Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,7,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(69.9364414204\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5090x^{6} + 8905881x^{4} + 5831691048x^{2} + 827887219200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.8 | ||
Root | \(42.5965i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.7.e.c.113.1 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 42.5965i | 1.57765i | 0.614618 | + | 0.788825i | \(0.289310\pi\) | ||||
−0.614618 | + | 0.788825i | \(0.710690\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 103.439 | 0.827513 | 0.413756 | − | 0.910388i | \(-0.364217\pi\) | ||||
0.413756 | + | 0.910388i | \(0.364217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 619.422 | 1.80589 | 0.902947 | − | 0.429752i | \(-0.141399\pi\) | ||||
0.902947 | + | 0.429752i | \(0.141399\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1085.46 | −1.48898 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 57.6072 | 0.0432811 | 0.0216406 | − | 0.999766i | \(-0.493111\pi\) | ||||
0.0216406 | + | 0.999766i | \(0.493111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 481.215i | − | 0.219033i | −0.993985 | − | 0.109516i | \(-0.965070\pi\) | ||
0.993985 | − | 0.109516i | \(-0.0349302\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4406.15i | 1.30552i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2339.07 | −0.476098 | −0.238049 | − | 0.971253i | \(-0.576508\pi\) | ||||
−0.238049 | + | 0.971253i | \(0.576508\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4359.73 | − | 5295.16i | −0.635621 | − | 0.772001i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26385.2i | 2.84907i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8694.38 | 0.714587 | 0.357293 | − | 0.933992i | \(-0.383700\pi\) | ||||
0.357293 | + | 0.933992i | \(0.383700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4925.35 | −0.315222 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 15184.1i | − | 0.771434i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46018.1i | 1.88684i | 0.331603 | + | 0.943419i | \(0.392410\pi\) | ||||
−0.331603 | + | 0.943419i | \(0.607590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36728.1i | 1.23286i | 0.787410 | + | 0.616430i | \(0.211421\pi\) | ||||
−0.787410 | + | 0.616430i | \(0.788579\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2453.87i | 0.0682824i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 64072.4 | 1.49440 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 40458.4i | − | 0.798737i | −0.916791 | − | 0.399368i | \(-0.869229\pi\) | ||
0.916791 | − | 0.399368i | \(-0.130771\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20498.1 | 0.345557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 61518.9i | 0.892600i | 0.894883 | + | 0.446300i | \(0.147259\pi\) | ||||
−0.894883 | + | 0.446300i | \(0.852741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64375.2 | 0.809680 | 0.404840 | − | 0.914388i | \(-0.367327\pi\) | ||||
0.404840 | + | 0.914388i | \(0.367327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −112279. | −1.23215 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 93996.5 | 0.905353 | 0.452676 | − | 0.891675i | \(-0.350469\pi\) | ||||
0.452676 | + | 0.891675i | \(0.350469\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 266034. | 2.26125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 99636.2i | − | 0.751115i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 97805.1i | 0.656952i | 0.944512 | + | 0.328476i | \(0.106535\pi\) | ||||
−0.944512 | + | 0.328476i | \(0.893465\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5958.83 | 0.0358157 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 225555. | − | 185709.i | 1.21795 | − | 1.00279i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 132484.i | 0.645070i | 0.946558 | + | 0.322535i | \(0.104535\pi\) | ||||
−0.946558 | + | 0.322535i | \(0.895465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1921.32 | −0.00846469 | −0.00423235 | − | 0.999991i | \(-0.501347\pi\) | ||||
−0.00423235 | + | 0.999991i | \(0.501347\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −672360. | −2.68893 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 49776.4i | − | 0.181252i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 378794.i | 1.25944i | 0.776821 | + | 0.629721i | \(0.216831\pi\) | ||||
−0.776821 | + | 0.629721i | \(0.783169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 370350.i | 1.12737i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 451799.i | 1.26232i | 0.775652 | + | 0.631161i | \(0.217421\pi\) | ||||
−0.775652 | + | 0.631161i | \(0.782579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −669896. | −1.72202 | −0.861011 | − | 0.508587i | \(-0.830168\pi\) | ||||
−0.861011 | + | 0.508587i | \(0.830168\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 209803.i | − | 0.497310i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35683.1 | 0.0781611 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 747688.i | 1.51649i | 0.651971 | + | 0.758244i | \(0.273942\pi\) | ||||
−0.651971 | + | 0.758244i | \(0.726058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −144512. | −0.271925 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 495260. | 0.866161 | 0.433081 | − | 0.901355i | \(-0.357427\pi\) | ||||
0.433081 | + | 0.901355i | \(0.357427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −241951. | −0.393977 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.96021e6 | −2.97677 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.35076e6i | − | 1.91606i | −0.286672 | − | 0.958029i | \(-0.592549\pi\) | ||
0.286672 | − | 0.958029i | \(-0.407451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 298075.i | − | 0.395550i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.56449e6 | −1.94502 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −450966. | − | 547726.i | −0.525985 | − | 0.638841i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 75990.3i | 0.0832612i | 0.999133 | + | 0.0416306i | \(0.0132553\pi\) | ||||
−0.999133 | + | 0.0416306i | \(0.986745\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −62530.5 | −0.0644446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.08825e6 | 1.05624 | 0.528121 | − | 0.849169i | \(-0.322897\pi\) | ||||
0.528121 | + | 0.849169i | \(0.322897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.69273e6i | − | 1.54909i | −0.632518 | − | 0.774545i | \(-0.717979\pi\) | ||
0.632518 | − | 0.774545i | \(-0.282021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.72926e6i | 2.35764i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 624544.i | 0.509814i | 0.966966 | + | 0.254907i | \(0.0820448\pi\) | ||||
