Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + 80362197690736 x^{8} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.18 | ||
Root | \(13.1339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.3 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.1339i | 1.64174i | 0.571114 | + | 0.820871i | \(0.306512\pi\) | ||||
−0.571114 | + | 0.820871i | \(0.693488\pi\) | |||||||
\(3\) | − | 22.6278i | − | 0.838068i | −0.907970 | − | 0.419034i | \(-0.862369\pi\) | ||
0.907970 | − | 0.419034i | \(-0.137631\pi\) | |||||||
\(4\) | −108.500 | −1.69532 | ||||||||
\(5\) | − | 138.961i | − | 1.11168i | −0.831288 | − | 0.555842i | \(-0.812396\pi\) | ||
0.831288 | − | 0.555842i | \(-0.187604\pi\) | |||||||
\(6\) | 297.193 | 1.37589 | ||||||||
\(7\) | 295.441i | 0.861345i | 0.902508 | + | 0.430672i | \(0.141724\pi\) | ||||
−0.902508 | + | 0.430672i | \(0.858276\pi\) | |||||||
\(8\) | − | 584.463i | − | 1.14153i | ||||||
\(9\) | 216.980 | 0.297641 | ||||||||
\(10\) | 1825.10 | 1.82510 | ||||||||
\(11\) | 1638.85 | 1.23129 | 0.615646 | − | 0.788023i | \(-0.288895\pi\) | ||||
0.615646 | + | 0.788023i | \(0.288895\pi\) | |||||||
\(12\) | 2455.13i | 1.42079i | ||||||||
\(13\) | 3924.21 | 1.78617 | 0.893084 | − | 0.449889i | \(-0.148536\pi\) | ||||
0.893084 | + | 0.449889i | \(0.148536\pi\) | |||||||
\(14\) | −3880.31 | −1.41411 | ||||||||
\(15\) | −3144.38 | −0.931667 | ||||||||
\(16\) | 732.289 | 0.178782 | ||||||||
\(17\) | −3266.76 | −0.664923 | −0.332461 | − | 0.943117i | \(-0.607879\pi\) | ||||
−0.332461 | + | 0.943117i | \(0.607879\pi\) | |||||||
\(18\) | 2849.81i | 0.488650i | ||||||||
\(19\) | − | 8538.82i | − | 1.24491i | −0.782657 | − | 0.622454i | \(-0.786136\pi\) | ||
0.782657 | − | 0.622454i | \(-0.213864\pi\) | |||||||
\(20\) | 15077.3i | 1.88466i | ||||||||
\(21\) | 6685.20 | 0.721866 | ||||||||
\(22\) | 21524.6i | 2.02146i | ||||||||
\(23\) | 9920.10 | 0.815328 | 0.407664 | − | 0.913132i | \(-0.366343\pi\) | ||||
0.407664 | + | 0.913132i | \(0.366343\pi\) | |||||||
\(24\) | −13225.2 | −0.956680 | ||||||||
\(25\) | −3685.02 | −0.235842 | ||||||||
\(26\) | 51540.4i | 2.93243i | ||||||||
\(27\) | − | 21405.5i | − | 1.08751i | ||||||
\(28\) | − | 32055.5i | − | 1.46025i | ||||||
\(29\) | 10554.6i | 0.432759i | 0.976309 | + | 0.216380i | \(0.0694249\pi\) | ||||
−0.976309 | + | 0.216380i | \(0.930575\pi\) | |||||||
\(30\) | − | 41298.0i | − | 1.52956i | ||||||
\(31\) | 18861.5 | 0.633128 | 0.316564 | − | 0.948571i | \(-0.397471\pi\) | ||||
0.316564 | + | 0.948571i | \(0.397471\pi\) | |||||||
\(32\) | − | 27787.8i | − | 0.848017i | ||||||
\(33\) | − | 37083.7i | − | 1.03191i | ||||||
\(34\) | − | 42905.5i | − | 1.09163i | ||||||
\(35\) | 41054.7 | 0.957543 | ||||||||
\(36\) | −23542.4 | −0.504596 | ||||||||
\(37\) | 9016.52i | 0.178006i | 0.996031 | + | 0.0890029i | \(0.0283680\pi\) | ||||
−0.996031 | + | 0.0890029i | \(0.971632\pi\) | |||||||
\(38\) | 112148. | 2.04382 | ||||||||
\(39\) | − | 88796.5i | − | 1.49693i | ||||||
\(40\) | −81217.3 | −1.26902 | ||||||||
\(41\) | −83955.2 | −1.21814 | −0.609068 | − | 0.793118i | \(-0.708457\pi\) | ||||
−0.609068 | + | 0.793118i | \(0.708457\pi\) | |||||||
\(42\) | 87803.0i | 1.18512i | ||||||||
\(43\) | −49574.1 | + | 62159.2i | −0.623519 | + | 0.781808i | ||||
\(44\) | −177816. | −2.08743 | ||||||||
\(45\) | − | 30151.7i | − | 0.330883i | ||||||
\(46\) | 130290.i | 1.33856i | ||||||||
\(47\) | 98965.6 | 0.953215 | 0.476607 | − | 0.879116i | \(-0.341866\pi\) | ||||
0.476607 | + | 0.879116i | \(0.341866\pi\) | |||||||
\(48\) | − | 16570.1i | − | 0.149831i | ||||||
\(49\) | 30363.5 | 0.258085 | ||||||||
\(50\) | − | 48398.9i | − | 0.387191i | ||||||
\(51\) | 73919.9i | 0.557251i | ||||||||
\(52\) | −425778. | −3.02812 | ||||||||
\(53\) | 49401.5 | 0.331828 | 0.165914 | − | 0.986140i | \(-0.446943\pi\) | ||||
0.165914 | + | 0.986140i | \(0.446943\pi\) | |||||||
\(54\) | 281138. | 1.78541 | ||||||||
\(55\) | − | 227736.i | − | 1.36881i | ||||||
\(56\) | 172675. | 0.983251 | ||||||||
\(57\) | −193215. | −1.04332 | ||||||||
\(58\) | −138623. | −0.710479 | ||||||||
\(59\) | −32952.4 | −0.160447 | −0.0802234 | − | 0.996777i | \(-0.525563\pi\) | ||||
−0.0802234 | + | 0.996777i | \(0.525563\pi\) | |||||||
\(60\) | 341166. | 1.57947 | ||||||||
\(61\) | 294417.i | 1.29710i | 0.761172 | + | 0.648550i | \(0.224624\pi\) | ||||
−0.761172 | + | 0.648550i | \(0.775376\pi\) | |||||||
\(62\) | 247726.i | 1.03943i | ||||||||
\(63\) | 64105.0i | 0.256372i | ||||||||
\(64\) | 411830. | 1.57101 | ||||||||
\(65\) | − | 545311.i | − | 1.98566i | ||||||
\(66\) | 487054. | 1.69413 | ||||||||
\(67\) | −352200. | −1.17102 | −0.585510 | − | 0.810665i | \(-0.699106\pi\) | ||||
−0.585510 | + | 0.810665i | \(0.699106\pi\) | |||||||
\(68\) | 354445. | 1.12725 | ||||||||
\(69\) | − | 224470.i | − | 0.683301i | ||||||
\(70\) | 539209.i | 1.57204i | ||||||||
\(71\) | − | 412839.i | − | 1.15347i | −0.816932 | − | 0.576735i | \(-0.804327\pi\) | ||
0.816932 | − | 0.576735i | \(-0.195673\pi\) | |||||||
\(72\) | − | 126817.i | − | 0.339766i | ||||||
\(73\) | 380514.i | 0.978141i | 0.872244 | + | 0.489071i | \(0.162664\pi\) | ||||
−0.872244 | + | 0.489071i | \(0.837336\pi\) | |||||||
\(74\) | −118422. | −0.292239 | ||||||||
\(75\) | 83384.2i | 0.197651i | ||||||||
\(76\) | 926464.i | 2.11051i | ||||||||
\(77\) | 484184.i | 1.06057i | ||||||||
\(78\) | 1.16625e6 | 2.45758 | ||||||||
\(79\) | −752994. | −1.52725 | −0.763625 | − | 0.645660i | \(-0.776582\pi\) | ||||
−0.763625 | + | 0.645660i | \(0.776582\pi\) | |||||||
\(80\) | − | 101759.i | − | 0.198749i | ||||||
\(81\) | −326182. | −0.613768 | ||||||||
\(82\) | − | 1.10266e6i | − | 1.99987i | ||||||
\(83\) | −164914. | −0.288418 | −0.144209 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144209 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(84\) | −725346. | −1.22379 | ||||||||
\(85\) | 453951.i | 0.739184i | ||||||||
\(86\) | −816395. | − | 651103.i | −1.28353 | − | 1.02366i | ||||
\(87\) | 238827. | 0.362682 | ||||||||
\(88\) | − | 957848.i | − | 1.40556i | ||||||
\(89\) | − | 904693.i | − | 1.28331i | −0.766994 | − | 0.641655i | \(-0.778248\pi\) | ||
0.766994 | − | 0.641655i | \(-0.221752\pi\) | |||||||
\(90\) | 396011. | 0.543225 | ||||||||
\(91\) | 1.15937e6i | 1.53851i | ||||||||
\(92\) | −1.07633e6 | −1.38224 | ||||||||
\(93\) | − | 426795.i | − | 0.530604i | ||||||
\(94\) | 1.29981e6i | 1.56493i | ||||||||
\(95\) | −1.18656e6 | −1.38394 | ||||||||
\(96\) | −628779. | −0.710696 | ||||||||
\(97\) | 977097. | 1.07059 | 0.535294 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535294 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(98\) | 398792.i | 0.423709i | ||||||||
\(99\) | 355599. | 0.366484 | ||||||||
\(100\) | 399826. | 0.399826 | ||||||||
\(101\) | 1.36505e6 | 1.32490 | 0.662450 | − | 0.749106i | \(-0.269517\pi\) | ||||
0.662450 | + | 0.749106i | \(0.269517\pi\) | |||||||
\(102\) | −970859. | −0.914862 | ||||||||
\(103\) | −481251. | −0.440413 | −0.220207 | − | 0.975453i | \(-0.570673\pi\) | ||||
−0.220207 | + | 0.975453i | \(0.570673\pi\) | |||||||
\(104\) | − | 2.29356e6i | − | 2.03897i | ||||||
\(105\) | − | 928979.i | − | 0.802487i | ||||||
\(106\) | 648837.i | 0.544776i | ||||||||
\(107\) | 839996. | 0.685687 | 0.342843 | − | 0.939393i | \(-0.388610\pi\) | ||||
0.342843 | + | 0.939393i | \(0.388610\pi\) | |||||||
\(108\) | 2.32250e6i | 1.84368i | ||||||||
\(109\) | −1.81764e6 | −1.40355 | −0.701776 | − | 0.712398i | \(-0.747609\pi\) | ||||
−0.701776 | + | 0.712398i | \(0.747609\pi\) | |||||||
\(110\) | 2.99106e6 | 2.24723 | ||||||||
\(111\) | 204025. | 0.149181 | ||||||||
\(112\) | 216348.i | 0.153993i | ||||||||
