Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,7,Mod(91,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.91");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.c (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: | \(41.4097350516\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.14 | ||
Character | \(\chi\) | \(=\) | 180.91 |
Dual form | 180.7.c.b.91.13 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.331992 | + | 7.99311i | −0.0414990 | + | 0.999139i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −63.7796 | − | 5.30729i | −0.996556 | − | 0.0829264i | ||||
\(5\) | 55.9017 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 552.003i | − | 1.60934i | −0.593723 | − | 0.804669i | \(-0.702343\pi\) | ||
0.593723 | − | 0.804669i | \(-0.297657\pi\) | |||||||
\(8\) | 63.5960 | − | 508.035i | 0.124211 | − | 0.992256i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.5589 | + | 446.828i | −0.0185589 | + | 0.446828i | ||||
\(11\) | − | 1284.63i | − | 0.965162i | −0.875851 | − | 0.482581i | \(-0.839699\pi\) | ||
0.875851 | − | 0.482581i | \(-0.160301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2513.57 | −1.14409 | −0.572046 | − | 0.820221i | \(-0.693850\pi\) | ||||
−0.572046 | + | 0.820221i | \(0.693850\pi\) | |||||||
\(14\) | 4412.22 | + | 183.260i | 1.60795 | + | 0.0667859i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4039.67 | + | 676.993i | 0.986246 | + | 0.165282i | ||||
\(17\) | −4597.01 | −0.935684 | −0.467842 | − | 0.883812i | \(-0.654968\pi\) | ||||
−0.467842 | + | 0.883812i | \(0.654968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9800.21i | 1.42881i | 0.699732 | + | 0.714405i | \(0.253303\pi\) | ||||
−0.699732 | + | 0.714405i | \(0.746697\pi\) | |||||||
\(20\) | −3565.39 | − | 296.687i | −0.445673 | − | 0.0370858i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10268.2 | + | 426.487i | 0.964330 | + | 0.0400532i | ||||
\(23\) | 15217.2i | 1.25070i | 0.780345 | + | 0.625349i | \(0.215043\pi\) | ||||
−0.780345 | + | 0.625349i | \(0.784957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | 834.485 | − | 20091.2i | 0.0474787 | − | 1.14311i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2929.64 | + | 35206.5i | −0.133457 | + | 1.60380i | ||||
\(29\) | 14380.1 | 0.589614 | 0.294807 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294807 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34497.8i | 1.15800i | 0.815329 | + | 0.578998i | \(0.196556\pi\) | ||||
−0.815329 | + | 0.578998i | \(0.803444\pi\) | |||||||
\(32\) | −6752.42 | + | 32064.7i | −0.206067 | + | 0.978538i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1526.17 | − | 36744.4i | 0.0388299 | − | 0.934878i | ||||
\(35\) | − | 30857.9i | − | 0.719718i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −71409.5 | −1.40978 | −0.704889 | − | 0.709318i | \(-0.749003\pi\) | ||||
−0.704889 | + | 0.709318i | \(0.749003\pi\) | |||||||
\(38\) | −78334.2 | − | 3253.59i | −1.42758 | − | 0.0592942i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3555.13 | − | 28400.0i | 0.0555489 | − | 0.443750i | ||||
\(41\) | 37657.2 | 0.546383 | 0.273191 | − | 0.961960i | \(-0.411921\pi\) | ||||
0.273191 | + | 0.961960i | \(0.411921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1535.15i | 0.0193083i | 0.999953 | + | 0.00965417i | \(0.00307307\pi\) | ||||
−0.999953 | + | 0.00965417i | \(0.996927\pi\) | |||||||
\(44\) | −6817.91 | + | 81933.1i | −0.0800374 | + | 0.961837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −121633. | − | 5052.00i | −1.24962 | − | 0.0519027i | ||||
\(47\) | 131297.i | 1.26463i | 0.774713 | + | 0.632313i | \(0.217894\pi\) | ||||
−0.774713 | + | 0.632313i | \(0.782106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −187058. | −1.58997 | ||||||||
\(50\) | −1037.47 | + | 24978.5i | −0.00829979 | + | 0.199828i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 160314. | + | 13340.3i | 1.14015 | + | 0.0948755i | ||||
\(53\) | 228206. | 1.53285 | 0.766424 | − | 0.642336i | \(-0.222034\pi\) | ||||
0.766424 | + | 0.642336i | \(0.222034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 71813.0i | − | 0.431633i | ||||||
\(56\) | −280437. | − | 35105.2i | −1.59688 | − | 0.199898i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4774.07 | + | 114942.i | −0.0244684 | + | 0.589106i | ||||
\(59\) | 271199.i | 1.32048i | 0.751053 | + | 0.660241i | \(0.229546\pi\) | ||||
−0.751053 | + | 0.660241i | \(0.770454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −252456. | −1.11223 | −0.556116 | − | 0.831105i | \(-0.687709\pi\) | ||||
−0.556116 | + | 0.831105i | \(0.687709\pi\) | |||||||
\(62\) | −275745. | − | 11453.0i | −1.15700 | − | 0.0480556i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −254055. | − | 64618.0i | −0.969143 | − | 0.246498i | ||||
\(65\) | −140513. | −0.511654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 71786.4i | 0.238681i | 0.992853 | + | 0.119340i | \(0.0380780\pi\) | ||||
−0.992853 | + | 0.119340i | \(0.961922\pi\) | |||||||
\(68\) | 293196. | + | 24397.7i | 0.932461 | + | 0.0775929i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 246651. | + | 10244.6i | 0.719098 | + | 0.0298676i | ||||
\(71\) | − | 193845.i | − | 0.541601i | −0.962635 | − | 0.270801i | \(-0.912712\pi\) | ||
0.962635 | − | 0.270801i | \(-0.0872884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125558. | 0.322758 | 0.161379 | − | 0.986893i | \(-0.448406\pi\) | ||||
0.161379 | + | 0.986893i | \(0.448406\pi\) | |||||||
\(74\) | 23707.4 | − | 570784.i | 0.0585043 | − | 1.40856i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 52012.6 | − | 625053.i | 0.118486 | − | 1.42389i | ||||
\(77\) | −709120. | −1.55327 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 609914.i | − | 1.23705i | −0.785765 | − | 0.618525i | \(-0.787730\pi\) | ||
0.785765 | − | 0.618525i | \(-0.212270\pi\) | |||||||
\(80\) | 225824. | + | 37845.1i | 0.441063 | + | 0.0739162i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12501.9 | + | 300998.i | −0.0226743 | + | 0.545912i | ||||
\(83\) | − | 592195.i | − | 1.03569i | −0.855474 | − | 0.517846i | \(-0.826734\pi\) | ||
0.855474 | − | 0.517846i | \(-0.173266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −256981. | −0.418451 | ||||||||
\(86\) | −12270.6 | − | 509.657i | −0.0192917 | − | 0.000801276i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −652637. | − | 81697.4i | −0.957687 | − | 0.119884i | ||||
\(89\) | 154289. | 0.218859 | 0.109429 | − | 0.993995i | \(-0.465098\pi\) | ||||
0.109429 | + | 0.993995i | \(0.465098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.38750e6i | 1.84123i | ||||||||
\(92\) | 80762.4 | − | 970549.i | 0.103716 | − | 1.24639i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.04947e6 | − | 43589.6i | −1.26354 | − | 0.0524807i | ||||
\(95\) | 547849.i | 0.638984i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46175e6 | −1.60162 | −0.800810 | − | 0.598919i | \(-0.795597\pi\) | ||||
−0.800810 | + | 0.598919i | \(0.795597\pi\) | |||||||
\(98\) | 62101.9 | − | 1.49518e6i | 0.0659821 | − | 1.58860i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −199311. | − | 16585.3i | −0.199311 | − | 0.0165853i | ||||
\(101\) | −963761. | −0.935417 | −0.467708 | − | 0.883883i | \(-0.654920\pi\) | ||||
−0.467708 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.01542e6i | 0.929250i | 0.885508 | + | 0.464625i | \(0.153811\pi\) | ||||
−0.885508 | + | 0.464625i | \(0.846189\pi\) | |||||||
\(104\) | −159853. | + | 1.27698e6i | −0.142109 | + | 1.13523i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −75762.4 | + | 1.82407e6i | −0.0636116 | + | 1.53153i | ||||
\(107\) | 509249.i | 0.415699i | 0.978161 | + | 0.207849i | \(0.0666463\pi\) | ||||
−0.978161 | + | 0.207849i | \(0.933354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.13481e6 | 1.64846 | 0.824231 | − | 0.566254i | \(-0.191608\pi\) | ||||
0.824231 | + | 0.566254i | \(0.191608\pi\) | |||||||
\(110\) | 574009. | + | 23841.3i | 0.431262 | + | 0.0179123i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 373703. | − | 2.22991e6i | 0.265994 | − | 1.58720i | ||||
\(113\) | −178688. | −0.123840 | −0.0619200 | − | 0.998081i | \(-0.519722\pi\) | ||||
