Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,6,Mod(1,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.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: | \(57.8985589525\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 19) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.1521 | 1.79465 | 0.897324 | − | 0.441372i | \(-0.145508\pi\) | ||||
0.897324 | + | 0.441372i | \(0.145508\pi\) | |||||||
\(3\) | −16.4562 | −1.05567 | −0.527833 | − | 0.849348i | \(-0.676995\pi\) | ||||
−0.527833 | + | 0.849348i | \(0.676995\pi\) | |||||||
\(4\) | 71.0645 | 2.22076 | ||||||||
\(5\) | −99.7603 | −1.78457 | −0.892284 | − | 0.451475i | \(-0.850898\pi\) | ||||
−0.892284 | + | 0.451475i | \(0.850898\pi\) | |||||||
\(6\) | −167.064 | −1.89455 | ||||||||
\(7\) | −57.1289 | −0.440668 | −0.220334 | − | 0.975425i | \(-0.570715\pi\) | ||||
−0.220334 | + | 0.975425i | \(0.570715\pi\) | |||||||
\(8\) | 396.585 | 2.19084 | ||||||||
\(9\) | 27.8066 | 0.114430 | ||||||||
\(10\) | −1012.77 | −3.20267 | ||||||||
\(11\) | −438.977 | −1.09386 | −0.546928 | − | 0.837180i | \(-0.684203\pi\) | ||||
−0.546928 | + | 0.837180i | \(0.684203\pi\) | |||||||
\(12\) | −1169.45 | −2.34439 | ||||||||
\(13\) | 477.590 | 0.783785 | 0.391892 | − | 0.920011i | \(-0.371821\pi\) | ||||
0.391892 | + | 0.920011i | \(0.371821\pi\) | |||||||
\(14\) | −579.977 | −0.790844 | ||||||||
\(15\) | 1641.68 | 1.88391 | ||||||||
\(16\) | 1752.10 | 1.71103 | ||||||||
\(17\) | 1671.39 | 1.40267 | 0.701334 | − | 0.712833i | \(-0.252588\pi\) | ||||
0.701334 | + | 0.712833i | \(0.252588\pi\) | |||||||
\(18\) | 282.294 | 0.205362 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −7089.42 | −3.96310 | ||||||||
\(21\) | 940.125 | 0.465198 | ||||||||
\(22\) | −4456.52 | −1.96309 | ||||||||
\(23\) | 459.514 | 0.181125 | 0.0905627 | − | 0.995891i | \(-0.471133\pi\) | ||||
0.0905627 | + | 0.995891i | \(0.471133\pi\) | |||||||
\(24\) | −6526.29 | −2.31280 | ||||||||
\(25\) | 6827.12 | 2.18468 | ||||||||
\(26\) | 4848.53 | 1.40662 | ||||||||
\(27\) | 3541.27 | 0.934866 | ||||||||
\(28\) | −4059.84 | −0.978619 | ||||||||
\(29\) | 2696.78 | 0.595457 | 0.297729 | − | 0.954651i | \(-0.403771\pi\) | ||||
0.297729 | + | 0.954651i | \(0.403771\pi\) | |||||||
\(30\) | 16666.4 | 3.38095 | ||||||||
\(31\) | 2314.43 | 0.432553 | 0.216277 | − | 0.976332i | \(-0.430609\pi\) | ||||
0.216277 | + | 0.976332i | \(0.430609\pi\) | |||||||
\(32\) | 5096.67 | 0.879856 | ||||||||
\(33\) | 7223.89 | 1.15475 | ||||||||
\(34\) | 16968.0 | 2.51730 | ||||||||
\(35\) | 5699.20 | 0.786401 | ||||||||
\(36\) | 1976.06 | 0.254123 | ||||||||
\(37\) | −3022.51 | −0.362964 | −0.181482 | − | 0.983394i | \(-0.558089\pi\) | ||||
−0.181482 | + | 0.983394i | \(0.558089\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7859.32 | −0.827415 | ||||||||
\(40\) | −39563.5 | −3.90971 | ||||||||
\(41\) | −5483.05 | −0.509404 | −0.254702 | − | 0.967020i | \(-0.581977\pi\) | ||||
−0.254702 | + | 0.967020i | \(0.581977\pi\) | |||||||
\(42\) | 9544.22 | 0.834867 | ||||||||
\(43\) | 5101.80 | 0.420777 | 0.210388 | − | 0.977618i | \(-0.432527\pi\) | ||||
0.210388 | + | 0.977618i | \(0.432527\pi\) | |||||||
\(44\) | −31195.7 | −2.42920 | ||||||||
\(45\) | −2773.99 | −0.204209 | ||||||||
\(46\) | 4665.02 | 0.325057 | ||||||||
\(47\) | 5803.63 | 0.383226 | 0.191613 | − | 0.981471i | \(-0.438628\pi\) | ||||
0.191613 | + | 0.981471i | \(0.438628\pi\) | |||||||
\(48\) | −28832.8 | −1.80628 | ||||||||
\(49\) | −13543.3 | −0.805812 | ||||||||
\(50\) | 69309.4 | 3.92073 | ||||||||
\(51\) | −27504.7 | −1.48075 | ||||||||
\(52\) | 33939.7 | 1.74060 | ||||||||
\(53\) | 23207.5 | 1.13485 | 0.567426 | − | 0.823424i | \(-0.307939\pi\) | ||||
0.567426 | + | 0.823424i | \(0.307939\pi\) | |||||||
\(54\) | 35951.2 | 1.67776 | ||||||||
\(55\) | 43792.5 | 1.95206 | ||||||||
\(56\) | −22656.5 | −0.965434 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 27377.9 | 1.06864 | ||||||||
\(59\) | 32849.5 | 1.22857 | 0.614284 | − | 0.789085i | \(-0.289445\pi\) | ||||
0.614284 | + | 0.789085i | \(0.289445\pi\) | |||||||
\(60\) | 116665. | 4.18371 | ||||||||
\(61\) | −46911.5 | −1.61419 | −0.807095 | − | 0.590422i | \(-0.798961\pi\) | ||||
−0.807095 | + | 0.590422i | \(0.798961\pi\) | |||||||
\(62\) | 23496.2 | 0.776281 | ||||||||
\(63\) | −1588.56 | −0.0504258 | ||||||||
\(64\) | −4325.31 | −0.131998 | ||||||||
\(65\) | −47644.5 | −1.39872 | ||||||||
\(66\) | 73337.4 | 2.07236 | ||||||||
\(67\) | 3565.12 | 0.0970257 | 0.0485128 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485128 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(68\) | 118776. | 3.11499 | ||||||||
\(69\) | −7561.86 | −0.191208 | ||||||||
\(70\) | 57858.7 | 1.41131 | ||||||||
\(71\) | −2346.44 | −0.0552413 | −0.0276207 | − | 0.999618i | \(-0.508793\pi\) | ||||
−0.0276207 | + | 0.999618i | \(0.508793\pi\) | |||||||
\(72\) | 11027.7 | 0.250699 | ||||||||
\(73\) | 57370.0 | 1.26002 | 0.630010 | − | 0.776587i | \(-0.283051\pi\) | ||||
0.630010 | + | 0.776587i | \(0.283051\pi\) | |||||||
\(74\) | −30684.7 | −0.651393 | ||||||||
\(75\) | −112349. | −2.30629 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25078.3 | 0.482027 | ||||||||
\(78\) | −79788.3 | −1.48492 | ||||||||
\(79\) | 29715.8 | 0.535698 | 0.267849 | − | 0.963461i | \(-0.413687\pi\) | ||||
0.267849 | + | 0.963461i | \(0.413687\pi\) | |||||||
\(80\) | −174790. | −3.05345 | ||||||||
\(81\) | −65032.8 | −1.10134 | ||||||||
\(82\) | −55664.3 | −0.914202 | ||||||||
\(83\) | 60526.0 | 0.964377 | 0.482188 | − | 0.876068i | \(-0.339842\pi\) | ||||
0.482188 | + | 0.876068i | \(0.339842\pi\) | |||||||
\(84\) | 66809.5 | 1.03309 | ||||||||
\(85\) | −166738. | −2.50315 | ||||||||
\(86\) | 51793.8 | 0.755147 | ||||||||
\(87\) | −44378.8 | −0.628604 | ||||||||
\(88\) | −174092. | −2.39647 | ||||||||
\(89\) | −19134.9 | −0.256066 | −0.128033 | − | 0.991770i | \(-0.540866\pi\) | ||||
−0.128033 | + | 0.991770i | \(0.540866\pi\) | |||||||
\(90\) | −28161.8 | −0.366483 | ||||||||
\(91\) | −27284.2 | −0.345389 | ||||||||
\(92\) | 32655.1 | 0.402237 | ||||||||
\(93\) | −38086.7 | −0.456631 | ||||||||
\(94\) | 58918.9 | 0.687756 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −83871.9 | −0.928834 | ||||||||
\(97\) | 43189.4 | 0.466067 | 0.233033 | − | 0.972469i | \(-0.425135\pi\) | ||||
0.233033 | + | 0.972469i | \(0.425135\pi\) | |||||||
\(98\) | −137492. | −1.44615 | ||||||||
\(99\) | −12206.4 | −0.125170 | ||||||||
\(100\) | 485166. | 4.85166 | ||||||||
\(101\) | −55330.5 | −0.539711 | −0.269855 | − | 0.962901i | \(-0.586976\pi\) | ||||
−0.269855 | + | 0.962901i | \(0.586976\pi\) | |||||||
\(102\) | −279229. | −2.65742 | ||||||||
\(103\) | 205641. | 1.90993 | 0.954964 | − | 0.296722i | \(-0.0958933\pi\) | ||||
0.954964 | + | 0.296722i | \(0.0958933\pi\) | |||||||
\(104\) | 189405. | 1.71715 | ||||||||
\(105\) | −93787.2 | −0.830177 | ||||||||
\(106\) | 235604. | 2.03666 | ||||||||
\(107\) | −181889. | −1.53585 | −0.767923 | − | 0.640543i | \(-0.778709\pi\) | ||||
−0.767923 | + | 0.640543i | \(0.778709\pi\) | |||||||
\(108\) | 251658. | 2.07612 | ||||||||
\(109\) | −24288.8 | −0.195813 | −0.0979063 | − | 0.995196i | \(-0.531215\pi\) | ||||
−0.0979063 | + | 0.995196i | \(0.531215\pi\) | |||||||
\(110\) | 444584. | 3.50326 | ||||||||
