Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7056,2,Mod(1,7056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7056.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: | \(56.3424436662\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7056.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27492 | −1.91180 | −0.955901 | − | 0.293691i | \(-0.905116\pi\) | ||||
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.27492 | −1.28894 | −0.644468 | − | 0.764631i | \(-0.722921\pi\) | ||||
−0.644468 | + | 0.764631i | \(0.722921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.27492 | 0.353598 | 0.176799 | − | 0.984247i | \(-0.443426\pi\) | ||||
0.176799 | + | 0.984247i | \(0.443426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.27492 | 0.292486 | 0.146243 | − | 0.989249i | \(-0.453282\pi\) | ||||
0.146243 | + | 0.989249i | \(0.453282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.2749 | 2.65498 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27492 | 0.422442 | 0.211221 | − | 0.977438i | \(-0.432256\pi\) | ||||
0.211221 | + | 0.977438i | \(0.432256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.27492 | 0.867191 | 0.433596 | − | 0.901108i | \(-0.357245\pi\) | ||||
0.433596 | + | 0.901108i | \(0.357245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5498 | 1.64761 | 0.823804 | − | 0.566875i | \(-0.191848\pi\) | ||||
0.823804 | + | 0.566875i | \(0.191848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.27492 | 1.10941 | 0.554707 | − | 0.832046i | \(-0.312830\pi\) | ||||
0.554707 | + | 0.832046i | \(0.312830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.72508 | −0.236958 | −0.118479 | − | 0.992957i | \(-0.537802\pi\) | ||||
−0.118479 | + | 0.992957i | \(0.537802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.2749 | 2.46419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.27492 | −0.816925 | −0.408462 | − | 0.912775i | \(-0.633935\pi\) | ||||
−0.408462 | + | 0.912775i | \(0.633935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.45017 | −0.676010 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.27492 | −0.888773 | −0.444386 | − | 0.895835i | \(-0.646578\pi\) | ||||
−0.444386 | + | 0.895835i | \(0.646578\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.27492 | −0.383300 | −0.191650 | − | 0.981463i | \(-0.561384\pi\) | ||||
−0.191650 | + | 0.981463i | \(0.561384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.54983 | 0.399388 | 0.199694 | − | 0.979858i | \(-0.436005\pi\) | ||||
0.199694 | + | 0.979858i | \(0.436005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.274917 | 0.0301761 | 0.0150880 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150880 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.0997 | 1.85472 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.54983 | 0.482281 | 0.241141 | − | 0.970490i | \(-0.422478\pi\) | ||||
0.241141 | + | 0.970490i | \(0.422478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.45017 | −0.559175 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2749 | −1.65247 | −0.826234 | − | 0.563327i | \(-0.809521\pi\) | ||||
−0.826234 | + | 0.563327i | \(0.809521\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8248 | −1.16513 | −0.582564 | − | 0.812785i | \(-0.697950\pi\) | ||||
−0.582564 | + | 0.812785i | \(0.697950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.82475 | 0.659774 | 0.329887 | − | 0.944020i | \(-0.392989\pi\) | ||||
0.329887 | + | 0.944020i | \(0.392989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.82475 | −0.557910 | −0.278955 | − | 0.960304i | \(-0.589988\pi\) | ||||
−0.278955 | + | 0.960304i | \(0.589988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5498 | −0.992445 | −0.496222 | − | 0.868195i | \(-0.665280\pi\) | ||||
−0.496222 | + | 0.868195i | \(0.665280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.0997 | −1.59455 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.27492 | 0.661356 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35.3746 | −3.16400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.5498 | 1.91224 | 0.956119 | − | 0.292978i | \(-0.0946462\pi\) | ||||
0.956119 | + | 0.292978i | \(0.0946462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.274917 | 0.0240196 | 0.0120098 | − | 0.999928i | \(-0.496177\pi\) | ||||
