Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | 1.1 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −1.93543 | −1.11742 | −0.558711 | − | 0.829362i | \(-0.688704\pi\) | ||||
−0.558711 | + | 0.829362i | \(0.688704\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.93543 | 1.86542 | 0.932709 | − | 0.360630i | \(-0.117438\pi\) | ||||
0.932709 | + | 0.360630i | \(0.117438\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.745898 | 0.248633 | ||||||||
\(10\) | 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 | \(-0.577840\pi\) | ||||
−0.242113 | + | 0.970248i | \(0.577840\pi\) | |||||||
\(14\) | 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 | \(-0.714668\pi\) | ||||
−0.624428 | + | 0.781083i | \(0.714668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.55220 | −2.08446 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.36266 | 0.839595 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.66492 | −0.309169 | −0.154584 | − | 0.987980i | \(-0.549404\pi\) | ||||
−0.154584 | + | 0.987980i | \(0.549404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61676 | 0.290379 | 0.145190 | − | 0.989404i | \(-0.453621\pi\) | ||||
0.145190 | + | 0.989404i | \(0.453621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.44364 | 0.251305 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.34625 | −0.714520 | −0.357260 | − | 0.934005i | \(-0.616289\pi\) | ||||
−0.357260 | + | 0.934005i | \(0.616289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.37907 | 0.541084 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.95184 | −1.08569 | −0.542847 | − | 0.839831i | \(-0.682654\pi\) | ||||
−0.542847 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(42\) | 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 | \(-0.437349\pi\) | ||||
0.195556 | + | 0.980693i | \(0.437349\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.3585 | 2.47978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.8227 | −1.65551 | ||||||||
\(52\) | 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 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.5358 | 1.39550 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 3.68133 | 0.463804 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1044 | 1.60096 | 0.800478 | − | 0.599362i | \(-0.204579\pi\) | ||||
0.800478 | + | 0.599362i | \(0.204579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.93543 | 0.232999 | ||||||||
\(70\) | 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 | \(-0.608208\pi\) | ||||
−0.333435 | + | 0.942773i | \(0.608208\pi\) | |||||||
\(74\) | 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 | \(-0.698462\pi\) | ||||
−0.583868 | + | 0.811848i | \(0.698462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6813 | −1.18681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.637339 | 0.0699570 | 0.0349785 | − | 0.999388i | \(-0.488864\pi\) | ||||
0.0349785 | + | 0.999388i | \(0.488864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.22235 | 0.345472 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.72532 | 0.288884 | 0.144442 | − | 0.989513i | \(-0.453861\pi\) | ||||
0.144442 | + | 0.989513i | \(0.453861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.61676 | −0.903282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.12914 | −0.324476 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.12497 | −0.723431 | −0.361715 | − | 0.932289i | \(-0.617809\pi\) | ||||
−0.361715 | + | 0.932289i | \(0.617809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.556364 | −0.0559167 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9753 | 1.49009 | 0.745047 | − | 0.667012i | \(-0.232427\pi\) | ||||
0.745047 | + | 0.667012i | \(0.232427\pi\) | |||||||
\(102\) | 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 | \(-0.617950\pi\) | ||||
−0.362130 | + | 0.932128i | \(0.617950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3309 | −1.75578 | −0.877891 | − | 0.478860i | \(-0.841050\pi\) | ||||
−0.877891 | + | 0.478860i | \(0.841050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.41188 | 0.798420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.379068 | −0.0356597 | −0.0178299 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178299 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.30226 | −0.120394 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.1484 | 2.76370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4436 | −0.949421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4548 | 1.21318 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64852 | 0.235018 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.70892 | −0.854822 | ||||||||
\(130\) | 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 | \(-0.156995\pi\) | ||||
0.880815 | + | 0.473460i | \(0.156995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.18953 | −0.437038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.30226 | 0.108901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33.5962 | −2.77097 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.06457 | −0.0872128 | −0.0436064 | − | 0.999049i | \(-0.513885\pi\) | ||||
−0.0436064 | + | 0.999049i | \(0.513885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6608 | 1.03032 | 0.515159 | − | 0.857095i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857095i | \(0.327733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.55636 | 0.368360 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.8873 | −1.18813 | −0.594067 | − | 0.804416i | \(-0.702479\pi\) | ||||
