Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.93543 | 1.86542 | 0.932709 | − | 0.360630i | \(-0.117438\pi\) | ||||
0.932709 | + | 0.360630i | \(0.117438\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.745898 | −0.224897 | −0.112448 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112448 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74590 | 0.484225 | 0.242113 | − | 0.970248i | \(-0.422160\pi\) | ||||
0.242113 | + | 0.970248i | \(0.422160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.10856 | 1.48154 | 0.740772 | − | 0.671757i | \(-0.234460\pi\) | ||||
0.740772 | + | 0.671757i | \(0.234460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.44364 | 1.24886 | 0.624428 | − | 0.781083i | \(-0.285332\pi\) | ||||
0.624428 | + | 0.781083i | \(0.285332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.66492 | 0.309169 | 0.154584 | − | 0.987980i | \(-0.450596\pi\) | ||||
0.154584 | + | 0.987980i | \(0.450596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.61676 | −0.290379 | −0.145190 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145190 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.93543 | −0.834240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.34625 | 0.714520 | 0.357260 | − | 0.934005i | \(-0.383711\pi\) | ||||
0.357260 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.95184 | 1.08569 | 0.542847 | − | 0.839831i | \(-0.317346\pi\) | ||||
0.542847 | + | 0.839831i | \(0.317346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01641 | 0.764995 | 0.382497 | − | 0.923957i | \(-0.375064\pi\) | ||||
0.382497 | + | 0.923957i | \(0.375064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.68133 | −0.391112 | −0.195556 | − | 0.980693i | \(-0.562651\pi\) | ||||
−0.195556 | + | 0.980693i | \(0.562651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.3585 | 2.47978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.7417 | −1.88757 | −0.943786 | − | 0.330558i | \(-0.892763\pi\) | ||||
−0.943786 | + | 0.330558i | \(0.892763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.745898 | 0.100577 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2171 | −1.59053 | −0.795267 | − | 0.606260i | \(-0.792669\pi\) | ||||
−0.795267 | + | 0.606260i | \(0.792669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9794 | −1.78988 | −0.894941 | − | 0.446185i | \(-0.852782\pi\) | ||||
−0.894941 | + | 0.446185i | \(0.852782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.74590 | −0.216552 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1044 | 1.60096 | 0.800478 | − | 0.599362i | \(-0.204579\pi\) | ||||
0.800478 | + | 0.599362i | \(0.204579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.67716 | 1.14847 | 0.574234 | − | 0.818691i | \(-0.305300\pi\) | ||||
0.574234 | + | 0.818691i | \(0.305300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.69774 | 0.666870 | 0.333435 | − | 0.942773i | \(-0.391792\pi\) | ||||
0.333435 | + | 0.942773i | \(0.391792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.68133 | −0.419527 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3791 | 1.16774 | 0.583868 | − | 0.811848i | \(-0.301538\pi\) | ||||
0.583868 | + | 0.811848i | \(0.301538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.637339 | −0.0699570 | −0.0349785 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349785 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.10856 | −0.662566 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.72532 | −0.288884 | −0.144442 | − | 0.989513i | \(-0.546139\pi\) | ||||
−0.144442 | + | 0.989513i | \(0.546139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.61676 | 0.903282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.44364 | −0.558505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.12497 | 0.723431 | 0.361715 | − | 0.932289i | \(-0.382191\pi\) | ||||
0.361715 | + | 0.932289i | \(0.382191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9753 | −1.49009 | −0.745047 | − | 0.667012i | \(-0.767573\pi\) | ||||
−0.745047 | + | 0.667012i | \(0.767573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8667 | −1.07073 | −0.535364 | − | 0.844622i | \(-0.679825\pi\) | ||||
−0.535364 | + | 0.844622i | \(0.679825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.49180 | 0.724259 | 0.362130 | − | 0.932128i | \(-0.382050\pi\) | ||||
0.362130 | + | 0.932128i | \(0.382050\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3309 | −1.75578 | −0.877891 | − | 0.478860i | \(-0.841050\pi\) | ||||
−0.877891 | + | 0.478860i | \(0.841050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.379068 | −0.0356597 | −0.0178299 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178299 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.1484 | 2.76370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4436 | −0.949421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64852 | 0.235018 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.53579 | 0.483664 | 0.241832 | − | 0.970318i | \(-0.422252\pi\) | ||||
0.241832 | + | 0.970318i | \(0.422252\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.8667 | 2.32964 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.16896 | −0.527050 | −0.263525 | − | 0.964653i | \(-0.584885\pi\) | ||||
−0.263525 | + | 0.964653i | \(0.584885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.7693 | −1.76163 | −0.880815 | − | 0.473460i | \(-0.843005\pi\) | ||||
