Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −1.80194 | −1.04035 | −0.520175 | − | 0.854060i | \(-0.674133\pi\) | ||||
−0.520175 | + | 0.854060i | \(0.674133\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80194 | −0.681068 | −0.340534 | − | 0.940232i | \(-0.610608\pi\) | ||||
−0.340534 | + | 0.940232i | \(0.610608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.246980 | 0.0823265 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.55496 | 0.468838 | 0.234419 | − | 0.972136i | \(-0.424681\pi\) | ||||
0.234419 | + | 0.972136i | \(0.424681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.80194 | 0.465258 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.911854 | 0.221157 | 0.110579 | − | 0.993867i | \(-0.464730\pi\) | ||||
0.110579 | + | 0.993867i | \(0.464730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.69202 | 0.388176 | 0.194088 | − | 0.980984i | \(-0.437825\pi\) | ||||
0.194088 | + | 0.980984i | \(0.437825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.24698 | 0.708549 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.246980 | 0.0514988 | 0.0257494 | − | 0.999668i | \(-0.491803\pi\) | ||||
0.0257494 | + | 0.999668i | \(0.491803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.96077 | 0.954701 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.29590 | −0.983423 | −0.491712 | − | 0.870758i | \(-0.663629\pi\) | ||||
−0.491712 | + | 0.870758i | \(0.663629\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.08815 | −0.195437 | −0.0977184 | − | 0.995214i | \(-0.531154\pi\) | ||||
−0.0977184 | + | 0.995214i | \(0.531154\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.80194 | −0.487755 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.80194 | 0.304583 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.96077 | 1.08709 | 0.543545 | − | 0.839380i | \(-0.317082\pi\) | ||||
0.543545 | + | 0.839380i | \(0.317082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.26875 | 0.345981 | 0.172991 | − | 0.984923i | \(-0.444657\pi\) | ||||
0.172991 | + | 0.984923i | \(0.444657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.246980 | −0.0368175 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.52111 | 1.24293 | 0.621466 | − | 0.783441i | \(-0.286538\pi\) | ||||
0.621466 | + | 0.783441i | \(0.286538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.75302 | −0.536146 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.64310 | −0.230081 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.92692 | 0.951486 | 0.475743 | − | 0.879584i | \(-0.342179\pi\) | ||||
0.475743 | + | 0.879584i | \(0.342179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.55496 | −0.209671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.04892 | −0.403839 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.7017 | −1.91400 | −0.957000 | − | 0.290089i | \(-0.906315\pi\) | ||||
−0.957000 | + | 0.290089i | \(0.906315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.55496 | −1.22339 | −0.611694 | − | 0.791095i | \(-0.709511\pi\) | ||||
−0.611694 | + | 0.791095i | \(0.709511\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.445042 | −0.0560700 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.21983 | 0.637704 | 0.318852 | − | 0.947805i | \(-0.396703\pi\) | ||||
0.318852 | + | 0.947805i | \(0.396703\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.445042 | −0.0535767 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.74094 | −0.681324 | −0.340662 | − | 0.940186i | \(-0.610651\pi\) | ||||
−0.340662 | + | 0.940186i | \(0.610651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.5918 | 1.70784 | 0.853920 | − | 0.520404i | \(-0.174219\pi\) | ||||
0.853920 | + | 0.520404i | \(0.174219\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.80194 | −0.208070 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.80194 | −0.319310 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.75063 | 0.872014 | 0.436007 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436007 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.67994 | −1.07555 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.94869 | 0.543189 | 0.271595 | − | 0.962412i | \(-0.412449\pi\) | ||||
0.271595 | + | 0.962412i | \(0.412449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.911854 | −0.0989045 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.54288 | 1.02310 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9095 | −1.26240 | −0.631200 | − | 0.775620i | \(-0.717437\pi\) | ||||
−0.631200 | + | 0.775620i | \(0.717437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.96077 | 0.203323 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69202 | −0.173598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.17390 | −0.931468 | −0.465734 | − | 0.884925i | \(-0.654210\pi\) | ||||
−0.465734 | + | 0.884925i | \(0.654210\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.384043 | 0.0385978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.18060 | −0.216978 | −0.108489 | − | 0.994098i | \(-0.534601\pi\) | ||||
−0.108489 | + | 0.994098i | \(0.534601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.58211 | −0.944153 | −0.472076 | − | 0.881558i | \(-0.656495\pi\) | ||||
−0.472076 | + | 0.881558i | \(0.656495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.24698 | −0.316873 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.03684 | 0.583603 | 0.291801 | − | 0.956479i | \(-0.405745\pi\) | ||||
0.291801 | + | 0.956479i | \(0.405745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6703 | −1.02202 | −0.511012 | − | 0.859573i | \(-0.670729\pi\) | ||||
−0.511012 | + | 0.859573i | \(0.670729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.40581 | −0.513097 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.6136 | −1.65694 | −0.828472 | − | 0.560030i | \(-0.810790\pi\) | ||||
