Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(401,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.4 | ||
Character | \(\chi\) | \(=\) | 4020.401 |
Dual form | 4020.2.f.b.401.3 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68102 | + | 0.417348i | −0.970536 | + | 0.240956i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.42754i | − | 0.917525i | −0.888559 | − | 0.458763i | \(-0.848293\pi\) | ||
0.888559 | − | 0.458763i | \(-0.151707\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.65164 | − | 1.40314i | 0.883881 | − | 0.467712i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.52837 | −0.762333 | −0.381167 | − | 0.924506i | \(-0.624478\pi\) | ||||
−0.381167 | + | 0.924506i | \(0.624478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.420456i | − | 0.116614i | −0.998299 | − | 0.0583068i | \(-0.981430\pi\) | ||
0.998299 | − | 0.0583068i | \(-0.0185702\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68102 | + | 0.417348i | −0.434037 | + | 0.107759i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.53240i | 0.371661i | 0.982582 | + | 0.185830i | \(0.0594975\pi\) | ||||
−0.982582 | + | 0.185830i | \(0.940503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.99037 | −0.456623 | −0.228311 | − | 0.973588i | \(-0.573320\pi\) | ||||
−0.228311 | + | 0.973588i | \(0.573320\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.01313 | + | 4.08074i | 0.221083 | + | 0.890492i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.90732i | 0.606219i | 0.952956 | + | 0.303109i | \(0.0980248\pi\) | ||||
−0.952956 | + | 0.303109i | \(0.901975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.87186 | + | 3.46536i | −0.745140 | + | 0.666908i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32422i | 0.245902i | 0.992413 | + | 0.122951i | \(0.0392358\pi\) | ||||
−0.992413 | + | 0.122951i | \(0.960764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.77115i | 0.856925i | 0.903560 | + | 0.428462i | \(0.140945\pi\) | ||||
−0.903560 | + | 0.428462i | \(0.859055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.25024 | − | 1.05521i | 0.739872 | − | 0.183689i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.42754i | − | 0.410330i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.45031 | 1.55362 | 0.776810 | − | 0.629735i | \(-0.216836\pi\) | ||||
0.776810 | + | 0.629735i | \(0.216836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.175476 | + | 0.706795i | 0.0280987 | + | 0.113178i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00106 | 0.312513 | 0.156256 | − | 0.987717i | \(-0.450057\pi\) | ||||
0.156256 | + | 0.987717i | \(0.450057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.63886i | − | 0.402422i | −0.979548 | − | 0.201211i | \(-0.935512\pi\) | ||
0.979548 | − | 0.201211i | \(-0.0644877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.65164 | − | 1.40314i | 0.395283 | − | 0.209167i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60954i | 0.380641i | 0.981722 | + | 0.190321i | \(0.0609528\pi\) | ||||
−0.981722 | + | 0.190321i | \(0.939047\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.10703 | 0.158147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.639542 | − | 2.57598i | −0.0895538 | − | 0.360710i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37490 | 0.188858 | 0.0944289 | − | 0.995532i | \(-0.469898\pi\) | ||||
0.0944289 | + | 0.995532i | \(0.469898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.52837 | −0.340926 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.34585 | − | 0.830677i | 0.443169 | − | 0.110026i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2114i | 1.85017i | 0.379758 | + | 0.925086i | \(0.376007\pi\) | ||||
−0.379758 | + | 0.925086i | \(0.623993\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.2815i | − | 1.44444i | −0.691662 | − | 0.722221i | \(-0.743121\pi\) | ||
0.691662 | − | 0.722221i | \(-0.256879\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.40618 | − | 6.43698i | −0.429138 | − | 0.810983i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.420456i | − | 0.0521512i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34375 | + | 3.61516i | 0.897182 | + | 0.441662i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.21336 | − | 4.88726i | −0.146072 | − | 0.588357i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.60277i | 0.427570i | 0.976881 | + | 0.213785i | \(0.0685793\pi\) | ||||
−0.976881 | + | 0.213785i | \(0.931421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.92733 | −0.225577 | −0.112789 | − | 0.993619i | \(-0.535978\pi\) | ||||
−0.112789 | + | 0.993619i | \(0.535978\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.68102 | + | 0.417348i | −0.194107 | + | 0.0481911i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.13774i | 0.699460i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.44491i | − | 0.837618i | −0.908074 | − | 0.418809i | \(-0.862448\pi\) | ||
0.908074 | − | 0.418809i | \(-0.137552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.06241 | − | 7.44124i | 0.562490 | − | 0.826804i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.4573i | − | 1.47713i | −0.674183 | − | 0.738565i | \(-0.735504\pi\) | ||
0.674183 | − | 0.738565i | \(-0.264496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.53240i | 0.166212i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.552661 | − | 2.22604i | −0.0592515 | − | 0.238657i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.46697i | − | 0.261498i | −0.991416 | − | 0.130749i | \(-0.958262\pi\) | ||
0.991416 | − | 0.130749i | \(-0.0417382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.02068 | −0.106996 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.99123 | − | 8.02040i | −0.206481 | − | 0.831676i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.99037 | −0.204208 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.51661i | − | 0.458593i | −0.973357 | − | 0.229296i | \(-0.926357\pi\) | ||
0.973357 | − | 0.229296i | \(-0.0736425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.70434 | + | 3.54766i | −0.673812 | + | 0.356553i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.70241 | −0.766419 | −0.383209 | − | 0.923662i | \(-0.625181\pi\) | ||||
−0.383209 | + | 0.923662i | \(0.625181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.858145 | −0.0845556 | −0.0422778 | − | 0.999106i | \(-0.513461\pi\) | ||||
−0.0422778 | + | 0.999106i | \(0.513461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.01313 | + | 4.08074i | 0.0988713 | + | 0.398240i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.38436i | − | 0.713873i | −0.934129 | − | 0.356937i | \(-0.883821\pi\) | ||
0.934129 | − | 0.356937i | \(-0.116179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.74050i | − | 0.837188i | −0.908173 | − | 0.418594i | \(-0.862523\pi\) | ||
0.908173 | − | 0.418594i | \(-0.137477\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.8861 | + | 3.94406i | −1.50785 | + | 0.374354i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.82442 | 0.830132 | 0.415066 | − | 0.909791i | \(-0.363758\pi\) | ||||
