||
−0.903428 | + | 0.428741i | \(0.858957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.77551i | − | 0.930688i | −0.885130 | − | 0.465344i | \(-0.845931\pi\) | ||
0.885130 | − | 0.465344i | \(-0.154069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.270718 | − | 1.37380i | 0.0365036 | − | 0.185243i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.593923 | 0.0773221 | 0.0386611 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386611 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.13536 | 0.913589 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0462 | + | 2.37380i | 1.49415 | + | 0.294434i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.79383i | 0.707829i | 0.935278 | + | 0.353915i | \(0.115150\pi\) | ||||
−0.935278 | + | 0.353915i | \(0.884850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.52311 | 0.655473 | 0.327737 | − | 0.944769i | \(-0.393714\pi\) | ||||
0.327737 | + | 0.944769i | \(0.393714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.72928i | 0.436479i | 0.975895 | + | 0.218240i | \(0.0700315\pi\) | ||||
−0.975895 | + | 0.218240i | \(0.929969\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.626198i | 0.0713619i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.67243 | −0.638198 | −0.319099 | − | 0.947721i | \(-0.603380\pi\) | ||||
−0.319099 | + | 0.947721i | \(0.603380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.4340i | 1.91363i | 0.290700 | + | 0.956814i | \(0.406112\pi\) | ||||
−0.290700 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.96772 | + | 0.387755i | 0.213430 | + | 0.0420580i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2986 | 1.51565 | 0.757826 | − | 0.652457i | \(-0.226262\pi\) | ||||
0.757826 | + | 0.652457i | \(0.226262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.49084 | −0.575596 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.76156 | + | 14.0140i | −0.283330 | + | 1.43780i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.1493i | − | 1.03051i | −0.857038 | − | 0.515253i | \(-0.827698\pi\) | ||
0.857038 | − | 0.515253i | \(-0.172302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.64015 | −0.959231 | −0.479615 | − | 0.877479i | \(-0.659224\pi\) | ||||
−0.479615 | + | 0.877479i | \(0.659224\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.626198i | − | 0.0617011i | −0.999524 | − | 0.0308506i | \(-0.990178\pi\) | ||
0.999524 | − | 0.0308506i | \(-0.00982160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9248 | −1.81267 | −0.906335 | − | 0.422561i | \(-0.861131\pi\) | ||||
−0.906335 | + | 0.422561i | \(0.861131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.04623i | − | 0.0984209i | −0.998788 | − | 0.0492105i | \(-0.984329\pi\) | ||
0.998788 | − | 0.0492105i | \(-0.0156705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.18159 | − | 1.61224i | −0.762937 | − | 0.150343i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.896916 | −0.0822202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6079 | −0.964352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.16160 | − | 9.32924i | 0.551110 | − | 0.834432i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2803i | 1.88832i | 0.329485 | + | 0.944161i | \(0.393125\pi\) | ||||
−0.329485 | + | 0.944161i | \(0.606875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.91087 | −0.865917 | −0.432958 | − | 0.901414i | \(-0.642530\pi\) | ||||
−0.432958 | + | 0.901414i | \(0.642530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.38776i | − | 0.553889i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.45856i | − | 0.295485i | −0.989026 | − | 0.147743i | \(-0.952799\pi\) | ||
0.989026 | − | 0.147743i | \(-0.0472007\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4157 | −1.73163 | −0.865817 | − | 0.500361i | \(-0.833201\pi\) | ||||
−0.865817 | + | 0.500361i | \(0.833201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.43835i | 0.287530i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.40608 | − | 17.2847i | 0.282859 | − | 1.43541i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0462 | −1.39648 | −0.698241 | − | 0.715863i | \(-0.746033\pi\) | ||||
−0.698241 | + | 0.715863i | \(0.746033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89692 | −0.235748 | −0.117874 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117874 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.25240 | − | 16.5048i | 0.261239 | − | 1.32570i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1170i | 0.807427i | 0.914885 | + | 0.403714i | \(0.132281\pi\) | ||||
−0.914885 | + | 0.403714i | \(0.867719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.72928 | 0.293909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.476886i | 0.0373526i | 0.999826 | + | 0.0186763i | \(0.00594519\pi\) | ||||
−0.999826 | + | 0.0186763i | \(0.994055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.1676i | − | 1.01894i | −0.860488 | − | 0.509471i | \(-0.829841\pi\) | ||
