Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.93322\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.93322 | 0.347651 | 0.173825 | − | 0.984776i | \(-0.444387\pi\) | ||||
0.173825 | + | 0.984776i | \(0.444387\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −112.530 | −0.879139 | ||||||||
\(5\) | −305.648 | −1.09352 | −0.546760 | − | 0.837289i | \(-0.684139\pi\) | ||||
−0.546760 | + | 0.837289i | \(0.684139\pi\) | |||||||
\(6\) | 106.197 | 0.200716 | ||||||||
\(7\) | −1406.85 | −1.55026 | −0.775128 | − | 0.631804i | \(-0.782315\pi\) | ||||
−0.775128 | + | 0.631804i | \(0.782315\pi\) | |||||||
\(8\) | −946.057 | −0.653284 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1202.18 | −0.380163 | ||||||||
\(11\) | 322.020 | 0.0729472 | 0.0364736 | − | 0.999335i | \(-0.488388\pi\) | ||||
0.0364736 | + | 0.999335i | \(0.488388\pi\) | |||||||
\(12\) | −3038.30 | −0.507571 | ||||||||
\(13\) | −6387.28 | −0.806333 | −0.403167 | − | 0.915127i | \(-0.632090\pi\) | ||||
−0.403167 | + | 0.915127i | \(0.632090\pi\) | |||||||
\(14\) | −5533.44 | −0.538948 | ||||||||
\(15\) | −8252.50 | −0.631344 | ||||||||
\(16\) | 10682.8 | 0.652024 | ||||||||
\(17\) | −14848.7 | −0.733023 | −0.366512 | − | 0.930413i | \(-0.619448\pi\) | ||||
−0.366512 | + | 0.930413i | \(0.619448\pi\) | |||||||
\(18\) | 2867.32 | 0.115884 | ||||||||
\(19\) | −12707.1 | −0.425019 | −0.212509 | − | 0.977159i | \(-0.568164\pi\) | ||||
−0.212509 | + | 0.977159i | \(0.568164\pi\) | |||||||
\(20\) | 34394.5 | 0.961356 | ||||||||
\(21\) | −37984.9 | −0.895041 | ||||||||
\(22\) | 1266.58 | 0.0253601 | ||||||||
\(23\) | −17301.0 | −0.296499 | −0.148250 | − | 0.988950i | \(-0.547364\pi\) | ||||
−0.148250 | + | 0.988950i | \(0.547364\pi\) | |||||||
\(24\) | −25543.5 | −0.377174 | ||||||||
\(25\) | 15295.9 | 0.195787 | ||||||||
\(26\) | −25122.6 | −0.280322 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 158312. | 1.36289 | ||||||||
\(29\) | −68692.0 | −0.523013 | −0.261507 | − | 0.965202i | \(-0.584219\pi\) | ||||
−0.261507 | + | 0.965202i | \(0.584219\pi\) | |||||||
\(30\) | −32458.9 | −0.219487 | ||||||||
\(31\) | 153138. | 0.923244 | 0.461622 | − | 0.887077i | \(-0.347268\pi\) | ||||
0.461622 | + | 0.887077i | \(0.347268\pi\) | |||||||
\(32\) | 163113. | 0.879961 | ||||||||
\(33\) | 8694.54 | 0.0421161 | ||||||||
\(34\) | −58403.3 | −0.254836 | ||||||||
\(35\) | 430000. | 1.69524 | ||||||||
\(36\) | −82034.2 | −0.293046 | ||||||||
\(37\) | 198033. | 0.642736 | 0.321368 | − | 0.946954i | \(-0.395857\pi\) | ||||
0.321368 | + | 0.946954i | \(0.395857\pi\) | |||||||
\(38\) | −49979.8 | −0.147758 | ||||||||
\(39\) | −172457. | −0.465537 | ||||||||
\(40\) | 289161. | 0.714380 | ||||||||
\(41\) | 419043. | 0.949544 | 0.474772 | − | 0.880109i | \(-0.342531\pi\) | ||||
0.474772 | + | 0.880109i | \(0.342531\pi\) | |||||||
\(42\) | −149403. | −0.311162 | ||||||||
\(43\) | 104716. | 0.200851 | 0.100426 | − | 0.994945i | \(-0.467980\pi\) | ||||
0.100426 | + | 0.994945i | \(0.467980\pi\) | |||||||
\(44\) | −36236.8 | −0.0641307 | ||||||||
\(45\) | −222818. | −0.364507 | ||||||||
\(46\) | −68048.6 | −0.103078 | ||||||||
\(47\) | −738804. | −1.03797 | −0.518987 | − | 0.854782i | \(-0.673691\pi\) | ||||
−0.518987 | + | 0.854782i | \(0.673691\pi\) | |||||||
\(48\) | 288435. | 0.376446 | ||||||||
\(49\) | 1.15568e6 | 1.40330 | ||||||||
\(50\) | 60162.0 | 0.0680656 | ||||||||
\(51\) | −400916. | −0.423211 | ||||||||
\(52\) | 718760. | 0.708879 | ||||||||
\(53\) | 248408. | 0.229192 | 0.114596 | − | 0.993412i | \(-0.463443\pi\) | ||||
0.114596 | + | 0.993412i | \(0.463443\pi\) | |||||||
\(54\) | 77417.6 | 0.0669054 | ||||||||
\(55\) | −98424.9 | −0.0797692 | ||||||||
\(56\) | 1.33096e6 | 1.01276 | ||||||||
\(57\) | −343091. | −0.245385 | ||||||||
\(58\) | −270181. | −0.181826 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 928652. | 0.555039 | ||||||||
\(61\) | 915348. | 0.516335 | 0.258168 | − | 0.966100i | \(-0.416881\pi\) | ||||
0.258168 | + | 0.966100i | \(0.416881\pi\) | |||||||
\(62\) | 602325. | 0.320966 | ||||||||
\(63\) | −1.02559e6 | −0.516752 | ||||||||
\(64\) | −725835. | −0.346105 | ||||||||
\(65\) | 1.95226e6 | 0.881742 | ||||||||
\(66\) | 34197.5 | 0.0146417 | ||||||||
\(67\) | −828193. | −0.336411 | −0.168205 | − | 0.985752i | \(-0.553797\pi\) | ||||
−0.168205 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(68\) | 1.67092e6 | 0.644429 | ||||||||
\(69\) | −467127. | −0.171184 | ||||||||
\(70\) | 1.69129e6 | 0.589351 | ||||||||
\(71\) | −302314. | −0.100243 | −0.0501215 | − | 0.998743i | \(-0.515961\pi\) | ||||
−0.0501215 | + | 0.998743i | \(0.515961\pi\) | |||||||
\(72\) | −689675. | −0.217761 | ||||||||
\(73\) | −3.36995e6 | −1.01390 | −0.506948 | − | 0.861977i | \(-0.669226\pi\) | ||||
−0.506948 | + | 0.861977i | \(0.669226\pi\) | |||||||
\(74\) | 778909. | 0.223448 | ||||||||
\(75\) | 412989. | 0.113038 | ||||||||
\(76\) | 1.42993e6 | 0.373651 | ||||||||
\(77\) | −453033. | −0.113087 | ||||||||
\(78\) | −678310. | −0.161844 | ||||||||
\(79\) | −608944. | −0.138958 | −0.0694789 | − | 0.997583i | \(-0.522134\pi\) | ||||
−0.0694789 | + | 0.997583i | \(0.522134\pi\) | |||||||
\(80\) | −3.26517e6 | −0.713002 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.64819e6 | 0.330110 | ||||||||
\(83\) | −3.11831e6 | −0.598614 | −0.299307 | − | 0.954157i | \(-0.596755\pi\) | ||||
−0.299307 | + | 0.954157i | \(0.596755\pi\) | |||||||
\(84\) | 4.27443e6 | 0.786866 | ||||||||
\(85\) | 4.53849e6 | 0.801576 | ||||||||
\(86\) | 411872. | 0.0698260 | ||||||||
\(87\) | −1.85468e6 | −0.301962 | ||||||||
\(88\) | −304649. | −0.0476552 | ||||||||
\(89\) | −8.70611e6 | −1.30906 | −0.654529 | − | 0.756037i | \(-0.727133\pi\) | ||||
−0.654529 | + | 0.756037i | \(0.727133\pi\) | |||||||
\(90\) | −876391. | −0.126721 | ||||||||
\(91\) | 8.98593e6 | 1.25002 | ||||||||
\(92\) | 1.94688e6 | 0.260664 | ||||||||
\(93\) | 4.13472e6 | 0.533035 | ||||||||
\(94\) | −2.90588e6 | −0.360852 | ||||||||
\(95\) | 3.88390e6 | 0.464767 | ||||||||
\(96\) | 4.40405e6 | 0.508046 | ||||||||
\(97\) | −1.80756e6 | −0.201091 | −0.100545 | − | 0.994932i | \(-0.532059\pi\) | ||||
−0.100545 | + | 0.994932i | \(0.532059\pi\) | |||||||
\(98\) | 4.54552e6 | 0.487857 | ||||||||
\(99\) | 234753. | 0.0243157 | ||||||||
\(100\) | −1.72124e6 | −0.172124 | ||||||||
\(101\) | 8.27630e6 | 0.799303 | 0.399651 | − | 0.916667i | \(-0.369131\pi\) | ||||
0.399651 | + | 0.916667i | \(0.369131\pi\) | |||||||
\(102\) | −1.57689e6 | −0.147130 | ||||||||
\(103\) | 1.84311e7 | 1.66197 | 0.830983 | − | 0.556298i | \(-0.187779\pi\) | ||||
0.830983 | + | 0.556298i | \(0.187779\pi\) | |||||||
\(104\) | 6.04273e6 | 0.526765 | ||||||||
\(105\) | 1.16100e7 | 0.978746 | ||||||||
\(106\) | 977042. | 0.0796788 | ||||||||
\(107\) | 6.61305e6 | 0.521866 | 0.260933 | − | 0.965357i | \(-0.415970\pi\) | ||||
0.260933 | + | 0.965357i | \(0.415970\pi\) | |||||||
\(108\) | −2.21492e6 | −0.169190 | ||||||||
\(109\) | 1.30251e7 | 0.963359 | 0.481679 | − | 0.876347i | \(-0.340027\pi\) | ||||
0.481679 | + | 0.876347i | \(0.340027\pi\) | |||||||
\(110\) | −387127. | −0.0277318 | ||||||||
\(111\) | 5.34690e6 | 0.371084 | ||||||||
\(112\) | −1.50290e7 | −1.01080 | ||||||||
\(113\) | −7.28274e6 | −0.474810 | −0.237405 | − | 0.971411i | \(-0.576297\pi\) | ||||
−0.237405 | + | 0.971411i | \(0.576297\pi\) | |||||||
\(114\) | −1.34945e6 | −0.0853082 | ||||||||
