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: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1150) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) 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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56155 | 0.590211 | 0.295106 | − | 0.955465i | \(-0.404645\pi\) | ||||
0.295106 | + | 0.955465i | \(0.404645\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | 0.987797 | 0.493899 | − | 0.869520i | \(-0.335571\pi\) | ||||
0.493899 | + | 0.869520i | \(0.335571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.43845 | 0.348875 | 0.174437 | − | 0.984668i | \(-0.444189\pi\) | ||||
0.174437 | + | 0.984668i | \(0.444189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.56155 | 1.03275 | 0.516377 | − | 0.856361i | \(-0.327280\pi\) | ||||
0.516377 | + | 0.856361i | \(0.327280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.12311 | −0.560926 | −0.280463 | − | 0.959865i | \(-0.590488\pi\) | ||||
−0.280463 | + | 0.959865i | \(0.590488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.12311 | −0.842233 | −0.421117 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421117 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.12311 | −1.46087 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1231 | −1.58096 | −0.790482 | − | 0.612486i | \(-0.790170\pi\) | ||||
−0.790482 | + | 0.612486i | \(0.790170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.68466 | 0.714404 | 0.357202 | − | 0.934027i | \(-0.383731\pi\) | ||||
0.357202 | + | 0.934027i | \(0.383731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.68466 | −0.515955 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.876894 | 0.120451 | 0.0602254 | − | 0.998185i | \(-0.480818\pi\) | ||||
0.0602254 | + | 0.998185i | \(0.480818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.2462 | −1.82404 | −0.912020 | − | 0.410145i | \(-0.865478\pi\) | ||||
−0.912020 | + | 0.410145i | \(0.865478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.56155 | 0.700690 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.43845 | 0.175734 | 0.0878671 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878671 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.56155 | 0.308375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.12311 | 0.845357 | 0.422679 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422679 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.12311 | 0.248491 | 0.124245 | − | 0.992252i | \(-0.460349\pi\) | ||||
0.124245 | + | 0.992252i | \(0.460349\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56155 | 0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9309 | 1.45484 | 0.727418 | − | 0.686194i | \(-0.240720\pi\) | ||||
0.727418 | + | 0.686194i | \(0.240720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.12311 | 0.233041 | 0.116521 | − | 0.993188i | \(-0.462826\pi\) | ||||
0.116521 | + | 0.993188i | \(0.462826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.2462 | −1.52735 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.5616 | −1.33152 | −0.665761 | − | 0.746165i | \(-0.731893\pi\) | ||||
−0.665761 | + | 0.746165i | \(0.731893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.56155 | 0.583009 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.24621 | −0.837276 | −0.418638 | − | 0.908153i | \(-0.637492\pi\) | ||||
−0.418638 | + | 0.908153i | \(0.637492\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.56155 | 0.357950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3693 | −1.33030 | −0.665148 | − | 0.746711i | \(-0.731632\pi\) | ||||
−0.665148 | + | 0.746711i | \(0.731632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.68466 | −0.658659 | −0.329329 | − | 0.944215i | \(-0.606823\pi\) | ||||
−0.329329 | + | 0.944215i | \(0.606823\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.80776 | 0.464784 | 0.232392 | − | 0.972622i | \(-0.425345\pi\) | ||||
0.232392 | + | 0.972622i | \(0.425345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3693 | 1.47211 | 0.736057 | − | 0.676920i | \(-0.236686\pi\) | ||||
0.736057 | + | 0.676920i | \(0.236686\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.1231 | 1.24559 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.9309 | 1.87494 | 0.937469 | − | 0.348068i | \(-0.113162\pi\) | ||||
0.937469 | + | 0.348068i | \(0.113162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.6847 | 1.17270 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.24621 | 0.205910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.9309 | 2.33811 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.75379 | 0.155624 | 0.0778118 | − | 0.996968i | \(-0.475207\pi\) | ||||
0.0778118 | + | 0.996968i | \(0.475207\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | −1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.12311 | −0.622349 | −0.311174 | − | 0.950353i | \(-0.600722\pi\) | ||||
−0.311174 | + | 0.950353i | \(0.600722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68466 | −0.406211 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8078 | 0.923370 | 0.461685 | − | 0.887044i | \(-0.347245\pi\) | ||||
