Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(127,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.o (of order \(4\), degree \(2\), 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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.2 | ||
Character | \(\chi\) | \(=\) | 315.253 |
Dual form | 315.3.o.b.127.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41688 | + | 2.41688i | −1.20844 | + | 1.20844i | −0.236905 | + | 0.971533i | \(0.576133\pi\) |
−0.971533 | + | 0.236905i | \(0.923867\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 7.68258i | − | 1.92065i | ||||||
\(5\) | −4.18124 | − | 2.74175i | −0.836249 | − | 0.548350i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87083 | + | 1.87083i | −0.267261 | + | 0.267261i | ||||
\(8\) | 8.90034 | + | 8.90034i | 1.11254 | + | 1.11254i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 16.7320 | − | 3.47908i | 1.67320 | − | 0.347908i | ||||
\(11\) | 20.9312 | 1.90284 | 0.951420 | − | 0.307897i | \(-0.0996252\pi\) | ||||
0.951420 | + | 0.307897i | \(0.0996252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.34319 | − | 9.34319i | −0.718707 | − | 0.718707i | 0.249633 | − | 0.968340i | \(-0.419690\pi\) |
−0.968340 | + | 0.249633i | \(0.919690\pi\) | |||||||
\(14\) | − | 9.04312i | − | 0.645937i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.2917 | −0.768233 | ||||||||
\(17\) | −7.08868 | + | 7.08868i | −0.416981 | + | 0.416981i | −0.884162 | − | 0.467181i | \(-0.845270\pi\) |
0.467181 | + | 0.884162i | \(0.345270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.9507i | 0.786881i | 0.919350 | + | 0.393440i | \(0.128715\pi\) | ||||
−0.919350 | + | 0.393440i | \(0.871285\pi\) | |||||||
\(20\) | −21.0637 | + | 32.1228i | −1.05319 | + | 1.60614i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −50.5882 | + | 50.5882i | −2.29946 | + | 2.29946i | ||||
\(23\) | −12.9691 | − | 12.9691i | −0.563874 | − | 0.563874i | 0.366531 | − | 0.930406i | \(-0.380545\pi\) |
−0.930406 | + | 0.366531i | \(0.880545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.96562 | + | 22.9279i | 0.398625 | + | 0.917114i | ||||
\(26\) | 45.1627 | 1.73703 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.3728 | + | 14.3728i | 0.513314 | + | 0.513314i | ||||
\(29\) | 39.6296i | 1.36654i | 0.730168 | + | 0.683268i | \(0.239442\pi\) | ||||
−0.730168 | + | 0.683268i | \(0.760558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.8776 | 0.415405 | 0.207703 | − | 0.978192i | \(-0.433401\pi\) | ||||
0.207703 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(32\) | −5.89378 | + | 5.89378i | −0.184181 | + | 0.184181i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 34.2649i | − | 1.00779i | ||||||
\(35\) | 12.9517 | − | 2.69305i | 0.370050 | − | 0.0769443i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −31.7205 | + | 31.7205i | −0.857312 | + | 0.857312i | −0.991021 | − | 0.133709i | \(-0.957311\pi\) |
0.133709 | + | 0.991021i | \(0.457311\pi\) | |||||||
\(38\) | −36.1341 | − | 36.1341i | −0.950897 | − | 0.950897i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.8120 | − | 61.6170i | −0.320300 | − | 1.54043i | ||||
\(41\) | −69.4519 | −1.69395 | −0.846974 | − | 0.531634i | \(-0.821578\pi\) | ||||
−0.846974 | + | 0.531634i | \(0.821578\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.46880 | + | 4.46880i | 0.103926 | + | 0.103926i | 0.757158 | − | 0.653232i | \(-0.226587\pi\) |
−0.653232 | + | 0.757158i | \(0.726587\pi\) | |||||||
\(44\) | − | 160.806i | − | 3.65468i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 62.6895 | 1.36281 | ||||||||
\(47\) | 4.41044 | − | 4.41044i | 0.0938392 | − | 0.0938392i | −0.658629 | − | 0.752468i | \(-0.728863\pi\) |
0.752468 | + | 0.658629i | \(0.228863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | −79.4994 | − | 31.3281i | −1.58999 | − | 0.626562i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −71.7798 | + | 71.7798i | −1.38038 | + | 1.38038i | ||||
\(53\) | 48.5314 | + | 48.5314i | 0.915687 | + | 0.915687i | 0.996712 | − | 0.0810246i | \(-0.0258192\pi\) |
−0.0810246 | + | 0.996712i | \(0.525819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −87.5186 | − | 57.3882i | −1.59125 | − | 1.04342i | ||||
\(56\) | −33.3020 | −0.594679 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −95.7797 | − | 95.7797i | −1.65137 | − | 1.65137i | ||||
\(59\) | 29.4254i | 0.498736i | 0.968409 | + | 0.249368i | \(0.0802229\pi\) | ||||
−0.968409 | + | 0.249368i | \(0.919777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09295 | 0.116278 | 0.0581389 | − | 0.998309i | \(-0.481483\pi\) | ||||
0.0581389 | + | 0.998309i | \(0.481483\pi\) | |||||||
\(62\) | −31.1235 | + | 31.1235i | −0.501992 | + | 0.501992i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 77.6560i | − | 1.21338i | ||||||
\(65\) | 13.4495 | + | 64.6829i | 0.206915 | + | 0.995121i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.39800 | + | 1.39800i | −0.0208657 | + | 0.0208657i | −0.717463 | − | 0.696597i | \(-0.754697\pi\) |
0.696597 | + | 0.717463i | \(0.254697\pi\) | |||||||
\(68\) | 54.4593 | + | 54.4593i | 0.800873 | + | 0.800873i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −24.7940 | + | 37.8115i | −0.354200 | + | 0.540164i | ||||
\(71\) | 15.9437 | 0.224559 | 0.112279 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112279 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 32.4160 | + | 32.4160i | 0.444055 | + | 0.444055i | 0.893372 | − | 0.449317i | \(-0.148333\pi\) |
−0.449317 | + | 0.893372i | \(0.648333\pi\) | |||||||
\(74\) | − | 153.329i | − | 2.07202i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 114.860 | 1.51132 | ||||||||
\(77\) | −39.1588 | + | 39.1588i | −0.508555 | + | 0.508555i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 66.1155i | 0.836905i | 0.908239 | + | 0.418453i | \(0.137427\pi\) | ||||
−0.908239 | + | 0.418453i | \(0.862573\pi\) | |||||||
\(80\) | 51.3947 | + | 33.7009i | 0.642434 | + | 0.421261i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 167.857 | − | 167.857i | 2.04703 | − | 2.04703i | ||||
\(83\) | 83.6744 | + | 83.6744i | 1.00812 | + | 1.00812i | 0.999967 | + | 0.00815803i | \(0.00259681\pi\) |
0.00815803 | + | 0.999967i | \(0.497403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.0749 | − | 10.2041i | 0.577352 | − | 0.120048i | ||||
\(86\) | −21.6011 | −0.251175 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 186.295 | + | 186.295i | 2.11699 | + | 2.11699i | ||||
\(89\) | 62.7487i | 0.705042i | 0.935804 | + | 0.352521i | \(0.114675\pi\) | ||||
−0.935804 | + | 0.352521i | \(0.885325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.9590 | 0.384165 | ||||||||
\(92\) | −99.6363 | + | 99.6363i | −1.08300 | + | 1.08300i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 21.3190i | 0.226798i | ||||||||
\(95\) | 40.9912 | − | 62.5127i | 0.431486 | − | 0.658028i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −85.4547 | + | 85.4547i | −0.880976 | + | 0.880976i | −0.993634 | − | 0.112658i | \(-0.964064\pi\) |
0.112658 | + | 0.993634i | \(0.464064\pi\) | |||||||
\(98\) | 16.9181 | + | 16.9181i | 0.172634 | + | 0.172634i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 176.145 | − | 76.5617i | 1.76145 | − | 0.765617i | ||||
\(101\) | −145.641 | −1.44199 | −0.720997 | − | 0.692938i | \(-0.756316\pi\) | ||||
−0.720997 | + | 0.692938i | \(0.756316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 62.2547 | + | 62.2547i | 0.604414 | + | 0.604414i | 0.941481 | − | 0.337067i | \(-0.109435\pi\) |
−0.337067 | + | 0.941481i | \(0.609435\pi\) | |||||||
\(104\) | − | 166.315i | − | 1.59918i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −234.589 | −2.21310 | ||||||||
\(107\) | 4.15809 | − | 4.15809i | 0.0388607 | − | 0.0388607i | −0.687409 | − | 0.726270i | \(-0.741252\pi\) |
0.726270 | + | 0.687409i | \(0.241252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 78.6347i | − | 0.721419i | −0.932678 | − | 0.360710i | \(-0.882535\pi\) | ||
0.932678 | − | 0.360710i | \(-0.117465\pi\) | |||||||
\(110\) | 350.222 | − | 72.8215i | 3.18383 | − | 0.662013i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 22.9957 | − | 22.9957i | 0.205319 | − | 0.205319i | ||||