−0.0619200 | + | 0.998081i | \(0.519722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 850670.i | 0.559329i | ||||||||
\(116\) | −917156. | − | 76319.3i | −0.587583 | − | 0.0488946i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.16773e6 | − | 90036.0i | −1.31935 | − | 0.0547987i | ||||
\(119\) | 2.53757e6i | 1.50583i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121287. | 0.0684633 | ||||||||
\(122\) | 83813.2 | − | 2.01790e6i | 0.0461565 | − | 1.11127i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 183090. | − | 2.20026e6i | 0.0960284 | − | 1.15401i | ||||
\(125\) | 174693. | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.94450e6i | − | 0.949286i | −0.880178 | − | 0.474643i | \(-0.842577\pi\) | ||
0.880178 | − | 0.474643i | \(-0.157423\pi\) | |||||||
\(128\) | 600843. | − | 2.00924e6i | 0.286504 | − | 0.958079i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 46649.1 | − | 1.12313e6i | 0.0212331 | − | 0.511213i | ||||
\(131\) | 3.66180e6i | 1.62885i | 0.580270 | + | 0.814424i | \(0.302947\pi\) | ||||
−0.580270 | + | 0.814424i | \(0.697053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.40975e6 | 2.29944 | ||||||||
\(134\) | −573796. | − | 23832.5i | −0.238475 | − | 0.00990501i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −292352. | + | 2.33544e6i | −0.116222 | + | 0.928438i | ||||
\(137\) | −477013. | −0.185510 | −0.0927552 | − | 0.995689i | \(-0.529567\pi\) | ||||
−0.0927552 | + | 0.995689i | \(0.529567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 874957.i | − | 0.325793i | −0.986643 | − | 0.162897i | \(-0.947916\pi\) | ||
0.986643 | − | 0.162897i | \(-0.0520837\pi\) | |||||||
\(140\) | −163772. | + | 1.96810e6i | −0.0596837 | + | 0.717239i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.54942e6 | + | 64354.9i | 0.541135 | + | 0.0224759i | ||||
\(143\) | 3.22901e6i | 1.10423i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 803871. | 0.263683 | ||||||||
\(146\) | −41684.3 | + | 1.00360e6i | −0.0133941 | + | 0.322480i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.55447e6 | + | 378991.i | 1.40492 | + | 0.116908i | ||||
\(149\) | 2.52851e6 | 0.764375 | 0.382187 | − | 0.924085i | \(-0.375171\pi\) | ||||
0.382187 | + | 0.924085i | \(0.375171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.24281e6i | 0.941869i | 0.882168 | + | 0.470934i | \(0.156083\pi\) | ||||
−0.882168 | + | 0.470934i | \(0.843917\pi\) | |||||||
\(152\) | 4.97885e6 | + | 623255.i | 1.41775 | + | 0.177474i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 235422. | − | 5.66807e6i | 0.0644592 | − | 1.55193i | ||||
\(155\) | 1.92849e6i | 0.517871i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.96596e6 | −1.54164 | −0.770818 | − | 0.637056i | \(-0.780152\pi\) | ||||
−0.770818 | + | 0.637056i | \(0.780152\pi\) | |||||||
\(158\) | 4.87511e6 | + | 202487.i | 1.23599 | + | 0.0513363i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −377472. | + | 1.79247e6i | −0.0921562 | + | 0.437615i | ||||
\(161\) | 8.39997e6 | 2.01280 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.08504e6i | 0.943265i | 0.881795 | + | 0.471632i | \(0.156335\pi\) | ||||
−0.881795 | + | 0.471632i | \(0.843665\pi\) | |||||||
\(164\) | −2.40176e6 | − | 199858.i | −0.544501 | − | 0.0453096i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.73348e6 | + | 196604.i | 1.03480 | + | 0.0429801i | ||||
\(167\) | − | 2.47808e6i | − | 0.532067i | −0.963964 | − | 0.266034i | \(-0.914287\pi\) | ||
0.963964 | − | 0.266034i | \(-0.0857132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.49123e6 | 0.308948 | ||||||||
\(170\) | 85315.5 | − | 2.05408e6i | 0.0173653 | − | 0.418090i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8147.48 | − | 97911.1i | 0.00160117 | − | 0.0192418i | ||||
\(173\) | −8.20504e6 | −1.58468 | −0.792341 | − | 0.610078i | \(-0.791138\pi\) | ||||
−0.792341 | + | 0.610078i | \(0.791138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.72501e6i | − | 0.321868i | ||||||
\(176\) | 869686. | − | 5.18948e6i | 0.159523 | − | 0.951887i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −51222.6 | + | 1.23325e6i | −0.00908241 | + | 0.218670i | ||||
\(179\) | 3.09966e6i | 0.540450i | 0.962797 | + | 0.270225i | \(0.0870981\pi\) | ||||
−0.962797 | + | 0.270225i | \(0.912902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.47886e6 | −0.418038 | −0.209019 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209019 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(182\) | −1.10904e7 | − | 460638.i | −1.83965 | − | 0.0764092i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.73089e6 | + | 967757.i | 1.24101 | + | 0.155351i | ||||
\(185\) | −3.99191e6 | −0.630472 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.90546e6i | 0.903086i | ||||||||
\(188\) | 696833. | − | 8.37408e6i | 0.104871 | − | 1.26027i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.37901e6 | − | 181881.i | −0.638433 | − | 0.0265172i | ||||
\(191\) | 1.42970e6i | 0.205185i | 0.994723 | + | 0.102592i | \(0.0327137\pi\) | ||||
−0.994723 | + | 0.102592i | \(0.967286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.81356e6 | −0.252266 | −0.126133 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126133 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(194\) | 485291. | − | 1.16840e7i | 0.0664656 | − | 1.60024i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.19305e7 | + | 992774.i | 1.58449 | + | 0.131851i | ||||
\(197\) | 8.69647e6 | 1.13748 | 0.568740 | − | 0.822517i | \(-0.307431\pi\) | ||||
0.568740 | + | 0.822517i | \(0.307431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.01570e6i | − | 0.636462i | −0.948013 | − | 0.318231i | \(-0.896911\pi\) | ||
0.948013 | − | 0.318231i | \(-0.103089\pi\) | |||||||
\(200\) | 198738. | − | 1.58761e6i | 0.0248422 | − | 0.198451i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 319961. | − | 7.70344e6i | 0.0388188 | − | 0.934611i | ||||
\(203\) | − | 7.93785e6i | − | 0.948888i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.10510e6 | 0.244350 | ||||||||
\(206\) | −8.11634e6 | − | 337110.i | −0.928450 | − | 0.0385629i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.01540e7 | − | 1.70167e6i | −1.12836 | − | 0.189097i | ||||
\(209\) | 1.25896e7 | 1.37903 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.77795e6i | 0.721525i | 0.932658 | + | 0.360762i | \(0.117483\pi\) | ||||
−0.932658 | + | 0.360762i | \(0.882517\pi\) | |||||||
\(212\) | −1.45549e7 | − | 1.21115e6i | −1.52757 | − | 0.127114i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.07048e6 | − | 169066.i | −0.415340 | − | 0.0172511i | ||||
\(215\) | 85817.4i | 0.00863495i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.90429e7 | 1.86361 | ||||||||
\(218\) | −708738. | + | 1.70637e7i | −0.0684095 | + | 1.64704i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −381133. | + | 4.58020e6i | −0.0357938 | + | 0.430147i | ||||
\(221\) | 1.15549e7 | 1.07051 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.21767e7i | − | 1.09803i | −0.835812 | − | 0.549016i | \(-0.815003\pi\) | ||
0.835812 | − | 0.549016i | \(-0.184997\pi\) | |||||||
\(224\) | 1.76998e7 | + | 3.72736e6i | 1.57480 | + | 0.331632i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 59323.1 | − | 1.42828e6i | 0.00513923 | − | 0.123733i | ||||
\(227\) | 8.92756e6i | 0.763230i | 0.924321 | + | 0.381615i | \(0.124632\pi\) | ||||
−0.924321 | + | 0.381615i | \(0.875368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.61284e7 | −1.34302 | −0.671512 | − | 0.740994i | \(-0.734355\pi\) | ||||
−0.671512 | + | 0.740994i | \(0.734355\pi\) | |||||||
\(230\) | −6.79950e6 | − | 282415.i | −0.558847 | − | 0.0232116i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 914517. | − | 7.30559e6i | 0.0732365 | − | 0.585048i | ||||
\(233\) | −5.66976e6 | −0.448226 | −0.224113 | − | 0.974563i | \(-0.571948\pi\) | ||||
−0.224113 | + | 0.974563i | \(0.571948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.33974e6i | 0.565558i | ||||||||
\(236\) | 1.43933e6 | − | 1.72970e7i | 0.109503 | − | 1.31593i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.02830e7 | − | 842451.i | −1.50453 | − | 0.0624905i | ||||
