Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(349,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 145) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.349 |
Dual form | 725.2.b.c.349.2 |
$q$-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 \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).
\(n\) | \(176\) | \(552\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214i | 0.292893i | 0.989219 | + | 0.146447i | \(0.0467837\pi\) | ||||
−0.989219 | + | 0.146447i | \(0.953216\pi\) | |||||||
\(3\) | 2.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.828427 | −0.338204 | ||||||||
\(7\) | − 4.82843i | − 1.82497i | −0.409106 | − | 0.912487i | \(-0.634159\pi\) | ||||
0.409106 | − | 0.912487i | \(-0.365841\pi\) | |||||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 3.65685i | 1.05564i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | − 0.414214i | − 0.0976311i | ||||||||
\(19\) | 4.82843 | 1.10772 | 0.553859 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553859 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.65685 | 2.10730 | ||||||||
\(22\) | 0.343146i | 0.0731589i | ||||||||
\(23\) | 3.17157i | 0.661319i | 0.943750 | + | 0.330659i | \(0.107271\pi\) | ||||
−0.943750 | + | 0.330659i | \(0.892729\pi\) | |||||||
\(24\) | −3.17157 | −0.647395 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.828427 | −0.162468 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 8.82843i | − 1.66842i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.48528 | 1.16479 | 0.582395 | − | 0.812906i | \(-0.302116\pi\) | ||||
0.582395 | + | 0.812906i | \(0.302116\pi\) | |||||||
\(32\) | 4.41421i | 0.780330i | ||||||||
\(33\) | 1.65685i | 0.288421i | ||||||||
\(34\) | −1.17157 | −0.200923 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | − 8.48528i | − 1.39497i | −0.716599 | − | 0.697486i | \(-0.754302\pi\) | ||||
0.716599 | − | 0.697486i | \(-0.245698\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 4.00000i | 0.617213i | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 1.51472 | 0.228352 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.31371 | −0.193696 | ||||||||
\(47\) | − 11.6569i | − 1.70033i | −0.526519 | − | 0.850163i | \(-0.676503\pi\) | ||||
0.526519 | − | 0.850163i | \(-0.323497\pi\) | |||||||
\(48\) | 6.00000i | 0.866025i | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.65685 | −0.792118 | ||||||||
\(52\) | 3.65685i | 0.507114i | ||||||||
\(53\) | 3.65685i | 0.502308i | 0.967947 | + | 0.251154i | \(0.0808100\pi\) | ||||
−0.967947 | + | 0.251154i | \(0.919190\pi\) | |||||||
\(54\) | −1.65685 | −0.225469 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.65685 | 1.02319 | ||||||||
\(57\) | 9.65685i | 1.27908i | ||||||||
\(58\) | − 0.414214i | − 0.0543889i | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.65685 | −0.468212 | −0.234106 | − | 0.972211i | \(-0.575216\pi\) | ||||
−0.234106 | + | 0.972211i | \(0.575216\pi\) | |||||||
\(62\) | 2.68629i | 0.341159i | ||||||||
\(63\) | 4.82843i | 0.608325i | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.686292 | −0.0844766 | ||||||||
\(67\) | 6.48528i | 0.792303i | 0.918185 | + | 0.396152i | \(0.129655\pi\) | ||||
−0.918185 | + | 0.396152i | \(0.870345\pi\) | |||||||
\(68\) | 5.17157i | 0.627145i | ||||||||
\(69\) | −6.34315 | −0.763625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.3137 | −1.81740 | −0.908701 | − | 0.417447i | \(-0.862925\pi\) | ||||
−0.908701 | + | 0.417447i | \(0.862925\pi\) | |||||||
\(72\) | − 1.58579i | − 0.186887i | ||||||||
\(73\) | − 8.48528i | − 0.993127i | −0.868000 | − | 0.496564i | \(-0.834595\pi\) | ||||
0.868000 | − | 0.496564i | \(-0.165405\pi\) | |||||||
\(74\) | 3.51472 | 0.408578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.82843 | 1.01269 | ||||||||
\(77\) | − 4.00000i | − 0.455842i | ||||||||
\(78\) | − 1.65685i | − 0.187602i | ||||||||
\(79\) | 2.48528 | 0.279616 | 0.139808 | − | 0.990179i | \(-0.455351\pi\) | ||||
0.139808 | + | 0.990179i | \(0.455351\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − 2.48528i | − 0.274453i | ||||||||
\(83\) | − 7.17157i | − 0.787182i | −0.919286 | − | 0.393591i | \(-0.871233\pi\) | ||||
0.919286 | − | 0.393591i | \(-0.128767\pi\) | |||||||
\(84\) | 17.6569 | 1.92652 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.48528 | −0.267995 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | 1.31371i | 0.140042i | ||||||||
\(89\) | 7.65685 | 0.811625 | 0.405812 | − | 0.913956i | \(-0.366989\pi\) | ||||
0.405812 | + | 0.913956i | \(0.366989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.65685 | 1.01231 | ||||||||
\(92\) | 5.79899i | 0.604586i | ||||||||
\(93\) | 12.9706i | 1.34498i | ||||||||
\(94\) | 4.82843 | 0.498014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.82843 | −0.901048 | ||||||||
\(97\) | − 12.4853i | − 1.26769i | −0.773461 | − | 0.633844i | \(-0.781476\pi\) | ||||
0.773461 | − | 0.633844i | \(-0.218524\pi\) | |||||||
\(98\) | − 6.75736i | − 0.682596i | ||||||||
\(99\) | −0.828427 | −0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6569 | 1.55792 | 0.778958 | − | 0.627077i | \(-0.215749\pi\) | ||||
0.778958 | + | 0.627077i | \(0.215749\pi\) | |||||||
\(102\) | − 2.34315i | − 0.232006i | ||||||||
\(103\) | − 16.1421i | − 1.59053i | −0.606261 | − | 0.795266i | \(-0.707331\pi\) | ||||
0.606261 | − | 0.795266i | \(-0.292669\pi\) | |||||||
\(104\) | −3.17157 | −0.310998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.51472 | −0.147122 | ||||||||
\(107\) | 20.1421i | 1.94721i | 0.228232 | + | 0.973607i | \(0.426706\pi\) | ||||
−0.228232 | + | 0.973607i | \(0.573294\pi\) | |||||||
\(108\) | 7.31371i | 0.703762i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.9706 | 1.61077 | ||||||||
\(112\) | − 14.4853i | − 1.36873i | ||||||||
\(113\) | 2.82843i | 0.266076i | 0.991111 | + | 0.133038i | \(0.0424732\pi\) | ||||
−0.991111 | + | 0.133038i | \(0.957527\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.82843 | −0.169765 | ||||||||
\(117\) | − 2.00000i | − 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | − 1.51472i | − 0.137136i | ||||||||
\(123\) | − 12.0000i | − 1.08200i | ||||||||
\(124\) | 11.8579 | 1.06487 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | 10.5563i | 0.933058i | ||||||||
\(129\) | −12.0000 | −1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.1421 | −1.06086 | −0.530432 | − | 0.847728i | \(-0.677970\pi\) | ||||
−0.530432 | + | 0.847728i | \(0.677970\pi\) | |||||||
\(132\) | 3.02944i | 0.263679i | ||||||||