\(113\) | 107.343 | + | 107.343i | 0.949938 | + | 0.949938i | 0.998805 | − | 0.0488672i | \(-0.0155611\pi\) |
−0.0488672 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.6690 | + | 89.7851i | 0.162339 | + | 0.780740i | ||||
\(116\) | 304.457 | 2.62463 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −71.1176 | − | 71.1176i | −0.602692 | − | 0.602692i | ||||
\(119\) | − | 26.5234i | − | 0.222886i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 317.117 | 2.62080 | ||||||||
\(122\) | −17.1428 | + | 17.1428i | −0.140515 | + | 0.140515i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 98.9329i | − | 0.797846i | ||||||
\(125\) | 21.1937 | − | 123.190i | 0.169550 | − | 0.985522i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −116.651 | + | 116.651i | −0.918514 | + | 0.918514i | −0.996921 | − | 0.0784074i | \(-0.975017\pi\) |
0.0784074 | + | 0.996921i | \(0.475017\pi\) | |||||||
\(128\) | 164.110 | + | 164.110i | 1.28211 | + | 1.28211i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −188.836 | − | 123.825i | −1.45259 | − | 0.952498i | ||||
\(131\) | −139.820 | −1.06733 | −0.533664 | − | 0.845697i | \(-0.679185\pi\) | ||||
−0.533664 | + | 0.845697i | \(0.679185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.9703 | − | 27.9703i | −0.210303 | − | 0.210303i | ||||
\(134\) | − | 6.75760i | − | 0.0504298i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −126.183 | −0.927819 | ||||||||
\(137\) | 161.119 | − | 161.119i | 1.17605 | − | 1.17605i | 0.195313 | − | 0.980741i | \(-0.437428\pi\) |
0.980741 | − | 0.195313i | \(-0.0625723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 201.129i | 1.44697i | 0.690340 | + | 0.723485i | \(0.257461\pi\) | ||||
−0.690340 | + | 0.723485i | \(0.742539\pi\) | |||||||
\(140\) | −20.6896 | − | 99.5028i | −0.147783 | − | 0.710734i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −38.5339 | + | 38.5339i | −0.271365 | + | 0.271365i | ||||
\(143\) | −195.565 | − | 195.565i | −1.36758 | − | 1.36758i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 108.654 | − | 165.701i | 0.749340 | − | 1.14276i | ||||
\(146\) | −156.691 | −1.07323 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 243.696 | + | 243.696i | 1.64659 | + | 1.64659i | ||||
\(149\) | 23.2371i | 0.155954i | 0.996955 | + | 0.0779768i | \(0.0248460\pi\) | ||||
−0.996955 | + | 0.0779768i | \(0.975154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −39.3517 | −0.260607 | −0.130304 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130304 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(152\) | −133.067 | + | 133.067i | −0.875439 | + | 0.875439i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 189.284i | − | 1.22912i | ||||||
\(155\) | −53.8443 | − | 35.3071i | −0.347382 | − | 0.227787i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 51.1623 | − | 51.1623i | 0.325874 | − | 0.325874i | −0.525141 | − | 0.851015i | \(-0.675987\pi\) |
0.851015 | + | 0.525141i | \(0.175987\pi\) | |||||||
\(158\) | −159.793 | − | 159.793i | −1.01135 | − | 1.01135i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 40.8026 | − | 8.48407i | 0.255016 | − | 0.0530254i | ||||
\(161\) | 48.5260 | 0.301404 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −40.2804 | − | 40.2804i | −0.247119 | − | 0.247119i | 0.572668 | − | 0.819787i | \(-0.305908\pi\) |
−0.819787 | + | 0.572668i | \(0.805908\pi\) | |||||||
\(164\) | 533.570i | 3.25347i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −404.461 | −2.43651 | ||||||||
\(167\) | 66.9974 | − | 66.9974i | 0.401182 | − | 0.401182i | −0.477467 | − | 0.878649i | \(-0.658445\pi\) |
0.878649 | + | 0.477467i | \(0.158445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.59045i | 0.0330796i | ||||||||
\(170\) | −93.9458 | + | 143.270i | −0.552622 | + | 0.842765i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34.3319 | − | 34.3319i | 0.199604 | − | 0.199604i | ||||
\(173\) | −221.843 | − | 221.843i | −1.28233 | − | 1.28233i | −0.939339 | − | 0.342991i | \(-0.888560\pi\) |
−0.342991 | − | 0.939339i | \(-0.611440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −61.5380 | − | 24.2501i | −0.351646 | − | 0.138572i | ||||
\(176\) | −257.281 | −1.46182 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −151.656 | − | 151.656i | −0.851999 | − | 0.851999i | ||||
\(179\) | 129.207i | 0.721827i | 0.932599 | + | 0.360914i | \(0.117535\pi\) | ||||
−0.932599 | + | 0.360914i | \(0.882465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28.8400 | 0.159337 | 0.0796685 | − | 0.996821i | \(-0.474614\pi\) | ||||
0.0796685 | + | 0.996821i | \(0.474614\pi\) | |||||||
\(182\) | −84.4916 | + | 84.4916i | −0.464240 | + | 0.464240i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 230.859i | − | 1.25467i | ||||||
\(185\) | 219.601 | − | 45.6616i | 1.18703 | − | 0.246819i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −148.375 | + | 148.375i | −0.793448 | + | 0.793448i | ||||
\(188\) | −33.8836 | − | 33.8836i | −0.180232 | − | 0.180232i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 52.0148 | + | 250.156i | 0.273762 | + | 1.31661i | ||||
\(191\) | −29.9221 | −0.156660 | −0.0783302 | − | 0.996927i | \(-0.524959\pi\) | ||||
−0.0783302 | + | 0.996927i | \(0.524959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42.5417 | − | 42.5417i | −0.220423 | − | 0.220423i | 0.588253 | − | 0.808677i | \(-0.299816\pi\) |
−0.808677 | + | 0.588253i | \(0.799816\pi\) | |||||||
\(194\) | − | 413.067i | − | 2.12921i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −53.7781 | −0.274378 | ||||||||
\(197\) | −249.093 | + | 249.093i | −1.26443 | + | 1.26443i | −0.315509 | + | 0.948922i | \(0.602175\pi\) |
−0.948922 | + | 0.315509i | \(0.897825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.7548i | − | 0.0841949i | −0.999114 | − | 0.0420974i | \(-0.986596\pi\) | ||
0.999114 | − | 0.0420974i | \(-0.0134040\pi\) | |||||||
\(200\) | −115.368 | + | 292.763i | −0.576842 | + | 1.46382i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 351.997 | − | 351.997i | 1.74256 | − | 1.74256i | ||||
\(203\) | −74.1401 | − | 74.1401i | −0.365222 | − | 0.365222i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 290.395 | + | 190.420i | 1.41656 | + | 0.928876i | ||||
\(206\) | −300.924 | −1.46079 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 114.844 | + | 114.844i | 0.552135 | + | 0.552135i | ||||
\(209\) | 312.937i | 1.49731i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.0276 | 0.365060 | 0.182530 | − | 0.983200i | \(-0.441571\pi\) | ||||
0.182530 | + | 0.983200i | \(0.441571\pi\) | |||||||
\(212\) | 372.847 | − | 372.847i | 1.75871 | − | 1.75871i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.0992i | 0.0939214i | ||||||||
\(215\) | −6.43281 | − | 30.9375i | −0.0299201 | − | 0.143895i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0917 | + | 24.0917i | −0.111022 | + | 0.111022i | ||||
\(218\) | 190.050 | + | 190.050i | 0.871791 | + | 0.871791i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −440.890 | + | 672.369i | −2.00404 | + | 3.05622i | ||||
\(221\) | 132.462 | 0.599374 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −44.1625 | − | 44.1625i | −0.198038 | − | 0.198038i | 0.601120 | − | 0.799158i | \(-0.294721\pi\) |
−0.799158 | + | 0.601120i | \(0.794721\pi\) | |||||||
\(224\) | − | 22.0525i | − | 0.0984487i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −518.869 | −2.29588 | ||||||||
\(227\) | 176.500 | − | 176.500i | 0.777533 | − | 0.777533i | −0.201878 | − | 0.979411i | \(-0.564704\pi\) |
0.979411 | + | 0.201878i | \(0.0647044\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 296.743i | − | 1.29582i | −0.761716 | − | 0.647911i | \(-0.775643\pi\) | ||
0.761716 | − | 0.647911i | \(-0.224357\pi\) | |||||||
\(230\) | −262.120 | − | 171.879i | −1.13965 | − | 0.747299i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −352.717 | + | 352.717i | −1.52033 | + | 1.52033i | ||||
\(233\) | 88.1651 | + | 88.1651i | 0.378391 | + | 0.378391i | 0.870521 | − | 0.492131i | \(-0.163782\pi\) |
−0.492131 | + | 0.870521i | \(0.663782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.5335 | + | 6.34881i | −0.129930 | + | 0.0270162i | ||||
\(236\) | 226.063 | 0.957895 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 64.1038 | + | 64.1038i | 0.269344 | + | 0.269344i | ||||