0.0120098 | + | 0.999928i | \(0.496177\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.5498 | −1.41395 | −0.706974 | − | 0.707240i | \(-0.749940\pi\) | ||||
−0.706974 | + | 0.707240i | \(0.749940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.725083 | 0.0615007 | 0.0307504 | − | 0.999527i | \(-0.490210\pi\) | ||||
0.0307504 | + | 0.999527i | \(0.490210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.45017 | −0.455766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.72508 | −0.807624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.549834 | −0.0450442 | −0.0225221 | − | 0.999746i | \(-0.507170\pi\) | ||||
−0.0225221 | + | 0.999746i | \(0.507170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3746 | 1.25117 | 0.625583 | − | 0.780158i | \(-0.284861\pi\) | ||||
0.625583 | + | 0.780158i | \(0.284861\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.27492 | 0.343370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5498 | −1.16120 | −0.580602 | − | 0.814188i | \(-0.697183\pi\) | ||||
−0.580602 | + | 0.814188i | \(0.697183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3746 | −0.874968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.45017 | −0.566426 | −0.283213 | − | 0.959057i | \(-0.591400\pi\) | ||||
−0.283213 | + | 0.959057i | \(0.591400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.45017 | −0.108390 | −0.0541952 | − | 0.998530i | \(-0.517259\pi\) | ||||
−0.0541952 | + | 0.998530i | \(0.517259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.82475 | −0.284292 | −0.142146 | − | 0.989846i | \(-0.545400\pi\) | ||||
−0.142146 | + | 0.989846i | \(0.545400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.5498 | −1.65790 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.0997 | 1.25045 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5498 | −0.763359 | −0.381680 | − | 0.924295i | \(-0.624654\pi\) | ||||
−0.381680 | + | 0.924295i | \(0.624654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5498 | 1.11930 | 0.559651 | − | 0.828729i | \(-0.310935\pi\) | ||||
0.559651 | + | 0.828729i | \(0.310935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5498 | 1.17913 | 0.589563 | − | 0.807722i | \(-0.299300\pi\) | ||||
0.589563 | + | 0.807722i | \(0.299300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0997 | 1.77927 | 0.889634 | − | 0.456674i | \(-0.150959\pi\) | ||||
0.889634 | + | 0.456674i | \(0.150959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −45.0997 | −3.14990 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.45017 | −0.376996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.6495 | −1.21504 | −0.607521 | − | 0.794304i | \(-0.707836\pi\) | ||||
−0.607521 | + | 0.794304i | \(0.707836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.0997 | −2.12098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.09967 | −0.343041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.27492 | 0.420200 | 0.210100 | − | 0.977680i | \(-0.432621\pi\) | ||||
0.210100 | + | 0.977680i | \(0.432621\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.72508 | 0.247242 | 0.123621 | − | 0.992329i | \(-0.460549\pi\) | ||||
0.123621 | + | 0.992329i | \(0.460549\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7251 | −0.708733 | −0.354367 | − | 0.935107i | \(-0.615304\pi\) | ||||
−0.354367 | + | 0.935107i | \(0.615304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5498 | −0.953191 | −0.476596 | − | 0.879123i | \(-0.658129\pi\) | ||||
−0.476596 | + | 0.879123i | \(0.658129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.6495 | −1.67319 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.5498 | 1.97610 | 0.988052 | − | 0.154119i | \(-0.0492540\pi\) | ||||
0.988052 | + | 0.154119i | \(0.0492540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8248 | 0.826115 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.62541 | 0.103423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.3746 | −1.22291 | −0.611457 | − | 0.791278i | \(-0.709416\pi\) | ||||
−0.611457 | + | 0.791278i | \(0.709416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0997 | −1.07505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0997 | −1.19140 | −0.595702 | − | 0.803205i | \(-0.703126\pi\) | ||||
−0.595702 | + | 0.803205i | \(0.703126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.5498 | −1.51381 | −0.756904 | − | 0.653526i | \(-0.773289\pi\) | ||||
