Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1064390625.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 271.2 | ||
Root | \(1.31557 + 1.28500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.271 |
Dual form | 450.2.h.d.181.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 2.12459 | − | 0.697217i | 0.950146 | − | 0.311805i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.25729 | −1.60910 | −0.804552 | − | 0.593882i | \(-0.797594\pi\) | ||||
−0.804552 | + | 0.593882i | \(0.797594\pi\) | |||||||
\(8\) | −0.809017 | + | 0.587785i | −0.286031 | + | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.00655751 | − | 2.23606i | −0.00207367 | − | 0.707104i | ||||
\(11\) | 1.51061 | − | 4.64918i | 0.455466 | − | 1.40178i | −0.415121 | − | 0.909766i | \(-0.636261\pi\) |
0.870587 | − | 0.492014i | \(-0.163739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.43361 | − | 4.41219i | −0.397611 | − | 1.22372i | −0.926909 | − | 0.375286i | \(-0.877544\pi\) |
0.529298 | − | 0.848436i | \(-0.322456\pi\) | |||||||
\(14\) | −1.31557 | + | 4.04892i | −0.351602 | + | 1.08212i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −0.815575 | + | 0.592550i | −0.197806 | + | 0.143714i | −0.682279 | − | 0.731092i | \(-0.739011\pi\) |
0.484473 | + | 0.874806i | \(0.339011\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 0.726543i | 0.229416 | − | 0.166680i | −0.467139 | − | 0.884184i | \(-0.654715\pi\) |
0.696555 | + | 0.717504i | \(0.254715\pi\) | |||||||
\(20\) | −2.12864 | − | 0.684743i | −0.475979 | − | 0.153113i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.95483 | − | 2.87335i | −0.843172 | − | 0.612601i | ||||
\(23\) | 1.38197 | − | 4.25325i | 0.288160 | − | 0.886865i | −0.697274 | − | 0.716805i | \(-0.745604\pi\) |
0.985434 | − | 0.170060i | \(-0.0543961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.02778 | − | 2.96260i | 0.805556 | − | 0.592520i | ||||
\(26\) | −4.63925 | −0.909833 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.44422 | + | 2.50237i | 0.650896 | + | 0.472904i | ||||
\(29\) | 3.42049 | + | 2.48513i | 0.635170 | + | 0.461478i | 0.858187 | − | 0.513337i | \(-0.171591\pi\) |
−0.223018 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.826185 | + | 0.600258i | −0.148387 | + | 0.107810i | −0.659502 | − | 0.751703i | \(-0.729233\pi\) |
0.511115 | + | 0.859513i | \(0.329233\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.311522 | + | 0.958765i | 0.0534255 | + | 0.164427i | ||||
\(35\) | −9.04500 | + | 2.96825i | −1.52888 | + | 0.501726i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.31152 | + | 10.1918i | 0.544411 | + | 1.67552i | 0.722387 | + | 0.691489i | \(0.243045\pi\) |
−0.177976 | + | 0.984035i | \(0.556955\pi\) | |||||||
\(38\) | −0.381966 | − | 1.17557i | −0.0619631 | − | 0.190703i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.30902 | + | 1.81286i | −0.206974 | + | 0.286639i | ||||
\(41\) | −1.42049 | − | 4.37183i | −0.221844 | − | 0.682765i | −0.998597 | − | 0.0529595i | \(-0.983135\pi\) |
0.776753 | − | 0.629806i | \(-0.216865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4984 | −1.60099 | −0.800493 | − | 0.599342i | \(-0.795429\pi\) | ||||
−0.800493 | + | 0.599342i | \(0.795429\pi\) | |||||||
\(44\) | −3.95483 | + | 2.87335i | −0.596213 | + | 0.433174i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.61803 | − | 2.62866i | −0.533450 | − | 0.387574i | ||||
\(47\) | −1.63925 | − | 1.19099i | −0.239110 | − | 0.173723i | 0.461777 | − | 0.886996i | \(-0.347212\pi\) |
−0.700887 | + | 0.713273i | \(0.747212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.1245 | 1.58922 | ||||||||
\(50\) | −1.57295 | − | 4.74614i | −0.222449 | − | 0.671205i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.43361 | + | 4.41219i | −0.198806 | + | 0.611861i | ||||
\(53\) | 8.94413 | + | 6.49829i | 1.22857 | + | 0.892609i | 0.996782 | − | 0.0801570i | \(-0.0255422\pi\) |
0.231789 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0320560 | − | 10.9308i | −0.00432242 | − | 1.47391i | ||||
\(56\) | 3.44422 | − | 2.50237i | 0.460253 | − | 0.334393i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.42049 | − | 2.48513i | 0.449133 | − | 0.326314i | ||||
\(59\) | 0.656508 | + | 2.02052i | 0.0854701 | + | 0.263050i | 0.984653 | − | 0.174523i | \(-0.0558383\pi\) |
−0.899183 | + | 0.437573i | \(0.855838\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.19754 | − | 3.68565i | 0.153329 | − | 0.471899i | −0.844658 | − | 0.535306i | \(-0.820196\pi\) |
0.997988 | + | 0.0634064i | \(0.0201964\pi\) | |||||||
\(62\) | 0.315575 | + | 0.971238i | 0.0400780 | + | 0.123347i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −6.12209 | − | 8.37457i | −0.759351 | − | 1.03874i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.03434 | + | 2.20457i | −0.370703 | + | 0.269332i | −0.757502 | − | 0.652832i | \(-0.773581\pi\) |
0.386799 | + | 0.922164i | \(0.373581\pi\) | |||||||
\(68\) | 1.00811 | 0.122251 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0279172 | + | 9.51955i | 0.00333674 | + | 1.13780i | ||||
\(71\) | 10.1457 | + | 7.37130i | 1.20408 | + | 0.874813i | 0.994679 | − | 0.103018i | \(-0.0328500\pi\) |
0.209397 | + | 0.977831i | \(0.432850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.05975 | − | 3.26157i | 0.124034 | − | 0.381738i | −0.869690 | − | 0.493599i | \(-0.835681\pi\) |
0.993724 | + | 0.111861i | \(0.0356811\pi\) | |||||||
\(74\) | 10.7163 | 1.24575 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | −6.43110 | + | 19.7929i | −0.732892 | + | 2.25561i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.16968 | − | 3.75599i | −0.581634 | − | 0.422582i | 0.257679 | − | 0.966231i | \(-0.417042\pi\) |
−0.839313 | + | 0.543649i | \(0.817042\pi\) | |||||||
\(80\) | 1.31963 | + | 1.80515i | 0.147539 | + | 0.201822i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.59681 | −0.507633 | ||||||||
\(83\) | 5.70151 | − | 4.14239i | 0.625822 | − | 0.454686i | −0.229128 | − | 0.973396i | \(-0.573588\pi\) |
0.854950 | + | 0.518710i | \(0.173588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31963 | + | 1.82756i | −0.143134 | + | 0.198226i | ||||
\(86\) | −3.24417 | + | 9.98454i | −0.349828 | + | 1.07666i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.51061 | + | 4.64918i | 0.161032 | + | 0.495604i | ||||
\(89\) | −0.693488 | + | 2.13434i | −0.0735096 | + | 0.226239i | −0.981060 | − | 0.193704i | \(-0.937950\pi\) |
0.907551 | + | 0.419943i | \(0.137950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.10328 | + | 18.7840i | 0.639798 | + | 1.96910i | ||||
\(92\) | −3.61803 | + | 2.62866i | −0.377206 | + | 0.274056i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.63925 | + | 1.19099i | −0.169076 | + | 0.122841i | ||||
\(95\) | 1.61803 | − | 2.24082i | 0.166007 | − | 0.229904i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.49586 | + | 4.71952i | 0.659555 | + | 0.479195i | 0.866513 | − | 0.499155i | \(-0.166356\pi\) |
−0.206958 | + | 0.978350i | \(0.566356\pi\) | |||||||
\(98\) | 3.43766 | − | 10.5800i | 0.347256 | − | 1.06874i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.99991 | + | 0.0293259i | −0.499991 | + | 0.00293259i | ||||
\(101\) | 17.6310 | 1.75435 | 0.877174 | − | 0.480173i | \(-0.159426\pi\) | ||||
0.877174 | + | 0.480173i | \(0.159426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9376 | + | 11.5793i | 1.57038 | + | 1.14094i | 0.926795 | + | 0.375566i | \(0.122552\pi\) |
0.643580 | + | 0.765378i | \(0.277448\pi\) | |||||||
\(104\) | 3.75324 | + | 2.72689i | 0.368035 | + | 0.267393i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.94413 | − | 6.49829i | 0.868731 | − | 0.631170i | ||||
\(107\) | −6.16695 | −0.596181 | −0.298091 | − | 0.954538i | \(-0.596350\pi\) | ||||
−0.298091 | + | 0.954538i | \(0.596350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.44982 | + | 7.53977i | 0.234650 | + | 0.722179i | 0.997168 | + | 0.0752113i | \(0.0239631\pi\) |
−0.762517 | + | 0.646968i | \(0.776037\pi\) | |||||||
\(110\) | −10.4057 | − | 3.34733i | −0.992149 | − | 0.319155i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.31557 | − | 4.04892i | −0.124310 | − | 0.382587i | ||||
\(113\) | −2.08857 | − | 6.42795i | −0.196476 | − | 0.604691i | −0.999956 | − | 0.00935951i | \(-0.997021\pi\) |
0.803480 | − | 0.595332i | \(-0.202979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0293261 | − | 9.99996i | −0.00273467 | − | 0.932501i | ||||
\(116\) | −1.30651 | − | 4.02103i | −0.121307 | − | 0.373343i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.12451 | 0.195577 | ||||||||
\(119\) | 3.47214 | − | 2.52265i | 0.318290 | − | 0.231251i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4337 | − | 7.58056i | −0.948523 | − | 0.689142i | ||||
