Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1569,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.l (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.15 | ||
Character | \(\chi\) | \(=\) | 2240.1569 |
Dual form | 2240.2.l.c.1569.16 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.09381 | 0.631512 | 0.315756 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315756 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20510 | + | 0.370875i | −0.986149 | + | 0.165860i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.80358 | −0.601193 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.07385i | − | 0.323779i | −0.986809 | − | 0.161889i | \(-0.948241\pi\) | ||
0.986809 | − | 0.161889i | \(-0.0517588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.77197 | 1.04616 | 0.523078 | − | 0.852285i | \(-0.324784\pi\) | ||||
0.523078 | + | 0.852285i | \(0.324784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41196 | + | 0.405667i | −0.622765 | + | 0.104743i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.08737i | − | 1.23387i | −0.787015 | − | 0.616934i | \(-0.788375\pi\) | ||
0.787015 | − | 0.616934i | \(-0.211625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.279623i | − | 0.0641499i | −0.999485 | − | 0.0320750i | \(-0.989788\pi\) | ||
0.999485 | − | 0.0320750i | \(-0.0102115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.09381i | 0.238689i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.13057i | 0.861283i | 0.902523 | + | 0.430642i | \(0.141713\pi\) | ||||
−0.902523 | + | 0.430642i | \(0.858287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.72490 | − | 1.63563i | 0.944981 | − | 0.327126i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.25421 | −1.01117 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.87012i | 0.904359i | 0.891927 | + | 0.452180i | \(0.149353\pi\) | ||||
−0.891927 | + | 0.452180i | \(0.850647\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1243 | 1.81838 | 0.909191 | − | 0.416378i | \(-0.136701\pi\) | ||||
0.909191 | + | 0.416378i | \(0.136701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.17459i | − | 0.204470i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.370875 | − | 2.20510i | −0.0626894 | − | 0.372729i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.19379 | −0.360657 | −0.180329 | − | 0.983606i | \(-0.557716\pi\) | ||||
−0.180329 | + | 0.983606i | \(0.557716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.12582 | 0.660660 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0451 | 1.72495 | 0.862476 | − | 0.506097i | \(-0.168912\pi\) | ||||
0.862476 | + | 0.506097i | \(0.168912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86758 | 0.284804 | 0.142402 | − | 0.989809i | \(-0.454517\pi\) | ||||
0.142402 | + | 0.989809i | \(0.454517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.97706 | − | 0.668903i | 0.592866 | − | 0.0997141i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.78644i | 0.698174i | 0.937090 | + | 0.349087i | \(0.113508\pi\) | ||||
−0.937090 | + | 0.349087i | \(0.886492\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 5.56462i | − | 0.779202i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.30210 | −0.728299 | −0.364150 | − | 0.931340i | \(-0.618640\pi\) | ||||
−0.364150 | + | 0.931340i | \(0.618640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.398266 | + | 2.36795i | 0.0537021 | + | 0.319294i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.305855i | − | 0.0405114i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.22153i | − | 0.679785i | −0.940464 | − | 0.339893i | \(-0.889609\pi\) | ||
0.940464 | − | 0.339893i | \(-0.110391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5860i | 1.86755i | 0.357863 | + | 0.933774i | \(0.383505\pi\) | ||||
−0.357863 | + | 0.933774i | \(0.616495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.80358i | − | 0.227229i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.31755 | + | 1.39893i | −1.03167 | + | 0.173516i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.74025 | 1.18996 | 0.594980 | − | 0.803740i | \(-0.297160\pi\) | ||||
0.594980 | + | 0.803740i | \(0.297160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.51806i | 0.543911i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.18240 | 0.496360 | 0.248180 | − | 0.968714i | \(-0.420168\pi\) | ||||
0.248180 | + | 0.968714i | \(0.420168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4860i | 1.46138i | 0.682709 | + | 0.730690i | \(0.260802\pi\) | ||||
−0.682709 | + | 0.730690i | \(0.739198\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.16815 | − | 1.78907i | 0.596767 | − | 0.206584i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07385 | 0.122377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4280 | 1.39826 | 0.699131 | − | 0.714994i | \(-0.253571\pi\) | ||||
0.699131 | + | 0.714994i | \(0.253571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.336372 | −0.0373747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.13284 | 0.234110 | 0.117055 | − | 0.993125i | \(-0.462655\pi\) | ||||
0.117055 | + | 0.993125i | \(0.462655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88678 | + | 11.2181i | 0.204650 | + | 1.21678i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.32699i | 0.571114i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.20284 | 0.869500 | 0.434750 | − | 0.900551i | \(-0.356837\pi\) | ||||
0.434750 | + | 0.900551i | \(0.356837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.77197i | 0.395410i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.0741 | 1.14833 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.103705 | + | 0.616596i | 0.0106399 | + | 0.0632614i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.92547i | 1.00778i | 0.863768 | + | 0.503889i | \(0.168098\pi\) | ||||
−0.863768 | + | 0.503889i | \(0.831902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.93678i | 0.194654i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.68390i | − | 0.366562i | −0.983061 | − | 0.183281i | \(-0.941328\pi\) | ||
0.983061 | − | 0.183281i | \(-0.0586718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.1850i | − | 1.69329i | −0.532157 | − | 0.846646i | \(-0.678618\pi\) | ||
0.532157 | − | 0.846646i | \(-0.321382\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.405667 | − | 2.41196i | −0.0395891 | − | 0.235383i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.64783 | −0.932691 | −0.466346 | − | 0.884603i | \(-0.654430\pi\) | ||||
−0.466346 | + | 0.884603i | \(0.654430\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.25100i | − | 0.119824i | −0.998204 | − | 0.0599121i | \(-0.980918\pi\) | ||
0.998204 | − | 0.0599121i | \(-0.0190820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.39959 | −0.227759 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9327i | 1.21661i | 0.793704 | + | 0.608305i | \(0.208150\pi\) | ||||
