Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(26,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.bk (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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.796594176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 5x^{6} - 2x^{5} + 63x^{4} - 64x^{3} + 46x^{2} - 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(2.62039 - 0.935532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1151 |
Dual form | 1575.2.bk.d.26.4 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29129 | − | 1.32288i | 0.866025 | − | 0.500000i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | + | 1.41421i | 0.738549 | + | 0.426401i | 0.821541 | − | 0.570149i | \(-0.193114\pi\) |
−0.0829925 | + | 0.996550i | \(0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575i | 0.733799i | 0.930261 | + | 0.366900i | \(0.119581\pi\) | ||||
−0.930261 | + | 0.366900i | \(0.880419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 1.87083 | − | 3.24037i | 0.453743 | − | 0.785905i | −0.544872 | − | 0.838519i | \(-0.683422\pi\) |
0.998615 | + | 0.0526138i | \(0.0167552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.61249 | − | 3.24037i | 1.17028 | − | 0.675664i | 0.216537 | − | 0.976274i | \(-0.430524\pi\) |
0.953747 | + | 0.300610i | \(0.0971904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150i | 1.00000i | ||||||||
\(29\) | − | 1.41421i | − | 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 2.59808i | 0.808224 | + | 0.466628i | 0.846339 | − | 0.532645i | \(-0.178802\pi\) |
−0.0381148 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.29129 | + | 3.96863i | 0.376685 | + | 0.652438i | 0.990578 | − | 0.136951i | \(-0.0437304\pi\) |
−0.613892 | + | 0.789390i | \(0.710397\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.58258 | −0.698836 | −0.349418 | − | 0.936967i | \(-0.613621\pi\) | ||||
−0.349418 | + | 0.936967i | \(0.613621\pi\) | |||||||
\(44\) | −4.89898 | + | 2.82843i | −0.738549 | + | 0.426401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.87083 | + | 3.24037i | 0.272888 | + | 0.472657i | 0.969600 | − | 0.244695i | \(-0.0786877\pi\) |
−0.696712 | + | 0.717351i | \(0.745354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.58258 | − | 2.64575i | −0.635489 | − | 0.366900i | ||||
\(53\) | 11.2250 | + | 6.48074i | 1.54187 | + | 0.890198i | 0.998721 | + | 0.0505609i | \(0.0161009\pi\) |
0.543148 | + | 0.839637i | \(0.317232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.67423 | − | 6.36396i | 0.478345 | − | 0.828517i | −0.521347 | − | 0.853345i | \(-0.674570\pi\) |
0.999692 | + | 0.0248275i | \(0.00790366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | + | 5.19615i | −1.15233 | + | 0.665299i | −0.949454 | − | 0.313905i | \(-0.898363\pi\) |
−0.202878 | + | 0.979204i | \(0.565029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.87386 | + | 11.9059i | −0.839776 | + | 1.45453i | 0.0503056 | + | 0.998734i | \(0.483980\pi\) |
−0.890082 | + | 0.455801i | \(0.849353\pi\) | |||||||
\(68\) | 3.74166 | + | 6.48074i | 0.453743 | + | 0.785905i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.3137i | − | 1.34269i | −0.741145 | − | 0.671345i | \(-0.765717\pi\) | ||
0.741145 | − | 0.671345i | \(-0.234283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4564 | + | 6.61438i | 1.34087 | + | 0.774154i | 0.986936 | − | 0.161114i | \(-0.0515087\pi\) |
0.353939 | + | 0.935269i | \(0.384842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | 7.48331 | 0.852803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50000 | − | 6.06218i | −0.393781 | − | 0.682048i | 0.599164 | − | 0.800626i | \(-0.295500\pi\) |
−0.992945 | + | 0.118578i | \(0.962166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9666 | 1.64280 | 0.821401 | − | 0.570352i | \(-0.193193\pi\) | ||||
0.821401 | + | 0.570352i | \(0.193193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.57321 | + | 14.8492i | 0.908759 | + | 1.57402i | 0.815791 | + | 0.578347i | \(0.196302\pi\) |
0.0929683 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | + | 6.06218i | 0.366900 | + | 0.635489i | ||||
\(92\) | 12.9615i | 1.35133i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.29150i | 0.537271i | 0.963242 | + | 0.268635i | \(0.0865727\pi\) | ||||
−0.963242 | + | 0.268635i | \(0.913427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.89898 | + | 8.48528i | −0.487467 | + | 0.844317i | −0.999896 | − | 0.0144123i | \(-0.995412\pi\) |
0.512429 | + | 0.858729i | \(0.328746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4564 | + | 6.61438i | −1.12884 | + | 0.651734i | −0.943642 | − | 0.330968i | \(-0.892625\pi\) |
−0.185194 | + | 0.982702i | \(0.559292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.61249 | − | 3.24037i | 0.542580 | − | 0.313258i | −0.203544 | − | 0.979066i | \(-0.565246\pi\) |
0.746124 | + | 0.665807i | \(0.231913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | + | 6.06218i | −0.335239 | + | 0.580651i | −0.983531 | − | 0.180741i | \(-0.942150\pi\) |
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.16515 | − | 5.29150i | −0.866025 | − | 0.500000i | ||||
\(113\) | − | 6.48074i | − | 0.609657i | −0.952407 | − | 0.304828i | \(-0.901401\pi\) | ||
