Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 8 x^{10} + 4 x^{9} + 36 x^{8} - 128 x^{7} + 232 x^{6} + 104 x^{5} + 324 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.9 | ||
Root | \(0.280289 + 0.280289i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.k.2431.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.20519i | 0.833482i | 0.909025 | + | 0.416741i | \(0.136828\pi\) | ||||
−0.909025 | + | 0.416741i | \(0.863172\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.04806i | − | 1.22054i | −0.792195 | − | 0.610268i | \(-0.791062\pi\) | ||
0.792195 | − | 0.610268i | \(-0.208938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.23424i | − | 0.342316i | −0.985244 | − | 0.171158i | \(-0.945249\pi\) | ||
0.985244 | − | 0.171158i | \(-0.0547508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.40345 | −1.06799 | −0.533997 | − | 0.845486i | \(-0.679311\pi\) | ||||
−0.533997 | + | 0.845486i | \(0.679311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.61178 | − | 2.44030i | 0.828598 | − | 0.559844i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.20519i | 0.481211i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.21663i | 1.92180i | 0.276894 | + | 0.960901i | \(0.410695\pi\) | ||||
−0.276894 | + | 0.960901i | \(0.589305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.22295i | 1.52696i | 0.645830 | + | 0.763481i | \(0.276512\pi\) | ||||
−0.645830 | + | 0.763481i | \(0.723488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.30698 | −1.31237 | −0.656186 | − | 0.754599i | \(-0.727831\pi\) | ||||
−0.656186 | + | 0.754599i | \(0.727831\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.04806i | − | 0.704677i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.20519i | − | 0.372744i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.55426i | 0.584318i | 0.956370 | + | 0.292159i | \(0.0943736\pi\) | ||||
−0.956370 | + | 0.292159i | \(0.905626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.23424i | − | 0.197636i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.31329i | 0.673623i | 0.941572 | + | 0.336811i | \(0.109348\pi\) | ||||
−0.941572 | + | 0.336811i | \(0.890652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.01837i | − | 1.07029i | −0.844760 | − | 0.535145i | \(-0.820257\pi\) | ||
0.844760 | − | 0.535145i | \(-0.179743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4035i | 1.51750i | 0.651382 | + | 0.758750i | \(0.274190\pi\) | ||||
−0.651382 | + | 0.758750i | \(0.725810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.13716 | 0.305308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.40345 | −0.616607 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.55958i | − | 1.03839i | −0.854656 | − | 0.519194i | \(-0.826232\pi\) | ||
0.854656 | − | 0.519194i | \(-0.173768\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.04806i | 0.545841i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.61178 | − | 2.44030i | 0.478391 | − | 0.323226i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.470233 | −0.0612192 | −0.0306096 | − | 0.999531i | \(-0.509745\pi\) | ||||
−0.0306096 | + | 0.999531i | \(0.509745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.970304 | 0.124235 | 0.0621174 | − | 0.998069i | \(-0.480215\pi\) | ||||
0.0621174 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.20519i | 0.277827i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.23424i | 0.153088i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.8255 | −1.68905 | −0.844524 | − | 0.535518i | \(-0.820117\pi\) | ||||
−0.844524 | + | 0.535518i | \(0.820117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.21663i | 1.10955i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6510 | 1.85744 | 0.928718 | − | 0.370786i | \(-0.120912\pi\) | ||||
0.928718 | + | 0.370786i | \(0.120912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.320027 | 0.0374564 | 0.0187282 | − | 0.999825i | \(-0.494038\pi\) | ||||
0.0187282 | + | 0.999825i | \(0.494038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.92673 | 1.01730 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4452 | 1.28769 | 0.643843 | − | 0.765158i | \(-0.277339\pi\) | ||||
0.643843 | + | 0.765158i | \(0.277339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.32538i | 1.02359i | 0.859106 | + | 0.511797i | \(0.171020\pi\) | ||||
−0.859106 | + | 0.511797i | \(0.828980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.40345 | 0.477622 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.22295i | 0.881592i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.17986i | 0.443065i | 0.975153 | + | 0.221532i | \(0.0711058\pi\) | ||||
−0.975153 | + | 0.221532i | \(0.928894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.72172 | 0.285314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.30698 | −0.757698 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.61178 | + | 2.44030i | −0.370560 | + | 0.250370i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6504i | 1.18292i | 0.806335 | + | 0.591459i | \(0.201448\pi\) | ||||
−0.806335 | + | 0.591459i | \(0.798552\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.04806i | − | 0.406846i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9156 | 1.48416 | 0.742078 | − | 0.670314i | \(-0.233840\pi\) | ||||
0.742078 | + | 0.670314i | \(0.233840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4655 | −1.42533 | −0.712664 | − | 0.701505i | \(-0.752512\pi\) | ||||
−0.712664 | + | 0.701505i | \(0.752512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.20519i | − | 0.215204i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4989 | 1.40166 | 0.700832 | − | 0.713326i | \(-0.252812\pi\) | ||||
0.700832 | + | 0.713326i | \(0.252812\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.28922i | − | 0.506615i | −0.967386 | − | 0.253308i | \(-0.918482\pi\) | ||
0.967386 | − | 0.253308i | \(-0.0815185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.55426i | 0.337356i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8980i | 1.30742i | 0.756747 | + | 0.653708i | \(0.226787\pi\) | ||||
−0.756747 | + | 0.653708i | \(0.773213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.21663i | − | 0.859456i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.23424i | − | 0.114105i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.71043i | − | 0.890154i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.38681 | −0.489710 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.31329i | 0.388916i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3384 | −1.27233 | −0.636165 | − | 0.771553i | \(-0.719480\pi\) | ||||
