Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.32 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.b.449.31 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 2.79495 | + | 1.09006i | 0.931652 | + | 0.363353i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.95266 | + | 1.54158i | 0.658777 | + | 0.256929i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 6.62354 | + | 6.09333i | 0.735949 | + | 0.677037i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.30912i | 0.300830i | 0.988623 | + | 0.150415i | \(0.0480609\pi\) | ||||
−0.988623 | + | 0.150415i | \(0.951939\pi\) | |||||||
\(12\) | 5.58991 | + | 2.18012i | 0.465826 | + | 0.181677i | ||||
\(13\) | 13.2159i | 1.01661i | 0.861177 | + | 0.508306i | \(0.169728\pi\) | ||||
−0.861177 | + | 0.508306i | \(0.830272\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 14.2264 | 0.836850 | 0.418425 | − | 0.908251i | \(-0.362582\pi\) | ||||
0.418425 | + | 0.908251i | \(0.362582\pi\) | |||||||
\(18\) | 9.36710 | + | 8.61727i | 0.520395 | + | 0.478737i | ||||
\(19\) | −7.45106 | −0.392161 | −0.196081 | − | 0.980588i | \(-0.562821\pi\) | ||||
−0.196081 | + | 0.980588i | \(0.562821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.88403 | − | 7.39475i | 0.137335 | − | 0.352131i | ||||
\(22\) | 4.67981i | 0.212719i | ||||||||
\(23\) | 7.07387 | 0.307559 | 0.153780 | − | 0.988105i | \(-0.450855\pi\) | ||||
0.153780 | + | 0.988105i | \(0.450855\pi\) | |||||||
\(24\) | 7.90533 | + | 3.08315i | 0.329389 | + | 0.128465i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 18.6902i | 0.718853i | ||||||||
\(27\) | 11.8704 | + | 24.2506i | 0.439645 | + | 0.898172i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | 25.7409i | 0.887619i | 0.896121 | + | 0.443809i | \(0.146373\pi\) | ||||
−0.896121 | + | 0.443809i | \(0.853627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.5150 | 1.33919 | 0.669597 | − | 0.742724i | \(-0.266467\pi\) | ||||
0.669597 | + | 0.742724i | \(0.266467\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | −3.60714 | + | 9.24885i | −0.109307 | + | 0.280268i | ||||
\(34\) | 20.1192 | 0.591742 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.2471 | + | 12.1867i | 0.367975 | + | 0.338518i | ||||
\(37\) | − | 27.7055i | − | 0.748797i | −0.927268 | − | 0.374398i | \(-0.877849\pi\) | ||
0.927268 | − | 0.374398i | \(-0.122151\pi\) | |||||||
\(38\) | −10.5374 | −0.277300 | ||||||||
\(39\) | −14.4062 | + | 36.9380i | −0.369389 | + | 0.947127i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.25580i | 0.0306292i | 0.999883 | + | 0.0153146i | \(0.00487497\pi\) | ||||
−0.999883 | + | 0.0153146i | \(0.995125\pi\) | |||||||
\(42\) | 4.07863 | − | 10.4578i | 0.0971102 | − | 0.248994i | ||||
\(43\) | − | 2.12678i | − | 0.0494599i | −0.999694 | − | 0.0247300i | \(-0.992127\pi\) | ||
0.999694 | − | 0.0247300i | \(-0.00787259\pi\) | |||||||
\(44\) | 6.61825i | 0.150415i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.0040 | 0.217477 | ||||||||
\(47\) | −54.8353 | −1.16671 | −0.583355 | − | 0.812218i | \(-0.698260\pi\) | ||||
−0.583355 | + | 0.812218i | \(0.698260\pi\) | |||||||
\(48\) | 11.1798 | + | 4.36024i | 0.232913 | + | 0.0908383i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 39.7623 | + | 15.5077i | 0.779653 | + | 0.304072i | ||||
\(52\) | 26.4319i | 0.508306i | ||||||||
\(53\) | 62.3147 | 1.17575 | 0.587874 | − | 0.808952i | \(-0.299965\pi\) | ||||
0.587874 | + | 0.808952i | \(0.299965\pi\) | |||||||
\(54\) | 16.7873 | + | 34.2956i | 0.310876 | + | 0.635103i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | −20.8254 | − | 8.12210i | −0.365357 | − | 0.142493i | ||||
\(58\) | 36.4032i | 0.627641i | ||||||||
\(59\) | − | 21.7601i | − | 0.368815i | −0.982850 | − | 0.184407i | \(-0.940963\pi\) | ||
0.982850 | − | 0.184407i | \(-0.0590366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 84.8047 | 1.39024 | 0.695121 | − | 0.718893i | \(-0.255351\pi\) | ||||
0.695121 | + | 0.718893i | \(0.255351\pi\) | |||||||
\(62\) | 58.7111 | 0.946954 | ||||||||
\(63\) | 16.1214 | − | 17.5242i | 0.255896 | − | 0.278163i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.10127 | + | 13.0799i | −0.0772919 | + | 0.198180i | ||||
\(67\) | 54.7450i | 0.817089i | 0.912738 | + | 0.408545i | \(0.133964\pi\) | ||||
−0.912738 | + | 0.408545i | \(0.866036\pi\) | |||||||
\(68\) | 28.4529 | 0.418425 | ||||||||
\(69\) | 19.7711 | + | 7.71093i | 0.286538 | + | 0.111753i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 100.282i | − | 1.41243i | −0.707999 | − | 0.706213i | \(-0.750402\pi\) | ||
0.707999 | − | 0.706213i | \(-0.249598\pi\) | |||||||
\(72\) | 18.7342 | + | 17.2345i | 0.260197 | + | 0.239369i | ||||
\(73\) | − | 63.2034i | − | 0.865800i | −0.901442 | − | 0.432900i | \(-0.857490\pi\) | ||
0.901442 | − | 0.432900i | \(-0.142510\pi\) | |||||||
\(74\) | − | 39.1815i | − | 0.529479i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9021 | −0.196081 | ||||||||
\(77\) | 8.75512 | 0.113703 | ||||||||
\(78\) | −20.3734 | + | 52.2382i | −0.261197 | + | 0.669720i | ||||
\(79\) | −116.942 | −1.48028 | −0.740138 | − | 0.672455i | \(-0.765240\pi\) | ||||
−0.740138 | + | 0.672455i | \(0.765240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.74263 | + | 80.7189i | 0.0832423 | + | 0.996529i | ||||
\(82\) | 1.77596i | 0.0216581i | ||||||||
\(83\) | −23.7433 | −0.286064 | −0.143032 | − | 0.989718i | \(-0.545685\pi\) | ||||
−0.143032 | + | 0.989718i | \(0.545685\pi\) | |||||||
\(84\) | 5.76805 | − | 14.7895i | 0.0686673 | − | 0.176066i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 3.00772i | − | 0.0349734i | ||||||
\(87\) | −28.0592 | + | 71.9448i | −0.322519 | + | 0.826952i | ||||
\(88\) | 9.35962i | 0.106359i | ||||||||
\(89\) | − | 3.26308i | − | 0.0366638i | −0.999832 | − | 0.0183319i | \(-0.994164\pi\) | ||
0.999832 | − | 0.0183319i | \(-0.00583555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.9661 | 0.384243 | ||||||||
\(92\) | 14.1477 | 0.153780 | ||||||||
\(93\) | 116.033 | + | 45.2538i | 1.24766 | + | 0.486600i | ||||
\(94\) | −77.5489 | −0.824988 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.8107 | + | 6.16631i | 0.164694 | + | 0.0642323i | ||||
\(97\) | 55.5754i | 0.572942i | 0.958089 | + | 0.286471i | \(0.0924822\pi\) | ||||
−0.958089 | + | 0.286471i | \(0.907518\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | −20.1636 | + | 21.9181i | −0.203673 | + | 0.221395i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 124.810i | − | 1.23574i | −0.786280 | − | 0.617870i | \(-0.787996\pi\) | ||
0.786280 | − | 0.617870i | \(-0.212004\pi\) | |||||||
\(102\) | 56.2324 | + | 21.9312i | 0.551298 | + | 0.215011i | ||||
\(103\) | 112.881i | 1.09593i | 0.836500 | + | 0.547967i | \(0.184598\pi\) | ||||
−0.836500 | + | 0.547967i | \(0.815402\pi\) | |||||||
\(104\) | 37.3803i | 0.359426i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 88.1263 | 0.831380 | ||||||||
\(107\) | −84.6754 | −0.791359 | −0.395680 | − | 0.918389i | \(-0.629491\pi\) | ||||
−0.395680 | + | 0.918389i | \(0.629491\pi\) | |||||||
\(108\) | 23.7408 | + | 48.5013i | 0.219822 | + | 0.449086i | ||||
\(109\) | −165.164 | −1.51527 | −0.757634 | − | 0.652680i | \(-0.773645\pi\) | ||||
−0.757634 | + | 0.652680i | \(0.773645\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.2006 | − | 77.4356i | 0.272078 | − | 0.697618i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | −55.8626 | −0.494359 | −0.247179 | − | 0.968970i | \(-0.579504\pi\) | ||||
−0.247179 | + | 0.968970i | \(0.579504\pi\) | |||||||
\(114\) | −29.4515 | − | 11.4864i | −0.258347 | − | 0.100758i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 51.4819i | 0.443809i | ||||||||
\(117\) | −80.5291 | + | 87.5364i | −0.688283 | + | 0.748174i | ||||
\(118\) | − | 30.7734i | − | 0.260791i | ||||||
\(119\) | − | 37.6396i | − | 0.316300i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 110.050 | 0.909502 | ||||||||
\(122\) | 119.932 | 0.983049 | ||||||||
