Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (of order \(3\), degree \(2\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.2 | ||
Root | \(0.500000 - 1.51496i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.f.67.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.227452 | + | 0.393958i | −0.101720 | + | 0.176184i | −0.912393 | − | 0.409315i | \(-0.865768\pi\) |
0.810674 | + | 0.585498i | \(0.199101\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.227452 | + | 2.63596i | −0.0859688 | + | 0.996298i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.227452 | − | 0.393958i | −0.0719267 | − | 0.124581i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 0.909808 | 0.252335 | 0.126168 | − | 0.992009i | \(-0.459732\pi\) | ||||
0.126168 | + | 0.992009i | \(0.459732\pi\) | |||||||
\(14\) | −2.16908 | − | 1.51496i | −0.579711 | − | 0.404889i | ||||
\(15\) | 0.454904 | 0.117456 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | 0.799000 | − | 0.601331i | \(-0.205363\pi\) |
−0.920268 | + | 0.391289i | \(0.872029\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −1.94163 | + | 3.36300i | −0.445440 | + | 0.771524i | −0.998083 | − | 0.0618938i | \(-0.980286\pi\) |
0.552643 | + | 0.833418i | \(0.313619\pi\) | |||||||
\(20\) | 0.454904 | 0.101720 | ||||||||
\(21\) | 2.39653 | − | 1.12100i | 0.522966 | − | 0.244622i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −4.16908 | + | 7.22106i | −0.869313 | + | 1.50569i | −0.00661323 | + | 0.999978i | \(0.502105\pi\) |
−0.862700 | + | 0.505716i | \(0.831228\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.39653 | + | 4.15091i | 0.479306 | + | 0.830183i | ||||
\(26\) | −0.454904 | + | 0.787917i | −0.0892140 | + | 0.154523i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.39653 | − | 1.12100i | 0.452902 | − | 0.211849i | ||||
\(29\) | −2.79306 | −0.518659 | −0.259329 | − | 0.965789i | \(-0.583502\pi\) | ||||
−0.259329 | + | 0.965789i | \(0.583502\pi\) | |||||||
\(30\) | −0.227452 | + | 0.393958i | −0.0415269 | + | 0.0719267i | ||||
\(31\) | 4.79306 | + | 8.30183i | 0.860859 | + | 1.49105i | 0.871101 | + | 0.491105i | \(0.163407\pi\) |
−0.0102412 | + | 0.999948i | \(0.503260\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −0.986723 | − | 0.689160i | −0.166787 | − | 0.116489i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.94163 | + | 6.82710i | −0.647999 | + | 1.12237i | 0.335601 | + | 0.942004i | \(0.391061\pi\) |
−0.983600 | + | 0.180364i | \(0.942273\pi\) | |||||||
\(38\) | −1.94163 | − | 3.36300i | −0.314973 | − | 0.545550i | ||||
\(39\) | −0.454904 | − | 0.787917i | −0.0728430 | − | 0.126168i | ||||
\(40\) | −0.227452 | + | 0.393958i | −0.0359633 | + | 0.0622903i | ||||
\(41\) | −1.79306 | −0.280029 | −0.140015 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140015 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(42\) | −0.227452 | + | 2.63596i | −0.0350966 | + | 0.406737i | ||||
\(43\) | 7.88325 | 1.20218 | 0.601092 | − | 0.799179i | \(-0.294732\pi\) | ||||
0.601092 | + | 0.799179i | \(0.294732\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −0.227452 | − | 0.393958i | −0.0339065 | − | 0.0587279i | ||||
\(46\) | −4.16908 | − | 7.22106i | −0.614697 | − | 1.06469i | ||||
\(47\) | −0.169079 | + | 0.292854i | −0.0246627 | + | 0.0427171i | −0.878093 | − | 0.478489i | \(-0.841185\pi\) |
0.853431 | + | 0.521206i | \(0.174518\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.89653 | − | 1.19911i | −0.985219 | − | 0.171301i | ||||
\(50\) | −4.79306 | −0.677841 | ||||||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | −0.454904 | − | 0.787917i | −0.0630838 | − | 0.109264i | ||||
\(53\) | −0.454904 | − | 0.787917i | −0.0624859 | − | 0.108229i | 0.833090 | − | 0.553137i | \(-0.186570\pi\) |
−0.895576 | + | 0.444909i | \(0.853236\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0.454904 | 0.0613393 | ||||||||
\(56\) | −0.227452 | + | 2.63596i | −0.0303946 | + | 0.352244i | ||||
\(57\) | 3.88325 | 0.514350 | ||||||||
\(58\) | 1.39653 | − | 2.41886i | 0.183374 | − | 0.317612i | ||||
\(59\) | −3.48672 | − | 6.03918i | −0.453933 | − | 0.786234i | 0.544693 | − | 0.838635i | \(-0.316646\pi\) |
−0.998626 | + | 0.0524008i | \(0.983313\pi\) | |||||||
\(60\) | −0.227452 | − | 0.393958i | −0.0293639 | − | 0.0508598i | ||||
\(61\) | 7.02051 | − | 12.1599i | 0.898885 | − | 1.55691i | 0.0699629 | − | 0.997550i | \(-0.477712\pi\) |
0.828922 | − | 0.559364i | \(-0.188955\pi\) | |||||||
\(62\) | −9.58612 | −1.21744 | ||||||||
\(63\) | −2.16908 | − | 1.51496i | −0.273278 | − | 0.190867i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.206938 | + | 0.358427i | −0.0256675 | + | 0.0444574i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | 1.89653 | + | 3.28489i | 0.231698 | + | 0.401313i | 0.958308 | − | 0.285737i | \(-0.0922385\pi\) |
−0.726610 | + | 0.687050i | \(0.758905\pi\) | |||||||
\(68\) | −0.500000 | + | 0.866025i | −0.0606339 | + | 0.105021i | ||||
\(69\) | 8.33816 | 1.00380 | ||||||||
\(70\) | 1.09019 | − | 0.509947i | 0.130303 | − | 0.0609503i | ||||
\(71\) | −4.79306 | −0.568832 | −0.284416 | − | 0.958701i | \(-0.591800\pi\) | ||||
−0.284416 | + | 0.958701i | \(0.591800\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −5.33816 | − | 9.24596i | −0.624784 | − | 1.08216i | −0.988583 | − | 0.150680i | \(-0.951854\pi\) |
0.363798 | − | 0.931478i | \(-0.381480\pi\) | |||||||
\(74\) | −3.94163 | − | 6.82710i | −0.458205 | − | 0.793634i | ||||
\(75\) | 2.39653 | − | 4.15091i | 0.276728 | − | 0.479306i | ||||
\(76\) | 3.88325 | 0.445440 | ||||||||
\(77\) | 2.39653 | − | 1.12100i | 0.273110 | − | 0.127750i | ||||
\(78\) | 0.909808 | 0.103015 | ||||||||
\(79\) | −2.68236 | + | 4.64598i | −0.301789 | + | 0.522713i | −0.976541 | − | 0.215331i | \(-0.930917\pi\) |
0.674753 | + | 0.738044i | \(0.264250\pi\) | |||||||
\(80\) | −0.227452 | − | 0.393958i | −0.0254299 | − | 0.0440459i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.896531 | − | 1.55284i | 0.0990053 | − | 0.171482i | ||||
\(83\) | 1.97345 | 0.216614 | 0.108307 | − | 0.994118i | \(-0.465457\pi\) | ||||
0.108307 | + | 0.994118i | \(0.465457\pi\) | |||||||
\(84\) | −2.16908 | − | 1.51496i | −0.236666 | − | 0.165295i | ||||
\(85\) | 0.454904 | 0.0493413 | ||||||||
\(86\) | −3.94163 | + | 6.82710i | −0.425037 | + | 0.736185i | ||||
\(87\) | 1.39653 | + | 2.41886i | 0.149724 | + | 0.259329i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 5.54510 | − | 9.60439i | 0.587779 | − | 1.01806i | −0.406744 | − | 0.913542i | \(-0.633336\pi\) |
0.994523 | − | 0.104521i | \(-0.0333309\pi\) | |||||||
\(90\) | 0.454904 | 0.0479511 | ||||||||
\(91\) | −0.206938 | + | 2.39821i | −0.0216930 | + | 0.251401i | ||||
\(92\) | 8.33816 | 0.869313 | ||||||||
\(93\) | 4.79306 | − | 8.30183i | 0.497017 | − | 0.860859i | ||||
\(94\) | −0.169079 | − | 0.292854i | −0.0174392 | − | 0.0302055i | ||||
\(95\) | −0.883254 | − | 1.52984i | −0.0906200 | − | 0.156958i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 14.5861 | 1.48100 | 0.740498 | − | 0.672058i | \(-0.234590\pi\) | ||||
0.740498 | + | 0.672058i | \(0.234590\pi\) | |||||||
\(98\) | 4.48672 | − | 5.37302i | 0.453227 | − | 0.542757i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 2.39653 | − | 4.15091i | 0.239653 | − | 0.415091i | ||||
\(101\) | 4.03182 | + | 6.98332i | 0.401181 | + | 0.694866i | 0.993869 | − | 0.110566i | \(-0.0352665\pi\) |
−0.592688 | + | 0.805432i | \(0.701933\pi\) | |||||||
\(102\) | −0.500000 | − | 0.866025i | −0.0495074 | − | 0.0857493i | ||||
\(103\) | −2.88325 | + | 4.99394i | −0.284095 | + | 0.492068i | −0.972389 | − | 0.233364i | \(-0.925027\pi\) |
0.688294 | + | 0.725432i | \(0.258360\pi\) | |||||||
\(104\) | 0.909808 | 0.0892140 | ||||||||
\(105\) | −0.103469 | + | 1.19911i | −0.0100975 | + | 0.117021i | ||||
\(106\) | 0.909808 | 0.0883684 | ||||||||
\(107\) | −7.80634 | + | 13.5210i | −0.754667 | + | 1.30712i | 0.190872 | + | 0.981615i | \(0.438868\pi\) |
−0.945540 | + | 0.325507i | \(0.894465\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.02051 | − | 12.1599i | −0.672443 | − | 1.16471i | −0.977209 | − | 0.212279i | \(-0.931912\pi\) |
0.304766 | − | 0.952427i | \(-0.401422\pi\) | |||||||
\(110\) | −0.227452 | + | 0.393958i | −0.0216867 | + | 0.0375625i | ||||
\(111\) | 7.88325 | 0.748245 | ||||||||
\(112\) | −2.16908 | − | 1.51496i | −0.204959 | − | 0.143150i | ||||
\(113\) | 7.58612 | 0.713643 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(114\) | −1.94163 | + | 3.36300i | −0.181850 | + | 0.314973i | ||||
\(115\) | −1.89653 | − | 3.28489i | −0.176852 | − | 0.306317i | ||||
\(116\) | 1.39653 | + | 2.41886i | 0.129665 | + | 0.224586i | ||||
\(117\) | −0.454904 | + | 0.787917i | −0.0420559 | + | 0.0728430i | ||||
\(118\) | 6.97345 | 0.641958 | ||||||||
\(119\) | 2.39653 | − | 1.12100i | 0.219690 | − | 0.102762i | ||||
\(120\) | 0.454904 | 0.0415269 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 7.02051 | + | 12.1599i | 0.635608 | + | 1.10090i | ||||
\(123\) | 0.896531 | + | 1.55284i | 0.0808375 | + | 0.140015i | ||||
\(124\) | 4.79306 | − | 8.30183i | 0.430430 | − | 0.745526i | ||||
\(125\) | −4.45490 | −0.398459 | ||||||||
\(126\) | 2.39653 | − | 1.12100i | 0.213500 | − | 0.0998665i | ||||
\(127\) | 7.42835 | 0.659159 | 0.329580 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329580 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.94163 | − | 6.82710i | −0.347041 | − | 0.601092i | ||||