−0.636165 | + | 0.771553i | \(0.719480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.01837i | − | 0.617933i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6624i | 1.54317i | 0.636127 | + | 0.771584i | \(0.280535\pi\) | ||||
−0.636127 | + | 0.771584i | \(0.719465\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.38132 | + | 7.96464i | 0.466620 | + | 0.690622i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6157 | −1.24870 | −0.624352 | − | 0.781143i | \(-0.714637\pi\) | ||||
−0.624352 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.86064i | 0.666731i | 0.942798 | + | 0.333365i | \(0.108184\pi\) | ||||
−0.942798 | + | 0.333365i | \(0.891816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4035i | 0.876129i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.99627 | −0.417809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.22295i | − | 0.682879i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.13716 | 0.176270 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5175 | 1.43509 | 0.717544 | − | 0.696513i | \(-0.245266\pi\) | ||||
0.717544 | + | 0.696513i | \(0.245266\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3374 | −1.24814 | −0.624071 | − | 0.781367i | \(-0.714523\pi\) | ||||
−0.624071 | + | 0.781367i | \(0.714523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.40345 | −0.355998 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.30698 | 0.586911 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9126 | −0.870921 | −0.435461 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435461 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 7.55958i | − | 0.599514i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.3244 | −1.60179 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9737i | 1.25116i | 0.780161 | + | 0.625579i | \(0.215137\pi\) | ||||
−0.780161 | + | 0.625579i | \(0.784863\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.04806i | 0.315141i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.356216 | −0.0275648 | −0.0137824 | − | 0.999905i | \(-0.504387\pi\) | ||||
−0.0137824 | + | 0.999905i | \(0.504387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4767 | 0.882820 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.61178 | − | 2.44030i | 0.276199 | − | 0.186615i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.81713i | − | 0.366240i | −0.983091 | − | 0.183120i | \(-0.941380\pi\) | ||
0.983091 | − | 0.183120i | \(-0.0586196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.20519i | 0.166696i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.470233 | −0.0353449 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.3596 | −1.67123 | −0.835616 | − | 0.549313i | \(-0.814889\pi\) | ||||
−0.835616 | + | 0.549313i | \(0.814889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.96763i | − | 0.740888i | −0.928855 | − | 0.370444i | \(-0.879206\pi\) | ||
0.928855 | − | 0.370444i | \(-0.120794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.970304 | 0.0717270 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.55426i | − | 0.261315i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.8255i | 1.30353i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.20519i | 0.160404i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1221i | 1.60070i | 0.599534 | + | 0.800349i | \(0.295353\pi\) | ||||
−0.599534 | + | 0.800349i | \(0.704647\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.52803i | − | 0.325934i | −0.986631 | − | 0.162967i | \(-0.947894\pi\) | ||
0.986631 | − | 0.162967i | \(-0.0521065\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23424i | 0.0883856i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.46460 | −0.603078 | −0.301539 | − | 0.953454i | \(-0.597500\pi\) | ||||
−0.301539 | + | 0.953454i | \(0.597500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21423i | 0.511403i | 0.966756 | + | 0.255702i | \(0.0823065\pi\) | ||||
−0.966756 | + | 0.255702i | \(0.917694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.8255 | −0.975172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.1331 | −1.27270 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.31329i | − | 0.301253i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.21663i | 0.640600i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.87849 | − | 14.6207i | −0.683310 | − | 1.01133i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9776 | −1.03110 | −0.515549 | − | 0.856860i | \(-0.672412\pi\) | ||||
−0.515549 | + | 0.856860i | \(0.672412\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.6510 | 1.07239 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.01837i | 0.478649i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.1132i | − | 1.09384i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.320027 | 0.0216254 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.43491i | 0.365591i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.24952 | −0.619394 | −0.309697 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309697 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.8867 | −1.58541 | −0.792707 | − | 0.609603i | \(-0.791329\pi\) | ||||
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4239 | 0.820994 | 0.410497 | − | 0.911862i | \(-0.365355\pi\) | ||||
0.410497 | + | 0.911862i | \(0.365355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.92673 | 0.587336 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.1146 | 1.90736 | 0.953682 | − | 0.300816i | \(-0.0972592\pi\) | ||||
0.953682 | + | 0.300816i | \(0.0972592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 10.4035i | − | 0.678646i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.4452 | 0.743446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.27796i | 0.212034i | 0.994364 | + | 0.106017i | \(0.0338098\pi\) | ||||
−0.994364 | + | 0.106017i | \(0.966190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.28166i | − | 0.0825587i | −0.999148 | − | 0.0412794i | \(-0.986857\pi\) | ||