0.860488 | − | 0.509471i | \(-0.170159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.1493 | −1.31918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9677i | 1.06195i | 0.847389 | + | 0.530973i | \(0.178174\pi\) | ||||
−0.847389 | + | 0.530973i | \(0.821826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.89692 | + | 4.62620i | −0.143393 | + | 0.349708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.45856 | −0.557479 | −0.278740 | − | 0.960367i | \(-0.589917\pi\) | ||||
−0.278740 | + | 0.960367i | \(0.589917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1170 | −1.04931 | −0.524656 | − | 0.851315i | \(-0.675806\pi\) | ||||
−0.524656 | + | 0.851315i | \(0.675806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.1633 | − | 2.59392i | −0.967783 | − | 0.190709i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.561647i | 0.0410717i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.42003 | −0.609252 | −0.304626 | − | 0.952472i | \(-0.598531\pi\) | ||||
−0.304626 | + | 0.952472i | \(0.598531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.2986i | 1.60509i | 0.596591 | + | 0.802545i | \(0.296521\pi\) | ||||
−0.596591 | + | 0.802545i | \(0.703479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.3632i | − | 1.87830i | −0.343509 | − | 0.939149i | \(-0.611616\pi\) | ||
0.343509 | − | 0.939149i | \(-0.388384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4402 | 1.59075 | 0.795373 | − | 0.606120i | \(-0.207275\pi\) | ||||
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.87859i | 0.552969i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.34153 | − | 16.9571i | 0.233382 | − | 1.18434i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1955 | 1.04610 | 0.523052 | − | 0.852301i | \(-0.324793\pi\) | ||||
0.523052 | + | 0.852301i | \(0.324793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.79383 | − | 0.747604i | −0.258737 | − | 0.0509862i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.52311i | 0.510702i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.92482 | −0.331279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.89692i | − | 0.461852i | −0.972971 | − | 0.230926i | \(-0.925825\pi\) | ||
0.972971 | − | 0.230926i | \(-0.0741755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.77988i | − | 0.184507i | −0.995736 | − | 0.0922535i | \(-0.970593\pi\) | ||
0.995736 | − | 0.0922535i | \(-0.0294070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6585 | −1.23299 | −0.616493 | − | 0.787360i | \(-0.711447\pi\) | ||||
−0.616493 | + | 0.787360i | \(0.711447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.0462i | − | 0.723663i | −0.932244 | − | 0.361831i | \(-0.882152\pi\) | ||
0.932244 | − | 0.361831i | \(-0.117848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8969 | − | 2.54144i | −0.841302 | − | 0.165785i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1493 | 1.30335 | 0.651675 | − | 0.758498i | \(-0.274066\pi\) | ||||
0.651675 | + | 0.758498i | \(0.274066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.72928 | 0.240224 | 0.120112 | − | 0.992760i | \(-0.461675\pi\) | ||||
0.120112 | + | 0.992760i | \(0.461675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.432320 | − | 2.19388i | 0.0276199 | − | 0.140162i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 35.0741i | − | 2.23171i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4985 | −1.35698 | −0.678488 | − | 0.734612i | \(-0.737364\pi\) | ||||
−0.678488 | + | 0.734612i | \(0.737364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.33527i | − | 0.146817i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4.27072i | − | 0.266400i | −0.991089 | − | 0.133200i | \(-0.957475\pi\) | ||
0.991089 | − | 0.133200i | \(-0.0425253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4586i | 0.706565i | 0.935517 | + | 0.353283i | \(0.114935\pi\) | ||||
−0.935517 | + | 0.353283i | \(0.885065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.8646 | + | 2.92919i | 0.913128 | + | 0.179939i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.07081 | −0.431115 | −0.215557 | − | 0.976491i | \(-0.569157\pi\) | ||||
−0.215557 | + | 0.976491i | \(0.569157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0096 | −1.03326 | −0.516629 | − | 0.856209i | \(-0.672813\pi\) | ||||
−0.516629 | + | 0.856209i | \(0.672813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.89692 | + | 1.18785i | 0.174691 | + | 0.0716298i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.7755i | − | 1.12811i | −0.825737 | − | 0.564056i | \(-0.809240\pi\) | ||
0.825737 | − | 0.564056i | \(-0.190760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.59829 | 0.274311 | 0.137156 | − | 0.990550i | \(-0.456204\pi\) | ||||
0.137156 | + | 0.990550i | \(0.456204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.5833i | − | 0.807443i | −0.914882 | − | 0.403722i | \(-0.867716\pi\) | ||
