Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.5 | ||
Root | \(1.50426 + 2.60546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.508 |
Dual form | 637.2.e.m.79.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00426 | + | 1.73943i | 0.710121 | + | 1.22997i | 0.964812 | + | 0.262942i | \(0.0846930\pi\) |
−0.254691 | + | 0.967023i | \(0.581974\pi\) | |||||||
\(3\) | 0.879528 | − | 1.52339i | 0.507796 | − | 0.879528i | −0.492164 | − | 0.870503i | \(-0.663794\pi\) |
0.999959 | − | 0.00902528i | \(-0.00287288\pi\) | |||||||
\(4\) | −1.01709 | + | 1.76164i | −0.508543 | + | 0.880822i | ||||
\(5\) | 0.452861 | + | 0.784378i | 0.202526 | + | 0.350784i | 0.949342 | − | 0.314246i | \(-0.101752\pi\) |
−0.746816 | + | 0.665031i | \(0.768418\pi\) | |||||||
\(6\) | 3.53311 | 1.44238 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.0686323 | −0.0242652 | ||||||||
\(9\) | −0.0471392 | − | 0.0816475i | −0.0157131 | − | 0.0272158i | ||||
\(10\) | −0.909582 | + | 1.57544i | −0.287635 | + | 0.498199i | ||||
\(11\) | −0.358181 | + | 0.620387i | −0.107996 | + | 0.187054i | −0.914958 | − | 0.403549i | \(-0.867777\pi\) |
0.806963 | + | 0.590603i | \(0.201110\pi\) | |||||||
\(12\) | 1.78911 | + | 3.09883i | 0.516472 | + | 0.894555i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.59322 | 0.411366 | ||||||||
\(16\) | 1.96525 | + | 3.40391i | 0.491311 | + | 0.850976i | ||||
\(17\) | 1.17614 | − | 2.03713i | 0.285255 | − | 0.494076i | −0.687416 | − | 0.726264i | \(-0.741255\pi\) |
0.972671 | + | 0.232188i | \(0.0745885\pi\) | |||||||
\(18\) | 0.0946802 | − | 0.163991i | 0.0223163 | − | 0.0386530i | ||||
\(19\) | 3.31796 | + | 5.74687i | 0.761191 | + | 1.31842i | 0.942237 | + | 0.334947i | \(0.108718\pi\) |
−0.181046 | + | 0.983475i | \(0.557948\pi\) | |||||||
\(20\) | −1.84239 | −0.411971 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.43883 | −0.306759 | ||||||||
\(23\) | −1.87953 | − | 3.25544i | −0.391909 | − | 0.678806i | 0.600793 | − | 0.799405i | \(-0.294852\pi\) |
−0.992701 | + | 0.120599i | \(0.961518\pi\) | |||||||
\(24\) | −0.0603641 | + | 0.104554i | −0.0123218 | + | 0.0213419i | ||||
\(25\) | 2.08983 | − | 3.61970i | 0.417967 | − | 0.723940i | ||||
\(26\) | −1.00426 | − | 1.73943i | −0.196952 | − | 0.341131i | ||||
\(27\) | 5.11133 | 0.983675 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.25799 | 0.604994 | 0.302497 | − | 0.953150i | \(-0.402180\pi\) | ||||
0.302497 | + | 0.953150i | \(0.402180\pi\) | |||||||
\(30\) | 1.60001 | + | 2.77129i | 0.292120 | + | 0.505966i | ||||
\(31\) | 0.785250 | − | 1.36009i | 0.141035 | − | 0.244280i | −0.786852 | − | 0.617142i | \(-0.788290\pi\) |
0.927887 | + | 0.372862i | \(0.121624\pi\) | |||||||
\(32\) | −4.01588 | + | 6.95570i | −0.709913 | + | 1.22961i | ||||
\(33\) | 0.630060 | + | 1.09130i | 0.109679 | + | 0.189970i | ||||
\(34\) | 4.72459 | 0.810261 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.191778 | 0.0319631 | ||||||||
\(37\) | −2.60441 | − | 4.51098i | −0.428163 | − | 0.741600i | 0.568547 | − | 0.822651i | \(-0.307506\pi\) |
−0.996710 | + | 0.0810508i | \(0.974172\pi\) | |||||||
\(38\) | −6.66419 | + | 11.5427i | −1.08108 | + | 1.87248i | ||||
\(39\) | −0.879528 | + | 1.52339i | −0.140837 | + | 0.243937i | ||||
\(40\) | −0.0310809 | − | 0.0538337i | −0.00491432 | − | 0.00851185i | ||||
\(41\) | −4.92168 | −0.768637 | −0.384318 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384318 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.43766 | −1.43923 | −0.719615 | − | 0.694373i | \(-0.755682\pi\) | ||||
−0.719615 | + | 0.694373i | \(0.755682\pi\) | |||||||
\(44\) | −0.728600 | − | 1.26197i | −0.109841 | − | 0.190250i | ||||
\(45\) | 0.0426950 | − | 0.0739499i | 0.00636459 | − | 0.0110238i | ||||
\(46\) | 3.77508 | − | 6.53863i | 0.556605 | − | 0.964068i | ||||
\(47\) | −4.15993 | − | 7.20521i | −0.606788 | − | 1.05099i | −0.991766 | − | 0.128062i | \(-0.959124\pi\) |
0.384978 | − | 0.922926i | \(-0.374209\pi\) | |||||||
\(48\) | 6.91395 | 0.997943 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.39497 | 1.18723 | ||||||||
\(51\) | −2.06889 | − | 3.58342i | −0.289702 | − | 0.501779i | ||||
\(52\) | 1.01709 | − | 1.76164i | 0.141044 | − | 0.244296i | ||||
\(53\) | −7.04163 | + | 12.1965i | −0.967243 | + | 1.67531i | −0.263777 | + | 0.964584i | \(0.584968\pi\) |
−0.703465 | + | 0.710729i | \(0.748365\pi\) | |||||||
\(54\) | 5.13311 | + | 8.89081i | 0.698528 | + | 1.20989i | ||||
\(55\) | −0.648824 | −0.0874874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.6729 | 1.54612 | ||||||||
\(58\) | 3.27188 | + | 5.66706i | 0.429619 | + | 0.744122i | ||||
\(59\) | 0.358181 | − | 0.620387i | 0.0466311 | − | 0.0807675i | −0.841768 | − | 0.539840i | \(-0.818485\pi\) |
0.888399 | + | 0.459072i | \(0.151818\pi\) | |||||||
\(60\) | −1.62044 | + | 2.80668i | −0.209197 | + | 0.362340i | ||||
\(61\) | −5.82633 | − | 10.0915i | −0.745986 | − | 1.29208i | −0.949733 | − | 0.313061i | \(-0.898645\pi\) |
0.203747 | − | 0.979024i | \(-0.434688\pi\) | |||||||
\(62\) | 3.15439 | 0.400607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.27099 | −1.03387 | ||||||||
\(65\) | −0.452861 | − | 0.784378i | −0.0561705 | − | 0.0972901i | ||||
\(66\) | −1.26549 | + | 2.19189i | −0.155771 | + | 0.269803i | ||||
\(67\) | −4.69587 | + | 8.13349i | −0.573692 | + | 0.993664i | 0.422490 | + | 0.906367i | \(0.361156\pi\) |
−0.996182 | + | 0.0872964i | \(0.972177\pi\) | |||||||
\(68\) | 2.39246 | + | 4.14386i | 0.290128 | + | 0.502517i | ||||
\(69\) | −6.61239 | −0.796038 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9914 | 1.30444 | 0.652220 | − | 0.758030i | \(-0.273838\pi\) | ||||
0.652220 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(72\) | 0.00323527 | + | 0.00560366i | 0.000381281 | + | 0.000660397i | ||||
\(73\) | −1.73650 | + | 3.00771i | −0.203242 | + | 0.352025i | −0.949571 | − | 0.313552i | \(-0.898481\pi\) |
0.746329 | + | 0.665577i | \(0.231814\pi\) | |||||||
\(74\) | 5.23103 | − | 9.06041i | 0.608095 | − | 1.05325i | ||||
\(75\) | −3.67614 | − | 6.36725i | −0.424484 | − | 0.735227i | ||||
\(76\) | −13.4986 | −1.54839 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.53311 | −0.400046 | ||||||||
\(79\) | −6.50408 | − | 11.2654i | −0.731766 | − | 1.26746i | −0.956128 | − | 0.292950i | \(-0.905363\pi\) |
0.224361 | − | 0.974506i | \(-0.427970\pi\) | |||||||
\(80\) | −1.77997 | + | 3.08299i | −0.199006 | + | 0.344689i | ||||
\(81\) | 4.63697 | − | 8.03147i | 0.515219 | − | 0.892386i | ||||
\(82\) | −4.94265 | − | 8.56093i | −0.545825 | − | 0.945396i | ||||
\(83\) | −3.54083 | −0.388656 | −0.194328 | − | 0.980937i | \(-0.562253\pi\) | ||||
−0.194328 | + | 0.980937i | \(0.562253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.13050 | 0.231085 | ||||||||
\(86\) | −9.47789 | − | 16.4162i | −1.02203 | − | 1.77020i | ||||
\(87\) | 2.86550 | − | 4.96318i | 0.307213 | − | 0.532109i | ||||
\(88\) | 0.0245828 | − | 0.0425786i | 0.00262053 | − | 0.00453889i | ||||
\(89\) | 6.02503 | + | 10.4357i | 0.638651 | + | 1.10618i | 0.985729 | + | 0.168340i | \(0.0538408\pi\) |
−0.347077 | + | 0.937836i | \(0.612826\pi\) | |||||||
\(90\) | 0.171508 | 0.0180785 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.64656 | 0.797209 | ||||||||
\(93\) | −1.38130 | − | 2.39248i | −0.143234 | − | 0.248088i | ||||
\(94\) | 8.35532 | − | 14.4718i | 0.861786 | − | 1.49266i | ||||
\(95\) | −3.00514 | + | 5.20506i | −0.308321 | + | 0.534028i | ||||
\(96\) | 7.06415 | + | 12.2355i | 0.720982 | + | 1.24878i | ||||
\(97\) | −7.43766 | −0.755180 | −0.377590 | − | 0.925973i | \(-0.623247\pi\) | ||||
−0.377590 | + | 0.925973i | \(0.623247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0675374 | 0.00678776 | ||||||||
\(100\) | 4.25108 | + | 7.36309i | 0.425108 | + | 0.736309i | ||||
\(101\) | −0.599526 | + | 1.03841i | −0.0596551 | + | 0.103326i | −0.894311 | − | 0.447447i | \(-0.852333\pi\) |
0.834656 | + | 0.550772i | \(0.185667\pi\) | |||||||
\(102\) | 4.15541 | − | 7.19739i | 0.411447 | − | 0.712647i | ||||
\(103\) | −7.20615 | − | 12.4814i | −0.710043 | − | 1.22983i | −0.964840 | − | 0.262837i | \(-0.915342\pi\) |
0.254797 | − | 0.966995i | \(-0.417991\pi\) | |||||||
\(104\) | 0.0686323 | 0.00672995 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.2866 | −2.74744 | ||||||||
\(107\) | −6.79661 | − | 11.7721i | −0.657053 | − | 1.13805i | −0.981375 | − | 0.192102i | \(-0.938469\pi\) |
0.324322 | − | 0.945947i | \(-0.394864\pi\) | |||||||
\(108\) | −5.19866 | + | 9.00434i | −0.500241 | + | 0.866443i | ||||
\(109\) | 6.86241 | − | 11.8860i | 0.657299 | − | 1.13848i | −0.324013 | − | 0.946053i | \(-0.605032\pi\) |
0.981312 | − | 0.192423i | \(-0.0616346\pi\) | |||||||
\(110\) | −0.651589 | − | 1.12859i | −0.0621266 | − | 0.107606i | ||||
\(111\) | −9.16262 | −0.869677 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25799 | −0.306486 | −0.153243 | − | 0.988189i | \(-0.548972\pi\) | ||||
−0.153243 | + | 0.988189i | \(0.548972\pi\) | |||||||
\(114\) | 11.7227 | + | 20.3043i | 1.09793 | + | 1.90167i | ||||
