Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.67513 | 0.749141 | 0.374571 | − | 0.927198i | \(-0.377790\pi\) | ||||
0.374571 | + | 0.927198i | \(0.377790\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35026 | 1.26628 | 0.633140 | − | 0.774037i | \(-0.281766\pi\) | ||||
0.633140 | + | 0.774037i | \(0.281766\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19394 | 0.359985 | 0.179993 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179993 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.96239 | −0.821619 | −0.410809 | − | 0.911721i | \(-0.634754\pi\) | ||||
−0.410809 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.324869 | −0.0787923 | −0.0393962 | − | 0.999224i | \(-0.512543\pi\) | ||||
−0.0393962 | + | 0.999224i | \(0.512543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61213 | −0.369847 | −0.184924 | − | 0.982753i | \(-0.559204\pi\) | ||||
−0.184924 | + | 0.982753i | \(0.559204\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.92478 | −1.23540 | −0.617701 | − | 0.786413i | \(-0.711936\pi\) | ||||
−0.617701 | + | 0.786413i | \(0.711936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.19394 | −0.438787 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.70052 | 1.24426 | 0.622128 | − | 0.782916i | \(-0.286268\pi\) | ||||
0.622128 | + | 0.782916i | \(0.286268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.31265 | 1.49300 | 0.746498 | − | 0.665388i | \(-0.231734\pi\) | ||||
0.746498 | + | 0.665388i | \(0.231734\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.61213 | 0.948623 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.574515 | −0.0944498 | −0.0472249 | − | 0.998884i | \(-0.515038\pi\) | ||||
−0.0472249 | + | 0.998884i | \(0.515038\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.06300 | 0.946882 | 0.473441 | − | 0.880825i | \(-0.343012\pi\) | ||||
0.473441 | + | 0.880825i | \(0.343012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36248 | −0.207776 | −0.103888 | − | 0.994589i | \(-0.533128\pi\) | ||||
−0.103888 | + | 0.994589i | \(0.533128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19394 | −0.757614 | −0.378807 | − | 0.925476i | \(-0.623665\pi\) | ||||
−0.378807 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22425 | 0.603465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2120 | 1.54009 | 0.770046 | − | 0.637989i | \(-0.220233\pi\) | ||||
0.770046 | + | 0.637989i | \(0.220233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.64974 | 0.605344 | 0.302672 | − | 0.953095i | \(-0.402121\pi\) | ||||
0.302672 | + | 0.953095i | \(0.402121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.806063 | −0.103206 | −0.0516029 | − | 0.998668i | \(-0.516433\pi\) | ||||
−0.0516029 | + | 0.998668i | \(0.516433\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.96239 | −0.615509 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28726 | 0.645941 | 0.322971 | − | 0.946409i | \(-0.395318\pi\) | ||||
0.322971 | + | 0.946409i | \(0.395318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.61213 | −0.422767 | −0.211384 | − | 0.977403i | \(-0.567797\pi\) | ||||
−0.211384 | + | 0.977403i | \(0.567797\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1744 | 1.36973 | 0.684865 | − | 0.728670i | \(-0.259861\pi\) | ||||
0.684865 | + | 0.728670i | \(0.259861\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6629 | 1.28017 | 0.640085 | − | 0.768304i | \(-0.278899\pi\) | ||||
0.640085 | + | 0.768304i | \(0.278899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.544198 | −0.0590266 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.7005 | 1.13425 | 0.567127 | − | 0.823631i | \(-0.308055\pi\) | ||||
0.567127 | + | 0.823631i | \(0.308055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.92478 | −1.04040 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.70052 | −0.277068 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0508 | 1.62971 | 0.814855 | − | 0.579665i | \(-0.196816\pi\) | ||||
0.814855 | + | 0.579665i | \(0.196816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.98778 | 0.197792 | 0.0988958 | − | 0.995098i | \(-0.468469\pi\) | ||||
0.0988958 | + | 0.995098i | \(0.468469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.02539 | 0.692233 | 0.346116 | − | 0.938192i | \(-0.387500\pi\) | ||||
0.346116 | + | 0.938192i | \(0.387500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3430 | 0.999892 | 0.499946 | − | 0.866056i | \(-0.333353\pi\) | ||||
0.499946 | + | 0.866056i | \(0.333353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35026 | 0.129332 | 0.0646658 | − | 0.997907i | \(-0.479402\pi\) | ||||
0.0646658 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4133 | 1.07367 | 0.536835 | − | 0.843687i | \(-0.319620\pi\) | ||||
