Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.41342275584.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.901794 - 1.56195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.q.577.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.207107 | + | 0.358719i | −0.119573 | + | 0.207107i | −0.919599 | − | 0.392859i | \(-0.871486\pi\) |
0.800025 | + | 0.599966i | \(0.204819\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60890 | + | 2.78670i | −0.719522 | + | 1.24625i | 0.241667 | + | 0.970359i | \(0.422306\pi\) |
−0.961189 | + | 0.275890i | \(0.911027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.13644 | 1.18546 | 0.592732 | − | 0.805399i | \(-0.298049\pi\) | ||||
0.592732 | + | 0.805399i | \(0.298049\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.21780 | 0.668692 | 0.334346 | − | 0.942450i | \(-0.391485\pi\) | ||||
0.334346 | + | 0.942450i | \(0.391485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37354 | − | 2.37903i | −0.380950 | − | 0.659825i | 0.610248 | − | 0.792210i | \(-0.291070\pi\) |
−0.991198 | + | 0.132385i | \(0.957736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.666429 | − | 1.15429i | −0.172071 | − | 0.298036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.59134 | − | 6.22038i | 0.871027 | − | 1.50866i | 0.0100916 | − | 0.999949i | \(-0.496788\pi\) |
0.860935 | − | 0.508714i | \(-0.169879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.32670 | − | 0.528817i | 0.992614 | − | 0.121319i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.649579 | + | 1.12510i | −0.141750 | + | 0.245518i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.29844 | + | 7.44512i | 0.896287 | + | 1.55242i | 0.832203 | + | 0.554471i | \(0.187079\pi\) |
0.0640843 | + | 0.997944i | \(0.479587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.67712 | − | 4.63691i | −0.535425 | − | 0.927383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.33113 | + | 5.76969i | 0.618576 | + | 1.07140i | 0.989746 | + | 0.142840i | \(0.0456233\pi\) |
−0.371170 | + | 0.928565i | \(0.621043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.7933 | −1.93853 | −0.969267 | − | 0.246012i | \(-0.920880\pi\) | ||||
−0.969267 | + | 0.246012i | \(0.920880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.459322 | + | 0.795569i | −0.0799576 | + | 0.138491i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.04623 | + | 8.74032i | −0.852968 | + | 1.47738i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.308018 | 0.0506378 | 0.0253189 | − | 0.999679i | \(-0.491940\pi\) | ||||
0.0253189 | + | 0.999679i | \(0.491940\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.13787 | 0.182206 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.30359 | − | 3.98993i | 0.359760 | − | 0.623123i | −0.628161 | − | 0.778084i | \(-0.716192\pi\) |
0.987921 | + | 0.154961i | \(0.0495252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.31601 | + | 7.47554i | −0.658185 | + | 1.14001i | 0.322900 | + | 0.946433i | \(0.395342\pi\) |
−0.981085 | + | 0.193577i | \(0.937991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.10132 | −1.35674 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.47002 | + | 4.27819i | 0.360289 | + | 0.624039i | 0.988008 | − | 0.154401i | \(-0.0493448\pi\) |
−0.627719 | + | 0.778440i | \(0.716011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.83729 | 0.405327 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.48758 | + | 2.57656i | 0.208303 | + | 0.360791i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00555 | − | 6.93782i | −0.550205 | − | 0.952982i | −0.998259 | − | 0.0589763i | \(-0.981216\pi\) |
0.448055 | − | 0.894006i | \(-0.352117\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.56822 | + | 6.18034i | −0.481139 | + | 0.833357i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.706392 | + | 1.66159i | −0.0935639 | + | 0.220083i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.01069 | − | 1.75057i | 0.131581 | − | 0.227905i | −0.792705 | − | 0.609605i | \(-0.791328\pi\) |
0.924286 | + | 0.381700i | \(0.124661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.780474 | − | 1.35182i | −0.0999294 | − | 0.173083i | 0.811726 | − | 0.584039i | \(-0.198528\pi\) |
−0.911655 | + | 0.410956i | \(0.865195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.43560 | + | 7.68269i | 0.558833 | + | 0.967928i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.83953 | 1.09641 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.81428 | + | 6.60653i | 0.465989 | + | 0.807116i | 0.999246 | − | 0.0388372i | \(-0.0123654\pi\) |
−0.533257 | + | 0.845953i | \(0.679032\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.56095 | −0.428688 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.84183 | − | 8.38629i | 0.574619 | − | 0.995270i | −0.421464 | − | 0.906845i | \(-0.638484\pi\) |
0.996083 | − | 0.0884243i | \(-0.0281831\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.85425 | + | 8.40780i | −0.568147 | + | 0.984059i | 0.428603 | + | 0.903493i | \(0.359006\pi\) |
−0.996749 | + | 0.0805657i | \(0.974327\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.21780 | 0.256090 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.95601 | 0.792711 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.98315 | + | 5.16697i | −0.335631 | + | 0.581329i | −0.983606 | − | 0.180332i | \(-0.942283\pi\) |
0.647975 | + | 0.761662i | \(0.275616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.49069 | 0.712446 | 0.356223 | − | 0.934401i | \(-0.384064\pi\) | ||||
0.356223 | + | 0.934401i | \(0.384064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5562 | + | 20.0159i | 1.25345 | + | 2.17103i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.75960 | −0.295860 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.762910 | + | 1.32140i | 0.0808683 | + | 0.140068i | 0.903623 | − | 0.428328i | \(-0.140897\pi\) |
−0.822755 | + | 0.568396i | \(0.807564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.30802 | − | 7.46171i | −0.451603 | − | 0.782199i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.23537 | − | 3.87177i | 0.231797 | − | 0.401483i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.48758 | + | 12.9080i | −0.563014 | + | 1.32434i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.69296 | + | 4.66435i | −0.273429 | + | 0.473593i | −0.969738 | − | 0.244150i | \(-0.921491\pi\) |
0.696309 | + | 0.717742i | \(0.254824\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.13644 | + | 5.43248i | 0.315225 | + | 0.545985i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24092 | − | 7.34548i | −0.421987 | − | 0.730903i | 0.574147 | − | 0.818752i | \(-0.305334\pi\) |
−0.996134 | + | 0.0878496i | \(0.972001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0925 | 0.994439 | 0.497220 | − | 0.867625i | \(-0.334354\pi\) | ||||
0.497220 | + | 0.867625i | \(0.334354\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.09022 | − | 3.62036i | −0.203984 | − | 0.353311i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5983 | 1.41127 | 0.705636 | − | 0.708574i | \(-0.250661\pi\) | ||||
0.705636 | + | 0.708574i | \(0.250661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.15228 | − | 5.45992i | 0.301934 | − | 0.522965i | −0.674640 | − | 0.738147i | \(-0.735701\pi\) |
0.976574 | + | 0.215182i | \(0.0690344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0637926 | + | 0.110492i | −0.00605492 | + | 0.0104874i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1124 | −1.89202 | −0.946009 | − | 0.324142i | \(-0.894925\pi\) | ||||
