Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(47,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{65}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.3 | ||
Root | \(-10.8505 - 10.2794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.63 |
Dual form | 80.6.n.d.47.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.68301 | + | 9.68301i | −0.621165 | + | 0.621165i | −0.945829 | − | 0.324664i | \(-0.894749\pi\) |
0.324664 | + | 0.945829i | \(0.394749\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −49.1893 | + | 26.5597i | −0.879924 | + | 0.475114i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −48.6629 | − | 48.6629i | −0.375364 | − | 0.375364i | 0.494062 | − | 0.869427i | \(-0.335512\pi\) |
−0.869427 | + | 0.494062i | \(0.835512\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 55.4787i | 0.228307i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 463.177i | − | 1.15416i | −0.816688 | − | 0.577080i | \(-0.804192\pi\) | ||
0.816688 | − | 0.577080i | \(-0.195808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 320.800 | + | 320.800i | 0.526473 | + | 0.526473i | 0.919519 | − | 0.393046i | \(-0.128579\pi\) |
−0.393046 | + | 0.919519i | \(0.628579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 219.122 | − | 733.478i | 0.251454 | − | 0.841703i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1045.30 | − | 1045.30i | 0.877238 | − | 0.877238i | −0.116010 | − | 0.993248i | \(-0.537011\pi\) |
0.993248 | + | 0.116010i | \(0.0370106\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −701.290 | −0.445670 | −0.222835 | − | 0.974856i | \(-0.571531\pi\) | ||||
−0.222835 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 942.407 | 0.466327 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2001.88 | − | 2001.88i | 0.789076 | − | 0.789076i | −0.192266 | − | 0.981343i | \(-0.561584\pi\) |
0.981343 | + | 0.192266i | \(0.0615838\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1714.16 | − | 2612.90i | 0.548533 | − | 0.836129i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2890.17 | − | 2890.17i | −0.762982 | − | 0.762982i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3567.76i | 0.787773i | 0.919159 | + | 0.393886i | \(0.128870\pi\) | ||||
−0.919159 | + | 0.393886i | \(0.871130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9044.72i | − | 1.69041i | −0.534446 | − | 0.845203i | \(-0.679480\pi\) | ||
0.534446 | − | 0.845203i | \(-0.320520\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4484.95 | + | 4484.95i | 0.716924 | + | 0.716924i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3686.17 | + | 1101.22i | 0.508633 | + | 0.151951i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1642.14 | − | 1642.14i | 0.197199 | − | 0.197199i | −0.601599 | − | 0.798798i | \(-0.705470\pi\) |
0.798798 | + | 0.601599i | \(0.205470\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6212.62 | −0.654054 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14338.6 | −1.33213 | −0.666067 | − | 0.745892i | \(-0.732024\pi\) | ||||
−0.666067 | + | 0.745892i | \(0.732024\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3941.99 | + | 3941.99i | −0.325120 | + | 0.325120i | −0.850727 | − | 0.525607i | \(-0.823838\pi\) |
0.525607 | + | 0.850727i | \(0.323838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1473.50 | − | 2728.95i | −0.108472 | − | 0.200893i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7944.15 | + | 7944.15i | 0.524569 | + | 0.524569i | 0.918948 | − | 0.394379i | \(-0.129040\pi\) |
−0.394379 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12070.8i | − | 0.718203i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20243.2i | 1.08982i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11621.9 | + | 11621.9i | 0.568313 | + | 0.568313i | 0.931656 | − | 0.363342i | \(-0.118364\pi\) |
−0.363342 | + | 0.931656i | \(0.618364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12301.9 | + | 22783.3i | 0.548358 | + | 1.01557i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6790.60 | − | 6790.60i | 0.276835 | − | 0.276835i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1121.30 | −0.0419365 | −0.0209683 | − | 0.999780i | \(-0.506675\pi\) | ||||
−0.0209683 | + | 0.999780i | \(0.506675\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29320.4 | −1.00889 | −0.504447 | − | 0.863442i | \(-0.668304\pi\) | ||||
−0.504447 | + | 0.863442i | \(0.668304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2699.75 | − | 2699.75i | 0.0856984 | − | 0.0856984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24300.3 | − | 7259.56i | −0.713391 | − | 0.213121i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9199.75 | − | 9199.75i | −0.250374 | − | 0.250374i | 0.570750 | − | 0.821124i | \(-0.306653\pi\) |
−0.821124 | + | 0.570750i | \(0.806653\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38768.5i | 0.980294i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52643.9i | 1.23937i | 0.784849 | + | 0.619687i | \(0.212740\pi\) | ||||
−0.784849 | + | 0.619687i | \(0.787260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27965.6 | − | 27965.6i | −0.614209 | − | 0.614209i | 0.329831 | − | 0.944040i | \(-0.393008\pi\) |
−0.944040 | + | 0.329831i | \(0.893008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8702.49 | + | 41899.0i | 0.178645 | + | 0.860104i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22539.6 | + | 22539.6i | −0.433230 | + | 0.433230i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −82263.7 | −1.48300 | −0.741499 | − | 0.670954i | \(-0.765885\pi\) | ||||
−0.741499 | + | 0.670954i | \(0.765885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 42489.8 | 0.719569 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77236.8 | − | 77236.8i | 1.23063 | − | 1.23063i | 0.266914 | − | 0.963720i | \(-0.413996\pi\) |
0.963720 | − | 0.266914i | \(-0.0860039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23654.6 | + | 79180.1i | −0.355114 | + | 1.18869i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −34546.7 | − | 34546.7i | −0.489337 | − | 0.489337i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145955.i | − | 1.95318i | −0.215100 | − | 0.976592i | \(-0.569008\pi\) | ||
0.215100 | − | 0.976592i | \(-0.430992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 31222.2i | − | 0.395239i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 87580.1 | + | 87580.1i | 1.05002 | + | 1.05002i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34495.9 | − | 18626.1i | 0.392156 | − | 0.211744i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 97856.7 | − | 97856.7i | 1.05599 | − | 1.05599i | 0.0576570 | − | 0.998336i | \(-0.481637\pi\) |
0.998336 | − | 0.0576570i | \(-0.0183630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25696.5 | 0.263503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 86555.1 | 0.844286 | 0.422143 | − | 0.906529i | \(-0.361278\pi\) | ||||
0.422143 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 125928. | − | 125928.i | 1.16958 | − | 1.16958i | 0.187273 | − | 0.982308i | \(-0.440035\pi\) |
0.982308 | − | 0.187273i | \(-0.0599650\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46356.3 | + | 25030.1i | −0.410332 | + | 0.221559i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −152309. | − | 152309.i | −1.28607 | − | 1.28607i | −0.937154 | − | 0.348917i | \(-0.886550\pi\) |
−0.348917 | − | 0.937154i | \(-0.613450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 62440.1i | − | 0.503382i | −0.967808 | − | 0.251691i | \(-0.919013\pi\) | ||
0.967808 | − | 0.251691i | \(-0.0809866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31801.6i | 0.244986i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 32875.2 | + | 32875.2i | 0.242199 | + | 0.242199i | 0.817759 | − | 0.575560i | \(-0.195216\pi\) |