−0.594067 | + | 0.804416i | \(0.702479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.5962 | 2.10921 | ||||||||
\(160\) | 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 | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.95184 | −0.765526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.06040 | −0.310506 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8503 | 1.20508 | 0.602538 | − | 0.798091i | \(-0.294156\pi\) | ||||
0.602538 | + | 0.798091i | \(0.294156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.6454 | 1.77730 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 27.0562 | 2.00005 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.55636 | −0.333194 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.5316 | 1.56619 | ||||||||
\(190\) | 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 | \(-0.496161\pi\) | ||||
0.0120597 | + | 0.999927i | \(0.496161\pi\) | |||||||
\(194\) | 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 | \(-0.701983\pi\) | ||||
−0.592813 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.3627 | −1.78894 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.21712 | −0.576729 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.745898 | −0.0518435 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.06040 | 0.280864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3955 | 0.922183 | 0.461091 | − | 0.887353i | \(-0.347458\pi\) | ||||
0.461091 | + | 0.887353i | \(0.347458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.7295 | −1.28332 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.97942 | 0.541679 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0276 | 0.745175 | ||||||||
\(220\) | 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 | \(-0.462096\pi\) | ||||
0.118799 | + | 0.992918i | \(0.462096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4119 | 0.688036 | 0.344018 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344018 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.12497 | 0.468788 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.06040 | −0.200493 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.0880 | 1.30485 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 7.58501 | 0.486579 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.50403 | 0.604727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.23353 | −0.0781715 | ||||||||
\(250\) | 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 | ||||||||
\(261\) | −1.24186 | −0.0768694 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2294 | 1.74070 | 0.870348 | − | 0.492437i | \(-0.163894\pi\) | ||||
0.870348 | + | 0.492437i | \(0.163894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.27468 | −0.322805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.4395 | −1.18525 | −0.592623 | − | 0.805480i | \(-0.701907\pi\) | ||||
−0.592623 | + | 0.805480i | \(0.701907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.42723 | 0.390426 | 0.195213 | − | 0.980761i | \(-0.437460\pi\) | ||||
0.195213 | + | 0.980761i | \(0.437460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.6772 | 1.00935 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.08514 | −0.245452 | −0.122726 | − | 0.992441i | \(-0.539164\pi\) | ||||
−0.122726 | + | 0.992441i | \(0.539164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.20594 | 0.0721978 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.38741 | −0.381041 | −0.190520 | − | 0.981683i | \(-0.561018\pi\) | ||||
−0.190520 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(282\) | 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 | ||||||||
\(291\) | 13.7899 | 0.808378 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1208 | 0.941787 | 0.470894 | − | 0.882190i | \(-0.343932\pi\) | ||||
0.470894 | + | 0.882190i | \(0.343932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.25410 | −0.188822 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74590 | 0.100968 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.7581 | 1.42704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.9836 | −1.66506 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.96302 | −0.397400 | −0.198700 | − | 0.980060i | \(-0.563672\pi\) | ||||
−0.198700 | + | 0.980060i | \(0.563672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.0318 | 1.19645 | ||||||||
\(310\) | 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 | \(-0.556661\pi\) | ||||
−0.177067 | + | 0.984199i | \(0.556661\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 14.4999 | 0.809304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.2528 | −1.85023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 35.4782 | 1.96195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2335 | 0.729588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3023 | 0.786123 | 0.393062 | − | 0.919512i | \(-0.371416\pi\) | ||||
0.393062 | + | 0.919512i | \(0.371416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.24186 | −0.177653 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.34731 | 0.182340 | 0.0911699 | − | 0.995835i | \(-0.470939\pi\) | ||||
