Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1249,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3120.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.l (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.57815240704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.8 | ||
Root | \(-2.15569 - 2.15569i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1249 |
Dual form | 3120.2.l.n.1249.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times\).
\(n\) | \(1951\) | \(2081\) | \(2341\) | \(2497\) | \(2641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.15569 | − | 0.594137i | 0.964054 | − | 0.265706i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.633776i | − | 0.239545i | −0.992801 | − | 0.119772i | \(-0.961784\pi\) | ||
0.992801 | − | 0.119772i | \(-0.0382165\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.177949 | 0.0536537 | 0.0268269 | − | 0.999640i | \(-0.491460\pi\) | ||||
0.0268269 | + | 0.999640i | \(0.491460\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.594137 | + | 2.15569i | 0.153406 | + | 0.556597i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.48933i | − | 1.08882i | −0.838818 | − | 0.544411i | \(-0.816753\pi\) | ||
0.838818 | − | 0.544411i | \(-0.183247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.633776 | 0.138301 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.48933i | 1.35312i | 0.736388 | + | 0.676559i | \(0.236530\pi\) | ||||
−0.736388 | + | 0.676559i | \(0.763470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29400 | − | 2.56155i | 0.858800 | − | 0.512311i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.49966 | 0.649870 | 0.324935 | − | 0.945736i | \(-0.394658\pi\) | ||||
0.324935 | + | 0.945736i | \(0.394658\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.177949i | 0.0309770i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.376550 | − | 1.36622i | −0.0636486 | − | 0.230934i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.75688i | − | 0.288830i | −0.989517 | − | 0.144415i | \(-0.953870\pi\) | ||
0.989517 | − | 0.144415i | \(-0.0461299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.67760 | 1.19904 | 0.599520 | − | 0.800360i | \(-0.295358\pi\) | ||||
0.599520 | + | 0.800360i | \(0.295358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.49966i | 1.14369i | 0.820363 | + | 0.571843i | \(0.193772\pi\) | ||||
−0.820363 | + | 0.571843i | \(0.806228\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.15569 | + | 0.594137i | −0.321351 | + | 0.0885688i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.18827i | − | 0.465058i | −0.972589 | − | 0.232529i | \(-0.925300\pi\) | ||
0.972589 | − | 0.232529i | \(-0.0747000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59833 | 0.942618 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.48933 | 0.628632 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.75688i | − | 0.241326i | −0.992694 | − | 0.120663i | \(-0.961498\pi\) | ||
0.992694 | − | 0.120663i | \(-0.0385021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.383604 | − | 0.105726i | 0.0517251 | − | 0.0142561i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.93483 | 0.512271 | 0.256136 | − | 0.966641i | \(-0.417551\pi\) | ||||
0.256136 | + | 0.966641i | \(0.417551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01033 | 0.385433 | 0.192716 | − | 0.981255i | \(-0.438270\pi\) | ||||
0.192716 | + | 0.981255i | \(0.438270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.633776i | 0.0798482i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.594137 | + | 2.15569i | 0.0736937 | + | 0.267380i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.62345i | − | 0.198336i | −0.995071 | − | 0.0991680i | \(-0.968382\pi\) | ||
0.995071 | − | 0.0991680i | \(-0.0316181\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.48933 | −0.781224 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41005 | 0.523377 | 0.261689 | − | 0.965152i | \(-0.415721\pi\) | ||||
0.261689 | + | 0.965152i | \(0.415721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.85555i | − | 0.451258i | −0.974213 | − | 0.225629i | \(-0.927556\pi\) | ||
0.974213 | − | 0.225629i | \(-0.0724438\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.56155 | + | 4.29400i | 0.295783 | + | 0.495829i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.112780i | − | 0.0128525i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.63309 | 1.08381 | 0.541903 | − | 0.840441i | \(-0.317704\pi\) | ||||
0.541903 | + | 0.840441i | \(0.317704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.72338i | 0.189165i | 0.995517 | + | 0.0945827i | \(0.0301517\pi\) | ||||
−0.995517 | + | 0.0945827i | \(0.969848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.66728 | − | 9.67760i | −0.289307 | − | 1.04968i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.49966i | 0.375202i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.589258 | 0.0624612 | 0.0312306 | − | 0.999512i | \(-0.490057\pi\) | ||||
0.0312306 | + | 0.999512i | \(0.490057\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.633776 | 0.0664378 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.45457i | 0.452293i | 0.974093 | + | 0.226147i | \(0.0726128\pi\) | ||||
−0.974093 | + | 0.226147i | \(0.927387\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.177949 | −0.0178846 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4783 | 1.63965 | 0.819827 | − | 0.572612i | \(-0.194070\pi\) | ||||
0.819827 | + | 0.572612i | \(0.194070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.86966i | − | 0.578355i | −0.957276 | − | 0.289177i | \(-0.906618\pi\) | ||
0.957276 | − | 0.289177i | \(-0.0933818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.36622 | − | 0.376550i | 0.133330 | − | 0.0367475i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.509981i | 0.0493017i | 0.999696 | + | 0.0246509i | \(0.00784741\pi\) | ||||
−0.999696 | + | 0.0246509i | \(0.992153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.35590 | −0.608785 | −0.304392 | − | 0.952547i | \(-0.598453\pi\) | ||||
−0.304392 | + | 0.952547i | \(0.598453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.75688 | 0.166756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.71111i | − | 0.913544i | −0.889584 | − | 0.456772i | \(-0.849005\pi\) | ||