\(133\) | − 23.3137i | − 2.02155i | ||||||||
\(134\) | −2.68629 | −0.232060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.48528 | −0.384610 | ||||||||
\(137\) | − 5.17157i | − 0.441837i | −0.975292 | − | 0.220919i | \(-0.929094\pi\) | ||||
0.975292 | − | 0.220919i | \(-0.0709055\pi\) | |||||||
\(138\) | − 2.62742i | − 0.223661i | ||||||||
\(139\) | −21.6569 | −1.83691 | −0.918455 | − | 0.395525i | \(-0.870563\pi\) | ||||
−0.918455 | + | 0.395525i | \(0.870563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.3137 | 1.96337 | ||||||||
\(142\) | − 6.34315i | − 0.532305i | ||||||||
\(143\) | 1.65685i | 0.138553i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.51472 | 0.290880 | ||||||||
\(147\) | − 32.6274i | − 2.69106i | ||||||||
\(148\) | − 15.5147i | − 1.27530i | ||||||||
\(149\) | −9.31371 | −0.763009 | −0.381504 | − | 0.924367i | \(-0.624594\pi\) | ||||
−0.381504 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 7.65685i | 0.621053i | ||||||||
\(153\) | − 2.82843i | − 0.228665i | ||||||||
\(154\) | 1.65685 | 0.133513 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.31371 | −0.585565 | ||||||||
\(157\) | 0.485281i | 0.0387297i | 0.999812 | + | 0.0193648i | \(0.00616440\pi\) | ||||
−0.999812 | + | 0.0193648i | \(0.993836\pi\) | |||||||
\(158\) | 1.02944i | 0.0818976i | ||||||||
\(159\) | −7.31371 | −0.580015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3137 | 1.20689 | ||||||||
\(162\) | − 4.55635i | − 0.357981i | ||||||||
\(163\) | 8.34315i | 0.653486i | 0.945113 | + | 0.326743i | \(0.105951\pi\) | ||||
−0.945113 | + | 0.326743i | \(0.894049\pi\) | |||||||
\(164\) | −10.9706 | −0.856657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.97056 | 0.230560 | ||||||||
\(167\) | − 2.48528i | − 0.192317i | −0.995366 | − | 0.0961584i | \(-0.969344\pi\) | ||||
0.995366 | − | 0.0961584i | \(-0.0306555\pi\) | |||||||
\(168\) | 15.3137i | 1.18148i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.82843 | −0.369239 | ||||||||
\(172\) | 10.9706i | 0.836498i | ||||||||
\(173\) | − 17.3137i | − 1.31634i | −0.752871 | − | 0.658168i | \(-0.771331\pi\) | ||||
0.752871 | − | 0.658168i | \(-0.228669\pi\) | |||||||
\(174\) | 0.828427 | 0.0628029 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48528 | 0.187335 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.17157i | 0.237719i | ||||||||
\(179\) | 23.3137 | 1.74255 | 0.871274 | − | 0.490797i | \(-0.163294\pi\) | ||||
0.871274 | + | 0.490797i | \(0.163294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | − 7.31371i | − 0.540645i | ||||||||
\(184\) | −5.02944 | −0.370775 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.37258 | −0.393937 | ||||||||
\(187\) | 2.34315i | 0.171348i | ||||||||
\(188\) | − 21.3137i | − 1.55446i | ||||||||
\(189\) | 19.3137 | 1.40487 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8284 | −1.50709 | −0.753546 | − | 0.657395i | \(-0.771658\pi\) | ||||
−0.753546 | + | 0.657395i | \(0.771658\pi\) | |||||||
\(192\) | 8.34315i | 0.602115i | ||||||||
\(193\) | − 4.48528i | − 0.322858i | −0.986884 | − | 0.161429i | \(-0.948390\pi\) | ||||
0.986884 | − | 0.161429i | \(-0.0516102\pi\) | |||||||
\(194\) | 5.17157 | 0.371297 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | − 19.6569i | − 1.40049i | −0.713901 | − | 0.700246i | \(-0.753073\pi\) | ||||
0.713901 | − | 0.700246i | \(-0.246927\pi\) | |||||||
\(198\) | − 0.343146i | − 0.0243863i | ||||||||
\(199\) | −12.0000 | −0.850657 | −0.425329 | − | 0.905039i | \(-0.639842\pi\) | ||||
−0.425329 | + | 0.905039i | \(0.639842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9706 | −0.914873 | ||||||||
\(202\) | 6.48528i | 0.456303i | ||||||||
\(203\) | 4.82843i | 0.338889i | ||||||||
\(204\) | −10.3431 | −0.724165 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.68629 | 0.465856 | ||||||||
\(207\) | − 3.17157i | − 0.220440i | ||||||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.828427 | −0.0570313 | −0.0285156 | − | 0.999593i | \(-0.509078\pi\) | ||||
−0.0285156 | + | 0.999593i | \(0.509078\pi\) | |||||||
\(212\) | 6.68629i | 0.459216i | ||||||||
\(213\) | − 30.6274i | − 2.09856i | ||||||||
\(214\) | −8.34315 | −0.570326 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.34315 | −0.431596 | ||||||||
\(217\) | − 31.3137i | − 2.12571i | ||||||||
\(218\) | − 0.828427i | − 0.0561082i | ||||||||
\(219\) | 16.9706 | 1.14676 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 7.02944i | 0.471785i | ||||||||
\(223\) | 17.7990i | 1.19191i | 0.803018 | + | 0.595954i | \(0.203226\pi\) | ||||
−0.803018 | + | 0.595954i | \(0.796774\pi\) | |||||||
\(224\) | 21.3137 | 1.42408 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.17157 | −0.0779319 | ||||||||
\(227\) | 20.1421i | 1.33688i | 0.743766 | + | 0.668440i | \(0.233038\pi\) | ||||
−0.743766 | + | 0.668440i | \(0.766962\pi\) | |||||||
\(228\) | 17.6569i | 1.16935i | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | − 1.58579i | − 0.104112i | ||||||||
\(233\) | − 18.0000i | − 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0.828427 | 0.0541560 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.97056i | 0.322873i | ||||||||
\(238\) | 5.65685i | 0.366679i | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | − 4.27208i | − 0.274620i | ||||||||
\(243\) | − 10.0000i | − 0.641500i | ||||||||
\(244\) | −6.68629 | −0.428046 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.97056 | 0.316912 | ||||||||
\(247\) | 9.65685i | 0.614451i | ||||||||
\(248\) | 10.2843i | 0.653052i | ||||||||
\(249\) | 14.3431 | 0.908960 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.82843 | 0.557245 | 0.278623 | − | 0.960401i | \(-0.410122\pi\) | ||||
0.278623 | + | 0.960401i | \(0.410122\pi\) | |||||||
\(252\) | 8.82843i | 0.556139i | ||||||||
\(253\) | 2.62742i | 0.165184i | ||||||||
\(254\) | −2.48528 | −0.155940 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 6.68629i | 0.417079i | 0.978014 | + | 0.208540i | \(0.0668710\pi\) | ||||
−0.978014 | + | 0.208540i | \(0.933129\pi\) | |||||||
\(258\) | − 4.97056i | − 0.309454i | ||||||||
\(259\) | −40.9706 | −2.54579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | − 5.02944i | − 0.310720i | ||||||||
\(263\) | 19.6569i | 1.21209i | 0.795429 | + | 0.606047i | \(0.207246\pi\) | ||||
−0.795429 | + | 0.606047i | \(0.792754\pi\) | |||||||
\(264\) | −2.62742 | −0.161706 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.65685 | 0.592100 | ||||||||
\(267\) | 15.3137i | 0.937184i | ||||||||
\(268\) | 11.8579i | 0.724334i | ||||||||
