Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.a (trivial) |
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: | yes |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.874032 | −0.504623 | −0.252311 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45052 | 1.51170 | 0.755852 | − | 0.654743i | \(-0.227223\pi\) | ||||
0.755852 | + | 0.654743i | \(0.227223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.40492 | 1.79596 | 0.897978 | − | 0.440040i | \(-0.145036\pi\) | ||||
0.897978 | + | 0.440040i | \(0.145036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.47214 | 0.539464 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.08036 | 0.225271 | 0.112636 | − | 0.993636i | \(-0.464071\pi\) | ||||
0.112636 | + | 0.993636i | \(0.464071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57649 | 0.880746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.667701 | 0.116232 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.62210 | 0.431070 | 0.215535 | − | 0.976496i | \(-0.430850\pi\) | ||||
0.215535 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.76393 | −0.762840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.48528 | −1.23771 | −0.618853 | − | 0.785507i | \(-0.712402\pi\) | ||||
−0.618853 | + | 0.785507i | \(0.712402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.62210 | −0.360173 | −0.180086 | − | 0.983651i | \(-0.557638\pi\) | ||||
−0.180086 | + | 0.983651i | \(0.557638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.874032 | 0.115768 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.52786 | −0.198911 | −0.0994555 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994555 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7082 | −1.49908 | −0.749541 | − | 0.661958i | \(-0.769726\pi\) | ||||
−0.749541 | + | 0.661958i | \(0.769726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.32456 | 0.796819 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1074 | −1.35698 | −0.678491 | − | 0.734609i | \(-0.737366\pi\) | ||||
−0.678491 | + | 0.734609i | \(0.737366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.944272 | −0.113677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4721 | −1.24281 | −0.621407 | − | 0.783488i | \(-0.713439\pi\) | ||||
−0.621407 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.24419 | −0.613786 | −0.306893 | − | 0.951744i | \(-0.599289\pi\) | ||||
−0.306893 | + | 0.951744i | \(0.599289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16073 | 0.246238 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4164 | 1.73448 | 0.867241 | − | 0.497889i | \(-0.165891\pi\) | ||||
0.867241 | + | 0.497889i | \(0.165891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7295 | −1.50701 | −0.753503 | − | 0.657445i | \(-0.771637\pi\) | ||||
−0.753503 | + | 0.657445i | \(0.771637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.90879 | 0.419066 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.94427 | 0.312092 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4164 | −1.61608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.49613 | 0.362532 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9358 | −1.41497 | −0.707483 | − | 0.706730i | \(-0.750170\pi\) | ||||
−0.707483 | + | 0.706730i | \(0.750170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.70820 | 0.171681 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23607 | 0.521008 | 0.260504 | − | 0.965473i | \(-0.416111\pi\) | ||||
0.260504 | + | 0.965473i | \(0.416111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.86319 | 0.577717 | 0.288858 | − | 0.957372i | \(-0.406724\pi\) | ||||
0.288858 | + | 0.957372i | \(0.406724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2681 | 1.28268 | 0.641338 | − | 0.767258i | \(-0.278380\pi\) | ||||
0.641338 | + | 0.767258i | \(0.278380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.29180 | −0.217528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3516 | 1.53823 | 0.769113 | − | 0.639113i | \(-0.220698\pi\) | ||||
0.769113 | + | 0.639113i | \(0.220698\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.1877 | −1.12676 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.9443 | −1.91996 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.24419 | 0.472853 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.5927 | 1.73857 | 0.869284 | − | 0.494314i | \(-0.164581\pi\) | ||||
0.869284 | + | 0.494314i | \(0.164581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.41641 | 0.652978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.40492 | 0.632645 | 0.316322 | − | 0.948652i | \(-0.397552\pi\) | ||||
0.316322 | + | 0.948652i | \(0.397552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.29180 | 0.194388 | 0.0971938 | − | 0.995265i | \(-0.469013\pi\) | ||||