−0.828472 | + | 0.560030i | \(0.810790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.246980 | −0.0230310 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.64310 | −0.150623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.58211 | −0.780191 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.5429 | −1.13095 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.4644 | −1.90466 | −0.952330 | − | 0.305071i | \(-0.901320\pi\) | ||||
−0.952330 | + | 0.305071i | \(0.901320\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.08815 | −0.359941 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.94869 | 0.694480 | 0.347240 | − | 0.937776i | \(-0.387119\pi\) | ||||
0.347240 | + | 0.937776i | \(0.387119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.04892 | −0.264375 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.96077 | −0.426955 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.39075 | −0.118820 | −0.0594098 | − | 0.998234i | \(-0.518922\pi\) | ||||
−0.0594098 | + | 0.998234i | \(0.518922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1008 | 1.70493 | 0.852465 | − | 0.522785i | \(-0.175107\pi\) | ||||
0.852465 | + | 0.522785i | \(0.175107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3545 | −1.29308 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.29590 | 0.439800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.76271 | 0.557779 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.34050 | 0.601357 | 0.300679 | − | 0.953725i | \(-0.402787\pi\) | ||||
0.300679 | + | 0.953725i | \(0.402787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.46011 | 0.688474 | 0.344237 | − | 0.938883i | \(-0.388138\pi\) | ||||
0.344237 | + | 0.938883i | \(0.388138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.225209 | 0.0182071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.08815 | 0.0874020 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.7681 | −1.41805 | −0.709024 | − | 0.705185i | \(-0.750864\pi\) | ||||
−0.709024 | + | 0.705185i | \(0.750864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4819 | −0.989877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.445042 | −0.0350742 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6286 | 0.910825 | 0.455412 | − | 0.890281i | \(-0.349492\pi\) | ||||
0.455412 | + | 0.890281i | \(0.349492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.80194 | 0.218131 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.20237 | 0.712101 | 0.356051 | − | 0.934467i | \(-0.384123\pi\) | ||||
0.356051 | + | 0.934467i | \(0.384123\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.417895 | 0.0319572 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.4601 | −1.17541 | −0.587705 | − | 0.809075i | \(-0.699968\pi\) | ||||
−0.587705 | + | 0.809075i | \(0.699968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.80194 | −0.136214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.4916 | 1.99123 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.0519 | −1.57349 | −0.786746 | − | 0.617276i | \(-0.788236\pi\) | ||||
−0.786746 | + | 0.617276i | \(0.788236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9608 | −1.11203 | −0.556013 | − | 0.831174i | \(-0.687669\pi\) | ||||
−0.556013 | + | 0.831174i | \(0.687669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.2174 | 1.27275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41789 | 0.103687 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.93900 | −0.650217 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.15452 | 0.228253 | 0.114127 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114127 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.04892 | −0.291447 | −0.145724 | − | 0.989325i | \(-0.546551\pi\) | ||||
−0.145724 | + | 0.989325i | \(0.546551\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.20775 | 0.371037 | 0.185518 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185518 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.5013 | −1.59507 | −0.797536 | − | 0.603272i | \(-0.793864\pi\) | ||||
−0.797536 | + | 0.603272i | \(0.793864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.40581 | −0.663435 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.54288 | 0.669779 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.96077 | −0.486161 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0609989 | 0.00423972 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.63102 | 0.181992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0435405 | −0.00299745 | −0.00149873 | − | 0.999999i | \(-0.500477\pi\) | ||||
−0.00149873 | + | 0.999999i | \(0.500477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.3448 | 0.708815 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.26875 | −0.154727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.96077 | 0.133106 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.2935 | −1.77675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0911 | −1.07754 | −0.538771 | − | 0.842452i | \(-0.681111\pi\) | ||||
−0.538771 | + | 0.842452i | \(0.681111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.246980 | 0.0164653 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.08575 | −0.0720640 | −0.0360320 | − | 0.999351i | \(-0.511472\pi\) | ||||
−0.0360320 | + | 0.999351i | \(0.511472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.2620 | −1.66936 | −0.834681 | − | 0.550733i | \(-0.814348\pi\) | ||||
−0.834681 | + | 0.550733i | \(0.814348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.04892 | 0.332194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.9879 | −1.57150 | −0.785750 | − | 0.618544i | \(-0.787723\pi\) | ||||
−0.785750 | + | 0.618544i | \(0.787723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.52111 | −0.555856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9661 | −0.907199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.88769 | 0.251474 | 0.125737 | − | 0.992064i | \(-0.459870\pi\) | ||||