\(115\) | 1.70233 | − | 2.94852i | 0.158743 | − | 0.274951i | ||||
\(116\) | −3.31366 | + | 5.73942i | −0.307665 | + | 0.532892i | ||||
\(117\) | 0.0471392 | + | 0.0816475i | 0.00435802 | + | 0.00754831i | ||||
\(118\) | 1.43883 | 0.132455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.109346 | −0.00998189 | ||||||||
\(121\) | 5.24341 | + | 9.08186i | 0.476674 | + | 0.825623i | ||||
\(122\) | 11.7023 | − | 20.2690i | 1.05948 | − | 1.83507i | ||||
\(123\) | −4.32875 | + | 7.49762i | −0.390310 | + | 0.676037i | ||||
\(124\) | 1.59733 | + | 2.76666i | 0.143445 | + | 0.248453i | ||||
\(125\) | 8.31422 | 0.743647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.950834 | −0.0843729 | −0.0421865 | − | 0.999110i | \(-0.513432\pi\) | ||||
−0.0421865 | + | 0.999110i | \(0.513432\pi\) | |||||||
\(128\) | −0.274489 | − | 0.475429i | −0.0242617 | − | 0.0420224i | ||||
\(129\) | −8.30069 | + | 14.3772i | −0.730835 | + | 1.26584i | ||||
\(130\) | 0.909582 | − | 1.57544i | 0.0797756 | − | 0.138175i | ||||
\(131\) | −9.40980 | − | 16.2983i | −0.822138 | − | 1.42399i | −0.904087 | − | 0.427349i | \(-0.859448\pi\) |
0.0819487 | − | 0.996637i | \(-0.473886\pi\) | |||||||
\(132\) | −2.56330 | −0.223106 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.8635 | −1.62956 | ||||||||
\(135\) | 2.31472 | + | 4.00921i | 0.199219 | + | 0.345058i | ||||
\(136\) | −0.0807209 | + | 0.139813i | −0.00692176 | + | 0.0119888i | ||||
\(137\) | −3.09090 | + | 5.35359i | −0.264073 | + | 0.457388i | −0.967320 | − | 0.253557i | \(-0.918399\pi\) |
0.703247 | + | 0.710945i | \(0.251733\pi\) | |||||||
\(138\) | −6.64057 | − | 11.5018i | −0.565283 | − | 0.979099i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.6351 | −1.23250 | ||||||||
\(142\) | 11.0383 | + | 19.1188i | 0.926309 | + | 1.60441i | ||||
\(143\) | 0.358181 | − | 0.620387i | 0.0299526 | − | 0.0518794i | ||||
\(144\) | 0.185280 | − | 0.320915i | 0.0154400 | − | 0.0267429i | ||||
\(145\) | 1.47542 | + | 2.55550i | 0.122527 | + | 0.212223i | ||||
\(146\) | −6.97560 | −0.577305 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5956 | 0.870956 | ||||||||
\(149\) | 10.5385 | + | 18.2533i | 0.863351 | + | 1.49537i | 0.868675 | + | 0.495382i | \(0.164972\pi\) |
−0.00532425 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(150\) | 7.38361 | − | 12.7888i | 0.602869 | − | 1.04420i | ||||
\(151\) | 7.86171 | − | 13.6169i | 0.639777 | − | 1.10813i | −0.345704 | − | 0.938344i | \(-0.612360\pi\) |
0.985481 | − | 0.169783i | \(-0.0543067\pi\) | |||||||
\(152\) | −0.227719 | − | 0.394421i | −0.0184705 | − | 0.0319918i | ||||
\(153\) | −0.221768 | −0.0179289 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.42244 | 0.114253 | ||||||||
\(156\) | −1.78911 | − | 3.09883i | −0.143243 | − | 0.248105i | ||||
\(157\) | −3.89250 | + | 6.74200i | −0.310655 | + | 0.538070i | −0.978504 | − | 0.206226i | \(-0.933882\pi\) |
0.667849 | + | 0.744297i | \(0.267215\pi\) | |||||||
\(158\) | 13.0636 | − | 22.6268i | 1.03928 | − | 1.80009i | ||||
\(159\) | 12.3866 | + | 21.4543i | 0.982323 | + | 1.70143i | ||||
\(160\) | −7.27453 | −0.575102 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18.6269 | 1.46347 | ||||||||
\(163\) | −0.844956 | − | 1.46351i | −0.0661820 | − | 0.114631i | 0.831036 | − | 0.556219i | \(-0.187748\pi\) |
−0.897218 | + | 0.441588i | \(0.854415\pi\) | |||||||
\(164\) | 5.00576 | − | 8.67024i | 0.390884 | − | 0.677032i | ||||
\(165\) | −0.570659 | + | 0.988410i | −0.0444257 | + | 0.0769476i | ||||
\(166\) | −3.55592 | − | 6.15903i | −0.275993 | − | 0.478034i | ||||
\(167\) | 21.8667 | 1.69210 | 0.846049 | − | 0.533105i | \(-0.178975\pi\) | ||||
0.846049 | + | 0.533105i | \(0.178975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.13958 | + | 3.70587i | 0.164099 | + | 0.284227i | ||||
\(171\) | 0.312812 | − | 0.541805i | 0.0239213 | − | 0.0414329i | ||||
\(172\) | 9.59891 | − | 16.6258i | 0.731910 | − | 1.26770i | ||||
\(173\) | 2.92061 | + | 5.05865i | 0.222050 | + | 0.384602i | 0.955430 | − | 0.295217i | \(-0.0953918\pi\) |
−0.733380 | + | 0.679819i | \(0.762058\pi\) | |||||||
\(174\) | 11.5108 | 0.872634 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.81565 | −0.212238 | ||||||||
\(177\) | −0.630060 | − | 1.09130i | −0.0473582 | − | 0.0820268i | ||||
\(178\) | −12.1014 | + | 20.9603i | −0.907039 | + | 1.57104i | ||||
\(179\) | −1.26714 | + | 2.19475i | −0.0947103 | + | 0.164043i | −0.909488 | − | 0.415731i | \(-0.863526\pi\) |
0.814777 | + | 0.579774i | \(0.196859\pi\) | |||||||
\(180\) | 0.0868489 | + | 0.150427i | 0.00647333 | + | 0.0112121i | ||||
\(181\) | 10.7248 | 0.797169 | 0.398585 | − | 0.917132i | \(-0.369502\pi\) | ||||
0.398585 | + | 0.917132i | \(0.369502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.4977 | −1.51523 | ||||||||
\(184\) | 0.128996 | + | 0.223428i | 0.00950974 | + | 0.0164714i | ||||
\(185\) | 2.35887 | − | 4.08569i | 0.173428 | − | 0.300386i | ||||
\(186\) | 2.77437 | − | 4.80535i | 0.203427 | − | 0.352345i | ||||
\(187\) | 0.842538 | + | 1.45932i | 0.0616125 | + | 0.106716i | ||||
\(188\) | 16.9240 | 1.23431 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0718 | −0.875781 | ||||||||
\(191\) | 0.839303 | + | 1.45371i | 0.0607298 | + | 0.105187i | 0.894792 | − | 0.446484i | \(-0.147324\pi\) |
−0.834062 | + | 0.551671i | \(0.813991\pi\) | |||||||
\(192\) | −7.27457 | + | 12.5999i | −0.524997 | + | 0.909321i | ||||
\(193\) | 3.22408 | − | 5.58427i | 0.232074 | − | 0.401964i | −0.726344 | − | 0.687331i | \(-0.758782\pi\) |
0.958418 | + | 0.285367i | \(0.0921154\pi\) | |||||||
\(194\) | −7.46936 | − | 12.9373i | −0.536269 | − | 0.928845i | ||||
\(195\) | −1.59322 | −0.114093 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.87251 | 0.133411 | 0.0667054 | − | 0.997773i | \(-0.478751\pi\) | ||||
0.0667054 | + | 0.997773i | \(0.478751\pi\) | |||||||
\(198\) | 0.0678252 | + | 0.117477i | 0.00482013 | + | 0.00834871i | ||||
\(199\) | −5.69833 | + | 9.86979i | −0.403944 | + | 0.699651i | −0.994198 | − | 0.107566i | \(-0.965694\pi\) |
0.590254 | + | 0.807217i | \(0.299028\pi\) | |||||||
\(200\) | −0.143430 | + | 0.248428i | −0.0101420 | + | 0.0175665i | ||||
\(201\) | 8.26030 | + | 14.3073i | 0.582637 | + | 1.00916i | ||||
\(202\) | −2.40833 | −0.169449 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.41694 | 0.589304 | ||||||||
\(205\) | −2.22883 | − | 3.86045i | −0.155669 | − | 0.269626i | ||||
\(206\) | 14.4737 | − | 25.0692i | 1.00843 | − | 1.74666i | ||||
\(207\) | −0.177199 | + | 0.306918i | −0.0123162 | + | 0.0213322i | ||||
\(208\) | −1.96525 | − | 3.40391i | −0.136265 | − | 0.236018i | ||||
\(209\) | −4.75371 | −0.328821 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.53599 | 0.518799 | 0.259400 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259400 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(212\) | −14.3239 | − | 24.8097i | −0.983768 | − | 1.70394i | ||||
\(213\) | 9.66725 | − | 16.7442i | 0.662389 | − | 1.14729i | ||||
\(214\) | 13.6512 | − | 23.6445i | 0.933174 | − | 1.61630i | ||||
\(215\) | −4.27395 | − | 7.40269i | −0.291481 | − | 0.504859i | ||||
\(216\) | −0.350802 | −0.0238691 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.5666 | 1.86705 | ||||||||
\(219\) | 3.05460 | + | 5.29072i | 0.206411 | + | 0.357514i | ||||
\(220\) | 0.659909 | − | 1.14300i | 0.0444911 | − | 0.0770608i | ||||
\(221\) | −1.17614 | + | 2.03713i | −0.0791154 | + | 0.137032i | ||||
\(222\) | −9.20167 | − | 15.9378i | −0.617576 | − | 1.06967i | ||||
\(223\) | −17.6349 | −1.18092 | −0.590459 | − | 0.807067i | \(-0.701053\pi\) | ||||
−0.590459 | + | 0.807067i | \(0.701053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.394052 | −0.0262702 | ||||||||
\(226\) | −3.27188 | − | 5.66706i | −0.217642 | − | 0.376967i | ||||
\(227\) | −2.66452 | + | 4.61509i | −0.176851 | + | 0.306314i | −0.940800 | − | 0.338962i | \(-0.889924\pi\) |
0.763950 | + | 0.645276i | \(0.223258\pi\) | |||||||
\(228\) | −11.8724 | + | 20.5636i | −0.786267 | + | 1.36185i | ||||
\(229\) | −4.25950 | − | 7.37767i | −0.281476 | − | 0.487530i | 0.690273 | − | 0.723549i | \(-0.257491\pi\) |
−0.971748 | + | 0.236019i | \(0.924157\pi\) | |||||||
\(230\) | 6.83834 | 0.450907 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.223604 | −0.0146803 | ||||||||
\(233\) | −2.37685 | − | 4.11683i | −0.155713 | − | 0.269703i | 0.777605 | − | 0.628752i | \(-0.216434\pi\) |
−0.933318 | + | 0.359050i | \(0.883101\pi\) | |||||||
\(234\) | −0.0946802 | + | 0.163991i | −0.00618944 | + | 0.0107204i | ||||
\(235\) | 3.76774 | − | 6.52592i | 0.245780 | − | 0.425704i | ||||
\(236\) | 0.728600 | + | 1.26197i | 0.0474278 | + | 0.0821474i | ||||
\(237\) | −22.8821 | −1.48635 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8314 | 0.959365 | 0.479682 | − | 0.877442i | \(-0.340752\pi\) | ||||
0.479682 | + | 0.877442i | \(0.340752\pi\) | |||||||
\(240\) | 3.13106 | + | 5.42315i | 0.202109 | + | 0.350063i | ||||
\(241\) | −3.06066 | + | 5.30121i | −0.197154 | + | 0.341481i | −0.947605 | − | 0.319446i | \(-0.896503\pi\) |