−0.575560 | + | 0.817759i | \(0.695216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −45301.7 | + | 151641.i | −0.319426 | + | 1.06923i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17797.6 | + | 17797.6i | −0.120198 | + | 0.120198i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −101734. | −0.658568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53482.3 | −0.332083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 138841. | − | 138841.i | 0.827476 | − | 0.827476i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14920.6 | + | 174054.i | −0.0854102 | + | 0.996346i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −120503. | − | 120503.i | −0.662960 | − | 0.662960i | 0.293116 | − | 0.956077i | \(-0.405308\pi\) |
−0.956077 | + | 0.293116i | \(0.905308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 76340.6i | − | 0.403907i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 88630.4i | 0.451237i | 0.974216 | + | 0.225618i | \(0.0724402\pi\) | ||||
−0.974216 | + | 0.225618i | \(0.927560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34126.8 | + | 34126.8i | 0.167289 | + | 0.167289i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 218927. | + | 65403.3i | 1.03387 | + | 0.308862i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −46725.7 | + | 46725.7i | −0.212694 | + | 0.212694i | −0.805411 | − | 0.592717i | \(-0.798055\pi\) |
0.592717 | + | 0.805411i | \(0.298055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −280242. | −1.23026 | −0.615128 | − | 0.788427i | \(-0.710896\pi\) | ||||
−0.615128 | + | 0.788427i | \(0.710896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −153846. | −0.651688 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 148587. | − | 148587.i | 0.607634 | − | 0.607634i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −94758.7 | − | 175496.i | −0.374282 | − | 0.693180i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 116882. | + | 116882.i | 0.446123 | + | 0.446123i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 114782.i | 0.423555i | 0.977318 | + | 0.211777i | \(0.0679251\pi\) | ||||
−0.977318 | + | 0.211777i | \(0.932075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 388996.i | 1.38836i | 0.719801 | + | 0.694181i | \(0.244233\pi\) | ||||
−0.719801 | + | 0.694181i | \(0.755767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 57991.7 | + | 57991.7i | 0.200280 | + | 0.200280i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 240225. | + | 444903.i | 0.803136 | + | 1.48743i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 230322. | − | 230322.i | 0.745738 | − | 0.745738i | −0.227938 | − | 0.973676i | \(-0.573198\pi\) |
0.973676 | + | 0.227938i | \(0.0731984\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −225070. | −0.706033 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −194835. | −0.592382 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −334147. | + | 334147.i | −0.985073 | + | 0.985073i | −0.999890 | − | 0.0148175i | \(-0.995283\pi\) |
0.0148175 | + | 0.999890i | \(0.495283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −339730. | − | 101492.i | −0.971459 | − | 0.290218i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 287959. | + | 287959.i | 0.798987 | + | 0.798987i | 0.982936 | − | 0.183949i | \(-0.0588880\pi\) |
−0.183949 | + | 0.982936i | \(0.558888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 165467.i | − | 0.445652i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 38906.6i | − | 0.101750i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 176255. | + | 176255.i | 0.447741 | + | 0.447741i | 0.894603 | − | 0.446862i | \(-0.147458\pi\) |
−0.446862 | + | 0.894603i | \(0.647458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −210568. | + | 43735.3i | −0.519753 | + | 0.107953i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10857.6 | − | 10857.6i | 0.0260495 | − | 0.0260495i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 409192. | 0.954540 | 0.477270 | − | 0.878757i | \(-0.341626\pi\) | ||||
0.477270 | + | 0.878757i | \(0.341626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −607951. | −1.37934 | −0.689671 | − | 0.724123i | \(-0.742245\pi\) | ||||
−0.689671 | + | 0.724123i | \(0.742245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 283910. | − | 283910.i | 0.626691 | − | 0.626691i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −37160.8 | + | 124390.i | −0.0798281 | + | 0.267212i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −484158. | − | 484158.i | −1.01247 | − | 1.01247i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 281288.i | 0.572793i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 67781.7i | − | 0.134440i | −0.997738 | − | 0.0672201i | \(-0.978587\pi\) | ||
0.997738 | − | 0.0672201i | \(-0.0214130\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 373274. | + | 373274.i | 0.721330 | + | 0.721330i | 0.968876 | − | 0.247546i | \(-0.0796241\pi\) |
−0.247546 | + | 0.968876i | \(0.579624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 305594. | − | 165005.i | 0.575518 | − | 0.310750i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 76924.7 | − | 76924.7i | 0.141221 | − | 0.141221i | −0.632962 | − | 0.774183i | \(-0.718161\pi\) |
0.774183 | + | 0.632962i | \(0.218161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −908495. | −1.62626 | −0.813130 | − | 0.582083i | \(-0.802238\pi\) | ||||
−0.813130 | + | 0.582083i | \(0.802238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 178162. | 0.311047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 173618. | − | 173618.i | 0.295702 | − | 0.295702i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 705306. | − | 380830.i | 1.17218 | − | 0.632916i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 111062. | + | 111062.i | 0.180152 | + | 0.180152i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 324822.i | 0.514374i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 732879.i | − | 1.13325i | −0.823975 | − | 0.566626i | \(-0.808249\pi\) | ||
0.823975 | − | 0.566626i | \(-0.191751\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −509751. | − | 509751.i | −0.769856 | − | 0.769856i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 89205.4 | − | 298601.i | 0.131612 | − | 0.440550i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −440143. | + | 440143.i | −0.634518 | + | 0.634518i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 541581. | 0.763051 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 670663. | 0.923684 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −346705. | + | 346705.i | −0.466872 | + | 0.466872i | −0.900900 | − | 0.434027i | \(-0.857092\pi\) |
0.434027 | + | 0.900900i | \(0.357092\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 144960. | + | 95099.6i | 0.190894 | + | 0.125234i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −262744. | − | 262744.i | −0.338429 | − | 0.338429i | 0.517347 | − | 0.855776i | \(-0.326920\pi\) |
−0.855776 | + | 0.517347i | \(0.826920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.36759e6i | − | 1.72332i | −0.507487 | − | 0.861660i | \(-0.669425\pi\) | ||
0.507487 | − | 0.861660i | \(-0.330575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 436502.i | − | 0.538215i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 171228. | + | 171228.i | 0.206626 | + | 0.206626i | 0.802832 | − | 0.596206i | \(-0.203326\pi\) |
−0.596206 | + | 0.802832i | \(0.703326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −601761. | − | 179772.i | −0.710811 | − | 0.212351i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 796560. | − | 796560.i | 0.921187 | − | 0.921187i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.31148e6 | 1.48514 | 0.742569 | − | 0.669769i | \(-0.233607\pi\) | ||||