\(115\) | 5.28802e6 | 0.324228 | ||||||||
\(116\) | 7.72989e6 | 0.459802 | ||||||||
\(117\) | −4.65633e6 | −0.268778 | ||||||||
\(118\) | 807801. | 0.0452603 | ||||||||
\(119\) | 2.08899e7 | 1.13637 | ||||||||
\(120\) | 7.80733e6 | 0.412447 | ||||||||
\(121\) | −1.93835e7 | −0.994679 | ||||||||
\(122\) | 3.60026e6 | 0.179504 | ||||||||
\(123\) | 1.13142e7 | 0.548219 | ||||||||
\(124\) | −1.72326e7 | −0.811660 | ||||||||
\(125\) | 1.92036e7 | 0.879423 | ||||||||
\(126\) | −4.03388e6 | −0.179649 | ||||||||
\(127\) | 3.11648e7 | 1.35006 | 0.675028 | − | 0.737792i | \(-0.264131\pi\) | ||||
0.675028 | + | 0.737792i | \(0.264131\pi\) | |||||||
\(128\) | −2.37333e7 | −1.00028 | ||||||||
\(129\) | 2.82734e6 | 0.115961 | ||||||||
\(130\) | 7.67868e6 | 0.306538 | ||||||||
\(131\) | −2.99857e7 | −1.16537 | −0.582687 | − | 0.812697i | \(-0.697999\pi\) | ||||
−0.582687 | + | 0.812697i | \(0.697999\pi\) | |||||||
\(132\) | −978395. | −0.0370259 | ||||||||
\(133\) | 1.78769e7 | 0.658889 | ||||||||
\(134\) | −3.25747e6 | −0.116953 | ||||||||
\(135\) | −6.01608e6 | −0.210448 | ||||||||
\(136\) | 1.40477e7 | 0.478873 | ||||||||
\(137\) | 1.65933e7 | 0.551329 | 0.275664 | − | 0.961254i | \(-0.411102\pi\) | ||||
0.275664 | + | 0.961254i | \(0.411102\pi\) | |||||||
\(138\) | −1.83731e6 | −0.0595122 | ||||||||
\(139\) | −5.13930e7 | −1.62313 | −0.811563 | − | 0.584264i | \(-0.801383\pi\) | ||||
−0.811563 | + | 0.584264i | \(0.801383\pi\) | |||||||
\(140\) | −4.83878e7 | −1.49035 | ||||||||
\(141\) | −1.99477e7 | −0.599275 | ||||||||
\(142\) | −1.18907e6 | −0.0348496 | ||||||||
\(143\) | −2.05683e6 | −0.0588197 | ||||||||
\(144\) | 7.78773e6 | 0.217341 | ||||||||
\(145\) | 2.09956e7 | 0.571926 | ||||||||
\(146\) | −1.32547e7 | −0.352481 | ||||||||
\(147\) | 3.12032e7 | 0.810194 | ||||||||
\(148\) | −2.22847e7 | −0.565054 | ||||||||
\(149\) | −2.55525e7 | −0.632821 | −0.316410 | − | 0.948622i | \(-0.602478\pi\) | ||||
−0.316410 | + | 0.948622i | \(0.602478\pi\) | |||||||
\(150\) | 1.62437e6 | 0.0392977 | ||||||||
\(151\) | −2.50959e6 | −0.0593176 | −0.0296588 | − | 0.999560i | \(-0.509442\pi\) | ||||
−0.0296588 | + | 0.999560i | \(0.509442\pi\) | |||||||
\(152\) | 1.20216e7 | 0.277658 | ||||||||
\(153\) | −1.08247e7 | −0.244341 | ||||||||
\(154\) | −1.78188e6 | −0.0393147 | ||||||||
\(155\) | −4.68063e7 | −1.00959 | ||||||||
\(156\) | 1.94065e7 | 0.409271 | ||||||||
\(157\) | −1.51685e7 | −0.312819 | −0.156409 | − | 0.987692i | \(-0.549992\pi\) | ||||
−0.156409 | + | 0.987692i | \(0.549992\pi\) | |||||||
\(158\) | −2.39511e6 | −0.0483088 | ||||||||
\(159\) | 6.70701e6 | 0.132324 | ||||||||
\(160\) | −4.98552e7 | −0.962255 | ||||||||
\(161\) | 2.43398e7 | 0.459650 | ||||||||
\(162\) | 2.09027e6 | 0.0386279 | ||||||||
\(163\) | 1.10949e7 | 0.200664 | 0.100332 | − | 0.994954i | \(-0.468010\pi\) | ||||
0.100332 | + | 0.994954i | \(0.468010\pi\) | |||||||
\(164\) | −4.71548e7 | −0.834781 | ||||||||
\(165\) | −2.65747e6 | −0.0460548 | ||||||||
\(166\) | −1.22650e7 | −0.208108 | ||||||||
\(167\) | 8.97494e7 | 1.49116 | 0.745579 | − | 0.666417i | \(-0.232173\pi\) | ||||
0.745579 | + | 0.666417i | \(0.232173\pi\) | |||||||
\(168\) | 3.59358e7 | 0.584716 | ||||||||
\(169\) | −2.19511e7 | −0.349827 | ||||||||
\(170\) | 1.78509e7 | 0.278669 | ||||||||
\(171\) | −9.26346e6 | −0.141673 | ||||||||
\(172\) | −1.17837e7 | −0.176576 | ||||||||
\(173\) | 9.67840e7 | 1.42116 | 0.710578 | − | 0.703618i | \(-0.248433\pi\) | ||||
0.710578 | + | 0.703618i | \(0.248433\pi\) | |||||||
\(174\) | −7.29488e6 | −0.104977 | ||||||||
\(175\) | −2.15189e7 | −0.303520 | ||||||||
\(176\) | 3.44006e6 | 0.0475633 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −3.42430e7 | −0.455095 | ||||||||
\(179\) | −3.95244e7 | −0.515086 | −0.257543 | − | 0.966267i | \(-0.582913\pi\) | ||||
−0.257543 | + | 0.966267i | \(0.582913\pi\) | |||||||
\(180\) | 2.50736e7 | 0.320452 | ||||||||
\(181\) | −7.62592e6 | −0.0955910 | −0.0477955 | − | 0.998857i | \(-0.515220\pi\) | ||||
−0.0477955 | + | 0.998857i | \(0.515220\pi\) | |||||||
\(182\) | 3.53436e7 | 0.434572 | ||||||||
\(183\) | 2.47144e7 | 0.298106 | ||||||||
\(184\) | 1.63677e7 | 0.193698 | ||||||||
\(185\) | −6.05286e7 | −0.702845 | ||||||||
\(186\) | 1.62628e7 | 0.185310 | ||||||||
\(187\) | −4.78159e6 | −0.0534720 | ||||||||
\(188\) | 8.31374e7 | 0.912523 | ||||||||
\(189\) | −2.76910e7 | −0.298347 | ||||||||
\(190\) | 1.52762e7 | 0.161577 | ||||||||
\(191\) | −7.01758e7 | −0.728736 | −0.364368 | − | 0.931255i | \(-0.618715\pi\) | ||||
−0.364368 | + | 0.931255i | \(0.618715\pi\) | |||||||
\(192\) | −1.95975e7 | −0.199824 | ||||||||
\(193\) | −1.47888e8 | −1.48076 | −0.740378 | − | 0.672191i | \(-0.765353\pi\) | ||||
−0.740378 | + | 0.672191i | \(0.765353\pi\) | |||||||
\(194\) | −7.10954e6 | −0.0699094 | ||||||||
\(195\) | 5.27111e7 | 0.509074 | ||||||||
\(196\) | −1.30048e8 | −1.23369 | ||||||||
\(197\) | −2.42261e7 | −0.225762 | −0.112881 | − | 0.993608i | \(-0.536008\pi\) | ||||
−0.112881 | + | 0.993608i | \(0.536008\pi\) | |||||||
\(198\) | 923334. | 0.00845338 | ||||||||
\(199\) | −1.19894e8 | −1.07847 | −0.539237 | − | 0.842154i | \(-0.681287\pi\) | ||||
−0.539237 | + | 0.842154i | \(0.681287\pi\) | |||||||
\(200\) | −1.44708e7 | −0.127905 | ||||||||
\(201\) | −2.23612e7 | −0.194227 | ||||||||
\(202\) | 3.25525e7 | 0.277878 | ||||||||
\(203\) | 9.66391e7 | 0.810805 | ||||||||
\(204\) | 4.51149e7 | 0.372062 | ||||||||
\(205\) | −1.28080e8 | −1.03835 | ||||||||
\(206\) | 7.24937e7 | 0.577783 | ||||||||
\(207\) | −1.26124e7 | −0.0988331 | ||||||||
\(208\) | −6.82338e7 | −0.525749 | ||||||||
\(209\) | −4.09194e6 | −0.0310039 | ||||||||
\(210\) | 4.56647e7 | 0.340262 | ||||||||
\(211\) | −1.87566e8 | −1.37456 | −0.687281 | − | 0.726391i | \(-0.741196\pi\) | ||||
−0.687281 | + | 0.726391i | \(0.741196\pi\) | |||||||
\(212\) | −2.79533e7 | −0.201492 | ||||||||
\(213\) | −8.16249e6 | −0.0578754 | ||||||||
\(214\) | 2.60106e7 | 0.181427 | ||||||||
\(215\) | −3.20063e7 | −0.219635 | ||||||||
\(216\) | −1.86212e7 | −0.125725 | ||||||||
\(217\) | −2.15441e8 | −1.43127 | ||||||||
\(218\) | 5.12306e7 | 0.334912 | ||||||||
\(219\) | −9.09886e7 | −0.585373 | ||||||||
\(220\) | 1.10757e7 | 0.0701282 | ||||||||
\(221\) | 9.48430e7 | 0.591061 | ||||||||
\(222\) | 2.10305e7 | 0.129008 | ||||||||
\(223\) | 5.60154e7 | 0.338252 | 0.169126 | − | 0.985594i | \(-0.445905\pi\) | ||||
0.169126 | + | 0.985594i | \(0.445905\pi\) | |||||||
\(224\) | −2.29475e8 | −1.36417 | ||||||||
\(225\) | 1.11507e7 | 0.0652624 | ||||||||
\(226\) | −2.86446e7 | −0.165068 | ||||||||
\(227\) | 1.96404e8 | 1.11445 | 0.557224 | − | 0.830362i | \(-0.311866\pi\) | ||||
0.557224 | + | 0.830362i | \(0.311866\pi\) | |||||||
\(228\) | 3.86080e7 | 0.215727 | ||||||||
\(229\) | 4.38337e7 | 0.241203 | 0.120602 | − | 0.992701i | \(-0.461518\pi\) | ||||
0.120602 | + | 0.992701i | \(0.461518\pi\) | |||||||
\(230\) | 2.07989e7 | 0.112718 | ||||||||
\(231\) | −1.22319e7 | −0.0652907 | ||||||||
\(232\) | 6.49865e7 | 0.341676 | ||||||||
\(233\) | 1.57505e7 | 0.0815732 | 0.0407866 | − | 0.999168i | \(-0.487014\pi\) | ||||
0.0407866 | + | 0.999168i | \(0.487014\pi\) | |||||||
\(234\) | −1.83144e7 | −0.0934408 | ||||||||
\(235\) | 2.25814e8 | 1.13505 | ||||||||
\(236\) | −2.31113e7 | −0.114454 | ||||||||
\(237\) | −1.64415e7 | −0.0802273 | ||||||||
\(238\) | 8.21645e7 | 0.395062 | ||||||||
\(239\) | −1.02176e8 | −0.484126 | −0.242063 | − | 0.970261i | \(-0.577824\pi\) | ||||
