Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(19,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bf (of order \(6\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(1.39564 + 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.199 |
Dual form | 252.2.bf.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39564 | + | 0.228425i | −0.986869 | + | 0.161521i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.89564 | − | 0.637600i | 0.947822 | − | 0.318800i | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29129 | + | 1.32288i | 0.866025 | + | 0.500000i | ||||
\(8\) | −2.50000 | + | 1.32288i | −0.883883 | + | 0.467707i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.89564 | + | 1.55130i | −0.599455 | + | 0.490564i | ||||
\(11\) | −2.29129 | − | 1.32288i | −0.690849 | − | 0.398862i | 0.113081 | − | 0.993586i | \(-0.463928\pi\) |
−0.803930 | + | 0.594724i | \(0.797261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | −3.50000 | − | 1.32288i | −0.935414 | − | 0.353553i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.18693 | − | 2.41733i | 0.796733 | − | 0.604332i | ||||
\(17\) | 6.00000 | + | 3.46410i | 1.45521 | + | 0.840168i | 0.998770 | − | 0.0495842i | \(-0.0157896\pi\) |
0.456444 | + | 0.889752i | \(0.349123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 2.29129 | − | 2.59808i | 0.512348 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.50000 | + | 1.32288i | 0.746203 | + | 0.282038i | ||||
\(23\) | 4.58258 | − | 2.64575i | 0.955533 | − | 0.551677i | 0.0607377 | − | 0.998154i | \(-0.480655\pi\) |
0.894795 | + | 0.446476i | \(0.147321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0.791288 | + | 4.83465i | 0.155184 | + | 0.948153i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.18693 | + | 1.04678i | 0.980238 | + | 0.197822i | ||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.29129 | + | 3.96863i | −0.411527 | + | 0.712786i | −0.995057 | − | 0.0993055i | \(-0.968338\pi\) |
0.583530 | + | 0.812092i | \(0.301671\pi\) | |||||||
\(32\) | −3.89564 | + | 4.10170i | −0.688659 | + | 0.725085i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.16515 | − | 3.46410i | −1.57181 | − | 0.594089i | ||||
\(35\) | 4.58258 | 0.774597 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.60436 | + | 4.14938i | −0.411785 | + | 0.656074i | ||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.5830i | − | 1.61389i | −0.590624 | − | 0.806947i | \(-0.701119\pi\) | ||
0.590624 | − | 0.806947i | \(-0.298881\pi\) | |||||||
\(44\) | −5.18693 | − | 1.04678i | −0.781959 | − | 0.157807i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.79129 | + | 4.73930i | −0.853879 | + | 0.698772i | ||||
\(47\) | −4.58258 | − | 7.93725i | −0.668437 | − | 1.15777i | −0.978341 | − | 0.207000i | \(-0.933630\pi\) |
0.309904 | − | 0.950768i | \(-0.399703\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | 1.00000 | − | 2.64575i | 0.141421 | − | 0.374166i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.20871 | − | 6.56670i | −0.306293 | − | 0.910638i | ||||
\(53\) | −3.50000 | + | 6.06218i | −0.480762 | + | 0.832704i | −0.999756 | − | 0.0220735i | \(-0.992973\pi\) |
0.518994 | + | 0.854778i | \(0.326307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.58258 | −0.617914 | ||||||||
\(56\) | −7.47822 | − | 0.276100i | −0.999319 | − | 0.0368954i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.97822 | + | 1.14213i | −0.916285 | + | 0.149968i | ||||
\(59\) | −6.87386 | + | 11.9059i | −0.894901 | + | 1.55001i | −0.0609735 | + | 0.998139i | \(0.519421\pi\) |
−0.833927 | + | 0.551874i | \(0.813913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | + | 5.19615i | −1.15233 | + | 0.665299i | −0.949454 | − | 0.313905i | \(-0.898363\pi\) |
−0.202878 | + | 0.979204i | \(0.565029\pi\) | |||||||
\(62\) | 2.29129 | − | 6.06218i | 0.290994 | − | 0.769897i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.50000 | − | 6.61438i | 0.562500 | − | 0.826797i | ||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 13.5826 | + | 2.74110i | 1.64713 | + | 0.332407i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.39564 | + | 1.04678i | −0.764426 | + | 0.125114i | ||||
\(71\) | 5.29150i | 0.627986i | 0.949425 | + | 0.313993i | \(0.101667\pi\) | ||||
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 3.46410i | −0.702247 | − | 0.405442i | 0.105937 | − | 0.994373i | \(-0.466216\pi\) |
−0.808184 | + | 0.588930i | \(0.799549\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.50000 | − | 6.06218i | −0.398862 | − | 0.690849i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.87386 | + | 3.96863i | −0.773370 | + | 0.446505i | −0.834075 | − | 0.551650i | \(-0.813998\pi\) |
0.0607054 | + | 0.998156i | \(0.480665\pi\) | |||||||
\(80\) | 2.68693 | − | 6.38595i | 0.300408 | − | 0.713971i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.791288 | + | 4.83465i | 0.0873831 | + | 0.533898i | ||||
\(83\) | −4.58258 | −0.503003 | −0.251502 | − | 0.967857i | \(-0.580924\pi\) | ||||
−0.251502 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 2.41742 | + | 14.7701i | 0.260678 | + | 1.59270i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.47822 | + | 0.276100i | 0.797181 | + | 0.0294324i | ||||
\(89\) | −9.00000 | + | 5.19615i | −0.953998 | + | 0.550791i | −0.894321 | − | 0.447427i | \(-0.852341\pi\) |
−0.0596775 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.58258 | − | 7.93725i | 0.480384 | − | 0.832050i | ||||
\(92\) | 7.00000 | − | 7.93725i | 0.729800 | − | 0.827516i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.20871 | + | 10.0308i | 0.846664 | + | 1.03460i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.66025i | − | 0.879316i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) | ||
0.898165 | − | 0.439658i | \(-0.144900\pi\) | |||||||
\(98\) | −6.26951 | − | 7.66115i | −0.633316 | − | 0.773893i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.791288 | + | 3.92095i | −0.0791288 | + | 0.392095i | ||||
\(101\) | −6.00000 | − | 3.46410i | −0.597022 | − | 0.344691i | 0.170847 | − | 0.985298i | \(-0.445350\pi\) |
−0.767869 | + | 0.640607i | \(0.778683\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16515 | + | 15.8745i | 0.903069 | + | 1.56416i | 0.823488 | + | 0.567333i | \(0.192025\pi\) |
0.0795810 | + | 0.996828i | \(0.474642\pi\) | |||||||
\(104\) | 4.58258 | + | 8.66025i | 0.449359 | + | 0.849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.50000 | − | 9.26013i | 0.339950 | − | 0.899423i | ||||
\(107\) | 16.0390 | − | 9.26013i | 1.55055 | − | 0.895211i | 0.552453 | − | 0.833544i | \(-0.313692\pi\) |
0.998097 | − | 0.0616667i | \(-0.0196416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 6.39564 | − | 1.04678i | 0.609801 | − | 0.0998061i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5000 | − | 1.32288i | 0.992157 | − | 0.125000i | ||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.58258 | − | 7.93725i | 0.427327 | − | 0.740153i | ||||
\(116\) | 9.47822 | − | 3.18800i | 0.880031 | − | 0.295998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.87386 | − | 18.1865i | 0.632790 | − | 1.67421i | ||||
\(119\) | 9.16515 | + | 15.8745i | 0.840168 | + | 1.45521i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | − | 3.46410i | −0.181818 | − | 0.314918i | ||||
\(122\) | 11.3739 | − | 9.30780i | 1.02974 | − | 0.842689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.81307 | + | 8.98403i | −0.162818 | + | 0.806790i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.93725i | 0.704317i | 0.935940 | + | 0.352159i | \(0.114552\pi\) | ||||
−0.935940 | + | 0.352159i | \(0.885448\pi\) | |||||||
\(128\) | −4.76951 | + | 10.2592i | −0.421569 | + | 0.906796i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.37386 | + | 6.56670i | 0.471319 | + | 0.575938i | ||||