\(130\) | −0.206938 | − | 0.358427i | −0.0181496 | − | 0.0314361i | ||||
\(131\) | 9.70287 | − | 16.8059i | 0.847744 | − | 1.46834i | −0.0354732 | − | 0.999371i | \(-0.511294\pi\) |
0.883217 | − | 0.468965i | \(-0.155373\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −8.42309 | − | 5.88296i | −0.730374 | − | 0.510118i | ||||
\(134\) | −3.79306 | −0.327671 | ||||||||
\(135\) | −0.227452 | + | 0.393958i | −0.0195760 | + | 0.0339065i | ||||
\(136\) | −0.500000 | − | 0.866025i | −0.0428746 | − | 0.0742611i | ||||
\(137\) | −0.454904 | − | 0.787917i | −0.0388651 | − | 0.0673163i | 0.845939 | − | 0.533280i | \(-0.179041\pi\) |
−0.884804 | + | 0.465964i | \(0.845708\pi\) | |||||||
\(138\) | −4.16908 | + | 7.22106i | −0.354896 | + | 0.614697i | ||||
\(139\) | −8.37919 | −0.710713 | −0.355357 | − | 0.934731i | \(-0.615641\pi\) | ||||
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(140\) | −0.103469 | + | 1.19911i | −0.00874472 | + | 0.101343i | ||||
\(141\) | 0.338158 | 0.0284781 | ||||||||
\(142\) | 2.39653 | − | 4.15091i | 0.201112 | − | 0.348337i | ||||
\(143\) | −0.454904 | − | 0.787917i | −0.0380410 | − | 0.0658889i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.635288 | − | 1.10035i | 0.0527578 | − | 0.0913791i | ||||
\(146\) | 10.6763 | 0.883578 | ||||||||
\(147\) | 2.40981 | + | 6.57212i | 0.198758 | + | 0.542060i | ||||
\(148\) | 7.88325 | 0.647999 | ||||||||
\(149\) | −2.05837 | + | 3.56521i | −0.168628 | + | 0.292073i | −0.937938 | − | 0.346803i | \(-0.887267\pi\) |
0.769309 | + | 0.638876i | \(0.220600\pi\) | |||||||
\(150\) | 2.39653 | + | 4.15091i | 0.195676 | + | 0.338921i | ||||
\(151\) | 3.07889 | + | 5.33279i | 0.250556 | + | 0.433976i | 0.963679 | − | 0.267063i | \(-0.0860531\pi\) |
−0.713123 | + | 0.701039i | \(0.752720\pi\) | |||||||
\(152\) | −1.94163 | + | 3.36300i | −0.157487 | + | 0.272775i | ||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.227452 | + | 2.63596i | −0.0183286 | + | 0.212411i | ||||
\(155\) | −4.36077 | −0.350265 | ||||||||
\(156\) | −0.454904 | + | 0.787917i | −0.0364215 | + | 0.0630838i | ||||
\(157\) | 8.82488 | + | 15.2851i | 0.704302 | + | 1.21989i | 0.966943 | + | 0.254993i | \(0.0820733\pi\) |
−0.262641 | + | 0.964894i | \(0.584593\pi\) | |||||||
\(158\) | −2.68236 | − | 4.64598i | −0.213397 | − | 0.369614i | ||||
\(159\) | −0.454904 | + | 0.787917i | −0.0360762 | + | 0.0624859i | ||||
\(160\) | 0.454904 | 0.0359633 | ||||||||
\(161\) | −18.0861 | − | 12.6320i | −1.42539 | − | 0.995537i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.80634 | − | 10.0569i | 0.454788 | − | 0.787715i | −0.543888 | − | 0.839158i | \(-0.683049\pi\) |
0.998676 | + | 0.0514424i | \(0.0163818\pi\) | |||||||
\(164\) | 0.896531 | + | 1.55284i | 0.0700073 | + | 0.121256i | ||||
\(165\) | −0.227452 | − | 0.393958i | −0.0177071 | − | 0.0306696i | ||||
\(166\) | −0.986723 | + | 1.70905i | −0.0765846 | + | 0.132648i | ||||
\(167\) | −4.85670 | −0.375823 | −0.187911 | − | 0.982186i | \(-0.560172\pi\) | ||||
−0.187911 | + | 0.982186i | \(0.560172\pi\) | |||||||
\(168\) | 2.39653 | − | 1.12100i | 0.184896 | − | 0.0864869i | ||||
\(169\) | −12.1722 | −0.936327 | ||||||||
\(170\) | −0.227452 | + | 0.393958i | −0.0174448 | + | 0.0302152i | ||||
\(171\) | −1.94163 | − | 3.36300i | −0.148480 | − | 0.257175i | ||||
\(172\) | −3.94163 | − | 6.82710i | −0.300546 | − | 0.520561i | ||||
\(173\) | 12.7931 | − | 22.1582i | 0.972639 | − | 1.68466i | 0.285121 | − | 0.958492i | \(-0.407966\pi\) |
0.687518 | − | 0.726168i | \(-0.258700\pi\) | |||||||
\(174\) | −2.79306 | −0.211742 | ||||||||
\(175\) | −11.4867 | + | 5.37302i | −0.868315 | + | 0.406162i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −3.48672 | + | 6.03918i | −0.262078 | + | 0.453933i | ||||
\(178\) | 5.54510 | + | 9.60439i | 0.415623 | + | 0.719879i | ||||
\(179\) | 7.85144 | + | 13.5991i | 0.586844 | + | 1.01644i | 0.994643 | + | 0.103372i | \(0.0329631\pi\) |
−0.407799 | + | 0.913072i | \(0.633704\pi\) | |||||||
\(180\) | −0.227452 | + | 0.393958i | −0.0169533 | + | 0.0293639i | ||||
\(181\) | −2.49593 | −0.185521 | −0.0927606 | − | 0.995688i | \(-0.529569\pi\) | ||||
−0.0927606 | + | 0.995688i | \(0.529569\pi\) | |||||||
\(182\) | −1.97345 | − | 1.37832i | −0.146282 | − | 0.102168i | ||||
\(183\) | −14.0410 | −1.03794 | ||||||||
\(184\) | −4.16908 | + | 7.22106i | −0.307349 | + | 0.532343i | ||||
\(185\) | −1.79306 | − | 3.10567i | −0.131829 | − | 0.228334i | ||||
\(186\) | 4.79306 | + | 8.30183i | 0.351444 | + | 0.608720i | ||||
\(187\) | −0.500000 | + | 0.866025i | −0.0365636 | + | 0.0633300i | ||||
\(188\) | 0.338158 | 0.0246627 | ||||||||
\(189\) | −0.227452 | + | 2.63596i | −0.0165447 | + | 0.191738i | ||||
\(190\) | 1.76651 | 0.128156 | ||||||||
\(191\) | −4.90981 | + | 8.50404i | −0.355261 | + | 0.615331i | −0.987163 | − | 0.159718i | \(-0.948941\pi\) |
0.631901 | + | 0.775049i | \(0.282275\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −3.42835 | − | 5.93808i | −0.246778 | − | 0.427432i | 0.715852 | − | 0.698252i | \(-0.246039\pi\) |
−0.962630 | + | 0.270820i | \(0.912705\pi\) | |||||||
\(194\) | −7.29306 | + | 12.6320i | −0.523611 | + | 0.906921i | ||||
\(195\) | 0.413875 | 0.0296382 | ||||||||
\(196\) | 2.40981 | + | 6.57212i | 0.172129 | + | 0.469437i | ||||
\(197\) | 23.4694 | 1.67212 | 0.836062 | − | 0.548635i | \(-0.184852\pi\) | ||||
0.836062 | + | 0.548635i | \(0.184852\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | 1.11675 | + | 1.93426i | 0.0791640 | + | 0.137116i | 0.902889 | − | 0.429873i | \(-0.141442\pi\) |
−0.823725 | + | 0.566989i | \(0.808108\pi\) | |||||||
\(200\) | 2.39653 | + | 4.15091i | 0.169460 | + | 0.293514i | ||||
\(201\) | 1.89653 | − | 3.28489i | 0.133771 | − | 0.231698i | ||||
\(202\) | −8.06364 | −0.567356 | ||||||||
\(203\) | 0.635288 | − | 7.36239i | 0.0445885 | − | 0.516738i | ||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 0.407836 | − | 0.706392i | 0.0284845 | − | 0.0493366i | ||||
\(206\) | −2.88325 | − | 4.99394i | −0.200886 | − | 0.347944i | ||||
\(207\) | −4.16908 | − | 7.22106i | −0.289771 | − | 0.501898i | ||||
\(208\) | −0.454904 | + | 0.787917i | −0.0315419 | + | 0.0546322i | ||||
\(209\) | 3.88325 | 0.268610 | ||||||||
\(210\) | −0.986723 | − | 0.689160i | −0.0680904 | − | 0.0475566i | ||||
\(211\) | −18.2624 | −1.25724 | −0.628619 | − | 0.777713i | \(-0.716380\pi\) | ||||
−0.628619 | + | 0.777713i | \(0.716380\pi\) | |||||||
\(212\) | −0.454904 | + | 0.787917i | −0.0312429 | + | 0.0541144i | ||||
\(213\) | 2.39653 | + | 4.15091i | 0.164208 | + | 0.284416i | ||||
\(214\) | −7.80634 | − | 13.5210i | −0.533630 | − | 0.924275i | ||||
\(215\) | −1.79306 | + | 3.10567i | −0.122286 | + | 0.211805i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −22.9734 | + | 10.7460i | −1.55954 | + | 0.729488i | ||||
\(218\) | 14.0410 | 0.950978 | ||||||||
\(219\) | −5.33816 | + | 9.24596i | −0.360719 | + | 0.624784i | ||||
\(220\) | −0.227452 | − | 0.393958i | −0.0153348 | − | 0.0265607i | ||||
\(221\) | −0.454904 | − | 0.787917i | −0.0306002 | − | 0.0530010i | ||||
\(222\) | −3.94163 | + | 6.82710i | −0.264545 | + | 0.458205i | ||||
\(223\) | 12.4959 | 0.836790 | 0.418395 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418395 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(224\) | 2.39653 | − | 1.12100i | 0.160125 | − | 0.0748999i | ||||
\(225\) | −4.79306 | −0.319537 | ||||||||
\(226\) | −3.79306 | + | 6.56978i | −0.252311 | + | 0.437015i | ||||
\(227\) | −4.89653 | − | 8.48104i | −0.324994 | − | 0.562906i | 0.656517 | − | 0.754311i | \(-0.272029\pi\) |
−0.981511 | + | 0.191405i | \(0.938696\pi\) | |||||||
\(228\) | −1.94163 | − | 3.36300i | −0.128587 | − | 0.222720i | ||||
\(229\) | −4.33816 | + | 7.51391i | −0.286674 | + | 0.496533i | −0.973014 | − | 0.230748i | \(-0.925883\pi\) |
0.686340 | + | 0.727281i | \(0.259216\pi\) | |||||||
\(230\) | 3.79306 | 0.250107 | ||||||||
\(231\) | −2.16908 | − | 1.51496i | −0.142715 | − | 0.0996769i | ||||
\(232\) | −2.79306 | −0.183374 | ||||||||
\(233\) | −8.38325 | + | 14.5202i | −0.549205 | + | 0.951251i | 0.449124 | + | 0.893469i | \(0.351736\pi\) |
−0.998329 | + | 0.0577819i | \(0.981597\pi\) | |||||||
\(234\) | −0.454904 | − | 0.787917i | −0.0297380 | − | 0.0515077i | ||||
\(235\) | −0.0769148 | − | 0.133220i | −0.00501737 | − | 0.00869033i | ||||
\(236\) | −3.48672 | + | 6.03918i | −0.226966 | + | 0.393117i | ||||
\(237\) | 5.36471 | 0.348476 | ||||||||
\(238\) | −0.227452 | + | 2.63596i | −0.0147435 | + | 0.170864i | ||||
\(239\) | −26.2624 | −1.69878 | −0.849388 | − | 0.527769i | \(-0.823029\pi\) | ||||
−0.849388 | + | 0.527769i | \(0.823029\pi\) | |||||||
\(240\) | −0.227452 | + | 0.393958i | −0.0146820 | + | 0.0254299i | ||||
\(241\) | −3.97345 | − | 6.88221i | −0.255952 | − | 0.443322i | 0.709202 | − | 0.705006i | \(-0.249056\pi\) |
−0.965154 | + | 0.261684i | \(0.915722\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −14.0410 | −0.898885 | ||||||||
\(245\) | 2.04103 | − | 2.44421i | 0.130397 | − | 0.156155i | ||||
\(246\) | −1.79306 | −0.114321 | ||||||||
\(247\) | −1.76651 | + | 3.05968i | −0.112400 | + | 0.194683i | ||||
\(248\) | 4.79306 | + | 8.30183i | 0.304360 | + | 0.527167i | ||||
\(249\) | −0.986723 | − | 1.70905i | −0.0625310 | − | 0.108307i | ||||
\(250\) | 2.22745 | − | 3.85806i | 0.140876 | − | 0.244005i | ||||
\(251\) | −3.93636 | −0.248461 | −0.124230 | − | 0.992253i | \(-0.539646\pi\) | ||||
−0.124230 | + | 0.992253i | \(0.539646\pi\) | |||||||
