Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.4270373191\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 957 x^{8} + 1224 x^{7} + 310102 x^{6} - 241884 x^{5} - 40367312 x^{4} + 11067840 x^{3} + 1840757376 x^{2} + 541859072 x - 4516262912 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(10.4944\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.49443 | 0.750808 | 0.375404 | − | 0.926861i | \(-0.377504\pi\) | ||||
0.375404 | + | 0.926861i | \(0.377504\pi\) | |||||||
\(3\) | 45.4613 | 0.972115 | 0.486058 | − | 0.873927i | \(-0.338435\pi\) | ||||
0.486058 | + | 0.873927i | \(0.338435\pi\) | |||||||
\(4\) | −55.8447 | −0.436287 | ||||||||
\(5\) | −130.405 | −0.466553 | −0.233276 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233276 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(6\) | 386.168 | 0.729872 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −1561.66 | −1.07838 | ||||||||
\(9\) | −120.267 | −0.0549919 | ||||||||
\(10\) | −1107.72 | −0.350292 | ||||||||
\(11\) | 1042.49 | 0.236155 | 0.118078 | − | 0.993004i | \(-0.462327\pi\) | ||||
0.118078 | + | 0.993004i | \(0.462327\pi\) | |||||||
\(12\) | −2538.77 | −0.424121 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 2913.59 | 0.283779 | ||||||||
\(15\) | −5928.40 | −0.453543 | ||||||||
\(16\) | −6117.25 | −0.373367 | ||||||||
\(17\) | −29763.8 | −1.46932 | −0.734661 | − | 0.678435i | \(-0.762659\pi\) | ||||
−0.734661 | + | 0.678435i | \(0.762659\pi\) | |||||||
\(18\) | −1021.60 | −0.0412884 | ||||||||
\(19\) | 5796.19 | 0.193867 | 0.0969337 | − | 0.995291i | \(-0.469097\pi\) | ||||
0.0969337 | + | 0.995291i | \(0.469097\pi\) | |||||||
\(20\) | 7282.45 | 0.203551 | ||||||||
\(21\) | 15593.2 | 0.367425 | ||||||||
\(22\) | 8855.36 | 0.177307 | ||||||||
\(23\) | −92127.5 | −1.57885 | −0.789427 | − | 0.613844i | \(-0.789622\pi\) | ||||
−0.789427 | + | 0.613844i | \(0.789622\pi\) | |||||||
\(24\) | −70994.9 | −1.04831 | ||||||||
\(25\) | −61119.4 | −0.782329 | ||||||||
\(26\) | −18662.3 | −0.208237 | ||||||||
\(27\) | −104891. | −1.02557 | ||||||||
\(28\) | −19154.7 | −0.164901 | ||||||||
\(29\) | −34842.8 | −0.265289 | −0.132645 | − | 0.991164i | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(30\) | −50358.4 | −0.340524 | ||||||||
\(31\) | 186908. | 1.12684 | 0.563419 | − | 0.826172i | \(-0.309486\pi\) | ||||
0.563419 | + | 0.826172i | \(0.309486\pi\) | |||||||
\(32\) | 147929. | 0.798049 | ||||||||
\(33\) | 47393.0 | 0.229570 | ||||||||
\(34\) | −252826. | −1.10318 | ||||||||
\(35\) | −44729.1 | −0.176340 | ||||||||
\(36\) | 6716.28 | 0.0239922 | ||||||||
\(37\) | 38460.8 | 0.124828 | 0.0624140 | − | 0.998050i | \(-0.480120\pi\) | ||||
0.0624140 | + | 0.998050i | \(0.480120\pi\) | |||||||
\(38\) | 49235.3 | 0.145557 | ||||||||
\(39\) | −99878.5 | −0.269616 | ||||||||
\(40\) | 203648. | 0.503119 | ||||||||
\(41\) | 9960.74 | 0.0225709 | 0.0112854 | − | 0.999936i | \(-0.496408\pi\) | ||||
0.0112854 | + | 0.999936i | \(0.496408\pi\) | |||||||
\(42\) | 132456. | 0.275866 | ||||||||
\(43\) | −33656.3 | −0.0645545 | −0.0322773 | − | 0.999479i | \(-0.510276\pi\) | ||||
−0.0322773 | + | 0.999479i | \(0.510276\pi\) | |||||||
\(44\) | −58217.6 | −0.103031 | ||||||||
\(45\) | 15683.5 | 0.0256566 | ||||||||
\(46\) | −782571. | −1.18542 | ||||||||
\(47\) | 409530. | 0.575364 | 0.287682 | − | 0.957726i | \(-0.407115\pi\) | ||||
0.287682 | + | 0.957726i | \(0.407115\pi\) | |||||||
\(48\) | −278098. | −0.362956 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −519175. | −0.587379 | ||||||||
\(51\) | −1.35310e6 | −1.42835 | ||||||||
\(52\) | 122691. | 0.121004 | ||||||||
\(53\) | −1.24539e6 | −1.14905 | −0.574524 | − | 0.818488i | \(-0.694813\pi\) | ||||
−0.574524 | + | 0.818488i | \(0.694813\pi\) | |||||||
\(54\) | −890993. | −0.770009 | ||||||||
\(55\) | −135946. | −0.110179 | ||||||||
\(56\) | −535648. | −0.407588 | ||||||||
\(57\) | 263502. | 0.188461 | ||||||||
\(58\) | −295969. | −0.199181 | ||||||||
\(59\) | −1.59698e6 | −1.01232 | −0.506161 | − | 0.862439i | \(-0.668936\pi\) | ||||
−0.506161 | + | 0.862439i | \(0.668936\pi\) | |||||||
\(60\) | 331070. | 0.197875 | ||||||||
\(61\) | 1.14496e6 | 0.645856 | 0.322928 | − | 0.946424i | \(-0.395333\pi\) | ||||
0.322928 | + | 0.946424i | \(0.395333\pi\) | |||||||
\(62\) | 1.58767e6 | 0.846039 | ||||||||
\(63\) | −41251.6 | −0.0207850 | ||||||||
\(64\) | 2.03958e6 | 0.972549 | ||||||||
\(65\) | 286501. | 0.129398 | ||||||||
\(66\) | 402577. | 0.172363 | ||||||||
\(67\) | −1.72469e6 | −0.700566 | −0.350283 | − | 0.936644i | \(-0.613915\pi\) | ||||
−0.350283 | + | 0.936644i | \(0.613915\pi\) | |||||||
\(68\) | 1.66215e6 | 0.641045 | ||||||||
\(69\) | −4.18824e6 | −1.53483 | ||||||||
\(70\) | −379948. | −0.132398 | ||||||||
\(71\) | −1.80050e6 | −0.597019 | −0.298509 | − | 0.954407i | \(-0.596489\pi\) | ||||
−0.298509 | + | 0.954407i | \(0.596489\pi\) | |||||||
\(72\) | 187816. | 0.0593019 | ||||||||
\(73\) | 6.02038e6 | 1.81132 | 0.905658 | − | 0.424010i | \(-0.139378\pi\) | ||||
0.905658 | + | 0.424010i | \(0.139378\pi\) | |||||||
\(74\) | 326702. | 0.0937219 | ||||||||
\(75\) | −2.77857e6 | −0.760514 | ||||||||
\(76\) | −323686. | −0.0845817 | ||||||||
\(77\) | 357574. | 0.0892584 | ||||||||
\(78\) | −848411. | −0.202430 | ||||||||
\(79\) | 4.01302e6 | 0.915748 | 0.457874 | − | 0.889017i | \(-0.348611\pi\) | ||||
0.457874 | + | 0.889017i | \(0.348611\pi\) | |||||||
\(80\) | 797723. | 0.174195 | ||||||||
\(81\) | −4.50548e6 | −0.941984 | ||||||||
\(82\) | 84610.8 | 0.0169464 | ||||||||
\(83\) | 2.81688e6 | 0.540749 | 0.270374 | − | 0.962755i | \(-0.412853\pi\) | ||||
0.270374 | + | 0.962755i | \(0.412853\pi\) | |||||||
\(84\) | −870799. | −0.160303 | ||||||||
\(85\) | 3.88136e6 | 0.685516 | ||||||||
\(86\) | −285891. | −0.0484681 | ||||||||
\(87\) | −1.58400e6 | −0.257892 | ||||||||
\(88\) | −1.62801e6 | −0.254664 | ||||||||
\(89\) | −4.78900e6 | −0.720078 | −0.360039 | − | 0.932937i | \(-0.617237\pi\) | ||||
−0.360039 | + | 0.932937i | \(0.617237\pi\) | |||||||
\(90\) | 133222. | 0.0192632 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 5.14483e6 | 0.688833 | ||||||||
\(93\) | 8.49707e6 | 1.09542 | ||||||||
\(94\) | 3.47872e6 | 0.431988 | ||||||||
\(95\) | −755854. | −0.0904493 | ||||||||
\(96\) | 6.72507e6 | 0.775795 | ||||||||
\(97\) | −4.85052e6 | −0.539620 | −0.269810 | − | 0.962914i | \(-0.586961\pi\) | ||||
−0.269810 | + | 0.962914i | \(0.586961\pi\) | |||||||
\(98\) | 999361. | 0.107258 | ||||||||
\(99\) | −125377. | −0.0129866 | ||||||||
\(100\) | 3.41320e6 | 0.341320 | ||||||||
\(101\) | 1.01297e7 | 0.978298 | 0.489149 | − | 0.872200i | \(-0.337307\pi\) | ||||
0.489149 | + | 0.872200i | \(0.337307\pi\) | |||||||
\(102\) | −1.14938e7 | −1.07242 | ||||||||
\(103\) | −7.80641e6 | −0.703916 | −0.351958 | − | 0.936016i | \(-0.614484\pi\) | ||||
−0.351958 | + | 0.936016i | \(0.614484\pi\) | |||||||
\(104\) | 3.43096e6 | 0.299088 | ||||||||
\(105\) | −2.03344e6 | −0.171423 | ||||||||
\(106\) | −1.05788e7 | −0.862715 | ||||||||
\(107\) | 1.89287e7 | 1.49375 | 0.746874 | − | 0.664966i | \(-0.231554\pi\) | ||||
0.746874 | + | 0.664966i | \(0.231554\pi\) | |||||||
\(108\) | 5.85763e6 | 0.447444 | ||||||||
\(109\) | 1.46063e7 | 1.08031 | 0.540154 | − | 0.841566i | \(-0.318366\pi\) | ||||
0.540154 | + | 0.841566i | \(0.318366\pi\) | |||||||
\(110\) | −1.15479e6 | −0.0827233 | ||||||||
\(111\) | 1.74848e6 | 0.121347 | ||||||||
\(112\) | −2.09822e6 | −0.141120 | ||||||||
