Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7220,2,Mod(1,7220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7220, 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("7220.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7220.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: | \(57.6519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.19869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7220.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.364448 | −0.210414 | −0.105207 | − | 0.994450i | \(-0.533551\pi\) | ||||
−0.105207 | + | 0.994450i | \(0.533551\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.635552 | 0.240216 | 0.120108 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120108 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86718 | −0.955726 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63555 | 0.493137 | 0.246569 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246569 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.364448 | 0.0941001 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.59607 | −1.59978 | −0.799891 | − | 0.600145i | \(-0.795110\pi\) | ||||
−0.799891 | + | 0.600145i | \(0.795110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.231626 | −0.0505449 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.867178 | 0.180819 | 0.0904095 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904095 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13828 | 0.411512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.09880 | −1.68961 | −0.844803 | − | 0.535078i | \(-0.820282\pi\) | ||||
−0.844803 | + | 0.535078i | \(0.820282\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.86718 | −0.335355 | −0.167677 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167677 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.596074 | −0.103763 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.635552 | −0.107428 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.635552 | 0.104484 | 0.0522420 | − | 0.998634i | \(-0.483363\pi\) | ||||
0.0522420 | + | 0.998634i | \(0.483363\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.364448 | 0.0583584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.90666 | 0.297770 | 0.148885 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148885 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.96052 | 0.603974 | 0.301987 | − | 0.953312i | \(-0.402350\pi\) | ||||
0.301987 | + | 0.953312i | \(0.402350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.86718 | 0.427414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.09880 | 1.32720 | 0.663598 | − | 0.748089i | \(-0.269028\pi\) | ||||
0.663598 | + | 0.748089i | \(0.269028\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59607 | −0.942296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.40393 | 0.336617 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.86718 | −1.35536 | −0.677681 | − | 0.735356i | \(-0.737015\pi\) | ||||
−0.677681 | + | 0.735356i | \(0.737015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.63555 | −0.220538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.09880 | 1.18456 | 0.592282 | − | 0.805731i | \(-0.298227\pi\) | ||||
0.592282 | + | 0.805731i | \(0.298227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.27110 | 0.290785 | 0.145393 | − | 0.989374i | \(-0.453555\pi\) | ||||
0.145393 | + | 0.989374i | \(0.453555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.82224 | −0.229581 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4633 | 1.52263 | 0.761314 | − | 0.648383i | \(-0.224554\pi\) | ||||
0.761314 | + | 0.648383i | \(0.224554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.316041 | −0.0380469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.50273 | 0.297019 | 0.148510 | − | 0.988911i | \(-0.452552\pi\) | ||||
0.148510 | + | 0.988911i | \(0.452552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.403926 | −0.0472760 | −0.0236380 | − | 0.999721i | \(-0.507525\pi\) | ||||
−0.0236380 | + | 0.999721i | \(0.507525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.364448 | −0.0420828 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.03948 | 0.118460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7289 | 1.20710 | 0.603548 | − | 0.797327i | \(-0.293753\pi\) | ||||
0.603548 | + | 0.797327i | \(0.293753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82224 | 0.869138 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8672 | −1.74165 | −0.870825 | − | 0.491594i | \(-0.836414\pi\) | ||||
−0.870825 | + | 0.491594i | \(0.836414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.59607 | 0.715445 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.31604 | 0.355517 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.542208 | 0.0574739 | 0.0287370 | − | 0.999587i | \(-0.490851\pi\) | ||||
0.0287370 | + | 0.999587i | \(0.490851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.635552 | −0.0666239 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.680489 | 0.0705634 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.36991 | −0.748301 | −0.374150 | − | 0.927368i | \(-0.622066\pi\) | ||||
−0.374150 | + | 0.927368i | \(0.622066\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.68942 | −0.471304 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.32497 | −0.927869 | −0.463935 | − | 0.885869i | \(-0.653563\pi\) | ||||
−0.463935 | + | 0.885869i | \(0.653563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8672 | −1.07077 | −0.535387 | − | 0.844607i | \(-0.679834\pi\) | ||||
−0.535387 | + | 0.844607i | \(0.679834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.231626 | 0.0226044 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3304 | 1.09535 | 0.547677 | − | 0.836690i | \(-0.315512\pi\) | ||||
0.547677 | + | 0.836690i | \(0.315512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2316 | 1.26736 | 0.633680 | − | 0.773595i | \(-0.281544\pi\) | ||||
0.633680 | + | 0.773595i | \(0.281544\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.231626 | −0.0219849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.09334 | 0.667286 | 0.333643 | − | 0.942700i | \(-0.391722\pi\) | ||||