\(111\) | 49739.0 | 0.383169 | ||||||||
\(112\) | −100095. | −0.753996 | ||||||||
\(113\) | 229667. | 1.69201 | 0.846006 | − | 0.533174i | \(-0.179001\pi\) | ||||
0.846006 | + | 0.533174i | \(0.179001\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −45841.3 | −0.323231 | ||||||||
\(116\) | 191645. | 1.32237 | ||||||||
\(117\) | 13280.1 | 0.0896888 | ||||||||
\(118\) | 333491. | 2.20485 | ||||||||
\(119\) | −95484.6 | −0.618110 | ||||||||
\(120\) | 651064. | 4.12735 | ||||||||
\(121\) | 31649.7 | 0.196520 | ||||||||
\(122\) | −476248. | −2.89690 | ||||||||
\(123\) | 90230.2 | 0.537761 | ||||||||
\(124\) | 164474. | 0.960599 | ||||||||
\(125\) | −369325. | −2.11414 | ||||||||
\(126\) | −16127.2 | −0.0904965 | ||||||||
\(127\) | −8086.69 | −0.0444899 | −0.0222450 | − | 0.999753i | \(-0.507081\pi\) | ||||
−0.0222450 | + | 0.999753i | \(0.507081\pi\) | |||||||
\(128\) | −207004. | −1.11675 | ||||||||
\(129\) | −83956.2 | −0.444200 | ||||||||
\(130\) | −483691. | −2.51021 | ||||||||
\(131\) | 118712. | 0.604390 | 0.302195 | − | 0.953246i | \(-0.402281\pi\) | ||||
0.302195 | + | 0.953246i | \(0.402281\pi\) | |||||||
\(132\) | 513362. | 2.56442 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 36193.3 | 0.174127 | ||||||||
\(135\) | −353278. | −1.66833 | ||||||||
\(136\) | 662847. | 3.07303 | ||||||||
\(137\) | 65348.7 | 0.297465 | 0.148732 | − | 0.988877i | \(-0.452481\pi\) | ||||
0.148732 | + | 0.988877i | \(0.452481\pi\) | |||||||
\(138\) | −76768.5 | −0.343151 | ||||||||
\(139\) | −28437.6 | −0.124841 | −0.0624203 | − | 0.998050i | \(-0.519882\pi\) | ||||
−0.0624203 | + | 0.998050i | \(0.519882\pi\) | |||||||
\(140\) | 405011. | 1.74641 | ||||||||
\(141\) | −95505.7 | −0.404559 | ||||||||
\(142\) | −23821.3 | −0.0991388 | ||||||||
\(143\) | −209651. | −0.857347 | ||||||||
\(144\) | 48719.8 | 0.195794 | ||||||||
\(145\) | −269032. | −1.06263 | ||||||||
\(146\) | 582424. | 2.26130 | ||||||||
\(147\) | 222871. | 0.850668 | ||||||||
\(148\) | −214793. | −0.806057 | ||||||||
\(149\) | 115852. | 0.427502 | 0.213751 | − | 0.976888i | \(-0.431432\pi\) | ||||
0.213751 | + | 0.976888i | \(0.431432\pi\) | |||||||
\(150\) | −1.14057e6 | −4.13898 | ||||||||
\(151\) | −35980.9 | −0.128419 | −0.0642096 | − | 0.997936i | \(-0.520453\pi\) | ||||
−0.0642096 | + | 0.997936i | \(0.520453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 46475.6 | 0.160508 | ||||||||
\(154\) | 254596. | 0.865069 | ||||||||
\(155\) | −230888. | −0.771920 | ||||||||
\(156\) | −558518. | −1.83749 | ||||||||
\(157\) | 566234. | 1.83336 | 0.916678 | − | 0.399627i | \(-0.130860\pi\) | ||||
0.916678 | + | 0.399627i | \(0.130860\pi\) | |||||||
\(158\) | 301677. | 0.961390 | ||||||||
\(159\) | −381908. | −1.19802 | ||||||||
\(160\) | −508446. | −1.57016 | ||||||||
\(161\) | −26251.6 | −0.0798161 | ||||||||
\(162\) | −660217. | −1.97651 | ||||||||
\(163\) | −307841. | −0.907523 | −0.453761 | − | 0.891123i | \(-0.649918\pi\) | ||||
−0.453761 | + | 0.891123i | \(0.649918\pi\) | |||||||
\(164\) | −389650. | −1.13127 | ||||||||
\(165\) | −720658. | −2.06072 | ||||||||
\(166\) | 614464. | 1.73072 | ||||||||
\(167\) | −126991. | −0.352357 | −0.176179 | − | 0.984358i | \(-0.556374\pi\) | ||||
−0.176179 | + | 0.984358i | \(0.556374\pi\) | |||||||
\(168\) | 372840. | 1.01918 | ||||||||
\(169\) | −143201. | −0.385681 | ||||||||
\(170\) | −1.69274e6 | −4.49228 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 362556. | 0.934446 | ||||||||
\(173\) | 582515. | 1.47976 | 0.739881 | − | 0.672738i | \(-0.234882\pi\) | ||||
0.739881 | + | 0.672738i | \(0.234882\pi\) | |||||||
\(174\) | −450536. | −1.12812 | ||||||||
\(175\) | −390026. | −0.962718 | ||||||||
\(176\) | −769130. | −1.87162 | ||||||||
\(177\) | −540579. | −1.29696 | ||||||||
\(178\) | −194259. | −0.459548 | ||||||||
\(179\) | 233819. | 0.545440 | 0.272720 | − | 0.962093i | \(-0.412077\pi\) | ||||
0.272720 | + | 0.962093i | \(0.412077\pi\) | |||||||
\(180\) | −197132. | −0.453500 | ||||||||
\(181\) | −318180. | −0.721899 | −0.360950 | − | 0.932585i | \(-0.617547\pi\) | ||||
−0.360950 | + | 0.932585i | \(0.617547\pi\) | |||||||
\(182\) | −276991. | −0.619851 | ||||||||
\(183\) | 771985. | 1.70404 | ||||||||
\(184\) | 182237. | 0.396818 | ||||||||
\(185\) | 301527. | 0.647734 | ||||||||
\(186\) | −386659. | −0.819493 | ||||||||
\(187\) | −733700. | −1.53432 | ||||||||
\(188\) | 412432. | 0.851055 | ||||||||
\(189\) | −202309. | −0.411965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −182032. | −0.361047 | −0.180523 | − | 0.983571i | \(-0.557779\pi\) | ||||
−0.180523 | + | 0.983571i | \(0.557779\pi\) | |||||||
\(192\) | 71178.2 | 0.139346 | ||||||||
\(193\) | −286026. | −0.552729 | −0.276365 | − | 0.961053i | \(-0.589130\pi\) | ||||
−0.276365 | + | 0.961053i | \(0.589130\pi\) | |||||||
\(194\) | 438462. | 0.836426 | ||||||||
\(195\) | 784048. | 1.47658 | ||||||||
\(196\) | −962446. | −1.78952 | ||||||||
\(197\) | −465880. | −0.855281 | −0.427640 | − | 0.903949i | \(-0.640655\pi\) | ||||
−0.427640 | + | 0.903949i | \(0.640655\pi\) | |||||||
\(198\) | −123921. | −0.224637 | ||||||||
\(199\) | 1.06447e6 | 1.90547 | 0.952736 | − | 0.303798i | \(-0.0982548\pi\) | ||||
0.952736 | + | 0.303798i | \(0.0982548\pi\) | |||||||
\(200\) | 2.70754e6 | 4.78629 | ||||||||
\(201\) | −58668.3 | −0.102427 | ||||||||
\(202\) | −561719. | −0.968591 | ||||||||
\(203\) | −154064. | −0.262399 | ||||||||
\(204\) | −1.95461e6 | −3.28839 | ||||||||
\(205\) | 546991. | 0.909067 | ||||||||
\(206\) | 2.08768e6 | 3.42765 | ||||||||
\(207\) | 12777.5 | 0.0207263 | ||||||||
\(208\) | 836784. | 1.34108 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −952134. | −1.48988 | ||||||||
\(211\) | −1.00586e6 | −1.55536 | −0.777679 | − | 0.628662i | \(-0.783603\pi\) | ||||
−0.777679 | + | 0.628662i | \(0.783603\pi\) | |||||||
\(212\) | 1.64923e6 | 2.52024 | ||||||||
\(213\) | 38613.5 | 0.0583164 | ||||||||
\(214\) | −1.84655e6 | −2.75630 | ||||||||
\(215\) | −508957. | −0.750905 | ||||||||
\(216\) | 1.40441e6 | 2.04814 | ||||||||
\(217\) | −132221. | −0.190612 | ||||||||
\(218\) | −246582. | −0.351415 | ||||||||
\(219\) | −944092. | −1.33016 | ||||||||
\(220\) | 3.11209e6 | 4.33506 | ||||||||
\(221\) | 798238. | 1.09939 | ||||||||
\(222\) | 504954. | 0.687653 | ||||||||
\(223\) | 377403. | 0.508210 | 0.254105 | − | 0.967177i | \(-0.418219\pi\) | ||||
0.254105 | + | 0.967177i | \(0.418219\pi\) | |||||||
\(224\) | −291167. | −0.387724 | ||||||||
\(225\) | 189839. | 0.249994 | ||||||||
\(226\) | 2.33160e6 | 3.03657 | ||||||||
\(227\) | 1.28433e6 | 1.65429 | 0.827145 | − | 0.561989i | \(-0.189964\pi\) | ||||
0.827145 | + | 0.561989i | \(0.189964\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 299103. | 0.376905 | 0.188452 | − | 0.982082i | \(-0.439653\pi\) | ||||
0.188452 | + | 0.982082i | \(0.439653\pi\) | |||||||
\(230\) | −465384. | −0.580085 | ||||||||
\(231\) | −412693. | −0.508859 | ||||||||
\(232\) | 1.06950e6 | 1.30455 | ||||||||
\(233\) | 564942. | 0.681732 | 0.340866 | − | 0.940112i | \(-0.389280\pi\) | ||||
0.340866 | + | 0.940112i | \(0.389280\pi\) | |||||||
\(234\) | 134821. | 0.160960 | ||||||||
\(235\) | −578972. | −0.683893 | ||||||||
\(236\) | 2.33443e6 | 2.72836 | ||||||||
\(237\) | −489010. | −0.565518 | ||||||||
\(238\) | −969366. | −1.10929 | ||||||||