−0.793704 | + | 0.608305i | \(0.791850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.53193 | − | 9.10831i | −0.142853 | − | 0.849354i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.80304 | −0.628941 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08737 | 0.466358 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.84684 | 0.895167 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.0812 | 1.08933 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.81225 | + | 5.35908i | −0.877635 | + | 0.479330i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.66938i | − | 0.769283i | −0.923066 | − | 0.384641i | \(-0.874325\pi\) | ||
0.923066 | − | 0.384641i | \(-0.125675\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.04278 | 0.179857 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7893i | 1.37952i | 0.724040 | + | 0.689758i | \(0.242283\pi\) | ||||
−0.724040 | + | 0.689758i | \(0.757717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.279623 | 0.0242464 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.5860 | − | 1.94865i | 0.997167 | − | 0.167714i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.1779i | − | 1.21130i | −0.795730 | − | 0.605652i | \(-0.792913\pi\) | ||
0.795730 | − | 0.605652i | \(-0.207087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.8789i | − | 1.60129i | −0.599141 | − | 0.800644i | \(-0.704491\pi\) | ||
0.599141 | − | 0.800644i | \(-0.295509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.23546i | 0.440905i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.05054i | − | 0.338723i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.80621 | − | 10.7391i | −0.149997 | − | 0.891833i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.09381 | −0.0902160 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.60627i | 0.459283i | 0.973275 | + | 0.229642i | \(0.0737554\pi\) | ||||
−0.973275 | + | 0.229642i | \(0.926245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8279 | 1.04392 | 0.521959 | − | 0.852971i | \(-0.325201\pi\) | ||||
0.521959 | + | 0.852971i | \(0.325201\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.17547i | 0.741792i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.3251 | + | 3.75486i | −1.79320 | + | 0.301598i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.49231 | −0.438334 | −0.219167 | − | 0.975687i | \(-0.570334\pi\) | ||||
−0.219167 | + | 0.975687i | \(0.570334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.79949 | −0.459930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.13057 | −0.325535 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.7379 | 1.38934 | 0.694670 | − | 0.719329i | \(-0.255550\pi\) | ||||
0.694670 | + | 0.719329i | \(0.255550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.435627 | + | 2.59009i | 0.0339135 | + | 0.201638i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.70432i | 0.286649i | 0.989676 | + | 0.143325i | \(0.0457793\pi\) | ||||
−0.989676 | + | 0.143325i | \(0.954221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.22774 | 0.0944413 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.504322i | 0.0385665i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.57366 | −0.651843 | −0.325922 | − | 0.945397i | \(-0.605675\pi\) | ||||
−0.325922 | + | 0.945397i | \(0.605675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63563 | + | 4.72490i | 0.123642 | + | 0.357169i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.71136i | − | 0.429292i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.5839i | − | 1.31428i | −0.753768 | − | 0.657141i | \(-0.771766\pi\) | ||
0.753768 | − | 0.657141i | \(-0.228234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.02458i | − | 0.373474i | −0.982410 | − | 0.186737i | \(-0.940209\pi\) | ||
0.982410 | − | 0.186737i | \(-0.0597913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.9543i | 1.17938i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.83752 | − | 0.813623i | 0.355662 | − | 0.0598188i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.46309 | −0.399501 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5.25421i | − | 0.382187i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.983348 | 0.0711525 | 0.0355763 | − | 0.999367i | \(-0.488673\pi\) | ||||
0.0355763 | + | 0.999367i | \(0.488673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.55980i | − | 0.472185i | −0.971731 | − | 0.236092i | \(-0.924133\pi\) | ||
0.971731 | − | 0.236092i | \(-0.0758668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.09783 | + | 1.53016i | −0.651509 | + | 0.109577i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.24696 | −0.373831 | −0.186915 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186915 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.69606 | −0.474671 | −0.237336 | − | 0.971428i | \(-0.576274\pi\) | ||||
−0.237336 | + | 0.971428i | \(0.576274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6540 | 0.751474 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.87012 | −0.341816 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.3555 | + | 4.09635i | −1.70106 | + | 0.286101i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.44981i | − | 0.517797i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.300274 | −0.0207704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.43877i | 0.374420i | 0.982320 | + | 0.187210i | \(0.0599445\pi\) | ||||
−0.982320 | + | 0.187210i | \(0.940056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.57476 | 0.313457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.11820 | + | 0.692641i | −0.280859 | + | 0.0472377i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1243i | 0.687284i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6574i | 0.922879i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.1894i | − | 1.29082i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.81776i | 0.121726i | 0.998146 | + | 0.0608630i | \(0.0193853\pi\) | ||||
−0.998146 | + | 0.0608630i | \(0.980615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.52173 | + | 2.94999i | −0.568115 | + | 0.196666i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2918 | −0.749463 | −0.374732 | − | 0.927133i | \(-0.622265\pi\) | ||||
−0.374732 | + | 0.927133i | \(0.622265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4723i | 1.08852i | 0.838916 | + | 0.544262i | \(0.183190\pi\) | ||||
−0.838916 | + | 0.544262i | \(0.816810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.17459 | 0.0772825 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.41351i | − | 0.289139i | −0.989495 | − | 0.144569i | \(-0.953820\pi\) | ||
0.989495 | − | 0.144569i | \(-0.0461797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.77517 | − | 10.5546i | −0.115800 | − | 0.688504i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5939 | 0.883019 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8480 | 0.766385 | 0.383192 | − | 0.923669i | \(-0.374825\pi\) | ||||
