Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(139,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("690.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.d (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.2 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.139 |
Dual form | 690.2.d.c.139.5 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.539189 | + | 2.17009i | −0.241133 | + | 0.970492i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 4.34017i | − | 1.64043i | −0.572055 | − | 0.820216i | \(-0.693853\pi\) | ||
0.572055 | − | 0.820216i | \(-0.306147\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.17009 | + | 0.539189i | 0.686242 | + | 0.170506i | ||||
\(11\) | −1.07838 | −0.325143 | −0.162572 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162572 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 2.34017i | − | 0.649047i | −0.945878 | − | 0.324524i | \(-0.894796\pi\) | ||
0.945878 | − | 0.324524i | \(-0.105204\pi\) | |||||||
\(14\) | −4.34017 | −1.15996 | ||||||||
\(15\) | 2.17009 | + | 0.539189i | 0.560314 | + | 0.139218i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.921622i | − | 0.223526i | −0.993735 | − | 0.111763i | \(-0.964350\pi\) | ||
0.993735 | − | 0.111763i | \(-0.0356498\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.34017 | −0.536873 | −0.268436 | − | 0.963297i | \(-0.586507\pi\) | ||||
−0.268436 | + | 0.963297i | \(0.586507\pi\) | |||||||
\(20\) | 0.539189 | − | 2.17009i | 0.120566 | − | 0.485246i | ||||
\(21\) | −4.34017 | −0.947103 | ||||||||
\(22\) | 1.07838i | 0.229911i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.41855 | − | 2.34017i | −0.883710 | − | 0.468035i | ||||
\(26\) | −2.34017 | −0.458946 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 4.34017i | 0.820216i | ||||||||
\(29\) | −10.4969 | −1.94923 | −0.974615 | − | 0.223886i | \(-0.928126\pi\) | ||||
−0.974615 | + | 0.223886i | \(0.928126\pi\) | |||||||
\(30\) | 0.539189 | − | 2.17009i | 0.0984420 | − | 0.396202i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.07838i | 0.187721i | ||||||||
\(34\) | −0.921622 | −0.158057 | ||||||||
\(35\) | 9.41855 | + | 2.34017i | 1.59203 | + | 0.395561i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 2.58145i | − | 0.424388i | −0.977228 | − | 0.212194i | \(-0.931939\pi\) | ||
0.977228 | − | 0.212194i | \(-0.0680608\pi\) | |||||||
\(38\) | 2.34017i | 0.379626i | ||||||||
\(39\) | −2.34017 | −0.374728 | ||||||||
\(40\) | −2.17009 | − | 0.539189i | −0.343121 | − | 0.0852532i | ||||
\(41\) | 0.156755 | 0.0244811 | 0.0122405 | − | 0.999925i | \(-0.496104\pi\) | ||||
0.0122405 | + | 0.999925i | \(0.496104\pi\) | |||||||
\(42\) | 4.34017i | 0.669703i | ||||||||
\(43\) | 0.738205i | 0.112575i | 0.998415 | + | 0.0562876i | \(0.0179264\pi\) | ||||
−0.998415 | + | 0.0562876i | \(0.982074\pi\) | |||||||
\(44\) | 1.07838 | 0.162572 | ||||||||
\(45\) | 0.539189 | − | 2.17009i | 0.0803775 | − | 0.323497i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − | 6.83710i | − | 0.997294i | −0.866805 | − | 0.498647i | \(-0.833830\pi\) | ||
0.866805 | − | 0.498647i | \(-0.166170\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −11.8371 | −1.69101 | ||||||||
\(50\) | −2.34017 | + | 4.41855i | −0.330950 | + | 0.624877i | ||||
\(51\) | −0.921622 | −0.129053 | ||||||||
\(52\) | 2.34017i | 0.324524i | ||||||||
\(53\) | − | 0.340173i | − | 0.0467264i | −0.999727 | − | 0.0233632i | \(-0.992563\pi\) | ||
0.999727 | − | 0.0233632i | \(-0.00743741\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.581449 | − | 2.34017i | 0.0784026 | − | 0.315549i | ||||
\(56\) | 4.34017 | 0.579980 | ||||||||
\(57\) | 2.34017i | 0.309963i | ||||||||
\(58\) | 10.4969i | 1.37831i | ||||||||
\(59\) | 8.83710 | 1.15049 | 0.575246 | − | 0.817980i | \(-0.304906\pi\) | ||||
0.575246 | + | 0.817980i | \(0.304906\pi\) | |||||||
\(60\) | −2.17009 | − | 0.539189i | −0.280157 | − | 0.0696090i | ||||
\(61\) | −11.5753 | −1.48207 | −0.741033 | − | 0.671469i | \(-0.765664\pi\) | ||||
−0.741033 | + | 0.671469i | \(0.765664\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | 4.34017i | 0.546810i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.07838 | + | 1.26180i | 0.629895 | + | 0.156506i | ||||
\(66\) | 1.07838 | 0.132739 | ||||||||
\(67\) | − | 2.58145i | − | 0.315374i | −0.987489 | − | 0.157687i | \(-0.949596\pi\) | ||
0.987489 | − | 0.157687i | \(-0.0504037\pi\) | |||||||
\(68\) | 0.921622i | 0.111763i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 2.34017 | − | 9.41855i | 0.279704 | − | 1.12573i | ||||
\(71\) | 15.1773 | 1.80121 | 0.900606 | − | 0.434637i | \(-0.143123\pi\) | ||||
0.900606 | + | 0.434637i | \(0.143123\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 4.68035i | − | 0.547793i | −0.961759 | − | 0.273897i | \(-0.911687\pi\) | ||
0.961759 | − | 0.273897i | \(-0.0883126\pi\) | |||||||
\(74\) | −2.58145 | −0.300087 | ||||||||
\(75\) | −2.34017 | + | 4.41855i | −0.270220 | + | 0.510210i | ||||
\(76\) | 2.34017 | 0.268436 | ||||||||
\(77\) | 4.68035i | 0.533375i | ||||||||
\(78\) | 2.34017i | 0.264972i | ||||||||
\(79\) | 11.9155 | 1.34060 | 0.670298 | − | 0.742092i | \(-0.266166\pi\) | ||||
0.670298 | + | 0.742092i | \(0.266166\pi\) | |||||||
\(80\) | −0.539189 | + | 2.17009i | −0.0602831 | + | 0.242623i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.156755i | − | 0.0173107i | ||||||
\(83\) | 11.4186i | 1.25335i | 0.779281 | + | 0.626674i | \(0.215584\pi\) | ||||
−0.779281 | + | 0.626674i | \(0.784416\pi\) | |||||||
\(84\) | 4.34017 | 0.473552 | ||||||||
\(85\) | 2.00000 | + | 0.496928i | 0.216930 | + | 0.0538995i | ||||
\(86\) | 0.738205 | 0.0796027 | ||||||||
\(87\) | 10.4969i | 1.12539i | ||||||||
\(88\) | − | 1.07838i | − | 0.114955i | ||||||
\(89\) | 4.68035 | 0.496116 | 0.248058 | − | 0.968745i | \(-0.420208\pi\) | ||||
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(90\) | −2.17009 | − | 0.539189i | −0.228747 | − | 0.0568355i | ||||
\(91\) | −10.1568 | −1.06472 | ||||||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | −6.83710 | −0.705193 | ||||||||
\(95\) | 1.26180 | − | 5.07838i | 0.129457 | − | 0.521031i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 9.02052i | − | 0.915895i | −0.888979 | − | 0.457947i | \(-0.848585\pi\) | ||
0.888979 | − | 0.457947i | \(-0.151415\pi\) | |||||||
\(98\) | 11.8371i | 1.19573i | ||||||||
\(99\) | 1.07838 | 0.108381 | ||||||||
\(100\) | 4.41855 | + | 2.34017i | 0.441855 | + | 0.234017i | ||||
\(101\) | 1.50307 | 0.149561 | 0.0747806 | − | 0.997200i | \(-0.476174\pi\) | ||||
0.0747806 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(102\) | 0.921622i | 0.0912542i | ||||||||
\(103\) | − | 2.49693i | − | 0.246030i | −0.992405 | − | 0.123015i | \(-0.960744\pi\) | ||
0.992405 | − | 0.123015i | \(-0.0392563\pi\) | |||||||
\(104\) | 2.34017 | 0.229473 | ||||||||
\(105\) | 2.34017 | − | 9.41855i | 0.228377 | − | 0.919156i | ||||
\(106\) | −0.340173 | −0.0330405 | ||||||||
\(107\) | − | 9.57531i | − | 0.925680i | −0.886442 | − | 0.462840i | \(-0.846830\pi\) | ||
0.886442 | − | 0.462840i | \(-0.153170\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 9.78539 | 0.937270 | 0.468635 | − | 0.883392i | \(-0.344746\pi\) | ||||
0.468635 | + | 0.883392i | \(0.344746\pi\) | |||||||
\(110\) | −2.34017 | − | 0.581449i | −0.223127 | − | 0.0554390i | ||||
\(111\) | −2.58145 | −0.245020 | ||||||||
\(112\) | − | 4.34017i | − | 0.410108i | ||||||
\(113\) | 8.92162i | 0.839276i | 0.907692 | + | 0.419638i | \(0.137843\pi\) | ||||
−0.907692 | + | 0.419638i | \(0.862157\pi\) | |||||||
\(114\) | 2.34017 | 0.219177 | ||||||||
\(115\) | −2.17009 | − | 0.539189i | −0.202362 | − | 0.0502796i | ||||
\(116\) | 10.4969 | 0.974615 | ||||||||
\(117\) | 2.34017i | 0.216349i | ||||||||
\(118\) | − | 8.83710i | − | 0.813521i | ||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | −0.539189 | + | 2.17009i | −0.0492210 | + | 0.198101i | ||||
\(121\) | −9.83710 | −0.894282 | ||||||||
\(122\) | 11.5753i | 1.04798i | ||||||||
