Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(4049,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.b (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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 7x^{2} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(-2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.4049 |
Dual form | 4400.2.b.y.4049.4 |
$q$-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 \(\left(\mathbb{Z}/4400\mathbb{Z}\right)^\times\).
\(n\) | \(177\) | \(1201\) | \(2751\) | \(3301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.30278i | − 1.32951i | −0.747062 | − | 0.664754i | \(-0.768536\pi\) | ||||
0.747062 | − | 0.664754i | \(-0.231464\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.697224i | 0.263526i | 0.991281 | + | 0.131763i | \(0.0420638\pi\) | ||||
−0.991281 | + | 0.131763i | \(0.957936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.30278 | −0.767592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.90833i | − 1.67552i | −0.546042 | − | 0.837758i | \(-0.683866\pi\) | ||||
0.546042 | − | 0.837758i | \(-0.316134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.60555 | 0.350360 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.30278i | 1.52273i | 0.648321 | + | 0.761367i | \(0.275471\pi\) | ||||
−0.648321 | + | 0.761367i | \(0.724529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.60555i | − 0.308988i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.908327 | −0.168672 | −0.0843360 | − | 0.996437i | \(-0.526877\pi\) | ||||
−0.0843360 | + | 0.996437i | \(0.526877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2111 | −1.83397 | −0.916984 | − | 0.398924i | \(-0.869384\pi\) | ||||
−0.916984 | + | 0.398924i | \(0.869384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.30278i | − 0.400862i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.39445i | − 0.393645i | −0.980439 | − | 0.196822i | \(-0.936938\pi\) | ||||
0.980439 | − | 0.196822i | \(-0.0630623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.5139 | 1.84370 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.60555 | −0.875440 | −0.437720 | − | 0.899111i | \(-0.644214\pi\) | ||||
−0.437720 | + | 0.899111i | \(0.644214\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.21110i | − 1.09968i | −0.835269 | − | 0.549841i | \(-0.814688\pi\) | ||||
0.835269 | − | 0.549841i | \(-0.185312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.00000i | − 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.51388 | 0.930554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.9083 | −2.22761 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.30278i | − 0.178950i | −0.995989 | − | 0.0894750i | \(-0.971481\pi\) | ||||
0.995989 | − | 0.0894750i | \(-0.0285189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.30278i | 0.305010i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2111 | −1.85013 | −0.925064 | − | 0.379811i | \(-0.875989\pi\) | ||||
−0.925064 | + | 0.379811i | \(0.875989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.90833 | −1.01256 | −0.506279 | − | 0.862370i | \(-0.668979\pi\) | ||||
−0.506279 | + | 0.862370i | \(0.668979\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.60555i | − 0.202280i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.8167 | 2.02449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.60555 | 0.309222 | 0.154611 | − | 0.987975i | \(-0.450588\pi\) | ||||
0.154611 | + | 0.987975i | \(0.450588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.90833i | − 0.925600i | −0.886463 | − | 0.462800i | \(-0.846845\pi\) | ||||
0.886463 | − | 0.462800i | \(-0.153155\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.697224i | 0.0794561i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9083 | −1.22728 | −0.613641 | − | 0.789585i | \(-0.710296\pi\) | ||||
−0.613641 | + | 0.789585i | \(0.710296\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.51388i | 0.385698i | 0.981228 | + | 0.192849i | \(0.0617728\pi\) | ||||
−0.981228 | + | 0.192849i | \(0.938227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.09167i | 0.224251i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.69722 | −0.179905 | −0.0899527 | − | 0.995946i | \(-0.528672\pi\) | ||||
−0.0899527 | + | 0.995946i | \(0.528672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.48612 | −0.365445 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.5139i | 2.43828i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 15.3028i | − 1.55376i | −0.629648 | − | 0.776881i | \(-0.716801\pi\) | ||||
0.629648 | − | 0.776881i | \(-0.283199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.30278 | −0.231438 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.513878 | −0.0511328 | −0.0255664 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255664 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.90833i | − 0.286566i | −0.989682 | − | 0.143283i | \(-0.954234\pi\) | ||||
0.989682 | − | 0.143283i | \(-0.0457659\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.00000i | − 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5139 | −1.10283 | −0.551415 | − | 0.834231i | \(-0.685912\pi\) | ||||
−0.551415 | + | 0.834231i | \(0.685912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.51388 | −0.523354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 10.8167i | − 1.01755i | −0.860901 | − | 0.508773i | \(-0.830099\pi\) | ||||