0.461685 | + | 0.887044i | \(0.347245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.43845 | 0.461283 | 0.230642 | − | 0.973039i | \(-0.425918\pi\) | ||||
0.230642 | + | 0.973039i | \(0.425918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.3693 | 1.29433 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.56155 | 0.297832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.6847 | 0.963734 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3693 | −1.73901 | −0.869505 | − | 0.493924i | \(-0.835562\pi\) | ||||
−0.869505 | + | 0.493924i | \(0.835562\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.12311 | 0.414179 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.24621 | −0.178136 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.56155 | −0.123068 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.80776 | −0.533225 | −0.266613 | − | 0.963804i | \(-0.585904\pi\) | ||||
−0.266613 | + | 0.963804i | \(0.585904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0000 | −0.773823 | −0.386912 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386912 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.6847 | −0.817076 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.0540 | 1.67673 | 0.838366 | − | 0.545107i | \(-0.183511\pi\) | ||||
0.838366 | + | 0.545107i | \(0.183511\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2462 | 0.770152 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8078 | 1.10678 | 0.553392 | − | 0.832921i | \(-0.313333\pi\) | ||||
0.553392 | + | 0.832921i | \(0.313333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.3693 | 1.43971 | 0.719855 | − | 0.694124i | \(-0.244208\pi\) | ||||
0.719855 | + | 0.694124i | \(0.244208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 36.4924 | 2.69760 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.43845 | 0.105190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.24621 | −0.163388 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0540 | −1.59577 | −0.797885 | − | 0.602810i | \(-0.794048\pi\) | ||||
−0.797885 | + | 0.602810i | \(0.794048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.9309 | 1.14673 | 0.573365 | − | 0.819300i | \(-0.305638\pi\) | ||||
0.573365 | + | 0.819300i | \(0.305638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.684658 | −0.0487799 | −0.0243899 | − | 0.999703i | \(-0.507764\pi\) | ||||
−0.0243899 | + | 0.999703i | \(0.507764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6847 | 1.04097 | 0.520484 | − | 0.853871i | \(-0.325752\pi\) | ||||
0.520484 | + | 0.853871i | \(0.325752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.68466 | −0.259896 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.68466 | 0.609544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.56155 | −0.247545 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.31534 | −0.434766 | −0.217383 | − | 0.976086i | \(-0.569752\pi\) | ||||
−0.217383 | + | 0.976086i | \(0.569752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.2462 | −1.25021 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.87689 | −0.331065 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.43845 | −0.367496 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.12311 | 0.344617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.6155 | −1.58141 | −0.790706 | − | 0.612196i | \(-0.790287\pi\) | ||||
−0.790706 | + | 0.612196i | \(0.790287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.75379 | −0.647382 | −0.323691 | − | 0.946163i | \(-0.604924\pi\) | ||||
−0.323691 | + | 0.946163i | \(0.604924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.31534 | −0.610268 | −0.305134 | − | 0.952309i | \(-0.598701\pi\) | ||||
−0.305134 | + | 0.952309i | \(0.598701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.1231 | −2.15158 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2462 | −1.05088 | −0.525440 | − | 0.850831i | \(-0.676099\pi\) | ||||
−0.525440 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6847 | −0.881506 | −0.440753 | − | 0.897628i | \(-0.645289\pi\) | ||||
−0.440753 | + | 0.897628i | \(0.645289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6847 | −0.679849 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.43845 | −0.344648 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6847 | 0.737529 | 0.368765 | − | 0.929523i | \(-0.379781\pi\) | ||||
0.368765 | + | 0.929523i | \(0.379781\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.4924 | −0.904012 | −0.452006 | − | 0.892015i | \(-0.649292\pi\) | ||||
−0.452006 | + | 0.892015i | \(0.649292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.8078 | 1.22607 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.75379 | 0.354794 | 0.177397 | − | 0.984139i | \(-0.443232\pi\) | ||||
0.177397 | + | 0.984139i | \(0.443232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.1771 | 1.96921 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1771 | 0.925363 | 0.462681 | − | 0.886525i | \(-0.346887\pi\) | ||||