−0.946009 | + | 0.324142i | \(0.894925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.6631 | −2.57960 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.88494 | − | 6.72892i | 0.359163 | − | 0.622089i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.2640 | − | 19.5099i | 1.03257 | − | 1.78847i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.08136 | −0.552851 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.954177 | + | 1.65268i | 0.0860353 | + | 0.149017i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.13989 | 0.101955 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.961761 | − | 1.66582i | −0.0853425 | − | 0.147818i | 0.820195 | − | 0.572085i | \(-0.193865\pi\) |
−0.905537 | + | 0.424267i | \(0.860532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.78775 | − | 3.09647i | −0.157403 | − | 0.272629i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.656448 | − | 1.13700i | 0.0573542 | − | 0.0993403i | −0.835923 | − | 0.548847i | \(-0.815067\pi\) |
0.893277 | + | 0.449507i | \(0.148400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5705 | − | 1.65861i | 1.17671 | − | 0.143819i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.88423 | − | 6.72768i | 0.334301 | − | 0.579027i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.393804 | + | 0.682089i | 0.0336450 | + | 0.0582748i | 0.882358 | − | 0.470580i | \(-0.155955\pi\) |
−0.848713 | + | 0.528854i | \(0.822622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.22850 | − | 2.12782i | −0.104200 | − | 0.180479i | 0.809211 | − | 0.587518i | \(-0.199895\pi\) |
−0.913411 | + | 0.407039i | \(0.866561\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.04623 | −0.172324 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.04623 | − | 5.27622i | −0.254738 | − | 0.441220i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.4378 | −1.78032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.587621 | + | 1.01779i | −0.0484662 | + | 0.0839459i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.77018 | − | 8.26220i | 0.390789 | − | 0.676866i | −0.601765 | − | 0.798673i | \(-0.705536\pi\) |
0.992554 | + | 0.121807i | \(0.0388690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8449 | −1.12669 | −0.563343 | − | 0.826223i | \(-0.690485\pi\) | ||||
−0.563343 | + | 0.826223i | \(0.690485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.3157 | 1.64242 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.3653 | − | 30.0777i | 1.39482 | − | 2.41590i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.61273 | − | 4.52537i | 0.208518 | − | 0.361164i | −0.742730 | − | 0.669591i | \(-0.766469\pi\) |
0.951248 | + | 0.308427i | \(0.0998026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.31831 | 0.263159 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.4818 | + | 23.3512i | 1.06252 | + | 1.84033i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.60177 | −0.752068 | −0.376034 | − | 0.926606i | \(-0.622712\pi\) | ||||
−0.376034 | + | 0.926606i | \(0.622712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.47801 | − | 2.55998i | −0.115063 | − | 0.199294i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.95147 | + | 8.57620i | 0.383156 | + | 0.663646i | 0.991512 | − | 0.130019i | \(-0.0415037\pi\) |
−0.608355 | + | 0.793665i | \(0.708170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.72680 | − | 4.72296i | 0.209754 | − | 0.363305i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.41421 | + | 9.85035i | 0.566979 | + | 0.753275i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00555 | + | 3.47372i | −0.152479 | + | 0.264102i | −0.932138 | − | 0.362103i | \(-0.882059\pi\) |
0.779659 | + | 0.626204i | \(0.215392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.39665 | − | 14.5434i | −0.634727 | − | 1.09938i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.418643 | + | 0.725112i | 0.0314672 | + | 0.0545027i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.33970 | −0.249621 | −0.124810 | − | 0.992181i | \(-0.539832\pi\) | ||||
−0.124810 | + | 0.992181i | \(0.539832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.32084 | − | 16.1442i | −0.692813 | − | 1.19999i | −0.970912 | − | 0.239435i | \(-0.923038\pi\) |
0.278100 | − | 0.960552i | \(-0.410295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.646566 | 0.0477955 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.495570 | + | 0.858353i | −0.0364350 | + | 0.0631073i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.96487 | − | 13.7956i | 0.582449 | − | 1.00883i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.57205 | −0.550785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.95932 | − | 12.0539i | 0.500943 | − | 0.867659i | −0.499056 | − | 0.866569i | \(-0.666320\pi\) |
0.999999 | − | 0.00108916i | \(-0.000346689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.83073 | + | 3.17091i | −0.131101 | + | 0.227074i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.03513 | −0.144997 | −0.0724984 | − | 0.997369i | \(-0.523097\pi\) | ||||
−0.0724984 | + | 0.997369i | \(0.523097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.34085 | + | 7.51857i | 0.307714 | + | 0.532977i | 0.977862 | − | 0.209251i | \(-0.0671025\pi\) |
−0.670148 | + | 0.742228i | \(0.733769\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.15986 | −0.222879 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4479 | + | 18.0963i | 0.733300 | + | 1.27011i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.41249 | + | 12.8388i | 0.517711 | + | 0.896701i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.1578 | + | 21.0580i | −0.845028 | + | 1.46363i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.59577 | − | 1.17281i | 0.663753 | − | 0.0811251i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.47729 | − | 2.55874i | 0.101701 | − | 0.176151i | −0.810685 | − | 0.585483i | \(-0.800905\pi\) |
0.912386 | + | 0.409332i | \(0.134238\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00555 | + | 3.47372i | 0.137418 | + | 0.238015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.8881 | − | 24.0548i | −0.947158 | − | 1.64052i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.8526 | −2.29806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.01069 | − | 3.48263i | −0.135870 | − | 0.235334i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.7313 | −1.32727 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.252215 | + | 0.436849i | −0.0168896 | + | 0.0292536i | −0.874347 | − | 0.485302i | \(-0.838710\pi\) |
0.857457 | + | 0.514555i | \(0.172043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.57205 | − | 13.1152i | 0.504803 | − | 0.874345i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.6933 | −1.77170 | −0.885849 | − | 0.463973i | \(-0.846423\pi\) | ||||
−0.885849 | + | 0.463973i | \(0.846423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.3157 | 1.34250 | 0.671249 | − | 0.741232i | \(-0.265758\pi\) | ||||
0.671249 | + | 0.741232i | \(0.265758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.44064 | + | 2.49526i | −0.0947870 | + | 0.164176i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.65783 | − | 6.33555i | 0.239633 | − | 0.415056i | −0.720976 | − | 0.692960i | \(-0.756306\pi\) |
0.960609 | + | 0.277904i | \(0.0896397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8960 | −1.03694 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.23566 | − | 2.14023i | −0.0802648 | − | 0.139023i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.29151 | 0.471648 | 0.235824 | − | 0.971796i | \(-0.424221\pi\) | ||||
0.235824 | + | 0.971796i | \(0.424221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.99557 | + | 3.45643i | 0.128546 | + | 0.222648i | 0.923113 | − | 0.384528i | \(-0.125636\pi\) |