0.860901 | − | 0.508773i | \(-0.169901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 11.5139i | − 1.06446i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.81665 | 0.441542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.9083i | 1.16390i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.11943i | 0.720483i | 0.932859 | + | 0.360241i | \(0.117306\pi\) | ||||
−0.932859 | + | 0.360241i | \(0.882694\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.6056 | −1.46204 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.90833 | 0.865695 | 0.432847 | − | 0.901467i | \(-0.357509\pi\) | ||||
0.432847 | + | 0.901467i | \(0.357509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.697224i | − 0.0604570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9083i | 1.10283i | 0.834230 | + | 0.551416i | \(0.185912\pi\) | ||||
−0.834230 | + | 0.551416i | \(0.814088\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.21110 | −0.526819 | −0.263409 | − | 0.964684i | \(-0.584847\pi\) | ||||
−0.263409 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.90833 | −0.581786 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.00000i | 0.418121i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 15.0000i | − 1.23718i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2111 | −1.40999 | −0.704994 | − | 0.709213i | \(-0.749050\pi\) | ||||
−0.704994 | + | 0.709213i | \(0.749050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.816654 | −0.0664583 | −0.0332292 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332292 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.9083i | 1.28611i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 19.2111i | − 1.53321i | −0.642117 | − | 0.766606i | \(-0.721944\pi\) | ||||
0.642117 | − | 0.766606i | \(-0.278056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.09167 | −0.401280 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.30278i | − 0.728650i | −0.931272 | − | 0.364325i | \(-0.881300\pi\) | ||||
0.931272 | − | 0.364325i | \(-0.118700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4222i | 1.03864i | 0.854579 | + | 0.519321i | \(0.173815\pi\) | ||||
−0.854579 | + | 0.519321i | \(0.826185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.30278 | 0.176098 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.81665i | − 0.366203i | −0.983094 | − | 0.183102i | \(-0.941386\pi\) | ||||
0.983094 | − | 0.183102i | \(-0.0586138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.7250i | 2.45976i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5139 | 0.935331 | 0.467666 | − | 0.883905i | \(-0.345095\pi\) | ||||
0.467666 | + | 0.883905i | \(0.345095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9083 | −1.47977 | −0.739887 | − | 0.672731i | \(-0.765121\pi\) | ||||
−0.739887 | + | 0.672731i | \(0.765121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.2111i | 1.34620i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.90833i | − 0.505187i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.11943 | 0.0814265 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3028 | −0.745483 | −0.372741 | − | 0.927935i | \(-0.621582\pi\) | ||||
−0.372741 | + | 0.927935i | \(0.621582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2111i | 0.950956i | 0.879728 | + | 0.475478i | \(0.157725\pi\) | ||||
−0.879728 | + | 0.475478i | \(0.842275\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.3028i | − 0.947784i | −0.880583 | − | 0.473892i | \(-0.842849\pi\) | ||||
0.880583 | − | 0.473892i | \(-0.157151\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.48612 | −0.459789 | −0.229894 | − | 0.973216i | \(-0.573838\pi\) | ||||
−0.229894 | + | 0.973216i | \(0.573838\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.21110 | −0.649701 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.633308i | − 0.0444495i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 16.8167i | − 1.16884i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2389 | 1.73751 | 0.868757 | − | 0.495238i | \(-0.164919\pi\) | ||||
0.868757 | + | 0.495238i | \(0.164919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.00000i | − 0.411113i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 7.11943i | − 0.483298i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.2111 | −1.23059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.5416 | 2.32352 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6333i | 1.51564i | 0.652465 | + | 0.757819i | \(0.273735\pi\) | ||||
−0.652465 | + | 0.757819i | \(0.726265\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.69722i | 0.112649i | 0.998413 | + | 0.0563244i | \(0.0179381\pi\) | ||||
−0.998413 | + | 0.0563244i | \(0.982062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7250 | 1.23738 | 0.618691 | − | 0.785635i | \(-0.287663\pi\) | ||||
0.618691 | + | 0.785635i | \(0.287663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.60555 | 0.105638 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9083i | 1.04219i | 0.853499 | + | 0.521095i | \(0.174476\pi\) | ||||
−0.853499 | + | 0.521095i | \(0.825524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.1194i | 1.63168i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1194 | 1.36610 | 0.683051 | − | 0.730371i | \(-0.260653\pi\) | ||||
0.683051 | + | 0.730371i | \(0.260653\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9361 | 1.41303 | 0.706514 | − | 0.707699i | \(-0.250267\pi\) | ||||
