Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.2 | ||
Root | \(-1.07992 - 0.623490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.316 |
Dual form | 507.2.j.h.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07992 | − | 0.623490i | −0.763616 | − | 0.440874i | 0.0669766 | − | 0.997755i | \(-0.478665\pi\) |
−0.830593 | + | 0.556881i | \(0.811998\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.222521 | − | 0.385418i | −0.111260 | − | 0.192709i | ||||
\(5\) | − | 2.80194i | − | 1.25306i | −0.779395 | − | 0.626532i | \(-0.784474\pi\) | ||
0.779395 | − | 0.626532i | \(-0.215526\pi\) | |||||||
\(6\) | 1.07992 | − | 0.623490i | 0.440874 | − | 0.254539i | ||||
\(7\) | 4.15860 | − | 2.40097i | 1.57180 | − | 0.907481i | 0.575855 | − | 0.817552i | \(-0.304669\pi\) |
0.995948 | − | 0.0899290i | \(-0.0286640\pi\) | |||||||
\(8\) | 3.04892i | 1.07796i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.74698 | + | 3.02586i | −0.552443 | + | 0.956860i | ||||
\(11\) | 1.27030 | + | 0.733406i | 0.383009 | + | 0.221130i | 0.679127 | − | 0.734021i | \(-0.262359\pi\) |
−0.296118 | + | 0.955151i | \(0.595692\pi\) | |||||||
\(12\) | 0.445042 | 0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.98792 | −1.60034 | ||||||||
\(15\) | 2.42655 | + | 1.40097i | 0.626532 | + | 0.361729i | ||||
\(16\) | 1.45593 | − | 2.52174i | 0.363982 | − | 0.630435i | ||||
\(17\) | −1.22252 | − | 2.11747i | −0.296505 | − | 0.513562i | 0.678829 | − | 0.734296i | \(-0.262488\pi\) |
−0.975334 | + | 0.220735i | \(0.929154\pi\) | |||||||
\(18\) | 1.24698i | 0.293916i | ||||||||
\(19\) | 2.20220 | − | 1.27144i | 0.505218 | − | 0.291688i | −0.225648 | − | 0.974209i | \(-0.572450\pi\) |
0.730866 | + | 0.682521i | \(0.239116\pi\) | |||||||
\(20\) | −1.07992 | + | 0.623490i | −0.241477 | + | 0.139417i | ||||
\(21\) | 4.80194i | 1.04787i | ||||||||
\(22\) | −0.914542 | − | 1.58403i | −0.194981 | − | 0.337717i | ||||
\(23\) | −1.75786 | + | 3.04471i | −0.366540 | + | 0.634866i | −0.989022 | − | 0.147768i | \(-0.952791\pi\) |
0.622482 | + | 0.782634i | \(0.286124\pi\) | |||||||
\(24\) | −2.64044 | − | 1.52446i | −0.538978 | − | 0.311179i | ||||
\(25\) | −2.85086 | −0.570171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.85075 | − | 1.06853i | −0.349759 | − | 0.201934i | ||||
\(29\) | −0.925428 | + | 1.60289i | −0.171848 | + | 0.297649i | −0.939066 | − | 0.343737i | \(-0.888307\pi\) |
0.767218 | + | 0.641386i | \(0.221640\pi\) | |||||||
\(30\) | −1.74698 | − | 3.02586i | −0.318953 | − | 0.552443i | ||||
\(31\) | − | 7.63102i | − | 1.37057i | −0.728274 | − | 0.685286i | \(-0.759677\pi\) | ||
0.728274 | − | 0.685286i | \(-0.240323\pi\) | |||||||
\(32\) | 2.13632 | − | 1.23341i | 0.377652 | − | 0.218037i | ||||
\(33\) | −1.27030 | + | 0.733406i | −0.221130 | + | 0.127670i | ||||
\(34\) | 3.04892i | 0.522885i | ||||||||
\(35\) | −6.72737 | − | 11.6521i | −1.13713 | − | 1.96957i | ||||
\(36\) | −0.222521 | + | 0.385418i | −0.0370868 | + | 0.0642363i | ||||
\(37\) | −3.94471 | − | 2.27748i | −0.648506 | − | 0.374415i | 0.139377 | − | 0.990239i | \(-0.455490\pi\) |
−0.787884 | + | 0.615824i | \(0.788823\pi\) | |||||||
\(38\) | −3.17092 | −0.514390 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.54288 | 1.35075 | ||||||||
\(41\) | −1.07992 | − | 0.623490i | −0.168655 | − | 0.0973727i | 0.413297 | − | 0.910596i | \(-0.364377\pi\) |
−0.581951 | + | 0.813224i | \(0.697711\pi\) | |||||||
\(42\) | 2.99396 | − | 5.18569i | 0.461978 | − | 0.800169i | ||||
\(43\) | 1.19202 | + | 2.06464i | 0.181782 | + | 0.314855i | 0.942487 | − | 0.334242i | \(-0.108480\pi\) |
−0.760706 | + | 0.649097i | \(0.775147\pi\) | |||||||
\(44\) | − | 0.652793i | − | 0.0984122i | ||||||
\(45\) | −2.42655 | + | 1.40097i | −0.361729 | + | 0.208844i | ||||
\(46\) | 3.79669 | − | 2.19202i | 0.559792 | − | 0.323196i | ||||
\(47\) | − | 12.8170i | − | 1.86955i | −0.355238 | − | 0.934776i | \(-0.615600\pi\) | ||
0.355238 | − | 0.934776i | \(-0.384400\pi\) | |||||||
\(48\) | 1.45593 | + | 2.52174i | 0.210145 | + | 0.363982i | ||||
\(49\) | 8.02930 | − | 13.9072i | 1.14704 | − | 1.98674i | ||||
\(50\) | 3.07868 | + | 1.77748i | 0.435392 | + | 0.251374i | ||||
\(51\) | 2.44504 | 0.342374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.85086 | −1.21576 | −0.607879 | − | 0.794030i | \(-0.707980\pi\) | ||||
−0.607879 | + | 0.794030i | \(0.707980\pi\) | |||||||
\(54\) | −1.07992 | − | 0.623490i | −0.146958 | − | 0.0848462i | ||||
\(55\) | 2.05496 | − | 3.55929i | 0.277090 | − | 0.479935i | ||||
\(56\) | 7.32036 | + | 12.6792i | 0.978224 | + | 1.69433i | ||||
\(57\) | 2.54288i | 0.336812i | ||||||||
\(58\) | 1.99877 | − | 1.15399i | 0.262451 | − | 0.151526i | ||||
\(59\) | −1.88472 | + | 1.08815i | −0.245370 | + | 0.141665i | −0.617642 | − | 0.786459i | \(-0.711912\pi\) |
0.372272 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(60\) | − | 1.24698i | − | 0.160984i | ||||||
\(61\) | 3.91454 | + | 6.78019i | 0.501206 | + | 0.868114i | 0.999999 | + | 0.00139289i | \(0.000443372\pi\) |
−0.498793 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(62\) | −4.75786 | + | 8.24086i | −0.604249 | + | 1.04659i | ||||
\(63\) | −4.15860 | − | 2.40097i | −0.523934 | − | 0.302494i | ||||
\(64\) | −8.89977 | −1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.82908 | 0.225145 | ||||||||
\(67\) | 3.10219 | + | 1.79105i | 0.378993 | + | 0.218812i | 0.677380 | − | 0.735633i | \(-0.263115\pi\) |
−0.298387 | + | 0.954445i | \(0.596449\pi\) | |||||||
\(68\) | −0.544073 | + | 0.942362i | −0.0659785 | + | 0.114278i | ||||
\(69\) | −1.75786 | − | 3.04471i | −0.211622 | − | 0.366540i | ||||
\(70\) | 16.7778i | 2.00533i | ||||||||
\(71\) | −7.65460 | + | 4.41939i | −0.908434 | + | 0.524485i | −0.879927 | − | 0.475109i | \(-0.842409\pi\) |
−0.0285072 | + | 0.999594i | \(0.509075\pi\) | |||||||
\(72\) | 2.64044 | − | 1.52446i | 0.311179 | − | 0.179659i | ||||
\(73\) | 7.69202i | 0.900283i | 0.892957 | + | 0.450142i | \(0.148626\pi\) | ||||
−0.892957 | + | 0.450142i | \(0.851374\pi\) | |||||||
\(74\) | 2.83997 | + | 4.91897i | 0.330140 | + | 0.571819i | ||||
\(75\) | 1.42543 | − | 2.46891i | 0.164594 | − | 0.285086i | ||||
\(76\) | −0.980069 | − | 0.565843i | −0.112422 | − | 0.0649067i | ||||
\(77\) | 7.04354 | 0.802686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.02177 | −0.452485 | −0.226242 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226242 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(80\) | −7.06576 | − | 4.07942i | −0.789976 | − | 0.456093i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.777479 | + | 1.34663i | 0.0858582 | + | 0.148711i | ||||
\(83\) | − | 0.652793i | − | 0.0716533i | −0.999358 | − | 0.0358267i | \(-0.988594\pi\) | ||
0.999358 | − | 0.0358267i | \(-0.0114064\pi\) | |||||||
\(84\) | 1.85075 | − | 1.06853i | 0.201934 | − | 0.116586i | ||||
\(85\) | −5.93301 | + | 3.42543i | −0.643526 | + | 0.371540i | ||||
\(86\) | − | 2.97285i | − | 0.320571i | ||||||
\(87\) | −0.925428 | − | 1.60289i | −0.0992162 | − | 0.171848i | ||||
\(88\) | −2.23609 | + | 3.87303i | −0.238368 | + | 0.412866i | ||||
\(89\) | 5.45241 | + | 3.14795i | 0.577954 | + | 0.333682i | 0.760320 | − | 0.649549i | \(-0.225042\pi\) |
−0.182366 | + | 0.983231i | \(0.558376\pi\) | |||||||
\(90\) | 3.49396 | 0.368296 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.56465 | 0.163126 | ||||||||
\(93\) | 6.60866 | + | 3.81551i | 0.685286 | + | 0.395650i | ||||
\(94\) | −7.99127 | + | 13.8413i | −0.824237 | + | 1.42762i | ||||
\(95\) | −3.56249 | − | 6.17042i | −0.365504 | − | 0.633071i | ||||
\(96\) | 2.46681i | 0.251768i | ||||||||
\(97\) | −8.68750 | + | 5.01573i | −0.882082 | + | 0.509270i | −0.871344 | − | 0.490672i | \(-0.836751\pi\) |
−0.0107376 | + | 0.999942i | \(0.503418\pi\) | |||||||
\(98\) | −17.3419 | + | 10.0124i | −1.75180 | + | 1.01140i | ||||
\(99\) | − | 1.46681i | − | 0.147420i | ||||||
\(100\) | 0.634375 | + | 1.09877i | 0.0634375 | + | 0.109877i | ||||
\(101\) | 6.94385 | − | 12.0271i | 0.690938 | − | 1.19674i | −0.280592 | − | 0.959827i | \(-0.590531\pi\) |
0.971531 | − | 0.236913i | \(-0.0761358\pi\) | |||||||
\(102\) | −2.64044 | − | 1.52446i | −0.261443 | − | 0.150944i | ||||
\(103\) | 17.4034 | 1.71481 | 0.857405 | − | 0.514642i | \(-0.172075\pi\) | ||||
0.857405 | + | 0.514642i | \(0.172075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.4547 | 1.31305 | ||||||||
\(106\) | 9.55818 | + | 5.51842i | 0.928373 | + | 0.535996i | ||||
\(107\) | −5.27628 | + | 9.13879i | −0.510077 | + | 0.883480i | 0.489854 | + | 0.871804i | \(0.337050\pi\) |
−0.999932 | + | 0.0116758i | \(0.996283\pi\) | |||||||
\(108\) | −0.222521 | − | 0.385418i | −0.0214121 | − | 0.0370868i | ||||
\(109\) | 1.07069i | 0.102553i | 0.998684 | + | 0.0512766i | \(0.0163290\pi\) | ||||
−0.998684 | + | 0.0512766i | \(0.983671\pi\) | |||||||
\(110\) | −4.43836 | + | 2.56249i | −0.423181 | + | 0.244324i | ||||
\(111\) | 3.94471 | − | 2.27748i | 0.374415 | − | 0.216169i | ||||
\(112\) | − | 13.9825i | − | 1.32123i | ||||||
\(113\) | 8.26540 | + | 14.3161i | 0.777543 | + | 1.34674i | 0.933354 | + | 0.358957i | \(0.116868\pi\) |
−0.155811 | + | 0.987787i | \(0.549799\pi\) | |||||||
\(114\) | 1.58546 | − | 2.74609i | 0.148492 | − | 0.257195i | ||||
\(115\) | 8.53109 | + | 4.92543i | 0.795528 | + | 0.459298i | ||||
\(116\) | 0.823708 | 0.0764794 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.71379 | 0.249825 | ||||||||
