Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,7,Mod(145,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.145");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bh (of order \(6\), degree \(2\), 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: | \(77.2981720963\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3\cdot 7 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(2.26350 + 3.92050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.145 |
Dual form | 336.7.bh.d.241.2 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 13.5000 | − | 7.79423i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −57.9943 | − | 33.4830i | −0.463955 | − | 0.267864i | 0.249751 | − | 0.968310i | \(-0.419651\pi\) |
−0.713706 | + | 0.700446i | \(0.752985\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 240.457 | + | 244.600i | 0.701042 | + | 0.713120i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 121.500 | − | 210.444i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 862.868 | + | 1494.53i | 0.648285 | + | 1.12286i | 0.983532 | + | 0.180733i | \(0.0578470\pi\) |
−0.335247 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2807.43i | 1.27785i | 0.769271 | + | 0.638923i | \(0.220620\pi\) | ||||
−0.769271 | + | 0.638923i | \(0.779380\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1043.90 | −0.309303 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5323.58 | + | 3073.57i | −1.08357 | + | 0.625599i | −0.931857 | − | 0.362826i | \(-0.881812\pi\) |
−0.151712 | + | 0.988425i | \(0.548479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7737.30 | − | 4467.13i | −1.12805 | − | 0.651281i | −0.184607 | − | 0.982812i | \(-0.559101\pi\) |
−0.943444 | + | 0.331532i | \(0.892435\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5152.64 | + | 1427.92i | 0.556381 | + | 0.154187i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4950.64 | − | 8574.76i | 0.406891 | − | 0.704755i | −0.587649 | − | 0.809116i | \(-0.699946\pi\) |
0.994540 | + | 0.104361i | \(0.0332796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5570.27 | − | 9648.00i | −0.356497 | − | 0.617472i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13610.4 | −0.558054 | −0.279027 | − | 0.960283i | \(-0.590012\pi\) | ||||
−0.279027 | + | 0.960283i | \(0.590012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21833.0 | − | 12605.3i | 0.732871 | − | 0.423123i | −0.0866007 | − | 0.996243i | \(-0.527600\pi\) |
0.819472 | + | 0.573120i | \(0.194267\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23297.4 | + | 13450.8i | 0.648285 | + | 0.374288i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5755.21 | − | 22236.7i | −0.134232 | − | 0.518639i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11366.4 | + | 19687.1i | −0.224397 | + | 0.388666i | −0.956138 | − | 0.292916i | \(-0.905374\pi\) |
0.731742 | + | 0.681582i | \(0.238708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 21881.7 | + | 37900.2i | 0.368882 | + | 0.638923i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 37897.2i | − | 0.549865i | −0.961464 | − | 0.274932i | \(-0.911345\pi\) | ||
0.961464 | − | 0.274932i | \(-0.0886554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −73646.2 | −0.926286 | −0.463143 | − | 0.886284i | \(-0.653278\pi\) | ||||
−0.463143 | + | 0.886284i | \(0.653278\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14092.6 | + | 8136.38i | −0.154652 | + | 0.0892881i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120523. | − | 69583.9i | −1.16085 | − | 0.670216i | −0.209342 | − | 0.977843i | \(-0.567132\pi\) |
−0.951507 | + | 0.307626i | \(0.900465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2009.47 | + | 117632.i | −0.0170802 | + | 0.999854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −47912.2 | + | 82986.3i | −0.361190 | + | 0.625599i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8258.79 | + | 14304.7i | 0.0554739 | + | 0.0960837i | 0.892429 | − | 0.451188i | \(-0.149000\pi\) |
−0.836955 | + | 0.547272i | \(0.815666\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 115566.i | − | 0.694610i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −139271. | −0.752034 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61989.7 | − | 35789.8i | 0.301831 | − | 0.174262i | −0.341434 | − | 0.939906i | \(-0.610913\pi\) |
0.643265 | + | 0.765644i | \(0.277579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −228557. | − | 131958.i | −1.00695 | − | 0.581360i | −0.0966496 | − | 0.995318i | \(-0.530813\pi\) |
−0.910296 | + | 0.413958i | \(0.864146\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 80690.3 | − | 20883.9i | 0.322700 | − | 0.0835201i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 94001.1 | − | 162815.i | 0.342289 | − | 0.592862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 274333. | + | 475159.i | 0.912125 | + | 1.57985i | 0.811057 | + | 0.584967i | \(0.198893\pi\) |
0.101068 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 154346.i | − | 0.469837i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −465655. | −1.30103 | −0.650517 | − | 0.759491i | \(-0.725448\pi\) | ||||
−0.650517 | + | 0.759491i | \(0.725448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −289020. | + | 166866.i | −0.742950 | + | 0.428942i | −0.823141 | − | 0.567837i | \(-0.807780\pi\) |
0.0801910 | + | 0.996780i | \(0.474447\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −150397. | − | 86832.0i | −0.356497 | − | 0.205824i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −158080. | + | 570429.i | −0.346261 | + | 1.24948i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −205012. | + | 355091.i | −0.415813 | + | 0.720209i | −0.995513 | − | 0.0946203i | \(-0.969836\pi\) |
0.579700 | + | 0.814830i | \(0.303170\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29524.5 | − | 51137.9i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 71948.9i | − | 0.125832i | −0.998019 | − | 0.0629158i | \(-0.979960\pi\) | ||
0.998019 | − | 0.0629158i | \(-0.0200400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 411649. | 0.670302 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −183740. | + | 106082.i | −0.279027 | + | 0.161096i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −141505. | − | 81698.0i | −0.200725 | − | 0.115889i | 0.396269 | − | 0.918135i | \(-0.370305\pi\) |
−0.596994 | + | 0.802246i | \(0.703638\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −686697. | + | 675066.i | −0.911257 | + | 0.895823i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 196497. | − | 340342.i | 0.244290 | − | 0.423123i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 299146. | + | 518137.i | 0.348910 | + | 0.604329i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 651914.i | 0.714291i | 0.934049 | + | 0.357146i | \(0.116250\pi\) | ||||
−0.934049 | + | 0.357146i | \(0.883750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 419354. | 0.432190 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 883850. | − | 510291.i | 0.857856 | − | 0.495283i | −0.00543765 | − | 0.999985i | \(-0.501731\pi\) |
0.863294 | + | 0.504702i | \(0.168398\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −363147. | − | 209663.i | −0.332331 | − | 0.191871i | 0.324545 | − | 0.945870i | \(-0.394789\pi\) |
−0.656875 | + | 0.753999i | \(0.728122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −251013. | − | 255338.i | −0.216834 | − | 0.220570i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.10621e6 | − | 1.91600e6i | 0.902993 | − | 1.56403i | 0.0794039 | − | 0.996843i | \(-0.474698\pi\) |
0.823589 | − | 0.567187i | \(-0.191968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −382955. | − | 663297.i | −0.295711 | − | 0.512187i | 0.679439 | − | 0.733732i | \(-0.262223\pi\) |
−0.975150 | + | 0.221545i | \(0.928890\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 354368.i | 0.259111i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.66096e6 | −1.84418 | −0.922090 | − | 0.386976i | \(-0.873520\pi\) | ||||