0.914882 | − | 0.403722i | \(-0.132284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.72928i | 0.456245i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1955 | 0.952679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8261i | 0.690889i | 0.938439 | + | 0.345444i | \(0.112272\pi\) | ||||
−0.938439 | + | 0.345444i | \(0.887728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.256765 | + | 1.30299i | −0.0149494 | + | 0.0758632i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.4769 | 1.18421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.72928 | 0.0996741 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.08476 | + | 15.6541i | −0.176633 | + | 0.896351i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9860i | 1.19774i | 0.800847 | + | 0.598868i | \(0.204383\pi\) | ||||
−0.800847 | + | 0.598868i | \(0.795617\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.5048 | −1.27613 | −0.638065 | − | 0.769983i | \(-0.720265\pi\) | ||||
−0.638065 | + | 0.769983i | \(0.720265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4846i | 0.705670i | 0.935686 | + | 0.352835i | \(0.114782\pi\) | ||||
−0.935686 | + | 0.352835i | \(0.885218\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.5231i | − | 1.43352i | −0.697319 | − | 0.716760i | \(-0.745624\pi\) | ||
0.697319 | − | 0.716760i | \(-0.254376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.93356 | 0.276226 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.72928i | − | 0.318786i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4157 | + | 25.4017i | −0.577757 | + | 1.40903i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.87859 | 0.324097 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.68305 | 0.147474 | 0.0737370 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737370 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7110 | − | 2.50479i | −0.694474 | − | 0.136851i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5048i | 0.681179i | 0.940212 | + | 0.340590i | \(0.110627\pi\) | ||||
−0.940212 | + | 0.340590i | \(0.889373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.71096 | 0.255113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 28.9450i | − | 1.55385i | −0.629593 | − | 0.776925i | \(-0.716778\pi\) | ||
0.629593 | − | 0.776925i | \(-0.283222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.1449 | −1.72068 | −0.860340 | − | 0.509721i | \(-0.829749\pi\) | ||||
−0.860340 | + | 0.509721i | \(0.829749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.17722i | 0.435229i | 0.976035 | + | 0.217615i | \(0.0698276\pi\) | ||||
−0.976035 | + | 0.217615i | \(0.930172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.38776 | + | 12.1170i | −0.126729 | + | 0.643106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.5048 | −0.976646 | −0.488323 | − | 0.872663i | \(-0.662391\pi\) | ||||
−0.488323 | + | 0.872663i | \(0.662391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.8034 | 1.14755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.18159 | − | 1.61224i | −0.428244 | − | 0.0843887i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4942i | 1.43518i | 0.696464 | + | 0.717592i | \(0.254756\pi\) | ||||
−0.696464 | + | 0.717592i | \(0.745244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.77551 | −0.351767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.06455i | − | 0.314011i | −0.987598 | − | 0.157005i | \(-0.949816\pi\) | ||
0.987598 | − | 0.157005i | \(-0.0501840\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.2601i | 2.22801i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.72928 | −0.294293 | −0.147147 | − | 0.989115i | \(-0.547009\pi\) | ||||
−0.147147 | + | 0.989115i | \(0.547009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.72928i | 0.0883622i | 0.999024 | + | 0.0441811i | \(0.0140679\pi\) | ||||
−0.999024 | + | 0.0441811i | \(0.985932\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37380 | − | 0.270718i | −0.0700154 | − | 0.0137971i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.7187 | −1.86171 | −0.930855 | − | 0.365389i | \(-0.880936\pi\) | ||||
−0.930855 | + | 0.365389i | \(0.880936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.34485 | 0.169157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.45231 | − | 12.4446i | 0.123389 | − | 0.626156i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.03228i | − | 0.101997i | −0.998699 | − | 0.0509985i | \(-0.983760\pi\) | ||
0.998699 | − | 0.0509985i | \(-0.0162404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.64452 | 0.0821234 | 0.0410617 | − | 0.999157i | \(-0.486926\pi\) | ||||
0.0410617 | + | 0.999157i | \(0.486926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.3082i | 2.05771i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.75719i | − | 0.186237i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.98168 | 0.246328 | 0.123164 | − | 0.992386i | \(-0.460696\pi\) | ||||