0.536835 | + | 0.843687i | \(0.319620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.92478 | −0.925490 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.08840 | −0.0997732 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.57452 | −0.870410 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0508 | −1.07785 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.962389 | −0.0853982 | −0.0426991 | − | 0.999088i | \(-0.513596\pi\) | ||||
−0.0426991 | + | 0.999088i | \(0.513596\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.27504 | −0.810364 | −0.405182 | − | 0.914236i | \(-0.632792\pi\) | ||||
−0.405182 | + | 0.914236i | \(0.632792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.40105 | −0.468330 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.64974 | 0.397254 | 0.198627 | − | 0.980075i | \(-0.436352\pi\) | ||||
0.198627 | + | 0.980075i | \(0.436352\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6751 | −1.49919 | −0.749593 | − | 0.661900i | \(-0.769751\pi\) | ||||
−0.749593 | + | 0.661900i | \(0.769751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.53690 | −0.295771 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2243 | 0.932124 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47390 | 0.448439 | 0.224220 | − | 0.974539i | \(-0.428017\pi\) | ||||
0.224220 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.33804 | −0.759919 | −0.379960 | − | 0.925003i | \(-0.624062\pi\) | ||||
−0.379960 | + | 0.925003i | \(0.624062\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.9248 | 1.11847 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0508 | −1.60023 | −0.800113 | − | 0.599849i | \(-0.795227\pi\) | ||||
−0.800113 | + | 0.599849i | \(0.795227\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8496 | −1.56436 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3004 | 1.43340 | 0.716700 | − | 0.697381i | \(-0.245652\pi\) | ||||
0.716700 | + | 0.697381i | \(0.245652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.22425 | −0.324943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.6121 | 1.33903 | 0.669513 | − | 0.742801i | \(-0.266503\pi\) | ||||
0.669513 | + | 0.742801i | \(0.266503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.35026 | −0.555628 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.3733 | −1.22380 | −0.611898 | − | 0.790936i | \(-0.709594\pi\) | ||||
−0.611898 | + | 0.790936i | \(0.709594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.43136 | 0.106392 | 0.0531962 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531962 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.962389 | −0.0707562 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.387873 | −0.0283641 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50659 | −0.109013 | −0.0545064 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545064 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.911603 | −0.0656186 | −0.0328093 | − | 0.999462i | \(-0.510445\pi\) | ||||
−0.0328093 | + | 0.999462i | \(0.510445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4641 | −0.959274 | −0.479637 | − | 0.877467i | \(-0.659232\pi\) | ||||
−0.479637 | + | 0.877467i | \(0.659232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3634 | −1.30175 | −0.650875 | − | 0.759185i | \(-0.725598\pi\) | ||||
−0.650875 | + | 0.759185i | \(0.725598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.4485 | 1.57558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1563 | 0.709349 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.92478 | −0.133140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.01317 | −0.482807 | −0.241403 | − | 0.970425i | \(-0.577608\pi\) | ||||
−0.241403 | + | 0.970425i | \(0.577608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.28233 | −0.155654 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.8496 | 1.89055 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.962389 | 0.0647373 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2750 | 1.42468 | 0.712341 | − | 0.701834i | \(-0.247635\pi\) | ||||
0.712341 | + | 0.701834i | \(0.247635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.03761 | 0.201613 | 0.100807 | − | 0.994906i | \(-0.467858\pi\) | ||||
0.100807 | + | 0.994906i | \(0.467858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8061 | −1.11058 | −0.555288 | − | 0.831658i | \(-0.687392\pi\) | ||||
−0.555288 | + | 0.831658i | \(0.687392\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.43866 | 0.552835 | 0.276417 | − | 0.961038i | \(-0.410853\pi\) | ||||
0.276417 | + | 0.961038i | \(0.410853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.70052 | −0.567560 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.2809 | −1.76466 | −0.882328 | − | 0.470635i | \(-0.844025\pi\) | ||||
