Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.5 | ||
Root | \(-0.671462 - 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.q.1549.6 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24464 | − | 0.671462i | 0.880096 | − | 0.474795i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.09828 | − | 1.67146i | 0.549139 | − | 0.835731i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.68585i | − | 1.77108i | −0.464560 | − | 0.885542i | \(-0.653787\pi\) | ||
0.464560 | − | 0.885542i | \(-0.346213\pi\) | |||||||
\(8\) | 0.244644 | − | 2.81783i | 0.0864948 | − | 0.996252i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29273i | 0.691284i | 0.938366 | + | 0.345642i | \(0.112339\pi\) | ||||
−0.938366 | + | 0.345642i | \(0.887661\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.97858 | −1.38081 | −0.690404 | − | 0.723424i | \(-0.742567\pi\) | ||||
−0.690404 | + | 0.723424i | \(0.742567\pi\) | |||||||
\(14\) | −3.14637 | − | 5.83221i | −0.840902 | − | 1.55872i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58757 | − | 3.67146i | −0.396892 | − | 0.917865i | ||||
\(17\) | − | 2.97858i | − | 0.722411i | −0.932486 | − | 0.361206i | \(-0.882365\pi\) | ||
0.932486 | − | 0.361206i | \(-0.117635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68585i | 0.616175i | 0.951358 | + | 0.308088i | \(0.0996890\pi\) | ||||
−0.951358 | + | 0.308088i | \(0.900311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.53948 | + | 2.85363i | 0.328218 | + | 0.608397i | ||||
\(23\) | − | 2.68585i | − | 0.560038i | −0.959995 | − | 0.280019i | \(-0.909659\pi\) | ||
0.959995 | − | 0.280019i | \(-0.0903407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.19656 | + | 3.34292i | −1.21524 | + | 0.655601i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.83221 | − | 5.14637i | −1.48015 | − | 0.972572i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.97858 | −1.25339 | −0.626695 | − | 0.779265i | \(-0.715593\pi\) | ||||
−0.626695 | + | 0.779265i | \(0.715593\pi\) | |||||||
\(32\) | −4.44120 | − | 3.50367i | −0.785101 | − | 0.619368i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 3.70727i | −0.342997 | − | 0.635791i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.39312 | −0.722224 | −0.361112 | − | 0.932523i | \(-0.617603\pi\) | ||||
−0.361112 | + | 0.932523i | \(0.617603\pi\) | |||||||
\(38\) | 1.80344 | + | 3.34292i | 0.292557 | + | 0.542294i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3717 | 1.77596 | 0.887980 | − | 0.459882i | \(-0.152108\pi\) | ||||
0.887980 | + | 0.459882i | \(0.152108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.37169 | 1.42917 | 0.714585 | − | 0.699549i | \(-0.246616\pi\) | ||||
0.714585 | + | 0.699549i | \(0.246616\pi\) | |||||||
\(44\) | 3.83221 | + | 2.51806i | 0.577728 | + | 0.379611i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.80344 | − | 3.34292i | −0.265903 | − | 0.492887i | ||||
\(47\) | 7.27131i | 1.06063i | 0.847801 | + | 0.530315i | \(0.177926\pi\) | ||||
−0.847801 | + | 0.530315i | \(0.822074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.9572 | −2.13674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.46787 | + | 8.32150i | −0.758257 | + | 1.15398i | ||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.2039 | − | 1.14637i | −1.76445 | − | 0.153190i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.34292 | − | 2.48929i | −0.176334 | − | 0.326860i | ||||
\(59\) | − | 1.70727i | − | 0.222267i | −0.993805 | − | 0.111134i | \(-0.964552\pi\) | ||
0.993805 | − | 0.111134i | \(-0.0354482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.58546i | − | 0.587108i | −0.955942 | − | 0.293554i | \(-0.905162\pi\) | ||
0.955942 | − | 0.293554i | \(-0.0948381\pi\) | |||||||
\(62\) | −8.68585 | + | 4.68585i | −1.10310 | + | 0.595103i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88030 | − | 1.37873i | −0.985037 | − | 0.172341i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −4.97858 | − | 3.27131i | −0.603741 | − | 0.396704i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.585462 | −0.0694816 | −0.0347408 | − | 0.999396i | \(-0.511061\pi\) | ||||
−0.0347408 | + | 0.999396i | \(0.511061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | −5.46787 | + | 2.94981i | −0.635626 | + | 0.342908i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.48929 | + | 2.94981i | 0.514957 | + | 0.338366i | ||||
\(77\) | 10.7434 | 1.22432 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.02142 | −0.114919 | −0.0574595 | − | 0.998348i | \(-0.518300\pi\) | ||||
−0.0574595 | + | 0.998348i | \(0.518300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.1537 | − | 7.63565i | 1.56302 | − | 0.843217i | ||||
\(83\) | 13.3717 | 1.46773 | 0.733867 | − | 0.679293i | \(-0.237714\pi\) | ||||
0.733867 | + | 0.679293i | \(0.237714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.6644 | − | 6.29273i | 1.25781 | − | 0.678563i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.46052 | + | 0.560904i | 0.688694 | + | 0.0597925i | ||||
\(89\) | 3.37169 | 0.357399 | 0.178699 | − | 0.983904i | \(-0.442811\pi\) | ||||
0.178699 | + | 0.983904i | \(0.442811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.3288i | 2.44553i | ||||||||
\(92\) | −4.48929 | − | 2.94981i | −0.468041 | − | 0.307539i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.88240 | + | 9.05019i | 0.503581 | + | 0.933456i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.95715i | 0.401788i | 0.979613 | + | 0.200894i | \(0.0643847\pi\) | ||||
−0.979613 | + | 0.200894i | \(0.935615\pi\) | |||||||
\(98\) | −18.6163 | + | 10.0432i | −1.88053 | + | 1.01451i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.00000i | − | 0.199007i | −0.995037 | − | 0.0995037i | \(-0.968274\pi\) | ||
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.6430i | − | 1.44282i | −0.692509 | − | 0.721409i | \(-0.743495\pi\) | ||
0.692509 | − | 0.721409i | \(-0.256505\pi\) | |||||||
\(104\) | −1.21798 | + | 14.0288i | −0.119433 | + | 1.37563i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.48929 | − | 1.34292i | 0.241781 | − | 0.130436i | ||||
\(107\) | −11.3288 | −1.09520 | −0.547600 | − | 0.836740i | \(-0.684459\pi\) | ||||
−0.547600 | + | 0.836740i | \(0.684459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.37169i | − | 0.897645i | −0.893621 | − | 0.448823i | \(-0.851843\pi\) | ||
0.893621 | − | 0.448823i | \(-0.148157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.2039 | + | 7.43910i | −1.62562 | + | 0.702929i | ||||
\(113\) | − | 19.7648i | − | 1.85932i | −0.368423 | − | 0.929658i | \(-0.620102\pi\) | ||
0.368423 | − | 0.929658i | \(-0.379898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.34292 | − | 2.19656i | −0.310383 | − | 0.203945i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.14637 | − | 2.12494i | −0.105531 | − | 0.195617i | ||||