0.123164 | + | 0.992386i | \(0.460696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 0.593923i | − | 0.0292250i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.2480 | − | 7.53707i | −1.87752 | − | 0.369980i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.9205 | −1.11974 | −0.559869 | − | 0.828581i | \(-0.689148\pi\) | ||||
−0.559869 | + | 0.828581i | \(0.689148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9527 | −1.02117 | −0.510587 | − | 0.859826i | \(-0.670572\pi\) | ||||
−0.510587 | + | 0.859826i | \(0.670572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.70138 | + | 4.14931i | −0.0825288 | + | 0.201271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.13536i | − | 0.345304i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.1589 | 1.59721 | 0.798604 | − | 0.601857i | \(-0.205572\pi\) | ||||
0.798604 | + | 0.601857i | \(0.205572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5414i | 0.891045i | 0.895271 | + | 0.445522i | \(0.146982\pi\) | ||||
−0.895271 | + | 0.445522i | \(0.853018\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.8217i | 1.13955i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.8401 | −0.994642 | −0.497321 | − | 0.867567i | \(-0.665683\pi\) | ||||
−0.497321 | + | 0.867567i | \(0.665683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.5510i | − | 0.833874i | −0.908935 | − | 0.416937i | \(-0.863104\pi\) | ||
0.908935 | − | 0.416937i | \(-0.136896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.18159 | + | 31.3694i | −0.293035 | + | 1.48705i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.1955 | −0.622736 | −0.311368 | − | 0.950289i | \(-0.600787\pi\) | ||||
−0.311368 | + | 0.950289i | \(0.600787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84006 | 0.227910 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.37380 | − | 12.0462i | 0.111286 | − | 0.564736i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.1020i | − | 1.36134i | −0.732592 | − | 0.680668i | \(-0.761690\pi\) | ||
0.732592 | − | 0.680668i | \(-0.238310\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8280 | 0.876907 | 0.438454 | − | 0.898754i | \(-0.355526\pi\) | ||||
0.438454 | + | 0.898754i | \(0.355526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.0925i | − | 0.654932i | −0.944863 | − | 0.327466i | \(-0.893805\pi\) | ||
0.944863 | − | 0.327466i | \(-0.106195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.2663i | − | 0.567619i | −0.958881 | − | 0.283809i | \(-0.908402\pi\) | ||
0.958881 | − | 0.283809i | \(-0.0915983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.79383 | 0.267534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.08287i | − | 0.0497905i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.5510 | − | 12.1170i | −1.35589 | − | 0.555968i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1570 | 0.646850 | 0.323425 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323425 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.9450 | 1.50216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.2663 | + | 4.38776i | 1.01106 | + | 0.199238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.2341i | − | 1.37004i | −0.728526 | − | 0.685018i | \(-0.759794\pi\) | ||
0.728526 | − | 0.685018i | \(-0.240206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.9065 | 1.80096 | 0.900478 | − | 0.434902i | \(-0.143217\pi\) | ||||
0.900478 | + | 0.434902i | \(0.143217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.06644i | 0.318256i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.52311i | − | 0.247746i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3246 | 1.22322 | 0.611610 | − | 0.791160i | \(-0.290522\pi\) | ||||
0.611610 | + | 0.791160i | \(0.290522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.40171i | − | 0.0624991i | −0.999512 | − | 0.0312495i | \(-0.990051\pi\) | ||
0.999512 | − | 0.0312495i | \(-0.00994866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.16763 | − | 21.1493i | 0.185457 | − | 0.941132i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6585 | 0.827022 | 0.413511 | − | 0.910499i | \(-0.364302\pi\) | ||||
0.413511 | + | 0.910499i | \(0.364302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72928 | 0.164974 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.37380 | + | 0.270718i | 0.0605369 | + | 0.0119293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.68116i | − | 0.161897i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.02791 | 0.176466 | 0.0882329 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882329 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.4436i | 1.68102i | 0.541796 | + | 0.840510i | \(0.317744\pi\) | ||||
−0.541796 | + | 0.840510i | \(0.682256\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.74760i | 0.293930i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.09246 | 0.395324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.4402i | 1.83829i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.626198 | 0.0269723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4846 | 0.536754 | 0.268377 | − | 0.963314i | \(-0.413513\pi\) | ||||