0.415066 | + | 0.909791i | \(0.363758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.90732i | 0.271109i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.589958 | − | 1.11490i | −0.0545417 | − | 0.103073i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.71996 | 0.341008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.60733 | −0.418848 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.36381 | + | 0.835137i | −0.303305 | + | 0.0753018i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6506 | 1.03383 | 0.516913 | − | 0.856038i | \(-0.327081\pi\) | ||||
0.516913 | + | 0.856038i | \(0.327081\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.10132 | + | 4.43597i | 0.0969659 | + | 0.390565i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.95159i | − | 0.607363i | −0.952774 | − | 0.303681i | \(-0.901784\pi\) | ||
0.952774 | − | 0.303681i | \(-0.0982158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.83172i | 0.418963i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.87186 | + | 3.46536i | −0.333237 | + | 0.298250i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3836 | 1.31431 | 0.657154 | − | 0.753757i | \(-0.271760\pi\) | ||||
0.657154 | + | 0.753757i | \(0.271760\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.5800i | − | 1.15184i | −0.817504 | − | 0.575922i | \(-0.804643\pi\) | ||
0.817504 | − | 0.575922i | \(-0.195357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.08909 | − | 4.38669i | −0.0917177 | − | 0.369426i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.06307i | 0.0888985i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.32422i | 0.109971i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.86094 | + | 0.462016i | −0.153487 | + | 0.0381065i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.4796i | 1.59583i | 0.602767 | + | 0.797917i | \(0.294065\pi\) | ||||
−0.602767 | + | 0.797917i | \(0.705935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.96107 | 0.810621 | 0.405310 | − | 0.914179i | \(-0.367163\pi\) | ||||
0.405310 | + | 0.914179i | \(0.367163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.15016 | + | 4.06337i | 0.173830 | + | 0.328504i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.77115i | 0.383228i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.59295 | 0.685792 | 0.342896 | − | 0.939373i | \(-0.388592\pi\) | ||||
0.342896 | + | 0.939373i | \(0.388592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.31124 | + | 0.573813i | −0.183293 | + | 0.0455063i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.05766 | 0.556221 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2882 | 0.805832 | 0.402916 | − | 0.915237i | \(-0.367997\pi\) | ||||
0.402916 | + | 0.915237i | \(0.367997\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.25024 | − | 1.05521i | 0.330881 | − | 0.0821480i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.722509i | 0.0559094i | 0.999609 | + | 0.0279547i | \(0.00889942\pi\) | ||||
−0.999609 | + | 0.0279547i | \(0.991101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8232 | 0.986401 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.27776 | + | 2.79277i | −0.403600 | + | 0.213568i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.18108i | − | 0.698024i | −0.937118 | − | 0.349012i | \(-0.886517\pi\) | ||
0.937118 | − | 0.349012i | \(-0.113483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.42754i | − | 0.183505i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.93111 | − | 23.8897i | −0.445809 | − | 1.79566i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.77495 | −0.506384 | −0.253192 | − | 0.967416i | \(-0.581480\pi\) | ||||
−0.253192 | + | 0.967416i | \(0.581480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.55595 | −0.561630 | −0.280815 | − | 0.959762i | \(-0.590605\pi\) | ||||
−0.280815 | + | 0.959762i | \(0.590605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.70829 | + | 18.9643i | 0.348047 | + | 1.40188i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.45031 | 0.694800 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.87447i | − | 0.283329i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.41230 | + | 9.39911i | 0.611905 | + | 0.683685i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9026 | −0.861240 | −0.430620 | − | 0.902533i | \(-0.641705\pi\) | ||||
−0.430620 | + | 0.902533i | \(0.641705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2551 | 0.954121 | 0.477061 | − | 0.878870i | \(-0.341702\pi\) | ||||
0.477061 | + | 0.878870i | \(0.341702\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.175476 | + | 0.706795i | 0.0125661 | + | 0.0506146i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.58564 | 0.397961 | 0.198980 | − | 0.980003i | \(-0.436237\pi\) | ||||
0.198980 | + | 0.980003i | \(0.436237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0996 | 1.14127 | 0.570634 | − | 0.821205i | \(-0.306698\pi\) | ||||
0.570634 | + | 0.821205i | \(0.306698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.8537 | − | 3.01225i | −0.977168 | − | 0.212468i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.21461 | 0.225621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00106 | 0.139760 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.07937 | + | 7.70918i | 0.283536 | + | 0.535825i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.03241 | 0.348099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0275 | −1.51644 | −0.758218 | − | 0.652001i | \(-0.773930\pi\) | ||||
−0.758218 | + | 0.652001i | \(0.773930\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.50361 | − | 6.05632i | −0.103026 | − | 0.414972i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.63886i | − | 0.179969i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5822 | 0.786250 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.23988 | − | 0.804368i | 0.218931 | − | 0.0543541i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.644306 | 0.0433407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.09341 | −0.140185 | −0.0700926 | − | 0.997540i | \(-0.522329\pi\) | ||||
−0.0700926 | + | 0.997540i | \(0.522329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.65164 | − | 1.40314i | 0.176776 | − | 0.0935425i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 0.0320395i | − | 0.00212653i | −0.999999 | − | 0.00106327i | \(-0.999662\pi\) | ||
0.999999 | − | 0.00106327i | \(-0.000338448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.71101i | 0.245230i | 0.992454 | + | 0.122615i | \(0.0391281\pi\) | ||||
−0.992454 | + | 0.122615i | \(0.960872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.56157 | − | 10.3176i | −0.168539 | − | 0.678851i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0674 | 1.18364 | 0.591819 | − | 0.806071i | \(-0.298410\pi\) | ||||
0.591819 | + | 0.806071i | \(0.298410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.60954i | 0.170228i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.10711 | + | 12.5150i | 0.201829 | + | 0.812938i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.57206 | 0.360427 | 0.180213 | − | 0.983628i | \(-0.442321\pi\) | ||||