0.125737 | + | 0.992064i | \(0.459870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5894 | 1.58394 | 0.791971 | − | 0.610558i | \(-0.209055\pi\) | ||||
0.791971 | + | 0.610558i | \(0.209055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.56033 | 0.164246 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.75302 | 0.239772 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.91723 | −0.565107 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.5090 | −0.915802 | −0.457901 | − | 0.889003i | \(-0.651399\pi\) | ||||
−0.457901 | + | 0.889003i | \(0.651399\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384043 | 0.0241446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.64310 | 0.102895 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.19700 | −0.324180 | −0.162090 | − | 0.986776i | \(-0.551823\pi\) | ||||
−0.162090 | + | 0.986776i | \(0.551823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.40581 | −0.335901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.30798 | −0.0809618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.86294 | 0.484849 | 0.242425 | − | 0.970170i | \(-0.422057\pi\) | ||||
0.242425 | + | 0.970170i | \(0.422057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.92692 | −0.425517 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.4601 | 1.31334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.81700 | 0.415640 | 0.207820 | − | 0.978167i | \(-0.433363\pi\) | ||||
0.207820 | + | 0.978167i | \(0.433363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2228 | 0.985466 | 0.492733 | − | 0.870181i | \(-0.335998\pi\) | ||||
0.492733 | + | 0.870181i | \(0.335998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.55496 | 0.0937675 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.15644 | 0.129568 | 0.0647840 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647840 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.268750 | −0.0160896 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7235 | 0.639709 | 0.319855 | − | 0.947467i | \(-0.396366\pi\) | ||||
0.319855 | + | 0.947467i | \(0.396366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.50902 | −0.327478 | −0.163739 | − | 0.986504i | \(-0.552355\pi\) | ||||
−0.163739 | + | 0.986504i | \(0.552355\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.04892 | 0.180602 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5429 | −0.740383 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1685 | −0.951090 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5308 | 0.969052 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.80864 | 0.105662 | 0.0528310 | − | 0.998603i | \(-0.483176\pi\) | ||||
0.0528310 | + | 0.998603i | \(0.483176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7017 | 0.855967 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.71379 | 0.447600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.08815 | −0.235637 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.92931 | 0.225733 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.55496 | 0.547115 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9414 | 0.624458 | 0.312229 | − | 0.950007i | \(-0.398924\pi\) | ||||
0.312229 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2664 | 0.982249 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.95646 | −0.167645 | −0.0838227 | − | 0.996481i | \(-0.526713\pi\) | ||||
−0.0838227 | + | 0.996481i | \(0.526713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.17523 | −0.0664278 | −0.0332139 | − | 0.999448i | \(-0.510574\pi\) | ||||
−0.0332139 | + | 0.999448i | \(0.510574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.445042 | 0.0250753 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.4620 | −0.980765 | −0.490383 | − | 0.871507i | \(-0.663143\pi\) | ||||
−0.490383 | + | 0.871507i | \(0.663143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.23490 | −0.461066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.8780 | −0.607151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.54288 | 0.0858479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.2271 | 1.06326 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3545 | −0.846521 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.7289 | −0.644676 | −0.322338 | − | 0.946625i | \(-0.604469\pi\) | ||||
−0.322338 | + | 0.946625i | \(0.604469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.740939 | 0.0406032 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.21983 | −0.285190 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.1879 | −1.53549 | −0.767746 | − | 0.640754i | \(-0.778622\pi\) | ||||
−0.767746 | + | 0.640754i | \(0.778622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.7385 | 1.72380 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.69202 | −0.0916281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3763 | 1.04622 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.445042 | 0.0239602 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.92394 | 0.264331 | 0.132165 | − | 0.991228i | \(-0.457807\pi\) | ||||
0.132165 | + | 0.991228i | \(0.457807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3220 | −0.766638 | −0.383319 | − | 0.923616i | \(-0.625219\pi\) | ||||
−0.383319 | + | 0.923616i | \(0.625219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.57242 | 0.243365 | 0.121683 | − | 0.992569i | \(-0.461171\pi\) | ||||
0.121683 | + | 0.992569i | \(0.461171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.74094 | 0.304697 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.96077 | 0.156701 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.0315 | −1.53222 | −0.766111 | − | 0.642708i | \(-0.777811\pi\) | ||||
−0.766111 | + | 0.642708i | \(0.777811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1371 | −0.849319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.4644 | 0.811672 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.5918 | −0.763769 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.8297 | 1.45270 | 0.726349 | − | 0.687326i | \(-0.241216\pi\) | ||||