0.0971938 | + | 0.995265i | \(0.469013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.41641 | 0.624574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.16383 | −0.348197 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.874032 | −0.0720889 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6525 | −1.03653 | −0.518266 | − | 0.855220i | \(-0.673422\pi\) | ||||
−0.518266 | + | 0.855220i | \(0.673422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.5579 | −1.33863 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.412662 | 0.0329340 | 0.0164670 | − | 0.999864i | \(-0.494758\pi\) | ||||
0.0164670 | + | 0.999864i | \(0.494758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.29180 | 0.181751 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.05573 | −0.240825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.4319 | −1.34892 | −0.674462 | − | 0.738310i | \(-0.735624\pi\) | ||||
−0.674462 | + | 0.738310i | \(0.735624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7082 | 1.28525 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.23607 | 0.170996 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.94665 | −0.680201 | −0.340101 | − | 0.940389i | \(-0.610461\pi\) | ||||
−0.340101 | + | 0.940389i | \(0.610461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.33540 | 0.100375 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.4721 | −1.67965 | −0.839823 | − | 0.542860i | \(-0.817341\pi\) | ||||
−0.839823 | + | 0.542860i | \(0.817341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.2333 | 0.756471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.65685 | −0.413670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.9443 | −0.941557 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.05573 | −0.221105 | −0.110552 | − | 0.993870i | \(-0.535262\pi\) | ||||
−0.110552 | + | 0.993870i | \(0.535262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.9358 | −1.00312 | −0.501561 | − | 0.865123i | \(-0.667241\pi\) | ||||
−0.501561 | + | 0.865123i | \(0.667241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6491 | −0.901212 | −0.450606 | − | 0.892723i | \(-0.648792\pi\) | ||||
−0.450606 | + | 0.892723i | \(0.648792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.70820 | 0.684764 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6491 | 0.887794 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.41577 | −0.167907 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.763932 | 0.0528423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4164 | 1.06131 | 0.530655 | − | 0.847588i | \(-0.321946\pi\) | ||||
0.530655 | + | 0.847588i | \(0.321946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.15298 | 0.627152 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137 | 0.768025 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.58359 | 0.309730 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.3607 | 2.71495 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7673 | −1.25675 | −0.628377 | − | 0.777909i | \(-0.716280\pi\) | ||||
−0.628377 | + | 0.777909i | \(0.716280\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.86319 | −0.389153 | −0.194577 | − | 0.980887i | \(-0.562333\pi\) | ||||
−0.194577 | + | 0.980887i | \(0.562333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.70820 | 0.509372 | 0.254686 | − | 0.967024i | \(-0.418028\pi\) | ||||
0.254686 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.88854 | −0.124257 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.6491 | 0.828671 | 0.414335 | − | 0.910124i | \(-0.364014\pi\) | ||||
0.414335 | + | 0.910124i | \(0.364014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4744 | −0.875259 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.8885 | −1.93333 | −0.966665 | − | 0.256046i | \(-0.917580\pi\) | ||||
−0.966665 | + | 0.256046i | \(0.917580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.8328 | −1.85728 | −0.928642 | − | 0.370976i | \(-0.879023\pi\) | ||||
−0.928642 | + | 0.370976i | \(0.879023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0965 | −1.03259 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.45052 | −0.346808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.88854 | −0.371682 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.825324 | −0.0518877 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.4319 | 1.08737 | 0.543687 | − | 0.839288i | \(-0.317028\pi\) | ||||
0.543687 | + | 0.839288i | \(0.317028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.41641 | −0.460833 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.8902 | −0.979832 | −0.489916 | − | 0.871770i | \(-0.662973\pi\) | ||||
−0.489916 | + | 0.871770i | \(0.662973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.57339 | −0.157489 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.9443 | 0.911168 | 0.455584 | − | 0.890193i | \(-0.349430\pi\) | ||||
0.455584 | + | 0.890193i | \(0.349430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1246 | 1.28323 | 0.641614 | − | 0.767027i | \(-0.278265\pi\) | ||||