0.706514 | + | 0.707699i | \(0.250267\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6056i | 1.25770i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.00000i | − 0.318142i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.09167 | 0.512789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.90833 | −0.436050 | −0.218025 | − | 0.975943i | \(-0.569961\pi\) | ||||
−0.218025 | + | 0.975943i | \(0.569961\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.30278i | 0.459122i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66947 | 0.103736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.09167 | 0.129471 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.8167i | 1.40694i | 0.710727 | + | 0.703468i | \(0.248366\pi\) | ||||
−0.710727 | + | 0.703468i | \(0.751634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.90833i | 0.239186i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.72498 | −0.531971 | −0.265986 | − | 0.963977i | \(-0.585697\pi\) | ||||
−0.265986 | + | 0.963977i | \(0.585697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.211103 | 0.0128236 | 0.00641178 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641178 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.02776i | 0.485862i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 14.3944i | − 0.864879i | −0.901663 | − | 0.432439i | \(-0.857653\pi\) | ||||
0.901663 | − | 0.432439i | \(-0.142347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.5139 | 1.40774 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.18335 | −0.0705925 | −0.0352963 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352963 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.30278i | − 0.374661i | −0.982297 | − | 0.187331i | \(-0.940016\pi\) | ||||
0.982297 | − | 0.187331i | \(-0.0599836\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.90833i | − 0.230701i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30.7250 | −1.80735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.2389 | −2.06574 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.788897i | 0.0460879i | 0.999734 | + | 0.0230439i | \(0.00733576\pi\) | ||||
−0.999734 | + | 0.0230439i | \(0.992664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1.60555i | − 0.0931635i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −36.5139 | −2.11165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.02776 | 0.289795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.18335i | 0.0679815i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.9083i | − 0.965009i | −0.875893 | − | 0.482505i | \(-0.839727\pi\) | ||||
0.875893 | − | 0.482505i | \(-0.160273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.69722 | −0.380992 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.81665 | −0.273127 | −0.136564 | − | 0.990631i | \(-0.543606\pi\) | ||||
−0.136564 | + | 0.990631i | \(0.543606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.183346i | 0.0103633i | 0.999987 | + | 0.00518167i | \(0.00164938\pi\) | ||||
−0.999987 | + | 0.00518167i | \(0.998351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.908327i | 0.0510167i | 0.999675 | + | 0.0255084i | \(0.00812044\pi\) | ||||
−0.999675 | + | 0.0255084i | \(0.991880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.908327 | −0.0508565 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.90833 | −0.385585 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.90833i | 0.384390i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.5139i | 1.46622i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.09167 | 0.115318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6056 | 1.18755 | 0.593774 | − | 0.804632i | \(-0.297637\pi\) | ||||
0.593774 | + | 0.804632i | \(0.297637\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.51388i | 0.302159i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.8444i | 1.68020i | 0.542430 | + | 0.840101i | \(0.317504\pi\) | ||||
−0.542430 | + | 0.840101i | \(0.682496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.9083 | −1.35283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2111 | −0.552962 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.42221i | 0.508751i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 12.5139i | − 0.671780i | −0.941901 | − | 0.335890i | \(-0.890963\pi\) | ||||
0.941901 | − | 0.335890i | \(-0.109037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.18335 | 0.277458 | 0.138729 | − | 0.990330i | \(-0.455698\pi\) | ||||
0.138729 | + | 0.990330i | \(0.455698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.02776 | 0.428490 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.6333i | 0.991751i | 0.868394 | + | 0.495875i | \(0.165153\pi\) | ||||
−0.868394 | + | 0.495875i | \(0.834847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 11.0917i | − 0.587034i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.788897 | 0.0416364 | 0.0208182 | − | 0.999783i | \(-0.493373\pi\) | ||||
0.0208182 | + | 0.999783i | \(0.493373\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.30278i | − 0.120864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 20.6972i | − 1.08039i | −0.841541 | − | 0.540193i | \(-0.818351\pi\) | ||||
0.841541 | − | 0.540193i | \(-0.181649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.9083 | 0.671981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.908327 | 0.0471580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.4222i | 1.41987i | 0.704268 | + | 0.709934i | \(0.251275\pi\) | ||||