0.726349 | + | 0.687326i | \(0.241216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.71917 | 0.0894963 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4819 | −0.648027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1588 | −0.836673 | −0.418336 | − | 0.908292i | \(-0.637387\pi\) | ||||
−0.418336 | + | 0.908292i | \(0.637387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.80194 | 0.0930517 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.05861 | −0.208477 | −0.104238 | − | 0.994552i | \(-0.533240\pi\) | ||||
−0.104238 | + | 0.994552i | \(0.533240\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.6775 | 1.98151 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9269 | −0.660535 | −0.330267 | − | 0.943887i | \(-0.607139\pi\) | ||||
−0.330267 | + | 0.943887i | \(0.607139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.80194 | 0.142800 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.560335 | 0.0284834 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2784 | 0.521138 | 0.260569 | − | 0.965455i | \(-0.416090\pi\) | ||||
0.260569 | + | 0.965455i | \(0.416090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.225209 | 0.0113893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.3230 | −0.722502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.75063 | −0.389976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0694 | 0.756309 | 0.378155 | − | 0.925742i | \(-0.376559\pi\) | ||||
0.378155 | + | 0.925742i | \(0.376559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.49396 | 0.275042 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.25129 | 0.0624865 | 0.0312433 | − | 0.999512i | \(-0.490053\pi\) | ||||
0.0312433 | + | 0.999512i | \(0.490053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.67994 | 0.481000 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.66487 | 0.231229 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.4849 | 0.666783 | 0.333392 | − | 0.942788i | \(-0.391807\pi\) | ||||
0.333392 | + | 0.942788i | \(0.391807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.50604 | 0.123614 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.4916 | 1.30356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.94869 | −0.242922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.2204 | −1.77372 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.84846 | −0.432276 | −0.216138 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216138 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.39373 | 0.214137 | 0.107069 | − | 0.994252i | \(-0.465854\pi\) | ||||
0.107069 | + | 0.994252i | \(0.465854\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.10454 | 0.102326 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.911854 | 0.0442314 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.2174 | 0.833210 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7235 | −0.853710 | −0.426855 | − | 0.904320i | \(-0.640379\pi\) | ||||
−0.426855 | + | 0.904320i | \(0.640379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.81402 | −0.375518 | −0.187759 | − | 0.982215i | \(-0.560122\pi\) | ||||
−0.187759 | + | 0.982215i | \(0.560122\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.54288 | −0.457546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.417895 | 0.0199906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.64178 | −0.269267 | −0.134634 | − | 0.990895i | \(-0.542986\pi\) | ||||
−0.134634 | + | 0.990895i | \(0.542986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.926919 | −0.0441390 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.3491 | 1.25188 | 0.625942 | − | 0.779869i | \(-0.284715\pi\) | ||||
0.625942 | + | 0.779869i | \(0.284715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.9095 | 0.564563 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.2271 | −0.625622 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.0941 | −1.84497 | −0.922483 | − | 0.386039i | \(-0.873843\pi\) | ||||
−0.922483 | + | 0.386039i | \(0.873843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8237 | 0.509669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.2446 | −0.716253 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6025 | 0.916968 | 0.458484 | − | 0.888703i | \(-0.348393\pi\) | ||||
0.458484 | + | 0.888703i | \(0.348393\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.52350 | 0.211139 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.5435 | 1.88830 | 0.944149 | − | 0.329520i | \(-0.106887\pi\) | ||||
0.944149 | + | 0.329520i | \(0.106887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4959 | −1.46374 | −0.731869 | − | 0.681446i | \(-0.761352\pi\) | ||||
−0.731869 | + | 0.681446i | \(0.761352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.96077 | −0.0909286 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.6189 | 1.64825 | 0.824124 | − | 0.566409i | \(-0.191668\pi\) | ||||
0.824124 | + | 0.566409i | \(0.191668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.40581 | −0.434320 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.0170 | 1.47526 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.52781 | 0.162209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.69202 | 0.0776353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.71081 | 0.0783325 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.698726 | −0.0319256 | −0.0159628 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159628 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.801938 | 0.0364894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.17390 | 0.416565 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.49263 | −0.430152 | −0.215076 | − | 0.976597i | \(-0.569000\pi\) | ||||
−0.215076 | + | 0.976597i | \(0.569000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.9541 | −0.947576 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0261 | 1.03915 | 0.519576 | − | 0.854424i | \(-0.326090\pi\) | ||||
