Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,7,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, 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("22.21");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(5.06118983964\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 1781x^{4} + 14500x^{3} + 786532x^{2} - 11444432x + 42080676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.4 | ||
Root | \(-32.5131 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.7.b.a.21.1 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685i | 0.707107i | ||||||||
\(3\) | −41.5131 | −1.53752 | −0.768761 | − | 0.639536i | \(-0.779126\pi\) | ||||
−0.768761 | + | 0.639536i | \(0.779126\pi\) | |||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | 155.573 | 1.24459 | 0.622294 | − | 0.782784i | \(-0.286201\pi\) | ||||
0.622294 | + | 0.782784i | \(0.286201\pi\) | |||||||
\(6\) | − | 234.833i | − | 1.08719i | ||||||
\(7\) | − | 562.567i | − | 1.64014i | −0.572266 | − | 0.820068i | \(-0.693935\pi\) | ||
0.572266 | − | 0.820068i | \(-0.306065\pi\) | |||||||
\(8\) | − | 181.019i | − | 0.353553i | ||||||
\(9\) | 994.336 | 1.36397 | ||||||||
\(10\) | 880.056i | 0.880056i | ||||||||
\(11\) | −1173.59 | + | 627.888i | −0.881737 | + | 0.471741i | ||||
\(12\) | 1328.42 | 0.768761 | ||||||||
\(13\) | − | 3272.55i | − | 1.48956i | −0.667313 | − | 0.744778i | \(-0.732556\pi\) | ||
0.667313 | − | 0.744778i | \(-0.267444\pi\) | |||||||
\(14\) | 3182.36 | 1.15975 | ||||||||
\(15\) | −6458.33 | −1.91358 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 1751.31i | 0.356463i | 0.983989 | + | 0.178232i | \(0.0570377\pi\) | ||||
−0.983989 | + | 0.178232i | \(0.942962\pi\) | |||||||
\(18\) | 5624.81i | 0.964474i | ||||||||
\(19\) | − | 8806.02i | − | 1.28386i | −0.766762 | − | 0.641932i | \(-0.778133\pi\) | ||
0.766762 | − | 0.641932i | \(-0.221867\pi\) | |||||||
\(20\) | −4978.35 | −0.622294 | ||||||||
\(21\) | 23353.9i | 2.52175i | ||||||||
\(22\) | −3551.87 | − | 6638.84i | −0.333572 | − | 0.623482i | ||||
\(23\) | −4919.08 | −0.404297 | −0.202148 | − | 0.979355i | \(-0.564792\pi\) | ||||
−0.202148 | + | 0.979355i | \(0.564792\pi\) | |||||||
\(24\) | 7514.67i | 0.543596i | ||||||||
\(25\) | 8578.08 | 0.548997 | ||||||||
\(26\) | 18512.4 | 1.05327 | ||||||||
\(27\) | −11014.9 | −0.559616 | ||||||||
\(28\) | 18002.1i | 0.820068i | ||||||||
\(29\) | − | 15064.6i | − | 0.617678i | −0.951114 | − | 0.308839i | \(-0.900060\pi\) | ||
0.951114 | − | 0.308839i | \(-0.0999405\pi\) | |||||||
\(30\) | − | 36533.8i | − | 1.35310i | ||||||
\(31\) | −4422.42 | −0.148448 | −0.0742240 | − | 0.997242i | \(-0.523648\pi\) | ||||
−0.0742240 | + | 0.997242i | \(0.523648\pi\) | |||||||
\(32\) | 5792.62i | 0.176777i | ||||||||
\(33\) | 48719.4 | − | 26065.6i | 1.35569 | − | 0.725313i | ||||
\(34\) | −9906.88 | −0.252058 | ||||||||
\(35\) | − | 87520.4i | − | 2.04129i | ||||||
\(36\) | −31818.8 | −0.681986 | ||||||||
\(37\) | −27378.8 | −0.540517 | −0.270259 | − | 0.962788i | \(-0.587109\pi\) | ||||
−0.270259 | + | 0.962788i | \(0.587109\pi\) | |||||||
\(38\) | 49814.4 | 0.907829 | ||||||||
\(39\) | 135854.i | 2.29022i | ||||||||
\(40\) | − | 28161.8i | − | 0.440028i | ||||||
\(41\) | 40130.1i | 0.582262i | 0.956683 | + | 0.291131i | \(0.0940316\pi\) | ||||
−0.956683 | + | 0.291131i | \(0.905968\pi\) | |||||||
\(42\) | −132110. | −1.78314 | ||||||||
\(43\) | 13388.3i | 0.168391i | 0.996449 | + | 0.0841957i | \(0.0268321\pi\) | ||||
−0.996449 | + | 0.0841957i | \(0.973168\pi\) | |||||||
\(44\) | 37554.9 | − | 20092.4i | 0.440868 | − | 0.235871i | ||||
\(45\) | 154692. | 1.69758 | ||||||||
\(46\) | − | 27826.5i | − | 0.285881i | ||||||
\(47\) | 125948. | 1.21310 | 0.606551 | − | 0.795045i | \(-0.292553\pi\) | ||||
0.606551 | + | 0.795045i | \(0.292553\pi\) | |||||||
\(48\) | −42509.4 | −0.384380 | ||||||||
\(49\) | −198832. | −1.69005 | ||||||||
\(50\) | 48524.9i | 0.388199i | ||||||||
\(51\) | − | 72702.1i | − | 0.548070i | ||||||
\(52\) | 104722.i | 0.744778i | ||||||||
\(53\) | 100119. | 0.672497 | 0.336249 | − | 0.941773i | \(-0.390842\pi\) | ||||
0.336249 | + | 0.941773i | \(0.390842\pi\) | |||||||
\(54\) | − | 62309.8i | − | 0.395708i | ||||||
\(55\) | −182580. | + | 97682.6i | −1.09740 | + | 0.587123i | ||||
\(56\) | −101835. | −0.579876 | ||||||||
\(57\) | 365565.i | 1.97397i | ||||||||
\(58\) | 85218.0 | 0.436765 | ||||||||
\(59\) | −337180. | −1.64175 | −0.820873 | − | 0.571110i | \(-0.806513\pi\) | ||||
−0.820873 | + | 0.571110i | \(0.806513\pi\) | |||||||
\(60\) | 206667. | 0.956790 | ||||||||
\(61\) | 53782.3i | 0.236946i | 0.992957 | + | 0.118473i | \(0.0377999\pi\) | ||||
−0.992957 | + | 0.118473i | \(0.962200\pi\) | |||||||
\(62\) | − | 25017.0i | − | 0.104969i | ||||||
\(63\) | − | 559380.i | − | 2.23710i | ||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | − | 509122.i | − | 1.85388i | ||||||
\(66\) | 147449. | + | 275599.i | 0.512873 | + | 0.958617i | ||||
\(67\) | 153989. | 0.511993 | 0.255997 | − | 0.966678i | \(-0.417596\pi\) | ||||
0.255997 | + | 0.966678i | \(0.417596\pi\) | |||||||
\(68\) | − | 56041.8i | − | 0.178232i | ||||||
\(69\) | 204206. | 0.621615 | ||||||||
\(70\) | 495090. | 1.44341 | ||||||||
\(71\) | 118037. | 0.329795 | 0.164897 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164897 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(72\) | − | 179994.i | − | 0.482237i | ||||||
\(73\) | − | 402389.i | − | 1.03437i | −0.855873 | − | 0.517187i | \(-0.826979\pi\) | ||
0.855873 | − | 0.517187i | \(-0.173021\pi\) | |||||||
\(74\) | − | 154878.i | − | 0.382203i | ||||||
\(75\) | −356102. | −0.844095 | ||||||||
\(76\) | 281793.i | 0.641932i | ||||||||
\(77\) | 353229. | + | 660224.i | 0.773720 | + | 1.44617i | ||||
\(78\) | −768505. | −1.61943 | ||||||||
\(79\) | 561206.i | 1.13826i | 0.822248 | + | 0.569129i | \(0.192720\pi\) | ||||
−0.822248 | + | 0.569129i | \(0.807280\pi\) | |||||||
\(80\) | 159307. | 0.311147 | ||||||||
\(81\) | −267608. | −0.503552 | ||||||||
\(82\) | −227010. | −0.411722 | ||||||||
\(83\) | − | 569941.i | − | 0.996771i | −0.866955 | − | 0.498386i | \(-0.833926\pi\) | ||
0.866955 | − | 0.498386i | \(-0.166074\pi\) | |||||||
\(84\) | − | 747324.i | − | 1.26087i | ||||||
\(85\) | 272456.i | 0.443650i | ||||||||
\(86\) | −75735.6 | −0.119071 | ||||||||
\(87\) | 625376.i | 0.949694i | ||||||||
\(88\) | 113660. | + | 212443.i | 0.166786 | + | 0.311741i | ||||
\(89\) | 805884. | 1.14315 | 0.571574 | − | 0.820550i | \(-0.306333\pi\) | ||||
0.571574 | + | 0.820550i | \(0.306333\pi\) | |||||||
\(90\) | 875071.i | 1.20037i | ||||||||
\(91\) | −1.84103e6 | −2.44307 | ||||||||
\(92\) | 157411. | 0.202148 | ||||||||
\(93\) | 183588. | 0.228242 | ||||||||
\(94\) | 712469.i | 0.857793i | ||||||||
\(95\) | − | 1.36998e6i | − | 1.59788i | ||||||
\(96\) | − | 240469.i | − | 0.271798i | ||||||
\(97\) | 1.00183e6 | 1.09769 | 0.548844 | − | 0.835925i | \(-0.315068\pi\) | ||||
0.548844 | + | 0.835925i | \(0.315068\pi\) | |||||||
\(98\) | − | 1.12477e6i | − | 1.19504i | ||||||
\(99\) | −1.16694e6 | + | 624331.i | −1.20266 | + | 0.643442i | ||||
\(100\) | −274498. | −0.274498 | ||||||||
\(101\) | 320013.i | 0.310601i | 0.987867 | + | 0.155301i | \(0.0496346\pi\) | ||||
−0.987867 | + | 0.155301i | \(0.950365\pi\) | |||||||
\(102\) | 411265. | 0.387544 | ||||||||
\(103\) | 1.88724e6 | 1.72709 | 0.863547 | − | 0.504268i | \(-0.168238\pi\) | ||||
0.863547 | + | 0.504268i | \(0.168238\pi\) | |||||||
\(104\) | −592395. | −0.526637 | ||||||||
\(105\) | 3.63324e6i | 3.13853i | ||||||||
\(106\) | 566361.i | 0.475528i | ||||||||
\(107\) | − | 1.21527e6i | − | 0.992025i | −0.868315 | − | 0.496012i | \(-0.834797\pi\) | ||
0.868315 | − | 0.496012i | \(-0.165203\pi\) | |||||||
\(108\) | 352477. | 0.279808 | ||||||||
\(109\) | − | 747494.i | − | 0.577203i | −0.957449 | − | 0.288601i | \(-0.906810\pi\) | ||
0.957449 | − | 0.288601i | \(-0.0931902\pi\) | |||||||
\(110\) | −552576. | − | 1.03283e6i | −0.415159 | − | 0.775978i | ||||
\(111\) | 1.13658e6 | 0.831057 | ||||||||