−0.242063 | + | 0.970261i | \(0.577824\pi\) | |||||||
\(240\) | −8.81595e7 | −0.411652 | ||||||||
\(241\) | 1.57502e7 | 0.0724813 | 0.0362407 | − | 0.999343i | \(-0.488462\pi\) | ||||
0.0362407 | + | 0.999343i | \(0.488462\pi\) | |||||||
\(242\) | −7.62395e7 | −0.345801 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −1.03004e8 | −0.453930 | ||||||||
\(245\) | −3.53230e8 | −1.53453 | ||||||||
\(246\) | 4.45011e7 | 0.190589 | ||||||||
\(247\) | 8.11638e7 | 0.342707 | ||||||||
\(248\) | −1.44877e8 | −0.603141 | ||||||||
\(249\) | −8.41945e7 | −0.345610 | ||||||||
\(250\) | 7.55320e7 | 0.305732 | ||||||||
\(251\) | 1.52785e8 | 0.609848 | 0.304924 | − | 0.952377i | \(-0.401369\pi\) | ||||
0.304924 | + | 0.952377i | \(0.401369\pi\) | |||||||
\(252\) | 1.15410e8 | 0.454297 | ||||||||
\(253\) | −5.57127e6 | −0.0216288 | ||||||||
\(254\) | 1.22578e8 | 0.469348 | ||||||||
\(255\) | 1.22539e8 | 0.462790 | ||||||||
\(256\) | −441486. | −0.00164466 | ||||||||
\(257\) | 2.55028e8 | 0.937176 | 0.468588 | − | 0.883417i | \(-0.344763\pi\) | ||||
0.468588 | + | 0.883417i | \(0.344763\pi\) | |||||||
\(258\) | 1.11205e7 | 0.0403141 | ||||||||
\(259\) | −2.78603e8 | −0.996405 | ||||||||
\(260\) | −2.19688e8 | −0.775174 | ||||||||
\(261\) | −5.00764e7 | −0.174338 | ||||||||
\(262\) | −1.17941e8 | −0.405143 | ||||||||
\(263\) | 3.21627e8 | 1.09020 | 0.545101 | − | 0.838370i | \(-0.316491\pi\) | ||||
0.545101 | + | 0.838370i | \(0.316491\pi\) | |||||||
\(264\) | −8.22553e6 | −0.0275138 | ||||||||
\(265\) | −7.59254e7 | −0.250626 | ||||||||
\(266\) | 7.03139e7 | 0.229063 | ||||||||
\(267\) | −2.35065e8 | −0.755785 | ||||||||
\(268\) | 9.31964e7 | 0.295752 | ||||||||
\(269\) | 2.32732e8 | 0.728992 | 0.364496 | − | 0.931205i | \(-0.381241\pi\) | ||||
0.364496 | + | 0.931205i | \(0.381241\pi\) | |||||||
\(270\) | −2.36625e7 | −0.0731625 | ||||||||
\(271\) | 1.17634e8 | 0.359036 | 0.179518 | − | 0.983755i | \(-0.442546\pi\) | ||||
0.179518 | + | 0.983755i | \(0.442546\pi\) | |||||||
\(272\) | −1.58625e8 | −0.477949 | ||||||||
\(273\) | 2.42620e8 | 0.721701 | ||||||||
\(274\) | 6.52651e7 | 0.191670 | ||||||||
\(275\) | 4.92558e6 | 0.0142821 | ||||||||
\(276\) | 5.25657e7 | 0.150494 | ||||||||
\(277\) | 2.49236e8 | 0.704583 | 0.352291 | − | 0.935890i | \(-0.385403\pi\) | ||||
0.352291 | + | 0.935890i | \(0.385403\pi\) | |||||||
\(278\) | −2.02140e8 | −0.564281 | ||||||||
\(279\) | 1.11637e8 | 0.307748 | ||||||||
\(280\) | −4.06805e8 | −1.10747 | ||||||||
\(281\) | 4.06099e8 | 1.09184 | 0.545921 | − | 0.837837i | \(-0.316180\pi\) | ||||
0.545921 | + | 0.837837i | \(0.316180\pi\) | |||||||
\(282\) | −7.84587e7 | −0.208338 | ||||||||
\(283\) | −7.10346e8 | −1.86302 | −0.931510 | − | 0.363717i | \(-0.881508\pi\) | ||||
−0.931510 | + | 0.363717i | \(0.881508\pi\) | |||||||
\(284\) | 3.40194e7 | 0.0881276 | ||||||||
\(285\) | 1.04865e8 | 0.268333 | ||||||||
\(286\) | −8.08998e6 | −0.0204487 | ||||||||
\(287\) | −5.89529e8 | −1.47204 | ||||||||
\(288\) | 1.18909e8 | 0.293320 | ||||||||
\(289\) | −1.89854e8 | −0.462677 | ||||||||
\(290\) | 8.25802e7 | 0.198831 | ||||||||
\(291\) | −4.88042e7 | −0.116100 | ||||||||
\(292\) | 3.79219e8 | 0.891355 | ||||||||
\(293\) | 9.92751e7 | 0.230571 | 0.115285 | − | 0.993332i | \(-0.463222\pi\) | ||||
0.115285 | + | 0.993332i | \(0.463222\pi\) | |||||||
\(294\) | 1.22729e8 | 0.281664 | ||||||||
\(295\) | −6.27737e7 | −0.142364 | ||||||||
\(296\) | −1.87351e8 | −0.419889 | ||||||||
\(297\) | 6.33832e6 | 0.0140387 | ||||||||
\(298\) | −1.00503e8 | −0.220001 | ||||||||
\(299\) | 1.10506e8 | 0.239077 | ||||||||
\(300\) | −4.64735e7 | −0.0993759 | ||||||||
\(301\) | −1.47320e8 | −0.311371 | ||||||||
\(302\) | −9.87078e6 | −0.0206218 | ||||||||
\(303\) | 2.23460e8 | 0.461478 | ||||||||
\(304\) | −1.35747e8 | −0.277123 | ||||||||
\(305\) | −2.79775e8 | −0.564623 | ||||||||
\(306\) | −4.25760e7 | −0.0849454 | ||||||||
\(307\) | 9.45615e8 | 1.86522 | 0.932610 | − | 0.360885i | \(-0.117525\pi\) | ||||
0.932610 | + | 0.360885i | \(0.117525\pi\) | |||||||
\(308\) | 5.09797e7 | 0.0994191 | ||||||||
\(309\) | 4.97641e8 | 0.959536 | ||||||||
\(310\) | −1.84099e8 | −0.350983 | ||||||||
\(311\) | 3.51898e8 | 0.663370 | 0.331685 | − | 0.943390i | \(-0.392383\pi\) | ||||
0.331685 | + | 0.943390i | \(0.392383\pi\) | |||||||
\(312\) | 1.63154e8 | 0.304128 | ||||||||
\(313\) | 4.30491e8 | 0.793521 | 0.396761 | − | 0.917922i | \(-0.370134\pi\) | ||||
0.396761 | + | 0.917922i | \(0.370134\pi\) | |||||||
\(314\) | −5.96609e7 | −0.108752 | ||||||||
\(315\) | 3.13470e8 | 0.565079 | ||||||||
\(316\) | 6.85244e7 | 0.122163 | ||||||||
\(317\) | 9.07736e8 | 1.60049 | 0.800243 | − | 0.599676i | \(-0.204704\pi\) | ||||
0.800243 | + | 0.599676i | \(0.204704\pi\) | |||||||
\(318\) | 2.63801e7 | 0.0460026 | ||||||||
\(319\) | −2.21202e7 | −0.0381524 | ||||||||
\(320\) | 2.21850e8 | 0.378473 | ||||||||
\(321\) | 1.78552e8 | 0.301299 | ||||||||
\(322\) | 9.57340e7 | 0.159798 | ||||||||
\(323\) | 1.88684e8 | 0.311549 | ||||||||
\(324\) | −5.98029e7 | −0.0976821 | ||||||||
\(325\) | −9.76991e7 | −0.157870 | ||||||||
\(326\) | 4.36389e7 | 0.0697609 | ||||||||
\(327\) | 3.51678e8 | 0.556195 | ||||||||
\(328\) | −3.96438e8 | −0.620322 | ||||||||
\(329\) | 1.03938e9 | 1.60913 | ||||||||
\(330\) | −1.04524e7 | −0.0160110 | ||||||||
\(331\) | −6.30152e8 | −0.955096 | −0.477548 | − | 0.878606i | \(-0.658474\pi\) | ||||
−0.477548 | + | 0.878606i | \(0.658474\pi\) | |||||||
\(332\) | 3.50903e8 | 0.526264 | ||||||||
\(333\) | 1.44366e8 | 0.214245 | ||||||||
\(334\) | 3.53004e8 | 0.518402 | ||||||||
\(335\) | 2.53136e8 | 0.367872 | ||||||||
\(336\) | −4.05783e8 | −0.583589 | ||||||||
\(337\) | 5.99949e8 | 0.853905 | 0.426952 | − | 0.904274i | \(-0.359587\pi\) | ||||
0.426952 | + | 0.904274i | \(0.359587\pi\) | |||||||
\(338\) | −8.63386e7 | −0.121618 | ||||||||
\(339\) | −1.96634e8 | −0.274132 | ||||||||
\(340\) | −5.10715e8 | −0.704697 | ||||||||
\(341\) | 4.93134e7 | 0.0673480 | ||||||||
\(342\) | −3.64352e7 | −0.0492527 | ||||||||
\(343\) | −4.67259e8 | −0.625213 | ||||||||
\(344\) | −9.90674e7 | −0.131213 | ||||||||
\(345\) | 1.42776e8 | 0.187193 | ||||||||
\(346\) | 3.80673e8 | 0.494066 | ||||||||
\(347\) | 9.73412e8 | 1.25067 | 0.625336 | − | 0.780355i | \(-0.284962\pi\) | ||||
0.625336 | + | 0.780355i | \(0.284962\pi\) | |||||||
\(348\) | 2.08707e8 | 0.265467 | ||||||||
\(349\) | 4.28531e7 | 0.0539627 | 0.0269813 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269813 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(350\) | −8.46388e7 | −0.105519 | ||||||||
\(351\) | −1.25721e8 | −0.155179 | ||||||||
\(352\) | 5.25256e7 | 0.0641907 | ||||||||
\(353\) | 1.33381e9 | 1.61393 | 0.806963 | − | 0.590603i | \(-0.201110\pi\) | ||||
0.806963 | + | 0.590603i | \(0.201110\pi\) | |||||||
\(354\) | 2.18106e7 | 0.0261310 | ||||||||
\(355\) | 9.24018e7 | 0.109618 | ||||||||
\(356\) | 9.79697e8 | 1.15084 | ||||||||
\(357\) | 5.64027e8 | 0.656086 | ||||||||
\(358\) | −1.55458e8 | −0.179070 | ||||||||
\(359\) | 5.52883e8 | 0.630671 | 0.315336 | − | 0.948980i | \(-0.397883\pi\) | ||||
0.315336 | + | 0.948980i | \(0.397883\pi\) | |||||||
\(360\) | 2.10798e8 | 0.238127 | ||||||||
\(361\) | −7.32402e8 | −0.819359 | ||||||||
\(362\) | −2.99944e7 | −0.0332323 | ||||||||
\(363\) | −5.23354e8 | −0.574278 | ||||||||
\(364\) | −1.01118e9 | −1.09894 | ||||||||