0.889584 | − | 0.456772i | \(-0.150995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.85555 | + | 13.9890i | 0.359532 | + | 1.30448i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.84523 | −0.260822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9683 | −0.997121 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.67760i | 0.692266i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.73462 | − | 8.07314i | 0.691806 | − | 0.722084i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.1231i | − | 0.987016i | −0.869741 | − | 0.493508i | \(-0.835714\pi\) | ||
0.869741 | − | 0.493508i | \(-0.164286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.49966 | −0.660308 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.9439 | −1.13091 | −0.565457 | − | 0.824778i | \(-0.691300\pi\) | ||||
−0.565457 | + | 0.824778i | \(0.691300\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.594137 | − | 2.15569i | −0.0511352 | − | 0.185532i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7904i | 1.00732i | 0.863902 | + | 0.503660i | \(0.168014\pi\) | ||||
−0.863902 | + | 0.503660i | \(0.831986\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.112780 | 0.00956587 | 0.00478293 | − | 0.999989i | \(-0.498478\pi\) | ||||
0.00478293 | + | 0.999989i | \(0.498478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18827 | 0.268501 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.177949i | 0.0148809i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.54417 | − | 2.07928i | 0.626510 | − | 0.172675i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.59833i | 0.544221i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.30829 | −0.189102 | −0.0945512 | − | 0.995520i | \(-0.530142\pi\) | ||||
−0.0945512 | + | 0.995520i | \(0.530142\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7318 | 1.44299 | 0.721495 | − | 0.692420i | \(-0.243455\pi\) | ||||
0.721495 | + | 0.692420i | \(0.243455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.48933i | 0.362941i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.8549i | − | 1.02593i | −0.858410 | − | 0.512965i | \(-0.828547\pi\) | ||
0.858410 | − | 0.512965i | \(-0.171453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.75688 | 0.139330 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.11278 | 0.324132 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3308i | 1.12247i | 0.827655 | + | 0.561237i | \(0.189674\pi\) | ||||
−0.827655 | + | 0.561237i | \(0.810326\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.105726 | + | 0.383604i | 0.00823078 | + | 0.0298635i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.43449i | 0.111004i | 0.998459 | + | 0.0555019i | \(0.0176759\pi\) | ||||
−0.998459 | + | 0.0555019i | \(0.982324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.24690i | − | 0.0948001i | −0.998876 | − | 0.0474000i | \(-0.984906\pi\) | ||
0.998876 | − | 0.0474000i | \(-0.0150936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.62345 | − | 2.72143i | −0.122721 | − | 0.205721i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.93483i | 0.295760i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.87621 | −0.588695 | −0.294348 | − | 0.955698i | \(-0.595102\pi\) | ||||
−0.294348 | + | 0.955698i | \(0.595102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3796 | 0.771513 | 0.385756 | − | 0.922601i | \(-0.373941\pi\) | ||||
0.385756 | + | 0.922601i | \(0.373941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.01033i | 0.222530i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.04383 | − | 3.78729i | −0.0767438 | − | 0.278447i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.798873i | − | 0.0584194i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.633776 | −0.0461004 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7318 | −0.993595 | −0.496798 | − | 0.867866i | \(-0.665491\pi\) | ||||
−0.496798 | + | 0.867866i | \(0.665491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.34488i | − | 0.456715i | −0.973577 | − | 0.228357i | \(-0.926665\pi\) | ||
0.973577 | − | 0.228357i | \(-0.0733355\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.15569 | + | 0.594137i | −0.154372 | + | 0.0425471i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.2966i | 1.51732i | 0.651487 | + | 0.758659i | \(0.274145\pi\) | ||||
−0.651487 | + | 0.758659i | \(0.725855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2108 | 0.794710 | 0.397355 | − | 0.917665i | \(-0.369928\pi\) | ||||
0.397355 | + | 0.917665i | \(0.369928\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.62345 | 0.114509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.21800i | − | 0.155673i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.5505 | − | 4.56155i | 1.15594 | − | 0.318593i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.48933i | − | 0.451040i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2810 | 1.39620 | 0.698100 | − | 0.716000i | \(-0.254029\pi\) | ||||
0.698100 | + | 0.716000i | \(0.254029\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.41005i | 0.302172i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.45583 | + | 16.1669i | 0.303885 | + | 1.10258i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.85555 | 0.260534 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.48933 | 0.301985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.3900i | − | 0.762729i | −0.924425 | − | 0.381364i | \(-0.875454\pi\) | ||
0.924425 | − | 0.381364i | \(-0.124546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.29400 | + | 2.56155i | −0.286267 | + | 0.170770i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.7020i | − | 0.975809i | −0.872897 | − | 0.487904i | \(-0.837762\pi\) | ||
0.872897 | − | 0.487904i | \(-0.162238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.84145 | −0.650341 | −0.325171 | − | 0.945655i | \(-0.605422\pi\) | ||||
−0.325171 | + | 0.945655i | \(0.605422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.112780 | 0.00742038 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.8439i | 1.49655i | 0.663388 | + | 0.748275i | \(0.269118\pi\) | ||||
−0.663388 | + | 0.748275i | \(0.730882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.89427 | − | 6.87293i | −0.123569 | − | 0.448341i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.63309i | 0.625736i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1907 | −1.56476 | −0.782382 | − | 0.622798i | \(-0.785996\pi\) | ||||
−0.782382 | + | 0.622798i | \(0.785996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.8896 | −1.47445 | −0.737225 | − | 0.675647i | \(-0.763864\pi\) | ||||