−0.922090 | + | 0.386976i | \(0.873520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −574218. | + | 331525.i | −0.377558 | + | 0.217983i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 590806. | + | 341102.i | 0.368882 | + | 0.212974i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.03189e6 | − | 563085.i | −1.20575 | − | 0.334144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −603302. | + | 1.04495e6i | −0.340548 | + | 0.589847i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −295380. | − | 511612.i | −0.158732 | − | 0.274932i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.79238e6i | 0.917700i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.11648e6 | 0.545055 | 0.272527 | − | 0.962148i | \(-0.412141\pi\) | ||||
0.272527 | + | 0.962148i | \(0.412141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −994224. | + | 574015.i | −0.463143 | + | 0.267396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −247826. | − | 143083.i | −0.110239 | − | 0.0636463i | 0.443867 | − | 0.896093i | \(-0.353606\pi\) |
−0.554106 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −767830. | − | 2.96670e6i | −0.326370 | − | 1.26101i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −126834. | + | 219682.i | −0.0515505 | + | 0.0892881i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.86697e6 | + | 3.23368e6i | 0.726063 | + | 1.25758i | 0.958535 | + | 0.284975i | \(0.0919854\pi\) |
−0.232472 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 618216.i | − | 0.230195i | −0.993354 | − | 0.115097i | \(-0.963282\pi\) | ||
0.993354 | − | 0.115097i | \(-0.0367180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.16941e6 | −0.773899 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.19579e6 | + | 2.42244e6i | −1.43485 | + | 0.828408i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 789324. | + | 455716.i | 0.258911 | + | 0.149483i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 889722. | + | 1.60369e6i | 0.280093 | + | 0.504858i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.86160e6 | + | 3.22438e6i | −0.562765 | + | 0.974737i | 0.434489 | + | 0.900677i | \(0.356929\pi\) |
−0.997254 | + | 0.0740601i | \(0.976404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.27599e6 | − | 2.21009e6i | −0.370611 | − | 0.641917i | 0.619049 | − | 0.785352i | \(-0.287518\pi\) |
−0.989660 | + | 0.143436i | \(0.954185\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.49375e6i | 0.417066i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.68825e6 | −0.453358 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.87057e6 | + | 3.38938e6i | −1.51699 | + | 0.875832i | −0.517186 | + | 0.855873i | \(0.673020\pi\) |
−0.999801 | + | 0.0199592i | \(0.993646\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 222987. | + | 128742.i | 0.0554739 | + | 0.0320279i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28781e6 | − | 850937.i | 0.787823 | − | 0.203901i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.13571e6 | + | 7.16325e6i | −0.954964 | + | 1.65405i | −0.220513 | + | 0.975384i | \(0.570773\pi\) |
−0.734451 | + | 0.678662i | \(0.762560\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −900746. | − | 1.56014e6i | −0.200517 | − | 0.347305i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59960e6i | 0.558158i | 0.960268 | + | 0.279079i | \(0.0900291\pi\) | ||||
−0.960268 | + | 0.279079i | \(0.909971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05483e6 | −0.632888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.88016e6 | + | 1.08551e6i | −0.376017 | + | 0.217094i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.10612e6 | − | 4.10272e6i | −1.37244 | − | 0.792380i | −0.381208 | − | 0.924489i | \(-0.624492\pi\) |
−0.991235 | + | 0.132109i | \(0.957825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.02049e6 | − | 3.68242e6i | 0.190412 | − | 0.687099i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 557907. | − | 966324.i | 0.100610 | − | 0.174262i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.09401e6 | + | 7.09104e6i | 0.713822 | + | 1.23638i | 0.963412 | + | 0.268025i | \(0.0863709\pi\) |
−0.249590 | + | 0.968352i | \(0.580296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.25606e6i | − | 0.549106i | −0.961572 | − | 0.274553i | \(-0.911470\pi\) | ||
0.961572 | − | 0.274553i | \(-0.0885298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.11403e6 | −0.671297 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.31837e6 | − | 761161.i | 0.208220 | − | 0.120216i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.18709e6 | − | 5.30417e6i | −1.40492 | − | 0.811133i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 926544. | − | 910851.i | 0.137240 | − | 0.134916i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.30425e6 | − | 7.45518e6i | 0.617728 | − | 1.06994i | −0.372171 | − | 0.928164i | \(-0.621386\pi\) |
0.989899 | − | 0.141773i | \(-0.0452802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89943.0 | + | 155786.i | 0.0125111 | + | 0.0216699i | 0.872213 | − | 0.489126i | \(-0.162684\pi\) |
−0.859702 | + | 0.510796i | \(0.829351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.93067e6i | − | 0.395241i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.69333e6 | 0.352283 | 0.176141 | − | 0.984365i | \(-0.443638\pi\) | ||||
0.176141 | + | 0.984365i | \(0.443638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.23271e6 | + | 3.02111e6i | −0.663999 | + | 0.383360i | −0.793799 | − | 0.608180i | \(-0.791900\pi\) |
0.129800 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.40700e6 | + | 4.27643e6i | 0.912125 | + | 0.526616i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.27271e6 | − | 3.32910e6i | −0.391219 | − | 0.397959i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.26891e6 | + | 2.19782e6i | −0.147289 | + | 0.255112i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.20301e6 | − | 2.08367e6i | −0.135630 | − | 0.234918i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.54182e7i | − | 1.68886i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.38113e7 | 1.47024 | 0.735118 | − | 0.677939i | \(-0.237127\pi\) | ||||
0.735118 | + | 0.677939i | \(0.237127\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.28634e6 | + | 3.62942e6i | −0.650517 | + | 0.375576i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.27106e6 | + | 2.46590e6i | 0.429755 | + | 0.248119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.33314e6 | + | 2.30932e6i | 0.815511 | + | 0.225998i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.60118e6 | + | 4.50538e6i | −0.247650 | + | 0.428942i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.62881e6 | − | 1.49455e7i | −0.799419 | − | 1.38463i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.81400e6i | 0.884976i | 0.896774 | + | 0.442488i | \(0.145904\pi\) | ||||
−0.896774 | + | 0.442488i | \(0.854096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70715e6 | −0.237665 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.26217e7 | − | 7.28715e6i | 1.07905 | − | 0.622989i | 0.148408 | − | 0.988926i | \(-0.452585\pi\) |
0.930639 | + | 0.365938i | \(0.119252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.27292e7 | + | 7.34923e6i | 1.05998 | + | 0.611978i | 0.925426 | − | 0.378929i | \(-0.123708\pi\) |
0.134551 | + | 0.990907i | \(0.457041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.31198e6 | + | 8.93290e6i | 0.187563 | + | 0.724697i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.87597e6 | + | 4.98133e6i | −0.227362 | + | 0.393802i | −0.957025 | − | 0.290004i | \(-0.906343\pi\) |
0.729664 | + | 0.683806i | \(0.239677\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.65976e6 | + | 8.07094e6i | 0.359054 | + | 0.621900i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.39164e6i | 0.480140i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.60167e7 | −1.17322 | −0.586610 | − | 0.809869i | \(-0.699538\pi\) | ||||