0.999148 | − | 0.0412794i | \(-0.0131434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.13716 | −0.136538 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.01191 | − | 4.45779i | −0.191643 | − | 0.283642i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.32538i | 0.590972i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.323718i | − | 0.0204329i | −0.999948 | − | 0.0102165i | \(-0.996748\pi\) | ||
0.999948 | − | 0.0102165i | \(-0.00325206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.3095 | 2.34563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.40345 | 0.275755 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3497i | 0.707976i | 0.935250 | + | 0.353988i | \(0.115175\pi\) | ||||
−0.935250 | + | 0.353988i | \(0.884825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.83781 | −0.487018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.22295i | 0.508988i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.2534i | − | 0.693912i | −0.937881 | − | 0.346956i | \(-0.887215\pi\) | ||
0.937881 | − | 0.346956i | \(-0.112785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.55958i | 0.464381i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.17986i | 0.255803i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.0809i | 0.919500i | 0.888048 | + | 0.459750i | \(0.152061\pi\) | ||||
−0.888048 | + | 0.459750i | \(0.847939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9368i | 1.87928i | 0.342169 | + | 0.939638i | \(0.388838\pi\) | ||||
−0.342169 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.72172 | 0.164726 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.04806i | − | 0.244107i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.96077 | 0.598485 | 0.299242 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299242 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.30698 | −0.437457 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.42360i | − | 0.204235i | −0.994772 | − | 0.102117i | \(-0.967438\pi\) | ||
0.994772 | − | 0.102117i | \(-0.0325617\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.15914i | − | 0.366123i | −0.983102 | − | 0.183061i | \(-0.941399\pi\) | ||
0.983102 | − | 0.183061i | \(-0.0586007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.61178 | + | 2.44030i | −0.213943 | + | 0.144551i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.51161 | −0.561452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.39040 | 0.140612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6504i | 0.682958i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.7112i | 1.44364i | 0.692079 | + | 0.721822i | \(0.256695\pi\) | ||||
−0.692079 | + | 0.721822i | \(0.743305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.470233 | 0.0273780 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.04806i | − | 0.234892i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3755 | 0.657863 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4768 | 0.892068 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.9156 | 0.856878 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.970304 | −0.0555595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.93681 | 0.452978 | 0.226489 | − | 0.974014i | \(-0.427275\pi\) | ||||
0.226489 | + | 0.974014i | \(0.427275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.4655 | −0.822914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.578158i | 0.0327843i | 0.999866 | + | 0.0163922i | \(0.00521802\pi\) | ||||
−0.999866 | + | 0.0163922i | \(0.994782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.18892 | 0.406342 | 0.203171 | − | 0.979143i | \(-0.434875\pi\) | ||||
0.203171 | + | 0.979143i | \(0.434875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.20519i | − | 0.124248i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.24733i | 0.0700568i | 0.999386 | + | 0.0350284i | \(0.0111522\pi\) | ||||
−0.999386 | + | 0.0350284i | \(0.988848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.2870 | 1.86371 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4989 | 0.809252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.9043 | + | 10.7458i | −0.884938 | + | 0.597910i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.23424i | − | 0.0684632i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.28922i | − | 0.292494i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.9415 | −1.26481 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4754 | −0.685713 | −0.342856 | − | 0.939388i | \(-0.611394\pi\) | ||||
−0.342856 | + | 0.939388i | \(0.611394\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.55426i | 0.194773i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.8255 | 0.755365 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.5603i | − | 1.11999i | −0.828496 | − | 0.559994i | \(-0.810803\pi\) | ||
0.828496 | − | 0.559994i | \(-0.189197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8980i | 0.754837i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.5791i | 1.60180i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1491i | 1.08795i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 9.21663i | − | 0.496207i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.00585i | − | 0.161362i | −0.996740 | − | 0.0806812i | \(-0.974290\pi\) | ||
0.996740 | − | 0.0806812i | \(-0.0257096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9230 | 0.852339 | 0.426169 | − | 0.904643i | \(-0.359863\pi\) | ||||
0.426169 | + | 0.904643i | \(0.359863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.23424i | − | 0.0658787i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.4303 | 1.40674 | 0.703372 | − | 0.710822i | \(-0.251677\pi\) | ||||
0.703372 | + | 0.710822i | \(0.251677\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.6510 | −0.830671 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 9.71043i | − | 0.513931i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.5186i | − | 1.39960i | −0.714339 | − | 0.699800i | \(-0.753272\pi\) | ||
0.714339 | − | 0.699800i | \(-0.246728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.08985 | − | 17.6276i | 0.373150 | − | 0.927771i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.38681 | −0.282734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.320027 | −0.0167510 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.3776i | − | 1.32470i | −0.749195 | − | 0.662350i | \(-0.769559\pi\) | ||
0.749195 | − | 0.662350i | \(-0.230441\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.31329i | 0.224541i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.6703 | 0.865478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.9214i | − | 0.927936i | −0.885852 | − | 0.463968i | \(-0.846425\pi\) | ||
