Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 172x^{6} + 13179x^{4} - 522628x^{2} + 8755681 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.6 | ||
Root | \(6.86097 + 3.28347i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.7.h.f.65.8 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 22.4164 | − | 15.0501i | 0.830237 | − | 0.557410i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 122.733 | 0.981863 | 0.490931 | − | 0.871198i | \(-0.336657\pi\) | ||||
0.490931 | + | 0.871198i | \(0.336657\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −206.594 | −0.602315 | −0.301157 | − | 0.953574i | \(-0.597373\pi\) | ||||
−0.301157 | + | 0.953574i | \(0.597373\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 275.991 | − | 674.737i | 0.378588 | − | 0.925565i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −142.827 | −0.107308 | −0.0536539 | − | 0.998560i | \(-0.517087\pi\) | ||||
−0.0536539 | + | 0.998560i | \(0.517087\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3499.27i | − | 1.59275i | −0.604804 | − | 0.796374i | \(-0.706749\pi\) | ||
0.604804 | − | 0.796374i | \(-0.293251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2751.23 | − | 1847.14i | 0.815179 | − | 0.547300i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3382.86i | − | 0.688554i | −0.938868 | − | 0.344277i | \(-0.888124\pi\) | ||
0.938868 | − | 0.344277i | \(-0.111876\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 755.858i | − | 0.110200i | −0.998481 | − | 0.0550998i | \(-0.982452\pi\) | ||
0.998481 | − | 0.0550998i | \(-0.0175477\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4631.09 | + | 3109.25i | −0.500064 | + | 0.335736i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16911.3i | 1.38993i | 0.719042 | + | 0.694967i | \(0.244581\pi\) | ||||
−0.719042 | + | 0.694967i | \(0.755419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −561.656 | −0.0359460 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3968.12 | − | 19278.9i | −0.201601 | − | 0.979468i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −41131.3 | −1.68647 | −0.843235 | − | 0.537546i | \(-0.819352\pi\) | ||||
−0.843235 | + | 0.537546i | \(0.819352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22916.1 | 0.769229 | 0.384615 | − | 0.923077i | \(-0.374334\pi\) | ||||
0.384615 | + | 0.923077i | \(0.374334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3201.66 | + | 2149.55i | −0.0890909 | + | 0.0598144i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −25355.8 | −0.591390 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 26835.0i | − | 0.529780i | −0.964279 | − | 0.264890i | \(-0.914664\pi\) | ||
0.964279 | − | 0.264890i | \(-0.0853357\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −52664.2 | − | 78441.0i | −0.887814 | − | 1.32236i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40460.6i | 0.587057i | 0.955950 | + | 0.293528i | \(0.0948296\pi\) | ||||
−0.955950 | + | 0.293528i | \(0.905170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 128319.i | − | 1.61393i | −0.590599 | − | 0.806965i | \(-0.701108\pi\) | ||
0.590599 | − | 0.806965i | \(-0.298892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 33873.1 | − | 82812.4i | 0.371721 | − | 0.908778i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 60668.5i | 0.584345i | 0.956366 | + | 0.292173i | \(0.0943782\pi\) | ||||
−0.956366 | + | 0.292173i | \(0.905622\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −74968.0 | −0.637217 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −50912.4 | − | 75831.7i | −0.383807 | − | 0.571663i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5295.60 | 0.0355703 | 0.0177852 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177852 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17529.5 | −0.105361 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11375.7 | − | 16943.6i | −0.0614263 | − | 0.0914917i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −97392.6 | −0.474209 | −0.237105 | − | 0.971484i | \(-0.576198\pi\) | ||||
−0.237105 | + | 0.971484i | \(0.576198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 213477.i | 0.940506i | 0.882532 | + | 0.470253i | \(0.155837\pi\) | ||||
−0.882532 | + | 0.470253i | \(0.844163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −57018.0 | + | 139397.i | −0.228029 | + | 0.557481i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 429475.i | − | 1.56386i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 385320.i | − | 1.28114i | −0.767898 | − | 0.640572i | \(-0.778697\pi\) | ||
0.767898 | − | 0.640572i | \(-0.221303\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 254517. | + | 379091.i | 0.774763 | + | 1.15397i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 356373.i | − | 0.995703i | −0.867262 | − | 0.497851i | \(-0.834123\pi\) | ||
0.867262 | − | 0.497851i | \(-0.165877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −141507. | −0.363754 | −0.181877 | − | 0.983321i | \(-0.558217\pi\) | ||||
−0.181877 | + | 0.983321i | \(0.558217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12590.3 | + | 8452.97i | −0.0298437 | + | 0.0200367i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29507.1 | 0.0646330 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 722207. | 1.46481 | 0.732403 | − | 0.680871i | \(-0.238399\pi\) | ||||
0.732403 | + | 0.680871i | \(0.238399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −379099. | − | 372442.i | −0.713342 | − | 0.700816i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8040.09 | −0.0140613 | −0.00703067 | − | 0.999975i | \(-0.502238\pi\) | ||||
−0.00703067 | + | 0.999975i | \(0.502238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 415188.i | − | 0.676065i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −922016. | + | 619029.i | −1.40017 | + | 0.940055i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 410420.i | 0.582181i | 0.956695 | + | 0.291091i | \(0.0940182\pi\) | ||||
−0.956695 | + | 0.291091i | \(0.905982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 722927.i | 0.959335i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 513697. | − | 344889.i | 0.638643 | − | 0.428776i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 92768.6i | − | 0.108201i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.52876e6 | −1.67504 | −0.837520 | − | 0.546407i | \(-0.815995\pi\) | ||||
−0.837520 | + | 0.546407i | \(0.815995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39418.8 | + | 96370.4i | −0.0406254 | + | 0.0993203i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −175149. | −0.169998 | −0.0849992 | − | 0.996381i | \(-0.527089\pi\) | ||||
−0.0849992 | + | 0.996381i | \(0.527089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33846e6 | 1.22488 | 0.612440 | − | 0.790517i | \(-0.290188\pi\) | ||||
0.612440 | + | 0.790517i | \(0.290188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −568387. | + | 381607.i | −0.490994 | + | 0.329647i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.06224e6 | 0.867103 | 0.433552 | − | 0.901129i | \(-0.357260\pi\) | ||||
0.433552 | + | 0.901129i | \(0.357260\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 390541.i | 0.301570i | 0.988567 | + | 0.150785i | \(0.0481801\pi\) | ||||