−0.704268 | + | 0.709934i | \(0.748725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.54163i | − 0.233906i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18335 | 0.163518 | 0.0817588 | − | 0.996652i | \(-0.473946\pi\) | ||||
0.0817588 | + | 0.996652i | \(0.473946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6972 | 0.957888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 21.6333i | − 1.10541i | −0.833377 | − | 0.552705i | \(-0.813596\pi\) | ||||
0.833377 | − | 0.552705i | \(-0.186404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.6056i | 0.844108i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.4500 | 2.55136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 22.8167i | − 1.15095i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 21.6972i | − 1.08895i | −0.838776 | − | 0.544476i | \(-0.816728\pi\) | ||||
0.838776 | − | 0.544476i | \(-0.183272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.60555 | −0.0803781 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7889 | −0.638647 | −0.319324 | − | 0.947646i | \(-0.603456\pi\) | ||||
−0.319324 | + | 0.947646i | \(0.603456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 51.0555i | − 2.54326i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.39445i | − 0.118688i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.21110 | 0.307119 | 0.153560 | − | 0.988139i | \(-0.450926\pi\) | ||||
0.153560 | + | 0.988139i | \(0.450926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.7250 | 1.46623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 9.90833i | − 0.487557i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3028i | 0.700410i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.39445 | 0.312389 | 0.156195 | − | 0.987726i | \(-0.450077\pi\) | ||||
0.156195 | + | 0.987726i | \(0.450077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.697224 | 0.0339806 | 0.0169903 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169903 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.90833i | 0.335894i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.51388i | − 0.266835i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.5139 | 0.555895 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000i | 0.240285i | 0.992757 | + | 0.120142i | \(0.0383351\pi\) | ||||
−0.992757 | + | 0.120142i | \(0.961665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.30278i | − 0.349339i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.3028 | 1.15991 | 0.579954 | − | 0.814649i | \(-0.303070\pi\) | ||||
0.579954 | + | 0.814649i | \(0.303070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.60555i | 0.408862i | 0.978881 | + | 0.204431i | \(0.0655344\pi\) | ||||
−0.978881 | + | 0.204431i | \(0.934466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.6333i | 1.87459i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.4861 | −1.10838 | −0.554189 | − | 0.832391i | \(-0.686972\pi\) | ||||
−0.554189 | + | 0.832391i | \(0.686972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.60555 | −0.263955 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.88057i | 0.0883569i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6972i | 0.968175i | 0.875020 | + | 0.484088i | \(0.160848\pi\) | ||||
−0.875020 | + | 0.484088i | \(0.839152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.0917 | −0.517715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.2111 | 1.50022 | 0.750110 | − | 0.661313i | \(-0.230000\pi\) | ||||
0.750110 | + | 0.661313i | \(0.230000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.7889i | − 0.547877i | −0.961747 | − | 0.273938i | \(-0.911674\pi\) | ||||
0.961747 | − | 0.273938i | \(-0.0883264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 18.6333i | − 0.862247i | −0.902293 | − | 0.431123i | \(-0.858117\pi\) | ||||
0.902293 | − | 0.431123i | \(-0.141883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.78890 | 0.128779 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.2389 | −2.03842 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.21110i | − 0.331567i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000i | 0.137361i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.8167 | −1.59081 | −0.795407 | − | 0.606076i | \(-0.792743\pi\) | ||||
−0.795407 | + | 0.606076i | \(0.792743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9722 | 0.545887 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.7250i | 0.533505i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.21110i | 0.190823i | 0.995438 | + | 0.0954116i | \(0.0304167\pi\) | ||||
−0.995438 | + | 0.0954116i | \(0.969583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.4222 | −0.968746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.78890 | 0.441767 | 0.220883 | − | 0.975300i | \(-0.429106\pi\) | ||||
0.220883 | + | 0.975300i | \(0.429106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.27502i | 0.282613i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.81665i | 0.0814881i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.48612 | −0.156060 | −0.0780301 | − | 0.996951i | \(-0.524863\pi\) | ||||
−0.0780301 | + | 0.996951i | \(0.524863\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.9083 | 1.38088 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 9.39445i | − 0.418878i | −0.977822 | − | 0.209439i | \(-0.932836\pi\) | ||||