\(123\) | −1.36889 | + | 3.50989i | −0.0111292 | + | 0.0285357i | ||||
\(124\) | 83.0301 | 0.669597 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.7992 | − | 24.7830i | 0.180946 | − | 0.196691i | ||||
\(127\) | 166.400i | 1.31023i | 0.755527 | + | 0.655117i | \(0.227381\pi\) | ||||
−0.755527 | + | 0.655117i | \(0.772619\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 2.31831 | − | 5.94424i | 0.0179714 | − | 0.0460794i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 229.177i | − | 1.74944i | −0.484626 | − | 0.874721i | \(-0.661044\pi\) | ||
0.484626 | − | 0.874721i | \(-0.338956\pi\) | |||||||
\(132\) | −7.21428 | + | 18.4977i | −0.0546537 | + | 0.140134i | ||||
\(133\) | 19.7137i | 0.148223i | ||||||||
\(134\) | 77.4211i | 0.577769i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 40.2385 | 0.295871 | ||||||||
\(137\) | −123.559 | −0.901889 | −0.450945 | − | 0.892552i | \(-0.648913\pi\) | ||||
−0.450945 | + | 0.892552i | \(0.648913\pi\) | |||||||
\(138\) | 27.9606 | + | 10.9049i | 0.202613 | + | 0.0790211i | ||||
\(139\) | −169.795 | −1.22155 | −0.610774 | − | 0.791805i | \(-0.709141\pi\) | ||||
−0.610774 | + | 0.791805i | \(0.709141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −153.262 | − | 59.7738i | −1.08697 | − | 0.423927i | ||||
\(142\) | − | 141.821i | − | 0.998736i | ||||||
\(143\) | −43.7332 | −0.305827 | ||||||||
\(144\) | 26.4942 | + | 24.3733i | 0.183987 | + | 0.169259i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 89.3832i | − | 0.612213i | ||||||
\(147\) | −19.5647 | − | 7.63041i | −0.133093 | − | 0.0519076i | ||||
\(148\) | − | 55.4110i | − | 0.374398i | ||||||
\(149\) | − | 237.791i | − | 1.59592i | −0.602713 | − | 0.797958i | \(-0.705914\pi\) | ||
0.602713 | − | 0.797958i | \(-0.294086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 117.067 | 0.775281 | 0.387640 | − | 0.921811i | \(-0.373290\pi\) | ||||
0.387640 | + | 0.921811i | \(0.373290\pi\) | |||||||
\(152\) | −21.0748 | −0.138650 | ||||||||
\(153\) | 94.2295 | + | 86.6865i | 0.615879 | + | 0.566578i | ||||
\(154\) | 12.3816 | 0.0804001 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −28.8123 | + | 73.8759i | −0.184694 | + | 0.473564i | ||||
\(157\) | 31.6151i | 0.201370i | 0.994918 | + | 0.100685i | \(0.0321035\pi\) | ||||
−0.994918 | + | 0.100685i | \(0.967897\pi\) | |||||||
\(158\) | −165.381 | −1.04671 | ||||||||
\(159\) | 174.167 | + | 67.9267i | 1.09539 | + | 0.427212i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 18.7157i | − | 0.116247i | ||||||
\(162\) | 9.53552 | + | 114.154i | 0.0588612 | + | 0.704653i | ||||
\(163\) | 107.553i | 0.659833i | 0.944010 | + | 0.329917i | \(0.107021\pi\) | ||||
−0.944010 | + | 0.329917i | \(0.892979\pi\) | |||||||
\(164\) | 2.51159i | 0.0153146i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.5781 | −0.202278 | ||||||||
\(167\) | 116.906 | 0.700036 | 0.350018 | − | 0.936743i | \(-0.386175\pi\) | ||||
0.350018 | + | 0.936743i | \(0.386175\pi\) | |||||||
\(168\) | 8.15726 | − | 20.9155i | 0.0485551 | − | 0.124497i | ||||
\(169\) | −5.66117 | −0.0334980 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −49.3524 | − | 45.4018i | −0.288611 | − | 0.265508i | ||||
\(172\) | − | 4.25355i | − | 0.0247300i | ||||||
\(173\) | −317.805 | −1.83702 | −0.918512 | − | 0.395392i | \(-0.870609\pi\) | ||||
−0.918512 | + | 0.395392i | \(0.870609\pi\) | |||||||
\(174\) | −39.6816 | + | 101.745i | −0.228055 | + | 0.584743i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.2365i | 0.0752074i | ||||||||
\(177\) | 23.7198 | − | 60.8184i | 0.134010 | − | 0.343607i | ||||
\(178\) | − | 4.61469i | − | 0.0259252i | ||||||
\(179\) | − | 325.244i | − | 1.81700i | −0.417880 | − | 0.908502i | \(-0.637227\pi\) | ||
0.417880 | − | 0.908502i | \(-0.362773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −34.5370 | −0.190812 | −0.0954060 | − | 0.995438i | \(-0.530415\pi\) | ||||
−0.0954060 | + | 0.995438i | \(0.530415\pi\) | |||||||
\(182\) | 49.4495 | 0.271701 | ||||||||
\(183\) | 237.025 | + | 92.4421i | 1.29522 | + | 0.505148i | ||||
\(184\) | 20.0079 | 0.108739 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 164.095 | + | 63.9986i | 0.882231 | + | 0.344079i | ||||
\(187\) | 47.0771i | 0.251749i | ||||||||
\(188\) | −109.671 | −0.583355 | ||||||||
\(189\) | 64.1612 | − | 31.4062i | 0.339477 | − | 0.166170i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 80.5748i | − | 0.421858i | −0.977501 | − | 0.210929i | \(-0.932351\pi\) | ||
0.977501 | − | 0.210929i | \(-0.0676489\pi\) | |||||||
\(192\) | 22.3596 | + | 8.72047i | 0.116456 | + | 0.0454191i | ||||
\(193\) | − | 102.042i | − | 0.528717i | −0.964424 | − | 0.264359i | \(-0.914840\pi\) | ||
0.964424 | − | 0.264359i | \(-0.0851602\pi\) | |||||||
\(194\) | 78.5954i | 0.405131i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 50.5512 | 0.256605 | 0.128303 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(198\) | −28.5156 | + | 30.9969i | −0.144018 | + | 0.156550i | ||||
\(199\) | 10.1649 | 0.0510800 | 0.0255400 | − | 0.999674i | \(-0.491869\pi\) | ||||
0.0255400 | + | 0.999674i | \(0.491869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −59.6752 | + | 153.010i | −0.296892 | + | 0.761242i | ||||
\(202\) | − | 176.508i | − | 0.873801i | ||||||
\(203\) | 68.1041 | 0.335488 | ||||||||
\(204\) | 79.5246 | + | 31.0153i | 0.389826 | + | 0.152036i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 159.638i | 0.774943i | ||||||||
\(207\) | 46.8541 | + | 43.1034i | 0.226348 | + | 0.208229i | ||||
\(208\) | 52.8638i | 0.254153i | ||||||||
\(209\) | − | 24.6565i | − | 0.117974i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −305.386 | −1.44733 | −0.723665 | − | 0.690152i | \(-0.757544\pi\) | ||||
−0.723665 | + | 0.690152i | \(0.757544\pi\) | |||||||
\(212\) | 124.629 | 0.587874 | ||||||||
\(213\) | 109.314 | − | 280.284i | 0.513209 | − | 1.31589i | ||||
\(214\) | −119.749 | −0.559575 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 33.5746 | + | 68.5912i | 0.155438 | + | 0.317552i | ||||
\(217\) | − | 109.838i | − | 0.506168i | ||||||
\(218\) | −233.577 | −1.07146 | ||||||||
\(219\) | 68.8955 | − | 176.651i | 0.314591 | − | 0.806624i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 188.016i | 0.850751i | ||||||||
\(222\) | 42.7101 | − | 109.510i | 0.192388 | − | 0.493290i | ||||
\(223\) | 103.856i | 0.465724i | 0.972510 | + | 0.232862i | \(0.0748090\pi\) | ||||
−0.972510 | + | 0.232862i | \(0.925191\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −79.0016 | −0.349565 | ||||||||
\(227\) | 392.738 | 1.73012 | 0.865062 | − | 0.501664i | \(-0.167279\pi\) | ||||
0.865062 | + | 0.501664i | \(0.167279\pi\) | |||||||
\(228\) | −41.6508 | − | 16.2442i | −0.182679 | − | 0.0712465i | ||||
\(229\) | 427.149 | 1.86528 | 0.932641 | − | 0.360806i | \(-0.117498\pi\) | ||||
0.932641 | + | 0.360806i | \(0.117498\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.4702 | + | 9.54360i | 0.105931 | + | 0.0413143i | ||||
\(232\) | 72.8064i | 0.313821i | ||||||||
\(233\) | −57.7328 | −0.247780 | −0.123890 | − | 0.992296i | \(-0.539537\pi\) | ||||
−0.123890 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(234\) | −113.885 | + | 123.795i | −0.486690 | + | 0.529039i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 43.5201i | − | 0.184407i | ||||||
\(237\) | −326.847 | − | 127.473i | −1.37910 | − | 0.537863i | ||||
\(238\) | − | 53.2305i | − | 0.223658i | ||||||
\(239\) | 52.9710i | 0.221636i | 0.993841 | + | 0.110818i | \(0.0353471\pi\) | ||||
−0.993841 | + | 0.110818i | \(0.964653\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −157.253 | −0.652502 | −0.326251 | − | 0.945283i | \(-0.605785\pi\) | ||||
−0.326251 | + | 0.945283i | \(0.605785\pi\) | |||||||
\(242\) | 155.634 | 0.643115 | ||||||||
\(243\) | −69.1430 | + | 232.955i | −0.284539 | + | 0.958664i | ||||
\(244\) | 169.609 | 0.695121 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.93591 | + | 4.96374i | −0.00786953 | + | 0.0201778i | ||||