0.268377 | + | 0.963314i | \(0.413513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.18159 | − | 41.5187i | 0.350461 | − | 1.77847i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.7851i | − | 1.61557i | −0.589474 | − | 0.807787i | \(-0.700665\pi\) | ||
0.589474 | − | 0.807787i | \(-0.299335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.3265 | −2.14398 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.67243i | 0.241216i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.93545i | − | 0.0820076i | −0.999159 | − | 0.0410038i | \(-0.986944\pi\) | ||
0.999159 | − | 0.0410038i | \(-0.0130556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.49521 | 0.401604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8463i | 1.25787i | 0.777457 | + | 0.628936i | \(0.216509\pi\) | ||||
−0.777457 | + | 0.628936i | \(0.783491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.29530 | + | 0.452306i | 0.0965639 | + | 0.0190287i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3449 | 0.643290 | 0.321645 | − | 0.946860i | \(-0.395764\pi\) | ||||
0.321645 | + | 0.946860i | \(0.395764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.8217 | −1.49909 | −0.749547 | − | 0.661952i | \(-0.769728\pi\) | ||||
−0.749547 | + | 0.661952i | \(0.769728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.07414 | − | 17.2524i | 0.295012 | − | 0.719475i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.92482i | 0.121762i | 0.998145 | + | 0.0608810i | \(0.0193910\pi\) | ||||
−0.998145 | + | 0.0608810i | \(0.980609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.4340 | 0.723284 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.24281i | 0.175719i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5756i | 0.807972i | 0.914765 | + | 0.403986i | \(0.132375\pi\) | ||||
−0.914765 | + | 0.403986i | \(0.867625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0558 | −1.98011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00770i | 0.328837i | 0.986391 | + | 0.164418i | \(0.0525747\pi\) | ||||
−0.986391 | + | 0.164418i | \(0.947425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.387755 | − | 1.96772i | 0.0158964 | − | 0.0806688i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.3005 | 1.19719 | 0.598593 | − | 0.801053i | \(-0.295727\pi\) | ||||
0.598593 | + | 0.801053i | \(0.295727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3449 | 0.870675 | 0.435337 | − | 0.900267i | \(-0.356629\pi\) | ||||
0.435337 | + | 0.900267i | \(0.356629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.58600 | − | 23.2724i | 0.186447 | − | 0.946157i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.53081i | − | 0.386844i | −0.981116 | − | 0.193422i | \(-0.938041\pi\) | ||
0.981116 | − | 0.193422i | \(-0.0619586\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.2784 | 1.30584 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.75719i | 0.394089i | 0.980395 | + | 0.197045i | \(0.0631344\pi\) | ||||
−0.980395 | + | 0.197045i | \(0.936866\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.9267i | 1.52687i | 0.645884 | + | 0.763436i | \(0.276489\pi\) | ||||
−0.645884 | + | 0.763436i | \(0.723511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.9109 | 1.68454 | 0.842270 | − | 0.539056i | \(-0.181219\pi\) | ||||
0.842270 | + | 0.539056i | \(0.181219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 14.2986i | − | 0.572862i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | + | 17.5510i | 0.712137 | + | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.38150 | 0.214574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.42003 | 0.335196 | 0.167598 | − | 0.985855i | \(-0.446399\pi\) | ||||
0.167598 | + | 0.985855i | \(0.446399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.6864 | − | 9.19991i | −1.85269 | − | 0.365087i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.49084i | 0.217555i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.07707 | 0.0820392 | 0.0410196 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410196 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.2480i | − | 1.07456i | −0.843405 | − | 0.537279i | \(-0.819452\pi\) | ||
0.843405 | − | 0.537279i | \(-0.180548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3632i | 0.486047i | 0.970020 | + | 0.243023i | \(0.0781391\pi\) | ||||
−0.970020 | + | 0.243023i | \(0.921861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.371913 | −0.0145989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.3449i | 1.46142i | 0.682690 | + | 0.730709i | \(0.260810\pi\) | ||||
−0.682690 | + | 0.730709i | \(0.739190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28467 | − | 21.7432i | 0.167416 | − | 0.849578i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1772 | 0.552266 | 0.276133 | − | 0.961119i | \(-0.410947\pi\) | ||||
