Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(449,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("560.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.g (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: | \(4.47162251319\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(0.432320 + 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.449 |
Dual form | 560.2.g.f.449.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.76156i | 1.01704i | 0.861052 | + | 0.508518i | \(0.169806\pi\) | ||||
−0.861052 | + | 0.508518i | \(0.830194\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.432320 | − | 2.19388i | 0.193340 | − | 0.981132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.103084 | −0.0343612 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.626198 | 0.188806 | 0.0944029 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944029 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.49084i | − | 1.52288i | −0.648233 | − | 0.761442i | \(-0.724492\pi\) | ||
0.648233 | − | 0.761442i | \(-0.275508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.86464 | + | 0.761557i | 0.997846 | + | 0.196633i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.896916i | 0.217534i | 0.994067 | + | 0.108767i | \(0.0346903\pi\) | ||||
−0.994067 | + | 0.108767i | \(0.965310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38776 | 1.46545 | 0.732726 | − | 0.680524i | \(-0.238248\pi\) | ||||
0.732726 | + | 0.680524i | \(0.238248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76156 | 0.384403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.72928i | − | 0.777609i | −0.921320 | − | 0.388805i | \(-0.872888\pi\) | ||
0.921320 | − | 0.388805i | \(-0.127112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | − | 1.89692i | −0.925240 | − | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10308i | 0.982089i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.87859 | 1.46302 | 0.731509 | − | 0.681832i | \(-0.238816\pi\) | ||||
0.731509 | + | 0.681832i | \(0.238816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52311 | −1.35119 | −0.675596 | − | 0.737272i | \(-0.736113\pi\) | ||||
−0.675596 | + | 0.737272i | \(0.736113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.10308i | 0.192022i | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 9.67243 | 1.54883 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.72928 | 1.20711 | 0.603556 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603556 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.72928i | 0.263713i | 0.991269 | + | 0.131856i | \(0.0420938\pi\) | ||||
−0.991269 | + | 0.131856i | \(0.957906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0445652 | + | 0.226153i | −0.00664339 | + | 0.0337129i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.87859i | − | 0.857481i | −0.903428 | − | 0.428741i | \(-0.858957\pi\) | ||
0.903428 | − | 0.428741i | \(-0.141043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.57997 | −0.221240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.77551i | 0.930688i | 0.885130 | + | 0.465344i | \(0.154069\pi\) | ||||
−0.885130 | + | 0.465344i | \(0.845931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.270718 | − | 1.37380i | 0.0365036 | − | 0.185243i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2524i | 1.49042i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.593923 | −0.0773221 | −0.0386611 | − | 0.999252i | \(-0.512309\pi\) | ||||
−0.0386611 | + | 0.999252i | \(0.512309\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.13536 | 0.913589 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.103084i | 0.0129873i | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 6.56934 | 0.790856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.52311 | −0.655473 | −0.327737 | − | 0.944769i | \(-0.606286\pi\) | ||||
−0.327737 | + | 0.944769i | \(0.606286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.72928i | 0.436479i | 0.975895 | + | 0.218240i | \(0.0700315\pi\) | ||||
−0.975895 | + | 0.218240i | \(0.929969\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.34153 | − | 8.14931i | 0.385846 | − | 0.941002i | ||||
\(76\) | 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 | ||||||||
\(81\) | −9.29862 | −1.03318 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.4340i | − | 1.91363i | −0.290700 | − | 0.956814i | \(-0.593888\pi\) | ||
0.290700 | − | 0.956814i | \(-0.406112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.96772 | + | 0.387755i | 0.213430 | + | 0.0420580i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.8786i | 1.48794i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.2986 | −1.51565 | −0.757826 | − | 0.652457i | \(-0.773738\pi\) | ||||
−0.757826 | + | 0.652457i | \(0.773738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.49084 | −0.575596 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 13.2524i | − | 1.37421i | ||||||
\(94\) | 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 | ||||||||
\(99\) | −0.0645508 | −0.00648760 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.64015 | 0.959231 | 0.479615 | − | 0.877479i | \(-0.340776\pi\) | ||||
0.479615 | + | 0.877479i | \(0.340776\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.626198i | − | 0.0617011i | −0.999524 | − | 0.0308506i | \(-0.990178\pi\) | ||
0.999524 | − | 0.0308506i | \(-0.00982160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.761557 | − | 3.86464i | 0.0743204 | − | 0.377150i | ||||
\(106\) | 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 | ||||||||
