Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
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: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.43449.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1400) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.31553\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.31553 | −1.91422 | −0.957112 | − | 0.289719i | \(-0.906438\pi\) | ||||
−0.957112 | + | 0.289719i | \(0.906438\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.99276 | 2.66425 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24536 | −1.28002 | −0.640012 | − | 0.768365i | \(-0.721071\pi\) | ||||
−0.640012 | + | 0.768365i | \(0.721071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.10909 | 1.41701 | 0.708503 | − | 0.705708i | \(-0.249371\pi\) | ||||
0.708503 | + | 0.705708i | \(0.249371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.883667 | −0.214321 | −0.107160 | − | 0.994242i | \(-0.534176\pi\) | ||||
−0.107160 | + | 0.994242i | \(0.534176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.54096 | 1.50060 | 0.750299 | − | 0.661099i | \(-0.229909\pi\) | ||||
0.750299 | + | 0.661099i | \(0.229909\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.33547 | −1.11252 | −0.556261 | − | 0.831008i | \(-0.687764\pi\) | ||||
−0.556261 | + | 0.831008i | \(0.687764\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.5536 | −3.18575 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54096 | 0.843234 | 0.421617 | − | 0.906774i | \(-0.361463\pi\) | ||||
0.421617 | + | 0.906774i | \(0.361463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.677224 | −0.121633 | −0.0608165 | − | 0.998149i | \(-0.519370\pi\) | ||||
−0.0608165 | + | 0.998149i | \(0.519370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.0756 | 2.45025 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.52198 | −0.250211 | −0.125106 | − | 0.992143i | \(-0.539927\pi\) | ||||
−0.125106 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.9394 | −2.71247 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.92666 | 0.925589 | 0.462795 | − | 0.886466i | \(-0.346847\pi\) | ||||
0.462795 | + | 0.886466i | \(0.346847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.49796 | 0.838431 | 0.419215 | − | 0.907887i | \(-0.362305\pi\) | ||||
0.419215 | + | 0.907887i | \(0.362305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.26937 | 1.06035 | 0.530174 | − | 0.847889i | \(-0.322127\pi\) | ||||
0.530174 | + | 0.847889i | \(0.322127\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.92983 | 0.410258 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.56813 | −0.352760 | −0.176380 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176380 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.6868 | −2.87248 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.94660 | 1.03456 | 0.517279 | − | 0.855817i | \(-0.326945\pi\) | ||||
0.517279 | + | 0.855817i | \(0.326945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01993 | 1.15488 | 0.577442 | − | 0.816432i | \(-0.304051\pi\) | ||||
0.577442 | + | 0.816432i | \(0.304051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.04395 | −0.371878 | −0.185939 | − | 0.982561i | \(-0.559533\pi\) | ||||
−0.185939 | + | 0.982561i | \(0.559533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6899 | 2.12962 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.39840 | 0.640672 | 0.320336 | − | 0.947304i | \(-0.396204\pi\) | ||||
0.320336 | + | 0.947304i | \(0.396204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.85965 | 0.451738 | 0.225869 | − | 0.974158i | \(-0.427478\pi\) | ||||
0.225869 | + | 0.974158i | \(0.427478\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.704402 | 0.0792514 | 0.0396257 | − | 0.999215i | \(-0.487383\pi\) | ||||
0.0396257 | + | 0.999215i | \(0.487383\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.9059 | 3.43399 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8135 | −1.18693 | −0.593467 | − | 0.804858i | \(-0.702241\pi\) | ||||
−0.593467 | + | 0.804858i | \(0.702241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.0557 | −1.61414 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.40564 | 0.890996 | 0.445498 | − | 0.895283i | \(-0.353027\pi\) | ||||
0.445498 | + | 0.895283i | \(0.353027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.24536 | 0.232833 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.614293 | 0.0623720 | 0.0311860 | − | 0.999514i | \(-0.490072\pi\) | ||||
0.0311860 | + | 0.999514i | \(0.490072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −33.9321 | −3.41031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.65100 | −0.562295 | −0.281148 | − | 0.959664i | \(-0.590715\pi\) | ||||
−0.281148 | + | 0.959664i | \(0.590715\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.34176 | −0.230740 | −0.115370 | − | 0.993323i | \(-0.536805\pi\) | ||||