0.641614 | + | 0.767027i | \(0.278265\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.4744 | 0.815510 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2148 | 1.33476 | 0.667378 | − | 0.744719i | \(-0.267417\pi\) | ||||
0.667378 | + | 0.744719i | \(0.267417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.94427 | 0.535480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.4164 | −1.51622 | −0.758108 | − | 0.652129i | \(-0.773876\pi\) | ||||
−0.758108 | + | 0.652129i | \(0.773876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.41577 | 0.143602 | 0.0718012 | − | 0.997419i | \(-0.477125\pi\) | ||||
0.0718012 | + | 0.997419i | \(0.477125\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706 | 1.00174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.8328 | 2.22546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1803 | 0.714024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.62210 | −0.153184 | −0.0765922 | − | 0.997062i | \(-0.524404\pi\) | ||||
−0.0765922 | + | 0.997062i | \(0.524404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.49613 | −0.202866 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.88854 | 0.340543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.57649 | −0.262913 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.45052 | 0.311078 | 0.155539 | − | 0.987830i | \(-0.450289\pi\) | ||||
0.155539 | + | 0.987830i | \(0.450289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.12461 | −0.291529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.70820 | −0.550502 | −0.275251 | − | 0.961372i | \(-0.588761\pi\) | ||||
−0.275251 | + | 0.961372i | \(0.588761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4884 | 0.592839 | 0.296419 | − | 0.955058i | \(-0.404207\pi\) | ||||
0.296419 | + | 0.955058i | \(0.404207\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.94665 | 0.502494 | 0.251247 | − | 0.967923i | \(-0.419159\pi\) | ||||
0.251247 | + | 0.967923i | \(0.419159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.41641 | 0.191282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.5967 | −0.647267 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.40492 | −0.412021 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.74806 | −0.0966682 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.41641 | 0.407643 | 0.203821 | − | 0.979008i | \(-0.434664\pi\) | ||||
0.203821 | + | 0.979008i | \(0.434664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.86319 | −0.321301 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7642 | −0.913206 | −0.456603 | − | 0.889671i | \(-0.650934\pi\) | ||||
−0.456603 | + | 0.889671i | \(0.650934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2918 | −0.776224 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.05573 | 0.165477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.40802 | 0.505049 | 0.252525 | − | 0.967590i | \(-0.418739\pi\) | ||||
0.252525 | + | 0.967590i | \(0.418739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4164 | 1.36051 | 0.680255 | − | 0.732976i | \(-0.261869\pi\) | ||||
0.680255 | + | 0.732976i | \(0.261869\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.9443 | 1.33143 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.56564 | −0.509128 | −0.254564 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254564 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.3060 | 0.968854 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1246 | 1.53714 | 0.768569 | − | 0.639767i | \(-0.220969\pi\) | ||||
0.768569 | + | 0.639767i | \(0.220969\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.10427 | 0.477850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.48528 | −0.442928 | −0.221464 | − | 0.975169i | \(-0.571084\pi\) | ||||
−0.221464 | + | 0.975169i | \(0.571084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.4164 | 0.698430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.41641 | 0.385041 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.1105 | −0.678835 | −0.339417 | − | 0.940636i | \(-0.610230\pi\) | ||||
−0.339417 | + | 0.940636i | \(0.610230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.3755 | −1.25540 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1246 | −0.877320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.4056 | 1.86024 | 0.930120 | − | 0.367257i | \(-0.119703\pi\) | ||||
0.930120 | + | 0.367257i | \(0.119703\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.9737 | 0.964486 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.9443 | −0.757705 | −0.378852 | − | 0.925457i | \(-0.623681\pi\) | ||||
−0.378852 | + | 0.925457i | \(0.623681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7264 | −0.588530 | −0.294265 | − | 0.955724i | \(-0.595075\pi\) | ||||
