Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(4049,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4400.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.b (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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 17x^{2} + 64 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(-3.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.4049 |
Dual form | 4400.2.b.p.4049.4 |
$q$-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 \(\left(\mathbb{Z}/4400\mathbb{Z}\right)^\times\).
\(n\) | \(177\) | \(1201\) | \(2751\) | \(3301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 3.37228i | − 1.94699i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) | ||||
0.228714 | − | 0.973494i | \(-0.426548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.37228i | − 1.27460i | −0.770615 | − | 0.637301i | \(-0.780051\pi\) | ||||
0.770615 | − | 0.637301i | \(-0.219949\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.37228 | −2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.37228i | 0.332827i | 0.986056 | + | 0.166414i | \(0.0532187\pi\) | ||||
−0.986056 | + | 0.166414i | \(0.946781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.627719 | 0.144009 | 0.0720043 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720043 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.3723 | −2.48164 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.74456i | 0.572281i | 0.958188 | + | 0.286140i | \(0.0923724\pi\) | ||||
−0.958188 | + | 0.286140i | \(0.907628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.1168i | 3.48659i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.37228 | −0.254826 | −0.127413 | − | 0.991850i | \(-0.540667\pi\) | ||||
−0.127413 | + | 0.991850i | \(0.540667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37228 | −0.605680 | −0.302840 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302840 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 3.37228i | − 0.587039i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.37228i | 1.54079i | 0.637565 | + | 0.770397i | \(0.279942\pi\) | ||||
−0.637565 | + | 0.770397i | \(0.720058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.74456 | −1.07999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4891 | −1.79430 | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.74456i | − 0.400336i | −0.979762 | − | 0.200168i | \(-0.935851\pi\) | ||||
0.979762 | − | 0.200168i | \(-0.0641487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.37228 | −0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.62772 | 0.648010 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.11684i | 0.565492i | 0.959195 | + | 0.282746i | \(0.0912454\pi\) | ||||
−0.959195 | + | 0.282746i | \(0.908755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.11684i | − 0.280383i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.37228 | −0.687850 | −0.343925 | − | 0.938997i | \(-0.611757\pi\) | ||||
−0.343925 | + | 0.938997i | \(0.611757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 28.2337i | 3.55711i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.25544 | 1.11422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1168 | −1.20065 | −0.600324 | − | 0.799757i | \(-0.704962\pi\) | ||||
−0.600324 | + | 0.799757i | \(0.704962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4891i | 1.81286i | 0.422351 | + | 0.906432i | \(0.361205\pi\) | ||||
−0.422351 | + | 0.906432i | \(0.638795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.37228i | − 0.384307i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.25544 | −0.141248 | −0.0706239 | − | 0.997503i | \(-0.522499\pi\) | ||||
−0.0706239 | + | 0.997503i | \(0.522499\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.74456i | − 0.301255i | −0.988591 | − | 0.150627i | \(-0.951871\pi\) | ||||
0.988591 | − | 0.150627i | \(-0.0481294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.62772i | 0.496144i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.37228 | 0.145462 | 0.0727308 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727308 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.74456 | −0.707022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.3723i | 1.17925i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 12.7446i | − 1.29401i | −0.762484 | − | 0.647007i | \(-0.776020\pi\) | ||||
0.762484 | − | 0.647007i | \(-0.223980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.37228 | −0.841446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.48913i | − 0.934991i | −0.883995 | − | 0.467496i | \(-0.845156\pi\) | ||||
0.883995 | − | 0.467496i | \(-0.154844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4891 | 1.48359 | 0.741795 | − | 0.670627i | \(-0.233975\pi\) | ||||
0.741795 | + | 0.670627i | \(0.233975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.6060 | 2.99991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 3.25544i | − 0.306246i | −0.988207 | − | 0.153123i | \(-0.951067\pi\) | ||||