−0.794567 | + | 0.607176i | \(0.792302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.17157 | − | 8.95743i | −0.331757 | − | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.56491 | + | 7.90666i | −0.291642 | + | 0.505138i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.20095 | − | 9.56702i | −0.458186 | − | 0.608735i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.34427 | + | 2.32834i | −0.0851894 | + | 0.147552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.120340 | + | 0.208435i | 0.00759581 | + | 0.0131563i | 0.869798 | − | 0.493407i | \(-0.164249\pi\) |
−0.862203 | + | 0.506564i | \(0.830915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.53309 | + | 16.5118i | 0.599341 | + | 1.03809i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.57348 | −0.599514 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.68267 | + | 8.11063i | 0.292097 | + | 0.505927i | 0.974305 | − | 0.225231i | \(-0.0723136\pi\) |
−0.682208 | + | 0.731158i | \(0.738980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.966081 | 0.0600293 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.42186 | + | 16.3191i | −0.583199 | + | 1.01013i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.74434 | − | 8.21743i | 0.292548 | − | 0.506708i | −0.681863 | − | 0.731480i | \(-0.738830\pi\) |
0.974412 | + | 0.224771i | \(0.0721635\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.7781 | 1.58354 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.632015 | −0.0386787 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4749 | − | 23.3391i | 0.821576 | − | 1.42301i | −0.0829318 | − | 0.996555i | \(-0.526428\pi\) |
0.904508 | − | 0.426457i | \(-0.140238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.05925 | − | 5.29878i | 0.185836 | − | 0.321878i | −0.758022 | − | 0.652229i | \(-0.773834\pi\) |
0.943858 | + | 0.330351i | \(0.107167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.56888 | 0.215998 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.93733 | − | 10.2838i | −0.358034 | − | 0.620134i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.06905 | 0.544906 | 0.272453 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272453 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.2640 | − | 26.4381i | −0.913834 | − | 1.58281i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.29675 | + | 14.3704i | 0.494943 | + | 0.857266i | 0.999983 | − | 0.00583003i | \(-0.00185577\pi\) |
−0.505040 | + | 0.863096i | \(0.668522\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.78403 | − | 15.2144i | 0.522157 | − | 0.904402i | −0.477511 | − | 0.878626i | \(-0.658461\pi\) |
0.999668 | − | 0.0257761i | \(-0.00820568\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.49385 | − | 4.64184i | −0.206958 | − | 0.274959i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.22508 | − | 12.5142i | 0.426483 | − | 0.738690i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.2954 | − | 29.9565i | −1.01738 | − | 1.76215i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.11546 | − | 1.93204i | −0.0653895 | − | 0.113258i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0573 | −1.40544 | −0.702722 | − | 0.711464i | \(-0.748032\pi\) | ||||
−0.702722 | + | 0.711464i | \(0.748032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.25221 | + | 5.63300i | 0.189351 | + | 0.327966i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.35425 | −0.310685 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.8081 | − | 20.4523i | 0.682882 | − | 1.18279i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.5369 | + | 23.4466i | −0.780255 | + | 1.35144i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.51329 | 0.201833 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.02282 | 0.287606 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.88047 | + | 17.1135i | −0.563908 | + | 0.976718i | 0.433242 | + | 0.901278i | \(0.357370\pi\) |
−0.997150 | + | 0.0754402i | \(0.975964\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.09022 | + | 3.62036i | −0.118908 | + | 0.205955i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2358 | 0.977353 | 0.488676 | − | 0.872465i | \(-0.337480\pi\) | ||||
0.488676 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.96044 | − | 8.59174i | −0.280381 | − | 0.485634i | 0.691098 | − | 0.722761i | \(-0.257127\pi\) |
−0.971479 | + | 0.237128i | \(0.923794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.5458 | −1.60837 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.33496 | + | 16.1686i | 0.524303 | + | 0.908120i | 0.999600 | + | 0.0282944i | \(0.00900758\pi\) |
−0.475296 | + | 0.879826i | \(0.657659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.38779 | + | 12.7960i | 0.413637 | + | 0.716440i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.02341 | + | 5.23670i | −0.168750 | + | 0.292284i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2492 | − | 28.8129i | 0.681564 | − | 1.60319i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.35425 | + | 12.7379i | −0.407940 | + | 0.706573i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.30572 | + | 2.26157i | 0.0722064 | + | 0.125065i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.74707 | + | 13.4183i | 0.427110 | + | 0.739776i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.7341 | 1.30455 | 0.652273 | − | 0.757984i | \(-0.273815\pi\) | ||||
0.652273 | + | 0.757984i | \(0.273815\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.435603 | + | 0.754486i | 0.0238709 | + | 0.0413456i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.5472 | −1.34116 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.82400 | − | 15.2836i | 0.480674 | − | 0.832551i | −0.519080 | − | 0.854725i | \(-0.673725\pi\) |
0.999754 | + | 0.0221741i | \(0.00705880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.16542 | − | 7.21472i | 0.226234 | − | 0.391850i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.9374 | −1.29628 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0561 | −0.704964 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.72921 | − | 9.92328i | 0.308450 | − | 0.534252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.02443 | + | 1.77437i | −0.0549945 | + | 0.0952532i | −0.892212 | − | 0.451617i | \(-0.850847\pi\) |
0.837218 | + | 0.546870i | \(0.184181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.00975744 | −0.000522304 | −0.000261152 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000261152 | 1.00000i | \(0.500083\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.31601 | + | 5.74349i | 0.176995 | + | 0.306565i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.47418 | 0.291361 | 0.145681 | − | 0.989332i | \(-0.453463\pi\) | ||||
0.145681 | + | 0.989332i | \(0.453463\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5800 | + | 26.9854i | 0.826903 | + | 1.43224i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.66571 | + | 8.08125i | 0.246936 | + | 0.427705i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.92701 | − | 8.53383i | 0.260038 | − | 0.450398i | −0.706214 | − | 0.707998i | \(-0.749598\pi\) |
0.966252 | + | 0.257600i | \(0.0829317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4407 | − | 4.57607i | 0.970563 | − | 0.240846i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.25949 | − | 2.18150i | 0.0661061 | − | 0.114499i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6200 | − | 27.0546i | −0.817588 | − | 1.41610i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4046 | − | 23.2175i | −0.699716 | − | 1.21194i | −0.968565 | − | 0.248762i | \(-0.919976\pi\) |