\(239\) | − | 370.319i | − | 1.54945i | −0.632297 | − | 0.774726i | \(-0.717888\pi\) | ||
0.632297 | − | 0.774726i | \(-0.282112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −202.313 | −0.839471 | −0.419736 | − | 0.907646i | \(-0.637877\pi\) | ||||
−0.419736 | + | 0.907646i | \(0.637877\pi\) | |||||||
\(242\) | −766.431 | + | 766.431i | −3.16707 | + | 3.16707i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 54.4921i | − | 0.223328i | ||||||
\(245\) | −19.1922 | + | 29.2687i | −0.0783357 | + | 0.119464i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 139.688 | − | 139.688i | 0.565537 | − | 0.565537i | ||||
\(248\) | 114.615 | + | 114.615i | 0.462156 | + | 0.462156i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 246.513 | + | 348.958i | 0.986051 | + | 1.39583i | ||||
\(251\) | 358.910 | 1.42992 | 0.714960 | − | 0.699165i | \(-0.246445\pi\) | ||||
0.714960 | + | 0.699165i | \(0.246445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −271.459 | − | 271.459i | −1.07296 | − | 1.07296i | ||||
\(254\) | − | 563.863i | − | 2.21993i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −482.642 | −1.88532 | ||||||||
\(257\) | 157.946 | − | 157.946i | 0.614576 | − | 0.614576i | −0.329559 | − | 0.944135i | \(-0.606900\pi\) |
0.944135 | + | 0.329559i | \(0.106900\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 118.687i | − | 0.458252i | ||||||
\(260\) | 496.931 | − | 103.327i | 1.91127 | − | 0.397410i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 337.927 | − | 337.927i | 1.28980 | − | 1.28980i | ||||
\(263\) | −9.79809 | − | 9.79809i | −0.0372551 | − | 0.0372551i | 0.688234 | − | 0.725489i | \(-0.258386\pi\) |
−0.725489 | + | 0.688234i | \(0.758386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −69.8608 | − | 335.983i | −0.263626 | − | 1.26786i | ||||
\(266\) | 135.201 | 0.508276 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.7403 | + | 10.7403i | 0.0400756 | + | 0.0400756i | ||||
\(269\) | − | 143.504i | − | 0.533473i | −0.963770 | − | 0.266736i | \(-0.914055\pi\) | ||
0.963770 | − | 0.266736i | \(-0.0859453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.4732 | −0.108757 | −0.0543785 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543785 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(272\) | 87.1321 | − | 87.1321i | 0.320339 | − | 0.320339i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 778.811i | 2.84238i | ||||||||
\(275\) | 208.593 | + | 479.908i | 0.758519 | + | 1.74512i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 189.827 | − | 189.827i | 0.685295 | − | 0.685295i | −0.275894 | − | 0.961188i | \(-0.588974\pi\) |
0.961188 | + | 0.275894i | \(0.0889738\pi\) | |||||||
\(278\) | −486.103 | − | 486.103i | −1.74857 | − | 1.74857i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 139.244 | + | 91.3058i | 0.497300 | + | 0.326092i | ||||
\(281\) | 61.2502 | 0.217972 | 0.108986 | − | 0.994043i | \(-0.465240\pi\) | ||||
0.108986 | + | 0.994043i | \(0.465240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −176.415 | − | 176.415i | −0.623375 | − | 0.623375i | 0.323018 | − | 0.946393i | \(-0.395303\pi\) |
−0.946393 | + | 0.323018i | \(0.895303\pi\) | |||||||
\(284\) | − | 122.489i | − | 0.431298i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 945.310 | 3.30528 | ||||||||
\(287\) | 129.933 | − | 129.933i | 0.452727 | − | 0.452727i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 188.501i | 0.652254i | ||||||||
\(290\) | 137.874 | + | 663.083i | 0.475429 | + | 2.28649i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 249.039 | − | 249.039i | 0.852873 | − | 0.852873i | ||||
\(293\) | 92.7415 | + | 92.7415i | 0.316524 | + | 0.316524i | 0.847430 | − | 0.530907i | \(-0.178148\pi\) |
−0.530907 | + | 0.847430i | \(0.678148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 80.6772 | − | 123.035i | 0.273482 | − | 0.417068i | ||||
\(296\) | −564.647 | −1.90759 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −56.1612 | − | 56.1612i | −0.188460 | − | 0.188460i | ||||
\(299\) | 242.346i | 0.810521i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.7207 | −0.0555505 | ||||||||
\(302\) | 95.1081 | − | 95.1081i | 0.314927 | − | 0.314927i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 183.770i | − | 0.604508i | ||||||
\(305\) | −29.6573 | − | 19.4471i | −0.0972372 | − | 0.0637609i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −228.867 | + | 228.867i | −0.745494 | + | 0.745494i | −0.973629 | − | 0.228135i | \(-0.926737\pi\) |
0.228135 | + | 0.973629i | \(0.426737\pi\) | |||||||
\(308\) | 300.840 | + | 300.840i | 0.976754 | + | 0.976754i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 215.468 | − | 44.8021i | 0.695057 | − | 0.144523i | ||||
\(311\) | −291.118 | −0.936070 | −0.468035 | − | 0.883710i | \(-0.655038\pi\) | ||||
−0.468035 | + | 0.883710i | \(0.655038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 251.667 | + | 251.667i | 0.804049 | + | 0.804049i | 0.983726 | − | 0.179677i | \(-0.0575052\pi\) |
−0.179677 | + | 0.983726i | \(0.557505\pi\) | |||||||
\(314\) | 247.306i | 0.787598i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 507.938 | 1.60740 | ||||||||
\(317\) | −30.4080 | + | 30.4080i | −0.0959244 | + | 0.0959244i | −0.753440 | − | 0.657516i | \(-0.771607\pi\) |
0.657516 | + | 0.753440i | \(0.271607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 829.495i | 2.60030i | ||||||||
\(320\) | −212.913 | + | 324.699i | −0.665354 | + | 1.01468i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −117.281 | + | 117.281i | −0.364228 | + | 0.364228i | ||||
\(323\) | −105.981 | − | 105.981i | −0.328114 | − | 0.328114i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 121.109 | − | 307.330i | 0.372642 | − | 0.945631i | ||||
\(326\) | 194.705 | 0.597255 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −618.146 | − | 618.146i | −1.88459 | − | 1.88459i | ||||
\(329\) | 16.5024i | 0.0501592i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −600.898 | −1.81540 | −0.907701 | − | 0.419617i | \(-0.862164\pi\) | ||||
−0.907701 | + | 0.419617i | \(0.862164\pi\) | |||||||
\(332\) | 642.835 | − | 642.835i | 1.93625 | − | 1.93625i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 323.849i | 0.969607i | ||||||||
\(335\) | 9.67836 | − | 2.01242i | 0.0288906 | − | 0.00600722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3744 | + | 18.3744i | −0.0545235 | + | 0.0545235i | −0.733843 | − | 0.679319i | \(-0.762275\pi\) |
0.679319 | + | 0.733843i | \(0.262275\pi\) | |||||||
\(338\) | −13.5114 | − | 13.5114i | −0.0399746 | − | 0.0399746i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −78.3940 | − | 377.022i | −0.230570 | − | 1.10889i | ||||
\(341\) | 269.543 | 0.790450 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0958 | + | 13.0958i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 79.5477i | 0.231243i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1072.33 | 3.09923 | ||||||||
\(347\) | −274.252 | + | 274.252i | −0.790351 | + | 0.790351i | −0.981551 | − | 0.191200i | \(-0.938762\pi\) |
0.191200 | + | 0.981551i | \(0.438762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 218.995i | 0.627494i | 0.949507 | + | 0.313747i | \(0.101584\pi\) | ||||
−0.949507 | + | 0.313747i | \(0.898416\pi\) | |||||||
\(350\) | 207.339 | − | 90.1203i | 0.592398 | − | 0.257487i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −123.364 | + | 123.364i | −0.350466 | + | 0.350466i | ||||
\(353\) | −77.0417 | − | 77.0417i | −0.218248 | − | 0.218248i | 0.589512 | − | 0.807760i | \(-0.299320\pi\) |
−0.807760 | + | 0.589512i | \(0.799320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −66.6644 | − | 43.7136i | −0.187787 | − | 0.123137i | ||||
\(356\) | 482.072 | 1.35413 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −312.277 | − | 312.277i | −0.872283 | − | 0.872283i | ||||
\(359\) | 532.713i | 1.48388i | 0.670466 | + | 0.741940i | \(0.266094\pi\) | ||||
−0.670466 | + | 0.741940i | \(0.733906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 137.476 | 0.380819 | ||||||||
\(362\) | −69.7027 | + | 69.7027i | −0.192549 | + | 0.192549i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 268.576i | − | 0.737845i | ||||||