−0.115370 | + | 0.993323i | \(0.536805\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.992756 | −0.0959734 | −0.0479867 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479867 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.1386 | −1.73736 | −0.868679 | − | 0.495375i | \(-0.835031\pi\) | ||||
−0.868679 | + | 0.495375i | \(0.835031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.04616 | 0.478960 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.22638 | 0.585728 | 0.292864 | − | 0.956154i | \(-0.405392\pi\) | ||||
0.292864 | + | 0.956154i | \(0.405392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40.8357 | 3.77526 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.02306 | 0.638460 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.6500 | −1.77178 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.62382 | 0.144091 | 0.0720454 | − | 0.997401i | \(-0.477047\pi\) | ||||
0.0720454 | + | 0.997401i | \(0.477047\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.2287 | −1.60494 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.28206 | −0.548867 | −0.274433 | − | 0.961606i | \(-0.588490\pi\) | ||||
−0.274433 | + | 0.961606i | \(0.588490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.9122 | −1.53034 | −0.765170 | − | 0.643828i | \(-0.777345\pi\) | ||||
−0.765170 | + | 0.643828i | \(0.777345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.0023 | −1.95103 | −0.975514 | − | 0.219936i | \(-0.929415\pi\) | ||||
−0.975514 | + | 0.219936i | \(0.929415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.1018 | −2.02974 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.6899 | −1.81380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4006 | −0.852051 | −0.426025 | − | 0.904711i | \(-0.640087\pi\) | ||||
−0.426025 | + | 0.904711i | \(0.640087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1720 | 1.72295 | 0.861477 | − | 0.507796i | \(-0.169540\pi\) | ||||
0.861477 | + | 0.507796i | \(0.169540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.06293 | −0.571004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.82074 | 0.624163 | 0.312081 | − | 0.950055i | \(-0.398974\pi\) | ||||
0.312081 | + | 0.950055i | \(0.398974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.51473 | 0.675262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.2811 | −1.74519 | −0.872596 | − | 0.488443i | \(-0.837565\pi\) | ||||
−0.872596 | + | 0.488443i | \(0.837565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8180 | 1.84309 | 0.921546 | − | 0.388270i | \(-0.126927\pi\) | ||||
0.921546 | + | 0.388270i | \(0.126927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.1028 | 1.00791 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 52.2803 | 3.99797 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.29247 | −0.554436 | −0.277218 | − | 0.960807i | \(-0.589412\pi\) | ||||
−0.277218 | + | 0.960807i | \(0.589412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.3472 | −1.98038 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.8452 | 1.33381 | 0.666905 | − | 0.745143i | \(-0.267619\pi\) | ||||
0.666905 | + | 0.745143i | \(0.267619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.62478 | 0.715404 | 0.357702 | − | 0.933836i | \(-0.383560\pi\) | ||||
0.357702 | + | 0.933836i | \(0.383560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.9059 | −2.21071 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.75148 | 0.274335 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4364 | −1.26165 | −0.630825 | − | 0.775925i | \(-0.717284\pi\) | ||||
−0.630825 | + | 0.775925i | \(0.717284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.61208 | −0.188022 | −0.0940110 | − | 0.995571i | \(-0.529969\pi\) | ||||
−0.0940110 | + | 0.995571i | \(0.529969\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.4853 | −1.31703 | −0.658513 | − | 0.752569i | \(-0.728814\pi\) | ||||
−0.658513 | + | 0.752569i | \(0.728814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5274 | 1.52604 | 0.763019 | − | 0.646376i | \(-0.223716\pi\) | ||||
0.763019 | + | 0.646376i | \(0.223716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0923 | 0.711857 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −42.6451 | −2.96404 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.7687 | −1.92080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3200 | 1.26120 | 0.630601 | − | 0.776107i | \(-0.282808\pi\) | ||||
0.630601 | + | 0.776107i | \(0.282808\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.8986 | −1.22639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7968 | −0.864727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.51473 | −0.303694 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.61429 | 0.175066 | 0.0875330 | − | 0.996162i | \(-0.472102\pi\) | ||||
0.0875330 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.02402 | −0.399828 | −0.199914 | − | 0.979813i | \(-0.564066\pi\) | ||||
−0.199914 | + | 0.979813i | \(0.564066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0430 | 0.994069 | 0.497035 | − | 0.867731i | \(-0.334422\pi\) | ||||
0.497035 | + | 0.867731i | \(0.334422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.70124 | 0.111452 | 0.0557260 | − | 0.998446i | \(-0.482253\pi\) | ||||