\(119\) | −13.9572 | −1.27945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.74338 | 0.522126 | ||||||||
\(122\) | −3.07896 | − | 5.70727i | −0.278756 | − | 0.516712i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.66442 | + | 11.6644i | −0.688286 | + | 1.04750i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.64300i | − | 0.589471i | −0.955579 | − | 0.294735i | \(-0.904768\pi\) | ||
0.955579 | − | 0.294735i | \(-0.0952315\pi\) | |||||||
\(128\) | −10.7339 | + | 3.57529i | −0.948755 | + | 0.316014i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07896i | 0.618492i | 0.950982 | + | 0.309246i | \(0.100077\pi\) | ||||
−0.950982 | + | 0.309246i | \(0.899923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5855 | 1.09130 | ||||||||
\(134\) | −4.97858 | + | 2.68585i | −0.430084 | + | 0.232022i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.39312 | − | 0.728692i | −0.719704 | − | 0.0624848i | ||||
\(137\) | − | 14.9786i | − | 1.27971i | −0.768497 | − | 0.639853i | \(-0.778995\pi\) | ||
0.768497 | − | 0.639853i | \(-0.221005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.64300i | 0.393814i | 0.980422 | + | 0.196907i | \(0.0630897\pi\) | ||||
−0.980422 | + | 0.196907i | \(0.936910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.728692 | + | 0.393115i | −0.0611505 | + | 0.0329895i | ||||
\(143\) | − | 11.4145i | − | 0.954532i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.02877 | − | 7.46787i | −0.333423 | − | 0.618045i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.82487 | + | 7.34292i | −0.396601 | + | 0.603585i | ||||
\(149\) | − | 2.00000i | − | 0.163846i | −0.996639 | − | 0.0819232i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819232i | \(-0.0261062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.35027 | −0.679535 | −0.339768 | − | 0.940509i | \(-0.610348\pi\) | ||||
−0.339768 | + | 0.940509i | \(0.610348\pi\) | |||||||
\(152\) | 7.56825 | + | 0.657077i | 0.613866 | + | 0.0532960i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.3717 | − | 7.21377i | 1.07752 | − | 0.581302i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3503 | 1.78375 | 0.891873 | − | 0.452286i | \(-0.149391\pi\) | ||||
0.891873 | + | 0.452286i | \(0.149391\pi\) | |||||||
\(158\) | −1.27131 | + | 0.685846i | −0.101140 | + | 0.0545630i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5855 | −0.991873 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.37169 | −0.107439 | −0.0537196 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537196 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(164\) | 12.4893 | − | 19.0073i | 0.975250 | − | 1.48422i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6430 | − | 8.97858i | 1.29175 | − | 0.696873i | ||||
\(167\) | 11.2713i | 0.872200i | 0.899898 | + | 0.436100i | \(0.143641\pi\) | ||||
−0.899898 | + | 0.436100i | \(0.856359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7862 | 0.906633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.2927 | − | 15.6644i | 0.784813 | − | 1.19440i | ||||
\(173\) | 10.7862 | 0.820062 | 0.410031 | − | 0.912072i | \(-0.365518\pi\) | ||||
0.410031 | + | 0.912072i | \(0.365518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.41767 | − | 3.63986i | 0.634506 | − | 0.274365i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.19656 | − | 2.26396i | 0.314545 | − | 0.169691i | ||||
\(179\) | − | 3.66442i | − | 0.273892i | −0.990579 | − | 0.136946i | \(-0.956271\pi\) | ||
0.990579 | − | 0.136946i | \(-0.0437287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.62831i | 0.492678i | 0.969184 | + | 0.246339i | \(0.0792277\pi\) | ||||
−0.969184 | + | 0.246339i | \(0.920772\pi\) | |||||||
\(182\) | 15.6644 | + | 29.0361i | 1.16112 | + | 2.15230i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.56825 | − | 0.657077i | −0.557939 | − | 0.0484404i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82908 | 0.499392 | ||||||||
\(188\) | 12.1537 | + | 7.98592i | 0.886401 | + | 0.582433i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.21377i | 0.0873690i | 0.999045 | + | 0.0436845i | \(0.0139096\pi\) | ||||
−0.999045 | + | 0.0436845i | \(0.986090\pi\) | |||||||
\(194\) | 2.65708 | + | 4.92525i | 0.190767 | + | 0.353612i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.4271 | + | 25.0003i | −1.17337 | + | 1.78574i | ||||
\(197\) | 23.9572 | 1.70688 | 0.853438 | − | 0.521194i | \(-0.174513\pi\) | ||||
0.853438 | + | 0.521194i | \(0.174513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.350269 | −0.0248299 | −0.0124150 | − | 0.999923i | \(-0.503952\pi\) | ||||
−0.0124150 | + | 0.999923i | \(0.503952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.34292 | − | 2.48929i | −0.0944877 | − | 0.175146i | ||||
\(203\) | −9.37169 | −0.657764 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.83221 | − | 18.2253i | −0.685043 | − | 1.26982i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.90383 | + | 18.2787i | 0.548032 | + | 1.26740i | ||||
\(209\) | −6.15792 | −0.425952 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.1004i | − | 0.970710i | −0.874317 | − | 0.485355i | \(-0.838690\pi\) | ||
0.874317 | − | 0.485355i | \(-0.161310\pi\) | |||||||
\(212\) | 2.19656 | − | 3.34292i | 0.150860 | − | 0.229593i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.1004 | + | 7.60688i | −0.963882 | + | 0.519996i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.7005i | 2.21986i | ||||||||
\(218\) | −6.29273 | − | 11.6644i | −0.426198 | − | 0.790014i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8291i | 0.997512i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.72869i | − | 0.450587i | −0.974291 | − | 0.225293i | \(-0.927666\pi\) | ||
0.974291 | − | 0.225293i | \(-0.0723340\pi\) | |||||||
\(224\) | −16.4177 | + | 20.8108i | −1.09695 | + | 1.39048i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.2713 | − | 24.6002i | −0.882794 | − | 1.63638i | ||||
\(227\) | 9.95715 | 0.660880 | 0.330440 | − | 0.943827i | \(-0.392803\pi\) | ||||
0.330440 | + | 0.943827i | \(0.392803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.3288i | − | 0.748631i | −0.927301 | − | 0.374316i | \(-0.877878\pi\) | ||
0.927301 | − | 0.374316i | \(-0.122122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.63565 | − | 0.489289i | −0.369999 | − | 0.0321234i | ||||
\(233\) | 18.9786i | 1.24333i | 0.783284 | + | 0.621664i | \(0.213543\pi\) | ||||
−0.783284 | + | 0.621664i | \(0.786457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.85363 | − | 1.87506i | −0.185756 | − | 0.122056i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.3717 | + | 9.37169i | −1.12604 | + | 0.607477i | ||||
