Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.7 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.7 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.925496 | − | 0.925496i | −0.413894 | − | 0.413894i | 0.469198 | − | 0.883093i | \(-0.344543\pi\) |
−0.883093 | + | 0.469198i | \(0.844543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72403 | + | 1.72403i | −0.519815 | + | 0.519815i | −0.917515 | − | 0.397701i | \(-0.869808\pi\) |
0.397701 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.328273 | + | 0.328273i | 0.0910464 | + | 0.0910464i | 0.751163 | − | 0.660117i | \(-0.229493\pi\) |
−0.660117 | + | 0.751163i | \(0.729493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.34181i | − | 0.567973i | −0.958828 | − | 0.283986i | \(-0.908343\pi\) | ||
0.958828 | − | 0.283986i | \(-0.0916570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77976 | − | 1.77976i | 0.408306 | − | 0.408306i | −0.472842 | − | 0.881147i | \(-0.656772\pi\) |
0.881147 | + | 0.472842i | \(0.156772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.17143i | 1.28683i | 0.765517 | + | 0.643416i | \(0.222483\pi\) | ||||
−0.765517 | + | 0.643416i | \(0.777517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.28691i | − | 0.657383i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.122671 | − | 0.122671i | 0.0227794 | − | 0.0227794i | −0.695625 | − | 0.718405i | \(-0.744873\pi\) |
0.718405 | + | 0.695625i | \(0.244873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.74700i | − | 0.313770i | −0.987617 | − | 0.156885i | \(-0.949855\pi\) | ||
0.987617 | − | 0.156885i | \(-0.0501452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.925496 | + | 0.925496i | 0.156437 | + | 0.156437i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.68105 | + | 1.68105i | −0.276363 | + | 0.276363i | −0.831655 | − | 0.555292i | \(-0.812606\pi\) |
0.555292 | + | 0.831655i | \(0.312606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.88812 | −0.451048 | −0.225524 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225524 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.77330 | − | 2.77330i | −0.422924 | − | 0.422924i | 0.463285 | − | 0.886209i | \(-0.346670\pi\) |
−0.886209 | + | 0.463285i | \(0.846670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.92184 | 0.863789 | 0.431894 | − | 0.901924i | \(-0.357845\pi\) | ||||
0.431894 | + | 0.901924i | \(0.357845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.973689 | + | 0.973689i | 0.133746 | + | 0.133746i | 0.770811 | − | 0.637064i | \(-0.219851\pi\) |
−0.637064 | + | 0.770811i | \(0.719851\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.19117 | 0.430297 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.33124 | + | 8.33124i | −1.08464 | + | 1.08464i | −0.0885647 | + | 0.996070i | \(0.528228\pi\) |
−0.996070 | + | 0.0885647i | \(0.971772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.28808 | + | 4.28808i | 0.549033 | + | 0.549033i | 0.926161 | − | 0.377128i | \(-0.123088\pi\) |
−0.377128 | + | 0.926161i | \(0.623088\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.607630i | − | 0.0753672i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.78259 | + | 1.78259i | −0.217778 | + | 0.217778i | −0.807561 | − | 0.589783i | \(-0.799213\pi\) |
0.589783 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.57053i | 1.01713i | 0.861022 | + | 0.508567i | \(0.169825\pi\) | ||||
−0.861022 | + | 0.508567i | \(0.830175\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.41750i | 0.751112i | 0.926800 | + | 0.375556i | \(0.122548\pi\) | ||||
−0.926800 | + | 0.375556i | \(0.877452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.72403 | − | 1.72403i | 0.196471 | − | 0.196471i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.38299i | − | 0.605633i | −0.953049 | − | 0.302817i | \(-0.902073\pi\) | ||
0.953049 | − | 0.302817i | \(-0.0979270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46360 | − | 3.46360i | −0.380179 | − | 0.380179i | 0.490987 | − | 0.871167i | \(-0.336636\pi\) |
−0.871167 | + | 0.490987i | \(0.836636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.16734 | + | 2.16734i | −0.235081 | + | 0.235081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.51391 | 0.160474 | 0.0802368 | − | 0.996776i | \(-0.474432\pi\) | ||||
0.0802368 | + | 0.996776i | \(0.474432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.328273 | − | 0.328273i | −0.0344123 | − | 0.0344123i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.29433 | −0.337991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.7177 | 1.59589 | 0.797943 | − | 0.602732i | \(-0.205921\pi\) | ||||
0.797943 | + | 0.602732i | \(0.205921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6438 | + | 13.6438i | 1.35760 | + | 1.35760i | 0.876861 | + | 0.480744i | \(0.159633\pi\) |
0.480744 | + | 0.876861i | \(0.340367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.9238 | 1.17489 | 0.587445 | − | 0.809264i | \(-0.300134\pi\) | ||||
0.587445 | + | 0.809264i | \(0.300134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6108 | + | 13.6108i | −1.31580 | + | 1.31580i | −0.398740 | + | 0.917064i | \(0.630553\pi\) |
−0.917064 | + | 0.398740i | \(0.869447\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.97865 | + | 4.97865i | 0.476868 | + | 0.476868i | 0.904129 | − | 0.427260i | \(-0.140521\pi\) |
−0.427260 | + | 0.904129i | \(0.640521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0768901i | 0.00723322i | 0.999993 | + | 0.00361661i | \(0.00115120\pi\) | ||||