\(131\) | −6.87386 | − | 11.9059i | −0.600572 | − | 1.04022i | −0.992734 | − | 0.120326i | \(-0.961606\pi\) |
0.392162 | − | 0.919896i | \(-0.371727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.5826 | − | 0.723000i | −1.67919 | − | 0.0619967i | ||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.16515 | −0.777378 | −0.388689 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388689 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(140\) | 8.68693 | − | 2.92185i | 0.734180 | − | 0.246942i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.20871 | − | 7.38505i | −0.101433 | − | 0.619740i | ||||
\(143\) | −4.58258 | + | 7.93725i | −0.383214 | + | 0.663747i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.50000 | − | 4.33013i | 0.622841 | − | 0.359597i | ||||
\(146\) | 9.16515 | + | 3.46410i | 0.758513 | + | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.00000 | − | 12.1244i | −0.573462 | − | 0.993266i | −0.996207 | − | 0.0870170i | \(-0.972267\pi\) |
0.422744 | − | 0.906249i | \(-0.361067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4564 | + | 6.61438i | 0.932312 | + | 0.538270i | 0.887542 | − | 0.460727i | \(-0.152411\pi\) |
0.0447698 | + | 0.998997i | \(0.485745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.26951 | + | 7.66115i | 0.505211 | + | 0.617353i | ||||
\(155\) | 7.93725i | 0.637536i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | + | 3.46410i | 0.478852 | + | 0.276465i | 0.719938 | − | 0.694038i | \(-0.244170\pi\) |
−0.241086 | + | 0.970504i | \(0.577504\pi\) | |||||||
\(158\) | 8.68693 | − | 7.10895i | 0.691095 | − | 0.565558i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.29129 | + | 9.52628i | −0.181142 | + | 0.753119i | ||||
\(161\) | 14.0000 | 1.10335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7477 | − | 7.93725i | 1.07681 | − | 0.621694i | 0.146772 | − | 0.989170i | \(-0.453112\pi\) |
0.930033 | + | 0.367477i | \(0.119778\pi\) | |||||||
\(164\) | −2.20871 | − | 6.56670i | −0.172471 | − | 0.512773i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.39564 | − | 1.04678i | 0.496398 | − | 0.0812455i | ||||
\(167\) | −18.3303 | −1.41844 | −0.709221 | − | 0.704987i | \(-0.750953\pi\) | ||||
−0.709221 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −16.7477 | + | 2.74110i | −1.28449 | + | 0.210233i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.74773 | − | 20.0616i | −0.514509 | − | 1.52968i | ||||
\(173\) | −12.0000 | + | 6.92820i | −0.912343 | + | 0.526742i | −0.881184 | − | 0.472773i | \(-0.843253\pi\) |
−0.0311588 | + | 0.999514i | \(0.509920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.58258 | + | 2.64575i | −0.346410 | + | 0.200000i | ||||
\(176\) | −10.5000 | + | 1.32288i | −0.791467 | + | 0.0997155i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.3739 | − | 9.30780i | 0.852507 | − | 0.697649i | ||||
\(179\) | −4.58258 | − | 2.64575i | −0.342518 | − | 0.197753i | 0.318867 | − | 0.947799i | \(-0.396698\pi\) |
−0.661385 | + | 0.750047i | \(0.730031\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | −4.58258 | + | 12.1244i | −0.339683 | + | 0.898717i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.95644 | + | 12.6766i | −0.586556 | + | 0.934528i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.16515 | − | 15.8745i | −0.670222 | − | 1.16086i | ||||
\(188\) | −13.7477 | − | 12.1244i | −1.00266 | − | 0.884260i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.16515 | − | 5.29150i | 0.663167 | − | 0.382880i | −0.130316 | − | 0.991473i | \(-0.541599\pi\) |
0.793483 | + | 0.608593i | \(0.208266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.50000 | + | 2.59808i | −0.107972 | + | 0.187014i | −0.914949 | − | 0.403570i | \(-0.867769\pi\) |
0.806976 | + | 0.590584i | \(0.201102\pi\) | |||||||
\(194\) | 1.97822 | + | 12.0866i | 0.142028 | + | 0.867770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5000 | + | 9.26013i | 0.750000 | + | 0.661438i | ||||
\(197\) | 14.0000 | 0.997459 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.16515 | + | 15.8745i | −0.649700 | + | 1.12531i | 0.333494 | + | 0.942752i | \(0.391772\pi\) |
−0.983194 | + | 0.182562i | \(0.941561\pi\) | |||||||
\(200\) | 0.208712 | − | 5.65300i | 0.0147582 | − | 0.399728i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.16515 | + | 3.46410i | 0.644858 | + | 0.243733i | ||||
\(203\) | 11.4564 | + | 6.61438i | 0.804084 | + | 0.464238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −16.4174 | − | 20.0616i | −1.14386 | − | 1.39776i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.37386 | − | 11.0399i | −0.580623 | − | 0.765476i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.29150i | − | 0.364282i | −0.983272 | − | 0.182141i | \(-0.941697\pi\) | ||
0.983272 | − | 0.182141i | \(-0.0583027\pi\) | |||||||
\(212\) | −2.76951 | + | 13.7233i | −0.190211 | + | 0.942522i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.2695 | + | 16.5876i | −1.38560 | + | 1.13390i | ||||
\(215\) | −9.16515 | − | 15.8745i | −0.625058 | − | 1.08263i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5000 | + | 6.06218i | −0.712786 | + | 0.411527i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.68693 | + | 2.92185i | −0.585673 | + | 0.196991i | ||||
\(221\) | 12.0000 | − | 20.7846i | 0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.58258 | −0.306872 | −0.153436 | − | 0.988159i | \(-0.549034\pi\) | ||||
−0.153436 | + | 0.988159i | \(0.549034\pi\) | |||||||
\(224\) | −14.3521 | + | 4.24473i | −0.958939 | + | 0.283613i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.5390 | − | 3.19795i | 1.29972 | − | 0.212725i | ||||
\(227\) | 2.29129 | − | 3.96863i | 0.152078 | − | 0.263407i | −0.779913 | − | 0.625888i | \(-0.784737\pi\) |
0.931991 | + | 0.362481i | \(0.118070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.00000 | + | 5.19615i | −0.594737 | + | 0.343371i | −0.766968 | − | 0.641685i | \(-0.778236\pi\) |
0.172231 | + | 0.985057i | \(0.444902\pi\) | |||||||
\(230\) | −4.58258 | + | 12.1244i | −0.302166 | + | 0.799456i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.5000 | + | 6.61438i | −0.820665 | + | 0.434255i | ||||
\(233\) | 10.0000 | + | 17.3205i | 0.655122 | + | 1.13470i | 0.981863 | + | 0.189590i | \(0.0607160\pi\) |
−0.326741 | + | 0.945114i | \(0.605951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.7477 | − | 7.93725i | −0.896803 | − | 0.517769i | ||||
\(236\) | −5.43920 | + | 26.9521i | −0.354062 | + | 1.75443i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.4174 | − | 20.0616i | −1.06418 | − | 1.30040i | ||||
\(239\) | − | 5.29150i | − | 0.342279i | −0.985247 | − | 0.171139i | \(-0.945255\pi\) | ||
0.985247 | − | 0.171139i | \(-0.0547449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | − | 2.59808i | −0.289870 | − | 0.167357i | 0.348013 | − | 0.937490i | \(-0.386857\pi\) |
−0.637883 | + | 0.770133i | \(0.720190\pi\) | |||||||
\(242\) | 3.58258 | + | 4.37780i | 0.230297 | + | 0.281416i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.7477 | + | 15.5885i | −0.880108 | + | 0.997949i | ||||
\(245\) | 10.5000 | + | 6.06218i | 0.670820 | + | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.478220 | − | 12.9527i | 0.0303670 | − | 0.822494i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.76951 | − | 16.9213i | −0.175159 | − | 1.07020i | ||||
\(251\) | 4.58258 | 0.289250 | 0.144625 | − | 0.989487i | \(-0.453802\pi\) | ||||
0.144625 | + | 0.989487i | \(0.453802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0000 | −0.880172 | ||||||||
\(254\) | −1.81307 | − | 11.0776i | −0.113762 | − | 0.695069i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.31307 | − | 15.4077i | 0.269567 | − | 0.962982i | ||||
