Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,7,Mod(48,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.48");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.2726500974\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 48.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.48 |
Dual form | 49.7.b.a.48.2 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.0000 | −1.50000 | −0.750000 | − | 0.661438i | \(-0.769947\pi\) | ||||
−0.750000 | + | 0.661438i | \(0.769947\pi\) | |||||||
\(3\) | − 12.1244i | − 0.449050i | −0.974468 | − | 0.224525i | \(-0.927917\pi\) | ||||
0.974468 | − | 0.224525i | \(-0.0720831\pi\) | |||||||
\(4\) | 80.0000 | 1.25000 | ||||||||
\(5\) | − 181.865i | − 1.45492i | −0.686149 | − | 0.727461i | \(-0.740700\pi\) | ||||
0.686149 | − | 0.727461i | \(-0.259300\pi\) | |||||||
\(6\) | 145.492i | 0.673575i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −192.000 | −0.375000 | ||||||||
\(9\) | 582.000 | 0.798354 | ||||||||
\(10\) | 2182.38i | 2.18238i | ||||||||
\(11\) | 1479.00 | 1.11119 | 0.555597 | − | 0.831452i | \(-0.312490\pi\) | ||||
0.555597 | + | 0.831452i | \(0.312490\pi\) | |||||||
\(12\) | − 969.948i | − 0.561313i | ||||||||
\(13\) | − 484.974i | − 0.220744i | −0.993890 | − | 0.110372i | \(-0.964796\pi\) | ||||
0.993890 | − | 0.110372i | \(-0.0352042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2205.00 | −0.653333 | ||||||||
\(16\) | −2816.00 | −0.687500 | ||||||||
\(17\) | − 3018.96i | − 0.614485i | −0.951631 | − | 0.307242i | \(-0.900594\pi\) | ||||
0.951631 | − | 0.307242i | \(-0.0994063\pi\) | |||||||
\(18\) | −6984.00 | −1.19753 | ||||||||
\(19\) | − 6874.51i | − 1.00226i | −0.865372 | − | 0.501131i | \(-0.832918\pi\) | ||||
0.865372 | − | 0.501131i | \(-0.167082\pi\) | |||||||
\(20\) | − 14549.2i | − 1.81865i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17748.0 | −1.66679 | ||||||||
\(23\) | −5913.00 | −0.485987 | −0.242993 | − | 0.970028i | \(-0.578129\pi\) | ||||
−0.242993 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(24\) | 2327.88i | 0.168394i | ||||||||
\(25\) | −17450.0 | −1.11680 | ||||||||
\(26\) | 5819.69i | 0.331116i | ||||||||
\(27\) | − 15895.0i | − 0.807551i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3978.00 | 0.163106 | 0.0815532 | − | 0.996669i | \(-0.474012\pi\) | ||||
0.0815532 | + | 0.996669i | \(0.474012\pi\) | |||||||
\(30\) | 26460.0 | 0.980000 | ||||||||
\(31\) | − 12815.4i | − 0.430178i | −0.976594 | − | 0.215089i | \(-0.930996\pi\) | ||||
0.976594 | − | 0.215089i | \(-0.0690042\pi\) | |||||||
\(32\) | 46080.0 | 1.40625 | ||||||||
\(33\) | − 17931.9i | − 0.498982i | ||||||||
\(34\) | 36227.6i | 0.921727i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 46560.0 | 0.997942 | ||||||||
\(37\) | −61577.0 | −1.21566 | −0.607832 | − | 0.794066i | \(-0.707960\pi\) | ||||
−0.607832 | + | 0.794066i | \(0.707960\pi\) | |||||||
\(38\) | 82494.1i | 1.50339i | ||||||||
\(39\) | −5880.00 | −0.0991251 | ||||||||
\(40\) | 34918.1i | 0.545596i | ||||||||
\(41\) | 110574.i | 1.60436i | 0.597082 | + | 0.802180i | \(0.296327\pi\) | ||||
−0.597082 | + | 0.802180i | \(0.703673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17414.0 | −0.219025 | −0.109512 | − | 0.993985i | \(-0.534929\pi\) | ||||
−0.109512 | + | 0.993985i | \(0.534929\pi\) | |||||||
\(44\) | 118320. | 1.38899 | ||||||||
\(45\) | − 105846.i | − 1.16154i | ||||||||
\(46\) | 70956.0 | 0.728980 | ||||||||
\(47\) | 30662.5i | 0.295334i | 0.989037 | + | 0.147667i | \(0.0471764\pi\) | ||||
−0.989037 | + | 0.147667i | \(0.952824\pi\) | |||||||
\(48\) | 34142.2i | 0.308722i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 209400. | 1.67520 | ||||||||
\(51\) | −36603.0 | −0.275935 | ||||||||
\(52\) | − 38797.9i | − 0.275930i | ||||||||
\(53\) | −60513.0 | −0.406463 | −0.203232 | − | 0.979131i | \(-0.565144\pi\) | ||||
−0.203232 | + | 0.979131i | \(0.565144\pi\) | |||||||
\(54\) | 190740.i | 1.21133i | ||||||||
\(55\) | − 268979.i | − 1.61670i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −83349.0 | −0.450066 | ||||||||
\(58\) | −47736.0 | −0.244659 | ||||||||
\(59\) | − 215729.i | − 1.05039i | −0.850981 | − | 0.525196i | \(-0.823992\pi\) | ||||
0.850981 | − | 0.525196i | \(-0.176008\pi\) | |||||||
\(60\) | −176400. | −0.816667 | ||||||||
\(61\) | − 162745.i | − 0.716999i | −0.933530 | − | 0.358500i | \(-0.883288\pi\) | ||||
0.933530 | − | 0.358500i | \(-0.116712\pi\) | |||||||
\(62\) | 153785.i | 0.645268i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −372736. | −1.42188 | ||||||||
\(65\) | −88200.0 | −0.321165 | ||||||||
\(66\) | 215183.i | 0.748473i | ||||||||
\(67\) | −268777. | −0.893650 | −0.446825 | − | 0.894621i | \(-0.647445\pi\) | ||||
−0.446825 | + | 0.894621i | \(0.647445\pi\) | |||||||
\(68\) | − 241517.i | − 0.768106i | ||||||||
\(69\) | 71691.3i | 0.218232i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 101922. | 0.284769 | 0.142385 | − | 0.989811i | \(-0.454523\pi\) | ||||
0.142385 | + | 0.989811i | \(0.454523\pi\) | |||||||
\(72\) | −111744. | −0.299383 | ||||||||
\(73\) | 317646.i | 0.816535i | 0.912862 | + | 0.408267i | \(0.133867\pi\) | ||||
−0.912862 | + | 0.408267i | \(0.866133\pi\) | |||||||
\(74\) | 738924. | 1.82350 | ||||||||
\(75\) | 211570.i | 0.501499i | ||||||||
\(76\) | − 549961.i | − 1.25283i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 70560.0 | 0.148688 | ||||||||
\(79\) | 362231. | 0.734690 | 0.367345 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367345 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(80\) | 512133.i | 1.00026i | ||||||||
\(81\) | 231561. | 0.435723 | ||||||||
\(82\) | − 1.32689e6i | − 2.40654i | ||||||||
\(83\) | − 216783.i | − 0.379133i | −0.981868 | − | 0.189567i | \(-0.939292\pi\) | ||||
0.981868 | − | 0.189567i | \(-0.0607083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −549045. | −0.894028 | ||||||||
\(86\) | 208968. | 0.328537 | ||||||||
\(87\) | − 48230.7i | − 0.0732429i | ||||||||
\(88\) | −283968. | −0.416698 | ||||||||
\(89\) | 1.33456e6i | 1.89308i | 0.322583 | + | 0.946541i | \(0.395449\pi\) | ||||
−0.322583 | + | 0.946541i | \(0.604551\pi\) | |||||||
\(90\) | 1.27015e6i | 1.74231i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −473040. | −0.607483 | ||||||||
\(93\) | −155379. | −0.193172 | ||||||||
\(94\) | − 367950.i | − 0.443001i | ||||||||
\(95\) | −1.25024e6 | −1.45821 | ||||||||
\(96\) | − 558690.i | − 0.631477i | ||||||||
\(97\) | − 1.51409e6i | − 1.65896i | −0.558535 | − | 0.829481i | \(-0.688636\pi\) | ||||
0.558535 | − | 0.829481i | \(-0.311364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 860778. | 0.887127 | ||||||||
\(100\) | −1.39600e6 | −1.39600 | ||||||||
\(101\) | − 1.32467e6i | − 1.28571i | −0.765987 | − | 0.642856i | \(-0.777749\pi\) | ||||
0.765987 | − | 0.642856i | \(-0.222251\pi\) | |||||||
\(102\) | 439236. | 0.413902 | ||||||||
\(103\) | − 64004.5i | − 0.0585732i | −0.999571 | − | 0.0292866i | \(-0.990676\pi\) | ||||
0.999571 | − | 0.0292866i | \(-0.00932354\pi\) | |||||||
\(104\) | 93115.1i | 0.0827789i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 726156. | 0.609695 | ||||||||
\(107\) | 660543. | 0.539200 | 0.269600 | − | 0.962972i | \(-0.413109\pi\) | ||||
0.269600 | + | 0.962972i | \(0.413109\pi\) | |||||||
\(108\) | − 1.27160e6i | − 1.00944i | ||||||||
\(109\) | −73169.0 | −0.0564999 | −0.0282499 | − | 0.999601i | \(-0.508993\pi\) | ||||
−0.0282499 | + | 0.999601i | \(0.508993\pi\) | |||||||
