Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,3,Mod(323,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.323");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.b (of order \(2\), degree \(1\), 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: | \(10.2997539928\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(-0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.323 |
Dual form | 378.3.b.c.323.7 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0.672556i | 0.134511i | 0.997736 | + | 0.0672556i | \(0.0214243\pi\) | ||||
−0.997736 | + | 0.0672556i | \(0.978576\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.951138 | 0.0951138 | ||||||||
\(11\) | 13.2647i | 1.20588i | 0.797786 | + | 0.602941i | \(0.206004\pi\) | ||||
−0.797786 | + | 0.602941i | \(0.793996\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.62808 | 0.356006 | 0.178003 | − | 0.984030i | \(-0.443036\pi\) | ||||
0.178003 | + | 0.984030i | \(0.443036\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 15.2020i | 0.894232i | 0.894476 | + | 0.447116i | \(0.147549\pi\) | ||||
−0.894476 | + | 0.447116i | \(0.852451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.04508 | 0.212899 | 0.106449 | − | 0.994318i | \(-0.466052\pi\) | ||||
0.106449 | + | 0.994318i | \(0.466052\pi\) | |||||||
\(20\) | − 1.34511i | − 0.0672556i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.7591 | 0.852687 | ||||||||
\(23\) | − 9.26566i | − 0.402855i | −0.979503 | − | 0.201427i | \(-0.935442\pi\) | ||||
0.979503 | − | 0.201427i | \(-0.0645580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.5477 | 0.981907 | ||||||||
\(26\) | − 6.54510i | − 0.251735i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.29150 | −0.188982 | ||||||||
\(29\) | 27.5450i | 0.949829i | 0.880032 | + | 0.474914i | \(0.157521\pi\) | ||||
−0.880032 | + | 0.474914i | \(0.842479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.0486 | 1.42092 | 0.710461 | − | 0.703736i | \(-0.248486\pi\) | ||||
0.710461 | + | 0.703736i | \(0.248486\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 21.4988 | 0.632318 | ||||||||
\(35\) | 1.77942i | 0.0508405i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.90984 | −0.0786445 | −0.0393222 | − | 0.999227i | \(-0.512520\pi\) | ||||
−0.0393222 | + | 0.999227i | \(0.512520\pi\) | |||||||
\(38\) | − 5.72060i | − 0.150542i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.90228 | −0.0475569 | ||||||||
\(41\) | − 23.9470i | − 0.584073i | −0.956407 | − | 0.292037i | \(-0.905667\pi\) | ||||
0.956407 | − | 0.292037i | \(-0.0943329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.8940 | 1.46265 | 0.731326 | − | 0.682028i | \(-0.238902\pi\) | ||||
0.731326 | + | 0.682028i | \(0.238902\pi\) | |||||||
\(44\) | − 26.5294i | − 0.602941i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.1036 | −0.284861 | ||||||||
\(47\) | 55.1568i | 1.17355i | 0.809751 | + | 0.586774i | \(0.199602\pi\) | ||||
−0.809751 | + | 0.586774i | \(0.800398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | − 34.7156i | − 0.694313i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.25617 | −0.178003 | ||||||||
\(53\) | 1.84323i | 0.0347779i | 0.999849 | + | 0.0173889i | \(0.00553535\pi\) | ||||
−0.999849 | + | 0.0173889i | \(0.994465\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.92125 | −0.162205 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 38.9546 | 0.671630 | ||||||||
\(59\) | − 13.2450i | − 0.224492i | −0.993680 | − | 0.112246i | \(-0.964196\pi\) | ||||
0.993680 | − | 0.112246i | \(-0.0358044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.5346 | −0.336633 | −0.168316 | − | 0.985733i | \(-0.553833\pi\) | ||||
−0.168316 | + | 0.985733i | \(0.553833\pi\) | |||||||
\(62\) | − 62.2941i | − 1.00474i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 3.11265i | 0.0478869i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −75.2985 | −1.12386 | −0.561929 | − | 0.827185i | \(-0.689941\pi\) | ||||
−0.561929 | + | 0.827185i | \(0.689941\pi\) | |||||||
\(68\) | − 30.4039i | − 0.447116i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.51647 | 0.0359496 | ||||||||
\(71\) | − 91.3391i | − 1.28647i | −0.765670 | − | 0.643233i | \(-0.777593\pi\) | ||||
0.765670 | − | 0.643233i | \(-0.222407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.4610 | 0.554261 | 0.277130 | − | 0.960832i | \(-0.410617\pi\) | ||||
0.277130 | + | 0.960832i | \(0.410617\pi\) | |||||||
\(74\) | 4.11514i | 0.0556100i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.09016 | −0.106449 | ||||||||
\(77\) | 35.0951i | 0.455780i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −84.4365 | −1.06882 | −0.534408 | − | 0.845226i | \(-0.679466\pi\) | ||||
−0.534408 | + | 0.845226i | \(0.679466\pi\) | |||||||
\(80\) | 2.69022i | 0.0336278i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −33.8662 | −0.413002 | ||||||||
\(83\) | 80.0194i | 0.964089i | 0.876147 | + | 0.482045i | \(0.160106\pi\) | ||||
−0.876147 | + | 0.482045i | \(0.839894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2242 | −0.120284 | ||||||||
\(86\) | − 88.9456i | − 1.03425i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −37.5182 | −0.426344 | ||||||||
\(89\) | 109.600i | 1.23146i | 0.787957 | + | 0.615730i | \(0.211139\pi\) | ||||
−0.787957 | + | 0.615730i | \(0.788861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2448 | 0.134558 | ||||||||
\(92\) | 18.5313i | 0.201427i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 78.0035 | 0.829824 | ||||||||
\(95\) | 2.72054i | 0.0286373i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 126.396 | 1.30306 | 0.651528 | − | 0.758624i | \(-0.274128\pi\) | ||||
0.651528 | + | 0.758624i | \(0.274128\pi\) | |||||||
\(98\) | − 9.89949i | − 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −49.0953 | −0.490953 | ||||||||
\(101\) | 119.202i | 1.18022i | 0.807324 | + | 0.590108i | \(0.200915\pi\) | ||||
−0.807324 | + | 0.590108i | \(0.799085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −132.242 | −1.28390 | −0.641952 | − | 0.766745i | \(-0.721875\pi\) | ||||
−0.641952 | + | 0.766745i | \(0.721875\pi\) | |||||||
\(104\) | 13.0902i | 0.125867i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.60672 | 0.0245917 | ||||||||
\(107\) | − 109.283i | − 1.02134i | −0.859777 | − | 0.510669i | \(-0.829398\pi\) | ||||
0.859777 | − | 0.510669i | \(-0.170602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −184.589 | −1.69347 | −0.846736 | − | 0.532013i | \(-0.821436\pi\) | ||||
−0.846736 | + | 0.532013i | \(0.821436\pi\) | |||||||
\(110\) | 12.6166i | 0.114696i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5830 | 0.0944911 | ||||||||
\(113\) | − 35.8528i | − 0.317281i | −0.987336 | − | 0.158641i | \(-0.949289\pi\) | ||||
0.987336 | − | 0.158641i | \(-0.0507111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.23168 | 0.0541885 | ||||||||