0.180213 | + | 0.983628i | \(0.442321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3553 | 1.37562 | 0.687809 | − | 0.725892i | \(-0.258573\pi\) | ||||
0.687809 | + | 0.725892i | \(0.258573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.40442 | + | 14.6216i | −0.346694 | + | 0.937978i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.10703 | 0.0707255 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.836865i | 0.0532485i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.61637 | + | 22.6219i | 0.355923 | + | 1.43361i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0803 | 0.636265 | 0.318133 | − | 0.948046i | \(-0.396944\pi\) | ||||
0.318133 | + | 0.948046i | \(0.396944\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.35080i | − | 0.462141i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.639542 | − | 2.57598i | −0.0400497 | − | 0.161314i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.37780i | − | 0.460214i | −0.973165 | − | 0.230107i | \(-0.926092\pi\) | ||
0.973165 | − | 0.230107i | \(-0.0739077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 22.9410i | − | 1.42549i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.85807 | + | 3.51136i | 0.115011 | + | 0.217348i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.74055i | − | 0.538965i | −0.963005 | − | 0.269483i | \(-0.913147\pi\) | ||
0.963005 | − | 0.269483i | \(-0.0868527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37490 | 0.0844597 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.02958 | + | 4.14702i | 0.0630094 | + | 0.253793i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.21198i | − | 0.0738958i | −0.999317 | − | 0.0369479i | \(-0.988236\pi\) | ||
0.999317 | − | 0.0369479i | \(-0.0117636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.452403i | − | 0.0274816i | −0.999906 | − | 0.0137408i | \(-0.995626\pi\) | ||
0.999906 | − | 0.0137408i | \(-0.00437396\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.71578 | − | 0.425977i | 0.103843 | − | 0.0257813i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.52837 | −0.152467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7483 | 0.826053 | 0.413027 | − | 0.910719i | \(-0.364472\pi\) | ||||
0.413027 | + | 0.910719i | \(0.364472\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.69459 | + | 12.6514i | 0.400794 | + | 0.757419i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6935 | −0.697574 | −0.348787 | − | 0.937202i | \(-0.613406\pi\) | ||||
−0.348787 | + | 0.937202i | \(0.613406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4059 | 0.796901 | 0.398450 | − | 0.917190i | \(-0.369548\pi\) | ||||
0.398450 | + | 0.917190i | \(0.369548\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.34585 | − | 0.830677i | 0.198191 | − | 0.0492051i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.85766i | − | 0.286738i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.6518 | 0.861868 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.88500 | + | 7.59251i | 0.110501 | + | 0.445081i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 16.2764i | − | 0.950879i | −0.879748 | − | 0.475440i | \(-0.842289\pi\) | ||
0.879748 | − | 0.475440i | \(-0.157711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2114i | 0.827422i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.78951 | − | 8.76171i | 0.568045 | − | 0.508406i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.22240 | 0.0706934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.40594 | −0.369232 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9479 | − | 3.21458i | 0.743837 | − | 0.184673i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 11.2815i | − | 0.645974i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.07309 | −0.118318 | −0.0591589 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591589 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.44256 | − | 0.358145i | 0.0820642 | − | 0.0203742i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.0659 | 1.25124 | 0.625622 | − | 0.780126i | \(-0.284845\pi\) | ||||
0.625622 | + | 0.780126i | \(0.284845\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5417i | 0.765424i | 0.923868 | + | 0.382712i | \(0.125010\pi\) | ||||
−0.923868 | + | 0.382712i | \(0.874990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.40618 | − | 6.43698i | −0.191916 | − | 0.362683i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.4476i | 1.14845i | 0.818696 | + | 0.574227i | \(0.194697\pi\) | ||||
−0.818696 | + | 0.574227i | \(0.805303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.34813i | − | 0.187459i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.08185 | + | 12.4132i | 0.172012 | + | 0.692840i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.05004i | − | 0.169709i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.420456i | − | 0.0233227i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.64783 | + | 14.6929i | 0.201725 | + | 0.812522i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.33478 | 0.349248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5476i | 1.34926i | 0.738156 | + | 0.674630i | \(0.235697\pi\) | ||||
−0.738156 | + | 0.674630i | \(0.764303\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.0588 | − | 13.2601i | 1.37322 | − | 0.726648i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.34375 | + | 3.61516i | 0.401232 | + | 0.197517i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0872i | 0.549484i | 0.961518 | + | 0.274742i | \(0.0885924\pi\) | ||||
−0.961518 | + | 0.274742i | \(0.911408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.8340 | + | 3.68285i | −0.805673 | + | 0.200025i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.0633i | − | 0.653262i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.6802i | − | 1.06263i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.21336 | − | 4.88726i | −0.0653254 | − | 0.263121i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.82450 | 0.205310 | 0.102655 | − | 0.994717i | \(-0.467266\pi\) | ||||
0.102655 | + | 0.994717i | \(0.467266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.49170 | 0.186907 | 0.0934533 | − | 0.995624i | \(-0.470209\pi\) | ||||
0.0934533 | + | 0.995624i | \(0.470209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45703 | + | 1.62795i | 0.0777706 | + | 0.0868935i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.7386 | 1.63605 | 0.818026 | − | 0.575182i | \(-0.195069\pi\) | ||||
0.818026 | + | 0.575182i | \(0.195069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.60277i | 0.191215i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.25332 | + | 1.55252i | −0.330961 | + | 0.0821678i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.84544i | − | 0.466845i | −0.972375 | − | 0.233422i | \(-0.925008\pi\) | ||
0.972375 | − | 0.233422i | \(-0.0749924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0384 | −0.791495 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.74500 | − | 1.92286i | 0.406507 | − | 0.100924i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.92733 | −0.100881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.7003i | − | 0.558551i | −0.960211 | − | 0.279275i | \(-0.909906\pi\) | ||