0.742569 | + | 0.669769i | \(0.233607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.31737e6 | 1.46105 | 0.730526 | − | 0.682884i | \(-0.239275\pi\) | ||||
0.730526 | + | 0.682884i | \(0.239275\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 290883. | − | 290883.i | 0.316011 | − | 0.316011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 320598. | + | 593755.i | 0.341229 | + | 0.631964i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −224974. | − | 224974.i | −0.234633 | − | 0.234633i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.49577e6i | 1.52885i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 188218.i | − | 0.188572i | −0.995545 | − | 0.0942859i | \(-0.969943\pi\) | ||
0.995545 | − | 0.0942859i | \(-0.0300568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −927227. | − | 927227.i | −0.910720 | − | 0.910720i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −537654. | − | 995750.i | −0.517789 | − | 0.958958i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −784122. | + | 784122.i | −0.740544 | + | 0.740544i | −0.972683 | − | 0.232139i | \(-0.925428\pi\) |
0.232139 | + | 0.972683i | \(0.425428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −159822. | −0.148043 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −197935. | −0.179854 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −554379. | + | 554379.i | −0.494217 | + | 0.494217i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −880348. | − | 262999.i | −0.770086 | − | 0.230059i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.41328e6 | + | 1.41328e6i | 1.21325 | + | 1.21325i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 146638.i | − | 0.123557i | −0.998090 | − | 0.0617785i | \(-0.980323\pi\) | ||
0.998090 | − | 0.0617785i | \(-0.0196772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 620115.i | 0.512919i | 0.966555 | + | 0.256460i | \(0.0825560\pi\) | ||||
−0.966555 | + | 0.256460i | \(0.917444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 302324. | + | 302324.i | 0.245509 | + | 0.245509i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.21024e6 | − | 793962.i | −0.965026 | − | 0.633094i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −571067. | + | 571067.i | −0.447185 | + | 0.447185i | −0.894418 | − | 0.447233i | \(-0.852410\pi\) |
0.447233 | + | 0.894418i | \(0.352410\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 501789. | 0.385932 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −623155. | −0.470793 | −0.235397 | − | 0.971899i | \(-0.575639\pi\) | ||||
−0.235397 | + | 0.971899i | \(0.575639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.66016e6 | + | 1.66016e6i | −1.23221 | + | 1.23221i | −0.269091 | + | 0.963115i | \(0.586723\pi\) |
−0.963115 | + | 0.269091i | \(0.913277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −153668. | + | 514381.i | −0.112065 | + | 0.375122i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 697760. | + | 697760.i | 0.500036 | + | 0.500036i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 765434.i | − | 0.539092i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.89509e6i | 1.31189i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.72577e6 | − | 1.72577e6i | −1.17439 | − | 1.17439i | −0.981151 | − | 0.193242i | \(-0.938100\pi\) |
−0.193242 | − | 0.981151i | \(-0.561900\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 55156.0 | − | 29781.4i | 0.0369010 | − | 0.0199247i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.33866e6 | + | 1.33866e6i | −0.880602 | + | 0.880602i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.28441e6 | 0.830855 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 383657. | 0.244077 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −838114. | + | 838114.i | −0.524441 | + | 0.524441i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.44225e6 | − | 778742.i | 0.887751 | − | 0.479340i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 693642. | + | 693642.i | 0.420039 | + | 0.420039i | 0.885217 | − | 0.465178i | \(-0.154010\pi\) |
−0.465178 | + | 0.885217i | \(0.654010\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.43873e6i | 1.45301i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 839243.i | − | 0.492024i | −0.969267 | − | 0.246012i | \(-0.920880\pi\) | ||
0.969267 | − | 0.246012i | \(-0.0791203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.45976e6 | − | 1.45976e6i | −0.842208 | − | 0.842208i | 0.146938 | − | 0.989146i | \(-0.453058\pi\) |
−0.989146 | + | 0.146938i | \(0.953058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −61094.2 | + | 204504.i | −0.0346916 | + | 0.116125i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 768911. | − | 768911.i | 0.429762 | − | 0.429762i | −0.458785 | − | 0.888547i | \(-0.651715\pi\) |
0.888547 | + | 0.458785i | \(0.151715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65251e6 | 0.909215 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.94961e6 | 1.59772 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −733056. | + | 733056.i | −0.390959 | + | 0.390959i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.38812e6 | − | 288316.i | 0.728987 | − | 0.151412i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 604608. | + | 604608.i | 0.312683 | + | 0.312683i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 773171.i | − | 0.393809i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.53718e6i | − | 0.771179i | −0.922671 | − | 0.385589i | \(-0.873998\pi\) | ||
0.922671 | − | 0.385589i | \(-0.126002\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 91103.5 | + | 91103.5i | 0.0450220 | + | 0.0450220i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 696871. | + | 208186.i | 0.339266 | + | 0.101354i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −600219. | + | 600219.i | −0.287895 | + | 0.287895i | −0.836248 | − | 0.548352i | \(-0.815255\pi\) |
0.548352 | + | 0.836248i | \(0.315255\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −636661. | −0.300891 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.18931e6 | −1.95100 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.40528e6 | + | 1.40528e6i | −0.644952 | + | 0.644952i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.02968e6 | − | 1.90699e6i | −0.465752 | − | 0.862584i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15540.8 | − | 15540.8i | −0.00692868 | − | 0.00692868i | 0.703634 | − | 0.710563i | \(-0.251560\pi\) |
−0.710563 | + | 0.703634i | \(0.751560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.37621e6i | 0.604815i | 0.953179 | + | 0.302407i | \(0.0977903\pi\) | ||||
−0.953179 | + | 0.302407i | \(0.902210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.85434e6i | − | 0.803379i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.13095e6 | + | 2.13095e6i | 0.910198 | + | 0.910198i | 0.996287 | − | 0.0860896i | \(-0.0274371\pi\) |
−0.0860896 | + | 0.996287i | \(0.527437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.39821e6 | − | 2.58951e6i | −0.588844 | − | 1.09055i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 985095. | − | 985095.i | 0.409079 | − | 0.409079i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 346230. | 0.141785 | 0.0708923 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708923 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.98429e6 | −0.801378 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 517870. | − | 517870.i | 0.206278 | − | 0.206278i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.11836e6 | + | 632848.i | 0.832277 | + | 0.248638i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −857952. | − | 857952.i | −0.332505 | − | 0.332505i | 0.521032 | − | 0.853537i | \(-0.325547\pi\) |