\(122\) | −3.13520 | − | 2.27786i | −0.283848 | − | 0.206228i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.02122 | 0.0917083 | ||||||||
\(125\) | 6.49181 | − | 9.10255i | 0.580645 | − | 0.814157i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.12054 | − | 9.60403i | 0.276903 | − | 0.852220i | −0.711807 | − | 0.702376i | \(-0.752123\pi\) |
0.988710 | − | 0.149844i | \(-0.0478773\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.85652 | + | 3.23457i | −0.864474 | + | 0.283690i | ||||
\(131\) | 5.43780 | − | 3.95079i | 0.475103 | − | 0.345182i | −0.324324 | − | 0.945946i | \(-0.605137\pi\) |
0.799427 | + | 0.600764i | \(0.205137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.25729 | + | 3.09310i | −0.369154 | + | 0.268206i | ||||
\(134\) | 1.15901 | + | 3.56708i | 0.100123 | + | 0.308148i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.311522 | − | 0.958765i | 0.0267128 | − | 0.0822134i | ||||
\(137\) | −5.44672 | − | 16.7633i | −0.465345 | − | 1.43218i | −0.858548 | − | 0.512733i | \(-0.828633\pi\) |
0.393203 | − | 0.919452i | \(-0.371367\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.51976 | + | 7.75502i | −0.213723 | + | 0.657772i | 0.785519 | + | 0.618838i | \(0.212396\pi\) |
−0.999242 | + | 0.0389342i | \(0.987604\pi\) | |||||||
\(140\) | 9.06225 | + | 2.91515i | 0.765900 | + | 0.246375i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.1457 | − | 7.37130i | 0.851410 | − | 0.618586i | ||||
\(143\) | −22.6787 | −1.89649 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.99983 | + | 2.89507i | 0.747395 | + | 0.240422i | ||||
\(146\) | −2.77446 | − | 2.01576i | −0.229616 | − | 0.166826i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.31152 | − | 10.1918i | 0.272205 | − | 0.837762i | ||||
\(149\) | −10.2230 | −0.837497 | −0.418748 | − | 0.908102i | \(-0.637531\pi\) | ||||
−0.418748 | + | 0.908102i | \(0.637531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2016 | 1.39984 | 0.699922 | − | 0.714220i | \(-0.253218\pi\) | ||||
0.699922 | + | 0.714220i | \(0.253218\pi\) | |||||||
\(152\) | −0.381966 | + | 1.17557i | −0.0309815 | + | 0.0953514i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.8368 | + | 12.2327i | 1.35675 | + | 0.985738i | ||||
\(155\) | −1.33680 | + | 1.85133i | −0.107374 | + | 0.148703i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7425 | −1.49582 | −0.747909 | − | 0.663802i | \(-0.768942\pi\) | ||||
−0.747909 | + | 0.663802i | \(0.768942\pi\) | |||||||
\(158\) | −5.16968 | + | 3.75599i | −0.411277 | + | 0.298811i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.12459 | − | 0.697217i | 0.167964 | − | 0.0551198i | ||||
\(161\) | −5.88343 | + | 18.1073i | −0.463679 | + | 1.42706i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.32624 | − | 13.3148i | −0.338857 | − | 1.04289i | −0.964791 | − | 0.263019i | \(-0.915282\pi\) |
0.625934 | − | 0.779876i | \(-0.284718\pi\) | |||||||
\(164\) | −1.42049 | + | 4.37183i | −0.110922 | + | 0.341383i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.17778 | − | 6.70252i | −0.169029 | − | 0.520217i | ||||
\(167\) | −10.9309 | + | 7.94175i | −0.845857 | + | 0.614551i | −0.924001 | − | 0.382391i | \(-0.875101\pi\) |
0.0781438 | + | 0.996942i | \(0.475101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.89500 | + | 5.00951i | −0.530384 | + | 0.385347i | ||||
\(170\) | 1.33032 | + | 1.81979i | 0.102031 | + | 0.139571i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.49336 | + | 6.17078i | 0.647612 | + | 0.470518i | ||||
\(173\) | 2.77609 | − | 8.54393i | 0.211062 | − | 0.649583i | −0.788348 | − | 0.615230i | \(-0.789063\pi\) |
0.999410 | − | 0.0343526i | \(-0.0109369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.1474 | + | 12.6126i | −1.29622 | + | 0.953426i | ||||
\(176\) | 4.88844 | 0.368480 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.81557 | + | 1.31909i | 0.136083 | + | 0.0988701i | ||||
\(179\) | 5.68029 | + | 4.12697i | 0.424565 | + | 0.308464i | 0.779472 | − | 0.626437i | \(-0.215488\pi\) |
−0.354907 | + | 0.934902i | \(0.615488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.66968 | − | 7.02543i | 0.718741 | − | 0.522196i | −0.167240 | − | 0.985916i | \(-0.553486\pi\) |
0.885982 | + | 0.463720i | \(0.153486\pi\) | |||||||
\(182\) | 19.7506 | 1.46402 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.38197 | + | 4.25325i | 0.101880 | + | 0.313554i | ||||
\(185\) | 14.1415 | + | 19.3446i | 1.03971 | + | 1.42224i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.52285 | + | 4.68686i | 0.111362 | + | 0.342737i | ||||
\(188\) | 0.626140 | + | 1.92706i | 0.0456659 | + | 0.140545i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.63115 | − | 2.23129i | −0.118336 | − | 0.161875i | ||||
\(191\) | −1.00000 | − | 3.07768i | −0.0723575 | − | 0.222693i | 0.908337 | − | 0.418239i | \(-0.137352\pi\) |
−0.980695 | + | 0.195545i | \(0.937352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.60802 | −0.547637 | −0.273818 | − | 0.961781i | \(-0.588287\pi\) | ||||
−0.273818 | + | 0.961781i | \(0.588287\pi\) | |||||||
\(194\) | 6.49586 | − | 4.71952i | 0.466376 | − | 0.338842i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.99991 | − | 6.53882i | −0.642851 | − | 0.467059i | ||||
\(197\) | 3.81549 | + | 2.77211i | 0.271842 | + | 0.197505i | 0.715351 | − | 0.698765i | \(-0.246267\pi\) |
−0.443509 | + | 0.896270i | \(0.646267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9276 | −1.12908 | −0.564539 | − | 0.825406i | \(-0.690946\pi\) | ||||
−0.564539 | + | 0.825406i | \(0.690946\pi\) | |||||||
\(200\) | −1.51717 | + | 4.76426i | −0.107280 | + | 0.336884i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.44827 | − | 16.7681i | 0.383339 | − | 1.17980i | ||||
\(203\) | −14.5620 | − | 10.5799i | −1.02205 | − | 0.742566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.06608 | − | 8.29796i | −0.423673 | − | 0.579555i | ||||
\(206\) | 15.9376 | − | 11.5793i | 1.11042 | − | 0.806770i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.75324 | − | 2.72689i | 0.260240 | − | 0.189075i | ||||
\(209\) | −1.86722 | − | 5.74670i | −0.129158 | − | 0.397508i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.73443 | + | 11.4934i | −0.257089 | + | 0.791239i | 0.736322 | + | 0.676631i | \(0.236561\pi\) |
−0.993411 | + | 0.114607i | \(0.963439\pi\) | |||||||
\(212\) | −3.41635 | − | 10.5145i | −0.234636 | − | 0.722136i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.90569 | + | 5.86511i | −0.130270 | + | 0.400931i | ||||
\(215\) | −22.3047 | + | 7.31963i | −1.52117 | + | 0.499195i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.51731 | − | 2.55547i | 0.238770 | − | 0.173477i | ||||
\(218\) | 7.92778 | 0.536937 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.39905 | + | 8.86207i | −0.431424 | + | 0.597481i | ||||
\(221\) | 3.78366 | + | 2.74899i | 0.254516 | + | 0.184917i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.89258 | + | 8.90243i | −0.193701 | + | 0.596151i | 0.806288 | + | 0.591523i | \(0.201473\pi\) |
−0.999989 | + | 0.00462801i | \(0.998527\pi\) | |||||||
\(224\) | −4.25729 | −0.284452 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.75875 | −0.449585 | ||||||||
\(227\) | −3.12864 | + | 9.62898i | −0.207655 | + | 0.639098i | 0.791938 | + | 0.610601i | \(0.209072\pi\) |
−0.999594 | + | 0.0284967i | \(0.990928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.99741 | − | 4.35737i | −0.396320 | − | 0.287943i | 0.371720 | − | 0.928345i | \(-0.378768\pi\) |
−0.768040 | + | 0.640401i | \(0.778768\pi\) | |||||||
\(230\) | −9.51959 | − | 3.06227i | −0.627703 | − | 0.201920i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.22796 | −0.277579 | ||||||||
\(233\) | −4.79568 | + | 3.48426i | −0.314175 | + | 0.228262i | −0.733686 | − | 0.679489i | \(-0.762202\pi\) |
0.419511 | + | 0.907750i | \(0.362202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.31312 | − | 1.38745i | −0.281357 | − | 0.0905071i | ||||
\(236\) | 0.656508 | − | 2.02052i | 0.0427351 | − | 0.131525i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.32624 | − | 4.08174i | −0.0859672 | − | 0.264580i | ||||
\(239\) | 5.10328 | − | 15.7063i | 0.330104 | − | 1.01596i | −0.638980 | − | 0.769224i | \(-0.720643\pi\) |
0.969084 | − | 0.246732i | \(-0.0793568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.48120 | − | 7.63634i | −0.159828 | − | 0.491900i | 0.838790 | − | 0.544455i | \(-0.183264\pi\) |
−0.998618 | + | 0.0525550i | \(0.983264\pi\) | |||||||
\(242\) | −10.4337 | + | 7.58056i | −0.670707 | + | 0.487297i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.13520 | + | 2.27786i | −0.200711 | + | 0.145825i | ||||