0.0557260 | + | 0.998446i | \(0.482253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.33547 | −0.151705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8208 | −1.67021 | −0.835105 | − | 0.550091i | \(-0.814593\pi\) | ||||
−0.835105 | + | 0.550091i | \(0.814593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0851 | 0.714052 | 0.357026 | − | 0.934094i | \(-0.383791\pi\) | ||||
0.357026 | + | 0.934094i | \(0.383791\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −52.8085 | −3.38767 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.4183 | 2.12636 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.8525 | 2.27206 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.96558 | −0.439663 | −0.219832 | − | 0.975538i | \(-0.570551\pi\) | ||||
−0.219832 | + | 0.975538i | \(0.570551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.6510 | 1.42405 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.02946 | −0.188973 | −0.0944864 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944864 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.2948 | 2.24659 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.33768 | 0.452460 | 0.226230 | − | 0.974074i | \(-0.427360\pi\) | ||||
0.226230 | + | 0.974074i | \(0.427360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.8692 | −1.70557 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.4142 | −0.939821 | −0.469911 | − | 0.882714i | \(-0.655714\pi\) | ||||
−0.469911 | + | 0.882714i | \(0.655714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.60933 | −0.401488 | −0.200744 | − | 0.979644i | \(-0.564336\pi\) | ||||
−0.200744 | + | 0.979644i | \(0.564336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7579 | −0.646378 | −0.323189 | − | 0.946334i | \(-0.604755\pi\) | ||||
−0.323189 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.41289 | −0.324061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3033 | 1.50947 | 0.754735 | − | 0.656030i | \(-0.227765\pi\) | ||||
0.754735 | + | 0.656030i | \(0.227765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.34500 | 0.377171 | 0.188585 | − | 0.982057i | \(-0.439610\pi\) | ||||
0.188585 | + | 0.982057i | \(0.439610\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2191 | −0.954067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.03671 | −0.119394 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.3589 | −1.18938 | −0.594691 | − | 0.803954i | \(-0.702726\pi\) | ||||
−0.594691 | + | 0.803954i | \(0.702726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 70.2762 | 4.07784 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.2594 | −1.57645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.7361 | 1.07636 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.5695 | −1.68762 | −0.843809 | − | 0.536643i | \(-0.819692\pi\) | ||||
−0.843809 | + | 0.536643i | \(0.819692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.76417 | 0.441688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4831 | 0.707849 | 0.353925 | − | 0.935274i | \(-0.384847\pi\) | ||||
0.353925 | + | 0.935274i | \(0.384847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.05340 | −0.0595418 | −0.0297709 | − | 0.999557i | \(-0.509478\pi\) | ||||
−0.0297709 | + | 0.999557i | \(0.509478\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.61933 | −0.147116 | −0.0735581 | − | 0.997291i | \(-0.523435\pi\) | ||||
−0.0735581 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.2780 | −1.07936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.29152 | 0.183715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.78002 | −0.321609 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 60.1390 | 3.32569 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2739 | 1.05939 | 0.529694 | − | 0.848189i | \(-0.322307\pi\) | ||||
0.529694 | + | 0.848189i | \(0.322307\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.1648 | −0.666626 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2979 | 0.560961 | 0.280481 | − | 0.959860i | \(-0.409506\pi\) | ||||
0.280481 | + | 0.959860i | \(0.409506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.6438 | −1.12121 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.87506 | 0.155693 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3051 | 1.09004 | 0.545018 | − | 0.838424i | \(-0.316523\pi\) | ||||
0.545018 | + | 0.838424i | \(0.316523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.62249 | 0.140379 | 0.0701893 | − | 0.997534i | \(-0.477640\pi\) | ||||
0.0701893 | + | 0.997534i | \(0.477640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −84.5741 | −4.51423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.72526 | −0.464399 | −0.232199 | − | 0.972668i | \(-0.574592\pi\) | ||||
−0.232199 | + | 0.972668i | \(0.574592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0494 | −0.635943 | −0.317971 | − | 0.948100i | \(-0.603002\pi\) | ||||