\(113\) | 2.22062e6 | 0.144777 | 0.0723886 | − | 0.997377i | \(-0.476938\pi\) | ||||
0.0723886 | + | 0.997377i | \(0.476938\pi\) | |||||||
\(114\) | 2.23830e6 | 0.141498 | ||||||||
\(115\) | 1.20139e7 | 0.736619 | ||||||||
\(116\) | 1.94578e6 | 0.115742 | ||||||||
\(117\) | 264227. | 0.0152520 | ||||||||
\(118\) | −1.35655e7 | −0.760060 | ||||||||
\(119\) | −1.02090e7 | −0.555351 | ||||||||
\(120\) | 9.25812e6 | 0.489090 | ||||||||
\(121\) | −1.84004e7 | −0.944231 | ||||||||
\(122\) | 9.72577e6 | 0.484914 | ||||||||
\(123\) | 452829. | 0.0219415 | ||||||||
\(124\) | −1.04378e7 | −0.491624 | ||||||||
\(125\) | 1.81582e7 | 0.831550 | ||||||||
\(126\) | −350409. | −0.0156055 | ||||||||
\(127\) | 1.81924e7 | 0.788092 | 0.394046 | − | 0.919091i | \(-0.371075\pi\) | ||||
0.394046 | + | 0.919091i | \(0.371075\pi\) | |||||||
\(128\) | −1.60986e6 | −0.0678507 | ||||||||
\(129\) | −1.53006e6 | −0.0627544 | ||||||||
\(130\) | 2.43366e6 | 0.0971534 | ||||||||
\(131\) | 1.42608e7 | 0.554236 | 0.277118 | − | 0.960836i | \(-0.410621\pi\) | ||||
0.277118 | + | 0.960836i | \(0.410621\pi\) | |||||||
\(132\) | −2.64665e6 | −0.100158 | ||||||||
\(133\) | 1.98809e6 | 0.0732750 | ||||||||
\(134\) | −1.46503e7 | −0.525991 | ||||||||
\(135\) | 1.36784e7 | 0.478484 | ||||||||
\(136\) | 4.64808e7 | 1.58448 | ||||||||
\(137\) | 3.67856e7 | 1.22224 | 0.611119 | − | 0.791539i | \(-0.290720\pi\) | ||||
0.611119 | + | 0.791539i | \(0.290720\pi\) | |||||||
\(138\) | −3.55767e7 | −1.15236 | ||||||||
\(139\) | −4.81539e7 | −1.52083 | −0.760413 | − | 0.649440i | \(-0.775003\pi\) | ||||
−0.760413 | + | 0.649440i | \(0.775003\pi\) | |||||||
\(140\) | 2.49788e6 | 0.0769349 | ||||||||
\(141\) | 1.86178e7 | 0.559320 | ||||||||
\(142\) | −1.52942e7 | −0.448247 | ||||||||
\(143\) | −2.29035e6 | −0.0654977 | ||||||||
\(144\) | 735705. | 0.0205322 | ||||||||
\(145\) | 4.54369e6 | 0.123771 | ||||||||
\(146\) | 5.11397e7 | 1.35995 | ||||||||
\(147\) | 5.34848e6 | 0.138874 | ||||||||
\(148\) | −2.14783e6 | −0.0544608 | ||||||||
\(149\) | −4.45417e7 | −1.10310 | −0.551550 | − | 0.834142i | \(-0.685964\pi\) | ||||
−0.551550 | + | 0.834142i | \(0.685964\pi\) | |||||||
\(150\) | −2.36024e7 | −0.571000 | ||||||||
\(151\) | −6.93213e7 | −1.63850 | −0.819252 | − | 0.573434i | \(-0.805611\pi\) | ||||
−0.819252 | + | 0.573434i | \(0.805611\pi\) | |||||||
\(152\) | −9.05164e6 | −0.209062 | ||||||||
\(153\) | 3.57960e6 | 0.0808007 | ||||||||
\(154\) | 3.03739e6 | 0.0670159 | ||||||||
\(155\) | −2.43738e7 | −0.525729 | ||||||||
\(156\) | 5.57769e6 | 0.117630 | ||||||||
\(157\) | −3.74846e6 | −0.0773044 | −0.0386522 | − | 0.999253i | \(-0.512306\pi\) | ||||
−0.0386522 | + | 0.999253i | \(0.512306\pi\) | |||||||
\(158\) | 3.40883e7 | 0.687551 | ||||||||
\(159\) | −5.66169e7 | −1.11701 | ||||||||
\(160\) | −1.92908e7 | −0.372332 | ||||||||
\(161\) | −3.15997e7 | −0.596751 | ||||||||
\(162\) | −3.82715e7 | −0.707250 | ||||||||
\(163\) | −1.74242e7 | −0.315135 | −0.157567 | − | 0.987508i | \(-0.550365\pi\) | ||||
−0.157567 | + | 0.987508i | \(0.550365\pi\) | |||||||
\(164\) | −556254. | −0.00984737 | ||||||||
\(165\) | −6.18031e6 | −0.107107 | ||||||||
\(166\) | 2.39278e7 | 0.405999 | ||||||||
\(167\) | −1.07364e8 | −1.78382 | −0.891909 | − | 0.452214i | \(-0.850634\pi\) | ||||
−0.891909 | + | 0.452214i | \(0.850634\pi\) | |||||||
\(168\) | −2.43513e7 | −0.396222 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 3.29699e7 | 0.514691 | ||||||||
\(171\) | −697091. | −0.0106611 | ||||||||
\(172\) | 1.87952e6 | 0.0281643 | ||||||||
\(173\) | −891764. | −0.0130945 | −0.00654724 | − | 0.999979i | \(-0.502084\pi\) | ||||
−0.00654724 | + | 0.999979i | \(0.502084\pi\) | |||||||
\(174\) | −1.34552e7 | −0.193627 | ||||||||
\(175\) | −2.09640e7 | −0.295692 | ||||||||
\(176\) | −6.37718e6 | −0.0881727 | ||||||||
\(177\) | −7.26011e7 | −0.984094 | ||||||||
\(178\) | −4.06798e7 | −0.540641 | ||||||||
\(179\) | −1.25293e8 | −1.63283 | −0.816414 | − | 0.577467i | \(-0.804041\pi\) | ||||
−0.816414 | + | 0.577467i | \(0.804041\pi\) | |||||||
\(180\) | −875840. | −0.0111936 | ||||||||
\(181\) | −8.11620e6 | −0.101737 | −0.0508684 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508684 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(182\) | −6.40115e6 | −0.0787061 | ||||||||
\(183\) | 5.20514e7 | 0.627846 | ||||||||
\(184\) | 1.43871e8 | 1.70260 | ||||||||
\(185\) | −5.01549e6 | −0.0582388 | ||||||||
\(186\) | 7.21778e7 | 0.822447 | ||||||||
\(187\) | −3.10285e7 | −0.346988 | ||||||||
\(188\) | −2.28701e7 | −0.251024 | ||||||||
\(189\) | −3.59778e7 | −0.387630 | ||||||||
\(190\) | −6.42055e6 | −0.0679101 | ||||||||
\(191\) | −2.83512e6 | −0.0294411 | −0.0147206 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147206 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(192\) | 9.27222e7 | 0.945430 | ||||||||
\(193\) | −7.16084e7 | −0.716990 | −0.358495 | − | 0.933532i | \(-0.616710\pi\) | ||||
−0.358495 | + | 0.933532i | \(0.616710\pi\) | |||||||
\(194\) | −4.12024e7 | −0.405151 | ||||||||
\(195\) | 1.30247e7 | 0.125790 | ||||||||
\(196\) | −6.57007e6 | −0.0623267 | ||||||||
\(197\) | 1.95714e8 | 1.82386 | 0.911928 | − | 0.410350i | \(-0.134593\pi\) | ||||
0.911928 | + | 0.410350i | \(0.134593\pi\) | |||||||
\(198\) | −1.06501e6 | −0.00975047 | ||||||||
\(199\) | −2.07334e8 | −1.86502 | −0.932512 | − | 0.361140i | \(-0.882388\pi\) | ||||
−0.932512 | + | 0.361140i | \(0.882388\pi\) | |||||||
\(200\) | 9.54475e7 | 0.843645 | ||||||||
\(201\) | −7.84067e7 | −0.681031 | ||||||||
\(202\) | 8.60459e7 | 0.734515 | ||||||||
\(203\) | −1.19511e7 | −0.100270 | ||||||||
\(204\) | 7.55635e7 | 0.623170 | ||||||||
\(205\) | −1.29893e6 | −0.0105305 | ||||||||
\(206\) | −6.63110e7 | −0.528506 | ||||||||
\(207\) | 1.10799e7 | 0.0868241 | ||||||||
\(208\) | 1.34396e7 | 0.103553 | ||||||||
\(209\) | 6.04247e6 | 0.0457828 | ||||||||
\(210\) | −1.72729e7 | −0.128706 | ||||||||
\(211\) | 2.61035e8 | 1.91298 | 0.956488 | − | 0.291771i | \(-0.0942446\pi\) | ||||
0.956488 | + | 0.291771i | \(0.0942446\pi\) | |||||||
\(212\) | 6.95482e7 | 0.501315 | ||||||||
\(213\) | −8.18529e7 | −0.580371 | ||||||||
\(214\) | 1.60788e8 | 1.12152 | ||||||||
\(215\) | 4.38896e6 | 0.0301181 | ||||||||
\(216\) | 1.63804e8 | 1.10595 | ||||||||
\(217\) | 6.41093e7 | 0.425904 | ||||||||
\(218\) | 1.24072e8 | 0.811105 | ||||||||
\(219\) | 2.73695e8 | 1.76081 | ||||||||
\(220\) | 7.59189e6 | 0.0480696 | ||||||||
\(221\) | 6.53910e7 | 0.407516 | ||||||||
\(222\) | 1.48523e7 | 0.0911085 | ||||||||
\(223\) | 5.01041e7 | 0.302556 | 0.151278 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151278 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(224\) | 5.07398e7 | 0.301634 | ||||||||
\(225\) | 7.35066e6 | 0.0430217 | ||||||||
\(226\) | 1.88629e7 | 0.108700 | ||||||||
\(227\) | −2.39460e8 | −1.35876 | −0.679379 | − | 0.733788i | \(-0.737751\pi\) | ||||
−0.679379 | + | 0.733788i | \(0.737751\pi\) | |||||||
\(228\) | −1.47152e7 | −0.0822232 | ||||||||
\(229\) | −1.85129e8 | −1.01871 | −0.509355 | − | 0.860557i | \(-0.670116\pi\) | ||||
−0.509355 | + | 0.860557i | \(0.670116\pi\) | |||||||
\(230\) | 1.02051e8 | 0.553059 | ||||||||
\(231\) | 1.62558e7 | 0.0867694 | ||||||||
\(232\) | 5.44124e7 | 0.286082 | ||||||||
\(233\) | −4.61056e7 | −0.238786 | −0.119393 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119393 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(234\) | 2.24446e6 | 0.0114513 | ||||||||