0.885852 | − | 0.463968i | \(-0.153575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.1491 | 0.522704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3455 | 1.30191 | 0.650957 | − | 0.759115i | \(-0.274368\pi\) | ||||
0.650957 | + | 0.759115i | \(0.274368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3384 | −0.734580 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.0924 | −1.12887 | −0.564436 | − | 0.825477i | \(-0.690906\pi\) | ||||
−0.564436 | + | 0.825477i | \(0.690906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.92673 | −0.454948 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.01837i | − | 0.356764i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.2984 | −1.23198 | −0.615989 | − | 0.787754i | \(-0.711244\pi\) | ||||
−0.615989 | + | 0.787754i | \(0.711244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 40.5850i | − | 2.05247i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.6624i | 0.890949i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.4452 | −0.575871 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.02883 | −0.202201 | −0.101101 | − | 0.994876i | \(-0.532236\pi\) | ||||
−0.101101 | + | 0.994876i | \(0.532236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.38132 | + | 7.96464i | 0.269403 | + | 0.398731i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.14264i | 0.306749i | 0.988168 | + | 0.153374i | \(0.0490140\pi\) | ||||
−0.988168 | + | 0.153374i | \(0.950986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.01855i | 0.449246i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.3879 | 0.713181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 31.1883i | − | 1.54216i | −0.636736 | − | 0.771082i | \(-0.719716\pi\) | ||
0.636736 | − | 0.771082i | \(-0.280284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6157 | −0.720940 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.03695i | − | 0.0510251i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.32538i | − | 0.457765i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.86064i | 0.384937i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.977475i | 0.0477528i | 0.999715 | + | 0.0238764i | \(0.00760081\pi\) | ||||
−0.999715 | + | 0.0238764i | \(0.992399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.8086i | 1.84268i | 0.388761 | + | 0.921339i | \(0.372903\pi\) | ||||
−0.388761 | + | 0.921339i | \(0.627097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.4035i | 0.505833i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.40345 | −0.213599 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.13970i | 0.103547i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.99627 | −0.241222 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.8298 | −1.09967 | −0.549837 | − | 0.835272i | \(-0.685310\pi\) | ||||
−0.549837 | + | 0.835272i | \(0.685310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.0259i | − | 1.73129i | −0.500654 | − | 0.865647i | \(-0.666907\pi\) | ||
0.500654 | − | 0.865647i | \(-0.333093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 8.22295i | − | 0.394260i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.4914 | + | 33.2884i | 1.07591 | + | 1.59240i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8206 | −1.13690 | −0.568448 | − | 0.822719i | \(-0.692456\pi\) | ||||
−0.568448 | + | 0.822719i | \(0.692456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.13716 | 0.101769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.7105i | − | 0.841452i | −0.907188 | − | 0.420726i | \(-0.861775\pi\) | ||
0.907188 | − | 0.420726i | \(-0.138225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4.17986i | − | 0.198145i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.5175 | 0.828548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.21702i | − | 0.151821i | −0.997115 | − | 0.0759104i | \(-0.975814\pi\) | ||
0.997115 | − | 0.0759104i | \(-0.0241863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4605 | 0.822181 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.3374 | −0.720616 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.72172 | −0.127596 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.93491 | 0.184067 | 0.0920336 | − | 0.995756i | \(-0.470663\pi\) | ||||
0.0920336 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.40345 | −0.205536 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.0719 | 1.35401 | 0.677007 | − | 0.735977i | \(-0.263277\pi\) | ||||
0.677007 | + | 0.735977i | \(0.263277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.13917i | − | 0.145890i | −0.997336 | − | 0.0729448i | \(-0.976760\pi\) | ||
0.997336 | − | 0.0729448i | \(-0.0232397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.30698 | 0.338853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0274i | 0.695384i | 0.937609 | + | 0.347692i | \(0.113034\pi\) | ||||
−0.937609 | + | 0.347692i | \(0.886966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.4877i | − | 1.40779i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9126 | −0.502827 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.4108 | −1.30633 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.61178 | − | 2.44030i | 0.165720 | − | 0.111969i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.55958i | − | 0.346129i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.457146i | 0.0208875i | 0.999945 | + | 0.0104438i | \(0.00332441\pi\) | ||||
−0.999945 | + | 0.0104438i | \(0.996676\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.38681 | 0.200021 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.3244 | −0.924792 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11.6504i | − | 0.529017i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.0347 | 1.85946 | 0.929729 | − | 0.368243i | \(-0.120041\pi\) | ||||
0.929729 | + | 0.368243i | \(0.120041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.9737i | 0.722357i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.3616i | − | 0.828648i | −0.910130 | − | 0.414324i | \(-0.864018\pi\) | ||
0.910130 | − | 0.414324i | \(-0.135982\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 36.2094i | − | 1.63079i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.04806i | 0.181947i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.5134i | 1.54814i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.6857i | − | 1.55275i | −0.630273 | − | 0.776374i | \(-0.717057\pi\) | ||