−0.988567 | + | 0.150785i | \(0.951820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −403868. | − | 601544.i | −0.295305 | − | 0.439843i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.53393e6i | − | 1.75614i | −0.478533 | − | 0.878070i | \(-0.658831\pi\) | ||
0.478533 | − | 0.878070i | \(-0.341169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.07557e6i | 1.36472i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.36109e6 | − | 965765.i | −1.47419 | − | 0.602995i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 698879.i | 0.414726i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.75116e6 | −0.988485 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 608934. | + | 906980.i | 0.327231 | + | 0.487397i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.98663e6 | −1.01716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.59182e6 | −1.26530 | −0.632649 | − | 0.774439i | \(-0.718032\pi\) | ||||
−0.632649 | + | 0.774439i | \(0.718032\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.93121e6 | − | 2.87645e6i | −0.899621 | − | 1.33995i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91522.7 | 0.0407113 | 0.0203557 | − | 0.999793i | \(-0.493520\pi\) | ||||
0.0203557 | + | 0.999793i | \(0.493520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 156156.i | 0.0663748i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −487019. | − | 2.36615e6i | −0.197945 | − | 0.961703i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.50257e6i | − | 0.973249i | −0.873611 | − | 0.486624i | \(-0.838228\pi\) | ||
0.873611 | − | 0.486624i | \(-0.161772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 988914.i | 0.368226i | 0.982905 | + | 0.184113i | \(0.0589412\pi\) | ||||
−0.982905 | + | 0.184113i | \(0.941059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 913065. | + | 1.35997e6i | 0.325720 | + | 0.485145i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 499789.i | 0.170914i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.04816e6 | −1.65588 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.68051e6 | + | 1.12827e6i | −0.529042 | + | 0.355191i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.84935e6 | 1.46597 | 0.732985 | − | 0.680245i | \(-0.238127\pi\) | ||||
0.732985 | + | 0.680245i | \(0.238127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.63349e6 | 1.05534 | 0.527671 | − | 0.849449i | \(-0.323065\pi\) | ||||
0.527671 | + | 0.849449i | \(0.323065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.28254e6 | − | 933639.i | −0.637301 | − | 0.260678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.81256e6 | 0.755278 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.51450e6i | − | 1.16657i | −0.812268 | − | 0.583285i | \(-0.801767\pi\) | ||
0.812268 | − | 0.583285i | \(-0.198233\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 118708. | − | 79699.2i | 0.0295318 | − | 0.0198273i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.49377e6i | − | 0.837177i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.64963e6i | − | 1.30454i | −0.757987 | − | 0.652269i | \(-0.773817\pi\) | ||
0.757987 | − | 0.652269i | \(-0.226183\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −392949. | + | 263820.i | −0.0874750 | + | 0.0587295i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.42913e6i | 0.950975i | 0.879723 | + | 0.475487i | \(0.157728\pi\) | ||||
−0.879723 | + | 0.475487i | \(0.842272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.41807e6 | −1.53685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −510006. | − | 208610.i | −0.101997 | − | 0.0417202i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.66599e6 | 0.321762 | 0.160881 | − | 0.986974i | \(-0.448566\pi\) | ||||
0.160881 | + | 0.986974i | \(0.448566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 116035. | 0.0216508 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.18319e6 | + | 1.46577e6i | −0.393706 | + | 0.264329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.85953e6 | −0.847296 | −0.423648 | − | 0.905827i | \(-0.639251\pi\) | ||||
−0.423648 | + | 0.905827i | \(0.639251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.92904e6i | 1.50581i | 0.658132 | + | 0.752903i | \(0.271347\pi\) | ||||
−0.658132 | + | 0.752903i | \(0.728653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.21285e6 | + | 4.78539e6i | 0.524248 | + | 0.780843i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.29353e6i | − | 0.520171i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 483163.i | 0.0738871i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 819790. | + | 3.98289e6i | 0.121427 | + | 0.589948i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.88180e6i | − | 1.13116i | −0.824692 | − | 0.565582i | \(-0.808652\pi\) | ||
0.824692 | − | 0.565582i | \(-0.191348\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.97521e6 | −0.831154 | −0.415577 | − | 0.909558i | \(-0.636420\pi\) | ||||
−0.415577 | + | 0.909558i | \(0.636420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.46363e6 | − | 9.62729e6i | −0.871711 | − | 1.29837i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.16081e6 | 0.544226 | 0.272113 | − | 0.962265i | \(-0.412278\pi\) | ||||
0.272113 | + | 0.962265i | \(0.412278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.21801e7 | −1.54558 | −0.772792 | − | 0.634660i | \(-0.781140\pi\) | ||||
−0.772792 | + | 0.634660i | \(0.781140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.79910e6 | − | 8.63750e6i | −0.714122 | − | 1.06365i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.49747e6 | 1.01578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.96584e6i | 0.576409i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.14107e7 | + | 4.66737e6i | 1.28647 | + | 0.526212i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 107957.i | 0.0118253i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.27411e7i | − | 1.35631i | −0.734919 | − | 0.678154i | \(-0.762780\pi\) | ||
0.734919 | − | 0.678154i | \(-0.237220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.36344e6 | − | 7.98860e6i | −0.555015 | − | 0.826669i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.57489e7i | − | 1.58466i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.73433e6 | −0.463318 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.17207e6 | + | 2.12969e6i | −0.302003 | + | 0.202760i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.18375e7 | −1.09669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.46685e6 | −0.763497 | −0.381749 | − | 0.924266i | \(-0.624678\pi\) | ||||
−0.381749 | + | 0.924266i | \(0.624678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −155012. | + | 378970.i | −0.0136087 | + | 0.0332704i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.29952e6 | −0.624046 | −0.312023 | − | 0.950075i | \(-0.601007\pi\) | ||||
−0.312023 | + | 0.950075i | \(0.601007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.83981e7i | − | 1.53202i | −0.642826 | − | 0.766012i | \(-0.722238\pi\) | ||
0.642826 | − | 0.766012i | \(-0.277762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 661443. | − | 444084.i | 0.0536607 | − | 0.0360271i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.00421e7i | − | 1.58444i | −0.610237 | − | 0.792219i | \(-0.708926\pi\) | ||