−0.999993 | + | 0.00361661i | \(0.998849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.71163 | − | 5.71163i | 0.532612 | − | 0.532612i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34181i | 0.214673i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.05544i | 0.459585i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.66951 | + | 7.66951i | −0.685981 | + | 0.685981i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0611i | 1.33646i | 0.743956 | + | 0.668229i | \(0.232947\pi\) | ||||
−0.743956 | + | 0.668229i | \(0.767053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.87027 | + | 3.87027i | 0.338147 | + | 0.338147i | 0.855670 | − | 0.517522i | \(-0.173146\pi\) |
−0.517522 | + | 0.855670i | \(0.673146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.77976 | + | 1.77976i | −0.154325 | + | 0.154325i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.47491 | 0.467753 | 0.233877 | − | 0.972266i | \(-0.424859\pi\) | ||||
0.233877 | + | 0.972266i | \(0.424859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1117 | − | 11.1117i | −0.942478 | − | 0.942478i | 0.0559554 | − | 0.998433i | \(-0.482180\pi\) |
−0.998433 | + | 0.0559554i | \(0.982180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.13190 | −0.0946545 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.227063 | −0.0188565 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.2234 | + | 10.2234i | 0.837535 | + | 0.837535i | 0.988534 | − | 0.150999i | \(-0.0482490\pi\) |
−0.150999 | + | 0.988534i | \(0.548249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.98993 | −0.487454 | −0.243727 | − | 0.969844i | \(-0.578370\pi\) | ||||
−0.243727 | + | 0.969844i | \(0.578370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.61684 | + | 1.61684i | −0.129868 | + | 0.129868i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.57922 | + | 9.57922i | 0.764505 | + | 0.764505i | 0.977133 | − | 0.212628i | \(-0.0682023\pi\) |
−0.212628 | + | 0.977133i | \(0.568202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.17143i | − | 0.486377i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.81085 | − | 7.81085i | 0.611793 | − | 0.611793i | −0.331620 | − | 0.943413i | \(-0.607595\pi\) |
0.943413 | + | 0.331620i | \(0.107595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.28108i | − | 0.408662i | −0.978902 | − | 0.204331i | \(-0.934498\pi\) | ||
0.978902 | − | 0.204331i | \(-0.0655019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7845i | − | 0.983421i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8893 | + | 11.8893i | −0.903929 | + | 0.903929i | −0.995773 | − | 0.0918444i | \(-0.970724\pi\) |
0.0918444 | + | 0.995773i | \(0.470724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.28691i | 0.248467i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.38837 | + | 6.38837i | 0.477489 | + | 0.477489i | 0.904328 | − | 0.426839i | \(-0.140373\pi\) |
−0.426839 | + | 0.904328i | \(0.640373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.56367 | − | 5.56367i | 0.413545 | − | 0.413545i | −0.469427 | − | 0.882971i | \(-0.655539\pi\) |
0.882971 | + | 0.469427i | \(0.155539\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.11161 | 0.228770 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.03735 | + | 4.03735i | 0.295240 | + | 0.295240i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.43241 | 0.176003 | 0.0880014 | − | 0.996120i | \(-0.471952\pi\) | ||||
0.0880014 | + | 0.996120i | \(0.471952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.8507 | 1.78879 | 0.894397 | − | 0.447273i | \(-0.147605\pi\) | ||||
0.894397 | + | 0.447273i | \(0.147605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.77151 | − | 1.77151i | −0.126215 | − | 0.126215i | 0.641178 | − | 0.767393i | \(-0.278446\pi\) |
−0.767393 | + | 0.641178i | \(0.778446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8970 | 0.985130 | 0.492565 | − | 0.870276i | \(-0.336059\pi\) | ||||
0.492565 | + | 0.870276i | \(0.336059\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.122671 | + | 0.122671i | −0.00860980 | + | 0.00860980i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.67294 | + | 2.67294i | 0.186686 | + | 0.186686i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.13673i | 0.424487i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.243974 | − | 0.243974i | 0.0167959 | − | 0.0167959i | −0.698659 | − | 0.715455i | \(-0.746220\pi\) |
0.715455 | + | 0.698659i | \(0.246220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.13335i | 0.350091i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.74700i | 0.118594i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.768752 | − | 0.768752i | 0.0517119 | − | 0.0517119i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.07187i | 0.473568i | 0.971562 | + | 0.236784i | \(0.0760933\pi\) | ||||
−0.971562 | + | 0.236784i | \(0.923907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.15348 | − | 2.15348i | −0.142932 | − | 0.142932i | 0.632020 | − | 0.774952i | \(-0.282226\pi\) |
−0.774952 | + | 0.632020i | \(0.782226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4509 | + | 14.4509i | −0.954943 | + | 0.954943i | −0.999028 | − | 0.0440845i | \(-0.985963\pi\) |
0.0440845 | + | 0.999028i | \(0.485963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.7969 | −1.16591 | −0.582955 | − | 0.812504i | \(-0.698104\pi\) | ||||
−0.582955 | + | 0.812504i | \(0.698104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.48063 | − | 5.48063i | −0.357517 | − | 0.357517i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.62147 | 0.622361 | 0.311180 | − | 0.950351i | \(-0.399276\pi\) | ||||
