Newspace parameters
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
Defining polynomial: | \(x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + 33122051904 x^{8} - 6210397064704 x^{7} - 2735256748800 x^{6} + 288860762071040 x^{5} - 34502173230080 x^{4} - 5633463408885760 x^{3} + 4719471961341952 x^{2} + 37636623107620864 x - 58321181718347776\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.39686\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.396855 | −0.0350774 | −0.0175387 | − | 0.999846i | \(-0.505583\pi\) | ||||
−0.0175387 | + | 0.999846i | \(0.505583\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −127.843 | −0.998770 | ||||||||
\(5\) | −247.233 | −0.884527 | −0.442264 | − | 0.896885i | \(-0.645824\pi\) | ||||
−0.442264 | + | 0.896885i | \(0.645824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −652.929 | −0.719487 | −0.359743 | − | 0.933051i | \(-0.617136\pi\) | ||||
−0.359743 | + | 0.933051i | \(0.617136\pi\) | |||||||
\(8\) | 101.532 | 0.0701116 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 98.1157 | 0.0310269 | ||||||||
\(11\) | 2477.11 | 0.561140 | 0.280570 | − | 0.959834i | \(-0.409476\pi\) | ||||
0.280570 | + | 0.959834i | \(0.409476\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9417.61 | 1.18888 | 0.594442 | − | 0.804139i | \(-0.297373\pi\) | ||||
0.594442 | + | 0.804139i | \(0.297373\pi\) | |||||||
\(14\) | 259.118 | 0.0252377 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16323.5 | 0.996310 | ||||||||
\(17\) | −12577.2 | −0.620889 | −0.310444 | − | 0.950592i | \(-0.600478\pi\) | ||||
−0.310444 | + | 0.950592i | \(0.600478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −41390.0 | −1.38439 | −0.692194 | − | 0.721711i | \(-0.743356\pi\) | ||||
−0.692194 | + | 0.721711i | \(0.743356\pi\) | |||||||
\(20\) | 31606.9 | 0.883439 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −983.055 | −0.0196833 | ||||||||
\(23\) | 59781.4 | 1.02452 | 0.512258 | − | 0.858832i | \(-0.328809\pi\) | ||||
0.512258 | + | 0.858832i | \(0.328809\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17000.9 | −0.217611 | ||||||||
\(26\) | −3737.43 | −0.0417029 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 83472.1 | 0.718602 | ||||||||
\(29\) | −212559. | −1.61840 | −0.809199 | − | 0.587534i | \(-0.800099\pi\) | ||||
−0.809199 | + | 0.587534i | \(0.800099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7793.74 | −0.0469872 | −0.0234936 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234936 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(32\) | −19474.2 | −0.105060 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4991.34 | 0.0217792 | ||||||||
\(35\) | 161426. | 0.636406 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −447343. | −1.45189 | −0.725946 | − | 0.687751i | \(-0.758598\pi\) | ||||
−0.725946 | + | 0.687751i | \(0.758598\pi\) | |||||||
\(38\) | 16425.8 | 0.0485607 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −25102.2 | −0.0620156 | ||||||||
\(41\) | −14016.1 | −0.0317602 | −0.0158801 | − | 0.999874i | \(-0.505055\pi\) | ||||
−0.0158801 | + | 0.999874i | \(0.505055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −896369. | −1.71928 | −0.859641 | − | 0.510899i | \(-0.829313\pi\) | ||||
−0.859641 | + | 0.510899i | \(0.829313\pi\) | |||||||
\(44\) | −316680. | −0.560450 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23724.6 | −0.0359373 | ||||||||
\(47\) | −21326.5 | −0.0299624 | −0.0149812 | − | 0.999888i | \(-0.504769\pi\) | ||||
−0.0149812 | + | 0.999888i | \(0.504769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −397227. | −0.482339 | ||||||||
\(50\) | 6746.89 | 0.00763324 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.20397e6 | −1.18742 | ||||||||
\(53\) | −910896. | −0.840433 | −0.420217 | − | 0.907424i | \(-0.638046\pi\) | ||||
−0.420217 | + | 0.907424i | \(0.638046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −612424. | −0.496344 | ||||||||
\(56\) | −66293.5 | −0.0504444 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 84355.0 | 0.0567692 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 810282. | 0.457069 | 0.228535 | − | 0.973536i | \(-0.426607\pi\) | ||||
0.228535 | + | 0.973536i | \(0.426607\pi\) | |||||||
\(62\) | 3092.99 | 0.00164819 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.08169e6 | −0.992625 | ||||||||
\(65\) | −2.32834e6 | −1.05160 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.83166e6 | −1.55641 | −0.778207 | − | 0.628007i | \(-0.783871\pi\) | ||||
−0.778207 | + | 0.628007i | \(0.783871\pi\) | |||||||
\(68\) | 1.60791e6 | 0.620125 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −64062.6 | −0.0223234 | ||||||||