\(239\) | −1.03635e6 | −1.17358 | −0.586789 | − | 0.809740i | \(-0.699608\pi\) | ||||
−0.586789 | + | 0.809740i | \(0.699608\pi\) | |||||||
\(240\) | 2.87637e6 | 3.22342 | ||||||||
\(241\) | −821274. | −0.910847 | −0.455423 | − | 0.890275i | \(-0.650512\pi\) | ||||
−0.455423 | + | 0.890275i | \(0.650512\pi\) | |||||||
\(242\) | 321310. | 0.352684 | ||||||||
\(243\) | 209665. | 0.227777 | ||||||||
\(244\) | −3.33374e6 | −3.58473 | ||||||||
\(245\) | 1.35108e6 | 1.43803 | ||||||||
\(246\) | 916023. | 0.965092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 917868. | 0.947656 | ||||||||
\(249\) | −996028. | −1.01806 | ||||||||
\(250\) | −3.74941e6 | −3.79414 | ||||||||
\(251\) | 1.23062e6 | 1.23293 | 0.616467 | − | 0.787380i | \(-0.288563\pi\) | ||||
0.616467 | + | 0.787380i | \(0.288563\pi\) | |||||||
\(252\) | −112890. | −0.111984 | ||||||||
\(253\) | −201716. | −0.198125 | ||||||||
\(254\) | −82096.7 | −0.0798438 | ||||||||
\(255\) | 2.74388e6 | 2.64249 | ||||||||
\(256\) | −1.96311e6 | −1.87217 | ||||||||
\(257\) | 1.05206e6 | 0.993592 | 0.496796 | − | 0.867867i | \(-0.334510\pi\) | ||||
0.496796 | + | 0.867867i | \(0.334510\pi\) | |||||||
\(258\) | −852329. | −0.797183 | ||||||||
\(259\) | 172673. | 0.159946 | ||||||||
\(260\) | −3.38583e6 | −3.10622 | ||||||||
\(261\) | 74988.2 | 0.0681384 | ||||||||
\(262\) | 1.20517e6 | 1.08467 | ||||||||
\(263\) | 1.88157e6 | 1.67738 | 0.838688 | − | 0.544612i | \(-0.183323\pi\) | ||||
0.838688 | + | 0.544612i | \(0.183323\pi\) | |||||||
\(264\) | 2.86489e6 | 2.52987 | ||||||||
\(265\) | −2.31519e6 | −2.02522 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 314888. | 0.270320 | ||||||||
\(268\) | 253353. | 0.215471 | ||||||||
\(269\) | 1.05389e6 | 0.888002 | 0.444001 | − | 0.896026i | \(-0.353559\pi\) | ||||
0.444001 | + | 0.896026i | \(0.353559\pi\) | |||||||
\(270\) | −3.58650e6 | −2.99407 | ||||||||
\(271\) | 688686. | 0.569637 | 0.284818 | − | 0.958581i | \(-0.408067\pi\) | ||||
0.284818 | + | 0.958581i | \(0.408067\pi\) | |||||||
\(272\) | 2.92843e6 | 2.40001 | ||||||||
\(273\) | 448995. | 0.364615 | ||||||||
\(274\) | 663425. | 0.533845 | ||||||||
\(275\) | −2.99695e6 | −2.38972 | ||||||||
\(276\) | −537380. | −0.424628 | ||||||||
\(277\) | −522720. | −0.409326 | −0.204663 | − | 0.978832i | \(-0.565610\pi\) | ||||
−0.204663 | + | 0.978832i | \(0.565610\pi\) | |||||||
\(278\) | −288701. | −0.224045 | ||||||||
\(279\) | 64356.3 | 0.0494972 | ||||||||
\(280\) | 2.26022e6 | 1.72288 | ||||||||
\(281\) | 2.00251e6 | 1.51290 | 0.756448 | − | 0.654053i | \(-0.226933\pi\) | ||||
0.756448 | + | 0.654053i | \(0.226933\pi\) | |||||||
\(282\) | −969581. | −0.726041 | ||||||||
\(283\) | −2.25219e6 | −1.67163 | −0.835813 | − | 0.549014i | \(-0.815003\pi\) | ||||
−0.835813 | + | 0.549014i | \(0.815003\pi\) | |||||||
\(284\) | −166749. | −0.122678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.12839e6 | −1.53864 | ||||||||
\(287\) | 313241. | 0.224478 | ||||||||
\(288\) | 141721. | 0.100682 | ||||||||
\(289\) | 1.37368e6 | 0.967476 | ||||||||
\(290\) | −2.73123e6 | −1.90705 | ||||||||
\(291\) | −710734. | −0.492011 | ||||||||
\(292\) | 4.07697e6 | 2.79821 | ||||||||
\(293\) | −1.76627e6 | −1.20195 | −0.600976 | − | 0.799267i | \(-0.705221\pi\) | ||||
−0.600976 | + | 0.799267i | \(0.705221\pi\) | |||||||
\(294\) | 2.26260e6 | 1.52665 | ||||||||
\(295\) | −3.27708e6 | −2.19246 | ||||||||
\(296\) | −1.19868e6 | −0.795197 | ||||||||
\(297\) | −1.55453e6 | −1.02261 | ||||||||
\(298\) | 1.17614e6 | 0.767216 | ||||||||
\(299\) | 219459. | 0.141963 | ||||||||
\(300\) | −7.98399e6 | −5.12173 | ||||||||
\(301\) | −291460. | −0.185423 | ||||||||
\(302\) | −365281. | −0.230467 | ||||||||
\(303\) | 910530. | 0.569754 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.67990e6 | 2.88063 | ||||||||
\(306\) | 471823. | 0.288055 | ||||||||
\(307\) | 1.71867e6 | 1.04075 | 0.520376 | − | 0.853937i | \(-0.325792\pi\) | ||||
0.520376 | + | 0.853937i | \(0.325792\pi\) | |||||||
\(308\) | 1.78218e6 | 1.07047 | ||||||||
\(309\) | −3.38407e6 | −2.01625 | ||||||||
\(310\) | −2.34399e6 | −1.38533 | ||||||||
\(311\) | 1.58149e6 | 0.927182 | 0.463591 | − | 0.886049i | \(-0.346561\pi\) | ||||
0.463591 | + | 0.886049i | \(0.346561\pi\) | |||||||
\(312\) | −3.11689e6 | −1.81274 | ||||||||
\(313\) | 54617.0 | 0.0315114 | 0.0157557 | − | 0.999876i | \(-0.494985\pi\) | ||||
0.0157557 | + | 0.999876i | \(0.494985\pi\) | |||||||
\(314\) | 5.74844e6 | 3.29023 | ||||||||
\(315\) | 158475. | 0.0899882 | ||||||||
\(316\) | 2.11174e6 | 1.18966 | ||||||||
\(317\) | 1.03467e6 | 0.578303 | 0.289151 | − | 0.957283i | \(-0.406627\pi\) | ||||
0.289151 | + | 0.957283i | \(0.406627\pi\) | |||||||
\(318\) | −3.87715e6 | −2.15003 | ||||||||
\(319\) | −1.18382e6 | −0.651344 | ||||||||
\(320\) | 431495. | 0.235559 | ||||||||
\(321\) | 2.99321e6 | 1.62134 | ||||||||
\(322\) | −266508. | −0.143242 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.62152e6 | −2.44581 | ||||||||
\(325\) | 3.26057e6 | 1.71232 | ||||||||
\(326\) | −3.12522e6 | −1.62868 | ||||||||
\(327\) | 399702. | 0.206713 | ||||||||
\(328\) | −2.17450e6 | −1.11603 | ||||||||
\(329\) | −331555. | −0.168875 | ||||||||
\(330\) | −7.31617e6 | −3.69827 | ||||||||
\(331\) | −2.03987e6 | −1.02337 | −0.511685 | − | 0.859173i | \(-0.670979\pi\) | ||||
−0.511685 | + | 0.859173i | \(0.670979\pi\) | |||||||
\(332\) | 4.30125e6 | 2.14165 | ||||||||
\(333\) | −84045.7 | −0.0415341 | ||||||||
\(334\) | −1.28923e6 | −0.632358 | ||||||||
\(335\) | −355657. | −0.173149 | ||||||||
\(336\) | 1.64719e6 | 0.795968 | ||||||||
\(337\) | −1.22774e6 | −0.588887 | −0.294444 | − | 0.955669i | \(-0.595134\pi\) | ||||
−0.294444 | + | 0.955669i | \(0.595134\pi\) | |||||||
\(338\) | −1.45378e6 | −0.692162 | ||||||||
\(339\) | −3.77945e6 | −1.78620 | ||||||||
\(340\) | −1.18492e7 | −5.55892 | ||||||||
\(341\) | −1.01598e6 | −0.473150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.73388e6 | 0.795763 | ||||||||
\(344\) | 2.02330e6 | 0.921857 | ||||||||
\(345\) | 754374. | 0.341223 | ||||||||
\(346\) | 5.91373e6 | 2.65565 | ||||||||
\(347\) | 3.93267e6 | 1.75333 | 0.876665 | − | 0.481101i | \(-0.159763\pi\) | ||||
0.876665 | + | 0.481101i | \(0.159763\pi\) | |||||||
\(348\) | −3.15375e6 | −1.39598 | ||||||||
\(349\) | −3.46176e6 | −1.52136 | −0.760682 | − | 0.649125i | \(-0.775135\pi\) | ||||
−0.760682 | + | 0.649125i | \(0.775135\pi\) | |||||||
\(350\) | −3.95957e6 | −1.72774 | ||||||||
\(351\) | 1.69127e6 | 0.732734 | ||||||||
\(352\) | −2.23732e6 | −0.962436 | ||||||||
\(353\) | −3.91227e6 | −1.67106 | −0.835531 | − | 0.549443i | \(-0.814840\pi\) | ||||
−0.835531 | + | 0.549443i | \(0.814840\pi\) | |||||||
\(354\) | −5.48799e6 | −2.32758 | ||||||||
\(355\) | 234082. | 0.0985819 | ||||||||
\(356\) | −1.35981e6 | −0.568662 | ||||||||
\(357\) | 1.57131e6 | 0.652518 | ||||||||
\(358\) | 2.37375e6 | 0.978874 | ||||||||
\(359\) | −949856. | −0.388975 | −0.194487 | − | 0.980905i | \(-0.562304\pi\) | ||||
−0.194487 | + | 0.980905i | \(0.562304\pi\) | |||||||
\(360\) | −1.10012e6 | −0.447389 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −3.23018e6 | −1.29556 | ||||||||
\(363\) | −520834. | −0.207459 | ||||||||
\(364\) | −1.93894e6 | −0.767027 | ||||||||
\(365\) | −5.72325e6 | −2.24859 | ||||||||