−0.756904 | + | 0.653526i | \(0.773289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.37459 | 0.453017 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.2749 | 1.72395 | 0.861976 | − | 0.506949i | \(-0.169227\pi\) | ||||
0.861976 | + | 0.506949i | \(0.169227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.27492 | −0.381174 | −0.190587 | − | 0.981670i | \(-0.561039\pi\) | ||||
−0.190587 | + | 0.981670i | \(0.561039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −56.7492 | −3.42210 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.17525 | −0.250866 | −0.125433 | − | 0.992102i | \(-0.540032\pi\) | ||||
−0.125433 | + | 0.992102i | \(0.540032\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4502 | 0.683060 | 0.341530 | − | 0.939871i | \(-0.389055\pi\) | ||||
0.341530 | + | 0.939871i | \(0.389055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9244 | 1.60049 | 0.800245 | − | 0.599673i | \(-0.204703\pi\) | ||||
0.800245 | + | 0.599673i | \(0.204703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.17525 | −0.302341 | −0.151171 | − | 0.988508i | \(-0.548304\pi\) | ||||
−0.151171 | + | 0.988508i | \(0.548304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8248 | 1.56180 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.09967 | 0.294921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.7492 | 2.44781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3746 | −1.50528 | −0.752639 | − | 0.658434i | \(-0.771219\pi\) | ||||
−0.752639 | + | 0.658434i | \(0.771219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5498 | −0.598226 | −0.299113 | − | 0.954218i | \(-0.596691\pi\) | ||||
−0.299113 | + | 0.954218i | \(0.596691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.45017 | 0.251538 | 0.125769 | − | 0.992060i | \(-0.459860\pi\) | ||||
0.125769 | + | 0.992060i | \(0.459860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.17525 | 0.290671 | 0.145335 | − | 0.989382i | \(-0.453574\pi\) | ||||
0.145335 | + | 0.989382i | \(0.453574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.72508 | −0.544500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.09967 | −0.283753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9244 | 0.938798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.8248 | −1.30953 | −0.654763 | − | 0.755834i | \(-0.727232\pi\) | ||||
−0.654763 | + | 0.755834i | \(0.727232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.0997 | 1.69916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.09967 | 0.332270 | 0.166135 | − | 0.986103i | \(-0.446871\pi\) | ||||
0.166135 | + | 0.986103i | \(0.446871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.27492 | 0.231500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.1993 | −1.62119 | −0.810593 | − | 0.585610i | \(-0.800855\pi\) | ||||
−0.810593 | + | 0.585610i | \(0.800855\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.45017 | −0.290083 | −0.145042 | − | 0.989426i | \(-0.546332\pi\) | ||||
−0.145042 | + | 0.989426i | \(0.546332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.54983 | −0.453778 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.6495 | 1.35373 | 0.676865 | − | 0.736108i | \(-0.263338\pi\) | ||||
0.676865 | + | 0.736108i | \(0.263338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3746 | −0.914452 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.09967 | −0.422799 | −0.211400 | − | 0.977400i | \(-0.567802\pi\) | ||||
−0.211400 | + | 0.977400i | \(0.567802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.27492 | 0.0660127 | 0.0330064 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330064 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.90033 | 0.149375 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.8248 | −1.84019 | −0.920097 | − | 0.391691i | \(-0.871890\pi\) | ||||
−0.920097 | + | 0.391691i | \(0.871890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.54983 | 0.232486 | 0.116243 | − | 0.993221i | \(-0.462915\pi\) | ||||
0.116243 | + | 0.993221i | \(0.462915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00000 | 0.101404 | 0.0507020 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507020 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1752 | −0.763550 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.3746 | −1.72521 | −0.862606 | − | 0.505877i | \(-0.831169\pi\) | ||||