−0.882328 | + | 0.470635i | \(0.844025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.9380 | −1.47756 | −0.738782 | − | 0.673945i | \(-0.764599\pi\) | ||||
−0.738782 | + | 0.673945i | \(0.764599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.07618 | 0.452080 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.77575 | 0.303873 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.11283 | 0.322719 | 0.161360 | − | 0.986896i | \(-0.448412\pi\) | ||||
0.161360 | + | 0.986896i | \(0.448412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.07381 | −0.444727 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.5623 | −1.03313 | −0.516564 | − | 0.856249i | \(-0.672789\pi\) | ||||
−0.516564 | + | 0.856249i | \(0.672789\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.92478 | −0.119600 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.8872 | 1.65793 | 0.828967 | − | 0.559298i | \(-0.188929\pi\) | ||||
0.828967 | + | 0.559298i | \(0.188929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.7816 | 1.15375 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1890 | 1.10900 | 0.554502 | − | 0.832183i | \(-0.312909\pi\) | ||||
0.554502 | + | 0.832183i | \(0.312909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.5623 | 1.12758 | 0.563790 | − | 0.825918i | \(-0.309343\pi\) | ||||
0.563790 | + | 0.825918i | \(0.309343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.61942 | −0.157957 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.09825 | 0.0659872 | 0.0329936 | − | 0.999456i | \(-0.489496\pi\) | ||||
0.0329936 | + | 0.999456i | \(0.489496\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1114 | 0.841817 | 0.420908 | − | 0.907103i | \(-0.361711\pi\) | ||||
0.420908 | + | 0.907103i | \(0.361711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2374 | 1.08410 | 0.542051 | − | 0.840345i | \(-0.317648\pi\) | ||||
0.542051 | + | 0.840345i | \(0.317648\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.3127 | 1.19902 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8945 | −0.993792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.92478 | −0.346129 | −0.173065 | − | 0.984910i | \(-0.555367\pi\) | ||||
−0.173065 | + | 0.984910i | \(0.555367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.78892 | 0.453488 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5515 | 1.01503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.56467 | −0.263103 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.35026 | −0.0773158 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0484 | −0.573493 | −0.286747 | − | 0.958006i | \(-0.592574\pi\) | ||||
−0.286747 | + | 0.958006i | \(0.592574\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.8872 | 1.52463 | 0.762316 | − | 0.647205i | \(-0.224062\pi\) | ||||
0.762316 | + | 0.647205i | \(0.224062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.44851 | 0.477538 | 0.238769 | − | 0.971076i | \(-0.423256\pi\) | ||||
0.238769 | + | 0.971076i | \(0.423256\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.83638 | 0.271638 | 0.135819 | − | 0.990734i | \(-0.456633\pi\) | ||||
0.135819 | + | 0.990734i | \(0.456633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.523730 | 0.0291411 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.49929 | 0.360516 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.4010 | −0.959351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.787965 | 0.0433105 | 0.0216552 | − | 0.999765i | \(-0.493106\pi\) | ||||
0.0216552 | + | 0.999765i | \(0.493106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.85685 | 0.483901 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4241 | −0.676782 | −0.338391 | − | 0.941006i | \(-0.609883\pi\) | ||||
−0.338391 | + | 0.941006i | \(0.609883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.92478 | 0.537457 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.29948 | −0.502125 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.27504 | −0.283179 | −0.141589 | − | 0.989925i | \(-0.545221\pi\) | ||||
−0.141589 | + | 0.989925i | \(0.545221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5745 | −0.887213 | −0.443607 | − | 0.896222i | \(-0.646301\pi\) | ||||
−0.443607 | + | 0.896222i | \(0.646301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.58769 | 0.297403 | 0.148701 | − | 0.988882i | \(-0.452491\pi\) | ||||
0.148701 | + | 0.988882i | \(0.452491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.70052 | 0.355627 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5501 | 0.556812 | 0.278406 | − | 0.960464i | \(-0.410194\pi\) | ||||
0.278406 | + | 0.960464i | \(0.410194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4010 | −0.863213 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.05079 | −0.316713 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.6107 | −1.18027 | −0.590135 | − | 0.807305i | \(-0.700925\pi\) | ||||