\(365\) | 1.03002e9 | 1.10872 | ||||||||
\(366\) | 9.72071e7 | 0.103637 | ||||||||
\(367\) | −8.45526e8 | −0.892885 | −0.446443 | − | 0.894812i | \(-0.647309\pi\) | ||||
−0.446443 | + | 0.894812i | \(0.647309\pi\) | |||||||
\(368\) | −1.84822e8 | −0.193325 | ||||||||
\(369\) | 3.05482e8 | 0.316515 | ||||||||
\(370\) | −2.38072e8 | −0.244345 | ||||||||
\(371\) | −3.49471e8 | −0.355306 | ||||||||
\(372\) | −4.65279e8 | −0.468612 | ||||||||
\(373\) | −1.80814e9 | −1.80406 | −0.902031 | − | 0.431671i | \(-0.857924\pi\) | ||||
−0.902031 | + | 0.431671i | \(0.857924\pi\) | |||||||
\(374\) | −1.88070e7 | −0.0185896 | ||||||||
\(375\) | 5.18498e8 | 0.507735 | ||||||||
\(376\) | 6.98950e8 | 0.678092 | ||||||||
\(377\) | 4.38755e8 | 0.421723 | ||||||||
\(378\) | −1.08915e8 | −0.103721 | ||||||||
\(379\) | −1.25199e9 | −1.18131 | −0.590653 | − | 0.806925i | \(-0.701130\pi\) | ||||
−0.590653 | + | 0.806925i | \(0.701130\pi\) | |||||||
\(380\) | −4.37054e8 | −0.408595 | ||||||||
\(381\) | 8.41451e8 | 0.779455 | ||||||||
\(382\) | −2.76017e8 | −0.253346 | ||||||||
\(383\) | 2.12795e6 | 0.00193537 | 0.000967687 | − | 1.00000i | \(-0.499692\pi\) | ||||
0.000967687 | 1.00000i | \(0.499692\pi\) | ||||||||
\(384\) | −6.40800e8 | −0.577515 | ||||||||
\(385\) | 1.38469e8 | 0.123663 | ||||||||
\(386\) | −5.81677e8 | −0.514786 | ||||||||
\(387\) | 7.63381e7 | 0.0669503 | ||||||||
\(388\) | 2.03405e8 | 0.176787 | ||||||||
\(389\) | 2.97352e8 | 0.256122 | 0.128061 | − | 0.991766i | \(-0.459125\pi\) | ||||
0.128061 | + | 0.991766i | \(0.459125\pi\) | |||||||
\(390\) | 2.07324e8 | 0.176980 | ||||||||
\(391\) | 2.56898e8 | 0.217341 | ||||||||
\(392\) | −1.09333e9 | −0.916751 | ||||||||
\(393\) | −8.09615e8 | −0.672829 | ||||||||
\(394\) | −9.52865e7 | −0.0784865 | ||||||||
\(395\) | 1.86123e8 | 0.151953 | ||||||||
\(396\) | −2.64167e7 | −0.0213769 | ||||||||
\(397\) | 7.60962e8 | 0.610374 | 0.305187 | − | 0.952292i | \(-0.401281\pi\) | ||||
0.305187 | + | 0.952292i | \(0.401281\pi\) | |||||||
\(398\) | −4.71568e8 | −0.374933 | ||||||||
\(399\) | 4.82677e8 | 0.380409 | ||||||||
\(400\) | 1.63402e8 | 0.127658 | ||||||||
\(401\) | 4.16579e8 | 0.322620 | 0.161310 | − | 0.986904i | \(-0.448428\pi\) | ||||
0.161310 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(402\) | −8.79516e7 | −0.0675231 | ||||||||
\(403\) | −9.78134e8 | −0.744442 | ||||||||
\(404\) | −9.31330e8 | −0.702698 | ||||||||
\(405\) | −1.62434e8 | −0.121502 | ||||||||
\(406\) | 3.80103e8 | 0.281877 | ||||||||
\(407\) | 6.37707e7 | 0.0468858 | ||||||||
\(408\) | 3.79289e8 | 0.276477 | ||||||||
\(409\) | −2.40984e9 | −1.74163 | −0.870815 | − | 0.491611i | \(-0.836408\pi\) | ||||
−0.870815 | + | 0.491611i | \(0.836408\pi\) | |||||||
\(410\) | −5.03766e8 | −0.360982 | ||||||||
\(411\) | 4.48019e8 | 0.318310 | ||||||||
\(412\) | −2.07405e9 | −1.46110 | ||||||||
\(413\) | −2.88937e8 | −0.201826 | ||||||||
\(414\) | −4.96074e7 | −0.0343594 | ||||||||
\(415\) | 9.53107e8 | 0.654596 | ||||||||
\(416\) | −1.04185e9 | −0.709542 | ||||||||
\(417\) | −1.38761e9 | −0.937113 | ||||||||
\(418\) | −1.60945e7 | −0.0107785 | ||||||||
\(419\) | −2.79997e8 | −0.185953 | −0.0929767 | − | 0.995668i | \(-0.529638\pi\) | ||||
−0.0929767 | + | 0.995668i | \(0.529638\pi\) | |||||||
\(420\) | −1.30647e9 | −0.860454 | ||||||||
\(421\) | 1.28732e9 | 0.840810 | 0.420405 | − | 0.907337i | \(-0.361888\pi\) | ||||
0.420405 | + | 0.907337i | \(0.361888\pi\) | |||||||
\(422\) | −7.37736e8 | −0.477868 | ||||||||
\(423\) | −5.38588e8 | −0.345991 | ||||||||
\(424\) | −2.35008e8 | −0.149727 | ||||||||
\(425\) | −2.27124e8 | −0.143517 | ||||||||
\(426\) | −3.21049e7 | −0.0201204 | ||||||||
\(427\) | −1.28775e9 | −0.800452 | ||||||||
\(428\) | −7.44165e8 | −0.458792 | ||||||||
\(429\) | −5.55345e7 | −0.0339596 | ||||||||
\(430\) | −1.25888e8 | −0.0763562 | ||||||||
\(431\) | −1.52813e9 | −0.919367 | −0.459684 | − | 0.888083i | \(-0.652037\pi\) | ||||
−0.459684 | + | 0.888083i | \(0.652037\pi\) | |||||||
\(432\) | 2.10269e8 | 0.125482 | ||||||||
\(433\) | 3.05014e9 | 1.80556 | 0.902780 | − | 0.430103i | \(-0.141523\pi\) | ||||
0.902780 | + | 0.430103i | \(0.141523\pi\) | |||||||
\(434\) | −8.47378e8 | −0.497580 | ||||||||
\(435\) | 5.66881e8 | 0.330202 | ||||||||
\(436\) | −1.46571e9 | −0.846926 | ||||||||
\(437\) | 2.19845e8 | 0.126018 | ||||||||
\(438\) | −3.57878e8 | −0.203505 | ||||||||
\(439\) | 1.16263e9 | 0.655864 | 0.327932 | − | 0.944701i | \(-0.393648\pi\) | ||||
0.327932 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(440\) | 9.31155e7 | 0.0521120 | ||||||||
\(441\) | 8.42487e8 | 0.467766 | ||||||||
\(442\) | 3.73038e8 | 0.205483 | ||||||||
\(443\) | −1.39964e9 | −0.764900 | −0.382450 | − | 0.923976i | \(-0.624920\pi\) | ||||
−0.382450 | + | 0.923976i | \(0.624920\pi\) | |||||||
\(444\) | −6.01686e8 | −0.326234 | ||||||||
\(445\) | 2.66101e9 | 1.43148 | ||||||||
\(446\) | 2.20321e8 | 0.117594 | ||||||||
\(447\) | −6.89916e8 | −0.365359 | ||||||||
\(448\) | 1.02114e9 | 0.536552 | ||||||||
\(449\) | −9.56624e8 | −0.498746 | −0.249373 | − | 0.968408i | \(-0.580224\pi\) | ||||
−0.249373 | + | 0.968408i | \(0.580224\pi\) | |||||||
\(450\) | 4.38581e7 | 0.0226885 | ||||||||
\(451\) | 1.34940e8 | 0.0692665 | ||||||||
\(452\) | 8.19525e8 | 0.417424 | ||||||||
\(453\) | −6.77590e7 | −0.0342471 | ||||||||
\(454\) | 7.72500e8 | 0.387439 | ||||||||
\(455\) | −2.74653e9 | −1.36693 | ||||||||
\(456\) | 3.24584e8 | 0.160306 | ||||||||
\(457\) | 2.44936e9 | 1.20045 | 0.600227 | − | 0.799830i | \(-0.295077\pi\) | ||||
0.600227 | + | 0.799830i | \(0.295077\pi\) | |||||||
\(458\) | 1.72407e8 | 0.0838546 | ||||||||
\(459\) | −2.92267e8 | −0.141070 | ||||||||
\(460\) | −5.95060e8 | −0.285041 | ||||||||
\(461\) | 3.14456e9 | 1.49488 | 0.747441 | − | 0.664329i | \(-0.231282\pi\) | ||||
0.747441 | + | 0.664329i | \(0.231282\pi\) | |||||||
\(462\) | −4.81107e7 | −0.0226984 | ||||||||
\(463\) | 3.16804e9 | 1.48340 | 0.741699 | − | 0.670733i | \(-0.234020\pi\) | ||||
0.741699 | + | 0.670733i | \(0.234020\pi\) | |||||||
\(464\) | −7.33820e8 | −0.341017 | ||||||||
\(465\) | −1.26377e9 | −0.582885 | ||||||||
\(466\) | 6.19500e7 | 0.0283590 | ||||||||
\(467\) | −1.93980e9 | −0.881350 | −0.440675 | − | 0.897667i | \(-0.645261\pi\) | ||||
−0.440675 | + | 0.897667i | \(0.645261\pi\) | |||||||
\(468\) | 5.23976e8 | 0.236293 | ||||||||
\(469\) | 1.16514e9 | 0.521523 | ||||||||
\(470\) | 8.88176e8 | 0.394600 | ||||||||
\(471\) | −4.09548e8 | −0.180606 | ||||||||
\(472\) | −1.94300e8 | −0.0850504 | ||||||||
\(473\) | 3.37207e7 | 0.0146515 | ||||||||
\(474\) | −6.46680e7 | −0.0278911 | ||||||||
\(475\) | −1.94366e8 | −0.0832133 | ||||||||
\(476\) | −2.35073e9 | −0.999031 | ||||||||
\(477\) | 1.81089e8 | 0.0763973 | ||||||||
\(478\) | −4.01882e8 | −0.168307 | ||||||||
\(479\) | −1.57859e9 | −0.656287 | −0.328143 | − | 0.944628i | \(-0.606423\pi\) | ||||
−0.328143 | + | 0.944628i | \(0.606423\pi\) | |||||||
\(480\) | −1.34609e9 | −0.555558 | ||||||||
\(481\) | −1.26490e9 | −0.518259 | ||||||||
\(482\) | 6.19490e7 | 0.0251982 | ||||||||
\(483\) | 6.57176e8 | 0.265379 | ||||||||
\(484\) | 2.18122e9 | 0.874461 | ||||||||
\(485\) | 5.52478e8 | 0.219897 | ||||||||
\(486\) | 5.64374e7 | 0.0223018 | ||||||||
\(487\) | 1.69122e9 | 0.663512 | 0.331756 | − | 0.943365i | \(-0.392359\pi\) | ||||
0.331756 | + | 0.943365i | \(0.392359\pi\) | |||||||
\(488\) | −8.65971e8 | −0.337314 | ||||||||