\(239\) | − | 1.01650e7i | − | 0.744583i | −0.928116 | − | 0.372291i | \(-0.878572\pi\) | ||
0.928116 | − | 0.372291i | \(-0.121428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.87229e7 | −1.33759 | −0.668795 | − | 0.743447i | \(-0.733189\pi\) | ||||
−0.668795 | + | 0.743447i | \(0.733189\pi\) | |||||||
\(242\) | −40266.2 | + | 969459.i | −0.00284115 | + | 0.0684043i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.61015e7 | + | 1.33986e6i | 1.10840 | + | 0.0922335i | ||||
\(245\) | −1.04569e7 | −0.711057 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.46335e7i | − | 1.63469i | ||||||
\(248\) | 1.75261e7 | + | 2.19393e6i | 1.14903 | + | 0.143836i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −57996.6 | + | 1.39634e6i | −0.00371178 | + | 0.0893657i | ||||
\(251\) | 3.39034e6i | 0.214398i | 0.994238 | + | 0.107199i | \(0.0341883\pi\) | ||||
−0.994238 | + | 0.107199i | \(0.965812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.95485e7 | 1.20713 | ||||||||
\(254\) | 1.55426e7 | + | 645559.i | 0.948468 | + | 0.0393944i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.58606e7 | + | 5.46965e6i | 0.945364 | + | 0.326017i | ||||
\(257\) | −2.79800e7 | −1.64835 | −0.824173 | − | 0.566338i | \(-0.808360\pi\) | ||||
−0.824173 | + | 0.566338i | \(0.808360\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.94183e7i | 2.26881i | ||||||||
\(260\) | 8.96185e6 | + | 745743.i | 0.509891 | + | 0.0424296i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.92692e7 | − | 1.21569e6i | −1.62745 | − | 0.0675955i | ||||
\(263\) | 2.67037e7i | 1.46793i | 0.679189 | + | 0.733963i | \(0.262331\pi\) | ||||
−0.679189 | + | 0.733963i | \(0.737669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.27571e7 | 0.685510 | ||||||||
\(266\) | −1.79599e6 | + | 4.32407e7i | −0.0954244 | + | 2.29746i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 380991. | − | 4.57850e6i | 0.0197929 | − | 0.237859i | ||||
\(269\) | −2.74962e7 | −1.41259 | −0.706295 | − | 0.707917i | \(-0.749635\pi\) | ||||
−0.706295 | + | 0.707917i | \(0.749635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.82244e6i | − | 0.393038i | −0.980500 | − | 0.196519i | \(-0.937036\pi\) | ||
0.980500 | − | 0.196519i | \(-0.0629637\pi\) | |||||||
\(272\) | −1.85704e7 | − | 3.11215e6i | −0.922815 | − | 0.154651i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 158364. | − | 3.81281e6i | 0.00769849 | − | 0.185351i | ||||
\(275\) | − | 4.01447e6i | − | 0.193032i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.48863e7 | −1.64140 | −0.820702 | − | 0.571356i | \(-0.806418\pi\) | ||||
−0.820702 | + | 0.571356i | \(0.806418\pi\) | |||||||
\(278\) | 6.99362e6 | + | 290478.i | 0.325513 | + | 0.0135201i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.56769e7 | − | 1.96244e6i | −0.714144 | − | 0.0893969i | ||||
\(281\) | 2.43392e6 | 0.109695 | 0.0548476 | − | 0.998495i | \(-0.482533\pi\) | ||||
0.0548476 | + | 0.998495i | \(0.482533\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.82558e7i | − | 1.68787i | −0.536447 | − | 0.843934i | \(-0.680234\pi\) | ||
0.536447 | − | 0.843934i | \(-0.319766\pi\) | |||||||
\(284\) | −1.02879e6 | + | 1.23634e7i | −0.0449131 | + | 0.539736i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.58098e7 | − | 1.07200e6i | −1.10328 | − | 0.0458246i | ||||
\(287\) | − | 2.07869e7i | − | 0.879315i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00503e6 | −0.124496 | ||||||||
\(290\) | −266879. | + | 6.42543e6i | −0.0109426 | + | 0.263456i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.00805e6 | − | 666374.i | −0.321646 | − | 0.0267651i | ||||
\(293\) | −2.04358e7 | −0.812436 | −0.406218 | − | 0.913776i | \(-0.633153\pi\) | ||||
−0.406218 | + | 0.913776i | \(0.633153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51605e7i | 0.590538i | ||||||||
\(296\) | −4.54136e6 | + | 3.62785e7i | −0.175110 | + | 1.39886i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −839445. | + | 2.02107e7i | −0.0317208 | + | 0.763716i | ||||
\(299\) | − | 3.82496e7i | − | 1.43091i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 847407. | 0.0310737 | ||||||||
\(302\) | −2.59201e7 | − | 1.07659e6i | −0.941058 | − | 0.0390866i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.63468e6 | + | 3.95896e7i | −0.236156 | + | 1.40916i | ||||
\(305\) | −1.41127e7 | −0.497405 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.54158e6i | 0.329765i | 0.986313 | + | 0.164883i | \(0.0527246\pi\) | ||||
−0.986313 | + | 0.164883i | \(0.947275\pi\) | |||||||
\(308\) | 4.52273e7 | + | 3.76351e6i | 1.54792 | + | 0.128807i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.54146e7 | − | 640242.i | −0.517425 | − | 0.0214911i | ||||
\(311\) | 2.91657e6i | 0.0969595i | 0.998824 | + | 0.0484798i | \(0.0154376\pi\) | ||||
−0.998824 | + | 0.0484798i | \(0.984562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.93741e7 | 0.631814 | 0.315907 | − | 0.948790i | \(-0.397691\pi\) | ||||
0.315907 | + | 0.948790i | \(0.397691\pi\) | |||||||
\(314\) | 1.98065e6 | − | 4.76866e7i | 0.0639763 | − | 1.54031i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.23699e6 | + | 3.89001e7i | −0.102584 | + | 1.23279i | ||||
\(317\) | −6.50536e6 | −0.204218 | −0.102109 | − | 0.994773i | \(-0.532559\pi\) | ||||
−0.102109 | + | 0.994773i | \(0.532559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.84731e7i | − | 0.569072i | ||||||
\(320\) | −1.42021e7 | − | 3.61226e6i | −0.433414 | − | 0.110237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.78872e6 | + | 6.71419e7i | −0.0835290 | + | 2.01106i | ||||
\(323\) | − | 4.50517e7i | − | 1.33692i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.85491e6 | −0.228818 | ||||||||
\(326\) | −3.26522e7 | − | 1.35620e6i | −0.942452 | − | 0.0391445i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.39485e6 | − | 1.91312e7i | 0.0678668 | − | 0.542151i | ||||
\(329\) | 7.24765e7 | 2.03521 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.30862e7i | − | 0.636603i | −0.947990 | − | 0.318301i | \(-0.896888\pi\) | ||
0.947990 | − | 0.318301i | \(-0.103112\pi\) | |||||||
\(332\) | −3.14295e6 | + | 3.77699e7i | −0.0858862 | + | 1.03212i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.98076e7 | + | 822703.i | 0.531609 | + | 0.0220802i | ||||
\(335\) | 4.01298e6i | 0.106741i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.43828e7 | −1.15965 | −0.579823 | − | 0.814743i | \(-0.696878\pi\) | ||||
−0.579823 | + | 0.814743i | \(0.696878\pi\) | |||||||
\(338\) | −495076. | + | 1.19196e7i | −0.0128210 | + | 0.308681i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.63901e7 | + | 1.36387e6i | 0.417009 | + | 0.0347006i | ||||
\(341\) | 4.43170e7 | 1.11765 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.83142e7i | 0.949463i | ||||||||
\(344\) | 779909. | + | 97629.4i | 0.0191588 | + | 0.00239831i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.72400e6 | − | 6.55838e7i | 0.0657627 | − | 1.58332i | ||||
\(347\) | − | 2.62548e7i | − | 0.628376i | −0.949361 | − | 0.314188i | \(-0.898268\pi\) | ||
0.949361 | − | 0.314188i | \(-0.101732\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.54811e7 | 1.77567 | 0.887834 | − | 0.460164i | \(-0.152209\pi\) | ||||
0.887834 | + | 0.460164i | \(0.152209\pi\) | |||||||
\(350\) | 1.37882e7 | + | 572689.i | 0.321590 | + | 0.0133572i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.11913e7 | + | 8.67436e6i | 0.944447 | + | 0.198888i | ||||
\(353\) | 7.31900e6 | 0.166390 | 0.0831951 | − | 0.996533i | \(-0.473488\pi\) | ||||
0.0831951 | + | 0.996533i | \(0.473488\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.08363e7i | − | 0.242211i | ||||||
\(356\) | −9.84046e6 | − | 818855.i | −0.218105 | − | 0.0181492i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.47759e7 | − | 1.02906e6i | −0.539984 | − | 0.0224281i | ||||
\(359\) | 4.02979e7i | 0.870961i | 0.900198 | + | 0.435480i | \(0.143421\pi\) | ||||
−0.900198 | + | 0.435480i | \(0.856579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.89983e7 | −1.04150 | ||||||||
\(362\) | 822960. | − | 1.98138e7i | 0.0173482 | − | 0.417678i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.36386e6 | − | 8.84941e7i | 0.152687 | − | 1.83489i | ||||