\(119\) | −10.1680 | − | 5.87047i | −0.932095 | − | 0.538145i | ||||
\(120\) | −4.27144 | + | 7.39835i | −0.389927 | + | 0.675374i | ||||
\(121\) | −4.42423 | − | 7.66299i | −0.402203 | − | 0.696636i | ||||
\(122\) | − | 9.76271i | − | 0.883874i | ||||||
\(123\) | 1.07992 | − | 0.623490i | 0.0973727 | − | 0.0562182i | ||||
\(124\) | −2.94113 | + | 1.69806i | −0.264121 | + | 0.152490i | ||||
\(125\) | − | 6.02177i | − | 0.538604i | ||||||
\(126\) | 2.99396 | + | 5.18569i | 0.266723 | + | 0.461978i | ||||
\(127\) | −4.76875 | + | 8.25972i | −0.423158 | + | 0.732931i | −0.996246 | − | 0.0865622i | \(-0.972412\pi\) |
0.573088 | + | 0.819494i | \(0.305745\pi\) | |||||||
\(128\) | 5.33836 | + | 3.08211i | 0.471849 | + | 0.272422i | ||||
\(129\) | −2.38404 | −0.209903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.50902 | −0.481326 | −0.240663 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240663 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(132\) | 0.565335 | + | 0.326396i | 0.0492061 | + | 0.0284092i | ||||
\(133\) | 6.10537 | − | 10.5748i | 0.529402 | − | 0.916952i | ||||
\(134\) | −2.23341 | − | 3.86837i | −0.192937 | − | 0.334177i | ||||
\(135\) | − | 2.80194i | − | 0.241152i | ||||||
\(136\) | 6.45599 | − | 3.72737i | 0.553596 | − | 0.319619i | ||||
\(137\) | 14.0154 | − | 8.09179i | 1.19742 | − | 0.691329i | 0.237438 | − | 0.971403i | \(-0.423692\pi\) |
0.959978 | + | 0.280074i | \(0.0903590\pi\) | |||||||
\(138\) | 4.38404i | 0.373195i | ||||||||
\(139\) | 5.25451 | + | 9.10108i | 0.445682 | + | 0.771944i | 0.998099 | − | 0.0616238i | \(-0.0196279\pi\) |
−0.552418 | + | 0.833568i | \(0.686295\pi\) | |||||||
\(140\) | −2.99396 | + | 5.18569i | −0.253036 | + | 0.438271i | ||||
\(141\) | 11.0999 | + | 6.40850i | 0.934776 | + | 0.539693i | ||||
\(142\) | 11.0218 | 0.924926 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | 4.49119 | + | 2.59299i | 0.372973 | + | 0.215336i | ||||
\(146\) | 4.79590 | − | 8.30674i | 0.396911 | − | 0.687470i | ||||
\(147\) | 8.02930 | + | 13.9072i | 0.662246 | + | 1.14704i | ||||
\(148\) | 2.02715i | 0.166630i | ||||||||
\(149\) | 12.4276 | − | 7.17510i | 1.01811 | − | 0.587807i | 0.104555 | − | 0.994519i | \(-0.466658\pi\) |
0.913556 | + | 0.406712i | \(0.133325\pi\) | |||||||
\(150\) | −3.07868 | + | 1.77748i | −0.251374 | + | 0.145131i | ||||
\(151\) | − | 1.96615i | − | 0.160003i | −0.996795 | − | 0.0800014i | \(-0.974508\pi\) | ||
0.996795 | − | 0.0800014i | \(-0.0254925\pi\) | |||||||
\(152\) | 3.87651 | + | 6.71431i | 0.314426 | + | 0.544603i | ||||
\(153\) | −1.22252 | + | 2.11747i | −0.0988350 | + | 0.171187i | ||||
\(154\) | −7.60643 | − | 4.39158i | −0.612944 | − | 0.353883i | ||||
\(155\) | −21.3817 | −1.71742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7017 | 0.854089 | 0.427045 | − | 0.904231i | \(-0.359555\pi\) | ||||
0.427045 | + | 0.904231i | \(0.359555\pi\) | |||||||
\(158\) | 4.34317 | + | 2.50753i | 0.345524 | + | 0.199489i | ||||
\(159\) | 4.42543 | − | 7.66507i | 0.350959 | − | 0.607879i | ||||
\(160\) | −3.45593 | − | 5.98584i | −0.273215 | − | 0.473222i | ||||
\(161\) | 16.8823i | 1.33051i | ||||||||
\(162\) | 1.07992 | − | 0.623490i | 0.0848462 | − | 0.0489860i | ||||
\(163\) | −3.37730 | + | 1.94989i | −0.264531 | + | 0.152727i | −0.626400 | − | 0.779502i | \(-0.715472\pi\) |
0.361869 | + | 0.932229i | \(0.382139\pi\) | |||||||
\(164\) | 0.554958i | 0.0433349i | ||||||||
\(165\) | 2.05496 | + | 3.55929i | 0.159978 | + | 0.277090i | ||||
\(166\) | −0.407010 | + | 0.704961i | −0.0315901 | + | 0.0547156i | ||||
\(167\) | 18.2033 | + | 10.5097i | 1.40861 | + | 0.813264i | 0.995255 | − | 0.0973035i | \(-0.0310218\pi\) |
0.413360 | + | 0.910568i | \(0.364355\pi\) | |||||||
\(168\) | −14.6407 | −1.12956 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.54288 | 0.655209 | ||||||||
\(171\) | −2.20220 | − | 1.27144i | −0.168406 | − | 0.0972293i | ||||
\(172\) | 0.530499 | − | 0.918852i | 0.0404502 | − | 0.0700618i | ||||
\(173\) | 6.61745 | + | 11.4618i | 0.503115 | + | 0.871421i | 0.999994 | + | 0.00360102i | \(0.00114624\pi\) |
−0.496878 | + | 0.867820i | \(0.665520\pi\) | |||||||
\(174\) | 2.30798i | 0.174967i | ||||||||
\(175\) | −11.8556 | + | 6.84481i | −0.896197 | + | 0.517419i | ||||
\(176\) | 3.69892 | − | 2.13557i | 0.278816 | − | 0.160975i | ||||
\(177\) | − | 2.17629i | − | 0.163580i | ||||||
\(178\) | −3.92543 | − | 6.79904i | −0.294223 | − | 0.509610i | ||||
\(179\) | 4.26391 | − | 7.38530i | 0.318699 | − | 0.552003i | −0.661518 | − | 0.749930i | \(-0.730087\pi\) |
0.980217 | + | 0.197926i | \(0.0634207\pi\) | |||||||
\(180\) | 1.07992 | + | 0.623490i | 0.0804922 | + | 0.0464722i | ||||
\(181\) | 3.63640 | 0.270291 | 0.135146 | − | 0.990826i | \(-0.456850\pi\) | ||||
0.135146 | + | 0.990826i | \(0.456850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.82908 | −0.578743 | ||||||||
\(184\) | −9.28307 | − | 5.35958i | −0.684357 | − | 0.395114i | ||||
\(185\) | −6.38135 | + | 11.0528i | −0.469167 | + | 0.812620i | ||||
\(186\) | −4.75786 | − | 8.24086i | −0.348864 | − | 0.604249i | ||||
\(187\) | − | 3.58642i | − | 0.262265i | ||||||
\(188\) | −4.93990 | + | 2.85205i | −0.360279 | + | 0.208007i | ||||
\(189\) | 4.15860 | − | 2.40097i | 0.302494 | − | 0.174645i | ||||
\(190\) | 8.88471i | 0.644564i | ||||||||
\(191\) | −10.6908 | − | 18.5171i | −0.773561 | − | 1.33985i | −0.935600 | − | 0.353062i | \(-0.885140\pi\) |
0.162039 | − | 0.986784i | \(-0.448193\pi\) | |||||||
\(192\) | 4.44989 | − | 7.70743i | 0.321143 | − | 0.556236i | ||||
\(193\) | −7.29850 | − | 4.21379i | −0.525358 | − | 0.303315i | 0.213766 | − | 0.976885i | \(-0.431427\pi\) |
−0.739124 | + | 0.673569i | \(0.764760\pi\) | |||||||
\(194\) | 12.5090 | 0.898096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.14675 | −0.510482 | ||||||||
\(197\) | 22.9293 | + | 13.2383i | 1.63365 | + | 0.943186i | 0.982955 | + | 0.183844i | \(0.0588540\pi\) |
0.650691 | + | 0.759343i | \(0.274479\pi\) | |||||||
\(198\) | −0.914542 | + | 1.58403i | −0.0649937 | + | 0.112572i | ||||
\(199\) | −7.12618 | − | 12.3429i | −0.505161 | − | 0.874965i | −0.999982 | − | 0.00597014i | \(-0.998100\pi\) |
0.494821 | − | 0.868995i | \(-0.335234\pi\) | |||||||
\(200\) | − | 8.69202i | − | 0.614619i | ||||||
\(201\) | −3.10219 | + | 1.79105i | −0.218812 | + | 0.126331i | ||||
\(202\) | −14.9975 | + | 8.65883i | −1.05522 | + | 0.609233i | ||||
\(203\) | 8.88769i | 0.623794i | ||||||||
\(204\) | −0.544073 | − | 0.942362i | −0.0380927 | − | 0.0659785i | ||||
\(205\) | −1.74698 | + | 3.02586i | −0.122014 | + | 0.211335i | ||||
\(206\) | −18.7942 | − | 10.8509i | −1.30946 | − | 0.756015i | ||||
\(207\) | 3.51573 | 0.244360 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.72992 | 0.258004 | ||||||||
\(210\) | −14.5300 | − | 8.38889i | −1.00266 | − | 0.578888i | ||||
\(211\) | −0.925428 | + | 1.60289i | −0.0637091 | + | 0.110347i | −0.896121 | − | 0.443811i | \(-0.853626\pi\) |
0.832412 | + | 0.554158i | \(0.186960\pi\) | |||||||
\(212\) | 1.96950 | + | 3.41127i | 0.135266 | + | 0.234287i | ||||
\(213\) | − | 8.83877i | − | 0.605623i | ||||||
\(214\) | 11.3959 | − | 6.57942i | 0.779007 | − | 0.449760i | ||||
\(215\) | 5.78500 | − | 3.33997i | 0.394534 | − | 0.227784i | ||||
\(216\) | 3.04892i | 0.207453i | ||||||||
\(217\) | −18.3218 | − | 31.7344i | −1.24377 | − | 2.15427i | ||||
\(218\) | 0.667563 | − | 1.15625i | 0.0452131 | − | 0.0783113i | ||||
\(219\) | −6.66149 | − | 3.84601i | −0.450142 | − | 0.259889i | ||||
\(220\) | −1.82908 | −0.123317 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.67994 | −0.381213 | ||||||||
\(223\) | −16.1517 | − | 9.32520i | −1.08160 | − | 0.624462i | −0.150272 | − | 0.988645i | \(-0.548015\pi\) |
−0.931327 | + | 0.364183i | \(0.881348\pi\) | |||||||
\(224\) | 5.92274 | − | 10.2585i | 0.395730 | − | 0.685424i | ||||
\(225\) | 1.42543 | + | 2.46891i | 0.0950285 | + | 0.164594i | ||||
\(226\) | − | 20.6136i | − | 1.37119i | ||||||
\(227\) | 8.45010 | − | 4.87867i | 0.560853 | − | 0.323808i | −0.192635 | − | 0.981270i | \(-0.561703\pi\) |
0.753488 | + | 0.657462i | \(0.228370\pi\) | |||||||
\(228\) | 0.980069 | − | 0.565843i | 0.0649067 | − | 0.0374739i | ||||
\(229\) | 2.86294i | 0.189188i | 0.995516 | + | 0.0945941i | \(0.0301553\pi\) | ||||
−0.995516 | + | 0.0945941i | \(0.969845\pi\) | |||||||
\(230\) | −6.14191 | − | 10.6381i | −0.404985 | − | 0.701455i | ||||
\(231\) | −3.52177 | + | 6.09989i | −0.231715 | + | 0.401343i | ||||
\(232\) | −4.88707 | − | 2.82155i | −0.320852 | − | 0.185244i | ||||
\(233\) | 5.78554 | 0.379024 | 0.189512 | − | 0.981878i | \(-0.439309\pi\) | ||||
0.189512 | + | 0.981878i | \(0.439309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9124 | −2.34267 | ||||||||
\(236\) | 0.838781 | + | 0.484271i | 0.0546000 | + | 0.0315233i | ||||
\(237\) | 2.01089 | − | 3.48296i | 0.130621 | − | 0.226242i | ||||
\(238\) | 7.32036 | + | 12.6792i | 0.474508 | + | 0.821872i | ||||
\(239\) | 7.09246i | 0.458773i | 0.973335 | + | 0.229386i | \(0.0736720\pi\) | ||||
−0.973335 | + | 0.229386i | \(0.926328\pi\) | |||||||
\(240\) | 7.06576 | − | 4.07942i | 0.456093 | − | 0.263325i | ||||
\(241\) | −3.37730 | + | 1.94989i | −0.217551 | + | 0.125603i | −0.604816 | − | 0.796365i | \(-0.706753\pi\) |
0.387265 | + | 0.921969i | \(0.373420\pi\) | |||||||