0.383192 | + | 0.923669i | \(0.374825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.85453 | −0.505955 | −0.252977 | − | 0.967472i | \(-0.581410\pi\) | ||||
−0.252977 | + | 0.967472i | \(0.581410\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3947 | 0.987570 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.20510 | − | 0.370875i | 0.140878 | − | 0.0236944i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.05473i | − | 0.0671108i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.33292 | 0.147843 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.3008i | − | 1.47073i | −0.677671 | − | 0.735365i | \(-0.737011\pi\) | ||
0.677671 | − | 0.735365i | \(-0.262989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.43563 | 0.278865 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.06378 | + | 12.2705i | 0.129239 | + | 0.768410i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.07004i | − | 0.129126i | −0.997914 | − | 0.0645629i | \(-0.979435\pi\) | ||
0.997914 | − | 0.0645629i | \(-0.0205653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.19379i | − | 0.136316i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 8.78365i | − | 0.543694i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 30.4778i | − | 1.87934i | −0.342084 | − | 0.939669i | \(-0.611133\pi\) | ||
0.342084 | − | 0.939669i | \(-0.388867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6916 | − | 1.96642i | 0.718212 | − | 0.120796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.97236 | 0.549099 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1810i | 1.35240i | 0.736718 | + | 0.676200i | \(0.236375\pi\) | ||||
−0.736718 | + | 0.676200i | \(0.763625\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.03998 | 0.245411 | 0.122706 | − | 0.992443i | \(-0.460843\pi\) | ||||
0.122706 | + | 0.992443i | \(0.460843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.12582i | 0.249706i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.75643 | − | 5.07385i | −0.105917 | − | 0.305965i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0433 | −0.963946 | −0.481973 | − | 0.876186i | \(-0.660080\pi\) | ||||
−0.481973 | + | 0.876186i | \(0.660080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.2600 | −1.09320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.48827 | 0.387058 | 0.193529 | − | 0.981095i | \(-0.438007\pi\) | ||||
0.193529 | + | 0.981095i | \(0.438007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.48606 | −0.445000 | −0.222500 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222500 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.113434 | + | 0.674439i | 0.00671925 | + | 0.0399503i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.0451i | 0.651971i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.88131 | −0.522430 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8566i | 0.636424i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.3728 | 1.13177 | 0.565885 | − | 0.824484i | \(-0.308535\pi\) | ||||
0.565885 | + | 0.824484i | \(0.308535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.93654 | + | 11.5140i | 0.112749 | + | 0.670370i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.64225i | 0.327396i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.5804i | 0.901036i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.86758i | 0.107646i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.02949i | − | 0.231488i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.40959 | − | 32.1636i | −0.309752 | − | 1.84168i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9673 | −1.19667 | −0.598335 | − | 0.801246i | \(-0.704171\pi\) | ||||
−0.598335 | + | 0.801246i | \(0.704171\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18.7972i | − | 1.06933i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9522 | −0.904566 | −0.452283 | − | 0.891875i | \(-0.649390\pi\) | ||||
−0.452283 | + | 0.891875i | \(0.649390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8486i | 0.613199i | 0.951839 | + | 0.306599i | \(0.0991912\pi\) | ||||
−0.951839 | + | 0.306599i | \(0.900809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.668903 | + | 3.97706i | 0.0376884 | + | 0.224082i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4714 | 0.588132 | 0.294066 | − | 0.955785i | \(-0.404991\pi\) | ||||
0.294066 | + | 0.955785i | \(0.404991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.22980 | 0.292812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.5529 | −0.589006 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.42255 | −0.0791525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8222 | − | 6.16955i | 0.988597 | − | 0.342225i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.36836i | − | 0.0756704i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.78644 | −0.263885 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.2958i | 1.55528i | 0.628710 | + | 0.777640i | \(0.283583\pi\) | ||||
−0.628710 | + | 0.777640i | \(0.716417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.95667 | 0.216824 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.4782 | + | 3.61242i | −1.17348 | + | 0.197367i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.5822i | − | 1.23013i | −0.788477 | − | 0.615064i | \(-0.789130\pi\) | ||
0.788477 | − | 0.615064i | \(-0.210870\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1460i | 0.768303i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.8720i | − | 0.588754i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.67564 | − | 9.96276i | −0.0902133 | − | 0.536377i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.5947 | 1.53505 | 0.767523 | − | 0.641022i | \(-0.221489\pi\) | ||||
0.767523 | + | 0.641022i | \(0.221489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.5209i | − | 0.830812i | −0.909636 | − | 0.415406i | \(-0.863639\pi\) | ||
0.909636 | − | 0.415406i | \(-0.136361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8187 | −1.05784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.7066i | 1.58112i | 0.612383 | + | 0.790561i | \(0.290211\pi\) | ||||
−0.612383 | + | 0.790561i | \(0.709789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.22261 | + | 1.55115i | −0.489485 | + | 0.0823265i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.56462 | 0.294511 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.4817 | −1.18654 | −0.593270 | − | 0.805003i | \(-0.702163\pi\) | ||||
−0.593270 | + | 0.805003i | \(0.702163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9218 | 0.995885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7706 | 0.565309 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.63076 | − | 27.5329i | −0.242385 | − | 1.44114i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8919i | 1.24715i | 0.781764 | + | 0.623574i | \(0.214320\pi\) | ||||