\(247\) | − | 98.4728i | − | 0.398675i | ||||||
\(248\) | 117.422 | 0.473477 | ||||||||
\(249\) | −66.3614 | − | 25.8816i | −0.266512 | − | 0.103942i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 150.522i | − | 0.599688i | −0.953988 | − | 0.299844i | \(-0.903065\pi\) | ||
0.953988 | − | 0.299844i | \(-0.0969346\pi\) | |||||||
\(252\) | 32.2429 | − | 35.0485i | 0.127948 | − | 0.139081i | ||||
\(253\) | 23.4083i | 0.0925230i | ||||||||
\(254\) | 235.325i | 0.926476i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −313.116 | −1.21835 | −0.609175 | − | 0.793036i | \(-0.708499\pi\) | ||||
−0.609175 | + | 0.793036i | \(0.708499\pi\) | |||||||
\(258\) | 3.27859 | − | 8.40643i | 0.0127077 | − | 0.0325831i | ||||
\(259\) | −73.3018 | −0.283019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −156.848 | + | 170.496i | −0.600951 | + | 0.653242i | ||||
\(262\) | − | 324.105i | − | 1.23704i | ||||||
\(263\) | −413.301 | −1.57149 | −0.785744 | − | 0.618552i | \(-0.787720\pi\) | ||||
−0.785744 | + | 0.618552i | \(0.787720\pi\) | |||||||
\(264\) | −10.2025 | + | 26.1597i | −0.0386460 | + | 0.0990898i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 27.8793i | 0.104809i | ||||||||
\(267\) | 3.55695 | − | 9.12016i | 0.0133219 | − | 0.0341579i | ||||
\(268\) | 109.490i | 0.408545i | ||||||||
\(269\) | − | 77.5114i | − | 0.288147i | −0.989567 | − | 0.144073i | \(-0.953980\pi\) | ||
0.989567 | − | 0.144073i | \(-0.0460201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 277.456 | 1.02382 | 0.511912 | − | 0.859038i | \(-0.328938\pi\) | ||||
0.511912 | + | 0.859038i | \(0.328938\pi\) | |||||||
\(272\) | 56.9058 | 0.209212 | ||||||||
\(273\) | 97.7287 | + | 38.1151i | 0.357980 | + | 0.139616i | ||||
\(274\) | −174.739 | −0.637732 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 39.5423 | + | 15.4219i | 0.143269 | + | 0.0558763i | ||||
\(277\) | − | 64.2751i | − | 0.232040i | −0.993247 | − | 0.116020i | \(-0.962986\pi\) | ||
0.993247 | − | 0.116020i | \(-0.0370137\pi\) | |||||||
\(278\) | −240.127 | −0.863764 | ||||||||
\(279\) | 274.977 | + | 252.965i | 0.985579 | + | 0.906684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 238.377i | 0.848315i | 0.905588 | + | 0.424158i | \(0.139430\pi\) | ||||
−0.905588 | + | 0.424158i | \(0.860570\pi\) | |||||||
\(282\) | −216.746 | − | 84.5329i | −0.768601 | − | 0.299762i | ||||
\(283\) | − | 295.213i | − | 1.04315i | −0.853204 | − | 0.521577i | \(-0.825344\pi\) | ||
0.853204 | − | 0.521577i | \(-0.174656\pi\) | |||||||
\(284\) | − | 200.564i | − | 0.706213i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −61.8481 | −0.216252 | ||||||||
\(287\) | 3.32252 | 0.0115767 | ||||||||
\(288\) | 37.4684 | + | 34.4691i | 0.130099 | + | 0.119684i | ||||
\(289\) | −86.6082 | −0.299682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −60.5804 | + | 155.331i | −0.208180 | + | 0.533782i | ||||
\(292\) | − | 126.407i | − | 0.432900i | ||||||
\(293\) | 358.351 | 1.22304 | 0.611521 | − | 0.791228i | \(-0.290558\pi\) | ||||
0.611521 | + | 0.791228i | \(0.290558\pi\) | |||||||
\(294\) | −27.6686 | − | 10.7910i | −0.0941110 | − | 0.0367042i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 78.3629i | − | 0.264740i | ||||||
\(297\) | −80.2484 | + | 39.2807i | −0.270197 | + | 0.132258i | ||||
\(298\) | − | 336.288i | − | 1.12848i | ||||||
\(299\) | 93.4878i | 0.312668i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.62692 | −0.0186941 | ||||||||
\(302\) | 165.558 | 0.548206 | ||||||||
\(303\) | 136.050 | − | 348.838i | 0.449010 | − | 1.15128i | ||||
\(304\) | −29.8042 | −0.0980403 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 133.261 | + | 122.593i | 0.435492 | + | 0.400631i | ||||
\(307\) | − | 531.675i | − | 1.73184i | −0.500182 | − | 0.865920i | \(-0.666733\pi\) | ||
0.500182 | − | 0.865920i | \(-0.333267\pi\) | |||||||
\(308\) | 17.5102 | 0.0568514 | ||||||||
\(309\) | −123.047 | + | 315.498i | −0.398211 | + | 1.02103i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 418.127i | − | 1.34446i | −0.740343 | − | 0.672229i | \(-0.765337\pi\) | ||
0.740343 | − | 0.672229i | \(-0.234663\pi\) | |||||||
\(312\) | −40.7468 | + | 104.476i | −0.130599 | + | 0.334860i | ||||
\(313\) | − | 306.865i | − | 0.980399i | −0.871610 | − | 0.490199i | \(-0.836924\pi\) | ||
0.871610 | − | 0.490199i | \(-0.163076\pi\) | |||||||
\(314\) | 44.7105i | 0.142390i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −233.884 | −0.740138 | ||||||||
\(317\) | 83.8149 | 0.264400 | 0.132200 | − | 0.991223i | \(-0.457796\pi\) | ||||
0.132200 | + | 0.991223i | \(0.457796\pi\) | |||||||
\(318\) | 246.309 | + | 96.0628i | 0.774556 | + | 0.302084i | ||||
\(319\) | −85.1800 | −0.267022 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −236.664 | − | 92.3012i | −0.737271 | − | 0.287543i | ||||
\(322\) | − | 26.4680i | − | 0.0821987i | ||||||
\(323\) | −106.002 | −0.328180 | ||||||||
\(324\) | 13.4853 | + | 161.438i | 0.0416212 | + | 0.498265i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 152.103i | 0.466572i | ||||||||
\(327\) | −461.626 | − | 180.039i | −1.41170 | − | 0.550577i | ||||
\(328\) | 3.55193i | 0.0108290i | ||||||||
\(329\) | 145.081i | 0.440975i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 145.013 | 0.438105 | 0.219052 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219052 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(332\) | −47.4866 | −0.143032 | ||||||||
\(333\) | 168.819 | − | 183.508i | 0.506963 | − | 0.551076i | ||||
\(334\) | 165.330 | 0.495000 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11.5361 | − | 29.5790i | 0.0343336 | − | 0.0880328i | ||||
\(337\) | 610.894i | 1.81274i | 0.422483 | + | 0.906371i | \(0.361159\pi\) | ||||
−0.422483 | + | 0.906371i | \(0.638841\pi\) | |||||||
\(338\) | −8.00610 | −0.0236867 | ||||||||
\(339\) | −156.133 | − | 60.8935i | −0.460570 | − | 0.179627i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 137.378i | 0.402869i | ||||||||
\(342\) | −69.7949 | − | 64.2078i | −0.204079 | − | 0.187742i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 6.01543i | − | 0.0174867i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −449.445 | −1.29897 | ||||||||
\(347\) | −70.0988 | −0.202014 | −0.101007 | − | 0.994886i | \(-0.532206\pi\) | ||||
−0.101007 | + | 0.994886i | \(0.532206\pi\) | |||||||
\(348\) | −56.1183 | + | 143.890i | −0.161260 | + | 0.413476i | ||||
\(349\) | 564.413 | 1.61723 | 0.808614 | − | 0.588340i | \(-0.200218\pi\) | ||||
0.808614 | + | 0.588340i | \(0.200218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −320.495 | + | 156.879i | −0.913091 | + | 0.446948i | ||||
\(352\) | 18.7192i | 0.0531796i | ||||||||
\(353\) | 1.65210 | 0.00468018 | 0.00234009 | − | 0.999997i | \(-0.499255\pi\) | ||||
0.00234009 | + | 0.999997i | \(0.499255\pi\) | |||||||
\(354\) | 33.5448 | − | 86.0102i | 0.0947593 | − | 0.242967i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.52616i | − | 0.0183319i | ||||||
\(357\) | 41.0294 | − | 105.201i | 0.114928 | − | 0.294681i | ||||
\(358\) | − | 459.964i | − | 1.28482i | ||||||
\(359\) | − | 396.146i | − | 1.10347i | −0.834020 | − | 0.551735i | \(-0.813966\pi\) | ||
0.834020 | − | 0.551735i | \(-0.186034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −305.482 | −0.846210 | ||||||||
\(362\) | −48.8427 | −0.134925 | ||||||||
\(363\) | 307.584 | + | 119.961i | 0.847339 | + | 0.330470i | ||||
\(364\) | 69.9322 | 0.192121 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 335.204 | + | 130.733i | 0.915859 | + | 0.357194i | ||||
\(367\) | 363.378i | 0.990131i | 0.868856 | + | 0.495066i | \(0.164856\pi\) | ||||
−0.868856 | + | 0.495066i | \(0.835144\pi\) | |||||||
\(368\) | 28.2955 | 0.0768899 | ||||||||
\(369\) | −7.65198 | + | 8.31782i | −0.0207371 | + | 0.0225415i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 164.869i | − | 0.444391i | ||||||
\(372\) | 232.065 | + | 90.5077i | 0.623831 | + | 0.243300i | ||||