\(123\) | − | 0.156755i | − | 0.0141342i | ||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | 7.46081 | − | 8.32684i | 0.667315 | − | 0.744775i | ||||
\(126\) | 4.34017 | 0.386653 | ||||||||
\(127\) | − | 17.1773i | − | 1.52424i | −0.647438 | − | 0.762118i | \(-0.724159\pi\) | ||
0.647438 | − | 0.762118i | \(-0.275841\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0.738205 | 0.0649953 | ||||||||
\(130\) | 1.26180 | − | 5.07838i | 0.110667 | − | 0.445403i | ||||
\(131\) | −6.68035 | −0.583665 | −0.291832 | − | 0.956470i | \(-0.594265\pi\) | ||||
−0.291832 | + | 0.956470i | \(0.594265\pi\) | |||||||
\(132\) | − | 1.07838i | − | 0.0938607i | ||||||
\(133\) | 10.1568i | 0.880702i | ||||||||
\(134\) | −2.58145 | −0.223003 | ||||||||
\(135\) | −2.17009 | − | 0.539189i | −0.186771 | − | 0.0464060i | ||||
\(136\) | 0.921622 | 0.0790285 | ||||||||
\(137\) | − | 22.2823i | − | 1.90371i | −0.306554 | − | 0.951853i | \(-0.599176\pi\) | ||
0.306554 | − | 0.951853i | \(-0.400824\pi\) | |||||||
\(138\) | − | 1.00000i | − | 0.0851257i | ||||||
\(139\) | 10.5236 | 0.892599 | 0.446300 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446300 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(140\) | −9.41855 | − | 2.34017i | −0.796013 | − | 0.197781i | ||||
\(141\) | −6.83710 | −0.575788 | ||||||||
\(142\) | − | 15.1773i | − | 1.27365i | ||||||
\(143\) | 2.52359i | 0.211033i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 5.65983 | − | 22.7792i | 0.470023 | − | 1.89171i | ||||
\(146\) | −4.68035 | −0.387348 | ||||||||
\(147\) | 11.8371i | 0.976308i | ||||||||
\(148\) | 2.58145i | 0.212194i | ||||||||
\(149\) | −6.92162 | −0.567041 | −0.283521 | − | 0.958966i | \(-0.591502\pi\) | ||||
−0.283521 | + | 0.958966i | \(0.591502\pi\) | |||||||
\(150\) | 4.41855 | + | 2.34017i | 0.360773 | + | 0.191074i | ||||
\(151\) | 6.15676 | 0.501030 | 0.250515 | − | 0.968113i | \(-0.419400\pi\) | ||||
0.250515 | + | 0.968113i | \(0.419400\pi\) | |||||||
\(152\) | − | 2.34017i | − | 0.189813i | ||||||
\(153\) | 0.921622i | 0.0745087i | ||||||||
\(154\) | 4.68035 | 0.377153 | ||||||||
\(155\) | 2.15676 | − | 8.68035i | 0.173235 | − | 0.697222i | ||||
\(156\) | 2.34017 | 0.187364 | ||||||||
\(157\) | − | 2.89496i | − | 0.231043i | −0.993305 | − | 0.115521i | \(-0.963146\pi\) | ||
0.993305 | − | 0.115521i | \(-0.0368539\pi\) | |||||||
\(158\) | − | 11.9155i | − | 0.947945i | ||||||
\(159\) | −0.340173 | −0.0269775 | ||||||||
\(160\) | 2.17009 | + | 0.539189i | 0.171560 | + | 0.0426266i | ||||
\(161\) | 4.34017 | 0.342054 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 6.52359i | 0.510967i | 0.966813 | + | 0.255484i | \(0.0822347\pi\) | ||||
−0.966813 | + | 0.255484i | \(0.917765\pi\) | |||||||
\(164\) | −0.156755 | −0.0122405 | ||||||||
\(165\) | −2.34017 | − | 0.581449i | −0.182182 | − | 0.0452658i | ||||
\(166\) | 11.4186 | 0.886251 | ||||||||
\(167\) | − | 5.47641i | − | 0.423777i | −0.977294 | − | 0.211889i | \(-0.932039\pi\) | ||
0.977294 | − | 0.211889i | \(-0.0679614\pi\) | |||||||
\(168\) | − | 4.34017i | − | 0.334852i | ||||||
\(169\) | 7.52359 | 0.578738 | ||||||||
\(170\) | 0.496928 | − | 2.00000i | 0.0381127 | − | 0.153393i | ||||
\(171\) | 2.34017 | 0.178958 | ||||||||
\(172\) | − | 0.738205i | − | 0.0562876i | ||||||
\(173\) | − | 15.6742i | − | 1.19169i | −0.803100 | − | 0.595844i | \(-0.796818\pi\) | ||
0.803100 | − | 0.595844i | \(-0.203182\pi\) | |||||||
\(174\) | 10.4969 | 0.795770 | ||||||||
\(175\) | −10.1568 | + | 19.1773i | −0.767779 | + | 1.44967i | ||||
\(176\) | −1.07838 | −0.0812858 | ||||||||
\(177\) | − | 8.83710i | − | 0.664237i | ||||||
\(178\) | − | 4.68035i | − | 0.350807i | ||||||
\(179\) | −15.3607 | −1.14811 | −0.574056 | − | 0.818816i | \(-0.694631\pi\) | ||||
−0.574056 | + | 0.818816i | \(0.694631\pi\) | |||||||
\(180\) | −0.539189 | + | 2.17009i | −0.0401888 | + | 0.161749i | ||||
\(181\) | 21.6163 | 1.60673 | 0.803365 | − | 0.595487i | \(-0.203041\pi\) | ||||
0.803365 | + | 0.595487i | \(0.203041\pi\) | |||||||
\(182\) | 10.1568i | 0.752869i | ||||||||
\(183\) | 11.5753i | 0.855671i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 5.60197 | + | 1.39189i | 0.411865 | + | 0.102334i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | 0.993857i | 0.0726780i | ||||||||
\(188\) | 6.83710i | 0.498647i | ||||||||
\(189\) | 4.34017 | 0.315701 | ||||||||
\(190\) | −5.07838 | − | 1.26180i | −0.368424 | − | 0.0915402i | ||||
\(191\) | 4.36683 | 0.315973 | 0.157987 | − | 0.987441i | \(-0.449500\pi\) | ||||
0.157987 | + | 0.987441i | \(0.449500\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 8.68035i | − | 0.624825i | −0.949947 | − | 0.312412i | \(-0.898863\pi\) | ||
0.949947 | − | 0.312412i | \(-0.101137\pi\) | |||||||
\(194\) | −9.02052 | −0.647636 | ||||||||
\(195\) | 1.26180 | − | 5.07838i | 0.0903590 | − | 0.363670i | ||||
\(196\) | 11.8371 | 0.845507 | ||||||||
\(197\) | 22.6803i | 1.61591i | 0.589246 | + | 0.807954i | \(0.299425\pi\) | ||||
−0.589246 | + | 0.807954i | \(0.700575\pi\) | |||||||
\(198\) | − | 1.07838i | − | 0.0766370i | ||||||
\(199\) | 5.44521 | 0.386001 | 0.193000 | − | 0.981199i | \(-0.438178\pi\) | ||||
0.193000 | + | 0.981199i | \(0.438178\pi\) | |||||||
\(200\) | 2.34017 | − | 4.41855i | 0.165475 | − | 0.312439i | ||||
\(201\) | −2.58145 | −0.182081 | ||||||||
\(202\) | − | 1.50307i | − | 0.105756i | ||||||
\(203\) | 45.5585i | 3.19758i | ||||||||
\(204\) | 0.921622 | 0.0645265 | ||||||||
\(205\) | −0.0845208 | + | 0.340173i | −0.00590319 | + | 0.0237587i | ||||
\(206\) | −2.49693 | −0.173969 | ||||||||
\(207\) | − | 1.00000i | − | 0.0695048i | ||||||
\(208\) | − | 2.34017i | − | 0.162262i | ||||||
\(209\) | 2.52359 | 0.174560 | ||||||||
\(210\) | −9.41855 | − | 2.34017i | −0.649942 | − | 0.161487i | ||||
\(211\) | −22.0410 | −1.51737 | −0.758684 | − | 0.651459i | \(-0.774157\pi\) | ||||
−0.758684 | + | 0.651459i | \(0.774157\pi\) | |||||||
\(212\) | 0.340173i | 0.0233632i | ||||||||
\(213\) | − | 15.1773i | − | 1.03993i | ||||||
\(214\) | −9.57531 | −0.654554 | ||||||||
\(215\) | −1.60197 | − | 0.398032i | −0.109253 | − | 0.0271455i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 17.3607i | 1.17852i | ||||||||
\(218\) | − | 9.78539i | − | 0.662750i | ||||||
\(219\) | −4.68035 | −0.316268 | ||||||||
\(220\) | −0.581449 | + | 2.34017i | −0.0392013 | + | 0.157774i | ||||
\(221\) | −2.15676 | −0.145079 | ||||||||
\(222\) | 2.58145i | 0.173256i | ||||||||
\(223\) | 21.1773i | 1.41814i | 0.705141 | + | 0.709068i | \(0.250884\pi\) | ||||
−0.705141 | + | 0.709068i | \(0.749116\pi\) | |||||||
\(224\) | −4.34017 | −0.289990 | ||||||||
\(225\) | 4.41855 | + | 2.34017i | 0.294570 | + | 0.156012i | ||||
\(226\) | 8.92162 | 0.593457 | ||||||||
\(227\) | 11.7854i | 0.782224i | 0.920343 | + | 0.391112i | \(0.127909\pi\) | ||||
−0.920343 | + | 0.391112i | \(0.872091\pi\) | |||||||
\(228\) | − | 2.34017i | − | 0.154982i | ||||||
\(229\) | −1.78539 | −0.117982 | −0.0589908 | − | 0.998259i | \(-0.518788\pi\) | ||||
−0.0589908 | + | 0.998259i | \(0.518788\pi\) | |||||||
\(230\) | −0.539189 | + | 2.17009i | −0.0355531 | + | 0.143091i | ||||
\(231\) | 4.68035 | 0.307944 | ||||||||
\(232\) | − | 10.4969i | − | 0.689157i | ||||||
\(233\) | 18.3135i | 1.19976i | 0.800091 | + | 0.599879i | \(0.204785\pi\) | ||||
−0.800091 | + | 0.599879i | \(0.795215\pi\) | |||||||
\(234\) | 2.34017 | 0.152982 | ||||||||
\(235\) | 14.8371 | + | 3.68649i | 0.967866 | + | 0.240480i | ||||
\(236\) | −8.83710 | −0.575246 | ||||||||
\(237\) | − | 11.9155i | − | 0.773994i | ||||||
\(238\) | 4.00000i | 0.259281i | ||||||||
\(239\) | 5.33403 | 0.345030 | 0.172515 | − | 0.985007i | \(-0.444811\pi\) | ||||
0.172515 | + | 0.985007i | \(0.444811\pi\) | |||||||
\(240\) | 2.17009 | + | 0.539189i | 0.140078 | + | 0.0348045i | ||||
\(241\) | 26.1978 | 1.68755 | 0.843774 | − | 0.536698i | \(-0.180329\pi\) | ||||
0.843774 | + | 0.536698i | \(0.180329\pi\) | |||||||
\(242\) | 9.83710i | 0.632353i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 11.5753 | 0.741033 | ||||||||