\(365\) | −46.6627 | − | 224.416i | −0.127843 | − | 0.614838i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 367.459 | − | 367.459i | 1.00125 | − | 1.00125i | 0.00125078 | − | 0.999999i | \(-0.499602\pi\) |
0.999999 | − | 0.00125078i | \(-0.000398137\pi\) | |||||||
\(368\) | 159.413 | + | 159.413i | 0.433187 | + | 0.433187i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −420.390 | + | 641.107i | −1.13619 | + | 1.73272i | ||||
\(371\) | −181.588 | −0.489456 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1723 | + | 30.1723i | 0.0808908 | + | 0.0808908i | 0.746395 | − | 0.665504i | \(-0.231783\pi\) |
−0.665504 | + | 0.746395i | \(0.731783\pi\) | |||||||
\(374\) | − | 717.207i | − | 1.91767i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 78.5089 | 0.208800 | ||||||||
\(377\) | 370.267 | − | 370.267i | 0.982139 | − | 0.982139i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 254.898i | − | 0.672555i | −0.941763 | − | 0.336277i | \(-0.890832\pi\) | ||
0.941763 | − | 0.336277i | \(-0.109168\pi\) | |||||||
\(380\) | −480.259 | − | 314.918i | −1.26384 | − | 0.828732i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 72.3181 | − | 72.3181i | 0.189314 | − | 0.189314i | ||||
\(383\) | −104.737 | − | 104.737i | −0.273465 | − | 0.273465i | 0.557028 | − | 0.830493i | \(-0.311941\pi\) |
−0.830493 | + | 0.557028i | \(0.811941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 271.096 | − | 56.3688i | 0.704145 | − | 0.146413i | ||||
\(386\) | 205.636 | 0.532736 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 656.512 | + | 656.512i | 1.69204 | + | 1.69204i | ||||
\(389\) | − | 667.039i | − | 1.71475i | −0.514689 | − | 0.857377i | \(-0.672092\pi\) | ||
0.514689 | − | 0.857377i | \(-0.327908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 183.868 | 0.470250 | ||||||||
\(392\) | 62.3024 | − | 62.3024i | 0.158935 | − | 0.158935i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 1204.05i | − | 3.05598i | ||||||
\(395\) | 181.272 | − | 276.445i | 0.458917 | − | 0.699861i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −171.665 | + | 171.665i | −0.432406 | + | 0.432406i | −0.889446 | − | 0.457040i | \(-0.848910\pi\) |
0.457040 | + | 0.889446i | \(0.348910\pi\) | |||||||
\(398\) | 40.4942 | + | 40.4942i | 0.101744 | + | 0.101744i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −122.495 | − | 281.823i | −0.306237 | − | 0.704558i | ||||
\(401\) | −686.098 | −1.71097 | −0.855484 | − | 0.517829i | \(-0.826740\pi\) | ||||
−0.855484 | + | 0.517829i | \(0.826740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −120.318 | − | 120.318i | −0.298555 | − | 0.298555i | ||||
\(404\) | 1118.90i | 2.76956i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 358.375 | 0.882697 | ||||||||
\(407\) | −663.950 | + | 663.950i | −1.63133 | + | 1.63133i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 556.252i | 1.36003i | 0.733198 | + | 0.680015i | \(0.238027\pi\) | ||||
−0.733198 | + | 0.680015i | \(0.761973\pi\) | |||||||
\(410\) | −1162.07 | + | 241.629i | −2.83432 | + | 0.589339i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 478.277 | − | 478.277i | 1.16087 | − | 1.16087i | ||||
\(413\) | −55.0499 | − | 55.0499i | −0.133293 | − | 0.133293i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −120.449 | − | 579.277i | −0.290238 | − | 1.39585i | ||||
\(416\) | 110.133 | 0.264744 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −756.331 | − | 756.331i | −1.80940 | − | 1.80940i | ||||
\(419\) | 143.631i | 0.342794i | 0.985202 | + | 0.171397i | \(0.0548280\pi\) | ||||
−0.985202 | + | 0.171397i | \(0.945172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 110.369 | 0.262159 | 0.131080 | − | 0.991372i | \(-0.458156\pi\) | ||||
0.131080 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(422\) | −186.166 | + | 186.166i | −0.441152 | + | 0.441152i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 863.893i | 2.03748i | ||||||||
\(425\) | −233.171 | − | 91.8851i | −0.548638 | − | 0.216200i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2697 | + | 13.2697i | −0.0310766 | + | 0.0310766i | ||||
\(428\) | −31.9449 | − | 31.9449i | −0.0746376 | − | 0.0746376i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 90.3193 | + | 59.2247i | 0.210045 | + | 0.137732i | ||||
\(431\) | −439.840 | −1.02051 | −0.510255 | − | 0.860023i | \(-0.670449\pi\) | ||||
−0.510255 | + | 0.860023i | \(0.670449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −118.543 | − | 118.543i | −0.273770 | − | 0.273770i | 0.556846 | − | 0.830616i | \(-0.312011\pi\) |
−0.830616 | + | 0.556846i | \(0.812011\pi\) | |||||||
\(434\) | − | 116.453i | − | 0.268326i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −604.118 | −1.38559 | ||||||||
\(437\) | 193.898 | − | 193.898i | 0.443702 | − | 0.443702i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 351.519i | − | 0.800727i | −0.916356 | − | 0.400363i | \(-0.868884\pi\) | ||
0.916356 | − | 0.400363i | \(-0.131116\pi\) | |||||||
\(440\) | −268.171 | − | 1289.72i | −0.609480 | − | 2.93118i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −320.144 | + | 320.144i | −0.724307 | + | 0.724307i | ||||
\(443\) | 41.1332 | + | 41.1332i | 0.0928514 | + | 0.0928514i | 0.752007 | − | 0.659155i | \(-0.229086\pi\) |
−0.659155 | + | 0.752007i | \(0.729086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 172.041 | − | 262.368i | 0.386610 | − | 0.589590i | ||||
\(446\) | 213.470 | 0.478633 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 145.281 | + | 145.281i | 0.324288 | + | 0.324288i | ||||
\(449\) | 209.909i | 0.467503i | 0.972296 | + | 0.233751i | \(0.0751002\pi\) | ||||
−0.972296 | + | 0.233751i | \(0.924900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1453.71 | −3.22331 | ||||||||
\(452\) | 824.671 | − | 824.671i | 1.82449 | − | 1.82449i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 853.157i | 1.87920i | ||||||||
\(455\) | −146.172 | − | 95.8489i | −0.321258 | − | 0.210657i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −156.842 | + | 156.842i | −0.343199 | + | 0.343199i | −0.857568 | − | 0.514370i | \(-0.828026\pi\) |
0.514370 | + | 0.857568i | \(0.328026\pi\) | |||||||
\(458\) | 717.192 | + | 717.192i | 1.56592 | + | 1.56592i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 689.781 | − | 143.426i | 1.49952 | − | 0.311795i | ||||
\(461\) | −274.147 | −0.594680 | −0.297340 | − | 0.954772i | \(-0.596099\pi\) | ||||
−0.297340 | + | 0.954772i | \(0.596099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 483.190 | + | 483.190i | 1.04361 | + | 1.04361i | 0.999005 | + | 0.0446032i | \(0.0142023\pi\) |
0.0446032 | + | 0.999005i | \(0.485798\pi\) | |||||||
\(464\) | − | 487.116i | − | 1.04982i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −426.168 | −0.914524 | ||||||||
\(467\) | −8.70901 | + | 8.70901i | −0.0186489 | + | 0.0186489i | −0.716370 | − | 0.697721i | \(-0.754198\pi\) |
0.697721 | + | 0.716370i | \(0.254198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.23085i | − | 0.0111532i | ||||||
\(470\) | 58.4513 | − | 89.1399i | 0.124365 | − | 0.189659i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −261.896 | + | 261.896i | −0.554865 | + | 0.554865i | ||||
\(473\) | 93.5374 | + | 93.5374i | 0.197754 | + | 0.197754i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −342.788 | + | 148.993i | −0.721659 | + | 0.313670i | ||||
\(476\) | −203.768 | −0.428084 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 895.015 | + | 895.015i | 1.87242 | + | 1.87242i | ||||
\(479\) | 806.280i | 1.68326i | 0.540056 | + | 0.841629i | \(0.318403\pi\) | ||||
−0.540056 | + | 0.841629i | \(0.681597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 592.742 | 1.23231 | ||||||||
\(482\) | 488.965 | − | 488.965i | 1.01445 | − | 1.01445i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 2436.27i | − | 5.03362i | ||||||
\(485\) | 591.602 | − | 123.012i | 1.21980 | − | 0.253632i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −153.496 | + | 153.496i | −0.315186 | + | 0.315186i | −0.846915 | − | 0.531729i | \(-0.821543\pi\) |
0.531729 | + | 0.846915i | \(0.321543\pi\) | |||||||
\(488\) | 63.1297 | + | 63.1297i | 0.129364 | + | 0.129364i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −24.3536 | − | 117.124i | −0.0497012 | − | 0.239029i | ||||
