Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.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: | \(59.4086991038\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 5x + 3 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 465) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.42801 | −0.917700 | −0.458850 | − | 0.888514i | \(-0.651739\pi\) | ||||
−0.458850 | + | 0.888514i | \(0.651739\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.14399 | −0.344925 | −0.172462 | − | 0.985016i | \(-0.555172\pi\) | ||||
−0.172462 | + | 0.985016i | \(0.555172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57199 | 0.435992 | 0.217996 | − | 0.975950i | \(-0.430048\pi\) | ||||
0.217996 | + | 0.975950i | \(0.430048\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.67282 | 1.13333 | 0.566663 | − | 0.823950i | \(-0.308234\pi\) | ||||
0.566663 | + | 0.823950i | \(0.308234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.34565 | −1.22638 | −0.613188 | − | 0.789937i | \(-0.710113\pi\) | ||||
−0.613188 | + | 0.789937i | \(0.710113\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.42801 | −0.529835 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81681 | 0.378831 | 0.189416 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189416 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.95684 | 0.363377 | 0.181688 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181688 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.14399 | −0.199142 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.42801 | 0.410408 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.57199 | 0.587232 | 0.293616 | − | 0.955923i | \(-0.405141\pi\) | ||||
0.293616 | + | 0.955923i | \(0.405141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57199 | 0.251720 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.14399 | −0.491008 | −0.245504 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245504 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.85601 | −0.435538 | −0.217769 | − | 0.976000i | \(-0.569878\pi\) | ||||
−0.217769 | + | 0.976000i | \(0.569878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.16246 | −1.04475 | −0.522376 | − | 0.852715i | \(-0.674954\pi\) | ||||
−0.522376 | + | 0.852715i | \(0.674954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.10478 | −0.157826 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.67282 | 0.654326 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.81681 | −0.524279 | −0.262140 | − | 0.965030i | \(-0.584428\pi\) | ||||
−0.262140 | + | 0.965030i | \(0.584428\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14399 | 0.154255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.34565 | −0.708048 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.24482 | 0.813006 | 0.406503 | − | 0.913649i | \(-0.366748\pi\) | ||||
0.406503 | + | 0.913649i | \(0.366748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.42801 | −0.305900 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.57199 | −0.194982 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.917641 | 0.112108 | 0.0560538 | − | 0.998428i | \(-0.482148\pi\) | ||||
0.0560538 | + | 0.998428i | \(0.482148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.81681 | 0.218718 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.44648 | 0.765056 | 0.382528 | − | 0.923944i | \(-0.375054\pi\) | ||||
0.382528 | + | 0.923944i | \(0.375054\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.71598 | 0.786046 | 0.393023 | − | 0.919529i | \(-0.371429\pi\) | ||||
0.393023 | + | 0.919529i | \(0.371429\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.77761 | 0.316538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.52884 | −1.07208 | −0.536039 | − | 0.844193i | \(-0.680080\pi\) | ||||
−0.536039 | + | 0.844193i | \(0.680080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16246 | 0.347125 | 0.173562 | − | 0.984823i | \(-0.444472\pi\) | ||||
0.173562 | + | 0.984823i | \(0.444472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.67282 | −0.506839 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.95684 | 0.209796 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2241 | −1.61375 | −0.806875 | − | 0.590722i | \(-0.798843\pi\) | ||||
−0.806875 | + | 0.590722i | \(0.798843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.81681 | −0.400110 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.34565 | 0.548452 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7776 | 1.09430 | 0.547150 | − | 0.837035i | \(-0.315713\pi\) | ||||
0.547150 | + | 0.837035i | \(0.315713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.14399 | −0.114975 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.51037 | −0.349294 | −0.174647 | − | 0.984631i | \(-0.555879\pi\) | ||||
−0.174647 | + | 0.984631i | \(0.555879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.2633 | −1.79954 | −0.899768 | − | 0.436369i | \(-0.856264\pi\) | ||||
−0.899768 | + | 0.436369i | \(0.856264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.42801 | 0.236949 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.96080 | 0.479578 | 0.239789 | − | 0.970825i | \(-0.422922\pi\) | ||||
0.239789 | + | 0.970825i | \(0.422922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.30644 | 0.604048 | 0.302024 | − | 0.953300i | \(-0.402338\pi\) | ||||
0.302024 | + | 0.953300i | \(0.402338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.57199 | 0.339039 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.43196 | −0.322852 | −0.161426 | − | 0.986885i | \(-0.551609\pi\) | ||||
−0.161426 | + | 0.986885i | \(0.551609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.81681 | −0.169418 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.57199 | 0.145331 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3456 | −1.04005 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.69129 | −0.881027 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.14399 | −0.283484 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8353 | −1.22768 | −0.613841 | − | 0.789429i | \(-0.710377\pi\) | ||||