\(71\) | 3.35674e6 | 1.11305 | 0.556524 | − | 0.830832i | \(-0.312135\pi\) | ||||
0.556524 | + | 0.830832i | \(0.312135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 461542. | 0.138861 | 0.0694306 | − | 0.997587i | \(-0.477882\pi\) | ||||
0.0694306 | + | 0.997587i | \(0.477882\pi\) | |||||||
\(74\) | 177530. | 0.0509286 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.29140e6 | 1.38269 | ||||||||
\(77\) | −1.61738e6 | −0.403733 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.37060e6 | −0.312762 | −0.156381 | − | 0.987697i | \(-0.549983\pi\) | ||||
−0.156381 | + | 0.987697i | \(0.549983\pi\) | |||||||
\(80\) | −4.03572e6 | −0.881264 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5562.36 | 0.00111407 | ||||||||
\(83\) | 7.63422e6 | 1.46552 | 0.732759 | − | 0.680488i | \(-0.238232\pi\) | ||||
0.732759 | + | 0.680488i | \(0.238232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.10951e6 | 0.549193 | ||||||||
\(86\) | 355729. | 0.0603079 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 251507. | 0.0393424 | ||||||||
\(89\) | 5.26057e6 | 0.790984 | 0.395492 | − | 0.918469i | \(-0.370574\pi\) | ||||
0.395492 | + | 0.918469i | \(0.370574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.14903e6 | −0.855386 | ||||||||
\(92\) | −7.64260e6 | −1.02326 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8463.51 | 0.00105100 | ||||||||
\(95\) | 1.02330e7 | 1.22453 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.23173e6 | −1.02703 | −0.513514 | − | 0.858081i | \(-0.671657\pi\) | ||||
−0.513514 | + | 0.858081i | \(0.671657\pi\) | |||||||
\(98\) | 157641. | 0.0169192 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.17344e6 | 0.217344 | ||||||||
\(101\) | −4.85554e6 | −0.468935 | −0.234468 | − | 0.972124i | \(-0.575335\pi\) | ||||
−0.234468 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.34436e6 | −0.391738 | −0.195869 | − | 0.980630i | \(-0.562753\pi\) | ||||
−0.195869 | + | 0.980630i | \(0.562753\pi\) | |||||||
\(104\) | 956193. | 0.0833545 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 361494. | 0.0294802 | ||||||||
\(107\) | 6.60510e6 | 0.521238 | 0.260619 | − | 0.965442i | \(-0.416073\pi\) | ||||
0.260619 | + | 0.965442i | \(0.416073\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.74784e6 | −0.203235 | −0.101617 | − | 0.994824i | \(-0.532402\pi\) | ||||
−0.101617 | + | 0.994824i | \(0.532402\pi\) | |||||||
\(110\) | 243044. | 0.0174104 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.06581e7 | −0.716832 | ||||||||
\(113\) | 3.08697e6 | 0.201260 | 0.100630 | − | 0.994924i | \(-0.467914\pi\) | ||||
0.100630 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.47799e7 | −0.906212 | ||||||||
\(116\) | 2.71740e7 | 1.61641 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −81505.7 | −0.00456669 | ||||||||
\(119\) | 8.21204e6 | 0.446721 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.33511e7 | −0.685122 | ||||||||
\(122\) | −321565. | −0.0160328 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 996371. | 0.0469294 | ||||||||
\(125\) | 2.35182e7 | 1.07701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.02662e7 | 0.444731 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(128\) | 3.31883e6 | 0.139878 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 924016. | 0.0368874 | ||||||||
\(131\) | 3.04995e7 | 1.18534 | 0.592671 | − | 0.805445i | \(-0.298073\pi\) | ||||
0.592671 | + | 0.805445i | \(0.298073\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.70247e7 | 0.996049 | ||||||||
\(134\) | 1.52062e6 | 0.0545950 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.27700e6 | −0.0435315 | ||||||||
\(137\) | −2.18105e7 | −0.724676 | −0.362338 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362338 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.59222e7 | 1.76617 | 0.883085 | − | 0.469213i | \(-0.155462\pi\) | ||||
0.883085 | + | 0.469213i | \(0.155462\pi\) | |||||||
\(140\) | −2.06370e7 | −0.635623 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.33214e6 | −0.0390428 | ||||||||
\(143\) | 2.33285e7 | 0.667130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.25515e7 | 1.43152 | ||||||||
\(146\) | −183165. | −0.00487089 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.71894e7 | 1.45011 | ||||||||
\(149\) | −4.25096e7 | −1.05277 | −0.526387 | − | 0.850245i | \(-0.676454\pi\) | ||||
−0.526387 | + | 0.850245i | \(0.676454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.69136e7 | −0.636140 | −0.318070 | − | 0.948067i | \(-0.603035\pi\) | ||||
−0.318070 | + | 0.948067i | \(0.603035\pi\) | |||||||
\(152\) | −4.20243e6 | −0.0970617 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 641865. | 0.0141619 | ||||||||