\(111\) | −10.5693 | −1.00320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.04623i | 0.0984209i | 0.998788 | + | 0.0492105i | \(0.0156705\pi\) | ||||
−0.998788 | + | 0.0492105i | \(0.984329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.18159 | − | 1.61224i | −0.762937 | − | 0.150343i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.566016i | 0.0523282i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.896916 | 0.0822202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6079 | −0.964352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.6156i | 1.22767i | ||||||||
\(124\) | 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 | ||||||||
\(129\) | −3.04623 | −0.268205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.91087 | 0.865917 | 0.432958 | − | 0.901414i | \(-0.357470\pi\) | ||||
0.432958 | + | 0.901414i | \(0.357470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.38776i | − | 0.553889i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.1955 | + | 2.20617i | 0.963559 | + | 0.189877i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.45856i | 0.295485i | 0.989026 | + | 0.147743i | \(0.0472007\pi\) | ||||
−0.989026 | + | 0.147743i | \(0.952799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4157 | −1.73163 | −0.865817 | − | 0.500361i | \(-0.833201\pi\) | ||||
−0.865817 | + | 0.500361i | \(0.833201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.3555 | 0.872089 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.43835i | − | 0.287530i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.40608 | − | 17.2847i | 0.282859 | − | 1.43541i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.76156i | − | 0.145291i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0462 | 1.39648 | 0.698241 | − | 0.715863i | \(-0.253967\pi\) | ||||
0.698241 | + | 0.715863i | \(0.253967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89692 | −0.235748 | −0.117874 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117874 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.0924575i | − | 0.00747474i | ||||||
\(154\) | 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 | ||||||||
\(159\) | −11.9354 | −0.946543 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 2.42003 | + | 0.476886i | 0.188399 | + | 0.0371255i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1676i | 1.01894i | 0.860488 | + | 0.509471i | \(0.170159\pi\) | ||||
−0.860488 | + | 0.509471i | \(0.829841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.1493 | −1.31918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.658473 | −0.0503547 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 13.9677i | − | 1.06195i | −0.847389 | − | 0.530973i | \(-0.821826\pi\) | ||
0.847389 | − | 0.530973i | \(-0.178174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.89692 | + | 4.62620i | −0.143393 | + | 0.349708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.04623i | − | 0.0786394i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.45856 | 0.557479 | 0.278740 | − | 0.960367i | \(-0.410083\pi\) | ||||
0.278740 | + | 0.960367i | \(0.410083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1170 | −1.04931 | −0.524656 | − | 0.851315i | \(-0.675806\pi\) | ||||
−0.524656 | + | 0.851315i | \(0.675806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5693i | 0.929153i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.1633 | + | 2.59392i | 0.967783 | + | 0.190709i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.561647i | 0.0410717i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.10308 | 0.371195 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.42003 | 0.609252 | 0.304626 | − | 0.952472i | \(-0.401469\pi\) | ||||
0.304626 | + | 0.952472i | \(0.401469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.2986i | 1.60509i | 0.596591 | + | 0.802545i | \(0.296521\pi\) | ||||
−0.596591 | + | 0.802545i | \(0.703479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.18159 | − | 21.2201i | 0.299450 | − | 1.51960i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.3632i | 1.87830i | 0.343509 | + | 0.939149i | \(0.388384\pi\) | ||||
−0.343509 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4402 | 1.59075 | 0.795373 | − | 0.606120i | \(-0.207275\pi\) | ||||
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2062 | −0.719888 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.87859i | − | 0.552969i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.34153 | − | 16.9571i | 0.233382 | − | 1.18434i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.384428i | 0.0267196i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − | 9.72928i | − | 0.666639i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.79383 | + | 0.747604i | 0.258737 | + | 0.0509862i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.52311i | 0.510702i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.56934 | −0.443915 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0.476886 | + | 0.195541i | 0.0317924 | + | 0.0130361i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.77988i | 0.184507i | 0.995736 | + | 0.0922535i | \(0.0294070\pi\) | ||||
−0.995736 | + | 0.0922535i | \(0.970593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6585 | −1.23299 | −0.616493 | − | 0.787360i | \(-0.711447\pi\) | ||||
−0.616493 | + | 0.787360i | \(0.711447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.10308 | 0.0725776 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0462i | 0.723663i | 0.932244 | + | 0.361831i | \(0.117848\pi\) | ||||