0.952407 | − | 0.304828i | \(-0.0985991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.44949 | + | 1.41421i | 0.227429 | + | 0.131306i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.89949i | − | 0.907485i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | − | 2.59808i | −0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | + | 5.19615i | −0.808224 | + | 0.466628i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7477 | 1.21991 | 0.609957 | − | 0.792435i | \(-0.291187\pi\) | ||||
0.609957 | + | 0.792435i | \(0.291187\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.57321 | + | 14.8492i | 0.749045 | + | 1.29738i | 0.948281 | + | 0.317433i | \(0.102821\pi\) |
−0.199236 | + | 0.979952i | \(0.563846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.29129 | + | 3.96863i | −0.198680 | + | 0.344124i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.61249 | − | 3.24037i | −0.479507 | − | 0.276844i | 0.240704 | − | 0.970599i | \(-0.422622\pi\) |
−0.720211 | + | 0.693755i | \(0.755955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.66025i | 0.734553i | 0.930112 | + | 0.367277i | \(0.119710\pi\) | ||||
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.74166 | + | 6.48074i | −0.312893 | + | 0.541947i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.16515 | −0.753371 | ||||||||
\(149\) | −12.2474 | + | 7.07107i | −1.00335 | + | 0.579284i | −0.909238 | − | 0.416277i | \(-0.863335\pi\) |
−0.0941123 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.58258 | − | 2.64575i | −0.365729 | − | 0.211154i | 0.305862 | − | 0.952076i | \(-0.401055\pi\) |
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.57321 | − | 14.8492i | 0.675664 | − | 1.17028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.58258 | + | 7.93725i | 0.358935 | + | 0.621694i | 0.987783 | − | 0.155834i | \(-0.0498066\pi\) |
−0.628848 | + | 0.777528i | \(0.716473\pi\) | |||||||
\(164\) | 4.89898 | − | 8.48528i | 0.382546 | − | 0.662589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.48331 | 0.579076 | 0.289538 | − | 0.957166i | \(-0.406498\pi\) | ||||
0.289538 | + | 0.957166i | \(0.406498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | 0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.58258 | − | 7.93725i | 0.349418 | − | 0.605210i | ||||
\(173\) | −7.48331 | − | 12.9615i | −0.568946 | − | 0.985443i | −0.996671 | − | 0.0815341i | \(-0.974018\pi\) |
0.427725 | − | 0.903909i | \(-0.359315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 11.3137i | − | 0.852803i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.12372 | − | 3.53553i | −0.457709 | − | 0.264258i | 0.253372 | − | 0.967369i | \(-0.418460\pi\) |
−0.711080 | + | 0.703111i | \(0.751794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.5885i | − | 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.16515 | − | 5.29150i | 0.670222 | − | 0.386953i | ||||
\(188\) | −7.48331 | −0.545777 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4722 | + | 7.77817i | −0.974814 | + | 0.562809i | −0.900700 | − | 0.434441i | \(-0.856946\pi\) |
−0.0741134 | + | 0.997250i | \(0.523613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.87386 | − | 11.9059i | 0.494792 | − | 0.857004i | −0.505190 | − | 0.863008i | \(-0.668578\pi\) |
0.999982 | + | 0.00600382i | \(0.00191109\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(197\) | − | 19.4422i | − | 1.38520i | −0.721321 | − | 0.692600i | \(-0.756465\pi\) | ||
0.721321 | − | 0.692600i | \(-0.243535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.00000 | − | 3.46410i | −0.425329 | − | 0.245564i | 0.272026 | − | 0.962290i | \(-0.412306\pi\) |
−0.697355 | + | 0.716726i | \(0.745640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.87083 | − | 3.24037i | −0.131306 | − | 0.227429i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.16515 | − | 5.29150i | 0.635489 | − | 0.366900i | ||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −22.4499 | + | 12.9615i | −1.54187 | + | 0.890198i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.7477 | 0.933257 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.57321 | + | 4.94975i | 0.576697 | + | 0.332956i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.29150i | − | 0.354345i | −0.984180 | − | 0.177173i | \(-0.943305\pi\) | ||
0.984180 | − | 0.177173i | \(-0.0566951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.48331 | − | 12.9615i | 0.496685 | − | 0.860284i | −0.503308 | − | 0.864107i | \(-0.667884\pi\) |
0.999993 | + | 0.00382356i | \(0.00121708\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.50000 | − | 0.866025i | 0.0991228 | − | 0.0572286i | −0.449619 | − | 0.893220i | \(-0.648440\pi\) |
0.548742 | + | 0.835992i | \(0.315107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.61249 | + | 3.24037i | −0.367686 | + | 0.212284i | −0.672447 | − | 0.740145i | \(-0.734757\pi\) |
0.304761 | + | 0.952429i | \(0.401423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.34847 | + | 12.7279i | 0.478345 | + | 0.828517i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.3848i | − | 1.18921i | −0.804017 | − | 0.594606i | \(-0.797308\pi\) | ||
0.804017 | − | 0.594606i | \(-0.202692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0000 | − | 8.66025i | −0.966235 | − | 0.557856i | −0.0681486 | − | 0.997675i | \(-0.521709\pi\) |
−0.898086 | + | 0.439819i | \(0.855043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 20.7846i | − | 1.33060i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.29129 | − | 3.96863i | −0.145791 | − | 0.252518i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0454 | −1.39149 | −0.695747 | − | 0.718287i | \(-0.744926\pi\) | ||||