−0.294265 | + | 0.955724i | \(0.595075\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.47214 | −0.123762 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.47214 | −0.223328 | −0.111664 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111664 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8021 | −1.08604 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00310 | −0.0992901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4164 | 0.861186 | 0.430593 | − | 0.902546i | \(-0.358304\pi\) | ||||
0.430593 | + | 0.902546i | \(0.358304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.47214 | −0.319247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.32145 | 0.212645 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.00310 | −0.0980924 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.9443 | −1.02319 | −0.511597 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511597 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.9737 | 0.922531 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.1158 | 1.60259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.63932 | 0.175708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.52786 | 0.0735946 | 0.0367973 | − | 0.999323i | \(-0.488284\pi\) | ||||
0.0367973 | + | 0.999323i | \(0.488284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4906 | 1.36917 | 0.684585 | − | 0.728933i | \(-0.259983\pi\) | ||||
0.684585 | + | 0.728933i | \(0.259983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.08036 | −0.0516808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8328 | −0.898841 | −0.449421 | − | 0.893320i | \(-0.648370\pi\) | ||||
−0.449421 | + | 0.893320i | \(0.648370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23607 | −0.106479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7295 | 0.652307 | 0.326153 | − | 0.945317i | \(-0.394247\pi\) | ||||
0.326153 | + | 0.945317i | \(0.394247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.0587 | 0.523057 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.4721 | −0.777368 | −0.388684 | − | 0.921371i | \(-0.627070\pi\) | ||||
−0.388684 | + | 0.921371i | \(0.627070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.58359 | 0.215833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.99226 | 0.328525 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.9473 | −1.77510 | −0.887551 | − | 0.460710i | \(-0.847595\pi\) | ||||
−0.887551 | + | 0.460710i | \(0.847595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.8885 | 1.58178 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.8885 | 1.11260 | 0.556300 | − | 0.830981i | \(-0.312220\pi\) | ||||
0.556300 | + | 0.830981i | \(0.312220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5548 | −0.676419 | −0.338209 | − | 0.941071i | \(-0.609821\pi\) | ||||
−0.338209 | + | 0.941071i | \(0.609821\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.7000 | −1.42063 | −0.710314 | − | 0.703885i | \(-0.751447\pi\) | ||||
−0.710314 | + | 0.703885i | \(0.751447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.4164 | 1.45067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.360680 | −0.0166192 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.48218 | 0.298051 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.86319 | 0.268457 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.2361 | 0.513389 | 0.256695 | − | 0.966493i | \(-0.417367\pi\) | ||||
0.256695 | + | 0.966493i | \(0.417367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2918 | 0.651650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.67080 | 0.121526 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6947 | 0.484624 | 0.242312 | − | 0.970198i | \(-0.422094\pi\) | ||||
0.242312 | + | 0.970198i | \(0.422094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.41641 | −0.335382 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.88854 | 0.265746 | 0.132873 | − | 0.991133i | \(-0.457580\pi\) | ||||
0.132873 | + | 0.991133i | \(0.457580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.1158 | −1.49146 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.6197 | 1.32862 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1246 | −0.766603 | −0.383301 | − | 0.923623i | \(-0.625213\pi\) | ||||
−0.383301 | + | 0.923623i | \(0.625213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.2361 | 0.680697 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.2117 | −0.901193 | −0.450597 | − | 0.892728i | \(-0.648789\pi\) | ||||
−0.450597 | + | 0.892728i | \(0.648789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.6035 | −0.648564 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5836 | −0.469109 | −0.234555 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8328 | 0.656165 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.57649 | −0.202057 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.48218 | 0.285086 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.81966 | 0.343245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.111456 | 0.00488298 | 0.00244149 | − | 0.999997i | \(-0.499223\pi\) | ||||
