Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(89,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bb (of order \(6\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.9 | ||
Character | \(\chi\) | \(=\) | 315.89 |
Dual form | 315.2.bb.b.269.9 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.956572 | − | 1.65683i | 0.676399 | − | 1.17156i | −0.299659 | − | 0.954046i | \(-0.596873\pi\) |
0.976058 | − | 0.217511i | \(-0.0697937\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.830062 | − | 1.43771i | −0.415031 | − | 0.718854i | ||||
\(5\) | 1.54260 | + | 1.61876i | 0.689873 | + | 0.723930i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.11878 | + | 2.39757i | 0.422859 | + | 0.906196i | ||||
\(8\) | 0.650234 | 0.229892 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.15762 | − | 1.00738i | 1.31476 | − | 0.318560i | ||||
\(11\) | 2.79501 | − | 1.61370i | 0.842728 | − | 0.486549i | −0.0154625 | − | 0.999880i | \(-0.504922\pi\) |
0.858191 | + | 0.513331i | \(0.171589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.86146 | −1.34833 | −0.674164 | − | 0.738582i | \(-0.735496\pi\) | ||||
−0.674164 | + | 0.738582i | \(0.735496\pi\) | |||||||
\(14\) | 5.04256 | + | 0.439817i | 1.34768 | + | 0.117546i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.28212 | − | 3.95275i | 0.570530 | − | 0.988186i | ||||
\(17\) | 0.631456 | − | 0.364571i | 0.153150 | − | 0.0884215i | −0.421466 | − | 0.906844i | \(-0.638484\pi\) |
0.574617 | + | 0.818423i | \(0.305151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.81691 | − | 3.93574i | −1.56391 | − | 0.902922i | −0.996856 | − | 0.0792390i | \(-0.974751\pi\) |
−0.567051 | − | 0.823683i | \(-0.691916\pi\) | |||||||
\(20\) | 1.04685 | − | 3.56148i | 0.234082 | − | 0.796372i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.17449i | − | 1.31641i | ||||||
\(23\) | −2.43410 | + | 4.21599i | −0.507545 | + | 0.879094i | 0.492417 | + | 0.870360i | \(0.336114\pi\) |
−0.999962 | + | 0.00873433i | \(0.997220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.240749 | + | 4.99420i | −0.0481499 | + | 0.998840i | ||||
\(26\) | −4.65034 | + | 8.05463i | −0.912007 | + | 1.57964i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.51835 | − | 3.59861i | 0.475923 | − | 0.680073i | ||||
\(29\) | − | 7.75958i | − | 1.44092i | −0.693498 | − | 0.720459i | \(-0.743931\pi\) | ||
0.693498 | − | 0.720459i | \(-0.256069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.23751 | + | 0.714478i | −0.222264 | + | 0.128324i | −0.606998 | − | 0.794703i | \(-0.707626\pi\) |
0.384734 | + | 0.923027i | \(0.374293\pi\) | |||||||
\(32\) | −3.71579 | − | 6.43594i | −0.656865 | − | 1.13772i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.39495i | − | 0.239233i | ||||||
\(35\) | −2.15525 | + | 5.50953i | −0.364303 | + | 0.931280i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.74130 | + | 1.58269i | 0.450667 | + | 0.260193i | 0.708112 | − | 0.706100i | \(-0.249547\pi\) |
−0.257445 | + | 0.966293i | \(0.582881\pi\) | |||||||
\(38\) | −13.0417 | + | 7.52965i | −2.11565 | + | 1.22147i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00305 | + | 1.05257i | 0.158597 | + | 0.166426i | ||||
\(41\) | 1.40264 | 0.219056 | 0.109528 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109528 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.42489i | − | 0.979787i | −0.871782 | − | 0.489893i | \(-0.837036\pi\) | ||
0.871782 | − | 0.489893i | \(-0.162964\pi\) | |||||||
\(44\) | −4.64007 | − | 2.67894i | −0.699516 | − | 0.403866i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.65679 | + | 8.06579i | 0.686606 | + | 1.18924i | ||||
\(47\) | 4.21797 | + | 2.43524i | 0.615254 | + | 0.355217i | 0.775019 | − | 0.631938i | \(-0.217740\pi\) |
−0.159765 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.49666 | + | 5.36470i | −0.642381 | + | 0.766386i | ||||
\(50\) | 8.04426 | + | 5.17620i | 1.13763 | + | 0.732025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.03531 | + | 6.98937i | 0.559597 | + | 0.969251i | ||||
\(53\) | 0.760733 | + | 1.31763i | 0.104495 | + | 0.180990i | 0.913532 | − | 0.406768i | \(-0.133344\pi\) |
−0.809037 | + | 0.587758i | \(0.800011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92379 | + | 2.03515i | 0.933603 | + | 0.274419i | ||||
\(56\) | 0.727468 | + | 1.55898i | 0.0972120 | + | 0.208327i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.8563 | − | 7.42260i | −1.68812 | − | 0.974635i | ||||
\(59\) | −3.15081 | − | 5.45737i | −0.410201 | − | 0.710489i | 0.584711 | − | 0.811242i | \(-0.301208\pi\) |
−0.994911 | + | 0.100753i | \(0.967875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05442 | − | 1.18612i | −0.263042 | − | 0.151867i | 0.362680 | − | 0.931914i | \(-0.381862\pi\) |
−0.625721 | + | 0.780047i | \(0.715195\pi\) | |||||||
\(62\) | 2.73380i | 0.347193i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.08921 | −0.636152 | ||||||||
\(65\) | −7.49931 | − | 7.86953i | −0.930175 | − | 0.976095i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.63531 | + | 5.56295i | −1.17714 | + | 0.679622i | −0.955351 | − | 0.295472i | \(-0.904523\pi\) |
−0.221789 | + | 0.975095i | \(0.571190\pi\) | |||||||
\(68\) | −1.04829 | − | 0.605233i | −0.127124 | − | 0.0733953i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.06671 | + | 8.84115i | 0.844634 | + | 1.05672i | ||||
\(71\) | − | 10.1351i | − | 1.20282i | −0.798942 | − | 0.601408i | \(-0.794607\pi\) | ||
0.798942 | − | 0.601408i | \(-0.205393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.91195 | + | 11.9718i | 0.808982 | + | 1.40120i | 0.913570 | + | 0.406683i | \(0.133314\pi\) |
−0.104587 | + | 0.994516i | \(0.533352\pi\) | |||||||
\(74\) | 5.24450 | − | 3.02792i | 0.609661 | − | 0.351988i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.0676i | 1.49896i | ||||||||
\(77\) | 6.99596 | + | 4.89586i | 0.797264 | + | 0.557935i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.99018 | + | 3.44710i | −0.223913 | + | 0.387829i | −0.955993 | − | 0.293390i | \(-0.905217\pi\) |
0.732080 | + | 0.681219i | \(0.238550\pi\) | |||||||
\(80\) | 9.91894 | − | 2.40332i | 1.10897 | − | 0.268700i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.34173 | − | 2.32395i | 0.148169 | − | 0.256637i | ||||
\(83\) | − | 4.19208i | − | 0.460141i | −0.973174 | − | 0.230070i | \(-0.926104\pi\) | ||
0.973174 | − | 0.230070i | \(-0.0738957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56424 | + | 0.459785i | 0.169665 | + | 0.0498706i | ||||
\(86\) | −10.6450 | − | 6.14587i | −1.14788 | − | 0.662727i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.81741 | − | 1.04928i | 0.193737 | − | 0.111854i | ||||
\(89\) | −5.63672 | + | 9.76309i | −0.597491 | + | 1.03489i | 0.395699 | + | 0.918380i | \(0.370502\pi\) |
−0.993190 | + | 0.116505i | \(0.962831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.43891 | − | 11.6557i | −0.570152 | − | 1.22185i | ||||
\(92\) | 8.08181 | 0.842587 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.06958 | − | 4.65898i | 0.832314 | − | 0.480537i | ||||
\(95\) | −4.14477 | − | 17.1062i | −0.425245 | − | 1.75506i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.21388 | 0.224785 | 0.112393 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112393 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(98\) | 4.58702 | + | 12.5819i | 0.463359 | + | 1.27097i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.38004 | − | 3.79937i | 0.738004 | − | 0.379937i | ||||
\(101\) | 5.85104 | + | 10.1343i | 0.582201 | + | 1.00840i | 0.995218 | + | 0.0976779i | \(0.0311415\pi\) |
−0.413017 | + | 0.910723i | \(0.635525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.292630 | − | 0.506851i | 0.0288337 | − | 0.0499415i | −0.851248 | − | 0.524763i | \(-0.824154\pi\) |
0.880082 | + | 0.474821i | \(0.157487\pi\) | |||||||
\(104\) | −3.16109 | −0.309970 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.91079 | 0.282721 | ||||||||
\(107\) | 0.846073 | − | 1.46544i | 0.0817929 | − | 0.141670i | −0.822227 | − | 0.569159i | \(-0.807269\pi\) |
0.904020 | + | 0.427490i | \(0.140602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.70139 | + | 11.6072i | 0.641877 | + | 1.11176i | 0.985013 | + | 0.172478i | \(0.0551774\pi\) |
−0.343136 | + | 0.939286i | \(0.611489\pi\) | |||||||
\(110\) | 9.99500 | − | 9.52479i | 0.952986 | − | 0.908153i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0302 | + | 1.04928i | 1.13674 | + | 0.0991479i | ||||
\(113\) | −14.2129 | −1.33704 | −0.668520 | − | 0.743694i | \(-0.733072\pi\) | ||||
−0.668520 | + | 0.743694i | \(0.733072\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.5795 | + | 2.56338i | −0.986544 | + | 0.239036i | ||||
\(116\) | −11.1560 | + | 6.44093i | −1.03581 | + | 0.598025i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.0559 | −1.10984 | ||||||||