0.977822 | − | 0.209439i | \(-0.0671637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.6333i | 1.22724i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6972 | 1.00604 | 0.503018 | − | 0.864276i | \(-0.332223\pi\) | ||||
0.503018 | + | 0.864276i | \(0.332223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.51388 | 0.243920 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.60555i | 0.0708868i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.00000i | − 0.131940i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.0917 | −0.486870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4500 | −1.81596 | −0.907978 | − | 0.419018i | \(-0.862374\pi\) | ||||
−0.907978 | + | 0.419018i | \(0.862374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4222i | 1.41772i | 0.705347 | + | 0.708862i | \(0.250791\pi\) | ||||
−0.705347 | + | 0.708862i | \(0.749209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 70.5416i | 3.07284i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −30.3305 | −1.31872 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.7250 | 1.42014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 28.0278i | − 1.21402i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 28.8167i | − 1.24353i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.51388 | 0.280573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7250 | 1.10600 | 0.553002 | − | 0.833180i | \(-0.313482\pi\) | ||||
0.553002 | + | 0.833180i | \(0.313482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.8444i | 1.96737i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7.11943i | − 0.304405i | −0.988349 | − | 0.152202i | \(-0.951363\pi\) | ||||
0.988349 | − | 0.152202i | \(-0.0486366\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.2111 | 0.777231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.908327 | 0.0386960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 7.60555i | − 0.323421i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19.4222i | − 0.822945i | −0.911422 | − | 0.411473i | \(-0.865015\pi\) | ||||
0.911422 | − | 0.411473i | \(-0.134985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0555 | 1.52499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.9083 | −0.671650 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8.09167i | − 0.341023i | −0.985356 | − | 0.170512i | \(-0.945458\pi\) | ||||
0.985356 | − | 0.170512i | \(-0.0545421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.39445i | − 0.310538i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.1472 | 1.93459 | 0.967295 | − | 0.253653i | \(-0.0816321\pi\) | ||||
0.967295 | + | 0.253653i | \(0.0816321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3305 | −0.934504 | −0.467252 | − | 0.884124i | \(-0.654756\pi\) | ||||
−0.467252 | + | 0.884124i | \(0.654756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7250i | 0.991125i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 44.3583i | − 1.84666i | −0.384008 | − | 0.923330i | \(-0.625456\pi\) | ||||
0.384008 | − | 0.923330i | \(-0.374544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.4222 | 1.26430 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44996 | −0.101642 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.30278i | − 0.0539555i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5416i | 0.682746i | 0.939928 | + | 0.341373i | \(0.110892\pi\) | ||||
−0.939928 | + | 0.341373i | \(0.889108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2111 | 0.420741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.6333 | −1.26009 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6.39445i | − 0.262589i | −0.991343 | − | 0.131294i | \(-0.958087\pi\) | ||||
0.991343 | − | 0.131294i | \(-0.0419133\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9361i | 0.611293i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.9083 | −1.01773 | −0.508863 | − | 0.860847i | \(-0.669934\pi\) | ||||
−0.508863 | + | 0.860847i | \(0.669934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.90833 | −0.0778423 | −0.0389211 | − | 0.999242i | \(-0.512392\pi\) | ||||
−0.0389211 | + | 0.999242i | \(0.512392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.21110i | 0.375105i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.21110i | 0.292690i | 0.989234 | + | 0.146345i | \(0.0467509\pi\) | ||||
−0.989234 | + | 0.146345i | \(0.953249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.45837 | −0.0590959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 15.8806i | − 0.641410i | −0.947179 | − | 0.320705i | \(-0.896080\pi\) | ||||
0.947179 | − | 0.320705i | \(-0.103920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 3.39445i | − 0.136655i | −0.997663 | − | 0.0683277i | \(-0.978234\pi\) | ||||
0.997663 | − | 0.0683277i | \(-0.0217663\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4222 | −0.459097 | −0.229549 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229549 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7250 | 0.470507 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.18335i | − 0.0474098i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.30278i | 0.0919640i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.5416 | −0.659558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.93608 | −0.276121 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 58.1194i | − 2.31004i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5694i | 1.29045i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7889 | 1.09760 | 0.548798 | − | 0.835955i | \(-0.315086\pi\) | ||||