\(257\) | 9.00000 | − | 5.19615i | 0.561405 | − | 0.324127i | −0.192304 | − | 0.981335i | \(-0.561596\pi\) |
0.753709 | + | 0.657208i | \(0.228263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.00000 | − | 7.93725i | −0.558156 | − | 0.492248i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3131 | + | 15.0462i | 0.760704 | + | 0.929558i | ||||
\(263\) | 9.16515 | + | 5.29150i | 0.565147 | + | 0.326288i | 0.755209 | − | 0.655484i | \(-0.227535\pi\) |
−0.190061 | + | 0.981772i | \(0.560869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1244i | 0.744793i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5000 | + | 9.52628i | 1.00602 | + | 0.580828i | 0.910025 | − | 0.414554i | \(-0.136062\pi\) |
0.0959980 | + | 0.995382i | \(0.469396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.87386 | − | 11.9059i | −0.417557 | − | 0.723231i | 0.578136 | − | 0.815941i | \(-0.303780\pi\) |
−0.995693 | + | 0.0927099i | \(0.970447\pi\) | |||||||
\(272\) | 27.4955 | − | 3.46410i | 1.66716 | − | 0.210042i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | + | 5.29150i | −0.120824 | + | 0.319671i | ||||
\(275\) | 4.58258 | − | 2.64575i | 0.276340 | − | 0.159545i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | − | 3.46410i | 0.120168 | − | 0.208138i | −0.799666 | − | 0.600446i | \(-0.794990\pi\) |
0.919834 | + | 0.392308i | \(0.128323\pi\) | |||||||
\(278\) | 12.7913 | − | 2.09355i | 0.767170 | − | 0.125563i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.4564 | + | 6.06218i | −0.684653 | + | 0.362284i | ||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.16515 | − | 15.8745i | 0.544812 | − | 0.943642i | −0.453807 | − | 0.891100i | \(-0.649934\pi\) |
0.998619 | − | 0.0525416i | \(-0.0167322\pi\) | |||||||
\(284\) | 3.37386 | + | 10.0308i | 0.200202 | + | 0.595219i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.58258 | − | 12.1244i | 0.270973 | − | 0.716928i | ||||
\(287\) | 4.58258 | − | 7.93725i | 0.270501 | − | 0.468521i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5000 | + | 26.8468i | 0.911765 | + | 1.57922i | ||||
\(290\) | −9.47822 | + | 7.75650i | −0.556580 | + | 0.455478i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.5826 | − | 2.74110i | −0.794860 | − | 0.160411i | ||||
\(293\) | 15.5885i | 0.910687i | 0.890316 | + | 0.455344i | \(0.150484\pi\) | ||||
−0.890316 | + | 0.455344i | \(0.849516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.8118i | 1.38637i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.5390 | + | 15.3223i | 0.726366 | + | 0.887597i | ||||
\(299\) | −9.16515 | − | 15.8745i | −0.530034 | − | 0.918046i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0000 | − | 24.2487i | 0.806947 | − | 1.39767i | ||||
\(302\) | −17.5000 | − | 6.61438i | −1.00701 | − | 0.380615i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.00000 | + | 15.5885i | −0.515339 | + | 0.892592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.4955 | 1.56925 | 0.784624 | − | 0.619972i | \(-0.212856\pi\) | ||||
0.784624 | + | 0.619972i | \(0.212856\pi\) | |||||||
\(308\) | −10.5000 | − | 9.26013i | −0.598293 | − | 0.527645i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.81307 | − | 11.0776i | −0.102975 | − | 0.629164i | ||||
\(311\) | −4.58258 | + | 7.93725i | −0.259854 | + | 0.450080i | −0.966203 | − | 0.257784i | \(-0.917008\pi\) |
0.706349 | + | 0.707864i | \(0.250341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5000 | − | 11.2583i | 1.10221 | − | 0.636358i | 0.165406 | − | 0.986226i | \(-0.447107\pi\) |
0.936799 | + | 0.349867i | \(0.113773\pi\) | |||||||
\(314\) | −9.16515 | − | 3.46410i | −0.517219 | − | 0.195491i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5000 | + | 11.9059i | −0.590671 | + | 0.669758i | ||||
\(317\) | −3.50000 | − | 6.06218i | −0.196580 | − | 0.340486i | 0.750838 | − | 0.660487i | \(-0.229650\pi\) |
−0.947417 | + | 0.320001i | \(0.896317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.4564 | − | 6.61438i | −0.641437 | − | 0.370334i | ||||
\(320\) | 1.02178 | − | 13.8187i | 0.0571193 | − | 0.772488i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −19.5390 | + | 3.19795i | −1.08887 | + | 0.178215i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | + | 3.46410i | 0.332820 | + | 0.192154i | ||||
\(326\) | −17.3739 | + | 14.2179i | −0.962249 | + | 0.787457i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.58258 | + | 8.66025i | 0.253030 | + | 0.478183i | ||||
\(329\) | − | 24.2487i | − | 1.33687i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.16515 | + | 5.29150i | −0.503762 | + | 0.290847i | −0.730266 | − | 0.683163i | \(-0.760604\pi\) |
0.226504 | + | 0.974010i | \(0.427270\pi\) | |||||||
\(332\) | −8.68693 | + | 2.92185i | −0.476757 | + | 0.160357i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.5826 | − | 4.18710i | 1.39982 | − | 0.229108i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0000 | −1.14394 | −0.571971 | − | 0.820274i | \(-0.693821\pi\) | ||||
−0.571971 | + | 0.820274i | \(0.693821\pi\) | |||||||
\(338\) | −1.39564 | + | 0.228425i | −0.0759130 | + | 0.0124247i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.7477 | − | 7.65120i | 1.23367 | − | 0.414945i | ||||
\(341\) | 10.5000 | − | 6.06218i | 0.568607 | − | 0.328285i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 1.00000i | ||||||||
\(344\) | 14.0000 | + | 26.4575i | 0.754829 | + | 1.42649i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1652 | − | 12.4104i | 0.815284 | − | 0.667188i | ||||
\(347\) | −4.58258 | − | 2.64575i | −0.246006 | − | 0.142031i | 0.371928 | − | 0.928261i | \(-0.378697\pi\) |
−0.617934 | + | 0.786230i | \(0.712030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7846i | 1.11257i | 0.830990 | + | 0.556287i | \(0.187775\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812225\pi\) | |||||||
\(350\) | 5.79129 | − | 4.73930i | 0.309557 | − | 0.253326i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.3521 | − | 4.24473i | 0.764969 | − | 0.226245i | ||||
\(353\) | −6.00000 | − | 3.46410i | −0.319348 | − | 0.184376i | 0.331754 | − | 0.943366i | \(-0.392360\pi\) |
−0.651102 | + | 0.758990i | \(0.725693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.58258 | + | 7.93725i | 0.243218 | + | 0.421266i | ||||
\(356\) | −13.7477 | + | 15.5885i | −0.728628 | + | 0.826187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.00000 | + | 2.64575i | 0.369961 | + | 0.139832i | ||||
\(359\) | 9.16515 | − | 5.29150i | 0.483718 | − | 0.279275i | −0.238247 | − | 0.971205i | \(-0.576573\pi\) |
0.721965 | + | 0.691930i | \(0.243239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | −0.791288 | − | 4.83465i | −0.0415892 | − | 0.254104i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.62614 | − | 17.9681i | 0.190061 | − | 0.941782i | ||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29129 | − | 3.96863i | 0.119604 | − | 0.207161i | −0.800007 | − | 0.599991i | \(-0.795171\pi\) |
0.919611 | + | 0.392831i | \(0.128504\pi\) | |||||||
\(368\) | 8.20871 | − | 19.5094i | 0.427909 | − | 1.01700i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0390 | + | 9.26013i | −0.832704 | + | 0.480762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0000 | − | 29.4449i | −0.880227 | − | 1.52460i | −0.851089 | − | 0.525022i | \(-0.824057\pi\) |
−0.0291379 | − | 0.999575i | \(-0.509276\pi\) | |||||||
\(374\) | 16.4174 | + | 20.0616i | 0.848925 | + | 1.03736i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.9564 | + | 13.7810i | 1.13232 | + | 0.710699i | ||||
\(377\) | − | 17.3205i | − | 0.892052i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.29150i | − | 0.271806i | −0.990722 | − | 0.135903i | \(-0.956606\pi\) | ||