−0.966966 | + | 0.254907i | \(0.917955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.40732e6i | 1.08671i | 0.839503 | + | 0.543356i | \(0.182846\pi\) | ||||
−0.839503 | + | 0.543356i | \(0.817154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.72339e6 | 1.26013 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.11788e6i | − | 0.774749i | −0.921922 | − | 0.387375i | \(-0.873382\pi\) | ||
0.921922 | − | 0.387375i | \(-0.126618\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 899339. | 0.591330 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 522341.i | 0.326135i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44887e6 | −0.859782 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.76824e6 | −0.998127 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.62049e6 | −1.40821 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.12571e6 | −1.08836 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.06130e6i | 1.00631i | 0.864198 | + | 0.503153i | \(0.167827\pi\) | ||||
−0.864198 | + | 0.503153i | \(0.832173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.74216e6i | 1.27739i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.33564e6 | 1.03894 | 0.519471 | − | 0.854488i | \(-0.326129\pi\) | ||||
0.519471 | + | 0.854488i | \(0.326129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.70051e6 | − | 3.27993e6i | −1.14786 | − | 1.39415i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.57063e6i | − | 0.638371i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.26330e6 | −1.26910 | −0.634550 | − | 0.772882i | \(-0.718815\pi\) | ||||
−0.634550 | + | 0.772882i | \(0.718815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −114357. | −0.0425813 | −0.0212907 | − | 0.999773i | \(-0.506778\pi\) | ||||
−0.0212907 | + | 0.999773i | \(0.506778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00392e6i | 1.42833i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 27721.4i | − | 0.00947998i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.76007e6i | 1.56138i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.13321e7i | 3.56746i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.12978e6 | 1.24844 | 0.624221 | − | 0.781248i | \(-0.285417\pi\) | ||||
0.624221 | + | 0.781248i | \(0.285417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 504349.i | − | 0.146487i | −0.997314 | − | 0.0732437i | \(-0.976665\pi\) | ||
0.997314 | − | 0.0732437i | \(-0.0233351\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.53898e6 | 0.708899 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.79912e6i | 1.02021i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.09258e6 | 0.799138 | 0.399569 | − | 0.916703i | \(-0.369160\pi\) | ||||
0.399569 | + | 0.916703i | \(0.369160\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.16616e6 | −1.03644 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.38549e6 | 1.29047 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 587796. | 0.135726 | 0.0678632 | − | 0.997695i | \(-0.478382\pi\) | ||||
0.0678632 | + | 0.997695i | \(0.478382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 253826.i | 0.0565046i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.10037e6i | − | 1.73922i | −0.493736 | − | 0.869612i | \(-0.664369\pi\) | ||
0.493736 | − | 0.869612i | \(-0.335631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.59524e6 | 0.952025 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.73233e6 | + | 5.74770e6i | 0.946425 | + | 1.14949i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.92729e6i | − | 0.372229i | −0.982528 | − | 0.186114i | \(-0.940411\pi\) | ||
0.982528 | − | 0.186114i | \(-0.0595895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.05087e6 | −0.569258 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.64335e6 | −1.01769 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.82927e6i | − | 0.842020i | −0.907056 | − | 0.421010i | \(-0.861676\pi\) | ||
0.907056 | − | 0.421010i | \(-0.138324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.36727e6i | 0.567862i | 0.958845 | + | 0.283931i | \(0.0916387\pi\) | ||||
−0.958845 | + | 0.283931i | \(0.908361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 81841.7i | − | 0.0133543i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.18498e6i | − | 0.660965i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −134747. | −0.0206061 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 9.40538e6i | − | 1.39313i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65880e6 | −0.812128 | −0.406064 | − | 0.913845i | \(-0.633099\pi\) | ||||
−0.406064 | + | 0.913845i | \(0.633099\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.02483e7i | − | 1.42554i | −0.701400 | − | 0.712768i | \(-0.747441\pi\) | ||
0.701400 | − | 0.712768i | \(-0.252559\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.12030e6 | 0.285953 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.47915e7 | 1.93470 | 0.967351 | − | 0.253441i | \(-0.0815622\pi\) | ||||
0.967351 | + | 0.253441i | \(0.0815622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.92464e6 | 0.624907 | 0.312453 | − | 0.949933i | \(-0.398849\pi\) | ||||
0.312453 | + | 0.949933i | \(0.398849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.61353e7 | −1.98696 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.85046e7i | 3.40743i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.36346e6i | 0.738638i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.43744e6 | −1.06400 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −251152. | − | 305039.i | −0.0275104 | − | 0.0334131i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 997042.i | 0.106137i | 0.998591 | + | 0.0530684i | \(0.0169001\pi\) | ||||
−0.998591 | + | 0.0530684i | \(0.983100\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.92451e7 | −1.99150 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.65892e6 | 0.670021 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.27502e7i | 2.22641i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.85352e7i | − | 2.71675i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.12559e6i | 0.104281i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.24527e7i | − | 1.12292i | −0.827502 | − | 0.561462i | \(-0.810239\pi\) | ||
0.827502 | − | 0.561462i | \(-0.189761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.34629e6 | 0.469359 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.22930e6i | − | 0.618043i | −0.951055 | − | 0.309022i | \(-0.899998\pi\) | ||
0.951055 | − | 0.309022i | \(-0.100002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.79865e6 | 0.399588 | 0.199794 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199794 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.51998e6i | 0.123311i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.55746e6 | −0.202181 | −0.101091 | − | 0.994877i | \(-0.532233\pi\) | ||||