−0.737225 | + | 0.675647i | \(0.763864\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.2240 | − | 3.92031i | 0.908735 | − | 0.250460i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.72338 | −0.109215 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6763 | 0.737005 | 0.368502 | − | 0.929627i | \(-0.379871\pi\) | ||||
0.368502 | + | 0.929627i | \(0.379871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15477i | 0.0725999i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.67760 | − | 2.66728i | 0.606035 | − | 0.167031i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.9993i | 1.55941i | 0.626144 | + | 0.779707i | \(0.284632\pi\) | ||||
−0.626144 | + | 0.779707i | \(0.715368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.11347 | −0.0691876 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.49966 | −0.216623 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.12965i | 0.439633i | 0.975541 | + | 0.219817i | \(0.0705459\pi\) | ||||
−0.975541 | + | 0.219817i | \(0.929454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.04383 | − | 3.78729i | −0.0641219 | − | 0.232652i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.589258i | 0.0360620i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.47832 | 0.516932 | 0.258466 | − | 0.966020i | \(-0.416783\pi\) | ||||
0.258466 | + | 0.966020i | \(0.416783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.60142 | −0.340262 | −0.170131 | − | 0.985421i | \(-0.554419\pi\) | ||||
−0.170131 | + | 0.985421i | \(0.554419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.633776i | 0.0383579i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.764114 | − | 0.455826i | 0.0460778 | − | 0.0274874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2991i | 1.45999i | 0.683451 | + | 0.729996i | \(0.260478\pi\) | ||||
−0.683451 | + | 0.729996i | \(0.739522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6318 | 0.693897 | 0.346948 | − | 0.937884i | \(-0.387218\pi\) | ||||
0.346948 | + | 0.937884i | \(0.387218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.197345i | − | 0.0117310i | −0.999983 | − | 0.00586549i | \(-0.998133\pi\) | ||
0.999983 | − | 0.00586549i | \(-0.00186705\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.86588i | − | 0.287224i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.15408 | −0.185534 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.45457 | −0.261132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.3918i | 1.71709i | 0.512740 | + | 0.858544i | \(0.328630\pi\) | ||||
−0.512740 | + | 0.858544i | \(0.671370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48228 | − | 2.33783i | 0.493857 | − | 0.136114i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.177949i | − | 0.0103257i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.48933 | −0.375288 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.75310 | 0.273964 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.4783i | 0.946654i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.48933 | − | 1.78855i | 0.371578 | − | 0.102412i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.1997i | − | 1.66652i | −0.552883 | − | 0.833259i | \(-0.686472\pi\) | ||
0.552883 | − | 0.833259i | \(-0.313528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.86966 | 0.333913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3346 | 0.756133 | 0.378067 | − | 0.925778i | \(-0.376589\pi\) | ||||
0.378067 | + | 0.925778i | \(0.376589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.16441i | − | 0.291910i | −0.989291 | − | 0.145955i | \(-0.953375\pi\) | ||
0.989291 | − | 0.145955i | \(-0.0466254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.376550 | + | 1.36622i | 0.0212162 | + | 0.0769780i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.3461i | 1.59208i | 0.605245 | + | 0.796039i | \(0.293075\pi\) | ||||
−0.605245 | + | 0.796039i | \(0.706925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.622761 | 0.0348679 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.509981 | −0.0284644 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.56155 | + | 4.29400i | 0.142089 | + | 0.238188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.35590i | − | 0.351482i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.02065 | −0.111402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1296 | 0.611741 | 0.305870 | − | 0.952073i | \(-0.401053\pi\) | ||||
0.305870 | + | 0.952073i | \(0.401053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.75688i | 0.0962765i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.964553 | − | 3.49966i | −0.0526991 | − | 0.191207i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.0529i | − | 0.656563i | −0.944580 | − | 0.328282i | \(-0.893530\pi\) | ||
0.944580 | − | 0.328282i | \(-0.106470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.71111 | 0.527435 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.61829i | − | 0.465344i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.9890 | + | 3.85555i | −0.753142 | + | 0.207576i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.62654i | 0.409414i | 0.978823 | + | 0.204707i | \(0.0656242\pi\) | ||||
−0.978823 | + | 0.204707i | \(0.934376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2455 | 0.816074 | 0.408037 | − | 0.912965i | \(-0.366213\pi\) | ||||
0.408037 | + | 0.912965i | \(0.366213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.83238i | − | 0.257201i | −0.991696 | − | 0.128601i | \(-0.958951\pi\) | ||
0.991696 | − | 0.128601i | \(-0.0410486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.50671 | − | 2.62018i | 0.504564 | − | 0.139065i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.84523i | − | 0.150585i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.25528 | 0.382919 | 0.191460 | − | 0.981501i | \(-0.438678\pi\) | ||||
0.191460 | + | 0.981501i | \(0.438678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.9683i | − | 0.575688i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.29073 | − | 8.31138i | −0.119902 | − | 0.435038i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.5808i | − | 1.75290i | −0.481491 | − | 0.876451i | \(-0.659905\pi\) | ||
0.481491 | − | 0.876451i | \(-0.340095\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.67760 | −0.399680 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.11347 | −0.0578084 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.78131i | 0.144011i | 0.997404 | + | 0.0720055i | \(0.0229399\pi\) | ||||