0.988207 | − | 0.153123i | \(-0.0489330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7446i | 1.54804i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.62772 | 0.424222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38.7446i | 3.49348i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.00000i | − 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.4891 | −1.18765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.1168 | −1.93236 | −0.966179 | − | 0.257873i | \(-0.916978\pi\) | ||||
−0.966179 | + | 0.257873i | \(0.916978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.11684i | − 0.183554i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.74456i | 0.747098i | 0.927610 | + | 0.373549i | \(0.121859\pi\) | ||||
−0.927610 | + | 0.373549i | \(0.878141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.25544 | −0.779448 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.00000i | − 0.167248i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.7446i | 1.21611i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.6060 | −1.77003 | −0.885015 | − | 0.465563i | \(-0.845852\pi\) | ||||
−0.885015 | + | 0.465563i | \(0.845852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2337 | 0.995563 | 0.497782 | − | 0.867302i | \(-0.334148\pi\) | ||||
0.497782 | + | 0.867302i | \(0.334148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 11.4891i | − 0.928841i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.37228i | 0.747989i | 0.927431 | + | 0.373995i | \(0.122012\pi\) | ||||
−0.927431 | + | 0.373995i | \(0.877988\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.8832 | 1.10101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.25544 | 0.729431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.88316i | − 0.460804i | −0.973095 | − | 0.230402i | \(-0.925996\pi\) | ||||
0.973095 | − | 0.230402i | \(-0.0740042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.62772i | 0.358104i | 0.983840 | + | 0.179052i | \(0.0573030\pi\) | ||||
−0.983840 | + | 0.179052i | \(0.942697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.25544 | −0.401893 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.25544i | 0.695681i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1168i | 1.33924i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.37228i | 0.100351i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 61.0951 | 4.44401 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.48913 | 0.397179 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 14.8614i | − 1.06975i | −0.844932 | − | 0.534874i | \(-0.820359\pi\) | ||||
0.844932 | − | 0.534874i | \(-0.179641\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.7446i | − 1.47799i | −0.673712 | − | 0.738994i | \(-0.735301\pi\) | ||||
0.673712 | − | 0.738994i | \(-0.264699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1168 | 1.28427 | 0.642135 | − | 0.766592i | \(-0.278049\pi\) | ||||
0.642135 | + | 0.766592i | \(0.278049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.9783 | −1.90290 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.62772i | 0.324802i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 22.9783i | − 1.59710i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.627719 | 0.0434202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.11684 | −0.421101 | −0.210550 | − | 0.977583i | \(-0.567526\pi\) | ||||
−0.210550 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.1168i | 2.33765i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3723i | 0.772001i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 52.2337 | 3.52963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.74456 | 0.184619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 18.7446i | − 1.25523i | −0.778524 | − | 0.627614i | \(-0.784031\pi\) | ||||
0.778524 | − | 0.627614i | \(-0.215969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74456i | 0.182163i | 0.995843 | + | 0.0910815i | \(0.0290324\pi\) | ||||
−0.995843 | + | 0.0910815i | \(0.970968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.3723 | −0.748241 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.37228i | − 0.0899011i | −0.998989 | − | 0.0449506i | \(-0.985687\pi\) | ||||
0.998989 | − | 0.0449506i | \(-0.0143130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.23369i | 0.275008i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7446 | −0.953746 | −0.476873 | − | 0.878972i | \(-0.658230\pi\) | ||||
−0.476873 | + | 0.878972i | \(0.658230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 66.9783i | − 4.29666i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.25544i | − 0.0798816i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.25544 | −0.586540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.74456 | −0.173235 | −0.0866176 | − | 0.996242i | \(-0.527606\pi\) | ||||
−0.0866176 | + | 0.996242i | \(0.527606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.74456i | 0.172549i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.6060 | 1.96390 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4891 | 0.711159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 24.8614i | − 1.53302i | −0.642232 | − | 0.766510i | \(-0.721992\pi\) | ||||