−0.101091 | + | 0.994877i | \(0.532233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.72291e6 | 0.749191 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.18489e7 | −2.39249 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.36214e7 | −1.73026 | −0.865132 | − | 0.501544i | \(-0.832765\pi\) | ||||
−0.865132 | + | 0.501544i | \(0.832765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.86092e7i | − | 1.32946i | −0.747082 | − | 0.664732i | \(-0.768546\pi\) | ||
0.747082 | − | 0.664732i | \(-0.231454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.72249e7i | − | 1.20044i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.75183e7 | 1.87122 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.54811e6 | + | 2.09796e6i | −0.169093 | + | 0.139222i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.10963e7i | 1.36650i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.87813e7 | −1.18769 | −0.593846 | − | 0.804578i | \(-0.702391\pi\) | ||||
−0.593846 | + | 0.804578i | \(0.702391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 500859. | 0.0309281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.03063e7i | − | 0.621558i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.43001e7i | − | 0.842441i | −0.906958 | − | 0.421220i | \(-0.861602\pi\) | ||
0.906958 | − | 0.421220i | \(-0.138398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.50608e7i | − | 1.44243i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 4.99510e7i | − | 2.80946i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.68886e7 | 1.47809 | 0.739044 | − | 0.673657i | \(-0.235278\pi\) | ||||
0.739044 | + | 0.673657i | \(0.235278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.01169e7i | 0.543636i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.75377e7 | 3.02287 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.30414e7i | − | 0.669986i | −0.942221 | − | 0.334993i | \(-0.891266\pi\) | ||
0.942221 | − | 0.334993i | \(-0.108734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.69825e7 | 0.853284 | 0.426642 | − | 0.904421i | \(-0.359697\pi\) | ||||
0.426642 | + | 0.904421i | \(0.359697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.26970e7 | 0.624039 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −283736. | −0.0136432 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.95844e6 | 0.327395 | 0.163698 | − | 0.986511i | \(-0.447658\pi\) | ||||
0.163698 | + | 0.986511i | \(0.447658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.98670e7i | − | 1.83570i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.61455e6i | 0.343183i | 0.985168 | + | 0.171591i | \(0.0548908\pi\) | ||||
−0.985168 | + | 0.171591i | \(0.945109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.19767e7 | 0.528418 | 0.264209 | − | 0.964465i | \(-0.414889\pi\) | ||||
0.264209 | + | 0.964465i | \(0.414889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.33312e7 | − | 1.92096e7i | 1.00787 | − | 0.829819i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.81061e7i | 1.61194i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.86663e7 | −0.773331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.23692e6 | −0.131357 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.84558e6i | − | 0.272149i | −0.990699 | − | 0.136075i | \(-0.956551\pi\) | ||
0.990699 | − | 0.136075i | \(-0.0434487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.37040e7i | 0.533804i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 874715.i | − | 0.0333885i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 4.18386e6i | − | 0.156518i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.98754e7 | 1.46220 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.63555e7i | 1.66638i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −198740. | −0.00700464 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.30979e7i | − | 0.452675i | −0.974049 | − | 0.226338i | \(-0.927325\pi\) | ||
0.974049 | − | 0.226338i | \(-0.0726753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.21046e7 | 2.44392 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.13128e6 | 0.104097 | 0.0520487 | − | 0.998645i | \(-0.483425\pi\) | ||||
0.0520487 | + | 0.998645i | \(0.483425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.85162e7 | −0.929948 | −0.464974 | − | 0.885324i | \(-0.653936\pi\) | ||||
−0.464974 | + | 0.885324i | \(0.653936\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.95483e7 | −2.22513 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.08011e6i | − | 0.0652993i | −0.999467 | − | 0.0326497i | \(-0.989605\pi\) | ||
0.999467 | − | 0.0326497i | \(-0.0103946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.65097e6i | 0.0816645i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.66034e7 | −0.804307 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.01977e7 | + | 1.23857e7i | 0.302618 | + | 0.367548i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.37015e6i | 0.0690440i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.99471e7 | −1.71445 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.82234e7 | 1.63497 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68996e6i | 0.239626i | 0.992796 | + | 0.119813i | \(0.0382295\pi\) | ||||
−0.992796 | + | 0.119813i | \(0.961770\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.39161e7i | 1.18930i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.91821e7i | 1.04220i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.62302e7i | 0.424066i | 0.977262 | + | 0.212033i | \(0.0680085\pi\) | ||||
−0.977262 | + | 0.212033i | \(0.931992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.76179e7 | 1.22228 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.11580e6i | 0.0533595i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.19130e7 | 2.27769 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.83087e7i | 0.932911i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.91081e7 | −1.65402 | −0.827010 | − | 0.562188i | \(-0.809960\pi\) | ||||
−0.827010 | + | 0.562188i | \(0.809960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.74773e7 | 0.411148 | 0.205574 | − | 0.978642i | \(-0.434094\pi\) | ||||
0.205574 | + | 0.978642i | \(0.434094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.30683e6 | −0.168969 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.02764e7 | −0.460964 | −0.230482 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230482 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.67337e7i | 1.04459i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.17168e7i | − | 1.35643i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.66182e7 | 1.43982 | 0.719912 | − | 0.694065i | \(-0.244182\pi\) | ||||