−0.997404 | + | 0.0720055i | \(0.977060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.07314 | + | 7.73462i | 0.416895 | + | 0.399414i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.49966i | 0.180241i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.0268 | −1.74784 | −0.873921 | − | 0.486069i | \(-0.838430\pi\) | ||||
−0.873921 | + | 0.486069i | \(0.838430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.1231 | 0.569854 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.45332i | 0.431944i | 0.976400 | + | 0.215972i | \(0.0692920\pi\) | ||||
−0.976400 | + | 0.215972i | \(0.930708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0670068 | − | 0.243119i | −0.00341498 | − | 0.0123905i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.49966i | − | 0.381229i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.2991 | 0.724994 | 0.362497 | − | 0.931985i | \(-0.381924\pi\) | ||||
0.362497 | + | 0.931985i | \(0.381924\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.1327 | 1.47331 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.9439i | − | 0.652933i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.7660 | − | 5.72338i | 1.04485 | − | 0.287974i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.97488i | − | 0.199493i | −0.995013 | − | 0.0997467i | \(-0.968197\pi\) | ||
0.995013 | − | 0.0997467i | \(-0.0318033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2560 | −0.512159 | −0.256079 | − | 0.966656i | \(-0.582431\pi\) | ||||
−0.256079 | + | 0.966656i | \(0.582431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.15569 | − | 0.594137i | 0.107117 | − | 0.0295229i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.312636i | − | 0.0154968i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.6296 | −0.970623 | −0.485311 | − | 0.874341i | \(-0.661294\pi\) | ||||
−0.485311 | + | 0.874341i | \(0.661294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7904 | −0.581577 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.49380i | − | 0.122712i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.02392 | + | 3.71507i | 0.0502624 | + | 0.182366i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.112780i | 0.00552286i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.7238 | 1.15899 | 0.579493 | − | 0.814977i | \(-0.303251\pi\) | ||||
0.579493 | + | 0.814977i | \(0.303251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8697 | 0.870914 | 0.435457 | − | 0.900210i | \(-0.356587\pi\) | ||||
0.435457 | + | 0.900210i | \(0.356587\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.18827i | 0.155019i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4997 | − | 19.2772i | −0.557815 | − | 0.935081i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.90787i | − | 0.0923284i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.177949 | −0.00859147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.9476 | −1.73153 | −0.865767 | − | 0.500448i | \(-0.833169\pi\) | ||||
−0.865767 | + | 0.500448i | \(0.833169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.21396i | − | 0.394738i | −0.980329 | − | 0.197369i | \(-0.936760\pi\) | ||
0.980329 | − | 0.197369i | \(-0.0632397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.07928 | + | 7.54417i | 0.0996937 | + | 0.361715i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0914 | −1.19755 | −0.598775 | − | 0.800918i | \(-0.704345\pi\) | ||||
−0.598775 | + | 0.800918i | \(0.704345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.59833 | −0.314206 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.75619i | − | 0.130951i | −0.997854 | − | 0.0654753i | \(-0.979144\pi\) | ||
0.997854 | − | 0.0654753i | \(-0.0208564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.27026 | − | 0.350100i | 0.0602160 | − | 0.0165963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.30829i | − | 0.109178i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.7639 | −1.87657 | −0.938287 | − | 0.345858i | \(-0.887588\pi\) | ||||
−0.938287 | + | 0.345858i | \(0.887588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.36622 | 0.0643330 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.7318i | 0.833111i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.36622 | − | 0.376550i | 0.0640496 | − | 0.0176529i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.72143i | − | 0.407971i | −0.978974 | − | 0.203986i | \(-0.934610\pi\) | ||
0.978974 | − | 0.203986i | \(-0.0653896\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.48933 | −0.209544 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5332 | 0.816601 | 0.408300 | − | 0.912848i | \(-0.366122\pi\) | ||||
0.408300 | + | 0.912848i | \(0.366122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.1049i | − | 0.841404i | −0.907199 | − | 0.420702i | \(-0.861784\pi\) | ||
0.907199 | − | 0.420702i | \(-0.138216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0451i | 0.511106i | 0.966795 | + | 0.255553i | \(0.0822575\pi\) | ||||
−0.966795 | + | 0.255553i | \(0.917743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.02890 | −0.0475103 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8549 | 0.592321 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.33456i | 0.0613631i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.75688i | 0.0804421i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.3887 | −1.52557 | −0.762785 | − | 0.646653i | \(-0.776168\pi\) | ||||
−0.762785 | + | 0.646653i | \(0.776168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.75688 | 0.0801069 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.11278i | 0.187138i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.64663 | + | 9.60268i | 0.120177 | + | 0.436035i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.7414i | − | 1.61960i | −0.586708 | − | 0.809799i | \(-0.699576\pi\) | ||
0.586708 | − | 0.809799i | \(-0.300424\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.3308 | −0.648060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.9914 | −1.66940 | −0.834699 | − | 0.550706i | \(-0.814358\pi\) | ||||
−0.834699 | + | 0.550706i | \(0.814358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 15.7111i | − | 0.707593i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.383604 | + | 0.105726i | −0.0172417 | + | 0.00475205i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.79498i | − | 0.125372i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0670 | −0.898323 | −0.449161 | − | 0.893451i | \(-0.648277\pi\) | ||||