−0.613841 | + | 0.789429i | \(0.710377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.85601 | −0.251458 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.79213 | −0.855542 | −0.427771 | − | 0.903887i | \(-0.640701\pi\) | ||||
−0.427771 | + | 0.903887i | \(0.640701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9793 | 1.12545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3641 | 1.31265 | 0.656323 | − | 0.754480i | \(-0.272111\pi\) | ||||
0.656323 | + | 0.754480i | \(0.272111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.1809 | 1.62691 | 0.813453 | − | 0.581631i | \(-0.197585\pi\) | ||||
0.813453 | + | 0.581631i | \(0.197585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.16246 | −0.603188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.79834 | −0.150385 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.95684 | −0.162507 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.10478 | −0.0911210 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.5473 | −0.945992 | −0.472996 | − | 0.881064i | \(-0.656828\pi\) | ||||
−0.472996 | + | 0.881064i | \(0.656828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.61515 | −0.456954 | −0.228477 | − | 0.973549i | \(-0.573375\pi\) | ||||
−0.228477 | + | 0.973549i | \(0.573375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.67282 | 0.377775 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1233 | −1.28678 | −0.643388 | − | 0.765540i | \(-0.722472\pi\) | ||||
−0.643388 | + | 0.765540i | \(0.722472\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.81681 | −0.302693 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.41123 | −0.347653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.71598 | −0.526036 | −0.263018 | − | 0.964791i | \(-0.584718\pi\) | ||||
−0.263018 | + | 0.964791i | \(0.584718\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.14399 | 0.0890592 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.16472 | −0.167511 | −0.0837555 | − | 0.996486i | \(-0.526691\pi\) | ||||
−0.0837555 | + | 0.996486i | \(0.526691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5288 | −0.809911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.34565 | −0.408792 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8560 | −1.12948 | −0.564741 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564741 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.42801 | −0.183540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.24482 | 0.469389 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0369 | −1.49763 | −0.748816 | − | 0.662778i | \(-0.769377\pi\) | ||||
−0.748816 | + | 0.662778i | \(0.769377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.287973 | −0.0214049 | −0.0107024 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107024 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.57199 | −0.262618 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.34565 | −0.390912 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.42801 | −0.176612 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2448 | −0.741289 | −0.370644 | − | 0.928775i | \(-0.620863\pi\) | ||||
−0.370644 | + | 0.928775i | \(0.620863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8353 | 1.28381 | 0.641906 | − | 0.766783i | \(-0.278144\pi\) | ||||
0.641906 | + | 0.766783i | \(0.278144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.57199 | −0.112573 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.32718 | 0.237051 | 0.118526 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118526 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65209 | 0.400666 | 0.200333 | − | 0.979728i | \(-0.435798\pi\) | ||||
0.200333 | + | 0.979728i | \(0.435798\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.917641 | 0.0647254 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.75123 | −0.333471 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.14399 | 0.219586 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.81681 | 0.126277 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.11535 | 0.423008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6050 | 1.55619 | 0.778096 | − | 0.628146i | \(-0.216186\pi\) | ||||
0.778096 | + | 0.628146i | \(0.216186\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.44648 | 0.441705 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.85601 | 0.194779 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.42801 | 0.164824 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.71598 | 0.453824 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34565 | 0.494122 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.69129 | 0.314152 | 0.157076 | − | 0.987586i | \(-0.449793\pi\) | ||||
0.157076 | + | 0.987586i | \(0.449793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.90312 | −0.126315 | −0.0631573 | − | 0.998004i | \(-0.520117\pi\) | ||||
−0.0631573 | + | 0.998004i | \(0.520117\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.1440 | −1.39723 | −0.698617 | − | 0.715496i | \(-0.746201\pi\) | ||||
−0.698617 | + | 0.715496i | \(0.746201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.77761 | 0.182753 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.7882 | −1.75495 | −0.877476 | − | 0.479621i | \(-0.840774\pi\) | ||||
−0.877476 | + | 0.479621i | \(0.840774\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.16246 | 0.467227 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.52884 | −0.618964 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.3249 | −1.57345 | −0.786724 | − | 0.617305i | \(-0.788224\pi\) | ||||
−0.786724 | + | 0.617305i | \(0.788224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.48963 | 0.418034 | 0.209017 | − | 0.977912i | \(-0.432974\pi\) | ||||
0.209017 | + | 0.977912i | \(0.432974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.10478 | 0.0705820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.40332 | −0.534691 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.16246 | 0.200413 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9216 | 1.38368 | 0.691839 | − | 0.722051i | \(-0.256801\pi\) | ||||