0.642232 | − | 0.766510i | \(-0.278008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4.62772i | − 0.283212i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.74456 | 0.533165 | 0.266583 | − | 0.963812i | \(-0.414105\pi\) | ||||
0.266583 | + | 0.963812i | \(0.414105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.7446i | 1.37656i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.7446i | − 0.765747i | −0.923801 | − | 0.382873i | \(-0.874935\pi\) | ||||
0.923801 | − | 0.382873i | \(-0.125065\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.2337 | 1.69031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.25544i | 0.312403i | 0.987725 | + | 0.156202i | \(0.0499250\pi\) | ||||
−0.987725 | + | 0.156202i | \(0.950075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.7446i | 2.28702i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1168 | 0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42.9783 | −2.51943 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 23.4891i | − 1.37225i | −0.727484 | − | 0.686125i | \(-0.759310\pi\) | ||||
0.727484 | − | 0.686125i | \(-0.240690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.1168i | 1.05125i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.48913 | 0.317444 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4891 | −0.777500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 20.2337i | − 1.16240i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.25544i | − 0.299944i | −0.988690 | − | 0.149972i | \(-0.952082\pi\) | ||||
0.988690 | − | 0.149972i | \(-0.0479183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.0000 | −1.82042 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.3723 | −1.09850 | −0.549251 | − | 0.835658i | \(-0.685087\pi\) | ||||
−0.549251 | + | 0.835658i | \(0.685087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0000i | 1.24351i | 0.783210 | + | 0.621757i | \(0.213581\pi\) | ||||
−0.783210 | + | 0.621757i | \(0.786419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 24.3505i | − 1.36766i | −0.729640 | − | 0.683831i | \(-0.760313\pi\) | ||||
0.729640 | − | 0.683831i | \(-0.239687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.37228 | −0.0768330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.4674 | 2.25867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.861407i | 0.0479299i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 52.2337i | − 2.88853i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.25544 | −0.510269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.9783 | −1.70272 | −0.851359 | − | 0.524583i | \(-0.824221\pi\) | ||||
−0.851359 | + | 0.524583i | \(0.824221\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 78.4674i | − 4.29999i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1168i | 1.31373i | 0.754009 | + | 0.656864i | \(0.228117\pi\) | ||||
−0.754009 | + | 0.656864i | \(0.771883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9783 | −0.596257 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.37228 | −0.182619 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 8.86141i | − 0.478471i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.2337i | 1.73040i | 0.501431 | + | 0.865198i | \(0.332807\pi\) | ||||
−0.501431 | + | 0.865198i | \(0.667193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.4891 | −1.04323 | −0.521614 | − | 0.853181i | \(-0.674670\pi\) | ||||
−0.521614 | + | 0.853181i | \(0.674670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.2337 | 1.93401 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.510875i | 0.0271911i | 0.999908 | + | 0.0135956i | \(0.00432773\pi\) | ||||
−0.999908 | + | 0.0135956i | \(0.995672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 15.6060i | − 0.825955i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.37228i | − 0.176999i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000i | 0.208798i | 0.994535 | + | 0.104399i | \(0.0332919\pi\) | ||||
−0.994535 | + | 0.104399i | \(0.966708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 96.1902 | 5.00746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.8832 | 0.720778 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 31.4891i | − 1.63045i | −0.579148 | − | 0.815223i | \(-0.696615\pi\) | ||||
0.579148 | − | 0.815223i | \(-0.303385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.74456i | 0.141352i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.233688 | −0.0120037 | −0.00600187 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00600187 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.9783 | −1.38214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.2337i | 1.64706i | 0.567269 | + | 0.823532i | \(0.308000\pi\) | ||||
−0.567269 | + | 0.823532i | \(0.692000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.4891i | 1.70235i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.76631 | −0.190471 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 74.5842i | 3.76228i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9783i | 1.25362i | 0.779171 | + | 0.626811i | \(0.215640\pi\) | ||||
−0.779171 | + | 0.626811i | \(0.784360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.13859 | −0.357377 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3723 | 0.667780 | 0.333890 | − | 0.942612i | \(-0.391639\pi\) | ||||