\(365\) | 7.01892e6 | 0.144342 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.15750e7i | − | 0.436469i | −0.975896 | − | 0.218234i | \(-0.929970\pi\) | ||
0.975896 | − | 0.218234i | \(-0.0700297\pi\) | |||||||
\(368\) | −1.03020e7 | + | 6.14726e7i | −0.206717 | + | 1.23350i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.32528e6 | − | 3.19078e7i | 0.0261639 | − | 0.629929i | ||||
\(371\) | − | 1.25970e8i | − | 2.46687i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.20071e7 | 1.00216 | 0.501079 | − | 0.865401i | \(-0.332937\pi\) | ||||
0.501079 | + | 0.865401i | \(0.332937\pi\) | |||||||
\(374\) | −4.72030e7 | − | 1.96056e6i | −0.902308 | − | 0.0374771i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.67036e7 | + | 8.34999e6i | 1.25483 | + | 0.157081i | ||||
\(377\) | −3.61454e7 | −0.674573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.39645e6i | − | 0.172602i | −0.996269 | − | 0.0863010i | \(-0.972495\pi\) | ||
0.996269 | − | 0.0863010i | \(-0.0275047\pi\) | |||||||
\(380\) | 2.90759e6 | − | 3.49415e7i | 0.0529886 | − | 0.636783i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.14277e7 | − | 474649.i | −0.205008 | − | 0.00851495i | ||||
\(383\) | − | 1.54516e7i | − | 0.275028i | −0.990500 | − | 0.137514i | \(-0.956089\pi\) | ||
0.990500 | − | 0.137514i | \(-0.0439112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.96410e7 | −0.694644 | ||||||||
\(386\) | 602086. | − | 1.44960e7i | 0.0104688 | − | 0.252049i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.32301e7 | + | 7.75796e6i | 1.59610 | + | 0.132817i | ||||
\(389\) | 5.51480e7 | 0.936873 | 0.468437 | − | 0.883497i | \(-0.344817\pi\) | ||||
0.468437 | + | 0.883497i | \(0.344817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.99539e7i | − | 1.17026i | ||||||
\(392\) | −1.18962e7 | + | 9.50322e7i | −0.197492 | + | 1.57766i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.88715e6 | + | 6.95118e7i | −0.0472043 | + | 1.13650i | ||||
\(395\) | − | 3.40952e7i | − | 0.553226i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.29579e7 | −1.48564 | −0.742822 | − | 0.669489i | \(-0.766513\pi\) | ||||
−0.742822 | + | 0.669489i | \(0.766513\pi\) | |||||||
\(398\) | 4.00910e7 | + | 1.66517e6i | 0.635914 | + | 0.0264125i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.26240e7 | + | 2.11560e6i | 0.197249 | + | 0.0330563i | ||||
\(401\) | −1.17915e8 | −1.82867 | −0.914334 | − | 0.404960i | \(-0.867285\pi\) | ||||
−0.914334 | + | 0.404960i | \(0.867285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.67128e7i | − | 1.32485i | ||||||
\(404\) | 6.14682e7 | + | 5.11496e6i | 0.932195 | + | 0.0775708i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.34481e7 | + | 2.63530e6i | 0.948071 | + | 0.0393779i | ||||
\(407\) | 9.17348e7i | 1.36066i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.08808e7 | 0.889836 | 0.444918 | − | 0.895571i | \(-0.353233\pi\) | ||||
0.444918 | + | 0.895571i | \(0.353233\pi\) | |||||||
\(410\) | −698877. | + | 1.68263e7i | −0.0101403 | + | 0.244139i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.38911e6 | − | 6.47628e7i | 0.0770594 | − | 0.926050i | ||||
\(413\) | 1.49703e8 | 2.12510 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.31047e7i | − | 0.463175i | ||||||
\(416\) | 1.69727e7 | − | 8.05970e7i | 0.235760 | − | 1.11954i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.17966e6 | + | 1.00630e8i | −0.0572285 | + | 1.37785i | ||||
\(419\) | 3.24991e7i | 0.441803i | 0.975296 | + | 0.220902i | \(0.0709000\pi\) | ||||
−0.975296 | + | 0.220902i | \(0.929100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.14006e7 | 0.554830 | 0.277415 | − | 0.960750i | \(-0.410522\pi\) | ||||
0.277415 | + | 0.960750i | \(0.410522\pi\) | |||||||
\(422\) | −5.41769e7 | − | 2.25022e6i | −0.720903 | − | 0.0299425i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.45130e7 | − | 1.15936e8i | 0.190397 | − | 1.52098i | ||||
\(425\) | −1.43657e7 | −0.187137 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.39356e8i | 1.78996i | ||||||||
\(428\) | 2.70273e6 | − | 3.24797e7i | 0.0344724 | − | 0.414267i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −685948. | − | 28490.7i | −0.00862752 | − | 0.000358342i | ||||
\(431\) | 2.64521e7i | 0.330391i | 0.986261 | + | 0.165196i | \(0.0528255\pi\) | ||||
−0.986261 | + | 0.165196i | \(0.947174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.52090e7 | −0.310521 | −0.155261 | − | 0.987874i | \(-0.549622\pi\) | ||||
−0.155261 | + | 0.987874i | \(0.549622\pi\) | |||||||
\(434\) | −6.32209e6 | + | 1.52212e8i | −0.0773377 | + | 1.86200i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.36157e8 | − | 1.13300e7i | −1.64278 | − | 0.136701i | ||||
\(437\) | −1.49132e8 | −1.78701 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.58533e8i | 1.87381i | 0.349589 | + | 0.936903i | \(0.386321\pi\) | ||||
−0.349589 | + | 0.936903i | \(0.613679\pi\) | |||||||
\(440\) | −3.64835e7 | − | 4.56702e6i | −0.428291 | − | 0.0536136i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.83614e6 | + | 9.23598e7i | −0.0444250 | + | 1.06959i | ||||
\(443\) | − | 1.05332e8i | − | 1.21157i | −0.795627 | − | 0.605787i | \(-0.792858\pi\) | ||
0.795627 | − | 0.605787i | \(-0.207142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.62500e6 | 0.0978766 | ||||||||
\(446\) | 9.73297e7 | + | 4.04256e6i | 1.09709 | + | 0.0455672i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.56694e7 | + | 1.40239e8i | −0.396699 | + | 1.55968i | ||||
\(449\) | 1.45273e8 | 1.60490 | 0.802448 | − | 0.596722i | \(-0.203530\pi\) | ||||
0.802448 | + | 0.596722i | \(0.203530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.83756e7i | − | 0.527348i | ||||||
\(452\) | 1.13967e7 | + | 948351.i | 0.123413 | + | 0.0102696i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.13590e7 | − | 2.96388e6i | −0.762572 | − | 0.0316732i | ||||
\(455\) | 7.75636e7i | 0.823424i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00926e8 | 1.05744 | 0.528718 | − | 0.848797i | \(-0.322673\pi\) | ||||
0.528718 | + | 0.848797i | \(0.322673\pi\) | |||||||
\(458\) | 5.35448e6 | − | 1.28916e8i | 0.0557341 | − | 1.34187i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.51475e6 | − | 5.42554e7i | 0.0463832 | − | 0.557403i | ||||
\(461\) | 1.04798e8 | 1.06968 | 0.534838 | − | 0.844955i | \(-0.320373\pi\) | ||||
0.534838 | + | 0.844955i | \(0.320373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.32165e7i | − | 0.838430i | −0.907887 | − | 0.419215i | \(-0.862305\pi\) | ||
0.907887 | − | 0.419215i | \(-0.137695\pi\) | |||||||
\(464\) | 5.80907e7 | + | 9.73523e6i | 0.581504 | + | 0.0974523i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.88231e6 | − | 4.53190e7i | 0.0186009 | − | 0.447840i | ||||
\(467\) | 7.13276e6i | 0.0700337i | 0.999387 | + | 0.0350168i | \(0.0111485\pi\) | ||||
−0.999387 | + | 0.0350168i | \(0.988852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.96263e7 | 0.384118 | ||||||||
\(470\) | −5.86673e7 | − | 2.43673e6i | −0.565071 | − | 0.0234701i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.37779e8 | + | 1.72472e7i | 1.31026 | + | 0.164019i | ||||
\(473\) | 1.97210e6 | 0.0186357 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.06257e7i | 0.285762i | ||||||||
\(476\) | 1.34676e7 | − | 1.61845e8i | 0.124873 | − | 1.50065i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.12498e7 | + | 3.37469e6i | 0.743941 | + | 0.0308994i | ||||
\(479\) | 1.02247e8i | 0.930346i | 0.885220 | + | 0.465173i | \(0.154008\pi\) | ||||
−0.885220 | + | 0.465173i | \(0.845992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.79493e8 | 1.61292 | ||||||||
\(482\) | 6.21586e6 | − | 1.49654e8i | 0.0555086 | − | 1.33644i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.73562e6 | − | 643705.i | −0.0682274 | − | 0.00567741i | ||||
\(485\) | −8.17146e7 | −0.716266 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.59619e6i | 0.0657671i | 0.999459 | + | 0.0328836i | \(0.0104691\pi\) | ||||
−0.999459 | + | 0.0328836i | \(0.989531\pi\) | |||||||
\(488\) | −1.60552e7 | + | 1.28256e8i | −0.138152 | + | 1.10362i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.47160e6 | − | 8.35830e7i | 0.0295081 | − | 0.710444i | ||||