−0.862606 | + | 0.505877i | \(0.831169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0000 | −1.19850 | −0.599251 | − | 0.800561i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800561i | \(0.704535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.27492 | −0.0635082 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.5498 | −1.11775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.5498 | −1.26336 | −0.631679 | − | 0.775230i | \(-0.717634\pi\) | ||||
−0.631679 | + | 0.775230i | \(0.717634\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.17525 | −0.0576907 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4502 | −0.657084 | −0.328542 | − | 0.944489i | \(-0.606557\pi\) | ||||
−0.328542 | + | 0.944489i | \(0.606557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8248 | −0.673777 | −0.336889 | − | 0.941545i | \(-0.609375\pi\) | ||||
−0.336889 | + | 0.941545i | \(0.609375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −53.0997 | −2.57571 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.6495 | 1.33183 | 0.665915 | − | 0.746028i | \(-0.268041\pi\) | ||||
0.665915 | + | 0.746028i | \(0.268041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8248 | −1.24106 | −0.620529 | − | 0.784183i | \(-0.713082\pi\) | ||||
−0.620529 | + | 0.784183i | \(0.713082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.09967 | 0.243950 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.72508 | 0.464153 | 0.232076 | − | 0.972698i | \(-0.425448\pi\) | ||||
0.232076 | + | 0.972698i | \(0.425448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3746 | 1.49065 | 0.745326 | − | 0.666700i | \(-0.232294\pi\) | ||||
0.745326 | + | 0.666700i | \(0.232294\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4502 | −0.922026 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45017 | −0.257209 | −0.128605 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128605 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −45.0997 | −2.12366 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.64950 | −0.404607 | −0.202303 | − | 0.979323i | \(-0.564843\pi\) | ||||
−0.202303 | + | 0.979323i | \(0.564843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.6495 | 1.93981 | 0.969905 | − | 0.243482i | \(-0.0782897\pi\) | ||||
0.969905 | + | 0.243482i | \(0.0782897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.8248 | −1.66492 | −0.832459 | − | 0.554087i | \(-0.813067\pi\) | ||||
−0.832459 | + | 0.554087i | \(0.813067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4502 | −1.17769 | −0.588847 | − | 0.808245i | \(-0.700418\pi\) | ||||
−0.588847 | + | 0.808245i | \(0.700418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.0997 | −1.42996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9244 | 0.776546 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.5498 | 0.938946 | 0.469473 | − | 0.882947i | \(-0.344444\pi\) | ||||
0.469473 | + | 0.882947i | \(0.344444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.72508 | 0.306637 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 69.5739 | 3.15919 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | −0.0453143 | −0.0226572 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226572 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9244 | −0.718659 | −0.359330 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.09967 | −0.409828 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7251 | −1.10685 | −0.553423 | − | 0.832900i | \(-0.686679\pi\) | ||||
−0.553423 | + | 0.832900i | \(0.686679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.64950 | −0.341074 | −0.170537 | − | 0.985351i | \(-0.554550\pi\) | ||||
−0.170537 | + | 0.985351i | \(0.554550\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6495 | 1.14139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.72508 | −0.165111 | −0.0825557 | − | 0.996586i | \(-0.526308\pi\) | ||||
−0.0825557 | + | 0.996586i | \(0.526308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.5498 | 2.22749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.6495 | −1.12806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.549834 | 0.0240887 | 0.0120443 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120443 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.2749 | −1.10519 | −0.552597 | − | 0.833448i | \(-0.686363\pi\) | ||||