0.719912 | + | 0.694065i | \(0.244182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.03146e6 | + | 4.61709e7i | −0.191971 | + | 0.981401i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.53210e7i | − | 1.57469i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.92934e7 | −1.42499 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.30816e7 | 0.466948 | 0.233474 | − | 0.972363i | \(-0.424991\pi\) | ||||
0.233474 | + | 0.972363i | \(0.424991\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.67766e7i | − | 1.32906i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.05826e7i | 1.18639i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.39871e7i | − | 1.61840i | −0.587532 | − | 0.809201i | \(-0.699900\pi\) | ||
0.587532 | − | 0.809201i | \(-0.300100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.05479e7i | − | 1.71706i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.21446e7 | 0.413279 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.57993e7i | − | 1.75973i | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||
0.475228 | − | 0.879863i | \(-0.342366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.78042e7 | −1.58760 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.84087e7i | 1.03964i | 0.854277 | + | 0.519818i | \(0.174000\pi\) | ||||
−0.854277 | + | 0.519818i | \(0.826000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.69103e6 | 0.0646793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.98770e7 | −1.20559 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.66058e7 | 0.791755 | 0.395878 | − | 0.918303i | \(-0.370440\pi\) | ||||
0.395878 | + | 0.918303i | \(0.370440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.03368e7 | −0.340213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.94900e7i | 1.63909i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.73401e7i | 1.25491i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.42232e6 | −0.0546952 | −0.0273476 | − | 0.999626i | \(-0.508706\pi\) | ||||
−0.0273476 | + | 0.999626i | \(0.508706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.39714e8 | − | 1.15032e8i | 2.19948 | − | 1.81093i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.36234e7i | − | 0.521444i | −0.965414 | − | 0.260722i | \(-0.916039\pi\) | ||
0.965414 | − | 0.260722i | \(-0.0839607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.76741e7 | 0.270036 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.49482e7 | −0.225021 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.33069e6i | − | 0.0345702i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.29912e7i | − | 0.482201i | −0.970500 | − | 0.241100i | \(-0.922492\pi\) | ||
0.970500 | − | 0.241100i | \(-0.0775083\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.39005e8i | − | 2.00219i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.20633e7i | 1.16493i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.12292e7 | 0.716760 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.87122e6i | − | 0.0671784i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.94603e7 | −1.08021 | −0.540105 | − | 0.841598i | \(-0.681615\pi\) | ||||
−0.540105 | + | 0.841598i | \(0.681615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.20635e8i | 1.61669i | 0.588706 | + | 0.808347i | \(0.299638\pi\) | ||||
−0.588706 | + | 0.808347i | \(0.700362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.02030e8 | −1.34805 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.15207e7 | 0.150077 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19011e6 | −0.0152863 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.18084e6 | 0.0149561 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.08169e8i | − | 1.35105i | −0.737337 | − | 0.675525i | \(-0.763917\pi\) | ||
0.737337 | − | 0.675525i | \(-0.236083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.91296e7i | 0.728352i | 0.931330 | + | 0.364176i | \(0.118649\pi\) | ||||
−0.931330 | + | 0.364176i | \(0.881351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.02762e8 | −2.46331 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.79051e7 | − | 4.60381e7i | −0.454207 | − | 0.551662i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.06497e8i | 1.25877i | 0.777094 | + | 0.629384i | \(0.216693\pi\) | ||||
−0.777094 | + | 0.629384i | \(0.783307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.88771e8 | −3.36695 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.08889e7 | −0.125248 | −0.0626242 | − | 0.998037i | \(-0.519947\pi\) | ||||
−0.0626242 | + | 0.998037i | \(0.519947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.39722e8i | − | 1.58556i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.75914e8i | 1.96960i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.25704e7i | − | 0.138870i | −0.997586 | − | 0.0694351i | \(-0.977880\pi\) | ||
0.997586 | − | 0.0694351i | \(-0.0221197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.54393e6i | 0.0386327i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.14835e7 | 0.231106 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.08326e7i | − | 0.327323i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.27105e7 | 0.342719 | 0.171359 | − | 0.985209i | \(-0.445184\pi\) | ||||
0.171359 | + | 0.985209i | \(0.445184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.55167e7i | 0.367278i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.30874e7 | 0.643932 | 0.321966 | − | 0.946751i | \(-0.395656\pi\) | ||||
0.321966 | + | 0.946751i | \(0.395656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.48175e8 | −1.49290 | −0.746450 | − | 0.665441i | \(-0.768243\pi\) | ||||
−0.746450 | + | 0.665441i | \(0.768243\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.61829e8 | −1.60953 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.45801e7 | −0.634086 | −0.317043 | − | 0.948411i | \(-0.602690\pi\) | ||||
−0.317043 | + | 0.948411i | \(0.602690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.34633e8i | 2.27442i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.31733e8i | 1.26076i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.70847e6 | 0.0350439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.14732e7 | + | 2.60805e7i | 0.200362 | + | 0.243352i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.06164e8i | − | 0.978187i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.70533e8 | 1.55168 | 0.775838 | − | 0.630932i | \(-0.217328\pi\) | ||||
0.775838 | + | 0.630932i | \(0.217328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.94692e7 | −0.174949 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.29403e8i | 2.03591i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.86037e6i | 0.0688997i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.79460e8i | 1.55375i | 0.629657 | + | 0.776873i | \(0.283195\pi\) | ||||