−0.695747 | + | 0.718287i | \(0.744926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.3303 | 1.15242 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.74166 | − | 6.48074i | −0.233398 | − | 0.404257i | 0.725408 | − | 0.688319i | \(-0.241651\pi\) |
−0.958806 | + | 0.284062i | \(0.908318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5000 | + | 6.06218i | 0.652438 | + | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.2250 | − | 6.48074i | −0.692161 | − | 0.399620i | 0.112260 | − | 0.993679i | \(-0.464191\pi\) |
−0.804421 | + | 0.594059i | \(0.797524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.7477 | − | 23.8118i | −0.839776 | − | 1.45453i | ||||
\(269\) | −8.57321 | + | 14.8492i | −0.522718 | + | 0.905374i | 0.476932 | + | 0.878940i | \(0.341749\pi\) |
−0.999651 | + | 0.0264343i | \(0.991585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | + | 6.92820i | −0.728948 | + | 0.420858i | −0.818037 | − | 0.575165i | \(-0.804938\pi\) |
0.0890891 | + | 0.996024i | \(0.471604\pi\) | |||||||
\(272\) | −14.9666 | −0.907485 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.29129 | − | 3.96863i | 0.137670 | − | 0.238452i | −0.788944 | − | 0.614465i | \(-0.789372\pi\) |
0.926614 | + | 0.376013i | \(0.122705\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.2843i | − | 1.68730i | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||
0.536895 | − | 0.843649i | \(-0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.0390 | − | 9.26013i | −0.953420 | − | 0.550458i | −0.0592787 | − | 0.998241i | \(-0.518880\pi\) |
−0.894142 | + | 0.447784i | \(0.852213\pi\) | |||||||
\(284\) | 19.5959 | + | 11.3137i | 1.16280 | + | 0.671345i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.2250 | + | 6.48074i | −0.662589 | + | 0.382546i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.50000 | + | 2.59808i | 0.0882353 | + | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.9129 | + | 13.2288i | −1.34087 | + | 0.774154i | ||||
\(293\) | −29.9333 | −1.74872 | −0.874360 | − | 0.485278i | \(-0.838718\pi\) | ||||
−0.874360 | + | 0.485278i | \(0.838718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.57321 | + | 14.8492i | 0.495802 | + | 0.858754i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5000 | + | 6.06218i | −0.605210 | + | 0.349418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000 | + | 3.46410i | 0.344124 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.64575i | − | 0.151001i | −0.997146 | − | 0.0755005i | \(-0.975945\pi\) | ||
0.997146 | − | 0.0755005i | \(-0.0240554\pi\) | |||||||
\(308\) | −7.48331 | + | 12.9615i | −0.426401 | + | 0.738549i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0390 | − | 9.26013i | 0.906579 | − | 0.523413i | 0.0272499 | − | 0.999629i | \(-0.491325\pi\) |
0.879329 | + | 0.476215i | \(0.157992\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 16.8375 | − | 9.72111i | 0.945686 | − | 0.545992i | 0.0539477 | − | 0.998544i | \(-0.482820\pi\) |
0.891738 | + | 0.452552i | \(0.149486\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.48074i | 0.360598i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.57321 | + | 4.94975i | 0.472657 | + | 0.272888i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | −14.9666 | + | 25.9230i | −0.821401 | + | 1.42271i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.0780 | −1.74740 | −0.873701 | − | 0.486464i | \(-0.838287\pi\) | ||||
−0.873701 | + | 0.486464i | \(0.838287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.34847 | + | 12.7279i | 0.397942 | + | 0.689256i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.46410i | − | 0.185429i | −0.995693 | − | 0.0927146i | \(-0.970446\pi\) | ||
0.995693 | − | 0.0927146i | \(-0.0295544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.74166 | − | 6.48074i | 0.199148 | − | 0.344935i | −0.749104 | − | 0.662452i | \(-0.769516\pi\) |
0.948253 | + | 0.317517i | \(0.102849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −34.2929 | −1.81752 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4722 | − | 7.77817i | 0.711035 | − | 0.410516i | −0.100409 | − | 0.994946i | \(-0.532015\pi\) |
0.811444 | + | 0.584430i | \(0.198682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.0000 | −0.733799 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0390 | + | 9.26013i | 0.837230 | + | 0.483375i | 0.856322 | − | 0.516443i | \(-0.172744\pi\) |
−0.0190919 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(368\) | −22.4499 | − | 12.9615i | −1.17028 | − | 0.675664i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.2929 | 1.78040 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.29129 | + | 3.96863i | 0.118638 | + | 0.205488i | 0.919228 | − | 0.393725i | \(-0.128814\pi\) |
−0.800590 | + | 0.599213i | \(0.795480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.74166 | 0.192705 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.74166 | + | 6.48074i | 0.191190 | + | 0.331150i | 0.945645 | − | 0.325201i | \(-0.105432\pi\) |
−0.754455 | + | 0.656352i | \(0.772099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.16515 | − | 5.29150i | −0.465290 | − | 0.268635i | ||||
\(389\) | −2.44949 | − | 1.41421i | −0.124194 | − | 0.0717035i | 0.436616 | − | 0.899648i | \(-0.356177\pi\) |
−0.560810 | + | 0.827945i | \(0.689510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 24.2487i | − | 1.22631i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.2042 | − | 14.5516i | 1.26496 | − | 0.730325i | 0.290931 | − | 0.956744i | \(-0.406035\pi\) |