−0.853537 | + | 0.521032i | \(0.825547\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 795488.i | − | 0.304136i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.13111e6i | − | 0.426649i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92433e6 | + | 1.92433e6i | 0.716157 | + | 0.716157i | 0.967816 | − | 0.251659i | \(-0.0809762\pi\) |
−0.251659 | + | 0.967816i | \(0.580976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.54090e6 | − | 1.82985e6i | −0.565842 | − | 0.671949i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.14454e6 | + | 1.14454e6i | −0.414741 | + | 0.414741i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5919.00 | 0.00211666 | 0.00105833 | − | 0.999999i | \(-0.499663\pi\) | ||||
0.00105833 | + | 0.999999i | \(0.499663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.33366e6 | 0.823616 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −121366. | + | 121366.i | −0.0422767 | + | 0.0422767i | −0.727929 | − | 0.685652i | \(-0.759517\pi\) |
0.685652 | + | 0.727929i | \(0.259517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 510060. | − | 1.70735e6i | 0.175376 | − | 0.587044i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −218696. | − | 218696.i | −0.0742273 | − | 0.0742273i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.60692e6i | 0.873482i | 0.899587 | + | 0.436741i | \(0.143867\pi\) | ||||
−0.899587 | + | 0.436741i | \(0.856133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.18512e6i | − | 1.38442i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −858209. | − | 858209.i | −0.280293 | − | 0.280293i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.04649e6 | − | 2.18490e6i | 1.30493 | − | 0.704593i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.66197e6 | − | 2.66197e6i | 0.847669 | − | 0.847669i | −0.142173 | − | 0.989842i | \(-0.545409\pi\) |
0.989842 | + | 0.142173i | \(0.0454089\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −660901. | −0.207828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.31838e6 | 1.03054 | 0.515270 | − | 0.857028i | \(-0.327692\pi\) | ||||
0.515270 | + | 0.857028i | \(0.327692\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.90155e6 | − | 2.90155e6i | 0.889953 | − | 0.889953i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.09004e6 | + | 1.12852e6i | −0.633166 | + | 0.341877i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −760600. | − | 760600.i | −0.227599 | − | 0.227599i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.71967e6i | − | 0.508319i | −0.967162 | − | 0.254159i | \(-0.918201\pi\) | ||
0.967162 | − | 0.254159i | \(-0.0817988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 904891.i | − | 0.264236i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 54565.8 | + | 54565.8i | 0.0157415 | + | 0.0157415i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.74783e6 | + | 5.85061e6i | −0.498173 | + | 1.66756i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.71358e6 | − | 2.71358e6i | 0.764193 | − | 0.764193i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.43886e6 | −0.678660 | −0.339330 | − | 0.940667i | \(-0.610200\pi\) | ||||
−0.339330 | + | 0.940667i | \(0.610200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.76737e6 | −0.760961 | −0.380480 | − | 0.924789i | \(-0.624241\pi\) | ||||
−0.380480 | + | 0.924789i | \(0.624241\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −440731. | + | 440731.i | −0.119763 | + | 0.119763i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −939449. | − | 4.52307e6i | −0.252290 | − | 1.21468i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.42682e6 | + | 1.42682e6i | 0.378703 | + | 0.378703i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.87755e6i | 0.754882i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.98814e6i | 1.03413i | 0.855945 | + | 0.517067i | \(0.172976\pi\) | ||||
−0.855945 | + | 0.517067i | \(0.827024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 386926. | + | 386926.i | 0.0991765 | + | 0.0991765i | 0.754954 | − | 0.655778i | \(-0.227659\pi\) |
−0.655778 | + | 0.754954i | \(0.727659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.61688e6 | + | 781776.i | 0.663071 | + | 0.198088i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.40390e6 | + | 1.40390e6i | −0.351668 | + | 0.351668i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.85711e6 | 0.459913 | 0.229956 | − | 0.973201i | \(-0.426142\pi\) | ||||
0.229956 | + | 0.973201i | \(0.426142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 669674. | 0.163971 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.58101e6 | + | 2.58101e6i | −0.624857 | + | 0.624857i | −0.946769 | − | 0.321913i | \(-0.895674\pi\) |
0.321913 | + | 0.946769i | \(0.395674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.87651e6 | + | 7.17940e6i | 0.927986 | + | 1.71865i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.11144e6 | − | 1.11144e6i | −0.263097 | − | 0.263097i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.66935e6i | − | 1.09305i | −0.837443 | − | 0.546525i | \(-0.815950\pi\) | ||
0.837443 | − | 0.546525i | \(-0.184050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.64133e6i | 1.53749i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.76665e6 | − | 3.76665e6i | −0.862402 | − | 0.862402i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 829251. | + | 1.53579e6i | 0.187784 | + | 0.347780i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.03755e6 | + | 5.03755e6i | −1.12831 | + | 1.12831i | −0.137858 | + | 0.990452i | \(0.544022\pi\) |
−0.990452 | + | 0.137858i | \(0.955978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.04217e6 | −1.33863 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.77546e6 | −0.608250 | −0.304125 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304125 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.00377e6 | − | 6.00377e6i | 1.30158 | − | 1.30158i | 0.374258 | − | 0.927325i | \(-0.377897\pi\) |
0.927325 | − | 0.374258i | \(-0.122103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.63410e6 | − | 1.98190e6i | −1.42282 | − | 0.425059i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.93586e6 | − | 2.93586e6i | −0.622935 | − | 0.622935i | 0.323346 | − | 0.946281i | \(-0.395192\pi\) |
−0.946281 | + | 0.323346i | \(0.895192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 895373.i | 0.187963i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.46042e6i | 0.926453i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.82584e6 | + | 1.82584e6i | 0.375240 | + | 0.375240i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20213e6 | + | 1.83240e6i | −0.244465 | + | 0.372638i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −644768. | + | 644768.i | −0.129750 | + | 0.129750i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 850769. | 0.169423 | 0.0847116 | − | 0.996406i | \(-0.473003\pi\) | ||||
0.0847116 | + | 0.996406i | \(0.473003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05360e6 | 0.207640 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.88659e6 | − | 1.88659e6i | 0.367967 | − | 0.367967i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.21445e6 | + | 7.41254e6i | −0.427476 | + | 1.43091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.08676e6 | + | 2.08676e6i | 0.398704 | + | 0.398704i | 0.877776 | − | 0.479072i | \(-0.159027\pi\) |
−0.479072 | + | 0.877776i | \(0.659027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.47109e6i | − | 1.22379i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.55745e6i | 0.665940i | 0.942937 | + | 0.332970i | \(0.108051\pi\) | ||||