−0.317971 | + | 0.948100i | \(0.603002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.7841 | 1.25180 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.2852 | −1.22216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.48527 | −0.181930 | −0.0909648 | − | 0.995854i | \(-0.528995\pi\) | ||||
−0.0909648 | + | 0.995854i | \(0.528995\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 47.3704 | 2.46600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.5696 | 1.94528 | 0.972639 | − | 0.232320i | \(-0.0746316\pi\) | ||||
0.972639 | + | 0.232320i | \(0.0746316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.2002 | 1.19487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.48935 | −0.127869 | −0.0639347 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639347 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.38383 | −0.275822 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.4753 | 1.09734 | 0.548668 | − | 0.836041i | \(-0.315135\pi\) | ||||
0.548668 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43.9438 | 2.23379 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3576 | 0.575854 | 0.287927 | − | 0.957652i | \(-0.407034\pi\) | ||||
0.287927 | + | 0.957652i | \(0.407034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.71477 | 0.238436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.8284 | 1.05065 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.9040 | −1.24990 | −0.624948 | − | 0.780666i | \(-0.714880\pi\) | ||||
−0.624948 | + | 0.780666i | \(0.714880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.36989 | 0.467910 | 0.233955 | − | 0.972247i | \(-0.424833\pi\) | ||||
0.233955 | + | 0.972247i | \(0.424833\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46000 | −0.172355 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46133 | 0.320276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0145 | 0.643525 | 0.321762 | − | 0.946820i | \(-0.395725\pi\) | ||||
0.321762 | + | 0.946820i | \(0.395725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 59.3884 | 2.92941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 76.2648 | 3.73470 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.76954 | −0.477273 | −0.238637 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238637 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5881 | −1.05214 | −0.526069 | − | 0.850442i | \(-0.676335\pi\) | ||||
−0.526069 | + | 0.850442i | \(0.676335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 58.1023 | 2.82503 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 71.9136 | 3.47202 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9969 | 0.866879 | 0.433439 | − | 0.901183i | \(-0.357300\pi\) | ||||
0.433439 | + | 0.901183i | \(0.357300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2236 | 1.16411 | 0.582057 | − | 0.813148i | \(-0.302248\pi\) | ||||
0.582057 | + | 0.813148i | \(0.302248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.8991 | −1.66945 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.01490 | 0.0484385 | 0.0242192 | − | 0.999707i | \(-0.492290\pi\) | ||||
0.0242192 | + | 0.999707i | \(0.492290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0095 | 0.665613 | 0.332806 | − | 0.942995i | \(-0.392004\pi\) | ||||
0.332806 | + | 0.942995i | \(0.392004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.4835 | 1.63102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.76134 | −0.460666 | −0.230333 | − | 0.973112i | \(-0.573982\pi\) | ||||
−0.230333 | + | 0.973112i | \(0.573982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.1608 | −1.18478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −70.1965 | −3.29812 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7298 | 1.20359 | 0.601794 | − | 0.798651i | \(-0.294453\pi\) | ||||
0.601794 | + | 0.798651i | \(0.294453\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.6279 | 0.682772 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3115 | −1.17888 | −0.589438 | − | 0.807814i | \(-0.700651\pi\) | ||||
−0.589438 | + | 0.807814i | \(0.700651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8484 | 1.66602 | 0.833008 | − | 0.553261i | \(-0.186617\pi\) | ||||
0.833008 | + | 0.553261i | \(0.186617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.65732 | 0.169241 | 0.0846204 | − | 0.996413i | \(-0.473032\pi\) | ||||
0.0846204 | + | 0.996413i | \(0.473032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.9299 | −1.19479 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.3408 | −1.07321 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.5265 | −0.939842 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.87101 | −0.0854886 | −0.0427443 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427443 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.77591 | −0.354551 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.38255 | 0.425164 | 0.212582 | − | 0.977143i | \(-0.431813\pi\) | ||||
0.212582 | + | 0.977143i | \(0.431813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 73.8738 | 3.34069 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6545 | −1.74445 | −0.872227 | − | 0.489100i | \(-0.837325\pi\) | ||||