0.691839 | + | 0.722051i | \(0.256801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.07841 | −0.130668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.67282 | −0.292624 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.73050 | −0.482215 | −0.241108 | − | 0.970498i | \(-0.577511\pi\) | ||||
−0.241108 | + | 0.970498i | \(0.577511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.67282 | −0.538903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.95684 | 0.121126 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.4689 | −1.57048 | −0.785240 | − | 0.619192i | \(-0.787460\pi\) | ||||
−0.785240 | + | 0.619192i | \(0.787460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.81681 | 0.234465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2241 | −0.931699 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.75518 | −0.228958 | −0.114479 | − | 0.993426i | \(-0.536520\pi\) | ||||
−0.114479 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6257 | 0.827703 | 0.413852 | − | 0.910344i | \(-0.364183\pi\) | ||||
0.413852 | + | 0.910344i | \(0.364183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.81681 | −0.231004 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.14399 | −0.0689850 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.3994 | −1.16560 | −0.582798 | − | 0.812617i | \(-0.698042\pi\) | ||||
−0.582798 | + | 0.812617i | \(0.698042\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.14399 | −0.545485 | −0.272742 | − | 0.962087i | \(-0.587931\pi\) | ||||
−0.272742 | + | 0.962087i | \(0.587931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0616 | −1.31143 | −0.655714 | − | 0.755010i | \(-0.727632\pi\) | ||||
−0.655714 | + | 0.755010i | \(0.727632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.34565 | 0.316649 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.63362 | 0.450598 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.83528 | 0.284428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.7776 | 0.631795 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.90312 | −0.461705 | −0.230853 | − | 0.972989i | \(-0.574152\pi\) | ||||
−0.230853 | + | 0.972989i | \(0.574152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24482 | −0.363587 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.14399 | −0.0663808 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.85601 | 0.165168 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.93442 | 0.399693 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.51037 | −0.201665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.3865 | 1.39181 | 0.695907 | − | 0.718132i | \(-0.255003\pi\) | ||||
0.695907 | + | 0.718132i | \(0.255003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.2633 | −1.03896 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.3681 | −1.83542 | −0.917712 | − | 0.397245i | \(-0.869966\pi\) | ||||
−0.917712 | + | 0.397245i | \(0.869966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8313 | 0.612223 | 0.306111 | − | 0.951996i | \(-0.400972\pi\) | ||||
0.306111 | + | 0.951996i | \(0.400972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.42801 | 0.136803 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.3641 | −0.862935 | −0.431467 | − | 0.902129i | \(-0.642004\pi\) | ||||
−0.431467 | + | 0.902129i | \(0.642004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.23860 | −0.125338 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.96080 | 0.276885 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.9793 | −1.38988 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57199 | 0.0871985 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.30644 | 0.348747 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3905 | 0.958769 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1417 | −1.21702 | −0.608510 | − | 0.793546i | \(-0.708232\pi\) | ||||
−0.608510 | + | 0.793546i | \(0.708232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.57199 | 0.195744 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.917641 | −0.0501361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.6873 | 1.39928 | 0.699639 | − | 0.714496i | \(-0.253344\pi\) | ||||
0.699639 | + | 0.714496i | \(0.253344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.43196 | −0.186398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14399 | 0.0619503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6785 | 1.06254 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.81681 | −0.0978138 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2593 | −0.926530 | −0.463265 | − | 0.886220i | \(-0.653322\pi\) | ||||
−0.463265 | + | 0.886220i | \(0.653322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.7098 | −1.64386 | −0.821928 | − | 0.569591i | \(-0.807101\pi\) | ||||
−0.821928 | + | 0.569591i | \(0.807101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57199 | 0.0839068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1338 | −1.71031 | −0.855155 | − | 0.518372i | \(-0.826538\pi\) | ||||
−0.855155 | + | 0.518372i | \(0.826538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.44648 | −0.342144 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.3456 | −0.600475 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.0594 | 1.32258 | 0.661291 | − | 0.750129i | \(-0.270009\pi\) | ||||
0.661291 | + | 0.750129i | \(0.270009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.57595 | 0.503997 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.69129 | −0.508661 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.71598 | −0.351530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71203 | 0.0893671 | 0.0446835 | − | 0.999001i | \(-0.485772\pi\) | ||||
0.0446835 | + | 0.999001i | \(0.485772\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.14399 | −0.163669 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.26724 | 0.481131 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.4482 | −1.68010 | −0.840051 | − | 0.542507i | \(-0.817475\pi\) | ||||
