Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (of order \(2\), degree \(1\), not 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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.a.449.2 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 8.00000i | − 0.513200i | −0.966518 | − | 0.256600i | \(-0.917398\pi\) | ||||
0.966518 | − | 0.256600i | \(-0.0826023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 208.000i | 1.60442i | 0.597042 | + | 0.802210i | \(0.296343\pi\) | ||||
−0.597042 | + | 0.802210i | \(0.703657\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 179.000 | 0.736626 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −536.000 | −1.33562 | −0.667810 | − | 0.744332i | \(-0.732768\pi\) | ||||
−0.667810 | + | 0.744332i | \(0.732768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 694.000i | 1.13894i | 0.822012 | + | 0.569470i | \(0.192852\pi\) | ||||
−0.822012 | + | 0.569470i | \(0.807148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1278.00i | 1.07253i | 0.844050 | + | 0.536264i | \(0.180165\pi\) | ||||
−0.844050 | + | 0.536264i | \(0.819835\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1112.00 | −0.706677 | −0.353338 | − | 0.935496i | \(-0.614954\pi\) | ||||
−0.353338 | + | 0.935496i | \(0.614954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1664.00 | 0.823389 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3216.00i | 1.26764i | 0.773480 | + | 0.633821i | \(0.218514\pi\) | ||||
−0.773480 | + | 0.633821i | \(0.781486\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3376.00i | − 0.891237i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2918.00 | −0.644303 | −0.322152 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322152 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2624.00 | −0.490410 | −0.245205 | − | 0.969471i | \(-0.578855\pi\) | ||||
−0.245205 | + | 0.969471i | \(0.578855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4288.00i | 0.685441i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9458.00i | 1.13578i | 0.823104 | + | 0.567891i | \(0.192241\pi\) | ||||
−0.823104 | + | 0.567891i | \(0.807759\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5552.00 | 0.584505 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 170.000 | 0.0157939 | 0.00789695 | − | 0.999969i | \(-0.497486\pi\) | ||||
0.00789695 | + | 0.999969i | \(0.497486\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 19928.0i | − 1.64359i | −0.569786 | − | 0.821793i | \(-0.692974\pi\) | ||||
0.569786 | − | 0.821793i | \(-0.307026\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 32.0000i | − 0.00211303i | −0.999999 | − | 0.00105651i | \(-0.999664\pi\) | ||||
0.999999 | − | 0.00105651i | \(-0.000336299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26457.0 | −1.57417 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10224.0 | 0.550422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 22178.0i | − 1.08451i | −0.840215 | − | 0.542254i | \(-0.817571\pi\) | ||||
0.840215 | − | 0.542254i | \(-0.182429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8896.00i | 0.362667i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −41480.0 | −1.55135 | −0.775673 | − | 0.631135i | \(-0.782589\pi\) | ||||
−0.775673 | + | 0.631135i | \(0.782589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15462.0 | 0.532036 | 0.266018 | − | 0.963968i | \(-0.414292\pi\) | ||||
0.266018 | + | 0.963968i | \(0.414292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37232.0i | 1.18186i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20744.0i | 0.564554i | 0.959333 | + | 0.282277i | \(0.0910897\pi\) | ||||
−0.959333 | + | 0.282277i | \(0.908910\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25728.0 | 0.650554 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28592.0 | 0.673130 | 0.336565 | − | 0.941660i | \(-0.390735\pi\) | ||||
0.336565 | + | 0.941660i | \(0.390735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 53670.0i | − 1.17876i | −0.807857 | − | 0.589379i | \(-0.799373\pi\) | ||||
0.807857 | − | 0.589379i | \(-0.200627\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 111488.i | − 2.14290i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69152.0 | 1.24663 | 0.623314 | − | 0.781971i | \(-0.285786\pi\) | ||||
0.623314 | + | 0.781971i | \(0.285786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16489.0 | 0.279243 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 37800.0i | − 0.602277i | −0.953580 | − | 0.301139i | \(-0.902633\pi\) | ||||
0.953580 | − | 0.301139i | \(-0.0973667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23344.0i | 0.330657i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126806. | 1.69693 | 0.848467 | − | 0.529249i | \(-0.177526\pi\) | ||||
0.848467 | + | 0.529249i | \(0.177526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −144352. | −1.82734 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20992.0i | 0.251679i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 62290.0i | − 0.672185i | −0.941829 | − | 0.336093i | \(-0.890894\pi\) | ||||
0.941829 | − | 0.336093i | \(-0.109106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −95944.0 | −0.983852 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6414.00 | 0.0625641 | 0.0312821 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312821 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 108432.i | − 1.00708i | −0.863972 | − | 0.503541i | \(-0.832030\pi\) | ||||
0.863972 | − | 0.503541i | \(-0.167970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 103976.i | − 0.877958i | −0.898497 | − | 0.438979i | \(-0.855340\pi\) | ||||
0.898497 | − | 0.438979i | \(-0.144660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2486.00 | −0.0200417 | −0.0100209 | − | 0.999950i | \(-0.503190\pi\) | ||||