−0.872227 | + | 0.489100i | \(0.837325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.01269 | −0.180723 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.10596 | 0.183808 | 0.0919040 | − | 0.995768i | \(-0.470705\pi\) | ||||
0.0919040 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −78.9693 | −3.52809 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.6922 | 1.19015 | 0.595073 | − | 0.803672i | \(-0.297123\pi\) | ||||
0.595073 | + | 0.803672i | \(0.297123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43.4428 | −1.92936 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8094 | 0.567766 | 0.283883 | − | 0.958859i | \(-0.408377\pi\) | ||||
0.283883 | + | 0.958859i | \(0.408377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −108.277 | −4.78053 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.8611 | −1.35727 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.1784 | 1.06131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.8211 | −1.04362 | −0.521811 | − | 0.853061i | \(-0.674743\pi\) | ||||
−0.521811 | + | 0.853061i | \(0.674743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7687 | 0.558335 | 0.279167 | − | 0.960242i | \(-0.409942\pi\) | ||||
0.279167 | + | 0.960242i | \(0.409942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.598440 | 0.0260685 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.46721 | 0.237705 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.5152 | 2.75633 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.2799 | 1.31157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −59.1662 | −2.55321 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6836 | −0.760277 | −0.380138 | − | 0.924930i | \(-0.624124\pi\) | ||||
−0.380138 | + | 0.924930i | \(0.624124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.9113 | −1.36944 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.0580 | 1.02864 | 0.514322 | − | 0.857597i | \(-0.328044\pi\) | ||||
0.514322 | + | 0.857597i | \(0.328044\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 72.0941 | 3.07690 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.7022 | 1.26536 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.86248 | 0.206030 | 0.103015 | − | 0.994680i | \(-0.467151\pi\) | ||||
0.103015 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.0896 | 1.18806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4382 | −0.525139 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.0847 | −0.467163 | −0.233581 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233581 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9571 | −0.710878 | −0.355439 | − | 0.934700i | \(-0.615669\pi\) | ||||
−0.355439 | + | 0.934700i | \(0.615669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3450 | 0.851412 | 0.425706 | − | 0.904862i | \(-0.360026\pi\) | ||||
0.425706 | + | 0.904862i | \(0.360026\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.8108 | 2.41508 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.7643 | 1.73867 | 0.869335 | − | 0.494223i | \(-0.164548\pi\) | ||||
0.869335 | + | 0.494223i | \(0.164548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.66045 | 0.359916 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.9026 | 0.451542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.6858 | −1.59674 | −0.798368 | − | 0.602170i | \(-0.794303\pi\) | ||||
−0.798368 | + | 0.602170i | \(0.794303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.42969 | −0.182522 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 61.2888 | 2.52108 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.5963 | 0.763660 | 0.381830 | − | 0.924233i | \(-0.375294\pi\) | ||||
0.381830 | + | 0.924233i | \(0.375294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −71.3749 | −2.92118 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.0538 | −0.901093 | −0.450547 | − | 0.892753i | \(-0.648771\pi\) | ||||
−0.450547 | + | 0.892753i | \(0.648771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6533 | 0.842465 | 0.421233 | − | 0.906953i | \(-0.361598\pi\) | ||||
0.421233 | + | 0.906953i | \(0.361598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.3296 | −0.990776 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.1712 | −0.981078 | −0.490539 | − | 0.871419i | \(-0.663200\pi\) | ||||
−0.490539 | + | 0.871419i | \(0.663200\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.1399 | 1.50252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.8765 | 1.85293 | 0.926467 | − | 0.376376i | \(-0.122830\pi\) | ||||
0.926467 | + | 0.376376i | \(0.122830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8072 | 1.03896 | 0.519479 | − | 0.854483i | \(-0.326126\pi\) | ||||
0.519479 | + | 0.854483i | \(0.326126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.0431 | 1.73005 | 0.865024 | − | 0.501730i | \(-0.167303\pi\) | ||||