\(245\) | 6.38243 | − | 25.6875i | 0.407759 | − | 1.64112i | ||||
\(246\) | −0.156755 | −0.00999437 | ||||||||
\(247\) | 5.47641i | 0.348456i | ||||||||
\(248\) | − | 4.00000i | − | 0.254000i | ||||||
\(249\) | 11.4186 | 0.723621 | ||||||||
\(250\) | −8.32684 | − | 7.46081i | −0.526636 | − | 0.471863i | ||||
\(251\) | 27.4329 | 1.73155 | 0.865775 | − | 0.500433i | \(-0.166826\pi\) | ||||
0.865775 | + | 0.500433i | \(0.166826\pi\) | |||||||
\(252\) | − | 4.34017i | − | 0.273405i | ||||||
\(253\) | − | 1.07838i | − | 0.0677970i | ||||||
\(254\) | −17.1773 | −1.07780 | ||||||||
\(255\) | 0.496928 | − | 2.00000i | 0.0311189 | − | 0.125245i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.3135i | 0.643339i | 0.946852 | + | 0.321670i | \(0.104244\pi\) | ||||
−0.946852 | + | 0.321670i | \(0.895756\pi\) | |||||||
\(258\) | − | 0.738205i | − | 0.0459586i | ||||||
\(259\) | −11.2039 | −0.696179 | ||||||||
\(260\) | −5.07838 | − | 1.26180i | −0.314948 | − | 0.0782532i | ||||
\(261\) | 10.4969 | 0.649744 | ||||||||
\(262\) | 6.68035i | 0.412713i | ||||||||
\(263\) | − | 20.9939i | − | 1.29454i | −0.762262 | − | 0.647268i | \(-0.775911\pi\) | ||
0.762262 | − | 0.647268i | \(-0.224089\pi\) | |||||||
\(264\) | −1.07838 | −0.0663696 | ||||||||
\(265\) | 0.738205 | + | 0.183417i | 0.0453476 | + | 0.0112672i | ||||
\(266\) | 10.1568 | 0.622751 | ||||||||
\(267\) | − | 4.68035i | − | 0.286433i | ||||||
\(268\) | 2.58145i | 0.157687i | ||||||||
\(269\) | −25.3874 | −1.54789 | −0.773947 | − | 0.633250i | \(-0.781720\pi\) | ||||
−0.773947 | + | 0.633250i | \(0.781720\pi\) | |||||||
\(270\) | −0.539189 | + | 2.17009i | −0.0328140 | + | 0.132067i | ||||
\(271\) | −32.5646 | −1.97816 | −0.989080 | − | 0.147379i | \(-0.952916\pi\) | ||||
−0.989080 | + | 0.147379i | \(0.952916\pi\) | |||||||
\(272\) | − | 0.921622i | − | 0.0558816i | ||||||
\(273\) | 10.1568i | 0.614715i | ||||||||
\(274\) | −22.2823 | −1.34612 | ||||||||
\(275\) | 4.76487 | + | 2.52359i | 0.287332 | + | 0.152178i | ||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | − | 15.7009i | − | 0.943374i | −0.881766 | − | 0.471687i | \(-0.843645\pi\) | ||
0.881766 | − | 0.471687i | \(-0.156355\pi\) | |||||||
\(278\) | − | 10.5236i | − | 0.631163i | ||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | −2.34017 | + | 9.41855i | −0.139852 | + | 0.562866i | ||||
\(281\) | −9.36069 | −0.558412 | −0.279206 | − | 0.960231i | \(-0.590071\pi\) | ||||
−0.279206 | + | 0.960231i | \(0.590071\pi\) | |||||||
\(282\) | 6.83710i | 0.407143i | ||||||||
\(283\) | − | 17.4186i | − | 1.03543i | −0.855555 | − | 0.517713i | \(-0.826784\pi\) | ||
0.855555 | − | 0.517713i | \(-0.173216\pi\) | |||||||
\(284\) | −15.1773 | −0.900606 | ||||||||
\(285\) | −5.07838 | − | 1.26180i | −0.300817 | − | 0.0747423i | ||||
\(286\) | 2.52359 | 0.149223 | ||||||||
\(287\) | − | 0.680346i | − | 0.0401596i | ||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.1506 | 0.950036 | ||||||||
\(290\) | −22.7792 | − | 5.65983i | −1.33764 | − | 0.332356i | ||||
\(291\) | −9.02052 | −0.528792 | ||||||||
\(292\) | 4.68035i | 0.273897i | ||||||||
\(293\) | − | 16.3402i | − | 0.954603i | −0.878740 | − | 0.477302i | \(-0.841615\pi\) | ||
0.878740 | − | 0.477302i | \(-0.158385\pi\) | |||||||
\(294\) | 11.8371 | 0.690354 | ||||||||
\(295\) | −4.76487 | + | 19.1773i | −0.277421 | + | 1.11654i | ||||
\(296\) | 2.58145 | 0.150044 | ||||||||
\(297\) | − | 1.07838i | − | 0.0625738i | ||||||
\(298\) | 6.92162i | 0.400959i | ||||||||
\(299\) | 2.34017 | 0.135336 | ||||||||
\(300\) | 2.34017 | − | 4.41855i | 0.135110 | − | 0.255105i | ||||
\(301\) | 3.20394 | 0.184672 | ||||||||
\(302\) | − | 6.15676i | − | 0.354281i | ||||||
\(303\) | − | 1.50307i | − | 0.0863492i | ||||||
\(304\) | −2.34017 | −0.134218 | ||||||||
\(305\) | 6.24128 | − | 25.1194i | 0.357374 | − | 1.43833i | ||||
\(306\) | 0.921622 | 0.0526856 | ||||||||
\(307\) | 3.20394i | 0.182858i | 0.995812 | + | 0.0914292i | \(0.0291435\pi\) | ||||
−0.995812 | + | 0.0914292i | \(0.970856\pi\) | |||||||
\(308\) | − | 4.68035i | − | 0.266687i | ||||||
\(309\) | −2.49693 | −0.142045 | ||||||||
\(310\) | −8.68035 | − | 2.15676i | −0.493011 | − | 0.122495i | ||||
\(311\) | 12.6537 | 0.717525 | 0.358762 | − | 0.933429i | \(-0.383199\pi\) | ||||
0.358762 | + | 0.933429i | \(0.383199\pi\) | |||||||
\(312\) | − | 2.34017i | − | 0.132486i | ||||||
\(313\) | 33.2183i | 1.87761i | 0.344449 | + | 0.938805i | \(0.388066\pi\) | ||||
−0.344449 | + | 0.938805i | \(0.611934\pi\) | |||||||
\(314\) | −2.89496 | −0.163372 | ||||||||
\(315\) | −9.41855 | − | 2.34017i | −0.530675 | − | 0.131854i | ||||
\(316\) | −11.9155 | −0.670298 | ||||||||
\(317\) | 6.99386i | 0.392814i | 0.980522 | + | 0.196407i | \(0.0629274\pi\) | ||||
−0.980522 | + | 0.196407i | \(0.937073\pi\) | |||||||
\(318\) | 0.340173i | 0.0190760i | ||||||||
\(319\) | 11.3197 | 0.633779 | ||||||||
\(320\) | 0.539189 | − | 2.17009i | 0.0301416 | − | 0.121312i | ||||
\(321\) | −9.57531 | −0.534441 | ||||||||
\(322\) | − | 4.34017i | − | 0.241868i | ||||||
\(323\) | 2.15676i | 0.120005i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −5.47641 | + | 10.3402i | −0.303777 | + | 0.573570i | ||||
\(326\) | 6.52359 | 0.361308 | ||||||||
\(327\) | − | 9.78539i | − | 0.541133i | ||||||
\(328\) | 0.156755i | 0.00865537i | ||||||||
\(329\) | −29.6742 | −1.63599 | ||||||||
\(330\) | −0.581449 | + | 2.34017i | −0.0320077 | + | 0.128822i | ||||
\(331\) | −29.7275 | −1.63397 | −0.816986 | − | 0.576657i | \(-0.804357\pi\) | ||||
−0.816986 | + | 0.576657i | \(0.804357\pi\) | |||||||
\(332\) | − | 11.4186i | − | 0.626674i | ||||||
\(333\) | 2.58145i | 0.141463i | ||||||||
\(334\) | −5.47641 | −0.299656 | ||||||||
\(335\) | 5.60197 | + | 1.39189i | 0.306068 | + | 0.0760470i | ||||
\(336\) | −4.34017 | −0.236776 | ||||||||
\(337\) | − | 28.3402i | − | 1.54379i | −0.635751 | − | 0.771894i | \(-0.719310\pi\) | ||
0.635751 | − | 0.771894i | \(-0.280690\pi\) | |||||||
\(338\) | − | 7.52359i | − | 0.409229i | ||||||
\(339\) | 8.92162 | 0.484556 | ||||||||
\(340\) | −2.00000 | − | 0.496928i | −0.108465 | − | 0.0269497i | ||||
\(341\) | 4.31351 | 0.233590 | ||||||||
\(342\) | − | 2.34017i | − | 0.126542i | ||||||
\(343\) | 20.9939i | 1.13356i | ||||||||
\(344\) | −0.738205 | −0.0398013 | ||||||||
\(345\) | −0.539189 | + | 2.17009i | −0.0290290 | + | 0.116834i | ||||
\(346\) | −15.6742 | −0.842650 | ||||||||
\(347\) | 22.5236i | 1.20913i | 0.796556 | + | 0.604565i | \(0.206653\pi\) | ||||
−0.796556 | + | 0.604565i | \(0.793347\pi\) | |||||||
\(348\) | − | 10.4969i | − | 0.562694i | ||||||
\(349\) | −15.6742 | −0.839021 | −0.419510 | − | 0.907751i | \(-0.637798\pi\) | ||||
−0.419510 | + | 0.907751i | \(0.637798\pi\) | |||||||
\(350\) | 19.1773 | + | 10.1568i | 1.02507 | + | 0.542901i | ||||
\(351\) | 2.34017 | 0.124909 | ||||||||
\(352\) | 1.07838i | 0.0574777i | ||||||||
\(353\) | 26.3135i | 1.40053i | 0.713885 | + | 0.700263i | \(0.246934\pi\) | ||||
−0.713885 | + | 0.700263i | \(0.753066\pi\) | |||||||
\(354\) | −8.83710 | −0.469687 | ||||||||
\(355\) | −8.18342 | + | 32.9360i | −0.434331 | + | 1.74806i | ||||
\(356\) | −4.68035 | −0.248058 | ||||||||
\(357\) | 4.00000i | 0.211702i | ||||||||
\(358\) | 15.3607i | 0.811838i | ||||||||
\(359\) | 0.796064 | 0.0420146 | 0.0210073 | − | 0.999779i | \(-0.493313\pi\) | ||||
0.0210073 | + | 0.999779i | \(0.493313\pi\) | |||||||
\(360\) | 2.17009 | + | 0.539189i | 0.114374 | + | 0.0284177i | ||||
\(361\) | −13.5236 | −0.711768 | ||||||||
\(362\) | − | 21.6163i | − | 1.13613i | ||||||
\(363\) | 9.83710i | 0.516314i | ||||||||
\(364\) | 10.1568 | 0.532359 | ||||||||
\(365\) | 10.1568 | + | 2.52359i | 0.531629 | + | 0.132091i | ||||
\(366\) | 11.5753 | 0.605051 | ||||||||
\(367\) | − | 13.7009i | − | 0.715179i | −0.933879 | − | 0.357590i | \(-0.883599\pi\) | ||
0.933879 | − | 0.357590i | \(-0.116401\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | −0.156755 | −0.00816036 | ||||||||
\(370\) | 1.39189 | − | 5.60197i | 0.0723608 | − | 0.291232i | ||||