\(235\) | −5.34049e7 | −0.268438 | ||||||||
\(236\) | 8.91831e7 | 0.441663 | ||||||||
\(237\) | 1.82437e8 | 0.890213 | ||||||||
\(238\) | −8.67194e7 | −0.416962 | ||||||||
\(239\) | −6.41048e7 | −0.303737 | −0.151869 | − | 0.988401i | \(-0.548529\pi\) | ||||
−0.151869 | + | 0.988401i | \(0.548529\pi\) | |||||||
\(240\) | 3.62655e7 | 0.169338 | ||||||||
\(241\) | −1.61560e8 | −0.743486 | −0.371743 | − | 0.928336i | \(-0.621240\pi\) | ||||
−0.371743 | + | 0.928336i | \(0.621240\pi\) | |||||||
\(242\) | −1.56301e8 | −0.708936 | ||||||||
\(243\) | 2.45724e7 | 0.109857 | ||||||||
\(244\) | −6.39399e7 | −0.281778 | ||||||||
\(245\) | −1.53421e7 | −0.0666504 | ||||||||
\(246\) | 3.84652e6 | 0.0164738 | ||||||||
\(247\) | −1.27342e7 | −0.0537691 | ||||||||
\(248\) | −2.91885e8 | −1.21515 | ||||||||
\(249\) | 1.28059e8 | 0.525670 | ||||||||
\(250\) | 1.54244e8 | 0.624335 | ||||||||
\(251\) | −1.95835e8 | −0.781687 | −0.390844 | − | 0.920457i | \(-0.627817\pi\) | ||||
−0.390844 | + | 0.920457i | \(0.627817\pi\) | |||||||
\(252\) | 2.30369e6 | 0.00906820 | ||||||||
\(253\) | −9.60421e7 | −0.372855 | ||||||||
\(254\) | 1.54534e8 | 0.591706 | ||||||||
\(255\) | 1.76452e8 | 0.666400 | ||||||||
\(256\) | −2.74742e8 | −1.02349 | ||||||||
\(257\) | −7.76172e7 | −0.285228 | −0.142614 | − | 0.989778i | \(-0.545551\pi\) | ||||
−0.142614 | + | 0.989778i | \(0.545551\pi\) | |||||||
\(258\) | −1.29970e7 | −0.0471166 | ||||||||
\(259\) | 1.31920e7 | 0.0471806 | ||||||||
\(260\) | −1.59995e7 | −0.0564548 | ||||||||
\(261\) | 4.19044e6 | 0.0145887 | ||||||||
\(262\) | 1.21138e8 | 0.416125 | ||||||||
\(263\) | 8.67584e7 | 0.294081 | 0.147040 | − | 0.989131i | \(-0.453025\pi\) | ||||
0.147040 | + | 0.989131i | \(0.453025\pi\) | |||||||
\(264\) | −7.40116e7 | −0.247563 | ||||||||
\(265\) | 1.62405e8 | 0.536092 | ||||||||
\(266\) | 1.68877e7 | 0.0550155 | ||||||||
\(267\) | −2.17714e8 | −0.699999 | ||||||||
\(268\) | 9.63148e7 | 0.305648 | ||||||||
\(269\) | 2.09851e8 | 0.657322 | 0.328661 | − | 0.944448i | \(-0.393403\pi\) | ||||
0.328661 | + | 0.944448i | \(0.393403\pi\) | |||||||
\(270\) | 1.16190e8 | 0.359250 | ||||||||
\(271\) | −5.33514e8 | −1.62837 | −0.814185 | − | 0.580605i | \(-0.802816\pi\) | ||||
−0.814185 | + | 0.580605i | \(0.802816\pi\) | |||||||
\(272\) | 1.82072e8 | 0.548596 | ||||||||
\(273\) | −3.42583e7 | −0.101905 | ||||||||
\(274\) | 3.12473e8 | 0.917667 | ||||||||
\(275\) | −6.37164e7 | −0.184751 | ||||||||
\(276\) | 2.33891e8 | 0.669625 | ||||||||
\(277\) | −4.09080e7 | −0.115646 | −0.0578228 | − | 0.998327i | \(-0.518416\pi\) | ||||
−0.0578228 | + | 0.998327i | \(0.518416\pi\) | |||||||
\(278\) | −4.09040e8 | −1.14185 | ||||||||
\(279\) | −2.24789e7 | −0.0619669 | ||||||||
\(280\) | 6.98514e7 | 0.190161 | ||||||||
\(281\) | 3.56604e8 | 0.958768 | 0.479384 | − | 0.877605i | \(-0.340860\pi\) | ||||
0.479384 | + | 0.877605i | \(0.340860\pi\) | |||||||
\(282\) | 1.58147e8 | 0.419942 | ||||||||
\(283\) | −3.28921e8 | −0.862660 | −0.431330 | − | 0.902194i | \(-0.641955\pi\) | ||||
−0.431330 | + | 0.902194i | \(0.641955\pi\) | |||||||
\(284\) | 1.00548e8 | 0.260471 | ||||||||
\(285\) | −3.43621e7 | −0.0879272 | ||||||||
\(286\) | −1.94552e7 | −0.0491762 | ||||||||
\(287\) | 3.41653e6 | 0.00853098 | ||||||||
\(288\) | −1.77910e7 | −0.0438862 | ||||||||
\(289\) | 4.75543e8 | 1.15890 | ||||||||
\(290\) | 3.85960e7 | 0.0929286 | ||||||||
\(291\) | −2.20511e8 | −0.524572 | ||||||||
\(292\) | −3.36206e8 | −0.790253 | ||||||||
\(293\) | −3.19794e8 | −0.742735 | −0.371368 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371368 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(294\) | 4.54323e7 | 0.104267 | ||||||||
\(295\) | 2.08255e8 | 0.472301 | ||||||||
\(296\) | −6.00625e7 | −0.134612 | ||||||||
\(297\) | −1.09348e8 | −0.242195 | ||||||||
\(298\) | −3.78357e8 | −0.828217 | ||||||||
\(299\) | 2.02404e8 | 0.437895 | ||||||||
\(300\) | 1.55168e8 | 0.331802 | ||||||||
\(301\) | −1.15441e7 | −0.0243993 | ||||||||
\(302\) | −5.88845e8 | −1.23020 | ||||||||
\(303\) | 4.60509e8 | 0.951019 | ||||||||
\(304\) | −3.54567e7 | −0.0723837 | ||||||||
\(305\) | −1.49309e8 | −0.301326 | ||||||||
\(306\) | 3.04067e7 | 0.0606658 | ||||||||
\(307\) | 6.60284e8 | 1.30241 | 0.651203 | − | 0.758903i | \(-0.274265\pi\) | ||||
0.651203 | + | 0.758903i | \(0.274265\pi\) | |||||||
\(308\) | −1.99686e7 | −0.0389422 | ||||||||
\(309\) | −3.54890e8 | −0.684288 | ||||||||
\(310\) | −2.07041e8 | −0.394722 | ||||||||
\(311\) | −1.05295e9 | −1.98493 | −0.992467 | − | 0.122514i | \(-0.960904\pi\) | ||||
−0.992467 | + | 0.122514i | \(0.960904\pi\) | |||||||
\(312\) | 1.55976e8 | 0.290748 | ||||||||
\(313\) | 1.95767e8 | 0.360856 | 0.180428 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180428 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(314\) | −3.18410e7 | −0.0580408 | ||||||||
\(315\) | 5.37944e6 | 0.00969728 | ||||||||
\(316\) | −2.24106e8 | −0.399529 | ||||||||
\(317\) | −1.66457e8 | −0.293491 | −0.146745 | − | 0.989174i | \(-0.546880\pi\) | ||||
−0.146745 | + | 0.989174i | \(0.546880\pi\) | |||||||
\(318\) | −4.80928e8 | −0.838659 | ||||||||
\(319\) | −3.63233e7 | −0.0626495 | ||||||||
\(320\) | −2.65973e8 | −0.453745 | ||||||||
\(321\) | 8.60523e8 | 1.45210 | ||||||||
\(322\) | −2.68422e8 | −0.448046 | ||||||||
\(323\) | −1.72516e8 | −0.284853 | ||||||||
\(324\) | 2.51607e8 | 0.410975 | ||||||||
\(325\) | 1.34279e8 | 0.216979 | ||||||||
\(326\) | −1.48009e8 | −0.236606 | ||||||||
\(327\) | 6.64023e8 | 1.05018 | ||||||||
\(328\) | −1.55552e7 | −0.0243399 | ||||||||
\(329\) | 1.40469e8 | 0.217467 | ||||||||
\(330\) | −5.24982e7 | −0.0804165 | ||||||||
\(331\) | 8.87071e8 | 1.34450 | 0.672249 | − | 0.740325i | \(-0.265328\pi\) | ||||
0.672249 | + | 0.740325i | \(0.265328\pi\) | |||||||
\(332\) | −1.57308e8 | −0.235921 | ||||||||
\(333\) | −4.62557e6 | −0.00686453 | ||||||||
\(334\) | −9.11995e8 | −1.33931 | ||||||||
\(335\) | 2.24909e8 | 0.326851 | ||||||||
\(336\) | −9.53877e7 | −0.137185 | ||||||||
\(337\) | 1.53476e8 | 0.218441 | 0.109221 | − | 0.994018i | \(-0.465164\pi\) | ||||
0.109221 | + | 0.994018i | \(0.465164\pi\) | |||||||
\(338\) | 4.10010e7 | 0.0577545 | ||||||||
\(339\) | 1.00952e8 | 0.140740 | ||||||||
\(340\) | −2.16753e8 | −0.299081 | ||||||||
\(341\) | 1.94850e8 | 0.266109 | ||||||||
\(342\) | −5.92139e6 | −0.00800446 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 5.25595e7 | 0.0696140 | ||||||||
\(345\) | 5.46169e8 | 0.716078 | ||||||||
\(346\) | −7.57502e6 | −0.00983145 | ||||||||
\(347\) | −1.15732e9 | −1.48697 | −0.743483 | − | 0.668754i | \(-0.766828\pi\) | ||||
−0.743483 | + | 0.668754i | \(0.766828\pi\) | |||||||
\(348\) | 8.84579e7 | 0.112515 | ||||||||
\(349\) | 5.73828e8 | 0.722592 | 0.361296 | − | 0.932451i | \(-0.382334\pi\) | ||||
0.361296 | + | 0.932451i | \(0.382334\pi\) | |||||||
\(350\) | −1.78077e8 | −0.222008 | ||||||||
\(351\) | 2.30446e8 | 0.284443 | ||||||||
\(352\) | 1.54215e8 | 0.188464 | ||||||||
\(353\) | −1.05519e9 | −1.27679 | −0.638396 | − | 0.769708i | \(-0.720402\pi\) | ||||
−0.638396 | + | 0.769708i | \(0.720402\pi\) | |||||||
\(354\) | −6.16704e8 | −0.738866 | ||||||||
\(355\) | 2.34794e8 | 0.278541 | ||||||||
\(356\) | 2.67440e8 | 0.314161 | ||||||||
\(357\) | −4.64113e8 | −0.539865 | ||||||||
\(358\) | −1.06429e9 | −1.22594 | ||||||||
\(359\) | 1.40542e9 | 1.60315 | 0.801577 | − | 0.597892i | \(-0.203995\pi\) | ||||
0.801577 | + | 0.597892i | \(0.203995\pi\) | |||||||