\(116\) | − 55.0901i | − 0.474914i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.7313 | −0.158739 | ||||||||
\(119\) | 40.2206i | 0.337988i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.9522 | −0.454150 | ||||||||
\(122\) | 29.0403i | 0.238035i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −88.0972 | −0.710461 | ||||||||
\(125\) | 33.3236i | 0.266589i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96.3439 | 0.758613 | 0.379307 | − | 0.925271i | \(-0.376163\pi\) | ||||
0.379307 | + | 0.925271i | \(0.376163\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.40195 | 0.0338611 | ||||||||
\(131\) | − 76.2958i | − 0.582411i | −0.956661 | − | 0.291205i | \(-0.905944\pi\) | ||||
0.956661 | − | 0.291205i | \(-0.0940563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.7023 | 0.0804682 | ||||||||
\(134\) | 106.488i | 0.794688i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −42.9976 | −0.316159 | ||||||||
\(137\) | 173.775i | 1.26843i | 0.773156 | + | 0.634216i | \(0.218677\pi\) | ||||
−0.773156 | + | 0.634216i | \(0.781323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −85.9389 | −0.618265 | −0.309133 | − | 0.951019i | \(-0.600039\pi\) | ||||
−0.309133 | + | 0.951019i | \(0.600039\pi\) | |||||||
\(140\) | − 3.55883i | − 0.0254202i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −129.173 | −0.909669 | ||||||||
\(143\) | 61.3901i | 0.429302i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.5256 | −0.127763 | ||||||||
\(146\) | − 57.2205i | − 0.391921i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.81969 | 0.0393222 | ||||||||
\(149\) | − 0.416605i | − 0.00279600i | −0.999999 | − | 0.00139800i | \(-0.999555\pi\) | ||||
0.999999 | − | 0.00139800i | \(-0.000444998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −170.051 | −1.12617 | −0.563084 | − | 0.826400i | \(-0.690385\pi\) | ||||
−0.563084 | + | 0.826400i | \(0.690385\pi\) | |||||||
\(152\) | 11.4412i | 0.0752711i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 49.6320 | 0.322285 | ||||||||
\(155\) | 29.6252i | 0.191130i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −146.513 | −0.933202 | −0.466601 | − | 0.884468i | \(-0.654522\pi\) | ||||
−0.466601 | + | 0.884468i | \(0.654522\pi\) | |||||||
\(158\) | 119.411i | 0.755767i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.80455 | 0.0237785 | ||||||||
\(161\) | − 24.5146i | − 0.152265i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 85.8374 | 0.526610 | 0.263305 | − | 0.964713i | \(-0.415188\pi\) | ||||
0.263305 | + | 0.964713i | \(0.415188\pi\) | |||||||
\(164\) | 47.8940i | 0.292037i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 113.165 | 0.681714 | ||||||||
\(167\) | − 244.178i | − 1.46214i | −0.682300 | − | 0.731072i | \(-0.739020\pi\) | ||||
0.682300 | − | 0.731072i | \(-0.260980\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −147.581 | −0.873259 | ||||||||
\(170\) | 14.4592i | 0.0850539i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −125.788 | −0.731326 | ||||||||
\(173\) | 144.775i | 0.836847i | 0.908252 | + | 0.418424i | \(0.137417\pi\) | ||||
−0.908252 | + | 0.418424i | \(0.862583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 64.9470 | 0.371126 | ||||||||
\(176\) | 53.0588i | 0.301470i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 154.998 | 0.870774 | ||||||||
\(179\) | − 192.258i | − 1.07407i | −0.843561 | − | 0.537033i | \(-0.819545\pi\) | ||||
0.843561 | − | 0.537033i | \(-0.180455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 298.952 | 1.65167 | 0.825835 | − | 0.563912i | \(-0.190704\pi\) | ||||
0.825835 | + | 0.563912i | \(0.190704\pi\) | |||||||
\(182\) | − 17.3167i | − 0.0951467i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.2072 | 0.142431 | ||||||||
\(185\) | − 1.95703i | − 0.0105786i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −201.649 | −1.07834 | ||||||||
\(188\) | − 110.314i | − 0.586774i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.84743 | 0.0202496 | ||||||||
\(191\) | − 225.355i | − 1.17987i | −0.807451 | − | 0.589935i | \(-0.799154\pi\) | ||||
0.807451 | − | 0.589935i | \(-0.200846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −343.910 | −1.78192 | −0.890958 | − | 0.454086i | \(-0.849966\pi\) | ||||
−0.890958 | + | 0.454086i | \(0.849966\pi\) | |||||||
\(194\) | − 178.752i | − 0.921400i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | − 111.867i | − 0.567851i | −0.958846 | − | 0.283926i | \(-0.908363\pi\) | ||||
0.958846 | − | 0.283926i | \(-0.0916369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 240.040 | 1.20623 | 0.603116 | − | 0.797654i | \(-0.293926\pi\) | ||||
0.603116 | + | 0.797654i | \(0.293926\pi\) | |||||||
\(200\) | 69.4313i | 0.347156i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 168.577 | 0.834539 | ||||||||
\(203\) | 72.8773i | 0.359002i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.1057 | 0.0785644 | ||||||||
\(206\) | 187.018i | 0.907857i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.5123 | 0.0890016 | ||||||||
\(209\) | 53.6567i | 0.256731i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 216.294 | 1.02509 | 0.512544 | − | 0.858661i | \(-0.328703\pi\) | ||||
0.512544 | + | 0.858661i | \(0.328703\pi\) | |||||||
\(212\) | − 3.68645i | − 0.0173889i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −154.550 | −0.722195 | ||||||||
\(215\) | 42.2998i | 0.196743i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 116.542 | 0.537058 | ||||||||
\(218\) | 261.048i | 1.19747i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.8425 | 0.0811023 | ||||||||
\(221\) | 70.3559i | 0.318352i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 410.400 | 1.84036 | 0.920180 | − | 0.391495i | \(-0.128042\pi\) | ||||
0.920180 | + | 0.391495i | \(0.128042\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.7035 | −0.224352 | ||||||||
\(227\) | − 418.066i | − 1.84170i | −0.389916 | − | 0.920850i | \(-0.627496\pi\) | ||||
0.389916 | − | 0.920850i | \(-0.372504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −38.0368 | −0.166099 | −0.0830497 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830497 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(230\) | − 8.81292i | − 0.0383171i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −77.9091 | −0.335815 | ||||||||
\(233\) | 101.421i | 0.435281i | 0.976029 | + | 0.217641i | \(0.0698361\pi\) | ||||
−0.976029 | + | 0.217641i | \(0.930164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.0960 | −0.157855 | ||||||||
\(236\) | 26.4900i | 0.112246i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 56.8805 | 0.238994 | ||||||||
\(239\) | − 403.709i | − 1.68916i | −0.535431 | − | 0.844579i | \(-0.679851\pi\) | ||||
0.535431 | − | 0.844579i | \(-0.320149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 452.244 | 1.87653 | 0.938266 | − | 0.345914i | \(-0.112431\pi\) | ||||