0.462681 | + | 0.886525i | \(0.346887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.75379 | −0.228026 | −0.114013 | − | 0.993479i | \(-0.536371\pi\) | ||||
−0.114013 | + | 0.993479i | \(0.536371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.2462 | −0.862220 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.05398 | 0.363748 | 0.181874 | − | 0.983322i | \(-0.441784\pi\) | ||||
0.181874 | + | 0.983322i | \(0.441784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.1231 | −0.665923 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2462 | 1.44641 | 0.723204 | − | 0.690635i | \(-0.242669\pi\) | ||||
0.723204 | + | 0.690635i | \(0.242669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1771 | 1.43718 | 0.718589 | − | 0.695435i | \(-0.244788\pi\) | ||||
0.718589 | + | 0.695435i | \(0.244788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.8078 | −0.933103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9309 | −0.878286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.1231 | 1.23826 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.4924 | 1.19718 | 0.598590 | − | 0.801056i | \(-0.295728\pi\) | ||||
0.598590 | + | 0.801056i | \(0.295728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.43845 | −0.0834672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.56155 | −0.205970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.31534 | 0.421649 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.2462 | 1.96739 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.9309 | 1.70824 | 0.854122 | − | 0.520072i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520072i | \(0.174095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.1231 | 0.974099 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.630683 | −0.0357628 | −0.0178814 | − | 0.999840i | \(-0.505692\pi\) | ||||
−0.0178814 | + | 0.999840i | \(0.505692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1231 | 1.19395 | 0.596974 | − | 0.802260i | \(-0.296369\pi\) | ||||
0.596974 | + | 0.802260i | \(0.296369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.5616 | 0.986355 | 0.493178 | − | 0.869929i | \(-0.335835\pi\) | ||||
0.493178 | + | 0.869929i | \(0.335835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.56155 | 0.311387 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3153 | −0.687375 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.31534 | −0.240112 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.3693 | −2.17713 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.36932 | −0.516547 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3002 | 1.28069 | 0.640347 | − | 0.768086i | \(-0.278791\pi\) | ||||
0.640347 | + | 0.768086i | \(0.278791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.2462 | −0.999886 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5616 | −1.55585 | −0.777923 | − | 0.628359i | \(-0.783727\pi\) | ||||
−0.777923 | + | 0.628359i | \(0.783727\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −51.0540 | −2.77287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.12311 | −0.169126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0540 | −0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.5616 | −1.64063 | −0.820315 | − | 0.571912i | \(-0.806202\pi\) | ||||
−0.820315 | + | 0.571912i | \(0.806202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0540 | −0.859350 | −0.429675 | − | 0.902984i | \(-0.641372\pi\) | ||||
−0.429675 | + | 0.902984i | \(0.641372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.12311 | −0.273451 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.4233 | −1.56604 | −0.783022 | − | 0.621994i | \(-0.786323\pi\) | ||||
−0.783022 | + | 0.621994i | \(0.786323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.75379 | −0.304523 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.5616 | 0.926863 | 0.463432 | − | 0.886133i | \(-0.346618\pi\) | ||||
0.463432 | + | 0.886133i | \(0.346618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.6155 | 1.34447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4384 | 0.649282 | 0.324641 | − | 0.945837i | \(-0.394757\pi\) | ||||
0.324641 | + | 0.945837i | \(0.394757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.0540 | −1.87689 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.36932 | 0.0710914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4924 | −0.853945 | −0.426973 | − | 0.904265i | \(-0.640420\pi\) | ||||
−0.426973 | + | 0.904265i | \(0.640420\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.8078 | 1.02015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8078 | −0.657891 | −0.328945 | − | 0.944349i | \(-0.606693\pi\) | ||||
−0.328945 | + | 0.944349i | \(0.606693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.49242 | −0.230154 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8078 | −0.909934 | −0.454967 | − | 0.890508i | \(-0.650349\pi\) | ||||
−0.454967 | + | 0.890508i | \(0.650349\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.6847 | 0.848129 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.1231 | −1.57800 | −0.789002 | − | 0.614391i | \(-0.789402\pi\) | ||||