\(155\) | 1.92687e6 | 0.0415615 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.09453e7 | −1.25687 | −0.628436 | − | 0.777861i | \(-0.716305\pi\) | ||||
−0.628436 | + | 0.777861i | \(0.716305\pi\) | |||||||
\(158\) | 543928. | 0.0109709 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.81467e6 | 0.0929281 | ||||||||
\(161\) | −3.90330e7 | −0.737126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.43192e7 | 0.439839 | 0.219919 | − | 0.975518i | \(-0.429421\pi\) | ||||
0.219919 | + | 0.975518i | \(0.429421\pi\) | |||||||
\(164\) | 1.79185e6 | 0.0317212 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.02968e6 | −0.0514066 | ||||||||
\(167\) | −2.18099e7 | −0.362366 | −0.181183 | − | 0.983449i | \(-0.557993\pi\) | ||||
−0.181183 | + | 0.983449i | \(0.557993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.59429e7 | 0.413443 | ||||||||
\(170\) | −1.23402e6 | −0.0192643 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.14594e8 | 1.71717 | ||||||||
\(173\) | −7.57905e7 | −1.11289 | −0.556446 | − | 0.830884i | \(-0.687836\pi\) | ||||
−0.556446 | + | 0.830884i | \(0.687836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.11004e7 | 0.156568 | ||||||||
\(176\) | 4.04353e7 | 0.559070 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.08769e6 | −0.0277457 | ||||||||
\(179\) | 1.14237e6 | 0.0148874 | 0.00744372 | − | 0.999972i | \(-0.497631\pi\) | ||||
0.00744372 | + | 0.999972i | \(0.497631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.35346e8 | 1.69656 | 0.848280 | − | 0.529548i | \(-0.177638\pi\) | ||||
0.848280 | + | 0.529548i | \(0.177638\pi\) | |||||||
\(182\) | 2.44028e6 | 0.0300047 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.06975e6 | 0.0718304 | ||||||||
\(185\) | 1.10598e8 | 1.28424 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.11552e7 | −0.348406 | ||||||||
\(188\) | 2.72643e6 | 0.0299255 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.06101e6 | −0.0429533 | ||||||||
\(191\) | −1.11443e8 | −1.15727 | −0.578637 | − | 0.815585i | \(-0.696415\pi\) | ||||
−0.578637 | + | 0.815585i | \(0.696415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.58821e7 | −0.459402 | −0.229701 | − | 0.973261i | \(-0.573775\pi\) | ||||
−0.229701 | + | 0.973261i | \(0.573775\pi\) | |||||||
\(194\) | 3.66366e6 | 0.0360254 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.07824e7 | 0.481745 | ||||||||
\(197\) | −1.22654e8 | −1.14301 | −0.571504 | − | 0.820600i | \(-0.693640\pi\) | ||||
−0.571504 | + | 0.820600i | \(0.693640\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.02506e7 | −0.0922072 | −0.0461036 | − | 0.998937i | \(-0.514680\pi\) | ||||
−0.0461036 | + | 0.998937i | \(0.514680\pi\) | |||||||
\(200\) | −1.72614e6 | −0.0152571 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.92695e6 | 0.0164490 | ||||||||
\(203\) | 1.38786e8 | 1.16442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46524e6 | 0.0280928 | ||||||||
\(206\) | 1.72408e6 | 0.0137411 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.53729e8 | 1.18450 | ||||||||
\(209\) | −1.02528e8 | −0.776836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.63127e8 | −1.19547 | −0.597734 | − | 0.801694i | \(-0.703932\pi\) | ||||
−0.597734 | + | 0.801694i | \(0.703932\pi\) | |||||||
\(212\) | 1.16451e8 | 0.839399 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.62127e6 | −0.0182837 | ||||||||
\(215\) | 2.21612e8 | 1.52075 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.08876e6 | 0.0338067 | ||||||||
\(218\) | 1.09049e6 | 0.00712895 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.82938e7 | 0.495733 | ||||||||
\(221\) | −1.18448e8 | −0.738164 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.16056e8 | 1.30466 | 0.652332 | − | 0.757933i | \(-0.273791\pi\) | ||||
0.652332 | + | 0.757933i | \(0.273791\pi\) | |||||||
\(224\) | 1.27153e7 | 0.0755890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.22508e6 | −0.00705968 | ||||||||
\(227\) | 9.46539e7 | 0.537091 | 0.268546 | − | 0.963267i | \(-0.413457\pi\) | ||||
0.268546 | + | 0.963267i | \(0.413457\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.62090e7 | 0.309301 | 0.154651 | − | 0.987969i | \(-0.450575\pi\) | ||||
0.154651 | + | 0.987969i | \(0.450575\pi\) | |||||||
\(230\) | 5.86549e6 | 0.0317876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.15816e7 | −0.113469 | ||||||||
\(233\) | −3.12602e8 | −1.61900 | −0.809500 | − | 0.587120i | \(-0.800261\pi\) | ||||
−0.809500 | + | 0.587120i | \(0.800261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.27260e6 | 0.0265025 | ||||||||
\(236\) | −2.62562e7 | −0.130029 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.25899e6 | −0.0156698 | ||||||||