−0.0100209 | + | 0.999950i | \(0.503190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 75664.0 | 0.582884 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15794.0i | 0.116358i | 0.998306 | + | 0.0581790i | \(0.0185294\pi\) | ||||
−0.998306 | + | 0.0581790i | \(0.981471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 124226.i | 0.838973i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −265824. | −1.72079 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 126245. | 0.783882 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1360.00i | − 0.00810543i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1024.00i | − 0.00563366i | −0.999996 | − | 0.00281683i | \(-0.999103\pi\) | ||||
0.999996 | − | 0.00281683i | \(-0.000896626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −159424. | −0.843489 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22664.0 | −0.115387 | −0.0576937 | − | 0.998334i | \(-0.518375\pi\) | ||||
−0.0576937 | + | 0.998334i | \(0.518375\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 231296.i | − 1.13381i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 53238.0i | 0.242337i | 0.992632 | + | 0.121169i | \(0.0386642\pi\) | ||||
−0.992632 | + | 0.121169i | \(0.961336\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19816.0 | −0.0869919 | −0.0434960 | − | 0.999054i | \(-0.513850\pi\) | ||||
−0.0434960 | + | 0.999054i | \(0.513850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −256.000 | −0.00108441 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 371984.i | − 1.52119i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 211656.i | 0.807862i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −452190. | −1.66861 | −0.834306 | − | 0.551302i | \(-0.814131\pi\) | ||||
−0.834306 | + | 0.551302i | \(0.814131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −263280. | −0.939670 | −0.469835 | − | 0.882754i | \(-0.655687\pi\) | ||||
−0.469835 | + | 0.882754i | \(0.655687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 228762.i | 0.790051i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 353530.i | 1.14466i | 0.820023 | + | 0.572331i | \(0.193961\pi\) | ||||
−0.820023 | + | 0.572331i | \(0.806039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −177424. | −0.556570 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −668928. | −2.03383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 100936.i | − 0.297562i | −0.988870 | − | 0.148781i | \(-0.952465\pi\) | ||||
0.988870 | − | 0.148781i | \(-0.0475349\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 284944.i | 0.790621i | 0.918548 | + | 0.395310i | \(0.129363\pi\) | ||||
−0.918548 | + | 0.395310i | \(0.870637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −110343. | −0.297186 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −199048. | −0.520556 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 484374.i | 1.23045i | 0.788350 | + | 0.615227i | \(0.210936\pi\) | ||||
−0.788350 | + | 0.615227i | \(0.789064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 331840.i | 0.796151i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −406680. | −0.948681 | −0.474341 | − | 0.880341i | \(-0.657313\pi\) | ||||
−0.474341 | + | 0.880341i | \(0.657313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 570302. | 1.29392 | 0.646962 | − | 0.762523i | \(-0.276039\pi\) | ||||
0.646962 | + | 0.762523i | \(0.276039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 123696.i | − 0.273041i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 685008.i | − 1.43249i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 702208. | 1.42992 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 138624. | 0.274951 | 0.137475 | − | 0.990505i | \(-0.456101\pi\) | ||||
0.137475 | + | 0.990505i | \(0.456101\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34482.0i | 0.0666345i | 0.999445 | + | 0.0333173i | \(0.0106072\pi\) | ||||
−0.999445 | + | 0.0333173i | \(0.989393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 643598.i | − 1.18154i | −0.806839 | − | 0.590771i | \(-0.798824\pi\) | ||||
0.806839 | − | 0.590771i | \(-0.201176\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.10738e6 | −1.98227 | −0.991134 | − | 0.132865i | \(-0.957582\pi\) | ||||
−0.991134 | + | 0.132865i | \(0.957582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 165952. | 0.289729 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 606944.i | − 1.03373i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 575664.i | 0.933777i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 596032. | 0.943852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 229976. | 0.355612 | 0.177806 | − | 0.984066i | \(-0.443100\pi\) | ||||
0.177806 | + | 0.984066i | \(0.443100\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 228736.i | − 0.345450i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 545792.i | − 0.786824i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −429360. | −0.604939 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −886932. | −1.22155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.08947e6i | − 1.46708i | −0.679646 | − | 0.733540i | \(-0.737867\pi\) | ||||
0.679646 | − | 0.733540i | \(-0.262133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 687048.i | 0.884958i | 0.896779 | + | 0.442479i | \(0.145901\pi\) | ||||
−0.896779 | + | 0.442479i | \(0.854099\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 699730. | 0.881743 | 0.440871 | − | 0.897570i | \(-0.354670\pi\) | ||||
0.440871 | + | 0.897570i | \(0.354670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −891904. | −1.09974 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 937722.i | 1.13158i | 0.824550 | + | 0.565789i | \(0.191428\pi\) | ||||