−0.880815 | + | 0.473460i | \(0.843005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.30226 | −0.108901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.66492 | −0.138264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.06457 | 0.0872128 | 0.0436064 | − | 0.999049i | \(-0.486115\pi\) | ||||
0.0436064 | + | 0.999049i | \(0.486115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6608 | −1.03032 | −0.515159 | − | 0.857095i | \(-0.672267\pi\) | ||||
−0.515159 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.61676 | 0.129862 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8873 | 1.18813 | 0.594067 | − | 0.804416i | \(-0.297521\pi\) | ||||
0.594067 | + | 0.804416i | \(0.297521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.93543 | 0.388967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.72949 | 0.527094 | 0.263547 | − | 0.964646i | \(-0.415108\pi\) | ||||
0.263547 | + | 0.964646i | \(0.415108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.98359 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.95184 | −0.765526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8503 | 1.20508 | 0.602538 | − | 0.798091i | \(-0.294156\pi\) | ||||
0.602538 | + | 0.798091i | \(0.294156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.93543 | 0.373084 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.02759 | −0.226292 | −0.113146 | − | 0.993578i | \(-0.536093\pi\) | ||||
−0.113146 | + | 0.993578i | \(0.536093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.82270 | 0.135481 | 0.0677403 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677403 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.34625 | −0.319543 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.55636 | −0.333194 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.6126 | −1.41912 | −0.709559 | − | 0.704646i | \(-0.751106\pi\) | ||||
−0.709559 | + | 0.704646i | \(0.751106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.335076 | −0.0241193 | −0.0120597 | − | 0.999927i | \(-0.503839\pi\) | ||||
−0.0120597 | + | 0.999927i | \(0.503839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.5316 | 1.46282 | 0.731409 | − | 0.681939i | \(-0.238863\pi\) | ||||
0.731409 | + | 0.681939i | \(0.238863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7253 | 1.18563 | 0.592813 | − | 0.805340i | \(-0.298017\pi\) | ||||
0.592813 | + | 0.805340i | \(0.298017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.21712 | 0.576729 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.95184 | −0.485538 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.06040 | −0.280864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3955 | −0.922183 | −0.461091 | − | 0.887353i | \(-0.652542\pi\) | ||||
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.01641 | −0.342116 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.97942 | −0.541679 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6649 | 0.717400 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27468 | 0.0853587 | 0.0426794 | − | 0.999089i | \(-0.486411\pi\) | ||||
0.0426794 | + | 0.999089i | \(0.486411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.57978 | −0.237598 | −0.118799 | − | 0.992918i | \(-0.537904\pi\) | ||||
−0.118799 | + | 0.992918i | \(0.537904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4119 | 0.688036 | 0.344018 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344018 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.06040 | −0.200493 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.68133 | 0.174911 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1895 | 1.24127 | 0.620634 | − | 0.784100i | \(-0.286875\pi\) | ||||
0.620634 | + | 0.784100i | \(0.286875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.346255 | 0.0223042 | 0.0111521 | − | 0.999938i | \(-0.496450\pi\) | ||||
0.0111521 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.3585 | −1.10899 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.50403 | 0.604727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3861 | −0.908041 | −0.454021 | − | 0.890991i | \(-0.650011\pi\) | ||||
−0.454021 | + | 0.890991i | \(0.650011\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.745898 | −0.0468942 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.28586 | −0.0802095 | −0.0401047 | − | 0.999195i | \(-0.512769\pi\) | ||||
−0.0401047 | + | 0.999195i | \(0.512769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4506 | 1.33288 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.2294 | −1.74070 | −0.870348 | − | 0.492437i | \(-0.836106\pi\) | ||||
−0.870348 | + | 0.492437i | \(0.836106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.7417 | 0.844148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4395 | 1.18525 | 0.592623 | − | 0.805480i | \(-0.298093\pi\) | ||||
0.592623 | + | 0.805480i | \(0.298093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.42723 | −0.390426 | −0.195213 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195213 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.745898 | −0.0449794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.08514 | 0.245452 | 0.122726 | − | 0.992441i | \(-0.460836\pi\) | ||||
0.122726 | + | 0.992441i | \(0.460836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.38741 | 0.381041 | 0.190520 | − | 0.981683i | \(-0.438982\pi\) | ||||