0.276133 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76925 | −0.0688160 | −0.0344080 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344080 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0140 | + | 2.76156i | 0.543438 | + | 0.107089i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29.3815i | − | 1.13766i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.46815 | −0.172491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.05581i | − | 0.156340i | −0.996940 | − | 0.0781701i | \(-0.975092\pi\) | ||
0.996940 | − | 0.0781701i | \(-0.0249077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.37713i | 0.360392i | 0.983631 | + | 0.180196i | \(0.0576733\pi\) | ||||
−0.983631 | + | 0.180196i | \(0.942327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1493 | −0.389495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.49521i | 0.210268i | 0.994458 | + | 0.105134i | \(0.0335272\pi\) | ||||
−0.994458 | + | 0.105134i | \(0.966473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.58767 | + | 1.49521i | 0.289910 | + | 0.0571290i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.2032 | −1.41733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.03416 | 0.115425 | 0.0577125 | − | 0.998333i | \(-0.481619\pi\) | ||||
0.0577125 | + | 0.998333i | \(0.481619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.82611 | − | 44.7895i | 0.334793 | − | 1.69896i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.93252i | 0.262588i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.2234 | −1.33037 | −0.665186 | − | 0.746678i | \(-0.731648\pi\) | ||||
−0.665186 | + | 0.746678i | \(0.731648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.3265i | 1.44551i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.64015i | 0.362555i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7187 | −1.07855 | −0.539276 | − | 0.842129i | \(-0.681302\pi\) | ||||
−0.539276 | + | 0.842129i | \(0.681302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 28.0558i | − | 1.05070i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.54333 | − | 1.48647i | −0.282104 | − | 0.0555908i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.60599 | 0.320949 | 0.160475 | − | 0.987040i | \(-0.448698\pi\) | ||||
0.160475 | + | 0.987040i | \(0.448698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.626198 | −0.0233208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.4479 | + | 14.9450i | 1.35364 | + | 0.555045i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2803i | 0.566715i | 0.959014 | + | 0.283358i | \(0.0914483\pi\) | ||||
−0.959014 | + | 0.283358i | \(0.908552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.55102 | 0.0573666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.0235i | 1.69992i | 0.526849 | + | 0.849959i | \(0.323373\pi\) | ||||
−0.526849 | + | 0.849959i | \(0.676627\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.62809i | − | 0.133642i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.3467 | 1.70489 | 0.852446 | − | 0.522815i | \(-0.175118\pi\) | ||||
0.852446 | + | 0.522815i | \(0.175118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10.7755i | − | 0.395315i | −0.980271 | − | 0.197658i | \(-0.936667\pi\) | ||
0.980271 | − | 0.197658i | \(-0.0633334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.36943 | − | 37.3973i | 0.269995 | − | 1.37013i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.76781 | −0.100999 | −0.0504995 | − | 0.998724i | \(-0.516081\pi\) | ||||
−0.0504995 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.25240 | − | 6.35548i | 0.0455794 | − | 0.231300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8401i | 0.539371i | 0.962948 | + | 0.269686i | \(0.0869198\pi\) | ||||
−0.962948 | + | 0.269686i | \(0.913080\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3169 | −1.13524 | −0.567619 | − | 0.823291i | \(-0.692135\pi\) | ||||
−0.567619 | + | 0.823291i | \(0.692135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.9248i | 0.685125i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.26113i | − | 0.117753i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.92586 | −0.321875 | −0.160937 | − | 0.986965i | \(-0.551452\pi\) | ||||
−0.160937 | + | 0.986965i | \(0.551452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.7711i | 1.32257i | 0.750136 | + | 0.661283i | \(0.229988\pi\) | ||||
−0.750136 | + | 0.661283i | \(0.770012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.8034 | + | 14.2707i | 1.25018 | + | 0.512619i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.3728 | −1.76896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.45856 | −0.123757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.1955 | − | 4.37380i | −0.792193 | − | 0.156108i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6.53707i | − | 0.233021i | −0.993189 | − | 0.116511i | \(-0.962829\pi\) | ||
0.993189 | − | 0.116511i | \(-0.0371709\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.04623 | −0.0371996 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 39.1791i | − | 1.39129i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.82611i | − | 0.277215i | −0.990347 | − | 0.138607i | \(-0.955737\pi\) | ||