\(366\) | 7.83724e6 | 3.05816 | ||||||||
\(367\) | 3.72584e6 | 1.44397 | 0.721986 | − | 0.691908i | \(-0.243230\pi\) | ||||
0.721986 | + | 0.691908i | \(0.243230\pi\) | |||||||
\(368\) | 805113. | 0.309911 | ||||||||
\(369\) | −152465. | −0.0582914 | ||||||||
\(370\) | 3.06112e6 | 1.16245 | ||||||||
\(371\) | −1.32582e6 | −0.500093 | ||||||||
\(372\) | −2.70661e6 | −1.01407 | ||||||||
\(373\) | 4.15376e6 | 1.54586 | 0.772929 | − | 0.634493i | \(-0.218791\pi\) | ||||
0.772929 | + | 0.634493i | \(0.218791\pi\) | |||||||
\(374\) | −7.44857e6 | −2.75356 | ||||||||
\(375\) | 6.07769e6 | 2.23183 | ||||||||
\(376\) | 2.30163e6 | 0.839589 | ||||||||
\(377\) | 1.28796e6 | 0.466710 | ||||||||
\(378\) | −2.05385e6 | −0.739332 | ||||||||
\(379\) | −2.29264e6 | −0.819857 | −0.409928 | − | 0.912118i | \(-0.634446\pi\) | ||||
−0.409928 | + | 0.912118i | \(0.634446\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 133076. | 0.0469665 | ||||||||
\(382\) | −1.84800e6 | −0.647952 | ||||||||
\(383\) | −3.09365e6 | −1.07764 | −0.538821 | − | 0.842420i | \(-0.681130\pi\) | ||||
−0.538821 | + | 0.842420i | \(0.681130\pi\) | |||||||
\(384\) | 3.40651e6 | 1.17891 | ||||||||
\(385\) | −2.50182e6 | −0.860209 | ||||||||
\(386\) | −2.90376e6 | −0.991955 | ||||||||
\(387\) | 141864. | 0.0481497 | ||||||||
\(388\) | 3.06923e6 | 1.03502 | ||||||||
\(389\) | −4.53732e6 | −1.52029 | −0.760144 | − | 0.649755i | \(-0.774871\pi\) | ||||
−0.760144 | + | 0.649755i | \(0.774871\pi\) | |||||||
\(390\) | 7.95971e6 | 2.64994 | ||||||||
\(391\) | 768026. | 0.254059 | ||||||||
\(392\) | −5.37107e6 | −1.76541 | ||||||||
\(393\) | −1.95355e6 | −0.638034 | ||||||||
\(394\) | −4.72965e6 | −1.53493 | ||||||||
\(395\) | −2.96446e6 | −0.955989 | ||||||||
\(396\) | −867445. | −0.277974 | ||||||||
\(397\) | −404604. | −0.128841 | −0.0644205 | − | 0.997923i | \(-0.520520\pi\) | ||||
−0.0644205 | + | 0.997923i | \(0.520520\pi\) | |||||||
\(398\) | 1.08066e7 | 3.41965 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.19618e7 | 3.73806 | ||||||||
\(401\) | 5.08752e6 | 1.57996 | 0.789978 | − | 0.613135i | \(-0.210092\pi\) | ||||
0.789978 | + | 0.613135i | \(0.210092\pi\) | |||||||
\(402\) | −595604. | −0.183820 | ||||||||
\(403\) | 1.10535e6 | 0.339029 | ||||||||
\(404\) | −3.93203e6 | −1.19857 | ||||||||
\(405\) | 6.48769e6 | 1.96541 | ||||||||
\(406\) | −1.56407e6 | −0.470913 | ||||||||
\(407\) | 1.32681e6 | 0.397030 | ||||||||
\(408\) | −1.09079e7 | −3.24409 | ||||||||
\(409\) | −367772. | −0.108710 | −0.0543551 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543551 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(410\) | 5.55309e6 | 1.63146 | ||||||||
\(411\) | −1.07539e6 | −0.314024 | ||||||||
\(412\) | 1.46138e7 | 4.24150 | ||||||||
\(413\) | −1.87666e6 | −0.541390 | ||||||||
\(414\) | 129718. | 0.0371964 | ||||||||
\(415\) | −6.03809e6 | −1.72099 | ||||||||
\(416\) | 2.43412e6 | 0.689618 | ||||||||
\(417\) | 467975. | 0.131790 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.12612e6 | −1.14817 | −0.574086 | − | 0.818795i | \(-0.694643\pi\) | ||||
−0.574086 | + | 0.818795i | \(0.694643\pi\) | |||||||
\(420\) | −6.66494e6 | −1.84363 | ||||||||
\(421\) | 2.05918e6 | 0.566224 | 0.283112 | − | 0.959087i | \(-0.408633\pi\) | ||||
0.283112 | + | 0.959087i | \(0.408633\pi\) | |||||||
\(422\) | −1.02115e7 | −2.79132 | ||||||||
\(423\) | 161379. | 0.0438527 | ||||||||
\(424\) | 9.20376e6 | 2.48628 | ||||||||
\(425\) | 1.14108e7 | 3.06438 | ||||||||
\(426\) | 392007. | 0.104657 | ||||||||
\(427\) | 2.68000e6 | 0.711321 | ||||||||
\(428\) | −1.29259e7 | −3.41075 | ||||||||
\(429\) | 3.45006e6 | 0.905072 | ||||||||
\(430\) | −5.16696e6 | −1.34761 | ||||||||
\(431\) | 3.23089e6 | 0.837777 | 0.418889 | − | 0.908038i | \(-0.362420\pi\) | ||||
0.418889 | + | 0.908038i | \(0.362420\pi\) | |||||||
\(432\) | 6.20464e6 | 1.59958 | ||||||||
\(433\) | 4.46477e6 | 1.14440 | 0.572202 | − | 0.820113i | \(-0.306089\pi\) | ||||
0.572202 | + | 0.820113i | \(0.306089\pi\) | |||||||
\(434\) | −1.34231e6 | −0.342082 | ||||||||
\(435\) | 4.42724e6 | 1.12179 | ||||||||
\(436\) | −1.72607e6 | −0.434854 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.58449e6 | −2.38717 | ||||||||
\(439\) | −3.96204e6 | −0.981201 | −0.490601 | − | 0.871385i | \(-0.663223\pi\) | ||||
−0.490601 | + | 0.871385i | \(0.663223\pi\) | |||||||
\(440\) | 1.73674e7 | 4.27666 | ||||||||
\(441\) | −376592. | −0.0922094 | ||||||||
\(442\) | 8.10376e6 | 1.97302 | ||||||||
\(443\) | 5.87689e6 | 1.42278 | 0.711391 | − | 0.702797i | \(-0.248066\pi\) | ||||
0.711391 | + | 0.702797i | \(0.248066\pi\) | |||||||
\(444\) | 3.53468e6 | 0.850927 | ||||||||
\(445\) | 1.90890e6 | 0.456966 | ||||||||
\(446\) | 3.83142e6 | 0.912059 | ||||||||
\(447\) | −1.90649e6 | −0.451299 | ||||||||
\(448\) | 247101. | 0.0581673 | ||||||||
\(449\) | 2.62215e6 | 0.613820 | 0.306910 | − | 0.951739i | \(-0.400705\pi\) | ||||
0.306910 | + | 0.951739i | \(0.400705\pi\) | |||||||
\(450\) | 1.92726e6 | 0.448651 | ||||||||
\(451\) | 2.40693e6 | 0.557215 | ||||||||
\(452\) | 1.63212e7 | 3.75756 | ||||||||
\(453\) | 592109. | 0.135568 | ||||||||
\(454\) | 1.30386e7 | 2.96887 | ||||||||
\(455\) | 2.72188e6 | 0.616369 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.12578e6 | 1.14807 | 0.574037 | − | 0.818830i | \(-0.305377\pi\) | ||||
0.574037 | + | 0.818830i | \(0.305377\pi\) | |||||||
\(458\) | 3.03651e6 | 0.676411 | ||||||||
\(459\) | 5.91883e6 | 1.31131 | ||||||||
\(460\) | −3.25769e6 | −0.717819 | ||||||||
\(461\) | 2.65571e6 | 0.582008 | 0.291004 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291004 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(462\) | −4.18969e6 | −0.913223 | ||||||||
\(463\) | −2.94632e6 | −0.638744 | −0.319372 | − | 0.947629i | \(-0.603472\pi\) | ||||
−0.319372 | + | 0.947629i | \(0.603472\pi\) | |||||||
\(464\) | 4.72502e6 | 1.01885 | ||||||||
\(465\) | 3.79954e6 | 0.814890 | ||||||||
\(466\) | 5.73533e6 | 1.22347 | ||||||||
\(467\) | 1.82563e6 | 0.387364 | 0.193682 | − | 0.981064i | \(-0.437957\pi\) | ||||
0.193682 | + | 0.981064i | \(0.437957\pi\) | |||||||
\(468\) | 943747. | 0.199178 | ||||||||
\(469\) | −203671. | −0.0427561 | ||||||||
\(470\) | −5.87776e6 | −1.22735 | ||||||||
\(471\) | −9.31806e6 | −1.93541 | ||||||||
\(472\) | 1.30276e7 | 2.69160 | ||||||||
\(473\) | −2.23957e6 | −0.460269 | ||||||||
\(474\) | −4.96446e6 | −1.01491 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.78556e6 | −1.37268 | ||||||||
\(477\) | 645322. | 0.129862 | ||||||||
\(478\) | −1.05211e7 | −2.10616 | ||||||||
\(479\) | 5.92850e6 | 1.18061 | 0.590304 | − | 0.807181i | \(-0.299008\pi\) | ||||
0.590304 | + | 0.807181i | \(0.299008\pi\) | |||||||
\(480\) | 8.36709e6 | 1.65757 | ||||||||
\(481\) | −1.44352e6 | −0.284486 | ||||||||
\(482\) | −8.33763e6 | −1.63465 | ||||||||
\(483\) | 432001. | 0.0842592 | ||||||||
\(484\) | 2.24917e6 | 0.436424 | ||||||||
\(485\) | −4.30859e6 | −0.831727 | ||||||||
\(486\) | 2.12853e6 | 0.408780 | ||||||||
\(487\) | 3.61261e6 | 0.690237 | 0.345118 | − | 0.938559i | \(-0.387839\pi\) | ||||
0.345118 | + | 0.938559i | \(0.387839\pi\) | |||||||
\(488\) | −1.86044e7 | −3.53644 | ||||||||
\(489\) | 5.06589e6 | 0.958041 | ||||||||
\(490\) | 1.37163e7 | 2.58075 | ||||||||
