Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(81,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("440.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.y (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 201.3 | ||
Root | \(-0.220438 - 0.678438i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.201 |
Dual form | 440.2.y.d.81.3 |
$q$-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 \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(221\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.220438 | + | 0.678438i | 0.127270 | + | 0.391696i | 0.994308 | − | 0.106546i | \(-0.0339791\pi\) |
−0.867038 | + | 0.498242i | \(0.833979\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.116244 | − | 0.357761i | 0.0439359 | − | 0.135221i | −0.926682 | − | 0.375846i | \(-0.877352\pi\) |
0.970618 | + | 0.240625i | \(0.0773523\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.01537 | − | 1.46425i | 0.671789 | − | 0.488083i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.107091 | − | 3.31490i | −0.0322892 | − | 0.999479i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28815 | − | 1.66244i | 0.634619 | − | 0.461077i | −0.223379 | − | 0.974732i | \(-0.571709\pi\) |
0.857997 | + | 0.513654i | \(0.171709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.220438 | − | 0.678438i | 0.0569168 | − | 0.175172i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.91377 | + | 2.84352i | 0.949228 | + | 0.689655i | 0.950624 | − | 0.310344i | \(-0.100444\pi\) |
−0.00139602 | + | 0.999999i | \(0.500444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.905388 | + | 2.78650i | 0.207710 | + | 0.639267i | 0.999591 | + | 0.0285910i | \(0.00910205\pi\) |
−0.791881 | + | 0.610676i | \(0.790898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.268343 | 0.0585573 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.77226 | 0.786571 | 0.393285 | − | 0.919416i | \(-0.371338\pi\) | ||||
0.393285 | + | 0.919416i | \(0.371338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.16901 | + | 2.30242i | 0.609876 | + | 0.443101i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.60933 | − | 8.03068i | 0.484540 | − | 1.49126i | −0.348107 | − | 0.937455i | \(-0.613175\pi\) |
0.832646 | − | 0.553805i | \(-0.186825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.50458 | + | 4.72586i | −1.16826 | + | 0.848789i | −0.990799 | − | 0.135340i | \(-0.956787\pi\) |
−0.177458 | + | 0.984128i | \(0.556787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.22534 | − | 0.803383i | 0.387383 | − | 0.139851i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.304330 | + | 0.221108i | −0.0514411 | + | 0.0373742i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.877578 | − | 2.70091i | 0.144273 | − | 0.444026i | −0.852644 | − | 0.522492i | \(-0.825002\pi\) |
0.996917 | + | 0.0784662i | \(0.0250023\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.63226 | + | 1.18590i | 0.261370 | + | 0.189897i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.14965 | − | 3.53825i | −0.179545 | − | 0.552583i | 0.820267 | − | 0.571981i | \(-0.193825\pi\) |
−0.999812 | + | 0.0193984i | \(0.993825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.48484 | −0.988929 | −0.494465 | − | 0.869198i | \(-0.664636\pi\) | ||||
−0.494465 | + | 0.869198i | \(0.664636\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.49113 | −0.371356 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.800034 | + | 2.46225i | 0.116697 | + | 0.359157i | 0.992297 | − | 0.123880i | \(-0.0395338\pi\) |
−0.875600 | + | 0.483037i | \(0.839534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.54864 | + | 4.03132i | 0.792663 | + | 0.575903i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.06641 | + | 3.28207i | −0.149327 | + | 0.459582i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0394497 | − | 0.0286619i | 0.00541884 | − | 0.00393702i | −0.585073 | − | 0.810981i | \(-0.698934\pi\) |
0.590491 | + | 0.807044i | \(0.298934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.86181 | + | 2.74475i | −0.251046 | + | 0.370102i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.69089 | + | 1.22850i | −0.223963 | + | 0.162719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.509660 | + | 1.56857i | −0.0663521 | + | 0.204211i | −0.978736 | − | 0.205126i | \(-0.934240\pi\) |
0.912384 | + | 0.409336i | \(0.134240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.03606 | − | 5.11200i | −0.900875 | − | 0.654524i | 0.0378153 | − | 0.999285i | \(-0.487960\pi\) |
−0.938691 | + | 0.344760i | \(0.887960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.289578 | − | 0.891229i | −0.0364834 | − | 0.112284i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.82831 | −0.350809 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4395 | 1.39756 | 0.698779 | − | 0.715338i | \(-0.253727\pi\) | ||||
0.698779 | + | 0.715338i | \(0.253727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.831550 | + | 2.55925i | 0.100107 | + | 0.308097i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4246 | − | 8.30046i | −1.35585 | − | 0.985084i | −0.998697 | − | 0.0510383i | \(-0.983747\pi\) |
−0.357155 | − | 0.934045i | \(-0.616253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.158595 | − | 0.488106i | 0.0185622 | − | 0.0571284i | −0.941346 | − | 0.337442i | \(-0.890438\pi\) |
0.959909 | + | 0.280313i | \(0.0904384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.577114 | + | 0.419298i | −0.0666394 | + | 0.0484163i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.19839 | − | 0.347022i | −0.136569 | − | 0.0395469i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5029 | + | 7.63082i | −1.18167 | + | 0.858534i | −0.992359 | − | 0.123383i | \(-0.960626\pi\) |
−0.189312 | + | 0.981917i | \(0.560626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.44592 | − | 4.45010i | 0.160658 | − | 0.494455i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.21418 | − | 1.60869i | −0.243037 | − | 0.176577i | 0.459598 | − | 0.888127i | \(-0.347993\pi\) |
−0.702635 | + | 0.711550i | \(0.747993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.49493 | − | 4.60091i | −0.162148 | − | 0.499039i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.02351 | 0.645789 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0195 | 1.27407 | 0.637034 | − | 0.770835i | \(-0.280161\pi\) | ||||
0.637034 | + | 0.770835i | \(0.280161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.328773 | − | 1.01186i | −0.0344648 | − | 0.106072i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.64006 | − | 3.37120i | −0.481152 | − | 0.349577i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.905388 | − | 2.78650i | 0.0928909 | − | 0.285889i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0046 | + | 9.44836i | −1.32041 | + | 0.959336i | −0.320486 | + | 0.947253i | \(0.603846\pi\) |
−0.999927 | + | 0.0120825i | \(0.996154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.06966 | − | 6.52392i | −0.509520 | − | 0.655678i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6112 | + | 9.16257i | −1.25486 | + | 0.911709i | −0.998493 | − | 0.0548702i | \(-0.982525\pi\) |
−0.256367 | + | 0.966580i | \(0.582525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.86121 | + | 8.80590i | −0.281923 | + | 0.867671i | 0.705381 | + | 0.708829i | \(0.250776\pi\) |
−0.987304 | + | 0.158842i | \(0.949224\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.217094 | − | 0.157728i | −0.0211862 | − | 0.0153927i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.667222 | − | 2.05350i | −0.0645027 | − | 0.198519i | 0.913611 | − | 0.406589i | \(-0.133282\pi\) |
−0.978114 | + | 0.208070i | \(0.933282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.79052 | −0.554631 | −0.277315 | − | 0.960779i | \(-0.589445\pi\) | ||||
−0.277315 | + | 0.960779i | \(0.589445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.02585 | 0.192285 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.87590 | + | 18.0842i | 0.552758 | + | 1.70121i | 0.701792 | + | 0.712382i | \(0.252384\pi\) |
