Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,8,Mod(1,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.a (trivial) |
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: | yes |
Analytic conductor: | \(43.1091335168\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-65.5856\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 138.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 340.987 | 1.21995 | 0.609976 | − | 0.792420i | \(-0.291179\pi\) | ||||
0.609976 | + | 0.792420i | \(0.291179\pi\) | |||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | 1267.12 | 1.39629 | 0.698143 | − | 0.715958i | \(-0.254010\pi\) | ||||
0.698143 | + | 0.715958i | \(0.254010\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2727.89 | 0.862636 | ||||||||
\(11\) | 5101.25 | 1.15559 | 0.577793 | − | 0.816183i | \(-0.303914\pi\) | ||||
0.577793 | + | 0.816183i | \(0.303914\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −5814.29 | −0.733998 | −0.366999 | − | 0.930221i | \(-0.619615\pi\) | ||||
−0.366999 | + | 0.930221i | \(0.619615\pi\) | |||||||
\(14\) | 10137.0 | 0.987324 | ||||||||
\(15\) | 9206.64 | 0.704339 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 6404.73 | 0.316177 | 0.158088 | − | 0.987425i | \(-0.449467\pi\) | ||||
0.158088 | + | 0.987425i | \(0.449467\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −38566.6 | −1.28995 | −0.644977 | − | 0.764202i | \(-0.723133\pi\) | ||||
−0.644977 | + | 0.764202i | \(0.723133\pi\) | |||||||
\(20\) | 21823.2 | 0.609976 | ||||||||
\(21\) | 34212.2 | 0.806147 | ||||||||
\(22\) | 40810.0 | 0.817122 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 38147.0 | 0.488281 | ||||||||
\(26\) | −46514.3 | −0.519015 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 81095.7 | 0.698143 | ||||||||
\(29\) | −208061. | −1.58415 | −0.792077 | − | 0.610422i | \(-0.791000\pi\) | ||||
−0.792077 | + | 0.610422i | \(0.791000\pi\) | |||||||
\(30\) | 73653.1 | 0.498043 | ||||||||
\(31\) | 3653.78 | 0.0220281 | 0.0110140 | − | 0.999939i | \(-0.496494\pi\) | ||||
0.0110140 | + | 0.999939i | \(0.496494\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 137734. | 0.667178 | ||||||||
\(34\) | 51237.9 | 0.223571 | ||||||||
\(35\) | 432071. | 1.70340 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 23930.9 | 0.0776699 | 0.0388350 | − | 0.999246i | \(-0.487635\pi\) | ||||
0.0388350 | + | 0.999246i | \(0.487635\pi\) | |||||||
\(38\) | −308533. | −0.912135 | ||||||||
\(39\) | −156986. | −0.423774 | ||||||||
\(40\) | 174585. | 0.431318 | ||||||||
\(41\) | −1151.50 | −0.00260928 | −0.00130464 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130464 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(42\) | 273698. | 0.570032 | ||||||||
\(43\) | −489302. | −0.938506 | −0.469253 | − | 0.883064i | \(-0.655477\pi\) | ||||
−0.469253 | + | 0.883064i | \(0.655477\pi\) | |||||||
\(44\) | 326480. | 0.577793 | ||||||||
\(45\) | 248579. | 0.406650 | ||||||||
\(46\) | −97336.0 | −0.147442 | ||||||||
\(47\) | 988907. | 1.38935 | 0.694677 | − | 0.719322i | \(-0.255547\pi\) | ||||
0.694677 | + | 0.719322i | \(0.255547\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 782050. | 0.949617 | ||||||||
\(50\) | 305176. | 0.345267 | ||||||||
\(51\) | 172928. | 0.182545 | ||||||||
\(52\) | −372115. | −0.366999 | ||||||||
\(53\) | −777027. | −0.716920 | −0.358460 | − | 0.933545i | \(-0.616698\pi\) | ||||
−0.358460 | + | 0.933545i | \(0.616698\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | 1.73946e6 | 1.40976 | ||||||||
\(56\) | 648766. | 0.493662 | ||||||||
\(57\) | −1.04130e6 | −0.744755 | ||||||||
\(58\) | −1.66449e6 | −1.12017 | ||||||||
\(59\) | 1.61187e6 | 1.02176 | 0.510879 | − | 0.859652i | \(-0.329320\pi\) | ||||
0.510879 | + | 0.859652i | \(0.329320\pi\) | |||||||
\(60\) | 589225. | 0.352170 | ||||||||
\(61\) | −1.04092e6 | −0.587171 | −0.293586 | − | 0.955933i | \(-0.594849\pi\) | ||||
−0.293586 | + | 0.955933i | \(0.594849\pi\) | |||||||
\(62\) | 29230.2 | 0.0155762 | ||||||||
\(63\) | 923731. | 0.465429 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −1.98260e6 | −0.895442 | ||||||||
\(66\) | 1.10187e6 | 0.471766 | ||||||||
\(67\) | −2.06066e6 | −0.837036 | −0.418518 | − | 0.908209i | \(-0.637450\pi\) | ||||
−0.418518 | + | 0.908209i | \(0.637450\pi\) | |||||||
\(68\) | 409903. | 0.158088 | ||||||||
\(69\) | −328509. | −0.120386 | ||||||||
\(70\) | 3.45657e6 | 1.20449 | ||||||||
\(71\) | 3.58392e6 | 1.18838 | 0.594189 | − | 0.804325i | \(-0.297473\pi\) | ||||
0.594189 | + | 0.804325i | \(0.297473\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −975850. | −0.293598 | −0.146799 | − | 0.989166i | \(-0.546897\pi\) | ||||
−0.146799 | + | 0.989166i | \(0.546897\pi\) | |||||||
\(74\) | 191447. | 0.0549209 | ||||||||
\(75\) | 1.02997e6 | 0.281909 | ||||||||
\(76\) | −2.46826e6 | −0.644977 | ||||||||
\(77\) | 6.46390e6 | 1.61353 | ||||||||
\(78\) | −1.25589e6 | −0.299653 | ||||||||
\(79\) | 6.00359e6 | 1.36999 | 0.684993 | − | 0.728550i | \(-0.259805\pi\) | ||||
0.684993 | + | 0.728550i | \(0.259805\pi\) | |||||||
\(80\) | 1.39668e6 | 0.304988 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −9212.01 | −0.00184504 | ||||||||
\(83\) | −5.40252e6 | −1.03711 | −0.518553 | − | 0.855046i | \(-0.673529\pi\) | ||||
−0.518553 | + | 0.855046i | \(0.673529\pi\) | |||||||
\(84\) | 2.18958e6 | 0.403073 | ||||||||
\(85\) | 2.18393e6 | 0.385720 | ||||||||
\(86\) | −3.91441e6 | −0.663624 | ||||||||
\(87\) | −5.61764e6 | −0.914611 | ||||||||
\(88\) | 2.61184e6 | 0.408561 | ||||||||
\(89\) | −4.13911e6 | −0.622361 | −0.311180 | − | 0.950351i | \(-0.600724\pi\) | ||||
−0.311180 | + | 0.950351i | \(0.600724\pi\) | |||||||
\(90\) | 1.98863e6 | 0.287545 | ||||||||
\(91\) | −7.36740e6 | −1.02487 | ||||||||
\(92\) | −778688. | −0.104257 | ||||||||
\(93\) | 98652.1 | 0.0127179 | ||||||||
\(94\) | 7.91125e6 | 0.982422 | ||||||||
\(95\) | −1.31507e7 | −1.57368 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | 1.18844e7 | 1.32214 | 0.661070 | − | 0.750324i | \(-0.270103\pi\) | ||||
0.661070 | + | 0.750324i | \(0.270103\pi\) | |||||||
\(98\) | 6.25640e6 | 0.671481 | ||||||||
\(99\) | 3.71881e6 | 0.385195 | ||||||||
\(100\) | 2.44141e6 | 0.244141 | ||||||||
\(101\) | 9.54327e6 | 0.921663 | 0.460832 | − | 0.887488i | \(-0.347551\pi\) | ||||
0.460832 | + | 0.887488i | \(0.347551\pi\) | |||||||
\(102\) | 1.38342e6 | 0.129079 | ||||||||
\(103\) | −3.12347e6 | −0.281648 | −0.140824 | − | 0.990035i | \(-0.544975\pi\) | ||||
−0.140824 | + | 0.990035i | \(0.544975\pi\) | |||||||
\(104\) | −2.97692e6 | −0.259508 | ||||||||
\(105\) | 1.16659e7 | 0.983460 | ||||||||
\(106\) | −6.21621e6 | −0.506939 | ||||||||
\(107\) | 1.02468e7 | 0.808620 | 0.404310 | − | 0.914622i | \(-0.367512\pi\) | ||||
0.404310 | + | 0.914622i | \(0.367512\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −1.26733e7 | −0.937337 | −0.468668 | − | 0.883374i | \(-0.655266\pi\) | ||||
−0.468668 | + | 0.883374i | \(0.655266\pi\) | |||||||
\(110\) | 1.39157e7 | 0.996850 | ||||||||
\(111\) | 646134. | 0.0448427 | ||||||||
\(112\) | 5.19012e6 | 0.349072 | ||||||||
\(113\) | 543321. | 0.0354227 | 0.0177114 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177114 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(114\) | −8.33039e6 | −0.526621 | ||||||||
\(115\) | −4.14879e6 | −0.254377 | ||||||||
\(116\) | −1.33159e7 | −0.792077 | ||||||||