−0.932244 | + | 0.361831i | \(0.882152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8969 | − | 2.54144i | −0.841302 | − | 0.165785i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.99230i | − | 0.649070i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.1493 | −1.30335 | −0.651675 | − | 0.758498i | \(-0.725934\pi\) | ||||
−0.651675 | + | 0.758498i | \(0.725934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.72928 | 0.240224 | 0.120112 | − | 0.992760i | \(-0.461675\pi\) | ||||
0.120112 | + | 0.992760i | \(0.461675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.07081i | − | 0.0686924i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.432320 | + | 2.19388i | −0.0276199 | + | 0.140162i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 35.0741i | − | 2.23171i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.7110 | 1.94623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4985 | 1.35698 | 0.678488 | − | 0.734612i | \(-0.262636\pi\) | ||||
0.678488 | + | 0.734612i | \(0.262636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.33527i | − | 0.146817i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.683053 | + | 3.46626i | −0.0427744 | + | 0.217066i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.27072i | 0.266400i | 0.991089 | + | 0.133200i | \(0.0425253\pi\) | ||||
−0.991089 | + | 0.133200i | \(0.957475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.812155 | −0.0502711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.4586i | − | 0.706565i | −0.935517 | − | 0.353283i | \(-0.885065\pi\) | ||
0.935517 | − | 0.353283i | \(-0.114935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.8646 | + | 2.92919i | 0.913128 | + | 0.179939i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 25.1878i | − | 1.54147i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.07081 | 0.431115 | 0.215557 | − | 0.976491i | \(-0.430843\pi\) | ||||
0.215557 | + | 0.976491i | \(0.430843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0096 | −1.03326 | −0.516629 | − | 0.856209i | \(-0.672813\pi\) | ||||
−0.516629 | + | 0.856209i | \(0.672813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.67243i | − | 0.585402i | ||||||
\(274\) | 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 | ||||||||
\(279\) | 0.775511 | 0.0464286 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.59829 | −0.274311 | −0.137156 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137156 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.5833i | − | 0.807443i | −0.914882 | − | 0.403722i | \(-0.867716\pi\) | ||
0.914882 | − | 0.403722i | \(-0.132284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.6864 | + | 4.86464i | 1.46229 | + | 0.288156i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.72928i | − | 0.456245i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1955 | 0.952679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8786 | 1.04806 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.8261i | − | 0.690889i | −0.938439 | − | 0.345444i | \(-0.887728\pi\) | ||
0.938439 | − | 0.345444i | \(-0.112272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.256765 | + | 1.30299i | −0.0149494 | + | 0.0758632i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.19554i | 0.185424i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.4769 | −1.18421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.72928 | 0.0996741 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.9817i | 0.975572i | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 1.10308 | 0.0627522 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5048 | 1.27613 | 0.638065 | − | 0.769983i | \(-0.279735\pi\) | ||||
0.638065 | + | 0.769983i | \(0.279735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4846i | 0.705670i | 0.935686 | + | 0.352835i | \(0.114782\pi\) | ||||
−0.935686 | + | 0.352835i | \(0.885218\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.226153 | + | 0.0445652i | 0.0127423 | + | 0.00251096i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.5231i | 1.43352i | 0.697319 | + | 0.716760i | \(0.254376\pi\) | ||||
−0.697319 | + | 0.716760i | \(0.745624\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | − | 33.3372i | − | 1.84355i | ||||||
\(328\) | 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 | ||||||||
\(333\) | − | 0.618502i | − | 0.0338937i | ||||||
\(334\) | 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 | ||||||||
\(339\) | −1.84299 | −0.100098 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.71096 | −0.255113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.84006 | − | 14.4123i | 0.152904 | − | 0.775934i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.9450i | 1.55385i | 0.629593 | + | 0.776925i | \(0.283222\pi\) | ||||
−0.629593 | + | 0.776925i | \(0.716778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.1449 | −1.72068 | −0.860340 | − | 0.509721i | \(-0.829749\pi\) | ||||
−0.860340 | + | 0.509721i | \(0.829749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.0202 | 1.49561 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.17722i | − | 0.435229i | −0.976035 | − | 0.217615i | \(-0.930172\pi\) | ||
0.976035 | − | 0.217615i | \(-0.0698276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.38776 | + | 12.1170i | −0.126729 | + | 0.643106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.57997i | 0.0836208i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.5048 | 0.976646 | 0.488323 | − | 0.872663i | \(-0.337609\pi\) | ||||