0.960211 | − | 0.279275i | \(-0.0900942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.30609 | − | 2.80776i | 0.276224 | − | 0.146166i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.33764i | − | 0.173282i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.8227i | − | 0.715713i | −0.933777 | − | 0.357857i | \(-0.883508\pi\) | ||
0.933777 | − | 0.357857i | \(-0.116492\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.68102 | + | 0.417348i | −0.0868074 | + | 0.0215517i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.556778 | 0.0286755 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5521i | 0.798859i | 0.916764 | + | 0.399429i | \(0.130792\pi\) | ||||
−0.916764 | + | 0.399429i | \(0.869208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.5849 | + | 4.86236i | −1.00336 | + | 0.249106i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.2968 | 0.934920 | 0.467460 | − | 0.884014i | \(-0.345169\pi\) | ||||
0.467460 | + | 0.884014i | \(0.345169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.13774i | 0.312808i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.70268 | − | 6.99731i | −0.188218 | − | 0.355693i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 0.443282i | − | 0.0224753i | −0.999937 | − | 0.0112376i | \(-0.996423\pi\) | ||
0.999937 | − | 0.0112376i | \(-0.00357713\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.45517 | −0.225308 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.90123 | + | 11.6857i | 0.146348 | + | 0.589468i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 7.44491i | − | 0.374594i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8994 | −0.547023 | −0.273512 | − | 0.961869i | \(-0.588185\pi\) | ||||
−0.273512 | + | 0.961869i | \(0.588185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.01651 | − | 8.12221i | −0.100952 | − | 0.406619i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4840 | −1.27261 | −0.636304 | − | 0.771438i | \(-0.719538\pi\) | ||||
−0.636304 | + | 0.771438i | \(0.719538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00606 | 0.0999291 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.06241 | − | 7.44124i | 0.251553 | − | 0.369758i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.8939 | −1.18438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5766i | 0.522979i | 0.965206 | + | 0.261489i | \(0.0842137\pi\) | ||||
−0.965206 | + | 0.261489i | \(0.915786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.8601 | + | 6.42030i | −1.27558 | + | 0.316690i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.4989 | 1.69758 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.4573i | − | 0.660592i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.66760 | + | 22.8283i | 0.277544 | + | 1.11791i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 39.1762i | − | 1.91389i | −0.290277 | − | 0.956943i | \(-0.593748\pi\) | ||
0.290277 | − | 0.956943i | \(-0.406252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.4203 | −1.43386 | −0.716929 | − | 0.697146i | \(-0.754453\pi\) | ||||
−0.716929 | + | 0.697146i | \(0.754453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.66155 | + | 6.91958i | 0.178031 | + | 0.336441i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.53240i | 0.0743321i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.3862 | −1.32531 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.443670 | − | 1.78704i | −0.0214206 | − | 0.0862792i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5435i | 1.08588i | 0.839771 | + | 0.542941i | \(0.182689\pi\) | ||||
−0.839771 | + | 0.542941i | \(0.817311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.4052i | 1.74952i | 0.484553 | + | 0.874762i | \(0.338982\pi\) | ||||
−0.484553 | + | 0.874762i | \(0.661018\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.552661 | − | 2.22604i | −0.0264981 | − | 0.106730i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.78666i | − | 0.276813i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.22089 | 0.249180 | 0.124590 | − | 0.992208i | \(-0.460239\pi\) | ||||
0.124590 | + | 0.992208i | \(0.460239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.93545 | − | 1.55332i | 0.139783 | − | 0.0739674i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.1367 | 1.09926 | 0.549628 | − | 0.835410i | \(-0.314770\pi\) | ||||
0.549628 | + | 0.835410i | \(0.314770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.46697i | − | 0.116945i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.12978 | − | 32.7456i | −0.384525 | − | 1.54881i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.5127i | − | 0.732091i | −0.930597 | − | 0.366045i | \(-0.880712\pi\) | ||
0.930597 | − | 0.366045i | \(-0.119288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.05942 | −0.238239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.7447 | + | 4.15723i | −0.786737 | + | 0.195324i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.02068 | −0.0478501 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0892 | 0.892955 | 0.446477 | − | 0.894795i | \(-0.352678\pi\) | ||||
0.446477 | + | 0.894795i | \(0.352678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.31030 | − | 5.93322i | −0.247863 | − | 0.276939i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.79717i | − | 0.363150i | −0.983377 | − | 0.181575i | \(-0.941880\pi\) | ||
0.983377 | − | 0.181575i | \(-0.0581195\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.4365i | − | 0.624449i | −0.950008 | − | 0.312224i | \(-0.898926\pi\) | ||
0.950008 | − | 0.312224i | \(-0.101074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.99123 | − | 8.02040i | −0.0923411 | − | 0.371937i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.4705i | 0.762163i | 0.924542 | + | 0.381081i | \(0.124448\pi\) | ||||
−0.924542 | + | 0.381081i | \(0.875552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.77596 | − | 17.8273i | 0.405236 | − | 0.823187i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.4449 | + | 3.58625i | −0.665586 | + | 0.165246i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.67202i | 0.306780i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.99037 | −0.0913246 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.64576 | − | 1.92918i | 0.166928 | − | 0.0883311i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 13.6228i | − | 0.622443i | −0.950337 | − | 0.311221i | \(-0.899262\pi\) | ||
0.950337 | − | 0.311221i | \(-0.100738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.97344i | − | 0.181173i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.8640 | + | 2.94550i | −0.539833 | + | 0.134025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.51661i | − | 0.205089i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0846i | 1.54452i | 0.635305 | + | 0.772261i | \(0.280874\pi\) | ||||