\(117\) | −4.23862e6 | −0.244666 | ||||||||
\(118\) | 1.28950e7 | 0.722493 | ||||||||
\(119\) | 8.11557e6 | 0.441473 | ||||||||
\(120\) | 4.71380e6 | 0.249022 | ||||||||
\(121\) | 6.53557e6 | 0.335378 | ||||||||
\(122\) | −8.32740e6 | −0.415193 | ||||||||
\(123\) | −31090.5 | −0.00150647 | ||||||||
\(124\) | 233842. | 0.0110140 | ||||||||
\(125\) | −1.36320e7 | −0.624272 | ||||||||
\(126\) | 7.38984e6 | 0.329108 | ||||||||
\(127\) | −6.08628e6 | −0.263657 | −0.131828 | − | 0.991273i | \(-0.542085\pi\) | ||||
−0.131828 | + | 0.991273i | \(0.542085\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −1.32111e7 | −0.541847 | ||||||||
\(130\) | −1.58608e7 | −0.633173 | ||||||||
\(131\) | −2.60740e7 | −1.01335 | −0.506674 | − | 0.862138i | \(-0.669125\pi\) | ||||
−0.506674 | + | 0.862138i | \(0.669125\pi\) | |||||||
\(132\) | 8.81496e6 | 0.333589 | ||||||||
\(133\) | −4.88686e7 | −1.80115 | ||||||||
\(134\) | −1.64853e7 | −0.591874 | ||||||||
\(135\) | 6.71164e6 | 0.234780 | ||||||||
\(136\) | 3.27922e6 | 0.111785 | ||||||||
\(137\) | 4.55380e7 | 1.51304 | 0.756522 | − | 0.653968i | \(-0.226897\pi\) | ||||
0.756522 | + | 0.653968i | \(0.226897\pi\) | |||||||
\(138\) | −2.62807e6 | −0.0851257 | ||||||||
\(139\) | −4.36079e7 | −1.37725 | −0.688626 | − | 0.725116i | \(-0.741786\pi\) | ||||
−0.688626 | + | 0.725116i | \(0.741786\pi\) | |||||||
\(140\) | 2.76526e7 | 0.851701 | ||||||||
\(141\) | 2.67005e7 | 0.802144 | ||||||||
\(142\) | 2.86714e7 | 0.840310 | ||||||||
\(143\) | −2.96601e7 | −0.848198 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −7.09460e7 | −1.93259 | ||||||||
\(146\) | −7.80680e6 | −0.207605 | ||||||||
\(147\) | 2.11154e7 | 0.548262 | ||||||||
\(148\) | 1.53158e6 | 0.0388350 | ||||||||
\(149\) | −7.44370e7 | −1.84347 | −0.921737 | − | 0.387816i | \(-0.873230\pi\) | ||||
−0.921737 | + | 0.387816i | \(0.873230\pi\) | |||||||
\(150\) | 8.23975e6 | 0.199340 | ||||||||
\(151\) | 2.77945e7 | 0.656962 | 0.328481 | − | 0.944511i | \(-0.393463\pi\) | ||||
0.328481 | + | 0.944511i | \(0.393463\pi\) | |||||||
\(152\) | −1.97461e7 | −0.456067 | ||||||||
\(153\) | 4.66905e6 | 0.105392 | ||||||||
\(154\) | 5.17112e7 | 1.14094 | ||||||||
\(155\) | 1.24589e6 | 0.0268732 | ||||||||
\(156\) | −1.00471e7 | −0.211887 | ||||||||
\(157\) | 3.33077e7 | 0.686904 | 0.343452 | − | 0.939170i | \(-0.388404\pi\) | ||||
0.343452 | + | 0.939170i | \(0.388404\pi\) | |||||||
\(158\) | 4.80287e7 | 0.968726 | ||||||||
\(159\) | −2.09797e7 | −0.413914 | ||||||||
\(160\) | 1.11735e7 | 0.215659 | ||||||||
\(161\) | −1.54171e7 | −0.291146 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −1.45963e7 | −0.263989 | −0.131994 | − | 0.991250i | \(-0.542138\pi\) | ||||
−0.131994 | + | 0.991250i | \(0.542138\pi\) | |||||||
\(164\) | −73696.1 | −0.00130464 | ||||||||
\(165\) | 4.69654e7 | 0.813924 | ||||||||
\(166\) | −4.32201e7 | −0.733344 | ||||||||
\(167\) | −7.61604e7 | −1.26538 | −0.632691 | − | 0.774404i | \(-0.718050\pi\) | ||||
−0.632691 | + | 0.774404i | \(0.718050\pi\) | |||||||
\(168\) | 1.75167e7 | 0.285016 | ||||||||
\(169\) | −2.89426e7 | −0.461247 | ||||||||
\(170\) | 1.74714e7 | 0.272745 | ||||||||
\(171\) | −2.81151e7 | −0.429985 | ||||||||
\(172\) | −3.13153e7 | −0.469253 | ||||||||
\(173\) | −1.17815e8 | −1.72997 | −0.864983 | − | 0.501801i | \(-0.832671\pi\) | ||||
−0.864983 | + | 0.501801i | \(0.832671\pi\) | |||||||
\(174\) | −4.49411e7 | −0.646728 | ||||||||
\(175\) | 4.83368e7 | 0.681781 | ||||||||
\(176\) | 2.08947e7 | 0.288896 | ||||||||
\(177\) | 4.35205e7 | 0.589913 | ||||||||
\(178\) | −3.31129e7 | −0.440075 | ||||||||
\(179\) | 2.34279e7 | 0.305314 | 0.152657 | − | 0.988279i | \(-0.451217\pi\) | ||||
0.152657 | + | 0.988279i | \(0.451217\pi\) | |||||||
\(180\) | 1.59091e7 | 0.203325 | ||||||||
\(181\) | −5.66147e7 | −0.709667 | −0.354833 | − | 0.934930i | \(-0.615462\pi\) | ||||
−0.354833 | + | 0.934930i | \(0.615462\pi\) | |||||||
\(182\) | −5.89392e7 | −0.724694 | ||||||||
\(183\) | −2.81050e7 | −0.339004 | ||||||||
\(184\) | −6.22950e6 | −0.0737210 | ||||||||
\(185\) | 8.16012e6 | 0.0947535 | ||||||||
\(186\) | 789217. | 0.00899292 | ||||||||
\(187\) | 3.26721e7 | 0.365369 | ||||||||
\(188\) | 6.32900e7 | 0.694677 | ||||||||
\(189\) | 2.49407e7 | 0.268716 | ||||||||
\(190\) | −1.05206e8 | −1.11276 | ||||||||
\(191\) | −1.26851e8 | −1.31727 | −0.658636 | − | 0.752461i | \(-0.728866\pi\) | ||||
−0.658636 | + | 0.752461i | \(0.728866\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | 1.36553e8 | 1.36726 | 0.683630 | − | 0.729828i | \(-0.260400\pi\) | ||||
0.683630 | + | 0.729828i | \(0.260400\pi\) | |||||||
\(194\) | 9.50755e7 | 0.934894 | ||||||||
\(195\) | −5.35301e7 | −0.516984 | ||||||||
\(196\) | 5.00512e7 | 0.474808 | ||||||||
\(197\) | −1.16049e8 | −1.08146 | −0.540729 | − | 0.841197i | \(-0.681852\pi\) | ||||
−0.540729 | + | 0.841197i | \(0.681852\pi\) | |||||||
\(198\) | 2.97505e7 | 0.272374 | ||||||||
\(199\) | 1.41367e7 | 0.127163 | 0.0635816 | − | 0.997977i | \(-0.479748\pi\) | ||||
0.0635816 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(200\) | 1.95312e7 | 0.172633 | ||||||||
\(201\) | −5.56377e7 | −0.483263 | ||||||||
\(202\) | 7.63462e7 | 0.651714 | ||||||||
\(203\) | −2.63638e8 | −2.21193 | ||||||||
\(204\) | 1.10674e7 | 0.0912723 | ||||||||
\(205\) | −392647. | −0.00318320 | ||||||||
\(206\) | −2.49877e7 | −0.199155 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | −2.38153e7 | −0.183500 | ||||||||
\(209\) | −1.96738e8 | −1.49065 | ||||||||
\(210\) | 9.33274e7 | 0.695411 | ||||||||
\(211\) | 1.88579e8 | 1.38199 | 0.690993 | − | 0.722861i | \(-0.257173\pi\) | ||||
0.690993 | + | 0.722861i | \(0.257173\pi\) | |||||||
\(212\) | −4.97297e7 | −0.358460 | ||||||||
\(213\) | 9.67660e7 | 0.686110 | ||||||||
\(214\) | 8.19743e7 | 0.571781 | ||||||||
\(215\) | −1.66845e8 | −1.14493 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 4.62978e6 | 0.0307575 | ||||||||
\(218\) | −1.01386e8 | −0.662797 | ||||||||
\(219\) | −2.63479e7 | −0.169509 | ||||||||
\(220\) | 1.11325e8 | 0.704879 | ||||||||
\(221\) | −3.72390e7 | −0.232073 | ||||||||
\(222\) | 5.16907e6 | 0.0317086 | ||||||||
\(223\) | 3.17153e8 | 1.91515 | 0.957573 | − | 0.288192i | \(-0.0930542\pi\) | ||||
0.957573 | + | 0.288192i | \(0.0930542\pi\) | |||||||
\(224\) | 4.15210e7 | 0.246831 | ||||||||
\(225\) | 2.78091e7 | 0.162760 | ||||||||
\(226\) | 4.34657e6 | 0.0250476 | ||||||||
\(227\) | 9.71697e6 | 0.0551366 | 0.0275683 | − | 0.999620i | \(-0.491224\pi\) | ||||
0.0275683 | + | 0.999620i | \(0.491224\pi\) | |||||||
\(228\) | −6.66431e7 | −0.372378 | ||||||||
\(229\) | 2.54644e8 | 1.40123 | 0.700614 | − | 0.713540i | \(-0.252909\pi\) | ||||
0.700614 | + | 0.713540i | \(0.252909\pi\) | |||||||
\(230\) | −3.31903e7 | −0.179872 | ||||||||
\(231\) | 1.74525e8 | 0.931571 | ||||||||
\(232\) | −1.06527e8 | −0.560083 | ||||||||
\(233\) | 2.64155e7 | 0.136808 | 0.0684042 | − | 0.997658i | \(-0.478209\pi\) | ||||
0.0684042 | + | 0.997658i | \(0.478209\pi\) | |||||||
\(234\) | −3.39089e7 | −0.173005 | ||||||||
\(235\) | 3.37204e8 | 1.69494 | ||||||||
\(236\) | 1.03160e8 | 0.510879 | ||||||||
\(237\) | 1.62097e8 | 0.790962 | ||||||||
\(238\) | 6.49245e7 | 0.312169 | ||||||||
\(239\) | −1.27674e7 | −0.0604936 | −0.0302468 | − | 0.999542i | \(-0.509629\pi\) | ||||
−0.0302468 | + | 0.999542i | \(0.509629\pi\) | |||||||