−0.629657 | + | 0.776873i | \(0.716805\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.50381e7i | 0.214129i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.53625e8 | 1.29783 | 0.648913 | − | 0.760863i | \(-0.275224\pi\) | ||||
0.648913 | + | 0.760863i | \(0.275224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.07639e8i | − | 0.898320i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.46810e6 | −0.0533287 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.79854e8i | 2.27962i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34585e7 | 0.108317 | 0.0541584 | − | 0.998532i | \(-0.482752\pi\) | ||||
0.0541584 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.45048e8 | 2.74388 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.76561e7 | −0.453045 | −0.226523 | − | 0.974006i | \(-0.572736\pi\) | ||||
−0.226523 | + | 0.974006i | \(0.572736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.12567e8 | 0.874054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.95741e8i | 1.50196i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.15748e8i | − | 1.63604i | −0.575193 | − | 0.818018i | \(-0.695073\pi\) | ||
0.575193 | − | 0.818018i | \(-0.304927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.14948e8 | −3.10979 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.04023e7 | + | 6.61987e7i | −0.595548 | + | 0.490340i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.75095e8i | − | 1.28189i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.41487e6 | 0.0391847 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.20961e7 | 0.587246 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.48064e7i | 0.599674i | 0.953990 | + | 0.299837i | \(0.0969323\pi\) | ||||
−0.953990 | + | 0.299837i | \(0.903068\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.36947e7i | − | 0.165633i | −0.996565 | − | 0.0828165i | \(-0.973608\pi\) | ||
0.996565 | − | 0.0828165i | \(-0.0263915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.29956e8i | − | 0.898090i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.59096e7i | − | 0.586962i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.24437e7 | −0.489366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.43806e8i | − | 0.960494i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.96038e7 | 0.195509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.46022e7i | 0.421877i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.05710e8 | 1.32841 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.53255e7 | 0.0978696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29774e8 | −1.45114 | −0.725569 | − | 0.688149i | \(-0.758423\pi\) | ||||
−0.725569 | + | 0.688149i | \(0.758423\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.43434e8 | −0.895887 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.45572e8i | 0.899268i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.04309e8i | 0.637326i | 0.947868 | + | 0.318663i | \(0.103234\pi\) | ||||
−0.947868 | + | 0.318663i | \(0.896766\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.08553e6 | 0.0126037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.43673e8 | − | 2.00626e8i | 1.45664 | − | 1.19931i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.63134e8i | 2.73862i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.78266e8 | 1.04277 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.31503e8 | 0.760973 | 0.380486 | − | 0.924787i | \(-0.375757\pi\) | ||||
0.380486 | + | 0.924787i | \(0.375757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.09783e7i | − | 0.177346i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.73976e6i | − | 0.0325091i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.60307e7i | 0.426053i | 0.977046 | + | 0.213027i | \(0.0683321\pi\) | ||||
−0.977046 | + | 0.213027i | \(0.931668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.15633e8i | − | 0.641115i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.95138e7 | −0.491067 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.84138e8i | − | 0.999553i | −0.866155 | − | 0.499776i | \(-0.833416\pi\) | ||
0.866155 | − | 0.499776i | \(-0.166584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94513e8 | 1.04482 | 0.522409 | − | 0.852695i | \(-0.325033\pi\) | ||||
0.522409 | + | 0.852695i | \(0.325033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.41045e8i | − | 1.28125i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.28229e7 | −0.225254 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 230318. | 0.00119895 | 0.000599475 | − | 1.00000i | \(-0.499809\pi\) | ||||
0.000599475 | 1.00000i | \(0.499809\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.36540e8 | 2.24900 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.06775e8 | 1.56420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.63427e6i | 0.0284336i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.40305e7i | 0.269881i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.41690e8 | 1.19493 | 0.597466 | − | 0.801894i | \(-0.296174\pi\) | ||||
0.597466 | + | 0.801894i | \(0.296174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.94481e8 | − | 1.60124e8i | 0.951768 | − | 0.783631i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.30067e8i | 3.05228i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.16180e8 | −1.03669 | −0.518347 | − | 0.855170i | \(-0.673453\pi\) | ||||
−0.518347 | + | 0.855170i | \(0.673453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.49870e8 | −0.711481 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.09772e8i | 0.985883i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.80059e8i | − | 0.837788i | −0.908035 | − | 0.418894i | \(-0.862418\pi\) | ||
0.908035 | − | 0.418894i | \(-0.137582\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.65025e8i | 1.22085i | 0.792072 | + | 0.610427i | \(0.209002\pi\) | ||||
−0.792072 | + | 0.610427i | \(0.790998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.11167e8i | − | 1.87528i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.82905e8 | −0.825963 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.33490e7i | − | 0.327965i | −0.986463 | − | 0.163983i | \(-0.947566\pi\) | ||
0.986463 | − | 0.163983i | \(-0.0524341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.21420e9 | −5.37573 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.52325e7i | − | 0.198302i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.14007e8 | 0.929064 | 0.464532 | − | 0.885556i | \(-0.346223\pi\) | ||||
0.464532 | + | 0.885556i | \(0.346223\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.71061e8 | −1.16531 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.01185e8 | 1.28226 | 0.641132 | − | 0.767430i | \(-0.278465\pi\) | ||||