0.974030 | + | 0.226419i | \(0.0727017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.89898 | − | 2.82843i | 0.244643 | − | 0.141245i | −0.372666 | − | 0.927966i | \(-0.621556\pi\) |
0.617309 | + | 0.786721i | \(0.288223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.87386 | + | 11.9059i | −0.342412 | + | 0.593074i | ||||
\(404\) | −9.79796 | − | 16.9706i | −0.487467 | − | 0.844317i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9615i | 0.642477i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 2.59808i | 0.222511 | + | 0.128467i | 0.607112 | − | 0.794616i | \(-0.292328\pi\) |
−0.384602 | + | 0.923083i | \(0.625661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 26.4575i | − | 1.30347i | ||||||
\(413\) | − | 19.4422i | − | 0.956689i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1464 | −0.837658 | −0.418829 | − | 0.908065i | \(-0.637559\pi\) | ||||
−0.418829 | + | 0.908065i | \(0.637559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0000 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7477 | + | 23.8118i | −0.665299 | + | 1.15233i | ||||
\(428\) | 12.9615i | 0.626517i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.12372 | + | 3.53553i | 0.294969 | + | 0.170301i | 0.640181 | − | 0.768224i | \(-0.278859\pi\) |
−0.345211 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.2288i | − | 0.635733i | −0.948135 | − | 0.317867i | \(-0.897034\pi\) | ||
0.948135 | − | 0.317867i | \(-0.102966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | −5.61249 | + | 9.72111i | −0.268482 | + | 0.465024i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.00000 | + | 5.19615i | −0.429547 | + | 0.247999i | −0.699153 | − | 0.714972i | \(-0.746440\pi\) |
0.269607 | + | 0.962970i | \(0.413106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.6749 | + | 19.4422i | −1.59994 | + | 0.923728i | −0.608447 | + | 0.793594i | \(0.708207\pi\) |
−0.991496 | + | 0.130133i | \(0.958459\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.3303 | − | 10.5830i | 0.866025 | − | 0.500000i | ||||
\(449\) | − | 18.3848i | − | 0.867631i | −0.901002 | − | 0.433816i | \(-0.857167\pi\) | ||
0.901002 | − | 0.433816i | \(-0.142833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | − | 6.92820i | −0.565058 | − | 0.326236i | ||||
\(452\) | 11.2250 | + | 6.48074i | 0.527978 | + | 0.304828i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.87386 | − | 11.9059i | −0.321546 | − | 0.556934i | 0.659261 | − | 0.751914i | \(-0.270869\pi\) |
−0.980807 | + | 0.194980i | \(0.937536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.1464 | −0.798589 | −0.399294 | − | 0.916823i | \(-0.630745\pi\) | ||||
−0.399294 | + | 0.916823i | \(0.630745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58258 | 0.212970 | 0.106485 | − | 0.994314i | \(-0.466040\pi\) | ||||
0.106485 | + | 0.994314i | \(0.466040\pi\) | |||||||
\(464\) | −4.89898 | + | 2.82843i | −0.227429 | + | 0.131306i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.87083 | + | 3.24037i | 0.0865716 | + | 0.149946i | 0.906060 | − | 0.423150i | \(-0.139076\pi\) |
−0.819488 | + | 0.573096i | \(0.805742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.3731i | 1.67955i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2250 | − | 6.48074i | −0.516125 | − | 0.297985i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.1464 | + | 9.89949i | 0.785905 | + | 0.453743i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.1464 | + | 29.6985i | −0.783440 | + | 1.35696i | 0.146486 | + | 0.989213i | \(0.453204\pi\) |
−0.929926 | + | 0.367746i | \(0.880130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5000 | + | 6.06218i | −0.478759 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.00000 | 0.272727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4564 | − | 19.8431i | 0.519141 | − | 0.899178i | −0.480612 | − | 0.876933i | \(-0.659585\pi\) |
0.999753 | − | 0.0222448i | \(-0.00708132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.3137i | − | 0.510581i | −0.966864 | − | 0.255290i | \(-0.917829\pi\) | ||
0.966864 | − | 0.255290i | \(-0.0821710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.58258 | − | 2.64575i | −0.206389 | − | 0.119159i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.7846i | − | 0.933257i | ||||||
\(497\) | −14.9666 | − | 25.9230i | −0.671345 | − | 1.16280i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.50000 | − | 11.2583i | −0.290980 | − | 0.503992i | 0.683062 | − | 0.730361i | \(-0.260648\pi\) |
−0.974042 | + | 0.226369i | \(0.927315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.74166 | 0.166832 | 0.0834161 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834161 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.7477 | + | 23.8118i | −0.609957 | + | 1.05648i | ||||
\(509\) | −8.57321 | − | 14.8492i | −0.380001 | − | 0.658181i | 0.611061 | − | 0.791584i | \(-0.290743\pi\) |
−0.991062 | + | 0.133402i | \(0.957410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.0000 | 1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5830i | 0.465440i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1464 | + | 29.6985i | −0.751199 | + | 1.30111i | 0.196043 | + | 0.980595i | \(0.437191\pi\) |
−0.947242 | + | 0.320519i | \(0.896143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.4564 | + | 6.61438i | −0.500955 | + | 0.289227i | −0.729108 | − | 0.684399i | \(-0.760065\pi\) |