0.488323 | + | 0.872663i | \(0.337609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.8034 | 1.14755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 18.6864i | − | 0.980781i | ||||||
\(364\) | 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 | ||||||||
\(369\) | −0.796763 | −0.0414778 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | −16.4340 | − | 10.8540i | −0.848647 | − | 0.560499i | ||||
\(376\) | 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 | ||||||||
\(381\) | −37.4865 | −1.92049 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.72928i | − | 0.0883622i | −0.999024 | − | 0.0441811i | \(-0.985932\pi\) | ||
0.999024 | − | 0.0441811i | \(-0.0140679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37380 | − | 0.270718i | −0.0700154 | − | 0.0137971i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.178261i | − | 0.00906150i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.7187 | 1.86171 | 0.930855 | − | 0.365389i | \(-0.119064\pi\) | ||||
0.930855 | + | 0.365389i | \(0.119064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.34485 | 0.169157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4586i | 0.880668i | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 11.2524 | 0.563324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.64452 | −0.0821234 | −0.0410617 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410617 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.3082i | 2.05771i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.01999 | + | 20.4000i | −0.199755 | + | 1.01369i | ||||
\(406\) | 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 | ||||||||
\(411\) | −6.09246 | −0.300519 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.593923i | 0.0292250i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.2480 | − | 7.53707i | −1.87752 | − | 0.369980i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 35.9634i | − | 1.76113i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.9205 | 1.11974 | 0.559869 | − | 0.828581i | \(-0.310852\pi\) | ||||
0.559869 | + | 0.828581i | \(0.310852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9527 | −1.02117 | −0.510587 | − | 0.859826i | \(-0.670572\pi\) | ||||
−0.510587 | + | 0.859826i | \(0.670572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.605987i | 0.0294641i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.70138 | − | 4.14931i | 0.0825288 | − | 0.201271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.13536i | − | 0.345304i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.05685 | 0.292428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.1589 | −1.59721 | −0.798604 | − | 0.601857i | \(-0.794428\pi\) | ||||
−0.798604 | + | 0.601857i | \(0.794428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5414i | 0.891045i | 0.895271 | + | 0.445522i | \(0.146982\pi\) | ||||
−0.895271 | + | 0.445522i | \(0.853018\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.4479 | + | 6.00000i | 1.45987 | + | 0.287678i | ||||
\(436\) | 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 | ||||||||
\(441\) | 0.103084 | 0.00490875 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.5510i | 0.833874i | 0.908935 | + | 0.416937i | \(0.136896\pi\) | ||||
−0.908935 | + | 0.416937i | \(0.863104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.18159 | + | 31.3694i | −0.293035 | + | 1.48705i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.0279i | 1.42027i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1955 | 0.622736 | 0.311368 | − | 0.950289i | \(-0.399213\pi\) | ||||
0.311368 | + | 0.950289i | \(0.399213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84006 | 0.227910 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5.10308i | − | 0.239764i | ||||||
\(454\) | 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 | ||||||||
\(459\) | −4.57704 | −0.213638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8280 | −0.876907 | −0.438454 | − | 0.898754i | \(-0.644474\pi\) | ||||
−0.438454 | + | 0.898754i | \(0.644474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.0925i | − | 0.654932i | −0.944863 | − | 0.327466i | \(-0.893805\pi\) | ||
0.944863 | − | 0.327466i | \(-0.106195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −29.0741 | − | 5.72928i | −1.34828 | − | 0.265689i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2663i | 0.567619i | 0.958881 | + | 0.283809i | \(0.0915983\pi\) | ||||
−0.958881 | + | 0.283809i | \(0.908402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.79383 | 0.267534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8217 | −0.821182 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.08287i | 0.0497905i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.5510 | − | 12.1170i | −1.35589 | − | 0.555968i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.698445i | − | 0.0319796i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.1570 | −0.646850 | −0.323425 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323425 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.9450 | 1.50216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 6.56934i | − | 0.298915i | ||||||
\(484\) | 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 | ||||||||
\(489\) | −0.840061 | −0.0379889 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.9065 | −1.80096 | −0.900478 | − | 0.434902i | \(-0.856783\pi\) | ||||
−0.900478 | + | 0.434902i | \(0.856783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.06644i | 0.318256i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0279066 | + | 0.141617i | −0.00125431 | + | 0.00636519i | ||||