\(360\) | −2.44922e7 | −0.0276675 | ||||||||
\(361\) | −8.60276e8 | −0.962415 | ||||||||
\(362\) | −6.89425e7 | −0.0763848 | ||||||||
\(363\) | −8.36506e8 | −0.917901 | ||||||||
\(364\) | 4.20829e7 | 0.0457353 | ||||||||
\(365\) | −7.85090e8 | −0.845074 | ||||||||
\(366\) | 4.42147e8 | 0.471392 | ||||||||
\(367\) | 2.16768e8 | 0.228909 | 0.114455 | − | 0.993428i | \(-0.463488\pi\) | ||||
0.114455 | + | 0.993428i | \(0.463488\pi\) | |||||||
\(368\) | 5.63567e8 | 0.589493 | ||||||||
\(369\) | −1.19795e6 | −0.00124121 | ||||||||
\(370\) | −4.26038e7 | −0.0437262 | ||||||||
\(371\) | −4.27167e8 | −0.434300 | ||||||||
\(372\) | −4.74516e8 | −0.477915 | ||||||||
\(373\) | −4.50926e8 | −0.449909 | −0.224954 | − | 0.974369i | \(-0.572223\pi\) | ||||
−0.224954 | + | 0.974369i | \(0.572223\pi\) | |||||||
\(374\) | −2.63569e8 | −0.260522 | ||||||||
\(375\) | 8.25497e8 | 0.808363 | ||||||||
\(376\) | −6.39544e8 | −0.620459 | ||||||||
\(377\) | 7.65496e7 | 0.0735780 | ||||||||
\(378\) | −3.05611e8 | −0.291036 | ||||||||
\(379\) | 3.61271e8 | 0.340875 | 0.170438 | − | 0.985368i | \(-0.445482\pi\) | ||||
0.170438 | + | 0.985368i | \(0.445482\pi\) | |||||||
\(380\) | 4.22104e7 | 0.0394618 | ||||||||
\(381\) | 8.27051e8 | 0.766117 | ||||||||
\(382\) | −2.40827e7 | −0.0221046 | ||||||||
\(383\) | −5.84010e8 | −0.531159 | −0.265580 | − | 0.964089i | \(-0.585563\pi\) | ||||
−0.265580 | + | 0.964089i | \(0.585563\pi\) | |||||||
\(384\) | −7.31866e7 | −0.0659587 | ||||||||
\(385\) | −4.66296e7 | −0.0416437 | ||||||||
\(386\) | −6.08272e8 | −0.538322 | ||||||||
\(387\) | 4.04775e6 | 0.00354997 | ||||||||
\(388\) | 2.70876e8 | 0.235429 | ||||||||
\(389\) | −1.27226e9 | −1.09585 | −0.547926 | − | 0.836527i | \(-0.684582\pi\) | ||||
−0.547926 | + | 0.836527i | \(0.684582\pi\) | |||||||
\(390\) | 1.10637e8 | 0.0944443 | ||||||||
\(391\) | 2.74206e9 | 2.31984 | ||||||||
\(392\) | −1.83727e8 | −0.154054 | ||||||||
\(393\) | 6.48316e8 | 0.538782 | ||||||||
\(394\) | 1.66248e9 | 1.36937 | ||||||||
\(395\) | −5.23319e8 | −0.427245 | ||||||||
\(396\) | 7.00167e6 | 0.00566589 | ||||||||
\(397\) | 8.15517e8 | 0.654133 | 0.327067 | − | 0.945001i | \(-0.393940\pi\) | ||||
0.327067 | + | 0.945001i | \(0.393940\pi\) | |||||||
\(398\) | −1.76118e9 | −1.40028 | ||||||||
\(399\) | 9.03813e7 | 0.0712317 | ||||||||
\(400\) | 3.73883e8 | 0.292096 | ||||||||
\(401\) | 6.46821e7 | 0.0500932 | 0.0250466 | − | 0.999686i | \(-0.492027\pi\) | ||||
0.0250466 | + | 0.999686i | \(0.492027\pi\) | |||||||
\(402\) | −6.66020e8 | −0.511324 | ||||||||
\(403\) | −4.10636e8 | −0.312528 | ||||||||
\(404\) | −5.65689e8 | −0.426818 | ||||||||
\(405\) | 5.87539e8 | 0.439485 | ||||||||
\(406\) | −1.01517e8 | −0.0752835 | ||||||||
\(407\) | 4.00950e7 | 0.0294788 | ||||||||
\(408\) | 2.11308e9 | 1.54030 | ||||||||
\(409\) | 8.76118e8 | 0.633186 | 0.316593 | − | 0.948562i | \(-0.397461\pi\) | ||||
0.316593 | + | 0.948562i | \(0.397461\pi\) | |||||||
\(410\) | −1.10337e7 | −0.00790638 | ||||||||
\(411\) | 1.67232e9 | 1.18816 | ||||||||
\(412\) | 4.35946e8 | 0.307109 | ||||||||
\(413\) | −5.47766e8 | −0.382622 | ||||||||
\(414\) | 9.41176e7 | 0.0651883 | ||||||||
\(415\) | −3.67337e8 | −0.252288 | ||||||||
\(416\) | −3.25001e8 | −0.221339 | ||||||||
\(417\) | −2.18914e9 | −1.47842 | ||||||||
\(418\) | 5.13273e7 | 0.0343741 | ||||||||
\(419\) | 8.56812e8 | 0.569032 | 0.284516 | − | 0.958671i | \(-0.408167\pi\) | ||||
0.284516 | + | 0.958671i | \(0.408167\pi\) | |||||||
\(420\) | 1.13557e8 | 0.0747896 | ||||||||
\(421\) | 1.04415e9 | 0.681987 | 0.340994 | − | 0.940066i | \(-0.389237\pi\) | ||||
0.340994 | + | 0.940066i | \(0.389237\pi\) | |||||||
\(422\) | 2.21734e9 | 1.43628 | ||||||||
\(423\) | −4.92530e7 | −0.0316403 | ||||||||
\(424\) | 1.94486e9 | 1.23911 | ||||||||
\(425\) | 1.81914e9 | 1.14949 | ||||||||
\(426\) | −6.95294e8 | −0.435747 | ||||||||
\(427\) | 3.92721e8 | 0.244111 | ||||||||
\(428\) | −1.05707e9 | −0.651702 | ||||||||
\(429\) | −1.04122e8 | −0.0636713 | ||||||||
\(430\) | 3.72817e7 | 0.0226129 | ||||||||
\(431\) | −1.35707e9 | −0.816456 | −0.408228 | − | 0.912880i | \(-0.633853\pi\) | ||||
−0.408228 | + | 0.912880i | \(0.633853\pi\) | |||||||
\(432\) | 6.41647e8 | 0.382916 | ||||||||
\(433\) | 2.21225e9 | 1.30956 | 0.654781 | − | 0.755819i | \(-0.272761\pi\) | ||||
0.654781 | + | 0.755819i | \(0.272761\pi\) | |||||||
\(434\) | 5.44572e8 | 0.319773 | ||||||||
\(435\) | 2.06562e8 | 0.120320 | ||||||||
\(436\) | −8.15685e8 | −0.471324 | ||||||||
\(437\) | −5.33988e8 | −0.306088 | ||||||||
\(438\) | 2.32488e9 | 1.32203 | ||||||||
\(439\) | 4.10584e7 | 0.0231620 | 0.0115810 | − | 0.999933i | \(-0.496314\pi\) | ||||
0.0115810 | + | 0.999933i | \(0.496314\pi\) | |||||||
\(440\) | 2.12302e8 | 0.118814 | ||||||||
\(441\) | −1.41493e7 | −0.00785598 | ||||||||
\(442\) | 5.55459e8 | 0.305967 | ||||||||
\(443\) | 1.19657e9 | 0.653920 | 0.326960 | − | 0.945038i | \(-0.393976\pi\) | ||||
0.326960 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(444\) | −9.76432e7 | −0.0529422 | ||||||||
\(445\) | 6.24511e8 | 0.335954 | ||||||||
\(446\) | 4.25606e8 | 0.227162 | ||||||||
\(447\) | −2.02493e9 | −1.07234 | ||||||||
\(448\) | 6.99577e8 | 0.367589 | ||||||||
\(449\) | −8.48590e8 | −0.442421 | −0.221210 | − | 0.975226i | \(-0.571001\pi\) | ||||
−0.221210 | + | 0.975226i | \(0.571001\pi\) | |||||||
\(450\) | 6.24397e7 | 0.0323011 | ||||||||
\(451\) | 1.03840e7 | 0.00533023 | ||||||||
\(452\) | −1.24010e8 | −0.0631644 | ||||||||
\(453\) | −3.15144e9 | −1.59281 | ||||||||
\(454\) | −2.03407e9 | −1.02017 | ||||||||
\(455\) | 9.82697e7 | 0.0489080 | ||||||||
\(456\) | −4.11500e8 | −0.203232 | ||||||||
\(457\) | 1.07158e9 | 0.525192 | 0.262596 | − | 0.964906i | \(-0.415421\pi\) | ||||
0.262596 | + | 0.964906i | \(0.415421\pi\) | |||||||
\(458\) | −1.57257e9 | −0.764856 | ||||||||
\(459\) | 3.12196e9 | 1.50690 | ||||||||
\(460\) | −6.70914e8 | −0.321377 | ||||||||
\(461\) | −1.77089e8 | −0.0841857 | −0.0420929 | − | 0.999114i | \(-0.513403\pi\) | ||||
−0.0420929 | + | 0.999114i | \(0.513403\pi\) | |||||||
\(462\) | 1.38084e8 | 0.0651472 | ||||||||
\(463\) | −5.19209e7 | −0.0243113 | −0.0121557 | − | 0.999926i | \(-0.503869\pi\) | ||||
−0.0121557 | + | 0.999926i | \(0.503869\pi\) | |||||||
\(464\) | 2.13142e8 | 0.0990503 | ||||||||
\(465\) | −1.10806e9 | −0.511069 | ||||||||
\(466\) | −3.91641e8 | −0.179282 | ||||||||
\(467\) | −6.33313e8 | −0.287746 | −0.143873 | − | 0.989596i | \(-0.545956\pi\) | ||||
−0.143873 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(468\) | −1.47557e7 | −0.00665424 | ||||||||
\(469\) | −5.91569e8 | −0.264789 | ||||||||
\(470\) | −4.53644e8 | −0.201545 | ||||||||
\(471\) | −1.70410e8 | −0.0751488 | ||||||||
\(472\) | 2.49394e9 | 1.09166 | ||||||||
\(473\) | −3.50864e7 | −0.0152449 | ||||||||
\(474\) | 1.54970e9 | 0.668379 | ||||||||
\(475\) | −3.54260e8 | −0.151668 | ||||||||
\(476\) | 5.70117e8 | 0.242292 | ||||||||
\(477\) | 1.49779e8 | 0.0631883 | ||||||||
\(478\) | −5.44533e8 | −0.228048 | ||||||||
\(479\) | 2.66856e9 | 1.10944 | 0.554718 | − | 0.832038i | \(-0.312826\pi\) | ||||
0.554718 | + | 0.832038i | \(0.312826\pi\) | |||||||
\(480\) | −8.76985e8 | −0.361949 | ||||||||
\(481\) | −8.44983e7 | −0.0346211 | ||||||||
\(482\) | −1.37236e9 | −0.558216 | ||||||||
\(483\) | −1.43657e9 | −0.580111 | ||||||||
\(484\) | 1.02756e9 | 0.411955 | ||||||||
\(485\) | 6.32535e8 | 0.251761 | ||||||||
\(486\) | 2.08729e8 | 0.0824813 | ||||||||