\(252\) | −0.227452 | + | 2.63596i | −0.0143281 | + | 0.166050i | ||||
\(253\) | 8.33816 | 0.524216 | ||||||||
\(254\) | −3.71417 | + | 6.43314i | −0.233048 | + | 0.403651i | ||||
\(255\) | −0.227452 | − | 0.393958i | −0.0142436 | − | 0.0246706i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.54510 | − | 13.0685i | 0.470650 | − | 0.815190i | −0.528786 | − | 0.848755i | \(-0.677353\pi\) |
0.999437 | + | 0.0335650i | \(0.0106861\pi\) | |||||||
\(258\) | 7.88325 | 0.490790 | ||||||||
\(259\) | −17.0994 | − | 11.9428i | −1.06251 | − | 0.742089i | ||||
\(260\) | 0.413875 | 0.0256675 | ||||||||
\(261\) | 1.39653 | − | 2.41886i | 0.0864431 | − | 0.149724i | ||||
\(262\) | 9.70287 | + | 16.8059i | 0.599445 | + | 1.03827i | ||||
\(263\) | 14.3116 | + | 24.7884i | 0.882491 | + | 1.52852i | 0.848562 | + | 0.529096i | \(0.177469\pi\) |
0.0339291 | + | 0.999424i | \(0.489198\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 0.413875 | 0.0254242 | ||||||||
\(266\) | 9.30634 | − | 4.35312i | 0.570608 | − | 0.266907i | ||||
\(267\) | −11.0902 | −0.678709 | ||||||||
\(268\) | 1.89653 | − | 3.28489i | 0.115849 | − | 0.200656i | ||||
\(269\) | 11.4754 | + | 19.8760i | 0.699669 | + | 1.21186i | 0.968581 | + | 0.248697i | \(0.0800023\pi\) |
−0.268913 | + | 0.963165i | \(0.586664\pi\) | |||||||
\(270\) | −0.227452 | − | 0.393958i | −0.0138423 | − | 0.0239756i | ||||
\(271\) | −4.90981 | + | 8.50404i | −0.298250 | + | 0.516583i | −0.975736 | − | 0.218952i | \(-0.929736\pi\) |
0.677486 | + | 0.735536i | \(0.263069\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 2.18038 | − | 1.01989i | 0.131963 | − | 0.0617268i | ||||
\(274\) | 0.909808 | 0.0549635 | ||||||||
\(275\) | 2.39653 | − | 4.15091i | 0.144516 | − | 0.250310i | ||||
\(276\) | −4.16908 | − | 7.22106i | −0.250949 | − | 0.434657i | ||||
\(277\) | −5.36471 | − | 9.29195i | −0.322334 | − | 0.558299i | 0.658635 | − | 0.752463i | \(-0.271134\pi\) |
−0.980969 | + | 0.194163i | \(0.937801\pi\) | |||||||
\(278\) | 4.18959 | − | 7.25659i | 0.251275 | − | 0.435221i | ||||
\(279\) | −9.58612 | −0.573906 | ||||||||
\(280\) | −0.986723 | − | 0.689160i | −0.0589680 | − | 0.0411852i | ||||
\(281\) | 2.58612 | 0.154275 | 0.0771376 | − | 0.997020i | \(-0.475422\pi\) | ||||
0.0771376 | + | 0.997020i | \(0.475422\pi\) | |||||||
\(282\) | −0.169079 | + | 0.292854i | −0.0100685 | + | 0.0174392i | ||||
\(283\) | 10.0410 | + | 17.3916i | 0.596877 | + | 1.03382i | 0.993279 | + | 0.115745i | \(0.0369254\pi\) |
−0.396402 | + | 0.918077i | \(0.629741\pi\) | |||||||
\(284\) | 2.39653 | + | 4.15091i | 0.142208 | + | 0.246311i | ||||
\(285\) | −0.883254 | + | 1.52984i | −0.0523195 | + | 0.0906200i | ||||
\(286\) | 0.909808 | 0.0537981 | ||||||||
\(287\) | 0.407836 | − | 4.72643i | 0.0240738 | − | 0.278993i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 0.635288 | + | 1.10035i | 0.0373054 | + | 0.0646148i | ||||
\(291\) | −7.29306 | − | 12.6320i | −0.427527 | − | 0.740498i | ||||
\(292\) | −5.33816 | + | 9.24596i | −0.312392 | + | 0.541079i | ||||
\(293\) | 10.3792 | 0.606359 | 0.303179 | − | 0.952934i | \(-0.401952\pi\) | ||||
0.303179 | + | 0.952934i | \(0.401952\pi\) | |||||||
\(294\) | −6.89653 | − | 1.19911i | −0.402214 | − | 0.0699334i | ||||
\(295\) | 3.17225 | 0.184695 | ||||||||
\(296\) | −3.94163 | + | 6.82710i | −0.229102 | + | 0.396817i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −2.05837 | − | 3.56521i | −0.119238 | − | 0.206527i | ||||
\(299\) | −3.79306 | + | 6.56978i | −0.219358 | + | 0.379940i | ||||
\(300\) | −4.79306 | −0.276728 | ||||||||
\(301\) | −1.79306 | + | 20.7799i | −0.103350 | + | 1.19773i | ||||
\(302\) | −6.15777 | −0.354340 | ||||||||
\(303\) | 4.03182 | − | 6.98332i | 0.231622 | − | 0.401181i | ||||
\(304\) | −1.94163 | − | 3.36300i | −0.111360 | − | 0.192881i | ||||
\(305\) | 3.19366 | + | 5.53158i | 0.182868 | + | 0.316737i | ||||
\(306\) | −0.500000 | + | 0.866025i | −0.0285831 | + | 0.0495074i | ||||
\(307\) | 9.76651 | 0.557404 | 0.278702 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278702 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(308\) | −2.16908 | − | 1.51496i | −0.123595 | − | 0.0863227i | ||||
\(309\) | 5.76651 | 0.328045 | ||||||||
\(310\) | 2.18038 | − | 3.77654i | 0.123837 | − | 0.214493i | ||||
\(311\) | 3.25927 | + | 5.64522i | 0.184816 | + | 0.320111i | 0.943515 | − | 0.331331i | \(-0.107498\pi\) |
−0.758698 | + | 0.651442i | \(0.774164\pi\) | |||||||
\(312\) | −0.454904 | − | 0.787917i | −0.0257539 | − | 0.0446070i | ||||
\(313\) | −15.3965 | + | 26.6676i | −0.870263 | + | 1.50734i | −0.00853913 | + | 0.999964i | \(0.502718\pi\) |
−0.861724 | + | 0.507377i | \(0.830615\pi\) | |||||||
\(314\) | −17.6498 | −0.996034 | ||||||||
\(315\) | 1.09019 | − | 0.509947i | 0.0614254 | − | 0.0287323i | ||||
\(316\) | 5.36471 | 0.301789 | ||||||||
\(317\) | 13.8136 | − | 23.9258i | 0.775848 | − | 1.34381i | −0.158469 | − | 0.987364i | \(-0.550656\pi\) |
0.934317 | − | 0.356444i | \(-0.116011\pi\) | |||||||
\(318\) | −0.454904 | − | 0.787917i | −0.0255098 | − | 0.0441842i | ||||
\(319\) | 1.39653 | + | 2.41886i | 0.0781907 | + | 0.135430i | ||||
\(320\) | −0.227452 | + | 0.393958i | −0.0127150 | + | 0.0220229i | ||||
\(321\) | 15.6127 | 0.871415 | ||||||||
\(322\) | 19.9827 | − | 9.34707i | 1.11359 | − | 0.520892i | ||||
\(323\) | 3.88325 | 0.216070 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 2.18038 | + | 3.77654i | 0.120946 | + | 0.209484i | ||||
\(326\) | 5.80634 | + | 10.0569i | 0.321583 | + | 0.556999i | ||||
\(327\) | −7.02051 | + | 12.1599i | −0.388235 | + | 0.672443i | ||||
\(328\) | −1.79306 | −0.0990053 | ||||||||
\(329\) | −0.733492 | − | 0.512295i | −0.0404387 | − | 0.0282438i | ||||
\(330\) | 0.454904 | 0.0250416 | ||||||||
\(331\) | 14.4827 | − | 25.0847i | 0.796039 | − | 1.37878i | −0.126139 | − | 0.992013i | \(-0.540258\pi\) |
0.922177 | − | 0.386767i | \(-0.126408\pi\) | |||||||
\(332\) | −0.986723 | − | 1.70905i | −0.0541535 | − | 0.0937965i | ||||
\(333\) | −3.94163 | − | 6.82710i | −0.216000 | − | 0.374123i | ||||
\(334\) | 2.42835 | − | 4.20603i | 0.132873 | − | 0.230143i | ||||
\(335\) | −1.72548 | −0.0942730 | ||||||||
\(336\) | −0.227452 | + | 2.63596i | −0.0124085 | + | 0.143803i | ||||
\(337\) | −9.03708 | −0.492281 | −0.246141 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246141 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(338\) | 6.08612 | − | 10.5415i | 0.331042 | − | 0.573381i | ||||
\(339\) | −3.79306 | − | 6.56978i | −0.206011 | − | 0.356821i | ||||
\(340\) | −0.227452 | − | 0.393958i | −0.0123353 | − | 0.0213654i | ||||
\(341\) | 4.79306 | − | 8.30183i | 0.259559 | − | 0.449569i | ||||
\(342\) | 3.88325 | 0.209982 | ||||||||
\(343\) | 4.72942 | − | 17.9062i | 0.255365 | − | 0.966845i | ||||
\(344\) | 7.88325 | 0.425037 | ||||||||
\(345\) | −1.89653 | + | 3.28489i | −0.102106 | + | 0.176852i | ||||
\(346\) | 12.7931 | + | 22.1582i | 0.687759 | + | 1.19123i | ||||
\(347\) | 10.8063 | + | 18.7171i | 0.580115 | + | 1.00479i | 0.995465 | + | 0.0951267i | \(0.0303256\pi\) |
−0.415350 | + | 0.909661i | \(0.636341\pi\) | |||||||
\(348\) | 1.39653 | − | 2.41886i | 0.0748619 | − | 0.129665i | ||||
\(349\) | 14.2745 | 0.764098 | 0.382049 | − | 0.924142i | \(-0.375219\pi\) | ||||
0.382049 | + | 0.924142i | \(0.375219\pi\) | |||||||
\(350\) | 1.09019 | − | 12.6343i | 0.0582732 | − | 0.675332i | ||||
\(351\) | 0.909808 | 0.0485620 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 14.2480 | + | 24.6782i | 0.758343 | + | 1.31349i | 0.943695 | + | 0.330816i | \(0.107324\pi\) |
−0.185353 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(354\) | −3.48672 | − | 6.03918i | −0.185317 | − | 0.320979i | ||||
\(355\) | 1.09019 | − | 1.88827i | 0.0578614 | − | 0.100219i | ||||
\(356\) | −11.0902 | −0.587779 | ||||||||
\(357\) | −2.16908 | − | 1.51496i | −0.114800 | − | 0.0801800i | ||||
\(358\) | −15.7029 | −0.829922 | ||||||||
\(359\) | 6.81962 | − | 11.8119i | 0.359926 | − | 0.623409i | −0.628022 | − | 0.778195i | \(-0.716135\pi\) |
0.987948 | + | 0.154786i | \(0.0494687\pi\) | |||||||
\(360\) | −0.227452 | − | 0.393958i | −0.0119878 | − | 0.0207634i | ||||
\(361\) | 1.96017 | + | 3.39511i | 0.103167 | + | 0.178690i | ||||
\(362\) | 1.24797 | − | 2.16154i | 0.0655917 | − | 0.113608i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 2.18038 | − | 1.01989i | 0.114283 | − | 0.0534570i | ||||
\(365\) | 4.85670 | 0.254211 | ||||||||
\(366\) | 7.02051 | − | 12.1599i | 0.366968 | − | 0.635608i | ||||
\(367\) | −11.3647 | − | 19.6843i | −0.593233 | − | 1.02751i | −0.993794 | − | 0.111240i | \(-0.964518\pi\) |
0.400560 | − | 0.916270i | \(-0.368815\pi\) | |||||||
\(368\) | −4.16908 | − | 7.22106i | −0.217328 | − | 0.376424i | ||||
\(369\) | 0.896531 | − | 1.55284i | 0.0466715 | − | 0.0808375i | ||||
\(370\) | 3.58612 | 0.186434 | ||||||||
\(371\) | 2.18038 | − | 1.01989i | 0.113200 | − | 0.0529503i | ||||
\(372\) | −9.58612 | −0.497017 | ||||||||
\(373\) | −5.20090 | + | 9.00822i | −0.269292 | + | 0.466428i | −0.968679 | − | 0.248315i | \(-0.920123\pi\) |
0.699387 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(374\) | −0.500000 | − | 0.866025i | −0.0258544 | − | 0.0447811i | ||||
\(375\) | 2.22745 | + | 3.85806i | 0.115025 | + | 0.199229i | ||||
\(376\) | −0.169079 | + | 0.292854i | −0.00871959 | + | 0.0151028i | ||||
\(377\) | −2.54115 | −0.130876 | ||||||||
\(378\) | −2.16908 | − | 1.51496i | −0.111565 | − | 0.0779210i | ||||