\(245\) | 23.6350 | − | 7.75619i | 1.50999 | − | 0.495525i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.63925 | − | 3.37062i | −0.295189 | − | 0.214467i | ||||
\(248\) | 0.315575 | − | 0.971238i | 0.0200390 | − | 0.0616737i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.65096 | − | 8.98692i | −0.420644 | − | 0.568383i | ||||
\(251\) | −14.4639 | −0.912951 | −0.456475 | − | 0.889736i | \(-0.650888\pi\) | ||||
−0.456475 | + | 0.889736i | \(0.650888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.6865 | − | 12.8500i | −1.11194 | − | 0.807874i | ||||
\(254\) | −8.16968 | − | 5.93562i | −0.512611 | − | 0.372434i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 1.36075 | 0.0848810 | 0.0424405 | − | 0.999099i | \(-0.486487\pi\) | ||||
0.0424405 | + | 0.999099i | \(0.486487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.0981 | − | 43.3895i | −0.876014 | − | 2.69609i | ||||
\(260\) | 0.0304219 | + | 10.3736i | 0.00188669 | + | 0.643346i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.07705 | − | 6.39252i | −0.128321 | − | 0.394931i | ||||
\(263\) | 2.09518 | + | 6.44830i | 0.129194 | + | 0.397619i | 0.994642 | − | 0.103380i | \(-0.0329659\pi\) |
−0.865448 | + | 0.500999i | \(0.832966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.5333 | + | 7.57022i | 1.44564 | + | 0.465035i | ||||
\(266\) | 1.62614 | + | 5.00474i | 0.0997050 | + | 0.306860i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.75065 | 0.229107 | ||||||||
\(269\) | −3.19745 | + | 2.32309i | −0.194952 | + | 0.141641i | −0.680979 | − | 0.732303i | \(-0.738446\pi\) |
0.486027 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.28521 | − | 6.01955i | −0.503290 | − | 0.365662i | 0.306982 | − | 0.951715i | \(-0.400681\pi\) |
−0.810272 | + | 0.586053i | \(0.800681\pi\) | |||||||
\(272\) | −0.815575 | − | 0.592550i | −0.0494515 | − | 0.0359286i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.6260 | −1.06482 | ||||||||
\(275\) | −7.68926 | − | 23.2012i | −0.463680 | − | 1.39909i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.18684 | + | 9.80810i | −0.191479 | + | 0.589311i | 0.808521 | + | 0.588468i | \(0.200269\pi\) |
−1.00000 | 0.000843804i | \(0.999731\pi\) | ||||||||
\(278\) | 6.59681 | + | 4.79287i | 0.395651 | + | 0.287457i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.57286 | − | 7.71788i | 0.333042 | − | 0.461232i | ||||
\(281\) | −2.88602 | + | 2.09682i | −0.172165 | + | 0.125086i | −0.670531 | − | 0.741881i | \(-0.733934\pi\) |
0.498366 | + | 0.866967i | \(0.333934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2571 | − | 16.8973i | 1.38249 | − | 1.00444i | 0.385850 | − | 0.922562i | \(-0.373908\pi\) |
0.996642 | − | 0.0818776i | \(-0.0260917\pi\) | |||||||
\(284\) | −3.87532 | − | 11.9270i | −0.229958 | − | 0.707738i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.00811 | + | 21.5687i | −0.414398 | + | 1.27539i | ||||
\(287\) | 6.04745 | + | 18.6121i | 0.356970 | + | 1.09864i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.93924 | + | 15.2014i | −0.290544 | + | 0.894201i | ||||
\(290\) | 5.53447 | − | 7.66472i | 0.324996 | − | 0.450088i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.77446 | + | 2.01576i | −0.162363 | + | 0.117963i | ||||
\(293\) | −1.78543 | −0.104306 | −0.0521530 | − | 0.998639i | \(-0.516608\pi\) | ||||
−0.0521530 | + | 0.998639i | \(0.516608\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.80356 | + | 3.83506i | 0.163229 | + | 0.223286i | ||||
\(296\) | −8.66968 | − | 6.29889i | −0.503915 | − | 0.366115i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.15907 | + | 9.72261i | −0.183000 | + | 0.563215i | ||||
\(299\) | −20.7474 | −1.19985 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 44.6946 | 2.57615 | ||||||||
\(302\) | 5.31557 | − | 16.3597i | 0.305877 | − | 0.941392i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | + | 0.726543i | 0.0573539 | + | 0.0416701i | ||||
\(305\) | −0.0254125 | − | 8.66545i | −0.00145511 | − | 0.496182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2752 | 0.928877 | 0.464439 | − | 0.885605i | \(-0.346256\pi\) | ||||
0.464439 | + | 0.885605i | \(0.346256\pi\) | |||||||
\(308\) | 16.8368 | − | 12.2327i | 0.959368 | − | 0.697022i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.34763 | + | 1.84346i | 0.0765403 | + | 0.104702i | ||||
\(311\) | −4.00501 | + | 12.3262i | −0.227103 | + | 0.698952i | 0.770968 | + | 0.636874i | \(0.219773\pi\) |
−0.998071 | + | 0.0620781i | \(0.980227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.29075 | − | 3.97253i | −0.0729577 | − | 0.224541i | 0.907928 | − | 0.419127i | \(-0.137664\pi\) |
−0.980885 | + | 0.194586i | \(0.937664\pi\) | |||||||
\(314\) | −5.79176 | + | 17.8252i | −0.326848 | + | 1.00594i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.97464 | + | 6.07732i | 0.111082 | + | 0.341876i | ||||
\(317\) | 24.4480 | − | 17.7625i | 1.37314 | − | 0.997643i | 0.375653 | − | 0.926761i | \(-0.377419\pi\) |
0.997485 | − | 0.0708820i | \(-0.0225814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.7209 | − | 12.1484i | 0.936189 | − | 0.680181i | ||||
\(320\) | −0.00655751 | − | 2.23606i | −0.000366576 | − | 0.124999i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.4030 | + | 11.1909i | 0.858376 | + | 0.623647i | ||||
\(323\) | −0.385062 | + | 1.18510i | −0.0214254 | + | 0.0659407i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.8458 | − | 13.5241i | −1.04538 | − | 0.750183i | ||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.71890 | + | 2.70194i | 0.205342 | + | 0.149190i | ||||
\(329\) | 6.97878 | + | 5.07038i | 0.384753 | + | 0.279539i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3949 | + | 8.27889i | −0.626321 | + | 0.455049i | −0.855124 | − | 0.518424i | \(-0.826519\pi\) |
0.228803 | + | 0.973473i | \(0.426519\pi\) | |||||||
\(332\) | −7.04745 | −0.386779 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.17522 | + | 12.8500i | 0.228458 | + | 0.703122i | ||||
\(335\) | −4.90966 | + | 6.79941i | −0.268243 | + | 0.371491i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.15155 | + | 12.7772i | 0.226149 | + | 0.696016i | 0.998173 | + | 0.0604224i | \(0.0192448\pi\) |
−0.772023 | + | 0.635594i | \(0.780755\pi\) | |||||||
\(338\) | 2.63365 | + | 8.10555i | 0.143252 | + | 0.440884i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.14181 | − | 0.702868i | 0.116156 | − | 0.0381184i | ||||
\(341\) | 1.54267 | + | 4.74784i | 0.0835401 | + | 0.257110i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5592 | −0.948108 | ||||||||
\(344\) | 8.49336 | − | 6.17078i | 0.457931 | − | 0.332706i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.26790 | − | 5.28044i | −0.390725 | − | 0.283878i | ||||
\(347\) | 4.55975 | + | 3.31285i | 0.244780 | + | 0.177843i | 0.703410 | − | 0.710784i | \(-0.251660\pi\) |
−0.458630 | + | 0.888627i | \(0.651660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.1159 | 1.29090 | 0.645449 | − | 0.763804i | \(-0.276670\pi\) | ||||
0.645449 | + | 0.763804i | \(0.276670\pi\) | |||||||
\(350\) | 6.69650 | + | 20.2057i | 0.357943 | + | 1.08004i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.51061 | − | 4.64918i | 0.0805158 | − | 0.247802i | ||||
\(353\) | 19.1672 | + | 13.9258i | 1.02017 | + | 0.741196i | 0.966317 | − | 0.257353i | \(-0.0828504\pi\) |
0.0538510 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.6949 | + | 8.58724i | 1.41682 | + | 0.455763i | ||||
\(356\) | 1.81557 | − | 1.31909i | 0.0962253 | − | 0.0699117i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.68029 | − | 4.12697i | 0.300212 | − | 0.218117i | ||||
\(359\) | 0.849092 | + | 2.61324i | 0.0448134 | + | 0.137921i | 0.970960 | − | 0.239243i | \(-0.0768992\pi\) |
−0.926146 | + | 0.377164i | \(0.876899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39919 | + | 16.6170i | −0.284168 | + | 0.874578i | ||||
\(362\) | −3.69349 | − | 11.3674i | −0.194125 | − | 0.597457i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.10328 | − | 18.7840i | 0.319899 | − | 0.984548i | ||||
\(365\) | −0.0224884 | − | 7.66838i | −0.00117710 | − | 0.401381i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.33266 | − | 3.14786i | 0.226163 | − | 0.164317i | −0.468934 | − | 0.883233i | \(-0.655362\pi\) |
0.695096 | + | 0.718917i | \(0.255362\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.7678 | − | 7.47159i | 1.18364 | − | 0.388429i | ||||
\(371\) | −38.0778 | − | 27.6651i | −1.97690 | − | 1.43630i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.66048 | + | 26.6542i | −0.448422 | + | 1.38010i | 0.430264 | + | 0.902703i | \(0.358420\pi\) |
−0.878687 | + | 0.477399i | \(0.841580\pi\) | |||||||