\(491\) | −4.32852e6 | −0.810281 | −0.405140 | − | 0.914255i | \(-0.632777\pi\) | ||||
−0.405140 | + | 0.914255i | \(0.632777\pi\) | |||||||
\(492\) | 6.41216e6 | 1.19424 | ||||||||
\(493\) | 4.50736e6 | 0.835228 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.21772e6 | 0.223375 | ||||||||
\(496\) | 4.05510e6 | 0.740112 | ||||||||
\(497\) | 134050. | 0.0243431 | ||||||||
\(498\) | −1.01117e7 | −1.82706 | ||||||||
\(499\) | −4.93615e6 | −0.887435 | −0.443718 | − | 0.896167i | \(-0.646341\pi\) | ||||
−0.443718 | + | 0.896167i | \(0.646341\pi\) | |||||||
\(500\) | −2.62459e7 | −4.69501 | ||||||||
\(501\) | 2.08980e6 | 0.371972 | ||||||||
\(502\) | 1.24933e7 | 2.21268 | ||||||||
\(503\) | 1.03023e6 | 0.181557 | 0.0907786 | − | 0.995871i | \(-0.471064\pi\) | ||||
0.0907786 | + | 0.995871i | \(0.471064\pi\) | |||||||
\(504\) | −630000. | −0.110475 | ||||||||
\(505\) | 5.51979e6 | 0.963150 | ||||||||
\(506\) | −2.04784e6 | −0.355565 | ||||||||
\(507\) | 2.35654e6 | 0.407151 | ||||||||
\(508\) | −574677. | −0.0988017 | ||||||||
\(509\) | −4.99120e6 | −0.853907 | −0.426954 | − | 0.904274i | \(-0.640413\pi\) | ||||
−0.426954 | + | 0.904274i | \(0.640413\pi\) | |||||||
\(510\) | 2.78560e7 | 4.74235 | ||||||||
\(511\) | −3.27749e6 | −0.555250 | ||||||||
\(512\) | −1.33055e7 | −2.24314 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.06806e7 | 1.78315 | ||||||||
\(515\) | −2.05148e7 | −3.40839 | ||||||||
\(516\) | −5.96630e6 | −0.986463 | ||||||||
\(517\) | −2.54766e6 | −0.419194 | ||||||||
\(518\) | 1.75299e6 | 0.287048 | ||||||||
\(519\) | −9.58598e6 | −1.56213 | ||||||||
\(520\) | −1.88951e7 | −3.06437 | ||||||||
\(521\) | −9.78050e6 | −1.57858 | −0.789291 | − | 0.614020i | \(-0.789551\pi\) | ||||
−0.789291 | + | 0.614020i | \(0.789551\pi\) | |||||||
\(522\) | 761286. | 0.122284 | ||||||||
\(523\) | 6.73157e6 | 1.07612 | 0.538062 | − | 0.842905i | \(-0.319157\pi\) | ||||
0.538062 | + | 0.842905i | \(0.319157\pi\) | |||||||
\(524\) | 8.43622e6 | 1.34221 | ||||||||
\(525\) | 6.41835e6 | 1.01631 | ||||||||
\(526\) | 1.91018e7 | 3.01030 | ||||||||
\(527\) | 3.86830e6 | 0.606728 | ||||||||
\(528\) | 1.26570e7 | 1.97581 | ||||||||
\(529\) | −6.22519e6 | −0.967194 | ||||||||
\(530\) | −2.35040e7 | −3.63456 | ||||||||
\(531\) | 913433. | 0.140586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.61865e6 | −0.399264 | ||||||||
\(534\) | 3.19676e6 | 0.485129 | ||||||||
\(535\) | 1.81453e7 | 2.74082 | ||||||||
\(536\) | 1.41387e6 | 0.212568 | ||||||||
\(537\) | −3.84777e6 | −0.575803 | ||||||||
\(538\) | 1.06991e7 | 1.59365 | ||||||||
\(539\) | 5.94519e6 | 0.881442 | ||||||||
\(540\) | −2.51055e7 | −3.70497 | ||||||||
\(541\) | −6.68215e6 | −0.981574 | −0.490787 | − | 0.871280i | \(-0.663291\pi\) | ||||
−0.490787 | + | 0.871280i | \(0.663291\pi\) | |||||||
\(542\) | 6.99159e6 | 1.02230 | ||||||||
\(543\) | 5.23603e6 | 0.762084 | ||||||||
\(544\) | 8.51851e6 | 1.23415 | ||||||||
\(545\) | 2.42306e6 | 0.349441 | ||||||||
\(546\) | 4.55822e6 | 0.654356 | ||||||||
\(547\) | 235187. | 0.0336081 | 0.0168041 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168041 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(548\) | 4.64397e6 | 0.660600 | ||||||||
\(549\) | −1.30445e6 | −0.184712 | ||||||||
\(550\) | −3.04252e7 | −4.28872 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.99892e6 | −0.418907 | ||||||||
\(553\) | −1.69763e6 | −0.236065 | ||||||||
\(554\) | −5.30668e6 | −0.734597 | ||||||||
\(555\) | −4.96198e6 | −0.683790 | ||||||||
\(556\) | −2.02090e6 | −0.277242 | ||||||||
\(557\) | −4.80203e6 | −0.655824 | −0.327912 | − | 0.944708i | \(-0.606345\pi\) | ||||
−0.327912 | + | 0.944708i | \(0.606345\pi\) | |||||||
\(558\) | 653350. | 0.0888301 | ||||||||
\(559\) | 2.43657e6 | 0.329799 | ||||||||
\(560\) | 9.98555e6 | 1.34556 | ||||||||
\(561\) | 1.20739e7 | 1.61972 | ||||||||
\(562\) | 2.03296e7 | 2.71512 | ||||||||
\(563\) | 8.37831e6 | 1.11400 | 0.557000 | − | 0.830512i | \(-0.311952\pi\) | ||||
0.557000 | + | 0.830512i | \(0.311952\pi\) | |||||||
\(564\) | −6.78706e6 | −0.898430 | ||||||||
\(565\) | −2.29117e7 | −3.01951 | ||||||||
\(566\) | −2.28644e7 | −2.99998 | ||||||||
\(567\) | 3.71525e6 | 0.485323 | ||||||||
\(568\) | −930565. | −0.121025 | ||||||||
\(569\) | 8.38130e6 | 1.08525 | 0.542626 | − | 0.839974i | \(-0.317430\pi\) | ||||
0.542626 | + | 0.839974i | \(0.317430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.97400e6 | 0.510079 | 0.255040 | − | 0.966931i | \(-0.417912\pi\) | ||||
0.255040 | + | 0.966931i | \(0.417912\pi\) | |||||||
\(572\) | −1.48987e7 | −1.90397 | ||||||||
\(573\) | 2.99555e6 | 0.381145 | ||||||||
\(574\) | 3.18004e6 | 0.402859 | ||||||||
\(575\) | 3.13716e6 | 0.395701 | ||||||||
\(576\) | −120272. | −0.0151046 | ||||||||
\(577\) | 1.40884e7 | 1.76166 | 0.880830 | − | 0.473432i | \(-0.156985\pi\) | ||||
0.880830 | + | 0.473432i | \(0.156985\pi\) | |||||||
\(578\) | 1.39457e7 | 1.73628 | ||||||||
\(579\) | 4.70690e6 | 0.583497 | ||||||||
\(580\) | −1.91186e7 | −2.35986 | ||||||||
\(581\) | −3.45779e6 | −0.424970 | ||||||||
\(582\) | −7.21542e6 | −0.882986 | ||||||||
\(583\) | −1.01876e7 | −1.24136 | ||||||||
\(584\) | 2.27521e7 | 2.76051 | ||||||||
\(585\) | −1.32483e6 | −0.160056 | ||||||||
\(586\) | −1.79313e7 | −2.15708 | ||||||||
\(587\) | 3.14647e6 | 0.376901 | 0.188451 | − | 0.982083i | \(-0.439653\pi\) | ||||
0.188451 | + | 0.982083i | \(0.439653\pi\) | |||||||
\(588\) | 1.58382e7 | 1.88913 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.32691e7 | −3.93470 | ||||||||
\(591\) | 7.66662e6 | 0.902891 | ||||||||
\(592\) | −5.29573e6 | −0.621043 | ||||||||
\(593\) | −4.29402e6 | −0.501450 | −0.250725 | − | 0.968058i | \(-0.580669\pi\) | ||||
−0.250725 | + | 0.968058i | \(0.580669\pi\) | |||||||
\(594\) | −1.57817e7 | −1.83522 | ||||||||
\(595\) | 9.52557e6 | 1.10306 | ||||||||
\(596\) | 8.23297e6 | 0.949382 | ||||||||
\(597\) | −1.75172e7 | −2.01154 | ||||||||
\(598\) | 2.22797e6 | 0.254774 | ||||||||
\(599\) | 6.82650e6 | 0.777376 | 0.388688 | − | 0.921370i | \(-0.372928\pi\) | ||||
0.388688 | + | 0.921370i | \(0.372928\pi\) | |||||||
\(600\) | −4.45558e7 | −5.05273 | ||||||||
\(601\) | −1.82575e6 | −0.206184 | −0.103092 | − | 0.994672i | \(-0.532874\pi\) | ||||
−0.103092 | + | 0.994672i | \(0.532874\pi\) | |||||||
\(602\) | −2.95892e6 | −0.332769 | ||||||||
\(603\) | 99133.7 | 0.0111027 | ||||||||
\(604\) | −2.55697e6 | −0.285189 | ||||||||
\(605\) | −3.15738e6 | −0.350703 | ||||||||
\(606\) | 9.24376e6 | 1.02251 | ||||||||
\(607\) | 2.44884e6 | 0.269767 | 0.134883 | − | 0.990861i | \(-0.456934\pi\) | ||||
0.134883 | + | 0.990861i | \(0.456934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.53531e6 | 0.277005 | ||||||||
\(610\) | 4.75107e7 | 5.16972 | ||||||||
\(611\) | 2.77176e6 | 0.300367 | ||||||||
\(612\) | 3.30276e6 | 0.356450 | ||||||||
\(613\) | −6.05994e6 | −0.651354 | −0.325677 | − | 0.945481i | \(-0.605592\pi\) | ||||
−0.325677 | + | 0.945481i | \(0.605592\pi\) | |||||||
\(614\) | 1.74481e7 | 1.86778 | ||||||||
\(615\) | −9.00140e6 | −0.959670 | ||||||||
\(616\) | 9.94568e6 | 1.05605 | ||||||||
\(617\) | 9.33155e6 | 0.986827 | 0.493414 | − | 0.869795i | \(-0.335749\pi\) | ||||
0.493414 | + | 0.869795i | \(0.335749\pi\) | |||||||
\(618\) | −3.43553e7 | −3.61845 | ||||||||