0.938266 | + | 0.345914i | \(0.112431\pi\) | |||||||
\(242\) | 77.7142i | 0.321133i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 41.0692 | 0.168316 | ||||||||
\(245\) | 4.70789i | 0.0192159i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.7210 | 0.0757933 | ||||||||
\(248\) | 124.588i | 0.502372i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 47.1267 | 0.188507 | ||||||||
\(251\) | 55.2568i | 0.220146i | 0.993923 | + | 0.110073i | \(0.0351085\pi\) | ||||
−0.993923 | + | 0.110073i | \(0.964891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 122.906 | 0.485795 | ||||||||
\(254\) | − 136.251i | − 0.536421i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 66.7940i | − 0.259899i | −0.991521 | − | 0.129949i | \(-0.958519\pi\) | ||||
0.991521 | − | 0.129949i | \(-0.0414815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.69873 | −0.0297248 | ||||||||
\(260\) | − 6.22529i | − 0.0239434i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −107.899 | −0.411827 | ||||||||
\(263\) | − 361.502i | − 1.37453i | −0.726406 | − | 0.687265i | \(-0.758811\pi\) | ||||
0.726406 | − | 0.687265i | \(-0.241189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.23967 | −0.00467801 | ||||||||
\(266\) | − 15.1353i | − 0.0568996i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 150.597 | 0.561929 | ||||||||
\(269\) | − 172.459i | − 0.641111i | −0.947230 | − | 0.320555i | \(-0.896130\pi\) | ||||
0.947230 | − | 0.320555i | \(-0.103870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91.2119 | 0.336575 | 0.168288 | − | 0.985738i | \(-0.446176\pi\) | ||||
0.168288 | + | 0.985738i | \(0.446176\pi\) | |||||||
\(272\) | 60.8078i | 0.223558i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 245.755 | 0.896917 | ||||||||
\(275\) | 325.617i | 1.18406i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −52.0409 | −0.187873 | −0.0939367 | − | 0.995578i | \(-0.529945\pi\) | ||||
−0.0939367 | + | 0.995578i | \(0.529945\pi\) | |||||||
\(278\) | 121.536i | 0.437180i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.03295 | −0.0179748 | ||||||||
\(281\) | − 413.083i | − 1.47005i | −0.678042 | − | 0.735023i | \(-0.737171\pi\) | ||||
0.678042 | − | 0.735023i | \(-0.262829\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 108.973 | 0.385063 | 0.192531 | − | 0.981291i | \(-0.438330\pi\) | ||||
0.192531 | + | 0.981291i | \(0.438330\pi\) | |||||||
\(284\) | 182.678i | 0.643233i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 86.8187 | 0.303562 | ||||||||
\(287\) | − 63.3578i | − 0.220759i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 57.9007 | 0.200348 | ||||||||
\(290\) | 26.1991i | 0.0903418i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −80.9221 | −0.277130 | ||||||||
\(293\) | 403.517i | 1.37719i | 0.725145 | + | 0.688596i | \(0.241773\pi\) | ||||
−0.725145 | + | 0.688596i | \(0.758227\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.90801 | 0.0301966 | ||||||||
\(296\) | − 8.23028i | − 0.0278050i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.589168 | −0.00197707 | ||||||||
\(299\) | − 42.8822i | − 0.143419i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 166.402 | 0.552830 | ||||||||
\(302\) | 240.489i | 0.796321i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.1803 | 0.0532247 | ||||||||
\(305\) | − 13.8107i | − 0.0452809i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −91.2879 | −0.297355 | −0.148677 | − | 0.988886i | \(-0.547502\pi\) | ||||
−0.148677 | + | 0.988886i | \(0.547502\pi\) | |||||||
\(308\) | − 70.1902i | − 0.227890i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 41.8963 | 0.135149 | ||||||||
\(311\) | 12.1248i | 0.0389864i | 0.999810 | + | 0.0194932i | \(0.00620527\pi\) | ||||
−0.999810 | + | 0.0194932i | \(0.993795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 87.0221 | 0.278026 | 0.139013 | − | 0.990291i | \(-0.455607\pi\) | ||||
0.139013 | + | 0.990291i | \(0.455607\pi\) | |||||||
\(314\) | 207.200i | 0.659874i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 168.873 | 0.534408 | ||||||||
\(317\) | 193.797i | 0.611348i | 0.952136 | + | 0.305674i | \(0.0988817\pi\) | ||||
−0.952136 | + | 0.305674i | \(0.901118\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −365.377 | −1.14538 | ||||||||
\(320\) | − 5.38045i | − 0.0168139i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.6689 | −0.107667 | ||||||||
\(323\) | 61.4931i | 0.190381i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 113.609 | 0.349565 | ||||||||
\(326\) | − 121.392i | − 0.372369i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 67.7323 | 0.206501 | ||||||||
\(329\) | 145.931i | 0.443560i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −417.814 | −1.26228 | −0.631138 | − | 0.775670i | \(-0.717412\pi\) | ||||
−0.631138 | + | 0.775670i | \(0.717412\pi\) | |||||||
\(332\) | − 160.039i | − 0.482045i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −345.320 | −1.03389 | ||||||||
\(335\) | − 50.6425i | − 0.151172i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 63.6695 | 0.188930 | 0.0944652 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944652 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(338\) | 208.711i | 0.617488i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.4483 | 0.0601422 | ||||||||
\(341\) | 584.291i | 1.71346i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | 177.891i | 0.517125i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 204.742 | 0.591740 | ||||||||
\(347\) | 310.877i | 0.895901i | 0.894058 | + | 0.447950i | \(0.147846\pi\) | ||||
−0.894058 | + | 0.447950i | \(0.852154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 415.607 | 1.19085 | 0.595426 | − | 0.803410i | \(-0.296983\pi\) | ||||
0.595426 | + | 0.803410i | \(0.296983\pi\) | |||||||
\(350\) | − 91.8490i | − 0.262426i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 75.0365 | 0.213172 | ||||||||
\(353\) | − 150.239i | − 0.425605i | −0.977095 | − | 0.212803i | \(-0.931741\pi\) | ||||
0.977095 | − | 0.212803i | \(-0.0682591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 61.4307 | 0.173044 | ||||||||
\(356\) | − 219.200i | − 0.615730i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −271.894 | −0.759479 | ||||||||
\(359\) | − 14.0939i | − 0.0392589i | −0.999807 | − | 0.0196294i | \(-0.993751\pi\) | ||||
0.999807 | − | 0.0196294i | \(-0.00624865\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −344.637 | −0.954674 | ||||||||
\(362\) | − 422.782i | − 1.16791i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.4895 | −0.0672789 | ||||||||
\(365\) | 27.2123i | 0.0745543i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44.6289 | −0.121605 | −0.0608024 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608024 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(368\) | − 37.0626i | − 0.100714i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.76766 | −0.00748017 | ||||||||