\(487\) | −6.98548e7 | −0.0274060 | −0.0137030 | − | 0.999906i | \(-0.504362\pi\) | ||||
−0.0137030 | + | 0.999906i | \(0.504362\pi\) | |||||||
\(488\) | −1.78803e9 | −0.696475 | ||||||||
\(489\) | −7.92128e8 | −0.306347 | ||||||||
\(490\) | −1.30322e8 | −0.0500417 | ||||||||
\(491\) | 2.78944e9 | 1.06348 | 0.531742 | − | 0.846906i | \(-0.321538\pi\) | ||||
0.531742 | + | 0.846906i | \(0.321538\pi\) | |||||||
\(492\) | −2.52881e7 | −0.00957277 | ||||||||
\(493\) | 1.03705e9 | 0.389795 | ||||||||
\(494\) | −1.08170e8 | −0.0403703 | ||||||||
\(495\) | 1.63499e7 | 0.00605894 | ||||||||
\(496\) | −1.14336e9 | −0.420724 | ||||||||
\(497\) | −6.17570e8 | −0.225652 | ||||||||
\(498\) | 1.08779e9 | 0.394678 | ||||||||
\(499\) | −3.61891e9 | −1.30385 | −0.651923 | − | 0.758286i | \(-0.726037\pi\) | ||||
−0.651923 | + | 0.758286i | \(0.726037\pi\) | |||||||
\(500\) | −1.01404e9 | −0.362794 | ||||||||
\(501\) | −4.88091e9 | −1.73408 | ||||||||
\(502\) | −1.66351e9 | −0.586897 | ||||||||
\(503\) | −6.21040e8 | −0.217586 | −0.108793 | − | 0.994064i | \(-0.534699\pi\) | ||||
−0.108793 | + | 0.994064i | \(0.534699\pi\) | |||||||
\(504\) | 6.44209e7 | 0.0224140 | ||||||||
\(505\) | −1.32097e9 | −0.456428 | ||||||||
\(506\) | −8.15823e8 | −0.279943 | ||||||||
\(507\) | 2.19433e8 | 0.0747781 | ||||||||
\(508\) | −1.01595e9 | −0.343834 | ||||||||
\(509\) | −6.97982e8 | −0.234602 | −0.117301 | − | 0.993096i | \(-0.537424\pi\) | ||||
−0.117301 | + | 0.993096i | \(0.537424\pi\) | |||||||
\(510\) | 1.49886e9 | 0.500339 | ||||||||
\(511\) | 2.06499e9 | 0.684613 | ||||||||
\(512\) | −2.12771e9 | −0.700596 | ||||||||
\(513\) | −6.07970e8 | −0.198825 | ||||||||
\(514\) | −6.59314e8 | −0.214151 | ||||||||
\(515\) | 1.01800e9 | 0.328414 | ||||||||
\(516\) | 8.54457e7 | 0.0273789 | ||||||||
\(517\) | 4.26931e8 | 0.135875 | ||||||||
\(518\) | 1.12059e8 | 0.0354236 | ||||||||
\(519\) | −4.05408e7 | −0.0127293 | ||||||||
\(520\) | −4.47415e8 | −0.139540 | ||||||||
\(521\) | −3.31626e9 | −1.02735 | −0.513673 | − | 0.857986i | \(-0.671715\pi\) | ||||
−0.513673 | + | 0.857986i | \(0.671715\pi\) | |||||||
\(522\) | 3.55954e7 | 0.0109534 | ||||||||
\(523\) | 1.38363e9 | 0.422926 | 0.211463 | − | 0.977386i | \(-0.432177\pi\) | ||||
0.211463 | + | 0.977386i | \(0.432177\pi\) | |||||||
\(524\) | −7.96391e8 | −0.241806 | ||||||||
\(525\) | −9.53050e8 | −0.287447 | ||||||||
\(526\) | 7.36963e8 | 0.220798 | ||||||||
\(527\) | −5.56308e9 | −1.65569 | ||||||||
\(528\) | −2.89915e8 | −0.0857140 | ||||||||
\(529\) | 5.08266e9 | 1.49278 | ||||||||
\(530\) | 1.37954e9 | 0.402502 | ||||||||
\(531\) | 1.92065e8 | 0.0556695 | ||||||||
\(532\) | −1.11024e8 | −0.0319689 | ||||||||
\(533\) | −2.18837e7 | −0.00626003 | ||||||||
\(534\) | −1.84936e9 | −0.525565 | ||||||||
\(535\) | −2.46840e9 | −0.696912 | ||||||||
\(536\) | 2.69337e9 | 0.755474 | ||||||||
\(537\) | −5.69598e9 | −1.58730 | ||||||||
\(538\) | 1.78257e9 | 0.493523 | ||||||||
\(539\) | 1.22648e8 | 0.0337365 | ||||||||
\(540\) | −7.63867e8 | −0.208756 | ||||||||
\(541\) | 6.14028e9 | 1.66724 | 0.833620 | − | 0.552339i | \(-0.186265\pi\) | ||||
0.833620 | + | 0.552339i | \(0.186265\pi\) | |||||||
\(542\) | −4.53190e9 | −1.22259 | ||||||||
\(543\) | −3.68973e8 | −0.0988998 | ||||||||
\(544\) | −4.40294e9 | −1.17259 | ||||||||
\(545\) | −1.90474e9 | −0.504021 | ||||||||
\(546\) | −2.91005e8 | −0.0765114 | ||||||||
\(547\) | 6.08930e9 | 1.59079 | 0.795393 | − | 0.606094i | \(-0.207265\pi\) | ||||
0.795393 | + | 0.606094i | \(0.207265\pi\) | |||||||
\(548\) | −2.05428e9 | −0.533246 | ||||||||
\(549\) | −1.37701e8 | −0.0355168 | ||||||||
\(550\) | −5.41235e8 | −0.138713 | ||||||||
\(551\) | −2.01955e8 | −0.0514309 | ||||||||
\(552\) | 6.54059e9 | 1.65512 | ||||||||
\(553\) | 1.37646e9 | 0.346120 | ||||||||
\(554\) | −3.47490e8 | −0.0868278 | ||||||||
\(555\) | −2.28011e8 | −0.0566149 | ||||||||
\(556\) | 2.68914e9 | 0.663516 | ||||||||
\(557\) | −4.90112e9 | −1.20172 | −0.600858 | − | 0.799356i | \(-0.705174\pi\) | ||||
−0.600858 | + | 0.799356i | \(0.705174\pi\) | |||||||
\(558\) | −1.90945e8 | −0.0465253 | ||||||||
\(559\) | 7.39429e7 | 0.0179042 | ||||||||
\(560\) | 2.73619e8 | 0.0658397 | ||||||||
\(561\) | −1.41060e9 | −0.337312 | ||||||||
\(562\) | 3.02914e9 | 0.719851 | ||||||||
\(563\) | 3.19645e9 | 0.754899 | 0.377450 | − | 0.926030i | \(-0.376801\pi\) | ||||
0.377450 | + | 0.926030i | \(0.376801\pi\) | |||||||
\(564\) | −1.03970e9 | −0.244024 | ||||||||
\(565\) | −2.89581e8 | −0.0675462 | ||||||||
\(566\) | −2.79400e9 | −0.647692 | ||||||||
\(567\) | −1.54538e9 | −0.356037 | ||||||||
\(568\) | 2.81175e9 | 0.643811 | ||||||||
\(569\) | −7.74869e9 | −1.76334 | −0.881668 | − | 0.471870i | \(-0.843579\pi\) | ||||
−0.881668 | + | 0.471870i | \(0.843579\pi\) | |||||||
\(570\) | −2.91887e8 | −0.0660165 | ||||||||
\(571\) | 6.14695e9 | 1.38176 | 0.690881 | − | 0.722968i | \(-0.257223\pi\) | ||||
0.690881 | + | 0.722968i | \(0.257223\pi\) | |||||||
\(572\) | 1.27904e8 | 0.0285758 | ||||||||
\(573\) | −1.28888e8 | −0.0286202 | ||||||||
\(574\) | 2.90215e7 | 0.00640513 | ||||||||
\(575\) | 5.63078e9 | 1.23518 | ||||||||
\(576\) | −2.45295e8 | −0.0534823 | ||||||||
\(577\) | −3.50140e9 | −0.758797 | −0.379399 | − | 0.925233i | \(-0.623869\pi\) | ||||
−0.379399 | + | 0.925233i | \(0.623869\pi\) | |||||||
\(578\) | 4.03947e9 | 0.870115 | ||||||||
\(579\) | −3.25541e9 | −0.696997 | ||||||||
\(580\) | −2.53741e8 | −0.0539998 | ||||||||
\(581\) | 9.66191e8 | 0.204384 | ||||||||
\(582\) | −1.87312e9 | −0.393853 | ||||||||
\(583\) | −1.29830e9 | −0.271354 | ||||||||
\(584\) | −9.40176e9 | −1.95328 | ||||||||
\(585\) | −3.44566e7 | −0.00711586 | ||||||||
\(586\) | −2.71647e9 | −0.557652 | ||||||||
\(587\) | 5.64465e9 | 1.15187 | 0.575935 | − | 0.817495i | \(-0.304638\pi\) | ||||
0.575935 | + | 0.817495i | \(0.304638\pi\) | |||||||
\(588\) | −2.98684e8 | −0.0605887 | ||||||||
\(589\) | 1.08335e9 | 0.218457 | ||||||||
\(590\) | 1.76901e9 | 0.354608 | ||||||||
\(591\) | 8.89743e9 | 1.77300 | ||||||||
\(592\) | −2.35274e8 | −0.0466067 | ||||||||
\(593\) | −8.67330e9 | −1.70802 | −0.854010 | − | 0.520256i | \(-0.825836\pi\) | ||||
−0.854010 | + | 0.520256i | \(0.825836\pi\) | |||||||
\(594\) | −9.28852e8 | −0.181842 | ||||||||
\(595\) | 1.33131e9 | 0.259101 | ||||||||
\(596\) | 2.48742e9 | 0.481268 | ||||||||
\(597\) | −9.42567e9 | −1.81302 | ||||||||
\(598\) | 1.71931e9 | 0.328776 | ||||||||
\(599\) | −4.08098e9 | −0.775837 | −0.387918 | − | 0.921694i | \(-0.626806\pi\) | ||||
−0.387918 | + | 0.921694i | \(0.626806\pi\) | |||||||
\(600\) | 4.33917e9 | 0.820120 | ||||||||
\(601\) | −3.62520e9 | −0.681196 | −0.340598 | − | 0.940209i | \(-0.610629\pi\) | ||||
−0.340598 | + | 0.940209i | \(0.610629\pi\) | |||||||
\(602\) | −9.80606e7 | −0.0183192 | ||||||||
\(603\) | 2.07424e8 | 0.0385255 | ||||||||
\(604\) | 3.87123e9 | 0.714857 | ||||||||
\(605\) | 2.39951e9 | 0.440533 | ||||||||
\(606\) | 3.91176e9 | 0.714033 | ||||||||
\(607\) | 8.74425e9 | 1.58695 | 0.793473 | − | 0.608605i | \(-0.208271\pi\) | ||||
0.793473 | + | 0.608605i | \(0.208271\pi\) | |||||||
\(608\) | 8.57426e8 | 0.154716 | ||||||||
\(609\) | −5.43312e8 | −0.0974739 | ||||||||
\(610\) | −1.26829e9 | −0.226238 | ||||||||
\(611\) | −8.99737e8 | −0.159577 | ||||||||
\(612\) | −1.99902e8 | −0.0352523 | ||||||||
\(613\) | −7.68701e9 | −1.34786 | −0.673932 | − | 0.738794i | \(-0.735396\pi\) | ||||
−0.673932 | + | 0.738794i | \(0.735396\pi\) | |||||||