−0.552597 | + | 0.833448i | \(0.686363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4502 | 0.582591 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.1752 | −1.26136 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.725083 | −0.0311737 | −0.0155869 | − | 0.999879i | \(-0.504962\pi\) | ||||
−0.0155869 | + | 0.999879i | \(0.504962\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.9003 | 1.06661 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.90033 | 0.123558 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.17525 | 0.304025 | 0.152013 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152013 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.27492 | 0.392287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.72508 | −0.325573 | −0.162787 | − | 0.986661i | \(-0.552048\pi\) | ||||
−0.162787 | + | 0.986661i | \(0.552048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.0997 | 1.89736 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.5498 | −1.11303 | −0.556513 | − | 0.830839i | \(-0.687861\pi\) | ||||
−0.556513 | + | 0.830839i | \(0.687861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.725083 | −0.0303438 | −0.0151719 | − | 0.999885i | \(-0.504830\pi\) | ||||
−0.0151719 | + | 0.999885i | \(0.504830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.0997 | 2.21441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000 | 1.04076 | 0.520382 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520382 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.37459 | 0.305424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.72508 | −0.0712018 | −0.0356009 | − | 0.999366i | \(-0.511335\pi\) | ||||
−0.0356009 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.27492 | −0.0525320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.5498 | 0.597490 | 0.298745 | − | 0.954333i | \(-0.403432\pi\) | ||||
0.298745 | + | 0.954333i | \(0.403432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.45017 | 0.304406 | 0.152203 | − | 0.988349i | \(-0.451363\pi\) | ||||
0.152203 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0997 | 1.06463 | 0.532314 | − | 0.846547i | \(-0.321323\pi\) | ||||
0.532314 | + | 0.846547i | \(0.321323\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.0997 | −1.26438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.00000 | −0.284121 | −0.142061 | − | 0.989858i | \(-0.545373\pi\) | ||||
−0.142061 | + | 0.989858i | \(0.545373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.64950 | 0.309466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.54983 | 0.264545 | 0.132273 | − | 0.991213i | \(-0.457773\pi\) | ||||
0.132273 | + | 0.991213i | \(0.457773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.17525 | 0.248204 | 0.124102 | − | 0.992269i | \(-0.460395\pi\) | ||||
0.124102 | + | 0.992269i | \(0.460395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 84.8488 | 3.39395 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0997 | −0.841299 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.82475 | 0.112452 | 0.0562258 | − | 0.998418i | \(-0.482093\pi\) | ||||
0.0562258 | + | 0.998418i | \(0.482093\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −92.1238 | −3.65582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.6495 | −1.64506 | −0.822528 | − | 0.568724i | \(-0.807437\pi\) | ||||
−0.822528 | + | 0.568724i | \(0.807437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.3746 | −1.27673 | −0.638365 | − | 0.769734i | \(-0.720389\pi\) | ||||
−0.638365 | + | 0.769734i | \(0.720389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.0000 | 1.33668 | 0.668339 | − | 0.743857i | \(-0.267006\pi\) | ||||
0.668339 | + | 0.743857i | \(0.267006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.8248 | 1.05296 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.9244 | −1.79716 | −0.898581 | − | 0.438808i | \(-0.855401\pi\) | ||||
−0.898581 | + | 0.438808i | \(0.855401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.17525 | −0.0459208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1993 | 0.708946 | 0.354473 | − | 0.935066i | \(-0.384660\pi\) | ||||
0.354473 | + | 0.935066i | \(0.384660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.8248 | −1.16005 | −0.580024 | − | 0.814599i | \(-0.696957\pi\) | ||||
−0.580024 | + | 0.814599i | \(0.696957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.09967 | 0.352341 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.7492 | 1.65031 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.4502 | 1.01958 | 0.509789 | − | 0.860299i | \(-0.329723\pi\) | ||||