0.610237 | − | 0.792219i | \(-0.291074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.44601e6i | 0.573747i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.61893e7 | − | 1.08693e7i | 1.21614 | − | 0.816498i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.39694e7i | 1.75575i | 0.478887 | + | 0.877877i | \(0.341040\pi\) | ||||
−0.478887 | + | 0.877877i | \(0.658960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.88680e6 | 0.420560 | 0.210280 | − | 0.977641i | \(-0.432562\pi\) | ||||
0.210280 | + | 0.977641i | \(0.432562\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.41033e7 | − | 2.64335e6i | −0.982885 | − | 0.184219i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.20103e6 | −0.625660 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.64495e6 | −0.175520 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −180230. | + | 121004.i | −0.0116743 | + | 0.00783793i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.80782e7 | 1.77561 | 0.887807 | − | 0.460217i | \(-0.152228\pi\) | ||||
0.887807 | + | 0.460217i | \(0.152228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.41539e6i | − | 0.149151i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.24862e6 | − | 9.30703e6i | −0.376845 | − | 0.561294i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62429e7i | 0.956894i | 0.878116 | + | 0.478447i | \(0.158800\pi\) | ||||
−0.878116 | + | 0.478447i | \(0.841200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.54394e6i | 0.319094i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13519e7 | + | 2.77528e7i | −0.638477 | + | 1.56094i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 572672.i | 0.0314803i | 0.999876 | + | 0.0157401i | \(0.00501045\pi\) | ||||
−0.999876 | + | 0.0157401i | \(0.994990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 649944. | 0.0349252 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.17685e6 | + | 9.20014e6i | 0.324514 | + | 0.483349i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.60268e7 | −0.823358 | −0.411679 | − | 0.911329i | \(-0.635057\pi\) | ||||
−0.411679 | + | 0.911329i | \(0.635057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.21330e7 | 1.11207 | 0.556035 | − | 0.831159i | \(-0.312322\pi\) | ||||
0.556035 | + | 0.831159i | \(0.312322\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.08801e7 | + | 1.62054e7i | 0.534743 | + | 0.796476i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 80219.5 | 0.00385728 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 329177.i | − | 0.0154878i | −0.999970 | − | 0.00774392i | \(-0.997535\pi\) | ||
0.999970 | − | 0.00774392i | \(-0.00246499\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.32463e6 | − | 1.54624e7i | 0.291221 | − | 0.711972i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.42415e7i | 1.09255i | 0.837607 | + | 0.546274i | \(0.183954\pi\) | ||||
−0.837607 | + | 0.546274i | \(0.816046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.32930e7i | 1.02770i | 0.857880 | + | 0.513850i | \(0.171781\pi\) | ||||
−0.857880 | + | 0.513850i | \(0.828219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.39617e6 | − | 2.07954e6i | −0.0603122 | − | 0.0898323i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.35890e6i | − | 0.353593i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26938e7 | 0.525894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.42694e7 | + | 2.30080e7i | −1.39068 | + | 0.933684i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.21239e7 | 0.481993 | 0.240996 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240996 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19533e7 | −0.465608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 566753. | + | 2.75353e6i | 0.0216334 | + | 0.105104i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.91772e7 | 2.21381 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65099e7i | 0.972094i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.92622e6 | + | 2.63601e6i | −0.141139 | + | 0.0947588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.62006e7i | 0.923448i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.04782e7i | − | 0.362136i | −0.983471 | − | 0.181068i | \(-0.942045\pi\) | ||
0.983471 | − | 0.181068i | \(-0.0579555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.00035e7 | − | 2.01439e7i | 1.01694 | − | 0.682761i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.87497e7i | 1.95310i | 0.215292 | + | 0.976550i | \(0.430930\pi\) | ||||
−0.215292 | + | 0.976550i | \(0.569070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.12380e7 | 1.67093 | 0.835467 | − | 0.549540i | \(-0.185197\pi\) | ||||
0.835467 | + | 0.549540i | \(0.185197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.99798e6 | + | 1.71085e7i | −0.223893 | + | 0.547370i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.13280e7 | 1.61130 | 0.805651 | − | 0.592390i | \(-0.201816\pi\) | ||||
0.805651 | + | 0.592390i | \(0.201816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.87464e6 | 0.180971 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.38116e7 | − | 1.59868e7i | 0.719901 | − | 0.483332i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.55697e6 | −0.0758783 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.96539e6i | 0.0572529i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.87768e6 | + | 8.75454e6i | 0.168098 | + | 0.250374i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.25337e7i | − | 0.351960i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.26211e7i | 1.45103i | 0.688207 | + | 0.725515i | \(0.258398\pi\) | ||||
−0.688207 | + | 0.725515i | \(0.741602\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.81065e7 | − | 7.40620e6i | −0.490346 | − | 0.200569i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.72915e7i | − | 1.25791i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.13406e7 | 0.818876 | 0.409438 | − | 0.912338i | \(-0.365725\pi\) | ||||
0.409438 | + | 0.912338i | \(0.365725\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.81358e7 | − | 5.68016e7i | −0.978890 | − | 1.45801i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.27303e6 | −0.0825443 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.97935e7 | 0.986120 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.12375e7 | + | 4.65269e7i | 0.760710 | + | 1.13304i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.67725e7 | 1.35878 | 0.679391 | − | 0.733777i | \(-0.262244\pi\) | ||||
0.679391 | + | 0.733777i | \(0.262244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.45512e6i | − | 0.222429i | −0.993796 | − | 0.111214i | \(-0.964526\pi\) | ||
0.993796 | − | 0.111214i | \(-0.0354740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.74619e7 | + | 1.38855e7i | −1.56005 | + | 0.321100i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.84722e7i | − | 0.419948i | −0.977707 | − | 0.209974i | \(-0.932662\pi\) | ||
0.977707 | − | 0.209974i | \(-0.0673379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.37386e7i | − | 0.977643i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.05182e7 | + | 1.56664e7i | 0.231172 | + | 0.344321i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.02076e7i | − | 1.73353i | −0.498714 | − | 0.866767i | \(-0.666194\pi\) | ||
0.498714 | − | 0.866767i | \(-0.333806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.64746e7 | 0.987856 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.92548e7 | + | 2.63551e7i | −0.820677 | + | 0.550992i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.73675e7 | −0.357157 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.88440e6 | −0.139273 | −0.0696366 | − | 0.997572i | \(-0.522184\pi\) | ||||