0.333643 | + | 0.942700i | \(0.391722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.867178 | −0.0808647 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.86718 | 0.265071 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.19215 | −0.384294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.32497 | −0.756815 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.694877 | −0.0626550 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.2766 | 1.44431 | 0.722156 | − | 0.691731i | \(-0.243151\pi\) | ||||
0.722156 | + | 0.691731i | \(0.243151\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.44340 | −0.127085 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6356 | −0.929232 | −0.464616 | − | 0.885512i | \(-0.653808\pi\) | ||||
−0.464616 | + | 0.885512i | \(0.653808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13828 | −0.184034 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.49727 | 0.298792 | 0.149396 | − | 0.988777i | \(-0.452267\pi\) | ||||
0.149396 | + | 0.988777i | \(0.452267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.734355 | 0.0622872 | 0.0311436 | − | 0.999515i | \(-0.490085\pi\) | ||||
0.0311436 | + | 0.999515i | \(0.490085\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31604 | −0.279261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.63555 | −0.136772 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.09880 | 0.755614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.40393 | 0.198272 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1383 | 0.830560 | 0.415280 | − | 0.909694i | \(-0.363684\pi\) | ||||
0.415280 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.81331 | 0.228944 | 0.114472 | − | 0.993426i | \(-0.463482\pi\) | ||||
0.114472 | + | 0.993426i | \(0.463482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.9121 | 1.52895 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.86718 | 0.149975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.960522 | 0.0766580 | 0.0383290 | − | 0.999265i | \(-0.487797\pi\) | ||||
0.0383290 | + | 0.999265i | \(0.487797\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.59607 | 0.285187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.551136 | 0.0434356 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.13828 | 0.245809 | 0.122905 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122905 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.596074 | 0.0464043 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.6356 | −0.823004 | −0.411502 | − | 0.911409i | \(-0.634996\pi\) | ||||
−0.411502 | + | 0.911409i | \(0.634996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3699 | 0.940467 | 0.470233 | − | 0.882542i | \(-0.344170\pi\) | ||||
0.470233 | + | 0.882542i | \(0.344170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.635552 | 0.0480432 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.31604 | −0.249249 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.324970 | −0.0242894 | −0.0121447 | − | 0.999926i | \(-0.503866\pi\) | ||||
−0.0121447 | + | 0.999926i | \(0.503866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.81331 | 0.655088 | 0.327544 | − | 0.944836i | \(-0.393779\pi\) | ||||
0.327544 | + | 0.944836i | \(0.393779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.827699 | −0.0611853 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.635552 | −0.0467267 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7882 | −0.788913 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.35899 | 0.0988519 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.1921 | 1.82284 | 0.911420 | − | 0.411478i | \(-0.134987\pi\) | ||||
0.911420 | + | 0.411478i | \(0.134987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8726 | −1.35848 | −0.679241 | − | 0.733915i | \(-0.737691\pi\) | ||||
−0.679241 | + | 0.733915i | \(0.737691\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.364448 | −0.0260987 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.36445 | −0.524695 | −0.262348 | − | 0.964973i | \(-0.584497\pi\) | ||||
−0.262348 | + | 0.964973i | \(0.584497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.76837 | 0.196245 | 0.0981224 | − | 0.995174i | \(-0.468716\pi\) | ||||
0.0981224 | + | 0.995174i | \(0.468716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.54221 | −0.320383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.78276 | −0.405870 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.90666 | −0.133167 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.48635 | −0.172813 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9265 | 1.16527 | 0.582634 | − | 0.812734i | \(-0.302022\pi\) | ||||
0.582634 | + | 0.812734i | \(0.302022\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.912115 | −0.0624971 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.96052 | −0.270105 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.18669 | −0.0805577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.147210 | 0.00994754 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.59607 | 0.443700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.64101 | 0.578645 | 0.289322 | − | 0.957232i | \(-0.406570\pi\) | ||||
0.289322 | + | 0.957232i | \(0.406570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.86718 | −0.191145 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9265 | 1.38894 | 0.694470 | − | 0.719521i | \(-0.255639\pi\) | ||||
0.694470 | + | 0.719521i | \(0.255639\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3754 | 1.47861 | 0.739303 | − | 0.673373i | \(-0.235155\pi\) | ||||
0.739303 | + | 0.673373i | \(0.235155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.378836 | −0.0249256 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.2371 | −1.26026 | −0.630132 | − | 0.776488i | \(-0.716999\pi\) | ||||
−0.630132 | + | 0.776488i | \(0.716999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.09880 | −0.593540 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.91013 | −0.253990 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.13282 | −0.137961 | −0.0689804 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689804 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4633 | 1.57582 | 0.787908 | − | 0.615793i | \(-0.211164\pi\) | ||||