0.228153 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(524\) | −34.2929 | −1.49809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.8375 | − | 9.72111i | 0.733451 | − | 0.423458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.58258 | − | 7.93725i | −0.198680 | − | 0.344124i | ||||
\(533\) | − | 12.9615i | − | 0.561424i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.1464 | − | 9.89949i | 0.738549 | − | 0.426401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.50000 | + | 6.06218i | 0.150477 | + | 0.260633i | 0.931403 | − | 0.363990i | \(-0.118586\pi\) |
−0.780926 | + | 0.624623i | \(0.785252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3303 | 0.783747 | 0.391874 | − | 0.920019i | \(-0.371827\pi\) | ||||
0.391874 | + | 0.920019i | \(0.371827\pi\) | |||||||
\(548\) | 11.2250 | − | 6.48074i | 0.479507 | − | 0.276844i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.22474 | + | 2.12132i | 0.0521759 | + | 0.0903713i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.0390 | − | 9.26013i | −0.682048 | − | 0.393781i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0000 | − | 8.66025i | −0.636142 | − | 0.367277i | ||||
\(557\) | 5.61249 | + | 3.24037i | 0.237809 | + | 0.137299i | 0.614169 | − | 0.789174i | \(-0.289491\pi\) |
−0.376360 | + | 0.926473i | \(0.622825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.1244i | − | 0.512806i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.35414 | − | 16.2019i | 0.394230 | − | 0.682827i | −0.598772 | − | 0.800919i | \(-0.704345\pi\) |
0.993003 | + | 0.118093i | \(0.0376780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.1918 | − | 22.6274i | 1.64301 | − | 0.948591i | 0.663251 | − | 0.748397i | \(-0.269176\pi\) |
0.979756 | − | 0.200194i | \(-0.0641571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50000 | + | 14.7224i | −0.355714 | + | 0.616115i | −0.987240 | − | 0.159240i | \(-0.949096\pi\) |
0.631526 | + | 0.775355i | \(0.282429\pi\) | |||||||
\(572\) | −7.48331 | − | 12.9615i | −0.312893 | − | 0.541947i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.7867 | + | 17.1974i | 1.24004 | + | 0.715936i | 0.969102 | − | 0.246661i | \(-0.0793334\pi\) |
0.270936 | + | 0.962597i | \(0.412667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.2929 | − | 19.7990i | 1.42271 | − | 0.821401i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.3303 | + | 31.7490i | 0.759164 | + | 1.31491i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.1916 | −1.08104 | −0.540522 | − | 0.841330i | \(-0.681773\pi\) | ||||
−0.540522 | + | 0.841330i | \(0.681773\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.16515 | − | 15.8745i | 0.376685 | − | 0.652438i | ||||
\(593\) | −7.48331 | − | 12.9615i | −0.307303 | − | 0.532264i | 0.670468 | − | 0.741938i | \(-0.266093\pi\) |
−0.977771 | + | 0.209674i | \(0.932760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 28.2843i | − | 1.15857i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.44949 | − | 1.41421i | −0.100083 | − | 0.0577832i | 0.449123 | − | 0.893470i | \(-0.351737\pi\) |
−0.549206 | + | 0.835687i | \(0.685070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66025i | 0.353259i | 0.984277 | + | 0.176630i | \(0.0565195\pi\) | ||||
−0.984277 | + | 0.176630i | \(0.943481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | + | 17.3205i | 0.406894 | + | 0.704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7867 | + | 17.1974i | −1.20901 | + | 0.698020i | −0.962542 | − | 0.271132i | \(-0.912602\pi\) |
−0.246464 | + | 0.969152i | \(0.579269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.57321 | + | 4.94975i | −0.346835 | + | 0.200245i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.16515 | − | 15.8745i | 0.370177 | − | 0.641165i | −0.619416 | − | 0.785063i | \(-0.712630\pi\) |
0.989593 | + | 0.143898i | \(0.0459637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.4037i | − | 1.30452i | −0.757994 | − | 0.652262i | \(-0.773820\pi\) | ||
0.757994 | − | 0.652262i | \(-0.226180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5000 | − | 14.7224i | −1.02493 | − | 0.591744i | −0.109403 | − | 0.993997i | \(-0.534894\pi\) |
−0.915529 | + | 0.402253i | \(0.868227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.2874 | + | 22.6826i | 1.57402 | + | 0.908759i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.16515 | − | 5.29150i | 0.365729 | − | 0.211154i | ||||
\(629\) | 17.1464 | 0.683673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0390 | + | 9.26013i | 0.635489 | + | 0.366900i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.2702 | − | 13.4350i | −0.919116 | − | 0.530652i | −0.0357629 | − | 0.999360i | \(-0.511386\pi\) |
−0.883353 | + | 0.468709i | \(0.844719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.64575i | 0.104338i | 0.998638 | + | 0.0521691i | \(0.0166135\pi\) | ||||
−0.998638 | + | 0.0521691i | \(0.983387\pi\) | |||||||
\(644\) | 17.1464 | + | 29.6985i | 0.675664 | + | 1.17028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.48331 | − | 12.9615i | 0.294199 | − | 0.509568i | −0.680599 | − | 0.732656i | \(-0.738280\pi\) |
0.974798 | + | 0.223088i | \(0.0716137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | − | 10.3923i | 0.706562 | − | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.3303 | −0.717870 | ||||||||