\(110\) | 3.22775e6i | 2.42505i | ||||||||
\(111\) | 746581.i | 0.545894i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.60351e6 | 1.11131 | 0.555655 | − | 0.831413i | \(-0.312468\pi\) | ||||
0.555655 | + | 0.831413i | \(0.312468\pi\) | |||||||
\(114\) | 1.00019e6 | 0.675098 | ||||||||
\(115\) | 1.07537e6i | 0.707073i | ||||||||
\(116\) | 318240. | 0.203883 | ||||||||
\(117\) | − 282255.i | − 0.176232i | ||||||||
\(118\) | 2.58874e6i | 1.57559i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 423360. | 0.245000 | ||||||||
\(121\) | 415880. | 0.234753 | ||||||||
\(122\) | 1.95294e6i | 1.07550i | ||||||||
\(123\) | 1.34064e6 | 0.720438 | ||||||||
\(124\) | − 1.02524e6i | − 0.537723i | ||||||||
\(125\) | 331904.i | 0.169935i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.22997e6 | −1.57684 | −0.788418 | − | 0.615139i | \(-0.789100\pi\) | ||||
−0.788418 | + | 0.615139i | \(0.789100\pi\) | |||||||
\(128\) | 1.52371e6 | 0.726562 | ||||||||
\(129\) | 211134.i | 0.0983531i | ||||||||
\(130\) | 1.05840e6 | 0.481748 | ||||||||
\(131\) | − 1.99546e6i | − 0.887625i | −0.896120 | − | 0.443813i | \(-0.853626\pi\) | ||||
0.896120 | − | 0.443813i | \(-0.146374\pi\) | |||||||
\(132\) | − 1.43455e6i | − 0.623728i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.22532e6 | 1.34048 | ||||||||
\(135\) | −2.89076e6 | −1.17492 | ||||||||
\(136\) | 579641.i | 0.230432i | ||||||||
\(137\) | 1.42158e6 | 0.552854 | 0.276427 | − | 0.961035i | \(-0.410850\pi\) | ||||
0.276427 | + | 0.961035i | \(0.410850\pi\) | |||||||
\(138\) | − 860296.i | − 0.327349i | ||||||||
\(139\) | 2.43603e6i | 0.907063i | 0.891240 | + | 0.453531i | \(0.149836\pi\) | ||||
−0.891240 | + | 0.453531i | \(0.850164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 371763. | 0.132620 | ||||||||
\(142\) | −1.22306e6 | −0.427154 | ||||||||
\(143\) | − 717277.i | − 0.245289i | ||||||||
\(144\) | −1.63891e6 | −0.548868 | ||||||||
\(145\) | − 723460.i | − 0.237307i | ||||||||
\(146\) | − 3.81175e6i | − 1.22480i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.92616e6 | −1.51958 | ||||||||
\(149\) | 3.14375e6 | 0.950363 | 0.475181 | − | 0.879888i | \(-0.342382\pi\) | ||||
0.475181 | + | 0.879888i | \(0.342382\pi\) | |||||||
\(150\) | − 2.53884e6i | − 0.752249i | ||||||||
\(151\) | −2.28220e6 | −0.662862 | −0.331431 | − | 0.943479i | \(-0.607531\pi\) | ||||
−0.331431 | + | 0.943479i | \(0.607531\pi\) | |||||||
\(152\) | 1.31991e6i | 0.375848i | ||||||||
\(153\) | − 1.75704e6i | − 0.490576i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.33068e6 | −0.625876 | ||||||||
\(156\) | −470400. | −0.123906 | ||||||||
\(157\) | − 148511.i | − 0.0383761i | −0.999816 | − | 0.0191880i | \(-0.993892\pi\) | ||||
0.999816 | − | 0.0191880i | \(-0.00610811\pi\) | |||||||
\(158\) | −4.34677e6 | −1.10204 | ||||||||
\(159\) | 733681.i | 0.182522i | ||||||||
\(160\) | − 8.38035e6i | − 2.04599i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.77873e6 | −0.653584 | ||||||||
\(163\) | −7.09747e6 | −1.63886 | −0.819428 | − | 0.573182i | \(-0.805709\pi\) | ||||
−0.819428 | + | 0.573182i | \(0.805709\pi\) | |||||||
\(164\) | 8.84593e6i | 2.00545i | ||||||||
\(165\) | −3.26120e6 | −0.725980 | ||||||||
\(166\) | 2.60140e6i | 0.568700i | ||||||||
\(167\) | 645986.i | 0.138699i | 0.997592 | + | 0.0693495i | \(0.0220924\pi\) | ||||
−0.997592 | + | 0.0693495i | \(0.977908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.59161e6 | 0.951272 | ||||||||
\(170\) | 6.58854e6 | 1.34104 | ||||||||
\(171\) | − 4.00096e6i | − 0.800159i | ||||||||
\(172\) | −1.39312e6 | −0.273781 | ||||||||
\(173\) | − 3.13583e6i | − 0.605640i | −0.953048 | − | 0.302820i | \(-0.902072\pi\) | ||||
0.953048 | − | 0.302820i | \(-0.0979281\pi\) | |||||||
\(174\) | 578768.i | 0.109864i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.16486e6 | −0.763946 | ||||||||
\(177\) | −2.61557e6 | −0.471679 | ||||||||
\(178\) | − 1.60148e7i | − 2.83962i | ||||||||
\(179\) | 1.01628e7 | 1.77196 | 0.885980 | − | 0.463724i | \(-0.153487\pi\) | ||||
0.885980 | + | 0.463724i | \(0.153487\pi\) | |||||||
\(180\) | − 8.46765e6i | − 1.45193i | ||||||||
\(181\) | 8.72517e6i | 1.47143i | 0.677294 | + | 0.735713i | \(0.263153\pi\) | ||||
−0.677294 | + | 0.735713i | \(0.736847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.97318e6 | −0.321969 | ||||||||
\(184\) | 1.13530e6 | 0.182245 | ||||||||
\(185\) | 1.11987e7i | 1.76870i | ||||||||
\(186\) | 1.86455e6 | 0.289758 | ||||||||
\(187\) | − 4.46505e6i | − 0.682812i | ||||||||
\(188\) | 2.45300e6i | 0.369168i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.50028e7 | 2.18732 | ||||||||
\(191\) | 4.23844e6 | 0.608283 | 0.304142 | − | 0.952627i | \(-0.401630\pi\) | ||||
0.304142 | + | 0.952627i | \(0.401630\pi\) | |||||||
\(192\) | 4.51918e6i | 0.638493i | ||||||||
\(193\) | 6.14821e6 | 0.855217 | 0.427609 | − | 0.903964i | \(-0.359356\pi\) | ||||
0.427609 | + | 0.903964i | \(0.359356\pi\) | |||||||
\(194\) | 1.81691e7i | 2.48844i | ||||||||
\(195\) | 1.06937e6i | 0.144219i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 790554. | 0.103403 | 0.0517015 | − | 0.998663i | \(-0.483536\pi\) | ||||
0.0517015 | + | 0.998663i | \(0.483536\pi\) | |||||||
\(198\) | −1.03293e7 | −1.33069 | ||||||||
\(199\) | 8.12583e6i | 1.03112i | 0.856854 | + | 0.515559i | \(0.172416\pi\) | ||||
−0.856854 | + | 0.515559i | \(0.827584\pi\) | |||||||
\(200\) | 3.35040e6 | 0.418800 | ||||||||
\(201\) | 3.25875e6i | 0.401294i | ||||||||
\(202\) | 1.58960e7i | 1.92857i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.92824e6 | −0.344918 | ||||||||
\(205\) | 2.01096e7 | 2.33422 | ||||||||
\(206\) | 768054.i | 0.0878597i | ||||||||
\(207\) | −3.44137e6 | −0.387989 | ||||||||
\(208\) | 1.36569e6i | 0.151761i | ||||||||
\(209\) | − 1.01674e7i | − 1.11371i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16724e7 | 1.24254 | 0.621271 | − | 0.783595i | \(-0.286616\pi\) | ||||
0.621271 | + | 0.783595i | \(0.286616\pi\) | |||||||
\(212\) | −4.84104e6 | −0.508079 | ||||||||
\(213\) | − 1.23574e6i | − 0.127876i | ||||||||
\(214\) | −7.92652e6 | −0.808800 | ||||||||
\(215\) | 3.16700e6i | 0.318664i | ||||||||
\(216\) | 3.05185e6i | 0.302832i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 878028. | 0.0847498 | ||||||||
\(219\) | 3.85125e6 | 0.366665 | ||||||||
\(220\) | − 2.15183e7i | − 2.02088i | ||||||||
\(221\) | −1.46412e6 | −0.135644 | ||||||||
\(222\) | − 8.95898e6i | − 0.818841i | ||||||||
\(223\) | 2.89821e6i | 0.261345i | 0.991426 | + | 0.130673i | \(0.0417137\pi\) | ||||
−0.991426 | + | 0.130673i | \(0.958286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.01559e7 | −0.891602 | ||||||||
\(226\) | −1.92421e7 | −1.66697 | ||||||||
\(227\) | − 1.67710e7i | − 1.43378i | −0.697188 | − | 0.716888i | \(-0.745566\pi\) | ||||
0.697188 | − | 0.716888i | \(-0.254434\pi\) | |||||||
\(228\) | −6.66792e6 | −0.562582 | ||||||||
\(229\) | 1.74779e7i | 1.45540i | 0.685895 | + | 0.727701i | \(0.259411\pi\) | ||||
−0.685895 | + | 0.727701i | \(0.740589\pi\) | |||||||
\(230\) | − 1.29044e7i | − 1.06061i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −763776. | −0.0611649 | ||||||||
\(233\) | −1.02044e7 | −0.806711 | −0.403355 | − | 0.915043i | \(-0.632156\pi\) | ||||
−0.403355 | + | 0.915043i | \(0.632156\pi\) | |||||||
\(234\) | 3.38706e6i | 0.264348i | ||||||||
\(235\) | 5.57644e6 | 0.429689 | ||||||||
\(236\) | − 1.72583e7i | − 1.31299i | ||||||||