\(491\) | 4.78138e7i | 0.403932i | 0.979393 | + | 0.201966i | \(0.0647331\pi\) | ||||
−0.979393 | + | 0.201966i | \(0.935267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.61055e7 | −0.551692 | ||||||||
\(494\) | 1.96899e8 | + | 8.17813e6i | 1.63328 | + | 0.0678380i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.33548e7 | + | 1.39360e8i | −0.191395 | + | 1.14207i | ||||
\(497\) | −1.07003e8 | −0.871620 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.03458e7i | 0.566157i | 0.959097 | + | 0.283078i | \(0.0913556\pi\) | ||||
−0.959097 | + | 0.283078i | \(0.908644\pi\) | |||||||
\(500\) | −1.11418e7 | − | 927146.i | −0.0891346 | − | 0.00741717i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.70993e7 | − | 1.12556e6i | −0.214214 | − | 0.00889731i | ||||
\(503\) | − | 1.29972e7i | − | 0.102128i | −0.998695 | − | 0.0510639i | \(-0.983739\pi\) | ||
0.998695 | − | 0.0510639i | \(-0.0162612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.38759e7 | −0.418331 | ||||||||
\(506\) | −6.48995e6 | + | 1.56254e8i | −0.0500945 | + | 1.20609i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.03200e7 | + | 1.24019e8i | −0.0787209 | + | 0.946017i | ||||
\(509\) | −1.39419e8 | −1.05723 | −0.528616 | − | 0.848861i | \(-0.677289\pi\) | ||||
−0.528616 | + | 0.848861i | \(0.677289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.93085e7i | − | 0.519426i | ||||||
\(512\) | −4.89851e7 | + | 1.24959e8i | −0.364968 | + | 0.931020i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.28913e6 | − | 2.23647e8i | 0.0684047 | − | 1.64693i | ||||
\(515\) | 5.67635e7i | 0.415573i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.68668e8 | 1.22057 | ||||||||
\(518\) | −3.15074e8 | − | 1.30865e7i | −2.26686 | − | 0.0941533i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.93606e6 | + | 7.13855e7i | −0.0635530 | + | 0.507691i | ||||
\(521\) | 1.76371e6 | 0.0124714 | 0.00623570 | − | 0.999981i | \(-0.498015\pi\) | ||||
0.00623570 | + | 0.999981i | \(0.498015\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.26098e8i | 1.58049i | 0.612792 | + | 0.790244i | \(0.290046\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(524\) | 1.94342e7 | − | 2.33548e8i | 0.135075 | − | 1.62324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.13446e8 | − | 8.86541e6i | −1.46666 | − | 0.0609174i | ||||
\(527\) | − | 1.58587e8i | − | 1.08352i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.35287e7 | −0.564246 | ||||||||
\(530\) | −4.23525e6 | + | 1.01969e8i | −0.0284480 | + | 0.684920i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.45031e8 | − | 2.87111e7i | −2.29152 | − | 0.190684i | ||||
\(533\) | −9.46542e7 | −0.625112 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.84679e7i | 0.185906i | ||||||||
\(536\) | 3.64700e7 | + | 4.56533e6i | 0.236832 | + | 0.0296468i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.12852e6 | − | 2.19780e8i | 0.0586210 | − | 1.41137i | ||||
\(539\) | 2.40301e8i | 1.53458i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06341e8 | 0.671596 | 0.335798 | − | 0.941934i | \(-0.390994\pi\) | ||||
0.335798 | + | 0.941934i | \(0.390994\pi\) | |||||||
\(542\) | 6.25256e7 | + | 2.59699e6i | 0.392699 | + | 0.0163107i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.10410e7 | − | 1.47402e8i | 0.192814 | − | 0.915602i | ||||
\(545\) | 1.19339e8 | 0.737215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.70542e7i | − | 0.104200i | −0.998642 | − | 0.0521002i | \(-0.983408\pi\) | ||
0.998642 | − | 0.0521002i | \(-0.0165915\pi\) | |||||||
\(548\) | 3.04237e7 | + | 2.53165e6i | 0.184871 | + | 0.0153837i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.20881e7 | + | 1.33277e6i | 0.192866 | + | 0.00801064i | ||||
\(551\) | 1.40928e8i | 0.842446i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.36675e8 | −1.99083 | ||||||||
\(554\) | 1.15820e7 | − | 2.78850e8i | 0.0681166 | − | 1.63999i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.64365e6 | + | 5.58043e7i | −0.0270169 | + | 0.324671i | ||||
\(557\) | 1.31701e8 | 0.762118 | 0.381059 | − | 0.924551i | \(-0.375559\pi\) | ||||
0.381059 | + | 0.924551i | \(0.375559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.85871e6i | − | 0.0220905i | ||||||
\(560\) | 2.08906e7 | − | 1.24656e8i | 0.118956 | − | 0.709819i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −808042. | + | 1.94546e7i | −0.00455224 | + | 0.109601i | ||||
\(563\) | 9.70061e7i | 0.543593i | 0.962355 | + | 0.271797i | \(0.0876178\pi\) | ||||
−0.962355 | + | 0.271797i | \(0.912382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.98898e6 | −0.0553829 | ||||||||
\(566\) | 3.05783e8 | + | 1.27006e7i | 1.68641 | + | 0.0700448i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.84801e7 | − | 1.23278e7i | −0.537407 | − | 0.0672728i | ||||
\(569\) | −2.37401e8 | −1.28868 | −0.644341 | − | 0.764738i | \(-0.722868\pi\) | ||||
−0.644341 | + | 0.764738i | \(0.722868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.85844e7i | 0.475827i | 0.971286 | + | 0.237913i | \(0.0764635\pi\) | ||||
−0.971286 | + | 0.237913i | \(0.923537\pi\) | |||||||
\(572\) | 1.71373e7 | − | 2.05945e8i | 0.0915702 | − | 1.10043i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.66152e8 | + | 6.90108e6i | 0.878557 | + | 0.0364907i | ||||
\(575\) | 4.75539e7i | 0.250140i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.33160e8 | −1.21374 | −0.606871 | − | 0.794800i | \(-0.707576\pi\) | ||||
−0.606871 | + | 0.794800i | \(0.707576\pi\) | |||||||
\(578\) | 997644. | − | 2.40195e7i | 0.00516645 | − | 0.124389i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.12706e7 | − | 4.26638e6i | −0.262775 | − | 0.0218663i | ||||
\(581\) | −3.26893e8 | −1.66678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.93160e8i | − | 1.47945i | ||||||
\(584\) | 7.98500e6 | − | 6.37880e7i | 0.0400901 | − | 0.320258i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.78452e6 | − | 1.63346e8i | 0.0337152 | − | 0.811736i | ||||
\(587\) | 3.20487e8i | 1.58451i | 0.610187 | + | 0.792257i | \(0.291094\pi\) | ||||
−0.610187 | + | 0.792257i | \(0.708906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.38086e8 | −1.65456 | ||||||||
\(590\) | −1.21180e8 | − | 5.03316e6i | −0.590029 | − | 0.0245067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.88470e8 | − | 4.83438e7i | −1.39039 | − | 0.233010i | ||||
\(593\) | 2.06932e8 | 0.992345 | 0.496173 | − | 0.868224i | \(-0.334738\pi\) | ||||
0.496173 | + | 0.868224i | \(0.334738\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.41854e8i | 0.673429i | ||||||||
\(596\) | −1.61267e8 | − | 1.34196e7i | −0.761742 | − | 0.0633869i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.05733e8 | + | 1.26986e7i | 1.42968 | + | 0.0593815i | ||||
\(599\) | 1.70428e8i | 0.792976i | 0.918040 | + | 0.396488i | \(0.129771\pi\) | ||||
−0.918040 | + | 0.396488i | \(0.870229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.51778e8 | −1.15983 | −0.579914 | − | 0.814678i | \(-0.696914\pi\) | ||||
−0.579914 | + | 0.814678i | \(0.696914\pi\) | |||||||
\(602\) | −281332. | + | 6.77342e6i | −0.00128953 | + | 0.0310469i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.72105e7 | − | 2.06825e8i | 0.0781058 | − | 0.938625i | ||||
\(605\) | 6.78014e6 | 0.0306177 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.60842e8i | − | 1.61343i | −0.590940 | − | 0.806716i | \(-0.701243\pi\) | ||
0.590940 | − | 0.806716i | \(-0.298757\pi\) | |||||||
\(608\) | −3.14241e8 | − | 6.61751e7i | −1.39815 | − | 0.294431i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.68530e6 | − | 1.12804e8i | 0.0206418 | − | 0.496977i | ||||
\(611\) | − | 3.30025e8i | − | 1.44685i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.76049e6 | 0.0119841 | 0.00599203 | − | 0.999982i | \(-0.498093\pi\) | ||||
0.00599203 | + | 0.999982i | \(0.498093\pi\) | |||||||
\(614\) | −7.62669e7 | − | 3.16773e6i | −0.329481 | − | 0.0136849i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.50972e7 | + | 3.60258e8i | −0.192933 | + | 1.54124i | ||||
\(617\) | 5.86892e7 | 0.249863 | 0.124932 | − | 0.992165i | \(-0.460129\pi\) | ||||