−0.586610 | + | 0.809869i | \(0.699538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.23613e7 | + | 1.29103e7i | −1.59752 | + | 0.922327i | −0.605553 | + | 0.795805i | \(0.707048\pi\) |
−0.991964 | + | 0.126522i | \(0.959618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −797162. | − | 460241.i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.05521e6 | − | 6.75469e6i | 0.275750 | − | 0.459312i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.25411e7 | − | 2.17219e7i | 0.832236 | − | 1.44147i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −560786. | − | 971311.i | −0.0363245 | − | 0.0629158i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.51912e6i | − | 0.601971i | −0.953629 | − | 0.300985i | \(-0.902684\pi\) | ||
0.953629 | − | 0.300985i | \(-0.0973156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.70870e7 | 1.05513 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.55727e6 | − | 3.20849e6i | 0.335151 | − | 0.193500i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.93872e7 | + | 1.11932e7i | 1.14213 | + | 0.659408i | 0.946957 | − | 0.321361i | \(-0.104140\pi\) |
0.195171 | + | 0.980769i | \(0.437474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.54860e6 | + | 1.95370e6i | −0.434477 | + | 0.112450i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.65366e6 | + | 2.86422e6i | −0.0930089 | + | 0.161096i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.24659e6 | + | 9.08736e6i | 0.288410 | + | 0.499540i | 0.973430 | − | 0.228983i | \(-0.0735402\pi\) |
−0.685021 | + | 0.728524i | \(0.740207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.10612e6i | − | 0.0594380i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.54709e6 | −0.133817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.33663e7 | − | 1.34905e7i | 1.20042 | − | 0.693063i | 0.239772 | − | 0.970829i | \(-0.422927\pi\) |
0.960649 | + | 0.277766i | \(0.0895941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.09955e6 | + | 634826.i | 0.0552468 | + | 0.0318968i | 0.527369 | − | 0.849636i | \(-0.323179\pi\) |
−0.472122 | + | 0.881533i | \(0.656512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00878e6 | + | 1.44657e7i | −0.197027 | + | 0.710969i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.61282e6 | − | 1.66499e7i | 0.462224 | − | 0.800596i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.35016e6 | + | 5.80265e6i | 0.157626 | + | 0.273016i | 0.934012 | − | 0.357242i | \(-0.116283\pi\) |
−0.776386 | + | 0.630257i | \(0.782949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 6.12616e6i | − | 0.282082i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −321000. | −0.0144673 | −0.00723363 | − | 0.999974i | \(-0.502303\pi\) | ||||
−0.00723363 | + | 0.999974i | \(0.502303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.77311e6 | + | 1.60105e6i | −0.122351 | + | 0.0706394i | −0.559926 | − | 0.828542i | \(-0.689171\pi\) |
0.437575 | + | 0.899182i | \(0.355837\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.07695e6 | + | 4.66323e6i | 0.348910 | + | 0.201443i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.26967e6 | − | 9.11267e6i | 0.392119 | − | 0.385478i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.82485e6 | − | 1.18210e7i | 0.282748 | − | 0.489734i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.08117e6 | + | 8.80084e6i | 0.206198 | + | 0.357146i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.67440e6i | 0.106322i | 0.998586 | + | 0.0531610i | \(0.0169297\pi\) | ||||
−0.998586 | + | 0.0531610i | \(0.983070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.79340e6 | −0.186714 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.66128e6 | − | 3.26854e6i | 0.216095 | − | 0.124763i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.40730e7 | + | 1.38986e7i | 0.900568 | + | 0.519943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77088e7 | − | 1.80139e7i | −0.649365 | − | 0.660553i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.95465e6 | − | 1.37779e7i | 0.285952 | − | 0.495283i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.83669e6 | + | 1.53056e7i | 0.311451 | + | 0.539449i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.98765e7i | 0.686950i | 0.939162 | + | 0.343475i | \(0.111604\pi\) | ||||
−0.939162 | + | 0.343475i | \(0.888396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.53664e6 | −0.221554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.36580e7 | − | 7.88548e6i | 0.454054 | − | 0.262148i | −0.255487 | − | 0.966813i | \(-0.582236\pi\) |
0.709541 | + | 0.704664i | \(0.248902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.13939e6 | − | 5.27663e6i | −0.298047 | − | 0.172077i | 0.343518 | − | 0.939146i | \(-0.388381\pi\) |
−0.641565 | + | 0.767069i | \(0.721715\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.37883e6 | − | 1.49060e6i | −0.172090 | − | 0.0476904i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.61613e7 | − | 2.79923e7i | 0.507341 | − | 0.878740i | −0.492623 | − | 0.870243i | \(-0.663962\pi\) |
0.999964 | − | 0.00849733i | \(-0.00270482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17440e7 | − | 2.03411e7i | −0.361778 | − | 0.626618i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3.44881e7i | − | 1.04269i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.49201e7 | 1.62976 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70860e7 | − | 1.56381e7i | 0.789033 | − | 0.455549i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.03398e7 | − | 5.96968e6i | −0.295711 | − | 0.170729i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.19604e7 | − | 4.62119e7i | −0.335859 | − | 1.29767i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00165e7 | − | 1.73490e7i | 0.276205 | − | 0.478400i | −0.694234 | − | 0.719750i | \(-0.744257\pi\) |
0.970438 | + | 0.241349i | \(0.0775899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.76203e6 | + | 4.78397e6i | 0.0747989 | + | 0.129555i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.67421e7i | − | 0.977303i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.66702e6 | −0.0958128 | −0.0479064 | − | 0.998852i | \(-0.515255\pi\) | ||||
−0.0479064 | + | 0.998852i | \(0.515255\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.59230e7 | + | 2.07401e7i | −0.922090 | + | 0.532369i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.76779e7 | + | 2.17534e7i | 0.950219 | + | 0.548609i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.92560e7 | + | 2.77939e7i | −0.724990 | + | 0.688760i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.16796e6 | + | 8.95117e6i | −0.125853 | + | 0.217983i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.22802e6 | + | 5.59109e6i | 0.0772587 | + | 0.133816i | 0.902066 | − | 0.431598i | \(-0.142050\pi\) |
−0.824808 | + | 0.565414i | \(0.808717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.01536e7i | 0.944600i | 0.881438 | + | 0.472300i | \(0.156576\pi\) | ||||
−0.881438 | + | 0.472300i | \(0.843424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06345e7 | 0.245921 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.02915e6 | − | 4.05828e6i | 0.159801 | − | 0.0922610i | −0.417967 | − | 0.908462i | \(-0.637257\pi\) |
0.577768 | + | 0.816201i | \(0.303924\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.70053e7 | + | 1.55915e7i | 0.603621 | + | 0.348501i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.18193e7 | + | 8.23535e6i | −0.699336 | + | 0.181000i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.84586e7 | − | 3.19712e7i | 0.398946 | − | 0.690996i | −0.594650 | − | 0.803985i | \(-0.702709\pi\) |
0.993596 | + | 0.112989i | \(0.0360426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.63876e7 | + | 2.83842e7i | 0.348333 | + | 0.603330i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.88091e7i | 0.393231i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.23487e7 | 0.459593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.70742e7 | + | 9.85777e6i | −0.345415 | + | 0.199425i | −0.662664 | − | 0.748917i | \(-0.730574\pi\) |