−0.0696366 | + | 0.997572i | \(0.522184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.73002e7 | + | 1.11667e7i | 0.543360 | + | 0.222253i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.09404e6 | −0.0214245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.53815e7i | 0.874485i | 0.899344 | + | 0.437243i | \(0.144045\pi\) | ||||
−0.899344 | + | 0.437243i | \(0.855955\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.45332e7 | + | 2.98990e7i | −0.844481 | + | 0.566973i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.43929e8i | 2.68612i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.51053e7i | − | 0.277467i | −0.990330 | − | 0.138734i | \(-0.955697\pi\) | ||
0.990330 | − | 0.138734i | \(-0.0443032\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.80992e7 | + | 3.90070e7i | −1.05050 | + | 0.705290i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.37036e7i | 0.421908i | 0.977496 | + | 0.210954i | \(0.0676570\pi\) | ||||
−0.977496 | + | 0.210954i | \(0.932343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.62149e6 | 0.0634607 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.65814e7 | − | 3.54148e7i | −1.49380 | − | 0.611015i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.21550e7 | −0.546261 | −0.273130 | − | 0.961977i | \(-0.588059\pi\) | ||||
−0.273130 | + | 0.961977i | \(0.588059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.72087e7 | 0.957044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.05161e6 | − | 1.37742e6i | 0.0338000 | − | 0.0226929i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.86385e7 | 1.43824 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.01939e8i | − | 1.62918i | −0.580035 | − | 0.814591i | \(-0.696961\pi\) | ||
0.580035 | − | 0.814591i | \(-0.303039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.35015e6 | + | 3.50045e6i | 0.0369980 | + | 0.0551068i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.78698e7i | 0.432215i | 0.976370 | + | 0.216108i | \(0.0693362\pi\) | ||||
−0.976370 | + | 0.216108i | \(0.930664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.01896e7i | − | 1.22519i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.65279e7 | − | 4.57109e7i | −0.700404 | − | 0.688105i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.83275e6i | 0.0568495i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07187e8 | 1.56665 | 0.783326 | − | 0.621611i | \(-0.213522\pi\) | ||||
0.783326 | + | 0.621611i | \(0.213522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.76638e7 | − | 5.60986e7i | −0.542499 | − | 0.808028i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.01207e7 | 0.285623 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −986783. | −0.0138063 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.48832e7 | + | 2.21679e7i | 0.205253 | + | 0.305715i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.69022e6 | 0.0909491 | 0.0454745 | − | 0.998965i | \(-0.485520\pi\) | ||||
0.0454745 | + | 0.998965i | \(0.485520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 5.45684e7i | − | 0.731299i | −0.930753 | − | 0.365649i | \(-0.880847\pi\) | ||
0.930753 | − | 0.365649i | \(-0.119153\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.09353e7 | + | 1.67439e7i | 0.540850 | + | 0.221226i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.90001e6i | 0.0247508i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.41031e7i | − | 0.566481i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.52185e6 | + | 1.12035e7i | 0.0952693 | + | 0.141899i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.58145e7i | 0.572231i | 0.958195 | + | 0.286115i | \(0.0923641\pi\) | ||||
−0.958195 | + | 0.286115i | \(0.907636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.27032e6 | −0.0772372 | −0.0386186 | − | 0.999254i | \(-0.512296\pi\) | ||||
−0.0386186 | + | 0.999254i | \(0.512296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13162e8 | + | 7.59752e7i | −1.37477 | + | 0.923005i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.27826e7 | 0.153170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.02491e7 | −0.475732 | −0.237866 | − | 0.971298i | \(-0.576448\pi\) | ||||
−0.237866 | + | 0.971298i | \(0.576448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.06905e7 | + | 5.05837e7i | −0.241243 | + | 0.589786i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.03746e7 | 0.809477 | 0.404739 | − | 0.914432i | \(-0.367363\pi\) | ||||
0.404739 | + | 0.914432i | \(0.367363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.03720e7i | 0.571622i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.08705e8 | − | 7.29831e7i | 1.21710 | − | 0.817146i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.22328e8i | − | 1.35141i | −0.737170 | − | 0.675707i | \(-0.763838\pi\) | ||
0.737170 | − | 0.675707i | \(-0.236162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.77884e6i | − | 0.0629958i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.14498e7 | − | 5.46843e7i | 0.876184 | − | 0.588258i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.87269e7i | 0.941935i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.10853e6 | −0.0116144 | −0.00580722 | − | 0.999983i | \(-0.501849\pi\) | ||||
−0.00580722 | + | 0.999983i | \(0.501849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.52178e7 | + | 1.34236e7i | −0.674416 | + | 0.138813i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.08136e7 | 0.416583 | 0.208292 | − | 0.978067i | \(-0.433210\pi\) | ||||
0.208292 | + | 0.978067i | \(0.433210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.22650e7 | 0.325079 | 0.162540 | − | 0.986702i | \(-0.448031\pi\) | ||||
0.162540 | + | 0.986702i | \(0.448031\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.30475e7 | − | 4.23292e7i | 0.627060 | − | 0.420999i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.16957e7 | 0.900323 | 0.450162 | − | 0.892947i | \(-0.351366\pi\) | ||||
0.450162 | + | 0.892947i | \(0.351366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.96049e7i | 0.771651i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.79435e7 | − | 1.01199e8i | −0.650257 | − | 0.968529i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.83273e7i | 0.173187i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 424533.i | 0.00396123i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.46154e6 | − | 3.57314e6i | 0.0134665 | − | 0.0329227i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.72123e7i | 0.338594i | 0.985565 | + | 0.169297i | \(0.0541498\pi\) | ||||
−0.985565 | + | 0.169297i | \(0.945850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.39027e7 | −0.843807 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.25816e7 | − | 7.83179e7i | −0.466651 | − | 0.695056i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.87629e8 | −1.64466 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.89081e8 | −1.63705 | −0.818525 | − | 0.574471i | \(-0.805208\pi\) | ||||
−0.818525 | + | 0.574471i | \(0.805208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.50273e7 | − | 1.26644e8i | −0.727163 | − | 1.08308i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.81333e8 | 1.53190 | 0.765952 | − | 0.642898i | \(-0.222268\pi\) | ||||