0.268848 | − | 0.963183i | \(-0.413357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0311 | 0.678370 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.5632 | − | 21.7601i | −0.652248 | − | 1.12973i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1510 | −1.19871 | −0.599357 | − | 0.800482i | \(-0.704577\pi\) | ||||
−0.599357 | + | 0.800482i | \(0.704577\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.236080 | + | 0.408902i | −0.0121911 | + | 0.0211156i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.15086 | − | 15.8497i | 0.471293 | − | 0.816303i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6968 | 1.11449 | 0.557244 | − | 0.830349i | \(-0.311859\pi\) | ||||
0.557244 | + | 0.830349i | \(0.311859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.796749 | 0.0408187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.62785 | − | 14.9439i | 0.440863 | − | 0.763596i | −0.556891 | − | 0.830586i | \(-0.688006\pi\) |
0.997754 | + | 0.0669891i | \(0.0213393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.1915 | + | 19.3843i | −0.570373 | + | 0.987916i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.4150 | −1.24109 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.90423 | + | 3.29823i | 0.0965485 | + | 0.167227i | 0.910254 | − | 0.414051i | \(-0.135886\pi\) |
−0.813705 | + | 0.581278i | \(0.802553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.7486 | 3.12276 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.271910 | + | 0.470962i | 0.0137160 | + | 0.0237569i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.59919 | − | 16.6263i | −0.482987 | − | 0.836559i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6517 | − | 18.4493i | 0.534592 | − | 0.925941i | −0.464590 | − | 0.885526i | \(-0.653798\pi\) |
0.999183 | − | 0.0404157i | \(-0.0128682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.21556 | + | 5.21150i | −0.110917 | + | 0.260901i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4277 | − | 19.7934i | 0.570673 | − | 0.988435i | −0.425824 | − | 0.904806i | \(-0.640016\pi\) |
0.996497 | − | 0.0836289i | \(-0.0266510\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.8250 | + | 25.6776i | 0.738485 | + | 1.27909i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.0431 | − | 20.8592i | −0.598425 | − | 1.03650i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.683122 | 0.0338611 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.919092 | − | 1.59191i | −0.0454462 | − | 0.0787151i | 0.842408 | − | 0.538841i | \(-0.181138\pi\) |
−0.887854 | + | 0.460126i | \(0.847804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.326238 | −0.0160921 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.16999 | − | 5.49058i | 0.155985 | − | 0.270174i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4429 | + | 18.0876i | −0.512621 | + | 0.887885i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.01772 | 0.0498379 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4053 | 1.58310 | 0.791550 | − | 0.611104i | \(-0.209274\pi\) | ||||
0.791550 | + | 0.611104i | \(0.209274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.47246 | − | 16.4068i | 0.461659 | − | 0.799617i | −0.537385 | − | 0.843337i | \(-0.680588\pi\) |
0.999044 | + | 0.0437200i | \(0.0139210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.98626 | + | 12.1006i | −0.339684 | + | 0.588349i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38.4578 | −1.86548 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.44791 | − | 4.23991i | −0.118463 | − | 0.205184i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.52358 | 0.121840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.13333 | − | 10.6232i | −0.295432 | − | 0.511704i | 0.679653 | − | 0.733534i | \(-0.262130\pi\) |
−0.975085 | + | 0.221830i | \(0.928797\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.43005 | + | 9.40513i | 0.260952 | + | 0.451982i | 0.966495 | − | 0.256685i | \(-0.0826303\pi\) |
−0.705543 | + | 0.708667i | \(0.749297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.43992 | − | 7.69017i | 0.212878 | − | 0.368716i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.5352 | + | 29.9397i | 1.07800 | + | 1.43221i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.734047 | + | 1.27141i | −0.0350341 | + | 0.0606809i | −0.883011 | − | 0.469353i | \(-0.844487\pi\) |
0.847977 | + | 0.530034i | \(0.177821\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.01253 | + | 6.94991i | 0.191073 | + | 0.330948i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0004 | + | 27.7135i | 0.760202 | + | 1.31671i | 0.942746 | + | 0.333511i | \(0.108233\pi\) |
−0.182544 | + | 0.983198i | \(0.558433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.90978 | −0.232746 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.97588 | + | 3.42232i | 0.0934557 | + | 0.161870i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4556 | −1.81483 | −0.907415 | − | 0.420235i | \(-0.861947\pi\) | ||||
−0.907415 | + | 0.420235i | \(0.861947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.10890 | − | 8.84888i | 0.240569 | − | 0.416677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.86738 | − | 4.96645i | 0.134721 | − | 0.233344i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.7247 | 1.29975 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2948 | −1.08969 | −0.544843 | − | 0.838538i | \(-0.683411\pi\) | ||||
−0.544843 | + | 0.838538i | \(0.683411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.67025 | + | 15.0173i | −0.404693 | + | 0.700948i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5879 | + | 25.2670i | −0.679426 | + | 1.17680i | 0.295728 | + | 0.955272i | \(0.404438\pi\) |
−0.975154 | + | 0.221528i | \(0.928896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.28461 | 0.0597008 | 0.0298504 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298504 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.19296 | + | 12.4586i | 0.333566 | + | 0.577753i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3289 | −0.524238 | −0.262119 | − | 0.965036i | \(-0.584421\pi\) | ||||
−0.262119 | + | 0.965036i | \(0.584421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.9633 | + | 20.7210i | 0.552413 | + | 0.956808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.08223 | + | 1.87447i | 0.0498664 | + | 0.0863711i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.57205 | + | 16.5793i | −0.440123 | + | 0.762316i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0352 | − | 18.6468i | −0.643979 | − | 0.855575i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3294 | − | 19.6231i | 0.518738 | − | 0.898480i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.97827 | − | 12.0867i | −0.318845 | − | 0.552256i | 0.661402 | − | 0.750032i | \(-0.269962\pi\) |
−0.980247 | + | 0.197775i | \(0.936628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.423073 | − | 0.732785i | −0.0192905 | − | 0.0334121i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.1687 | −0.508194 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.66542 | − | 15.0089i | −0.393476 | − | 0.681521i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1139 | −0.820819 | −0.410410 | − | 0.911901i | \(-0.634614\pi\) | ||||
−0.410410 | + | 0.911901i | \(0.634614\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.98859 | − | 3.44434i | 0.0899272 | − | 0.155758i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9928 | + | 32.8965i | −0.857134 | + | 1.48460i | 0.0175169 | + | 0.999847i | \(0.494424\pi\) |