\(269\) | 21.3137 | 1.29952 | 0.649760 | − | 0.760140i | \(-0.274869\pi\) | ||||
0.649760 | + | 0.760140i | \(0.274869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.79899 | −0.595246 | −0.297623 | − | 0.954683i | \(-0.596194\pi\) | ||||
−0.297623 | + | 0.954683i | \(0.596194\pi\) | |||||||
\(272\) | 8.48528i | 0.514496i | ||||||||
\(273\) | 19.3137i | 1.16892i | ||||||||
\(274\) | 2.14214 | 0.129411 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.5980 | −0.698116 | ||||||||
\(277\) | − 3.65685i | − 0.219719i | −0.993947 | − | 0.109860i | \(-0.964960\pi\) | ||||
0.993947 | − | 0.109860i | \(-0.0350401\pi\) | |||||||
\(278\) | − 8.97056i | − 0.538019i | ||||||||
\(279\) | −6.48528 | −0.388264 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3137 | −1.74871 | −0.874355 | − | 0.485288i | \(-0.838715\pi\) | ||||
−0.874355 | + | 0.485288i | \(0.838715\pi\) | |||||||
\(282\) | 9.65685i | 0.575057i | ||||||||
\(283\) | − 4.82843i | − 0.287020i | −0.989649 | − | 0.143510i | \(-0.954161\pi\) | ||||
0.989649 | − | 0.143510i | \(-0.0458390\pi\) | |||||||
\(284\) | −28.0000 | −1.66149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.686292 | −0.0405813 | ||||||||
\(287\) | 28.9706i | 1.71008i | ||||||||
\(288\) | − 4.41421i | − 0.260110i | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.9706 | 1.46380 | ||||||||
\(292\) | − 15.5147i | − 0.907930i | ||||||||
\(293\) | − 8.48528i | − 0.495715i | −0.968796 | − | 0.247858i | \(-0.920273\pi\) | ||||
0.968796 | − | 0.247858i | \(-0.0797265\pi\) | |||||||
\(294\) | 13.5147 | 0.788194 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.4558 | 0.782105 | ||||||||
\(297\) | 3.31371i | 0.192281i | ||||||||
\(298\) | − 3.85786i | − 0.223480i | ||||||||
\(299\) | −6.34315 | −0.366834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.9706 | 1.66984 | ||||||||
\(302\) | − 4.97056i | − 0.286024i | ||||||||
\(303\) | 31.3137i | 1.79893i | ||||||||
\(304\) | 14.4853 | 0.830788 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.17157 | 0.0669744 | ||||||||
\(307\) | − 22.9706i | − 1.31100i | −0.755195 | − | 0.655500i | \(-0.772458\pi\) | ||||
0.755195 | − | 0.655500i | \(-0.227542\pi\) | |||||||
\(308\) | − 7.31371i | − 0.416737i | ||||||||
\(309\) | 32.2843 | 1.83659 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4853 | 0.821385 | 0.410692 | − | 0.911774i | \(-0.365287\pi\) | ||||
0.410692 | + | 0.911774i | \(0.365287\pi\) | |||||||
\(312\) | − 6.34315i | − 0.359110i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −0.201010 | −0.0113437 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.54416 | 0.255629 | ||||||||
\(317\) | 2.82843i | 0.158860i | 0.996840 | + | 0.0794301i | \(0.0253101\pi\) | ||||
−0.996840 | + | 0.0794301i | \(0.974690\pi\) | |||||||
\(318\) | − 3.02944i | − 0.169882i | ||||||||
\(319\) | −0.828427 | −0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.2843 | −2.24845 | ||||||||
\(322\) | 6.34315i | 0.353490i | ||||||||
\(323\) | 13.6569i | 0.759888i | ||||||||
\(324\) | −20.1127 | −1.11737 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.45584 | −0.191402 | ||||||||
\(327\) | − 4.00000i | − 0.221201i | ||||||||
\(328\) | − 9.51472i | − 0.525362i | ||||||||
\(329\) | −56.2843 | −3.10305 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7990 | 1.19818 | 0.599090 | − | 0.800681i | \(-0.295529\pi\) | ||||
0.599090 | + | 0.800681i | \(0.295529\pi\) | |||||||
\(332\) | − 13.1127i | − 0.719653i | ||||||||
\(333\) | 8.48528i | 0.464991i | ||||||||
\(334\) | 1.02944 | 0.0563283 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 28.9706 | 1.58047 | ||||||||
\(337\) | − 1.17157i | − 0.0638196i | −0.999491 | − | 0.0319098i | \(-0.989841\pi\) | ||||
0.999491 | − | 0.0319098i | \(-0.0101589\pi\) | |||||||
\(338\) | 3.72792i | 0.202772i | ||||||||
\(339\) | −5.65685 | −0.307238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.37258 | 0.290942 | ||||||||
\(342\) | − 2.00000i | − 0.108148i | ||||||||
\(343\) | 44.9706i | 2.42818i | ||||||||
\(344\) | −9.51472 | −0.512999 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.17157 | 0.385546 | ||||||||
\(347\) | − 8.14214i | − 0.437093i | −0.975827 | − | 0.218546i | \(-0.929869\pi\) | ||||
0.975827 | − | 0.218546i | \(-0.0701315\pi\) | |||||||
\(348\) | − 3.65685i | − 0.196028i | ||||||||
\(349\) | −20.6274 | −1.10416 | −0.552080 | − | 0.833791i | \(-0.686166\pi\) | ||||
−0.552080 | + | 0.833791i | \(0.686166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 3.65685i | 0.194911i | ||||||||
\(353\) | 4.34315i | 0.231162i | 0.993298 | + | 0.115581i | \(0.0368730\pi\) | ||||
−0.993298 | + | 0.115581i | \(0.963127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 27.3137i | 1.44559i | ||||||||
\(358\) | 9.65685i | 0.510381i | ||||||||
\(359\) | 3.85786 | 0.203610 | 0.101805 | − | 0.994804i | \(-0.467538\pi\) | ||||
0.101805 | + | 0.994804i | \(0.467538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | − 2.48528i | − 0.130623i | ||||||||
\(363\) | − 20.6274i | − 1.08266i | ||||||||
\(364\) | 17.6569 | 0.925471 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.02944 | 0.158351 | ||||||||
\(367\) | 18.0000i | 0.939592i | 0.882775 | + | 0.469796i | \(0.155673\pi\) | ||||
−0.882775 | + | 0.469796i | \(0.844327\pi\) | |||||||
\(368\) | 9.51472i | 0.495989i | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6569 | 0.916698 | ||||||||
\(372\) | 23.7157i | 1.22960i | ||||||||
\(373\) | 6.97056i | 0.360922i | 0.983582 | + | 0.180461i | \(0.0577590\pi\) | ||||
−0.983582 | + | 0.180461i | \(0.942241\pi\) | |||||||
\(374\) | −0.970563 | −0.0501866 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.4853 | 0.953306 | ||||||||
\(377\) | − 2.00000i | − 0.103005i | ||||||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | −22.4853 | −1.15499 | −0.577496 | − | 0.816394i | \(-0.695970\pi\) | ||||
−0.577496 | + | 0.816394i | \(0.695970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0000 | −0.614779 | ||||||||
\(382\) | − 8.62742i | − 0.441417i | ||||||||
\(383\) | − 2.48528i | − 0.126992i | −0.997982 | − | 0.0634960i | \(-0.979775\pi\) | ||||
0.997982 | − | 0.0634960i | \(-0.0202250\pi\) | |||||||
\(384\) | −21.1127 | −1.07740 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.85786 | 0.0945628 | ||||||||
\(387\) | − 6.00000i | − 0.304997i | ||||||||
\(388\) | − 22.8284i | − 1.15894i | ||||||||
\(389\) | 29.3137 | 1.48626 | 0.743132 | − | 0.669145i | \(-0.233339\pi\) | ||||
0.743132 | + | 0.669145i | \(0.233339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.97056 | −0.453661 | ||||||||