\(242\) | 11.0339i | 0.709283i | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 1.74214 | − | 3.01747i | 0.111529 | − | 0.193174i | ||||
\(245\) | −38.9670 | − | 22.4976i | −2.48951 | − | 1.43732i | ||||
\(246\) | −1.55496 | −0.0991405 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.2664 | 1.47742 | ||||||||
\(249\) | 0.565335 | + | 0.326396i | 0.0358267 | + | 0.0206845i | ||||
\(250\) | −3.75451 | + | 6.50301i | −0.237456 | + | 0.411286i | ||||
\(251\) | −1.22252 | − | 2.11747i | −0.0771648 | − | 0.133653i | 0.824861 | − | 0.565336i | \(-0.191253\pi\) |
−0.902026 | + | 0.431682i | \(0.857920\pi\) | |||||||
\(252\) | 2.13706i | 0.134622i | ||||||||
\(253\) | −4.46602 | + | 2.57846i | −0.280776 | + | 0.162106i | ||||
\(254\) | 10.2997 | − | 5.94653i | 0.646261 | − | 0.373119i | ||||
\(255\) | − | 6.85086i | − | 0.429017i | ||||||
\(256\) | 5.05645 | + | 8.75803i | 0.316028 | + | 0.547377i | ||||
\(257\) | −7.06518 | + | 12.2372i | −0.440714 | + | 0.763339i | −0.997743 | − | 0.0671545i | \(-0.978608\pi\) |
0.557029 | + | 0.830493i | \(0.311941\pi\) | |||||||
\(258\) | 2.57457 | + | 1.48643i | 0.160285 | + | 0.0925409i | ||||
\(259\) | −21.8726 | −1.35910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.85086 | 0.114565 | ||||||||
\(262\) | 5.94928 | + | 3.43482i | 0.367548 | + | 0.212204i | ||||
\(263\) | 11.8617 | − | 20.5451i | 0.731426 | − | 1.26687i | −0.224847 | − | 0.974394i | \(-0.572188\pi\) |
0.956274 | − | 0.292473i | \(-0.0944783\pi\) | |||||||
\(264\) | −2.23609 | − | 3.87303i | −0.137622 | − | 0.238368i | ||||
\(265\) | 24.7995i | 1.52342i | ||||||||
\(266\) | −13.1866 | + | 7.61327i | −0.808520 | + | 0.466799i | ||||
\(267\) | −5.45241 | + | 3.14795i | −0.333682 | + | 0.192651i | ||||
\(268\) | − | 1.59419i | − | 0.0973805i | ||||||
\(269\) | 2.95808 | + | 5.12355i | 0.180357 | + | 0.312388i | 0.942002 | − | 0.335606i | \(-0.108941\pi\) |
−0.761645 | + | 0.647995i | \(0.775608\pi\) | |||||||
\(270\) | −1.74698 | + | 3.02586i | −0.106318 | + | 0.184148i | ||||
\(271\) | 2.76287 | + | 1.59515i | 0.167833 | + | 0.0968982i | 0.581563 | − | 0.813501i | \(-0.302441\pi\) |
−0.413731 | + | 0.910399i | \(0.635775\pi\) | |||||||
\(272\) | −7.11960 | −0.431689 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1806 | −1.21915 | ||||||||
\(275\) | −3.62143 | − | 2.09083i | −0.218381 | − | 0.126082i | ||||
\(276\) | −0.782323 | + | 1.35502i | −0.0470903 | + | 0.0815629i | ||||
\(277\) | 10.9683 | + | 18.9977i | 0.659022 | + | 1.14146i | 0.980869 | + | 0.194667i | \(0.0623627\pi\) |
−0.321848 | + | 0.946791i | \(0.604304\pi\) | |||||||
\(278\) | − | 13.1045i | − | 0.785958i | ||||||
\(279\) | −6.60866 | + | 3.81551i | −0.395650 | + | 0.228429i | ||||
\(280\) | 35.5264 | − | 20.5112i | 2.12311 | − | 1.22578i | ||||
\(281\) | 11.9903i | 0.715282i | 0.933859 | + | 0.357641i | \(0.116419\pi\) | ||||
−0.933859 | + | 0.357641i | \(0.883581\pi\) | |||||||
\(282\) | −7.99127 | − | 13.8413i | −0.475873 | − | 0.824237i | ||||
\(283\) | −7.18329 | + | 12.4418i | −0.427002 | + | 0.739590i | −0.996605 | − | 0.0823303i | \(-0.973764\pi\) |
0.569603 | + | 0.821920i | \(0.307097\pi\) | |||||||
\(284\) | 3.40662 | + | 1.96681i | 0.202146 | + | 0.116709i | ||||
\(285\) | 7.12498 | 0.422047 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.98792 | −0.353456 | ||||||||
\(288\) | −2.13632 | − | 1.23341i | −0.125884 | − | 0.0726791i | ||||
\(289\) | 5.51089 | − | 9.54513i | 0.324170 | − | 0.561478i | ||||
\(290\) | −3.23341 | − | 5.60042i | −0.189872 | − | 0.328868i | ||||
\(291\) | − | 10.0315i | − | 0.588055i | ||||||
\(292\) | 2.96464 | − | 1.71164i | 0.173492 | − | 0.100166i | ||||
\(293\) | 16.2452 | − | 9.37920i | 0.949058 | − | 0.547939i | 0.0562695 | − | 0.998416i | \(-0.482079\pi\) |
0.892788 | + | 0.450477i | \(0.148746\pi\) | |||||||
\(294\) | − | 20.0248i | − | 1.16787i | ||||||
\(295\) | 3.04892 | + | 5.28088i | 0.177515 | + | 0.307465i | ||||
\(296\) | 6.94385 | − | 12.0271i | 0.403603 | − | 0.699061i | ||||
\(297\) | 1.27030 | + | 0.733406i | 0.0737101 | + | 0.0425565i | ||||
\(298\) | −17.8944 | −1.03659 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.26875 | −0.0732513 | ||||||||
\(301\) | 9.91428 | + | 5.72401i | 0.571450 | + | 0.329927i | ||||
\(302\) | −1.22587 | + | 2.12327i | −0.0705411 | + | 0.122181i | ||||
\(303\) | 6.94385 | + | 12.0271i | 0.398913 | + | 0.690938i | ||||
\(304\) | − | 7.40449i | − | 0.424676i | ||||||
\(305\) | 18.9977 | − | 10.9683i | 1.08780 | − | 0.628043i | ||||
\(306\) | 2.64044 | − | 1.52446i | 0.150944 | − | 0.0871475i | ||||
\(307\) | 25.6262i | 1.46257i | 0.682074 | + | 0.731283i | \(0.261078\pi\) | ||||
−0.682074 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(308\) | −1.56734 | − | 2.71470i | −0.0893072 | − | 0.154685i | ||||
\(309\) | −8.70171 | + | 15.0718i | −0.495023 | + | 0.857405i | ||||
\(310\) | 23.0904 | + | 13.3312i | 1.31145 | + | 0.757164i | ||||
\(311\) | −11.3817 | −0.645394 | −0.322697 | − | 0.946502i | \(-0.604590\pi\) | ||||
−0.322697 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.5743 | 1.55859 | 0.779297 | − | 0.626655i | \(-0.215576\pi\) | ||||
0.779297 | + | 0.626655i | \(0.215576\pi\) | |||||||
\(314\) | −11.5569 | − | 6.67241i | −0.652196 | − | 0.376546i | ||||
\(315\) | −6.72737 | + | 11.6521i | −0.379044 | + | 0.656524i | ||||
\(316\) | 0.894928 | + | 1.55006i | 0.0503436 | + | 0.0871977i | ||||
\(317\) | 11.2597i | 0.632405i | 0.948692 | + | 0.316203i | \(0.102408\pi\) | ||||
−0.948692 | + | 0.316203i | \(0.897592\pi\) | |||||||
\(318\) | −9.55818 | + | 5.51842i | −0.535996 | + | 0.309458i | ||||
\(319\) | −2.35113 | + | 1.35743i | −0.131638 | + | 0.0760014i | ||||
\(320\) | 24.9366i | 1.39400i | ||||||||
\(321\) | −5.27628 | − | 9.13879i | −0.294493 | − | 0.510077i | ||||
\(322\) | 10.5260 | − | 18.2315i | 0.586588 | − | 1.01600i | ||||
\(323\) | −5.38446 | − | 3.10872i | −0.299599 | − | 0.172974i | ||||
\(324\) | 0.445042 | 0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.86294 | 0.269333 | ||||||||
\(327\) | −0.927243 | − | 0.535344i | −0.0512766 | − | 0.0296046i | ||||
\(328\) | 1.90097 | − | 3.29257i | 0.104963 | − | 0.181802i | ||||
\(329\) | −30.7732 | − | 53.3008i | −1.69658 | − | 2.93857i | ||||
\(330\) | − | 5.12498i | − | 0.282121i | ||||||
\(331\) | 10.3113 | − | 5.95324i | 0.566761 | − | 0.327220i | −0.189094 | − | 0.981959i | \(-0.560555\pi\) |
0.755855 | + | 0.654739i | \(0.227222\pi\) | |||||||
\(332\) | −0.251598 | + | 0.145260i | −0.0138082 | + | 0.00797218i | ||||
\(333\) | 4.55496i | 0.249610i | ||||||||
\(334\) | −13.1054 | − | 22.6992i | −0.717094 | − | 1.24204i | ||||
\(335\) | 5.01842 | − | 8.69215i | 0.274185 | − | 0.474903i | ||||
\(336\) | 12.1092 | + | 6.99127i | 0.660613 | + | 0.381405i | ||||
\(337\) | −17.1672 | −0.935157 | −0.467578 | − | 0.883952i | \(-0.654873\pi\) | ||||
−0.467578 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5308 | −0.897830 | ||||||||
\(340\) | 2.64044 | + | 1.52446i | 0.143198 | + | 0.0826754i | ||||
\(341\) | 5.59664 | − | 9.69366i | 0.303075 | − | 0.524941i | ||||
\(342\) | 1.58546 | + | 2.74609i | 0.0857317 | + | 0.148492i | ||||
\(343\) | − | 43.4989i | − | 2.34872i | ||||||
\(344\) | −6.29492 | + | 3.63437i | −0.339399 | + | 0.195952i | ||||
\(345\) | −8.53109 | + | 4.92543i | −0.459298 | + | 0.265176i | ||||
\(346\) | − | 16.5036i | − | 0.887242i | ||||||
\(347\) | 12.1380 | + | 21.0237i | 0.651603 | + | 1.12861i | 0.982734 | + | 0.185025i | \(0.0592366\pi\) |
−0.331131 | + | 0.943585i | \(0.607430\pi\) | |||||||
\(348\) | −0.411854 | + | 0.713352i | −0.0220777 | + | 0.0382397i | ||||
\(349\) | 3.95983 | + | 2.28621i | 0.211965 | + | 0.122378i | 0.602224 | − | 0.798327i | \(-0.294281\pi\) |
−0.390259 | + | 0.920705i | \(0.627615\pi\) | |||||||
\(350\) | 17.0707 | 0.912467 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.61835 | 0.192859 | ||||||||
\(353\) | −5.26203 | − | 3.03803i | −0.280069 | − | 0.161698i | 0.353385 | − | 0.935478i | \(-0.385030\pi\) |
−0.633455 | + | 0.773780i | \(0.718364\pi\) | |||||||
\(354\) | −1.35690 | + | 2.35021i | −0.0721182 | + | 0.124912i | ||||
\(355\) | 12.3828 | + | 21.4477i | 0.657213 | + | 1.13833i | ||||
\(356\) | − | 2.80194i | − | 0.148502i | ||||||
\(357\) | 10.1680 | − | 5.87047i | 0.538145 | − | 0.310698i | ||||
\(358\) | −9.20932 | + | 5.31700i | −0.486728 | + | 0.281012i | ||||
\(359\) | − | 14.9661i | − | 0.789883i | −0.918706 | − | 0.394942i | \(-0.870765\pi\) | ||
0.918706 | − | 0.394942i | \(-0.129235\pi\) | |||||||
\(360\) | −4.27144 | − | 7.39835i | −0.225125 | − | 0.389927i | ||||
\(361\) | −6.26689 | + | 10.8546i | −0.329836 | + | 0.571293i | ||||
\(362\) | −3.92701 | − | 2.26726i | −0.206399 | − | 0.119164i | ||||
\(363\) | 8.84846 | 0.464424 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.5526 | 1.12811 | ||||||||
\(366\) | 8.45475 | + | 4.88135i | 0.441937 | + | 0.255152i | ||||
\(367\) | −18.5417 | + | 32.1151i | −0.967868 | + | 1.67640i | −0.266164 | + | 0.963928i | \(0.585756\pi\) |
−0.701704 | + | 0.712468i | \(0.747577\pi\) | |||||||
\(368\) | 5.11865 | + | 8.86575i | 0.266828 | + | 0.462159i | ||||
\(369\) | 1.24698i | 0.0649152i | ||||||||
\(370\) | 13.7827 | − | 7.95742i | 0.716526 | − | 0.413687i | ||||
\(371\) | −36.8072 | + | 21.2506i | −1.91093 | + | 1.10328i | ||||
\(372\) | − | 3.39612i | − | 0.176081i | ||||||