0.865024 | + | 0.501730i | \(0.167303\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 88.3214 | 3.54422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 92.0680 | 3.67684 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.34492 | 0.0536254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.8872 | 0.831508 | 0.415754 | − | 0.909477i | \(-0.363518\pi\) | ||||
0.415754 | + | 0.909477i | \(0.363518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −60.7406 | −2.41422 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.1481 | 1.70691 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.8932 | −1.25971 | −0.629853 | − | 0.776714i | \(-0.716885\pi\) | ||||
−0.629853 | + | 0.776714i | \(0.716885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.850088 | 0.0335242 | 0.0167621 | − | 0.999860i | \(-0.494664\pi\) | ||||
0.0167621 | + | 0.999860i | \(0.494664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.3589 | 1.35079 | 0.675395 | − | 0.737456i | \(-0.263973\pi\) | ||||
0.675395 | + | 0.737456i | \(0.263973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7362 | −1.32426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.0484 | 0.862822 | 0.431411 | − | 0.902155i | \(-0.358016\pi\) | ||||
0.431411 | + | 0.902155i | \(0.358016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.8492 | 1.20354 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9046 | −0.658508 | −0.329254 | − | 0.944241i | \(-0.606797\pi\) | ||||
−0.329254 | + | 0.944241i | \(0.606797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8973 | −0.579437 | −0.289718 | − | 0.957112i | \(-0.593562\pi\) | ||||
−0.289718 | + | 0.957112i | \(0.593562\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9687 | 0.581338 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.2281 | −0.938117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.66777 | −0.335115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.2928 | −1.47828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1490 | 1.00797 | 0.503984 | − | 0.863713i | \(-0.331867\pi\) | ||||
0.503984 | + | 0.863713i | \(0.331867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.4405 | 1.24679 | 0.623394 | − | 0.781908i | \(-0.285753\pi\) | ||||
0.623394 | + | 0.781908i | \(0.285753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.9728 | 0.765360 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.2540 | 1.69333 | 0.846667 | − | 0.532123i | \(-0.178606\pi\) | ||||
0.846667 | + | 0.532123i | \(0.178606\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −49.8755 | −1.90287 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.1208 | −0.499864 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3586 | 1.45923 | 0.729616 | − | 0.683857i | \(-0.239699\pi\) | ||||
0.729616 | + | 0.683857i | \(0.239699\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.23719 | −0.198373 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.64052 | −0.213344 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0696 | 0.493633 | 0.246817 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246817 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.95517 | −0.375466 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.95918 | −0.374025 | −0.187012 | − | 0.982358i | \(-0.559880\pi\) | ||||
−0.187012 | + | 0.982358i | \(0.559880\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.63011 | 0.211146 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.61331 | 0.135319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 85.6097 | 3.19715 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.4595 | −1.76994 | −0.884971 | − | 0.465646i | \(-0.845822\pi\) | ||||
−0.884971 | + | 0.465646i | \(0.845822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.7529 | −1.36686 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.84829 | 0.142725 | 0.0713626 | − | 0.997450i | \(-0.477265\pi\) | ||||
0.0713626 | + | 0.997450i | \(0.477265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 82.3708 | 3.05077 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.85836 | −0.179693 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.26076 | −0.120439 | −0.0602196 | − | 0.998185i | \(-0.519180\pi\) | ||||
−0.0602196 | + | 0.998185i | \(0.519180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9227 | 0.476012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0013 | −0.698975 | −0.349488 | − | 0.936941i | \(-0.613644\pi\) | ||||
−0.349488 | + | 0.936941i | \(0.613644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −110.800 | −4.07032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.02310 | −0.147593 | −0.0737965 | − | 0.997273i | \(-0.523512\pi\) | ||||
−0.0737965 | + | 0.997273i | \(0.523512\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −86.4296 | −3.16229 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.690791 | −0.0252073 | −0.0126037 | − | 0.999921i | \(-0.504012\pi\) | ||||
−0.0126037 | + | 0.999921i | \(0.504012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.0946 | 0.841614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5723 | 0.856751 | 0.428375 | − | 0.903601i | \(-0.359086\pi\) | ||||
