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 | 42.12 | ||
Root | \(2.98785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.98785i | 0.373482i | 0.982409 | + | 0.186741i | \(0.0597925\pi\) | ||||
−0.982409 | + | 0.186741i | \(0.940208\pi\) | |||||||
\(3\) | − | 41.6692i | − | 1.54330i | −0.636044 | − | 0.771652i | \(-0.719431\pi\) | ||
0.636044 | − | 0.771652i | \(-0.280569\pi\) | |||||||
\(4\) | 55.0727 | 0.860511 | ||||||||
\(5\) | − | 126.319i | − | 1.01055i | −0.862958 | − | 0.505275i | \(-0.831391\pi\) | ||
0.862958 | − | 0.505275i | \(-0.168609\pi\) | |||||||
\(6\) | 124.502 | 0.576396 | ||||||||
\(7\) | − | 69.5744i | − | 0.202841i | −0.994844 | − | 0.101420i | \(-0.967661\pi\) | ||
0.994844 | − | 0.101420i | \(-0.0323387\pi\) | |||||||
\(8\) | 355.772i | 0.694867i | ||||||||
\(9\) | −1007.32 | −1.38179 | ||||||||
\(10\) | 377.422 | 0.377422 | ||||||||
\(11\) | −100.569 | −0.0755589 | −0.0377795 | − | 0.999286i | \(-0.512028\pi\) | ||||
−0.0377795 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(12\) | − | 2294.84i | − | 1.32803i | ||||||
\(13\) | −1723.32 | −0.784396 | −0.392198 | − | 0.919881i | \(-0.628285\pi\) | ||||
−0.392198 | + | 0.919881i | \(0.628285\pi\) | |||||||
\(14\) | 207.878 | 0.0757573 | ||||||||
\(15\) | −5263.61 | −1.55959 | ||||||||
\(16\) | 2461.66 | 0.600991 | ||||||||
\(17\) | −115.904 | −0.0235912 | −0.0117956 | − | 0.999930i | \(-0.503755\pi\) | ||||
−0.0117956 | + | 0.999930i | \(0.503755\pi\) | |||||||
\(18\) | − | 3009.74i | − | 0.516073i | ||||||
\(19\) | − | 9219.04i | − | 1.34408i | −0.740515 | − | 0.672039i | \(-0.765419\pi\) | ||
0.740515 | − | 0.672039i | \(-0.234581\pi\) | |||||||
\(20\) | − | 6956.72i | − | 0.869590i | ||||||
\(21\) | −2899.11 | −0.313045 | ||||||||
\(22\) | − | 300.485i | − | 0.0282199i | ||||||
\(23\) | 6392.18 | 0.525370 | 0.262685 | − | 0.964882i | \(-0.415392\pi\) | ||||
0.262685 | + | 0.964882i | \(0.415392\pi\) | |||||||
\(24\) | 14824.7 | 1.07239 | ||||||||
\(25\) | −331.444 | −0.0212124 | ||||||||
\(26\) | − | 5149.02i | − | 0.292957i | ||||||
\(27\) | 11597.6i | 0.589218i | ||||||||
\(28\) | − | 3831.65i | − | 0.174547i | ||||||
\(29\) | 15483.4i | 0.634851i | 0.948283 | + | 0.317426i | \(0.102818\pi\) | ||||
−0.948283 | + | 0.317426i | \(0.897182\pi\) | |||||||
\(30\) | − | 15726.9i | − | 0.582477i | ||||||
\(31\) | −42010.7 | −1.41018 | −0.705091 | − | 0.709117i | \(-0.749094\pi\) | ||||
−0.705091 | + | 0.709117i | \(0.749094\pi\) | |||||||
\(32\) | 30124.5i | 0.919326i | ||||||||
\(33\) | 4190.63i | 0.116610i | ||||||||
\(34\) | − | 346.304i | − | 0.00881090i | ||||||
\(35\) | −8788.56 | −0.204981 | ||||||||
\(36\) | −55476.1 | −1.18905 | ||||||||
\(37\) | 38260.7i | 0.755350i | 0.925938 | + | 0.377675i | \(0.123276\pi\) | ||||
−0.925938 | + | 0.377675i | \(0.876724\pi\) | |||||||
\(38\) | 27545.1 | 0.501989 | ||||||||
\(39\) | 71809.3i | 1.21056i | ||||||||
\(40\) | 44940.7 | 0.702198 | ||||||||
\(41\) | 78659.7 | 1.14130 | 0.570651 | − | 0.821193i | \(-0.306691\pi\) | ||||
0.570651 | + | 0.821193i | \(0.306691\pi\) | |||||||
\(42\) | − | 8662.12i | − | 0.116917i | ||||||
\(43\) | 35141.8 | − | 71319.1i | 0.441996 | − | 0.897017i | ||||
\(44\) | −5538.60 | −0.0650193 | ||||||||
\(45\) | 127244.i | 1.39637i | ||||||||
\(46\) | 19098.9i | 0.196216i | ||||||||
\(47\) | 138058. | 1.32974 | 0.664871 | − | 0.746958i | \(-0.268486\pi\) | ||||
0.664871 | + | 0.746958i | \(0.268486\pi\) | |||||||
\(48\) | − | 102576.i | − | 0.927513i | ||||||
\(49\) | 112808. | 0.958856 | ||||||||
\(50\) | − | 990.307i | − | 0.00792245i | ||||||
\(51\) | 4829.62i | 0.0364085i | ||||||||
\(52\) | −94907.8 | −0.674981 | ||||||||
\(53\) | 54847.1 | 0.368406 | 0.184203 | − | 0.982888i | \(-0.441030\pi\) | ||||
0.184203 | + | 0.982888i | \(0.441030\pi\) | |||||||
\(54\) | −34651.8 | −0.220062 | ||||||||
\(55\) | 12703.7i | 0.0763561i | ||||||||
\(56\) | 24752.6 | 0.140947 | ||||||||
\(57\) | −384150. | −2.07432 | ||||||||
\(58\) | −46262.1 | −0.237105 | ||||||||
\(59\) | −177043. | −0.862029 | −0.431015 | − | 0.902345i | \(-0.641844\pi\) | ||||
−0.431015 | + | 0.902345i | \(0.641844\pi\) | |||||||
\(60\) | −289881. | −1.34204 | ||||||||
\(61\) | − | 372244.i | − | 1.63998i | −0.572377 | − | 0.819990i | \(-0.693979\pi\) | ||
0.572377 | − | 0.819990i | \(-0.306021\pi\) | |||||||
\(62\) | − | 125522.i | − | 0.526677i | ||||||
\(63\) | 70084.0i | 0.280283i | ||||||||
\(64\) | 67538.8 | 0.257640 | ||||||||
\(65\) | 217687.i | 0.792671i | ||||||||
\(66\) | −12521.0 | −0.0435519 | ||||||||
\(67\) | 575276. | 1.91272 | 0.956361 | − | 0.292189i | \(-0.0943836\pi\) | ||||
0.956361 | + | 0.292189i | \(0.0943836\pi\) | |||||||
\(68\) | −6383.14 | −0.0203005 | ||||||||
\(69\) | − | 266357.i | − | 0.810806i | ||||||
\(70\) | − | 26258.9i | − | 0.0765566i | ||||||
\(71\) | 367418.i | 1.02656i | 0.858220 | + | 0.513282i | \(0.171570\pi\) | ||||
−0.858220 | + | 0.513282i | \(0.828430\pi\) | |||||||
\(72\) | − | 358378.i | − | 0.960160i | ||||||
\(73\) | 47584.3i | 0.122319i | 0.998128 | + | 0.0611597i | \(0.0194799\pi\) | ||||
−0.998128 | + | 0.0611597i | \(0.980520\pi\) | |||||||
\(74\) | −114317. | −0.282109 | ||||||||
\(75\) | 13811.0i | 0.0327373i | ||||||||
\(76\) | − | 507718.i | − | 1.15660i | ||||||
\(77\) | 6997.02i | 0.0153264i | ||||||||
\(78\) | −214556. | −0.452123 | ||||||||
\(79\) | 234069. | 0.474748 | 0.237374 | − | 0.971418i | \(-0.423713\pi\) | ||||
0.237374 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(80\) | − | 310954.i | − | 0.607332i | ||||||
\(81\) | −251078. | −0.472447 | ||||||||
\(82\) | 235023.i | 0.426255i | ||||||||
\(83\) | −68786.3 | −0.120301 | −0.0601503 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601503 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(84\) | −159662. | −0.269379 | ||||||||
\(85\) | 14640.8i | 0.0238401i | ||||||||
\(86\) | 213091. | + | 104998.i | 0.335019 | + | 0.165077i | ||||
\(87\) | 645181. | 0.979769 | ||||||||
\(88\) | − | 35779.6i | − | 0.0525034i | ||||||
\(89\) | 33503.7i | 0.0475251i | 0.999718 | + | 0.0237625i | \(0.00756456\pi\) | ||||
−0.999718 | + | 0.0237625i | \(0.992435\pi\) | |||||||
\(90\) | −380187. | −0.521518 | ||||||||
\(91\) | 119899.i | 0.159107i | ||||||||
\(92\) | 352035. | 0.452087 | ||||||||
\(93\) | 1.75055e6i | 2.17634i | ||||||||
\(94\) | 412497.i | 0.496634i | ||||||||
\(95\) | −1.16454e6 | −1.35826 | ||||||||
\(96\) | 1.25526e6 | 1.41880 | ||||||||
\(97\) | 341432. | 0.374101 | 0.187051 | − | 0.982350i | \(-0.440107\pi\) | ||||
0.187051 | + | 0.982350i | \(0.440107\pi\) | |||||||
\(98\) | 337055.i | 0.358115i | ||||||||
\(99\) | 101306. | 0.104407 | ||||||||
\(100\) | −18253.5 | −0.0182535 | ||||||||
\(101\) | −785657. | −0.762551 | −0.381275 | − | 0.924462i | \(-0.624515\pi\) | ||||
−0.381275 | + | 0.924462i | \(0.624515\pi\) | |||||||
\(102\) | −14430.2 | −0.0135979 | ||||||||
\(103\) | 51634.9 | 0.0472532 | 0.0236266 | − | 0.999721i | \(-0.492479\pi\) | ||||
0.0236266 | + | 0.999721i | \(0.492479\pi\) | |||||||
\(104\) | − | 613108.i | − | 0.545051i | ||||||
\(105\) | 366212.i | 0.316348i | ||||||||
\(106\) | 163875.i | 0.137593i | ||||||||
\(107\) | 1.82956e6 | 1.49347 | 0.746733 | − | 0.665124i | \(-0.231621\pi\) | ||||
0.746733 | + | 0.665124i | \(0.231621\pi\) | |||||||
\(108\) | 638710.i | 0.507029i | ||||||||
\(109\) | −2.10066e6 | −1.62209 | −0.811046 | − | 0.584982i | \(-0.801102\pi\) | ||||
−0.811046 | + | 0.584982i | \(0.801102\pi\) | |||||||
\(110\) | −37956.9 | −0.0285176 | ||||||||
\(111\) | 1.59430e6 | 1.16574 | ||||||||
\(112\) | − | 171269.i | − | 0.121906i | ||||||
\(113\) | 2.18163e6i | 1.51198i | 0.654583 | + | 0.755990i | \(0.272844\pi\) | ||||
−0.654583 | + | 0.755990i | \(0.727156\pi\) | |||||||
\(114\) | − | 1.14778e6i | − | 0.774722i | ||||||
\(115\) | − | 807452.i | − | 0.530913i | ||||||
\(116\) | 852712.i | 0.546297i | ||||||||
\(117\) | 1.73594e6 | 1.08387 | ||||||||
\(118\) | − | 528978.i | − | 0.321952i | ||||||
\(119\) | 8063.94i | 0.00478527i | ||||||||
\(120\) | − | 1.87264e6i | − | 1.08371i | ||||||
\(121\) | −1.76145e6 | −0.994291 | ||||||||
\(122\) | 1.11221e6 | 0.612503 | ||||||||
\(123\) | − | 3.27769e6i | − | 1.76138i | ||||||
\(124\) | −2.31365e6 | −1.21348 | ||||||||
\(125\) | − | 1.93186e6i | − | 0.989114i | ||||||
\(126\) | −209401. | −0.104681 | ||||||||
\(127\) | 1.20370e6 | 0.587636 | 0.293818 | − | 0.955861i | \(-0.405074\pi\) | ||||
0.293818 | + | 0.955861i | \(0.405074\pi\) | |||||||
\(128\) | 2.12976e6i | 1.01555i | ||||||||
\(129\) | −2.97181e6 | − | 1.46433e6i | −1.38437 | − | 0.682134i | ||||
\(130\) | −650418. | −0.296048 | ||||||||
\(131\) | 2.57371e6i | 1.14484i | 0.819960 | + | 0.572421i | \(0.193996\pi\) | ||||
−0.819960 | + | 0.572421i | \(0.806004\pi\) | |||||||
\(132\) | 230789.i | 0.100345i | ||||||||
\(133\) | −641409. | −0.272634 | ||||||||
\(134\) | 1.71884e6i | 0.714366i | ||||||||
\(135\) | 1.46499e6 | 0.595434 | ||||||||
\(136\) | − | 41235.3i | − | 0.0163928i | ||||||
\(137\) | 996805.i | 0.387658i | 0.981035 | + | 0.193829i | \(0.0620906\pi\) | ||||
−0.981035 | + | 0.193829i | \(0.937909\pi\) | |||||||
\(138\) | 795836. | 0.302821 | ||||||||
\(139\) | −1.90604e6 | −0.709720 | −0.354860 | − | 0.934920i | \(-0.615471\pi\) | ||||
−0.354860 | + | 0.934920i | \(0.615471\pi\) | |||||||
\(140\) | −484010. | −0.176388 | ||||||||
\(141\) | − | 5.75276e6i | − | 2.05220i | ||||||
\(142\) | −1.09779e6 | −0.383403 | ||||||||
\(143\) | 173312. | 0.0592681 | ||||||||
\(144\) | −2.47969e6 | −0.830444 | ||||||||
\(145\) | 1.95584e6 | 0.641549 | ||||||||
\(146\) | −142175. | −0.0456841 | ||||||||
\(147\) | − | 4.70064e6i | − | 1.47981i | ||||||
\(148\) | 2.10712e6i | 0.649987i | ||||||||
\(149\) | − | 192908.i | − | 0.0583165i | −0.999575 | − | 0.0291582i | \(-0.990717\pi\) | ||
0.999575 | − | 0.0291582i | \(-0.00928267\pi\) | |||||||
\(150\) | −41265.3 | −0.0122268 | ||||||||
\(151\) | − | 2.12036e6i | − | 0.615856i | −0.951410 | − | 0.307928i | \(-0.900364\pi\) | ||
0.951410 | − | 0.307928i | \(-0.0996356\pi\) | |||||||
\(152\) | 3.27987e6 | 0.933956 | ||||||||
\(153\) | 116753. | 0.0325981 | ||||||||
\(154\) | −20906.1 | −0.00572414 | ||||||||
\(155\) | 5.30675e6i | 1.42506i | ||||||||
\(156\) | 3.95473e6i | 1.04170i | ||||||||
\(157\) | − | 4.75453e6i | − | 1.22860i | −0.789074 | − | 0.614298i | \(-0.789439\pi\) | ||
0.789074 | − | 0.614298i | \(-0.210561\pi\) | |||||||
\(158\) | 699364.i | 0.177309i | ||||||||
\(159\) | − | 2.28544e6i | − | 0.568562i | ||||||
\(160\) | 3.80529e6 | 0.929026 | ||||||||
\(161\) | − | 444732.i | − | 0.106567i | ||||||
\(162\) | − | 750183.i | − | 0.176450i | ||||||
\(163\) | − | 663761.i | − | 0.153267i | −0.997059 | − | 0.0766335i | \(-0.975583\pi\) | ||
0.997059 | − | 0.0766335i | \(-0.0244172\pi\) | |||||||
\(164\) | 4.33200e6 | 0.982103 | ||||||||
\(165\) | 529355. | 0.117841 | ||||||||
\(166\) | − | 205523.i | − | 0.0449301i | ||||||
\(167\) | 2.20047e6 | 0.472460 | 0.236230 | − | 0.971697i | \(-0.424088\pi\) | ||||
0.236230 | + | 0.971697i | \(0.424088\pi\) | |||||||
\(168\) | − | 1.03142e6i | − | 0.217525i | ||||||
\(169\) | −1.85699e6 | −0.384723 | ||||||||
\(170\) | −43744.7 | −0.00890386 | ||||||||
\(171\) | 9.28656e6i | 1.85723i | ||||||||
\(172\) | 1.93535e6 | − | 3.92774e6i | 0.380343 | − | 0.771893i | ||||
\(173\) | −8.81032e6 | −1.70158 | −0.850792 | − | 0.525502i | \(-0.823878\pi\) | ||||
−0.850792 | + | 0.525502i | \(0.823878\pi\) | |||||||
\(174\) | 1.92770e6i | 0.365926i | ||||||||
\(175\) | 23060.0i | 0.00430275i | ||||||||
\(176\) | −247567. | −0.0454103 | ||||||||
\(177\) | 7.37723e6i | 1.33037i | ||||||||
\(178\) | −100104. | −0.0177497 | ||||||||
\(179\) | 8.87459e6i | 1.54735i | 0.633582 | + | 0.773676i | \(0.281584\pi\) | ||||
−0.633582 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(180\) | 7.00768e6i | 1.20159i | ||||||||
\(181\) | 3.01860e6 | 0.509060 | 0.254530 | − | 0.967065i | \(-0.418079\pi\) | ||||
0.254530 | + | 0.967065i | \(0.418079\pi\) | |||||||
\(182\) | −358240. | −0.0594237 | ||||||||
\(183\) | −1.55111e7 | −2.53099 | ||||||||
\(184\) | 2.27416e6i | 0.365062i | ||||||||
\(185\) | 4.83305e6 | 0.763319 | ||||||||
\(186\) | −5.23040e6 | −0.812823 | ||||||||
\(187\) | 11656.3 | 0.00178253 | ||||||||
\(188\) | 7.60322e6 | 1.14426 | ||||||||
\(189\) | 806894. | 0.119517 | ||||||||
\(190\) | − | 3.47947e6i | − | 0.507285i | ||||||
\(191\) | 1.43958e6i | 0.206602i | 0.994650 | + | 0.103301i | \(0.0329405\pi\) | ||||
−0.994650 | + | 0.103301i | \(0.967060\pi\) | |||||||
\(192\) | − | 2.81429e6i | − | 0.397617i | ||||||
\(193\) | −7.10710e6 | −0.988599 | −0.494300 | − | 0.869292i | \(-0.664575\pi\) | ||||
−0.494300 | + | 0.869292i | \(0.664575\pi\) | |||||||
\(194\) | 1.02015e6i | 0.139720i | ||||||||
\(195\) | 9.07087e6 | 1.22333 | ||||||||
\(196\) | 6.21267e6 | 0.825106 | ||||||||
\(197\) | 1.16308e7 | 1.52128 | 0.760640 | − | 0.649173i | \(-0.224885\pi\) | ||||
0.760640 | + | 0.649173i | \(0.224885\pi\) | |||||||
\(198\) | 302686.i | 0.0389939i | ||||||||
\(199\) | 9.37093e6i | 1.18911i | 0.804054 | + | 0.594557i | \(0.202672\pi\) | ||||
−0.804054 | + | 0.594557i | \(0.797328\pi\) | |||||||
\(200\) | − | 117919.i | − | 0.0147398i | ||||||
\(201\) | − | 2.39713e7i | − | 2.95191i | ||||||
\(202\) | − | 2.34743e6i | − | 0.284799i | ||||||
\(203\) | 1.07725e6 | 0.128774 | ||||||||
\(204\) | 265980.i | 0.0313299i | ||||||||
\(205\) | − | 9.93619e6i | − | 1.15334i | ||||||
\(206\) | 154277.i | 0.0176482i | ||||||||
\(207\) | −6.43900e6 | −0.725951 | ||||||||
\(208\) | −4.24222e6 | −0.471415 | ||||||||
\(209\) | 927148.i | 0.101557i | ||||||||
\(210\) | −1.09419e6 | −0.118150 | ||||||||
\(211\) | − | 1.53230e7i | − | 1.63116i | −0.578644 | − | 0.815580i | \(-0.696418\pi\) | ||
0.578644 | − | 0.815580i | \(-0.303582\pi\) | |||||||
\(212\) | 3.02058e6 | 0.317017 | ||||||||
\(213\) | 1.53100e7 | 1.58430 | ||||||||
\(214\) | 5.46645e6i | 0.557782i | ||||||||
\(215\) | −9.00895e6 | − | 4.43907e6i | −0.906481 | − | 0.446659i | ||||
\(216\) | −4.12609e6 | −0.409428 | ||||||||
\(217\) | 2.92287e6i | 0.286043i | ||||||||
\(218\) | − | 6.27646e6i | − | 0.605822i | ||||||
\(219\) | 1.98280e6 | 0.188776 | ||||||||
\(220\) | 699630.i | 0.0657053i | ||||||||
\(221\) | 199739. | 0.0185049 | ||||||||
\(222\) | 4.76352e6i | 0.435381i | ||||||||
\(223\) | 1.92740e7i | 1.73803i | 0.494789 | + | 0.869013i | \(0.335245\pi\) | ||||
−0.494789 | + | 0.869013i | \(0.664755\pi\) | |||||||
\(224\) | 2.09589e6 | 0.186477 | ||||||||
\(225\) | 333872. | 0.0293111 | ||||||||
\(226\) | −6.51839e6 | −0.564697 | ||||||||
\(227\) | 1.18617e7i | 1.01407i | 0.861924 | + | 0.507037i | \(0.169259\pi\) | ||||
−0.861924 | + | 0.507037i | \(0.830741\pi\) | |||||||
\(228\) | −2.11562e7 | −1.78498 | ||||||||
\(229\) | 4.46227e6 | 0.371577 | 0.185789 | − | 0.982590i | \(-0.440516\pi\) | ||||
0.185789 | + | 0.982590i | \(0.440516\pi\) | |||||||
\(230\) | 2.41255e6 | 0.198286 | ||||||||
\(231\) | 291561. | 0.0236534 | ||||||||
\(232\) | −5.50855e6 | −0.441137 | ||||||||
\(233\) | − | 2.31494e7i | − | 1.83009i | −0.403351 | − | 0.915045i | \(-0.632155\pi\) | ||
0.403351 | − | 0.915045i | \(-0.367845\pi\) | |||||||
\(234\) | 5.18673e6i | 0.404805i | ||||||||
\(235\) | − | 1.74393e7i | − | 1.34377i | ||||||
\(236\) | −9.75023e6 | −0.741786 | ||||||||
\(237\) | − | 9.75348e6i | − | 0.732680i | ||||||
\(238\) | −24093.9 | −0.00178721 | ||||||||
\(239\) | −1.52813e7 | −1.11935 | −0.559674 | − | 0.828713i | \(-0.689074\pi\) | ||||
−0.559674 | + | 0.828713i | \(0.689074\pi\) | |||||||
\(240\) | −1.29572e7 | −0.937299 | ||||||||
\(241\) | 1.36802e7i | 0.977330i | 0.872472 | + | 0.488665i | \(0.162516\pi\) | ||||
−0.872472 | + | 0.488665i | \(0.837484\pi\) | |||||||
\(242\) | − | 5.26294e6i | − | 0.371349i | ||||||
\(243\) | 1.89168e7i | 1.31835i | ||||||||
\(244\) | − | 2.05005e7i | − | 1.41122i | ||||||
\(245\) | − | 1.42498e7i | − | 0.968972i | ||||||
\(246\) | 9.79325e6 | 0.657842 | ||||||||
\(247\) | 1.58873e7i | 1.05429i | ||||||||
\(248\) | − | 1.49462e7i | − | 0.979889i | ||||||
\(249\) | 2.86627e6i | 0.185661i | ||||||||
\(250\) | 5.77213e6 | 0.369416 | ||||||||
\(251\) | 1.66557e7 | 1.05328 | 0.526638 | − | 0.850089i | \(-0.323452\pi\) | ||||
0.526638 | + | 0.850089i | \(0.323452\pi\) | |||||||
\(252\) | 3.85972e6i | 0.241187i | ||||||||
\(253\) | −642854. | −0.0396964 | ||||||||
\(254\) | 3.59649e6i | 0.219471i | ||||||||
\(255\) | 610072. | 0.0367926 | ||||||||
\(256\) | −2.04094e6 | −0.121649 | ||||||||
\(257\) | 1.62803e7i | 0.959101i | 0.877514 | + | 0.479550i | \(0.159200\pi\) | ||||
−0.877514 | + | 0.479550i | \(0.840800\pi\) | |||||||
\(258\) | 4.37520e6 | − | 8.87934e6i | 0.254765 | − | 0.517037i | ||||
\(259\) | 2.66197e6 | 0.153216 | ||||||||
\(260\) | 1.19886e7i | 0.682103i | ||||||||
\(261\) | − | 1.55968e7i | − | 0.877231i | ||||||
\(262\) | −7.68987e6 | −0.427578 | ||||||||
\(263\) | 2.85794e7i | 1.57104i | 0.618839 | + | 0.785518i | \(0.287603\pi\) | ||||
−0.618839 | + | 0.785518i | \(0.712397\pi\) | |||||||
\(264\) | −1.49091e6 | −0.0810287 | ||||||||
\(265\) | − | 6.92822e6i | − | 0.372292i | ||||||
\(266\) | − | 1.91644e6i | − | 0.101824i | ||||||
\(267\) | 1.39607e6 | 0.0733457 | ||||||||
\(268\) | 3.16820e7 | 1.64592 | ||||||||
\(269\) | 2.80627e7 | 1.44169 | 0.720846 | − | 0.693095i | \(-0.243753\pi\) | ||||
0.720846 | + | 0.693095i | \(0.243753\pi\) | |||||||
\(270\) | 4.37718e6i | 0.222384i | ||||||||
\(271\) | −1.61533e7 | −0.811622 | −0.405811 | − | 0.913957i | \(-0.633011\pi\) | ||||
−0.405811 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(272\) | −285316. | −0.0141781 | ||||||||
\(273\) | 4.99609e6 | 0.245551 | ||||||||
\(274\) | −2.97831e6 | −0.144783 | ||||||||
\(275\) | 33333.0 | 0.00160279 | ||||||||
\(276\) | − | 1.46690e7i | − | 0.697708i | ||||||
\(277\) | 3.22384e7i | 1.51682i | 0.651777 | + | 0.758410i | \(0.274024\pi\) | ||||
−0.651777 | + | 0.758410i | \(0.725976\pi\) | |||||||
\(278\) | − | 5.69496e6i | − | 0.265067i | ||||||
\(279\) | 4.23184e7 | 1.94858 | ||||||||
\(280\) | − | 3.12672e6i | − | 0.142434i | ||||||
\(281\) | −2.09764e7 | −0.945393 | −0.472697 | − | 0.881225i | \(-0.656719\pi\) | ||||
−0.472697 | + | 0.881225i | \(0.656719\pi\) | |||||||
\(282\) | 1.71884e7 | 0.766458 | ||||||||
\(283\) | 1.16336e7 | 0.513282 | 0.256641 | − | 0.966507i | \(-0.417384\pi\) | ||||
0.256641 | + | 0.966507i | \(0.417384\pi\) | |||||||
\(284\) | 2.02347e7i | 0.883370i | ||||||||
\(285\) | 4.85254e7i | 2.09621i | ||||||||
\(286\) | 517831.i | 0.0221355i | ||||||||
\(287\) | − | 5.47270e6i | − | 0.231503i | ||||||
\(288\) | − | 3.03451e7i | − | 1.27032i | ||||||
\(289\) | −2.41241e7 | −0.999443 | ||||||||
\(290\) | 5.84377e6i | 0.239607i | ||||||||
\(291\) | − | 1.42272e7i | − | 0.577352i | ||||||
\(292\) | 2.62060e6i | 0.105257i | ||||||||
\(293\) | −2.45473e7 | −0.975888 | −0.487944 | − | 0.872875i | \(-0.662253\pi\) | ||||
−0.487944 | + | 0.872875i | \(0.662253\pi\) | |||||||
\(294\) | 1.40448e7 | 0.552681 | ||||||||
\(295\) | 2.23638e7i | 0.871124i | ||||||||
\(296\) | −1.36121e7 | −0.524868 | ||||||||
\(297\) | − | 1.16636e6i | − | 0.0445206i | ||||||
\(298\) | 576381. | 0.0217801 | ||||||||
\(299\) | −1.10157e7 | −0.412098 | ||||||||
\(300\) | 760611.i | 0.0281708i | ||||||||
\(301\) | −4.96199e6 | − | 2.44497e6i | −0.181952 | − | 0.0896548i | ||||
\(302\) | 6.33533e6 | 0.230011 | ||||||||
\(303\) | 3.27377e7i | 1.17685i | ||||||||
\(304\) | − | 2.26941e7i | − | 0.807780i | ||||||
\(305\) | −4.70215e7 | −1.65728 | ||||||||
\(306\) | 348840.i | 0.0121748i | ||||||||
\(307\) | 1.50700e7 | 0.520831 | 0.260416 | − | 0.965497i | \(-0.416140\pi\) | ||||
0.260416 | + | 0.965497i | \(0.416140\pi\) | |||||||
\(308\) | 385345.i | 0.0131886i | ||||||||
\(309\) | − | 2.15159e6i | − | 0.0729262i | ||||||
\(310\) | −1.58558e7 | −0.532234 | ||||||||
\(311\) | 1.25190e7 | 0.416186 | 0.208093 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208093 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(312\) | −2.55477e7 | −0.841179 | ||||||||
\(313\) | − | 2.09806e7i | − | 0.684201i | −0.939663 | − | 0.342101i | \(-0.888862\pi\) | ||
0.939663 | − | 0.342101i | \(-0.111138\pi\) | |||||||
\(314\) | 1.42058e7 | 0.458858 | ||||||||
\(315\) | 8.85293e6 | 0.283241 | ||||||||
\(316\) | 1.28908e7 | 0.408526 | ||||||||
\(317\) | −3.56390e7 | −1.11879 | −0.559394 | − | 0.828902i | \(-0.688966\pi\) | ||||
−0.559394 | + | 0.828902i | \(0.688966\pi\) | |||||||
\(318\) | 6.82855e6 | 0.212347 | ||||||||
\(319\) | − | 1.55715e6i | − | 0.0479687i | ||||||
\(320\) | − | 8.53142e6i | − | 0.260358i | ||||||
\(321\) | − | 7.62363e7i | − | 2.30487i | ||||||
\(322\) | 1.32879e6 | 0.0398006 | ||||||||
\(323\) | 1.06852e6i | 0.0317085i | ||||||||
\(324\) | −1.38275e7 | −0.406546 | ||||||||
\(325\) | 571184. | 0.0166389 | ||||||||
\(326\) | 1.98322e6 | 0.0572424 | ||||||||
\(327\) | 8.75328e7i | 2.50338i | ||||||||
\(328\) | 2.79849e7i | 0.793053i | ||||||||
\(329\) | − | 9.60529e6i | − | 0.269726i | ||||||
\(330\) | 1.58164e6i | 0.0440113i | ||||||||
\(331\) | − | 4.51562e6i | − | 0.124518i | −0.998060 | − | 0.0622592i | \(-0.980169\pi\) | ||
0.998060 | − | 0.0622592i | \(-0.0198306\pi\) | |||||||
\(332\) | −3.78825e6 | −0.103520 | ||||||||
\(333\) | − | 3.85410e7i | − | 1.04373i | ||||||
\(334\) | 6.57467e6i | 0.176455i | ||||||||
\(335\) | − | 7.26682e7i | − | 1.93290i | ||||||
\(336\) | −7.13663e6 | −0.188138 | ||||||||
\(337\) | 3.54358e7 | 0.925876 | 0.462938 | − | 0.886391i | \(-0.346795\pi\) | ||||
0.462938 | + | 0.886391i | \(0.346795\pi\) | |||||||
\(338\) | − | 5.54840e6i | − | 0.143687i | ||||||
\(339\) | 9.09069e7 | 2.33345 | ||||||||
\(340\) | 806311.i | 0.0205147i | ||||||||
\(341\) | 4.22497e6 | 0.106552 | ||||||||
\(342\) | −2.77469e7 | −0.693643 | ||||||||
\(343\) | − | 1.60339e7i | − | 0.397336i | ||||||
\(344\) | 2.53733e7 | + | 1.25025e7i | 0.623307 | + | 0.307128i | ||||
\(345\) | −3.36459e7 | −0.819361 | ||||||||
\(346\) | − | 2.63240e7i | − | 0.635511i | ||||||
\(347\) | − | 7.07630e7i | − | 1.69363i | −0.531889 | − | 0.846814i | \(-0.678518\pi\) | ||
0.531889 | − | 0.846814i | \(-0.321482\pi\) | |||||||
\(348\) | 3.55319e7 | 0.843102 | ||||||||
\(349\) | 5.72662e6i | 0.134717i | 0.997729 | + | 0.0673585i | \(0.0214571\pi\) | ||||
−0.997729 | + | 0.0673585i | \(0.978543\pi\) | |||||||
\(350\) | −68900.0 | −0.00160700 | ||||||||
\(351\) | − | 1.99863e7i | − | 0.462180i | ||||||
\(352\) | − | 3.02959e6i | − | 0.0694633i | ||||||
\(353\) | −3.74887e7 | −0.852268 | −0.426134 | − | 0.904660i | \(-0.640125\pi\) | ||||
−0.426134 | + | 0.904660i | \(0.640125\pi\) | |||||||
\(354\) | −2.20421e7 | −0.496870 | ||||||||
\(355\) | 4.64119e7 | 1.03739 | ||||||||
\(356\) | 1.84514e6i | 0.0408959i | ||||||||
\(357\) | 336018. | 0.00738513 | ||||||||
\(358\) | −2.65160e7 | −0.577907 | ||||||||
\(359\) | 6.27195e6 | 0.135556 | 0.0677781 | − | 0.997700i | \(-0.478409\pi\) | ||||
0.0677781 | + | 0.997700i | \(0.478409\pi\) | |||||||
\(360\) | −4.52699e7 | −0.970290 | ||||||||
\(361\) | −3.79448e7 | −0.806548 | ||||||||
\(362\) | 9.01912e6i | 0.190125i | ||||||||
\(363\) | 7.33981e7i | 1.53449i | ||||||||
\(364\) | 6.60315e6i | 0.136914i | ||||||||
\(365\) | 6.01080e6 | 0.123610 | ||||||||
\(366\) | − | 4.63450e7i | − | 0.945278i | ||||||
\(367\) | −6.87779e6 | −0.139140 | −0.0695698 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695698 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(368\) | 1.57354e7 | 0.315743 | ||||||||
\(369\) | −7.92358e7 | −1.57704 | ||||||||
\(370\) | 1.44404e7i | 0.285086i | ||||||||
\(371\) | − | 3.81596e6i | − | 0.0747277i | ||||||
\(372\) | 9.64078e7i | 1.87277i | ||||||||
\(373\) | 9.99739e6i | 0.192646i | 0.995350 | + | 0.0963231i | \(0.0307082\pi\) | ||||
−0.995350 | + | 0.0963231i | \(0.969292\pi\) | |||||||
\(374\) | 34827.4i | 0.000665742i | ||||||||
\(375\) | −8.04993e7 | −1.52650 | ||||||||
\(376\) | 4.91171e7i | 0.923994i | ||||||||
\(377\) | − | 2.66828e7i | − | 0.497974i | ||||||
\(378\) | 2.41088e6i | 0.0446376i | ||||||||
\(379\) | 9.50197e7 | 1.74540 | 0.872702 | − | 0.488253i | \(-0.162366\pi\) | ||||
0.872702 | + | 0.488253i | \(0.162366\pi\) | |||||||
\(380\) | −6.41343e7 | −1.16880 | ||||||||
\(381\) | − | 5.01574e7i | − | 0.906902i | ||||||
\(382\) | −4.30124e6 | −0.0771620 | ||||||||
\(383\) | − | 4.30196e7i | − | 0.765720i | −0.923806 | − | 0.382860i | \(-0.874939\pi\) | ||
0.923806 | − | 0.382860i | \(-0.125061\pi\) | |||||||
\(384\) | 8.87456e7 | 1.56730 | ||||||||
\(385\) | 883856. | 0.0154881 | ||||||||
\(386\) | − | 2.12350e7i | − | 0.369224i | ||||||
\(387\) | −3.53992e7 | + | 7.18415e7i | −0.610745 | + | 1.23949i | ||||
\(388\) | 1.88036e7 | 0.321919 | ||||||||
\(389\) | 3.21983e6i | 0.0546996i | 0.999626 | + | 0.0273498i | \(0.00870680\pi\) | ||||
−0.999626 | + | 0.0273498i | \(0.991293\pi\) | |||||||
\(390\) | 2.71024e7i | 0.456893i | ||||||||
\(391\) | −740878. | −0.0123941 | ||||||||
\(392\) | 4.01341e7i | 0.666277i | ||||||||
\(393\) | 1.07244e8 | 1.76684 | ||||||||
\(394\) | 3.47510e7i | 0.568170i | ||||||||
\(395\) | − | 2.95673e7i | − | 0.479756i | ||||||
\(396\) | 5.57917e6 | 0.0898430 | ||||||||
\(397\) | −5.56628e7 | −0.889597 | −0.444799 | − | 0.895631i | \(-0.646725\pi\) | ||||
−0.444799 | + | 0.895631i | \(0.646725\pi\) | |||||||
\(398\) | −2.79990e7 | −0.444112 | ||||||||
\(399\) | 2.67270e7i | 0.420758i | ||||||||
\(400\) | −815903. | −0.0127485 | ||||||||
\(401\) | 1.03598e8 | 1.60664 | 0.803319 | − | 0.595549i | \(-0.203065\pi\) | ||||
0.803319 | + | 0.595549i | \(0.203065\pi\) | |||||||
\(402\) | 7.16227e7 | 1.10248 | ||||||||
\(403\) | 7.23978e7 | 1.10614 | ||||||||
\(404\) | −4.32683e7 | −0.656184 | ||||||||
\(405\) | 3.17158e7i | 0.477432i | ||||||||
\(406\) | 3.21866e6i | 0.0480946i | ||||||||
\(407\) | − | 3.84784e6i | − | 0.0570734i | ||||||
\(408\) | −1.71824e6 | −0.0252990 | ||||||||
\(409\) | 4.89797e7i | 0.715890i | 0.933743 | + | 0.357945i | \(0.116522\pi\) | ||||
−0.933743 | + | 0.357945i | \(0.883478\pi\) | |||||||
\(410\) | 2.96879e7 | 0.430752 | ||||||||
\(411\) | 4.15361e7 | 0.598274 | ||||||||
\(412\) | 2.84367e6 | 0.0406620 | ||||||||
\(413\) | 1.23176e7i | 0.174855i | ||||||||
\(414\) | − | 1.92388e7i | − | 0.271129i | ||||||
\(415\) | 8.68901e6i | 0.121570i | ||||||||
\(416\) | − | 5.19140e7i | − | 0.721115i | ||||||
\(417\) | 7.94231e7i | 1.09531i | ||||||||
\(418\) | −2.77018e6 | −0.0379297 | ||||||||
\(419\) | − | 1.02750e8i | − | 1.39682i | −0.715699 | − | 0.698408i | \(-0.753892\pi\) | ||
0.715699 | − | 0.698408i | \(-0.246108\pi\) | |||||||
\(420\) | 2.01683e7i | 0.272221i | ||||||||
\(421\) | 5.62844e7i | 0.754296i | 0.926153 | + | 0.377148i | \(0.123095\pi\) | ||||
−0.926153 | + | 0.377148i | \(0.876905\pi\) | |||||||
\(422\) | 4.57829e7 | 0.609208 | ||||||||
\(423\) | −1.39069e8 | −1.83742 | ||||||||
\(424\) | 1.95131e7i | 0.255993i | ||||||||
\(425\) | 38415.6 | 0.000500428 | ||||||||
\(426\) | 4.57442e7i | 0.591707i | ||||||||
\(427\) | −2.58987e7 | −0.332655 | ||||||||
\(428\) | 1.00759e8 | 1.28514 | ||||||||
\(429\) | − | 7.22178e6i | − | 0.0914687i | ||||||
\(430\) | 1.32633e7 | − | 2.69174e7i | 0.166819 | − | 0.338554i | ||||
\(431\) | −7.60304e7 | −0.949632 | −0.474816 | − | 0.880085i | \(-0.657485\pi\) | ||||
−0.474816 | + | 0.880085i | \(0.657485\pi\) | |||||||
\(432\) | 2.85493e7i | 0.354115i | ||||||||
\(433\) | − | 1.14226e7i | − | 0.140702i | −0.997522 | − | 0.0703511i | \(-0.977588\pi\) | ||
0.997522 | − | 0.0703511i | \(-0.0224120\pi\) | |||||||
\(434\) | −8.73311e6 | −0.106832 | ||||||||
\(435\) | − | 8.14985e7i | − | 0.990106i | ||||||
\(436\) | −1.15689e8 | −1.39583 | ||||||||
\(437\) | − | 5.89297e7i | − | 0.706139i | ||||||
\(438\) | 5.92432e6i | 0.0705044i | ||||||||
\(439\) | −2.07515e7 | −0.245277 | −0.122638 | − | 0.992451i | \(-0.539136\pi\) | ||||
−0.122638 | + | 0.992451i | \(0.539136\pi\) | |||||||
\(440\) | −4.51963e6 | −0.0530573 | ||||||||
\(441\) | −1.13635e8 | −1.32494 | ||||||||
\(442\) | 596791.i | 0.00691123i | ||||||||
\(443\) | −1.36002e7 | −0.156435 | −0.0782175 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782175 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(444\) | 8.78022e7 | 1.00313 | ||||||||
\(445\) | 4.23215e6 | 0.0480265 | ||||||||
\(446\) | −5.75878e7 | −0.649121 | ||||||||
\(447\) | −8.03832e6 | −0.0900001 | ||||||||
\(448\) | − | 4.69897e6i | − | 0.0522599i | ||||||
\(449\) | − | 1.38176e8i | − | 1.52649i | −0.646107 | − | 0.763246i | \(-0.723604\pi\) | ||
0.646107 | − | 0.763246i | \(-0.276396\pi\) | |||||||
\(450\) | 997560.i | 0.0109472i | ||||||||
\(451\) | −7.91072e6 | −0.0862355 | ||||||||
\(452\) | 1.20148e8i | 1.30108i | ||||||||
\(453\) | −8.83538e7 | −0.950453 | ||||||||
\(454\) | −3.54410e7 | −0.378738 | ||||||||
\(455\) | 1.51455e7 | 0.160786 | ||||||||
\(456\) | − | 1.36670e8i | − | 1.44138i | ||||||
\(457\) | 1.58547e7i | 0.166116i | 0.996545 | + | 0.0830578i | \(0.0264686\pi\) | ||||
−0.996545 | + | 0.0830578i | \(0.973531\pi\) | |||||||
\(458\) | 1.33326e7i | 0.138777i | ||||||||
\(459\) | − | 1.34420e6i | − | 0.0139004i | ||||||
\(460\) | − | 4.44686e7i | − | 0.456857i | ||||||
\(461\) | 1.06966e8 | 1.09180 | 0.545901 | − | 0.837849i | \(-0.316187\pi\) | ||||
0.545901 | + | 0.837849i | \(0.316187\pi\) | |||||||
\(462\) | 871140.i | 0.00883409i | ||||||||
\(463\) | 6.74339e7i | 0.679415i | 0.940531 | + | 0.339707i | \(0.110328\pi\) | ||||
−0.940531 | + | 0.339707i | \(0.889672\pi\) | |||||||
\(464\) | 3.81148e7i | 0.381540i | ||||||||
\(465\) | 2.21128e8 | 2.19930 | ||||||||
\(466\) | 6.91671e7 | 0.683505 | ||||||||
\(467\) | 1.09689e8i | 1.07699i | 0.842627 | + | 0.538497i | \(0.181008\pi\) | ||||
−0.842627 | + | 0.538497i | \(0.818992\pi\) | |||||||
\(468\) | 9.56030e7 | 0.932682 | ||||||||
\(469\) | − | 4.00245e7i | − | 0.387978i | ||||||
\(470\) | 5.21061e7 | 0.501874 | ||||||||
\(471\) | −1.98118e8 | −1.89610 | ||||||||
\(472\) | − | 6.29868e7i | − | 0.598996i | ||||||
\(473\) | −3.53417e6 | + | 7.17249e6i | −0.0333967 | + | 0.0677776i | ||||
\(474\) | 2.91420e7 | 0.273643 | ||||||||
\(475\) | 3.05560e6i | 0.0285112i | ||||||||
\(476\) | 444103.i | 0.00411778i | ||||||||
\(477\) | −5.52488e7 | −0.509059 | ||||||||
\(478\) | − | 4.56582e7i | − | 0.418056i | ||||||
\(479\) | −1.79146e8 | −1.63005 | −0.815026 | − | 0.579425i | \(-0.803277\pi\) | ||||
−0.815026 | + | 0.579425i | \(0.803277\pi\) | |||||||
\(480\) | − | 1.58563e8i | − | 1.43377i | ||||||
\(481\) | − | 6.59354e7i | − | 0.592493i | ||||||
\(482\) | −4.08744e7 | −0.365015 | ||||||||
\(483\) | −1.85316e7 | −0.164465 | ||||||||
\(484\) | −9.70077e7 | −0.855599 | ||||||||
\(485\) | − | 4.31293e7i | − | 0.378048i | ||||||
\(486\) | −5.65208e7 | −0.492379 | ||||||||
\(487\) | 2.19363e8 | 1.89922 | 0.949612 | − | 0.313428i | \(-0.101477\pi\) | ||||
0.949612 | + | 0.313428i | \(0.101477\pi\) | |||||||
\(488\) | 1.32434e8 | 1.13957 | ||||||||
\(489\) | −2.76584e7 | −0.236538 | ||||||||
\(490\) | 4.25764e7 | 0.361893 | ||||||||
\(491\) | 4.75542e7i | 0.401740i | 0.979618 | + | 0.200870i | \(0.0643768\pi\) | ||||
−0.979618 | + | 0.200870i | \(0.935623\pi\) | |||||||
\(492\) | − | 1.80511e8i | − | 1.51568i | ||||||
\(493\) | − | 1.79458e6i | − | 0.0149769i | ||||||
\(494\) | −4.74690e7 | −0.393758 | ||||||||
\(495\) | − | 1.27968e7i | − | 0.105508i | ||||||
\(496\) | −1.03416e8 | −0.847507 | ||||||||
\(497\) | 2.55629e7 | 0.208229 | ||||||||
\(498\) | −8.56401e6 | −0.0693408 | ||||||||
\(499\) | − | 1.26074e8i | − | 1.01467i | −0.861750 | − | 0.507333i | \(-0.830632\pi\) | ||
0.861750 | − | 0.507333i | \(-0.169368\pi\) | |||||||
\(500\) | − | 1.06393e8i | − | 0.851144i | ||||||
\(501\) | − | 9.16917e7i | − | 0.729150i | ||||||
\(502\) | 4.97649e7i | 0.393380i | ||||||||
\(503\) | 1.56016e8i | 1.22593i | 0.790110 | + | 0.612965i | \(0.210023\pi\) | ||||
−0.790110 | + | 0.612965i | \(0.789977\pi\) | |||||||
\(504\) | −2.49339e7 | −0.194760 | ||||||||
\(505\) | 9.92432e7i | 0.770596i | ||||||||
\(506\) | − | 1.92075e6i | − | 0.0148259i | ||||||
\(507\) | 7.73792e7i | 0.593746i | ||||||||
\(508\) | 6.62913e7 | 0.505668 | ||||||||
\(509\) | −3.00795e7 | −0.228096 | −0.114048 | − | 0.993475i | \(-0.536382\pi\) | ||||
−0.114048 | + | 0.993475i | \(0.536382\pi\) | |||||||
\(510\) | 1.82281e6i | 0.0137414i | ||||||||
\(511\) | 3.31065e6 | 0.0248114 | ||||||||
\(512\) | 1.30207e8i | 0.970116i | ||||||||
\(513\) | 1.06918e8 | 0.791955 | ||||||||
\(514\) | −4.86433e7 | −0.358206 | ||||||||
\(515\) | − | 6.52246e6i | − | 0.0477518i | ||||||
\(516\) | −1.63666e8 | − | 8.06447e7i | −1.19127 | − | 0.586984i | ||||
\(517\) | −1.38843e7 | −0.100474 | ||||||||
\(518\) | 7.95357e6i | 0.0572233i | ||||||||
\(519\) | 3.67119e8i | 2.62606i | ||||||||
\(520\) | −7.74470e7 | −0.550801 | ||||||||
\(521\) | − | 7.50174e7i | − | 0.530455i | −0.964186 | − | 0.265228i | \(-0.914553\pi\) | ||
0.964186 | − | 0.265228i | \(-0.0854471\pi\) | |||||||
\(522\) | 4.66009e7 | 0.327630 | ||||||||
\(523\) | − | 7.31971e6i | − | 0.0511668i | −0.999673 | − | 0.0255834i | \(-0.991856\pi\) | ||
0.999673 | − | 0.0255834i | \(-0.00814435\pi\) | |||||||
\(524\) | 1.41741e8i | 0.985150i | ||||||||
\(525\) | 960894. | 0.00664045 | ||||||||
\(526\) | −8.53911e7 | −0.586753 | ||||||||
\(527\) | 4.86920e6 | 0.0332680 | ||||||||
\(528\) | 1.03159e7i | 0.0700819i | ||||||||
\(529\) | −1.07176e8 | −0.723986 | ||||||||
\(530\) | 2.07005e7 | 0.139044 | ||||||||
\(531\) | 1.78339e8 | 1.19114 | ||||||||
\(532\) | −3.53242e7 | −0.234605 | ||||||||
\(533\) | −1.35556e8 | −0.895232 | ||||||||
\(534\) | 4.17126e6i | 0.0273933i | ||||||||
\(535\) | − | 2.31108e8i | − | 1.50922i | ||||||
\(536\) | 2.04667e8i | 1.32909i | ||||||||
\(537\) | 3.69797e8 | 2.38804 | ||||||||
\(538\) | 8.38472e7i | 0.538446i | ||||||||
\(539\) | −1.13450e7 | −0.0724501 | ||||||||
\(540\) | 8.06811e7 | 0.512378 | ||||||||
\(541\) | −1.94691e7 | −0.122957 | −0.0614785 | − | 0.998108i | \(-0.519582\pi\) | ||||
−0.0614785 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(542\) | − | 4.82638e7i | − | 0.303126i | ||||||
\(543\) | − | 1.25783e8i | − | 0.785635i | ||||||
\(544\) | − | 3.49154e6i | − | 0.0216880i | ||||||
\(545\) | 2.65353e8i | 1.63921i | ||||||||
\(546\) | 1.49276e7i | 0.0917089i | ||||||||
\(547\) | 9.15424e7 | 0.559320 | 0.279660 | − | 0.960099i | \(-0.409778\pi\) | ||||
0.279660 | + | 0.960099i | \(0.409778\pi\) | |||||||
\(548\) | 5.48968e7i | 0.333584i | ||||||||
\(549\) | 3.74971e8i | 2.26611i | ||||||||
\(550\) | 99594.1i | 0.000598612i | ||||||||
\(551\) | 1.42742e8 | 0.853290 | ||||||||
\(552\) | 9.47624e7 | 0.563402 | ||||||||
\(553\) | − | 1.62852e7i | − | 0.0962982i | ||||||
\(554\) | −9.63236e7 | −0.566505 | ||||||||
\(555\) | − | 2.01390e8i | − | 1.17803i | ||||||
\(556\) | −1.04971e8 | −0.610722 | ||||||||
\(557\) | 2.38280e7 | 0.137886 | 0.0689432 | − | 0.997621i | \(-0.478037\pi\) | ||||
0.0689432 | + | 0.997621i | \(0.478037\pi\) | |||||||
\(558\) | 1.26441e8i | 0.727757i | ||||||||
\(559\) | −6.05604e7 | + | 1.22905e8i | −0.346700 | + | 0.703616i | ||||
\(560\) | −2.16344e7 | −0.123192 | ||||||||
\(561\) | − | 485710.i | − | 0.00275099i | ||||||
\(562\) | − | 6.26745e7i | − | 0.353087i | ||||||
\(563\) | −1.26545e8 | −0.709123 | −0.354561 | − | 0.935033i | \(-0.615370\pi\) | ||||
−0.354561 | + | 0.935033i | \(0.615370\pi\) | |||||||
\(564\) | − | 3.16820e8i | − | 1.76594i | ||||||
\(565\) | 2.75581e8 | 1.52793 | ||||||||
\(566\) | 3.47596e7i | 0.191701i | ||||||||
\(567\) | 1.74686e7i | 0.0958316i | ||||||||
\(568\) | −1.30717e8 | −0.713325 | ||||||||
\(569\) | 2.44261e8 | 1.32592 | 0.662959 | − | 0.748656i | \(-0.269300\pi\) | ||||
0.662959 | + | 0.748656i | \(0.269300\pi\) | |||||||
\(570\) | −1.44987e8 | −0.782895 | ||||||||
\(571\) | − | 2.69338e8i | − | 1.44674i | −0.690462 | − | 0.723368i | \(-0.742593\pi\) | ||
0.690462 | − | 0.723368i | \(-0.257407\pi\) | |||||||
\(572\) | 9.54477e6 | 0.0510009 | ||||||||
\(573\) | 5.99860e7 | 0.318850 | ||||||||
\(574\) | 1.63516e7 | 0.0864620 | ||||||||
\(575\) | −2.11865e6 | −0.0111444 | ||||||||
\(576\) | −6.80335e7 | −0.356004 | ||||||||
\(577\) | 1.55241e8i | 0.808126i | 0.914731 | + | 0.404063i | \(0.132402\pi\) | ||||
−0.914731 | + | 0.404063i | \(0.867598\pi\) | |||||||
\(578\) | − | 7.20794e7i | − | 0.373274i | ||||||
\(579\) | 2.96147e8i | 1.52571i | ||||||||
\(580\) | 1.07714e8 | 0.552060 | ||||||||
\(581\) | 4.78577e6i | 0.0244019i | ||||||||
\(582\) | 4.25088e7 | 0.215631 | ||||||||
\(583\) | −5.51591e6 | −0.0278363 | ||||||||
\(584\) | −1.69292e7 | −0.0849957 | ||||||||
\(585\) | − | 2.19282e8i | − | 1.09531i | ||||||
\(586\) | − | 7.33436e7i | − | 0.364476i | ||||||
\(587\) | − | 1.52542e8i | − | 0.754179i | −0.926177 | − | 0.377090i | \(-0.876925\pi\) | ||
0.926177 | − | 0.377090i | \(-0.123075\pi\) | |||||||
\(588\) | − | 2.58877e8i | − | 1.27339i | ||||||
\(589\) | 3.87299e8i | 1.89540i | ||||||||
\(590\) | −6.68198e7 | −0.325349 | ||||||||
\(591\) | − | 4.84645e8i | − | 2.34780i | ||||||
\(592\) | 9.41850e7i | 0.453959i | ||||||||
\(593\) | 2.05477e8i | 0.985369i | 0.870208 | + | 0.492685i | \(0.163984\pi\) | ||||
−0.870208 | + | 0.492685i | \(0.836016\pi\) | |||||||
\(594\) | 3.48490e6 | 0.0166276 | ||||||||
\(595\) | 1.01863e6 | 0.00483576 | ||||||||
\(596\) | − | 1.06240e7i | − | 0.0501820i | ||||||
\(597\) | 3.90479e8 | 1.83516 | ||||||||
\(598\) | − | 3.29134e7i | − | 0.153911i | ||||||
\(599\) | 2.54531e8 | 1.18430 | 0.592149 | − | 0.805829i | \(-0.298280\pi\) | ||||
0.592149 | + | 0.805829i | \(0.298280\pi\) | |||||||
\(600\) | −4.91357e6 | −0.0227480 | ||||||||
\(601\) | − | 1.86617e8i | − | 0.859661i | −0.902910 | − | 0.429831i | \(-0.858573\pi\) | ||
0.902910 | − | 0.429831i | \(-0.141427\pi\) | |||||||
\(602\) | 7.30520e6 | − | 1.48257e7i | 0.0334844 | − | 0.0679556i | ||||
\(603\) | −5.79489e8 | −2.64298 | ||||||||
\(604\) | − | 1.16774e8i | − | 0.529951i | ||||||
\(605\) | 2.22504e8i | 1.00478i | ||||||||
\(606\) | −9.78155e7 | −0.439531 | ||||||||
\(607\) | 5.73996e7i | 0.256651i | 0.991732 | + | 0.128325i | \(0.0409602\pi\) | ||||
−0.991732 | + | 0.128325i | \(0.959040\pi\) | |||||||
\(608\) | 2.77719e8 | 1.23565 | ||||||||
\(609\) | − | 4.48881e7i | − | 0.198737i | ||||||
\(610\) | − | 1.40493e8i | − | 0.618965i | ||||||
\(611\) | −2.37917e8 | −1.04304 | ||||||||
\(612\) | 6.42989e6 | 0.0280511 | ||||||||
\(613\) | −1.23866e8 | −0.537739 | −0.268869 | − | 0.963177i | \(-0.586650\pi\) | ||||
−0.268869 | + | 0.963177i | \(0.586650\pi\) | |||||||
\(614\) | 4.50268e7i | 0.194521i | ||||||||
\(615\) | −4.14034e8 | −1.77996 | ||||||||
\(616\) | −2.48934e6 | −0.0106498 | ||||||||
\(617\) | −2.71924e7 | −0.115769 | −0.0578845 | − | 0.998323i | \(-0.518436\pi\) | ||||
−0.0578845 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(618\) | 6.42862e6 | 0.0272366 | ||||||||
\(619\) | −2.18698e8 | −0.922091 | −0.461045 | − | 0.887377i | \(-0.652525\pi\) | ||||
−0.461045 | + | 0.887377i | \(0.652525\pi\) | |||||||
\(620\) | 2.92257e8i | 1.22628i | ||||||||
\(621\) | 7.41337e7i | 0.309557i | ||||||||
\(622\) | 3.74049e7i | 0.155438i | ||||||||
\(623\) | 2.33100e6 | 0.00964003 | ||||||||
\(624\) | 1.76770e8i | 0.727537i | ||||||||
\(625\) | −2.49210e8 | −1.02076 | ||||||||
\(626\) | 6.26868e7 | 0.255537 | ||||||||
\(627\) | 3.86336e7 | 0.156734 | ||||||||
\(628\) | − | 2.61845e8i | − | 1.05722i | ||||||
\(629\) | − | 4.43456e6i | − | 0.0178196i | ||||||
\(630\) | 2.64513e7i | 0.105785i | ||||||||
\(631\) | 3.08632e8i | 1.22844i | 0.789135 | + | 0.614219i | \(0.210529\pi\) | ||||
−0.789135 | + | 0.614219i | \(0.789471\pi\) | |||||||
\(632\) | 8.32752e7i | 0.329886i | ||||||||
\(633\) | −6.38498e8 | −2.51738 | ||||||||
\(634\) | − | 1.06484e8i | − | 0.417847i | ||||||
\(635\) | − | 1.52051e8i | − | 0.593836i | ||||||
\(636\) | − | 1.25865e8i | − | 0.489254i | ||||||
\(637\) | −1.94405e8 | −0.752122 | ||||||||
\(638\) | 4.65253e6 | 0.0179154 | ||||||||
\(639\) | − | 3.70110e8i | − | 1.41849i | ||||||
\(640\) | 2.69029e8 | 1.02626 | ||||||||
\(641\) | − | 2.78366e8i | − | 1.05692i | −0.848958 | − | 0.528460i | \(-0.822770\pi\) | ||
0.848958 | − | 0.528460i | \(-0.177230\pi\) | |||||||
\(642\) | 2.27783e8 | 0.860827 | ||||||||
\(643\) | 3.11174e8 | 1.17050 | 0.585248 | − | 0.810855i | \(-0.300997\pi\) | ||||
0.585248 | + | 0.810855i | \(0.300997\pi\) | |||||||
\(644\) | − | 2.44926e7i | − | 0.0917017i | ||||||
\(645\) | −1.84972e8 | + | 3.75396e8i | −0.689331 | + | 1.39898i | ||||
\(646\) | −3.19258e6 | −0.0118425 | ||||||||
\(647\) | − | 4.55247e8i | − | 1.68087i | −0.541913 | − | 0.840435i | \(-0.682300\pi\) | ||
0.541913 | − | 0.840435i | \(-0.317700\pi\) | |||||||
\(648\) | − | 8.93264e7i | − | 0.328288i | ||||||
\(649\) | 1.78050e7 | 0.0651340 | ||||||||
\(650\) | 1.70661e6i | 0.00621434i | ||||||||
\(651\) | 1.21794e8 | 0.441451 | ||||||||
\(652\) | − | 3.65551e7i | − | 0.131888i | ||||||
\(653\) | − | 1.72465e8i | − | 0.619386i | −0.950837 | − | 0.309693i | \(-0.899774\pi\) | ||
0.950837 | − | 0.309693i | \(-0.100226\pi\) | |||||||
\(654\) | −2.61535e8 | −0.934968 | ||||||||
\(655\) | 3.25108e8 | 1.15692 | ||||||||
\(656\) | 1.93633e8 | 0.685913 | ||||||||
\(657\) | − | 4.79329e7i | − | 0.169020i | ||||||
\(658\) | 2.86992e7 | 0.100738 | ||||||||
\(659\) | −3.61115e7 | −0.126180 | −0.0630898 | − | 0.998008i | \(-0.520095\pi\) | ||||
−0.0630898 | + | 0.998008i | \(0.520095\pi\) | |||||||
\(660\) | 2.91530e7 | 0.101403 | ||||||||
\(661\) | −4.17097e8 | −1.44422 | −0.722109 | − | 0.691779i | \(-0.756827\pi\) | ||||
−0.722109 | + | 0.691779i | \(0.756827\pi\) | |||||||
\(662\) | 1.34920e7 | 0.0465054 | ||||||||
\(663\) | − | 8.32297e6i | − | 0.0285587i | ||||||
\(664\) | − | 2.44722e7i | − | 0.0835929i | ||||||
\(665\) | 8.10220e7i | 0.275511i | ||||||||
\(666\) | 1.15155e8 | 0.389816 | ||||||||
\(667\) | 9.89725e7i | 0.333532i | ||||||||
\(668\) | 1.21186e8 | 0.406557 | ||||||||
\(669\) | 8.03131e8 | 2.68230 | ||||||||
\(670\) | 2.17122e8 | 0.721903 | ||||||||
\(671\) | 3.74362e7i | 0.123915i | ||||||||
\(672\) | − | 8.73342e7i | − | 0.287791i | ||||||
\(673\) | − | 5.11802e8i | − | 1.67902i | −0.543341 | − | 0.839512i | \(-0.682841\pi\) | ||
0.543341 | − | 0.839512i | \(-0.317159\pi\) | |||||||
\(674\) | 1.05877e8i | 0.345798i | ||||||||
\(675\) | − | 3.84395e6i | − | 0.0124987i | ||||||
\(676\) | −1.02269e8 | −0.331059 | ||||||||
\(677\) | 1.81913e8i | 0.586269i | 0.956071 | + | 0.293134i | \(0.0946984\pi\) | ||||
−0.956071 | + | 0.293134i | \(0.905302\pi\) | |||||||
\(678\) | 2.71616e8i | 0.871499i | ||||||||
\(679\) | − | 2.37549e7i | − | 0.0758830i | ||||||
\(680\) | −5.20880e6 | −0.0165657 | ||||||||
\(681\) | 4.94268e8 | 1.56502 | ||||||||
\(682\) | 1.26236e7i | 0.0397951i | ||||||||
\(683\) | 4.25041e8 | 1.33404 | 0.667020 | − | 0.745040i | \(-0.267569\pi\) | ||||
0.667020 | + | 0.745040i | \(0.267569\pi\) | |||||||
\(684\) | 5.11436e8i | 1.59817i | ||||||||
\(685\) | 1.25915e8 | 0.391748 | ||||||||
\(686\) | 4.79071e7 | 0.148398 | ||||||||
\(687\) | − | 1.85939e8i | − | 0.573457i | ||||||
\(688\) | 8.65071e7 | − | 1.75564e8i | 0.265636 | − | 0.539100i | ||||
\(689\) | −9.45190e7 | −0.288976 | ||||||||
\(690\) | − | 1.00529e8i | − | 0.306016i | ||||||
\(691\) | 1.14153e8i | 0.345982i | 0.984923 | + | 0.172991i | \(0.0553432\pi\) | ||||
−0.984923 | + | 0.172991i | \(0.944657\pi\) | |||||||
\(692\) | −4.85209e8 | −1.46423 | ||||||||
\(693\) | − | 7.04827e6i | − | 0.0211779i | ||||||
\(694\) | 2.11430e8 | 0.632539 | ||||||||
\(695\) | 2.40768e8i | 0.717208i | ||||||||
\(696\) | 2.29537e8i | 0.680809i | ||||||||
\(697\) | −9.11695e6 | −0.0269247 | ||||||||
\(698\) | −1.71103e7 | −0.0503143 | ||||||||
\(699\) | −9.64619e8 | −2.82439 | ||||||||
\(700\) | 1.26998e6i | 0.00370256i | ||||||||
\(701\) | −2.36723e8 | −0.687204 | −0.343602 | − | 0.939115i | \(-0.611647\pi\) | ||||
−0.343602 | + | 0.939115i | \(0.611647\pi\) | |||||||
\(702\) | 5.97161e7 | 0.172616 | ||||||||
\(703\) | 3.52727e8 | 1.01525 | ||||||||
\(704\) | −6.79230e6 | −0.0194670 | ||||||||
\(705\) | −7.26682e8 | −2.07385 | ||||||||
\(706\) | − | 1.12011e8i | − | 0.318306i | ||||||
\(707\) | 5.46616e7i | 0.154676i | ||||||||
\(708\) | 4.06284e8i | 1.14480i | ||||||||
\(709\) | 4.51159e7 | 0.126588 | 0.0632938 | − | 0.997995i | \(-0.479839\pi\) | ||||
0.0632938 | + | 0.997995i | \(0.479839\pi\) | |||||||
\(710\) | 1.38672e8i | 0.387448i | ||||||||
\(711\) | −2.35784e8 | −0.656001 | ||||||||
\(712\) | −1.19197e7 | −0.0330236 | ||||||||
\(713\) | −2.68540e8 | −0.740867 | ||||||||
\(714\) | 1.00397e6i | 0.00275821i | ||||||||
\(715\) | − | 2.18926e7i | − | 0.0598934i | ||||||
\(716\) | 4.88748e8i | 1.33151i | ||||||||
\(717\) | 6.36758e8i | 1.72750i | ||||||||
\(718\) | 1.87397e7i | 0.0506277i | ||||||||
\(719\) | 6.75759e8 | 1.81805 | 0.909024 | − | 0.416744i | \(-0.136829\pi\) | ||||
0.909024 | + | 0.416744i | \(0.136829\pi\) | |||||||
\(720\) | 3.13232e8i | 0.839205i | ||||||||
\(721\) | − | 3.59247e6i | − | 0.00958489i | ||||||
\(722\) | − | 1.13373e8i | − | 0.301231i | ||||||
\(723\) | 5.70043e8 | 1.50832 | ||||||||
\(724\) | 1.66242e8 | 0.438052 | ||||||||
\(725\) | − | 5.13188e6i | − | 0.0134667i | ||||||
\(726\) | −2.19303e8 | −0.573105 | ||||||||
\(727\) | 1.12489e8i | 0.292758i | 0.989229 | + | 0.146379i | \(0.0467618\pi\) | ||||
−0.989229 | + | 0.146379i | \(0.953238\pi\) | |||||||
\(728\) | −4.26566e7 | −0.110559 | ||||||||
\(729\) | 6.05215e8 | 1.56216 | ||||||||
\(730\) | 1.79594e7i | 0.0461660i | ||||||||
\(731\) | −4.07306e6 | + | 8.26616e6i | −0.0104272 | + | 0.0211618i | ||||
\(732\) | −8.54241e8 | −2.17795 | ||||||||
\(733\) | 6.77003e8i | 1.71901i | 0.511126 | + | 0.859506i | \(0.329229\pi\) | ||||
−0.511126 | + | 0.859506i | \(0.670771\pi\) | |||||||
\(734\) | − | 2.05498e7i | − | 0.0519661i | ||||||
\(735\) | −5.93779e8 | −1.49542 | ||||||||
\(736\) | 1.92561e8i | 0.482986i | ||||||||
\(737\) | −5.78549e7 | −0.144523 | ||||||||
\(738\) | − | 2.36745e8i | − | 0.588995i | ||||||
\(739\) | − | 5.36084e8i | − | 1.32831i | −0.747595 | − | 0.664155i | \(-0.768791\pi\) | ||
0.747595 | − | 0.664155i | \(-0.231209\pi\) | |||||||
\(740\) | 2.66169e8 | 0.656845 | ||||||||
\(741\) | 6.62013e8 | 1.62709 | ||||||||
\(742\) | 1.14015e7 | 0.0279094 | ||||||||
\(743\) | − | 2.50988e7i | − | 0.0611909i | −0.999532 | − | 0.0305955i | \(-0.990260\pi\) | ||
0.999532 | − | 0.0305955i | \(-0.00974036\pi\) | |||||||
\(744\) | −6.22798e8 | −1.51227 | ||||||||
\(745\) | −2.43679e7 | −0.0589318 | ||||||||
\(746\) | −2.98707e7 | −0.0719498 | ||||||||
\(747\) | 6.92902e7 | 0.166230 | ||||||||
\(748\) | 641945. | 0.00153389 | ||||||||
\(749\) | − | 1.27291e8i | − | 0.302936i | ||||||
\(750\) | − | 2.40520e8i | − | 0.570122i | ||||||
\(751\) | − | 6.06389e8i | − | 1.43163i | −0.698289 | − | 0.715816i | \(-0.746055\pi\) | ||
0.698289 | − | 0.715816i | \(-0.253945\pi\) | |||||||
\(752\) | 3.39852e8 | 0.799164 | ||||||||
\(753\) | − | 6.94031e8i | − | 1.62553i | ||||||
\(754\) | 7.97242e7 | 0.185984 | ||||||||
\(755\) | −2.67842e8 | −0.622354 | ||||||||
\(756\) | 4.44379e7 | 0.102846 | ||||||||
\(757\) | 4.02328e7i | 0.0927454i | 0.998924 | + | 0.0463727i | \(0.0147662\pi\) | ||||
−0.998924 | + | 0.0463727i | \(0.985234\pi\) | |||||||
\(758\) | 2.83905e8i | 0.651876i | ||||||||
\(759\) | 2.67872e7i | 0.0612636i | ||||||||
\(760\) | − | 4.14310e8i | − | 0.943810i | ||||||
\(761\) | − | 1.17921e8i | − | 0.267571i | −0.991010 | − | 0.133785i | \(-0.957287\pi\) | ||
0.991010 | − | 0.133785i | \(-0.0427133\pi\) | |||||||
\(762\) | 1.49863e8 | 0.338711 | ||||||||
\(763\) | 1.46152e8i | 0.329027i | ||||||||
\(764\) | 7.92813e7i | 0.177783i | ||||||||
\(765\) | − | 1.47481e7i | − | 0.0329421i | ||||||
\(766\) | 1.28536e8 | 0.285983 | ||||||||
\(767\) | 3.05101e8 | 0.676172 | ||||||||
\(768\) | 8.50442e7i | 0.187742i | ||||||||
\(769\) | −2.78052e8 | −0.611430 | −0.305715 | − | 0.952123i | \(-0.598895\pi\) | ||||
−0.305715 | + | 0.952123i | \(0.598895\pi\) | |||||||
\(770\) | 2.64083e6i | 0.00578453i | ||||||||
\(771\) | 6.78389e8 | 1.48018 | ||||||||
\(772\) | −3.91407e8 | −0.850701 | ||||||||
\(773\) | − | 3.45546e8i | − | 0.748114i | −0.927406 | − | 0.374057i | \(-0.877966\pi\) | ||
0.927406 | − | 0.374057i | \(-0.122034\pi\) | |||||||
\(774\) | −2.14652e8 | − | 1.05768e8i | −0.462926 | − | 0.228102i | ||||
\(775\) | 1.39242e7 | 0.0299134 | ||||||||
\(776\) | 1.21472e8i | 0.259951i | ||||||||
\(777\) | − | 1.10922e8i | − | 0.236459i | ||||||
\(778\) | −9.62038e6 | −0.0204293 | ||||||||
\(779\) | − | 7.25166e8i | − | 1.53400i | ||||||
\(780\) | 4.99557e8 | 1.05269 | ||||||||
\(781\) | − | 3.69509e7i | − | 0.0775660i | ||||||
\(782\) | − | 2.21363e6i | − | 0.00462898i | ||||||
\(783\) | −1.79570e8 | −0.374066 | ||||||||
\(784\) | 2.77696e8 | 0.576264 | ||||||||
\(785\) | −6.00587e8 | −1.24156 | ||||||||
\(786\) | 3.20431e8i | 0.659882i | ||||||||
\(787\) | −7.53528e8 | −1.54588 | −0.772939 | − | 0.634480i | \(-0.781214\pi\) | ||||
−0.772939 | + | 0.634480i | \(0.781214\pi\) | |||||||
\(788\) | 6.40538e8 | 1.30908 | ||||||||
\(789\) | 1.19088e9 | 2.42459 | ||||||||
\(790\) | 8.83428e7 | 0.179180 | ||||||||
\(791\) | 1.51786e8 | 0.306691 | ||||||||
\(792\) | 3.60417e7i | 0.0725486i | ||||||||
\(793\) | 6.41495e8i | 1.28639i | ||||||||
\(794\) | − | 1.66312e8i | − | 0.332248i | ||||||
\(795\) | −2.88694e8 | −0.574561 | ||||||||
\(796\) | 5.16083e8i | 1.02325i | ||||||||
\(797\) | −4.13846e8 | −0.817456 | −0.408728 | − | 0.912656i | \(-0.634027\pi\) | ||||
−0.408728 | + | 0.912656i | \(0.634027\pi\) | |||||||
\(798\) | −7.98564e7 | −0.157145 | ||||||||
\(799\) | −1.60014e7 | −0.0313703 | ||||||||
\(800\) | − | 9.98459e6i | − | 0.0195011i | ||||||
\(801\) | − | 3.37491e7i | − | 0.0656696i | ||||||
\(802\) | 3.09536e8i | 0.600050i | ||||||||
\(803\) | − | 4.78550e6i | − | 0.00924232i | ||||||
\(804\) | − | 1.32016e9i | − | 2.54015i | ||||||
\(805\) | −5.61780e7 | −0.107691 | ||||||||
\(806\) | 2.16314e8i | 0.413123i | ||||||||
\(807\) | − | 1.16935e9i | − | 2.22497i | ||||||
\(808\) | − | 2.79515e8i | − | 0.529871i | ||||||
\(809\) | −3.98175e8 | −0.752018 | −0.376009 | − | 0.926616i | \(-0.622704\pi\) | ||||
−0.376009 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(810\) | −9.47623e7 | −0.178312 | ||||||||
\(811\) | 7.81142e8i | 1.46443i | 0.681076 | + | 0.732213i | \(0.261512\pi\) | ||||
−0.681076 | + | 0.732213i | \(0.738488\pi\) | |||||||
\(812\) | 5.93270e7 | 0.110811 | ||||||||
\(813\) | 6.73097e8i | 1.25258i | ||||||||
\(814\) | 1.14968e7 | 0.0213159 | ||||||||
\(815\) | −8.38455e7 | −0.154884 | ||||||||
\(816\) | 1.18889e7i | 0.0218812i | ||||||||
\(817\) | −6.57494e8 | − | 3.23973e8i | −1.20566 | − | 0.594077i | ||||
\(818\) | −1.46344e8 | −0.267372 | ||||||||
\(819\) | − | 1.20777e8i | − | 0.219853i | ||||||
\(820\) | − | 5.47213e8i | − | 0.992465i | ||||||
\(821\) | −4.44865e8 | −0.803893 | −0.401947 | − | 0.915663i | \(-0.631666\pi\) | ||||
−0.401947 | + | 0.915663i | \(0.631666\pi\) | |||||||
\(822\) | 1.24104e8i | 0.223444i | ||||||||
\(823\) | −8.76142e8 | −1.57172 | −0.785859 | − | 0.618405i | \(-0.787779\pi\) | ||||
−0.785859 | + | 0.618405i | \(0.787779\pi\) | |||||||
\(824\) | 1.83702e7i | 0.0328347i | ||||||||
\(825\) | − | 1.38896e6i | − | 0.00247359i | ||||||
\(826\) | −3.68033e7 | −0.0653050 | ||||||||
\(827\) | −7.26669e8 | −1.28475 | −0.642377 | − | 0.766388i | \(-0.722052\pi\) | ||||
−0.642377 | + | 0.766388i | \(0.722052\pi\) | |||||||
\(828\) | −3.54613e8 | −0.624689 | ||||||||
\(829\) | 7.35131e8i | 1.29033i | 0.764043 | + | 0.645166i | \(0.223212\pi\) | ||||
−0.764043 | + | 0.645166i | \(0.776788\pi\) | |||||||
\(830\) | −2.59615e7 | −0.0454041 | ||||||||
\(831\) | 1.34335e9 | 2.34092 | ||||||||
\(832\) | −1.16391e8 | −0.202092 | ||||||||
\(833\) | −1.30749e7 | −0.0226206 | ||||||||
\(834\) | −2.37304e8 | −0.409080 | ||||||||
\(835\) | − | 2.77960e8i | − | 0.477445i | ||||||
\(836\) | 5.10606e7i | 0.0873911i | ||||||||
\(837\) | − | 4.87223e8i | − | 0.830904i | ||||||
\(838\) | 3.07002e8 | 0.521685 | ||||||||
\(839\) | − | 9.99532e8i | − | 1.69243i | −0.532841 | − | 0.846215i | \(-0.678876\pi\) | ||
0.532841 | − | 0.846215i | \(-0.321124\pi\) | |||||||
\(840\) | −1.30288e8 | −0.219820 | ||||||||
\(841\) | 3.55088e8 | 0.596964 | ||||||||
\(842\) | −1.68170e8 | −0.281716 | ||||||||
\(843\) | 8.74071e8i | 1.45903i | ||||||||
\(844\) | − | 8.43880e8i | − | 1.40363i | ||||||
\(845\) | 2.34572e8i | 0.388783i | ||||||||
\(846\) | − | 4.15518e8i | − | 0.686244i | ||||||
\(847\) | 1.22552e8i | 0.201683i | ||||||||
\(848\) | 1.35015e8 | 0.221409 | ||||||||
\(849\) | − | 4.84764e8i | − | 0.792150i | ||||||
\(850\) | 114780.i | 0.000186901i | ||||||||
\(851\) | 2.44569e8i | 0.396838i | ||||||||
\(852\) | 8.43166e8 | 1.36331 | ||||||||
\(853\) | −2.44606e8 | −0.394112 | −0.197056 | − | 0.980392i | \(-0.563138\pi\) | ||||
−0.197056 | + | 0.980392i | \(0.563138\pi\) | |||||||
\(854\) | − | 7.73815e7i | − | 0.124241i | ||||||
\(855\) | 1.17307e9 | 1.87683 | ||||||||
\(856\) | 6.50906e8i | 1.03776i | ||||||||
\(857\) | 1.71598e8 | 0.272627 | 0.136314 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136314 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(858\) | 2.15776e7 | 0.0341619 | ||||||||
\(859\) | 8.07434e8i | 1.27388i | 0.770915 | + | 0.636938i | \(0.219799\pi\) | ||||
−0.770915 | + | 0.636938i | \(0.780201\pi\) | |||||||
\(860\) | −4.96147e8 | − | 2.44472e8i | −0.780037 | − | 0.384355i | ||||
\(861\) | −2.28043e8 | −0.357279 | ||||||||
\(862\) | − | 2.27168e8i | − | 0.354670i | ||||||
\(863\) | − | 1.46709e8i | − | 0.228257i | −0.993466 | − | 0.114129i | \(-0.963592\pi\) | ||
0.993466 | − | 0.114129i | \(-0.0364076\pi\) | |||||||
\(864\) | −3.49371e8 | −0.541683 | ||||||||
\(865\) | 1.11291e9i | 1.71954i | ||||||||
\(866\) | 3.41290e7 | 0.0525497 | ||||||||
\(867\) | 1.00523e9i | 1.54245i | ||||||||
\(868\) | 1.60971e8i | 0.246143i | ||||||||
\(869\) | −2.35401e7 | −0.0358714 | ||||||||
\(870\) | 2.43505e8 | 0.369786 | ||||||||
\(871\) | −9.91383e8 | −1.50033 | ||||||||
\(872\) | − | 7.47355e8i | − | 1.12714i | ||||||
\(873\) | −3.43933e8 | −0.516929 | ||||||||
\(874\) | 1.76073e8 | 0.263730 | ||||||||
\(875\) | −1.34408e8 | −0.200633 | ||||||||
\(876\) | 1.09198e8 | 0.162444 | ||||||||
\(877\) | 1.89159e8 | 0.280432 | 0.140216 | − | 0.990121i | \(-0.455220\pi\) | ||||
0.140216 | + | 0.990121i | \(0.455220\pi\) | |||||||
\(878\) | − | 6.20025e7i | − | 0.0916063i | ||||||
\(879\) | 1.02287e9i | 1.50609i | ||||||||
\(880\) | 3.12723e7i | 0.0458894i | ||||||||
\(881\) | 5.04119e8 | 0.737234 | 0.368617 | − | 0.929581i | \(-0.379831\pi\) | ||||
0.368617 | + | 0.929581i | \(0.379831\pi\) | |||||||
\(882\) | − | 3.39524e8i | − | 0.494840i | ||||||
\(883\) | 3.57290e8 | 0.518966 | 0.259483 | − | 0.965748i | \(-0.416448\pi\) | ||||
0.259483 | + | 0.965748i | \(0.416448\pi\) | |||||||
\(884\) | 1.10002e7 | 0.0159237 | ||||||||
\(885\) | 9.31883e8 | 1.34441 | ||||||||
\(886\) | − | 4.06354e7i | − | 0.0584256i | ||||||
\(887\) | 1.88076e8i | 0.269502i | 0.990879 | + | 0.134751i | \(0.0430235\pi\) | ||||
−0.990879 | + | 0.134751i | \(0.956977\pi\) | |||||||
\(888\) | 5.67205e8i | 0.810031i | ||||||||
\(889\) | − | 8.37470e7i | − | 0.119197i | ||||||
\(890\) | 1.26450e7i | 0.0179370i | ||||||||
\(891\) | 2.52506e7 | 0.0356976 | ||||||||
\(892\) | 1.06147e9i | 1.49559i | ||||||||
\(893\) | − | 1.27276e9i | − | 1.78728i | ||||||
\(894\) | − | 2.40173e7i | − | 0.0336134i | ||||||
\(895\) | 1.12103e9 | 1.56368 | ||||||||
\(896\) | 1.48177e8 | 0.205995 | ||||||||
\(897\) | 4.59018e8i | 0.635993i | ||||||||
\(898\) | 4.12851e8 | 0.570117 | ||||||||
\(899\) | − | 6.50468e8i | − | 0.895256i | ||||||
\(900\) | 1.83872e7 | 0.0252226 | ||||||||
\(901\) | −6.35699e6 | −0.00869115 | ||||||||
\(902\) | − | 2.36361e7i | − | 0.0322074i | ||||||
\(903\) | −1.01880e8 | + | 2.06762e8i | −0.138365 | + | 0.280807i | ||||
\(904\) | −7.76163e8 | −1.05062 | ||||||||
\(905\) | − | 3.81306e8i | − | 0.514431i | ||||||
\(906\) | − | 2.63988e8i | − | 0.354977i | ||||||
\(907\) | 3.41940e8 | 0.458277 | 0.229139 | − | 0.973394i | \(-0.426409\pi\) | ||||
0.229139 | + | 0.973394i | \(0.426409\pi\) | |||||||
\(908\) | 6.53256e8i | 0.872622i | ||||||||
\(909\) | 7.91411e8 | 1.05368 | ||||||||
\(910\) | 4.52524e7i | 0.0600507i | ||||||||
\(911\) | 7.37566e8i | 0.975542i | 0.872972 | + | 0.487771i | \(0.162190\pi\) | ||||
−0.872972 | + | 0.487771i | \(0.837810\pi\) | |||||||
\(912\) | −9.45647e8 | −1.24665 | ||||||||
\(913\) | 6.91777e6 | 0.00908979 | ||||||||
\(914\) | −4.73716e7 | −0.0620412 | ||||||||
\(915\) | 1.95935e9i | 2.55769i | ||||||||
\(916\) | 2.45749e8 | 0.319747 | ||||||||
\(917\) | 1.79064e8 | 0.232221 | ||||||||
\(918\) | 4.01628e6 | 0.00519154 | ||||||||
\(919\) | 5.04014e8 | 0.649376 | 0.324688 | − | 0.945821i | \(-0.394741\pi\) | ||||
0.324688 | + | 0.945821i | \(0.394741\pi\) | |||||||
\(920\) | 2.87269e8 | 0.368914 | ||||||||
\(921\) | − | 6.27954e8i | − | 0.803801i | ||||||
\(922\) | 3.19600e8i | 0.407768i | ||||||||
\(923\) | − | 6.33178e8i | − | 0.805232i | ||||||
\(924\) | 1.60570e7 | 0.0203540 | ||||||||
\(925\) | − | 1.26813e7i | − | 0.0160228i | ||||||
\(926\) | −2.01482e8 | −0.253749 | ||||||||
\(927\) | −5.20131e7 | −0.0652940 | ||||||||
\(928\) | −4.66429e8 | −0.583635 | ||||||||
\(929\) | 1.02260e9i | 1.27543i | 0.770271 | + | 0.637717i | \(0.220121\pi\) | ||||
−0.770271 | + | 0.637717i | \(0.779879\pi\) | |||||||
\(930\) | 6.60698e8i | 0.821399i | ||||||||
\(931\) | − | 1.03998e9i | − | 1.28878i | ||||||
\(932\) | − | 1.27490e9i | − | 1.57481i | ||||||
\(933\) | − | 5.21656e8i | − | 0.642302i | ||||||
\(934\) | −3.27735e8 | −0.402237 | ||||||||
\(935\) | − | 1.47241e6i | − | 0.00180134i | ||||||
\(936\) | 6.17599e8i | 0.753145i | ||||||||
\(937\) | 4.71718e7i | 0.0573408i | 0.999589 | + | 0.0286704i | \(0.00912733\pi\) | ||||
−0.999589 | + | 0.0286704i | \(0.990873\pi\) | |||||||
\(938\) | 1.19587e8 | 0.144903 | ||||||||
\(939\) | −8.74243e8 | −1.05593 | ||||||||
\(940\) | − | 9.60430e8i | − | 1.15633i | ||||||
\(941\) | −1.66410e8 | −0.199715 | −0.0998576 | − | 0.995002i | \(-0.531839\pi\) | ||||
−0.0998576 | + | 0.995002i | \(0.531839\pi\) | |||||||
\(942\) | − | 5.91946e8i | − | 0.708157i | ||||||
\(943\) | 5.02806e8 | 0.599606 | ||||||||
\(944\) | −4.35819e8 | −0.518072 | ||||||||
\(945\) | − | 1.01926e8i | − | 0.120778i | ||||||
\(946\) | −2.14303e7 | − | 1.05596e7i | −0.0253137 | − | 0.0124731i | ||||
\(947\) | −1.17982e9 | −1.38921 | −0.694603 | − | 0.719393i | \(-0.744420\pi\) | ||||
−0.694603 | + | 0.719393i | \(0.744420\pi\) | |||||||
\(948\) | − | 5.37151e8i | − | 0.630480i | ||||||
\(949\) | − | 8.20029e7i | − | 0.0959468i | ||||||
\(950\) | −9.12968e6 | −0.0106484 | ||||||||
\(951\) | 1.48505e9i | 1.72663i | ||||||||
\(952\) | −2.86892e6 | −0.00332512 | ||||||||
\(953\) | − | 2.13184e8i | − | 0.246306i | −0.992388 | − | 0.123153i | \(-0.960699\pi\) | ||
0.992388 | − | 0.123153i | \(-0.0393006\pi\) | |||||||
\(954\) | − | 1.65075e8i | − | 0.190124i | ||||||
\(955\) | 1.81845e8 | 0.208782 | ||||||||
\(956\) | −8.41581e8 | −0.963212 | ||||||||
\(957\) | −6.48851e7 | −0.0740303 | ||||||||
\(958\) | − | 5.35263e8i | − | 0.608794i | ||||||
\(959\) | 6.93521e7 | 0.0786328 | ||||||||
\(960\) | −3.55498e8 | −0.401812 | ||||||||
\(961\) | 8.77398e8 | 0.988614 | ||||||||
\(962\) | 1.97005e8 | 0.221285 | ||||||||
\(963\) | −1.84296e9 | −2.06365 | ||||||||
\(964\) | 7.53406e8i | 0.841003i | ||||||||
\(965\) | 8.97760e8i | 0.999030i | ||||||||
\(966\) | − | 5.53698e7i | − | 0.0614245i | ||||||
\(967\) | 1.26871e9 | 1.40308 | 0.701542 | − | 0.712628i | \(-0.252495\pi\) | ||||
0.701542 | + | 0.712628i | \(0.252495\pi\) | |||||||
\(968\) | − | 6.26673e8i | − | 0.690900i | ||||||
\(969\) | 4.45245e7 | 0.0489359 | ||||||||
\(970\) | 1.28864e8 | 0.141194 | ||||||||
\(971\) | −3.71047e8 | −0.405295 | −0.202648 | − | 0.979252i | \(-0.564955\pi\) | ||||
−0.202648 | + | 0.979252i | \(0.564955\pi\) | |||||||
\(972\) | 1.04180e9i | 1.13445i | ||||||||
\(973\) | 1.32611e8i | 0.143960i | ||||||||
\(974\) | 6.55424e8i | 0.709325i | ||||||||
\(975\) | − | 2.38008e7i | − | 0.0256790i | ||||||
\(976\) | − | 9.16340e8i | − | 0.985614i | ||||||
\(977\) | −1.44365e9 | −1.54803 | −0.774015 | − | 0.633167i | \(-0.781755\pi\) | ||||
−0.774015 | + | 0.633167i | \(0.781755\pi\) | |||||||
\(978\) | − | 8.26393e7i | − | 0.0883425i | ||||||
\(979\) | − | 3.36943e6i | − | 0.00359094i | ||||||
\(980\) | − | 7.84777e8i | − | 0.833812i | ||||||
\(981\) | 2.11604e9 | 2.24139 | ||||||||
\(982\) | −1.42085e8 | −0.150042 | ||||||||
\(983\) | − | 5.80712e8i | − | 0.611365i | −0.952134 | − | 0.305682i | \(-0.901115\pi\) | ||
0.952134 | − | 0.305682i | \(-0.0988846\pi\) | |||||||
\(984\) | 1.16611e9 | 1.22392 | ||||||||
\(985\) | − | 1.46918e9i | − | 1.53733i | ||||||
\(986\) | 5.36195e6 | 0.00559361 | ||||||||
\(987\) | −4.00245e8 | −0.416270 | ||||||||
\(988\) | 8.74958e8i | 0.907228i | ||||||||
\(989\) | 2.24632e8 | − | 4.55885e8i | 0.232211 | − | 0.471266i | ||||
\(990\) | 3.82349e7 | 0.0394053 | ||||||||
\(991\) | 1.54780e9i | 1.59035i | 0.606380 | + | 0.795175i | \(0.292621\pi\) | ||||
−0.606380 | + | 0.795175i | \(0.707379\pi\) | |||||||
\(992\) | − | 1.26555e9i | − | 1.29642i | ||||||
\(993\) | −1.88163e8 | −0.192170 | ||||||||
\(994\) | 7.63782e7i | 0.0777697i | ||||||||
\(995\) | 1.18372e9 | 1.20166 | ||||||||
\(996\) | 1.57854e8i | 0.159763i | ||||||||
\(997\) | − | 3.37310e8i | − | 0.340364i | −0.985413 | − | 0.170182i | \(-0.945564\pi\) | ||
0.985413 | − | 0.170182i | \(-0.0544356\pi\) | |||||||
\(998\) | 3.76690e8 | 0.378959 | ||||||||
\(999\) | −4.43732e8 | −0.445066 |
(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.42.12 | yes | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.9 | ✓ | 20 | 43.42 | odd | 2 | inner | |
43.7.b.b.42.12 | yes | 20 | 1.1 | even | 1 | trivial |