−0.942937 | + | 0.332970i | \(0.891949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.72937e6 | + | 3.72937e6i | 0.691064 | + | 0.691064i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26399e6 | + | 682490.i | −0.231863 | + | 0.125194i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.56181e6 | − | 2.56181e6i | 0.465217 | − | 0.465217i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.06234e6 | 0.730339 | 0.365170 | − | 0.930941i | \(-0.381011\pi\) | ||||
0.365170 | + | 0.930941i | \(0.381011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.57662e6 | −0.992606 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.25876e6 | + | 2.25876e6i | −0.398061 | + | 0.398061i | −0.877549 | − | 0.479488i | \(-0.840823\pi\) |
0.479488 | + | 0.877549i | \(0.340823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.25758e6 | + | 2.29888e6i | −0.742907 | + | 0.401132i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.60222e6 | + | 1.60222e6i | 0.276824 | + | 0.276824i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5.20653e6i | − | 0.890746i | −0.895345 | − | 0.445373i | \(-0.853071\pi\) | ||
0.895345 | − | 0.445373i | \(-0.146929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.72177e6i | 0.461105i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.02685e6 | + | 2.02685e6i | 0.340038 | + | 0.340038i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.84970e6 | + | 9.53894e6i | −0.473458 | + | 1.58483i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.67955e6 | − | 3.67955e6i | 0.605436 | − | 0.605436i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.41336e6 | −0.556242 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.82071e6 | 0.293864 | 0.146932 | − | 0.989147i | \(-0.453060\pi\) | ||||
0.146932 | + | 0.989147i | \(0.453060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.25978e6 | − | 3.25978e6i | 0.521116 | − | 0.521116i | −0.396793 | − | 0.917908i | \(-0.629877\pi\) |
0.917908 | + | 0.396793i | \(0.129877\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.61544e6 | − | 2.46242e6i | 0.255796 | − | 0.389909i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.45442e6 | − | 9.45442e6i | −1.48289 | − | 1.48289i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.57872e6i | − | 0.245283i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 62208.3i | − | 0.00957442i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.59983e6 | − | 4.59983e6i | −0.701333 | − | 0.701333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.15372e7 | + | 3.44667e6i | 1.74268 | + | 0.520614i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.96221e6 | + | 3.96221e6i | −0.592927 | + | 0.592927i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.59094e6 | −0.828920 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.09633e6 | 0.895520 | 0.447760 | − | 0.894154i | \(-0.352222\pi\) | ||||
0.447760 | + | 0.894154i | \(0.352222\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.88679e6 | − | 5.88679e6i | 0.856799 | − | 0.856799i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.65839e6 | + | 3.07138e6i | 0.239164 | + | 0.442938i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00865e6 | + | 2.00865e6i | 0.287036 | + | 0.287036i | 0.835907 | − | 0.548871i | \(-0.184942\pi\) |
−0.548871 | + | 0.835907i | \(0.684942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.62666e6i | − | 0.230338i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.50204e6i | − | 0.351087i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00319e6 | + | 4.00319e6i | 0.556665 | + | 0.556665i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −844642. | − | 1.56430e6i | −0.116397 | − | 0.215569i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00540e7 | − | 1.00540e7i | 1.37309 | − | 1.37309i | 0.517272 | − | 0.855821i | \(-0.326948\pi\) |
0.855821 | − | 0.517272i | \(-0.173052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.52918e6 | −0.342334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.37621e6 | 1.25782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.99182e6 | − | 6.99182e6i | 0.929650 | − | 0.929650i | −0.0680335 | − | 0.997683i | \(-0.521672\pi\) |
0.997683 | + | 0.0680335i | \(0.0216725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.49026e6 | − | 743951.i | −0.328189 | − | 0.0980444i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.06768e6 | − | 2.06768e6i | −0.270100 | − | 0.270100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.15878e6i | 0.409015i | 0.978865 | + | 0.204507i | \(0.0655592\pi\) | ||||
−0.978865 | + | 0.204507i | \(0.934441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.35381e6i | − | 1.20060i | −0.799775 | − | 0.600300i | \(-0.795048\pi\) | ||
0.799775 | − | 0.600300i | \(-0.204952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 656331. | + | 656331.i | 0.0835095 | + | 0.0835095i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.79917e6 | − | 8.66228e6i | −0.226935 | − | 1.09260i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00683e7 | + | 1.00683e7i | −1.25897 | + | 1.25897i | −0.307391 | + | 0.951583i | \(0.599456\pi\) |
−0.951583 | + | 0.307391i | \(0.900544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.22883e6 | −0.896131 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.51714e6 | −0.923873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.38301e6 | − | 5.38301e6i | 0.655924 | − | 0.655924i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 402751. | − | 1.34815e6i | 0.0486572 | − | 0.162872i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.87805e6 | − | 9.87805e6i | −1.18325 | − | 1.18325i | −0.978898 | − | 0.204351i | \(-0.934492\pi\) |
−0.204351 | − | 0.978898i | \(-0.565508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.34297e6i | 0.753364i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.48972e6i | 0.175444i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.47163e6 | + | 6.47163e6i | 0.755748 | + | 0.755748i | 0.975546 | − | 0.219797i | \(-0.0705396\pi\) |
−0.219797 | + | 0.975546i | \(0.570540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.00424e6 | − | 2.70204e6i | 0.579490 | − | 0.312895i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.79696e6 | − | 8.79696e6i | 1.01018 | − | 1.01018i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.49595e6 | −0.625858 | −0.312929 | − | 0.949777i | \(-0.601310\pi\) | ||||
−0.312929 | + | 0.949777i | \(0.601310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.92293e6 | −0.330090 | −0.165045 | − | 0.986286i | \(-0.552777\pi\) | ||||
−0.165045 | + | 0.986286i | \(0.552777\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 510390. | − | 510390.i | 0.0571622 | − | 0.0571622i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.63075e6 | − | 1.42047e6i | 0.292208 | − | 0.157777i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.15887e6 | + | 3.15887e6i | 0.347984 | + | 0.347984i | 0.859358 | − | 0.511374i | \(-0.170863\pi\) |
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.36229e6i | 0.367360i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.09697e6i | 0.552343i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.01465e6 | + | 1.01465e6i | 0.109060 | + | 0.109060i | 0.759531 | − | 0.650471i | \(-0.225429\pi\) |
−0.650471 | + | 0.759531i | \(0.725429\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.14191e6 | + | 1.05171e7i | −0.334970 | + | 1.12126i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.48588e6 | − | 2.48588e6i | 0.262886 | − | 0.262886i | −0.563340 | − | 0.826226i | \(-0.690484\pi\) |
0.826226 | + | 0.563340i | \(0.190484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.49651e6 | 0.471682 | 0.235841 | − | 0.971792i | \(-0.424216\pi\) | ||||