−0.449161 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.43449 | −0.0640881 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.3332i | 0.683673i | 0.939759 | + | 0.341836i | \(0.111049\pi\) | ||||
−0.939759 | + | 0.341836i | \(0.888951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.5221 | − | 9.79038i | 1.58071 | − | 0.435666i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.0476 | −1.33184 | −0.665918 | − | 0.746025i | \(-0.731960\pi\) | ||||
−0.665918 | + | 0.746025i | \(0.731960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.44356 | −0.108097 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.48739 | − | 12.6532i | −0.153673 | − | 0.557565i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.567351i | − | 0.0249521i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.24690 | 0.0547328 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.8263 | −1.35052 | −0.675262 | − | 0.737578i | \(-0.735970\pi\) | ||||
−0.675262 | + | 0.737578i | \(0.735970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0141i | 0.525340i | 0.964886 | + | 0.262670i | \(0.0846031\pi\) | ||||
−0.964886 | + | 0.262670i | \(0.915397\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.72143 | − | 1.62345i | 0.118773 | − | 0.0708532i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.1114 | −0.830931 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.93483 | −0.170757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.67760i | 0.332554i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.302999 | + | 1.09936i | 0.0130998 | + | 0.0475295i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7.87621i | − | 0.339883i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.17417 | 0.0505750 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3132 | 0.701360 | 0.350680 | − | 0.936495i | \(-0.385950\pi\) | ||||
0.350680 | + | 0.936495i | \(0.385950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3796i | 0.445433i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.7013 | + | 3.77628i | −0.586901 | + | 0.161758i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.239667i | − | 0.0102474i | −0.999987 | − | 0.00512371i | \(-0.998369\pi\) | ||
0.999987 | − | 0.00512371i | \(-0.00163094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.01033 | −0.128478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.10522i | − | 0.259620i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.78729 | − | 1.04383i | 0.160762 | − | 0.0443081i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0304i | 0.425002i | 0.977161 | + | 0.212501i | \(0.0681609\pi\) | ||||
−0.977161 | + | 0.212501i | \(0.931839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.49966 | −0.317202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.798873 | 0.0337284 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 0.310125i | − | 0.0130702i | −0.999979 | − | 0.00653511i | \(-0.997920\pi\) | ||
0.999979 | − | 0.00653511i | \(-0.00208021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.76973 | − | 20.9341i | −0.242735 | − | 0.880706i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.633776i | − | 0.0266161i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.2850 | −0.515014 | −0.257507 | − | 0.966276i | \(-0.582901\pi\) | ||||
−0.257507 | + | 0.966276i | \(0.582901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.6124 | 1.32294 | 0.661470 | − | 0.749972i | \(-0.269933\pi\) | ||||
0.661470 | + | 0.749972i | \(0.269933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.7318i | − | 0.573652i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6228 | + | 27.8652i | 0.693217 | + | 1.16206i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.36691i | 0.265058i | 0.991179 | + | 0.132529i | \(0.0423098\pi\) | ||||
−0.991179 | + | 0.132529i | \(0.957690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.34488 | 0.263684 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.09224 | 0.0453136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.312636i | − | 0.0129481i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.594137 | − | 2.15569i | −0.0245646 | − | 0.0891268i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 14.8103i | − | 0.611288i | −0.952146 | − | 0.305644i | \(-0.901128\pi\) | ||
0.952146 | − | 0.305644i | \(-0.0988718\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.2966 | −0.876024 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.9864i | − | 1.39565i | −0.716267 | − | 0.697826i | \(-0.754151\pi\) | ||
0.716267 | − | 0.697826i | \(-0.245849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.13343 | + | 1.69046i | −0.251446 | + | 0.0693020i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.2108i | 0.458826i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.10900 | −0.0453124 | −0.0226562 | − | 0.999743i | \(-0.507212\pi\) | ||||
−0.0226562 | + | 0.999743i | \(0.507212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.9670 | −1.95661 | −0.978306 | − | 0.207163i | \(-0.933577\pi\) | ||||
−0.978306 | + | 0.207163i | \(0.933577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.62345i | 0.0661120i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.6443 | + | 6.51670i | −0.961279 | + | 0.264941i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.5319i | − | 1.44220i | −0.692833 | − | 0.721098i | \(-0.743638\pi\) | ||
0.692833 | − | 0.721098i | \(-0.256362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.21800 | 0.0898778 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.18827 | 0.128984 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.4955i | − | 0.827806i | −0.910321 | − | 0.413903i | \(-0.864165\pi\) | ||
0.910321 | − | 0.413903i | \(-0.135835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.56155 | + | 16.5505i | 0.183940 | + | 0.667382i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6119i | 0.427218i | 0.976919 | + | 0.213609i | \(0.0685218\pi\) | ||||
−0.976919 | + | 0.213609i | \(0.931478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5312 | −1.14677 | −0.573383 | − | 0.819287i | \(-0.694369\pi\) | ||||
