Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,6,Mod(505,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.505");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(109.702532752\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 17616 x^{16} - 456301 x^{15} + 216301789 x^{14} - 6076762674 x^{13} + \cdots + 55\!\cdots\!41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.6 | ||
Root | \(19.0963 - 31.3437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.577 |
Dual form | 684.6.k.f.505.6 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.0963 | + | 31.3437i | 0.323717 | + | 0.560694i | 0.981252 | − | 0.192730i | \(-0.0617342\pi\) |
−0.657535 | + | 0.753424i | \(0.728401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −208.885 | −1.61125 | −0.805624 | − | 0.592427i | \(-0.798170\pi\) | ||||
−0.805624 | + | 0.592427i | \(0.798170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 204.444 | 0.509440 | 0.254720 | − | 0.967015i | \(-0.418017\pi\) | ||||
0.254720 | + | 0.967015i | \(0.418017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −146.736 | + | 254.155i | −0.240813 | + | 0.417100i | −0.960946 | − | 0.276736i | \(-0.910747\pi\) |
0.720133 | + | 0.693836i | \(0.244081\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 850.109 | + | 1472.43i | 0.713432 | + | 1.23570i | 0.963561 | + | 0.267488i | \(0.0861935\pi\) |
−0.250130 | + | 0.968212i | \(0.580473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1329.36 | + | 841.960i | 0.844810 | + | 0.535066i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1768.22 | − | 3062.65i | 0.696975 | − | 1.20720i | −0.272535 | − | 0.962146i | \(-0.587862\pi\) |
0.969510 | − | 0.245051i | \(-0.0788046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 907.547 | − | 1571.92i | 0.290415 | − | 0.503013i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3204.96 | − | 5551.15i | 0.707664 | − | 1.22571i | −0.258058 | − | 0.966130i | \(-0.583082\pi\) |
0.965722 | − | 0.259580i | \(-0.0835842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2731.24 | −0.510452 | −0.255226 | − | 0.966881i | \(-0.582150\pi\) | ||||
−0.255226 | + | 0.966881i | \(0.582150\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3780.05 | − | 6547.24i | −0.521588 | − | 0.903417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5427.82 | −0.651811 | −0.325905 | − | 0.945402i | \(-0.605669\pi\) | ||||
−0.325905 | + | 0.945402i | \(0.605669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3692.75 | + | 6396.03i | 0.343076 | + | 0.594225i | 0.985002 | − | 0.172541i | \(-0.0551979\pi\) |
−0.641926 | + | 0.766766i | \(0.721865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7870.13 | + | 13631.5i | 0.649099 | + | 1.12427i | 0.983339 | + | 0.181784i | \(0.0581871\pi\) |
−0.334240 | + | 0.942488i | \(0.608480\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9723.97 | + | 16842.4i | −0.642094 | + | 1.11214i | 0.342870 | + | 0.939383i | \(0.388601\pi\) |
−0.984964 | + | 0.172757i | \(0.944732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26826.0 | 1.59612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4290.51 | − | 7431.39i | 0.209807 | − | 0.363396i | −0.741847 | − | 0.670569i | \(-0.766050\pi\) |
0.951654 | + | 0.307173i | \(0.0993832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3699.69 | + | 6408.05i | 0.164914 | + | 0.285640i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13969.1 | − | 24195.1i | −0.522441 | − | 0.904894i | −0.999659 | − | 0.0261092i | \(-0.991688\pi\) |
0.477218 | − | 0.878785i | \(-0.341645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15366.2 | + | 26615.0i | −0.528739 | + | 0.915803i | 0.470700 | + | 0.882294i | \(0.344002\pi\) |
−0.999438 | + | 0.0335090i | \(0.989332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10621.5 | −0.311820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24126.9 | + | 41788.9i | −0.656619 | + | 1.13730i | 0.324866 | + | 0.945760i | \(0.394681\pi\) |
−0.981485 | + | 0.191538i | \(0.938652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3430.92 | + | 5942.53i | 0.0807727 | + | 0.139902i | 0.903582 | − | 0.428415i | \(-0.140928\pi\) |
−0.822809 | + | 0.568317i | \(0.807595\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 19300.4 | + | 33429.3i | 0.423897 | + | 0.734210i | 0.996317 | − | 0.0857501i | \(-0.0273287\pi\) |
−0.572420 | + | 0.819961i | \(0.693995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42705.4 | −0.820834 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −32155.8 | − | 55695.5i | −0.579684 | − | 1.00404i | −0.995515 | − | 0.0946008i | \(-0.969843\pi\) |
0.415831 | − | 0.909442i | \(-0.363491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −71525.2 | −1.13963 | −0.569815 | − | 0.821773i | \(-0.692985\pi\) | ||||
−0.569815 | + | 0.821773i | \(0.692985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30767.7 | + | 53291.2i | −0.461900 | + | 0.800034i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 23256.6 | − | 40281.7i | 0.311223 | − | 0.539054i | −0.667404 | − | 0.744696i | \(-0.732595\pi\) |
0.978627 | + | 0.205641i | \(0.0659280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30651.0 | − | 53089.2i | 0.388009 | − | 0.672051i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2333.64 | + | 56903.5i | −0.0265292 | + | 0.646890i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −45206.3 | − | 78299.6i | −0.487831 | − | 0.844949i | 0.512071 | − | 0.858943i | \(-0.328879\pi\) |
−0.999902 | + | 0.0139945i | \(0.995545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −73036.4 | + | 126503.i | −0.712420 | + | 1.23395i | 0.251527 | + | 0.967850i | \(0.419067\pi\) |
−0.963946 | + | 0.266097i | \(0.914266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −85248.6 | −0.791761 | −0.395880 | − | 0.918302i | \(-0.629561\pi\) | ||||