0.311180 | + | 0.950351i | \(0.399276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.3786 | 1.76361 | 0.881805 | − | 0.471614i | \(-0.156329\pi\) | ||||
0.881805 | + | 0.471614i | \(0.156329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.925496 | − | 0.925496i | −0.0591278 | − | 0.0591278i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.16849 | 0.0743495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.56293 | − | 6.56293i | 0.414249 | − | 0.414249i | −0.468967 | − | 0.883216i | \(-0.655374\pi\) |
0.883216 | + | 0.468967i | \(0.155374\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.6397 | − | 10.6397i | −0.668914 | − | 0.668914i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6808i | 0.853383i | 0.904397 | + | 0.426691i | \(0.140321\pi\) | ||||
−0.904397 | + | 0.426691i | \(0.859679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68105 | − | 1.68105i | 0.104455 | − | 0.104455i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 26.5064i | − | 1.63445i | −0.576317 | − | 0.817226i | \(-0.695511\pi\) | ||
0.576317 | − | 0.817226i | \(-0.304489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.80229i | − | 0.110714i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.7053 | + | 11.7053i | −0.713684 | + | 0.713684i | −0.967304 | − | 0.253620i | \(-0.918379\pi\) |
0.253620 | + | 0.967304i | \(0.418379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7904i | 1.62740i | 0.581286 | + | 0.813700i | \(0.302550\pi\) | ||||
−0.581286 | + | 0.813700i | \(0.697450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.66674 | + | 5.66674i | 0.341717 | + | 0.341717i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.376534 | + | 0.376534i | −0.0226237 | + | 0.0226237i | −0.718328 | − | 0.695704i | \(-0.755092\pi\) |
0.695704 | + | 0.718328i | \(0.255092\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8174 | −0.645314 | −0.322657 | − | 0.946516i | \(-0.604576\pi\) | ||||
−0.322657 | + | 0.946516i | \(0.604576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.954650 | − | 0.954650i | −0.0567481 | − | 0.0567481i | 0.678163 | − | 0.734911i | \(-0.262776\pi\) |
−0.734911 | + | 0.678163i | \(0.762776\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.88812 | 0.170480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.5159 | 0.677407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4106 | + | 14.4106i | 0.841877 | + | 0.841877i | 0.989103 | − | 0.147226i | \(-0.0470346\pi\) |
−0.147226 | + | 0.989103i | \(0.547035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.4211 | 0.897849 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.02591 | + | 2.02591i | −0.117161 | + | 0.117161i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.77330 | + | 2.77330i | 0.159850 | + | 0.159850i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 7.93721i | − | 0.454483i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9801 | + | 15.9801i | −0.912034 | + | 0.912034i | −0.996432 | − | 0.0843977i | \(-0.973103\pi\) |
0.0843977 | + | 0.996432i | \(0.473103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.61653i | 0.431894i | 0.976405 | + | 0.215947i | \(0.0692838\pi\) | ||||
−0.976405 | + | 0.215947i | \(0.930716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 30.7549i | − | 1.73837i | −0.494490 | − | 0.869184i | \(-0.664645\pi\) | ||
0.494490 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.52751 | − | 4.52751i | 0.254291 | − | 0.254291i | −0.568437 | − | 0.822727i | \(-0.692452\pi\) |
0.822727 | + | 0.568437i | \(0.192452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.422976i | 0.0236821i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.16787 | − | 4.16787i | −0.231906 | − | 0.231906i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.07900 | − | 1.07900i | 0.0598524 | − | 0.0598524i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.92184 | −0.326481 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4312 | − | 11.4312i | −0.628318 | − | 0.628318i | 0.319326 | − | 0.947645i | \(-0.396543\pi\) |
−0.947645 | + | 0.319326i | \(0.896543\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.29956 | 0.180274 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.7569 | −0.585964 | −0.292982 | − | 0.956118i | \(-0.594648\pi\) | ||||
−0.292982 | + | 0.956118i | \(0.594648\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.01187 | + | 3.01187i | 0.163102 | + | 0.163102i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3589 | + | 16.3589i | −0.878193 | + | 0.878193i | −0.993348 | − | 0.115154i | \(-0.963264\pi\) |
0.115154 | + | 0.993348i | \(0.463264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.8389 | − | 25.8389i | −1.38312 | − | 1.38312i | −0.839013 | − | 0.544112i | \(-0.816867\pi\) |
−0.544112 | − | 0.839013i | \(-0.683133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5770i | 1.30810i | 0.756451 | + | 0.654051i | \(0.226932\pi\) | ||||
−0.756451 | + | 0.654051i | \(0.773068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.93199 | − | 7.93199i | 0.420986 | − | 0.420986i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.5485i | 0.926176i | 0.886312 | + | 0.463088i | \(0.153259\pi\) | ||||
−0.886312 | + | 0.463088i | \(0.846741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6649i | 0.666573i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.93937 | − | 5.93937i | 0.310881 | − | 0.310881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.7849i | 0.823964i | 0.911192 | + | 0.411982i | \(0.135163\pi\) | ||||