0.787908 | + | 0.615793i | \(0.211164\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.26564 | −0.594391 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.59607 | 0.421408 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.78276 | 0.366468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.28003 | 0.207034 | 0.103517 | − | 0.994628i | \(-0.466990\pi\) | ||||
0.103517 | + | 0.994628i | \(0.466990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41831 | 0.0891686 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.40393 | −0.150540 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.63555 | −0.476293 | −0.238146 | − | 0.971229i | \(-0.576540\pi\) | ||||
−0.238146 | + | 0.971229i | \(0.576540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.403926 | 0.0250988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.0879 | 1.61480 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.7289 | 0.908223 | 0.454111 | − | 0.890945i | \(-0.349957\pi\) | ||||
0.454111 | + | 0.890945i | \(0.349957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.86718 | 0.606136 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.197607 | −0.0120933 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4633 | −0.820869 | −0.410434 | − | 0.911890i | \(-0.634623\pi\) | ||||
−0.410434 | + | 0.911890i | \(0.634623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.86172 | 0.234583 | 0.117291 | − | 0.993098i | \(-0.462579\pi\) | ||||
0.117291 | + | 0.993098i | \(0.462579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.231626 | 0.0140186 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.63555 | 0.0986275 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2766 | −1.45864 | −0.729319 | − | 0.684174i | \(-0.760163\pi\) | ||||
−0.729319 | + | 0.684174i | \(0.760163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.35353 | 0.320507 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.497270 | 0.0296647 | 0.0148323 | − | 0.999890i | \(-0.495279\pi\) | ||||
0.0148323 | + | 0.999890i | \(0.495279\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1581 | −0.901057 | −0.450529 | − | 0.892762i | \(-0.648764\pi\) | ||||
−0.450529 | + | 0.892762i | \(0.648764\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21178 | 0.0715290 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.5082 | 1.55931 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.68595 | 0.157453 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4094 | −0.783385 | −0.391692 | − | 0.920096i | \(-0.628110\pi\) | ||||
−0.391692 | + | 0.920096i | \(0.628110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.09880 | −0.529753 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.49727 | 0.202932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.867178 | −0.0501502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.51712 | 0.145084 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.39847 | 0.195237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.27110 | −0.130043 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2065 | 1.83812 | 0.919062 | − | 0.394113i | \(-0.128948\pi\) | ||||
0.919062 | + | 0.394113i | \(0.128948\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.96052 | 0.225306 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3699 | 0.701433 | 0.350717 | − | 0.936482i | \(-0.385938\pi\) | ||||
0.350717 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7882 | 1.40111 | 0.700557 | − | 0.713597i | \(-0.252935\pi\) | ||||
0.700557 | + | 0.713597i | \(0.252935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82224 | 0.102672 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.31058 | 0.410603 | 0.205302 | − | 0.978699i | \(-0.434182\pi\) | ||||
0.205302 | + | 0.978699i | \(0.434182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8816 | −0.833208 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.12935 | −0.230478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.82224 | −0.266670 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.78276 | 0.318814 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4722 | 1.01532 | 0.507661 | − | 0.861557i | \(-0.330510\pi\) | ||||
0.507661 | + | 0.861557i | \(0.330510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.82224 | −0.0998582 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4633 | −0.680940 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.4633 | 1.65944 | 0.829720 | − | 0.558181i | \(-0.188500\pi\) | ||||
0.829720 | + | 0.558181i | \(0.188500\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.58516 | −0.140406 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.05387 | −0.165376 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.64101 | −0.466571 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.316041 | 0.0170151 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.3215 | 1.25196 | 0.625982 | − | 0.779838i | \(-0.284698\pi\) | ||||
0.625982 | + | 0.779838i | \(0.284698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.6894 | −0.946893 | −0.473446 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473446 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.13828 | −0.114133 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.13828 | −0.379932 | −0.189966 | − | 0.981791i | \(-0.560838\pi\) | ||||
−0.189966 | + | 0.981791i | \(0.560838\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.50273 | −0.132831 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.52782 | 0.0808608 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.1437 | −1.59093 | −0.795463 | − | 0.606002i | \(-0.792772\pi\) | ||||
−0.795463 | + | 0.606002i | \(0.792772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.03402 | 0.159245 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.403926 | 0.0211425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.2031 | −1.57659 | −0.788294 | − | 0.615299i | \(-0.789035\pi\) | ||||