\(379\) | 7.61268 | 0.391037 | 0.195519 | − | 0.980700i | \(-0.437361\pi\) | ||||
0.195519 | + | 0.980700i | \(0.437361\pi\) | |||||||
\(380\) | −0.883254 | + | 1.52984i | −0.0453100 | + | 0.0784792i | ||||
\(381\) | −3.71417 | − | 6.43314i | −0.190283 | − | 0.329580i | ||||
\(382\) | −4.90981 | − | 8.50404i | −0.251208 | − | 0.435104i | ||||
\(383\) | 11.0728 | − | 19.1787i | 0.565796 | − | 0.979988i | −0.431179 | − | 0.902266i | \(-0.641902\pi\) |
0.996975 | − | 0.0777212i | \(-0.0247644\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.103469 | + | 1.19911i | −0.00527326 | + | 0.0611122i | ||||
\(386\) | 6.85670 | 0.348997 | ||||||||
\(387\) | −3.94163 | + | 6.82710i | −0.200364 | + | 0.347041i | ||||
\(388\) | −7.29306 | − | 12.6320i | −0.370249 | − | 0.641290i | ||||
\(389\) | 1.77255 | + | 3.07014i | 0.0898717 | + | 0.155662i | 0.907457 | − | 0.420145i | \(-0.138021\pi\) |
−0.817585 | + | 0.575808i | \(0.804688\pi\) | |||||||
\(390\) | −0.206938 | + | 0.358427i | −0.0104787 | + | 0.0181496i | ||||
\(391\) | 8.33816 | 0.421679 | ||||||||
\(392\) | −6.89653 | − | 1.19911i | −0.348327 | − | 0.0605641i | ||||
\(393\) | −19.4057 | −0.978890 | ||||||||
\(394\) | −11.7347 | + | 20.3251i | −0.591185 | + | 1.02396i | ||||
\(395\) | −1.22021 | − | 2.11347i | −0.0613957 | − | 0.106340i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 1.27979 | − | 2.21665i | 0.0642306 | − | 0.111251i | −0.832122 | − | 0.554593i | \(-0.812874\pi\) |
0.896352 | + | 0.443342i | \(0.146207\pi\) | |||||||
\(398\) | −2.23349 | −0.111955 | ||||||||
\(399\) | −0.883254 | + | 10.2361i | −0.0442180 | + | 0.512445i | ||||
\(400\) | −4.79306 | −0.239653 | ||||||||
\(401\) | −5.24797 | + | 9.08974i | −0.262071 | + | 0.453920i | −0.966792 | − | 0.255564i | \(-0.917739\pi\) |
0.704721 | + | 0.709484i | \(0.251072\pi\) | |||||||
\(402\) | 1.89653 | + | 3.28489i | 0.0945904 | + | 0.163835i | ||||
\(403\) | 4.36077 | + | 7.55307i | 0.217225 | + | 0.376245i | ||||
\(404\) | 4.03182 | − | 6.98332i | 0.200590 | − | 0.347433i | ||||
\(405\) | 0.454904 | 0.0226044 | ||||||||
\(406\) | 6.05837 | + | 4.23137i | 0.300672 | + | 0.209999i | ||||
\(407\) | 7.88325 | 0.390758 | ||||||||
\(408\) | −0.500000 | + | 0.866025i | −0.0247537 | + | 0.0428746i | ||||
\(409\) | −7.92428 | − | 13.7253i | −0.391831 | − | 0.678670i | 0.600860 | − | 0.799354i | \(-0.294825\pi\) |
−0.992691 | + | 0.120683i | \(0.961491\pi\) | |||||||
\(410\) | 0.407836 | + | 0.706392i | 0.0201416 | + | 0.0348862i | ||||
\(411\) | −0.454904 | + | 0.787917i | −0.0224388 | + | 0.0388651i | ||||
\(412\) | 5.76651 | 0.284095 | ||||||||
\(413\) | 16.7121 | − | 7.81723i | 0.822348 | − | 0.384661i | ||||
\(414\) | 8.33816 | 0.409798 | ||||||||
\(415\) | −0.448864 | + | 0.777456i | −0.0220339 | + | 0.0381638i | ||||
\(416\) | −0.454904 | − | 0.787917i | −0.0223035 | − | 0.0386308i | ||||
\(417\) | 4.18959 | + | 7.25659i | 0.205165 | + | 0.355357i | ||||
\(418\) | −1.94163 | + | 3.36300i | −0.0949681 | + | 0.164490i | ||||
\(419\) | −9.52249 | −0.465204 | −0.232602 | − | 0.972572i | \(-0.574724\pi\) | ||||
−0.232602 | + | 0.972572i | \(0.574724\pi\) | |||||||
\(420\) | 1.09019 | − | 0.509947i | 0.0531959 | − | 0.0248829i | ||||
\(421\) | −0.530621 | −0.0258609 | −0.0129305 | − | 0.999916i | \(-0.504116\pi\) | ||||
−0.0129305 | + | 0.999916i | \(0.504116\pi\) | |||||||
\(422\) | 9.13122 | − | 15.8157i | 0.444501 | − | 0.769898i | ||||
\(423\) | −0.169079 | − | 0.292854i | −0.00822091 | − | 0.0142390i | ||||
\(424\) | −0.454904 | − | 0.787917i | −0.0220921 | − | 0.0382646i | ||||
\(425\) | 2.39653 | − | 4.15091i | 0.116249 | − | 0.201349i | ||||
\(426\) | −4.79306 | −0.232225 | ||||||||
\(427\) | 30.4561 | + | 21.2716i | 1.47387 | + | 1.02940i | ||||
\(428\) | 15.6127 | 0.754667 | ||||||||
\(429\) | −0.454904 | + | 0.787917i | −0.0219630 | + | 0.0380410i | ||||
\(430\) | −1.79306 | − | 3.10567i | −0.0864691 | − | 0.149769i | ||||
\(431\) | −10.4018 | − | 18.0164i | −0.501037 | − | 0.867821i | −0.999999 | − | 0.00119770i | \(-0.999619\pi\) |
0.498962 | − | 0.866624i | \(-0.333715\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −4.40574 | −0.211726 | −0.105863 | − | 0.994381i | \(-0.533761\pi\) | ||||
−0.105863 | + | 0.994381i | \(0.533761\pi\) | |||||||
\(434\) | 2.18038 | − | 25.2686i | 0.104662 | − | 1.21293i | ||||
\(435\) | −1.27058 | −0.0609194 | ||||||||
\(436\) | −7.02051 | + | 12.1599i | −0.336222 | + | 0.582353i | ||||
\(437\) | −16.1896 | − | 28.0412i | −0.774453 | − | 1.34139i | ||||
\(438\) | −5.33816 | − | 9.24596i | −0.255067 | − | 0.441789i | ||||
\(439\) | 7.59743 | − | 13.1591i | 0.362606 | − | 0.628051i | −0.625783 | − | 0.779997i | \(-0.715221\pi\) |
0.988389 | + | 0.151946i | \(0.0485539\pi\) | |||||||
\(440\) | 0.454904 | 0.0216867 | ||||||||
\(441\) | 4.48672 | − | 5.37302i | 0.213653 | − | 0.255858i | ||||
\(442\) | 0.909808 | 0.0432752 | ||||||||
\(443\) | 5.69366 | − | 9.86171i | 0.270514 | − | 0.468544i | −0.698480 | − | 0.715630i | \(-0.746140\pi\) |
0.968994 | + | 0.247086i | \(0.0794730\pi\) | |||||||
\(444\) | −3.94163 | − | 6.82710i | −0.187061 | − | 0.324000i | ||||
\(445\) | 2.52249 | + | 4.36908i | 0.119577 | + | 0.207114i | ||||
\(446\) | −6.24797 | + | 10.8218i | −0.295850 | + | 0.512427i | ||||
\(447\) | 4.11675 | 0.194715 | ||||||||
\(448\) | −0.227452 | + | 2.63596i | −0.0107461 | + | 0.124537i | ||||
\(449\) | −24.0821 | −1.13650 | −0.568251 | − | 0.822855i | \(-0.692380\pi\) | ||||
−0.568251 | + | 0.822855i | \(0.692380\pi\) | |||||||
\(450\) | 2.39653 | − | 4.15091i | 0.112974 | − | 0.195676i | ||||
\(451\) | 0.896531 | + | 1.55284i | 0.0422160 | + | 0.0731203i | ||||
\(452\) | −3.79306 | − | 6.56978i | −0.178411 | − | 0.309016i | ||||
\(453\) | 3.07889 | − | 5.33279i | 0.144659 | − | 0.250556i | ||||
\(454\) | 9.79306 | 0.459611 | ||||||||
\(455\) | −0.897729 | − | 0.627004i | −0.0420862 | − | 0.0293944i | ||||
\(456\) | 3.88325 | 0.181850 | ||||||||
\(457\) | 14.7665 | − | 25.5763i | 0.690748 | − | 1.19641i | −0.280845 | − | 0.959753i | \(-0.590615\pi\) |
0.971593 | − | 0.236658i | \(-0.0760520\pi\) | |||||||
\(458\) | −4.33816 | − | 7.51391i | −0.202709 | − | 0.351102i | ||||
\(459\) | −0.500000 | − | 0.866025i | −0.0233380 | − | 0.0404226i | ||||
\(460\) | −1.89653 | + | 3.28489i | −0.0884262 | + | 0.153159i | ||||
\(461\) | 4.14569 | 0.193084 | 0.0965421 | − | 0.995329i | \(-0.469222\pi\) | ||||
0.0965421 | + | 0.995329i | \(0.469222\pi\) | |||||||
\(462\) | 2.39653 | − | 1.12100i | 0.111497 | − | 0.0521536i | ||||
\(463\) | −9.32368 | −0.433308 | −0.216654 | − | 0.976248i | \(-0.569514\pi\) | ||||
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(464\) | 1.39653 | − | 2.41886i | 0.0648323 | − | 0.112293i | ||||
\(465\) | 2.18038 | + | 3.77654i | 0.101113 | + | 0.175133i | ||||
\(466\) | −8.38325 | − | 14.5202i | −0.388347 | − | 0.672636i | ||||
\(467\) | −18.2798 | + | 31.6615i | −0.845888 | + | 1.46512i | 0.0389606 | + | 0.999241i | \(0.487595\pi\) |
−0.884848 | + | 0.465880i | \(0.845738\pi\) | |||||||
\(468\) | 0.909808 | 0.0420559 | ||||||||
\(469\) | −9.09019 | + | 4.25202i | −0.419746 | + | 0.196340i | ||||
\(470\) | 0.153830 | 0.00709563 | ||||||||
\(471\) | 8.82488 | − | 15.2851i | 0.406629 | − | 0.704302i | ||||
\(472\) | −3.48672 | − | 6.03918i | −0.160489 | − | 0.277976i | ||||
\(473\) | −3.94163 | − | 6.82710i | −0.181236 | − | 0.313910i | ||||
\(474\) | −2.68236 | + | 4.64598i | −0.123205 | + | 0.213397i | ||||
\(475\) | −18.6127 | −0.854008 | ||||||||
\(476\) | −2.16908 | − | 1.51496i | −0.0994196 | − | 0.0694380i | ||||
\(477\) | 0.909808 | 0.0416573 | ||||||||
\(478\) | 13.1312 | − | 22.7439i | 0.600608 | − | 1.04028i | ||||
\(479\) | −0.364712 | − | 0.631700i | −0.0166641 | − | 0.0288631i | 0.857573 | − | 0.514362i | \(-0.171971\pi\) |
−0.874237 | + | 0.485499i | \(0.838638\pi\) | |||||||
\(480\) | −0.227452 | − | 0.393958i | −0.0103817 | − | 0.0179817i | ||||
\(481\) | −3.58612 | + | 6.21135i | −0.163513 | + | 0.283213i | ||||
\(482\) | 7.94689 | 0.361971 | ||||||||
\(483\) | −1.89653 | + | 21.9790i | −0.0862952 | + | 1.00008i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −3.31764 | + | 5.74633i | −0.150646 | + | 0.260927i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 18.4283 | + | 31.9188i | 0.835068 | + | 1.44638i | 0.893975 | + | 0.448117i | \(0.147905\pi\) |
−0.0589066 | + | 0.998263i | \(0.518761\pi\) | |||||||
\(488\) | 7.02051 | − | 12.1599i | 0.317804 | − | 0.550452i | ||||
\(489\) | −11.6127 | −0.525143 | ||||||||
\(490\) | 1.09623 | + | 2.98969i | 0.0495227 | + | 0.135060i | ||||
\(491\) | 25.5065 | 1.15109 | 0.575545 | − | 0.817770i | \(-0.304790\pi\) | ||||
0.575545 | + | 0.817770i | \(0.304790\pi\) | |||||||
\(492\) | 0.896531 | − | 1.55284i | 0.0404187 | − | 0.0700073i | ||||
\(493\) | 1.39653 | + | 2.41886i | 0.0628966 | + | 0.108940i | ||||
\(494\) | −1.76651 | − | 3.05968i | −0.0794790 | − | 0.137662i | ||||
\(495\) | −0.227452 | + | 0.393958i | −0.0102232 | + | 0.0177071i | ||||
\(496\) | −9.58612 | −0.430430 | ||||||||
\(497\) | 1.09019 | − | 12.6343i | 0.0489018 | − | 0.566726i | ||||
\(498\) | 1.97345 | 0.0884322 | ||||||||
\(499\) | 2.06364 | − | 3.57433i | 0.0923811 | − | 0.160009i | −0.816131 | − | 0.577866i | \(-0.803886\pi\) |
0.908513 | + | 0.417857i | \(0.137219\pi\) | |||||||
\(500\) | 2.22745 | + | 3.85806i | 0.0996147 | + | 0.172538i | ||||
\(501\) | 2.42835 | + | 4.20603i | 0.108491 | + | 0.187911i | ||||