\(491\) | 180.954 | 0.368543 | 0.184271 | − | 0.982875i | \(-0.441007\pi\) | ||||
0.184271 | + | 0.982875i | \(0.441007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −280.921 | − | 280.921i | −0.569820 | − | 0.569820i | ||||
\(494\) | 675.215i | 1.36683i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.288 | −0.319128 | ||||||||
\(497\) | −29.8279 | + | 29.8279i | −0.0600159 | + | 0.0600159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.9603i | − | 0.0279765i | −0.999902 | − | 0.0139883i | \(-0.995547\pi\) | ||
0.999902 | − | 0.0139883i | \(-0.00445275\pi\) | |||||||
\(500\) | −946.419 | − | 162.823i | −1.89284 | − | 0.325645i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −867.441 | + | 867.441i | −1.72797 | + | 1.72797i | ||||
\(503\) | −358.510 | − | 358.510i | −0.712743 | − | 0.712743i | 0.254365 | − | 0.967108i | \(-0.418134\pi\) |
−0.967108 | + | 0.254365i | \(0.918134\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 608.962 | + | 399.312i | 1.20587 | + | 0.790717i | ||||
\(506\) | 1312.17 | 2.59322 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 896.183 | + | 896.183i | 1.76414 | + | 1.76414i | ||||
\(509\) | − | 446.506i | − | 0.877223i | −0.898677 | − | 0.438611i | \(-0.855470\pi\) | ||
0.898677 | − | 0.438611i | \(-0.144530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −121.290 | −0.237357 | ||||||||
\(512\) | 510.047 | − | 510.047i | 0.996186 | − | 0.996186i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 763.472i | 1.48535i | ||||||||
\(515\) | −89.6153 | − | 430.989i | −0.174010 | − | 0.836871i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 92.3160 | − | 92.3160i | 0.178561 | − | 0.178561i | ||||
\(518\) | 286.853 | + | 286.853i | 0.553770 | + | 0.553770i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −455.995 | + | 695.405i | −0.876913 | + | 1.33732i | ||||
\(521\) | 682.112 | 1.30924 | 0.654618 | − | 0.755960i | \(-0.272829\pi\) | ||||
0.654618 | + | 0.755960i | \(0.272829\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −252.224 | − | 252.224i | −0.482263 | − | 0.482263i | 0.423591 | − | 0.905854i | \(-0.360769\pi\) |
−0.905854 | + | 0.423591i | \(0.860769\pi\) | |||||||
\(524\) | 1074.18i | 2.04996i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.3615 | 0.0900410 | ||||||||
\(527\) | −91.2849 | + | 91.2849i | −0.173216 | + | 0.173216i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 192.604i | − | 0.364091i | ||||||
\(530\) | 980.874 | + | 643.184i | 1.85071 | + | 1.21356i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −214.884 | + | 214.884i | −0.403917 | + | 0.403917i | ||||
\(533\) | 648.902 | + | 648.902i | 1.21745 | + | 1.21745i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.7864 | + | 5.98555i | −0.0538064 | + | 0.0111879i | ||||
\(536\) | −24.8854 | −0.0464280 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 346.832 | + | 346.832i | 0.644669 | + | 0.644669i | ||||
\(539\) | − | 146.519i | − | 0.271834i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 225.356 | 0.416554 | 0.208277 | − | 0.978070i | \(-0.433214\pi\) | ||||
0.208277 | + | 0.978070i | \(0.433214\pi\) | |||||||
\(542\) | 71.2330 | − | 71.2330i | 0.131426 | − | 0.131426i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 83.5582i | − | 0.153600i | ||||||
\(545\) | −215.597 | + | 328.791i | −0.395590 | + | 0.603286i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 211.802 | − | 211.802i | 0.387207 | − | 0.387207i | −0.486483 | − | 0.873690i | \(-0.661720\pi\) |
0.873690 | + | 0.486483i | \(0.161720\pi\) | |||||||
\(548\) | −1237.81 | − | 1237.81i | −2.25878 | − | 2.25878i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1664.02 | − | 655.736i | −3.02549 | − | 1.19225i | ||||
\(551\) | −592.491 | −1.07530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −123.691 | − | 123.691i | −0.223672 | − | 0.223672i | ||||
\(554\) | 917.575i | 1.65627i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1545.19 | 2.77912 | ||||||||
\(557\) | 74.4003 | − | 74.4003i | 0.133573 | − | 0.133573i | −0.637159 | − | 0.770732i | \(-0.719891\pi\) |
0.770732 | + | 0.637159i | \(0.219891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 83.5057i | − | 0.149384i | ||||||
\(560\) | −159.199 | + | 33.1022i | −0.284284 | + | 0.0591111i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −148.034 | + | 148.034i | −0.263406 | + | 0.263406i | ||||
\(563\) | 340.172 | + | 340.172i | 0.604214 | + | 0.604214i | 0.941428 | − | 0.337214i | \(-0.109485\pi\) |
−0.337214 | + | 0.941428i | \(0.609485\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −154.520 | − | 743.135i | −0.273486 | − | 1.31528i | ||||
\(566\) | 852.747 | 1.50662 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 141.904 | + | 141.904i | 0.249831 | + | 0.249831i | ||||
\(569\) | 672.360i | 1.18165i | 0.806799 | + | 0.590826i | \(0.201198\pi\) | ||||
−0.806799 | + | 0.590826i | \(0.798802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 613.562 | 1.07454 | 0.537269 | − | 0.843411i | \(-0.319456\pi\) | ||||
0.537269 | + | 0.843411i | \(0.319456\pi\) | |||||||
\(572\) | −1502.44 | + | 1502.44i | −2.62664 | + | 2.62664i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 628.062i | 1.09418i | ||||||||
\(575\) | 168.109 | − | 426.599i | 0.292363 | − | 0.741911i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −81.3337 | + | 81.3337i | −0.140960 | + | 0.140960i | −0.774065 | − | 0.633106i | \(-0.781780\pi\) |
0.633106 | + | 0.774065i | \(0.281780\pi\) | |||||||
\(578\) | −455.584 | − | 455.584i | −0.788208 | − | 0.788208i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1273.01 | − | 834.746i | −2.19485 | − | 1.43922i | ||||
\(581\) | −313.081 | −0.538865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1015.82 | + | 1015.82i | 1.74241 | + | 1.74241i | ||||
\(584\) | 577.028i | 0.988061i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −448.289 | −0.764999 | ||||||||
\(587\) | −819.321 | + | 819.321i | −1.39578 | + | 1.39578i | −0.584082 | + | 0.811694i | \(0.698546\pi\) |
−0.811694 | + | 0.584082i | \(0.801454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 192.529i | 0.326874i | ||||||||
\(590\) | 102.373 | + | 492.347i | 0.173514 | + | 0.834486i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 389.900 | − | 389.900i | 0.658615 | − | 0.658615i | ||||
\(593\) | 308.110 | + | 308.110i | 0.519578 | + | 0.519578i | 0.917444 | − | 0.397865i | \(-0.130249\pi\) |
−0.397865 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −72.7205 | + | 110.901i | −0.122219 | + | 0.186388i | ||||
\(596\) | 178.521 | 0.299532 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −585.720 | − | 585.720i | −0.979464 | − | 0.979464i | ||||
\(599\) | 458.753i | 0.765864i | 0.923776 | + | 0.382932i | \(0.125086\pi\) | ||||
−0.923776 | + | 0.382932i | \(0.874914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 829.765 | 1.38064 | 0.690320 | − | 0.723504i | \(-0.257470\pi\) | ||||
0.690320 | + | 0.723504i | \(0.257470\pi\) | |||||||
\(602\) | 40.4119 | − | 40.4119i | 0.0671294 | − | 0.0671294i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 302.322i | 0.500534i | ||||||||
\(605\) | −1325.94 | − | 869.454i | −2.19164 | − | 1.43711i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −249.775 | + | 249.775i | −0.411490 | + | 0.411490i | −0.882258 | − | 0.470767i | \(-0.843977\pi\) |
0.470767 | + | 0.882258i | \(0.343977\pi\) | |||||||
\(608\) | −88.1163 | − | 88.1163i | −0.144928 | − | 0.144928i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 118.679 | − | 24.6769i | 0.194556 | − | 0.0404540i | ||||
\(611\) | −82.4152 | −0.134886 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 90.9769 | + | 90.9769i | 0.148413 | + | 0.148413i | 0.777409 | − | 0.628996i | \(-0.216534\pi\) |
−0.628996 | + | 0.777409i | \(0.716534\pi\) | |||||||
\(614\) | − | 1106.29i | − | 1.80177i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −697.053 | −1.13158 | ||||||||
\(617\) | 445.593 | − | 445.593i | 0.722193 | − | 0.722193i | −0.246858 | − | 0.969052i | \(-0.579398\pi\) |
0.969052 | + | 0.246858i | \(0.0793983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 943.969i | − | 1.52499i | −0.646994 | − | 0.762495i | \(-0.723974\pi\) | ||