−0.824550 | + | 0.565789i | \(0.808572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 553216.i | − 0.639770i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −643488. | −0.728695 | −0.364347 | − | 0.931263i | \(-0.618708\pi\) | ||||
−0.364347 | + | 0.931263i | \(0.618708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 157282. | 0.174436 | 0.0872181 | − | 0.996189i | \(-0.472202\pi\) | ||||
0.0872181 | + | 0.996189i | \(0.472202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 952280.i | − 1.03454i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 771728.i | − 0.804863i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −302400. | −0.309089 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.58604e6 | −1.58902 | −0.794511 | − | 0.607250i | \(-0.792273\pi\) | ||||
−0.794511 | + | 0.607250i | \(0.792273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.72378e6i | − 1.69309i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 654334.i | 0.617969i | 0.951067 | + | 0.308984i | \(0.0999891\pi\) | ||||
−0.951067 | + | 0.308984i | \(0.900011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.96726e6 | −1.82227 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −522322. | −0.474610 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 330192.i | − 0.294359i | −0.989110 | − | 0.147179i | \(-0.952981\pi\) | ||||
0.989110 | − | 0.147179i | \(-0.0470195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.01445e6i | − 0.870867i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.56956e6 | −1.32250 | −0.661252 | − | 0.750164i | \(-0.729974\pi\) | ||||
−0.661252 | + | 0.750164i | \(0.729974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 957792. | 0.792224 | 0.396112 | − | 0.918202i | \(-0.370359\pi\) | ||||
0.396112 | + | 0.918202i | \(0.370359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15482e6i | 0.937791i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 565438.i | − 0.442778i | −0.975186 | − | 0.221389i | \(-0.928941\pi\) | ||||
0.975186 | − | 0.221389i | \(-0.0710590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −469696. | −0.361249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34127e6 | −1.01333 | −0.506664 | − | 0.862143i | \(-0.669122\pi\) | ||||
−0.506664 | + | 0.862143i | \(0.669122\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 734264.i | − 0.544987i | −0.962158 | − | 0.272494i | \(-0.912152\pi\) | ||||
0.962158 | − | 0.272494i | \(-0.0878483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35360.0i | 0.0253401i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −213427. | −0.150316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −498320. | −0.344966 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.13320e6i | − 0.771149i | −0.922677 | − | 0.385574i | \(-0.874003\pi\) | ||||
0.922677 | − | 0.385574i | \(-0.125997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.80954e6i | 1.19035i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.23190e6 | −1.44377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.14502e6 | 2.63700 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 51312.0i | − 0.0321079i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.91377e6i | 1.76445i | 0.470829 | + | 0.882224i | \(0.343955\pi\) | ||||
−0.470829 | + | 0.882224i | \(0.656045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −867456. | −0.516834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.43813e6 | −0.843134 | −0.421567 | − | 0.906797i | \(-0.638520\pi\) | ||||
−0.421567 | + | 0.906797i | \(0.638520\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.37601e6i | − 0.793888i | −0.917843 | − | 0.396944i | \(-0.870071\pi\) | ||||
0.917843 | − | 0.396944i | \(-0.129929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.23494e6i | 0.690235i | 0.938559 | + | 0.345118i | \(0.112161\pi\) | ||||
−0.938559 | + | 0.345118i | \(0.887839\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56405e6 | 0.860545 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −831808. | −0.450568 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.42114e6i | − 0.757930i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19888.0i | 0.0102854i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6656.00 | 0.00339019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48930e6 | −0.747160 | −0.373580 | − | 0.927598i | \(-0.621870\pi\) | ||||
−0.373580 | + | 0.927598i | \(0.621870\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.69298e6i | 0.836646i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 838226.i | − 0.402056i | −0.979586 | − | 0.201028i | \(-0.935572\pi\) | ||||
0.979586 | − | 0.201028i | \(-0.0644282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126352. | 0.0597149 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.40646e6 | 0.655002 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.00720e6i | − 0.921203i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 350008.i | 0.156047i | 0.996952 | + | 0.0780233i | \(0.0248609\pi\) | ||||
−0.996952 | + | 0.0780233i | \(0.975139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 383642. | 0.168602 | 0.0843010 | − | 0.996440i | \(-0.473134\pi\) | ||||
0.0843010 | + | 0.996440i | \(0.473134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34294e6 | 1.01507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.09309e6i | 1.74829i | 0.485661 | + | 0.874147i | \(0.338579\pi\) | ||||
−0.485661 | + | 0.874147i | \(0.661421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12659e6i | 0.883108i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.14430e6 | −1.28762 | −0.643811 | − | 0.765185i | \(-0.722648\pi\) | ||||
−0.643811 | + | 0.765185i | \(0.722648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.23955e6 | −0.500608 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.00996e6i | − 0.402288i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47619e6i | 0.572108i | 0.958214 | + | 0.286054i | \(0.0923436\pi\) | ||||