\(614\) | 5.60874e9 | 0.977858 | ||||||||
\(615\) | −5.90513e7 | −0.0102369 | ||||||||
\(616\) | −5.58408e8 | −0.0962541 | ||||||||
\(617\) | 6.45616e9 | 1.10656 | 0.553282 | − | 0.832994i | \(-0.313375\pi\) | ||||
0.553282 | + | 0.832994i | \(0.313375\pi\) | |||||||
\(618\) | −3.01458e9 | −0.513769 | ||||||||
\(619\) | −3.22485e9 | −0.546502 | −0.273251 | − | 0.961943i | \(-0.588099\pi\) | ||||
−0.273251 | + | 0.961943i | \(0.588099\pi\) | |||||||
\(620\) | 1.36115e9 | 0.229368 | ||||||||
\(621\) | 9.66339e9 | 1.61923 | ||||||||
\(622\) | −8.94420e9 | −1.49030 | ||||||||
\(623\) | −1.64263e9 | −0.272164 | ||||||||
\(624\) | 6.10982e8 | 0.100666 | ||||||||
\(625\) | 2.40702e9 | 0.394367 | ||||||||
\(626\) | 1.66293e9 | 0.270934 | ||||||||
\(627\) | 2.74699e8 | 0.0445062 | ||||||||
\(628\) | 2.09332e8 | 0.0337269 | ||||||||
\(629\) | −1.14474e9 | −0.183412 | ||||||||
\(630\) | 4.56953e7 | 0.00728080 | ||||||||
\(631\) | 3.24674e9 | 0.514452 | 0.257226 | − | 0.966351i | \(-0.417192\pi\) | ||||
0.257226 | + | 0.966351i | \(0.417192\pi\) | |||||||
\(632\) | −6.26695e9 | −0.987521 | ||||||||
\(633\) | 1.18670e10 | 1.85963 | ||||||||
\(634\) | −1.41396e9 | −0.220355 | ||||||||
\(635\) | −2.37239e9 | −0.367686 | ||||||||
\(636\) | 3.16175e9 | 0.487336 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −3.08545e8 | −0.0470378 | ||||||||
\(639\) | 2.16541e8 | 0.0328312 | ||||||||
\(640\) | 2.09935e8 | 0.0316559 | ||||||||
\(641\) | 6.88178e9 | 1.03204 | 0.516022 | − | 0.856576i | \(-0.327412\pi\) | ||||
0.516022 | + | 0.856576i | \(0.327412\pi\) | |||||||
\(642\) | 7.30965e9 | 1.09025 | ||||||||
\(643\) | 4.29735e9 | 0.637473 | 0.318737 | − | 0.947843i | \(-0.396741\pi\) | ||||
0.318737 | + | 0.947843i | \(0.396741\pi\) | |||||||
\(644\) | 1.76468e9 | 0.260354 | ||||||||
\(645\) | 1.99528e8 | 0.0292782 | ||||||||
\(646\) | −1.46543e9 | −0.213870 | ||||||||
\(647\) | 1.11221e10 | 1.61444 | 0.807218 | − | 0.590254i | \(-0.200972\pi\) | ||||
0.807218 | + | 0.590254i | \(0.200972\pi\) | |||||||
\(648\) | 7.03601e9 | 1.01581 | ||||||||
\(649\) | −1.66484e9 | −0.239065 | ||||||||
\(650\) | 1.14063e9 | 0.162910 | ||||||||
\(651\) | 2.91450e9 | 0.414028 | ||||||||
\(652\) | 9.73050e8 | 0.137489 | ||||||||
\(653\) | −1.26139e10 | −1.77277 | −0.886387 | − | 0.462945i | \(-0.846793\pi\) | ||||
−0.886387 | + | 0.462945i | \(0.846793\pi\) | |||||||
\(654\) | 5.64049e9 | 0.788488 | ||||||||
\(655\) | −1.85969e9 | −0.258580 | ||||||||
\(656\) | −6.09323e7 | −0.00842722 | ||||||||
\(657\) | −7.24054e8 | −0.0996076 | ||||||||
\(658\) | 1.19320e9 | 0.163276 | ||||||||
\(659\) | −7.31188e9 | −0.995245 | −0.497623 | − | 0.867394i | \(-0.665794\pi\) | ||||
−0.497623 | + | 0.867394i | \(0.665794\pi\) | |||||||
\(660\) | 3.45137e8 | 0.0467292 | ||||||||
\(661\) | −8.30130e9 | −1.11800 | −0.558999 | − | 0.829168i | \(-0.688815\pi\) | ||||
−0.558999 | + | 0.829168i | \(0.688815\pi\) | |||||||
\(662\) | 7.53516e9 | 1.00946 | ||||||||
\(663\) | 2.97276e9 | 0.396153 | ||||||||
\(664\) | −4.39900e9 | −0.583131 | ||||||||
\(665\) | −2.59258e8 | −0.0341866 | ||||||||
\(666\) | −3.92916e7 | −0.00515394 | ||||||||
\(667\) | 3.20998e9 | 0.418853 | ||||||||
\(668\) | 5.99570e9 | 0.778256 | ||||||||
\(669\) | 2.27780e9 | 0.294120 | ||||||||
\(670\) | 1.91047e9 | 0.245403 | ||||||||
\(671\) | 1.19361e9 | 0.152522 | ||||||||
\(672\) | 2.30670e9 | 0.293223 | ||||||||
\(673\) | 9.26631e9 | 1.17180 | 0.585901 | − | 0.810383i | \(-0.300741\pi\) | ||||
0.585901 | + | 0.810383i | \(0.300741\pi\) | |||||||
\(674\) | 1.30369e9 | 0.164008 | ||||||||
\(675\) | 6.41090e9 | 0.802336 | ||||||||
\(676\) | −2.69552e8 | −0.0335605 | ||||||||
\(677\) | 1.22345e10 | 1.51539 | 0.757695 | − | 0.652609i | \(-0.226326\pi\) | ||||
0.757695 | + | 0.652609i | \(0.226326\pi\) | |||||||
\(678\) | 8.57534e8 | 0.105669 | ||||||||
\(679\) | −1.66373e9 | −0.203957 | ||||||||
\(680\) | −6.06134e9 | −0.739244 | ||||||||
\(681\) | −1.08862e10 | −1.32087 | ||||||||
\(682\) | 1.65514e9 | 0.199797 | ||||||||
\(683\) | −6.37930e9 | −0.766127 | −0.383064 | − | 0.923722i | \(-0.625131\pi\) | ||||
−0.383064 | + | 0.923722i | \(0.625131\pi\) | |||||||
\(684\) | 3.89288e7 | 0.00465131 | ||||||||
\(685\) | −4.79704e9 | −0.570238 | ||||||||
\(686\) | 3.42781e8 | 0.0405398 | ||||||||
\(687\) | −8.41622e9 | −0.990303 | ||||||||
\(688\) | 2.05884e8 | 0.0241025 | ||||||||
\(689\) | 2.73611e9 | 0.318689 | ||||||||
\(690\) | 4.63940e9 | 0.537638 | ||||||||
\(691\) | −3.63823e9 | −0.419486 | −0.209743 | − | 0.977757i | \(-0.567263\pi\) | ||||
−0.209743 | + | 0.977757i | \(0.567263\pi\) | |||||||
\(692\) | 4.98003e7 | 0.00571295 | ||||||||
\(693\) | −4.30045e7 | −0.00490848 | ||||||||
\(694\) | −9.83079e9 | −1.11643 | ||||||||
\(695\) | 6.27953e9 | 0.709545 | ||||||||
\(696\) | 2.47366e9 | 0.278104 | ||||||||
\(697\) | −2.96469e8 | −0.0331638 | ||||||||
\(698\) | 4.87434e9 | 0.542528 | ||||||||
\(699\) | −2.09602e9 | −0.232127 | ||||||||
\(700\) | 1.17073e9 | 0.129007 | ||||||||
\(701\) | −1.08142e10 | −1.18572 | −0.592858 | − | 0.805307i | \(-0.702001\pi\) | ||||
−0.592858 | + | 0.805307i | \(0.702001\pi\) | |||||||
\(702\) | 1.95751e9 | 0.213562 | ||||||||
\(703\) | 2.22926e8 | 0.0242001 | ||||||||
\(704\) | 2.12625e9 | 0.229673 | ||||||||
\(705\) | −2.42786e9 | −0.260952 | ||||||||
\(706\) | −8.96326e9 | −0.958626 | ||||||||
\(707\) | 3.47448e9 | 0.369762 | ||||||||
\(708\) | 4.05438e9 | 0.429347 | ||||||||
\(709\) | −7.50891e9 | −0.791252 | −0.395626 | − | 0.918412i | \(-0.629472\pi\) | ||||
−0.395626 | + | 0.918412i | \(0.629472\pi\) | |||||||
\(710\) | 1.99444e9 | 0.209131 | ||||||||
\(711\) | −4.82634e8 | −0.0503587 | ||||||||
\(712\) | 7.47877e9 | 0.776515 | ||||||||
\(713\) | −1.72193e10 | −1.77911 | ||||||||
\(714\) | −3.94238e9 | −0.405335 | ||||||||
\(715\) | 2.98674e8 | 0.0305581 | ||||||||
\(716\) | 6.99694e9 | 0.712381 | ||||||||
\(717\) | −2.91429e9 | −0.295267 | ||||||||
\(718\) | 1.19382e10 | 1.20366 | ||||||||
\(719\) | 6.47250e9 | 0.649413 | 0.324707 | − | 0.945815i | \(-0.394734\pi\) | ||||
0.324707 | + | 0.945815i | \(0.394734\pi\) | |||||||
\(720\) | −9.59399e7 | −0.00957933 | ||||||||
\(721\) | −2.67760e9 | −0.266055 | ||||||||
\(722\) | −7.30755e9 | −0.722590 | ||||||||
\(723\) | −7.34471e9 | −0.722754 | ||||||||
\(724\) | 4.53247e8 | 0.0443864 | ||||||||
\(725\) | 2.12957e9 | 0.207543 | ||||||||
\(726\) | −7.10564e9 | −0.689168 | ||||||||
\(727\) | −1.98504e10 | −1.91602 | −0.958009 | − | 0.286739i | \(-0.907429\pi\) | ||||
−0.958009 | + | 0.286739i | \(0.907429\pi\) | |||||||
\(728\) | 1.17682e9 | 0.113045 | ||||||||
\(729\) | 1.09706e10 | 1.04878 | ||||||||
\(730\) | −6.66889e9 | −0.634489 | ||||||||
\(731\) | 1.00174e9 | 0.0948513 | ||||||||
\(732\) | −2.90679e9 | −0.273921 | ||||||||
\(733\) | −1.49386e10 | −1.40102 | −0.700511 | − | 0.713642i | \(-0.747045\pi\) | ||||
−0.700511 | + | 0.713642i | \(0.747045\pi\) | |||||||
\(734\) | 1.84132e9 | 0.171867 | ||||||||
\(735\) | −6.97471e8 | −0.0647918 | ||||||||
\(736\) | −1.36284e10 | −1.26000 | ||||||||
\(737\) | −1.79797e9 | −0.165443 | ||||||||
\(738\) | −1.01759e7 | −0.000931914 0 | ||||||||
\(739\) | −1.03698e10 | −0.945182 | −0.472591 | − | 0.881282i | \(-0.656681\pi\) | ||||
−0.472591 | + | 0.881282i | \(0.656681\pi\) | |||||||
\(740\) | 2.80089e8 | 0.0254088 | ||||||||
\(741\) | −5.78915e8 | −0.0522698 | ||||||||
\(742\) | −3.62854e9 | −0.326076 | ||||||||
\(743\) | −6.40768e9 | −0.573112 | −0.286556 | − | 0.958063i | \(-0.592511\pi\) | ||||