\(237\) | − 4.39182e6i | − 0.329913i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.43114e6 | 0.104831 | 0.0524153 | − | 0.998625i | \(-0.483308\pi\) | ||||
0.0524153 | + | 0.998625i | \(0.483308\pi\) | |||||||
\(240\) | 6.20928e6 | 0.449167 | ||||||||
\(241\) | 1.55039e7i | 1.10762i | 0.832643 | + | 0.553810i | \(0.186827\pi\) | ||||
−0.832643 | + | 0.553810i | \(0.813173\pi\) | |||||||
\(242\) | −4.99056e6 | −0.352130 | ||||||||
\(243\) | − 1.43950e7i | − 1.00321i | ||||||||
\(244\) | − 1.30196e7i | − 0.896249i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.60877e7 | −1.08066 | ||||||||
\(247\) | −3.33396e6 | −0.221243 | ||||||||
\(248\) | 2.46057e6i | 0.161317i | ||||||||
\(249\) | −2.62836e6 | −0.170250 | ||||||||
\(250\) | − 3.98285e6i | − 0.254902i | ||||||||
\(251\) | − 3.44089e6i | − 0.217595i | −0.994064 | − | 0.108798i | \(-0.965300\pi\) | ||||
0.994064 | − | 0.108798i | \(-0.0347001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.74533e6 | −0.540026 | ||||||||
\(254\) | 3.87596e7 | 2.36526 | ||||||||
\(255\) | 6.65682e6i | 0.401464i | ||||||||
\(256\) | 5.57056e6 | 0.332031 | ||||||||
\(257\) | 2.32527e7i | 1.36985i | 0.728613 | + | 0.684926i | \(0.240166\pi\) | ||||
−0.728613 | + | 0.684926i | \(0.759834\pi\) | |||||||
\(258\) | − 2.53360e6i | − 0.147530i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.05600e6 | −0.401457 | ||||||||
\(261\) | 2.31520e6 | 0.130217 | ||||||||
\(262\) | 2.39456e7i | 1.33144i | ||||||||
\(263\) | −2.82618e7 | −1.55358 | −0.776789 | − | 0.629761i | \(-0.783153\pi\) | ||||
−0.776789 | + | 0.629761i | \(0.783153\pi\) | |||||||
\(264\) | 3.44293e6i | 0.187118i | ||||||||
\(265\) | 1.10052e7i | 0.591372i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.61807e7 | 0.850089 | ||||||||
\(268\) | −2.15022e7 | −1.11706 | ||||||||
\(269\) | 1.58102e7i | 0.812235i | 0.913821 | + | 0.406118i | \(0.133118\pi\) | ||||
−0.913821 | + | 0.406118i | \(0.866882\pi\) | |||||||
\(270\) | 3.46891e7 | 1.76239 | ||||||||
\(271\) | − 3.65028e7i | − 1.83408i | −0.398793 | − | 0.917041i | \(-0.630571\pi\) | ||||
0.398793 | − | 0.917041i | \(-0.369429\pi\) | |||||||
\(272\) | 8.50140e6i | 0.422458i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.70590e7 | −0.829281 | ||||||||
\(275\) | −2.58086e7 | −1.24098 | ||||||||
\(276\) | 5.73531e6i | 0.272791i | ||||||||
\(277\) | 3.14807e7 | 1.48117 | 0.740585 | − | 0.671962i | \(-0.234548\pi\) | ||||
0.740585 | + | 0.671962i | \(0.234548\pi\) | |||||||
\(278\) | − 2.92323e7i | − 1.36059i | ||||||||
\(279\) | − 7.45859e6i | − 0.343435i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.62368e6 | 0.298525 | 0.149262 | − | 0.988798i | \(-0.452310\pi\) | ||||
0.149262 | + | 0.988798i | \(0.452310\pi\) | |||||||
\(282\) | −4.46116e6 | −0.198930 | ||||||||
\(283\) | − 4.02480e7i | − 1.77576i | −0.460071 | − | 0.887882i | \(-0.652176\pi\) | ||||
0.460071 | − | 0.887882i | \(-0.347824\pi\) | |||||||
\(284\) | 8.15376e6 | 0.355961 | ||||||||
\(285\) | 1.51583e7i | 0.654811i | ||||||||
\(286\) | 8.60732e6i | 0.367934i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.68186e7 | 1.12269 | ||||||||
\(289\) | 1.50234e7 | 0.622408 | ||||||||
\(290\) | 8.68152e6i | 0.355961i | ||||||||
\(291\) | −1.83574e7 | −0.744957 | ||||||||
\(292\) | 2.54117e7i | 1.02067i | ||||||||
\(293\) | − 1.26797e7i | − 0.504086i | −0.967716 | − | 0.252043i | \(-0.918898\pi\) | ||||
0.967716 | − | 0.252043i | \(-0.0811024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.92336e7 | −1.52824 | ||||||||
\(296\) | 1.18228e7 | 0.455874 | ||||||||
\(297\) | − 2.35087e7i | − 0.897347i | ||||||||
\(298\) | −3.77250e7 | −1.42554 | ||||||||
\(299\) | 2.86765e6i | 0.107279i | ||||||||
\(300\) | 1.69256e7i | 0.626874i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.73864e7 | 0.994293 | ||||||||
\(303\) | −1.60608e7 | −0.577349 | ||||||||
\(304\) | 1.93586e7i | 0.689055i | ||||||||
\(305\) | −2.95977e7 | −1.04318 | ||||||||
\(306\) | 2.10844e7i | 0.735865i | ||||||||
\(307\) | − 1.77258e6i | − 0.0612620i | −0.999531 | − | 0.0306310i | \(-0.990248\pi\) | ||||
0.999531 | − | 0.0306310i | \(-0.00975167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −776013. | −0.0263023 | ||||||||
\(310\) | 2.79682e7 | 0.938814 | ||||||||
\(311\) | − 3.65265e7i | − 1.21430i | −0.794586 | − | 0.607152i | \(-0.792312\pi\) | ||||
0.794586 | − | 0.607152i | \(-0.207688\pi\) | |||||||
\(312\) | 1.12896e6 | 0.0371719 | ||||||||
\(313\) | − 1.16049e7i | − 0.378451i | −0.981934 | − | 0.189226i | \(-0.939402\pi\) | ||||
0.981934 | − | 0.189226i | \(-0.0605977\pi\) | |||||||
\(314\) | 1.78213e6i | 0.0575641i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.89785e7 | 0.918363 | ||||||||
\(317\) | 2.11641e7 | 0.664388 | 0.332194 | − | 0.943211i | \(-0.392211\pi\) | ||||
0.332194 | + | 0.943211i | \(0.392211\pi\) | |||||||
\(318\) | − 8.80417e6i | − 0.273783i | ||||||||
\(319\) | 5.88346e6 | 0.181243 | ||||||||
\(320\) | 6.77878e7i | 2.06872i | ||||||||
\(321\) | − 8.00866e6i | − 0.242128i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.07539e7 | −0.615874 | ||||||||
\(324\) | 1.85249e7 | 0.544654 | ||||||||
\(325\) | 8.46280e6i | 0.246527i | ||||||||
\(326\) | 8.51697e7 | 2.45828 | ||||||||
\(327\) | 887127.i | 0.0253713i | ||||||||
\(328\) | − 2.12302e7i | − 0.601635i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.91343e7 | 1.08897 | ||||||||
\(331\) | −5.92199e7 | −1.63299 | −0.816496 | − | 0.577352i | \(-0.804086\pi\) | ||||
−0.816496 | + | 0.577352i | \(0.804086\pi\) | |||||||
\(332\) | − 1.73427e7i | − 0.473917i | ||||||||
\(333\) | −3.58378e7 | −0.970530 | ||||||||
\(334\) | − 7.75183e6i | − 0.208049i | ||||||||
\(335\) | 4.88812e7i | 1.30019i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.67798e7 | 0.960992 | 0.480496 | − | 0.876997i | \(-0.340457\pi\) | ||||
0.480496 | + | 0.876997i | \(0.340457\pi\) | |||||||
\(338\) | −5.50993e7 | −1.42691 | ||||||||
\(339\) | − 1.94415e7i | − 0.499034i | ||||||||
\(340\) | −4.39236e7 | −1.11754 | ||||||||
\(341\) | − 1.89540e7i | − 0.478012i | ||||||||
\(342\) | 4.80116e7i | 1.20024i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.34349e6 | 0.0821343 | ||||||||
\(345\) | 1.30382e7 | 0.317511 | ||||||||
\(346\) | 3.76300e7i | 0.908460i | ||||||||
\(347\) | 3.39775e7 | 0.813210 | 0.406605 | − | 0.913604i | \(-0.366713\pi\) | ||||
0.406605 | + | 0.913604i | \(0.366713\pi\) | |||||||
\(348\) | − 3.85845e6i | − 0.0915537i | ||||||||
\(349\) | − 5.48045e7i | − 1.28926i | −0.764495 | − | 0.644629i | \(-0.777012\pi\) | ||||
0.764495 | − | 0.644629i | \(-0.222988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.70868e6 | −0.178262 | ||||||||
\(352\) | 6.81523e7 | 1.56262 | ||||||||
\(353\) | − 4.76003e6i | − 0.108215i | −0.998535 | − | 0.0541073i | \(-0.982769\pi\) | ||||
0.998535 | − | 0.0541073i | \(-0.0172313\pi\) | |||||||
\(354\) | 3.13869e7 | 0.707519 | ||||||||
\(355\) | − 1.85361e7i | − 0.414317i | ||||||||
\(356\) | 1.06765e8i | 2.36635i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.21953e8 | −2.65794 | ||||||||
\(359\) | −5.31169e6 | −0.114802 | −0.0574010 | − | 0.998351i | \(-0.518281\pi\) | ||||
−0.0574010 | + | 0.998351i | \(0.518281\pi\) | |||||||
\(360\) | 2.03224e7i | 0.435579i | ||||||||
\(361\) | −213002. | −0.00452754 | ||||||||
\(362\) | − 1.04702e8i | − 2.20714i | ||||||||
\(363\) | − 5.04228e6i | − 0.105416i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.77688e7 | 1.18800 | ||||||||