0.235841 | + | 0.971792i | \(0.424216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.15716e7 | −1.20410 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.10259e6 | + | 7.10259e6i | −0.733156 | + | 0.733156i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.88890e6 | − | 8.95789e6i | −0.398224 | − | 0.917288i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.14525e6 | − | 3.14525e6i | −0.319512 | − | 0.319512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.43304e6i | − | 0.345981i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.34293e6i | − | 0.834152i | −0.908872 | − | 0.417076i | \(-0.863055\pi\) | ||
0.908872 | − | 0.417076i | \(-0.136945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.09648e6 | + | 7.09648e6i | 0.703936 | + | 0.703936i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.12795e6 | + | 2.72692e6i | 0.898337 | + | 0.268373i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.87233e6 | − | 3.87233e6i | 0.378115 | − | 0.378115i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.92061e6 | −0.282958 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.67634e6 | −0.449532 | −0.224766 | − | 0.974413i | \(-0.572162\pi\) | ||||
−0.224766 | + | 0.974413i | \(0.572162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.95020e6 | + | 1.95020e6i | −0.186017 | + | 0.186017i | −0.793972 | − | 0.607955i | \(-0.791990\pi\) |
0.607955 | + | 0.793972i | \(0.291990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.02758e6 | + | 3.75514e6i | 0.191902 | + | 0.355407i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.09333e6 | + | 7.09333e6i | 0.666177 | + | 0.666177i | 0.956829 | − | 0.290652i | \(-0.0938722\pi\) |
−0.290652 | + | 0.956829i | \(0.593872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 519362.i | 0.0484014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 8.52381e6i | − | 0.788281i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02700e7 | − | 1.02700e7i | −0.942516 | − | 0.942516i | 0.0559194 | − | 0.998435i | \(-0.482191\pi\) |
−0.998435 | + | 0.0559194i | \(0.982191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.35400e6 | − | 4.35966e6i | −0.214389 | − | 0.397054i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.55149e6 | − | 1.55149e6i | 0.140228 | − | 0.140228i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.21615e7 | 1.98786 | 0.993930 | − | 0.110013i | \(-0.0350891\pi\) | ||||
0.993930 | + | 0.110013i | \(0.0350891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.85454e6 | 0.343138 | 0.171569 | − | 0.985172i | \(-0.445116\pi\) | ||||
0.171569 | + | 0.985172i | \(0.445116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.49403e6 | + | 6.49403e6i | −0.573761 | + | 0.573761i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.58507e6 | − | 772275.i | −0.226683 | − | 0.0677201i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.14224e6 | + | 7.14224e6i | 0.621613 | + | 0.621613i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6.71430e6i | − | 0.580010i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.35806e7i | 1.16443i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.70626e6 | + | 8.70626e6i | 0.740958 | + | 0.740958i | 0.972762 | − | 0.231804i | \(-0.0744629\pi\) |
−0.231804 | + | 0.972762i | \(0.574463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.25060e7 | + | 2.59751e6i | −1.05647 | + | 0.219431i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.81144e6 | + | 2.81144e6i | −0.235753 | + | 0.235753i | −0.815089 | − | 0.579336i | \(-0.803312\pi\) |
0.579336 | + | 0.815089i | \(0.303312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.52399e6 | −0.792765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.08830e6 | 0.420441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.19141e6 | + | 8.19141e6i | −0.671903 | + | 0.671903i | −0.958155 | − | 0.286251i | \(-0.907591\pi\) |
0.286251 | + | 0.958155i | \(0.407591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.05738e6 | − | 3.53942e6i | 0.0861004 | − | 0.288208i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.32423e7 | + | 1.32423e7i | 1.07047 | + | 1.07047i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.45662e6i | 0.598403i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.47639e6i | 0.515986i | 0.966147 | + | 0.257993i | \(0.0830611\pi\) | ||||
−0.966147 | + | 0.257993i | \(0.916939\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.25047e6 | − | 1.25047e6i | −0.0989096 | − | 0.0989096i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.37849e7 | − | 7.44313e6i | 1.08253 | − | 0.584512i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.49881e7 | + | 1.49881e7i | −1.16860 | + | 1.16860i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.31600e6 | −0.256697 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.17245e7 | −0.901155 | −0.450578 | − | 0.892737i | \(-0.648782\pi\) | ||||
−0.450578 | + | 0.892737i | \(0.648782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.15161e6 | + | 1.15161e6i | −0.0878858 | + | 0.0878858i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.56759e6 | − | 4.08612e6i | 0.573436 | − | 0.309626i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.21203e6 | − | 4.21203e6i | −0.316915 | − | 0.316915i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.40476e6i | − | 0.403795i | −0.979407 | − | 0.201897i | \(-0.935289\pi\) | ||
0.979407 | − | 0.201897i | \(-0.0647107\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.56388e6i | − | 0.338579i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.81065e7 | − | 1.81065e7i | −1.33386 | − | 1.33386i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.36247e6 | + | 1.12553e7i | −0.245976 | + | 0.823367i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.26991e7 | + | 1.26991e7i | −0.922516 | + | 0.922516i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.95216e6 | −0.357250 | −0.178625 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178625 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.22561e7 | −0.878038 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.27561e7 | + | 1.27561e7i | −0.907555 | + | 0.907555i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.32222e6 | + | 6.11573e6i | 0.658680 | + | 0.432119i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 824940. | + | 824940.i | 0.0578877 | + | 0.0578877i | 0.735458 | − | 0.677570i | \(-0.236967\pi\) |
−0.677570 | + | 0.735458i | \(0.736967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59583e7i | 1.11216i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.24109e6i | 0.570415i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.29259e7 | − | 1.29259e7i | −0.888590 | − | 0.888590i | 0.105798 | − | 0.994388i | \(-0.466260\pi\) |
−0.994388 | + | 0.105798i | \(0.966260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.85369e6 | − | 2.64499e6i | −0.604514 | − | 0.180595i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.26111e6 | + | 4.26111e6i | −0.288971 | + | 0.288971i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48270e7 | 0.998714 | 0.499357 | − | 0.866396i | \(-0.333570\pi\) | ||||
0.499357 | + | 0.866396i | \(0.333570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.35685e6 | 0.291492 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.13856e6 | − | 2.13856e6i | 0.142118 | − | 0.142118i | −0.632468 | − | 0.774586i | \(-0.717958\pi\) |
0.774586 | + | 0.632468i | \(0.217958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.04858e6 | − | 5.64606e6i | −0.201237 | − | 0.372696i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.28499e6 | + | 4.28499e6i | 0.280963 | + | 0.280963i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.48236e7i | 0.965491i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 499674.i | − | 0.0323286i | −0.999869 | − | 0.0161643i | \(-0.994855\pi\) | ||