−0.840051 | + | 0.542507i | \(0.817475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.07615 | 0.158430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.51827 | 0.0779884 | 0.0389942 | − | 0.999239i | \(-0.487585\pi\) | ||||
0.0389942 | + | 0.999239i | \(0.487585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8353 | −0.708803 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.2201 | −1.54418 | −0.772088 | − | 0.635515i | \(-0.780788\pi\) | ||||
−0.772088 | + | 0.635515i | \(0.780788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.77761 | −0.141560 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.85601 | −0.145179 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.67678 | 0.389228 | 0.194614 | − | 0.980880i | \(-0.437655\pi\) | ||||
0.194614 | + | 0.980880i | \(0.437655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.48963 | 0.429339 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.79213 | −0.493947 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.52884 | 0.479448 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.3664 | −0.721028 | −0.360514 | − | 0.932754i | \(-0.617399\pi\) | ||||
−0.360514 | + | 0.932754i | \(0.617399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.9793 | 0.649776 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2448 | 0.511602 | 0.255801 | − | 0.966729i | \(-0.417661\pi\) | ||||
0.255801 | + | 0.966729i | \(0.417661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.57199 | −0.0783066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.08631 | −0.202551 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.2880 | −1.20096 | −0.600481 | − | 0.799639i | \(-0.705024\pi\) | ||||
−0.600481 | + | 0.799639i | \(0.705024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.3641 | 0.757856 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.1625 | −0.746096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.16246 | −0.155239 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.1809 | 0.939294 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.9938 | 1.85612 | 0.928059 | − | 0.372433i | \(-0.121476\pi\) | ||||
0.928059 | + | 0.372433i | \(0.121476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5658 | 1.53842 | 0.769211 | − | 0.638995i | \(-0.220650\pi\) | ||||
0.769211 | + | 0.638995i | \(0.220650\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.16246 | −0.348251 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.67282 | 0.226665 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.85601 | 0.234999 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.79834 | −0.0868246 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8992 | 0.717668 | 0.358834 | − | 0.933401i | \(-0.383174\pi\) | ||||
0.358834 | + | 0.933401i | \(0.383174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.9753 | −0.767725 | −0.383862 | − | 0.923390i | \(-0.625406\pi\) | ||||
−0.383862 | + | 0.923390i | \(0.625406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.95684 | −0.0938235 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.71203 | −0.464589 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0739 | 1.53080 | 0.765401 | − | 0.643553i | \(-0.222540\pi\) | ||||
0.765401 | + | 0.643553i | \(0.222540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.10478 | −0.0526087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5944 | 0.598379 | 0.299189 | − | 0.954194i | \(-0.403284\pi\) | ||||
0.299189 | + | 0.954194i | \(0.403284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2241 | 0.721691 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.5473 | −0.546169 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.46721 | −0.352399 | −0.176200 | − | 0.984354i | \(-0.556380\pi\) | ||||
−0.176200 | + | 0.984354i | \(0.556380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.59668 | 0.169361 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.61515 | −0.263823 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.81681 | 0.178935 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.1849 | −0.944209 | −0.472104 | − | 0.881543i | \(-0.656505\pi\) | ||||
−0.472104 | + | 0.881543i | \(0.656505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.67282 | 0.218109 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0017 | 1.30417 | 0.652084 | − | 0.758146i | \(-0.273895\pi\) | ||||
0.652084 | + | 0.758146i | \(0.273895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4896 | 1.78876 | 0.894382 | − | 0.447303i | \(-0.147615\pi\) | ||||
0.894382 | + | 0.447303i | \(0.147615\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.2985 | 0.939304 | 0.469652 | − | 0.882852i | \(-0.344379\pi\) | ||||
0.469652 | + | 0.882852i | \(0.344379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.22804 | −0.102881 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.1233 | −0.742920 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.26724 | 0.150228 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.34565 | −0.245275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.81681 | −0.174760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0594 | 0.870845 | 0.435422 | − | 0.900226i | \(-0.356599\pi\) | ||||
0.435422 | + | 0.900226i | \(0.356599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.61515 | 0.256029 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.41123 | −0.200718 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.7776 | −0.489386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0656 | −0.592058 | −0.296029 | − | 0.955179i | \(-0.595662\pi\) | ||||
−0.296029 | + | 0.955179i | \(0.595662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.71598 | −0.303707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.3170 | −1.09741 | −0.548706 | − | 0.836016i | \(-0.684879\pi\) | ||||
−0.548706 | + | 0.836016i | \(0.684879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.14399 | 0.411824 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.14399 | 0.0514184 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6521 | −0.702092 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4033 | 0.734314 | 0.367157 | − | 0.930159i | \(-0.380331\pi\) | ||||
