Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.2 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.b.1187.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.42143 | − | 1.39801i | −1.08289 | − | 0.625209i | −0.151219 | − | 0.988500i | \(-0.548320\pi\) |
−0.931676 | + | 0.363291i | \(0.881653\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62875 | − | 0.299420i | −0.993576 | − | 0.113170i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.42143 | + | 1.39801i | −0.765722 | + | 0.442090i | ||||
\(11\) | 1.36985 | + | 3.02052i | 0.413024 | + | 0.910720i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.20191i | 0.888050i | 0.896015 | + | 0.444025i | \(0.146450\pi\) | ||||
−0.896015 | + | 0.444025i | \(0.853550\pi\) | |||||||
\(14\) | −1.57368 | + | 2.12686i | −0.420584 | + | 0.568427i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.05881 | − | 3.56596i | −0.499334 | − | 0.864872i | 0.500666 | − | 0.865641i | \(-0.333089\pi\) |
−1.00000 | 0.000768905i | \(0.999755\pi\) | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82770 | + | 1.05522i | 0.419304 | + | 0.242085i | 0.694779 | − | 0.719223i | \(-0.255502\pi\) |
−0.275476 | + | 0.961308i | \(0.588835\pi\) | |||||||
\(20\) | 2.79602i | 0.625209i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.30077 | + | 0.323937i | 0.703726 | + | 0.0690637i | ||||
\(23\) | −0.902766 | − | 0.521212i | −0.188240 | − | 0.108680i | 0.402919 | − | 0.915236i | \(-0.367996\pi\) |
−0.591158 | + | 0.806556i | \(0.701329\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.40887 | + | 2.44023i | 0.281773 | + | 0.488046i | ||||
\(26\) | 2.77293 | + | 1.60095i | 0.543817 | + | 0.313973i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.05507 | + | 2.42628i | 0.199390 | + | 0.458523i | ||||
\(29\) | 9.40956 | 1.74731 | 0.873655 | − | 0.486545i | \(-0.161743\pi\) | ||||
0.873655 | + | 0.486545i | \(0.161743\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.58777 | + | 6.21420i | 0.644383 | + | 1.11610i | 0.984444 | + | 0.175701i | \(0.0562191\pi\) |
−0.340061 | + | 0.940404i | \(0.610448\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.11761 | −0.706165 | ||||||||
\(35\) | 5.94674 | + | 4.40005i | 1.00518 | + | 0.743744i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.60502 | + | 7.97612i | −0.757060 | + | 1.31127i | 0.187284 | + | 0.982306i | \(0.440032\pi\) |
−0.944344 | + | 0.328961i | \(0.893302\pi\) | |||||||
\(38\) | 1.82770 | − | 1.05522i | 0.296492 | − | 0.171180i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.42143 | + | 1.39801i | 0.382861 | + | 0.221045i | ||||
\(41\) | −0.110771 | −0.0172995 | −0.00864977 | − | 0.999963i | \(-0.502753\pi\) | ||||
−0.00864977 | + | 0.999963i | \(0.502753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.20415i | 0.641127i | 0.947227 | + | 0.320564i | \(0.103872\pi\) | ||||
−0.947227 | + | 0.320564i | \(0.896128\pi\) | |||||||
\(44\) | 1.93092 | − | 2.69658i | 0.291097 | − | 0.406525i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.902766 | + | 0.521212i | −0.133106 | + | 0.0768485i | ||||
\(47\) | −7.27267 | − | 4.19888i | −1.06083 | − | 0.612469i | −0.135167 | − | 0.990823i | \(-0.543157\pi\) |
−0.925661 | + | 0.378353i | \(0.876490\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82070 | + | 1.57420i | 0.974385 | + | 0.224886i | ||||
\(50\) | 2.81773 | 0.398488 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.77293 | − | 1.60095i | 0.384537 | − | 0.222012i | ||||
\(53\) | 10.3301 | − | 5.96410i | 1.41895 | − | 0.819232i | 0.422745 | − | 0.906249i | \(-0.361067\pi\) |
0.996207 | + | 0.0870162i | \(0.0277332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.905736 | − | 9.22901i | 0.122129 | − | 1.24444i | ||||
\(56\) | 2.62875 | + | 0.299420i | 0.351282 | + | 0.0400117i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.70478 | − | 8.14891i | 0.617768 | − | 1.07000i | ||||
\(59\) | −6.34962 | + | 3.66595i | −0.826650 | + | 0.477266i | −0.852704 | − | 0.522394i | \(-0.825039\pi\) |
0.0260545 | + | 0.999661i | \(0.491706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.21987 | + | 5.32310i | 1.18048 | + | 0.681553i | 0.956126 | − | 0.292954i | \(-0.0946383\pi\) |
0.224357 | + | 0.974507i | \(0.427972\pi\) | |||||||
\(62\) | 7.17555 | 0.911295 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.47630 | − | 7.75318i | 0.555217 | − | 0.961664i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97143 | − | 6.87872i | −0.485188 | − | 0.840370i | 0.514667 | − | 0.857390i | \(-0.327915\pi\) |
−0.999855 | + | 0.0170201i | \(0.994582\pi\) | |||||||
\(68\) | −2.05881 | + | 3.56596i | −0.249667 | + | 0.432436i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.78392 | − | 2.95000i | 0.810834 | − | 0.352593i | ||||
\(71\) | 11.0925i | 1.31643i | 0.752828 | + | 0.658217i | \(0.228689\pi\) | ||||
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.46860 | + | 3.15730i | −0.640052 | + | 0.369534i | −0.784634 | − | 0.619959i | \(-0.787149\pi\) |
0.144583 | + | 0.989493i | \(0.453816\pi\) | |||||||
\(74\) | 4.60502 | + | 7.97612i | 0.535322 | + | 0.927205i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.11045i | − | 0.242085i | ||||||
\(77\) | −2.69658 | − | 8.35036i | −0.307304 | − | 0.951611i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4344 | + | 7.17899i | 1.39898 | + | 0.807700i | 0.994286 | − | 0.106753i | \(-0.0340455\pi\) |
0.404692 | + | 0.914453i | \(0.367379\pi\) | |||||||
\(80\) | 2.42143 | − | 1.39801i | 0.270724 | − | 0.156302i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.0553856 | + | 0.0959306i | −0.00611631 | + | 0.0105938i | ||||
\(83\) | 14.2335 | 1.56234 | 0.781168 | − | 0.624321i | \(-0.214624\pi\) | ||||
0.781168 | + | 0.624321i | \(0.214624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5129i | 1.24875i | ||||||||
\(86\) | 3.64090 | + | 2.10208i | 0.392609 | + | 0.226673i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.36985 | − | 3.02052i | −0.146026 | − | 0.321988i | ||||
\(89\) | −10.3472 | − | 5.97394i | −1.09680 | − | 0.633236i | −0.161419 | − | 0.986886i | \(-0.551607\pi\) |
−0.935378 | + | 0.353650i | \(0.884940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.958715 | − | 8.41703i | 0.100501 | − | 0.882344i | ||||
\(92\) | 1.04242i | 0.108680i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.27267 | + | 4.19888i | −0.750119 | + | 0.433081i | ||||
\(95\) | −2.95043 | − | 5.11029i | −0.302708 | − | 0.524305i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.6911 | −1.79626 | −0.898129 | − | 0.439733i | \(-0.855073\pi\) | ||||
−0.898129 | + | 0.439733i | \(0.855073\pi\) | |||||||
\(98\) | 4.77365 | − | 5.11979i | 0.482211 | − | 0.517177i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.40887 | − | 2.44023i | 0.140887 | − | 0.244023i | ||||
\(101\) | 0.117005 | + | 0.202659i | 0.0116425 | + | 0.0201653i | 0.871788 | − | 0.489883i | \(-0.162961\pi\) |
−0.860145 | + | 0.510049i | \(0.829627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.27192 | + | 10.8633i | −0.617991 | + | 1.07039i | 0.371861 | + | 0.928288i | \(0.378720\pi\) |
−0.989852 | + | 0.142103i | \(0.954614\pi\) | |||||||
\(104\) | − | 3.20191i | − | 0.313973i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.9282i | − | 1.15857i | ||||||
\(107\) | −6.54545 | + | 11.3370i | −0.632772 | + | 1.09599i | 0.354210 | + | 0.935166i | \(0.384750\pi\) |
−0.986982 | + | 0.160828i | \(0.948584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.63480 | + | 3.25325i | −0.539716 | + | 0.311605i | −0.744964 | − | 0.667105i | \(-0.767533\pi\) |
0.205248 | + | 0.978710i | \(0.434200\pi\) | |||||||
\(110\) | −7.53969 | − | 5.39890i | −0.718881 | − | 0.514765i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.57368 | − | 2.12686i | 0.148699 | − | 0.200969i | ||||
\(113\) | 0.871772i | 0.0820094i | 0.999159 | + | 0.0410047i | \(0.0130559\pi\) | ||||
−0.999159 | + | 0.0410047i | \(0.986944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45732 | + | 2.52415i | 0.135896 | + | 0.235378i | ||||
\(116\) | −4.70478 | − | 8.14891i | −0.436828 | − | 0.756608i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.33191i | 0.674957i | ||||||||
\(119\) | 4.34438 | + | 9.99047i | 0.398248 | + | 0.915825i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.24705 | + | 8.27528i | −0.658822 | + | 0.752299i | ||||