−0.781764 | + | 0.623574i | \(0.785680\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.9207 | −1.03703 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.30210i | − | 0.275271i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.52111 | 0.182316 | 0.0911581 | − | 0.995836i | \(-0.470943\pi\) | ||||
0.0911581 | + | 0.995836i | \(0.470943\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.7327 | + | 5.86181i | −0.554237 | + | 0.302703i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.3699i | 0.946100i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.35864i | 0.121155i | 0.998163 | + | 0.0605775i | \(0.0192942\pi\) | ||||
−0.998163 | + | 0.0605775i | \(0.980706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 9.48266i | − | 0.485811i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.63272i | − | 0.441111i | −0.975374 | − | 0.220556i | \(-0.929213\pi\) | ||
0.975374 | − | 0.220556i | \(-0.0707871\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.36795 | + | 0.398266i | −0.120682 | + | 0.0202975i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.36833 | −0.171222 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 16.3195i | − | 0.827430i | −0.910406 | − | 0.413715i | \(-0.864231\pi\) | ||
0.910406 | − | 0.413715i | \(-0.135769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0137 | 1.06271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.2705i | 0.871181i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.4050 | + | 4.60925i | −1.37889 | + | 0.231916i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.404753 | 0.0203139 | 0.0101570 | − | 0.999948i | \(-0.496767\pi\) | ||||
0.0101570 | + | 0.999948i | \(0.496767\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.305855 | 0.0153119 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.0436 | −1.25062 | −0.625308 | − | 0.780378i | \(-0.715027\pi\) | ||||
−0.625308 | + | 0.780378i | \(0.715027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.1886 | 1.90231 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.741733 | − | 0.124752i | 0.0368570 | − | 0.00619898i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.35581i | 0.116773i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8580 | 0.685236 | 0.342618 | − | 0.939475i | \(-0.388686\pi\) | ||||
0.342618 | + | 0.939475i | \(0.388686\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 15.5080i | − | 0.764952i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.22153 | 0.256935 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.70312 | + | 0.791018i | −0.230867 | + | 0.0388295i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 20.6499i | − | 1.01123i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.9313i | 1.31568i | 0.753158 | + | 0.657839i | \(0.228529\pi\) | ||||
−0.753158 | + | 0.657839i | \(0.771471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5126i | 1.68204i | 0.541002 | + | 0.841022i | \(0.318045\pi\) | ||||
−0.541002 | + | 0.841022i | \(0.681955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.63272i | − | 0.419737i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.32106 | − | 24.0373i | −0.403631 | − | 1.16598i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5860 | −0.705867 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 4.43052i | − | 0.213908i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0970 | −0.823532 | −0.411766 | − | 0.911290i | \(-0.635088\pi\) | ||||
−0.411766 | + | 0.911290i | \(0.635088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2904i | 1.26344i | 0.775197 | + | 0.631719i | \(0.217650\pi\) | ||||
−0.775197 | + | 0.631719i | \(0.782350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.97565 | − | 11.7465i | −0.0947252 | − | 0.563203i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.15500 | 0.0552513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.881339 | −0.0420640 | −0.0210320 | − | 0.999779i | \(-0.506695\pi\) | ||||
−0.0210320 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.80358 | 0.0858847 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.3910 | 1.82401 | 0.912005 | − | 0.410178i | \(-0.134534\pi\) | ||||
0.912005 | + | 0.410178i | \(0.134534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0881 | + | 3.04223i | −0.857456 | + | 0.144216i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.13219i | 0.290043i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −42.1553 | −1.98943 | −0.994716 | − | 0.102667i | \(-0.967262\pi\) | ||||
−0.994716 | + | 0.102667i | \(0.967262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.8608i | − | 0.558503i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.0313 | 0.659247 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.39893 | − | 8.31755i | −0.0655828 | − | 0.389933i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.6832i | − | 1.01430i | −0.861858 | − | 0.507149i | \(-0.830699\pi\) | ||
0.861858 | − | 0.507149i | \(-0.169301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.7301i | 1.24765i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.8367i | − | 1.57593i | −0.615718 | − | 0.787966i | \(-0.711134\pi\) | ||
0.615718 | − | 0.787966i | \(-0.288866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.1430i | − | 1.07555i | −0.843089 | − | 0.537773i | \(-0.819266\pi\) | ||
0.843089 | − | 0.537773i | \(-0.180734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.4195 | + | 4.10711i | −1.13243 | + | 0.190463i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0911 | 0.929706 | 0.464853 | − | 0.885388i | \(-0.346107\pi\) | ||||
0.464853 | + | 0.885388i | \(0.346107\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.74025i | 0.449763i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00755 | −0.276813 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.00551i | − | 0.0922135i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.457360 | − | 1.32119i | −0.0209851 | − | 0.0606204i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.56275 | 0.437848 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.3459 | −1.20378 | −0.601888 | − | 0.798580i | \(-0.705585\pi\) | ||||
−0.601888 | + | 0.798580i | \(0.705585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.27491 | −0.377303 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.51806 | −0.205579 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.68111 | − | 21.8866i | −0.167151 | − | 0.993820i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.00797075i | − | 0.000361189i | −1.00000 | 0.000180595i | \(-0.999943\pi\) | |||
1.00000 | 0.000180595i | \(-5.74850e-5\pi\) | ||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.4019 | 0.877385 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3750i | 0.874379i | 0.899369 | + | 0.437190i | \(0.144026\pi\) | ||||