−0.911192 | + | 0.411982i | \(0.864837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.973689 | − | 0.973689i | −0.0505514 | − | 0.0505514i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5837 | + | 11.5837i | −0.599781 | + | 0.599781i | −0.940254 | − | 0.340473i | \(-0.889413\pi\) |
0.340473 | + | 0.940254i | \(0.389413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0805389 | 0.00414796 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.84371 | + | 1.84371i | 0.0947049 | + | 0.0947049i | 0.752872 | − | 0.658167i | \(-0.228668\pi\) |
−0.658167 | + | 0.752872i | \(0.728668\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.04073 | 0.206472 | 0.103236 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103236 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.19117 | −0.162637 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.92444 | − | 2.92444i | −0.148275 | − | 0.148275i | 0.629072 | − | 0.777347i | \(-0.283435\pi\) |
−0.777347 | + | 0.629072i | \(0.783435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4523 | 0.730885 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.98193 | + | 4.98193i | −0.250668 | + | 0.250668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9555 | − | 21.9555i | −1.10191 | − | 1.10191i | −0.994180 | − | 0.107735i | \(-0.965640\pi\) |
−0.107735 | − | 0.994180i | \(-0.534360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.18398i | 0.159000i | 0.996835 | + | 0.0795001i | \(0.0253324\pi\) | ||||
−0.996835 | + | 0.0795001i | \(0.974668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.573491 | − | 0.573491i | 0.0285676 | − | 0.0285676i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.79636i | − | 0.287315i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1001i | 0.746650i | 0.927701 | + | 0.373325i | \(0.121782\pi\) | ||||
−0.927701 | + | 0.373325i | \(0.878218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.33124 | − | 8.33124i | 0.409954 | − | 0.409954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.41109i | 0.314708i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.19389 | − | 2.19389i | −0.107178 | − | 0.107178i | 0.651484 | − | 0.758662i | \(-0.274147\pi\) |
−0.758662 | + | 0.651484i | \(0.774147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8539 | + | 16.8539i | −0.821410 | + | 0.821410i | −0.986310 | − | 0.164900i | \(-0.947270\pi\) |
0.164900 | + | 0.986310i | \(0.447270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.69733 | −0.373376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.28808 | − | 4.28808i | −0.207515 | − | 0.207515i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.9661 | 0.961735 | 0.480868 | − | 0.876793i | \(-0.340322\pi\) | ||||
0.480868 | + | 0.876793i | \(0.340322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.83212 | −0.184160 | −0.0920800 | − | 0.995752i | \(-0.529352\pi\) | ||||
−0.0920800 | + | 0.995752i | \(0.529352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.9837 | + | 10.9837i | 0.525421 | + | 0.525421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.0120 | 1.09830 | 0.549151 | − | 0.835723i | \(-0.314951\pi\) | ||||
0.549151 | + | 0.835723i | \(0.314951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6982 | + | 13.6982i | −0.650821 | + | 0.650821i | −0.953191 | − | 0.302370i | \(-0.902222\pi\) |
0.302370 | + | 0.953191i | \(0.402222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.40111 | − | 1.40111i | −0.0664191 | − | 0.0664191i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.3194i | − | 1.28928i | −0.764486 | − | 0.644640i | \(-0.777007\pi\) | ||
0.764486 | − | 0.644640i | \(-0.222993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.97920 | − | 4.97920i | 0.234462 | − | 0.234462i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.607630i | 0.0284861i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 30.4516i | − | 1.42447i | −0.701942 | − | 0.712234i | \(-0.747684\pi\) | ||
0.701942 | − | 0.712234i | \(-0.252316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8016 | + | 17.8016i | −0.829101 | + | 0.829101i | −0.987392 | − | 0.158291i | \(-0.949402\pi\) |
0.158291 | + | 0.987392i | \(0.449402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.43314i | 0.391921i | 0.980612 | + | 0.195961i | \(0.0627825\pi\) | ||||
−0.980612 | + | 0.195961i | \(0.937218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.17711 | − | 3.17711i | −0.147019 | − | 0.147019i | 0.629766 | − | 0.776785i | \(-0.283151\pi\) |
−0.776785 | + | 0.629766i | \(0.783151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.78259 | − | 1.78259i | 0.0823124 | − | 0.0823124i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.56249 | 0.439684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.84993 | − | 5.84993i | −0.268413 | − | 0.268413i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.550076 | −0.0251336 | −0.0125668 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125668 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.10368 | −0.0503237 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5466 | − | 14.5466i | −0.660528 | − | 0.660528i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1678 | −0.823262 | −0.411631 | − | 0.911351i | \(-0.635041\pi\) | ||||
−0.411631 | + | 0.911351i | \(0.635041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.4565 | − | 12.4565i | 0.562156 | − | 0.562156i | −0.367764 | − | 0.929919i | \(-0.619876\pi\) |