0.990347 | − | 0.138607i | \(-0.0442626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.27261 | 0.186531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.33527i | − | 0.0824099i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61224 | + | 8.18159i | −0.0568242 | + | 0.288363i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.4113 | 1.35047 | 0.675235 | − | 0.737603i | \(-0.264042\pi\) | ||||
0.675235 | + | 0.737603i | \(0.264042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.64015 | −0.268282 | −0.134141 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134141 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.04623 | − | 0.206167i | −0.0366478 | − | 0.00722173i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0462i | 0.386459i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.56165 | −0.0894021 | −0.0447011 | − | 0.999000i | \(-0.514234\pi\) | ||||
−0.0447011 | + | 0.999000i | \(0.514234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.784248i | 0.0273372i | 0.999907 | + | 0.0136686i | \(0.00435098\pi\) | ||||
−0.999907 | + | 0.0136686i | \(0.995649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.28904i | 0.253465i | 0.991937 | + | 0.126732i | \(0.0404489\pi\) | ||||
−0.991937 | + | 0.126732i | \(0.959551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0708 | 0.384505 | 0.192253 | − | 0.981345i | \(-0.438421\pi\) | ||||
0.192253 | + | 0.981345i | \(0.438421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.896916i | 0.0310763i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.8882 | + | 5.69264i | 0.999717 | + | 0.197002i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.55976 | 0.191944 | 0.0959721 | − | 0.995384i | \(-0.469404\pi\) | ||||
0.0959721 | + | 0.995384i | \(0.469404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0722 | 1.14042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.41400 | − | 37.6235i | 0.255049 | − | 1.29429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6079i | 0.364491i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.3757 | −0.767029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.0804i | − | 0.550582i | −0.961361 | − | 0.275291i | \(-0.911226\pi\) | ||
0.961361 | − | 0.275291i | \(-0.0887742\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.58767i | − | 0.0542336i | −0.999632 | − | 0.0271168i | \(-0.991367\pi\) | ||
0.999632 | − | 0.0271168i | \(-0.00863261\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.94171 | 0.168609 | 0.0843044 | − | 0.996440i | \(-0.473133\pi\) | ||||
0.0843044 | + | 0.996440i | \(0.473133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6647i | 1.28212i | 0.767490 | + | 0.641061i | \(0.221506\pi\) | ||||
−0.767490 | + | 0.641061i | \(0.778494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.6435 | − | 6.03853i | −1.04191 | − | 0.205316i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.55206 | 0.120495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.8130 | 1.07794 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.32924 | − | 6.16160i | −0.315386 | − | 0.208300i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.66473i | − | 0.123749i | −0.998084 | − | 0.0618746i | \(-0.980292\pi\) | ||
0.998084 | − | 0.0618746i | \(-0.0197079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4373 | 1.46344 | 0.731720 | − | 0.681605i | \(-0.238718\pi\) | ||||
0.731720 | + | 0.681605i | \(0.238718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.3853i | − | 1.59464i | −0.603556 | − | 0.797321i | \(-0.706250\pi\) | ||
0.603556 | − | 0.797321i | \(-0.293750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3169i | 0.715753i | 0.933769 | + | 0.357877i | \(0.116499\pi\) | ||||
−0.933769 | + | 0.357877i | \(0.883501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.2803 | 0.713718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.5510i | 1.25660i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.22449 | − | 16.3632i | 0.107783 | − | 0.546961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.2716 | 1.97682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.07707 | −0.202456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.10308 | − | 30.9711i | 0.202873 | − | 1.02951i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9325i | 0.628644i | 0.949316 | + | 0.314322i | \(0.101777\pi\) | ||||
−0.949316 | + | 0.314322i | \(0.898223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.6705 | −0.419794 | −0.209897 | − | 0.977724i | \(-0.567313\pi\) | ||||
−0.209897 | + | 0.977724i | \(0.567313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.9171i | − | 0.361304i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.91087i | 0.327286i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.8690 | 0.754379 | 0.377190 | − | 0.926136i | \(-0.376891\pi\) | ||||