\(119\) | 1.58054 | + | 1.10608i | 0.144888 | + | 0.101394i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.291934 | + | 0.505645i | −0.0265395 | + | 0.0459677i | ||||
\(122\) | −3.93041 | + | 2.26922i | −0.355842 | + | 0.205446i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.05442 | + | 1.18612i | 0.184493 | + | 0.106517i | ||||
\(125\) | −8.45578 | + | 7.31436i | −0.756308 | + | 0.654216i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.08954i | 0.185417i | 0.995693 | + | 0.0927084i | \(0.0295524\pi\) | ||||
−0.995693 | + | 0.0927084i | \(0.970448\pi\) | |||||||
\(128\) | 2.56338 | − | 4.43990i | 0.226573 | − | 0.392436i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −20.2121 | + | 4.89732i | −1.77272 | + | 0.429524i | ||||
\(131\) | 5.60241 | − | 9.70365i | 0.489484 | − | 0.847812i | −0.510442 | − | 0.859912i | \(-0.670518\pi\) |
0.999927 | + | 0.0121001i | \(0.00385167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.80960 | − | 20.7472i | 0.156912 | − | 1.79901i | ||||
\(134\) | 21.2855i | 1.83878i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.410594 | − | 0.237056i | 0.0352081 | − | 0.0203274i | ||||
\(137\) | −3.51995 | − | 6.09673i | −0.300730 | − | 0.520879i | 0.675572 | − | 0.737294i | \(-0.263897\pi\) |
−0.976301 | + | 0.216415i | \(0.930564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.45903i | − | 0.547848i | −0.961751 | − | 0.273924i | \(-0.911678\pi\) | ||
0.961751 | − | 0.273924i | \(-0.0883216\pi\) | |||||||
\(140\) | 9.71009 | − | 1.47463i | 0.820652 | − | 0.124629i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.7922 | − | 9.69496i | −1.40917 | − | 0.813583i | ||||
\(143\) | −13.5879 | + | 7.84495i | −1.13627 | + | 0.656028i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5609 | − | 11.9699i | 1.04312 | − | 0.994050i | ||||
\(146\) | 26.4471 | 2.18878 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.25492i | − | 0.431952i | ||||||
\(149\) | 20.3962 | + | 11.7758i | 1.67092 | + | 0.964709i | 0.967122 | + | 0.254312i | \(0.0818491\pi\) |
0.703802 | + | 0.710396i | \(0.251484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.05442 | − | 15.6827i | −0.736838 | − | 1.27624i | −0.953912 | − | 0.300086i | \(-0.902985\pi\) |
0.217074 | − | 0.976155i | \(-0.430349\pi\) | |||||||
\(152\) | −4.43258 | − | 2.55915i | −0.359530 | − | 0.207575i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.8038 | − | 6.90789i | 1.19292 | − | 0.556654i | ||||
\(155\) | −3.06556 | − | 0.901075i | −0.246231 | − | 0.0723761i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.24227 | − | 2.15168i | −0.0991441 | − | 0.171723i | 0.812187 | − | 0.583398i | \(-0.198277\pi\) |
−0.911331 | + | 0.411675i | \(0.864944\pi\) | |||||||
\(158\) | 3.80751 | + | 6.59480i | 0.302909 | + | 0.524654i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.68623 | − | 15.9431i | 0.370479 | − | 1.26041i | ||||
\(161\) | −12.8313 | − | 1.11916i | −1.01125 | − | 0.0882023i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.41015 | − | 1.96885i | −0.267104 | − | 0.154212i | 0.360467 | − | 0.932772i | \(-0.382617\pi\) |
−0.627571 | + | 0.778560i | \(0.715951\pi\) | |||||||
\(164\) | −1.16428 | − | 2.01659i | −0.0909151 | − | 0.157470i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.94558 | − | 4.01003i | −0.539081 | − | 0.311239i | ||||
\(167\) | − | 5.31832i | − | 0.411544i | −0.978600 | − | 0.205772i | \(-0.934029\pi\) | ||
0.978600 | − | 0.205772i | \(-0.0659705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6338 | 0.817986 | ||||||||
\(170\) | 2.25809 | − | 2.15186i | 0.173188 | − | 0.165040i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.23712 | + | 5.33306i | −0.704324 | + | 0.406642i | ||||
\(173\) | −6.45623 | − | 3.72751i | −0.490858 | − | 0.283397i | 0.234072 | − | 0.972219i | \(-0.424795\pi\) |
−0.724930 | + | 0.688822i | \(0.758128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2433 | + | 5.01020i | −0.925505 | + | 0.378735i | ||||
\(176\) | − | 14.7306i | − | 1.11036i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.7839 | + | 18.6782i | 0.808285 | + | 1.39999i | ||||
\(179\) | −11.5242 | + | 6.65349i | −0.861358 | + | 0.497305i | −0.864467 | − | 0.502690i | \(-0.832344\pi\) |
0.00310866 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.95814i | − | 0.740183i | −0.928995 | − | 0.370091i | \(-0.879326\pi\) | ||
0.928995 | − | 0.370091i | \(-0.120674\pi\) | |||||||
\(182\) | −24.5142 | − | 2.13816i | −1.81712 | − | 0.158491i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.58273 | + | 2.74138i | −0.116681 | + | 0.202097i | ||||
\(185\) | 1.66675 | + | 6.87896i | 0.122542 | + | 0.505751i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17662 | − | 2.03796i | 0.0860428 | − | 0.149031i | ||||
\(188\) | − | 8.08561i | − | 0.589704i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −32.3069 | − | 9.49614i | −2.34379 | − | 0.688922i | ||||
\(191\) | 21.3140 | + | 12.3056i | 1.54223 | + | 0.890404i | 0.998698 | + | 0.0510125i | \(0.0162448\pi\) |
0.543527 | + | 0.839392i | \(0.317089\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8377 | − | 6.25714i | 0.780113 | − | 0.450399i | −0.0563571 | − | 0.998411i | \(-0.517949\pi\) |
0.836470 | + | 0.548012i | \(0.184615\pi\) | |||||||
\(194\) | 2.11773 | − | 3.66802i | 0.152044 | − | 0.263349i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.4454 | + | 2.01186i | 0.817528 | + | 0.143704i | ||||
\(197\) | 15.6968 | 1.11835 | 0.559177 | − | 0.829049i | \(-0.311117\pi\) | ||||
0.559177 | + | 0.829049i | \(0.311117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1436 | − | 9.89788i | 1.21528 | − | 0.701642i | 0.251375 | − | 0.967890i | \(-0.419117\pi\) |
0.963905 | + | 0.266247i | \(0.0857838\pi\) | |||||||
\(200\) | −0.156543 | + | 3.24740i | −0.0110693 | + | 0.229626i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.3878 | 1.57520 | ||||||||
\(203\) | 18.6041 | − | 8.68126i | 1.30575 | − | 0.609305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.16372 | + | 2.27054i | 0.151121 | + | 0.158581i | ||||
\(206\) | −0.559844 | − | 0.969678i | −0.0390062 | − | 0.0675607i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.0944 | + | 19.2161i | −0.769261 | + | 1.33240i | ||||
\(209\) | −25.4045 | −1.75726 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5839 | 0.797466 | 0.398733 | − | 0.917067i | \(-0.369450\pi\) | ||||
0.398733 | + | 0.917067i | \(0.369450\pi\) | |||||||
\(212\) | 1.26291 | − | 2.18743i | 0.0867371 | − | 0.150233i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.61866 | − | 2.80360i | −0.110649 | − | 0.191650i | ||||
\(215\) | 10.4003 | − | 9.91106i | 0.709297 | − | 0.675929i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.09751 | − | 2.16768i | −0.210273 | − | 0.147151i | ||||
\(218\) | 25.6415 | 1.73666 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.82122 | − | 11.6437i | −0.190207 | − | 0.785017i | ||||
\(221\) | −3.06980 | + | 1.77235i | −0.206497 | + | 0.119221i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.1321 | −1.61600 | −0.808002 | − | 0.589180i | \(-0.799451\pi\) | ||||
−0.808002 | + | 0.589180i | \(0.799451\pi\) | |||||||
\(224\) | 11.2734 | − | 16.1093i | 0.753239 | − | 1.07634i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.5957 | + | 23.5484i | −0.904372 | + | 1.56642i | ||||
\(227\) | 8.82377 | − | 5.09441i | 0.585654 | − | 0.338128i | −0.177723 | − | 0.984081i | \(-0.556873\pi\) |
0.763377 | + | 0.645953i | \(0.223540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.7373 | + | 13.1274i | 1.50252 | + | 0.867483i | 0.999996 | + | 0.00292226i | \(0.000930186\pi\) |
0.502529 | + | 0.864561i | \(0.332403\pi\) | |||||||
\(230\) | −5.87298 | + | 19.9805i | −0.387253 | + | 1.31748i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 5.04554i | − | 0.331256i | ||||||
\(233\) | 9.19667 | − | 15.9291i | 0.602494 | − | 1.04355i | −0.389948 | − | 0.920837i | \(-0.627507\pi\) |
0.992442 | − | 0.122713i | \(-0.0391595\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.56458 | + | 10.5845i | 0.167295 | + | 0.690455i | ||||
\(236\) | −5.23074 | + | 9.05990i | −0.340492 | + | 0.589749i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.34450 | − | 1.56065i | 0.216792 | − | 0.101162i | ||||
\(239\) | − | 0.961317i | − | 0.0621824i | −0.999517 | − | 0.0310912i | \(-0.990102\pi\) | ||
0.999517 | − | 0.0310912i | \(-0.00989824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.63829 | + | 3.25527i | −0.363194 | + | 0.209690i | −0.670481 | − | 0.741927i | \(-0.733912\pi\) |
0.307287 | + | 0.951617i | \(0.400579\pi\) | |||||||
\(242\) | 0.558512 | + | 0.967371i | 0.0359025 | + | 0.0621850i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.93821i | 0.252118i | ||||||||