0.990722 | − | 0.135903i | \(-0.0433936\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.5826 | + | 9.47860i | −0.592616 | + | 0.484968i | ||||
\(383\) | 13.7477 | + | 23.8118i | 0.702476 | + | 1.21672i | 0.967595 | + | 0.252508i | \(0.0812555\pi\) |
−0.265119 | + | 0.964216i | \(0.585411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5000 | − | 6.06218i | −0.535130 | − | 0.308957i | ||||
\(386\) | 1.50000 | − | 3.96863i | 0.0763480 | − | 0.201998i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.52178 | − | 16.4168i | −0.280326 | − | 0.833435i | ||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.6606 | 1.85401 | ||||||||
\(392\) | −16.7695 | − | 10.5254i | −0.846988 | − | 0.531612i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −19.5390 | + | 3.19795i | −0.984361 | + | 0.161110i | ||||
\(395\) | −6.87386 | + | 11.9059i | −0.345862 | + | 0.599050i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0000 | − | 6.92820i | 0.602263 | − | 0.347717i | −0.167668 | − | 0.985843i | \(-0.553624\pi\) |
0.769931 | + | 0.638127i | \(0.220290\pi\) | |||||||
\(398\) | 9.16515 | − | 24.2487i | 0.459408 | − | 1.21548i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | + | 7.93725i | 0.0500000 | + | 0.396863i | ||||
\(401\) | −4.00000 | − | 6.92820i | −0.199750 | − | 0.345978i | 0.748697 | − | 0.662912i | \(-0.230680\pi\) |
−0.948447 | + | 0.316934i | \(0.897346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.7477 | + | 7.93725i | 0.684823 | + | 0.395383i | ||||
\(404\) | −13.5826 | − | 2.74110i | −0.675758 | − | 0.136375i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5000 | − | 6.61438i | −0.868510 | − | 0.328266i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 2.59808i | 0.222511 | + | 0.128467i | 0.607112 | − | 0.794616i | \(-0.292328\pi\) |
−0.384602 | + | 0.923083i | \(0.625661\pi\) | |||||||
\(410\) | 5.37386 | + | 6.56670i | 0.265396 | + | 0.324306i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.4955 | + | 24.2487i | 1.35460 | + | 1.19465i | ||||
\(413\) | −31.5000 | + | 18.1865i | −1.55001 | + | 0.894901i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.87386 | + | 3.96863i | −0.337425 | + | 0.194812i | ||||
\(416\) | 14.2087 | + | 13.4949i | 0.696639 | + | 0.661642i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 1.20871 | + | 7.38505i | 0.0588392 | + | 0.359499i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.730493 | − | 19.7855i | 0.0354759 | − | 0.960869i | ||||
\(425\) | −12.0000 | + | 6.92820i | −0.582086 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.4955 | −1.33060 | ||||||||
\(428\) | 24.5000 | − | 27.7804i | 1.18425 | − | 1.34282i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.4174 | + | 20.0616i | 0.791719 | + | 0.967457i | ||||
\(431\) | −22.9129 | − | 13.2288i | −1.10367 | − | 0.637207i | −0.166491 | − | 0.986043i | \(-0.553244\pi\) |
−0.937184 | + | 0.348836i | \(0.886577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.7846i | − | 0.998845i | −0.866359 | − | 0.499422i | \(-0.833546\pi\) | ||
0.866359 | − | 0.499422i | \(-0.166454\pi\) | |||||||
\(434\) | 13.2695 | − | 10.8591i | 0.636957 | − | 0.521254i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.29129 | + | 3.96863i | 0.109357 | + | 0.189412i | 0.915510 | − | 0.402295i | \(-0.131787\pi\) |
−0.806153 | + | 0.591707i | \(0.798454\pi\) | |||||||
\(440\) | 11.4564 | − | 6.06218i | 0.546164 | − | 0.289003i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | + | 31.7490i | −0.570782 | + | 1.51015i | ||||
\(443\) | −16.0390 | + | 9.26013i | −0.762037 | + | 0.439962i | −0.830026 | − | 0.557724i | \(-0.811675\pi\) |
0.0679899 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 6.39564 | − | 1.04678i | 0.302843 | − | 0.0495663i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.0608 | − | 9.20250i | 0.900538 | − | 0.434777i | ||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58258 | + | 7.93725i | −0.215785 | + | 0.373751i | ||||
\(452\) | −26.5390 | + | 8.92640i | −1.24829 | + | 0.419863i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.29129 | + | 6.06218i | −0.107535 | + | 0.284512i | ||||
\(455\) | − | 15.8745i | − | 0.744208i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.5000 | + | 23.3827i | 0.631503 | + | 1.09380i | 0.987245 | + | 0.159211i | \(0.0508951\pi\) |
−0.355741 | + | 0.934585i | \(0.615772\pi\) | |||||||
\(458\) | 11.3739 | − | 9.30780i | 0.531466 | − | 0.434925i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.62614 | − | 17.9681i | 0.169069 | − | 0.837765i | ||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.8745i | − | 0.737751i | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||
0.929479 | − | 0.368875i | \(-0.120257\pi\) | |||||||
\(464\) | 15.9347 | − | 12.0866i | 0.739748 | − | 0.561108i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9129 | − | 21.8890i | −0.829798 | − | 1.01399i | ||||
\(467\) | 18.3303 | + | 31.7490i | 0.848225 | + | 1.46917i | 0.882791 | + | 0.469767i | \(0.155662\pi\) |
−0.0345653 | + | 0.999402i | \(0.511005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 21.0000 | + | 7.93725i | 0.968658 | + | 0.366118i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.43466 | − | 38.8580i | 0.0660355 | − | 1.78858i | ||||
\(473\) | −14.0000 | + | 24.2487i | −0.643721 | + | 1.11496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 27.4955 | + | 24.2487i | 1.26025 | + | 1.11144i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.20871 | + | 7.38505i | 0.0552852 | + | 0.337784i | ||||
\(479\) | 9.16515 | − | 15.8745i | 0.418766 | − | 0.725325i | −0.577049 | − | 0.816709i | \(-0.695796\pi\) |
0.995816 | + | 0.0913846i | \(0.0291293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.87386 | + | 2.59808i | 0.313096 | + | 0.118339i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.00000 | − | 5.29150i | −0.272727 | − | 0.240523i | ||||
\(485\) | −7.50000 | − | 12.9904i | −0.340557 | − | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29129 | + | 1.32288i | 0.103828 | + | 0.0599452i | 0.551015 | − | 0.834495i | \(-0.314241\pi\) |
−0.447187 | + | 0.894441i | \(0.647574\pi\) | |||||||
\(488\) | 15.6261 | − | 24.8963i | 0.707362 | − | 1.12700i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.0390 | − | 6.06218i | −0.724569 | − | 0.273861i | ||||
\(491\) | 2.64575i | 0.119401i | 0.998216 | + | 0.0597005i | \(0.0190146\pi\) | ||||
−0.998216 | + | 0.0597005i | \(0.980985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.0000 | + | 17.3205i | 1.35113 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.29129 | + | 18.1865i | 0.102882 | + | 0.816599i | ||||
\(497\) | −7.00000 | + | 12.1244i | −0.313993 | + | 0.543852i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.58258 | + | 2.64575i | −0.205144 | + | 0.118440i | −0.599053 | − | 0.800710i | \(-0.704456\pi\) |
0.393908 | + | 0.919150i | \(0.371123\pi\) | |||||||
\(500\) | 7.73049 | + | 22.9835i | 0.345718 | + | 1.02785i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.39564 | + | 1.04678i | −0.285452 | + | 0.0467199i | ||||
\(503\) | 36.6606 | 1.63462 | 0.817308 | − | 0.576201i | \(-0.195466\pi\) | ||||
0.817308 | + | 0.576201i | \(0.195466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 19.5390 | − | 3.19795i | 0.868615 | − | 0.142166i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.06080 | + | 15.0462i | 0.224536 | + | 0.667567i | ||||
\(509\) | −1.50000 | + | 0.866025i | −0.0664863 | + | 0.0383859i | −0.532875 | − | 0.846194i | \(-0.678888\pi\) |
0.466388 | + | 0.884580i | \(0.345555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.16515 | − | 15.8745i | −0.405442 | − | 0.702247i | ||||
\(512\) | −2.50000 | + | 22.4889i | −0.110485 | + | 0.993878i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.3739 | + | 9.30780i | −0.501680 | + | 0.410550i | ||||