0.765952 | + | 0.642898i | \(0.222268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.39142e8i | 1.16122i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.83798e6 | + | 1.18278e7i | −0.0398886 | + | 0.0975189i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.36245e7i | 0.599726i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.73596e8i | 1.39713i | 0.715546 | + | 0.698566i | \(0.246178\pi\) | ||||
−0.715546 | + | 0.698566i | \(0.753822\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.66587e7 | + | 9.92852e7i | 0.530083 | + | 0.789535i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.79058e7i | − | 0.690739i | −0.938467 | − | 0.345369i | \(-0.887754\pi\) | ||
0.938467 | − | 0.345369i | \(-0.112246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.14966e7 | −0.166915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.66286e8 | + | 1.11642e8i | −1.27595 | + | 0.856654i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.69584e8 | 1.28597 | 0.642987 | − | 0.765877i | \(-0.277695\pi\) | ||||
0.642987 | + | 0.765877i | \(0.277695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.92344e7 | 0.219095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.45721e7 | + | 2.99934e6i | −0.107937 | + | 0.0222164i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.64273e8 | 1.20266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.66507e6i | − | 0.0627048i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.73456e7 | − | 2.50733e7i | 0.267139 | − | 0.179354i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.96877e8i | − | 1.39213i | −0.717977 | − | 0.696067i | \(-0.754932\pi\) | ||
0.717977 | − | 0.696067i | \(-0.245068\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.70811e8i | 1.19402i | 0.802235 | + | 0.597008i | \(0.203644\pi\) | ||||
−0.802235 | + | 0.597008i | \(0.796356\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.60108e6 | − | 1.74633e6i | 0.0179753 | − | 0.0120684i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.75221e7i | − | 0.529656i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.37957e8 | −0.931914 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.68795e7 | + | 6.57144e7i | −0.179530 | + | 0.438912i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.41582e8 | 0.935034 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.30372e8 | 0.851376 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.08933e8 | + | 7.31363e7i | −0.703457 | + | 0.472291i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.07074e7 | 0.0683783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.09184e8i | − | 0.689555i | −0.938684 | − | 0.344778i | \(-0.887954\pi\) | ||
0.938684 | − | 0.344778i | \(-0.112046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.34383e8 | + | 2.00157e8i | 0.839351 | + | 1.25018i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.79323e7i | 0.296100i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.10962e7i | − | 0.128897i | −0.997921 | − | 0.0644483i | \(-0.979471\pi\) | ||
0.997921 | − | 0.0644483i | \(-0.0205287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.44041e8 | + | 5.89177e7i | 0.870500 | + | 0.356064i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.10894e7i | 0.185848i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.49203e8 | −0.882274 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.95679e7 | − | 7.38291e7i | −0.289949 | − | 0.431866i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.31350e8 | −1.33876 | −0.669381 | − | 0.742919i | \(-0.733441\pi\) | ||||
−0.669381 | + | 0.742919i | \(0.733441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.49022e8 | −2.57058 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.27164e6 | + | 1.08308e7i | 0.0411854 | + | 0.0613439i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.49317e8 | 1.39709 | 0.698547 | − | 0.715564i | \(-0.253830\pi\) | ||||
0.698547 | + | 0.715564i | \(0.253830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.10996e8i | − | 1.72429i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.83196e7 | + | 7.69443e7i | 0.429656 | + | 0.422112i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.88477e8i | − | 1.02311i | −0.859252 | − | 0.511553i | \(-0.829070\pi\) | ||
0.859252 | − | 0.511553i | \(-0.170930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.38897e7i | 0.343181i | 0.985168 | + | 0.171590i | \(0.0548905\pi\) | ||||
−0.985168 | + | 0.171590i | \(0.945109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.18622e8 | − | 1.76682e8i | −0.630522 | − | 0.939134i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.49835e6i | − | 0.0499625i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.64150e8 | −1.37506 | −0.687531 | − | 0.726155i | \(-0.741306\pi\) | ||||
−0.687531 | + | 0.726155i | \(0.741306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.33943e8 | + | 8.99274e7i | −0.690055 | + | 0.463294i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.66103e6 | 0.00846935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −756353. | −0.00381697 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.89783e8 | − | 1.18531e8i | −1.44745 | − | 0.592059i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.84017e7 | 0.338184 | 0.169092 | − | 0.985600i | \(-0.445917\pi\) | ||||
0.169092 | + | 0.985600i | \(0.445917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.73213e7i | − | 0.0847687i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.32704e7 | − | 6.26205e7i | 0.451837 | − | 0.303357i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.30466e7i | − | 0.110521i | −0.998472 | − | 0.0552604i | \(-0.982401\pi\) | ||
0.998472 | − | 0.0552604i | \(-0.0175989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.57754e7i | 0.407204i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.73035e8 | + | 1.83312e8i | −1.28320 | + | 0.861524i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.25012e8i | − | 1.04695i | −0.852042 | − | 0.523474i | \(-0.824636\pi\) | ||
0.852042 | − | 0.523474i | \(-0.175364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.08740e7 | −0.372551 | −0.186275 | − | 0.982498i | \(-0.559642\pi\) | ||||
−0.186275 | + | 0.982498i | \(0.559642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.59990e8 | − | 1.06345e8i | −1.18578 | − | 0.485026i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.14925e8 | −0.970556 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.86741e8 | 1.28211 | 0.641054 | − | 0.767496i | \(-0.278498\pi\) | ||||
0.641054 | + | 0.767496i | \(0.278498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.90483e8 | − | 1.27888e8i | 0.843343 | − | 0.566209i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.12295e8 | 0.930715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.51391e8i | 1.52549i | 0.646699 | + | 0.762745i | \(0.276149\pi\) | ||||
−0.646699 | + | 0.762745i | \(0.723851\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.47362e7 | + | 1.11316e8i | 0.321296 | + | 0.478556i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.46355e8i | − | 1.47457i | −0.675580 | − | 0.737287i | \(-0.736107\pi\) | ||
0.675580 | − | 0.737287i | \(-0.263893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.14225e8i | − | 1.32486i | −0.749126 | − | 0.662428i | \(-0.769526\pi\) | ||