0.548798 | + | 0.835955i | \(0.315086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0000i | 0.867595i | 0.901010 | + | 0.433798i | \(0.142827\pi\) | ||||
−0.901010 | + | 0.433798i | \(0.857173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 33.2389i | − 1.30675i | −0.757033 | − | 0.653377i | \(-0.773352\pi\) | ||||
0.757033 | − | 0.653377i | \(-0.226648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.2111 | −0.557835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3944 | −0.642549 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.11943i | 0.239472i | 0.992806 | + | 0.119736i | \(0.0382048\pi\) | ||||
−0.992806 | + | 0.119736i | \(0.961795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.2111i | 0.710483i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.9083 | −1.20402 | −0.602009 | − | 0.798489i | \(-0.705633\pi\) | ||||
−0.602009 | + | 0.798489i | \(0.705633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.81665 | −0.342928 | −0.171464 | − | 0.985190i | \(-0.554850\pi\) | ||||
−0.171464 | + | 0.985190i | \(0.554850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 79.5416i | − 3.08914i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.63331i | − 0.256843i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.1194 | 2.01505 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.90833 | −0.305298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0278i | 1.15748i | 0.815510 | + | 0.578742i | \(0.196456\pi\) | ||||
−0.815510 | + | 0.578742i | \(0.803544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 24.2389i | − 0.931575i | −0.884897 | − | 0.465788i | \(-0.845771\pi\) | ||||
0.884897 | − | 0.465788i | \(-0.154229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6695 | 0.409457 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.90833 | 0.149767 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 47.8444i | − 1.83072i | −0.402642 | − | 0.915358i | \(-0.631908\pi\) | ||||
0.402642 | − | 0.915358i | \(-0.368092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 43.1194i | − 1.64511i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.51388 | 0.248159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.5416 | −1.04773 | −0.523867 | − | 0.851800i | \(-0.675511\pi\) | ||||
−0.523867 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.60555i | − 0.0609898i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.7250i | 1.46681i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.6333 | 1.38560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2111 | −1.55652 | −0.778261 | − | 0.627941i | \(-0.783898\pi\) | ||||
−0.778261 | + | 0.627941i | \(0.783898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.39445i | 0.0903083i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.358288i | − 0.0134748i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.6333 | 1.18801 | 0.594007 | − | 0.804460i | \(-0.297545\pi\) | ||||
0.594007 | + | 0.804460i | \(0.297545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.1194 | 0.942052 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 74.5694i | − 2.79265i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 48.6333i | − 1.81624i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.18335 | 0.267894 | 0.133947 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133947 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.02776 | 0.0755176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 50.5139i | − 1.87863i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 39.3305i | − 1.45869i | −0.684147 | − | 0.729344i | \(-0.739825\pi\) | ||||
0.684147 | − | 0.729344i | \(-0.260175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.3305 | 0.493723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.8167 | −1.84254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6056i | 0.724148i | 0.932149 | + | 0.362074i | \(0.117931\pi\) | ||||
−0.932149 | + | 0.362074i | \(0.882069\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.00000i | − 0.147342i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.1194 | 1.29189 | 0.645945 | − | 0.763384i | \(-0.276464\pi\) | ||||
0.645945 | + | 0.763384i | \(0.276464\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.5139 | −0.422973 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 40.6972i | − 1.49304i | −0.665365 | − | 0.746518i | \(-0.731724\pi\) | ||||
0.665365 | − | 0.746518i | \(-0.268276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.09167i | − 0.296059i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.09167 | 0.0764281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.3305 | 1.65413 | 0.827067 | − | 0.562103i | \(-0.190008\pi\) | ||||
0.827067 | + | 0.562103i | \(0.190008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.9083i | 0.579732i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 49.0555i | − 1.78295i | −0.453067 | − | 0.891476i | \(-0.649670\pi\) | ||||
0.453067 | − | 0.891476i | \(-0.350330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.8167 | 0.610406 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5778 | −0.492195 | −0.246097 | − | 0.969245i | \(-0.579148\pi\) | ||||