\(496\) | 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 | ||||||||
\(501\) | −23.1955 | −1.03630 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.40171i | 0.0624991i | 0.999512 | + | 0.0312495i | \(0.00994866\pi\) | ||||
−0.999512 | + | 0.0312495i | \(0.990051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.16763 | − | 21.1493i | 0.185457 | − | 0.941132i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 30.2095i | − | 1.34165i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6585 | −0.827022 | −0.413511 | − | 0.910499i | \(-0.635698\pi\) | ||||
−0.413511 | + | 0.910499i | \(0.635698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72928 | 0.164974 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.5972i | 1.43920i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.37380 | − | 0.270718i | −0.0605369 | − | 0.0119293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.68116i | − | 0.161897i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.6049 | 1.08004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.02791 | −0.176466 | −0.0882329 | − | 0.996100i | \(-0.528122\pi\) | ||||
−0.0882329 | + | 0.996100i | \(0.528122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.4436i | 1.68102i | 0.541796 | + | 0.840510i | \(0.317744\pi\) | ||||
−0.541796 | + | 0.840510i | \(0.682256\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.14931 | − | 3.34153i | −0.355665 | − | 0.145836i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.74760i | − | 0.293930i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.09246 | 0.395324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0612237 | 0.00265688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 42.4402i | − | 1.83829i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1387i | 0.566976i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 24.8680i | − | 1.06719i | ||||||
\(544\) | 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 | ||||||||
\(549\) | −0.735539 | −0.0313921 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.3265 | 2.14398 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.67243i | 0.241216i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.56934 | + | 23.1878i | −0.193958 | + | 0.984269i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93545i | 0.0820076i | 0.999159 | + | 0.0410038i | \(0.0130556\pi\) | ||||
−0.999159 | + | 0.0410038i | \(0.986944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.49521 | 0.401604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.989374 | −0.0417714 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 29.8463i | − | 1.25787i | −0.777457 | − | 0.628936i | \(-0.783491\pi\) | ||
0.777457 | − | 0.628936i | \(-0.216509\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.29530 | + | 0.452306i | 0.0965639 | + | 0.0190287i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.29862i | 0.390506i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.3449 | −0.643290 | −0.321645 | − | 0.946860i | \(-0.604236\pi\) | ||||
−0.321645 | + | 0.946860i | \(0.604236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.8217 | −1.49909 | −0.749547 | − | 0.661952i | \(-0.769728\pi\) | ||||
−0.749547 | + | 0.661952i | \(0.769728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.8324i | 0.619631i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −39.2803 | −1.63243 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.4340 | −0.723284 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.24281i | 0.175719i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.24177 | + | 0.244700i | 0.0513409 | + | 0.0101171i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.5756i | − | 0.807972i | −0.914765 | − | 0.403986i | \(-0.867625\pi\) | ||
0.914765 | − | 0.403986i | \(-0.132375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0558 | −1.98011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.4402 | −1.91030 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00770i | − | 0.328837i | −0.986391 | − | 0.164418i | \(-0.947425\pi\) | ||
0.986391 | − | 0.164418i | \(-0.0525747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.387755 | − | 1.96772i | 0.0158964 | − | 0.0806688i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.5298i | 1.61785i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.3005 | −1.19719 | −0.598593 | − | 0.801053i | \(-0.704273\pi\) | ||||
−0.598593 | + | 0.801053i | \(0.704273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3449 | 0.870675 | 0.435337 | − | 0.900267i | \(-0.356629\pi\) | ||||
0.435337 | + | 0.900267i | \(0.356629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.597250i | − | 0.0243219i | ||||||
\(604\) | 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 | ||||||||
\(609\) | 13.8786 | 0.562389 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 29.8709 | + | 5.88629i | 1.20451 | + | 0.237358i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 37.9267i | − | 1.52687i | −0.645884 | − | 0.763436i | \(-0.723511\pi\) | ||
0.645884 | − | 0.763436i | \(-0.276489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.9109 | 1.68454 | 0.842270 | − | 0.539056i | \(-0.181219\pi\) | ||||