\(373\) | 18.2545 | + | 31.6177i | 0.945183 | + | 1.63710i | 0.755385 | + | 0.655282i | \(0.227450\pi\) |
0.189798 | + | 0.981823i | \(0.439217\pi\) | |||||||
\(374\) | −2.23609 | + | 3.87303i | −0.115626 | + | 0.200270i | ||||
\(375\) | 5.21501 | + | 3.01089i | 0.269302 | + | 0.155481i | ||||
\(376\) | 39.0780 | 2.01529 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.98792 | −0.307985 | ||||||||
\(379\) | −23.0234 | − | 13.2925i | −1.18263 | − | 0.682792i | −0.226009 | − | 0.974125i | \(-0.572568\pi\) |
−0.956622 | + | 0.291333i | \(0.905901\pi\) | |||||||
\(380\) | −1.58546 | + | 2.74609i | −0.0813323 | + | 0.140872i | ||||
\(381\) | −4.76875 | − | 8.25972i | −0.244310 | − | 0.423158i | ||||
\(382\) | 26.6625i | 1.36417i | ||||||||
\(383\) | 12.4276 | − | 7.17510i | 0.635022 | − | 0.366630i | −0.147672 | − | 0.989036i | \(-0.547178\pi\) |
0.782694 | + | 0.622406i | \(0.213845\pi\) | |||||||
\(384\) | −5.33836 | + | 3.08211i | −0.272422 | + | 0.157283i | ||||
\(385\) | − | 19.7356i | − | 1.00582i | ||||||
\(386\) | 5.25451 | + | 9.10108i | 0.267448 | + | 0.463233i | ||||
\(387\) | 1.19202 | − | 2.06464i | 0.0605939 | − | 0.104952i | ||||
\(388\) | 3.86630 | + | 2.23221i | 0.196282 | + | 0.113323i | ||||
\(389\) | 22.6582 | 1.14881 | 0.574407 | − | 0.818570i | \(-0.305233\pi\) | ||||
0.574407 | + | 0.818570i | \(0.305233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.59611 | 0.434724 | ||||||||
\(392\) | 42.4018 | + | 24.4807i | 2.14161 | + | 1.23646i | ||||
\(393\) | 2.75451 | − | 4.77096i | 0.138947 | − | 0.240663i | ||||
\(394\) | −16.5078 | − | 28.5924i | −0.831652 | − | 1.44046i | ||||
\(395\) | 11.2687i | 0.566992i | ||||||||
\(396\) | −0.565335 | + | 0.326396i | −0.0284092 | + | 0.0164020i | ||||
\(397\) | 6.84813 | − | 3.95377i | 0.343698 | − | 0.198434i | −0.318208 | − | 0.948021i | \(-0.603081\pi\) |
0.661906 | + | 0.749587i | \(0.269748\pi\) | |||||||
\(398\) | 17.7724i | 0.890850i | ||||||||
\(399\) | 6.10537 | + | 10.5748i | 0.305651 | + | 0.529402i | ||||
\(400\) | −4.15064 | + | 7.18911i | −0.207532 | + | 0.359456i | ||||
\(401\) | −2.54318 | − | 1.46830i | −0.127000 | − | 0.0733236i | 0.435154 | − | 0.900356i | \(-0.356694\pi\) |
−0.562154 | + | 0.827032i | \(0.690027\pi\) | |||||||
\(402\) | 4.46681 | 0.222784 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.18060 | −0.307497 | ||||||||
\(405\) | 2.42655 | + | 1.40097i | 0.120576 | + | 0.0696147i | ||||
\(406\) | 5.54138 | − | 9.59796i | 0.275014 | − | 0.476339i | ||||
\(407\) | −3.34063 | − | 5.78615i | −0.165589 | − | 0.286809i | ||||
\(408\) | 7.45473i | 0.369064i | ||||||||
\(409\) | −10.1801 | + | 5.87747i | −0.503372 | + | 0.290622i | −0.730105 | − | 0.683335i | \(-0.760529\pi\) |
0.226733 | + | 0.973957i | \(0.427196\pi\) | |||||||
\(410\) | 3.77318 | − | 2.17845i | 0.186344 | − | 0.107586i | ||||
\(411\) | 16.1836i | 0.798278i | ||||||||
\(412\) | −3.87263 | − | 6.70758i | −0.190791 | − | 0.330459i | ||||
\(413\) | −5.22521 | + | 9.05033i | −0.257116 | + | 0.445338i | ||||
\(414\) | −3.79669 | − | 2.19202i | −0.186597 | − | 0.107732i | ||||
\(415\) | −1.82908 | −0.0897862 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.5090 | −0.514629 | ||||||||
\(418\) | −4.02800 | − | 2.32557i | −0.197016 | − | 0.113747i | ||||
\(419\) | −3.67092 | + | 6.35821i | −0.179336 | + | 0.310619i | −0.941653 | − | 0.336584i | \(-0.890728\pi\) |
0.762317 | + | 0.647203i | \(0.224062\pi\) | |||||||
\(420\) | −2.99396 | − | 5.18569i | −0.146090 | − | 0.253036i | ||||
\(421\) | − | 25.6963i | − | 1.25236i | −0.779677 | − | 0.626181i | \(-0.784617\pi\) | ||
0.779677 | − | 0.626181i | \(-0.215383\pi\) | |||||||
\(422\) | 1.99877 | − | 1.15399i | 0.0972985 | − | 0.0561753i | ||||
\(423\) | −11.0999 | + | 6.40850i | −0.539693 | + | 0.311592i | ||||
\(424\) | − | 26.9855i | − | 1.31053i | ||||||
\(425\) | 3.48523 | + | 6.03660i | 0.169058 | + | 0.292818i | ||||
\(426\) | −5.51089 | + | 9.54513i | −0.267003 | + | 0.462463i | ||||
\(427\) | 32.5580 | + | 18.7974i | 1.57559 | + | 0.909669i | ||||
\(428\) | 4.69633 | 0.227006 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.32975 | −0.401696 | ||||||||
\(431\) | 7.74399 | + | 4.47099i | 0.373015 | + | 0.215360i | 0.674775 | − | 0.738024i | \(-0.264241\pi\) |
−0.301760 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(432\) | 1.45593 | − | 2.52174i | 0.0700483 | − | 0.121327i | ||||
\(433\) | 1.45742 | + | 2.52432i | 0.0700391 | + | 0.121311i | 0.898918 | − | 0.438116i | \(-0.144354\pi\) |
−0.828879 | + | 0.559428i | \(0.811021\pi\) | |||||||
\(434\) | 45.6939i | 2.19338i | ||||||||
\(435\) | −4.49119 | + | 2.59299i | −0.215336 | + | 0.124324i | ||||
\(436\) | 0.412662 | − | 0.238250i | 0.0197629 | − | 0.0114101i | ||||
\(437\) | 8.94007i | 0.427661i | ||||||||
\(438\) | 4.79590 | + | 8.30674i | 0.229157 | + | 0.396911i | ||||
\(439\) | 4.52930 | − | 7.84498i | 0.216172 | − | 0.374421i | −0.737463 | − | 0.675388i | \(-0.763976\pi\) |
0.953634 | + | 0.300967i | \(0.0973095\pi\) | |||||||
\(440\) | 10.8520 | + | 6.26540i | 0.517348 | + | 0.298691i | ||||
\(441\) | −16.0586 | −0.764696 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2325 | 0.533672 | 0.266836 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266836 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(444\) | −1.75556 | − | 1.01357i | −0.0833152 | − | 0.0481021i | ||||
\(445\) | 8.82036 | − | 15.2773i | 0.418125 | − | 0.724214i | ||||
\(446\) | 11.6283 | + | 20.1409i | 0.550618 | + | 0.953698i | ||||
\(447\) | 14.3502i | 0.678741i | ||||||||
\(448\) | −37.0106 | + | 21.3681i | −1.74859 | + | 1.00955i | ||||
\(449\) | 24.9051 | − | 14.3790i | 1.17534 | − | 0.678585i | 0.220411 | − | 0.975407i | \(-0.429260\pi\) |
0.954933 | + | 0.296822i | \(0.0959268\pi\) | |||||||
\(450\) | − | 3.55496i | − | 0.167582i | ||||||
\(451\) | −0.914542 | − | 1.58403i | −0.0430641 | − | 0.0745892i | ||||
\(452\) | 3.67845 | − | 6.37126i | 0.173020 | − | 0.299679i | ||||
\(453\) | 1.70273 | + | 0.983074i | 0.0800014 | + | 0.0461888i | ||||
\(454\) | −12.1672 | −0.571035 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.75302 | −0.363068 | ||||||||
\(457\) | −16.5204 | − | 9.53803i | −0.772790 | − | 0.446170i | 0.0610792 | − | 0.998133i | \(-0.480546\pi\) |
−0.833869 | + | 0.551963i | \(0.813879\pi\) | |||||||
\(458\) | 1.78501 | − | 3.09173i | 0.0834081 | − | 0.144467i | ||||
\(459\) | −1.22252 | − | 2.11747i | −0.0570624 | − | 0.0988350i | ||||
\(460\) | − | 4.38404i | − | 0.204407i | ||||||
\(461\) | −27.4817 | + | 15.8666i | −1.27995 | + | 0.738981i | −0.976839 | − | 0.213974i | \(-0.931359\pi\) |
−0.303113 | + | 0.952955i | \(0.598026\pi\) | |||||||
\(462\) | 7.60643 | − | 4.39158i | 0.353883 | − | 0.204315i | ||||
\(463\) | − | 36.4784i | − | 1.69530i | −0.530559 | − | 0.847648i | \(-0.678018\pi\) | ||
0.530559 | − | 0.847648i | \(-0.321982\pi\) | |||||||
\(464\) | 2.69471 | + | 4.66737i | 0.125099 | + | 0.216677i | ||||
\(465\) | 10.6908 | − | 18.5171i | 0.495775 | − | 0.858708i | ||||
\(466\) | −6.24790 | − | 3.60723i | −0.289428 | − | 0.167102i | ||||
\(467\) | −13.0000 | −0.601568 | −0.300784 | − | 0.953692i | \(-0.597248\pi\) | ||||
−0.300784 | + | 0.953692i | \(0.597248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.2010 | 0.794271 | ||||||||
\(470\) | 38.7824 | + | 22.3910i | 1.78890 | + | 1.03282i | ||||
\(471\) | −5.35086 | + | 9.26795i | −0.246554 | + | 0.427045i | ||||
\(472\) | −3.31767 | − | 5.74637i | −0.152708 | − | 0.264498i | ||||
\(473\) | 3.49694i | 0.160790i | ||||||||
\(474\) | −4.34317 | + | 2.50753i | −0.199489 | + | 0.115175i | ||||
\(475\) | −6.27814 | + | 3.62469i | −0.288061 | + | 0.166312i | ||||
\(476\) | 5.22521i | 0.239497i | ||||||||
\(477\) | 4.42543 | + | 7.66507i | 0.202626 | + | 0.350959i | ||||
\(478\) | 4.42208 | − | 7.65926i | 0.202261 | − | 0.350326i | ||||
\(479\) | −4.86407 | − | 2.80827i | −0.222245 | − | 0.128313i | 0.384744 | − | 0.923023i | \(-0.374290\pi\) |
−0.606989 | + | 0.794710i | \(0.707623\pi\) | |||||||
\(480\) | 6.91185 | 0.315482 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.86294 | 0.221501 | ||||||||
\(483\) | −14.6205 | − | 8.44116i | −0.665256 | − | 0.384086i | ||||
\(484\) | −1.96897 | + | 3.41035i | −0.0894985 | + | 0.155016i | ||||
\(485\) | 14.0538 | + | 24.3418i | 0.638148 | + | 1.10531i | ||||
\(486\) | 1.24698i | 0.0565641i | ||||||||
\(487\) | 8.45010 | − | 4.87867i | 0.382910 | − | 0.221073i | −0.296173 | − | 0.955134i | \(-0.595711\pi\) |
0.679084 | + | 0.734061i | \(0.262377\pi\) | |||||||
\(488\) | −20.6722 | + | 11.9351i | −0.935788 | + | 0.540277i | ||||
\(489\) | − | 3.89977i | − | 0.176354i | ||||||
\(490\) | 28.0541 | + | 48.5911i | 1.26735 | + | 2.19512i | ||||
\(491\) | −3.69418 | + | 6.39850i | −0.166716 | + | 0.288760i | −0.937263 | − | 0.348622i | \(-0.886650\pi\) |
0.770547 | + | 0.637383i | \(0.219983\pi\) | |||||||
\(492\) | −0.480608 | − | 0.277479i | −0.0216675 | − | 0.0125097i | ||||
\(493\) | 4.52542 | 0.203815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.10992 | −0.184727 | ||||||||
\(496\) | −19.2435 | − | 11.1102i | −0.864056 | − | 0.498863i | ||||
\(497\) | −21.2216 | + | 36.7569i | −0.951920 | + | 1.64877i | ||||
\(498\) | −0.407010 | − | 0.704961i | −0.0182385 | − | 0.0315901i | ||||
\(499\) | 43.2814i | 1.93754i | 0.247956 | + | 0.968771i | \(0.420241\pi\) | ||||