\(113\) | − | 1.55685e6i | − | 1.07897i | −0.841994 | − | 0.539486i | \(-0.818618\pi\) | ||
0.841994 | − | 0.539486i | \(-0.181382\pi\) | |||||||
\(114\) | − | 2.53767e6i | − | 1.71286i | ||||||
\(115\) | − | 1.37850e6i | − | 0.906387i | ||||||
\(116\) | − | 1.14517e6i | − | 0.733664i | ||||||
\(117\) | 851478. | 0.531638 | ||||||||
\(118\) | − | 432795.i | − | 0.263412i | ||||||
\(119\) | − | 965137.i | − | 0.572728i | ||||||
\(120\) | 1.83777e6i | 1.06353i | ||||||||
\(121\) | 914270. | 0.516082 | ||||||||
\(122\) | −3.86686e6 | −2.12950 | ||||||||
\(123\) | 1.89973e6i | 1.02088i | ||||||||
\(124\) | −2.04648e6 | −1.07335 | ||||||||
\(125\) | − | 1.65919e6i | − | 0.849503i | ||||||
\(126\) | −841951. | −0.420896 | ||||||||
\(127\) | −960451. | −0.468882 | −0.234441 | − | 0.972130i | \(-0.575326\pi\) | ||||
−0.234441 | + | 0.972130i | \(0.575326\pi\) | |||||||
\(128\) | 3.63053e6i | 1.73117i | ||||||||
\(129\) | 1.40653e6 | + | 1.12176e6i | 0.655209 | + | 0.522551i | ||||
\(130\) | 7.16207e6 | 3.25993 | ||||||||
\(131\) | 3.57250e6i | 1.58913i | 0.607182 | + | 0.794563i | \(0.292300\pi\) | ||||
−0.607182 | + | 0.794563i | \(0.707700\pi\) | |||||||
\(132\) | 4.02359e6i | 1.74941i | ||||||||
\(133\) | 2.52272e6 | 1.07229 | ||||||||
\(134\) | − | 4.62577e6i | − | 1.92251i | ||||||
\(135\) | −2.97452e6 | −1.20897 | ||||||||
\(136\) | 1.90930e6i | 0.759029i | ||||||||
\(137\) | 4.56853e6i | 1.77670i | 0.459164 | + | 0.888351i | \(0.348149\pi\) | ||||
−0.459164 | + | 0.888351i | \(0.651851\pi\) | |||||||
\(138\) | 2.94818e6 | 1.12180 | ||||||||
\(139\) | −3.61640e6 | −1.34658 | −0.673290 | − | 0.739378i | \(-0.735120\pi\) | ||||
−0.673290 | + | 0.739378i | \(0.735120\pi\) | |||||||
\(140\) | −4.45444e6 | −1.62334 | ||||||||
\(141\) | − | 2.23938e6i | − | 0.798859i | ||||||
\(142\) | 5.42220e6 | 1.89370 | ||||||||
\(143\) | 6.43120e6 | 2.19930 | ||||||||
\(144\) | 158892. | 0.0532128 | ||||||||
\(145\) | 1.46667e6 | 0.481092 | ||||||||
\(146\) | −4.99764e6 | −1.60586 | ||||||||
\(147\) | − | 687060.i | − | 0.216293i | ||||||
\(148\) | − | 978295.i | − | 0.301776i | ||||||
\(149\) | 2.60224e6i | 0.786663i | 0.919397 | + | 0.393331i | \(0.128677\pi\) | ||||
−0.919397 | + | 0.393331i | \(0.871323\pi\) | |||||||
\(150\) | −1.09516e6 | −0.324492 | ||||||||
\(151\) | − | 2.66549e6i | − | 0.774188i | −0.922040 | − | 0.387094i | \(-0.873479\pi\) | ||
0.922040 | − | 0.387094i | \(-0.126521\pi\) | |||||||
\(152\) | −4.99063e6 | −1.42110 | ||||||||
\(153\) | −708824. | −0.197908 | ||||||||
\(154\) | −6.35924e6 | −1.74118 | ||||||||
\(155\) | − | 2.62100e6i | − | 0.703838i | ||||||
\(156\) | 9.63444e6i | 2.53777i | ||||||||
\(157\) | 5.69323e6i | 1.47116i | 0.677438 | + | 0.735580i | \(0.263090\pi\) | ||||
−0.677438 | + | 0.735580i | \(0.736910\pi\) | |||||||
\(158\) | − | 9.88977e6i | − | 2.50735i | ||||||
\(159\) | − | 1.11785e6i | − | 0.278095i | ||||||
\(160\) | −3.86141e6 | −0.942727 | ||||||||
\(161\) | 2.93081e6i | 0.702279i | ||||||||
\(162\) | − | 4.28405e6i | − | 1.00765i | ||||||
\(163\) | − | 3.64901e6i | − | 0.842582i | −0.906926 | − | 0.421291i | \(-0.861577\pi\) | ||
0.906926 | − | 0.421291i | \(-0.138423\pi\) | |||||||
\(164\) | 9.10916e6 | 2.06513 | ||||||||
\(165\) | −5.15316e6 | −1.14716 | ||||||||
\(166\) | − | 2.16596e6i | − | 0.473508i | ||||||
\(167\) | 3.21802e6 | 0.690938 | 0.345469 | − | 0.938430i | \(-0.387720\pi\) | ||||
0.345469 | + | 0.938430i | \(0.387720\pi\) | |||||||
\(168\) | − | 3.90726e6i | − | 0.824032i | ||||||
\(169\) | 1.05726e7 | 2.19040 | ||||||||
\(170\) | −5.96217e6 | −1.21355 | ||||||||
\(171\) | − | 1.85276e6i | − | 0.370536i | ||||||
\(172\) | 5.37880e6 | − | 6.74429e6i | 1.05706 | − | 1.32541i | ||||
\(173\) | 3.00030e6 | 0.579464 | 0.289732 | − | 0.957108i | \(-0.406434\pi\) | ||||
0.289732 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(174\) | 3.13674e6i | 0.595430i | ||||||||
\(175\) | − | 1.08871e6i | − | 0.203141i | ||||||
\(176\) | 1.20011e6 | 0.220132 | ||||||||
\(177\) | 745642.i | 0.134465i | ||||||||
\(178\) | 1.18822e7 | 2.10686 | ||||||||
\(179\) | 2.48400e6i | 0.433104i | 0.976271 | + | 0.216552i | \(0.0694811\pi\) | ||||
−0.976271 | + | 0.216552i | \(0.930519\pi\) | |||||||
\(180\) | 3.27147e6i | 0.560951i | ||||||||
\(181\) | −9.37063e6 | −1.58028 | −0.790138 | − | 0.612929i | \(-0.789991\pi\) | ||||
−0.790138 | + | 0.612929i | \(0.789991\pi\) | |||||||
\(182\) | −1.52272e7 | −2.52583 | ||||||||
\(183\) | 6.66203e6 | 1.08706 | ||||||||
\(184\) | − | 5.79793e6i | − | 0.930722i | ||||||
\(185\) | 1.25294e6 | 0.197886 | ||||||||
\(186\) | 5.60550e6 | 0.871115 | ||||||||
\(187\) | −5.35374e6 | −0.818714 | ||||||||
\(188\) | −1.07378e7 | −1.61600 | ||||||||
\(189\) | 6.32407e6 | 0.936723 | ||||||||
\(190\) | − | 1.55842e7i | − | 2.27208i | ||||||
\(191\) | − | 5.54978e6i | − | 0.796482i | −0.917281 | − | 0.398241i | \(-0.869621\pi\) | ||
0.917281 | − | 0.398241i | \(-0.130379\pi\) | |||||||
\(192\) | − | 9.31883e6i | − | 1.31661i | ||||||
\(193\) | −86852.8 | −0.0120812 | −0.00604062 | − | 0.999982i | \(-0.501923\pi\) | ||||
−0.00604062 | + | 0.999982i | \(0.501923\pi\) | |||||||
\(194\) | 1.28331e7i | 1.75763i | ||||||||
\(195\) | −1.23392e7 | −1.66412 | ||||||||
\(196\) | −3.29444e6 | −0.437536 | ||||||||
\(197\) | −9.72532e6 | −1.27205 | −0.636026 | − | 0.771667i | \(-0.719423\pi\) | ||||
−0.636026 | + | 0.771667i | \(0.719423\pi\) | |||||||
\(198\) | 4.67041e6i | 0.601671i | ||||||||
\(199\) | 1.24242e7i | 1.57656i | 0.615318 | + | 0.788279i | \(0.289028\pi\) | ||||
−0.615318 | + | 0.788279i | \(0.710972\pi\) | |||||||
\(200\) | 2.15376e6i | 0.269220i | ||||||||
\(201\) | 7.96952e6i | 0.981395i | ||||||||
\(202\) | 1.79284e7i | 2.17514i | ||||||||
\(203\) | −3.11826e6 | −0.372755 | ||||||||
\(204\) | − | 8.02032e6i | − | 0.944716i | ||||||
\(205\) | 1.16665e7i | 1.35418i | ||||||||
\(206\) | − | 6.32072e6i | − | 0.723045i | ||||||
\(207\) | 2.15247e6 | 0.242675 | ||||||||
\(208\) | 2.87366e6 | 0.319334 | ||||||||
\(209\) | − | 1.39938e7i | − | 1.53285i | ||||||
\(210\) | 1.22011e7 | 1.31748 | ||||||||
\(211\) | − | 1.09760e6i | − | 0.116842i | −0.998292 | − | 0.0584209i | \(-0.981393\pi\) | ||
0.998292 | − | 0.0584209i | \(-0.0186065\pi\) | |||||||
\(212\) | −5.36008e6 | −0.562553 | ||||||||
\(213\) | −9.34166e6 | −0.966686 | ||||||||
\(214\) | 1.10325e7i | 1.12572i | ||||||||
\(215\) | 8.63768e6 | + | 6.88884e6i | 0.869124 | + | 0.693156i | ||||
\(216\) | −1.25107e7 | −1.24143 | ||||||||
\(217\) | 5.57247e6i | 0.545341i | ||||||||
\(218\) | − | 2.38728e7i | − | 2.30427i | ||||||
\(219\) | 8.61021e6 | 0.819750 | ||||||||
\(220\) | 2.47094e7i | 2.32056i | ||||||||
\(221\) | −1.28195e7 | −1.18766 | ||||||||
\(222\) | 2.67964e6i | 0.244917i | ||||||||
\(223\) | − | 1.37225e7i | − | 1.23743i | −0.785616 | − | 0.618714i | \(-0.787654\pi\) | ||
0.785616 | − | 0.618714i | \(-0.212346\pi\) | |||||||
\(224\) | 8.20967e6 | 0.730435 | ||||||||
\(225\) | −799578. | −0.0701962 | ||||||||
\(226\) | 2.04475e7 | 1.77140 | ||||||||
\(227\) | 3.65964e6i | 0.312868i | 0.987688 | + | 0.156434i | \(0.0499998\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(228\) | 2.09639e7 | 1.76875 | ||||||||
\(229\) | 8.39728e6 | 0.699250 | 0.349625 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349625 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(230\) | 1.81052e7 | 1.48805 | ||||||||
\(231\) | 1.09560e7 | 0.888828 | ||||||||
\(232\) | 6.16876e6 | 0.494008 | ||||||||
\(233\) | − | 8.63710e6i | − | 0.682811i | −0.939916 | − | 0.341405i | \(-0.889097\pi\) | ||
0.939916 | − | 0.341405i | \(-0.110903\pi\) | |||||||
\(234\) | 1.11833e7i | 0.872812i | ||||||||
\(235\) | − | 1.37523e7i | − | 1.05967i | ||||||
\(236\) | 3.57534e6 | 0.272008 | ||||||||