\(373\) | − | 207.182i | − | 0.555448i | −0.960661 | − | 0.277724i | \(-0.910420\pi\) | ||
0.960661 | − | 0.277724i | \(-0.0895800\pi\) | |||||||
\(374\) | 66.5771i | 0.178014i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −155.098 | −0.412494 | ||||||||
\(377\) | −340.191 | −0.902363 | ||||||||
\(378\) | 90.7376 | − | 44.4150i | 0.240046 | − | 0.117500i | ||||
\(379\) | −489.449 | −1.29142 | −0.645712 | − | 0.763581i | \(-0.723439\pi\) | ||||
−0.645712 | + | 0.763581i | \(0.723439\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −181.386 | + | 465.080i | −0.476078 | + | 1.22068i | ||||
\(382\) | − | 113.950i | − | 0.298299i | ||||||
\(383\) | −210.772 | −0.550318 | −0.275159 | − | 0.961399i | \(-0.588731\pi\) | ||||
−0.275159 | + | 0.961399i | \(0.588731\pi\) | |||||||
\(384\) | 31.6213 | + | 12.3326i | 0.0823471 | + | 0.0321162i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 144.310i | − | 0.373859i | ||||||
\(387\) | 12.9592 | − | 14.0868i | 0.0334862 | − | 0.0364000i | ||||
\(388\) | 111.151i | 0.286471i | ||||||||
\(389\) | − | 328.979i | − | 0.845704i | −0.906199 | − | 0.422852i | \(-0.861029\pi\) | ||
0.906199 | − | 0.422852i | \(-0.138971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 100.636 | 0.257381 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 249.816 | − | 640.539i | 0.635665 | − | 1.62987i | ||||
\(394\) | 71.4902 | 0.181447 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −40.3272 | + | 43.8363i | −0.101836 | + | 0.110698i | ||||
\(397\) | 32.3623i | 0.0815172i | 0.999169 | + | 0.0407586i | \(0.0129775\pi\) | ||||
−0.999169 | + | 0.0407586i | \(0.987023\pi\) | |||||||
\(398\) | 14.3754 | 0.0361190 | ||||||||
\(399\) | −21.4890 | + | 55.0988i | −0.0538573 | + | 0.138092i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 233.517i | 0.582338i | 0.956672 | + | 0.291169i | \(0.0940441\pi\) | ||||
−0.956672 | + | 0.291169i | \(0.905956\pi\) | |||||||
\(402\) | −84.3935 | + | 216.388i | −0.209934 | + | 0.538280i | ||||
\(403\) | 548.660i | 1.36144i | ||||||||
\(404\) | − | 249.620i | − | 0.617870i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 96.3138 | 0.237226 | ||||||||
\(407\) | 91.6809 | 0.225260 | ||||||||
\(408\) | 112.465 | + | 43.8623i | 0.275649 | + | 0.107506i | ||||
\(409\) | 30.2404 | 0.0739375 | 0.0369687 | − | 0.999316i | \(-0.488230\pi\) | ||||
0.0369687 | + | 0.999316i | \(0.488230\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −345.341 | − | 134.686i | −0.840246 | − | 0.327704i | ||||
\(412\) | 225.763i | 0.547967i | ||||||||
\(413\) | −57.5717 | −0.139399 | ||||||||
\(414\) | 66.2616 | + | 60.9574i | 0.160052 | + | 0.147240i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 74.7607i | 0.179713i | ||||||||
\(417\) | −474.570 | − | 185.087i | −1.13806 | − | 0.443853i | ||||
\(418\) | − | 34.8695i | − | 0.0834200i | ||||||
\(419\) | − | 690.640i | − | 1.64831i | −0.566367 | − | 0.824153i | \(-0.691652\pi\) | ||
0.566367 | − | 0.824153i | \(-0.308348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −637.548 | −1.51437 | −0.757183 | − | 0.653203i | \(-0.773425\pi\) | ||||
−0.757183 | + | 0.653203i | \(0.773425\pi\) | |||||||
\(422\) | −431.882 | −1.02342 | ||||||||
\(423\) | −363.204 | − | 334.130i | −0.858639 | − | 0.789905i | ||||
\(424\) | 176.253 | 0.415690 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 154.593 | − | 396.382i | 0.362894 | − | 0.930474i | ||||
\(427\) | − | 224.372i | − | 0.525462i | ||||||
\(428\) | −169.351 | −0.395680 | ||||||||
\(429\) | −122.232 | − | 47.6718i | −0.284924 | − | 0.111123i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 474.481i | 1.10088i | 0.834874 | + | 0.550442i | \(0.185541\pi\) | ||||
−0.834874 | + | 0.550442i | \(0.814459\pi\) | |||||||
\(432\) | 47.4816 | + | 97.0025i | 0.109911 | + | 0.224543i | ||||
\(433\) | − | 66.7488i | − | 0.154154i | −0.997025 | − | 0.0770772i | \(-0.975441\pi\) | ||
0.997025 | − | 0.0770772i | \(-0.0245588\pi\) | |||||||
\(434\) | − | 155.335i | − | 0.357915i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −330.328 | −0.757634 | ||||||||
\(437\) | −52.7078 | −0.120613 | ||||||||
\(438\) | 97.4329 | − | 249.822i | 0.222450 | − | 0.570370i | ||||
\(439\) | 361.090 | 0.822528 | 0.411264 | − | 0.911516i | \(-0.365087\pi\) | ||||
0.411264 | + | 0.911516i | \(0.365087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.3648 | − | 42.6533i | −0.105136 | − | 0.0967195i | ||||
\(442\) | 265.895i | 0.601572i | ||||||||
\(443\) | −415.163 | −0.937163 | −0.468581 | − | 0.883420i | \(-0.655235\pi\) | ||||
−0.468581 | + | 0.883420i | \(0.655235\pi\) | |||||||
\(444\) | 60.4012 | − | 154.871i | 0.136039 | − | 0.348809i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 146.875i | 0.329316i | ||||||||
\(447\) | 259.207 | − | 664.616i | 0.579881 | − | 1.48684i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | 538.703i | 1.19978i | 0.800081 | + | 0.599892i | \(0.204790\pi\) | ||||
−0.800081 | + | 0.599892i | \(0.795210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.15559 | −0.00921416 | ||||||||
\(452\) | −111.725 | −0.247179 | ||||||||
\(453\) | 327.198 | + | 127.610i | 0.722292 | + | 0.281701i | ||||
\(454\) | 555.416 | 1.22338 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −58.9031 | − | 22.9728i | −0.129173 | − | 0.0503789i | ||||
\(457\) | − | 666.562i | − | 1.45856i | −0.684216 | − | 0.729280i | \(-0.739855\pi\) | ||
0.684216 | − | 0.729280i | \(-0.260145\pi\) | |||||||
\(458\) | 604.081 | 1.31895 | ||||||||
\(459\) | 168.874 | + | 345.000i | 0.367917 | + | 0.751635i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 246.725i | − | 0.535196i | −0.963531 | − | 0.267598i | \(-0.913770\pi\) | ||
0.963531 | − | 0.267598i | \(-0.0862299\pi\) | |||||||
\(462\) | 34.6060 | + | 13.4967i | 0.0749048 | + | 0.0292136i | ||||
\(463\) | − | 278.772i | − | 0.602099i | −0.953609 | − | 0.301049i | \(-0.902663\pi\) | ||
0.953609 | − | 0.301049i | \(-0.0973369\pi\) | |||||||
\(464\) | 102.964i | 0.221905i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −81.6465 | −0.175207 | ||||||||
\(467\) | −263.485 | −0.564208 | −0.282104 | − | 0.959384i | \(-0.591032\pi\) | ||||
−0.282104 | + | 0.959384i | \(0.591032\pi\) | |||||||
\(468\) | −161.058 | + | 175.073i | −0.344142 | + | 0.374087i | ||||
\(469\) | 144.842 | 0.308831 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.4623 | + | 88.3628i | −0.0731685 | + | 0.187607i | ||||
\(472\) | − | 61.5468i | − | 0.130396i | ||||||
\(473\) | 7.03777 | 0.0148790 | ||||||||
\(474\) | −462.231 | − | 180.275i | −0.975172 | − | 0.380326i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 75.2793i | − | 0.158150i | ||||||
\(477\) | 412.744 | + | 379.704i | 0.865291 | + | 0.796025i | ||||
\(478\) | 74.9123i | 0.156720i | ||||||||
\(479\) | 163.187i | 0.340683i | 0.985385 | + | 0.170342i | \(0.0544871\pi\) | ||||
−0.985385 | + | 0.170342i | \(0.945513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 366.154 | 0.761235 | ||||||||
\(482\) | −222.389 | −0.461388 | ||||||||
\(483\) | 20.4012 | − | 52.3095i | 0.0422385 | − | 0.108301i | ||||
\(484\) | 220.099 | 0.454751 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −97.7830 | + | 329.449i | −0.201200 | + | 0.677878i | ||||
\(487\) | 752.251i | 1.54466i | 0.635219 | + | 0.772332i | \(0.280910\pi\) | ||||
−0.635219 | + | 0.772332i | \(0.719090\pi\) | |||||||
\(488\) | 239.864 | 0.491524 | ||||||||
\(489\) | −117.239 | + | 300.605i | −0.239752 | + | 0.614735i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 67.2107i | 0.136885i | 0.997655 | + | 0.0684427i | \(0.0218030\pi\) | ||||
−0.997655 | + | 0.0684427i | \(0.978197\pi\) | |||||||
\(492\) | −2.73778 | + | 7.01978i | −0.00556460 | + | 0.0142679i | ||||
\(493\) | 366.202i | 0.742804i | ||||||||
\(494\) | − | 139.262i | − | 0.281906i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 166.060 | 0.334799 | ||||||||
\(497\) | −265.322 | −0.533847 | ||||||||
\(498\) | −93.8492 | − | 36.6021i | −0.188452 | − | 0.0734982i | ||||