\(371\) | 4.87672i | 0.0131448i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −259.881 | −0.696732 | −0.348366 | − | 0.937359i | \(-0.613263\pi\) | ||||
−0.348366 | + | 0.937359i | \(0.613263\pi\) | |||||||
\(374\) | 285.175i | 0.762500i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −156.007 | −0.414912 | ||||||||
\(377\) | 127.481i | 0.338145i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −185.662 | −0.489872 | −0.244936 | − | 0.969539i | \(-0.578767\pi\) | ||||
−0.244936 | + | 0.969539i | \(0.578767\pi\) | |||||||
\(380\) | − 5.44108i | − 0.0143186i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −318.700 | −0.834294 | ||||||||
\(383\) | − 604.452i | − 1.57820i | −0.614262 | − | 0.789102i | \(-0.710546\pi\) | ||||
0.614262 | − | 0.789102i | \(-0.289454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.6034 | −0.0613076 | ||||||||
\(386\) | 486.362i | 1.26000i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −252.793 | −0.651528 | ||||||||
\(389\) | − 506.617i | − 1.30236i | −0.758924 | − | 0.651179i | \(-0.774275\pi\) | ||||
0.758924 | − | 0.651179i | \(-0.225725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 140.856 | 0.360246 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −158.203 | −0.401531 | ||||||||
\(395\) | − 56.7883i | − 0.143768i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −232.366 | −0.585305 | −0.292652 | − | 0.956219i | \(-0.594538\pi\) | ||||
−0.292652 | + | 0.956219i | \(0.594538\pi\) | |||||||
\(398\) | − 339.468i | − 0.852935i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 98.1907 | 0.245477 | ||||||||
\(401\) | 647.469i | 1.61464i | 0.590116 | + | 0.807318i | \(0.299082\pi\) | ||||
−0.590116 | + | 0.807318i | \(0.700918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 203.861 | 0.505857 | ||||||||
\(404\) | − 238.404i | − 0.590108i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 103.064 | 0.253852 | ||||||||
\(407\) | − 38.5982i | − 0.0948359i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −148.863 | −0.363967 | −0.181984 | − | 0.983302i | \(-0.558252\pi\) | ||||
−0.181984 | + | 0.983302i | \(0.558252\pi\) | |||||||
\(410\) | − 22.7769i | − 0.0555534i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 264.484 | 0.641952 | ||||||||
\(413\) | − 35.0430i | − 0.0848498i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −53.8175 | −0.129681 | ||||||||
\(416\) | − 26.1804i | − 0.0629336i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 75.8821 | 0.181536 | ||||||||
\(419\) | 418.288i | 0.998301i | 0.866515 | + | 0.499150i | \(0.166355\pi\) | ||||
−0.866515 | + | 0.499150i | \(0.833645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 494.465 | 1.17450 | 0.587251 | − | 0.809405i | \(-0.300210\pi\) | ||||
0.587251 | + | 0.809405i | \(0.300210\pi\) | |||||||
\(422\) | − 305.885i | − 0.724847i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.21343 | −0.0122958 | ||||||||
\(425\) | 373.172i | 0.878053i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.3294 | −0.127235 | ||||||||
\(428\) | 218.566i | 0.510669i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 59.8209 | 0.139118 | ||||||||
\(431\) | − 804.276i | − 1.86607i | −0.359786 | − | 0.933035i | \(-0.617150\pi\) | ||||
0.359786 | − | 0.933035i | \(-0.382850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −855.394 | −1.97551 | −0.987753 | − | 0.156023i | \(-0.950133\pi\) | ||||
−0.987753 | + | 0.156023i | \(0.950133\pi\) | |||||||
\(434\) | − 164.815i | − 0.379757i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 369.177 | 0.846736 | ||||||||
\(437\) | − 37.4803i | − 0.0857673i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −736.810 | −1.67838 | −0.839191 | − | 0.543837i | \(-0.816971\pi\) | ||||
−0.839191 | + | 0.543837i | \(0.816971\pi\) | |||||||
\(440\) | − 25.2331i | − 0.0573480i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 99.4983 | 0.225109 | ||||||||
\(443\) | − 138.024i | − 0.311566i | −0.987791 | − | 0.155783i | \(-0.950210\pi\) | ||||
0.987791 | − | 0.155783i | \(-0.0497900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −73.7121 | −0.165645 | ||||||||
\(446\) | − 580.394i | − 1.30133i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.1660 | −0.0472456 | ||||||||
\(449\) | 488.441i | 1.08784i | 0.839137 | + | 0.543921i | \(0.183061\pi\) | ||||
−0.839137 | + | 0.543921i | \(0.816939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 317.650 | 0.704323 | ||||||||
\(452\) | 71.7055i | 0.158641i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −591.235 | −1.30228 | ||||||||
\(455\) | 8.23529i | 0.0180995i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −331.337 | −0.725026 | −0.362513 | − | 0.931979i | \(-0.618081\pi\) | ||||
−0.362513 | + | 0.931979i | \(0.618081\pi\) | |||||||
\(458\) | 53.7921i | 0.117450i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.4634 | −0.0270943 | ||||||||
\(461\) | − 20.8885i | − 0.0453112i | −0.999743 | − | 0.0226556i | \(-0.992788\pi\) | ||||
0.999743 | − | 0.0226556i | \(-0.00721212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 106.427 | 0.229864 | 0.114932 | − | 0.993373i | \(-0.463335\pi\) | ||||
0.114932 | + | 0.993373i | \(0.463335\pi\) | |||||||
\(464\) | 110.180i | 0.237457i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 143.430 | 0.307790 | ||||||||
\(467\) | 472.833i | 1.01249i | 0.862390 | + | 0.506245i | \(0.168967\pi\) | ||||
−0.862390 | + | 0.506245i | \(0.831033\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −199.221 | −0.424779 | ||||||||
\(470\) | 52.4617i | 0.111621i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 37.4625 | 0.0793697 | ||||||||
\(473\) | 834.270i | 1.76378i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 99.2972 | 0.209047 | ||||||||
\(476\) | − 80.4412i | − 0.168994i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −570.930 | −1.19442 | ||||||||
\(479\) | − 373.539i | − 0.779832i | −0.920850 | − | 0.389916i | \(-0.872504\pi\) | ||||
0.920850 | − | 0.389916i | \(-0.127496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4670 | −0.0279979 | ||||||||
\(482\) | − 639.570i | − 1.32691i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 109.904 | 0.227075 | ||||||||
\(485\) | 85.0087i | 0.175276i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −642.695 | −1.31970 | −0.659851 | − | 0.751396i | \(-0.729381\pi\) | ||||
−0.659851 | + | 0.751396i | \(0.729381\pi\) | |||||||
\(488\) | − 58.0806i | − 0.119018i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.65797 | 0.0135877 | ||||||||
\(491\) | − 805.881i | − 1.64131i | −0.571427 | − | 0.820653i | \(-0.693610\pi\) | ||||
0.571427 | − | 0.820653i | \(-0.306390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −418.738 | −0.849368 | ||||||||