−0.573383 | + | 0.819287i | \(0.694369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.48933 | 0.260408 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.373457i | − | 0.0149623i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8769 | − | 21.9986i | 0.475076 | − | 0.879945i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.88722 | −0.314484 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.71111 | 0.306974 | 0.153487 | − | 0.988151i | \(-0.450950\pi\) | ||||
0.153487 | + | 0.988151i | \(0.450950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.2810i | 0.806096i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.60865 | − | 23.9780i | −0.262256 | − | 0.951537i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.59833i | 0.261435i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.41005 | −0.174459 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.5124 | −1.08667 | −0.543337 | − | 0.839515i | \(-0.682839\pi\) | ||||
−0.543337 | + | 0.839515i | \(0.682839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.1798i | − | 0.953558i | −0.879023 | − | 0.476779i | \(-0.841804\pi\) | ||
0.879023 | − | 0.476779i | \(-0.158196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.1669 | + | 4.45583i | −0.636572 | + | 0.175448i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.9347i | 1.09823i | 0.835748 | + | 0.549113i | \(0.185034\pi\) | ||||
−0.835748 | + | 0.549113i | \(0.814966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.700200 | 0.0274853 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.2868i | − | 1.06782i | −0.845543 | − | 0.533908i | \(-0.820723\pi\) | ||
0.845543 | − | 0.533908i | \(-0.179277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.9030 | + | 7.69046i | −1.09026 | + | 0.300491i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.85555i | 0.150419i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.3198 | −1.18109 | −0.590545 | − | 0.807005i | \(-0.701087\pi\) | ||||
−0.590545 | + | 0.807005i | \(0.701087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7104 | 0.649960 | 0.324980 | − | 0.945721i | \(-0.394642\pi\) | ||||
0.324980 | + | 0.945721i | \(0.394642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.48933i | 0.174351i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.7104i | 0.879351i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.3900 | 0.440362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.535685 | 0.0206799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.950445i | 0.0366370i | 0.999832 | + | 0.0183185i | \(0.00583128\pi\) | ||||
−0.999832 | + | 0.0183185i | \(0.994169\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56155 | − | 4.29400i | −0.0985942 | − | 0.165276i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 34.1991i | − | 1.31438i | −0.753726 | − | 0.657188i | \(-0.771746\pi\) | ||
0.753726 | − | 0.657188i | \(-0.228254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.82320 | 0.108344 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7020 | 0.563383 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.68208i | − | 0.217419i | −0.994074 | − | 0.108709i | \(-0.965328\pi\) | ||
0.994074 | − | 0.108709i | \(-0.0346718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.00511 | + | 25.4164i | 0.267651 | + | 0.971111i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.84145i | − | 0.375475i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.75688 | 0.0669319 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.7795 | 0.524197 | 0.262098 | − | 0.965041i | \(-0.415586\pi\) | ||||
0.262098 | + | 0.965041i | \(0.415586\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.112780i | 0.00428416i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.243119 | − | 0.0670068i | 0.00922201 | − | 0.00254171i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 34.4673i | − | 1.30554i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.8439 | −0.864034 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4113 | 0.770924 | 0.385462 | − | 0.922724i | \(-0.374042\pi\) | ||||
0.385462 | + | 0.922724i | \(0.374042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.87293 | − | 1.89427i | 0.258850 | − | 0.0713425i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 10.4436i | − | 0.392770i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.17852 | −0.119372 | −0.0596858 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596858 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.63309 | −0.361269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.105726 | + | 0.383604i | 0.00395394 | + | 0.0143460i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 24.1907i | − | 0.903417i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5312 | −1.51156 | −0.755780 | − | 0.654826i | \(-0.772742\pi\) | ||||
−0.755780 | + | 0.654826i | \(0.772742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.72005 | −0.138542 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 22.8896i | − | 0.851274i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0275 | − | 8.96455i | 0.558108 | − | 0.332935i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.39066i | − | 0.162840i | −0.996680 | − | 0.0814202i | \(-0.974054\pi\) | ||
0.996680 | − | 0.0814202i | \(-0.0259456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.6684 | 1.24527 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.1823i | − | 1.11481i | −0.830241 | − | 0.557404i | \(-0.811797\pi\) | ||
0.830241 | − | 0.557404i | \(-0.188203\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.92031 | + | 14.2240i | 0.144603 | + | 0.524658i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.288892i | − | 0.0106415i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.1565 | −1.80825 | −0.904125 | − | 0.427267i | \(-0.859476\pi\) | ||||
−0.904125 | + | 0.427267i | \(0.859476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.8317i | − | 0.800927i | −0.916313 | − | 0.400463i | \(-0.868849\pi\) | ||
0.916313 | − | 0.400463i | \(-0.131151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.97595 | + | 1.37144i | −0.182305 | + | 0.0502457i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.72338i | − | 0.0630551i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.323214 | 0.0118100 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8170 | 0.832605 | 0.416302 | − | 0.909226i | \(-0.363326\pi\) | ||||