\(239\) | 2.62831 | 0.170011 | 0.0850055 | − | 0.996380i | \(-0.472909\pi\) | ||||
0.0850055 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7862 | 0.694802 | 0.347401 | − | 0.937717i | \(-0.387064\pi\) | ||||
0.347401 | + | 0.937717i | \(0.387064\pi\) | |||||||
\(242\) | 7.14847 | − | 3.85646i | 0.459521 | − | 0.247903i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.66442 | − | 5.03612i | −0.490664 | − | 0.322404i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.3717i | − | 0.850820i | ||||||
\(248\) | −1.70727 | + | 19.6644i | −0.108412 | + | 1.24869i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.9933i | 1.95628i | 0.207952 | + | 0.978139i | \(0.433320\pi\) | ||||
−0.207952 | + | 0.978139i | \(0.566680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.15792 | 0.387145 | ||||||||
\(254\) | −4.46052 | − | 8.26817i | −0.279878 | − | 0.518791i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9593 | + | 11.6574i | −0.684954 | + | 0.728587i | ||||
\(257\) | 20.9357i | 1.30594i | 0.757386 | + | 0.652968i | \(0.226476\pi\) | ||||
−0.757386 | + | 0.652968i | \(0.773524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5855i | 1.27912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.75325 | + | 8.81079i | 0.293657 | + | 0.544332i | ||||
\(263\) | 19.2713i | 1.18832i | 0.804347 | + | 0.594160i | \(0.202515\pi\) | ||||
−0.804347 | + | 0.594160i | \(0.797485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.6644 | − | 8.45065i | 0.960447 | − | 0.518143i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.39312 | + | 6.68585i | −0.268352 | + | 0.408403i | ||||
\(269\) | 24.7434i | 1.50863i | 0.656512 | + | 0.754315i | \(0.272031\pi\) | ||||
−0.656512 | + | 0.754315i | \(0.727969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.5640 | 1.67440 | 0.837198 | − | 0.546900i | \(-0.184192\pi\) | ||||
0.837198 | + | 0.546900i | \(0.184192\pi\) | |||||||
\(272\) | −10.9357 | + | 4.72869i | −0.663076 | + | 0.286719i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0575 | − | 18.6430i | −0.607598 | − | 1.12626i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3074 | 1.22015 | 0.610077 | − | 0.792342i | \(-0.291138\pi\) | ||||
0.610077 | + | 0.792342i | \(0.291138\pi\) | |||||||
\(278\) | 3.11760 | + | 5.77888i | 0.186981 | + | 0.346594i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7862 | 0.643453 | 0.321726 | − | 0.946833i | \(-0.395737\pi\) | ||||
0.321726 | + | 0.946833i | \(0.395737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | −0.643000 | + | 0.978577i | −0.0381551 | + | 0.0580679i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.66442 | − | 14.2070i | −0.453207 | − | 0.840080i | ||||
\(287\) | − | 53.2860i | − | 3.14537i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.12808 | 0.478122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.0288 | − | 6.58967i | −0.586889 | − | 0.385631i | ||||
\(293\) | 21.9143 | 1.28025 | 0.640124 | − | 0.768272i | \(-0.278883\pi\) | ||||
0.640124 | + | 0.768272i | \(0.278883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.07475 | + | 12.3790i | −0.0624686 | + | 0.719517i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.34292 | − | 2.48929i | −0.0777934 | − | 0.144201i | ||||
\(299\) | 13.3717i | 0.773305i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 43.9143i | − | 2.53118i | ||||||
\(302\) | −10.3931 | + | 5.60688i | −0.598057 | + | 0.322640i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.86098 | − | 4.26396i | 0.565566 | − | 0.244555i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5426 | −1.51487 | −0.757434 | − | 0.652912i | \(-0.773547\pi\) | ||||
−0.757434 | + | 0.652912i | \(0.773547\pi\) | |||||||
\(308\) | 11.7992 | − | 17.9572i | 0.672324 | − | 1.02320i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2008 | −0.691842 | −0.345921 | − | 0.938264i | \(-0.612434\pi\) | ||||
−0.345921 | + | 0.938264i | \(0.612434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9572i | 0.901952i | 0.892536 | + | 0.450976i | \(0.148924\pi\) | ||||
−0.892536 | + | 0.450976i | \(0.851076\pi\) | |||||||
\(314\) | 27.8181 | − | 15.0073i | 1.56987 | − | 0.846914i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.12181 | + | 1.70727i | −0.0631066 | + | 0.0960414i | ||||
\(317\) | −33.5296 | −1.88321 | −0.941605 | − | 0.336718i | \(-0.890683\pi\) | ||||
−0.941605 | + | 0.336718i | \(0.890683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.58546 | 0.256737 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.6644 | + | 8.45065i | −0.872944 | + | 0.470937i | ||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.70727 | + | 0.921039i | −0.0945569 | + | 0.0510116i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.78202 | − | 32.0435i | 0.153611 | − | 1.76930i | ||||
\(329\) | 34.0722 | 1.87846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8568i | 1.09143i | 0.837972 | + | 0.545713i | \(0.183741\pi\) | ||||
−0.837972 | + | 0.545713i | \(0.816259\pi\) | |||||||
\(332\) | 14.6858 | − | 22.3503i | 0.805991 | − | 1.22663i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.56825 | + | 14.0288i | 0.414116 | + | 0.767620i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.17092i | − | 0.390625i | −0.980741 | − | 0.195313i | \(-0.937428\pi\) | ||
0.980741 | − | 0.195313i | \(-0.0625721\pi\) | |||||||
\(338\) | 14.6697 | − | 7.91400i | 0.797925 | − | 0.430465i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.0000i | − | 0.866449i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.2860i | 2.01325i | ||||||||
\(344\) | 2.29273 | − | 26.4078i | 0.123616 | − | 1.42381i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4250 | − | 7.24254i | 0.721734 | − | 0.389361i | ||||
\(347\) | 0.786230 | 0.0422071 | 0.0211035 | − | 0.999777i | \(-0.493282\pi\) | ||||
0.0211035 | + | 0.999777i | \(0.493282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.15792i | 0.329626i | 0.986325 | + | 0.164813i | \(0.0527021\pi\) | ||||
−0.986325 | + | 0.164813i | \(0.947298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.03298 | − | 10.1825i | 0.428159 | − | 0.542728i | ||||
\(353\) | − | 21.7220i | − | 1.15614i | −0.815986 | − | 0.578072i | \(-0.803805\pi\) | ||
0.815986 | − | 0.578072i | \(-0.196195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.70306 | − | 5.63565i | 0.196262 | − | 0.298689i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.46052 | − | 4.56090i | −0.130042 | − | 0.241051i | ||||
\(359\) | 0.585462 | 0.0308995 | 0.0154498 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154498 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7862 | 0.620328 | ||||||||
\(362\) | 4.45065 | + | 8.24989i | 0.233921 | + | 0.433604i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 38.9933 | + | 25.6216i | 2.04380 | + | 1.34294i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.485078i | 0.0253209i | 0.999920 | + | 0.0126604i | \(0.00403005\pi\) | ||||