0.519576 | + | 0.854424i | \(0.326090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.82908 | −0.217491 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.384043 | −0.0172614 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3448 | 0.464028 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5109 | 0.694365 | 0.347183 | − | 0.937798i | \(-0.387138\pi\) | ||||
0.347183 | + | 0.937798i | \(0.387138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.5821 | −0.740834 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.8538 | −1.24194 | −0.620971 | − | 0.783834i | \(-0.713261\pi\) | ||||
−0.620971 | + | 0.783834i | \(0.713261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.18060 | 0.0970356 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.6474 | −0.915181 | −0.457590 | − | 0.889163i | \(-0.651287\pi\) | ||||
−0.457590 | + | 0.889163i | \(0.651287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.2935 | −1.16316 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.39373 | 0.370592 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.58211 | 0.422238 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2500 | 0.582733 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.8582 | 1.22284 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.5700 | 1.20786 | 0.603932 | − | 0.797036i | \(-0.293600\pi\) | ||||
0.603932 | + | 0.797036i | \(0.293600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2427 | 0.622788 | 0.311394 | − | 0.950281i | \(-0.399204\pi\) | ||||
0.311394 | + | 0.950281i | \(0.399204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.24698 | 0.141710 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.992230 | −0.0432222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9390 | −0.997348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.63102 | −0.157573 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.03684 | −0.260995 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.9342 | 1.63698 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.83579 | −0.251365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9667 | −1.15939 | −0.579695 | − | 0.814833i | \(-0.696828\pi\) | ||||
−0.579695 | + | 0.814833i | \(0.696828\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.9584 | 1.15689 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.6703 | 0.457063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.7294 | −1.39941 | −0.699705 | − | 0.714432i | \(-0.746685\pi\) | ||||
−0.699705 | + | 0.714432i | \(0.746685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.35988 | −0.100717 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.96077 | −0.381742 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.9661 | −0.593901 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.40581 | 0.229464 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.7603 | 1.76944 | 0.884721 | − | 0.466122i | \(-0.154349\pi\) | ||||
0.884721 | + | 0.466122i | \(0.154349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.55496 | −0.107870 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.8834 | 1.04871 | 0.524355 | − | 0.851500i | \(-0.324307\pi\) | ||||
0.524355 | + | 0.851500i | \(0.324307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.6136 | 0.741008 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.4426 | 0.732522 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2271 | 1.18334 | 0.591671 | − | 0.806179i | \(-0.298468\pi\) | ||||
0.591671 | + | 0.806179i | \(0.298468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4316 | 0.938735 | 0.469367 | − | 0.883003i | \(-0.344482\pi\) | ||||
0.469367 | + | 0.883003i | \(0.344482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.68425 | −0.237463 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.246980 | 0.0102998 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.8437 | −1.53382 | −0.766911 | − | 0.641753i | \(-0.778207\pi\) | ||||
−0.766911 | + | 0.641753i | \(0.778207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.29590 | 0.303207 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.91723 | −0.369949 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.7711 | 0.446092 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.4480 | 1.83457 | 0.917283 | − | 0.398236i | \(-0.130377\pi\) | ||||
0.917283 | + | 0.398236i | \(0.130377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.84117 | −0.0758639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.38404 | −0.386008 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.6276 | 0.847073 | 0.423536 | − | 0.905879i | \(-0.360789\pi\) | ||||
0.423536 | + | 0.905879i | \(0.360789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.64310 | 0.0673607 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.5459 | 1.65943 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2674 | 1.27755 | 0.638776 | − | 0.769393i | \(-0.279441\pi\) | ||||
0.638776 | + | 0.769393i | \(0.279441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.94438 | −0.324058 | −0.162029 | − | 0.986786i | \(-0.551804\pi\) | ||||
−0.162029 | + | 0.986786i | \(0.551804\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.28919 | 0.0525000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.58211 | 0.348912 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.97690 | −0.161417 | −0.0807087 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807087 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.1957 | −0.696804 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.0062 | −1.45428 | −0.727139 | − | 0.686490i | \(-0.759150\pi\) | ||||
−0.727139 | + | 0.686490i | \(0.759150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.5429 | 0.505778 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.14808 | 0.126737 | 0.0633685 | − | 0.997990i | \(-0.479816\pi\) | ||||