0.999869 | − | 0.0161643i | \(-0.00514548\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.82252e6 | + | 1.82252e6i | 0.117134 | + | 0.117134i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.03316e7 | − | 1.91344e7i | −0.659630 | − | 1.22165i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51219e7 | − | 1.51219e7i | 0.959105 | − | 0.959105i | −0.0400909 | − | 0.999196i | \(-0.512765\pi\) |
0.999196 | + | 0.0400909i | \(0.0127647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.79567e7 | 1.13141 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.08023e7 | 1.92806 | 0.964032 | − | 0.265788i | \(-0.0856321\pi\) | ||||
0.964032 | + | 0.265788i | \(0.0856321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.03852e6 | + | 3.03852e6i | −0.188952 | + | 0.188952i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.39281e6 | − | 1.31233e6i | −0.271387 | − | 0.0810752i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −359714. | − | 359714.i | −0.0220785 | − | 0.0220785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.19605e6i | − | 0.377832i | −0.981993 | − | 0.188916i | \(-0.939503\pi\) | ||
0.981993 | − | 0.188916i | \(-0.0604975\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.51853e7i | − | 0.920001i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.65596e6 | + | 6.65596e6i | 0.400647 | + | 0.400647i | 0.878461 | − | 0.477814i | \(-0.158571\pi\) |
−0.477814 | + | 0.878461i | \(0.658571\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.36330e7 | − | 1.55041e7i | −1.41340 | − | 0.927243i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.54756e6 | − | 1.54756e6i | 0.0919592 | − | 0.0919592i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00555e7 | 0.593693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.43835e7 | 1.43043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.03114e7 | − | 1.03114e7i | 0.601056 | − | 0.601056i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.21208e6 | + | 1.74466e7i | −0.301882 | + | 1.01050i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.68934e6 | − | 2.68934e6i | −0.154778 | − | 0.154778i | 0.625470 | − | 0.780248i | \(-0.284907\pi\) |
−0.780248 | + | 0.625470i | \(0.784907\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.07361e7i | − | 0.613981i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.19961e6i | − | 0.181826i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.40600e6 | − | 9.40600e6i | −0.531156 | − | 0.531156i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.10710e7 | − | 5.97780e6i | 0.621256 | − | 0.335446i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.61839e6 | − | 3.61839e6i | 0.201776 | − | 0.201776i | −0.598984 | − | 0.800761i | \(-0.704429\pi\) |
0.800761 | + | 0.598984i | \(0.204429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.66080e7 | 0.920343 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.09738e6 | 0.445926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.29530e7 | + | 1.29530e7i | −0.708895 | + | 0.708895i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.58379e6 | − | 5.17476e6i | 0.521252 | − | 0.281449i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.41990e6 | + | 1.41990e6i | 0.0767493 | + | 0.0767493i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.19735e7i | − | 0.643204i | −0.946875 | − | 0.321602i | \(-0.895779\pi\) | ||
0.946875 | − | 0.321602i | \(-0.104221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.43266e7i | − | 0.764876i | −0.923981 | − | 0.382438i | \(-0.875085\pi\) | ||
0.923981 | − | 0.382438i | \(-0.124915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00458e6 | − | 6.00458e6i | −0.318608 | − | 0.318608i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.56159e6 | − | 2.53113e7i | 0.398767 | − | 1.33481i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.76448e6 | − | 2.76448e6i | 0.144896 | − | 0.144896i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.73216e6 | 0.0902359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.43974e6 | 0.333434 | 0.166717 | − | 0.986005i | \(-0.446683\pi\) | ||||
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.25915e7 | + | 1.25915e7i | −0.648002 | + | 0.648002i | −0.952510 | − | 0.304508i | \(-0.901508\pi\) |
0.304508 | + | 0.952510i | \(0.401508\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.94067e7 | − | 4.03080e6i | 0.992697 | − | 0.206185i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.91817e6 | + | 1.91817e6i | 0.0975268 | + | 0.0975268i | 0.754187 | − | 0.656660i | \(-0.228031\pi\) |
−0.656660 | + | 0.754187i | \(0.728031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.88830e7i | 0.954300i | 0.878822 | + | 0.477150i | \(0.158330\pi\) | ||||
−0.878822 | + | 0.477150i | \(0.841670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.10593e7i | − | 0.555552i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.26176e7 | − | 1.26176e7i | −0.630035 | − | 0.630035i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.18126e7 | − | 6.51639e6i | −1.08266 | − | 0.323438i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.61408e7 | + | 2.61408e7i | −1.28975 | + | 1.28975i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −468493. | −0.0229772 | −0.0114886 | − | 0.999934i | \(-0.503657\pi\) | ||||
−0.0114886 | + | 0.999934i | \(0.503657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.78221e6 | 0.379414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.03402e6 | − | 6.03402e6i | 0.292441 | − | 0.292441i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.39477e6 | + | 8.13922e6i | 0.211736 | + | 0.392140i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.60261e6 | + | 2.60261e6i | 0.124652 | + | 0.124652i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 3.21507e7i | − | 1.53081i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.57473e6i | − | 0.311210i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.66492e7 | + | 1.66492e7i | 0.783466 | + | 0.783466i | 0.980414 | − | 0.196948i | \(-0.0631030\pi\) |
−0.196948 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.03335e6 | + | 1.91379e6i | 0.0483428 | + | 0.0895321i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.05630e7 | − | 2.05630e7i | 0.956391 | − | 0.956391i | −0.0426973 | − | 0.999088i | \(-0.513595\pi\) |
0.999088 | + | 0.0426973i | \(0.0135951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.68768e7 | −1.70518 | −0.852589 | − | 0.522582i | \(-0.824969\pi\) | ||||
−0.852589 | + | 0.522582i | \(0.824969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.35128e7 | −0.621210 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.56410e6 | + | 8.56410e6i | −0.391431 | + | 0.391431i | −0.875197 | − | 0.483767i | \(-0.839268\pi\) |
0.483767 | + | 0.875197i | \(0.339268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.33512e7 | − | 3.98858e6i | −0.606706 | − | 0.181250i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.41170e6 | + | 7.41170e6i | 0.334865 | + | 0.334865i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.81027e7i | 1.71162i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.90256e6i | − | 0.263630i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.42896e6 | + | 5.42896e6i | 0.241091 | + | 0.241091i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.19608e6 | − | 7.74392e6i | 0.406053 | − | 0.341933i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.83761e7 | + | 1.83761e7i | −0.806779 | + | 0.806779i | −0.984145 | − | 0.177366i | \(-0.943242\pi\) |
0.177366 | + | 0.984145i | \(0.443242\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.34213e7 | 1.45898 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.58839e7 | −0.689472 | −0.344736 | − | 0.938700i | \(-0.612032\pi\) | ||||