0.190520 | + | 0.981683i | \(0.438982\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.4835 | −1.27706 | −0.638530 | − | 0.769597i | \(-0.720457\pi\) | ||||
−0.638530 | + | 0.769597i | \(0.720457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.3103 | 2.02527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.3145 | 1.19497 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1208 | 0.941787 | 0.470894 | − | 0.882190i | \(-0.343932\pi\) | ||||
0.470894 | + | 0.882190i | \(0.343932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2171 | 0.711308 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74590 | 0.100968 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.7581 | 1.42704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9794 | 0.800460 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.96302 | −0.397400 | −0.198700 | − | 0.980060i | \(-0.563672\pi\) | ||||
−0.198700 | + | 0.980060i | \(0.563672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.14031 | 0.234776 | 0.117388 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117388 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.26528 | 0.354135 | 0.177067 | − | 0.984199i | \(-0.443339\pi\) | ||||
0.177067 | + | 0.984199i | \(0.443339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.53996 | −0.535817 | −0.267909 | − | 0.963444i | \(-0.586333\pi\) | ||||
−0.267909 | + | 0.963444i | \(0.586333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.24186 | −0.0695310 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.2528 | 1.85023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.74590 | 0.0968450 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.2335 | −0.729588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3023 | −0.786123 | −0.393062 | − | 0.919512i | \(-0.628584\pi\) | ||||
−0.393062 | + | 0.919512i | \(0.628584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.1044 | −0.715969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.34731 | −0.182340 | −0.0911699 | − | 0.995835i | \(-0.529061\pi\) | ||||
−0.0911699 | + | 0.995835i | \(0.529061\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.20594 | 0.0653054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 51.1236 | 2.76042 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.9383 | 1.28507 | 0.642537 | − | 0.766255i | \(-0.277882\pi\) | ||||
0.642537 | + | 0.766255i | \(0.277882\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9149 | −0.637788 | −0.318894 | − | 0.947790i | \(-0.603311\pi\) | ||||
−0.318894 | + | 0.947790i | \(0.603311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2447 | 1.34364 | 0.671820 | − | 0.740714i | \(-0.265513\pi\) | ||||
0.671820 | + | 0.740714i | \(0.265513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.67716 | −0.513610 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4671 | −1.08021 | −0.540105 | − | 0.841598i | \(-0.681615\pi\) | ||||
−0.540105 | + | 0.841598i | \(0.681615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6332 | 0.559641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.69774 | −0.298233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.4999 | −1.90528 | −0.952639 | − | 0.304104i | \(-0.901643\pi\) | ||||
−0.952639 | + | 0.304104i | \(0.901643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −67.8214 | −3.52111 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.57978 | −0.288910 | −0.144455 | − | 0.989511i | \(-0.546143\pi\) | ||||
−0.144455 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.90679 | 0.149707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.6168 | 1.88088 | 0.940438 | − | 0.339964i | \(-0.110415\pi\) | ||||
0.940438 | + | 0.339964i | \(0.110415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7581 | 1.46947 | 0.734736 | − | 0.678353i | \(-0.237306\pi\) | ||||
0.734736 | + | 0.678353i | \(0.237306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.68133 | 0.187618 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3913 | −1.33809 | −0.669046 | − | 0.743221i | \(-0.733297\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.10856 | 0.308923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3791 | −0.522228 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.08931 | 0.0546710 | 0.0273355 | − | 0.999626i | \(-0.491298\pi\) | ||||
0.0273355 | + | 0.999626i | \(0.491298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5962 | 1.12840 | 0.564200 | − | 0.825638i | \(-0.309185\pi\) | ||||
0.564200 | + | 0.825638i | \(0.309185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.82270 | −0.140609 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.24186 | −0.160693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0510 | −0.793671 | −0.396835 | − | 0.917890i | \(-0.629892\pi\) | ||||
−0.396835 | + | 0.917890i | \(0.629892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −60.2968 | −2.96701 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.637339 | 0.0312857 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4342 | 1.19369 | 0.596845 | − | 0.802356i | \(-0.296421\pi\) | ||||
0.596845 | + | 0.802356i | \(0.296421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3473 | −0.553034 | −0.276517 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276517 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.10856 | 0.296309 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −68.9945 | −3.33888 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.83805 | −0.377546 | −0.188773 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188773 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.9023 | −1.82147 | −0.910735 | − | 0.412990i | \(-0.864484\pi\) | ||||