\(489\) | 2.99564e8 | 0.115853 | ||||||||
\(490\) | −1.38933e9 | −0.533482 | ||||||||
\(491\) | 3.03523e9 | 1.15720 | 0.578598 | − | 0.815613i | \(-0.303600\pi\) | ||||
0.578598 | + | 0.815613i | \(0.303600\pi\) | |||||||
\(492\) | −1.27318e9 | −0.481961 | ||||||||
\(493\) | 1.01999e9 | 0.383381 | ||||||||
\(494\) | 3.19235e8 | 0.119142 | ||||||||
\(495\) | −7.17517e7 | −0.0265897 | ||||||||
\(496\) | 1.63593e9 | 0.601977 | ||||||||
\(497\) | 4.25310e8 | 0.155403 | ||||||||
\(498\) | −3.31155e8 | −0.120151 | ||||||||
\(499\) | −2.19815e9 | −0.791966 | −0.395983 | − | 0.918258i | \(-0.629596\pi\) | ||||
−0.395983 | + | 0.918258i | \(0.629596\pi\) | |||||||
\(500\) | −2.16098e9 | −0.773135 | ||||||||
\(501\) | 2.42323e9 | 0.860921 | ||||||||
\(502\) | 6.00936e8 | 0.212014 | ||||||||
\(503\) | −4.49246e9 | −1.57397 | −0.786984 | − | 0.616973i | \(-0.788359\pi\) | ||||
−0.786984 | + | 0.616973i | \(0.788359\pi\) | |||||||
\(504\) | 9.70267e8 | 0.337586 | ||||||||
\(505\) | −2.52964e9 | −0.874054 | ||||||||
\(506\) | −2.19130e7 | −0.00751926 | ||||||||
\(507\) | −5.92680e8 | −0.201973 | ||||||||
\(508\) | −3.50697e9 | −1.18689 | ||||||||
\(509\) | −4.25095e9 | −1.42881 | −0.714403 | − | 0.699734i | \(-0.753302\pi\) | ||||
−0.714403 | + | 0.699734i | \(0.753302\pi\) | |||||||
\(510\) | 4.81973e8 | 0.160889 | ||||||||
\(511\) | 4.74100e9 | 1.57180 | ||||||||
\(512\) | 3.03613e9 | 0.999713 | ||||||||
\(513\) | −2.50114e8 | −0.0817949 | ||||||||
\(514\) | 1.00308e9 | 0.325810 | ||||||||
\(515\) | −5.63345e9 | −1.81739 | ||||||||
\(516\) | −3.18159e8 | −0.101946 | ||||||||
\(517\) | −2.37910e8 | −0.0757173 | ||||||||
\(518\) | −1.09581e9 | −0.346401 | ||||||||
\(519\) | 2.61317e9 | 0.820505 | ||||||||
\(520\) | −1.84695e9 | −0.576028 | ||||||||
\(521\) | 6.47770e8 | 0.200673 | 0.100336 | − | 0.994954i | \(-0.468008\pi\) | ||||
0.100336 | + | 0.994954i | \(0.468008\pi\) | |||||||
\(522\) | −1.96962e8 | −0.0606087 | ||||||||
\(523\) | 2.31099e9 | 0.706386 | 0.353193 | − | 0.935551i | \(-0.385096\pi\) | ||||
0.353193 | + | 0.935551i | \(0.385096\pi\) | |||||||
\(524\) | 3.37429e9 | 1.02453 | ||||||||
\(525\) | −5.81012e8 | −0.175238 | ||||||||
\(526\) | 1.26503e9 | 0.379010 | ||||||||
\(527\) | −2.27390e9 | −0.676759 | ||||||||
\(528\) | 9.28817e7 | 0.0274607 | ||||||||
\(529\) | −3.10550e9 | −0.912088 | ||||||||
\(530\) | −2.98631e8 | −0.0871304 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | −2.01169e9 | −0.579255 | ||||||||
\(533\) | −2.67655e9 | −0.765648 | ||||||||
\(534\) | −9.24562e8 | −0.262749 | ||||||||
\(535\) | −2.02127e9 | −0.570671 | ||||||||
\(536\) | 7.83518e8 | 0.219772 | ||||||||
\(537\) | −1.06716e9 | −0.297385 | ||||||||
\(538\) | 9.15386e8 | 0.253435 | ||||||||
\(539\) | 3.72151e8 | 0.102367 | ||||||||
\(540\) | 6.76988e8 | 0.185013 | ||||||||
\(541\) | 2.47612e8 | 0.0672329 | 0.0336165 | − | 0.999435i | \(-0.489298\pi\) | ||||
0.0336165 | + | 0.999435i | \(0.489298\pi\) | |||||||
\(542\) | 4.62678e8 | 0.124819 | ||||||||
\(543\) | −2.05900e8 | −0.0551895 | ||||||||
\(544\) | −2.42202e9 | −0.645032 | ||||||||
\(545\) | −3.98110e9 | −1.05345 | ||||||||
\(546\) | 9.54278e8 | 0.250900 | ||||||||
\(547\) | −2.13776e9 | −0.558474 | −0.279237 | − | 0.960222i | \(-0.590082\pi\) | ||||
−0.279237 | + | 0.960222i | \(0.590082\pi\) | |||||||
\(548\) | −1.86724e9 | −0.484694 | ||||||||
\(549\) | 6.67289e8 | 0.172112 | ||||||||
\(550\) | 1.93734e7 | 0.00496519 | ||||||||
\(551\) | 8.72874e8 | 0.222291 | ||||||||
\(552\) | 4.41928e8 | 0.111832 | ||||||||
\(553\) | 8.56691e8 | 0.215420 | ||||||||
\(554\) | 9.80301e8 | 0.244949 | ||||||||
\(555\) | −1.63427e9 | −0.405788 | ||||||||
\(556\) | 5.78325e9 | 1.42695 | ||||||||
\(557\) | 6.39469e9 | 1.56793 | 0.783964 | − | 0.620806i | \(-0.213194\pi\) | ||||
0.783964 | + | 0.620806i | \(0.213194\pi\) | |||||||
\(558\) | 4.39095e8 | 0.106989 | ||||||||
\(559\) | −6.68852e8 | −0.161953 | ||||||||
\(560\) | 4.59359e9 | 1.10534 | ||||||||
\(561\) | −1.29103e8 | −0.0308721 | ||||||||
\(562\) | 1.59728e9 | 0.379580 | ||||||||
\(563\) | 7.78393e9 | 1.83831 | 0.919156 | − | 0.393893i | \(-0.128872\pi\) | ||||
0.919156 | + | 0.393893i | \(0.128872\pi\) | |||||||
\(564\) | 2.24471e9 | 0.526846 | ||||||||
\(565\) | 2.22596e9 | 0.519215 | ||||||||
\(566\) | −2.79395e9 | −0.647680 | ||||||||
\(567\) | −7.47656e8 | −0.172251 | ||||||||
\(568\) | 2.86006e8 | 0.0654872 | ||||||||
\(569\) | 1.45339e9 | 0.330742 | 0.165371 | − | 0.986231i | \(-0.447118\pi\) | ||||
0.165371 | + | 0.986231i | \(0.447118\pi\) | |||||||
\(570\) | 4.12458e8 | 0.0932863 | ||||||||
\(571\) | 6.80957e9 | 1.53071 | 0.765356 | − | 0.643608i | \(-0.222563\pi\) | ||||
0.765356 | + | 0.643608i | \(0.222563\pi\) | |||||||
\(572\) | 2.31455e8 | 0.0517107 | ||||||||
\(573\) | −1.89475e9 | −0.420736 | ||||||||
\(574\) | −2.31875e9 | −0.511755 | ||||||||
\(575\) | −2.64634e8 | −0.0580507 | ||||||||
\(576\) | −5.29134e8 | −0.115368 | ||||||||
\(577\) | −2.47806e9 | −0.537027 | −0.268513 | − | 0.963276i | \(-0.586532\pi\) | ||||
−0.268513 | + | 0.963276i | \(0.586532\pi\) | |||||||
\(578\) | −7.46738e8 | −0.160850 | ||||||||
\(579\) | −3.99298e9 | −0.854915 | ||||||||
\(580\) | −2.36263e9 | −0.502802 | ||||||||
\(581\) | 4.38699e9 | 0.928005 | ||||||||
\(582\) | −1.91958e8 | −0.0403622 | ||||||||
\(583\) | 7.99922e7 | 0.0167189 | ||||||||
\(584\) | 3.18816e9 | 0.662362 | ||||||||
\(585\) | 1.42320e9 | 0.293914 | ||||||||
\(586\) | 3.90471e8 | 0.0801580 | ||||||||
\(587\) | −1.40629e9 | −0.286974 | −0.143487 | − | 0.989652i | \(-0.545832\pi\) | ||||
−0.143487 | + | 0.989652i | \(0.545832\pi\) | |||||||
\(588\) | −3.51129e9 | −0.712273 | ||||||||
\(589\) | −1.94593e9 | −0.392396 | ||||||||
\(590\) | −2.46903e8 | −0.0494930 | ||||||||
\(591\) | −6.54104e8 | −0.130344 | ||||||||
\(592\) | 2.11554e9 | 0.419079 | ||||||||
\(593\) | 1.46308e8 | 0.0288123 | 0.0144062 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144062 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(594\) | 2.49300e7 | 0.00488056 | ||||||||
\(595\) | −6.38496e9 | −1.24265 | ||||||||
\(596\) | 2.87541e9 | 0.556337 | ||||||||
\(597\) | −3.23713e9 | −0.622658 | ||||||||
\(598\) | 4.34646e8 | 0.0831154 | ||||||||
\(599\) | −5.20381e9 | −0.989299 | −0.494649 | − | 0.869093i | \(-0.664703\pi\) | ||||
−0.494649 | + | 0.869093i | \(0.664703\pi\) | |||||||
\(600\) | −3.90710e8 | −0.0738458 | ||||||||
\(601\) | 3.88435e9 | 0.729891 | 0.364945 | − | 0.931029i | \(-0.381088\pi\) | ||||
0.364945 | + | 0.931029i | \(0.381088\pi\) | |||||||
\(602\) | −5.79440e8 | −0.108248 | ||||||||
\(603\) | −6.03753e8 | −0.112137 | ||||||||
\(604\) | 2.82404e8 | 0.0521484 | ||||||||
\(605\) | 5.92453e9 | 1.08770 | ||||||||
\(606\) | 8.78917e8 | 0.160433 | ||||||||
\(607\) | 9.88692e9 | 1.79432 | 0.897161 | − | 0.441703i | \(-0.145626\pi\) | ||||
0.897161 | + | 0.441703i | \(0.145626\pi\) | |||||||
\(608\) | −2.07269e9 | −0.374000 | ||||||||
\(609\) | 2.60925e9 | 0.468119 | ||||||||
\(610\) | −1.10041e9 | −0.196292 | ||||||||
\(611\) | 4.71895e9 | 0.836953 | ||||||||
\(612\) | 1.21810e9 | 0.214810 | ||||||||
\(613\) | 3.19394e9 | 0.560035 | 0.280018 | − | 0.959995i | \(-0.409660\pi\) | ||||
0.280018 | + | 0.959995i | \(0.409660\pi\) | |||||||
\(614\) | 3.71931e9 | 0.648445 | ||||||||
\(615\) | −3.45815e9 | −0.599489 | ||||||||
\(616\) | 4.28595e8 | 0.0738779 | ||||||||
\(617\) | −1.12180e10 | −1.92272 | −0.961360 | − | 0.275295i | \(-0.911225\pi\) | ||||