\(366\) | 2.36782e7 | 0.482953 | ||||||||
\(367\) | 7.98359e7i | 1.61510i | 0.589798 | + | 0.807551i | \(0.299207\pi\) | ||||
−0.589798 | + | 0.807551i | \(0.700793\pi\) | |||||||
\(368\) | 1.66510e7 | 0.334116 | ||||||||
\(369\) | 6.43541e7i | 1.28085i | ||||||||
\(370\) | − 1.34385e8i | − 2.65304i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.24303e7 | −0.241465 | ||||||||
\(373\) | 4.22601e7 | 0.814336 | 0.407168 | − | 0.913353i | \(-0.366516\pi\) | ||||
0.407168 | + | 0.913353i | \(0.366516\pi\) | |||||||
\(374\) | 5.35806e7i | 1.02422i | ||||||||
\(375\) | 4.02413e6 | 0.0763093 | ||||||||
\(376\) | − 5.88720e6i | − 0.110750i | ||||||||
\(377\) | − 1.92923e6i | − 0.0360047i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.28840e7 | 0.236664 | 0.118332 | − | 0.992974i | \(-0.462245\pi\) | ||||
0.118332 | + | 0.992974i | \(0.462245\pi\) | |||||||
\(380\) | −1.00019e8 | −1.82277 | ||||||||
\(381\) | 3.91613e7i | 0.708079i | ||||||||
\(382\) | −5.08613e7 | −0.912425 | ||||||||
\(383\) | 2.67570e7i | 0.476257i | 0.971234 | + | 0.238128i | \(0.0765339\pi\) | ||||
−0.971234 | + | 0.238128i | \(0.923466\pi\) | |||||||
\(384\) | − 1.84740e7i | − 0.326263i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.37785e7 | −1.28283 | ||||||||
\(387\) | −1.01349e7 | −0.174859 | ||||||||
\(388\) | − 1.21127e8i | − 2.07370i | ||||||||
\(389\) | −1.07557e7 | −0.182722 | −0.0913610 | − | 0.995818i | \(-0.529122\pi\) | ||||
−0.0913610 | + | 0.995818i | \(0.529122\pi\) | |||||||
\(390\) | − 1.28324e7i | − 0.216329i | ||||||||
\(391\) | 1.78511e7i | 0.298632i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.41937e7 | −0.398588 | ||||||||
\(394\) | −9.48665e6 | −0.155104 | ||||||||
\(395\) | − 6.58773e7i | − 1.06892i | ||||||||
\(396\) | 6.88622e7 | 1.10891 | ||||||||
\(397\) | − 9.52333e6i | − 0.152201i | −0.997100 | − | 0.0761005i | \(-0.975753\pi\) | ||||
0.997100 | − | 0.0761005i | \(-0.0242470\pi\) | |||||||
\(398\) | − 9.75099e7i | − 1.54668i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.91392e7 | 0.767800 | ||||||||
\(401\) | 7.67884e7 | 1.19086 | 0.595432 | − | 0.803405i | \(-0.296981\pi\) | ||||
0.595432 | + | 0.803405i | \(0.296981\pi\) | |||||||
\(402\) | − 3.91050e7i | − 0.601941i | ||||||||
\(403\) | −6.21516e6 | −0.0949592 | ||||||||
\(404\) | − 1.05974e8i | − 1.60714i | ||||||||
\(405\) | − 4.21129e7i | − 0.633943i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.10724e7 | −1.35084 | ||||||||
\(408\) | 7.02778e6 | 0.103475 | ||||||||
\(409\) | 3.00588e7i | 0.439341i | 0.975574 | + | 0.219670i | \(0.0704982\pi\) | ||||
−0.975574 | + | 0.219670i | \(0.929502\pi\) | |||||||
\(410\) | −2.41315e8 | −3.50133 | ||||||||
\(411\) | − 1.72358e7i | − 0.248259i | ||||||||
\(412\) | − 5.12036e6i | − 0.0732165i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.12964e7 | 0.581984 | ||||||||
\(415\) | −3.94254e7 | −0.551610 | ||||||||
\(416\) | − 2.23476e7i | − 0.310421i | ||||||||
\(417\) | 2.95352e7 | 0.407317 | ||||||||
\(418\) | 1.22009e8i | 1.67056i | ||||||||
\(419\) | 4.76385e7i | 0.647614i | 0.946123 | + | 0.323807i | \(0.104963\pi\) | ||||
−0.946123 | + | 0.323807i | \(0.895037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79191e7 | −0.374158 | −0.187079 | − | 0.982345i | \(-0.559902\pi\) | ||||
−0.187079 | + | 0.982345i | \(0.559902\pi\) | |||||||
\(422\) | −1.40068e8 | −1.86381 | ||||||||
\(423\) | 1.78456e7i | 0.235781i | ||||||||
\(424\) | 1.16185e7 | 0.152424 | ||||||||
\(425\) | 5.26809e7i | 0.686257i | ||||||||
\(426\) | 1.48289e7i | 0.191813i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.28434e7 | 0.674000 | ||||||||
\(429\) | −8.69652e6 | −0.110147 | ||||||||
\(430\) | − 3.80040e7i | − 0.477996i | ||||||||
\(431\) | 3.31444e6 | 0.0413979 | 0.0206989 | − | 0.999786i | \(-0.493411\pi\) | ||||
0.0206989 | + | 0.999786i | \(0.493411\pi\) | |||||||
\(432\) | 4.47604e7i | 0.555191i | ||||||||
\(433\) | 4.59746e7i | 0.566310i | 0.959074 | + | 0.283155i | \(0.0913811\pi\) | ||||
−0.959074 | + | 0.283155i | \(0.908619\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.77149e6 | −0.106563 | ||||||||
\(436\) | −5.85352e6 | −0.0706249 | ||||||||
\(437\) | 4.06490e7i | 0.487086i | ||||||||
\(438\) | −4.62150e7 | −0.549998 | ||||||||
\(439\) | − 5.44399e7i | − 0.643463i | −0.946831 | − | 0.321732i | \(-0.895735\pi\) | ||||
0.946831 | − | 0.321732i | \(-0.104265\pi\) | |||||||
\(440\) | 5.16439e7i | 0.606263i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.75694e7 | 0.203466 | ||||||||
\(443\) | 1.05887e8 | 1.21796 | 0.608978 | − | 0.793187i | \(-0.291580\pi\) | ||||
0.608978 | + | 0.793187i | \(0.291580\pi\) | |||||||
\(444\) | 5.97265e7i | 0.682367i | ||||||||
\(445\) | 2.42711e8 | 2.75429 | ||||||||
\(446\) | − 3.47785e7i | − 0.392018i | ||||||||
\(447\) | − 3.81160e7i | − 0.426761i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.14053e8 | 1.26000 | 0.629998 | − | 0.776597i | \(-0.283056\pi\) | ||||
0.629998 | + | 0.776597i | \(0.283056\pi\) | |||||||
\(450\) | 1.21871e8 | 1.33740 | ||||||||
\(451\) | 1.63539e8i | 1.78276i | ||||||||
\(452\) | 1.28280e8 | 1.38914 | ||||||||
\(453\) | 2.76702e7i | 0.297658i | ||||||||
\(454\) | 2.01252e8i | 2.15066i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.60030e7 | 0.168775 | ||||||||
\(457\) | 9.84729e7 | 1.03174 | 0.515868 | − | 0.856668i | \(-0.327470\pi\) | ||||
0.515868 | + | 0.856668i | \(0.327470\pi\) | |||||||
\(458\) | − 2.09735e8i | − 2.18310i | ||||||||
\(459\) | −4.79865e7 | −0.496228 | ||||||||
\(460\) | 8.60296e7i | 0.883841i | ||||||||
\(461\) | 3.58333e7i | 0.365750i | 0.983136 | + | 0.182875i | \(0.0585403\pi\) | ||||
−0.983136 | + | 0.182875i | \(0.941460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.81000e8 | 1.82362 | 0.911810 | − | 0.410612i | \(-0.134685\pi\) | ||||
0.911810 | + | 0.410612i | \(0.134685\pi\) | |||||||
\(464\) | −1.12020e7 | −0.112136 | ||||||||
\(465\) | 2.82581e7i | 0.281050i | ||||||||
\(466\) | 1.22452e8 | 1.21007 | ||||||||
\(467\) | − 8.48539e7i | − 0.833146i | −0.909102 | − | 0.416573i | \(-0.863231\pi\) | ||||
0.909102 | − | 0.416573i | \(-0.136769\pi\) | |||||||
\(468\) | − 2.25804e7i | − 0.220290i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.69173e7 | −0.644533 | ||||||||
\(471\) | −1.80060e6 | −0.0172328 | ||||||||
\(472\) | 4.14199e7i | 0.393897i | ||||||||
\(473\) | −2.57553e7 | −0.243379 | ||||||||
\(474\) | 5.27018e7i | 0.494869i | ||||||||
\(475\) | 1.19960e8i | 1.11933i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.52186e7 | −0.324501 | ||||||||
\(478\) | −1.71737e7 | −0.157246 | ||||||||
\(479\) | − 1.59224e8i | − 1.44878i | −0.689390 | − | 0.724390i | \(-0.742121\pi\) | ||||
0.689390 | − | 0.724390i | \(-0.257879\pi\) | |||||||
\(480\) | −1.01606e8 | −0.918750 | ||||||||
\(481\) | 2.98633e7i | 0.268350i | ||||||||
\(482\) | − 1.86047e8i | − 1.66143i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.32704e7 | 0.293442 | ||||||||
\(485\) | −2.75360e8 | −2.41366 | ||||||||
\(486\) | 1.72740e8i | 1.50482i | ||||||||
\(487\) | −8.06142e7 | −0.697951 | −0.348975 | − | 0.937132i | \(-0.613470\pi\) | ||||
−0.348975 | + | 0.937132i | \(0.613470\pi\) | |||||||
\(488\) | 3.12471e7i | 0.268875i | ||||||||
\(489\) | 8.60523e7i | 0.735929i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.46544e7 | −0.123800 | −0.0619002 | − | 0.998082i | \(-0.519716\pi\) | ||||
−0.0619002 | + | 0.998082i | \(0.519716\pi\) | |||||||