\(245\) | −15.6207 | + | 0.996599i | −0.997971 | + | 0.0636704i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.1402 | + | 19.1335i | 2.10866 | + | 1.21743i | ||||
\(248\) | −0.804672 | + | 0.464578i | −0.0510967 | + | 0.0295007i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.03010 | + | 21.0065i | 0.254886 | + | 1.32857i | ||||
\(251\) | −2.02506 | −0.127820 | −0.0639102 | − | 0.997956i | \(-0.520357\pi\) | ||||
−0.0639102 | + | 0.997956i | \(0.520357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.7116i | 0.987783i | ||||||||
\(254\) | 3.46202 | + | 1.99880i | 0.217226 | + | 0.125416i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.99333 | − | 17.3090i | −0.624583 | − | 1.08181i | ||||
\(257\) | 15.7532 | + | 9.09510i | 0.982656 | + | 0.567337i | 0.903071 | − | 0.429491i | \(-0.141307\pi\) |
0.0795849 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.727697 | + | 8.34313i | −0.0452169 | + | 0.518417i | ||||
\(260\) | −5.08920 | + | 17.3140i | −0.315619 | + | 1.07377i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.7182 | − | 18.5645i | −0.662173 | − | 1.14692i | ||||
\(263\) | 9.78034 | + | 16.9400i | 0.603082 | + | 1.04457i | 0.992351 | + | 0.123444i | \(0.0393940\pi\) |
−0.389270 | + | 0.921124i | \(0.627273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.959411 | + | 3.26402i | −0.0589362 | + | 0.200507i | ||||
\(266\) | −32.6437 | − | 22.8444i | −2.00151 | − | 1.40068i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.9958 | + | 9.23518i | 0.977099 | + | 0.564128i | ||||
\(269\) | 2.30801 | + | 3.99759i | 0.140722 | + | 0.243738i | 0.927769 | − | 0.373156i | \(-0.121724\pi\) |
−0.787047 | + | 0.616893i | \(0.788391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.33654 | − | 5.39045i | −0.567154 | − | 0.327447i | 0.188858 | − | 0.982004i | \(-0.439522\pi\) |
−0.756012 | + | 0.654558i | \(0.772855\pi\) | |||||||
\(272\) | − | 3.32798i | − | 0.201788i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.4684 | −0.813653 | ||||||||
\(275\) | 7.38625 | + | 14.3474i | 0.445408 | + | 0.865178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.7594 | + | 10.2534i | −1.06706 | + | 0.616067i | −0.927376 | − | 0.374130i | \(-0.877941\pi\) |
−0.139682 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(278\) | −10.7015 | − | 6.17853i | −0.641835 | − | 0.370564i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.40141 | + | 3.58248i | −0.0837505 | + | 0.214094i | ||||
\(281\) | 0.714666i | 0.0426334i | 0.999773 | + | 0.0213167i | \(0.00678583\pi\) | ||||
−0.999773 | + | 0.0213167i | \(0.993214\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0110 | + | 24.2677i | 0.832866 | + | 1.44257i | 0.895756 | + | 0.444545i | \(0.146635\pi\) |
−0.0628908 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(284\) | −14.5713 | + | 8.41276i | −0.864649 | + | 0.499206i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.0171i | 1.77495i | ||||||||
\(287\) | 1.56925 | + | 3.36293i | 0.0926299 | + | 0.198508i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.23418 | + | 14.2620i | −0.484363 | + | 0.838942i | ||||
\(290\) | −7.81681 | − | 32.2614i | −0.459019 | − | 1.89445i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.4747 | − | 19.8747i | 0.671505 | − | 1.16308i | ||||
\(293\) | − | 9.79171i | − | 0.572038i | −0.958224 | − | 0.286019i | \(-0.907668\pi\) | ||
0.958224 | − | 0.286019i | \(-0.0923321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.97370 | − | 13.5190i | 0.231358 | − | 0.787104i | ||||
\(296\) | 1.78249 | + | 1.02912i | 0.103605 | + | 0.0598163i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 39.0209 | − | 22.5287i | 2.26042 | − | 1.30506i | ||||
\(299\) | 11.8333 | − | 20.4959i | 0.684337 | − | 1.18531i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4041 | − | 7.18804i | 0.887878 | − | 0.414312i | ||||
\(302\) | −34.6448 | −1.99359 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −31.1140 | + | 17.9637i | −1.78451 | + | 1.03029i | ||||
\(305\) | −1.24912 | − | 5.15533i | −0.0715242 | − | 0.295193i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4778 | −1.45410 | −0.727048 | − | 0.686586i | \(-0.759108\pi\) | ||||
−0.727048 | + | 0.686586i | \(0.759108\pi\) | |||||||
\(308\) | 1.23174 | − | 14.1220i | 0.0701847 | − | 0.804677i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.42536 | + | 4.21717i | −0.251343 | + | 0.239519i | ||||
\(311\) | 5.05422 | + | 8.75417i | 0.286599 | + | 0.496404i | 0.972996 | − | 0.230824i | \(-0.0741420\pi\) |
−0.686397 | + | 0.727227i | \(0.740809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7375 | − | 20.3300i | 0.663445 | − | 1.14912i | −0.316260 | − | 0.948673i | \(-0.602427\pi\) |
0.979705 | − | 0.200447i | \(-0.0642395\pi\) | |||||||
\(314\) | −4.75329 | −0.268244 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.60790 | 0.371724 | ||||||||
\(317\) | −15.7156 | + | 27.2202i | −0.882677 | + | 1.52884i | −0.0343235 | + | 0.999411i | \(0.510928\pi\) |
−0.848353 | + | 0.529430i | \(0.822406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5216 | − | 21.6881i | −0.701077 | − | 1.21430i | ||||
\(320\) | −7.85064 | − | 8.23820i | −0.438864 | − | 0.460529i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.1284 | + | 20.1888i | −0.787343 | + | 1.12508i | ||||
\(323\) | −5.73943 | −0.319351 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.17039 | − | 24.2791i | 0.0649218 | − | 1.34676i | ||||
\(326\) | −6.52412 | + | 3.76670i | −0.361337 | + | 0.208618i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.912047 | 0.0503593 | ||||||||
\(329\) | −1.11969 | + | 12.8374i | −0.0617304 | + | 0.707747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.589214 | − | 1.02055i | 0.0323861 | − | 0.0560944i | −0.849378 | − | 0.527785i | \(-0.823023\pi\) |
0.881764 | + | 0.471691i | \(0.156356\pi\) | |||||||
\(332\) | −6.02700 | + | 3.47969i | −0.330774 | + | 0.190973i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.81156 | − | 5.08736i | −0.482147 | − | 0.278368i | ||||
\(335\) | −23.8685 | − | 7.01580i | −1.30408 | − | 0.383314i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.92868i | 0.214009i | 0.994259 | + | 0.107004i | \(0.0341259\pi\) | ||||
−0.994259 | + | 0.107004i | \(0.965874\pi\) | |||||||
\(338\) | 10.1720 | − | 17.6185i | 0.553285 | − | 0.958318i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.637377 | − | 2.63057i | −0.0345666 | − | 0.142663i | ||||
\(341\) | −2.30591 | + | 3.99395i | −0.124872 | + | 0.216285i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8930 | − | 4.77914i | −0.966132 | − | 0.258049i | ||||
\(344\) | − | 4.17768i | − | 0.225245i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3517 | + | 7.13126i | −0.664032 | + | 0.383379i | ||||
\(347\) | 2.41532 | + | 4.18346i | 0.129661 | + | 0.224580i | 0.923545 | − | 0.383489i | \(-0.125278\pi\) |
−0.793884 | + | 0.608069i | \(0.791944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.0461i | − | 0.858927i | −0.903084 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903084 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(350\) | −3.41053 | + | 25.0777i | −0.182300 | + | 1.34046i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.7714 | − | 11.9924i | −1.10712 | − | 0.639195i | ||||
\(353\) | 5.09305 | − | 2.94047i | 0.271075 | − | 0.156505i | −0.358301 | − | 0.933606i | \(-0.616644\pi\) |
0.629376 | + | 0.777101i | \(0.283310\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.4063 | − | 15.6344i | 0.870755 | − | 0.829790i | ||||
\(356\) | 18.7153 | 0.991909 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.4582i | 1.34551i | ||||||||
\(359\) | −7.00295 | − | 4.04315i | −0.369601 | − | 0.213389i | 0.303683 | − | 0.952773i | \(-0.401784\pi\) |
−0.673284 | + | 0.739384i | \(0.735117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.4802 | + | 37.2048i | 1.13054 | + | 1.95815i | ||||
\(362\) | −16.4990 | − | 9.52569i | −0.867167 | − | 0.500659i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.2429 | + | 17.4945i | −0.641700 | + | 0.916961i | ||||
\(365\) | −8.71711 | + | 29.6566i | −0.456275 | + | 1.55230i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.28484 | − | 16.0818i | −0.484665 | − | 0.839464i | 0.515180 | − | 0.857082i | \(-0.327725\pi\) |
−0.999845 | + | 0.0176181i | \(0.994392\pi\) | |||||||
\(368\) | 11.1098 | + | 19.2428i | 0.579139 | + | 1.00310i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.9916 | + | 3.81870i | 0.675404 | + | 0.198525i | ||||
\(371\) | −2.30801 | + | 3.29805i | −0.119826 | + | 0.171226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28930 | + | 1.32173i | 0.118536 | + | 0.0684365i | 0.558095 | − | 0.829777i | \(-0.311532\pi\) |
−0.439560 | + | 0.898213i | \(0.644866\pi\) | |||||||