0.367157 | + | 0.930159i | \(0.380331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.16472 | −0.0967125 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.837542 | 0.0373442 | 0.0186721 | − | 0.999826i | \(-0.494056\pi\) | ||||
0.0186721 | + | 0.999826i | \(0.494056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.51037 | 0.156209 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5288 | −0.467602 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.38880 | −0.0615576 | −0.0307788 | − | 0.999526i | \(-0.509799\pi\) | ||||
−0.0307788 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3064 | −0.721355 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.34565 | −0.236016 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.2633 | 0.804777 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.19376 | 0.360361 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8560 | −0.652107 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.1025 | 1.45025 | 0.725124 | − | 0.688618i | \(-0.241782\pi\) | ||||
0.725124 | + | 0.688618i | \(0.241782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.62571 | −0.0710875 | −0.0355438 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355438 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.42801 | −0.105967 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.67282 | −0.203551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6992 | −0.856487 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.24482 | 0.271002 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.94233 | −0.214076 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.96080 | −0.214474 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.0369 | −0.864658 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26386 | 0.0544382 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.5865 | 1.14304 | 0.571522 | − | 0.820587i | \(-0.306353\pi\) | ||||
0.571522 | + | 0.820587i | \(0.306353\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.287973 | −0.0123581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.30644 | −0.270138 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9753 | 0.854083 | 0.427041 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427041 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4606 | −0.445636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.1361 | 0.983846 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.57199 | −0.151623 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.2488 | −1.23931 | −0.619655 | − | 0.784874i | \(-0.712728\pi\) | ||||
−0.619655 | + | 0.784874i | \(0.712728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.48963 | −0.189891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.34565 | −0.225693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.960797 | −0.0404928 | −0.0202464 | − | 0.999795i | \(-0.506445\pi\) | ||||
−0.0202464 | + | 0.999795i | \(0.506445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.43196 | 0.144384 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.42801 | −0.101967 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.87844 | −0.162593 | −0.0812963 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812963 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.20166 | 0.259531 | 0.129766 | − | 0.991545i | \(-0.458577\pi\) | ||||
0.129766 | + | 0.991545i | \(0.458577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.2448 | −0.427983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.81681 | 0.0757662 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.6336 | 1.48345 | 0.741724 | − | 0.670706i | \(-0.234009\pi\) | ||||
0.741724 | + | 0.670706i | \(0.234009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.8353 | 0.741209 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.67847 | −0.318557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.36638 | 0.180837 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.57199 | −0.0649939 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.7569 | 1.80604 | 0.903020 | − | 0.429599i | \(-0.141345\pi\) | ||||
0.903020 | + | 0.429599i | \(0.141345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.34565 | 0.220264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.32718 | 0.136862 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.3536 | 0.712625 | 0.356313 | − | 0.934367i | \(-0.384034\pi\) | ||||
0.356313 | + | 0.934367i | \(0.384034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3456 | 0.465126 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65209 | 0.231325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.7552 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661292\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.9506 | −1.71120 | −0.855601 | − | 0.517636i | \(-0.826812\pi\) | ||||
−0.855601 | + | 0.517636i | \(0.826812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.917641 | 0.0373692 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.69129 | 0.394007 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.25538 | 0.172721 | 0.0863603 | − | 0.996264i | \(-0.472476\pi\) | ||||
0.0863603 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.75123 | −0.192530 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.2593 | −0.455504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7367 | 0.474041 | 0.237021 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237021 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.14399 | 0.126778 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.5759 | −0.425772 | −0.212886 | − | 0.977077i | \(-0.568286\pi\) | ||||
−0.212886 | + | 0.977077i | \(0.568286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.1994 | −1.17362 | −0.586811 | − | 0.809724i | \(-0.699617\pi\) | ||||