−0.899369 | + | 0.437190i | \(0.855974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.7761 | 1.11586 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.718303 | − | 4.27078i | −0.0322853 | − | 0.191957i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.18240i | 0.187606i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.6514i | − | 0.924484i | −0.886754 | − | 0.462242i | \(-0.847045\pi\) | ||
0.886754 | − | 0.462242i | \(-0.152955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.05183i | 0.181022i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.6811i | 0.699184i | 0.936902 | + | 0.349592i | \(0.113680\pi\) | ||||
−0.936902 | + | 0.349592i | \(0.886320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.36627 | + | 8.12336i | 0.0607981 | + | 0.361485i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34291 | 0.0596408 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 28.3123i | − | 1.25492i | −0.778648 | − | 0.627461i | \(-0.784094\pi\) | ||
0.778648 | − | 0.627461i | \(-0.215906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4860 | −0.552350 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.46920i | 0.0648666i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.37351 | + | 37.8947i | 0.280850 | + | 1.66984i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.13994 | 0.226054 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.37796 | −0.411647 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.94766 | 0.392004 | 0.196002 | − | 0.980604i | \(-0.437204\pi\) | ||||
0.196002 | + | 0.980604i | \(0.437204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.7287 | 1.47485 | 0.737425 | − | 0.675429i | \(-0.236041\pi\) | ||||
0.737425 | + | 0.675429i | \(0.236041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.78907 | + | 5.16815i | 0.0780815 | + | 0.225557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 51.5062i | − | 2.24364i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.93839 | 0.258191 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.41743i | 0.408682i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.6617 | 1.80457 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.2744 | − | 3.57814i | 0.919773 | − | 0.154697i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 19.2335i | − | 0.829985i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.07385i | 0.0462541i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4226i | 1.35096i | 0.737378 | + | 0.675481i | \(0.236064\pi\) | ||||
−0.737378 | + | 0.675481i | \(0.763936\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.49594i | − | 0.235853i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.463966 | + | 2.75858i | 0.0198741 | + | 0.118165i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8319 | −1.48930 | −0.744652 | − | 0.667453i | \(-0.767385\pi\) | ||||
−0.744652 | + | 0.667453i | \(0.767385\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 26.3070i | − | 1.12276i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.36180 | 0.0580146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.4280i | 0.528493i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.29134 | − | 0.889950i | 0.224605 | − | 0.0377763i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.1339 | −1.27682 | −0.638408 | − | 0.769698i | \(-0.720407\pi\) | ||||
−0.638408 | + | 0.769698i | \(0.720407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.04447 | 0.297949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.97558 | −0.252289 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.7846 | −0.580951 | −0.290476 | − | 0.956882i | \(-0.593814\pi\) | ||||
−0.290476 | + | 0.956882i | \(0.593814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.79643 | − | 28.5179i | −0.201787 | − | 1.19976i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.336372i | − | 0.0141263i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.4658 | 1.06758 | 0.533791 | − | 0.845616i | \(-0.320767\pi\) | ||||
0.533791 | + | 0.845616i | \(0.320767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.8001i | − | 0.661213i | −0.943769 | − | 0.330606i | \(-0.892747\pi\) | ||
0.943769 | − | 0.330606i | \(-0.107253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.07560 | 0.0449337 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.75609 | + | 19.5165i | 0.281749 | + | 0.813896i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1131i | 0.754057i | 0.926202 | + | 0.377028i | \(0.123054\pi\) | ||||
−0.926202 | + | 0.377028i | \(0.876946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 7.17518i | − | 0.298190i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.13284i | 0.0884851i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.69368i | 0.235808i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0014 | − | 2.52308i | 0.620230 | − | 0.104316i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.8724 | −1.56316 | −0.781581 | − | 0.623804i | \(-0.785586\pi\) | ||||
−0.781581 | + | 0.623804i | \(0.785586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.83100i | − | 0.116649i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.73918 | −0.236078 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.1567i | − | 0.745604i | −0.927911 | − | 0.372802i | \(-0.878397\pi\) | ||
0.927911 | − | 0.372802i | \(-0.121603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2181 | + | 1.88678i | −0.459899 | + | 0.0773504i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.32422 | −0.299761 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.8947 | −0.894592 | −0.447296 | − | 0.894386i | \(-0.647613\pi\) | ||||
−0.447296 | + | 0.894386i | \(0.647613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.1613 | −1.18951 | −0.594757 | − | 0.803906i | \(-0.702752\pi\) | ||||
−0.594757 | + | 0.803906i | \(0.702752\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.5673 | −0.715395 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.7132 | + | 3.65195i | −0.882768 | + | 0.148473i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0842i | 1.13990i | 0.821679 | + | 0.569950i | \(0.193038\pi\) | ||||
−0.821679 | + | 0.569950i | \(0.806962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.32699 | −0.215861 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0543i | 0.730399i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1906 | −0.694321 | −0.347160 | − | 0.937806i | \(-0.612854\pi\) | ||||
−0.347160 | + | 0.937806i | \(0.612854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.6403 | + | 4.48063i | −1.07424 | + | 0.180676i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5274i | 0.584851i | 0.956288 | + | 0.292425i | \(0.0944623\pi\) | ||||
−0.956288 | + | 0.292425i | \(0.905538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.9968i | − | 0.522387i | −0.965287 | − | 0.261193i | \(-0.915884\pi\) | ||