\(374\) | 4.92806 | 0.254824 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.02623 | 0.104495 | ||||||||
\(377\) | 6.06124 | − | 18.6546i | 0.312170 | − | 0.960760i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.20145 | + | 1.59945i | 0.113081 | + | 0.0821582i | 0.642889 | − | 0.765960i | \(-0.277736\pi\) |
−0.529807 | + | 0.848118i | \(0.677736\pi\) | |||||||
\(380\) | −2.62614 | + | 0.861807i | −0.134718 | + | 0.0442098i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.23607 | −0.165572 | ||||||||
\(383\) | 13.6522 | − | 9.91890i | 0.697595 | − | 0.506832i | −0.181553 | − | 0.983381i | \(-0.558112\pi\) |
0.879148 | + | 0.476549i | \(0.158112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.136471 | + | 46.5357i | 0.00695523 | + | 2.37168i | ||||
\(386\) | −2.35101 | + | 7.23565i | −0.119663 | + | 0.368285i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.48120 | − | 7.63634i | −0.125964 | − | 0.387677i | ||||
\(389\) | −11.9654 | + | 36.8258i | −0.606672 | + | 1.86714i | −0.121810 | + | 0.992553i | \(0.538870\pi\) |
−0.484862 | + | 0.874590i | \(0.661130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39317 | + | 4.28773i | 0.0704555 | + | 0.216840i | ||||
\(392\) | −8.99991 | + | 6.53882i | −0.454564 | + | 0.330260i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.81549 | − | 2.77211i | 0.192222 | − | 0.139657i | ||||
\(395\) | −13.6022 | − | 4.37556i | −0.684400 | − | 0.220158i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0261 | − | 14.5498i | −1.00508 | − | 0.730233i | −0.0419078 | − | 0.999121i | \(-0.513344\pi\) |
−0.963171 | + | 0.268889i | \(0.913344\pi\) | |||||||
\(398\) | −4.92190 | + | 15.1481i | −0.246713 | + | 0.759304i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.06225 | + | 2.91515i | 0.203113 | + | 0.145758i | ||||
\(401\) | 3.31830 | 0.165708 | 0.0828541 | − | 0.996562i | \(-0.473596\pi\) | ||||
0.0828541 | + | 0.996562i | \(0.473596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.83288 | + | 2.78475i | 0.190929 | + | 0.138718i | ||||
\(404\) | −14.2638 | − | 10.3632i | −0.709649 | − | 0.515590i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.5620 | + | 10.5799i | −0.722701 | + | 0.525073i | ||||
\(407\) | 52.3860 | 2.59668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.76950 | − | 26.9897i | −0.433624 | − | 1.33456i | −0.894490 | − | 0.447087i | \(-0.852461\pi\) |
0.460866 | − | 0.887470i | \(-0.347539\pi\) | |||||||
\(410\) | −9.76635 | + | 3.20497i | −0.482326 | + | 0.158282i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.08761 | − | 18.7357i | −0.299915 | − | 0.923044i | ||||
\(413\) | −2.79495 | − | 8.60196i | −0.137530 | − | 0.423275i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.22523 | − | 12.7761i | 0.452849 | − | 0.627152i | ||||
\(416\) | −1.43361 | − | 4.41219i | −0.0702884 | − | 0.216326i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.04244 | −0.295545 | ||||||||
\(419\) | 11.9931 | − | 8.71352i | 0.585903 | − | 0.425683i | −0.254945 | − | 0.966956i | \(-0.582057\pi\) |
0.840847 | + | 0.541272i | \(0.182057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7255 | − | 10.6987i | −0.717677 | − | 0.521423i | 0.167964 | − | 0.985793i | \(-0.446281\pi\) |
−0.885641 | + | 0.464370i | \(0.846281\pi\) | |||||||
\(422\) | 9.77688 | + | 7.10332i | 0.475931 | + | 0.345784i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.0556 | −0.536905 | ||||||||
\(425\) | −1.52947 | + | 4.80288i | −0.0741900 | + | 0.232974i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.09828 | + | 15.6909i | −0.246723 | + | 0.759335i | ||||
\(428\) | 4.98916 | + | 3.62484i | 0.241160 | + | 0.175213i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0688431 | + | 23.4750i | 0.00331991 | + | 1.13206i | ||||
\(431\) | 14.3606 | − | 10.4336i | 0.691724 | − | 0.502567i | −0.185502 | − | 0.982644i | \(-0.559391\pi\) |
0.877227 | + | 0.480077i | \(0.159391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5703 | + | 12.7656i | −0.844373 | + | 0.613473i | −0.923589 | − | 0.383384i | \(-0.874758\pi\) |
0.0792155 | + | 0.996858i | \(0.474758\pi\) | |||||||
\(434\) | −1.34349 | − | 4.13484i | −0.0644897 | − | 0.198479i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.44982 | − | 7.53977i | 0.117325 | − | 0.361089i | ||||
\(437\) | −1.70820 | − | 5.25731i | −0.0817145 | − | 0.251491i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.31399 | − | 10.1994i | 0.158168 | − | 0.486792i | −0.840300 | − | 0.542122i | \(-0.817621\pi\) |
0.998468 | + | 0.0553300i | \(0.0176211\pi\) | |||||||
\(440\) | 6.45092 | + | 8.82439i | 0.307535 | + | 0.420686i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.78366 | − | 2.74899i | 0.179970 | − | 0.130756i | ||||
\(443\) | −25.5092 | −1.21198 | −0.605990 | − | 0.795472i | \(-0.707223\pi\) | ||||
−0.605990 | + | 0.795472i | \(0.707223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0147162 | + | 5.01810i | 0.000697614 | + | 0.237881i | ||||
\(446\) | 7.57286 | + | 5.50201i | 0.358585 | + | 0.260528i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.31557 | + | 4.04892i | −0.0621551 | + | 0.191294i | ||||
\(449\) | 12.5619 | 0.592831 | 0.296415 | − | 0.955059i | \(-0.404209\pi\) | ||||
0.296415 | + | 0.955059i | \(0.404209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4712 | −1.05813 | ||||||||
\(452\) | −2.08857 | + | 6.42795i | −0.0982380 | + | 0.302346i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.19090 | + | 5.95104i | 0.384418 | + | 0.279296i | ||||
\(455\) | 26.0635 | + | 35.6530i | 1.22188 | + | 1.67144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.04289 | 0.142340 | 0.0711702 | − | 0.997464i | \(-0.477327\pi\) | ||||
0.0711702 | + | 0.997464i | \(0.477327\pi\) | |||||||
\(458\) | −5.99741 | + | 4.35737i | −0.280241 | + | 0.203607i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.85410 | + | 8.10737i | −0.272949 | + | 0.378008i | ||||
\(461\) | 8.52674 | − | 26.2426i | 0.397130 | − | 1.22224i | −0.530161 | − | 0.847897i | \(-0.677868\pi\) |
0.927291 | − | 0.374342i | \(-0.122132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.33417 | + | 28.7276i | 0.433796 | + | 1.33509i | 0.894316 | + | 0.447437i | \(0.147663\pi\) |
−0.460520 | + | 0.887649i | \(0.652337\pi\) | |||||||
\(464\) | −1.30651 | + | 4.02103i | −0.0606533 | + | 0.186672i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.83179 | + | 5.63766i | 0.0848558 | + | 0.261159i | ||||
\(467\) | 24.1271 | − | 17.5293i | 1.11647 | − | 0.811161i | 0.132797 | − | 0.991143i | \(-0.457604\pi\) |
0.983670 | + | 0.179982i | \(0.0576040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9180 | − | 9.38551i | 0.596500 | − | 0.433382i | ||||
\(470\) | −2.65237 | + | 3.67328i | −0.122345 | + | 0.169436i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.71876 | − | 1.24875i | −0.0791124 | − | 0.0574785i | ||||
\(473\) | −15.8589 | + | 48.8088i | −0.729195 | + | 2.24423i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.87532 | − | 5.88895i | 0.0860457 | − | 0.270204i | ||||
\(476\) | −4.29180 | −0.196714 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.3606 | − | 9.70702i | −0.611098 | − | 0.443989i | ||||
\(479\) | 5.27040 | + | 3.82917i | 0.240811 | + | 0.174959i | 0.701644 | − | 0.712527i | \(-0.252450\pi\) |
−0.460834 | + | 0.887487i | \(0.652450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.2208 | − | 29.2221i | 1.83391 | − | 1.33242i | ||||
\(482\) | −8.02933 | −0.365726 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.98534 | + | 12.2656i | 0.181152 | + | 0.557528i | ||||
\(485\) | 17.0916 | + | 5.49803i | 0.776089 | + | 0.249653i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4222 | + | 38.2315i | 0.562903 | + | 1.73244i | 0.674102 | + | 0.738638i | \(0.264531\pi\) |
−0.111199 | + | 0.993798i | \(0.535469\pi\) | |||||||
\(488\) | 1.19754 | + | 3.68565i | 0.0542101 | + | 0.166842i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0729490 | − | 24.8750i | −0.00329550 | − | 1.12374i | ||||
\(491\) | 11.3187 | + | 34.8353i | 0.510804 | + | 1.57209i | 0.790788 | + | 0.612090i | \(0.209671\pi\) |
−0.279984 | + | 0.960005i | \(0.590329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.26223 | −0.191961 | ||||||||
\(494\) | −4.63925 | + | 3.37062i | −0.208730 | + | 0.151651i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.826185 | − | 0.600258i | −0.0370968 | − | 0.0269524i | ||||
\(497\) | −43.1933 | − | 31.3818i | −1.93748 | − | 1.40766i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.9343 | −1.11621 | −0.558105 | − | 0.829770i | \(-0.688471\pi\) | ||||
−0.558105 | + | 0.829770i | \(0.688471\pi\) | |||||||