\(239\) | −3.24955e8 | −1.53968 | −0.769840 | − | 0.638237i | \(-0.779664\pi\) | ||||
−0.769840 | + | 0.638237i | \(0.779664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.55841e8 | 1.17737 | 0.588683 | − | 0.808364i | \(-0.299647\pi\) | ||||
0.588683 | + | 0.808364i | \(0.299647\pi\) | |||||||
\(242\) | 5.29845e6 | 0.0240323 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.03589e8 | −0.456507 | ||||||||
\(245\) | 9.82075e7 | 0.426642 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.89795e8 | −1.64588 | ||||||||
\(248\) | −791317. | −0.00329435 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.33334e6 | −0.0377787 | ||||||||
\(251\) | −1.47199e8 | −0.587552 | −0.293776 | − | 0.955874i | \(-0.594912\pi\) | ||||
−0.293776 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.48085e8 | 0.574897 | ||||||||
\(254\) | −4.07420e6 | −0.0156000 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.65139e8 | 0.987718 | ||||||||
\(257\) | 3.26518e8 | 1.19989 | 0.599944 | − | 0.800042i | \(-0.295190\pi\) | ||||
0.599944 | + | 0.800042i | \(0.295190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.92083e8 | 1.04462 | ||||||||
\(260\) | 2.97661e8 | 1.05031 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.21039e7 | −0.0415787 | ||||||||
\(263\) | 1.12281e8 | 0.380592 | 0.190296 | − | 0.981727i | \(-0.439055\pi\) | ||||
0.190296 | + | 0.981727i | \(0.439055\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.25203e8 | 0.743386 | ||||||||
\(266\) | −1.07249e7 | −0.0349388 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.89849e8 | 1.55450 | ||||||||
\(269\) | 5.12589e7 | 0.160560 | 0.0802798 | − | 0.996772i | \(-0.474419\pi\) | ||||
0.0802798 | + | 0.996772i | \(0.474419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.28326e8 | −1.61254 | −0.806269 | − | 0.591549i | \(-0.798516\pi\) | ||||
−0.806269 | + | 0.591549i | \(0.798516\pi\) | |||||||
\(272\) | −2.05305e8 | −0.618598 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.65561e6 | 0.0254197 | ||||||||
\(275\) | −4.21131e7 | −0.122110 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.48700e7 | −0.126846 | −0.0634230 | − | 0.997987i | \(-0.520202\pi\) | ||||
−0.0634230 | + | 0.997987i | \(0.520202\pi\) | |||||||
\(278\) | −2.21930e7 | −0.0619526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.63899e7 | 0.0446194 | ||||||||
\(281\) | 5.27134e8 | 1.41726 | 0.708629 | − | 0.705581i | \(-0.249314\pi\) | ||||
0.708629 | + | 0.705581i | \(0.249314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.08524e8 | 0.809163 | 0.404582 | − | 0.914502i | \(-0.367417\pi\) | ||||
0.404582 | + | 0.914502i | \(0.367417\pi\) | |||||||
\(284\) | −4.29134e8 | −1.11168 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.25804e6 | −0.0234012 | ||||||||
\(287\) | 9.15152e6 | 0.0228511 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.52152e8 | −0.614497 | ||||||||
\(290\) | −2.08553e7 | −0.0502139 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.90047e7 | −0.138690 | ||||||||
\(293\) | 8.22037e8 | 1.90921 | 0.954607 | − | 0.297869i | \(-0.0962760\pi\) | ||||
0.954607 | + | 0.297869i | \(0.0962760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.07764e7 | −0.115156 | ||||||||
\(296\) | −4.54198e7 | −0.101795 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.68702e7 | 0.0369285 | ||||||||
\(299\) | 5.62998e8 | 1.21803 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.85265e8 | 1.23700 | ||||||||
\(302\) | 1.06808e7 | 0.0223141 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.75632e8 | −1.37928 | ||||||||
\(305\) | −2.00328e8 | −0.404290 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.21225e8 | 0.239116 | 0.119558 | − | 0.992827i | \(-0.461852\pi\) | ||||
0.119558 | + | 0.992827i | \(0.461852\pi\) | |||||||
\(308\) | 2.06770e8 | 0.403236 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −764688. | −0.00145787 | ||||||||
\(311\) | 4.99117e8 | 0.940894 | 0.470447 | − | 0.882428i | \(-0.344093\pi\) | ||||
0.470447 | + | 0.882428i | \(0.344093\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.71603e8 | 1.23796 | 0.618981 | − | 0.785406i | \(-0.287546\pi\) | ||||
0.618981 | + | 0.785406i | \(0.287546\pi\) | |||||||
\(314\) | 2.41865e7 | 0.0440878 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.75220e8 | 0.312377 | ||||||||
\(317\) | 7.55861e8 | 1.33271 | 0.666353 | − | 0.745636i | \(-0.267854\pi\) | ||||
0.666353 | + | 0.745636i | \(0.267854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.26531e8 | −0.908149 | ||||||||
\(320\) | 5.14661e8 | 0.878004 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.54905e7 | 0.0258564 | ||||||||
\(323\) | 5.20572e8 | 0.859552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.60108e8 | −0.258714 | ||||||||