\(515\) | 27.4955 | + | 15.8745i | 1.21159 | + | 0.699514i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.2487i | 1.06646i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.3739 | + | 9.02175i | 0.630336 | + | 0.395630i | ||||
\(521\) | −6.00000 | − | 3.46410i | −0.262865 | − | 0.151765i | 0.362776 | − | 0.931876i | \(-0.381829\pi\) |
−0.625641 | + | 0.780111i | \(0.715162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7477 | − | 23.8118i | −0.601146 | − | 1.04122i | −0.992648 | − | 0.121038i | \(-0.961378\pi\) |
0.391502 | − | 0.920177i | \(-0.371956\pi\) | |||||||
\(524\) | −20.6216 | − | 18.1865i | −0.900858 | − | 0.794482i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0000 | − | 5.29150i | −0.610429 | − | 0.230720i | ||||
\(527\) | −27.4955 | + | 15.8745i | −1.19772 | + | 0.691504i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50000 | − | 4.33013i | 0.108696 | − | 0.188266i | ||||
\(530\) | −2.76951 | − | 16.9213i | −0.120300 | − | 0.735014i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0390 | − | 27.7804i | 0.693427 | − | 1.20105i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.2042 | − | 9.52628i | −1.08663 | − | 0.410707i | ||||
\(539\) | − | 18.5203i | − | 0.797724i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | \(-0.221681\pi\) |
−0.939110 | + | 0.343617i | \(0.888348\pi\) | |||||||
\(542\) | 12.3131 | + | 15.0462i | 0.528892 | + | 0.646290i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −37.5826 | + | 11.1153i | −1.61134 | + | 0.476565i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7490i | 1.35749i | 0.734374 | + | 0.678745i | \(0.237476\pi\) | ||||
−0.734374 | + | 0.678745i | \(0.762524\pi\) | |||||||
\(548\) | 1.58258 | − | 7.84190i | 0.0676043 | − | 0.334990i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.79129 | + | 4.73930i | −0.246941 | + | 0.202085i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0000 | −0.893011 | ||||||||
\(554\) | −2.00000 | + | 5.29150i | −0.0849719 | + | 0.224814i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.3739 | + | 5.84370i | −0.736816 | + | 0.247828i | ||||
\(557\) | 3.50000 | − | 6.06218i | 0.148300 | − | 0.256863i | −0.782299 | − | 0.622903i | \(-0.785953\pi\) |
0.930599 | + | 0.366040i | \(0.119287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.6606 | −1.55058 | ||||||||
\(560\) | 14.6044 | − | 11.0776i | 0.617147 | − | 0.468113i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.3303 | + | 3.65480i | −0.941947 | + | 0.154169i | ||||
\(563\) | 11.4564 | − | 19.8431i | 0.482831 | − | 0.836288i | −0.516974 | − | 0.856001i | \(-0.672942\pi\) |
0.999806 | + | 0.0197125i | \(0.00627508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.0000 | + | 12.1244i | −0.883477 | + | 0.510075i | ||||
\(566\) | −9.16515 | + | 24.2487i | −0.385240 | + | 1.01925i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.00000 | − | 13.2288i | −0.293713 | − | 0.555066i | ||||
\(569\) | 4.00000 | + | 6.92820i | 0.167689 | + | 0.290445i | 0.937607 | − | 0.347697i | \(-0.113036\pi\) |
−0.769918 | + | 0.638143i | \(0.779703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.7477 | − | 7.93725i | −0.575324 | − | 0.332164i | 0.183949 | − | 0.982936i | \(-0.441112\pi\) |
−0.759273 | + | 0.650772i | \(0.774445\pi\) | |||||||
\(572\) | −3.62614 | + | 17.9681i | −0.151616 | + | 0.751282i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.58258 | + | 12.1244i | −0.191273 | + | 0.506061i | ||||
\(575\) | 10.5830i | 0.441342i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.5000 | − | 21.6506i | −1.56115 | − | 0.901328i | −0.997142 | − | 0.0755556i | \(-0.975927\pi\) |
−0.564004 | − | 0.825772i | \(-0.690740\pi\) | |||||||
\(578\) | −27.7650 | − | 33.9280i | −1.15487 | − | 1.41122i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.4564 | − | 12.9904i | 0.475703 | − | 0.539396i | ||||
\(581\) | −10.5000 | − | 6.06218i | −0.435613 | − | 0.251502i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0390 | − | 9.26013i | 0.664268 | − | 0.383515i | ||||
\(584\) | 19.5826 | + | 0.723000i | 0.810333 | + | 0.0299180i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.56080 | − | 21.7559i | −0.147095 | − | 0.898729i | ||||
\(587\) | −22.9129 | −0.945716 | −0.472858 | − | 0.881139i | \(-0.656778\pi\) | ||||
−0.472858 | + | 0.881139i | \(0.656778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5.43920 | − | 33.2327i | −0.223929 | − | 1.36817i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | − | 5.19615i | 0.369586 | − | 0.213380i | −0.303692 | − | 0.952770i | \(-0.598219\pi\) |
0.673277 | + | 0.739390i | \(0.264886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.4955 | + | 15.8745i | 1.12720 | + | 0.650791i | ||||
\(596\) | −21.0000 | − | 18.5203i | −0.860194 | − | 0.758619i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.4174 | + | 20.0616i | 0.671358 | + | 0.820380i | ||||
\(599\) | −9.16515 | − | 5.29150i | −0.374478 | − | 0.216205i | 0.300935 | − | 0.953645i | \(-0.402701\pi\) |
−0.675413 | + | 0.737440i | \(0.736035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66025i | 0.353259i | 0.984277 | + | 0.176630i | \(0.0565195\pi\) | ||||
−0.984277 | + | 0.176630i | \(0.943481\pi\) | |||||||
\(602\) | −14.0000 | + | 37.0405i | −0.570597 | + | 1.50966i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25.9347 | + | 5.23388i | 1.05527 | + | 0.212963i | ||||
\(605\) | −6.00000 | − | 3.46410i | −0.243935 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.87386 | − | 11.9059i | −0.279002 | − | 0.483245i | 0.692135 | − | 0.721768i | \(-0.256670\pi\) |
−0.971137 | + | 0.238523i | \(0.923337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.00000 | − | 23.8118i | 0.364399 | − | 0.964110i | ||||
\(611\) | −27.4955 | + | 15.8745i | −1.11235 | + | 0.642214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.00000 | + | 12.1244i | −0.282727 | + | 0.489698i | −0.972056 | − | 0.234751i | \(-0.924572\pi\) |
0.689328 | + | 0.724449i | \(0.257906\pi\) | |||||||
\(614\) | −38.3739 | + | 6.28065i | −1.54864 | + | 0.253467i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.7695 | + | 10.5254i | 0.675663 | + | 0.424080i | ||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7477 | + | 23.8118i | −0.552568 | + | 0.957076i | 0.445521 | + | 0.895272i | \(0.353019\pi\) |
−0.998088 | + | 0.0618038i | \(0.980315\pi\) | |||||||
\(620\) | 5.06080 | + | 15.0462i | 0.203246 | + | 0.604270i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.58258 | − | 12.1244i | 0.183745 | − | 0.486142i | ||||
\(623\) | −27.4955 | −1.10158 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −24.6434 | + | 20.1669i | −0.984947 | + | 0.806032i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5826 | + | 2.74110i | 0.542004 | + | 0.109382i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.93725i | 0.315977i | 0.987441 | + | 0.157989i | \(0.0505009\pi\) | ||||
−0.987441 | + | 0.157989i | \(0.949499\pi\) | |||||||
\(632\) | 11.9347 | − | 19.0148i | 0.474735 | − | 0.756369i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.26951 | + | 7.66115i | 0.248994 | + | 0.304263i | ||||
\(635\) | 6.87386 | + | 11.9059i | 0.272781 | + | 0.472470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.0000 | − | 12.1244i | 0.832050 | − | 0.480384i | ||||
\(638\) | 17.5000 | + | 6.61438i | 0.692832 | + | 0.261866i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73049 | + | 19.5194i | 0.0684037 | + | 0.771570i | ||||
\(641\) | 19.0000 | − | 32.9090i | 0.750455 | − | 1.29983i | −0.197148 | − | 0.980374i | \(-0.563168\pi\) |
0.947602 | − | 0.319452i | \(-0.103499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.3303 | −0.722877 | −0.361438 | − | 0.932396i | \(-0.617714\pi\) | ||||