−0.874651 | + | 0.484753i | \(0.838909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.8529 | 2.15518 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.1849 | −0.907244 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.1861 | − | 26.3031i | 0.681191 | − | 1.17986i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8728 | + | 24.0284i | −0.621033 | + | 1.07566i | 0.368261 | + | 0.929722i | \(0.379953\pi\) |
−0.989294 | + | 0.145938i | \(0.953380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.10193 | −0.183261 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.7092 | − | 20.2809i | −0.522088 | − | 0.904283i | −0.999670 | − | 0.0256954i | \(-0.991820\pi\) |
0.477582 | − | 0.878587i | \(-0.341513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.2929 | 1.21452 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.12948 | + | 1.95631i | 0.0501619 | + | 0.0868829i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.8588 | + | 32.6644i | 0.835902 | + | 1.44783i | 0.893294 | + | 0.449474i | \(0.148388\pi\) |
−0.0573913 | + | 0.998352i | \(0.518278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.2251 | + | 26.3706i | −0.673518 | + | 1.16657i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.4456 | + | 1.27668i | −0.461184 | + | 0.0563667i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.2378 | + | 28.1246i | −0.715521 | + | 1.23932i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.47801 | + | 9.48818i | 0.240922 | + | 0.417290i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.830726 | − | 1.43886i | −0.0364648 | − | 0.0631589i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8376 | −0.650046 | −0.325023 | − | 0.945706i | \(-0.605372\pi\) | ||||
−0.325023 | + | 0.945706i | \(0.605372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7964 | − | 32.5563i | −0.821910 | − | 1.42359i | −0.904258 | − | 0.426986i | \(-0.859575\pi\) |
0.0823488 | − | 0.996604i | \(-0.473758\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.95601 | 0.303585 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.7624 | + | 67.1384i | −1.68852 | + | 2.92459i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.4532 | + | 44.0863i | −1.10666 | + | 1.91680i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.71735 | 0.248112 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6562 | −0.548202 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4872 | + | 40.6811i | −1.01544 | + | 1.75880i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.691674 | − | 1.19801i | 0.0298479 | − | 0.0516981i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.29254 | 0.271039 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5473 | − | 25.1967i | −0.625439 | − | 1.08329i | −0.988456 | − | 0.151510i | \(-0.951586\pi\) |
0.363016 | − | 0.931783i | \(-0.381747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.72164 | 0.331367 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1434 | + | 17.5689i | 0.434497 | + | 0.752570i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2974 | + | 19.5677i | 0.483042 | + | 0.836652i | 0.999810 | − | 0.0194725i | \(-0.00619868\pi\) |
−0.516769 | + | 0.856125i | \(0.672865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.20751 | − | 3.82352i | 0.0942143 | − | 0.163184i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4639 | + | 23.2022i | 0.743988 | + | 0.988446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.35649 | + | 16.2059i | −0.397878 | + | 0.689145i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.205272 | − | 0.355541i | −0.00871331 | − | 0.0150919i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.12548 | + | 12.3417i | 0.301916 | + | 0.522935i | 0.976570 | − | 0.215200i | \(-0.0690403\pi\) |
−0.674654 | + | 0.738135i | \(0.735707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.7128 | 1.00294 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.29916 | + | 5.71431i | 0.139291 | + | 0.241258i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.0196 | 1.34947 | 0.674734 | − | 0.738061i | \(-0.264258\pi\) | ||||
0.674734 | + | 0.738061i | \(0.264258\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.3589 | − | 56.0472i | 1.36135 | − | 2.35792i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.7386 | + | 20.3318i | −0.492974 | + | 0.853857i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.59636 | 0.234611 | 0.117306 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117306 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.8521 | −0.956331 | −0.478166 | − | 0.878270i | \(-0.658698\pi\) | ||||
−0.478166 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.65685 | + | 2.86976i | −0.0692161 | + | 0.119886i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.0149 | − | 39.8630i | 0.959789 | − | 1.66240i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5489 | −1.06362 | −0.531808 | − | 0.846865i | \(-0.678487\pi\) | ||||
−0.531808 | + | 0.846865i | \(0.678487\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.88265 | + | 4.99289i | 0.119799 | + | 0.207497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3577 | 0.844580 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.88352 | − | 15.3867i | −0.367918 | − | 0.637252i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.5010 | + | 21.6523i | 0.516852 | + | 0.895214i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7040 | − | 18.5398i | 0.441799 | − | 0.765219i | −0.556024 | − | 0.831166i | \(-0.687674\pi\) |
0.997823 | + | 0.0659474i | \(0.0210070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.6994 | + | 5.70768i | −1.92421 | + | 0.235181i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.421489 | − | 0.730040i | 0.0173377 | − | 0.0300298i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.31469 | + | 2.27711i | 0.0539878 | + | 0.0935096i | 0.891756 | − | 0.452516i | \(-0.149473\pi\) |
−0.837768 | + | 0.546026i | \(0.816140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.2454 | + | 62.7789i | 1.48592 | + | 2.57368i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.59608 | −0.147178 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0421 | + | 29.5177i | 0.696320 | + | 1.20606i | 0.969734 | + | 0.244165i | \(0.0785138\pi\) |
−0.273414 | + | 0.961896i | \(0.588153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9251 | 1.05751 | 0.528753 | − | 0.848776i | \(-0.322660\pi\) | ||||
0.528753 | + | 0.848776i | \(0.322660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7884 | + | 18.6861i | −0.439338 | + | 0.760957i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.78430 | − | 16.9469i | 0.397788 | − | 0.688990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.1695 | 1.02160 | 0.510799 | − | 0.859700i | \(-0.329350\pi\) | ||||
0.510799 | + | 0.859700i | \(0.329350\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.65533 | −0.350732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.78531 | − | 11.7525i | 0.274504 | − | 0.475455i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.50653 | − | 14.7337i | 0.343576 | − | 0.595090i | −0.641518 | − | 0.767108i | \(-0.721695\pi\) |
0.985094 | + | 0.172017i | \(0.0550285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.14071 | −0.247617 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.21682 | − | 7.30375i | −0.169763 | − | 0.294038i | 0.768574 | − | 0.639761i | \(-0.220967\pi\) |
−0.938336 | + | 0.345724i | \(0.887634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.9297 | −1.28336 | −0.641682 | − | 0.766970i | \(-0.721763\pi\) | ||||