\(237\) | 1.70386e7i | 1.27994i | ||||||||
\(238\) | 1.26760e7 | 0.940271 | ||||||||
\(239\) | −2.41978e7 | −1.77248 | −0.886240 | − | 0.463226i | \(-0.846692\pi\) | ||||
−0.886240 | + | 0.463226i | \(0.846692\pi\) | |||||||
\(240\) | −2.30259e6 | −0.166565 | ||||||||
\(241\) | 2.77131e7i | 1.97985i | 0.141576 | + | 0.989927i | \(0.454783\pi\) | ||||
−0.141576 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(242\) | 1.20080e7i | 0.847273i | ||||||||
\(243\) | − | 8.22382e6i | − | 0.573132i | ||||||
\(244\) | − | 3.19443e7i | − | 2.19900i | ||||||
\(245\) | − | 4.21932e6i | − | 0.286909i | ||||||
\(246\) | −2.49509e7 | −1.67602 | ||||||||
\(247\) | − | 3.35081e7i | − | 2.22361i | ||||||
\(248\) | − | 1.10239e7i | − | 0.722734i | ||||||
\(249\) | 3.73164e6i | 0.241714i | ||||||||
\(250\) | 2.17916e7 | 1.39466 | ||||||||
\(251\) | −7.61274e6 | −0.481415 | −0.240708 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240708 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(252\) | − | 6.95541e6i | − | 0.434631i | ||||||
\(253\) | 1.62576e7 | 1.00391 | ||||||||
\(254\) | − | 1.26145e7i | − | 0.769784i | ||||||
\(255\) | 1.02719e7 | 0.619487 | ||||||||
\(256\) | −2.13260e7 | −1.27113 | ||||||||
\(257\) | − | 6.67289e6i | − | 0.393111i | −0.980493 | − | 0.196555i | \(-0.937024\pi\) | ||
0.980493 | − | 0.196555i | \(-0.0629755\pi\) | |||||||
\(258\) | −1.47331e7 | + | 1.84733e7i | −0.857894 | + | 1.07568i | ||||
\(259\) | −2.66385e6 | −0.153324 | ||||||||
\(260\) | 5.91663e7i | 3.36631i | ||||||||
\(261\) | 2.29014e6i | 0.128807i | ||||||||
\(262\) | −4.69210e7 | −2.60894 | ||||||||
\(263\) | − | 1.90916e7i | − | 1.04948i | −0.851262 | − | 0.524741i | \(-0.824162\pi\) | ||
0.851262 | − | 0.524741i | \(-0.175838\pi\) | |||||||
\(264\) | −2.16740e7 | −1.17795 | ||||||||
\(265\) | − | 6.86486e6i | − | 0.368888i | ||||||
\(266\) | 3.31332e7i | 1.76043i | ||||||||
\(267\) | −2.04713e7 | −1.07550 | ||||||||
\(268\) | 3.82137e7 | 1.98525 | ||||||||
\(269\) | 3.35363e7 | 1.72289 | 0.861446 | − | 0.507849i | \(-0.169559\pi\) | ||||
0.861446 | + | 0.507849i | \(0.169559\pi\) | |||||||
\(270\) | − | 3.90671e7i | − | 1.98482i | ||||||
\(271\) | −3.07340e7 | −1.54423 | −0.772114 | − | 0.635484i | \(-0.780800\pi\) | ||||
−0.772114 | + | 0.635484i | \(0.780800\pi\) | |||||||
\(272\) | −2.39222e6 | −0.118876 | ||||||||
\(273\) | 2.62342e7 | 1.28937 | ||||||||
\(274\) | −6.00028e7 | −2.91689 | ||||||||
\(275\) | −6.03920e6 | −0.290390 | ||||||||
\(276\) | 2.43551e7i | 1.15841i | ||||||||
\(277\) | − | 5.66158e6i | − | 0.266378i | −0.991091 | − | 0.133189i | \(-0.957478\pi\) | ||
0.991091 | − | 0.133189i | \(-0.0425217\pi\) | |||||||
\(278\) | − | 4.74976e7i | − | 2.21074i | ||||||
\(279\) | 4.09258e6 | 0.188445 | ||||||||
\(280\) | − | 2.39950e7i | − | 1.09306i | ||||||
\(281\) | 1.65801e7 | 0.747253 | 0.373627 | − | 0.927579i | \(-0.378114\pi\) | ||||
0.373627 | + | 0.927579i | \(0.378114\pi\) | |||||||
\(282\) | 2.94119e7 | 1.31152 | ||||||||
\(283\) | −2.42978e7 | −1.07203 | −0.536016 | − | 0.844208i | \(-0.680071\pi\) | ||||
−0.536016 | + | 0.844208i | \(0.680071\pi\) | |||||||
\(284\) | 4.47932e7i | 1.95550i | ||||||||
\(285\) | 2.68493e7i | 1.15984i | ||||||||
\(286\) | 8.44670e7i | 3.61068i | ||||||||
\(287\) | − | 2.48038e7i | − | 1.04924i | ||||||
\(288\) | − | 6.02942e6i | − | 0.252405i | ||||||
\(289\) | −1.34658e7 | −0.557878 | ||||||||
\(290\) | 1.92631e7i | 0.789829i | ||||||||
\(291\) | − | 2.21096e7i | − | 0.897226i | ||||||
\(292\) | − | 4.12858e7i | − | 1.65826i | ||||||
\(293\) | −3.69429e7 | −1.46868 | −0.734342 | − | 0.678779i | \(-0.762509\pi\) | ||||
−0.734342 | + | 0.678779i | \(0.762509\pi\) | |||||||
\(294\) | 9.02380e6 | 0.355097 | ||||||||
\(295\) | 4.57908e6i | 0.178366i | ||||||||
\(296\) | 5.26983e6 | 0.203199 | ||||||||
\(297\) | − | 3.50804e7i | − | 1.33905i | ||||||
\(298\) | −3.41777e7 | −1.29150 | ||||||||
\(299\) | 3.89286e7 | 1.45631 | ||||||||
\(300\) | − | 9.04720e6i | − | 0.335082i | ||||||
\(301\) | −1.83644e7 | − | 1.46462e7i | −0.673407 | − | 0.537065i | ||||
\(302\) | 3.50084e7 | 1.27102 | ||||||||
\(303\) | − | 3.08880e7i | − | 1.11036i | ||||||
\(304\) | − | 6.25288e6i | − | 0.222566i | ||||||
\(305\) | 4.09124e7 | 1.44197 | ||||||||
\(306\) | − | 9.30965e6i | − | 0.324915i | ||||||
\(307\) | −1.07968e7 | −0.373148 | −0.186574 | − | 0.982441i | \(-0.559738\pi\) | ||||
−0.186574 | + | 0.982441i | \(0.559738\pi\) | |||||||
\(308\) | − | 5.25341e7i | − | 1.79800i | ||||||
\(309\) | 1.08897e7i | 0.369096i | ||||||||
\(310\) | 3.44241e7 | 1.15552 | ||||||||
\(311\) | 1.93935e7 | 0.644727 | 0.322363 | − | 0.946616i | \(-0.395523\pi\) | ||||
0.322363 | + | 0.946616i | \(0.395523\pi\) | |||||||
\(312\) | −5.18983e7 | −1.70879 | ||||||||
\(313\) | − | 1.28612e6i | − | 0.0419420i | −0.999780 | − | 0.0209710i | \(-0.993324\pi\) | ||
0.999780 | − | 0.0209710i | \(-0.00667576\pi\) | |||||||
\(314\) | −7.47745e7 | −2.41526 | ||||||||
\(315\) | 8.90806e6 | 0.285004 | ||||||||
\(316\) | 8.17000e7 | 2.58917 | ||||||||
\(317\) | 4.25006e7 | 1.33419 | 0.667094 | − | 0.744974i | \(-0.267538\pi\) | ||||
0.667094 | + | 0.744974i | \(0.267538\pi\) | |||||||
\(318\) | 1.46818e7 | 0.456559 | ||||||||
\(319\) | 1.72974e7i | 0.532854i | ||||||||
\(320\) | − | 5.72281e7i | − | 1.74646i | ||||||
\(321\) | − | 1.90073e7i | − | 0.574653i | ||||||
\(322\) | −3.84930e7 | −1.15296 | ||||||||
\(323\) | 2.78943e7i | 0.827767i | ||||||||
\(324\) | 3.53908e7 | 1.04053 | ||||||||
\(325\) | −1.44608e7 | −0.421253 | ||||||||
\(326\) | 4.79259e7 | 1.38330 | ||||||||
\(327\) | 4.11293e7i | 1.17627i | ||||||||
\(328\) | 4.90688e7i | 1.39054i | ||||||||
\(329\) | 2.92385e7i | 0.821046i | ||||||||
\(330\) | − | 6.76813e7i | − | 1.88333i | ||||||
\(331\) | 4.77276e7i | 1.31609i | 0.752979 | + | 0.658045i | \(0.228616\pi\) | ||||
−0.752979 | + | 0.658045i | \(0.771384\pi\) | |||||||
\(332\) | 1.78932e7 | 0.488960 | ||||||||
\(333\) | 1.95641e6i | 0.0529818i | ||||||||
\(334\) | 4.22652e7i | 1.13434i | ||||||||
\(335\) | 4.89418e7i | 1.30180i | ||||||||
\(336\) | 4.89550e6 | 0.129056 | ||||||||
\(337\) | −2.31815e7 | −0.605692 | −0.302846 | − | 0.953040i | \(-0.597937\pi\) | ||||
−0.302846 | + | 0.953040i | \(0.597937\pi\) | |||||||
\(338\) | 1.38860e8i | 3.59607i | ||||||||
\(339\) | −3.52281e7 | −0.904253 | ||||||||
\(340\) | − | 4.92538e7i | − | 1.25315i | ||||||
\(341\) | 3.09112e7 | 0.779566 | ||||||||
\(342\) | 2.43340e7 | 0.608324 | ||||||||
\(343\) | 4.37290e7i | 1.08365i | ||||||||
\(344\) | 3.63298e7 | + | 2.89743e7i | 0.892458 | + | 0.711765i | ||||
\(345\) | −3.11925e7 | −0.759615 | ||||||||
\(346\) | 3.94058e7i | 0.951330i | ||||||||
\(347\) | − | 4.51753e7i | − | 1.08122i | −0.841275 | − | 0.540608i | \(-0.818194\pi\) | ||
0.841275 | − | 0.540608i | \(-0.181806\pi\) | |||||||
\(348\) | −2.59128e7 | −0.614861 | ||||||||
\(349\) | 3.63458e7i | 0.855024i | 0.904010 | + | 0.427512i | \(0.140610\pi\) | ||||
−0.904010 | + | 0.427512i | \(0.859390\pi\) | |||||||
\(350\) | 1.42990e7 | 0.333505 | ||||||||
\(351\) | − | 8.39998e7i | − | 1.94248i | ||||||
\(352\) | − | 4.55401e7i | − | 1.04416i | ||||||
\(353\) | 6.26609e6 | 0.142453 | 0.0712266 | − | 0.997460i | \(-0.477309\pi\) | ||||
0.0712266 | + | 0.997460i | \(0.477309\pi\) | |||||||
\(354\) | −9.79322e6 | −0.220758 | ||||||||
\(355\) | −5.73684e7 | −1.28229 | ||||||||
\(356\) | 9.81594e7i | 2.17562i | ||||||||
\(357\) | −2.18390e7 | −0.479985 | ||||||||
\(358\) | −3.26247e7 | −0.711045 | ||||||||
\(359\) | −7.60423e7 | −1.64351 | −0.821754 | − | 0.569843i | \(-0.807004\pi\) | ||||
−0.821754 | + | 0.569843i | \(0.807004\pi\) | |||||||
\(360\) | −1.76226e7 | −0.377713 | ||||||||