\(492\) | 1.07251e8 | 0.900548 | ||||||||
\(493\) | − 1.20094e7i | − 0.100226i | ||||||||
\(494\) | 4.00075e7 | 0.331864 | ||||||||
\(495\) | − 1.56546e8i | − 1.29070i | ||||||||
\(496\) | 3.60883e7i | 0.295748i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.15403e7 | 0.255375 | ||||||||
\(499\) | −3.12556e7 | −0.251551 | −0.125776 | − | 0.992059i | \(-0.540142\pi\) | ||||
−0.125776 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(500\) | 2.65523e7i | 0.212419i | ||||||||
\(501\) | 7.83216e6 | 0.0622828 | ||||||||
\(502\) | 4.12907e7i | 0.326393i | ||||||||
\(503\) | − 1.42620e8i | − 1.12067i | −0.828267 | − | 0.560334i | \(-0.810673\pi\) | ||||
0.828267 | − | 0.560334i | \(-0.189327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.40912e8 | −1.87061 | ||||||||
\(506\) | 1.04944e8 | 0.810039 | ||||||||
\(507\) | − 5.56703e7i | − 0.427169i | ||||||||
\(508\) | −2.58397e8 | −1.97105 | ||||||||
\(509\) | 1.04526e7i | 0.0792628i | 0.999214 | + | 0.0396314i | \(0.0126184\pi\) | ||||
−0.999214 | + | 0.0396314i | \(0.987382\pi\) | |||||||
\(510\) | − 7.98818e7i | − 0.602195i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.64364e8 | −1.22461 | ||||||||
\(513\) | −1.09271e8 | −0.809377 | ||||||||
\(514\) | − 2.79032e8i | − 2.05478i | ||||||||
\(515\) | −1.16402e7 | −0.0852194 | ||||||||
\(516\) | 1.68907e7i | 0.122941i | ||||||||
\(517\) | 4.53498e7i | 0.328174i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.80199e7 | −0.271963 | ||||||||
\(520\) | 1.69344e7 | 0.120437 | ||||||||
\(521\) | 2.72001e6i | 0.0192335i | 0.999954 | + | 0.00961674i | \(0.00306115\pi\) | ||||
−0.999954 | + | 0.00961674i | \(0.996939\pi\) | |||||||
\(522\) | −2.77824e7 | −0.195325 | ||||||||
\(523\) | 2.29072e8i | 1.60128i | 0.599145 | + | 0.800640i | \(0.295507\pi\) | ||||
−0.599145 | + | 0.800640i | \(0.704493\pi\) | |||||||
\(524\) | − 1.59637e8i | − 1.10953i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.39142e8 | 2.33037 | ||||||||
\(527\) | −3.86894e7 | −0.264338 | ||||||||
\(528\) | 5.04963e7i | 0.343050i | ||||||||
\(529\) | −1.13072e8 | −0.763817 | ||||||||
\(530\) | − 1.32063e8i | − 0.887058i | ||||||||
\(531\) | − 1.25554e8i | − 0.838585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.36256e7 | 0.354153 | ||||||||
\(534\) | −1.94169e8 | −1.27513 | ||||||||
\(535\) | − 1.20130e8i | − 0.784494i | ||||||||
\(536\) | 5.16052e7 | 0.335119 | ||||||||
\(537\) | − 1.23217e8i | − 0.795699i | ||||||||
\(538\) | − 1.89723e8i | − 1.21835i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.31260e8 | −1.46866 | ||||||||
\(541\) | 2.29389e8 | 1.44871 | 0.724355 | − | 0.689428i | \(-0.242138\pi\) | ||||
0.724355 | + | 0.689428i | \(0.242138\pi\) | |||||||
\(542\) | 4.38034e8i | 2.75112i | ||||||||
\(543\) | 1.05787e8 | 0.660744 | ||||||||
\(544\) | − 1.39114e8i | − 0.864119i | ||||||||
\(545\) | 1.33069e7i | 0.0822030i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.87986e7 | 0.481456 | 0.240728 | − | 0.970593i | \(-0.422614\pi\) | ||||
0.240728 | + | 0.970593i | \(0.422614\pi\) | |||||||
\(548\) | 1.13727e8 | 0.691068 | ||||||||
\(549\) | − 9.47177e7i | − 0.572419i | ||||||||
\(550\) | 3.09703e8 | 1.86147 | ||||||||
\(551\) | − 2.73468e7i | − 0.163475i | ||||||||
\(552\) | − 1.37647e7i | − 0.0818372i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.77768e8 | −2.22176 | ||||||||
\(555\) | 1.35777e8 | 0.794233 | ||||||||
\(556\) | 1.94882e8i | 1.13383i | ||||||||
\(557\) | −1.07355e8 | −0.621236 | −0.310618 | − | 0.950535i | \(-0.600536\pi\) | ||||
−0.310618 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(558\) | 8.95031e7i | 0.515152i | ||||||||
\(559\) | 8.44534e6i | 0.0483484i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.41358e7 | −0.306617 | ||||||||
\(562\) | −7.94842e7 | −0.447787 | ||||||||
\(563\) | 2.29315e8i | 1.28501i | 0.766280 | + | 0.642507i | \(0.222106\pi\) | ||||
−0.766280 | + | 0.642507i | \(0.777894\pi\) | |||||||
\(564\) | 2.97410e7 | 0.165775 | ||||||||
\(565\) | − 2.91622e8i | − 1.61687i | ||||||||
\(566\) | 4.82976e8i | 2.66365i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.95690e7 | −0.106788 | ||||||||
\(569\) | −1.47105e8 | −0.798526 | −0.399263 | − | 0.916836i | \(-0.630734\pi\) | ||||
−0.399263 | + | 0.916836i | \(0.630734\pi\) | |||||||
\(570\) | − 1.81900e8i | − 0.982216i | ||||||||
\(571\) | 2.75556e6 | 0.0148014 | 0.00740068 | − | 0.999973i | \(-0.497644\pi\) | ||||
0.00740068 | + | 0.999973i | \(0.497644\pi\) | |||||||
\(572\) | − 5.73822e7i | − 0.306612i | ||||||||
\(573\) | − 5.13883e7i | − 0.273150i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03182e8 | 0.542750 | ||||||||
\(576\) | −2.16932e8 | −1.13516 | ||||||||
\(577\) | − 3.19900e6i | − 0.0166528i | −0.999965 | − | 0.00832639i | \(-0.997350\pi\) | ||||
0.999965 | − | 0.00832639i | \(-0.00265040\pi\) | |||||||
\(578\) | −1.80281e8 | −0.933612 | ||||||||
\(579\) | − 7.45430e7i | − 0.384036i | ||||||||
\(580\) | − 5.78768e7i | − 0.296634i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.20288e8 | 1.11744 | ||||||||
\(583\) | −8.94987e7 | −0.451660 | ||||||||
\(584\) | − 6.09880e7i | − 0.306201i | ||||||||
\(585\) | −5.13324e7 | −0.256404 | ||||||||
\(586\) | 1.52156e8i | 0.756129i | ||||||||
\(587\) | 2.39854e8i | 1.18586i | 0.805254 | + | 0.592929i | \(0.202029\pi\) | ||||
−0.805254 | + | 0.592929i | \(0.797971\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.80999e7 | −0.431151 | ||||||||
\(590\) | 4.70803e8 | 2.29236 | ||||||||
\(591\) | − 9.58496e6i | − 0.0464331i | ||||||||
\(592\) | 1.73401e8 | 0.835769 | ||||||||
\(593\) | 1.89913e8i | 0.910734i | 0.890304 | + | 0.455367i | \(0.150492\pi\) | ||||
−0.890304 | + | 0.455367i | \(0.849508\pi\) | |||||||
\(594\) | 2.82105e8i | 1.34602i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.51500e8 | 1.18795 | ||||||||
\(597\) | 9.85204e7 | 0.463024 | ||||||||
\(598\) | − 3.44118e7i | − 0.160918i | ||||||||
\(599\) | 3.85151e8 | 1.79205 | 0.896025 | − | 0.444004i | \(-0.146442\pi\) | ||||
0.896025 | + | 0.444004i | \(0.146442\pi\) | |||||||
\(600\) | − 4.06214e7i | − 0.188062i | ||||||||
\(601\) | − 2.97376e8i | − 1.36988i | −0.728598 | − | 0.684941i | \(-0.759828\pi\) | ||||
0.728598 | − | 0.684941i | \(-0.240172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.56428e8 | −0.713449 | ||||||||
\(604\) | −1.82576e8 | −0.828577 | ||||||||
\(605\) | − 7.56342e7i | − 0.341548i | ||||||||
\(606\) | 1.92729e8 | 0.866024 | ||||||||
\(607\) | 2.95316e8i | 1.32045i | 0.751069 | + | 0.660223i | \(0.229538\pi\) | ||||
−0.751069 | + | 0.660223i | \(0.770462\pi\) | |||||||
\(608\) | − 3.16777e8i | − 1.40943i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.55173e8 | 1.56477 | ||||||||
\(611\) | 1.48705e7 | 0.0651932 | ||||||||
\(612\) | − 1.40563e8i | − 0.613221i | ||||||||
\(613\) | −3.37212e8 | −1.46394 | −0.731968 | − | 0.681339i | \(-0.761398\pi\) | ||||
−0.731968 | + | 0.681339i | \(0.761398\pi\) | |||||||
\(614\) | 2.12710e7i | 0.0918929i | ||||||||
\(615\) | − 2.43816e8i | − 1.04818i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.68150e8 | 1.56736 | 0.783682 | − | 0.621163i | \(-0.213339\pi\) | ||||
0.783682 | + | 0.621163i | \(0.213339\pi\) | |||||||
\(618\) | 9.31216e6 | 0.0394534 | ||||||||
\(619\) | − 3.10795e7i | − 0.131039i | −0.997851 | − | 0.0655197i | \(-0.979129\pi\) | ||||
0.997851 | − | 0.0655197i | \(-0.0208705\pi\) | |||||||
\(620\) | −1.86455e8 | −0.782345 | ||||||||