\(494\) | − 26.4754i | − 0.0535940i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 176.194 | 0.355231 | ||||||||
\(497\) | − 241.661i | − 0.486239i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 408.219 | 0.818075 | 0.409037 | − | 0.912518i | \(-0.365865\pi\) | ||||
0.409037 | + | 0.912518i | \(0.365865\pi\) | |||||||
\(500\) | − 66.6472i | − 0.133294i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 78.1449 | 0.155667 | ||||||||
\(503\) | 708.495i | 1.40854i | 0.709933 | + | 0.704269i | \(0.248725\pi\) | ||||
−0.709933 | + | 0.704269i | \(0.751275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −80.1699 | −0.158752 | ||||||||
\(506\) | − 173.816i | − 0.343509i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −192.688 | −0.379307 | ||||||||
\(509\) | − 842.863i | − 1.65592i | −0.560787 | − | 0.827960i | \(-0.689501\pi\) | ||||
0.560787 | − | 0.827960i | \(-0.310499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 107.050 | 0.209491 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −94.4610 | −0.183776 | ||||||||
\(515\) | − 88.9402i | − 0.172699i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −731.638 | −1.41516 | ||||||||
\(518\) | 10.8876i | 0.0210186i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.80389 | −0.0169306 | ||||||||
\(521\) | − 798.331i | − 1.53231i | −0.642659 | − | 0.766153i | \(-0.722169\pi\) | ||||
0.642659 | − | 0.766153i | \(-0.277831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 101.371 | 0.193825 | 0.0969127 | − | 0.995293i | \(-0.469103\pi\) | ||||
0.0969127 | + | 0.995293i | \(0.469103\pi\) | |||||||
\(524\) | 152.592i | 0.291205i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −511.240 | −0.971940 | ||||||||
\(527\) | 669.625i | 1.27063i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 443.148 | 0.837708 | ||||||||
\(530\) | 1.75316i | 0.00330786i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.4045 | −0.0402341 | ||||||||
\(533\) | − 110.829i | − 0.207934i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 73.4991 | 0.137381 | ||||||||
\(536\) | − 212.976i | − 0.397344i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −243.894 | −0.453334 | ||||||||
\(539\) | 92.8529i | 0.172269i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 469.805 | 0.868402 | 0.434201 | − | 0.900816i | \(-0.357031\pi\) | ||||
0.434201 | + | 0.900816i | \(0.357031\pi\) | |||||||
\(542\) | − 128.993i | − 0.237995i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 85.9952 | 0.158079 | ||||||||
\(545\) | − 124.146i | − 0.227791i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −742.985 | −1.35829 | −0.679145 | − | 0.734004i | \(-0.737649\pi\) | ||||
−0.679145 | + | 0.734004i | \(0.737649\pi\) | |||||||
\(548\) | − 347.551i | − 0.634216i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 460.493 | 0.837259 | ||||||||
\(551\) | 111.422i | 0.202217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −223.398 | −0.403975 | ||||||||
\(554\) | 73.5970i | 0.132847i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 171.878 | 0.309133 | ||||||||
\(557\) | 506.745i | 0.909775i | 0.890549 | + | 0.454887i | \(0.150321\pi\) | ||||
−0.890549 | + | 0.454887i | \(0.849679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 291.079 | 0.520713 | ||||||||
\(560\) | 7.11767i | 0.0127101i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −584.187 | −1.03948 | ||||||||
\(563\) | 900.954i | 1.60027i | 0.599818 | + | 0.800137i | \(0.295240\pi\) | ||||
−0.599818 | + | 0.800137i | \(0.704760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.1130 | 0.0426779 | ||||||||
\(566\) | − 154.111i | − 0.272281i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 258.346 | 0.454835 | ||||||||
\(569\) | 590.261i | 1.03737i | 0.854967 | + | 0.518683i | \(0.173577\pi\) | ||||
−0.854967 | + | 0.518683i | \(0.826423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 941.922 | 1.64960 | 0.824800 | − | 0.565425i | \(-0.191288\pi\) | ||||
0.824800 | + | 0.565425i | \(0.191288\pi\) | |||||||
\(572\) | − 122.780i | − 0.214651i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −89.6014 | −0.156100 | ||||||||
\(575\) | − 227.450i | − 0.395566i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 236.677 | 0.410185 | 0.205092 | − | 0.978743i | \(-0.434251\pi\) | ||||
0.205092 | + | 0.978743i | \(0.434251\pi\) | |||||||
\(578\) | − 81.8839i | − 0.141668i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 37.0512 | 0.0638813 | ||||||||
\(581\) | 211.711i | 0.364391i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.4499 | −0.0419380 | ||||||||
\(584\) | 114.441i | 0.195961i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 570.660 | 0.973822 | ||||||||
\(587\) | 920.582i | 1.56828i | 0.620582 | + | 0.784141i | \(0.286896\pi\) | ||||
−0.620582 | + | 0.784141i | \(0.713104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 178.180 | 0.302513 | ||||||||
\(590\) | − 12.5978i | − 0.0213522i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.6394 | −0.0196611 | ||||||||
\(593\) | 760.444i | 1.28237i | 0.767388 | + | 0.641184i | \(0.221556\pi\) | ||||
−0.767388 | + | 0.641184i | \(0.778444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.0506 | −0.0454632 | ||||||||
\(596\) | 0.833209i | 0.00139800i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −60.6447 | −0.101412 | ||||||||
\(599\) | − 399.798i | − 0.667442i | −0.942672 | − | 0.333721i | \(-0.891696\pi\) | ||||
0.942672 | − | 0.333721i | \(-0.108304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 664.811 | 1.10617 | 0.553087 | − | 0.833124i | \(-0.313450\pi\) | ||||
0.553087 | + | 0.833124i | \(0.313450\pi\) | |||||||
\(602\) | − 235.328i | − 0.390910i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 340.103 | 0.563084 | ||||||||
\(605\) | − 36.9584i | − 0.0610883i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 372.670 | 0.613954 | 0.306977 | − | 0.951717i | \(-0.400682\pi\) | ||||
0.306977 | + | 0.951717i | \(0.400682\pi\) | |||||||
\(608\) | − 22.8824i | − 0.0376355i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.5312 | −0.0320184 | ||||||||
\(611\) | 255.270i | 0.417791i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 512.686 | 0.836356 | 0.418178 | − | 0.908365i | \(-0.362669\pi\) | ||||
0.418178 | + | 0.908365i | \(0.362669\pi\) | |||||||
\(614\) | 129.101i | 0.210262i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −99.2639 | −0.161143 | ||||||||
\(617\) | − 921.484i | − 1.49349i | −0.665110 | − | 0.746745i | \(-0.731615\pi\) | ||||
0.665110 | − | 0.746745i | \(-0.268385\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1104.63 | −1.78454 | −0.892270 | − | 0.451503i | \(-0.850888\pi\) | ||||
−0.892270 | + | 0.451503i | \(0.850888\pi\) | |||||||
\(620\) | − 59.2503i | − 0.0955650i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1470 | 0.0275676 | ||||||||