0.750450 | + | 0.660927i | \(0.229837\pi\) | |||||||
\(242\) | −10.5315 | + | 18.2411i | −0.676992 | + | 1.17258i | ||||
\(243\) | −0.489705 | − | 0.848195i | −0.0314146 | − | 0.0544117i | ||||
\(244\) | 23.7035 | 1.51746 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.3888 | −1.10867 | ||||||||
\(247\) | −3.31796 | − | 5.74687i | −0.211116 | − | 0.365664i | ||||
\(248\) | −0.0538935 | + | 0.0933463i | −0.00342224 | + | 0.00592750i | ||||
\(249\) | −3.11426 | + | 5.39405i | −0.197358 | + | 0.341834i | ||||
\(250\) | 8.34966 | + | 14.4620i | 0.528079 | + | 0.914660i | ||||
\(251\) | 13.9708 | 0.881832 | 0.440916 | − | 0.897548i | \(-0.354654\pi\) | ||||
0.440916 | + | 0.897548i | \(0.354654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.69284 | 0.169298 | ||||||||
\(254\) | −0.954887 | − | 1.65391i | −0.0599149 | − | 0.103776i | ||||
\(255\) | 1.87384 | − | 3.24558i | 0.117344 | − | 0.203246i | ||||
\(256\) | −7.71967 | + | 13.3709i | −0.482479 | + | 0.835679i | ||||
\(257\) | 8.63253 | + | 14.9520i | 0.538482 | + | 0.932679i | 0.998986 | + | 0.0450210i | \(0.0143355\pi\) |
−0.460504 | + | 0.887658i | \(0.652331\pi\) | |||||||
\(258\) | −33.3443 | −2.07592 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.84239 | 0.114260 | ||||||||
\(261\) | −0.153579 | − | 0.266007i | −0.00950631 | − | 0.0164654i | ||||
\(262\) | 18.8998 | − | 32.7354i | 1.16763 | − | 2.02240i | ||||
\(263\) | 1.30336 | − | 2.25749i | 0.0803687 | − | 0.139203i | −0.823040 | − | 0.567984i | \(-0.807724\pi\) |
0.903408 | + | 0.428781i | \(0.141057\pi\) | |||||||
\(264\) | −0.0432425 | − | 0.0748982i | −0.00266139 | − | 0.00460966i | ||||
\(265\) | −12.7555 | −0.783565 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.1967 | 1.29722 | ||||||||
\(268\) | −9.55221 | − | 16.5449i | −0.583494 | − | 1.01064i | ||||
\(269\) | −7.24477 | + | 12.5483i | −0.441721 | + | 0.765084i | −0.997817 | − | 0.0660343i | \(-0.978965\pi\) |
0.556096 | + | 0.831118i | \(0.312299\pi\) | |||||||
\(270\) | −4.64917 | + | 8.05260i | −0.282940 | + | 0.490066i | ||||
\(271\) | −4.31796 | − | 7.47892i | −0.262297 | − | 0.454312i | 0.704555 | − | 0.709650i | \(-0.251147\pi\) |
−0.966852 | + | 0.255338i | \(0.917813\pi\) | |||||||
\(272\) | 9.24558 | 0.560596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4163 | −0.750095 | ||||||||
\(275\) | 1.49708 | + | 2.59301i | 0.0902771 | + | 0.156364i | ||||
\(276\) | 6.72537 | − | 11.6487i | 0.404819 | − | 0.701168i | ||||
\(277\) | −6.11349 | + | 10.5889i | −0.367324 | + | 0.636223i | −0.989146 | − | 0.146935i | \(-0.953059\pi\) |
0.621822 | + | 0.783158i | \(0.286393\pi\) | |||||||
\(278\) | 4.01705 | + | 6.95773i | 0.240927 | + | 0.417297i | ||||
\(279\) | −0.148064 | −0.00886437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1822 | −1.44259 | −0.721293 | − | 0.692630i | \(-0.756452\pi\) | ||||
−0.721293 | + | 0.692630i | \(0.756452\pi\) | |||||||
\(282\) | −14.6975 | − | 25.4568i | −0.875222 | − | 1.51593i | ||||
\(283\) | −15.3842 | + | 26.6461i | −0.914493 | + | 1.58395i | −0.106851 | + | 0.994275i | \(0.534077\pi\) |
−0.807642 | + | 0.589674i | \(0.799256\pi\) | |||||||
\(284\) | −11.1792 | + | 19.3629i | −0.663363 | + | 1.14898i | ||||
\(285\) | 5.28622 | + | 9.15599i | 0.313128 | + | 0.542354i | ||||
\(286\) | 1.43883 | 0.0850797 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.757221 | 0.0446197 | ||||||||
\(289\) | 5.73341 | + | 9.93056i | 0.337259 | + | 0.584150i | ||||
\(290\) | −2.96341 | + | 5.13278i | −0.174018 | + | 0.301407i | ||||
\(291\) | −6.54163 | + | 11.3304i | −0.383477 | + | 0.664202i | ||||
\(292\) | −3.53234 | − | 6.11819i | −0.206714 | − | 0.358040i | ||||
\(293\) | 31.8295 | 1.85950 | 0.929749 | − | 0.368193i | \(-0.120024\pi\) | ||||
0.929749 | + | 0.368193i | \(0.120024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.648824 | 0.0377760 | ||||||||
\(296\) | 0.178747 | + | 0.309599i | 0.0103895 | + | 0.0179951i | ||||
\(297\) | −1.83078 | + | 3.17100i | −0.106233 | + | 0.184000i | ||||
\(298\) | −21.1669 | + | 36.6622i | −1.22617 | + | 2.12378i | ||||
\(299\) | 1.87953 | + | 3.25544i | 0.108696 | + | 0.188267i | ||||
\(300\) | 14.9558 | 0.863472 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 31.5809 | 1.81728 | ||||||||
\(303\) | 1.05460 | + | 1.82662i | 0.0605852 | + | 0.104937i | ||||
\(304\) | −13.0412 | + | 22.5880i | −0.747964 | + | 1.29551i | ||||
\(305\) | 5.27704 | − | 9.14010i | 0.302162 | − | 0.523360i | ||||
\(306\) | −0.222714 | − | 0.385751i | −0.0127317 | − | 0.0220519i | ||||
\(307\) | −28.7884 | −1.64304 | −0.821520 | − | 0.570179i | \(-0.806874\pi\) | ||||
−0.821520 | + | 0.570179i | \(0.806874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.3521 | −1.44223 | ||||||||
\(310\) | 1.42850 | + | 2.47423i | 0.0811332 | + | 0.140527i | ||||
\(311\) | 2.75931 | − | 4.77927i | 0.156466 | − | 0.271007i | −0.777126 | − | 0.629345i | \(-0.783323\pi\) |
0.933592 | + | 0.358338i | \(0.116656\pi\) | |||||||
\(312\) | 0.0603641 | − | 0.104554i | 0.00341744 | − | 0.00591918i | ||||
\(313\) | −2.42399 | − | 4.19848i | −0.137012 | − | 0.237312i | 0.789352 | − | 0.613941i | \(-0.210417\pi\) |
−0.926364 | + | 0.376629i | \(0.877083\pi\) | |||||||
\(314\) | −15.6363 | −0.882410 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.4608 | 1.48854 | ||||||||
\(317\) | 3.82756 | + | 6.62952i | 0.214977 | + | 0.372351i | 0.953265 | − | 0.302134i | \(-0.0976990\pi\) |
−0.738288 | + | 0.674485i | \(0.764366\pi\) | |||||||
\(318\) | −24.8788 | + | 43.0914i | −1.39514 | + | 2.41645i | ||||
\(319\) | −1.16695 | + | 2.02122i | −0.0653366 | + | 0.113166i | ||||
\(320\) | −3.74561 | − | 6.48758i | −0.209386 | − | 0.362667i | ||||
\(321\) | −23.9112 | −1.33459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.6095 | 0.868534 | ||||||||
\(324\) | 9.43239 | + | 16.3374i | 0.524022 | + | 0.907633i | ||||
\(325\) | −2.08983 | + | 3.61970i | −0.115923 | + | 0.200785i | ||||
\(326\) | 1.69711 | − | 2.93949i | 0.0939945 | − | 0.162803i | ||||
\(327\) | −12.0714 | − | 20.9082i | −0.667548 | − | 1.15623i | ||||
\(328\) | 0.337786 | 0.0186511 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.29236 | −0.126190 | ||||||||
\(331\) | −5.67159 | − | 9.82348i | −0.311739 | − | 0.539947i | 0.667000 | − | 0.745058i | \(-0.267578\pi\) |
−0.978739 | + | 0.205110i | \(0.934245\pi\) | |||||||
\(332\) | 3.60132 | − | 6.23768i | 0.197648 | − | 0.342337i | ||||
\(333\) | −0.245540 | + | 0.425288i | −0.0134555 | + | 0.0233056i | ||||
\(334\) | 21.9599 | + | 38.0357i | 1.20159 | + | 2.08122i | ||||
\(335\) | −8.50631 | −0.464749 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.74149 | 0.0948649 | 0.0474324 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474324 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(338\) | 1.00426 | + | 1.73943i | 0.0546247 | + | 0.0946127i | ||||
\(339\) | −2.86550 | + | 4.96318i | −0.155632 | + | 0.269563i | ||||
\(340\) | −2.16690 | + | 3.75319i | −0.117517 | + | 0.203545i | ||||
\(341\) | 0.562522 | + | 0.974317i | 0.0304623 | + | 0.0527622i | ||||
\(342\) | 1.25658 | 0.0679480 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.647729 | 0.0349232 | ||||||||
\(345\) | −2.99449 | − | 5.18661i | −0.161218 | − | 0.279238i | ||||
\(346\) | −5.86612 | + | 10.1604i | −0.315365 | + | 0.546228i | ||||
\(347\) | −10.5251 | + | 18.2301i | −0.565019 | + | 0.978641i | 0.432029 | + | 0.901860i | \(0.357798\pi\) |
−0.997048 | + | 0.0767814i | \(0.975536\pi\) | |||||||
\(348\) | 5.82891 | + | 10.0960i | 0.312462 | + | 0.541200i | ||||
\(349\) | 8.35601 | 0.447287 | 0.223643 | − | 0.974671i | \(-0.428205\pi\) | ||||
0.223643 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11133 | −0.272822 | ||||||||
\(352\) | −2.87682 | − | 4.98279i | −0.153335 | − | 0.265584i | ||||
\(353\) | −4.26677 | + | 7.39027i | −0.227097 | + | 0.393344i | −0.956947 | − | 0.290264i | \(-0.906257\pi\) |
0.729849 | + | 0.683608i | \(0.239590\pi\) | |||||||
\(354\) | 1.26549 | − | 2.19189i | 0.0672601 | − | 0.116498i | ||||
\(355\) | 4.97758 | + | 8.62141i | 0.264182 | + | 0.457577i | ||||
\(356\) | −24.5119 | −1.29913 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.09015 | −0.269023 | ||||||||
\(359\) | 8.08565 | + | 14.0047i | 0.426744 | + | 0.739142i | 0.996582 | − | 0.0826150i | \(-0.0263272\pi\) |
−0.569837 | + | 0.821757i | \(0.692994\pi\) | |||||||
\(360\) | −0.00293026 | + | 0.00507535i | −0.000154438 | + | 0.000267495i | ||||
\(361\) | −12.5177 | + | 21.6812i | −0.658824 | + | 1.14112i | ||||
\(362\) | 10.7705 | + | 18.6551i | 0.566086 | + | 0.980490i | ||||
\(363\) | 18.4469 | 0.968212 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.14557 | −0.164647 | ||||||||
\(366\) | −20.5851 | − | 35.6544i | −1.07600 | − | 1.86368i | ||||
\(367\) | 14.0770 | − | 24.3821i | 0.734813 | − | 1.27273i | −0.219992 | − | 0.975502i | \(-0.570603\pi\) |
0.954805 | − | 0.297232i | \(-0.0960636\pi\) | |||||||
\(368\) | 7.38747 | − | 12.7955i | 0.385098 | − | 0.667010i | ||||
\(369\) | 0.232004 | + | 0.401842i | 0.0120776 | + | 0.0209191i | ||||