0.333890 | + | 0.942612i | \(0.391639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.74456i | 0.335971i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.37228i | 0.464567i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.76631 | 0.0873385 | 0.0436693 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436693 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.4891 | 1.45459 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.25544i | 0.455430i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4891i | 0.660565i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2337 | 0.498759 | 0.249380 | − | 0.968406i | \(-0.419773\pi\) | ||||
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.9783i | 1.11724i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1168i | 0.876736i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.74456 | −0.325631 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.9783 | 1.68484 | 0.842422 | − | 0.538819i | \(-0.181129\pi\) | ||||
0.842422 | + | 0.538819i | \(0.181129\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 27.7228i | − 1.33227i | −0.745830 | − | 0.666137i | \(-0.767947\pi\) | ||||
0.745830 | − | 0.666137i | \(-0.232053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.72281i | 0.0824133i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9783 | 0.905782 | 0.452891 | − | 0.891566i | \(-0.350393\pi\) | ||||
0.452891 | + | 0.891566i | \(0.350393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.6060 | 1.74314 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.4891i | 1.40107i | 0.713618 | + | 0.700535i | \(0.247055\pi\) | ||||
−0.713618 | + | 0.700535i | \(0.752945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 72.8614i | 3.44623i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.9783 | −1.36757 | −0.683784 | − | 0.729684i | \(-0.739667\pi\) | ||||
−0.683784 | + | 0.729684i | \(0.739667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4891 | −0.541002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 41.2554i | − 1.93835i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 16.3505i | − 0.764846i | −0.923987 | − | 0.382423i | \(-0.875090\pi\) | ||||
0.923987 | − | 0.382423i | \(-0.124910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.8614 | −1.16043 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1168 | 0.750636 | 0.375318 | − | 0.926896i | \(-0.377533\pi\) | ||||
0.375318 | + | 0.926896i | \(0.377533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 0.233688i | − 0.0108604i | −0.999985 | − | 0.00543020i | \(-0.998272\pi\) | ||||
0.999985 | − | 0.00543020i | \(-0.00172849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3723i | 0.896442i | 0.893923 | + | 0.448221i | \(0.147942\pi\) | ||||
−0.893923 | + | 0.448221i | \(0.852058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.9783 | −1.24574 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.6060 | 1.45633 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.00000i | − 0.183920i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 34.4674i | − 1.57815i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.48913 | 0.250805 | 0.125402 | − | 0.992106i | \(-0.459978\pi\) | ||||
0.125402 | + | 0.992106i | \(0.459978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7446 | 0.854678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 31.2119i | − 1.42019i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 20.0000i | − 0.906287i | −0.891438 | − | 0.453143i | \(-0.850303\pi\) | ||||
0.891438 | − | 0.453143i | \(-0.149697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.8397 | −0.897180 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.37228 | 0.332706 | 0.166353 | − | 0.986066i | \(-0.446801\pi\) | ||||
0.166353 | + | 0.986066i | \(0.446801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.88316i | − 0.0848131i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.1168i | 1.53035i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.4891 | −1.49918 | −0.749590 | − | 0.661903i | \(-0.769749\pi\) | ||||
−0.749590 | + | 0.661903i | \(0.769749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.6060 | 0.697223 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 34.9783i | − 1.55960i | −0.626027 | − | 0.779802i | \(-0.715320\pi\) | ||||
0.626027 | − | 0.779802i | \(-0.284680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 30.3505i | − 1.34791i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.76631 | −0.432884 | −0.216442 | − | 0.976295i | \(-0.569445\pi\) | ||||
−0.216442 | + | 0.976295i | \(0.569445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 52.2337 | 2.31068 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.3723i | 0.502098i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.74456i | − 0.120706i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2337 | 0.888160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5109 | 0.548111 | 0.274056 | − | 0.961714i | \(-0.411635\pi\) | ||||
0.274056 | + | 0.961714i | \(0.411635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.9783i | 1.35458i | 0.735714 | + | 0.677292i | \(0.236847\pi\) | ||||