\(240\) | 3.77104e7 | 0.176085 | ||||||||
\(241\) | 1.47494e8 | 0.678757 | 0.339379 | − | 0.940650i | \(-0.389783\pi\) | ||||
0.339379 | + | 0.940650i | \(0.389783\pi\) | |||||||
\(242\) | 5.22845e7 | 0.237148 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −6.66192e7 | −0.293586 | ||||||||
\(245\) | 2.66669e8 | 1.15849 | ||||||||
\(246\) | −248724. | −0.00106524 | ||||||||
\(247\) | 2.24238e8 | 0.946823 | ||||||||
\(248\) | 1.87074e6 | 0.00778810 | ||||||||
\(249\) | −1.45868e8 | −0.598773 | ||||||||
\(250\) | −1.09056e8 | −0.441427 | ||||||||
\(251\) | 2.67374e8 | 1.06724 | 0.533618 | − | 0.845726i | \(-0.320832\pi\) | ||||
0.533618 | + | 0.845726i | \(0.320832\pi\) | |||||||
\(252\) | 5.91188e7 | 0.232714 | ||||||||
\(253\) | −6.20669e7 | −0.240956 | ||||||||
\(254\) | −4.86902e7 | −0.186433 | ||||||||
\(255\) | 5.89661e7 | 0.222696 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −1.37033e8 | −0.503568 | −0.251784 | − | 0.967784i | \(-0.581017\pi\) | ||||
−0.251784 | + | 0.967784i | \(0.581017\pi\) | |||||||
\(258\) | −1.05689e8 | −0.383143 | ||||||||
\(259\) | 3.03233e7 | 0.108449 | ||||||||
\(260\) | −1.26886e8 | −0.447721 | ||||||||
\(261\) | −1.51676e8 | −0.528051 | ||||||||
\(262\) | −2.08592e8 | −0.716545 | ||||||||
\(263\) | 1.60586e8 | 0.544329 | 0.272165 | − | 0.962251i | \(-0.412260\pi\) | ||||
0.272165 | + | 0.962251i | \(0.412260\pi\) | |||||||
\(264\) | 7.05197e7 | 0.235883 | ||||||||
\(265\) | −2.64956e8 | −0.874607 | ||||||||
\(266\) | −3.90948e8 | −1.27360 | ||||||||
\(267\) | −1.11756e8 | −0.359320 | ||||||||
\(268\) | −1.31882e8 | −0.418518 | ||||||||
\(269\) | 4.67109e8 | 1.46314 | 0.731568 | − | 0.681768i | \(-0.238789\pi\) | ||||
0.731568 | + | 0.681768i | \(0.238789\pi\) | |||||||
\(270\) | 5.36931e7 | 0.166014 | ||||||||
\(271\) | 5.51685e8 | 1.68383 | 0.841916 | − | 0.539609i | \(-0.181428\pi\) | ||||
0.841916 | + | 0.539609i | \(0.181428\pi\) | |||||||
\(272\) | 2.62338e7 | 0.0790442 | ||||||||
\(273\) | −1.98920e8 | −0.591710 | ||||||||
\(274\) | 3.64304e8 | 1.06988 | ||||||||
\(275\) | 1.94597e8 | 0.564251 | ||||||||
\(276\) | −2.10246e7 | −0.0601929 | ||||||||
\(277\) | 4.78153e8 | 1.35172 | 0.675862 | − | 0.737028i | \(-0.263772\pi\) | ||||
0.675862 | + | 0.737028i | \(0.263772\pi\) | |||||||
\(278\) | −3.48863e8 | −0.973865 | ||||||||
\(279\) | 2.66361e6 | 0.00734269 | ||||||||
\(280\) | 2.21220e8 | 0.602244 | ||||||||
\(281\) | 7.37447e8 | 1.98271 | 0.991354 | − | 0.131218i | \(-0.0418887\pi\) | ||||
0.991354 | + | 0.131218i | \(0.0418887\pi\) | |||||||
\(282\) | 2.13604e8 | 0.567201 | ||||||||
\(283\) | −6.82950e8 | −1.79117 | −0.895584 | − | 0.444893i | \(-0.853242\pi\) | ||||
−0.895584 | + | 0.444893i | \(0.853242\pi\) | |||||||
\(284\) | 2.29371e8 | 0.594189 | ||||||||
\(285\) | −3.55069e8 | −0.908565 | ||||||||
\(286\) | −2.37281e8 | −0.599766 | ||||||||
\(287\) | −1.45909e6 | −0.00364331 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.69318e8 | −0.900032 | ||||||||
\(290\) | −5.67568e8 | −1.36655 | ||||||||
\(291\) | 3.20880e8 | 0.763338 | ||||||||
\(292\) | −6.24544e7 | −0.146799 | ||||||||
\(293\) | −4.73242e7 | −0.109912 | −0.0549562 | − | 0.998489i | \(-0.517502\pi\) | ||||
−0.0549562 | + | 0.998489i | \(0.517502\pi\) | |||||||
\(294\) | 1.68923e8 | 0.387680 | ||||||||
\(295\) | 5.49627e8 | 1.24650 | ||||||||
\(296\) | 1.22526e7 | 0.0274605 | ||||||||
\(297\) | 1.00408e8 | 0.222393 | ||||||||
\(298\) | −5.95496e8 | −1.30353 | ||||||||
\(299\) | 7.07425e7 | 0.153049 | ||||||||
\(300\) | 6.59180e7 | 0.140955 | ||||||||
\(301\) | −6.20004e8 | −1.31042 | ||||||||
\(302\) | 2.22356e8 | 0.464542 | ||||||||
\(303\) | 2.57668e8 | 0.532123 | ||||||||
\(304\) | −1.57969e8 | −0.322488 | ||||||||
\(305\) | −3.54942e8 | −0.716321 | ||||||||
\(306\) | 3.73524e7 | 0.0745236 | ||||||||
\(307\) | 3.47596e8 | 0.685630 | 0.342815 | − | 0.939403i | \(-0.388620\pi\) | ||||
0.342815 | + | 0.939403i | \(0.388620\pi\) | |||||||
\(308\) | 4.13689e8 | 0.806764 | ||||||||
\(309\) | −8.43336e7 | −0.162610 | ||||||||
\(310\) | 9.96713e6 | 0.0190022 | ||||||||
\(311\) | −8.46459e8 | −1.59568 | −0.797838 | − | 0.602873i | \(-0.794023\pi\) | ||||
−0.797838 | + | 0.602873i | \(0.794023\pi\) | |||||||
\(312\) | −8.03767e7 | −0.149827 | ||||||||
\(313\) | 5.31447e8 | 0.979613 | 0.489806 | − | 0.871831i | \(-0.337067\pi\) | ||||
0.489806 | + | 0.871831i | \(0.337067\pi\) | |||||||
\(314\) | 2.66462e8 | 0.485715 | ||||||||
\(315\) | 3.14980e8 | 0.567801 | ||||||||
\(316\) | 3.84230e8 | 0.684993 | ||||||||
\(317\) | −7.52971e8 | −1.32761 | −0.663806 | − | 0.747905i | \(-0.731060\pi\) | ||||
−0.663806 | + | 0.747905i | \(0.731060\pi\) | |||||||
\(318\) | −1.67838e8 | −0.292681 | ||||||||
\(319\) | −1.06137e9 | −1.83062 | ||||||||
\(320\) | 8.93876e7 | 0.152494 | ||||||||
\(321\) | 2.76663e8 | 0.466857 | ||||||||
\(322\) | −1.23336e8 | −0.205871 | ||||||||
\(323\) | −2.47009e8 | −0.407853 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −2.21798e8 | −0.358398 | ||||||||
\(326\) | −1.16770e8 | −0.186668 | ||||||||
\(327\) | −3.42178e8 | −0.541172 | ||||||||
\(328\) | −589569. | −0.000922521 0 | ||||||||
\(329\) | 1.25306e9 | 1.93994 | ||||||||
\(330\) | 3.75723e8 | 0.575531 | ||||||||
\(331\) | −1.86489e8 | −0.282654 | −0.141327 | − | 0.989963i | \(-0.545137\pi\) | ||||
−0.141327 | + | 0.989963i | \(0.545137\pi\) | |||||||
\(332\) | −3.45761e8 | −0.518553 | ||||||||
\(333\) | 1.74456e7 | 0.0258900 | ||||||||
\(334\) | −6.09284e8 | −0.894760 | ||||||||
\(335\) | −7.02657e8 | −1.02114 | ||||||||
\(336\) | 1.40133e8 | 0.201537 | ||||||||
\(337\) | −7.20597e8 | −1.02562 | −0.512811 | − | 0.858501i | \(-0.671396\pi\) | ||||
−0.512811 | + | 0.858501i | \(0.671396\pi\) | |||||||
\(338\) | −2.31540e8 | −0.326151 | ||||||||
\(339\) | 1.46697e7 | 0.0204513 | ||||||||
\(340\) | 1.39771e8 | 0.192860 | ||||||||
\(341\) | 1.86388e7 | 0.0254553 | ||||||||
\(342\) | −2.24921e8 | −0.304045 | ||||||||
\(343\) | −5.25761e7 | −0.0703491 | ||||||||
\(344\) | −2.50522e8 | −0.331812 | ||||||||
\(345\) | −1.12017e8 | −0.146865 | ||||||||
\(346\) | −9.42517e8 | −1.22327 | ||||||||
\(347\) | −8.14326e8 | −1.04627 | −0.523137 | − | 0.852249i | \(-0.675238\pi\) | ||||
−0.523137 | + | 0.852249i | \(0.675238\pi\) | |||||||
\(348\) | −3.59529e8 | −0.457306 | ||||||||
\(349\) | −4.25035e8 | −0.535224 | −0.267612 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267612 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(350\) | 3.86694e8 | 0.482092 | ||||||||
\(351\) | −1.14443e8 | −0.141258 | ||||||||
\(352\) | 1.67158e8 | 0.204281 | ||||||||
\(353\) | −2.10866e8 | −0.255149 | −0.127575 | − | 0.991829i | \(-0.540719\pi\) | ||||
−0.127575 | + | 0.991829i | \(0.540719\pi\) | |||||||
\(354\) | 3.48164e8 | 0.417131 | ||||||||
\(355\) | 1.22207e9 | 1.44976 | ||||||||
\(356\) | −2.64903e8 | −0.311180 | ||||||||
\(357\) | 2.19120e8 | 0.254885 | ||||||||
\(358\) | 1.87423e8 | 0.215890 | ||||||||
\(359\) | −9.62505e8 | −1.09792 | −0.548962 | − | 0.835847i | \(-0.684977\pi\) | ||||
−0.548962 | + | 0.835847i | \(0.684977\pi\) | |||||||
\(360\) | 1.27273e8 | 0.143773 | ||||||||
\(361\) | 5.93513e8 | 0.663980 | ||||||||
\(362\) | −4.52918e8 | −0.501810 | ||||||||
\(363\) | 1.76460e8 | 0.193631 | ||||||||
\(364\) | −4.71514e8 | −0.512436 | ||||||||
\(365\) | −3.32752e8 | −0.358175 | ||||||||
\(366\) | −2.24840e8 | −0.239712 | ||||||||