−0.961360 | + | 0.275295i | \(0.911225\pi\) | |||||||
\(618\) | 1.95733e9 | 0.333583 | ||||||||
\(619\) | 7.74489e9 | 1.31250 | 0.656248 | − | 0.754545i | \(-0.272142\pi\) | ||||
0.656248 | + | 0.754545i | \(0.272142\pi\) | |||||||
\(620\) | 5.26710e9 | 0.887566 | ||||||||
\(621\) | −3.40535e8 | −0.0570613 | ||||||||
\(622\) | 1.38409e9 | 0.230621 | ||||||||
\(623\) | 1.22482e10 | 2.02938 | ||||||||
\(624\) | −1.84231e9 | −0.303541 | ||||||||
\(625\) | −7.06454e9 | −1.15745 | ||||||||
\(626\) | 1.69321e9 | 0.275868 | ||||||||
\(627\) | −1.10482e8 | −0.0179001 | ||||||||
\(628\) | 1.70690e9 | 0.275011 | ||||||||
\(629\) | −2.94054e9 | −0.471140 | ||||||||
\(630\) | 1.23295e9 | 0.196450 | ||||||||
\(631\) | 6.77645e9 | 1.07374 | 0.536871 | − | 0.843665i | \(-0.319606\pi\) | ||||
0.536871 | + | 0.843665i | \(0.319606\pi\) | |||||||
\(632\) | 5.76096e8 | 0.0907789 | ||||||||
\(633\) | −5.06427e9 | −0.793604 | ||||||||
\(634\) | 3.57032e9 | 0.556410 | ||||||||
\(635\) | −9.52548e9 | −1.47631 | ||||||||
\(636\) | −7.54738e8 | −0.116331 | ||||||||
\(637\) | −7.38162e9 | −1.13152 | ||||||||
\(638\) | −8.70036e7 | −0.0132637 | ||||||||
\(639\) | −2.20387e8 | −0.0334144 | ||||||||
\(640\) | 7.25405e9 | 1.09383 | ||||||||
\(641\) | 8.18828e7 | 0.0122797 | 0.00613987 | − | 0.999981i | \(-0.498046\pi\) | ||||
0.00613987 | + | 0.999981i | \(0.498046\pi\) | |||||||
\(642\) | 7.02286e8 | 0.104747 | ||||||||
\(643\) | 2.87560e9 | 0.426570 | 0.213285 | − | 0.976990i | \(-0.431584\pi\) | ||||
0.213285 | + | 0.976990i | \(0.431584\pi\) | |||||||
\(644\) | −2.73896e9 | −0.404096 | ||||||||
\(645\) | −8.64170e8 | −0.126806 | ||||||||
\(646\) | 7.42136e8 | 0.108310 | ||||||||
\(647\) | −4.48392e9 | −0.650869 | −0.325434 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325434 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(648\) | −5.02773e8 | −0.0725871 | ||||||||
\(649\) | 6.61362e7 | 0.00949691 | ||||||||
\(650\) | −3.84272e8 | −0.0548835 | ||||||||
\(651\) | −5.81692e9 | −0.826341 | ||||||||
\(652\) | −1.24851e9 | −0.176411 | ||||||||
\(653\) | −5.52310e9 | −0.776224 | −0.388112 | − | 0.921612i | \(-0.626873\pi\) | ||||
−0.388112 | + | 0.921612i | \(0.626873\pi\) | |||||||
\(654\) | 1.38322e9 | 0.193362 | ||||||||
\(655\) | 9.16509e9 | 1.27436 | ||||||||
\(656\) | 4.47654e9 | 0.619125 | ||||||||
\(657\) | −2.45669e9 | −0.337965 | ||||||||
\(658\) | 4.08812e9 | 0.559414 | ||||||||
\(659\) | 5.93057e9 | 0.807230 | 0.403615 | − | 0.914929i | \(-0.367753\pi\) | ||||
0.403615 | + | 0.914929i | \(0.367753\pi\) | |||||||
\(660\) | 2.99045e8 | 0.0404886 | ||||||||
\(661\) | −1.03877e10 | −1.39898 | −0.699492 | − | 0.714641i | \(-0.746590\pi\) | ||||
−0.699492 | + | 0.714641i | \(0.746590\pi\) | |||||||
\(662\) | −2.47852e9 | −0.332040 | ||||||||
\(663\) | 2.56076e9 | 0.341249 | ||||||||
\(664\) | 2.95010e9 | 0.391065 | ||||||||
\(665\) | −5.46405e9 | −0.720508 | ||||||||
\(666\) | 5.67825e8 | 0.0744825 | ||||||||
\(667\) | 1.18844e9 | 0.155073 | ||||||||
\(668\) | −1.00995e10 | −1.31094 | ||||||||
\(669\) | 1.51242e9 | 0.195290 | ||||||||
\(670\) | 9.95639e8 | 0.127891 | ||||||||
\(671\) | 2.94760e8 | 0.0376652 | ||||||||
\(672\) | −6.19582e9 | −0.787601 | ||||||||
\(673\) | −1.00404e9 | −0.126969 | −0.0634843 | − | 0.997983i | \(-0.520221\pi\) | ||||
−0.0634843 | + | 0.997983i | \(0.520221\pi\) | |||||||
\(674\) | 2.35973e9 | 0.296861 | ||||||||
\(675\) | 3.01069e8 | 0.0376793 | ||||||||
\(676\) | 2.47015e9 | 0.307546 | ||||||||
\(677\) | 4.85982e9 | 0.601950 | 0.300975 | − | 0.953632i | \(-0.402688\pi\) | ||||
0.300975 | + | 0.953632i | \(0.402688\pi\) | |||||||
\(678\) | −7.73405e8 | −0.0953022 | ||||||||
\(679\) | 2.54296e9 | 0.311742 | ||||||||
\(680\) | −4.29366e9 | −0.523657 | ||||||||
\(681\) | 5.30291e9 | 0.643427 | ||||||||
\(682\) | 1.93961e8 | 0.0234136 | ||||||||
\(683\) | 1.18996e10 | 1.42909 | 0.714543 | − | 0.699592i | \(-0.246635\pi\) | ||||
0.714543 | + | 0.699592i | \(0.246635\pi\) | |||||||
\(684\) | 1.04242e9 | 0.124550 | ||||||||
\(685\) | −5.07171e9 | −0.602889 | ||||||||
\(686\) | −1.83783e9 | −0.217356 | ||||||||
\(687\) | 1.18351e9 | 0.139259 | ||||||||
\(688\) | 1.11866e9 | 0.130960 | ||||||||
\(689\) | −1.58665e9 | −0.184805 | ||||||||
\(690\) | 5.61571e8 | 0.0650778 | ||||||||
\(691\) | 3.67203e9 | 0.423383 | 0.211691 | − | 0.977337i | \(-0.432103\pi\) | ||||
0.211691 | + | 0.977337i | \(0.432103\pi\) | |||||||
\(692\) | −1.08911e10 | −1.24939 | ||||||||
\(693\) | −3.30261e8 | −0.0376956 | ||||||||
\(694\) | 3.82864e9 | 0.434797 | ||||||||
\(695\) | 1.57082e10 | 1.77492 | ||||||||
\(696\) | 1.75463e9 | 0.197267 | ||||||||
\(697\) | −6.22225e9 | −0.696038 | ||||||||
\(698\) | 1.68551e8 | 0.0187602 | ||||||||
\(699\) | 4.25262e8 | 0.0470963 | ||||||||
\(700\) | 2.42152e9 | 0.266837 | ||||||||
\(701\) | 1.31260e10 | 1.43919 | 0.719595 | − | 0.694394i | \(-0.244328\pi\) | ||||
0.719595 | + | 0.694394i | \(0.244328\pi\) | |||||||
\(702\) | −4.94488e8 | −0.0539481 | ||||||||
\(703\) | −2.51643e9 | −0.273175 | ||||||||
\(704\) | −2.33733e8 | −0.0252474 | ||||||||
\(705\) | 6.09698e9 | 0.655319 | ||||||||
\(706\) | 5.24618e9 | 0.561082 | ||||||||
\(707\) | −1.16435e10 | −1.23912 | ||||||||
\(708\) | −6.24004e8 | −0.0660801 | ||||||||
\(709\) | 1.38490e10 | 1.45934 | 0.729668 | − | 0.683801i | \(-0.239675\pi\) | ||||
0.729668 | + | 0.683801i | \(0.239675\pi\) | |||||||
\(710\) | 3.63437e8 | 0.0381087 | ||||||||
\(711\) | −4.43920e8 | −0.0463192 | ||||||||
\(712\) | 8.23647e9 | 0.855187 | ||||||||
\(713\) | −2.64944e9 | −0.273741 | ||||||||
\(714\) | 2.21844e9 | 0.228089 | ||||||||
\(715\) | 6.28668e8 | 0.0643206 | ||||||||
\(716\) | 4.44767e9 | 0.452832 | ||||||||
\(717\) | −2.75876e9 | −0.279510 | ||||||||
\(718\) | 2.17461e9 | 0.219253 | ||||||||
\(719\) | 5.91612e9 | 0.593589 | 0.296795 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296795 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(720\) | −2.38031e9 | −0.237667 | ||||||||
\(721\) | −2.59298e10 | −2.57647 | ||||||||
\(722\) | −2.88070e9 | −0.284851 | ||||||||
\(723\) | 4.25255e8 | 0.0418471 | ||||||||
\(724\) | 8.58143e8 | 0.0840378 | ||||||||
\(725\) | −1.05070e9 | −0.102399 | ||||||||
\(726\) | −2.05847e9 | −0.199648 | ||||||||
\(727\) | −5.62356e8 | −0.0542801 | −0.0271401 | − | 0.999632i | \(-0.508640\pi\) | ||||
−0.0271401 | + | 0.999632i | \(0.508640\pi\) | |||||||
\(728\) | −8.50120e9 | −0.816621 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 4.05129e9 | 0.385446 | ||||||||
\(731\) | −1.55490e9 | −0.147229 | ||||||||
\(732\) | −2.78111e9 | −0.262077 | ||||||||
\(733\) | −4.63518e9 | −0.434713 | −0.217356 | − | 0.976092i | \(-0.569743\pi\) | ||||
−0.217356 | + | 0.976092i | \(0.569743\pi\) | |||||||
\(734\) | −3.32564e9 | −0.310412 | ||||||||
\(735\) | −9.53721e9 | −0.885963 | ||||||||
\(736\) | −2.82201e9 | −0.260908 | ||||||||
\(737\) | −2.66695e8 | −0.0245402 | ||||||||
\(738\) | 1.20153e9 | 0.110037 | ||||||||
\(739\) | 8.68070e9 | 0.791224 | 0.395612 | − | 0.918418i | \(-0.370533\pi\) | ||||
0.395612 | + | 0.918418i | \(0.370533\pi\) | |||||||
\(740\) | 6.81127e9 | 0.617898 | ||||||||
\(741\) | 2.19142e9 | 0.197862 | ||||||||
\(742\) | −1.37455e9 | −0.123523 | ||||||||
\(743\) | −7.23578e9 | −0.647179 | −0.323589 | − | 0.946198i | \(-0.604890\pi\) | ||||
−0.323589 | + | 0.946198i | \(0.604890\pi\) | |||||||
\(744\) | −3.91168e9 | −0.348223 | ||||||||