0.124932 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.86112e8i | 1.20632i | 0.797619 | + | 0.603161i | \(0.206093\pi\) | ||||
−0.797619 | + | 0.603161i | \(0.793907\pi\) | |||||||
\(620\) | 1.02350e7 | − | 1.22998e8i | 0.0429452 | − | 0.516087i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.33124e7 | − | 968275.i | −0.0968760 | − | 0.00402372i | ||||
\(623\) | − | 8.51678e7i | − | 0.352218i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | −6.43205e6 | + | 1.54859e8i | −0.0262196 | + | 0.631269i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.80507e8 | + | 3.16631e7i | 1.53633 | + | 0.127842i | ||||
\(629\) | 3.28270e8 | 1.31911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.43261e8i | 0.968244i | 0.875001 | + | 0.484122i | \(0.160861\pi\) | ||||
−0.875001 | + | 0.484122i | \(0.839139\pi\) | |||||||
\(632\) | −3.09858e8 | − | 3.87881e7i | −1.22747 | − | 0.153655i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.15972e6 | − | 5.19980e7i | 0.00847482 | − | 0.204042i | ||||
\(635\) | − | 1.08701e8i | − | 0.424534i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.70185e8 | 1.81907 | ||||||||
\(638\) | 1.47657e8 | + | 6.13291e6i | 0.568582 | + | 0.0236159i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.35882e7 | − | 1.12320e8i | 0.128129 | − | 0.428466i | ||||
\(641\) | −1.54539e8 | −0.586766 | −0.293383 | − | 0.955995i | \(-0.594781\pi\) | ||||
−0.293383 | + | 0.955995i | \(0.594781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.73101e8i | − | 0.651130i | −0.945520 | − | 0.325565i | \(-0.894445\pi\) | ||
0.945520 | − | 0.325565i | \(-0.105555\pi\) | |||||||
\(644\) | −5.35746e8 | − | 4.45811e7i | −2.00586 | − | 0.166914i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.60103e8 | + | 1.49568e7i | 1.33576 | + | 0.0554806i | ||||
\(647\) | − | 2.97783e8i | − | 1.09948i | −0.835336 | − | 0.549740i | \(-0.814727\pi\) | ||
0.835336 | − | 0.549740i | \(-0.185273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.48391e8 | 1.27448 | ||||||||
\(650\) | 2.60777e6 | − | 6.27851e7i | 0.00949573 | − | 0.228621i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.16805e7 | − | 2.60542e8i | 0.0782216 | − | 0.940016i | ||||
\(653\) | 4.67892e8 | 1.68038 | 0.840188 | − | 0.542296i | \(-0.182445\pi\) | ||||
0.840188 | + | 0.542296i | \(0.182445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.04701e8i | 0.728443i | ||||||||
\(656\) | 1.52123e8 | + | 2.54937e7i | 0.538868 | + | 0.0903070i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.40616e7 | + | 5.79313e8i | −0.0844592 | + | 2.03346i | ||||
\(659\) | − | 3.65042e8i | − | 1.27552i | −0.770236 | − | 0.637759i | \(-0.779862\pi\) | ||
0.770236 | − | 0.637759i | \(-0.220138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50270e7 | 0.0866573 | 0.0433287 | − | 0.999061i | \(-0.486204\pi\) | ||||
0.0433287 | + | 0.999061i | \(0.486204\pi\) | |||||||
\(662\) | 1.84530e8 | + | 7.66443e6i | 0.636054 | + | 0.0264183i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.00856e8 | − | 3.76612e7i | −1.02767 | − | 0.128644i | ||||
\(665\) | 3.02414e8 | 1.02834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.18825e8i | 0.737429i | ||||||||
\(668\) | −1.31519e7 | + | 1.58051e8i | −0.0441224 | + | 0.530234i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.20762e7 | − | 1.33228e6i | −0.106649 | − | 0.00442965i | ||||
\(671\) | 3.24312e8i | 1.07348i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.07582e8 | −1.33712 | −0.668559 | − | 0.743659i | \(-0.733088\pi\) | ||||
−0.668559 | + | 0.743659i | \(0.733088\pi\) | |||||||
\(674\) | 1.47347e7 | − | 3.54757e8i | 0.0481241 | − | 1.15865i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.51101e7 | − | 7.91440e6i | −0.307883 | − | 0.0256199i | ||||
\(677\) | 3.08100e8 | 0.992946 | 0.496473 | − | 0.868052i | \(-0.334628\pi\) | ||||
0.496473 | + | 0.868052i | \(0.334628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.06893e8i | 2.57755i | ||||||||
\(680\) | −1.63430e7 | + | 1.30555e8i | −0.0519762 | + | 0.415210i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.47129e7 | + | 3.54230e8i | −0.0463814 | + | 1.11669i | ||||
\(683\) | 2.86032e8i | 0.897744i | 0.893596 | + | 0.448872i | \(0.148174\pi\) | ||||
−0.893596 | + | 0.448872i | \(0.851826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.66658e7 | −0.0829628 | ||||||||
\(686\) | −3.06250e8 | − | 1.27200e7i | −0.948645 | − | 0.0394017i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.03929e6 | + | 6.20149e6i | −0.00319131 | + | 0.0190428i | ||||
\(689\) | −5.73611e8 | −1.75372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.17632e8i | − | 1.87196i | −0.352059 | − | 0.935978i | \(-0.614518\pi\) | ||
0.352059 | − | 0.935978i | \(-0.385482\pi\) | |||||||
\(692\) | 5.23314e8 | + | 4.35465e7i | 1.57922 | + | 0.131412i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.09857e8 | + | 8.71636e6i | 0.627835 | + | 0.0260770i | ||||
\(695\) | − | 4.89116e7i | − | 0.145699i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.73111e8 | −0.511241 | ||||||||
\(698\) | −2.50591e7 | + | 6.03328e8i | −0.0736884 | + | 1.77414i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.15513e6 | + | 1.10020e8i | −0.0266913 | + | 0.320759i | ||||
\(701\) | 2.90668e8 | 0.843808 | 0.421904 | − | 0.906641i | \(-0.361362\pi\) | ||||
0.421904 | + | 0.906641i | \(0.361362\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.99828e8i | − | 2.01431i | ||||||
\(704\) | −8.30103e7 | + | 3.26367e8i | −0.237911 | + | 0.935380i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.42985e6 | + | 5.85016e7i | −0.00690502 | + | 0.166247i | ||||
\(707\) | 5.31999e8i | 1.50540i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.33660e7 | 0.149736 | 0.0748679 | − | 0.997193i | \(-0.476146\pi\) | ||||
0.0748679 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(710\) | 8.66155e7 | + | 3.59755e6i | 0.242003 | + | 0.0100515i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.81215e6 | − | 7.83840e7i | 0.0271847 | − | 0.217164i | ||||
\(713\) | −5.24962e8 | −1.44830 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.80507e8i | 0.493828i | ||||||||
\(716\) | 1.64508e7 | − | 1.97695e8i | 0.0448176 | − | 0.538588i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.22105e8 | − | 1.33786e7i | −0.870210 | − | 0.0361440i | ||||
\(719\) | 8.54538e7i | 0.229903i | 0.993371 | + | 0.114951i | \(0.0366713\pi\) | ||||
−0.993371 | + | 0.114951i | \(0.963329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.60513e8 | 1.49548 | ||||||||
\(722\) | 1.62670e7 | − | 3.91649e8i | 0.0432212 | − | 1.04060i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.58100e8 | + | 1.31560e7i | 0.416598 | + | 0.0346664i | ||||
\(725\) | 4.49378e7 | 0.117923 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.69711e8i | − | 1.22244i | −0.791461 | − | 0.611220i | \(-0.790679\pi\) | ||
0.791461 | − | 0.611220i | \(-0.209321\pi\) | |||||||
\(728\) | 7.04898e8 | + | 8.82395e7i | 1.82697 | + | 0.228701i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.33022e6 | + | 5.61030e7i | −0.00599003 | + | 0.144217i | ||||
\(731\) | − | 7.05710e6i | − | 0.0180665i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.65700e8 | 0.928567 | 0.464283 | − | 0.885687i | \(-0.346312\pi\) | ||||
0.464283 | + | 0.885687i | \(0.346312\pi\) | |||||||
\(734\) | 1.72452e8 | + | 7.16273e6i | 0.436093 | + | 0.0181130i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.87937e8 | − | 1.02753e8i | −1.22386 | − | 0.257728i | ||||
\(737\) | 9.22189e7 | 0.230366 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.87643e8i | 1.20828i | 0.796877 | + | 0.604142i | \(0.206484\pi\) | ||||
−0.796877 | + | 0.604142i | \(0.793516\pi\) | |||||||
\(740\) | 2.54602e8 | + | 2.11862e7i | 0.628300 | + | 0.0522828i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.00689e9 | + | 4.18211e7i | 2.46474 | + | 0.102373i | ||||
\(743\) | − | 7.13753e8i | − | 1.74013i | −0.492939 | − | 0.870064i | \(-0.664077\pi\) | ||
0.492939 | − | 0.870064i | \(-0.335923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.41348e8 | 0.341839 | ||||||||