\(367\) | −5.91557e7 | −0.0624691 | −0.0312345 | − | 0.999512i | \(-0.509944\pi\) | ||||
−0.0312345 | + | 0.999512i | \(0.509944\pi\) | |||||||
\(368\) | −4.98360e7 | −0.0521286 | ||||||||
\(369\) | −839445. | −0.000869761 0 | ||||||||
\(370\) | 6.52809e7 | 0.0670009 | ||||||||
\(371\) | −9.84586e8 | −1.00103 | ||||||||
\(372\) | 6.31373e6 | 0.00635896 | ||||||||
\(373\) | −7.57694e8 | −0.755984 | −0.377992 | − | 0.925809i | \(-0.623385\pi\) | ||||
−0.377992 | + | 0.925809i | \(0.623385\pi\) | |||||||
\(374\) | 2.61377e8 | 0.258355 | ||||||||
\(375\) | −3.68063e8 | −0.360424 | ||||||||
\(376\) | 5.06320e8 | 0.491211 | ||||||||
\(377\) | 1.20973e9 | 1.16277 | ||||||||
\(378\) | 1.99526e8 | 0.190011 | ||||||||
\(379\) | −2.47156e8 | −0.233203 | −0.116601 | − | 0.993179i | \(-0.537200\pi\) | ||||
−0.116601 | + | 0.993179i | \(0.537200\pi\) | |||||||
\(380\) | −8.41645e8 | −0.786840 | ||||||||
\(381\) | −1.64330e8 | −0.152222 | ||||||||
\(382\) | −1.01480e9 | −0.931452 | ||||||||
\(383\) | −1.95064e9 | −1.77411 | −0.887056 | − | 0.461662i | \(-0.847253\pi\) | ||||
−0.887056 | + | 0.461662i | \(0.847253\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 2.20410e9 | 1.96843 | ||||||||
\(386\) | 1.09243e9 | 0.966799 | ||||||||
\(387\) | −3.56701e8 | −0.312835 | ||||||||
\(388\) | 7.60604e8 | 0.661070 | ||||||||
\(389\) | 1.70660e9 | 1.46997 | 0.734987 | − | 0.678082i | \(-0.237188\pi\) | ||||
0.734987 | + | 0.678082i | \(0.237188\pi\) | |||||||
\(390\) | −4.28241e8 | −0.365563 | ||||||||
\(391\) | −7.79264e7 | −0.0659274 | ||||||||
\(392\) | 4.00410e8 | 0.335740 | ||||||||
\(393\) | −7.03998e8 | −0.585056 | ||||||||
\(394\) | −9.28392e8 | −0.764706 | ||||||||
\(395\) | 2.04714e9 | 1.67132 | ||||||||
\(396\) | 2.38004e8 | 0.192598 | ||||||||
\(397\) | 9.51729e8 | 0.763390 | 0.381695 | − | 0.924288i | \(-0.375340\pi\) | ||||
0.381695 | + | 0.924288i | \(0.375340\pi\) | |||||||
\(398\) | 1.13093e8 | 0.0899179 | ||||||||
\(399\) | −1.31945e9 | −1.03989 | ||||||||
\(400\) | 1.56250e8 | 0.122070 | ||||||||
\(401\) | 1.03883e9 | 0.804522 | 0.402261 | − | 0.915525i | \(-0.368225\pi\) | ||||
0.402261 | + | 0.915525i | \(0.368225\pi\) | |||||||
\(402\) | −4.45102e8 | −0.341718 | ||||||||
\(403\) | −2.12441e7 | −0.0161686 | ||||||||
\(404\) | 6.10769e8 | 0.460832 | ||||||||
\(405\) | 1.81214e8 | 0.135550 | ||||||||
\(406\) | −2.10910e9 | −1.56407 | ||||||||
\(407\) | 1.22077e8 | 0.0897542 | ||||||||
\(408\) | 8.85390e7 | 0.0645393 | ||||||||
\(409\) | 2.67559e9 | 1.93370 | 0.966849 | − | 0.255348i | \(-0.0821899\pi\) | ||||
0.966849 | + | 0.255348i | \(0.0821899\pi\) | |||||||
\(410\) | −3.14117e6 | −0.00225086 | ||||||||
\(411\) | 1.22953e9 | 0.873557 | ||||||||
\(412\) | −1.99902e8 | −0.140824 | ||||||||
\(413\) | 2.04243e9 | 1.42667 | ||||||||
\(414\) | −7.09579e7 | −0.0491473 | ||||||||
\(415\) | −1.84219e9 | −1.26522 | ||||||||
\(416\) | −1.90523e8 | −0.129754 | ||||||||
\(417\) | −1.17741e9 | −0.795157 | ||||||||
\(418\) | −1.57390e9 | −1.05405 | ||||||||
\(419\) | 3.41769e8 | 0.226978 | 0.113489 | − | 0.993539i | \(-0.463797\pi\) | ||||
0.113489 | + | 0.993539i | \(0.463797\pi\) | |||||||
\(420\) | 7.46619e8 | 0.491730 | ||||||||
\(421\) | 1.83184e9 | 1.19646 | 0.598232 | − | 0.801323i | \(-0.295870\pi\) | ||||
0.598232 | + | 0.801323i | \(0.295870\pi\) | |||||||
\(422\) | 1.50863e9 | 0.977212 | ||||||||
\(423\) | 7.20913e8 | 0.463118 | ||||||||
\(424\) | −3.97838e8 | −0.253469 | ||||||||
\(425\) | 2.44321e8 | 0.154383 | ||||||||
\(426\) | 7.74128e8 | 0.485153 | ||||||||
\(427\) | −1.31898e9 | −0.819860 | ||||||||
\(428\) | 6.55794e8 | 0.404310 | ||||||||
\(429\) | −8.00824e8 | −0.489707 | ||||||||
\(430\) | −1.33476e9 | −0.809589 | ||||||||
\(431\) | −1.20261e9 | −0.723529 | −0.361764 | − | 0.932270i | \(-0.617826\pi\) | ||||
−0.361764 | + | 0.932270i | \(0.617826\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 1.83198e9 | 1.08446 | 0.542228 | − | 0.840231i | \(-0.317581\pi\) | ||||
0.542228 | + | 0.840231i | \(0.317581\pi\) | |||||||
\(434\) | 3.70382e7 | 0.0217488 | ||||||||
\(435\) | −1.91554e9 | −1.11578 | ||||||||
\(436\) | −8.11089e8 | −0.468668 | ||||||||
\(437\) | 4.69240e8 | 0.268974 | ||||||||
\(438\) | −2.10784e8 | −0.119861 | ||||||||
\(439\) | −1.50903e9 | −0.851277 | −0.425639 | − | 0.904893i | \(-0.639951\pi\) | ||||
−0.425639 | + | 0.904893i | \(0.639951\pi\) | |||||||
\(440\) | 8.90603e8 | 0.498425 | ||||||||
\(441\) | 5.70115e8 | 0.316539 | ||||||||
\(442\) | −2.97912e8 | −0.164100 | ||||||||
\(443\) | 2.98792e9 | 1.63289 | 0.816444 | − | 0.577425i | \(-0.195942\pi\) | ||||
0.816444 | + | 0.577425i | \(0.195942\pi\) | |||||||
\(444\) | 4.13526e7 | 0.0224214 | ||||||||
\(445\) | −1.41138e9 | −0.759250 | ||||||||
\(446\) | 2.53722e9 | 1.35421 | ||||||||
\(447\) | −2.00980e9 | −1.06433 | ||||||||
\(448\) | 3.32168e8 | 0.174536 | ||||||||
\(449\) | 1.91998e9 | 1.00100 | 0.500500 | − | 0.865737i | \(-0.333150\pi\) | ||||
0.500500 | + | 0.865737i | \(0.333150\pi\) | |||||||
\(450\) | 2.22473e8 | 0.115089 | ||||||||
\(451\) | −5.87410e6 | −0.00301525 | ||||||||
\(452\) | 3.47725e7 | 0.0177114 | ||||||||
\(453\) | 7.50452e8 | 0.379297 | ||||||||
\(454\) | 7.77358e7 | 0.0389875 | ||||||||
\(455\) | −2.51219e9 | −1.25029 | ||||||||
\(456\) | −5.33145e8 | −0.263311 | ||||||||
\(457\) | −1.94014e9 | −0.950883 | −0.475441 | − | 0.879747i | \(-0.657712\pi\) | ||||
−0.475441 | + | 0.879747i | \(0.657712\pi\) | |||||||
\(458\) | 2.03715e9 | 0.990818 | ||||||||
\(459\) | 1.26064e8 | 0.0608482 | ||||||||
\(460\) | −2.65522e8 | −0.127189 | ||||||||
\(461\) | −8.14499e8 | −0.387202 | −0.193601 | − | 0.981080i | \(-0.562017\pi\) | ||||
−0.193601 | + | 0.981080i | \(0.562017\pi\) | |||||||
\(462\) | 1.39620e9 | 0.658720 | ||||||||
\(463\) | −6.61468e7 | −0.0309724 | −0.0154862 | − | 0.999880i | \(-0.504930\pi\) | ||||
−0.0154862 | + | 0.999880i | \(0.504930\pi\) | |||||||
\(464\) | −8.52217e8 | −0.396038 | ||||||||
\(465\) | 3.36390e7 | 0.0155152 | ||||||||
\(466\) | 2.11324e8 | 0.0967382 | ||||||||
\(467\) | −2.88027e9 | −1.30865 | −0.654327 | − | 0.756212i | \(-0.727048\pi\) | ||||
−0.654327 | + | 0.756212i | \(0.727048\pi\) | |||||||
\(468\) | −2.71272e8 | −0.122333 | ||||||||
\(469\) | −2.61110e9 | −1.16874 | ||||||||
\(470\) | 2.69763e9 | 1.19851 | ||||||||
\(471\) | 8.99308e8 | 0.396584 | ||||||||
\(472\) | 8.25278e8 | 0.361246 | ||||||||
\(473\) | −2.49605e9 | −1.08452 | ||||||||
\(474\) | 1.29677e9 | 0.559294 | ||||||||
\(475\) | −1.47120e9 | −0.629860 | ||||||||
\(476\) | 5.19396e8 | 0.220737 | ||||||||
\(477\) | −5.66453e8 | −0.238973 | ||||||||
\(478\) | −1.02139e8 | −0.0427754 | ||||||||
\(479\) | −3.40043e9 | −1.41371 | −0.706854 | − | 0.707360i | \(-0.749886\pi\) | ||||
−0.706854 | + | 0.707360i | \(0.749886\pi\) | |||||||
\(480\) | 3.01683e8 | 0.124511 | ||||||||
\(481\) | −1.39141e8 | −0.0570096 | ||||||||
\(482\) | 1.17995e9 | 0.479954 | ||||||||
\(483\) | −4.16260e8 | −0.168093 | ||||||||
\(484\) | 4.18276e8 | 0.167689 | ||||||||
\(485\) | 4.05243e9 | 1.61295 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | 3.01213e9 | 1.18174 | 0.590871 | − | 0.806766i | \(-0.298784\pi\) | ||||
0.590871 | + | 0.806766i | \(0.298784\pi\) | |||||||
\(488\) | −5.32954e8 | −0.207596 | ||||||||
\(489\) | −3.94100e8 | −0.152414 | ||||||||
\(490\) | 2.13335e9 | 0.819174 | ||||||||
\(491\) | −835191. | −0.000318420 0 | −0.000159210 | − | 1.00000i | \(-0.500051\pi\) | ||||