\(623\) | 289.974i | 0.465448i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 591.280 | 0.946048 | ||||||||
\(626\) | − 123.068i | − 0.196594i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 293.026 | 0.466601 | ||||||||
\(629\) | − 44.2353i | − 0.0703264i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 119.817 | 0.189884 | 0.0949418 | − | 0.995483i | \(-0.469733\pi\) | ||||
0.0949418 | + | 0.995483i | \(0.469733\pi\) | |||||||
\(632\) | − 238.823i | − 0.377884i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 274.071 | 0.432288 | ||||||||
\(635\) | 64.7967i | 0.102042i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.3966 | 0.0508581 | ||||||||
\(638\) | 516.721i | 0.809907i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.60910 | −0.0118892 | ||||||||
\(641\) | 82.6281i | 0.128905i | 0.997921 | + | 0.0644525i | \(0.0205301\pi\) | ||||
−0.997921 | + | 0.0644525i | \(0.979470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 126.741 | 0.197109 | 0.0985547 | − | 0.995132i | \(-0.468578\pi\) | ||||
0.0985547 | + | 0.995132i | \(0.468578\pi\) | |||||||
\(644\) | 49.0293i | 0.0761324i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 86.9643 | 0.134620 | ||||||||
\(647\) | − 738.224i | − 1.14099i | −0.821299 | − | 0.570497i | \(-0.806750\pi\) | ||||
0.821299 | − | 0.570497i | \(-0.193250\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 175.691 | 0.270710 | ||||||||
\(650\) | − 160.667i | − 0.247180i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −171.675 | −0.263305 | ||||||||
\(653\) | 69.1073i | 0.105831i | 0.998599 | + | 0.0529153i | \(0.0168513\pi\) | ||||
−0.998599 | + | 0.0529153i | \(0.983149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.3132 | 0.0783408 | ||||||||
\(656\) | − 95.7880i | − 0.146018i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 206.378 | 0.313644 | ||||||||
\(659\) | 427.081i | 0.648075i | 0.946044 | + | 0.324037i | \(0.105040\pi\) | ||||
−0.946044 | + | 0.324037i | \(0.894960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 93.3442 | 0.141217 | 0.0706083 | − | 0.997504i | \(-0.477506\pi\) | ||||
0.0706083 | + | 0.997504i | \(0.477506\pi\) | |||||||
\(662\) | 590.878i | 0.892565i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −226.329 | −0.340857 | ||||||||
\(665\) | 7.19788i | 0.0108239i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 255.223 | 0.382643 | ||||||||
\(668\) | 488.356i | 0.731072i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −71.6193 | −0.106894 | ||||||||
\(671\) | − 272.385i | − 0.405939i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 468.530 | 0.696181 | 0.348091 | − | 0.937461i | \(-0.386830\pi\) | ||||
0.348091 | + | 0.937461i | \(0.386830\pi\) | |||||||
\(674\) | − 90.0423i | − 0.133594i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 295.162 | 0.436630 | ||||||||
\(677\) | 1286.77i | 1.90070i | 0.311183 | + | 0.950350i | \(0.399275\pi\) | ||||
−0.311183 | + | 0.950350i | \(0.600725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 334.414 | 0.492509 | ||||||||
\(680\) | − 28.9183i | − 0.0425269i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 826.313 | 1.21160 | ||||||||
\(683\) | − 478.532i | − 0.700632i | −0.936632 | − | 0.350316i | \(-0.886074\pi\) | ||||
0.936632 | − | 0.350316i | \(-0.113926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −116.874 | −0.170618 | ||||||||
\(686\) | − 26.1916i | − 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 251.576 | 0.365663 | ||||||||
\(689\) | 8.53061i | 0.0123811i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 886.514 | 1.28294 | 0.641471 | − | 0.767147i | \(-0.278324\pi\) | ||||
0.641471 | + | 0.767147i | \(0.278324\pi\) | |||||||
\(692\) | − 289.549i | − 0.418424i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 439.647 | 0.633497 | ||||||||
\(695\) | − 57.7987i | − 0.0831636i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 364.041 | 0.522297 | ||||||||
\(698\) | − 587.758i | − 0.842060i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −129.894 | −0.185563 | ||||||||
\(701\) | − 503.322i | − 0.718006i | −0.933336 | − | 0.359003i | \(-0.883117\pi\) | ||||
0.933336 | − | 0.359003i | \(-0.116883\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.7705 | −0.0167433 | ||||||||
\(704\) | − 106.118i | − 0.150735i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −212.470 | −0.300948 | ||||||||
\(707\) | 315.378i | 0.446080i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −102.128 | −0.144046 | −0.0720229 | − | 0.997403i | \(-0.522945\pi\) | ||||
−0.0720229 | + | 0.997403i | \(0.522945\pi\) | |||||||
\(710\) | − 86.8761i | − 0.122361i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −309.996 | −0.435387 | ||||||||
\(713\) | − 408.139i | − 0.572425i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.2883 | −0.0577459 | ||||||||
\(716\) | 384.516i | 0.537033i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.9318 | −0.0277602 | ||||||||
\(719\) | 375.610i | 0.522406i | 0.965284 | + | 0.261203i | \(0.0841192\pi\) | ||||
−0.965284 | + | 0.261203i | \(0.915881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −349.880 | −0.485270 | ||||||||
\(722\) | 487.391i | 0.675057i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −597.904 | −0.825835 | ||||||||
\(725\) | 676.166i | 0.932643i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −967.189 | −1.33038 | −0.665192 | − | 0.746672i | \(-0.731650\pi\) | ||||
−0.665192 | + | 0.746672i | \(0.731650\pi\) | |||||||
\(728\) | 34.6334i | 0.0475734i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.4840 | 0.0527178 | ||||||||
\(731\) | 956.112i | 1.30795i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.8714 | 0.0612162 | 0.0306081 | − | 0.999531i | \(-0.490256\pi\) | ||||
0.0306081 | + | 0.999531i | \(0.490256\pi\) | |||||||
\(734\) | 63.1148i | 0.0859875i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.4145 | −0.0712153 | ||||||||
\(737\) | − 998.812i | − 1.35524i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 790.331 | 1.06946 | 0.534730 | − | 0.845023i | \(-0.320413\pi\) | ||||
0.534730 | + | 0.845023i | \(0.320413\pi\) | |||||||
\(740\) | 3.91407i | 0.00528928i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.89673 | 0.00929478 | ||||||||
\(743\) | − 198.537i | − 0.267210i | −0.991035 | − | 0.133605i | \(-0.957345\pi\) | ||||
0.991035 | − | 0.133605i | \(-0.0426554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.280190 | 0.000376094 0 | ||||||||
\(746\) | 367.527i | 0.492664i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 403.299 | 0.539169 | ||||||||
\(749\) | − 289.136i | − 0.386030i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 527.315 | 0.702151 | 0.351076 | − | 0.936347i | \(-0.385816\pi\) | ||||
0.351076 | + | 0.936347i | \(0.385816\pi\) | |||||||