\(619\) | −9.73252e6 | −1.02094 | −0.510468 | − | 0.859897i | \(-0.670528\pi\) | ||||
−0.510468 | + | 0.859897i | \(0.670528\pi\) | |||||||
\(620\) | −1.64079e7 | −1.71425 | ||||||||
\(621\) | 1.62726e6 | 0.169328 | ||||||||
\(622\) | 1.60554e7 | 1.66397 | ||||||||
\(623\) | 1.09316e6 | 0.112840 | ||||||||
\(624\) | −1.37703e7 | −1.41573 | ||||||||
\(625\) | 1.55092e7 | 1.58815 | ||||||||
\(626\) | 554475. | 0.0565518 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.02391e7 | 4.07145 | ||||||||
\(629\) | −5.05178e6 | −0.509118 | ||||||||
\(630\) | 1.60885e6 | 0.161497 | ||||||||
\(631\) | 8.09784e6 | 0.809647 | 0.404824 | − | 0.914395i | \(-0.367333\pi\) | ||||
0.404824 | + | 0.914395i | \(0.367333\pi\) | |||||||
\(632\) | 1.17849e7 | 1.17363 | ||||||||
\(633\) | 1.65526e7 | 1.64194 | ||||||||
\(634\) | 1.05041e7 | 1.03785 | ||||||||
\(635\) | 806731. | 0.0793953 | ||||||||
\(636\) | −2.71401e7 | −2.66053 | ||||||||
\(637\) | −6.46814e6 | −0.631583 | ||||||||
\(638\) | −1.20183e7 | −1.16893 | ||||||||
\(639\) | −65246.6 | −0.00632129 | ||||||||
\(640\) | 2.06508e7 | 1.99291 | ||||||||
\(641\) | 1.54883e7 | 1.48887 | 0.744436 | − | 0.667694i | \(-0.232718\pi\) | ||||
0.744436 | + | 0.667694i | \(0.232718\pi\) | |||||||
\(642\) | 3.03872e7 | 2.90973 | ||||||||
\(643\) | 1.43966e7 | 1.37320 | 0.686600 | − | 0.727036i | \(-0.259103\pi\) | ||||
0.686600 | + | 0.727036i | \(0.259103\pi\) | |||||||
\(644\) | −1.86555e6 | −0.177253 | ||||||||
\(645\) | 8.37550e6 | 0.792704 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.47992e6 | −0.608568 | −0.304284 | − | 0.952581i | \(-0.598417\pi\) | ||||
−0.304284 | + | 0.952581i | \(0.598417\pi\) | |||||||
\(648\) | −2.57910e7 | −2.41286 | ||||||||
\(649\) | −1.44202e7 | −1.34388 | ||||||||
\(650\) | 3.31015e7 | 3.07301 | ||||||||
\(651\) | 2.17585e6 | 0.201223 | ||||||||
\(652\) | −2.18766e7 | −2.01539 | ||||||||
\(653\) | −7.89619e6 | −0.724660 | −0.362330 | − | 0.932050i | \(-0.618019\pi\) | ||||
−0.362330 | + | 0.932050i | \(0.618019\pi\) | |||||||
\(654\) | 4.05780e6 | 0.370977 | ||||||||
\(655\) | −1.18428e7 | −1.07857 | ||||||||
\(656\) | −9.60683e6 | −0.871607 | ||||||||
\(657\) | 1.59526e6 | 0.144185 | ||||||||
\(658\) | −3.36597e6 | −0.303072 | ||||||||
\(659\) | 1.08756e7 | 0.975530 | 0.487765 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487765 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(660\) | −5.12132e7 | −4.57638 | ||||||||
\(661\) | 8.09950e6 | 0.721032 | 0.360516 | − | 0.932753i | \(-0.382601\pi\) | ||||
0.360516 | + | 0.932753i | \(0.382601\pi\) | |||||||
\(662\) | −2.07089e7 | −1.83659 | ||||||||
\(663\) | −1.31360e7 | −1.16059 | ||||||||
\(664\) | 2.40037e7 | 2.11280 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −853238. | −0.0745391 | ||||||||
\(667\) | 1.23921e6 | 0.107852 | ||||||||
\(668\) | −9.02458e6 | −0.782503 | ||||||||
\(669\) | −6.21062e6 | −0.536500 | ||||||||
\(670\) | −3.61066e6 | −0.310741 | ||||||||
\(671\) | 2.05930e7 | 1.76569 | ||||||||
\(672\) | 4.79151e6 | 0.409307 | ||||||||
\(673\) | −6.23497e6 | −0.530636 | −0.265318 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265318 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(674\) | −1.24641e7 | −1.05685 | ||||||||
\(675\) | 2.41767e7 | 2.04238 | ||||||||
\(676\) | −1.01765e7 | −0.856507 | ||||||||
\(677\) | −1.16588e7 | −0.977649 | −0.488824 | − | 0.872382i | \(-0.662574\pi\) | ||||
−0.488824 | + | 0.872382i | \(0.662574\pi\) | |||||||
\(678\) | −3.83693e7 | −3.20560 | ||||||||
\(679\) | −2.46737e6 | −0.205380 | ||||||||
\(680\) | −6.61259e7 | −5.48402 | ||||||||
\(681\) | −2.11352e7 | −1.74638 | ||||||||
\(682\) | −1.03143e7 | −0.849139 | ||||||||
\(683\) | 1.22340e6 | 0.100350 | 0.0501748 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501748 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.51921e6 | −0.530846 | ||||||||
\(686\) | 1.76025e7 | 1.42811 | ||||||||
\(687\) | −4.92209e6 | −0.397885 | ||||||||
\(688\) | 8.93884e6 | 0.719962 | ||||||||
\(689\) | 1.10837e7 | 0.889480 | ||||||||
\(690\) | 7.65845e6 | 0.612376 | ||||||||
\(691\) | −5.82015e6 | −0.463702 | −0.231851 | − | 0.972751i | \(-0.574478\pi\) | ||||
−0.231851 | + | 0.972751i | \(0.574478\pi\) | |||||||
\(692\) | 4.13961e7 | 3.28620 | ||||||||
\(693\) | 697341. | 0.0551585 | ||||||||
\(694\) | 3.99247e7 | 3.14661 | ||||||||
\(695\) | 2.83695e6 | 0.222787 | ||||||||
\(696\) | −1.76000e7 | −1.37717 | ||||||||
\(697\) | −9.16430e6 | −0.714525 | ||||||||
\(698\) | −3.51440e7 | −2.73031 | ||||||||
\(699\) | −9.29680e6 | −0.719682 | ||||||||
\(700\) | −2.77170e7 | −2.13797 | ||||||||
\(701\) | 9.44191e6 | 0.725713 | 0.362856 | − | 0.931845i | \(-0.381802\pi\) | ||||
0.362856 | + | 0.931845i | \(0.381802\pi\) | |||||||
\(702\) | 1.71699e7 | 1.31500 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.89871e6 | 0.144387 | ||||||||
\(705\) | 9.52768e6 | 0.721962 | ||||||||
\(706\) | −3.97177e7 | −2.99897 | ||||||||
\(707\) | 3.16097e6 | 0.237833 | ||||||||
\(708\) | −3.84159e7 | −2.88024 | ||||||||
\(709\) | 7.88964e6 | 0.589443 | 0.294721 | − | 0.955583i | \(-0.404773\pi\) | ||||
0.294721 | + | 0.955583i | \(0.404773\pi\) | |||||||
\(710\) | 2.37642e6 | 0.176920 | ||||||||
\(711\) | 826296. | 0.0613002 | ||||||||
\(712\) | −7.58862e6 | −0.561000 | ||||||||
\(713\) | 1.06351e6 | 0.0783464 | ||||||||
\(714\) | 1.59521e7 | 1.17104 | ||||||||
\(715\) | 2.09149e7 | 1.52999 | ||||||||
\(716\) | 1.66162e7 | 1.21129 | ||||||||
\(717\) | 1.70544e7 | 1.23891 | ||||||||
\(718\) | −9.64300e6 | −0.698073 | ||||||||
\(719\) | 1.89500e7 | 1.36706 | 0.683530 | − | 0.729922i | \(-0.260444\pi\) | ||||
0.683530 | + | 0.729922i | \(0.260444\pi\) | |||||||
\(720\) | −4.86030e6 | −0.349408 | ||||||||
\(721\) | −1.17481e7 | −0.841643 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.35150e7 | 0.961550 | ||||||||
\(724\) | −2.26113e7 | −1.60317 | ||||||||
\(725\) | 1.84113e7 | 1.30088 | ||||||||
\(726\) | −5.28754e6 | −0.372316 | ||||||||
\(727\) | 6.46947e6 | 0.453976 | 0.226988 | − | 0.973898i | \(-0.427112\pi\) | ||||
0.226988 | + | 0.973898i | \(0.427112\pi\) | |||||||
\(728\) | −1.08205e7 | −0.756693 | ||||||||
\(729\) | 1.23527e7 | 0.860879 | ||||||||
\(730\) | −5.81028e7 | −4.03543 | ||||||||
\(731\) | 8.52707e6 | 0.590210 | ||||||||
\(732\) | 5.48607e7 | 3.78428 | ||||||||
\(733\) | 6.39936e6 | 0.439923 | 0.219962 | − | 0.975509i | \(-0.429407\pi\) | ||||
0.219962 | + | 0.975509i | \(0.429407\pi\) | |||||||
\(734\) | 3.78249e7 | 2.59142 | ||||||||
\(735\) | −2.22337e7 | −1.51807 | ||||||||
\(736\) | 2.34199e6 | 0.159364 | ||||||||
\(737\) | −1.56500e6 | −0.106132 | ||||||||
\(738\) | −1.54783e6 | −0.104613 | ||||||||
\(739\) | −1.28565e7 | −0.865987 | −0.432993 | − | 0.901397i | \(-0.642543\pi\) | ||||
−0.432993 | + | 0.901397i | \(0.642543\pi\) | |||||||
\(740\) | 2.14278e7 | 1.43846 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.34598e7 | −0.897491 | ||||||||
\(743\) | 2.19966e7 | 1.46179 | 0.730893 | − | 0.682492i | \(-0.239104\pi\) | ||||
0.730893 | + | 0.682492i | \(0.239104\pi\) | |||||||
\(744\) | −1.51046e7 | −1.00041 | ||||||||
\(745\) | −1.15574e7 | −0.762906 | ||||||||
\(746\) | 4.21693e7 | 2.77427 | ||||||||
\(747\) | 1.68302e6 | 0.110354 | ||||||||
\(748\) | −5.21400e7 | −3.40735 | ||||||||