\(371\) | −1.47641 | −0.0766514 | ||||||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 4.25565i | 0.220349i | 0.993912 | + | 0.110175i | \(0.0351410\pi\) | ||||
−0.993912 | + | 0.110175i | \(0.964859\pi\) | |||||||
\(374\) | 0.993857 | 0.0513911 | ||||||||
\(375\) | −8.32684 | − | 7.46081i | −0.429996 | − | 0.385275i | ||||
\(376\) | 6.83710 | 0.352597 | ||||||||
\(377\) | 24.5646i | 1.26514i | ||||||||
\(378\) | − | 4.34017i | − | 0.223234i | ||||||
\(379\) | 30.6537 | 1.57457 | 0.787287 | − | 0.616587i | \(-0.211485\pi\) | ||||
0.787287 | + | 0.616587i | \(0.211485\pi\) | |||||||
\(380\) | −1.26180 | + | 5.07838i | −0.0647287 | + | 0.260515i | ||||
\(381\) | −17.1773 | −0.880018 | ||||||||
\(382\) | − | 4.36683i | − | 0.223427i | ||||||
\(383\) | − | 20.8781i | − | 1.06682i | −0.845856 | − | 0.533412i | \(-0.820910\pi\) | ||
0.845856 | − | 0.533412i | \(-0.179090\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −10.1568 | − | 2.52359i | −0.517636 | − | 0.128614i | ||||
\(386\) | −8.68035 | −0.441818 | ||||||||
\(387\) | − | 0.738205i | − | 0.0375251i | ||||||
\(388\) | 9.02052i | 0.457947i | ||||||||
\(389\) | 16.9627 | 0.860041 | 0.430021 | − | 0.902819i | \(-0.358506\pi\) | ||||
0.430021 | + | 0.902819i | \(0.358506\pi\) | |||||||
\(390\) | −5.07838 | − | 1.26180i | −0.257154 | − | 0.0638935i | ||||
\(391\) | 0.921622 | 0.0466084 | ||||||||
\(392\) | − | 11.8371i | − | 0.597864i | ||||||
\(393\) | 6.68035i | 0.336979i | ||||||||
\(394\) | 22.6803 | 1.14262 | ||||||||
\(395\) | −6.42469 | + | 25.8576i | −0.323261 | + | 1.30104i | ||||
\(396\) | −1.07838 | −0.0541905 | ||||||||
\(397\) | 16.4969i | 0.827957i | 0.910287 | + | 0.413979i | \(0.135861\pi\) | ||||
−0.910287 | + | 0.413979i | \(0.864139\pi\) | |||||||
\(398\) | − | 5.44521i | − | 0.272944i | ||||||
\(399\) | 10.1568 | 0.508474 | ||||||||
\(400\) | −4.41855 | − | 2.34017i | −0.220928 | − | 0.117009i | ||||
\(401\) | −35.2039 | −1.75800 | −0.879000 | − | 0.476821i | \(-0.841789\pi\) | ||||
−0.879000 | + | 0.476821i | \(0.841789\pi\) | |||||||
\(402\) | 2.58145i | 0.128751i | ||||||||
\(403\) | 9.36069i | 0.466289i | ||||||||
\(404\) | −1.50307 | −0.0747806 | ||||||||
\(405\) | −0.539189 | + | 2.17009i | −0.0267925 | + | 0.107832i | ||||
\(406\) | 45.5585 | 2.26103 | ||||||||
\(407\) | 2.78378i | 0.137987i | ||||||||
\(408\) | − | 0.921622i | − | 0.0456271i | ||||||
\(409\) | −11.3607 | −0.561750 | −0.280875 | − | 0.959744i | \(-0.590625\pi\) | ||||
−0.280875 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(410\) | 0.340173 | + | 0.0845208i | 0.0167999 | + | 0.00417419i | ||||
\(411\) | −22.2823 | −1.09911 | ||||||||
\(412\) | 2.49693i | 0.123015i | ||||||||
\(413\) | − | 38.3545i | − | 1.88730i | ||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −24.7792 | − | 6.15676i | −1.21637 | − | 0.302223i | ||||
\(416\) | −2.34017 | −0.114736 | ||||||||
\(417\) | − | 10.5236i | − | 0.515342i | ||||||
\(418\) | − | 2.52359i | − | 0.123433i | ||||||
\(419\) | 18.1256 | 0.885491 | 0.442746 | − | 0.896647i | \(-0.354004\pi\) | ||||
0.442746 | + | 0.896647i | \(0.354004\pi\) | |||||||
\(420\) | −2.34017 | + | 9.41855i | −0.114189 | + | 0.459578i | ||||
\(421\) | 2.58145 | 0.125812 | 0.0629061 | − | 0.998019i | \(-0.479963\pi\) | ||||
0.0629061 | + | 0.998019i | \(0.479963\pi\) | |||||||
\(422\) | 22.0410i | 1.07294i | ||||||||
\(423\) | 6.83710i | 0.332431i | ||||||||
\(424\) | 0.340173 | 0.0165203 | ||||||||
\(425\) | −2.15676 | + | 4.07223i | −0.104618 | + | 0.197532i | ||||
\(426\) | −15.1773 | −0.735341 | ||||||||
\(427\) | 50.2388i | 2.43123i | ||||||||
\(428\) | 9.57531i | 0.462840i | ||||||||
\(429\) | 2.52359 | 0.121840 | ||||||||
\(430\) | −0.398032 | + | 1.60197i | −0.0191948 | + | 0.0772538i | ||||
\(431\) | −33.9877 | −1.63713 | −0.818565 | − | 0.574414i | \(-0.805230\pi\) | ||||
−0.818565 | + | 0.574414i | \(0.805230\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 8.28685i | − | 0.398241i | −0.979975 | − | 0.199120i | \(-0.936192\pi\) | ||
0.979975 | − | 0.199120i | \(-0.0638084\pi\) | |||||||
\(434\) | 17.3607 | 0.833340 | ||||||||
\(435\) | −22.7792 | − | 5.65983i | −1.09218 | − | 0.271368i | ||||
\(436\) | −9.78539 | −0.468635 | ||||||||
\(437\) | − | 2.34017i | − | 0.111946i | ||||||
\(438\) | 4.68035i | 0.223636i | ||||||||
\(439\) | 28.9939 | 1.38380 | 0.691901 | − | 0.721993i | \(-0.256774\pi\) | ||||
0.691901 | + | 0.721993i | \(0.256774\pi\) | |||||||
\(440\) | 2.34017 | + | 0.581449i | 0.111563 | + | 0.0277195i | ||||
\(441\) | 11.8371 | 0.563671 | ||||||||
\(442\) | 2.15676i | 0.102586i | ||||||||
\(443\) | − | 3.20394i | − | 0.152224i | −0.997099 | − | 0.0761118i | \(-0.975749\pi\) | ||
0.997099 | − | 0.0761118i | \(-0.0242506\pi\) | |||||||
\(444\) | 2.58145 | 0.122510 | ||||||||
\(445\) | −2.52359 | + | 10.1568i | −0.119630 | + | 0.481476i | ||||
\(446\) | 21.1773 | 1.00277 | ||||||||
\(447\) | 6.92162i | 0.327381i | ||||||||
\(448\) | 4.34017i | 0.205054i | ||||||||
\(449\) | −28.1568 | −1.32880 | −0.664400 | − | 0.747377i | \(-0.731313\pi\) | ||||
−0.664400 | + | 0.747377i | \(0.731313\pi\) | |||||||
\(450\) | 2.34017 | − | 4.41855i | 0.110317 | − | 0.208292i | ||||
\(451\) | −0.169042 | −0.00795986 | ||||||||
\(452\) | − | 8.92162i | − | 0.419638i | ||||||
\(453\) | − | 6.15676i | − | 0.289270i | ||||||
\(454\) | 11.7854 | 0.553116 | ||||||||
\(455\) | 5.47641 | − | 22.0410i | 0.256738 | − | 1.03330i | ||||
\(456\) | −2.34017 | −0.109589 | ||||||||
\(457\) | 23.1773i | 1.08419i | 0.840318 | + | 0.542094i | \(0.182368\pi\) | ||||
−0.840318 | + | 0.542094i | \(0.817632\pi\) | |||||||
\(458\) | 1.78539i | 0.0834256i | ||||||||
\(459\) | 0.921622 | 0.0430176 | ||||||||
\(460\) | 2.17009 | + | 0.539189i | 0.101181 | + | 0.0251398i | ||||
\(461\) | −42.3279 | −1.97141 | −0.985703 | − | 0.168491i | \(-0.946110\pi\) | ||||
−0.985703 | + | 0.168491i | \(0.946110\pi\) | |||||||
\(462\) | − | 4.68035i | − | 0.217749i | ||||||
\(463\) | − | 34.9048i | − | 1.62216i | −0.584933 | − | 0.811082i | \(-0.698879\pi\) | ||
0.584933 | − | 0.811082i | \(-0.301121\pi\) | |||||||
\(464\) | −10.4969 | −0.487308 | ||||||||
\(465\) | −8.68035 | − | 2.15676i | −0.402541 | − | 0.100017i | ||||
\(466\) | 18.3135 | 0.848357 | ||||||||
\(467\) | 37.7731i | 1.74793i | 0.485988 | + | 0.873965i | \(0.338460\pi\) | ||||
−0.485988 | + | 0.873965i | \(0.661540\pi\) | |||||||
\(468\) | − | 2.34017i | − | 0.108175i | ||||||
\(469\) | −11.2039 | −0.517350 | ||||||||
\(470\) | 3.68649 | − | 14.8371i | 0.170045 | − | 0.684384i | ||||
\(471\) | −2.89496 | −0.133393 | ||||||||
\(472\) | 8.83710i | 0.406761i | ||||||||
\(473\) | − | 0.796064i | − | 0.0366030i | ||||||
\(474\) | −11.9155 | −0.547296 | ||||||||
\(475\) | 10.3402 | + | 5.47641i | 0.474440 | + | 0.251275i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0.340173i | 0.0155755i | ||||||||
\(478\) | − | 5.33403i | − | 0.243973i | ||||||
\(479\) | 28.1978 | 1.28839 | 0.644195 | − | 0.764861i | \(-0.277193\pi\) | ||||
0.644195 | + | 0.764861i | \(0.277193\pi\) | |||||||
\(480\) | 0.539189 | − | 2.17009i | 0.0246105 | − | 0.0990504i | ||||
\(481\) | −6.04104 | −0.275448 | ||||||||
\(482\) | − | 26.1978i | − | 1.19328i | ||||||
\(483\) | − | 4.34017i | − | 0.197485i | ||||||
\(484\) | 9.83710 | 0.447141 | ||||||||
\(485\) | 19.5753 | + | 4.86376i | 0.888869 | + | 0.220852i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − | 38.2245i | − | 1.73212i | −0.499944 | − | 0.866058i | \(-0.666646\pi\) | ||
0.499944 | − | 0.866058i | \(-0.333354\pi\) | |||||||
\(488\) | − | 11.5753i | − | 0.523989i | ||||||
\(489\) | 6.52359 | 0.295007 | ||||||||
\(490\) | −25.6875 | − | 6.38243i | −1.16044 | − | 0.288329i | ||||
\(491\) | 11.3074 | 0.510294 | 0.255147 | − | 0.966902i | \(-0.417876\pi\) | ||||
0.255147 | + | 0.966902i | \(0.417876\pi\) | |||||||
\(492\) | 0.156755i | 0.00706708i | ||||||||
\(493\) | 9.67420i | 0.435704i | ||||||||
\(494\) | 5.47641 | 0.246395 | ||||||||