0.0633685 | + | 0.997990i | \(0.479816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.9594 | −1.00320 | −0.501602 | − | 0.865098i | \(-0.667256\pi\) | ||||
−0.501602 | + | 0.865098i | \(0.667256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.22521 | 0.0491660 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.4601 | 0.859781 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.74094 | −0.189335 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.73556 | 0.109074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34960 | 0.0537267 | 0.0268634 | − | 0.999639i | \(-0.491448\pi\) | ||||
0.0268634 | + | 0.999639i | \(0.491448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0784573 | 0.00311840 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.4644 | 0.851789 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.41789 | −0.0560911 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.7808 | 1.21577 | 0.607883 | − | 0.794026i | \(-0.292019\pi\) | ||||
0.607883 | + | 0.794026i | \(0.292019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.528402 | 0.0208381 | 0.0104191 | − | 0.999946i | \(-0.496683\pi\) | ||||
0.0104191 | + | 0.999946i | \(0.496683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.08815 | 0.160971 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7114 | −0.499737 | −0.249868 | − | 0.968280i | \(-0.580387\pi\) | ||||
−0.249868 | + | 0.968280i | \(0.580387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.8605 | −0.897355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.53319 | −0.138477 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.2241 | 0.634900 | 0.317450 | − | 0.948275i | \(-0.397173\pi\) | ||||
0.317450 | + | 0.948275i | \(0.397173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.94869 | −0.310581 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.60388 | 0.140601 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.5478 | −1.42370 | −0.711850 | − | 0.702332i | \(-0.752142\pi\) | ||||
−0.711850 | + | 0.702332i | \(0.752142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.94810 | −0.309145 | −0.154573 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154573 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04892 | 0.118232 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.30798 | −0.0506451 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.9952 | 1.12102 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.8576 | −0.573570 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0771 | −0.388445 | −0.194222 | − | 0.980958i | \(-0.562218\pi\) | ||||
−0.194222 | + | 0.980958i | \(0.562218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.96077 | 0.190940 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.3236 | −1.43446 | −0.717232 | − | 0.696835i | \(-0.754591\pi\) | ||||
−0.717232 | + | 0.696835i | \(0.754591\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5308 | 0.634394 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.95646 | 0.0749717 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.8237 | 0.414158 | 0.207079 | − | 0.978324i | \(-0.433604\pi\) | ||||
0.207079 | + | 0.978324i | \(0.433604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.39075 | 0.0531377 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.5206 | 1.73672 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.4838 | −0.931408 | −0.465704 | − | 0.884941i | \(-0.654199\pi\) | ||||
−0.465704 | + | 0.884941i | \(0.654199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.692021 | −0.0262877 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.1008 | −0.762468 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.34721 | 0.240418 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.2247 | 1.63491 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9554 | 1.16917 | 0.584585 | − | 0.811333i | \(-0.301258\pi\) | ||||
0.584585 | + | 0.811333i | \(0.301258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.07606 | 0.191447 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.3545 | 0.578284 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.92931 | 0.147777 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.6396 | 0.812694 | 0.406347 | − | 0.913719i | \(-0.366802\pi\) | ||||
0.406347 | + | 0.913719i | \(0.366802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.91425 | 0.0717899 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.268750 | −0.0100648 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.00538 | −0.261621 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.2556 | −0.419763 | −0.209882 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209882 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2664 | 0.643033 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −44.3086 | −1.64785 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.29590 | −0.196685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6485 | 0.691634 | 0.345817 | − | 0.938302i | \(-0.387602\pi\) | ||||
0.345817 | + | 0.938302i | \(0.387602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4263 | 0.904676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.06877 | 0.0765162 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.01639 | 0.185285 | 0.0926424 | − | 0.995699i | \(-0.470469\pi\) | ||||
0.0926424 | + | 0.995699i | \(0.470469\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.76271 | −0.249446 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.11662 | 0.298980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.4276 | −0.972154 | −0.486077 | − | 0.873916i | \(-0.661573\pi\) | ||||
−0.486077 | + | 0.873916i | \(0.661573\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.25129 | 0.0825919 | 0.0412959 | − | 0.999147i | \(-0.486851\pi\) | ||||
0.0412959 | + | 0.999147i | \(0.486851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.34050 | −0.268935 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22223 | 0.0447189 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8780 | −0.397474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7375 | 1.08514 | 0.542568 | − | 0.840012i | \(-0.317452\pi\) | ||||