−0.789002 | + | 0.614391i | \(0.789402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.43845 | −0.0727454 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.2462 | 0.920400 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1231 | −0.759007 | −0.379503 | − | 0.925190i | \(-0.623905\pi\) | ||||
−0.379503 | + | 0.925190i | \(0.623905\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | 0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6847 | 0.783254 | 0.391627 | − | 0.920124i | \(-0.371912\pi\) | ||||
0.391627 | + | 0.920124i | \(0.371912\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.1231 | −0.554081 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.12311 | −0.253943 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7538 | −0.630634 | −0.315317 | − | 0.948986i | \(-0.602111\pi\) | ||||
−0.315317 | + | 0.948986i | \(0.602111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.6847 | −1.36558 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.24621 | −0.307356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.9309 | −0.682198 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.8769 | −0.580224 | −0.290112 | − | 0.956993i | \(-0.593693\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7538 | −0.767793 | −0.383896 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383896 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.3693 | −1.03901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.2462 | −1.07657 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.12311 | −0.440468 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2462 | −0.878889 | −0.439445 | − | 0.898270i | \(-0.644825\pi\) | ||||
−0.439445 | + | 0.898270i | \(0.644825\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.3002 | −1.21585 | −0.607925 | − | 0.793995i | \(-0.707998\pi\) | ||||
−0.607925 | + | 0.793995i | \(0.707998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8769 | −1.47367 | −0.736837 | − | 0.676071i | \(-0.763681\pi\) | ||||
−0.736837 | + | 0.676071i | \(0.763681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.2462 | −0.773629 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.80776 | −0.133401 | −0.0667004 | − | 0.997773i | \(-0.521247\pi\) | ||||
−0.0667004 | + | 0.997773i | \(0.521247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 46.1080 | 2.18083 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4233 | 1.15261 | 0.576303 | − | 0.817236i | \(-0.304495\pi\) | ||||
0.576303 | + | 0.817236i | \(0.304495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.1231 | −0.476678 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 54.7386 | 2.57185 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1771 | −1.22451 | −0.612256 | − | 0.790660i | \(-0.709738\pi\) | ||||
−0.612256 | + | 0.790660i | \(0.709738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.06913 | −0.0965787 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.1771 | −0.613718 | −0.306859 | − | 0.951755i | \(-0.599278\pi\) | ||||
−0.306859 | + | 0.951755i | \(0.599278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.63068 | −0.215206 | −0.107603 | − | 0.994194i | \(-0.534318\pi\) | ||||
−0.107603 | + | 0.994194i | \(0.534318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.68466 | −0.216780 | −0.108390 | − | 0.994108i | \(-0.534570\pi\) | ||||
−0.108390 | + | 0.994108i | \(0.534570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.24621 | 0.103720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.3693 | 0.708181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.68466 | 0.215401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.12311 | 0.142997 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.93087 | 0.133915 | 0.0669574 | − | 0.997756i | \(-0.478671\pi\) | ||||
0.0669574 | + | 0.997756i | \(0.478671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2462 | −0.831956 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.24621 | −0.192414 | −0.0962071 | − | 0.995361i | \(-0.530671\pi\) | ||||
−0.0962071 | + | 0.995361i | \(0.530671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.4384 | 0.788594 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.24621 | −0.281888 | −0.140944 | − | 0.990018i | \(-0.545014\pi\) | ||||
−0.140944 | + | 0.990018i | \(0.545014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | 0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.1231 | 0.498939 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.8617 | −1.51586 | −0.757930 | − | 0.652336i | \(-0.773789\pi\) | ||||
−0.757930 | + | 0.652336i | \(0.773789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.6155 | 1.14442 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5616 | −0.961382 | −0.480691 | − | 0.876890i | \(-0.659614\pi\) | ||||
−0.480691 | + | 0.876890i | \(0.659614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.807764 | 0.0358741 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.8769 | −0.748055 | −0.374028 | − | 0.927418i | \(-0.622023\pi\) | ||||