\(749\) | 1.03911e7 | 0.676797 | ||||||||
\(750\) | 6.17011e7 | 4.00534 | ||||||||
\(751\) | −4.73982e6 | −0.306663 | −0.153332 | − | 0.988175i | \(-0.549000\pi\) | ||||
−0.153332 | + | 0.988175i | \(0.549000\pi\) | |||||||
\(752\) | 1.01685e7 | 0.655712 | ||||||||
\(753\) | −2.02514e7 | −1.30157 | ||||||||
\(754\) | 1.30754e7 | 0.837581 | ||||||||
\(755\) | 3.58947e6 | 0.229173 | ||||||||
\(756\) | −1.43770e7 | −0.914877 | ||||||||
\(757\) | −8.15849e6 | −0.517452 | −0.258726 | − | 0.965951i | \(-0.583303\pi\) | ||||
−0.258726 | + | 0.965951i | \(0.583303\pi\) | |||||||
\(758\) | −2.32750e7 | −1.47135 | ||||||||
\(759\) | 3.31948e6 | 0.209154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.40805e7 | −1.50731 | −0.753657 | − | 0.657268i | \(-0.771712\pi\) | ||||
−0.753657 | + | 0.657268i | \(0.771712\pi\) | |||||||
\(762\) | 1.35100e6 | 0.0842884 | ||||||||
\(763\) | 1.38760e6 | 0.0862883 | ||||||||
\(764\) | −1.29360e7 | −0.801800 | ||||||||
\(765\) | −4.63642e6 | −0.286437 | ||||||||
\(766\) | −3.14069e7 | −1.93399 | ||||||||
\(767\) | 1.56886e7 | 0.962933 | ||||||||
\(768\) | 3.23054e7 | 1.97639 | ||||||||
\(769\) | −3.57395e6 | −0.217938 | −0.108969 | − | 0.994045i | \(-0.534755\pi\) | ||||
−0.108969 | + | 0.994045i | \(0.534755\pi\) | |||||||
\(770\) | −2.53986e7 | −1.54377 | ||||||||
\(771\) | −1.73129e7 | −1.04890 | ||||||||
\(772\) | −2.03263e7 | −1.22748 | ||||||||
\(773\) | −1.38262e7 | −0.832251 | −0.416126 | − | 0.909307i | \(-0.636612\pi\) | ||||
−0.416126 | + | 0.909307i | \(0.636612\pi\) | |||||||
\(774\) | 1.44021e6 | 0.0864117 | ||||||||
\(775\) | 1.58009e7 | 0.944990 | ||||||||
\(776\) | 1.71283e7 | 1.02108 | ||||||||
\(777\) | −2.84154e6 | −0.168850 | ||||||||
\(778\) | −4.60632e7 | −2.72838 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 5.57180e7 | 3.27913 | ||||||||
\(781\) | 1.03003e6 | 0.0604260 | ||||||||
\(782\) | 7.79705e6 | 0.455946 | ||||||||
\(783\) | 9.55002e6 | 0.556672 | ||||||||
\(784\) | −2.37291e7 | −1.37877 | ||||||||
\(785\) | −5.64877e7 | −3.27175 | ||||||||
\(786\) | −1.98326e7 | −1.14505 | ||||||||
\(787\) | −2.52043e7 | −1.45057 | −0.725283 | − | 0.688451i | \(-0.758291\pi\) | ||||
−0.725283 | + | 0.688451i | \(0.758291\pi\) | |||||||
\(788\) | −3.31075e7 | −1.89938 | ||||||||
\(789\) | −3.09635e7 | −1.77075 | ||||||||
\(790\) | −3.00954e7 | −1.71567 | ||||||||
\(791\) | −1.31207e7 | −0.745615 | ||||||||
\(792\) | −4.84090e6 | −0.274229 | ||||||||
\(793\) | −2.24045e7 | −1.26518 | ||||||||
\(794\) | −4.10757e6 | −0.231224 | ||||||||
\(795\) | 3.80993e7 | 2.13796 | ||||||||
\(796\) | 7.56464e7 | 4.23161 | ||||||||
\(797\) | −3.37562e7 | −1.88238 | −0.941190 | − | 0.337877i | \(-0.890291\pi\) | ||||
−0.941190 | + | 0.337877i | \(0.890291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.70011e6 | 0.537539 | ||||||||
\(800\) | 3.47956e7 | 1.92220 | ||||||||
\(801\) | −532076. | −0.0293017 | ||||||||
\(802\) | 5.16488e7 | 2.83547 | ||||||||
\(803\) | −2.51841e7 | −1.37828 | ||||||||
\(804\) | −4.16923e6 | −0.227466 | ||||||||
\(805\) | 2.61887e6 | 0.142437 | ||||||||
\(806\) | 1.12216e7 | 0.608437 | ||||||||
\(807\) | −1.73430e7 | −0.937433 | ||||||||
\(808\) | −2.19433e7 | −1.18242 | ||||||||
\(809\) | −2.10318e7 | −1.12981 | −0.564906 | − | 0.825155i | \(-0.691088\pi\) | ||||
−0.564906 | + | 0.825155i | \(0.691088\pi\) | |||||||
\(810\) | 6.58635e7 | 3.52722 | ||||||||
\(811\) | 2.27692e7 | 1.21561 | 0.607807 | − | 0.794085i | \(-0.292050\pi\) | ||||
0.607807 | + | 0.794085i | \(0.292050\pi\) | |||||||
\(812\) | −1.09485e7 | −0.582726 | ||||||||
\(813\) | −1.13332e7 | −0.601346 | ||||||||
\(814\) | 1.34699e7 | 0.712530 | ||||||||
\(815\) | 3.07103e7 | 1.61954 | ||||||||
\(816\) | −4.81908e7 | −2.53361 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.73365e6 | −0.195097 | ||||||||
\(819\) | −758681. | −0.0395230 | ||||||||
\(820\) | 3.88716e7 | 2.01882 | ||||||||
\(821\) | −2.30273e7 | −1.19230 | −0.596149 | − | 0.802874i | \(-0.703303\pi\) | ||||
−0.596149 | + | 0.802874i | \(0.703303\pi\) | |||||||
\(822\) | −1.09175e7 | −0.563562 | ||||||||
\(823\) | −1.70408e7 | −0.876979 | −0.438490 | − | 0.898736i | \(-0.644486\pi\) | ||||
−0.438490 | + | 0.898736i | \(0.644486\pi\) | |||||||
\(824\) | 8.15542e7 | 4.18435 | ||||||||
\(825\) | 4.93184e7 | 2.52275 | ||||||||
\(826\) | −1.90520e7 | −0.971605 | ||||||||
\(827\) | −3.62225e6 | −0.184168 | −0.0920840 | − | 0.995751i | \(-0.529353\pi\) | ||||
−0.0920840 | + | 0.995751i | \(0.529353\pi\) | |||||||
\(828\) | 908028. | 0.0460281 | ||||||||
\(829\) | −1.36980e7 | −0.692261 | −0.346131 | − | 0.938186i | \(-0.612505\pi\) | ||||
−0.346131 | + | 0.938186i | \(0.612505\pi\) | |||||||
\(830\) | −6.12991e7 | −3.08858 | ||||||||
\(831\) | 8.60198e6 | 0.432112 | ||||||||
\(832\) | −2.06573e6 | −0.103458 | ||||||||
\(833\) | −2.26361e7 | −1.13029 | ||||||||
\(834\) | 4.75091e6 | 0.236517 | ||||||||
\(835\) | 1.26687e7 | 0.628805 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.19600e6 | 0.404379 | ||||||||
\(838\) | −4.18887e7 | −2.06057 | ||||||||
\(839\) | 8.15272e6 | 0.399850 | 0.199925 | − | 0.979811i | \(-0.435930\pi\) | ||||
0.199925 | + | 0.979811i | \(0.435930\pi\) | |||||||
\(840\) | −3.71946e7 | −1.81879 | ||||||||
\(841\) | −1.32385e7 | −0.645431 | ||||||||
\(842\) | 2.09049e7 | 1.01617 | ||||||||
\(843\) | −3.29537e7 | −1.59711 | ||||||||
\(844\) | −7.14807e7 | −3.45408 | ||||||||
\(845\) | 1.42858e7 | 0.688274 | ||||||||
\(846\) | 1.63833e6 | 0.0787002 | ||||||||
\(847\) | −1.80811e6 | −0.0865999 | ||||||||
\(848\) | 4.06618e7 | 1.94177 | ||||||||
\(849\) | 3.70625e7 | 1.76468 | ||||||||
\(850\) | 1.15843e8 | 5.49948 | ||||||||
\(851\) | −1.38889e6 | −0.0657420 | ||||||||
\(852\) | 2.74405e6 | 0.129507 | ||||||||
\(853\) | −3.76514e7 | −1.77178 | −0.885888 | − | 0.463899i | \(-0.846450\pi\) | ||||
−0.885888 | + | 0.463899i | \(0.846450\pi\) | |||||||
\(854\) | 2.72076e7 | 1.27657 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.21345e7 | −3.36480 | ||||||||
\(857\) | −1.18679e7 | −0.551980 | −0.275990 | − | 0.961160i | \(-0.589006\pi\) | ||||
−0.275990 | + | 0.961160i | \(0.589006\pi\) | |||||||
\(858\) | 3.50252e7 | 1.62429 | ||||||||
\(859\) | −8.63985e6 | −0.399506 | −0.199753 | − | 0.979846i | \(-0.564014\pi\) | ||||
−0.199753 | + | 0.979846i | \(0.564014\pi\) | |||||||
\(860\) | −3.61687e7 | −1.66758 | ||||||||
\(861\) | −5.15476e6 | −0.236974 | ||||||||
\(862\) | 3.28002e7 | 1.50352 | ||||||||
\(863\) | 1.39409e7 | 0.637181 | 0.318591 | − | 0.947892i | \(-0.396790\pi\) | ||||
0.318591 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(864\) | 1.80487e7 | 0.822547 | ||||||||
\(865\) | −5.81119e7 | −2.64073 | ||||||||
\(866\) | 4.53267e7 | 2.05380 | ||||||||
\(867\) | −2.26055e7 | −1.02133 | ||||||||
\(868\) | −9.39620e6 | −0.423305 | ||||||||
\(869\) | −1.30446e7 | −0.585976 | ||||||||
\(870\) | 4.49456e7 | 2.01321 | ||||||||
\(871\) | 1.70266e6 | 0.0760473 | ||||||||
\(872\) | −9.63260e6 | −0.428995 | ||||||||
\(873\) | 1.20095e6 | 0.0533322 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.10992e7 | 0.931633 | ||||||||
\(876\) | −6.70914e7 | −2.95397 | ||||||||
\(877\) | −2.92561e7 | −1.28445 | −0.642224 | − | 0.766517i | \(-0.721988\pi\) | ||||
−0.642224 | + | 0.766517i | \(0.721988\pi\) | |||||||