\(370\) | 9.47571 | 0.492619 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.61959 | 0.291362 | ||||||||
\(373\) | 14.2518 | + | 24.6849i | 0.737932 | + | 1.27814i | 0.953425 | + | 0.301630i | \(0.0975308\pi\) |
−0.215493 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(374\) | −1.69226 | + | 2.93108i | −0.0875046 | + | 0.151562i | ||||
\(375\) | 7.31259 | − | 12.6658i | 0.377621 | − | 0.654058i | ||||
\(376\) | 0.285506 | + | 0.494511i | 0.0147238 | + | 0.0255024i | ||||
\(377\) | −3.25799 | −0.167795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.26263 | −0.373056 | −0.186528 | − | 0.982450i | \(-0.559724\pi\) | ||||
−0.186528 | + | 0.982450i | \(0.559724\pi\) | |||||||
\(380\) | −6.11297 | − | 10.5880i | −0.313589 | − | 0.543152i | ||||
\(381\) | −0.836286 | + | 1.44849i | −0.0428442 | + | 0.0742083i | ||||
\(382\) | −1.68576 | + | 2.91982i | −0.0862510 | + | 0.149391i | ||||
\(383\) | 6.46627 | + | 11.1999i | 0.330411 | + | 0.572289i | 0.982592 | − | 0.185774i | \(-0.0594793\pi\) |
−0.652181 | + | 0.758063i | \(0.726146\pi\) | |||||||
\(384\) | −0.965684 | −0.0492799 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9513 | 0.659203 | ||||||||
\(387\) | 0.444884 | + | 0.770561i | 0.0226147 | + | 0.0391698i | ||||
\(388\) | 7.56474 | − | 13.1025i | 0.384041 | − | 0.665179i | ||||
\(389\) | 10.5679 | − | 18.3041i | 0.535811 | − | 0.928053i | −0.463312 | − | 0.886195i | \(-0.653339\pi\) |
0.999124 | − | 0.0418574i | \(-0.0133275\pi\) | |||||||
\(390\) | −1.60001 | − | 2.77129i | −0.0810194 | − | 0.140330i | ||||
\(391\) | −8.84232 | −0.447175 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.1047 | −1.66991 | ||||||||
\(394\) | 1.88049 | + | 3.25711i | 0.0947378 | + | 0.164091i | ||||
\(395\) | 5.89089 | − | 10.2033i | 0.296403 | − | 0.513384i | ||||
\(396\) | −0.0686913 | + | 0.118977i | −0.00345187 | + | 0.00597881i | ||||
\(397\) | 9.60366 | + | 16.6340i | 0.481994 | + | 0.834838i | 0.999786 | − | 0.0206683i | \(-0.00657938\pi\) |
−0.517792 | + | 0.855506i | \(0.673246\pi\) | |||||||
\(398\) | −22.8905 | −1.14740 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.4282 | 0.821408 | ||||||||
\(401\) | −8.33460 | − | 14.4360i | −0.416210 | − | 0.720897i | 0.579344 | − | 0.815083i | \(-0.303309\pi\) |
−0.995555 | + | 0.0941856i | \(0.969975\pi\) | |||||||
\(402\) | −16.5910 | + | 28.7365i | −0.827485 | + | 1.43325i | ||||
\(403\) | −0.785250 | + | 1.36009i | −0.0391161 | + | 0.0677510i | ||||
\(404\) | −1.21954 | − | 2.11230i | −0.0606743 | − | 0.105091i | ||||
\(405\) | 8.39961 | 0.417380 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.73140 | 0.184959 | ||||||||
\(408\) | 0.141993 | + | 0.245939i | 0.00702968 | + | 0.0121758i | ||||
\(409\) | 6.17416 | − | 10.6940i | 0.305293 | − | 0.528782i | −0.672034 | − | 0.740520i | \(-0.734579\pi\) |
0.977326 | + | 0.211738i | \(0.0679124\pi\) | |||||||
\(410\) | 4.47667 | − | 7.75382i | 0.221087 | − | 0.382934i | ||||
\(411\) | 5.43706 | + | 9.41727i | 0.268190 | + | 0.464520i | ||||
\(412\) | 29.3171 | 1.44435 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.711817 | −0.0349839 | ||||||||
\(415\) | −1.60350 | − | 2.77735i | −0.0787128 | − | 0.136335i | ||||
\(416\) | 4.01588 | − | 6.95570i | 0.196895 | − | 0.341031i | ||||
\(417\) | 3.51811 | − | 6.09355i | 0.172283 | − | 0.298402i | ||||
\(418\) | −4.77397 | − | 8.26876i | −0.233502 | − | 0.404438i | ||||
\(419\) | −4.35934 | −0.212968 | −0.106484 | − | 0.994314i | \(-0.533959\pi\) | ||||
−0.106484 | + | 0.994314i | \(0.533959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 7.56811 | + | 13.1084i | 0.368410 | + | 0.638105i | ||||
\(423\) | −0.392192 | + | 0.679296i | −0.0190690 | + | 0.0330285i | ||||
\(424\) | 0.483284 | − | 0.837072i | 0.0234703 | − | 0.0406518i | ||||
\(425\) | −4.91586 | − | 8.51451i | −0.238454 | − | 0.413015i | ||||
\(426\) | 38.8338 | 1.88150 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.6509 | 1.33656 | ||||||||
\(429\) | −0.630060 | − | 1.09130i | −0.0304196 | − | 0.0526882i | ||||
\(430\) | 8.58433 | − | 14.8685i | 0.413973 | − | 0.717022i | ||||
\(431\) | 11.6813 | − | 20.2326i | 0.562667 | − | 0.974569i | −0.434595 | − | 0.900626i | \(-0.643109\pi\) |
0.997262 | − | 0.0739426i | \(-0.0235582\pi\) | |||||||
\(432\) | 10.0450 | + | 17.3985i | 0.483291 | + | 0.837084i | ||||
\(433\) | 2.71285 | 0.130371 | 0.0651856 | − | 0.997873i | \(-0.479236\pi\) | ||||
0.0651856 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.19068 | 0.248874 | ||||||||
\(436\) | 13.9593 | + | 24.1782i | 0.668529 | + | 1.15793i | ||||
\(437\) | 12.4724 | − | 21.6028i | 0.596635 | − | 1.03340i | ||||
\(438\) | −6.13524 | + | 10.6265i | −0.293153 | + | 0.507756i | ||||
\(439\) | −4.41760 | − | 7.65150i | −0.210840 | − | 0.365186i | 0.741137 | − | 0.671353i | \(-0.234287\pi\) |
−0.951978 | + | 0.306167i | \(0.900953\pi\) | |||||||
\(440\) | 0.0445303 | 0.00212290 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.72459 | −0.224726 | ||||||||
\(443\) | 1.45279 | + | 2.51630i | 0.0690240 | + | 0.119553i | 0.898472 | − | 0.439031i | \(-0.144678\pi\) |
−0.829448 | + | 0.558584i | \(0.811345\pi\) | |||||||
\(444\) | 9.31917 | − | 16.1413i | 0.442268 | − | 0.766031i | ||||
\(445\) | −5.45700 | + | 9.45179i | −0.258686 | + | 0.448058i | ||||
\(446\) | −17.7100 | − | 30.6747i | −0.838595 | − | 1.45249i | ||||
\(447\) | 37.0758 | 1.75362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.2777 | −0.720998 | −0.360499 | − | 0.932760i | \(-0.617394\pi\) | ||||
−0.360499 | + | 0.932760i | \(0.617394\pi\) | |||||||
\(450\) | −0.395732 | − | 0.685428i | −0.0186550 | − | 0.0323114i | ||||
\(451\) | 1.76285 | − | 3.05334i | 0.0830093 | − | 0.143776i | ||||
\(452\) | 3.31366 | − | 5.73942i | 0.155861 | − | 0.269960i | ||||
\(453\) | −13.8292 | − | 23.9529i | −0.649752 | − | 1.12540i | ||||
\(454\) | −10.7035 | −0.502341 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.801141 | −0.0375169 | ||||||||
\(457\) | −11.8300 | − | 20.4902i | −0.553384 | − | 0.958489i | −0.998027 | − | 0.0627815i | \(-0.980003\pi\) |
0.444643 | − | 0.895708i | \(-0.353330\pi\) | |||||||
\(458\) | 8.55531 | − | 14.8182i | 0.399763 | − | 0.692410i | ||||
\(459\) | 6.01161 | − | 10.4124i | 0.280598 | − | 0.486010i | ||||
\(460\) | 3.46283 | + | 5.99779i | 0.161455 | + | 0.279649i | ||||
\(461\) | 26.6170 | 1.23968 | 0.619839 | − | 0.784729i | \(-0.287198\pi\) | ||||
0.619839 | + | 0.784729i | \(0.287198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44250 | −0.0670385 | −0.0335193 | − | 0.999438i | \(-0.510672\pi\) | ||||
−0.0335193 | + | 0.999438i | \(0.510672\pi\) | |||||||
\(464\) | 6.40276 | + | 11.0899i | 0.297240 | + | 0.514836i | ||||
\(465\) | 1.25107 | − | 2.16692i | 0.0580171 | − | 0.100488i | ||||
\(466\) | 4.77397 | − | 8.26876i | 0.221150 | − | 0.383043i | ||||
\(467\) | −4.19480 | − | 7.26560i | −0.194112 | − | 0.336212i | 0.752497 | − | 0.658596i | \(-0.228849\pi\) |
−0.946609 | + | 0.322384i | \(0.895516\pi\) | |||||||
\(468\) | −0.191778 | −0.00886496 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.1352 | 0.698135 | ||||||||
\(471\) | 6.84712 | + | 11.8596i | 0.315499 | + | 0.546460i | ||||
\(472\) | −0.0245828 | + | 0.0425786i | −0.00113151 | + | 0.00195984i | ||||
\(473\) | 3.38039 | − | 5.85500i | 0.155430 | − | 0.269213i | ||||
\(474\) | −22.9796 | − | 39.8019i | −1.05549 | − | 1.82816i | ||||
\(475\) | 27.7359 | 1.27261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.32775 | 0.0607934 | ||||||||
\(478\) | 14.8946 | + | 25.7983i | 0.681265 | + | 1.17999i | ||||
\(479\) | 6.30608 | − | 10.9225i | 0.288132 | − | 0.499060i | −0.685232 | − | 0.728325i | \(-0.740299\pi\) |
0.973364 | + | 0.229265i | \(0.0736324\pi\) | |||||||
\(480\) | −6.39815 | + | 11.0819i | −0.292034 | + | 0.505819i | ||||
\(481\) | 2.60441 | + | 4.51098i | 0.118751 | + | 0.205683i | ||||
\(482\) | −12.2948 | −0.560013 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.3320 | −0.969636 | ||||||||
\(485\) | −3.36823 | − | 5.83394i | −0.152943 | − | 0.264905i | ||||
\(486\) | 0.983585 | − | 1.70362i | 0.0446163 | − | 0.0772778i | ||||
\(487\) | −10.7840 | + | 18.6785i | −0.488671 | + | 0.846403i | −0.999915 | − | 0.0130329i | \(-0.995851\pi\) |
0.511244 | + | 0.859435i | \(0.329185\pi\) | |||||||
\(488\) | 0.399875 | + | 0.692604i | 0.0181015 | + | 0.0313527i | ||||
\(489\) | −2.97265 | −0.134428 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.2347 | 1.77064 | 0.885318 | − | 0.464987i | \(-0.153941\pi\) | ||||
0.885318 | + | 0.464987i | \(0.153941\pi\) | |||||||
\(492\) | −8.80542 | − | 15.2514i | −0.396979 | − | 0.687588i | ||||
\(493\) | 3.83184 | − | 6.63694i | 0.172577 | − | 0.298913i | ||||
\(494\) | 6.66419 | − | 11.5427i | 0.299836 | − | 0.519332i | ||||
\(495\) | 0.0305850 | + | 0.0529748i | 0.00137469 | + | 0.00238104i | ||||
\(496\) | 6.17283 | 0.277168 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.5101 | −0.560592 | ||||||||
\(499\) | −4.58407 | − | 7.93984i | −0.205211 | − | 0.355436i | 0.744989 | − | 0.667077i | \(-0.232455\pi\) |