0.646994 | − | 0.762495i | \(-0.276026\pi\) | |||||||
\(620\) | −271.249 | + | 413.663i | −0.437499 | + | 0.667198i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 703.595 | − | 703.595i | 1.13118 | − | 1.13118i | ||||
\(623\) | −117.392 | − | 117.392i | −0.188430 | − | 0.188430i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −426.373 | + | 456.980i | −0.682197 | + | 0.731169i | ||||
\(626\) | −1216.50 | −1.94329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −393.058 | − | 393.058i | −0.625889 | − | 0.625889i | ||||
\(629\) | − | 449.713i | − | 0.714965i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1001.49 | −1.58714 | −0.793570 | − | 0.608478i | \(-0.791780\pi\) | ||||
−0.793570 | + | 0.608478i | \(0.791780\pi\) | |||||||
\(632\) | −588.451 | + | 588.451i | −0.931093 | + | 0.931093i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 146.985i | − | 0.231837i | ||||||
\(635\) | 807.576 | − | 167.919i | 1.27177 | − | 0.264439i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −65.4023 | + | 65.4023i | −0.102672 | + | 0.102672i | ||||
\(638\) | −2004.79 | − | 2004.79i | −3.14230 | − | 3.14230i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −236.235 | − | 1136.13i | −0.369118 | − | 1.77521i | ||||
\(641\) | 878.051 | 1.36981 | 0.684907 | − | 0.728630i | \(-0.259843\pi\) | ||||
0.684907 | + | 0.728630i | \(0.259843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −551.380 | − | 551.380i | −0.857511 | − | 0.857511i | 0.133533 | − | 0.991044i | \(-0.457368\pi\) |
−0.991044 | + | 0.133533i | \(0.957368\pi\) | |||||||
\(644\) | − | 372.805i | − | 0.578889i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 512.286 | 0.793012 | ||||||||
\(647\) | −315.391 | + | 315.391i | −0.487466 | + | 0.487466i | −0.907506 | − | 0.420039i | \(-0.862016\pi\) |
0.420039 | + | 0.907506i | \(0.362016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 615.911i | 0.949015i | ||||||||
\(650\) | 450.074 | + | 1035.48i | 0.692421 | + | 1.59305i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −309.457 | + | 309.457i | −0.474628 | + | 0.474628i | ||||
\(653\) | 825.176 | + | 825.176i | 1.26367 | + | 1.26367i | 0.949301 | + | 0.314368i | \(0.101793\pi\) |
0.314368 | + | 0.949301i | \(0.398207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 584.621 | + | 383.351i | 0.892552 | + | 0.585269i | ||||
\(656\) | 853.684 | 1.30135 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −39.8842 | − | 39.8842i | −0.0606143 | − | 0.0606143i | ||||
\(659\) | − | 956.471i | − | 1.45140i | −0.688012 | − | 0.725699i | \(-0.741517\pi\) | ||
0.688012 | − | 0.725699i | \(-0.258483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2815 | 0.0276573 | 0.0138286 | − | 0.999904i | \(-0.495598\pi\) | ||||
0.0138286 | + | 0.999904i | \(0.495598\pi\) | |||||||
\(662\) | 1452.30 | − | 1452.30i | 2.19380 | − | 2.19380i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1489.46i | 2.24316i | ||||||||
\(665\) | 40.2631 | + | 193.638i | 0.0605460 | + | 0.291185i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 513.960 | − | 513.960i | 0.770555 | − | 0.770555i | ||||
\(668\) | −514.713 | − | 514.713i | −0.770528 | − | 0.770528i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.5276 | + | 28.2552i | −0.0276532 | + | 0.0421719i | ||||
\(671\) | 148.464 | 0.221258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −829.059 | − | 829.059i | −1.23189 | − | 1.23189i | −0.963239 | − | 0.268647i | \(-0.913424\pi\) |
−0.268647 | − | 0.963239i | \(-0.586576\pi\) | |||||||
\(674\) | − | 88.8173i | − | 0.131776i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.9491 | 0.0635342 | ||||||||
\(677\) | 421.712 | − | 421.712i | 0.622913 | − | 0.622913i | −0.323362 | − | 0.946275i | \(-0.604813\pi\) |
0.946275 | + | 0.323362i | \(0.104813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 319.742i | − | 0.470901i | ||||||
\(680\) | 527.603 | + | 345.963i | 0.775887 | + | 0.508769i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −651.453 | + | 651.453i | −0.955209 | + | 0.955209i | ||||
\(683\) | 40.2821 | + | 40.2821i | 0.0589782 | + | 0.0589782i | 0.735981 | − | 0.677003i | \(-0.236721\pi\) |
−0.677003 | + | 0.735981i | \(0.736721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1115.43 | + | 231.931i | −1.62836 | + | 0.338585i | ||||
\(686\) | −63.3019 | −0.0922768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −54.9293 | − | 54.9293i | −0.0798390 | − | 0.0798390i | ||||
\(689\) | − | 906.877i | − | 1.31622i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 499.429 | 0.722763 | 0.361381 | − | 0.932418i | \(-0.382305\pi\) | ||||
0.361381 | + | 0.932418i | \(0.382305\pi\) | |||||||
\(692\) | −1704.33 | + | 1704.33i | −2.46290 | + | 2.46290i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1325.67i | − | 1.91018i | ||||||
\(695\) | 551.445 | − | 840.969i | 0.793446 | − | 1.21003i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 492.322 | − | 492.322i | 0.706344 | − | 0.706344i | ||||
\(698\) | −529.285 | − | 529.285i | −0.758287 | − | 0.758287i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −186.304 | + | 472.771i | −0.266148 | + | 0.675387i | ||||
\(701\) | −29.9935 | −0.0427867 | −0.0213934 | − | 0.999771i | \(-0.506810\pi\) | ||||
−0.0213934 | + | 0.999771i | \(0.506810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −474.245 | − | 474.245i | −0.674602 | − | 0.674602i | ||||
\(704\) | − | 1625.44i | − | 2.30886i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 372.401 | 0.527480 | ||||||||
\(707\) | 272.470 | − | 272.470i | 0.385389 | − | 0.385389i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 983.508i | 1.38718i | 0.720372 | + | 0.693588i | \(0.243971\pi\) | ||||
−0.720372 | + | 0.693588i | \(0.756029\pi\) | |||||||
\(710\) | 266.770 | − | 55.4694i | 0.375732 | − | 0.0781259i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −558.485 | + | 558.485i | −0.784389 | + | 0.784389i | ||||
\(713\) | −167.011 | − | 167.011i | −0.234236 | − | 0.234236i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 281.514 | + | 1353.89i | 0.393726 | + | 1.89356i | ||||
\(716\) | 992.644 | 1.38637 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1287.50 | − | 1287.50i | −1.79318 | − | 1.79318i | ||||
\(719\) | 59.3020i | 0.0824784i | 0.999149 | + | 0.0412392i | \(0.0131306\pi\) | ||||
−0.999149 | + | 0.0412392i | \(0.986869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −232.936 | −0.323073 | ||||||||
\(722\) | −332.261 | + | 332.261i | −0.460196 | + | 0.460196i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 221.566i | − | 0.306030i | ||||||
\(725\) | −908.621 | + | 394.933i | −1.25327 | + | 0.544735i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.0937 | + | 25.0937i | −0.0345168 | + | 0.0345168i | −0.724155 | − | 0.689638i | \(-0.757770\pi\) |
0.689638 | + | 0.724155i | \(0.257770\pi\) | |||||||
\(728\) | 311.147 | + | 311.147i | 0.427400 | + | 0.427400i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 655.164 | + | 429.608i | 0.897485 | + | 0.588504i | ||||
\(731\) | −63.3557 | −0.0866699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 611.839 | + | 611.839i | 0.834706 | + | 0.834706i | 0.988156 | − | 0.153451i | \(-0.0490386\pi\) |
−0.153451 | + | 0.988156i | \(0.549039\pi\) | |||||||
\(734\) | 1776.20i | 2.41990i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 152.874 | 0.207709 | ||||||||
\(737\) | −29.2619 | + | 29.2619i | −0.0397041 | + | 0.0397041i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 566.278i | − | 0.766277i | −0.923691 | − | 0.383138i | \(-0.874843\pi\) | ||
0.923691 | − | 0.383138i | \(-0.125157\pi\) | |||||||
\(740\) | −350.799 | − | 1687.10i | −0.474052 | − | 2.27987i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 438.876 | − | 438.876i | 0.591477 | − | 0.591477i | ||||
\(743\) | −65.5539 | − | 65.5539i | −0.0882287 | − | 0.0882287i | 0.661615 | − | 0.749844i | \(-0.269871\pi\) |
−0.749844 | + | 0.661615i | \(0.769871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.7103 | − | 97.1600i | 0.0855172 | − | 0.130416i | ||||
\(746\) | −145.845 | −0.195503 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1139.90 | + | 1139.90i | 1.52393 | + | 1.52393i | ||||