0.641132 | + | 0.767430i | \(0.278465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.15883e8 | 1.33185 | 0.665924 | − | 0.746019i | \(-0.268037\pi\) | ||||
0.665924 | + | 0.746019i | \(0.268037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.32017e8i | − | 0.551257i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8.36691e8i | − | 3.46020i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.42923e8 | −0.585412 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.29936e7 | − | 1.06982e7i | 0.0527141 | − | 0.0434018i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.46350e7i | 0.380277i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.94706e8 | −0.774980 | −0.387490 | − | 0.921874i | \(-0.626658\pi\) | ||||
−0.387490 | + | 0.921874i | \(0.626658\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.24705e7 | −0.167447 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.13219e8i | 0.832731i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.28020e8i | − | 0.495288i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.90411e8i | − | 1.87957i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.53818e8i | − | 1.72309i | −0.507684 | − | 0.861543i | \(-0.669498\pi\) | ||
0.507684 | − | 0.861543i | \(-0.330502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.37859e8 | −0.518564 | −0.259282 | − | 0.965802i | \(-0.583486\pi\) | ||||
−0.259282 | + | 0.965802i | \(0.583486\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.83647e8i | 1.05706i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.74047e7 | 0.359639 | 0.179820 | − | 0.983700i | \(-0.442449\pi\) | ||||
0.179820 | + | 0.983700i | \(0.442449\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.63202e6i | 0.0279193i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.69079e8 | −3.51250 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.31439e7 | −0.0831184 | −0.0415592 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415592 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.41596e8 | 0.859738 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.27148e8 | 2.56405 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.21467e8i | 0.773844i | 0.922112 | + | 0.386922i | \(0.126462\pi\) | ||||
−0.922112 | + | 0.386922i | \(0.873538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.13083e8i | − | 0.737811i | −0.929467 | − | 0.368906i | \(-0.879733\pi\) | ||
0.929467 | − | 0.368906i | \(-0.120267\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.79464e7 | −0.164519 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.79338e8 | − | 3.39273e8i | −0.949873 | − | 1.15368i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00099e8i | 1.34831i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.30444e8 | 1.77158 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −110682. | −0.000366361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.52414e8i | 0.500011i | 0.968244 | + | 0.250006i | \(0.0804325\pi\) | ||||
−0.968244 | + | 0.250006i | \(0.919568\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.47872e7i | 0.243173i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.86309e7i | − | 0.317868i | −0.987289 | − | 0.158934i | \(-0.949194\pi\) | ||
0.987289 | − | 0.158934i | \(-0.0508057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.70700e7i | 0.150361i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.07943e8 | 0.975055 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.83544e8i | − | 0.576074i | −0.957619 | − | 0.288037i | \(-0.906997\pi\) | ||
0.957619 | − | 0.288037i | \(-0.0930026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.37553e8 | −1.05020 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.04406e8i | 0.630410i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.70653e7 | 0.143894 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.11147e7 | −0.276156 | −0.138078 | − | 0.990421i | \(-0.544092\pi\) | ||||
−0.138078 | + | 0.990421i | \(0.544092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.87328e7 | −0.116380 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.18290e7 | −0.0352366 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.43897e8i | − | 0.424965i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.08939e8i | − | 0.318971i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.14272e8 | −1.20263 | −0.601315 | − | 0.799012i | \(-0.705356\pi\) | ||||
−0.601315 | + | 0.799012i | \(0.705356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14234e8 | + | 1.76388e8i | −0.616625 | + | 0.507694i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.14162e8i | 1.18196i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.74084e8 | 1.90746 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.21198e8 | −0.901226 | −0.450613 | − | 0.892719i | \(-0.648795\pi\) | ||||
−0.450613 | + | 0.892719i | \(0.648795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.11588e8i | − | 2.25802i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.19328e8i | 0.880985i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.86748e6i | − | 0.00784481i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.00619e9i | − | 2.72975i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.98125e8 | 1.07111 | 0.535553 | − | 0.844502i | \(-0.320103\pi\) | ||||
0.535553 | + | 0.844502i | \(0.320103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.04852e9i | − | 2.79749i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.92687e8 | 2.09743 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.26655e8i | − | 0.594774i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.93307e8 | −0.763343 | −0.381672 | − | 0.924298i | \(-0.624651\pi\) | ||||
−0.381672 | + | 0.924298i | \(0.624651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.28373e8 | 1.62194 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50578e8 | −0.385487 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.75660e8 | 1.20777 | 0.603886 | − | 0.797071i | \(-0.293618\pi\) | ||||
0.603886 | + | 0.797071i | \(0.293618\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.17219e9i | 2.95212i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.18212e7i | 0.0545101i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.86348e8 | −0.709515 | −0.354757 | − | 0.934958i | \(-0.615437\pi\) | ||||
−0.354757 | + | 0.934958i | \(0.615437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.93660e7 | − | 1.08541e8i | −0.219643 | − | 0.266770i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.29617e8i | − | 1.53501i | −0.641045 | − | 0.767503i | \(-0.721499\pi\) | ||