0.965287 | − | 0.261193i | \(-0.0841160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 21.7029i | − | 0.870906i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.20284i | 0.328640i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6494 | − | 15.4564i | 0.785977 | − | 0.618256i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.328443 | −0.0131168 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1606i | 0.445003i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.6079 | −0.621341 | −0.310671 | − | 0.950518i | \(-0.600554\pi\) | ||||
−0.310671 | + | 0.950518i | \(0.600554\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.94898i | 0.236451i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.21526 | + | 19.1168i | 0.127594 | + | 0.758628i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.77197 | −0.149451 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.54329 | −0.298408 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6906 | −0.975222 | −0.487611 | − | 0.873061i | \(-0.662132\pi\) | ||||
−0.487611 | + | 0.873061i | \(0.662132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8495 | −0.979969 | −0.489984 | − | 0.871731i | \(-0.662998\pi\) | ||||
−0.489984 | + | 0.871731i | \(0.662998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.50453 | + | 0.757618i | −0.177366 | + | 0.0298312i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.76410i | − | 0.0693539i | −0.999399 | − | 0.0346770i | \(-0.988960\pi\) | ||
0.999399 | − | 0.0346770i | \(-0.0110402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.60716 | −0.220100 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0741i | 0.434028i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.2584 | −1.45803 | −0.729017 | − | 0.684496i | \(-0.760022\pi\) | ||||
−0.729017 | + | 0.684496i | \(0.760022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.85586 | − | 34.8169i | −0.228807 | − | 1.36041i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 22.5196i | − | 0.878571i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 35.5909i | − | 1.38642i | −0.720734 | − | 0.693212i | \(-0.756195\pi\) | ||
0.720734 | − | 0.693212i | \(-0.243805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23.9986i | − | 0.933438i | −0.884406 | − | 0.466719i | \(-0.845436\pi\) | ||
0.884406 | − | 0.466719i | \(-0.154564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 20.9896i | − | 0.815167i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.616596 | + | 0.103705i | −0.0239106 | + | 0.00402152i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.1164 | −0.778910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.98828i | 0.0768714i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.6632 | 0.604673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6776i | 1.10544i | 0.833367 | + | 0.552720i | \(0.186410\pi\) | ||||
−0.833367 | + | 0.552720i | \(0.813590\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.8256 | + | 8.59395i | −0.955538 | + | 0.330781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.2371 | −1.27741 | −0.638703 | − | 0.769454i | \(-0.720529\pi\) | ||||
−0.638703 | + | 0.769454i | \(0.720529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.92547 | −0.380905 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.3511 | −0.473295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.6848 | 1.40370 | 0.701852 | − | 0.712322i | \(-0.252357\pi\) | ||||
0.701852 | + | 0.712322i | \(0.252357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.25825 | + | 31.2637i | 0.200907 | + | 1.19453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.0176i | 0.687415i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.9993 | −0.761914 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.0123i | − | 0.913471i | −0.889602 | − | 0.456736i | \(-0.849019\pi\) | ||
0.889602 | − | 0.456736i | \(-0.150981\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.93678 | −0.0735721 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.00172 | + | 41.6298i | 0.265590 | + | 1.57911i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 56.1904i | − | 2.12836i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 4.82754i | − | 0.182595i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.8234i | − | 0.937566i | −0.883313 | − | 0.468783i | \(-0.844693\pi\) | ||
0.883313 | − | 0.468783i | \(-0.155307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.613435i | 0.0231361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.94170 | − | 11.5447i | −0.0731288 | − | 0.434798i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.68390 | 0.138547 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.61054i | − | 0.248264i | −0.992266 | − | 0.124132i | \(-0.960385\pi\) | ||
0.992266 | − | 0.124132i | \(-0.0396146\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.4149 | −0.840625 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.8192i | 1.56614i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.50225 | + | 8.93183i | 0.0561808 | + | 0.334032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9595 | 0.483981 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.9038 | 0.966050 | 0.483025 | − | 0.875607i | \(-0.339538\pi\) | ||||
0.483025 | + | 0.875607i | \(0.339538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1850 | 0.640004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.59137 | −0.319516 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.96573 | + | 23.0109i | 0.295840 | + | 0.854602i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.35460i | 0.272767i | 0.990656 | + | 0.136383i | \(0.0435479\pi\) | ||||
−0.990656 | + | 0.136383i | \(0.956452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.8480 | 0.661037 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.50109i | − | 0.351410i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.12528 | −0.300114 | −0.150057 | − | 0.988677i | \(-0.547946\pi\) | ||||
−0.150057 | + | 0.988677i | \(0.547946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.41196 | − | 0.405667i | 0.0889664 | − | 0.0149633i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.4596i | − | 0.385284i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.7064i | 1.23991i | 0.784637 | + | 0.619955i | \(0.212849\pi\) | ||||
−0.784637 | + | 0.619955i | \(0.787151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.15367i | − | 0.0423813i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.46383i | − | 0.0537028i | −0.999639 | − | 0.0268514i | \(-0.991452\pi\) | ||
0.999639 | − | 0.0268514i | \(-0.00854809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.07923 | − | 12.3624i | −0.0761769 | − | 0.452922i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.84674 | −0.140745 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 9.64783i | − | 0.352524i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5655 | −0.750444 | −0.375222 | − | 0.926935i | \(-0.622434\pi\) | ||||