−0.247956 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(500\) | −2.32090 | + | 1.33997i | −0.103794 | + | 0.0599253i | ||||
\(501\) | −18.2033 | + | 10.5097i | −0.813264 | + | 0.469538i | ||||
\(502\) | 3.04892i | 0.136080i | ||||||||
\(503\) | −5.38351 | − | 9.32451i | −0.240039 | − | 0.415760i | 0.720686 | − | 0.693261i | \(-0.243827\pi\) |
−0.960725 | + | 0.277502i | \(0.910494\pi\) | |||||||
\(504\) | 7.32036 | − | 12.6792i | 0.326075 | − | 0.564778i | ||||
\(505\) | −33.6992 | − | 19.4562i | −1.49959 | − | 0.865791i | ||||
\(506\) | 6.43057 | 0.285874 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.24459 | 0.188323 | ||||||||
\(509\) | −35.9788 | − | 20.7724i | −1.59473 | − | 0.920720i | −0.992479 | − | 0.122417i | \(-0.960935\pi\) |
−0.602256 | − | 0.798303i | \(-0.705731\pi\) | |||||||
\(510\) | −4.27144 | + | 7.39835i | −0.189142 | + | 0.327604i | ||||
\(511\) | 18.4683 | + | 31.9880i | 0.816990 | + | 1.41507i | ||||
\(512\) | − | 24.9390i | − | 1.10216i | ||||||
\(513\) | 2.20220 | − | 1.27144i | 0.0972293 | − | 0.0561354i | ||||
\(514\) | 15.2596 | − | 8.81013i | 0.673072 | − | 0.388598i | ||||
\(515\) | − | 48.7633i | − | 2.14877i | ||||||
\(516\) | 0.530499 | + | 0.918852i | 0.0233539 | + | 0.0404502i | ||||
\(517\) | 9.40007 | − | 16.2814i | 0.413415 | − | 0.716055i | ||||
\(518\) | 23.6206 | + | 13.6374i | 1.03783 | + | 0.599191i | ||||
\(519\) | −13.2349 | −0.580948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7198 | 1.12680 | 0.563402 | − | 0.826183i | \(-0.309492\pi\) | ||||
0.563402 | + | 0.826183i | \(0.309492\pi\) | |||||||
\(522\) | −1.99877 | − | 1.15399i | −0.0874837 | − | 0.0505087i | ||||
\(523\) | −4.29643 | + | 7.44163i | −0.187870 | + | 0.325400i | −0.944540 | − | 0.328397i | \(-0.893492\pi\) |
0.756670 | + | 0.653797i | \(0.226825\pi\) | |||||||
\(524\) | 1.22587 | + | 2.12327i | 0.0535525 | + | 0.0927557i | ||||
\(525\) | − | 13.6896i | − | 0.597464i | ||||||
\(526\) | −25.6194 | + | 14.7913i | −1.11706 | + | 0.644933i | ||||
\(527\) | −16.1584 | + | 9.32908i | −0.703873 | + | 0.406381i | ||||
\(528\) | 4.27114i | 0.185878i | ||||||||
\(529\) | 5.31982 | + | 9.21420i | 0.231297 | + | 0.400618i | ||||
\(530\) | 15.4623 | − | 26.7814i | 0.671638 | − | 1.16331i | ||||
\(531\) | 1.88472 | + | 1.08815i | 0.0817901 | + | 0.0472215i | ||||
\(532\) | −5.43429 | −0.235606 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.85086 | 0.339740 | ||||||||
\(535\) | 25.6063 | + | 14.7838i | 1.10706 | + | 0.639160i | ||||
\(536\) | −5.46077 | + | 9.45833i | −0.235869 | + | 0.408538i | ||||
\(537\) | 4.26391 | + | 7.38530i | 0.184001 | + | 0.318699i | ||||
\(538\) | − | 7.37734i | − | 0.318060i | ||||||
\(539\) | 20.3992 | − | 11.7775i | 0.878655 | − | 0.507292i | ||||
\(540\) | −1.07992 | + | 0.623490i | −0.0464722 | + | 0.0268307i | ||||
\(541\) | 31.3534i | 1.34799i | 0.738736 | + | 0.673995i | \(0.235423\pi\) | ||||
−0.738736 | + | 0.673995i | \(0.764577\pi\) | |||||||
\(542\) | −1.98911 | − | 3.44525i | −0.0854398 | − | 0.147986i | ||||
\(543\) | −1.81820 | + | 3.14921i | −0.0780264 | + | 0.135146i | ||||
\(544\) | −5.22340 | − | 3.01573i | −0.223951 | − | 0.129298i | ||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9342 | 0.852325 | 0.426163 | − | 0.904647i | \(-0.359865\pi\) | ||||
0.426163 | + | 0.904647i | \(0.359865\pi\) | |||||||
\(548\) | −6.23744 | − | 3.60119i | −0.266450 | − | 0.153835i | ||||
\(549\) | 3.91454 | − | 6.78019i | 0.167069 | − | 0.289371i | ||||
\(550\) | 2.60723 | + | 4.51585i | 0.111173 | + | 0.192557i | ||||
\(551\) | 4.70650i | 0.200503i | ||||||||
\(552\) | 9.28307 | − | 5.35958i | 0.395114 | − | 0.228119i | ||||
\(553\) | −16.7249 | + | 9.65615i | −0.711217 | + | 0.410621i | ||||
\(554\) | − | 27.3545i | − | 1.16218i | ||||||
\(555\) | −6.38135 | − | 11.0528i | −0.270873 | − | 0.469167i | ||||
\(556\) | 2.33848 | − | 4.05036i | 0.0991736 | − | 0.171774i | ||||
\(557\) | −28.7823 | − | 16.6174i | −1.21954 | − | 0.704104i | −0.254723 | − | 0.967014i | \(-0.581984\pi\) |
−0.964820 | + | 0.262910i | \(0.915318\pi\) | |||||||
\(558\) | 9.51573 | 0.402833 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −39.1782 | −1.65558 | ||||||||
\(561\) | 3.10593 | + | 1.79321i | 0.131132 | + | 0.0757093i | ||||
\(562\) | 7.47584 | − | 12.9485i | 0.315349 | − | 0.546201i | ||||
\(563\) | 1.93565 | + | 3.35264i | 0.0815779 | + | 0.141297i | 0.903928 | − | 0.427685i | \(-0.140671\pi\) |
−0.822350 | + | 0.568982i | \(0.807337\pi\) | |||||||
\(564\) | − | 5.70410i | − | 0.240186i | ||||||
\(565\) | 40.1128 | − | 23.1591i | 1.68756 | − | 0.974312i | ||||
\(566\) | 15.5147 | − | 8.95742i | 0.652132 | − | 0.376508i | ||||
\(567\) | 4.80194i | 0.201662i | ||||||||
\(568\) | −13.4743 | − | 23.3382i | −0.565371 | − | 0.979251i | ||||
\(569\) | 10.0728 | − | 17.4467i | 0.422276 | − | 0.731403i | −0.573886 | − | 0.818935i | \(-0.694565\pi\) |
0.996162 | + | 0.0875324i | \(0.0278981\pi\) | |||||||
\(570\) | −7.69438 | − | 4.44235i | −0.322282 | − | 0.186070i | ||||
\(571\) | 32.1269 | 1.34447 | 0.672234 | − | 0.740338i | \(-0.265335\pi\) | ||||
0.672234 | + | 0.740338i | \(0.265335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3817 | 0.893231 | ||||||||
\(574\) | 6.46645 | + | 3.73341i | 0.269904 | + | 0.155829i | ||||
\(575\) | 5.01142 | − | 8.68003i | 0.208991 | − | 0.361982i | ||||
\(576\) | 4.44989 | + | 7.70743i | 0.185412 | + | 0.321143i | ||||
\(577\) | 16.7506i | 0.697338i | 0.937246 | + | 0.348669i | \(0.113366\pi\) | ||||
−0.937246 | + | 0.348669i | \(0.886634\pi\) | |||||||
\(578\) | −11.9026 | + | 6.87196i | −0.495082 | + | 0.285836i | ||||
\(579\) | 7.29850 | − | 4.21379i | 0.303315 | − | 0.175119i | ||||
\(580\) | − | 2.30798i | − | 0.0958336i | ||||||
\(581\) | −1.56734 | − | 2.71470i | −0.0650240 | − | 0.112625i | ||||
\(582\) | −6.25451 | + | 10.8331i | −0.259258 | + | 0.449048i | ||||
\(583\) | −11.2432 | − | 6.49127i | −0.465646 | − | 0.268841i | ||||
\(584\) | −23.4523 | −0.970465 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.3913 | −0.966287 | ||||||||
\(587\) | −5.83524 | − | 3.36898i | −0.240846 | − | 0.139053i | 0.374719 | − | 0.927138i | \(-0.377739\pi\) |
−0.615566 | + | 0.788086i | \(0.711072\pi\) | |||||||
\(588\) | 3.57338 | − | 6.18927i | 0.147364 | − | 0.255241i | ||||
\(589\) | −9.70237 | − | 16.8050i | −0.399779 | − | 0.692438i | ||||
\(590\) | − | 7.60388i | − | 0.313047i | ||||||
\(591\) | −22.9293 | + | 13.2383i | −0.943186 | + | 0.544549i | ||||
\(592\) | −11.4864 | + | 6.63169i | −0.472089 | + | 0.272561i | ||||
\(593\) | 18.1172i | 0.743985i | 0.928236 | + | 0.371992i | \(0.121325\pi\) | ||||
−0.928236 | + | 0.371992i | \(0.878675\pi\) | |||||||
\(594\) | −0.914542 | − | 1.58403i | −0.0375241 | − | 0.0649937i | ||||
\(595\) | −16.4487 | + | 28.4900i | −0.674331 | + | 1.16797i | ||||
\(596\) | −5.53082 | − | 3.19322i | −0.226551 | − | 0.130799i | ||||
\(597\) | 14.2524 | 0.583310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7851 | −1.09441 | −0.547204 | − | 0.836999i | \(-0.684308\pi\) | ||||
−0.547204 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(600\) | 7.52751 | + | 4.34601i | 0.307309 | + | 0.177425i | ||||
\(601\) | 2.35086 | − | 4.07180i | 0.0958934 | − | 0.166092i | −0.814088 | − | 0.580742i | \(-0.802763\pi\) |
0.909981 | + | 0.414650i | \(0.136096\pi\) | |||||||
\(602\) | −7.13773 | − | 12.3629i | −0.290912 | − | 0.503874i | ||||
\(603\) | − | 3.58211i | − | 0.145875i | ||||||
\(604\) | −0.757788 | + | 0.437509i | −0.0308340 | + | 0.0178020i | ||||
\(605\) | −21.4712 | + | 12.3964i | −0.872930 | + | 0.503986i | ||||
\(606\) | − | 17.3177i | − | 0.703482i | ||||||
\(607\) | −13.8198 | − | 23.9366i | −0.560929 | − | 0.971558i | −0.997416 | − | 0.0718472i | \(-0.977111\pi\) |
0.436486 | − | 0.899711i | \(-0.356223\pi\) | |||||||
\(608\) | 3.13640 | − | 5.43240i | 0.127198 | − | 0.220313i | ||||
\(609\) | −7.69697 | − | 4.44385i | −0.311897 | − | 0.180074i | ||||
\(610\) | −27.3545 | −1.10755 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.08815 | 0.0439857 | ||||||||
\(613\) | 41.7236 | + | 24.0891i | 1.68520 | + | 0.972950i | 0.958108 | + | 0.286409i | \(0.0924615\pi\) |
0.727091 | + | 0.686541i | \(0.240872\pi\) | |||||||
\(614\) | 15.9777 | − | 27.6742i | 0.644807 | − | 1.11684i | ||||
\(615\) | −1.74698 | − | 3.02586i | −0.0704450 | − | 0.122014i | ||||
\(616\) | 21.4752i | 0.865259i | ||||||||
\(617\) | −26.2443 | + | 15.1521i | −1.05655 | + | 0.610002i | −0.924477 | − | 0.381238i | \(-0.875498\pi\) |
−0.132077 | + | 0.991239i | \(0.542165\pi\) | |||||||
\(618\) | 18.7942 | − | 10.8509i | 0.756015 | − | 0.436485i | ||||
\(619\) | − | 10.9041i | − | 0.438272i | −0.975694 | − | 0.219136i | \(-0.929676\pi\) | ||
0.975694 | − | 0.219136i | \(-0.0703239\pi\) | |||||||
\(620\) | 4.75786 | + | 8.24086i | 0.191080 | + | 0.330961i | ||||
\(621\) | −1.75786 | + | 3.04471i | −0.0705407 | + | 0.122180i | ||||
\(622\) | 12.2912 | + | 7.09634i | 0.492833 | + | 0.284537i | ||||
\(623\) | 30.2325 | 1.21124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1269 | −1.24508 | ||||||||
\(626\) | −29.7780 | − | 17.1923i | −1.19017 | − | 0.687143i | ||||
\(627\) | −1.86496 | + | 3.23021i | −0.0744794 | + | 0.129002i | ||||
\(628\) | −2.38135 | − | 4.12463i | −0.0950264 | − | 0.164591i | ||||
\(629\) | 11.1371i | 0.444064i | ||||||||
\(630\) | 14.5300 | − | 8.38889i | 0.578888 | − | 0.334221i | ||||