−0.395880 | + | 0.918302i | \(0.629561\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 28226.4 | 0.238339 | 0.119170 | − | 0.992874i | \(-0.461977\pi\) | ||||
0.119170 | + | 0.992874i | \(0.461977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 109018. | + | 188825.i | 0.878888 | + | 1.52228i | 0.852563 | + | 0.522625i | \(0.175047\pi\) |
0.0263250 | + | 0.999653i | \(0.491620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 174546. | 1.28592 | 0.642958 | − | 0.765901i | \(-0.277707\pi\) | ||||
0.642958 | + | 0.765901i | \(0.277707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 127993. | 0.902490 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −177575. | − | 307569.i | −1.14952 | − | 1.99102i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119254. | −0.740471 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 178795. | 1.02348 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −71846.8 | + | 124442.i | −0.395274 | + | 0.684634i | −0.993136 | − | 0.116965i | \(-0.962684\pi\) |
0.597862 | + | 0.801599i | \(0.296017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2867.13 | − | 4966.01i | −0.0145972 | − | 0.0252830i | 0.858635 | − | 0.512588i | \(-0.171313\pi\) |
−0.873232 | + | 0.487305i | \(0.837980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −277684. | − | 175873.i | −1.36120 | − | 0.862125i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −150187. | + | 260131.i | −0.683645 | + | 1.18411i | 0.290216 | + | 0.956961i | \(0.406273\pi\) |
−0.973861 | + | 0.227146i | \(0.927061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 218624. | − | 378668.i | 0.959757 | − | 1.66235i | 0.236670 | − | 0.971590i | \(-0.423944\pi\) |
0.723087 | − | 0.690757i | \(-0.242723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29999.4 | + | 51960.5i | −0.122680 | + | 0.212487i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 231992. | 0.916331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4540.46 | − | 7864.31i | −0.0167546 | − | 0.0290198i | 0.857527 | − | 0.514440i | \(-0.172000\pi\) |
−0.874281 | + | 0.485420i | \(0.838667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 43328.1 | 0.154642 | 0.0773209 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773209 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −49425.3 | − | 85607.2i | −0.165242 | − | 0.286208i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −50402.1 | − | 87299.0i | −0.163192 | − | 0.282657i | 0.772820 | − | 0.634626i | \(-0.218846\pi\) |
−0.936012 | + | 0.351968i | \(0.885512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −369355. | + | 639742.i | −1.12300 | + | 1.94509i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −315707. | −0.930712 | −0.465356 | − | 0.885124i | \(-0.654074\pi\) | ||||
−0.465356 | + | 0.885124i | \(0.654074\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −280911. | + | 486551.i | −0.779430 | + | 1.35001i | 0.152841 | + | 0.988251i | \(0.451158\pi\) |
−0.932271 | + | 0.361761i | \(0.882176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142583. | + | 246962.i | 0.384019 | + | 0.665140i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 323128. | + | 559674.i | 0.820842 | + | 1.42174i | 0.905056 | + | 0.425292i | \(0.139829\pi\) |
−0.0842143 | + | 0.996448i | \(0.526838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −189573. | + | 328350.i | −0.467930 | + | 0.810479i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −391686. | −0.913704 | −0.456852 | − | 0.889543i | \(-0.651023\pi\) | ||||
−0.456852 | + | 0.889543i | \(0.651023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −356595. | + | 617641.i | −0.809057 | + | 1.40133i | 0.104461 | + | 0.994529i | \(0.466688\pi\) |
−0.913518 | + | 0.406798i | \(0.866645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −98223.6 | − | 170128.i | −0.211002 | − | 0.365466i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 173800. | + | 301030.i | 0.363451 | + | 0.629515i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −73696.8 | −0.146172 | −0.0730862 | − | 0.997326i | \(-0.523285\pi\) | ||||
−0.0730862 | + | 0.997326i | \(0.523285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −281706. | − | 487929.i | −0.544381 | − | 0.942896i | −0.998646 | − | 0.0520289i | \(-0.983431\pi\) |
0.454264 | − | 0.890867i | \(-0.349902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −227957. | −0.418491 | −0.209246 | − | 0.977863i | \(-0.567101\pi\) | ||||
−0.209246 | + | 0.977863i | \(0.567101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −305231. | + | 528676.i | −0.546382 | + | 0.946361i | 0.452137 | + | 0.891949i | \(0.350662\pi\) |
−0.998519 | + | 0.0544126i | \(0.982671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −669468. | + | 1.15955e6i | −1.14022 | + | 1.97492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −133650. | + | 231489.i | −0.222119 | + | 0.384721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 271780. | + | 172134.i | 0.430380 | + | 0.272584i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −340640. | − | 590006.i | −0.526732 | − | 0.912327i | −0.999515 | − | 0.0311480i | \(-0.990084\pi\) |
0.472782 | − | 0.881179i | \(-0.343250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −284841. | + | 493359.i | −0.420248 | + | 0.727891i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 570515. | 0.822466 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −498968. | −0.687214 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −464769. | − | 805003.i | −0.625856 | − | 1.08402i | −0.988375 | − | 0.152038i | \(-0.951416\pi\) |
0.362518 | − | 0.931977i | \(-0.381917\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 836852. | 1.07791 | 0.538957 | − | 0.842333i | \(-0.318819\pi\) | ||||
0.538957 | + | 0.842333i | \(0.318819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −43953.2 | −0.0553862 | −0.0276931 | − | 0.999616i | \(-0.508816\pi\) | ||||