−0.641682 | + | 0.766970i | \(0.721763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3774 | − | 17.9741i | −0.416429 | − | 0.721276i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.39282 | + | 4.14449i | 0.0958665 | + | 0.166046i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.5516 | − | 20.0080i | 0.462066 | − | 0.800321i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.56664 | + | 3.68509i | −0.0625655 | + | 0.147168i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.10620 | − | 1.91599i | 0.0441069 | − | 0.0763954i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3584 | − | 21.4054i | −0.491981 | − | 0.852135i | 0.507977 | − | 0.861371i | \(-0.330394\pi\) |
−0.999957 | + | 0.00923543i | \(0.997060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.611914 | + | 1.05987i | 0.0243214 | + | 0.0421259i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.18951 | 0.245623 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.89711 | − | 6.75000i | −0.154409 | − | 0.267445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.3895 | 1.08351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6013 | − | 23.5582i | 0.537220 | − | 0.930492i | −0.461833 | − | 0.886967i | \(-0.652808\pi\) |
0.999052 | − | 0.0435248i | \(-0.0138587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1988 | − | 29.7892i | 0.678254 | − | 1.17477i | −0.297253 | − | 0.954799i | \(-0.596070\pi\) |
0.975506 | − | 0.219971i | \(-0.0705962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5052 | 0.453018 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.7415 | 1.60171 | 0.800857 | − | 0.598855i | \(-0.204378\pi\) | ||||
0.800857 | + | 0.598855i | \(0.204378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.24152 | − | 3.88243i | 0.0879874 | − | 0.152399i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.01110 | − | 12.1436i | 0.274787 | − | 0.475945i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.7465 | −1.47713 | −0.738566 | − | 0.674181i | \(-0.764497\pi\) | ||||
−0.738566 | + | 0.674181i | \(0.764497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.11232 | + | 3.65865i | 0.0825352 | + | 0.142955i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.4598 | −1.07131 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.61915 | − | 4.53650i | −0.102027 | − | 0.176717i | 0.810492 | − | 0.585749i | \(-0.199200\pi\) |
−0.912520 | + | 0.409032i | \(0.865866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.46982 | − | 16.4022i | −0.368333 | − | 0.637972i | 0.620972 | − | 0.783833i | \(-0.286738\pi\) |
−0.989305 | + | 0.145861i | \(0.953405\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.08649 | − | 7.07801i | 0.158706 | − | 0.274887i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.2115 | + | 40.4853i | −0.667433 | + | 1.56995i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.6374 | + | 49.6014i | −1.10884 | + | 1.92057i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.104471 | − | 0.180949i | −0.00403908 | − | 0.00699589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.73094 | − | 2.99807i | −0.0668220 | − | 0.115739i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.32739 | 0.0511670 | 0.0255835 | − | 0.999673i | \(-0.491856\pi\) | ||||
0.0255835 | + | 0.999673i | \(0.491856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.46315 | + | 11.1945i | 0.248767 | + | 0.430876i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.2385 | 0.700963 | 0.350482 | − | 0.936570i | \(-0.386018\pi\) | ||||
0.350482 | + | 0.936570i | \(0.386018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.44633 | + | 14.6295i | −0.324140 | + | 0.561428i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.52837 | − | 9.57542i | 0.211848 | − | 0.366931i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.92284 | 0.150103 | 0.0750517 | − | 0.997180i | \(-0.476088\pi\) | ||||
0.0750517 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.53437 | −0.0968332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.20751 | + | 7.28763i | −0.160527 | + | 0.278040i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0035 | + | 19.0587i | −0.419201 | + | 0.726078i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.65685 | −0.0630297 | −0.0315149 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315149 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.83729 | + | 17.0387i | 0.373688 | + | 0.647246i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.90611 | 0.299896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.5459 | − | 28.6584i | −0.626721 | − | 1.08551i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.51512 | + | 2.62427i | 0.0573073 | + | 0.0992591i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.23551 | − | 5.60406i | 0.122203 | − | 0.211662i | −0.798433 | − | 0.602084i | \(-0.794337\pi\) |
0.920636 | + | 0.390421i | \(0.127671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.33270 | − | 0.162885i | 0.0502638 | − | 0.00614333i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.29218 | − | 5.70222i | 0.123991 | − | 0.214758i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.3014 | − | 23.0387i | −0.500251 | − | 0.866459i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1975 | + | 36.7151i | 0.796087 | + | 1.37886i | 0.922146 | + | 0.386841i | \(0.126434\pi\) |
−0.126059 | + | 0.992023i | \(0.540233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8752 | −0.632871 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −46.3944 | − | 80.3574i | −1.73748 | − | 3.00941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.6043 | 0.733160 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.51012 | + | 2.61561i | −0.0563965 | + | 0.0976816i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.08590 | − | 15.7372i | 0.338847 | − | 0.586900i | −0.645369 | − | 0.763871i | \(-0.723297\pi\) |
0.984216 | + | 0.176971i | \(0.0566298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.6544 | 1.17887 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.65318 | −0.0614826 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.8357 | − | 30.8923i | 0.662401 | − | 1.14731i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.21746 | + | 9.03691i | −0.193505 | + | 0.335160i | −0.946409 | − | 0.322969i | \(-0.895319\pi\) |
0.752904 | + | 0.658130i | \(0.228652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.0005 | + | 53.6944i | 1.14659 | + | 1.98596i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.6625 | 0.910932 | 0.455466 | − | 0.890253i | \(-0.349473\pi\) | ||||
0.455466 | + | 0.890253i | \(0.349473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.89085 | − | 3.27505i | −0.0697450 | − | 0.120802i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.45932 | + | 14.6520i | 0.311603 | + | 0.539712i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9259 | − | 25.8524i | 0.549058 | − | 0.950996i | −0.449282 | − | 0.893390i | \(-0.648320\pi\) |
0.998339 | − | 0.0576057i | \(-0.0183466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.92324 | − | 0.601727i | 0.180860 | − | 0.0221050i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.10405 | + | 14.0366i | −0.297309 | + | 0.514954i | −0.975519 | − | 0.219914i | \(-0.929422\pi\) |
0.678210 | + | 0.734868i | \(0.262756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3495 | + | 26.5861i | 0.562362 | + | 0.974040i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.17922 | + | 15.8989i | 0.335850 | + | 0.581710i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.7868 | 1.67301 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.42220 | + | 4.19538i | 0.0883875 | + | 0.153092i | 0.906830 | − | 0.421497i | \(-0.138495\pi\) |