−0.149034 | + | 0.988832i | \(0.547616\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.05182 | − | 2.21728i | −0.284584 | − | 0.206762i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.17724 | − | 6.70084i | 0.201285 | − | 0.619493i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.47225 | − | 1.06965i | 0.134961 | − | 0.0980549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9771 | + | 0.709993i | −0.997915 | + | 0.0645448i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.14706 | − | 1.55993i | 0.193594 | − | 0.140654i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.16891 | + | 5.93506i | 0.724873 | + | 0.526651i | 0.887937 | − | 0.459964i | \(-0.152138\pi\) |
−0.163064 | + | 0.986615i | \(0.552138\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.42950 | − | 4.39956i | −0.125861 | − | 0.387360i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.29651 | −0.550128 | −0.275064 | − | 0.961426i | \(-0.588699\pi\) | ||||
−0.275064 | + | 0.961426i | \(0.588699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.10215 | 0.0955682 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.21045 | − | 3.72539i | −0.104179 | − | 0.320631i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.69323 | + | 4.86292i | 0.571842 | + | 0.415467i | 0.835774 | − | 0.549074i | \(-0.185019\pi\) |
−0.263932 | + | 0.964541i | \(0.585019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17270 | + | 9.76458i | −0.269105 | + | 0.828221i | 0.721614 | + | 0.692296i | \(0.243401\pi\) |
−0.990719 | + | 0.135925i | \(0.956599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.49413 | + | 1.08555i | −0.125828 | + | 0.0914196i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.75585 | − | 7.40694i | −0.481328 | − | 0.619400i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.83130 | + | 4.96323i | −0.567309 | + | 0.412174i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.51187 | + | 4.65306i | −0.124697 | + | 0.383778i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.96547 | + | 2.88109i | 0.324864 | + | 0.236028i | 0.738248 | − | 0.674529i | \(-0.235653\pi\) |
−0.413384 | + | 0.910557i | \(0.635653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89124 | − | 8.89833i | −0.235286 | − | 0.724136i | −0.997083 | − | 0.0763203i | \(-0.975683\pi\) |
0.761797 | − | 0.647815i | \(-0.224317\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0513 | 0.974289 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.04011 | 0.645797 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.98454 | + | 9.18547i | 0.238192 | + | 0.733080i | 0.996682 | + | 0.0813952i | \(0.0259376\pi\) |
−0.758490 | + | 0.651685i | \(0.774062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0281416 | + | 0.0204460i | 0.00223177 | + | 0.00162148i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.438501 | − | 1.34957i | 0.0345587 | − | 0.106361i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.63088 | + | 2.63799i | −0.284393 | + | 0.206623i | −0.720831 | − | 0.693111i | \(-0.756240\pi\) |
0.436438 | + | 0.899734i | \(0.356240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.27256 | − | 0.658074i | −0.176918 | − | 0.0512310i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9889 | − | 13.7962i | 1.46940 | − | 1.06759i | 0.488619 | − | 0.872497i | \(-0.337501\pi\) |
0.980786 | − | 0.195088i | \(-0.0624992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.54529 | + | 4.75592i | −0.118869 | + | 0.365840i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.90482 | + | 4.29010i | 0.451553 | + | 0.328072i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00204 | − | 12.3170i | −0.304270 | − | 0.936445i | −0.979949 | − | 0.199250i | \(-0.936150\pi\) |
0.675679 | − | 0.737196i | \(-0.263850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.376172 | 0.0284359 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.17653 | −0.0884332 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.09062 | − | 3.35659i | −0.0815170 | − | 0.250884i | 0.901989 | − | 0.431759i | \(-0.142107\pi\) |
−0.983506 | + | 0.180875i | \(0.942107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.44958 | − | 1.05318i | −0.107746 | − | 0.0782824i | 0.532607 | − | 0.846362i | \(-0.321212\pi\) |
−0.640354 | + | 0.768080i | \(0.721212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.91716 | − | 5.90041i | 0.141721 | − | 0.436171i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.29753 | + | 1.66925i | −0.168918 | + | 0.122726i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00684 | − | 13.2782i | 0.658645 | − | 0.971002i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.19209 | − | 0.866106i | 0.0867120 | − | 0.0629999i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.05101 | − | 3.23466i | 0.0760481 | − | 0.234052i | −0.905805 | − | 0.423695i | \(-0.860733\pi\) |
0.981853 | + | 0.189643i | \(0.0607329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.29046 | + | 4.57028i | 0.452797 | + | 0.328976i | 0.790699 | − | 0.612205i | \(-0.209717\pi\) |
−0.337902 | + | 0.941181i | \(0.609717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.623466 | − | 1.91883i | −0.0446474 | − | 0.137410i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.09410 | −0.505434 | −0.252717 | − | 0.967540i | \(-0.581324\pi\) | ||||
−0.252717 | + | 0.967540i | \(0.581324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7734 | 0.905481 | 0.452740 | − | 0.891642i | \(-0.350446\pi\) | ||||
0.452740 | + | 0.891642i | \(0.350446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.52170 | + | 7.76100i | 0.177867 | + | 0.547418i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.56975 | − | 1.86703i | −0.180361 | − | 0.131040i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.14965 | + | 3.53825i | −0.0802949 | + | 0.247122i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.60249 | − | 5.52353i | 0.528409 | − | 0.383912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.13999 | − | 3.29968i | 0.632227 | − | 0.228243i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.93856 | + | 4.31462i | −0.408828 | + | 0.297031i | −0.773127 | − | 0.634251i | \(-0.781308\pi\) |
0.364299 | + | 0.931282i | \(0.381308\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.11293 | − | 9.58062i | 0.213295 | − | 0.656454i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.24635 | + | 3.81169i | 0.357798 | + | 0.259955i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.934611 | + | 2.87644i | 0.0634455 | + | 0.195265i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.366110 | 0.0247394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.6825 | 0.920382 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.02059 | + | 6.21872i | 0.135308 | + | 0.416436i | 0.995638 | − | 0.0933019i | \(-0.0297422\pi\) |
−0.860329 | + | 0.509738i | \(0.829742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.01537 | + | 1.46425i | 0.134358 | + | 0.0976166i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.34910 | − | 19.5405i | 0.421405 | − | 1.29695i | −0.484990 | − | 0.874520i | \(-0.661177\pi\) |
0.906395 | − | 0.422431i | \(-0.138823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50380 | − | 2.54566i | 0.231538 | − | 0.168222i | −0.465967 | − | 0.884802i | \(-0.654294\pi\) |
0.697505 | + | 0.716580i | \(0.254294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0287372 | − | 0.889530i | −0.00189077 | − | 0.0585268i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.1860 | + | 16.8456i | −1.51897 | + | 1.10360i | −0.556973 | + | 0.830531i | \(0.688037\pi\) |
−0.961996 | + | 0.273064i | \(0.911963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.800034 | − | 2.46225i | 0.0521885 | − | 0.160620i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.49228 | − | 5.44346i | −0.486676 | − | 0.353591i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.23746 | − | 9.96387i | −0.209414 | − | 0.644509i | −0.999503 | − | 0.0315175i | \(-0.989966\pi\) |