−0.361438 | + | 0.932396i | \(0.617714\pi\) | |||||||
\(644\) | 26.5390 | − | 8.92640i | 1.04578 | − | 0.351750i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.58258 | + | 7.93725i | −0.180160 | + | 0.312046i | −0.941935 | − | 0.335796i | \(-0.890995\pi\) |
0.761775 | + | 0.647842i | \(0.224328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5000 | − | 18.1865i | 1.23648 | − | 0.713884i | ||||
\(650\) | −9.16515 | − | 3.46410i | −0.359487 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.0000 | − | 23.8118i | 0.822423 | − | 0.932541i | ||||
\(653\) | 21.5000 | + | 37.2391i | 0.841360 | + | 1.45728i | 0.888745 | + | 0.458402i | \(0.151578\pi\) |
−0.0473852 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6216 | − | 11.9059i | −0.805752 | − | 0.465201i | ||||
\(656\) | −8.37386 | − | 11.0399i | −0.326944 | − | 0.431034i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.53901 | + | 33.8426i | 0.215933 | + | 1.31932i | ||||
\(659\) | − | 26.4575i | − | 1.03064i | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515319i | \(-0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | + | 3.46410i | 0.233373 | + | 0.134738i | 0.612127 | − | 0.790759i | \(-0.290314\pi\) |
−0.378754 | + | 0.925497i | \(0.623647\pi\) | |||||||
\(662\) | 11.5826 | − | 9.47860i | 0.450170 | − | 0.368396i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.4564 | − | 6.06218i | 0.444596 | − | 0.235258i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.9129 | − | 13.2288i | 0.887190 | − | 0.512219i | ||||
\(668\) | −34.7477 | + | 11.6874i | −1.34443 | + | 0.452199i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.4955 | 1.06145 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0000 | 0.809491 | 0.404745 | − | 0.914429i | \(-0.367360\pi\) | ||||
0.404745 | + | 0.914429i | \(0.367360\pi\) | |||||||
\(674\) | 29.3085 | − | 4.79693i | 1.12892 | − | 0.184771i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.89564 | − | 0.637600i | 0.0729094 | − | 0.0245231i | ||||
\(677\) | 19.5000 | − | 11.2583i | 0.749446 | − | 0.432693i | −0.0760478 | − | 0.997104i | \(-0.524230\pi\) |
0.825494 | + | 0.564411i | \(0.190897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4564 | − | 19.8431i | 0.439658 | − | 0.761510i | ||||
\(680\) | −30.0000 | + | 15.8745i | −1.15045 | + | 0.608760i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.2695 | + | 10.8591i | −0.508116 | + | 0.415817i | ||||
\(683\) | −2.29129 | − | 1.32288i | −0.0876737 | − | 0.0506184i | 0.455522 | − | 0.890224i | \(-0.349453\pi\) |
−0.543196 | + | 0.839606i | \(0.682786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.92820i | − | 0.264713i | ||||||
\(686\) | −4.23049 | − | 25.8477i | −0.161521 | − | 0.986869i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.5826 | − | 33.7273i | −0.975327 | − | 1.28584i | ||||
\(689\) | 21.0000 | + | 12.1244i | 0.800036 | + | 0.461901i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9129 | + | 39.6863i | 0.871647 | + | 1.50974i | 0.860292 | + | 0.509801i | \(0.170281\pi\) |
0.0113548 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(692\) | −18.3303 | + | 20.7846i | −0.696814 | + | 0.790112i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.00000 | + | 2.64575i | 0.265716 | + | 0.100431i | ||||
\(695\) | −13.7477 | + | 7.93725i | −0.521481 | + | 0.301077i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | − | 20.7846i | 0.454532 | − | 0.787273i | ||||
\(698\) | −4.74773 | − | 29.0079i | −0.179704 | − | 1.09797i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.00000 | + | 7.93725i | −0.264575 | + | 0.300000i | ||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −19.0608 | + | 9.20250i | −0.718381 | + | 0.346832i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.16515 | + | 3.46410i | 0.344935 | + | 0.130373i | ||||
\(707\) | −9.16515 | − | 15.8745i | −0.344691 | − | 0.597022i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.0000 | − | 36.3731i | −0.788672 | − | 1.36602i | −0.926781 | − | 0.375602i | \(-0.877436\pi\) |
0.138109 | − | 0.990417i | \(-0.455897\pi\) | |||||||
\(710\) | −8.20871 | − | 10.0308i | −0.308067 | − | 0.376449i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.6261 | − | 24.8963i | 0.585614 | − | 0.933027i | ||||
\(713\) | 24.2487i | 0.908121i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8745i | 0.593673i | ||||||||
\(716\) | −10.3739 | − | 2.09355i | −0.387689 | − | 0.0782397i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.5826 | + | 9.47860i | −0.432258 | + | 0.353738i | ||||
\(719\) | 13.7477 | + | 23.8118i | 0.512704 | + | 0.888029i | 0.999891 | + | 0.0147316i | \(0.00468939\pi\) |
−0.487188 | + | 0.873297i | \(0.661977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.4974i | 1.80614i | ||||||||
\(722\) | −9.50000 | + | 25.1346i | −0.353553 | + | 0.935414i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.20871 | + | 6.56670i | 0.0820861 | + | 0.244050i | ||||
\(725\) | −5.00000 | + | 8.66025i | −0.185695 | + | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7477 | 0.509875 | 0.254937 | − | 0.966958i | \(-0.417945\pi\) | ||||
0.254937 | + | 0.966958i | \(0.417945\pi\) | |||||||
\(728\) | −0.956439 | + | 25.9053i | −0.0354480 | + | 0.960115i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.7477 | − | 2.74110i | 0.619861 | − | 0.101453i | ||||
\(731\) | 36.6606 | − | 63.4980i | 1.35594 | − | 2.34856i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0000 | + | 17.3205i | −1.10808 | + | 0.639748i | −0.938330 | − | 0.345740i | \(-0.887628\pi\) |
−0.169745 | + | 0.985488i | \(0.554294\pi\) | |||||||
\(734\) | −2.29129 | + | 6.06218i | −0.0845730 | + | 0.223759i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | + | 29.1033i | −0.258023 | + | 1.07276i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.2432 | + | 23.8118i | 1.51715 | + | 0.875930i | 0.999797 | + | 0.0201609i | \(0.00641784\pi\) |
0.517358 | + | 0.855769i | \(0.326915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.2695 | − | 16.5876i | 0.744117 | − | 0.608948i | ||||
\(743\) | − | 21.1660i | − | 0.776506i | −0.921553 | − | 0.388253i | \(-0.873079\pi\) | ||
0.921553 | − | 0.388253i | \(-0.126921\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0000 | − | 12.1244i | −0.769380 | − | 0.444202i | ||||
\(746\) | 30.4519 | + | 37.2113i | 1.11492 | + | 1.36240i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.4955 | − | 24.2487i | −1.00533 | − | 0.886621i | ||||
\(749\) | 49.0000 | 1.79042 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4564 | − | 6.61438i | 0.418051 | − | 0.241362i | −0.276192 | − | 0.961103i | \(-0.589073\pi\) |
0.694243 | + | 0.719740i | \(0.255739\pi\) | |||||||
\(752\) | −33.7913 | − | 14.2179i | −1.23224 | − | 0.518474i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.95644 | + | 24.1733i | 0.144085 | + | 0.880338i | ||||
\(755\) | 22.9129 | 0.833885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 1.20871 | + | 7.38505i | 0.0439024 | + | 0.268237i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.0000 | − | 19.0526i | 1.19625 | − | 0.690655i | 0.236532 | − | 0.971624i | \(-0.423989\pi\) |
0.959717 | + | 0.280969i | \(0.0906558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.0000 | − | 15.8745i | 0.506502 | − | 0.574320i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.6261 | − | 30.0924i | −0.889778 | − | 1.08728i | ||||
\(767\) | 41.2432 | + | 23.8118i | 1.48920 | + | 0.859793i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.9090i | − | 1.18673i | −0.804934 | − | 0.593364i | \(-0.797800\pi\) | ||
0.804934 | − | 0.593364i | \(-0.202200\pi\) | |||||||