\(326\) | −9.65122e6 | −0.0154284 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.42309e6 | −0.00222676 | ||||||||
\(329\) | 1.39247e7 | 0.0215575 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.06940e7 | 0.107148 | 0.0535740 | − | 0.998564i | \(-0.482939\pi\) | ||||
0.0535740 | + | 0.998564i | \(0.482939\pi\) | |||||||
\(332\) | −9.75978e8 | −1.46372 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.65539e6 | 0.0127108 | ||||||||
\(335\) | 9.47313e8 | 1.37669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.96987e8 | −0.992020 | −0.496010 | − | 0.868317i | \(-0.665202\pi\) | ||||
−0.496010 | + | 0.868317i | \(0.665202\pi\) | |||||||
\(338\) | −1.02956e7 | −0.0145025 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.97527e8 | −0.548518 | ||||||||
\(341\) | −1.93060e7 | −0.0263664 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.97076e8 | 1.06652 | ||||||||
\(344\) | −9.10105e7 | −0.120542 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00778e7 | 0.0390374 | ||||||||
\(347\) | 3.13443e8 | 0.402721 | 0.201361 | − | 0.979517i | \(-0.435464\pi\) | ||||
0.201361 | + | 0.979517i | \(0.435464\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.69924e8 | 0.843599 | 0.421800 | − | 0.906689i | \(-0.361399\pi\) | ||||
0.421800 | + | 0.906689i | \(0.361399\pi\) | |||||||
\(350\) | −4.40524e6 | −0.00549201 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.82399e7 | −0.0589531 | ||||||||
\(353\) | 1.16673e9 | 1.41175 | 0.705875 | − | 0.708336i | \(-0.250554\pi\) | ||||
0.705875 | + | 0.708336i | \(0.250554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.29897e8 | −0.984521 | ||||||||
\(356\) | −6.72525e8 | −0.790011 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −453354. | −0.000522212 0 | ||||||||
\(359\) | −1.70302e9 | −1.94263 | −0.971316 | − | 0.237794i | \(-0.923576\pi\) | ||||
−0.971316 | + | 0.237794i | \(0.923576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.19262e8 | 0.916532 | ||||||||
\(362\) | −5.37126e7 | −0.0595109 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.86108e8 | 0.854333 | ||||||||
\(365\) | −1.14108e8 | −0.122827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.54527e8 | 1.00799 | 0.503996 | − | 0.863706i | \(-0.331863\pi\) | ||||
0.503996 | + | 0.863706i | \(0.331863\pi\) | |||||||
\(368\) | 9.75845e8 | 1.02074 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.38914e7 | −0.0450477 | ||||||||
\(371\) | 5.94751e8 | 0.604681 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.42139e9 | 1.41819 | 0.709093 | − | 0.705115i | \(-0.249105\pi\) | ||||
0.709093 | + | 0.705115i | \(0.249105\pi\) | |||||||
\(374\) | 1.23641e7 | 0.0122212 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.16533e6 | −0.00210071 | ||||||||
\(377\) | −2.00179e9 | −1.92409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.98909e8 | 0.282035 | 0.141017 | − | 0.990007i | \(-0.454963\pi\) | ||||
0.141017 | + | 0.990007i | \(0.454963\pi\) | |||||||
\(380\) | −1.30821e9 | −1.22302 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.42268e7 | 0.0405941 | ||||||||
\(383\) | 2.63974e8 | 0.240086 | 0.120043 | − | 0.992769i | \(-0.461697\pi\) | ||||
0.120043 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.99869e8 | 0.357113 | ||||||||
\(386\) | 1.82086e7 | 0.0161146 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.18021e9 | 1.02576 | ||||||||
\(389\) | 1.71619e9 | 1.47823 | 0.739116 | − | 0.673578i | \(-0.235243\pi\) | ||||
0.739116 | + | 0.673578i | \(0.235243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.51885e8 | −0.636111 | ||||||||
\(392\) | −4.03314e7 | −0.0338175 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.86758e7 | 0.0400937 | ||||||||
\(395\) | 3.38856e8 | 0.276647 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.74825e8 | 0.461072 | 0.230536 | − | 0.973064i | \(-0.425952\pi\) | ||||
0.230536 | + | 0.973064i | \(0.425952\pi\) | |||||||
\(398\) | 4.06802e6 | 0.00323439 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.77515e8 | −0.216808 | ||||||||
\(401\) | 1.14785e9 | 0.888953 | 0.444476 | − | 0.895791i | \(-0.353390\pi\) | ||||
0.444476 | + | 0.895791i | \(0.353390\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.33984e7 | −0.0558623 | ||||||||
\(404\) | 6.20745e8 | 0.468358 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.50778e7 | −0.0408447 | ||||||||
\(407\) | −1.10812e9 | −0.814715 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.45907e6 | −0.00322265 | −0.00161132 | − | 0.999999i | \(-0.500513\pi\) | ||||
−0.00161132 | + | 0.999999i | \(0.500513\pi\) | |||||||
\(410\) | −1.37520e6 | −0.000985422 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.55394e8 | 0.391256 | ||||||||