0.630273 | − | 0.776374i | \(-0.282943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.356216 | −0.0159145 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4735i | 1.09122i | 0.838040 | + | 0.545609i | \(0.183702\pi\) | ||||
−0.838040 | + | 0.545609i | \(0.816298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.9156 | −0.663735 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4767 | 0.509696 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.1023i | − | 1.60020i | −0.599864 | − | 0.800102i | \(-0.704779\pi\) | ||
0.599864 | − | 0.800102i | \(-0.295221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.705720i | 0.0312192i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.61178 | − | 2.44030i | 0.159464 | − | 0.107742i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.4655 | 0.637426 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.1138 | 1.85216 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.81713i | − | 0.211449i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 25.9388i | − | 1.13640i | −0.822891 | − | 0.568200i | \(-0.807640\pi\) | ||
0.822891 | − | 0.568200i | \(-0.192360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.59448 | 0.0697219 | 0.0348609 | − | 0.999392i | \(-0.488901\pi\) | ||||
0.0348609 | + | 0.999392i | \(0.488901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.20519i | 0.0962422i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.1759 | 1.40161 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −61.9464 | −2.69332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.470233 | −0.0204064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.32363 | 0.230592 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4989 | −0.626844 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.3596 | −0.964887 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.65135i | − | 0.372640i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.1720 | 1.94210 | 0.971049 | − | 0.238881i | \(-0.0767806\pi\) | ||||
0.971049 | + | 0.238881i | \(0.0767806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 9.96763i | − | 0.427752i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.28922i | 0.226565i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.6483 | −1.52421 | −0.762106 | − | 0.647452i | \(-0.775835\pi\) | ||||
−0.762106 | + | 0.647452i | \(0.775835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.970304 | 0.0414116 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0665 | + | 29.6994i | 0.854861 | + | 1.26524i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.2388i | 1.07326i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3.55426i | − | 0.150870i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.2984 | −1.66513 | −0.832563 | − | 0.553930i | \(-0.813127\pi\) | ||||
−0.832563 | + | 0.553930i | \(0.813127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.66233 | −0.366378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.8255i | 0.752591i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.81444 | 0.413629 | 0.206815 | − | 0.978380i | \(-0.433690\pi\) | ||||
0.206815 | + | 0.978380i | \(0.433690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 13.8980i | − | 0.584694i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.20519i | 0.0926091i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.3042i | − | 1.10273i | −0.834265 | − | 0.551364i | \(-0.814107\pi\) | ||
0.834265 | − | 0.551364i | \(-0.185893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3658i | 1.01968i | 0.860270 | + | 0.509839i | \(0.170295\pi\) | ||||
−0.860270 | + | 0.509839i | \(0.829705\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.1221i | 0.924164i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.21663i | 0.384360i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.4885 | 1.14436 | 0.572182 | − | 0.820127i | \(-0.306097\pi\) | ||||
0.572182 | + | 0.820127i | \(0.306097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.52803i | − | 0.188178i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.5642 | −0.853147 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.6017 | −1.26739 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.23424i | 0.0510294i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.523540i | 0.0216088i | 0.999942 | + | 0.0108044i | \(0.00343921\pi\) | ||||
−0.999942 | + | 0.0108044i | \(0.996561\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.3912 | + | 17.8312i | −1.08743 | + | 0.734723i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.46460 | −0.348187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4009 | 0.468180 | 0.234090 | − | 0.972215i | \(-0.424789\pi\) | ||||
0.234090 | + | 0.972215i | \(0.424789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.71043i | 0.398089i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.21423i | 0.295259i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.1713 | 0.701601 | 0.350800 | − | 0.936450i | \(-0.385910\pi\) | ||||
0.350800 | + | 0.936450i | \(0.385910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8582i | 1.62585i | 0.582369 | + | 0.812924i | \(0.302126\pi\) | ||||
−0.582369 | + | 0.812924i | \(0.697874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.8255 | −0.563016 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.38681 | 0.219005 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.19661 | 0.129746 | 0.0648732 | − | 0.997894i | \(-0.479336\pi\) | ||||
0.0648732 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.1331 | −0.734791 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.8403 | 0.519464 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.3847 | −0.580994 | −0.290497 | − | 0.956876i | \(-0.593821\pi\) | ||||
−0.290497 | + | 0.956876i | \(0.593821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.31329i | − | 0.173929i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4439 | −0.541232 | −0.270616 | − | 0.962687i | \(-0.587227\pi\) | ||||
−0.270616 | + | 0.962687i | \(0.587227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.8410i | − | 0.596511i | −0.954486 | − | 0.298256i | \(-0.903595\pi\) | ||