−0.999920 | + | 0.0126604i | \(0.995970\pi\) | |||||||
\(368\) | −9.86098 | + | 4.26396i | −0.514039 | + | 0.222274i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.37169i | − | 0.486554i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3931 | −0.641691 | −0.320846 | − | 0.947132i | \(-0.603967\pi\) | ||||
−0.320846 | + | 0.947132i | \(0.603967\pi\) | |||||||
\(374\) | 8.49977 | − | 4.58546i | 0.439513 | − | 0.237109i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.4893 | + | 1.77888i | 1.05665 | + | 0.0917389i | ||||
\(377\) | 9.95715i | 0.512820i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.0147i | − | 1.33629i | −0.744033 | − | 0.668143i | \(-0.767090\pi\) | ||
0.744033 | − | 0.668143i | \(-0.232910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.95715 | − | 5.37169i | 0.509452 | − | 0.274840i | ||||
\(383\) | − | 6.68585i | − | 0.341631i | −0.985303 | − | 0.170815i | \(-0.945360\pi\) | ||
0.985303 | − | 0.170815i | \(-0.0546402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.815000 | + | 1.51071i | 0.0414824 | + | 0.0768932i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.61423 | + | 4.34606i | 0.335787 | + | 0.220638i | ||||
\(389\) | − | 29.9143i | − | 1.51672i | −0.651838 | − | 0.758358i | \(-0.726002\pi\) | ||
0.651838 | − | 0.758358i | \(-0.273998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −3.65918 | + | 42.1467i | −0.184817 | + | 2.12873i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.8181 | − | 16.0863i | 1.50222 | − | 0.810416i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.76481 | −0.490082 | −0.245041 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245041 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(398\) | −0.435961 | + | 0.235192i | −0.0218527 | + | 0.0117891i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.58546 | 0.328862 | 0.164431 | − | 0.986389i | \(-0.447421\pi\) | ||||
0.164431 | + | 0.986389i | \(0.447421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.7434 | 1.73069 | ||||||||
\(404\) | −3.34292 | − | 2.19656i | −0.166317 | − | 0.109283i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.6644 | + | 6.29273i | −0.578896 | + | 0.312303i | ||||
\(407\) | − | 10.0722i | − | 0.499262i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9143 | 1.28138 | 0.640690 | − | 0.767800i | \(-0.278648\pi\) | ||||
0.640690 | + | 0.767800i | \(0.278648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.4752 | − | 16.0821i | −1.20581 | − | 0.792308i | ||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22.1109 | + | 17.4433i | 1.08407 | + | 0.855229i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.66442 | + | 4.13481i | −0.374879 | + | 0.202240i | ||||
\(419\) | 12.2499i | 0.598446i | 0.954183 | + | 0.299223i | \(0.0967275\pi\) | ||||
−0.954183 | + | 0.299223i | \(0.903273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.67115i | 0.227658i | 0.993500 | + | 0.113829i | \(0.0363116\pi\) | ||||
−0.993500 | + | 0.113829i | \(0.963688\pi\) | |||||||
\(422\) | −9.46787 | − | 17.5500i | −0.460888 | − | 0.854319i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.489289 | − | 5.63565i | 0.0237620 | − | 0.273692i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4868 | −1.03982 | ||||||||
\(428\) | −12.4422 | + | 18.9357i | −0.601418 | + | 0.915293i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.585462 | −0.0282007 | −0.0141004 | − | 0.999901i | \(-0.504488\pi\) | ||||
−0.0141004 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.9143i | − | 1.05313i | −0.850133 | − | 0.526567i | \(-0.823479\pi\) | ||
0.850133 | − | 0.526567i | \(-0.176521\pi\) | |||||||
\(434\) | 21.9572 | + | 40.7005i | 1.05398 | + | 1.95369i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.6644 | − | 10.2927i | −0.750190 | − | 0.492932i | ||||
\(437\) | 7.21377 | 0.345081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.39312 | 0.114217 | 0.0571086 | − | 0.998368i | \(-0.481812\pi\) | ||||
0.0571086 | + | 0.998368i | \(0.481812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.95715 | + | 18.4569i | 0.473614 | + | 0.877906i | ||||
\(443\) | 20.7005 | 0.983512 | 0.491756 | − | 0.870733i | \(-0.336355\pi\) | ||||
0.491756 | + | 0.870733i | \(0.336355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.51806 | − | 8.37483i | −0.213936 | − | 0.396560i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.46052 | + | 36.9259i | −0.305231 | + | 1.74458i | ||||
\(449\) | −37.9143 | −1.78929 | −0.894643 | − | 0.446781i | \(-0.852570\pi\) | ||||
−0.894643 | + | 0.446781i | \(0.852570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0722i | 1.22769i | ||||||||
\(452\) | −33.0361 | − | 21.7073i | −1.55389 | − | 1.02102i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.3931 | − | 6.68585i | 0.581638 | − | 0.313782i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 38.7005i | − | 1.81033i | −0.425055 | − | 0.905167i | \(-0.639745\pi\) | ||
0.425055 | − | 0.905167i | \(-0.360255\pi\) | |||||||
\(458\) | −7.60688 | − | 14.1004i | −0.355446 | − | 0.658868i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.74338i | − | 0.220921i | −0.993880 | − | 0.110461i | \(-0.964767\pi\) | ||
0.993880 | − | 0.110461i | \(-0.0352326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3142i | 0.711709i | 0.934541 | + | 0.355855i | \(0.115810\pi\) | ||||
−0.934541 | + | 0.355855i | \(0.884190\pi\) | |||||||
\(464\) | −7.34292 | + | 3.17513i | −0.340887 | + | 0.147402i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7434 | + | 23.6216i | 0.590326 | + | 1.09425i | ||||
\(467\) | −30.5426 | −1.41334 | −0.706672 | − | 0.707541i | \(-0.749804\pi\) | ||||
−0.706672 | + | 0.707541i | \(0.749804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7434i | 0.865489i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.81079 | − | 0.417674i | −0.221435 | − | 0.0192250i | ||||
\(473\) | 21.4868i | 0.987963i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.3288 | + | 23.3288i | −0.702597 | + | 1.06928i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.27131 | − | 1.76481i | 0.149626 | − | 0.0807204i | ||||
\(479\) | 3.32885 | 0.152099 | 0.0760494 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760494 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.8715 | 0.997253 | ||||||||
\(482\) | 13.4250 | − | 7.24254i | 0.611493 | − | 0.329889i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.30784 | − | 9.59985i | 0.286720 | − | 0.436357i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1004i | 0.548321i | 0.961684 | + | 0.274160i | \(0.0883999\pi\) | ||||
−0.961684 | + | 0.274160i | \(0.911600\pi\) | |||||||