\(499\) | 247.715 | 0.496423 | 0.248212 | − | 0.968706i | \(-0.420157\pi\) | ||||
0.248212 | + | 0.968706i | \(0.420157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 326.747 | + | 127.435i | 0.652190 | + | 0.254360i | ||||
\(502\) | − | 212.870i | − | 0.424043i | ||||||
\(503\) | −142.465 | −0.283231 | −0.141616 | − | 0.989922i | \(-0.545230\pi\) | ||||
−0.141616 | + | 0.989922i | \(0.545230\pi\) | |||||||
\(504\) | 45.5983 | − | 49.5661i | 0.0904728 | − | 0.0983453i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.1043i | 0.0654236i | ||||||||
\(507\) | −15.8227 | − | 6.17101i | −0.0312085 | − | 0.0121716i | ||||
\(508\) | 332.800i | 0.655117i | ||||||||
\(509\) | 541.364i | 1.06358i | 0.846875 | + | 0.531792i | \(0.178481\pi\) | ||||
−0.846875 | + | 0.531792i | \(0.821519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −167.221 | −0.327242 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −88.4471 | − | 180.693i | −0.172412 | − | 0.352228i | ||||
\(514\) | −442.813 | −0.861504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.63662 | − | 11.8885i | 0.00898571 | − | 0.0230397i | ||||
\(517\) | − | 181.457i | − | 0.350981i | ||||||
\(518\) | −103.664 | −0.200124 | ||||||||
\(519\) | −888.251 | − | 346.427i | −1.71147 | − | 0.667489i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 796.131i | − | 1.52808i | −0.645168 | − | 0.764041i | \(-0.723213\pi\) | ||
0.645168 | − | 0.764041i | \(-0.276787\pi\) | |||||||
\(522\) | −221.817 | + | 241.118i | −0.424936 | + | 0.461912i | ||||
\(523\) | 382.162i | 0.730711i | 0.930868 | + | 0.365355i | \(0.119053\pi\) | ||||
−0.930868 | + | 0.365355i | \(0.880947\pi\) | |||||||
\(524\) | − | 458.354i | − | 0.874721i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −584.496 | −1.11121 | ||||||||
\(527\) | 590.612 | 1.12071 | ||||||||
\(528\) | −14.4286 | + | 36.9954i | −0.0273268 | + | 0.0700671i | ||||
\(529\) | −478.960 | −0.905407 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 132.591 | − | 144.129i | 0.249701 | − | 0.271429i | ||||
\(532\) | 39.4273i | 0.0741115i | ||||||||
\(533\) | −16.5965 | −0.0311380 | ||||||||
\(534\) | 5.03029 | − | 12.8979i | 0.00942001 | − | 0.0241533i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 154.842i | 0.288885i | ||||||||
\(537\) | 354.535 | − | 909.042i | 0.660214 | − | 1.69282i | ||||
\(538\) | − | 109.618i | − | 0.203750i | ||||||
\(539\) | − | 23.1639i | − | 0.0429756i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 781.905 | 1.44530 | 0.722648 | − | 0.691217i | \(-0.242925\pi\) | ||||
0.722648 | + | 0.691217i | \(0.242925\pi\) | |||||||
\(542\) | 392.382 | 0.723952 | ||||||||
\(543\) | −96.5293 | − | 37.6474i | −0.177770 | − | 0.0693321i | ||||
\(544\) | 80.4769 | 0.147936 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 138.209 | + | 53.9029i | 0.253130 | + | 0.0987233i | ||||
\(547\) | 836.992i | 1.53015i | 0.643942 | + | 0.765075i | \(0.277298\pi\) | ||||
−0.643942 | + | 0.765075i | \(0.722702\pi\) | |||||||
\(548\) | −247.118 | −0.450945 | ||||||||
\(549\) | 561.708 | + | 516.743i | 1.02315 | + | 0.941244i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 191.797i | − | 0.348090i | ||||||
\(552\) | 55.9212 | + | 21.8098i | 0.101307 | + | 0.0395105i | ||||
\(553\) | 309.399i | 0.559492i | ||||||||
\(554\) | − | 90.8988i | − | 0.164077i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −339.590 | −0.610774 | ||||||||
\(557\) | −151.652 | −0.272267 | −0.136133 | − | 0.990691i | \(-0.543468\pi\) | ||||
−0.136133 | + | 0.990691i | \(0.543468\pi\) | |||||||
\(558\) | 388.876 | + | 357.746i | 0.696910 | + | 0.641123i | ||||
\(559\) | 28.1074 | 0.0502815 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −51.3168 | + | 131.578i | −0.0914738 | + | 0.234542i | ||||
\(562\) | 337.115i | 0.599850i | ||||||||
\(563\) | −830.912 | −1.47586 | −0.737932 | − | 0.674875i | \(-0.764198\pi\) | ||||
−0.737932 | + | 0.674875i | \(0.764198\pi\) | |||||||
\(564\) | −306.525 | − | 119.548i | −0.543483 | − | 0.211964i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 417.494i | − | 0.737621i | ||||||
\(567\) | 213.562 | − | 17.8393i | 0.376653 | − | 0.0314626i | ||||
\(568\) | − | 283.641i | − | 0.499368i | ||||||
\(569\) | 76.3013i | 0.134097i | 0.997750 | + | 0.0670486i | \(0.0213583\pi\) | ||||
−0.997750 | + | 0.0670486i | \(0.978642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −273.471 | −0.478933 | −0.239467 | − | 0.970905i | \(-0.576973\pi\) | ||||
−0.239467 | + | 0.970905i | \(0.576973\pi\) | |||||||
\(572\) | −87.4664 | −0.152913 | ||||||||
\(573\) | 87.8313 | − | 225.203i | 0.153283 | − | 0.393025i | ||||
\(574\) | 4.69876 | 0.00818599 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 52.9883 | + | 48.7466i | 0.0919936 | + | 0.0846296i | ||||
\(577\) | 783.907i | 1.35859i | 0.733865 | + | 0.679295i | \(0.237714\pi\) | ||||
−0.733865 | + | 0.679295i | \(0.762286\pi\) | |||||||
\(578\) | −122.482 | −0.211907 | ||||||||
\(579\) | 111.232 | − | 285.204i | 0.192111 | − | 0.492580i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.8189i | 0.108122i | ||||||||
\(582\) | −85.6736 | + | 219.671i | −0.147206 | + | 0.377441i | ||||
\(583\) | 206.207i | 0.353700i | ||||||||
\(584\) | − | 178.766i | − | 0.306107i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 506.786 | 0.864822 | ||||||||
\(587\) | 552.525 | 0.941269 | 0.470634 | − | 0.882328i | \(-0.344025\pi\) | ||||
0.470634 | + | 0.882328i | \(0.344025\pi\) | |||||||
\(588\) | −39.1294 | − | 15.2608i | −0.0665465 | − | 0.0259538i | ||||
\(589\) | −309.331 | −0.525180 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 141.288 | + | 55.1038i | 0.239067 | + | 0.0932382i | ||||
\(592\) | − | 110.822i | − | 0.187199i | ||||||
\(593\) | 236.428 | 0.398699 | 0.199349 | − | 0.979928i | \(-0.436117\pi\) | ||||
0.199349 | + | 0.979928i | \(0.436117\pi\) | |||||||
\(594\) | −113.488 | + | 55.5512i | −0.191058 | + | 0.0935206i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 475.583i | − | 0.797958i | ||||||
\(597\) | 28.4105 | + | 11.0804i | 0.0475888 | + | 0.0185601i | ||||
\(598\) | 132.212i | 0.221090i | ||||||||
\(599\) | 1179.57i | 1.96923i | 0.174727 | + | 0.984617i | \(0.444096\pi\) | ||||
−0.174727 | + | 0.984617i | \(0.555904\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1090.04 | 1.81370 | 0.906851 | − | 0.421451i | \(-0.138479\pi\) | ||||
0.906851 | + | 0.421451i | \(0.138479\pi\) | |||||||
\(602\) | −7.95767 | −0.0132187 | ||||||||
\(603\) | −333.579 | + | 362.606i | −0.553199 | + | 0.601336i | ||||
\(604\) | 234.135 | 0.387640 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 192.404 | − | 493.331i | 0.317498 | − | 0.814078i | ||||
\(607\) | − | 1077.37i | − | 1.77491i | −0.460892 | − | 0.887456i | \(-0.652470\pi\) | ||
0.460892 | − | 0.887456i | \(-0.347530\pi\) | |||||||
\(608\) | −42.1496 | −0.0693249 | ||||||||
\(609\) | 190.348 | + | 74.2375i | 0.312558 | + | 0.121901i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 724.701i | − | 1.18609i | ||||||
\(612\) | 188.459 | + | 173.373i | 0.307939 | + | 0.283289i | ||||
\(613\) | 942.291i | 1.53718i | 0.639742 | + | 0.768590i | \(0.279041\pi\) | ||||
−0.639742 | + | 0.768590i | \(0.720959\pi\) | |||||||
\(614\) | − | 751.902i | − | 1.22460i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.7632 | 0.0402000 | ||||||||
\(617\) | 863.672 | 1.39979 | 0.699896 | − | 0.714245i | \(-0.253230\pi\) | ||||
0.699896 | + | 0.714245i | \(0.253230\pi\) | |||||||
\(618\) | −174.015 | + | 446.182i | −0.281578 | + | 0.721977i | ||||
\(619\) | −626.507 | −1.01213 | −0.506064 | − | 0.862496i | \(-0.668900\pi\) | ||||
−0.506064 | + | 0.862496i | \(0.668900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 83.9697 | + | 171.546i | 0.135217 | + | 0.276241i | ||||
\(622\) | − | 591.320i | − | 0.950676i | ||||||
\(623\) | −8.63330 | −0.0138576 | ||||||||