\(112\) | − | 576068.i | − | 0.410034i | ||||||
\(113\) | 599923. | 0.415777 | 0.207888 | − | 0.978153i | \(-0.433341\pi\) | ||||
0.207888 | + | 0.978153i | \(0.433341\pi\) | |||||||
\(114\) | −2.06795e6 | −1.39581 | ||||||||
\(115\) | −765278. | −0.503183 | ||||||||
\(116\) | 482066.i | 0.308839i | ||||||||
\(117\) | − | 3.25402e6i | − | 2.03171i | ||||||
\(118\) | − | 1.90738e6i | − | 1.16089i | ||||||
\(119\) | 985226. | 0.584649 | ||||||||
\(120\) | 1.16908e6i | 0.676552i | ||||||||
\(121\) | 983075. | − | 1.47377e6i | 0.554920 | − | 0.831904i | ||||
\(122\) | −304239. | −0.167546 | ||||||||
\(123\) | − | 1.66592e6i | − | 0.895241i | ||||||
\(124\) | 141517. | 0.0742240 | ||||||||
\(125\) | −1.09631e6 | −0.561313 | ||||||||
\(126\) | 3.16433e6 | 1.58187 | ||||||||
\(127\) | 2.88684e6i | 1.40933i | 0.709541 | + | 0.704664i | \(0.248902\pi\) | ||||
−0.709541 | + | 0.704664i | \(0.751098\pi\) | |||||||
\(128\) | − | 185364.i | − | 0.0883883i | ||||||
\(129\) | − | 555789.i | − | 0.258905i | ||||||
\(130\) | 2.88003e6 | 1.31089 | ||||||||
\(131\) | 1.00234e6i | 0.445863i | 0.974834 | + | 0.222932i | \(0.0715626\pi\) | ||||
−0.974834 | + | 0.222932i | \(0.928437\pi\) | |||||||
\(132\) | −1.55902e6 | + | 834098.i | −0.677845 | + | 0.362656i | ||||
\(133\) | −4.95398e6 | −2.10571 | ||||||||
\(134\) | 871091.i | 0.362034i | ||||||||
\(135\) | −1.71363e6 | −0.696490 | ||||||||
\(136\) | 317020. | 0.126029 | ||||||||
\(137\) | −415951. | −0.161764 | −0.0808818 | − | 0.996724i | \(-0.525774\pi\) | ||||
−0.0808818 | + | 0.996724i | \(0.525774\pi\) | |||||||
\(138\) | 1.15516e6i | 0.439548i | ||||||||
\(139\) | 3.13482e6i | 1.16726i | 0.812019 | + | 0.583631i | \(0.198368\pi\) | ||||
−0.812019 | + | 0.583631i | \(0.801632\pi\) | |||||||
\(140\) | 2.80065e6i | 1.02065i | ||||||||
\(141\) | −5.22848e6 | −1.86517 | ||||||||
\(142\) | 667720.i | 0.233200i | ||||||||
\(143\) | 2.05480e6 | + | 3.84064e6i | 0.702685 | + | 1.31340i | ||||
\(144\) | 1.01820e6 | 0.340993 | ||||||||
\(145\) | − | 2.34364e6i | − | 0.768755i | ||||||
\(146\) | 2.27626e6 | 0.731413 | ||||||||
\(147\) | 8.25415e6 | 2.59849 | ||||||||
\(148\) | 876122. | 0.270259 | ||||||||
\(149\) | − | 1.12693e6i | − | 0.340675i | −0.985386 | − | 0.170337i | \(-0.945514\pi\) | ||
0.985386 | − | 0.170337i | \(-0.0544857\pi\) | |||||||
\(150\) | − | 2.01442e6i | − | 0.596865i | ||||||
\(151\) | − | 5.47157e6i | − | 1.58921i | −0.607127 | − | 0.794605i | \(-0.707678\pi\) | ||
0.607127 | − | 0.794605i | \(-0.292322\pi\) | |||||||
\(152\) | −1.59406e6 | −0.453914 | ||||||||
\(153\) | 1.74139e6i | 0.486206i | ||||||||
\(154\) | −3.73479e6 | + | 1.99816e6i | −1.02260 | + | 0.547103i | ||||
\(155\) | −688010. | −0.184756 | ||||||||
\(156\) | − | 4.34732e6i | − | 1.14511i | ||||||
\(157\) | −5.05000e6 | −1.30495 | −0.652473 | − | 0.757812i | \(-0.726268\pi\) | ||||
−0.652473 | + | 0.757812i | \(0.726268\pi\) | |||||||
\(158\) | −3.17466e6 | −0.804870 | ||||||||
\(159\) | −4.15627e6 | −1.03398 | ||||||||
\(160\) | 901177.i | 0.220014i | ||||||||
\(161\) | 2.76731e6i | 0.663102i | ||||||||
\(162\) | − | 1.51382e6i | − | 0.356065i | ||||||
\(163\) | 3.61048e6 | 0.833686 | 0.416843 | − | 0.908979i | \(-0.363137\pi\) | ||||
0.416843 | + | 0.908979i | \(0.363137\pi\) | |||||||
\(164\) | − | 1.28416e6i | − | 0.291131i | ||||||
\(165\) | 7.57944e6 | − | 4.05511e6i | 1.68727 | − | 0.902715i | ||||
\(166\) | 3.22407e6 | 0.704824 | ||||||||
\(167\) | 8.85321e6i | 1.90086i | 0.310932 | + | 0.950432i | \(0.399359\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(168\) | 4.22750e6 | 0.891572 | ||||||||
\(169\) | −5.88279e6 | −1.21877 | ||||||||
\(170\) | −1.54125e6 | −0.313708 | ||||||||
\(171\) | − | 8.75614e6i | − | 1.75116i | ||||||
\(172\) | − | 428425.i | − | 0.0841957i | ||||||
\(173\) | 2.78711e6i | 0.538290i | 0.963100 | + | 0.269145i | \(0.0867410\pi\) | ||||
−0.963100 | + | 0.269145i | \(0.913259\pi\) | |||||||
\(174\) | −3.53766e6 | −0.671535 | ||||||||
\(175\) | − | 4.82574e6i | − | 0.900430i | ||||||
\(176\) | −1.20176e6 | + | 642957.i | −0.220434 | + | 0.117935i | ||||
\(177\) | 1.39974e7 | 2.52422 | ||||||||
\(178\) | 4.55877e6i | 0.808328i | ||||||||
\(179\) | 2.05899e6 | 0.359001 | 0.179501 | − | 0.983758i | \(-0.442552\pi\) | ||||
0.179501 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(180\) | −4.95015e6 | −0.848791 | ||||||||
\(181\) | 2.44164e6 | 0.411762 | 0.205881 | − | 0.978577i | \(-0.433994\pi\) | ||||
0.205881 | + | 0.978577i | \(0.433994\pi\) | |||||||
\(182\) | − | 1.04144e7i | − | 1.72751i | ||||||
\(183\) | − | 2.23267e6i | − | 0.364310i | ||||||
\(184\) | 890449.i | 0.142941i | ||||||||
\(185\) | −4.25941e6 | −0.672720 | ||||||||
\(186\) | 1.03853e6i | 0.161391i | ||||||||
\(187\) | −1.09962e6 | − | 2.05532e6i | −0.168159 | − | 0.314307i | ||||
\(188\) | −4.03033e6 | −0.606551 | ||||||||
\(189\) | 6.19663e6i | 0.917846i | ||||||||
\(190\) | 7.74979e6 | 1.12987 | ||||||||
\(191\) | 1.46170e6 | 0.209778 | 0.104889 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104889 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(192\) | 1.36030e6 | 0.192190 | ||||||||
\(193\) | − | 7.05871e6i | − | 0.981869i | −0.871196 | − | 0.490935i | \(-0.836655\pi\) | ||
0.871196 | − | 0.490935i | \(-0.163345\pi\) | |||||||
\(194\) | 5.66721e6i | 0.776183i | ||||||||
\(195\) | 2.11352e7i | 2.85038i | ||||||||
\(196\) | 6.36264e6 | 0.845024 | ||||||||
\(197\) | − | 8.27203e6i | − | 1.08197i | −0.841034 | − | 0.540983i | \(-0.818052\pi\) | ||
0.841034 | − | 0.540983i | \(-0.181948\pi\) | |||||||
\(198\) | −3.53175e6 | − | 6.60124e6i | −0.454982 | − | 0.850413i | ||||
\(199\) | −1.24256e6 | −0.157673 | −0.0788366 | − | 0.996888i | \(-0.525121\pi\) | ||||
−0.0788366 | + | 0.996888i | \(0.525121\pi\) | |||||||
\(200\) | − | 1.55280e6i | − | 0.194100i | ||||||
\(201\) | −6.39254e6 | −0.787201 | ||||||||
\(202\) | −1.81027e6 | −0.219628 | ||||||||
\(203\) | −8.47482e6 | −1.01308 | ||||||||
\(204\) | 2.32647e6i | 0.274035i | ||||||||
\(205\) | 6.24318e6i | 0.724676i | ||||||||
\(206\) | 1.06759e7i | 1.22124i | ||||||||
\(207\) | −4.89122e6 | −0.551450 | ||||||||
\(208\) | − | 3.35109e6i | − | 0.372389i | ||||||
\(209\) | 5.52919e6 | + | 1.03347e7i | 0.605652 | + | 1.13203i | ||||
\(210\) | −2.05527e7 | −2.21928 | ||||||||
\(211\) | − | 1.63465e7i | − | 1.74011i | −0.492953 | − | 0.870056i | \(-0.664083\pi\) | ||
0.492953 | − | 0.870056i | \(-0.335917\pi\) | |||||||
\(212\) | −3.20382e6 | −0.336249 | ||||||||
\(213\) | −4.90009e6 | −0.507067 | ||||||||
\(214\) | 6.87462e6 | 0.701467 | ||||||||
\(215\) | 2.08286e6i | 0.209578i | ||||||||
\(216\) | 1.99391e6i | 0.197854i | ||||||||
\(217\) | 2.48790e6i | 0.243475i | ||||||||
\(218\) | 4.22847e6 | 0.408144 | ||||||||
\(219\) | 1.67044e7i | 1.59037i | ||||||||
\(220\) | 5.84255e6 | − | 3.12584e6i | 0.548699 | − | 0.293562i | ||||
\(221\) | 5.73124e6 | 0.530972 | ||||||||
\(222\) | 6.42946e6i | 0.587646i | ||||||||
\(223\) | 1.29219e7 | 1.16523 | 0.582615 | − | 0.812748i | \(-0.302030\pi\) | ||||
0.582615 | + | 0.812748i | \(0.302030\pi\) | |||||||
\(224\) | 3.25874e6 | 0.289938 | ||||||||
\(225\) | 8.52949e6 | 0.748817 | ||||||||
\(226\) | 3.39368e6i | 0.293998i | ||||||||
\(227\) | 4.31943e6i | 0.369274i | 0.982807 | + | 0.184637i | \(0.0591109\pi\) | ||||
−0.982807 | + | 0.184637i | \(0.940889\pi\) | |||||||
\(228\) | − | 1.16981e7i | − | 0.986984i | ||||||
\(229\) | −1.73096e7 | −1.44138 | −0.720692 | − | 0.693255i | \(-0.756176\pi\) | ||||
−0.720692 | + | 0.693255i | \(0.756176\pi\) | |||||||
\(230\) | − | 4.32907e6i | − | 0.355804i | ||||||
\(231\) | −1.46636e7 | − | 2.74079e7i | −1.18961 | − | 2.22352i | ||||
\(232\) | −2.72698e6 | −0.218382 | ||||||||
\(233\) | − | 1.81640e7i | − | 1.43596i | −0.696063 | − | 0.717981i | \(-0.745067\pi\) | ||
0.696063 | − | 0.717981i | \(-0.254933\pi\) | |||||||
\(234\) | 1.84075e7 | 1.43664 | ||||||||
\(235\) | 1.95941e7 | 1.50981 | ||||||||
\(236\) | 1.07898e7 | 0.820873 | ||||||||