\(374\) | −2.25104 | − | 3.89892i | −0.116399 | − | 0.201608i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.74266 | + | 1.58348i | 0.141442 | + | 0.0816617i | ||||
\(377\) | 37.7229i | 1.94283i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8582 | −1.22551 | −0.612756 | − | 0.790272i | \(-0.709939\pi\) | ||||
−0.612756 | + | 0.790272i | \(0.709939\pi\) | |||||||
\(380\) | −21.1533 | + | 20.1582i | −1.08514 | + | 1.03409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.7767 | − | 23.5425i | 2.08632 | − | 1.20454i | ||||
\(383\) | 9.62590 | + | 5.55752i | 0.491861 | + | 0.283976i | 0.725346 | − | 0.688384i | \(-0.241680\pi\) |
−0.233485 | + | 0.972360i | \(0.575013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.86679 | + | 18.8771i | 0.146105 | + | 0.962068i | ||||
\(386\) | − | 23.9416i | − | 1.21860i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.83765 | − | 3.18291i | −0.0932928 | − | 0.161588i | ||||
\(389\) | 10.8957 | − | 6.29064i | 0.552434 | − | 0.318948i | −0.197669 | − | 0.980269i | \(-0.563337\pi\) |
0.750103 | + | 0.661321i | \(0.230004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.54961i | 0.179512i | ||||||||
\(392\) | −2.92388 | + | 3.48831i | −0.147678 | + | 0.176186i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.0152 | − | 26.0070i | 0.756453 | − | 1.31021i | ||||
\(395\) | −8.65008 | + | 2.09588i | −0.435233 | + | 0.105455i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.3154 | + | 24.7951i | −0.718471 | + | 1.24443i | 0.243134 | + | 0.969993i | \(0.421825\pi\) |
−0.961605 | + | 0.274436i | \(0.911509\pi\) | |||||||
\(398\) | − | 37.8722i | − | 1.89836i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1914 | + | 12.3490i | 0.959569 | + | 0.617449i | ||||
\(401\) | −10.2994 | − | 5.94639i | −0.514330 | − | 0.296948i | 0.220282 | − | 0.975436i | \(-0.429302\pi\) |
−0.734612 | + | 0.678488i | \(0.762636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.01612 | − | 3.47341i | 0.299684 | − | 0.173023i | ||||
\(404\) | 9.71345 | − | 16.8242i | 0.483262 | − | 0.837035i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.41280 | − | 39.1281i | 0.169374 | − | 1.94190i | ||||
\(407\) | 10.2160 | 0.506386 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4855 | + | 7.20852i | −0.617369 | + | 0.356438i | −0.775844 | − | 0.630925i | \(-0.782676\pi\) |
0.158475 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(410\) | 5.83166 | − | 1.41299i | 0.288005 | − | 0.0697826i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.971605 | −0.0478675 | ||||||||
\(413\) | 9.55934 | − | 13.6599i | 0.470384 | − | 0.672159i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.78596 | − | 6.46672i | 0.333110 | − | 0.317439i | ||||
\(416\) | 18.0642 | + | 31.2881i | 0.885669 | + | 1.53402i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −24.3012 | + | 42.0909i | −1.18861 | + | 2.05874i | ||||
\(419\) | 34.9400 | 1.70693 | 0.853466 | − | 0.521149i | \(-0.174496\pi\) | ||||
0.853466 | + | 0.521149i | \(0.174496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8515 | 1.16245 | 0.581226 | − | 0.813742i | \(-0.302573\pi\) | ||||
0.581226 | + | 0.813742i | \(0.302573\pi\) | |||||||
\(422\) | 11.0808 | − | 19.1925i | 0.539405 | − | 0.934277i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.494655 | + | 0.856767i | 0.0240225 | + | 0.0416083i | ||||
\(425\) | 1.66872 | + | 3.24139i | 0.0809447 | + | 0.157230i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.545360 | − | 6.25262i | 0.0263918 | − | 0.302586i | ||||
\(428\) | −2.80917 | −0.135786 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.47228 | − | 26.7123i | −0.312121 | − | 1.28818i | ||||
\(431\) | 7.06551 | − | 4.07928i | 0.340334 | − | 0.196492i | −0.320086 | − | 0.947389i | \(-0.603712\pi\) |
0.660420 | + | 0.750897i | \(0.270378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2667 | 1.21424 | 0.607121 | − | 0.794610i | \(-0.292324\pi\) | ||||
0.607121 | + | 0.794610i | \(0.292324\pi\) | |||||||
\(434\) | −6.55447 | + | 3.05852i | −0.314625 | + | 0.146814i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.1251 | − | 19.2693i | 0.532798 | − | 0.922832i | ||||
\(437\) | 33.1861 | − | 19.1600i | 1.58751 | − | 0.916547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.688243 | − | 0.397357i | −0.0328480 | − | 0.0189648i | 0.483486 | − | 0.875352i | \(-0.339370\pi\) |
−0.516334 | + | 0.856387i | \(0.672704\pi\) | |||||||
\(440\) | 4.50208 | + | 1.32332i | 0.214628 | + | 0.0630868i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.78152i | 0.322564i | ||||||||
\(443\) | −11.3244 | + | 19.6145i | −0.538040 | + | 0.931913i | 0.460970 | + | 0.887416i | \(0.347502\pi\) |
−0.999010 | + | 0.0444966i | \(0.985832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.4993 | + | 5.93609i | −1.16138 | + | 0.281398i | ||||
\(446\) | −23.0841 | + | 39.9828i | −1.09306 | + | 1.89324i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.69371 | − | 12.2017i | −0.269002 | − | 0.576478i | ||||
\(449\) | 2.15664i | 0.101778i | 0.998704 | + | 0.0508891i | \(0.0162055\pi\) | ||||
−0.998704 | + | 0.0508891i | \(0.983794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.92041 | − | 2.26345i | 0.184605 | − | 0.106582i | ||||
\(452\) | 11.7976 | + | 20.4340i | 0.554913 | + | 0.961137i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 19.4927i | − | 0.914836i | ||||||
\(455\) | 10.4777 | − | 26.7844i | 0.491200 | − | 1.25567i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.74004 | + | 2.73666i | 0.221730 | + | 0.128016i | 0.606751 | − | 0.794892i | \(-0.292473\pi\) |
−0.385021 | + | 0.922908i | \(0.625806\pi\) | |||||||
\(458\) | 43.4998 | − | 25.1146i | 2.03261 | − | 1.17353i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.4670 | + | 13.0825i | 0.581278 | + | 0.609974i | ||||
\(461\) | 10.1084 | 0.470797 | 0.235399 | − | 0.971899i | \(-0.424360\pi\) | ||||
0.235399 | + | 0.971899i | \(0.424360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0455i | 0.559800i | 0.960029 | + | 0.279900i | \(0.0903014\pi\) | ||||
−0.960029 | + | 0.279900i | \(0.909699\pi\) | |||||||
\(464\) | −30.6716 | − | 17.7083i | −1.42389 | − | 0.822086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5946 | − | 30.4747i | −0.815052 | − | 1.41171i | ||||
\(467\) | −17.2622 | − | 9.96636i | −0.798801 | − | 0.461188i | 0.0442505 | − | 0.999020i | \(-0.485910\pi\) |
−0.843052 | + | 0.537832i | \(0.819243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.1173 | − | 16.8776i | −1.11363 | − | 0.779335i | ||||
\(470\) | 19.9899 | + | 5.87574i | 0.922066 | + | 0.271028i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.04876 | − | 3.54856i | −0.0943020 | − | 0.163336i | ||||
\(473\) | −10.3679 | − | 17.9577i | −0.476715 | − | 0.825694i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.2971 | − | 33.0975i | 0.977176 | − | 1.51862i | ||||
\(476\) | 0.278277 | − | 3.19048i | 0.0127548 | − | 0.146235i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.59274 | − | 0.919569i | −0.0728503 | − | 0.0420601i | ||||
\(479\) | −9.69290 | − | 16.7886i | −0.442880 | − | 0.767091i | 0.555022 | − | 0.831836i | \(-0.312710\pi\) |
−0.997902 | + | 0.0647451i | \(0.979377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3267 | − | 7.69419i | −0.607646 | − | 0.350825i | ||||
\(482\) | 12.4556i | 0.567337i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.969293 | 0.0440588 | ||||||||
\(485\) | 3.41513 | + | 3.58373i | 0.155073 | + | 0.162729i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.60056 | + | 0.924082i | −0.0725282 | + | 0.0418742i | −0.535826 | − | 0.844329i | \(-0.680000\pi\) |
0.463297 | + | 0.886203i | \(0.346666\pi\) | |||||||
\(488\) | −1.33585 | − | 0.771256i | −0.0604713 | − | 0.0349131i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.2912 | + | 26.8342i | −0.600433 | + | 1.21225i | ||||
\(491\) | − | 25.4836i | − | 1.15006i | −0.818133 | − | 0.575030i | \(-0.804991\pi\) | ||
0.818133 | − | 0.575030i | \(-0.195009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.82892 | − | 4.89983i | −0.127408 | − | 0.220677i | ||||
\(494\) | 63.4019 | − | 36.6051i | 2.85259 | − | 1.64694i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.52209i | 0.292851i | ||||||||
\(497\) | 24.2996 | − | 11.3390i | 1.08999 | − | 0.508621i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1142 | − | 22.7144i | 0.587072 | − | 1.01684i | −0.407542 | − | 0.913187i | \(-0.633614\pi\) |
0.994614 | − | 0.103652i | \(-0.0330527\pi\) | |||||||
\(500\) | 17.5347 | + | 6.08558i | 0.784177 | + | 0.272155i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.93711 | + | 3.35518i | −0.0864576 | + | 0.149749i | ||||
\(503\) | − | 4.25713i | − | 0.189816i | −0.995486 | − | 0.0949081i | \(-0.969744\pi\) | ||