\(500\) | −10.6023 | + | 3.54833i | −0.474151 | + | 0.158686i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.46958 | + | 13.7559i | −0.199487 | + | 0.613958i | ||||
\(503\) | 34.9784 | + | 25.4133i | 1.55961 | + | 1.13312i | 0.936327 | + | 0.351128i | \(0.114202\pi\) |
0.623284 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.4586 | − | 12.2926i | 1.66689 | − | 0.547014i | ||||
\(506\) | −17.6865 | + | 12.8500i | −0.786262 | + | 0.571253i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.16968 | + | 5.93562i | −0.362471 | + | 0.263350i | ||||
\(509\) | −9.55465 | − | 29.4062i | −0.423503 | − | 1.30341i | −0.904421 | − | 0.426641i | \(-0.859697\pi\) |
0.480918 | − | 0.876765i | \(-0.340303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.51165 | + | 13.8854i | −0.199584 | + | 0.614256i | ||||
\(512\) | 0.309017 | + | 0.951057i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.420493 | − | 1.29415i | 0.0185472 | − | 0.0570823i | ||||
\(515\) | 41.9341 | + | 13.4894i | 1.84784 | + | 0.594414i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.01339 | + | 5.82207i | −0.352429 | + | 0.256054i | ||||
\(518\) | −45.6224 | −2.00453 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.87532 | + | 3.17670i | 0.433062 | + | 0.139307i | ||||
\(521\) | −23.9548 | − | 17.4042i | −1.04948 | − | 0.762491i | −0.0773654 | − | 0.997003i | \(-0.524651\pi\) |
−0.972113 | + | 0.234512i | \(0.924651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.64736 | − | 11.2254i | 0.159488 | − | 0.490853i | −0.839100 | − | 0.543977i | \(-0.816918\pi\) |
0.998588 | + | 0.0531238i | \(0.0169178\pi\) | |||||||
\(524\) | −6.72149 | −0.293630 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.78014 | 0.295628 | ||||||||
\(527\) | 0.318132 | − | 0.979111i | 0.0138581 | − | 0.0426507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.42705 | + | 1.76336i | 0.105524 | + | 0.0766676i | ||||
\(530\) | 14.4719 | − | 20.0422i | 0.628620 | − | 0.870578i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.26230 | 0.228150 | ||||||||
\(533\) | −17.2529 | + | 12.5350i | −0.747307 | + | 0.542950i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1022 | + | 4.29970i | −0.566459 | + | 0.185892i | ||||
\(536\) | 1.15901 | − | 3.56708i | 0.0500617 | − | 0.154074i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.22132 | + | 3.75883i | 0.0526548 | + | 0.162055i | ||||
\(539\) | 16.8048 | − | 51.7198i | 0.723834 | − | 2.22773i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.69039 | + | 14.4355i | 0.201656 | + | 0.620632i | 0.999834 | + | 0.0182113i | \(0.00579717\pi\) |
−0.798178 | + | 0.602421i | \(0.794203\pi\) | |||||||
\(542\) | −8.28521 | + | 6.01955i | −0.355880 | + | 0.258562i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.815575 | + | 0.592550i | −0.0349675 | + | 0.0254054i | ||||
\(545\) | 10.4617 | + | 14.3109i | 0.448131 | + | 0.613011i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.2147 | − | 20.4992i | −1.20637 | − | 0.876481i | −0.211476 | − | 0.977383i | \(-0.567827\pi\) |
−0.994896 | + | 0.100902i | \(0.967827\pi\) | |||||||
\(548\) | −5.44672 | + | 16.7633i | −0.232672 | + | 0.716092i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.4418 | + | 0.143358i | −1.04220 | + | 0.00611281i | ||||
\(551\) | 5.22605 | 0.222637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0088 | + | 15.9903i | 0.935910 | + | 0.679978i | ||||
\(554\) | 8.34327 | + | 6.06174i | 0.354471 | + | 0.257539i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.59681 | − | 4.79287i | 0.279767 | − | 0.203263i | ||||
\(557\) | −31.4820 | −1.33393 | −0.666967 | − | 0.745087i | \(-0.732408\pi\) | ||||
−0.666967 | + | 0.745087i | \(0.732408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0505 | + | 46.3208i | 0.636570 | + | 1.95916i | ||||
\(560\) | −5.61803 | − | 7.68506i | −0.237405 | − | 0.324753i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.10236 | + | 3.39272i | 0.0465003 | + | 0.143113i | ||||
\(563\) | −0.272961 | − | 0.840089i | −0.0115040 | − | 0.0354055i | 0.945140 | − | 0.326666i | \(-0.105925\pi\) |
−0.956644 | + | 0.291261i | \(0.905925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.91903 | − | 12.2006i | −0.375226 | − | 0.513283i | ||||
\(566\) | −8.88343 | − | 27.3404i | −0.373398 | − | 1.14920i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.5408 | −0.526201 | ||||||||
\(569\) | −4.94008 | + | 3.58918i | −0.207099 | + | 0.150466i | −0.686500 | − | 0.727130i | \(-0.740854\pi\) |
0.479401 | + | 0.877596i | \(0.340854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0293261 | + | 0.0213066i | 0.00122726 | + | 0.000891655i | 0.588399 | − | 0.808571i | \(-0.299759\pi\) |
−0.587171 | + | 0.809463i | \(0.699759\pi\) | |||||||
\(572\) | 18.3475 | + | 13.3302i | 0.767146 | + | 0.557364i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.5700 | 0.816834 | ||||||||
\(575\) | −7.03444 | − | 21.2254i | −0.293357 | − | 0.885159i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3368 | − | 37.9688i | 0.513587 | − | 1.58066i | −0.272250 | − | 0.962227i | \(-0.587768\pi\) |
0.785837 | − | 0.618433i | \(-0.212232\pi\) | |||||||
\(578\) | 12.9311 | + | 9.39500i | 0.537863 | + | 0.390780i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.57933 | − | 7.63213i | −0.231669 | − | 0.316907i | ||||
\(581\) | −24.2730 | + | 17.6353i | −1.00701 | + | 0.731637i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.7228 | − | 31.7665i | 1.81081 | − | 1.31563i | ||||
\(584\) | 1.05975 | + | 3.26157i | 0.0438527 | + | 0.134965i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.551728 | + | 1.69805i | −0.0227917 | + | 0.0701456i | ||||
\(587\) | 5.39111 | + | 16.5921i | 0.222515 | + | 0.684831i | 0.998534 | + | 0.0541218i | \(0.0172359\pi\) |
−0.776019 | + | 0.630709i | \(0.782764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.390072 | + | 1.20052i | −0.0160726 | + | 0.0494664i | ||||
\(590\) | 4.51371 | − | 1.48124i | 0.185826 | − | 0.0609817i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.66968 | + | 6.29889i | −0.356322 | + | 0.258883i | ||||
\(593\) | 5.43780 | 0.223304 | 0.111652 | − | 0.993747i | \(-0.464386\pi\) | ||||
0.111652 | + | 0.993747i | \(0.464386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.61803 | − | 7.78044i | 0.230317 | − | 0.318967i | ||||
\(596\) | 8.27054 | + | 6.00890i | 0.338775 | + | 0.246134i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.41129 | + | 19.7319i | −0.262177 | + | 0.806899i | ||||
\(599\) | −28.7804 | −1.17593 | −0.587967 | − | 0.808885i | \(-0.700071\pi\) | ||||
−0.587967 | + | 0.808885i | \(0.700071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.4162 | −1.68940 | −0.844702 | − | 0.535237i | \(-0.820222\pi\) | ||||
−0.844702 | + | 0.535237i | \(0.820222\pi\) | |||||||
\(602\) | 13.8114 | − | 42.5071i | 0.562910 | − | 1.73246i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.9164 | − | 10.1108i | −0.566248 | − | 0.411404i | ||||
\(605\) | −27.4527 | − | 8.83101i | −1.11611 | − | 0.359032i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.9868 | 0.973595 | 0.486797 | − | 0.873515i | \(-0.338165\pi\) | ||||
0.486797 | + | 0.873515i | \(0.338165\pi\) | |||||||
\(608\) | 1.00000 | − | 0.726543i | 0.0405554 | − | 0.0294652i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.24918 | − | 2.65360i | −0.334000 | − | 0.107441i | ||||
\(611\) | −2.90482 | + | 8.94012i | −0.117516 | + | 0.361678i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.131288 | + | 0.404063i | 0.00530268 | + | 0.0163200i | 0.953673 | − | 0.300846i | \(-0.0972689\pi\) |
−0.948370 | + | 0.317166i | \(0.897269\pi\) | |||||||
\(614\) | 5.02933 | − | 15.4787i | 0.202967 | − | 0.624668i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.43110 | − | 19.7929i | −0.259117 | − | 0.797479i | ||||
\(617\) | 26.5991 | − | 19.3253i | 1.07084 | − | 0.778009i | 0.0947752 | − | 0.995499i | \(-0.469787\pi\) |
0.976063 | + | 0.217489i | \(0.0697868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.53580 | + | 6.92816i | −0.383276 | + | 0.278466i | −0.762695 | − | 0.646759i | \(-0.776124\pi\) |
0.379419 | + | 0.925225i | \(0.376124\pi\) | |||||||
\(620\) | 2.16968 | − | 0.712012i | 0.0871363 | − | 0.0285951i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.4853 | + | 7.61798i | 0.420420 | + | 0.305453i | ||||
\(623\) | 2.95238 | − | 9.08648i | 0.118285 | − | 0.364042i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.44599 | − | 23.8654i | 0.297840 | − | 0.954616i | ||||
\(626\) | −4.17697 | −0.166945 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.1630 | + | 11.0166i | 0.605071 | + | 0.439610i | ||||