\(746\) | −1.72659e7 | + | 4.15699e8i | −0.0415885 | + | 1.00129i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.13420e7 | − | 3.76648e8i | 0.0748897 | − | 0.899975i | ||||
\(749\) | 2.81107e8 | 0.669000 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.91873e8i | 0.925180i | 0.886572 | + | 0.462590i | \(0.153080\pi\) | ||||
−0.886572 | + | 0.462590i | \(0.846920\pi\) | |||||||
\(752\) | −8.88874e7 | + | 5.30397e8i | −0.209019 | + | 1.24723i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.20000e7 | − | 2.88914e8i | 0.0279941 | − | 0.673991i | ||||
\(755\) | 1.81279e8i | 0.421217i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.04521e7 | 0.0471466 | 0.0235733 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235733 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(758\) | 7.51068e7 | + | 3.11954e6i | 0.172453 | + | 0.00716281i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.78326e8 | + | 3.48410e7i | 0.634035 | + | 0.0793688i | ||||
\(761\) | −5.17521e8 | −1.17429 | −0.587143 | − | 0.809483i | \(-0.699748\pi\) | ||||
−0.587143 | + | 0.809483i | \(0.699748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.17842e9i | − | 2.65293i | ||||||
\(764\) | 7.58784e6 | − | 9.11857e7i | 0.0170152 | − | 0.204478i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.23506e8 | + | 5.12980e6i | 0.274791 | + | 0.0114134i | ||||
\(767\) | − | 6.81679e8i | − | 1.51075i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.63067e8 | −0.578478 | −0.289239 | − | 0.957257i | \(-0.593402\pi\) | ||||
−0.289239 | + | 0.957257i | \(0.593402\pi\) | |||||||
\(770\) | 1.31605e7 | − | 3.16855e8i | 0.0288270 | − | 0.694046i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.15668e8 | + | 9.62508e6i | 0.251397 | + | 0.0209196i | ||||
\(773\) | −5.41479e8 | −1.17231 | −0.586155 | − | 0.810199i | \(-0.699359\pi\) | ||||
−0.586155 | + | 0.810199i | \(0.699359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.07806e8i | 0.231599i | ||||||||
\(776\) | −9.29618e7 | + | 7.42623e8i | −0.198939 | + | 1.58922i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.83087e7 | + | 4.40804e8i | −0.0388793 | + | 0.936066i | ||||
\(779\) | 3.69049e8i | 0.780678i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.49019e8 | −0.522733 | ||||||||
\(782\) | 5.59149e8 | + | 2.32241e7i | 1.16925 | + | 0.0485645i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.55654e8 | − | 1.26637e8i | −1.56810 | − | 0.262793i | ||||
\(785\) | −3.33508e8 | −0.689440 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.07996e7i | 0.0426709i | 0.999772 | + | 0.0213354i | \(0.00679179\pi\) | ||||
−0.999772 | + | 0.0213354i | \(0.993208\pi\) | |||||||
\(788\) | −5.54657e8 | − | 4.61547e7i | −1.13356 | − | 0.0943272i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.72527e8 | + | 1.13193e7i | 0.552749 | + | 0.0229583i | ||||
\(791\) | 9.86365e7i | 0.199300i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.34565e8 | 1.27250 | ||||||||
\(794\) | 3.08613e7 | − | 7.43023e8i | 0.0616527 | − | 1.48436i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.66198e7 | + | 3.19899e8i | −0.0527795 | + | 0.634270i | ||||
\(797\) | −6.81937e8 | −1.34701 | −0.673503 | − | 0.739185i | \(-0.735211\pi\) | ||||
−0.673503 | + | 0.739185i | \(0.735211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.03575e8i | − | 1.18329i | ||||||
\(800\) | −2.11013e7 | + | 1.00202e8i | −0.0412135 | + | 0.195708i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.91467e7 | − | 9.42505e8i | 0.0758879 | − | 1.82709i | ||||
\(803\) | − | 1.61296e8i | − | 0.311513i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.69572e8 | 0.900150 | ||||||||
\(806\) | 6.93105e8 | + | 2.87879e7i | 1.32371 | + | 0.0549801i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.12914e7 | + | 4.89624e8i | −0.116189 | + | 0.928173i | ||||
\(809\) | 7.38152e7 | 0.139412 | 0.0697060 | − | 0.997568i | \(-0.477794\pi\) | ||||
0.0697060 | + | 0.997568i | \(0.477794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.60157e8i | − | 0.300250i | −0.988667 | − | 0.150125i | \(-0.952032\pi\) | ||
0.988667 | − | 0.150125i | \(-0.0479675\pi\) | |||||||
\(812\) | −4.21285e7 | + | 5.06273e8i | −0.0786879 | + | 0.945620i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.33246e8 | − | 3.04552e7i | −1.35949 | − | 0.0564661i | ||||
\(815\) | 2.28361e8i | 0.421841i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50448e7 | −0.0275880 | ||||||||
\(818\) | −2.02119e7 | + | 4.86626e8i | −0.0369273 | + | 0.889070i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.34263e8 | − | 1.11724e7i | −0.243508 | − | 0.0202631i | ||||
\(821\) | 7.70613e8 | 1.39254 | 0.696269 | − | 0.717781i | \(-0.254842\pi\) | ||||
0.696269 | + | 0.717781i | \(0.254842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.88839e8i | 1.59450i | 0.603652 | + | 0.797248i | \(0.293712\pi\) | ||||
−0.603652 | + | 0.797248i | \(0.706288\pi\) | |||||||
\(824\) | 5.15867e8 | + | 6.45765e7i | 0.922054 | + | 0.115423i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.97001e7 | + | 1.19659e9i | −0.0881896 | + | 2.12327i | ||||
\(827\) | − | 7.22792e8i | − | 1.27790i | −0.769248 | − | 0.638950i | \(-0.779369\pi\) | ||
0.769248 | − | 0.638950i | \(-0.220631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.80531e8 | 1.37002 | 0.685009 | − | 0.728534i | \(-0.259798\pi\) | ||||
0.685009 | + | 0.728534i | \(0.259798\pi\) | |||||||
\(830\) | 2.64609e8 | + | 1.09905e7i | 0.462776 | + | 0.0192213i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.38586e8 | + | 1.62422e8i | 1.10879 | + | 0.282017i | ||||
\(833\) | 8.59910e8 | 1.48771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.38529e8i | − | 0.237948i | ||||||
\(836\) | −8.02962e8 | − | 6.68169e7i | −1.37428 | − | 0.114358i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.59769e8 | − | 1.07894e7i | −0.441423 | − | 0.0183344i | ||||
\(839\) | − | 3.58594e8i | − | 0.607180i | −0.952803 | − | 0.303590i | \(-0.901815\pi\) | ||
0.952803 | − | 0.303590i | \(-0.0981853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.88036e8 | −0.652356 | ||||||||
\(842\) | −1.37446e7 | + | 3.30919e8i | −0.0230249 | + | 0.554352i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.59726e7 | − | 4.32295e8i | 0.0598335 | − | 0.719039i | ||||
\(845\) | 8.33623e7 | 0.138166 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.69507e7i | − | 0.110181i | ||||||
\(848\) | 9.21875e8 | + | 1.54494e8i | 1.51176 | + | 0.253351i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.76928e6 | − | 1.14826e8i | 0.00776598 | − | 0.186976i | ||||
\(851\) | − | 1.08666e9i | − | 1.76321i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.64679e8 | 1.23206 | 0.616031 | − | 0.787722i | \(-0.288740\pi\) | ||||
0.616031 | + | 0.787722i | \(0.288740\pi\) | |||||||
\(854\) | −1.11389e9 | − | 4.62651e7i | −1.78842 | − | 0.0742814i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.58716e8 | + | 3.23862e7i | 0.412479 | + | 0.0516343i | ||||
\(857\) | 7.39540e8 | 1.17495 | 0.587474 | − | 0.809243i | \(-0.300122\pi\) | ||||
0.587474 | + | 0.809243i | \(0.300122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.38366e8i | 0.376067i | 0.982163 | + | 0.188034i | \(0.0602114\pi\) | ||||
−0.982163 | + | 0.188034i | \(0.939789\pi\) | |||||||
\(860\) | 455458. | − | 5.47340e6i | 0.000716066 | − | 0.00860521i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.11435e8 | − | 8.78188e6i | −0.330107 | − | 0.0137109i | ||||
\(863\) | − | 1.16251e9i | − | 1.80870i | −0.426794 | − | 0.904349i | \(-0.640357\pi\) | ||
0.426794 | − | 0.904349i | \(-0.359643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.58676e8 | −0.708692 | ||||||||
\(866\) | 8.36917e6 | − | 2.01498e8i | 0.0128863 | − | 0.310254i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.21455e9 | − | 1.01066e8i | −1.85719 | − | 0.154542i | ||||
\(869\) | −7.83514e8 | −1.19395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.80440e8i | − | 0.273073i | ||||||
\(872\) | 1.35765e8 | − | 1.08456e9i | 0.204757 | − | 1.63570i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.95107e7 | − | 1.19203e9i | 0.0741591 | − | 1.78547i | ||||
\(875\) | − | 9.64310e7i | − | 0.143944i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.18584e8 | 0.175803 | 0.0879016 | − | 0.996129i | \(-0.471984\pi\) | ||||