\(488\) | −12.9210 | − | 1.12181i | −0.584908 | − | 0.0507818i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2927i | 0.645022i | 0.946566 | + | 0.322511i | \(0.104527\pi\) | ||||
−0.946566 | + | 0.322511i | \(0.895473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.95715 | −0.268297 | ||||||||
\(494\) | −8.97858 | − | 16.6430i | −0.403965 | − | 0.748804i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.0790 | + | 25.6216i | 0.497460 | + | 1.15044i | ||||
\(497\) | 2.74338i | 0.123058i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.22846i | − | 0.413123i | −0.978434 | − | 0.206561i | \(-0.933773\pi\) | ||
0.978434 | − | 0.206561i | \(-0.0662273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.8108 | + | 38.5756i | 0.928831 | + | 1.72171i | ||||
\(503\) | 14.1004i | 0.628705i | 0.949306 | + | 0.314353i | \(0.101787\pi\) | ||||
−0.949306 | + | 0.314353i | \(0.898213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.66442 | − | 4.13481i | 0.340725 | − | 0.183815i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.1035 | − | 7.29587i | −0.492639 | − | 0.323702i | ||||
\(509\) | − | 43.4011i | − | 1.92372i | −0.273544 | − | 0.961859i | \(-0.588196\pi\) | ||
0.273544 | − | 0.961859i | \(-0.411804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1151 | −1.24374 | ||||||||
\(512\) | −5.81289 | + | 21.8680i | −0.256896 | + | 0.966439i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.0575 | + | 26.0575i | 0.620051 | + | 1.14935i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6712 | −0.733196 | ||||||||
\(518\) | 13.8223 | + | 25.6216i | 0.607319 | + | 1.12575i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5725 | −0.593482 | −0.296741 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296741 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(524\) | 11.8322 | + | 7.77467i | 0.516893 | + | 0.339638i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9399 | + | 23.9859i | 0.564208 | + | 1.04584i | ||||
\(527\) | 20.7862i | 0.905462i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7862 | 0.686358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.8223 | − | 21.0361i | 0.599275 | − | 0.912031i | ||||
\(533\) | −56.6148 | −2.45226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.978577 | + | 11.2713i | −0.0422681 | + | 0.486846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.6142 | + | 30.7967i | 0.716290 | + | 1.32774i | ||||
\(539\) | − | 34.2927i | − | 1.47709i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 37.2860i | − | 1.60305i | −0.597961 | − | 0.801525i | \(-0.704022\pi\) | ||
0.597961 | − | 0.801525i | \(-0.295978\pi\) | |||||||
\(542\) | 34.3074 | − | 18.5082i | 1.47363 | − | 0.794995i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.4360 | + | 13.2285i | −0.447438 | + | 0.567166i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.200768 | −0.00858424 | −0.00429212 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429212 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(548\) | −25.0361 | − | 16.4507i | −1.06949 | − | 0.702737i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.37169 | 0.228842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.78623i | 0.203531i | ||||||||
\(554\) | 25.2755 | − | 13.6357i | 1.07385 | − | 0.579323i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.76060 | + | 5.09931i | 0.329123 | + | 0.216259i | ||||
\(557\) | −9.21377 | −0.390400 | −0.195200 | − | 0.980763i | \(-0.562536\pi\) | ||||
−0.195200 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.6577 | −1.97341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.4250 | − | 7.24254i | 0.566300 | − | 0.305508i | ||||
\(563\) | −36.7005 | −1.54674 | −0.773372 | − | 0.633953i | \(-0.781431\pi\) | ||||
−0.773372 | + | 0.633953i | \(0.781431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.8929 | + | 13.4292i | −1.04633 | + | 0.564473i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.143230 | + | 1.64973i | −0.00600979 | + | 0.0692212i | ||||
\(569\) | 13.4145 | 0.562367 | 0.281183 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281183 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6858i | 0.781978i | 0.920395 | + | 0.390989i | \(0.127867\pi\) | ||||
−0.920395 | + | 0.390989i | \(0.872133\pi\) | |||||||
\(572\) | −19.0790 | − | 12.5363i | −0.797731 | − | 0.524171i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −35.7795 | − | 66.3221i | −1.49341 | − | 2.76823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.78623i | 0.115992i | 0.998317 | + | 0.0579961i | \(0.0184711\pi\) | ||||
−0.998317 | + | 0.0579961i | \(0.981529\pi\) | |||||||
\(578\) | 10.1166 | − | 5.45769i | 0.420794 | − | 0.227010i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 62.6577i | − | 2.59948i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.58546i | 0.189910i | ||||||||
\(584\) | −16.9070 | − | 1.46787i | −0.699615 | − | 0.0607407i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.2755 | − | 14.7146i | 1.12674 | − | 0.607855i | ||||
\(587\) | 27.3288 | 1.12798 | 0.563991 | − | 0.825781i | \(-0.309265\pi\) | ||||
0.563991 | + | 0.825781i | \(0.309265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18.7434i | − | 0.772308i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.97437 | + | 16.1292i | 0.286645 | + | 0.662904i | ||||
\(593\) | 6.97858i | 0.286576i | 0.989681 | + | 0.143288i | \(0.0457675\pi\) | ||||
−0.989681 | + | 0.143288i | \(0.954233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.34292 | − | 2.19656i | −0.136931 | − | 0.0899745i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.97858 | + | 16.6430i | 0.367161 | + | 0.680583i | ||||
\(599\) | 36.4998 | 1.49134 | 0.745670 | − | 0.666315i | \(-0.232130\pi\) | ||||
0.745670 | + | 0.666315i | \(0.232130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5725 | −0.635214 | −0.317607 | − | 0.948222i | \(-0.602879\pi\) | ||||
−0.317607 | + | 0.948222i | \(0.602879\pi\) | |||||||
\(602\) | −29.4868 | − | 54.6577i | −1.20179 | − | 2.22768i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.17092 | + | 13.9572i | −0.373160 | + | 0.567909i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2285i | 1.26752i | 0.773528 | + | 0.633762i | \(0.218490\pi\) | ||||
−0.773528 | + | 0.633762i | \(0.781510\pi\) | |||||||
\(608\) | 9.41033 | − | 11.9284i | 0.381639 | − | 0.483760i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 36.2008i | − | 1.46453i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.978577 | 0.0395244 | 0.0197622 | − | 0.999805i | \(-0.493709\pi\) | ||||
0.0197622 | + | 0.999805i | \(0.493709\pi\) | |||||||
\(614\) | −33.0361 | + | 17.8223i | −1.33323 | + | 0.719251i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.62831 | − | 30.2730i | 0.105898 | − | 1.21973i | ||||