0.416302 | + | 0.909226i | \(0.363326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.6763i | 0.425510i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.2242 | − | 10.5351i | 1.39112 | − | 0.383412i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.4649i | 0.416699i | 0.978054 | + | 0.208349i | \(0.0668091\pi\) | ||||
−0.978054 | + | 0.208349i | \(0.933191\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.15477 | −0.0419156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.9005 | −0.975143 | −0.487571 | − | 0.873083i | \(-0.662117\pi\) | ||||
−0.487571 | + | 0.873083i | \(0.662117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.02821i | 0.145831i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.66728 | + | 9.67760i | 0.0964357 | + | 0.349895i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.93483i | 0.142079i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.9298 | −0.466260 | −0.233130 | − | 0.972446i | \(-0.574897\pi\) | ||||
−0.233130 | + | 0.972446i | \(0.574897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9993 | −0.900328 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 7.56231i | − | 0.271998i | −0.990709 | − | 0.135999i | \(-0.956576\pi\) | ||
0.990709 | − | 0.135999i | \(-0.0434243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.11347i | − | 0.0399455i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.784766 | 0.0280811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.49966i | − | 0.125067i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.63756 | − | 27.7111i | −0.272596 | − | 0.989052i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.3318i | 1.90107i | 0.310612 | + | 0.950537i | \(0.399466\pi\) | ||||
−0.310612 | + | 0.950537i | \(0.600534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.12965 | −0.253822 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.15466 | −0.218835 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.01033i | 0.106900i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.78729 | − | 1.04383i | 0.134321 | − | 0.0370208i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.9391i | 1.66267i | 0.555774 | + | 0.831334i | \(0.312422\pi\) | ||||
−0.555774 | + | 0.831334i | \(0.687578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.3132 | −0.506365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.589258 | −0.0208204 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 0.686093i | − | 0.0242117i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.86588 | − | 2.44356i | 0.312481 | − | 0.0861241i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.47832i | 0.298451i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.1365 | −0.637646 | −0.318823 | − | 0.947814i | \(-0.603288\pi\) | ||||
−0.318823 | + | 0.947814i | \(0.603288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.6664 | −1.77914 | −0.889568 | − | 0.456802i | \(-0.848995\pi\) | ||||
−0.889568 | + | 0.456802i | \(0.848995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.60142i | − | 0.196450i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.51445 | + | 30.8927i | 0.298248 | + | 1.08212i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.633776 | −0.0221459 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.1986 | 1.26334 | 0.631670 | − | 0.775237i | \(-0.282370\pi\) | ||||
0.631670 | + | 0.775237i | \(0.282370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.307033i | − | 0.0107025i | −0.999986 | − | 0.00535124i | \(-0.998297\pi\) | ||
0.999986 | − | 0.00535124i | \(-0.00170336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.455826 | + | 0.764114i | 0.0158698 | + | 0.0266030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.9733i | 1.94638i | 0.230000 | + | 0.973191i | \(0.426127\pi\) | ||||
−0.230000 | + | 0.973191i | \(0.573873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1912 | 1.29171 | 0.645853 | − | 0.763462i | \(-0.276502\pi\) | ||||
0.645853 | + | 0.763462i | \(0.276502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.2991 | −0.842927 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 29.6221i | − | 1.02634i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.852282 | + | 3.09231i | 0.0294944 | + | 0.107014i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.2570 | 1.07911 | 0.539556 | − | 0.841950i | \(-0.318592\pi\) | ||||
0.539556 | + | 0.841950i | \(0.318592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.7524 | −0.577669 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.6318i | 0.400622i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.15569 | + | 0.594137i | −0.0741580 | + | 0.0204390i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.95146i | 0.238855i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.197345 | 0.00677288 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4010 | 0.390821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7066i | 1.29105i | 0.763739 | + | 0.645525i | \(0.223362\pi\) | ||||
−0.763739 | + | 0.645525i | \(0.776638\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5364i | 0.667350i | 0.942688 | + | 0.333675i | \(0.108289\pi\) | ||||
−0.942688 | + | 0.333675i | \(0.891711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.0340 | 1.16122 | 0.580612 | − | 0.814180i | \(-0.302813\pi\) | ||||
0.580612 | + | 0.814180i | \(0.302813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.86588 | 0.165829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9482i | 0.576925i | 0.957491 | + | 0.288463i | \(0.0931441\pi\) | ||||
−0.957491 | + | 0.288463i | \(0.906856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.740830 | − | 2.68793i | −0.0251890 | − | 0.0913924i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.15408i | − | 0.107118i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.71420 | 0.0581503 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.62345 | 0.0550085 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.45457i | − | 0.150764i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.11656 | − | 4.90202i | −0.172971 | − | 0.165718i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30.3339i | − | 1.02430i | −0.858895 | − | 0.512151i | \(-0.828849\pi\) | ||
0.858895 | − | 0.512151i | \(-0.171151\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.3918 | −0.991361 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.66544 | −0.291946 | −0.145973 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145973 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.6898i | 0.427045i | 0.976938 | + | 0.213522i | \(0.0684936\pi\) | ||||