0.317249 | + | 0.948342i | \(0.397241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.97525e6 | − | 4.60451e6i | −0.158732 | − | 0.0916441i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.51303e6 | + | 5.45976e6i | −0.0296296 | + | 0.106918i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.21653e6 | + | 9.03530e6i | −0.100521 | + | 0.174107i | −0.911899 | − | 0.410414i | \(-0.865384\pi\) |
0.811379 | + | 0.584521i | \(0.198718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.39702e7 | + | 2.41972e7i | 0.264917 | + | 0.458850i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.82101e7i | − | 0.713106i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.26018e7 | 0.966235 | 0.483118 | − | 0.875556i | \(-0.339504\pi\) | ||||
0.483118 | + | 0.875556i | \(0.339504\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50725e7 | − | 8.70210e6i | 0.272527 | − | 0.157344i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.36846e7 | − | 3.67683e7i | −1.13354 | − | 0.654451i | −0.188719 | − | 0.982031i | \(-0.560434\pi\) |
−0.944823 | + | 0.327580i | \(0.893767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.82674e7 | − | 2.77886e7i | 0.495340 | − | 0.486951i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.94802e6 | + | 1.54984e7i | −0.154381 | + | 0.267396i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.60695e6 | − | 1.49077e7i | −0.146218 | − | 0.253257i | 0.783609 | − | 0.621255i | \(-0.213377\pi\) |
−0.929827 | + | 0.367998i | \(0.880043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.08645e7i | 1.01820i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.46088e6 | −0.0734924 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.37791e7 | − | 1.37289e7i | 0.385837 | − | 0.222763i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.31024e7 | − | 3.06587e7i | −0.848678 | − | 0.489984i | 0.0115267 | − | 0.999934i | \(-0.496331\pi\) |
−0.860205 | + | 0.509949i | \(0.829664\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.34888e7 | − | 3.40658e7i | −0.527207 | − | 0.536290i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.30735e7 | − | 3.99645e7i | 0.357833 | − | 0.619785i | −0.629765 | − | 0.776785i | \(-0.716849\pi\) |
0.987599 | + | 0.157000i | \(0.0501823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.53883e7 | + | 6.12944e7i | 0.540686 | + | 0.936495i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.95428e6i | 0.0595254i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.92307e7 | −0.581892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.25613e7 | + | 3.03463e7i | −0.768239 | + | 0.443543i | −0.832246 | − | 0.554406i | \(-0.812945\pi\) |
0.0640071 | + | 0.997949i | \(0.479612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.04081e7 | + | 2.91031e7i | 0.726063 | + | 0.419193i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.36601e7 | + | 6.55677e6i | 0.335866 | + | 0.0930765i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.40907e6 | + | 4.17263e6i | −0.0337058 | + | 0.0583802i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.81852e6 | − | 8.34592e6i | −0.0664516 | − | 0.115097i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.17371e8i | − | 1.59558i | −0.602939 | − | 0.797788i | \(-0.706004\pi\) | ||
0.602939 | − | 0.797788i | \(-0.293996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28510e7 | −0.172222 | −0.0861111 | − | 0.996286i | \(-0.527444\pi\) | ||||
−0.0861111 | + | 0.996286i | \(0.527444\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.92870e7 | + | 1.69089e7i | −0.386950 | + | 0.223405i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.93075e7 | + | 3.42412e7i | 0.772579 | + | 0.446049i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.26815e7 | − | 8.76354e7i | −0.291331 | − | 1.12563i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.77621e7 | + | 6.54058e7i | −0.478282 | + | 0.828408i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.69282e7 | − | 9.86026e7i | −0.711043 | − | 1.23156i | −0.964466 | − | 0.264207i | \(-0.914890\pi\) |
0.253423 | − | 0.967356i | \(-0.418444\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.76112e7i | 0.340111i | 0.985434 | + | 0.170056i | \(0.0543947\pi\) | ||||
−0.985434 | + | 0.170056i | \(0.945605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.42078e7 | 0.172608 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.66092e7 | + | 4.42303e7i | −0.917987 | + | 0.530000i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.22452e7 | − | 3.59373e7i | −0.735720 | − | 0.424768i | 0.0847914 | − | 0.996399i | \(-0.472978\pi\) |
−0.820511 | + | 0.571631i | \(0.806311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.45108e7 | + | 1.47151e7i | 0.285786 | + | 0.171573i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.75145e7 | + | 8.22975e7i | −0.546531 | + | 0.946620i | 0.451978 | + | 0.892029i | \(0.350719\pi\) |
−0.998509 | + | 0.0545904i | \(0.982615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.47099e6 | + | 9.47603e6i | 0.0620849 | + | 0.107534i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.80389e7i | 0.649825i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.15401e8 | 1.27488 | 0.637440 | − | 0.770500i | \(-0.279993\pi\) | ||||
0.637440 | + | 0.770500i | \(0.279993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.66386e7 | − | 3.27003e7i | 0.617423 | − | 0.356469i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.44518e7 | − | 1.98908e7i | −0.370611 | − | 0.213972i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.24278e7 | − | 1.61573e7i | 0.662741 | − | 0.171528i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.58763e6 | + | 7.94601e6i | −0.0480662 | + | 0.0832531i | −0.889058 | − | 0.457796i | \(-0.848639\pi\) |
0.840991 | + | 0.541049i | \(0.181973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.16427e7 | + | 2.01657e7i | 0.120397 | + | 0.208533i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.79354e7i | 0.591346i | 0.955289 | + | 0.295673i | \(0.0955438\pi\) | ||||
−0.955289 | + | 0.295673i | \(0.904456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.51781e7 | −0.656687 | −0.328344 | − | 0.944558i | \(-0.606490\pi\) | ||||
−0.328344 | + | 0.944558i | \(0.606490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.27914e7 | + | 1.31586e7i | −0.226679 | + | 0.130873i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.46749e8 | + | 8.47258e7i | 1.44087 | + | 0.831888i | 0.997908 | − | 0.0646508i | \(-0.0205933\pi\) |
0.442965 | + | 0.896539i | \(0.353927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.02586e7 | + | 1.81358e8i | −0.487182 | + | 1.75799i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.28352e7 | + | 9.15132e7i | −0.505662 | + | 0.875832i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.35470e7 | − | 1.10067e8i | −0.600498 | − | 1.04009i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.95326e7i | 0.928719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.01377e6 | 0.0369826 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.92689e7 | − | 4.57659e7i | 0.721268 | − | 0.416424i | −0.0939514 | − | 0.995577i | \(-0.529950\pi\) |
0.815219 | + | 0.579153i | \(0.196617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52701e7 | − | 3.19102e7i | −0.496656 | − | 0.286744i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.77530e7 | − | 3.71136e7i | 0.335050 | − | 0.329375i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.18281e7 | − | 3.78073e7i | 0.191333 | − | 0.331399i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.56199e7 | − | 1.13657e8i | −0.568131 | − | 0.984032i | −0.996751 | − | 0.0805467i | \(-0.974333\pi\) |
0.428620 | − | 0.903485i | \(-0.359000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.28939e8i | 1.10270i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.81776e7 | 0.744927 | 0.372463 | − | 0.928047i | \(-0.378513\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.24558e7 | − | 4.18324e7i | 0.604690 | − | 0.349118i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.43201e7 | − | 1.40412e7i | −0.200517 | − | 0.115768i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.11970e8 | − | 1.13899e8i | −0.912080 | − | 0.927794i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.14235e8 | + | 1.97862e8i | −0.919389 | + | 1.59243i | −0.119043 | + | 0.992889i | \(0.537983\pi\) |