\(413\) | −1.34098e8 | −0.0936692 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.88743e9 | −1.29629 | ||||||||
\(416\) | −1.83401e8 | −0.124904 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.06887e7 | 0.0272494 | ||||||||
\(419\) | −2.72506e9 | −1.80978 | −0.904892 | − | 0.425642i | \(-0.860048\pi\) | ||||
−0.904892 | + | 0.425642i | \(0.860048\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.98552e9 | −1.29684 | −0.648420 | − | 0.761283i | \(-0.724570\pi\) | ||||
−0.648420 | + | 0.761283i | \(0.724570\pi\) | |||||||
\(422\) | 6.47379e7 | 0.0419339 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.24855e7 | −0.0589241 | ||||||||
\(425\) | 2.13824e8 | 0.135112 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.29057e8 | −0.328855 | ||||||||
\(428\) | −8.44413e8 | −0.520597 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.79478e7 | −0.0533440 | ||||||||
\(431\) | 8.94337e8 | 0.538060 | 0.269030 | − | 0.963132i | \(-0.413297\pi\) | ||||
0.269030 | + | 0.963132i | \(0.413297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.81913e9 | −1.66881 | −0.834405 | − | 0.551152i | \(-0.814188\pi\) | ||||
−0.834405 | + | 0.551152i | \(0.814188\pi\) | |||||||
\(434\) | −2.01950e6 | −0.00118585 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.51290e8 | 0.202985 | ||||||||
\(437\) | −2.47435e9 | −1.41833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.50706e9 | 0.850166 | 0.425083 | − | 0.905154i | \(-0.360245\pi\) | ||||
0.425083 | + | 0.905154i | \(0.360245\pi\) | |||||||
\(440\) | −6.21809e7 | −0.0347995 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.70065e7 | 0.0258929 | ||||||||
\(443\) | −1.30737e9 | −0.714471 | −0.357235 | − | 0.934014i | \(-0.616281\pi\) | ||||
−0.357235 | + | 0.934014i | \(0.616281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.30059e9 | −0.699647 | ||||||||
\(446\) | −8.57428e7 | −0.0457642 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.35919e9 | 0.714181 | ||||||||
\(449\) | 2.59024e9 | 1.35045 | 0.675223 | − | 0.737613i | \(-0.264047\pi\) | ||||
0.675223 | + | 0.737613i | \(0.264047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.47195e7 | −0.0178219 | ||||||||
\(452\) | −3.94646e8 | −0.201012 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.75639e7 | −0.0188397 | ||||||||
\(455\) | 1.52024e9 | 0.756612 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00834e9 | −1.47442 | −0.737208 | − | 0.675666i | \(-0.763856\pi\) | ||||
−0.737208 | + | 0.675666i | \(0.763856\pi\) | |||||||
\(458\) | −2.23068e7 | −0.0108495 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.88950e9 | 0.905097 | ||||||||
\(461\) | −1.29563e9 | −0.615926 | −0.307963 | − | 0.951398i | \(-0.599647\pi\) | ||||
−0.307963 | + | 0.951398i | \(0.599647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.89028e7 | 0.0369453 | 0.0184726 | − | 0.999829i | \(-0.494120\pi\) | ||||
0.0184726 | + | 0.999829i | \(0.494120\pi\) | |||||||
\(464\) | −3.46971e9 | −1.61243 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.24058e8 | 0.0567903 | ||||||||
\(467\) | 1.97263e9 | 0.896264 | 0.448132 | − | 0.893967i | \(-0.352089\pi\) | ||||
0.448132 | + | 0.893967i | \(0.352089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.50180e9 | 1.11982 | ||||||||
\(470\) | −2.09246e6 | −0.000929639 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.08526e7 | 0.00912775 | ||||||||
\(473\) | −2.22041e9 | −0.964758 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.03667e8 | 0.301259 | ||||||||
\(476\) | −1.04985e9 | −0.446172 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.28960e8 | 0.0540080 | ||||||||
\(479\) | −8.20556e7 | −0.0341141 | −0.0170571 | − | 0.999855i | \(-0.505430\pi\) | ||||
−0.0170571 | + | 0.999855i | \(0.505430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.21290e9 | −1.72613 | ||||||||
\(482\) | −1.01532e8 | −0.0412989 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.70684e9 | 0.684279 | ||||||||
\(485\) | 2.28239e9 | 0.908434 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.81731e9 | 1.10531 | 0.552655 | − | 0.833410i | \(-0.313615\pi\) | ||||
0.552655 | + | 0.833410i | \(0.313615\pi\) | |||||||
\(488\) | 8.22699e7 | 0.0320458 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.89742e7 | −0.0149655 | ||||||||
\(491\) | 4.34251e9 | 1.65560 | 0.827800 | − | 0.561023i | \(-0.189592\pi\) | ||||
0.827800 | + | 0.561023i | \(0.189592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.67340e9 | 1.00485 | ||||||||
\(494\) | 1.54692e8 | 0.0577330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27221e8 | −0.0468138 | ||||||||
\(497\) | −2.19171e9 | −0.800823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.81881e9 | −1.01558 | −0.507789 | − | 0.861481i | \(-0.669537\pi\) | ||||