0.842270 | + | 0.539056i | \(0.181219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.0308 | 0.763681 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.2986i | 0.572862i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | + | 17.5510i | 0.712137 | + | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.04623i | 0.281399i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 26.7678i | 1.06393i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.6864 | + | 9.19991i | 1.85269 | + | 0.365087i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.49084i | 0.217555i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.569343 | 0.0225229 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.07707 | −0.0820392 | −0.0410196 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410196 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.2480i | − | 1.07456i | −0.843405 | − | 0.537279i | \(-0.819452\pi\) | ||
0.843405 | − | 0.537279i | \(-0.180548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.31695 | + | 6.68305i | −0.0518547 | + | 0.263145i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.3632i | − | 0.486047i | −0.970020 | − | 0.243023i | \(-0.921861\pi\) | ||
0.970020 | − | 0.243023i | \(-0.0781391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.371913 | −0.0145989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2524 | −0.519402 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 37.3449i | − | 1.46142i | −0.682690 | − | 0.730709i | \(-0.739190\pi\) | ||
0.682690 | − | 0.730709i | \(-0.260810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28467 | − | 21.7432i | 0.167416 | − | 0.849578i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.384428i | − | 0.0149980i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1772 | −0.552266 | −0.276133 | − | 0.961119i | \(-0.589053\pi\) | ||||
−0.276133 | + | 0.961119i | \(0.589053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76925 | −0.0688160 | −0.0344080 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344080 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.67536i | 0.336923i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.0140 | − | 2.76156i | −0.543438 | − | 0.107089i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29.3815i | − | 1.13766i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1493 | 0.469720 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 9.68012 | − | 23.6079i | 0.372588 | − | 0.908668i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.37713i | − | 0.360392i | −0.983631 | − | 0.180196i | \(-0.942327\pi\) | ||
0.983631 | − | 0.180196i | \(-0.0576733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1493 | −0.389495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.89692 | −0.187650 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.49521i | − | 0.210268i | −0.994458 | − | 0.105134i | \(-0.966473\pi\) | ||
0.994458 | − | 0.105134i | \(-0.0335272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.58767 | + | 1.49521i | 0.289910 | + | 0.0571290i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 32.8680i | − | 1.25399i | ||||||
\(688\) | 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 | ||||||||
\(693\) | 0.0645508i | 0.00245208i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.82611 | + | 44.7895i | −0.334793 | + | 1.69896i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.93252i | 0.262588i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.4586 | −0.735990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2234 | 1.33037 | 0.665186 | − | 0.746678i | \(-0.268352\pi\) | ||||
0.665186 | + | 0.746678i | \(0.268352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.3265i | 1.44551i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.47689 | − | 22.7187i | 0.168609 | − | 0.855634i | ||||
\(706\) | 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 | ||||||||
\(711\) | 0.584735 | 0.0219293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0558i | 1.05070i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.54333 | − | 1.48647i | −0.282104 | − | 0.0555908i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 35.4942i | − | 1.32555i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.60599 | −0.320949 | −0.160475 | − | 0.987040i | \(-0.551302\pi\) | ||||
−0.160475 | + | 0.987040i | \(0.551302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.626198 | −0.0233208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.56934i | 0.244316i | ||||||||
\(724\) | 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 | ||||||||
\(729\) | −26.0096 | −0.963318 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | −3.86464 | − | 0.761557i | −0.142549 | − | 0.0280905i | ||||
\(736\) | 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 | ||||||||
\(741\) | 61.7851 | 2.26973 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7755i | 0.395315i | 0.980271 | + | 0.197658i | \(0.0633334\pi\) | ||||
−0.980271 | + | 0.197658i | \(0.936667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.36943 | − | 37.3973i | 0.269995 | − | 1.37013i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.79716i | 0.0657546i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 37.8709i | 1.38009i | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 4.11371 | 0.149318 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3169 | 1.13524 | 0.567619 | − | 0.823291i | \(-0.307865\pi\) | ||||
0.567619 | + | 0.823291i | \(0.307865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.9248i | 0.685125i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.202840 | − | 0.0399712i | −0.00733371 | − | 0.00144516i | ||||
\(766\) | 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 | ||||||||
\(771\) | −7.52311 | −0.270938 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36.7711i | − | 1.32257i | −0.750136 | − | 0.661283i | \(-0.770012\pi\) | ||