0.954486 | − | 0.298256i | \(-0.0964048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.21663i | 0.369851i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.21737 | −0.369286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.87849 | − | 14.6207i | −0.394509 | − | 0.583894i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 15.6510i | − | 0.624048i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.16341i | − | 0.364789i | −0.983225 | − | 0.182395i | \(-0.941615\pi\) | ||
0.983225 | − | 0.182395i | \(-0.0583849\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9776 | −0.595305 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.3384 | 0.569003 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.63776i | − | 0.104512i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.6510 | 0.619146 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.7951i | − | 0.900353i | −0.892940 | − | 0.450176i | \(-0.851361\pi\) | ||
0.892940 | − | 0.450176i | \(-0.148639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.9599i | 1.69417i | 0.531456 | + | 0.847086i | \(0.321645\pi\) | ||||
−0.531456 | + | 0.847086i | \(0.678355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.01837i | 0.276348i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.17729i | 0.242854i | 0.992600 | + | 0.121427i | \(0.0387471\pi\) | ||||
−0.992600 | + | 0.121427i | \(0.961253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.90353i | 0.0747203i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 16.1132i | − | 0.631528i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.7151 | −0.614979 | −0.307490 | − | 0.951551i | \(-0.599489\pi\) | ||||
−0.307490 | + | 0.951551i | \(0.599489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.6624i | − | 0.690126i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.320027 | 0.0124855 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.7943 | 0.926896 | 0.463448 | − | 0.886124i | \(-0.346612\pi\) | ||||
0.463448 | + | 0.886124i | \(0.346612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.30405i | 0.128513i | 0.997933 | + | 0.0642564i | \(0.0204676\pi\) | ||||
−0.997933 | + | 0.0642564i | \(0.979532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.43491i | 0.211074i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.38132 | − | 7.96464i | −0.208679 | − | 0.308855i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −75.7879 | −2.93452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.24952 | −0.357607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.92785i | − | 0.151633i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.9847i | 1.34856i | 0.738475 | + | 0.674281i | \(0.235546\pi\) | ||||
−0.738475 | + | 0.674281i | \(0.764454\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.4637i | − | 1.28611i | −0.765818 | − | 0.643057i | \(-0.777666\pi\) | ||
0.765818 | − | 0.643057i | \(-0.222334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.6913 | −0.985940 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.8867 | −0.915339 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.9199 | 1.48923 | 0.744615 | − | 0.667494i | \(-0.232633\pi\) | ||||
0.744615 | + | 0.667494i | \(0.232633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6157 | 0.558438 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4239 | 0.474001 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.33032 | −0.355457 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.35686i | 0.165743i | 0.996560 | + | 0.0828714i | \(0.0264091\pi\) | ||||
−0.996560 | + | 0.0828714i | \(0.973591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.92673 | 0.339098 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.86064i | − | 0.298171i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.9934i | − | 0.719425i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.1146 | 1.10122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.49337 | −0.0564039 | −0.0282020 | − | 0.999602i | \(-0.508978\pi\) | ||||
−0.0282020 | + | 0.999602i | \(0.508978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.67348 | + | 12.8372i | 0.327126 | + | 0.484164i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 10.4035i | − | 0.391817i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.8916i | 1.23702i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.1781 | −1.65914 | −0.829571 | − | 0.558401i | \(-0.811415\pi\) | ||||
−0.829571 | + | 0.558401i | \(0.811415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4452 | 0.429229 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 67.3457i | − | 2.52212i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.99627 | 0.186850 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.27796i | 0.122418i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 48.9398i | − | 1.82515i | −0.408911 | − | 0.912574i | \(-0.634091\pi\) | ||
0.408911 | − | 0.912574i | \(-0.365909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 31.8991i | − | 1.18799i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.28166i | − | 0.0476653i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.22295i | 0.305393i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 30.2687i | − | 1.12260i | −0.827611 | − | 0.561302i | \(-0.810301\pi\) | ||
0.827611 | − | 0.561302i | \(-0.189699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.9051i | 1.14306i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4834 | 0.608827 | 0.304413 | − | 0.952540i | \(-0.401540\pi\) | ||||
0.304413 | + | 0.952540i | \(0.401540\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.13716 | −0.0788302 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 55.9663i | 2.06155i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 36.2349i | − | 1.33292i | −0.745540 | − | 0.666461i | \(-0.767808\pi\) | ||
0.745540 | − | 0.666461i | \(-0.232192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.01191 | − | 4.45779i | −0.110645 | − | 0.163761i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5620 | −0.791032 | −0.395516 | − | 0.918459i | \(-0.629434\pi\) | ||||
−0.395516 | + | 0.918459i | \(0.629434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5175 | −0.641791 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.32538i | 0.341198i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.9728i | 1.16826i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5768 | 0.787348 | 0.393674 | − | 0.919250i | \(-0.371204\pi\) | ||||