−0.375222 | + | 0.926935i | \(0.622434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 25.4866i | − | 0.928784i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.2867 | + | 4.75754i | −1.02946 | + | 0.173145i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6397 | −0.750162 | −0.375081 | − | 0.926992i | \(-0.622385\pi\) | ||||
−0.375081 | + | 0.926992i | \(0.622385\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.85174 | 0.176107 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.18178 | 0.0428396 | 0.0214198 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214198 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.25100 | 0.0452893 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.40295 | − | 20.2328i | −0.123034 | − | 0.731518i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 19.6954i | − | 0.711161i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.15898 | −0.222098 | −0.111049 | − | 0.993815i | \(-0.535421\pi\) | ||||
−0.111049 | + | 0.993815i | \(0.535421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.26424i | − | 0.0815445i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.3637 | 1.16404 | 0.582022 | − | 0.813173i | \(-0.302262\pi\) | ||||
0.582022 | + | 0.813173i | \(0.302262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.8365 | − | 16.5597i | 1.71834 | − | 0.594841i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.39959i | − | 0.0860849i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.08846i | − | 0.110656i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.49129i | − | 0.160711i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 25.5886i | − | 0.914463i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1111 | − | 2.03696i | 0.432263 | − | 0.0727023i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1116 | −0.503024 | −0.251512 | − | 0.967854i | \(-0.580928\pi\) | ||||
−0.251512 | + | 0.967854i | \(0.580928\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 33.3369i | − | 1.18682i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9327 | −0.459835 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.0180i | 1.95375i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7884 | − | 2.15089i | 0.453559 | − | 0.0762842i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.3283 | 1.46392 | 0.731961 | − | 0.681347i | \(-0.238605\pi\) | ||||
0.731961 | + | 0.681347i | \(0.238605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.3504 | 0.861455 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7945 | −0.522737 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.4082 | 0.473164 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.10831 | − | 1.53193i | 0.321026 | − | 0.0539933i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.2618i | 0.854057i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.8798 | 0.980201 | 0.490100 | − | 0.871666i | \(-0.336960\pi\) | ||||
0.490100 | + | 0.871666i | \(0.336960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.8990i | − | 1.01478i | −0.861716 | − | 0.507391i | \(-0.830610\pi\) | ||
0.861716 | − | 0.507391i | \(-0.169390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.41897 | 0.154980 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.1138 | + | 6.57855i | −1.37010 | + | 0.230437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.522219i | − | 0.0182701i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 6.80304i | − | 0.237717i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2968i | 0.638564i | 0.947660 | + | 0.319282i | \(0.103442\pi\) | ||||
−0.947660 | + | 0.319282i | \(0.896558\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 56.5497i | − | 1.97120i | −0.169102 | − | 0.985599i | \(-0.554087\pi\) | ||
0.169102 | − | 0.985599i | \(-0.445913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.92120 | − | 5.54984i | −0.0668876 | − | 0.193220i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.93726 | −0.102138 | −0.0510692 | − | 0.998695i | \(-0.516263\pi\) | ||||
−0.0510692 | + | 0.998695i | \(0.516263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.5110i | 1.47647i | 0.674544 | + | 0.738234i | \(0.264340\pi\) | ||||
−0.674544 | + | 0.738234i | \(0.735660\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5483 | −0.608743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.08737i | 0.176267i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.37384 | − | 8.16839i | −0.0475438 | − | 0.282679i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −53.1953 | −1.83870 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.39641 | 0.0827331 | 0.0413666 | − | 0.999144i | \(-0.486829\pi\) | ||||
0.0413666 | + | 0.999144i | \(0.486829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.28191 | 0.182135 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.09694 | 0.244431 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.70728 | + | 0.455337i | −0.0931332 | + | 0.0156641i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.84684i | 0.338341i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.18833 | −0.281023 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 9.06161i | − | 0.310628i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.83044 | 0.131152 | 0.0655759 | − | 0.997848i | \(-0.479112\pi\) | ||||
0.0655759 | + | 0.997848i | \(0.479112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.187041 | − | 1.11208i | −0.00639665 | − | 0.0380323i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 55.4188i | 1.89307i | 0.322602 | + | 0.946535i | \(0.395442\pi\) | ||||
−0.322602 | + | 0.946535i | \(0.604558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.13603i | − | 0.0387607i | −0.999812 | − | 0.0193803i | \(-0.993831\pi\) | ||
0.999812 | − | 0.0193803i | \(-0.00616934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0812i | 0.411727i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45.8120i | − | 1.55946i | −0.626117 | − | 0.779729i | \(-0.715357\pi\) | ||
0.626117 | − | 0.779729i | \(-0.284643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9057 | − | 3.17976i | 0.642815 | − | 0.108115i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.71448 | −0.329921 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.3459i | − | 0.452728i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.7399 | 1.24488 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 17.9014i | − | 0.605869i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.35908 | − | 9.81225i | −0.181170 | − | 0.331715i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.4124 | 1.66854 | 0.834269 | − | 0.551358i | \(-0.185890\pi\) | ||||
0.834269 | + | 0.551358i | \(0.185890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.1902 | 0.714726 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.6973 | −1.67435 | −0.837173 | − | 0.546939i | \(-0.815793\pi\) | ||||
−0.837173 | + | 0.546939i | \(0.815793\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.8249 | 1.54213 | 0.771066 | − | 0.636756i | \(-0.219724\pi\) | ||||