\(752\) | 220.627i | 0.293387i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 180.285 | 0.239105 | ||||||||
\(755\) | − 114.369i | − 0.151482i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −986.410 | −1.30305 | −0.651526 | − | 0.758626i | \(-0.725871\pi\) | ||||
−0.651526 | + | 0.758626i | \(0.725871\pi\) | |||||||
\(758\) | 262.565i | 0.346392i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.69485 | −0.0101248 | ||||||||
\(761\) | − 1431.24i | − 1.88073i | −0.340166 | − | 0.940366i | \(-0.610483\pi\) | ||||
0.340166 | − | 0.940366i | \(-0.389517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −488.375 | −0.640073 | ||||||||
\(764\) | 450.710i | 0.589935i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −854.825 | −1.11596 | ||||||||
\(767\) | − 61.2990i | − 0.0799204i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 321.382 | 0.417922 | 0.208961 | − | 0.977924i | \(-0.432992\pi\) | ||||
0.208961 | + | 0.977924i | \(0.432992\pi\) | |||||||
\(770\) | 33.3803i | 0.0433510i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 687.819 | 0.890958 | ||||||||
\(773\) | − 731.933i | − 0.946873i | −0.880828 | − | 0.473436i | \(-0.843013\pi\) | ||||
0.880828 | − | 0.473436i | \(-0.156987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1081.29 | 1.39521 | ||||||||
\(776\) | 357.503i | 0.460700i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −716.465 | −0.920906 | ||||||||
\(779\) | − 96.8674i | − 0.124348i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1211.59 | 1.55133 | ||||||||
\(782\) | − 199.201i | − 0.254732i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | − 98.5381i | − 0.125526i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −790.685 | −1.00468 | −0.502341 | − | 0.864669i | \(-0.667528\pi\) | ||||
−0.502341 | + | 0.864669i | \(0.667528\pi\) | |||||||
\(788\) | 223.733i | 0.283926i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −80.3108 | −0.101659 | ||||||||
\(791\) | − 94.8575i | − 0.119921i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −95.0358 | −0.119843 | ||||||||
\(794\) | 328.615i | 0.413873i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −480.080 | −0.603116 | ||||||||
\(797\) | − 1157.18i | − 1.45192i | −0.687739 | − | 0.725958i | \(-0.741397\pi\) | ||||
0.687739 | − | 0.725958i | \(-0.258603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −838.491 | −1.04943 | ||||||||
\(800\) | − 138.863i | − 0.173578i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 915.660 | 1.14172 | ||||||||
\(803\) | 536.703i | 0.668373i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4875 | 0.0204813 | ||||||||
\(806\) | − 288.302i | − 0.357695i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −337.154 | −0.417269 | ||||||||
\(809\) | − 951.837i | − 1.17656i | −0.808658 | − | 0.588280i | \(-0.799805\pi\) | ||||
0.808658 | − | 0.588280i | \(-0.200195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −737.263 | −0.909079 | −0.454540 | − | 0.890727i | \(-0.650196\pi\) | ||||
−0.454540 | + | 0.890727i | \(0.650196\pi\) | |||||||
\(812\) | − 145.755i | − 0.179501i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −54.5861 | −0.0670591 | ||||||||
\(815\) | 57.7304i | 0.0708349i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 254.411 | 0.311397 | ||||||||
\(818\) | 210.523i | 0.257364i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −32.2114 | −0.0392822 | ||||||||
\(821\) | − 1089.87i | − 1.32750i | −0.747957 | − | 0.663748i | \(-0.768965\pi\) | ||||
0.747957 | − | 0.663748i | \(-0.231035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1121.28 | 1.36243 | 0.681216 | − | 0.732083i | \(-0.261452\pi\) | ||||
0.681216 | + | 0.732083i | \(0.261452\pi\) | |||||||
\(824\) | − 374.037i | − 0.453928i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −49.5583 | −0.0599979 | ||||||||
\(827\) | 1322.75i | 1.59946i | 0.600362 | + | 0.799729i | \(0.295023\pi\) | ||||
−0.600362 | + | 0.799729i | \(0.704977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −303.153 | −0.365686 | −0.182843 | − | 0.983142i | \(-0.558530\pi\) | ||||
−0.182843 | + | 0.983142i | \(0.558530\pi\) | |||||||
\(830\) | 76.1095i | 0.0916982i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.0247 | −0.0445008 | ||||||||
\(833\) | 106.414i | 0.127747i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 164.224 | 0.196675 | ||||||||
\(836\) | − 107.313i | − 0.128365i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 591.549 | 0.705905 | ||||||||
\(839\) | 48.7743i | 0.0581339i | 0.999577 | + | 0.0290669i | \(0.00925360\pi\) | ||||
−0.999577 | + | 0.0290669i | \(0.990746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.2710 | 0.0978252 | ||||||||
\(842\) | − 699.279i | − 0.830498i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −432.587 | −0.512544 | ||||||||
\(845\) | − 99.2564i | − 0.117463i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −145.390 | −0.171653 | ||||||||
\(848\) | 7.37291i | 0.00869447i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 527.746 | 0.620877 | ||||||||
\(851\) | 26.9616i | 0.0316823i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −795.011 | −0.932017 | −0.466009 | − | 0.884780i | \(-0.654308\pi\) | ||||
−0.466009 | + | 0.884780i | \(0.654308\pi\) | |||||||
\(854\) | 76.8334i | 0.0899689i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 309.100 | 0.361098 | ||||||||
\(857\) | 515.098i | 0.601048i | 0.953774 | + | 0.300524i | \(0.0971616\pi\) | ||||
−0.953774 | + | 0.300524i | \(0.902838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 731.616 | 0.851706 | 0.425853 | − | 0.904792i | \(-0.359974\pi\) | ||||
0.425853 | + | 0.904792i | \(0.359974\pi\) | |||||||
\(860\) | − 84.5995i | − 0.0983715i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1137.42 | −1.31951 | ||||||||
\(863\) | − 1675.40i | − 1.94137i | −0.240350 | − | 0.970686i | \(-0.577262\pi\) | ||||
0.240350 | − | 0.970686i | \(-0.422738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −97.3691 | −0.112565 | ||||||||
\(866\) | 1209.71i | 1.39689i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −233.083 | −0.268529 | ||||||||
\(869\) | − 1120.02i | − 1.28887i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −348.488 | −0.400101 | ||||||||
\(872\) | − 522.095i | − 0.598733i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.0052 | −0.0606467 | ||||||||
\(875\) | 88.1659i | 0.100761i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1563.11 | −1.78234 | −0.891170 | − | 0.453670i | \(-0.850115\pi\) | ||||
−0.891170 | + | 0.453670i | \(0.850115\pi\) | |||||||
\(878\) | 1042.01i | 1.18680i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35.6850 | −0.0405512 | ||||||||
\(881\) | 751.835i | 0.853389i | 0.904396 | + | 0.426694i | \(0.140322\pi\) | ||||