\(361\) | −2.58655e7 | −0.549794 | ||||||||
\(362\) | − | 1.23073e8i | − | 2.59440i | ||||||
\(363\) | − | 2.06880e7i | − | 0.432512i | ||||||
\(364\) | − | 1.25792e8i | − | 2.60826i | ||||||
\(365\) | 5.28764e7 | 1.08738 | ||||||||
\(366\) | 8.74987e7i | 1.78467i | ||||||||
\(367\) | 1.84223e6 | 0.0372688 | 0.0186344 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186344 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(368\) | 7.26438e6 | 0.145766 | ||||||||
\(369\) | −1.82166e7 | −0.362568 | ||||||||
\(370\) | 1.64560e7i | 0.324878i | ||||||||
\(371\) | 1.45953e7i | 0.285818i | ||||||||
\(372\) | 4.63074e7i | 0.899542i | ||||||||
\(373\) | − | 3.24275e7i | − | 0.624865i | −0.949940 | − | 0.312433i | \(-0.898856\pi\) | ||
0.949940 | − | 0.312433i | \(-0.101144\pi\) | |||||||
\(374\) | − | 7.03157e7i | − | 1.34412i | ||||||
\(375\) | −3.75438e7 | −0.711942 | ||||||||
\(376\) | − | 5.78418e7i | − | 1.08812i | ||||||
\(377\) | 4.14184e7i | 0.772981i | ||||||||
\(378\) | 8.30599e7i | 1.53786i | ||||||||
\(379\) | 5.84087e6 | 0.107290 | 0.0536451 | − | 0.998560i | \(-0.482916\pi\) | ||||
0.0536451 | + | 0.998560i | \(0.482916\pi\) | |||||||
\(380\) | 1.28742e8 | 2.34622 | ||||||||
\(381\) | 2.17329e7i | 0.392956i | ||||||||
\(382\) | 7.28905e7 | 1.30762 | ||||||||
\(383\) | − | 3.08598e7i | − | 0.549284i | −0.961547 | − | 0.274642i | \(-0.911441\pi\) | ||
0.961547 | − | 0.274642i | \(-0.0885593\pi\) | |||||||
\(384\) | 8.21510e7 | 1.45084 | ||||||||
\(385\) | 6.72825e7 | 1.17902 | ||||||||
\(386\) | − | 1.14072e6i | − | 0.0198343i | ||||||
\(387\) | −1.07566e7 | + | 1.34873e7i | −0.185585 | + | 0.232698i | ||||
\(388\) | −1.06015e8 | −1.81499 | ||||||||
\(389\) | 8.63120e7i | 1.46630i | 0.680068 | + | 0.733149i | \(0.261950\pi\) | ||||
−0.680068 | + | 0.733149i | \(0.738050\pi\) | |||||||
\(390\) | − | 1.62062e8i | − | 2.73205i | ||||||
\(391\) | −3.24066e7 | −0.542130 | ||||||||
\(392\) | − | 1.77463e7i | − | 0.294612i | ||||||
\(393\) | 8.08380e7 | 1.33180 | ||||||||
\(394\) | − | 1.27732e8i | − | 2.08838i | ||||||
\(395\) | 1.04636e8i | 1.69782i | ||||||||
\(396\) | −3.85825e7 | −0.621306 | ||||||||
\(397\) | 6.88256e7 | 1.09996 | 0.549982 | − | 0.835176i | \(-0.314634\pi\) | ||||
0.549982 | + | 0.835176i | \(0.314634\pi\) | |||||||
\(398\) | −1.63179e8 | −2.58830 | ||||||||
\(399\) | − | 5.70837e7i | − | 0.898656i | ||||||
\(400\) | −2.69850e6 | −0.0421641 | ||||||||
\(401\) | 2.18197e7 | 0.338389 | 0.169194 | − | 0.985583i | \(-0.445883\pi\) | ||||
0.169194 | + | 0.985583i | \(0.445883\pi\) | |||||||
\(402\) | −1.04671e8 | −1.61120 | ||||||||
\(403\) | 7.40166e7 | 1.13087 | ||||||||
\(404\) | −1.48108e8 | −2.24612 | ||||||||
\(405\) | 4.53264e7i | 0.682317i | ||||||||
\(406\) | − | 4.09550e7i | − | 0.611968i | ||||||
\(407\) | 1.47767e7i | 0.219177i | ||||||||
\(408\) | 4.32035e7 | 0.636119 | ||||||||
\(409\) | − | 3.33427e7i | − | 0.487339i | −0.969858 | − | 0.243669i | \(-0.921649\pi\) | ||
0.969858 | − | 0.243669i | \(-0.0783512\pi\) | |||||||
\(410\) | −1.53227e8 | −2.22322 | ||||||||
\(411\) | 1.03376e8 | 1.48900 | ||||||||
\(412\) | 5.22159e7 | 0.746639 | ||||||||
\(413\) | − | 9.73550e6i | − | 0.138200i | ||||||
\(414\) | 2.82704e7i | 0.398410i | ||||||||
\(415\) | 2.29165e7i | 0.320630i | ||||||||
\(416\) | − | 1.09045e8i | − | 1.51470i | ||||||
\(417\) | 8.18314e7i | 1.12853i | ||||||||
\(418\) | 1.83794e8 | 2.51654 | ||||||||
\(419\) | − | 9.15691e7i | − | 1.24482i | −0.782691 | − | 0.622411i | \(-0.786153\pi\) | ||
0.782691 | − | 0.622411i | \(-0.213847\pi\) | |||||||
\(420\) | 1.00794e8i | 1.36047i | ||||||||
\(421\) | 9.23221e6i | 0.123726i | 0.998085 | + | 0.0618628i | \(0.0197041\pi\) | ||||
−0.998085 | + | 0.0618628i | \(0.980296\pi\) | |||||||
\(422\) | 1.44159e7 | 0.191824 | ||||||||
\(423\) | 2.14736e7 | 0.283716 | ||||||||
\(424\) | − | 2.88734e7i | − | 0.378792i | ||||||
\(425\) | 1.20381e7 | 0.156816 | ||||||||
\(426\) | − | 1.22693e8i | − | 1.58705i | ||||||
\(427\) | −8.69830e7 | −1.11725 | ||||||||
\(428\) | −9.11398e7 | −1.16246 | ||||||||
\(429\) | − | 1.45524e8i | − | 1.84316i | ||||||
\(430\) | −9.04776e7 | + | 1.13447e8i | −1.13798 | + | 1.42688i | ||||
\(431\) | −1.01039e8 | −1.26199 | −0.630996 | − | 0.775786i | \(-0.717354\pi\) | ||||
−0.630996 | + | 0.775786i | \(0.717354\pi\) | |||||||
\(432\) | − | 1.56750e7i | − | 0.194427i | ||||||
\(433\) | 5.06133e7i | 0.623449i | 0.950173 | + | 0.311724i | \(0.100907\pi\) | ||||
−0.950173 | + | 0.311724i | \(0.899093\pi\) | |||||||
\(434\) | −7.31884e7 | −0.895310 | ||||||||
\(435\) | − | 3.31875e7i | − | 0.403188i | ||||||
\(436\) | 1.97214e8 | 2.37946 | ||||||||
\(437\) | − | 8.47059e7i | − | 1.01501i | ||||||
\(438\) | 1.13086e8i | 1.34582i | ||||||||
\(439\) | 1.13037e8 | 1.33606 | 0.668031 | − | 0.744133i | \(-0.267137\pi\) | ||||
0.668031 | + | 0.744133i | \(0.267137\pi\) | |||||||
\(440\) | −1.33103e8 | −1.56254 | ||||||||
\(441\) | 6.58828e6 | 0.0768168 | ||||||||
\(442\) | − | 1.68370e8i | − | 1.94984i | ||||||
\(443\) | 2.36191e6 | 0.0271677 | 0.0135838 | − | 0.999908i | \(-0.495676\pi\) | ||||
0.0135838 | + | 0.999908i | \(0.495676\pi\) | |||||||
\(444\) | −2.21367e7 | −0.252909 | ||||||||
\(445\) | −1.25717e8 | −1.42663 | ||||||||
\(446\) | 1.80231e8 | 2.03154 | ||||||||
\(447\) | 5.88831e7 | 0.659277 | ||||||||
\(448\) | 1.21672e8i | 1.35318i | ||||||||
\(449\) | 4.84461e7i | 0.535204i | 0.963529 | + | 0.267602i | \(0.0862313\pi\) | ||||
−0.963529 | + | 0.267602i | \(0.913769\pi\) | |||||||
\(450\) | − | 1.05016e7i | − | 0.115244i | ||||||
\(451\) | −1.37590e8 | −1.49988 | ||||||||
\(452\) | 1.68918e8i | 1.82920i | ||||||||
\(453\) | −6.03144e7 | −0.648823 | ||||||||
\(454\) | −4.80655e7 | −0.513648 | ||||||||
\(455\) | 1.61107e8 | 1.71033 | ||||||||
\(456\) | 1.12927e8i | 1.19098i | ||||||||
\(457\) | 8.69144e7i | 0.910632i | 0.890330 | + | 0.455316i | \(0.150474\pi\) | ||||
−0.890330 | + | 0.455316i | \(0.849526\pi\) | |||||||
\(458\) | 1.10289e8i | 1.14799i | ||||||||
\(459\) | 6.99267e7i | 0.723111i | ||||||||
\(460\) | 1.49568e8i | 1.53661i | ||||||||
\(461\) | 8.68002e7 | 0.885968 | 0.442984 | − | 0.896530i | \(-0.353920\pi\) | ||||
0.442984 | + | 0.896530i | \(0.353920\pi\) | |||||||
\(462\) | 1.43896e8i | 1.45923i | ||||||||
\(463\) | − | 1.01559e8i | − | 1.02324i | −0.859212 | − | 0.511619i | \(-0.829046\pi\) | ||
0.859212 | − | 0.511619i | \(-0.170954\pi\) | |||||||
\(464\) | 7.72900e6i | 0.0773694i | ||||||||
\(465\) | −5.93077e7 | −0.589864 | ||||||||
\(466\) | 1.13439e8 | 1.12100 | ||||||||
\(467\) | − | 7.61686e7i | − | 0.747869i | −0.927455 | − | 0.373934i | \(-0.878009\pi\) | ||
0.927455 | − | 0.373934i | \(-0.121991\pi\) | |||||||
\(468\) | −9.23855e7 | −0.901294 | ||||||||
\(469\) | − | 1.04054e8i | − | 1.00865i | ||||||
\(470\) | 1.80622e8 | 1.73971 | ||||||||
\(471\) | 1.28826e8 | 1.23293 | ||||||||
\(472\) | 1.92595e7i | 0.183155i | ||||||||
\(473\) | −8.12445e7 | + | 1.01870e8i | −0.767734 | + | 0.962635i | ||||
\(474\) | −2.23784e8 | −2.10133 | ||||||||
\(475\) | 3.14657e7i | 0.293601i | ||||||||
\(476\) | 1.04718e8i | 0.970955i | ||||||||
\(477\) | 1.07192e7 | 0.0987657 | ||||||||
\(478\) | − | 3.17812e8i | − | 2.90995i | ||||||
\(479\) | 6.83393e7 | 0.621819 | 0.310910 | − | 0.950439i | \(-0.399366\pi\) | ||||
0.310910 | + | 0.950439i | \(0.399366\pi\) | |||||||
\(480\) | 8.73754e7i | 0.790070i | ||||||||
\(481\) | 3.53828e7i | 0.317948i | ||||||||
\(482\) | −3.63982e8 | −3.25041 | ||||||||
\(483\) | 6.63178e7 | 0.588558 | ||||||||
\(484\) | −9.91986e7 | −0.874922 | ||||||||
\(485\) | − | 1.35778e8i | − | 1.19016i | ||||||
\(486\) | 1.08011e8 | 0.940935 | ||||||||
\(487\) | 1.15513e8 | 1.00010 | 0.500050 | − | 0.865997i | \(-0.333315\pi\) | ||||