0.00244149 | + | 0.999997i | \(0.499223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8369 | 1.08604 | 0.543020 | − | 0.839720i | \(-0.317281\pi\) | ||||
0.543020 | + | 0.839720i | \(0.317281\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.6197 | −1.29025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8328 | −0.949253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.41641 | 0.148259 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.7031 | −1.41653 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.6414 | 0.847588 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.763932 | −0.0329049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7082 | 0.503375 | 0.251688 | − | 0.967809i | \(-0.419014\pi\) | ||||
0.251688 | + | 0.967809i | \(0.419014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.24419 | −0.225050 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.27895 | 0.353982 | 0.176991 | − | 0.984212i | \(-0.443364\pi\) | ||||
0.176991 | + | 0.984212i | \(0.443364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.1803 | 1.11735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.47214 | 0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.6042 | −1.85424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.0540 | −0.849716 | −0.424858 | − | 0.905260i | \(-0.639676\pi\) | ||||
−0.424858 | + | 0.905260i | \(0.639676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.2492 | −1.95613 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.94427 | 0.208747 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.0810 | −1.26776 | −0.633882 | − | 0.773429i | \(-0.718540\pi\) | ||||
−0.633882 | + | 0.773429i | \(0.718540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.65996 | −0.321688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.9443 | −1.63263 | −0.816314 | − | 0.577608i | \(-0.803986\pi\) | ||||
−0.816314 | + | 0.577608i | \(0.803986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1246 | 1.05143 | 0.525716 | − | 0.850660i | \(-0.323797\pi\) | ||||
0.525716 | + | 0.850660i | \(0.323797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.67080 | 0.111574 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65685 | 0.235498 | 0.117749 | − | 0.993043i | \(-0.462432\pi\) | ||||
0.117749 | + | 0.993043i | \(0.462432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1803 | 0.506198 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.8328 | 1.61106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00310 | 0.0829601 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.40182 | −0.222957 | −0.111478 | − | 0.993767i | \(-0.535559\pi\) | ||||
−0.111478 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0557 | 0.454772 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.16073 | 0.0887304 | 0.0443652 | − | 0.999015i | \(-0.485873\pi\) | ||||
0.0443652 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9845 | 0.572348 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.8328 | 0.686625 | 0.343312 | − | 0.939221i | \(-0.388451\pi\) | ||||
0.343312 | + | 0.939221i | \(0.388451\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.8369 | 1.01143 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.4211 | −0.910044 | −0.455022 | − | 0.890480i | \(-0.650369\pi\) | ||||
−0.455022 | + | 0.890480i | \(0.650369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.0557 | −0.448001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.2492 | −1.87104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.1853 | 1.58268 | 0.791340 | − | 0.611376i | \(-0.209384\pi\) | ||||
0.791340 | + | 0.611376i | \(0.209384\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.08347 | −0.124136 | −0.0620678 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620678 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.1246 | 1.65294 | 0.826469 | − | 0.562982i | \(-0.190346\pi\) | ||||
0.826469 | + | 0.562982i | \(0.190346\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.94427 | 0.198407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.32766 | −0.333641 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.667701 | −0.0266654 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.4164 | 0.774183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.70820 | −0.0680025 | −0.0340013 | − | 0.999422i | \(-0.510825\pi\) | ||||
−0.0340013 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.4744 | −0.535561 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.45052 | 0.215958 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.4164 | 0.926339 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1115 | −0.478374 | −0.239187 | − | 0.970974i | \(-0.576881\pi\) | ||||