−0.800346 | + | 0.599539i | \(0.795351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.02619e7 | + | 3.50946e7i | 0.161126 | + | 0.279079i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 2.07735e8i | − | 1.63232i | −0.577824 | − | 0.816161i | \(-0.696098\pi\) | ||
0.577824 | − | 0.816161i | \(-0.303902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.83444e7 | −0.530675 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.12402e7 | + | 2.38100e7i | −0.316444 | + | 0.182699i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.74960e7 | − | 2.74218e7i | −0.360167 | − | 0.207942i | 0.308987 | − | 0.951066i | \(-0.400010\pi\) |
−0.669154 | + | 0.743124i | \(0.733343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.10312e8 | − | 3.05702e7i | −0.826726 | − | 0.229106i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.69215e7 | + | 2.93089e7i | −0.125339 | + | 0.217094i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.40403e7 | + | 2.43185e7i | 0.102791 | + | 0.178039i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.40167e8i | − | 1.73797i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.27910e8 | −0.914962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.47035e7 | + | 1.42626e7i | −0.174681 | + | 0.100852i | −0.584791 | − | 0.811184i | \(-0.698824\pi\) |
0.410110 | + | 0.912036i | \(0.365490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.32394e7 | + | 5.38318e7i | 0.651770 | + | 0.376300i | 0.789134 | − | 0.614221i | \(-0.210530\pi\) |
−0.137364 | + | 0.990521i | \(0.543863\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.49251e7 | − | 5.76666e7i | −0.103143 | − | 0.398517i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.74863e7 | + | 1.34210e8i | −0.529411 | + | 0.916966i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50003e7 | + | 4.33018e7i | 0.168880 | + | 0.292509i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.73938e7i | − | 0.116175i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06394e8 | 0.702642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28307e8 | + | 7.40782e7i | −0.837895 | + | 0.483759i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.10538e8 | + | 6.38193e7i | 0.713822 | + | 0.412125i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.77538e8 | + | 9.84975e7i | −1.13377 | + | 0.629012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.77877e7 | + | 4.81297e7i | −0.175493 | + | 0.303963i | −0.940332 | − | 0.340259i | \(-0.889485\pi\) |
0.764839 | + | 0.644222i | \(0.222819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.53784e7 | − | 4.39567e7i | −0.158513 | − | 0.274553i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.12900e7i | 0.316842i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.44170e7 | −0.332485 | −0.166243 | − | 0.986085i | \(-0.553163\pi\) | ||||
−0.166243 | + | 0.986085i | \(0.553163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.55395e7 | + | 3.20657e7i | −0.335648 | + | 0.193787i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.05308e8 | + | 6.07993e7i | 0.629513 | + | 0.363449i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.36152e8 | + | 3.52384e7i | −0.805098 | + | 0.208372i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.18653e7 | − | 2.05513e7i | 0.0694066 | − | 0.120216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.26135e6 | − | 1.08450e7i | −0.0362329 | − | 0.0627571i | 0.847340 | − | 0.531050i | \(-0.178202\pi\) |
−0.883573 | + | 0.468293i | \(0.844869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.06756e8i | − | 1.18365i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65368e8 | −0.936616 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.50742e8 | + | 8.70310e7i | −0.844713 | + | 0.487695i | −0.858864 | − | 0.512204i | \(-0.828829\pi\) |
0.0141502 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54321e8 | + | 8.90971e7i | 0.855616 | + | 0.493990i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.40896e6 | − | 1.95182e7i | 0.0296732 | − | 0.107076i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.37803e7 | + | 4.11886e7i | −0.129086 | + | 0.223584i | −0.923323 | − | 0.384025i | \(-0.874538\pi\) |
0.794237 | + | 0.607609i | \(0.207871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.27707e7 | + | 1.43363e8i | 0.444599 | + | 0.770068i | 0.998024 | − | 0.0628311i | \(-0.0200129\pi\) |
−0.553425 | + | 0.832899i | \(0.686680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.34193e8i | − | 0.713291i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.10306e8 | −0.580222 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.44692e7 | + | 2.56743e7i | −0.231490 | + | 0.133651i | −0.611259 | − | 0.791431i | \(-0.709337\pi\) |
0.379769 | + | 0.925081i | \(0.376003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.42846e6 | + | 1.40207e6i | 0.0125111 | + | 0.00722328i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.75987e7 | − | 1.73007e7i | 0.0897331 | − | 0.0882133i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.42525e7 | + | 2.46861e7i | −0.0719259 | + | 0.124579i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.28423e7 | − | 3.95640e7i | −0.114096 | − | 0.197621i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37624e8i | 1.17483i | 0.809285 | + | 0.587416i | \(0.199855\pi\) | ||||
−0.809285 | + | 0.587416i | \(0.800145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.25238e8 | −1.10229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.63600e7 | − | 2.09925e7i | 0.176141 | − | 0.101695i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.20624e8 | − | 1.85112e8i | −1.53756 | − | 0.887711i | −0.998981 | − | 0.0451361i | \(-0.985628\pi\) |
−0.538579 | − | 0.842575i | \(-0.681039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.89842e7 | + | 1.00690e8i | 0.469910 | + | 0.478006i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.70944e7 | + | 8.15699e7i | −0.221333 | + | 0.383360i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.87938e7 | − | 3.25519e7i | −0.0874451 | − | 0.151459i | 0.818985 | − | 0.573814i | \(-0.194537\pi\) |
−0.906430 | + | 0.422355i | \(0.861204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.67605e7i | − | 0.123274i | −0.998099 | − | 0.0616369i | \(-0.980368\pi\) | ||
0.998099 | − | 0.0616369i | \(-0.0196321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.33326e8 | 0.608083 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.99761e7 | − | 4.04007e7i | 0.315998 | − | 0.182441i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.69071e7 | − | 3.86288e7i | −0.299162 | − | 0.172721i | 0.342905 | − | 0.939370i | \(-0.388589\pi\) |
−0.642066 | + | 0.766649i | \(0.721923\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.01294e7 | − | 1.94345e7i | −0.310490 | − | 0.0860444i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.95352e8 | − | 3.38359e8i | 0.856433 | − | 1.48338i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.76486e8 | + | 3.05682e8i | 0.766174 | + | 1.32705i | 0.939623 | + | 0.342210i | \(0.111175\pi\) |
−0.173449 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.95608e7i | 0.170075i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.82109e8 | 0.775310 | 0.387655 | − | 0.921805i | \(-0.373285\pi\) | ||||
0.387655 | + | 0.921805i | \(0.373285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.43335e7 | + | 4.86900e7i | −0.355573 | + | 0.205290i | −0.667137 | − | 0.744935i | \(-0.732480\pi\) |