\(617\) | 32.9357i | 1.32594i | 0.748645 | + | 0.662971i | \(0.230705\pi\) | ||||
−0.748645 | + | 0.662971i | \(0.769295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.35700i | − | 0.134929i | −0.997722 | − | 0.0674646i | \(-0.978509\pi\) | ||
0.997722 | − | 0.0674646i | \(-0.0214910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.1856 | + | 8.19235i | −0.608888 | + | 0.328483i | ||||
\(623\) | − | 15.7992i | − | 0.632983i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.7146 | + | 19.8610i | 0.428242 | + | 0.793804i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.5468 | − | 37.3576i | 0.979525 | − | 1.49073i | ||||
\(629\) | 13.0852i | 0.521742i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.7648 | −1.10530 | −0.552650 | − | 0.833414i | \(-0.686383\pi\) | ||||
−0.552650 | + | 0.833414i | \(0.686383\pi\) | |||||||
\(632\) | −0.249885 | + | 2.87819i | −0.00993990 | + | 0.114488i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.7324 | + | 22.5138i | −1.65741 | + | 0.894139i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 74.4653 | 2.95042 | ||||||||
\(638\) | 5.70727 | − | 3.07896i | 0.225953 | − | 0.121897i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.1281 | 0.834509 | 0.417254 | − | 0.908790i | \(-0.362992\pi\) | ||||
0.417254 | + | 0.908790i | \(0.362992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2860 | 1.15493 | 0.577464 | − | 0.816416i | \(-0.304043\pi\) | ||||
0.577464 | + | 0.816416i | \(0.304043\pi\) | |||||||
\(644\) | −13.8223 | + | 21.0361i | −0.544677 | + | 0.828939i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.95715 | − | 5.37169i | 0.391759 | − | 0.211346i | ||||
\(647\) | 15.6728i | 0.616163i | 0.951360 | + | 0.308082i | \(0.0996870\pi\) | ||||
−0.951360 | + | 0.308082i | \(0.900313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.91431 | 0.153650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.50650 | + | 2.29273i | −0.0589991 | + | 0.0897903i | ||||
\(653\) | −17.5296 | −0.685987 | −0.342993 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342993 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.0533 | − | 41.7507i | −0.704864 | − | 1.63009i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 42.4078 | − | 22.8782i | 1.65323 | − | 0.891885i | ||||
\(659\) | 23.8652i | 0.929656i | 0.885401 | + | 0.464828i | \(0.153884\pi\) | ||||
−0.885401 | + | 0.464828i | \(0.846116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.1579i | 1.17301i | 0.809947 | + | 0.586504i | \(0.199496\pi\) | ||||
−0.809947 | + | 0.586504i | \(0.800504\pi\) | |||||||
\(662\) | 13.3331 | + | 24.7146i | 0.518204 | + | 0.960561i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.27131 | − | 37.6791i | 0.126951 | − | 1.46223i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.37169 | −0.207993 | ||||||||
\(668\) | 18.8396 | + | 12.3790i | 0.728924 | + | 0.478959i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5132 | 0.405859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.0000i | − | 0.693849i | −0.937893 | − | 0.346925i | \(-0.887226\pi\) | ||
0.937893 | − | 0.346925i | \(-0.112774\pi\) | |||||||
\(674\) | −4.81500 | − | 8.92525i | −0.185467 | − | 0.343788i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.9446 | − | 19.7002i | 0.497868 | − | 0.757701i | ||||
\(677\) | 9.61531 | 0.369546 | 0.184773 | − | 0.982781i | \(-0.440845\pi\) | ||||
0.184773 | + | 0.982781i | \(0.440845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5426 | 0.711600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.7434 | − | 19.9143i | −0.411385 | − | 0.762558i | ||||
\(683\) | −18.6283 | −0.712792 | −0.356396 | − | 0.934335i | \(-0.615995\pi\) | ||||
−0.356396 | + | 0.934335i | \(0.615995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.0361 | + | 46.4078i | 0.955883 | + | 1.77186i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.8782 | − | 34.4078i | −0.567226 | − | 1.31179i | ||||
\(689\) | −9.95715 | −0.379337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4292i | 0.510872i | 0.966826 | + | 0.255436i | \(0.0822190\pi\) | ||||
−0.966826 | + | 0.255436i | \(0.917781\pi\) | |||||||
\(692\) | 11.8463 | − | 18.0288i | 0.450328 | − | 0.685351i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.978577 | − | 0.527923i | 0.0371463 | − | 0.0200397i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.8715i | − | 1.28297i | ||||||
\(698\) | 4.13481 | + | 7.66442i | 0.156505 | + | 0.290103i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1709i | 0.724076i | 0.932163 | + | 0.362038i | \(0.117919\pi\) | ||||
−0.932163 | + | 0.362038i | \(0.882081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.7992i | − | 0.445016i | ||||||
\(704\) | 3.16106 | − | 18.0674i | 0.119137 | − | 0.680941i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.5855 | − | 27.0361i | −0.548931 | − | 1.01752i | ||||
\(707\) | −9.37169 | −0.352459 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4145i | 0.578905i | 0.957192 | + | 0.289453i | \(0.0934732\pi\) | ||||
−0.957192 | + | 0.289453i | \(0.906527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.824865 | − | 9.50085i | 0.0309131 | − | 0.356059i | ||||
\(713\) | 18.7434i | 0.701945i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.12494 | − | 4.02456i | −0.228900 | − | 0.150405i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.728692 | − | 0.393115i | 0.0271945 | − | 0.0146709i | ||||
\(719\) | 20.7862 | 0.775196 | 0.387598 | − | 0.921829i | \(-0.373305\pi\) | ||||
0.387598 | + | 0.921829i | \(0.373305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −68.6148 | −2.55535 | ||||||||
\(722\) | 14.6697 | − | 7.91400i | 0.545948 | − | 0.294529i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0790 | + | 7.27973i | 0.411746 | + | 0.270549i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.3012i | − | 0.456224i | −0.973635 | − | 0.228112i | \(-0.926745\pi\) | ||
0.973635 | − | 0.228112i | \(-0.0732553\pi\) | |||||||
\(728\) | 65.7367 | + | 5.70727i | 2.43636 | + | 0.211525i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 27.9143i | − | 1.03245i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.9227 | −1.32684 | −0.663418 | − | 0.748249i | \(-0.730895\pi\) | ||||
−0.663418 | + | 0.748249i | \(0.730895\pi\) | |||||||
\(734\) | 0.325711 | + | 0.603749i | 0.0120222 | + | 0.0222848i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.41033 | + | 11.9284i | −0.346869 | + | 0.439686i | ||||
\(737\) | − | 9.17092i | − | 0.337815i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.0277i | 1.06780i | 0.845547 | + | 0.533900i | \(0.179274\pi\) | ||||
−0.845547 | + | 0.533900i | \(0.820726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.29273 | − | 11.6644i | −0.231013 | − | 0.428214i | ||||