−0.239187 | + | 0.970974i | \(0.576881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7000 | 1.21069 | 0.605346 | − | 0.795963i | \(-0.293035\pi\) | ||||
0.605346 | + | 0.795963i | \(0.293035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.40802 | 0.369867 | 0.184934 | − | 0.982751i | \(-0.440793\pi\) | ||||
0.184934 | + | 0.982751i | \(0.440793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.16718 | 0.0458160 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.88854 | −0.387563 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.2148 | 0.869331 | 0.434665 | − | 0.900592i | \(-0.356867\pi\) | ||||
0.434665 | + | 0.900592i | \(0.356867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.7264 | 0.457489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.9443 | −1.75078 | −0.875390 | − | 0.483417i | \(-0.839395\pi\) | ||||
−0.875390 | + | 0.483417i | \(0.839395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.2765 | −1.37003 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.83153 | −0.187078 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4033 | 0.634186 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.94427 | 0.345290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.62520 | 0.178288 | 0.0891442 | − | 0.996019i | \(-0.471587\pi\) | ||||
0.0891442 | + | 0.996019i | \(0.471587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.7302 | −1.64225 | −0.821127 | − | 0.570746i | \(-0.806654\pi\) | ||||
−0.821127 | + | 0.570746i | \(0.806654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.4164 | 1.51266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.12461 | 0.196376 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5927 | −0.749692 | −0.374846 | − | 0.927087i | \(-0.622304\pi\) | ||||
−0.374846 | + | 0.927087i | \(0.622304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.73722 | −0.257041 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.2918 | −0.544474 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1246 | 0.955785 | 0.477893 | − | 0.878418i | \(-0.341401\pi\) | ||||
0.477893 | + | 0.878418i | \(0.341401\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.83153 | −0.183535 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.4295 | −1.68289 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.0557 | −0.418166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.875388 | 0.0330630 | 0.0165315 | − | 0.999863i | \(-0.494738\pi\) | ||||
0.0165315 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.62210 | −0.0988942 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.8098 | −0.556981 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.4164 | 1.25498 | 0.627490 | − | 0.778625i | \(-0.284082\pi\) | ||||
0.627490 | + | 0.778625i | \(0.284082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.4721 | −1.29281 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.32145 | −0.161840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.1235 | 0.975602 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.5967 | 1.02919 | 0.514593 | − | 0.857435i | \(-0.327943\pi\) | ||||
0.514593 | + | 0.857435i | \(0.327943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5836 | −0.617605 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.2008 | 0.937228 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.48528 | −0.314702 | −0.157351 | − | 0.987543i | \(-0.550295\pi\) | ||||
−0.157351 | + | 0.987543i | \(0.550295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94427 | 0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.8328 | −2.32396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9411 | 1.25364 | 0.626822 | − | 0.779162i | \(-0.284355\pi\) | ||||
0.626822 | + | 0.779162i | \(0.284355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.48528 | 0.312559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.8328 | −0.692776 | −0.346388 | − | 0.938091i | \(-0.612592\pi\) | ||||
−0.346388 | + | 0.938091i | \(0.612592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.76393 | 0.175007 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.62210 | 0.0961954 | 0.0480977 | − | 0.998843i | \(-0.484684\pi\) | ||||
0.0480977 | + | 0.998843i | \(0.484684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.7000 | 1.12326 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.5279 | −1.37124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.5836 | 0.751106 | 0.375553 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375553 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.14678 | 0.187559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.7727 | 1.40922 | 0.704608 | − | 0.709597i | \(-0.251123\pi\) | ||||
0.704608 | + | 0.709597i | \(0.251123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.721360 | 0.0261837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.5410 | −1.54211 | −0.771055 | − | 0.636768i | \(-0.780271\pi\) | ||||