0.393674 | + | 0.919250i | \(0.371204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 0.323718i | − | 0.0117970i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.3374 | 0.558187 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.1484 | −0.841341 | −0.420671 | − | 0.907213i | \(-0.638205\pi\) | ||||
−0.420671 | + | 0.907213i | \(0.638205\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.3095 | 1.35425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.89987 | 0.213870 | 0.106935 | − | 0.994266i | \(-0.465896\pi\) | ||||
0.106935 | + | 0.994266i | \(0.465896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6637 | 0.422254 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.40345 | 0.159207 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.580380i | 0.0209563i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8068 | 0.497885 | 0.248942 | − | 0.968518i | \(-0.419917\pi\) | ||||
0.248942 | + | 0.968518i | \(0.419917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3497i | 0.408750i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3296i | 0.839109i | 0.907730 | + | 0.419554i | \(0.137814\pi\) | ||||
−0.907730 | + | 0.419554i | \(0.862186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.30698 | −0.262474 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.83781 | −0.281180 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.5257 | + | 15.5786i | 0.377123 | + | 0.558163i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 63.3564i | − | 2.26707i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.22295i | 0.293864i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9126 | 0.389488 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6037 | 1.16220 | 0.581098 | − | 0.813834i | \(-0.302623\pi\) | ||||
0.581098 | + | 0.813834i | \(0.302623\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 11.2534i | − | 0.400630i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.6477 | −1.08971 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.19759i | − | 0.0425275i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.55958i | 0.268111i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.9938i | 0.672794i | 0.941720 | + | 0.336397i | \(0.109208\pi\) | ||||
−0.941720 | + | 0.336397i | \(0.890792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 45.8111i | − | 1.62068i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.17986i | 0.147688i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.29549i | − | 0.0457169i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.3244 | 0.716341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0809i | 0.530873i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.7741 | −1.25775 | −0.628875 | − | 0.777507i | \(-0.716484\pi\) | ||||
−0.628875 | + | 0.777507i | \(0.716484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.7302 | 1.00885 | 0.504427 | − | 0.863455i | \(-0.331704\pi\) | ||||
0.504427 | + | 0.863455i | \(0.331704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.9368i | 1.08500i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.9737i | − | 0.559535i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1269 | − | 25.3488i | −0.599196 | − | 0.886841i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.72172 | 0.0951047 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.2681 | 0.707360 | 0.353680 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353680 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4615i | 0.538953i | 0.963007 | + | 0.269476i | \(0.0868506\pi\) | ||||
−0.963007 | + | 0.269476i | \(0.913149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.04806i | − | 0.140935i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.0865 | −1.67213 | −0.836065 | − | 0.548630i | \(-0.815150\pi\) | ||||
−0.836065 | + | 0.548630i | \(0.815150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9194i | 0.657096i | 0.944487 | + | 0.328548i | \(0.106559\pi\) | ||||
−0.944487 | + | 0.328548i | \(0.893441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.96077 | 0.345535 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.41087 | −0.326067 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.356216 | 0.0123273 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.30698 | −0.252566 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.51947 | 0.0524580 | 0.0262290 | − | 0.999656i | \(-0.491650\pi\) | ||||
0.0262290 | + | 0.999656i | \(0.491650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.6169 | −1.33162 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 3.42360i | − | 0.117915i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4767 | −0.394809 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.8789i | − | 0.408164i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 6.15914i | − | 0.211381i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.7584 | −1.12294 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.3427 | 0.901957 | 0.450978 | − | 0.892535i | \(-0.351075\pi\) | ||||
0.450978 | + | 0.892535i | \(0.351075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.61178 | + | 2.44030i | −0.123520 | + | 0.0834566i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.88515i | 0.201033i | 0.994935 | + | 0.100516i | \(0.0320495\pi\) | ||||
−0.994935 | + | 0.100516i | \(0.967950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3191i | 0.625040i | 0.949911 | + | 0.312520i | \(0.101173\pi\) | ||||
−0.949911 | + | 0.312520i | \(0.898827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.51161 | −0.324155 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.6356 | 1.58750 | 0.793748 | − | 0.608247i | \(-0.208127\pi\) | ||||
0.793748 | + | 0.608247i | \(0.208127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.81713i | 0.163787i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.39040 | 0.0811824 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 46.3309i | − | 1.57167i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0639i | 0.578188i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6504i | 0.394306i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.20519i | − | 0.0745489i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.5433i | 0.997607i | 0.866715 | + | 0.498803i | \(0.166227\pi\) | ||||
−0.866715 | + | 0.498803i | \(0.833773\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.7112i | 0.833488i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7237 | −0.866653 | −0.433327 | − | 0.901237i | \(-0.642660\pi\) | ||||