0.995486 | − | 0.0949081i | \(-0.0302557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.37914 | + | 25.1046i | −0.328367 | + | 1.11714i | ||||
\(506\) | 26.0316 | + | 15.0293i | 1.15724 | + | 0.668135i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.00415 | − | 1.73445i | 0.133288 | − | 0.0769537i | ||||
\(509\) | 9.55960 | − | 16.5577i | 0.423722 | − | 0.733907i | −0.572578 | − | 0.819850i | \(-0.694057\pi\) |
0.996300 | + | 0.0859425i | \(0.0273901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.9704 | + | 29.9657i | −0.927674 | + | 1.32561i | ||||
\(512\) | −27.9839 | −1.23672 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.1381 | − | 17.4002i | 1.32933 | − | 0.767492i | ||||
\(515\) | 1.27188 | − | 0.308172i | 0.0560457 | − | 0.0135797i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7190 | 0.691322 | ||||||||
\(518\) | 13.1271 | + | 9.18648i | 0.576771 | + | 0.403631i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.87630 | − | 5.11703i | −0.213840 | − | 0.224397i | ||||
\(521\) | −11.4068 | − | 19.7571i | −0.499739 | − | 0.865573i | 0.500261 | − | 0.865875i | \(-0.333237\pi\) |
−1.00000 | 0.000301478i | \(0.999904\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.56468 | − | 2.71011i | 0.0684188 | − | 0.118505i | −0.829787 | − | 0.558081i | \(-0.811538\pi\) |
0.898205 | + | 0.439576i | \(0.144871\pi\) | |||||||
\(524\) | −18.6014 | −0.812604 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.4224 | 1.63169 | ||||||||
\(527\) | −0.520956 | + | 0.902322i | −0.0226932 | + | 0.0393058i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.349692 | − | 0.605685i | −0.0152040 | − | 0.0263341i | ||||
\(530\) | 4.49019 | + | 4.71186i | 0.195041 | + | 0.204670i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −31.3306 | + | 14.6198i | −1.35835 | + | 0.633849i | ||||
\(533\) | −6.81890 | −0.295359 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.67735 | − | 0.891008i | 0.158986 | − | 0.0385216i | ||||
\(536\) | −6.26520 | + | 3.61722i | −0.270616 | + | 0.156240i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.83112 | 0.380737 | ||||||||
\(539\) | −3.91121 | + | 22.2507i | −0.168468 | + | 0.958405i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2308 | − | 19.4524i | 0.482852 | − | 0.836323i | −0.516955 | − | 0.856013i | \(-0.672934\pi\) |
0.999806 | + | 0.0196894i | \(0.00626775\pi\) | |||||||
\(542\) | −17.8622 | + | 10.3127i | −0.767245 | + | 0.442969i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.69271 | − | 2.70934i | −0.201198 | − | 0.116162i | ||||
\(545\) | −8.45157 | + | 28.7532i | −0.362026 | + | 1.23165i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4567i | 0.447097i | 0.974693 | + | 0.223549i | \(0.0717642\pi\) | ||||
−0.974693 | + | 0.223549i | \(0.928236\pi\) | |||||||
\(548\) | −5.84355 | + | 10.1213i | −0.249624 | + | 0.432362i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.8366 | + | 1.48650i | 1.31488 | + | 0.0633848i | ||||
\(551\) | −30.5397 | + | 52.8963i | −1.30104 | + | 2.25346i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.4912 | − | 0.915056i | −0.446133 | − | 0.0389122i | ||||
\(554\) | 39.2324i | 1.66683i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.28620 | + | 5.36139i | −0.393823 | + | 0.227374i | ||||
\(557\) | −15.6239 | − | 27.0614i | −0.662006 | − | 1.14663i | −0.980088 | − | 0.198564i | \(-0.936372\pi\) |
0.318082 | − | 0.948063i | \(-0.396961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.2344i | 1.32107i | ||||||||
\(560\) | 16.8592 | + | 21.0925i | 0.712433 | + | 0.891323i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.18408 | + | 0.683630i | 0.0499475 | + | 0.0288372i | ||||
\(563\) | −25.8689 | + | 14.9354i | −1.09024 | + | 0.629452i | −0.933641 | − | 0.358210i | \(-0.883387\pi\) |
−0.156601 | + | 0.987662i | \(0.550054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.9249 | − | 23.0073i | −0.922388 | − | 0.967923i | ||||
\(566\) | 53.6100 | 2.25340 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.59019i | − | 0.276518i | ||||||
\(569\) | −25.0218 | − | 14.4464i | −1.04897 | − | 0.605623i | −0.126608 | − | 0.991953i | \(-0.540409\pi\) |
−0.922361 | + | 0.386330i | \(0.873743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.68844 | + | 6.38856i | 0.154356 | + | 0.267353i | 0.932824 | − | 0.360331i | \(-0.117336\pi\) |
−0.778468 | + | 0.627684i | \(0.784003\pi\) | |||||||
\(572\) | 22.5575 | + | 13.0236i | 0.943177 | + | 0.544543i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.07292 | + | 0.616907i | 0.295218 | + | 0.0257492i | ||||
\(575\) | −20.4695 | − | 13.1714i | −0.853636 | − | 0.549285i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.03785 | − | 15.6540i | −0.376251 | − | 0.651686i | 0.614263 | − | 0.789102i | \(-0.289454\pi\) |
−0.990513 | + | 0.137416i | \(0.956120\pi\) | |||||||
\(578\) | 15.7532 | + | 27.2853i | 0.655246 | + | 1.13492i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.6356 | − | 8.12308i | −1.14751 | − | 0.337292i | ||||
\(581\) | 10.0508 | − | 4.69002i | 0.416978 | − | 0.194575i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.25252 | + | 2.45519i | 0.176121 | + | 0.101684i | ||||
\(584\) | 4.49438 | + | 7.78450i | 0.185979 | + | 0.322125i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2232 | − | 9.36648i | −0.670175 | − | 0.386926i | ||||
\(587\) | − | 35.0876i | − | 1.44822i | −0.689684 | − | 0.724111i | \(-0.742250\pi\) | ||
0.689684 | − | 0.724111i | \(-0.257750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2480 | 0.463466 | ||||||||
\(590\) | −18.5975 | − | 19.5156i | −0.765647 | − | 0.803445i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.5119 | − | 7.22377i | 0.514238 | − | 0.296895i | ||||
\(593\) | 6.11233 | + | 3.52896i | 0.251003 | + | 0.144917i | 0.620224 | − | 0.784425i | \(-0.287042\pi\) |
−0.369220 | + | 0.929342i | \(0.620375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.647672 | + | 4.26476i | 0.0265520 | + | 0.174838i | ||||
\(596\) | − | 39.0984i | − | 1.60153i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.6388 | − | 39.2115i | −0.925769 | − | 1.60348i | ||||
\(599\) | −4.23198 | + | 2.44333i | −0.172914 | + | 0.0998318i | −0.583959 | − | 0.811783i | \(-0.698497\pi\) |
0.411045 | + | 0.911615i | \(0.365164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1905i | 1.47624i | 0.674669 | + | 0.738121i | \(0.264286\pi\) | ||||
−0.674669 | + | 0.738121i | \(0.735714\pi\) | |||||||
\(602\) | 2.82578 | − | 32.3979i | 0.115170 | − | 1.32044i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.0315 | + | 26.0352i | −0.611621 | + | 1.05936i | ||||
\(605\) | −1.26885 | + | 0.307439i | −0.0515863 | + | 0.0124992i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.46272 | − | 14.6579i | 0.343491 | − | 0.594944i | −0.641587 | − | 0.767050i | \(-0.721724\pi\) |
0.985078 | + | 0.172106i | \(0.0550572\pi\) | |||||||
\(608\) | 58.4976i | 2.37239i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.73638 | − | 2.86187i | −0.394214 | − | 0.115874i | ||||
\(611\) | −20.5055 | − | 11.8389i | −0.829563 | − | 0.478949i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.1128 | − | 9.30275i | 0.650792 | − | 0.375735i | −0.137968 | − | 0.990437i | \(-0.544057\pi\) |
0.788759 | + | 0.614702i | \(0.210724\pi\) | |||||||
\(614\) | −24.3714 | + | 42.2125i | −0.983549 | + | 1.70356i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.54901 | + | 3.18345i | 0.183285 | + | 0.128265i | ||||
\(617\) | −44.6022 | −1.79562 | −0.897809 | − | 0.440384i | \(-0.854842\pi\) | ||||
−0.897809 | + | 0.440384i | \(0.854842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.80175 | + | 5.65904i | −0.393966 | + | 0.227456i | −0.683877 | − | 0.729597i | \(-0.739707\pi\) |
0.289911 | + | 0.957053i | \(0.406374\pi\) | |||||||
\(620\) | 1.24912 | + | 5.15533i | 0.0501657 | + | 0.207043i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.3389 | 0.775420 | ||||||||
\(623\) | −29.7139 | − | 2.59168i | −1.19046 | − | 0.103833i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8841 | − | 2.40470i | −0.995363 | − | 0.0961880i | ||||
\(626\) | −22.4556 | − | 38.8942i | −0.897506 | − | 1.55453i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.06233 | + | 3.57205i | −0.0822957 | + | 0.142540i | ||||
\(629\) | 2.30801 | 0.0920265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.29394 | −0.250558 | −0.125279 | − | 0.992122i | \(-0.539983\pi\) | ||||
−0.125279 | + | 0.992122i | \(0.539983\pi\) | |||||||
\(632\) | −1.29409 | + | 2.24142i | −0.0514759 | + | 0.0891589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.0662 | + | 52.0763i | 1.19408 | + | 2.06821i | ||||
\(635\) | −3.38246 | + | 3.22333i | −0.134229 | + | 0.127914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.8604 | − | 26.0803i | 0.866139 | − | 1.03334i | ||||