−0.590135 | + | 0.807305i | \(0.700925\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.5633 | 1.95019 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.66291 | 0.0861023 | 0.0430512 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430512 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.8496 | −1.02230 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8618 | 0.917498 | 0.458749 | − | 0.888566i | \(-0.348298\pi\) | ||||
0.458749 | + | 0.888566i | \(0.348298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.67021 | −0.238636 | −0.119318 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119318 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.70052 | 0.341490 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.78797 | −0.141355 | −0.0706777 | − | 0.997499i | \(-0.522516\pi\) | ||||
−0.0706777 | + | 0.997499i | \(0.522516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.92478 | 0.0973402 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.3938 | 1.02612 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0303 | 0.603784 | 0.301892 | − | 0.953342i | \(-0.402382\pi\) | ||||
0.301892 | + | 0.953342i | \(0.402382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.3235 | 1.96372 | 0.981860 | − | 0.189608i | \(-0.0607218\pi\) | ||||
0.981860 | + | 0.189608i | \(0.0607218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.6253 | −1.22667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.685935 | −0.0340005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.956509 | −0.0472963 | −0.0236482 | − | 0.999720i | \(-0.507528\pi\) | ||||
−0.0236482 | + | 0.999720i | \(0.507528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5778 | 0.766535 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.5369 | 0.959029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.49341 | −0.317224 | −0.158612 | − | 0.987341i | \(-0.550702\pi\) | ||||
−0.158612 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.8251 | −1.45359 | −0.726794 | − | 0.686856i | \(-0.758990\pi\) | ||||
−0.726794 | + | 0.686856i | \(0.758990\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.712742 | 0.0345731 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.70052 | −0.130687 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.2882 | −1.16992 | −0.584961 | − | 0.811061i | \(-0.698890\pi\) | ||||
−0.584961 | + | 0.811061i | \(0.698890\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2677 | −0.877892 | −0.438946 | − | 0.898513i | \(-0.644648\pi\) | ||||
−0.438946 | + | 0.898513i | \(0.644648\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.55149 | 0.456910 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.5623 | −0.981385 | −0.490692 | − | 0.871333i | \(-0.663256\pi\) | ||||
−0.490692 | + | 0.871333i | \(0.663256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.0771 | 1.90412 | 0.952061 | − | 0.305908i | \(-0.0989601\pi\) | ||||
0.952061 | + | 0.305908i | \(0.0989601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9248 | 0.849716 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4993 | −0.967421 | −0.483711 | − | 0.875228i | \(-0.660711\pi\) | ||||
−0.483711 | + | 0.875228i | \(0.660711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.23884 | 0.340864 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.6253 | −0.779406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4763 | −1.00462 | −0.502309 | − | 0.864688i | \(-0.667516\pi\) | ||||
−0.502309 | + | 0.864688i | \(0.667516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.48612 | −0.0692155 | −0.0346077 | − | 0.999401i | \(-0.511018\pi\) | ||||
−0.0346077 | + | 0.999401i | \(0.511018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.6982 | −1.14782 | −0.573910 | − | 0.818918i | \(-0.694574\pi\) | ||||
−0.573910 | + | 0.818918i | \(0.694574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.14903 | −0.238269 | −0.119134 | − | 0.992878i | \(-0.538012\pi\) | ||||
−0.119134 | + | 0.992878i | \(0.538012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7137 | 0.817943 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.62672 | −0.0747964 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.53690 | 0.162284 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8773 | 0.953909 | 0.476954 | − | 0.878928i | \(-0.341741\pi\) | ||||