−0.818442 | + | 0.574589i | \(0.805162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0996931 | −0.00363302 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.2751 | − | 38.5817i | 0.810675 | − | 1.40413i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.82512 | + | 17.0176i | −0.357100 | + | 0.618515i | −0.987475 | − | 0.157775i | \(-0.949568\pi\) |
0.630375 | + | 0.776291i | \(0.282901\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.89747 | −0.286660 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.5702 | 1.10817 | 0.554085 | − | 0.832460i | \(-0.313068\pi\) | ||||
0.554085 | + | 0.832460i | \(0.313068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.88697 | − | 17.1247i | 0.357932 | − | 0.619957i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.6859 | + | 56.6136i | −1.18176 | + | 2.04687i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.55290 | −0.200504 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.9284 | − | 22.3926i | −0.466210 | − | 0.807499i | 0.533045 | − | 0.846087i | \(-0.321047\pi\) |
−0.999255 | + | 0.0385875i | \(0.987714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.87925 | −0.139708 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2326 | − | 28.1157i | −0.583846 | − | 1.01125i | −0.995018 | − | 0.0996927i | \(-0.968214\pi\) |
0.411173 | − | 0.911557i | \(-0.365119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.8950 | + | 50.0476i | 1.03794 | + | 1.79776i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.200082 | + | 0.346552i | −0.00717790 | + | 0.0124325i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.85699 | − | 18.4814i | 0.281506 | − | 0.662166i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7382 | − | 18.5991i | 0.384243 | − | 0.665529i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.04206 | − | 13.9293i | −0.287400 | − | 0.497791i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.40723 | + | 14.5618i | 0.300067 | + | 0.519731i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.6534 | −0.807507 | −0.403753 | − | 0.914868i | \(-0.632295\pi\) | ||||
−0.403753 | + | 0.914868i | \(0.632295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.96517 | + | 3.40377i | 0.0699618 | + | 0.121177i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.0815 | −2.24292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.14402 | + | 3.71354i | −0.0761362 | + | 0.131872i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.33883 | + | 9.24712i | −0.189349 | + | 0.327961i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.55181 | 0.0903896 | 0.0451948 | − | 0.998978i | \(-0.485609\pi\) | ||||
0.0451948 | + | 0.998978i | \(0.485609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.4826 | 1.25529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.15783 | + | 3.73748i | −0.0762433 | + | 0.132057i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.7658 | + | 18.6468i | −0.379915 | + | 0.658033i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −86.7637 | −3.05802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.58147 | + | 9.66738i | 0.196477 | + | 0.340308i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.8734 | 1.29640 | 0.648201 | − | 0.761470i | \(-0.275522\pi\) | ||||
0.648201 | + | 0.761470i | \(0.275522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.25949 | − | 2.18150i | −0.0442267 | − | 0.0766029i | 0.843065 | − | 0.537812i | \(-0.180749\pi\) |
−0.887291 | + | 0.461209i | \(0.847416\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.26718 | + | 2.19483i | 0.0444421 | + | 0.0769759i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.4483 | − | 26.7572i | 0.541130 | − | 0.937265i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.7209 | + | 34.6268i | −0.515018 | + | 1.21144i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.1849 | − | 21.1049i | 0.425775 | − | 0.737465i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.27642 | + | 3.94287i | 0.0794476 | + | 0.137607i | 0.903012 | − | 0.429616i | \(-0.141351\pi\) |
−0.823564 | + | 0.567223i | \(0.808018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.43594 | − | 2.48712i | −0.0500538 | − | 0.0866957i | 0.839913 | − | 0.542721i | \(-0.182606\pi\) |
−0.889967 | + | 0.456025i | \(0.849273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.91864 | 0.171245 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.4097 | + | 23.2264i | 0.466302 | + | 0.807659i | 0.999259 | − | 0.0384830i | \(-0.0122525\pi\) |
−0.532957 | + | 0.846142i | \(0.678919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.8817 | −1.24622 | −0.623111 | − | 0.782133i | \(-0.714132\pi\) | ||||
−0.623111 | + | 0.782133i | \(0.714132\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.87826 | + | 3.25324i | −0.0651562 | + | 0.112854i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.1897 | − | 17.6490i | 0.353051 | − | 0.611501i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.8657 | −1.10276 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.0573 | 0.900673 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.3309 | − | 24.8219i | 0.494759 | − | 0.856947i | −0.505223 | − | 0.862989i | \(-0.668590\pi\) |
0.999982 | + | 0.00604151i | \(0.00192308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.69288 | + | 13.3245i | −0.265272 | + | 0.459464i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.87325 | −0.236727 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.77431 | + | 15.1975i | 0.301845 | + | 0.522811i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0738 | −0.655385 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.63847 | + | 6.30201i | 0.124872 | + | 0.216284i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.32400 | + | 2.29323i | 0.0453860 | + | 0.0786109i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.1924 | + | 47.0987i | −0.931051 | + | 1.61263i | −0.149522 | + | 0.988758i | \(0.547773\pi\) |
−0.781529 | + | 0.623869i | \(0.785560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −39.3787 | + | 4.81293i | −1.34672 | + | 0.164599i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.30847 | − | 16.1227i | 0.317971 | − | 0.550742i | −0.662093 | − | 0.749421i | \(-0.730332\pi\) |
0.980065 | + | 0.198679i | \(0.0636651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5174 | + | 32.0730i | 0.631804 | + | 1.09432i | 0.987183 | + | 0.159595i | \(0.0510187\pi\) |
−0.355378 | + | 0.934723i | \(0.615648\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.99272 | + | 5.18355i | 0.101992 | + | 0.176655i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.7053 | 0.840979 | 0.420490 | − | 0.907297i | \(-0.361858\pi\) | ||||
0.420490 | + | 0.907297i | \(0.361858\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.45346 | − | 11.1777i | −0.219424 | − | 0.380054i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.3280 | 0.486604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.61604 | + | 11.4593i | −0.224434 | + | 0.388730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4781 | − | 18.1486i | 0.355037 | − | 0.614942i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.2337 | −0.515582 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.57522 | 0.120864 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6668 | + | 39.2600i | −0.765402 | + | 1.32572i | 0.174632 | + | 0.984634i | \(0.444127\pi\) |
−0.940034 | + | 0.341082i | \(0.889207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.98244 | − | 8.62983i | 0.168053 | − | 0.291077i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.632076 | −0.0212952 | −0.0106476 | − | 0.999943i | \(-0.503389\pi\) | ||||