−0.433327 | + | 0.901237i | \(0.642660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.5906i | − | 1.53425i | −0.641499 | − | 0.767124i | \(-0.721687\pi\) | ||
0.641499 | − | 0.767124i | \(-0.278313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.470233 | 0.0158067 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.1405 | 1.24706 | 0.623528 | − | 0.781801i | \(-0.285699\pi\) | ||||
0.623528 | + | 0.781801i | \(0.285699\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 31.6189i | − | 1.06046i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.04806i | − | 0.135615i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.3876 | + | 37.5749i | 0.849563 | + | 1.25740i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.3596 | 0.747398 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.3755 | 0.379817 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 60.0849i | − | 2.00394i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.2883i | 1.10899i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.4768 | 0.515036 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.96763i | 0.331335i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.9876 | 1.85904 | 0.929519 | − | 0.368775i | \(-0.120223\pi\) | ||||
0.929519 | + | 0.368775i | \(0.120223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.9156 | 0.494719 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5424 | 0.945651 | 0.472826 | − | 0.881156i | \(-0.343234\pi\) | ||||
0.472826 | + | 0.881156i | \(0.343234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.7497 | 1.24933 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.970304 | −0.0320773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.9488 | −1.28620 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.4320i | − | 1.00386i | −0.864909 | − | 0.501929i | \(-0.832624\pi\) | ||
0.864909 | − | 0.501929i | \(-0.167376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.93681 | 0.261527 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19.3171i | − | 0.635830i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.55426i | 0.116864i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.4655 | −0.475110 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.0254 | 1.05072 | 0.525359 | − | 0.850881i | \(-0.323931\pi\) | ||||
0.525359 | + | 0.850881i | \(0.323931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.71893 | − | 5.21531i | 0.252978 | − | 0.170925i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.578158i | 0.0189280i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 17.8255i | − | 0.582955i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2194 | 1.57526 | 0.787629 | − | 0.616149i | \(-0.211308\pi\) | ||||
0.787629 | + | 0.616149i | \(0.211308\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.18892 | 0.234601 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.2280i | 1.93078i | 0.260815 | + | 0.965389i | \(0.416009\pi\) | ||||
−0.260815 | + | 0.965389i | \(0.583991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.7540 | −1.29457 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 2.20519i | − | 0.0717347i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 44.1262i | − | 1.43391i | −0.697121 | − | 0.716954i | \(-0.745536\pi\) | ||
0.697121 | − | 0.716954i | \(-0.254464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.394990i | − | 0.0128219i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.24733i | 0.0404473i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.2648i | − | 0.364903i | −0.983215 | − | 0.182451i | \(-0.941597\pi\) | ||
0.983215 | − | 0.182451i | \(-0.0584032\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 22.1221i | − | 0.715854i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.2870 | 1.07602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 32.2304i | − | 1.04077i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3919 | 0.722320 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.4989 | 0.467222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.52803i | 0.145762i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.2657i | − | 0.362282i | −0.983457 | − | 0.181141i | \(-0.942021\pi\) | ||
0.983457 | − | 0.181141i | \(-0.0579790\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.9043 | + | 10.7458i | −0.510919 | + | 0.345203i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0946 | −1.06206 | −0.531028 | − | 0.847354i | \(-0.678194\pi\) | ||||
−0.531028 | + | 0.847354i | \(0.678194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.3342 | −0.555708 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.23424i | − | 0.0395272i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7074i | 0.694482i | 0.937776 | + | 0.347241i | \(0.112881\pi\) | ||||
−0.937776 | + | 0.347241i | \(0.887119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9203 | 0.540777 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 5.28922i | − | 0.168872i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.2350 | −0.996242 | −0.498121 | − | 0.867107i | \(-0.665977\pi\) | ||||
−0.498121 | + | 0.867107i | \(0.665977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.46460 | 0.269705 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.9415 | −0.730237 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.6857 | 2.05689 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.6036 | −1.54394 | −0.771972 | − | 0.635657i | \(-0.780729\pi\) | ||||
−0.771972 | + | 0.635657i | \(0.780729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.4754 | −0.395896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.21423i | − | 0.228707i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5887 | 0.652050 | 0.326025 | − | 0.945361i | \(-0.394291\pi\) | ||||
0.326025 | + | 0.945361i | \(0.394291\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.55426i | 0.112452i |
(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 | 4560.2.d.k.2431.9 | yes | 12 | |
4.3 | odd | 2 | 4560.2.d.i.2431.4 | ✓ | 12 | ||
19.18 | odd | 2 | 4560.2.d.i.2431.9 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.k.2431.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.i.2431.4 | ✓ | 12 | 4.3 | odd | 2 | ||
4560.2.d.i.2431.9 | yes | 12 | 19.18 | odd | 2 | ||
4560.2.d.k.2431.4 | yes | 12 | 76.75 | even | 2 | inner | |
4560.2.d.k.2431.9 | yes | 12 | 1.1 | even | 1 | trivial |