0.509789 | + | 0.860299i | \(0.329723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.72508 | −0.220033 | −0.110016 | − | 0.993930i | \(-0.535090\pi\) | ||||
−0.110016 | + | 0.993930i | \(0.535090\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.8248 | 1.33253 | 0.666266 | − | 0.745714i | \(-0.267892\pi\) | ||||
0.666266 | + | 0.745714i | \(0.267892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.7492 | 2.70319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.19934 | −0.0837881 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8248 | 0.449835 | 0.224917 | − | 0.974378i | \(-0.427789\pi\) | ||||
0.224917 | + | 0.974378i | \(0.427789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.09967 | −0.117577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.1993 | −1.59841 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.9244 | −1.50792 | −0.753962 | − | 0.656918i | \(-0.771860\pi\) | ||||
−0.753962 | + | 0.656918i | \(0.771860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.72508 | 0.253641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.1993 | 1.20927 | 0.604636 | − | 0.796502i | \(-0.293319\pi\) | ||||
0.604636 | + | 0.796502i | \(0.293319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.2990 | 0.871333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.1993 | 1.20083 | 0.600416 | − | 0.799688i | \(-0.295002\pi\) | ||||
0.600416 | + | 0.799688i | \(0.295002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.1993 | 1.12158 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4502 | 0.610103 | 0.305051 | − | 0.952336i | \(-0.401326\pi\) | ||||
0.305051 | + | 0.952336i | \(0.401326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.0997 | −1.07629 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.9244 | 1.73319 | 0.866597 | − | 0.499010i | \(-0.166303\pi\) | ||||
0.866597 | + | 0.499010i | \(0.166303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.0997 | 1.14557 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.3746 | 1.33806 | 0.669030 | − | 0.743235i | \(-0.266710\pi\) | ||||
0.669030 | + | 0.743235i | \(0.266710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1993 | 0.594296 | 0.297148 | − | 0.954831i | \(-0.403965\pi\) | ||||
0.297148 | + | 0.954831i | \(0.403965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.35050 | 0.0861155 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5498 | 0.932327 | 0.466163 | − | 0.884699i | \(-0.345636\pi\) | ||||
0.466163 | + | 0.884699i | \(0.345636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −65.7251 | −2.39198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.09967 | 0.184863 | 0.0924314 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924314 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6495 | −0.456153 | −0.228076 | − | 0.973643i | \(-0.573244\pi\) | ||||
−0.228076 | + | 0.973643i | \(0.573244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0997 | −0.974707 | −0.487354 | − | 0.873205i | \(-0.662038\pi\) | ||||
−0.487354 | + | 0.873205i | \(0.662038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.2749 | −0.476849 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.4502 | 0.481902 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.54983 | −0.305937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 62.1993 | 2.21999 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5498 | −0.447353 | −0.223677 | − | 0.974663i | \(-0.571806\pi\) | ||||
−0.223677 | + | 0.974663i | \(0.571806\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7492 | −0.452736 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.4743 | 1.29198 | 0.645992 | − | 0.763344i | \(-0.276444\pi\) | ||||
0.645992 | + | 0.763344i | \(0.276444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.0000 | 0.494049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.6495 | −0.550207 | −0.275104 | − | 0.961415i | \(-0.588712\pi\) | ||||
−0.275104 | + | 0.961415i | \(0.588712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4502 | −0.963906 | −0.481953 | − | 0.876197i | \(-0.660072\pi\) | ||||
−0.481953 | + | 0.876197i | \(0.660072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.2990 | −1.79693 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.27492 | 0.324488 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.2749 | −0.707599 | −0.353800 | − | 0.935321i | \(-0.615111\pi\) | ||||