\(653\) | 22.4499 | − | 12.9615i | 0.878534 | − | 0.507222i | 0.00835938 | − | 0.999965i | \(-0.497339\pi\) |
0.870175 | + | 0.492743i | \(0.164006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.79796 | + | 16.9706i | 0.382546 | + | 0.662589i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2843i | 1.10180i | 0.834572 | + | 0.550899i | \(0.185715\pi\) | ||||
−0.834572 | + | 0.550899i | \(0.814285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50000 | − | 2.59808i | −0.175030 | − | 0.101053i | 0.409926 | − | 0.912119i | \(-0.365555\pi\) |
−0.584955 | + | 0.811065i | \(0.698888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.58258 | − | 7.93725i | −0.177438 | − | 0.307332i | ||||
\(668\) | −7.48331 | + | 12.9615i | −0.289538 | + | 0.501495i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3939 | −1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9129 | 0.883227 | 0.441613 | − | 0.897206i | \(-0.354406\pi\) | ||||
0.441613 | + | 0.897206i | \(0.354406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 1.87083 | + | 3.24037i | 0.0719018 | + | 0.124538i | 0.899735 | − | 0.436437i | \(-0.143760\pi\) |
−0.827833 | + | 0.560975i | \(0.810427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | + | 12.1244i | 0.268635 | + | 0.465290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0624 | + | 16.2019i | 1.07378 | + | 0.619947i | 0.929212 | − | 0.369548i | \(-0.120488\pi\) |
0.144568 | + | 0.989495i | \(0.453821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.16515 | + | 15.8745i | 0.349418 | + | 0.605210i | ||||
\(689\) | −17.1464 | + | 29.6985i | −0.653227 | + | 1.13142i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.5000 | + | 23.3827i | −1.54069 | + | 0.889519i | −0.541897 | + | 0.840445i | \(0.682294\pi\) |
−0.998795 | + | 0.0490747i | \(0.984373\pi\) | |||||||
\(692\) | 29.9333 | 1.13789 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.16515 | + | 15.8745i | −0.347155 | + | 0.601290i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41421i | 0.0534141i | 0.999643 | + | 0.0267071i | \(0.00850213\pi\) | ||||
−0.999643 | + | 0.0267071i | \(0.991498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.87386 | − | 3.96863i | −0.259253 | − | 0.149680i | ||||
\(704\) | 19.5959 | + | 11.3137i | 0.738549 | + | 0.426401i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.9230i | 0.974933i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | + | 6.92820i | 0.150223 | + | 0.260194i | 0.931309 | − | 0.364229i | \(-0.118667\pi\) |
−0.781086 | + | 0.624423i | \(0.785334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.6749 | 1.26114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.2474 | − | 7.07107i | 0.457709 | − | 0.264258i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.22474 | + | 2.12132i | 0.0456753 | + | 0.0791119i | 0.887959 | − | 0.459922i | \(-0.152123\pi\) |
−0.842284 | + | 0.539034i | \(0.818789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5000 | + | 30.3109i | −0.651734 | + | 1.12884i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.0000 | + | 15.5885i | 1.00345 | + | 0.579340i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1033i | 1.07938i | 0.841864 | + | 0.539690i | \(0.181459\pi\) | ||||
−0.841864 | + | 0.539690i | \(0.818541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.57321 | + | 14.8492i | −0.317092 | + | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4564 | + | 6.61438i | −0.423153 | + | 0.244308i | −0.696426 | − | 0.717629i | \(-0.745227\pi\) |
0.273272 | + | 0.961937i | \(0.411894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.6749 | + | 19.4422i | −1.24043 | + | 0.716163i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.50000 | − | 14.7224i | 0.312678 | − | 0.541573i | −0.666264 | − | 0.745716i | \(-0.732107\pi\) |
0.978941 | + | 0.204143i | \(0.0654407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.8459i | 1.90204i | 0.309125 | + | 0.951021i | \(0.399964\pi\) | ||||
−0.309125 | + | 0.951021i | \(0.600036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.1660i | 0.773906i | ||||||||
\(749\) | 8.57321 | − | 14.8492i | 0.313258 | − | 0.542580i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.50000 | + | 6.06218i | 0.127717 | + | 0.221212i | 0.922792 | − | 0.385299i | \(-0.125902\pi\) |
−0.795075 | + | 0.606511i | \(0.792568\pi\) | |||||||
\(752\) | 7.48331 | − | 12.9615i | 0.272888 | − | 0.472657i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.57321 | + | 14.8492i | 0.310779 | + | 0.538285i | 0.978531 | − | 0.206099i | \(-0.0660768\pi\) |
−0.667752 | + | 0.744383i | \(0.732744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.5203i | 0.670478i | ||||||||
\(764\) | − | 31.1127i | − | 1.12562i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.8375 | + | 9.72111i | 0.607965 | + | 0.351009i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.9090i | − | 1.18673i | −0.804934 | − | 0.593364i | \(-0.797800\pi\) | ||
0.804934 | − | 0.593364i | \(-0.202200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.7477 | + | 23.8118i | 0.494792 | + | 0.857004i | ||||
\(773\) | 14.9666 | − | 25.9230i | 0.538312 | − | 0.932384i | −0.460683 | − | 0.887565i | \(-0.652395\pi\) |
0.998995 | − | 0.0448193i | \(-0.0142712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.34847 | − | 4.24264i | 0.263286 | − | 0.152008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.8258 | − | 26.4575i | −1.63351 | − | 0.943108i | −0.982998 | − | 0.183614i | \(-0.941220\pi\) |