\(770\) | 16.0390 | + | 6.06218i | 0.578006 | + | 0.218466i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.18693 | + | 5.88143i | −0.0427186 | + | 0.211677i | ||||
\(773\) | −36.0000 | − | 20.7846i | −1.29483 | − | 0.747570i | −0.315324 | − | 0.948984i | \(-0.602113\pi\) |
−0.979506 | + | 0.201414i | \(0.935446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.58258 | − | 7.93725i | −0.164611 | − | 0.285115i | ||||
\(776\) | 11.4564 | + | 21.6506i | 0.411262 | + | 0.777213i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.00000 | − | 13.2288i | 0.179259 | − | 0.474274i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.00000 | − | 12.1244i | 0.250480 | − | 0.433844i | ||||
\(782\) | −51.1652 | + | 8.37420i | −1.82966 | + | 0.299461i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.8085 | + | 10.8591i | 0.921733 | + | 0.387825i | ||||
\(785\) | 12.0000 | 0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7477 | + | 23.8118i | −0.490054 | + | 0.848798i | −0.999934 | − | 0.0114473i | \(-0.996356\pi\) |
0.509881 | + | 0.860245i | \(0.329689\pi\) | |||||||
\(788\) | 26.5390 | − | 8.92640i | 0.945413 | − | 0.317990i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.87386 | − | 18.1865i | 0.244561 | − | 0.647048i | ||||
\(791\) | −32.0780 | − | 18.5203i | −1.14056 | − | 0.658505i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | + | 31.1769i | 0.639199 | + | 1.10712i | ||||
\(794\) | −15.1652 | + | 12.4104i | −0.538191 | + | 0.440429i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.25227 | + | 35.9361i | −0.257050 | + | 1.27372i | ||||
\(797\) | 15.5885i | 0.552171i | 0.961133 | + | 0.276086i | \(0.0890374\pi\) | ||||
−0.961133 | + | 0.276086i | \(0.910963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 63.4980i | − | 2.24640i | ||||||
\(800\) | −3.20871 | − | 10.8492i | −0.113445 | − | 0.383576i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.16515 | + | 8.75560i | 0.253010 | + | 0.309171i | ||||
\(803\) | 9.16515 | + | 15.8745i | 0.323431 | + | 0.560199i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0000 | − | 12.1244i | 0.740153 | − | 0.427327i | ||||
\(806\) | −21.0000 | − | 7.93725i | −0.739693 | − | 0.279578i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.5826 | + | 0.723000i | 0.688913 | + | 0.0254351i | ||||
\(809\) | 14.0000 | − | 24.2487i | 0.492214 | − | 0.852539i | −0.507746 | − | 0.861507i | \(-0.669521\pi\) |
0.999960 | + | 0.00896753i | \(0.00285449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.6606 | −1.28733 | −0.643664 | − | 0.765308i | \(-0.722587\pi\) | ||||
−0.643664 | + | 0.765308i | \(0.722587\pi\) | |||||||
\(812\) | 25.9347 | + | 5.23388i | 0.910128 | + | 0.183673i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7477 | − | 23.8118i | 0.481562 | − | 0.834090i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.87386 | − | 2.59808i | −0.240339 | − | 0.0908396i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | − | 7.93725i | −0.314294 | − | 0.277181i | ||||
\(821\) | 24.5000 | + | 42.4352i | 0.855056 | + | 1.48100i | 0.876593 | + | 0.481232i | \(0.159811\pi\) |
−0.0215373 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.2432 | + | 23.8118i | 1.43765 | + | 0.830026i | 0.997686 | − | 0.0679910i | \(-0.0216589\pi\) |
0.439961 | + | 0.898017i | \(0.354992\pi\) | |||||||
\(824\) | −43.9129 | − | 27.5619i | −1.52978 | − | 0.960165i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39.8085 | − | 32.5773i | 1.38512 | − | 1.13351i | ||||
\(827\) | − | 34.3948i | − | 1.19602i | −0.801487 | − | 0.598012i | \(-0.795958\pi\) | ||
0.801487 | − | 0.598012i | \(-0.204042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.00000 | + | 3.46410i | 0.208389 | + | 0.120313i | 0.600562 | − | 0.799578i | \(-0.294943\pi\) |
−0.392174 | + | 0.919891i | \(0.628277\pi\) | |||||||
\(830\) | 8.68693 | − | 7.10895i | 0.301528 | − | 0.246755i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.9129 | − | 15.5885i | −0.794361 | − | 0.540433i | ||||
\(833\) | 48.4974i | 1.68034i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.4955 | + | 15.8745i | −0.951519 | + | 0.549360i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.6606 | −1.26566 | −0.632832 | − | 0.774289i | \(-0.718108\pi\) | ||||
−0.632832 | + | 0.774289i | \(0.718108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 2.79129 | − | 0.456850i | 0.0961941 | − | 0.0157441i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.37386 | − | 10.0308i | −0.116133 | − | 0.345275i | ||||
\(845\) | 1.50000 | − | 0.866025i | 0.0516016 | − | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.5830i | − | 0.363636i | ||||||
\(848\) | 3.50000 | + | 27.7804i | 0.120190 | + | 0.953982i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.1652 | − | 12.4104i | 0.520160 | − | 0.425673i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.7128i | − | 0.948869i | −0.880291 | − | 0.474434i | \(-0.842653\pi\) | ||
0.880291 | − | 0.474434i | \(-0.157347\pi\) | |||||||
\(854\) | 38.3739 | − | 6.28065i | 1.31313 | − | 0.214920i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.8475 | + | 44.3679i | −0.951809 | + | 1.51647i | ||||
\(857\) | −27.0000 | − | 15.5885i | −0.922302 | − | 0.532492i | −0.0379336 | − | 0.999280i | \(-0.512078\pi\) |
−0.884369 | + | 0.466789i | \(0.845411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3303 | + | 31.7490i | 0.625422 | + | 1.08326i | 0.988459 | + | 0.151488i | \(0.0484064\pi\) |
−0.363037 | + | 0.931775i | \(0.618260\pi\) | |||||||
\(860\) | −27.4955 | − | 24.2487i | −0.937587 | − | 0.826874i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.0000 | + | 13.2288i | 1.19210 | + | 0.450573i | ||||
\(863\) | −22.9129 | + | 13.2288i | −0.779963 | + | 0.450312i | −0.836417 | − | 0.548093i | \(-0.815354\pi\) |
0.0564539 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | + | 20.7846i | −0.408012 | + | 0.706698i | ||||
\(866\) | 4.74773 | + | 29.0079i | 0.161334 | + | 0.985729i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.0390 | + | 18.1865i | −0.544400 | + | 0.617291i | ||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.0390 | + | 27.7804i | −0.542218 | + | 0.939149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.0000 | − | 24.2487i | −0.472746 | − | 0.818821i | 0.526767 | − | 0.850010i | \(-0.323404\pi\) |
−0.999514 | + | 0.0311889i | \(0.990071\pi\) | |||||||
\(878\) | −4.10436 | − | 5.01540i | −0.138515 | − | 0.169262i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14.6044 | + | 11.0776i | −0.492313 | + | 0.373425i | ||||
\(881\) | − | 27.7128i | − | 0.933668i | −0.884345 | − | 0.466834i | \(-0.845394\pi\) | ||
0.884345 | − | 0.466834i | \(-0.154606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.29150i | 0.178073i | 0.996028 | + | 0.0890366i | \(0.0283788\pi\) | ||||
−0.996028 | + | 0.0890366i | \(0.971621\pi\) | |||||||
\(884\) | 9.49545 | − | 47.0514i | 0.319367 | − | 1.58251i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.2695 | − | 16.5876i | 0.680967 | − | 0.557270i | ||||
\(887\) | 13.7477 | + | 23.8118i | 0.461603 | + | 0.799521i | 0.999041 | − | 0.0437828i | \(-0.0139410\pi\) |
−0.537438 | + | 0.843304i | \(0.680608\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.5000 | + | 18.1865i | −0.352159 | + | 0.609957i | ||||
\(890\) | 9.00000 | − | 23.8118i | 0.301681 | − | 0.798172i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.68693 | + | 2.92185i | −0.290860 | + | 0.0978308i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.16515 | −0.306357 | ||||||||
\(896\) | −24.5000 | + | 17.1974i | −0.818488 | + | 0.574524i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5390 | − | 3.19795i | 0.652025 | − | 0.106717i | ||||
\(899\) | −11.4564 | + | 19.8431i | −0.382094 | + | 0.661806i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.0000 | + | 24.2487i | −1.39922 | + | 0.807842i | ||||