−0.950200 | + | 0.311641i | \(0.899121\pi\) | |||||||
\(500\) | −8.45627 | + | 14.6467i | −0.378176 | + | 0.655020i | ||||
\(501\) | 19.2324 | − | 33.3115i | 0.859240 | − | 1.48825i | ||||
\(502\) | 14.0304 | + | 24.3013i | 0.626207 | + | 1.08462i | ||||
\(503\) | −24.9370 | −1.11188 | −0.555942 | − | 0.831221i | \(-0.687642\pi\) | ||||
−0.555942 | + | 0.831221i | \(0.687642\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.08601 | −0.0483267 | ||||||||
\(506\) | 2.70432 | + | 4.68402i | 0.120222 | + | 0.208230i | ||||
\(507\) | 0.879528 | − | 1.52339i | 0.0390612 | − | 0.0676560i | ||||
\(508\) | 0.967080 | − | 1.67503i | 0.0429072 | − | 0.0743175i | ||||
\(509\) | 2.94904 | + | 5.10788i | 0.130714 | + | 0.226403i | 0.923952 | − | 0.382509i | \(-0.124940\pi\) |
−0.793238 | + | 0.608912i | \(0.791606\pi\) | |||||||
\(510\) | 7.52730 | 0.333314 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.1083 | −1.41900 | ||||||||
\(513\) | 16.9592 | + | 29.3741i | 0.748765 | + | 1.29690i | ||||
\(514\) | −17.3386 | + | 30.0314i | −0.764775 | + | 1.32463i | ||||
\(515\) | 6.52677 | − | 11.3047i | 0.287604 | − | 0.498144i | ||||
\(516\) | −16.8850 | − | 29.2457i | −0.743321 | − | 1.28747i | ||||
\(517\) | 5.96003 | 0.262122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.2750 | 0.451024 | ||||||||
\(520\) | 0.0310809 | + | 0.0538337i | 0.00136299 | + | 0.00236076i | ||||
\(521\) | −18.5948 | + | 32.2071i | −0.814652 | + | 1.41102i | 0.0949259 | + | 0.995484i | \(0.469739\pi\) |
−0.909578 | + | 0.415534i | \(0.863595\pi\) | |||||||
\(522\) | 0.308468 | − | 0.534281i | 0.0135013 | − | 0.0233849i | ||||
\(523\) | −2.54540 | − | 4.40876i | −0.111303 | − | 0.192782i | 0.804993 | − | 0.593284i | \(-0.202169\pi\) |
−0.916296 | + | 0.400502i | \(0.868836\pi\) | |||||||
\(524\) | 38.2823 | 1.67237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.23567 | 0.228286 | ||||||||
\(527\) | −1.84712 | − | 3.19931i | −0.0804618 | − | 0.139364i | ||||
\(528\) | −2.47644 | + | 4.28933i | −0.107773 | + | 0.186669i | ||||
\(529\) | 4.43475 | − | 7.68121i | 0.192815 | − | 0.333966i | ||||
\(530\) | −12.8099 | − | 22.1874i | −0.556426 | − | 0.963758i | ||||
\(531\) | −0.0675374 | −0.00293087 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.92168 | 0.213181 | ||||||||
\(534\) | 21.2871 | + | 36.8703i | 0.921181 | + | 1.59553i | ||||
\(535\) | 6.15583 | − | 10.6622i | 0.266140 | − | 0.460968i | ||||
\(536\) | 0.322289 | − | 0.558220i | 0.0139208 | − | 0.0241114i | ||||
\(537\) | 2.22897 | + | 3.86068i | 0.0961870 | + | 0.166601i | ||||
\(538\) | −29.1026 | −1.25470 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.41707 | −0.405246 | ||||||||
\(541\) | 0.383425 | + | 0.664111i | 0.0164847 | + | 0.0285524i | 0.874150 | − | 0.485656i | \(-0.161419\pi\) |
−0.857665 | + | 0.514208i | \(0.828086\pi\) | |||||||
\(542\) | 8.67272 | − | 15.0216i | 0.372525 | − | 0.645232i | ||||
\(543\) | 9.43277 | − | 16.3380i | 0.404799 | − | 0.701133i | ||||
\(544\) | 9.44643 | + | 16.3617i | 0.405012 | + | 0.701502i | ||||
\(545\) | 12.4309 | 0.532480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.1428 | 0.604702 | 0.302351 | − | 0.953197i | \(-0.402229\pi\) | ||||
0.302351 | + | 0.953197i | \(0.402229\pi\) | |||||||
\(548\) | −6.28741 | − | 10.8901i | −0.268585 | − | 0.465203i | ||||
\(549\) | −0.549297 | + | 0.951411i | −0.0234434 | + | 0.0406052i | ||||
\(550\) | −3.00691 | + | 5.20813i | −0.128215 | + | 0.222075i | ||||
\(551\) | 10.8099 | + | 18.7233i | 0.460516 | + | 0.797637i | ||||
\(552\) | 0.453824 | 0.0193160 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −24.5582 | −1.04338 | ||||||||
\(555\) | −4.14939 | − | 7.18696i | −0.176132 | − | 0.305069i | ||||
\(556\) | −4.06834 | + | 7.04657i | −0.172536 | + | 0.298841i | ||||
\(557\) | 12.4314 | − | 21.5317i | 0.526733 | − | 0.912329i | −0.472782 | − | 0.881180i | \(-0.656750\pi\) |
0.999515 | − | 0.0311490i | \(-0.00991664\pi\) | |||||||
\(558\) | −0.148695 | − | 0.257548i | −0.00629477 | − | 0.0109029i | ||||
\(559\) | 9.43766 | 0.399171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.96414 | 0.125146 | ||||||||
\(562\) | −24.2852 | − | 42.0633i | −1.02441 | − | 1.77433i | ||||
\(563\) | 22.0047 | − | 38.1133i | 0.927388 | − | 1.60628i | 0.139713 | − | 0.990192i | \(-0.455382\pi\) |
0.787675 | − | 0.616091i | \(-0.211285\pi\) | |||||||
\(564\) | 14.8852 | − | 25.7818i | 0.626778 | − | 1.08561i | ||||
\(565\) | −1.47542 | − | 2.55550i | −0.0620713 | − | 0.107511i | ||||
\(566\) | −61.7989 | −2.59760 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.754366 | −0.0316525 | ||||||||
\(569\) | 16.6308 | + | 28.8054i | 0.697199 | + | 1.20758i | 0.969434 | + | 0.245353i | \(0.0789040\pi\) |
−0.272235 | + | 0.962231i | \(0.587763\pi\) | |||||||
\(570\) | −10.6175 | + | 18.3900i | −0.444718 | + | 0.770274i | ||||
\(571\) | 6.17699 | − | 10.6989i | 0.258499 | − | 0.447734i | −0.707341 | − | 0.706873i | \(-0.750105\pi\) |
0.965840 | + | 0.259139i | \(0.0834387\pi\) | |||||||
\(572\) | 0.728600 | + | 1.26197i | 0.0304643 | + | 0.0527657i | ||||
\(573\) | 2.95276 | 0.123353 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.7116 | −0.655219 | ||||||||
\(576\) | 0.389888 | + | 0.675306i | 0.0162453 | + | 0.0281377i | ||||
\(577\) | −12.9829 | + | 22.4871i | −0.540486 | + | 0.936150i | 0.458390 | + | 0.888751i | \(0.348426\pi\) |
−0.998876 | + | 0.0473984i | \(0.984907\pi\) | |||||||
\(578\) | −11.5157 | + | 19.9458i | −0.478990 | + | 0.829635i | ||||
\(579\) | −5.67133 | − | 9.82304i | −0.235693 | − | 0.408232i | ||||
\(580\) | −6.00250 | −0.249240 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26.2781 | −1.08926 | ||||||||
\(583\) | −5.04435 | − | 8.73707i | −0.208916 | − | 0.361853i | ||||
\(584\) | 0.119180 | − | 0.206426i | 0.00493171 | − | 0.00854196i | ||||
\(585\) | −0.0426950 | + | 0.0739499i | −0.00176522 | + | 0.00305745i | ||||
\(586\) | 31.9652 | + | 55.3653i | 1.32047 | + | 2.28712i | ||||
\(587\) | 23.9747 | 0.989543 | 0.494771 | − | 0.869023i | \(-0.335252\pi\) | ||||
0.494771 | + | 0.869023i | \(0.335252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.4217 | 0.429418 | ||||||||
\(590\) | 0.651589 | + | 1.12859i | 0.0268255 | + | 0.0464631i | ||||
\(591\) | 1.64693 | − | 2.85256i | 0.0677454 | − | 0.117339i | ||||
\(592\) | 10.2366 | − | 17.7304i | 0.420723 | − | 0.728713i | ||||
\(593\) | 23.5240 | + | 40.7448i | 0.966015 | + | 1.67319i | 0.706862 | + | 0.707352i | \(0.250110\pi\) |
0.259154 | + | 0.965836i | \(0.416556\pi\) | |||||||
\(594\) | −7.35433 | −0.301752 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −42.8744 | −1.75620 | ||||||||
\(597\) | 10.0237 | + | 17.3615i | 0.410242 | + | 0.710560i | ||||
\(598\) | −3.77508 | + | 6.53863i | −0.154374 | + | 0.267384i | ||||
\(599\) | −10.0868 | + | 17.4708i | −0.412135 | + | 0.713840i | −0.995123 | − | 0.0986415i | \(-0.968550\pi\) |
0.582988 | + | 0.812481i | \(0.301884\pi\) | |||||||
\(600\) | 0.252302 | + | 0.437000i | 0.0103002 | + | 0.0178404i | ||||
\(601\) | −29.5773 | −1.20648 | −0.603242 | − | 0.797558i | \(-0.706125\pi\) | ||||
−0.603242 | + | 0.797558i | \(0.706125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.885439 | 0.0360579 | ||||||||
\(604\) | 15.9921 | + | 27.6991i | 0.650708 | + | 1.12706i | ||||
\(605\) | −4.74907 | + | 8.22564i | −0.193077 | + | 0.334420i | ||||
\(606\) | −2.11819 | + | 3.66881i | −0.0860456 | + | 0.149035i | ||||
\(607\) | −7.72099 | − | 13.3732i | −0.313385 | − | 0.542799i | 0.665708 | − | 0.746213i | \(-0.268130\pi\) |
−0.979093 | + | 0.203413i | \(0.934796\pi\) | |||||||
\(608\) | −53.2980 | −2.16152 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.1981 | 0.858287 | ||||||||
\(611\) | 4.15993 | + | 7.20521i | 0.168293 | + | 0.291492i | ||||
\(612\) | 0.225557 | − | 0.390677i | 0.00911762 | − | 0.0157922i | ||||
\(613\) | −0.997423 | + | 1.72759i | −0.0402855 | + | 0.0697766i | −0.885465 | − | 0.464706i | \(-0.846160\pi\) |
0.845180 | + | 0.534482i | \(0.179493\pi\) | |||||||
\(614\) | −28.9111 | − | 50.0755i | −1.16676 | − | 2.02088i | ||||
\(615\) | −7.84129 | −0.316191 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.85584 | −0.114972 | −0.0574858 | − | 0.998346i | \(-0.518308\pi\) | ||||
−0.0574858 | + | 0.998346i | \(0.518308\pi\) | |||||||
\(618\) | −25.4601 | − | 44.0982i | −1.02416 | − | 1.77389i | ||||
\(619\) | 15.9911 | − | 27.6975i | 0.642738 | − | 1.11326i | −0.342080 | − | 0.939671i | \(-0.611132\pi\) |
0.984819 | − | 0.173585i | \(-0.0555351\pi\) | |||||||
\(620\) | −1.44674 | + | 2.50582i | −0.0581024 | + | 0.100636i | ||||
\(621\) | −9.60688 | − | 16.6396i | −0.385511 | − | 0.667725i | ||||
\(622\) | 11.0843 | 0.444440 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.91395 | −0.276780 | ||||||||
\(625\) | −6.68398 | − | 11.5770i | −0.267359 | − | 0.463080i | ||||
\(626\) | 4.86865 | − | 8.43275i | 0.194590 | − | 0.337040i | ||||
\(627\) | −4.18102 | + | 7.24174i | −0.166974 | + | 0.289207i | ||||