\(392\) | − 25.8701i | − 1.30664i | ||||||||
\(393\) | − 24.2843i | − 1.22498i | ||||||||
\(394\) | 8.14214 | 0.410195 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.51472 | −0.0761175 | ||||||||
\(397\) | − 19.6569i | − 0.986549i | −0.869874 | − | 0.493275i | \(-0.835800\pi\) | ||||
0.869874 | − | 0.493275i | \(-0.164200\pi\) | |||||||
\(398\) | − 4.97056i | − 0.249152i | ||||||||
\(399\) | 46.6274 | 2.33429 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.68629 | −0.333897 | −0.166949 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166949 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(402\) | − 5.37258i | − 0.267960i | ||||||||
\(403\) | 12.9706i | 0.646110i | ||||||||
\(404\) | 28.6274 | 1.42427 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | − 7.02944i | − 0.348436i | ||||||||
\(408\) | − 8.97056i | − 0.444109i | ||||||||
\(409\) | 2.97056 | 0.146885 | 0.0734424 | − | 0.997299i | \(-0.476601\pi\) | ||||
0.0734424 | + | 0.997299i | \(0.476601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.3431 | 0.510190 | ||||||||
\(412\) | − 29.5147i | − 1.45409i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.31371 | 0.0645653 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.82843 | −0.432849 | ||||||||
\(417\) | − 43.3137i | − 2.12108i | ||||||||
\(418\) | 1.65685i | 0.0810394i | ||||||||
\(419\) | −28.9706 | −1.41530 | −0.707652 | − | 0.706561i | \(-0.750246\pi\) | ||||
−0.707652 | + | 0.706561i | \(0.750246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9706 | 0.924569 | 0.462284 | − | 0.886732i | \(-0.347030\pi\) | ||||
0.462284 | + | 0.886732i | \(0.347030\pi\) | |||||||
\(422\) | − 0.343146i | − 0.0167041i | ||||||||
\(423\) | 11.6569i | 0.566776i | ||||||||
\(424\) | −5.79899 | −0.281624 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.6863 | 0.614653 | ||||||||
\(427\) | 17.6569i | 0.854475i | ||||||||
\(428\) | 36.8284i | 1.78017i | ||||||||
\(429\) | −3.31371 | −0.159987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31371 | 0.159616 | 0.0798079 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798079 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(432\) | 12.0000i | 0.577350i | ||||||||
\(433\) | 29.1716i | 1.40190i | 0.713212 | + | 0.700948i | \(0.247240\pi\) | ||||
−0.713212 | + | 0.700948i | \(0.752760\pi\) | |||||||
\(434\) | 12.9706 | 0.622607 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.65685 | −0.175132 | ||||||||
\(437\) | 15.3137i | 0.732554i | ||||||||
\(438\) | 7.02944i | 0.335880i | ||||||||
\(439\) | 10.3431 | 0.493651 | 0.246826 | − | 0.969060i | \(-0.420612\pi\) | ||||
0.246826 | + | 0.969060i | \(0.420612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | − 2.34315i | − 0.111452i | ||||||||
\(443\) | 7.65685i | 0.363788i | 0.983318 | + | 0.181894i | \(0.0582228\pi\) | ||||
−0.983318 | + | 0.181894i | \(0.941777\pi\) | |||||||
\(444\) | 31.0294 | 1.47259 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.37258 | −0.349102 | ||||||||
\(447\) | − 18.6274i | − 0.881047i | ||||||||
\(448\) | − 20.1421i | − 0.951626i | ||||||||
\(449\) | −11.6569 | −0.550121 | −0.275060 | − | 0.961427i | \(-0.588698\pi\) | ||||
−0.275060 | + | 0.961427i | \(0.588698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.97056 | −0.234055 | ||||||||
\(452\) | 5.17157i | 0.243250i | ||||||||
\(453\) | − 24.0000i | − 1.12762i | ||||||||
\(454\) | −8.34315 | −0.391563 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.3137 | −0.717130 | ||||||||
\(457\) | 19.6569i | 0.919509i | 0.888046 | + | 0.459754i | \(0.152063\pi\) | ||||
−0.888046 | + | 0.459754i | \(0.847937\pi\) | |||||||
\(458\) | 0.828427i | 0.0387099i | ||||||||
\(459\) | −11.3137 | −0.528079 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.6569 | −1.66071 | −0.830353 | − | 0.557238i | \(-0.811861\pi\) | ||||
−0.830353 | + | 0.557238i | \(0.811861\pi\) | |||||||
\(462\) | 3.31371i | 0.154168i | ||||||||
\(463\) | − 21.7990i | − 1.01308i | −0.862215 | − | 0.506542i | \(-0.830923\pi\) | ||||
0.862215 | − | 0.506542i | \(-0.169077\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.45584 | 0.345385 | ||||||||
\(467\) | 10.9706i | 0.507657i | 0.967249 | + | 0.253829i | \(0.0816899\pi\) | ||||
−0.967249 | + | 0.253829i | \(0.918310\pi\) | |||||||
\(468\) | − 3.65685i | − 0.169038i | ||||||||
\(469\) | 31.3137 | 1.44593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.970563 | −0.0447212 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.97056i | 0.228547i | ||||||||
\(474\) | −2.05887 | −0.0945672 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.9706 | 1.14452 | ||||||||
\(477\) | − 3.65685i | − 0.167436i | ||||||||
\(478\) | 0.284271i | 0.0130023i | ||||||||
\(479\) | −7.17157 | −0.327678 | −0.163839 | − | 0.986487i | \(-0.552388\pi\) | ||||
−0.163839 | + | 0.986487i | \(0.552388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9706 | 0.773791 | ||||||||
\(482\) | 4.14214i | 0.188669i | ||||||||
\(483\) | 30.6274i | 1.39360i | ||||||||
\(484\) | −18.8579 | −0.857176 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.14214 | 0.187891 | ||||||||
\(487\) | 9.79899i | 0.444035i | 0.975043 | + | 0.222017i | \(0.0712641\pi\) | ||||
−0.975043 | + | 0.222017i | \(0.928736\pi\) | |||||||
\(488\) | − 5.79899i | − 0.262508i | ||||||||
\(489\) | −16.6863 | −0.754580 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.45584 | −0.336478 | −0.168239 | − | 0.985746i | \(-0.553808\pi\) | ||||
−0.168239 | + | 0.985746i | \(0.553808\pi\) | |||||||
\(492\) | − 21.9411i | − 0.989182i | ||||||||
\(493\) | − 2.82843i | − 0.127386i | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.4558 | 0.873593 | ||||||||
\(497\) | 73.9411i | 3.31671i | ||||||||
\(498\) | 5.94113i | 0.266228i | ||||||||
\(499\) | −36.0000 | −1.61158 | −0.805791 | − | 0.592200i | \(-0.798259\pi\) | ||||
−0.805791 | + | 0.592200i | \(0.798259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.97056 | 0.222068 | ||||||||
\(502\) | 3.65685i | 0.163213i | ||||||||
\(503\) | 30.0000i | 1.33763i | 0.743427 | + | 0.668817i | \(0.233199\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(504\) | −7.65685 | −0.341063 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.08831 | −0.0483814 | ||||||||
\(507\) | 18.0000i | 0.799408i | ||||||||
\(508\) | 10.9706i | 0.486740i | ||||||||
\(509\) | −0.627417 | −0.0278098 | −0.0139049 | − | 0.999903i | \(-0.504426\pi\) | ||||
−0.0139049 | + | 0.999903i | \(0.504426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.9706 | −1.81243 | ||||||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | 19.3137i | 0.852721i | ||||||||