−0.958214 | + | 0.286054i | \(0.907656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30430.0 | 0.0116342 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.61302e6 | 1.74001 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.73981e6i | − 1.39180i | −0.718138 | − | 0.695901i | \(-0.755005\pi\) | ||||
0.718138 | − | 0.695901i | \(-0.244995\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.02509e6i | − 0.733823i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.89966e6 | −0.679324 | −0.339662 | − | 0.940548i | \(-0.610313\pi\) | ||||
−0.339662 | + | 0.940548i | \(0.610313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8192.00 | −0.00289120 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.74310e6i | 0.607192i | 0.952801 | + | 0.303596i | \(0.0981874\pi\) | ||||
−0.952801 | + | 0.303596i | \(0.901813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.56711e6i | − 1.21071i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.69147e6 | 0.901812 | 0.450906 | − | 0.892571i | \(-0.351101\pi\) | ||||
0.450906 | + | 0.892571i | \(0.351101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.11005e6 | −1.35958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 181312.i | 0.0592168i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.37353e6i | − 1.71113i | −0.517695 | − | 0.855565i | \(-0.673210\pi\) | ||||
0.517695 | − | 0.855565i | \(-0.326790\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.85037e6 | −0.581870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 156418. | 0.0485765 | 0.0242882 | − | 0.999705i | \(-0.492268\pi\) | ||||
0.0242882 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.82106e6i | − 0.558548i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.06949e6i | − 1.51697i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 306086. | 0.0904764 | 0.0452382 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452382 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 425904. | 0.124368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.62784e6i | − 2.48901i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 158528.i | 0.0446443i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.70868e6 | 1.86682 | 0.933409 | − | 0.358814i | \(-0.116819\pi\) | ||||
0.933409 | + | 0.358814i | \(0.116819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.02347e6 | 1.10636 | 0.553179 | − | 0.833063i | \(-0.313415\pi\) | ||||
0.553179 | + | 0.833063i | \(0.313415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 5728.00i | − 0.00155651i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.21610e6i | 0.853610i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.97587e6 | −0.780676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.04304e6 | −1.82628 | −0.913139 | − | 0.407648i | \(-0.866349\pi\) | ||||
−0.913139 | + | 0.407648i | \(0.866349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.25142e6i | − 0.320763i | −0.987055 | − | 0.160381i | \(-0.948728\pi\) | ||||
0.987055 | − | 0.160381i | \(-0.0512724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.57619e6i | − 0.895813i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.25406e6 | 0.310569 | 0.155285 | − | 0.987870i | \(-0.450371\pi\) | ||||
0.155285 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.73580e6 | −1.15957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.18081e6i | 1.25426i | 0.778914 | + | 0.627131i | \(0.215771\pi\) | ||||
−0.778914 | + | 0.627131i | \(0.784229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.61752e6i | 0.856332i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.73064e6 | 1.34149 | 0.670745 | − | 0.741688i | \(-0.265975\pi\) | ||||
0.670745 | + | 0.741688i | \(0.265975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −91120.0 | −0.0210947 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.10624e6i | 0.482239i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.24153e6i | 1.17400i | 0.809588 | + | 0.586999i | \(0.199691\pi\) | ||||
−0.809588 | + | 0.586999i | \(0.800309\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.31453e6 | 0.955876 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −173994. | −0.0381313 | −0.0190657 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190657 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.01277e6i | 0.869945i | 0.900444 | + | 0.434972i | \(0.143242\pi\) | ||||
−0.900444 | + | 0.434972i | \(0.856758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 774616.i | − 0.164359i | −0.996618 | − | 0.0821796i | \(-0.973812\pi\) | ||||
0.996618 | − | 0.0821796i | \(-0.0261881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.31475e6 | −0.905782 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.82824e6 | 0.587441 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.06814e7i | 2.19521i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.96986e6i | − 0.798876i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.33530e6 | −0.465054 | −0.232527 | − | 0.972590i | \(-0.574699\pi\) | ||||
−0.232527 | + | 0.972590i | \(0.574699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.56385e6 | −1.29359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.35142e6i | 1.04376i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.03947e6i | − 0.198605i | −0.995057 | − | 0.0993025i | \(-0.968339\pi\) | ||||
0.995057 | − | 0.0993025i | \(-0.0316612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −807488. | −0.152709 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.85092e6 | 1.46966 | 0.734830 | − | 0.678251i | \(-0.237262\pi\) | ||||
0.734830 | + | 0.678251i | \(0.237262\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.72920e6i | − 0.691033i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.94714e6i | 1.07998i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.71644e6 | −0.488370 | −0.244185 | − | 0.969729i | \(-0.578520\pi\) | ||||