\(628\) | −7.91800 | − | 13.7144i | −0.315963 | − | 0.547263i | ||||
\(629\) | −12.2526 | −0.488542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.1115 | 1.27834 | 0.639169 | − | 0.769066i | \(-0.279278\pi\) | ||||
0.639169 | + | 0.769066i | \(0.279278\pi\) | |||||||
\(632\) | 0.446390 | + | 0.773171i | 0.0177565 | + | 0.0307551i | ||||
\(633\) | 6.62812 | − | 11.4802i | 0.263444 | − | 0.456298i | ||||
\(634\) | −7.68774 | + | 13.3156i | −0.305319 | + | 0.528828i | ||||
\(635\) | −0.430596 | − | 0.745814i | −0.0170877 | − | 0.0295967i | ||||
\(636\) | −50.3930 | −1.99821 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.68769 | −0.185588 | ||||||||
\(639\) | −0.518126 | − | 0.897420i | −0.0204967 | − | 0.0355014i | ||||
\(640\) | 0.248611 | − | 0.430607i | 0.00982721 | − | 0.0170212i | ||||
\(641\) | −16.5124 | + | 28.6003i | −0.652200 | + | 1.12964i | 0.330387 | + | 0.943845i | \(0.392821\pi\) |
−0.982588 | + | 0.185799i | \(0.940513\pi\) | |||||||
\(642\) | −24.0131 | − | 41.5920i | −0.947723 | − | 1.64150i | ||||
\(643\) | −15.7942 | −0.622863 | −0.311432 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311432 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.0362 | −0.592051 | ||||||||
\(646\) | 15.6760 | + | 27.1516i | 0.616764 | + | 1.06827i | ||||
\(647\) | −2.32036 | + | 4.01898i | −0.0912227 | + | 0.158002i | −0.908026 | − | 0.418914i | \(-0.862411\pi\) |
0.816803 | + | 0.576916i | \(0.195744\pi\) | |||||||
\(648\) | −0.318246 | + | 0.551219i | −0.0125019 | + | 0.0216539i | ||||
\(649\) | 0.256587 | + | 0.444421i | 0.0100719 | + | 0.0174451i | ||||
\(650\) | −8.39497 | −0.329278 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.43757 | 0.134626 | ||||||||
\(653\) | −13.4143 | − | 23.2342i | −0.524941 | − | 0.909225i | −0.999578 | − | 0.0290430i | \(-0.990754\pi\) |
0.474637 | − | 0.880182i | \(-0.342579\pi\) | |||||||
\(654\) | 24.2456 | − | 41.9946i | 0.948079 | − | 1.64212i | ||||
\(655\) | 8.52266 | − | 14.7617i | 0.333008 | − | 0.576787i | ||||
\(656\) | −9.67230 | − | 16.7529i | −0.377640 | − | 0.654092i | ||||
\(657\) | 0.327429 | 0.0127742 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.9889 | −1.67461 | −0.837306 | − | 0.546735i | \(-0.815871\pi\) | ||||
−0.837306 | + | 0.546735i | \(0.815871\pi\) | |||||||
\(660\) | −1.16082 | − | 2.01059i | −0.0451847 | − | 0.0782623i | ||||
\(661\) | −14.7349 | + | 25.5216i | −0.573122 | + | 0.992676i | 0.423121 | + | 0.906073i | \(0.360934\pi\) |
−0.996243 | + | 0.0866030i | \(0.972399\pi\) | |||||||
\(662\) | 11.3915 | − | 19.7307i | 0.442744 | − | 0.766855i | ||||
\(663\) | 2.06889 | + | 3.58342i | 0.0803490 | + | 0.139169i | ||||
\(664\) | 0.243015 | 0.00943082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.986346 | −0.0382201 | ||||||||
\(667\) | −6.12349 | − | 10.6062i | −0.237102 | − | 0.410673i | ||||
\(668\) | −22.2403 | + | 38.5214i | −0.860504 | + | 1.49044i | ||||
\(669\) | −15.5104 | + | 26.8647i | −0.599666 | + | 1.03865i | ||||
\(670\) | −8.54256 | − | 14.7962i | −0.330028 | − | 0.571625i | ||||
\(671\) | 8.34752 | 0.322252 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1702 | −0.777504 | −0.388752 | − | 0.921342i | \(-0.627094\pi\) | ||||
−0.388752 | + | 0.921342i | \(0.627094\pi\) | |||||||
\(674\) | 1.74891 | + | 3.02920i | 0.0673655 | + | 0.116680i | ||||
\(675\) | 10.6818 | − | 18.5015i | 0.411144 | − | 0.712122i | ||||
\(676\) | −1.01709 | + | 1.76164i | −0.0391187 | + | 0.0677555i | ||||
\(677\) | −3.10241 | − | 5.37353i | −0.119235 | − | 0.206521i | 0.800230 | − | 0.599694i | \(-0.204711\pi\) |
−0.919465 | + | 0.393172i | \(0.871378\pi\) | |||||||
\(678\) | −11.5108 | −0.442071 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.146221 | −0.00560733 | ||||||||
\(681\) | 4.68704 | + | 8.11820i | 0.179608 | + | 0.311090i | ||||
\(682\) | −1.12984 | + | 1.95694i | −0.0432638 | + | 0.0749351i | ||||
\(683\) | 0.884758 | − | 1.53245i | 0.0338543 | − | 0.0586374i | −0.848602 | − | 0.529032i | \(-0.822555\pi\) |
0.882456 | + | 0.470395i | \(0.155888\pi\) | |||||||
\(684\) | 0.636312 | + | 1.10212i | 0.0243300 | + | 0.0421408i | ||||
\(685\) | −5.59899 | −0.213926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9854 | −0.571729 | ||||||||
\(688\) | −18.5473 | − | 32.1249i | −0.707110 | − | 1.22475i | ||||
\(689\) | 7.04163 | − | 12.1965i | 0.268265 | − | 0.464648i | ||||
\(690\) | 6.01451 | − | 10.4174i | 0.228969 | − | 0.396585i | ||||
\(691\) | 22.4658 | + | 38.9120i | 0.854641 | + | 1.48028i | 0.876977 | + | 0.480531i | \(0.159556\pi\) |
−0.0223363 | + | 0.999751i | \(0.507110\pi\) | |||||||
\(692\) | −11.8820 | −0.451688 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.2800 | −1.60493 | ||||||||
\(695\) | 1.81144 | + | 3.13751i | 0.0687120 | + | 0.119013i | ||||
\(696\) | −0.196666 | + | 0.340635i | −0.00745459 | + | 0.0129117i | ||||
\(697\) | −5.78856 | + | 10.0261i | −0.219257 | + | 0.379765i | ||||
\(698\) | 8.39162 | + | 14.5347i | 0.317628 | + | 0.550147i | ||||
\(699\) | −8.36204 | −0.316281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.5707 | 1.45679 | 0.728397 | − | 0.685156i | \(-0.240266\pi\) | ||||
0.728397 | + | 0.685156i | \(0.240266\pi\) | |||||||
\(702\) | −5.13311 | − | 8.89081i | −0.193737 | − | 0.335562i | ||||
\(703\) | 17.2827 | − | 29.9344i | 0.651828 | − | 1.12900i | ||||
\(704\) | 2.96251 | − | 5.13121i | 0.111654 | − | 0.193390i | ||||
\(705\) | −6.62767 | − | 11.4795i | −0.249612 | − | 0.432341i | ||||
\(706\) | −17.1398 | −0.645066 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.56330 | 0.0963346 | ||||||||
\(709\) | −4.38866 | − | 7.60137i | −0.164819 | − | 0.285476i | 0.771772 | − | 0.635900i | \(-0.219371\pi\) |
−0.936591 | + | 0.350424i | \(0.886037\pi\) | |||||||
\(710\) | −9.99758 | + | 17.3163i | −0.375203 | + | 0.649870i | ||||
\(711\) | −0.613194 | + | 1.06208i | −0.0229966 | + | 0.0398312i | ||||
\(712\) | −0.413512 | − | 0.716223i | −0.0154970 | − | 0.0268416i | ||||
\(713\) | −5.90360 | −0.221091 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.648824 | 0.0242646 | ||||||||
\(716\) | −2.57757 | − | 4.46449i | −0.0963284 | − | 0.166846i | ||||
\(717\) | 13.0447 | − | 22.5940i | 0.487161 | − | 0.843788i | ||||
\(718\) | −16.2402 | + | 28.1289i | −0.606080 | + | 1.04976i | ||||
\(719\) | 2.10218 | + | 3.64109i | 0.0783982 | + | 0.135790i | 0.902559 | − | 0.430566i | \(-0.141686\pi\) |
−0.824161 | + | 0.566356i | \(0.808353\pi\) | |||||||
\(720\) | 0.335625 | 0.0125080 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −50.2840 | −1.87138 | ||||||||
\(723\) | 5.38386 | + | 9.32513i | 0.200228 | + | 0.346805i | ||||
\(724\) | −10.9080 | + | 18.8933i | −0.405394 | + | 0.702164i | ||||
\(725\) | 6.80866 | − | 11.7930i | 0.252867 | − | 0.437979i | ||||
\(726\) | 18.5255 | + | 32.0872i | 0.687547 | + | 1.19087i | ||||
\(727\) | 28.9856 | 1.07502 | 0.537509 | − | 0.843258i | \(-0.319366\pi\) | ||||
0.537509 | + | 0.843258i | \(0.319366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0990 | 0.966630 | ||||||||
\(730\) | −3.15898 | − | 5.47151i | −0.116919 | − | 0.202510i | ||||
\(731\) | −11.1000 | + | 19.2257i | −0.410547 | + | 0.711089i | ||||
\(732\) | 20.8479 | − | 36.1096i | 0.770561 | − | 1.33465i | ||||
\(733\) | −12.0172 | − | 20.8145i | −0.443867 | − | 0.768800i | 0.554106 | − | 0.832446i | \(-0.313060\pi\) |
−0.997972 | + | 0.0636467i | \(0.979727\pi\) | |||||||
\(734\) | 56.5480 | 2.08722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.1918 | 1.11288 | ||||||||
\(737\) | −3.36394 | − | 5.82652i | −0.123912 | − | 0.214622i | ||||
\(738\) | −0.465985 | + | 0.807110i | −0.0171532 | + | 0.0297101i | ||||
\(739\) | −5.90276 | + | 10.2239i | −0.217136 | + | 0.376091i | −0.953931 | − | 0.300025i | \(-0.903005\pi\) |
0.736795 | + | 0.676116i | \(0.236338\pi\) | |||||||
\(740\) | 4.79835 | + | 8.31099i | 0.176391 | + | 0.305518i | ||||
\(741\) | −11.6729 | −0.428816 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.2786 | 1.73448 | 0.867241 | − | 0.497888i | \(-0.165891\pi\) | ||||
0.867241 | + | 0.497888i | \(0.165891\pi\) | |||||||
\(744\) | 0.0948017 | + | 0.164201i | 0.00347560 | + | 0.00601992i | ||||
\(745\) | −9.54499 | + | 16.5324i | −0.349701 | + | 0.605700i | ||||
\(746\) | −28.6252 | + | 49.5802i | −1.04804 | + | 1.81526i | ||||
\(747\) | 0.166912 | + | 0.289100i | 0.00610698 | + | 0.0105776i | ||||
\(748\) | −3.42773 | −0.125330 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 29.3750 | 1.07262 | ||||||||
\(751\) | −2.73850 | − | 4.74322i | −0.0999294 | − | 0.173083i | 0.811726 | − | 0.584039i | \(-0.198528\pi\) |
−0.911655 | + | 0.410956i | \(0.865195\pi\) | |||||||
\(752\) | 16.3506 | − | 28.3200i | 0.596244 | − | 1.03273i | ||||
\(753\) | 12.2877 | − | 21.2830i | 0.447790 | − | 0.775596i | ||||
\(754\) | −3.27188 | − | 5.66706i | −0.119155 | − | 0.206382i | ||||
\(755\) | 14.2410 | 0.518285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7453 | 0.390546 | 0.195273 | − | 0.980749i | \(-0.437441\pi\) | ||||
0.195273 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(758\) | −7.29358 | − | 12.6329i | −0.264915 | − | 0.458846i | ||||