0.311564 | + | 0.950225i | \(0.399147\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.24811e7 | − | 1.87530e7i | −0.135630 | − | 0.0783062i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.40426e7 | − | 5.42570e7i | −0.0580742 | − | 0.224384i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.70211e7 | + | 4.68019e7i | −0.110678 | + | 0.191701i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.20173e8 | − | 2.08145e8i | −0.487533 | − | 0.844431i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.39741e8i | − | 0.561529i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.37285e8 | 0.546430 | 0.273215 | − | 0.961953i | \(-0.411913\pi\) | ||||
0.273215 | + | 0.961953i | \(0.411913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.86453e8 | − | 1.07648e8i | 0.735118 | − | 0.424421i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.47495e7 | − | 3.73832e7i | −0.252881 | − | 0.146001i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.30243e8 | − | 5.64143e6i | −1.27766 | − | 0.0218258i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65770e7 | + | 9.79943e7i | −0.216839 | + | 0.375576i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04673e8 | + | 1.81298e8i | 0.397428 | + | 0.688366i | 0.993408 | − | 0.114633i | \(-0.0365693\pi\) |
−0.595979 | + | 0.803000i | \(0.703236\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.49818e8i | − | 1.31586i | −0.753079 | − | 0.657930i | \(-0.771432\pi\) | ||
0.753079 | − | 0.657930i | \(-0.228568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.68791e7 | 0.286503 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.20197e8 | + | 1.84866e8i | −1.18224 | + | 0.682566i | −0.956531 | − | 0.291630i | \(-0.905803\pi\) |
−0.225707 | + | 0.974195i | \(0.572469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06978e8 | + | 6.17637e7i | 0.391345 | + | 0.225943i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.30497e8 | − | 3.37747e7i | 0.472995 | − | 0.122419i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.97623e7 | − | 3.42293e7i | 0.0709737 | − | 0.122930i | −0.828355 | − | 0.560204i | \(-0.810723\pi\) |
0.899328 | + | 0.437274i | \(0.144056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.58169e6 | + | 1.65960e7i | 0.0340971 | + | 0.0590580i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.10968e7i | 0.285962i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.29124e8 | 1.15002 | 0.575008 | − | 0.818148i | \(-0.304999\pi\) | ||||
0.575008 | + | 0.818148i | \(0.304999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39292e8 | + | 8.04205e7i | −0.482306 | + | 0.278460i | −0.721377 | − | 0.692543i | \(-0.756491\pi\) |
0.239071 | + | 0.971002i | \(0.423157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.32978e8 | − | 1.34510e8i | −0.799419 | − | 0.461545i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.48044e7 | + | 1.97761e8i | −0.186359 | + | 0.672474i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.73800e7 | + | 1.16706e8i | −0.227067 | + | 0.393291i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.64926e7 | + | 1.32489e8i | 0.255471 | + | 0.442488i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.55448e8i | − | 1.50755i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.32162e8 | 1.74582 | 0.872908 | − | 0.487886i | \(-0.162232\pi\) | ||||
0.872908 | + | 0.487886i | \(0.162232\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.65466e7 | + | 2.11002e7i | −0.118832 | + | 0.0686080i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.68878e8 | − | 2.70707e8i | −1.51110 | − | 0.872435i | −0.999916 | − | 0.0129645i | \(-0.995873\pi\) |
−0.511186 | − | 0.859470i | \(-0.670794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.59458e8 | + | 1.56758e8i | −0.509375 | + | 0.500748i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.13595e8 | − | 1.96753e8i | 0.359683 | − | 0.622989i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.24469e8 | + | 2.15587e8i | 0.390662 | + | 0.676646i | 0.992537 | − | 0.121944i | \(-0.0389129\pi\) |
−0.601875 | + | 0.798590i | \(0.705580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.50047e8i | − | 0.777946i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.29126e8 | 0.706651 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.01592e7 | + | 2.31860e7i | −0.122780 | + | 0.0708871i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00565e7 | − | 4.62206e7i | −0.242640 | − | 0.140088i | 0.373749 | − | 0.927530i | \(-0.378072\pi\) |
−0.616390 | + | 0.787441i | \(0.711405\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00837e8 | + | 1.02574e8i | 0.302984 | + | 0.308204i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.06997e7 | + | 3.58530e7i | −0.0616610 | + | 0.106800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.16480e8 | + | 2.01749e8i | 0.343995 | + | 0.595816i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.96640e7i | 0.262535i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.38435e8 | 1.56307 | 0.781537 | − | 0.623859i | \(-0.214436\pi\) | ||||
0.781537 | + | 0.623859i | \(0.214436\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75890e8 | − | 1.01550e8i | 0.506262 | − | 0.292290i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.25813e8 | + | 7.26384e7i | 0.359054 | + | 0.207300i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.37346e8 | + | 9.34866e7i | 0.954590 | + | 0.264540i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.53455e7 | + | 6.12202e7i | −0.0991735 | + | 0.171773i | −0.911343 | − | 0.411648i | \(-0.864953\pi\) |
0.812169 | + | 0.583422i | \(0.198287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.98179e7 | + | 8.62872e7i | 0.138604 | + | 0.240070i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.49616e8i | − | 0.688660i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.24442e8 | 0.887604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.16226e8 | + | 1.24838e8i | −0.586610 | + | 0.338680i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.38940e8 | + | 1.95687e8i | 0.911876 | + | 0.526472i | 0.881034 | − | 0.473053i | \(-0.156848\pi\) |
0.0308415 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.60378e7 | − | 1.39241e8i | −0.0961506 | − | 0.371501i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.01252e8 | + | 3.48578e8i | −0.532506 | + | 0.922327i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.58135e7 | + | 1.31313e8i | 0.198945 | + | 0.344582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.83550e8i | − | 1.25846i | −0.777221 | − | 0.629228i | \(-0.783371\pi\) | ||
0.777221 | − | 0.629228i | \(-0.216629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.92061e8 | − | 2.26357e8i | 1.00369 | − | 0.579484i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.76711e8 | − | 1.59759e8i | −0.702611 | − | 0.405653i | 0.105708 | − | 0.994397i | \(-0.466289\pi\) |
−0.808319 | + | 0.588745i | \(0.799622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.09768e6 | − | 1.22796e8i | 0.00528295 | − | 0.309258i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.73427e8 | + | 8.20000e8i | −1.18263 | + | 2.04838i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.76757e8 | + | 3.06151e8i | 0.437968 | + | 0.758582i | 0.997533 | − | 0.0702042i | \(-0.0223651\pi\) |
−0.559565 | + | 0.828787i | \(0.689032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.90994e8i | − | 0.960983i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.63396e8 | −1.12976 | −0.564880 | − | 0.825173i | \(-0.691077\pi\) | ||||
−0.564880 | + | 0.825173i | \(0.691077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.15924e8 | − | 1.24664e8i | 0.522195 | − | 0.301489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.51412e7 | − | 8.74179e6i | −0.0363245 | − | 0.0209719i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.34650e8 | − | 1.90139e8i | 1.74838 | − | 0.452508i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.48510e7 | + | 2.57226e7i | −0.0350618 | + | 0.0607289i | −0.883024 | − | 0.469328i | \(-0.844496\pi\) |
0.847962 | + | 0.530057i | \(0.177829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.41942e7 | − | 1.28508e8i | −0.173774 | − | 0.300985i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.70897e8i | 0.397093i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.11235e8 | 1.63955 | 0.819776 | − | 0.572684i | \(-0.194098\pi\) | ||||