\(631\) | −9.05199 | + | 5.22617i | −0.360354 | + | 0.208050i | −0.669236 | − | 0.743050i | \(-0.733379\pi\) |
0.308882 | + | 0.951100i | \(0.400045\pi\) | |||||||
\(632\) | − | 12.2620i | − | 0.487758i | ||||||
\(633\) | −0.925428 | − | 1.60289i | −0.0367824 | − | 0.0637091i | ||||
\(634\) | 7.02028 | − | 12.1595i | 0.278811 | − | 0.482915i | ||||
\(635\) | 23.1432 | + | 13.3617i | 0.918410 | + | 0.530244i | ||||
\(636\) | −3.93900 | −0.156192 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.38537 | 0.134028 | ||||||||
\(639\) | 7.65460 | + | 4.41939i | 0.302811 | + | 0.174828i | ||||
\(640\) | 8.63587 | − | 14.9578i | 0.341363 | − | 0.591257i | ||||
\(641\) | −8.79709 | − | 15.2370i | −0.347464 | − | 0.601826i | 0.638334 | − | 0.769760i | \(-0.279624\pi\) |
−0.985798 | + | 0.167934i | \(0.946291\pi\) | |||||||
\(642\) | 13.1588i | 0.519338i | ||||||||
\(643\) | −19.5772 | + | 11.3029i | −0.772049 | + | 0.445743i | −0.833605 | − | 0.552361i | \(-0.813727\pi\) |
0.0615560 | + | 0.998104i | \(0.480394\pi\) | |||||||
\(644\) | 6.50674 | − | 3.75667i | 0.256401 | − | 0.148033i | ||||
\(645\) | 6.67994i | 0.263022i | ||||||||
\(646\) | 3.87651 | + | 6.71431i | 0.152519 | + | 0.264171i | ||||
\(647\) | −12.3959 | + | 21.4703i | −0.487333 | + | 0.844085i | −0.999894 | − | 0.0145658i | \(-0.995363\pi\) |
0.512561 | + | 0.858651i | \(0.328697\pi\) | |||||||
\(648\) | −2.64044 | − | 1.52446i | −0.103726 | − | 0.0598864i | ||||
\(649\) | −3.19221 | −0.125305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6437 | 1.43618 | ||||||||
\(652\) | 1.50304 | + | 0.867781i | 0.0588636 | + | 0.0339849i | ||||
\(653\) | 10.9053 | − | 18.8885i | 0.426757 | − | 0.739164i | −0.569826 | − | 0.821765i | \(-0.692989\pi\) |
0.996583 | + | 0.0826012i | \(0.0263228\pi\) | |||||||
\(654\) | 0.667563 | + | 1.15625i | 0.0261038 | + | 0.0452131i | ||||
\(655\) | 15.4359i | 0.603132i | ||||||||
\(656\) | −3.14456 | + | 1.81551i | −0.122774 | + | 0.0708838i | ||||
\(657\) | 6.66149 | − | 3.84601i | 0.259889 | − | 0.150047i | ||||
\(658\) | 76.7472i | 2.99192i | ||||||||
\(659\) | −8.27628 | − | 14.3349i | −0.322398 | − | 0.558410i | 0.658584 | − | 0.752507i | \(-0.271156\pi\) |
−0.980982 | + | 0.194097i | \(0.937822\pi\) | |||||||
\(660\) | 0.914542 | − | 1.58403i | 0.0355985 | − | 0.0616584i | ||||
\(661\) | 13.8166 | + | 7.97703i | 0.537405 | + | 0.310271i | 0.744026 | − | 0.668150i | \(-0.232914\pi\) |
−0.206622 | + | 0.978421i | \(0.566247\pi\) | |||||||
\(662\) | −14.8471 | −0.577050 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.99031 | 0.0772391 | ||||||||
\(665\) | −29.6299 | − | 17.1069i | −1.14900 | − | 0.663376i | ||||
\(666\) | 2.83997 | − | 4.91897i | 0.110047 | − | 0.190606i | ||||
\(667\) | −3.25355 | − | 5.63532i | −0.125978 | − | 0.218200i | ||||
\(668\) | − | 9.35450i | − | 0.361937i | ||||||
\(669\) | 16.1517 | − | 9.32520i | 0.624462 | − | 0.360533i | ||||
\(670\) | −10.8389 | + | 6.25786i | −0.418745 | + | 0.241762i | ||||
\(671\) | 11.4838i | 0.443327i | ||||||||
\(672\) | 5.92274 | + | 10.2585i | 0.228475 | + | 0.395730i | ||||
\(673\) | −3.69418 | + | 6.39850i | −0.142400 | + | 0.246644i | −0.928400 | − | 0.371583i | \(-0.878815\pi\) |
0.786000 | + | 0.618227i | \(0.212149\pi\) | |||||||
\(674\) | 18.5391 | + | 10.7036i | 0.714101 | + | 0.412286i | ||||
\(675\) | −2.85086 | −0.109729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1454 | −0.851118 | −0.425559 | − | 0.904931i | \(-0.639922\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639922\pi\) | |||||||
\(678\) | 17.8519 | + | 10.3068i | 0.685597 | + | 0.395830i | ||||
\(679\) | −24.0852 | + | 41.7168i | −0.924306 | + | 1.60094i | ||||
\(680\) | −10.4438 | − | 18.0893i | −0.400503 | − | 0.693692i | ||||
\(681\) | 9.75733i | 0.373902i | ||||||||
\(682\) | −12.0878 | + | 6.97889i | −0.462866 | + | 0.267236i | ||||
\(683\) | 7.88103 | − | 4.55011i | 0.301559 | − | 0.174105i | −0.341584 | − | 0.939851i | \(-0.610963\pi\) |
0.643143 | + | 0.765746i | \(0.277630\pi\) | |||||||
\(684\) | 1.13169i | 0.0432711i | ||||||||
\(685\) | −22.6727 | − | 39.2703i | −0.866279 | − | 1.50044i | ||||
\(686\) | −27.1211 | + | 46.9751i | −1.03549 | + | 1.79352i | ||||
\(687\) | −2.47938 | − | 1.43147i | −0.0945941 | − | 0.0546139i | ||||
\(688\) | 6.94198 | 0.264661 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.2838 | 0.467637 | ||||||||
\(691\) | 11.9261 | + | 6.88553i | 0.453690 | + | 0.261938i | 0.709387 | − | 0.704819i | \(-0.248972\pi\) |
−0.255697 | + | 0.966757i | \(0.582305\pi\) | |||||||
\(692\) | 2.94504 | − | 5.10096i | 0.111954 | − | 0.193909i | ||||
\(693\) | −3.52177 | − | 6.09989i | −0.133781 | − | 0.231715i | ||||
\(694\) | − | 30.2717i | − | 1.14910i | ||||||
\(695\) | 25.5007 | − | 14.7228i | 0.967295 | − | 0.558468i | ||||
\(696\) | 4.88707 | − | 2.82155i | 0.185244 | − | 0.106951i | ||||
\(697\) | 3.04892i | 0.115486i | ||||||||
\(698\) | −2.85086 | − | 4.93783i | −0.107906 | − | 0.186899i | ||||
\(699\) | −2.89277 | + | 5.01043i | −0.109415 | + | 0.189512i | ||||
\(700\) | 5.27622 | + | 3.04623i | 0.199422 | + | 0.115137i | ||||
\(701\) | −46.5090 | −1.75662 | −0.878311 | − | 0.478090i | \(-0.841329\pi\) | ||||
−0.878311 | + | 0.478090i | \(0.841329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5827 | −0.436850 | ||||||||
\(704\) | −11.3054 | − | 6.52715i | −0.426086 | − | 0.246001i | ||||
\(705\) | 17.9562 | − | 31.1011i | 0.676270 | − | 1.17133i | ||||
\(706\) | 3.78836 | + | 6.56164i | 0.142577 | + | 0.246951i | ||||
\(707\) | − | 66.6878i | − | 2.50805i | ||||||
\(708\) | −0.838781 | + | 0.484271i | −0.0315233 | + | 0.0182000i | ||||
\(709\) | 6.27492 | − | 3.62283i | 0.235660 | − | 0.136058i | −0.377521 | − | 0.926001i | \(-0.623223\pi\) |
0.613180 | + | 0.789943i | \(0.289890\pi\) | |||||||
\(710\) | − | 30.8823i | − | 1.15899i | ||||||
\(711\) | 2.01089 | + | 3.48296i | 0.0754141 | + | 0.130621i | ||||
\(712\) | −9.59783 | + | 16.6239i | −0.359694 | + | 0.623008i | ||||
\(713\) | 23.2343 | + | 13.4143i | 0.870130 | + | 0.502370i | ||||
\(714\) | −14.6407 | −0.547915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.79523 | −0.141835 | ||||||||
\(717\) | −6.14225 | − | 3.54623i | −0.229386 | − | 0.132436i | ||||
\(718\) | −9.33124 | + | 16.1622i | −0.348239 | + | 0.603167i | ||||
\(719\) | 12.7573 | + | 22.0963i | 0.475768 | + | 0.824055i | 0.999615 | − | 0.0277580i | \(-0.00883678\pi\) |
−0.523846 | + | 0.851813i | \(0.675503\pi\) | |||||||
\(720\) | 8.15883i | 0.304062i | ||||||||
\(721\) | 72.3739 | − | 41.7851i | 2.69534 | − | 1.55616i | ||||
\(722\) | 13.5354 | − | 7.81468i | 0.503736 | − | 0.290832i | ||||
\(723\) | − | 3.89977i | − | 0.145034i | ||||||
\(724\) | −0.809175 | − | 1.40153i | −0.0300728 | − | 0.0520875i | ||||
\(725\) | 2.63826 | − | 4.56960i | 0.0979825 | − | 0.169711i | ||||
\(726\) | −9.55560 | − | 5.51693i | −0.354641 | − | 0.204752i | ||||
\(727\) | 14.4873 | 0.537303 | 0.268651 | − | 0.963238i | \(-0.413422\pi\) | ||||
0.268651 | + | 0.963238i | \(0.413422\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.2750 | − | 13.4378i | −0.861445 | − | 0.497355i | ||||
\(731\) | 2.91454 | − | 5.04814i | 0.107798 | − | 0.186712i | ||||
\(732\) | 1.74214 | + | 3.01747i | 0.0643912 | + | 0.111529i | ||||
\(733\) | − | 37.5036i | − | 1.38523i | −0.721308 | − | 0.692614i | \(-0.756459\pi\) | ||
0.721308 | − | 0.692614i | \(-0.243541\pi\) | |||||||
\(734\) | 40.0469 | − | 23.1211i | 1.47816 | − | 0.853415i | ||||
\(735\) | 38.9670 | − | 22.4976i | 1.43732 | − | 0.829837i | ||||
\(736\) | 8.67264i | 0.319678i | ||||||||
\(737\) | 2.62714 | + | 4.55034i | 0.0967719 | + | 0.167614i | ||||
\(738\) | 0.777479 | − | 1.34663i | 0.0286194 | − | 0.0495703i | ||||
\(739\) | −37.4016 | − | 21.5938i | −1.37584 | − | 0.794341i | −0.384184 | − | 0.923257i | \(-0.625517\pi\) |
−0.991656 | + | 0.128915i | \(0.958851\pi\) | |||||||
\(740\) | 5.67994 | 0.208799 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.9982 | 1.94563 | ||||||||
\(743\) | 11.6710 | + | 6.73825i | 0.428167 | + | 0.247202i | 0.698566 | − | 0.715546i | \(-0.253822\pi\) |
−0.270398 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(744\) | −11.6332 | + | 20.1493i | −0.426493 | + | 0.738708i | ||||
\(745\) | −20.1042 | − | 34.8214i | −0.736560 | − | 1.27576i | ||||
\(746\) | − | 45.5260i | − | 1.66683i | ||||||
\(747\) | −0.565335 | + | 0.326396i | −0.0206845 | + | 0.0119422i | ||||
\(748\) | −1.38227 | + | 0.798053i | −0.0505407 | + | 0.0291797i | ||||
\(749\) | 50.6728i | 1.85154i | ||||||||
\(750\) | −3.75451 | − | 6.50301i | −0.137095 | − | 0.237456i | ||||
\(751\) | 17.7947 | − | 30.8213i | 0.649338 | − | 1.12469i | −0.333943 | − | 0.942593i | \(-0.608379\pi\) |
0.983281 | − | 0.182093i | \(-0.0582872\pi\) | |||||||
\(752\) | −32.3211 | − | 18.6606i | −1.17863 | − | 0.680483i | ||||
\(753\) | 2.44504 | 0.0891023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.50902 | −0.200494 | ||||||||
\(756\) | −1.85075 | − | 1.06853i | −0.0673112 | − | 0.0388621i | ||||
\(757\) | 6.10537 | − | 10.5748i | 0.221903 | − | 0.384348i | −0.733483 | − | 0.679708i | \(-0.762106\pi\) |
0.955386 | + | 0.295360i | \(0.0954397\pi\) | |||||||
\(758\) | 16.5755 | + | 28.7097i | 0.602050 | + | 1.04278i | ||||
\(759\) | − | 5.15691i | − | 0.187184i | ||||||
\(760\) | 18.8131 | − | 10.8617i | 0.682422 | − | 0.393997i | ||||