−0.586811 | + | 0.809724i | \(0.699617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.81681 | 0.0729061 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.9642 | 1.48094 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.11535 | 0.244224 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.6913 | 0.665526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6706 | −0.783073 | −0.391536 | − | 0.920163i | \(-0.628056\pi\) | ||||
−0.391536 | + | 0.920163i | \(0.628056\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.6050 | 0.898467 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8353 | 0.549036 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73671 | −0.0688110 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.44648 | 0.255019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.3681 | 1.59444 | 0.797221 | − | 0.603687i | \(-0.206302\pi\) | ||||
0.797221 | + | 0.603687i | \(0.206302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.20166 | −0.0868250 | −0.0434125 | − | 0.999057i | \(-0.513823\pi\) | ||||
−0.0434125 | + | 0.999057i | \(0.513823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.85601 | 0.112455 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.0162 | −1.61251 | −0.806257 | − | 0.591566i | \(-0.798510\pi\) | ||||
−0.806257 | + | 0.591566i | \(0.798510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.14399 | −0.280426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.42801 | 0.0951611 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.00226 | −0.195754 | −0.0978768 | − | 0.995199i | \(-0.531205\pi\) | ||||
−0.0978768 | + | 0.995199i | \(0.531205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.79213 | 0.382610 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.71598 | 0.262015 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.5826 | −0.451192 | −0.225596 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.2386 | 1.87626 | 0.938132 | − | 0.346278i | \(-0.112554\pi\) | ||||
0.938132 | + | 0.346278i | \(0.112554\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.34565 | 0.285281 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.9793 | −0.503314 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.55521 | 0.137658 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.69129 | 0.181376 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.28797 | 0.0883262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3417 | 0.707020 | 0.353510 | − | 0.935431i | \(-0.384988\pi\) | ||||
0.353510 | + | 0.935431i | \(0.384988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.33508 | 0.205044 | 0.102522 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102522 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.1681 | −1.00424 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.90312 | −0.0729278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.2695 | −0.546007 | −0.273004 | − | 0.962013i | \(-0.588017\pi\) | ||||
−0.273004 | + | 0.962013i | \(0.588017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.3641 | −0.587033 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.1440 | −0.806693 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1233 | 0.917692 | 0.458846 | − | 0.888516i | \(-0.348263\pi\) | ||||
0.458846 | + | 0.888516i | \(0.348263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.77761 | 0.105513 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1809 | −0.727574 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.6913 | −0.556472 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.7882 | −1.01322 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.26724 | −0.123402 | −0.0617010 | − | 0.998095i | \(-0.519653\pi\) | ||||
−0.0617010 | + | 0.998095i | \(0.519653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.0946 | −0.720167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.16246 | 0.269754 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.52319 | 0.320548 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.1104 | 1.84438 | 0.922190 | − | 0.386736i | \(-0.126398\pi\) | ||||
0.922190 | + | 0.386736i | \(0.126398\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.52884 | −0.357359 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.81681 | −0.0680401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.79834 | 0.0672541 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.3249 | −0.908431 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.4320 | −0.426340 | −0.213170 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213170 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.3434 | 1.65143 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.48963 | 0.241352 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.95684 | 0.0726754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.514319 | 0.0190750 | 0.00953752 | − | 0.999955i | \(-0.496964\pi\) | ||||
0.00953752 | + | 0.999955i | \(0.496964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3456 | −0.493607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7859 | 1.32178 | 0.660891 | − | 0.750482i | \(-0.270178\pi\) | ||||
0.660891 | + | 0.750482i | \(0.270178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.10478 | 0.0407505 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.04977 | −0.0386687 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.2857 | −1.22443 | −0.612217 | − | 0.790690i | \(-0.709722\pi\) | ||||
−0.612217 | + | 0.790690i | \(0.709722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.40332 | −0.308704 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.0448 | −1.39573 | −0.697865 | − | 0.716229i | \(-0.745866\pi\) | ||||
−0.697865 | + | 0.716229i | \(0.745866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5473 | 0.423061 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.16246 | 0.115708 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0448 | −0.440109 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.20166 | 0.226302 | 0.113151 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113151 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.9216 | 0.798867 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.61515 | 0.204356 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.522225 | −0.0189806 | −0.00949029 | − | 0.999955i | \(-0.503021\pi\) | ||||