−0.635305 | + | 0.772261i | \(0.719126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2946 | + | 4.29374i | −0.782089 | + | 0.194170i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 37.7437i | − | 1.70335i | −0.524070 | − | 0.851675i | \(-0.675587\pi\) | ||
0.524070 | − | 0.851675i | \(-0.324413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.02923 | −0.0913920 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.70434 | + | 3.54766i | −0.301338 | + | 0.159455i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.74589 | 0.392307 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.2910i | 1.75891i | 0.475986 | + | 0.879453i | \(0.342091\pi\) | ||||
−0.475986 | + | 0.879453i | \(0.657909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.301537 | − | 1.21455i | −0.0134717 | − | 0.0542621i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.34751 | 0.193846 | 0.0969230 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969230 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.70241 | −0.342753 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.5561 | + | 5.35174i | −0.957338 | + | 0.237679i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.7652i | 1.27499i | 0.770453 | + | 0.637497i | \(0.220030\pi\) | ||||
−0.770453 | + | 0.637497i | \(0.779970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.67868i | 0.206973i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.70645 | − | 6.89735i | 0.340248 | − | 0.304525i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.858145 | −0.0378144 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.59790i | − | 0.290176i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.83170 | + | 15.4336i | 0.168193 | + | 0.677458i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.51176 | −0.285286 | −0.142643 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142643 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.0962 | −1.31602 | −0.658008 | − | 0.753011i | \(-0.728601\pi\) | ||||
−0.658008 | + | 0.753011i | \(0.728601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.01313 | + | 4.08074i | 0.0442166 | + | 0.178098i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.31130 | −0.318485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5475 | 0.632499 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.9406 | + | 37.6836i | 0.865348 | + | 1.63533i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.841358i | − | 0.0364433i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.38436i | − | 0.319254i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.3888 | − | 2.82751i | 0.491464 | − | 0.122016i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.79899 | −0.120561 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.8023i | − | 1.66824i | −0.551583 | − | 0.834120i | \(-0.685976\pi\) | ||
0.551583 | − | 0.834120i | \(-0.314024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7017 | − | 3.15346i | 0.545082 | − | 0.135328i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.74050i | − | 0.374402i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.7743i | − | 0.931003i | −0.885047 | − | 0.465502i | \(-0.845874\pi\) | ||
0.885047 | − | 0.465502i | \(-0.154126\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.8294 | − | 29.9144i | −0.675584 | − | 1.27671i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.63570i | − | 0.112284i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.0728 | −0.768535 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.8861 | + | 3.94406i | −0.674329 | + | 0.167416i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.9112i | − | 1.35212i | −0.736847 | − | 0.676060i | \(-0.763686\pi\) | ||
0.736847 | − | 0.676060i | \(-0.236314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.10952 | −0.0469279 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.61700 | + | 6.51305i | 0.0682698 | + | 0.274981i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.9040 | 1.47103 | 0.735513 | − | 0.677510i | \(-0.236941\pi\) | ||||
0.735513 | + | 0.677510i | \(0.236941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.82442 | 0.371246 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0639 | − | 12.2892i | −0.758614 | − | 0.516099i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.51890i | 0.315209i | 0.987502 | + | 0.157604i | \(0.0503771\pi\) | ||||
−0.987502 | + | 0.157604i | \(0.949623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.31988 | −0.222630 | −0.111315 | − | 0.993785i | \(-0.535506\pi\) | ||||
−0.111315 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.0084 | − | 4.96751i | 0.835864 | − | 0.207521i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.90732i | 0.121244i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.43497i | − | 0.267891i | −0.990989 | − | 0.133946i | \(-0.957235\pi\) | ||
0.990989 | − | 0.133946i | \(-0.0427648\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.2820 | + | 5.53197i | −0.926009 | + | 0.229901i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.6682 | −1.35530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.47627 | −0.143973 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.589958 | − | 1.11490i | −0.0243918 | − | 0.0460954i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.508051 | 0.0209695 | 0.0104848 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104848 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.49638i | − | 0.391291i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.38957 | + | 2.33115i | −0.386235 | + | 0.0958909i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.25928 | 0.257038 | 0.128519 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128519 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.71996 | 0.152503 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.0636 | + | 6.71911i | −1.10764 | + | 0.274995i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9213 | 0.773105 | 0.386552 | − | 0.922267i | \(-0.373666\pi\) | ||||
0.386552 | + | 0.922267i | \(0.373666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9349 | −0.731581 | −0.365791 | − | 0.930697i | \(-0.619201\pi\) | ||||
−0.365791 | + | 0.930697i | \(0.619201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.5456 | − | 0.718183i | 0.999572 | − | 0.0292467i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.60733 | −0.187314 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7897 | −1.20913 | −0.604564 | − | 0.796556i | \(-0.706653\pi\) | ||||
−0.604564 | + | 0.796556i | \(0.706653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.40381 | + | 1.34161i | −0.218974 | + | 0.0543647i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.09720 | 0.0443880 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.42785 | −0.340398 | −0.170199 | − | 0.985410i | \(-0.554441\pi\) | ||||
−0.170199 | + | 0.985410i | \(0.554441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.36381 | + | 0.835137i | −0.135642 | + | 0.0336760i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1035i | 1.57425i | 0.616795 | + | 0.787124i | \(0.288431\pi\) | ||||