−0.000159210 | 1.00000i | \(0.500051\pi\) | ||||||||
\(492\) | −1.98979e6 | −0.000753235 0 | ||||||||
\(493\) | −1.33257e9 | −0.500872 | ||||||||
\(494\) | 1.79390e9 | 0.669505 | ||||||||
\(495\) | 1.26807e9 | 0.469919 | ||||||||
\(496\) | 1.49659e7 | 0.00550702 | ||||||||
\(497\) | 4.54126e9 | 1.65932 | ||||||||
\(498\) | −1.16694e9 | −0.423396 | ||||||||
\(499\) | −4.35806e9 | −1.57015 | −0.785075 | − | 0.619401i | \(-0.787375\pi\) | ||||
−0.785075 | + | 0.619401i | \(0.787375\pi\) | |||||||
\(500\) | −8.72447e8 | −0.312136 | ||||||||
\(501\) | −2.05633e9 | −0.730569 | ||||||||
\(502\) | 2.13899e9 | 0.754650 | ||||||||
\(503\) | −2.40286e8 | −0.0841862 | −0.0420931 | − | 0.999114i | \(-0.513403\pi\) | ||||
−0.0420931 | + | 0.999114i | \(0.513403\pi\) | |||||||
\(504\) | 4.72950e8 | 0.164554 | ||||||||
\(505\) | 3.25413e9 | 1.12438 | ||||||||
\(506\) | −4.96535e8 | −0.170382 | ||||||||
\(507\) | −7.81449e8 | −0.266301 | ||||||||
\(508\) | −3.89522e8 | −0.131828 | ||||||||
\(509\) | −3.36572e9 | −1.13127 | −0.565634 | − | 0.824656i | \(-0.691369\pi\) | ||||
−0.565634 | + | 0.824656i | \(0.691369\pi\) | |||||||
\(510\) | 4.71729e8 | 0.157470 | ||||||||
\(511\) | −1.23652e9 | −0.409947 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −7.59107e8 | −0.248252 | ||||||||
\(514\) | −1.09626e9 | −0.356076 | ||||||||
\(515\) | −1.06506e9 | −0.343597 | ||||||||
\(516\) | −8.45513e8 | −0.270923 | ||||||||
\(517\) | 5.04466e9 | 1.60552 | ||||||||
\(518\) | 2.42587e8 | 0.0766854 | ||||||||
\(519\) | −3.18099e9 | −0.998797 | ||||||||
\(520\) | −1.01509e9 | −0.316587 | ||||||||
\(521\) | 6.69390e8 | 0.207371 | 0.103685 | − | 0.994610i | \(-0.466937\pi\) | ||||
0.103685 | + | 0.994610i | \(0.466937\pi\) | |||||||
\(522\) | −1.21341e9 | −0.373388 | ||||||||
\(523\) | 6.04759e9 | 1.84853 | 0.924265 | − | 0.381752i | \(-0.124679\pi\) | ||||
0.924265 | + | 0.381752i | \(0.124679\pi\) | |||||||
\(524\) | −1.66874e9 | −0.506674 | ||||||||
\(525\) | 1.30509e9 | 0.393626 | ||||||||
\(526\) | 1.28469e9 | 0.384899 | ||||||||
\(527\) | 2.34015e7 | 0.00696476 | ||||||||
\(528\) | 5.64157e8 | 0.166794 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | −2.11965e9 | −0.618441 | ||||||||
\(531\) | 1.17505e9 | 0.340586 | ||||||||
\(532\) | −3.12759e9 | −0.900573 | ||||||||
\(533\) | 6.69516e6 | 0.00191521 | ||||||||
\(534\) | −8.94048e8 | −0.254078 | ||||||||
\(535\) | 3.49402e9 | 0.986477 | ||||||||
\(536\) | −1.05506e9 | −0.295937 | ||||||||
\(537\) | 6.32553e8 | 0.176273 | ||||||||
\(538\) | 3.73687e9 | 1.03459 | ||||||||
\(539\) | 3.98943e9 | 1.09736 | ||||||||
\(540\) | 4.29545e8 | 0.117390 | ||||||||
\(541\) | 9.56170e8 | 0.259624 | 0.129812 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129812 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(542\) | 4.41348e9 | 1.19065 | ||||||||
\(543\) | −1.52860e9 | −0.409726 | ||||||||
\(544\) | 2.09870e8 | 0.0558927 | ||||||||
\(545\) | −4.32141e9 | −1.14351 | ||||||||
\(546\) | −1.59136e9 | −0.418402 | ||||||||
\(547\) | −7.50590e9 | −1.96086 | −0.980431 | − | 0.196864i | \(-0.936924\pi\) | ||||
−0.980431 | + | 0.196864i | \(0.936924\pi\) | |||||||
\(548\) | 2.91443e9 | 0.756522 | ||||||||
\(549\) | −7.58834e8 | −0.195724 | ||||||||
\(550\) | 1.55678e9 | 0.398986 | ||||||||
\(551\) | 8.02420e9 | 2.04348 | ||||||||
\(552\) | −1.68197e8 | −0.0425628 | ||||||||
\(553\) | 7.60727e9 | 1.91289 | ||||||||
\(554\) | 3.82523e9 | 0.955813 | ||||||||
\(555\) | 2.20323e8 | 0.0547060 | ||||||||
\(556\) | −2.79091e9 | −0.688626 | ||||||||
\(557\) | 2.30925e9 | 0.566209 | 0.283105 | − | 0.959089i | \(-0.408636\pi\) | ||||
0.283105 | + | 0.959089i | \(0.408636\pi\) | |||||||
\(558\) | 2.13088e7 | 0.00519207 | ||||||||
\(559\) | 2.84494e9 | 0.688862 | ||||||||
\(560\) | 1.76976e9 | 0.425851 | ||||||||
\(561\) | 8.82148e8 | 0.210946 | ||||||||
\(562\) | 5.89957e9 | 1.40199 | ||||||||
\(563\) | 2.20676e9 | 0.521166 | 0.260583 | − | 0.965451i | \(-0.416085\pi\) | ||||
0.260583 | + | 0.965451i | \(0.416085\pi\) | |||||||
\(564\) | 1.70883e9 | 0.401072 | ||||||||
\(565\) | 1.85265e8 | 0.0432140 | ||||||||
\(566\) | −5.46360e9 | −1.26655 | ||||||||
\(567\) | 6.73400e8 | 0.155143 | ||||||||
\(568\) | 1.83497e9 | 0.420155 | ||||||||
\(569\) | −2.56775e9 | −0.584332 | −0.292166 | − | 0.956368i | \(-0.594376\pi\) | ||||
−0.292166 | + | 0.956368i | \(0.594376\pi\) | |||||||
\(570\) | −2.84055e9 | −0.642452 | ||||||||
\(571\) | −3.30249e9 | −0.742360 | −0.371180 | − | 0.928561i | \(-0.621047\pi\) | ||||
−0.371180 | + | 0.928561i | \(0.621047\pi\) | |||||||
\(572\) | −1.89825e9 | −0.424099 | ||||||||
\(573\) | −3.42497e9 | −0.760528 | ||||||||
\(574\) | −1.16727e7 | −0.00257621 | ||||||||
\(575\) | −4.64134e8 | −0.101814 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −4.83666e9 | −1.04817 | −0.524083 | − | 0.851667i | \(-0.675592\pi\) | ||||
−0.524083 | + | 0.851667i | \(0.675592\pi\) | |||||||
\(578\) | −2.95454e9 | −0.636419 | ||||||||
\(579\) | 3.68694e9 | 0.789388 | ||||||||
\(580\) | −4.54054e9 | −0.966295 | ||||||||
\(581\) | −6.84564e9 | −1.44810 | ||||||||
\(582\) | 2.56704e9 | 0.539761 | ||||||||
\(583\) | −3.96381e9 | −0.828462 | ||||||||
\(584\) | −4.99635e8 | −0.103803 | ||||||||
\(585\) | −1.44531e9 | −0.298481 | ||||||||
\(586\) | −3.78593e8 | −0.0777198 | ||||||||
\(587\) | 8.36248e9 | 1.70648 | 0.853241 | − | 0.521517i | \(-0.174634\pi\) | ||||
0.853241 | + | 0.521517i | \(0.174634\pi\) | |||||||
\(588\) | 1.35138e9 | 0.274131 | ||||||||
\(589\) | −1.40914e8 | −0.0284152 | ||||||||
\(590\) | 4.39702e9 | 0.881406 | ||||||||
\(591\) | −3.13332e9 | −0.624380 | ||||||||
\(592\) | 9.80209e7 | 0.0194175 | ||||||||
\(593\) | −7.18982e9 | −1.41588 | −0.707941 | − | 0.706272i | \(-0.750376\pi\) | ||||
−0.707941 | + | 0.706272i | \(0.750376\pi\) | |||||||
\(594\) | 8.03263e8 | 0.157255 | ||||||||
\(595\) | 2.76730e9 | 0.538576 | ||||||||
\(596\) | −4.76397e9 | −0.921737 | ||||||||
\(597\) | 3.81690e8 | 0.0734177 | ||||||||
\(598\) | 5.65940e8 | 0.108222 | ||||||||
\(599\) | 7.64624e9 | 1.45363 | 0.726815 | − | 0.686833i | \(-0.241000\pi\) | ||||
0.726815 | + | 0.686833i | \(0.241000\pi\) | |||||||
\(600\) | 5.27344e8 | 0.0996700 | ||||||||
\(601\) | 1.72237e9 | 0.323643 | 0.161821 | − | 0.986820i | \(-0.448263\pi\) | ||||
0.161821 | + | 0.986820i | \(0.448263\pi\) | |||||||
\(602\) | −4.96003e9 | −0.926609 | ||||||||
\(603\) | −1.50222e9 | −0.279012 | ||||||||
\(604\) | 1.77885e9 | 0.328481 | ||||||||
\(605\) | 2.22854e9 | 0.409145 | ||||||||
\(606\) | 2.06135e9 | 0.376268 | ||||||||
\(607\) | −4.96333e9 | −0.900768 | −0.450384 | − | 0.892835i | \(-0.648713\pi\) | ||||
−0.450384 | + | 0.892835i | \(0.648713\pi\) | |||||||
\(608\) | −1.26375e9 | −0.228034 | ||||||||
\(609\) | −7.11823e9 | −1.27706 | ||||||||
\(610\) | −2.83953e9 | −0.506515 | ||||||||
\(611\) | −5.74979e9 | −1.01978 | ||||||||
\(612\) | 2.98819e8 | 0.0526961 | ||||||||
\(613\) | 5.74407e9 | 1.00718 | 0.503591 | − | 0.863942i | \(-0.332012\pi\) | ||||
0.503591 | + | 0.863942i | \(0.332012\pi\) | |||||||
\(614\) | 2.78076e9 | 0.484814 | ||||||||
\(615\) | −1.06015e7 | −0.00183782 | ||||||||
\(616\) | 3.30951e9 | 0.570469 | ||||||||
\(617\) | −1.05462e10 | −1.80758 | −0.903788 | − | 0.427981i | \(-0.859225\pi\) | ||||
−0.903788 | + | 0.427981i | \(0.859225\pi\) | |||||||
\(618\) | −6.74669e8 | −0.114982 | ||||||||