\(495\) | −0.581449 | + | 2.34017i | −0.0261342 | + | 0.105183i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | − | 65.8720i | − | 2.95476i | ||||||
\(498\) | − | 11.4186i | − | 0.511677i | ||||||
\(499\) | 2.47027 | 0.110584 | 0.0552922 | − | 0.998470i | \(-0.482391\pi\) | ||||
0.0552922 | + | 0.998470i | \(0.482391\pi\) | |||||||
\(500\) | −7.46081 | + | 8.32684i | −0.333658 | + | 0.372388i | ||||
\(501\) | −5.47641 | −0.244668 | ||||||||
\(502\) | − | 27.4329i | − | 1.22439i | ||||||
\(503\) | − | 20.6270i | − | 0.919713i | −0.887993 | − | 0.459857i | \(-0.847901\pi\) | ||
0.887993 | − | 0.459857i | \(-0.152099\pi\) | |||||||
\(504\) | −4.34017 | −0.193327 | ||||||||
\(505\) | −0.810439 | + | 3.26180i | −0.0360641 | + | 0.145148i | ||||
\(506\) | −1.07838 | −0.0479397 | ||||||||
\(507\) | − | 7.52359i | − | 0.334134i | ||||||
\(508\) | 17.1773i | 0.762118i | ||||||||
\(509\) | 32.2245 | 1.42832 | 0.714162 | − | 0.699981i | \(-0.246808\pi\) | ||||
0.714162 | + | 0.699981i | \(0.246808\pi\) | |||||||
\(510\) | −2.00000 | − | 0.496928i | −0.0885615 | − | 0.0220044i | ||||
\(511\) | −20.3135 | −0.898617 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 2.34017i | − | 0.103321i | ||||||
\(514\) | 10.3135 | 0.454909 | ||||||||
\(515\) | 5.41855 | + | 1.34632i | 0.238770 | + | 0.0593258i | ||||
\(516\) | −0.738205 | −0.0324977 | ||||||||
\(517\) | 7.37298i | 0.324263i | ||||||||
\(518\) | 11.2039i | 0.492273i | ||||||||
\(519\) | −15.6742 | −0.688021 | ||||||||
\(520\) | −1.26180 | + | 5.07838i | −0.0553334 | + | 0.222702i | ||||
\(521\) | −3.51745 | −0.154102 | −0.0770511 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770511 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(522\) | − | 10.4969i | − | 0.459438i | ||||||
\(523\) | − | 35.9421i | − | 1.57164i | −0.618455 | − | 0.785820i | \(-0.712241\pi\) | ||
0.618455 | − | 0.785820i | \(-0.287759\pi\) | |||||||
\(524\) | 6.68035 | 0.291832 | ||||||||
\(525\) | 19.1773 | + | 10.1568i | 0.836965 | + | 0.443277i | ||||
\(526\) | −20.9939 | −0.915376 | ||||||||
\(527\) | 3.68649i | 0.160586i | ||||||||
\(528\) | 1.07838i | 0.0469304i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0.183417 | − | 0.738205i | 0.00796715 | − | 0.0320656i | ||||
\(531\) | −8.83710 | −0.383498 | ||||||||
\(532\) | − | 10.1568i | − | 0.440351i | ||||||
\(533\) | − | 0.366835i | − | 0.0158894i | ||||||
\(534\) | −4.68035 | −0.202538 | ||||||||
\(535\) | 20.7792 | + | 5.16290i | 0.898365 | + | 0.223212i | ||||
\(536\) | 2.58145 | 0.111502 | ||||||||
\(537\) | 15.3607i | 0.662863i | ||||||||
\(538\) | 25.3874i | 1.09453i | ||||||||
\(539\) | 12.7649 | 0.549822 | ||||||||
\(540\) | 2.17009 | + | 0.539189i | 0.0933857 | + | 0.0232030i | ||||
\(541\) | 31.7275 | 1.36407 | 0.682036 | − | 0.731318i | \(-0.261095\pi\) | ||||
0.682036 | + | 0.731318i | \(0.261095\pi\) | |||||||
\(542\) | 32.5646i | 1.39877i | ||||||||
\(543\) | − | 21.6163i | − | 0.927646i | ||||||
\(544\) | −0.921622 | −0.0395142 | ||||||||
\(545\) | −5.27617 | + | 21.2351i | −0.226006 | + | 0.909613i | ||||
\(546\) | 10.1568 | 0.434669 | ||||||||
\(547\) | 9.84324i | 0.420867i | 0.977608 | + | 0.210433i | \(0.0674875\pi\) | ||||
−0.977608 | + | 0.210433i | \(0.932512\pi\) | |||||||
\(548\) | 22.2823i | 0.951853i | ||||||||
\(549\) | 11.5753 | 0.494022 | ||||||||
\(550\) | 2.52359 | − | 4.76487i | 0.107606 | − | 0.203175i | ||||
\(551\) | 24.5646 | 1.04649 | ||||||||
\(552\) | 1.00000i | 0.0425628i | ||||||||
\(553\) | − | 51.7152i | − | 2.19916i | ||||||
\(554\) | −15.7009 | −0.667066 | ||||||||
\(555\) | 1.39189 | − | 5.60197i | 0.0590824 | − | 0.237790i | ||||
\(556\) | −10.5236 | −0.446300 | ||||||||
\(557\) | − | 26.3279i | − | 1.11555i | −0.829993 | − | 0.557774i | \(-0.811656\pi\) | ||
0.829993 | − | 0.557774i | \(-0.188344\pi\) | |||||||
\(558\) | − | 4.00000i | − | 0.169334i | ||||||
\(559\) | 1.72753 | 0.0730666 | ||||||||
\(560\) | 9.41855 | + | 2.34017i | 0.398006 | + | 0.0988904i | ||||
\(561\) | 0.993857 | 0.0419607 | ||||||||
\(562\) | 9.36069i | 0.394857i | ||||||||
\(563\) | − | 30.2557i | − | 1.27512i | −0.770399 | − | 0.637562i | \(-0.779943\pi\) | ||
0.770399 | − | 0.637562i | \(-0.220057\pi\) | |||||||
\(564\) | 6.83710 | 0.287894 | ||||||||
\(565\) | −19.3607 | − | 4.81044i | −0.814510 | − | 0.202377i | ||||
\(566\) | −17.4186 | −0.732156 | ||||||||
\(567\) | − | 4.34017i | − | 0.182270i | ||||||
\(568\) | 15.1773i | 0.636824i | ||||||||
\(569\) | −33.8720 | −1.41999 | −0.709994 | − | 0.704208i | \(-0.751302\pi\) | ||||
−0.709994 | + | 0.704208i | \(0.751302\pi\) | |||||||
\(570\) | −1.26180 | + | 5.07838i | −0.0528508 | + | 0.212710i | ||||
\(571\) | 35.1650 | 1.47161 | 0.735804 | − | 0.677194i | \(-0.236804\pi\) | ||||
0.735804 | + | 0.677194i | \(0.236804\pi\) | |||||||
\(572\) | − | 2.52359i | − | 0.105517i | ||||||
\(573\) | − | 4.36683i | − | 0.182427i | ||||||
\(574\) | −0.680346 | −0.0283971 | ||||||||
\(575\) | 2.34017 | − | 4.41855i | 0.0975920 | − | 0.184266i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.00000i | 0.166522i | 0.996528 | + | 0.0832611i | \(0.0265335\pi\) | ||||
−0.996528 | + | 0.0832611i | \(0.973466\pi\) | |||||||
\(578\) | − | 16.1506i | − | 0.671777i | ||||||
\(579\) | −8.68035 | −0.360743 | ||||||||
\(580\) | −5.65983 | + | 22.7792i | −0.235012 | + | 0.945857i | ||||
\(581\) | 49.5585 | 2.05603 | ||||||||
\(582\) | 9.02052i | 0.373913i | ||||||||
\(583\) | 0.366835i | 0.0151928i | ||||||||
\(584\) | 4.68035 | 0.193674 | ||||||||
\(585\) | −5.07838 | − | 1.26180i | −0.209965 | − | 0.0521688i | ||||
\(586\) | −16.3402 | −0.675006 | ||||||||
\(587\) | − | 9.30737i | − | 0.384156i | −0.981380 | − | 0.192078i | \(-0.938477\pi\) | ||
0.981380 | − | 0.192078i | \(-0.0615227\pi\) | |||||||
\(588\) | − | 11.8371i | − | 0.488154i | ||||||
\(589\) | 9.36069 | 0.385701 | ||||||||
\(590\) | 19.1773 | + | 4.76487i | 0.789516 | + | 0.196166i | ||||
\(591\) | 22.6803 | 0.932945 | ||||||||
\(592\) | − | 2.58145i | − | 0.106097i | ||||||
\(593\) | 33.0349i | 1.35658i | 0.734794 | + | 0.678290i | \(0.237279\pi\) | ||||
−0.734794 | + | 0.678290i | \(0.762721\pi\) | |||||||
\(594\) | −1.07838 | −0.0442464 | ||||||||
\(595\) | 2.15676 | − | 8.68035i | 0.0884184 | − | 0.355859i | ||||
\(596\) | 6.92162 | 0.283521 | ||||||||
\(597\) | − | 5.44521i | − | 0.222858i | ||||||
\(598\) | − | 2.34017i | − | 0.0956968i | ||||||
\(599\) | −13.6475 | −0.557623 | −0.278812 | − | 0.960346i | \(-0.589941\pi\) | ||||
−0.278812 | + | 0.960346i | \(0.589941\pi\) | |||||||
\(600\) | −4.41855 | − | 2.34017i | −0.180387 | − | 0.0955372i | ||||
\(601\) | 1.68649 | 0.0687933 | 0.0343967 | − | 0.999408i | \(-0.489049\pi\) | ||||
0.0343967 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(602\) | − | 3.20394i | − | 0.130583i | ||||||
\(603\) | 2.58145i | 0.105125i | ||||||||
\(604\) | −6.15676 | −0.250515 | ||||||||
\(605\) | 5.30406 | − | 21.3474i | 0.215641 | − | 0.867894i | ||||
\(606\) | −1.50307 | −0.0610581 | ||||||||
\(607\) | 47.2183i | 1.91653i | 0.285878 | + | 0.958266i | \(0.407715\pi\) | ||||
−0.285878 | + | 0.958266i | \(0.592285\pi\) | |||||||
\(608\) | 2.34017i | 0.0949065i | ||||||||
\(609\) | 45.5585 | 1.84612 | ||||||||
\(610\) | −25.1194 | − | 6.24128i | −1.01706 | − | 0.252702i | ||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | − | 0.921622i | − | 0.0372544i | ||||||
\(613\) | − | 7.45959i | − | 0.301290i | −0.988588 | − | 0.150645i | \(-0.951865\pi\) | ||
0.988588 | − | 0.150645i | \(-0.0481350\pi\) | |||||||
\(614\) | 3.20394 | 0.129300 | ||||||||
\(615\) | 0.340173 | + | 0.0845208i | 0.0137171 | + | 0.00340821i | ||||
\(616\) | −4.68035 | −0.188577 | ||||||||
\(617\) | − | 15.8120i | − | 0.636569i | −0.947995 | − | 0.318285i | \(-0.896893\pi\) | ||
0.947995 | − | 0.318285i | \(-0.103107\pi\) | |||||||
\(618\) | 2.49693i | 0.100441i | ||||||||
\(619\) | 26.3402 | 1.05870 | 0.529350 | − | 0.848403i | \(-0.322436\pi\) | ||||
0.529350 | + | 0.848403i | \(0.322436\pi\) | |||||||
\(620\) | −2.15676 | + | 8.68035i | −0.0866174 | + | 0.348611i | ||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | − | 12.6537i | − | 0.507367i | ||||||