\(122\) | 9.21987 | − | 5.32310i | 0.834728 | − | 0.481931i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.58777 | − | 6.21420i | 0.322192 | − | 0.558052i | ||||
\(125\) | 6.10167i | 0.545750i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.15849i | 0.812685i | 0.913721 | + | 0.406342i | \(0.133196\pi\) | ||||
−0.913721 | + | 0.406342i | \(0.866804\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.47630 | − | 7.75318i | −0.392598 | − | 0.679999i | ||||
\(131\) | 3.87340 | − | 6.70892i | 0.338420 | − | 0.586161i | −0.645716 | − | 0.763578i | \(-0.723441\pi\) |
0.984136 | + | 0.177417i | \(0.0567741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.48862 | − | 3.32118i | −0.389213 | − | 0.287982i | ||||
\(134\) | −7.94287 | −0.686159 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.05881 | + | 3.56596i | 0.176541 | + | 0.305778i | ||||
\(137\) | 6.78091 | − | 3.91496i | 0.579333 | − | 0.334478i | −0.181536 | − | 0.983384i | \(-0.558107\pi\) |
0.760868 | + | 0.648907i | \(0.224773\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.11030i | 0.263812i | 0.991262 | + | 0.131906i | \(0.0421097\pi\) | ||||
−0.991262 | + | 0.131906i | \(0.957890\pi\) | |||||||
\(140\) | 0.837184 | − | 7.35005i | 0.0707550 | − | 0.621193i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.60636 | + | 5.54624i | 0.806148 | + | 0.465430i | ||||
\(143\) | −9.67142 | + | 4.38612i | −0.808765 | + | 0.366786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.7845 | − | 13.1547i | −1.89215 | − | 1.09243i | ||||
\(146\) | 6.31460i | 0.522600i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.21003 | 0.757060 | ||||||||
\(149\) | −4.08541 | + | 7.07613i | −0.334690 | + | 0.579699i | −0.983425 | − | 0.181314i | \(-0.941965\pi\) |
0.648736 | + | 0.761014i | \(0.275298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.93139 | + | 3.42449i | −0.482690 | + | 0.278681i | −0.721537 | − | 0.692376i | \(-0.756564\pi\) |
0.238847 | + | 0.971057i | \(0.423231\pi\) | |||||||
\(152\) | −1.82770 | − | 1.05522i | −0.148246 | − | 0.0855900i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.57991 | − | 1.83987i | −0.691389 | − | 0.148261i | ||||
\(155\) | − | 20.0630i | − | 1.61150i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.04332 | + | 7.00324i | 0.322692 | + | 0.558920i | 0.981043 | − | 0.193792i | \(-0.0620787\pi\) |
−0.658350 | + | 0.752712i | \(0.728745\pi\) | |||||||
\(158\) | 12.4344 | − | 7.17899i | 0.989226 | − | 0.571130i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.79602i | − | 0.221045i | ||||||
\(161\) | 2.21709 | + | 1.64044i | 0.174731 | + | 0.129285i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.682357 | + | 1.18188i | −0.0534463 | + | 0.0925717i | −0.891511 | − | 0.453000i | \(-0.850354\pi\) |
0.838064 | + | 0.545571i | \(0.183687\pi\) | |||||||
\(164\) | 0.0553856 | + | 0.0959306i | 0.00432489 | + | 0.00749092i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.11677 | − | 12.3266i | 0.552369 | − | 0.956731i | ||||
\(167\) | −7.34655 | −0.568493 | −0.284247 | − | 0.958751i | \(-0.591743\pi\) | ||||
−0.284247 | + | 0.958751i | \(0.591743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.74778 | 0.211368 | ||||||||
\(170\) | 9.97049 | + | 5.75647i | 0.764702 | + | 0.441501i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.64090 | − | 2.10208i | 0.277616 | − | 0.160282i | ||||
\(173\) | 0.327674 | − | 0.567548i | 0.0249126 | − | 0.0431498i | −0.853300 | − | 0.521420i | \(-0.825403\pi\) |
0.878213 | + | 0.478270i | \(0.158736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.97291 | − | 6.83660i | −0.224731 | − | 0.516799i | ||||
\(176\) | −3.30077 | − | 0.323937i | −0.248805 | − | 0.0244177i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.3472 | + | 5.97394i | −0.775553 | + | 0.447765i | ||||
\(179\) | −3.55106 | + | 2.05021i | −0.265419 | + | 0.153240i | −0.626804 | − | 0.779177i | \(-0.715637\pi\) |
0.361385 | + | 0.932417i | \(0.382304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0064 | −0.818102 | −0.409051 | − | 0.912511i | \(-0.634140\pi\) | ||||
−0.409051 | + | 0.912511i | \(0.634140\pi\) | |||||||
\(182\) | −6.81000 | − | 5.03879i | −0.504791 | − | 0.373500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.902766 | + | 0.521212i | 0.0665528 | + | 0.0384243i | ||||
\(185\) | 22.3014 | − | 12.8757i | 1.63963 | − | 0.946642i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.95079 | − | 11.1035i | 0.581419 | − | 0.811966i | ||||
\(188\) | 8.39776i | 0.612469i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.90086 | −0.428093 | ||||||||
\(191\) | 18.8331 | + | 10.8733i | 1.36271 | + | 0.786763i | 0.989984 | − | 0.141178i | \(-0.0450890\pi\) |
0.372728 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3131 | − | 11.1504i | 1.39019 | − | 0.802625i | 0.396852 | − | 0.917882i | \(-0.370102\pi\) |
0.993336 | + | 0.115257i | \(0.0367692\pi\) | |||||||
\(194\) | −8.84554 | + | 15.3209i | −0.635073 | + | 1.09998i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.04705 | − | 6.69400i | −0.146218 | − | 0.478143i | ||||
\(197\) | −11.0036 | −0.783972 | −0.391986 | − | 0.919971i | \(-0.628212\pi\) | ||||
−0.391986 | + | 0.919971i | \(0.628212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.22506 | − | 14.2462i | −0.583059 | − | 1.00989i | −0.995114 | − | 0.0987290i | \(-0.968522\pi\) |
0.412055 | − | 0.911159i | \(-0.364811\pi\) | |||||||
\(200\) | −1.40887 | − | 2.44023i | −0.0996219 | − | 0.172550i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.234010 | 0.0164649 | ||||||||
\(203\) | −24.7354 | − | 2.81741i | −1.73609 | − | 0.197743i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.268224 | + | 0.154859i | 0.0187336 | + | 0.0108158i | ||||
\(206\) | 6.27192 | + | 10.8633i | 0.436986 | + | 0.756881i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.77293 | − | 1.60095i | −0.192268 | − | 0.111006i | ||||
\(209\) | −0.683653 | + | 6.96610i | −0.0472893 | + | 0.481855i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.618822i | − | 0.0426015i | −0.999773 | − | 0.0213007i | \(-0.993219\pi\) | ||
0.999773 | − | 0.0213007i | \(-0.00678075\pi\) | |||||||
\(212\) | −10.3301 | − | 5.96410i | −0.709476 | − | 0.409616i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.54545 | + | 11.3370i | 0.447438 | + | 0.774985i | ||||
\(215\) | 5.87745 | − | 10.1800i | 0.400839 | − | 0.694273i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.57072 | − | 17.4099i | −0.513934 | − | 1.18186i | ||||
\(218\) | 6.50650i | 0.440676i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.44543 | + | 3.83012i | −0.569391 | + | 0.258226i | ||||
\(221\) | 11.4179 | − | 6.59211i | 0.768049 | − | 0.443433i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3553 | 0.693443 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(224\) | −1.05507 | − | 2.42628i | −0.0704949 | − | 0.162112i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.754977 | + | 0.435886i | 0.0502203 | + | 0.0289947i | ||||
\(227\) | −6.46564 | − | 11.1988i | −0.429140 | − | 0.743292i | 0.567657 | − | 0.823265i | \(-0.307850\pi\) |
−0.996797 | + | 0.0799731i | \(0.974517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.73849 | + | 4.74320i | −0.180964 | + | 0.313439i | −0.942209 | − | 0.335025i | \(-0.891255\pi\) |
0.761245 | + | 0.648465i | \(0.224589\pi\) | |||||||
\(230\) | 2.91464 | 0.192186 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.40956 | −0.617768 | ||||||||
\(233\) | −13.7588 | + | 23.8310i | −0.901372 | + | 1.56122i | −0.0756568 | + | 0.997134i | \(0.524105\pi\) |
−0.825715 | + | 0.564088i | \(0.809228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7402 | + | 20.3345i | 0.765843 | + | 1.32648i | ||||
\(236\) | 6.34962 | + | 3.66595i | 0.413325 | + | 0.238633i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.8242 | + | 1.23290i | 0.701628 | + | 0.0799167i | ||||
\(239\) | −13.3339 | −0.862499 | −0.431249 | − | 0.902233i | \(-0.641927\pi\) | ||||
−0.431249 | + | 0.902233i | \(0.641927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7035 | − | 9.06641i | 1.01155 | − | 0.584019i | 0.0999053 | − | 0.994997i | \(-0.468146\pi\) |
0.911645 | + | 0.410978i | \(0.134813\pi\) | |||||||
\(242\) | 3.54308 | + | 10.4138i | 0.227758 | + | 0.669422i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10.6462i | − | 0.681553i | ||||||
\(245\) | −14.3151 | − | 13.3472i | −0.914555 | − | 0.852722i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.37873 | + | 5.85213i | −0.214984 | + | 0.372362i | ||||