−0.244185 | + | 0.969729i | \(0.578520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.27955e6 | 0.405747 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4.62034e6i | − 0.814242i | −0.913374 | − | 0.407121i | \(-0.866533\pi\) | ||||
0.913374 | − | 0.407121i | \(-0.133467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 882744.i | 0.152516i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.46198e6 | 0.763366 | 0.381683 | − | 0.924293i | \(-0.375345\pi\) | ||||
0.381683 | + | 0.924293i | \(0.375345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.11634e7 | 1.89122 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.75411e6i | 0.629816i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17152.0i | 0.00282220i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.87499e6 | 0.631470 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.74375e6 | 0.604245 | 0.302122 | − | 0.953269i | \(-0.402305\pi\) | ||||
0.302122 | + | 0.953269i | \(0.402305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.28433e6i | 1.48421i | 0.670282 | + | 0.742107i | \(0.266173\pi\) | ||||
−0.670282 | + | 0.742107i | \(0.733827\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.35347e6i | − 0.525979i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.90631e6 | −0.606915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.42492e6 | −1.14276 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 117980.i | 0.0179883i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.25344e6i | 0.486863i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.41810e7 | 2.10249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 862150. | 0.126645 | 0.0633227 | − | 0.997993i | \(-0.479830\pi\) | ||||
0.0633227 | + | 0.997993i | \(0.479830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 4.56242e6i | − 0.664042i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.75442e6i | − 0.250707i | −0.992112 | − | 0.125353i | \(-0.959994\pi\) | ||||
0.992112 | − | 0.125353i | \(-0.0400065\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.76770e6 | 0.391911 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24482e6 | 0.455314 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.43836e7i | 2.00012i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00292e7i | 1.36971i | 0.728678 | + | 0.684856i | \(0.240135\pi\) | ||||
−0.728678 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38300e7 | 1.87195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.48006e6 | −0.735154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.27460e6i | − 0.701324i | −0.936502 | − | 0.350662i | \(-0.885957\pi\) | ||||
0.936502 | − | 0.350662i | \(-0.114043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.42971e6i | 0.448023i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.36940e6 | −1.08371 | −0.541856 | − | 0.840471i | \(-0.682278\pi\) | ||||
−0.541856 | + | 0.840471i | \(0.682278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.02702e6 | 0.516884 | 0.258442 | − | 0.966027i | \(-0.416791\pi\) | ||||
0.258442 | + | 0.966027i | \(0.416791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.10899e6i | − 0.141105i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 2.37568e6i | − 0.297063i | −0.988908 | − | 0.148532i | \(-0.952545\pi\) | ||||
0.988908 | − | 0.148532i | \(-0.0474547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 275856. | 0.0341968 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.86240e6 | 0.966306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.18874e7i | 1.44849i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.44028e6i | 0.412096i | 0.978542 | + | 0.206048i | \(0.0660603\pi\) | ||||
−0.978542 | + | 0.206048i | \(0.933940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.91789e6 | 0.346562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.14878e6 | −0.606368 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 3.22942e6i | − 0.377127i | −0.982061 | − | 0.188564i | \(-0.939617\pi\) | ||||
0.982061 | − | 0.188564i | \(-0.0603832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.85901e6i | 1.01730i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.29714e6 | 1.05872 | 0.529361 | − | 0.848397i | \(-0.322432\pi\) | ||||
0.529361 | + | 0.848397i | \(0.322432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.12782e7 | −1.27366 | −0.636828 | − | 0.771006i | \(-0.719754\pi\) | ||||
−0.636828 | + | 0.771006i | \(0.719754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.71318e6i | 0.415865i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 7.00115e6i | − 0.771255i | −0.922655 | − | 0.385627i | \(-0.873985\pi\) | ||||
0.922655 | − | 0.385627i | \(-0.126015\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.85555e6 | −0.530512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22208.0 | 0.00240661 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.19432e6i | − 0.665798i | −0.942962 | − | 0.332899i | \(-0.891973\pi\) | ||||
0.942962 | − | 0.332899i | \(-0.108027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.62407e6i | 0.277500i | 0.990327 | + | 0.138750i | \(0.0443084\pi\) | ||||
−0.990327 | + | 0.138750i | \(0.955692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.83721e6 | 0.297622 | 0.148811 | − | 0.988866i | \(-0.452455\pi\) | ||||
0.148811 | + | 0.988866i | \(0.452455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08572e7 | 1.12977 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.63756e7i | 2.72259i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.76826e6i | − 0.484385i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.20873e7 | −1.21816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.29656e7 | 1.29634 | 0.648170 | − | 0.761496i | \(-0.275535\pi\) | ||||