\(502\) | 1.96818 | − | 3.40899i | 0.0878442 | − | 0.152151i | ||||
\(503\) | −6.85670 | −0.305725 | −0.152863 | − | 0.988247i | \(-0.548849\pi\) | ||||
−0.152863 | + | 0.988247i | \(0.548849\pi\) | |||||||
\(504\) | −2.16908 | − | 1.51496i | −0.0966185 | − | 0.0674816i | ||||
\(505\) | −3.66818 | −0.163232 | ||||||||
\(506\) | −4.16908 | + | 7.22106i | −0.185338 | + | 0.321015i | ||||
\(507\) | 6.08612 | + | 10.5415i | 0.270294 | + | 0.468163i | ||||
\(508\) | −3.71417 | − | 6.43314i | −0.164790 | − | 0.285424i | ||||
\(509\) | −8.22141 | + | 14.2399i | −0.364408 | + | 0.631173i | −0.988681 | − | 0.150033i | \(-0.952062\pi\) |
0.624273 | + | 0.781206i | \(0.285395\pi\) | |||||||
\(510\) | 0.454904 | 0.0201435 | ||||||||
\(511\) | 25.5861 | − | 11.9681i | 1.13186 | − | 0.529439i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.94163 | + | 3.36300i | −0.0857249 | + | 0.148480i | ||||
\(514\) | 7.54510 | + | 13.0685i | 0.332800 | + | 0.576426i | ||||
\(515\) | −1.31160 | − | 2.27176i | −0.0577962 | − | 0.100106i | ||||
\(516\) | −3.94163 | + | 6.82710i | −0.173520 | + | 0.300546i | ||||
\(517\) | 0.338158 | 0.0148722 | ||||||||
\(518\) | 18.8925 | − | 8.83712i | 0.830087 | − | 0.388281i | ||||
\(519\) | −25.5861 | −1.12311 | ||||||||
\(520\) | −0.206938 | + | 0.358427i | −0.00907482 | + | 0.0157180i | ||||
\(521\) | 2.81962 | + | 4.88372i | 0.123530 | + | 0.213960i | 0.921157 | − | 0.389191i | \(-0.127245\pi\) |
−0.797628 | + | 0.603150i | \(0.793912\pi\) | |||||||
\(522\) | 1.39653 | + | 2.41886i | 0.0611245 | + | 0.105871i | ||||
\(523\) | 2.04103 | − | 3.53517i | 0.0892480 | − | 0.154582i | −0.817946 | − | 0.575296i | \(-0.804887\pi\) |
0.907193 | + | 0.420714i | \(0.138220\pi\) | |||||||
\(524\) | −19.4057 | −0.847744 | ||||||||
\(525\) | 10.3965 | + | 7.26129i | 0.453742 | + | 0.316908i | ||||
\(526\) | −28.6232 | −1.24803 | ||||||||
\(527\) | 4.79306 | − | 8.30183i | 0.208789 | − | 0.361633i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | −23.2624 | − | 40.2917i | −1.01141 | − | 1.75181i | ||||
\(530\) | −0.206938 | + | 0.358427i | −0.00898880 | + | 0.0155691i | ||||
\(531\) | 6.97345 | 0.302622 | ||||||||
\(532\) | −0.883254 | + | 10.2361i | −0.0382939 | + | 0.443791i | ||||
\(533\) | −1.63134 | −0.0706613 | ||||||||
\(534\) | 5.54510 | − | 9.60439i | 0.239960 | − | 0.415623i | ||||
\(535\) | −3.55114 | − | 6.15075i | −0.153529 | − | 0.265920i | ||||
\(536\) | 1.89653 | + | 3.28489i | 0.0819177 | + | 0.141886i | ||||
\(537\) | 7.85144 | − | 13.5991i | 0.338814 | − | 0.586844i | ||||
\(538\) | −22.9508 | −0.989481 | ||||||||
\(539\) | 2.40981 | + | 6.57212i | 0.103798 | + | 0.283081i | ||||
\(540\) | 0.454904 | 0.0195760 | ||||||||
\(541\) | 2.44886 | − | 4.24156i | 0.105285 | − | 0.182359i | −0.808570 | − | 0.588400i | \(-0.799758\pi\) |
0.913855 | + | 0.406042i | \(0.133091\pi\) | |||||||
\(542\) | −4.90981 | − | 8.50404i | −0.210894 | − | 0.365280i | ||||
\(543\) | 1.24797 | + | 2.16154i | 0.0535554 | + | 0.0927606i | ||||
\(544\) | −0.500000 | + | 0.866025i | −0.0214373 | + | 0.0371305i | ||||
\(545\) | 6.38732 | 0.273603 | ||||||||
\(546\) | −0.206938 | + | 2.39821i | −0.00885612 | + | 0.102634i | ||||
\(547\) | 21.4694 | 0.917964 | 0.458982 | − | 0.888445i | \(-0.348214\pi\) | ||||
0.458982 | + | 0.888445i | \(0.348214\pi\) | |||||||
\(548\) | −0.454904 | + | 0.787917i | −0.0194325 | + | 0.0336581i | ||||
\(549\) | 7.02051 | + | 12.1599i | 0.299628 | + | 0.518971i | ||||
\(550\) | 2.39653 | + | 4.15091i | 0.102188 | + | 0.176996i | ||||
\(551\) | 5.42309 | − | 9.39306i | 0.231031 | − | 0.400158i | ||||
\(552\) | 8.33816 | 0.354896 | ||||||||
\(553\) | −11.6365 | − | 8.12731i | −0.494834 | − | 0.345608i | ||||
\(554\) | 10.7294 | 0.455850 | ||||||||
\(555\) | −1.79306 | + | 3.10567i | −0.0761113 | + | 0.131829i | ||||
\(556\) | 4.18959 | + | 7.25659i | 0.177678 | + | 0.307748i | ||||
\(557\) | 19.7347 | + | 34.1815i | 0.836186 | + | 1.44832i | 0.893061 | + | 0.449935i | \(0.148553\pi\) |
−0.0568758 | + | 0.998381i | \(0.518114\pi\) | |||||||
\(558\) | 4.79306 | − | 8.30183i | 0.202907 | − | 0.351444i | ||||
\(559\) | 7.17225 | 0.303354 | ||||||||
\(560\) | 1.09019 | − | 0.509947i | 0.0460690 | − | 0.0215492i | ||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −1.29306 | + | 2.23965i | −0.0545445 | + | 0.0944739i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | −0.169079 | − | 0.292854i | −0.00711951 | − | 0.0123314i | ||||
\(565\) | −1.72548 | + | 2.98862i | −0.0725915 | + | 0.125732i | ||||
\(566\) | −20.0821 | −0.844112 | ||||||||
\(567\) | 2.39653 | − | 1.12100i | 0.100645 | − | 0.0470775i | ||||
\(568\) | −4.79306 | −0.201112 | ||||||||
\(569\) | −17.0994 | + | 29.6170i | −0.716844 | + | 1.24161i | 0.245400 | + | 0.969422i | \(0.421081\pi\) |
−0.962244 | + | 0.272189i | \(0.912253\pi\) | |||||||
\(570\) | −0.883254 | − | 1.52984i | −0.0369954 | − | 0.0640780i | ||||
\(571\) | −7.39653 | − | 12.8112i | −0.309535 | − | 0.536131i | 0.668726 | − | 0.743509i | \(-0.266840\pi\) |
−0.978261 | + | 0.207379i | \(0.933507\pi\) | |||||||
\(572\) | −0.454904 | + | 0.787917i | −0.0190205 | + | 0.0329445i | ||||
\(573\) | 9.81962 | 0.410220 | ||||||||
\(574\) | 3.88929 | + | 2.71641i | 0.162336 | + | 0.113381i | ||||
\(575\) | −39.9653 | −1.66667 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 3.59940 | + | 6.23435i | 0.149845 | + | 0.259539i | 0.931170 | − | 0.364585i | \(-0.118789\pi\) |
−0.781325 | + | 0.624124i | \(0.785456\pi\) | |||||||
\(578\) | 8.00000 | + | 13.8564i | 0.332756 | + | 0.576351i | ||||
\(579\) | −3.42835 | + | 5.93808i | −0.142477 | + | 0.246778i | ||||
\(580\) | −1.27058 | −0.0527578 | ||||||||
\(581\) | −0.448864 | + | 5.20192i | −0.0186220 | + | 0.215812i | ||||
\(582\) | 14.5861 | 0.604614 | ||||||||
\(583\) | −0.454904 | + | 0.787917i | −0.0188402 | + | 0.0326322i | ||||
\(584\) | −5.33816 | − | 9.24596i | −0.220895 | − | 0.382601i | ||||
\(585\) | −0.206938 | − | 0.358427i | −0.00855582 | − | 0.0148191i | ||||
\(586\) | −5.18959 | + | 8.98864i | −0.214380 | + | 0.371317i | ||||
\(587\) | −44.4959 | −1.83654 | −0.918272 | − | 0.395951i | \(-0.870415\pi\) | ||||
−0.918272 | + | 0.395951i | \(0.870415\pi\) | |||||||
\(588\) | 4.48672 | − | 5.37302i | 0.185029 | − | 0.221580i | ||||
\(589\) | −37.2254 | −1.53384 | ||||||||
\(590\) | −1.58612 | + | 2.74725i | −0.0652997 | + | 0.113102i | ||||
\(591\) | −11.7347 | − | 20.3251i | −0.482701 | − | 0.836062i | ||||
\(592\) | −3.94163 | − | 6.82710i | −0.162000 | − | 0.280592i | ||||
\(593\) | −8.98266 | + | 15.5584i | −0.368873 | + | 0.638908i | −0.989390 | − | 0.145286i | \(-0.953590\pi\) |
0.620516 | + | 0.784194i | \(0.286923\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −0.103469 | + | 1.19911i | −0.00424181 | + | 0.0491586i | ||||
\(596\) | 4.11675 | 0.168628 | ||||||||
\(597\) | 1.11675 | − | 1.93426i | 0.0457054 | − | 0.0791640i | ||||
\(598\) | −3.79306 | − | 6.56978i | −0.155110 | − | 0.268658i | ||||
\(599\) | 12.9038 | + | 22.3500i | 0.527234 | + | 0.913196i | 0.999496 | + | 0.0317376i | \(0.0101041\pi\) |
−0.472263 | + | 0.881458i | \(0.656563\pi\) | |||||||
\(600\) | 2.39653 | − | 4.15091i | 0.0978380 | − | 0.169460i | ||||
\(601\) | 10.4139 | 0.424791 | 0.212395 | − | 0.977184i | \(-0.431874\pi\) | ||||
0.212395 | + | 0.977184i | \(0.431874\pi\) | |||||||
\(602\) | −17.0994 | − | 11.9428i | −0.696920 | − | 0.486752i | ||||
\(603\) | −3.79306 | −0.154465 | ||||||||
\(604\) | 3.07889 | − | 5.33279i | 0.125278 | − | 0.216988i | ||||
\(605\) | −0.227452 | − | 0.393958i | −0.00924724 | − | 0.0160167i | ||||
\(606\) | 4.03182 | + | 6.98332i | 0.163781 | + | 0.283678i | ||||
\(607\) | 4.44886 | − | 7.70566i | 0.180574 | − | 0.312763i | −0.761502 | − | 0.648162i | \(-0.775538\pi\) |
0.942076 | + | 0.335399i | \(0.108871\pi\) | |||||||
\(608\) | 3.88325 | 0.157487 | ||||||||
\(609\) | −6.69366 | + | 3.13102i | −0.271241 | + | 0.126875i | ||||
\(610\) | −6.38732 | −0.258615 | ||||||||
\(611\) | −0.153830 | + | 0.266441i | −0.00622328 | + | 0.0107790i | ||||
\(612\) | −0.500000 | − | 0.866025i | −0.0202113 | − | 0.0350070i | ||||
\(613\) | 11.8136 | + | 20.4617i | 0.477146 | + | 0.826441i | 0.999657 | − | 0.0261916i | \(-0.00833800\pi\) |
−0.522511 | + | 0.852632i | \(0.675005\pi\) | |||||||
\(614\) | −4.88325 | + | 8.45804i | −0.197072 | + | 0.341339i | ||||
\(615\) | −0.815671 | −0.0328910 | ||||||||
\(616\) | 2.39653 | − | 1.12100i | 0.0965590 | − | 0.0451663i | ||||
\(617\) | −35.8486 | −1.44321 | −0.721604 | − | 0.692306i | \(-0.756595\pi\) | ||||
−0.721604 | + | 0.692306i | \(0.756595\pi\) | |||||||
\(618\) | −2.88325 | + | 4.99394i | −0.115981 | + | 0.200886i | ||||
\(619\) | −13.9602 | − | 24.1797i | −0.561107 | − | 0.971865i | −0.997400 | − | 0.0720607i | \(-0.977042\pi\) |
0.436294 | − | 0.899804i | \(-0.356291\pi\) | |||||||
\(620\) | 2.18038 | + | 3.77654i | 0.0875663 | + | 0.151669i | ||||
\(621\) | −4.16908 | + | 7.22106i | −0.167299 | + | 0.289771i | ||||
\(622\) | −6.51854 | −0.261370 | ||||||||
\(623\) | 24.0555 | + | 16.8012i | 0.963763 | + | 0.673125i | ||||
\(624\) | 0.909808 | 0.0364215 | ||||||||
\(625\) | −10.9694 | + | 18.9995i | −0.438775 | + | 0.759981i | ||||
\(626\) | −15.3965 | − | 26.6676i | −0.615369 | − | 1.06585i | ||||
\(627\) | −1.94163 | − | 3.36300i | −0.0775411 | − | 0.134305i | ||||
\(628\) | 8.82488 | − | 15.2851i | 0.352151 | − | 0.609944i | ||||
\(629\) | 7.88325 | 0.314326 | ||||||||