\(514\) | −2.76955 | −0.122160 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.9411 | −0.965904 | ||||||||
\(517\) | − 9.65685i | − 0.424708i | ||||||||
\(518\) | − 16.9706i | − 0.745644i | ||||||||
\(519\) | 34.6274 | 1.51997 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3137 | −0.933771 | −0.466885 | − | 0.884318i | \(-0.654624\pi\) | ||||
−0.466885 | + | 0.884318i | \(0.654624\pi\) | |||||||
\(522\) | 0.414214i | 0.0181296i | ||||||||
\(523\) | − 2.48528i | − 0.108674i | −0.998523 | − | 0.0543369i | \(-0.982696\pi\) | ||||
0.998523 | − | 0.0543369i | \(-0.0173045\pi\) | |||||||
\(524\) | −22.2010 | −0.969856 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.14214 | −0.355014 | ||||||||
\(527\) | 18.3431i | 0.799040i | ||||||||
\(528\) | 4.97056i | 0.216316i | ||||||||
\(529\) | 12.9411 | 0.562658 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 42.6274i | − 1.84813i | ||||||||
\(533\) | − 12.0000i | − 0.519778i | ||||||||
\(534\) | −6.34315 | −0.274495 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.2843 | −0.444213 | ||||||||
\(537\) | 46.6274i | 2.01212i | ||||||||
\(538\) | 8.82843i | 0.380621i | ||||||||
\(539\) | −13.5147 | −0.582120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.02944 | −0.216232 | −0.108116 | − | 0.994138i | \(-0.534482\pi\) | ||||
−0.108116 | + | 0.994138i | \(0.534482\pi\) | |||||||
\(542\) | − 4.05887i | − 0.174344i | ||||||||
\(543\) | − 12.0000i | − 0.514969i | ||||||||
\(544\) | −12.4853 | −0.535302 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.00000 | −0.342368 | ||||||||
\(547\) | − 2.48528i | − 0.106263i | −0.998588 | − | 0.0531315i | \(-0.983080\pi\) | ||||
0.998588 | − | 0.0531315i | \(-0.0169202\pi\) | |||||||
\(548\) | − 9.45584i | − 0.403934i | ||||||||
\(549\) | 3.65685 | 0.156071 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.82843 | −0.205698 | ||||||||
\(552\) | − 10.0589i | − 0.428134i | ||||||||
\(553\) | − 12.0000i | − 0.510292i | ||||||||
\(554\) | 1.51472 | 0.0643542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −39.5980 | −1.67933 | ||||||||
\(557\) | − 27.9411i | − 1.18390i | −0.805973 | − | 0.591952i | \(-0.798358\pi\) | ||||
0.805973 | − | 0.591952i | \(-0.201642\pi\) | |||||||
\(558\) | − 2.68629i | − 0.113720i | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.68629 | −0.197855 | ||||||||
\(562\) | − 12.1421i | − 0.512185i | ||||||||
\(563\) | − 7.65685i | − 0.322698i | −0.986897 | − | 0.161349i | \(-0.948416\pi\) | ||||
0.986897 | − | 0.161349i | \(-0.0515845\pi\) | |||||||
\(564\) | 42.6274 | 1.79494 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.00000 | 0.0840663 | ||||||||
\(567\) | 53.1127i | 2.23052i | ||||||||
\(568\) | − 24.2843i | − 1.01895i | ||||||||
\(569\) | −27.6569 | −1.15944 | −0.579718 | − | 0.814817i | \(-0.696837\pi\) | ||||
−0.579718 | + | 0.814817i | \(0.696837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 3.02944i | 0.126667i | ||||||||
\(573\) | − 41.6569i | − 1.74024i | ||||||||
\(574\) | −12.0000 | −0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | 23.7990i | 0.990765i | 0.868675 | + | 0.495382i | \(0.164972\pi\) | ||||
−0.868675 | + | 0.495382i | \(0.835028\pi\) | |||||||
\(578\) | 3.72792i | 0.155061i | ||||||||
\(579\) | 8.97056 | 0.372804 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.6274 | −1.43659 | ||||||||
\(582\) | 10.3431i | 0.428737i | ||||||||
\(583\) | 3.02944i | 0.125466i | ||||||||
\(584\) | 13.4558 | 0.556807 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.51472 | 0.145192 | ||||||||
\(587\) | − 29.7990i | − 1.22994i | −0.788552 | − | 0.614968i | \(-0.789169\pi\) | ||||
0.788552 | − | 0.614968i | \(-0.210831\pi\) | |||||||
\(588\) | − 59.6569i | − 2.46021i | ||||||||
\(589\) | 31.3137 | 1.29026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.3137 | 1.61715 | ||||||||
\(592\) | − 25.4558i | − 1.04623i | ||||||||
\(593\) | 7.65685i | 0.314429i | 0.987564 | + | 0.157215i | \(0.0502515\pi\) | ||||
−0.987564 | + | 0.157215i | \(0.949749\pi\) | |||||||
\(594\) | −1.37258 | −0.0563178 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.0294 | −0.697553 | ||||||||
\(597\) | − 24.0000i | − 0.982255i | ||||||||
\(598\) | − 2.62742i | − 0.107443i | ||||||||
\(599\) | 37.7990 | 1.54442 | 0.772212 | − | 0.635364i | \(-0.219150\pi\) | ||||
0.772212 | + | 0.635364i | \(0.219150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 12.0000i | 0.489083i | ||||||||
\(603\) | − 6.48528i | − 0.264101i | ||||||||
\(604\) | −21.9411 | −0.892772 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.9706 | −0.526893 | ||||||||
\(607\) | 9.02944i | 0.366494i | 0.983067 | + | 0.183247i | \(0.0586607\pi\) | ||||
−0.983067 | + | 0.183247i | \(0.941339\pi\) | |||||||
\(608\) | 21.3137i | 0.864385i | ||||||||
\(609\) | −9.65685 | −0.391315 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3137 | 0.943172 | ||||||||
\(612\) | − 5.17157i | − 0.209048i | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | 9.51472 | 0.383983 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.34315 | 0.255573 | ||||||||
\(617\) | − 9.17157i | − 0.369234i | −0.982811 | − | 0.184617i | \(-0.940896\pi\) | ||||
0.982811 | − | 0.184617i | \(-0.0591044\pi\) | |||||||
\(618\) | 13.3726i | 0.537924i | ||||||||
\(619\) | 9.79899 | 0.393855 | 0.196927 | − | 0.980418i | \(-0.436904\pi\) | ||||
0.196927 | + | 0.980418i | \(0.436904\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.6863 | −0.509083 | ||||||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | − 36.9706i | − 1.48119i | ||||||||
\(624\) | −12.0000 | −0.480384 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.48528 | −0.0993318 | ||||||||
\(627\) | 8.00000i | 0.319489i | ||||||||
\(628\) | 0.887302i | 0.0354072i | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.9706 | 1.47177 | 0.735887 | − | 0.677104i | \(-0.236765\pi\) | ||||
0.735887 | + | 0.677104i | \(0.236765\pi\) | |||||||
\(632\) | 3.94113i | 0.156770i | ||||||||
\(633\) | − 1.65685i | − 0.0658540i | ||||||||
\(634\) | −1.17157 | −0.0465291 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.3726 | −0.530257 | ||||||||
\(637\) | − 32.6274i | − 1.29275i | ||||||||
\(638\) | − 0.343146i | − 0.0135853i | ||||||||
\(639\) | 15.3137 | 0.605801 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.627417 | 0.0247815 | 0.0123907 | − | 0.999923i | \(-0.496056\pi\) | ||||
0.0123907 | + | 0.999923i | \(0.496056\pi\) | |||||||
\(642\) | − 16.6863i | − 0.658555i | ||||||||