0.0911699 | + | 0.995835i | \(0.470939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.733661 | 0.0398470 | ||||||||
\(340\) | 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 | \(-0.722118\pi\) | ||||
−0.642537 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9149 | −0.637788 | −0.318894 | − | 0.947790i | \(-0.603311\pi\) | ||||
−0.318894 | + | 0.947790i | \(0.603311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.61676 | −0.406553 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2447 | 1.34364 | 0.671820 | − | 0.740714i | \(-0.265513\pi\) | ||||
0.671820 | + | 0.740714i | \(0.265513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −58.3502 | −3.08822 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 20.2130 | 1.06090 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.4999 | −1.90528 | −0.952639 | − | 0.304104i | \(-0.901643\pi\) | ||||
−0.952639 | + | 0.304104i | \(0.901643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.18537 | −0.269939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −67.8214 | −3.52111 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.57978 | 0.288910 | 0.144455 | − | 0.989511i | \(-0.453857\pi\) | ||||
0.144455 | + | 0.989511i | \(0.453857\pi\) | |||||||
\(374\) | 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 | \(-0.889585\pi\) | ||||
−0.940438 | + | 0.339964i | \(0.889585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.12603 | −0.262614 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.7581 | −1.46947 | −0.734736 | − | 0.678353i | \(-0.762694\pi\) | ||||
−0.734736 | + | 0.678353i | \(0.762694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.74173 | 0.190203 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.3913 | 1.33809 | 0.669046 | − | 0.743221i | \(-0.266703\pi\) | ||||
0.669046 | + | 0.743221i | \(0.266703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.10856 | −0.308923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.7141 | −0.540457 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.08931 | −0.0546710 | −0.0273355 | − | 0.999626i | \(-0.508702\pi\) | ||||
−0.0273355 | + | 0.999626i | \(0.508702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 51.9987 | 2.60319 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5962 | −1.12840 | −0.564200 | − | 0.825638i | \(-0.690815\pi\) | ||||
−0.564200 | + | 0.825638i | \(0.690815\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 11.9396 | 0.588937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −60.2968 | −2.96701 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.1976 | −1.96849 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 2.00000 | 0.0972433 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −68.9945 | −3.33888 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.52044 | −0.121688 | ||||||||
\(430\) | 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 | \(-0.135516\pi\) | ||||
0.910735 | + | 0.412990i | \(0.135516\pi\) | |||||||
\(434\) | 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 | \(-0.360602\pi\) | ||||
0.424067 | + | 0.905631i | \(0.360602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9477 | 0.616556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9466 | 0.805158 | 0.402579 | − | 0.915385i | \(-0.368114\pi\) | ||||
0.402579 | + | 0.915385i | \(0.368114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.06040 | 0.0974535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.0890 | −0.995253 | −0.497627 | − | 0.867391i | \(-0.665795\pi\) | ||||
−0.497627 | + | 0.867391i | \(0.665795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.18537 | 0.244169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.5040 | −1.15130 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1372 | −0.614532 | −0.307266 | − | 0.951624i | \(-0.599414\pi\) | ||||
−0.307266 | + | 0.951624i | \(0.599414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.6496 | 1.24390 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5439 | −0.677375 | −0.338687 | − | 0.940899i | \(-0.609983\pi\) | ||||
−0.338687 | + | 0.940899i | \(0.609983\pi\) | |||||||
\(462\) | 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 | \(-0.526637\pi\) | ||||
−0.0835855 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 64.6758 | 2.98645 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.8133 | 1.32765 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.74173 | −0.172045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.2499 | −0.469312 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 9.55220 | 0.434640 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.7693 | −1.12240 | −0.561202 | − | 0.827679i | \(-0.689661\pi\) | ||||
−0.561202 | + | 0.827679i | \(0.689661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.0245 | −0.588987 | ||||||||
\(490\) | 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 | \(-0.749443\pi\) | ||||
−0.705868 | + | 0.708344i | \(0.749443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.77454 | 0.257988 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.2346 | −1.43727 | −0.718635 | − | 0.695388i | \(-0.755233\pi\) | ||||
−0.718635 | + | 0.695388i | \(0.755233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2611 | 0.855416 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.302263 | 0.0133976 | 0.00669878 | − | 0.999978i | \(-0.497868\pi\) | ||||