−0.735714 | + | 0.677292i | \(0.763153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.62772i | − 0.201587i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4674 | 0.672495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.9783 | 0.997171 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.9783i | 0.995299i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.4674i | 1.74630i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.37228 | −0.188327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1168 | −0.864891 | −0.432445 | − | 0.901660i | \(-0.642349\pi\) | ||||
−0.432445 | + | 0.901660i | \(0.642349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.7228i | 1.44718i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.0000i | − 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 44.9783 | 1.91962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.861407 | −0.0366972 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.23369i | 0.180035i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.97825i | 0.210935i | 0.994423 | + | 0.105468i | \(0.0336339\pi\) | ||||
−0.994423 | + | 0.105468i | \(0.966366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.62772 | 0.195382 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8.23369i | − 0.347009i | −0.984833 | − | 0.173504i | \(-0.944491\pi\) | ||||
0.984833 | − | 0.173504i | \(-0.0555090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 121.329i | − 5.09533i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.2554 | 0.639541 | 0.319771 | − | 0.947495i | \(-0.396394\pi\) | ||||
0.319771 | + | 0.947495i | \(0.396394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.3723 | −0.643310 | −0.321655 | − | 0.946857i | \(-0.604239\pi\) | ||||
−0.321655 | + | 0.946857i | \(0.604239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 18.5109i | − 0.773303i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9783i | 1.53942i | 0.638391 | + | 0.769712i | \(0.279600\pi\) | ||||
−0.638391 | + | 0.769712i | \(0.720400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −50.1168 | −2.08278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.25544 | −0.383980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.11684i | 0.170502i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 24.8614i | − 1.02614i | −0.858347 | − | 0.513070i | \(-0.828508\pi\) | ||||
0.858347 | − | 0.513070i | \(-0.171492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.11684 | −0.0872230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −69.9565 | −2.87763 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5109i | 0.513760i | 0.966443 | + | 0.256880i | \(0.0826945\pi\) | ||||
−0.966443 | + | 0.256880i | \(0.917305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 61.0951i | − 2.50046i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.6060 | −1.61826 | −0.809128 | − | 0.587632i | \(-0.800060\pi\) | ||||
−0.809128 | + | 0.587632i | \(0.800060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5109 | −0.673493 | −0.336746 | − | 0.941595i | \(-0.609326\pi\) | ||||
−0.336746 | + | 0.941595i | \(0.609326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.9783i | 2.72757i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.88316i | 0.238790i | 0.992847 | + | 0.119395i | \(0.0380955\pi\) | ||||
−0.992847 | + | 0.119395i | \(0.961905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.6060 | 0.632386 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.48913 | −0.222066 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.5109i | − 0.828426i | −0.910180 | − | 0.414213i | \(-0.864057\pi\) | ||||
0.910180 | − | 0.414213i | \(-0.135943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 2.23369i | − 0.0899249i | −0.998989 | − | 0.0449624i | \(-0.985683\pi\) | ||||
0.998989 | − | 0.0449624i | \(-0.0143168\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.4674 | −1.78729 | −0.893647 | − | 0.448770i | \(-0.851862\pi\) | ||||
−0.893647 | + | 0.448770i | \(0.851862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7228 | −1.99531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 4.62772i | − 0.185406i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.11684i | − 0.0845386i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.8614 | −0.512818 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.1168 | −1.67665 | −0.838323 | − | 0.545175i | \(-0.816463\pi\) | ||||
−0.838323 | + | 0.545175i | \(0.816463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.6277i | 0.819878i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.74456i | 0.346472i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 84.7011 | 3.35072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0951 | −1.07019 | −0.535096 | − | 0.844791i | \(-0.679725\pi\) | ||||
−0.535096 | + | 0.844791i | \(0.679725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.88316i | − 0.232009i | −0.993249 | − | 0.116005i | \(-0.962991\pi\) | ||||
0.993249 | − | 0.116005i | \(-0.0370087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.7228i | 1.48304i | 0.670933 | + | 0.741518i | \(0.265894\pi\) | ||||