\(629\) | −8.73995 | − | 6.34994i | −0.348485 | − | 0.253189i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0900 | + | 19.6820i | −1.07844 | + | 0.783529i | −0.977410 | − | 0.211354i | \(-0.932213\pi\) |
−0.101026 | + | 0.994884i | \(0.532213\pi\) | |||||||
\(632\) | 6.39007 | 0.254183 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.33831 | − | 28.7404i | −0.370872 | − | 1.14143i | ||||
\(635\) | −0.0662195 | − | 22.5803i | −0.00262784 | − | 0.896073i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9482 | − | 49.0835i | −0.631890 | − | 1.94476i | ||||
\(638\) | −6.38680 | − | 19.6566i | −0.252856 | − | 0.778211i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12864 | − | 0.684743i | −0.0841421 | − | 0.0270669i | ||||
\(641\) | 5.17714 | + | 15.9336i | 0.204485 | + | 0.629339i | 0.999734 | + | 0.0230567i | \(0.00733983\pi\) |
−0.795250 | + | 0.606282i | \(0.792660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5246 | 0.572794 | 0.286397 | − | 0.958111i | \(-0.407542\pi\) | ||||
0.286397 | + | 0.958111i | \(0.407542\pi\) | |||||||
\(644\) | 15.4030 | − | 11.1909i | 0.606964 | − | 0.440985i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.00811 | + | 0.732432i | 0.0396634 | + | 0.0288171i | ||||
\(647\) | 12.8965 | + | 9.36989i | 0.507015 | + | 0.368368i | 0.811690 | − | 0.584088i | \(-0.198548\pi\) |
−0.304675 | + | 0.952456i | \(0.598548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3855 | 0.407667 | ||||||||
\(650\) | −18.6859 | + | 13.7443i | −0.732921 | + | 0.539094i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.32624 | + | 13.3148i | −0.169429 | + | 0.521447i | ||||
\(653\) | −20.3233 | − | 14.7657i | −0.795312 | − | 0.577828i | 0.114223 | − | 0.993455i | \(-0.463562\pi\) |
−0.909535 | + | 0.415627i | \(0.863562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.79855 | − | 12.1851i | 0.343788 | − | 0.476113i | ||||
\(656\) | 3.71890 | − | 2.70194i | 0.145199 | − | 0.105493i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.97878 | − | 5.07038i | 0.272061 | − | 0.197664i | ||||
\(659\) | 3.40766 | + | 10.4877i | 0.132744 | + | 0.408543i | 0.995232 | − | 0.0975338i | \(-0.0310954\pi\) |
−0.862489 | + | 0.506076i | \(0.831095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.20173 | + | 12.9316i | −0.163428 | + | 0.502981i | −0.998917 | − | 0.0465267i | \(-0.985185\pi\) |
0.835489 | + | 0.549508i | \(0.185185\pi\) | |||||||
\(662\) | 4.35247 | + | 13.3955i | 0.169163 | + | 0.520632i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.17778 | + | 6.70252i | −0.0845143 | + | 0.260108i | ||||
\(665\) | −6.88844 | + | 9.53983i | −0.267122 | + | 0.369939i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.2969 | − | 11.1139i | 0.592299 | − | 0.430330i | ||||
\(668\) | 13.5113 | 0.522768 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.94945 | + | 6.77049i | 0.191214 | + | 0.261567i | ||||
\(671\) | −15.3262 | − | 11.1352i | −0.591663 | − | 0.429868i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.81053 | + | 20.9607i | −0.262527 | + | 0.807974i | 0.729726 | + | 0.683740i | \(0.239648\pi\) |
−0.992253 | + | 0.124235i | \(0.960352\pi\) | |||||||
\(674\) | 13.4347 | 0.517485 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.52268 | 0.327795 | ||||||||
\(677\) | −10.3185 | + | 31.7571i | −0.396572 | + | 1.22052i | 0.531158 | + | 0.847273i | \(0.321757\pi\) |
−0.927730 | + | 0.373251i | \(0.878243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.6548 | − | 20.0924i | −1.06129 | − | 0.771074i | ||||
\(680\) | −0.00661066 | − | 2.25418i | −0.000253507 | − | 0.0864440i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.99217 | 0.191160 | ||||||||
\(683\) | 2.88616 | − | 2.09692i | 0.110436 | − | 0.0802363i | −0.531197 | − | 0.847249i | \(-0.678257\pi\) |
0.641632 | + | 0.767012i | \(0.278257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.2597 | − | 31.8176i | −0.888708 | − | 1.21569i | ||||
\(686\) | −5.42609 | + | 16.6998i | −0.207169 | + | 0.637601i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.24417 | − | 9.98454i | −0.123683 | − | 0.380657i | ||||
\(689\) | 15.8493 | − | 48.7792i | 0.603812 | − | 1.85834i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6129 | − | 35.7407i | −0.441774 | − | 1.35964i | −0.885983 | − | 0.463717i | \(-0.846515\pi\) |
0.444210 | − | 0.895923i | \(-0.353485\pi\) | |||||||
\(692\) | −7.26790 | + | 5.28044i | −0.276284 | + | 0.200732i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.55975 | − | 3.31285i | 0.173086 | − | 0.125754i | ||||
\(695\) | 0.0534706 | + | 18.2331i | 0.00202826 | + | 0.691620i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.74904 | + | 2.72384i | 0.142005 | + | 0.103173i | ||||
\(698\) | 7.45224 | − | 22.9356i | 0.282071 | − | 0.868126i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.2861 | − | 0.124849i | 0.804538 | − | 0.00471885i | ||||
\(701\) | −26.4948 | −1.00070 | −0.500348 | − | 0.865825i | \(-0.666795\pi\) | ||||
−0.500348 | + | 0.865825i | \(0.666795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7163 | + | 7.78585i | 0.404173 | + | 0.293649i | ||||
\(704\) | −3.95483 | − | 2.87335i | −0.149053 | − | 0.108294i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.1672 | − | 13.9258i | 0.721368 | − | 0.524105i | ||||
\(707\) | −75.0602 | −2.82293 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5055 | + | 35.4104i | 0.432100 | + | 1.32987i | 0.896029 | + | 0.443995i | \(0.146439\pi\) |
−0.463930 | + | 0.885872i | \(0.653561\pi\) | |||||||
\(710\) | 16.4161 | − | 22.7348i | 0.616086 | − | 0.853221i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.693488 | − | 2.13434i | −0.0259896 | − | 0.0799876i | ||||
\(713\) | 1.41129 | + | 4.34351i | 0.0528533 | + | 0.162666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.1830 | + | 15.8120i | −1.80194 | + | 0.591334i | ||||
\(716\) | −2.16968 | − | 6.67758i | −0.0810846 | − | 0.249553i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.74772 | 0.102544 | ||||||||
\(719\) | −0.501912 | + | 0.364661i | −0.0187182 | + | 0.0135995i | −0.597105 | − | 0.802163i | \(-0.703682\pi\) |
0.578387 | + | 0.815763i | \(0.303682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.8509 | − | 49.2965i | −2.52690 | − | 1.83590i | ||||
\(722\) | 14.1353 | + | 10.2699i | 0.526060 | + | 0.382205i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.9524 | −0.444207 | ||||||||
\(725\) | 21.1394 | − | 0.123989i | 0.785099 | − | 0.00460483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.0770549 | + | 0.237151i | −0.00285781 | + | 0.00879543i | −0.952475 | − | 0.304616i | \(-0.901472\pi\) |
0.949617 | + | 0.313411i | \(0.101472\pi\) | |||||||
\(728\) | −15.9786 | − | 11.6091i | −0.592207 | − | 0.430263i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.30001 | − | 2.34827i | −0.270185 | − | 0.0869134i | ||||
\(731\) | 8.56220 | − | 6.22080i | 0.316684 | − | 0.230085i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.4927 | + | 25.0604i | −1.27402 | + | 0.925628i | −0.999355 | − | 0.0359121i | \(-0.988566\pi\) |
−0.274663 | + | 0.961540i | \(0.588566\pi\) | |||||||
\(734\) | −1.65493 | − | 5.09334i | −0.0610845 | − | 0.187999i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.38197 | − | 4.25325i | 0.0509399 | − | 0.156777i | ||||
\(737\) | 5.66576 | + | 17.4374i | 0.208701 | + | 0.642316i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.86029 | − | 14.9584i | 0.178789 | − | 0.550255i | −0.820997 | − | 0.570932i | \(-0.806582\pi\) |
0.999786 | + | 0.0206765i | \(0.00658202\pi\) | |||||||
\(740\) | −0.0702723 | − | 23.9623i | −0.00258326 | − | 0.880871i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −38.0778 | + | 27.6651i | −1.39788 | + | 1.01562i | ||||
\(743\) | 45.9731 | 1.68659 | 0.843294 | − | 0.537452i | \(-0.180613\pi\) | ||||
0.843294 | + | 0.537452i | \(0.180613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.7196 | + | 7.12761i | −0.795745 | + | 0.261136i | ||||
\(746\) | 22.6734 | + | 16.4732i | 0.830133 | + | 0.603127i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.52285 | − | 4.68686i | 0.0556811 | − | 0.171369i | ||||
\(749\) | 26.2545 | 0.959317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.09608 | 0.258940 | 0.129470 | − | 0.991583i | \(-0.458672\pi\) | ||||
0.129470 | + | 0.991583i | \(0.458672\pi\) | |||||||
\(752\) | 0.626140 | − | 1.92706i | 0.0228330 | − | 0.0702726i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.8685 | − | 11.5292i | −0.577898 | − | 0.419868i | ||||
\(755\) | 36.5463 | − | 11.9932i | 1.33006 | − | 0.436478i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7795 | 0.864281 | 0.432141 | − | 0.901806i | \(-0.357758\pi\) | ||||
0.432141 | + | 0.901806i | \(0.357758\pi\) | |||||||