0.929919 | + | 0.367764i | \(0.119876\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.287272 | − | 0.287272i | −0.0129381 | − | 0.0129381i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.57053i | − | 0.384441i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1835 | − | 23.1835i | 1.03784 | − | 1.03784i | 0.0385798 | − | 0.999256i | \(-0.487717\pi\) |
0.999256 | − | 0.0385798i | \(-0.0122834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.4375i | − | 1.75843i | −0.476426 | − | 0.879215i | \(-0.658068\pi\) | ||
0.476426 | − | 0.879215i | \(-0.341932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.2545i | − | 1.12381i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.26193 | − | 1.26193i | 0.0559340 | − | 0.0559340i | −0.678587 | − | 0.734520i | \(-0.737407\pi\) |
0.734520 | + | 0.678587i | \(0.237407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.41750i | − | 0.283894i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0355 | − | 11.0355i | −0.486280 | − | 0.486280i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2094 | + | 10.2094i | −0.449010 | + | 0.449010i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.2672 | −1.19460 | −0.597300 | − | 0.802018i | \(-0.703760\pi\) | ||||
−0.597300 | + | 0.802018i | \(0.703760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1608 | + | 31.1608i | 1.36257 | + | 1.36257i | 0.870633 | + | 0.491933i | \(0.163709\pi\) |
0.491933 | + | 0.870633i | \(0.336291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.09113 | −0.178213 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0865 | −0.655936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.948090 | − | 0.948090i | −0.0410663 | − | 0.0410663i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.1935 | 1.08921 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.72403 | + | 1.72403i | −0.0742592 | + | 0.0742592i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9117 | + | 12.9117i | 0.555119 | + | 0.555119i | 0.927914 | − | 0.372795i | \(-0.121600\pi\) |
−0.372795 | + | 0.927914i | \(0.621600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.21544i | − | 0.394746i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6998 | − | 17.6998i | 0.756790 | − | 0.756790i | −0.218947 | − | 0.975737i | \(-0.570262\pi\) |
0.975737 | + | 0.218947i | \(0.0702622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.436650i | − | 0.0186019i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.38299i | 0.228908i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.90087 | + | 3.90087i | −0.165285 | + | 0.165285i | −0.784903 | − | 0.619618i | \(-0.787287\pi\) |
0.619618 | + | 0.784903i | \(0.287287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.82079i | − | 0.0770114i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4905 | + | 27.4905i | 1.15859 | + | 1.15859i | 0.984780 | + | 0.173807i | \(0.0556068\pi\) |
0.173807 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0711615 | − | 0.0711615i | 0.00299379 | − | 0.00299379i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.2030 | 0.805031 | 0.402516 | − | 0.915413i | \(-0.368136\pi\) | ||||
0.402516 | + | 0.915413i | \(0.368136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.2363 | − | 23.2363i | −0.972408 | − | 0.972408i | 0.0272217 | − | 0.999629i | \(-0.491334\pi\) |
−0.999629 | + | 0.0272217i | \(0.991334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.2850 | 0.845941 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0676 | 1.04358 | 0.521789 | − | 0.853074i | \(-0.325265\pi\) | ||||
0.521789 | + | 0.853074i | \(0.325265\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.46360 | + | 3.46360i | 0.143694 | + | 0.143694i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.35734 | −0.139047 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.53626 | − | 6.53626i | 0.269780 | − | 0.269780i | −0.559231 | − | 0.829012i | \(-0.688904\pi\) |
0.829012 | + | 0.559231i | \(0.188904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.10924 | − | 3.10924i | −0.128114 | − | 0.128114i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.1162i | − | 0.620749i | −0.950614 | − | 0.310375i | \(-0.899545\pi\) | ||
0.950614 | − | 0.310375i | \(-0.100455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.16734 | − | 2.16734i | 0.0888521 | − | 0.0888521i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 29.1264i | − | 1.19007i | −0.803700 | − | 0.595035i | \(-0.797138\pi\) | ||
0.803700 | − | 0.595035i | \(-0.202862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2202i | 0.580053i | 0.957019 | + | 0.290026i | \(0.0936641\pi\) | ||||
−0.957019 | + | 0.290026i | \(0.906336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.67879 | − | 4.67879i | 0.190220 | − | 0.190220i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8584i | 1.09015i | 0.838387 | + | 0.545075i | \(0.183499\pi\) | ||||
−0.838387 | + | 0.545075i | \(0.816501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.94398 | + | 1.94398i | 0.0786448 | + | 0.0786448i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.2483 | + | 28.2483i | −1.14094 | + | 1.14094i | −0.152659 | + | 0.988279i | \(0.548784\pi\) |
−0.988279 | + | 0.152659i | \(0.951216\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.4617 | −1.26660 | −0.633300 | − | 0.773906i | \(-0.718300\pi\) | ||||
−0.633300 | + | 0.773906i | \(0.718300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.3846 | − | 13.3846i | −0.537973 | − | 0.537973i | 0.384961 | − | 0.922933i | \(-0.374215\pi\) |