0.542568 | + | 0.840012i | \(0.317452\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.1444 | 0.952753 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.46011 | −0.307895 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.9764 | 0.907784 | 0.453892 | − | 0.891057i | \(-0.350035\pi\) | ||||
0.453892 | + | 0.891057i | \(0.350035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.692021 | −0.0251188 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.37090 | 0.267195 | 0.133597 | − | 0.991036i | \(-0.457347\pi\) | ||||
0.133597 | + | 0.991036i | \(0.457347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.2271 | 0.696069 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.225209 | −0.00814246 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −55.2780 | −1.99337 | −0.996687 | − | 0.0813304i | \(-0.974083\pi\) | ||||
−0.996687 | + | 0.0813304i | \(0.974083\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.36467 | 0.337260 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 54.5120 | 1.96066 | 0.980330 | − | 0.197364i | \(-0.0632380\pi\) | ||||
0.980330 | + | 0.197364i | \(0.0632380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08815 | −0.0390874 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.74094 | 0.349454 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.7778 | 0.421983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.92692 | −0.319430 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.2717 | −0.938875 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.7681 | 0.634170 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.7493 | 1.95160 | 0.975801 | − | 0.218661i | \(-0.0701689\pi\) | ||||
0.975801 | + | 0.218661i | \(0.0701689\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.1685 | −0.504413 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.7385 | 1.12849 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.4819 | 0.442687 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.9982 | 1.20428 | 0.602139 | − | 0.798391i | \(-0.294315\pi\) | ||||
0.602139 | + | 0.798391i | \(0.294315\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.77000 | 0.274883 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.94139 | −0.103929 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.6896 | 0.800700 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.445042 | 0.0156857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.2838 | −0.432411 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.3532 | −0.399156 | −0.199578 | − | 0.979882i | \(-0.563957\pi\) | ||||
−0.199578 | + | 0.979882i | \(0.563957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.6082 | 1.14503 | 0.572514 | − | 0.819895i | \(-0.305968\pi\) | ||||
0.572514 | + | 0.819895i | \(0.305968\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.2325 | −1.02523 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.6286 | −0.407333 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.83877 | 0.134302 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.6377 | −0.475960 | −0.237980 | − | 0.971270i | \(-0.576485\pi\) | ||||
−0.237980 | + | 0.971270i | \(0.576485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.4077 | −1.16452 | −0.582260 | − | 0.813003i | \(-0.697831\pi\) | ||||
−0.582260 | + | 0.813003i | \(0.697831\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.80194 | −0.0975510 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.9801 | −0.486137 | −0.243069 | − | 0.970009i | \(-0.578154\pi\) | ||||
−0.243069 | + | 0.970009i | \(0.578154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8528 | 1.27995 | 0.639975 | − | 0.768396i | \(-0.278945\pi\) | ||||
0.639975 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.88577 | −0.134796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.42221 | −0.118572 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.20237 | −0.318461 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.39804 | −0.186584 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.58775 | 0.123863 | 0.0619314 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619314 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.953476 | −0.0328785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.3230 | −0.665521 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4644 | 0.531364 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.92692 | 0.340691 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.740939 | 0.0253991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.2723 | −1.61857 | −0.809287 | − | 0.587414i | \(-0.800146\pi\) | ||||
−0.809287 | + | 0.587414i | \(0.800146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.417895 | −0.0142917 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.5435 | −0.701751 | −0.350876 | − | 0.936422i | \(-0.614116\pi\) | ||||
−0.350876 | + | 0.936422i | \(0.614116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0597 | 0.684427 | 0.342214 | − | 0.939622i | \(-0.388823\pi\) | ||||
0.342214 | + | 0.939622i | \(0.388823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.6015 | 0.770256 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.7103 | −1.48792 | −0.743959 | − | 0.668226i | \(-0.767054\pi\) | ||||
−0.743959 | + | 0.668226i | \(0.767054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4601 | 0.525659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.1347 | 0.989465 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0519 | 0.408833 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.26577 | −0.0766846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.80194 | 0.0609166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.6655 | −0.799126 | −0.399563 | − | 0.916706i | \(-0.630838\pi\) | ||||