\(761\) | 26.7663 | − | 15.4535i | 0.970278 | − | 0.560190i | 0.0709569 | − | 0.997479i | \(-0.477395\pi\) |
0.899321 | + | 0.437289i | \(0.144061\pi\) | |||||||
\(762\) | 11.8931i | 0.430840i | ||||||||
\(763\) | 2.57069 | + | 4.45256i | 0.0930651 | + | 0.161194i | ||||
\(764\) | −4.75786 | + | 8.24086i | −0.172134 | + | 0.298144i | ||||
\(765\) | 5.93301 | + | 3.42543i | 0.214509 | + | 0.123847i | ||||
\(766\) | −17.8944 | −0.646551 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.1129 | −0.364918 | ||||||||
\(769\) | 10.3830 | + | 5.99462i | 0.374420 | + | 0.216172i | 0.675388 | − | 0.737463i | \(-0.263976\pi\) |
−0.300968 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(770\) | −12.3049 | + | 21.3127i | −0.443439 | + | 0.768058i | ||||
\(771\) | −7.06518 | − | 12.2372i | −0.254446 | − | 0.440714i | ||||
\(772\) | 3.75063i | 0.134988i | ||||||||
\(773\) | −38.0758 | + | 21.9831i | −1.36949 | + | 0.790676i | −0.990863 | − | 0.134873i | \(-0.956938\pi\) |
−0.378628 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(774\) | −2.57457 | + | 1.48643i | −0.0925409 | + | 0.0534285i | ||||
\(775\) | 21.7549i | 0.781460i | ||||||||
\(776\) | −15.2925 | − | 26.4875i | −0.548970 | − | 0.950845i | ||||
\(777\) | 10.9363 | − | 18.9422i | 0.392338 | − | 0.679549i | ||||
\(778\) | −24.4689 | − | 14.1271i | −0.877253 | − | 0.506482i | ||||
\(779\) | −3.17092 | −0.113610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9648 | −0.463918 | ||||||||
\(782\) | −9.28307 | − | 5.35958i | −0.331962 | − | 0.191658i | ||||
\(783\) | −0.925428 | + | 1.60289i | −0.0330721 | + | 0.0572825i | ||||
\(784\) | −23.3802 | − | 40.4956i | −0.835006 | − | 1.44627i | ||||
\(785\) | − | 29.9855i | − | 1.07023i | ||||||
\(786\) | −5.94928 | + | 3.43482i | −0.212204 | + | 0.122516i | ||||
\(787\) | 26.3066 | − | 15.1881i | 0.937730 | − | 0.541399i | 0.0484819 | − | 0.998824i | \(-0.484562\pi\) |
0.889248 | + | 0.457425i | \(0.151228\pi\) | |||||||
\(788\) | − | 11.7832i | − | 0.419757i | ||||||
\(789\) | 11.8617 | + | 20.5451i | 0.422289 | + | 0.731426i | ||||
\(790\) | 7.02595 | − | 12.1693i | 0.249972 | − | 0.432964i | ||||
\(791\) | 68.7450 | + | 39.6899i | 2.44429 | + | 1.41121i | ||||
\(792\) | 4.47219 | 0.158912 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.86054 | −0.349938 | ||||||||
\(795\) | −21.4770 | − | 12.3998i | −0.761712 | − | 0.439775i | ||||
\(796\) | −3.17145 | + | 5.49311i | −0.112409 | + | 0.194698i | ||||
\(797\) | 26.2881 | + | 45.5324i | 0.931173 | + | 1.61284i | 0.781320 | + | 0.624131i | \(0.214547\pi\) |
0.149854 | + | 0.988708i | \(0.452120\pi\) | |||||||
\(798\) | − | 15.2265i | − | 0.539014i | ||||||
\(799\) | −27.1396 | + | 15.6691i | −0.960130 | + | 0.554331i | ||||
\(800\) | −6.09034 | + | 3.51626i | −0.215326 | + | 0.124319i | ||||
\(801\) | − | 6.29590i | − | 0.222455i | ||||||
\(802\) | 1.83095 | + | 3.17129i | 0.0646529 | + | 0.111982i | ||||
\(803\) | −5.64138 | + | 9.77115i | −0.199080 | + | 0.344816i | ||||
\(804\) | 1.38061 | + | 0.797093i | 0.0486902 | + | 0.0281113i | ||||
\(805\) | 47.3032 | 1.66722 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.91617 | −0.208259 | ||||||||
\(808\) | 36.6696 | + | 21.1712i | 1.29003 | + | 0.744801i | ||||
\(809\) | −24.7107 | + | 42.8002i | −0.868783 | + | 1.50478i | −0.00554214 | + | 0.999985i | \(0.501764\pi\) |
−0.863241 | + | 0.504792i | \(0.831569\pi\) | |||||||
\(810\) | −1.74698 | − | 3.02586i | −0.0613826 | − | 0.106318i | ||||
\(811\) | 1.36526i | 0.0479406i | 0.999713 | + | 0.0239703i | \(0.00763072\pi\) | ||||
−0.999713 | + | 0.0239703i | \(0.992369\pi\) | |||||||
\(812\) | 3.42547 | − | 1.97770i | 0.120211 | − | 0.0694036i | ||||
\(813\) | −2.76287 | + | 1.59515i | −0.0968982 | + | 0.0559442i | ||||
\(814\) | 8.33140i | 0.292016i | ||||||||
\(815\) | 5.46346 | + | 9.46299i | 0.191377 | + | 0.331474i | ||||
\(816\) | 3.55980 | − | 6.16576i | 0.124618 | − | 0.215845i | ||||
\(817\) | 5.25013 | + | 3.03116i | 0.183679 | + | 0.106047i | ||||
\(818\) | 14.6582 | 0.512511 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.55496 | 0.0543015 | ||||||||
\(821\) | 0.576720 | + | 0.332970i | 0.0201277 | + | 0.0116207i | 0.510030 | − | 0.860157i | \(-0.329634\pi\) |
−0.489902 | + | 0.871777i | \(0.662968\pi\) | |||||||
\(822\) | 10.0903 | − | 17.4769i | 0.351940 | − | 0.609577i | ||||
\(823\) | −5.02960 | − | 8.71152i | −0.175321 | − | 0.303665i | 0.764951 | − | 0.644088i | \(-0.222763\pi\) |
−0.940272 | + | 0.340423i | \(0.889430\pi\) | |||||||
\(824\) | 53.0616i | 1.84849i | ||||||||
\(825\) | 3.62143 | − | 2.09083i | 0.126082 | − | 0.0727935i | ||||
\(826\) | 11.2856 | − | 6.51573i | 0.392675 | − | 0.226711i | ||||
\(827\) | − | 37.3038i | − | 1.29718i | −0.761138 | − | 0.648590i | \(-0.775359\pi\) | ||
0.761138 | − | 0.648590i | \(-0.224641\pi\) | |||||||
\(828\) | −0.782323 | − | 1.35502i | −0.0271876 | − | 0.0470903i | ||||
\(829\) | −21.3104 | + | 36.9107i | −0.740142 | + | 1.28196i | 0.212289 | + | 0.977207i | \(0.431908\pi\) |
−0.952430 | + | 0.304756i | \(0.901425\pi\) | |||||||
\(830\) | 1.97526 | + | 1.14042i | 0.0685622 | + | 0.0395844i | ||||
\(831\) | −21.9366 | −0.760973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.2640 | −1.36042 | ||||||||
\(834\) | 11.3489 | + | 6.55227i | 0.392979 | + | 0.226887i | ||||
\(835\) | 29.4475 | − | 51.0046i | 1.01907 | − | 1.76509i | ||||
\(836\) | −0.829986 | − | 1.43758i | −0.0287057 | − | 0.0497197i | ||||
\(837\) | − | 7.63102i | − | 0.263767i | ||||||
\(838\) | 7.92856 | − | 4.57756i | 0.273888 | − | 0.158129i | ||||
\(839\) | 3.58539 | − | 2.07002i | 0.123781 | − | 0.0714652i | −0.436831 | − | 0.899544i | \(-0.643899\pi\) |
0.560612 | + | 0.828078i | \(0.310566\pi\) | |||||||
\(840\) | 41.0224i | 1.41541i | ||||||||
\(841\) | 12.7872 | + | 22.1480i | 0.440937 | + | 0.763725i | ||||
\(842\) | −16.0214 | + | 27.7499i | −0.552134 | + | 0.956324i | ||||
\(843\) | −10.3839 | − | 5.99516i | −0.357641 | − | 0.206484i | ||||
\(844\) | 0.823708 | 0.0283532 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.9825 | 0.549491 | ||||||||
\(847\) | −36.7972 | − | 21.2449i | −1.26437 | − | 0.729983i | ||||
\(848\) | −12.8862 | + | 22.3196i | −0.442514 | + | 0.766457i | ||||
\(849\) | −7.18329 | − | 12.4418i | −0.246530 | − | 0.427002i | ||||
\(850\) | − | 8.69202i | − | 0.298134i | ||||||
\(851\) | 13.8685 | − | 8.00700i | 0.475407 | − | 0.274476i | ||||
\(852\) | −3.40662 | + | 1.96681i | −0.116709 | + | 0.0673819i | ||||
\(853\) | 17.3502i | 0.594059i | 0.954868 | + | 0.297030i | \(0.0959960\pi\) | ||||
−0.954868 | + | 0.297030i | \(0.904004\pi\) | |||||||
\(854\) | −23.4400 | − | 40.5992i | −0.802099 | − | 1.38928i | ||||
\(855\) | −3.56249 | + | 6.17042i | −0.121835 | + | 0.211024i | ||||
\(856\) | −27.8634 | − | 16.0869i | −0.952352 | − | 0.549841i | ||||
\(857\) | −41.0180 | −1.40115 | −0.700575 | − | 0.713579i | \(-0.747073\pi\) | ||||
−0.700575 | + | 0.713579i | \(0.747073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.59286 | 0.224945 | 0.112473 | − | 0.993655i | \(-0.464123\pi\) | ||||
0.112473 | + | 0.993655i | \(0.464123\pi\) | |||||||
\(860\) | −2.57457 | − | 1.48643i | −0.0877920 | − | 0.0506867i | ||||
\(861\) | 2.99396 | − | 5.18569i | 0.102034 | − | 0.176728i | ||||
\(862\) | −5.57524 | − | 9.65659i | −0.189893 | − | 0.328905i | ||||
\(863\) | 16.6455i | 0.566619i | 0.959028 | + | 0.283310i | \(0.0914324\pi\) | ||||
−0.959028 | + | 0.283310i | \(0.908568\pi\) | |||||||
\(864\) | 2.13632 | − | 1.23341i | 0.0726791 | − | 0.0419613i | ||||
\(865\) | 32.1151 | − | 18.5417i | 1.09195 | − | 0.630436i | ||||
\(866\) | − | 3.63474i | − | 0.123514i | ||||||
\(867\) | 5.51089 | + | 9.54513i | 0.187159 | + | 0.324170i | ||||
\(868\) | −8.15399 | + | 14.1231i | −0.276764 | + | 0.479370i | ||||
\(869\) | −5.10884 | − | 2.94959i | −0.173306 | − | 0.100058i | ||||
\(870\) | 6.46681 | 0.219245 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.26444 | −0.110548 | ||||||||
\(873\) | 8.68750 | + | 5.01573i | 0.294027 | + | 0.169757i | ||||
\(874\) | 5.57404 | − | 9.65452i | 0.188545 | − | 0.326569i | ||||
\(875\) | −14.4581 | − | 25.0421i | −0.488772 | − | 0.846579i | ||||
\(876\) | 3.42327i | 0.115662i | ||||||||
\(877\) | −47.1953 | + | 27.2482i | −1.59367 | + | 0.920108i | −0.601004 | + | 0.799246i | \(0.705232\pi\) |
−0.992669 | + | 0.120861i | \(0.961434\pi\) | |||||||
\(878\) | −9.78253 | + | 5.64795i | −0.330145 | + | 0.190609i | ||||
\(879\) | 18.7584i | 0.632705i | ||||||||
\(880\) | −5.98374 | − | 10.3641i | −0.201712 | − | 0.349375i | ||||
\(881\) | −4.50335 | + | 7.80004i | −0.151722 | + | 0.262790i | −0.931861 | − | 0.362817i | \(-0.881815\pi\) |
0.780139 | + | 0.625607i | \(0.215148\pi\) | |||||||
\(882\) | 17.3419 | + | 10.0124i | 0.583934 | + | 0.337134i | ||||
\(883\) | −18.8907 | −0.635722 | −0.317861 | − | 0.948137i | \(-0.602965\pi\) | ||||
−0.317861 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.09783 | −0.204976 | ||||||||
\(886\) | −12.1302 | − | 7.00335i | −0.407521 | − | 0.235282i | ||||
\(887\) | 23.4562 | − | 40.6274i | 0.787583 | − | 1.36413i | −0.139861 | − | 0.990171i | \(-0.544666\pi\) |
0.927444 | − | 0.373962i | \(-0.122001\pi\) | |||||||
\(888\) | 6.94385 | + | 12.0271i | 0.233020 | + | 0.403603i | ||||
\(889\) | 45.7985i | 1.53603i | ||||||||
\(890\) | −19.0505 | + | 10.9988i | −0.638574 | + | 0.368681i | ||||