\(643\) | − 19.4558i | − 0.767264i | −0.923486 | − | 0.383632i | \(-0.874673\pi\) | ||||
0.923486 | − | 0.383632i | \(-0.125327\pi\) | |||||||
\(644\) | 28.0000 | 1.10335 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.65685 | −0.222566 | ||||||||
\(647\) | − 41.1127i | − 1.61631i | −0.588972 | − | 0.808153i | \(-0.700467\pi\) | ||||
0.588972 | − | 0.808153i | \(-0.299533\pi\) | |||||||
\(648\) | − 17.4437i | − 0.685251i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 62.6274 | 2.45456 | ||||||||
\(652\) | 15.2548i | 0.597425i | ||||||||
\(653\) | 17.1716i | 0.671976i | 0.941866 | + | 0.335988i | \(0.109070\pi\) | ||||
−0.941866 | + | 0.335988i | \(0.890930\pi\) | |||||||
\(654\) | 1.65685 | 0.0647881 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | 8.48528i | 0.331042i | ||||||||
\(658\) | − 23.3137i | − 0.908863i | ||||||||
\(659\) | −1.79899 | −0.0700787 | −0.0350393 | − | 0.999386i | \(-0.511156\pi\) | ||||
−0.0350393 | + | 0.999386i | \(0.511156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | 9.02944i | 0.350939i | ||||||||
\(663\) | − 11.3137i | − 0.439388i | ||||||||
\(664\) | 11.3726 | 0.441342 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.51472 | −0.136193 | ||||||||
\(667\) | − 3.17157i | − 0.122804i | ||||||||
\(668\) | − 4.54416i | − 0.175819i | ||||||||
\(669\) | −35.5980 | −1.37630 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.02944 | −0.116950 | ||||||||
\(672\) | 42.6274i | 1.64439i | ||||||||
\(673\) | − 22.9706i | − 0.885450i | −0.896657 | − | 0.442725i | \(-0.854012\pi\) | ||||
0.896657 | − | 0.442725i | \(-0.145988\pi\) | |||||||
\(674\) | 0.485281 | 0.0186923 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.4558 | 0.632917 | ||||||||
\(677\) | − 36.7696i | − 1.41317i | −0.707629 | − | 0.706584i | \(-0.750235\pi\) | ||||
0.707629 | − | 0.706584i | \(-0.249765\pi\) | |||||||
\(678\) | − 2.34315i | − 0.0899880i | ||||||||
\(679\) | −60.2843 | −2.31350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.2843 | −1.54370 | ||||||||
\(682\) | 2.22540i | 0.0852148i | ||||||||
\(683\) | − 11.8579i | − 0.453729i | −0.973926 | − | 0.226864i | \(-0.927153\pi\) | ||||
0.973926 | − | 0.226864i | \(-0.0728474\pi\) | |||||||
\(684\) | −8.82843 | −0.337563 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.6274 | −0.711198 | ||||||||
\(687\) | 4.00000i | 0.152610i | ||||||||
\(688\) | 18.0000i | 0.686244i | ||||||||
\(689\) | −7.31371 | −0.278630 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.9706 | −1.71076 | −0.855380 | − | 0.518000i | \(-0.826677\pi\) | ||||
−0.855380 | + | 0.518000i | \(0.826677\pi\) | |||||||
\(692\) | − 31.6569i | − 1.20341i | ||||||||
\(693\) | 4.00000i | 0.151947i | ||||||||
\(694\) | 3.37258 | 0.128022 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.17157 | 0.120218 | ||||||||
\(697\) | − 16.9706i | − 0.642806i | ||||||||
\(698\) | − 8.54416i | − 0.323401i | ||||||||
\(699\) | 36.0000 | 1.36165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.68629 | 0.252538 | 0.126269 | − | 0.991996i | \(-0.459700\pi\) | ||||
0.126269 | + | 0.991996i | \(0.459700\pi\) | |||||||
\(702\) | − 3.31371i | − 0.125068i | ||||||||
\(703\) | − 40.9706i | − 1.54523i | ||||||||
\(704\) | 3.45584 | 0.130247 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.79899 | −0.0677059 | ||||||||
\(707\) | − 75.5980i | − 2.84315i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | 0.826227 | 0.413114 | − | 0.910679i | \(-0.364441\pi\) | ||||
0.413114 | + | 0.910679i | \(0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.48528 | −0.0932053 | ||||||||
\(712\) | 12.1421i | 0.455046i | ||||||||
\(713\) | 20.5685i | 0.770298i | ||||||||
\(714\) | −11.3137 | −0.423405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.6274 | 1.59306 | ||||||||
\(717\) | 1.37258i | 0.0512601i | ||||||||
\(718\) | 1.59798i | 0.0596361i | ||||||||
\(719\) | 34.6274 | 1.29138 | 0.645692 | − | 0.763598i | \(-0.276569\pi\) | ||||
0.645692 | + | 0.763598i | \(0.276569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −77.9411 | −2.90268 | ||||||||
\(722\) | 1.78680i | 0.0664977i | ||||||||
\(723\) | 20.0000i | 0.743808i | ||||||||
\(724\) | −10.9706 | −0.407718 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.54416 | 0.317103 | ||||||||
\(727\) | − 23.9411i | − 0.887927i | −0.896045 | − | 0.443964i | \(-0.853572\pi\) | ||||
0.896045 | − | 0.443964i | \(-0.146428\pi\) | |||||||
\(728\) | 15.3137i | 0.567564i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9706 | −0.627679 | ||||||||
\(732\) | − 13.3726i | − 0.494265i | ||||||||
\(733\) | 22.8284i | 0.843187i | 0.906785 | + | 0.421594i | \(0.138529\pi\) | ||||
−0.906785 | + | 0.421594i | \(0.861471\pi\) | |||||||
\(734\) | −7.45584 | −0.275200 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0000 | −0.516047 | ||||||||
\(737\) | 5.37258i | 0.197902i | ||||||||
\(738\) | 2.48528i | 0.0914845i | ||||||||
\(739\) | −14.4853 | −0.532850 | −0.266425 | − | 0.963856i | \(-0.585842\pi\) | ||||
−0.266425 | + | 0.963856i | \(0.585842\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.3137 | −0.709507 | ||||||||
\(742\) | 7.31371i | 0.268495i | ||||||||
\(743\) | 52.6274i | 1.93071i | 0.260935 | + | 0.965356i | \(0.415969\pi\) | ||||
−0.260935 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(744\) | −20.5685 | −0.754079 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.88730 | −0.105712 | ||||||||
\(747\) | 7.17157i | 0.262394i | ||||||||
\(748\) | 4.28427i | 0.156648i | ||||||||
\(749\) | 97.2548 | 3.55361 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1421 | 0.589035 | 0.294517 | − | 0.955646i | \(-0.404841\pi\) | ||||
0.294517 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(752\) | − 34.9706i | − 1.27525i | ||||||||
\(753\) | 17.6569i | 0.643452i | ||||||||
\(754\) | 0.828427 | 0.0301695 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 35.3137 | 1.28435 | ||||||||
\(757\) | 19.5147i | 0.709275i | 0.935004 | + | 0.354637i | \(0.115396\pi\) | ||||
−0.935004 | + | 0.354637i | \(0.884604\pi\) | |||||||
\(758\) | − 9.31371i | − 0.338289i | ||||||||
\(759\) | −5.25483 | −0.190738 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.62742 | 0.312744 | 0.156372 | − | 0.987698i | \(-0.450020\pi\) | ||||
0.156372 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(762\) | − 4.97056i | − 0.180064i | ||||||||
\(763\) | 9.65685i | 0.349602i | ||||||||
\(764\) | −38.0833 | −1.37780 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.02944 | 0.0371951 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 7.94113i | 0.286551i | ||||||||