\(237\) | − | 2.32974e7i | − | 1.75010i | ||||||
\(238\) | 5.57328e6i | 0.413409i | ||||||||
\(239\) | − | 1.63745e6i | − | 0.119943i | −0.998200 | − | 0.0599716i | \(-0.980899\pi\) | ||
0.998200 | − | 0.0599716i | \(-0.0191010\pi\) | |||||||
\(240\) | −6.61333e6 | −0.478395 | ||||||||
\(241\) | 1.08289e7i | 0.773633i | 0.922157 | + | 0.386816i | \(0.126425\pi\) | ||||
−0.922157 | + | 0.386816i | \(0.873575\pi\) | |||||||
\(242\) | 8.33689e6 | + | 5.56111e6i | 0.588245 | + | 0.392388i | ||||
\(243\) | 1.91391e7 | 1.33384 | ||||||||
\(244\) | − | 1.72103e6i | − | 0.118473i | ||||||
\(245\) | −3.09330e7 | −2.10341 | ||||||||
\(246\) | 9.42389e6 | 0.633031 | ||||||||
\(247\) | −2.88182e7 | −1.91239 | ||||||||
\(248\) | 800543.i | 0.0524843i | ||||||||
\(249\) | 2.36600e7i | 1.53256i | ||||||||
\(250\) | − | 6.20169e6i | − | 0.396908i | ||||||
\(251\) | 1.79196e7 | 1.13320 | 0.566601 | − | 0.823993i | \(-0.308258\pi\) | ||||
0.566601 | + | 0.823993i | \(0.308258\pi\) | |||||||
\(252\) | 1.79002e7i | 1.11855i | ||||||||
\(253\) | 5.77299e6 | − | 3.08863e6i | 0.356484 | − | 0.190724i | ||||
\(254\) | −1.63304e7 | −0.996545 | ||||||||
\(255\) | − | 1.13105e7i | − | 0.682121i | ||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | −2.11042e7 | −1.24328 | −0.621641 | − | 0.783302i | \(-0.713534\pi\) | ||||
−0.621641 | + | 0.783302i | \(0.713534\pi\) | |||||||
\(258\) | 3.14402e6 | 0.183074 | ||||||||
\(259\) | 1.54024e7i | 0.886522i | ||||||||
\(260\) | 1.62919e7i | 0.926941i | ||||||||
\(261\) | − | 1.49792e7i | − | 0.842496i | ||||||
\(262\) | −5.67010e6 | −0.315273 | ||||||||
\(263\) | − | 2.18105e7i | − | 1.19894i | −0.800396 | − | 0.599472i | \(-0.795377\pi\) | ||
0.800396 | − | 0.599472i | \(-0.204623\pi\) | |||||||
\(264\) | −4.71837e6 | − | 8.81916e6i | −0.256437 | − | 0.479309i | ||||
\(265\) | 1.55759e7 | 0.836982 | ||||||||
\(266\) | − | 2.80239e7i | − | 1.48896i | ||||||
\(267\) | −3.34547e7 | −1.75762 | ||||||||
\(268\) | −4.92764e6 | −0.255997 | ||||||||
\(269\) | 2.11114e7 | 1.08458 | 0.542288 | − | 0.840192i | \(-0.317558\pi\) | ||||
0.542288 | + | 0.840192i | \(0.317558\pi\) | |||||||
\(270\) | − | 9.69374e6i | − | 0.492493i | ||||||
\(271\) | 3.75101e7i | 1.88469i | 0.334640 | + | 0.942346i | \(0.391385\pi\) | ||||
−0.334640 | + | 0.942346i | \(0.608615\pi\) | |||||||
\(272\) | 1.79334e6i | 0.0891159i | ||||||||
\(273\) | 7.64268e7 | 3.75628 | ||||||||
\(274\) | − | 2.35298e6i | − | 0.114384i | ||||||
\(275\) | −1.00672e7 | + | 5.38607e6i | −0.484071 | + | 0.258985i | ||||
\(276\) | −6.53460e6 | −0.310808 | ||||||||
\(277\) | 4.60892e6i | 0.216850i | 0.994105 | + | 0.108425i | \(0.0345808\pi\) | ||||
−0.994105 | + | 0.108425i | \(0.965419\pi\) | |||||||
\(278\) | −1.77332e7 | −0.825378 | ||||||||
\(279\) | −4.39737e6 | −0.202479 | ||||||||
\(280\) | −1.58429e7 | −0.721706 | ||||||||
\(281\) | 2.57781e7i | 1.16180i | 0.813975 | + | 0.580900i | \(0.197299\pi\) | ||||
−0.813975 | + | 0.580900i | \(0.802701\pi\) | |||||||
\(282\) | − | 2.95768e7i | − | 1.31887i | ||||||
\(283\) | − | 4.26850e6i | − | 0.188328i | −0.995557 | − | 0.0941642i | \(-0.969982\pi\) | ||
0.995557 | − | 0.0941642i | \(-0.0300179\pi\) | |||||||
\(284\) | −3.77719e6 | −0.164897 | ||||||||
\(285\) | 5.68722e7i | 2.45678i | ||||||||
\(286\) | −2.17259e7 | + | 1.16237e7i | −0.928711 | + | 0.496873i | ||||
\(287\) | 2.25759e7 | 0.954990 | ||||||||
\(288\) | 5.75981e6i | 0.241119i | ||||||||
\(289\) | 2.10705e7 | 0.872934 | ||||||||
\(290\) | 1.32577e7 | 0.543592 | ||||||||
\(291\) | −4.15891e7 | −1.68772 | ||||||||
\(292\) | 1.28764e7i | 0.517187i | ||||||||
\(293\) | − | 2.82205e7i | − | 1.12192i | −0.827843 | − | 0.560959i | \(-0.810432\pi\) | ||
0.827843 | − | 0.560959i | \(-0.189568\pi\) | |||||||
\(294\) | 4.66925e7i | 1.83741i | ||||||||
\(295\) | −5.24563e7 | −2.04330 | ||||||||
\(296\) | 4.95609e6i | 0.191102i | ||||||||
\(297\) | 1.29270e7 | − | 6.91613e6i | 0.493434 | − | 0.263994i | ||||
\(298\) | 6.37490e6 | 0.240893 | ||||||||
\(299\) | 1.60980e7i | 0.602223i | ||||||||
\(300\) | 1.13953e7 | 0.422047 | ||||||||
\(301\) | 7.53181e6 | 0.276185 | ||||||||
\(302\) | 3.09519e7 | 1.12374 | ||||||||
\(303\) | − | 1.32847e7i | − | 0.477556i | ||||||
\(304\) | − | 9.01737e6i | − | 0.320966i | ||||||
\(305\) | 8.36709e6i | 0.294900i | ||||||||
\(306\) | −9.85076e6 | −0.343800 | ||||||||
\(307\) | − | 5.22991e7i | − | 1.80750i | −0.428057 | − | 0.903752i | \(-0.640802\pi\) | ||
0.428057 | − | 0.903752i | \(-0.359198\pi\) | |||||||
\(308\) | −1.13033e7 | − | 2.11272e7i | −0.386860 | − | 0.723085i | ||||
\(309\) | −7.83453e7 | −2.65545 | ||||||||
\(310\) | − | 3.89197e6i | − | 0.130643i | ||||||
\(311\) | 4.28332e7 | 1.42396 | 0.711982 | − | 0.702197i | \(-0.247798\pi\) | ||||
0.711982 | + | 0.702197i | \(0.247798\pi\) | |||||||
\(312\) | 2.45922e7 | 0.809716 | ||||||||
\(313\) | 3.32457e7 | 1.08418 | 0.542091 | − | 0.840320i | \(-0.317633\pi\) | ||||
0.542091 | + | 0.840320i | \(0.317633\pi\) | |||||||
\(314\) | − | 2.85671e7i | − | 0.922736i | ||||||
\(315\) | − | 8.70247e7i | − | 2.78427i | ||||||
\(316\) | − | 1.79586e7i | − | 0.569129i | ||||||
\(317\) | 1.49771e7 | 0.470166 | 0.235083 | − | 0.971975i | \(-0.424464\pi\) | ||||
0.235083 | + | 0.971975i | \(0.424464\pi\) | |||||||
\(318\) | − | 2.35114e7i | − | 0.731134i | ||||||
\(319\) | 9.45885e6 | + | 1.76796e7i | 0.291384 | + | 0.544630i | ||||
\(320\) | −5.09783e6 | −0.155573 | ||||||||
\(321\) | 5.04497e7i | 1.52526i | ||||||||
\(322\) | −1.56543e7 | −0.468884 | ||||||||
\(323\) | 1.54220e7 | 0.457651 | ||||||||
\(324\) | 8.56345e6 | 0.251776 | ||||||||
\(325\) | − | 2.80722e7i | − | 0.817761i | ||||||
\(326\) | 2.04240e7i | 0.589505i | ||||||||
\(327\) | 3.10308e7i | 0.887462i | ||||||||
\(328\) | 7.26433e6 | 0.205861 | ||||||||
\(329\) | − | 7.08541e7i | − | 1.98965i | ||||||
\(330\) | 2.29391e7 | + | 4.28758e7i | 0.638316 | + | 1.19308i | ||||
\(331\) | −5.72143e6 | −0.157768 | −0.0788842 | − | 0.996884i | \(-0.525136\pi\) | ||||
−0.0788842 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(332\) | 1.82381e7i | 0.498386i | ||||||||
\(333\) | −2.72237e7 | −0.737250 | ||||||||
\(334\) | −5.00813e7 | −1.34411 | ||||||||
\(335\) | 2.39565e7 | 0.637220 | ||||||||
\(336\) | 2.39144e7i | 0.630436i | ||||||||
\(337\) | 3.20214e7i | 0.836664i | 0.908294 | + | 0.418332i | \(0.137385\pi\) | ||||
−0.908294 | + | 0.418332i | \(0.862615\pi\) | |||||||
\(338\) | − | 3.32781e7i | − | 0.861804i | ||||||
\(339\) | −2.49046e7 | −0.639266 | ||||||||
\(340\) | − | 8.71861e6i | − | 0.221825i | ||||||
\(341\) | 5.19011e6 | − | 2.77678e6i | 0.130892 | − | 0.0700291i | ||||
\(342\) | 4.95322e7 | 1.23825 | ||||||||
\(343\) | 4.56711e7i | 1.13177i | ||||||||
\(344\) | 2.42354e6 | 0.0595353 | ||||||||
\(345\) | 3.17691e7 | 0.773654 | ||||||||
\(346\) | −1.57663e7 | −0.380628 | ||||||||
\(347\) | 8.53561e6i | 0.204290i | 0.994770 | + | 0.102145i | \(0.0325705\pi\) | ||||
−0.994770 | + | 0.102145i | \(0.967429\pi\) | |||||||
\(348\) | − | 2.00120e7i | − | 0.474847i | ||||||
\(349\) | − | 1.70635e7i | − | 0.401414i | −0.979651 | − | 0.200707i | \(-0.935676\pi\) | ||
0.979651 | − | 0.200707i | \(-0.0643240\pi\) | |||||||
\(350\) | 2.72985e7 | 0.636700 | ||||||||
\(351\) | 3.60469e7i | 0.833578i | ||||||||
\(352\) | −3.63711e6 | − | 6.79817e6i | −0.0833929 | − | 0.155871i | ||||
\(353\) | −4.60075e7 | −1.04594 | −0.522968 | − | 0.852352i | \(-0.675175\pi\) | ||||
−0.522968 | + | 0.852352i | \(0.675175\pi\) | |||||||
\(354\) | 7.91812e7i | 1.78489i | ||||||||
\(355\) | 1.83635e7 | 0.410459 | ||||||||
\(356\) | −2.57883e7 | −0.571574 | ||||||||
\(357\) | −4.08998e7 | −0.898910 | ||||||||
\(358\) | 1.16474e7i | 0.253852i | ||||||||
\(359\) | − | 1.15691e7i | − | 0.250043i | −0.992154 | − | 0.125022i | \(-0.960100\pi\) | ||
0.992154 | − | 0.125022i | \(-0.0399001\pi\) | |||||||
\(360\) | − | 2.80023e7i | − | 0.600186i | ||||||
\(361\) | −3.05002e7 | −0.648307 | ||||||||
\(362\) | 1.38120e7i | 0.291160i | ||||||||
\(363\) | −4.08105e7 | + | 6.11807e7i | −0.853202 | + | 1.27907i | ||||