\(248\) | −3.58777 | − | 6.21420i | −0.227824 | − | 0.394602i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.28420 | + | 3.05083i | 0.334202 | + | 0.192952i | ||||
\(251\) | 18.5540i | 1.17112i | 0.810630 | + | 0.585559i | \(0.199125\pi\) | ||||
−0.810630 | + | 0.585559i | \(0.800875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.337680 | − | 3.44080i | 0.0212298 | − | 0.216321i | ||||
\(254\) | 7.93149 | + | 4.57925i | 0.497666 | + | 0.287327i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −23.4582 | − | 13.5436i | −1.46328 | − | 0.844826i | −0.464120 | − | 0.885773i | \(-0.653629\pi\) |
−0.999161 | + | 0.0409470i | \(0.986963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4937 | − | 19.5884i | 0.900593 | − | 1.21717i | ||||
\(260\) | −8.95260 | −0.555217 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.87340 | − | 6.70892i | −0.239299 | − | 0.414478i | ||||
\(263\) | 5.53418 | + | 9.58548i | 0.341252 | + | 0.591066i | 0.984665 | − | 0.174453i | \(-0.0558157\pi\) |
−0.643414 | + | 0.765519i | \(0.722482\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.3515 | −2.04877 | ||||||||
\(266\) | −5.12053 | + | 2.22667i | −0.313960 | + | 0.136526i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.97143 | + | 6.87872i | −0.242594 | + | 0.420185i | ||||
\(269\) | −8.44523 | + | 4.87586i | −0.514915 | + | 0.297286i | −0.734852 | − | 0.678228i | \(-0.762748\pi\) |
0.219937 | + | 0.975514i | \(0.429415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.91324 | − | 1.68196i | −0.176967 | − | 0.102172i | 0.408900 | − | 0.912579i | \(-0.365912\pi\) |
−0.585867 | + | 0.810407i | \(0.699246\pi\) | |||||||
\(272\) | 4.11761 | 0.249667 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 7.82992i | − | 0.473023i | ||||||
\(275\) | −5.44082 | + | 7.59824i | −0.328094 | + | 0.458191i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3722 | − | 8.29777i | 0.863539 | − | 0.498564i | −0.00165684 | − | 0.999999i | \(-0.500527\pi\) |
0.865196 | + | 0.501434i | \(0.167194\pi\) | |||||||
\(278\) | 2.69360 | + | 1.55515i | 0.161551 | + | 0.0932716i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.94674 | − | 4.40005i | −0.355386 | − | 0.262953i | ||||
\(281\) | −5.58641 | −0.333257 | −0.166629 | − | 0.986020i | \(-0.553288\pi\) | ||||
−0.166629 | + | 0.986020i | \(0.553288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.33852 | − | 1.35014i | 0.139010 | − | 0.0802577i | −0.428882 | − | 0.903361i | \(-0.641092\pi\) |
0.567892 | + | 0.823103i | \(0.307759\pi\) | |||||||
\(284\) | 9.60636 | − | 5.54624i | 0.570033 | − | 0.329109i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.03722 | + | 10.5688i | −0.0613320 | + | 0.624944i | ||||
\(287\) | 0.291190 | + | 0.0331671i | 0.0171884 | + | 0.00195779i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0226302 | − | 0.0391967i | 0.00133119 | − | 0.00230569i | ||||
\(290\) | −22.7845 | + | 13.1547i | −1.33795 | + | 0.772468i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.46860 | + | 3.15730i | 0.320026 | + | 0.184767i | ||||
\(293\) | −15.8185 | −0.924125 | −0.462062 | − | 0.886847i | \(-0.652890\pi\) | ||||
−0.462062 | + | 0.886847i | \(0.652890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.5002 | 1.19357 | ||||||||
\(296\) | 4.60502 | − | 7.97612i | 0.267661 | − | 0.463603i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.08541 | + | 7.07613i | 0.236661 | + | 0.409909i | ||||
\(299\) | 1.66887 | − | 2.89057i | 0.0965134 | − | 0.167166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.25881 | − | 11.0517i | 0.0725564 | − | 0.637008i | ||||
\(302\) | 6.84898i | 0.394115i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.82770 | + | 1.05522i | −0.104826 | + | 0.0605213i | ||||
\(305\) | −14.8835 | − | 25.7790i | −0.852226 | − | 1.47610i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.2813i | − | 0.700932i | −0.936575 | − | 0.350466i | \(-0.886023\pi\) | ||
0.936575 | − | 0.350466i | \(-0.113977\pi\) | |||||||
\(308\) | −5.88333 | + | 6.51049i | −0.335234 | + | 0.370969i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.3750 | − | 10.0315i | −0.986836 | − | 0.569750i | ||||
\(311\) | 17.6592 | − | 10.1956i | 1.00136 | − | 0.578137i | 0.0927112 | − | 0.995693i | \(-0.470447\pi\) |
0.908651 | + | 0.417556i | \(0.137113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62210 | − | 2.80957i | 0.0916867 | − | 0.158806i | −0.816534 | − | 0.577297i | \(-0.804108\pi\) |
0.908221 | + | 0.418491i | \(0.137441\pi\) | |||||||
\(314\) | 8.08665 | 0.456356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 14.3580i | − | 0.807700i | ||||||
\(317\) | −9.57584 | − | 5.52861i | −0.537833 | − | 0.310518i | 0.206368 | − | 0.978475i | \(-0.433836\pi\) |
−0.744200 | + | 0.667957i | \(0.767169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8896 | + | 28.4217i | 0.721681 | + | 1.59131i | ||||
\(320\) | −2.42143 | − | 1.39801i | −0.135362 | − | 0.0781512i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.52921 | − | 1.09983i | 0.140947 | − | 0.0612913i | ||||
\(323\) | − | 8.69001i | − | 0.483525i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.81339 | + | 4.51106i | −0.433409 | + | 0.250229i | ||||
\(326\) | 0.682357 | + | 1.18188i | 0.0377922 | + | 0.0654581i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.110771 | 0.00611631 | ||||||||
\(329\) | 17.8608 | + | 13.2154i | 0.984700 | + | 0.728589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.27038 | − | 12.5927i | 0.399616 | − | 0.692156i | −0.594062 | − | 0.804419i | \(-0.702477\pi\) |
0.993678 | + | 0.112263i | \(0.0358100\pi\) | |||||||
\(332\) | −7.11677 | − | 12.3266i | −0.390584 | − | 0.676511i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.67328 | + | 6.36230i | −0.200993 | + | 0.348130i | ||||
\(335\) | 22.2084i | 1.21338i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0460i | 1.09198i | 0.837793 | + | 0.545988i | \(0.183846\pi\) | ||||
−0.837793 | + | 0.545988i | \(0.816154\pi\) | |||||||
\(338\) | 1.37389 | − | 2.37965i | 0.0747299 | − | 0.129436i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.97049 | − | 5.75647i | 0.540726 | − | 0.312188i | ||||
\(341\) | −13.8554 | + | 19.3494i | −0.750313 | + | 1.04783i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4586 | − | 6.18044i | −0.942675 | − | 0.333713i | ||||
\(344\) | − | 4.20415i | − | 0.226673i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.327674 | − | 0.567548i | −0.0176158 | − | 0.0305115i | ||||
\(347\) | −6.04444 | − | 10.4693i | −0.324482 | − | 0.562020i | 0.656925 | − | 0.753956i | \(-0.271857\pi\) |
−0.981407 | + | 0.191936i | \(0.938523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.92511i | − | 0.263635i | −0.991274 | − | 0.131818i | \(-0.957919\pi\) | ||
0.991274 | − | 0.131818i | \(-0.0420813\pi\) | |||||||
\(350\) | −7.40713 | − | 0.843685i | −0.395928 | − | 0.0450969i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.93092 | + | 2.69658i | −0.102918 | + | 0.143728i | ||||
\(353\) | 8.28001 | − | 4.78047i | 0.440700 | − | 0.254438i | −0.263194 | − | 0.964743i | \(-0.584776\pi\) |
0.703895 | + | 0.710304i | \(0.251443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5074 | − | 26.8596i | 0.823047 | − | 1.42556i | ||||
\(356\) | 11.9479i | 0.633236i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.10041i | 0.216714i | ||||||||
\(359\) | 4.14103 | − | 7.17248i | 0.218555 | − | 0.378549i | −0.735811 | − | 0.677187i | \(-0.763199\pi\) |
0.954366 | + | 0.298638i | \(0.0965323\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.27300 | − | 12.5972i | −0.382790 | − | 0.663011i | ||||
\(362\) | −5.50322 | + | 9.53186i | −0.289243 | + | 0.500983i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.76872 | + | 3.37824i | −0.407191 | + | 0.177068i | ||||
\(365\) | 17.6558 | 0.924144 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.6919 | + | 32.3753i | 0.975710 | + | 1.68998i | 0.677572 | + | 0.735457i | \(0.263032\pi\) |
0.298138 | + | 0.954523i | \(0.403634\pi\) | |||||||
\(368\) | 0.902766 | − | 0.521212i | 0.0470599 | − | 0.0271701i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 25.7514i | − | 1.33875i | ||||||
\(371\) | −28.9411 | + | 12.5851i | −1.50255 | + | 0.653386i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6889 | + | 11.9447i | 1.07123 | + | 0.618475i | 0.928517 | − | 0.371289i | \(-0.121084\pi\) |
0.142713 | + | 0.989764i | \(0.454417\pi\) | |||||||