0.641045 | − | 0.767503i | \(-0.278501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.27181e8 | 1.03310 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.37587e8 | −1.28969 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.86856e8i | 0.920669i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.36049e8i | − | 1.26557i | −0.774329 | − | 0.632783i | \(-0.781913\pi\) | ||
0.774329 | − | 0.632783i | \(-0.218087\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.00018e8i | − | 1.87376i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.21694e7i | − | 0.121220i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.72181e7 | −0.108848 | −0.0544240 | − | 0.998518i | \(-0.517332\pi\) | ||||
−0.0544240 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.13348e7i | 0.0487937i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.01530e8 | 0.684189 | 0.342095 | − | 0.939666i | \(-0.388864\pi\) | ||||
0.342095 | + | 0.939666i | \(0.388864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.71726e8i | 1.96249i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.62629e8 | 0.586623 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.37532e7 | 0.141291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.09285e8 | −1.55970 | −0.779851 | − | 0.625965i | \(-0.784705\pi\) | ||||
−0.779851 | + | 0.625965i | \(0.784705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.09134e8 | 1.32908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.38166e8i | 0.948638i | 0.880353 | + | 0.474319i | \(0.157306\pi\) | ||||
−0.880353 | + | 0.474319i | \(0.842694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.80899e8i | − | 0.388625i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.06750e9 | 2.27565 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.25752e8 | − | 2.68206e8i | 0.689088 | − | 0.567356i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.60269e7i | 0.0546347i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.98745e8 | 1.45557 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.19893e8 | 0.661297 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.08238e8i | − | 0.837509i | −0.908099 | − | 0.418755i | \(-0.862467\pi\) | ||
0.908099 | − | 0.418755i | \(-0.137533\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.14536e9i | 2.33190i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.92441e8i | − | 1.39911i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 924569.i | 0.00185404i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.30944e8 | −0.857668 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.93088e8i | − | 0.776452i | −0.921564 | − | 0.388226i | \(-0.873088\pi\) | ||
0.921564 | − | 0.388226i | \(-0.126912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.19864e8 | −0.431037 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.46620e9i | 2.85297i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.85908e7 | −0.0745310 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.57070e8 | 1.06788 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.55517e8 | 1.05700 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.89585e8 | −0.358062 | −0.179031 | − | 0.983843i | \(-0.557296\pi\) | ||||
−0.179031 | + | 0.983843i | \(0.557296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.61235e8i | 0.677217i | 0.940927 | + | 0.338608i | \(0.109956\pi\) | ||||
−0.940927 | + | 0.338608i | \(0.890044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.23395e8i | 1.34618i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.08011e7 | 0.112315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.80658e8 | − | 3.40877e8i | −0.514650 | − | 0.625074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.23550e8i | 0.588964i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.28100e8 | −1.67712 | −0.838562 | − | 0.544806i | \(-0.816603\pi\) | ||||
−0.838562 | + | 0.544806i | \(0.816603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.88701e8 | 1.05608 | 0.528038 | − | 0.849221i | \(-0.322928\pi\) | ||||
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.20861e7i | − | 0.0215242i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.62734e8i | 0.641316i | 0.947195 | + | 0.320658i | \(0.103904\pi\) | ||||
−0.947195 | + | 0.320658i | \(0.896096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.99074e8i | 0.524946i | 0.964939 | + | 0.262473i | \(0.0845381\pi\) | ||||
−0.964939 | + | 0.262473i | \(0.915462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.96405e8i | 0.516515i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.22272e8 | −1.07658 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 8.37895e8i | − | 1.43923i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.57684e8 | 0.951069 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.24397e8i | 1.56521i | 0.622518 | + | 0.782605i | \(0.286110\pi\) | ||||
−0.622518 | + | 0.782605i | \(0.713890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.52284e9 | −2.56016 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.24353e8 | −0.541422 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.75328e8 | 0.787813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.09529e9 | −1.80251 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.10166e8i | 0.833659i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.51761e8i | − | 0.570767i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.56120e8 | 1.54051 | 0.770256 | − | 0.637734i | \(-0.220128\pi\) | ||||
0.770256 | + | 0.637734i | \(0.220128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.89508e8 | + | 5.94537e8i | 0.783179 | + | 0.951219i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.58039e8i | − | 1.20434i | −0.798368 | − | 0.602170i | \(-0.794303\pi\) | ||
0.798368 | − | 0.602170i | \(-0.205697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.10887e9 | 1.74945 | 0.874724 | − | 0.484621i | \(-0.161043\pi\) | ||||
0.874724 | + | 0.484621i | \(0.161043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.62319e9 | −2.54308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.02345e8i | 0.470403i | 0.971947 | + | 0.235201i | \(0.0755750\pi\) | ||||
−0.971947 | + | 0.235201i | \(0.924425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.99358e8i | − | 0.308024i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 7.95121e8i | − | 1.22004i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.30722e7i | 0.0656353i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.82281e8 | 0.275859 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.24847e7i | − | 0.123974i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.31671e9 | −1.96547 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 7.86910e7i | − | 0.116661i | −0.998297 | − | 0.0583306i | \(-0.981422\pi\) | ||