\(769\) | 15.6569 | 0.564601 | 0.282300 | − | 0.959326i | \(-0.408903\pi\) | ||||
0.282300 | + | 0.959326i | \(0.408903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3726 | −0.481602 | ||||||||
\(772\) | − 8.20101i | − 0.295161i | ||||||||
\(773\) | 8.48528i | 0.305194i | 0.988288 | + | 0.152597i | \(0.0487637\pi\) | ||||
−0.988288 | + | 0.152597i | \(0.951236\pi\) | |||||||
\(774\) | 2.48528 | 0.0893316 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 19.7990 | 0.710742 | ||||||||
\(777\) | − 81.9411i | − 2.93962i | ||||||||
\(778\) | 12.1421i | 0.435317i | ||||||||
\(779\) | −28.9706 | −1.03798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6863 | −0.453951 | ||||||||
\(782\) | − 3.71573i | − 0.132874i | ||||||||
\(783\) | − 4.00000i | − 0.142948i | ||||||||
\(784\) | −48.9411 | −1.74790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.0589 | 0.358788 | ||||||||
\(787\) | 17.7990i | 0.634465i | 0.948348 | + | 0.317233i | \(0.102754\pi\) | ||||
−0.948348 | + | 0.317233i | \(0.897246\pi\) | |||||||
\(788\) | − 35.9411i | − 1.28035i | ||||||||
\(789\) | −39.3137 | −1.39961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6569 | 0.485582 | ||||||||
\(792\) | − 1.31371i | − 0.0466806i | ||||||||
\(793\) | − 7.31371i | − 0.259717i | ||||||||
\(794\) | 8.14214 | 0.288954 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.9411 | −0.777683 | ||||||||
\(797\) | − 5.85786i | − 0.207496i | −0.994604 | − | 0.103748i | \(-0.966916\pi\) | ||||
0.994604 | − | 0.103748i | \(-0.0330836\pi\) | |||||||
\(798\) | 19.3137i | 0.683698i | ||||||||
\(799\) | 32.9706 | 1.16641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | − 2.76955i | − 0.0977963i | ||||||||
\(803\) | − 7.02944i | − 0.248063i | ||||||||
\(804\) | −23.7157 | −0.836389 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.37258 | −0.189241 | ||||||||
\(807\) | 42.6274i | 1.50056i | ||||||||
\(808\) | 24.8284i | 0.873461i | ||||||||
\(809\) | −42.2843 | −1.48664 | −0.743318 | − | 0.668938i | \(-0.766749\pi\) | ||||
−0.743318 | + | 0.668938i | \(0.766749\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.6569 | 1.32231 | 0.661155 | − | 0.750249i | \(-0.270066\pi\) | ||||
0.661155 | + | 0.750249i | \(0.270066\pi\) | |||||||
\(812\) | 8.82843i | 0.309817i | ||||||||
\(813\) | − 19.5980i | − 0.687331i | ||||||||
\(814\) | 2.91169 | 0.102055 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −16.9706 | −0.594089 | ||||||||
\(817\) | 28.9706i | 1.01355i | ||||||||
\(818\) | 1.23045i | 0.0430216i | ||||||||
\(819\) | −9.65685 | −0.337438 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.6863 | −0.791757 | −0.395879 | − | 0.918303i | \(-0.629560\pi\) | ||||
−0.395879 | + | 0.918303i | \(0.629560\pi\) | |||||||
\(822\) | 4.28427i | 0.149431i | ||||||||
\(823\) | 30.9706i | 1.07957i | 0.841804 | + | 0.539783i | \(0.181494\pi\) | ||||
−0.841804 | + | 0.539783i | \(0.818506\pi\) | |||||||
\(824\) | 25.5980 | 0.891748 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3137i | 0.602057i | 0.953615 | + | 0.301028i | \(0.0973299\pi\) | ||||
−0.953615 | + | 0.301028i | \(0.902670\pi\) | |||||||
\(828\) | − 5.79899i | − 0.201529i | ||||||||
\(829\) | −20.6274 | −0.716420 | −0.358210 | − | 0.933641i | \(-0.616613\pi\) | ||||
−0.358210 | + | 0.933641i | \(0.616613\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.31371 | 0.253710 | ||||||||
\(832\) | 8.34315i | 0.289247i | ||||||||
\(833\) | − 46.1421i | − 1.59873i | ||||||||
\(834\) | 17.9411 | 0.621250 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.31371 | 0.252950 | ||||||||
\(837\) | 25.9411i | 0.896656i | ||||||||
\(838\) | − 12.0000i | − 0.414533i | ||||||||
\(839\) | −2.48528 | −0.0858014 | −0.0429007 | − | 0.999079i | \(-0.513660\pi\) | ||||
−0.0429007 | + | 0.999079i | \(0.513660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 7.85786i | 0.270800i | ||||||||
\(843\) | − 58.6274i | − 2.01924i | ||||||||
\(844\) | −1.51472 | −0.0521388 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | −0.166005 | ||||||||
\(847\) | 49.7990i | 1.71111i | ||||||||
\(848\) | 10.9706i | 0.376731i | ||||||||
\(849\) | 9.65685 | 0.331422 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.9117 | 0.922521 | ||||||||
\(852\) | − 56.0000i | − 1.91853i | ||||||||
\(853\) | − 51.1127i | − 1.75007i | −0.484064 | − | 0.875033i | \(-0.660840\pi\) | ||||
0.484064 | − | 0.875033i | \(-0.339160\pi\) | |||||||
\(854\) | −7.31371 | −0.250270 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.9411 | −1.09173 | ||||||||
\(857\) | 3.37258i | 0.115205i | 0.998340 | + | 0.0576026i | \(0.0183456\pi\) | ||||
−0.998340 | + | 0.0576026i | \(0.981654\pi\) | |||||||
\(858\) | − 1.37258i | − 0.0468592i | ||||||||
\(859\) | 56.4264 | 1.92524 | 0.962622 | − | 0.270848i | \(-0.0873041\pi\) | ||||
0.962622 | + | 0.270848i | \(0.0873041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −57.9411 | −1.97463 | ||||||||
\(862\) | 1.37258i | 0.0467504i | ||||||||
\(863\) | 36.1421i | 1.23029i | 0.788413 | + | 0.615146i | \(0.210903\pi\) | ||||
−0.788413 | + | 0.615146i | \(0.789097\pi\) | |||||||
\(864\) | −17.6569 | −0.600698 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.0833 | −0.410606 | ||||||||
\(867\) | 18.0000i | 0.611312i | ||||||||
\(868\) | − 57.2548i | − 1.94336i | ||||||||
\(869\) | 2.05887 | 0.0698425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9706 | −0.439491 | ||||||||
\(872\) | − 3.17157i | − 0.107403i | ||||||||
\(873\) | 12.4853i | 0.422563i | ||||||||
\(874\) | −6.34315 | −0.214560 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 31.0294 | 1.04839 | ||||||||
\(877\) | 38.2843i | 1.29277i | 0.763012 | + | 0.646384i | \(0.223720\pi\) | ||||
−0.763012 | + | 0.646384i | \(0.776280\pi\) | |||||||
\(878\) | 4.28427i | 0.144587i | ||||||||
\(879\) | 16.9706 | 0.572403 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3137 | 0.987604 | 0.493802 | − | 0.869574i | \(-0.335607\pi\) | ||||
0.493802 | + | 0.869574i | \(0.335607\pi\) | |||||||
\(882\) | 6.75736i | 0.227532i | ||||||||
\(883\) | 14.4853i | 0.487469i | 0.969842 | + | 0.243734i | \(0.0783725\pi\) | ||||
−0.969842 | + | 0.243734i | \(0.921628\pi\) | |||||||
\(884\) | −10.3431 | −0.347878 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.17157 | −0.106551 | ||||||||
\(887\) | − 6.68629i | − 0.224504i | −0.993680 | − | 0.112252i | \(-0.964194\pi\) | ||||
0.993680 | − | 0.112252i | \(-0.0358063\pi\) | |||||||
\(888\) | 26.9117i | 0.903097i | ||||||||