0.476954 | + | 0.878928i | \(0.341741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.70194 | 0.0776017 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.8872 | 1.22088 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8373 | 0.536401 | 0.268200 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268200 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3576 | 0.557689 | 0.278844 | − | 0.960336i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960336i | \(0.410049\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.17679 | −0.0980378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4010 | 0.601119 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5853 | 1.05582 | 0.527912 | − | 0.849299i | \(-0.322975\pi\) | ||||
0.527912 | + | 0.849299i | \(0.322975\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0449056 | 0.00200224 | 0.00100112 | − | 0.999999i | \(-0.499681\pi\) | ||||
0.00100112 | + | 0.999999i | \(0.499681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.32979 | 0.148174 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.4387 | 1.08322 | 0.541612 | − | 0.840628i | \(-0.317814\pi\) | ||||
0.541612 | + | 0.840628i | \(0.317814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1016 | −0.535342 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.7685 | 0.518580 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.20123 | −0.272730 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2252 | −0.798461 | −0.399230 | − | 0.916851i | \(-0.630723\pi\) | ||||
−0.399230 | + | 0.916851i | \(0.630723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.3112 | 1.28169 | 0.640845 | − | 0.767670i | \(-0.278584\pi\) | ||||
0.640845 | + | 0.767670i | \(0.278584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.70052 | −0.117637 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.1030 | 0.526217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.9610 | −0.777976 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3258 | 0.749061 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.04349 | 0.217239 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.9887 | 1.07435 | 0.537175 | − | 0.843471i | \(-0.319492\pi\) | ||||
0.537175 | + | 0.843471i | \(0.319492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.26187 | 0.0968877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.10062 | −0.0470589 | −0.0235295 | − | 0.999723i | \(-0.507490\pi\) | ||||
−0.0235295 | + | 0.999723i | \(0.507490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.8021 | −0.460185 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.7875 | 1.73446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.4993 | −1.88550 | −0.942748 | − | 0.333507i | \(-0.891768\pi\) | ||||
−0.942748 | + | 0.333507i | \(0.891768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.03620 | 0.170713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.4372 | 1.57779 | 0.788896 | − | 0.614527i | \(-0.210653\pi\) | ||||
0.788896 | + | 0.614527i | \(0.210653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1187 | 0.804330 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.1744 | −1.09729 | −0.548644 | − | 0.836056i | \(-0.684856\pi\) | ||||
−0.548644 | + | 0.836056i | \(0.684856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.92715 | 0.0806486 | 0.0403243 | − | 0.999187i | \(-0.487161\pi\) | ||||
0.0403243 | + | 0.999187i | \(0.487161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.9986 | 0.542078 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4934 | −0.686630 | −0.343315 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343315 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.0738 | 1.62105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3865 | 0.554410 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2130 | 0.916828 | 0.458414 | − | 0.888739i | \(-0.348418\pi\) | ||||
0.458414 | + | 0.888739i | \(0.348418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4010 | −0.552181 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.90080 | −0.160187 | −0.0800933 | − | 0.996787i | \(-0.525522\pi\) | ||||
−0.0800933 | + | 0.996787i | \(0.525522\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.82321 | −0.0747442 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.4010 | 1.20129 | 0.600647 | − | 0.799514i | \(-0.294910\pi\) | ||||
0.600647 | + | 0.799514i | \(0.294910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8496 | 0.564935 | 0.282468 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282468 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.0386 | −0.652060 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2022 | 0.779393 | 0.389696 | − | 0.920943i | \(-0.372580\pi\) | ||||
0.389696 | + | 0.920943i | \(0.372580\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.3865 | 0.622469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.1319 | 0.490002 | 0.245001 | − | 0.969523i | \(-0.421212\pi\) | ||||
0.245001 | + | 0.969523i | \(0.421212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0620 | 0.445341 | 0.222671 | − | 0.974894i | \(-0.428523\pi\) | ||||