−0.616795 | + | 0.787124i | \(0.711569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0283 | −0.885391 | −0.442696 | − | 0.896672i | \(-0.645978\pi\) | ||||
−0.442696 | + | 0.896672i | \(0.645978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0749 | − | 11.2568i | −0.404292 | − | 0.451718i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.98867 | −0.239931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.45957 | + | 2.10026i | −0.337843 | + | 0.0838764i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.4816i | 0.577420i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4627i | 0.615561i | 0.951457 | + | 0.307781i | \(0.0995863\pi\) | ||||
−0.951457 | + | 0.307781i | \(0.900414\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.0286 | − | 9.19313i | 1.47176 | − | 0.365394i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6506 | 0.462341 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.465458i | − | 0.0184421i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.05518 | + | 9.55326i | 0.199980 | + | 0.377921i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2575 | −0.523638 | −0.261819 | − | 0.965117i | \(-0.584322\pi\) | ||||
−0.261819 | + | 0.965117i | \(0.584322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.05881 | −0.317809 | −0.158904 | − | 0.987294i | \(-0.550796\pi\) | ||||
−0.158904 | + | 0.987294i | \(0.550796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.10132 | + | 4.43597i | 0.0433645 | + | 0.174666i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.4596 | −1.15818 | −0.579088 | − | 0.815265i | \(-0.696591\pi\) | ||||
−0.579088 | + | 0.815265i | \(0.696591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 35.9318i | − | 1.41045i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.4699 | + | 4.83380i | −0.763084 | + | 0.189452i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.97875 | 0.0774344 | 0.0387172 | − | 0.999250i | \(-0.487673\pi\) | ||||
0.0387172 | + | 0.999250i | \(0.487673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.95159i | − | 0.271621i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.11060 | + | 2.70431i | −0.199383 | + | 0.105505i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 14.6853i | − | 0.572056i | −0.958221 | − | 0.286028i | \(-0.907665\pi\) | ||
0.958221 | − | 0.286028i | \(-0.0923351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5712i | 1.18908i | 0.804065 | + | 0.594542i | \(0.202666\pi\) | ||||
−0.804065 | + | 0.594542i | \(0.797334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.08309 | + | 0.268899i | −0.0420637 | + | 0.0104432i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.83172i | 0.187366i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.84994 | −0.149070 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.51906 | − | 0.873680i | 0.136055 | − | 0.0337784i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.5237i | 1.10115i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2408i | 0.780225i | 0.920767 | + | 0.390112i | \(0.127564\pi\) | ||||
−0.920767 | + | 0.390112i | \(0.872436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.87186 | + | 3.46536i | −0.149028 | + | 0.133382i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6761 | 0.448750 | 0.224375 | − | 0.974503i | \(-0.427966\pi\) | ||||
0.224375 | + | 0.974503i | \(0.427966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9643 | −0.420771 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0133716 | + | 0.0538589i | 0.000512401 | + | 0.00206388i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.5015 | 0.631412 | 0.315706 | − | 0.948857i | \(-0.397759\pi\) | ||||
0.315706 | + | 0.948857i | \(0.397759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3836 | 0.587776 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.54878 | − | 6.23827i | −0.0590896 | − | 0.238005i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.578088i | − | 0.0220234i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.5174 | −0.590309 | −0.295154 | − | 0.955450i | \(-0.595371\pi\) | ||||
−0.295154 | + | 0.955450i | \(0.595371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.61209 | + | 16.2751i | 0.327146 | + | 0.618239i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 13.5800i | − | 0.515121i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.06641i | 0.116149i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.3717 | + | 7.54041i | −1.14876 | + | 0.285204i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7546 | −1.23712 | −0.618562 | − | 0.785736i | \(-0.712284\pi\) | ||||
−0.618562 | + | 0.785736i | \(0.712284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.8096 | −0.709419 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.08909 | − | 4.38669i | −0.0410174 | − | 0.165212i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.6979i | 0.703209i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6450 | 0.399780 | 0.199890 | − | 0.979818i | \(-0.435941\pi\) | ||||
0.199890 | + | 0.979818i | \(0.435941\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4462 | − | 19.7412i | −0.391764 | − | 0.740354i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8713 | −0.519484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.06307i | 0.0397566i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.36673 | + | 2.32549i | −0.349807 | + | 0.0868469i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 23.7738i | − | 0.886613i | −0.896370 | − | 0.443307i | \(-0.853805\pi\) | ||
0.896370 | − | 0.443307i | \(-0.146195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.08319i | 0.0775819i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.8987 | + | 8.91260i | −1.33509 | + | 0.331463i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32422i | 0.0491804i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.3179i | − | 0.456847i | −0.973562 | − | 0.228424i | \(-0.926643\pi\) | ||
0.973562 | − | 0.228424i | \(-0.0733571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.98262 | − | 26.8348i | 0.110467 | − | 0.993880i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.04378 | 0.149564 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.5859i | 1.60988i | 0.593355 | + | 0.804941i | \(0.297803\pi\) | ||||
−0.593355 | + | 0.804941i | \(0.702197\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.86094 | + | 0.462016i | −0.0686417 | + | 0.0170417i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.5677 | − | 9.14047i | −0.683952 | − | 0.336694i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.9495i | − | 0.623498i | −0.950165 | − | 0.311749i | \(-0.899085\pi\) | ||
0.950165 | − | 0.311749i | \(-0.100915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.349264 | − | 1.40679i | −0.0128305 | − | 0.0516796i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 19.6974i | − | 0.722629i | −0.932444 | − | 0.361315i | \(-0.882328\pi\) | ||
0.932444 | − | 0.361315i | \(-0.117672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.4796i | 0.713679i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.8824 | − | 35.6839i | −0.690872 | − | 1.30561i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.9259 | −0.654997 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.2894 | −0.849841 | −0.424920 | − | 0.905231i | \(-0.639698\pi\) | ||||