\(743\) | − | 2.60015i | − | 0.0953904i | −0.998862 | − | 0.0476952i | \(-0.984812\pi\) | ||
0.998862 | − | 0.0476952i | \(-0.0151876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4250 | + | 8.32150i | −0.564750 | + | 0.304672i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.50023 | − | 11.4145i | 0.274236 | − | 0.417357i | ||||
\(749\) | 53.0852i | 1.93969i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8929 | −0.397487 | −0.198744 | − | 0.980052i | \(-0.563686\pi\) | ||||
−0.198744 | + | 0.980052i | \(0.563686\pi\) | |||||||
\(752\) | 26.6963 | − | 11.5437i | 0.973515 | − | 0.420955i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.68585 | + | 12.3931i | 0.243484 | + | 0.451331i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.3503 | −1.24848 | −0.624241 | − | 0.781232i | \(-0.714592\pi\) | ||||
−0.624241 | + | 0.781232i | \(0.714592\pi\) | |||||||
\(758\) | −17.4679 | − | 32.3790i | −0.634461 | − | 1.17606i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0852 | 0.691839 | 0.345920 | − | 0.938264i | \(-0.387567\pi\) | ||||
0.345920 | + | 0.938264i | \(0.387567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.9143 | −1.58980 | ||||||||
\(764\) | 8.78623 | − | 13.3717i | 0.317875 | − | 0.483771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.48929 | − | 8.32150i | −0.162205 | − | 0.300668i | ||||
\(767\) | 8.49977i | 0.306909i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.8715 | −1.14931 | −0.574657 | − | 0.818394i | \(-0.694865\pi\) | ||||
−0.574657 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.02877 | + | 1.33306i | 0.0730170 | + | 0.0479778i | ||||
\(773\) | 11.9572 | 0.430069 | 0.215034 | − | 0.976606i | \(-0.431014\pi\) | ||||
0.215034 | + | 0.976606i | \(0.431014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.1506 | + | 0.968095i | 0.400282 | + | 0.0347526i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.0863 | − | 37.2327i | −0.720129 | − | 1.33486i | ||||
\(779\) | 30.5426i | 1.09430i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.34231i | − | 0.0480315i | ||||||
\(782\) | −9.95715 | + | 5.37169i | −0.356067 | + | 0.192091i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.7455 | + | 54.9146i | 0.848053 | + | 1.96124i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.0852 | −1.17936 | −0.589681 | − | 0.807637i | \(-0.700746\pi\) | ||||
−0.589681 | + | 0.807637i | \(0.700746\pi\) | |||||||
\(788\) | 26.3116 | − | 40.0435i | 0.937313 | − | 1.42649i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.6148 | −3.29300 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8291i | 0.810684i | ||||||||
\(794\) | −12.1537 | + | 6.55669i | −0.431319 | + | 0.232688i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.384694 | + | 0.585462i | −0.0136351 | + | 0.0207511i | ||||
\(797\) | −10.0000 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.6582 | 0.766210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.19656 | − | 4.42188i | 0.289431 | − | 0.156142i | ||||
\(803\) | 13.7564 | 0.485452 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.2432 | − | 23.3288i | 1.52318 | − | 0.821724i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.63565 | − | 0.489289i | −0.198262 | − | 0.0172131i | ||||
\(809\) | −30.6148 | −1.07636 | −0.538180 | − | 0.842830i | \(-0.680888\pi\) | ||||
−0.538180 | + | 0.842830i | \(0.680888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 53.9290i | − | 1.89370i | −0.321670 | − | 0.946852i | \(-0.604244\pi\) | ||
0.321670 | − | 0.946852i | \(-0.395756\pi\) | |||||||
\(812\) | −10.2927 | + | 15.6644i | −0.361204 | + | 0.549713i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.76312 | − | 12.5363i | −0.237047 | − | 0.439399i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.1709i | 0.880619i | ||||||||
\(818\) | 32.2541 | − | 17.4005i | 1.12774 | − | 0.608393i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.6577i | 0.441757i | 0.975301 | + | 0.220878i | \(0.0708924\pi\) | ||||
−0.975301 | + | 0.220878i | \(0.929108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.8139i | − | 0.690670i | −0.938479 | − | 0.345335i | \(-0.887765\pi\) | ||
0.938479 | − | 0.345335i | \(-0.112235\pi\) | |||||||
\(824\) | −41.2614 | − | 3.58233i | −1.43741 | − | 0.124796i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.95715 | + | 5.37169i | −0.346454 | + | 0.186905i | ||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.3717i | − | 1.43690i | −0.695580 | − | 0.718449i | \(-0.744852\pi\) | ||
0.695580 | − | 0.718449i | \(-0.255148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 39.2327 | + | 6.86412i | 1.36015 | + | 0.237970i | ||||
\(833\) | 44.5510i | 1.54360i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.76312 | + | 10.2927i | −0.233907 | + | 0.355982i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.22533 | + | 15.2467i | 0.284139 | + | 0.526690i | ||||
\(839\) | 20.9013 | 0.721593 | 0.360797 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360797 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 3.13650 | + | 5.81392i | 0.108091 | + | 0.200361i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.5682 | − | 15.4862i | −0.811253 | − | 0.533055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 26.9126i | − | 0.924728i | ||||||
\(848\) | −3.17513 | − | 7.34292i | −0.109035 | − | 0.252157i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7992i | 0.404472i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.63673 | 0.227237 | 0.113619 | − | 0.993524i | \(-0.463756\pi\) | ||||
0.113619 | + | 0.993524i | \(0.463756\pi\) | |||||||
\(854\) | −26.7434 | + | 14.4275i | −0.915140 | + | 0.493700i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.77154 | + | 31.9227i | −0.0947292 | + | 1.09110i | ||||
\(857\) | 9.80765i | 0.335023i | 0.985870 | + | 0.167512i | \(0.0535731\pi\) | ||||
−0.985870 | + | 0.167512i | \(0.946427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.3864i | 1.34385i | 0.740621 | + | 0.671923i | \(0.234531\pi\) | ||||
−0.740621 | + | 0.671923i | \(0.765469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.728692 | + | 0.393115i | −0.0248193 | + | 0.0133896i | ||||
\(863\) | − | 7.07054i | − | 0.240684i | −0.992732 | − | 0.120342i | \(-0.961601\pi\) | ||
0.992732 | − | 0.120342i | \(-0.0383991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.7146 | − | 27.2755i | −0.500023 | − | 0.926860i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 54.6577 | + | 35.9143i | 1.85520 | + | 1.21901i | ||||
\(869\) | − | 2.34185i | − | 0.0794417i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9143 | 0.674771 | ||||||||