0.819776 | + | 0.572684i | \(0.194098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.30674e8 | − | 1.33180e8i | 0.527563 | − | 0.304588i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.18255e8 | + | 1.83745e8i | 0.722140 | + | 0.416928i | 0.815540 | − | 0.578701i | \(-0.196440\pi\) |
−0.0933998 | + | 0.995629i | \(0.529773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.01583e7 | − | 2.53166e8i | 0.157945 | − | 0.569942i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.00154e7 | − | 8.66292e7i | 0.111717 | − | 0.193500i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.00477e8 | + | 1.74031e8i | 0.222680 | + | 0.385693i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.18891e8i | − | 0.701235i | −0.936519 | − | 0.350617i | \(-0.885972\pi\) | ||
0.936519 | − | 0.350617i | \(-0.114028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.48969e8 | 0.761419 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.35153e8 | − | 7.80307e7i | 0.292609 | − | 0.168938i | −0.346509 | − | 0.938047i | \(-0.612633\pi\) |
0.639118 | + | 0.769109i | \(0.279300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43231e8 | − | 1.40430e8i | −0.522533 | − | 0.301685i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.66785e7 | + | 8.52105e7i | −0.184777 | + | 0.181648i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.69292e8 | + | 2.93222e8i | −0.358116 | + | 0.620275i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.01798e8 | − | 6.95935e8i | −0.843442 | − | 1.46088i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.15560e7i | 0.107397i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.53947e8 | 0.938417 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.50044e8 | − | 3.75303e8i | 1.33358 | − | 0.769942i | 0.347733 | − | 0.937594i | \(-0.386952\pi\) |
0.985846 | + | 0.167651i | \(0.0536183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.41658e8 | + | 8.17862e7i | 0.288410 | + | 0.166513i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.39848e8 | − | 6.50872e8i | −1.29285 | − | 1.31512i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.70462e8 | − | 6.41658e8i | 0.742888 | − | 1.28672i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.62134e6 | − | 1.49326e7i | −0.0171583 | − | 0.0297190i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.08408e6i | 0.00214134i | 0.999999 | + | 0.00107067i | \(0.000340806\pi\) | ||||
−0.999999 | + | 0.00107067i | \(0.999659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.55483e8 | 1.67715 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.43857e7 | + | 1.98526e7i | −0.0669084 | + | 0.0386296i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.98772e8 | − | 2.87966e8i | −0.963287 | − | 0.556154i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.19166e8 | − | 6.07362e7i | −0.420132 | − | 0.116429i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.10297e8 | − | 3.64245e8i | 0.400140 | − | 0.693063i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.23887e8 | − | 3.87784e8i | −0.422847 | − | 0.732392i | 0.573370 | − | 0.819297i | \(-0.305636\pi\) |
−0.996217 | + | 0.0869044i | \(0.972303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.02416e8i | 1.31684i | 0.752652 | + | 0.658418i | \(0.228774\pi\) | ||||
−0.752652 | + | 0.658418i | \(0.771226\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.97919e7 | 0.0368312 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.79695e8 | − | 2.76952e8i | 0.886120 | − | 0.511601i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.69823e8 | + | 3.28987e8i | 1.04490 | + | 0.603272i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.86301e7 | + | 2.26532e8i | 0.106726 | + | 0.412361i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.31937e8 | + | 5.74932e8i | −0.599828 | + | 1.03893i | 0.393018 | + | 0.919531i | \(0.371431\pi\) |
−0.992846 | + | 0.119402i | \(0.961902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.08427e8 | + | 3.61007e8i | 0.373900 | + | 0.647614i | 0.990162 | − | 0.139928i | \(-0.0446870\pi\) |
−0.616262 | + | 0.787541i | \(0.711354\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.99698e8i | − | 0.533731i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.14598e8 | −0.202609 | −0.101305 | − | 0.994855i | \(-0.532302\pi\) | ||||
−0.101305 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.05381e8 | − | 2.34047e8i | 0.711541 | − | 0.410808i | −0.100090 | − | 0.994978i | \(-0.531913\pi\) |
0.811631 | + | 0.584170i | \(0.198580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.04544e7 | + | 5.22239e7i | 0.157626 | + | 0.0910052i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.50852e8 | − | 6.32398e8i | −0.607000 | − | 1.09410i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.70425e7 | − | 1.50762e8i | 0.149511 | − | 0.258960i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.77487e7 | − | 8.27031e7i | −0.0814301 | − | 0.141041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.49855e8i | − | 1.10035i | −0.835050 | − | 0.550174i | \(-0.814561\pi\) | ||
0.835050 | − | 0.550174i | \(-0.185439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.09581e8 | −0.688576 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.33350e6 | + | 2.50195e6i | −0.00723363 | + | 0.00417634i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.77163e8 | + | 1.02285e8i | 0.293631 | + | 0.169528i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00663e8 | + | 1.03698e8i | −0.659370 | + | 0.170656i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.49580e7 | + | 4.32285e7i | −0.0407837 | + | 0.0706394i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.12542e8 | + | 1.94928e8i | 0.182610 | + | 0.316290i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.47082e7i | − | 0.120371i | −0.998187 | − | 0.0601854i | \(-0.980831\pi\) | ||
0.998187 | − | 0.0601854i | \(-0.0191692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.45385e8 | 0.232606 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.50588e8 | + | 4.33352e8i | −1.19250 | + | 0.688491i | −0.958873 | − | 0.283835i | \(-0.908393\pi\) |
−0.233629 | + | 0.972326i | \(0.575060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.51273e7 | + | 8.73376e6i | 0.0238662 | + | 0.0137791i | 0.511886 | − | 0.859054i | \(-0.328947\pi\) |
−0.488019 | + | 0.872833i | \(0.662280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.41143e7 | − | 1.95271e8i | 0.0847817 | − | 0.305934i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.59542e8 | + | 9.69155e8i | −0.870563 | + | 1.50786i | −0.00914866 | + | 0.999958i | \(0.502912\pi\) |
−0.861415 | + | 0.507902i | \(0.830421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.74743e8 | + | 4.75869e8i | 0.424501 | + | 0.735257i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.12778e8i | − | 0.326489i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.07593e8 | −1.07826 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.33397e9 | + | 7.70171e8i | −2.01880 | + | 1.16555i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.37192e8 | + | 7.92076e7i | 0.206198 | + | 0.119049i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.38417e8 | + | 4.30992e8i | −0.654430 | + | 0.643346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.82730e8 | + | 1.00932e9i | −0.863910 | + | 1.49634i | 0.00421521 | + | 0.999991i | \(0.498658\pi\) |
−0.868125 | + | 0.496345i | \(0.834675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.08449e7 | + | 3.61044e7i | 0.0306925 | + | 0.0531610i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.07806e8i | 0.303900i | 0.988388 | + | 0.151950i | \(0.0485553\pi\) | ||||
−0.988388 | + | 0.151950i | \(0.951445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.48816e8 | 0.506657 | 0.253329 | − | 0.967380i | \(-0.418475\pi\) | ||||