\(749\) | 15.5582i | 0.0207719i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −99.3347 | −0.132270 | −0.0661350 | − | 0.997811i | \(-0.521067\pi\) | ||||
−0.0661350 | + | 0.997811i | \(0.521067\pi\) | |||||||
\(752\) | −54.2120 | + | 54.2120i | −0.0720904 | + | 0.0720904i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1789.78i | 2.37371i | ||||||||
\(755\) | 164.539 | + | 107.892i | 0.217932 | + | 0.142904i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 605.866 | − | 605.866i | 0.800351 | − | 0.800351i | −0.182799 | − | 0.983150i | \(-0.558516\pi\) |
0.983150 | + | 0.182799i | \(0.0585159\pi\) | |||||||
\(758\) | 616.058 | + | 616.058i | 0.812741 | + | 0.812741i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 921.220 | − | 191.549i | 1.21213 | − | 0.252038i | ||||
\(761\) | −126.096 | −0.165698 | −0.0828489 | − | 0.996562i | \(-0.526402\pi\) | ||||
−0.0828489 | + | 0.996562i | \(0.526402\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 147.112 | + | 147.112i | 0.192807 | + | 0.192807i | ||||
\(764\) | 229.879i | 0.300889i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 506.273 | 0.660931 | ||||||||
\(767\) | 274.927 | − | 274.927i | 0.358445 | − | 0.358445i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 115.901i | − | 0.150716i | −0.997157 | − | 0.0753582i | \(-0.975990\pi\) | ||
0.997157 | − | 0.0753582i | \(-0.0240100\pi\) | |||||||
\(770\) | −518.969 | + | 791.442i | −0.673985 | + | 1.02785i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −326.830 | + | 326.830i | −0.423355 | + | 0.423355i | ||||
\(773\) | −325.618 | − | 325.618i | −0.421240 | − | 0.421240i | 0.464391 | − | 0.885630i | \(-0.346273\pi\) |
−0.885630 | + | 0.464391i | \(0.846273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 128.333 | + | 295.255i | 0.165591 | + | 0.380974i | ||||
\(776\) | −1521.15 | −1.96025 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1612.15 | + | 1612.15i | 2.07217 | + | 2.07217i | ||||
\(779\) | − | 1038.36i | − | 1.33294i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 333.721 | 0.427299 | ||||||||
\(782\) | −444.385 | + | 444.385i | −0.568268 | + | 0.568268i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 86.0421i | 0.109748i | ||||||||
\(785\) | −354.196 | + | 73.6478i | −0.451205 | + | 0.0938189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −140.660 | + | 140.660i | −0.178730 | + | 0.178730i | −0.790802 | − | 0.612072i | \(-0.790336\pi\) |
0.612072 | + | 0.790802i | \(0.290336\pi\) | |||||||
\(788\) | 1913.68 | + | 1913.68i | 2.42852 | + | 2.42852i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 230.021 | + | 1106.25i | 0.291166 | + | 1.40031i | ||||
\(791\) | −401.641 | −0.507763 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −66.2708 | − | 66.2708i | −0.0835697 | − | 0.0835697i | ||||
\(794\) | − | 829.788i | − | 1.04507i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −128.720 | −0.161709 | ||||||||
\(797\) | 533.305 | − | 533.305i | 0.669141 | − | 0.669141i | −0.288376 | − | 0.957517i | \(-0.593115\pi\) |
0.957517 | + | 0.288376i | \(0.0931154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.5284i | 0.0782584i | ||||||||
\(800\) | −193.867 | − | 76.3966i | −0.242334 | − | 0.0954957i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1658.21 | − | 1658.21i | 2.06760 | − | 2.06760i | ||||
\(803\) | 678.507 | + | 678.507i | 0.844966 | + | 0.844966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −202.899 | − | 133.046i | −0.252048 | − | 0.165275i | ||||
\(806\) | 581.585 | 0.721570 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1296.26 | − | 1296.26i | −1.60428 | − | 1.60428i | ||||
\(809\) | 651.161i | 0.804896i | 0.915443 | + | 0.402448i | \(0.131841\pi\) | ||||
−0.915443 | + | 0.402448i | \(0.868159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 94.9703 | 0.117103 | 0.0585513 | − | 0.998284i | \(-0.481352\pi\) | ||||
0.0585513 | + | 0.998284i | \(0.481352\pi\) | |||||||
\(812\) | −569.587 | + | 569.587i | −0.701462 | + | 0.701462i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 3209.37i | − | 3.94271i | ||||||
\(815\) | 57.9834 | + | 278.861i | 0.0711453 | + | 0.342160i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −66.8118 | + | 66.8118i | −0.0817770 | + | 0.0817770i | ||||
\(818\) | −1344.39 | − | 1344.39i | −1.64351 | − | 1.64351i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1462.91 | − | 2230.99i | 1.78404 | − | 2.72071i | ||||
\(821\) | 368.589 | 0.448952 | 0.224476 | − | 0.974480i | \(-0.427933\pi\) | ||||
0.224476 | + | 0.974480i | \(0.427933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 494.462 | + | 494.462i | 0.600804 | + | 0.600804i | 0.940526 | − | 0.339722i | \(-0.110333\pi\) |
−0.339722 | + | 0.940526i | \(0.610333\pi\) | |||||||
\(824\) | 1108.18i | 1.34487i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 266.098 | 0.322152 | ||||||||
\(827\) | 191.666 | − | 191.666i | 0.231761 | − | 0.231761i | −0.581666 | − | 0.813427i | \(-0.697599\pi\) |
0.813427 | + | 0.581666i | \(0.197599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 110.729i | − | 0.133569i | −0.997767 | − | 0.0667847i | \(-0.978726\pi\) | ||
0.997767 | − | 0.0667847i | \(-0.0212741\pi\) | |||||||
\(830\) | 1691.15 | + | 1108.93i | 2.03753 | + | 1.33606i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −725.555 | + | 725.555i | −0.872061 | + | 0.872061i | ||||
\(833\) | 49.6207 | + | 49.6207i | 0.0595687 | + | 0.0595687i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −463.823 | + | 96.4424i | −0.555476 | + | 0.115500i | ||||
\(836\) | 2404.17 | 2.87580 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −347.137 | − | 347.137i | −0.414245 | − | 0.414245i | ||||
\(839\) | 184.793i | 0.220254i | 0.993918 | + | 0.110127i | \(0.0351258\pi\) | ||||
−0.993918 | + | 0.110127i | \(0.964874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −729.502 | −0.867422 | ||||||||
\(842\) | −266.748 | + | 266.748i | −0.316803 | + | 0.316803i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 591.771i | − | 0.701150i | ||||||
\(845\) | 15.3276 | − | 23.3750i | 0.0181392 | − | 0.0276628i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −593.271 | + | 593.271i | −0.700438 | + | 0.700438i | ||||
\(848\) | −596.535 | − | 596.535i | −0.703462 | − | 0.703462i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 785.621 | − | 341.471i | 0.924260 | − | 0.401731i | ||||
\(851\) | 822.774 | 0.966832 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.11065 | + | 3.11065i | 0.00364672 | + | 0.00364672i | 0.708928 | − | 0.705281i | \(-0.249179\pi\) |
−0.705281 | + | 0.708928i | \(0.749179\pi\) | |||||||
\(854\) | − | 64.1424i | − | 0.0751082i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 74.0169 | 0.0864683 | ||||||||
\(857\) | −141.310 | + | 141.310i | −0.164889 | + | 0.164889i | −0.784729 | − | 0.619840i | \(-0.787198\pi\) |
0.619840 | + | 0.784729i | \(0.287198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1054.78i | − | 1.22792i | −0.789338 | − | 0.613959i | \(-0.789576\pi\) | ||
0.789338 | − | 0.613959i | \(-0.210424\pi\) | |||||||
\(860\) | −237.680 | + | 49.4206i | −0.276372 | + | 0.0574658i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1063.04 | − | 1063.04i | 1.23322 | − | 1.23322i | ||||
\(863\) | 227.600 | + | 227.600i | 0.263732 | + | 0.263732i | 0.826568 | − | 0.562837i | \(-0.190290\pi\) |
−0.562837 | + | 0.826568i | \(0.690290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 319.342 | + | 1535.82i | 0.369181 | + | 1.77551i | ||||
\(866\) | 573.005 | 0.661669 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 185.087 | + | 185.087i | 0.213233 | + | 0.213233i | ||||
\(869\) | 1383.88i | 1.59250i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.1236 | 0.0299927 | ||||||||
\(872\) | 699.876 | − | 699.876i | 0.802610 | − | 0.802610i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 937.254i | 1.07237i | ||||||||
\(875\) | 190.818 | + | 270.118i | 0.218078 | + | 0.308706i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −71.4976 | + | 71.4976i | −0.0815252 | + | 0.0815252i | −0.746693 | − | 0.665168i | \(-0.768360\pi\) |
0.665168 | + | 0.746693i | \(0.268360\pi\) | |||||||