\(759\) | 2.36843 | − | 4.10224i | 0.0859686 | − | 0.148902i | ||||
\(760\) | 0.206250 | − | 0.357236i | 0.00748148 | − | 0.0129583i | ||||
\(761\) | −16.5200 | − | 28.6134i | −0.598848 | − | 1.03724i | −0.992991 | − | 0.118186i | \(-0.962292\pi\) |
0.394143 | − | 0.919049i | \(-0.371041\pi\) | |||||||
\(762\) | −3.35940 | −0.121698 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.41457 | −0.123535 | ||||||||
\(765\) | −0.100430 | − | 0.173950i | −0.00363106 | − | 0.00628918i | ||||
\(766\) | −12.9877 | + | 22.4953i | −0.469263 | + | 0.812788i | ||||
\(767\) | −0.358181 | + | 0.620387i | −0.0129332 | + | 0.0224009i | ||||
\(768\) | 13.5793 | + | 23.5201i | 0.490002 | + | 0.848708i | ||||
\(769\) | −2.98332 | −0.107581 | −0.0537907 | − | 0.998552i | \(-0.517130\pi\) | ||||
−0.0537907 | + | 0.998552i | \(0.517130\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.3702 | 1.09376 | ||||||||
\(772\) | 6.55833 | + | 11.3594i | 0.236039 | + | 0.408832i | ||||
\(773\) | −10.9543 | + | 18.9733i | −0.393998 | + | 0.682424i | −0.992973 | − | 0.118344i | \(-0.962242\pi\) |
0.598975 | + | 0.800768i | \(0.295575\pi\) | |||||||
\(774\) | −0.893560 | + | 1.54769i | −0.0321184 | + | 0.0556306i | ||||
\(775\) | −3.28208 | − | 5.68473i | −0.117896 | − | 0.204202i | ||||
\(776\) | 0.510464 | 0.0183246 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42.4516 | 1.52196 | ||||||||
\(779\) | −16.3299 | − | 28.2842i | −0.585079 | − | 1.01339i | ||||
\(780\) | 1.62044 | − | 2.80668i | 0.0580209 | − | 0.100495i | ||||
\(781\) | −3.93691 | + | 6.81892i | −0.140874 | + | 0.244000i | ||||
\(782\) | −8.88001 | − | 15.3806i | −0.317548 | − | 0.550010i | ||||
\(783\) | 16.6527 | 0.595118 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.05104 | −0.251662 | ||||||||
\(786\) | −33.2458 | − | 57.5835i | −1.18584 | − | 2.05393i | ||||
\(787\) | −6.68161 | + | 11.5729i | −0.238174 | + | 0.412529i | −0.960190 | − | 0.279347i | \(-0.909882\pi\) |
0.722017 | + | 0.691876i | \(0.243215\pi\) | |||||||
\(788\) | −1.90450 | + | 3.29869i | −0.0678451 | + | 0.117511i | ||||
\(789\) | −2.29269 | − | 3.97105i | −0.0816218 | − | 0.141373i | ||||
\(790\) | 23.6640 | 0.841927 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.00463525 | −0.000164706 | ||||||||
\(793\) | 5.82633 | + | 10.0915i | 0.206899 | + | 0.358360i | ||||
\(794\) | −19.2892 | + | 33.4099i | −0.684548 | + | 1.18567i | ||||
\(795\) | −11.2188 | + | 19.4316i | −0.397891 | + | 0.689167i | ||||
\(796\) | −11.5914 | − | 20.0768i | −0.410845 | − | 0.711605i | ||||
\(797\) | −32.5388 | −1.15258 | −0.576292 | − | 0.817244i | \(-0.695501\pi\) | ||||
−0.576292 | + | 0.817244i | \(0.695501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.5706 | −0.692357 | ||||||||
\(800\) | 16.7850 | + | 29.0725i | 0.593440 | + | 1.02787i | ||||
\(801\) | 0.568030 | − | 0.983857i | 0.0200703 | − | 0.0347629i | ||||
\(802\) | 16.7403 | − | 28.9950i | 0.591119 | − | 1.02385i | ||||
\(803\) | −1.24396 | − | 2.15460i | −0.0438984 | − | 0.0760343i | ||||
\(804\) | −33.6057 | −1.18518 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.15439 | −0.111109 | ||||||||
\(807\) | 12.7440 | + | 22.0732i | 0.448608 | + | 0.777013i | ||||
\(808\) | 0.0411469 | − | 0.0712685i | 0.00144754 | − | 0.00250722i | ||||
\(809\) | −3.84413 | + | 6.65824i | −0.135153 | + | 0.234091i | −0.925656 | − | 0.378367i | \(-0.876486\pi\) |
0.790503 | + | 0.612458i | \(0.209819\pi\) | |||||||
\(810\) | 8.43542 | + | 14.6106i | 0.296390 | + | 0.513363i | ||||
\(811\) | 48.3178 | 1.69667 | 0.848334 | − | 0.529461i | \(-0.177606\pi\) | ||||
0.848334 | + | 0.529461i | \(0.177606\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.1911 | −0.532773 | ||||||||
\(814\) | 3.74731 | + | 6.49052i | 0.131343 | + | 0.227493i | ||||
\(815\) | 0.765295 | − | 1.32553i | 0.0268071 | − | 0.0464313i | ||||
\(816\) | 8.13175 | − | 14.0846i | 0.284668 | − | 0.493060i | ||||
\(817\) | −31.3137 | − | 54.2370i | −1.09553 | − | 1.89751i | ||||
\(818\) | 24.8019 | 0.867178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.06766 | 0.316656 | ||||||||
\(821\) | 1.86721 | + | 3.23410i | 0.0651661 | + | 0.112871i | 0.896768 | − | 0.442502i | \(-0.145909\pi\) |
−0.831602 | + | 0.555373i | \(0.812576\pi\) | |||||||
\(822\) | −10.9205 | + | 18.9148i | −0.380895 | + | 0.659730i | ||||
\(823\) | −7.11590 | + | 12.3251i | −0.248045 | + | 0.429626i | −0.962983 | − | 0.269561i | \(-0.913121\pi\) |
0.714939 | + | 0.699187i | \(0.246455\pi\) | |||||||
\(824\) | 0.494575 | + | 0.856629i | 0.0172293 | + | 0.0298421i | ||||
\(825\) | 5.26688 | 0.183369 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.3016 | 1.67961 | 0.839805 | − | 0.542888i | \(-0.182669\pi\) | ||||
0.839805 | + | 0.542888i | \(0.182669\pi\) | |||||||
\(828\) | −0.360453 | − | 0.624323i | −0.0125266 | − | 0.0216967i | ||||
\(829\) | 5.75506 | − | 9.96806i | 0.199882 | − | 0.346205i | −0.748608 | − | 0.663013i | \(-0.769278\pi\) |
0.948490 | + | 0.316808i | \(0.102611\pi\) | |||||||
\(830\) | 3.22067 | − | 5.57837i | 0.111791 | − | 0.193628i | ||||
\(831\) | 10.7540 | + | 18.6264i | 0.373051 | + | 0.646143i | ||||
\(832\) | 8.27099 | 0.286745 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.1324 | 0.489366 | ||||||||
\(835\) | 9.90258 | + | 17.1518i | 0.342693 | + | 0.593562i | ||||
\(836\) | 4.83493 | − | 8.37434i | 0.167219 | − | 0.289633i | ||||
\(837\) | 4.01367 | − | 6.95188i | 0.138733 | − | 0.240292i | ||||
\(838\) | −4.37792 | − | 7.58278i | −0.151233 | − | 0.261943i | ||||
\(839\) | −13.1103 | −0.452616 | −0.226308 | − | 0.974056i | \(-0.572666\pi\) | ||||
−0.226308 | + | 0.974056i | \(0.572666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3855 | −0.633982 | ||||||||
\(842\) | −10.0426 | − | 17.3943i | −0.346092 | − | 0.599448i | ||||
\(843\) | −21.2689 | + | 36.8388i | −0.732539 | + | 1.26880i | ||||
\(844\) | −7.66475 | + | 13.2757i | −0.263831 | + | 0.456969i | ||||
\(845\) | 0.452861 | + | 0.784378i | 0.0155789 | + | 0.0269834i | ||||
\(846\) | −1.57545 | −0.0541652 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −55.3541 | −1.90087 | ||||||||
\(849\) | 27.0616 | + | 46.8721i | 0.928751 | + | 1.60864i | ||||
\(850\) | 9.87362 | − | 17.1016i | 0.338662 | − | 0.586580i | ||||
\(851\) | −9.79014 | + | 16.9570i | −0.335602 | + | 0.581279i | ||||
\(852\) | 19.6648 | + | 34.0605i | 0.673706 | + | 1.16689i | ||||
\(853\) | −8.80346 | −0.301425 | −0.150712 | − | 0.988578i | \(-0.548157\pi\) | ||||
−0.150712 | + | 0.988578i | \(0.548157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.566640 | 0.0193787 | ||||||||
\(856\) | 0.466467 | + | 0.807945i | 0.0159435 | + | 0.0276150i | ||||
\(857\) | 8.48254 | − | 14.6922i | 0.289758 | − | 0.501876i | −0.683994 | − | 0.729488i | \(-0.739758\pi\) |
0.973752 | + | 0.227612i | \(0.0730918\pi\) | |||||||
\(858\) | 1.26549 | − | 2.19189i | 0.0432031 | − | 0.0748300i | ||||
\(859\) | 7.27049 | + | 12.5929i | 0.248066 | + | 0.429663i | 0.962989 | − | 0.269540i | \(-0.0868717\pi\) |
−0.714923 | + | 0.699203i | \(0.753538\pi\) | |||||||
\(860\) | 17.3879 | 0.592922 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.9243 | 1.59825 | ||||||||
\(863\) | −19.5222 | − | 33.8135i | −0.664544 | − | 1.15102i | −0.979409 | − | 0.201887i | \(-0.935293\pi\) |
0.314865 | − | 0.949136i | \(-0.398041\pi\) | |||||||
\(864\) | −20.5265 | + | 35.5529i | −0.698324 | + | 1.20953i | ||||
\(865\) | −2.64526 | + | 4.58173i | −0.0899416 | + | 0.155783i | ||||
\(866\) | 2.72441 | + | 4.71882i | 0.0925793 | + | 0.160352i | ||||
\(867\) | 20.1708 | 0.685036 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.31854 | 0.316110 | ||||||||
\(870\) | 5.21281 | + | 9.02885i | 0.176731 | + | 0.306107i | ||||
\(871\) | 4.69587 | − | 8.13349i | 0.159114 | − | 0.275593i | ||||
\(872\) | −0.470983 | + | 0.815767i | −0.0159495 | + | 0.0276253i | ||||
\(873\) | 0.350605 | + | 0.607266i | 0.0118662 | + | 0.0205529i | ||||
\(874\) | 50.1022 | 1.69473 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4272 | −0.419875 | ||||||||
\(877\) | −16.2971 | − | 28.2273i | −0.550312 | − | 0.953169i | −0.998252 | − | 0.0591051i | \(-0.981175\pi\) |
0.447939 | − | 0.894064i | \(-0.352158\pi\) | |||||||
\(878\) | 8.87285 | − | 15.3682i | 0.299444 | − | 0.518652i | ||||
\(879\) | 27.9949 | − | 48.4886i | 0.944245 | − | 1.63548i | ||||
\(880\) | −1.27510 | − | 2.20853i | −0.0429835 | − | 0.0744497i | ||||
\(881\) | 43.4141 | 1.46266 | 0.731330 | − | 0.682024i | \(-0.238900\pi\) | ||||
0.731330 | + | 0.682024i | \(0.238900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2902 | 0.952040 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(884\) | −2.39246 | − | 4.14386i | −0.0804672 | − | 0.139373i | ||||
\(885\) | 0.570659 | − | 0.988410i | 0.0191825 | − | 0.0332250i | ||||
\(886\) | −2.91796 | + | 5.05406i | −0.0980308 | + | 0.169794i | ||||
\(887\) | −25.1325 | − | 43.5307i | −0.843866 | − | 1.46162i | −0.886602 | − | 0.462532i | \(-0.846941\pi\) |