\(619\) | 3.60119e9 | 0.610279 | 0.305140 | − | 0.952308i | \(-0.401297\pi\) | ||||
0.305140 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(620\) | 7.97370e7 | 0.0134366 | ||||||||
\(621\) | −2.39483e8 | −0.0401286 | ||||||||
\(622\) | −6.77167e9 | −1.12831 | ||||||||
\(623\) | −5.24475e9 | −0.868994 | ||||||||
\(624\) | −6.43014e8 | −0.105944 | ||||||||
\(625\) | −7.62856e9 | −1.24986 | ||||||||
\(626\) | 4.25157e9 | 0.692691 | ||||||||
\(627\) | −5.31193e9 | −0.860628 | ||||||||
\(628\) | 2.13169e9 | 0.343452 | ||||||||
\(629\) | 1.53271e8 | 0.0245574 | ||||||||
\(630\) | 2.51984e9 | 0.401496 | ||||||||
\(631\) | −2.99729e9 | −0.474926 | −0.237463 | − | 0.971397i | \(-0.576316\pi\) | ||||
−0.237463 | + | 0.971397i | \(0.576316\pi\) | |||||||
\(632\) | 3.07384e9 | 0.484363 | ||||||||
\(633\) | 5.09162e9 | 0.797890 | ||||||||
\(634\) | −6.02377e9 | −0.938763 | ||||||||
\(635\) | −2.07534e9 | −0.321648 | ||||||||
\(636\) | −1.34270e9 | −0.206957 | ||||||||
\(637\) | −4.54707e9 | −0.697017 | ||||||||
\(638\) | −8.49096e9 | −1.29445 | ||||||||
\(639\) | 2.61268e9 | 0.396126 | ||||||||
\(640\) | 7.15101e8 | 0.107829 | ||||||||
\(641\) | 1.30075e9 | 0.195069 | 0.0975347 | − | 0.995232i | \(-0.468904\pi\) | ||||
0.0975347 | + | 0.995232i | \(0.468904\pi\) | |||||||
\(642\) | 2.21331e9 | 0.330118 | ||||||||
\(643\) | −9.31677e9 | −1.38206 | −0.691030 | − | 0.722826i | \(-0.742843\pi\) | ||||
−0.691030 | + | 0.722826i | \(0.742843\pi\) | |||||||
\(644\) | −9.86691e8 | −0.145573 | ||||||||
\(645\) | −4.50482e9 | −0.661027 | ||||||||
\(646\) | −1.97607e9 | −0.288396 | ||||||||
\(647\) | −9.62984e9 | −1.39783 | −0.698914 | − | 0.715205i | \(-0.746333\pi\) | ||||
−0.698914 | + | 0.715205i | \(0.746333\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 8.22256e9 | 1.18073 | ||||||||
\(650\) | −1.77438e9 | −0.253425 | ||||||||
\(651\) | 1.25004e8 | 0.0177579 | ||||||||
\(652\) | −9.34162e8 | −0.131994 | ||||||||
\(653\) | 4.51671e9 | 0.634784 | 0.317392 | − | 0.948294i | \(-0.397193\pi\) | ||||
0.317392 | + | 0.948294i | \(0.397193\pi\) | |||||||
\(654\) | −2.73742e9 | −0.382666 | ||||||||
\(655\) | −8.89089e9 | −1.23623 | ||||||||
\(656\) | −4.71655e6 | −0.000652321 0 | ||||||||
\(657\) | −7.11395e8 | −0.0978660 | ||||||||
\(658\) | 1.00245e10 | 1.37174 | ||||||||
\(659\) | 6.60804e9 | 0.899443 | 0.449722 | − | 0.893169i | \(-0.351523\pi\) | ||||
0.449722 | + | 0.893169i | \(0.351523\pi\) | |||||||
\(660\) | 3.00578e9 | 0.406962 | ||||||||
\(661\) | 1.31054e10 | 1.76500 | 0.882502 | − | 0.470308i | \(-0.155857\pi\) | ||||
0.882502 | + | 0.470308i | \(0.155857\pi\) | |||||||
\(662\) | −1.49191e9 | −0.199867 | ||||||||
\(663\) | −1.00545e9 | −0.133987 | ||||||||
\(664\) | −2.76609e9 | −0.366672 | ||||||||
\(665\) | −1.66635e10 | −2.19731 | ||||||||
\(666\) | 1.39565e8 | 0.0183070 | ||||||||
\(667\) | 2.53148e9 | 0.330319 | ||||||||
\(668\) | −4.87427e9 | −0.632691 | ||||||||
\(669\) | 8.56313e9 | 1.10571 | ||||||||
\(670\) | −5.62125e9 | −0.722057 | ||||||||
\(671\) | −5.31002e9 | −0.678527 | ||||||||
\(672\) | 1.12107e9 | 0.142508 | ||||||||
\(673\) | −1.48862e9 | −0.188249 | −0.0941243 | − | 0.995560i | \(-0.530005\pi\) | ||||
−0.0941243 | + | 0.995560i | \(0.530005\pi\) | |||||||
\(674\) | −5.76477e9 | −0.725225 | ||||||||
\(675\) | 7.50847e8 | 0.0939698 | ||||||||
\(676\) | −1.85232e9 | −0.230623 | ||||||||
\(677\) | 1.38673e10 | 1.71763 | 0.858817 | − | 0.512282i | \(-0.171200\pi\) | ||||
0.858817 | + | 0.512282i | \(0.171200\pi\) | |||||||
\(678\) | 1.17357e8 | 0.0144613 | ||||||||
\(679\) | 1.50590e10 | 1.84609 | ||||||||
\(680\) | 1.11817e9 | 0.136373 | ||||||||
\(681\) | 2.62358e8 | 0.0318332 | ||||||||
\(682\) | 1.49111e8 | 0.0179996 | ||||||||
\(683\) | −6.45650e9 | −0.775398 | −0.387699 | − | 0.921786i | \(-0.626730\pi\) | ||||
−0.387699 | + | 0.921786i | \(0.626730\pi\) | |||||||
\(684\) | −1.79936e9 | −0.214992 | ||||||||
\(685\) | 1.55279e10 | 1.84584 | ||||||||
\(686\) | −4.20609e8 | −0.0497443 | ||||||||
\(687\) | 6.87538e9 | 0.809000 | ||||||||
\(688\) | −2.00418e9 | −0.234626 | ||||||||
\(689\) | 4.51786e9 | 0.526218 | ||||||||
\(690\) | −8.96138e8 | −0.103849 | ||||||||
\(691\) | −8.22490e8 | −0.0948325 | −0.0474163 | − | 0.998875i | \(-0.515099\pi\) | ||||
−0.0474163 | + | 0.998875i | \(0.515099\pi\) | |||||||
\(692\) | −7.54013e9 | −0.864983 | ||||||||
\(693\) | 4.71218e9 | 0.537843 | ||||||||
\(694\) | −6.51461e9 | −0.739827 | ||||||||
\(695\) | −1.48697e10 | −1.68018 | ||||||||
\(696\) | −2.87623e9 | −0.323364 | ||||||||
\(697\) | −7.37506e6 | −0.000824994 0 | ||||||||
\(698\) | −3.40028e9 | −0.378460 | ||||||||
\(699\) | 7.13218e8 | 0.0789864 | ||||||||
\(700\) | 3.09355e9 | 0.340890 | ||||||||
\(701\) | 1.78860e10 | 1.96111 | 0.980553 | − | 0.196252i | \(-0.0628772\pi\) | ||||
0.980553 | + | 0.196252i | \(0.0628772\pi\) | |||||||
\(702\) | −9.15541e8 | −0.0998845 | ||||||||
\(703\) | −9.22934e8 | −0.100191 | ||||||||
\(704\) | 1.33726e9 | 0.144448 | ||||||||
\(705\) | 9.10451e9 | 0.978576 | ||||||||
\(706\) | −1.68693e9 | −0.180418 | ||||||||
\(707\) | 1.20925e10 | 1.28691 | ||||||||
\(708\) | 2.78531e9 | 0.294956 | ||||||||
\(709\) | 1.14149e10 | 1.20285 | 0.601424 | − | 0.798930i | \(-0.294600\pi\) | ||||
0.601424 | + | 0.798930i | \(0.294600\pi\) | |||||||
\(710\) | 9.77657e9 | 1.02514 | ||||||||
\(711\) | 4.37661e9 | 0.456662 | ||||||||
\(712\) | −2.11923e9 | −0.220038 | ||||||||
\(713\) | −4.44555e7 | −0.00459317 | ||||||||
\(714\) | 1.75296e9 | 0.180231 | ||||||||
\(715\) | −1.01137e10 | −1.03476 | ||||||||
\(716\) | 1.49938e9 | 0.152657 | ||||||||
\(717\) | −3.44720e8 | −0.0349260 | ||||||||
\(718\) | −7.70004e9 | −0.776349 | ||||||||
\(719\) | −4.68698e9 | −0.470264 | −0.235132 | − | 0.971963i | \(-0.575552\pi\) | ||||
−0.235132 | + | 0.971963i | \(0.575552\pi\) | |||||||
\(720\) | 1.01818e9 | 0.101663 | ||||||||
\(721\) | −3.95781e9 | −0.393262 | ||||||||
\(722\) | 4.74811e9 | 0.469505 | ||||||||
\(723\) | 3.98234e9 | 0.391881 | ||||||||
\(724\) | −3.62334e9 | −0.354833 | ||||||||
\(725\) | −7.93689e9 | −0.773512 | ||||||||
\(726\) | 1.41168e9 | 0.136917 | ||||||||
\(727\) | −1.85231e10 | −1.78790 | −0.893951 | − | 0.448164i | \(-0.852078\pi\) | ||||
−0.893951 | + | 0.448164i | \(0.852078\pi\) | |||||||
\(728\) | −3.77211e9 | −0.362347 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −2.66201e9 | −0.253268 | ||||||||
\(731\) | −3.13385e9 | −0.296734 | ||||||||
\(732\) | −1.79872e9 | −0.169502 | ||||||||
\(733\) | 1.69649e9 | 0.159107 | 0.0795534 | − | 0.996831i | \(-0.474651\pi\) | ||||
0.0795534 | + | 0.996831i | \(0.474651\pi\) | |||||||
\(734\) | −4.73245e8 | −0.0441723 | ||||||||
\(735\) | 7.20006e9 | 0.668853 | ||||||||
\(736\) | −3.98688e8 | −0.0368605 | ||||||||
\(737\) | −1.05119e10 | −0.967266 | ||||||||
\(738\) | −6.71556e6 | −0.000615014 0 | ||||||||
\(739\) | −8.17586e9 | −0.745209 | −0.372604 | − | 0.927990i | \(-0.621535\pi\) | ||||
−0.372604 | + | 0.927990i | \(0.621535\pi\) | |||||||
\(740\) | 5.22247e8 | 0.0473768 | ||||||||
\(741\) | 6.05441e9 | 0.546649 | ||||||||
\(742\) | −7.87669e9 | −0.707832 | ||||||||
\(743\) | 1.95551e9 | 0.174904 | 0.0874519 | − | 0.996169i | \(-0.472128\pi\) | ||||
0.0874519 | + | 0.996169i | \(0.472128\pi\) | |||||||
\(744\) | 5.05099e7 | 0.00449646 | ||||||||
\(745\) | −2.53820e10 | −2.24895 | ||||||||
\(746\) | −6.06155e9 | −0.534562 | ||||||||