\(889\) | 28.9706 | 0.971641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.11270 | −0.305287 | ||||||||
\(892\) | 32.5442i | 1.08966i | ||||||||
\(893\) | − 56.2843i | − 1.88348i | ||||||||
\(894\) | 7.71573 | 0.258053 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.9706 | 1.70281 | ||||||||
\(897\) | − 12.6863i | − 0.423583i | ||||||||
\(898\) | − 4.82843i | − 0.161127i | ||||||||
\(899\) | −6.48528 | −0.216296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.3431 | −0.344580 | ||||||||
\(902\) | − 2.05887i | − 0.0685530i | ||||||||
\(903\) | 57.9411i | 1.92816i | ||||||||
\(904\) | −4.48528 | −0.149178 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.94113 | 0.330272 | ||||||||
\(907\) | − 10.0000i | − 0.332045i | −0.986122 | − | 0.166022i | \(-0.946908\pi\) | ||||
0.986122 | − | 0.166022i | \(-0.0530924\pi\) | |||||||
\(908\) | 36.8284i | 1.22219i | ||||||||
\(909\) | −15.6569 | −0.519305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.1421 | 1.06492 | 0.532458 | − | 0.846456i | \(-0.321268\pi\) | ||||
0.532458 | + | 0.846456i | \(0.321268\pi\) | |||||||
\(912\) | 28.9706i | 0.959311i | ||||||||
\(913\) | − 5.94113i | − 0.196623i | ||||||||
\(914\) | −8.14214 | −0.269318 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.65685 | 0.120826 | ||||||||
\(917\) | 58.6274i | 1.93605i | ||||||||
\(918\) | − 4.68629i | − 0.154671i | ||||||||
\(919\) | 36.0000 | 1.18753 | 0.593765 | − | 0.804638i | \(-0.297641\pi\) | ||||
0.593765 | + | 0.804638i | \(0.297641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.9411 | 1.51381 | ||||||||
\(922\) | − 14.7696i | − 0.486409i | ||||||||
\(923\) | − 30.6274i | − 1.00811i | ||||||||
\(924\) | 14.6274 | 0.481207 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.02944 | 0.296726 | ||||||||
\(927\) | 16.1421i | 0.530177i | ||||||||
\(928\) | − 4.41421i | − 0.144904i | ||||||||
\(929\) | 4.62742 | 0.151821 | 0.0759103 | − | 0.997115i | \(-0.475814\pi\) | ||||
0.0759103 | + | 0.997115i | \(0.475814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78.7696 | −2.58157 | ||||||||
\(932\) | − 32.9117i | − 1.07806i | ||||||||
\(933\) | 28.9706i | 0.948454i | ||||||||
\(934\) | −4.54416 | −0.148689 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.17157 | 0.103666 | ||||||||
\(937\) | 19.6569i | 0.642161i | 0.947052 | + | 0.321081i | \(0.104046\pi\) | ||||
−0.947052 | + | 0.321081i | \(0.895954\pi\) | |||||||
\(938\) | 12.9706i | 0.423504i | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.9411 | −0.910855 | −0.455427 | − | 0.890273i | \(-0.650514\pi\) | ||||
−0.455427 | + | 0.890273i | \(0.650514\pi\) | |||||||
\(942\) | − 0.402020i | − 0.0130985i | ||||||||
\(943\) | − 19.0294i | − 0.619684i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.05887 | −0.0669398 | ||||||||
\(947\) | 44.9117i | 1.45943i | 0.683749 | + | 0.729717i | \(0.260348\pi\) | ||||
−0.683749 | + | 0.729717i | \(0.739652\pi\) | |||||||
\(948\) | 9.08831i | 0.295175i | ||||||||
\(949\) | 16.9706 | 0.550888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.65685 | −0.183436 | ||||||||
\(952\) | 21.6569i | 0.701903i | ||||||||
\(953\) | − 29.3137i | − 0.949564i | −0.880103 | − | 0.474782i | \(-0.842527\pi\) | ||||
0.880103 | − | 0.474782i | \(-0.157473\pi\) | |||||||
\(954\) | 1.51472 | 0.0490408 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.25483 | 0.0405842 | ||||||||
\(957\) | − 1.65685i | − 0.0535585i | ||||||||
\(958\) | − 2.97056i | − 0.0959745i | ||||||||
\(959\) | −24.9706 | −0.806342 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0589 | 0.356738 | ||||||||
\(962\) | 7.02944i | 0.226638i | ||||||||
\(963\) | − 20.1421i | − 0.649071i | ||||||||
\(964\) | 18.2843 | 0.588897 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.6863 | −0.408175 | ||||||||
\(967\) | 14.9706i | 0.481421i | 0.970597 | + | 0.240710i | \(0.0773804\pi\) | ||||
−0.970597 | + | 0.240710i | \(0.922620\pi\) | |||||||
\(968\) | − 16.3553i | − 0.525681i | ||||||||
\(969\) | −27.3137 | −0.877443 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.1421 | 0.903124 | 0.451562 | − | 0.892240i | \(-0.350867\pi\) | ||||
0.451562 | + | 0.892240i | \(0.350867\pi\) | |||||||
\(972\) | − 18.2843i | − 0.586468i | ||||||||
\(973\) | 104.569i | 3.35231i | ||||||||
\(974\) | −4.05887 | −0.130055 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.9706 | −0.351159 | ||||||||
\(977\) | − 2.68629i | − 0.0859421i | −0.999076 | − | 0.0429710i | \(-0.986318\pi\) | ||||
0.999076 | − | 0.0429710i | \(-0.0136823\pi\) | |||||||
\(978\) | − 6.91169i | − 0.221011i | ||||||||
\(979\) | 6.34315 | 0.202728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | − 3.08831i | − 0.0985520i | ||||||||
\(983\) | 9.31371i | 0.297061i | 0.988908 | + | 0.148531i | \(0.0474543\pi\) | ||||
−0.988908 | + | 0.148531i | \(0.952546\pi\) | |||||||
\(984\) | 19.0294 | 0.606636 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.17157 | 0.0373105 | ||||||||
\(987\) | − 112.569i | − 3.58310i | ||||||||
\(988\) | 17.6569i | 0.561739i | ||||||||
\(989\) | −19.0294 | −0.605101 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 28.6274i | 0.908921i | ||||||||
\(993\) | 43.5980i | 1.38354i | ||||||||
\(994\) | −30.6274 | −0.971443 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 26.2254 | 0.830983 | ||||||||
\(997\) | 6.82843i | 0.216258i | 0.994137 | + | 0.108129i | \(0.0344860\pi\) | ||||
−0.994137 | + | 0.108129i | \(0.965514\pi\) | |||||||
\(998\) | − 14.9117i | − 0.472021i | ||||||||
\(999\) | 33.9411 | 1.07385 |
(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 | 725.2.b.c.349.3 | 4 | ||
5.2 | odd | 4 | 725.2.a.c.1.1 | 2 | |||
5.3 | odd | 4 | 145.2.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 725.2.b.c.349.2 | 4 | ||
15.2 | even | 4 | 6525.2.a.p.1.2 | 2 | |||
15.8 | even | 4 | 1305.2.a.n.1.1 | 2 | |||
20.3 | even | 4 | 2320.2.a.k.1.2 | 2 | |||
35.13 | even | 4 | 7105.2.a.e.1.2 | 2 | |||
40.3 | even | 4 | 9280.2.a.w.1.2 | 2 | |||
40.13 | odd | 4 | 9280.2.a.be.1.1 | 2 | |||
145.28 | odd | 4 | 4205.2.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
725.2.a.c.1.1 | 2 | 5.2 | odd | 4 | |||
725.2.b.c.349.2 | 4 | 5.4 | even | 2 | inner | ||
725.2.b.c.349.3 | 4 | 1.1 | even | 1 | trivial | ||
1305.2.a.n.1.1 | 2 | 15.8 | even | 4 | |||
2320.2.a.k.1.2 | 2 | 20.3 | even | 4 | |||
4205.2.a.d.1.1 | 2 | 145.28 | odd | 4 | |||
6525.2.a.p.1.2 | 2 | 15.2 | even | 4 | |||
7105.2.a.e.1.2 | 2 | 35.13 | even | 4 | |||
9280.2.a.w.1.2 | 2 | 40.3 | even | 4 | |||
9280.2.a.be.1.1 | 2 | 40.13 | odd | 4 |