\(638\) | −47.9114 | −1.89683 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1414 | − | 2.69952i | 0.440402 | − | 0.106708i | ||||
\(641\) | −0.511044 | + | 0.295051i | −0.0201850 | + | 0.0116538i | −0.510059 | − | 0.860140i | \(-0.670376\pi\) |
0.489874 | + | 0.871794i | \(0.337043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.7107 | −1.13224 | −0.566119 | − | 0.824323i | \(-0.691556\pi\) | ||||
−0.566119 | + | 0.824323i | \(0.691556\pi\) | |||||||
\(644\) | 9.04177 | + | 19.3767i | 0.356296 | + | 0.763549i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.49018 | + | 9.50928i | −0.216008 | + | 0.374138i | ||||
\(647\) | 10.3303 | − | 5.96420i | 0.406126 | − | 0.234477i | −0.282998 | − | 0.959121i | \(-0.591329\pi\) |
0.689124 | + | 0.724644i | \(0.257996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6131 | − | 10.1689i | −0.691375 | − | 0.399166i | ||||
\(650\) | −39.1069 | − | 25.1639i | −1.53390 | − | 0.987009i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.53708i | 0.256012i | ||||||||
\(653\) | 7.99647 | − | 13.8503i | 0.312926 | − | 0.542004i | −0.666068 | − | 0.745891i | \(-0.732024\pi\) |
0.978994 | + | 0.203887i | \(0.0653574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3501 | − | 5.89995i | 0.951439 | − | 0.230530i | ||||
\(656\) | 3.20100 | − | 5.54430i | 0.124978 | − | 0.216468i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.1983 | + | 14.1350i | 0.787412 | + | 0.551040i | ||||
\(659\) | 27.6958i | 1.07887i | 0.842026 | + | 0.539437i | \(0.181363\pi\) | ||||
−0.842026 | + | 0.539437i | \(0.818637\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.1490 | + | 20.8706i | −1.40603 | + | 0.811773i | −0.995003 | − | 0.0998487i | \(-0.968164\pi\) |
−0.411030 | + | 0.911622i | \(0.634831\pi\) | |||||||
\(662\) | −1.12725 | − | 1.95246i | −0.0438119 | − | 0.0758844i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.72583i | − | 0.105783i | ||||||
\(665\) | 36.3762 | − | 29.0755i | 1.41061 | − | 1.12750i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.7143 | + | 18.8876i | 1.26670 | + | 0.731330i | ||||
\(668\) | −7.64620 | + | 4.41453i | −0.295840 | + | 0.170803i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.4560 | + | 32.8350i | −1.33115 | + | 1.26853i | ||||
\(671\) | −7.65618 | −0.295564 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.91950i | 0.305274i | 0.988282 | + | 0.152637i | \(0.0487766\pi\) | ||||
−0.988282 | + | 0.152637i | \(0.951223\pi\) | |||||||
\(674\) | 6.50916 | + | 3.75807i | 0.250724 | + | 0.144755i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.82673 | − | 15.2883i | −0.339489 | − | 0.588013i | ||||
\(677\) | 9.23807 | + | 5.33360i | 0.355048 | + | 0.204987i | 0.666906 | − | 0.745142i | \(-0.267618\pi\) |
−0.311858 | + | 0.950129i | \(0.600951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.47684 | + | 5.30792i | 0.0950524 | + | 0.203699i | ||||
\(680\) | 1.01712 | + | 0.298967i | 0.0390048 | + | 0.0114649i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.41154 | + | 7.64100i | 0.168926 | + | 0.292589i | ||||
\(683\) | −1.10463 | − | 1.91327i | −0.0422674 | − | 0.0732093i | 0.844118 | − | 0.536158i | \(-0.180125\pi\) |
−0.886385 | + | 0.462948i | \(0.846791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.43924 | − | 15.1028i | 0.169615 | − | 0.577048i | ||||
\(686\) | −25.0342 | + | 25.0741i | −0.955810 | + | 0.957334i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.3960 | − | 14.6624i | −0.968212 | − | 0.558997i | ||||
\(689\) | −3.69828 | − | 6.40560i | −0.140893 | − | 0.244034i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.02498 | − | 4.63322i | −0.305284 | − | 0.176256i | 0.339530 | − | 0.940595i | \(-0.389732\pi\) |
−0.644814 | + | 0.764339i | \(0.723065\pi\) | |||||||
\(692\) | 12.3762i | 0.470474i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.24172 | 0.350811 | ||||||||
\(695\) | 10.4556 | − | 9.96372i | 0.396604 | − | 0.377945i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.885707 | − | 0.511363i | 0.0335486 | − | 0.0193693i | ||||
\(698\) | −26.5857 | − | 15.3492i | −1.00628 | − | 0.580977i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.3659 | + | 13.4435i | 0.656369 | + | 0.508117i | ||||
\(701\) | − | 6.99882i | − | 0.264342i | −0.991227 | − | 0.132171i | \(-0.957805\pi\) | ||
0.991227 | − | 0.132171i | \(-0.0421948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.4581 | − | 21.5781i | −0.469867 | − | 0.813834i | ||||
\(704\) | −14.2244 | + | 8.21247i | −0.536103 | + | 0.309519i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 11.2511i | − | 0.423441i | ||||||
\(707\) | −17.7517 | + | 25.3663i | −0.667620 | + | 0.953999i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5805 | − | 26.9863i | 0.585139 | − | 1.01349i | −0.409719 | − | 0.912212i | \(-0.634373\pi\) |
0.994858 | − | 0.101279i | \(-0.0322935\pi\) | |||||||
\(710\) | −10.2099 | − | 42.1379i | −0.383169 | − | 1.58141i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.66519 | + | 6.34829i | −0.137359 | + | 0.237912i | ||||
\(713\) | − | 6.95644i | − | 0.260521i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.6597 | − | 9.89379i | −1.25880 | − | 0.370007i | ||||
\(716\) | 19.1316 | + | 11.0456i | 0.714980 | + | 0.412794i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.3976 | + | 7.73514i | −0.499996 | + | 0.288673i | ||||
\(719\) | 4.53080 | − | 7.84758i | 0.168970 | − | 0.292665i | −0.769088 | − | 0.639143i | \(-0.779289\pi\) |
0.938058 | + | 0.346478i | \(0.112622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.54260 | + | 0.134547i | 0.0574493 | + | 0.00501079i | ||||
\(722\) | 82.1894 | 3.05877 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.3169 | + | 8.26587i | −0.532084 | + | 0.307199i | ||||
\(725\) | 38.7529 | + | 1.86811i | 1.43925 | + | 0.0693800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0567 | −0.632599 | −0.316300 | − | 0.948659i | \(-0.602441\pi\) | ||||
−0.316300 | + | 0.948659i | \(0.602441\pi\) | |||||||
\(728\) | −3.53656 | − | 7.57892i | −0.131074 | − | 0.280893i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 40.7974 | + | 42.8114i | 1.50998 | + | 1.58452i | ||||
\(731\) | −2.34233 | − | 4.05703i | −0.0866342 | − | 0.150055i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.98301 | − | 13.8270i | 0.294859 | − | 0.510711i | −0.680093 | − | 0.733126i | \(-0.738061\pi\) |
0.974952 | + | 0.222415i | \(0.0713939\pi\) | |||||||
\(734\) | −35.5265 | −1.31131 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.1784 | 1.33355 | ||||||||
\(737\) | −17.9539 | + | 31.0970i | −0.661340 | + | 1.14547i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.92575 | + | 11.9958i | 0.254768 | + | 0.441271i | 0.964832 | − | 0.262866i | \(-0.0846676\pi\) |
−0.710064 | + | 0.704137i | \(0.751334\pi\) | |||||||
\(740\) | 8.50644 | − | 8.10626i | 0.312703 | − | 0.297992i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.25653 | + | 6.97881i | 0.119551 | + | 0.256200i | ||||
\(743\) | 27.6801 | 1.01548 | 0.507741 | − | 0.861510i | \(-0.330481\pi\) | ||||
0.507741 | + | 0.861510i | \(0.330481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4012 | + | 51.1819i | 0.454344 | + | 1.87516i | ||||
\(746\) | 4.37976 | − | 2.52866i | 0.160355 | − | 0.0925807i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.90666 | −0.142842 | ||||||||
\(749\) | 4.46006 | + | 0.389011i | 0.162967 | + | 0.0142142i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.6666 | + | 28.8674i | −0.608173 | + | 1.05339i | 0.383368 | + | 0.923596i | \(0.374764\pi\) |
−0.991541 | + | 0.129791i | \(0.958569\pi\) | |||||||
\(752\) | 19.2518 | − | 11.1150i | 0.702041 | − | 0.405324i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 62.5005 | + | 36.0847i | 2.27613 | + | 1.31413i | ||||
\(755\) | 11.4191 | − | 38.8491i | 0.415585 | − | 1.41386i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1442i | 0.368697i | 0.982861 | + | 0.184348i | \(0.0590175\pi\) | ||||
−0.982861 | + | 0.184348i | \(0.940983\pi\) | |||||||
\(758\) | −22.8221 | + | 39.5290i | −0.828935 | + | 1.43576i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.69507 | − | 11.1230i | −0.0977605 | − | 0.403475i | ||||
\(761\) | −7.35057 | + | 12.7316i | −0.266458 | + | 0.461519i | −0.967945 | − | 0.251164i | \(-0.919187\pi\) |
0.701487 | + | 0.712683i | \(0.252520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.3316 | + | 29.0529i | −0.736052 | + | 1.05179i | ||||
\(764\) | − | 40.8577i | − | 1.47818i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4157 | − | 10.6323i | 0.665388 | − | 0.384162i | ||||
\(767\) | 15.3176 | + | 26.5308i | 0.553085 | + | 0.957971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4992i | 0.811340i | 0.914020 | + | 0.405670i | \(0.132962\pi\) | ||||