−0.374028 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.31534 | 0.146662 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.31534 | 0.190527 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −56.4924 | −2.47974 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.93087 | 0.0845929 | 0.0422965 | − | 0.999105i | \(-0.486533\pi\) | ||||
0.0422965 | + | 0.999105i | \(0.486533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.1080 | −1.53516 | −0.767582 | − | 0.640951i | \(-0.778540\pi\) | ||||
−0.767582 | + | 0.640951i | \(0.778540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.49242 | −0.195693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2462 | −0.618233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0540 | −1.56167 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.9309 | −1.63684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.56155 | −0.196480 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.68466 | −0.373383 | −0.186691 | − | 0.982419i | \(-0.559776\pi\) | ||||
−0.186691 | + | 0.982419i | \(0.559776\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −49.6155 | −2.12921 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.5616 | 0.537093 | 0.268547 | − | 0.963267i | \(-0.413457\pi\) | ||||
0.268547 | + | 0.963267i | \(0.413457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −50.7386 | −2.16547 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.6847 | −0.710790 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.1922 | 0.858661 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.3693 | −0.481733 | −0.240867 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240867 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.6847 | 0.705686 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.68466 | −0.155566 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8078 | −0.666218 | −0.333109 | − | 0.942888i | \(-0.608098\pi\) | ||||
−0.333109 | + | 0.942888i | \(0.608098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9309 | −0.459053 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.6847 | 1.49598 | 0.747989 | − | 0.663711i | \(-0.231019\pi\) | ||||
0.747989 | + | 0.663711i | \(0.231019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0000 | 1.50655 | 0.753277 | − | 0.657704i | \(-0.228472\pi\) | ||||
0.753277 | + | 0.657704i | \(0.228472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 56.4924 | 2.36000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8769 | 1.49357 | 0.746787 | − | 0.665063i | \(-0.231595\pi\) | ||||
0.746787 | + | 0.665063i | \(0.231595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.8078 | −1.69591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.31534 | 0.137544 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.876894 | 0.0363173 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.8078 | 1.51922 | 0.759610 | − | 0.650379i | \(-0.225390\pi\) | ||||
0.759610 | + | 0.650379i | \(0.225390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.36932 | 0.386056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.75379 | 0.0721412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.75379 | 0.195215 | 0.0976074 | − | 0.995225i | \(-0.468881\pi\) | ||||
0.0976074 | + | 0.995225i | \(0.468881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.6155 | −1.53950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.1231 | 1.27166 | 0.635828 | − | 0.771831i | \(-0.280659\pi\) | ||||
0.635828 | + | 0.771831i | \(0.280659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6847 | −1.04770 | −0.523850 | − | 0.851811i | \(-0.675505\pi\) | ||||
−0.523850 | + | 0.851811i | \(0.675505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.12311 | 0.208629 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.9848 | −1.25764 | −0.628818 | − | 0.777552i | \(-0.716461\pi\) | ||||
−0.628818 | + | 0.777552i | \(0.716461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.2462 | −0.901462 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.3693 | −0.864510 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.49242 | −0.181447 | −0.0907236 | − | 0.995876i | \(-0.528918\pi\) | ||||
−0.0907236 | + | 0.995876i | \(0.528918\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.8617 | 1.28271 | 0.641353 | − | 0.767246i | \(-0.278374\pi\) | ||||
0.641353 | + | 0.767246i | \(0.278374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9848 | −1.16500 | −0.582500 | − | 0.812831i | \(-0.697925\pi\) | ||||
−0.582500 | + | 0.812831i | \(0.697925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.6155 | −0.785880 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.68466 | 0.306896 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.36932 | −0.293834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.1771 | −1.71885 | −0.859426 | − | 0.511260i | \(-0.829179\pi\) | ||||
−0.859426 | + | 0.511260i | \(0.829179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.1771 | 0.642981 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.2462 | −0.643698 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.3693 | 1.00359 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8617 | 1.10047 | 0.550236 | − | 0.835009i | \(-0.314538\pi\) | ||||