0.648170 | + | 0.761496i | \(0.275535\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1.83981e6i | − 0.182500i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.83612e7i | − 1.79288i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.11797e6 | 0.495844 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.16798e7 | −1.12276 | −0.561382 | − | 0.827557i | \(-0.689730\pi\) | ||||
−0.561382 | + | 0.827557i | \(0.689730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.02732e6i | 0.670289i | 0.942167 | + | 0.335145i | \(0.108785\pi\) | ||||
−0.942167 | + | 0.335145i | \(0.891215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.72821e6i | 0.913634i | 0.889561 | + | 0.456817i | \(0.151011\pi\) | ||||
−0.889561 | + | 0.456817i | \(0.848989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.22333e7 | 2.07201 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.36634e6 | −0.403798 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9.81425e6i | − 0.900688i | −0.892855 | − | 0.450344i | \(-0.851301\pi\) | ||||
0.892855 | − | 0.450344i | \(-0.148699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 9.60693e6i | − 0.868303i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.46652e7 | −1.31545 | −0.657724 | − | 0.753259i | \(-0.728481\pi\) | ||||
−0.657724 | + | 0.753259i | \(0.728481\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41836e7 | −1.26265 | −0.631327 | − | 0.775517i | \(-0.717489\pi\) | ||||
−0.631327 | + | 0.775517i | \(0.717489\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.09546e6i | 0.626897i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.38429e6i | − 0.816745i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.71578e6 | −0.752906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.28763e6 | −0.710598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.49941e6i | 0.468035i | 0.972232 | + | 0.234018i | \(0.0751873\pi\) | ||||
−0.972232 | + | 0.234018i | \(0.924813\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.77375e7i | − 1.48737i | −0.668528 | − | 0.743687i | \(-0.733075\pi\) | ||||
0.668528 | − | 0.743687i | \(-0.266925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.29563e7 | 1.07847 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.49638e6 | 0.454160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.39670e6i | − 0.770768i | −0.922756 | − | 0.385384i | \(-0.874069\pi\) | ||||
0.922756 | − | 0.385384i | \(-0.125931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 5.59784e6i | − 0.452510i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.53915e7 | 1.23519 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.34767e7 | −1.07371 | −0.536857 | − | 0.843673i | \(-0.680389\pi\) | ||||
−0.536857 | + | 0.843673i | \(0.680389\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.99564e7i | − 1.57851i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 217260.i | 0.0169394i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.50178e6 | 0.580726 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.15594e7 | 1.65707 | 0.828536 | − | 0.559935i | \(-0.189174\pi\) | ||||
0.828536 | + | 0.559935i | \(0.189174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.05173e7i | − 0.802631i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.33411e6i | 0.100379i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.38165e6 | 0.476779 | 0.238390 | − | 0.971170i | \(-0.423380\pi\) | ||||
0.238390 | + | 0.971170i | \(0.423380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.23782e7 | 0.918298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.43878e6i | − 0.621664i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.14790e6i | 0.373966i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.63566e7 | 1.17997 | 0.589986 | − | 0.807413i | \(-0.299133\pi\) | ||||
0.589986 | + | 0.807413i | \(0.299133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.25539e7 | 1.61578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.25826e6i | − 0.0895207i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.13130e7i | 1.49558i | 0.663937 | + | 0.747788i | \(0.268884\pi\) | ||||
−0.663937 | + | 0.747788i | \(0.731116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.61141e6 | −0.251686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.54680e7 | 1.76279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.21571e7i | 0.835737i | 0.908507 | + | 0.417869i | \(0.137223\pi\) | ||||
−0.908507 | + | 0.417869i | \(0.862777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.11188e7i | − 0.754030i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.92337e7 | 1.29555 | 0.647773 | − | 0.761834i | \(-0.275701\pi\) | ||||
0.647773 | + | 0.761834i | \(0.275701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.17382e6 | −0.413056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.66565e6i | 0.110691i | 0.998467 | + | 0.0553454i | \(0.0176260\pi\) | ||||
−0.998467 | + | 0.0553454i | \(0.982374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.76620e6i | − 0.443653i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.16270e7 | 1.40861 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.81290e6 | 0.634888 | 0.317444 | − | 0.948277i | \(-0.397175\pi\) | ||||
0.317444 | + | 0.948277i | \(0.397175\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.26883e7i | 0.815486i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.92753e7i | 1.22254i | 0.791423 | + | 0.611269i | \(0.209341\pi\) | ||||
−0.791423 | + | 0.611269i | \(0.790659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.37902e7 | −0.868893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.17863e7 | −0.737762 | −0.368881 | − | 0.929477i | \(-0.620259\pi\) | ||||
−0.368881 | + | 0.929477i | \(0.620259\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 517088.i | − 0.0321553i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.87871e7i | − 1.76689i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.22941e7 | −0.749690 | −0.374845 | − | 0.927087i | \(-0.622304\pi\) | ||||