−0.00949029 | + | 0.999955i | \(0.503021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.07841 | −0.0754414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.07219 | −0.147617 | −0.0738084 | − | 0.997272i | \(-0.523515\pi\) | ||||
−0.0738084 | + | 0.997272i | \(0.523515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3121 | −0.554335 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.67282 | −0.168946 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.81681 | 0.354464 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.8089 | −0.714327 | −0.357164 | − | 0.934042i | \(-0.616256\pi\) | ||||
−0.357164 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.73050 | −0.278407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.3803 | −1.45238 | −0.726190 | − | 0.687494i | \(-0.758711\pi\) | ||||
−0.726190 | + | 0.687494i | \(0.758711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.67282 | −0.311136 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.8066 | 0.602160 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.37468 | −0.263887 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.95684 | 0.0699319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1233 | 0.575464 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1730 | −0.683444 | −0.341722 | − | 0.939801i | \(-0.611010\pi\) | ||||
−0.341722 | + | 0.939801i | \(0.611010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.4689 | −0.906717 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.33282 | 0.296281 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.14399 | −0.111646 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.81681 | 0.135368 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.0347 | 1.38268 | 0.691340 | − | 0.722530i | \(-0.257021\pi\) | ||||
0.691340 | + | 0.722530i | \(0.257021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.4689 | −1.18404 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2241 | −0.537917 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.68299 | −0.271127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.41123 | 0.155475 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.75518 | −0.132189 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.4627 | −0.895220 | −0.447610 | − | 0.894229i | \(-0.647725\pi\) | ||||
−0.447610 | + | 0.894229i | \(0.647725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.1440 | 1.51499 | 0.757495 | − | 0.652841i | \(-0.226423\pi\) | ||||
0.757495 | + | 0.652841i | \(0.226423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6257 | 0.477875 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.71598 | 0.235251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.2672 | 0.534133 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.81681 | −0.133370 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.2527 | 0.427623 | 0.213811 | − | 0.976875i | \(-0.431412\pi\) | ||||
0.213811 | + | 0.976875i | \(0.431412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.7569 | 1.17669 | 0.588345 | − | 0.808610i | \(-0.299780\pi\) | ||||
0.588345 | + | 0.808610i | \(0.299780\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.14399 | −0.0398285 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2778 | 1.29628 | 0.648138 | − | 0.761523i | \(-0.275548\pi\) | ||||
0.648138 | + | 0.761523i | \(0.275548\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.3170 | 0.914028 | 0.457014 | − | 0.889460i | \(-0.348919\pi\) | ||||
0.457014 | + | 0.889460i | \(0.348919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.3994 | −0.672957 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.16246 | −0.178869 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.16472 | 0.0749132 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.1664 | −0.972412 | −0.486206 | − | 0.873844i | \(-0.661620\pi\) | ||||
−0.486206 | + | 0.873844i | \(0.661620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1708 | −0.867957 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.14399 | −0.314936 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.5288 | 0.362203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5305 | 0.808519 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.0616 | −0.757153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.48963 | 0.222462 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.67056 | −0.262635 | −0.131318 | − | 0.991340i | \(-0.541921\pi\) | ||||
−0.131318 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.34565 | 0.182817 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.6992 | −1.45858 | −0.729288 | − | 0.684206i | \(-0.760149\pi\) | ||||
−0.729288 | + | 0.684206i | \(0.760149\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.2465 | 1.50967 | 0.754836 | − | 0.655914i | \(-0.227717\pi\) | ||||
0.754836 | + | 0.655914i | \(0.227717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.63362 | 0.260153 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.8639 | −0.778297 | −0.389148 | − | 0.921175i | \(-0.627231\pi\) | ||||
−0.389148 | + | 0.921175i | \(0.627231\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8560 | 0.505120 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.83528 | 0.164215 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9009 | 0.369786 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.44252 | 0.0488781 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.7776 | 0.364767 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.42801 | 0.0820816 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.0577 | 1.04874 | 0.524372 | − | 0.851490i | \(-0.324300\pi\) | ||||
0.524372 | + | 0.851490i | \(0.324300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.90312 | −0.266566 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.8784 | −0.602340 | −0.301170 | − | 0.953570i | \(-0.597377\pi\) | ||||
−0.301170 | + | 0.953570i | \(0.597377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2096 | 0.747411 | 0.373706 | − | 0.927547i | \(-0.378087\pi\) | ||||