0.749126 | − | 0.662428i | \(-0.230474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.26031e8 | − | 6.71062e7i | 1.36139 | − | 0.280213i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8.47902e7i | − | 0.350656i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.35049e8 | −0.962762 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.62476e6 | + | 2.42000e6i | 0.00659152 | + | 0.00981777i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.07791e7 | −0.364782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.41176e7 | 0.215402 | 0.107701 | − | 0.994183i | \(-0.465651\pi\) | ||||
0.107701 | + | 0.994183i | \(0.465651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.91754e8 | − | 2.85609e8i | −0.756020 | − | 1.12606i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.18101e8 | −1.24235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62333e8i | 1.01493i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.40458e8 | − | 9.83556e7i | −0.921588 | − | 0.376961i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.42947e8i | − | 0.542751i | −0.962474 | − | 0.271375i | \(-0.912522\pi\) | ||
0.962474 | − | 0.271375i | \(-0.0874785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.21812e7i | − | 0.196282i | −0.995173 | − | 0.0981411i | \(-0.968710\pi\) | ||
0.995173 | − | 0.0981411i | \(-0.0312897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.37022e8 | − | 3.53034e8i | −0.883304 | − | 1.31564i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.37963e8i | 1.61705i | 0.588460 | + | 0.808526i | \(0.299734\pi\) | ||||
−0.588460 | + | 0.808526i | \(0.700266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.39103e7 | 0.0508863 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.06127e8 | + | 7.12520e7i | −0.384664 | + | 0.258258i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.41321e7 | −0.0866674 | −0.0433337 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433337 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.12328e7 | 0.0399729 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.90545e7 | + | 9.54798e7i | −0.137713 | + | 0.336679i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.76788e8 | 0.967142 | 0.483571 | − | 0.875305i | \(-0.339339\pi\) | ||||
0.483571 | + | 0.875305i | \(0.339339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.29605e8i | − | 1.14127i | −0.821203 | − | 0.570636i | \(-0.806697\pi\) | ||
0.821203 | − | 0.570636i | \(-0.193303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.65355e8 | + | 1.78156e8i | −0.910515 | + | 0.611308i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.91654e7i | 0.0651709i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.95584e8i | − | 2.34408i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.89796e8 | + | 1.27427e8i | −0.633884 | + | 0.425581i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.04902e7i | − | 0.100924i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.21755e8 | −0.727493 | −0.363746 | − | 0.931498i | \(-0.618503\pi\) | ||||
−0.363746 | + | 0.931498i | \(0.618503\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.22872e6 | + | 1.08281e7i | 0.00724677 | + | 0.0352079i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.76656e8 | 1.85845 | 0.929225 | − | 0.369513i | \(-0.120476\pi\) | ||||
0.929225 | + | 0.369513i | \(0.120476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.15833e8 | 1.00890 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.63629e8 | + | 1.09858e8i | −0.518106 | + | 0.347850i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.03596e7 | −0.252218 | −0.126109 | − | 0.992016i | \(-0.540249\pi\) | ||||
−0.126109 | + | 0.992016i | \(0.540249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.07147e8i | − | 0.955597i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.76892e8 | − | 4.12418e8i | −0.853965 | − | 1.27194i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.85307e7i | − | 0.0566546i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.40157e8i | 0.727884i | 0.931422 | + | 0.363942i | \(0.118569\pi\) | ||||
−0.931422 | + | 0.363942i | \(0.881431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.14369e6 | − | 1.99095e7i | 0.0244693 | − | 0.0598221i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.21372e8i | 0.361547i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.36873e8 | 0.404220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.01635e8 | − | 4.49271e8i | −0.883181 | − | 1.31546i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.71751e8 | 1.36949 | 0.684744 | − | 0.728784i | \(-0.259914\pi\) | ||||
0.684744 | + | 0.728784i | \(0.259914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.02834e7 | −0.0583815 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.12063e8 | + | 1.66913e8i | 0.319812 | + | 0.476346i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.61848e7 | 0.102392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.03570e8i | 0.851765i | 0.904779 | + | 0.425882i | \(0.140036\pi\) | ||||
−0.904779 | + | 0.425882i | \(0.859964\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.99322e8 | − | 4.87300e8i | 0.554558 | − | 1.35577i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.87542e8i | 1.06918i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.13405e7i | 0.167814i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.60741e8 | + | 5.37308e8i | 0.978675 | + | 1.45769i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.70537e8i | 0.727846i | 0.931429 | + | 0.363923i | \(0.118563\pi\) | ||||
−0.931429 | + | 0.363923i | \(0.881437\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.76518e8 | −0.737763 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.31961e8 | − | 8.85967e7i | 0.349164 | − | 0.234424i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.31017e7 | 0.0606218 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.96563e8 | −1.03207 | −0.516035 | − | 0.856567i | \(-0.672593\pi\) | ||||
−0.516035 | + | 0.856567i | \(0.672593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.55929e8 | + | 1.53002e8i | −0.918714 | + | 0.394924i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.34085e8 | −1.11128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.12080e8i | − | 0.284589i | −0.989824 | − | 0.142295i | \(-0.954552\pi\) | ||
0.989824 | − | 0.142295i | \(-0.0454480\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.06254e8 | + | 1.38476e8i | −0.519446 | + | 0.348749i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.50340e7i | 0.137477i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.33774e8i | 0.579245i | 0.957141 | + | 0.289622i | \(0.0935297\pi\) | ||||
−0.957141 | + | 0.289622i | \(0.906470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.92903e7 | + | 3.98067e7i | −0.145723 | + | 0.0978367i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.99167e8i | − | 1.70457i | −0.523078 | − | 0.852285i | \(-0.675217\pi\) | ||
0.523078 | − | 0.852285i | \(-0.324783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.95175e8 | 1.43938 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.21899e6 | + | 5.42495e6i | −0.00532346 | + | 0.0130147i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.19452e8 | −0.522269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.11140e8 | 1.20676 | 0.603379 | − | 0.797455i | \(-0.293821\pi\) | ||||