\(374\) | −5.64049 | − | 12.4373i | −0.291663 | − | 0.643119i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.27267 | + | 4.19888i | 0.375059 | + | 0.216541i | ||||
\(377\) | 30.1285i | 1.55170i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.9926 | 0.924217 | 0.462109 | − | 0.886823i | \(-0.347093\pi\) | ||||
0.462109 | + | 0.886823i | \(0.347093\pi\) | |||||||
\(380\) | −2.95043 | + | 5.11029i | −0.151354 | + | 0.262153i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.8331 | − | 10.8733i | 0.963583 | − | 0.556325i | ||||
\(383\) | 14.6369 | + | 8.45064i | 0.747913 | + | 0.431808i | 0.824939 | − | 0.565221i | \(-0.191209\pi\) |
−0.0770265 | + | 0.997029i | \(0.524543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.14431 | + | 23.9896i | −0.262178 | + | 1.22262i | ||||
\(386\) | − | 22.3009i | − | 1.13508i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.84554 | + | 15.3209i | 0.449064 | + | 0.777802i | ||||
\(389\) | −9.20118 | + | 5.31230i | −0.466518 | + | 0.269344i | −0.714781 | − | 0.699348i | \(-0.753474\pi\) |
0.248263 | + | 0.968693i | \(0.420140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.29230i | 0.217071i | ||||||||
\(392\) | −6.82070 | − | 1.57420i | −0.344497 | − | 0.0795092i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.50179 | + | 9.52937i | −0.277176 | + | 0.480083i | ||||
\(395\) | −20.0726 | − | 34.7668i | −1.00996 | − | 1.74931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4791 | − | 19.8824i | 0.576120 | − | 0.997870i | −0.419799 | − | 0.907617i | \(-0.637899\pi\) |
0.995919 | − | 0.0902525i | \(-0.0287674\pi\) | |||||||
\(398\) | −16.4501 | −0.824570 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.81773 | −0.140887 | ||||||||
\(401\) | −8.28001 | − | 4.78047i | −0.413484 | − | 0.238725i | 0.278802 | − | 0.960349i | \(-0.410063\pi\) |
−0.692286 | + | 0.721624i | \(0.743396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.8973 | + | 11.4877i | −0.991156 | + | 0.572244i | ||||
\(404\) | 0.117005 | − | 0.202659i | 0.00582123 | − | 0.0100827i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.8077 | + | 20.0128i | −0.734891 | + | 0.993218i | ||||
\(407\) | −30.4002 | − | 2.98347i | −1.50688 | − | 0.147885i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.3509 | + | 6.55346i | −0.561267 | + | 0.324048i | −0.753654 | − | 0.657271i | \(-0.771711\pi\) |
0.192387 | + | 0.981319i | \(0.438377\pi\) | |||||||
\(410\) | 0.268224 | − | 0.154859i | 0.0132466 | − | 0.00764795i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.5438 | 0.617991 | ||||||||
\(413\) | 17.7892 | − | 7.73569i | 0.875351 | − | 0.380648i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.4655 | − | 19.8987i | −1.69184 | − | 0.976786i | ||||
\(416\) | −2.77293 | + | 1.60095i | −0.135954 | + | 0.0784932i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.69099 | + | 4.07511i | 0.278356 | + | 0.199320i | ||||
\(419\) | 4.51379i | 0.220513i | 0.993903 | + | 0.110256i | \(0.0351672\pi\) | ||||
−0.993903 | + | 0.110256i | \(0.964833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.3188 | −1.81881 | −0.909403 | − | 0.415917i | \(-0.863461\pi\) | ||||
−0.909403 | + | 0.415917i | \(0.863461\pi\) | |||||||
\(422\) | −0.535916 | − | 0.309411i | −0.0260880 | − | 0.0150619i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.3301 | + | 5.96410i | −0.501675 | + | 0.289642i | ||||
\(425\) | 5.80117 | − | 10.0479i | 0.281398 | − | 0.487395i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.6429 | − | 16.7537i | −1.09577 | − | 0.810770i | ||||
\(428\) | 13.0909 | 0.632772 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.87745 | − | 10.1800i | −0.283436 | − | 0.490925i | ||||
\(431\) | 13.8494 | + | 23.9878i | 0.667100 | + | 1.15545i | 0.978711 | + | 0.205242i | \(0.0657981\pi\) |
−0.311611 | + | 0.950210i | \(0.600869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.18187 | 0.393196 | 0.196598 | − | 0.980484i | \(-0.437011\pi\) | ||||
0.196598 | + | 0.980484i | \(0.437011\pi\) | |||||||
\(434\) | −18.8627 | − | 2.14850i | −0.905441 | − | 0.103131i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.63480 | + | 3.25325i | 0.269858 | + | 0.155802i | ||||
\(437\) | −1.09999 | − | 1.90524i | −0.0526197 | − | 0.0911400i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.16163 | + | 0.670668i | 0.0554416 | + | 0.0320092i | 0.527465 | − | 0.849577i | \(-0.323143\pi\) |
−0.472023 | + | 0.881586i | \(0.656476\pi\) | |||||||
\(440\) | −0.905736 | + | 9.22901i | −0.0431793 | + | 0.439976i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 13.1842i | − | 0.627109i | ||||||
\(443\) | 23.5122 | + | 13.5748i | 1.11710 | + | 0.644958i | 0.940659 | − | 0.339354i | \(-0.110208\pi\) |
0.176441 | + | 0.984311i | \(0.443542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.7033 | + | 28.9309i | 0.791810 | + | 1.37146i | ||||
\(446\) | 5.17766 | − | 8.96797i | 0.245169 | − | 0.424646i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.62875 | − | 0.299420i | −0.124197 | − | 0.0141463i | ||||
\(449\) | − | 37.3766i | − | 1.76391i | −0.471334 | − | 0.881955i | \(-0.656227\pi\) | ||
0.471334 | − | 0.881955i | \(-0.343773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.151739 | − | 0.334586i | −0.00714513 | − | 0.0157550i | ||||
\(452\) | 0.754977 | − | 0.435886i | 0.0355111 | − | 0.0205024i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.9313 | −0.606895 | ||||||||
\(455\) | −14.0886 | + | 19.0409i | −0.660481 | + | 0.892652i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4149 | + | 11.7865i | 0.954967 | + | 0.551350i | 0.894620 | − | 0.446827i | \(-0.147446\pi\) |
0.0603464 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(458\) | 2.73849 | + | 4.74320i | 0.127961 | + | 0.221635i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.45732 | − | 2.52415i | 0.0679479 | − | 0.117689i | ||||
\(461\) | −38.3140 | −1.78446 | −0.892231 | − | 0.451580i | \(-0.850861\pi\) | ||||
−0.892231 | + | 0.451580i | \(0.850861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.80424 | −0.455642 | −0.227821 | − | 0.973703i | \(-0.573160\pi\) | ||||
−0.227821 | + | 0.973703i | \(0.573160\pi\) | |||||||
\(464\) | −4.70478 | + | 8.14891i | −0.218414 | + | 0.378304i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7588 | + | 23.8310i | 0.637366 | + | 1.10395i | ||||
\(467\) | −10.8457 | − | 6.26175i | −0.501878 | − | 0.289759i | 0.227611 | − | 0.973752i | \(-0.426909\pi\) |
−0.729489 | + | 0.683993i | \(0.760242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.38029 | + | 19.2716i | 0.386966 | + | 0.889880i | ||||
\(470\) | 23.4803 | 1.08307 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.34962 | − | 3.66595i | 0.292265 | − | 0.168739i | ||||
\(473\) | −12.6987 | + | 5.75904i | −0.583887 | + | 0.264801i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.94668i | 0.272852i | ||||||||
\(476\) | 6.47982 | − | 8.75758i | 0.297002 | − | 0.401403i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.66695 | + | 11.5475i | −0.304939 | + | 0.528170i | ||||
\(479\) | 7.84197 | + | 13.5827i | 0.358309 | + | 0.620609i | 0.987678 | − | 0.156497i | \(-0.0500202\pi\) |
−0.629370 | + | 0.777106i | \(0.716687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.5388 | − | 14.7448i | −1.16447 | − | 0.672307i | ||||
\(482\) | − | 18.1328i | − | 0.825928i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7901 | + | 2.13848i | 0.490460 | + | 0.0972038i | ||||
\(485\) | 42.8376 | + | 24.7323i | 1.94516 | + | 1.12304i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0262 | + | 32.9544i | 0.862161 | + | 1.49331i | 0.869839 | + | 0.493336i | \(0.164223\pi\) |
−0.00767777 | + | 0.999971i | \(0.502444\pi\) | |||||||
\(488\) | −9.21987 | − | 5.32310i | −0.417364 | − | 0.240965i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.7166 | + | 5.72359i | −0.845528 | + | 0.258565i | ||||
\(491\) | −3.63565 | −0.164075 | −0.0820373 | − | 0.996629i | \(-0.526143\pi\) | ||||
−0.0820373 | + | 0.996629i | \(0.526143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.3725 | − | 33.5541i | −0.872492 | − | 1.51120i | ||||
\(494\) | 3.37873 | + | 5.85213i | 0.152016 | + | 0.263300i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.17555 | −0.322192 | ||||||||
\(497\) | 3.32131 | − | 29.1594i | 0.148981 | − | 1.30798i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.18656 | − | 15.9116i | 0.411247 | − | 0.712301i | −0.583779 | − | 0.811912i | \(-0.698427\pi\) |