−0.374845 | + | 0.927087i | \(0.622304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.23467e6 | 0.317142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.57086e6i | 0.154750i | 0.997002 | + | 0.0773749i | \(0.0246538\pi\) | ||||
−0.997002 | + | 0.0773749i | \(0.975346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.57381e7i | 0.935190i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −189040. | −0.0111612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.53253e7 | −0.899046 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.85117e6i | 0.574227i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.54594e6i | − 0.319182i | −0.987183 | − | 0.159591i | \(-0.948982\pi\) | ||||
0.987183 | − | 0.159591i | \(-0.0510176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.64154e6 | −0.151065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.28515e6 | −0.186687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07306e7i | 0.605958i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.09610e7i | − 1.16887i | −0.811440 | − | 0.584436i | \(-0.801316\pi\) | ||||
0.811440 | − | 0.584436i | \(-0.198684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40896.0 | 0.00226628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.26983e7 | 1.25000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.87671e7i | 1.57437i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.25565e7i | 0.678709i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.70297e7 | −1.45201 | −0.726005 | − | 0.687690i | \(-0.758625\pi\) | ||||
−0.726005 | + | 0.687690i | \(0.758625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.13052e6 | −0.113745 | −0.0568727 | − | 0.998381i | \(-0.518113\pi\) | ||||
−0.0568727 | + | 0.998381i | \(0.518113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.66234e6i | − 0.406570i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.21599e7i | 1.16148i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.58390e7 | −1.34607 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58060e7 | 0.818396 | 0.409198 | − | 0.912446i | \(-0.365809\pi\) | ||||
0.409198 | + | 0.912446i | \(0.365809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.28848e7i | − 1.17773i | −0.808230 | − | 0.588867i | \(-0.799574\pi\) | ||||
0.808230 | − | 0.588867i | \(-0.200426\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.55336e7i | 1.29822i | 0.760695 | + | 0.649109i | \(0.224858\pi\) | ||||
−0.760695 | + | 0.649109i | \(0.775142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.31786e6 | −0.420364 | −0.210182 | − | 0.977662i | \(-0.567406\pi\) | ||||
−0.210182 | + | 0.977662i | \(0.567406\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.52350e6 | −0.227234 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.38120e7i | − 1.68834i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.85862e6i | 0.437072i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.66261e7 | −1.79633 | −0.898164 | − | 0.439660i | \(-0.855099\pi\) | ||||
−0.898164 | + | 0.439660i | \(0.855099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.19964e7 | −0.584873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.07302e7i | 0.520041i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.62590e7i | 1.25768i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.87411e6 | −0.279687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.04169e7 | −1.43976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74802e7i | 0.822571i | 0.911507 | + | 0.411286i | \(0.134920\pi\) | ||||
−0.911507 | + | 0.411286i | \(0.865080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 9.31062e6i | − 0.433038i | −0.976278 | − | 0.216519i | \(-0.930530\pi\) | ||||
0.976278 | − | 0.216519i | \(-0.0694704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.49525e7 | 1.61620 | 0.808101 | − | 0.589045i | \(-0.200496\pi\) | ||||
0.808101 | + | 0.589045i | \(0.200496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 282880. | 0.0130045 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2.02349e7i | − 0.924858i | −0.886656 | − | 0.462429i | \(-0.846978\pi\) | ||||
0.886656 | − | 0.462429i | \(-0.153022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.70742e6i | 0.0771421i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.70655e7 | −1.66502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.43963e7 | −0.642994 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.11499e7i | − 0.495149i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.98342e7i | 0.870797i | 0.900238 | + | 0.435398i | \(0.143392\pi\) | ||||
−0.900238 | + | 0.435398i | \(0.856608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.06562e6 | −0.395754 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.81023e7 | −1.65391 | −0.826954 | − | 0.562270i | \(-0.809928\pi\) | ||||
−0.826954 | + | 0.562270i | \(0.809928\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.41560e7i | − 1.04261i | −0.853369 | − | 0.521307i | \(-0.825445\pi\) | ||||
0.853369 | − | 0.521307i | \(-0.174555\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.02368e7i | − 0.863638i | −0.901960 | − | 0.431819i | \(-0.857872\pi\) | ||||
0.901960 | − | 0.431819i | \(-0.142128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 212992. | 0.00903876 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.83810e6 | −0.372962 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35584.0i | 0.00149323i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.78552e7i | 0.740942i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.65683e6 | 0.315973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.83435e7 | 1.16316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.31602e7i | − 1.35331i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.97976e7i | − 0.799088i | −0.916714 | − | 0.399544i | \(-0.869169\pi\) | ||||