\(364\) | 5.89130e7 | 1.22154 | ||||||||
\(365\) | − | 6.26010e7i | − | 1.28737i | ||||||
\(366\) | 1.26299e7 | 0.257606 | ||||||||
\(367\) | −4.97883e6 | −0.100723 | −0.0503615 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503615 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(368\) | −5.03714e6 | −0.101074 | ||||||||
\(369\) | 3.99028e7i | 0.794190i | ||||||||
\(370\) | − | 2.40949e7i | − | 0.475685i | ||||||
\(371\) | − | 5.63239e7i | − | 1.10299i | ||||||
\(372\) | −5.87482e6 | −0.114121 | ||||||||
\(373\) | 2.36429e7i | 0.455590i | 0.973709 | + | 0.227795i | \(0.0731516\pi\) | ||||
−0.973709 | + | 0.227795i | \(0.926848\pi\) | |||||||
\(374\) | 1.16266e7 | − | 6.22041e6i | 0.222249 | − | 0.118906i | ||||
\(375\) | 4.55114e7 | 0.863030 | ||||||||
\(376\) | − | 2.27990e7i | − | 0.428896i | ||||||
\(377\) | −4.92996e7 | −0.920066 | ||||||||
\(378\) | −3.50534e7 | −0.649015 | ||||||||
\(379\) | 1.59004e7 | 0.292072 | 0.146036 | − | 0.989279i | \(-0.453348\pi\) | ||||
0.146036 | + | 0.989279i | \(0.453348\pi\) | |||||||
\(380\) | 4.38394e7i | 0.798940i | ||||||||
\(381\) | − | 1.19842e8i | − | 2.16687i | ||||||
\(382\) | 8.26865e6i | 0.148335i | ||||||||
\(383\) | −5.32888e7 | −0.948505 | −0.474252 | − | 0.880389i | \(-0.657282\pi\) | ||||
−0.474252 | + | 0.880389i | \(0.657282\pi\) | |||||||
\(384\) | 7.69502e6i | 0.135899i | ||||||||
\(385\) | 5.49530e7 | + | 1.02713e8i | 0.962962 | + | 1.79988i | ||||
\(386\) | 3.99301e7 | 0.694286 | ||||||||
\(387\) | 1.33125e7i | 0.229681i | ||||||||
\(388\) | −3.20586e7 | −0.548844 | ||||||||
\(389\) | −8.43359e7 | −1.43273 | −0.716363 | − | 0.697727i | \(-0.754195\pi\) | ||||
−0.716363 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(390\) | −1.19559e8 | −2.01552 | ||||||||
\(391\) | − | 8.61481e6i | − | 0.144117i | ||||||
\(392\) | 3.59925e7i | 0.597522i | ||||||||
\(393\) | − | 4.16102e7i | − | 0.685524i | ||||||
\(394\) | 4.67937e7 | 0.765065 | ||||||||
\(395\) | 8.73087e7i | 1.41666i | ||||||||
\(396\) | 3.73422e7 | − | 1.99786e7i | 0.601332 | − | 0.321721i | ||||
\(397\) | 1.39558e7 | 0.223040 | 0.111520 | − | 0.993762i | \(-0.464428\pi\) | ||||
0.111520 | + | 0.993762i | \(0.464428\pi\) | |||||||
\(398\) | − | 7.02898e6i | − | 0.111492i | ||||||
\(399\) | 2.05655e8 | 3.23758 | ||||||||
\(400\) | 8.78395e6 | 0.137249 | ||||||||
\(401\) | 5.35293e7 | 0.830153 | 0.415077 | − | 0.909786i | \(-0.363755\pi\) | ||||
0.415077 | + | 0.909786i | \(0.363755\pi\) | |||||||
\(402\) | − | 3.61617e7i | − | 0.556635i | ||||||
\(403\) | 1.44726e7i | 0.221122i | ||||||||
\(404\) | − | 1.02404e7i | − | 0.155301i | ||||||
\(405\) | −4.16327e7 | −0.626714 | ||||||||
\(406\) | − | 4.79408e7i | − | 0.716354i | ||||||
\(407\) | 3.21315e7 | − | 1.71908e7i | 0.476594 | − | 0.254984i | ||||
\(408\) | −1.31605e7 | −0.193772 | ||||||||
\(409\) | − | 6.32419e7i | − | 0.924347i | −0.886790 | − | 0.462173i | \(-0.847070\pi\) | ||
0.886790 | − | 0.462173i | \(-0.152930\pi\) | |||||||
\(410\) | −3.53167e7 | −0.512423 | ||||||||
\(411\) | 1.72674e7 | 0.248715 | ||||||||
\(412\) | −6.03918e7 | −0.863547 | ||||||||
\(413\) | 1.89686e8i | 2.69269i | ||||||||
\(414\) | − | 2.76689e7i | − | 0.389934i | ||||||
\(415\) | − | 8.86676e7i | − | 1.24057i | ||||||
\(416\) | 1.89567e7 | 0.263319 | ||||||||
\(417\) | − | 1.30136e8i | − | 1.79469i | ||||||
\(418\) | −5.84618e7 | + | 3.12778e7i | −0.800466 | + | 0.428260i | ||||
\(419\) | 9.31206e6 | 0.126591 | 0.0632956 | − | 0.997995i | \(-0.479839\pi\) | ||||
0.0632956 | + | 0.997995i | \(0.479839\pi\) | |||||||
\(420\) | − | 1.16264e8i | − | 1.56927i | ||||||
\(421\) | −2.19313e7 | −0.293912 | −0.146956 | − | 0.989143i | \(-0.546948\pi\) | ||||
−0.146956 | + | 0.989143i | \(0.546948\pi\) | |||||||
\(422\) | 9.24697e7 | 1.23044 | ||||||||
\(423\) | 1.25235e8 | 1.65464 | ||||||||
\(424\) | − | 1.81235e7i | − | 0.237764i | ||||||
\(425\) | 1.50228e7i | 0.195697i | ||||||||
\(426\) | − | 2.77191e7i | − | 0.358550i | ||||||
\(427\) | 3.02561e7 | 0.388624 | ||||||||
\(428\) | 3.88887e7i | 0.496012i | ||||||||
\(429\) | −8.53009e7 | − | 1.59437e8i | −1.08039 | − | 2.01937i | ||||
\(430\) | −1.17824e7 | −0.148194 | ||||||||
\(431\) | − | 4.16809e7i | − | 0.520601i | −0.965528 | − | 0.260300i | \(-0.916178\pi\) | ||
0.965528 | − | 0.260300i | \(-0.0838216\pi\) | |||||||
\(432\) | −1.12793e7 | −0.139904 | ||||||||
\(433\) | 1.37815e8 | 1.69760 | 0.848798 | − | 0.528718i | \(-0.177327\pi\) | ||||
0.848798 | + | 0.528718i | \(0.177327\pi\) | |||||||
\(434\) | −1.40737e7 | −0.172163 | ||||||||
\(435\) | 9.72919e7i | 1.18198i | ||||||||
\(436\) | 2.39198e7i | 0.288601i | ||||||||
\(437\) | 4.33175e7i | 0.519062i | ||||||||
\(438\) | −9.44944e7 | −1.12456 | ||||||||
\(439\) | 7.06075e7i | 0.834559i | 0.908778 | + | 0.417280i | \(0.137016\pi\) | ||||
−0.908778 | + | 0.417280i | \(0.862984\pi\) | |||||||
\(440\) | 1.76824e7 | + | 3.30504e7i | 0.207579 | + | 0.387989i | ||||
\(441\) | −1.97706e8 | −2.30518 | ||||||||
\(442\) | 3.24208e7i | 0.375454i | ||||||||
\(443\) | −4.33504e7 | −0.498634 | −0.249317 | − | 0.968422i | \(-0.580206\pi\) | ||||
−0.249317 | + | 0.968422i | \(0.580206\pi\) | |||||||
\(444\) | −3.63705e7 | −0.415528 | ||||||||
\(445\) | 1.25374e8 | 1.42275 | ||||||||
\(446\) | 7.30973e7i | 0.823942i | ||||||||
\(447\) | 4.67825e7i | 0.523794i | ||||||||
\(448\) | 1.84342e7i | 0.205017i | ||||||||
\(449\) | −4.32962e7 | −0.478312 | −0.239156 | − | 0.970981i | \(-0.576871\pi\) | ||||
−0.239156 | + | 0.970981i | \(0.576871\pi\) | |||||||
\(450\) | 4.82501e7i | 0.529493i | ||||||||
\(451\) | −2.51972e7 | − | 4.70964e7i | −0.274677 | − | 0.513402i | ||||
\(452\) | −1.91975e7 | −0.207888 | ||||||||
\(453\) | 2.27142e8i | 2.44344i | ||||||||
\(454\) | −2.44344e7 | −0.261116 | ||||||||
\(455\) | −2.86415e8 | −3.04062 | ||||||||
\(456\) | 6.61744e7 | 0.697903 | ||||||||
\(457\) | − | 1.73513e7i | − | 0.181796i | −0.995860 | − | 0.0908980i | \(-0.971026\pi\) | ||
0.995860 | − | 0.0908980i | \(-0.0289737\pi\) | |||||||
\(458\) | − | 9.79177e7i | − | 1.01921i | ||||||
\(459\) | − | 1.92905e7i | − | 0.199483i | ||||||
\(460\) | 2.44889e7 | 0.251591 | ||||||||
\(461\) | 3.21397e7i | 0.328050i | 0.986456 | + | 0.164025i | \(0.0524477\pi\) | ||||
−0.986456 | + | 0.164025i | \(0.947552\pi\) | |||||||
\(462\) | 1.55043e8 | − | 8.29499e7i | 1.57226 | − | 0.841182i | ||||
\(463\) | −1.40558e8 | −1.41616 | −0.708078 | − | 0.706134i | \(-0.750438\pi\) | ||||
−0.708078 | + | 0.706134i | \(0.750438\pi\) | |||||||
\(464\) | − | 1.54261e7i | − | 0.154420i | ||||||
\(465\) | 2.85614e7 | 0.284067 | ||||||||
\(466\) | 1.02751e8 | 1.01538 | ||||||||
\(467\) | −1.02465e8 | −1.00607 | −0.503033 | − | 0.864267i | \(-0.667782\pi\) | ||||
−0.503033 | + | 0.864267i | \(0.667782\pi\) | |||||||
\(468\) | 1.04129e8i | 1.01586i | ||||||||
\(469\) | − | 8.66289e7i | − | 0.839739i | ||||||
\(470\) | 1.10841e8i | 1.06760i | ||||||||
\(471\) | 2.09641e8 | 2.00638 | ||||||||
\(472\) | 6.10362e7i | 0.580445i | ||||||||
\(473\) | −8.40634e6 | − | 1.57124e7i | −0.0794372 | − | 0.148477i | ||||
\(474\) | 1.31790e8 | 1.23751 | ||||||||
\(475\) | − | 7.55387e7i | − | 0.704837i | ||||||
\(476\) | −3.15272e7 | −0.292324 | ||||||||
\(477\) | 9.95523e7 | 0.917268 | ||||||||
\(478\) | 9.26284e6 | 0.0848126 | ||||||||
\(479\) | − | 7.50766e7i | − | 0.683121i | −0.939860 | − | 0.341561i | \(-0.889045\pi\) | ||
0.939860 | − | 0.341561i | \(-0.110955\pi\) | |||||||
\(480\) | − | 3.74106e7i | − | 0.338276i | ||||||
\(481\) | 8.95986e7i | 0.805130i | ||||||||
\(482\) | −6.12577e7 | −0.547041 | ||||||||
\(483\) | − | 1.14880e8i | − | 1.01953i | ||||||
\(484\) | −3.14584e7 | + | 4.71606e7i | −0.277460 | + | 0.415952i | ||||
\(485\) | 1.55858e8 | 1.36617 | ||||||||
\(486\) | 1.08267e8i | 0.943165i | ||||||||
\(487\) | 2.45602e7 | 0.212640 | 0.106320 | − | 0.994332i | \(-0.466093\pi\) | ||||
0.106320 | + | 0.994332i | \(0.466093\pi\) | |||||||
\(488\) | 9.73564e6 | 0.0837732 | ||||||||
\(489\) | −1.49882e8 | −1.28181 | ||||||||