−0.910735 | + | 0.412990i | \(0.864484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.44364 | 0.260404 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7704 | −0.848134 | −0.424067 | − | 0.905631i | \(-0.639398\pi\) | ||||
−0.424067 | + | 0.905631i | \(0.639398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9466 | −0.805158 | −0.402579 | − | 0.915385i | \(-0.631886\pi\) | ||||
−0.402579 | + | 0.915385i | \(0.631886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.72532 | 0.129193 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0890 | 0.995253 | 0.497627 | − | 0.867391i | \(-0.334205\pi\) | ||||
0.497627 | + | 0.867391i | \(0.334205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.18537 | −0.244169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.61676 | −0.403960 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.1372 | 0.614532 | 0.307266 | − | 0.951624i | \(-0.400586\pi\) | ||||
0.307266 | + | 0.951624i | \(0.400586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5439 | 0.677375 | 0.338687 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338687 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.4283 | 0.902909 | 0.451455 | − | 0.892294i | \(-0.350905\pi\) | ||||
0.451455 | + | 0.892294i | \(0.350905\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.61259 | 0.167171 | 0.0835855 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835855 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 64.6758 | 2.98645 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.74173 | −0.172045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.44364 | 0.249771 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.13720 | −0.234725 | −0.117362 | − | 0.993089i | \(-0.537444\pi\) | ||||
−0.117362 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.58812 | 0.345988 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.12497 | −0.323528 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.7693 | −1.12240 | −0.561202 | − | 0.827679i | \(-0.689661\pi\) | ||||
−0.561202 | + | 0.827679i | \(0.689661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.54413 | −0.159944 | −0.0799721 | − | 0.996797i | \(-0.525483\pi\) | ||||
−0.0799721 | + | 0.996797i | \(0.525483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1703 | 0.458047 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.7610 | 2.14237 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5358 | 1.41174 | 0.705868 | − | 0.708344i | \(-0.250557\pi\) | ||||
0.705868 | + | 0.708344i | \(0.250557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2346 | 1.43727 | 0.718635 | − | 0.695388i | \(-0.244767\pi\) | ||||
0.718635 | + | 0.695388i | \(0.244767\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9753 | 0.666390 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.302263 | −0.0133976 | −0.00669878 | − | 0.999978i | \(-0.502132\pi\) | ||||
−0.00669878 | + | 0.999978i | \(0.502132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1208 | 1.24399 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8667 | 0.478844 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.3463 | 1.32949 | 0.664747 | − | 0.747069i | \(-0.268539\pi\) | ||||
0.664747 | + | 0.747069i | \(0.268539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.5878 | −1.86224 | −0.931118 | − | 0.364717i | \(-0.881166\pi\) | ||||
−0.931118 | + | 0.364717i | \(0.881166\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.87609 | −0.430209 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1372 | 0.525721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.49180 | −0.323899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.9477 | −0.557696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9313 | 1.67379 | 0.836893 | − | 0.547367i | \(-0.184370\pi\) | ||||
0.836893 | + | 0.547367i | \(0.184370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.3309 | 0.785210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6004 | 0.709780 | 0.354890 | − | 0.934908i | \(-0.384518\pi\) | ||||
0.354890 | + | 0.934908i | \(0.384518\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.06324 | 0.386107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.2252 | 2.17832 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4506 | −0.739408 | −0.369704 | − | 0.929150i | \(-0.620541\pi\) | ||||
−0.369704 | + | 0.929150i | \(0.620541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.75814 | 0.370430 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.25827 | −0.348045 | −0.174022 | − | 0.984742i | \(-0.555676\pi\) | ||||
−0.174022 | + | 0.984742i | \(0.555676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.379068 | 0.0159475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.4178 | 1.73633 | 0.868163 | − | 0.496279i | \(-0.165301\pi\) | ||||
0.868163 | + | 0.496279i | \(0.165301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.19059 | 0.300917 | 0.150458 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.3103 | 1.63651 | 0.818255 | − | 0.574855i | \(-0.194942\pi\) | ||||