0.222671 | + | 0.974894i | \(0.428523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.3150 | −0.414596 | −0.207298 | − | 0.978278i | \(-0.566467\pi\) | ||||
−0.207298 | + | 0.978278i | \(0.566467\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.8496 | 1.43628 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.21696 | −0.368678 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.186642 | 0.00744192 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4847 | −1.05434 | −0.527170 | − | 0.849760i | \(-0.676747\pi\) | ||||
−0.527170 | + | 0.849760i | \(0.676747\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.61213 | −0.0639753 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.5139 | −0.495818 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.3136 | −1.31581 | −0.657904 | − | 0.753102i | \(-0.728557\pi\) | ||||
−0.657904 | + | 0.753102i | \(0.728557\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9224 | 0.943408 | 0.471704 | − | 0.881757i | \(-0.343639\pi\) | ||||
0.471704 | + | 0.881757i | \(0.343639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.8021 | −1.36821 | −0.684106 | − | 0.729383i | \(-0.739807\pi\) | ||||
−0.684106 | + | 0.729383i | \(0.739807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.55149 | 0.217915 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.1622 | −0.945540 | −0.472770 | − | 0.881186i | \(-0.656746\pi\) | ||||
−0.472770 | + | 0.881186i | \(0.656746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5369 | −0.607077 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1721 | −0.396247 | −0.198123 | − | 0.980177i | \(-0.563485\pi\) | ||||
−0.198123 | + | 0.980177i | \(0.563485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.2736 | −1.56646 | −0.783231 | − | 0.621731i | \(-0.786430\pi\) | ||||
−0.783231 | + | 0.621731i | \(0.786430\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.04746 | −0.350845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.6991 | −1.53716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.962389 | −0.0371526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1490 | −0.583952 | −0.291976 | − | 0.956426i | \(-0.594313\pi\) | ||||
−0.291976 | + | 0.956426i | \(0.594313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6531 | −0.832195 | −0.416097 | − | 0.909320i | \(-0.636602\pi\) | ||||
−0.416097 | + | 0.909320i | \(0.636602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.7743 | 2.06367 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.63656 | −0.368733 | −0.184366 | − | 0.982858i | \(-0.559023\pi\) | ||||
−0.184366 | + | 0.982858i | \(0.559023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.78892 | 0.297599 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.2144 | −1.26537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4001 | −0.395638 | −0.197819 | − | 0.980239i | \(-0.563386\pi\) | ||||
−0.197819 | + | 0.980239i | \(0.563386\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.6082 | −1.12310 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.96968 | −0.0746071 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.6615 | −1.53576 | −0.767882 | − | 0.640592i | \(-0.778689\pi\) | ||||
−0.767882 | + | 0.640592i | \(0.778689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.926192 | 0.0349320 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.65959 | 0.250460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7367 | −1.07923 | −0.539615 | − | 0.841912i | \(-0.681430\pi\) | ||||
−0.539615 | + | 0.841912i | \(0.681430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −49.2506 | −1.84445 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.92478 | −0.221574 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8496 | 0.441914 | 0.220957 | − | 0.975284i | \(-0.429082\pi\) | ||||
0.220957 | + | 0.975284i | \(0.429082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.5369 | 0.876560 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.7005 | −0.545964 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.13681 | −0.116338 | −0.0581690 | − | 0.998307i | \(-0.518526\pi\) | ||||
−0.0581690 | + | 0.998307i | \(0.518526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.442628 | 0.0163712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1939 | 0.561201 | 0.280600 | − | 0.959825i | \(-0.409466\pi\) | ||||
0.280600 | + | 0.959825i | \(0.409466\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.31265 | 0.232529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9271 | 0.733032 | 0.366516 | − | 0.930412i | \(-0.380551\pi\) | ||||
0.366516 | + | 0.930412i | \(0.380551\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1490 | 0.482391 | 0.241196 | − | 0.970477i | \(-0.422460\pi\) | ||||