−0.771055 | + | 0.636768i | \(0.780271\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.65685 | −0.204792 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.32766 | −0.300694 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.5410 | −1.38982 | −0.694912 | − | 0.719094i | \(-0.744557\pi\) | ||||
−0.694912 | + | 0.719094i | \(0.744557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2361 | −0.548714 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.86319 | −0.210884 | −0.105442 | − | 0.994425i | \(-0.533626\pi\) | ||||
−0.105442 | + | 0.994425i | \(0.533626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.48218 | 0.232547 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.4667 | −0.731420 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.8369 | −0.885338 | −0.442669 | − | 0.896685i | \(-0.645968\pi\) | ||||
−0.442669 | + | 0.896685i | \(0.645968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.8885 | 0.494445 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.2492 | −1.64443 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63.8158 | −2.26617 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.2958 | 1.85241 | 0.926206 | − | 0.377018i | \(-0.123050\pi\) | ||||
0.926206 | + | 0.377018i | \(0.123050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −62.8328 | −2.22287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.58359 | −0.232620 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00621 | 0.141376 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0618 | −0.459796 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.52786 | −0.264666 | −0.132333 | − | 0.991205i | \(-0.542247\pi\) | ||||
−0.132333 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.4636 | −0.647546 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48528 | 0.296862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.4721 | 1.20455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.9443 | 1.35916 | 0.679582 | − | 0.733599i | \(-0.262161\pi\) | ||||
0.679582 | + | 0.733599i | \(0.262161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.9442 | 1.25294 | 0.626469 | − | 0.779447i | \(-0.284500\pi\) | ||||
0.626469 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.86629 | 0.273538 | 0.136769 | − | 0.990603i | \(-0.456328\pi\) | ||||
0.136769 | + | 0.990603i | \(0.456328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4164 | −0.673548 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.40492 | 0.256565 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.3060 | −0.632747 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.3050 | 1.70220 | 0.851098 | − | 0.525007i | \(-0.175937\pi\) | ||||
0.851098 | + | 0.525007i | \(0.175937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.2148 | 0.765117 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.4621 | 1.01233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.11146 | −0.0724650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83282 | 0.0971077 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.4589 | 0.940176 | 0.470088 | − | 0.882619i | \(-0.344222\pi\) | ||||
0.470088 | + | 0.882619i | \(0.344222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.3190 | −1.06984 | −0.534919 | − | 0.844903i | \(-0.679658\pi\) | ||||
−0.534919 | + | 0.844903i | \(0.679658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.8328 | −0.505501 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.86629 | −0.267772 | −0.133886 | − | 0.990997i | \(-0.542746\pi\) | ||||
−0.133886 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.0671 | −1.12302 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7771 | −0.399510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.5410 | −2.05135 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.1614 | 1.05465 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9358 | −0.470579 | −0.235289 | − | 0.971925i | \(-0.575604\pi\) | ||||
−0.235289 | + | 0.971925i | \(0.575604\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.29180 | 0.0773004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.652476 | 0.0219825 | 0.0109912 | − | 0.999940i | \(-0.496501\pi\) | ||||
0.0109912 | + | 0.999940i | \(0.496501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.9148 | 1.78072 | 0.890362 | − | 0.455253i | \(-0.150451\pi\) | ||||
0.890362 | + | 0.455253i | \(0.150451\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.0547 | 1.64710 | 0.823548 | − | 0.567247i | \(-0.191991\pi\) | ||||
0.823548 | + | 0.567247i | \(0.191991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55.4164 | −1.85861 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.06888 | −0.0693102 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.48528 | 0.283949 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.14678 | −0.171846 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8885 | 0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.4164 | −0.646854 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.9768 | −0.698063 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5663 | 1.28057 | 0.640287 | − | 0.768136i | \(-0.278815\pi\) | ||||