−0.788294 | + | 0.615299i | \(0.789035\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.46672 | −0.284586 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.27110 | −0.325579 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0449 | 1.50389 | 0.751945 | − | 0.659226i | \(-0.229116\pi\) | ||||
0.751945 | + | 0.659226i | \(0.229116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.364448 | 0.0188200 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.09880 | 0.468612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.76837 | 0.142202 | 0.0711009 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0711009 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.93196 | −0.303904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.6105 | 1.35973 | 0.679866 | − | 0.733337i | \(-0.262038\pi\) | ||||
0.679866 | + | 0.733337i | \(0.262038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.03948 | −0.0529767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3555 | −0.577233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.55660 | −0.281731 | −0.140865 | − | 0.990029i | \(-0.544988\pi\) | ||||
−0.140865 | + | 0.990029i | \(0.544988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.71997 | −0.289271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.87611 | 0.195524 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7289 | −0.539829 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.71451 | 0.136237 | 0.0681186 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681186 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8816 | −0.892963 | −0.446481 | − | 0.894793i | \(-0.647323\pi\) | ||||
−0.446481 | + | 0.894793i | \(0.647323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.86718 | 0.0930107 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.82224 | −0.388690 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.03948 | 0.0515250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3250 | 1.30169 | 0.650843 | − | 0.759212i | \(-0.274416\pi\) | ||||
0.650843 | + | 0.759212i | \(0.274416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27457 | −0.0628701 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.78276 | 0.284551 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8672 | 0.778889 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.267634 | −0.0131061 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3250 | 0.748674 | 0.374337 | − | 0.927293i | \(-0.377870\pi\) | ||||
0.374337 | + | 0.927293i | \(0.377870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8332 | 1.06408 | 0.532042 | − | 0.846718i | \(-0.321425\pi\) | ||||
0.532042 | + | 0.846718i | \(0.321425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.0879 | −1.26844 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.59607 | −0.319957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.44340 | 0.0698512 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.596074 | 0.0287787 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.2855 | 1.12162 | 0.560811 | − | 0.827944i | \(-0.310489\pi\) | ||||
0.560811 | + | 0.827944i | \(0.310489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.90120 | −0.187480 | −0.0937398 | − | 0.995597i | \(-0.529882\pi\) | ||||
−0.0937398 | + | 0.995597i | \(0.529882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.31604 | −0.158992 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4776 | −0.929617 | −0.464808 | − | 0.885411i | \(-0.653877\pi\) | ||||
−0.464808 | + | 0.885411i | \(0.653877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.9121 | 0.900577 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.90666 | 0.0905880 | 0.0452940 | − | 0.998974i | \(-0.485578\pi\) | ||||
0.0452940 | + | 0.998974i | \(0.485578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.542208 | −0.0257031 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.69488 | −0.174762 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.05933 | −0.380343 | −0.190172 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190172 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.11843 | 0.146841 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.02531 | −0.0481731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.635552 | 0.0297951 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3250 | 0.529760 | 0.264880 | − | 0.964281i | \(-0.414668\pi\) | ||||
0.264880 | + | 0.964281i | \(0.414668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.1043 | −0.658331 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.1043 | 0.936349 | 0.468174 | − | 0.883636i | \(-0.344912\pi\) | ||||
0.468174 | + | 0.883636i | \(0.344912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33043 | 0.0618303 | 0.0309151 | − | 0.999522i | \(-0.490158\pi\) | ||||
0.0309151 | + | 0.999522i | \(0.490158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.680489 | −0.0315569 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0844 | 0.466651 | 0.233326 | − | 0.972399i | \(-0.425039\pi\) | ||||
0.233326 | + | 0.972399i | \(0.425039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.92104 | 0.365760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.350060 | −0.0161299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.47764 | 0.297842 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.2910 | 1.29535 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.88157 | 0.405809 | 0.202905 | − | 0.979199i | \(-0.434962\pi\) | ||||
0.202905 | + | 0.979199i | \(0.434962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.635552 | −0.0289787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.200861 | −0.00913947 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.36991 | 0.334650 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.32497 | 0.241297 | 0.120649 | − | 0.992695i | \(-0.461503\pi\) | ||||
0.120649 | + | 0.992695i | \(0.461503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.14374 | −0.0517217 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4094 | −0.875933 | −0.437967 | − | 0.898991i | \(-0.644301\pi\) | ||||