\(745\) | 7.81006e9 | 0.692002 | ||||||||
\(746\) | −7.11182e9 | −0.627184 | ||||||||
\(747\) | −2.27325e9 | −0.199538 | ||||||||
\(748\) | 5.38071e8 | 0.0470093 | ||||||||
\(749\) | −9.30355e9 | −0.809026 | ||||||||
\(750\) | 2.03937e9 | 0.176515 | ||||||||
\(751\) | −1.53619e10 | −1.32344 | −0.661722 | − | 0.749750i | \(-0.730174\pi\) | ||||
−0.661722 | + | 0.749750i | \(0.730174\pi\) | |||||||
\(752\) | −7.89246e9 | −0.676784 | ||||||||
\(753\) | 4.12519e9 | 0.352096 | ||||||||
\(754\) | 1.72572e9 | 0.146612 | ||||||||
\(755\) | 7.67053e8 | 0.0648651 | ||||||||
\(756\) | 3.11606e9 | 0.262289 | ||||||||
\(757\) | −1.36460e10 | −1.14332 | −0.571661 | − | 0.820490i | \(-0.693701\pi\) | ||||
−0.571661 | + | 0.820490i | \(0.693701\pi\) | |||||||
\(758\) | −4.92434e9 | −0.410682 | ||||||||
\(759\) | −1.50424e8 | −0.0124874 | ||||||||
\(760\) | −3.67439e9 | −0.303625 | ||||||||
\(761\) | 1.05663e10 | 0.869112 | 0.434556 | − | 0.900645i | \(-0.356905\pi\) | ||||
0.434556 | + | 0.900645i | \(0.356905\pi\) | |||||||
\(762\) | 3.30961e9 | 0.270978 | ||||||||
\(763\) | −1.83243e10 | −1.49345 | ||||||||
\(764\) | 7.89686e9 | 0.640660 | ||||||||
\(765\) | 3.30856e9 | 0.267192 | ||||||||
\(766\) | 8.36968e6 | 0.000672834 0 | ||||||||
\(767\) | −1.31181e9 | −0.104976 | ||||||||
\(768\) | −1.19201e7 | −0.000949548 0 | ||||||||
\(769\) | −1.72180e10 | −1.36534 | −0.682668 | − | 0.730729i | \(-0.739180\pi\) | ||||
−0.682668 | + | 0.730729i | \(0.739180\pi\) | |||||||
\(770\) | 5.44628e8 | 0.0429915 | ||||||||
\(771\) | 6.88575e9 | 0.541079 | ||||||||
\(772\) | 1.66418e10 | 1.30179 | ||||||||
\(773\) | 1.20767e10 | 0.940419 | 0.470209 | − | 0.882555i | \(-0.344178\pi\) | ||||
0.470209 | + | 0.882555i | \(0.344178\pi\) | |||||||
\(774\) | 3.00254e8 | 0.0232753 | ||||||||
\(775\) | 2.34238e9 | 0.180759 | ||||||||
\(776\) | 1.71006e9 | 0.131369 | ||||||||
\(777\) | −7.52227e9 | −0.575275 | ||||||||
\(778\) | 1.16955e9 | 0.0890410 | ||||||||
\(779\) | −5.32481e9 | −0.403574 | ||||||||
\(780\) | −5.93157e9 | −0.447547 | ||||||||
\(781\) | −9.73513e7 | −0.00731245 | ||||||||
\(782\) | 1.01043e9 | 0.0755587 | ||||||||
\(783\) | −1.35206e9 | −0.100654 | ||||||||
\(784\) | 1.23458e10 | 0.914983 | ||||||||
\(785\) | 4.63621e9 | 0.342074 | ||||||||
\(786\) | −3.18439e9 | −0.233909 | ||||||||
\(787\) | 5.72468e9 | 0.418639 | 0.209319 | − | 0.977847i | \(-0.432875\pi\) | ||||
0.209319 | + | 0.977847i | \(0.432875\pi\) | |||||||
\(788\) | 2.72616e9 | 0.198476 | ||||||||
\(789\) | 8.68392e9 | 0.629428 | ||||||||
\(790\) | 7.32062e8 | 0.0528266 | ||||||||
\(791\) | 1.02457e10 | 0.736078 | ||||||||
\(792\) | −2.22089e8 | −0.0158851 | ||||||||
\(793\) | −5.84659e9 | −0.416338 | ||||||||
\(794\) | 2.99303e9 | 0.212197 | ||||||||
\(795\) | −2.04998e9 | −0.144699 | ||||||||
\(796\) | 1.34916e10 | 0.948129 | ||||||||
\(797\) | −1.13444e10 | −0.793740 | −0.396870 | − | 0.917875i | \(-0.629904\pi\) | ||||
−0.396870 | + | 0.917875i | \(0.629904\pi\) | |||||||
\(798\) | 1.89847e9 | 0.132250 | ||||||||
\(799\) | 1.09703e10 | 0.760859 | ||||||||
\(800\) | 2.49495e9 | 0.172285 | ||||||||
\(801\) | −6.34675e9 | −0.436353 | ||||||||
\(802\) | 1.63850e9 | 0.112159 | ||||||||
\(803\) | −1.08519e9 | −0.0739608 | ||||||||
\(804\) | 2.51630e9 | 0.170752 | ||||||||
\(805\) | −7.43943e9 | −0.502637 | ||||||||
\(806\) | −3.84722e9 | −0.258806 | ||||||||
\(807\) | 6.28376e9 | 0.420884 | ||||||||
\(808\) | −7.82984e9 | −0.522172 | ||||||||
\(809\) | 2.36003e10 | 1.56711 | 0.783553 | − | 0.621325i | \(-0.213405\pi\) | ||||
0.783553 | + | 0.621325i | \(0.213405\pi\) | |||||||
\(810\) | −6.38889e8 | −0.0422404 | ||||||||
\(811\) | −5.41251e9 | −0.356308 | −0.178154 | − | 0.984003i | \(-0.557013\pi\) | ||||
−0.178154 | + | 0.984003i | \(0.557013\pi\) | |||||||
\(812\) | −1.08748e10 | −0.712810 | ||||||||
\(813\) | 3.17610e9 | 0.207290 | ||||||||
\(814\) | 2.50824e8 | 0.0162999 | ||||||||
\(815\) | −3.39115e9 | −0.219430 | ||||||||
\(816\) | −4.28289e9 | −0.275944 | ||||||||
\(817\) | −1.33064e9 | −0.0853655 | ||||||||
\(818\) | −9.47841e9 | −0.605479 | ||||||||
\(819\) | 6.55074e9 | 0.416674 | ||||||||
\(820\) | 1.44128e10 | 0.912850 | ||||||||
\(821\) | 1.82304e9 | 0.114973 | 0.0574863 | − | 0.998346i | \(-0.481691\pi\) | ||||
0.0574863 | + | 0.998346i | \(0.481691\pi\) | |||||||
\(822\) | 1.76216e9 | 0.110661 | ||||||||
\(823\) | −1.51277e10 | −0.945960 | −0.472980 | − | 0.881073i | \(-0.656822\pi\) | ||||
−0.472980 | + | 0.881073i | \(0.656822\pi\) | |||||||
\(824\) | −1.74369e10 | −1.08574 | ||||||||
\(825\) | 1.32991e8 | 0.00824579 | ||||||||
\(826\) | −1.13645e9 | −0.0701651 | ||||||||
\(827\) | −2.65641e10 | −1.63315 | −0.816573 | − | 0.577242i | \(-0.804129\pi\) | ||||
−0.816573 | + | 0.577242i | \(0.804129\pi\) | |||||||
\(828\) | 1.41927e9 | 0.0868880 | ||||||||
\(829\) | −2.30465e10 | −1.40496 | −0.702479 | − | 0.711704i | \(-0.747924\pi\) | ||||
−0.702479 | + | 0.711704i | \(0.747924\pi\) | |||||||
\(830\) | 3.74878e9 | 0.227571 | ||||||||
\(831\) | 6.72938e9 | 0.406791 | ||||||||
\(832\) | 4.63611e9 | 0.279076 | ||||||||
\(833\) | −1.71603e10 | −1.02865 | ||||||||
\(834\) | −5.45778e9 | −0.325788 | ||||||||
\(835\) | −2.74317e10 | −1.63061 | ||||||||
\(836\) | 4.60465e8 | 0.0272568 | ||||||||
\(837\) | 3.01421e9 | 0.177678 | ||||||||
\(838\) | −1.10129e9 | −0.0646469 | ||||||||
\(839\) | −2.55035e10 | −1.49084 | −0.745422 | − | 0.666592i | \(-0.767752\pi\) | ||||
−0.745422 | + | 0.666592i | \(0.767752\pi\) | |||||||
\(840\) | −1.09837e10 | −0.639399 | ||||||||
\(841\) | −1.25313e10 | −0.726457 | ||||||||
\(842\) | 5.06330e9 | 0.292308 | ||||||||
\(843\) | 1.09647e10 | 0.630375 | ||||||||
\(844\) | 2.11067e10 | 1.20843 | ||||||||
\(845\) | 6.70932e9 | 0.382543 | ||||||||
\(846\) | −2.11838e9 | −0.120284 | ||||||||
\(847\) | 2.72696e10 | 1.54201 | ||||||||
\(848\) | 2.65368e9 | 0.149439 | ||||||||
\(849\) | −1.91793e10 | −1.07561 | ||||||||
\(850\) | −8.93329e8 | −0.0498937 | ||||||||
\(851\) | −3.42617e9 | −0.190571 | ||||||||
\(852\) | 9.18523e8 | 0.0508805 | ||||||||
\(853\) | −2.38277e10 | −1.31450 | −0.657250 | − | 0.753673i | \(-0.728280\pi\) | ||||
−0.657250 | + | 0.753673i | \(0.728280\pi\) | |||||||
\(854\) | −5.06502e9 | −0.278278 | ||||||||
\(855\) | 2.83136e9 | 0.154922 | ||||||||
\(856\) | −6.25632e9 | −0.340927 | ||||||||
\(857\) | 3.88776e9 | 0.210992 | 0.105496 | − | 0.994420i | \(-0.466357\pi\) | ||||
0.105496 | + | 0.994420i | \(0.466357\pi\) | |||||||
\(858\) | −2.18429e8 | −0.0118061 | ||||||||
\(859\) | 1.22415e10 | 0.658961 | 0.329480 | − | 0.944162i | \(-0.393126\pi\) | ||||
0.329480 | + | 0.944162i | \(0.393126\pi\) | |||||||
\(860\) | 3.60166e9 | 0.193089 | ||||||||
\(861\) | −1.59173e10 | −0.849881 | ||||||||
\(862\) | −6.01046e9 | −0.319619 | ||||||||
\(863\) | 1.45480e10 | 0.770489 | 0.385244 | − | 0.922815i | \(-0.374117\pi\) | ||||
0.385244 | + | 0.922815i | \(0.374117\pi\) | |||||||
\(864\) | 3.21055e9 | 0.169349 | ||||||||
\(865\) | −2.95818e10 | −1.55406 | ||||||||
\(866\) | 1.19969e10 | 0.627704 | ||||||||
\(867\) | −5.12606e9 | −0.267126 | ||||||||
\(868\) | 2.42436e10 | 1.25828 | ||||||||
\(869\) | −1.96092e8 | −0.0101366 | ||||||||
\(870\) | 2.22967e9 | 0.114795 | ||||||||
\(871\) | 5.28991e9 | 0.271259 | ||||||||
\(872\) | −1.23225e10 | −0.629347 | ||||||||
\(873\) | −1.31771e9 | −0.0670303 | ||||||||
\(874\) | 8.64699e8 | 0.0438102 | ||||||||