0.790090 | − | 0.612991i | \(-0.210034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5202 | 0.999745 | 0.499873 | − | 0.866099i | \(-0.333380\pi\) | ||||
0.499873 | + | 0.866099i | \(0.333380\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0892 | 0.967971 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.11939 | − | 6.52282i | −0.135403 | − | 0.416727i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.70405 | + | 4.87077i | 0.426568 | + | 0.309920i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.603310 | − | 1.85680i | 0.0382332 | − | 0.117670i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.68403 | − | 7.03586i | 0.611251 | − | 0.444100i | −0.238604 | − | 0.971117i | \(-0.576690\pi\) |
0.849854 | + | 0.527017i | \(0.176690\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.403976 | − | 12.5047i | −0.0253978 | − | 0.786161i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.79189 | − | 2.02843i | 0.174835 | − | 0.127025i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.61843 | + | 8.05870i | −0.163333 | + | 0.502688i | −0.998910 | − | 0.0466864i | \(-0.985134\pi\) |
0.835576 | + | 0.549374i | \(0.185134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.864266 | − | 0.627926i | −0.0537029 | − | 0.0390174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.50017 | − | 20.0055i | −0.402350 | − | 1.23831i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5189 | 0.771950 | 0.385975 | − | 0.922509i | \(-0.373865\pi\) | ||||
0.385975 | + | 0.922509i | \(0.373865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0487626 | −0.00299546 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.64956 | + | 8.15451i | 0.162151 | + | 0.499048i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4689 | + | 14.1450i | 1.18704 | + | 0.862434i | 0.992948 | − | 0.118549i | \(-0.0378244\pi\) |
0.194091 | + | 0.980984i | \(0.437824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.91162 | + | 8.96105i | −0.176868 | + | 0.544345i | −0.999714 | − | 0.0239201i | \(-0.992385\pi\) |
0.822845 | + | 0.568265i | \(0.192385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.614009 | − | 0.446104i | 0.0371615 | − | 0.0269994i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.11956 | − | 1.12621i | 0.188117 | − | 0.0679129i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2393 | + | 13.9782i | −1.15598 | + | 0.839867i | −0.989264 | − | 0.146138i | \(-0.953316\pi\) |
−0.166714 | + | 0.986005i | \(0.553316\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.18928 | + | 19.0487i | −0.370543 | + | 1.14041i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.402004 | − | 0.292073i | −0.0239815 | − | 0.0174236i | 0.575730 | − | 0.817640i | \(-0.304718\pi\) |
−0.599711 | + | 0.800216i | \(0.704718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.44629 | + | 4.45123i | 0.0859732 | + | 0.264598i | 0.984796 | − | 0.173713i | \(-0.0555766\pi\) |
−0.898823 | + | 0.438312i | \(0.855577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.09005 | 0.123804 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.39949 | −0.0826092 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.97869 | + | 6.08979i | 0.116394 | + | 0.358223i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.27683 | − | 6.74001i | −0.543817 | − | 0.395106i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.22865 | − | 16.0921i | 0.305461 | − | 0.940112i | −0.674044 | − | 0.738691i | \(-0.735444\pi\) |
0.979505 | − | 0.201421i | \(-0.0645559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.33431 | − | 0.969431i | 0.0776864 | − | 0.0564424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.29290 | − | 10.7515i | 0.423177 | − | 0.623865i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.63150 | − | 6.27115i | 0.499173 | − | 0.362670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.753821 | + | 2.32002i | −0.0434495 | + | 0.133724i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.99622 | − | 6.53614i | −0.516819 | − | 0.375491i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.68754 | + | 8.27139i | 0.153888 | + | 0.473618i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.3667 | −1.96141 | −0.980707 | − | 0.195486i | \(-0.937372\pi\) | ||||
−0.980707 | + | 0.195486i | \(0.937372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.60497 | −0.375744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.27681 | + | 7.00729i | 0.129106 | + | 0.397347i | 0.994627 | − | 0.103526i | \(-0.0330124\pi\) |
−0.865521 | + | 0.500873i | \(0.833012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2744 | + | 14.7302i | 1.14598 | + | 0.832602i | 0.987941 | − | 0.154831i | \(-0.0494834\pi\) |
0.158037 | + | 0.987433i | \(0.449483\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.289578 | + | 0.891229i | −0.0163159 | + | 0.0502150i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.7114 | + | 16.5008i | −1.27560 | + | 0.926777i | −0.999411 | − | 0.0343263i | \(-0.989071\pi\) |
−0.276189 | + | 0.961103i | \(0.589071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.9003 | − | 7.78963i | −1.50613 | − | 0.436135i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.24609 | − | 0.905337i | 0.0695499 | − | 0.0505310i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.37998 | + | 13.4802i | −0.243709 | + | 0.750058i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.28815 | + | 1.66244i | 0.126924 | + | 0.0922155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.27645 | − | 3.92851i | −0.0705878 | − | 0.217247i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.973897 | 0.0536927 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9644 | 1.20727 | 0.603637 | − | 0.797259i | \(-0.293718\pi\) | ||||
0.603637 | + | 0.797259i | \(0.293718\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.18616 | − | 6.72830i | −0.119801 | − | 0.368709i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.25475 | − | 6.72397i | −0.505641 | − | 0.367370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.91576 | − | 21.2845i | 0.376726 | − | 1.15944i | −0.565581 | − | 0.824693i | \(-0.691348\pi\) |
0.942307 | − | 0.334750i | \(-0.108652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9737 | + | 7.97287i | −0.596010 | + | 0.433027i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.3623 | + | 21.0559i | 0.886068 | + | 1.14024i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.21755 | − | 3.06423i | 0.227726 | − | 0.165453i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.831550 | − | 2.55925i | 0.0447691 | − | 0.137785i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0465 | + | 14.5646i | 1.07615 | + | 0.781869i | 0.977008 | − | 0.213204i | \(-0.0683898\pi\) |
0.0991431 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.89978 | − | 21.2354i | −0.369337 | − | 1.13670i | −0.947220 | − | 0.320583i | \(-0.896121\pi\) |
0.577883 | − | 0.816119i | \(-0.303879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.0788 | 0.591342 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.79232 | −0.308294 | −0.154147 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154147 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.36381 | + | 13.4304i | 0.231607 | + | 0.712813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.05023 | + | 0.763039i | 0.0555842 | + | 0.0403843i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.50069 | − | 20.0071i | 0.343094 | − | 1.05593i | −0.619503 | − | 0.784994i | \(-0.712666\pi\) |
0.962597 | − | 0.270939i | \(-0.0873342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.42648 | − | 6.12219i | 0.443499 | − | 0.322221i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.90145 | − | 7.29075i | −0.152286 | − | 0.382665i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.415207 | + | 0.301666i | −0.0217330 | + | 0.0157899i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.30007 | + | 22.4673i | −0.381061 | + | 1.17278i | 0.558237 | + | 0.829681i | \(0.311478\pi\) |