−0.0276931 | + | 0.999616i | \(0.508816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19649.6 | − | 34034.0i | −0.0237117 | − | 0.0410699i | 0.853926 | − | 0.520394i | \(-0.174215\pi\) |
−0.877638 | + | 0.479324i | \(0.840882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −703872. | −0.831427 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.14239e6 | −1.29365 | −0.646827 | − | 0.762637i | \(-0.723904\pi\) | ||||
−0.646827 | + | 0.762637i | \(0.723904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −142528. | + | 246866.i | −0.158073 | + | 0.273790i | −0.934174 | − | 0.356819i | \(-0.883861\pi\) |
0.776101 | + | 0.630609i | \(0.217195\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 485452. | + | 840827.i | 0.516691 | + | 0.894935i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −409054. | + | 214317.i | −0.426617 | + | 0.223519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 787154. | − | 1.36339e6i | 0.788634 | − | 1.36595i | −0.138169 | − | 0.990409i | \(-0.544122\pi\) |
0.926804 | − | 0.375546i | \(-0.122545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 361503. | − | 626141.i | 0.355067 | − | 0.614994i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −172908. | + | 299486.i | −0.163299 | + | 0.282842i | −0.936050 | − | 0.351867i | \(-0.885547\pi\) |
0.772751 | + | 0.634709i | \(0.218880\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13379e6 | 1.05023 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −494023. | − | 855673.i | −0.440411 | − | 0.762814i | 0.557309 | − | 0.830305i | \(-0.311834\pi\) |
−0.997720 | + | 0.0674913i | \(0.978501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 310570. | 0.271672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −418483. | − | 724833.i | −0.352612 | − | 0.610741i | 0.634094 | − | 0.773256i | \(-0.281373\pi\) |
−0.986706 | + | 0.162514i | \(0.948040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.04254e6 | + | 1.80574e6i | 0.862325 | + | 1.49359i | 0.869679 | + | 0.493618i | \(0.164326\pi\) |
−0.00735345 | + | 0.999973i | \(0.502341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 185543. | − | 321369.i | 0.147949 | − | 0.256255i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −654742. | −0.512709 | −0.256355 | − | 0.966583i | \(-0.582521\pi\) | ||||
−0.256355 | + | 0.966583i | \(0.582521\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −432664. | + | 749397.i | −0.326878 | + | 0.566169i | −0.981891 | − | 0.189449i | \(-0.939330\pi\) |
0.655013 | + | 0.755618i | \(0.272663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 840551. | + | 1.45588e6i | 0.623876 | + | 1.08058i | 0.988757 | + | 0.149530i | \(0.0477761\pi\) |
−0.364882 | + | 0.931054i | \(0.618891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −771360. | − | 1.33604e6i | −0.552780 | − | 0.957444i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −735443. | + | 1.27382e6i | −0.517970 | + | 0.897150i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −495850. | −0.337428 | −0.168714 | − | 0.985665i | \(-0.553961\pi\) | ||||
−0.168714 | + | 0.985665i | \(0.553961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 505577. | − | 875685.i | 0.338246 | − | 0.585859i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 518925. | + | 898805.i | 0.335681 | + | 0.581416i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.64395e6 | − | 2.84741e6i | −1.04586 | − | 1.81148i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.11228e6 | −0.684647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.22956e6 | + | 2.12967e6i | 0.744569 | + | 1.28963i | 0.950396 | + | 0.311043i | \(0.100678\pi\) |
−0.205826 | + | 0.978589i | \(0.565988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.82000e6 | −1.06702 | −0.533508 | − | 0.845795i | \(-0.679127\pi\) | ||||
−0.533508 | + | 0.845795i | \(0.679127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −847350. | + | 1.46765e6i | −0.488880 | + | 0.846765i | −0.999918 | − | 0.0127931i | \(-0.995928\pi\) |
0.511038 | + | 0.859558i | \(0.329261\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 785090. | − | 1.35982e6i | 0.438805 | − | 0.760033i | −0.558793 | − | 0.829307i | \(-0.688735\pi\) |
0.997598 | + | 0.0692749i | \(0.0220686\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 655235. | − | 1.13490e6i | 0.360512 | − | 0.624426i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −109627. | + | 2.67315e6i | −0.0584671 | + | 1.42567i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 266340. | + | 461315.i | 0.139871 | + | 0.242264i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.03119e6 | − | 3.51813e6i | 1.03457 | − | 1.79193i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.47267e6 | −0.738816 | −0.369408 | − | 0.929267i | \(-0.620440\pi\) | ||||
−0.369408 | + | 0.929267i | \(0.620440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.74643e6 | −0.850235 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.04852e6 | − | 1.81609e6i | −0.502922 | − | 0.871087i | −0.999994 | − | 0.00337788i | \(-0.998925\pi\) |
0.497072 | − | 0.867709i | \(-0.334409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −558386. | −0.260045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.09282e6 | −0.960498 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.08983e6 | + | 1.88764e6i | 0.485887 | + | 0.841582i | 0.999868 | − | 0.0162199i | \(-0.00516317\pi\) |
−0.513981 | + | 0.857802i | \(0.671830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80723e6 | 0.794238 | 0.397119 | − | 0.917767i | \(-0.370010\pi\) | ||||
0.397119 | + | 0.917767i | \(0.370010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.11807e6 | 0.904696 | 0.452348 | − | 0.891842i | \(-0.350586\pi\) | ||||
0.452348 | + | 0.891842i | \(0.350586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −124174. | + | 215076.i | −0.0522950 | + | 0.0905775i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.04610e6 | + | 1.81190e6i | 0.428388 | + | 0.741990i | 0.996730 | − | 0.0808022i | \(-0.0257482\pi\) |