0.428375 | + | 0.903601i | \(0.359086\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −75.1000 | −2.72596 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.72338 | −0.207472 | −0.103736 | − | 0.994605i | \(-0.533080\pi\) | ||||
−0.103736 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.5999 | 1.46598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.8252 | 1.25583 | 0.627915 | − | 0.778282i | \(-0.283909\pi\) | ||||
0.627915 | + | 0.778282i | \(0.283909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0443 | 0.361736 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.50204 | 0.233862 | 0.116931 | − | 0.993140i | \(-0.462694\pi\) | ||||
0.116931 | + | 0.993140i | \(0.462694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.7660 | 1.38894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9181 | −0.820075 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −75.1694 | −2.68633 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7306 | −0.917198 | −0.458599 | − | 0.888643i | \(-0.651649\pi\) | ||||
−0.458599 | + | 0.888643i | \(0.651649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.3283 | −0.866110 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.0837 | 1.63648 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.8212 | 1.58765 | 0.793825 | − | 0.608147i | \(-0.208087\pi\) | ||||
0.793825 | + | 0.608147i | \(0.208087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.42370 | −0.227254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 67.1842 | 2.37384 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3856 | −0.578235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 51.1063 | 1.79903 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3839 | 0.892450 | 0.446225 | − | 0.894921i | \(-0.352768\pi\) | ||||
0.446225 | + | 0.894921i | \(0.352768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.86499 | 0.241062 | 0.120531 | − | 0.992710i | \(-0.461540\pi\) | ||||
0.120531 | + | 0.992710i | \(0.461540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9135 | 0.768539 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.9619 | 1.25815 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.2507 | 1.09066 | 0.545328 | − | 0.838223i | \(-0.316405\pi\) | ||||
0.545328 | + | 0.838223i | \(0.316405\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4667 | −0.434562 | −0.217281 | − | 0.976109i | \(-0.569719\pi\) | ||||
−0.217281 | + | 0.976109i | \(0.569719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0893 | 0.698572 | 0.349286 | − | 0.937016i | \(-0.386424\pi\) | ||||
0.349286 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.2767 | 1.67672 | 0.838359 | − | 0.545118i | \(-0.183515\pi\) | ||||
0.838359 | + | 0.545118i | \(0.183515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.6681 | 1.23731 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.2105 | 0.387492 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.1020 | 1.93686 | 0.968429 | − | 0.249291i | \(-0.0801975\pi\) | ||||
0.968429 | + | 0.249291i | \(0.0801975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.37972 | −0.288956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −83.8940 | −2.88946 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.0370 | −0.721989 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.12045 | 0.278365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4092 | −0.561840 | −0.280920 | − | 0.959731i | \(-0.590640\pi\) | ||||
−0.280920 | + | 0.959731i | \(0.590640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.47307 | −0.152797 | −0.0763985 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763985 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5116 | 0.495128 | 0.247564 | − | 0.968871i | \(-0.420370\pi\) | ||||
0.247564 | + | 0.968871i | \(0.420370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5859 | 0.496508 | 0.248254 | − | 0.968695i | \(-0.420143\pi\) | ||||
0.248254 | + | 0.968695i | \(0.420143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 53.7751 | 1.82630 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.99044 | −0.101444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.5518 | −0.526953 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.90989 | 0.166175 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.6586 | −1.27164 | −0.635821 | − | 0.771837i | \(-0.719338\pi\) | ||||
−0.635821 | + | 0.771837i | \(0.719338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 67.5007 | 2.27674 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4007 | 1.49590 | 0.747949 | − | 0.663757i | \(-0.231039\pi\) | ||||
0.747949 | + | 0.663757i | \(0.231039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.7213 | 1.74056 | 0.870279 | − | 0.492558i | \(-0.163938\pi\) | ||||