0.550236 | + | 0.835009i | \(0.314538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −50.0540 | −1.97394 | −0.986968 | − | 0.160916i | \(-0.948555\pi\) | ||||
−0.986968 | + | 0.160916i | \(0.948555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.3693 | −1.46914 | −0.734570 | − | 0.678533i | \(-0.762616\pi\) | ||||
−0.734570 | + | 0.678533i | \(0.762616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.4924 | 0.489617 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0691 | 0.746233 | 0.373116 | − | 0.927785i | \(-0.378289\pi\) | ||||
0.373116 | + | 0.927785i | \(0.378289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.56155 | 0.295004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.7386 | −1.08054 | −0.540272 | − | 0.841491i | \(-0.681679\pi\) | ||||
−0.540272 | + | 0.841491i | \(0.681679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8617 | 1.16149 | 0.580744 | − | 0.814087i | \(-0.302762\pi\) | ||||
0.580744 | + | 0.814087i | \(0.302762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.1231 | −0.509659 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.56155 | −0.215344 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.4924 | 2.33877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2462 | −0.549969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.8078 | −1.45738 | −0.728691 | − | 0.684843i | \(-0.759871\pi\) | ||||
−0.728691 | + | 0.684843i | \(0.759871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1231 | −0.504362 | −0.252181 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252181 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.8769 | −0.494170 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9848 | 0.957421 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.68466 | −0.217517 | −0.108759 | − | 0.994068i | \(-0.534688\pi\) | ||||
−0.108759 | + | 0.994068i | \(0.534688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.6155 | −0.977293 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.12311 | 0.118981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.43845 | 0.206888 | 0.103444 | − | 0.994635i | \(-0.467014\pi\) | ||||
0.103444 | + | 0.994635i | \(0.467014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.56155 | 0.211266 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.5616 | −0.551558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.8617 | 0.902534 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.7538 | 0.670551 | 0.335276 | − | 0.942120i | \(-0.391171\pi\) | ||||
0.335276 | + | 0.942120i | \(0.391171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3693 | 0.579665 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.8769 | −0.785156 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.8617 | −1.12148 | −0.560741 | − | 0.827992i | \(-0.689483\pi\) | ||||
−0.560741 | + | 0.827992i | \(0.689483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.0540 | 1.72716 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.12311 | 0.116961 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.6155 | 1.55416 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7386 | 0.400483 | 0.200242 | − | 0.979747i | \(-0.435827\pi\) | ||||
0.200242 | + | 0.979747i | \(0.435827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4384 | −0.388748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.0540 | 1.30367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.24621 | −0.0833074 | −0.0416537 | − | 0.999132i | \(-0.513263\pi\) | ||||
−0.0416537 | + | 0.999132i | \(0.513263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.73863 | 0.249237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.43845 | 0.0529859 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8769 | 0.915111 | 0.457556 | − | 0.889181i | \(-0.348725\pi\) | ||||
0.457556 | + | 0.889181i | \(0.348725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.3693 | 1.00544 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6695 | 1.30859 | 0.654294 | − | 0.756241i | \(-0.272966\pi\) | ||||
0.654294 | + | 0.756241i | \(0.272966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.56155 | 0.276663 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.50758 | 0.274321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.8078 | −0.430871 | −0.215436 | − | 0.976518i | \(-0.569117\pi\) | ||||
−0.215436 | + | 0.976518i | \(0.569117\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.9309 | −1.09074 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2462 | −1.39008 | −0.695041 | − | 0.718970i | \(-0.744614\pi\) | ||||
−0.695041 | + | 0.718970i | \(0.744614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.56155 | 0.0929785 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.49242 | −0.126600 | −0.0633001 | − | 0.997995i | \(-0.520163\pi\) | ||||