−0.437967 | + | 0.898991i | \(0.644301\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 60.0164 | 2.70300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.68942 | 0.210774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.59061 | 0.0713488 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5871 | 0.518712 | 0.259356 | − | 0.965782i | \(-0.416490\pi\) | ||||
0.259356 | + | 0.965782i | \(0.416490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.87611 | 0.173172 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.1043 | 1.56522 | 0.782611 | − | 0.622511i | \(-0.213888\pi\) | ||||
0.782611 | + | 0.622511i | \(0.213888\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32497 | 0.414956 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.37338 | 0.194228 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8672 | −0.703300 | −0.351650 | − | 0.936131i | \(-0.614379\pi\) | ||||
−0.351650 | + | 0.936131i | \(0.614379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.256716 | −0.0113565 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8672 | 0.478865 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.8816 | 0.654490 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.50819 | −0.197888 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6949 | 1.60763 | 0.803816 | − | 0.594878i | \(-0.202800\pi\) | ||||
0.803816 | + | 0.594878i | \(0.202800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0253 | −1.35664 | −0.678321 | − | 0.734766i | \(-0.737292\pi\) | ||||
−0.678321 | + | 0.734766i | \(0.737292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.231626 | −0.0101090 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.3160 | 0.536495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2480 | −0.967304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0879 | −1.13212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.90666 | −0.0825864 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3304 | −0.489857 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.118435 | 0.00511083 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.7882 | −0.464682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.58715 | −0.326197 | −0.163098 | − | 0.986610i | \(-0.552149\pi\) | ||||
−0.163098 | + | 0.986610i | \(0.552149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.21199 | −0.137840 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.2316 | −0.566781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.7828 | −1.31618 | −0.658088 | − | 0.752941i | \(-0.728635\pi\) | ||||
−0.658088 | + | 0.752941i | \(0.728635\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.51166 | −0.277911 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.81877 | 0.289964 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.231626 | 0.00983196 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.0737 | 1.31664 | 0.658318 | − | 0.752740i | \(-0.271268\pi\) | ||||
0.658318 | + | 0.752740i | \(0.271268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96052 | −0.167512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.93175 | 0.165998 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.2766 | −0.980990 | −0.490495 | − | 0.871444i | \(-0.663184\pi\) | ||||
−0.490495 | + | 0.871444i | \(0.663184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.09334 | −0.298419 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.97144 | 0.208781 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1976 | 1.01442 | 0.507208 | − | 0.861824i | \(-0.330678\pi\) | ||||
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8475 | 1.24908 | 0.624540 | − | 0.780992i | \(-0.285286\pi\) | ||||
0.624540 | + | 0.780992i | \(0.285286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.18123 | −0.383551 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.867178 | 0.0361638 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7882 | 1.40662 | 0.703311 | − | 0.710882i | \(-0.251704\pi\) | ||||
0.703311 | + | 0.710882i | \(0.251704\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.87810 | 0.285844 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0844 | −0.418372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.1383 | −0.668379 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.86718 | −0.118543 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.6949 | −1.26691 | −0.633457 | − | 0.773778i | \(-0.718364\pi\) | ||||
−0.633457 | + | 0.773778i | \(0.718364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.68396 | 0.110403 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.99454 | 0.287231 | 0.143616 | − | 0.989634i | \(-0.454127\pi\) | ||||
0.143616 | + | 0.989634i | \(0.454127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.19215 | 0.171861 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.00893 | −0.0412927 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.53675 | −0.185367 | −0.0926833 | − | 0.995696i | \(-0.529544\pi\) | ||||
−0.0926833 | + | 0.995696i | \(0.529544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0790 | 0.655874 | 0.327937 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327937 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.7344 | −1.45522 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.32497 | 0.338458 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0702 | −1.38287 | −0.691434 | − | 0.722439i | \(-0.743021\pi\) | ||||
−0.691434 | + | 0.722439i | \(0.743021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.10752 | 0.0854009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.09880 | −0.368098 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.4382 | −1.59289 | −0.796446 | − | 0.604709i | \(-0.793289\pi\) | ||||
−0.796446 | + | 0.604709i | \(0.793289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.694877 | 0.0280201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.2515 | −1.58020 | −0.790102 | − | 0.612975i | \(-0.789973\pi\) | ||||
−0.790102 | + | 0.612975i | \(0.789973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.3644 | 0.979290 | 0.489645 | − | 0.871922i | \(-0.337126\pi\) | ||||
0.489645 | + | 0.871922i | \(0.337126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.85427 | 0.0744093 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.344601 | 0.0138062 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.19215 | −0.167152 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3898 | −1.40884 | −0.704422 | − | 0.709781i | \(-0.748794\pi\) | ||||