−0.650513 | − | 0.759495i | \(-0.725446\pi\) | |||||||
\(788\) | 33.6749 | + | 19.4422i | 1.19962 | + | 0.692600i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.57321 | − | 14.8492i | −0.304828 | − | 0.527978i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.7477 | − | 23.8118i | −0.488196 | − | 0.845580i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0000 | − | 6.92820i | 0.425329 | − | 0.245564i | ||||
\(797\) | 41.1582 | 1.45790 | 0.728950 | − | 0.684567i | \(-0.240009\pi\) | ||||
0.728950 | + | 0.684567i | \(0.240009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0000 | 0.495284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.7083 | + | 32.4037i | 0.660201 | + | 1.14350i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.1691 | − | 16.2635i | −0.990374 | − | 0.571793i | −0.0849879 | − | 0.996382i | \(-0.527085\pi\) |
−0.905386 | + | 0.424589i | \(0.860418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.7846i | − | 0.729846i | −0.931038 | − | 0.364923i | \(-0.881095\pi\) | ||
0.931038 | − | 0.364923i | \(-0.118905\pi\) | |||||||
\(812\) | 7.48331 | 0.262613 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.87386 | − | 3.96863i | 0.240486 | − | 0.138845i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.89898 | − | 2.82843i | 0.170976 | − | 0.0987128i | −0.412070 | − | 0.911152i | \(-0.635194\pi\) |
0.583046 | + | 0.812439i | \(0.301861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.7477 | + | 23.8118i | −0.479216 | + | 0.830026i | −0.999716 | − | 0.0238357i | \(-0.992412\pi\) |
0.520500 | + | 0.853862i | \(0.325745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4422i | 0.676072i | 0.941133 | + | 0.338036i | \(0.109763\pi\) | ||||
−0.941133 | + | 0.338036i | \(0.890237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.5000 | − | 21.6506i | −1.30243 | − | 0.751958i | −0.321609 | − | 0.946873i | \(-0.604224\pi\) |
−0.980820 | + | 0.194915i | \(0.937557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.1660i | 0.733799i | ||||||||
\(833\) | −13.0958 | − | 22.6826i | −0.453743 | − | 0.785905i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.89898 | − | 8.48528i | 0.169435 | − | 0.293470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2474 | −0.422829 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.0000 | + | 24.2487i | −0.481900 | + | 0.834675i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.87386 | − | 3.96863i | −0.236189 | − | 0.136364i | ||||
\(848\) | − | 51.8459i | − | 1.78040i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.7196 | + | 14.8492i | 0.881658 | + | 0.509025i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2693i | 1.72119i | 0.509292 | + | 0.860594i | \(0.329907\pi\) | ||||
−0.509292 | + | 0.860594i | \(0.670093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.35414 | + | 16.2019i | −0.319531 | + | 0.553445i | −0.980390 | − | 0.197065i | \(-0.936859\pi\) |
0.660859 | + | 0.750510i | \(0.270192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | + | 6.92820i | −0.409435 | + | 0.236387i | −0.690547 | − | 0.723288i | \(-0.742630\pi\) |
0.281112 | + | 0.959675i | \(0.409297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.0624 | − | 16.2019i | 0.955256 | − | 0.551517i | 0.0605464 | − | 0.998165i | \(-0.480716\pi\) |
0.894710 | + | 0.446648i | \(0.147382\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.7477 | + | 23.8118i | −0.466628 | + | 0.808224i | ||||
\(869\) | − | 19.7990i | − | 0.671635i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.5000 | − | 18.1865i | −1.06734 | − | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.58258 | + | 7.93725i | 0.154743 | + | 0.268022i | 0.932965 | − | 0.359966i | \(-0.117212\pi\) |
−0.778223 | + | 0.627988i | \(0.783879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3939 | −0.990305 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.2432 | −1.38794 | −0.693972 | − | 0.720002i | \(-0.744141\pi\) | ||||
−0.693972 | + | 0.720002i | \(0.744141\pi\) | |||||||
\(884\) | −17.1464 | + | 9.89949i | −0.576697 | + | 0.332956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.7083 | + | 32.4037i | 0.628163 | + | 1.08801i | 0.987920 | + | 0.154964i | \(0.0495261\pi\) |
−0.359757 | + | 0.933046i | \(0.617141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.5000 | − | 18.1865i | 1.05648 | − | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.16515 | + | 5.29150i | 0.306872 | + | 0.177173i | ||||
\(893\) | −5.61249 | − | 3.24037i | −0.187815 | − | 0.108435i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.67423 | − | 6.36396i | 0.122543 | − | 0.212250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.0000 | − | 24.2487i | 1.39922 | − | 0.807842i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4564 | + | 19.8431i | −0.380405 | + | 0.658880i | −0.991120 | − | 0.132970i | \(-0.957549\pi\) |
0.610715 | + | 0.791850i | \(0.290882\pi\) | |||||||
\(908\) | 14.9666 | + | 25.9230i | 0.496685 | + | 0.860284i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.0122i | − | 1.35879i | −0.733771 | − | 0.679397i | \(-0.762241\pi\) | ||
0.733771 | − | 0.679397i | \(-0.237759\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.6606 | + | 21.1660i | 1.21329 | + | 0.700493i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.46410i | 0.114457i | ||||||||