−0.0633001 | + | 0.997995i | \(0.520163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0000 | 0.868858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.2462 | −0.514401 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.4233 | 1.52982 | 0.764912 | − | 0.644135i | \(-0.222783\pi\) | ||||
0.764912 | + | 0.644135i | \(0.222783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1231 | 1.33696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.75379 | 0.206949 | 0.103475 | − | 0.994632i | \(-0.467004\pi\) | ||||
0.103475 | + | 0.994632i | \(0.467004\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.4924 | 0.735162 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.3693 | 1.08809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.12311 | 0.254885 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.00000 | −0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.94602 | −0.0693683 | −0.0346841 | − | 0.999398i | \(-0.511043\pi\) | ||||
−0.0346841 | + | 0.999398i | \(0.511043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.7386 | −0.524709 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1231 | 1.10661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.7386 | −1.80178 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.63068 | −0.164027 | −0.0820136 | − | 0.996631i | \(-0.526135\pi\) | ||||
−0.0820136 | + | 0.996631i | \(0.526135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.63068 | −0.305332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.7386 | −1.58076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.12311 | 0.0749228 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.8769 | −1.36853 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0691 | 0.389170 | 0.194585 | − | 0.980886i | \(-0.437664\pi\) | ||||
0.194585 | + | 0.980886i | \(0.437664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9848 | 0.736878 | 0.368439 | − | 0.929652i | \(-0.379892\pi\) | ||||
0.368439 | + | 0.929652i | \(0.379892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.61553 | 0.337231 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0540 | −0.491686 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.8078 | 0.692139 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3002 | −0.568880 | −0.284440 | − | 0.958694i | \(-0.591808\pi\) | ||||
−0.284440 | + | 0.958694i | \(0.591808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.3693 | −0.954034 | −0.477017 | − | 0.878894i | \(-0.658282\pi\) | ||||
−0.477017 | + | 0.878894i | \(0.658282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0000 | −0.730242 | −0.365121 | − | 0.930960i | \(-0.618972\pi\) | ||||
−0.365121 | + | 0.930960i | \(0.618972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1922 | −0.701305 | −0.350653 | − | 0.936506i | \(-0.614040\pi\) | ||||
−0.350653 | + | 0.936506i | \(0.614040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5076 | −0.537952 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.56155 | −0.227344 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.49242 | 0.155281 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9309 | −0.584519 | −0.292259 | − | 0.956339i | \(-0.594407\pi\) | ||||
−0.292259 | + | 0.956339i | \(0.594407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.93087 | 0.0665817 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −62.1080 | −2.13911 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.6155 | −0.536556 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −61.9309 | −2.12546 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.12311 | 0.175618 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.192236 | 0.00658203 | 0.00329102 | − | 0.999995i | \(-0.498952\pi\) | ||||
0.00329102 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9460 | 0.373909 | 0.186955 | − | 0.982369i | \(-0.440138\pi\) | ||||
0.186955 | + | 0.982369i | \(0.440138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1771 | 1.37082 | 0.685412 | − | 0.728155i | \(-0.259622\pi\) | ||||
0.685412 | + | 0.728155i | \(0.259622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.4924 | 1.37998 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.1231 | 1.19560 | 0.597802 | − | 0.801644i | \(-0.296041\pi\) | ||||
0.597802 | + | 0.801644i | \(0.296041\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.2462 | 1.29891 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9309 | 0.438650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.12311 | 0.173590 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.3693 | −0.994001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.49242 | −0.0841631 | −0.0420816 | − | 0.999114i | \(-0.513399\pi\) | ||||
−0.0420816 | + | 0.999114i | \(0.513399\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.4924 | −1.77053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.3693 | −1.59591 | −0.797956 | − | 0.602715i | \(-0.794086\pi\) | ||||
−0.797956 | + | 0.602715i | \(0.794086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.6847 | 1.73933 | 0.869664 | − | 0.493645i | \(-0.164336\pi\) | ||||