−0.939298 | + | 0.343103i | \(0.888522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.49785 | − | 5.44750i | −0.390322 | − | 0.283586i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.00566834 | − | 0.0174453i | −0.000294285 | − | 0.000905717i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7740 | −0.661411 | −0.330705 | − | 0.943734i | \(-0.607287\pi\) | ||||
−0.330705 | + | 0.943734i | \(0.607287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.713352 | 0.0368373 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.37998 | − | 22.7132i | −0.380088 | − | 1.16979i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0453 | − | 14.5637i | −1.02966 | − | 0.748089i | −0.0614167 | − | 0.998112i | \(-0.519562\pi\) |
−0.968240 | + | 0.250023i | \(0.919562\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.22583 | + | 6.85041i | −0.114033 | + | 0.350957i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8810 | + | 22.4363i | −1.57794 | + | 1.14644i | −0.658941 | + | 0.752195i | \(0.728995\pi\) |
−0.919004 | + | 0.394249i | \(0.871005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.765542 | + | 0.985142i | 0.0390157 | + | 0.0502075i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.0693 | + | 9.49542i | −0.664351 | + | 0.482679i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.744648 | − | 2.29179i | 0.0377551 | − | 0.116198i | −0.930403 | − | 0.366539i | \(-0.880543\pi\) |
0.968158 | + | 0.250341i | \(0.0805426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.7638 | + | 10.7265i | 0.746635 | + | 0.542462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.38799 | − | 4.27179i | −0.0700148 | − | 0.215483i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9823 | 0.653212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5456 | −0.579459 | −0.289729 | − | 0.957109i | \(-0.593565\pi\) | ||||
−0.289729 | + | 0.957109i | \(0.593565\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.242955 | + | 0.747738i | 0.0121630 | + | 0.0374337i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7114 | − | 15.0477i | −1.03428 | − | 0.751445i | −0.0651157 | − | 0.997878i | \(-0.520742\pi\) |
−0.969160 | + | 0.246432i | \(0.920742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.02702 | + | 21.6269i | −0.350041 | + | 1.07731i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.78548 | + | 2.75031i | −0.188102 | + | 0.136664i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.04720 | − | 2.61983i | −0.448453 | − | 0.129860i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.57539 | + | 5.50384i | −0.374579 | + | 0.272147i | −0.759107 | − | 0.650966i | \(-0.774364\pi\) |
0.384528 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.82375 | + | 5.61292i | −0.0899588 | + | 0.276865i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.501929 | + | 0.364673i | 0.0246983 | + | 0.0179444i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.845740 | + | 2.60292i | 0.0415157 | + | 0.127772i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.32405 | −0.358660 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.3716 | −1.04407 | −0.522035 | − | 0.852924i | \(-0.674827\pi\) | ||||
−0.522035 | + | 0.852924i | \(0.674827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.50429 | + | 26.1735i | 0.414474 | + | 1.27562i | 0.912721 | + | 0.408584i | \(0.133977\pi\) |
−0.498247 | + | 0.867035i | \(0.666023\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.21771 | + | 3.79089i | 0.253694 | + | 0.184319i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.49493 | + | 4.60091i | −0.0725146 | + | 0.223177i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.64677 | + | 1.92299i | −0.128086 | + | 0.0930601i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.75635 | − | 5.53776i | 0.181358 | − | 0.267366i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.12962 | + | 1.54726i | −0.102580 | + | 0.0745290i | −0.637893 | − | 0.770125i | \(-0.720194\pi\) |
0.535313 | + | 0.844654i | \(0.320194\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.08722 | − | 9.50147i | 0.148362 | − | 0.456612i | −0.849066 | − | 0.528287i | \(-0.822835\pi\) |
0.997428 | + | 0.0716753i | \(0.0228345\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.87313 | − | 3.54053i | −0.233648 | − | 0.169756i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.41536 | + | 10.5114i | 0.163379 | + | 0.502829i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.85957 | 0.136480 | 0.0682400 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682400 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.0854 | 0.813590 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.4551 | − | 38.3329i | −0.591761 | − | 1.82125i | −0.570232 | − | 0.821484i | \(-0.693147\pi\) |
−0.0215292 | − | 0.999768i | \(-0.506853\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.72401 | − | 7.06491i | −0.460962 | − | 0.334909i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.08050 | + | 3.32543i | −0.0511058 | + | 0.157287i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.57792 | − | 1.14642i | 0.0744665 | − | 0.0541031i | −0.549929 | − | 0.835211i | \(-0.685345\pi\) |
0.624396 | + | 0.781108i | \(0.285345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6058 | + | 4.18988i | −0.546497 | + | 0.197294i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.39963 | − | 3.92306i | 0.253697 | − | 0.184321i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.328773 | + | 1.01186i | −0.0154131 | + | 0.0474367i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.9438 | − | 21.0289i | −1.35393 | − | 0.983691i | −0.998805 | − | 0.0488733i | \(-0.984437\pi\) |
−0.355129 | − | 0.934817i | \(-0.615563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.85579 | + | 18.0223i | 0.273325 | + | 0.841207i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1433 | 0.705295 | 0.352648 | − | 0.935756i | \(-0.385281\pi\) | ||||
0.352648 | + | 0.935756i | \(0.385281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6301 | −0.586972 | −0.293486 | − | 0.955963i | \(-0.594815\pi\) | ||||
−0.293486 | + | 0.955963i | \(0.594815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.77234 | + | 5.45471i | 0.0821905 | + | 0.252956i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.3664 | − | 18.4298i | −1.17382 | − | 0.852829i | −0.182358 | − | 0.983232i | \(-0.558373\pi\) |
−0.991461 | + | 0.130403i | \(0.958373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.32977 | − | 4.09261i | 0.0614030 | − | 0.188979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.57387 | + | 4.04965i | −0.256830 | + | 0.186598i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.694470 | + | 21.4966i | 0.0319318 | + | 0.988413i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.37034 | + | 1.72215i | −0.108759 | + | 0.0790177i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0375375 | − | 0.115528i | 0.00171872 | − | 0.00528969i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.97966 | + | 7.25064i | 0.455982 | + | 0.331290i | 0.791953 | − | 0.610582i | \(-0.209064\pi\) |
−0.335971 | + | 0.941872i | \(0.609064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.48206 | − | 7.63900i | −0.113172 | − | 0.348308i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.01226 | 0.0460595 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0745 | 0.729906 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.77063 | − | 20.8379i | −0.306807 | − | 0.944254i | −0.978997 | − | 0.203875i | \(-0.934646\pi\) |
0.672190 | − | 0.740378i | \(-0.265354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.59010 | − | 1.88182i | −0.117128 | − | 0.0850987i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.45266 | + | 26.0146i | −0.381463 | + | 1.17402i | 0.557551 | + | 0.830143i | \(0.311741\pi\) |