\(490\) | − | 1.74984e8i | − | 1.48734i | ||||||
\(491\) | 1.63937e8i | 1.38494i | 0.721444 | + | 0.692472i | \(0.243479\pi\) | ||||
−0.721444 | + | 0.692472i | \(0.756521\pi\) | |||||||
\(492\) | 5.33096e7i | 0.447620i | ||||||||
\(493\) | 2.63826e7 | 0.220180 | ||||||||
\(494\) | − | 1.63020e8i | − | 1.35226i | ||||||
\(495\) | −1.81546e8 | + | 9.71293e7i | −1.49682 | + | 0.800820i | ||||
\(496\) | −4.52855e6 | −0.0371120 | ||||||||
\(497\) | − | 6.64038e7i | − | 0.540909i | ||||||
\(498\) | −1.33841e8 | −1.08368 | ||||||||
\(499\) | −3.35715e7 | −0.270190 | −0.135095 | − | 0.990833i | \(-0.543134\pi\) | ||||
−0.135095 | + | 0.990833i | \(0.543134\pi\) | |||||||
\(500\) | 3.50820e7 | 0.280656 | ||||||||
\(501\) | − | 3.67524e8i | − | 2.92262i | ||||||
\(502\) | 1.01369e8i | 0.801294i | ||||||||
\(503\) | 4.18394e7i | 0.328762i | 0.986397 | + | 0.164381i | \(0.0525626\pi\) | ||||
−0.986397 | + | 0.164381i | \(0.947437\pi\) | |||||||
\(504\) | −1.01259e8 | −0.790935 | ||||||||
\(505\) | 4.97855e7i | 0.386570i | ||||||||
\(506\) | 1.74719e7 | + | 3.26570e7i | 0.134862 | + | 0.252072i | ||||
\(507\) | 2.44213e8 | 1.87389 | ||||||||
\(508\) | − | 9.23790e7i | − | 0.704664i | ||||||
\(509\) | 1.93657e8 | 1.46852 | 0.734260 | − | 0.678868i | \(-0.237529\pi\) | ||||
0.734260 | + | 0.678868i | \(0.237529\pi\) | |||||||
\(510\) | 6.39819e7 | 0.482333 | ||||||||
\(511\) | −2.26371e8 | −1.69651 | ||||||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 9.69976e7i | 0.718470i | ||||||||
\(514\) | − | 1.19384e8i | − | 0.879134i | ||||||
\(515\) | 2.93605e8 | 2.14952 | ||||||||
\(516\) | 1.77853e7i | 0.129453i | ||||||||
\(517\) | −1.47811e8 | + | 7.90811e7i | −1.06964 | + | 0.572270i | ||||
\(518\) | −8.71292e7 | −0.626866 | ||||||||
\(519\) | − | 1.15702e8i | − | 0.827632i | ||||||
\(520\) | −9.21609e7 | −0.655446 | ||||||||
\(521\) | 4.32733e6 | 0.0305990 | 0.0152995 | − | 0.999883i | \(-0.495130\pi\) | ||||
0.0152995 | + | 0.999883i | \(0.495130\pi\) | |||||||
\(522\) | 8.47353e7 | 0.595735 | ||||||||
\(523\) | − | 1.83961e8i | − | 1.28594i | −0.765892 | − | 0.642969i | \(-0.777702\pi\) | ||
0.765892 | − | 0.642969i | \(-0.222298\pi\) | |||||||
\(524\) | − | 3.20749e7i | − | 0.222932i | ||||||
\(525\) | 2.00331e8i | 1.38443i | ||||||||
\(526\) | 1.23379e8 | 0.847782 | ||||||||
\(527\) | − | 7.74500e6i | − | 0.0529163i | ||||||
\(528\) | 4.98887e7 | − | 2.66911e7i | 0.338922 | − | 0.181328i | ||||
\(529\) | −1.23839e8 | −0.836544 | ||||||||
\(530\) | 8.81107e7i | 0.591835i | ||||||||
\(531\) | −3.35271e8 | −2.23930 | ||||||||
\(532\) | 1.58527e8 | 1.05286 | ||||||||
\(533\) | 1.31328e8 | 0.867312 | ||||||||
\(534\) | − | 1.89249e8i | − | 1.24282i | ||||||
\(535\) | − | 1.89064e8i | − | 1.23466i | ||||||
\(536\) | − | 2.78749e7i | − | 0.181017i | ||||||
\(537\) | −8.54752e7 | −0.551972 | ||||||||
\(538\) | 1.19424e8i | 0.766912i | ||||||||
\(539\) | 2.33348e8 | − | 1.24844e8i | 1.49018 | − | 0.797266i | ||||
\(540\) | 5.48361e7 | 0.348245 | ||||||||
\(541\) | 8.76383e7i | 0.553480i | 0.960945 | + | 0.276740i | \(0.0892541\pi\) | ||||
−0.960945 | + | 0.276740i | \(0.910746\pi\) | |||||||
\(542\) | −2.12189e8 | −1.33268 | ||||||||
\(543\) | −1.01360e8 | −0.633093 | ||||||||
\(544\) | −1.01446e7 | −0.0630144 | ||||||||
\(545\) | − | 1.16290e8i | − | 0.718379i | ||||||
\(546\) | 4.32335e8i | 2.65609i | ||||||||
\(547\) | − | 4.38238e6i | − | 0.0267762i | −0.999910 | − | 0.0133881i | \(-0.995738\pi\) | ||
0.999910 | − | 0.0133881i | \(-0.00426169\pi\) | |||||||
\(548\) | 1.33104e7 | 0.0808818 | ||||||||
\(549\) | 5.34777e7i | 0.323188i | ||||||||
\(550\) | −3.04682e7 | − | 5.69485e7i | −0.183130 | − | 0.342290i | ||||
\(551\) | −1.32659e8 | −0.793015 | ||||||||
\(552\) | − | 3.69653e7i | − | 0.219774i | ||||||
\(553\) | 3.15716e8 | 1.86690 | ||||||||
\(554\) | −2.60720e7 | −0.153336 | ||||||||
\(555\) | 1.76821e8 | 1.03432 | ||||||||
\(556\) | − | 1.00314e8i | − | 0.583631i | ||||||
\(557\) | 2.44031e8i | 1.41214i | 0.708140 | + | 0.706072i | \(0.249534\pi\) | ||||
−0.708140 | + | 0.706072i | \(0.750466\pi\) | |||||||
\(558\) | − | 2.48753e7i | − | 0.143174i | ||||||
\(559\) | 4.38139e7 | 0.250828 | ||||||||
\(560\) | − | 8.96209e7i | − | 0.510323i | ||||||
\(561\) | 4.56487e7 | + | 8.53226e7i | 0.258547 | + | 0.483254i | ||||
\(562\) | −1.45823e8 | −0.821517 | ||||||||
\(563\) | 3.18995e8i | 1.78755i | 0.448511 | + | 0.893777i | \(0.351955\pi\) | ||||
−0.448511 | + | 0.893777i | \(0.648045\pi\) | |||||||
\(564\) | 1.67312e8 | 0.932585 | ||||||||
\(565\) | 9.33320e7 | 0.517470 | ||||||||
\(566\) | 2.41463e7 | 0.133168 | ||||||||
\(567\) | 1.50547e8i | 0.825893i | ||||||||
\(568\) | − | 2.13670e7i | − | 0.116600i | ||||||
\(569\) | 4.87047e6i | 0.0264383i | 0.999913 | + | 0.0132192i | \(0.00420791\pi\) | ||||
−0.999913 | + | 0.0132192i | \(0.995792\pi\) | |||||||
\(570\) | −3.21718e8 | −1.73720 | ||||||||
\(571\) | 6.19484e7i | 0.332753i | 0.986062 | + | 0.166376i | \(0.0532067\pi\) | ||||
−0.986062 | + | 0.166376i | \(0.946793\pi\) | |||||||
\(572\) | −6.57535e7 | − | 1.22901e8i | −0.351342 | − | 0.656698i | ||||
\(573\) | −6.06798e7 | −0.322538 | ||||||||
\(574\) | 1.27708e8i | 0.675280i | ||||||||
\(575\) | −4.21963e7 | −0.221958 | ||||||||
\(576\) | −3.25824e7 | −0.170497 | ||||||||
\(577\) | −1.94815e7 | −0.101413 | −0.0507066 | − | 0.998714i | \(-0.516147\pi\) | ||||
−0.0507066 | + | 0.998714i | \(0.516147\pi\) | |||||||
\(578\) | 1.19193e8i | 0.617257i | ||||||||
\(579\) | 2.93029e8i | 1.50965i | ||||||||
\(580\) | 7.49966e7i | 0.384377i | ||||||||
\(581\) | −3.20630e8 | −1.63484 | ||||||||
\(582\) | − | 2.35263e8i | − | 1.19340i | ||||||
\(583\) | −1.17499e8 | + | 6.28638e7i | −0.592966 | + | 0.317245i | ||||
\(584\) | −7.28402e7 | −0.365706 | ||||||||
\(585\) | − | 5.06238e8i | − | 2.52864i | ||||||
\(586\) | 1.59639e8 | 0.793316 | ||||||||
\(587\) | −2.18801e8 | −1.08177 | −0.540885 | − | 0.841097i | \(-0.681911\pi\) | ||||
−0.540885 | + | 0.841097i | \(0.681911\pi\) | |||||||
\(588\) | −2.64133e8 | −1.29924 | ||||||||
\(589\) | 3.89439e7i | 0.190587i | ||||||||
\(590\) | − | 2.96738e8i | − | 1.44483i | ||||||
\(591\) | 3.43397e8i | 1.66354i | ||||||||
\(592\) | −2.80359e7 | −0.135129 | ||||||||
\(593\) | − | 1.46841e8i | − | 0.704177i | −0.935967 | − | 0.352089i | \(-0.885472\pi\) | ||
0.935967 | − | 0.352089i | \(-0.114528\pi\) | |||||||
\(594\) | 3.91235e7 | + | 7.31262e7i | 0.186672 | + | 0.348910i | ||||
\(595\) | 1.53275e8 | 0.727646 | ||||||||
\(596\) | 3.60619e7i | 0.170337i | ||||||||
\(597\) | 5.15825e7 | 0.242426 | ||||||||
\(598\) | −9.10638e7 | −0.425836 | ||||||||
\(599\) | 3.42767e8 | 1.59485 | 0.797423 | − | 0.603421i | \(-0.206196\pi\) | ||||
0.797423 | + | 0.603421i | \(0.206196\pi\) | |||||||
\(600\) | 6.44614e7i | 0.298433i | ||||||||
\(601\) | 3.62306e8i | 1.66898i | 0.551020 | + | 0.834492i | \(0.314239\pi\) | ||||
−0.551020 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(602\) | 4.26063e7i | 0.195292i | ||||||||
\(603\) | 1.53116e8 | 0.698345 | ||||||||
\(604\) | 1.75090e8i | 0.794605i | ||||||||
\(605\) | 1.52940e8 | − | 2.29279e8i | 0.690646 | − | 1.03538i | ||||
\(606\) | 7.51497e7 | 0.337683 | ||||||||
\(607\) | − | 2.33328e8i | − | 1.04328i | −0.853165 | − | 0.521640i | \(-0.825320\pi\) | ||
0.853165 | − | 0.521640i | \(-0.174680\pi\) | |||||||
\(608\) | 5.10099e7 | 0.226957 | ||||||||
\(609\) | 3.51816e8 | 1.55763 | ||||||||
\(610\) | −4.73314e7 | −0.208526 | ||||||||
\(611\) | − | 4.12171e8i | − | 1.80698i | ||||||
\(612\) | − | 5.57243e7i | − | 0.243103i | ||||||
\(613\) | − | 3.55486e8i | − | 1.54327i | −0.636066 | − | 0.771634i | \(-0.719440\pi\) | ||
0.636066 | − | 0.771634i | \(-0.280560\pi\) | |||||||
\(614\) | 2.95848e8 | 1.27810 | ||||||||
\(615\) | − | 2.59173e8i | − | 1.11421i | ||||||
\(616\) | 1.19513e8 | − | 6.39412e7i | 0.511298 | − | 0.273551i | ||||
\(617\) | −2.02737e8 | −0.863132 | −0.431566 | − | 0.902081i | \(-0.642039\pi\) | ||||
−0.431566 | + | 0.902081i | \(0.642039\pi\) | |||||||