0.750136 | − | 0.661283i | \(-0.229988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.8034 | + | 14.2707i | 1.25018 | + | 0.512619i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5693i | 0.379173i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 49.3728 | 1.76896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.45856 | −0.123757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.2051i | 1.43681i | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 20.1849 | 0.718602 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.04623 | 0.0371996 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 39.1791i | − | 1.39129i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.15994 | + | 26.1849i | −0.183004 | + | 0.928683i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.82611i | 0.277215i | 0.990347 | + | 0.138607i | \(0.0442626\pi\) | ||||
−0.990347 | + | 0.138607i | \(0.955737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.27261 | 0.186531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47396 | 0.0520796 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.33527i | 0.0824099i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61224 | + | 8.18159i | −0.0568242 | + | 0.288363i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.4556i | 0.438459i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.4113 | −1.35047 | −0.675235 | − | 0.737603i | \(-0.735958\pi\) | ||||
−0.675235 | + | 0.737603i | \(0.735958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.64015 | −0.268282 | −0.134141 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134141 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 29.9634i | − | 1.05086i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04623 | + | 0.206167i | 0.0366478 | + | 0.00722173i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0462i | 0.386459i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.566016 | 0.0197782 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.56165 | 0.0894021 | 0.0447011 | − | 0.999000i | \(-0.485766\pi\) | ||||
0.0447011 | + | 0.999000i | \(0.485766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.784248i | 0.0273372i | 0.999907 | + | 0.0136686i | \(0.00435098\pi\) | ||||
−0.999907 | + | 0.0136686i | \(0.995649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.09246 | − | 5.10308i | 0.0728500 | − | 0.177667i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.28904i | − | 0.253465i | −0.991937 | − | 0.126732i | \(-0.959551\pi\) | ||
0.991937 | − | 0.126732i | \(-0.0404489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0708 | 0.384505 | 0.192253 | − | 0.981345i | \(-0.438421\pi\) | ||||
0.192253 | + | 0.981345i | \(0.438421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.0741 | 1.14733 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.896916i | − | 0.0310763i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.8882 | + | 5.69264i | 0.999717 | + | 0.197002i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 38.3911i | − | 1.32699i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.55976 | −0.191944 | −0.0959721 | − | 0.995384i | \(-0.530596\pi\) | ||||
−0.0959721 | + | 0.995384i | \(0.530596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0722 | 1.14042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 8.10015i | − | 0.278984i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.41400 | + | 37.6235i | −0.255049 | + | 1.29429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6079i | 0.364491i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.9278 | 0.821198 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | −0.284672 | + | 1.44461i | −0.00973556 | + | 0.0494046i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.58767i | 0.0542336i | 0.999632 | + | 0.0271168i | \(0.00863261\pi\) | ||||
−0.999632 | + | 0.0271168i | \(0.991367\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.94171 | 0.168609 | 0.0843044 | − | 0.996440i | \(-0.473133\pi\) | ||||
0.0843044 | + | 0.996440i | \(0.473133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6156 | 0.464017 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 37.6647i | − | 1.28212i | −0.767490 | − | 0.641061i | \(-0.778494\pi\) | ||
0.767490 | − | 0.641061i | \(-0.221506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.6435 | − | 6.03853i | −1.04191 | − | 0.205316i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5294i | 0.968908i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.55206 | −0.120495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.8130 | 1.07794 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.04623i | 0.0354095i | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 20.8324 | 0.702658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.4373 | −1.46344 | −0.731720 | − | 0.681605i | \(-0.761282\pi\) | ||||
−0.731720 | + | 0.681605i | \(0.761282\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.3853i | − | 1.59464i | −0.603556 | − | 0.797321i | \(-0.706250\pi\) | ||
0.603556 | − | 0.797321i | \(-0.293750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.29530 | − | 0.452306i | −0.0771556 | − | 0.0152041i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 21.3169i | − | 0.715753i | −0.933769 | − | 0.357877i | \(-0.883501\pi\) | ||
0.933769 | − | 0.357877i | \(-0.116499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.2803 | 0.713718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.82278 | −0.195071 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 37.5510i | − | 1.25660i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.22449 | − | 16.3632i | 0.107783 | − | 0.546961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 36.0712i | − | 1.20438i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −59.2716 | −1.97682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.07707 | −0.202456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.04623i | 0.101372i | ||||||||