0.00669878 | + | 0.999978i | \(0.497868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1208 | −1.24399 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.7487 | −1.04853 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.6772 | −1.34658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3463 | −1.32949 | −0.664747 | − | 0.747069i | \(-0.731461\pi\) | ||||
−0.664747 | + | 0.747069i | \(0.731461\pi\) | |||||||
\(522\) | 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 | ||||||||
\(531\) | −9.11273 | −0.395459 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1372 | 0.525721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.85969 | 0.252864 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | −3.52772 | −0.151389 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6004 | 0.709780 | 0.354890 | − | 0.934908i | \(-0.384518\pi\) | ||||
0.354890 | + | 0.934908i | \(0.384518\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.4272 | −0.445023 | ||||||||
\(550\) | 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 | ||||||||
\(561\) | 8.81853 | 0.372319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.25827 | 0.348045 | 0.174022 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174022 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −52.7170 | −2.21391 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.4178 | −1.73633 | −0.868163 | − | 0.496279i | \(-0.834699\pi\) | ||||
−0.868163 | + | 0.496279i | \(0.834699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.19059 | −0.300917 | −0.150458 | − | 0.988616i | \(-0.548075\pi\) | ||||
−0.150458 | + | 0.988616i | \(0.548075\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.9588 | 1.58575 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.3103 | −1.63651 | −0.818255 | − | 0.574855i | \(-0.805058\pi\) | ||||
−0.818255 | + | 0.574855i | \(0.805058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.648517 | −0.0269515 | ||||||||
\(580\) | 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 | \(-0.297491\pi\) | ||||
0.594143 | + | 0.804359i | \(0.297491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.80107 | −0.362642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.7376 | −1.63458 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.8873 | 1.67904 | 0.839519 | − | 0.543330i | \(-0.182837\pi\) | ||||
0.839519 | + | 0.543330i | \(0.182837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.3707 | 1.32485 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 9.77454 | 0.398050 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1924 | 0.535462 | 0.267731 | − | 0.963494i | \(-0.413726\pi\) | ||||
0.267731 | + | 0.963494i | \(0.413726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.9037 | 0.644450 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.68133 | −0.189386 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.6207 | −1.31754 | −0.658768 | − | 0.752346i | \(-0.728922\pi\) | ||||
−0.658768 | + | 0.752346i | \(0.728922\pi\) | |||||||
\(614\) | 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 | \(-0.497830\pi\) | ||||
0.00681771 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.36266 | −0.175068 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.4506 | 0.538889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.85863 | −0.313843 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.5494 | −1.05859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.71725 | −0.147982 | −0.0739908 | − | 0.997259i | \(-0.523574\pi\) | ||||
−0.0739908 | + | 0.997259i | \(0.523574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.9260 | −1.03047 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.3062 | −1.20077 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.21818 | 0.285547 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.0328 | −0.870244 | −0.435122 | − | 0.900372i | \(-0.643295\pi\) | ||||
−0.435122 | + | 0.900372i | \(0.643295\pi\) | |||||||
\(642\) | 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 | \(-0.282058\pi\) | ||||
0.632428 | + | 0.774619i | \(0.282058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.11273 | 0.357706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4436 | −0.605284 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9466 | 1.05450 | 0.527251 | − | 0.849709i | \(-0.323223\pi\) | ||||
0.527251 | + | 0.849709i | \(0.323223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.24993 | −0.165806 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 20.6412 | 0.801639 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.66492 | 0.0644661 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.46705 | −0.0953817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4272 | 0.402539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4970 | −0.481725 | −0.240862 | − | 0.970559i | \(-0.577430\pi\) | ||||
−0.240862 | + | 0.970559i | \(0.577430\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | −6.92842 | −0.265498 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.72115 | −0.104122 | −0.0520610 | − | 0.998644i | \(-0.516579\pi\) | ||||
−0.0520610 | + | 0.998644i | \(0.516579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.1515 | −0.768827 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.9917 | 0.914010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.3051 | −1.45719 | −0.728597 | − | 0.684942i | \(-0.759827\pi\) | ||||