−0.286556 | + | 0.958063i | \(0.592511\pi\) | |||||||
\(744\) | −1.32695e10 | −1.18127 | ||||||||
\(745\) | 5.80848e9 | 0.514655 | ||||||||
\(746\) | −3.83036e9 | −0.337795 | ||||||||
\(747\) | −3.38779e8 | −0.0297368 | ||||||||
\(748\) | 1.73277e9 | 0.151386 | ||||||||
\(749\) | 6.49254e9 | 0.564584 | ||||||||
\(750\) | 7.01213e9 | 0.606925 | ||||||||
\(751\) | 3.61512e9 | 0.311446 | 0.155723 | − | 0.987801i | \(-0.450229\pi\) | ||||
0.155723 | + | 0.987801i | \(0.450229\pi\) | |||||||
\(752\) | −2.50520e9 | −0.214822 | ||||||||
\(753\) | −8.90294e9 | −0.759890 | ||||||||
\(754\) | 6.50245e8 | 0.0552430 | ||||||||
\(755\) | 9.03987e9 | 0.764448 | ||||||||
\(756\) | 2.00917e9 | 0.169118 | ||||||||
\(757\) | 4.97903e8 | 0.0417166 | 0.0208583 | − | 0.999782i | \(-0.493360\pi\) | ||||
0.0208583 | + | 0.999782i | \(0.493360\pi\) | |||||||
\(758\) | 3.06879e9 | 0.255932 | ||||||||
\(759\) | −4.36620e9 | −0.362458 | ||||||||
\(760\) | 1.18038e9 | 0.0975384 | ||||||||
\(761\) | 2.27559e9 | 0.187175 | 0.0935874 | − | 0.995611i | \(-0.470167\pi\) | ||||
0.0935874 | + | 0.995611i | \(0.470167\pi\) | |||||||
\(762\) | 7.02532e9 | 0.575207 | ||||||||
\(763\) | 5.00997e9 | 0.408318 | ||||||||
\(764\) | 1.58326e8 | 0.0128448 | ||||||||
\(765\) | −4.66800e8 | −0.0376978 | ||||||||
\(766\) | −4.96083e9 | −0.398799 | ||||||||
\(767\) | 3.50858e9 | 0.280768 | ||||||||
\(768\) | −1.24901e10 | −0.994952 | ||||||||
\(769\) | −1.17120e10 | −0.928726 | −0.464363 | − | 0.885645i | \(-0.653717\pi\) | ||||
−0.464363 | + | 0.885645i | \(0.653717\pi\) | |||||||
\(770\) | −3.96092e8 | −0.0312665 | ||||||||
\(771\) | −3.52858e9 | −0.277274 | ||||||||
\(772\) | 3.99895e9 | 0.312813 | ||||||||
\(773\) | 3.36168e9 | 0.261775 | 0.130887 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130887 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(774\) | 3.43833e7 | 0.00266535 | ||||||||
\(775\) | −1.14237e10 | −0.881557 | ||||||||
\(776\) | 7.57485e9 | 0.581913 | ||||||||
\(777\) | 5.99728e8 | 0.0458649 | ||||||||
\(778\) | −1.08071e10 | −0.822775 | ||||||||
\(779\) | 5.77343e7 | 0.00437575 | ||||||||
\(780\) | −7.27361e8 | −0.0548806 | ||||||||
\(781\) | −1.87700e9 | −0.140989 | ||||||||
\(782\) | 2.32923e10 | 1.74176 | ||||||||
\(783\) | 3.65471e9 | 0.272074 | ||||||||
\(784\) | −7.19688e8 | −0.0533382 | ||||||||
\(785\) | 4.88820e8 | 0.0360666 | ||||||||
\(786\) | 5.50707e9 | 0.404522 | ||||||||
\(787\) | 9.64652e9 | 0.705439 | 0.352719 | − | 0.935729i | \(-0.385257\pi\) | ||||
0.352719 | + | 0.935729i | \(0.385257\pi\) | |||||||
\(788\) | −1.09296e10 | −0.795724 | ||||||||
\(789\) | 3.94415e9 | 0.285880 | ||||||||
\(790\) | −4.44529e9 | −0.320779 | ||||||||
\(791\) | 7.61674e8 | 0.0547206 | ||||||||
\(792\) | 1.95796e8 | 0.0140045 | ||||||||
\(793\) | −2.51548e9 | −0.179128 | ||||||||
\(794\) | 6.92735e9 | 0.491129 | ||||||||
\(795\) | 7.38315e9 | 0.521143 | ||||||||
\(796\) | 1.15785e10 | 0.813685 | ||||||||
\(797\) | −9.41347e9 | −0.658636 | −0.329318 | − | 0.944219i | \(-0.606819\pi\) | ||||
−0.329318 | + | 0.944219i | \(0.606819\pi\) | |||||||
\(798\) | 7.67737e8 | 0.0534814 | ||||||||
\(799\) | −1.21891e10 | −0.845395 | ||||||||
\(800\) | −9.04136e9 | −0.624336 | ||||||||
\(801\) | 5.75959e8 | 0.0395984 | ||||||||
\(802\) | 5.49437e8 | 0.0376104 | ||||||||
\(803\) | 6.27619e9 | 0.427752 | ||||||||
\(804\) | 4.37860e9 | 0.297125 | ||||||||
\(805\) | 4.12078e9 | 0.278416 | ||||||||
\(806\) | −3.48812e9 | −0.234649 | ||||||||
\(807\) | 9.54011e9 | 0.638993 | ||||||||
\(808\) | −1.58191e10 | −1.05497 | ||||||||
\(809\) | −1.90105e8 | −0.0126233 | −0.00631167 | − | 0.999980i | \(-0.502009\pi\) | ||||
−0.00631167 | + | 0.999980i | \(0.502009\pi\) | |||||||
\(810\) | 4.99081e9 | 0.329969 | ||||||||
\(811\) | 1.18714e10 | 0.781501 | 0.390750 | − | 0.920497i | \(-0.372216\pi\) | ||||
0.390750 | + | 0.920497i | \(0.372216\pi\) | |||||||
\(812\) | 6.67404e8 | 0.0437464 | ||||||||
\(813\) | −2.42543e10 | −1.58296 | ||||||||
\(814\) | 3.40584e8 | 0.0221329 | ||||||||
\(815\) | 2.27221e9 | 0.147027 | ||||||||
\(816\) | 8.27725e9 | 0.533299 | ||||||||
\(817\) | −1.95078e8 | −0.0125150 | ||||||||
\(818\) | 7.44212e9 | 0.475401 | ||||||||
\(819\) | 9.06299e7 | 0.00576471 | ||||||||
\(820\) | 7.25386e7 | 0.00459431 | ||||||||
\(821\) | 2.50076e10 | 1.57714 | 0.788571 | − | 0.614944i | \(-0.210821\pi\) | ||||
0.788571 | + | 0.614944i | \(0.210821\pi\) | |||||||
\(822\) | 1.42054e10 | 0.892078 | ||||||||
\(823\) | 2.48122e10 | 1.55155 | 0.775776 | − | 0.631009i | \(-0.217359\pi\) | ||||
0.775776 | + | 0.631009i | \(0.217359\pi\) | |||||||
\(824\) | 1.21909e10 | 0.759086 | ||||||||
\(825\) | −2.89663e9 | −0.179599 | ||||||||
\(826\) | −4.65296e9 | −0.287276 | ||||||||
\(827\) | 1.77670e10 | 1.09231 | 0.546155 | − | 0.837684i | \(-0.316091\pi\) | ||||
0.546155 | + | 0.837684i | \(0.316091\pi\) | |||||||
\(828\) | −6.18755e8 | −0.0378802 | ||||||||
\(829\) | −9.96869e9 | −0.607711 | −0.303856 | − | 0.952718i | \(-0.598274\pi\) | ||||
−0.303856 | + | 0.952718i | \(0.598274\pi\) | |||||||
\(830\) | −3.12032e9 | −0.189420 | ||||||||
\(831\) | −1.85973e9 | −0.112421 | ||||||||
\(832\) | −4.48096e9 | −0.269737 | ||||||||
\(833\) | −3.50168e9 | −0.209903 | ||||||||
\(834\) | −1.85955e10 | −1.11001 | ||||||||
\(835\) | 1.40008e10 | 0.832245 | ||||||||
\(836\) | −3.37440e8 | −0.0199744 | ||||||||
\(837\) | −1.96050e10 | −1.15565 | ||||||||
\(838\) | 7.27813e9 | 0.427234 | ||||||||
\(839\) | −2.61866e10 | −1.53078 | −0.765390 | − | 0.643567i | \(-0.777454\pi\) | ||||
−0.765390 | + | 0.643567i | \(0.777454\pi\) | |||||||
\(840\) | 3.17554e9 | 0.184859 | ||||||||
\(841\) | −1.60359e10 | −0.929622 | ||||||||
\(842\) | 8.86947e9 | 0.512042 | ||||||||
\(843\) | 1.62117e10 | 0.932033 | ||||||||
\(844\) | −1.45774e10 | −0.834606 | ||||||||
\(845\) | −6.29442e8 | −0.0358887 | ||||||||
\(846\) | −4.18376e8 | −0.0237558 | ||||||||
\(847\) | −6.31133e9 | −0.356886 | ||||||||
\(848\) | 7.61834e9 | 0.429017 | ||||||||
\(849\) | −1.49532e10 | −0.838605 | ||||||||
\(850\) | 1.54526e10 | 0.863048 | ||||||||
\(851\) | −3.54330e9 | −0.197085 | ||||||||
\(852\) | 4.57105e9 | 0.253208 | ||||||||
\(853\) | 1.60269e9 | 0.0884151 | 0.0442076 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442076 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(854\) | 3.33594e9 | 0.183280 | ||||||||
\(855\) | 9.09044e7 | 0.00497398 | ||||||||
\(856\) | −2.95601e10 | −1.61082 | ||||||||
\(857\) | 5.04497e9 | 0.273795 | 0.136898 | − | 0.990585i | \(-0.456287\pi\) | ||||
0.136898 | + | 0.990585i | \(0.456287\pi\) | |||||||
\(858\) | −8.84461e8 | −0.0478050 | ||||||||
\(859\) | −6.78061e9 | −0.365000 | −0.182500 | − | 0.983206i | \(-0.558419\pi\) | ||||
−0.182500 | + | 0.983206i | \(0.558419\pi\) | |||||||
\(860\) | −2.45100e8 | −0.0131401 | ||||||||
\(861\) | 1.55320e8 | 0.00829310 | ||||||||
\(862\) | −1.15276e10 | −0.613002 | ||||||||
\(863\) | −7.09709e9 | −0.375874 | −0.187937 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187937 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(864\) | −1.55165e10 | −0.818458 | ||||||||
\(865\) | 1.16291e8 | 0.00610927 | ||||||||
\(866\) | 1.87918e10 | 0.983230 | ||||||||
\(867\) | 2.16188e10 | 1.12659 | ||||||||
\(868\) | −3.58017e9 | −0.185816 | ||||||||
\(869\) | 4.18353e9 | 0.216259 | ||||||||
\(870\) | 1.75463e9 | 0.0903373 | ||||||||
\(871\) | 3.78914e9 | 0.194302 | ||||||||
\(872\) | −2.28100e10 | −1.16498 | ||||||||