\(875\) | −2.70165e10 | −1.36333 | ||||||||
\(876\) | 1.02389e10 | 0.514624 | ||||||||
\(877\) | −1.79027e10 | −0.896231 | −0.448115 | − | 0.893976i | \(-0.647905\pi\) | ||||
−0.448115 | + | 0.893976i | \(0.647905\pi\) | |||||||
\(878\) | 4.57286e9 | 0.228012 | ||||||||
\(879\) | 2.68043e9 | 0.133120 | ||||||||
\(880\) | −1.05145e9 | −0.0520115 | ||||||||
\(881\) | −8.23369e9 | −0.405675 | −0.202838 | − | 0.979212i | \(-0.565016\pi\) | ||||
−0.202838 | + | 0.979212i | \(0.565016\pi\) | |||||||
\(882\) | 3.31369e9 | 0.162619 | ||||||||
\(883\) | −1.02587e10 | −0.501452 | −0.250726 | − | 0.968058i | \(-0.580669\pi\) | ||||
−0.250726 | + | 0.968058i | \(0.580669\pi\) | |||||||
\(884\) | −1.06727e10 | −0.519625 | ||||||||
\(885\) | −1.69489e9 | −0.0821940 | ||||||||
\(886\) | −5.50511e9 | −0.265918 | ||||||||
\(887\) | 8.18874e9 | 0.393989 | 0.196995 | − | 0.980405i | \(-0.436882\pi\) | ||||
0.196995 | + | 0.980405i | \(0.436882\pi\) | |||||||
\(888\) | −5.05847e9 | −0.242423 | ||||||||
\(889\) | −4.38442e10 | −2.09293 | ||||||||
\(890\) | 1.04663e10 | 0.497656 | ||||||||
\(891\) | 1.71135e8 | 0.00810524 | ||||||||
\(892\) | −6.30341e9 | −0.297371 | ||||||||
\(893\) | 9.38804e9 | 0.441159 | ||||||||
\(894\) | −2.71359e9 | −0.127017 | ||||||||
\(895\) | 1.20806e10 | 0.563257 | ||||||||
\(896\) | 3.33891e10 | 1.55070 | ||||||||
\(897\) | 2.98367e9 | 0.138031 | ||||||||
\(898\) | −3.76261e9 | −0.173389 | ||||||||
\(899\) | −1.05193e10 | −0.482869 | ||||||||
\(900\) | −1.25478e9 | −0.0573747 | ||||||||
\(901\) | −3.68854e9 | −0.168003 | ||||||||
\(902\) | 5.30749e8 | 0.0240806 | ||||||||
\(903\) | −3.97763e9 | −0.179770 | ||||||||
\(904\) | 6.88988e9 | 0.310186 | ||||||||
\(905\) | 2.33085e9 | 0.104531 | ||||||||
\(906\) | −2.66511e8 | −0.0119060 | ||||||||
\(907\) | −1.90356e10 | −0.847110 | −0.423555 | − | 0.905870i | \(-0.639218\pi\) | ||||
−0.423555 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(908\) | −2.21013e10 | −0.979755 | ||||||||
\(909\) | 6.03342e9 | 0.266434 | ||||||||
\(910\) | −1.08027e10 | −0.475213 | ||||||||
\(911\) | 1.11471e10 | 0.488483 | 0.244241 | − | 0.969714i | \(-0.421461\pi\) | ||||
0.244241 | + | 0.969714i | \(0.421461\pi\) | |||||||
\(912\) | −3.66516e9 | −0.159997 | ||||||||
\(913\) | −1.00416e9 | −0.0436672 | ||||||||
\(914\) | 9.63386e9 | 0.417339 | ||||||||
\(915\) | −7.55391e9 | −0.325985 | ||||||||
\(916\) | −4.93259e9 | −0.212051 | ||||||||
\(917\) | 4.21853e10 | 1.80663 | ||||||||
\(918\) | −1.14955e9 | −0.0490432 | ||||||||
\(919\) | 9.09748e9 | 0.386649 | 0.193324 | − | 0.981135i | \(-0.438073\pi\) | ||||
0.193324 | + | 0.981135i | \(0.438073\pi\) | |||||||
\(920\) | −5.00276e9 | −0.211813 | ||||||||
\(921\) | 2.55316e10 | 1.07689 | ||||||||
\(922\) | 1.23682e10 | 0.519697 | ||||||||
\(923\) | 1.93097e9 | 0.0808293 | ||||||||
\(924\) | 1.37645e9 | 0.0573996 | ||||||||
\(925\) | 3.02909e9 | 0.125839 | ||||||||
\(926\) | 1.24606e10 | 0.515705 | ||||||||
\(927\) | 1.34363e10 | 0.553988 | ||||||||
\(928\) | −1.12045e10 | −0.460231 | ||||||||
\(929\) | −2.50717e10 | −1.02596 | −0.512978 | − | 0.858402i | \(-0.671458\pi\) | ||||
−0.512978 | + | 0.858402i | \(0.671458\pi\) | |||||||
\(930\) | −4.97069e9 | −0.202640 | ||||||||
\(931\) | −1.46853e10 | −0.596428 | ||||||||
\(932\) | −1.77240e9 | −0.0717142 | ||||||||
\(933\) | 9.50126e9 | 0.382997 | ||||||||
\(934\) | −7.62967e9 | −0.306402 | ||||||||
\(935\) | 1.46148e9 | 0.0584727 | ||||||||
\(936\) | 4.40515e9 | 0.175588 | ||||||||
\(937\) | 4.32100e9 | 0.171591 | 0.0857957 | − | 0.996313i | \(-0.472657\pi\) | ||||
0.0857957 | + | 0.996313i | \(0.472657\pi\) | |||||||
\(938\) | 4.58276e9 | 0.181308 | ||||||||
\(939\) | 1.16232e10 | 0.458140 | ||||||||
\(940\) | −2.54108e10 | −0.997863 | ||||||||
\(941\) | 1.72767e10 | 0.675922 | 0.337961 | − | 0.941160i | \(-0.390263\pi\) | ||||
0.337961 | + | 0.941160i | \(0.390263\pi\) | |||||||
\(942\) | −1.61084e9 | −0.0627878 | ||||||||
\(943\) | −7.24986e9 | −0.281539 | ||||||||
\(944\) | 2.19402e9 | 0.0848863 | ||||||||
\(945\) | 8.46370e9 | 0.326249 | ||||||||
\(946\) | 1.32631e8 | 0.00509361 | ||||||||
\(947\) | −2.35290e10 | −0.900284 | −0.450142 | − | 0.892957i | \(-0.648627\pi\) | ||||
−0.450142 | + | 0.892957i | \(0.648627\pi\) | |||||||
\(948\) | 1.85016e9 | 0.0705309 | ||||||||
\(949\) | 2.15248e10 | 0.817537 | ||||||||
\(950\) | −7.64484e8 | −0.0289292 | ||||||||
\(951\) | 2.45089e10 | 0.924041 | ||||||||
\(952\) | −1.97630e10 | −0.742376 | ||||||||
\(953\) | 9.37890e9 | 0.351016 | 0.175508 | − | 0.984478i | \(-0.443843\pi\) | ||||
0.175508 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(954\) | 7.12263e8 | 0.0265596 | ||||||||
\(955\) | 2.14491e10 | 0.796888 | ||||||||
\(956\) | 1.14979e10 | 0.425614 | ||||||||
\(957\) | −5.97245e8 | −0.0220273 | ||||||||
\(958\) | −6.20892e9 | −0.228159 | ||||||||
\(959\) | −2.33442e10 | −0.854701 | ||||||||
\(960\) | 5.98996e9 | 0.218511 | ||||||||
\(961\) | −4.06144e9 | −0.147621 | ||||||||
\(962\) | −4.97511e9 | −0.180173 | ||||||||
\(963\) | 4.82091e9 | 0.173955 | ||||||||
\(964\) | −1.77237e9 | −0.0637212 | ||||||||
\(965\) | 4.52018e10 | 1.61924 | ||||||||
\(966\) | 2.58482e9 | 0.0922592 | ||||||||
\(967\) | 4.13184e10 | 1.46944 | 0.734718 | − | 0.678373i | \(-0.237315\pi\) | ||||
0.734718 | + | 0.678373i | \(0.237315\pi\) | |||||||
\(968\) | 1.83379e10 | 0.649808 | ||||||||
\(969\) | 5.09447e9 | 0.179873 | ||||||||
\(970\) | 2.17302e9 | 0.0764473 | ||||||||
\(971\) | 6.75904e9 | 0.236929 | 0.118464 | − | 0.992958i | \(-0.462203\pi\) | ||||
0.118464 | + | 0.992958i | \(0.462203\pi\) | |||||||
\(972\) | −1.61468e9 | −0.0563968 | ||||||||
\(973\) | 7.23021e10 | 2.51626 | ||||||||
\(974\) | 6.65194e9 | 0.230671 | ||||||||
\(975\) | −2.63788e9 | −0.0911461 | ||||||||
\(976\) | 9.77845e9 | 0.336663 | ||||||||
\(977\) | 2.83700e10 | 0.973258 | 0.486629 | − | 0.873609i | \(-0.338226\pi\) | ||||
0.486629 | + | 0.873609i | \(0.338226\pi\) | |||||||
\(978\) | 1.17825e9 | 0.0402765 | ||||||||
\(979\) | −2.80354e9 | −0.0954922 | ||||||||
\(980\) | 3.97489e10 | 1.34907 | ||||||||
\(981\) | 9.49529e9 | 0.321120 | ||||||||
\(982\) | 1.19382e10 | 0.402300 | ||||||||
\(983\) | 5.77572e10 | 1.93940 | 0.969702 | − | 0.244289i | \(-0.0785546\pi\) | ||||
0.969702 | + | 0.244289i | \(0.0785546\pi\) | |||||||
\(984\) | −1.07038e10 | −0.358143 | ||||||||
\(985\) | 7.40466e9 | 0.246876 | ||||||||
\(986\) | 4.01184e9 | 0.133283 | ||||||||
\(987\) | 2.80634e10 | 0.929030 | ||||||||
\(988\) | −9.13334e9 | −0.301287 | ||||||||
\(989\) | −1.81169e9 | −0.0595522 | ||||||||
\(990\) | −2.82215e8 | −0.00924395 | ||||||||
\(991\) | −2.44660e10 | −0.798554 | −0.399277 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399277 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(992\) | 2.49787e10 | 0.812418 | ||||||||
\(993\) | −1.70141e10 | −0.551425 | ||||||||
\(994\) | 1.67284e9 | 0.0540258 | ||||||||
\(995\) | 3.66453e10 | 1.17933 | ||||||||
\(996\) | 9.47439e9 | 0.303839 | ||||||||
\(997\) | −3.98637e10 | −1.27393 | −0.636964 | − | 0.770894i | \(-0.719810\pi\) | ||||
−0.636964 | + | 0.770894i | \(0.719810\pi\) | |||||||
\(998\) | −8.64583e9 | −0.275327 | ||||||||
\(999\) | 3.89789e9 | 0.123695 |
(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 | 177.8.a.d.1.10 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.10 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.9 | 18 | 3.2 | odd | 2 |