0.603379 | + | 0.797455i | \(0.293821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.29413e8 | − | 4.22579e8i | 1.47418 | − | 0.989745i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.45948e8 | 1.03620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.13325e8i | 1.18333i | 0.806185 | + | 0.591664i | \(0.201529\pi\) | ||||
−0.806185 | + | 0.591664i | \(0.798471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.63517e7 | − | 5.41443e7i | −0.0831380 | − | 0.123830i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.53837e7i | 0.216431i | 0.994127 | + | 0.108216i | \(0.0345137\pi\) | ||||
−0.994127 | + | 0.108216i | \(0.965486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.06835e7i | − | 0.181640i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.80143e8 | − | 1.14588e8i | −0.625742 | − | 0.255950i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.40803e8i | 0.755296i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.74508e8 | −0.383740 | −0.191870 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191870 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.44457e8 | + | 3.64107e8i | 0.533382 | + | 0.794449i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.01318e8 | −0.868860 | −0.434430 | − | 0.900706i | \(-0.643050\pi\) | ||||
−0.434430 | + | 0.900706i | \(0.643050\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.28710e7 | −0.0276507 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.34367e7 | + | 1.24275e8i | 0.177866 | + | 0.264924i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.05825e7 | 0.0646934 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.08995e7i | 0.106847i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.63214e8 | + | 7.92965e8i | 0.339995 | + | 1.65184i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.54077e8i | − | 1.14541i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.87876e7i | − | 0.161634i | −0.996729 | − | 0.0808172i | \(-0.974247\pi\) | ||
0.996729 | − | 0.0808172i | \(-0.0257530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.61875e6 | + | 1.28372e7i | 0.0175474 | + | 0.0261361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.23494e8i | 1.05775i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.47013e8 | 1.49799 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.45694e7 | − | 9.78171e6i | 0.0289962 | − | 0.0194676i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.55228e8 | −0.306616 | −0.153308 | − | 0.988178i | \(-0.548993\pi\) | ||||
−0.153308 | + | 0.988178i | \(0.548993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.05233e8 | 0.402353 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.76926e8 | + | 1.13272e8i | 0.538847 | + | 0.220407i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.02109e7 | 0.0390337 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 4.28801e8i | − | 0.821993i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.59262e8 | + | 2.41204e8i | −0.683582 | + | 0.458948i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.91494e8i | 1.30600i | 0.757358 | + | 0.653000i | \(0.226490\pi\) | ||||
−0.757358 | + | 0.653000i | \(0.773510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.19813e8i | 1.72440i | 0.506572 | + | 0.862198i | \(0.330912\pi\) | ||||
−0.506572 | + | 0.862198i | \(0.669088\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.96142e8 | − | 3.33103e8i | 0.923281 | − | 0.619879i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 6.93394e8i | − | 1.28088i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.69908e7 | −0.177854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.87786e8 | + | 1.99521e8i | 0.887928 | + | 0.363193i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.54626e8 | 0.640827 | 0.320414 | − | 0.947278i | \(-0.396178\pi\) | ||||
0.320414 | + | 0.947278i | \(0.396178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.29337e8 | 1.12897 | 0.564487 | − | 0.825442i | \(-0.309074\pi\) | ||||
0.564487 | + | 0.825442i | \(0.309074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.79823e6 | − | 1.20731e6i | 0.00320246 | − | 0.00215009i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.77055e8 | −1.55064 | −0.775318 | − | 0.631571i | \(-0.782411\pi\) | ||||
−0.775318 | + | 0.631571i | \(0.782411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.31492e8i | − | 0.406323i | −0.979145 | − | 0.203162i | \(-0.934878\pi\) | ||
0.979145 | − | 0.203162i | \(-0.0651217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.95414e6 | − | 7.37898e6i | −0.00863308 | − | 0.0128586i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.53606e8i | 0.438758i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.43600e8i | 0.933726i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.09339e7 | − | 4.41797e8i | −0.155078 | − | 0.753435i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.86832e8i | − | 0.485671i | −0.970068 | − | 0.242835i | \(-0.921923\pi\) | ||
0.970068 | − | 0.242835i | \(-0.0780775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09696e9 | 1.84418 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.64836e8 | + | 5.43407e8i | 0.608997 | + | 0.907073i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.10440e8 | −1.50897 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.61779e8 | 0.595379 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.50561e8 | + | 5.22145e8i | 0.572850 | + | 0.853234i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.53815e8 | 0.736359 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.87271e8i | − | 0.623976i | −0.950086 | − | 0.311988i | \(-0.899005\pi\) | ||
0.950086 | − | 0.311988i | \(-0.100995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.25944e7 | − | 2.56033e7i | −0.100147 | − | 0.0409635i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.83015e8i | 0.290767i | 0.989375 | + | 0.145383i | \(0.0464415\pi\) | ||||
−0.989375 | + | 0.145383i | \(0.953558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.26953e8i | − | 0.989135i | −0.869139 | − | 0.494567i | \(-0.835327\pi\) | ||
0.869139 | − | 0.494567i | \(-0.164673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.25802e8 | − | 1.87377e8i | −0.197096 | − | 0.293566i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.24437e8i | − | 0.971530i | −0.874089 | − | 0.485765i | \(-0.838541\pi\) | ||
0.874089 | − | 0.485765i | \(-0.161459\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.04472e8 | 0.315926 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.84549e8 | − | 1.91043e8i | 0.436617 | − | 0.293138i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03150e8 | −0.157185 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34834e9 | −2.04054 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.21924e8 | + | 1.03151e9i | −0.634150 | + | 1.55036i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.10426e8 | 0.612648 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.74884e8i | 0.704026i | 0.935995 | + | 0.352013i | \(0.114503\pi\) | ||||
−0.935995 | + | 0.352013i | \(0.885497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.71775e8 | − | 1.82466e8i | 0.400168 | − | 0.268668i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.64654e8i | 0.679520i | 0.940512 | + | 0.339760i | \(0.110346\pi\) | ||||