\(878\) | −4.02229e7 | −1.76091 | ||||||||
\(879\) | 2.90661e7 | 1.26886 | ||||||||
\(880\) | 7.67286e7 | 3.34003 | ||||||||
\(881\) | −1.44235e7 | −0.626081 | −0.313041 | − | 0.949740i | \(-0.601348\pi\) | ||||
−0.313041 | + | 0.949740i | \(0.601348\pi\) | |||||||
\(882\) | −3.82319e6 | −0.165483 | ||||||||
\(883\) | −4.94360e6 | −0.213374 | −0.106687 | − | 0.994293i | \(-0.534024\pi\) | ||||
−0.106687 | + | 0.994293i | \(0.534024\pi\) | |||||||
\(884\) | 5.67263e7 | 2.44149 | ||||||||
\(885\) | 5.39283e7 | 2.31451 | ||||||||
\(886\) | 5.96626e7 | 2.55339 | ||||||||
\(887\) | 1.32368e7 | 0.564903 | 0.282452 | − | 0.959282i | \(-0.408852\pi\) | ||||
0.282452 | + | 0.959282i | \(0.408852\pi\) | |||||||
\(888\) | 1.97258e7 | 0.839463 | ||||||||
\(889\) | 461984. | 0.0196053 | ||||||||
\(890\) | 1.93793e7 | 0.820094 | ||||||||
\(891\) | 2.85479e7 | 1.20470 | ||||||||
\(892\) | 2.68200e7 | 1.12862 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.93548e7 | −0.809924 | ||||||||
\(895\) | −2.33259e7 | −0.973375 | ||||||||
\(896\) | 1.18259e7 | 0.492114 | ||||||||
\(897\) | −3.61147e6 | −0.149866 | ||||||||
\(898\) | 2.66202e7 | 1.10159 | ||||||||
\(899\) | 6.24150e6 | 0.257567 | ||||||||
\(900\) | 1.34908e7 | 0.555177 | ||||||||
\(901\) | 3.87888e7 | 1.59182 | ||||||||
\(902\) | 2.44353e7 | 1.00001 | ||||||||
\(903\) | 4.79633e6 | 0.195744 | ||||||||
\(904\) | 9.10827e7 | 3.70693 | ||||||||
\(905\) | 3.17417e7 | 1.28828 | ||||||||
\(906\) | 6.01113e6 | 0.243297 | ||||||||
\(907\) | −7.51989e6 | −0.303524 | −0.151762 | − | 0.988417i | \(-0.548495\pi\) | ||||
−0.151762 | + | 0.988417i | \(0.548495\pi\) | |||||||
\(908\) | 9.12701e7 | 3.67379 | ||||||||
\(909\) | −1.53855e6 | −0.0617593 | ||||||||
\(910\) | 2.76327e7 | 1.10617 | ||||||||
\(911\) | −4.53248e7 | −1.80942 | −0.904710 | − | 0.426027i | \(-0.859913\pi\) | ||||
−0.904710 | + | 0.426027i | \(0.859913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.65695e7 | −1.05489 | ||||||||
\(914\) | 5.20373e7 | 2.06039 | ||||||||
\(915\) | −7.70134e7 | −3.04098 | ||||||||
\(916\) | 2.12556e7 | 0.837016 | ||||||||
\(917\) | −6.78190e6 | −0.266335 | ||||||||
\(918\) | 6.00883e7 | 2.35333 | ||||||||
\(919\) | 1.47088e7 | 0.574497 | 0.287249 | − | 0.957856i | \(-0.407259\pi\) | ||||
0.287249 | + | 0.957856i | \(0.407259\pi\) | |||||||
\(920\) | −1.81800e7 | −0.708148 | ||||||||
\(921\) | −2.82828e7 | −1.09869 | ||||||||
\(922\) | 2.69610e7 | 1.04450 | ||||||||
\(923\) | −1.12064e6 | −0.0432973 | ||||||||
\(924\) | −2.93278e7 | −1.13006 | ||||||||
\(925\) | −2.06351e7 | −0.792960 | ||||||||
\(926\) | −2.99112e7 | −1.14632 | ||||||||
\(927\) | 5.71818e6 | 0.218554 | ||||||||
\(928\) | 1.37446e7 | 0.523917 | ||||||||
\(929\) | −1.35395e7 | −0.514711 | −0.257356 | − | 0.966317i | \(-0.582851\pi\) | ||||
−0.257356 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(930\) | 3.85732e7 | 1.46244 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.01473e7 | 1.51397 | ||||||||
\(933\) | −2.60253e7 | −0.978795 | ||||||||
\(934\) | 1.85339e7 | 0.695183 | ||||||||
\(935\) | 7.31942e7 | 2.73809 | ||||||||
\(936\) | 5.26671e6 | 0.196494 | ||||||||
\(937\) | −1.21203e7 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(938\) | −2.06769e6 | −0.0767321 | ||||||||
\(939\) | −898788. | −0.0332655 | ||||||||
\(940\) | −4.11444e7 | −1.51877 | ||||||||
\(941\) | −2.61927e7 | −0.964288 | −0.482144 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482144 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(942\) | −9.45976e7 | −3.47338 | ||||||||
\(943\) | −2.51954e6 | −0.0922661 | ||||||||
\(944\) | 5.75555e7 | 2.10212 | ||||||||
\(945\) | 2.01824e7 | 0.735179 | ||||||||
\(946\) | −2.27363e7 | −0.826021 | ||||||||
\(947\) | −3.47875e7 | −1.26051 | −0.630257 | − | 0.776386i | \(-0.717051\pi\) | ||||
−0.630257 | + | 0.776386i | \(0.717051\pi\) | |||||||
\(948\) | −3.47512e7 | −1.25588 | ||||||||
\(949\) | 2.73993e7 | 0.987585 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.70268e7 | −0.610494 | ||||||||
\(952\) | −3.78678e7 | −1.35418 | ||||||||
\(953\) | −1.16268e7 | −0.414695 | −0.207347 | − | 0.978267i | \(-0.566483\pi\) | ||||
−0.207347 | + | 0.978267i | \(0.566483\pi\) | |||||||
\(954\) | 6.55136e6 | 0.233056 | ||||||||
\(955\) | 1.81595e7 | 0.644312 | ||||||||
\(956\) | −7.36477e7 | −2.60624 | ||||||||
\(957\) | 1.94812e7 | 0.687602 | ||||||||
\(958\) | 6.01865e7 | 2.11878 | ||||||||
\(959\) | −3.73330e6 | −0.131083 | ||||||||
\(960\) | −7.10077e6 | −0.248672 | ||||||||
\(961\) | −2.32726e7 | −0.812898 | ||||||||
\(962\) | −1.46547e7 | −0.510552 | ||||||||
\(963\) | −5.05772e6 | −0.175747 | ||||||||
\(964\) | −5.83634e7 | −2.02278 | ||||||||
\(965\) | 2.85341e7 | 0.986383 | ||||||||
\(966\) | 4.38570e6 | 0.151216 | ||||||||
\(967\) | −2.70316e7 | −0.929622 | −0.464811 | − | 0.885410i | \(-0.653878\pi\) | ||||
−0.464811 | + | 0.885410i | \(0.653878\pi\) | |||||||
\(968\) | 1.25518e7 | 0.430544 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.37411e7 | −1.49266 | ||||||||
\(971\) | 5.13472e6 | 0.174771 | 0.0873854 | − | 0.996175i | \(-0.472149\pi\) | ||||
0.0873854 | + | 0.996175i | \(0.472149\pi\) | |||||||
\(972\) | 1.48997e7 | 0.505840 | ||||||||
\(973\) | 1.62461e6 | 0.0550132 | ||||||||
\(974\) | 3.66754e7 | 1.23873 | ||||||||
\(975\) | −5.36565e7 | −1.80764 | ||||||||
\(976\) | −8.21934e7 | −2.76193 | ||||||||
\(977\) | 5.11922e6 | 0.171580 | 0.0857902 | − | 0.996313i | \(-0.472659\pi\) | ||||
0.0857902 | + | 0.996313i | \(0.472659\pi\) | |||||||
\(978\) | 5.14293e7 | 1.71935 | ||||||||
\(979\) | 8.39978e6 | 0.280099 | ||||||||
\(980\) | 9.60140e7 | 3.19352 | ||||||||
\(981\) | −675390. | −0.0224069 | ||||||||
\(982\) | −4.39434e7 | −1.45417 | ||||||||
\(983\) | −3.30087e7 | −1.08954 | −0.544771 | − | 0.838585i | \(-0.683384\pi\) | ||||
−0.544771 | + | 0.838585i | \(0.683384\pi\) | |||||||
\(984\) | 3.57840e7 | 1.17815 | ||||||||
\(985\) | 4.64764e7 | 1.52631 | ||||||||
\(986\) | 4.57590e7 | 1.49894 | ||||||||
\(987\) | 5.45614e6 | 0.178276 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.34435e6 | 0.0762134 | ||||||||
\(990\) | 1.23624e7 | 0.400879 | ||||||||
\(991\) | 3.54462e7 | 1.14653 | 0.573265 | − | 0.819370i | \(-0.305676\pi\) | ||||
0.573265 | + | 0.819370i | \(0.305676\pi\) | |||||||
\(992\) | 1.17959e7 | 0.380585 | ||||||||
\(993\) | 3.35685e7 | 1.08034 | ||||||||
\(994\) | 1.36088e6 | 0.0436873 | ||||||||
\(995\) | −1.06192e8 | −3.40044 | ||||||||
\(996\) | −7.07822e7 | −2.26087 | ||||||||
\(997\) | 4.51197e7 | 1.43757 | 0.718784 | − | 0.695233i | \(-0.244699\pi\) | ||||
0.718784 | + | 0.695233i | \(0.244699\pi\) | |||||||
\(998\) | −5.01121e7 | −1.59264 | ||||||||
\(999\) | −1.07035e7 | −0.339322 |
(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 | 361.6.a.d.1.2 | 2 | ||
19.18 | odd | 2 | 19.6.a.c.1.1 | ✓ | 2 | ||
57.56 | even | 2 | 171.6.a.f.1.2 | 2 | |||
76.75 | even | 2 | 304.6.a.g.1.1 | 2 | |||
95.94 | odd | 2 | 475.6.a.d.1.2 | 2 | |||
133.132 | even | 2 | 931.6.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.6.a.c.1.1 | ✓ | 2 | 19.18 | odd | 2 | ||
171.6.a.f.1.2 | 2 | 57.56 | even | 2 | |||
304.6.a.g.1.1 | 2 | 76.75 | even | 2 | |||
361.6.a.d.1.2 | 2 | 1.1 | even | 1 | trivial | ||
475.6.a.d.1.2 | 2 | 95.94 | odd | 2 | |||
931.6.a.c.1.1 | 2 | 133.132 | even | 2 |