\(878\) | 849.578 | + | 849.578i | 0.967629 | + | 0.967629i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1075.76 | + | 705.400i | 1.22245 | + | 0.801591i | ||||
\(881\) | −932.073 | −1.05797 | −0.528986 | − | 0.848631i | \(-0.677428\pi\) | ||||
−0.528986 | + | 0.848631i | \(0.677428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −616.640 | − | 616.640i | −0.698346 | − | 0.698346i | 0.265708 | − | 0.964054i | \(-0.414394\pi\) |
−0.964054 | + | 0.265708i | \(0.914394\pi\) | |||||||
\(884\) | − | 1017.65i | − | 1.15119i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −198.828 | −0.224410 | ||||||||
\(887\) | 990.320 | − | 990.320i | 1.11648 | − | 1.11648i | 0.124229 | − | 0.992254i | \(-0.460354\pi\) |
0.992254 | − | 0.124229i | \(-0.0396459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 436.469i | − | 0.490966i | ||||||
\(890\) | 218.308 | + | 1049.91i | 0.245290 | + | 1.17968i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −339.282 | + | 339.282i | −0.380361 | + | 0.380361i | ||||
\(893\) | 65.9394 | + | 65.9394i | 0.0738403 | + | 0.0738403i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 354.253 | − | 540.246i | 0.395814 | − | 0.603627i | ||||
\(896\) | −614.043 | −0.685316 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −507.323 | − | 507.323i | −0.564948 | − | 0.564948i | ||||
\(899\) | 510.332i | 0.567666i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −688.047 | −0.763649 | ||||||||
\(902\) | 3513.45 | − | 3513.45i | 3.89517 | − | 3.89517i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1910.78i | 2.11369i | ||||||||
\(905\) | −120.587 | − | 79.0721i | −0.133245 | − | 0.0873725i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −449.584 | + | 449.584i | −0.495682 | + | 0.495682i | −0.910091 | − | 0.414409i | \(-0.863988\pi\) |
0.414409 | + | 0.910091i | \(0.363988\pi\) | |||||||
\(908\) | −1355.98 | − | 1355.98i | −1.49336 | − | 1.49336i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 584.935 | − | 121.625i | 0.642786 | − | 0.133654i | ||||
\(911\) | −1065.29 | −1.16936 | −0.584680 | − | 0.811264i | \(-0.698780\pi\) | ||||
−0.584680 | + | 0.811264i | \(0.698780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1751.41 | + | 1751.41i | 1.91830 | + | 1.91830i | ||||
\(914\) | − | 758.134i | − | 0.829468i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2279.75 | −2.48881 | ||||||||
\(917\) | 261.579 | − | 261.579i | 0.285255 | − | 0.285255i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1080.05i | − | 1.17525i | −0.809135 | − | 0.587623i | \(-0.800064\pi\) | ||
0.809135 | − | 0.587623i | \(-0.199936\pi\) | |||||||
\(920\) | −632.958 | + | 965.278i | −0.687998 | + | 1.04922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 662.580 | − | 662.580i | 0.718634 | − | 0.718634i | ||||
\(923\) | −148.965 | − | 148.965i | −0.161392 | − | 0.161392i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1043.40 | − | 411.169i | −1.12800 | − | 0.444507i | ||||
\(926\) | −2335.62 | −2.52227 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −233.568 | − | 233.568i | −0.251690 | − | 0.251690i | ||||
\(929\) | 1513.19i | 1.62884i | 0.580278 | + | 0.814419i | \(0.302944\pi\) | ||||
−0.580278 | + | 0.814419i | \(0.697056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 104.655 | 0.112412 | ||||||||
\(932\) | 677.335 | − | 677.335i | 0.726755 | − | 0.726755i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 42.0972i | − | 0.0450720i | ||||||
\(935\) | 1027.20 | − | 213.585i | 1.09861 | − | 0.228433i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 754.545 | − | 754.545i | 0.805278 | − | 0.805278i | −0.178637 | − | 0.983915i | \(-0.557169\pi\) |
0.983915 | + | 0.178637i | \(0.0571688\pi\) | |||||||
\(938\) | 12.6423 | + | 12.6423i | 0.0134779 | + | 0.0134779i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48.7753 | + | 234.576i | 0.0518886 | + | 0.249549i | ||||
\(941\) | −1377.61 | −1.46399 | −0.731993 | − | 0.681312i | \(-0.761410\pi\) | ||||
−0.731993 | + | 0.681312i | \(0.761410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 900.729 | + | 900.729i | 0.955174 | + | 0.955174i | ||||
\(944\) | − | 361.690i | − | 0.383146i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −452.137 | −0.477946 | ||||||||
\(947\) | −133.593 | + | 133.593i | −0.141070 | + | 0.141070i | −0.774115 | − | 0.633045i | \(-0.781805\pi\) |
0.633045 | + | 0.774115i | \(0.281805\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 605.738i | − | 0.638291i | ||||||
\(950\) | 468.378 | − | 1188.58i | 0.493030 | − | 1.25113i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 236.067 | − | 236.067i | 0.247970 | − | 0.247970i | ||||
\(953\) | 498.927 | + | 498.927i | 0.523533 | + | 0.523533i | 0.918636 | − | 0.395104i | \(-0.129291\pi\) |
−0.395104 | + | 0.918636i | \(0.629291\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 125.112 | + | 82.0390i | 0.131007 | + | 0.0859047i | ||||
\(956\) | −2845.01 | −2.97595 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1948.68 | − | 1948.68i | −2.03411 | − | 2.03411i | ||||
\(959\) | 602.854i | 0.628627i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −795.168 | −0.827438 | ||||||||
\(962\) | −1432.58 | + | 1432.58i | −1.48917 | + | 1.48917i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1554.28i | 1.61233i | ||||||||
\(965\) | 61.2386 | + | 294.516i | 0.0634597 | + | 0.305198i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 506.991 | − | 506.991i | 0.524293 | − | 0.524293i | −0.394572 | − | 0.918865i | \(-0.629107\pi\) |
0.918865 | + | 0.394572i | \(0.129107\pi\) | |||||||
\(968\) | 2822.45 | + | 2822.45i | 2.91575 | + | 2.91575i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1132.53 | + | 1727.13i | −1.16755 | + | 1.78055i | ||||
\(971\) | 74.6256 | 0.0768543 | 0.0384272 | − | 0.999261i | \(-0.487765\pi\) | ||||
0.0384272 | + | 0.999261i | \(0.487765\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −376.277 | − | 376.277i | −0.386719 | − | 0.386719i | ||||
\(974\) | − | 741.960i | − | 0.761766i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −87.1846 | −0.0893285 | ||||||||
\(977\) | 291.427 | − | 291.427i | 0.298288 | − | 0.298288i | −0.542055 | − | 0.840343i | \(-0.682354\pi\) |
0.840343 | + | 0.542055i | \(0.182354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1313.41i | 1.34158i | ||||||||
\(980\) | 224.859 | + | 147.446i | 0.229448 | + | 0.150455i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −437.345 | + | 437.345i | −0.445361 | + | 0.445361i | ||||
\(983\) | 932.709 | + | 932.709i | 0.948839 | + | 0.948839i | 0.998754 | − | 0.0499141i | \(-0.0158948\pi\) |
−0.0499141 | + | 0.998754i | \(0.515895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1724.47 | − | 358.568i | 1.75073 | − | 0.364029i | ||||
\(986\) | 1357.90 | 1.37718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1073.16 | − | 1073.16i | −1.08620 | − | 1.08620i | ||||
\(989\) | − | 115.913i | − | 0.117202i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 294.340 | 0.297013 | 0.148507 | − | 0.988911i | \(-0.452553\pi\) | ||||
0.148507 | + | 0.988911i | \(0.452553\pi\) | |||||||
\(992\) | −75.8975 | + | 75.8975i | −0.0765096 | + | 0.0765096i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 144.181i | − | 0.145051i | ||||||
\(995\) | −45.9374 | + | 70.0559i | −0.0461683 | + | 0.0704079i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 678.292 | − | 678.292i | 0.680333 | − | 0.680333i | −0.279742 | − | 0.960075i | \(-0.590249\pi\) |
0.960075 | + | 0.279742i | \(0.0902489\pi\) | |||||||
\(998\) | 33.7403 | + | 33.7403i | 0.0338079 | + | 0.0338079i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.3.o.b.253.2 | 24 | ||
3.2 | odd | 2 | 105.3.l.a.43.11 | yes | 24 | ||
5.2 | odd | 4 | inner | 315.3.o.b.127.2 | 24 | ||
15.2 | even | 4 | 105.3.l.a.22.11 | ✓ | 24 | ||
15.8 | even | 4 | 525.3.l.e.232.2 | 24 | |||
15.14 | odd | 2 | 525.3.l.e.43.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.11 | ✓ | 24 | 15.2 | even | 4 | ||
105.3.l.a.43.11 | yes | 24 | 3.2 | odd | 2 | ||
315.3.o.b.127.2 | 24 | 5.2 | odd | 4 | inner | ||
315.3.o.b.253.2 | 24 | 1.1 | even | 1 | trivial | ||
525.3.l.e.43.2 | 24 | 15.14 | odd | 2 | |||
525.3.l.e.232.2 | 24 | 15.8 | even | 4 |