\(624\) | −57.6246 | + | 147.752i | −0.0923472 | + | 0.236782i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 433.972i | − | 0.693247i | ||||||
\(627\) | 26.8770 | − | 68.9138i | 0.0428661 | − | 0.109910i | ||||
\(628\) | 63.2302i | 0.100685i | ||||||||
\(629\) | − | 394.151i | − | 0.626630i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 612.214 | 0.970228 | 0.485114 | − | 0.874451i | \(-0.338778\pi\) | ||||
0.485114 | + | 0.874451i | \(0.338778\pi\) | |||||||
\(632\) | −330.761 | −0.523356 | ||||||||
\(633\) | −853.541 | − | 332.889i | −1.34841 | − | 0.525891i | ||||
\(634\) | 118.532 | 0.186959 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 348.333 | + | 135.853i | 0.547694 | + | 0.213606i | ||||
\(637\) | − | 92.5116i | − | 0.145230i | ||||||
\(638\) | −120.463 | −0.188813 | ||||||||
\(639\) | 611.053 | − | 664.224i | 0.956264 | − | 1.03947i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 804.983i | 1.25582i | 0.778284 | + | 0.627912i | \(0.216090\pi\) | ||||
−0.778284 | + | 0.627912i | \(0.783910\pi\) | |||||||
\(642\) | −334.693 | − | 130.534i | −0.521329 | − | 0.203323i | ||||
\(643\) | − | 71.5877i | − | 0.111334i | −0.998449 | − | 0.0556670i | \(-0.982271\pi\) | ||
0.998449 | − | 0.0556670i | \(-0.0177285\pi\) | |||||||
\(644\) | − | 37.4314i | − | 0.0581233i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −149.910 | −0.232058 | ||||||||
\(647\) | 579.969 | 0.896397 | 0.448199 | − | 0.893934i | \(-0.352066\pi\) | ||||
0.448199 | + | 0.893934i | \(0.352066\pi\) | |||||||
\(648\) | 19.0710 | + | 228.307i | 0.0294306 | + | 0.352326i | ||||
\(649\) | 72.0068 | 0.110950 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 119.730 | − | 306.994i | 0.183918 | − | 0.471572i | ||||
\(652\) | 215.106i | 0.329917i | ||||||||
\(653\) | 1063.75 | 1.62902 | 0.814511 | − | 0.580148i | \(-0.197005\pi\) | ||||
0.814511 | + | 0.580148i | \(0.197005\pi\) | |||||||
\(654\) | −652.838 | − | 254.613i | −0.998223 | − | 0.389317i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.02318i | 0.00765729i | ||||||||
\(657\) | 385.119 | − | 418.631i | 0.586179 | − | 0.637185i | ||||
\(658\) | 205.175i | 0.311816i | ||||||||
\(659\) | − | 227.741i | − | 0.345586i | −0.984958 | − | 0.172793i | \(-0.944721\pi\) | ||
0.984958 | − | 0.172793i | \(-0.0552792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 87.7668 | 0.132779 | 0.0663894 | − | 0.997794i | \(-0.478852\pi\) | ||||
0.0663894 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(662\) | 205.079 | 0.309787 | ||||||||
\(663\) | −204.948 | + | 525.496i | −0.309123 | + | 0.792603i | ||||
\(664\) | −67.1562 | −0.101139 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 238.746 | − | 259.520i | 0.358477 | − | 0.389670i | ||||
\(667\) | 182.088i | 0.272996i | ||||||||
\(668\) | 233.812 | 0.350018 | ||||||||
\(669\) | −113.210 | + | 290.274i | −0.169222 | + | 0.433892i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 280.629i | 0.418226i | ||||||||
\(672\) | 16.3145 | − | 41.8311i | 0.0242775 | − | 0.0622486i | ||||
\(673\) | 286.806i | 0.426160i | 0.977035 | + | 0.213080i | \(0.0683495\pi\) | ||||
−0.977035 | + | 0.213080i | \(0.931650\pi\) | |||||||
\(674\) | 863.935i | 1.28180i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3223 | −0.0167490 | ||||||||
\(677\) | 739.076 | 1.09169 | 0.545847 | − | 0.837885i | \(-0.316208\pi\) | ||||
0.545847 | + | 0.837885i | \(0.316208\pi\) | |||||||
\(678\) | −220.806 | − | 86.1164i | −0.325672 | − | 0.127015i | ||||
\(679\) | 147.039 | 0.216552 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1097.69 | + | 428.108i | 1.61187 | + | 0.628646i | ||||
\(682\) | 194.282i | 0.284872i | ||||||||
\(683\) | −384.541 | −0.563017 | −0.281509 | − | 0.959559i | \(-0.590835\pi\) | ||||
−0.281509 | + | 0.959559i | \(0.590835\pi\) | |||||||
\(684\) | −98.7048 | − | 90.8036i | −0.144305 | − | 0.132754i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 1193.86 | + | 465.618i | 1.73779 | + | 0.677756i | ||||
\(688\) | − | 8.50711i | − | 0.0123650i | ||||||
\(689\) | 823.547i | 1.19528i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1158.11 | 1.67599 | 0.837994 | − | 0.545680i | \(-0.183729\pi\) | ||||
0.837994 | + | 0.545680i | \(0.183729\pi\) | |||||||
\(692\) | −635.611 | −0.918512 | ||||||||
\(693\) | 57.9899 | + | 53.3479i | 0.0836795 | + | 0.0769810i | ||||
\(694\) | −99.1347 | −0.142845 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −79.3633 | + | 203.491i | −0.114028 | + | 0.292372i | ||||
\(697\) | 17.8655i | 0.0256320i | ||||||||
\(698\) | 798.200 | 1.14355 | ||||||||
\(699\) | −161.360 | − | 62.9321i | −0.230845 | − | 0.0900317i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1033.07i | 1.47371i | 0.676049 | + | 0.736856i | \(0.263691\pi\) | ||||
−0.676049 | + | 0.736856i | \(0.736309\pi\) | |||||||
\(702\) | −453.248 | + | 221.860i | −0.645653 | + | 0.316040i | ||||
\(703\) | 206.435i | 0.293649i | ||||||||
\(704\) | 26.4730i | 0.0376037i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.33643 | 0.00330939 | ||||||||
\(707\) | −330.216 | −0.467066 | ||||||||
\(708\) | 47.4395 | − | 121.637i | 0.0670050 | − | 0.171803i | ||||
\(709\) | 978.655 | 1.38033 | 0.690166 | − | 0.723651i | \(-0.257538\pi\) | ||||
0.690166 | + | 0.723651i | \(0.257538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −774.569 | − | 712.565i | −1.08941 | − | 1.00220i | ||||
\(712\) | − | 9.22938i | − | 0.0129626i | ||||||
\(713\) | 293.672 | 0.411882 | ||||||||
\(714\) | 58.0244 | − | 148.777i | 0.0812666 | − | 0.208371i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 650.488i | − | 0.908502i | ||||||
\(717\) | −57.7415 | + | 148.052i | −0.0805321 | + | 0.206488i | ||||
\(718\) | − | 560.235i | − | 0.780271i | ||||||
\(719\) | − | 1081.91i | − | 1.50474i | −0.658739 | − | 0.752372i | \(-0.728910\pi\) | ||
0.658739 | − | 0.752372i | \(-0.271090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 298.656 | 0.414224 | ||||||||
\(722\) | −432.016 | −0.598361 | ||||||||
\(723\) | −439.515 | − | 171.415i | −0.607904 | − | 0.237088i | ||||
\(724\) | −69.0740 | −0.0954060 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 434.989 | + | 169.650i | 0.599159 | + | 0.233678i | ||||
\(727\) | − | 416.273i | − | 0.572589i | −0.958142 | − | 0.286295i | \(-0.907576\pi\) | ||
0.958142 | − | 0.286295i | \(-0.0924237\pi\) | |||||||
\(728\) | 98.8991 | 0.135850 | ||||||||
\(729\) | −447.187 | + | 575.730i | −0.613425 | + | 0.789753i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 30.2565i | − | 0.0413905i | ||||||
\(732\) | 474.051 | + | 184.884i | 0.647610 | + | 0.252574i | ||||
\(733\) | − | 338.733i | − | 0.462118i | −0.972940 | − | 0.231059i | \(-0.925781\pi\) | ||
0.972940 | − | 0.231059i | \(-0.0742191\pi\) | |||||||
\(734\) | 513.894i | 0.700128i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.0158 | 0.0543693 | ||||||||
\(737\) | −181.158 | −0.245805 | ||||||||
\(738\) | −10.8215 | + | 11.7632i | −0.0146633 | + | 0.0159393i | ||||
\(739\) | −324.854 | −0.439586 | −0.219793 | − | 0.975547i | \(-0.570538\pi\) | ||||
−0.219793 | + | 0.975547i | \(0.570538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 107.341 | − | 275.227i | 0.144860 | − | 0.371426i | ||||
\(742\) | − | 233.160i | − | 0.314232i | ||||||
\(743\) | −857.635 | −1.15429 | −0.577143 | − | 0.816643i | \(-0.695833\pi\) | ||||
−0.577143 | + | 0.816643i | \(0.695833\pi\) | |||||||
\(744\) | 328.190 | + | 127.997i | 0.441115 | + | 0.172039i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 293.000i | − | 0.392761i | ||||||
\(747\) | −157.265 | − | 144.676i | −0.210528 | − | 0.193676i | ||||
\(748\) | 94.1542i | 0.125875i | ||||||||
\(749\) | 224.030i | 0.299106i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −356.621 | −0.474861 | −0.237431 | − | 0.971404i | \(-0.576305\pi\) | ||||
−0.237431 | + | 0.971404i | \(0.576305\pi\) | |||||||
\(752\) | −219.341 | −0.291677 | ||||||||
\(753\) | 164.077 | − | 420.701i | 0.217898 | − | 0.558700i | ||||