0.500050 | + | 0.865997i | \(0.333315\pi\) | |||||||
\(488\) | 1.72076e8 | 1.48068 | ||||||||
\(489\) | −8.25692e7 | −0.706141 | ||||||||
\(490\) | 5.54163e7 | 0.471031 | ||||||||
\(491\) | 4.76707e7i | 0.402724i | 0.979517 | + | 0.201362i | \(0.0645367\pi\) | ||||
−0.979517 | + | 0.201362i | \(0.935463\pi\) | |||||||
\(492\) | − | 2.06121e8i | − | 1.73072i | ||||||
\(493\) | − | 3.44793e7i | − | 0.287752i | ||||||
\(494\) | 4.40094e8 | 3.65060 | ||||||||
\(495\) | − | 4.94142e7i | − | 0.407414i | ||||||
\(496\) | 1.38121e7 | 0.113192 | ||||||||
\(497\) | 1.21970e8 | 0.993535 | ||||||||
\(498\) | −4.90111e7 | −0.396832 | ||||||||
\(499\) | 1.77336e8i | 1.42723i | 0.700537 | + | 0.713616i | \(0.252944\pi\) | ||||
−0.700537 | + | 0.713616i | \(0.747056\pi\) | |||||||
\(500\) | 1.80022e8i | 1.44018i | ||||||||
\(501\) | − | 7.28168e7i | − | 0.579053i | ||||||
\(502\) | − | 9.99852e7i | − | 0.790359i | ||||||
\(503\) | − | 2.49388e6i | − | 0.0195962i | −0.999952 | − | 0.00979809i | \(-0.996881\pi\) | ||
0.999952 | − | 0.00979809i | \(-0.00311888\pi\) | |||||||
\(504\) | 3.74670e7 | 0.292656 | ||||||||
\(505\) | − | 1.89687e8i | − | 1.47287i | ||||||
\(506\) | 2.13526e8i | 1.64816i | ||||||||
\(507\) | − | 2.39236e8i | − | 1.83570i | ||||||
\(508\) | 1.04209e8 | 0.794904 | ||||||||
\(509\) | −7.63361e7 | −0.578864 | −0.289432 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289432 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(510\) | 1.34911e8i | 1.01704i | ||||||||
\(511\) | −1.12419e8 | −0.842517 | ||||||||
\(512\) | − | 4.77405e7i | − | 0.355694i | ||||||
\(513\) | −1.82778e8 | −1.35385 | ||||||||
\(514\) | 8.76413e7 | 0.645386 | ||||||||
\(515\) | 6.68749e7i | 0.489600i | ||||||||
\(516\) | −1.52609e8 | − | 1.21711e8i | −1.11079 | − | 0.885890i | ||||
\(517\) | 1.62190e8 | 1.17369 | ||||||||
\(518\) | − | 3.49869e7i | − | 0.251719i | ||||||
\(519\) | − | 6.78904e7i | − | 0.485631i | ||||||
\(520\) | −3.18714e8 | −2.26669 | ||||||||
\(521\) | 5.85908e7i | 0.414301i | 0.978309 | + | 0.207151i | \(0.0664190\pi\) | ||||
−0.978309 | + | 0.207151i | \(0.933581\pi\) | |||||||
\(522\) | −3.00785e7 | −0.211468 | ||||||||
\(523\) | 1.14240e8i | 0.798568i | 0.916827 | + | 0.399284i | \(0.130741\pi\) | ||||
−0.916827 | + | 0.399284i | \(0.869259\pi\) | |||||||
\(524\) | − | 3.87617e8i | − | 2.69407i | ||||||
\(525\) | −2.46351e7 | −0.170246 | ||||||||
\(526\) | 2.50748e8 | 1.72298 | ||||||||
\(527\) | −6.16161e7 | −0.420981 | ||||||||
\(528\) | − | 2.71560e7i | − | 0.184486i | ||||||
\(529\) | −4.96275e7 | −0.335240 | ||||||||
\(530\) | 9.01627e7 | 0.605619 | ||||||||
\(531\) | −7.15003e6 | −0.0477556 | ||||||||
\(532\) | −2.73716e8 | −1.81788 | ||||||||
\(533\) | −3.29458e8 | −2.17580 | ||||||||
\(534\) | − | 2.68868e8i | − | 1.76569i | ||||||
\(535\) | − | 1.16726e8i | − | 0.762267i | ||||||
\(536\) | 2.05848e8i | 1.33676i | ||||||||
\(537\) | 5.62076e7 | 0.362971 | ||||||||
\(538\) | 4.40463e8i | 2.82854i | ||||||||
\(539\) | 4.97612e7 | 0.317778 | ||||||||
\(540\) | 3.22736e8 | 2.04959 | ||||||||
\(541\) | −6.24119e6 | −0.0394163 | −0.0197081 | − | 0.999806i | \(-0.506274\pi\) | ||||
−0.0197081 | + | 0.999806i | \(0.506274\pi\) | |||||||
\(542\) | − | 4.03658e8i | − | 2.53522i | ||||||
\(543\) | 2.12037e8i | 1.32438i | ||||||||
\(544\) | 9.07763e7i | 0.563866i | ||||||||
\(545\) | 2.52580e8i | 1.56031i | ||||||||
\(546\) | 3.44558e8i | 2.11682i | ||||||||
\(547\) | −9.45969e7 | −0.577983 | −0.288991 | − | 0.957332i | \(-0.593320\pi\) | ||||
−0.288991 | + | 0.957332i | \(0.593320\pi\) | |||||||
\(548\) | − | 4.95687e8i | − | 3.01207i | ||||||
\(549\) | 6.38828e7i | 0.386071i | ||||||||
\(550\) | − | 7.93185e7i | − | 0.476745i | ||||||
\(551\) | 9.01236e7 | 0.538745 | ||||||||
\(552\) | −1.31195e8 | −0.780009 | ||||||||
\(553\) | − | 2.22465e8i | − | 1.31549i | ||||||
\(554\) | 7.43588e7 | 0.437324 | ||||||||
\(555\) | − | 2.83514e7i | − | 0.165842i | ||||||
\(556\) | 3.92381e8 | 2.28288 | ||||||||
\(557\) | −3.64924e7 | −0.211172 | −0.105586 | − | 0.994410i | \(-0.533672\pi\) | ||||
−0.105586 | + | 0.994410i | \(0.533672\pi\) | |||||||
\(558\) | 5.37517e7i | 0.309378i | ||||||||
\(559\) | −1.94539e8 | + | 2.43926e8i | −1.11371 | + | 1.39644i | ||||
\(560\) | 3.00639e7 | 0.171191 | ||||||||
\(561\) | 1.21144e8i | 0.686139i | ||||||||
\(562\) | 2.17762e8i | 1.22680i | ||||||||
\(563\) | −8.39838e7 | −0.470620 | −0.235310 | − | 0.971920i | \(-0.575611\pi\) | ||||
−0.235310 | + | 0.971920i | \(0.575611\pi\) | |||||||
\(564\) | 2.42973e8i | 1.35432i | ||||||||
\(565\) | −2.16340e8 | −1.19948 | ||||||||
\(566\) | − | 3.19126e8i | − | 1.76000i | ||||||
\(567\) | − | 9.63675e7i | − | 0.528666i | ||||||
\(568\) | −2.41289e8 | −1.31672 | ||||||||
\(569\) | −1.07209e8 | −0.581963 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(570\) | −3.52637e8 | −1.90416 | ||||||||
\(571\) | 1.05706e8i | 0.567797i | 0.958854 | + | 0.283899i | \(0.0916279\pi\) | ||||
−0.958854 | + | 0.283899i | \(0.908372\pi\) | |||||||
\(572\) | −6.97787e8 | −3.72850 | ||||||||
\(573\) | −1.25580e8 | −0.667506 | ||||||||
\(574\) | 3.25772e8 | 1.72257 | ||||||||
\(575\) | −3.65558e7 | −0.192288 | ||||||||
\(576\) | 8.93591e7 | 0.467596 | ||||||||
\(577\) | − | 1.36661e8i | − | 0.711403i | −0.934600 | − | 0.355702i | \(-0.884242\pi\) | ||
0.934600 | − | 0.355702i | \(-0.115758\pi\) | |||||||
\(578\) | − | 1.76859e8i | − | 0.915891i | ||||||
\(579\) | 1.96529e6i | 0.0101249i | ||||||||
\(580\) | −1.59134e8 | −0.815603 | ||||||||
\(581\) | − | 4.87223e7i | − | 0.248427i | ||||||
\(582\) | 2.90386e8 | 1.47301 | ||||||||
\(583\) | 8.09618e7 | 0.408577 | ||||||||
\(584\) | 2.22396e8 | 1.11658 | ||||||||
\(585\) | − | 1.18322e8i | − | 0.591013i | ||||||
\(586\) | − | 4.85206e8i | − | 2.41120i | ||||||
\(587\) | − | 1.16599e8i | − | 0.576475i | −0.957559 | − | 0.288238i | \(-0.906931\pi\) | ||
0.957559 | − | 0.288238i | \(-0.0930693\pi\) | |||||||
\(588\) | 7.45461e7i | 0.366685i | ||||||||
\(589\) | − | 1.61055e8i | − | 0.788185i | ||||||
\(590\) | −6.01414e7 | −0.292831 | ||||||||
\(591\) | 2.20063e8i | 1.06607i | ||||||||
\(592\) | 6.60270e6i | 0.0318241i | ||||||||
\(593\) | 3.03405e8i | 1.45499i | 0.686115 | + | 0.727493i | \(0.259315\pi\) | ||||
−0.686115 | + | 0.727493i | \(0.740685\pi\) | |||||||
\(594\) | 4.60744e8 | 2.19837 | ||||||||
\(595\) | −1.34116e8 | −0.636692 | ||||||||
\(596\) | − | 2.82344e8i | − | 1.33364i | ||||||
\(597\) | 2.81133e8 | 1.32126 | ||||||||
\(598\) | 5.11285e8i | 2.39089i | ||||||||
\(599\) | −3.82574e8 | −1.78006 | −0.890030 | − | 0.455901i | \(-0.849317\pi\) | ||||
−0.890030 | + | 0.455901i | \(0.849317\pi\) | |||||||
\(600\) | 4.87350e7 | 0.225625 | ||||||||
\(601\) | − | 4.50470e7i | − | 0.207512i | −0.994603 | − | 0.103756i | \(-0.966914\pi\) | ||
0.994603 | − | 0.103756i | \(-0.0330861\pi\) | |||||||
\(602\) | 1.92363e8 | − | 2.41197e8i | 0.881721 | − | 1.10556i | ||||
\(603\) | −7.64204e7 | −0.348544 | ||||||||
\(604\) | 2.89207e8i | 1.31249i | ||||||||
\(605\) | − | 1.27047e8i | − | 0.573720i | ||||||
\(606\) | 4.05682e8 | 1.82292 | ||||||||
\(607\) | − | 1.78401e8i | − | 0.797685i | −0.917020 | − | 0.398842i | \(-0.869412\pi\) | ||
0.917020 | − | 0.398842i | \(-0.130588\pi\) | |||||||
\(608\) | −2.37275e8 | −1.05570 | ||||||||
\(609\) | 7.05594e7i | 0.312394i | ||||||||
\(610\) | 5.37340e8i | 2.36734i | ||||||||
\(611\) | 3.88362e8 | 1.70260 | ||||||||
\(612\) | 7.69076e7 | 0.335517 | ||||||||
\(613\) | 2.81992e8 | 1.22421 | 0.612104 | − | 0.790777i | \(-0.290323\pi\) | ||||
0.612104 | + | 0.790777i | \(0.290323\pi\) | |||||||
\(614\) | − | 1.41805e8i | − | 0.612612i | ||||||
\(615\) | 2.63987e8 | 1.13490 | ||||||||