−0.568342 | + | 0.822793i | \(0.692415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.05830e6 | + | 2.23854e6i | 0.427408 | + | 0.904059i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −698534. | + | 1.20990e6i | −0.274445 | + | 0.475352i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.45084e6 | + | 2.51293e6i | −0.562282 | + | 0.973901i | 0.435015 | + | 0.900423i | \(0.356743\pi\) |
−0.997297 | + | 0.0734776i | \(0.976590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −896224. | + | 1.55231e6i | −0.338051 | + | 0.585521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.15657e6 | −1.17474 | −0.587372 | − | 0.809317i | \(-0.699837\pi\) | ||||
−0.587372 | + | 0.809317i | \(0.699837\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 940567. | + | 1.62911e6i | 0.340829 | + | 0.590333i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.95334e6 | 1.41373 | 0.706864 | − | 0.707350i | \(-0.250109\pi\) | ||||
0.706864 | + | 0.707350i | \(0.250109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.93528e6 | − | 3.35201e6i | −0.674136 | − | 1.16764i | −0.976720 | − | 0.214516i | \(-0.931183\pi\) |
0.302584 | − | 0.953123i | \(-0.402151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −772810. | − | 1.33855e6i | −0.265718 | − | 0.460237i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.11143e6 | + | 1.92505e6i | −0.372399 | + | 0.645013i | −0.989934 | − | 0.141530i | \(-0.954798\pi\) |
0.617535 | + | 0.786543i | \(0.288131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.01273e6 | 1.98898 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.16380e6 | − | 2.01577e6i | 0.375307 | − | 0.650051i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −207721. | − | 359784.i | −0.0661462 | − | 0.114569i | 0.831056 | − | 0.556189i | \(-0.187737\pi\) |
−0.897202 | + | 0.441621i | \(0.854404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50770e6 | − | 2.61141e6i | −0.468224 | − | 0.810988i | 0.531116 | − | 0.847299i | \(-0.321773\pi\) |
−0.999341 | + | 0.0363107i | \(0.988439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 400772. | − | 694157.i | 0.122923 | − | 0.212910i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.10969e6 | −0.332058 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.89456e6 | + | 3.28148e6i | −0.560016 | + | 0.969976i | 0.437478 | + | 0.899229i | \(0.355872\pi\) |
−0.997494 | + | 0.0707474i | \(0.977462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.91793e6 | + | 5.05400e6i | 0.841782 | + | 1.45801i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.29434e6 | − | 2.24187e6i | −0.368917 | − | 0.638983i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −359202. | −0.0999549 | −0.0499774 | − | 0.998750i | \(-0.515915\pi\) | ||||
−0.0499774 | + | 0.998750i | \(0.515915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −272896. | − | 472669.i | −0.0750398 | − | 0.129973i | 0.826064 | − | 0.563577i | \(-0.190575\pi\) |
−0.901104 | + | 0.433604i | \(0.857242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.08606e6 | 0.828765 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.20977e6 | − | 5.55948e6i | 0.851930 | − | 1.47559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.14797e6 | − | 1.98834e6i | 0.297671 | − | 0.515581i | −0.677932 | − | 0.735125i | \(-0.737124\pi\) |
0.975603 | + | 0.219544i | \(0.0704569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.52128e6 | + | 4.36698e6i | −0.646251 | + | 1.11934i | 0.337760 | + | 0.941232i | \(0.390331\pi\) |
−0.984011 | + | 0.178107i | \(0.943003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.92924e6 | − | 2.58260e6i | 1.23474 | − | 0.646924i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.91644e6 | − | 6.78347e6i | −0.969907 | − | 1.67993i | −0.695810 | − | 0.718226i | \(-0.744955\pi\) |
−0.274097 | − | 0.961702i | \(-0.588379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.75654e6 | − | 4.77446e6i | 0.667351 | − | 1.15589i | −0.311291 | − | 0.950315i | \(-0.600761\pi\) |
0.978642 | − | 0.205571i | \(-0.0659052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.68344e6 | 0.402993 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.99055e6 | −1.40233 | −0.701166 | − | 0.712998i | \(-0.747337\pi\) | ||||
−0.701166 | + | 0.712998i | \(0.747337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 754961. | + | 1.30763e6i | 0.174777 | + | 0.302722i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.21868e6 | 0.502420 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 289587. | 0.0648617 | 0.0324308 | − | 0.999474i | \(-0.489675\pi\) | ||||
0.0324308 | + | 0.999474i | \(0.489675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.79574e6 | + | 3.11031e6i | 0.393542 | + | 0.681635i | 0.992914 | − | 0.118836i | \(-0.0379163\pi\) |
−0.599372 | + | 0.800471i | \(0.704583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 108518. | 0.0235260 | 0.0117630 | − | 0.999931i | \(-0.496256\pi\) | ||||
0.0117630 | + | 0.999931i | \(0.496256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.47855e6 | 0.950267 | 0.475133 | − | 0.879914i | \(-0.342400\pi\) | ||||
0.475133 | + | 0.879914i | \(0.342400\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.03974e6 | − | 8.72909e6i | 1.05798 | − | 1.83247i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.60900e6 | + | 2.78687e6i | 0.330677 | + | 0.572749i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.52995e6 | − | 1.32553e6i | 0.514491 | − | 0.269560i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.21830e6 | − | 5.57425e6i | 0.640896 | − | 1.11006i | −0.344337 | − | 0.938846i | \(-0.611896\pi\) |
0.985233 | − | 0.171218i | \(-0.0547703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 796459. | − | 1.37951e6i | 0.156964 | − | 0.271870i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.63614e6 | − | 2.83387e6i | 0.315838 | − | 0.547048i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −983792. | −0.187967 | −0.0939833 | − | 0.995574i | \(-0.529960\pi\) | ||||