−0.940512 | + | 0.339760i | \(0.889654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.30656e8i | 0.335028i | 0.985870 | + | 0.167514i | \(0.0535740\pi\) | ||||
−0.985870 | + | 0.167514i | \(0.946426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.67949e8 | + | 1.79898e8i | −0.386565 | + | 0.259535i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.94025e8i | − | 0.278027i | −0.990290 | − | 0.139014i | \(-0.955607\pi\) | ||
0.990290 | − | 0.139014i | \(-0.0443932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.35453e8 | 0.762108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.41455e7 | + | 5.31947e7i | 0.0765471 | + | 0.0752030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.58568e7 | 0.0643945 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.96424e8 | −0.831928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.32654e9 | − | 8.90621e8i | 1.83799 | − | 1.23400i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.42570e8 | −1.29728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.79143e7i | − | 0.0244921i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.98975e8 | + | 5.94256e8i | 0.541855 | + | 0.807069i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.09589e9i | 1.47849i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.19565e7i | − | 0.0294267i | −0.999892 | − | 0.0147133i | \(-0.995316\pi\) | ||
0.999892 | − | 0.0147133i | \(-0.00468357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.83396e7 | + | 1.18180e8i | −0.0643593 | + | 0.157345i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.15098e9i | 1.52235i | 0.648547 | + | 0.761175i | \(0.275377\pi\) | ||||
−0.648547 | + | 0.761175i | \(0.724623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14834e6 | 0.00150889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.94322e8 | + | 5.87324e8i | 0.514739 | + | 0.766681i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.89080e7 | −0.0245210 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.98945e8 | −0.771685 | −0.385843 | − | 0.922565i | \(-0.626089\pi\) | ||||
−0.385843 | + | 0.922565i | \(0.626089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.57698e8 | − | 2.34884e8i | −0.201858 | − | 0.300659i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.24704e9 | −1.58590 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.50720e7i | 0.0190435i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.69402e8 | − | 9.03109e8i | 0.463725 | − | 1.13371i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.34334e9i | 1.67548i | 0.546066 | + | 0.837742i | \(0.316125\pi\) | ||||
−0.546066 | + | 0.837742i | \(0.683875\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.66652e7i | 0.0702210i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.84187e8 | + | 1.31696e9i | 1.08868 | + | 1.62154i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.93000e7i | 0.0725470i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.14989e9 | 1.39777 | 0.698887 | − | 0.715232i | \(-0.253679\pi\) | ||||
0.698887 | + | 0.715232i | \(0.253679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.14857e9 | − | 7.71136e8i | 1.38727 | − | 0.931396i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.14092e7 | 0.0977023 | 0.0488511 | − | 0.998806i | \(-0.484444\pi\) | ||||
0.0488511 | + | 0.998806i | \(0.484444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.84241e8 | −0.815970 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00615e8 | + | 4.88832e8i | 0.119225 | + | 0.579247i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.31324e8 | −0.978860 | −0.489430 | − | 0.872043i | \(-0.662795\pi\) | ||||
−0.489430 | + | 0.872043i | \(0.662795\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.95170e8i | 0.579369i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.15059e9 | − | 7.72491e8i | 1.33776 | − | 0.898156i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.24911e9i | − | 1.44318i | −0.692319 | − | 0.721592i | \(-0.743411\pi\) | ||
0.692319 | − | 0.721592i | \(-0.256589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 9.67356e8i | − | 1.11065i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.31688e8 | − | 8.84138e7i | 0.150249 | − | 0.100875i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.17015e8i | 0.586202i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.62355e8 | −0.408286 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.93168e8 | − | 7.16732e8i | 0.328275 | − | 0.802560i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.33355e8 | −0.816079 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.42091e9 | 1.57140 | 0.785700 | − | 0.618607i | \(-0.212303\pi\) | ||||
0.785700 | + | 0.618607i | \(0.212303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.73180e7 | + | 3.84825e7i | −0.0629970 | + | 0.0422953i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.12527e8 | 0.778294 | 0.389147 | − | 0.921176i | \(-0.372770\pi\) | ||||
0.389147 | + | 0.921176i | \(0.372770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.04304e8i | − | 0.221788i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.95792e7 | + | 4.40569e7i | 0.0319134 | + | 0.0475335i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.18474e8i | − | 0.877650i | −0.898573 | − | 0.438825i | \(-0.855395\pi\) | ||
0.898573 | − | 0.438825i | \(-0.144605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.86189e7i | − | 0.0624726i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.63513e8 | + | 1.07786e8i | 0.279122 | + | 0.114171i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.48038e7i | − | 0.0155852i | −0.999970 | − | 0.00779260i | \(-0.997520\pi\) | ||
0.999970 | − | 0.00779260i | \(-0.00248049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.10668e8 | 0.534355 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88634e8 | − | 2.80961e8i | −0.196186 | − | 0.292210i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.17004e9 | 2.24326 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.84976e9 | −1.90062 | −0.950308 | − | 0.311310i | \(-0.899232\pi\) | ||||
−0.950308 | + | 0.311310i | \(0.899232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.91952e8 | + | 1.17958e9i | 0.808819 | + | 1.20470i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.49490e9 | −1.51755 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.00022e9i | − | 1.00928i | −0.863330 | − | 0.504640i | \(-0.831625\pi\) | ||
0.863330 | − | 0.504640i | \(-0.168375\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.17348e8 | + | 1.06484e8i | −0.518903 | + | 0.106805i |
(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 | 384.7.h.f.65.6 | yes | 8 | |
3.2 | odd | 2 | 384.7.h.e.65.1 | ✓ | 8 | ||
4.3 | odd | 2 | 384.7.h.e.65.4 | yes | 8 | ||
8.3 | odd | 2 | inner | 384.7.h.f.65.5 | yes | 8 | |
8.5 | even | 2 | 384.7.h.e.65.3 | yes | 8 | ||
12.11 | even | 2 | inner | 384.7.h.f.65.7 | yes | 8 | |
24.5 | odd | 2 | inner | 384.7.h.f.65.8 | yes | 8 | |
24.11 | even | 2 | 384.7.h.e.65.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.h.e.65.1 | ✓ | 8 | 3.2 | odd | 2 | ||
384.7.h.e.65.2 | yes | 8 | 24.11 | even | 2 | ||
384.7.h.e.65.3 | yes | 8 | 8.5 | even | 2 | ||
384.7.h.e.65.4 | yes | 8 | 4.3 | odd | 2 | ||
384.7.h.f.65.5 | yes | 8 | 8.3 | odd | 2 | inner | |
384.7.h.f.65.6 | yes | 8 | 1.1 | even | 1 | trivial | |
384.7.h.f.65.7 | yes | 8 | 12.11 | even | 2 | inner | |
384.7.h.f.65.8 | yes | 8 | 24.5 | odd | 2 | inner |