\(904\) | 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 | ||||||||
\(909\) | −0.993743 | −0.0329604 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6705 | 0.419794 | 0.209897 | − | 0.977724i | \(-0.432687\pi\) | ||||
0.209897 | + | 0.977724i | \(0.432687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.9171i | − | 0.361304i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.5756 | + | 5.43398i | 0.911621 | + | 0.179642i | ||||
\(916\) | 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 | ||||||||
\(921\) | −36.9681 | −1.21814 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.3265i | 0.998210i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3815 | − | 27.7572i | 0.374221 | − | 0.912651i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0645508i | 0.00212013i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.4190 | −1.65419 | −0.827097 | − | 0.562060i | \(-0.810009\pi\) | ||||
−0.827097 | + | 0.562060i | \(0.810009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.38776 | −0.209350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.6435i | 1.29787i | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −21.9923 | −0.717692 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.9667 | 1.95486 | 0.977429 | − | 0.211264i | \(-0.0677580\pi\) | ||||
0.977429 | + | 0.211264i | \(0.0677580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.8247i | − | 0.938660i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.20617 | − | 11.1955i | 0.0717666 | − | 0.364191i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.5231i | 0.894381i | 0.894439 | + | 0.447191i | \(0.147575\pi\) | ||||
−0.894439 | + | 0.447191i | \(0.852425\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.4769 | 0.664708 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.9604 | −1.45794 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.840061i | − | 0.0272123i | −0.999907 | − | 0.0136061i | \(-0.995669\pi\) | ||
0.999907 | − | 0.0136061i | \(-0.00433110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.64015 | − | 18.4725i | 0.117793 | − | 0.597757i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.69075i | 0.280932i | ||||||||
\(958\) | 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 | ||||||||
\(969\) | −10.0925 | −0.324216 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.4157 | −0.911902 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4157i | 0.654496i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −44.7466 | − | 18.3478i | −1.43304 | − | 0.587599i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.55102i | 0.305564i | 0.988260 | + | 0.152782i | \(0.0488233\pi\) | ||||
−0.988260 | + | 0.152782i | \(0.951177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.95377 | −0.286164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.95084 | 0.0622856 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 0.0443400i | − | 0.00141423i | −1.00000 | 0.000707113i | \(-0.999775\pi\) | |||
1.00000 | 0.000707113i | \(-0.000225081\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.8376 | + | 11.3973i | 1.84286 | + | 0.363149i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 10.3555i | − | 0.329619i | ||||||
\(988\) | 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 | ||||||||
\(993\) | 4.72635i | 0.149986i | ||||||||
\(994\) | 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 | ||||||||
\(999\) | −30.6185 | −0.968727 |
(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 | 560.2.g.f.449.5 | 6 | ||
3.2 | odd | 2 | 5040.2.t.y.1009.4 | 6 | |||
4.3 | odd | 2 | 280.2.g.b.169.2 | ✓ | 6 | ||
5.2 | odd | 4 | 2800.2.a.bq.1.3 | 3 | |||
5.3 | odd | 4 | 2800.2.a.br.1.1 | 3 | |||
5.4 | even | 2 | inner | 560.2.g.f.449.2 | 6 | ||
8.3 | odd | 2 | 2240.2.g.l.449.5 | 6 | |||
8.5 | even | 2 | 2240.2.g.m.449.2 | 6 | |||
12.11 | even | 2 | 2520.2.t.g.1009.4 | 6 | |||
15.14 | odd | 2 | 5040.2.t.y.1009.3 | 6 | |||
20.3 | even | 4 | 1400.2.a.s.1.3 | 3 | |||
20.7 | even | 4 | 1400.2.a.t.1.1 | 3 | |||
20.19 | odd | 2 | 280.2.g.b.169.5 | yes | 6 | ||
28.27 | even | 2 | 1960.2.g.c.1569.5 | 6 | |||
40.19 | odd | 2 | 2240.2.g.l.449.2 | 6 | |||
40.29 | even | 2 | 2240.2.g.m.449.5 | 6 | |||
60.59 | even | 2 | 2520.2.t.g.1009.3 | 6 | |||
140.27 | odd | 4 | 9800.2.a.cd.1.3 | 3 | |||
140.83 | odd | 4 | 9800.2.a.cg.1.1 | 3 | |||
140.139 | even | 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 | 4.3 | odd | 2 | ||
280.2.g.b.169.5 | yes | 6 | 20.19 | odd | 2 | ||
560.2.g.f.449.2 | 6 | 5.4 | even | 2 | inner | ||
560.2.g.f.449.5 | 6 | 1.1 | even | 1 | trivial | ||
1400.2.a.s.1.3 | 3 | 20.3 | even | 4 | |||
1400.2.a.t.1.1 | 3 | 20.7 | even | 4 | |||
1960.2.g.c.1569.2 | 6 | 140.139 | even | 2 | |||
1960.2.g.c.1569.5 | 6 | 28.27 | even | 2 | |||
2240.2.g.l.449.2 | 6 | 40.19 | odd | 2 | |||
2240.2.g.l.449.5 | 6 | 8.3 | odd | 2 | |||
2240.2.g.m.449.2 | 6 | 8.5 | even | 2 | |||
2240.2.g.m.449.5 | 6 | 40.29 | even | 2 | |||
2520.2.t.g.1009.3 | 6 | 60.59 | even | 2 | |||
2520.2.t.g.1009.4 | 6 | 12.11 | even | 2 | |||
2800.2.a.bq.1.3 | 3 | 5.2 | odd | 4 | |||
2800.2.a.br.1.1 | 3 | 5.3 | odd | 4 | |||
5040.2.t.y.1009.3 | 6 | 15.14 | odd | 2 | |||
5040.2.t.y.1009.4 | 6 | 3.2 | odd | 2 | |||
9800.2.a.cd.1.3 | 3 | 140.27 | odd | 4 | |||
9800.2.a.cg.1.1 | 3 | 140.83 | odd | 4 |