−0.0939833 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.28089e6 | − | 5.68267e6i | −0.614170 | − | 1.06377i | −0.990530 | − | 0.137300i | \(-0.956158\pi\) |
0.376360 | − | 0.926474i | \(-0.377176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.08983e7 | 2.01948 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −716668. | − | 1.24131e6i | −0.130145 | − | 0.225418i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.23268e6 | − | 3.86711e6i | −0.401398 | − | 0.695241i | 0.592497 | − | 0.805572i | \(-0.298142\pi\) |
−0.993895 | + | 0.110331i | \(0.964809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.44875e6 | − | 2.50931e6i | 0.255313 | − | 0.442215i | −0.709667 | − | 0.704537i | \(-0.751155\pi\) |
0.964981 | + | 0.262322i | \(0.0844881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.28676e6 | −0.922489 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.19919e6 | + | 5.54116e6i | −0.547325 | + | 0.947995i | 0.451131 | + | 0.892458i | \(0.351021\pi\) |
−0.998457 | + | 0.0555374i | \(0.982313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.03157e6 | − | 6.98289e6i | −0.683003 | − | 1.18300i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.54269e6 | − | 2.67201e6i | −0.256306 | − | 0.443936i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.98801e6 | + | 3.44333e6i | −0.327109 | + | 0.566569i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.13178e7 | 1.82671 | 0.913353 | − | 0.407168i | \(-0.133484\pi\) | ||||
0.913353 | + | 0.407168i | \(0.133484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −214962. | + | 372326.i | −0.0343643 | + | 0.0595208i | −0.882696 | − | 0.469944i | \(-0.844274\pi\) |
0.848332 | + | 0.529465i | \(0.177607\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.32185e6 | − | 4.02156e6i | −0.364173 | − | 0.630766i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.03505e6 | − | 5.25687e6i | −0.471549 | − | 0.816747i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.16744e6 | −0.330468 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 510794. | + | 884721.i | 0.0771545 | + | 0.133635i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.48442e6 | 0.813128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.05574e6 | − | 7.02475e6i | 0.595768 | − | 1.03190i | −0.397670 | − | 0.917529i | \(-0.630181\pi\) |
0.993438 | − | 0.114372i | \(-0.0364855\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.94566e6 | + | 6.83409e6i | −0.569021 | + | 0.985574i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.15311e6 | + | 7.19340e6i | −0.593479 | + | 1.02794i | 0.400281 | + | 0.916393i | \(0.368913\pi\) |
−0.993760 | + | 0.111543i | \(0.964421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.93439e6 | − | 4.68103e6i | 1.25368 | − | 0.656845i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.71687e6 | + | 1.16340e7i | 0.934015 | + | 1.61776i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.99228e6 | − | 3.45072e6i | 0.272089 | − | 0.471272i | −0.697307 | − | 0.716772i | \(-0.745619\pi\) |
0.969397 | + | 0.245500i | \(0.0789521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.61934e6 | −0.625245 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.11824e6 | −0.813496 | −0.406748 | − | 0.913540i | \(-0.633337\pi\) | ||||
−0.406748 | + | 0.913540i | \(0.633337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.15863e6 | + | 5.47091e6i | 0.416273 | + | 0.721005i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −908888. | −0.117687 | −0.0588436 | − | 0.998267i | \(-0.518741\pi\) | ||||
−0.0588436 | + | 0.998267i | \(0.518741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.83881e6 | 0.236019 | 0.118010 | − | 0.993012i | \(-0.462349\pi\) | ||||
0.118010 | + | 0.993012i | \(0.462349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.20949e6 | − | 5.55900e6i | −0.404824 | − | 0.701176i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.44901e6 | 0.681362 | 0.340681 | − | 0.940179i | \(-0.389342\pi\) | ||||
0.340681 | + | 0.940179i | \(0.389342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.49405e7 | 1.83623 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 877170. | − | 1.51930e6i | 0.106884 | − | 0.185128i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.89239e6 | + | 3.27772e6i | 0.226681 | + | 0.392623i | 0.956823 | − | 0.290673i | \(-0.0938791\pi\) |
−0.730141 | + | 0.683296i | \(0.760546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.63080e6 | − | 2.29959e6i | −0.431235 | − | 0.273126i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.72339e6 | + | 9.91320e6i | −0.668369 | + | 1.15765i | 0.309990 | + | 0.950740i | \(0.399674\pi\) |
−0.978360 | + | 0.206910i | \(0.933659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.42691e6 | − | 1.11317e7i | 0.744235 | − | 1.28905i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.14807e6 | − | 5.45262e6i | 0.358491 | − | 0.620924i | −0.629218 | − | 0.777229i | \(-0.716625\pi\) |
0.987709 | + | 0.156305i | \(0.0499582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.03647e6 | −0.342913 | −0.171456 | − | 0.985192i | \(-0.554847\pi\) | ||||
−0.171456 | + | 0.985192i | \(0.554847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.15805e6 | − | 3.73785e6i | −0.239703 | − | 0.415177i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.08106e7 | −1.19091 | −0.595454 | − | 0.803389i | \(-0.703028\pi\) | ||||
−0.595454 | + | 0.803389i | \(0.703028\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.85372e6 | − | 4.94279e6i | −0.309249 | − | 0.535635i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.94957e6 | + | 8.57291e6i | 0.532006 | + | 0.921461i | 0.999302 | + | 0.0373600i | \(0.0118948\pi\) |
−0.467296 | + | 0.884101i | \(0.654772\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −973579. | + | 1.68629e6i | −0.102958 | + | 0.178328i | −0.912902 | − | 0.408179i | \(-0.866164\pi\) |