0.0427364 | − | 0.999086i | \(-0.486392\pi\) | |||||||
\(888\) | 0.628852 | 0.0211029 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −21.9210 | −0.734794 | ||||||||
\(891\) | 3.32175 | + | 5.75344i | 0.111283 | + | 0.192747i | ||||
\(892\) | 17.9362 | − | 31.0664i | 0.600548 | − | 1.04018i | ||||
\(893\) | 27.6049 | − | 47.8131i | 0.923764 | − | 1.60001i | ||||
\(894\) | 37.2338 | + | 64.4908i | 1.24528 | + | 2.15690i | ||||
\(895\) | −2.29535 | −0.0767250 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.61239 | 0.220781 | ||||||||
\(898\) | −15.3428 | − | 26.5745i | −0.511996 | − | 0.886803i | ||||
\(899\) | 2.55834 | − | 4.43117i | 0.0853253 | − | 0.147788i | ||||
\(900\) | 0.400785 | − | 0.694180i | 0.0133595 | − | 0.0231393i | ||||
\(901\) | 16.5638 | + | 28.6894i | 0.551821 | + | 0.955782i | ||||
\(902\) | 7.08145 | 0.235786 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.223604 | 0.00743695 | ||||||||
\(905\) | 4.85685 | + | 8.41231i | 0.161447 | + | 0.279635i | ||||
\(906\) | 27.7763 | − | 48.1099i | 0.922805 | − | 1.59835i | ||||
\(907\) | −13.4138 | + | 23.2334i | −0.445399 | + | 0.771453i | −0.998080 | − | 0.0619394i | \(-0.980271\pi\) |
0.552681 | + | 0.833393i | \(0.313605\pi\) | |||||||
\(908\) | −5.42009 | − | 9.38787i | −0.179872 | − | 0.311548i | ||||
\(909\) | 0.113045 | 0.00374946 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.3560 | −0.740687 | −0.370344 | − | 0.928895i | \(-0.620760\pi\) | ||||
−0.370344 | + | 0.928895i | \(0.620760\pi\) | |||||||
\(912\) | 22.9402 | + | 39.7336i | 0.759626 | + | 1.31571i | ||||
\(913\) | 1.26826 | − | 2.19668i | 0.0419731 | − | 0.0726996i | ||||
\(914\) | 23.7608 | − | 41.1550i | 0.785939 | − | 1.36129i | ||||
\(915\) | −9.28260 | − | 16.0779i | −0.306873 | − | 0.531520i | ||||
\(916\) | 17.3291 | 0.572569 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.1489 | 0.797034 | ||||||||
\(919\) | 4.31122 | + | 7.46725i | 0.142214 | + | 0.246322i | 0.928330 | − | 0.371757i | \(-0.121245\pi\) |
−0.786116 | + | 0.618079i | \(0.787911\pi\) | |||||||
\(920\) | −0.116835 | + | 0.202364i | −0.00385193 | + | 0.00667174i | ||||
\(921\) | −25.3202 | + | 43.8559i | −0.834329 | + | 1.44510i | ||||
\(922\) | 26.7305 | + | 46.2985i | 0.880321 | + | 1.52476i | ||||
\(923\) | −10.9914 | −0.361786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7712 | −0.715832 | ||||||||
\(926\) | −1.44865 | − | 2.50913i | −0.0476054 | − | 0.0824550i | ||||
\(927\) | −0.679385 | + | 1.17673i | −0.0223139 | + | 0.0386488i | ||||
\(928\) | −13.0837 | + | 22.6616i | −0.429493 | + | 0.743904i | ||||
\(929\) | 20.6930 | + | 35.8414i | 0.678916 | + | 1.17592i | 0.975308 | + | 0.220851i | \(0.0708834\pi\) |
−0.296391 | + | 0.955067i | \(0.595783\pi\) | |||||||
\(930\) | 5.02562 | 0.164796 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.66985 | 0.316747 | ||||||||
\(933\) | −4.85379 | − | 8.40700i | −0.158906 | − | 0.275233i | ||||
\(934\) | 8.42535 | − | 14.5931i | 0.275686 | − | 0.477502i | ||||
\(935\) | −0.763105 | + | 1.32174i | −0.0249562 | + | 0.0432254i | ||||
\(936\) | −0.00323527 | − | 0.00560366i | −0.000105748 | − | 0.000183161i | ||||
\(937\) | −21.3818 | −0.698514 | −0.349257 | − | 0.937027i | \(-0.613566\pi\) | ||||
−0.349257 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.52788 | −0.278297 | ||||||||
\(940\) | 7.66423 | + | 13.2748i | 0.249979 | + | 0.432977i | ||||
\(941\) | −26.5740 | + | 46.0275i | −0.866288 | + | 1.50046i | −0.000525658 | 1.00000i | \(0.500167\pi\) | |
−0.865762 | + | 0.500455i | \(0.833166\pi\) | |||||||
\(942\) | −13.7526 | + | 23.8202i | −0.448084 | + | 0.776105i | ||||
\(943\) | 9.25043 | + | 16.0222i | 0.301235 | + | 0.521755i | ||||
\(944\) | 2.81565 | 0.0916416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.5792 | 0.441497 | ||||||||
\(947\) | 4.43468 | + | 7.68109i | 0.144108 | + | 0.249602i | 0.929040 | − | 0.369980i | \(-0.120635\pi\) |
−0.784932 | + | 0.619582i | \(0.787302\pi\) | |||||||
\(948\) | 23.2730 | − | 40.3101i | 0.755873 | − | 1.30921i | ||||
\(949\) | 1.73650 | − | 3.00771i | 0.0563692 | − | 0.0976343i | ||||
\(950\) | 27.8541 | + | 48.2448i | 0.903707 | + | 1.56527i | ||||
\(951\) | 13.4658 | 0.436658 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.8167 | −1.28979 | −0.644894 | − | 0.764272i | \(-0.723099\pi\) | ||||
−0.644894 | + | 0.764272i | \(0.723099\pi\) | |||||||
\(954\) | 1.33341 | + | 2.30953i | 0.0431706 | + | 0.0747737i | ||||
\(955\) | −0.760174 | + | 1.31666i | −0.0245987 | + | 0.0426061i | ||||
\(956\) | −15.0848 | + | 26.1277i | −0.487878 | + | 0.845029i | ||||
\(957\) | 2.05273 | + | 3.55543i | 0.0663553 | + | 0.114931i | ||||
\(958\) | 25.3319 | 0.818435 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.1775 | −0.425301 | ||||||||
\(961\) | 14.2668 | + | 24.7108i | 0.460218 | + | 0.797121i | ||||
\(962\) | −5.23103 | + | 9.06041i | −0.168655 | + | 0.292119i | ||||
\(963\) | −0.640773 | + | 1.10985i | −0.0206486 | + | 0.0357645i | ||||
\(964\) | −6.22589 | − | 10.7836i | −0.200523 | − | 0.347315i | ||||
\(965\) | 5.84024 | 0.188004 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1611 | −0.712652 | −0.356326 | − | 0.934362i | \(-0.615971\pi\) | ||||
−0.356326 | + | 0.934362i | \(0.615971\pi\) | |||||||
\(968\) | −0.359868 | − | 0.623309i | −0.0115666 | − | 0.0200339i | ||||
\(969\) | 13.7290 | − | 23.7793i | 0.441038 | − | 0.763900i | ||||
\(970\) | 6.76516 | − | 11.7176i | 0.217216 | − | 0.376230i | ||||
\(971\) | 18.0212 | + | 31.2136i | 0.578327 | + | 1.00169i | 0.995671 | + | 0.0929428i | \(0.0296274\pi\) |
−0.417345 | + | 0.908748i | \(0.637039\pi\) | |||||||
\(972\) | 1.99229 | 0.0639027 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −43.3199 | −1.38806 | ||||||||
\(975\) | 3.67614 | + | 6.36725i | 0.117731 | + | 0.203915i | ||||
\(976\) | 22.9004 | − | 39.6646i | 0.733022 | − | 1.26963i | ||||
\(977\) | −16.4708 | + | 28.5283i | −0.526947 | + | 0.912700i | 0.472559 | + | 0.881299i | \(0.343330\pi\) |
−0.999507 | + | 0.0314009i | \(0.990003\pi\) | |||||||
\(978\) | −2.98532 | − | 5.17072i | −0.0954600 | − | 0.165342i | ||||
\(979\) | −8.63219 | −0.275886 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.29395 | −0.0413128 | ||||||||
\(982\) | 39.4019 | + | 68.2461i | 1.25736 | + | 2.17782i | ||||
\(983\) | −2.09973 | + | 3.63683i | −0.0669709 | + | 0.115997i | −0.897567 | − | 0.440879i | \(-0.854667\pi\) |
0.830596 | + | 0.556876i | \(0.188000\pi\) | |||||||
\(984\) | 0.297092 | − | 0.514579i | 0.00947096 | − | 0.0164042i | ||||
\(985\) | 0.847986 | + | 1.46876i | 0.0270191 | + | 0.0467984i | ||||
\(986\) | 15.3927 | 0.490203 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.4986 | 0.429447 | ||||||||
\(989\) | 17.7383 | + | 30.7237i | 0.564047 | + | 0.976958i | ||||
\(990\) | −0.0614308 | + | 0.106401i | −0.00195240 | + | 0.00338165i | ||||
\(991\) | 6.70693 | − | 11.6167i | 0.213053 | − | 0.369018i | −0.739616 | − | 0.673029i | \(-0.764993\pi\) |
0.952668 | + | 0.304011i | \(0.0983261\pi\) | |||||||
\(992\) | 6.30693 | + | 10.9239i | 0.200245 | + | 0.346835i | ||||
\(993\) | −19.9533 | −0.633198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3222 | −0.327236 | ||||||||
\(996\) | −6.33493 | − | 10.9724i | −0.200730 | − | 0.347675i | ||||
\(997\) | −23.9434 | + | 41.4712i | −0.758295 | + | 1.31341i | 0.185424 | + | 0.982659i | \(0.440634\pi\) |
−0.943719 | + | 0.330747i | \(0.892699\pi\) | |||||||
\(998\) | 9.20722 | − | 15.9474i | 0.291449 | − | 0.504805i | ||||
\(999\) | −13.3120 | − | 23.0571i | −0.421173 | − | 0.729494i |
(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 | 637.2.e.m.508.5 | 10 | ||
7.2 | even | 3 | inner | 637.2.e.m.79.5 | 10 | ||
7.3 | odd | 6 | 637.2.a.l.1.1 | 5 | |||
7.4 | even | 3 | 637.2.a.k.1.1 | 5 | |||
7.5 | odd | 6 | 91.2.e.c.79.5 | yes | 10 | ||
7.6 | odd | 2 | 91.2.e.c.53.5 | ✓ | 10 | ||
21.5 | even | 6 | 819.2.j.h.352.1 | 10 | |||
21.11 | odd | 6 | 5733.2.a.bm.1.5 | 5 | |||
21.17 | even | 6 | 5733.2.a.bl.1.5 | 5 | |||
21.20 | even | 2 | 819.2.j.h.235.1 | 10 | |||
28.19 | even | 6 | 1456.2.r.p.625.4 | 10 | |||
28.27 | even | 2 | 1456.2.r.p.417.4 | 10 | |||
91.12 | odd | 6 | 1183.2.e.f.170.1 | 10 | |||
91.25 | even | 6 | 8281.2.a.bx.1.5 | 5 | |||
91.38 | odd | 6 | 8281.2.a.bw.1.5 | 5 | |||
91.90 | odd | 2 | 1183.2.e.f.508.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.5 | ✓ | 10 | 7.6 | odd | 2 | ||
91.2.e.c.79.5 | yes | 10 | 7.5 | odd | 6 | ||
637.2.a.k.1.1 | 5 | 7.4 | even | 3 | |||
637.2.a.l.1.1 | 5 | 7.3 | odd | 6 | |||
637.2.e.m.79.5 | 10 | 7.2 | even | 3 | inner | ||
637.2.e.m.508.5 | 10 | 1.1 | even | 1 | trivial | ||
819.2.j.h.235.1 | 10 | 21.20 | even | 2 | |||
819.2.j.h.352.1 | 10 | 21.5 | even | 6 | |||
1183.2.e.f.170.1 | 10 | 91.12 | odd | 6 | |||
1183.2.e.f.508.1 | 10 | 91.90 | odd | 2 | |||
1456.2.r.p.417.4 | 10 | 28.27 | even | 2 | |||
1456.2.r.p.625.4 | 10 | 28.19 | even | 6 | |||
5733.2.a.bl.1.5 | 5 | 21.17 | even | 6 | |||
5733.2.a.bm.1.5 | 5 | 21.11 | odd | 6 | |||
8281.2.a.bw.1.5 | 5 | 91.38 | odd | 6 | |||
8281.2.a.bx.1.5 | 5 | 91.25 | even | 6 |