0.241196 | + | 0.970477i | \(0.422460\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.16950 | 0.335944 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.6516 | 1.26614 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2252 | 0.883990 | 0.441995 | − | 0.897017i | \(-0.354271\pi\) | ||||
0.441995 | + | 0.897017i | \(0.354271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.6424 | −0.569287 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3272 | 0.593424 | 0.296712 | − | 0.954967i | \(-0.404110\pi\) | ||||
0.296712 | + | 0.954967i | \(0.404110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.2652 | −1.71336 | −0.856681 | − | 0.515847i | \(-0.827477\pi\) | ||||
−0.856681 | + | 0.515847i | \(0.827477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.52373 | 0.163770 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.7743 | −0.497362 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1504 | 0.366034 | 0.183017 | − | 0.983110i | \(-0.441414\pi\) | ||||
0.183017 | + | 0.983110i | \(0.441414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.0616 | −0.901403 | −0.450701 | − | 0.892675i | \(-0.648826\pi\) | ||||
−0.450701 | + | 0.892675i | \(0.648826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.2374 | −0.655108 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.77433 | −0.350202 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.77575 | 0.170890 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.5877 | −1.19880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5491 | 0.910728 | 0.455364 | − | 0.890305i | \(-0.349509\pi\) | ||||
0.455364 | + | 0.890305i | \(0.349509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.2374 | 1.35957 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.38787 | 0.0847959 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.2384 | −1.17736 | −0.588682 | − | 0.808365i | \(-0.700353\pi\) | ||||
−0.588682 | + | 0.808365i | \(0.700353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.68735 | 0.0596941 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.31265 | −0.152190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.2506 | −1.17193 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0997 | −0.355085 | −0.177543 | − | 0.984113i | \(-0.556815\pi\) | ||||
−0.177543 | + | 0.984113i | \(0.556815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.13681 | 0.250607 | 0.125304 | − | 0.992118i | \(-0.460009\pi\) | ||||
0.125304 | + | 0.992118i | \(0.460009\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.6556 | 1.07382 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.19649 | 0.0768455 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.9878 | −0.557977 | −0.278989 | − | 0.960294i | \(-0.589999\pi\) | ||||
−0.278989 | + | 0.960294i | \(0.589999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7377 | −1.31545 | −0.657726 | − | 0.753257i | \(-0.728482\pi\) | ||||
−0.657726 | + | 0.753257i | \(0.728482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.6155 | −0.786416 | −0.393208 | − | 0.919449i | \(-0.628635\pi\) | ||||
−0.393208 | + | 0.919449i | \(0.628635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.3503 | −0.741525 | −0.370763 | − | 0.928728i | \(-0.620904\pi\) | ||||
−0.370763 | + | 0.928728i | \(0.620904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.37233 | −0.0475484 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.67513 | −0.0579703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1187 | 0.936242 | 0.468121 | − | 0.883664i | \(-0.344931\pi\) | ||||
0.468121 | + | 0.883664i | \(0.344931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.8970 | 0.548173 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.07618 | −0.243428 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.0771 | −1.10218 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.40388 | 0.116683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1305 | 1.13437 | 0.567183 | − | 0.823592i | \(-0.308033\pi\) | ||||
0.567183 | + | 0.823592i | \(0.308033\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.9868 | −0.853534 | −0.426767 | − | 0.904362i | \(-0.640348\pi\) | ||||
−0.426767 | + | 0.904362i | \(0.640348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2896 | −0.794632 | −0.397316 | − | 0.917682i | \(-0.630058\pi\) | ||||
−0.397316 | + | 0.917682i | \(0.630058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0362 | 1.09052 | 0.545262 | − | 0.838265i | \(-0.316430\pi\) | ||||
0.545262 | + | 0.838265i | \(0.316430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.5026 | 1.00312 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.5355 | 0.493083 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6629 | −0.530718 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.3733 | −1.36487 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.1721 | −0.681162 | −0.340581 | − | 0.940215i | \(-0.610624\pi\) | ||||