−0.507789 | + | 0.861481i | \(0.669537\pi\) | |||||||
\(500\) | −3.00663e9 | −1.07569 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.84167e7 | 0.0206098 | ||||||||
\(503\) | −3.80145e9 | −1.33187 | −0.665933 | − | 0.746011i | \(-0.731967\pi\) | ||||
−0.665933 | + | 0.746011i | \(0.731967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.20045e9 | 0.414786 | ||||||||
\(506\) | −5.87684e7 | −0.0201659 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.31246e9 | −0.444184 | ||||||||
\(509\) | −1.38927e9 | −0.466956 | −0.233478 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233478 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.01354e8 | −0.0999089 | ||||||||
\(512\) | −5.30032e8 | −0.174525 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.29580e8 | −0.0420889 | ||||||||
\(515\) | 1.07407e9 | 0.346503 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.28280e7 | −0.0168131 | ||||||||
\(518\) | −1.15915e8 | −0.0366425 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.36402e8 | −0.0737293 | ||||||||
\(521\) | 2.67044e9 | 0.827277 | 0.413639 | − | 0.910441i | \(-0.364258\pi\) | ||||
0.413639 | + | 0.910441i | \(0.364258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.60473e8 | 0.0796173 | 0.0398086 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398086 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(524\) | −3.89914e9 | −1.18388 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.45592e7 | −0.0133502 | ||||||||
\(527\) | 9.80236e7 | 0.0291738 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.68991e8 | 0.0496327 | ||||||||
\(530\) | −8.93732e7 | −0.0260760 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.45491e9 | −0.994824 | ||||||||
\(533\) | −1.31998e8 | −0.0377592 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.63300e9 | −0.461049 | ||||||||
\(536\) | −3.89038e8 | −0.109123 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.03424e7 | −0.00563201 | ||||||||
\(539\) | −9.83975e8 | −0.270660 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.32970e7 | −0.0253324 | −0.0126662 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126662 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(542\) | 2.09669e8 | 0.0565636 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.44932e8 | 0.0652303 | ||||||||
\(545\) | 6.79356e8 | 0.179767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.23723e9 | 1.62943 | 0.814716 | − | 0.579861i | \(-0.196893\pi\) | ||||
0.814716 | + | 0.579861i | \(0.196893\pi\) | |||||||
\(548\) | 2.78831e9 | 0.723784 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.67128e7 | 0.00428332 | ||||||||
\(551\) | 8.79780e9 | 2.24049 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.94902e8 | 0.225028 | ||||||||
\(554\) | 1.78069e7 | 0.00444943 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.14923e9 | −1.76400 | ||||||||
\(557\) | −1.77646e9 | −0.435574 | −0.217787 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217787 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.44166e9 | −2.04403 | ||||||||
\(560\) | 2.63504e9 | 0.634058 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.09196e8 | −0.0497137 | ||||||||
\(563\) | −2.36725e9 | −0.559067 | −0.279534 | − | 0.960136i | \(-0.590180\pi\) | ||||
−0.279534 | + | 0.960136i | \(0.590180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.63200e8 | −0.178020 | ||||||||
\(566\) | −1.22439e8 | −0.0283833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.40818e8 | 0.0780375 | ||||||||
\(569\) | 4.20570e9 | 0.957073 | 0.478536 | − | 0.878068i | \(-0.341167\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.59664e9 | 1.25806 | 0.629029 | − | 0.777382i | \(-0.283453\pi\) | ||||
0.629029 | + | 0.777382i | \(0.283453\pi\) | |||||||
\(572\) | −2.98237e9 | −0.666309 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.63183e6 | −0.000801556 0 | ||||||||
\(575\) | −1.01634e9 | −0.222946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.81070e9 | −0.825828 | −0.412914 | − | 0.910770i | \(-0.635489\pi\) | ||||
−0.412914 | + | 0.910770i | \(0.635489\pi\) | |||||||
\(578\) | 1.00068e8 | 0.0215549 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.71831e9 | −1.42976 | ||||||||
\(581\) | −4.98460e9 | −1.05442 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.25639e9 | −0.471601 | ||||||||
\(584\) | 4.68615e7 | 0.00973579 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26230e8 | −0.0669702 | ||||||||
\(587\) | −1.29560e9 | −0.264386 | −0.132193 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132193 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22583e8 | 0.0650486 | ||||||||