\(891\) | −1.27030 | + | 0.733406i | −0.0425565 | + | 0.0245700i | ||||
\(892\) | 8.30021i | 0.277912i | ||||||||
\(893\) | −16.2960 | − | 28.2255i | −0.545326 | − | 0.944532i | ||||
\(894\) | 8.94720 | − | 15.4970i | 0.299239 | − | 0.518297i | ||||
\(895\) | −20.6932 | − | 11.9472i | −0.691696 | − | 0.399351i | ||||
\(896\) | 29.6002 | 0.988872 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.8605 | −1.19668 | ||||||||
\(899\) | 12.2317 | + | 7.06196i | 0.407949 | + | 0.235529i | ||||
\(900\) | 0.634375 | − | 1.09877i | 0.0211458 | − | 0.0366257i | ||||
\(901\) | 10.8204 | + | 18.7414i | 0.360478 | + | 0.624367i | ||||
\(902\) | 2.28083i | 0.0759434i | ||||||||
\(903\) | −9.91428 | + | 5.72401i | −0.329927 | + | 0.190483i | ||||
\(904\) | −43.6486 | + | 25.2005i | −1.45173 | + | 0.838157i | ||||
\(905\) | − | 10.1890i | − | 0.338693i | ||||||
\(906\) | −1.22587 | − | 2.12327i | −0.0407269 | − | 0.0705411i | ||||
\(907\) | −17.6506 | + | 30.5718i | −0.586080 | + | 1.01512i | 0.408660 | + | 0.912687i | \(0.365996\pi\) |
−0.994740 | + | 0.102433i | \(0.967337\pi\) | |||||||
\(908\) | −3.76065 | − | 2.17121i | −0.124801 | − | 0.0720542i | ||||
\(909\) | −13.8877 | −0.460626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.80731 | −0.324931 | −0.162465 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162465 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(912\) | 6.41247 | + | 3.70224i | 0.212338 | + | 0.122594i | ||||
\(913\) | 0.478762 | − | 0.829240i | 0.0158447 | − | 0.0274439i | ||||
\(914\) | 11.8937 | + | 20.6005i | 0.393410 | + | 0.681406i | ||||
\(915\) | 21.9366i | 0.725202i | ||||||||
\(916\) | 1.10343 | − | 0.637063i | 0.0364582 | − | 0.0210492i | ||||
\(917\) | −22.9098 | + | 13.2270i | −0.756549 | + | 0.436794i | ||||
\(918\) | 3.04892i | 0.100629i | ||||||||
\(919\) | −9.23274 | − | 15.9916i | −0.304560 | − | 0.527513i | 0.672603 | − | 0.740003i | \(-0.265176\pi\) |
−0.977163 | + | 0.212490i | \(0.931843\pi\) | |||||||
\(920\) | −15.0172 | + | 26.0106i | −0.495103 | + | 0.857544i | ||||
\(921\) | −22.1930 | − | 12.8131i | −0.731283 | − | 0.422207i | ||||
\(922\) | 39.5706 | 1.30319 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.13467 | 0.103123 | ||||||||
\(925\) | 11.2458 | + | 6.49276i | 0.369759 | + | 0.213481i | ||||
\(926\) | −22.7439 | + | 39.3936i | −0.747412 | + | 1.29455i | ||||
\(927\) | −8.70171 | − | 15.0718i | −0.285802 | − | 0.495023i | ||||
\(928\) | 4.56571i | 0.149877i | ||||||||
\(929\) | 22.1934 | − | 12.8134i | 0.728141 | − | 0.420393i | −0.0896005 | − | 0.995978i | \(-0.528559\pi\) |
0.817742 | + | 0.575585i | \(0.195226\pi\) | |||||||
\(930\) | −23.0904 | + | 13.3312i | −0.757164 | + | 0.437149i | ||||
\(931\) | − | 40.8351i | − | 1.33831i | ||||||
\(932\) | −1.28740 | − | 2.22985i | −0.0421703 | − | 0.0730412i | ||||
\(933\) | 5.69083 | − | 9.85680i | 0.186309 | − | 0.322697i | ||||
\(934\) | 14.0389 | + | 8.10537i | 0.459367 | + | 0.265216i | ||||
\(935\) | −10.0489 | −0.328635 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.54932 | 0.246625 | 0.123313 | − | 0.992368i | \(-0.460648\pi\) | ||||
0.123313 | + | 0.992368i | \(0.460648\pi\) | |||||||
\(938\) | −18.5757 | − | 10.7247i | −0.606518 | − | 0.350173i | ||||
\(939\) | −13.7872 | + | 23.8801i | −0.449927 | + | 0.779297i | ||||
\(940\) | 7.99127 | + | 13.8413i | 0.260647 | + | 0.451453i | ||||
\(941\) | 12.6418i | 0.412110i | 0.978540 | + | 0.206055i | \(0.0660626\pi\) | ||||
−0.978540 | + | 0.206055i | \(0.933937\pi\) | |||||||
\(942\) | 11.5569 | − | 6.67241i | 0.376546 | − | 0.217399i | ||||
\(943\) | 3.79669 | − | 2.19202i | 0.123637 | − | 0.0713820i | ||||
\(944\) | 6.33704i | 0.206253i | ||||||||
\(945\) | −6.72737 | − | 11.6521i | −0.218841 | − | 0.379044i | ||||
\(946\) | 2.18031 | − | 3.77640i | 0.0708879 | − | 0.122782i | ||||
\(947\) | −24.2315 | − | 13.9901i | −0.787419 | − | 0.454616i | 0.0516344 | − | 0.998666i | \(-0.483557\pi\) |
−0.839053 | + | 0.544050i | \(0.816890\pi\) | |||||||
\(948\) | −1.78986 | −0.0581318 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.03982 | 0.293290 | ||||||||
\(951\) | −9.75114 | − | 5.62983i | −0.316203 | − | 0.182560i | ||||
\(952\) | 17.8986 | − | 31.0012i | 0.580096 | − | 1.00476i | ||||
\(953\) | 2.00120 | + | 3.46617i | 0.0648251 | + | 0.112280i | 0.896616 | − | 0.442808i | \(-0.146018\pi\) |
−0.831791 | + | 0.555089i | \(0.812684\pi\) | |||||||
\(954\) | − | 11.0368i | − | 0.357331i | ||||||
\(955\) | −51.8836 | + | 29.9550i | −1.67891 | + | 0.969322i | ||||
\(956\) | 2.73356 | − | 1.57822i | 0.0884096 | − | 0.0510433i | ||||
\(957\) | − | 2.71486i | − | 0.0877589i | ||||||
\(958\) | 3.50186 | + | 6.06540i | 0.113140 | + | 0.195964i | ||||
\(959\) | 38.8563 | − | 67.3011i | 1.25474 | − | 2.17326i | ||||
\(960\) | −21.5957 | − | 12.4683i | −0.696999 | − | 0.402413i | ||||
\(961\) | −27.2325 | −0.878468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5526 | 0.340052 | ||||||||
\(964\) | 1.50304 | + | 0.867781i | 0.0484097 | + | 0.0279493i | ||||
\(965\) | −11.8068 | + | 20.4499i | −0.380074 | + | 0.658307i | ||||
\(966\) | 10.5260 | + | 18.2315i | 0.338667 | + | 0.586588i | ||||
\(967\) | − | 12.2239i | − | 0.393094i | −0.980494 | − | 0.196547i | \(-0.937027\pi\) | ||
0.980494 | − | 0.196547i | \(-0.0629728\pi\) | |||||||
\(968\) | 23.3638 | − | 13.4891i | 0.750942 | − | 0.433557i | ||||
\(969\) | 5.38446 | − | 3.10872i | 0.172974 | − | 0.0998665i | ||||
\(970\) | − | 35.0495i | − | 1.12537i | ||||||
\(971\) | 11.8201 | + | 20.4729i | 0.379324 | + | 0.657008i | 0.990964 | − | 0.134128i | \(-0.0428233\pi\) |
−0.611640 | + | 0.791136i | \(0.709490\pi\) | |||||||
\(972\) | −0.222521 | + | 0.385418i | −0.00713736 | + | 0.0123623i | ||||
\(973\) | 43.7028 | + | 25.2318i | 1.40105 | + | 0.808896i | ||||
\(974\) | −12.1672 | −0.389862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7972 | 0.729719 | ||||||||
\(977\) | 16.2217 | + | 9.36563i | 0.518979 | + | 0.299633i | 0.736517 | − | 0.676419i | \(-0.236469\pi\) |
−0.217538 | + | 0.976052i | \(0.569802\pi\) | |||||||
\(978\) | −2.43147 | + | 4.21143i | −0.0777498 | + | 0.134667i | ||||
\(979\) | 4.61745 | + | 7.99766i | 0.147574 | + | 0.255606i | ||||
\(980\) | 20.0248i | 0.639667i | ||||||||
\(981\) | 0.927243 | − | 0.535344i | 0.0296046 | − | 0.0170922i | ||||
\(982\) | 7.97880 | − | 4.60656i | 0.254614 | − | 0.147001i | ||||
\(983\) | 12.0954i | 0.385785i | 0.981220 | + | 0.192892i | \(0.0617868\pi\) | ||||
−0.981220 | + | 0.192892i | \(0.938213\pi\) | |||||||
\(984\) | 1.90097 | + | 3.29257i | 0.0606007 | + | 0.104963i | ||||
\(985\) | 37.0928 | − | 64.2465i | 1.18187 | − | 2.04706i | ||||
\(986\) | −4.88707 | − | 2.82155i | −0.155636 | − | 0.0898565i | ||||
\(987\) | 61.5465 | 1.95905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.38165 | −0.266521 | ||||||||
\(990\) | 4.43836 | + | 2.56249i | 0.141060 | + | 0.0814413i | ||||
\(991\) | 14.2763 | − | 24.7272i | 0.453501 | − | 0.785487i | −0.545100 | − | 0.838371i | \(-0.683508\pi\) |
0.998601 | + | 0.0528844i | \(0.0168415\pi\) | |||||||
\(992\) | −9.41215 | − | 16.3023i | −0.298836 | − | 0.517599i | ||||
\(993\) | 11.9065i | 0.377841i | ||||||||
\(994\) | 45.8351 | − | 26.4629i | 1.45380 | − | 0.839353i | ||||
\(995\) | −34.5840 | + | 19.9671i | −1.09639 | + | 0.633000i | ||||
\(996\) | − | 0.290520i | − | 0.00920548i | ||||||
\(997\) | 11.9673 | + | 20.7280i | 0.379010 | + | 0.656464i | 0.990918 | − | 0.134464i | \(-0.0429314\pi\) |
−0.611909 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(998\) | 26.9855 | − | 46.7403i | 0.854212 | − | 1.47954i | ||||
\(999\) | −3.94471 | − | 2.27748i | −0.124805 | − | 0.0720562i |
(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 | 507.2.j.h.316.2 | 12 | ||
13.2 | odd | 12 | 507.2.e.k.484.1 | 6 | |||
13.3 | even | 3 | inner | 507.2.j.h.361.5 | 12 | ||
13.4 | even | 6 | 507.2.b.g.337.2 | 6 | |||
13.5 | odd | 4 | 507.2.e.k.22.1 | 6 | |||
13.6 | odd | 12 | 507.2.a.j.1.3 | ✓ | 3 | ||
13.7 | odd | 12 | 507.2.a.k.1.1 | yes | 3 | ||
13.8 | odd | 4 | 507.2.e.j.22.3 | 6 | |||
13.9 | even | 3 | 507.2.b.g.337.5 | 6 | |||
13.10 | even | 6 | inner | 507.2.j.h.361.2 | 12 | ||
13.11 | odd | 12 | 507.2.e.j.484.3 | 6 | |||
13.12 | even | 2 | inner | 507.2.j.h.316.5 | 12 | ||
39.17 | odd | 6 | 1521.2.b.m.1351.5 | 6 | |||
39.20 | even | 12 | 1521.2.a.p.1.3 | 3 | |||
39.32 | even | 12 | 1521.2.a.q.1.1 | 3 | |||
39.35 | odd | 6 | 1521.2.b.m.1351.2 | 6 | |||
52.7 | even | 12 | 8112.2.a.cf.1.3 | 3 | |||
52.19 | even | 12 | 8112.2.a.by.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.3 | ✓ | 3 | 13.6 | odd | 12 | ||
507.2.a.k.1.1 | yes | 3 | 13.7 | odd | 12 | ||
507.2.b.g.337.2 | 6 | 13.4 | even | 6 | |||
507.2.b.g.337.5 | 6 | 13.9 | even | 3 | |||
507.2.e.j.22.3 | 6 | 13.8 | odd | 4 | |||
507.2.e.j.484.3 | 6 | 13.11 | odd | 12 | |||
507.2.e.k.22.1 | 6 | 13.5 | odd | 4 | |||
507.2.e.k.484.1 | 6 | 13.2 | odd | 12 | |||
507.2.j.h.316.2 | 12 | 1.1 | even | 1 | trivial | ||
507.2.j.h.316.5 | 12 | 13.12 | even | 2 | inner | ||
507.2.j.h.361.2 | 12 | 13.10 | even | 6 | inner | ||
507.2.j.h.361.5 | 12 | 13.3 | even | 3 | inner | ||
1521.2.a.p.1.3 | 3 | 39.20 | even | 12 | |||
1521.2.a.q.1.1 | 3 | 39.32 | even | 12 | |||
1521.2.b.m.1351.2 | 6 | 39.35 | odd | 6 | |||
1521.2.b.m.1351.5 | 6 | 39.17 | odd | 6 | |||
8112.2.a.by.1.1 | 3 | 52.19 | even | 12 | |||
8112.2.a.cf.1.3 | 3 | 52.7 | even | 12 |