\(618\) | − | 4.43188e8i | − | 1.87768i | ||||||
\(619\) | −2.08625e8 | −0.879618 | −0.439809 | − | 0.898091i | \(-0.644954\pi\) | ||||
−0.439809 | + | 0.898091i | \(0.644954\pi\) | |||||||
\(620\) | 2.20163e7 | 0.0923782 | ||||||||
\(621\) | 5.41833e7 | 0.226251 | ||||||||
\(622\) | 2.42301e8i | 1.00689i | ||||||||
\(623\) | − | 4.53364e8i | − | 1.87492i | ||||||
\(624\) | 1.39114e8i | 0.572556i | ||||||||
\(625\) | −3.04590e8 | −1.24760 | ||||||||
\(626\) | 1.88066e8i | 0.766632i | ||||||||
\(627\) | −2.29534e8 | − | 4.29024e8i | −0.931203 | − | 1.74052i | ||||
\(628\) | 1.61600e8 | 0.652473 | ||||||||
\(629\) | − | 4.79486e7i | − | 0.192675i | ||||||
\(630\) | 4.92286e8 | 1.96877 | ||||||||
\(631\) | −4.31963e8 | −1.71933 | −0.859663 | − | 0.510861i | \(-0.829327\pi\) | ||||
−0.859663 | + | 0.510861i | \(0.829327\pi\) | |||||||
\(632\) | 1.01589e8 | 0.402435 | ||||||||
\(633\) | 6.78593e8i | 2.67546i | ||||||||
\(634\) | 8.47235e7i | 0.332458i | ||||||||
\(635\) | 4.49116e8i | 1.75403i | ||||||||
\(636\) | 1.33000e8 | 0.516990 | ||||||||
\(637\) | 6.50690e8i | 2.51742i | ||||||||
\(638\) | −1.00011e8 | + | 5.35073e7i | −0.385111 | + | 0.206040i | ||||
\(639\) | 1.17369e8 | 0.449831 | ||||||||
\(640\) | − | 2.88377e7i | − | 0.110007i | ||||||
\(641\) | 8.83907e7 | 0.335608 | 0.167804 | − | 0.985820i | \(-0.446332\pi\) | ||||
0.167804 | + | 0.985820i | \(0.446332\pi\) | |||||||
\(642\) | −2.85387e8 | −1.07852 | ||||||||
\(643\) | −3.44806e8 | −1.29701 | −0.648503 | − | 0.761212i | \(-0.724605\pi\) | ||||
−0.648503 | + | 0.761212i | \(0.724605\pi\) | |||||||
\(644\) | − | 8.85540e7i | − | 0.331551i | ||||||
\(645\) | − | 8.64660e7i | − | 0.322230i | ||||||
\(646\) | 8.72402e7i | 0.323608i | ||||||||
\(647\) | 5.41898e7 | 0.200081 | 0.100040 | − | 0.994983i | \(-0.468103\pi\) | ||||
0.100040 | + | 0.994983i | \(0.468103\pi\) | |||||||
\(648\) | 4.84422e7i | 0.178032i | ||||||||
\(649\) | 3.95712e8 | − | 2.11711e8i | 1.44759 | − | 0.774480i | ||||
\(650\) | 1.58800e8 | 0.578245 | ||||||||
\(651\) | − | 1.03281e8i | − | 0.374348i | ||||||
\(652\) | −1.15535e8 | −0.416843 | ||||||||
\(653\) | 5.00498e8 | 1.79747 | 0.898737 | − | 0.438488i | \(-0.144486\pi\) | ||||
0.898737 | + | 0.438488i | \(0.144486\pi\) | |||||||
\(654\) | −1.75537e8 | −0.627530 | ||||||||
\(655\) | 1.55938e8i | 0.554915i | ||||||||
\(656\) | 4.10932e7i | 0.145566i | ||||||||
\(657\) | − | 4.00110e8i | − | 1.41086i | ||||||
\(658\) | 4.00811e8 | 1.40690 | ||||||||
\(659\) | − | 1.49050e7i | − | 0.0520804i | −0.999661 | − | 0.0260402i | \(-0.991710\pi\) | ||
0.999661 | − | 0.0260402i | \(-0.00828979\pi\) | |||||||
\(660\) | −2.42542e8 | + | 1.29763e8i | −0.843637 | + | 0.451357i | ||||
\(661\) | 4.79576e8 | 1.66056 | 0.830278 | − | 0.557350i | \(-0.188182\pi\) | ||||
0.830278 | + | 0.557350i | \(0.188182\pi\) | |||||||
\(662\) | − | 3.23653e7i | − | 0.111559i | ||||||
\(663\) | −2.37921e8 | −0.816381 | ||||||||
\(664\) | −1.03170e8 | −0.352412 | ||||||||
\(665\) | −7.70707e8 | −2.62074 | ||||||||
\(666\) | − | 1.54001e8i | − | 0.521315i | ||||||
\(667\) | 7.41038e7i | 0.249726i | ||||||||
\(668\) | − | 2.83303e8i | − | 0.950432i | ||||||
\(669\) | −5.36428e8 | −1.79157 | ||||||||
\(670\) | 1.35519e8i | 0.450583i | ||||||||
\(671\) | −3.37692e7 | − | 6.31185e7i | −0.111777 | − | 0.208924i | ||||
\(672\) | −1.35280e8 | −0.445786 | ||||||||
\(673\) | 4.12777e8i | 1.35416i | 0.735908 | + | 0.677081i | \(0.236755\pi\) | ||||
−0.735908 | + | 0.677081i | \(0.763245\pi\) | |||||||
\(674\) | −1.81141e8 | −0.591611 | ||||||||
\(675\) | −9.44868e7 | −0.307227 | ||||||||
\(676\) | 1.88249e8 | 0.609387 | ||||||||
\(677\) | − | 1.79192e8i | − | 0.577500i | −0.957405 | − | 0.288750i | \(-0.906760\pi\) | ||
0.957405 | − | 0.288750i | \(-0.0932396\pi\) | |||||||
\(678\) | − | 1.40882e8i | − | 0.452029i | ||||||
\(679\) | − | 5.63596e8i | − | 1.80036i | ||||||
\(680\) | 4.93199e7 | 0.156854 | ||||||||
\(681\) | − | 1.79313e8i | − | 0.567766i | ||||||
\(682\) | 1.57078e7 | + | 2.93597e7i | 0.0495180 | + | 0.0925547i | ||||
\(683\) | 3.83703e8 | 1.20430 | 0.602148 | − | 0.798384i | \(-0.294312\pi\) | ||||
0.602148 | + | 0.798384i | \(0.294312\pi\) | |||||||
\(684\) | 2.80197e8i | 0.875578i | ||||||||
\(685\) | −6.47109e7 | −0.201329 | ||||||||
\(686\) | −2.58355e8 | −0.800284 | ||||||||
\(687\) | 7.18573e8 | 2.21616 | ||||||||
\(688\) | 1.37096e7i | 0.0420978i | ||||||||
\(689\) | − | 3.27646e8i | − | 1.00172i | ||||||
\(690\) | 1.79713e8i | 0.547056i | ||||||||
\(691\) | −5.62227e8 | −1.70403 | −0.852015 | − | 0.523517i | \(-0.824619\pi\) | ||||
−0.852015 | + | 0.523517i | \(0.824619\pi\) | |||||||
\(692\) | − | 8.91876e7i | − | 0.269145i | ||||||
\(693\) | 3.51228e8 | + | 6.56484e8i | 1.05533 | + | 1.97253i | ||||
\(694\) | −4.82847e7 | −0.144455 | ||||||||
\(695\) | 4.87694e8i | 1.45276i | ||||||||
\(696\) | 1.13205e8 | 0.335767 | ||||||||
\(697\) | −7.02801e7 | −0.207555 | ||||||||
\(698\) | 9.65260e7 | 0.283843 | ||||||||
\(699\) | 7.54042e8i | 2.20782i | ||||||||
\(700\) | 1.54424e8i | 0.450215i | ||||||||
\(701\) | 8.52636e7i | 0.247520i | 0.992312 | + | 0.123760i | \(0.0394952\pi\) | ||||
−0.992312 | + | 0.123760i | \(0.960505\pi\) | |||||||
\(702\) | −2.03912e8 | −0.589429 | ||||||||
\(703\) | 2.41098e8i | 0.693950i | ||||||||
\(704\) | 3.84563e7 | − | 2.05746e7i | 0.110217 | − | 0.0589677i | ||||
\(705\) | −8.13413e8 | −2.32137 | ||||||||
\(706\) | − | 2.60258e8i | − | 0.739588i | ||||||
\(707\) | 1.80029e8 | 0.509428 | ||||||||
\(708\) | −4.47917e8 | −1.26211 | ||||||||
\(709\) | 1.23402e8 | 0.346246 | 0.173123 | − | 0.984900i | \(-0.444614\pi\) | ||||
0.173123 | + | 0.984900i | \(0.444614\pi\) | |||||||
\(710\) | 1.03879e8i | 0.290238i | ||||||||
\(711\) | 5.58027e8i | 1.55255i | ||||||||
\(712\) | − | 1.45881e8i | − | 0.404164i | ||||||
\(713\) | 2.17542e7 | 0.0600171 | ||||||||
\(714\) | − | 2.31364e8i | − | 0.635625i | ||||||
\(715\) | 3.19672e8 | + | 5.97502e8i | 0.874552 | + | 1.63464i | ||||
\(716\) | −6.58878e7 | −0.179501 | ||||||||
\(717\) | 6.79758e7i | 0.184415i | ||||||||
\(718\) | 6.54446e7 | 0.176807 | ||||||||
\(719\) | 4.85475e8 | 1.30611 | 0.653056 | − | 0.757310i | \(-0.273487\pi\) | ||||
0.653056 | + | 0.757310i | \(0.273487\pi\) | |||||||
\(720\) | 1.58405e8 | 0.424396 | ||||||||
\(721\) | − | 1.06170e9i | − | 2.83267i | ||||||
\(722\) | − | 1.72535e8i | − | 0.458422i | ||||||
\(723\) | − | 4.49543e8i | − | 1.18948i | ||||||
\(724\) | −7.81326e7 | −0.205881 | ||||||||
\(725\) | − | 1.29225e8i | − | 0.339104i | ||||||
\(726\) | −3.46090e8 | − | 2.30859e8i | −0.904439 | − | 0.603305i | ||||
\(727\) | 3.27708e7 | 0.0852871 | 0.0426436 | − | 0.999090i | \(-0.486422\pi\) | ||||
0.0426436 | + | 0.999090i | \(0.486422\pi\) | |||||||
\(728\) | 3.33262e8i | 0.863757i | ||||||||
\(729\) | −5.99437e8 | −1.54725 | ||||||||
\(730\) | 3.54125e8 | 0.910307 | ||||||||
\(731\) | −2.34470e7 | −0.0600254 | ||||||||
\(732\) | 7.14454e7i | 0.182155i | ||||||||
\(733\) | − | 6.33574e8i | − | 1.60874i | −0.594130 | − | 0.804369i | \(-0.702504\pi\) | ||
0.594130 | − | 0.804369i | \(-0.297496\pi\) | |||||||
\(734\) | − | 2.81645e7i | − | 0.0712219i | ||||||
\(735\) | 1.28413e9 | 3.23404 | ||||||||
\(736\) | − | 2.84944e7i | − | 0.0714703i | ||||||
\(737\) | −1.80720e8 | + | 9.66876e7i | −0.451443 | + | 0.241528i | ||||
\(738\) | −2.25724e8 | −0.561577 | ||||||||
\(739\) | − | 2.55770e8i | − | 0.633747i | −0.948468 | − | 0.316873i | \(-0.897367\pi\) | ||
0.948468 | − | 0.316873i | \(-0.102633\pi\) | |||||||
\(740\) | 1.36301e8 | 0.336360 | ||||||||
\(741\) | 1.19633e9 | 2.94034 | ||||||||
\(742\) | 3.18616e8 | 0.779930 | ||||||||
\(743\) | 1.05929e8i | 0.258254i | 0.991628 | + | 0.129127i | \(0.0412175\pi\) | ||||
−0.991628 | + | 0.129127i | \(0.958782\pi\) | |||||||
\(744\) | − | 3.32330e7i | − | 0.0806957i | ||||||
\(745\) | − | 1.75321e8i | − | 0.423999i | ||||||
\(746\) | −1.33744e8 | −0.322151 | ||||||||
\(747\) | − | 5.66713e8i | − | 1.35957i | ||||||
\(748\) | 3.51879e7 | + | 6.57702e7i | 0.0840793 | + | 0.157154i | ||||