0.995026 | + | 0.0996117i | \(0.0317601\pi\) | |||||||
\(500\) | 5.28420 | − | 3.05083i | 0.236316 | − | 0.136437i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.0682 | + | 9.27699i | 0.717160 | + | 0.414053i | ||||
\(503\) | 34.2342 | 1.52643 | 0.763213 | − | 0.646146i | \(-0.223620\pi\) | ||||
0.763213 | + | 0.646146i | \(0.223620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.654298i | − | 0.0291159i | ||||||
\(506\) | −2.81098 | − | 2.01284i | −0.124963 | − | 0.0894816i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.93149 | − | 4.57925i | 0.351903 | − | 0.203171i | ||||
\(509\) | 9.23009 | + | 5.32899i | 0.409116 | + | 0.236203i | 0.690410 | − | 0.723418i | \(-0.257430\pi\) |
−0.281294 | + | 0.959622i | \(0.590763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.3210 | − | 6.66236i | 0.677760 | − | 0.294725i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.4582 | + | 13.5436i | −1.03470 | + | 0.597382i | ||||
\(515\) | 30.3740 | − | 17.5364i | 1.33844 | − | 0.772747i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.72035 | − | 27.7190i | 0.119641 | − | 1.21908i | ||||
\(518\) | −9.71725 | − | 22.3461i | −0.426951 | − | 0.981831i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.47630 | + | 7.75318i | −0.196299 | + | 0.339999i | ||||
\(521\) | −18.3680 | + | 10.6048i | −0.804716 | + | 0.464603i | −0.845118 | − | 0.534581i | \(-0.820470\pi\) |
0.0404016 | + | 0.999184i | \(0.487136\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.1257 | − | 10.4649i | −0.792583 | − | 0.457598i | 0.0482882 | − | 0.998833i | \(-0.484623\pi\) |
−0.840871 | + | 0.541236i | \(0.817957\pi\) | |||||||
\(524\) | −7.74679 | −0.338420 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.0684 | 0.482603 | ||||||||
\(527\) | 14.7731 | − | 25.5877i | 0.643525 | − | 1.11462i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9567 | − | 18.9775i | −0.476377 | − | 0.825110i | ||||
\(530\) | −16.6758 | + | 28.8833i | −0.724348 | + | 1.25461i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.631910 | + | 5.54785i | −0.0273968 | + | 0.240530i | ||||
\(533\) | − | 0.354679i | − | 0.0153629i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.6986 | − | 18.3012i | 1.37045 | − | 0.791230i | ||||
\(536\) | 3.97143 | + | 6.87872i | 0.171540 | + | 0.297116i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.75172i | 0.420426i | ||||||||
\(539\) | 4.58839 | + | 22.7584i | 0.197636 | + | 0.980275i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.708020 | + | 0.408775i | 0.0304402 | + | 0.0175746i | 0.515143 | − | 0.857104i | \(-0.327739\pi\) |
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(542\) | −2.91324 | + | 1.68196i | −0.125134 | + | 0.0722463i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.05881 | − | 3.56596i | 0.0882706 | − | 0.152889i | ||||
\(545\) | 18.1923 | 0.779273 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.2530i | − | 0.694930i | −0.937693 | − | 0.347465i | \(-0.887043\pi\) | ||
0.937693 | − | 0.347465i | \(-0.112957\pi\) | |||||||
\(548\) | −6.78091 | − | 3.91496i | −0.289666 | − | 0.167239i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.85986 | + | 8.51101i | 0.164585 | + | 0.362911i | ||||
\(551\) | 17.1979 | + | 9.92919i | 0.732654 | + | 0.422998i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.5374 | − | 22.5949i | −1.29858 | − | 0.960833i | ||||
\(554\) | − | 16.5955i | − | 0.705077i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.69360 | − | 1.55515i | 0.114234 | − | 0.0659530i | ||||
\(557\) | −3.81751 | − | 6.61212i | −0.161753 | − | 0.280165i | 0.773744 | − | 0.633498i | \(-0.218381\pi\) |
−0.935498 | + | 0.353333i | \(0.885048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4613 | −0.569353 | ||||||||
\(560\) | −6.78392 | + | 2.95000i | −0.286673 | + | 0.124660i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.79320 | + | 4.83797i | −0.117824 | + | 0.204078i | ||||
\(563\) | 22.5824 | + | 39.1138i | 0.951734 | + | 1.64845i | 0.741672 | + | 0.670763i | \(0.234033\pi\) |
0.210061 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.21875 | − | 2.11093i | 0.0512731 | − | 0.0888075i | ||||
\(566\) | − | 2.70029i | − | 0.113502i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 11.0925i | − | 0.465430i | ||||||
\(569\) | −16.3937 | + | 28.3948i | −0.687261 | + | 1.19037i | 0.285459 | + | 0.958391i | \(0.407854\pi\) |
−0.972720 | + | 0.231981i | \(0.925479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.58774 | − | 2.64873i | 0.191991 | − | 0.110846i | −0.400923 | − | 0.916112i | \(-0.631311\pi\) |
0.592914 | + | 0.805266i | \(0.297977\pi\) | |||||||
\(572\) | 8.63420 | + | 6.18263i | 0.361014 | + | 0.258509i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.174319 | − | 0.235594i | 0.00727592 | − | 0.00983352i | ||||
\(575\) | − | 2.93727i | − | 0.122493i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.83877 | − | 11.8451i | −0.284702 | − | 0.493118i | 0.687835 | − | 0.725867i | \(-0.258561\pi\) |
−0.972537 | + | 0.232749i | \(0.925228\pi\) | |||||||
\(578\) | −0.0226302 | − | 0.0391967i | −0.000941294 | − | 0.00163037i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 26.3093i | 1.09243i | ||||||||
\(581\) | −37.4165 | − | 4.26181i | −1.55230 | − | 0.176810i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.1653 | + | 23.0324i | 1.33215 | + | 0.953906i | ||||
\(584\) | 5.46860 | − | 3.15730i | 0.226292 | − | 0.130650i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.90923 | + | 13.6992i | −0.326727 | + | 0.565909i | ||||
\(587\) | 24.5620i | 1.01378i | 0.862011 | + | 0.506890i | \(0.169205\pi\) | ||||
−0.862011 | + | 0.506890i | \(0.830795\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.1436i | 0.623982i | ||||||||
\(590\) | 10.2501 | − | 17.7537i | 0.421989 | − | 0.730907i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.60502 | − | 7.97612i | −0.189265 | − | 0.327817i | ||||
\(593\) | −2.76466 | + | 4.78853i | −0.113531 | + | 0.196641i | −0.917192 | − | 0.398447i | \(-0.869549\pi\) |
0.803661 | + | 0.595088i | \(0.202883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.44720 | − | 30.2647i | 0.141321 | − | 1.24073i | ||||
\(596\) | 8.17082 | 0.334690 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.66887 | − | 2.89057i | −0.0682453 | − | 0.118204i | ||||
\(599\) | 20.9741 | − | 12.1094i | 0.856977 | − | 0.494776i | −0.00602174 | − | 0.999982i | \(-0.501917\pi\) |
0.862999 | + | 0.505206i | \(0.168583\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7793i | 0.684443i | 0.939619 | + | 0.342222i | \(0.111179\pi\) | ||||
−0.939619 | + | 0.342222i | \(0.888821\pi\) | |||||||
\(602\) | −8.94163 | − | 6.61600i | −0.364434 | − | 0.269648i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.93139 | + | 3.42449i | 0.241345 | + | 0.139341i | ||||
\(605\) | 29.1171 | − | 9.90653i | 1.18378 | − | 0.402758i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9524 | + | 17.8704i | 1.25632 | + | 0.725337i | 0.972357 | − | 0.233498i | \(-0.0750174\pi\) |
0.283963 | + | 0.958835i | \(0.408351\pi\) | |||||||
\(608\) | 2.11045i | 0.0855900i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.7670 | −1.20523 | ||||||||
\(611\) | 13.4444 | − | 23.2864i | 0.543903 | − | 0.942068i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.82971 | − | 4.52049i | 0.316239 | − | 0.182581i | −0.333476 | − | 0.942759i | \(-0.608222\pi\) |
0.649715 | + | 0.760178i | \(0.274888\pi\) | |||||||
\(614\) | −10.6359 | − | 6.14066i | −0.429231 | − | 0.247817i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.69658 | + | 8.35036i | 0.108648 | + | 0.336445i | ||||
\(617\) | 11.5919i | 0.466672i | 0.972396 | + | 0.233336i | \(0.0749643\pi\) | ||||
−0.972396 | + | 0.233336i | \(0.925036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.200558 | + | 0.347377i | 0.00806111 | + | 0.0139622i | 0.870028 | − | 0.493003i | \(-0.164101\pi\) |
−0.861967 | + | 0.506965i | \(0.830767\pi\) | |||||||
\(620\) | −17.3750 | + | 10.0315i | −0.697799 | + | 0.402874i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 20.3911i | − | 0.817609i | ||||||
\(623\) | 25.4114 | + | 18.8022i | 1.01809 | + | 0.753292i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5745 | − | 26.9759i | 0.622981 | − | 1.07903i | ||||
\(626\) | −1.62210 | − | 2.80957i | −0.0648323 | − | 0.112293i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.04332 | − | 7.00324i | 0.161346 | − | 0.279460i | ||||