\(621\) | 9.39873e7i | 0.392459i | ||||||||
\(622\) | 4.38318e8i | 1.82146i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.65581e7 | 0.0681485 | ||||||||
\(625\) | −2.12294e8 | −0.869558 | ||||||||
\(626\) | 1.39259e8i | 0.567677i | ||||||||
\(627\) | −1.23273e8 | −0.500110 | ||||||||
\(628\) | − 1.18809e7i | − 0.0479701i | ||||||||
\(629\) | 1.85899e8i | 0.747007i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.25406e8 | −1.29520 | −0.647601 | − | 0.761980i | \(-0.724228\pi\) | ||||
−0.647601 | + | 0.761980i | \(0.724228\pi\) | |||||||
\(632\) | −6.95484e7 | −0.275509 | ||||||||
\(633\) | − 1.41520e8i | − 0.557964i | ||||||||
\(634\) | −2.53969e8 | −0.996583 | ||||||||
\(635\) | 5.87419e8i | 2.29418i | ||||||||
\(636\) | 5.86945e7i | 0.228153i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.06015e7 | −0.271864 | ||||||||
\(639\) | 5.93186e7 | 0.227347 | ||||||||
\(640\) | − 2.77110e8i | − 1.05709i | ||||||||
\(641\) | −5.55637e7 | −0.210968 | −0.105484 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105484 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(642\) | 9.61039e7i | 0.363192i | ||||||||
\(643\) | − 9.33357e7i | − 0.351087i | −0.984472 | − | 0.175544i | \(-0.943832\pi\) | ||||
0.984472 | − | 0.175544i | \(-0.0561683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.83979e7 | 0.143096 | ||||||||
\(646\) | 2.49047e8 | 0.923812 | ||||||||
\(647\) | − 1.93195e8i | − 0.713317i | −0.934235 | − | 0.356659i | \(-0.883916\pi\) | ||||
0.934235 | − | 0.356659i | \(-0.116084\pi\) | |||||||
\(648\) | −4.44597e7 | −0.163396 | ||||||||
\(649\) | − 3.19063e8i | − 1.16719i | ||||||||
\(650\) | − 1.01554e8i | − 0.369790i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.67798e8 | −2.04857 | ||||||||
\(653\) | 3.62447e8 | 1.30168 | 0.650842 | − | 0.759213i | \(-0.274416\pi\) | ||||
0.650842 | + | 0.759213i | \(0.274416\pi\) | |||||||
\(654\) | − 1.06455e7i | − 0.0380569i | ||||||||
\(655\) | −3.62906e8 | −1.29143 | ||||||||
\(656\) | − 3.11377e8i | − 1.10300i | ||||||||
\(657\) | 1.84870e8i | 0.651884i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.39985e8 | 0.838549 | 0.419274 | − | 0.907860i | \(-0.362285\pi\) | ||||
0.419274 | + | 0.907860i | \(0.362285\pi\) | |||||||
\(660\) | −2.60896e8 | −0.907476 | ||||||||
\(661\) | − 1.93221e7i | − 0.0669035i | −0.999440 | − | 0.0334518i | \(-0.989350\pi\) | ||||
0.999440 | − | 0.0334518i | \(-0.0106500\pi\) | |||||||
\(662\) | 7.10639e8 | 2.44949 | ||||||||
\(663\) | 1.77515e7i | 0.0609109i | ||||||||
\(664\) | 4.16224e7i | 0.142175i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.30054e8 | 1.45579 | ||||||||
\(667\) | −2.35219e7 | −0.0792675 | ||||||||
\(668\) | 5.16789e7i | 0.173374i | ||||||||
\(669\) | 3.51389e7 | 0.117357 | ||||||||
\(670\) | − 5.86575e8i | − 1.95029i | ||||||||
\(671\) | − 2.40700e8i | − 0.796726i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.27171e7 | −0.140138 | −0.0700692 | − | 0.997542i | \(-0.522322\pi\) | ||||
−0.0700692 | + | 0.997542i | \(0.522322\pi\) | |||||||
\(674\) | −4.41358e8 | −1.44149 | ||||||||
\(675\) | 2.77368e8i | 0.901873i | ||||||||
\(676\) | 3.67329e8 | 1.18909 | ||||||||
\(677\) | 2.90750e8i | 0.937032i | 0.883455 | + | 0.468516i | \(0.155211\pi\) | ||||
−0.883455 | + | 0.468516i | \(0.844789\pi\) | |||||||
\(678\) | 2.33298e8i | 0.748551i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.05417e8 | 0.335261 | ||||||||
\(681\) | −2.03338e8 | −0.643838 | ||||||||
\(682\) | 2.27448e8i | 0.717018i | ||||||||
\(683\) | 8.21931e7 | 0.257972 | 0.128986 | − | 0.991646i | \(-0.458828\pi\) | ||||
0.128986 | + | 0.991646i | \(0.458828\pi\) | |||||||
\(684\) | − 3.20077e8i | − 1.00020i | ||||||||
\(685\) | − 2.58537e8i | − 0.804360i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.11908e8 | 0.653548 | ||||||||
\(688\) | 4.90378e7 | 0.150580 | ||||||||
\(689\) | 2.93472e7i | 0.0897242i | ||||||||
\(690\) | −1.56458e8 | −0.476267 | ||||||||
\(691\) | − 3.47176e7i | − 0.105224i | −0.998615 | − | 0.0526122i | \(-0.983245\pi\) | ||||
0.998615 | − | 0.0526122i | \(-0.0167547\pi\) | |||||||
\(692\) | − 2.50866e8i | − 0.757050i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.07730e8 | −1.21981 | ||||||||
\(695\) | 4.43029e8 | 1.31971 | ||||||||
\(696\) | 9.26029e6i | 0.0274661i | ||||||||
\(697\) | 3.33819e8 | 0.985855 | ||||||||
\(698\) | 6.57654e8i | 1.93389i | ||||||||
\(699\) | 1.23721e8i | 0.362254i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.04543e8 | −0.884087 | −0.442044 | − | 0.896994i | \(-0.645746\pi\) | ||||
−0.442044 | + | 0.896994i | \(0.645746\pi\) | |||||||
\(702\) | 9.25042e7 | 0.267393 | ||||||||
\(703\) | 4.23312e8i | 1.21841i | ||||||||
\(704\) | −5.51277e8 | −1.57998 | ||||||||
\(705\) | − 6.76108e7i | − 0.192952i | ||||||||
\(706\) | 5.71204e7i | 0.162322i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.09246e8 | −0.589599 | ||||||||
\(709\) | −2.28892e8 | −0.642231 | −0.321116 | − | 0.947040i | \(-0.604058\pi\) | ||||
−0.321116 | + | 0.947040i | \(0.604058\pi\) | |||||||
\(710\) | 2.22433e8i | 0.621476i | ||||||||
\(711\) | 2.10818e8 | 0.586543 | ||||||||
\(712\) | − 2.56236e8i | − 0.709906i | ||||||||
\(713\) | 7.57777e7i | 0.209061i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.30448e8 | −0.356877 | ||||||||
\(716\) | 8.13023e8 | 2.21495 | ||||||||
\(717\) | − 1.73516e7i | − 0.0470742i | ||||||||
\(718\) | 6.37403e7 | 0.172203 | ||||||||
\(719\) | − 4.47898e8i | − 1.20501i | −0.798114 | − | 0.602507i | \(-0.794169\pi\) | ||||
0.798114 | − | 0.602507i | \(-0.205831\pi\) | |||||||
\(720\) | 2.98061e8i | 0.798561i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.55602e6 | 0.00679131 | ||||||||
\(723\) | 1.87975e8 | 0.497377 | ||||||||
\(724\) | 6.98014e8i | 1.83928i | ||||||||
\(725\) | −6.94161e7 | −0.182157 | ||||||||
\(726\) | 6.05073e7i | 0.158124i | ||||||||
\(727\) | 3.71752e7i | 0.0967498i | 0.998829 | + | 0.0483749i | \(0.0154042\pi\) | ||||
−0.998829 | + | 0.0483749i | \(0.984596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.72219e6 | −0.0147700 | ||||||||
\(730\) | −6.93226e8 | −1.78199 | ||||||||
\(731\) | 5.25722e7i | 0.134587i | ||||||||
\(732\) | −1.57854e8 | −0.402461 | ||||||||
\(733\) | − 6.05169e8i | − 1.53661i | −0.640081 | − | 0.768307i | \(-0.721099\pi\) | ||||
0.640081 | − | 0.768307i | \(-0.278901\pi\) | |||||||
\(734\) | − 9.58030e8i | − 2.42265i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.72471e8 | −0.683419 | ||||||||
\(737\) | −3.97521e8 | −0.993020 | ||||||||
\(738\) | − 7.72250e8i | − 1.92127i | ||||||||
\(739\) | −2.01787e8 | −0.499989 | −0.249994 | − | 0.968247i | \(-0.580429\pi\) | ||||
−0.249994 | + | 0.968247i | \(0.580429\pi\) | |||||||
\(740\) | 8.95898e8i | 2.21087i | ||||||||
\(741\) | 4.04221e7i | 0.0993492i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.81196e7 | −0.239216 | −0.119608 | − | 0.992821i | \(-0.538164\pi\) | ||||
−0.119608 | + | 0.992821i | \(0.538164\pi\) | |||||||
\(744\) | 2.98328e7 | 0.0724394 | ||||||||
\(745\) | − 5.71739e8i | − 1.38270i | ||||||||
\(746\) | −5.07121e8 | −1.22150 | ||||||||
\(747\) | − 1.26168e8i | − 0.302683i | ||||||||
\(748\) | − 3.57204e8i | − 0.853515i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.82895e7 | −0.114464 | ||||||||
\(751\) | −4.25827e8 | −1.00534 | −0.502670 | − | 0.864478i | \(-0.667649\pi\) | ||||
−0.502670 | + | 0.864478i | \(0.667649\pi\) | |||||||
\(752\) | − 8.63456e7i | − 0.203042i | ||||||||