\(873\) | 5.83359e8 | 0.0296747 | ||||||||
\(874\) | −4.53593e9 | −0.229814 | ||||||||
\(875\) | 6.22827e9 | 0.314296 | ||||||||
\(876\) | −1.52844e10 | −0.768217 | ||||||||
\(877\) | −6.12021e8 | −0.0306385 | −0.0153192 | − | 0.999883i | \(-0.504876\pi\) | ||||
−0.0153192 | + | 0.999883i | \(0.504876\pi\) | |||||||
\(878\) | 3.48768e8 | 0.0173903 | ||||||||
\(879\) | −1.45383e10 | −0.722024 | ||||||||
\(880\) | 8.31619e8 | 0.0411372 | ||||||||
\(881\) | 2.62029e10 | 1.29102 | 0.645512 | − | 0.763750i | \(-0.276644\pi\) | ||||
0.645512 | + | 0.763750i | \(0.276644\pi\) | |||||||
\(882\) | −1.20190e8 | −0.00589834 | ||||||||
\(883\) | 2.83780e10 | 1.38714 | 0.693569 | − | 0.720391i | \(-0.256037\pi\) | ||||
0.693569 | + | 0.720391i | \(0.256037\pi\) | |||||||
\(884\) | −3.65174e9 | −0.177794 | ||||||||
\(885\) | 9.46757e9 | 0.459131 | ||||||||
\(886\) | 1.01642e10 | 0.490969 | ||||||||
\(887\) | −2.43273e10 | −1.17047 | −0.585235 | − | 0.810864i | \(-0.698998\pi\) | ||||
−0.585235 | + | 0.810864i | \(0.698998\pi\) | |||||||
\(888\) | −2.73052e9 | −0.130858 | ||||||||
\(889\) | 6.23999e9 | 0.297871 | ||||||||
\(890\) | 5.30487e9 | 0.252237 | ||||||||
\(891\) | −4.69692e9 | −0.222455 | ||||||||
\(892\) | −2.79805e9 | −0.132001 | ||||||||
\(893\) | 2.37371e9 | 0.111544 | ||||||||
\(894\) | −1.72006e10 | −0.805123 | ||||||||
\(895\) | 1.63389e10 | 0.761800 | ||||||||
\(896\) | −5.52183e8 | −0.0256451 | ||||||||
\(897\) | 9.20156e9 | 0.425685 | ||||||||
\(898\) | −7.20828e9 | −0.332173 | ||||||||
\(899\) | −6.51238e9 | −0.298938 | ||||||||
\(900\) | −4.10495e8 | −0.0187698 | ||||||||
\(901\) | 3.70674e10 | 1.68832 | ||||||||
\(902\) | 8.82060e7 | 0.00400198 | ||||||||
\(903\) | −5.24810e8 | −0.0237189 | ||||||||
\(904\) | −3.46785e9 | −0.156124 | ||||||||
\(905\) | 1.05840e9 | 0.0474655 | ||||||||
\(906\) | −2.67697e10 | −1.19590 | ||||||||
\(907\) | 2.55913e10 | 1.13885 | 0.569425 | − | 0.822043i | \(-0.307166\pi\) | ||||
0.569425 | + | 0.822043i | \(0.307166\pi\) | |||||||
\(908\) | 1.33726e10 | 0.592808 | ||||||||
\(909\) | −1.21827e9 | −0.0537984 | ||||||||
\(910\) | 8.34745e8 | 0.0367205 | ||||||||
\(911\) | 3.22614e9 | 0.141374 | 0.0706869 | − | 0.997499i | \(-0.477481\pi\) | ||||
0.0706869 | + | 0.997499i | \(0.477481\pi\) | |||||||
\(912\) | −1.61191e9 | −0.0703653 | ||||||||
\(913\) | 2.93658e9 | 0.127701 | ||||||||
\(914\) | 9.10246e9 | 0.394319 | ||||||||
\(915\) | −6.78778e9 | −0.292923 | ||||||||
\(916\) | 1.03385e10 | 0.444449 | ||||||||
\(917\) | 4.89146e9 | 0.209482 | ||||||||
\(918\) | 2.65193e10 | 1.13139 | ||||||||
\(919\) | −2.19319e10 | −0.932122 | −0.466061 | − | 0.884753i | \(-0.654327\pi\) | ||||
−0.466061 | + | 0.884753i | \(0.654327\pi\) | |||||||
\(920\) | −1.87616e10 | −0.794352 | ||||||||
\(921\) | 3.00174e10 | 1.26609 | ||||||||
\(922\) | −1.50427e9 | −0.0632073 | ||||||||
\(923\) | 3.95569e9 | 0.165583 | ||||||||
\(924\) | −9.07801e8 | −0.0378563 | ||||||||
\(925\) | −2.35070e9 | −0.0976566 | ||||||||
\(926\) | −4.41038e8 | −0.0182531 | ||||||||
\(927\) | 9.38855e8 | 0.0387097 | ||||||||
\(928\) | −5.15427e9 | −0.211714 | ||||||||
\(929\) | −7.69802e9 | −0.315010 | −0.157505 | − | 0.987518i | \(-0.550345\pi\) | ||||
−0.157505 | + | 0.987518i | \(0.550345\pi\) | |||||||
\(930\) | −9.41237e9 | −0.383715 | ||||||||
\(931\) | 6.81915e8 | 0.0276953 | ||||||||
\(932\) | 2.57475e9 | 0.104179 | ||||||||
\(933\) | −4.78685e10 | −1.92958 | ||||||||
\(934\) | −5.37963e9 | −0.216042 | ||||||||
\(935\) | 4.04628e9 | 0.161888 | ||||||||
\(936\) | −4.12632e8 | −0.0164474 | ||||||||
\(937\) | 1.96480e10 | 0.780241 | 0.390121 | − | 0.920764i | \(-0.372433\pi\) | ||||
0.390121 | + | 0.920764i | \(0.372433\pi\) | |||||||
\(938\) | −5.02504e9 | −0.198806 | ||||||||
\(939\) | 8.89982e9 | 0.350794 | ||||||||
\(940\) | 2.98238e9 | 0.117116 | ||||||||
\(941\) | −8.52895e9 | −0.333681 | −0.166841 | − | 0.985984i | \(-0.553357\pi\) | ||||
−0.166841 | + | 0.985984i | \(0.553357\pi\) | |||||||
\(942\) | −1.44754e9 | −0.0564224 | ||||||||
\(943\) | −9.17658e8 | −0.0356361 | ||||||||
\(944\) | 9.76915e9 | 0.377968 | ||||||||
\(945\) | 4.69170e9 | 0.180850 | ||||||||
\(946\) | −2.98039e8 | −0.0114460 | ||||||||
\(947\) | 7.92096e8 | 0.0303077 | 0.0151539 | − | 0.999885i | \(-0.495176\pi\) | ||||
0.0151539 | + | 0.999885i | \(0.495176\pi\) | |||||||
\(948\) | −1.01881e10 | −0.388388 | ||||||||
\(949\) | −1.32268e10 | −0.502368 | ||||||||
\(950\) | −3.00923e9 | −0.113874 | ||||||||
\(951\) | −7.56735e9 | −0.285307 | ||||||||
\(952\) | 1.59429e10 | 0.598877 | ||||||||
\(953\) | 1.74946e10 | 0.654755 | 0.327377 | − | 0.944894i | \(-0.393835\pi\) | ||||
0.327377 | + | 0.944894i | \(0.393835\pi\) | |||||||
\(954\) | 1.27229e9 | 0.0474423 | ||||||||
\(955\) | 3.69715e8 | 0.0137358 | ||||||||
\(956\) | 3.57991e9 | 0.132516 | ||||||||
\(957\) | −1.65130e9 | −0.0609025 | ||||||||
\(958\) | 2.26679e10 | 0.832975 | ||||||||
\(959\) | 1.26175e10 | 0.461963 | ||||||||
\(960\) | −1.20915e10 | −0.441093 | ||||||||
\(961\) | 7.42186e9 | 0.269762 | ||||||||
\(962\) | −7.17765e8 | −0.0259938 | ||||||||
\(963\) | −2.27650e9 | −0.0821440 | ||||||||
\(964\) | 9.02224e9 | 0.324373 | ||||||||
\(965\) | 9.33812e9 | 0.334514 | ||||||||
\(966\) | −1.22028e10 | −0.435552 | ||||||||
\(967\) | −1.57615e9 | −0.0560537 | −0.0280269 | − | 0.999607i | \(-0.508922\pi\) | ||||
−0.0280269 | + | 0.999607i | \(0.508922\pi\) | |||||||
\(968\) | 2.87351e10 | 1.01824 | ||||||||
\(969\) | −7.84282e9 | −0.276910 | ||||||||
\(970\) | 5.37302e9 | 0.189024 | ||||||||
\(971\) | 8.34171e9 | 0.292407 | 0.146204 | − | 0.989255i | \(-0.453295\pi\) | ||||
0.146204 | + | 0.989255i | \(0.453295\pi\) | |||||||
\(972\) | −1.37224e9 | −0.0479290 | ||||||||
\(973\) | −1.65168e10 | −0.574818 | ||||||||
\(974\) | −5.93377e8 | −0.0205766 | ||||||||
\(975\) | 6.10452e9 | 0.210929 | ||||||||
\(976\) | −7.00400e9 | −0.241141 | ||||||||
\(977\) | 4.51998e10 | 1.55062 | 0.775311 | − | 0.631580i | \(-0.217593\pi\) | ||||
0.775311 | + | 0.631580i | \(0.217593\pi\) | |||||||
\(978\) | −6.72867e9 | −0.230008 | ||||||||
\(979\) | −4.99249e9 | −0.170050 | ||||||||
\(980\) | 8.56773e8 | 0.0290787 | ||||||||
\(981\) | −1.75666e9 | −0.0594082 | ||||||||
\(982\) | 2.36947e10 | 0.798473 | ||||||||
\(983\) | −4.03179e9 | −0.135382 | −0.0676909 | − | 0.997706i | \(-0.521563\pi\) | ||||
−0.0676909 | + | 0.997706i | \(0.521563\pi\) | |||||||
\(984\) | −7.07162e8 | −0.0236612 | ||||||||
\(985\) | −2.55222e10 | −0.850925 | ||||||||
\(986\) | 8.80916e9 | 0.292661 | ||||||||
\(987\) | 6.38589e9 | 0.211403 | ||||||||
\(988\) | 7.11139e8 | 0.0234588 | ||||||||
\(989\) | 3.10067e9 | 0.101922 | ||||||||
\(990\) | 1.38883e8 | 0.00454911 | ||||||||
\(991\) | −1.71004e10 | −0.558146 | −0.279073 | − | 0.960270i | \(-0.590027\pi\) | ||||
−0.279073 | + | 0.960270i | \(0.590027\pi\) | |||||||
\(992\) | 2.76491e10 | 0.899271 | ||||||||
\(993\) | 4.03274e10 | 1.30701 | ||||||||
\(994\) | −5.24590e9 | −0.169421 | ||||||||
\(995\) | 2.70374e10 | 0.870132 | ||||||||
\(996\) | −7.15143e9 | −0.229343 | ||||||||
\(997\) | 1.49544e10 | 0.477899 | 0.238949 | − | 0.971032i | \(-0.423197\pi\) | ||||
0.238949 | + | 0.971032i | \(0.423197\pi\) | |||||||
\(998\) | −3.07406e10 | −0.978938 | ||||||||
\(999\) | −4.03421e9 | −0.128020 |
(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 | 91.8.a.c.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.c.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |