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 | 42.6 | ||
Root | \(-8.33048i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 8.33048i | − | 1.04131i | −0.853767 | − | 0.520655i | \(-0.825688\pi\) | ||
0.853767 | − | 0.520655i | \(-0.174312\pi\) | |||||||
\(3\) | 16.8005i | 0.622239i | 0.950371 | + | 0.311120i | \(0.100704\pi\) | ||||
−0.950371 | + | 0.311120i | \(0.899296\pi\) | |||||||
\(4\) | −5.39690 | −0.0843265 | ||||||||
\(5\) | − | 47.9107i | − | 0.383286i | −0.981465 | − | 0.191643i | \(-0.938618\pi\) | ||
0.981465 | − | 0.191643i | \(-0.0613815\pi\) | |||||||
\(6\) | 139.956 | 0.647944 | ||||||||
\(7\) | 493.652i | 1.43922i | 0.694379 | + | 0.719609i | \(0.255679\pi\) | ||||
−0.694379 | + | 0.719609i | \(0.744321\pi\) | |||||||
\(8\) | − | 488.192i | − | 0.953500i | ||||||
\(9\) | 446.745 | 0.612818 | ||||||||
\(10\) | −399.119 | −0.399119 | ||||||||
\(11\) | 2011.69 | 1.51141 | 0.755704 | − | 0.654913i | \(-0.227295\pi\) | ||||
0.755704 | + | 0.654913i | \(0.227295\pi\) | |||||||
\(12\) | − | 90.6704i | − | 0.0524713i | ||||||
\(13\) | −124.091 | −0.0564818 | −0.0282409 | − | 0.999601i | \(-0.508991\pi\) | ||||
−0.0282409 | + | 0.999601i | \(0.508991\pi\) | |||||||
\(14\) | 4112.36 | 1.49867 | ||||||||
\(15\) | 804.922 | 0.238495 | ||||||||
\(16\) | −4412.28 | −1.07722 | ||||||||
\(17\) | 3857.23 | 0.785106 | 0.392553 | − | 0.919729i | \(-0.371592\pi\) | ||||
0.392553 | + | 0.919729i | \(0.371592\pi\) | |||||||
\(18\) | − | 3721.60i | − | 0.638134i | ||||||
\(19\) | − | 11142.3i | − | 1.62447i | −0.583328 | − | 0.812237i | \(-0.698250\pi\) | ||
0.583328 | − | 0.812237i | \(-0.301750\pi\) | |||||||
\(20\) | 258.569i | 0.0323212i | ||||||||
\(21\) | −8293.58 | −0.895538 | ||||||||
\(22\) | − | 16758.3i | − | 1.57385i | ||||||
\(23\) | −1130.75 | −0.0929361 | −0.0464681 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464681 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(24\) | 8201.85 | 0.593305 | ||||||||
\(25\) | 13329.6 | 0.853092 | ||||||||
\(26\) | 1033.73i | 0.0588151i | ||||||||
\(27\) | 19753.0i | 1.00356i | ||||||||
\(28\) | − | 2664.19i | − | 0.121364i | ||||||
\(29\) | 24367.1i | 0.999102i | 0.866284 | + | 0.499551i | \(0.166502\pi\) | ||||
−0.866284 | + | 0.499551i | \(0.833498\pi\) | |||||||
\(30\) | − | 6705.39i | − | 0.248348i | ||||||
\(31\) | −12408.9 | −0.416533 | −0.208266 | − | 0.978072i | \(-0.566782\pi\) | ||||
−0.208266 | + | 0.978072i | \(0.566782\pi\) | |||||||
\(32\) | 5512.08i | 0.168215i | ||||||||
\(33\) | 33797.2i | 0.940458i | ||||||||
\(34\) | − | 32132.6i | − | 0.817539i | ||||||
\(35\) | 23651.2 | 0.551632 | ||||||||
\(36\) | −2411.04 | −0.0516769 | ||||||||
\(37\) | 84686.2i | 1.67189i | 0.548814 | + | 0.835944i | \(0.315079\pi\) | ||||
−0.548814 | + | 0.835944i | \(0.684921\pi\) | |||||||
\(38\) | −92820.4 | −1.69158 | ||||||||
\(39\) | − | 2084.78i | − | 0.0351452i | ||||||
\(40\) | −23389.6 | −0.365463 | ||||||||
\(41\) | 125398. | 1.81944 | 0.909721 | − | 0.415221i | \(-0.136296\pi\) | ||||
0.909721 | + | 0.415221i | \(0.136296\pi\) | |||||||
\(42\) | 69089.5i | 0.932533i | ||||||||
\(43\) | −60660.4 | − | 51397.3i | −0.762957 | − | 0.646450i | ||||
\(44\) | −10856.9 | −0.127452 | ||||||||
\(45\) | − | 21403.9i | − | 0.234885i | ||||||
\(46\) | 9419.72i | 0.0967753i | ||||||||
\(47\) | −200638. | −1.93250 | −0.966250 | − | 0.257606i | \(-0.917066\pi\) | ||||
−0.966250 | + | 0.257606i | \(0.917066\pi\) | |||||||
\(48\) | − | 74128.2i | − | 0.670286i | ||||||
\(49\) | −126043. | −1.07135 | ||||||||
\(50\) | − | 111042.i | − | 0.888333i | ||||||
\(51\) | 64803.2i | 0.488524i | ||||||||
\(52\) | 669.704 | 0.00476291 | ||||||||
\(53\) | −124888. | −0.838865 | −0.419433 | − | 0.907786i | \(-0.637771\pi\) | ||||
−0.419433 | + | 0.907786i | \(0.637771\pi\) | |||||||
\(54\) | 164552. | 1.04502 | ||||||||
\(55\) | − | 96381.3i | − | 0.579301i | ||||||
\(56\) | 240997. | 1.37229 | ||||||||
\(57\) | 187195. | 1.01081 | ||||||||
\(58\) | 202990. | 1.04038 | ||||||||
\(59\) | −123831. | −0.602941 | −0.301470 | − | 0.953476i | \(-0.597477\pi\) | ||||
−0.301470 | + | 0.953476i | \(0.597477\pi\) | |||||||
\(60\) | −4344.08 | −0.0201115 | ||||||||
\(61\) | − | 28789.1i | − | 0.126835i | −0.997987 | − | 0.0634175i | \(-0.979800\pi\) | ||
0.997987 | − | 0.0634175i | \(-0.0202000\pi\) | |||||||
\(62\) | 103372.i | 0.433740i | ||||||||
\(63\) | 220536.i | 0.881980i | ||||||||
\(64\) | −236467. | −0.902051 | ||||||||
\(65\) | 5945.26i | 0.0216487i | ||||||||
\(66\) | 281547. | 0.979308 | ||||||||
\(67\) | 289876. | 0.963801 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(68\) | −20817.1 | −0.0662053 | ||||||||
\(69\) | − | 18997.2i | − | 0.0578285i | ||||||
\(70\) | − | 197026.i | − | 0.574420i | ||||||
\(71\) | − | 420644.i | − | 1.17528i | −0.809124 | − | 0.587638i | \(-0.800058\pi\) | ||
0.809124 | − | 0.587638i | \(-0.199942\pi\) | |||||||
\(72\) | − | 218097.i | − | 0.584322i | ||||||
\(73\) | − | 330369.i | − | 0.849240i | −0.905372 | − | 0.424620i | \(-0.860408\pi\) | ||
0.905372 | − | 0.424620i | \(-0.139592\pi\) | |||||||
\(74\) | 705476. | 1.74095 | ||||||||
\(75\) | 223943.i | 0.530827i | ||||||||
\(76\) | 60133.7i | 0.136986i | ||||||||
\(77\) | 993072.i | 2.17525i | ||||||||
\(78\) | −17367.2 | −0.0365970 | ||||||||
\(79\) | −647349. | −1.31298 | −0.656489 | − | 0.754336i | \(-0.727959\pi\) | ||||
−0.656489 | + | 0.754336i | \(0.727959\pi\) | |||||||
\(80\) | 211395.i | 0.412881i | ||||||||
\(81\) | −6183.39 | −0.0116351 | ||||||||
\(82\) | − | 1.04462e6i | − | 1.89460i | ||||||
\(83\) | −76719.5 | −0.134175 | −0.0670875 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670875 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(84\) | 44759.6 | 0.0755176 | ||||||||
\(85\) | − | 184802.i | − | 0.300920i | ||||||
\(86\) | −428164. | + | 505330.i | −0.673154 | + | 0.794474i | ||||
\(87\) | −409379. | −0.621681 | ||||||||
\(88\) | − | 982088.i | − | 1.44113i | ||||||
\(89\) | − | 16908.5i | − | 0.0239848i | −0.999928 | − | 0.0119924i | \(-0.996183\pi\) | ||
0.999928 | − | 0.0119924i | \(-0.00381739\pi\) | |||||||
\(90\) | −178304. | −0.244588 | ||||||||
\(91\) | − | 61257.5i | − | 0.0812897i | ||||||
\(92\) | 6102.56 | 0.00783698 | ||||||||
\(93\) | − | 208476.i | − | 0.259183i | ||||||
\(94\) | 1.67141e6i | 2.01233i | ||||||||
\(95\) | −533834. | −0.622637 | ||||||||
\(96\) | −92605.5 | −0.104670 | ||||||||
\(97\) | −1.10090e6 | −1.20623 | −0.603117 | − | 0.797653i | \(-0.706075\pi\) | ||||
−0.603117 | + | 0.797653i | \(0.706075\pi\) | |||||||
\(98\) | 1.05000e6i | 1.11561i | ||||||||
\(99\) | 898710. | 0.926219 | ||||||||
\(100\) | −71938.3 | −0.0719383 | ||||||||
\(101\) | −1.03617e6 | −1.00569 | −0.502846 | − | 0.864376i | \(-0.667714\pi\) | ||||
−0.502846 | + | 0.864376i | \(0.667714\pi\) | |||||||
\(102\) | 539842. | 0.508705 | ||||||||
\(103\) | 1.09074e6 | 0.998178 | 0.499089 | − | 0.866551i | \(-0.333668\pi\) | ||||
0.499089 | + | 0.866551i | \(0.333668\pi\) | |||||||
\(104\) | 60580.0i | 0.0538554i | ||||||||
\(105\) | 397351.i | 0.343247i | ||||||||
\(106\) | 1.04037e6i | 0.873519i | ||||||||
\(107\) | 788177. | 0.643387 | 0.321694 | − | 0.946844i | \(-0.395748\pi\) | ||||
0.321694 | + | 0.946844i | \(0.395748\pi\) | |||||||
\(108\) | − | 106605.i | − | 0.0846266i | ||||||
\(109\) | −17946.9 | −0.0138583 | −0.00692913 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692913 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(110\) | −802902. | −0.603232 | ||||||||
\(111\) | −1.42277e6 | −1.04031 | ||||||||
\(112\) | − | 2.17813e6i | − | 1.55035i | ||||||
\(113\) | 457458.i | 0.317041i | 0.987356 | + | 0.158521i | \(0.0506724\pi\) | ||||
−0.987356 | + | 0.158521i | \(0.949328\pi\) | |||||||
\(114\) | − | 1.55943e6i | − | 1.05257i | ||||||
\(115\) | 54175.2i | 0.0356211i | ||||||||
\(116\) | − | 131507.i | − | 0.0842509i | ||||||
\(117\) | −55436.8 | −0.0346131 | ||||||||
\(118\) | 1.03157e6i | 0.627848i | ||||||||
\(119\) | 1.90413e6i | 1.12994i | ||||||||
\(120\) | − | 392956.i | − | 0.227405i | ||||||
\(121\) | 2.27532e6 | 1.28436 | ||||||||
\(122\) | −239827. | −0.132075 | ||||||||
\(123\) | 2.10674e6i | 1.13213i | ||||||||
\(124\) | 66969.7 | 0.0351248 | ||||||||
\(125\) | − | 1.38723e6i | − | 0.710264i | ||||||
\(126\) | 1.83717e6 | 0.918414 | ||||||||
\(127\) | −1.91397e6 | −0.934383 | −0.467191 | − | 0.884156i | \(-0.654734\pi\) | ||||
−0.467191 | + | 0.884156i | \(0.654734\pi\) | |||||||
\(128\) | 2.32266e6i | 1.10753i | ||||||||
\(129\) | 863498. | − | 1.01912e6i | 0.402246 | − | 0.474742i | ||||
\(130\) | 49526.9 | 0.0225430 | ||||||||
\(131\) | − | 2.53980e6i | − | 1.12976i | −0.825174 | − | 0.564879i | \(-0.808923\pi\) | ||
0.825174 | − | 0.564879i | \(-0.191077\pi\) | |||||||
\(132\) | − | 182400.i | − | 0.0793055i | ||||||
\(133\) | 5.50040e6 | 2.33797 | ||||||||
\(134\) | − | 2.41480e6i | − | 1.00362i | ||||||
\(135\) | 946383. | 0.384650 | ||||||||
\(136\) | − | 1.88307e6i | − | 0.748599i | ||||||
\(137\) | − | 1.25787e6i | − | 0.489186i | −0.969626 | − | 0.244593i | \(-0.921346\pi\) | ||
0.969626 | − | 0.244593i | \(-0.0786544\pi\) | |||||||
\(138\) | −158256. | −0.0602174 | ||||||||
\(139\) | −1.15999e6 | −0.431927 | −0.215963 | − | 0.976401i | \(-0.569289\pi\) | ||||
−0.215963 | + | 0.976401i | \(0.569289\pi\) | |||||||
\(140\) | −127643. | −0.0465172 | ||||||||
\(141\) | − | 3.37081e6i | − | 1.20248i | ||||||
\(142\) | −3.50417e6 | −1.22383 | ||||||||
\(143\) | −249631. | −0.0853671 | ||||||||
\(144\) | −1.97116e6 | −0.660138 | ||||||||
\(145\) | 1.16745e6 | 0.382942 | ||||||||
\(146\) | −2.75213e6 | −0.884322 | ||||||||
\(147\) | − | 2.11758e6i | − | 0.666636i | ||||||
\(148\) | − | 457043.i | − | 0.140985i | ||||||
\(149\) | 6.01941e6i | 1.81968i | 0.414959 | + | 0.909840i | \(0.363796\pi\) | ||||
−0.414959 | + | 0.909840i | \(0.636204\pi\) | |||||||
\(150\) | 1.86555e6 | 0.552756 | ||||||||
\(151\) | − | 2.07076e6i | − | 0.601449i | −0.953711 | − | 0.300725i | \(-0.902771\pi\) | ||
0.953711 | − | 0.300725i | \(-0.0972285\pi\) | |||||||
\(152\) | −5.43956e6 | −1.54894 | ||||||||
\(153\) | 1.72320e6 | 0.481128 | ||||||||
\(154\) | 8.27277e6 | 2.26511 | ||||||||
\(155\) | 594520.i | 0.159651i | ||||||||
\(156\) | 11251.3i | 0.00296367i | ||||||||
\(157\) | − | 1.17682e6i | − | 0.304096i | −0.988373 | − | 0.152048i | \(-0.951413\pi\) | ||
0.988373 | − | 0.152048i | \(-0.0485869\pi\) | |||||||
\(158\) | 5.39273e6i | 1.36722i | ||||||||
\(159\) | − | 2.09817e6i | − | 0.521975i | ||||||
\(160\) | 264088. | 0.0644746 | ||||||||
\(161\) | − | 558199.i | − | 0.133755i | ||||||
\(162\) | 51510.6i | 0.0121158i | ||||||||
\(163\) | 2.85797e6i | 0.659925i | 0.943994 | + | 0.329962i | \(0.107036\pi\) | ||||
−0.943994 | + | 0.329962i | \(0.892964\pi\) | |||||||
\(164\) | −676759. | −0.153427 | ||||||||
\(165\) | 1.61925e6 | 0.360464 | ||||||||
\(166\) | 639110.i | 0.139718i | ||||||||
\(167\) | −1.92344e6 | −0.412980 | −0.206490 | − | 0.978449i | \(-0.566204\pi\) | ||||
−0.206490 | + | 0.978449i | \(0.566204\pi\) | |||||||
\(168\) | 4.04886e6i | 0.853896i | ||||||||
\(169\) | −4.81141e6 | −0.996810 | ||||||||
\(170\) | −1.53949e6 | −0.313351 | ||||||||
\(171\) | − | 4.97775e6i | − | 0.995507i | ||||||
\(172\) | 327378. | + | 277386.i | 0.0643375 | + | 0.0545129i | ||||
\(173\) | 4.93838e6 | 0.953775 | 0.476887 | − | 0.878964i | \(-0.341765\pi\) | ||||
0.476887 | + | 0.878964i | \(0.341765\pi\) | |||||||
\(174\) | 3.41032e6i | 0.647362i | ||||||||
\(175\) | 6.58017e6i | 1.22779i | ||||||||
\(176\) | −8.87611e6 | −1.62811 | ||||||||
\(177\) | − | 2.08042e6i | − | 0.375173i | ||||||
\(178\) | −140856. | −0.0249756 | ||||||||
\(179\) | 6.45397e6i | 1.12530i | 0.826695 | + | 0.562650i | \(0.190218\pi\) | ||||
−0.826695 | + | 0.562650i | \(0.809782\pi\) | |||||||
\(180\) | 115514.i | 0.0198070i | ||||||||
\(181\) | −807853. | −0.136238 | −0.0681188 | − | 0.997677i | \(-0.521700\pi\) | ||||
−0.0681188 | + | 0.997677i | \(0.521700\pi\) | |||||||
\(182\) | −510305. | −0.0846477 | ||||||||
\(183\) | 483671. | 0.0789217 | ||||||||
\(184\) | 552025.i | 0.0886146i | ||||||||
\(185\) | 4.05737e6 | 0.640811 | ||||||||
\(186\) | −1.73670e6 | −0.269890 | ||||||||
\(187\) | 7.75953e6 | 1.18662 | ||||||||
\(188\) | 1.08282e6 | 0.162961 | ||||||||
\(189\) | −9.75113e6 | −1.44434 | ||||||||
\(190\) | 4.44709e6i | 0.648359i | ||||||||
\(191\) | − | 1.42360e6i | − | 0.204310i | −0.994768 | − | 0.102155i | \(-0.967426\pi\) | ||
0.994768 | − | 0.102155i | \(-0.0325738\pi\) | |||||||
\(192\) | − | 3.97276e6i | − | 0.561292i | ||||||
\(193\) | 457518. | 0.0636409 | 0.0318204 | − | 0.999494i | \(-0.489870\pi\) | ||||
0.0318204 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(194\) | 9.17100e6i | 1.25606i | ||||||||
\(195\) | −99883.2 | −0.0134706 | ||||||||
\(196\) | 680243. | 0.0903432 | ||||||||
\(197\) | −6.24148e6 | −0.816373 | −0.408187 | − | 0.912898i | \(-0.633839\pi\) | ||||
−0.408187 | + | 0.912898i | \(0.633839\pi\) | |||||||
\(198\) | − | 7.48668e6i | − | 0.964481i | ||||||
\(199\) | − | 9.27567e6i | − | 1.17703i | −0.808488 | − | 0.588513i | \(-0.799714\pi\) | ||
0.808488 | − | 0.588513i | \(-0.200286\pi\) | |||||||
\(200\) | − | 6.50739e6i | − | 0.813423i | ||||||
\(201\) | 4.87004e6i | 0.599715i | ||||||||
\(202\) | 8.63176e6i | 1.04724i | ||||||||
\(203\) | −1.20289e7 | −1.43793 | ||||||||
\(204\) | − | 349736.i | − | 0.0411955i | ||||||
\(205\) | − | 6.00789e6i | − | 0.697366i | ||||||
\(206\) | − | 9.08635e6i | − | 1.03941i | ||||||
\(207\) | −505158. | −0.0569530 | ||||||||
\(208\) | 547521. | 0.0608431 | ||||||||
\(209\) | − | 2.24147e7i | − | 2.45524i | ||||||
\(210\) | 3.31013e6 | 0.357426 | ||||||||
\(211\) | 1.36638e7i | 1.45453i | 0.686354 | + | 0.727267i | \(0.259210\pi\) | ||||
−0.686354 | + | 0.727267i | \(0.740790\pi\) | |||||||
\(212\) | 674007. | 0.0707386 | ||||||||
\(213\) | 7.06701e6 | 0.731303 | ||||||||
\(214\) | − | 6.56589e6i | − | 0.669965i | ||||||
\(215\) | −2.46248e6 | + | 2.90628e6i | −0.247775 | + | 0.292430i | ||||
\(216\) | 9.64328e6 | 0.956893 | ||||||||
\(217\) | − | 6.12569e6i | − | 0.599482i | ||||||
\(218\) | 149506.i | 0.0144307i | ||||||||
\(219\) | 5.55034e6 | 0.528430 | ||||||||
\(220\) | 520160.i | 0.0488505i | ||||||||
\(221\) | −478645. | −0.0443442 | ||||||||
\(222\) | 1.18523e7i | 1.08329i | ||||||||
\(223\) | − | 1.05558e7i | − | 0.951865i | −0.879482 | − | 0.475933i | \(-0.842111\pi\) | ||
0.879482 | − | 0.475933i | \(-0.157889\pi\) | |||||||
\(224\) | −2.72105e6 | −0.242099 | ||||||||
\(225\) | 5.95491e6 | 0.522791 | ||||||||
\(226\) | 3.81084e6 | 0.330138 | ||||||||
\(227\) | 1.22631e7i | 1.04839i | 0.851599 | + | 0.524194i | \(0.175633\pi\) | ||||
−0.851599 | + | 0.524194i | \(0.824367\pi\) | |||||||
\(228\) | −1.01027e6 | −0.0852382 | ||||||||
\(229\) | 1.47550e7 | 1.22866 | 0.614332 | − | 0.789048i | \(-0.289426\pi\) | ||||
0.614332 | + | 0.789048i | \(0.289426\pi\) | |||||||
\(230\) | 451305. | 0.0370926 | ||||||||
\(231\) | −1.66841e7 | −1.35352 | ||||||||
\(232\) | 1.18958e7 | 0.952644 | ||||||||
\(233\) | 1.30644e7i | 1.03282i | 0.856343 | + | 0.516408i | \(0.172731\pi\) | ||||
−0.856343 | + | 0.516408i | \(0.827269\pi\) | |||||||
\(234\) | 461815.i | 0.0360430i | ||||||||
\(235\) | 9.61271e6i | 0.740700i | ||||||||
\(236\) | 668305. | 0.0508439 | ||||||||
\(237\) | − | 1.08758e7i | − | 0.816986i | ||||||
\(238\) | 1.58623e7 | 1.17662 | ||||||||
\(239\) | 1.34499e7 | 0.985199 | 0.492600 | − | 0.870256i | \(-0.336047\pi\) | ||||
0.492600 | + | 0.870256i | \(0.336047\pi\) | |||||||
\(240\) | −3.55154e6 | −0.256911 | ||||||||
\(241\) | − | 1.99696e7i | − | 1.42665i | −0.700832 | − | 0.713326i | \(-0.747188\pi\) | ||
0.700832 | − | 0.713326i | \(-0.252812\pi\) | |||||||
\(242\) | − | 1.89545e7i | − | 1.33741i | ||||||
\(243\) | 1.42961e7i | 0.996319i | ||||||||
\(244\) | 155372.i | 0.0106956i | ||||||||
\(245\) | 6.03882e6i | 0.410633i | ||||||||
\(246\) | 1.75501e7 | 1.17890 | ||||||||
\(247\) | 1.38265e6i | 0.0917532i | ||||||||
\(248\) | 6.05794e6i | 0.397164i | ||||||||
\(249\) | − | 1.28892e6i | − | 0.0834889i | ||||||
\(250\) | −1.15563e7 | −0.739605 | ||||||||
\(251\) | −3.10748e6 | −0.196511 | −0.0982554 | − | 0.995161i | \(-0.531326\pi\) | ||||
−0.0982554 | + | 0.995161i | \(0.531326\pi\) | |||||||
\(252\) | − | 1.19021e6i | − | 0.0743743i | ||||||
\(253\) | −2.27472e6 | −0.140464 | ||||||||
\(254\) | 1.59443e7i | 0.972982i | ||||||||
\(255\) | 3.10477e6 | 0.187244 | ||||||||
\(256\) | 4.21496e6 | 0.251231 | ||||||||
\(257\) | − | 795874.i | − | 0.0468862i | −0.999725 | − | 0.0234431i | \(-0.992537\pi\) | ||
0.999725 | − | 0.0234431i | \(-0.00746285\pi\) | |||||||
\(258\) | −8.48978e6 | − | 7.19335e6i | −0.494353 | − | 0.418863i | ||||
\(259\) | −4.18055e7 | −2.40621 | ||||||||
\(260\) | − | 32086.0i | − | 0.00182556i | ||||||
\(261\) | 1.08859e7i | 0.612268i | ||||||||
\(262\) | −2.11577e7 | −1.17643 | ||||||||
\(263\) | 2.05517e7i | 1.12974i | 0.825179 | + | 0.564871i | \(0.191074\pi\) | ||||
−0.825179 | + | 0.564871i | \(0.808926\pi\) | |||||||
\(264\) | 1.64995e7 | 0.896726 | ||||||||
\(265\) | 5.98346e6i | 0.321525i | ||||||||
\(266\) | − | 4.58210e7i | − | 2.43455i | ||||||
\(267\) | 284071. | 0.0149243 | ||||||||
\(268\) | −1.56443e6 | −0.0812740 | ||||||||
\(269\) | −5.28734e6 | −0.271632 | −0.135816 | − | 0.990734i | \(-0.543366\pi\) | ||||
−0.135816 | + | 0.990734i | \(0.543366\pi\) | |||||||
\(270\) | − | 7.88382e6i | − | 0.400540i | ||||||
\(271\) | −5.39678e6 | −0.271161 | −0.135580 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(272\) | −1.70191e7 | −0.845729 | ||||||||
\(273\) | 1.02915e6 | 0.0505816 | ||||||||
\(274\) | −1.04787e7 | −0.509395 | ||||||||
\(275\) | 2.68149e7 | 1.28937 | ||||||||
\(276\) | 102526.i | 0.00487648i | ||||||||
\(277\) | − | 7.82259e6i | − | 0.368054i | −0.982921 | − | 0.184027i | \(-0.941087\pi\) | ||
0.982921 | − | 0.184027i | \(-0.0589134\pi\) | |||||||
\(278\) | 9.66328e6i | 0.449770i | ||||||||
\(279\) | −5.54362e6 | −0.255259 | ||||||||
\(280\) | − | 1.15463e7i | − | 0.525981i | ||||||
\(281\) | −5.00396e6 | −0.225525 | −0.112763 | − | 0.993622i | \(-0.535970\pi\) | ||||
−0.112763 | + | 0.993622i | \(0.535970\pi\) | |||||||
\(282\) | −2.80805e7 | −1.25215 | ||||||||
\(283\) | −3.71907e7 | −1.64088 | −0.820438 | − | 0.571736i | \(-0.806270\pi\) | ||||
−0.820438 | + | 0.571736i | \(0.806270\pi\) | |||||||
\(284\) | 2.27017e6i | 0.0991069i | ||||||||
\(285\) | − | 8.96865e6i | − | 0.387429i | ||||||
\(286\) | 2.07955e6i | 0.0888936i | ||||||||
\(287\) | 6.19028e7i | 2.61857i | ||||||||
\(288\) | 2.46249e6i | 0.103086i | ||||||||
\(289\) | −9.25937e6 | −0.383608 | ||||||||
\(290\) | − | 9.72538e6i | − | 0.398761i | ||||||
\(291\) | − | 1.84956e7i | − | 0.750566i | ||||||
\(292\) | 1.78297e6i | 0.0716134i | ||||||||
\(293\) | 2.43355e7 | 0.967468 | 0.483734 | − | 0.875215i | \(-0.339280\pi\) | ||||
0.483734 | + | 0.875215i | \(0.339280\pi\) | |||||||
\(294\) | −1.76405e7 | −0.694175 | ||||||||
\(295\) | 5.93285e6i | 0.231098i | ||||||||
\(296\) | 4.13431e7 | 1.59415 | ||||||||
\(297\) | 3.97369e7i | 1.51679i | ||||||||
\(298\) | 5.01446e7 | 1.89485 | ||||||||
\(299\) | 140316. | 0.00524920 | ||||||||
\(300\) | − | 1.20860e6i | − | 0.0447628i | ||||||
\(301\) | 2.53724e7 | − | 2.99451e7i | 0.930382 | − | 1.09806i | ||||
\(302\) | −1.72504e7 | −0.626295 | ||||||||
\(303\) | − | 1.74081e7i | − | 0.625781i | ||||||
\(304\) | 4.91627e7i | 1.74991i | ||||||||
\(305\) | −1.37931e6 | −0.0486140 | ||||||||
\(306\) | − | 1.43550e7i | − | 0.501003i | ||||||
\(307\) | −5.56753e7 | −1.92419 | −0.962094 | − | 0.272718i | \(-0.912077\pi\) | ||||
−0.962094 | + | 0.272718i | \(0.912077\pi\) | |||||||
\(308\) | − | 5.35951e6i | − | 0.183431i | ||||||
\(309\) | 1.83249e7i | 0.621105i | ||||||||
\(310\) | 4.95264e6 | 0.166246 | ||||||||
\(311\) | 2.20696e7 | 0.733692 | 0.366846 | − | 0.930282i | \(-0.380438\pi\) | ||||
0.366846 | + | 0.930282i | \(0.380438\pi\) | |||||||
\(312\) | −1.01777e6 | −0.0335109 | ||||||||
\(313\) | 2.38515e7i | 0.777826i | 0.921275 | + | 0.388913i | \(0.127149\pi\) | ||||
−0.921275 | + | 0.388913i | \(0.872851\pi\) | |||||||
\(314\) | −9.80348e6 | −0.316659 | ||||||||
\(315\) | 1.05661e7 | 0.338050 | ||||||||
\(316\) | 3.49368e6 | 0.110719 | ||||||||
\(317\) | 4.51895e7 | 1.41860 | 0.709300 | − | 0.704906i | \(-0.249011\pi\) | ||||
0.709300 | + | 0.704906i | \(0.249011\pi\) | |||||||
\(318\) | −1.74788e7 | −0.543538 | ||||||||
\(319\) | 4.90190e7i | 1.51005i | ||||||||
\(320\) | 1.13293e7i | 0.345743i | ||||||||
\(321\) | 1.32417e7i | 0.400341i | ||||||||
\(322\) | −4.65006e6 | −0.139281 | ||||||||
\(323\) | − | 4.29782e7i | − | 1.27538i | ||||||
\(324\) | 33371.2 | 0.000981152 | ||||||||
\(325\) | −1.65407e6 | −0.0481842 | ||||||||
\(326\) | 2.38082e7 | 0.687186 | ||||||||
\(327\) | − | 301515.i | − | 0.00862315i | ||||||
\(328\) | − | 6.12182e7i | − | 1.73484i | ||||||
\(329\) | − | 9.90453e7i | − | 2.78129i | ||||||
\(330\) | − | 1.34891e7i | − | 0.375355i | ||||||
\(331\) | − | 4.81328e7i | − | 1.32726i | −0.748059 | − | 0.663632i | \(-0.769014\pi\) | ||
0.748059 | − | 0.663632i | \(-0.230986\pi\) | |||||||
\(332\) | 414047. | 0.0113145 | ||||||||
\(333\) | 3.78331e7i | 1.02456i | ||||||||
\(334\) | 1.60232e7i | 0.430040i | ||||||||
\(335\) | − | 1.38881e7i | − | 0.369411i | ||||||
\(336\) | 3.65935e7 | 0.964688 | ||||||||
\(337\) | 7.06937e7 | 1.84710 | 0.923551 | − | 0.383476i | \(-0.125273\pi\) | ||||
0.923551 | + | 0.383476i | \(0.125273\pi\) | |||||||
\(338\) | 4.00814e7i | 1.03799i | ||||||||
\(339\) | −7.68550e6 | −0.197275 | ||||||||
\(340\) | 997360.i | 0.0253755i | ||||||||
\(341\) | −2.49629e7 | −0.629551 | ||||||||
\(342\) | −4.14670e7 | −1.03663 | ||||||||
\(343\) | − | 4.14384e6i | − | 0.102688i | ||||||
\(344\) | −2.50917e7 | + | 2.96139e7i | −0.616390 | + | 0.727479i | ||||
\(345\) | −910168. | −0.0221648 | ||||||||
\(346\) | − | 4.11390e7i | − | 0.993175i | ||||||
\(347\) | − | 3.36102e7i | − | 0.804420i | −0.915547 | − | 0.402210i | \(-0.868242\pi\) | ||
0.915547 | − | 0.402210i | \(-0.131758\pi\) | |||||||
\(348\) | 2.20937e6 | 0.0524242 | ||||||||
\(349\) | − | 3.01730e7i | − | 0.709811i | −0.934902 | − | 0.354905i | \(-0.884513\pi\) | ||
0.934902 | − | 0.354905i | \(-0.115487\pi\) | |||||||
\(350\) | 5.48159e7 | 1.27851 | ||||||||
\(351\) | − | 2.45117e6i | − | 0.0566828i | ||||||
\(352\) | 1.10886e7i | 0.254242i | ||||||||
\(353\) | −1.35366e6 | −0.0307740 | −0.0153870 | − | 0.999882i | \(-0.504898\pi\) | ||||
−0.0153870 | + | 0.999882i | \(0.504898\pi\) | |||||||
\(354\) | −1.73309e7 | −0.390672 | ||||||||
\(355\) | −2.01534e7 | −0.450466 | ||||||||
\(356\) | 91253.6i | 0.00202255i | ||||||||
\(357\) | −3.19902e7 | −0.703093 | ||||||||
\(358\) | 5.37647e7 | 1.17179 | ||||||||
\(359\) | 4.50676e7 | 0.974050 | 0.487025 | − | 0.873388i | \(-0.338082\pi\) | ||||
0.487025 | + | 0.873388i | \(0.338082\pi\) | |||||||
\(360\) | −1.04492e7 | −0.223962 | ||||||||
\(361\) | −7.71042e7 | −1.63891 | ||||||||
\(362\) | 6.72981e6i | 0.141865i | ||||||||
\(363\) | 3.82263e7i | 0.799177i | ||||||||
\(364\) | 330601.i | 0.00685488i | ||||||||
\(365\) | −1.58282e7 | −0.325501 | ||||||||
\(366\) | − | 4.02921e6i | − | 0.0821820i | ||||||
\(367\) | −3.86047e7 | −0.780983 | −0.390492 | − | 0.920606i | \(-0.627695\pi\) | ||||
−0.390492 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(368\) | 4.98920e6 | 0.100112 | ||||||||
\(369\) | 5.60208e7 | 1.11499 | ||||||||
\(370\) | − | 3.37999e7i | − | 0.667283i | ||||||
\(371\) | − | 6.16511e7i | − | 1.20731i | ||||||
\(372\) | 1.12512e6i | 0.0218560i | ||||||||
\(373\) | 5.22223e7i | 1.00631i | 0.864198 | + | 0.503153i | \(0.167827\pi\) | ||||
−0.864198 | + | 0.503153i | \(0.832173\pi\) | |||||||
\(374\) | − | 6.46406e7i | − | 1.23564i | ||||||
\(375\) | 2.33062e7 | 0.441954 | ||||||||
\(376\) | 9.79498e7i | 1.84264i | ||||||||
\(377\) | − | 3.02373e6i | − | 0.0564311i | ||||||
\(378\) | 8.12316e7i | 1.50401i | ||||||||
\(379\) | −4.96049e7 | −0.911186 | −0.455593 | − | 0.890188i | \(-0.650573\pi\) | ||||
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(380\) | 2.88105e6 | 0.0525049 | ||||||||
\(381\) | − | 3.21556e7i | − | 0.581410i | ||||||
\(382\) | −1.18593e7 | −0.212750 | ||||||||
\(383\) | − | 7.72156e6i | − | 0.137439i | −0.997636 | − | 0.0687193i | \(-0.978109\pi\) | ||
0.997636 | − | 0.0687193i | \(-0.0218913\pi\) | |||||||
\(384\) | −3.90217e7 | −0.689149 | ||||||||
\(385\) | 4.75788e7 | 0.833741 | ||||||||
\(386\) | − | 3.81134e6i | − | 0.0662699i | ||||||
\(387\) | −2.70997e7 | − | 2.29615e7i | −0.467554 | − | 0.396156i | ||||
\(388\) | 5.94143e6 | 0.101717 | ||||||||
\(389\) | − | 7.60790e7i | − | 1.29246i | −0.763144 | − | 0.646228i | \(-0.776345\pi\) | ||
0.763144 | − | 0.646228i | \(-0.223655\pi\) | |||||||
\(390\) | 832075.i | 0.0140271i | ||||||||
\(391\) | −4.36157e6 | −0.0729647 | ||||||||
\(392\) | 6.15333e7i | 1.02153i | ||||||||
\(393\) | 4.26698e7 | 0.702979 | ||||||||
\(394\) | 5.19945e7i | 0.850098i | ||||||||
\(395\) | 3.10150e7i | 0.503246i | ||||||||
\(396\) | −4.85024e6 | −0.0781049 | ||||||||
\(397\) | 1.53245e7 | 0.244914 | 0.122457 | − | 0.992474i | \(-0.460923\pi\) | ||||
0.122457 | + | 0.992474i | \(0.460923\pi\) | |||||||
\(398\) | −7.72708e7 | −1.22565 | ||||||||
\(399\) | 9.24092e7i | 1.45478i | ||||||||
\(400\) | −5.88137e7 | −0.918964 | ||||||||
\(401\) | 2.42146e7 | 0.375530 | 0.187765 | − | 0.982214i | \(-0.439876\pi\) | ||||
0.187765 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(402\) | 4.05698e7 | 0.624489 | ||||||||
\(403\) | 1.53983e6 | 0.0235265 | ||||||||
\(404\) | 5.59208e6 | 0.0848066 | ||||||||
\(405\) | 296251.i | 0.00445959i | ||||||||
\(406\) | 1.00206e8i | 1.49733i | ||||||||
\(407\) | 1.70362e8i | 2.52691i | ||||||||
\(408\) | 3.16364e7 | 0.465807 | ||||||||
\(409\) | − | 9.87818e7i | − | 1.44380i | −0.691997 | − | 0.721900i | \(-0.743269\pi\) | ||
0.691997 | − | 0.721900i | \(-0.256731\pi\) | |||||||
\(410\) | −5.00486e7 | −0.726174 | ||||||||
\(411\) | 2.11328e7 | 0.304391 | ||||||||
\(412\) | −5.88659e6 | −0.0841729 | ||||||||
\(413\) | − | 6.11296e7i | − | 0.867763i | ||||||
\(414\) | 4.20821e6i | 0.0593057i | ||||||||
\(415\) | 3.67569e6i | 0.0514273i | ||||||||
\(416\) | − | 683997.i | − | 0.00950111i | ||||||
\(417\) | − | 1.94884e7i | − | 0.268762i | ||||||
\(418\) | −1.86725e8 | −2.55667 | ||||||||
\(419\) | − | 8.18950e7i | − | 1.11331i | −0.830745 | − | 0.556654i | \(-0.812085\pi\) | ||
0.830745 | − | 0.556654i | \(-0.187915\pi\) | |||||||
\(420\) | − | 2.14446e6i | − | 0.0289448i | ||||||
\(421\) | 3.91015e7i | 0.524019i | 0.965065 | + | 0.262010i | \(0.0843852\pi\) | ||||
−0.965065 | + | 0.262010i | \(0.915615\pi\) | |||||||
\(422\) | 1.13826e8 | 1.51462 | ||||||||
\(423\) | −8.96339e7 | −1.18427 | ||||||||
\(424\) | 6.09692e7i | 0.799858i | ||||||||
\(425\) | 5.14152e7 | 0.669768 | ||||||||
\(426\) | − | 5.88716e7i | − | 0.761513i | ||||||
\(427\) | 1.42118e7 | 0.182543 | ||||||||
\(428\) | −4.25371e6 | −0.0542546 | ||||||||
\(429\) | − | 4.19392e6i | − | 0.0531187i | ||||||
\(430\) | 2.42107e7 | + | 2.05136e7i | 0.304511 | + | 0.258010i | ||||
\(431\) | 1.04216e8 | 1.30167 | 0.650836 | − | 0.759218i | \(-0.274418\pi\) | ||||
0.650836 | + | 0.759218i | \(0.274418\pi\) | |||||||
\(432\) | − | 8.71559e7i | − | 1.08105i | ||||||
\(433\) | − | 1.75892e7i | − | 0.216662i | −0.994115 | − | 0.108331i | \(-0.965449\pi\) | ||
0.994115 | − | 0.108331i | \(-0.0345507\pi\) | |||||||
\(434\) | −5.10299e7 | −0.624246 | ||||||||
\(435\) | 1.96136e7i | 0.238281i | ||||||||
\(436\) | 96857.3 | 0.00116862 | ||||||||
\(437\) | 1.25992e7i | 0.150972i | ||||||||
\(438\) | − | 4.62370e7i | − | 0.550260i | ||||||
\(439\) | −4.59377e6 | −0.0542970 | −0.0271485 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271485 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(440\) | −4.70526e7 | −0.552364 | ||||||||
\(441\) | −5.63091e7 | −0.656543 | ||||||||
\(442\) | 3.98734e6i | 0.0461761i | ||||||||
\(443\) | −5.13129e7 | −0.590221 | −0.295111 | − | 0.955463i | \(-0.595357\pi\) | ||||
−0.295111 | + | 0.955463i | \(0.595357\pi\) | |||||||
\(444\) | 7.67853e6 | 0.0877261 | ||||||||
\(445\) | −810100. | −0.00919302 | ||||||||
\(446\) | −8.79346e7 | −0.991187 | ||||||||
\(447\) | −1.01129e8 | −1.13228 | ||||||||
\(448\) | − | 1.16733e8i | − | 1.29825i | ||||||
\(449\) | 1.08274e8i | 1.19615i | 0.801440 | + | 0.598076i | \(0.204068\pi\) | ||||
−0.801440 | + | 0.598076i | \(0.795932\pi\) | |||||||
\(450\) | − | 4.96073e7i | − | 0.544387i | ||||||
\(451\) | 2.52261e8 | 2.74992 | ||||||||
\(452\) | − | 2.46885e6i | − | 0.0267350i | ||||||
\(453\) | 3.47897e7 | 0.374245 | ||||||||
\(454\) | 1.02157e8 | 1.09170 | ||||||||
\(455\) | −2.93489e6 | −0.0311572 | ||||||||
\(456\) | − | 9.13872e7i | − | 0.963808i | ||||||
\(457\) | 7.81647e7i | 0.818958i | 0.912319 | + | 0.409479i | \(0.134290\pi\) | ||||
−0.912319 | + | 0.409479i | \(0.865710\pi\) | |||||||
\(458\) | − | 1.22916e8i | − | 1.27942i | ||||||
\(459\) | 7.61920e7i | 0.787900i | ||||||||
\(460\) | − | 292378.i | − | 0.00300380i | ||||||
\(461\) | 1.36693e8 | 1.39522 | 0.697609 | − | 0.716479i | \(-0.254247\pi\) | ||||
0.697609 | + | 0.716479i | \(0.254247\pi\) | |||||||
\(462\) | 1.38986e8i | 1.40944i | ||||||||
\(463\) | − | 1.22553e8i | − | 1.23476i | −0.786667 | − | 0.617378i | \(-0.788195\pi\) | ||
0.786667 | − | 0.617378i | \(-0.211805\pi\) | |||||||
\(464\) | − | 1.07514e8i | − | 1.07625i | ||||||
\(465\) | −9.98822e6 | −0.0993411 | ||||||||
\(466\) | 1.08833e8 | 1.07548 | ||||||||
\(467\) | 6.94572e6i | 0.0681972i | 0.999418 | + | 0.0340986i | \(0.0108560\pi\) | ||||
−0.999418 | + | 0.0340986i | \(0.989144\pi\) | |||||||
\(468\) | 299187. | 0.00291880 | ||||||||
\(469\) | 1.43098e8i | 1.38712i | ||||||||
\(470\) | 8.00785e7 | 0.771298 | ||||||||
\(471\) | 1.97711e7 | 0.189221 | ||||||||
\(472\) | 6.04535e7i | 0.574904i | ||||||||
\(473\) | −1.22030e8 | − | 1.03395e8i | −1.15314 | − | 0.977050i | ||||
\(474\) | −9.06003e7 | −0.850736 | ||||||||
\(475\) | − | 1.48522e8i | − | 1.38583i | ||||||
\(476\) | − | 1.02764e7i | − | 0.0952839i | ||||||
\(477\) | −5.57929e7 | −0.514072 | ||||||||
\(478\) | − | 1.12044e8i | − | 1.02590i | ||||||
\(479\) | 5.80479e6 | 0.0528178 | 0.0264089 | − | 0.999651i | \(-0.491593\pi\) | ||||
0.0264089 | + | 0.999651i | \(0.491593\pi\) | |||||||
\(480\) | 4.43680e6i | 0.0401186i | ||||||||
\(481\) | − | 1.05088e7i | − | 0.0944313i | ||||||
\(482\) | −1.66356e8 | −1.48559 | ||||||||
\(483\) | 9.37799e6 | 0.0832278 | ||||||||
\(484\) | −1.22796e7 | −0.108305 | ||||||||
\(485\) | 5.27447e7i | 0.462332i | ||||||||
\(486\) | 1.19093e8 | 1.03748 | ||||||||
\(487\) | 2.69087e7 | 0.232973 | 0.116487 | − | 0.993192i | \(-0.462837\pi\) | ||||
0.116487 | + | 0.993192i | \(0.462837\pi\) | |||||||
\(488\) | −1.40546e7 | −0.120937 | ||||||||
\(489\) | −4.80152e7 | −0.410631 | ||||||||
\(490\) | 5.03063e7 | 0.427596 | ||||||||
\(491\) | − | 2.15902e7i | − | 0.182395i | −0.995833 | − | 0.0911974i | \(-0.970931\pi\) | ||
0.995833 | − | 0.0911974i | \(-0.0290694\pi\) | |||||||
\(492\) | − | 1.13699e7i | − | 0.0954684i | ||||||
\(493\) | 9.39895e7i | 0.784402i | ||||||||
\(494\) | 1.15181e7 | 0.0955435 | ||||||||
\(495\) | − | 4.30578e7i | − | 0.355007i | ||||||
\(496\) | 5.47516e7 | 0.448696 | ||||||||
\(497\) | 2.07652e8 | 1.69148 | ||||||||
\(498\) | −1.07373e7 | −0.0869379 | ||||||||
\(499\) | 1.53896e8i | 1.23859i | 0.785160 | + | 0.619293i | \(0.212581\pi\) | ||||
−0.785160 | + | 0.619293i | \(0.787419\pi\) | |||||||
\(500\) | 7.48676e6i | 0.0598941i | ||||||||
\(501\) | − | 3.23147e7i | − | 0.256972i | ||||||
\(502\) | 2.58868e7i | 0.204629i | ||||||||
\(503\) | − | 2.00534e8i | − | 1.57574i | −0.615842 | − | 0.787870i | \(-0.711184\pi\) | ||
0.615842 | − | 0.787870i | \(-0.288816\pi\) | |||||||
\(504\) | 1.07664e8 | 0.840968 | ||||||||
\(505\) | 4.96435e7i | 0.385468i | ||||||||
\(506\) | 1.89495e7i | 0.146267i | ||||||||
\(507\) | − | 8.08339e7i | − | 0.620254i | ||||||
\(508\) | 1.03295e7 | 0.0787933 | ||||||||
\(509\) | −1.49488e8 | −1.13359 | −0.566793 | − | 0.823860i | \(-0.691816\pi\) | ||||
−0.566793 | + | 0.823860i | \(0.691816\pi\) | |||||||
\(510\) | − | 2.58642e7i | − | 0.194979i | ||||||
\(511\) | 1.63087e8 | 1.22224 | ||||||||
\(512\) | 1.13538e8i | 0.845921i | ||||||||
\(513\) | 2.20094e8 | 1.63025 | ||||||||
\(514\) | −6.63001e6 | −0.0488230 | ||||||||
\(515\) | − | 5.22579e7i | − | 0.382587i | ||||||
\(516\) | −4.66021e6 | + | 5.50010e6i | −0.0339200 | + | 0.0400333i | ||||
\(517\) | −4.03620e8 | −2.92080 | ||||||||
\(518\) | 3.48260e8i | 2.50561i | ||||||||
\(519\) | 8.29670e7i | 0.593476i | ||||||||
\(520\) | 2.90243e6 | 0.0206420 | ||||||||
\(521\) | 9.54093e7i | 0.674649i | 0.941388 | + | 0.337324i | \(0.109522\pi\) | ||||
−0.941388 | + | 0.337324i | \(0.890478\pi\) | |||||||
\(522\) | 9.06846e7 | 0.637561 | ||||||||
\(523\) | 2.34864e8i | 1.64176i | 0.571097 | + | 0.820882i | \(0.306518\pi\) | ||||
−0.571097 | + | 0.820882i | \(0.693482\pi\) | |||||||
\(524\) | 1.37070e7i | 0.0952686i | ||||||||
\(525\) | −1.10550e8 | −0.763976 | ||||||||
\(526\) | 1.71205e8 | 1.17641 | ||||||||
\(527\) | −4.78640e7 | −0.327022 | ||||||||
\(528\) | − | 1.49123e8i | − | 1.01308i | ||||||
\(529\) | −1.46757e8 | −0.991363 | ||||||||
\(530\) | 4.98451e7 | 0.334807 | ||||||||
\(531\) | −5.53210e7 | −0.369493 | ||||||||
\(532\) | −2.96851e7 | −0.197153 | ||||||||
\(533\) | −1.55607e7 | −0.102765 | ||||||||
\(534\) | − | 2.36645e6i | − | 0.0155408i | ||||||
\(535\) | − | 3.77621e7i | − | 0.246601i | ||||||
\(536\) | − | 1.41515e8i | − | 0.918984i | ||||||
\(537\) | −1.08430e8 | −0.700205 | ||||||||
\(538\) | 4.40461e7i | 0.282853i | ||||||||
\(539\) | −2.53559e8 | −1.61925 | ||||||||
\(540\) | −5.10753e6 | −0.0324362 | ||||||||
\(541\) | −1.30081e8 | −0.821529 | −0.410764 | − | 0.911742i | \(-0.634738\pi\) | ||||
−0.410764 | + | 0.911742i | \(0.634738\pi\) | |||||||
\(542\) | 4.49577e7i | 0.282362i | ||||||||
\(543\) | − | 1.35723e7i | − | 0.0847723i | ||||||
\(544\) | 2.12614e7i | 0.132067i | ||||||||
\(545\) | 859846.i | 0.00531167i | ||||||||
\(546\) | − | 8.57335e6i | − | 0.0526711i | ||||||
\(547\) | −3.76027e7 | −0.229751 | −0.114875 | − | 0.993380i | \(-0.536647\pi\) | ||||
−0.114875 | + | 0.993380i | \(0.536647\pi\) | |||||||
\(548\) | 6.78860e6i | 0.0412514i | ||||||||
\(549\) | − | 1.28614e7i | − | 0.0777268i | ||||||
\(550\) | − | 2.23381e8i | − | 1.34263i | ||||||
\(551\) | 2.71505e8 | 1.62302 | ||||||||
\(552\) | −9.27427e6 | −0.0551395 | ||||||||
\(553\) | − | 3.19565e8i | − | 1.88966i | ||||||
\(554\) | −6.51660e7 | −0.383258 | ||||||||
\(555\) | 6.81657e7i | 0.398738i | ||||||||
\(556\) | 6.26035e6 | 0.0364229 | ||||||||
\(557\) | −1.07813e8 | −0.623884 | −0.311942 | − | 0.950101i | \(-0.600979\pi\) | ||||
−0.311942 | + | 0.950101i | \(0.600979\pi\) | |||||||
\(558\) | 4.61810e7i | 0.265804i | ||||||||
\(559\) | 7.52738e6 | + | 6.37791e6i | 0.0430932 | + | 0.0365126i | ||||
\(560\) | −1.04356e8 | −0.594226 | ||||||||
\(561\) | 1.30364e8i | 0.738359i | ||||||||
\(562\) | 4.16854e7i | 0.234842i | ||||||||
\(563\) | −1.93573e8 | −1.08472 | −0.542362 | − | 0.840145i | \(-0.682470\pi\) | ||||
−0.542362 | + | 0.840145i | \(0.682470\pi\) | |||||||
\(564\) | 1.81919e7i | 0.101401i | ||||||||
\(565\) | 2.19171e7 | 0.121517 | ||||||||
\(566\) | 3.09817e8i | 1.70866i | ||||||||
\(567\) | − | 3.05244e6i | − | 0.0167455i | ||||||
\(568\) | −2.05355e8 | −1.12063 | ||||||||
\(569\) | 1.27767e8 | 0.693556 | 0.346778 | − | 0.937947i | \(-0.387276\pi\) | ||||
0.346778 | + | 0.937947i | \(0.387276\pi\) | |||||||
\(570\) | −7.47132e7 | −0.403434 | ||||||||
\(571\) | − | 1.71269e8i | − | 0.919965i | −0.887928 | − | 0.459982i | \(-0.847856\pi\) | ||
0.887928 | − | 0.459982i | \(-0.152144\pi\) | |||||||
\(572\) | 1.34723e6 | 0.00719871 | ||||||||
\(573\) | 2.39172e7 | 0.127130 | ||||||||
\(574\) | 5.15680e8 | 2.72675 | ||||||||
\(575\) | −1.50725e7 | −0.0792831 | ||||||||
\(576\) | −1.05640e8 | −0.552794 | ||||||||
\(577\) | − | 5.40566e7i | − | 0.281398i | −0.990052 | − | 0.140699i | \(-0.955065\pi\) | ||
0.990052 | − | 0.140699i | \(-0.0449350\pi\) | |||||||
\(578\) | 7.71350e7i | 0.399455i | ||||||||
\(579\) | 7.68651e6i | 0.0395998i | ||||||||
\(580\) | −6.30059e6 | −0.0322921 | ||||||||
\(581\) | − | 3.78727e7i | − | 0.193107i | ||||||
\(582\) | −1.54077e8 | −0.781571 | ||||||||
\(583\) | −2.51235e8 | −1.26787 | ||||||||
\(584\) | −1.61283e8 | −0.809750 | ||||||||
\(585\) | 2.65601e6i | 0.0132667i | ||||||||
\(586\) | − | 2.02726e8i | − | 1.00743i | ||||||
\(587\) | 1.30895e8i | 0.647155i | 0.946202 | + | 0.323578i | \(0.104886\pi\) | ||||
−0.946202 | + | 0.323578i | \(0.895114\pi\) | |||||||
\(588\) | 1.14284e7i | 0.0562151i | ||||||||
\(589\) | 1.38264e8i | 0.676646i | ||||||||
\(590\) | 4.94235e7 | 0.240645 | ||||||||
\(591\) | − | 1.04860e8i | − | 0.507980i | ||||||
\(592\) | − | 3.73659e8i | − | 1.80098i | ||||||
\(593\) | 2.81686e8i | 1.35083i | 0.737437 | + | 0.675416i | \(0.236036\pi\) | ||||
−0.737437 | + | 0.675416i | \(0.763964\pi\) | |||||||
\(594\) | 3.31028e8 | 1.57945 | ||||||||
\(595\) | 9.12281e7 | 0.433090 | ||||||||
\(596\) | − | 3.24861e7i | − | 0.153447i | ||||||
\(597\) | 1.55836e8 | 0.732392 | ||||||||
\(598\) | − | 1.16890e6i | − | 0.00546604i | ||||||
\(599\) | 1.77903e8 | 0.827758 | 0.413879 | − | 0.910332i | \(-0.364174\pi\) | ||||
0.413879 | + | 0.910332i | \(0.364174\pi\) | |||||||
\(600\) | 1.09327e8 | 0.506144 | ||||||||
\(601\) | 1.04686e8i | 0.482240i | 0.970495 | + | 0.241120i | \(0.0775147\pi\) | ||||
−0.970495 | + | 0.241120i | \(0.922485\pi\) | |||||||
\(602\) | −2.49457e8 | − | 2.11364e8i | −1.14342 | − | 0.968816i | ||||
\(603\) | 1.29500e8 | 0.590635 | ||||||||
\(604\) | 1.11757e7i | 0.0507181i | ||||||||
\(605\) | − | 1.09012e8i | − | 0.492275i | ||||||
\(606\) | −1.45018e8 | −0.651632 | ||||||||
\(607\) | 3.06425e8i | 1.37012i | 0.728488 | + | 0.685058i | \(0.240223\pi\) | ||||
−0.728488 | + | 0.685058i | \(0.759777\pi\) | |||||||
\(608\) | 6.14171e7 | 0.273262 | ||||||||
\(609\) | − | 2.02091e8i | − | 0.894734i | ||||||
\(610\) | 1.14903e7i | 0.0506223i | ||||||||
\(611\) | 2.48973e7 | 0.109151 | ||||||||
\(612\) | −9.29991e6 | −0.0405718 | ||||||||
\(613\) | −2.57269e7 | −0.111688 | −0.0558440 | − | 0.998440i | \(-0.517785\pi\) | ||||
−0.0558440 | + | 0.998440i | \(0.517785\pi\) | |||||||
\(614\) | 4.63802e8i | 2.00368i | ||||||||
\(615\) | 1.00935e8 | 0.433928 | ||||||||
\(616\) | 4.84810e8 | 2.07410 | ||||||||
\(617\) | −1.22820e8 | −0.522894 | −0.261447 | − | 0.965218i | \(-0.584200\pi\) | ||||
−0.261447 | + | 0.965218i | \(0.584200\pi\) | |||||||
\(618\) | 1.52655e8 | 0.646763 | ||||||||
\(619\) | −7.80094e7 | −0.328908 | −0.164454 | − | 0.986385i | \(-0.552586\pi\) | ||||
−0.164454 | + | 0.986385i | \(0.552586\pi\) | |||||||
\(620\) | − | 3.20857e6i | − | 0.0134628i | ||||||
\(621\) | − | 2.23358e7i | − | 0.0932668i | ||||||
\(622\) | − | 1.83851e8i | − | 0.764001i | ||||||
\(623\) | 8.34693e6 | 0.0345193 | ||||||||
\(624\) | 9.19861e6i | 0.0378589i | ||||||||
\(625\) | 1.41811e8 | 0.580858 | ||||||||
\(626\) | 1.98694e8 | 0.809958 | ||||||||
\(627\) | 3.76578e8 | 1.52775 | ||||||||
\(628\) | 6.35118e6i | 0.0256434i | ||||||||
\(629\) | 3.26654e8i | 1.31261i | ||||||||
\(630\) | − | 8.80203e7i | − | 0.352015i | ||||||
\(631\) | − | 2.93500e8i | − | 1.16821i | −0.811678 | − | 0.584105i | \(-0.801446\pi\) | ||
0.811678 | − | 0.584105i | \(-0.198554\pi\) | |||||||
\(632\) | 3.16031e8i | 1.25192i | ||||||||
\(633\) | −2.29558e8 | −0.905069 | ||||||||
\(634\) | − | 3.76451e8i | − | 1.47720i | ||||||
\(635\) | 9.16998e7i | 0.358136i | ||||||||
\(636\) | 1.13236e7i | 0.0440163i | ||||||||
\(637\) | 1.56408e7 | 0.0605118 | ||||||||
\(638\) | 4.08351e8 | 1.57243 | ||||||||
\(639\) | − | 1.87920e8i | − | 0.720231i | ||||||
\(640\) | 1.11280e8 | 0.424501 | ||||||||
\(641\) | − | 6.47635e7i | − | 0.245899i | −0.992413 | − | 0.122949i | \(-0.960765\pi\) | ||
0.992413 | − | 0.122949i | \(-0.0392353\pi\) | |||||||
\(642\) | 1.10310e8 | 0.416879 | ||||||||
\(643\) | 1.49102e8 | 0.560855 | 0.280427 | − | 0.959875i | \(-0.409524\pi\) | ||||
0.280427 | + | 0.959875i | \(0.409524\pi\) | |||||||
\(644\) | 3.01254e6i | 0.0112791i | ||||||||
\(645\) | −4.88269e7 | − | 4.13708e7i | −0.181962 | − | 0.154175i | ||||
\(646\) | −3.58029e8 | −1.32807 | ||||||||
\(647\) | − | 9.73636e7i | − | 0.359488i | −0.983713 | − | 0.179744i | \(-0.942473\pi\) | ||
0.983713 | − | 0.179744i | \(-0.0575269\pi\) | |||||||
\(648\) | 3.01868e6i | 0.0110941i | ||||||||
\(649\) | −2.49110e8 | −0.911290 | ||||||||
\(650\) | 1.37792e7i | 0.0501747i | ||||||||
\(651\) | 1.02914e8 | 0.373021 | ||||||||
\(652\) | − | 1.54242e7i | − | 0.0556492i | ||||||
\(653\) | − | 2.89942e8i | − | 1.04129i | −0.853773 | − | 0.520645i | \(-0.825692\pi\) | ||
0.853773 | − | 0.520645i | \(-0.174308\pi\) | |||||||
\(654\) | −2.51177e6 | −0.00897938 | ||||||||
\(655\) | −1.21684e8 | −0.433020 | ||||||||
\(656\) | −5.53289e8 | −1.95993 | ||||||||
\(657\) | − | 1.47590e8i | − | 0.520430i | ||||||
\(658\) | −8.25095e8 | −2.89619 | ||||||||
\(659\) | 3.85283e8 | 1.34624 | 0.673122 | − | 0.739532i | \(-0.264953\pi\) | ||||
0.673122 | + | 0.739532i | \(0.264953\pi\) | |||||||
\(660\) | −8.73892e6 | −0.0303967 | ||||||||
\(661\) | −1.05838e8 | −0.366470 | −0.183235 | − | 0.983069i | \(-0.558657\pi\) | ||||
−0.183235 | + | 0.983069i | \(0.558657\pi\) | |||||||
\(662\) | −4.00970e8 | −1.38209 | ||||||||
\(663\) | − | 8.04146e6i | − | 0.0275927i | ||||||
\(664\) | 3.74538e7i | 0.127936i | ||||||||
\(665\) | − | 2.63528e8i | − | 0.896111i | ||||||
\(666\) | 3.15168e8 | 1.06689 | ||||||||
\(667\) | − | 2.75532e7i | − | 0.0928527i | ||||||
\(668\) | 1.03806e7 | 0.0348252 | ||||||||
\(669\) | 1.77342e8 | 0.592288 | ||||||||
\(670\) | −1.15695e8 | −0.384671 | ||||||||
\(671\) | − | 5.79147e7i | − | 0.191700i | ||||||
\(672\) | − | 4.57149e7i | − | 0.150643i | ||||||
\(673\) | 3.67800e8i | 1.20661i | 0.797511 | + | 0.603304i | \(0.206149\pi\) | ||||
−0.797511 | + | 0.603304i | \(0.793851\pi\) | |||||||
\(674\) | − | 5.88912e8i | − | 1.92341i | ||||||
\(675\) | 2.63300e8i | 0.856128i | ||||||||
\(676\) | 2.59667e7 | 0.0840575 | ||||||||
\(677\) | 1.77988e8i | 0.573621i | 0.957987 | + | 0.286810i | \(0.0925950\pi\) | ||||
−0.957987 | + | 0.286810i | \(0.907405\pi\) | |||||||
\(678\) | 6.40239e7i | 0.205425i | ||||||||
\(679\) | − | 5.43460e8i | − | 1.73603i | ||||||
\(680\) | −9.02191e7 | −0.286927 | ||||||||
\(681\) | −2.06025e8 | −0.652348 | ||||||||
\(682\) | 2.07953e8i | 0.655558i | ||||||||
\(683\) | 4.22123e8 | 1.32488 | 0.662440 | − | 0.749115i | \(-0.269521\pi\) | ||||
0.662440 | + | 0.749115i | \(0.269521\pi\) | |||||||
\(684\) | 2.68644e7i | 0.0839477i | ||||||||
\(685\) | −6.02655e7 | −0.187498 | ||||||||
\(686\) | −3.45201e7 | −0.106930 | ||||||||
\(687\) | 2.47891e8i | 0.764523i | ||||||||
\(688\) | 2.67650e8 | + | 2.26779e8i | 0.821869 | + | 0.696366i | ||||
\(689\) | 1.54974e7 | 0.0473806 | ||||||||
\(690\) | 7.58214e6i | 0.0230805i | ||||||||
\(691\) | 3.29787e7i | 0.0999538i | 0.998750 | + | 0.0499769i | \(0.0159148\pi\) | ||||
−0.998750 | + | 0.0499769i | \(0.984085\pi\) | |||||||
\(692\) | −2.66519e7 | −0.0804285 | ||||||||
\(693\) | 4.43650e8i | 1.33303i | ||||||||
\(694\) | −2.79989e8 | −0.837651 | ||||||||
\(695\) | 5.55760e7i | 0.165551i | ||||||||
\(696\) | 1.99855e8i | 0.592773i | ||||||||
\(697\) | 4.83687e8 | 1.42845 | ||||||||
\(698\) | −2.51356e8 | −0.739133 | ||||||||
\(699\) | −2.19489e8 | −0.642659 | ||||||||
\(700\) | − | 3.55125e7i | − | 0.103535i | ||||||
\(701\) | −5.33584e8 | −1.54899 | −0.774496 | − | 0.632579i | \(-0.781996\pi\) | ||||
−0.774496 | + | 0.632579i | \(0.781996\pi\) | |||||||
\(702\) | −2.04194e7 | −0.0590244 | ||||||||
\(703\) | 9.43596e8 | 2.71594 | ||||||||
\(704\) | −4.75698e8 | −1.36337 | ||||||||
\(705\) | −1.61498e8 | −0.460892 | ||||||||
\(706\) | 1.12766e7i | 0.0320453i | ||||||||
\(707\) | − | 5.11505e8i | − | 1.44741i | ||||||
\(708\) | 1.12278e7i | 0.0316371i | ||||||||
\(709\) | 9.62028e7 | 0.269929 | 0.134964 | − | 0.990850i | \(-0.456908\pi\) | ||||
0.134964 | + | 0.990850i | \(0.456908\pi\) | |||||||
\(710\) | 1.67887e8i | 0.469075i | ||||||||
\(711\) | −2.89200e8 | −0.804617 | ||||||||
\(712\) | −8.25461e6 | −0.0228695 | ||||||||
\(713\) | 1.40314e7 | 0.0387109 | ||||||||
\(714\) | 2.66494e8i | 0.732137i | ||||||||
\(715\) | 1.19600e7i | 0.0327200i | ||||||||
\(716\) | − | 3.48314e7i | − | 0.0948926i | ||||||
\(717\) | 2.25964e8i | 0.613030i | ||||||||
\(718\) | − | 3.75435e8i | − | 1.01429i | ||||||
\(719\) | −5.90610e8 | −1.58896 | −0.794482 | − | 0.607288i | \(-0.792258\pi\) | ||||
−0.794482 | + | 0.607288i | \(0.792258\pi\) | |||||||
\(720\) | 9.44397e7i | 0.253021i | ||||||||
\(721\) | 5.38444e8i | 1.43660i | ||||||||
\(722\) | 6.42315e8i | 1.70662i | ||||||||
\(723\) | 3.35498e8 | 0.887719 | ||||||||
\(724\) | 4.35990e6 | 0.0114884 | ||||||||
\(725\) | 3.24803e8i | 0.852326i | ||||||||
\(726\) | 3.18444e8 | 0.832191 | ||||||||
\(727\) | − | 6.66392e8i | − | 1.73431i | −0.498040 | − | 0.867154i | \(-0.665947\pi\) | ||
0.498040 | − | 0.867154i | \(-0.334053\pi\) | |||||||
\(728\) | −2.99054e7 | −0.0775097 | ||||||||
\(729\) | −2.44689e8 | −0.631584 | ||||||||
\(730\) | 1.31856e8i | 0.338948i | ||||||||
\(731\) | −2.33981e8 | − | 1.98251e8i | −0.599002 | − | 0.507532i | ||||
\(732\) | −2.61032e6 | −0.00665520 | ||||||||
\(733\) | 1.91149e8i | 0.485357i | 0.970107 | + | 0.242678i | \(0.0780260\pi\) | ||||
−0.970107 | + | 0.242678i | \(0.921974\pi\) | |||||||
\(734\) | 3.21595e8i | 0.813246i | ||||||||
\(735\) | −1.01455e8 | −0.255512 | ||||||||
\(736\) | − | 6.23281e6i | − | 0.0156333i | ||||||
\(737\) | 5.83139e8 | 1.45670 | ||||||||
\(738\) | − | 4.66680e8i | − | 1.16105i | ||||||
\(739\) | 5.39175e8i | 1.33597i | 0.744175 | + | 0.667985i | \(0.232843\pi\) | ||||
−0.744175 | + | 0.667985i | \(0.767157\pi\) | |||||||
\(740\) | −2.18972e7 | −0.0540374 | ||||||||
\(741\) | −2.32291e7 | −0.0570924 | ||||||||
\(742\) | −5.13583e8 | −1.25718 | ||||||||
\(743\) | − | 2.06678e8i | − | 0.503881i | −0.967743 | − | 0.251940i | \(-0.918931\pi\) | ||
0.967743 | − | 0.251940i | \(-0.0810687\pi\) | |||||||
\(744\) | −1.01776e8 | −0.247131 | ||||||||
\(745\) | 2.88394e8 | 0.697457 | ||||||||
\(746\) | 4.35037e8 | 1.04788 | ||||||||
\(747\) | −3.42740e7 | −0.0822249 | ||||||||
\(748\) | −4.18774e7 | −0.100063 | ||||||||
\(749\) | 3.89085e8i | 0.925975i | ||||||||
\(750\) | − | 1.94152e8i | − | 0.460211i | ||||||
\(751\) | 1.65838e7i | 0.0391529i | 0.999808 | + | 0.0195765i | \(0.00623178\pi\) | ||||
−0.999808 | + | 0.0195765i | \(0.993768\pi\) | |||||||
\(752\) | 8.85270e8 | 2.08172 | ||||||||
\(753\) | − | 5.22070e7i | − | 0.122277i | ||||||
\(754\) | −2.51891e7 | −0.0587623 | ||||||||
\(755\) | −9.92116e7 | −0.230527 | ||||||||
\(756\) | 5.26259e7 | 0.121796 | ||||||||
\(757\) | 4.14585e8i | 0.955710i | 0.878439 | + | 0.477855i | \(0.158585\pi\) | ||||
−0.878439 | + | 0.477855i | \(0.841415\pi\) | |||||||
\(758\) | 4.13233e8i | 0.948827i | ||||||||
\(759\) | − | 3.82163e7i | − | 0.0874025i | ||||||
\(760\) | 2.60613e8i | 0.593685i | ||||||||
\(761\) | − | 4.74981e8i | − | 1.07776i | −0.842383 | − | 0.538880i | \(-0.818848\pi\) | ||
0.842383 | − | 0.538880i | \(-0.181152\pi\) | |||||||
\(762\) | −2.67872e8 | −0.605428 | ||||||||
\(763\) | − | 8.85950e6i | − | 0.0199451i | ||||||
\(764\) | 7.68305e6i | 0.0172287i | ||||||||
\(765\) | − | 8.25595e7i | − | 0.184409i | ||||||
\(766\) | −6.43243e7 | −0.143116 | ||||||||
\(767\) | 1.53663e7 | 0.0340552 | ||||||||
\(768\) | 7.08133e7i | 0.156326i | ||||||||
\(769\) | 5.57822e8 | 1.22664 | 0.613319 | − | 0.789835i | \(-0.289834\pi\) | ||||
0.613319 | + | 0.789835i | \(0.289834\pi\) | |||||||
\(770\) | − | 3.96354e8i | − | 0.868183i | ||||||
\(771\) | 1.33710e7 | 0.0291744 | ||||||||
\(772\) | −2.46918e6 | −0.00536661 | ||||||||
\(773\) | − | 2.66540e8i | − | 0.577063i | −0.957470 | − | 0.288532i | \(-0.906833\pi\) | ||
0.957470 | − | 0.288532i | \(-0.0931670\pi\) | |||||||
\(774\) | −1.91280e8 | + | 2.25754e8i | −0.412521 | + | 0.486869i | ||||
\(775\) | −1.65406e8 | −0.355341 | ||||||||
\(776\) | 5.37449e8i | 1.15014i | ||||||||
\(777\) | − | 7.02351e8i | − | 1.49724i | ||||||
\(778\) | −6.33775e8 | −1.34585 | ||||||||
\(779\) | − | 1.39721e9i | − | 2.95563i | ||||||
\(780\) | 539059. | 0.00113593 | ||||||||
\(781\) | − | 8.46203e8i | − | 1.77632i | ||||||
\(782\) | 3.63340e7i | 0.0759789i | ||||||||
\(783\) | −4.81325e8 | −1.00266 | ||||||||
\(784\) | 5.56137e8 | 1.15407 | ||||||||
\(785\) | −5.63823e7 | −0.116556 | ||||||||
\(786\) | − | 3.55460e8i | − | 0.732020i | ||||||
\(787\) | −2.64088e7 | −0.0541782 | −0.0270891 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270891 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(788\) | 3.36846e7 | 0.0688420 | ||||||||
\(789\) | −3.45277e8 | −0.702970 | ||||||||
\(790\) | 2.58370e8 | 0.524035 | ||||||||
\(791\) | −2.25825e8 | −0.456291 | ||||||||
\(792\) | − | 4.38743e8i | − | 0.883150i | ||||||
\(793\) | 3.57246e6i | 0.00716387i | ||||||||
\(794\) | − | 1.27660e8i | − | 0.255032i | ||||||
\(795\) | −1.00525e8 | −0.200065 | ||||||||
\(796\) | 5.00599e7i | 0.0992545i | ||||||||
\(797\) | −7.17908e7 | −0.141806 | −0.0709028 | − | 0.997483i | \(-0.522588\pi\) | ||||
−0.0709028 | + | 0.997483i | \(0.522588\pi\) | |||||||
\(798\) | 7.69813e8 | 1.51487 | ||||||||
\(799\) | −7.73906e8 | −1.51722 | ||||||||
\(800\) | 7.34737e7i | 0.143503i | ||||||||
\(801\) | − | 7.55379e6i | − | 0.0146983i | ||||||
\(802\) | − | 2.01719e8i | − | 0.391043i | ||||||
\(803\) | − | 6.64598e8i | − | 1.28355i | ||||||
\(804\) | − | 2.62831e7i | − | 0.0505719i | ||||||
\(805\) | −2.67437e7 | −0.0512665 | ||||||||
\(806\) | − | 1.28275e7i | − | 0.0244984i | ||||||
\(807\) | − | 8.88297e7i | − | 0.169020i | ||||||
\(808\) | 5.05848e8i | 0.958928i | ||||||||
\(809\) | 9.69352e8 | 1.83078 | 0.915390 | − | 0.402568i | \(-0.131882\pi\) | ||||
0.915390 | + | 0.402568i | \(0.131882\pi\) | |||||||
\(810\) | 2.46791e6 | 0.00464381 | ||||||||
\(811\) | 1.00965e9i | 1.89282i | 0.322961 | + | 0.946412i | \(0.395322\pi\) | ||||
−0.322961 | + | 0.946412i | \(0.604678\pi\) | |||||||
\(812\) | 6.49186e7 | 0.121255 | ||||||||
\(813\) | − | 9.06683e7i | − | 0.168727i | ||||||
\(814\) | 1.41920e9 | 2.63129 | ||||||||
\(815\) | 1.36927e8 | 0.252940 | ||||||||
\(816\) | − | 2.85929e8i | − | 0.526245i | ||||||
\(817\) | −5.72682e8 | + | 6.75894e8i | −1.05014 | + | 1.23940i | ||||
\(818\) | −8.22900e8 | −1.50344 | ||||||||
\(819\) | − | 2.73665e7i | − | 0.0498158i | ||||||
\(820\) | 3.24240e7i | 0.0588064i | ||||||||
\(821\) | 4.60743e8 | 0.832586 | 0.416293 | − | 0.909230i | \(-0.363329\pi\) | ||||
0.416293 | + | 0.909230i | \(0.363329\pi\) | |||||||
\(822\) | − | 1.76046e8i | − | 0.316965i | ||||||
\(823\) | 5.35351e8 | 0.960371 | 0.480186 | − | 0.877167i | \(-0.340569\pi\) | ||||
0.480186 | + | 0.877167i | \(0.340569\pi\) | |||||||
\(824\) | − | 5.32488e8i | − | 0.951763i | ||||||
\(825\) | 4.50502e8i | 0.802297i | ||||||||
\(826\) | −5.09239e8 | −0.903611 | ||||||||
\(827\) | 9.85479e8 | 1.74233 | 0.871166 | − | 0.490989i | \(-0.163364\pi\) | ||||
0.871166 | + | 0.490989i | \(0.163364\pi\) | |||||||
\(828\) | 2.72629e6 | 0.00480265 | ||||||||
\(829\) | − | 7.45480e7i | − | 0.130850i | −0.997858 | − | 0.0654248i | \(-0.979160\pi\) | ||
0.997858 | − | 0.0654248i | \(-0.0208402\pi\) | |||||||
\(830\) | 3.06202e7 | 0.0535518 | ||||||||
\(831\) | 1.31423e8 | 0.229018 | ||||||||
\(832\) | 2.93433e7 | 0.0509495 | ||||||||
\(833\) | −4.86177e8 | −0.841123 | ||||||||
\(834\) | −1.62348e8 | −0.279864 | ||||||||
\(835\) | 9.21534e7i | 0.158289i | ||||||||
\(836\) | 1.20970e8i | 0.207042i | ||||||||
\(837\) | − | 2.45114e8i | − | 0.418015i | ||||||
\(838\) | −6.82224e8 | −1.15930 | ||||||||
\(839\) | 7.40970e8i | 1.25463i | 0.778766 | + | 0.627314i | \(0.215846\pi\) | ||||
−0.778766 | + | 0.627314i | \(0.784154\pi\) | |||||||
\(840\) | 1.93984e8 | 0.327286 | ||||||||
\(841\) | 1.06723e6 | 0.00179420 | ||||||||
\(842\) | 3.25734e8 | 0.545667 | ||||||||
\(843\) | − | 8.40689e7i | − | 0.140331i | ||||||
\(844\) | − | 7.37422e7i | − | 0.122656i | ||||||
\(845\) | 2.30518e8i | 0.382063i | ||||||||
\(846\) | 7.46694e8i | 1.23319i | ||||||||
\(847\) | 1.12321e9i | 1.84847i | ||||||||
\(848\) | 5.51039e8 | 0.903639 | ||||||||
\(849\) | − | 6.24822e8i | − | 1.02102i | ||||||
\(850\) | − | 4.28313e8i | − | 0.697436i | ||||||
\(851\) | − | 9.57592e7i | − | 0.155379i | ||||||
\(852\) | −3.81400e7 | −0.0616682 | ||||||||
\(853\) | 1.10117e9 | 1.77422 | 0.887111 | − | 0.461556i | \(-0.152709\pi\) | ||||
0.887111 | + | 0.461556i | \(0.152709\pi\) | |||||||
\(854\) | − | 1.18391e8i | − | 0.190084i | ||||||
\(855\) | −2.38487e8 | −0.381564 | ||||||||
\(856\) | − | 3.84782e8i | − | 0.613470i | ||||||
\(857\) | 3.24078e8 | 0.514881 | 0.257441 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257441 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(858\) | −3.49373e7 | −0.0553131 | ||||||||
\(859\) | 5.90852e8i | 0.932178i | 0.884738 | + | 0.466089i | \(0.154337\pi\) | ||||
−0.884738 | + | 0.466089i | \(0.845663\pi\) | |||||||
\(860\) | 1.32898e7 | − | 1.56849e7i | 0.0208940 | − | 0.0246596i | ||||
\(861\) | −1.04000e9 | −1.62938 | ||||||||
\(862\) | − | 8.68168e8i | − | 1.35544i | ||||||
\(863\) | − | 7.18255e8i | − | 1.11750i | −0.829337 | − | 0.558748i | \(-0.811282\pi\) | ||
0.829337 | − | 0.558748i | \(-0.188718\pi\) | |||||||
\(864\) | −1.08880e8 | −0.168814 | ||||||||
\(865\) | − | 2.36601e8i | − | 0.365568i | ||||||
\(866\) | −1.46527e8 | −0.225613 | ||||||||
\(867\) | − | 1.55562e8i | − | 0.238696i | ||||||
\(868\) | 3.30597e7i | 0.0505522i | ||||||||
\(869\) | −1.30226e9 | −1.98445 | ||||||||
\(870\) | 1.63391e8 | 0.248125 | ||||||||
\(871\) | −3.59708e7 | −0.0544372 | ||||||||
\(872\) | 8.76151e6i | 0.0132139i | ||||||||
\(873\) | −4.91820e8 | −0.739202 | ||||||||
\(874\) | 1.04957e8 | 0.157209 | ||||||||
\(875\) | 6.84811e8 | 1.02222 | ||||||||
\(876\) | −2.99546e7 | −0.0445607 | ||||||||
\(877\) | −3.42343e8 | −0.507531 | −0.253766 | − | 0.967266i | \(-0.581669\pi\) | ||||
−0.253766 | + | 0.967266i | \(0.581669\pi\) | |||||||
\(878\) | 3.82683e7i | 0.0565400i | ||||||||
\(879\) | 4.08847e8i | 0.601996i | ||||||||
\(880\) | 4.25261e8i | 0.624032i | ||||||||
\(881\) | 4.41693e8 | 0.645941 | 0.322970 | − | 0.946409i | \(-0.395319\pi\) | ||||
0.322970 | + | 0.946409i | \(0.395319\pi\) | |||||||
\(882\) | 4.69082e8i | 0.683665i | ||||||||
\(883\) | −1.02932e9 | −1.49509 | −0.747544 | − | 0.664212i | \(-0.768767\pi\) | ||||
−0.747544 | + | 0.664212i | \(0.768767\pi\) | |||||||
\(884\) | 2.58320e6 | 0.00373939 | ||||||||
\(885\) | −9.96745e7 | −0.143799 | ||||||||
\(886\) | 4.27461e8i | 0.614604i | ||||||||
\(887\) | 1.36019e9i | 1.94907i | 0.224228 | + | 0.974537i | \(0.428014\pi\) | ||||
−0.224228 | + | 0.974537i | \(0.571986\pi\) | |||||||
\(888\) | 6.94583e8i | 0.991940i | ||||||||
\(889\) | − | 9.44837e8i | − | 1.34478i | ||||||
\(890\) | 6.74852e6i | 0.00957279i | ||||||||
\(891\) | −1.24390e7 | −0.0175855 | ||||||||
\(892\) | 5.69684e7i | 0.0802675i | ||||||||
\(893\) | 2.23556e9i | 3.13930i | ||||||||
\(894\) | 8.42452e8i | 1.17905i | ||||||||
\(895\) | 3.09214e8 | 0.431311 | ||||||||
\(896\) | −1.14659e9 | −1.59398 | ||||||||
\(897\) | 2.35737e6i | 0.00326626i | ||||||||
\(898\) | 9.01976e8 | 1.24556 | ||||||||
\(899\) | − | 3.02370e8i | − | 0.416159i | ||||||
\(900\) | −3.21381e7 | −0.0440851 | ||||||||
\(901\) | −4.81720e8 | −0.658598 | ||||||||
\(902\) | − | 2.10145e9i | − | 2.86352i | ||||||
\(903\) | 5.03092e8 | + | 4.26267e8i | 0.683257 | + | 0.578920i | ||||
\(904\) | 2.23327e8 | 0.302299 | ||||||||
\(905\) | 3.87048e7i | 0.0522179i | ||||||||
\(906\) | − | 2.89815e8i | − | 0.389705i | ||||||
\(907\) | −1.38587e9 | −1.85738 | −0.928689 | − | 0.370858i | \(-0.879064\pi\) | ||||
−0.928689 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(908\) | − | 6.61826e7i | − | 0.0884070i | ||||||
\(909\) | −4.62902e8 | −0.616307 | ||||||||
\(910\) | 2.44491e7i | 0.0324443i | ||||||||
\(911\) | − | 8.07099e8i | − | 1.06751i | −0.845639 | − | 0.533755i | \(-0.820781\pi\) | ||
0.845639 | − | 0.533755i | \(-0.179219\pi\) | |||||||
\(912\) | −8.25956e8 | −1.08886 | ||||||||
\(913\) | −1.54335e8 | −0.202793 | ||||||||
\(914\) | 6.51149e8 | 0.852790 | ||||||||
\(915\) | − | 2.31730e7i | − | 0.0302496i | ||||||
\(916\) | −7.96313e7 | −0.103609 | ||||||||
\(917\) | 1.25378e9 | 1.62597 | ||||||||
\(918\) | 6.34716e8 | 0.820448 | ||||||||
\(919\) | −4.84001e8 | −0.623591 | −0.311795 | − | 0.950149i | \(-0.600930\pi\) | ||||
−0.311795 | + | 0.950149i | \(0.600930\pi\) | |||||||
\(920\) | 2.64479e7 | 0.0339647 | ||||||||
\(921\) | − | 9.35371e8i | − | 1.19731i | ||||||
\(922\) | − | 1.13871e9i | − | 1.45285i | ||||||
\(923\) | 5.21979e7i | 0.0663817i | ||||||||
\(924\) | 9.00422e7 | 0.114138 | ||||||||
\(925\) | 1.12883e9i | 1.42627i | ||||||||
\(926\) | −1.02093e9 | −1.28576 | ||||||||
\(927\) | 4.87280e8 | 0.611702 | ||||||||
\(928\) | −1.34314e8 | −0.168064 | ||||||||
\(929\) | − | 1.33655e9i | − | 1.66701i | −0.552509 | − | 0.833507i | \(-0.686329\pi\) | ||
0.552509 | − | 0.833507i | \(-0.313671\pi\) | |||||||
\(930\) | 8.32066e7i | 0.103445i | ||||||||
\(931\) | 1.40441e9i | 1.74038i | ||||||||
\(932\) | − | 7.05074e7i | − | 0.0870938i | ||||||
\(933\) | 3.70780e8i | 0.456532i | ||||||||
\(934\) | 5.78612e7 | 0.0710144 | ||||||||
\(935\) | − | 3.71764e8i | − | 0.454813i | ||||||
\(936\) | 2.70638e7i | 0.0330036i | ||||||||
\(937\) | − | 1.16884e9i | − | 1.42081i | −0.703791 | − | 0.710407i | \(-0.748511\pi\) | ||
0.703791 | − | 0.710407i | \(-0.251489\pi\) | |||||||
\(938\) | 1.19207e9 | 1.44442 | ||||||||
\(939\) | −4.00716e8 | −0.483994 | ||||||||
\(940\) | − | 5.18788e7i | − | 0.0624606i | ||||||
\(941\) | −1.06839e9 | −1.28222 | −0.641109 | − | 0.767449i | \(-0.721526\pi\) | ||||
−0.641109 | + | 0.767449i | \(0.721526\pi\) | |||||||
\(942\) | − | 1.64703e8i | − | 0.197037i | ||||||
\(943\) | −1.41794e8 | −0.169092 | ||||||||
\(944\) | 5.46378e8 | 0.649497 | ||||||||
\(945\) | 4.67184e8i | 0.553595i | ||||||||
\(946\) | −8.61331e8 | + | 1.01657e9i | −1.01741 | + | 1.20078i | ||||
\(947\) | −8.39527e8 | −0.988519 | −0.494259 | − | 0.869315i | \(-0.664561\pi\) | ||||
−0.494259 | + | 0.869315i | \(0.664561\pi\) | |||||||
\(948\) | 5.86954e7i | 0.0688936i | ||||||||
\(949\) | 4.09956e7i | 0.0479666i | ||||||||
\(950\) | −1.23726e9 | −1.44307 | ||||||||
\(951\) | 7.59205e8i | 0.882709i | ||||||||
\(952\) | 9.29580e8 | 1.07740 | ||||||||
\(953\) | − | 2.74829e8i | − | 0.317529i | −0.987316 | − | 0.158764i | \(-0.949249\pi\) | ||
0.987316 | − | 0.158764i | \(-0.0507510\pi\) | |||||||
\(954\) | 4.64782e8i | 0.535308i | ||||||||
\(955\) | −6.82059e7 | −0.0783090 | ||||||||
\(956\) | −7.25875e7 | −0.0830785 | ||||||||
\(957\) | −8.23541e8 | −0.939614 | ||||||||
\(958\) | − | 4.83567e7i | − | 0.0549997i | ||||||
\(959\) | 6.20950e8 | 0.704046 | ||||||||
\(960\) | −1.90338e8 | −0.215135 | ||||||||
\(961\) | −7.33522e8 | −0.826500 | ||||||||
\(962\) | −8.75429e7 | −0.0983322 | ||||||||
\(963\) | 3.52114e8 | 0.394279 | ||||||||
\(964\) | 1.07774e8i | 0.120305i | ||||||||
\(965\) | − | 2.19200e7i | − | 0.0243926i | ||||||
\(966\) | − | 7.81232e7i | − | 0.0866660i | ||||||
\(967\) | 1.44614e9 | 1.59930 | 0.799651 | − | 0.600465i | \(-0.205018\pi\) | ||||
0.799651 | + | 0.600465i | \(0.205018\pi\) | |||||||
\(968\) | − | 1.11079e9i | − | 1.22463i | ||||||
\(969\) | 7.22054e8 | 0.793594 | ||||||||
\(970\) | 4.39389e8 | 0.481431 | ||||||||
\(971\) | 6.76504e8 | 0.738946 | 0.369473 | − | 0.929242i | \(-0.379538\pi\) | ||||
0.369473 | + | 0.929242i | \(0.379538\pi\) | |||||||
\(972\) | − | 7.71545e7i | − | 0.0840161i | ||||||
\(973\) | − | 5.72632e8i | − | 0.621637i | ||||||
\(974\) | − | 2.24162e8i | − | 0.242597i | ||||||
\(975\) | − | 2.77892e7i | − | 0.0299821i | ||||||
\(976\) | 1.27026e8i | 0.136629i | ||||||||
\(977\) | 1.12326e9 | 1.20448 | 0.602238 | − | 0.798317i | \(-0.294276\pi\) | ||||
0.602238 | + | 0.798317i | \(0.294276\pi\) | |||||||
\(978\) | 3.99989e8i | 0.427594i | ||||||||
\(979\) | − | 3.40146e7i | − | 0.0362508i | ||||||
\(980\) | − | 3.25909e7i | − | 0.0346273i | ||||||
\(981\) | −8.01766e6 | −0.00849260 | ||||||||
\(982\) | −1.79857e8 | −0.189929 | ||||||||
\(983\) | − | 1.17196e7i | − | 0.0123382i | −0.999981 | − | 0.00616910i | \(-0.998036\pi\) | ||
0.999981 | − | 0.00616910i | \(-0.00196370\pi\) | |||||||
\(984\) | 1.02849e9 | 1.07948 | ||||||||
\(985\) | 2.99034e8i | 0.312904i | ||||||||
\(986\) | 7.82977e8 | 0.816805 | ||||||||
\(987\) | 1.66401e9 | 1.73063 | ||||||||
\(988\) | − | 7.46202e6i | − | 0.00773723i | ||||||
\(989\) | 6.85920e7 | + | 5.81176e7i | 0.0709062 | + | 0.0600785i | ||||
\(990\) | −3.58692e8 | −0.369672 | ||||||||
\(991\) | − | 4.97809e8i | − | 0.511495i | −0.966744 | − | 0.255748i | \(-0.917678\pi\) | ||
0.966744 | − | 0.255748i | \(-0.0823216\pi\) | |||||||
\(992\) | − | 6.83990e7i | − | 0.0700672i | ||||||
\(993\) | 8.08654e8 | 0.825876 | ||||||||
\(994\) | − | 1.72984e9i | − | 1.76135i | ||||||
\(995\) | −4.44404e8 | −0.451137 | ||||||||
\(996\) | 6.95619e6i | 0.00704033i | ||||||||
\(997\) | − | 8.24314e8i | − | 0.831778i | −0.909415 | − | 0.415889i | \(-0.863470\pi\) | ||
0.909415 | − | 0.415889i | \(-0.136530\pi\) | |||||||
\(998\) | 1.28203e9 | 1.28975 | ||||||||
\(999\) | −1.67281e9 | −1.67784 |
(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.42.6 | ✓ | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.15 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
43.7.b.b.42.15 | yes | 20 | 43.42 | odd | 2 | inner |