−0.340581 | + | 0.940215i | \(0.610624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.3757 | −0.551710 | −0.275855 | − | 0.961199i | \(-0.588961\pi\) | ||||
−0.275855 | + | 0.961199i | \(0.588961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.98541 | 0.201425 | 0.100713 | − | 0.994916i | \(-0.467888\pi\) | ||||
0.100713 | + | 0.994916i | \(0.467888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −55.6093 | −1.86718 | −0.933589 | − | 0.358346i | \(-0.883341\pi\) | ||||
−0.933589 | + | 0.358346i | \(0.883341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.22425 | −0.108138 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.37328 | 0.280201 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.4274 | −0.916797 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.6991 | 1.85767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.64244 | −0.121347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.39772 | 0.0797030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.11283 | 0.302587 | 0.151293 | − | 0.988489i | \(-0.451656\pi\) | ||||
0.151293 | + | 0.988489i | \(0.451656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.6991 | 1.31529 | 0.657645 | − | 0.753328i | \(-0.271553\pi\) | ||||
0.657645 | + | 0.753328i | \(0.271553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.9248 | 0.460843 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.0738 | −1.02615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.79877 | 0.191284 | 0.0956419 | − | 0.995416i | \(-0.469510\pi\) | ||||
0.0956419 | + | 0.995416i | \(0.469510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8496 | −0.390033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26045 | 0.0414434 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.1636 | −1.41615 | −0.708076 | − | 0.706136i | \(-0.750437\pi\) | ||||
−0.708076 | + | 0.706136i | \(0.750437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.81003 | −0.223190 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.649738 | −0.0212487 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.1886 | 1.57425 | 0.787126 | − | 0.616793i | \(-0.211568\pi\) | ||||
0.787126 | + | 0.616793i | \(0.211568\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.31028 | −0.270907 | −0.135454 | − | 0.990784i | \(-0.543249\pi\) | ||||
−0.135454 | + | 0.990784i | \(0.543249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.9219 | −1.16978 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.66879 | −0.184211 | −0.0921055 | − | 0.995749i | \(-0.529360\pi\) | ||||
−0.0921055 | + | 0.995749i | \(0.529360\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7005 | 0.347354 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6869 | 0.832080 | 0.416040 | − | 0.909346i | \(-0.363418\pi\) | ||||
0.416040 | + | 0.909346i | \(0.363418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.52373 | −0.0816660 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.5778 | 0.503035 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.1002 | 1.22904 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.52705 | −0.0491576 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.6893 | −1.34064 | −0.670318 | − | 0.742074i | \(-0.733842\pi\) | ||||
−0.670318 | + | 0.742074i | \(0.733842\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.4993 | −1.55642 | −0.778208 | − | 0.628006i | \(-0.783871\pi\) | ||||
−0.778208 | + | 0.628006i | \(0.783871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.2163 | −1.89839 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.7851 | 0.984904 | 0.492452 | − | 0.870340i | \(-0.336101\pi\) | ||||
0.492452 | + | 0.870340i | \(0.336101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7757 | 0.408315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.2652 | −0.997205 | −0.498602 | − | 0.866831i | \(-0.666153\pi\) | ||||
−0.498602 | + | 0.866831i | \(0.666153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.5540 | −0.718632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.07239 | 0.256687 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.39868 | 0.235027 | 0.117513 | − | 0.993071i | \(-0.462508\pi\) | ||||
0.117513 | + | 0.993071i | \(0.462508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.7612 | −0.975194 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.2189 | 1.59045 | 0.795224 | − | 0.606316i | \(-0.207353\pi\) | ||||
0.795224 | + | 0.606316i | \(0.207353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6012.2.a.c.1.3 | yes | 3 | |
3.2 | odd | 2 | 6012.2.a.b.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.a.b.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
6012.2.a.c.1.3 | yes | 3 | 1.1 | even | 1 | trivial |