0.809944 | + | 0.586507i | \(0.199497\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.48976e6 | 0.366074 | 0.183037 | − | 0.983106i | \(-0.441407\pi\) | ||||
0.183037 | + | 0.983106i | \(0.441407\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.85797e6 | + | 8.41424e6i | −0.501458 | + | 0.868550i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 399448. | + | 691864.i | 0.0409034 | + | 0.0708468i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.61424e6 | − | 7.99210e6i | −0.465022 | − | 0.805442i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.65587e6 | + | 8.06421e6i | −0.465509 | + | 0.806285i | −0.999224 | − | 0.0393793i | \(-0.987462\pi\) |
0.533716 | + | 0.845664i | \(0.320795\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.20065e6 | −0.511827 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.93635e6 | + | 6.81796e6i | −0.384366 | + | 0.665741i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.98479e6 | − | 5.16981e6i | −0.286925 | − | 0.496969i | 0.686149 | − | 0.727461i | \(-0.259300\pi\) |
−0.973074 | + | 0.230492i | \(0.925966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.07253e6 | + | 1.57141e7i | 0.865368 | + | 1.49886i | 0.866681 | + | 0.498863i | \(0.166249\pi\) |
−0.00131239 | + | 0.999999i | \(0.500418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.03554e7 | −0.972537 | −0.486269 | − | 0.873809i | \(-0.661642\pi\) | ||||
−0.486269 | + | 0.873809i | \(0.661642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.85589e6 | − | 4.94655e6i | −0.266152 | − | 0.460989i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.38119e6 | −0.402077 | −0.201038 | − | 0.979583i | \(-0.564432\pi\) | ||||
−0.201038 | + | 0.979583i | \(0.564432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 103769. | − | 179733.i | 0.00945069 | − | 0.0163691i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.34358e6 | − | 1.27195e7i | 0.658710 | − | 1.14092i | −0.322239 | − | 0.946658i | \(-0.604436\pi\) |
0.980950 | − | 0.194262i | \(-0.0622311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.90277e6 | + | 3.29569e6i | −0.169388 | + | 0.293388i | −0.938205 | − | 0.346081i | \(-0.887512\pi\) |
0.768817 | + | 0.639469i | \(0.220846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 487462. | − | 1.18863e7i | 0.0427452 | − | 1.04230i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.13342e7 | − | 1.96313e7i | −0.986449 | − | 1.70858i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.14153e6 | + | 5.44128e6i | −0.269361 | + | 0.466547i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.15454e7 | 1.83365 | 0.916824 | − | 0.399291i | \(-0.130744\pi\) | ||||
0.916824 | + | 0.399291i | \(0.130744\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 182950. | 0.0153412 | 0.00767061 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767061 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.44293e6 | + | 1.63556e7i | 0.786017 | + | 1.36142i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.90678e7 | 1.56404 | 0.782021 | − | 0.623252i | \(-0.214189\pi\) | ||||
0.782021 | + | 0.623252i | \(0.214189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.08713e7 | −0.885229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.25915e6 | + | 2.18091e6i | 0.101048 | + | 0.175021i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.57718e7 | 1.25657 | 0.628285 | − | 0.777983i | \(-0.283757\pi\) | ||||
0.628285 | + | 0.777983i | \(0.283757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.58252e7 | 1.24276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.27848e6 | + | 1.08746e7i | −0.489522 | + | 0.847878i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.89878e6 | + | 1.54131e7i | 0.683967 | + | 1.18467i | 0.973760 | + | 0.227577i | \(0.0730802\pi\) |
−0.289793 | + | 0.957089i | \(0.593586\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.21554e6 | − | 4.57001e6i | −0.550656 | − | 0.348762i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.52562e7 | − | 2.64245e7i | 1.14788 | − | 1.98819i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.02786e6 | + | 1.78031e6i | −0.0767924 | + | 0.133008i | −0.901864 | − | 0.432019i | \(-0.857801\pi\) |
0.825072 | + | 0.565028i | \(0.191135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.82944e6 | + | 8.36483e6i | −0.355773 | + | 0.616217i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.17151e6 | −0.158854 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.09362e7 | − | 1.89420e7i | −0.788940 | − | 1.36648i | −0.926617 | − | 0.376007i | \(-0.877297\pi\) |
0.137676 | − | 0.990477i | \(-0.456037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.78072e7 | 1.27572 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.81729e6 | − | 1.00758e7i | −0.411032 | − | 0.711929i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17837e6 | + | 2.04099e6i | 0.0826884 | + | 0.143221i | 0.904404 | − | 0.426677i | \(-0.140316\pi\) |
−0.821715 | + | 0.569898i | \(0.806983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.33809e7 | + | 2.31765e7i | −0.926175 | + | 1.60418i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.16077e7 | 1.48541 | 0.742707 | − | 0.669616i | \(-0.233541\pi\) | ||||
0.742707 | + | 0.669616i | \(0.233541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.93260e6 | + | 8.54351e6i | −0.334508 | + | 0.579385i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.23082e6 | − | 3.86389e6i | −0.150263 | − | 0.260264i | 0.781061 | − | 0.624455i | \(-0.214679\pi\) |
−0.931324 | + | 0.364191i | \(0.881345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.70913e6 | + | 1.33526e7i | 0.512311 | + | 0.887348i | 0.999898 | + | 0.0142742i | \(0.00454377\pi\) |