−0.0106476 | + | 0.999943i | \(0.503389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.1308 | − | 46.9919i | −0.913023 | − | 1.58140i | −0.809770 | − | 0.586747i | \(-0.800408\pi\) |
−0.103252 | − | 0.994655i | \(-0.532925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.69422 | −0.0905653 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.9061 | − | 31.0142i | −0.601227 | − | 1.04135i | −0.992636 | − | 0.121138i | \(-0.961346\pi\) |
0.391409 | − | 0.920217i | \(-0.371988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.01651 | − | 5.22475i | −0.101171 | − | 0.175232i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.30043 | + | 14.3768i | −0.278075 | + | 0.481640i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9494 | + | 17.2043i | 0.433335 | + | 0.575719i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.37324 | − | 9.30672i | 0.179608 | − | 0.311089i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.89109 | + | 8.47161i | 0.163309 | + | 0.282859i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35.9539 | − | 62.2740i | −1.19913 | − | 2.07695i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.5411 | −1.91697 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.60718 | − | 9.71191i | −0.186595 | − | 0.323192i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59.9852 | 1.99398 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.1300 | + | 40.0623i | −0.768017 | + | 1.33025i | 0.170619 | + | 0.985337i | \(0.445423\pi\) |
−0.938636 | + | 0.344908i | \(0.887910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.9951 | − | 20.7762i | 0.397853 | − | 0.689102i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.0416 | −0.365824 | −0.182912 | − | 0.983129i | \(-0.558552\pi\) | ||||
−0.182912 | + | 0.983129i | \(0.558552\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3951 | 0.476407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.04026 | + | 1.80178i | −0.0343899 | + | 0.0595651i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.05891 | − | 3.56614i | 0.0679913 | − | 0.117764i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.2252 | −1.16197 | −0.580986 | − | 0.813914i | \(-0.697333\pi\) | ||||
−0.580986 | + | 0.813914i | \(0.697333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.09263 | − | 7.08864i | −0.134857 | − | 0.233578i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.6017 | −0.875605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.824602 | − | 1.42825i | −0.0271127 | − | 0.0469606i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2729 | + | 24.7214i | 0.468783 | + | 0.811956i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.6827 | − | 21.9670i | 0.416105 | − | 0.720715i | −0.579439 | − | 0.815016i | \(-0.696728\pi\) |
0.995544 | + | 0.0943008i | \(0.0300615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2761 | − | 1.50041i | 0.402333 | − | 0.0491738i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.56965 | + | 6.18282i | −0.116865 | + | 0.202416i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.6294 | + | 44.3914i | 0.838170 | + | 1.45175i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.8951 | + | 25.7990i | 0.486601 | + | 0.842817i | 0.999881 | − | 0.0154038i | \(-0.00490339\pi\) |
−0.513281 | + | 0.858221i | \(0.671570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.10936 | 0.134104 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7327 | − | 30.7139i | −0.578068 | − | 1.00124i | −0.995701 | − | 0.0926275i | \(-0.970473\pi\) |
0.417633 | − | 0.908616i | \(-0.362860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.6074 | 1.28979 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.1827 | − | 21.1010i | 0.396302 | − | 0.686416i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.00995 | + | 15.6057i | −0.292784 | + | 0.507117i | −0.974467 | − | 0.224531i | \(-0.927915\pi\) |
0.681683 | + | 0.731648i | \(0.261248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.6699 | 0.865742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.73333 | −0.250770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.19963 | + | 12.4701i | −0.233219 | + | 0.403947i | −0.958754 | − | 0.284239i | \(-0.908259\pi\) |
0.725535 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.8712 | + | 22.2936i | −0.416502 | + | 0.721403i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.12025 | −0.197839 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23515 | + | 2.13933i | 0.0398849 | + | 0.0690827i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 85.4953 | 2.75791 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.6451 | + | 35.7584i | 0.665280 | + | 1.15230i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.3937 | + | 38.7871i | 0.720879 | + | 1.24860i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2010 | + | 22.8647i | −0.424514 | + | 0.735280i | −0.996375 | − | 0.0850708i | \(-0.972888\pi\) |
0.571861 | + | 0.820351i | \(0.306222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.79885 | + | 10.3614i | 0.250535 | + | 0.332855i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3912 | − | 23.1943i | 0.429744 | − | 0.744339i | −0.567106 | − | 0.823645i | \(-0.691937\pi\) |
0.996850 | + | 0.0793058i | \(0.0252703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.85311 | − | 6.67378i | −0.123525 | − | 0.213952i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.04623 | − | 5.27622i | −0.0975574 | − | 0.168974i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.2049 | −1.22228 | −0.611141 | − | 0.791522i | \(-0.709289\pi\) | ||||
−0.611141 | + | 0.791522i | \(0.709289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.69198 | + | 2.93060i | 0.0540760 | + | 0.0936624i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.8320 | 0.569332 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.49327 | − | 11.2467i | 0.207103 | − | 0.358713i | −0.743698 | − | 0.668516i | \(-0.766930\pi\) |
0.950801 | + | 0.309803i | \(0.100263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.27432 | − | 5.67129i | 0.104328 | − | 0.180702i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.41788 | −0.204283 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −74.2085 | −2.35969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0328 | + | 19.1094i | −0.350469 | + | 0.607031i | −0.986332 | − | 0.164772i | \(-0.947311\pi\) |
0.635862 | + | 0.771802i | \(0.280645\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.91550 | + | 8.51390i | −0.155989 | + | 0.270180i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.9360 | −0.885630 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.61655 | − | 13.1923i | −0.241219 | − | 0.417803i | 0.719843 | − | 0.694137i | \(-0.244214\pi\) |
−0.961062 | + | 0.276334i | \(0.910880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.743621 | −0.0235271 |
(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 | 1216.2.i.q.961.1 | 8 | ||
4.3 | odd | 2 | 1216.2.i.o.961.3 | 8 | |||
8.3 | odd | 2 | 608.2.i.e.353.2 | yes | 8 | ||
8.5 | even | 2 | 608.2.i.c.353.4 | ✓ | 8 | ||
19.7 | even | 3 | inner | 1216.2.i.q.577.1 | 8 | ||
76.7 | odd | 6 | 1216.2.i.o.577.3 | 8 | |||
152.45 | even | 6 | 608.2.i.c.577.4 | yes | 8 | ||
152.83 | odd | 6 | 608.2.i.e.577.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.c.353.4 | ✓ | 8 | 8.5 | even | 2 | ||
608.2.i.c.577.4 | yes | 8 | 152.45 | even | 6 | ||
608.2.i.e.353.2 | yes | 8 | 8.3 | odd | 2 | ||
608.2.i.e.577.2 | yes | 8 | 152.83 | odd | 6 | ||
1216.2.i.o.577.3 | 8 | 76.7 | odd | 6 | |||
1216.2.i.o.961.3 | 8 | 4.3 | odd | 2 | |||
1216.2.i.q.577.1 | 8 | 19.7 | even | 3 | inner | ||
1216.2.i.q.961.1 | 8 | 1.1 | even | 1 | trivial |