0.870279 | + | 0.492558i | \(0.163938\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.489461 | 0.0164345 | 0.00821725 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821725 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −131.207 | −4.39558 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.5487 | 1.59116 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 90.3794 | 3.01768 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.07524 | −0.102565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.26937 | 0.0756038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.4541 | −1.44287 | −0.721435 | − | 0.692483i | \(-0.756517\pi\) | ||||
−0.721435 | + | 0.692483i | \(0.756517\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45.1671 | −1.49810 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.77049 | −0.158054 | −0.0790268 | − | 0.996872i | \(-0.525181\pi\) | ||||
−0.0790268 | + | 0.996872i | \(0.525181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.9071 | 1.51930 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.2350 | −1.36022 | −0.680109 | − | 0.733111i | \(-0.738068\pi\) | ||||
−0.680109 | + | 0.733111i | \(0.738068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 98.0385 | 3.23048 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.5809 | 0.907836 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.7171 | −0.614750 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.8922 | −1.04635 | −0.523175 | − | 0.852225i | \(-0.675253\pi\) | ||||
−0.523175 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −41.3880 | −1.35498 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2518 | 0.759602 | 0.379801 | − | 0.925068i | \(-0.375992\pi\) | ||||
0.379801 | + | 0.925068i | \(0.375992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.49259 | 0.113976 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6519 | −0.868828 | −0.434414 | − | 0.900713i | \(-0.643044\pi\) | ||||
−0.434414 | + | 0.900713i | \(0.643044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.6215 | −1.02974 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.21410 | −0.169435 | −0.0847177 | − | 0.996405i | \(-0.526999\pi\) | ||||
−0.0847177 | + | 0.996405i | \(0.526999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7193 | 0.640116 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.68447 | 0.281613 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.8674 | −1.22664 | −0.613322 | − | 0.789833i | \(-0.710167\pi\) | ||||
−0.613322 | + | 0.789833i | \(0.710167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 63.9168 | 2.06614 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5414 | −0.985205 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.93486 | −0.255697 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.7266 | 0.570049 | 0.285024 | − | 0.958520i | \(-0.407998\pi\) | ||||
0.285024 | + | 0.958520i | \(0.407998\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.1639 | 0.615632 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.7641 | −0.345436 | −0.172718 | − | 0.984971i | \(-0.555255\pi\) | ||||
−0.172718 | + | 0.984971i | \(0.555255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.5777 | 1.26620 | 0.633101 | − | 0.774069i | \(-0.281782\pi\) | ||||
0.633101 | + | 0.774069i | \(0.281782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.6850 | −1.14050 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −144.977 | −4.62876 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.9761 | −0.987983 | −0.493991 | − | 0.869467i | \(-0.664463\pi\) | ||||
−0.493991 | + | 0.869467i | \(0.664463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.3342 | −0.932773 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.1892 | −1.05429 | −0.527145 | − | 0.849775i | \(-0.676738\pi\) | ||||
−0.527145 | + | 0.849775i | \(0.676738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −63.9031 | −2.02790 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.83435 | −0.279787 | −0.139893 | − | 0.990167i | \(-0.544676\pi\) | ||||
−0.139893 | + | 0.990167i | \(0.544676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.1942 | 0.797111 |
(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 | 9800.2.a.ck.1.1 | 4 | ||
5.4 | even | 2 | 9800.2.a.cu.1.4 | 4 | |||
7.3 | odd | 6 | 1400.2.q.l.401.1 | ✓ | 8 | ||
7.5 | odd | 6 | 1400.2.q.l.1201.1 | yes | 8 | ||
7.6 | odd | 2 | 9800.2.a.ct.1.4 | 4 | |||
35.3 | even | 12 | 1400.2.bh.j.849.8 | 16 | |||
35.12 | even | 12 | 1400.2.bh.j.249.8 | 16 | |||
35.17 | even | 12 | 1400.2.bh.j.849.1 | 16 | |||
35.19 | odd | 6 | 1400.2.q.m.1201.4 | yes | 8 | ||
35.24 | odd | 6 | 1400.2.q.m.401.4 | yes | 8 | ||
35.33 | even | 12 | 1400.2.bh.j.249.1 | 16 | |||
35.34 | odd | 2 | 9800.2.a.cj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.l.401.1 | ✓ | 8 | 7.3 | odd | 6 | ||
1400.2.q.l.1201.1 | yes | 8 | 7.5 | odd | 6 | ||
1400.2.q.m.401.4 | yes | 8 | 35.24 | odd | 6 | ||
1400.2.q.m.1201.4 | yes | 8 | 35.19 | odd | 6 | ||
1400.2.bh.j.249.1 | 16 | 35.33 | even | 12 | |||
1400.2.bh.j.249.8 | 16 | 35.12 | even | 12 | |||
1400.2.bh.j.849.1 | 16 | 35.17 | even | 12 | |||
1400.2.bh.j.849.8 | 16 | 35.3 | even | 12 | |||
9800.2.a.cj.1.1 | 4 | 35.34 | odd | 2 | |||
9800.2.a.ck.1.1 | 4 | 1.1 | even | 1 | trivial | ||
9800.2.a.ct.1.4 | 4 | 7.6 | odd | 2 | |||
9800.2.a.cu.1.4 | 4 | 5.4 | even | 2 |