−0.424920 | + | 0.905231i | \(0.639698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.9452 | + | 4.20700i | −0.617518 | + | 0.153312i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.96107 | 0.362521 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.9943i | − | 0.435942i | −0.975955 | − | 0.217971i | \(-0.930056\pi\) | ||
0.975955 | − | 0.217971i | \(-0.0699438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.06784 | + | 12.3568i | 0.111356 | + | 0.448524i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.6678i | 1.43796i | 0.695033 | + | 0.718978i | \(0.255390\pi\) | ||||
−0.695033 | + | 0.718978i | \(0.744610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.2180 | −0.768142 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.15016 | + | 4.06337i | 0.0777393 | + | 0.146911i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.97529 | 0.215755 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.5436i | − | 0.452333i | −0.974089 | − | 0.226167i | \(-0.927381\pi\) | ||
0.974089 | − | 0.226167i | \(-0.0726194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.07911 | + | 12.4022i | 0.110891 | + | 0.446655i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.4721i | − | 0.772296i | −0.922437 | − | 0.386148i | \(-0.873805\pi\) | ||
0.922437 | − | 0.386148i | \(-0.126195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.77115i | 0.171385i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.57439 | + | 38.5643i | 0.343479 | + | 1.38349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.98285 | −0.142701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.10915i | − | 0.325951i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.58890 | − | 5.12720i | −0.163994 | − | 0.183231i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.59295 | 0.306695 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.5376i | 1.30242i | 0.758896 | + | 0.651212i | \(0.225739\pi\) | ||||
−0.758896 | + | 0.651212i | \(0.774261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.64785 | + | 14.6930i | 0.129867 | + | 0.523085i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 21.4217i | − | 0.761667i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.74336 | −0.168442 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.31124 | + | 0.573813i | −0.0819712 | + | 0.0203511i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.9887i | 1.02683i | 0.858140 | + | 0.513416i | \(0.171620\pi\) | ||||
−0.858140 | + | 0.513416i | \(0.828380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.99886 | −0.141469 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.46149 | − | 6.54151i | −0.122306 | − | 0.231133i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.87302 | 0.171965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.05766 | 0.248750 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.505817 | + | 2.03736i | 0.0178056 | + | 0.0717185i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.8104 | 0.766812 | 0.383406 | − | 0.923580i | \(-0.374751\pi\) | ||||
0.383406 | + | 0.923580i | \(0.374751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.8274i | − | 0.977153i | −0.872521 | − | 0.488576i | \(-0.837516\pi\) | ||
0.872521 | − | 0.488576i | \(-0.162484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.188809 | + | 0.760498i | 0.00662184 | + | 0.0266718i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.2882 | 0.360379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.25231i | 0.183755i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.70647 | + | 1.43215i | −0.0945717 | + | 0.0500434i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4600i | 1.55166i | 0.630940 | + | 0.775832i | \(0.282670\pi\) | ||||
−0.630940 | + | 0.775832i | \(0.717330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.01482 | 0.105090 | 0.0525450 | − | 0.998619i | \(-0.483267\pi\) | ||||
0.0525450 | + | 0.998619i | \(0.483267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.25024 | − | 1.05521i | 0.147974 | − | 0.0367377i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.3860i | 0.535024i | 0.963554 | + | 0.267512i | \(0.0862016\pi\) | ||||
−0.963554 | + | 0.267512i | \(0.913798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3596 | −0.394534 | −0.197267 | − | 0.980350i | \(-0.563207\pi\) | ||||
−0.197267 | + | 0.980350i | \(0.563207\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.1111 | + | 5.73781i | −0.801715 | + | 0.199042i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.69641i | 0.0587771i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.722509i | 0.0250034i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5337 | − | 18.4733i | −0.571490 | − | 0.638529i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 23.8599i | − | 0.823737i | −0.911243 | − | 0.411868i | \(-0.864876\pi\) | ||
0.911243 | − | 0.411868i | \(-0.135124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2464 | 0.939532 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.6569 | − | 4.88024i | 0.677021 | − | 0.168084i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.8232 | 0.441132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1845i | 0.384303i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.5356 | + | 5.59494i | −0.773421 | + | 0.192018i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.4751i | 0.941834i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.360566 | −0.0123456 | −0.00617278 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617278 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.27776 | + | 2.79277i | −0.180495 | + | 0.0955106i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.81250 | 0.266870 | 0.133435 | − | 0.991058i | \(-0.457399\pi\) | ||||
0.133435 | + | 0.991058i | \(0.457399\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.6578 | −0.807194 | −0.403597 | − | 0.914937i | \(-0.632240\pi\) | ||||
−0.403597 | + | 0.914937i | \(0.632240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.02733 | + | 8.16581i | 0.0690913 | + | 0.278290i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 5.00090i | − | 0.170233i | −0.996371 | − | 0.0851163i | \(-0.972874\pi\) | ||
0.996371 | − | 0.0851163i | \(-0.0271262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 9.18108i | − | 0.312166i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.6299 | + | 6.11488i | −0.836474 | + | 0.207672i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.8235i | 0.638544i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.52002 | − | 3.08773i | 0.0515038 | − | 0.104624i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.33743 | − | 11.9764i | −0.214490 | − | 0.405341i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.42754i | − | 0.0820660i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.40316 | −0.148684 | −0.0743421 | − | 0.997233i | \(-0.523686\pi\) | ||||