\(616\) | 2.82988e8 | 1.21067 | ||||||||
\(617\) | 3.33667e8 | 1.42055 | 0.710277 | − | 0.703923i | \(-0.248570\pi\) | ||||
0.710277 | + | 0.703923i | \(0.248570\pi\) | |||||||
\(618\) | −1.43024e8 | −0.605961 | ||||||||
\(619\) | 9.98403e7 | 0.420953 | 0.210477 | − | 0.977599i | \(-0.432498\pi\) | ||||
0.210477 | + | 0.977599i | \(0.432498\pi\) | |||||||
\(620\) | 2.84380e8i | 1.19323i | ||||||||
\(621\) | − | 2.12345e8i | − | 0.886679i | ||||||
\(622\) | 2.54713e8i | 1.05847i | ||||||||
\(623\) | 2.67284e8 | 1.10537 | ||||||||
\(624\) | − | 6.50247e7i | − | 0.267624i | ||||||
\(625\) | −2.88140e8 | −1.18022 | ||||||||
\(626\) | 1.68918e7 | 0.0688579 | ||||||||
\(627\) | −3.16651e8 | −1.28463 | ||||||||
\(628\) | − | 6.17717e8i | − | 2.49408i | ||||||
\(629\) | − | 2.94549e7i | − | 0.118360i | ||||||
\(630\) | 1.16998e8i | 0.467904i | ||||||||
\(631\) | − | 2.37989e8i | − | 0.947257i | −0.880725 | − | 0.473629i | \(-0.842944\pi\) | ||
0.880725 | − | 0.473629i | \(-0.157056\pi\) | |||||||
\(632\) | 4.40097e8i | 1.74340i | ||||||||
\(633\) | −2.48364e7 | −0.0979214 | ||||||||
\(634\) | 5.58200e8i | 2.19039i | ||||||||
\(635\) | 1.33465e8i | 0.521249i | ||||||||
\(636\) | 1.21287e8i | 0.471458i | ||||||||
\(637\) | 1.19153e8 | 0.460984 | ||||||||
\(638\) | −2.27182e8 | −0.874808 | ||||||||
\(639\) | − | 8.95781e7i | − | 0.343320i | ||||||
\(640\) | 5.04500e8 | 1.92451 | ||||||||
\(641\) | − | 9.09313e7i | − | 0.345254i | −0.984987 | − | 0.172627i | \(-0.944774\pi\) | ||
0.984987 | − | 0.172627i | \(-0.0552256\pi\) | |||||||
\(642\) | 2.49641e8 | 0.943431 | ||||||||
\(643\) | −9.69805e7 | −0.364797 | −0.182399 | − | 0.983225i | \(-0.558386\pi\) | ||||
−0.182399 | + | 0.983225i | \(0.558386\pi\) | |||||||
\(644\) | − | 3.17993e8i | − | 1.19058i | ||||||
\(645\) | 1.55880e8 | − | 1.95452e8i | 0.580912 | − | 0.728385i | ||||
\(646\) | −3.66362e8 | −1.35898 | ||||||||
\(647\) | 909696.i | 0.00335880i | 0.999999 | + | 0.00167940i | \(0.000534569\pi\) | ||||
−0.999999 | + | 0.00167940i | \(0.999465\pi\) | |||||||
\(648\) | 1.90641e8i | 0.700635i | ||||||||
\(649\) | −5.40041e7 | −0.197557 | ||||||||
\(650\) | − | 1.89927e8i | − | 0.691588i | ||||||
\(651\) | 1.26093e8 | 0.457033 | ||||||||
\(652\) | 3.95918e8i | 1.42844i | ||||||||
\(653\) | − | 1.20112e8i | − | 0.431367i | −0.976463 | − | 0.215683i | \(-0.930802\pi\) | ||
0.976463 | − | 0.215683i | \(-0.0691979\pi\) | |||||||
\(654\) | −5.40189e8 | −1.93113 | ||||||||
\(655\) | 4.96436e8 | 1.76661 | ||||||||
\(656\) | −6.14795e7 | −0.217780 | ||||||||
\(657\) | 8.25640e7i | 0.291135i | ||||||||
\(658\) | −3.84017e8 | −1.34795 | ||||||||
\(659\) | 2.23855e7 | 0.0782187 | 0.0391093 | − | 0.999235i | \(-0.487548\pi\) | ||||
0.0391093 | + | 0.999235i | \(0.487548\pi\) | |||||||
\(660\) | 5.59120e8 | 1.94479 | ||||||||
\(661\) | −4.33191e8 | −1.49994 | −0.749972 | − | 0.661469i | \(-0.769933\pi\) | ||||
−0.749972 | + | 0.661469i | \(0.769933\pi\) | |||||||
\(662\) | −6.26851e8 | −2.16068 | ||||||||
\(663\) | 2.90077e8i | 0.995344i | ||||||||
\(664\) | 9.63860e7i | 0.329238i | ||||||||
\(665\) | − | 3.50558e8i | − | 1.19205i | ||||||
\(666\) | −2.56954e7 | −0.0869825 | ||||||||
\(667\) | 1.04702e8i | 0.352841i | ||||||||
\(668\) | −3.49156e8 | −1.17136 | ||||||||
\(669\) | −3.10512e8 | −1.03705 | ||||||||
\(670\) | −6.42799e8 | −2.13723 | ||||||||
\(671\) | 4.82506e8i | 1.59711i | ||||||||
\(672\) | − | 1.85767e8i | − | 0.612155i | ||||||
\(673\) | − | 2.73875e8i | − | 0.898477i | −0.893412 | − | 0.449239i | \(-0.851695\pi\) | ||
0.893412 | − | 0.449239i | \(-0.148305\pi\) | |||||||
\(674\) | − | 3.04464e8i | − | 0.994390i | ||||||
\(675\) | 7.88798e7i | 0.256481i | ||||||||
\(676\) | −1.14713e9 | −3.71342 | ||||||||
\(677\) | − | 5.41280e7i | − | 0.174444i | −0.996189 | − | 0.0872219i | \(-0.972201\pi\) | ||
0.996189 | − | 0.0872219i | \(-0.0277989\pi\) | |||||||
\(678\) | − | 4.62684e8i | − | 1.48455i | ||||||
\(679\) | 2.88675e8i | 0.922146i | ||||||||
\(680\) | 2.65318e8 | 0.843801 | ||||||||
\(681\) | 8.28098e7 | 0.262205 | ||||||||
\(682\) | 4.05986e8i | 1.27985i | ||||||||
\(683\) | 5.00593e8 | 1.57117 | 0.785583 | − | 0.618756i | \(-0.212363\pi\) | ||||
0.785583 | + | 0.618756i | \(0.212363\pi\) | |||||||
\(684\) | 2.01025e8i | 0.628175i | ||||||||
\(685\) | 6.34845e8 | 1.97513 | ||||||||
\(686\) | −5.74334e8 | −1.77907 | ||||||||
\(687\) | − | 1.90012e8i | − | 0.586019i | ||||||
\(688\) | −3.63026e7 | + | 4.55185e7i | −0.111474 | + | 0.139773i | ||||
\(689\) | 1.93862e8 | 0.592701 | ||||||||
\(690\) | − | 4.09681e8i | − | 1.24709i | ||||||
\(691\) | 6.59368e8i | 1.99845i | 0.0393546 | + | 0.999225i | \(0.487470\pi\) | ||||
−0.0393546 | + | 0.999225i | \(0.512530\pi\) | |||||||
\(692\) | −3.25533e8 | −0.982375 | ||||||||
\(693\) | 1.05058e8i | 0.315669i | ||||||||
\(694\) | 5.93329e8 | 1.77508 | ||||||||
\(695\) | 5.02537e8i | 1.49697i | ||||||||
\(696\) | − | 1.39586e8i | − | 0.414012i | ||||||
\(697\) | 2.74262e8 | 0.809967 | ||||||||
\(698\) | −4.77364e8 | −1.40373 | ||||||||
\(699\) | −1.95439e8 | −0.572242 | ||||||||
\(700\) | 1.18125e8i | 0.344388i | ||||||||
\(701\) | −1.34774e8 | −0.391248 | −0.195624 | − | 0.980679i | \(-0.562673\pi\) | ||||
−0.195624 | + | 0.980679i | \(0.562673\pi\) | |||||||
\(702\) | 1.10325e9 | 3.18905 | ||||||||
\(703\) | 7.69905e7 | 0.221601 | ||||||||
\(704\) | 6.74928e8 | 1.93437 | ||||||||
\(705\) | −3.11185e8 | −0.888079 | ||||||||
\(706\) | 8.22984e7i | 0.233872i | ||||||||
\(707\) | 4.03291e8i | 1.14120i | ||||||||
\(708\) | − | 8.09024e7i | − | 0.227961i | ||||||
\(709\) | −1.73069e8 | −0.485601 | −0.242801 | − | 0.970076i | \(-0.578066\pi\) | ||||
−0.242801 | + | 0.970076i | \(0.578066\pi\) | |||||||
\(710\) | − | 7.53472e8i | − | 2.10519i | ||||||
\(711\) | −1.63385e8 | −0.454573 | ||||||||
\(712\) | −5.28760e8 | −1.46494 | ||||||||
\(713\) | 1.87108e8 | 0.516207 | ||||||||
\(714\) | − | 2.86832e8i | − | 0.788011i | ||||||
\(715\) | − | 8.93683e8i | − | 2.44492i | ||||||
\(716\) | − | 2.69515e8i | − | 0.734249i | ||||||
\(717\) | 5.47543e8i | 1.48546i | ||||||||
\(718\) | − | 9.98734e8i | − | 2.69821i | ||||||
\(719\) | −5.58345e7 | −0.150216 | −0.0751079 | − | 0.997175i | \(-0.523930\pi\) | ||||
−0.0751079 | + | 0.997175i | \(0.523930\pi\) | |||||||
\(720\) | − | 2.20798e7i | − | 0.0591558i | ||||||
\(721\) | − | 1.42181e8i | − | 0.379347i | ||||||
\(722\) | − | 3.39716e8i | − | 0.902620i | ||||||
\(723\) | 6.27087e8 | 1.65925 | ||||||||
\(724\) | 1.01672e9 | 2.67907 | ||||||||
\(725\) | − | 3.88938e7i | − | 0.102063i | ||||||
\(726\) | 2.71714e8 | 0.710073 | ||||||||
\(727\) | − | 6.04466e8i | − | 1.57314i | −0.617499 | − | 0.786572i | \(-0.711854\pi\) | ||
0.617499 | − | 0.786572i | \(-0.288146\pi\) | |||||||
\(728\) | 6.77612e8 | 1.75625 | ||||||||
\(729\) | −4.23874e8 | −1.09409 | ||||||||
\(730\) | 6.94475e8i | 1.78520i | ||||||||
\(731\) | 1.61947e8 | − | 2.03060e8i | 0.414592 | − | 0.519842i | ||||
\(732\) | −7.22832e8 | −1.84291 | ||||||||
\(733\) | − | 7.18216e8i | − | 1.82366i | −0.410572 | − | 0.911828i | \(-0.634671\pi\) | ||
0.410572 | − | 0.911828i | \(-0.365329\pi\) | |||||||
\(734\) | 2.41957e7i | 0.0611858i | ||||||||
\(735\) | −9.54742e7 | −0.240449 | ||||||||
\(736\) | − | 2.75658e8i | − | 0.691412i | ||||||
\(737\) | −5.77203e8 | −1.44187 | ||||||||
\(738\) | − | 2.39256e8i | − | 0.595243i | ||||||
\(739\) | − | 1.73211e8i | − | 0.429182i | −0.976704 | − | 0.214591i | \(-0.931158\pi\) | ||
0.976704 | − | 0.214591i | \(-0.0688418\pi\) | |||||||
\(740\) | −1.35944e8 | −0.335480 | ||||||||
\(741\) | −7.58217e8 | −1.86354 | ||||||||
\(742\) | −1.91693e8 | −0.469240 | ||||||||