\(623\) | − | 20.3135i | − | 0.813844i | ||||||
\(624\) | −2.34017 | −0.0936819 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 33.2183 | 1.32767 | ||||||||
\(627\) | − | 2.52359i | − | 0.100782i | ||||||
\(628\) | 2.89496i | 0.115521i | ||||||||
\(629\) | −2.37912 | −0.0948618 | ||||||||
\(630\) | −2.34017 | + | 9.41855i | −0.0932347 | + | 0.375244i | ||||
\(631\) | −14.4391 | −0.574810 | −0.287405 | − | 0.957809i | \(-0.592793\pi\) | ||||
−0.287405 | + | 0.957809i | \(0.592793\pi\) | |||||||
\(632\) | 11.9155i | 0.473972i | ||||||||
\(633\) | 22.0410i | 0.876053i | ||||||||
\(634\) | 6.99386 | 0.277762 | ||||||||
\(635\) | 37.2762 | + | 9.26180i | 1.47926 | + | 0.367543i | ||||
\(636\) | 0.340173 | 0.0134887 | ||||||||
\(637\) | 27.7009i | 1.09755i | ||||||||
\(638\) | − | 11.3197i | − | 0.448149i | ||||||
\(639\) | −15.1773 | −0.600404 | ||||||||
\(640\) | −2.17009 | − | 0.539189i | −0.0857802 | − | 0.0213133i | ||||
\(641\) | −5.78992 | −0.228688 | −0.114344 | − | 0.993441i | \(-0.536477\pi\) | ||||
−0.114344 | + | 0.993441i | \(0.536477\pi\) | |||||||
\(642\) | 9.57531i | 0.377907i | ||||||||
\(643\) | 23.4063i | 0.923053i | 0.887126 | + | 0.461526i | \(0.152698\pi\) | ||||
−0.887126 | + | 0.461526i | \(0.847302\pi\) | |||||||
\(644\) | −4.34017 | −0.171027 | ||||||||
\(645\) | −0.398032 | + | 1.60197i | −0.0156725 | + | 0.0630774i | ||||
\(646\) | 2.15676 | 0.0848564 | ||||||||
\(647\) | − | 25.9877i | − | 1.02168i | −0.859675 | − | 0.510841i | \(-0.829334\pi\) | ||
0.859675 | − | 0.510841i | \(-0.170666\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −9.52973 | −0.374075 | ||||||||
\(650\) | 10.3402 | + | 5.47641i | 0.405575 | + | 0.214802i | ||||
\(651\) | 17.3607 | 0.680419 | ||||||||
\(652\) | − | 6.52359i | − | 0.255484i | ||||||
\(653\) | − | 0.325797i | − | 0.0127494i | −0.999980 | − | 0.00637471i | \(-0.997971\pi\) | ||
0.999980 | − | 0.00637471i | \(-0.00202915\pi\) | |||||||
\(654\) | −9.78539 | −0.382639 | ||||||||
\(655\) | 3.60197 | − | 14.4969i | 0.140741 | − | 0.566442i | ||||
\(656\) | 0.156755 | 0.00612027 | ||||||||
\(657\) | 4.68035i | 0.182598i | ||||||||
\(658\) | 29.6742i | 1.15682i | ||||||||
\(659\) | 3.11942 | 0.121515 | 0.0607576 | − | 0.998153i | \(-0.480648\pi\) | ||||
0.0607576 | + | 0.998153i | \(0.480648\pi\) | |||||||
\(660\) | 2.34017 | + | 0.581449i | 0.0910911 | + | 0.0226329i | ||||
\(661\) | 24.1399 | 0.938935 | 0.469467 | − | 0.882950i | \(-0.344446\pi\) | ||||
0.469467 | + | 0.882950i | \(0.344446\pi\) | |||||||
\(662\) | 29.7275i | 1.15539i | ||||||||
\(663\) | 2.15676i | 0.0837614i | ||||||||
\(664\) | −11.4186 | −0.443126 | ||||||||
\(665\) | −22.0410 | − | 5.47641i | −0.854715 | − | 0.212366i | ||||
\(666\) | 2.58145 | 0.100029 | ||||||||
\(667\) | − | 10.4969i | − | 0.406443i | ||||||
\(668\) | 5.47641i | 0.211889i | ||||||||
\(669\) | 21.1773 | 0.818761 | ||||||||
\(670\) | 1.39189 | − | 5.60197i | 0.0537734 | − | 0.216423i | ||||
\(671\) | 12.4826 | 0.481884 | ||||||||
\(672\) | 4.34017i | 0.167426i | ||||||||
\(673\) | − | 45.6742i | − | 1.76061i | −0.474407 | − | 0.880306i | \(-0.657338\pi\) | ||
0.474407 | − | 0.880306i | \(-0.342662\pi\) | |||||||
\(674\) | −28.3402 | −1.09162 | ||||||||
\(675\) | 2.34017 | − | 4.41855i | 0.0900733 | − | 0.170070i | ||||
\(676\) | −7.52359 | −0.289369 | ||||||||
\(677\) | − | 9.38735i | − | 0.360785i | −0.983595 | − | 0.180393i | \(-0.942263\pi\) | ||
0.983595 | − | 0.180393i | \(-0.0577368\pi\) | |||||||
\(678\) | − | 8.92162i | − | 0.342633i | ||||||
\(679\) | −39.1506 | −1.50246 | ||||||||
\(680\) | −0.496928 | + | 2.00000i | −0.0190563 | + | 0.0766965i | ||||
\(681\) | 11.7854 | 0.451617 | ||||||||
\(682\) | − | 4.31351i | − | 0.165173i | ||||||
\(683\) | 20.9939i | 0.803308i | 0.915792 | + | 0.401654i | \(0.131564\pi\) | ||||
−0.915792 | + | 0.401654i | \(0.868436\pi\) | |||||||
\(684\) | −2.34017 | −0.0894788 | ||||||||
\(685\) | 48.3545 | + | 12.0144i | 1.84753 | + | 0.459046i | ||||
\(686\) | 20.9939 | 0.801549 | ||||||||
\(687\) | 1.78539i | 0.0681167i | ||||||||
\(688\) | 0.738205i | 0.0281438i | ||||||||
\(689\) | −0.796064 | −0.0303276 | ||||||||
\(690\) | 2.17009 | + | 0.539189i | 0.0826138 | + | 0.0205266i | ||||
\(691\) | −44.1445 | −1.67933 | −0.839667 | − | 0.543101i | \(-0.817250\pi\) | ||||
−0.839667 | + | 0.543101i | \(0.817250\pi\) | |||||||
\(692\) | 15.6742i | 0.595844i | ||||||||
\(693\) | − | 4.68035i | − | 0.177792i | ||||||
\(694\) | 22.5236 | 0.854984 | ||||||||
\(695\) | −5.67420 | + | 22.8371i | −0.215235 | + | 0.866261i | ||||
\(696\) | −10.4969 | −0.397885 | ||||||||
\(697\) | − | 0.144469i | − | 0.00547217i | ||||||
\(698\) | 15.6742i | 0.593277i | ||||||||
\(699\) | 18.3135 | 0.692681 | ||||||||
\(700\) | 10.1568 | − | 19.1773i | 0.383889 | − | 0.724833i | ||||
\(701\) | −27.7998 | −1.04998 | −0.524991 | − | 0.851108i | \(-0.675931\pi\) | ||||
−0.524991 | + | 0.851108i | \(0.675931\pi\) | |||||||
\(702\) | − | 2.34017i | − | 0.0883241i | ||||||
\(703\) | 6.04104i | 0.227842i | ||||||||
\(704\) | 1.07838 | 0.0406429 | ||||||||
\(705\) | 3.68649 | − | 14.8371i | 0.138841 | − | 0.558798i | ||||
\(706\) | 26.3135 | 0.990322 | ||||||||
\(707\) | − | 6.52359i | − | 0.245345i | ||||||
\(708\) | 8.83710i | 0.332119i | ||||||||
\(709\) | −4.30898 | −0.161827 | −0.0809135 | − | 0.996721i | \(-0.525784\pi\) | ||||
−0.0809135 | + | 0.996721i | \(0.525784\pi\) | |||||||
\(710\) | 32.9360 | + | 8.18342i | 1.23607 | + | 0.307118i | ||||
\(711\) | −11.9155 | −0.446865 | ||||||||
\(712\) | 4.68035i | 0.175403i | ||||||||
\(713\) | − | 4.00000i | − | 0.149801i | ||||||
\(714\) | 4.00000 | 0.149696 | ||||||||
\(715\) | −5.47641 | − | 1.36069i | −0.204806 | − | 0.0508870i | ||||
\(716\) | 15.3607 | 0.574056 | ||||||||
\(717\) | − | 5.33403i | − | 0.199203i | ||||||
\(718\) | − | 0.796064i | − | 0.0297088i | ||||||
\(719\) | −15.9733 | −0.595705 | −0.297852 | − | 0.954612i | \(-0.596270\pi\) | ||||
−0.297852 | + | 0.954612i | \(0.596270\pi\) | |||||||
\(720\) | 0.539189 | − | 2.17009i | 0.0200944 | − | 0.0808743i | ||||
\(721\) | −10.8371 | −0.403595 | ||||||||
\(722\) | 13.5236i | 0.503296i | ||||||||
\(723\) | − | 26.1978i | − | 0.974306i | ||||||
\(724\) | −21.6163 | −0.803365 | ||||||||
\(725\) | 46.3812 | + | 24.5646i | 1.72255 | + | 0.912307i | ||||
\(726\) | 9.83710 | 0.365089 | ||||||||
\(727\) | 0.340173i | 0.0126163i | 0.999980 | + | 0.00630816i | \(0.00200796\pi\) | ||||
−0.999980 | + | 0.00630816i | \(0.997992\pi\) | |||||||
\(728\) | − | 10.1568i | − | 0.376434i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 2.52359 | − | 10.1568i | 0.0934023 | − | 0.375918i | ||||
\(731\) | 0.680346 | 0.0251635 | ||||||||
\(732\) | − | 11.5753i | − | 0.427836i | ||||||
\(733\) | − | 19.2618i | − | 0.711451i | −0.934591 | − | 0.355725i | \(-0.884234\pi\) | ||
0.934591 | − | 0.355725i | \(-0.115766\pi\) | |||||||
\(734\) | −13.7009 | −0.505708 | ||||||||
\(735\) | −25.6875 | − | 6.38243i | −0.947499 | − | 0.235420i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 2.78378i | 0.102542i | ||||||||
\(738\) | 0.156755i | 0.00577025i | ||||||||
\(739\) | −25.5585 | −0.940184 | −0.470092 | − | 0.882617i | \(-0.655779\pi\) | ||||
−0.470092 | + | 0.882617i | \(0.655779\pi\) | |||||||
\(740\) | −5.60197 | − | 1.39189i | −0.205932 | − | 0.0511668i | ||||
\(741\) | 5.47641 | 0.201181 | ||||||||
\(742\) | 1.47641i | 0.0542007i | ||||||||
\(743\) | − | 36.8781i | − | 1.35293i | −0.736476 | − | 0.676464i | \(-0.763511\pi\) | ||
0.736476 | − | 0.676464i | \(-0.236489\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 3.73206 | − | 15.0205i | 0.136732 | − | 0.550309i | ||||
\(746\) | 4.25565 | 0.155810 | ||||||||
\(747\) | − | 11.4186i | − | 0.417783i | ||||||
\(748\) | − | 0.993857i | − | 0.0363390i | ||||||
\(749\) | −41.5585 | −1.51851 | ||||||||
\(750\) | −7.46081 | + | 8.32684i | −0.272430 | + | 0.304053i | ||||
\(751\) | 18.1256 | 0.661411 | 0.330706 | − | 0.943734i | \(-0.392713\pi\) | ||||