−0.0743421 | + | 0.997233i | \(0.523686\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.79293 | + | 27.3610i | 0.229120 | + | 0.922863i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.2289i | − | 0.782601i | −0.920263 | − | 0.391300i | \(-0.872025\pi\) | ||
0.920263 | − | 0.391300i | \(-0.127975\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0604i | 0.776045i | 0.921650 | + | 0.388023i | \(0.126842\pi\) | ||||
−0.921650 | + | 0.388023i | \(0.873158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.93111 | − | 23.8897i | −0.199372 | − | 0.803043i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.0386i | − | 0.504945i | −0.967604 | − | 0.252473i | \(-0.918756\pi\) | ||
0.967604 | − | 0.252473i | \(-0.0812438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28.2824i | − | 0.948561i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.7997 | + | 18.8142i | −0.428805 | + | 0.630300i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.19397i | − | 0.173810i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.77495 | −0.226462 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.05488 | + | 0.510167i | −0.0686105 | + | 0.0170340i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.31807 | −0.210719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.10690i | 0.0701910i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.7685 | − | 2.67351i | 0.358353 | − | 0.0889687i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.55595 | −0.251168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.42199 | 0.146830 | 0.0734149 | − | 0.997301i | \(-0.476610\pi\) | ||||
0.0734149 | + | 0.997301i | \(0.476610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.4240 | + | 10.8075i | −0.677423 | + | 0.358464i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1786i | 0.403496i | 0.979437 | + | 0.201748i | \(0.0646623\pi\) | ||||
−0.979437 | + | 0.201748i | \(0.935338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.0251i | 1.12606i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.70829 | + | 18.9643i | 0.155651 | + | 0.626941i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8753 | −0.557271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.8418i | 1.87504i | 0.347933 | + | 0.937519i | \(0.386884\pi\) | ||||
−0.347933 | + | 0.937519i | \(0.613116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.48491 | − | 0.865201i | 0.114832 | − | 0.0285093i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.51481 | 0.0498605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.45031 | 0.310724 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.27549 | + | 1.20410i | −0.0747370 | + | 0.0395477i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.21303 | −0.138225 | −0.0691124 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691124 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.20340 | −0.0722136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.0932 | + | 9.20916i | −1.21438 | + | 0.301494i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.87447i | − | 0.126709i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1901i | 0.332896i | 0.986050 | + | 0.166448i | \(0.0532298\pi\) | ||||
−0.986050 | + | 0.166448i | \(0.946770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.65161 | − | 22.7639i | −0.184433 | − | 0.742872i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3534 | 0.402710 | 0.201355 | − | 0.979518i | \(-0.435466\pi\) | ||||
0.201355 | + | 0.979518i | \(0.435466\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.81772i | 0.189451i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.41230 | + | 9.39911i | 0.273652 | + | 0.305753i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45.1800i | − | 1.46815i | −0.679067 | − | 0.734076i | \(-0.737615\pi\) | ||
0.679067 | − | 0.734076i | \(-0.262385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.810359i | 0.0263054i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.53377 | − | 34.3728i | −0.276727 | − | 1.11462i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.16355i | 0.167264i | 0.996497 | + | 0.0836320i | \(0.0266520\pi\) | ||||
−0.996497 | + | 0.0836320i | \(0.973348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9026 | −0.385158 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.39733 | + | 5.62826i | 0.0451694 | + | 0.181936i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 37.3443i | − | 1.20591i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.23608 | 0.265680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3613 | − | 19.5807i | −0.333887 | − | 0.630979i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.2551 | 0.426696 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9992 | −0.353709 | −0.176854 | − | 0.984237i | \(-0.556592\pi\) | ||||
−0.176854 | + | 0.984237i | \(0.556592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.27293 | + | 5.12717i | 0.0408923 | + | 0.164708i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 9.50261i | − | 0.304953i | −0.988307 | − | 0.152477i | \(-0.951275\pi\) | ||
0.988307 | − | 0.152477i | \(-0.0487249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.9662 | −1.05685 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.175476 | + | 0.706795i | 0.00561975 | + | 0.0226356i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 42.2127i | − | 1.35051i | −0.737586 | − | 0.675253i | \(-0.764035\pi\) | ||
0.737586 | − | 0.675253i | \(-0.235965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.23742i | 0.199349i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2641 | − | 23.1767i | −0.391563 | − | 0.739975i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4727 | 0.621084 | 0.310542 | − | 0.950560i | \(-0.399490\pi\) | ||||
0.310542 | + | 0.950560i | \(0.399490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.58564 | 0.177973 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6489 | + | 2.64381i | −0.338958 | + | 0.0841533i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.67201 | 0.243956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.0521i | 0.954635i | 0.878731 | + | 0.477318i | \(0.158391\pi\) | ||||
−0.878731 | + | 0.477318i | \(0.841609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.2449 | − | 41.2650i | −0.325112 | − | 1.30951i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0996 | 0.510390 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.3064 | −1.52988 | −0.764939 | − | 0.644103i | \(-0.777231\pi\) | ||||
−0.764939 | + | 0.644103i | \(0.777231\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.5903 | + | 32.7487i | −1.15767 | + | 1.03612i |
(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 | 4020.2.f.b.401.4 | yes | 46 | |
3.2 | odd | 2 | 4020.2.f.a.401.44 | yes | 46 | ||
67.66 | odd | 2 | 4020.2.f.a.401.43 | ✓ | 46 | ||
201.200 | even | 2 | inner | 4020.2.f.b.401.3 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.f.a.401.43 | ✓ | 46 | 67.66 | odd | 2 | ||
4020.2.f.a.401.44 | yes | 46 | 3.2 | odd | 2 | ||
4020.2.f.b.401.3 | yes | 46 | 201.200 | even | 2 | inner | |
4020.2.f.b.401.4 | yes | 46 | 1.1 | even | 1 | trivial |