−0.728597 | + | 0.684942i | \(0.759827\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.74590 | −0.104308 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.4657 | −1.60850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.92319 | 0.224036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.8472 | 1.50501 | 0.752504 | − | 0.658588i | \(-0.228846\pi\) | ||||
0.752504 | + | 0.658588i | \(0.228846\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | −7.74173 | −0.290338 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.61676 | −0.0605482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.1400 | −1.38702 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | −0.670152 | −0.0249232 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.9219 | −1.81441 | −0.907206 | − | 0.420687i | \(-0.861789\pi\) | ||||
−0.907206 | + | 0.420687i | \(0.861789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.3637 | 0.643101 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.6430 | 1.13337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1536 | 0.522776 | 0.261388 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261388 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(734\) | 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 | \(-0.526166\pi\) | ||||
−0.0821093 | + | 0.996623i | \(0.526166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.3944 | −0.675736 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.2898 | −1.25797 | −0.628985 | − | 0.777418i | \(-0.716529\pi\) | ||||
−0.628985 | + | 0.777418i | \(0.716529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.475390 | 0.0173936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.9753 | −1.35105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.28275 | 0.302242 | 0.151121 | − | 0.988515i | \(-0.451712\pi\) | ||||
0.151121 | + | 0.988515i | \(0.451712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.8433 | 1.01467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.32985 | −0.121025 | −0.0605127 | − | 0.998167i | \(-0.519274\pi\) | ||||
−0.0605127 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.44364 | −0.0524007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.4077 | −0.667279 | −0.333640 | − | 0.942701i | \(-0.608277\pi\) | ||||
−0.333640 | + | 0.942701i | \(0.608277\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | 2.48869 | 0.0896279 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.4506 | −0.627656 | −0.313828 | − | 0.949480i | \(-0.601612\pi\) | ||||
−0.313828 | + | 0.949480i | \(0.601612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 41.5163 | 1.48939 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.8433 | 1.35588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.21818 | −0.258287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.26350 | −0.259576 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2335 | −0.756893 | −0.378447 | − | 0.925623i | \(-0.623542\pi\) | ||||
−0.378447 | + | 0.925623i | \(0.623542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.6360 | −1.94509 | ||||||||
\(790\) | 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 | ||||||||
\(801\) | 2.03281 | 0.0718259 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24993 | 0.149977 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.6238 | 1.32442 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.14137 | 0.215919 | 0.107960 | − | 0.994155i | \(-0.465568\pi\) | ||||
0.107960 | + | 0.994155i | \(0.465568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5051 | −0.544457 | −0.272229 | − | 0.962233i | \(-0.587761\pi\) | ||||
−0.272229 | + | 0.962233i | \(0.587761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4395 | −0.436271 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.3075 | −0.955368 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.42723 | −0.224586 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4835 | −0.749778 | −0.374889 | − | 0.927070i | \(-0.622319\pi\) | ||||
−0.374889 | + | 0.927070i | \(0.622319\pi\) | |||||||
\(822\) | 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 | \(-0.269839\pi\) | ||||
0.661691 | + | 0.749777i | \(0.269839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.2580 | −1.78026 | −0.890132 | − | 0.455703i | \(-0.849388\pi\) | ||||
−0.890132 | + | 0.455703i | \(0.849388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.90652 | 0.274274 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 106.035 | 3.67391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.05339 | 0.243801 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 12.3624 | 0.425783 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −51.5439 | −1.77107 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.5798 | 1.42701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.34625 | 0.148988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.0867 | −1.37254 | −0.686270 | − | 0.727346i | \(-0.740753\pi\) | ||||
−0.686270 | + | 0.727346i | \(0.740753\pi\) | |||||||
\(854\) | 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 | \(-0.277250\pi\) | ||||