−0.353800 | + | 0.935321i | \(0.615111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.1993 | −0.913252 | −0.456626 | − | 0.889659i | \(-0.650942\pi\) | ||||
−0.456626 | + | 0.889659i | \(0.650942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.0241 | 1.35700 | 0.678500 | − | 0.734600i | \(-0.262630\pi\) | ||||
0.678500 | + | 0.734600i | \(0.262630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7251 | −0.789275 | −0.394637 | − | 0.918837i | \(-0.629130\pi\) | ||||
−0.394637 | + | 0.918837i | \(0.629130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.6495 | −0.887638 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1993 | −1.04260 | −0.521298 | − | 0.853374i | \(-0.674552\pi\) | ||||
−0.521298 | + | 0.853374i | \(0.674552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8248 | −0.821543 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.6254 | 1.67277 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0997 | 0.723287 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3746 | 0.834570 | 0.417285 | − | 0.908776i | \(-0.362982\pi\) | ||||
0.417285 | + | 0.908776i | \(0.362982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5498 | −0.975244 | −0.487622 | − | 0.873055i | \(-0.662136\pi\) | ||||
−0.487622 | + | 0.873055i | \(0.662136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3505 | −0.353154 | −0.176577 | − | 0.984287i | \(-0.556503\pi\) | ||||
−0.176577 | + | 0.984287i | \(0.556503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0997 | −0.377837 | −0.188919 | − | 0.981993i | \(-0.560498\pi\) | ||||
−0.188919 | + | 0.981993i | \(0.560498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.8488 | 1.08289 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1752 | −0.514785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.27492 | −0.314269 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.7492 | −0.970791 | −0.485395 | − | 0.874295i | \(-0.661324\pi\) | ||||
−0.485395 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.5498 | 0.827105 | 0.413552 | − | 0.910480i | \(-0.364288\pi\) | ||||
0.413552 | + | 0.910480i | \(0.364288\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.3746 | 1.02219 | 0.511093 | − | 0.859525i | \(-0.329241\pi\) | ||||
0.511093 | + | 0.859525i | \(0.329241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6495 | 0.391152 | 0.195576 | − | 0.980689i | \(-0.437342\pi\) | ||||
0.195576 | + | 0.980689i | \(0.437342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.64950 | 0.255981 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19934 | 0.207221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.27492 | −0.0758727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.90033 | 0.229883 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.3505 | 0.543509 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.2749 | 1.23769 | 0.618847 | − | 0.785512i | \(-0.287600\pi\) | ||||
0.618847 | + | 0.785512i | \(0.287600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8488 | −1.71783 | −0.858914 | − | 0.512119i | \(-0.828861\pi\) | ||||
−0.858914 | + | 0.512119i | \(0.828861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.17525 | −0.0388950 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8248 | −0.653958 | −0.326979 | − | 0.945032i | \(-0.606031\pi\) | ||||
−0.326979 | + | 0.945032i | \(0.606031\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.54983 | 0.0839288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.0241 | 2.30238 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1993 | 0.662719 | 0.331359 | − | 0.943505i | \(-0.392493\pi\) | ||||
0.331359 | + | 0.943505i | \(0.392493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −73.0997 | −2.39061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0997 | −0.787302 | −0.393651 | − | 0.919260i | \(-0.628788\pi\) | ||||
−0.393651 | + | 0.919260i | \(0.628788\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.1752 | 0.951086 | 0.475543 | − | 0.879693i | \(-0.342252\pi\) | ||||
0.475543 | + | 0.879693i | \(0.342252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.1993 | 1.37420 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.5498 | −1.12272 | −0.561359 | − | 0.827572i | \(-0.689721\pi\) | ||||