\(872\) | −26.4078 | − | 2.29273i | −0.894281 | − | 0.0776417i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.97858 | − | 4.84377i | 0.303705 | − | 0.163843i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.1365 | −0.781264 | −0.390632 | − | 0.920547i | \(-0.627744\pi\) | ||||
−0.390632 | + | 0.920547i | \(0.627744\pi\) | |||||||
\(878\) | 2.97858 | − | 1.60688i | 0.100522 | − | 0.0542297i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.4569 | −0.958738 | −0.479369 | − | 0.877613i | \(-0.659134\pi\) | ||||
−0.479369 | + | 0.877613i | \(0.659134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.2003 | −1.38650 | −0.693250 | − | 0.720697i | \(-0.743822\pi\) | ||||
−0.693250 | + | 0.720697i | \(0.743822\pi\) | |||||||
\(884\) | 24.7862 | + | 16.2865i | 0.833651 | + | 0.547773i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.7648 | − | 13.8996i | 0.865586 | − | 0.466967i | ||||
\(887\) | − | 3.55777i | − | 0.119458i | −0.998215 | − | 0.0597291i | \(-0.980976\pi\) | ||
0.998215 | − | 0.0597291i | \(-0.0190237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.1281 | −1.04400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.2467 | − | 7.38998i | −0.376569 | − | 0.247435i | ||||
\(893\) | −19.5296 | −0.653534 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.7533 | + | 50.2976i | 0.559687 | + | 1.68032i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47.1898 | + | 25.4580i | −1.57474 | + | 0.849544i | ||||
\(899\) | 13.9572i | 0.465497i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.95715i | − | 0.198462i | ||||||
\(902\) | 17.5065 | + | 32.4507i | 0.582903 | + | 1.08049i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −55.6938 | − | 4.83535i | −1.85235 | − | 0.160821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.6577 | 1.68206 | 0.841031 | − | 0.540988i | \(-0.181949\pi\) | ||||
0.841031 | + | 0.540988i | \(0.181949\pi\) | |||||||
\(908\) | 10.9357 | − | 16.6430i | 0.362915 | − | 0.552317i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.4569 | 0.876557 | 0.438279 | − | 0.898839i | \(-0.355588\pi\) | ||||
0.438279 | + | 0.898839i | \(0.355588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.6577i | 1.01462i | ||||||||
\(914\) | −25.9859 | − | 48.1684i | −0.859538 | − | 1.59327i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.9357 | − | 12.4422i | −0.625654 | − | 0.411103i | ||||
\(917\) | 33.1709 | 1.09540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.8077 | −0.983264 | −0.491632 | − | 0.870803i | \(-0.663599\pi\) | ||||
−0.491632 | + | 0.870803i | \(0.663599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.18500 | − | 5.90383i | −0.104892 | − | 0.194432i | ||||
\(923\) | 2.91477 | 0.0959407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.2829 | + | 19.0607i | 0.337916 | + | 0.626373i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.00735 | + | 8.88240i | −0.230027 | + | 0.291579i | ||||
\(929\) | −8.82908 | −0.289673 | −0.144836 | − | 0.989456i | \(-0.546266\pi\) | ||||
−0.144836 | + | 0.989456i | \(0.546266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 40.1726i | − | 1.31660i | ||||||
\(932\) | 31.7220 | + | 20.8438i | 1.03909 | + | 0.682760i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.0147 | + | 20.5082i | −1.24388 | + | 0.671049i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.2302i | 1.37960i | 0.724000 | + | 0.689799i | \(0.242301\pi\) | ||||
−0.724000 | + | 0.689799i | \(0.757699\pi\) | |||||||
\(938\) | 12.5855 | + | 23.3288i | 0.410930 | + | 0.761714i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.7434i | 1.06740i | 0.845673 | + | 0.533702i | \(0.179200\pi\) | ||||
−0.845673 | + | 0.533702i | \(0.820800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30.5426i | − | 0.994604i | ||||||
\(944\) | −6.26817 | + | 2.71040i | −0.204012 | + | 0.0882162i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.4275 | + | 26.7434i | 0.469080 | + | 0.869502i | ||||
\(947\) | −15.9143 | −0.517146 | −0.258573 | − | 0.965992i | \(-0.583252\pi\) | ||||
−0.258573 | + | 0.965992i | \(0.583252\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8715i | 0.969669i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.41454 | + | 39.3288i | −0.110666 | + | 1.27466i | ||||
\(953\) | − | 55.6791i | − | 1.80362i | −0.432129 | − | 0.901812i | \(-0.642238\pi\) | ||
0.432129 | − | 0.901812i | \(-0.357762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.88661 | − | 4.39312i | 0.0933598 | − | 0.142083i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.14323 | − | 2.23519i | 0.133862 | − | 0.0722158i | ||||
\(959\) | −70.1873 | −2.26647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7005 | 0.570985 | ||||||||
\(962\) | 27.2222 | − | 14.6858i | 0.877679 | − | 0.473491i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.8463 | − | 18.0288i | 0.381543 | − | 0.580668i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7581i | 1.76090i | 0.474138 | + | 0.880451i | \(0.342760\pi\) | ||||
−0.474138 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(968\) | 1.40509 | − | 16.1839i | 0.0451612 | − | 0.520169i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 30.3221i | − | 0.973083i | −0.873657 | − | 0.486542i | \(-0.838258\pi\) | ||
0.873657 | − | 0.486542i | \(-0.161742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.7564 | 0.697478 | ||||||||
\(974\) | 8.12494 | + | 15.0607i | 0.260340 | + | 0.482575i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.8353 | + | 7.27973i | −0.538886 | + | 0.233018i | ||||
\(977\) | − | 29.7220i | − | 0.950890i | −0.879746 | − | 0.475445i | \(-0.842287\pi\) | ||
0.879746 | − | 0.475445i | \(-0.157713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.73038i | 0.247064i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.59702 | + | 17.7894i | 0.306253 | + | 0.567681i | ||||
\(983\) | 49.5443i | 1.58022i | 0.612966 | + | 0.790109i | \(0.289976\pi\) | ||||
−0.612966 | + | 0.790109i | \(0.710024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.41454 | + | 4.00000i | −0.236127 | + | 0.127386i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.3503 | − | 14.6858i | −0.711057 | − | 0.467219i | ||||
\(989\) | − | 25.1709i | − | 0.800389i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0937 | 0.606530 | 0.303265 | − | 0.952906i | \(-0.401923\pi\) | ||||
0.303265 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(992\) | 30.9933 | + | 24.4507i | 0.984037 | + | 0.776309i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.84208 | + | 3.41454i | 0.0584271 | + | 0.108303i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.8500 | −1.23039 | −0.615197 | − | 0.788374i | \(-0.710923\pi\) | ||||
−0.615197 | + | 0.788374i | \(0.710923\pi\) | |||||||
\(998\) | −6.19656 | − | 11.4862i | −0.196149 | − | 0.363588i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))