\(754\) | −481.103 | −0.638067 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 128.322 | − | 62.8123i | 0.169739 | − | 0.0830851i | ||||
\(757\) | 1356.47i | 1.79191i | 0.444147 | + | 0.895954i | \(0.353507\pi\) | ||||
−0.444147 | + | 0.895954i | \(0.646493\pi\) | |||||||
\(758\) | −692.186 | −0.913174 | ||||||||
\(759\) | −25.5164 | + | 65.4252i | −0.0336185 | + | 0.0861992i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 106.889i | 0.140459i | 0.997531 | + | 0.0702294i | \(0.0223731\pi\) | ||||
−0.997531 | + | 0.0702294i | \(0.977627\pi\) | |||||||
\(762\) | −256.518 | + | 657.722i | −0.336638 | + | 0.863153i | ||||
\(763\) | 436.983i | 0.572717i | ||||||||
\(764\) | − | 161.150i | − | 0.210929i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −298.076 | −0.389134 | ||||||||
\(767\) | 287.580 | 0.374941 | ||||||||
\(768\) | 44.7193 | + | 17.4409i | 0.0582282 | + | 0.0227096i | ||||
\(769\) | −500.283 | −0.650563 | −0.325282 | − | 0.945617i | \(-0.605459\pi\) | ||||
−0.325282 | + | 0.945617i | \(0.605459\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −875.145 | − | 341.315i | −1.13508 | − | 0.442691i | ||||
\(772\) | − | 204.085i | − | 0.264359i | ||||||
\(773\) | 1146.06 | 1.48262 | 0.741309 | − | 0.671164i | \(-0.234206\pi\) | ||||
0.741309 | + | 0.671164i | \(0.234206\pi\) | |||||||
\(774\) | 18.3270 | − | 19.9217i | 0.0236783 | − | 0.0257387i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 157.191i | 0.202566i | ||||||||
\(777\) | −204.875 | − | 79.9033i | −0.263675 | − | 0.102836i | ||||
\(778\) | − | 465.246i | − | 0.598003i | ||||||
\(779\) | − | 9.35701i | − | 0.0120116i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 331.846 | 0.424899 | ||||||||
\(782\) | 142.321 | 0.181996 | ||||||||
\(783\) | −624.234 | + | 305.556i | −0.797234 | + | 0.390237i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 353.294 | − | 905.859i | 0.449483 | − | 1.15249i | ||||
\(787\) | 488.016i | 0.620097i | 0.950721 | + | 0.310048i | \(0.100345\pi\) | ||||
−0.950721 | + | 0.310048i | \(0.899655\pi\) | |||||||
\(788\) | 101.102 | 0.128303 | ||||||||
\(789\) | −1155.16 | − | 450.523i | −1.46408 | − | 0.571005i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 147.798i | 0.186850i | ||||||||
\(792\) | −57.0313 | + | 61.9938i | −0.0720092 | + | 0.0782750i | ||||
\(793\) | 1120.77i | 1.41333i | ||||||||
\(794\) | 45.7672i | 0.0576413i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3299 | 0.0255400 | ||||||||
\(797\) | 197.490 | 0.247792 | 0.123896 | − | 0.992295i | \(-0.460461\pi\) | ||||
0.123896 | + | 0.992295i | \(0.460461\pi\) | |||||||
\(798\) | −30.3901 | + | 77.9214i | −0.0380828 | + | 0.0976459i | ||||
\(799\) | −780.112 | −0.976361 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.8830 | − | 21.6131i | 0.0248228 | − | 0.0269827i | ||||
\(802\) | 330.243i | 0.411775i | ||||||||
\(803\) | 209.148 | 0.260458 | ||||||||
\(804\) | −119.350 | + | 306.019i | −0.148446 | + | 0.380621i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 775.923i | 0.962684i | ||||||||
\(807\) | 84.4920 | − | 216.641i | 0.104699 | − | 0.268452i | ||||
\(808\) | − | 353.015i | − | 0.436900i | ||||||
\(809\) | 982.627i | 1.21462i | 0.794465 | + | 0.607310i | \(0.207751\pi\) | ||||
−0.794465 | + | 0.607310i | \(0.792249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 344.348 | 0.424597 | 0.212298 | − | 0.977205i | \(-0.431905\pi\) | ||||
0.212298 | + | 0.977205i | \(0.431905\pi\) | |||||||
\(812\) | 136.208 | 0.167744 | ||||||||
\(813\) | 775.477 | + | 302.444i | 0.953846 | + | 0.372009i | ||||
\(814\) | 129.656 | 0.159283 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 159.049 | + | 62.0307i | 0.194913 | + | 0.0760180i | ||||
\(817\) | 15.8467i | 0.0193963i | ||||||||
\(818\) | 42.7664 | 0.0522817 | ||||||||
\(819\) | 231.599 | + | 213.060i | 0.282783 | + | 0.260147i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 616.490i | − | 0.750901i | −0.926842 | − | 0.375451i | \(-0.877488\pi\) | ||
0.926842 | − | 0.375451i | \(-0.122512\pi\) | |||||||
\(822\) | −488.386 | − | 190.475i | −0.594144 | − | 0.231722i | ||||
\(823\) | 638.840i | 0.776234i | 0.921610 | + | 0.388117i | \(0.126874\pi\) | ||||
−0.921610 | + | 0.388117i | \(0.873126\pi\) | |||||||
\(824\) | 319.276i | 0.387471i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −81.4187 | −0.0985699 | ||||||||
\(827\) | −1066.42 | −1.28951 | −0.644753 | − | 0.764391i | \(-0.723040\pi\) | ||||
−0.644753 | + | 0.764391i | \(0.723040\pi\) | |||||||
\(828\) | 93.7081 | + | 86.2068i | 0.113174 | + | 0.104115i | ||||
\(829\) | 625.285 | 0.754265 | 0.377132 | − | 0.926159i | \(-0.376910\pi\) | ||||
0.377132 | + | 0.926159i | \(0.376910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 70.0637 | − | 179.646i | 0.0843125 | − | 0.216181i | ||||
\(832\) | 105.728i | 0.127076i | ||||||||
\(833\) | −99.5851 | −0.119550 | ||||||||
\(834\) | −671.143 | − | 261.752i | −0.804727 | − | 0.313851i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 49.3130i | − | 0.0589868i | ||||||
\(837\) | 492.801 | + | 1006.77i | 0.588770 | + | 1.20283i | ||||
\(838\) | − | 976.713i | − | 1.16553i | ||||||
\(839\) | − | 387.376i | − | 0.461712i | −0.972988 | − | 0.230856i | \(-0.925847\pi\) | ||
0.972988 | − | 0.230856i | \(-0.0741526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 178.404 | 0.212133 | ||||||||
\(842\) | −901.629 | −1.07082 | ||||||||
\(843\) | −259.845 | + | 666.252i | −0.308238 | + | 0.790334i | ||||
\(844\) | −610.773 | −0.723665 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −513.648 | − | 472.531i | −0.607149 | − | 0.558547i | ||||
\(847\) | − | 291.164i | − | 0.343759i | ||||||
\(848\) | 249.259 | 0.293937 | ||||||||
\(849\) | 321.799 | − | 825.106i | 0.379033 | − | 0.971856i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 195.985i | − | 0.230299i | ||||||
\(852\) | 218.627 | − | 560.569i | 0.256605 | − | 0.657944i | ||||
\(853\) | 830.771i | 0.973940i | 0.873419 | + | 0.486970i | \(0.161898\pi\) | ||||
−0.873419 | + | 0.486970i | \(0.838102\pi\) | |||||||
\(854\) | − | 317.310i | − | 0.371558i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −239.498 | −0.279788 | ||||||||
\(857\) | 292.550 | 0.341365 | 0.170683 | − | 0.985326i | \(-0.445403\pi\) | ||||
0.170683 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(858\) | −172.863 | − | 67.4181i | −0.201472 | − | 0.0785758i | ||||
\(859\) | 672.801 | 0.783237 | 0.391619 | − | 0.920128i | \(-0.371915\pi\) | ||||
0.391619 | + | 0.920128i | \(0.371915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.28630 | + | 3.62175i | 0.0107855 | + | 0.00420644i | ||||
\(862\) | 671.017i | 0.778442i | ||||||||
\(863\) | 699.281 | 0.810291 | 0.405145 | − | 0.914252i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914252i | \(0.367221\pi\) | |||||||
\(864\) | 67.1492 | + | 137.182i | 0.0777190 | + | 0.158776i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 94.3971i | − | 0.109004i | ||||||
\(867\) | −242.066 | − | 94.4080i | −0.279199 | − | 0.108890i | ||||
\(868\) | − | 219.677i | − | 0.253084i | ||||||
\(869\) | − | 386.975i | − | 0.445311i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −723.506 | −0.830662 | ||||||||
\(872\) | −467.155 | −0.535728 | ||||||||
\(873\) | −338.639 | + | 368.106i | −0.387903 | + | 0.421656i | ||||
\(874\) | −74.5401 | −0.0852862 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 137.791 | − | 353.301i | 0.157296 | − | 0.403312i | ||||
\(877\) | − | 358.626i | − | 0.408924i | −0.978874 | − | 0.204462i | \(-0.934456\pi\) | ||
0.978874 | − | 0.204462i | \(-0.0655445\pi\) | |||||||
\(878\) | 510.658 | 0.581615 | ||||||||
\(879\) | 1001.58 | + | 390.624i | 1.13945 | + | 0.444396i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1550.04i | 1.75941i | 0.475522 | + | 0.879704i | \(0.342259\pi\) | ||||
−0.475522 | + | 0.879704i | \(0.657741\pi\) | |||||||
\(882\) | −65.5697 | − | 60.3209i | −0.0743421 | − | 0.0683910i | ||||