0.998297 | − | 0.0583306i | \(-0.0185777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.91598e8 | 0.429356 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.85796e7 | −0.0710438 | −0.0355219 | − | 0.999369i | \(-0.511309\pi\) | ||||
−0.0355219 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.43174e8 | 0.934214 | 0.467107 | − | 0.884201i | \(-0.345296\pi\) | ||||
0.467107 | + | 0.884201i | \(0.345296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.83743e8 | −0.842155 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.45733e8i | 1.21189i | 0.795507 | + | 0.605944i | \(0.207204\pi\) | ||||
−0.795507 | + | 0.605944i | \(0.792796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.27681e9i | 1.81728i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.32493e6 | −0.0117692 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.09799e8 | − | 4.97726e8i | −0.575462 | − | 0.698933i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.99536e8i | − | 0.696783i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.78218e8 | 0.246930 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.69016e9 | −2.32621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.28773e8i | − | 0.312774i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.69855e9i | 2.30683i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.48308e8i | 0.469913i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 6.28543e8i | − | 0.842390i | −0.906970 | − | 0.421195i | \(-0.861611\pi\) | ||
0.906970 | − | 0.421195i | \(-0.138389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.18125e9 | −1.57272 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.01606e9i | − | 1.34389i | −0.740601 | − | 0.671945i | \(-0.765459\pi\) | ||
0.740601 | − | 0.671945i | \(-0.234541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.85305e7 | 0.0374884 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 8.46563e6i | − | 0.0110509i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.44674e9 | 1.87622 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.64340e8 | −0.340578 | −0.170289 | − | 0.985394i | \(-0.554470\pi\) | ||||
−0.170289 | + | 0.985394i | \(0.554470\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.57926e8 | 0.714163 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.17412e8 | 0.276490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.99272e8i | 0.251780i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.83740e9i | 2.30656i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.45301e8 | 0.680126 | 0.340063 | − | 0.940403i | \(-0.389552\pi\) | ||||
0.340063 | + | 0.940403i | \(0.389552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.15984e9 | − | 1.40869e9i | −1.43730 | − | 1.74569i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.33381e8i | 0.164229i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39381e7 | −0.0170518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.24987e7 | −0.0516602 | −0.0258301 | − | 0.999666i | \(-0.508223\pi\) | ||||
−0.0258301 | + | 0.999666i | \(0.508223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.21469e9i | − | 1.46713i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.88776e8i | 0.346570i | 0.984872 | + | 0.173285i | \(0.0554382\pi\) | ||||
−0.984872 | + | 0.173285i | \(0.944562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.34869e8i | 0.637840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 9.72884e8i | − | 1.15283i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.44768e8 | −0.641449 | −0.320724 | − | 0.947173i | \(-0.603926\pi\) | ||||
−0.320724 | + | 0.947173i | \(0.603926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.22364e8i | 0.377179i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.86055e7 | 0.103019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 8.40684e8i | − | 0.971302i | −0.874153 | − | 0.485651i | \(-0.838583\pi\) | ||
0.874153 | − | 0.485651i | \(-0.161417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.85341e8 | −0.672046 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.12922e8 | −0.128838 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.02136e9 | −2.29186 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.61450e8 | −0.519941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.77920e8i | − | 0.759101i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.06007e9i | − | 1.17965i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.07252e8 | 0.560976 | 0.280488 | − | 0.959857i | \(-0.409504\pi\) | ||||
0.280488 | + | 0.959857i | \(0.409504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.27589e8 | + | 4.34387e8i | −0.579862 | + | 0.477425i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.79559e8i | 0.960743i | 0.877065 | + | 0.480371i | \(0.159498\pi\) | ||||
−0.877065 | + | 0.480371i | \(0.840502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.08353e7 | −0.0768973 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00960e8 | −0.108927 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.00687e9i | − | 1.07967i | −0.841771 | − | 0.539835i | \(-0.818487\pi\) | ||
0.841771 | − | 0.539835i | \(-0.181513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.78135e7i | − | 0.0829291i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.52760e9i | − | 1.61809i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.63063e9i | − | 1.71670i | −0.513066 | − | 0.858349i | \(-0.671491\pi\) | ||
0.513066 | − | 0.858349i | \(-0.328509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.53002e9 | 1.60099 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.48012e9i | 2.57941i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.59703e8 | 0.578587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.15200e8i | 0.426615i | 0.976985 | + | 0.213307i | \(0.0684236\pi\) | ||||
−0.976985 | + | 0.213307i | \(0.931576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.70162e8 | −0.378046 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.09400e8 | 0.517118 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.10642e9 | −1.11644 | −0.558218 | − | 0.829695i | \(-0.688515\pi\) | ||||
−0.558218 | + | 0.829695i | \(0.688515\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.14326e8 | −0.616172 |
(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 | 304.7.e.c.113.8 | 8 | ||
4.3 | odd | 2 | 76.7.c.b.37.1 | ✓ | 8 | ||
12.11 | even | 2 | 684.7.h.c.37.1 | 8 | |||
19.18 | odd | 2 | inner | 304.7.e.c.113.1 | 8 | ||
76.75 | even | 2 | 76.7.c.b.37.8 | yes | 8 | ||
228.227 | odd | 2 | 684.7.h.c.37.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.c.b.37.1 | ✓ | 8 | 4.3 | odd | 2 | ||
76.7.c.b.37.8 | yes | 8 | 76.75 | even | 2 | ||
304.7.e.c.113.1 | 8 | 19.18 | odd | 2 | inner | ||
304.7.e.c.113.8 | 8 | 1.1 | even | 1 | trivial | ||
684.7.h.c.37.1 | 8 | 12.11 | even | 2 | |||
684.7.h.c.37.2 | 8 | 228.227 | odd | 2 |