0.377190 | + | 0.926136i | \(0.376891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 30.3265i | − | 0.998210i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3815 | − | 27.7572i | 0.374221 | − | 0.912651i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.4190 | 1.65419 | 0.827097 | − | 0.562060i | \(-0.189991\pi\) | ||||
0.827097 | + | 0.562060i | \(0.189991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.38776 | −0.209350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.23219 | − | 0.242812i | −0.0402968 | − | 0.00794079i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47.9344i | − | 1.56595i | −0.622054 | − | 0.782974i | \(-0.713702\pi\) | ||
0.622054 | − | 0.782974i | \(-0.286298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.9667 | −1.95486 | −0.977429 | − | 0.211264i | \(-0.932242\pi\) | ||||
−0.977429 | + | 0.211264i | \(0.932242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.8247i | − | 0.938660i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 27.5231i | − | 0.894381i | −0.894439 | − | 0.447191i | \(-0.852425\pi\) | ||
0.894439 | − | 0.447191i | \(-0.147575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.4769 | 0.664708 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.840061i | 0.0272123i | 0.999907 | + | 0.0136061i | \(0.00433110\pi\) | ||||
−0.999907 | + | 0.0136061i | \(0.995669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.64015 | − | 18.4725i | 0.117793 | − | 0.597757i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.45856 | −0.111683 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5972 | 0.825718 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.9205 | − | 9.64015i | −1.57481 | − | 0.310327i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.8988i | − | 1.02580i | −0.858449 | − | 0.512898i | \(-0.828572\pi\) | ||
0.858449 | − | 0.512898i | \(-0.171428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.4157 | 0.911902 | 0.455951 | − | 0.890005i | \(-0.349299\pi\) | ||||
0.455951 | + | 0.890005i | \(0.349299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4157i | 0.654496i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 9.55102i | − | 0.305564i | −0.988260 | − | 0.152782i | \(-0.951177\pi\) | ||
0.988260 | − | 0.152782i | \(-0.0488233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.95377 | −0.286164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.0443400i | 0.00141423i | 1.00000 | 0.000707113i | \(0.000225081\pi\) | |||||
−1.00000 | 0.000707113i | \(0.999775\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.8376 | + | 11.3973i | 1.84286 | + | 0.363149i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.44898 | −0.205066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9913 | 0.444447 | 0.222224 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222224 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.70138 | + | 49.2311i | −0.307554 | + | 1.56073i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 19.0419i | − | 0.603062i | −0.953456 | − | 0.301531i | \(-0.902502\pi\) | ||
0.953456 | − | 0.301531i | \(-0.0974976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5040.2.t.y.1009.4 | 6 | ||
3.2 | odd | 2 | 560.2.g.f.449.5 | 6 | |||
4.3 | odd | 2 | 2520.2.t.g.1009.4 | 6 | |||
5.4 | even | 2 | inner | 5040.2.t.y.1009.3 | 6 | ||
12.11 | even | 2 | 280.2.g.b.169.2 | ✓ | 6 | ||
15.2 | even | 4 | 2800.2.a.bq.1.3 | 3 | |||
15.8 | even | 4 | 2800.2.a.br.1.1 | 3 | |||
15.14 | odd | 2 | 560.2.g.f.449.2 | 6 | |||
20.19 | odd | 2 | 2520.2.t.g.1009.3 | 6 | |||
24.5 | odd | 2 | 2240.2.g.m.449.2 | 6 | |||
24.11 | even | 2 | 2240.2.g.l.449.5 | 6 | |||
60.23 | odd | 4 | 1400.2.a.s.1.3 | 3 | |||
60.47 | odd | 4 | 1400.2.a.t.1.1 | 3 | |||
60.59 | even | 2 | 280.2.g.b.169.5 | yes | 6 | ||
84.83 | odd | 2 | 1960.2.g.c.1569.5 | 6 | |||
120.29 | odd | 2 | 2240.2.g.m.449.5 | 6 | |||
120.59 | even | 2 | 2240.2.g.l.449.2 | 6 | |||
420.83 | even | 4 | 9800.2.a.cg.1.1 | 3 | |||
420.167 | even | 4 | 9800.2.a.cd.1.3 | 3 | |||
420.419 | odd | 2 | 1960.2.g.c.1569.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.2 | ✓ | 6 | 12.11 | even | 2 | ||
280.2.g.b.169.5 | yes | 6 | 60.59 | even | 2 | ||
560.2.g.f.449.2 | 6 | 15.14 | odd | 2 | |||
560.2.g.f.449.5 | 6 | 3.2 | odd | 2 | |||
1400.2.a.s.1.3 | 3 | 60.23 | odd | 4 | |||
1400.2.a.t.1.1 | 3 | 60.47 | odd | 4 | |||
1960.2.g.c.1569.2 | 6 | 420.419 | odd | 2 | |||
1960.2.g.c.1569.5 | 6 | 84.83 | odd | 2 | |||
2240.2.g.l.449.2 | 6 | 120.59 | even | 2 | |||
2240.2.g.l.449.5 | 6 | 24.11 | even | 2 | |||
2240.2.g.m.449.2 | 6 | 24.5 | odd | 2 | |||
2240.2.g.m.449.5 | 6 | 120.29 | odd | 2 | |||
2520.2.t.g.1009.3 | 6 | 20.19 | odd | 2 | |||
2520.2.t.g.1009.4 | 6 | 4.3 | odd | 2 | |||
2800.2.a.bq.1.3 | 3 | 15.2 | even | 4 | |||
2800.2.a.br.1.1 | 3 | 15.8 | even | 4 | |||
5040.2.t.y.1009.3 | 6 | 5.4 | even | 2 | inner | ||
5040.2.t.y.1009.4 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cd.1.3 | 3 | 420.167 | even | 4 | |||
9800.2.a.cg.1.1 | 3 | 420.83 | even | 4 |