0.818255 | + | 0.574855i | \(0.194942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.14554 | −0.130499 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2499 | 0.424509 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.7899 | −1.18829 | −0.594143 | − | 0.804359i | \(-0.702509\pi\) | ||||
−0.594143 | + | 0.804359i | \(0.702509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.80107 | −0.362642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.8873 | 1.67904 | 0.839519 | − | 0.543330i | \(-0.182837\pi\) | ||||
0.839519 | + | 0.543330i | \(0.182837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.1484 | −1.23596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1801 | −0.783679 | −0.391840 | − | 0.920034i | \(-0.628161\pi\) | ||||
−0.391840 | + | 0.920034i | \(0.628161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.36683 | 0.137336 | 0.0686679 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686679 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.4436 | 0.424594 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1924 | 0.535462 | 0.267731 | − | 0.963494i | \(-0.413726\pi\) | ||||
0.267731 | + | 0.963494i | \(0.413726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.68133 | −0.189386 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.6207 | 1.31754 | 0.658768 | − | 0.752346i | \(-0.271078\pi\) | ||||
0.658768 | + | 0.752346i | \(0.271078\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.7212 | −1.67963 | −0.839815 | − | 0.542872i | \(-0.817337\pi\) | ||||
−0.839815 | + | 0.542872i | \(0.817337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.339245 | −0.0136354 | −0.00681771 | − | 0.999977i | \(-0.502170\pi\) | ||||
−0.00681771 | + | 0.999977i | \(0.502170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.4506 | −0.538889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.5494 | 1.05859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.71725 | 0.147982 | 0.0739908 | − | 0.997259i | \(-0.476426\pi\) | ||||
0.0739908 | + | 0.997259i | \(0.476426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.64852 | −0.105103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.3062 | 1.20077 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.0328 | 0.870244 | 0.435122 | − | 0.900372i | \(-0.356705\pi\) | ||||
0.435122 | + | 0.900372i | \(0.356705\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6842 | −0.973449 | −0.486724 | − | 0.873556i | \(-0.661808\pi\) | ||||
−0.486724 | + | 0.873556i | \(0.661808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.1731 | −1.26486 | −0.632428 | − | 0.774619i | \(-0.717942\pi\) | ||||
−0.632428 | + | 0.774619i | \(0.717942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.11273 | 0.357706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9466 | 1.05450 | 0.527251 | − | 0.849709i | \(-0.323223\pi\) | ||||
0.527251 | + | 0.849709i | \(0.323223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.53579 | −0.216301 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7417 | 0.769029 | 0.384514 | − | 0.923119i | \(-0.374369\pi\) | ||||
0.384514 | + | 0.923119i | \(0.374369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.28692 | −0.0500552 | −0.0250276 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250276 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.8667 | −1.04185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.66492 | 0.0644661 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4272 | 0.402539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4970 | 0.481725 | 0.240862 | − | 0.970559i | \(-0.422570\pi\) | ||||
0.240862 | + | 0.970559i | \(0.422570\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.69251 | 0.103482 | 0.0517408 | − | 0.998661i | \(-0.483523\pi\) | ||||
0.0517408 | + | 0.998661i | \(0.483523\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.1648 | 1.34950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.72115 | 0.104122 | 0.0520610 | − | 0.998644i | \(-0.483421\pi\) | ||||
0.0520610 | + | 0.998644i | \(0.483421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.16896 | 0.235704 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.9917 | −0.914010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3051 | 1.45719 | 0.728597 | − | 0.684942i | \(-0.240173\pi\) | ||||
0.728597 | + | 0.684942i | \(0.240173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.7693 | 0.787825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.4657 | 1.60850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.8472 | −1.50501 | −0.752504 | − | 0.658588i | \(-0.771154\pi\) | ||||
−0.752504 | + | 0.658588i | \(0.771154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.6594 | 0.892332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −73.9094 | −2.77965 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.8995 | −1.68624 | −0.843118 | − | 0.537728i | \(-0.819283\pi\) | ||||
−0.843118 | + | 0.537728i | \(0.819283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.61676 | −0.0605482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.30226 | 0.0487019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.5400 | 1.17624 | 0.588121 | − | 0.808773i | \(-0.299868\pi\) | ||||
0.588121 | + | 0.808773i | \(0.299868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.6318 | −1.99735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.66492 | 0.0618337 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.9219 | −1.81441 | −0.907206 | − | 0.420687i | \(-0.861789\pi\) | ||||