−0.704422 | + | 0.709781i | \(0.748794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.16883 | −0.245189 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.2766 | −0.645916 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.59607 | 0.261346 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.17577 | −0.283869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.7093 | 1.41043 | 0.705216 | − | 0.708993i | \(-0.250850\pi\) | ||||
0.705216 | + | 0.708993i | \(0.250850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.1097 | 0.832486 | 0.416243 | − | 0.909253i | \(-0.363347\pi\) | ||||
0.416243 | + | 0.909253i | \(0.363347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44340 | 0.0568340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.7058 | 1.71825 | 0.859126 | − | 0.511764i | \(-0.171008\pi\) | ||||
0.859126 | + | 0.511764i | \(0.171008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8816 | 0.584153 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.432486 | 0.0169505 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.1887 | −0.946576 | −0.473288 | − | 0.880908i | \(-0.656933\pi\) | ||||
−0.473288 | + | 0.880908i | \(0.656933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.6356 | 0.415565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.15813 | 0.0451829 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.9913 | 1.32411 | 0.662056 | − | 0.749454i | \(-0.269684\pi\) | ||||
0.662056 | + | 0.749454i | \(0.269684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.55660 | 0.177231 | 0.0886155 | − | 0.996066i | \(-0.471756\pi\) | ||||
0.0886155 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.40393 | −0.0933608 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.89028 | −0.305513 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.14920 | −0.121755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.71451 | 0.143397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7487 | −0.876900 | −0.438450 | − | 0.898756i | \(-0.644472\pi\) | ||||
−0.438450 | + | 0.898756i | \(0.644472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.13828 | 0.0823025 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6949 | −0.603203 | −0.301602 | − | 0.953434i | \(-0.597521\pi\) | ||||
−0.301602 | + | 0.953434i | \(0.597521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.68396 | −0.179754 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.62662 | −0.292253 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.82770 | −0.337783 | −0.168891 | − | 0.985635i | \(-0.554019\pi\) | ||||
−0.168891 | + | 0.985635i | \(0.554019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.49727 | −0.133624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.15466 | −0.311120 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.86718 | 0.375910 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0198 | −0.875716 | −0.437858 | − | 0.899044i | \(-0.644263\pi\) | ||||
−0.437858 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.98037 | −0.113215 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.734355 | −0.0278557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5764 | −0.476367 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.01092 | 0.265177 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.91211 | −0.374375 | −0.187188 | − | 0.982324i | \(-0.559937\pi\) | ||||
−0.187188 | + | 0.982324i | \(0.559937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.31604 | 0.124889 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.92650 | −0.222889 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.1043 | −1.35592 | −0.677962 | − | 0.735097i | \(-0.737137\pi\) | ||||
−0.677962 | + | 0.735097i | \(0.737137\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.7617 | −1.15365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.61917 | −0.0606386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63555 | 0.0611662 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.777303 | 0.0290289 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.0109 | −0.708988 | −0.354494 | − | 0.935058i | \(-0.615347\pi\) | ||||
−0.354494 | + | 0.935058i | \(0.615347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.90666 | −0.257217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.91558 | −0.331574 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.09880 | −0.337921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.88702 | −0.107074 | −0.0535369 | − | 0.998566i | \(-0.517049\pi\) | ||||
−0.0535369 | + | 0.998566i | \(0.517049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0899 | −0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.1239 | −0.966227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.9463 | 1.66013 | 0.830066 | − | 0.557666i | \(-0.188303\pi\) | ||||
0.830066 | + | 0.557666i | \(0.188303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.40393 | −0.0886702 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.3843 | 0.750865 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.9913 | 1.87574 | 0.937872 | − | 0.346980i | \(-0.112793\pi\) | ||||
0.937872 | + | 0.346980i | \(0.112793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8761 | 0.692497 | 0.346249 | − | 0.938143i | \(-0.387455\pi\) | ||||
0.346249 | + | 0.938143i | \(0.387455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.1383 | −0.371438 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.4940 | 1.66454 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.20108 | 0.263122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0253 | 0.949677 | 0.474838 | − | 0.880073i | \(-0.342506\pi\) | ||||
0.474838 | + | 0.880073i | \(0.342506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.19540 | −0.0435629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.81331 | −0.102387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9156 | −0.433079 | −0.216540 | − | 0.976274i | \(-0.569477\pi\) | ||||