0.253329 | + | 0.967380i | \(0.418475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.47109e7 | + | 3.73609e7i | −0.0933572 | + | 0.0538998i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.31382e8 | + | 4.22263e8i | 1.04803 | + | 0.605080i | 0.922097 | − | 0.386959i | \(-0.126475\pi\) |
0.125932 | + | 0.992039i | \(0.459808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.68466e8 | + | 2.73091e8i | 0.382106 | + | 0.388689i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.09515e7 | − | 8.82506e7i | 0.0720317 | − | 0.124763i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.21681e8 | + | 1.07678e9i | 0.872998 | + | 1.51208i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.48320e8i | − | 0.764830i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.33314e8 | 0.600379 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.97155e8 | + | 1.71562e8i | −0.408981 | + | 0.236125i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.79326e7 | − | 5.07679e7i | −0.120220 | − | 0.0694089i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.79473e8 | − | 1.05161e8i | −0.515368 | − | 0.142821i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.09023e8 | + | 1.88833e8i | −0.147086 | + | 0.254760i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.99924e8 | − | 6.92689e8i | −0.535989 | − | 0.928360i | −0.999115 | − | 0.0420677i | \(-0.986605\pi\) |
0.463126 | − | 0.886293i | \(-0.346728\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.48001e8i | − | 0.330189i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.54047e8 | −0.203750 | −0.101875 | − | 0.994797i | \(-0.532484\pi\) | ||||
−0.101875 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.07530e8 | − | 6.20824e7i | 0.141292 | − | 0.0815749i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.38591e8 | + | 1.37750e8i | 0.311451 | + | 0.179816i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.45937e7 | − | 9.50237e7i | −0.0318945 | − | 0.123232i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.43544e8 | − | 5.95036e8i | 0.442625 | − | 0.766649i | −0.555258 | − | 0.831678i | \(-0.687381\pi\) |
0.997883 | + | 0.0650288i | \(0.0207139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.54922e8 | + | 2.68333e8i | 0.198305 | + | 0.343475i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.30729e9i | − | 1.66252i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53255e8 | 0.319987 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.82447e7 | + | 5.09481e7i | −0.110777 | + | 0.0639571i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.27395e8 | + | 1.89021e8i | 0.408342 | + | 0.235757i | 0.690077 | − | 0.723736i | \(-0.257577\pi\) |
−0.281735 | + | 0.959492i | \(0.590910\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.41025e8 | − | 9.01176e8i | 0.670453 | − | 1.11676i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.22922e8 | − | 2.12908e8i | 0.151351 | − | 0.262148i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.55199e8 | + | 6.15223e8i | 0.434547 | + | 0.752658i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.27190e9i | − | 1.54609i | −0.634351 | − | 0.773045i | \(-0.718732\pi\) | ||
0.634351 | − | 0.773045i | \(-0.281268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.64509e8 | −0.198698 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.05181e8 | + | 3.49402e8i | −0.726301 | + | 0.419330i | −0.817067 | − | 0.576542i | \(-0.804402\pi\) |
0.0907665 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.24960e8 | − | 1.87615e8i | −0.387520 | − | 0.223735i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.42324e7 | + | 2.18007e7i | −0.0998122 | + | 0.0258330i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.95719e8 | + | 3.38995e8i | −0.230453 | + | 0.399157i | −0.957942 | − | 0.286963i | \(-0.907354\pi\) |
0.727488 | + | 0.686120i | \(0.240688\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.68464e8 | − | 8.11403e8i | −0.548122 | − | 0.949375i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 5.03861e8i | − | 0.585827i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.05418e8 | −1.04609 | −0.523047 | − | 0.852304i | \(-0.675205\pi\) | ||||
−0.523047 | + | 0.852304i | \(0.675205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.99244e8 | + | 2.88239e8i | −0.573196 | + | 0.330935i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.17087e8 | − | 1.83070e8i | −0.361778 | − | 0.208873i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.42033e8 | + | 1.23422e9i | −0.387803 | + | 1.39939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.25967e8 | + | 2.18180e8i | −0.141934 | + | 0.245836i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.68808e8 | − | 4.65589e8i | −0.300998 | − | 0.521343i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.20463e7i | − | 0.0134051i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.33523e9 | 1.47665 | 0.738323 | − | 0.674448i | \(-0.235618\pi\) | ||||
0.738323 | + | 0.674448i | \(0.235618\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.41422e8 | − | 4.28060e8i | 0.814881 | − | 0.470472i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.45806e8 | + | 3.15121e8i | 0.596184 | + | 0.344207i | 0.767539 | − | 0.641002i | \(-0.221481\pi\) |
−0.171355 | + | 0.985209i | \(0.554814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.51216e8 | − | 1.48655e8i | 0.164157 | − | 0.161376i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.43774e8 | − | 4.22229e8i | 0.263011 | − | 0.455549i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.04552e8 | + | 3.54294e8i | 0.219341 | + | 0.379910i | 0.954607 | − | 0.297869i | \(-0.0962760\pi\) |
−0.735266 | + | 0.677779i | \(0.762943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.81978e8i | − | 0.300516i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.86116e8 | −0.197141 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.95291e8 | + | 4.59161e8i | −0.837270 | + | 0.483398i | −0.856335 | − | 0.516420i | \(-0.827264\pi\) |
0.0190654 | + | 0.999818i | \(0.493931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.56198e8 | − | 9.01810e7i | −0.163443 | − | 0.0943640i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.21651e8 | − | 5.30638e8i | −0.542536 | − | 0.551883i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.64596e8 | + | 6.31499e8i | −0.376897 | + | 0.652805i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.59369e8 | − | 4.49241e8i | −0.266500 | − | 0.461592i | 0.701455 | − | 0.712713i | \(-0.252534\pi\) |
−0.967956 | + | 0.251122i | \(0.919201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.12283e8i | − | 0.318934i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.04623e8 | 0.410754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.12596e8 | − | 1.80477e8i | 0.315426 | − | 0.182111i | −0.333926 | − | 0.942599i | \(-0.608374\pi\) |
0.649352 | + | 0.760488i | \(0.275040\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.45747e7 | + | 4.30557e7i | 0.0747989 | + | 0.0431852i |
(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 | 336.7.bh.d.145.2 | 8 | ||
4.3 | odd | 2 | 21.7.f.a.19.2 | yes | 8 | ||
7.3 | odd | 6 | inner | 336.7.bh.d.241.2 | 8 | ||
12.11 | even | 2 | 63.7.m.d.19.3 | 8 | |||
28.3 | even | 6 | 21.7.f.a.10.2 | ✓ | 8 | ||
28.11 | odd | 6 | 147.7.f.d.31.2 | 8 | |||
28.19 | even | 6 | 147.7.d.b.97.6 | 8 | |||
28.23 | odd | 6 | 147.7.d.b.97.5 | 8 | |||
28.27 | even | 2 | 147.7.f.d.19.2 | 8 | |||
84.23 | even | 6 | 441.7.d.c.244.3 | 8 | |||
84.47 | odd | 6 | 441.7.d.c.244.4 | 8 | |||
84.59 | odd | 6 | 63.7.m.d.10.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.a.10.2 | ✓ | 8 | 28.3 | even | 6 | ||
21.7.f.a.19.2 | yes | 8 | 4.3 | odd | 2 | ||
63.7.m.d.10.3 | 8 | 84.59 | odd | 6 | |||
63.7.m.d.19.3 | 8 | 12.11 | even | 2 | |||
147.7.d.b.97.5 | 8 | 28.23 | odd | 6 | |||
147.7.d.b.97.6 | 8 | 28.19 | even | 6 | |||
147.7.f.d.19.2 | 8 | 28.27 | even | 2 | |||
147.7.f.d.31.2 | 8 | 28.11 | odd | 6 | |||
336.7.bh.d.145.2 | 8 | 1.1 | even | 1 | trivial | ||
336.7.bh.d.241.2 | 8 | 7.3 | odd | 6 | inner | ||
441.7.d.c.244.3 | 8 | 84.23 | even | 6 | |||
441.7.d.c.244.4 | 8 | 84.47 | odd | 6 |