−0.939014 | + | 0.343880i | \(0.888259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.0477 | − | 24.0106i | 1.48839 | − | 1.08138i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.266778 | + | 8.25783i | 0.0119908 | + | 0.371162i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.29762 | + | 3.12240i | −0.192775 | + | 0.140059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.21316 | + | 9.88908i | −0.143841 | + | 0.442696i | −0.996860 | − | 0.0791832i | \(-0.974769\pi\) |
0.853019 | + | 0.521879i | \(0.174769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5458 | + | 9.84158i | 0.605180 | + | 0.439689i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.20969 | − | 9.87840i | −0.143113 | − | 0.440456i | 0.853651 | − | 0.520846i | \(-0.174383\pi\) |
−0.996763 | + | 0.0803900i | \(0.974383\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5883 | 0.693670 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.56724 | −0.158427 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.13139 | + | 21.9482i | 0.316093 | + | 0.972835i | 0.975302 | + | 0.220875i | \(0.0708913\pi\) |
−0.659209 | + | 0.751960i | \(0.729109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.156189 | − | 0.113478i | −0.00690942 | − | 0.00501998i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.54650 | + | 10.9150i | −0.156582 | + | 0.481910i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.49074 | − | 5.44234i | 0.330082 | − | 0.239818i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.07643 | − | 2.91572i | 0.355201 | − | 0.128233i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.47413 | − | 5.43027i | 0.328078 | − | 0.238363i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.9451 | − | 33.6855i | 0.479513 | − | 1.47579i | −0.360260 | − | 0.932852i | \(-0.617312\pi\) |
0.839773 | − | 0.542938i | \(-0.182688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6855 | + | 10.6697i | 0.642153 | + | 0.466551i | 0.860589 | − | 0.509300i | \(-0.170096\pi\) |
−0.218436 | + | 0.975851i | \(0.570096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0829226 | + | 0.255210i | 0.00361904 | + | 0.0111383i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.8955 | −1.69431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.77004 | −0.381306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.26963 | + | 3.90751i | 0.0550972 | + | 0.169572i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.51270 | − | 6.18484i | −0.368726 | − | 0.267895i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.667222 | + | 2.05350i | −0.0288465 | + | 0.0887804i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.03683 | − | 1.47984i | 0.0878956 | − | 0.0638599i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7692 | − | 18.8249i | 0.550008 | − | 0.810845i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1542 | + | 9.55711i | −0.565545 | + | 0.410892i | −0.833484 | − | 0.552543i | \(-0.813657\pi\) |
0.267939 | + | 0.963436i | \(0.413657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.394976 | − | 1.21561i | 0.0169500 | − | 0.0521669i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.68463 | + | 3.40358i | 0.200667 | + | 0.145793i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.81979 | + | 14.8338i | 0.206079 | + | 0.634246i | 0.999667 | + | 0.0257912i | \(0.00821049\pi\) |
−0.793588 | + | 0.608455i | \(0.791790\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.6655 | −0.924660 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.7399 | 1.05396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50911 | + | 4.64457i | 0.0641740 | + | 0.197507i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.63895 | − | 1.19076i | −0.0695694 | − | 0.0505451i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.25243 | − | 10.0099i | 0.137810 | − | 0.424135i | −0.858207 | − | 0.513304i | \(-0.828421\pi\) |
0.996016 | + | 0.0891695i | \(0.0284213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.8383 | + | 10.7806i | −0.627593 | + | 0.455973i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.9939 | + | 3.18355i | 0.464164 | + | 0.134410i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.48416 | + | 6.89065i | −0.399710 | + | 0.290406i | −0.769423 | − | 0.638740i | \(-0.779456\pi\) |
0.369713 | + | 0.929146i | \(0.379456\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.87590 | − | 18.0842i | 0.247201 | − | 0.760806i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.42399 | − | 1.03459i | −0.0598020 | − | 0.0434487i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.95887 | − | 9.10646i | −0.124042 | − | 0.381763i | 0.869683 | − | 0.493610i | \(-0.164323\pi\) |
−0.993725 | + | 0.111848i | \(0.964323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0439 | 1.84318 | 0.921589 | − | 0.388166i | \(-0.126891\pi\) | ||||
0.921589 | + | 0.388166i | \(0.126891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.42620 | 0.101356 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.16569 | + | 3.58763i | 0.0486128 | + | 0.149615i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.6902 | + | 16.4854i | 0.944604 | + | 0.686295i | 0.949525 | − | 0.313693i | \(-0.101566\pi\) |
−0.00492032 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.71400 | + | 5.27515i | −0.0712314 | + | 0.219228i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.832911 | + | 0.605145i | −0.0345550 | + | 0.0251057i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0992360 | − | 0.127702i | −0.00410993 | − | 0.00528889i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.70008 | + | 4.14135i | −0.235669 | + | 0.171224i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.837247 | + | 2.57678i | −0.0345569 | + | 0.106355i | −0.966847 | − | 0.255356i | \(-0.917807\pi\) |
0.932290 | + | 0.361711i | \(0.117807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.0578 | − | 13.8463i | −0.785261 | − | 0.570526i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.56381 | − | 4.81291i | −0.0643265 | − | 0.197977i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.1817 | −1.44474 | −0.722369 | − | 0.691508i | \(-0.756947\pi\) | ||||
−0.722369 | + | 0.691508i | \(0.756947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.81980 | −0.0746046 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.81574 | + | 8.66595i | 0.115240 | + | 0.354674i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.2343 | + | 27.7788i | 1.56221 | + | 1.13501i | 0.934167 | + | 0.356835i | \(0.116144\pi\) |
0.628044 | + | 0.778178i | \(0.283856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.59792 | − | 11.0733i | 0.146762 | − | 0.451687i | −0.850471 | − | 0.526022i | \(-0.823683\pi\) |
0.997233 | + | 0.0743341i | \(0.0236831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.0548 | − | 16.7503i | 0.938863 | − | 0.682124i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.29795 | + | 5.87776i | 0.378016 | + | 0.238965i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.1632 | − | 27.0006i | 1.50841 | − | 1.09592i | 0.541528 | − | 0.840683i | \(-0.317846\pi\) |
0.966878 | − | 0.255238i | \(-0.0821539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.700195 | − | 2.15498i | 0.0283733 | − | 0.0873241i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.92394 | + | 4.30400i | 0.239657 | + | 0.174121i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.03724 | + | 3.19229i | 0.0418937 | + | 0.128935i | 0.969816 | − | 0.243839i | \(-0.0784067\pi\) |
−0.927922 | + | 0.372774i | \(0.878407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.65391 | −0.107016 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4880 | −0.663783 | −0.331892 | − | 0.943318i | \(-0.607687\pi\) | ||||
−0.331892 | + | 0.943318i | \(0.607687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.635849 | + | 1.95694i | 0.0255569 | + | 0.0786561i | 0.963021 | − | 0.269425i | \(-0.0868335\pi\) |