0.330706 | + | 0.943734i | \(0.392713\pi\) | |||||||
\(752\) | − | 6.83710i | − | 0.249323i | ||||||
\(753\) | − | 27.4329i | − | 0.999711i | ||||||
\(754\) | 24.5646 | 0.894591 | ||||||||
\(755\) | −3.31965 | + | 13.3607i | −0.120815 | + | 0.486245i | ||||
\(756\) | −4.34017 | −0.157851 | ||||||||
\(757\) | 17.4186i | 0.633088i | 0.948578 | + | 0.316544i | \(0.102522\pi\) | ||||
−0.948578 | + | 0.316544i | \(0.897478\pi\) | |||||||
\(758\) | − | 30.6537i | − | 1.11339i | ||||||
\(759\) | −1.07838 | −0.0391426 | ||||||||
\(760\) | 5.07838 | + | 1.26180i | 0.184212 | + | 0.0457701i | ||||
\(761\) | −23.4140 | −0.848757 | −0.424379 | − | 0.905485i | \(-0.639507\pi\) | ||||
−0.424379 | + | 0.905485i | \(0.639507\pi\) | |||||||
\(762\) | 17.1773i | 0.622267i | ||||||||
\(763\) | − | 42.4703i | − | 1.53753i | ||||||
\(764\) | −4.36683 | −0.157987 | ||||||||
\(765\) | −2.00000 | − | 0.496928i | −0.0723102 | − | 0.0179665i | ||||
\(766\) | −20.8781 | −0.754358 | ||||||||
\(767\) | − | 20.6803i | − | 0.746724i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 29.7152 | 1.07156 | 0.535779 | − | 0.844358i | \(-0.320018\pi\) | ||||
0.535779 | + | 0.844358i | \(0.320018\pi\) | |||||||
\(770\) | −2.52359 | + | 10.1568i | −0.0909439 | + | 0.366024i | ||||
\(771\) | 10.3135 | 0.371432 | ||||||||
\(772\) | 8.68035i | 0.312412i | ||||||||
\(773\) | 15.3463i | 0.551969i | 0.961162 | + | 0.275984i | \(0.0890038\pi\) | ||||
−0.961162 | + | 0.275984i | \(0.910996\pi\) | |||||||
\(774\) | −0.738205 | −0.0265342 | ||||||||
\(775\) | 17.6742 | + | 9.36069i | 0.634876 | + | 0.336246i | ||||
\(776\) | 9.02052 | 0.323818 | ||||||||
\(777\) | 11.2039i | 0.401939i | ||||||||
\(778\) | − | 16.9627i | − | 0.608141i | ||||||
\(779\) | −0.366835 | −0.0131432 | ||||||||
\(780\) | −1.26180 | + | 5.07838i | −0.0451795 | + | 0.181835i | ||||
\(781\) | −16.3668 | −0.585651 | ||||||||
\(782\) | − | 0.921622i | − | 0.0329571i | ||||||
\(783\) | − | 10.4969i | − | 0.375130i | ||||||
\(784\) | −11.8371 | −0.422754 | ||||||||
\(785\) | 6.28231 | + | 1.56093i | 0.224225 | + | 0.0557120i | ||||
\(786\) | 6.68035 | 0.238280 | ||||||||
\(787\) | 22.8950i | 0.816117i | 0.912956 | + | 0.408059i | \(0.133794\pi\) | ||||
−0.912956 | + | 0.408059i | \(0.866206\pi\) | |||||||
\(788\) | − | 22.6803i | − | 0.807954i | ||||||
\(789\) | −20.9939 | −0.747401 | ||||||||
\(790\) | 25.8576 | + | 6.42469i | 0.919973 | + | 0.228580i | ||||
\(791\) | 38.7214 | 1.37677 | ||||||||
\(792\) | 1.07838i | 0.0383185i | ||||||||
\(793\) | 27.0882i | 0.961931i | ||||||||
\(794\) | 16.4969 | 0.585454 | ||||||||
\(795\) | 0.183417 | − | 0.738205i | 0.00650515 | − | 0.0261814i | ||||
\(796\) | −5.44521 | −0.193000 | ||||||||
\(797\) | 7.60650i | 0.269436i | 0.990884 | + | 0.134718i | \(0.0430129\pi\) | ||||
−0.990884 | + | 0.134718i | \(0.956987\pi\) | |||||||
\(798\) | − | 10.1568i | − | 0.359545i | ||||||
\(799\) | −6.30122 | −0.222921 | ||||||||
\(800\) | −2.34017 | + | 4.41855i | −0.0827376 | + | 0.156219i | ||||
\(801\) | −4.68035 | −0.165372 | ||||||||
\(802\) | 35.2039i | 1.24309i | ||||||||
\(803\) | 5.04718i | 0.178111i | ||||||||
\(804\) | 2.58145 | 0.0910407 | ||||||||
\(805\) | −2.34017 | + | 9.41855i | −0.0824803 | + | 0.331960i | ||||
\(806\) | 9.36069 | 0.329716 | ||||||||
\(807\) | 25.3874i | 0.893677i | ||||||||
\(808\) | 1.50307i | 0.0528779i | ||||||||
\(809\) | −43.7275 | −1.53738 | −0.768689 | − | 0.639623i | \(-0.779091\pi\) | ||||
−0.768689 | + | 0.639623i | \(0.779091\pi\) | |||||||
\(810\) | 2.17009 | + | 0.539189i | 0.0762491 | + | 0.0189452i | ||||
\(811\) | −4.79606 | −0.168413 | −0.0842063 | − | 0.996448i | \(-0.526835\pi\) | ||||
−0.0842063 | + | 0.996448i | \(0.526835\pi\) | |||||||
\(812\) | − | 45.5585i | − | 1.59879i | ||||||
\(813\) | 32.5646i | 1.14209i | ||||||||
\(814\) | 2.78378 | 0.0975713 | ||||||||
\(815\) | −14.1568 | − | 3.51745i | −0.495890 | − | 0.123211i | ||||
\(816\) | −0.921622 | −0.0322632 | ||||||||
\(817\) | − | 1.72753i | − | 0.0604385i | ||||||
\(818\) | 11.3607i | 0.397217i | ||||||||
\(819\) | 10.1568 | 0.354906 | ||||||||
\(820\) | 0.0845208 | − | 0.340173i | 0.00295159 | − | 0.0118794i | ||||
\(821\) | −12.2245 | −0.426636 | −0.213318 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213318 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(822\) | 22.2823i | 0.777185i | ||||||||
\(823\) | − | 37.5441i | − | 1.30871i | −0.756189 | − | 0.654353i | \(-0.772941\pi\) | ||
0.756189 | − | 0.654353i | \(-0.227059\pi\) | |||||||
\(824\) | 2.49693 | 0.0869846 | ||||||||
\(825\) | 2.52359 | − | 4.76487i | 0.0878601 | − | 0.165891i | ||||
\(826\) | −38.3545 | −1.33453 | ||||||||
\(827\) | 38.3090i | 1.33213i | 0.745892 | + | 0.666067i | \(0.232023\pi\) | ||||
−0.745892 | + | 0.666067i | \(0.767977\pi\) | |||||||
\(828\) | 1.00000i | 0.0347524i | ||||||||
\(829\) | 31.4140 | 1.09105 | 0.545527 | − | 0.838093i | \(-0.316330\pi\) | ||||
0.545527 | + | 0.838093i | \(0.316330\pi\) | |||||||
\(830\) | −6.15676 | + | 24.7792i | −0.213704 | + | 0.860100i | ||||
\(831\) | −15.7009 | −0.544657 | ||||||||
\(832\) | 2.34017i | 0.0811309i | ||||||||
\(833\) | 10.9093i | 0.377986i | ||||||||
\(834\) | −10.5236 | −0.364402 | ||||||||
\(835\) | 11.8843 | + | 2.95282i | 0.411273 | + | 0.102187i | ||||
\(836\) | −2.52359 | −0.0872802 | ||||||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | − | 18.1256i | − | 0.626137i | ||||||
\(839\) | −23.1506 | −0.799248 | −0.399624 | − | 0.916679i | \(-0.630859\pi\) | ||||
−0.399624 | + | 0.916679i | \(0.630859\pi\) | |||||||
\(840\) | 9.41855 | + | 2.34017i | 0.324971 | + | 0.0807436i | ||||
\(841\) | 81.1855 | 2.79950 | ||||||||
\(842\) | − | 2.58145i | − | 0.0889626i | ||||||
\(843\) | 9.36069i | 0.322399i | ||||||||
\(844\) | 22.0410 | 0.758684 | ||||||||
\(845\) | −4.05664 | + | 16.3268i | −0.139553 | + | 0.561660i | ||||
\(846\) | 6.83710 | 0.235064 | ||||||||
\(847\) | 42.6947i | 1.46701i | ||||||||
\(848\) | − | 0.340173i | − | 0.0116816i | ||||||
\(849\) | −17.4186 | −0.597803 | ||||||||
\(850\) | 4.07223 | + | 2.15676i | 0.139676 | + | 0.0739761i | ||||
\(851\) | 2.58145 | 0.0884909 | ||||||||
\(852\) | 15.1773i | 0.519965i | ||||||||
\(853\) | − | 32.4969i | − | 1.11267i | −0.830957 | − | 0.556337i | \(-0.812206\pi\) | ||
0.830957 | − | 0.556337i | \(-0.187794\pi\) | |||||||
\(854\) | 50.2388 | 1.71914 | ||||||||
\(855\) | −1.26180 | + | 5.07838i | −0.0431525 | + | 0.173677i | ||||
\(856\) | 9.57531 | 0.327277 | ||||||||
\(857\) | − | 37.8310i | − | 1.29228i | −0.763219 | − | 0.646140i | \(-0.776382\pi\) | ||
0.763219 | − | 0.646140i | \(-0.223618\pi\) | |||||||
\(858\) | − | 2.52359i | − | 0.0861540i | ||||||
\(859\) | 28.1978 | 0.962096 | 0.481048 | − | 0.876694i | \(-0.340256\pi\) | ||||
0.481048 | + | 0.876694i | \(0.340256\pi\) | |||||||
\(860\) | 1.60197 | + | 0.398032i | 0.0546267 | + | 0.0135728i | ||||
\(861\) | −0.680346 | −0.0231861 | ||||||||
\(862\) | 33.9877i | 1.15763i | ||||||||
\(863\) | 32.0288i | 1.09027i | 0.838348 | + | 0.545136i | \(0.183522\pi\) | ||||
−0.838348 | + | 0.545136i | \(0.816478\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 34.0144 | + | 8.45136i | 1.15652 | + | 0.287355i | ||||
\(866\) | −8.28685 | −0.281599 | ||||||||
\(867\) | − | 16.1506i | − | 0.548504i | ||||||
\(868\) | − | 17.3607i | − | 0.589260i | ||||||
\(869\) | −12.8494 | −0.435886 | ||||||||
\(870\) | −5.65983 | + | 22.7792i | −0.191886 | + | 0.772289i | ||||
\(871\) | −6.04104 | −0.204693 | ||||||||
\(872\) | 9.78539i | 0.331375i | ||||||||
\(873\) | 9.02052i | 0.305298i | ||||||||
\(874\) | −2.34017 | −0.0791575 | ||||||||
\(875\) | −36.1399 | − | 32.3812i | −1.22175 | − | 1.09468i | ||||
\(876\) | 4.68035 | 0.158134 | ||||||||
\(877\) | − | 27.7009i | − | 0.935392i | −0.883889 | − | 0.467696i | \(-0.845084\pi\) | ||
0.883889 | − | 0.467696i | \(-0.154916\pi\) | |||||||
\(878\) | − | 28.9939i | − | 0.978495i | ||||||
\(879\) | −16.3402 | −0.551140 | ||||||||
\(880\) | 0.581449 | − | 2.34017i | 0.0196007 | − | 0.0788872i | ||||