−0.246097 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.02776i | − 0.290624i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 71.0555i | − 2.56567i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.18335 | 0.186916 | 0.0934581 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934581 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.4500 | 1.49278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.11943i | 0.112198i | 0.998425 | + | 0.0560990i | \(0.0178663\pi\) | ||||
−0.998425 | + | 0.0560990i | \(0.982134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3.84441i | − 0.137917i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.60555 | 0.200840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.60555 | 0.0932340 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.45837i | 0.0521177i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2111i | 0.363986i | 0.983300 | + | 0.181993i | \(0.0582549\pi\) | ||||
−0.983300 | + | 0.181993i | \(0.941745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 52.5416 | 1.87053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.54163 | 0.268150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 39.5416i | − 1.40416i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.51388i | − 0.124468i | −0.998062 | − | 0.0622340i | \(-0.980178\pi\) | ||||
0.998062 | − | 0.0622340i | \(-0.0198225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7250 | −0.733197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.90833 | 0.138094 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.90833i | − 0.279079i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0917i | 0.707260i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.6333 | −1.39343 | −0.696716 | − | 0.717347i | \(-0.745356\pi\) | ||||
−0.696716 | + | 0.717347i | \(0.745356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.8722 | −1.36499 | −0.682493 | − | 0.730892i | \(-0.739104\pi\) | ||||
−0.682493 | + | 0.730892i | \(0.739104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 0.486122i | − 0.0170490i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.21110i | 0.252285i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.02776 | 0.280513 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | 0.418803 | 0.209401 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209401 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 18.4222i | − 0.642158i | −0.947052 | − | 0.321079i | \(-0.895955\pi\) | ||||
0.947052 | − | 0.321079i | \(-0.104045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8167i | 0.480452i | 0.970717 | + | 0.240226i | \(0.0772216\pi\) | ||||
−0.970717 | + | 0.240226i | \(0.922778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.7527 | −1.03336 | −0.516678 | − | 0.856180i | \(-0.672831\pi\) | ||||
−0.516678 | + | 0.856180i | \(0.672831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.1472 | −1.14986 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 45.0000i | − 1.55916i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.3944i | 0.566675i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.11943 | −0.314838 | −0.157419 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157419 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1749 | −0.971550 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.72498i | 0.0938533i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.697224i | 0.0239569i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5139 | −0.498115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.4861 | 0.599417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 12.7250i | − 0.435695i | −0.975983 | − | 0.217848i | \(-0.930096\pi\) | ||||
0.975983 | − | 0.217848i | \(-0.0699035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000i | 0.102478i | 0.998686 | + | 0.0512390i | \(0.0163170\pi\) | ||||
−0.998686 | + | 0.0512390i | \(0.983683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3944 | 1.41236 | 0.706180 | − | 0.708032i | \(-0.250417\pi\) | ||||
0.706180 | + | 0.708032i | \(0.250417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | −0.306719 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3944i | 0.421912i | 0.977496 | + | 0.210956i | \(0.0676577\pi\) | ||||
−0.977496 | + | 0.210956i | \(0.932342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 70.7527i | 2.40289i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9083 | −0.370040 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2389i | 1.19265i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 20.0000i | − 0.675352i | −0.941262 | − | 0.337676i | \(-0.890359\pi\) | ||||
0.941262 | − | 0.337676i | \(-0.109641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.81665 | 0.0612742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5416 | 0.658374 | 0.329187 | − | 0.944265i | \(-0.393225\pi\) | ||||
0.329187 | + | 0.944265i | \(0.393225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52.4500i | − 1.76508i | −0.470236 | − | 0.882541i | \(-0.655831\pi\) | ||||
0.470236 | − | 0.882541i | \(-0.344169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.23886i | − 0.108750i | −0.998521 | − | 0.0543751i | \(-0.982683\pi\) | ||||
0.998521 | − | 0.0543751i | \(-0.0173167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.66106 | −0.189866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.6056 | −0.355299 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.00000i | 0.100391i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 84.0833i | 2.80746i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.27502 | 0.309339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 11.5778i | − 0.385285i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.00000i | − 0.132818i | −0.997792 | − | 0.0664089i | \(-0.978846\pi\) | ||||