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.51391 | −0.0606533 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.23838 | −0.0895353 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.93670 | + | 3.93670i | 0.156966 | + | 0.156966i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5279 | −0.618154 | −0.309077 | − | 0.951037i | \(-0.600020\pi\) | ||||
−0.309077 | + | 0.951037i | \(0.600020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.9390 | − | 13.9390i | 0.553152 | − | 0.553152i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.328273 | + | 0.328273i | 0.0130066 | + | 0.0130066i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 33.1261i | − | 1.30840i | −0.756320 | − | 0.654201i | \(-0.773005\pi\) | ||
0.756320 | − | 0.654201i | \(-0.226995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5683 | + | 28.5683i | −1.12662 | + | 1.12662i | −0.135902 | + | 0.990722i | \(0.543393\pi\) |
−0.990722 | + | 0.135902i | \(0.956607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.7052i | 1.91480i | 0.288765 | + | 0.957400i | \(0.406755\pi\) | ||||
−0.288765 | + | 0.957400i | \(0.593245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.7266i | − | 1.12762i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.67453 | + | 2.67453i | −0.104662 | + | 0.104662i | −0.757499 | − | 0.652836i | \(-0.773579\pi\) |
0.652836 | + | 0.757499i | \(0.273579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.16384i | − | 0.279915i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0589 | − | 20.0589i | −0.781384 | − | 0.781384i | 0.198680 | − | 0.980064i | \(-0.436334\pi\) |
−0.980064 | + | 0.198680i | \(0.936334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.44403 | − | 3.44403i | 0.133957 | − | 0.133957i | −0.636949 | − | 0.770906i | \(-0.719804\pi\) |
0.770906 | + | 0.636949i | \(0.219804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.29433 | 0.127749 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.757054 | + | 0.757054i | 0.0293132 | + | 0.0293132i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7856 | −0.570791 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.1701 | −1.24007 | −0.620033 | − | 0.784576i | \(-0.712881\pi\) | ||||
−0.620033 | + | 0.784576i | \(0.712881\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.59090 | − | 3.59090i | −0.138009 | − | 0.138009i | 0.634727 | − | 0.772736i | \(-0.281113\pi\) |
−0.772736 | + | 0.634727i | \(0.781113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7177 | −0.603188 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.35732 | − | 4.35732i | 0.166728 | − | 0.166728i | −0.618811 | − | 0.785540i | \(-0.712385\pi\) |
0.785540 | + | 0.618811i | \(0.212385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.06701 | − | 5.06701i | −0.193600 | − | 0.193600i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.639271i | 0.0243543i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.12084 | − | 9.12084i | 0.346973 | − | 0.346973i | −0.512008 | − | 0.858981i | \(-0.671098\pi\) |
0.858981 | + | 0.512008i | \(0.171098\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.5676i | 0.780173i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.76343i | 0.256183i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1832 | − | 13.1832i | 0.497923 | − | 0.497923i | −0.412868 | − | 0.910791i | \(-0.635473\pi\) |
0.910791 | + | 0.412868i | \(0.135473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.98374i | 0.225681i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6438 | − | 13.6438i | −0.513126 | − | 0.513126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95604 | − | 5.95604i | 0.223684 | − | 0.223684i | −0.586364 | − | 0.810048i | \(-0.699441\pi\) |
0.810048 | + | 0.586364i | \(0.199441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7815 | 0.403769 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.04757 | + | 1.04757i | 0.0391770 | + | 0.0391770i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.3917 | 1.43177 | 0.715884 | − | 0.698220i | \(-0.246024\pi\) | ||||
0.715884 | + | 0.698220i | \(0.246024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.9238 | −0.444067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.403208 | − | 0.403208i | −0.0149748 | − | 0.0149748i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.05200 | 0.187368 | 0.0936842 | − | 0.995602i | \(-0.470136\pi\) | ||||
0.0936842 | + | 0.995602i | \(0.470136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.49454 | + | 6.49454i | −0.240209 | + | 0.240209i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.73691 | + | 2.73691i | 0.101090 | + | 0.101090i | 0.755843 | − | 0.654753i | \(-0.227227\pi\) |
−0.654753 | + | 0.755843i | \(0.727227\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.14648i | − | 0.226408i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.5031 | + | 18.5031i | −0.680648 | + | 0.680648i | −0.960146 | − | 0.279498i | \(-0.909832\pi\) |
0.279498 | + | 0.960146i | \(0.409832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 41.1110i | − | 1.50822i | −0.656751 | − | 0.754108i | \(-0.728070\pi\) | ||
0.656751 | − | 0.754108i | \(-0.271930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 18.9235i | − | 0.693302i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.6108 | − | 13.6108i | 0.497327 | − | 0.497327i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.5241i | 1.00437i | 0.864760 | + | 0.502185i | \(0.167470\pi\) | ||||
−0.864760 | + | 0.502185i | \(0.832530\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.54366 | + | 5.54366i | 0.201754 | + | 0.201754i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.27349 | − | 6.27349i | 0.228014 | − | 0.228014i | −0.583849 | − | 0.811863i | \(-0.698454\pi\) |