\(881\) | 12.3135 | 0.414853 | 0.207426 | − | 0.978251i | \(-0.433491\pi\) | ||||
0.207426 | + | 0.978251i | \(0.433491\pi\) | |||||||
\(882\) | − | 11.8371i | − | 0.398576i | ||||||
\(883\) | 7.15061i | 0.240637i | 0.992735 | + | 0.120319i | \(0.0383916\pi\) | ||||
−0.992735 | + | 0.120319i | \(0.961608\pi\) | |||||||
\(884\) | 2.15676 | 0.0725395 | ||||||||
\(885\) | 19.1773 | + | 4.76487i | 0.644637 | + | 0.160169i | ||||
\(886\) | −3.20394 | −0.107638 | ||||||||
\(887\) | − | 9.19165i | − | 0.308625i | −0.988022 | − | 0.154313i | \(-0.950684\pi\) | ||
0.988022 | − | 0.154313i | \(-0.0493163\pi\) | |||||||
\(888\) | − | 2.58145i | − | 0.0866278i | ||||||
\(889\) | −74.5523 | −2.50041 | ||||||||
\(890\) | 10.1568 | + | 2.52359i | 0.340455 | + | 0.0845909i | ||||
\(891\) | −1.07838 | −0.0361270 | ||||||||
\(892\) | − | 21.1773i | − | 0.709068i | ||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | 6.92162 | 0.231494 | ||||||||
\(895\) | 8.28231 | − | 33.3340i | 0.276847 | − | 1.11423i | ||||
\(896\) | 4.34017 | 0.144995 | ||||||||
\(897\) | − | 2.34017i | − | 0.0781361i | ||||||
\(898\) | 28.1568i | 0.939603i | ||||||||
\(899\) | 41.9877 | 1.40037 | ||||||||
\(900\) | −4.41855 | − | 2.34017i | −0.147285 | − | 0.0780058i | ||||
\(901\) | −0.313511 | −0.0104446 | ||||||||
\(902\) | 0.169042i | 0.00562847i | ||||||||
\(903\) | − | 3.20394i | − | 0.106620i | ||||||
\(904\) | −8.92162 | −0.296729 | ||||||||
\(905\) | −11.6553 | + | 46.9093i | −0.387435 | + | 1.55932i | ||||
\(906\) | −6.15676 | −0.204545 | ||||||||
\(907\) | 14.0989i | 0.468146i | 0.972219 | + | 0.234073i | \(0.0752055\pi\) | ||||
−0.972219 | + | 0.234073i | \(0.924794\pi\) | |||||||
\(908\) | − | 11.7854i | − | 0.391112i | ||||||
\(909\) | −1.50307 | −0.0498537 | ||||||||
\(910\) | −22.0410 | − | 5.47641i | −0.730653 | − | 0.181541i | ||||
\(911\) | −20.9939 | −0.695558 | −0.347779 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347779 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(912\) | 2.34017i | 0.0774909i | ||||||||
\(913\) | − | 12.3135i | − | 0.407518i | ||||||
\(914\) | 23.1773 | 0.766636 | ||||||||
\(915\) | −25.1194 | − | 6.24128i | −0.830422 | − | 0.206330i | ||||
\(916\) | 1.78539 | 0.0589908 | ||||||||
\(917\) | 28.9939i | 0.957462i | ||||||||
\(918\) | − | 0.921622i | − | 0.0304181i | ||||||
\(919\) | 1.92777 | 0.0635911 | 0.0317956 | − | 0.999494i | \(-0.489877\pi\) | ||||
0.0317956 | + | 0.999494i | \(0.489877\pi\) | |||||||
\(920\) | 0.539189 | − | 2.17009i | 0.0177765 | − | 0.0715456i | ||||
\(921\) | 3.20394 | 0.105573 | ||||||||
\(922\) | 42.3279i | 1.39399i | ||||||||
\(923\) | − | 35.5174i | − | 1.16907i | ||||||
\(924\) | −4.68035 | −0.153972 | ||||||||
\(925\) | −6.04104 | + | 11.4063i | −0.198628 | + | 0.375036i | ||||
\(926\) | −34.9048 | −1.14704 | ||||||||
\(927\) | 2.49693i | 0.0820099i | ||||||||
\(928\) | 10.4969i | 0.344579i | ||||||||
\(929\) | −18.5646 | −0.609086 | −0.304543 | − | 0.952499i | \(-0.598504\pi\) | ||||
−0.304543 | + | 0.952499i | \(0.598504\pi\) | |||||||
\(930\) | −2.15676 | + | 8.68035i | −0.0707228 | + | 0.284640i | ||||
\(931\) | 27.7009 | 0.907859 | ||||||||
\(932\) | − | 18.3135i | − | 0.599879i | ||||||
\(933\) | − | 12.6537i | − | 0.414263i | ||||||
\(934\) | 37.7731 | 1.23597 | ||||||||
\(935\) | −2.15676 | − | 0.535877i | −0.0705334 | − | 0.0175250i | ||||
\(936\) | −2.34017 | −0.0764909 | ||||||||
\(937\) | − | 22.3279i | − | 0.729420i | −0.931121 | − | 0.364710i | \(-0.881168\pi\) | ||
0.931121 | − | 0.364710i | \(-0.118832\pi\) | |||||||
\(938\) | 11.2039i | 0.365821i | ||||||||
\(939\) | 33.2183 | 1.08404 | ||||||||
\(940\) | −14.8371 | − | 3.68649i | −0.483933 | − | 0.120240i | ||||
\(941\) | −11.0661 | −0.360744 | −0.180372 | − | 0.983598i | \(-0.557730\pi\) | ||||
−0.180372 | + | 0.983598i | \(0.557730\pi\) | |||||||
\(942\) | 2.89496i | 0.0943229i | ||||||||
\(943\) | 0.156755i | 0.00510466i | ||||||||
\(944\) | 8.83710 | 0.287623 | ||||||||
\(945\) | −2.34017 | + | 9.41855i | −0.0761258 | + | 0.306385i | ||||
\(946\) | −0.796064 | −0.0258823 | ||||||||
\(947\) | − | 8.05332i | − | 0.261698i | −0.991402 | − | 0.130849i | \(-0.958230\pi\) | ||
0.991402 | − | 0.130849i | \(-0.0417703\pi\) | |||||||
\(948\) | 11.9155i | 0.386997i | ||||||||
\(949\) | −10.9528 | −0.355544 | ||||||||
\(950\) | 5.47641 | − | 10.3402i | 0.177678 | − | 0.335480i | ||||
\(951\) | 6.99386 | 0.226791 | ||||||||
\(952\) | − | 4.00000i | − | 0.129641i | ||||||
\(953\) | 39.5897i | 1.28244i | 0.767359 | + | 0.641218i | \(0.221570\pi\) | ||||
−0.767359 | + | 0.641218i | \(0.778430\pi\) | |||||||
\(954\) | 0.340173 | 0.0110135 | ||||||||
\(955\) | −2.35455 | + | 9.47641i | −0.0761914 | + | 0.306649i | ||||
\(956\) | −5.33403 | −0.172515 | ||||||||
\(957\) | − | 11.3197i | − | 0.365912i | ||||||
\(958\) | − | 28.1978i | − | 0.911029i | ||||||
\(959\) | −96.7091 | −3.12290 | ||||||||
\(960\) | −2.17009 | − | 0.539189i | −0.0700392 | − | 0.0174022i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 6.04104i | 0.194771i | ||||||||
\(963\) | 9.57531i | 0.308560i | ||||||||
\(964\) | −26.1978 | −0.843774 | ||||||||
\(965\) | 18.8371 | + | 4.68035i | 0.606388 | + | 0.150666i | ||||
\(966\) | −4.34017 | −0.139643 | ||||||||
\(967\) | − | 48.2655i | − | 1.55211i | −0.630663 | − | 0.776057i | \(-0.717217\pi\) | ||
0.630663 | − | 0.776057i | \(-0.282783\pi\) | |||||||
\(968\) | − | 9.83710i | − | 0.316176i | ||||||
\(969\) | 2.15676 | 0.0692850 | ||||||||
\(970\) | 4.86376 | − | 19.5753i | 0.156166 | − | 0.628525i | ||||
\(971\) | 18.0722 | 0.579966 | 0.289983 | − | 0.957032i | \(-0.406350\pi\) | ||||
0.289983 | + | 0.957032i | \(0.406350\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 45.6742i | − | 1.46425i | ||||||
\(974\) | −38.2245 | −1.22479 | ||||||||
\(975\) | 10.3402 | + | 5.47641i | 0.331151 | + | 0.175385i | ||||
\(976\) | −11.5753 | −0.370517 | ||||||||
\(977\) | 45.9442i | 1.46989i | 0.678129 | + | 0.734943i | \(0.262791\pi\) | ||||
−0.678129 | + | 0.734943i | \(0.737209\pi\) | |||||||
\(978\) | − | 6.52359i | − | 0.208601i | ||||||
\(979\) | −5.04718 | −0.161309 | ||||||||
\(980\) | −6.38243 | + | 25.6875i | −0.203879 | + | 0.820558i | ||||
\(981\) | −9.78539 | −0.312423 | ||||||||
\(982\) | − | 11.3074i | − | 0.360833i | ||||||
\(983\) | 1.78992i | 0.0570896i | 0.999593 | + | 0.0285448i | \(0.00908733\pi\) | ||||
−0.999593 | + | 0.0285448i | \(0.990913\pi\) | |||||||
\(984\) | 0.156755 | 0.00499718 | ||||||||
\(985\) | −49.2183 | − | 12.2290i | −1.56823 | − | 0.389648i | ||||
\(986\) | 9.67420 | 0.308089 | ||||||||
\(987\) | 29.6742i | 0.944540i | ||||||||
\(988\) | − | 5.47641i | − | 0.174228i | ||||||
\(989\) | −0.738205 | −0.0234735 | ||||||||
\(990\) | 2.34017 | + | 0.581449i | 0.0743756 | + | 0.0184797i | ||||
\(991\) | 7.68649 | 0.244169 | 0.122085 | − | 0.992520i | \(-0.461042\pi\) | ||||
0.122085 | + | 0.992520i | \(0.461042\pi\) | |||||||
\(992\) | 4.00000i | 0.127000i | ||||||||
\(993\) | 29.7275i | 0.943375i | ||||||||
\(994\) | −65.8720 | −2.08933 | ||||||||
\(995\) | −2.93600 | + | 11.8166i | −0.0930774 | + | 0.374611i | ||||
\(996\) | −11.4186 | −0.361811 | ||||||||
\(997\) | 21.4908i | 0.680620i | 0.940313 | + | 0.340310i | \(0.110532\pi\) | ||||
−0.940313 | + | 0.340310i | \(0.889468\pi\) | |||||||
\(998\) | − | 2.47027i | − | 0.0781949i | ||||||
\(999\) | 2.58145 | 0.0816734 |
(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 | 690.2.d.c.139.2 | ✓ | 6 | |
3.2 | odd | 2 | 2070.2.d.e.829.5 | 6 | |||
5.2 | odd | 4 | 3450.2.a.bt.1.3 | 3 | |||
5.3 | odd | 4 | 3450.2.a.bo.1.1 | 3 | |||
5.4 | even | 2 | inner | 690.2.d.c.139.5 | yes | 6 | |
15.14 | odd | 2 | 2070.2.d.e.829.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.c.139.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
690.2.d.c.139.5 | yes | 6 | 5.4 | even | 2 | inner | |
2070.2.d.e.829.2 | 6 | 15.14 | odd | 2 | |||
2070.2.d.e.829.5 | 6 | 3.2 | odd | 2 | |||
3450.2.a.bo.1.1 | 3 | 5.3 | odd | 4 | |||
3450.2.a.bt.1.3 | 3 | 5.2 | odd | 4 |