\(917\) | 39.2874 | + | 22.6826i | 1.29738 | + | 0.749045i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5000 | + | 30.3109i | 0.577272 | + | 0.999864i | 0.995791 | + | 0.0916559i | \(0.0292160\pi\) |
−0.418519 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.9333 | 0.985265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.1244i | 0.397360i | ||||||||
\(932\) | − | 12.9615i | − | 0.424567i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.2693i | − | 1.64223i | −0.570766 | − | 0.821113i | \(-0.693354\pi\) | ||
0.570766 | − | 0.821113i | \(-0.306646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.67423 | + | 6.36396i | −0.119777 | + | 0.207459i | −0.919679 | − | 0.392671i | \(-0.871551\pi\) |
0.799902 | + | 0.600130i | \(0.204885\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.4955 | + | 15.8745i | −0.895375 | + | 0.516945i | ||||
\(944\) | −29.3939 | −0.956689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.6749 | − | 19.4422i | 1.09429 | − | 0.631787i | 0.159573 | − | 0.987186i | \(-0.448988\pi\) |
0.934715 | + | 0.355399i | \(0.115655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.5000 | + | 30.3109i | −0.568074 | + | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31.8434 | + | 18.3848i | 1.02989 | + | 0.594606i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1464 | −0.553687 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | − | 3.46410i | −0.0645161 | − | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.0000 | − | 17.3205i | 0.966235 | − | 0.557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.58258 | −0.147366 | −0.0736828 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736828 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.79796 | + | 16.9706i | 0.314431 | + | 0.544611i | 0.979316 | − | 0.202334i | \(-0.0648528\pi\) |
−0.664885 | + | 0.746946i | \(0.731519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.4564 | + | 19.8431i | 0.367277 | + | 0.636142i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.0000 | + | 20.7846i | 1.15233 | + | 0.665299i | ||||
\(977\) | −33.6749 | − | 19.4422i | −1.07736 | − | 0.622012i | −0.147174 | − | 0.989111i | \(-0.547018\pi\) |
−0.930182 | + | 0.367099i | \(0.880351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.4974i | 1.54998i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.3208 | + | 42.1248i | −0.775712 | + | 1.34357i | 0.158681 | + | 0.987330i | \(0.449276\pi\) |
−0.934393 | + | 0.356243i | \(0.884058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.16515 | 0.291582 | ||||||||
\(989\) | −25.7196 | + | 14.8492i | −0.817837 | + | 0.472178i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50000 | − | 6.06218i | 0.111181 | − | 0.192571i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) |
0.916247 | + | 0.400614i | \(0.131203\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.29129 | + | 1.32288i | 0.0725658 | + | 0.0418959i | 0.535844 | − | 0.844317i | \(-0.319994\pi\) |
−0.463278 | + | 0.886213i | \(0.653327\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.bk.d.1151.4 | 8 | ||
3.2 | odd | 2 | inner | 1575.2.bk.d.1151.3 | 8 | ||
5.2 | odd | 4 | 315.2.bb.a.269.2 | yes | 8 | ||
5.3 | odd | 4 | 315.2.bb.a.269.4 | yes | 8 | ||
5.4 | even | 2 | inner | 1575.2.bk.d.1151.2 | 8 | ||
7.5 | odd | 6 | inner | 1575.2.bk.d.26.3 | 8 | ||
15.2 | even | 4 | 315.2.bb.a.269.3 | yes | 8 | ||
15.8 | even | 4 | 315.2.bb.a.269.1 | yes | 8 | ||
15.14 | odd | 2 | inner | 1575.2.bk.d.1151.1 | 8 | ||
21.5 | even | 6 | inner | 1575.2.bk.d.26.4 | 8 | ||
35.3 | even | 12 | 2205.2.g.a.2204.5 | 8 | |||
35.12 | even | 12 | 315.2.bb.a.89.1 | ✓ | 8 | ||
35.17 | even | 12 | 2205.2.g.a.2204.7 | 8 | |||
35.18 | odd | 12 | 2205.2.g.a.2204.3 | 8 | |||
35.19 | odd | 6 | inner | 1575.2.bk.d.26.1 | 8 | ||
35.32 | odd | 12 | 2205.2.g.a.2204.1 | 8 | |||
35.33 | even | 12 | 315.2.bb.a.89.3 | yes | 8 | ||
105.17 | odd | 12 | 2205.2.g.a.2204.2 | 8 | |||
105.32 | even | 12 | 2205.2.g.a.2204.8 | 8 | |||
105.38 | odd | 12 | 2205.2.g.a.2204.4 | 8 | |||
105.47 | odd | 12 | 315.2.bb.a.89.4 | yes | 8 | ||
105.53 | even | 12 | 2205.2.g.a.2204.6 | 8 | |||
105.68 | odd | 12 | 315.2.bb.a.89.2 | yes | 8 | ||
105.89 | even | 6 | inner | 1575.2.bk.d.26.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.a.89.1 | ✓ | 8 | 35.12 | even | 12 | ||
315.2.bb.a.89.2 | yes | 8 | 105.68 | odd | 12 | ||
315.2.bb.a.89.3 | yes | 8 | 35.33 | even | 12 | ||
315.2.bb.a.89.4 | yes | 8 | 105.47 | odd | 12 | ||
315.2.bb.a.269.1 | yes | 8 | 15.8 | even | 4 | ||
315.2.bb.a.269.2 | yes | 8 | 5.2 | odd | 4 | ||
315.2.bb.a.269.3 | yes | 8 | 15.2 | even | 4 | ||
315.2.bb.a.269.4 | yes | 8 | 5.3 | odd | 4 | ||
1575.2.bk.d.26.1 | 8 | 35.19 | odd | 6 | inner | ||
1575.2.bk.d.26.2 | 8 | 105.89 | even | 6 | inner | ||
1575.2.bk.d.26.3 | 8 | 7.5 | odd | 6 | inner | ||
1575.2.bk.d.26.4 | 8 | 21.5 | even | 6 | inner | ||
1575.2.bk.d.1151.1 | 8 | 15.14 | odd | 2 | inner | ||
1575.2.bk.d.1151.2 | 8 | 5.4 | even | 2 | inner | ||
1575.2.bk.d.1151.3 | 8 | 3.2 | odd | 2 | inner | ||
1575.2.bk.d.1151.4 | 8 | 1.1 | even | 1 | trivial | ||
2205.2.g.a.2204.1 | 8 | 35.32 | odd | 12 | |||
2205.2.g.a.2204.2 | 8 | 105.17 | odd | 12 | |||
2205.2.g.a.2204.3 | 8 | 35.18 | odd | 12 | |||
2205.2.g.a.2204.4 | 8 | 105.38 | odd | 12 | |||
2205.2.g.a.2204.5 | 8 | 35.3 | even | 12 | |||
2205.2.g.a.2204.6 | 8 | 105.53 | even | 12 | |||
2205.2.g.a.2204.7 | 8 | 35.17 | even | 12 | |||
2205.2.g.a.2204.8 | 8 | 105.32 | even | 12 |