−0.399563 | + | 0.916706i | \(0.630838\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.25906 | −0.109925 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.5743 | −1.13115 | −0.565574 | − | 0.824698i | \(-0.691345\pi\) | ||||
−0.565574 | + | 0.824698i | \(0.691345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.10513 | −0.272759 | −0.136380 | − | 0.990657i | \(-0.543547\pi\) | ||||
−0.136380 | + | 0.990657i | \(0.543547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.4916 | −0.890504 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.9687 | 1.44275 | 0.721373 | − | 0.692547i | \(-0.243511\pi\) | ||||
0.721373 | + | 0.692547i | \(0.243511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.6775 | 1.29720 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.0519 | −0.504258 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.4179 | 0.482476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0519 | 0.703687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.76271 | 0.192197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.31634 | 0.210428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.36658 | 0.245145 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.9608 | 0.497313 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.9536 | −0.894979 | −0.447490 | − | 0.894289i | \(-0.647682\pi\) | ||||
−0.447490 | + | 0.894289i | \(0.647682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.538565 | −0.0178631 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.1909 | −1.00027 | −0.500134 | − | 0.865948i | \(-0.666716\pi\) | ||||
−0.500134 | + | 0.865948i | \(0.666716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.69501 | 0.254668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.2174 | −0.569191 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.3230 | −0.472989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.9336 | −0.954432 | −0.477216 | − | 0.878786i | \(-0.658354\pi\) | ||||
−0.477216 | + | 0.878786i | \(0.658354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.7157 | −0.649655 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.36658 | −0.0777288 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.34854 | −0.306715 | −0.153358 | − | 0.988171i | \(-0.549009\pi\) | ||||
−0.153358 | + | 0.988171i | \(0.549009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.35019 | −0.208119 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.32736 | 0.174410 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.41789 | −0.0463701 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7808 | −1.33225 | −0.666125 | − | 0.745840i | \(-0.732048\pi\) | ||||
−0.666125 | + | 0.745840i | \(0.732048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.11769 | 0.0691081 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.4161 | −1.21973 | −0.609865 | − | 0.792505i | \(-0.708776\pi\) | ||||
−0.609865 | + | 0.792505i | \(0.708776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.71917 | 0.0559838 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.93900 | 0.290786 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.4612 | −0.404934 | −0.202467 | − | 0.979289i | \(-0.564896\pi\) | ||||
−0.202467 | + | 0.979289i | \(0.564896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.4655 | 1.02034 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.66978 | −0.216055 | −0.108028 | − | 0.994148i | \(-0.534454\pi\) | ||||
−0.108028 | + | 0.994148i | \(0.534454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.15452 | −0.102078 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.8388 | 0.479669 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.50604 | 0.0809243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8159 | −0.961804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.49098 | 0.0480460 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.04892 | 0.130339 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.9584 | 1.47792 | 0.738961 | − | 0.673748i | \(-0.235317\pi\) | ||||
0.738961 | + | 0.673748i | \(0.235317\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.78017 | −0.0893118 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3991 | 1.45693 | 0.728463 | − | 0.685085i | \(-0.240235\pi\) | ||||
0.728463 | + | 0.685085i | \(0.240235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.2204 | −1.16117 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.2174 | −0.390871 | −0.195435 | − | 0.980717i | \(-0.562612\pi\) | ||||
−0.195435 | + | 0.980717i | \(0.562612\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.5187 | −0.591861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.63533 | −0.0841398 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.9081 | −1.68751 | −0.843754 | − | 0.536731i | \(-0.819659\pi\) | ||||
−0.843754 | + | 0.536731i | \(0.819659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.20775 | −0.165933 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.6679 | 0.880678 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.560335 | 0.0178176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9011 | −0.378051 | −0.189025 | − | 0.981972i | \(-0.560533\pi\) | ||||
−0.189025 | + | 0.981972i | \(0.560533\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.1347 | 0.670688 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.5013 | 0.713338 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.5937 | 1.03225 | 0.516127 | − | 0.856512i | \(-0.327373\pi\) | ||||
0.516127 | + | 0.856512i | \(0.327373\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.8823 | 0.470856 |
(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 | 3380.2.a.k.1.1 | ✓ | 3 | |
13.5 | odd | 4 | 3380.2.f.g.3041.2 | 6 | |||
13.8 | odd | 4 | 3380.2.f.g.3041.1 | 6 | |||
13.12 | even | 2 | 3380.2.a.l.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.k.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3380.2.a.l.1.1 | yes | 3 | 13.12 | even | 2 | ||
3380.2.f.g.3041.1 | 6 | 13.8 | odd | 4 | |||
3380.2.f.g.3041.2 | 6 | 13.5 | odd | 4 |