\(629\) | 37.9234 | 1.51210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7927 | 1.30546 | 0.652728 | − | 0.757592i | \(-0.273624\pi\) | ||||
0.652728 | + | 0.757592i | \(0.273624\pi\) | |||||||
\(632\) | −12.4344 | − | 7.17899i | −0.494613 | − | 0.285565i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.57584 | + | 5.52861i | −0.380305 | + | 0.219569i | ||||
\(635\) | 12.8037 | − | 22.1766i | 0.508098 | − | 0.880052i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.04045 | + | 21.8392i | −0.199710 | + | 0.865302i | ||||
\(638\) | 31.0588 | + | 3.04811i | 1.22963 | + | 0.120676i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.42143 | + | 1.39801i | −0.0957152 | + | 0.0552612i | ||||
\(641\) | 27.3662 | − | 15.7999i | 1.08090 | − | 0.624058i | 0.149761 | − | 0.988722i | \(-0.452150\pi\) |
0.931139 | + | 0.364664i | \(0.118816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.86178 | −0.191730 | −0.0958650 | − | 0.995394i | \(-0.530562\pi\) | ||||
−0.0958650 | + | 0.995394i | \(0.530562\pi\) | |||||||
\(644\) | 0.312123 | − | 2.74028i | 0.0122994 | − | 0.107982i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.52577 | − | 4.34501i | −0.296098 | − | 0.170952i | ||||
\(647\) | −18.9738 | + | 10.9545i | −0.745937 | + | 0.430667i | −0.824224 | − | 0.566264i | \(-0.808388\pi\) |
0.0782867 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7711 | − | 14.1573i | −0.776082 | − | 0.555724i | ||||
\(650\) | 9.02212i | 0.353877i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.36471 | 0.0534463 | ||||||||
\(653\) | −31.4813 | − | 18.1757i | −1.23196 | − | 0.711271i | −0.264520 | − | 0.964380i | \(-0.585214\pi\) |
−0.967438 | + | 0.253109i | \(0.918547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.7583 | + | 10.8301i | −0.732947 | + | 0.423167i | ||||
\(656\) | 0.0553856 | − | 0.0959306i | 0.00216244 | − | 0.00374546i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.3753 | − | 8.86024i | 0.794312 | − | 0.345408i | ||||
\(659\) | 1.25809 | 0.0490083 | 0.0245041 | − | 0.999700i | \(-0.492199\pi\) | ||||
0.0245041 | + | 0.999700i | \(0.492199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0453 | − | 32.9875i | −0.740778 | − | 1.28307i | −0.952141 | − | 0.305658i | \(-0.901124\pi\) |
0.211363 | − | 0.977408i | \(-0.432210\pi\) | |||||||
\(662\) | −7.27038 | − | 12.5927i | −0.282571 | − | 0.489428i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.2335 | −0.552369 | ||||||||
\(665\) | 6.22583 | + | 14.3171i | 0.241427 | + | 0.555194i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.49463 | − | 4.90437i | −0.328913 | − | 0.189898i | ||||
\(668\) | 3.67328 | + | 6.36230i | 0.142123 | + | 0.246165i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.2331 | + | 11.1042i | 0.743038 | + | 0.428993i | ||||
\(671\) | −3.44870 | + | 35.1406i | −0.133136 | + | 1.35659i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4116i | 0.748263i | 0.927376 | + | 0.374131i | \(0.122059\pi\) | ||||
−0.927376 | + | 0.374131i | \(0.877941\pi\) | |||||||
\(674\) | 17.3604 | + | 10.0230i | 0.668696 | + | 0.386072i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.37389 | − | 2.37965i | −0.0528420 | − | 0.0915250i | ||||
\(677\) | 5.25697 | − | 9.10535i | 0.202042 | − | 0.349947i | −0.747144 | − | 0.664662i | \(-0.768576\pi\) |
0.949186 | + | 0.314715i | \(0.101909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.5055 | + | 5.29706i | 1.78472 | + | 0.203283i | ||||
\(680\) | − | 11.5129i | − | 0.441501i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.82939 | + | 21.6739i | 0.376387 | + | 0.829935i | ||||
\(683\) | 37.1706 | − | 21.4605i | 1.42230 | − | 0.821163i | 0.425800 | − | 0.904817i | \(-0.359993\pi\) |
0.996495 | + | 0.0836546i | \(0.0266593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8926 | −0.836474 | ||||||||
\(686\) | −14.0817 | + | 12.0294i | −0.537642 | + | 0.459283i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.64090 | − | 2.10208i | −0.138808 | − | 0.0801409i | ||||
\(689\) | 19.0965 | + | 33.0761i | 0.727519 | + | 1.26010i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5279 | − | 40.7515i | 0.895043 | − | 1.55026i | 0.0612926 | − | 0.998120i | \(-0.480478\pi\) |
0.833751 | − | 0.552141i | \(-0.186189\pi\) | |||||||
\(692\) | −0.655347 | −0.0249126 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0889 | −0.458887 | ||||||||
\(695\) | 4.34823 | − | 7.53135i | 0.164938 | − | 0.285680i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.228056 | + | 0.395005i | 0.00863825 | + | 0.0149619i | ||||
\(698\) | −4.26527 | − | 2.46255i | −0.161443 | − | 0.0932091i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.43422 | + | 5.99292i | −0.167598 | + | 0.226511i | ||||
\(701\) | −1.94709 | −0.0735406 | −0.0367703 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367703 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.8332 | + | 9.71865i | −0.634876 | + | 0.366546i | ||||
\(704\) | 1.36985 | + | 3.02052i | 0.0516280 | + | 0.113840i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 9.56093i | − | 0.359830i | ||||||
\(707\) | −0.246898 | − | 0.567774i | −0.00928555 | − | 0.0213534i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4549 | + | 19.8405i | −0.430199 | + | 0.745126i | −0.996890 | − | 0.0788042i | \(-0.974890\pi\) |
0.566691 | + | 0.823930i | \(0.308223\pi\) | |||||||
\(710\) | −15.5074 | − | 26.8596i | −0.581982 | − | 1.00802i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.3472 | + | 5.97394i | 0.387776 | + | 0.223883i | ||||
\(713\) | − | 7.47996i | − | 0.280127i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.5505 | + | 2.90008i | 1.10512 | + | 0.108457i | ||||
\(716\) | 3.55106 | + | 2.05021i | 0.132709 | + | 0.0766199i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.14103 | − | 7.17248i | −0.154542 | − | 0.267674i | ||||
\(719\) | 1.87531 | + | 1.08271i | 0.0699372 | + | 0.0403782i | 0.534561 | − | 0.845130i | \(-0.320477\pi\) |
−0.464624 | + | 0.885508i | \(0.653810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7400 | − | 26.6790i | 0.735157 | − | 0.993577i | ||||
\(722\) | −14.5460 | −0.541346 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.50322 | + | 9.53186i | 0.204526 | + | 0.354249i | ||||
\(725\) | 13.2568 | + | 22.9615i | 0.492345 | + | 0.852767i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8670 | 0.736825 | 0.368412 | − | 0.929662i | \(-0.379901\pi\) | ||||
0.368412 | + | 0.929662i | \(0.379901\pi\) | |||||||
\(728\) | −0.958715 | + | 8.41703i | −0.0355323 | + | 0.311956i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.82788 | − | 15.2903i | 0.326734 | − | 0.565921i | ||||
\(731\) | 14.9918 | − | 8.65553i | 0.554493 | − | 0.320137i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.7695 | − | 18.3421i | −1.17343 | − | 0.677483i | −0.218948 | − | 0.975737i | \(-0.570262\pi\) |
−0.954487 | + | 0.298254i | \(0.903596\pi\) | |||||||
\(734\) | 37.3838 | 1.37986 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.04242i | − | 0.0384243i | ||||||
\(737\) | 15.3371 | − | 21.4186i | 0.564948 | − | 0.788963i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.5162 | + | 18.1959i | −1.15934 | + | 0.669346i | −0.951146 | − | 0.308742i | \(-0.900092\pi\) |
−0.208195 | + | 0.978087i | \(0.566759\pi\) | |||||||
\(740\) | −22.3014 | − | 12.8757i | −0.819816 | − | 0.473321i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.57154 | + | 31.3563i | −0.131115 | + | 1.15113i | ||||
\(743\) | 0.143528 | 0.00526553 | 0.00263276 | − | 0.999997i | \(-0.499162\pi\) | ||||
0.00263276 | + | 0.999997i | \(0.499162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.7850 | − | 11.4229i | 0.724867 | − | 0.418502i | ||||
\(746\) | 20.6889 | − | 11.9447i | 0.757474 | − | 0.437328i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.5913 | − | 1.33385i | −0.496947 | − | 0.0487704i | ||||
\(749\) | 20.6009 | − | 27.8425i | 0.752741 | − | 1.01734i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.63144 | − | 4.55779i | 0.0960226 | − | 0.166316i | −0.814012 | − | 0.580848i | \(-0.802721\pi\) |
0.910035 | + | 0.414532i | \(0.136055\pi\) | |||||||
\(752\) | 7.27267 | − | 4.19888i | 0.265207 | − | 0.153117i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.0921 | + | 15.0643i | 0.950217 | + | 0.548608i | ||||