0.916714 | − | 0.399544i | \(-0.130831\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.14811e6 | 0.0460863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.13242e7 | −0.851288 | −0.425644 | − | 0.904891i | \(-0.639952\pi\) | ||||
−0.425644 | + | 0.904891i | \(0.639952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.02608e7i | 0.804414i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.71411e6i | − 0.185130i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.49941e7 | −1.36680 | −0.683401 | − | 0.730043i | \(-0.739500\pi\) | ||||
−0.683401 | + | 0.730043i | \(0.739500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.33101e7 | 0.905515 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.98428e7i | 0.766655i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.94093e7i | − 0.741842i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.88107e7 | 1.09525 | 0.547627 | − | 0.836722i | \(-0.315531\pi\) | ||||
0.547627 | + | 0.836722i | \(0.315531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.94202e7 | 1.11243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.15050e7i | 0.432697i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.28854e7i | − 0.479457i | −0.970840 | − | 0.239729i | \(-0.922941\pi\) | ||||
0.970840 | − | 0.239729i | \(-0.0770585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.10080e7 | −0.407424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.27615e7 | −1.94242 | −0.971210 | − | 0.238227i | \(-0.923434\pi\) | ||||
−0.971210 | + | 0.238227i | \(0.923434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 546720.i | 0.0200210i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 5.53961e6i | − 0.200726i | −0.994951 | − | 0.100363i | \(-0.968000\pi\) | ||||
0.994951 | − | 0.100363i | \(-0.0320004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.72470e7 | 1.34253 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.87950e6 | 0.354229 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 228102.i | − 0.00813574i | −0.999992 | − | 0.00406787i | \(-0.998705\pi\) | ||||
0.999992 | − | 0.00406787i | \(-0.00129485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.25124e7i | − 0.441632i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.10735e7 | −0.388811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.17438e7 | −0.759498 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.86117e7i | − 0.646726i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7.36709e6i | − 0.253355i | −0.991944 | − | 0.126678i | \(-0.959569\pi\) | ||||
0.991944 | − | 0.126678i | \(-0.0404313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.13691e7 | −0.388970 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.91161e7 | −0.650654 | −0.325327 | − | 0.945602i | \(-0.605474\pi\) | ||||
−0.325327 | + | 0.945602i | \(0.605474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.12173e6i | − 0.139572i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 5.57040e7i | − 1.86702i | −0.358546 | − | 0.933512i | \(-0.616727\pi\) | ||||
0.358546 | − | 0.933512i | \(-0.383273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.79680e7 | −2.26646 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −444994. | −0.0147632 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.55469e7i | − 0.513167i | −0.966522 | − | 0.256584i | \(-0.917403\pi\) | ||||
0.966522 | − | 0.256584i | \(-0.0825969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 53248.0i | − 0.00173984i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.40884e7 | 2.08348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.36890e7 | 0.766237 | 0.383118 | − | 0.923699i | \(-0.374850\pi\) | ||||
0.383118 | + | 0.923699i | \(0.374850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.19144e7i | 0.383442i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.71720e6i | − 0.118434i | −0.998245 | − | 0.0592172i | \(-0.981140\pi\) | ||||
0.998245 | − | 0.0592172i | \(-0.0188605\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.19302e7 | 1.01225 |
(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 | 800.6.c.a.449.1 | 2 | ||
4.3 | odd | 2 | 800.6.c.b.449.2 | 2 | |||
5.2 | odd | 4 | 32.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 800.6.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 800.6.c.a.449.2 | 2 | ||
15.2 | even | 4 | 288.6.a.d.1.1 | 1 | |||
20.3 | even | 4 | 800.6.a.a.1.1 | 1 | |||
20.7 | even | 4 | 32.6.a.c.1.1 | yes | 1 | ||
20.19 | odd | 2 | 800.6.c.b.449.1 | 2 | |||
40.27 | even | 4 | 64.6.a.c.1.1 | 1 | |||
40.37 | odd | 4 | 64.6.a.e.1.1 | 1 | |||
60.47 | odd | 4 | 288.6.a.e.1.1 | 1 | |||
80.27 | even | 4 | 256.6.b.b.129.1 | 2 | |||
80.37 | odd | 4 | 256.6.b.h.129.2 | 2 | |||
80.67 | even | 4 | 256.6.b.b.129.2 | 2 | |||
80.77 | odd | 4 | 256.6.b.h.129.1 | 2 | |||
120.77 | even | 4 | 576.6.a.u.1.1 | 1 | |||
120.107 | odd | 4 | 576.6.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
32.6.a.c.1.1 | yes | 1 | 20.7 | even | 4 | ||
64.6.a.c.1.1 | 1 | 40.27 | even | 4 | |||
64.6.a.e.1.1 | 1 | 40.37 | odd | 4 | |||
256.6.b.b.129.1 | 2 | 80.27 | even | 4 | |||
256.6.b.b.129.2 | 2 | 80.67 | even | 4 | |||
256.6.b.h.129.1 | 2 | 80.77 | odd | 4 | |||
256.6.b.h.129.2 | 2 | 80.37 | odd | 4 | |||
288.6.a.d.1.1 | 1 | 15.2 | even | 4 | |||
288.6.a.e.1.1 | 1 | 60.47 | odd | 4 | |||
576.6.a.u.1.1 | 1 | 120.77 | even | 4 | |||
576.6.a.v.1.1 | 1 | 120.107 | odd | 4 | |||
800.6.a.a.1.1 | 1 | 20.3 | even | 4 | |||
800.6.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
800.6.c.a.449.1 | 2 | 1.1 | even | 1 | trivial | ||
800.6.c.a.449.2 | 2 | 5.4 | even | 2 | inner | ||
800.6.c.b.449.1 | 2 | 20.19 | odd | 2 | |||
800.6.c.b.449.2 | 2 | 4.3 | odd | 2 |