0.811863 | + | 0.583849i | \(0.198454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.6884 | −0.858704 | −0.429352 | − | 0.903137i | \(-0.641258\pi\) | ||||
−0.429352 | + | 0.903137i | \(0.641258\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.97865 | − | 4.97865i | −0.180239 | − | 0.180239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.46983 | −0.197504 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.74756 | −0.171201 | −0.0856006 | − | 0.996330i | \(-0.527281\pi\) | ||||
−0.0856006 | + | 0.996330i | \(0.527281\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.2666 | − | 18.2666i | −0.657005 | − | 0.657005i | 0.297666 | − | 0.954670i | \(-0.403792\pi\) |
−0.954670 | + | 0.297666i | \(0.903792\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.74223 | −0.206267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.14017 | + | 5.14017i | −0.184166 | + | 0.184166i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7759 | − | 14.7759i | −0.528722 | − | 0.528722i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 17.7311i | − | 0.632849i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1972 | + | 28.1972i | −1.00512 | + | 1.00512i | −0.00513510 | + | 0.999987i | \(0.501635\pi\) |
−0.999987 | + | 0.00513510i | \(0.998365\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.0768901i | − | 0.00273390i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.81532i | 0.0999749i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.8697 | − | 24.8697i | 0.880930 | − | 0.880930i | −0.112699 | − | 0.993629i | \(-0.535950\pi\) |
0.993629 | + | 0.112699i | \(0.0359496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 13.8678i | − | 0.490608i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0640 | − | 11.0640i | −0.390439 | − | 0.390439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.71163 | + | 5.71163i | −0.201309 | + | 0.201309i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.9141 | 1.57910 | 0.789548 | − | 0.613688i | \(-0.210315\pi\) | ||||
0.789548 | + | 0.613688i | \(0.210315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1446 | − | 13.1446i | −0.461570 | − | 0.461570i | 0.437600 | − | 0.899170i | \(-0.355829\pi\) |
−0.899170 | + | 0.437600i | \(0.855829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4578 | −0.506435 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.87162 | −0.345364 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0363 | + | 15.0363i | 0.524772 | + | 0.524772i | 0.919009 | − | 0.394237i | \(-0.128991\pi\) |
−0.394237 | + | 0.919009i | \(0.628991\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3186 | −0.429399 | −0.214699 | − | 0.976680i | \(-0.568877\pi\) | ||||
−0.214699 | + | 0.976680i | \(0.568877\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2509 | − | 29.2509i | 1.01715 | − | 1.01715i | 0.0173016 | − | 0.999850i | \(-0.494492\pi\) |
0.999850 | − | 0.0173016i | \(-0.00550753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.68627 | + | 3.68627i | 0.128029 | + | 0.128029i | 0.768218 | − | 0.640189i | \(-0.221144\pi\) |
−0.640189 | + | 0.768218i | \(0.721144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.34181i | − | 0.0811389i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.88761 | + | 4.88761i | −0.169143 | + | 0.169143i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.5841i | − | 0.917786i | −0.888492 | − | 0.458893i | \(-0.848246\pi\) | ||
0.888492 | − | 0.458893i | \(-0.151754\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9699i | 0.998962i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.8320 | + | 11.8320i | −0.407032 | + | 0.407032i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.05544i | − | 0.173707i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3745 | − | 10.3745i | −0.355632 | − | 0.355632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.95460 | − | 8.95460i | 0.306600 | − | 0.306600i | −0.536989 | − | 0.843589i | \(-0.680438\pi\) |
0.843589 | + | 0.536989i | \(0.180438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.9763 | 1.26309 | 0.631543 | − | 0.775341i | \(-0.282422\pi\) | ||||
0.631543 | + | 0.775341i | \(0.282422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.95338 | − | 1.95338i | −0.0666483 | − | 0.0666483i | 0.672997 | − | 0.739645i | \(-0.265007\pi\) |
−0.739645 | + | 0.672997i | \(0.765007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.1583 | 0.379835 | 0.189917 | − | 0.981800i | \(-0.439178\pi\) | ||||
0.189917 | + | 0.981800i | \(0.439178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0071 | 0.748262 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.28043 | + | 9.28043i | 0.314817 | + | 0.314817i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.17035 | −0.0396558 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.66951 | − | 7.66951i | 0.259277 | − | 0.259277i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5959 | + | 34.5959i | 1.16822 | + | 1.16822i | 0.982626 | + | 0.185595i | \(0.0594213\pi\) |
0.185595 | + | 0.982626i | \(0.440579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.6167i | − | 1.73901i | −0.493924 | − | 0.869505i | \(-0.664438\pi\) | ||
0.493924 | − | 0.869505i | \(-0.335562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.62392 | + | 6.62392i | −0.222913 | + | 0.222913i | −0.809724 | − | 0.586811i | \(-0.800383\pi\) |
0.586811 | + | 0.809724i | \(0.300383\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 41.8546i | − | 1.40534i | −0.711515 | − | 0.702671i | \(-0.751991\pi\) | ||
0.711515 | − | 0.702671i | \(-0.248009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 15.0611i | − | 0.505134i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5395 | − | 10.5395i | 0.352690 | − | 0.352690i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.8248i | − | 0.395260i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.214305 | − | 0.214305i | −0.00714748 | − | 0.00714748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.28020 | − | 2.28020i | 0.0759643 | − | 0.0759643i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.2983 | −0.342328 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.3030 | − | 20.3030i | −0.674150 | − | 0.674150i | 0.284520 | − | 0.958670i | \(-0.408166\pi\) |
−0.958670 | + | 0.284520i | \(0.908166\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0607824 | 0.00201381 | 0.00100691 | − | 0.999999i | \(-0.499679\pi\) | ||||
0.00100691 | + | 0.999999i | \(0.499679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.9427 | 0.395246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.87027 | − | 3.87027i | −0.127808 | − | 0.127808i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.3187 | −1.36298 | −0.681489 | − | 0.731828i | \(-0.738667\pi\) | ||||
−0.681489 | + | 0.731828i | \(0.738667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.81347 | + | 2.81347i | −0.0926065 | + | 0.0926065i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.52546 | + | 5.52546i | 0.181676 | + | 0.181676i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.2586i | 1.35365i | 0.736143 | + | 0.676826i | \(0.236645\pi\) | ||||
−0.736143 | + | 0.676826i | \(0.763355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77976 | − | 1.77976i | 0.0583294 | − | 0.0583294i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.47311i | − | 0.244397i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0095i | 1.73175i | 0.500264 | + | 0.865873i | \(0.333236\pi\) | ||||
−0.500264 | + | 0.865873i | \(0.666764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3743 | + | 24.3743i | −0.794580 | + | 0.794580i | −0.982235 | − | 0.187655i | \(-0.939911\pi\) |
0.187655 | + | 0.982235i | \(0.439911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17.8238i | − | 0.580423i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.4434 | − | 22.4434i | −0.729314 | − | 0.729314i | 0.241169 | − | 0.970483i | \(-0.422469\pi\) |
−0.970483 | + | 0.241169i | \(0.922469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.10669 | + | 2.10669i | −0.0683861 | + | 0.0683861i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.7067 | 0.379218 | 0.189609 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.25118 | − | 2.25118i | −0.0728466 | − | 0.0728466i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.47491 | −0.176794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.9480 | 0.901549 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.9992 | − | 22.9992i | −0.740372 | − | 0.740372i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.7319 | −1.72790 | −0.863951 | − | 0.503576i | \(-0.832017\pi\) | ||||
−0.863951 | + | 0.503576i | \(0.832017\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.49392 | + | 1.49392i | −0.0479423 | + | 0.0479423i | −0.730671 | − | 0.682729i | \(-0.760793\pi\) |
0.682729 | + | 0.730671i | \(0.260793\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1117 | + | 11.1117i | 0.356223 | + | 0.356223i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 35.4073i | − | 1.13278i | −0.824138 | − | 0.566390i | \(-0.808340\pi\) | ||
0.824138 | − | 0.566390i | \(-0.191660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.61002 | + | 2.61002i | −0.0834166 | + | 0.0834166i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.8771i | 0.570191i | 0.958499 | + | 0.285096i | \(0.0920254\pi\) | ||||
−0.958499 | + | 0.285096i | \(0.907975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.27905i | 0.104479i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.1152 | − | 17.1152i | 0.544232 | − | 0.544232i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 54.7193i | − | 1.73822i | −0.494623 | − | 0.869108i | \(-0.664694\pi\) | ||
0.494623 | − | 0.869108i | \(-0.335306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.8616 | − | 12.8616i | −0.407740 | − | 0.407740i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.1277 | − | 38.1277i | 1.20751 | − | 1.20751i | 0.235686 | − | 0.971829i | \(-0.424266\pi\) |
0.971829 | − | 0.235686i | \(-0.0757336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.e.1583.7 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.14 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.16 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.5 | ✓ | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.5 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.14 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.16 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.7 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.5 | ✓ | 40 | 12.11 | even | 2 | ||
1008.2.v.e.323.16 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.5 | yes | 40 | 16.5 | even | 4 | ||
1008.2.v.e.827.16 | yes | 40 | 48.5 | odd | 4 | ||
4032.2.v.e.1583.7 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.1583.14 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.7 | 40 | 48.11 | even | 4 | inner | ||
4032.2.v.e.3599.14 | 40 | 16.11 | odd | 4 | inner |