\(883\) | − | 1595.94i | − | 1.80741i | −0.428154 | − | 0.903706i | \(-0.640836\pi\) | ||
0.428154 | − | 0.903706i | \(-0.359164\pi\) | |||||||
\(884\) | 376.032i | 0.425375i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −587.129 | −0.662674 | ||||||||
\(887\) | 134.533 | 0.151671 | 0.0758357 | − | 0.997120i | \(-0.475838\pi\) | ||||
0.0758357 | + | 0.997120i | \(0.475838\pi\) | |||||||
\(888\) | 85.4202 | − | 219.021i | 0.0961939 | − | 0.246645i | ||||
\(889\) | 440.253 | 0.495222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −267.109 | + | 22.3122i | −0.299785 | + | 0.0250418i | ||||
\(892\) | 207.713i | 0.232862i | ||||||||
\(893\) | 408.581 | 0.457538 | ||||||||
\(894\) | 366.574 | − | 939.909i | 0.410038 | − | 1.05135i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −101.907 | + | 261.294i | −0.113609 | + | 0.291298i | ||||
\(898\) | 761.841i | 0.848375i | ||||||||
\(899\) | 1068.64i | 1.18869i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 886.517 | 0.983925 | ||||||||
\(902\) | −5.87688 | −0.00651539 | ||||||||
\(903\) | −15.7270 | − | 6.13368i | −0.0174164 | − | 0.00679256i | ||||
\(904\) | −158.003 | −0.174782 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 462.728 | + | 180.468i | 0.510737 | + | 0.199192i | ||||
\(907\) | 879.668i | 0.969865i | 0.874551 | + | 0.484933i | \(0.161156\pi\) | ||||
−0.874551 | + | 0.484933i | \(0.838844\pi\) | |||||||
\(908\) | 785.477 | 0.865062 | ||||||||
\(909\) | 760.507 | − | 826.683i | 0.836642 | − | 0.909442i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1522.40i | 1.67113i | 0.549391 | + | 0.835565i | \(0.314860\pi\) | ||||
−0.549391 | + | 0.835565i | \(0.685140\pi\) | |||||||
\(912\) | −83.3015 | − | 32.4884i | −0.0913394 | − | 0.0356232i | ||||
\(913\) | − | 78.5695i | − | 0.0860564i | ||||||
\(914\) | − | 942.661i | − | 1.03136i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 854.299 | 0.932641 | ||||||||
\(917\) | −606.345 | −0.661227 | ||||||||
\(918\) | 238.824 | + | 487.904i | 0.260156 | + | 0.531486i | ||||
\(919\) | −1178.73 | −1.28262 | −0.641309 | − | 0.767282i | \(-0.721608\pi\) | ||||
−0.641309 | + | 0.767282i | \(0.721608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 579.557 | − | 1486.01i | 0.629270 | − | 1.61347i | ||||
\(922\) | − | 348.922i | − | 0.378441i | ||||||
\(923\) | 1325.32 | 1.43589 | ||||||||
\(924\) | 48.9403 | + | 19.0872i | 0.0529657 | + | 0.0206571i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 394.243i | − | 0.425748i | ||||||
\(927\) | −687.823 | + | 747.674i | −0.741988 | + | 0.806552i | ||||
\(928\) | 145.613i | 0.156910i | ||||||||
\(929\) | 534.346i | 0.575184i | 0.957753 | + | 0.287592i | \(0.0928547\pi\) | ||||
−0.957753 | + | 0.287592i | \(0.907145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.1574 | 0.0560230 | ||||||||
\(932\) | −115.466 | −0.123890 | ||||||||
\(933\) | 455.783 | − | 1168.65i | 0.488513 | − | 1.25257i | ||||
\(934\) | −372.624 | −0.398955 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −227.771 | + | 247.590i | −0.243345 | + | 0.264519i | ||||
\(937\) | 1383.17i | 1.47616i | 0.674711 | + | 0.738082i | \(0.264268\pi\) | ||||
−0.674711 | + | 0.738082i | \(0.735732\pi\) | |||||||
\(938\) | 204.837 | 0.218376 | ||||||||
\(939\) | 334.501 | − | 857.673i | 0.356231 | − | 0.913390i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 562.997i | 0.598296i | 0.954207 | + | 0.299148i | \(0.0967024\pi\) | ||||
−0.954207 | + | 0.299148i | \(0.903298\pi\) | |||||||
\(942\) | −48.7371 | + | 124.964i | −0.0517379 | + | 0.132658i | ||||
\(943\) | 8.88333i | 0.00942029i | ||||||||
\(944\) | − | 87.0403i | − | 0.0922037i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.95291 | 0.0105210 | ||||||||
\(947\) | 722.442 | 0.762874 | 0.381437 | − | 0.924395i | \(-0.375429\pi\) | ||||
0.381437 | + | 0.924395i | \(0.375429\pi\) | |||||||
\(948\) | −653.694 | − | 254.947i | −0.689551 | − | 0.268931i | ||||
\(949\) | 835.293 | 0.880182 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 234.259 | + | 91.3632i | 0.246329 | + | 0.0960707i | ||||
\(952\) | − | 106.461i | − | 0.111829i | ||||||
\(953\) | 1567.96 | 1.64529 | 0.822644 | − | 0.568557i | \(-0.192498\pi\) | ||||
0.822644 | + | 0.568557i | \(0.192498\pi\) | |||||||
\(954\) | 583.708 | + | 536.983i | 0.611853 | + | 0.562875i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 105.942i | 0.110818i | ||||||||
\(957\) | −238.074 | − | 92.8512i | −0.248771 | − | 0.0970232i | ||||
\(958\) | 230.782i | 0.240899i | ||||||||
\(959\) | 326.906i | 0.340882i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 762.498 | 0.793443 | ||||||||
\(962\) | 517.820 | 0.538274 | ||||||||
\(963\) | −560.851 | − | 515.955i | −0.582400 | − | 0.535779i | ||||
\(964\) | −314.506 | −0.326251 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 28.8517 | − | 73.9768i | 0.0298672 | − | 0.0765806i | ||||
\(967\) | − | 1182.12i | − | 1.22246i | −0.791453 | − | 0.611230i | \(-0.790675\pi\) | ||
0.791453 | − | 0.611230i | \(-0.209325\pi\) | |||||||
\(968\) | 311.268 | 0.321557 | ||||||||
\(969\) | −296.271 | − | 115.549i | −0.305749 | − | 0.119245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1672.57i | − | 1.72252i | −0.508165 | − | 0.861260i | \(-0.669676\pi\) | ||
0.508165 | − | 0.861260i | \(-0.330324\pi\) | |||||||
\(972\) | −138.286 | + | 465.911i | −0.142270 | + | 0.479332i | ||||
\(973\) | 449.236i | 0.461702i | ||||||||
\(974\) | 1063.84i | 1.09224i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 339.219 | 0.347560 | ||||||||
\(977\) | −383.549 | −0.392578 | −0.196289 | − | 0.980546i | \(-0.562889\pi\) | ||||
−0.196289 | + | 0.980546i | \(0.562889\pi\) | |||||||
\(978\) | −165.801 | + | 425.120i | −0.169531 | + | 0.434683i | ||||
\(979\) | 10.7979 | 0.0110296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1093.97 | − | 1006.40i | −1.11516 | − | 1.02589i | ||||
\(982\) | 95.0503i | 0.0967925i | ||||||||
\(983\) | −68.4583 | −0.0696422 | −0.0348211 | − | 0.999394i | \(-0.511086\pi\) | ||||
−0.0348211 | + | 0.999394i | \(0.511086\pi\) | |||||||
\(984\) | −3.87181 | + | 9.92748i | −0.00393477 | + | 0.0100889i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 517.888i | 0.525242i | ||||||||
\(987\) | −158.147 | + | 405.494i | −0.160229 | + | 0.410835i | ||||
\(988\) | − | 196.946i | − | 0.199338i | ||||||
\(989\) | − | 15.0445i | − | 0.0152119i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −700.214 | −0.706573 | −0.353287 | − | 0.935515i | \(-0.614936\pi\) | ||||
−0.353287 | + | 0.935515i | \(0.614936\pi\) | |||||||
\(992\) | 234.845 | 0.236738 | ||||||||
\(993\) | 405.304 | + | 158.072i | 0.408161 | + | 0.159187i | ||||
\(994\) | −375.222 | −0.377487 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −132.723 | − | 51.7632i | −0.133256 | − | 0.0519711i | ||||
\(997\) | 1678.07i | 1.68312i | 0.540166 | + | 0.841558i | \(0.318361\pi\) | ||||
−0.540166 | + | 0.841558i | \(0.681639\pi\) | |||||||
\(998\) | 350.322 | 0.351024 | ||||||||
\(999\) | 671.875 | − | 328.875i | 0.672548 | − | 0.329205i |
(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 | 1050.3.c.b.449.32 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.b.449.2 | 32 | ||
5.2 | odd | 4 | 1050.3.e.c.701.13 | yes | 16 | ||
5.3 | odd | 4 | 1050.3.e.b.701.4 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1050.3.c.b.449.1 | 32 | ||
15.2 | even | 4 | 1050.3.e.c.701.5 | yes | 16 | ||
15.8 | even | 4 | 1050.3.e.b.701.12 | yes | 16 | ||
15.14 | odd | 2 | inner | 1050.3.c.b.449.31 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.c.b.449.1 | 32 | 5.4 | even | 2 | inner | ||
1050.3.c.b.449.2 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.b.449.31 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.c.b.449.32 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.e.b.701.4 | ✓ | 16 | 5.3 | odd | 4 | ||
1050.3.e.b.701.12 | yes | 16 | 15.8 | even | 4 | ||
1050.3.e.c.701.5 | yes | 16 | 15.2 | even | 4 | ||
1050.3.e.c.701.13 | yes | 16 | 5.2 | odd | 4 |