\(902\) | 4.58258 | − | 12.1244i | 0.152583 | − | 0.403697i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.0000 | − | 18.5203i | 1.16408 | − | 0.615975i | ||||
\(905\) | 3.00000 | + | 5.19615i | 0.0997234 | + | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0780 | − | 18.5203i | −1.06513 | − | 0.614955i | −0.138286 | − | 0.990392i | \(-0.544159\pi\) |
−0.926848 | + | 0.375437i | \(0.877493\pi\) | |||||||
\(908\) | 1.81307 | − | 8.98403i | 0.0601688 | − | 0.298145i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.62614 | + | 22.1552i | 0.120205 | + | 0.734436i | ||||
\(911\) | 5.29150i | 0.175315i | 0.996151 | + | 0.0876577i | \(0.0279382\pi\) | ||||
−0.996151 | + | 0.0876577i | \(0.972062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.5000 | + | 6.06218i | 0.347499 | + | 0.200629i | ||||
\(914\) | −24.1824 | − | 29.5502i | −0.799882 | − | 0.977433i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.7477 | + | 15.5885i | −0.454238 | + | 0.515057i | ||||
\(917\) | − | 36.3731i | − | 1.20114i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.58258 | − | 2.64575i | 0.151165 | − | 0.0872753i | −0.422510 | − | 0.906358i | \(-0.638851\pi\) |
0.573675 | + | 0.819083i | \(0.305517\pi\) | |||||||
\(920\) | −0.956439 | + | 25.9053i | −0.0315329 | + | 0.854073i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.33030 | + | 38.6772i | 0.208477 | + | 1.27377i | ||||
\(923\) | 18.3303 | 0.603349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.62614 | + | 22.1552i | 0.119162 | + | 0.728064i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19.4782 | + | 20.5085i | −0.639404 | + | 0.673225i | ||||
\(929\) | −30.0000 | + | 17.3205i | −0.984268 | + | 0.568267i | −0.903556 | − | 0.428470i | \(-0.859053\pi\) |
−0.0807121 | + | 0.996737i | \(0.525719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.0000 | + | 26.4575i | 0.982683 | + | 0.866645i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.8348 | − | 40.1232i | −1.07439 | − | 1.31287i | ||||
\(935\) | −27.4955 | − | 15.8745i | −0.899198 | − | 0.519152i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.5885i | − | 0.509253i | −0.967040 | − | 0.254626i | \(-0.918048\pi\) | ||
0.967040 | − | 0.254626i | \(-0.0819525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31.1216 | − | 6.28065i | −1.01507 | − | 0.204852i | ||||
\(941\) | −4.50000 | − | 2.59808i | −0.146696 | − | 0.0846949i | 0.424856 | − | 0.905261i | \(-0.360325\pi\) |
−0.571551 | + | 0.820566i | \(0.693658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.16515 | − | 15.8745i | −0.298458 | − | 0.516945i | ||||
\(944\) | 6.87386 | + | 54.5596i | 0.223725 | + | 1.77576i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.0000 | − | 37.0405i | 0.455179 | − | 1.20429i | ||||
\(947\) | −32.0780 | + | 18.5203i | −1.04240 | + | 0.601828i | −0.920511 | − | 0.390717i | \(-0.872227\pi\) |
−0.121885 | + | 0.992544i | \(0.538894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −43.9129 | − | 27.5619i | −1.42322 | − | 0.893287i | ||||
\(953\) | −28.0000 | −0.907009 | −0.453504 | − | 0.891254i | \(-0.649826\pi\) | ||||
−0.453504 | + | 0.891254i | \(0.649826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.16515 | − | 15.8745i | 0.296577 | − | 0.513687i | ||||
\(956\) | −3.37386 | − | 10.0308i | −0.109119 | − | 0.324419i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.16515 | + | 24.2487i | −0.296113 | + | 0.783440i | ||||
\(959\) | 9.16515 | − | 5.29150i | 0.295958 | − | 0.170872i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | + | 8.66025i | 0.161290 | + | 0.279363i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.1869 | − | 2.05583i | −0.328099 | − | 0.0662137i | ||||
\(965\) | 5.19615i | 0.167270i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.6863i | − | 1.27622i | −0.769943 | − | 0.638112i | \(-0.779716\pi\) | ||
0.769943 | − | 0.638112i | \(-0.220284\pi\) | |||||||
\(968\) | 9.58258 | + | 6.01450i | 0.307996 | + | 0.193313i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.4347 | + | 16.4168i | 0.431361 | + | 0.527110i | ||||
\(971\) | 2.29129 | + | 3.96863i | 0.0735309 | + | 0.127359i | 0.900446 | − | 0.434967i | \(-0.143240\pi\) |
−0.826916 | + | 0.562326i | \(0.809907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.0000 | − | 12.1244i | −0.673229 | − | 0.388689i | ||||
\(974\) | −3.50000 | − | 1.32288i | −0.112147 | − | 0.0423877i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.1216 | + | 38.3157i | −0.516040 | + | 1.22646i | ||||
\(977\) | 16.0000 | − | 27.7128i | 0.511885 | − | 0.886611i | −0.488020 | − | 0.872833i | \(-0.662281\pi\) |
0.999905 | − | 0.0137788i | \(-0.00438608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.4955 | 0.878759 | ||||||||
\(980\) | 23.7695 | + | 4.79693i | 0.759289 | + | 0.153232i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.604356 | − | 3.69253i | −0.0192858 | − | 0.117833i | ||||
\(983\) | 22.9129 | − | 39.6863i | 0.730807 | − | 1.26580i | −0.225731 | − | 0.974190i | \(-0.572477\pi\) |
0.956539 | − | 0.291606i | \(-0.0941895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.0000 | − | 12.1244i | 0.669116 | − | 0.386314i | ||||
\(986\) | −45.8258 | − | 17.3205i | −1.45939 | − | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0000 | − | 48.4974i | −0.890348 | − | 1.54213i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.5345 | − | 25.1346i | −1.38292 | − | 0.798428i | −0.390414 | − | 0.920639i | \(-0.627668\pi\) |
−0.992504 | + | 0.122211i | \(0.961001\pi\) | |||||||
\(992\) | −7.35208 | − | 24.8585i | −0.233429 | − | 0.789259i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.00000 | − | 18.5203i | 0.222027 | − | 0.587427i | ||||
\(995\) | 31.7490i | 1.00651i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.00000 | + | 3.46410i | 0.190022 | + | 0.109709i | 0.591993 | − | 0.805943i | \(-0.298341\pi\) |
−0.401971 | + | 0.915652i | \(0.631675\pi\) | |||||||
\(998\) | 5.79129 | − | 4.73930i | 0.183320 | − | 0.150020i | ||||
\(999\) | 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 | 252.2.bf.a.199.1 | yes | 4 | |
3.2 | odd | 2 | 252.2.bf.d.199.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 252.2.bf.a.199.2 | yes | 4 | |
7.3 | odd | 6 | 1764.2.b.h.1567.1 | 4 | |||
7.4 | even | 3 | 1764.2.b.h.1567.2 | 4 | |||
7.5 | odd | 6 | inner | 252.2.bf.a.19.2 | yes | 4 | |
12.11 | even | 2 | 252.2.bf.d.199.1 | yes | 4 | ||
21.5 | even | 6 | 252.2.bf.d.19.1 | yes | 4 | ||
21.11 | odd | 6 | 1764.2.b.b.1567.3 | 4 | |||
21.17 | even | 6 | 1764.2.b.b.1567.4 | 4 | |||
28.3 | even | 6 | 1764.2.b.h.1567.3 | 4 | |||
28.11 | odd | 6 | 1764.2.b.h.1567.4 | 4 | |||
28.19 | even | 6 | inner | 252.2.bf.a.19.1 | ✓ | 4 | |
84.11 | even | 6 | 1764.2.b.b.1567.1 | 4 | |||
84.47 | odd | 6 | 252.2.bf.d.19.2 | yes | 4 | ||
84.59 | odd | 6 | 1764.2.b.b.1567.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.bf.a.19.1 | ✓ | 4 | 28.19 | even | 6 | inner | |
252.2.bf.a.19.2 | yes | 4 | 7.5 | odd | 6 | inner | |
252.2.bf.a.199.1 | yes | 4 | 1.1 | even | 1 | trivial | |
252.2.bf.a.199.2 | yes | 4 | 4.3 | odd | 2 | inner | |
252.2.bf.d.19.1 | yes | 4 | 21.5 | even | 6 | ||
252.2.bf.d.19.2 | yes | 4 | 84.47 | odd | 6 | ||
252.2.bf.d.199.1 | yes | 4 | 12.11 | even | 2 | ||
252.2.bf.d.199.2 | yes | 4 | 3.2 | odd | 2 | ||
1764.2.b.b.1567.1 | 4 | 84.11 | even | 6 | |||
1764.2.b.b.1567.2 | 4 | 84.59 | odd | 6 | |||
1764.2.b.b.1567.3 | 4 | 21.11 | odd | 6 | |||
1764.2.b.b.1567.4 | 4 | 21.17 | even | 6 | |||
1764.2.b.h.1567.1 | 4 | 7.3 | odd | 6 | |||
1764.2.b.h.1567.2 | 4 | 7.4 | even | 3 | |||
1764.2.b.h.1567.3 | 4 | 28.3 | even | 6 | |||
1764.2.b.h.1567.4 | 4 | 28.11 | odd | 6 |