−0.561359 | + | 0.827572i | \(0.689721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.17525 | −0.135534 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3505 | −0.335285 | −0.167643 | − | 0.985848i | \(-0.553616\pi\) | ||||
−0.167643 | + | 0.985848i | \(0.553616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0997 | 1.45939 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −66.4743 | −2.13988 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.4502 | 1.23647 | 0.618237 | − | 0.785992i | \(-0.287847\pi\) | ||||
0.618237 | + | 0.785992i | \(0.287847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5739 | 1.33417 | 0.667085 | − | 0.744981i | \(-0.267542\pi\) | ||||
0.667085 | + | 0.744981i | \(0.267542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.0997 | −1.25091 | −0.625455 | − | 0.780261i | \(-0.715086\pi\) | ||||
−0.625455 | + | 0.780261i | \(0.715086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.4502 | −0.621630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.2990 | 1.63618 | 0.818092 | − | 0.575087i | \(-0.195032\pi\) | ||||
0.818092 | + | 0.575087i | \(0.195032\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.7492 | −2.25426 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.0997 | 0.925316 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0997 | −0.511423 | −0.255711 | − | 0.966753i | \(-0.582310\pi\) | ||||
−0.255711 | + | 0.966753i | \(0.582310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −107.299 | −3.40161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.1752 | 0.702297 | 0.351149 | − | 0.936320i | \(-0.385791\pi\) | ||||
0.351149 | + | 0.936320i | \(0.385791\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7056.2.a.ch.1.1 | 2 | ||
3.2 | odd | 2 | 2352.2.a.ba.1.2 | 2 | |||
4.3 | odd | 2 | 3528.2.a.bd.1.1 | 2 | |||
7.3 | odd | 6 | 1008.2.s.r.289.1 | 4 | |||
7.5 | odd | 6 | 1008.2.s.r.865.1 | 4 | |||
7.6 | odd | 2 | 7056.2.a.cu.1.2 | 2 | |||
12.11 | even | 2 | 1176.2.a.n.1.2 | 2 | |||
21.2 | odd | 6 | 2352.2.q.bf.1537.1 | 4 | |||
21.5 | even | 6 | 336.2.q.g.193.2 | 4 | |||
21.11 | odd | 6 | 2352.2.q.bf.961.1 | 4 | |||
21.17 | even | 6 | 336.2.q.g.289.2 | 4 | |||
21.20 | even | 2 | 2352.2.a.bf.1.1 | 2 | |||
24.5 | odd | 2 | 9408.2.a.dw.1.1 | 2 | |||
24.11 | even | 2 | 9408.2.a.dj.1.1 | 2 | |||
28.3 | even | 6 | 504.2.s.i.289.1 | 4 | |||
28.11 | odd | 6 | 3528.2.s.bk.3313.2 | 4 | |||
28.19 | even | 6 | 504.2.s.i.361.1 | 4 | |||
28.23 | odd | 6 | 3528.2.s.bk.361.2 | 4 | |||
28.27 | even | 2 | 3528.2.a.bk.1.2 | 2 | |||
84.11 | even | 6 | 1176.2.q.l.961.1 | 4 | |||
84.23 | even | 6 | 1176.2.q.l.361.1 | 4 | |||
84.47 | odd | 6 | 168.2.q.c.25.2 | ✓ | 4 | ||
84.59 | odd | 6 | 168.2.q.c.121.2 | yes | 4 | ||
84.83 | odd | 2 | 1176.2.a.k.1.1 | 2 | |||
168.5 | even | 6 | 1344.2.q.x.193.1 | 4 | |||
168.59 | odd | 6 | 1344.2.q.w.961.1 | 4 | |||
168.83 | odd | 2 | 9408.2.a.ec.1.2 | 2 | |||
168.101 | even | 6 | 1344.2.q.x.961.1 | 4 | |||
168.125 | even | 2 | 9408.2.a.dp.1.2 | 2 | |||
168.131 | odd | 6 | 1344.2.q.w.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.q.c.25.2 | ✓ | 4 | 84.47 | odd | 6 | ||
168.2.q.c.121.2 | yes | 4 | 84.59 | odd | 6 | ||
336.2.q.g.193.2 | 4 | 21.5 | even | 6 | |||
336.2.q.g.289.2 | 4 | 21.17 | even | 6 | |||
504.2.s.i.289.1 | 4 | 28.3 | even | 6 | |||
504.2.s.i.361.1 | 4 | 28.19 | even | 6 | |||
1008.2.s.r.289.1 | 4 | 7.3 | odd | 6 | |||
1008.2.s.r.865.1 | 4 | 7.5 | odd | 6 | |||
1176.2.a.k.1.1 | 2 | 84.83 | odd | 2 | |||
1176.2.a.n.1.2 | 2 | 12.11 | even | 2 | |||
1176.2.q.l.361.1 | 4 | 84.23 | even | 6 | |||
1176.2.q.l.961.1 | 4 | 84.11 | even | 6 | |||
1344.2.q.w.193.1 | 4 | 168.131 | odd | 6 | |||
1344.2.q.w.961.1 | 4 | 168.59 | odd | 6 | |||
1344.2.q.x.193.1 | 4 | 168.5 | even | 6 | |||
1344.2.q.x.961.1 | 4 | 168.101 | even | 6 | |||
2352.2.a.ba.1.2 | 2 | 3.2 | odd | 2 | |||
2352.2.a.bf.1.1 | 2 | 21.20 | even | 2 | |||
2352.2.q.bf.961.1 | 4 | 21.11 | odd | 6 | |||
2352.2.q.bf.1537.1 | 4 | 21.2 | odd | 6 | |||
3528.2.a.bd.1.1 | 2 | 4.3 | odd | 2 | |||
3528.2.a.bk.1.2 | 2 | 28.27 | even | 2 | |||
3528.2.s.bk.361.2 | 4 | 28.23 | odd | 6 | |||
3528.2.s.bk.3313.2 | 4 | 28.11 | odd | 6 | |||
7056.2.a.ch.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7056.2.a.cu.1.2 | 2 | 7.6 | odd | 2 | |||
9408.2.a.dj.1.1 | 2 | 24.11 | even | 2 | |||
9408.2.a.dp.1.2 | 2 | 168.125 | even | 2 | |||
9408.2.a.dw.1.1 | 2 | 24.5 | odd | 2 | |||
9408.2.a.ec.1.2 | 2 | 168.83 | odd | 2 |