\(747\) | −3.93843e9 | −0.345702 | ||||||||
\(748\) | 2.09102e9 | 0.182685 | ||||||||
\(749\) | 1.29839e10 | 1.12907 | ||||||||
\(750\) | −2.94451e9 | −0.254858 | ||||||||
\(751\) | 1.41485e10 | 1.21891 | 0.609453 | − | 0.792823i | \(-0.291389\pi\) | ||||
0.609453 | + | 0.792823i | \(0.291389\pi\) | |||||||
\(752\) | 4.05056e9 | 0.347338 | ||||||||
\(753\) | 7.21909e9 | 0.616169 | ||||||||
\(754\) | 9.67780e9 | 0.822199 | ||||||||
\(755\) | 9.47757e9 | 0.801461 | ||||||||
\(756\) | 1.59621e9 | 0.134358 | ||||||||
\(757\) | −3.50371e9 | −0.293557 | −0.146779 | − | 0.989169i | \(-0.546890\pi\) | ||||
−0.146779 | + | 0.989169i | \(0.546890\pi\) | |||||||
\(758\) | −1.97725e9 | −0.164899 | ||||||||
\(759\) | −1.67581e9 | −0.139116 | ||||||||
\(760\) | −6.73316e9 | −0.556380 | ||||||||
\(761\) | 1.18352e9 | 0.0973485 | 0.0486743 | − | 0.998815i | \(-0.484500\pi\) | ||||
0.0486743 | + | 0.998815i | \(0.484500\pi\) | |||||||
\(762\) | −1.31464e9 | −0.107637 | ||||||||
\(763\) | −1.60585e10 | −1.30879 | ||||||||
\(764\) | −8.11844e9 | −0.658636 | ||||||||
\(765\) | 1.59208e9 | 0.128573 | ||||||||
\(766\) | −1.56051e10 | −1.25449 | ||||||||
\(767\) | −9.37189e9 | −0.749969 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 1.26642e10 | 1.00424 | 0.502118 | − | 0.864799i | \(-0.332554\pi\) | ||||
0.502118 | + | 0.864799i | \(0.332554\pi\) | |||||||
\(770\) | 1.76328e10 | 1.39189 | ||||||||
\(771\) | −3.69988e9 | −0.290735 | ||||||||
\(772\) | 8.73941e9 | 0.683630 | ||||||||
\(773\) | −6.91080e9 | −0.538146 | −0.269073 | − | 0.963120i | \(-0.586717\pi\) | ||||
−0.269073 | + | 0.963120i | \(0.586717\pi\) | |||||||
\(774\) | −2.85361e9 | −0.221208 | ||||||||
\(775\) | 1.39381e8 | 0.0107559 | ||||||||
\(776\) | 6.08483e9 | 0.467447 | ||||||||
\(777\) | 8.18729e8 | 0.0626133 | ||||||||
\(778\) | 1.36528e10 | 1.03943 | ||||||||
\(779\) | 4.44095e7 | 0.00336585 | ||||||||
\(780\) | −3.42593e9 | −0.258492 | ||||||||
\(781\) | 1.82825e10 | 1.37327 | ||||||||
\(782\) | −6.23411e8 | −0.0466177 | ||||||||
\(783\) | −4.09526e9 | −0.304870 | ||||||||
\(784\) | 3.20328e9 | 0.237404 | ||||||||
\(785\) | 1.13575e10 | 0.837990 | ||||||||
\(786\) | −5.63199e9 | −0.413697 | ||||||||
\(787\) | 1.12082e10 | 0.819644 | 0.409822 | − | 0.912166i | \(-0.365591\pi\) | ||||
0.409822 | + | 0.912166i | \(0.365591\pi\) | |||||||
\(788\) | −7.42714e9 | −0.540729 | ||||||||
\(789\) | 4.33581e9 | 0.314269 | ||||||||
\(790\) | 1.63771e10 | 1.18180 | ||||||||
\(791\) | 6.88453e8 | 0.0494603 | ||||||||
\(792\) | 1.90403e9 | 0.136187 | ||||||||
\(793\) | 6.05224e9 | 0.430983 | ||||||||
\(794\) | 7.61383e9 | 0.539798 | ||||||||
\(795\) | −7.15381e9 | −0.504955 | ||||||||
\(796\) | 9.04747e8 | 0.0635816 | ||||||||
\(797\) | 2.00641e9 | 0.140383 | 0.0701917 | − | 0.997534i | \(-0.477639\pi\) | ||||
0.0701917 | + | 0.997534i | \(0.477639\pi\) | |||||||
\(798\) | −1.05556e10 | −0.735314 | ||||||||
\(799\) | 6.33368e9 | 0.439281 | ||||||||
\(800\) | 1.25000e9 | 0.0863167 | ||||||||
\(801\) | −3.01741e9 | −0.207454 | ||||||||
\(802\) | 8.31061e9 | 0.568883 | ||||||||
\(803\) | −4.97805e9 | −0.339278 | ||||||||
\(804\) | −3.56082e9 | −0.241631 | ||||||||
\(805\) | −5.25701e9 | −0.355184 | ||||||||
\(806\) | −1.69953e8 | −0.0114329 | ||||||||
\(807\) | 1.26119e10 | 0.844742 | ||||||||
\(808\) | 4.88615e9 | 0.325857 | ||||||||
\(809\) | −2.85624e9 | −0.189660 | −0.0948300 | − | 0.995493i | \(-0.530231\pi\) | ||||
−0.0948300 | + | 0.995493i | \(0.530231\pi\) | |||||||
\(810\) | 1.44971e9 | 0.0958484 | ||||||||
\(811\) | 1.97522e10 | 1.30030 | 0.650148 | − | 0.759808i | \(-0.274707\pi\) | ||||
0.650148 | + | 0.759808i | \(0.274707\pi\) | |||||||
\(812\) | −1.68728e10 | −1.10597 | ||||||||
\(813\) | 1.48955e10 | 0.972161 | ||||||||
\(814\) | 9.76619e8 | 0.0634658 | ||||||||
\(815\) | −4.97714e9 | −0.322054 | ||||||||
\(816\) | 7.08312e8 | 0.0456362 | ||||||||
\(817\) | 1.88707e10 | 1.21063 | ||||||||
\(818\) | 2.14048e10 | 1.36733 | ||||||||
\(819\) | −5.37084e9 | −0.341624 | ||||||||
\(820\) | −2.51294e7 | −0.00159160 | ||||||||
\(821\) | 1.99137e10 | 1.25589 | 0.627943 | − | 0.778260i | \(-0.283897\pi\) | ||||
0.627943 | + | 0.778260i | \(0.283897\pi\) | |||||||
\(822\) | 9.83621e9 | 0.617698 | ||||||||
\(823\) | 2.60455e10 | 1.62867 | 0.814336 | − | 0.580393i | \(-0.197101\pi\) | ||||
0.814336 | + | 0.580393i | \(0.197101\pi\) | |||||||
\(824\) | −1.59922e9 | −0.0995776 | ||||||||
\(825\) | 5.25412e9 | 0.325770 | ||||||||
\(826\) | 1.63395e10 | 1.00881 | ||||||||
\(827\) | 9.95427e9 | 0.611984 | 0.305992 | − | 0.952034i | \(-0.401012\pi\) | ||||
0.305992 | + | 0.952034i | \(0.401012\pi\) | |||||||
\(828\) | −5.67664e8 | −0.0347524 | ||||||||
\(829\) | −3.29779e9 | −0.201040 | −0.100520 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100520 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(830\) | −1.47375e10 | −0.894644 | ||||||||
\(831\) | 1.29101e10 | 0.780418 | ||||||||
\(832\) | −1.52418e9 | −0.0917498 | ||||||||
\(833\) | 5.00882e9 | 0.300247 | ||||||||
\(834\) | −9.41931e9 | −0.562261 | ||||||||
\(835\) | −2.59697e10 | −1.54370 | ||||||||
\(836\) | −1.25912e10 | −0.745326 | ||||||||
\(837\) | 7.19174e7 | 0.00423930 | ||||||||
\(838\) | 2.73415e9 | 0.160498 | ||||||||
\(839\) | 1.21672e9 | 0.0711252 | 0.0355626 | − | 0.999367i | \(-0.488678\pi\) | ||||
0.0355626 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(840\) | 5.97295e9 | 0.347705 | ||||||||
\(841\) | 2.60394e10 | 1.50954 | ||||||||
\(842\) | 1.46547e10 | 0.846028 | ||||||||
\(843\) | 1.99111e10 | 1.14472 | ||||||||
\(844\) | 1.20690e10 | 0.690993 | ||||||||
\(845\) | −9.86903e9 | −0.562699 | ||||||||
\(846\) | 5.76730e9 | 0.327474 | ||||||||
\(847\) | 8.28135e9 | 0.468284 | ||||||||
\(848\) | −3.18270e9 | −0.179230 | ||||||||
\(849\) | −1.84396e10 | −1.03413 | ||||||||
\(850\) | 1.95457e9 | 0.109165 | ||||||||
\(851\) | −2.91167e8 | −0.0161953 | ||||||||
\(852\) | 6.19302e9 | 0.343055 | ||||||||
\(853\) | −1.25896e10 | −0.694527 | −0.347264 | − | 0.937768i | \(-0.612889\pi\) | ||||
−0.347264 | + | 0.937768i | \(0.612889\pi\) | |||||||
\(854\) | −1.05518e10 | −0.579728 | ||||||||
\(855\) | −9.58687e9 | −0.524560 | ||||||||
\(856\) | 5.24636e9 | 0.285890 | ||||||||
\(857\) | −3.98461e9 | −0.216248 | −0.108124 | − | 0.994137i | \(-0.534484\pi\) | ||||
−0.108124 | + | 0.994137i | \(0.534484\pi\) | |||||||
\(858\) | −6.40659e9 | −0.346275 | ||||||||
\(859\) | −1.29735e10 | −0.698361 | −0.349181 | − | 0.937055i | \(-0.613540\pi\) | ||||
−0.349181 | + | 0.937055i | \(0.613540\pi\) | |||||||
\(860\) | −1.06781e10 | −0.572466 | ||||||||
\(861\) | −3.93955e7 | −0.00210346 | ||||||||
\(862\) | −9.62091e9 | −0.511612 | ||||||||
\(863\) | −2.90007e10 | −1.53593 | −0.767963 | − | 0.640495i | \(-0.778729\pi\) | ||||
−0.767963 | + | 0.640495i | \(0.778729\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | −4.01732e10 | −2.11048 | ||||||||
\(866\) | 1.46558e10 | 0.766826 | ||||||||
\(867\) | −9.97159e9 | −0.519634 | ||||||||
\(868\) | 2.96306e8 | 0.0153788 | ||||||||
\(869\) | 3.06258e10 | 1.58314 | ||||||||
\(870\) | −1.53243e10 | −0.788976 | ||||||||
\(871\) | 1.19813e10 | 0.614383 | ||||||||
\(872\) | −6.48871e9 | −0.331399 | ||||||||
\(873\) | 8.66375e9 | 0.440713 | ||||||||
\(874\) | 3.75392e9 | 0.190193 | ||||||||
\(875\) | −1.72734e10 | −0.871663 | ||||||||
\(876\) | −1.68627e9 | −0.0847544 | ||||||||