\(743\) | 1.73962e8i | 0.424119i | 0.977257 | + | 0.212060i | \(0.0680171\pi\) | ||||
−0.977257 | + | 0.212060i | \(0.931983\pi\) | |||||||
\(744\) | −2.49446e8 | −0.605701 | ||||||||
\(745\) | 3.61609e8 | 0.874521 | ||||||||
\(746\) | 4.25900e8 | 1.02587 | ||||||||
\(747\) | −3.57830e7 | −0.0858451 | ||||||||
\(748\) | 5.80882e8 | 1.38798 | ||||||||
\(749\) | 2.48169e8i | 0.590613i | ||||||||
\(750\) | − | 4.93098e8i | − | 1.16882i | ||||||
\(751\) | 8.34005e8i | 1.96901i | 0.175345 | + | 0.984507i | \(0.443896\pi\) | ||||
−0.175345 | + | 0.984507i | \(0.556104\pi\) | |||||||
\(752\) | 7.24714e7 | 0.170417 | ||||||||
\(753\) | 1.72260e8i | 0.403459i | ||||||||
\(754\) | −5.43986e8 | −1.26904 | ||||||||
\(755\) | −3.70398e8 | −0.860653 | ||||||||
\(756\) | −6.86163e8 | −1.58804 | ||||||||
\(757\) | 3.17760e8i | 0.732508i | 0.930515 | + | 0.366254i | \(0.119360\pi\) | ||||
−0.930515 | + | 0.366254i | \(0.880640\pi\) | |||||||
\(758\) | 7.67136e7i | 0.176143i | ||||||||
\(759\) | − | 3.67874e8i | − | 0.841343i | ||||||
\(760\) | 6.93500e8i | 1.57981i | ||||||||
\(761\) | − | 1.38371e8i | − | 0.313972i | −0.987601 | − | 0.156986i | \(-0.949822\pi\) | ||
0.987601 | − | 0.156986i | \(-0.0501777\pi\) | |||||||
\(762\) | −2.85439e8 | −0.645132 | ||||||||
\(763\) | − | 5.37006e8i | − | 1.20894i | ||||||
\(764\) | 6.02153e8i | 1.35029i | ||||||||
\(765\) | 9.84986e7i | 0.220012i | ||||||||
\(766\) | 4.05311e8 | 0.901782 | ||||||||
\(767\) | −1.29312e8 | −0.286585 | ||||||||
\(768\) | 4.82561e8i | 1.06529i | ||||||||
\(769\) | 6.44915e8 | 1.41815 | 0.709077 | − | 0.705131i | \(-0.249112\pi\) | ||||
0.709077 | + | 0.705131i | \(0.249112\pi\) | |||||||
\(770\) | 8.83684e8i | 1.93564i | ||||||||
\(771\) | −1.50993e8 | −0.329454 | ||||||||
\(772\) | 9.42355e6 | 0.0204815 | ||||||||
\(773\) | 5.45053e8i | 1.18005i | 0.807385 | + | 0.590025i | \(0.200882\pi\) | ||||
−0.807385 | + | 0.590025i | \(0.799118\pi\) | |||||||
\(774\) | −1.77142e8 | − | 1.41277e8i | −0.382031 | − | 0.304682i | ||||
\(775\) | −6.95051e7 | −0.149318 | ||||||||
\(776\) | − | 5.71078e8i | − | 1.22211i | ||||||
\(777\) | 6.02773e7i | 0.128496i | ||||||||
\(778\) | −1.13362e9 | −2.40728 | ||||||||
\(779\) | 7.16878e8i | 1.51647i | ||||||||
\(780\) | 1.33881e9 | 2.82120 | ||||||||
\(781\) | − | 6.76582e8i | − | 1.42026i | ||||||
\(782\) | − | 4.25627e8i | − | 0.890038i | ||||||
\(783\) | 2.25926e8 | 0.470631 | ||||||||
\(784\) | 2.22348e7 | 0.0461408 | ||||||||
\(785\) | 7.91134e8 | 1.63547 | ||||||||
\(786\) | 1.06172e9i | 2.18647i | ||||||||
\(787\) | 5.06991e8 | 1.04010 | 0.520051 | − | 0.854135i | \(-0.325913\pi\) | ||||
0.520051 | + | 0.854135i | \(0.325913\pi\) | |||||||
\(788\) | 1.05520e9 | 2.15653 | ||||||||
\(789\) | −4.32002e8 | −0.879538 | ||||||||
\(790\) | −1.37429e9 | −2.78738 | ||||||||
\(791\) | 4.59957e8 | 0.929368 | ||||||||
\(792\) | − | 2.07834e8i | − | 0.418352i | ||||||
\(793\) | 1.15536e9i | 2.31684i | ||||||||
\(794\) | 9.03951e8i | 1.80586i | ||||||||
\(795\) | −1.55337e8 | −0.309153 | ||||||||
\(796\) | − | 1.34803e9i | − | 2.67277i | ||||||
\(797\) | −2.78365e8 | −0.549844 | −0.274922 | − | 0.961467i | \(-0.588652\pi\) | ||||
−0.274922 | + | 0.961467i | \(0.588652\pi\) | |||||||
\(798\) | 7.49734e8 | 1.47536 | ||||||||
\(799\) | −3.23297e8 | −0.633814 | ||||||||
\(800\) | 1.02399e8i | 0.199998i | ||||||||
\(801\) | − | 1.96301e8i | − | 0.381966i | ||||||
\(802\) | 2.86579e8i | 0.555547i | ||||||||
\(803\) | 6.23605e8i | 1.20438i | ||||||||
\(804\) | − | 8.64695e8i | − | 1.66378i | ||||||
\(805\) | 4.07266e8 | 0.780712 | ||||||||
\(806\) | 9.72129e8i | 1.85660i | ||||||||
\(807\) | − | 7.58854e8i | − | 1.44390i | ||||||
\(808\) | − | 7.97819e8i | − | 1.51241i | ||||||
\(809\) | −8.49318e8 | −1.60408 | −0.802038 | − | 0.597273i | \(-0.796251\pi\) | ||||
−0.802038 | + | 0.597273i | \(0.796251\pi\) | |||||||
\(810\) | −5.95314e8 | −1.12019 | ||||||||
\(811\) | 5.11238e8i | 0.958430i | 0.877697 | + | 0.479215i | \(0.159079\pi\) | ||||
−0.877697 | + | 0.479215i | \(0.840921\pi\) | |||||||
\(812\) | 3.38332e8 | 0.631938 | ||||||||
\(813\) | 6.95444e8i | 1.29417i | ||||||||
\(814\) | −1.94077e8 | −0.359832 | ||||||||
\(815\) | −5.07068e8 | −0.936685 | ||||||||
\(816\) | 5.41307e7i | 0.0996261i | ||||||||
\(817\) | 5.30767e8 | + | 4.23304e8i | 0.973279 | + | 0.776223i | ||||
\(818\) | 4.37921e8 | 0.800084 | ||||||||
\(819\) | 2.51562e8i | 0.457923i | ||||||||
\(820\) | − | 1.26581e9i | − | 2.29577i | ||||||
\(821\) | −3.71408e8 | −0.671154 | −0.335577 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335577 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(822\) | 1.35773e9i | 2.44455i | ||||||||
\(823\) | −5.07441e8 | −0.910304 | −0.455152 | − | 0.890414i | \(-0.650415\pi\) | ||||
−0.455152 | + | 0.890414i | \(0.650415\pi\) | |||||||
\(824\) | 2.81274e8i | 0.502745i | ||||||||
\(825\) | 1.36654e8i | 0.243367i | ||||||||
\(826\) | 1.27865e8 | 0.226889 | ||||||||
\(827\) | 1.29378e8 | 0.228741 | 0.114370 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114370 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(828\) | −2.33543e8 | −0.411411 | ||||||||
\(829\) | − | 5.83787e8i | − | 1.02469i | −0.858781 | − | 0.512343i | \(-0.828778\pi\) | ||
0.858781 | − | 0.512343i | \(-0.171222\pi\) | |||||||
\(830\) | −3.00984e8 | −0.526391 | ||||||||
\(831\) | −1.28109e8 | −0.223243 | ||||||||
\(832\) | 1.61611e9 | 2.80608 | ||||||||
\(833\) | −9.91903e7 | −0.171607 | ||||||||
\(834\) | −1.07477e9 | −1.85275 | ||||||||
\(835\) | − | 4.47177e8i | − | 0.768104i | ||||||
\(836\) | 1.51834e9i | 2.59866i | ||||||||
\(837\) | − | 4.03740e8i | − | 0.688534i | ||||||
\(838\) | 1.20266e9 | 2.04367 | ||||||||
\(839\) | − | 9.70687e8i | − | 1.64359i | −0.569783 | − | 0.821795i | \(-0.692973\pi\) | ||
0.569783 | − | 0.821795i | \(-0.307027\pi\) | |||||||
\(840\) | −5.42954e8 | −0.916063 | ||||||||
\(841\) | 4.83424e8 | 0.812719 | ||||||||
\(842\) | −1.21255e8 | −0.203126 | ||||||||
\(843\) | − | 3.75172e8i | − | 0.626250i | ||||||
\(844\) | 1.19090e8i | 0.198084i | ||||||||
\(845\) | − | 1.46918e9i | − | 2.43503i | ||||||
\(846\) | 2.82033e8i | 0.465788i | ||||||||
\(847\) | 2.70113e8i | 0.444524i | ||||||||
\(848\) | 3.61762e7 | 0.0593247 | ||||||||
\(849\) | 5.49807e8i | 0.898436i | ||||||||
\(850\) | 1.58108e8i | 0.257452i | ||||||||
\(851\) | 8.94448e7i | 0.145133i | ||||||||
\(852\) | 1.01357e9 | 1.63884 | ||||||||
\(853\) | 3.44624e8 | 0.555263 | 0.277632 | − | 0.960688i | \(-0.410451\pi\) | ||||
0.277632 | + | 0.960688i | \(0.410451\pi\) | |||||||
\(854\) | − | 1.14243e9i | − | 1.83424i | ||||||
\(855\) | −2.57460e8 | −0.411919 | ||||||||
\(856\) | − | 4.90947e8i | − | 0.782732i | ||||||
\(857\) | 1.04607e9 | 1.66194 | 0.830972 | − | 0.556314i | \(-0.187785\pi\) | ||||
0.830972 | + | 0.556314i | \(0.187785\pi\) | |||||||
\(858\) | 1.91131e9 | 3.02600 | ||||||||
\(859\) | − | 6.80036e8i | − | 1.07288i | −0.843937 | − | 0.536442i | \(-0.819768\pi\) | ||
0.843937 | − | 0.536442i | \(-0.180232\pi\) | |||||||
\(860\) | −9.37191e8 | − | 7.47441e8i | −1.47344 | − | 1.17512i | ||||
\(861\) | −5.61257e8 | −0.879332 | ||||||||
\(862\) | − | 1.32704e9i | − | 2.07187i | ||||||
\(863\) | 1.85369e8i | 0.288407i | 0.989548 | + | 0.144203i | \(0.0460619\pi\) | ||||
−0.989548 | + | 0.144203i | \(0.953938\pi\) | |||||||
\(864\) | −5.94812e8 | −0.922229 | ||||||||
\(865\) | − | 4.16923e8i | − | 0.644181i | ||||||
\(866\) | −6.64752e8 | −1.02354 | ||||||||
\(867\) | 3.04702e8i | 0.467540i | ||||||||
\(868\) | − | 6.04614e8i | − | 0.924526i | ||||||
\(869\) | −1.23404e9 | −1.88049 | ||||||||
\(870\) | 4.35883e8 | 0.661930 | ||||||||
\(871\) | −1.38211e9 | −2.09164 | ||||||||
\(872\) | 1.06234e9i | 1.60220i | ||||||||