\(630\) | −0.103469 | + | 1.19911i | −0.00412230 | + | 0.0477736i | ||||
\(631\) | 43.6682 | 1.73840 | 0.869201 | − | 0.494458i | \(-0.164633\pi\) | ||||
0.869201 | + | 0.494458i | \(0.164633\pi\) | |||||||
\(632\) | −2.68236 | + | 4.64598i | −0.106698 | + | 0.184807i | ||||
\(633\) | 9.13122 | + | 15.8157i | 0.362933 | + | 0.628619i | ||||
\(634\) | 13.8136 | + | 23.9258i | 0.548607 | + | 0.950216i | ||||
\(635\) | −1.68959 | + | 2.92646i | −0.0670495 | + | 0.116133i | ||||
\(636\) | 0.909808 | 0.0360762 | ||||||||
\(637\) | −6.27452 | − | 1.09096i | −0.248606 | − | 0.0432253i | ||||
\(638\) | −2.79306 | −0.110578 | ||||||||
\(639\) | 2.39653 | − | 4.15091i | 0.0948053 | − | 0.164208i | ||||
\(640\) | −0.227452 | − | 0.393958i | −0.00899083 | − | 0.0155726i | ||||
\(641\) | 9.88325 | + | 17.1183i | 0.390365 | + | 0.676132i | 0.992498 | − | 0.122264i | \(-0.0390155\pi\) |
−0.602133 | + | 0.798396i | \(0.705682\pi\) | |||||||
\(642\) | −7.80634 | + | 13.5210i | −0.308092 | + | 0.533630i | ||||
\(643\) | 24.7584 | 0.976375 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(644\) | −1.89653 | + | 21.9790i | −0.0747338 | + | 0.866095i | ||||
\(645\) | 3.58612 | 0.141204 | ||||||||
\(646\) | −1.94163 | + | 3.36300i | −0.0763923 | + | 0.132315i | ||||
\(647\) | −15.5391 | − | 26.9144i | −0.610903 | − | 1.05812i | −0.991088 | − | 0.133205i | \(-0.957473\pi\) |
0.380185 | − | 0.924910i | \(-0.375860\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −3.48672 | + | 6.03918i | −0.136866 | + | 0.237059i | ||||
\(650\) | −4.36077 | −0.171043 | ||||||||
\(651\) | 20.7931 | + | 14.5226i | 0.814944 | + | 0.569184i | ||||
\(652\) | −11.6127 | −0.454788 | ||||||||
\(653\) | −11.3587 | + | 19.6738i | −0.444499 | + | 0.769895i | −0.998017 | − | 0.0629420i | \(-0.979952\pi\) |
0.553518 | + | 0.832837i | \(0.313285\pi\) | |||||||
\(654\) | −7.02051 | − | 12.1599i | −0.274524 | − | 0.475489i | ||||
\(655\) | 4.41388 | + | 7.64506i | 0.172464 | + | 0.298717i | ||||
\(656\) | 0.896531 | − | 1.55284i | 0.0350037 | − | 0.0606281i | ||||
\(657\) | 10.6763 | 0.416523 | ||||||||
\(658\) | 0.810407 | − | 0.379075i | 0.0315929 | − | 0.0147779i | ||||
\(659\) | 43.6127 | 1.69891 | 0.849454 | − | 0.527662i | \(-0.176931\pi\) | ||||
0.849454 | + | 0.527662i | \(0.176931\pi\) | |||||||
\(660\) | −0.227452 | + | 0.393958i | −0.00885356 | + | 0.0153348i | ||||
\(661\) | 3.96818 | + | 6.87309i | 0.154344 | + | 0.267332i | 0.932820 | − | 0.360342i | \(-0.117340\pi\) |
−0.778476 | + | 0.627675i | \(0.784007\pi\) | |||||||
\(662\) | 14.4827 | + | 25.0847i | 0.562884 | + | 0.974944i | ||||
\(663\) | −0.454904 | + | 0.787917i | −0.0176670 | + | 0.0306002i | ||||
\(664\) | 1.97345 | 0.0765846 | ||||||||
\(665\) | 4.23349 | − | 1.98025i | 0.164168 | − | 0.0767909i | ||||
\(666\) | 7.88325 | 0.305470 | ||||||||
\(667\) | 11.6445 | − | 20.1689i | 0.450877 | − | 0.780941i | ||||
\(668\) | 2.42835 | + | 4.20603i | 0.0939557 | + | 0.162736i | ||||
\(669\) | −6.24797 | − | 10.8218i | −0.241560 | − | 0.418395i | ||||
\(670\) | 0.862740 | − | 1.49431i | 0.0333305 | − | 0.0577302i | ||||
\(671\) | −14.0410 | −0.542048 | ||||||||
\(672\) | −2.16908 | − | 1.51496i | −0.0836740 | − | 0.0584408i | ||||
\(673\) | 36.9388 | 1.42388 | 0.711942 | − | 0.702238i | \(-0.247816\pi\) | ||||
0.711942 | + | 0.702238i | \(0.247816\pi\) | |||||||
\(674\) | 4.51854 | − | 7.82634i | 0.174048 | − | 0.301460i | ||||
\(675\) | 2.39653 | + | 4.15091i | 0.0922425 | + | 0.159769i | ||||
\(676\) | 6.08612 | + | 10.5415i | 0.234082 | + | 0.405441i | ||||
\(677\) | 19.8249 | − | 34.3377i | 0.761932 | − | 1.31971i | −0.179921 | − | 0.983681i | \(-0.557584\pi\) |
0.941853 | − | 0.336024i | \(-0.109082\pi\) | |||||||
\(678\) | 7.58612 | 0.291343 | ||||||||
\(679\) | −3.31764 | + | 38.4484i | −0.127319 | + | 1.47551i | ||||
\(680\) | 0.454904 | 0.0174448 | ||||||||
\(681\) | −4.89653 | + | 8.48104i | −0.187635 | + | 0.324994i | ||||
\(682\) | 4.79306 | + | 8.30183i | 0.183536 | + | 0.317893i | ||||
\(683\) | 22.7757 | + | 39.4487i | 0.871489 | + | 1.50946i | 0.860457 | + | 0.509523i | \(0.170178\pi\) |
0.0110318 | + | 0.999939i | \(0.496488\pi\) | |||||||
\(684\) | −1.94163 | + | 3.36300i | −0.0742400 | + | 0.128587i | ||||
\(685\) | 0.413875 | 0.0158134 | ||||||||
\(686\) | 13.1425 | + | 13.0489i | 0.501784 | + | 0.498210i | ||||
\(687\) | 8.67632 | 0.331022 | ||||||||
\(688\) | −3.94163 | + | 6.82710i | −0.150273 | + | 0.260281i | ||||
\(689\) | −0.413875 | − | 0.716853i | −0.0157674 | − | 0.0273099i | ||||
\(690\) | −1.89653 | − | 3.28489i | −0.0721997 | − | 0.125054i | ||||
\(691\) | 9.59940 | − | 16.6267i | 0.365178 | − | 0.632508i | −0.623626 | − | 0.781723i | \(-0.714341\pi\) |
0.988805 | + | 0.149215i | \(0.0476746\pi\) | |||||||
\(692\) | −25.5861 | −0.972639 | ||||||||
\(693\) | −0.227452 | + | 2.63596i | −0.00864019 | + | 0.100132i | ||||
\(694\) | −21.6127 | −0.820406 | ||||||||
\(695\) | 1.90586 | − | 3.30105i | 0.0722935 | − | 0.125216i | ||||
\(696\) | 1.39653 | + | 2.41886i | 0.0529354 | + | 0.0916868i | ||||
\(697\) | 0.896531 | + | 1.55284i | 0.0339585 | + | 0.0588179i | ||||
\(698\) | −7.13726 | + | 12.3621i | −0.270149 | + | 0.467912i | ||||
\(699\) | 16.7665 | 0.634168 | ||||||||
\(700\) | 10.3965 | + | 7.26129i | 0.392952 | + | 0.274451i | ||||
\(701\) | 23.2890 | 0.879613 | 0.439807 | − | 0.898093i | \(-0.355047\pi\) | ||||
0.439807 | + | 0.898093i | \(0.355047\pi\) | |||||||
\(702\) | −0.454904 | + | 0.787917i | −0.0171692 | + | 0.0297380i | ||||
\(703\) | −15.3063 | − | 26.5114i | −0.577290 | − | 0.999895i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | −0.0769148 | + | 0.133220i | −0.00289678 | + | 0.00501737i | ||||
\(706\) | −28.4959 | −1.07246 | ||||||||
\(707\) | −19.3248 | + | 9.03933i | −0.726782 | + | 0.339959i | ||||
\(708\) | 6.97345 | 0.262078 | ||||||||
\(709\) | 10.3965 | − | 18.0073i | 0.390450 | − | 0.676279i | −0.602059 | − | 0.798452i | \(-0.705653\pi\) |
0.992509 | + | 0.122173i | \(0.0389861\pi\) | |||||||
\(710\) | 1.09019 | + | 1.88827i | 0.0409142 | + | 0.0708654i | ||||
\(711\) | −2.68236 | − | 4.64598i | −0.100596 | − | 0.174238i | ||||
\(712\) | 5.54510 | − | 9.60439i | 0.207811 | − | 0.359940i | ||||
\(713\) | −79.9306 | −2.99343 | ||||||||
\(714\) | 2.39653 | − | 1.12100i | 0.0896879 | − | 0.0419523i | ||||
\(715\) | 0.413875 | 0.0154781 | ||||||||
\(716\) | 7.85144 | − | 13.5991i | 0.293422 | − | 0.508222i | ||||
\(717\) | 13.1312 | + | 22.7439i | 0.490394 | + | 0.849388i | ||||
\(718\) | 6.81962 | + | 11.8119i | 0.254506 | + | 0.440817i | ||||
\(719\) | 2.74073 | − | 4.74708i | 0.102212 | − | 0.177036i | −0.810384 | − | 0.585899i | \(-0.800741\pi\) |
0.912596 | + | 0.408863i | \(0.134075\pi\) | |||||||
\(720\) | 0.454904 | 0.0169533 | ||||||||
\(721\) | −12.5080 | − | 8.73601i | −0.465823 | − | 0.325346i | ||||
\(722\) | −3.92034 | −0.145900 | ||||||||
\(723\) | −3.97345 | + | 6.88221i | −0.147774 | + | 0.255952i | ||||
\(724\) | 1.24797 | + | 2.16154i | 0.0463803 | + | 0.0803330i | ||||
\(725\) | −6.69366 | − | 11.5938i | −0.248596 | − | 0.430581i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | 25.5330 | 0.946967 | 0.473484 | − | 0.880803i | \(-0.342996\pi\) | ||||
0.473484 | + | 0.880803i | \(0.342996\pi\) | |||||||
\(728\) | −0.206938 | + | 2.39821i | −0.00766962 | + | 0.0888837i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.42835 | + | 4.20603i | −0.0898773 | + | 0.155672i | ||||
\(731\) | −3.94163 | − | 6.82710i | −0.145786 | − | 0.252509i | ||||
\(732\) | 7.02051 | + | 12.1599i | 0.259486 | + | 0.449442i | ||||
\(733\) | −8.11071 | + | 14.0482i | −0.299576 | + | 0.518880i | −0.976039 | − | 0.217596i | \(-0.930178\pi\) |
0.676463 | + | 0.736476i | \(0.263512\pi\) | |||||||
\(734\) | 22.7294 | 0.838958 | ||||||||
\(735\) | −3.13726 | − | 0.545479i | −0.115720 | − | 0.0201203i | ||||
\(736\) | 8.33816 | 0.307349 | ||||||||
\(737\) | 1.89653 | − | 3.28489i | 0.0698596 | − | 0.121000i | ||||
\(738\) | 0.896531 | + | 1.55284i | 0.0330018 | + | 0.0571607i | ||||
\(739\) | −9.37919 | − | 16.2452i | −0.345019 | − | 0.597590i | 0.640338 | − | 0.768093i | \(-0.278794\pi\) |
−0.985357 | + | 0.170503i | \(0.945461\pi\) | |||||||
\(740\) | −1.79306 | + | 3.10567i | −0.0659143 | + | 0.114167i | ||||
\(741\) | 3.53302 | 0.129789 | ||||||||
\(742\) | −0.206938 | + | 2.39821i | −0.00759692 | + | 0.0880412i | ||||
\(743\) | −44.6763 | −1.63902 | −0.819508 | − | 0.573068i | \(-0.805753\pi\) | ||||
−0.819508 | + | 0.573068i | \(0.805753\pi\) | |||||||
\(744\) | 4.79306 | − | 8.30183i | 0.175722 | − | 0.304360i | ||||
\(745\) | −0.936362 | − | 1.62183i | −0.0343057 | − | 0.0594191i | ||||
\(746\) | −5.20090 | − | 9.00822i | −0.190418 | − | 0.329814i | ||||
\(747\) | −0.986723 | + | 1.70905i | −0.0361023 | + | 0.0625310i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −33.8651 | − | 23.6525i | −1.23741 | − | 0.864245i | ||||
\(750\) | −4.45490 | −0.162670 | ||||||||
\(751\) | 1.48146 | − | 2.56596i | 0.0540592 | − | 0.0936332i | −0.837729 | − | 0.546085i | \(-0.816117\pi\) |
0.891789 | + | 0.452452i | \(0.149451\pi\) | |||||||
\(752\) | −0.169079 | − | 0.292854i | −0.00616568 | − | 0.0106793i | ||||
\(753\) | 1.96818 | + | 3.40899i | 0.0717245 | + | 0.124230i | ||||
\(754\) | 1.27058 | − | 2.20070i | 0.0462716 | − | 0.0801448i | ||||
\(755\) | −2.80120 | −0.101946 | ||||||||
\(756\) | 2.39653 | − | 1.12100i | 0.0871610 | − | 0.0407703i | ||||