\(753\) | −4.17186e7 | −0.0977113 | ||||||||
\(754\) | 2.31507e7i | 0.0540071i | ||||||||
\(755\) | 4.15053e8i | 0.964413i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.07427e7 | 0.0708687 | 0.0354344 | − | 0.999372i | \(-0.488719\pi\) | ||||
0.0354344 | + | 0.999372i | \(0.488719\pi\) | |||||||
\(758\) | −1.54608e8 | −0.354996 | ||||||||
\(759\) | 1.06031e8i | 0.242499i | ||||||||
\(760\) | 2.40045e8 | 0.546830 | ||||||||
\(761\) | − 3.71229e8i | − 0.842340i | −0.906982 | − | 0.421170i | \(-0.861620\pi\) | ||||
0.906982 | − | 0.421170i | \(-0.138380\pi\) | |||||||
\(762\) | − 4.69935e8i | − 1.06212i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.39075e8 | 0.760354 | ||||||||
\(765\) | −3.19544e8 | −0.713751 | ||||||||
\(766\) | − 3.21084e8i | − 0.714385i | ||||||||
\(767\) | −1.04623e8 | −0.231868 | ||||||||
\(768\) | − 6.75395e7i | − 0.149099i | ||||||||
\(769\) | − 4.59933e8i | − 1.01138i | −0.862714 | − | 0.505691i | \(-0.831237\pi\) | ||||
0.862714 | − | 0.505691i | \(-0.168763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.81924e8 | 0.615132 | ||||||||
\(772\) | 4.91857e8 | 1.06902 | ||||||||
\(773\) | − 6.86231e8i | − 1.48570i | −0.669456 | − | 0.742852i | \(-0.733473\pi\) | ||||
0.669456 | − | 0.742852i | \(-0.266527\pi\) | |||||||
\(774\) | 1.21619e8 | 0.262289 | ||||||||
\(775\) | 2.23629e8i | 0.480423i | ||||||||
\(776\) | 2.90705e8i | 0.622111i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.29069e8 | 0.274083 | ||||||||
\(779\) | 7.60143e8 | 1.60799 | ||||||||
\(780\) | 8.55495e7i | 0.180274i | ||||||||
\(781\) | 1.50743e8 | 0.316434 | ||||||||
\(782\) | − 2.14214e8i | − 0.447947i | ||||||||
\(783\) | − 6.32304e7i | − 0.131717i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.70090e7 | −0.0558342 | ||||||||
\(786\) | 2.90324e8 | 0.597883 | ||||||||
\(787\) | − 5.62391e8i | − 1.15376i | −0.816830 | − | 0.576879i | \(-0.804271\pi\) | ||||
0.816830 | − | 0.576879i | \(-0.195729\pi\) | |||||||
\(788\) | 6.32443e7 | 0.129254 | ||||||||
\(789\) | 3.42657e8i | 0.697635i | ||||||||
\(790\) | 7.90527e8i | 1.60338i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.65269e8 | −0.332672 | ||||||||
\(793\) | −7.89272e7 | −0.158273 | ||||||||
\(794\) | 1.14280e8i | 0.228301i | ||||||||
\(795\) | 1.33431e8 | 0.265556 | ||||||||
\(796\) | 6.50066e8i | 1.28890i | ||||||||
\(797\) | 9.95198e8i | 1.96578i | 0.184200 | + | 0.982889i | \(0.441031\pi\) | ||||
−0.184200 | + | 0.982889i | \(0.558969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.25690e7 | 0.181478 | ||||||||
\(800\) | −8.04096e8 | −1.57050 | ||||||||
\(801\) | 7.76716e8i | 1.51135i | ||||||||
\(802\) | −9.21461e8 | −1.78630 | ||||||||
\(803\) | 4.69798e8i | 0.907329i | ||||||||
\(804\) | 2.60700e8i | 0.501617i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.45819e7 | 0.142439 | ||||||||
\(807\) | 1.91689e8 | 0.364734 | ||||||||
\(808\) | 2.54337e8i | 0.482142i | ||||||||
\(809\) | 7.15167e8 | 1.35071 | 0.675355 | − | 0.737493i | \(-0.263990\pi\) | ||||
0.675355 | + | 0.737493i | \(0.263990\pi\) | |||||||
\(810\) | 5.05355e8i | 0.950915i | ||||||||
\(811\) | − 3.33892e8i | − 0.625955i | −0.949761 | − | 0.312977i | \(-0.898674\pi\) | ||||
0.949761 | − | 0.312977i | \(-0.101326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.42573e8 | −0.823595 | ||||||||
\(814\) | 1.09287e9 | 2.02626 | ||||||||
\(815\) | 1.29078e9i | 2.38441i | ||||||||
\(816\) | 1.03074e8 | 0.189705 | ||||||||
\(817\) | 1.19713e8i | 0.219520i | ||||||||
\(818\) | − 3.60705e8i | − 0.659011i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.60877e9 | 2.91778 | ||||||||
\(821\) | −4.83959e8 | −0.874540 | −0.437270 | − | 0.899330i | \(-0.644055\pi\) | ||||
−0.437270 | + | 0.899330i | \(0.644055\pi\) | |||||||
\(822\) | 2.06829e8i | 0.372389i | ||||||||
\(823\) | 1.57007e8 | 0.281657 | 0.140829 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140829 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(824\) | 1.22889e7i | 0.0219649i | ||||||||
\(825\) | 3.12912e8i | 0.557263i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.84716e8 | 1.56418 | 0.782091 | − | 0.623164i | \(-0.214153\pi\) | ||||
0.782091 | + | 0.623164i | \(0.214153\pi\) | |||||||
\(828\) | −2.75309e8 | −0.484987 | ||||||||
\(829\) | − 8.14222e7i | − 0.142916i | −0.997444 | − | 0.0714578i | \(-0.977235\pi\) | ||||
0.997444 | − | 0.0714578i | \(-0.0227651\pi\) | |||||||
\(830\) | 4.73105e8 | 0.827414 | ||||||||
\(831\) | − 3.81683e8i | − 0.665120i | ||||||||
\(832\) | 1.80767e8i | 0.313870i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.54423e8 | −0.610975 | ||||||||
\(835\) | 1.17482e8 | 0.201796 | ||||||||
\(836\) | − 8.13392e8i | − 1.39213i | ||||||||
\(837\) | −2.03702e8 | −0.347391 | ||||||||
\(838\) | − 5.71662e8i | − 0.971421i | ||||||||
\(839\) | 4.66806e8i | 0.790407i | 0.918594 | + | 0.395203i | \(0.129326\pi\) | ||||
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.78999e8 | −0.973396 | ||||||||
\(842\) | 3.35029e8 | 0.561237 | ||||||||
\(843\) | − 8.03079e7i | − 0.134053i | ||||||||
\(844\) | 9.33789e8 | 1.55318 | ||||||||
\(845\) | − 8.35055e8i | − 1.38403i | ||||||||
\(846\) | − 2.14147e8i | − 0.353672i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.70405e8 | 0.279443 | ||||||||
\(849\) | −4.87981e8 | −0.797407 | ||||||||
\(850\) | − 6.32171e8i | − 1.02939i | ||||||||
\(851\) | 3.64105e8 | 0.590796 | ||||||||
\(852\) | − 9.88591e7i | − 0.159845i | ||||||||
\(853\) | 8.80430e8i | 1.41856i | 0.704926 | + | 0.709280i | \(0.250980\pi\) | ||||
−0.704926 | + | 0.709280i | \(0.749020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.27637e8 | −1.16417 | ||||||||
\(856\) | −1.26824e8 | −0.202200 | ||||||||
\(857\) | 1.79898e8i | 0.285815i | 0.989736 | + | 0.142907i | \(0.0456451\pi\) | ||||
−0.989736 | + | 0.142907i | \(0.954355\pi\) | |||||||
\(858\) | 1.04358e8 | 0.165221 | ||||||||
\(859\) | 9.06857e8i | 1.43074i | 0.698748 | + | 0.715368i | \(0.253741\pi\) | ||||
−0.698748 | + | 0.715368i | \(0.746259\pi\) | |||||||
\(860\) | 2.53360e8i | 0.398330i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.97733e7 | −0.0620968 | ||||||||
\(863\) | 5.44143e7 | 0.0846605 | 0.0423303 | − | 0.999104i | \(-0.486522\pi\) | ||||
0.0423303 | + | 0.999104i | \(0.486522\pi\) | |||||||
\(864\) | − 7.32443e8i | − 1.13562i | ||||||||
\(865\) | −5.70299e8 | −0.881159 | ||||||||
\(866\) | − 5.51695e8i | − 0.849465i | ||||||||
\(867\) | − 1.82149e8i | − 0.279493i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.35740e8 | 0.816384 | ||||||||
\(870\) | 1.05258e8 | 0.159844 | ||||||||
\(871\) | 1.30350e8i | 0.197268i | ||||||||
\(872\) | 1.40484e7 | 0.0211875 | ||||||||
\(873\) | − 8.81200e8i | − 1.32444i | ||||||||
\(874\) | − 4.87788e8i | − 0.730628i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.08100e8 | 0.458332 | ||||||||
\(877\) | −1.26037e8 | −0.186853 | −0.0934263 | − | 0.995626i | \(-0.529782\pi\) | ||||
−0.0934263 | + | 0.995626i | \(0.529782\pi\) | |||||||
\(878\) | 6.53279e8i | 0.965195i | ||||||||
\(879\) | −1.53733e8 | −0.226360 | ||||||||
\(880\) | 7.57444e8i | 1.11148i | ||||||||
\(881\) | 1.37857e8i | 0.201605i | 0.994906 | + | 0.100802i | \(0.0321410\pi\) | ||||
−0.994906 | + | 0.100802i | \(0.967859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.41288e8 | 1.07672 | 0.538362 | − | 0.842713i | \(-0.319043\pi\) | ||||
0.538362 | + | 0.842713i | \(0.319043\pi\) | |||||||
\(884\) | −1.17130e8 | −0.169555 | ||||||||