0.0879016 | + | 0.996129i | \(0.471984\pi\) | |||||||
\(878\) | −1.26717e9 | − | 5.26315e7i | −1.87219 | − | 0.0777610i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.86169e7 | − | 2.90100e8i | 0.0713411 | − | 0.425697i | ||||
\(881\) | 5.84028e8 | 0.854095 | 0.427047 | − | 0.904229i | \(-0.359554\pi\) | ||||
0.427047 | + | 0.904229i | \(0.359554\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.76901e8i | − | 0.547451i | −0.961808 | − | 0.273725i | \(-0.911744\pi\) | ||
0.961808 | − | 0.273725i | \(-0.0882560\pi\) | |||||||
\(884\) | −7.36968e8 | − | 6.13253e7i | −1.06682 | − | 0.0887735i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.41932e8 | + | 3.49694e7i | 1.21053 | + | 0.0502791i | ||||
\(887\) | − | 9.41273e8i | − | 1.34879i | −0.738370 | − | 0.674395i | \(-0.764404\pi\) | ||
0.738370 | − | 0.674395i | \(-0.235596\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.07337e9 | −1.52772 | ||||||||
\(890\) | −2.86343e6 | + | 6.89405e7i | −0.00406178 | + | 0.0977923i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.46253e7 | + | 7.76625e8i | −0.0910559 | + | 1.09425i | ||||
\(893\) | −1.28674e9 | −1.80691 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.73276e8i | 0.241697i | ||||||||
\(896\) | −1.10911e9 | − | 3.31667e8i | −1.54187 | − | 0.461082i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.82295e7 | + | 1.16119e9i | −0.0666015 | + | 1.60351i | ||||
\(899\) | 4.96082e8i | 0.682770i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.04906e9 | −1.43426 | ||||||||
\(902\) | 3.86672e8 | + | 1.60603e7i | 0.526893 | + | 0.0218844i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.13639e7 | + | 9.07799e7i | −0.0153823 | + | 0.122881i | ||||
\(905\) | −1.38572e8 | −0.186952 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.10117e9i | − | 1.47582i | −0.674902 | − | 0.737908i | \(-0.735814\pi\) | ||
0.674902 | − | 0.737908i | \(-0.264186\pi\) | |||||||
\(908\) | 4.73812e7 | − | 5.69396e8i | 0.0632919 | − | 0.760601i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.19974e8 | − | 2.57505e7i | −0.822715 | − | 0.0341712i | ||||
\(911\) | 5.43788e8i | 0.719241i | 0.933099 | + | 0.359621i | \(0.117094\pi\) | ||||
−0.933099 | + | 0.359621i | \(0.882906\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.60751e8 | −0.999609 | ||||||||
\(914\) | −3.35066e7 | + | 8.06712e8i | −0.0438825 | + | 1.05653i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.02866e9 | + | 8.55979e7i | 1.33840 | + | 0.111372i | ||||
\(917\) | 2.02132e9 | 2.62137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.23288e9i | 1.58845i | 0.607626 | + | 0.794224i | \(0.292122\pi\) | ||||
−0.607626 | + | 0.794224i | \(0.707878\pi\) | |||||||
\(920\) | 4.32170e8 | + | 5.40992e7i | 0.554998 | + | 0.0694749i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.47922e7 | + | 8.37665e8i | −0.0443904 | + | 1.06875i | ||||
\(923\) | 4.87243e8i | 0.619642i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.23155e8 | −0.281956 | ||||||||
\(926\) | 6.65159e8 | + | 2.76272e7i | 0.837707 | + | 0.0347940i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.71004e7 | + | 4.61094e8i | −0.121500 | + | 0.576959i | ||||
\(929\) | −5.78905e8 | −0.722038 | −0.361019 | − | 0.932558i | \(-0.617571\pi\) | ||||
−0.361019 | + | 0.932558i | \(0.617571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.83321e9i | − | 2.27177i | ||||||
\(932\) | 3.61615e8 | + | 3.00911e7i | 0.446682 | + | 0.0371698i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.70129e7 | − | 2.36802e6i | −0.0699733 | − | 0.00290633i | ||||
\(935\) | 3.30125e8i | 0.403872i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.59361e8 | −0.923059 | −0.461529 | − | 0.887125i | \(-0.652699\pi\) | ||||
−0.461529 | + | 0.887125i | \(0.652699\pi\) | |||||||
\(938\) | −1.31556e7 | + | 3.16737e8i | −0.0159405 | + | 0.383787i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.89541e7 | − | 4.68125e8i | 0.0468997 | − | 0.563610i | ||||
\(941\) | −5.09200e8 | −0.611110 | −0.305555 | − | 0.952174i | \(-0.598842\pi\) | ||||
−0.305555 | + | 0.952174i | \(0.598842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.73040e8i | 0.683360i | ||||||||
\(944\) | −1.83600e8 | + | 1.09556e9i | −0.218252 | + | 1.30232i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −654720. | + | 1.57632e7i | −0.000773361 | + | 0.0186196i | ||||
\(947\) | 5.18817e8i | 0.610892i | 0.952209 | + | 0.305446i | \(0.0988055\pi\) | ||||
−0.952209 | + | 0.305446i | \(0.901194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.15599e8 | −0.369265 | ||||||||
\(950\) | −2.44794e8 | − | 1.01675e7i | −0.285516 | − | 0.0118588i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.28917e9 | + | 1.61379e8i | 1.49417 | + | 0.187041i | ||||
\(953\) | −1.67690e9 | −1.93745 | −0.968723 | − | 0.248146i | \(-0.920179\pi\) | ||||
−0.968723 | + | 0.248146i | \(0.920179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.99227e7i | 0.0917614i | ||||||||
\(956\) | −5.39485e7 | + | 6.48318e8i | −0.0617456 | + | 0.742018i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.17272e8 | − | 3.39452e7i | −0.929544 | − | 0.0386084i | ||||
\(959\) | 2.63312e8i | 0.298549i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.02597e8 | −0.340953 | ||||||||
\(962\) | −5.95901e7 | + | 1.43471e9i | −0.0669344 | + | 1.61153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.19414e9 | + | 9.93681e7i | 1.33298 | + | 0.110922i | ||||
\(965\) | −1.01381e8 | −0.112817 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.67789e9i | 1.85560i | 0.373082 | + | 0.927798i | \(0.378301\pi\) | ||||
−0.373082 | + | 0.927798i | \(0.621699\pi\) | |||||||
\(968\) | 7.71336e6 | − | 6.16180e7i | 0.00850389 | − | 0.0679331i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.71286e7 | − | 6.53154e8i | 0.0297243 | − | 0.715649i | ||||
\(971\) | − | 5.10919e8i | − | 0.558078i | −0.960280 | − | 0.279039i | \(-0.909984\pi\) | ||
0.960280 | − | 0.279039i | \(-0.0900158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.82979e8 | −0.524312 | ||||||||
\(974\) | −6.07172e7 | − | 2.52187e6i | −0.0657105 | − | 0.00272927i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.01984e9 | − | 1.70911e8i | −1.09694 | − | 0.183832i | ||||
\(977\) | −3.24832e7 | −0.0348318 | −0.0174159 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174159 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.98204e8i | − | 0.211234i | ||||||
\(980\) | 6.66936e8 | + | 5.54977e7i | 0.708607 | + | 0.0589654i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.82181e8 | − | 1.58738e7i | −0.403584 | − | 0.0167628i | ||||
\(983\) | 7.49859e8i | 0.789439i | 0.918802 | + | 0.394720i | \(0.129158\pi\) | ||||
−0.918802 | + | 0.394720i | \(0.870842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.86147e8 | 0.508697 | ||||||||
\(986\) | 2.19465e7 | − | 5.28388e8i | 0.0228946 | − | 0.551217i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.30737e8 | + | 1.57112e9i | −0.135559 | + | 1.62906i | ||||
\(989\) | −2.33607e7 | −0.0241489 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.65908e8i | 0.684216i | 0.939661 | + | 0.342108i | \(0.111141\pi\) | ||||
−0.939661 | + | 0.342108i | \(0.888859\pi\) | |||||||
\(992\) | −1.10616e9 | − | 2.32944e8i | −1.13314 | − | 0.238625i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.55241e7 | − | 8.55287e8i | 0.0361713 | − | 0.870869i | ||||
\(995\) | − | 2.80386e8i | − | 0.284634i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.37105e8 | −0.642873 | −0.321437 | − | 0.946931i | \(-0.604166\pi\) | ||||
−0.321437 | + | 0.946931i | \(0.604166\pi\) | |||||||
\(998\) | −5.62282e8 | − | 2.33542e7i | −0.565669 | − | 0.0234949i | ||||
\(999\) | 0 | 0 |
(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 | 180.7.c.b.91.14 | 24 | ||
3.2 | odd | 2 | 60.7.c.a.31.11 | ✓ | 24 | ||
4.3 | odd | 2 | inner | 180.7.c.b.91.13 | 24 | ||
12.11 | even | 2 | 60.7.c.a.31.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.11 | ✓ | 24 | 3.2 | odd | 2 | ||
60.7.c.a.31.12 | yes | 24 | 12.11 | even | 2 | ||
180.7.c.b.91.13 | 24 | 4.3 | odd | 2 | inner | ||
180.7.c.b.91.14 | 24 | 1.1 | even | 1 | trivial |