0.771066 | + | 0.636756i | \(0.219724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.11820 | + | 12.5941i | 0.0712026 | + | 0.423346i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 31.4562i | − | 1.05619i | −0.849184 | − | 0.528097i | \(-0.822906\pi\) | ||
0.849184 | − | 0.528097i | \(-0.177094\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.66938 | 0.290762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.361214i | 0.0121011i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.33840 | 0.0447878 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.52143 | + | 38.7742i | 0.217987 | + | 1.29608i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.0420i | 0.569015i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.3067i | 1.64447i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.9737i | 0.898625i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.04278i | 0.0679796i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.86349 | + | 11.0797i | 0.0619446 | + | 0.368301i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.2056 | 1.33501 | 0.667503 | − | 0.744607i | \(-0.267363\pi\) | ||||
0.667503 | + | 0.744607i | \(0.267363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.64420i | 0.220374i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.19808 | 0.139089 | 0.0695444 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695444 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.29036i | − | 0.0757998i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.91707 | − | 35.1809i | −0.195612 | − | 1.16304i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.7893 | −0.521408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.1340 | 1.15896 | 0.579482 | − | 0.814985i | \(-0.303255\pi\) | ||||
0.579482 | + | 0.814985i | \(0.303255\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.9343 | −0.755711 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.7759 | 0.519270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3655 | + | 3.58824i | −0.340814 | + | 0.117980i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.9946i | 1.01799i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.36911 | 0.241773 | 0.120886 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120886 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.279623i | 0.00916427i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.4487 | −0.571244 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0466 | − | 2.02612i | 0.393967 | − | 0.0662613i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.99362i | 0.293809i | 0.989151 | + | 0.146904i | \(0.0469310\pi\) | ||||
−0.989151 | + | 0.146904i | \(0.953069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.8663i | 0.387242i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.4187i | 1.35021i | 0.737722 | + | 0.675105i | \(0.235902\pi\) | ||||
−0.737722 | + | 0.675105i | \(0.764098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.6225i | 1.48567i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.94865 | + | 11.5860i | 0.0633897 | + | 0.376894i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.8177 | 0.936449 | 0.468225 | − | 0.883609i | \(-0.344894\pi\) | ||||
0.468225 | + | 0.883609i | \(0.344894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.0969i | 1.52883i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.4537 | 0.371412 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.39709i | − | 0.239615i | −0.992797 | − | 0.119808i | \(-0.961772\pi\) | ||
0.992797 | − | 0.119808i | \(-0.0382278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.16838 | + | 0.364699i | −0.0701670 | + | 0.0118014i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.72041 | 0.184915 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.1779 | 0.457830 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.5020 | 2.30652 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.4006 | 0.560727 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.43287 | + | 14.4650i | 0.0783168 | + | 0.465645i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8031i | 0.765457i | 0.923861 | + | 0.382728i | \(0.125015\pi\) | ||||
−0.923861 | + | 0.382728i | \(0.874985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.55600 | −0.0499858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5025i | 0.946781i | 0.880853 | + | 0.473390i | \(0.156970\pi\) | ||||
−0.880853 | + | 0.473390i | \(0.843030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.8789 | 0.605230 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.4941 | − | 6.74832i | 0.624311 | − | 0.216119i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.48739i | 0.207550i | 0.994601 | + | 0.103775i | \(0.0330922\pi\) | ||||
−0.994601 | + | 0.103775i | \(0.966908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.80865i | − | 0.281526i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.25628i | 0.0720374i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.7636i | 0.470885i | 0.971888 | + | 0.235442i | \(0.0756539\pi\) | ||||
−0.971888 | + | 0.235442i | \(0.924346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5701 | − | 1.94597i | 0.368653 | − | 0.0620037i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.23546 | −0.166647 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.71419i | 0.245297i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.7476 | 1.64382 | 0.821909 | − | 0.569619i | \(-0.192909\pi\) | ||||
0.821909 | + | 0.569619i | \(0.192909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.9503i | 0.982178i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.7655 | − | 2.48340i | 0.468097 | − | 0.0787292i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.8514 | −1.73716 | −0.868580 | − | 0.495549i | \(-0.834967\pi\) | ||||
−0.868580 | + | 0.495549i | \(0.834967\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.5266 | 0.364687 |
(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 | 2240.2.l.c.1569.15 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.l.c.1569.10 | yes | 24 | |
5.4 | even | 2 | 2240.2.l.d.1569.10 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.l.d.1569.16 | yes | 24 | ||
8.5 | even | 2 | 2240.2.l.d.1569.9 | yes | 24 | ||
20.19 | odd | 2 | 2240.2.l.d.1569.15 | yes | 24 | ||
40.19 | odd | 2 | inner | 2240.2.l.c.1569.9 | ✓ | 24 | |
40.29 | even | 2 | inner | 2240.2.l.c.1569.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.l.c.1569.9 | ✓ | 24 | 40.19 | odd | 2 | inner | |
2240.2.l.c.1569.10 | yes | 24 | 4.3 | odd | 2 | inner | |
2240.2.l.c.1569.15 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.l.c.1569.16 | yes | 24 | 40.29 | even | 2 | inner | |
2240.2.l.d.1569.9 | yes | 24 | 8.5 | even | 2 | ||
2240.2.l.d.1569.10 | yes | 24 | 5.4 | even | 2 | ||
2240.2.l.d.1569.15 | yes | 24 | 20.19 | odd | 2 | ||
2240.2.l.d.1569.16 | yes | 24 | 8.3 | odd | 2 |