\(885\) | 4.75682e8i | 0.686257i | ||||||||
\(886\) | −1.27064e9 | −1.82693 | ||||||||
\(887\) | 3.49873e8i | 0.501348i | 0.968072 | + | 0.250674i | \(0.0806522\pi\) | ||||
−0.968072 | + | 0.250674i | \(0.919348\pi\) | |||||||
\(888\) | − 1.43344e8i | − 0.204710i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.91253e9 | −4.13143 | ||||||||
\(891\) | 3.42479e8 | 0.484173 | ||||||||
\(892\) | 2.31856e8i | 0.326682i | ||||||||
\(893\) | 2.10790e8 | 0.296002 | ||||||||
\(894\) | 4.57391e8i | 0.640141i | ||||||||
\(895\) | − 1.84826e9i | − 2.57806i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.47684e7 | 0.0481735 | ||||||||
\(898\) | −1.36864e9 | −1.88999 | ||||||||
\(899\) | − 5.09798e7i | − 0.0701648i | ||||||||
\(900\) | −8.12472e8 | −1.11450 | ||||||||
\(901\) | 1.82687e8i | 0.249765i | ||||||||
\(902\) | − 1.96247e9i | − 2.67413i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.07873e8 | −0.416741 | ||||||||
\(905\) | 1.58681e9 | 2.14081 | ||||||||
\(906\) | − 3.32043e8i | − 0.446487i | ||||||||
\(907\) | 7.32341e8 | 0.981503 | 0.490751 | − | 0.871300i | \(-0.336722\pi\) | ||||
0.490751 | + | 0.871300i | \(0.336722\pi\) | |||||||
\(908\) | − 1.34168e9i | − 1.79222i | ||||||||
\(909\) | − 7.70958e8i | − 1.02645i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.09031e8 | −1.07007 | −0.535033 | − | 0.844831i | \(-0.679701\pi\) | ||||
−0.535033 | + | 0.844831i | \(0.679701\pi\) | |||||||
\(912\) | 2.34711e8 | 0.309420 | ||||||||
\(913\) | − 3.20623e8i | − 0.421291i | ||||||||
\(914\) | −1.18168e9 | −1.54760 | ||||||||
\(915\) | 3.58853e8i | 0.468440i | ||||||||
\(916\) | 1.39823e9i | 1.81925i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.75838e8 | 0.744342 | ||||||||
\(919\) | 1.23948e9 | 1.59696 | 0.798479 | − | 0.602022i | \(-0.205638\pi\) | ||||
0.798479 | + | 0.602022i | \(0.205638\pi\) | |||||||
\(920\) | − 2.06471e8i | − 0.265152i | ||||||||
\(921\) | −2.14914e7 | −0.0275097 | ||||||||
\(922\) | − 4.29999e8i | − 0.548624i | ||||||||
\(923\) | − 4.94295e7i | − 0.0628610i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.07452e9 | 1.35765 | ||||||||
\(926\) | −2.17199e9 | −2.73543 | ||||||||
\(927\) | − 3.72506e7i | − 0.0467621i | ||||||||
\(928\) | 1.83306e8 | 0.229368 | ||||||||
\(929\) | 1.21156e9i | 1.51112i | 0.655082 | + | 0.755558i | \(0.272634\pi\) | ||||
−0.655082 | + | 0.755558i | \(0.727366\pi\) | |||||||
\(930\) | − 3.39097e8i | − 0.421575i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.16348e8 | −1.00839 | ||||||||
\(933\) | −4.42861e8 | −0.545283 | ||||||||
\(934\) | 1.01825e9i | 1.24972i | ||||||||
\(935\) | −8.12038e8 | −0.993439 | ||||||||
\(936\) | 5.41930e7i | 0.0660869i | ||||||||
\(937\) | 1.26862e8i | 0.154211i | 0.997023 | + | 0.0771053i | \(0.0245678\pi\) | ||||
−0.997023 | + | 0.0771053i | \(0.975432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.40702e8 | −0.169944 | ||||||||
\(940\) | 4.46116e8 | 0.537111 | ||||||||
\(941\) | − 4.23325e8i | − 0.508048i | −0.967198 | − | 0.254024i | \(-0.918246\pi\) | ||||
0.967198 | − | 0.254024i | \(-0.0817543\pi\) | |||||||
\(942\) | 2.16072e7 | 0.0258492 | ||||||||
\(943\) | − 6.53825e8i | − 0.779698i | ||||||||
\(944\) | 6.07492e8i | 0.722145i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.09064e8 | 0.365069 | ||||||||
\(947\) | −1.59549e9 | −1.87865 | −0.939324 | − | 0.343032i | \(-0.888546\pi\) | ||||
−0.939324 | + | 0.343032i | \(0.888546\pi\) | |||||||
\(948\) | − 3.51345e8i | − 0.412391i | ||||||||
\(949\) | 1.54050e8 | 0.180245 | ||||||||
\(950\) | − 1.43952e9i | − 1.67899i | ||||||||
\(951\) | − 2.56601e8i | − 0.298344i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.42254e8 | −0.395430 | −0.197715 | − | 0.980260i | \(-0.563352\pi\) | ||||
−0.197715 | + | 0.980260i | \(0.563352\pi\) | |||||||
\(954\) | 4.22623e8 | 0.486752 | ||||||||
\(955\) | − 7.70825e8i | − 0.885005i | ||||||||
\(956\) | 1.14491e8 | 0.131038 | ||||||||
\(957\) | − 7.13332e7i | − 0.0813871i | ||||||||
\(958\) | 1.91069e9i | 2.17317i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.21883e8 | 0.928958 | ||||||||
\(961\) | 7.23268e8 | 0.814947 | ||||||||
\(962\) | − 3.58359e8i | − 0.402525i | ||||||||
\(963\) | 3.84436e8 | 0.430472 | ||||||||
\(964\) | 1.24031e9i | 1.38453i | ||||||||
\(965\) | − 1.11815e9i | − 1.24428i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.56835e9 | −1.73445 | −0.867227 | − | 0.497914i | \(-0.834100\pi\) | ||||
−0.867227 | + | 0.497914i | \(0.834100\pi\) | |||||||
\(968\) | −7.98490e7 | −0.0880325 | ||||||||
\(969\) | 2.51628e8i | 0.276559i | ||||||||
\(970\) | 3.30432e9 | 3.62049 | ||||||||
\(971\) | − 6.00734e8i | − 0.656182i | −0.944646 | − | 0.328091i | \(-0.893595\pi\) | ||||
0.944646 | − | 0.328091i | \(-0.106405\pi\) | |||||||
\(972\) | − 1.15160e9i | − 1.25402i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.67371e8 | 1.04693 | ||||||||
\(975\) | 1.02606e8 | 0.110703 | ||||||||
\(976\) | 4.58291e8i | 0.492937i | ||||||||
\(977\) | −1.17902e8 | −0.126426 | −0.0632132 | − | 0.998000i | \(-0.520135\pi\) | ||||
−0.0632132 | + | 0.998000i | \(0.520135\pi\) | |||||||
\(978\) | − 1.03263e9i | − 1.10389i | ||||||||
\(979\) | 1.97382e9i | 2.10358i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.25844e7 | −0.0451069 | ||||||||
\(982\) | 1.75852e8 | 0.185701 | ||||||||
\(983\) | 1.04078e9i | 1.09572i | 0.836570 | + | 0.547860i | \(0.184558\pi\) | ||||
−0.836570 | + | 0.547860i | \(0.815442\pi\) | |||||||
\(984\) | −2.57403e8 | −0.270164 | ||||||||
\(985\) | − 1.43774e8i | − 0.150443i | ||||||||
\(986\) | 1.44113e8i | 0.150340i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.66717e8 | −0.276554 | ||||||||
\(989\) | 1.02969e8 | 0.106443 | ||||||||
\(990\) | 1.87855e9i | 1.93605i | ||||||||
\(991\) | −1.41876e9 | −1.45777 | −0.728883 | − | 0.684639i | \(-0.759960\pi\) | ||||
−0.728883 | + | 0.684639i | \(0.759960\pi\) | |||||||
\(992\) | − 5.90536e8i | − 0.604938i | ||||||||
\(993\) | 7.18003e8i | 0.733295i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.47781e9 | 1.50020 | ||||||||
\(996\) | −2.10269e8 | −0.212812 | ||||||||
\(997\) | 8.14278e8i | 0.821651i | 0.911714 | + | 0.410826i | \(0.134759\pi\) | ||||
−0.911714 | + | 0.410826i | \(0.865241\pi\) | |||||||
\(998\) | 3.75068e8 | 0.377327 | ||||||||
\(999\) | 9.78768e8i | 0.981710i |
(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 | 49.7.b.a.48.1 | 2 | ||
3.2 | odd | 2 | 441.7.d.a.244.2 | 2 | |||
7.2 | even | 3 | 49.7.d.b.31.1 | 2 | |||
7.3 | odd | 6 | 49.7.d.b.19.1 | 2 | |||
7.4 | even | 3 | 7.7.d.a.5.1 | yes | 2 | ||
7.5 | odd | 6 | 7.7.d.a.3.1 | ✓ | 2 | ||
7.6 | odd | 2 | inner | 49.7.b.a.48.2 | 2 | ||
21.5 | even | 6 | 63.7.m.a.10.1 | 2 | |||
21.11 | odd | 6 | 63.7.m.a.19.1 | 2 | |||
21.20 | even | 2 | 441.7.d.a.244.1 | 2 | |||
28.11 | odd | 6 | 112.7.s.a.33.1 | 2 | |||
28.19 | even | 6 | 112.7.s.a.17.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.7.d.a.3.1 | ✓ | 2 | 7.5 | odd | 6 | ||
7.7.d.a.5.1 | yes | 2 | 7.4 | even | 3 | ||
49.7.b.a.48.1 | 2 | 1.1 | even | 1 | trivial | ||
49.7.b.a.48.2 | 2 | 7.6 | odd | 2 | inner | ||
49.7.d.b.19.1 | 2 | 7.3 | odd | 6 | |||
49.7.d.b.31.1 | 2 | 7.2 | even | 3 | |||
63.7.m.a.10.1 | 2 | 21.5 | even | 6 | |||
63.7.m.a.19.1 | 2 | 21.11 | odd | 6 | |||
112.7.s.a.17.1 | 2 | 28.19 | even | 6 | |||
112.7.s.a.33.1 | 2 | 28.11 | odd | 6 | |||
441.7.d.a.244.1 | 2 | 21.20 | even | 2 | |||
441.7.d.a.244.2 | 2 | 3.2 | odd | 2 |