−0.216540 | + | 0.976274i | \(0.569477\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.516902 | −0.0187623 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.39500 | −0.0868186 | −0.0434093 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434093 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.40939 | 0.304440 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.9121 | −0.683769 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.09880 | −0.328539 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.32497 | 0.192023 | 0.0960117 | − | 0.995380i | \(-0.469391\pi\) | ||||
0.0960117 | + | 0.995380i | \(0.469391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78276 | 0.100219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4973 | −0.881106 | −0.440553 | − | 0.897727i | \(-0.645218\pi\) | ||||
−0.440553 | + | 0.897727i | \(0.645218\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.86718 | −0.0670710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.147210 | −0.00528113 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.09334 | 0.146471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.4558 | −0.695294 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.960522 | −0.0342825 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5171 | −0.731356 | −0.365678 | − | 0.930741i | \(-0.619163\pi\) | ||||
−0.365678 | + | 0.930741i | \(0.619163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.36792 | −0.191103 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.50819 | 0.160293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.27110 | −0.0806493 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.59607 | −0.127540 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0144 | −0.815211 | −0.407606 | − | 0.913158i | \(-0.633636\pi\) | ||||
−0.407606 | + | 0.913158i | \(0.633636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0164 | −2.12323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.55461 | −0.0549293 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.660642 | −0.0233136 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.551136 | −0.0194250 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.90666 | 0.172722 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3195 | −0.995661 | −0.497830 | − | 0.867274i | \(-0.665870\pi\) | ||||
−0.497830 | + | 0.867274i | \(0.665870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.5531 | 1.38890 | 0.694449 | − | 0.719542i | \(-0.255648\pi\) | ||||
0.694449 | + | 0.719542i | \(0.255648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.40740 | −0.0493595 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.13828 | −0.109929 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.82224 | 0.0636742 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.8026 | 1.07502 | 0.537509 | − | 0.843258i | \(-0.319365\pi\) | ||||
0.537509 | + | 0.843258i | \(0.319365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.596074 | −0.0207526 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.2855 | 0.705396 | 0.352698 | − | 0.935737i | \(-0.385264\pi\) | ||||
0.352698 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0792 | 1.53093 | 0.765466 | − | 0.643476i | \(-0.222508\pi\) | ||||
0.765466 | + | 0.643476i | \(0.222508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.84755 | 0.306918 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.5082 | 1.50747 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6356 | 0.368058 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.99255 | −0.138003 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.9069 | 1.86107 | 0.930536 | − | 0.366201i | \(-0.119342\pi\) | ||||
0.930536 | + | 0.366201i | \(0.119342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.7882 | 1.85477 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.181229 | −0.00624187 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.29095 | −0.181799 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.52435 | 0.189595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.551136 | 0.0188927 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0648 | 0.926681 | 0.463340 | − | 0.886180i | \(-0.346651\pi\) | ||||
0.463340 | + | 0.886180i | \(0.346651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.35353 | −0.114554 | −0.0572772 | − | 0.998358i | \(-0.518242\pi\) | ||||
−0.0572772 | + | 0.998358i | \(0.518242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.7058 | −1.83242 | −0.916209 | − | 0.400701i | \(-0.868767\pi\) | ||||
−0.916209 | + | 0.400701i | \(0.868767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.441630 | −0.0150507 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.1527 | −1.33277 | −0.666386 | − | 0.745607i | \(-0.732160\pi\) | ||||
−0.666386 | + | 0.745607i | \(0.732160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3699 | −0.420589 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.66086 | −0.328100 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.5477 | 0.595264 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4633 | −0.422301 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.1308 | 0.715170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.635552 | −0.0214856 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.6519 | −1.00127 | −0.500637 | − | 0.865657i | \(-0.666901\pi\) | ||||
−0.500637 | + | 0.865657i | \(0.666901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.88702 | 0.164835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.2820 | 1.45821 | 0.729104 | − | 0.684403i | \(-0.239937\pi\) | ||||
0.729104 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.9660 | 1.91706 | 0.958529 | − | 0.284995i | \(-0.0919920\pi\) | ||||
0.958529 | + | 0.284995i | \(0.0919920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.31604 | 0.111468 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.2316 | 0.679312 | 0.339656 | − | 0.940550i | \(-0.389689\pi\) | ||||