\(749\) | −6.83672e8 | −1.62706 | ||||||||
\(750\) | 2.57451e8i | 0.610255i | ||||||||
\(751\) | 2.47361e8 | 0.583999 | 0.292000 | − | 0.956418i | \(-0.405679\pi\) | ||||
0.292000 | + | 0.956418i | \(0.405679\pi\) | |||||||
\(752\) | 1.28971e8 | 0.303275 | ||||||||
\(753\) | −7.43897e8 | −1.74232 | ||||||||
\(754\) | − | 2.78880e8i | − | 0.650585i | ||||||
\(755\) | − | 8.51231e8i | − | 1.97791i | ||||||
\(756\) | − | 1.98292e8i | − | 0.458923i | ||||||
\(757\) | −1.73783e8 | −0.400608 | −0.200304 | − | 0.979734i | \(-0.564193\pi\) | ||||
−0.200304 | + | 0.979734i | \(0.564193\pi\) | |||||||
\(758\) | 8.99462e7i | 0.206526i | ||||||||
\(759\) | −2.39655e8 | + | 1.28219e8i | −0.548101 | + | 0.293242i | ||||
\(760\) | −2.47993e8 | −0.564936 | ||||||||
\(761\) | − | 1.14915e7i | − | 0.0260748i | −0.999915 | − | 0.0130374i | \(-0.995850\pi\) | ||
0.999915 | − | 0.0130374i | \(-0.00415005\pi\) | |||||||
\(762\) | 6.77927e8 | 1.53221 | ||||||||
\(763\) | −4.20516e8 | −0.946691 | ||||||||
\(764\) | −4.67745e7 | −0.104889 | ||||||||
\(765\) | 2.70913e8i | 0.605126i | ||||||||
\(766\) | − | 3.01447e8i | − | 0.670694i | ||||||
\(767\) | 1.10344e9i | 2.44547i | ||||||||
\(768\) | −4.35296e7 | −0.0960951 | ||||||||
\(769\) | 2.40729e8i | 0.529357i | 0.964337 | + | 0.264679i | \(0.0852659\pi\) | ||||
−0.964337 | + | 0.264679i | \(0.914734\pi\) | |||||||
\(770\) | −5.81034e8 | + | 3.10861e8i | −1.27271 | + | 0.680917i | ||||
\(771\) | 8.76101e8 | 1.91157 | ||||||||
\(772\) | 2.25879e8i | 0.490935i | ||||||||
\(773\) | −3.21248e8 | −0.695507 | −0.347753 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347753 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(774\) | −7.53066e7 | −0.162409 | ||||||||
\(775\) | −3.79358e7 | −0.0814975 | ||||||||
\(776\) | − | 1.81351e8i | − | 0.388091i | ||||||
\(777\) | − | 6.39402e8i | − | 1.36305i | ||||||
\(778\) | − | 4.77076e8i | − | 1.01309i | ||||||
\(779\) | 3.53387e8 | 0.747546 | ||||||||
\(780\) | − | 6.76327e8i | − | 1.42519i | ||||||
\(781\) | −1.38528e8 | + | 7.41141e7i | −0.290792 | + | 0.155578i | ||||
\(782\) | 4.87327e7 | 0.101906 | ||||||||
\(783\) | 1.65935e8i | 0.345662i | ||||||||
\(784\) | −2.03604e8 | −0.422512 | ||||||||
\(785\) | −7.85646e8 | −1.62412 | ||||||||
\(786\) | 2.35383e8 | 0.484739 | ||||||||
\(787\) | − | 2.07195e7i | − | 0.0425065i | −0.999774 | − | 0.0212532i | \(-0.993234\pi\) | ||
0.999774 | − | 0.0212532i | \(-0.00676562\pi\) | |||||||
\(788\) | 2.64705e8i | 0.540983i | ||||||||
\(789\) | 9.05422e8i | 1.84340i | ||||||||
\(790\) | −4.93893e8 | −1.00173 | ||||||||
\(791\) | − | 3.37497e8i | − | 0.681930i | ||||||
\(792\) | 1.13016e8 | + | 2.11240e8i | 0.227491 | + | 0.425206i | ||||
\(793\) | 1.76005e8 | 0.352945 | ||||||||
\(794\) | 7.89458e7i | 0.157713i | ||||||||
\(795\) | −6.46604e8 | −1.28688 | ||||||||
\(796\) | 3.97619e7 | 0.0788366 | ||||||||
\(797\) | 8.52877e8 | 1.68466 | 0.842328 | − | 0.538965i | \(-0.181185\pi\) | ||||
0.842328 | + | 0.538965i | \(0.181185\pi\) | |||||||
\(798\) | 1.16336e9i | 2.28931i | ||||||||
\(799\) | 2.20573e8i | 0.432427i | ||||||||
\(800\) | 4.96895e7i | 0.0970499i | ||||||||
\(801\) | 8.01320e8 | 1.55922 | ||||||||
\(802\) | 3.02807e8i | 0.587007i | ||||||||
\(803\) | 2.52655e8 | + | 4.72240e8i | 0.487957 | + | 0.912046i | ||||
\(804\) | 2.04561e8 | 0.393600 | ||||||||
\(805\) | 4.30520e8i | 0.825288i | ||||||||
\(806\) | −8.18693e7 | −0.156357 | ||||||||
\(807\) | −8.76400e8 | −1.66756 | ||||||||
\(808\) | 5.79285e7 | 0.109814 | ||||||||
\(809\) | 9.43038e8i | 1.78108i | 0.454905 | + | 0.890540i | \(0.349673\pi\) | ||||
−0.454905 | + | 0.890540i | \(0.650327\pi\) | |||||||
\(810\) | − | 2.35510e8i | − | 0.443153i | ||||||
\(811\) | − | 9.96885e8i | − | 1.86888i | −0.356114 | − | 0.934442i | \(-0.615899\pi\) | ||
0.356114 | − | 0.934442i | \(-0.384101\pi\) | |||||||
\(812\) | 2.71194e8 | 0.506538 | ||||||||
\(813\) | − | 1.55716e9i | − | 2.89776i | ||||||
\(814\) | 9.72460e7 | + | 1.81763e8i | 0.180301 | + | 0.337003i | ||||
\(815\) | 5.61695e8 | 1.03759 | ||||||||
\(816\) | − | 7.44469e7i | − | 0.137018i | ||||||
\(817\) | 1.17898e8 | 0.216192 | ||||||||
\(818\) | 3.57750e8 | 0.653612 | ||||||||
\(819\) | −1.83060e9 | −3.33229 | ||||||||
\(820\) | − | 1.99782e8i | − | 0.362338i | ||||||
\(821\) | 7.20740e8i | 1.30241i | 0.758900 | + | 0.651207i | \(0.225737\pi\) | ||||
−0.758900 | + | 0.651207i | \(0.774263\pi\) | |||||||
\(822\) | 9.76793e7i | 0.175868i | ||||||||
\(823\) | 8.95717e7 | 0.160683 | 0.0803417 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803417 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(824\) | − | 3.41627e8i | − | 0.610620i | ||||||
\(825\) | 4.17919e8 | − | 2.23592e8i | 0.744269 | − | 0.398194i | ||||
\(826\) | −1.07303e9 | −1.90402 | ||||||||
\(827\) | 2.54024e8i | 0.449115i | 0.974461 | + | 0.224557i | \(0.0720937\pi\) | ||||
−0.974461 | + | 0.224557i | \(0.927906\pi\) | |||||||
\(828\) | 1.56519e8 | 0.275725 | ||||||||
\(829\) | −2.37655e7 | −0.0417141 | −0.0208570 | − | 0.999782i | \(-0.506639\pi\) | ||||
−0.0208570 | + | 0.999782i | \(0.506639\pi\) | |||||||
\(830\) | 5.01580e8 | 0.877215 | ||||||||
\(831\) | − | 1.91331e8i | − | 0.333412i | ||||||
\(832\) | 1.07235e8i | 0.186194i | ||||||||
\(833\) | − | 3.48216e8i | − | 0.602440i | ||||||
\(834\) | 7.36160e8 | 1.26904 | ||||||||
\(835\) | 1.37732e9i | 2.36579i | ||||||||
\(836\) | −1.76934e8 | − | 3.30710e8i | −0.302826 | − | 0.566015i | ||||
\(837\) | 4.87125e7 | 0.0830738 | ||||||||
\(838\) | 5.26770e7i | 0.0895135i | ||||||||
\(839\) | −3.05248e8 | −0.516853 | −0.258427 | − | 0.966031i | \(-0.583204\pi\) | ||||
−0.258427 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(840\) | 6.57687e8 | 1.10964 | ||||||||
\(841\) | 3.67882e8 | 0.618473 | ||||||||
\(842\) | − | 1.24062e8i | − | 0.207827i | ||||||
\(843\) | − | 1.07013e9i | − | 1.78629i | ||||||
\(844\) | 5.23088e8i | 0.870056i | ||||||||
\(845\) | −9.15206e8 | −1.51687 | ||||||||
\(846\) | 7.08433e8i | 1.17001i | ||||||||
\(847\) | −8.29093e8 | − | 5.53045e8i | −1.36444 | − | 0.910145i | ||||
\(848\) | 1.02522e8 | 0.168124 | ||||||||
\(849\) | 1.77199e8i | 0.289559i | ||||||||
\(850\) | −8.49820e7 | −0.138379 | ||||||||
\(851\) | 1.34679e8 | 0.218529 | ||||||||
\(852\) | 1.56803e8 | 0.253533 | ||||||||
\(853\) | 6.59469e8i | 1.06254i | 0.847201 | + | 0.531272i | \(0.178286\pi\) | ||||
−0.847201 | + | 0.531272i | \(0.821714\pi\) | |||||||
\(854\) | 1.71155e8i | 0.274799i | ||||||||
\(855\) | − | 1.36222e9i | − | 2.17946i | ||||||
\(856\) | −2.19988e8 | −0.350734 | ||||||||
\(857\) | 2.21289e8i | 0.351575i | 0.984428 | + | 0.175788i | \(0.0562472\pi\) | ||||
−0.984428 | + | 0.175788i | \(0.943753\pi\) | |||||||
\(858\) | 9.01911e8 | − | 4.82535e8i | 1.42791 | − | 0.763953i | ||||
\(859\) | 1.23094e9 | 1.94204 | 0.971021 | − | 0.238995i | \(-0.0768178\pi\) | ||||
0.971021 | + | 0.238995i | \(0.0768178\pi\) | |||||||
\(860\) | − | 6.66516e7i | − | 0.104789i | ||||||
\(861\) | −9.37194e8 | −1.46832 | ||||||||
\(862\) | 2.35783e8 | 0.368120 | ||||||||
\(863\) | −1.21099e9 | −1.88411 | −0.942056 | − | 0.335455i | \(-0.891110\pi\) | ||||
−0.942056 | + | 0.335455i | \(0.891110\pi\) | |||||||
\(864\) | − | 6.38052e7i | − | 0.0989270i | ||||||
\(865\) | 4.33600e8i | 0.669948i | ||||||||
\(866\) | 7.79602e8i | 1.20038i | ||||||||
\(867\) | −8.74701e8 | −1.34215 | ||||||||
\(868\) | − | 7.96129e7i | − | 0.121738i | ||||||
\(869\) | −3.52374e8 | − | 6.58627e8i | −0.536964 | − | 1.00364i | ||||
\(870\) | −5.50366e8 | −0.835784 | ||||||||
\(871\) | − | 5.03936e8i | − | 0.762642i | ||||||
\(872\) | −1.35311e8 | −0.204072 | ||||||||
\(873\) | 9.96156e8 | 1.49722 | ||||||||
\(874\) | −2.45041e8 | −0.367032 | ||||||||
\(875\) | 6.16750e8i | 0.920629i | ||||||||
\(876\) | − | 5.34541e8i | − | 0.795186i | ||||||
\(877\) | − | 7.23871e8i | − | 1.07315i | −0.843851 | − | 0.536577i | \(-0.819717\pi\) | ||
0.843851 | − | 0.536577i | \(-0.180283\pi\) | |||||||
\(878\) | −3.99416e8 | −0.590123 | ||||||||