−0.670933 | + | 0.741518i | \(0.734106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74456 | −0.107734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.3505 | 1.50308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 10.6277i | − 0.415895i | −0.978140 | − | 0.207947i | \(-0.933322\pi\) | ||||
0.978140 | − | 0.207947i | \(-0.0666783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 129.679i | − 5.05927i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.8614 | 0.501009 | 0.250505 | − | 0.968115i | \(-0.419403\pi\) | ||||
0.250505 | + | 0.968115i | \(0.419403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.51087 | 0.331035 | 0.165517 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165517 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 9.25544i | − 0.359451i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.76631i | − 0.145832i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −63.2119 | −2.44391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.37228 | −0.207395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 14.8614i | − 0.572865i | −0.958100 | − | 0.286433i | \(-0.907531\pi\) | ||||
0.958100 | − | 0.286433i | \(-0.0924694\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.25544i | 0.125117i | 0.998041 | + | 0.0625583i | \(0.0199259\pi\) | ||||
−0.998041 | + | 0.0625583i | \(0.980074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.9783 | −1.64935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.25544 | 0.354669 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 28.6277i | − 1.09541i | −0.836672 | − | 0.547705i | \(-0.815502\pi\) | ||||
0.836672 | − | 0.547705i | \(-0.184498\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 33.7228i | − 1.28661i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.23369 | 0.313679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2337 | −1.53056 | −0.765281 | − | 0.643697i | \(-0.777400\pi\) | ||||
−0.765281 | + | 0.643697i | \(0.777400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.2337i | 1.07251i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 15.7663i | − 0.597192i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.62772 | −0.175036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3723 | −1.41153 | −0.705766 | − | 0.708445i | \(-0.749397\pi\) | ||||
−0.705766 | + | 0.708445i | \(0.749397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.88316i | 0.221887i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 20.2337i | − 0.760966i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.5109 | 0.394189 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 9.25544i | − 0.346619i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 49.7228i | 1.85693i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8832 | 0.517754 | 0.258877 | − | 0.965910i | \(-0.416648\pi\) | ||||
0.258877 | + | 0.965910i | \(0.416648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | −1.19174 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 74.1902i | 2.75916i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2337i | 0.898778i | 0.893336 | + | 0.449389i | \(0.148358\pi\) | ||||
−0.893336 | + | 0.449389i | \(0.851642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −117.935 | −4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.48913 | 0.203023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 46.2337i | − 1.70768i | −0.520535 | − | 0.853840i | \(-0.674268\pi\) | ||||
0.520535 | − | 0.853840i | \(-0.325732\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 8.00000i | − 0.294684i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4674 | −0.752905 | −0.376452 | − | 0.926436i | \(-0.622856\pi\) | ||||
−0.376452 | + | 0.926436i | \(0.622856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.23369 | −0.155528 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.62772i | − 0.169775i | −0.996391 | − | 0.0848873i | \(-0.972947\pi\) | ||||
0.996391 | − | 0.0848873i | \(-0.0270530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.9783i | 0.840730i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.4674 | 1.47865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.86141 | −0.323357 | −0.161679 | − | 0.986843i | \(-0.551691\pi\) | ||||
−0.161679 | + | 0.986843i | \(0.551691\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.25544i | 0.337287i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 20.9783i | − 0.762467i | −0.924479 | − | 0.381234i | \(-0.875499\pi\) | ||||
0.924479 | − | 0.381234i | \(-0.124501\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.25544 | 0.335951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.97825 | 0.180461 | 0.0902307 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902307 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 52.2337i | − 1.89099i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.48913i | 0.198201i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.7011 | 2.18610 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.6060i | 1.20872i | 0.796710 | + | 0.604361i | \(0.206572\pi\) | ||||