\(877\) | −2.05862e10 | −1.03057 | −0.515286 | − | 0.857018i | \(-0.672314\pi\) | ||||
−0.515286 | + | 0.857018i | \(0.672314\pi\) | |||||||
\(878\) | −1.20722e10 | −0.601944 | ||||||||
\(879\) | −1.27775e9 | −0.0634579 | ||||||||
\(880\) | 7.12482e9 | 0.352440 | ||||||||
\(881\) | 4.47154e9 | 0.220314 | 0.110157 | − | 0.993914i | \(-0.464865\pi\) | ||||
0.110157 | + | 0.993914i | \(0.464865\pi\) | |||||||
\(882\) | 4.56092e9 | 0.223827 | ||||||||
\(883\) | −6.15100e9 | −0.300665 | −0.150333 | − | 0.988635i | \(-0.548034\pi\) | ||||
−0.150333 | + | 0.988635i | \(0.548034\pi\) | |||||||
\(884\) | −2.38329e9 | −0.116037 | ||||||||
\(885\) | 1.48399e10 | 0.719665 | ||||||||
\(886\) | 2.39034e10 | 1.15463 | ||||||||
\(887\) | 2.96262e10 | 1.42542 | 0.712712 | − | 0.701457i | \(-0.247467\pi\) | ||||
0.712712 | + | 0.701457i | \(0.247467\pi\) | |||||||
\(888\) | 3.30821e8 | 0.0158543 | ||||||||
\(889\) | −7.71205e9 | −0.368140 | ||||||||
\(890\) | −1.12911e10 | −0.536871 | ||||||||
\(891\) | 2.71101e9 | 0.128398 | ||||||||
\(892\) | 2.02978e10 | 0.957573 | ||||||||
\(893\) | −3.81388e10 | −1.79220 | ||||||||
\(894\) | −1.60784e10 | −0.752595 | ||||||||
\(895\) | 7.98860e9 | 0.372469 | ||||||||
\(896\) | 2.65734e9 | 0.123415 | ||||||||
\(897\) | 1.91005e9 | 0.0883630 | ||||||||
\(898\) | 1.53598e10 | 0.707813 | ||||||||
\(899\) | −7.60208e8 | −0.0348958 | ||||||||
\(900\) | 1.77979e9 | 0.0813802 | ||||||||
\(901\) | −4.97665e9 | −0.226673 | ||||||||
\(902\) | −4.69928e7 | −0.00213210 | ||||||||
\(903\) | −1.67401e10 | −0.756573 | ||||||||
\(904\) | 2.78180e8 | 0.0125238 | ||||||||
\(905\) | −1.93049e10 | −0.865759 | ||||||||
\(906\) | 6.00362e9 | 0.268204 | ||||||||
\(907\) | 3.02880e10 | 1.34786 | 0.673930 | − | 0.738795i | \(-0.264605\pi\) | ||||
0.673930 | + | 0.738795i | \(0.264605\pi\) | |||||||
\(908\) | 6.21886e8 | 0.0275683 | ||||||||
\(909\) | 6.95704e9 | 0.307221 | ||||||||
\(910\) | −2.00975e10 | −0.884091 | ||||||||
\(911\) | 9.96481e9 | 0.436671 | 0.218336 | − | 0.975874i | \(-0.429937\pi\) | ||||
0.218336 | + | 0.975874i | \(0.429937\pi\) | |||||||
\(912\) | −4.26516e9 | −0.186189 | ||||||||
\(913\) | −2.75596e10 | −1.19846 | ||||||||
\(914\) | −1.55211e10 | −0.672376 | ||||||||
\(915\) | −9.58342e9 | −0.413568 | ||||||||
\(916\) | 1.62972e10 | 0.700614 | ||||||||
\(917\) | −3.30389e10 | −1.41492 | ||||||||
\(918\) | 1.00851e9 | 0.0430262 | ||||||||
\(919\) | −3.72161e10 | −1.58171 | −0.790855 | − | 0.612003i | \(-0.790364\pi\) | ||||
−0.790855 | + | 0.612003i | \(0.790364\pi\) | |||||||
\(920\) | −2.12418e9 | −0.0899360 | ||||||||
\(921\) | 9.38508e9 | 0.395849 | ||||||||
\(922\) | −6.51599e9 | −0.273793 | ||||||||
\(923\) | −2.08380e10 | −0.872267 | ||||||||
\(924\) | 1.11696e10 | 0.465786 | ||||||||
\(925\) | 9.12891e8 | 0.0379248 | ||||||||
\(926\) | −5.29174e8 | −0.0219008 | ||||||||
\(927\) | −2.27701e9 | −0.0938827 | ||||||||
\(928\) | −6.81773e9 | −0.280041 | ||||||||
\(929\) | 2.36879e9 | 0.0969328 | 0.0484664 | − | 0.998825i | \(-0.484567\pi\) | ||||
0.0484664 | + | 0.998825i | \(0.484567\pi\) | |||||||
\(930\) | 2.69112e8 | 0.0109709 | ||||||||
\(931\) | −3.01610e10 | −1.22496 | ||||||||
\(932\) | 1.69059e9 | 0.0684042 | ||||||||
\(933\) | −2.28544e10 | −0.921263 | ||||||||
\(934\) | −2.30422e10 | −0.925357 | ||||||||
\(935\) | 1.11408e10 | 0.445733 | ||||||||
\(936\) | −2.17017e9 | −0.0865025 | ||||||||
\(937\) | 2.37255e10 | 0.942166 | 0.471083 | − | 0.882089i | \(-0.343863\pi\) | ||||
0.471083 | + | 0.882089i | \(0.343863\pi\) | |||||||
\(938\) | −2.08888e10 | −0.826425 | ||||||||
\(939\) | 1.43491e10 | 0.565580 | ||||||||
\(940\) | 2.15811e10 | 0.847472 | ||||||||
\(941\) | −2.53391e10 | −0.991351 | −0.495676 | − | 0.868508i | \(-0.665079\pi\) | ||||
−0.495676 | + | 0.868508i | \(0.665079\pi\) | |||||||
\(942\) | 7.19447e9 | 0.280427 | ||||||||
\(943\) | 1.40103e7 | 0.000544073 0 | ||||||||
\(944\) | 6.60223e9 | 0.255440 | ||||||||
\(945\) | 8.50446e9 | 0.327820 | ||||||||
\(946\) | −1.99684e10 | −0.766874 | ||||||||
\(947\) | 3.19577e10 | 1.22278 | 0.611392 | − | 0.791328i | \(-0.290610\pi\) | ||||
0.611392 | + | 0.791328i | \(0.290610\pi\) | |||||||
\(948\) | 1.03742e10 | 0.395481 | ||||||||
\(949\) | 5.67387e9 | 0.215500 | ||||||||
\(950\) | −1.17696e10 | −0.445378 | ||||||||
\(951\) | −2.03302e10 | −0.766497 | ||||||||
\(952\) | 4.15517e9 | 0.156084 | ||||||||
\(953\) | 1.06573e10 | 0.398861 | 0.199431 | − | 0.979912i | \(-0.436091\pi\) | ||||
0.199431 | + | 0.979912i | \(0.436091\pi\) | |||||||
\(954\) | −4.53162e9 | −0.168980 | ||||||||
\(955\) | −4.32544e10 | −1.60701 | ||||||||
\(956\) | −8.17113e8 | −0.0302468 | ||||||||
\(957\) | −2.86570e10 | −1.05691 | ||||||||
\(958\) | −2.72034e10 | −0.999642 | ||||||||
\(959\) | 5.77021e10 | 2.11264 | ||||||||
\(960\) | 2.41347e9 | 0.0880424 | ||||||||
\(961\) | −2.74993e10 | −0.999515 | ||||||||
\(962\) | −1.11313e9 | −0.0403119 | ||||||||
\(963\) | 7.46991e9 | 0.269540 | ||||||||
\(964\) | 9.43961e9 | 0.339379 | ||||||||
\(965\) | 4.65628e10 | 1.66799 | ||||||||
\(966\) | −3.33008e9 | −0.118860 | ||||||||
\(967\) | 5.33089e10 | 1.89586 | 0.947932 | − | 0.318472i | \(-0.103170\pi\) | ||||
0.947932 | + | 0.318472i | \(0.103170\pi\) | |||||||
\(968\) | 3.34621e9 | 0.118574 | ||||||||
\(969\) | −6.66924e9 | −0.235474 | ||||||||
\(970\) | 3.24195e10 | 1.14053 | ||||||||
\(971\) | −5.29648e10 | −1.85661 | −0.928304 | − | 0.371823i | \(-0.878733\pi\) | ||||
−0.928304 | + | 0.371823i | \(0.878733\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −5.52565e10 | −1.92304 | ||||||||
\(974\) | 2.40970e10 | 0.835617 | ||||||||
\(975\) | −5.98853e9 | −0.206921 | ||||||||
\(976\) | −4.26363e9 | −0.146793 | ||||||||
\(977\) | −1.79920e10 | −0.617233 | −0.308616 | − | 0.951187i | \(-0.599866\pi\) | ||||
−0.308616 | + | 0.951187i | \(0.599866\pi\) | |||||||
\(978\) | −3.15280e9 | −0.107773 | ||||||||
\(979\) | −2.11146e10 | −0.719191 | ||||||||
\(980\) | 1.70668e10 | 0.579243 | ||||||||
\(981\) | −9.23881e9 | −0.312446 | ||||||||
\(982\) | −6.68153e6 | −0.000225157 0 | ||||||||
\(983\) | 1.56089e10 | 0.524124 | 0.262062 | − | 0.965051i | \(-0.415597\pi\) | ||||
0.262062 | + | 0.965051i | \(0.415597\pi\) | |||||||
\(984\) | −1.59184e7 | −0.000532618 0 | ||||||||
\(985\) | −3.95712e10 | −1.31933 | ||||||||
\(986\) | −1.06606e10 | −0.354170 | ||||||||
\(987\) | 3.38327e10 | 1.12002 | ||||||||
\(988\) | 1.43512e10 | 0.473412 | ||||||||
\(989\) | 5.95333e9 | 0.195692 | ||||||||
\(990\) | 1.01445e10 | 0.332283 | ||||||||
\(991\) | 4.73053e10 | 1.54402 | 0.772009 | − | 0.635612i | \(-0.219252\pi\) | ||||
0.772009 | + | 0.635612i | \(0.219252\pi\) | |||||||
\(992\) | 1.19727e8 | 0.00389405 | ||||||||
\(993\) | −5.03521e9 | −0.163191 | ||||||||
\(994\) | 3.63301e10 | 1.17331 | ||||||||
\(995\) | 4.82042e9 | 0.155133 | ||||||||
\(996\) | −9.33555e9 | −0.299386 | ||||||||
\(997\) | 3.63716e10 | 1.16233 | 0.581166 | − | 0.813785i | \(-0.302597\pi\) | ||||
0.581166 | + | 0.813785i | \(0.302597\pi\) | |||||||
\(998\) | −3.48645e10 | −1.11026 | ||||||||
\(999\) | 4.71032e8 | 0.0149476 |
(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 | 138.8.a.h.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 414.8.a.i.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.8.a.h.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
414.8.a.i.1.2 | 4 | 3.2 | odd | 2 |