−0.907206 | + | 0.420687i | \(0.861789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.6430 | 1.13337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1536 | −0.522776 | −0.261388 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261388 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.77454 | −0.360050 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.46421 | 0.164219 | 0.0821093 | − | 0.996623i | \(-0.473834\pi\) | ||||
0.0821093 | + | 0.996623i | \(0.473834\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2898 | 1.25797 | 0.628985 | − | 0.777418i | \(-0.283471\pi\) | ||||
0.628985 | + | 0.777418i | \(0.283471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.06457 | −0.0390027 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.9753 | 1.35105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.28275 | −0.302242 | −0.151121 | − | 0.988515i | \(-0.548288\pi\) | ||||
−0.151121 | + | 0.988515i | \(0.548288\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.6608 | 0.460772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.32985 | 0.121025 | 0.0605127 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605127 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4077 | 0.667279 | 0.333640 | − | 0.942701i | \(-0.391723\pi\) | ||||
0.333640 | + | 0.942701i | \(0.391723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −90.4710 | −3.27527 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.3298 | −0.770176 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.4506 | 1.85536 | 0.927679 | − | 0.373379i | \(-0.121801\pi\) | ||||
0.927679 | + | 0.373379i | \(0.121801\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.4506 | −0.627656 | −0.313828 | − | 0.949480i | \(-0.601612\pi\) | ||||
−0.313828 | + | 0.949480i | \(0.601612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.61676 | −0.0580758 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.8433 | 1.35588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.21818 | −0.258287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8873 | −0.531350 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2335 | −0.756893 | −0.378447 | − | 0.925623i | \(-0.623542\pi\) | ||||
−0.378447 | + | 0.925623i | \(0.623542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.87086 | −0.0665203 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.4067 | −0.866706 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.3215 | 0.896934 | 0.448467 | − | 0.893799i | \(-0.351970\pi\) | ||||
0.448467 | + | 0.893799i | \(0.351970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3791 | −0.579450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.24993 | −0.149977 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.93543 | −0.173951 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.14137 | −0.215919 | −0.107960 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107960 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5051 | 0.544457 | 0.272229 | − | 0.962233i | \(-0.412239\pi\) | ||||
0.272229 | + | 0.962233i | \(0.412239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.72949 | −0.235724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3075 | 0.955368 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4835 | 0.749778 | 0.374889 | − | 0.927070i | \(-0.377681\pi\) | ||||
0.374889 | + | 0.927070i | \(0.377681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1565 | 1.39977 | 0.699883 | − | 0.714258i | \(-0.253235\pi\) | ||||
0.699883 | + | 0.714258i | \(0.253235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.0573 | −1.32338 | −0.661691 | − | 0.749777i | \(-0.730161\pi\) | ||||
−0.661691 | + | 0.749777i | \(0.730161\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.2580 | −1.78026 | −0.890132 | − | 0.455703i | \(-0.849388\pi\) | ||||
−0.890132 | + | 0.455703i | \(0.849388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 106.035 | 3.67391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.98359 | −0.103252 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.4200 | −1.56807 | −0.784035 | − | 0.620716i | \(-0.786842\pi\) | ||||
−0.784035 | + | 0.620716i | \(0.786842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2280 | −0.904415 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.95184 | 0.342354 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −51.5439 | −1.77107 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.34625 | 0.148988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.0867 | 1.37254 | 0.686270 | − | 0.727346i | \(-0.259247\pi\) | ||||
0.686270 | + | 0.727346i | \(0.259247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.63423 | 0.124143 | 0.0620715 | − | 0.998072i | \(-0.480229\pi\) | ||||
0.0620715 | + | 0.998072i | \(0.480229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7529 | −1.28811 | −0.644056 | − | 0.764978i | \(-0.722750\pi\) | ||||
−0.644056 | + | 0.764978i | \(0.722750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.94555 | 0.134308 | 0.0671541 | − | 0.997743i | \(-0.478608\pi\) | ||||
0.0671541 | + | 0.997743i | \(0.478608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.8503 | −0.538926 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.74173 | −0.262620 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.8789 | 0.775223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.93543 | −0.166848 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.64958 | −0.292075 | −0.146038 | − | 0.989279i | \(-0.546652\pi\) | ||||