0.373706 | + | 0.927547i | \(0.378087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.24482 | −0.209917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.10478 | 0.137825 | 0.0689126 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689126 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.5922 | 1.12664 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.14399 | −0.0383250 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2880 | 1.28126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0369 | 0.669761 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.85601 | 0.0953595 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.95684 | −0.0652644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8353 | −0.594179 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.93442 | 0.230763 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.287973 | 0.00957255 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.62967 | −0.286543 | −0.143272 | − | 0.989683i | \(-0.545762\pi\) | ||||
−0.143272 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.51037 | −0.116431 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.83528 | −0.259594 | −0.129797 | − | 0.991541i | \(-0.541433\pi\) | ||||
−0.129797 | + | 0.991541i | \(0.541433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.61781 | −0.119732 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.7753 | 0.785131 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2514 | −0.503098 | −0.251549 | − | 0.967845i | \(-0.580940\pi\) | ||||
−0.251549 | + | 0.967845i | \(0.580940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.3865 | 0.803564 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1338 | 0.333559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.57199 | 0.117446 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.2633 | −0.599845 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.15850 | −0.136436 | −0.0682181 | − | 0.997670i | \(-0.521731\pi\) | ||||
−0.0682181 | + | 0.997670i | \(0.521731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.90578 | 0.193554 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.3681 | −1.05968 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.34565 | 0.174821 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2175 | −0.595139 | −0.297569 | − | 0.954700i | \(-0.596176\pi\) | ||||
−0.297569 | + | 0.954700i | \(0.596176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.8313 | 0.353467 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.84150 | −0.190427 | −0.0952137 | − | 0.995457i | \(-0.530353\pi\) | ||||
−0.0952137 | + | 0.995457i | \(0.530353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.71203 | −0.186009 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.42801 | 0.0789831 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.9276 | −1.88240 | −0.941198 | − | 0.337856i | \(-0.890298\pi\) | ||||
−0.941198 | + | 0.337856i | \(0.890298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5575 | 0.342710 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.3641 | −0.498216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9977 | 0.744970 | 0.372485 | − | 0.928038i | \(-0.378506\pi\) | ||||
0.372485 | + | 0.928038i | \(0.378506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.2448 | 0.331514 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.23860 | −0.0723638 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.3042 | −1.20461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.96080 | 0.159859 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8353 | −0.574138 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.2672 | −1.45570 | −0.727848 | − | 0.685738i | \(-0.759479\pi\) | ||||
−0.727848 | + | 0.685738i | \(0.759479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.9793 | −0.802450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.59837 | −0.243843 | −0.121922 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121922 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.5714 | −1.49301 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.57199 | 0.0503441 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.1519 | −0.612723 | −0.306362 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306362 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4161 | 0.556623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.30644 | 0.201349 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.20957 | −0.134264 | −0.0671322 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671322 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.32718 | −0.106013 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.3905 | 0.553546 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.18883 | −0.164995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.3121 | 1.18526 | 0.592629 | − | 0.805476i | \(-0.298090\pi\) | ||||
0.592629 | + | 0.805476i | \(0.298090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.1417 | −0.702646 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.65209 | −0.179183 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62.0034 | −1.96367 | −0.981833 | − | 0.189745i | \(-0.939234\pi\) | ||||
−0.981833 | + | 0.189745i | \(0.939234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.57199 | 0.113013 |
(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 | 7440.2.a.bs.1.2 | 3 | ||
4.3 | odd | 2 | 465.2.a.e.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 1395.2.a.j.1.2 | 3 | |||
20.3 | even | 4 | 2325.2.c.k.1024.3 | 6 | |||
20.7 | even | 4 | 2325.2.c.k.1024.4 | 6 | |||
20.19 | odd | 2 | 2325.2.a.r.1.2 | 3 | |||
60.59 | even | 2 | 6975.2.a.bf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.a.e.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
1395.2.a.j.1.2 | 3 | 12.11 | even | 2 | |||
2325.2.a.r.1.2 | 3 | 20.19 | odd | 2 | |||
2325.2.c.k.1024.3 | 6 | 20.3 | even | 4 | |||
2325.2.c.k.1024.4 | 6 | 20.7 | even | 4 | |||
6975.2.a.bf.1.2 | 3 | 60.59 | even | 2 | |||
7440.2.a.bs.1.2 | 3 | 1.1 | even | 1 | trivial |