−0.344736 | + | 0.938700i | \(0.612032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.53863e7 | − | 1.53863e7i | 0.664098 | − | 0.664098i | −0.292246 | − | 0.956343i | \(-0.594402\pi\) |
0.956343 | + | 0.292246i | \(0.0944025\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −245702. | + | 822450.i | −0.0105451 | + | 0.0352981i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.45205e7 | − | 2.45205e7i | −1.04645 | − | 1.04645i | −0.998867 | − | 0.0475864i | \(-0.984847\pi\) |
−0.0475864 | − | 0.998867i | \(-0.515153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.17280e7i | 0.497703i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.96803e7i | − | 0.830496i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.57115e6 | − | 5.57115e6i | −0.233785 | − | 0.233785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.01278e7 | + | 1.08680e7i | −0.839923 | + | 0.453516i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.24369e7 | + | 1.24369e7i | −0.516098 | + | 0.516098i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.22694e7 | 1.33166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.42967e7 | 0.997092 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.71496e6 | + | 3.71496e6i | −0.151612 | + | 0.151612i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.99046e7 | − | 1.61470e7i | 1.21372 | − | 0.655345i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.02264e7 | + | 2.02264e7i | 0.816394 | + | 0.816394i | 0.985584 | − | 0.169189i | \(-0.0541150\pi\) |
−0.169189 | + | 0.985584i | \(0.554115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.80196e6i | 0.192757i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.37080e7i | 1.34567i | 0.739795 | + | 0.672833i | \(0.234923\pi\) | ||||
−0.739795 | + | 0.672833i | \(0.765077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.57743e7 | − | 3.57743e7i | −1.42035 | − | 1.42035i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.42476e6 | + | 2.15059e7i | −0.253690 | + | 0.849190i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.31301e6 | − | 4.31301e6i | 0.169378 | − | 0.169378i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.78592e7 | −1.47871 | −0.739355 | − | 0.673315i | \(-0.764870\pi\) | ||||
−0.739355 | + | 0.673315i | \(0.764870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.34331e7 | −0.521827 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.68882e7 | + | 1.68882e7i | −0.652497 | + | 0.652497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.47585e6 | − | 7.10564e6i | −0.0567137 | − | 0.273054i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.98634e6 | + | 6.98634e6i | 0.267024 | + | 0.267024i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.07311e6i | 0.0407947i | 0.999792 | + | 0.0203973i | \(0.00649312\pi\) | ||||
−0.999792 | + | 0.0203973i | \(0.993507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.46516e6i | 0.320082i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.12639e6 | + | 8.12639e6i | 0.305628 | + | 0.305628i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.66744e7 | + | 1.09563e7i | 1.37194 | + | 0.409858i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.76810e7 | − | 1.76810e7i | 0.657898 | − | 0.657898i | −0.296985 | − | 0.954882i | \(-0.595981\pi\) |
0.954882 | + | 0.296985i | \(0.0959810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.82697e7 | 1.04630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.81767e7 | −1.03733 | −0.518664 | − | 0.854978i | \(-0.673571\pi\) | ||||
−0.518664 | + | 0.854978i | \(0.673571\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.87042e7 | + | 2.87042e7i | −1.05116 | + | 1.05116i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.47094e6 | − | 1.38364e7i | −0.272142 | − | 0.504014i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 812310. | + | 812310.i | 0.0294338 | + | 0.0294338i | 0.721671 | − | 0.692237i | \(-0.243375\pi\) |
−0.692237 | + | 0.721671i | \(0.743375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.79427e7i | − | 0.646729i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.48907e7i | 0.533906i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.90628e7 | + | 2.90628e7i | 1.03659 | + | 1.03659i | 0.999305 | + | 0.0372807i | \(0.0118696\pi\) |
0.0372807 | + | 0.999305i | \(0.488130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.80026e6 | + | 3.33413e6i | 0.0638744 | + | 0.118297i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.60012e7 | + | 1.60012e7i | −0.564773 | + | 0.564773i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.54762e6 | 0.159675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.31778e7 | −1.85747 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.44988e6 | − | 8.44988e6i | 0.293619 | − | 0.293619i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.82751e7 | − | 8.44702e6i | −0.977430 | − | 0.292002i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.81711e7 | + | 2.81711e7i | 0.968809 | + | 0.968809i | 0.999528 | − | 0.0307195i | \(-0.00977986\pi\) |
−0.0307195 | + | 0.999528i | \(0.509780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.41964e7i | − | 0.485700i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.42018e7i | 1.50450i | 0.658879 | + | 0.752249i | \(0.271031\pi\) | ||||
−0.658879 | + | 0.752249i | \(0.728969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.36374e7 | + | 1.36374e7i | 0.461795 | + | 0.461795i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.06495e7 | + | 1.62330e7i | −0.358770 | + | 0.546873i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.48781e7 | − | 1.48781e7i | 0.498667 | − | 0.498667i | −0.412356 | − | 0.911023i | \(-0.635294\pi\) |
0.911023 | + | 0.412356i | \(0.135294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.76029e7 | −2.25429 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.46409e6 | 0.114926 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −955948. | + | 955948.i | −0.0315537 | + | 0.0315537i | −0.722708 | − | 0.691154i | \(-0.757103\pi\) |
0.691154 | + | 0.722708i | \(0.257103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.74077e6 | + | 5.82696e6i | −0.0571677 | + | 0.191360i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.48662e6 | + | 7.48662e6i | 0.244621 | + | 0.244621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.57828e7i | 0.513089i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.39902e7i | − | 0.775978i | −0.921664 | − | 0.387989i | \(-0.873170\pi\) | ||
0.921664 | − | 0.387989i | \(-0.126830\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.48845e7 | + | 1.48845e7i | 0.479029 | + | 0.479029i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.46882e7 | − | 2.41293e7i | 1.43098 | − | 0.772659i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.04726e7 | − | 3.04726e7i | 0.970894 | − | 0.970894i | −0.0286939 | − | 0.999588i | \(-0.509135\pi\) |
0.999588 | + | 0.0286939i | \(0.00913479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.49211e6 | −0.300919 |
(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 | 80.6.n.d.63.3 | yes | 20 | |
4.3 | odd | 2 | inner | 80.6.n.d.63.8 | yes | 20 | |
5.2 | odd | 4 | inner | 80.6.n.d.47.8 | yes | 20 | |
5.3 | odd | 4 | 400.6.n.g.207.3 | 20 | |||
5.4 | even | 2 | 400.6.n.g.143.8 | 20 | |||
20.3 | even | 4 | 400.6.n.g.207.8 | 20 | |||
20.7 | even | 4 | inner | 80.6.n.d.47.3 | ✓ | 20 | |
20.19 | odd | 2 | 400.6.n.g.143.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.n.d.47.3 | ✓ | 20 | 20.7 | even | 4 | inner | |
80.6.n.d.47.8 | yes | 20 | 5.2 | odd | 4 | inner | |
80.6.n.d.63.3 | yes | 20 | 1.1 | even | 1 | trivial | |
80.6.n.d.63.8 | yes | 20 | 4.3 | odd | 2 | inner | |
400.6.n.g.143.3 | 20 | 20.19 | odd | 2 | |||
400.6.n.g.143.8 | 20 | 5.4 | even | 2 | |||
400.6.n.g.207.3 | 20 | 5.3 | odd | 4 | |||
400.6.n.g.207.8 | 20 | 20.3 | even | 4 |