−0.146038 | + | 0.989279i | \(0.546652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1760 | 1.89262 | 0.946308 | − | 0.323266i | \(-0.104781\pi\) | ||||
0.946308 | + | 0.323266i | \(0.104781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.1054 | −0.407381 | −0.203690 | − | 0.979035i | \(-0.565294\pi\) | ||||
−0.203690 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.7058 | 0.829540 | 0.414770 | − | 0.909926i | \(-0.363862\pi\) | ||||
0.414770 | + | 0.909926i | \(0.363862\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0716 | 0.438407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.5962 | −0.488443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.02759 | 0.101201 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.69179 | −0.0897761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −83.9422 | −2.79652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.82270 | −0.0605887 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7170 | 0.754305 | 0.377153 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377153 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3156 | 0.408033 | 0.204016 | − | 0.978967i | \(-0.434600\pi\) | ||||
0.204016 | + | 0.978967i | \(0.434600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.475390 | 0.0157331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3215 | 0.902236 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.2088 | 1.52429 | 0.762144 | − | 0.647408i | \(-0.224147\pi\) | ||||
0.762144 | + | 0.647408i | \(0.224147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8953 | 0.556117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.34625 | 0.142904 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.12391 | −0.299346 | −0.149673 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149673 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 94.4933 | 3.09689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.55636 | 0.149009 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.9190 | −1.10809 | −0.554043 | − | 0.832488i | \(-0.686916\pi\) | ||||
−0.554043 | + | 0.832488i | \(0.686916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2926 | 1.21570 | 0.607852 | − | 0.794050i | \(-0.292031\pi\) | ||||
0.607852 | + | 0.794050i | \(0.292031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.95184 | 0.226383 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.7047 | −1.09526 | −0.547629 | − | 0.836722i | \(-0.684469\pi\) | ||||
−0.547629 | + | 0.836722i | \(0.684469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.94767 | 0.322915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.4465 | 1.56934 | 0.784668 | − | 0.619917i | \(-0.212834\pi\) | ||||
0.784668 | + | 0.619917i | \(0.212834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.6126 | 0.634649 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.4465 | −0.983168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3861 | −0.915680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.335076 | 0.0107865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.2528 | −0.908548 | −0.454274 | − | 0.890862i | \(-0.650101\pi\) | ||||
−0.454274 | + | 0.890862i | \(0.650101\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.65553 | −0.0531284 | −0.0265642 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265642 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −102.506 | −3.28618 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.1630 | 0.357136 | 0.178568 | − | 0.983928i | \(-0.442854\pi\) | ||||
0.178568 | + | 0.983928i | \(0.442854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.03281 | 0.0649690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.0615 | −0.480386 | −0.240193 | − | 0.970725i | \(-0.577211\pi\) | ||||
−0.240193 | + | 0.970725i | \(0.577211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5316 | −0.654192 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.01641 | 0.159512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.8971 | −1.39444 | −0.697219 | − | 0.716858i | \(-0.745579\pi\) | ||||
−0.697219 | + | 0.716858i | \(0.745579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.7253 | −0.530228 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.5655 | 1.22138 | 0.610691 | − | 0.791869i | \(-0.290892\pi\) | ||||
0.610691 | + | 0.791869i | \(0.290892\pi\) | |||||||
\(998\) | 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 | 8280.2.a.bl.1.3 | 3 | ||
3.2 | odd | 2 | 920.2.a.i.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 1840.2.a.q.1.3 | 3 | |||
15.2 | even | 4 | 4600.2.e.q.4049.5 | 6 | |||
15.8 | even | 4 | 4600.2.e.q.4049.2 | 6 | |||
15.14 | odd | 2 | 4600.2.a.v.1.3 | 3 | |||
24.5 | odd | 2 | 7360.2.a.bw.1.3 | 3 | |||
24.11 | even | 2 | 7360.2.a.cf.1.1 | 3 | |||
60.59 | even | 2 | 9200.2.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1840.2.a.q.1.3 | 3 | 12.11 | even | 2 | |||
4600.2.a.v.1.3 | 3 | 15.14 | odd | 2 | |||
4600.2.e.q.4049.2 | 6 | 15.8 | even | 4 | |||
4600.2.e.q.4049.5 | 6 | 15.2 | even | 4 | |||
7360.2.a.bw.1.3 | 3 | 24.5 | odd | 2 | |||
7360.2.a.cf.1.1 | 3 | 24.11 | even | 2 | |||
8280.2.a.bl.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9200.2.a.ci.1.1 | 3 | 60.59 | even | 2 |