−0.976938 | + | 0.213522i | \(0.931506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.33783 | + | 8.48228i | 0.0785853 | + | 0.285129i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.8638i | 1.40565i | 0.711363 | + | 0.702825i | \(0.248078\pi\) | ||||
−0.711363 | + | 0.702825i | \(0.751922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.04955 | −0.236434 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.177949 | 0.00596153 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9787 | + | 4.67955i | −0.567534 | + | 0.156420i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.48933i | − | 0.216672i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.88722 | −0.262761 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.75310i | 0.158173i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.3753 | − | 6.16693i | 0.743780 | − | 0.204996i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.2531i | 0.639288i | 0.947538 | + | 0.319644i | \(0.103563\pi\) | ||||
−0.947538 | + | 0.319644i | \(0.896437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.4783 | −0.546551 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.30885 | 0.308416 | 0.154208 | − | 0.988038i | \(-0.450717\pi\) | ||||
0.154208 | + | 0.988038i | \(0.450717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.306674i | 0.0101494i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.78855 | + | 6.48933i | 0.0591276 | + | 0.214531i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.20353i | 0.270904i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.9282 | −0.459448 | −0.229724 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229724 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.1997 | 0.962164 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.41005i | 0.145159i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.50034 | − | 7.54405i | −0.147970 | − | 0.248047i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.86966i | 0.192785i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4734 | 0.343621 | 0.171810 | − | 0.985130i | \(-0.445038\pi\) | ||||
0.171810 | + | 0.985130i | \(0.445038\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.3346i | 0.436554i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.474640 | − | 1.72212i | −0.0155224 | − | 0.0563194i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.63825i | − | 0.216862i | −0.994104 | − | 0.108431i | \(-0.965417\pi\) | ||
0.994104 | − | 0.108431i | \(-0.0345827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.16441 | 0.168534 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.5538 | 1.41981 | 0.709907 | − | 0.704296i | \(-0.248737\pi\) | ||||
0.709907 | + | 0.704296i | \(0.248737\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.8225i | 1.62244i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.36622 | + | 0.376550i | −0.0444433 | + | 0.0122492i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 29.8379i | − | 0.969601i | −0.874625 | − | 0.484800i | \(-0.838892\pi\) | ||
0.874625 | − | 0.484800i | \(-0.161108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.85555 | 0.125157 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.3461 | −0.919187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.4285i | 0.532172i | 0.963949 | + | 0.266086i | \(0.0857304\pi\) | ||||
−0.963949 | + | 0.266086i | \(0.914270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.6014 | + | 8.15855i | −0.957879 | + | 0.264005i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.622761i | 0.0201310i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.47246 | 0.241298 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 0.509981i | − | 0.0164339i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.76973 | − | 13.6776i | −0.121352 | − | 0.440298i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.1011i | − | 1.25741i | −0.777646 | − | 0.628703i | \(-0.783586\pi\) | ||
0.777646 | − | 0.628703i | \(-0.216414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.0240 | −1.44489 | −0.722444 | − | 0.691429i | \(-0.756981\pi\) | ||||
−0.722444 | + | 0.691429i | \(0.756981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.0714772i | − | 0.00229145i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.29400 | + | 2.56155i | −0.137518 | + | 0.0820353i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.5616i | − | 0.849782i | −0.905245 | − | 0.424891i | \(-0.860312\pi\) | ||
0.905245 | − | 0.424891i | \(-0.139688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.104858 | 0.00335128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.35590 | 0.202928 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7420i | 0.406405i | 0.979137 | + | 0.203203i | \(0.0651351\pi\) | ||||
−0.979137 | + | 0.203203i | \(0.934865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6531 | + | 45.9088i | 0.403161 | + | 1.46278i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.02065i | − | 0.0643180i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.6677 | −1.54754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.0639 | 1.08208 | 0.541038 | − | 0.840998i | \(-0.318032\pi\) | ||||
0.541038 | + | 0.840998i | \(0.318032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.1296i | 0.353189i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.1669 | − | 6.66073i | 0.766143 | − | 0.211159i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17.5887i | − | 0.557039i | −0.960431 | − | 0.278520i | \(-0.910156\pi\) | ||
0.960431 | − | 0.278520i | \(-0.0898438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.75688 | −0.0555853 |
(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 | 3120.2.l.n.1249.8 | 8 | ||
4.3 | odd | 2 | 1560.2.l.d.1249.4 | ✓ | 8 | ||
5.4 | even | 2 | inner | 3120.2.l.n.1249.4 | 8 | ||
12.11 | even | 2 | 4680.2.l.g.2809.2 | 8 | |||
20.3 | even | 4 | 7800.2.a.by.1.2 | 4 | |||
20.7 | even | 4 | 7800.2.a.bt.1.3 | 4 | |||
20.19 | odd | 2 | 1560.2.l.d.1249.8 | yes | 8 | ||
60.59 | even | 2 | 4680.2.l.g.2809.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.d.1249.4 | ✓ | 8 | 4.3 | odd | 2 | ||
1560.2.l.d.1249.8 | yes | 8 | 20.19 | odd | 2 | ||
3120.2.l.n.1249.4 | 8 | 5.4 | even | 2 | inner | ||
3120.2.l.n.1249.8 | 8 | 1.1 | even | 1 | trivial | ||
4680.2.l.g.2809.1 | 8 | 60.59 | even | 2 | |||
4680.2.l.g.2809.2 | 8 | 12.11 | even | 2 | |||
7800.2.a.bt.1.3 | 4 | 20.7 | even | 4 | |||
7800.2.a.by.1.2 | 4 | 20.3 | even | 4 |