−0.487587 | + | 0.873074i | \(0.662123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 164331. | − | 284630.i | 0.0108475 | − | 0.0187884i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.89607e6 | −0.384024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.64269e6 | + | 2.84522e6i | −0.106281 | + | 0.184084i | −0.914261 | − | 0.405126i | \(-0.867228\pi\) |
0.807980 | + | 0.589210i | \(0.200561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 784079. | + | 1.35806e6i | 0.0500602 | + | 0.0867068i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.40092e6 | − | 9.35466e6i | −0.342553 | − | 0.593319i | 0.642353 | − | 0.766409i | \(-0.277958\pi\) |
−0.984906 | + | 0.173090i | \(0.944625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.38280e6 | 0.587315 | 0.293657 | − | 0.955911i | \(-0.405128\pi\) | ||||
0.293657 | + | 0.955911i | \(0.405128\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.27723e7 | − | 3.94428e7i | −1.41611 | − | 2.45277i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.19907e6 | 0.503241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.58311e6 | − | 4.47407e6i | 0.157517 | − | 0.272827i | −0.776456 | − | 0.630172i | \(-0.782985\pi\) |
0.933973 | + | 0.357345i | \(0.116318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.46904e6 | + | 4.27650e6i | −0.148621 | + | 0.257419i | −0.930718 | − | 0.365738i | \(-0.880817\pi\) |
0.782097 | + | 0.623156i | \(0.214150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.47873e6 | + | 4.29328e6i | −0.148243 | + | 0.256764i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −476204. | + | 1.16118e7i | −0.0281157 | + | 0.685575i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 701432. | + | 1.21492e6i | 0.0411489 | + | 0.0712719i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.82419e6 | − | 3.15958e6i | 0.105656 | − | 0.183002i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.65272e6 | −0.440432 | −0.220216 | − | 0.975451i | \(-0.570676\pi\) | ||||
−0.220216 | + | 0.975451i | \(0.570676\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.64600e7 | −2.07193 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.50955e6 | − | 7.81077e6i | −0.254654 | − | 0.441074i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.09086e7 | 0.608306 | 0.304153 | − | 0.952623i | \(-0.401627\pi\) | ||||
0.304153 | + | 0.952623i | \(0.401627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.30657e7 | −1.83236 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.94586e6 | + | 6.83443e6i | 0.215950 | + | 0.374036i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.67359e7 | −1.45414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.87426e7 | −1.54403 | −0.772013 | − | 0.635606i | \(-0.780750\pi\) | ||||
−0.772013 | + | 0.635606i | \(0.780750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.14408e6 | + | 1.58380e7i | −0.488189 | + | 0.845568i | −0.999908 | − | 0.0135852i | \(-0.995676\pi\) |
0.511719 | + | 0.859153i | \(0.329009\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.71314e6 | − | 9.89544e6i | −0.301287 | − | 0.521845i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01490e6 | + | 2.47475e7i | −0.0531949 | + | 1.29711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.63449e6 | + | 1.32233e7i | −0.395296 | + | 0.684672i | −0.993139 | − | 0.116941i | \(-0.962691\pi\) |
0.597843 | + | 0.801613i | \(0.296025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.66967e6 | − | 6.35605e6i | 0.188854 | − | 0.327105i | −0.756014 | − | 0.654555i | \(-0.772856\pi\) |
0.944869 | + | 0.327450i | \(0.106189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.35237e6 | + | 1.61988e7i | −0.475508 | + | 0.823605i | −0.999606 | − | 0.0280533i | \(-0.991069\pi\) |
0.524098 | + | 0.851658i | \(0.324403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.92855e7 | 0.974641 | 0.487320 | − | 0.873223i | \(-0.337974\pi\) | ||||
0.487320 | + | 0.873223i | \(0.337974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.28050e7 | + | 3.94995e7i | 1.13872 | + | 1.97233i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.03338e7 | −1.00926 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.24428e6 | − | 1.08154e7i | −0.306251 | − | 0.530442i | 0.671288 | − | 0.741196i | \(-0.265741\pi\) |
−0.977539 | + | 0.210754i | \(0.932408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.02879e7 | − | 1.78192e7i | −0.501576 | − | 0.868756i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.16047e6 | + | 8.93819e6i | −0.248626 | + | 0.430634i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.49103e7 | 1.19308 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.59760e6 | + | 1.66235e7i | −0.454296 | + | 0.786864i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.42614e6 | + | 5.93425e6i | 0.161225 | + | 0.279250i | 0.935308 | − | 0.353834i | \(-0.115122\pi\) |
−0.774083 | + | 0.633084i | \(0.781789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.61768e6 | + | 9.73011e6i | 0.261279 | + | 0.452549i | 0.966582 | − | 0.256357i | \(-0.0825223\pi\) |
−0.705303 | + | 0.708906i | \(0.749189\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.89450e6 | − | 3.28138e6i | 0.0876017 | − | 0.151731i | −0.818895 | − | 0.573943i | \(-0.805413\pi\) |
0.906497 | + | 0.422212i | \(0.138746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.08965e7 | 1.41215 | 0.706077 | − | 0.708135i | \(-0.250463\pi\) | ||||
0.706077 | + | 0.708135i | \(0.250463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.16949e7 | + | 2.02561e7i | −0.531441 | + | 0.920482i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.57407e6 | − | 1.13866e7i | −0.295314 | − | 0.511500i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.08057e6 | − | 1.22639e7i | −0.316244 | − | 0.547752i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.73476e7 | −1.64908 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06989e7 | + | 1.85310e7i | 0.469719 | + | 0.813577i | 0.999401 | − | 0.0346194i | \(-0.0110219\pi\) |