\(758\) | 2.20145 | − | 1.59945i | 0.0799604 | − | 0.0580946i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.00810552 | + | 2.76392i | 0.000294018 | + | 0.100258i | ||||
\(761\) | −1.62195 | + | 4.99184i | −0.0587956 | + | 0.180954i | −0.976141 | − | 0.217138i | \(-0.930328\pi\) |
0.917345 | + | 0.398093i | \(0.130328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4296 | − | 32.0990i | −0.377576 | − | 1.16206i | ||||
\(764\) | −1.00000 | + | 3.07768i | −0.0361787 | + | 0.111347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.21468 | − | 16.0491i | −0.188414 | − | 0.579878i | ||||
\(767\) | 7.97377 | − | 5.79328i | 0.287916 | − | 0.209183i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.43639 | − | 3.22323i | 0.159980 | − | 0.116233i | −0.504915 | − | 0.863169i | \(-0.668476\pi\) |
0.664895 | + | 0.746937i | \(0.268476\pi\) | |||||||
\(770\) | 44.3003 | + | 14.2505i | 1.59647 | + | 0.513553i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.15501 | + | 4.47188i | 0.221524 | + | 0.160946i | ||||
\(773\) | 3.60661 | − | 11.1000i | 0.129721 | − | 0.399239i | −0.865011 | − | 0.501753i | \(-0.832689\pi\) |
0.994732 | + | 0.102514i | \(0.0326886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.54936 | + | 4.86536i | −0.0556548 | + | 0.174769i | ||||
\(776\) | −8.02933 | −0.288236 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.3259 | + | 22.7596i | 1.12309 | + | 0.815972i | ||||
\(779\) | −4.59681 | − | 3.33978i | −0.164698 | − | 0.119660i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.5967 | − | 36.0341i | 1.77471 | − | 1.28940i | ||||
\(782\) | 4.50838 | 0.161220 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.43766 | + | 10.5800i | 0.122774 | + | 0.377858i | ||||
\(785\) | −39.8202 | + | 13.0676i | −1.42125 | + | 0.466403i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.63108 | − | 23.4861i | −0.272019 | − | 0.837188i | −0.989993 | − | 0.141118i | \(-0.954930\pi\) |
0.717974 | − | 0.696070i | \(-0.245070\pi\) | |||||||
\(788\) | −1.45739 | − | 4.48538i | −0.0519173 | − | 0.159785i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.36471 | + | 11.5843i | −0.297603 | + | 0.412152i | ||||
\(791\) | 8.89164 | + | 27.3657i | 0.316150 | + | 0.973011i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.9786 | −0.638439 | ||||||||
\(794\) | −20.0261 | + | 14.5498i | −0.710698 | + | 0.516352i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8857 | + | 9.36201i | 0.456722 | + | 0.331828i | ||||
\(797\) | 16.7427 | + | 12.1643i | 0.593056 | + | 0.430880i | 0.843407 | − | 0.537275i | \(-0.180546\pi\) |
−0.250351 | + | 0.968155i | \(0.580546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.04265 | 0.0722639 | ||||||||
\(800\) | 4.02778 | − | 2.96260i | 0.142403 | − | 0.104744i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.02541 | − | 3.15590i | 0.0362086 | − | 0.111439i | ||||
\(803\) | −13.5628 | − | 9.85392i | −0.478619 | − | 0.347737i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.124850 | + | 42.5727i | 0.00440037 | + | 1.50049i | ||||
\(806\) | 3.83288 | − | 2.78475i | 0.135007 | − | 0.0980887i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.2638 | + | 10.3632i | −0.501797 | + | 0.364577i | ||||
\(809\) | 0.948863 | + | 2.92030i | 0.0333602 | + | 0.102672i | 0.966350 | − | 0.257230i | \(-0.0828099\pi\) |
−0.932990 | + | 0.359903i | \(0.882810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3668 | + | 44.2164i | −0.504485 | + | 1.55265i | 0.297149 | + | 0.954831i | \(0.403964\pi\) |
−0.801634 | + | 0.597815i | \(0.796036\pi\) | |||||||
\(812\) | 5.56220 | + | 17.1187i | 0.195195 | + | 0.600748i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.1882 | − | 49.8221i | 0.567395 | − | 1.74626i | ||||
\(815\) | −18.4748 | − | 25.2722i | −0.647143 | − | 0.885245i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4984 | + | 7.62751i | −0.367291 | + | 0.266853i | ||||
\(818\) | −28.3787 | −0.992238 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0301436 | + | 10.2787i | 0.00105266 | + | 0.358949i | ||||
\(821\) | −14.3885 | − | 10.4539i | −0.502162 | − | 0.364842i | 0.307680 | − | 0.951490i | \(-0.400447\pi\) |
−0.809842 | + | 0.586648i | \(0.800447\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.89759 | − | 5.84017i | 0.0661457 | − | 0.203575i | −0.912521 | − | 0.409030i | \(-0.865867\pi\) |
0.978667 | + | 0.205454i | \(0.0658672\pi\) | |||||||
\(824\) | −19.6999 | −0.686279 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.04463 | −0.314703 | ||||||||
\(827\) | 9.06121 | − | 27.8875i | 0.315089 | − | 0.969745i | −0.660629 | − | 0.750713i | \(-0.729710\pi\) |
0.975718 | − | 0.219032i | \(-0.0702898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.1826 | + | 29.1944i | 1.39560 | + | 1.01396i | 0.995225 | + | 0.0976102i | \(0.0311199\pi\) |
0.400374 | + | 0.916352i | \(0.368880\pi\) | |||||||
\(830\) | −9.30001 | − | 12.7217i | −0.322808 | − | 0.441578i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.63925 | −0.160837 | ||||||||
\(833\) | −9.07286 | + | 6.59182i | −0.314356 | + | 0.228393i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.6865 | + | 24.4942i | −0.612068 | + | 0.847655i | ||||
\(836\) | −1.86722 | + | 5.74670i | −0.0645790 | + | 0.198754i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.58097 | − | 14.0988i | −0.158247 | − | 0.487034i | ||||
\(839\) | −8.60481 | + | 26.4829i | −0.297071 | + | 0.914291i | 0.685447 | + | 0.728123i | \(0.259607\pi\) |
−0.982518 | + | 0.186168i | \(0.940393\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.43761 | − | 10.5799i | −0.118538 | − | 0.364823i | ||||
\(842\) | −14.7255 | + | 10.6987i | −0.507475 | + | 0.368702i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.77688 | − | 7.10332i | 0.336534 | − | 0.244506i | ||||
\(845\) | −11.1563 | + | 15.4505i | −0.383790 | + | 0.531512i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.4195 | + | 32.2726i | 1.52627 | + | 1.10890i | ||||
\(848\) | −3.41635 | + | 10.5145i | −0.117318 | + | 0.361068i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.09518 | + | 2.93878i | 0.140463 | + | 0.100799i | ||||
\(851\) | 47.9248 | 1.64284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8857 | + | 18.8070i | 0.886309 | + | 0.643941i | 0.934913 | − | 0.354877i | \(-0.115477\pi\) |
−0.0486043 | + | 0.998818i | \(0.515477\pi\) | |||||||
\(854\) | 13.3475 | + | 9.69750i | 0.456741 | + | 0.331841i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.98916 | − | 3.62484i | 0.170526 | − | 0.123894i | ||||
\(857\) | −31.7769 | −1.08548 | −0.542739 | − | 0.839902i | \(-0.682613\pi\) | ||||
−0.542739 | + | 0.839902i | \(0.682613\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.55910 | + | 7.87611i | 0.0873155 | + | 0.268729i | 0.985175 | − | 0.171553i | \(-0.0548784\pi\) |
−0.897859 | + | 0.440282i | \(0.854878\pi\) | |||||||
\(860\) | 22.3473 | + | 7.18869i | 0.762036 | + | 0.245132i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.48525 | − | 16.8819i | −0.186828 | − | 0.574999i | ||||
\(863\) | 5.98671 | + | 18.4252i | 0.203790 | + | 0.627201i | 0.999761 | + | 0.0218664i | \(0.00696084\pi\) |
−0.795971 | + | 0.605335i | \(0.793039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0589101 | − | 20.0879i | −0.00200300 | − | 0.683009i | ||||
\(866\) | 6.71125 | + | 20.6551i | 0.228057 | + | 0.701889i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.34763 | −0.147568 | ||||||||
\(869\) | −25.2716 | + | 18.3609i | −0.857282 | + | 0.622852i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0771 | + | 10.2276i | 0.476983 | + | 0.346548i | ||||
\(872\) | −6.41371 | − | 4.65983i | −0.217196 | − | 0.157802i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.52786 | −0.186983 | ||||||||
\(875\) | −27.6375 | + | 38.7522i | −0.934318 | + | 1.31006i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.18634 | + | 28.2726i | −0.310201 | + | 0.954699i | 0.667485 | + | 0.744624i | \(0.267371\pi\) |
−0.977685 | + | 0.210076i | \(0.932629\pi\) | |||||||
\(878\) | −8.67615 | − | 6.30359i | −0.292806 | − | 0.212736i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.3859 | − | 3.40830i | 0.350110 | − | 0.114894i | ||||
\(881\) | 13.8537 | − | 10.0653i | 0.466741 | − | 0.339107i | −0.329429 | − | 0.944180i | \(-0.606856\pi\) |
0.796170 | + | 0.605073i | \(0.206856\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34718 | − | 1.70533i | 0.0789889 | − | 0.0573888i | −0.547590 | − | 0.836747i | \(-0.684455\pi\) |
0.626579 | + | 0.779358i | \(0.284455\pi\) | |||||||
\(884\) | −1.44523 | − | 4.44796i | −0.0486083 | − | 0.149601i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.88278 | + | 24.2607i | −0.264827 | + | 0.815055i | ||||