\(757\) | 26.1988 | 0.952212 | 0.476106 | − | 0.879388i | \(-0.342048\pi\) | ||||
0.476106 | + | 0.879388i | \(0.342048\pi\) | |||||||
\(758\) | −3.80634 | + | 6.59277i | −0.138252 | + | 0.239460i | ||||
\(759\) | −4.16908 | − | 7.22106i | −0.151328 | − | 0.262108i | ||||
\(760\) | −0.883254 | − | 1.52984i | −0.0320390 | − | 0.0554932i | ||||
\(761\) | −12.8965 | + | 22.3374i | −0.467499 | + | 0.809732i | −0.999310 | − | 0.0371309i | \(-0.988178\pi\) |
0.531812 | + | 0.846863i | \(0.321511\pi\) | |||||||
\(762\) | 7.42835 | 0.269101 | ||||||||
\(763\) | 33.6498 | − | 15.7400i | 1.21820 | − | 0.569825i | ||||
\(764\) | 9.81962 | 0.355261 | ||||||||
\(765\) | −0.227452 | + | 0.393958i | −0.00822355 | + | 0.0142436i | ||||
\(766\) | 11.0728 | + | 19.1787i | 0.400078 | + | 0.692956i | ||||
\(767\) | −3.17225 | − | 5.49450i | −0.114543 | − | 0.198395i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −37.2012 | −1.34151 | −0.670755 | − | 0.741679i | \(-0.734030\pi\) | ||||
−0.670755 | + | 0.741679i | \(0.734030\pi\) | |||||||
\(770\) | −0.986723 | − | 0.689160i | −0.0355590 | − | 0.0248356i | ||||
\(771\) | −15.0902 | −0.543460 | ||||||||
\(772\) | −3.42835 | + | 5.93808i | −0.123389 | + | 0.213716i | ||||
\(773\) | 20.3852 | + | 35.3082i | 0.733206 | + | 1.26995i | 0.955506 | + | 0.294971i | \(0.0953101\pi\) |
−0.222300 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(774\) | −3.94163 | − | 6.82710i | −0.141679 | − | 0.245395i | ||||
\(775\) | −22.9734 | + | 39.7912i | −0.825231 | + | 1.42934i | ||||
\(776\) | 14.5861 | 0.523611 | ||||||||
\(777\) | −1.79306 | + | 20.7799i | −0.0643258 | + | 0.745475i | ||||
\(778\) | −3.54510 | −0.127098 | ||||||||
\(779\) | 3.48146 | − | 6.03006i | 0.124736 | − | 0.216049i | ||||
\(780\) | −0.206938 | − | 0.358427i | −0.00740956 | − | 0.0128337i | ||||
\(781\) | 2.39653 | + | 4.15091i | 0.0857546 | + | 0.148531i | ||||
\(782\) | −4.16908 | + | 7.22106i | −0.149086 | + | 0.258224i | ||||
\(783\) | −2.79306 | −0.0998159 | ||||||||
\(784\) | 4.48672 | − | 5.37302i | 0.160240 | − | 0.191893i | ||||
\(785\) | −8.02895 | −0.286565 | ||||||||
\(786\) | 9.70287 | − | 16.8059i | 0.346090 | − | 0.599445i | ||||
\(787\) | −27.2943 | − | 47.2750i | −0.972935 | − | 1.68517i | −0.686587 | − | 0.727048i | \(-0.740892\pi\) |
−0.286348 | − | 0.958126i | \(-0.592441\pi\) | |||||||
\(788\) | −11.7347 | − | 20.3251i | −0.418031 | − | 0.724051i | ||||
\(789\) | 14.3116 | − | 24.7884i | 0.509507 | − | 0.882491i | ||||
\(790\) | 2.44043 | 0.0868266 | ||||||||
\(791\) | −1.72548 | + | 19.9967i | −0.0613510 | + | 0.711001i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 6.38732 | − | 11.0632i | 0.226820 | − | 0.392865i | ||||
\(794\) | 1.27979 | + | 2.21665i | 0.0454179 | + | 0.0786661i | ||||
\(795\) | −0.206938 | − | 0.358427i | −0.00733933 | − | 0.0127121i | ||||
\(796\) | 1.11675 | − | 1.93426i | 0.0395820 | − | 0.0685581i | ||||
\(797\) | −16.7705 | −0.594040 | −0.297020 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297020 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(798\) | −8.42309 | − | 5.88296i | −0.298174 | − | 0.208255i | ||||
\(799\) | 0.338158 | 0.0119632 | ||||||||
\(800\) | 2.39653 | − | 4.15091i | 0.0847302 | − | 0.146757i | ||||
\(801\) | 5.54510 | + | 9.60439i | 0.195926 | + | 0.339354i | ||||
\(802\) | −5.24797 | − | 9.08974i | −0.185312 | − | 0.320970i | ||||
\(803\) | −5.33816 | + | 9.24596i | −0.188380 | + | 0.326283i | ||||
\(804\) | −3.79306 | −0.133771 | ||||||||
\(805\) | 9.09019 | − | 4.25202i | 0.320387 | − | 0.149864i | ||||
\(806\) | −8.72153 | −0.307203 | ||||||||
\(807\) | 11.4754 | − | 19.8760i | 0.403954 | − | 0.699669i | ||||
\(808\) | 4.03182 | + | 6.98332i | 0.141839 | + | 0.245672i | ||||
\(809\) | 5.10347 | + | 8.83947i | 0.179428 | + | 0.310779i | 0.941685 | − | 0.336496i | \(-0.109242\pi\) |
−0.762257 | + | 0.647275i | \(0.775909\pi\) | |||||||
\(810\) | −0.227452 | + | 0.393958i | −0.00799185 | + | 0.0138423i | ||||
\(811\) | −28.4139 | −0.997746 | −0.498873 | − | 0.866675i | \(-0.666253\pi\) | ||||
−0.498873 | + | 0.866675i | \(0.666253\pi\) | |||||||
\(812\) | −6.69366 | + | 3.13102i | −0.234901 | + | 0.109877i | ||||
\(813\) | 9.81962 | 0.344389 | ||||||||
\(814\) | −3.94163 | + | 6.82710i | −0.138154 | + | 0.239290i | ||||
\(815\) | 2.64133 | + | 4.57491i | 0.0925217 | + | 0.160252i | ||||
\(816\) | −0.500000 | − | 0.866025i | −0.0175035 | − | 0.0303170i | ||||
\(817\) | −15.3063 | + | 26.5114i | −0.535501 | + | 0.927515i | ||||
\(818\) | 15.8486 | 0.554132 | ||||||||
\(819\) | −1.97345 | − | 1.37832i | −0.0689578 | − | 0.0481624i | ||||
\(820\) | −0.815671 | −0.0284845 | ||||||||
\(821\) | 1.70287 | − | 2.94946i | 0.0594306 | − | 0.102937i | −0.834779 | − | 0.550585i | \(-0.814405\pi\) |
0.894210 | + | 0.447648i | \(0.147738\pi\) | |||||||
\(822\) | −0.454904 | − | 0.787917i | −0.0158666 | − | 0.0274818i | ||||
\(823\) | 19.0145 | + | 32.9340i | 0.662803 | + | 1.14801i | 0.979876 | + | 0.199607i | \(0.0639666\pi\) |
−0.317073 | + | 0.948401i | \(0.602700\pi\) | |||||||
\(824\) | −2.88325 | + | 4.99394i | −0.100443 | + | 0.173972i | ||||
\(825\) | −4.79306 | −0.166873 | ||||||||
\(826\) | −1.58612 | + | 18.3817i | −0.0551883 | + | 0.639581i | ||||
\(827\) | −12.9653 | −0.450848 | −0.225424 | − | 0.974261i | \(-0.572377\pi\) | ||||
−0.225424 | + | 0.974261i | \(0.572377\pi\) | |||||||
\(828\) | −4.16908 | + | 7.22106i | −0.144886 | + | 0.250949i | ||||
\(829\) | −25.9416 | − | 44.9322i | −0.900990 | − | 1.56056i | −0.826211 | − | 0.563360i | \(-0.809508\pi\) |
−0.0747785 | − | 0.997200i | \(-0.523825\pi\) | |||||||
\(830\) | −0.448864 | − | 0.777456i | −0.0155803 | − | 0.0269859i | ||||
\(831\) | −5.36471 | + | 9.29195i | −0.186100 | + | 0.322334i | ||||
\(832\) | 0.909808 | 0.0315419 | ||||||||
\(833\) | 2.40981 | + | 6.57212i | 0.0834949 | + | 0.227711i | ||||
\(834\) | −8.37919 | −0.290148 | ||||||||
\(835\) | 1.10467 | − | 1.91334i | 0.0382286 | − | 0.0662138i | ||||
\(836\) | −1.94163 | − | 3.36300i | −0.0671526 | − | 0.116312i | ||||
\(837\) | 4.79306 | + | 8.30183i | 0.165672 | + | 0.286953i | ||||
\(838\) | 4.76124 | − | 8.24672i | 0.164474 | − | 0.284878i | ||||
\(839\) | −50.2504 | −1.73484 | −0.867418 | − | 0.497581i | \(-0.834222\pi\) | ||||
−0.867418 | + | 0.497581i | \(0.834222\pi\) | |||||||
\(840\) | −0.103469 | + | 1.19911i | −0.00357002 | + | 0.0413731i | ||||
\(841\) | −21.1988 | −0.730993 | ||||||||
\(842\) | 0.265311 | − | 0.459532i | 0.00914321 | − | 0.0158365i | ||||
\(843\) | −1.29306 | − | 2.23965i | −0.0445354 | − | 0.0771376i | ||||
\(844\) | 9.13122 | + | 15.8157i | 0.314310 | + | 0.544400i | ||||
\(845\) | 2.76860 | − | 4.79536i | 0.0952428 | − | 0.164965i | ||||
\(846\) | 0.338158 | 0.0116261 | ||||||||
\(847\) | −2.16908 | − | 1.51496i | −0.0745304 | − | 0.0520546i | ||||
\(848\) | 0.909808 | 0.0312429 | ||||||||
\(849\) | 10.0410 | − | 17.3916i | 0.344607 | − | 0.596877i | ||||
\(850\) | 2.39653 | + | 4.15091i | 0.0822003 | + | 0.142375i | ||||
\(851\) | −32.8659 | − | 56.9254i | −1.12663 | − | 1.95138i | ||||
\(852\) | 2.39653 | − | 4.15091i | 0.0821038 | − | 0.142208i | ||||
\(853\) | 13.3647 | 0.457599 | 0.228800 | − | 0.973474i | \(-0.426520\pi\) | ||||
0.228800 | + | 0.973474i | \(0.426520\pi\) | |||||||
\(854\) | −33.6498 | + | 15.7400i | −1.15147 | + | 0.538611i | ||||
\(855\) | 1.76651 | 0.0604133 | ||||||||
\(856\) | −7.80634 | + | 13.5210i | −0.266815 | + | 0.462137i | ||||
\(857\) | −13.1763 | − | 22.8220i | −0.450094 | − | 0.779586i | 0.548297 | − | 0.836284i | \(-0.315276\pi\) |
−0.998391 | + | 0.0566973i | \(0.981943\pi\) | |||||||
\(858\) | −0.454904 | − | 0.787917i | −0.0155302 | − | 0.0268990i | ||||
\(859\) | −0.986723 | + | 1.70905i | −0.0336666 | + | 0.0583122i | −0.882368 | − | 0.470560i | \(-0.844052\pi\) |
0.848701 | + | 0.528873i | \(0.177385\pi\) | |||||||
\(860\) | 3.58612 | 0.122286 | ||||||||
\(861\) | −4.29713 | + | 2.01002i | −0.146446 | + | 0.0685013i | ||||
\(862\) | 20.8036 | 0.708573 | ||||||||
\(863\) | 24.9038 | − | 43.1346i | 0.847734 | − | 1.46832i | −0.0354913 | − | 0.999370i | \(-0.511300\pi\) |
0.883225 | − | 0.468949i | \(-0.155367\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 5.81962 | + | 10.0799i | 0.197873 | + | 0.342726i | ||||
\(866\) | 2.20287 | − | 3.81548i | 0.0748566 | − | 0.129655i | ||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 20.7931 | + | 14.5226i | 0.705763 | + | 0.492928i | ||||
\(869\) | 5.36471 | 0.181985 | ||||||||
\(870\) | 0.635288 | − | 1.10035i | 0.0215383 | − | 0.0373054i | ||||
\(871\) | 1.72548 | + | 2.98862i | 0.0584656 | + | 0.101265i | ||||
\(872\) | −7.02051 | − | 12.1599i | −0.237745 | − | 0.411786i | ||||
\(873\) | −7.29306 | + | 12.6320i | −0.246833 | + | 0.427527i | ||||
\(874\) | 32.3792 | 1.09524 | ||||||||
\(875\) | 1.01328 | − | 11.7429i | 0.0342550 | − | 0.396984i | ||||
\(876\) | 10.6763 | 0.360719 | ||||||||
\(877\) | 12.2685 | − | 21.2496i | 0.414277 | − | 0.717549i | −0.581075 | − | 0.813850i | \(-0.697368\pi\) |
0.995352 | + | 0.0963008i | \(0.0307011\pi\) | |||||||
\(878\) | 7.59743 | + | 13.1591i | 0.256401 | + | 0.444099i | ||||
\(879\) | −5.18959 | − | 8.98864i | −0.175041 | − | 0.303179i | ||||
\(880\) | −0.227452 | + | 0.393958i | −0.00766741 | + | 0.0132803i | ||||
\(881\) | 11.5861 | 0.390346 | 0.195173 | − | 0.980769i | \(-0.437473\pi\) | ||||
0.195173 | + | 0.980769i | \(0.437473\pi\) | |||||||
\(882\) | 2.40981 | + | 6.57212i | 0.0811425 | + | 0.221295i | ||||