\(879\) | 1.17152e9i | 1.72497i | ||||||||
\(880\) | −1.86962e8 | + | 1.00027e8i | −0.274350 | + | 0.146781i | ||||
\(881\) | −1.55299e8 | −0.227112 | −0.113556 | − | 0.993532i | \(-0.536224\pi\) | ||||
−0.113556 | + | 0.993532i | \(0.536224\pi\) | |||||||
\(882\) | − | 1.11840e9i | − | 1.63001i | ||||||
\(883\) | 7.75077e8 | 1.12580 | 0.562902 | − | 0.826524i | \(-0.309685\pi\) | ||||
0.562902 | + | 0.826524i | \(0.309685\pi\) | |||||||
\(884\) | −1.83400e8 | −0.265486 | ||||||||
\(885\) | 2.17762e9 | 3.14161 | ||||||||
\(886\) | − | 2.45227e8i | − | 0.352587i | ||||||
\(887\) | 2.17717e8i | 0.311976i | 0.987759 | + | 0.155988i | \(0.0498561\pi\) | ||||
−0.987759 | + | 0.155988i | \(0.950144\pi\) | |||||||
\(888\) | − | 2.05743e8i | − | 0.293823i | ||||||
\(889\) | 1.62404e9 | 2.31149 | ||||||||
\(890\) | 7.09223e8i | 1.00603i | ||||||||
\(891\) | 3.14062e8 | − | 1.68028e8i | 0.444000 | − | 0.237546i | ||||
\(892\) | −4.13501e8 | −0.582615 | ||||||||
\(893\) | − | 1.10910e9i | − | 1.55746i | ||||||
\(894\) | −2.64642e8 | −0.370379 | ||||||||
\(895\) | 3.20325e8 | 0.446808 | ||||||||
\(896\) | −1.04280e8 | −0.144969 | ||||||||
\(897\) | − | 6.68276e8i | − | 0.925930i | ||||||
\(898\) | − | 2.44920e8i | − | 0.338217i | ||||||
\(899\) | 6.66217e7i | 0.0916931i | ||||||||
\(900\) | −2.72944e8 | −0.374408 | ||||||||
\(901\) | 1.75340e8i | 0.239721i | ||||||||
\(902\) | 2.66417e8 | − | 1.42537e8i | 0.363030 | − | 0.194226i | ||||
\(903\) | −3.12669e8 | −0.424640 | ||||||||
\(904\) | − | 1.08598e8i | − | 0.146999i | ||||||
\(905\) | 3.79855e8 | 0.512474 | ||||||||
\(906\) | −1.28491e9 | −1.72778 | ||||||||
\(907\) | 1.92503e8 | 0.257998 | 0.128999 | − | 0.991645i | \(-0.458824\pi\) | ||||
0.128999 | + | 0.991645i | \(0.458824\pi\) | |||||||
\(908\) | − | 1.38222e8i | − | 0.184637i | ||||||
\(909\) | 3.18200e8i | 0.423651i | ||||||||
\(910\) | − | 1.62021e9i | − | 2.15004i | ||||||
\(911\) | −4.80350e8 | −0.635335 | −0.317667 | − | 0.948202i | \(-0.602900\pi\) | ||||
−0.317667 | + | 0.948202i | \(0.602900\pi\) | |||||||
\(912\) | 3.74339e8i | 0.493492i | ||||||||
\(913\) | 3.57859e8 | + | 6.68878e8i | 0.470218 | + | 0.878890i | ||||
\(914\) | 9.81540e7 | 0.128549 | ||||||||
\(915\) | − | 3.47344e8i | − | 0.453415i | ||||||
\(916\) | 5.53906e8 | 0.720692 | ||||||||
\(917\) | 5.63884e8 | 0.731276 | ||||||||
\(918\) | 1.09123e8 | 0.141055 | ||||||||
\(919\) | − | 1.32400e9i | − | 1.70585i | −0.522033 | − | 0.852926i | \(-0.674826\pi\) | ||
0.522033 | − | 0.852926i | \(-0.325174\pi\) | |||||||
\(920\) | 1.38530e8i | 0.177902i | ||||||||
\(921\) | 2.17110e9i | 2.77908i | ||||||||
\(922\) | −1.81810e8 | −0.231966 | ||||||||
\(923\) | − | 3.86283e8i | − | 0.491248i | ||||||
\(924\) | 4.69236e8 | + | 8.77054e8i | 0.594806 | + | 1.11176i | ||||
\(925\) | −2.34858e8 | −0.296742 | ||||||||
\(926\) | − | 7.95114e8i | − | 1.00137i | ||||||
\(927\) | 1.87655e9 | 2.35571 | ||||||||
\(928\) | 8.72632e7 | 0.109191 | ||||||||
\(929\) | −6.17444e8 | −0.770106 | −0.385053 | − | 0.922894i | \(-0.625817\pi\) | ||||
−0.385053 | + | 0.922894i | \(0.625817\pi\) | |||||||
\(930\) | 1.61568e8i | 0.200866i | ||||||||
\(931\) | 1.75092e9i | 2.16979i | ||||||||
\(932\) | 5.81247e8i | 0.717981i | ||||||||
\(933\) | −1.77814e9 | −2.18938 | ||||||||
\(934\) | − | 5.79631e8i | − | 0.711396i | ||||||
\(935\) | −1.71072e8 | − | 3.19753e8i | −0.209288 | − | 0.391182i | ||||
\(936\) | −5.89040e8 | −0.718319 | ||||||||
\(937\) | 6.81980e8i | 0.828997i | 0.910050 | + | 0.414498i | \(0.136043\pi\) | ||||
−0.910050 | + | 0.414498i | \(0.863957\pi\) | |||||||
\(938\) | 4.90047e8 | 0.593785 | ||||||||
\(939\) | −1.38013e9 | −1.66695 | ||||||||
\(940\) | −6.27012e8 | −0.754905 | ||||||||
\(941\) | 1.58337e9i | 1.90026i | 0.311852 | + | 0.950131i | \(0.399051\pi\) | ||||
−0.311852 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(942\) | 1.18591e9i | 1.41873i | ||||||||
\(943\) | − | 1.97403e8i | − | 0.235407i | ||||||
\(944\) | −3.45273e8 | −0.410437 | ||||||||
\(945\) | 9.64030e8i | 1.14234i | ||||||||
\(946\) | 8.88827e7 | − | 4.75535e7i | 0.104989 | − | 0.0561706i | ||||
\(947\) | 2.95359e8 | 0.347776 | 0.173888 | − | 0.984765i | \(-0.444367\pi\) | ||||
0.173888 | + | 0.984765i | \(0.444367\pi\) | |||||||
\(948\) | 7.45516e8i | 0.875049i | ||||||||
\(949\) | −1.31684e9 | −1.54076 | ||||||||
\(950\) | 4.27312e8 | 0.498395 | ||||||||
\(951\) | −6.21747e8 | −0.722890 | ||||||||
\(952\) | − | 1.78345e8i | − | 0.206705i | ||||||
\(953\) | − | 1.25203e9i | − | 1.44656i | −0.690553 | − | 0.723282i | \(-0.742633\pi\) | ||
0.690553 | − | 0.723282i | \(-0.257367\pi\) | |||||||
\(954\) | 5.63153e8i | 0.648606i | ||||||||
\(955\) | 2.27402e8 | 0.261087 | ||||||||
\(956\) | 5.23985e7i | 0.0599716i | ||||||||
\(957\) | −3.92666e8 | − | 7.33937e8i | −0.448010 | − | 0.837380i | ||||
\(958\) | 4.24697e8 | 0.483040 | ||||||||
\(959\) | 2.34000e8i | 0.265314i | ||||||||
\(960\) | 2.11627e8 | 0.239197 | ||||||||
\(961\) | −8.67946e8 | −0.977963 | ||||||||
\(962\) | −5.06846e8 | −0.569313 | ||||||||
\(963\) | − | 1.20839e9i | − | 1.35309i | ||||||
\(964\) | − | 3.46526e8i | − | 0.386816i | ||||||
\(965\) | − | 1.09815e9i | − | 1.22202i | ||||||
\(966\) | 6.49857e8 | 0.720919 | ||||||||
\(967\) | − | 6.73829e8i | − | 0.745195i | −0.927993 | − | 0.372598i | \(-0.878467\pi\) | ||
0.927993 | − | 0.372598i | \(-0.121533\pi\) | |||||||
\(968\) | −2.66781e8 | − | 1.77956e8i | −0.294122 | − | 0.196194i | ||||
\(969\) | −6.40216e8 | −0.703648 | ||||||||
\(970\) | 8.81667e8i | 0.966027i | ||||||||
\(971\) | 1.46250e9 | 1.59749 | 0.798743 | − | 0.601672i | \(-0.205498\pi\) | ||||
0.798743 | + | 0.601672i | \(0.205498\pi\) | |||||||
\(972\) | −6.12451e8 | −0.666918 | ||||||||
\(973\) | 1.76354e9 | 1.91447 | ||||||||
\(974\) | 1.38934e8i | 0.150359i | ||||||||
\(975\) | 1.16536e9i | 1.25733i | ||||||||
\(976\) | 5.50731e7i | 0.0592366i | ||||||||
\(977\) | 5.82424e8 | 0.624534 | 0.312267 | − | 0.949994i | \(-0.398912\pi\) | ||||
0.312267 | + | 0.949994i | \(0.398912\pi\) | |||||||
\(978\) | − | 8.47862e8i | − | 0.906377i | ||||||
\(979\) | −9.45779e8 | + | 5.06005e8i | −1.00796 | + | 0.539270i | ||||
\(980\) | 9.89857e8 | 1.05171 | ||||||||
\(981\) | − | 7.43260e8i | − | 0.787289i | ||||||
\(982\) | −9.27367e8 | −0.979304 | ||||||||
\(983\) | −1.22564e9 | −1.29033 | −0.645165 | − | 0.764043i | \(-0.723212\pi\) | ||||
−0.645165 | + | 0.764043i | \(0.723212\pi\) | |||||||
\(984\) | −3.01565e8 | −0.316515 | ||||||||
\(985\) | − | 1.28691e9i | − | 1.34660i | ||||||
\(986\) | 1.49243e8i | 0.155691i | ||||||||
\(987\) | 2.94137e9i | 3.05913i | ||||||||
\(988\) | 9.22182e8 | 0.956193 | ||||||||
\(989\) | − | 6.58581e7i | − | 0.0680801i | ||||||
\(990\) | −5.49447e8 | − | 1.02698e9i | −0.566265 | − | 1.05841i | ||||
\(991\) | 4.01381e8 | 0.412416 | 0.206208 | − | 0.978508i | \(-0.433888\pi\) | ||||
0.206208 | + | 0.978508i | \(0.433888\pi\) | |||||||
\(992\) | − | 2.56174e7i | − | 0.0262422i | ||||||
\(993\) | 2.37514e8 | 0.242572 | ||||||||
\(994\) | 3.75637e8 | 0.382480 | ||||||||
\(995\) | −1.93309e8 | −0.196238 | ||||||||
\(996\) | − | 7.57120e8i | − | 0.766279i | ||||||
\(997\) | 1.60438e9i | 1.61891i | 0.587185 | + | 0.809453i | \(0.300236\pi\) | ||||
−0.587185 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(998\) | − | 1.89909e8i | − | 0.191053i | ||||||
\(999\) | 3.01575e8 | 0.302482 |
(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 | 22.7.b.a.21.4 | yes | 6 | |
3.2 | odd | 2 | 198.7.d.a.109.2 | 6 | |||
4.3 | odd | 2 | 176.7.h.e.65.6 | 6 | |||
11.10 | odd | 2 | inner | 22.7.b.a.21.1 | ✓ | 6 | |
33.32 | even | 2 | 198.7.d.a.109.5 | 6 | |||
44.43 | even | 2 | 176.7.h.e.65.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.7.b.a.21.1 | ✓ | 6 | 11.10 | odd | 2 | inner | |
22.7.b.a.21.4 | yes | 6 | 1.1 | even | 1 | trivial | |
176.7.h.e.65.5 | 6 | 44.43 | even | 2 | |||
176.7.h.e.65.6 | 6 | 4.3 | odd | 2 | |||
198.7.d.a.109.2 | 6 | 3.2 | odd | 2 | |||
198.7.d.a.109.5 | 6 | 33.32 | even | 2 |