−0.937465 | + | 0.348081i | \(0.886834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.9543 | + | 8.68533i | 0.479711 | + | 0.348530i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.39719 | − | 4.30012i | 0.0559774 | − | 0.172281i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.25343 | + | 5.47355i | 0.169866 | + | 0.218592i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1147 | − | 8.07531i | 0.443173 | − | 0.321984i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8822 | − | 33.4918i | 0.433212 | − | 1.33329i | −0.461696 | − | 0.887038i | \(-0.652759\pi\) |
0.894908 | − | 0.446251i | \(-0.147241\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.23629 | − | 3.07784i | −0.168377 | − | 0.122333i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.12025 | − | 9.60313i | −0.123823 | − | 0.381088i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.3979 | 0.768574 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.1787 | −1.39165 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4016 | − | 32.0128i | −0.410838 | − | 1.26443i | −0.915921 | − | 0.401359i | \(-0.868538\pi\) |
0.505083 | − | 0.863071i | \(-0.331462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.62876 | + | 1.18336i | 0.0642320 | + | 0.0466673i | 0.619438 | − | 0.785046i | \(-0.287361\pi\) |
−0.555206 | + | 0.831713i | \(0.687361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.42950 | + | 4.39956i | −0.0562867 | + | 0.173233i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.5398 | + | 20.0088i | −1.08270 | + | 0.786628i | −0.978152 | − | 0.207892i | \(-0.933340\pi\) |
−0.104548 | + | 0.994520i | \(0.533340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.25423 | + | 1.52149i | 0.206247 | + | 0.0597237i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.74546 | + | 1.26815i | −0.0684100 | + | 0.0497028i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.53960 | + | 20.1268i | −0.255914 | + | 0.787623i | 0.737734 | + | 0.675091i | \(0.235896\pi\) |
−0.993648 | + | 0.112531i | \(0.964104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.09398 | + | 3.70099i | 0.199038 | + | 0.144610i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.395081 | − | 1.21593i | −0.0154136 | − | 0.0474381i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3464 | 0.831539 | 0.415770 | − | 0.909470i | \(-0.363512\pi\) | ||||
0.415770 | + | 0.909470i | \(0.363512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3318 | 0.440757 | 0.220379 | − | 0.975414i | \(-0.429271\pi\) | ||||
0.220379 | + | 0.975414i | \(0.429271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.01613 | + | 9.28270i | 0.117137 | + | 0.360510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.891655 | − | 0.647825i | −0.0345769 | − | 0.0251216i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.84306 | − | 30.2938i | 0.381125 | − | 1.17298i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.77360 | + | 2.74168i | −0.145896 | + | 0.106000i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.1922 | + | 23.8713i | −0.625094 | + | 0.921540i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7639 | − | 11.4531i | 0.607653 | − | 0.441486i | −0.240934 | − | 0.970541i | \(-0.577454\pi\) |
0.848587 | + | 0.529056i | \(0.177454\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.21045 | + | 3.72539i | −0.0465904 | + | 0.143390i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8399 | + | 15.1411i | 0.800944 | + | 0.581920i | 0.911191 | − | 0.411985i | \(-0.135164\pi\) |
−0.110247 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.86856 | + | 5.75083i | 0.0717087 | + | 0.220697i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.6566 | 0.561643 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0179 | 0.498117 | 0.249059 | − | 0.968488i | \(-0.419879\pi\) | ||||
0.249059 | + | 0.968488i | \(0.419879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.55659 | − | 7.86837i | −0.0976822 | − | 0.300635i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.49945 | + | 1.81595i | 0.0953598 | + | 0.0692829i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0426183 | − | 0.131166i | 0.00162363 | − | 0.00499701i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4366 | − | 28.6523i | 1.50024 | − | 1.08999i | 0.529950 | − | 0.848029i | \(-0.322211\pi\) |
0.970287 | − | 0.241957i | \(-0.0777894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.92332 | + | 1.05536i | −0.111048 | + | 0.0400899i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.30625 | − | 6.03484i | 0.315074 | − | 0.228915i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.56164 | − | 17.1170i | 0.210662 | − | 0.648351i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.5398 | − | 12.0169i | −0.625593 | − | 0.454520i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9531 | + | 42.9432i | 0.527001 | + | 1.62194i | 0.760324 | + | 0.649544i | \(0.225040\pi\) |
−0.233322 | + | 0.972399i | \(0.574960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.32062 | 0.313818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.84684 | 0.0695562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.81204 | + | 5.57688i | 0.0681487 | + | 0.209740i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.34695 | + | 4.61133i | 0.238365 | + | 0.173182i | 0.700554 | − | 0.713599i | \(-0.252936\pi\) |
−0.462190 | + | 0.886781i | \(0.652936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.99381 | + | 30.7578i | −0.374797 | + | 1.15351i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.5370 | + | 17.8272i | −0.918917 | + | 0.667633i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.302887 | + | 9.37555i | 0.0113273 | + | 0.350626i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.04621 | − | 4.39283i | 0.225800 | − | 0.164053i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2597 | − | 34.6538i | 0.419916 | − | 1.29237i | −0.487864 | − | 0.872920i | \(-0.662224\pi\) |
0.907780 | − | 0.419447i | \(-0.137776\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81781 | + | 2.04726i | 0.104941 | + | 0.0762439i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.42124 | + | 10.5295i | 0.127237 | + | 0.391597i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.44396 | 0.313601 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.4970 | −0.574753 | −0.287376 | − | 0.957818i | \(-0.592783\pi\) | ||||
−0.287376 | + | 0.957818i | \(0.592783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.01155 | − | 3.11322i | −0.0374647 | − | 0.115304i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3802 | − | 18.4398i | −0.938719 | − | 0.682020i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0999 | − | 40.3172i | 0.483854 | − | 1.48915i | −0.349779 | − | 0.936832i | \(-0.613743\pi\) |
0.833633 | − | 0.552318i | \(-0.186257\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.95813 | − | 2.87575i | 0.145998 | − | 0.106074i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.22507 | − | 37.9208i | −0.0451261 | − | 1.39683i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5290 | − | 17.8214i | 0.902315 | − | 0.655570i | −0.0367444 | − | 0.999325i | \(-0.511699\pi\) |
0.939060 | + | 0.343754i | \(0.111699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.82669 | + | 5.62198i | −0.0671053 | + | 0.206529i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8518 | + | 12.2436i | 0.618234 | + | 0.449173i | 0.852304 | − | 0.523047i | \(-0.175205\pi\) |
−0.234070 | + | 0.972220i | \(0.575205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.51468 | − | 4.66169i | −0.0554934 | − | 0.170791i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.81790 | −0.249454 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.812221 | −0.0296779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.50988 | − | 29.2684i | −0.347020 | − | 1.06802i | −0.960493 | − | 0.278303i | \(-0.910228\pi\) |