−0.914020 | + | 0.405670i | \(0.867038\pi\) | |||||||
\(770\) | 34.0185 | + | 13.3075i | 1.22594 | + | 0.479571i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.9919 | − | 10.3876i | −0.647542 | − | 0.373859i | ||||
\(773\) | −18.4057 | + | 10.6266i | −0.662008 | + | 0.382211i | −0.793042 | − | 0.609167i | \(-0.791504\pi\) |
0.131034 | + | 0.991378i | \(0.458170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.27032 | − | 6.35239i | −0.117473 | − | 0.228185i | ||||
\(776\) | 1.43954 | 0.0516764 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 24.0698i | − | 0.862945i | ||||||
\(779\) | −9.56170 | − | 5.52045i | −0.342583 | − | 0.197791i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.3550 | − | 28.3278i | −0.585229 | − | 1.01365i | ||||
\(782\) | 5.88111 | + | 3.39546i | 0.210308 | + | 0.121421i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.9434 | + | 30.0171i | 0.390835 | + | 1.07204i | ||||
\(785\) | 1.56671 | − | 5.33012i | 0.0559183 | − | 0.190240i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.85952 | + | 13.6131i | 0.280162 | + | 0.485254i | 0.971424 | − | 0.237349i | \(-0.0762786\pi\) |
−0.691263 | + | 0.722603i | \(0.742945\pi\) | |||||||
\(788\) | −13.0293 | − | 22.5675i | −0.464151 | − | 0.803933i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.80190 | + | 16.3366i | −0.170844 | + | 0.581230i | ||||
\(791\) | −15.9011 | − | 34.0765i | −0.565379 | − | 1.21162i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.98750 | + | 5.76628i | 0.354666 | + | 0.204767i | ||||
\(794\) | 27.3875 | + | 47.4366i | 0.971946 | + | 1.68346i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −28.4605 | − | 16.4317i | −1.00876 | − | 0.582406i | ||||
\(797\) | − | 39.5812i | − | 1.40204i | −0.713143 | − | 0.701019i | \(-0.752729\pi\) | ||
0.713143 | − | 0.701019i | \(-0.247271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55128 | 0.125635 | ||||||||
\(800\) | 33.0369 | − | 17.0080i | 1.16803 | − | 0.601322i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.7043 | + | 11.3763i | −0.695784 | + | 0.401711i | ||||
\(803\) | 38.6380 | + | 22.3076i | 1.36350 | + | 0.787220i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.9820 | − | 22.4972i | −0.633783 | − | 0.792923i | ||||
\(806\) | − | 13.2903i | − | 0.468130i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.80455 | + | 6.58967i | 0.133843 | + | 0.231824i | ||||
\(809\) | −38.1053 | + | 22.0001i | −1.33971 | + | 0.773483i | −0.986764 | − | 0.162160i | \(-0.948154\pi\) |
−0.352947 | + | 0.935643i | \(0.614820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.9306i | 1.57773i | 0.614567 | + | 0.788864i | \(0.289331\pi\) | ||||
−0.614567 | + | 0.788864i | \(0.710669\pi\) | |||||||
\(812\) | −27.9237 | − | 19.5413i | −0.979929 | − | 0.685766i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.77230 | − | 16.9261i | 0.342519 | − | 0.593260i | ||||
\(815\) | −2.07342 | − | 8.55737i | −0.0726287 | − | 0.299752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.2867 | + | 43.7979i | −0.884671 | + | 1.53229i | ||||
\(818\) | 27.5819i | 0.964378i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.46835 | − | 4.99549i | 0.0512771 | − | 0.174450i | ||||
\(821\) | −13.1026 | − | 7.56481i | −0.457285 | − | 0.264014i | 0.253617 | − | 0.967305i | \(-0.418380\pi\) |
−0.710902 | + | 0.703291i | \(0.751713\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.3487 | + | 15.7898i | −0.953316 | + | 0.550397i | −0.894109 | − | 0.447848i | \(-0.852190\pi\) |
−0.0592066 | + | 0.998246i | \(0.518857\pi\) | |||||||
\(824\) | 0.190278 | − | 0.329571i | 0.00662865 | − | 0.0114812i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4879 | − | 28.9049i | −0.469305 | − | 1.00573i | ||||
\(827\) | 48.6368 | 1.69127 | 0.845633 | − | 0.533765i | \(-0.179223\pi\) | ||||
0.845633 | + | 0.533765i | \(0.179223\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.4900 | − | 23.3769i | 1.40628 | − | 0.811914i | 0.411249 | − | 0.911523i | \(-0.365093\pi\) |
0.995027 | + | 0.0996095i | \(0.0317594\pi\) | |||||||
\(830\) | −4.22301 | − | 17.4291i | −0.146583 | − | 0.604973i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.7410 | 0.857741 | ||||||||
\(833\) | −0.883629 | + | 5.02692i | −0.0306159 | + | 0.174173i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.60907 | − | 8.20406i | 0.297929 | − | 0.283913i | ||||
\(836\) | 21.0873 | + | 36.5242i | 0.729319 | + | 1.26322i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.4227 | − | 57.8898i | 1.15457 | − | 1.99977i | ||||
\(839\) | 29.1067 | 1.00488 | 0.502438 | − | 0.864613i | \(-0.332437\pi\) | ||||
0.502438 | + | 0.864613i | \(0.332437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.2110 | −1.07624 | ||||||||
\(842\) | 22.8157 | − | 39.5179i | 0.786281 | − | 1.36188i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.61532 | − | 16.6542i | −0.330973 | − | 0.573262i | ||||
\(845\) | 16.4038 | + | 17.2136i | 0.564307 | + | 0.592165i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.53893 | − | 0.134227i | −0.0528782 | − | 0.00461209i | ||||
\(848\) | 6.94434 | 0.238469 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.96668 | + | 0.335834i | 0.238955 | + | 0.0115190i | ||||
\(851\) | −13.3452 | + | 7.70485i | −0.457467 | + | 0.264119i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.4915 | 0.975531 | 0.487766 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487766 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(854\) | −9.83787 | − | 6.88466i | −0.336645 | − | 0.235588i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.550145 | − | 0.952879i | 0.0188036 | − | 0.0325687i | ||||
\(857\) | −35.1219 | + | 20.2776i | −1.19974 | + | 0.692670i | −0.960497 | − | 0.278290i | \(-0.910232\pi\) |
−0.239243 | + | 0.970960i | \(0.576899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.6686 | + | 18.8612i | 1.11464 | + | 0.643537i | 0.940027 | − | 0.341100i | \(-0.110800\pi\) |
0.174612 | + | 0.984637i | \(0.444133\pi\) | |||||||
\(860\) | −22.8821 | − | 6.72587i | −0.780274 | − | 0.229350i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 15.6085i | − | 0.531627i | ||||||
\(863\) | −12.8395 | + | 22.2387i | −0.437062 | + | 0.757014i | −0.997461 | − | 0.0712087i | \(-0.977314\pi\) |
0.560399 | + | 0.828223i | \(0.310648\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.92547 | − | 16.2011i | −0.133470 | − | 0.550855i | ||||
\(866\) | 24.1695 | − | 41.8627i | 0.821311 | − | 1.42255i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.545360 | + | 6.25262i | −0.0185107 | + | 0.212228i | ||||
\(869\) | 12.8463i | 0.435779i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.8417 | − | 27.0441i | 1.58717 | − | 0.916353i | ||||
\(872\) | 4.35747 | + | 7.54736i | 0.147563 | + | 0.255586i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 73.3117i | − | 2.47981i | ||||||
\(875\) | −26.9968 | − | 12.0902i | −0.912659 | − | 0.408722i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.4938 | − | 9.52270i | −0.556956 | − | 0.321559i | 0.194967 | − | 0.980810i | \(-0.437540\pi\) |
−0.751923 | + | 0.659251i | \(0.770873\pi\) | |||||||
\(878\) | −1.31671 | + | 0.760202i | −0.0444367 | + | 0.0256556i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.8453 | − | 22.7235i | 0.803826 | − | 0.766010i | ||||
\(881\) | 30.7115 | 1.03470 | 0.517349 | − | 0.855774i | \(-0.326919\pi\) | ||||
0.517349 | + | 0.855774i | \(0.326919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.8466i | − | 1.23999i | −0.784607 | − | 0.619993i | \(-0.787135\pi\) | ||
0.784607 | − | 0.619993i | \(-0.212865\pi\) | |||||||
\(884\) | 5.09624 | + | 2.94232i | 0.171405 | + | 0.0989608i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.6653 | + | 37.5254i | 0.727859 | + | 1.26069i | ||||
\(887\) | −29.3385 | − | 16.9386i | −0.985090 | − | 0.568742i | −0.0812870 | − | 0.996691i | \(-0.525903\pi\) |
−0.903803 | + | 0.427949i | \(0.859236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.00982 | + | 2.33774i | −0.168024 | + | 0.0784051i | ||||
\(890\) | −13.6002 | + | 46.2695i | −0.455881 | + | 1.55096i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0311 | + | 34.6949i | 0.670691 | + | 1.16167i | ||||
\(893\) | −19.1690 | − | 33.2017i | −0.641466 | − | 1.11105i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.5476 | − | 8.39116i | −0.954242 | − | 0.280486i | ||||
\(896\) | 13.5128 | + | 1.17860i | 0.451432 | + | 0.0393743i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.57319 | + | 2.06298i | 0.119239 | + | 0.0688427i | ||||
\(899\) | 5.54404 | + | 9.60257i | 0.184904 | + | 0.320264i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.960739 | + | 0.554683i | 0.0320068 | + | 0.0184792i | ||||
