Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 543.4 | ||
Root | \(-1.09445 - 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.543 |
Dual form | 1600.2.o.l.607.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.18890 | + | 2.18890i | 1.26376 | + | 1.26376i | 0.949255 | + | 0.314508i | \(0.101839\pi\) |
0.314508 | + | 0.949255i | \(0.398161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.79129 | − | 1.79129i | −0.677043 | − | 0.677043i | 0.282287 | − | 0.959330i | \(-0.408907\pi\) |
−0.959330 | + | 0.282287i | \(0.908907\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.58258i | 2.19419i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.913701 | 0.275491 | 0.137746 | − | 0.990468i | \(-0.456014\pi\) | ||||
0.137746 | + | 0.990468i | \(0.456014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73205 | + | 1.73205i | −0.480384 | + | 0.480384i | −0.905254 | − | 0.424870i | \(-0.860320\pi\) |
0.424870 | + | 0.905254i | \(0.360320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 3.00000i | −0.727607 | + | 0.727607i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.84190i | − | 1.71124i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.79129 | + | 3.79129i | −0.790538 | + | 0.790538i | −0.981582 | − | 0.191043i | \(-0.938813\pi\) |
0.191043 | + | 0.981582i | \(0.438813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.84190 | + | 7.84190i | −1.50918 | + | 1.50918i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29150 | 0.982607 | 0.491304 | − | 0.870988i | \(-0.336521\pi\) | ||||
0.491304 | + | 0.870988i | \(0.336521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.58258i | 1.36187i | 0.732343 | + | 0.680935i | \(0.238427\pi\) | ||||
−0.732343 | + | 0.680935i | \(0.761573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | + | 2.00000i | 0.348155 | + | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.19615 | − | 5.19615i | −0.854242 | − | 0.854242i | 0.136410 | − | 0.990652i | \(-0.456443\pi\) |
−0.990652 | + | 0.136410i | \(0.956443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.58258 | −1.21418 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.58258 | 0.247157 | 0.123578 | − | 0.992335i | \(-0.460563\pi\) | ||||
0.123578 | + | 0.992335i | \(0.460563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.361500 | + | 0.361500i | 0.0551282 | + | 0.0551282i | 0.734133 | − | 0.679005i | \(-0.237589\pi\) |
−0.679005 | + | 0.734133i | \(0.737589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.79129 | + | 3.79129i | 0.553016 | + | 0.553016i | 0.927310 | − | 0.374294i | \(-0.122115\pi\) |
−0.374294 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.582576i | − | 0.0832251i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.1334 | −1.83904 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.64575 | − | 2.64575i | 0.363422 | − | 0.363422i | −0.501649 | − | 0.865071i | \(-0.667273\pi\) |
0.865071 | + | 0.501649i | \(0.167273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.58258 | + | 7.58258i | −1.00434 | + | 1.00434i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.29150i | 0.688895i | 0.938806 | + | 0.344447i | \(0.111934\pi\) | ||||
−0.938806 | + | 0.344447i | \(0.888066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.20520i | 0.794495i | 0.917712 | + | 0.397247i | \(0.130035\pi\) | ||||
−0.917712 | + | 0.397247i | \(0.869965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.7913 | − | 11.7913i | 1.48556 | − | 1.48556i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.361500 | + | 0.361500i | −0.0441643 | + | 0.0441643i | −0.728844 | − | 0.684680i | \(-0.759942\pi\) |
0.684680 | + | 0.728844i | \(0.259942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.5975 | −1.99811 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41742i | 0.524252i | 0.965034 | + | 0.262126i | \(0.0844236\pi\) | ||||
−0.965034 | + | 0.262126i | \(0.915576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.58258 | + | 8.58258i | 1.00451 | + | 1.00451i | 0.999990 | + | 0.00452474i | \(0.00144028\pi\) |
0.00452474 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.63670 | − | 1.63670i | −0.186519 | − | 0.186519i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.5826 | −1.62029 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.10260 | + | 3.10260i | 0.340555 | + | 0.340555i | 0.856576 | − | 0.516021i | \(-0.172587\pi\) |
−0.516021 | + | 0.856576i | \(0.672587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.5826 | + | 11.5826i | 1.24178 | + | 1.24178i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.1652i | − | 1.60750i | −0.594965 | − | 0.803751i | \(-0.702834\pi\) | ||
0.594965 | − | 0.803751i | \(-0.297166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.20520 | 0.650482 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.5975 | + | 16.5975i | −1.72108 | + | 1.72108i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.58258 | − | 8.58258i | 0.871429 | − | 0.871429i | −0.121200 | − | 0.992628i | \(-0.538674\pi\) |
0.992628 | + | 0.121200i | \(0.0386741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.01450i | 0.604480i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 17.5112i | − | 1.74243i | −0.490901 | − | 0.871215i | \(-0.663332\pi\) | ||
0.490901 | − | 0.871215i | \(-0.336668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.37386 | − | 3.37386i | 0.332437 | − | 0.332437i | −0.521075 | − | 0.853511i | \(-0.674469\pi\) |
0.853511 | + | 0.521075i | \(0.174469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.361500 | + | 0.361500i | −0.0349475 | + | 0.0349475i | −0.724365 | − | 0.689417i | \(-0.757867\pi\) |
0.689417 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.66930 | −0.926151 | −0.463076 | − | 0.886319i | \(-0.653254\pi\) | ||||
−0.463076 | + | 0.886319i | \(0.653254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 22.7477i | − | 2.15912i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.58258 | − | 4.58258i | −0.431092 | − | 0.431092i | 0.457907 | − | 0.889000i | \(-0.348599\pi\) |
−0.889000 | + | 0.457907i | \(0.848599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.4014 | − | 11.4014i | −1.05406 | − | 1.05406i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7477 | 0.985243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1652 | −0.924105 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.46410 | + | 3.46410i | 0.312348 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.79129 | − | 5.79129i | −0.513894 | − | 0.513894i | 0.401823 | − | 0.915717i | \(-0.368377\pi\) |
−0.915717 | + | 0.401823i | \(0.868377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.58258i | 0.139338i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.01450 | −0.525490 | −0.262745 | − | 0.964865i | \(-0.584628\pi\) | ||||
−0.262745 | + | 0.964865i | \(0.584628\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.20520 | − | 6.20520i | 0.538059 | − | 0.538059i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.16515 | − | 6.16515i | 0.526724 | − | 0.526724i | −0.392870 | − | 0.919594i | \(-0.628518\pi\) |
0.919594 | + | 0.392870i | \(0.128518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 22.8027i | − | 1.93410i | −0.254585 | − | 0.967050i | \(-0.581939\pi\) | ||
0.254585 | − | 0.967050i | \(-0.418061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5975i | 1.39776i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.58258 | + | 1.58258i | −0.132342 | + | 0.132342i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.27520 | − | 1.27520i | 0.105177 | − | 0.105177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.913701 | 0.0748533 | 0.0374266 | − | 0.999299i | \(-0.488084\pi\) | ||||
0.0374266 | + | 0.999299i | \(0.488084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7477i | 1.20015i | 0.799943 | + | 0.600077i | \(0.204863\pi\) | ||||
−0.799943 | + | 0.600077i | \(0.795137\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.7477 | − | 19.7477i | −1.59651 | − | 1.59651i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.47315 | − | 4.47315i | −0.356996 | − | 0.356996i | 0.505708 | − | 0.862705i | \(-0.331231\pi\) |
−0.862705 | + | 0.505708i | \(0.831231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5826 | 0.918558 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5826 | 1.07046 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.361500 | + | 0.361500i | 0.0283149 | + | 0.0283149i | 0.721122 | − | 0.692808i | \(-0.243626\pi\) |
−0.692808 | + | 0.721122i | \(0.743626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7913 | + | 15.7913i | 1.22197 | + | 1.22197i | 0.966932 | + | 0.255035i | \(0.0820869\pi\) |
0.255035 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000i | 0.538462i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.8027 | −1.74377 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.66025 | − | 8.66025i | 0.658427 | − | 0.658427i | −0.296581 | − | 0.955008i | \(-0.595846\pi\) |
0.955008 | + | 0.296581i | \(0.0958464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.5826 | + | 11.5826i | −0.870600 | + | 0.870600i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 19.1479i | − | 1.43118i | −0.698520 | − | 0.715591i | \(-0.746157\pi\) | ||
0.698520 | − | 0.715591i | \(-0.253843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.5826 | + | 13.5826i | −1.00405 | + | 1.00405i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.74110 | + | 2.74110i | −0.200449 | + | 0.200449i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 28.0942 | 2.04355 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.41742i | − | 0.319634i | −0.987147 | − | 0.159817i | \(-0.948910\pi\) | ||
0.987147 | − | 0.159817i | \(-0.0510903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.16515 | + | 4.16515i | 0.299814 | + | 0.299814i | 0.840941 | − | 0.541127i | \(-0.182002\pi\) |
−0.541127 | + | 0.840941i | \(0.682002\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.64575 | + | 2.64575i | 0.188502 | + | 0.188502i | 0.795048 | − | 0.606546i | \(-0.207446\pi\) |
−0.606546 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.58258 | −0.111626 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.47860 | − | 9.47860i | −0.665268 | − | 0.665268i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.9564 | − | 24.9564i | −1.73459 | − | 1.73459i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.16515i | 0.218938i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5257 | 1.61958 | 0.809788 | − | 0.586722i | \(-0.199582\pi\) | ||||
0.809788 | + | 0.586722i | \(0.199582\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.66930 | + | 9.66930i | −0.662530 | + | 0.662530i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5826 | − | 13.5826i | 0.922045 | − | 0.922045i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.5728i | 2.53894i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.3923i | − | 0.699062i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.37386 | + | 1.37386i | −0.0920007 | + | 0.0920007i | −0.751609 | − | 0.659609i | \(-0.770722\pi\) |
0.659609 | + | 0.751609i | \(0.270722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.8582 | + | 11.8582i | −0.787057 | + | 0.787057i | −0.981011 | − | 0.193954i | \(-0.937869\pi\) |
0.193954 | + | 0.981011i | \(0.437869\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46410 | 0.228914 | 0.114457 | − | 0.993428i | \(-0.463487\pi\) | ||||
0.114457 | + | 0.993428i | \(0.463487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 7.16515i | − | 0.471432i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1652 | + | 12.1652i | 0.796966 | + | 0.796966i | 0.982616 | − | 0.185650i | \(-0.0594392\pi\) |
−0.185650 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.2668 | + | 26.2668i | 1.70621 | + | 1.70621i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1652 | −0.980952 | −0.490476 | − | 0.871455i | \(-0.663177\pi\) | ||||
−0.490476 | + | 0.871455i | \(0.663177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7477 | 1.07882 | 0.539408 | − | 0.842045i | \(-0.318648\pi\) | ||||
0.539408 | + | 0.842045i | \(0.318648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.39410 | − | 8.39410i | −0.538482 | − | 0.538482i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 6.00000i | −0.381771 | − | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5826i | 0.860761i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9427 | 0.816936 | 0.408468 | − | 0.912773i | \(-0.366063\pi\) | ||||
0.408468 | + | 0.912773i | \(0.366063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.46410 | + | 3.46410i | −0.217786 | + | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.74773 | + | 7.74773i | −0.483290 | + | 0.483290i | −0.906181 | − | 0.422891i | \(-0.861015\pi\) |
0.422891 | + | 0.906181i | \(0.361015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.6156i | 1.15672i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 34.8317i | 2.15603i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.2087 | + | 14.2087i | −0.876147 | + | 0.876147i | −0.993133 | − | 0.116987i | \(-0.962676\pi\) |
0.116987 | + | 0.993133i | \(0.462676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.1950 | − | 33.1950i | 2.03150 | − | 2.03150i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3241 | −0.812385 | −0.406193 | − | 0.913788i | \(-0.633144\pi\) | ||||
−0.406193 | + | 0.913788i | \(0.633144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7477i | 1.13884i | 0.822046 | + | 0.569422i | \(0.192833\pi\) | ||||
−0.822046 | + | 0.569422i | \(0.807167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.5826 | + | 13.5826i | 0.822055 | + | 0.822055i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7937 | + | 21.7937i | 1.30945 | + | 1.30945i | 0.921808 | + | 0.387646i | \(0.126712\pi\) |
0.387646 | + | 0.921808i | \(0.373288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −49.9129 | −2.98821 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7477 | 0.999086 | 0.499543 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499543 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4412 | + | 22.4412i | 1.33399 | + | 1.33399i | 0.901765 | + | 0.432226i | \(0.142272\pi\) |
0.432226 | + | 0.901765i | \(0.357728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.83485 | − | 2.83485i | −0.167336 | − | 0.167336i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.5728 | 2.20256 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.1389 | − | 18.1389i | 1.05968 | − | 1.05968i | 0.0615814 | − | 0.998102i | \(-0.480386\pi\) |
0.998102 | − | 0.0615814i | \(-0.0196144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.16515 | + | 7.16515i | −0.415764 | + | 0.415764i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 13.1334i | − | 0.759525i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.29510i | − | 0.0746484i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.3303 | − | 38.3303i | 2.20202 | − | 2.20202i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.56670 | − | 6.56670i | 0.374782 | − | 0.374782i | −0.494434 | − | 0.869215i | \(-0.664625\pi\) |
0.869215 | + | 0.494434i | \(0.164625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7701 | 0.840242 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5826i | 1.11043i | 0.831708 | + | 0.555213i | \(0.187363\pi\) | ||||
−0.831708 | + | 0.555213i | \(0.812637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.58258 | + | 6.58258i | 0.372069 | + | 0.372069i | 0.868230 | − | 0.496161i | \(-0.165258\pi\) |
−0.496161 | + | 0.868230i | \(0.665258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.1425 | − | 14.1425i | −0.794320 | − | 0.794320i | 0.187874 | − | 0.982193i | \(-0.439840\pi\) |
−0.982193 | + | 0.187874i | \(0.939840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.83485 | 0.270700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.58258 | −0.0883308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3923 | − | 10.3923i | −0.578243 | − | 0.578243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.1652 | − | 21.1652i | −1.17044 | − | 1.17044i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 13.5826i | − | 0.748832i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.66930 | −0.531473 | −0.265737 | − | 0.964046i | \(-0.585615\pi\) | ||||
−0.265737 | + | 0.964046i | \(0.585615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34.2041 | − | 34.2041i | 1.87437 | − | 1.87437i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.00000i | −0.0544735 | + | 0.0544735i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 20.0616i | − | 1.08960i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820i | 0.375183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5826 | + | 13.5826i | −0.733390 | + | 0.733390i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.27520 | + | 1.27520i | −0.0684564 | + | 0.0684564i | −0.740506 | − | 0.672050i | \(-0.765414\pi\) |
0.672050 | + | 0.740506i | \(0.265414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3923 | −0.556287 | −0.278144 | − | 0.960539i | \(-0.589719\pi\) | ||||
−0.278144 | + | 0.960539i | \(0.589719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 27.1652i | − | 1.44997i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.1652 | − | 24.1652i | −1.28618 | − | 1.28618i | −0.937088 | − | 0.349093i | \(-0.886490\pi\) |
−0.349093 | − | 0.937088i | \(-0.613510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.5257 | + | 23.5257i | 1.24511 | + | 1.24511i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.1652 | −1.43372 | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||||
−0.716861 | + | 0.697216i | \(0.754422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.2505 | − | 22.2505i | −1.16785 | − | 1.16785i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5390 | + | 16.5390i | 0.863330 | + | 0.863330i | 0.991723 | − | 0.128394i | \(-0.0409821\pi\) |
−0.128394 | + | 0.991723i | \(0.540982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4174i | 0.542309i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.47860 | −0.492105 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.19615 | + | 5.19615i | −0.269047 | + | 0.269047i | −0.828716 | − | 0.559669i | \(-0.810928\pi\) |
0.559669 | + | 0.828716i | \(0.310928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.16515 | + | 9.16515i | −0.472029 | + | 0.472029i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 25.3531i | − | 1.29888i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3739 | + | 17.3739i | −0.887763 | + | 0.887763i | −0.994308 | − | 0.106545i | \(-0.966021\pi\) |
0.106545 | + | 0.994308i | \(0.466021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.37960 | + | 2.37960i | −0.120962 | + | 0.120962i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.5547 | 1.80270 | 0.901348 | − | 0.433096i | \(-0.142579\pi\) | ||||
0.901348 | + | 0.433096i | \(0.142579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 22.7477i | − | 1.15040i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1652 | − | 13.1652i | −0.664094 | − | 0.664094i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.93725 | − | 7.93725i | −0.398359 | − | 0.398359i | 0.479295 | − | 0.877654i | \(-0.340893\pi\) |
−0.877654 | + | 0.479295i | \(0.840893\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.1652 | 1.35996 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3303 | −1.21500 | −0.607499 | − | 0.794321i | \(-0.707827\pi\) | ||||
−0.607499 | + | 0.794321i | \(0.707827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1334 | − | 13.1334i | −0.654222 | − | 0.654222i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.74773 | − | 4.74773i | −0.235336 | − | 0.235336i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.4174i | − | 0.811789i | −0.913920 | − | 0.405895i | \(-0.866960\pi\) | ||
0.913920 | − | 0.405895i | \(-0.133040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.9898 | 1.33131 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.47860 | − | 9.47860i | 0.466412 | − | 0.466412i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 49.9129 | − | 49.9129i | 2.44424 | − | 2.44424i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.9753i | − | 1.02471i | −0.858773 | − | 0.512355i | \(-0.828773\pi\) | ||
0.858773 | − | 0.512355i | \(-0.171227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1334i | 0.640083i | 0.947404 | + | 0.320042i | \(0.103697\pi\) | ||||
−0.947404 | + | 0.320042i | \(0.896303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.9564 | + | 24.9564i | −1.21342 | + | 1.21342i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1153 | − | 11.1153i | 0.537907 | − | 0.537907i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92820 | −0.334497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7477i | 0.517700i | 0.965918 | + | 0.258850i | \(0.0833435\pi\) | ||||
−0.965918 | + | 0.258850i | \(0.916656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.41742 | + | 5.41742i | 0.260345 | + | 0.260345i | 0.825194 | − | 0.564849i | \(-0.191066\pi\) |
−0.564849 | + | 0.825194i | \(0.691066\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1334 | − | 13.1334i | −0.628256 | − | 0.628256i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4955 | 1.21683 | 0.608416 | − | 0.793618i | \(-0.291805\pi\) | ||||
0.608416 | + | 0.793618i | \(0.291805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.83485 | 0.182612 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.4086 | − | 14.4086i | −0.684574 | − | 0.684574i | 0.276454 | − | 0.961027i | \(-0.410841\pi\) |
−0.961027 | + | 0.276454i | \(0.910841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000 | + | 2.00000i | 0.0945968 | + | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.5826i | − | 0.924159i | −0.886839 | − | 0.462079i | \(-0.847103\pi\) | ||
0.886839 | − | 0.462079i | \(-0.152897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.44600 | 0.0680895 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.2813 | + | 32.2813i | −1.51671 | + | 1.51671i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5826 | + | 12.5826i | −0.588588 | + | 0.588588i | −0.937249 | − | 0.348661i | \(-0.886636\pi\) |
0.348661 | + | 0.937249i | \(0.386636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 47.0514i | − | 2.19617i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.65480i | 0.170221i | 0.996372 | + | 0.0851106i | \(0.0271243\pi\) | ||||
−0.996372 | + | 0.0851106i | \(0.972876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2087 | − | 12.2087i | 0.567387 | − | 0.567387i | −0.364009 | − | 0.931396i | \(-0.618592\pi\) |
0.931396 | + | 0.364009i | \(0.118592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2360 | − | 16.2360i | 0.751313 | − | 0.751313i | −0.223411 | − | 0.974724i | \(-0.571719\pi\) |
0.974724 | + | 0.223411i | \(0.0717193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.29510 | 0.0598022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 19.5826i | − | 0.902317i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.330303 | + | 0.330303i | 0.0151873 | + | 0.0151873i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.4159 | + | 17.4159i | 0.797417 | + | 0.797417i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.4955 | 1.53045 | 0.765223 | − | 0.643765i | \(-0.222629\pi\) | ||||
0.765223 | + | 0.643765i | \(0.222629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.7309 | + | 29.7309i | 1.35280 | + | 1.35280i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3739 | + | 13.3739i | 0.606028 | + | 0.606028i | 0.941906 | − | 0.335878i | \(-0.109033\pi\) |
−0.335878 | + | 0.941906i | \(0.609033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.58258i | 0.0715665i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.1805 | −1.22664 | −0.613320 | − | 0.789835i | \(-0.710166\pi\) | ||||
−0.613320 | + | 0.789835i | \(0.710166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.8745 | + | 15.8745i | −0.714952 | + | 0.714952i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.91288 | − | 7.91288i | 0.354941 | − | 0.354941i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 69.1311i | 3.08855i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.5390 | − | 14.5390i | 0.648263 | − | 0.648263i | −0.304310 | − | 0.952573i | \(-0.598426\pi\) |
0.952573 | + | 0.304310i | \(0.0984260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3223 | + | 15.3223i | −0.680488 | + | 0.680488i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.84550 | −0.170449 | −0.0852244 | − | 0.996362i | \(-0.527161\pi\) | ||||
−0.0852244 | + | 0.996362i | \(0.527161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 30.7477i | − | 1.36020i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.1652 | − | 27.1652i | −1.19937 | − | 1.19937i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.46410 | + | 3.46410i | 0.152351 | + | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.9129 | 1.66419 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8348 | −0.649927 | −0.324963 | − | 0.945727i | \(-0.605352\pi\) | ||||
−0.324963 | + | 0.945727i | \(0.605352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8872 | + | 23.8872i | 1.04451 | + | 1.04451i | 0.998962 | + | 0.0455529i | \(0.0145050\pi\) |
0.0455529 | + | 0.998962i | \(0.485495\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.7477 | − | 22.7477i | −0.990907 | − | 0.990907i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5.74773i | − | 0.249901i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.8317 | −1.51157 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.74110 | + | 2.74110i | −0.118730 | + | 0.118730i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.9129 | − | 41.9129i | 1.80867 | − | 1.80867i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.532300i | − | 0.0229278i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1652 | − | 15.1652i | 0.650799 | − | 0.650799i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1642 | − | 23.1642i | 0.990430 | − | 0.990430i | −0.00952449 | − | 0.999955i | \(-0.503032\pi\) |
0.999955 | + | 0.00952449i | \(0.00303179\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.8462 | −1.74327 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.3303i | 0.780897i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.4955 | − | 21.4955i | −0.914080 | − | 0.914080i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.8800 | − | 20.8800i | −0.884712 | − | 0.884712i | 0.109297 | − | 0.994009i | \(-0.465140\pi\) |
−0.994009 | + | 0.109297i | \(0.965140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.25227 | −0.0529655 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6675 | − | 11.6675i | −0.491727 | − | 0.491727i | 0.417123 | − | 0.908850i | \(-0.363038\pi\) |
−0.908850 | + | 0.417123i | \(0.863038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.1216 | + | 26.1216i | 1.09700 | + | 1.09700i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.7477i | 0.953634i | 0.879002 | + | 0.476817i | \(0.158210\pi\) | ||||
−0.879002 | + | 0.476817i | \(0.841790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.22330 | 0.344135 | 0.172067 | − | 0.985085i | \(-0.444955\pi\) | ||||
0.172067 | + | 0.985085i | \(0.444955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.66930 | − | 9.66930i | 0.403941 | − | 0.403941i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7477 | + | 15.7477i | −0.655586 | + | 0.655586i | −0.954333 | − | 0.298746i | \(-0.903432\pi\) |
0.298746 | + | 0.954333i | \(0.403432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.2342i | 0.757788i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.1153i | − | 0.461141i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.41742 | − | 2.41742i | 0.100119 | − | 0.100119i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.54860 | + | 4.54860i | −0.187741 | + | 0.187741i | −0.794719 | − | 0.606978i | \(-0.792382\pi\) |
0.606978 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.2668 | −1.08231 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5826i | 0.476444i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.1652 | + | 18.1652i | 0.745953 | + | 0.745953i | 0.973717 | − | 0.227763i | \(-0.0731412\pi\) |
−0.227763 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.75560 | − | 8.75560i | −0.358343 | − | 0.358343i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.66970 | 0.231658 | 0.115829 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115829 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7477 | 1.00948 | 0.504740 | − | 0.863271i | \(-0.331588\pi\) | ||||
0.504740 | + | 0.863271i | \(0.331588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.37960 | − | 2.37960i | −0.0969049 | − | 0.0969049i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.37386 | − | 7.37386i | −0.299296 | − | 0.299296i | 0.541442 | − | 0.840738i | \(-0.317879\pi\) |
−0.840738 | + | 0.541442i | \(0.817879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 41.4955i | − | 1.68148i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.1334 | −0.531321 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.66025 | + | 8.66025i | −0.349784 | + | 0.349784i | −0.860029 | − | 0.510245i | \(-0.829555\pi\) |
0.510245 | + | 0.860029i | \(0.329555\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | + | 3.00000i | −0.120775 | + | 0.120775i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) |
0.644136 | + | 0.764911i | \(0.277217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.01810i | − | 0.0811143i | −0.999177 | − | 0.0405572i | \(-0.987087\pi\) | ||
0.999177 | − | 0.0405572i | \(-0.0129133\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 59.4618i | − | 2.38612i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.1652 | + | 27.1652i | −1.08835 | + | 1.08835i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.92820 | + | 6.92820i | −0.276686 | + | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1769 | 1.24310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.0780i | − | 0.679866i | −0.940450 | − | 0.339933i | \(-0.889596\pi\) | ||
0.940450 | − | 0.339933i | \(-0.110404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 51.4955 | + | 51.4955i | 2.04676 | + | 2.04676i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00905 | + | 1.00905i | 0.0399800 | + | 0.0399800i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.0780 | −1.15031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9129 | −0.786511 | −0.393256 | − | 0.919429i | \(-0.628651\pi\) | ||||
−0.393256 | + | 0.919429i | \(0.628651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.7538 | − | 10.7538i | −0.424089 | − | 0.424089i | 0.462520 | − | 0.886609i | \(-0.346945\pi\) |
−0.886609 | + | 0.462520i | \(0.846945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.5390 | + | 32.5390i | 1.27924 | + | 1.27924i | 0.941093 | + | 0.338148i | \(0.109800\pi\) |
0.338148 | + | 0.941093i | \(0.390200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.83485i | 0.189784i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.4618 | 2.33049 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.47315 | − | 4.47315i | 0.175048 | − | 0.175048i | −0.614145 | − | 0.789193i | \(-0.710499\pi\) |
0.789193 | + | 0.614145i | \(0.210499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −56.4955 | + | 56.4955i | −2.20410 | + | 2.20410i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.4865i | − | 1.49922i | −0.661879 | − | 0.749611i | \(-0.730241\pi\) | ||
0.661879 | − | 0.749611i | \(-0.269759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.9542i | − | 1.47625i | −0.674665 | − | 0.738124i | \(-0.735712\pi\) | ||
0.674665 | − | 0.738124i | \(-0.264288\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.7477 | − | 22.7477i | 0.883449 | − | 0.883449i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0616 | + | 20.0616i | −0.776789 | + | 0.776789i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.01450 | −0.232534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.66970i | 0.218876i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.41742 | + | 9.41742i | 0.363015 | + | 0.363015i | 0.864922 | − | 0.501907i | \(-0.167368\pi\) |
−0.501907 | + | 0.864922i | \(0.667368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.45505 | − | 2.45505i | −0.0943553 | − | 0.0943553i | 0.658354 | − | 0.752709i | \(-0.271253\pi\) |
−0.752709 | + | 0.658354i | \(0.771253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.7477 | −1.17999 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −51.9129 | −1.98931 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.8335 | − | 32.8335i | −1.25634 | − | 1.25634i | −0.952828 | − | 0.303512i | \(-0.901841\pi\) |
−0.303512 | − | 0.952828i | \(-0.598159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.58258 | + | 7.58258i | 0.289293 | + | 0.289293i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.16515i | 0.349164i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1515 | −0.576391 | −0.288195 | − | 0.957572i | \(-0.593055\pi\) | ||||
−0.288195 | + | 0.957572i | \(0.593055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7737 | − | 10.7737i | 0.409259 | − | 0.409259i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.74773 | + | 4.74773i | −0.179833 | + | 0.179833i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.2566i | 2.01435i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1624i | 0.950371i | 0.879886 | + | 0.475186i | \(0.157619\pi\) | ||||
−0.879886 | + | 0.475186i | \(0.842381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | − | 18.0000i | 0.678883 | − | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.3676 | + | 31.3676i | −1.17970 | + | 1.17970i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6591 | 1.37676 | 0.688381 | − | 0.725349i | \(-0.258322\pi\) | ||||
0.688381 | + | 0.725349i | \(0.258322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 78.9909i | 2.96239i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.7477 | − | 28.7477i | −1.07661 | − | 1.07661i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.1950 | − | 33.1950i | −1.23969 | − | 1.23969i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.8258 | −1.93277 | −0.966387 | − | 0.257091i | \(-0.917236\pi\) | ||||
−0.966387 | + | 0.257091i | \(0.917236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0871 | −0.450148 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6591 | + | 36.6591i | 1.36337 | + | 1.36337i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9564 | − | 16.9564i | −0.628880 | − | 0.628880i | 0.318907 | − | 0.947786i | \(-0.396684\pi\) |
−0.947786 | + | 0.318907i | \(0.896684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.16900 | −0.0802234 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1425 | − | 14.1425i | 0.522364 | − | 0.522364i | −0.395921 | − | 0.918285i | \(-0.629575\pi\) |
0.918285 | + | 0.395921i | \(0.129575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.330303 | + | 0.330303i | −0.0121669 | + | 0.0121669i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7309i | 1.09367i | 0.837241 | + | 0.546835i | \(0.184167\pi\) | ||||
−0.837241 | + | 0.546835i | \(0.815833\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 26.2668i | − | 0.964935i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.7913 | − | 21.7913i | 0.799445 | − | 0.799445i | −0.183563 | − | 0.983008i | \(-0.558763\pi\) |
0.983008 | + | 0.183563i | \(0.0587632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.4231 | + | 20.4231i | −0.747243 | + | 0.747243i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29510 | 0.0473220 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41.0780i | − | 1.49896i | −0.662028 | − | 0.749479i | \(-0.730304\pi\) | ||
0.662028 | − | 0.749479i | \(-0.269696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.3303 | + | 28.3303i | 1.03241 | + | 1.03241i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.2759 | + | 27.2759i | 0.991358 | + | 0.991358i | 0.999963 | − | 0.00860486i | \(-0.00273905\pi\) |
−0.00860486 | + | 0.999963i | \(0.502739\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.1652 | −0.550460 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.3205 | + | 17.3205i | 0.627044 | + | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.16515 | − | 9.16515i | −0.330934 | − | 0.330934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4955i | 0.630902i | 0.948942 | + | 0.315451i | \(0.102156\pi\) | ||||
−0.948942 | + | 0.315451i | \(0.897844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.9180 | −1.22153 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.4630 | − | 31.4630i | 1.13164 | − | 1.13164i | 0.141740 | − | 0.989904i | \(-0.454730\pi\) |
0.989904 | − | 0.141740i | \(-0.0452698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −40.7477 | + | 40.7477i | −1.46182 | + | 1.46182i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.48220i | 0.196420i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.03620i | 0.144427i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.4955 | + | 41.4955i | −1.48293 | + | 1.48293i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9771 | − | 18.9771i | 0.676461 | − | 0.676461i | −0.282737 | − | 0.959198i | \(-0.591242\pi\) |
0.959198 | + | 0.282737i | \(0.0912423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −62.2029 | −2.21448 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4174i | 0.583736i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7477 | − | 10.7477i | −0.381663 | − | 0.381663i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.17805 | − | 3.17805i | −0.112572 | − | 0.112572i | 0.648577 | − | 0.761149i | \(-0.275365\pi\) |
−0.761149 | + | 0.648577i | \(0.775365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7477 | −0.804757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 99.8258 | 3.52717 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.84190 | + | 7.84190i | 0.276735 | + | 0.276735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.1652 | − | 29.1652i | −1.02666 | − | 1.02666i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.33030i | − | 0.222562i | −0.993789 | − | 0.111281i | \(-0.964505\pi\) | ||
0.993789 | − | 0.111281i | \(-0.0354953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.7925 | −1.74845 | −0.874226 | − | 0.485519i | \(-0.838631\pi\) | ||||
−0.874226 | + | 0.485519i | \(0.838631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.0369 | + | 41.0369i | −1.43923 | + | 1.43923i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.25227 | + | 1.25227i | −0.0438115 | + | 0.0438115i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 40.8462i | 1.42728i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 17.8528i | − | 0.623067i | −0.950235 | − | 0.311534i | \(-0.899157\pi\) | ||
0.950235 | − | 0.311534i | \(-0.100843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.79129 | + | 7.79129i | −0.271587 | + | 0.271587i | −0.829739 | − | 0.558152i | \(-0.811511\pi\) |
0.558152 | + | 0.829739i | \(0.311511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.6428 | + | 32.6428i | −1.13510 | + | 1.13510i | −0.145786 | + | 0.989316i | \(0.546571\pi\) |
−0.989316 | + | 0.145786i | \(0.953429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.5257 | −0.817082 | −0.408541 | − | 0.912740i | \(-0.633962\pi\) | ||||
−0.408541 | + | 0.912740i | \(0.633962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 95.4083i | 3.30968i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.74773 | + | 1.74773i | 0.0605552 | + | 0.0605552i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −59.4618 | − | 59.4618i | −2.05530 | − | 2.05530i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.33030 | 0.218546 | 0.109273 | − | 0.994012i | \(-0.465148\pi\) | ||||
0.109273 | + | 0.994012i | \(0.465148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | −0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.6591 | + | 36.6591i | 1.26261 | + | 1.26261i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2087 | + | 18.2087i | 0.625659 | + | 0.625659i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 98.2432i | 3.37170i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.4002 | 1.35062 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5529 | + | 26.5529i | −0.909153 | + | 0.909153i | −0.996204 | − | 0.0870511i | \(-0.972256\pi\) |
0.0870511 | + | 0.996204i | \(0.472256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.66970 | + | 2.66970i | −0.0911951 | + | 0.0911951i | −0.751233 | − | 0.660038i | \(-0.770540\pi\) |
0.660038 | + | 0.751233i | \(0.270540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 29.7309i | − | 1.01441i | −0.861827 | − | 0.507203i | \(-0.830679\pi\) | ||
0.861827 | − | 0.507203i | \(-0.169321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 12.4104i | − | 0.422946i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7042 | − | 17.7042i | 0.602657 | − | 0.602657i | −0.338360 | − | 0.941017i | \(-0.609872\pi\) |
0.941017 | + | 0.338360i | \(0.109872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.18890 | − | 2.18890i | 0.0743390 | − | 0.0743390i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9644 | 0.371942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.25227i | − | 0.0424316i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 56.4955 | + | 56.4955i | 1.91208 | + | 1.91208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.6501 | + | 35.6501i | 1.20382 | + | 1.20382i | 0.972996 | + | 0.230821i | \(0.0741412\pi\) |
0.230821 | + | 0.972996i | \(0.425859\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 79.4083 | 2.67838 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.4174 | −1.56384 | −0.781921 | − | 0.623377i | \(-0.785760\pi\) | ||||
−0.781921 | + | 0.623377i | \(0.785760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.2179 | + | 14.2179i | 0.478471 | + | 0.478471i | 0.904642 | − | 0.426172i | \(-0.140138\pi\) |
−0.426172 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.956439 | − | 0.956439i | −0.0321141 | − | 0.0321141i | 0.690867 | − | 0.722981i | \(-0.257229\pi\) |
−0.722981 | + | 0.690867i | \(0.757229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7477i | 0.695856i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.3241 | −0.446374 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.1334 | + | 13.1334i | −0.439493 | + | 0.439493i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.7477 | − | 28.7477i | 0.959859 | − | 0.959859i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.1232i | 1.33818i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8745i | 0.528857i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.83485 | − | 2.83485i | 0.0943379 | − | 0.0943379i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7719 | + | 12.7719i | −0.424084 | + | 0.424084i | −0.886607 | − | 0.462523i | \(-0.846944\pi\) |
0.462523 | + | 0.886607i | \(0.346944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 115.269 | 3.82323 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.4174i | − | 1.33909i | −0.742772 | − | 0.669545i | \(-0.766489\pi\) | ||
0.742772 | − | 0.669545i | \(-0.233511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.83485 | + | 2.83485i | 0.0938198 | + | 0.0938198i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7737 | + | 10.7737i | 0.355779 | + | 0.355779i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.66970 | 0.187026 | 0.0935130 | − | 0.995618i | \(-0.470190\pi\) | ||||
0.0935130 | + | 0.995618i | \(0.470190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.7477 | 0.947270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.65120 | − | 7.65120i | −0.251842 | − | 0.251842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.2087 | + | 22.2087i | 0.729430 | + | 0.729430i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.9129i | 0.850174i | 0.905153 | + | 0.425087i | \(0.139756\pi\) | ||||
−0.905153 | + | 0.425087i | \(0.860244\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.01810 | 0.0661406 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.8643 | + | 42.8643i | −1.40331 | + | 1.40331i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8348 | + | 15.8348i | −0.517302 | + | 0.517302i | −0.916754 | − | 0.399452i | \(-0.869200\pi\) |
0.399452 | + | 0.916754i | \(0.369200\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.8172i | 0.940414i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.27340i | − | 0.106710i | −0.998576 | − | 0.0533549i | \(-0.983009\pi\) | ||
0.998576 | − | 0.0533549i | \(-0.0169915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | + | 6.00000i | −0.195387 | + | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.2831 | + | 30.2831i | −0.984069 | + | 0.984069i | −0.999875 | − | 0.0158061i | \(-0.994969\pi\) |
0.0158061 | + | 0.999875i | \(0.494969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.7309 | −0.965106 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 61.9129i | − | 2.00766i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.9129 | − | 34.9129i | −1.13094 | − | 1.13094i | −0.990021 | − | 0.140918i | \(-0.954995\pi\) |
−0.140918 | − | 0.990021i | \(-0.545005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.5830 | + | 10.5830i | 0.342100 | + | 0.342100i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.0871 | −0.713230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4955 | −0.854692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.37960 | − | 2.37960i | −0.0766816 | − | 0.0766816i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.20871 | − | 4.20871i | −0.135343 | − | 0.135343i | 0.636190 | − | 0.771533i | \(-0.280510\pi\) |
−0.771533 | + | 0.636190i | \(0.780510\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 45.4955i | − | 1.46152i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.532300 | −0.0170823 | −0.00854116 | − | 0.999964i | \(-0.502719\pi\) | ||||
−0.00854116 | + | 0.999964i | \(0.502719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8462 | + | 40.8462i | −1.30947 | + | 1.30947i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.4174 | + | 19.4174i | −0.621218 | + | 0.621218i | −0.945843 | − | 0.324625i | \(-0.894762\pi\) |
0.324625 | + | 0.945843i | \(0.394762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.8564i | − | 0.442853i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 63.6489i | − | 2.03215i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.7042 | + | 23.7042i | −0.756045 | + | 0.756045i | −0.975600 | − | 0.219555i | \(-0.929540\pi\) |
0.219555 | + | 0.975600i | \(0.429540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.7309 | − | 29.7309i | 0.946345 | − | 0.946345i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.74110 | −0.0871620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.7477i | 0.976734i | 0.872638 | + | 0.488367i | \(0.162407\pi\) | ||||
−0.872638 | + | 0.488367i | \(0.837593\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.1652 | − | 21.1652i | −0.671656 | − | 0.671656i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1425 | − | 14.1425i | −0.447896 | − | 0.447896i | 0.446758 | − | 0.894655i | \(-0.352578\pi\) |
−0.894655 | + | 0.446758i | \(0.852578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 81.4955 | 2.57840 |
(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 | 1600.2.o.l.543.4 | 8 | ||
4.3 | odd | 2 | 1600.2.o.e.543.1 | 8 | |||
5.2 | odd | 4 | 1600.2.o.e.607.4 | 8 | |||
5.3 | odd | 4 | 320.2.o.f.287.1 | yes | 8 | ||
5.4 | even | 2 | 320.2.o.e.223.1 | ✓ | 8 | ||
8.3 | odd | 2 | 1600.2.o.e.543.4 | 8 | |||
8.5 | even | 2 | inner | 1600.2.o.l.543.1 | 8 | ||
20.3 | even | 4 | 320.2.o.e.287.4 | yes | 8 | ||
20.7 | even | 4 | inner | 1600.2.o.l.607.1 | 8 | ||
20.19 | odd | 2 | 320.2.o.f.223.4 | yes | 8 | ||
40.3 | even | 4 | 320.2.o.e.287.1 | yes | 8 | ||
40.13 | odd | 4 | 320.2.o.f.287.4 | yes | 8 | ||
40.19 | odd | 2 | 320.2.o.f.223.1 | yes | 8 | ||
40.27 | even | 4 | inner | 1600.2.o.l.607.4 | 8 | ||
40.29 | even | 2 | 320.2.o.e.223.4 | yes | 8 | ||
40.37 | odd | 4 | 1600.2.o.e.607.1 | 8 | |||
80.3 | even | 4 | 1280.2.n.p.767.4 | 8 | |||
80.13 | odd | 4 | 1280.2.n.n.767.1 | 8 | |||
80.19 | odd | 4 | 1280.2.n.n.1023.1 | 8 | |||
80.29 | even | 4 | 1280.2.n.p.1023.4 | 8 | |||
80.43 | even | 4 | 1280.2.n.p.767.1 | 8 | |||
80.53 | odd | 4 | 1280.2.n.n.767.4 | 8 | |||
80.59 | odd | 4 | 1280.2.n.n.1023.4 | 8 | |||
80.69 | even | 4 | 1280.2.n.p.1023.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.o.e.223.1 | ✓ | 8 | 5.4 | even | 2 | ||
320.2.o.e.223.4 | yes | 8 | 40.29 | even | 2 | ||
320.2.o.e.287.1 | yes | 8 | 40.3 | even | 4 | ||
320.2.o.e.287.4 | yes | 8 | 20.3 | even | 4 | ||
320.2.o.f.223.1 | yes | 8 | 40.19 | odd | 2 | ||
320.2.o.f.223.4 | yes | 8 | 20.19 | odd | 2 | ||
320.2.o.f.287.1 | yes | 8 | 5.3 | odd | 4 | ||
320.2.o.f.287.4 | yes | 8 | 40.13 | odd | 4 | ||
1280.2.n.n.767.1 | 8 | 80.13 | odd | 4 | |||
1280.2.n.n.767.4 | 8 | 80.53 | odd | 4 | |||
1280.2.n.n.1023.1 | 8 | 80.19 | odd | 4 | |||
1280.2.n.n.1023.4 | 8 | 80.59 | odd | 4 | |||
1280.2.n.p.767.1 | 8 | 80.43 | even | 4 | |||
1280.2.n.p.767.4 | 8 | 80.3 | even | 4 | |||
1280.2.n.p.1023.1 | 8 | 80.69 | even | 4 | |||
1280.2.n.p.1023.4 | 8 | 80.29 | even | 4 | |||
1600.2.o.e.543.1 | 8 | 4.3 | odd | 2 | |||
1600.2.o.e.543.4 | 8 | 8.3 | odd | 2 | |||
1600.2.o.e.607.1 | 8 | 40.37 | odd | 4 | |||
1600.2.o.e.607.4 | 8 | 5.2 | odd | 4 | |||
1600.2.o.l.543.1 | 8 | 8.5 | even | 2 | inner | ||
1600.2.o.l.543.4 | 8 | 1.1 | even | 1 | trivial | ||
1600.2.o.l.607.1 | 8 | 20.7 | even | 4 | inner | ||
1600.2.o.l.607.4 | 8 | 40.27 | even | 4 | inner |