0.640287 | + | 0.768136i | \(0.278815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.7082 | −0.388337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4721 | −1.53969 | −0.769845 | − | 0.638231i | \(-0.779667\pi\) | ||||
−0.769845 | + | 0.638231i | \(0.779667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4884 | 0.347115 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8328 | 0.885133 | 0.442566 | − | 0.896736i | \(-0.354068\pi\) | ||||
0.442566 | + | 0.896736i | \(0.354068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.76393 | −0.156977 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57.0786 | −1.87877 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.1105 | −0.430605 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.52786 | 0.246981 | 0.123491 | − | 0.992346i | \(-0.460591\pi\) | ||||
0.123491 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.48528 | 0.277796 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.1915 | 1.41101 | 0.705503 | − | 0.708707i | \(-0.250721\pi\) | ||||
0.705503 | + | 0.708707i | \(0.250721\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.16718 | −0.299160 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.9443 | −1.26955 | −0.634773 | − | 0.772698i | \(-0.718907\pi\) | ||||
−0.634773 | + | 0.772698i | \(0.718907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.48218 | −0.211089 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.6706 | 1.54909 | 0.774543 | − | 0.632521i | \(-0.217980\pi\) | ||||
0.774543 | + | 0.632521i | \(0.217980\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.5836 | −0.927863 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.81966 | −0.253570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.5632 | 1.18440 | 0.592199 | − | 0.805791i | \(-0.298260\pi\) | ||||
0.592199 | + | 0.805791i | \(0.298260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.98605 | −0.0965253 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.9443 | −0.676326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.6684 | −0.956050 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41577 | 0.0776858 | 0.0388429 | − | 0.999245i | \(-0.487633\pi\) | ||||
0.0388429 | + | 0.999245i | \(0.487633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.47214 | 0.207915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.3607 | −1.29524 | −0.647618 | − | 0.761965i | \(-0.724235\pi\) | ||||
−0.647618 | + | 0.761965i | \(0.724235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.48218 | −0.207809 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.9945 | −0.799644 | −0.399822 | − | 0.916593i | \(-0.630928\pi\) | ||||
−0.399822 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.24922 | −0.0718855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.47214 | −0.142784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.2387 | 0.964464 | 0.482232 | − | 0.876044i | \(-0.339826\pi\) | ||||
0.482232 | + | 0.876044i | \(0.339826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.9768 | −0.667698 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.16718 | −0.291500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.8328 | 1.23357 | 0.616783 | − | 0.787134i | \(-0.288436\pi\) | ||||
0.616783 | + | 0.787134i | \(0.288436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.48218 | −0.205706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7264 | 0.371378 | 0.185689 | − | 0.982609i | \(-0.440548\pi\) | ||||
0.185689 | + | 0.982609i | \(0.440548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0000 | 0.379663 |
(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 | 1900.2.a.j.1.2 | 4 | ||
4.3 | odd | 2 | 7600.2.a.ce.1.3 | 4 | |||
5.2 | odd | 4 | 380.2.c.a.229.3 | yes | 4 | ||
5.3 | odd | 4 | 380.2.c.a.229.2 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1900.2.a.j.1.3 | 4 | ||
15.2 | even | 4 | 3420.2.f.a.1369.1 | 4 | |||
15.8 | even | 4 | 3420.2.f.a.1369.2 | 4 | |||
20.3 | even | 4 | 1520.2.d.f.609.3 | 4 | |||
20.7 | even | 4 | 1520.2.d.f.609.2 | 4 | |||
20.19 | odd | 2 | 7600.2.a.ce.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.a.229.2 | ✓ | 4 | 5.3 | odd | 4 | ||
380.2.c.a.229.3 | yes | 4 | 5.2 | odd | 4 | ||
1520.2.d.f.609.2 | 4 | 20.7 | even | 4 | |||
1520.2.d.f.609.3 | 4 | 20.3 | even | 4 | |||
1900.2.a.j.1.2 | 4 | 1.1 | even | 1 | trivial | ||
1900.2.a.j.1.3 | 4 | 5.4 | even | 2 | inner | ||
3420.2.f.a.1369.1 | 4 | 15.2 | even | 4 | |||
3420.2.f.a.1369.2 | 4 | 15.8 | even | 4 | |||
7600.2.a.ce.1.2 | 4 | 20.19 | odd | 2 | |||
7600.2.a.ce.1.3 | 4 | 4.3 | odd | 2 |