−0.796710 | + | 0.604361i | \(0.793428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 106.584i | − 3.82369i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.21194 | −0.258395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1168 | −0.362009 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 24.8614i | − 0.888474i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4674i | 1.58509i | 0.609813 | + | 0.792545i | \(0.291245\pi\) | ||||
−0.609813 | + | 0.792545i | \(0.708755\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −83.8397 | −2.98477 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.7446i | 0.381551i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4891i | 0.406966i | 0.979079 | + | 0.203483i | \(0.0652261\pi\) | ||||
−0.979079 | + | 0.203483i | \(0.934774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.76631 | 0.133243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4891 | −0.405948 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4891i | 0.546599i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 29.4891i | − 1.03807i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.8614 | −1.57530 | −0.787649 | − | 0.616125i | \(-0.788702\pi\) | ||||
−0.787649 | + | 0.616125i | \(0.788702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 53.9565i | − 1.89234i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 2.51087i | − 0.0878444i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 56.4674 | 1.97313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4891 | 0.400973 | 0.200487 | − | 0.979696i | \(-0.435748\pi\) | ||||
0.200487 | + | 0.979696i | \(0.435748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 28.0000i | − 0.976019i | −0.872838 | − | 0.488009i | \(-0.837723\pi\) | ||||
0.872838 | − | 0.488009i | \(-0.162277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 46.9783i | − 1.63359i | −0.576925 | − | 0.816797i | \(-0.695748\pi\) | ||||
0.576925 | − | 0.816797i | \(-0.304252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.7446 | 0.859414 | 0.429707 | − | 0.902968i | \(-0.358617\pi\) | ||||
0.429707 | + | 0.902968i | \(0.358617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.9783 | −1.49090 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.00000i | − 0.207888i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 61.0951i | − 2.11176i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.9783 | −0.379011 | −0.189506 | − | 0.981880i | \(-0.560689\pi\) | ||||
−0.189506 | + | 0.981880i | \(0.560689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 60.7011i | − 2.09066i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.37228i | − 0.115873i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.7228 | 0.608245 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7228 | −0.881767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.4674i | 1.31710i | 0.752538 | + | 0.658549i | \(0.228829\pi\) | ||||
−0.752538 | + | 0.658549i | \(0.771171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.3505i | 1.24171i | 0.783925 | + | 0.620855i | \(0.213215\pi\) | ||||
−0.783925 | + | 0.620855i | \(0.786785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.7446 | −1.45843 | −0.729213 | − | 0.684287i | \(-0.760114\pi\) | ||||
−0.729213 | + | 0.684287i | \(0.760114\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 130.658 | 4.45280 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.2554i | 0.723544i | 0.932267 | + | 0.361772i | \(0.117828\pi\) | ||||
−0.932267 | + | 0.361772i | \(0.882172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 50.9783i | − 1.73131i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.25544 | −0.0425878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 106.701i | 3.61128i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.9783i | 1.24867i | 0.781158 | + | 0.624333i | \(0.214629\pi\) | ||||
−0.781158 | + | 0.624333i | \(0.785371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79.2119 | −2.67175 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.37228i | 0.113486i | 0.998389 | + | 0.0567432i | \(0.0180716\pi\) | ||||
−0.998389 | + | 0.0567432i | \(0.981928\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.9783i | 0.368614i | 0.982869 | + | 0.184307i | \(0.0590040\pi\) | ||||
−0.982869 | + | 0.184307i | \(0.940996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.9783 | −0.904821 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.9783 | 1.20532 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.72281i | − 0.0576517i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 18.5109i | − 0.618060i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.62772 | 0.154343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64947 | −0.188211 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.4891i | 1.51378i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.394031i | 0.0130836i | 0.999979 | + | 0.00654179i | \(0.00208233\pi\) | ||||
−0.999979 | + | 0.00654179i | \(0.997918\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −50.2337 | −1.66615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.39403 | 0.278107 | 0.139053 | − | 0.990285i | \(-0.455594\pi\) | ||||