\(755\) | 19.1499 | 0.696936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6449 | −0.495932 | −0.247966 | − | 0.968769i | \(-0.579762\pi\) | ||||
−0.247966 | + | 0.968769i | \(0.579762\pi\) | |||||||
\(758\) | 8.99630 | − | 15.5820i | 0.326760 | − | 0.565965i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.95043 | + | 5.11029i | 0.107023 | + | 0.185370i | ||||
\(761\) | 14.3603 | − | 24.8727i | 0.520559 | − | 0.901635i | −0.479155 | − | 0.877730i | \(-0.659057\pi\) |
0.999714 | − | 0.0239048i | \(-0.00760986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.7866 | − | 6.86483i | 0.571513 | − | 0.248523i | ||||
\(764\) | − | 21.7465i | − | 0.786763i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.6369 | − | 8.45064i | 0.528854 | − | 0.305334i | ||||
\(767\) | −11.7380 | − | 20.3309i | −0.423836 | − | 0.734106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.9742i | 1.47757i | 0.673943 | + | 0.738783i | \(0.264599\pi\) | ||||
−0.673943 | + | 0.738783i | \(0.735401\pi\) | |||||||
\(770\) | 18.2035 | + | 16.4499i | 0.656007 | + | 0.592814i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.3131 | − | 11.1504i | −0.695094 | − | 0.401313i | ||||
\(773\) | 9.44578 | − | 5.45352i | 0.339741 | − | 0.196150i | −0.320416 | − | 0.947277i | \(-0.603823\pi\) |
0.660158 | + | 0.751127i | \(0.270490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.1094 | + | 17.5100i | −0.363140 | + | 0.628977i | ||||
\(776\) | 17.6911 | 0.635073 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6246i | 0.380911i | ||||||||
\(779\) | −0.202457 | − | 0.116888i | −0.00725376 | − | 0.00418796i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.5050 | + | 15.1950i | −1.19890 | + | 0.543719i | ||||
\(782\) | 3.71724 | + | 2.14615i | 0.132928 | + | 0.0767462i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.77365 | + | 5.11979i | −0.170487 | + | 0.182850i | ||||
\(785\) | − | 22.6104i | − | 0.807001i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.7122 | + | 9.64880i | −0.595726 | + | 0.343943i | −0.767358 | − | 0.641219i | \(-0.778429\pi\) |
0.171632 | + | 0.985161i | \(0.445096\pi\) | |||||||
\(788\) | 5.50179 | + | 9.52937i | 0.195993 | + | 0.339470i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −40.1452 | −1.42830 | ||||||||
\(791\) | 0.261026 | − | 2.29167i | 0.00928102 | − | 0.0814826i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.0441 | + | 29.5212i | −0.605253 | + | 1.04833i | ||||
\(794\) | −11.4791 | − | 19.8824i | −0.407379 | − | 0.705600i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.22506 | + | 14.2462i | −0.291529 | + | 0.504944i | ||||
\(797\) | − | 23.8010i | − | 0.843075i | −0.906811 | − | 0.421538i | \(-0.861491\pi\) | ||
0.906811 | − | 0.421538i | \(-0.138509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5787i | 1.22331i | ||||||||
\(800\) | −1.40887 | + | 2.44023i | −0.0498109 | + | 0.0862751i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.28001 | + | 4.78047i | −0.292377 | + | 0.168804i | ||||
\(803\) | −17.0278 | − | 12.1930i | −0.600899 | − | 0.430282i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.07515 | − | 7.07173i | −0.108385 | − | 0.249246i | ||||
\(806\) | 22.9754i | 0.809275i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.117005 | − | 0.202659i | −0.00411623 | − | 0.00712952i | ||||
\(809\) | −10.7545 | − | 18.6274i | −0.378109 | − | 0.654905i | 0.612678 | − | 0.790333i | \(-0.290092\pi\) |
−0.990787 | + | 0.135428i | \(0.956759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.4205i | 1.84073i | 0.391059 | + | 0.920366i | \(0.372109\pi\) | ||||
−0.391059 | + | 0.920366i | \(0.627891\pi\) | |||||||
\(812\) | 9.92776 | + | 22.8302i | 0.348396 | + | 0.801183i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.7839 | + | 24.8356i | −0.623324 | + | 0.870487i | ||||
\(815\) | 3.30455 | − | 1.90788i | 0.115753 | − | 0.0668302i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.43632 | + | 7.68394i | −0.155207 | + | 0.268827i | ||||
\(818\) | 13.1069i | 0.458273i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 0.309718i | − | 0.0108158i | ||||||
\(821\) | 24.4907 | − | 42.4191i | 0.854731 | − | 1.48044i | −0.0221630 | − | 0.999754i | \(-0.507055\pi\) |
0.876894 | − | 0.480683i | \(-0.159611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.61437 | − | 6.26027i | −0.125989 | − | 0.218219i | 0.796130 | − | 0.605126i | \(-0.206877\pi\) |
−0.922119 | + | 0.386906i | \(0.873544\pi\) | |||||||
\(824\) | 6.27192 | − | 10.8633i | 0.218493 | − | 0.378441i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19532 | − | 19.2738i | 0.0763849 | − | 0.670620i | ||||
\(827\) | −45.2699 | −1.57419 | −0.787095 | − | 0.616832i | \(-0.788416\pi\) | ||||
−0.787095 | + | 0.616832i | \(0.788416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5067 | + | 42.4468i | 0.851152 | + | 1.47424i | 0.880169 | + | 0.474660i | \(0.157429\pi\) |
−0.0290174 | + | 0.999579i | \(0.509238\pi\) | |||||||
\(830\) | −34.4655 | + | 19.8987i | −1.19631 | + | 0.690692i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.20191i | 0.111006i | ||||||||
\(833\) | −8.42895 | − | 27.5633i | −0.292046 | − | 0.955011i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7891 | + | 10.2706i | 0.615618 | + | 0.355427i | ||||
\(836\) | 6.37465 | − | 2.89099i | 0.220472 | − | 0.0999869i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.90905 | + | 2.25689i | 0.135036 | + | 0.0779631i | ||||
\(839\) | 2.44258i | 0.0843273i | 0.999111 | + | 0.0421637i | \(0.0134251\pi\) | ||||
−0.999111 | + | 0.0421637i | \(0.986575\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.5398 | 2.05309 | ||||||||
\(842\) | −18.6594 | + | 32.3190i | −0.643045 | + | 1.11379i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.535916 | + | 0.309411i | −0.0184470 | + | 0.0106504i | ||||
\(845\) | −6.65355 | − | 3.84143i | −0.228889 | − | 0.132149i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5285 | − | 19.5838i | 0.739728 | − | 0.672906i | ||||
\(848\) | 11.9282i | 0.409616i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.80117 | − | 10.0479i | −0.198978 | − | 0.344641i | ||||
\(851\) | 8.31450 | − | 4.80038i | 0.285017 | − | 0.164555i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.5500i | 1.28569i | 0.765997 | + | 0.642844i | \(0.222246\pi\) | ||||
−0.765997 | + | 0.642844i | \(0.777754\pi\) | |||||||
\(854\) | −25.8306 | + | 11.2325i | −0.883906 | + | 0.384368i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.54545 | − | 11.3370i | 0.223719 | − | 0.387492i | ||||
\(857\) | 21.4068 | + | 37.0777i | 0.731243 | + | 1.26655i | 0.956352 | + | 0.292217i | \(0.0943929\pi\) |
−0.225109 | + | 0.974334i | \(0.572274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.43313 | + | 9.41045i | −0.185376 | + | 0.321080i | −0.943703 | − | 0.330794i | \(-0.892684\pi\) |
0.758327 | + | 0.651874i | \(0.226017\pi\) | |||||||
\(860\) | −11.7549 | −0.400839 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.6987 | 0.943422 | ||||||||
\(863\) | 0.401363 | + | 0.231727i | 0.0136626 | + | 0.00788808i | 0.506816 | − | 0.862054i | \(-0.330822\pi\) |
−0.493153 | + | 0.869943i | \(0.664156\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.58687 | + | 0.916183i | −0.0539554 | + | 0.0311511i | ||||
\(866\) | 4.09094 | − | 7.08571i | 0.139016 | − | 0.240782i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.2920 | + | 15.2614i | −0.383276 | + | 0.518005i | ||||
\(869\) | −4.65109 | + | 47.3924i | −0.157777 | + | 1.60768i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.0250 | − | 12.7162i | 0.746290 | − | 0.430871i | ||||
\(872\) | 5.63480 | − | 3.25325i | 0.190818 | − | 0.110169i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.19998 | −0.0744155 | ||||||||
\(875\) | 1.82696 | − | 16.0398i | 0.0617625 | − | 0.542243i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.8492 | − | 9.15055i | −0.535190 | − | 0.308992i | 0.207937 | − | 0.978142i | \(-0.433325\pi\) |
−0.743127 | + | 0.669150i | \(0.766658\pi\) | |||||||
\(878\) | 1.16163 | − | 0.670668i | 0.0392031 | − | 0.0226339i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.53969 | + | 5.39890i | 0.254163 | + | 0.181997i | ||||
\(881\) | − | 26.3700i | − | 0.888426i | −0.895921 | − | 0.444213i | \(-0.853483\pi\) | ||
0.895921 | − | 0.444213i | \(-0.146517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2737 | −0.345738 | −0.172869 | − | 0.984945i | \(-0.555304\pi\) | ||||
−0.172869 | + | 0.984945i | \(0.555304\pi\) | |||||||