\(902\) | − | 8.66061i | − | 0.288367i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.24172 | −0.307375 | ||||||||
\(905\) | 16.1198 | − | 15.3615i | 0.535841 | − | 0.510632i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.923888 | + | 0.533407i | −0.0306772 | + | 0.0177115i | −0.515260 | − | 0.857034i | \(-0.672305\pi\) |
0.484583 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(908\) | −14.6485 | − | 8.45734i | −0.486129 | − | 0.280667i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −34.3546 | − | 42.9809i | −1.13884 | − | 1.42480i | ||||
\(911\) | 9.61157i | 0.318445i | 0.987243 | + | 0.159223i | \(0.0508988\pi\) | ||||
−0.987243 | + | 0.159223i | \(0.949101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.76477 | − | 11.7169i | −0.223881 | − | 0.387774i | ||||
\(914\) | 9.06839 | − | 5.23564i | 0.299956 | − | 0.173179i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 43.5862i | − | 1.44013i | ||||||
\(917\) | 29.5330 | + | 2.57590i | 0.975266 | + | 0.0850637i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.41594 | − | 5.91658i | 0.112681 | − | 0.195170i | −0.804169 | − | 0.594401i | \(-0.797389\pi\) |
0.916851 | + | 0.399231i | \(0.130723\pi\) | |||||||
\(920\) | −6.87915 | + | 1.66679i | −0.226799 | + | 0.0549526i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.66946 | − | 16.7480i | 0.318447 | − | 0.551566i | ||||
\(923\) | 49.2714i | 1.62179i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.56424 | + | 13.3096i | −0.281590 | + | 0.437616i | ||||
\(926\) | 19.9573 | + | 11.5224i | 0.655838 | + | 0.378648i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.9401 | + | 28.8330i | −1.63937 | + | 0.946488i | ||||
\(929\) | 26.9383 | − | 46.6585i | 0.883818 | − | 1.53082i | 0.0367547 | − | 0.999324i | \(-0.488298\pi\) |
0.847063 | − | 0.531493i | \(-0.178369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.7674 | − | 18.8730i | 1.69661 | − | 0.618536i | ||||
\(932\) | −30.5352 | −1.00021 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.0252 | + | 19.0671i | −1.08062 | + | 0.623894i | ||||
\(935\) | 5.11402 | − | 1.23911i | 0.167246 | − | 0.0405232i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6036 | −0.705759 | −0.352880 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352880 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(938\) | −51.0333 | + | 23.8137i | −1.66630 | + | 0.777546i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.0886 | − | 12.4729i | 0.426904 | − | 0.406821i | ||||
\(941\) | 29.1006 | + | 50.4038i | 0.948654 | + | 1.64312i | 0.748265 | + | 0.663400i | \(0.230887\pi\) |
0.200389 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.41418 | + | 5.91353i | −0.111181 | + | 0.192571i | ||||
\(944\) | −28.7621 | −0.936127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.6704 | −1.28980 | ||||||||
\(947\) | −10.2347 | + | 17.7271i | −0.332584 | + | 0.576053i | −0.983018 | − | 0.183510i | \(-0.941254\pi\) |
0.650434 | + | 0.759563i | \(0.274587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.6022 | − | 58.2007i | −1.09077 | − | 1.88927i | ||||
\(950\) | −34.4648 | − | 66.9458i | −1.11819 | − | 2.17201i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.02772 | + | 0.719212i | 0.0333087 | + | 0.0233098i | ||||
\(953\) | −10.4745 | −0.339303 | −0.169651 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169651 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.9592 | + | 53.4849i | 0.419349 | + | 1.73073i | ||||
\(956\) | −1.38209 | + | 0.797952i | −0.0447001 | + | 0.0258076i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.0879 | −1.19825 | ||||||||
\(959\) | 10.6793 | − | 15.2602i | 0.344852 | − | 0.492778i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.4790 | + | 25.0784i | −0.467066 | + | 0.808982i | ||||
\(962\) | −25.4960 | + | 14.7201i | −0.822023 | + | 0.474595i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.36026 | + | 5.40415i | 0.301474 | + | 0.174056i | ||||
\(965\) | 26.8470 | + | 7.89129i | 0.864236 | + | 0.254030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.1242i | − | 1.38678i | −0.720562 | − | 0.693391i | \(-0.756116\pi\) | ||
0.720562 | − | 0.693391i | \(-0.243884\pi\) | |||||||
\(968\) | −0.189825 | + | 0.328787i | −0.00610122 | + | 0.0105676i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.20446 | − | 2.23021i | 0.295537 | − | 0.0716076i | ||||
\(971\) | 4.17572 | − | 7.23256i | 0.134005 | − | 0.232104i | −0.791212 | − | 0.611542i | \(-0.790549\pi\) |
0.925217 | + | 0.379438i | \(0.123883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.4860 | − | 7.22623i | 0.496457 | − | 0.231662i | ||||
\(974\) | 3.53581i | 0.113295i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.37687 | + | 5.41374i | −0.300146 | + | 0.173290i | ||||
\(977\) | 13.4044 | + | 23.2171i | 0.428845 | + | 0.742781i | 0.996771 | − | 0.0802983i | \(-0.0255873\pi\) |
−0.567926 | + | 0.823080i | \(0.692254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.3840i | 1.16284i | ||||||||
\(980\) | 14.3990 | + | 21.6308i | 0.459958 | + | 0.690971i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.2221 | − | 24.3769i | −1.34736 | − | 0.777899i | ||||
\(983\) | 25.5109 | − | 14.7287i | 0.813671 | − | 0.469773i | −0.0345581 | − | 0.999403i | \(-0.511002\pi\) |
0.848229 | + | 0.529630i | \(0.177669\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2140 | + | 25.4094i | 0.771522 | + | 0.809610i | ||||
\(986\) | −10.8243 | −0.344714 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 63.5279i | − | 2.02109i | ||||||
\(989\) | 27.0873 | + | 15.6388i | 0.861325 | + | 0.497286i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.50334 | + | 4.33591i | 0.0795211 | + | 0.137735i | 0.903043 | − | 0.429549i | \(-0.141328\pi\) |
−0.823522 | + | 0.567284i | \(0.807994\pi\) | |||||||
\(992\) | 9.19667 | + | 5.30970i | 0.291995 | + | 0.168583i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.45760 | − | 51.1069i | 0.141386 | − | 1.62101i | ||||
\(995\) | 42.4681 | + | 12.4829i | 1.34633 | + | 0.395734i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.43960 | − | 7.68960i | −0.140603 | − | 0.243532i | 0.787121 | − | 0.616799i | \(-0.211571\pi\) |
−0.927724 | + | 0.373267i | \(0.878238\pi\) | |||||||
\(998\) | −25.0893 | − | 43.4560i | −0.794189 | − | 1.37558i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.bb.b.89.9 | yes | 24 | |
3.2 | odd | 2 | inner | 315.2.bb.b.89.4 | yes | 24 | |
5.2 | odd | 4 | 1575.2.bk.i.26.9 | 24 | |||
5.3 | odd | 4 | 1575.2.bk.i.26.3 | 24 | |||
5.4 | even | 2 | inner | 315.2.bb.b.89.3 | ✓ | 24 | |
7.2 | even | 3 | 2205.2.g.b.2204.7 | 24 | |||
7.3 | odd | 6 | inner | 315.2.bb.b.269.10 | yes | 24 | |
7.5 | odd | 6 | 2205.2.g.b.2204.8 | 24 | |||
15.2 | even | 4 | 1575.2.bk.i.26.4 | 24 | |||
15.8 | even | 4 | 1575.2.bk.i.26.10 | 24 | |||
15.14 | odd | 2 | inner | 315.2.bb.b.89.10 | yes | 24 | |
21.2 | odd | 6 | 2205.2.g.b.2204.17 | 24 | |||
21.5 | even | 6 | 2205.2.g.b.2204.18 | 24 | |||
21.17 | even | 6 | inner | 315.2.bb.b.269.3 | yes | 24 | |
35.3 | even | 12 | 1575.2.bk.i.1151.10 | 24 | |||
35.9 | even | 6 | 2205.2.g.b.2204.19 | 24 | |||
35.17 | even | 12 | 1575.2.bk.i.1151.4 | 24 | |||
35.19 | odd | 6 | 2205.2.g.b.2204.20 | 24 | |||
35.24 | odd | 6 | inner | 315.2.bb.b.269.4 | yes | 24 | |
105.17 | odd | 12 | 1575.2.bk.i.1151.9 | 24 | |||
105.38 | odd | 12 | 1575.2.bk.i.1151.3 | 24 | |||
105.44 | odd | 6 | 2205.2.g.b.2204.5 | 24 | |||
105.59 | even | 6 | inner | 315.2.bb.b.269.9 | yes | 24 | |
105.89 | even | 6 | 2205.2.g.b.2204.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.b.89.3 | ✓ | 24 | 5.4 | even | 2 | inner | |
315.2.bb.b.89.4 | yes | 24 | 3.2 | odd | 2 | inner | |
315.2.bb.b.89.9 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bb.b.89.10 | yes | 24 | 15.14 | odd | 2 | inner | |
315.2.bb.b.269.3 | yes | 24 | 21.17 | even | 6 | inner | |
315.2.bb.b.269.4 | yes | 24 | 35.24 | odd | 6 | inner | |
315.2.bb.b.269.9 | yes | 24 | 105.59 | even | 6 | inner | |
315.2.bb.b.269.10 | yes | 24 | 7.3 | odd | 6 | inner | |
1575.2.bk.i.26.3 | 24 | 5.3 | odd | 4 | |||
1575.2.bk.i.26.4 | 24 | 15.2 | even | 4 | |||
1575.2.bk.i.26.9 | 24 | 5.2 | odd | 4 | |||
1575.2.bk.i.26.10 | 24 | 15.8 | even | 4 | |||
1575.2.bk.i.1151.3 | 24 | 105.38 | odd | 12 | |||
1575.2.bk.i.1151.4 | 24 | 35.17 | even | 12 | |||
1575.2.bk.i.1151.9 | 24 | 105.17 | odd | 12 | |||
1575.2.bk.i.1151.10 | 24 | 35.3 | even | 12 | |||
2205.2.g.b.2204.5 | 24 | 105.44 | odd | 6 | |||
2205.2.g.b.2204.6 | 24 | 105.89 | even | 6 | |||
2205.2.g.b.2204.7 | 24 | 7.2 | even | 3 | |||
2205.2.g.b.2204.8 | 24 | 7.5 | odd | 6 | |||
2205.2.g.b.2204.17 | 24 | 21.2 | odd | 6 | |||
2205.2.g.b.2204.18 | 24 | 21.5 | even | 6 | |||
2205.2.g.b.2204.19 | 24 | 35.9 | even | 6 | |||
2205.2.g.b.2204.20 | 24 | 35.19 | odd | 6 |