\(887\) | 8.80338 | + | 27.0940i | 0.295589 | + | 0.909728i | 0.983023 | + | 0.183482i | \(0.0587369\pi\) |
−0.687434 | + | 0.726246i | \(0.741263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.2850 | + | 40.8871i | −0.445566 | + | 1.37131i | ||||
\(890\) | 4.77705 | + | 1.53668i | 0.160127 | + | 0.0515097i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.57286 | − | 5.50201i | 0.253558 | − | 0.184221i | ||||
\(893\) | −2.50456 | −0.0838118 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.9457 | + | 4.80773i | 0.499579 | + | 0.160705i | ||||
\(896\) | 3.44422 | + | 2.50237i | 0.115063 | + | 0.0835984i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.88183 | − | 11.9470i | 0.129538 | − | 0.398678i | ||||
\(899\) | −4.31768 | −0.144003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1452 | −0.371299 | ||||||||
\(902\) | −6.94399 | + | 21.3714i | −0.231210 | + | 0.711590i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.46794 | + | 3.97269i | 0.181861 | + | 0.132130i | ||||
\(905\) | 15.6459 | − | 21.6680i | 0.520086 | − | 0.720270i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.7343 | 1.85063 | 0.925314 | − | 0.379203i | \(-0.123802\pi\) | ||||
0.925314 | + | 0.379203i | \(0.123802\pi\) | |||||||
\(908\) | 8.19090 | − | 5.95104i | 0.271824 | − | 0.197492i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.9621 | − | 13.7705i | 1.39103 | − | 0.456487i | ||||
\(911\) | −0.506472 | + | 1.55876i | −0.0167801 | + | 0.0516440i | −0.959096 | − | 0.283081i | \(-0.908643\pi\) |
0.942316 | + | 0.334725i | \(0.108643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.6460 | − | 32.7649i | −0.352330 | − | 1.08436i | ||||
\(914\) | 0.940305 | − | 2.89396i | 0.0311025 | − | 0.0957237i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.29081 | + | 7.05038i | 0.0756904 | + | 0.232951i | ||||
\(917\) | −23.1503 | + | 16.8197i | −0.764490 | + | 0.555434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5965 | + | 20.7766i | −0.943310 | + | 0.685355i | −0.949215 | − | 0.314627i | \(-0.898120\pi\) |
0.00590477 | + | 0.999983i | \(0.498120\pi\) | |||||||
\(920\) | 5.90155 | + | 8.07290i | 0.194568 | + | 0.266156i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.3233 | − | 16.2188i | −0.735178 | − | 0.534138i | ||||
\(923\) | 17.9786 | − | 55.3325i | 0.591773 | − | 1.82129i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.5324 | + | 31.2397i | 1.43134 | + | 1.02715i | ||||
\(926\) | 30.2060 | 0.992631 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.42049 | + | 2.48513i | 0.112283 | + | 0.0815785i | ||||
\(929\) | −7.50256 | − | 5.45093i | −0.246151 | − | 0.178839i | 0.457868 | − | 0.889020i | \(-0.348613\pi\) |
−0.704019 | + | 0.710181i | \(0.748613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1245 | − | 8.08243i | 0.364591 | − | 0.264891i | ||||
\(932\) | 5.92778 | 0.194171 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.21572 | − | 28.3631i | −0.301548 | − | 0.928068i | ||||
\(935\) | 6.50320 | + | 8.89591i | 0.212677 | + | 0.290927i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.03856 | − | 9.35173i | −0.0992654 | − | 0.305508i | 0.889076 | − | 0.457759i | \(-0.151348\pi\) |
−0.988342 | + | 0.152251i | \(0.951348\pi\) | |||||||
\(938\) | −4.93425 | − | 15.1861i | −0.161109 | − | 0.495843i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.67387 | + | 3.65766i | 0.0872120 | + | 0.119300i | ||||
\(941\) | −18.0203 | − | 55.4607i | −0.587444 | − | 1.80797i | −0.589227 | − | 0.807968i | \(-0.700568\pi\) |
0.00178292 | − | 0.999998i | \(-0.499432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.5576 | −0.669447 | ||||||||
\(944\) | −1.71876 | + | 1.24875i | −0.0559409 | + | 0.0406434i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.5192 | + | 30.1655i | 1.34991 | + | 0.980765i | ||||
\(947\) | −35.0917 | − | 25.4956i | −1.14033 | − | 0.828496i | −0.153162 | − | 0.988201i | \(-0.548946\pi\) |
−0.987165 | + | 0.159705i | \(0.948946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.9099 | −0.516458 | ||||||||
\(950\) | −5.02122 | − | 3.60332i | −0.162910 | − | 0.116907i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.32624 | + | 4.08174i | −0.0429836 | + | 0.132290i | ||||
\(953\) | −8.14992 | − | 5.92126i | −0.264002 | − | 0.191808i | 0.447908 | − | 0.894080i | \(-0.352169\pi\) |
−0.711909 | + | 0.702271i | \(0.752169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.27040 | − | 5.84160i | −0.138187 | − | 0.189030i | ||||
\(956\) | −13.3606 | + | 9.70702i | −0.432112 | + | 0.313948i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.27040 | − | 3.82917i | 0.170279 | − | 0.123715i | ||||
\(959\) | 23.1883 | + | 71.3662i | 0.748788 | + | 2.30453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.25726 | + | 28.4909i | −0.298621 | + | 0.919061i | ||||
\(962\) | −15.3630 | − | 47.2824i | −0.495323 | − | 1.52445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.48120 | + | 7.63634i | −0.0799140 | + | 0.245950i | ||||
\(965\) | −16.1639 | + | 5.30443i | −0.520335 | + | 0.170756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3754 | − | 8.26469i | 0.365807 | − | 0.265775i | −0.389663 | − | 0.920958i | \(-0.627408\pi\) |
0.755470 | + | 0.655183i | \(0.227408\pi\) | |||||||
\(968\) | 12.8968 | 0.414520 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.5105 | − | 14.5561i | 0.337473 | − | 0.467367i | ||||
\(971\) | −24.3406 | − | 17.6845i | −0.781127 | − | 0.567522i | 0.124190 | − | 0.992258i | \(-0.460367\pi\) |
−0.905317 | + | 0.424737i | \(0.860367\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.7273 | − | 33.0154i | 0.343903 | − | 1.05842i | ||||
\(974\) | 40.1990 | 1.28806 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.87532 | 0.124046 | ||||||||
\(977\) | 3.66766 | − | 11.2879i | 0.117339 | − | 0.361131i | −0.875089 | − | 0.483962i | \(-0.839197\pi\) |
0.992428 | + | 0.122831i | \(0.0391972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.87532 | + | 6.44830i | 0.283657 | + | 0.206089i | ||||
\(980\) | −23.6801 | − | 7.61743i | −0.756434 | − | 0.243330i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.6280 | 1.16885 | ||||||||
\(983\) | −27.7898 | + | 20.1905i | −0.886358 | + | 0.643976i | −0.934926 | − | 0.354843i | \(-0.884534\pi\) |
0.0485682 | + | 0.998820i | \(0.484534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0391 | + | 3.22939i | 0.319873 | + | 0.102897i | ||||
\(986\) | −1.31710 | + | 4.05362i | −0.0419451 | + | 0.129094i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.77204 | + | 5.45377i | 0.0563760 | + | 0.173508i | ||||
\(989\) | −14.5084 | + | 44.6522i | −0.461340 | + | 1.41986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.76632 | + | 26.9800i | 0.278471 | + | 0.857046i | 0.988280 | + | 0.152652i | \(0.0487814\pi\) |
−0.709809 | + | 0.704394i | \(0.751219\pi\) | |||||||
\(992\) | −0.826185 | + | 0.600258i | −0.0262314 | + | 0.0190582i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −43.1933 | + | 31.3818i | −1.37001 | + | 0.995369i | ||||
\(995\) | −33.8397 | + | 11.1050i | −1.07279 | + | 0.352052i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.0128 | − | 26.8914i | −1.17221 | − | 0.851658i | −0.180935 | − | 0.983495i | \(-0.557912\pi\) |
−0.991271 | + | 0.131837i | \(0.957912\pi\) | |||||||
\(998\) | −7.70511 | + | 23.7139i | −0.243901 | + | 0.750650i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.h.d.271.2 | 8 | ||
3.2 | odd | 2 | 150.2.g.c.121.1 | yes | 8 | ||
15.2 | even | 4 | 750.2.h.e.649.1 | 16 | |||
15.8 | even | 4 | 750.2.h.e.649.4 | 16 | |||
15.14 | odd | 2 | 750.2.g.d.601.2 | 8 | |||
25.6 | even | 5 | inner | 450.2.h.d.181.2 | 8 | ||
75.8 | even | 20 | 750.2.h.e.349.2 | 16 | |||
75.17 | even | 20 | 750.2.h.e.349.3 | 16 | |||
75.38 | even | 20 | 3750.2.c.h.1249.8 | 8 | |||
75.41 | odd | 10 | 3750.2.a.l.1.1 | 4 | |||
75.44 | odd | 10 | 750.2.g.d.151.2 | 8 | |||
75.56 | odd | 10 | 150.2.g.c.31.1 | ✓ | 8 | ||
75.59 | odd | 10 | 3750.2.a.q.1.4 | 4 | |||
75.62 | even | 20 | 3750.2.c.h.1249.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.c.31.1 | ✓ | 8 | 75.56 | odd | 10 | ||
150.2.g.c.121.1 | yes | 8 | 3.2 | odd | 2 | ||
450.2.h.d.181.2 | 8 | 25.6 | even | 5 | inner | ||
450.2.h.d.271.2 | 8 | 1.1 | even | 1 | trivial | ||
750.2.g.d.151.2 | 8 | 75.44 | odd | 10 | |||
750.2.g.d.601.2 | 8 | 15.14 | odd | 2 | |||
750.2.h.e.349.2 | 16 | 75.8 | even | 20 | |||
750.2.h.e.349.3 | 16 | 75.17 | even | 20 | |||
750.2.h.e.649.1 | 16 | 15.2 | even | 4 | |||
750.2.h.e.649.4 | 16 | 15.8 | even | 4 | |||
3750.2.a.l.1.1 | 4 | 75.41 | odd | 10 | |||
3750.2.a.q.1.4 | 4 | 75.59 | odd | 10 | |||
3750.2.c.h.1249.1 | 8 | 75.62 | even | 20 | |||
3750.2.c.h.1249.8 | 8 | 75.38 | even | 20 |