0.613473 | − | 0.789716i | \(-0.289772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.90812 | + | 5.01905i | 0.251746 | + | 0.182904i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.89124 | + | 8.89833i | −0.105223 | + | 0.323843i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.5370 | − | 14.9210i | 0.746429 | − | 0.542312i | −0.148289 | − | 0.988944i | \(-0.547377\pi\) |
0.894718 | + | 0.446632i | \(0.147377\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.39458 | − | 3.03057i | 0.304704 | − | 0.110003i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2145 | + | 19.7725i | −0.986526 | + | 0.716753i | −0.959158 | − | 0.282872i | \(-0.908713\pi\) |
−0.0273686 | + | 0.999625i | \(0.508713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.673110 | + | 2.07162i | −0.0243682 | + | 0.0749977i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.74970 | − | 7.08357i | −0.352501 | − | 0.256107i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.44148 | + | 4.43641i | 0.0520487 | + | 0.160189i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.4388 | −1.06159 | −0.530795 | − | 0.847500i | \(-0.678107\pi\) | ||||
−0.530795 | + | 0.847500i | \(0.678107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.04453 | −0.217688 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.65080 | + | 23.5467i | 0.275180 | + | 0.846917i | 0.989172 | + | 0.146763i | \(0.0468855\pi\) |
−0.713992 | + | 0.700154i | \(0.753115\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.50458 | − | 4.72586i | −0.233651 | − | 0.169758i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.235492 | − | 0.724770i | 0.00844823 | − | 0.0260010i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.81846 | − | 6.40699i | 0.315954 | − | 0.229554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2917 | + | 38.7603i | −0.940791 | + | 1.38695i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.7590 | − | 19.4415i | 0.956287 | − | 0.694783i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.98454 | − | 9.18547i | 0.106523 | − | 0.327843i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3056 | − | 22.0183i | −1.08028 | − | 0.784869i | −0.102547 | − | 0.994728i | \(-0.532699\pi\) |
−0.977732 | + | 0.209860i | \(0.932699\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.75965 | + | 8.49332i | 0.0982460 | + | 0.302370i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.15284 | 0.254326 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.5979 | −0.873499 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0107491 | − | 0.0330824i | −0.000381232 | − | 0.00117331i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.9506 | + | 28.2993i | 1.37970 | + | 1.00241i | 0.996908 | + | 0.0785781i | \(0.0250380\pi\) |
0.382794 | + | 0.923834i | \(0.374962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.87031 | + | 11.9116i | −0.136922 | + | 0.421402i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.2238 | − | 17.5996i | 0.855905 | − | 0.621851i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.63500 | − | 0.473454i | −0.0576980 | − | 0.0167078i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.14801 | + | 0.834079i | −0.0404621 | + | 0.0293974i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.30481 | + | 16.3265i | −0.186738 | + | 0.574721i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.1663 | − | 21.9171i | −1.06059 | − | 0.770564i | −0.0863934 | − | 0.996261i | \(-0.527534\pi\) |
−0.974198 | + | 0.225697i | \(0.927534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.74285 | + | 8.44162i | 0.0963145 | + | 0.296425i | 0.987594 | − | 0.157029i | \(-0.0501916\pi\) |
−0.891280 | + | 0.453454i | \(0.850192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.72135 | −0.235728 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.48802 | 0.157208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.87130 | − | 18.0700i | −0.205411 | − | 0.632189i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.14421 | − | 1.55786i | −0.0749248 | − | 0.0544360i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.62682 | + | 29.6283i | −0.335978 | + | 1.03403i | 0.630260 | + | 0.776384i | \(0.282948\pi\) |
−0.966238 | + | 0.257650i | \(0.917052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4022 | − | 19.1823i | 0.920321 | − | 0.668653i | −0.0232827 | − | 0.999729i | \(-0.507412\pi\) |
0.943604 | + | 0.331076i | \(0.107412\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.45173 | + | 1.86817i | 0.0505428 | + | 0.0650413i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.2668 | − | 16.9043i | 0.809067 | − | 0.587822i | −0.104493 | − | 0.994526i | \(-0.533322\pi\) |
0.913560 | + | 0.406704i | \(0.133322\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.2250 | + | 40.7023i | −0.459323 | + | 1.41365i | 0.406661 | + | 0.913579i | \(0.366693\pi\) |
−0.865984 | + | 0.500071i | \(0.833307\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.7244 | − | 9.97136i | −0.476094 | − | 0.345903i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2529 | + | 31.5553i | 0.355243 | + | 1.09333i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.4716 | −0.812267 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.4940 | −1.08859 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.81709 | − | 27.1362i | −0.304400 | − | 0.936846i | −0.979900 | − | 0.199487i | \(-0.936072\pi\) |
0.675501 | − | 0.737359i | \(-0.263928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.2218 | − | 24.8636i | −1.18006 | − | 0.857364i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.109536 | − | 0.337119i | 0.00377264 | − | 0.0116110i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.04563 | − | 2.93932i | 0.139174 | − | 0.101116i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.02201 | + | 4.00970i | −0.0351165 | + | 0.137775i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.70107 | + | 1.96244i | −0.0927004 | + | 0.0673508i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.31045 | − | 10.1885i | 0.113481 | − | 0.349258i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.0293 | − | 19.6380i | −0.925466 | − | 0.672391i | 0.0194121 | − | 0.999812i | \(-0.493821\pi\) |
−0.944879 | + | 0.327421i | \(0.893821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.25544 | − | 6.94153i | −0.0771344 | − | 0.237395i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.9632 | 0.408656 | 0.204328 | − | 0.978902i | \(-0.434499\pi\) | ||||
0.204328 | + | 0.978902i | \(0.434499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.4984 | 0.801755 | 0.400878 | − | 0.916132i | \(-0.368705\pi\) | ||||
0.400878 | + | 0.916132i | \(0.368705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.308500 | − | 0.949467i | −0.0105137 | − | 0.0323577i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.31223 | − | 2.40647i | −0.112750 | − | 0.0819173i | 0.529982 | − | 0.848009i | \(-0.322199\pi\) |
−0.642731 | + | 0.766092i | \(0.722199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00204 | + | 12.3170i | −0.136073 | + | 0.418791i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.69536 | + | 2.68484i | −0.125501 | + | 0.0911819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.4201 | + | 33.9989i | 0.896242 | + | 1.15333i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.1753 | − | 19.0175i | 0.886916 | − | 0.644382i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.3742 | + | 38.0838i | −0.418803 | + | 1.28894i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.304330 | − | 0.221108i | −0.0102882 | − | 0.00747483i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7101 | + | 42.1952i | 0.462956 | + | 1.42483i | 0.861535 | + | 0.507698i | \(0.169503\pi\) |
−0.398579 | + | 0.917134i | \(0.630497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0701 | 0.407115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.0315 | −1.44977 | −0.724884 | − | 0.688871i | \(-0.758107\pi\) | ||||