−0.904396 | + | 0.426694i | \(0.859678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1005.78 | −1.13905 | −0.569527 | − | 0.821973i | \(-0.692873\pi\) | ||||
−0.569527 | + | 0.821973i | \(0.692873\pi\) | |||||||
\(884\) | − 140.712i | − 0.159176i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −195.195 | −0.220310 | ||||||||
\(887\) | − 1413.71i | − 1.59381i | −0.604106 | − | 0.796904i | \(-0.706470\pi\) | ||||
0.604106 | − | 0.796904i | \(-0.293530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 254.902 | 0.286729 | ||||||||
\(890\) | 104.245i | 0.117129i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −820.801 | −0.920180 | ||||||||
\(893\) | 223.113i | 0.249847i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 129.304 | 0.144474 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 690.760 | 0.769220 | ||||||||
\(899\) | 1213.32i | 1.34963i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.0207 | −0.0310995 | ||||||||
\(902\) | − 449.224i | − 0.498032i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 101.407 | 0.112176 | ||||||||
\(905\) | 201.062i | 0.222168i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −158.562 | −0.174821 | −0.0874104 | − | 0.996172i | \(-0.527859\pi\) | ||||
−0.0874104 | + | 0.996172i | \(0.527859\pi\) | |||||||
\(908\) | 836.132i | 0.920850i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.6465 | 0.0127983 | ||||||||
\(911\) | − 85.1896i | − 0.0935121i | −0.998906 | − | 0.0467561i | \(-0.985112\pi\) | ||||
0.998906 | − | 0.0467561i | \(-0.0148883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1061.43 | −1.16258 | ||||||||
\(914\) | 468.581i | 0.512671i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 76.0735 | 0.0830497 | ||||||||
\(917\) | − 201.860i | − 0.220131i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −89.1494 | −0.0970070 | −0.0485035 | − | 0.998823i | \(-0.515445\pi\) | ||||
−0.0485035 | + | 0.998823i | \(0.515445\pi\) | |||||||
\(920\) | 17.6258i | 0.0191585i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.5408 | −0.0320399 | ||||||||
\(923\) | − 422.725i | − 0.457990i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −71.4299 | −0.0772215 | ||||||||
\(926\) | − 150.511i | − 0.162538i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 155.818 | 0.167908 | ||||||||
\(929\) | − 271.528i | − 0.292280i | −0.989264 | − | 0.146140i | \(-0.953315\pi\) | ||||
0.989264 | − | 0.146140i | \(-0.0466850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.3155 | 0.0304141 | ||||||||
\(932\) | − 202.841i | − 0.217641i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 668.686 | 0.715938 | ||||||||
\(935\) | − 135.620i | − 0.145049i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1238.24 | −1.32149 | −0.660747 | − | 0.750609i | \(-0.729760\pi\) | ||||
−0.660747 | + | 0.750609i | \(0.729760\pi\) | |||||||
\(938\) | 281.741i | 0.300364i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 74.1921 | 0.0789277 | ||||||||
\(941\) | − 796.254i | − 0.846179i | −0.906088 | − | 0.423089i | \(-0.860946\pi\) | ||||
0.906088 | − | 0.423089i | \(-0.139054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −221.885 | −0.235297 | ||||||||
\(944\) | − 52.9800i | − 0.0561229i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1179.84 | 1.24718 | ||||||||
\(947\) | 716.676i | 0.756786i | 0.925645 | + | 0.378393i | \(0.123523\pi\) | ||||
−0.925645 | + | 0.378393i | \(0.876477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 187.257 | 0.197320 | ||||||||
\(950\) | − 140.427i | − 0.147818i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −113.761 | −0.119497 | ||||||||
\(953\) | − 1105.45i | − 1.15996i | −0.814629 | − | 0.579982i | \(-0.803060\pi\) | ||||
0.814629 | − | 0.579982i | \(-0.196940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 151.564 | 0.158706 | ||||||||
\(956\) | 807.418i | 0.844579i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −528.265 | −0.551424 | ||||||||
\(959\) | 459.766i | 0.479422i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 979.278 | 1.01902 | ||||||||
\(962\) | 19.0452i | 0.0197975i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −904.489 | −0.938266 | ||||||||
\(965\) | − 231.299i | − 0.239688i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 176.547 | 0.182572 | 0.0912858 | − | 0.995825i | \(-0.470902\pi\) | ||||
0.0912858 | + | 0.995825i | \(0.470902\pi\) | |||||||
\(968\) | − 155.428i | − 0.160566i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 120.220 | 0.123939 | ||||||||
\(971\) | 1493.78i | 1.53840i | 0.639009 | + | 0.769199i | \(0.279345\pi\) | ||||
−0.639009 | + | 0.769199i | \(0.720655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −227.373 | −0.233682 | ||||||||
\(974\) | 908.908i | 0.933171i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −82.1384 | −0.0841582 | ||||||||
\(977\) | 720.120i | 0.737073i | 0.929613 | + | 0.368536i | \(0.120141\pi\) | ||||
−0.929613 | + | 0.368536i | \(0.879859\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1453.81 | −1.48500 | ||||||||
\(980\) | − 9.41579i | − 0.00960795i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1139.69 | −1.16058 | ||||||||
\(983\) | − 727.718i | − 0.740303i | −0.928971 | − | 0.370151i | \(-0.879306\pi\) | ||||
0.928971 | − | 0.370151i | \(-0.120694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 75.2366 | 0.0763824 | ||||||||
\(986\) | 592.185i | 0.600594i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.4419 | −0.0378967 | ||||||||
\(989\) | − 582.755i | − 0.589236i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −682.016 | −0.688210 | −0.344105 | − | 0.938931i | \(-0.611818\pi\) | ||||
−0.344105 | + | 0.938931i | \(0.611818\pi\) | |||||||
\(992\) | − 249.176i | − 0.251186i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −341.760 | −0.343823 | ||||||||
\(995\) | 161.440i | 0.162252i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −210.841 | −0.211476 | −0.105738 | − | 0.994394i | \(-0.533720\pi\) | ||||
−0.105738 | + | 0.994394i | \(0.533720\pi\) | |||||||
\(998\) | − 577.309i | − 0.578466i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.3.b.c.323.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 378.3.b.c.323.7 | yes | 8 | |
4.3 | odd | 2 | 3024.3.d.h.1457.5 | 8 | |||
9.2 | odd | 6 | 1134.3.q.f.701.6 | 16 | |||
9.4 | even | 3 | 1134.3.q.f.1079.6 | 16 | |||
9.5 | odd | 6 | 1134.3.q.f.1079.3 | 16 | |||
9.7 | even | 3 | 1134.3.q.f.701.3 | 16 | |||
12.11 | even | 2 | 3024.3.d.h.1457.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.3.b.c.323.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
378.3.b.c.323.7 | yes | 8 | 3.2 | odd | 2 | inner | |
1134.3.q.f.701.3 | 16 | 9.7 | even | 3 | |||
1134.3.q.f.701.6 | 16 | 9.2 | odd | 6 | |||
1134.3.q.f.1079.3 | 16 | 9.5 | odd | 6 | |||
1134.3.q.f.1079.6 | 16 | 9.4 | even | 3 | |||
3024.3.d.h.1457.4 | 8 | 12.11 | even | 2 | |||
3024.3.d.h.1457.5 | 8 | 4.3 | odd | 2 |