\(873\) | 2.12011e8 | 0.318651 | ||||||||
\(874\) | 1.11252e9 | 1.66638 | ||||||||
\(875\) | 4.90192e8 | 0.731715 | ||||||||
\(876\) | −9.34210e8 | −1.38973 | ||||||||
\(877\) | −6.26510e8 | −0.928816 | −0.464408 | − | 0.885621i | \(-0.653733\pi\) | ||||
−0.464408 | + | 0.885621i | \(0.653733\pi\) | |||||||
\(878\) | 1.48462e9i | 2.19347i | ||||||||
\(879\) | 8.35939e8i | 1.23086i | ||||||||
\(880\) | − | 1.66768e8i | − | 0.244718i | ||||||
\(881\) | 1.13133e9 | 1.65448 | 0.827239 | − | 0.561851i | \(-0.189911\pi\) | ||||
0.827239 | + | 0.561851i | \(0.189911\pi\) | |||||||
\(882\) | 8.65300e7i | 0.126113i | ||||||||
\(883\) | 1.74569e8 | 0.253562 | 0.126781 | − | 0.991931i | \(-0.459535\pi\) | ||||
0.126781 | + | 0.991931i | \(0.459535\pi\) | |||||||
\(884\) | 1.39092e9 | 2.01347 | ||||||||
\(885\) | 1.03615e8 | 0.149483 | ||||||||
\(886\) | 3.10212e7i | 0.0446023i | ||||||||
\(887\) | 1.53622e8i | 0.220132i | 0.993924 | + | 0.110066i | \(0.0351063\pi\) | ||||
−0.993924 | + | 0.110066i | \(0.964894\pi\) | |||||||
\(888\) | − | 1.19245e8i | − | 0.170295i | ||||||
\(889\) | − | 2.83757e8i | − | 0.403869i | ||||||
\(890\) | − | 1.65115e9i | − | 2.34217i | ||||||
\(891\) | −5.34563e8 | −0.755729 | ||||||||
\(892\) | 1.48890e9i | 2.09783i | ||||||||
\(893\) | − | 8.45049e8i | − | 1.18666i | ||||||
\(894\) | 7.73367e8i | 1.08236i | ||||||||
\(895\) | 3.45178e8 | 0.481475 | ||||||||
\(896\) | −1.07261e9 | −1.49113 | ||||||||
\(897\) | − | 8.80870e8i | − | 1.22049i | ||||||
\(898\) | −6.36288e8 | −0.878668 | ||||||||
\(899\) | 1.99075e8i | 0.273992i | ||||||||
\(900\) | 8.67544e7 | 0.119005 | ||||||||
\(901\) | −1.61383e8 | −0.220640 | ||||||||
\(902\) | − | 1.80710e9i | − | 2.46242i | ||||||
\(903\) | −3.31413e8 | + | 4.15547e8i | −0.450097 | + | 0.564361i | ||||
\(904\) | −9.09920e8 | −1.23168 | ||||||||
\(905\) | 1.30215e9i | 1.75677i | ||||||||
\(906\) | − | 7.92165e8i | − | 1.06520i | ||||||
\(907\) | 9.11432e8 | 1.22152 | 0.610762 | − | 0.791814i | \(-0.290863\pi\) | ||||
0.610762 | + | 0.791814i | \(0.290863\pi\) | |||||||
\(908\) | − | 3.97072e8i | − | 0.530410i | ||||||
\(909\) | 2.96188e8 | 0.394345 | ||||||||
\(910\) | 2.11597e9i | 2.80793i | ||||||||
\(911\) | 4.94587e8i | 0.654166i | 0.944996 | + | 0.327083i | \(0.106066\pi\) | ||||
−0.944996 | + | 0.327083i | \(0.893934\pi\) | |||||||
\(912\) | −1.41489e8 | −0.186526 | ||||||||
\(913\) | −2.70269e8 | −0.355127 | ||||||||
\(914\) | −1.14153e9 | −1.49502 | ||||||||
\(915\) | − | 9.25759e8i | − | 1.20847i | ||||||
\(916\) | −9.11108e8 | −1.18545 | ||||||||
\(917\) | −1.05546e9 | −1.36879 | ||||||||
\(918\) | −9.18413e8 | −1.18716 | ||||||||
\(919\) | 1.14272e9 | 1.47230 | 0.736148 | − | 0.676821i | \(-0.236643\pi\) | ||||
0.736148 | + | 0.676821i | \(0.236643\pi\) | |||||||
\(920\) | −8.05684e8 | −1.03467 | ||||||||
\(921\) | 2.44309e8i | 0.312723i | ||||||||
\(922\) | 1.14003e9i | 1.45453i | ||||||||
\(923\) | − | 1.62007e9i | − | 2.06029i | ||||||
\(924\) | −1.18873e9 | −1.50685 | ||||||||
\(925\) | − | 3.32261e7i | − | 0.0419811i | ||||||
\(926\) | 1.33387e9 | 1.67989 | ||||||||
\(927\) | −1.04422e8 | −0.131085 | ||||||||
\(928\) | 2.93289e8 | 0.366987 | ||||||||
\(929\) | − | 5.82463e8i | − | 0.726475i | −0.931697 | − | 0.363238i | \(-0.881671\pi\) | ||
0.931697 | − | 0.363238i | \(-0.118329\pi\) | |||||||
\(930\) | − | 7.78944e8i | − | 0.968405i | ||||||
\(931\) | − | 2.59268e8i | − | 0.321292i | ||||||
\(932\) | 9.37128e8i | 1.15758i | ||||||||
\(933\) | − | 4.38834e8i | − | 0.540325i | ||||||
\(934\) | 1.00039e9 | 1.22781 | ||||||||
\(935\) | 7.43958e8i | 0.910152i | ||||||||
\(936\) | − | 4.97658e8i | − | 0.606880i | ||||||
\(937\) | − | 3.95212e8i | − | 0.480410i | −0.970722 | − | 0.240205i | \(-0.922785\pi\) | ||
0.970722 | − | 0.240205i | \(-0.0772146\pi\) | |||||||
\(938\) | 1.36664e9 | 1.65595 | ||||||||
\(939\) | −2.91022e7 | −0.0351502 | ||||||||
\(940\) | 1.49213e9i | 1.79648i | ||||||||
\(941\) | 2.47559e8 | 0.297104 | 0.148552 | − | 0.988905i | \(-0.452539\pi\) | ||||
0.148552 | + | 0.988905i | \(0.452539\pi\) | |||||||
\(942\) | 1.69199e9i | 2.02416i | ||||||||
\(943\) | −8.32844e8 | −0.993181 | ||||||||
\(944\) | −2.41307e7 | −0.0286849 | ||||||||
\(945\) | − | 8.78796e8i | − | 1.04134i | ||||||
\(946\) | −1.33795e9 | − | 1.06706e9i | −1.58040 | − | 1.26042i | ||||
\(947\) | 2.33236e8 | 0.274628 | 0.137314 | − | 0.990528i | \(-0.456153\pi\) | ||||
0.137314 | + | 0.990528i | \(0.456153\pi\) | |||||||
\(948\) | − | 1.84870e9i | − | 2.16990i | ||||||
\(949\) | 1.49322e9i | 1.74713i | ||||||||
\(950\) | −4.13269e8 | −0.482017 | ||||||||
\(951\) | − | 9.61696e8i | − | 1.11814i | ||||||
\(952\) | −5.64087e8 | −0.653786 | ||||||||
\(953\) | 1.15096e9i | 1.32978i | 0.746941 | + | 0.664890i | \(0.231522\pi\) | ||||
−0.746941 | + | 0.664890i | \(0.768478\pi\) | |||||||
\(954\) | 1.40785e8i | 0.162148i | ||||||||
\(955\) | −7.71200e8 | −0.885436 | ||||||||
\(956\) | 2.62546e9 | 3.00491 | ||||||||
\(957\) | 3.91402e8 | 0.446568 | ||||||||
\(958\) | 8.97564e8i | 1.02087i | ||||||||
\(959\) | −1.34973e9 | −1.53035 | ||||||||
\(960\) | −1.29495e9 | −1.46366 | ||||||||
\(961\) | −5.31747e8 | −0.599149 | ||||||||
\(962\) | −4.64715e8 | −0.521989 | ||||||||
\(963\) | 1.82263e8 | 0.204089 | ||||||||
\(964\) | − | 3.00687e9i | − | 3.35648i | ||||||
\(965\) | 1.20691e7i | 0.0134305i | ||||||||
\(966\) | 8.71014e8i | 0.966260i | ||||||||
\(967\) | −3.51599e8 | −0.388838 | −0.194419 | − | 0.980919i | \(-0.562282\pi\) | ||||
−0.194419 | + | 0.980919i | \(0.562282\pi\) | |||||||
\(968\) | − | 5.34358e8i | − | 0.589123i | ||||||
\(969\) | 6.31188e8 | 0.693725 | ||||||||
\(970\) | 1.78330e9 | 1.95393 | ||||||||
\(971\) | 6.33816e8 | 0.692318 | 0.346159 | − | 0.938176i | \(-0.387486\pi\) | ||||
0.346159 | + | 0.938176i | \(0.387486\pi\) | |||||||
\(972\) | 8.92287e8i | 0.971641i | ||||||||
\(973\) | − | 1.06843e9i | − | 1.15987i | ||||||
\(974\) | 1.51714e9i | 1.64191i | ||||||||
\(975\) | 3.27217e8i | 0.353039i | ||||||||
\(976\) | 2.15599e8i | 0.231898i | ||||||||
\(977\) | 1.38060e9 | 1.48042 | 0.740208 | − | 0.672378i | \(-0.234727\pi\) | ||||
0.740208 | + | 0.672378i | \(0.234727\pi\) | |||||||
\(978\) | − | 1.08446e9i | − | 1.15930i | ||||||
\(979\) | − | 1.48266e9i | − | 1.58013i | ||||||
\(980\) | 4.57797e8i | 0.486402i | ||||||||
\(981\) | −3.94392e8 | −0.417755 | ||||||||
\(982\) | −6.26104e8 | −0.661169 | ||||||||
\(983\) | − | 3.15144e7i | − | 0.0331779i | −0.999862 | − | 0.0165889i | \(-0.994719\pi\) | ||
0.999862 | − | 0.0165889i | \(-0.00528067\pi\) | |||||||
\(984\) | 1.11032e9 | 1.16537 | ||||||||
\(985\) | 1.35144e9i | 1.41412i | ||||||||
\(986\) | 4.52849e8 | 0.472414 | ||||||||
\(987\) | 6.61605e8 | 0.688093 | ||||||||
\(988\) | 3.63564e9i | 3.76973i | ||||||||
\(989\) | −4.91780e8 | + | 6.16626e8i | −0.508372 | + | 0.637430i | ||||
\(990\) | 6.49002e8 | 0.668868 | ||||||||
\(991\) | − | 5.62503e8i | − | 0.577968i | −0.957334 | − | 0.288984i | \(-0.906683\pi\) | ||
0.957334 | − | 0.288984i | \(-0.0933174\pi\) | |||||||
\(992\) | − | 5.24120e8i | − | 0.536903i | ||||||
\(993\) | 1.07997e9 | 1.10297 | ||||||||
\(994\) | 1.60194e9i | 1.63113i | ||||||||
\(995\) | 1.72648e9 | 1.75263 | ||||||||
\(996\) | − | 4.04884e8i | − | 0.409782i | ||||||
\(997\) | − | 6.86242e8i | − | 0.692455i | −0.938150 | − | 0.346228i | \(-0.887462\pi\) | ||
0.938150 | − | 0.346228i | \(-0.112538\pi\) | |||||||
\(998\) | −2.32912e9 | −2.34315 | ||||||||
\(999\) | 1.93003e8 | 0.193583 |
(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 | 43.7.b.b.42.18 | yes | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.3 | ✓ | 20 | 43.42 | odd | 2 | inner | |
43.7.b.b.42.18 | yes | 20 | 1.1 | even | 1 | trivial |