0.997792 | − | 0.0664089i | \(-0.0211542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.18335 | 0.0392491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7889 | 0.821293 | 0.410646 | − | 0.911795i | \(-0.365303\pi\) | ||||
0.410646 | + | 0.911795i | \(0.365303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.51388i | 0.116292i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.90833i | 0.228133i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.7889 | 0.883684 | 0.441842 | − | 0.897093i | \(-0.354325\pi\) | ||||
0.441842 | + | 0.897093i | \(0.354325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.9361 | −1.28299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0278i | 0.428814i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.69722i | 0.219966i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.6056 | −1.75874 | −0.879371 | − | 0.476138i | \(-0.842036\pi\) | ||||
−0.879371 | + | 0.476138i | \(0.842036\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.51388 | −0.213484 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0917i | 0.363125i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.21110i | 0.300914i | 0.988617 | + | 0.150457i | \(0.0480744\pi\) | ||||
−0.988617 | + | 0.150457i | \(0.951926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.422205 | 0.0137781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.6056 | 1.94309 | 0.971543 | − | 0.236864i | \(-0.0761197\pi\) | ||||
0.971543 | + | 0.236864i | \(0.0761197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 40.9361i | − 1.33306i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.63331i | 0.215554i | 0.994175 | + | 0.107777i | \(0.0343732\pi\) | ||||
−0.994175 | + | 0.107777i | \(0.965627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.5416 | 1.28358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.09167 | 0.0678271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.2666i | 1.20718i | 0.797293 | + | 0.603592i | \(0.206264\pi\) | ||||
−0.797293 | + | 0.603592i | \(0.793736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.09167i | 0.0676142i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | −0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.2666 | 2.36344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.90833i | 0.222618i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9083i | 0.479419i | 0.970845 | + | 0.239710i | \(0.0770523\pi\) | ||||
−0.970845 | + | 0.239710i | \(0.922948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.9083 | 0.511049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.3583 | −1.45562 | −0.727808 | − | 0.685781i | \(-0.759461\pi\) | ||||
−0.727808 | + | 0.685781i | \(0.759461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.33053i | − 0.138830i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.0278i | 1.66452i | 0.554389 | + | 0.832258i | \(0.312952\pi\) | ||||
−0.554389 | + | 0.832258i | \(0.687048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.69722 | −0.0542435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.5139 | 0.846523 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 8.84441i | − 0.282093i | −0.990003 | − | 0.141046i | \(-0.954953\pi\) | ||||
0.990003 | − | 0.141046i | \(-0.0450467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.81665i | − 0.153316i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.6611 | 1.67452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.9083 | 0.537111 | 0.268555 | − | 0.963264i | \(-0.413454\pi\) | ||||
0.268555 | + | 0.963264i | \(0.413454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 49.7527i | − 1.57886i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 46.7250i | − 1.47979i | −0.672720 | − | 0.739897i | \(-0.734874\pi\) | ||||
0.672720 | − | 0.739897i | \(-0.265126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.84441 | −0.121632 |
(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 | 4400.2.b.y.4049.1 | 4 | ||
4.3 | odd | 2 | 275.2.b.c.199.3 | 4 | |||
5.2 | odd | 4 | 4400.2.a.bh.1.1 | 2 | |||
5.3 | odd | 4 | 4400.2.a.bs.1.2 | 2 | |||
5.4 | even | 2 | inner | 4400.2.b.y.4049.4 | 4 | ||
12.11 | even | 2 | 2475.2.c.k.199.2 | 4 | |||
20.3 | even | 4 | 275.2.a.e.1.2 | ✓ | 2 | ||
20.7 | even | 4 | 275.2.a.f.1.1 | yes | 2 | ||
20.19 | odd | 2 | 275.2.b.c.199.2 | 4 | |||
60.23 | odd | 4 | 2475.2.a.t.1.1 | 2 | |||
60.47 | odd | 4 | 2475.2.a.o.1.2 | 2 | |||
60.59 | even | 2 | 2475.2.c.k.199.3 | 4 | |||
220.43 | odd | 4 | 3025.2.a.n.1.1 | 2 | |||
220.87 | odd | 4 | 3025.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.e.1.2 | ✓ | 2 | 20.3 | even | 4 | ||
275.2.a.f.1.1 | yes | 2 | 20.7 | even | 4 | ||
275.2.b.c.199.2 | 4 | 20.19 | odd | 2 | |||
275.2.b.c.199.3 | 4 | 4.3 | odd | 2 | |||
2475.2.a.o.1.2 | 2 | 60.47 | odd | 4 | |||
2475.2.a.t.1.1 | 2 | 60.23 | odd | 4 | |||
2475.2.c.k.199.2 | 4 | 12.11 | even | 2 | |||
2475.2.c.k.199.3 | 4 | 60.59 | even | 2 | |||
3025.2.a.h.1.2 | 2 | 220.87 | odd | 4 | |||
3025.2.a.n.1.1 | 2 | 220.43 | odd | 4 | |||
4400.2.a.bh.1.1 | 2 | 5.2 | odd | 4 | |||
4400.2.a.bs.1.2 | 2 | 5.3 | odd | 4 | |||
4400.2.b.y.4049.1 | 4 | 1.1 | even | 1 | trivial | ||
4400.2.b.y.4049.4 | 4 | 5.4 | even | 2 | inner |