0.339656 | + | 0.940550i | \(0.389689\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3446 | 0.346947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.7937 | 0.428604 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.324970 | 0.0108625 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.316041 | 0.0105523 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.9891 | 0.566618 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.0846 | 2.16828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.917359 | −0.0305278 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.81331 | −0.292964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | −0.332045 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.7363 | 0.886789 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.0109 | −1.82259 | −0.911297 | − | 0.411751i | \(-0.864917\pi\) | ||||
−0.911297 | + | 0.411751i | \(0.864917\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.9516 | −0.858872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.827699 | 0.0273629 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.75945 | −0.223217 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6159 | 1.60369 | 0.801846 | − | 0.597531i | \(-0.203852\pi\) | ||||
0.801846 | + | 0.597531i | \(0.203852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7376 | −0.386767 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.50273 | −0.0823783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.635552 | 0.0208968 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.1581 | 1.02337 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3215 | 0.371446 | 0.185723 | − | 0.982602i | \(-0.440537\pi\) | ||||
0.185723 | + | 0.982602i | \(0.440537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.50819 | −0.147591 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.7882 | 0.352813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.4973 | −0.342931 | −0.171465 | − | 0.985190i | \(-0.554850\pi\) | ||||
−0.171465 | + | 0.985190i | \(0.554850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.03402 | −0.294814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.81877 | −0.0918893 | −0.0459447 | − | 0.998944i | \(-0.514630\pi\) | ||||
−0.0459447 | + | 0.998944i | \(0.514630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.65341 | 0.0538424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.35899 | −0.0442079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.5136 | −1.47899 | −0.739497 | − | 0.673159i | \(-0.764937\pi\) | ||||
−0.739497 | + | 0.673159i | \(0.764937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.403926 | 0.0131120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.66433 | −0.0863967 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.7200 | −0.671186 | −0.335593 | − | 0.942007i | \(-0.608937\pi\) | ||||
−0.335593 | + | 0.942007i | \(0.608937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.1921 | −0.815199 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.42356 | 0.175319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.22270 | 0.0717746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5136 | −0.887537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.4864 | −1.04686 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.8726 | 0.607532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.4687 | −0.433125 | −0.216562 | − | 0.976269i | \(-0.569484\pi\) | ||||
−0.216562 | + | 0.976269i | \(0.569484\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.0504 | −1.50992 | −0.754960 | − | 0.655771i | \(-0.772344\pi\) | ||||
−0.754960 | + | 0.655771i | \(0.772344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.466721 | 0.0149624 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.364448 | 0.0116717 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.0648 | 1.37776 | 0.688882 | − | 0.724873i | \(-0.258102\pi\) | ||||
0.688882 | + | 0.724873i | \(0.258102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.886809 | 0.0283425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9374 | −1.21125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.0792 | −1.72486 | −0.862429 | − | 0.506178i | \(-0.831058\pi\) | ||||
−0.862429 | + | 0.506178i | \(0.831058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.36445 | 0.234651 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.10752 | −0.0670830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.43448 | 0.109210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.2711 | 1.31102 | 0.655510 | − | 0.755187i | \(-0.272454\pi\) | ||||
0.655510 | + | 0.755187i | \(0.272454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.73215 | −0.213638 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.76837 | −0.0877634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.08987 | −0.0345167 | −0.0172583 | − | 0.999851i | \(-0.505494\pi\) | ||||
−0.0172583 | + | 0.999851i | \(0.505494\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.35899 | 0.0429965 |
(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 | 7220.2.a.n.1.2 | 3 | ||
19.7 | even | 3 | 380.2.i.b.201.2 | yes | 6 | ||
19.11 | even | 3 | 380.2.i.b.121.2 | ✓ | 6 | ||
19.18 | odd | 2 | 7220.2.a.o.1.2 | 3 | |||
57.11 | odd | 6 | 3420.2.t.v.1261.2 | 6 | |||
57.26 | odd | 6 | 3420.2.t.v.3241.2 | 6 | |||
76.7 | odd | 6 | 1520.2.q.i.961.2 | 6 | |||
76.11 | odd | 6 | 1520.2.q.i.881.2 | 6 | |||
95.7 | odd | 12 | 1900.2.s.c.49.3 | 12 | |||
95.49 | even | 6 | 1900.2.i.c.501.2 | 6 | |||
95.64 | even | 6 | 1900.2.i.c.201.2 | 6 | |||
95.68 | odd | 12 | 1900.2.s.c.349.3 | 12 | |||
95.83 | odd | 12 | 1900.2.s.c.49.4 | 12 | |||
95.87 | odd | 12 | 1900.2.s.c.349.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.2 | ✓ | 6 | 19.11 | even | 3 | ||
380.2.i.b.201.2 | yes | 6 | 19.7 | even | 3 | ||
1520.2.q.i.881.2 | 6 | 76.11 | odd | 6 | |||
1520.2.q.i.961.2 | 6 | 76.7 | odd | 6 | |||
1900.2.i.c.201.2 | 6 | 95.64 | even | 6 | |||
1900.2.i.c.501.2 | 6 | 95.49 | even | 6 | |||
1900.2.s.c.49.3 | 12 | 95.7 | odd | 12 | |||
1900.2.s.c.49.4 | 12 | 95.83 | odd | 12 | |||
1900.2.s.c.349.3 | 12 | 95.68 | odd | 12 | |||
1900.2.s.c.349.4 | 12 | 95.87 | odd | 12 | |||
3420.2.t.v.1261.2 | 6 | 57.11 | odd | 6 | |||
3420.2.t.v.3241.2 | 6 | 57.26 | odd | 6 | |||
7220.2.a.n.1.2 | 3 | 1.1 | even | 1 | trivial | ||
7220.2.a.o.1.2 | 3 | 19.18 | odd | 2 |