0.644056 | + | 0.764978i | \(0.277250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 66.4053 | 2.26309 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.94555 | −0.134308 | −0.0671541 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671541 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.3173 | −1.33529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.74173 | 0.262620 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.8789 | −0.775223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.31450 | −0.179869 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.64958 | 0.292075 | 0.146038 | − | 0.989279i | \(-0.453348\pi\) | ||||
0.146038 | + | 0.989279i | \(0.453348\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.2007 | −1.05237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.1760 | −1.89262 | −0.946308 | − | 0.323266i | \(-0.895219\pi\) | ||||
−0.946308 | + | 0.323266i | \(0.895219\pi\) | |||||||
\(882\) | 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 | \(-0.636138\pi\) | ||||
−0.414770 | + | 0.909926i | \(0.636138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0716 | 0.438407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.96719 | 0.266911 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.5962 | −0.488443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.37907 | −0.112824 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.69179 | −0.0897761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −83.9422 | −2.79652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.9177 | −1.59460 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7170 | 0.754305 | 0.377153 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377153 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1700 | 0.370486 | ||||||||
\(910\) | 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 | \(-0.775853\pi\) | ||||
−0.762144 | + | 0.647408i | \(0.775853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.4764 | 0.444064 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.8953 | −0.556117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.10545 | −0.266218 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.12391 | 0.299346 | 0.149673 | − | 0.988736i | \(-0.452178\pi\) | ||||
0.149673 | + | 0.988736i | \(0.452178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −94.4933 | −3.09689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.01330 | −0.262344 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9190 | 1.10809 | 0.554043 | − | 0.832488i | \(-0.313084\pi\) | ||||
0.554043 | + | 0.832488i | \(0.313084\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.1260 | 0.395718 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.2926 | −1.21570 | −0.607852 | − | 0.794050i | \(-0.707969\pi\) | ||||
−0.607852 | + | 0.794050i | \(0.707969\pi\) | |||||||
\(942\) | 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 | \(-0.315531\pi\) | ||||
0.547629 | + | 0.836722i | \(0.315531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.94767 | 0.322915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.4639 | 0.598734 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.4465 | 1.56934 | 0.784668 | − | 0.619917i | \(-0.212834\pi\) | ||||
0.784668 | + | 0.619917i | \(0.212834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.40354 | −0.0776955 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.4465 | −0.983168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3861 | −0.915680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.58812 | −0.180075 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.2528 | −0.908548 | −0.454274 | − | 0.890862i | \(-0.650101\pi\) | ||||
−0.454274 | + | 0.890862i | \(0.650101\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 64.3585 | 2.06749 | ||||||||
\(970\) | 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 | ||||||||
\(981\) | −13.6730 | −0.436545 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.0615 | 0.480386 | 0.240193 | − | 0.970725i | \(-0.422789\pi\) | ||||
0.240193 | + | 0.970725i | \(0.422789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.6126 | −0.815258 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.01641 | −0.159512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.8971 | 1.39444 | 0.697219 | − | 0.716858i | \(-0.254421\pi\) | ||||
0.697219 | + | 0.716858i | \(0.254421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.6811 | −0.878432 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.5655 | −1.22138 | −0.610691 | − | 0.791869i | \(-0.709108\pi\) | ||||
−0.610691 | + | 0.791869i | \(0.709108\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.9612 | −0.599907 |
(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 | 9200.2.a.ci.1.1 | 3 | ||
4.3 | odd | 2 | 4600.2.a.v.1.3 | 3 | |||
5.4 | even | 2 | 1840.2.a.q.1.3 | 3 | |||
20.3 | even | 4 | 4600.2.e.q.4049.5 | 6 | |||
20.7 | even | 4 | 4600.2.e.q.4049.2 | 6 | |||
20.19 | odd | 2 | 920.2.a.i.1.1 | ✓ | 3 | ||
40.19 | odd | 2 | 7360.2.a.bw.1.3 | 3 | |||
40.29 | even | 2 | 7360.2.a.cf.1.1 | 3 | |||
60.59 | even | 2 | 8280.2.a.bl.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.1 | ✓ | 3 | 20.19 | odd | 2 | ||
1840.2.a.q.1.3 | 3 | 5.4 | even | 2 | |||
4600.2.a.v.1.3 | 3 | 4.3 | odd | 2 | |||
4600.2.e.q.4049.2 | 6 | 20.7 | even | 4 | |||
4600.2.e.q.4049.5 | 6 | 20.3 | even | 4 | |||
7360.2.a.bw.1.3 | 3 | 40.19 | odd | 2 | |||
7360.2.a.cf.1.1 | 3 | 40.29 | even | 2 | |||
8280.2.a.bl.1.3 | 3 | 60.59 | even | 2 | |||
9200.2.a.ci.1.1 | 3 | 1.1 | even | 1 | trivial |