−0.724884 | + | 0.688871i | \(0.758107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.2928 | − | 34.7558i | −0.380034 | − | 1.16963i | −0.940019 | − | 0.341122i | \(-0.889193\pi\) |
0.559985 | − | 0.828503i | \(-0.310807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.951831 | + | 0.691545i | 0.0319954 | + | 0.0232460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.554496 | + | 1.70656i | −0.0186181 | + | 0.0573008i | −0.959934 | − | 0.280226i | \(-0.909590\pi\) |
0.941316 | + | 0.337527i | \(0.109590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.07292 | − | 2.23260i | 0.103062 | − | 0.0748791i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9065 | − | 4.31652i | −0.499385 | − | 0.144609i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.13672 | + | 4.45859i | −0.205358 | + | 0.149201i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09062 | + | 3.35659i | −0.0364555 | + | 0.112199i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.15730 | + | 4.47354i | 0.205586 | + | 0.149367i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.9793 | + | 64.5675i | 0.699697 | + | 2.15345i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.235898 | 0.00785890 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.74016 | −0.0579090 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.553690 | + | 1.70408i | 0.0184053 | + | 0.0566457i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.4760 | + | 30.1341i | 1.37719 | + | 1.00059i | 0.997137 | + | 0.0756199i | \(0.0240936\pi\) |
0.380051 | + | 0.924966i | \(0.375906\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.9999 | + | 36.9318i | −0.398011 | + | 1.22495i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.4256 | + | 23.5586i | −1.07431 | + | 0.780531i | −0.976682 | − | 0.214692i | \(-0.931125\pi\) |
−0.0976273 | + | 0.995223i | \(0.531125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.09553 | + | 7.51204i | −0.168637 | + | 0.248612i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.01919 | + | 3.64665i | −0.165929 | + | 0.120555i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.731929 | + | 2.25264i | −0.0241704 | + | 0.0743889i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.876551 | − | 0.636852i | −0.0289147 | − | 0.0210078i | 0.573234 | − | 0.819392i | \(-0.305689\pi\) |
−0.602149 | + | 0.798384i | \(0.705689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.57573 | − | 23.3157i | −0.249629 | − | 0.768279i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.9402 | −1.31465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.83990 | 0.0933754 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.12764 | + | 21.9366i | 0.234102 | + | 0.720493i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.5480 | − | 8.39015i | −0.378879 | − | 0.275272i | 0.382004 | − | 0.924161i | \(-0.375234\pi\) |
−0.760883 | + | 0.648889i | \(0.775234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.20960 | + | 19.1112i | −0.203511 | + | 0.626344i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.25212 | + | 3.08935i | −0.139208 | + | 0.101141i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.0914 | + | 5.44824i | −0.493543 | + | 0.178177i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.5636 | − | 16.3934i | 0.737120 | − | 0.535549i | −0.154688 | − | 0.987963i | \(-0.549437\pi\) |
0.891808 | + | 0.452415i | \(0.149437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.52430 | + | 17.0020i | −0.180279 | + | 0.554841i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.93220 | − | 2.13037i | −0.0955869 | − | 0.0694480i | 0.538965 | − | 0.842328i | \(-0.318815\pi\) |
−0.634552 | + | 0.772880i | \(0.718815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.33678 | − | 13.3472i | −0.141225 | − | 0.434645i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.47351 | −0.0479332 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.9559 | −1.78583 | −0.892913 | − | 0.450230i | \(-0.851342\pi\) | ||||
−0.892913 | + | 0.450230i | \(0.851342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.448556 | − | 1.38051i | −0.0145607 | − | 0.0448134i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.2012 | − | 11.7709i | −0.525361 | − | 0.381697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.79241 | + | 8.59415i | −0.0904550 | + | 0.278392i | −0.986043 | − | 0.166493i | \(-0.946756\pi\) |
0.895588 | + | 0.444885i | \(0.146756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.75157 | + | 1.99913i | −0.0890387 | + | 0.0646904i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.645066 | − | 19.9673i | −0.0208520 | − | 0.645452i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.51781 | − | 1.82930i | 0.0813043 | − | 0.0590710i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.3964 | − | 31.9967i | 0.335366 | − | 1.03215i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.35153 | − | 3.16157i | −0.140226 | − | 0.101880i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.40274 | − | 7.39487i | −0.0773469 | − | 0.238049i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.4619 | −1.42980 | −0.714900 | − | 0.699227i | \(-0.753528\pi\) | ||||
−0.714900 | + | 0.699227i | \(0.753528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.1110 | −0.324812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.515647 | + | 1.58700i | 0.0165479 | + | 0.0509292i | 0.958990 | − | 0.283442i | \(-0.0914762\pi\) |
−0.942442 | + | 0.334371i | \(0.891476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12458 | + | 2.27014i | 0.100169 | + | 0.0727773i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.623466 | + | 1.91883i | −0.0199669 | + | 0.0614518i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.3272 | + | 13.3155i | −0.586339 | + | 0.426000i | −0.841004 | − | 0.541029i | \(-0.818035\pi\) |
0.254665 | + | 0.967029i | \(0.418035\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.28719 | − | 39.8435i | −0.0411387 | − | 1.27340i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6700 | + | 8.47876i | −0.372595 | + | 0.270706i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5087 | − | 44.6531i | 0.462754 | − | 1.42421i | −0.399031 | − | 0.916938i | \(-0.630653\pi\) |
0.861785 | − | 0.507274i | \(-0.169347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.73925 | + | 4.16981i | 0.182868 | + | 0.132861i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.214684 | + | 0.660729i | 0.00683346 | + | 0.0210312i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.4625 | −0.777863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.122612 | −0.00389489 | −0.00194745 | − | 0.999998i | \(-0.500620\pi\) | ||||
−0.00194745 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.84179 | + | 14.9015i | 0.153650 | + | 0.472885i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3339 | − | 7.50800i | −0.327606 | − | 0.238020i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.23692 | + | 19.1953i | −0.197525 | + | 0.607920i | 0.802413 | + | 0.596770i | \(0.203549\pi\) |
−0.999938 | + | 0.0111504i | \(0.996451\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.99967 | − | 6.53864i | 0.284737 | − | 0.206873i |
(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 | 440.2.y.d.201.3 | yes | 16 | |
4.3 | odd | 2 | 880.2.bo.k.641.2 | 16 | |||
11.2 | odd | 10 | 4840.2.a.bh.1.5 | 8 | |||
11.4 | even | 5 | inner | 440.2.y.d.81.3 | ✓ | 16 | |
11.9 | even | 5 | 4840.2.a.bg.1.5 | 8 | |||
44.15 | odd | 10 | 880.2.bo.k.81.2 | 16 | |||
44.31 | odd | 10 | 9680.2.a.df.1.4 | 8 | |||
44.35 | even | 10 | 9680.2.a.de.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.d.81.3 | ✓ | 16 | 11.4 | even | 5 | inner | |
440.2.y.d.201.3 | yes | 16 | 1.1 | even | 1 | trivial | |
880.2.bo.k.81.2 | 16 | 44.15 | odd | 10 | |||
880.2.bo.k.641.2 | 16 | 4.3 | odd | 2 | |||
4840.2.a.bg.1.5 | 8 | 11.9 | even | 5 | |||
4840.2.a.bh.1.5 | 8 | 11.2 | odd | 10 | |||
9680.2.a.de.1.4 | 8 | 44.35 | even | 10 | |||
9680.2.a.df.1.4 | 8 | 44.31 | odd | 10 |