\(883\) | −44.1376 | −1.48535 | −0.742674 | − | 0.669654i | \(-0.766443\pi\) | ||||
−0.742674 | + | 0.669654i | \(0.766443\pi\) | |||||||
\(884\) | −0.454904 | + | 0.787917i | −0.0153001 | + | 0.0265005i | ||||
\(885\) | −1.58612 | − | 2.74725i | −0.0533170 | − | 0.0923477i | ||||
\(886\) | 5.69366 | + | 9.86171i | 0.191282 | + | 0.331311i | ||||
\(887\) | 10.0145 | − | 17.3456i | 0.336253 | − | 0.582408i | −0.647472 | − | 0.762090i | \(-0.724174\pi\) |
0.983725 | + | 0.179682i | \(0.0575069\pi\) | |||||||
\(888\) | 7.88325 | 0.264545 | ||||||||
\(889\) | −1.68959 | + | 19.5808i | −0.0566671 | + | 0.656719i | ||||
\(890\) | −5.04497 | −0.169108 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −6.24797 | − | 10.8218i | −0.209197 | − | 0.362341i | ||||
\(893\) | −0.656577 | − | 1.13722i | −0.0219715 | − | 0.0380558i | ||||
\(894\) | −2.05837 | + | 3.56521i | −0.0688423 | + | 0.119238i | ||||
\(895\) | −7.14330 | −0.238774 | ||||||||
\(896\) | −2.16908 | − | 1.51496i | −0.0724638 | − | 0.0506112i | ||||
\(897\) | 7.58612 | 0.253293 | ||||||||
\(898\) | 12.0410 | − | 20.8557i | 0.401814 | − | 0.695963i | ||||
\(899\) | −13.3873 | − | 23.1875i | −0.446492 | − | 0.773347i | ||||
\(900\) | 2.39653 | + | 4.15091i | 0.0798844 | + | 0.138364i | ||||
\(901\) | −0.454904 | + | 0.787917i | −0.0151551 | + | 0.0262493i | ||||
\(902\) | −1.79306 | −0.0597024 | ||||||||
\(903\) | 18.8925 | − | 8.83712i | 0.628702 | − | 0.294081i | ||||
\(904\) | 7.58612 | 0.252311 | ||||||||
\(905\) | 0.567705 | − | 0.983294i | 0.0188712 | − | 0.0326858i | ||||
\(906\) | 3.07889 | + | 5.33279i | 0.102289 | + | 0.177170i | ||||
\(907\) | 8.96017 | + | 15.5195i | 0.297518 | + | 0.515315i | 0.975567 | − | 0.219700i | \(-0.0705080\pi\) |
−0.678050 | + | 0.735016i | \(0.737175\pi\) | |||||||
\(908\) | −4.89653 | + | 8.48104i | −0.162497 | + | 0.281453i | ||||
\(909\) | −8.06364 | −0.267454 | ||||||||
\(910\) | 0.991865 | − | 0.463954i | 0.0328800 | − | 0.0153799i | ||||
\(911\) | 13.9695 | 0.462830 | 0.231415 | − | 0.972855i | \(-0.425664\pi\) | ||||
0.231415 | + | 0.972855i | \(0.425664\pi\) | |||||||
\(912\) | −1.94163 | + | 3.36300i | −0.0642937 | + | 0.111360i | ||||
\(913\) | −0.986723 | − | 1.70905i | −0.0326558 | − | 0.0565614i | ||||
\(914\) | 14.7665 | + | 25.5763i | 0.488433 | + | 0.845990i | ||||
\(915\) | 3.19366 | − | 5.53158i | 0.105579 | − | 0.182868i | ||||
\(916\) | 8.67632 | 0.286674 | ||||||||
\(917\) | 42.0926 | + | 29.3989i | 1.39002 | + | 0.970836i | ||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 21.4807 | − | 37.2056i | 0.708582 | − | 1.22730i | −0.256801 | − | 0.966464i | \(-0.582668\pi\) |
0.965383 | − | 0.260836i | \(-0.0839983\pi\) | |||||||
\(920\) | −1.89653 | − | 3.28489i | −0.0625268 | − | 0.108300i | ||||
\(921\) | −4.88325 | − | 8.45804i | −0.160909 | − | 0.278702i | ||||
\(922\) | −2.07285 | + | 3.59028i | −0.0682656 | + | 0.118239i | ||||
\(923\) | −4.36077 | −0.143536 | ||||||||
\(924\) | −0.227452 | + | 2.63596i | −0.00748262 | + | 0.0867166i | ||||
\(925\) | −37.7849 | −1.24236 | ||||||||
\(926\) | 4.66184 | − | 8.07455i | 0.153198 | − | 0.265346i | ||||
\(927\) | −2.88325 | − | 4.99394i | −0.0946985 | − | 0.164023i | ||||
\(928\) | 1.39653 | + | 2.41886i | 0.0458434 | + | 0.0794031i | ||||
\(929\) | 12.8341 | − | 22.2293i | 0.421073 | − | 0.729320i | −0.574972 | − | 0.818173i | \(-0.694987\pi\) |
0.996045 | + | 0.0888536i | \(0.0283203\pi\) | |||||||
\(930\) | −4.36077 | −0.142995 | ||||||||
\(931\) | 17.4231 | − | 20.8648i | 0.571019 | − | 0.683816i | ||||
\(932\) | 16.7665 | 0.549205 | ||||||||
\(933\) | 3.25927 | − | 5.64522i | 0.106704 | − | 0.184816i | ||||
\(934\) | −18.2798 | − | 31.6615i | −0.598133 | − | 1.03600i | ||||
\(935\) | −0.227452 | − | 0.393958i | −0.00743848 | − | 0.0128838i | ||||
\(936\) | −0.454904 | + | 0.787917i | −0.0148690 | + | 0.0257539i | ||||
\(937\) | 26.7584 | 0.874158 | 0.437079 | − | 0.899423i | \(-0.356013\pi\) | ||||
0.437079 | + | 0.899423i | \(0.356013\pi\) | |||||||
\(938\) | 0.862740 | − | 9.99835i | 0.0281695 | − | 0.326458i | ||||
\(939\) | 30.7931 | 1.00489 | ||||||||
\(940\) | −0.0769148 | + | 0.133220i | −0.00250868 | + | 0.00434517i | ||||
\(941\) | 7.81041 | + | 13.5280i | 0.254612 | + | 0.441001i | 0.964790 | − | 0.263021i | \(-0.0847189\pi\) |
−0.710178 | + | 0.704022i | \(0.751386\pi\) | |||||||
\(942\) | 8.82488 | + | 15.2851i | 0.287530 | + | 0.498017i | ||||
\(943\) | 7.47542 | − | 12.9478i | 0.243433 | − | 0.421639i | ||||
\(944\) | 6.97345 | 0.226966 | ||||||||
\(945\) | −0.986723 | − | 0.689160i | −0.0320981 | − | 0.0224184i | ||||
\(946\) | 7.88325 | 0.256307 | ||||||||
\(947\) | −9.89246 | + | 17.1343i | −0.321462 | + | 0.556788i | −0.980790 | − | 0.195067i | \(-0.937508\pi\) |
0.659328 | + | 0.751855i | \(0.270841\pi\) | |||||||
\(948\) | −2.68236 | − | 4.64598i | −0.0871189 | − | 0.150894i | ||||
\(949\) | −4.85670 | − | 8.41205i | −0.157655 | − | 0.273067i | ||||
\(950\) | 9.30634 | − | 16.1191i | 0.301938 | − | 0.522971i | ||||
\(951\) | −27.6272 | −0.895872 | ||||||||
\(952\) | 2.39653 | − | 1.12100i | 0.0776720 | − | 0.0363318i | ||||
\(953\) | 43.5065 | 1.40931 | 0.704656 | − | 0.709549i | \(-0.251101\pi\) | ||||
0.704656 | + | 0.709549i | \(0.251101\pi\) | |||||||
\(954\) | −0.454904 | + | 0.787917i | −0.0147281 | + | 0.0255098i | ||||
\(955\) | −2.23349 | − | 3.86852i | −0.0722741 | − | 0.125182i | ||||
\(956\) | 13.1312 | + | 22.7439i | 0.424694 | + | 0.735592i | ||||
\(957\) | 1.39653 | − | 2.41886i | 0.0451434 | − | 0.0781907i | ||||
\(958\) | 0.729425 | 0.0235666 | ||||||||
\(959\) | 2.18038 | − | 1.01989i | 0.0704083 | − | 0.0329341i | ||||
\(960\) | 0.454904 | 0.0146820 | ||||||||
\(961\) | −30.4469 | + | 52.7356i | −0.982158 | + | 1.70115i | ||||
\(962\) | −3.58612 | − | 6.21135i | −0.115621 | − | 0.200262i | ||||
\(963\) | −7.80634 | − | 13.5210i | −0.251556 | − | 0.435707i | ||||
\(964\) | −3.97345 | + | 6.88221i | −0.127976 | + | 0.221661i | ||||
\(965\) | 3.11914 | 0.100409 | ||||||||
\(966\) | −18.0861 | − | 12.6320i | −0.581912 | − | 0.406426i | ||||
\(967\) | 34.5185 | 1.11004 | 0.555021 | − | 0.831837i | \(-0.312710\pi\) | ||||
0.555021 | + | 0.831837i | \(0.312710\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | −1.94163 | − | 3.36300i | −0.0623740 | − | 0.108035i | ||||
\(970\) | −3.31764 | − | 5.74633i | −0.106523 | − | 0.184503i | ||||
\(971\) | 22.4694 | − | 38.9181i | 0.721077 | − | 1.24894i | −0.239492 | − | 0.970898i | \(-0.576981\pi\) |
0.960569 | − | 0.278043i | \(-0.0896858\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.90586 | − | 22.0872i | 0.0610992 | − | 0.708082i | ||||
\(974\) | −36.8567 | −1.18096 | ||||||||
\(975\) | 2.18038 | − | 3.77654i | 0.0698282 | − | 0.120946i | ||||
\(976\) | 7.02051 | + | 12.1599i | 0.224721 | + | 0.389229i | ||||
\(977\) | −16.2624 | − | 28.1674i | −0.520282 | − | 0.901154i | −0.999722 | − | 0.0235797i | \(-0.992494\pi\) |
0.479440 | − | 0.877574i | \(-0.340840\pi\) | |||||||
\(978\) | 5.80634 | − | 10.0569i | 0.185666 | − | 0.321583i | ||||
\(979\) | −11.0902 | −0.354444 | ||||||||
\(980\) | −3.13726 | − | 0.545479i | −0.100216 | − | 0.0174247i | ||||
\(981\) | 14.0410 | 0.448296 | ||||||||
\(982\) | −12.7532 | + | 22.0892i | −0.406972 | + | 0.704896i | ||||
\(983\) | 23.5974 | + | 40.8719i | 0.752641 | + | 1.30361i | 0.946539 | + | 0.322591i | \(0.104554\pi\) |
−0.193897 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(984\) | 0.896531 | + | 1.55284i | 0.0285804 | + | 0.0495027i | ||||
\(985\) | −5.33816 | + | 9.24596i | −0.170088 | + | 0.294601i | ||||
\(986\) | −2.79306 | −0.0889492 | ||||||||
\(987\) | −0.0769148 | + | 0.891370i | −0.00244822 | + | 0.0283726i | ||||
\(988\) | 3.53302 | 0.112400 | ||||||||
\(989\) | −32.8659 | + | 56.9254i | −1.04508 | + | 1.81012i | ||||
\(990\) | −0.227452 | − | 0.393958i | −0.00722890 | − | 0.0125208i | ||||
\(991\) | −6.27452 | − | 10.8678i | −0.199317 | − | 0.345227i | 0.748990 | − | 0.662581i | \(-0.230539\pi\) |
−0.948307 | + | 0.317354i | \(0.897206\pi\) | |||||||
\(992\) | 4.79306 | − | 8.30183i | 0.152180 | − | 0.263583i | ||||
\(993\) | −28.9653 | −0.919186 | ||||||||
\(994\) | 10.3965 | + | 7.26129i | 0.329758 | + | 0.230314i | ||||
\(995\) | −1.01602 | −0.0322101 | ||||||||
\(996\) | −0.986723 | + | 1.70905i | −0.0312655 | + | 0.0541535i | ||||
\(997\) | −20.4549 | − | 35.4289i | −0.647813 | − | 1.12205i | −0.983644 | − | 0.180123i | \(-0.942350\pi\) |
0.335831 | − | 0.941922i | \(-0.390983\pi\) | |||||||
\(998\) | 2.06364 | + | 3.57433i | 0.0653233 | + | 0.113143i | ||||
\(999\) | −3.94163 | + | 6.82710i | −0.124708 | + | 0.216000i |
(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 | 462.2.i.f.331.2 | yes | 6 | |
3.2 | odd | 2 | 1386.2.k.w.793.2 | 6 | |||
7.2 | even | 3 | 3234.2.a.bi.1.2 | 3 | |||
7.4 | even | 3 | inner | 462.2.i.f.67.2 | ✓ | 6 | |
7.5 | odd | 6 | 3234.2.a.bg.1.2 | 3 | |||
21.2 | odd | 6 | 9702.2.a.dt.1.2 | 3 | |||
21.5 | even | 6 | 9702.2.a.du.1.2 | 3 | |||
21.11 | odd | 6 | 1386.2.k.w.991.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.2 | ✓ | 6 | 7.4 | even | 3 | inner | |
462.2.i.f.331.2 | yes | 6 | 1.1 | even | 1 | trivial | |
1386.2.k.w.793.2 | 6 | 3.2 | odd | 2 | |||
1386.2.k.w.991.2 | 6 | 21.11 | odd | 6 | |||
3234.2.a.bg.1.2 | 3 | 7.5 | odd | 6 | |||
3234.2.a.bi.1.2 | 3 | 7.2 | even | 3 | |||
9702.2.a.dt.1.2 | 3 | 21.2 | odd | 6 | |||
9702.2.a.du.1.2 | 3 | 21.5 | even | 6 |