\(884\) | −11.4179 | − | 6.59211i | −0.384024 | − | 0.221717i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.5122 | − | 13.5748i | 0.789909 | − | 0.456054i | ||||
\(887\) | 8.89664 | − | 15.4094i | 0.298720 | − | 0.517398i | −0.677123 | − | 0.735870i | \(-0.736774\pi\) |
0.975843 | + | 0.218471i | \(0.0701070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.74224 | − | 24.0754i | 0.0919716 | − | 0.807464i | ||||
\(890\) | 33.4065 | 1.11979 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.17766 | − | 8.96797i | −0.173361 | − | 0.300270i | ||||
\(893\) | −8.86152 | − | 15.3486i | −0.296539 | − | 0.513621i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.4648 | 0.383228 | ||||||||
\(896\) | −1.57368 | + | 2.12686i | −0.0525730 | + | 0.0710533i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.3691 | − | 18.6883i | −1.08017 | − | 0.623636i | ||||
\(899\) | 33.7594 | + | 58.4729i | 1.12594 | + | 1.95018i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.5355 | − | 24.5579i | −1.41706 | − | 0.818141i | ||||
\(902\) | −0.365630 | − | 0.0358829i | −0.0121741 | − | 0.00119477i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.871772i | − | 0.0289947i | ||||||
\(905\) | 26.6513 | + | 15.3871i | 0.885918 | + | 0.511485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.7926 | − | 29.0857i | −0.557590 | − | 0.965775i | −0.997697 | − | 0.0678291i | \(-0.978393\pi\) |
0.440107 | − | 0.897945i | \(-0.354941\pi\) | |||||||
\(908\) | −6.46564 | + | 11.1988i | −0.214570 | + | 0.371646i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.44564 | + | 21.7215i | 0.313120 | + | 0.720061i | ||||
\(911\) | − | 2.04771i | − | 0.0678437i | −0.999424 | − | 0.0339218i | \(-0.989200\pi\) | ||
0.999424 | − | 0.0339218i | \(-0.0107997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.4978 | + | 42.9927i | 0.645282 | + | 1.42285i | ||||
\(914\) | 20.4149 | − | 11.7865i | 0.675263 | − | 0.389864i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.47697 | 0.180964 | ||||||||
\(917\) | −12.1910 | + | 16.4763i | −0.402582 | + | 0.544096i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.2849 | − | 21.5264i | −1.22992 | − | 0.710092i | −0.262903 | − | 0.964822i | \(-0.584680\pi\) |
−0.967012 | + | 0.254731i | \(0.918013\pi\) | |||||||
\(920\) | −1.45732 | − | 2.52415i | −0.0480464 | − | 0.0832188i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1570 | + | 33.1809i | −0.630902 | + | 1.09275i | ||||
\(923\) | −35.5171 | −1.16906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.9514 | −0.853277 | ||||||||
\(926\) | −4.90212 | + | 8.49072i | −0.161094 | + | 0.279022i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.70478 | + | 8.14891i | 0.154442 | + | 0.267501i | ||||
\(929\) | −11.1033 | − | 6.41047i | −0.364286 | − | 0.210321i | 0.306673 | − | 0.951815i | \(-0.400784\pi\) |
−0.670959 | + | 0.741494i | \(0.734117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8051 | + | 10.0745i | 0.354122 | + | 0.330180i | ||||
\(932\) | 27.5177 | 0.901372 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.8457 | + | 6.26175i | −0.354881 | + | 0.204891i | ||||
\(935\) | −34.7750 | + | 15.7709i | −1.13726 | + | 0.515765i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.4540i | 1.55025i | 0.631805 | + | 0.775127i | \(0.282314\pi\) | ||||
−0.631805 | + | 0.775127i | \(0.717686\pi\) | |||||||
\(938\) | 20.8798 | + | 2.37825i | 0.681751 | + | 0.0776527i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.7402 | − | 20.3345i | 0.382922 | − | 0.663240i | ||||
\(941\) | 5.71859 | + | 9.90490i | 0.186421 | + | 0.322890i | 0.944054 | − | 0.329790i | \(-0.106978\pi\) |
−0.757634 | + | 0.652680i | \(0.773645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.100000 | + | 0.0577353i | 0.00325646 | + | 0.00188012i | ||||
\(944\) | − | 7.33191i | − | 0.238633i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36188 | + | 13.8769i | −0.0442786 | + | 0.451178i | ||||
\(947\) | 4.81239 | + | 2.77843i | 0.156382 | + | 0.0902869i | 0.576149 | − | 0.817345i | \(-0.304555\pi\) |
−0.419767 | + | 0.907632i | \(0.637888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1094 | − | 17.5100i | −0.328165 | − | 0.568398i | ||||
\(950\) | 5.14998 | + | 2.97334i | 0.167087 | + | 0.0964679i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.34438 | − | 9.99047i | −0.140802 | − | 0.323793i | ||||
\(953\) | 25.6550 | 0.831045 | 0.415523 | − | 0.909583i | \(-0.363599\pi\) | ||||
0.415523 | + | 0.909583i | \(0.363599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.4019 | − | 52.6576i | −0.983782 | − | 1.70396i | ||||
\(956\) | 6.66695 | + | 11.5475i | 0.215625 | + | 0.373473i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.6839 | 0.506725 | ||||||||
\(959\) | −18.9976 | + | 8.26113i | −0.613464 | + | 0.266766i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2442 | + | 17.7435i | −0.330459 | + | 0.572372i | ||||
\(962\) | −25.5388 | + | 14.7448i | −0.823404 | + | 0.475393i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.7035 | − | 9.06641i | −0.505775 | − | 0.292009i | ||||
\(965\) | −62.3537 | −2.00724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.1653i | − | 1.42026i | −0.704071 | − | 0.710130i | \(-0.748636\pi\) | ||
0.704071 | − | 0.710130i | \(-0.251364\pi\) | |||||||
\(968\) | 7.24705 | − | 8.27528i | 0.232929 | − | 0.265978i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42.8376 | − | 24.7323i | 1.37543 | − | 0.794107i | ||||
\(971\) | −47.3097 | − | 27.3143i | −1.51824 | − | 0.876557i | −0.999770 | − | 0.0214630i | \(-0.993168\pi\) |
−0.518472 | − | 0.855094i | \(-0.673499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.931285 | − | 8.17621i | 0.0298556 | − | 0.262117i | ||||
\(974\) | 38.0525 | 1.21928 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.21987 | + | 5.32310i | −0.295121 | + | 0.170388i | ||||
\(977\) | 0.164978 | − | 0.0952499i | 0.00527810 | − | 0.00304731i | −0.497359 | − | 0.867545i | \(-0.665697\pi\) |
0.502637 | + | 0.864498i | \(0.332363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.87036 | − | 39.4371i | 0.123697 | − | 1.26042i | ||||
\(980\) | −4.40150 | + | 19.0708i | −0.140601 | + | 0.609195i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.81783 | + | 3.14857i | −0.0580091 | + | 0.100475i | ||||
\(983\) | −37.5517 | + | 21.6805i | −1.19771 | + | 0.691500i | −0.960045 | − | 0.279847i | \(-0.909716\pi\) |
−0.237668 | + | 0.971346i | \(0.576383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.6443 | + | 15.3831i | 0.848959 | + | 0.490147i | ||||
\(986\) | −38.7449 | −1.23389 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.75746 | 0.214984 | ||||||||
\(989\) | 2.19125 | − | 3.79536i | 0.0696778 | − | 0.120686i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8052 | − | 25.6433i | −0.470302 | − | 0.814588i | 0.529121 | − | 0.848546i | \(-0.322522\pi\) |
−0.999423 | + | 0.0339589i | \(0.989188\pi\) | |||||||
\(992\) | −3.58777 | + | 6.21420i | −0.113912 | + | 0.197301i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.5921 | − | 17.4560i | −0.748296 | − | 0.553672i | ||||
\(995\) | 45.9949i | 1.45814i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.9359 | − | 28.2531i | 1.54981 | − | 0.894786i | 0.551659 | − | 0.834070i | \(-0.313995\pi\) |
0.998155 | − | 0.0607158i | \(-0.0193383\pi\) | |||||||
\(998\) | −9.18656 | − | 15.9116i | −0.290795 | − | 0.503673i | ||||
\(999\) | 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 | 1386.2.ba.b.989.2 | yes | 32 | |
3.2 | odd | 2 | 1386.2.ba.a.989.15 | yes | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.b.1187.15 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.a.989.2 | ✓ | 32 | ||
21.11 | odd | 6 | 1386.2.ba.a.1187.2 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.b.989.15 | yes | 32 | |
77.32 | odd | 6 | 1386.2.ba.a.1187.15 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.b.1187.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.2 | ✓ | 32 | 11.10 | odd | 2 | ||
1386.2.ba.a.989.15 | yes | 32 | 3.2 | odd | 2 | ||
1386.2.ba.a.1187.2 | yes | 32 | 21.11 | odd | 6 | ||
1386.2.ba.a.1187.15 | yes | 32 | 77.32 | odd | 6 | ||
1386.2.ba.b.989.2 | yes | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.b.989.15 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.b.1187.2 | yes | 32 | 231.32 | even | 6 | inner | |
1386.2.ba.b.1187.15 | yes | 32 | 7.4 | even | 3 | inner |