0.139053 | + | 0.990285i | \(0.455594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2.74456i | − 0.0908318i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74.5842i | 2.46299i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9783 | 0.626035 | 0.313017 | − | 0.949747i | \(-0.398660\pi\) | ||||
0.313017 | + | 0.949747i | \(0.398660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7228 | −0.583987 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.2337i | 0.666000i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 79.4456i | 2.60934i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.3505 | −0.798915 | −0.399458 | − | 0.916752i | \(-0.630801\pi\) | ||||
−0.399458 | + | 0.916752i | \(0.630801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74456 | −0.0899494 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.3288i | 2.13877i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 28.5109i | − 0.931410i | −0.884940 | − | 0.465705i | \(-0.845801\pi\) | ||||
0.884940 | − | 0.465705i | \(-0.154199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 74.1902 | 2.42111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0951 | −0.492086 | −0.246043 | − | 0.969259i | \(-0.579130\pi\) | ||||
−0.246043 | + | 0.969259i | \(0.579130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 31.5326i | − 1.02684i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 48.8614i | − 1.58778i | −0.608060 | − | 0.793891i | \(-0.708052\pi\) | ||||
0.608060 | − | 0.793891i | \(-0.291948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.9783 | 1.00560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82.1168 | −2.66282 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 40.1168i | − 1.29951i | −0.760143 | − | 0.649756i | \(-0.774871\pi\) | ||||
0.760143 | − | 0.649756i | \(-0.225129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.62772i | 0.149593i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.4891 | 0.952254 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 100.467i | − 3.23752i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 47.6060i | − 1.53090i | −0.643493 | − | 0.765452i | \(-0.722515\pi\) | ||||
0.643493 | − | 0.765452i | \(-0.277485\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.90491 | 0.0933190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.02175 | 0.0327895 | 0.0163947 | − | 0.999866i | \(-0.494781\pi\) | ||||
0.0163947 | + | 0.999866i | \(0.494781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.4891i | 0.432442i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.2337i | 0.455376i | 0.973734 | + | 0.227688i | \(0.0731166\pi\) | ||||
−0.973734 | + | 0.227688i | \(0.926883\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.37228 | 0.0438583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −129.679 | −4.14034 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 13.7228i | − 0.437690i | −0.975760 | − | 0.218845i | \(-0.929771\pi\) | ||||
0.975760 | − | 0.218845i | \(-0.0702289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.2119i | 0.993487i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.9783 | 0.349088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 104.467i | 3.31517i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.2337i | 0.704148i | 0.935972 | + | 0.352074i | \(0.114523\pi\) | ||||
−0.935972 | + | 0.352074i | \(0.885477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −169.796 | −5.37211 |
(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 | 4400.2.b.p.4049.1 | 4 | ||
4.3 | odd | 2 | 550.2.b.f.199.2 | 4 | |||
5.2 | odd | 4 | 4400.2.a.bl.1.1 | 2 | |||
5.3 | odd | 4 | 880.2.a.n.1.2 | 2 | |||
5.4 | even | 2 | inner | 4400.2.b.p.4049.4 | 4 | ||
12.11 | even | 2 | 4950.2.c.bc.199.4 | 4 | |||
15.8 | even | 4 | 7920.2.a.bq.1.1 | 2 | |||
20.3 | even | 4 | 110.2.a.d.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 550.2.a.n.1.2 | 2 | |||
20.19 | odd | 2 | 550.2.b.f.199.3 | 4 | |||
40.3 | even | 4 | 3520.2.a.bq.1.2 | 2 | |||
40.13 | odd | 4 | 3520.2.a.bj.1.1 | 2 | |||
55.43 | even | 4 | 9680.2.a.bt.1.2 | 2 | |||
60.23 | odd | 4 | 990.2.a.m.1.2 | 2 | |||
60.47 | odd | 4 | 4950.2.a.bw.1.1 | 2 | |||
60.59 | even | 2 | 4950.2.c.bc.199.1 | 4 | |||
140.83 | odd | 4 | 5390.2.a.bp.1.2 | 2 | |||
220.43 | odd | 4 | 1210.2.a.r.1.1 | 2 | |||
220.87 | odd | 4 | 6050.2.a.cb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.a.d.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
550.2.a.n.1.2 | 2 | 20.7 | even | 4 | |||
550.2.b.f.199.2 | 4 | 4.3 | odd | 2 | |||
550.2.b.f.199.3 | 4 | 20.19 | odd | 2 | |||
880.2.a.n.1.2 | 2 | 5.3 | odd | 4 | |||
990.2.a.m.1.2 | 2 | 60.23 | odd | 4 | |||
1210.2.a.r.1.1 | 2 | 220.43 | odd | 4 | |||
3520.2.a.bj.1.1 | 2 | 40.13 | odd | 4 | |||
3520.2.a.bq.1.2 | 2 | 40.3 | even | 4 | |||
4400.2.a.bl.1.1 | 2 | 5.2 | odd | 4 | |||
4400.2.b.p.4049.1 | 4 | 1.1 | even | 1 | trivial | ||
4400.2.b.p.4049.4 | 4 | 5.4 | even | 2 | inner | ||
4950.2.a.bw.1.1 | 2 | 60.47 | odd | 4 | |||
4950.2.c.bc.199.1 | 4 | 60.59 | even | 2 | |||
4950.2.c.bc.199.4 | 4 | 12.11 | even | 2 | |||
5390.2.a.bp.1.2 | 2 | 140.83 | odd | 4 | |||
6050.2.a.cb.1.2 | 2 | 220.87 | odd | 4 | |||
7920.2.a.bq.1.1 | 2 | 15.8 | even | 4 | |||
9680.2.a.bt.1.2 | 2 | 55.43 | even | 4 |