0.869664 | + | 0.493645i | \(0.164336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00000 | −0.134307 | −0.0671534 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671534 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.73863 | 0.0918508 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.00000 | −0.234509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0000 | 0.602347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.12311 | 0.304612 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3693 | −0.579299 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26137 | 0.0420222 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.7386 | −0.623583 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.6847 | −0.421187 | −0.210594 | − | 0.977574i | \(-0.567540\pi\) | ||||
−0.210594 | + | 0.977574i | \(0.567540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.6155 | −1.57931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.5464 | −1.74094 | −0.870470 | − | 0.492222i | \(-0.836185\pi\) | ||||
−0.870470 | + | 0.492222i | \(0.836185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.12311 | 0.0702645 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1231 | −0.367317 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7386 | 0.486183 | 0.243091 | − | 0.970003i | \(-0.421839\pi\) | ||||
0.243091 | + | 0.970003i | \(0.421839\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76.6695 | −2.52635 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.3693 | 0.835041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.8078 | −0.781950 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.9309 | 1.34290 | 0.671449 | − | 0.741051i | \(-0.265672\pi\) | ||||
0.671449 | + | 0.741051i | \(0.265672\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6847 | 0.448497 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.61553 | 0.0528900 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.9309 | 1.43516 | 0.717579 | − | 0.696477i | \(-0.245250\pi\) | ||||
0.717579 | + | 0.696477i | \(0.245250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.1080 | −1.76575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.8617 | 1.10386 | 0.551931 | − | 0.833890i | \(-0.313891\pi\) | ||||
0.551931 | + | 0.833890i | \(0.313891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1231 | 0.329654 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.1080 | −1.82326 | −0.911632 | − | 0.411008i | \(-0.865177\pi\) | ||||
−0.911632 | + | 0.411008i | \(0.865177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.56155 | 0.245458 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.9848 | −1.45873 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.5616 | −1.50828 | −0.754138 | − | 0.656716i | \(-0.771945\pi\) | ||||
−0.754138 | + | 0.656716i | \(0.771945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.2462 | −0.460515 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.8769 | 0.544983 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.1231 | 0.551784 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000 | 0.128631 | 0.0643157 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643157 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.0540 | 0.355105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.63068 | −0.309063 | −0.154532 | − | 0.987988i | \(-0.549387\pi\) | ||||
−0.154532 | + | 0.987988i | \(0.549387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.49242 | 0.272255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.05398 | 0.161691 | 0.0808455 | − | 0.996727i | \(-0.474238\pi\) | ||||
0.0808455 | + | 0.996727i | \(0.474238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5616 | −0.401469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.7386 | 1.74767 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.31534 | 0.297113 | 0.148557 | − | 0.988904i | \(-0.452537\pi\) | ||||
0.148557 | + | 0.988904i | \(0.452537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.0000 | 0.763928 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.68466 | −0.148963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.24621 | 0.134885 | 0.0674427 | − | 0.997723i | \(-0.478516\pi\) | ||||
0.0674427 | + | 0.997723i | \(0.478516\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.6847 | −1.89404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.822919 | −0.0260621 | −0.0130311 | − | 0.999915i | \(-0.504148\pi\) | ||||
−0.0130311 | + | 0.999915i | \(0.504148\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.36932 | 0.233155 |
(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.bp.1.1 | 2 | ||
4.3 | odd | 2 | 1150.2.a.p.1.2 | yes | 2 | ||
5.4 | even | 2 | 9200.2.a.bw.1.2 | 2 | |||
20.3 | even | 4 | 1150.2.b.h.599.2 | 4 | |||
20.7 | even | 4 | 1150.2.b.h.599.3 | 4 | |||
20.19 | odd | 2 | 1150.2.a.k.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.2.a.k.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
1150.2.a.p.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1150.2.b.h.599.2 | 4 | 20.3 | even | 4 | |||
1150.2.b.h.599.3 | 4 | 20.7 | even | 4 | |||
9200.2.a.bp.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9200.2.a.bw.1.2 | 2 | 5.4 | even | 2 |