−0.529682 | + | 0.848197i | \(0.677689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.47758e6 | −0.150951 | −0.0754756 | − | 0.997148i | \(-0.524048\pi\) | ||||
−0.0754756 | + | 0.997148i | \(0.524048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.52985e6 | + | 1.30421e7i | −0.325001 | + | 0.562918i | −0.981513 | − | 0.191398i | \(-0.938698\pi\) |
0.656512 | + | 0.754316i | \(0.272031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.37599e7 | + | 2.38328e7i | −0.587225 | + | 1.01710i | 0.407369 | + | 0.913264i | \(0.366446\pi\) |
−0.994594 | + | 0.103840i | \(0.966887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.50077e7 | − | 2.59941e7i | 0.636884 | − | 1.10312i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.71073e7 | + | 1.42025e7i | −1.13752 | + | 0.595984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.08807e6 | − | 1.22769e7i | −0.295781 | − | 0.512308i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.75350e6 | + | 1.51615e7i | −0.361229 | + | 0.625667i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45896e7 | 0.598731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.58122e7 | −1.04762 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.31824e7 | − | 2.28326e7i | −0.532079 | − | 0.921588i | −0.999299 | − | 0.0374469i | \(-0.988077\pi\) |
0.467219 | − | 0.884141i | \(-0.345256\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00749e6 | 0.239827 | 0.119913 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119913 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.46229e7 | −0.580573 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 598900. | + | 1.03733e6i | 0.0235197 | + | 0.0407372i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.21396e7 | 0.474150 | 0.237075 | − | 0.971491i | \(-0.423811\pi\) | ||||
0.237075 | + | 0.971491i | \(0.423811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.01376e6 | −0.0778044 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92600e6 | + | 8.53209e6i | −0.189296 | + | 0.327869i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.94616e6 | + | 8.56699e6i | 0.188031 | + | 0.325679i | 0.944594 | − | 0.328242i | \(-0.106456\pi\) |
−0.756563 | + | 0.653921i | \(0.773123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56614e7 | + | 2.25864e7i | 1.34842 | + | 0.854030i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.29028e6 | + | 1.08951e7i | −0.235310 | + | 0.407569i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.02564e7 | + | 1.77646e7i | −0.381632 | + | 0.661007i | −0.991296 | − | 0.131654i | \(-0.957971\pi\) |
0.609663 | + | 0.792660i | \(0.291305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.28320e7 | + | 3.95462e7i | −0.840562 | + | 1.45590i | 0.0488582 | + | 0.998806i | \(0.484442\pi\) |
−0.889420 | + | 0.457090i | \(0.848892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.61184e7 | 0.956462 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.04770e6 | + | 8.74287e6i | 0.182902 | + | 0.316796i | 0.942868 | − | 0.333168i | \(-0.108118\pi\) |
−0.759966 | + | 0.649963i | \(0.774784\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.13283e7 | −0.408319 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.33676e7 | + | 2.31533e7i | 0.476782 | + | 0.825811i | 0.999646 | − | 0.0266050i | \(-0.00846964\pi\) |
−0.522864 | + | 0.852416i | \(0.675136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.33364e6 | − | 2.30993e6i | −0.0473184 | − | 0.0819579i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.13718e7 | − | 5.43375e7i | 1.10152 | − | 1.90789i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.11695e7 | −0.739438 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.01957e7 | − | 1.76594e7i | 0.352451 | − | 0.610462i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.40549e6 | + | 7.63054e6i | 0.151505 | + | 0.262415i | 0.931781 | − | 0.363021i | \(-0.118255\pi\) |
−0.780276 | + | 0.625436i | \(0.784921\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.90262e7 | − | 3.29543e7i | −0.647594 | − | 1.12167i | −0.983696 | − | 0.179840i | \(-0.942442\pi\) |
0.336102 | − | 0.941826i | \(-0.390891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.56673e7 | + | 7.90981e7i | −1.54641 | + | 2.67845i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.16722e7 | 1.39672 | 0.698361 | − | 0.715746i | \(-0.253913\pi\) | ||||
0.698361 | + | 0.715746i | \(0.253913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.75469e6 | − | 8.23536e6i | 0.158550 | − | 0.274616i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.16371e7 | − | 3.74766e7i | −0.714194 | − | 1.23702i | −0.963270 | − | 0.268536i | \(-0.913460\pi\) |
0.249076 | − | 0.968484i | \(-0.419873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.12517e6 | − | 7.14501e6i | −0.135473 | − | 0.234646i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.56646e7 | 1.80962 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.59147e7 | + | 2.75651e7i | 0.514772 | + | 0.891611i | 0.999853 | + | 0.0171418i | \(0.00545668\pi\) |
−0.485081 | + | 0.874469i | \(0.661210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.20942e7 | −0.707492 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.67257e7 | − | 4.62903e7i | 0.851514 | − | 1.47487i | −0.0283272 | − | 0.999599i | \(-0.509018\pi\) |
0.879841 | − | 0.475267i | \(-0.157649\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.6.k.f.577.6 | 18 | ||
3.2 | odd | 2 | 76.6.e.a.45.9 | ✓ | 18 | ||
12.11 | even | 2 | 304.6.i.d.273.1 | 18 | |||
19.11 | even | 3 | inner | 684.6.k.f.505.6 | 18 | ||
57.11 | odd | 6 | 76.6.e.a.49.9 | yes | 18 | ||
228.11 | even | 6 | 304.6.i.d.49.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.9 | ✓ | 18 | 3.2 | odd | 2 | ||
76.6.e.a.49.9 | yes | 18 | 57.11 | odd | 6 | ||
304.6.i.d.49.1 | 18 | 228.11 | even | 6 | |||
304.6.i.d.273.1 | 18 | 12.11 | even | 2 | |||
684.6.k.f.505.6 | 18 | 19.11 | even | 3 | inner | ||
684.6.k.f.577.6 | 18 | 1.1 | even | 1 | trivial |