\(590\) | 2.01509e7 | 0.00403936 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.30222e9 | −1.44654 | ||||||||
\(593\) | −3.30125e9 | −0.650111 | −0.325055 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325055 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.03029e9 | −0.395137 | ||||||||
\(596\) | 5.43453e9 | 1.05148 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.23429e8 | −0.0427253 | ||||||||
\(599\) | −3.03218e9 | −0.576448 | −0.288224 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288224 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.17671e9 | 0.596922 | 0.298461 | − | 0.954422i | \(-0.403527\pi\) | ||||
0.298461 | + | 0.954422i | \(0.403527\pi\) | |||||||
\(602\) | −2.32266e8 | −0.0433908 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.44071e9 | 0.635358 | ||||||||
\(605\) | 3.30083e9 | 0.606009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.80510e9 | 0.509083 | 0.254541 | − | 0.967062i | \(-0.418075\pi\) | ||||
0.254541 | + | 0.967062i | \(0.418075\pi\) | |||||||
\(608\) | 8.06039e8 | 0.145443 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.95014e7 | 0.0141814 | ||||||||
\(611\) | −2.00844e8 | −0.0356218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.45694e9 | −1.65821 | −0.829104 | − | 0.559094i | \(-0.811149\pi\) | ||||
−0.829104 | + | 0.559094i | \(0.811149\pi\) | |||||||
\(614\) | −4.81088e7 | −0.00838755 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.64216e8 | −0.0283064 | ||||||||
\(617\) | −5.14249e9 | −0.881405 | −0.440702 | − | 0.897653i | \(-0.645271\pi\) | ||||
−0.440702 | + | 0.897653i | \(0.645271\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.42513e9 | 1.25831 | 0.629153 | − | 0.777281i | \(-0.283402\pi\) | ||||
0.629153 | + | 0.777281i | \(0.283402\pi\) | |||||||
\(620\) | −2.46336e8 | −0.0415103 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.98077e8 | −0.0330041 | ||||||||
\(623\) | −3.43478e9 | −0.569103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.48629e9 | −0.735034 | ||||||||
\(626\) | −2.66529e8 | −0.0434245 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.79140e9 | 1.25533 | ||||||||
\(629\) | 5.62634e9 | 0.901464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.01569e8 | 0.0953197 | 0.0476598 | − | 0.998864i | \(-0.484824\pi\) | ||||
0.0476598 | + | 0.998864i | \(0.484824\pi\) | |||||||
\(632\) | −1.39160e8 | −0.0219283 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.99967e8 | −0.0467479 | ||||||||
\(635\) | −2.53815e9 | −0.393377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.74093e9 | −0.573444 | ||||||||
\(638\) | 2.08957e8 | 0.0318555 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.20524e8 | −0.123726 | ||||||||
\(641\) | −3.94333e9 | −0.591371 | −0.295685 | − | 0.955285i | \(-0.595548\pi\) | ||||
−0.295685 | + | 0.955285i | \(0.595548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.67937e9 | 0.545802 | 0.272901 | − | 0.962042i | \(-0.412017\pi\) | ||||
0.272901 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(644\) | 4.99008e9 | 0.736219 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.06592e8 | −0.0301508 | ||||||||
\(647\) | −9.80484e9 | −1.42323 | −0.711616 | − | 0.702569i | \(-0.752036\pi\) | ||||
−0.711616 | + | 0.702569i | \(0.752036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.08747e8 | 0.0730542 | ||||||||
\(650\) | 6.35396e7 | 0.00907503 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.10903e9 | −0.439297 | ||||||||
\(653\) | 4.40696e9 | 0.619360 | 0.309680 | − | 0.950841i | \(-0.399778\pi\) | ||||
0.309680 | + | 0.950841i | \(0.399778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.54049e9 | −1.04847 | ||||||||
\(656\) | −2.28792e8 | −0.0316430 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.52607e6 | −0.000756182 0 | ||||||||
\(659\) | 1.35935e10 | 1.85025 | 0.925127 | − | 0.379657i | \(-0.123958\pi\) | ||||
0.925127 | + | 0.379657i | \(0.123958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.30552e9 | −0.714534 | −0.357267 | − | 0.934002i | \(-0.616291\pi\) | ||||
−0.357267 | + | 0.934002i | \(0.616291\pi\) | |||||||
\(662\) | −2.80553e7 | −0.00375847 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.75121e8 | 0.102750 | ||||||||
\(665\) | −6.68141e9 | −0.881033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.27070e10 | −1.65807 | ||||||||
\(668\) | 2.78824e9 | 0.361920 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.75946e8 | −0.0482907 | ||||||||
\(671\) | 2.00716e9 | 0.256480 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.77543e9 | 0.477434 | 0.238717 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238717 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(674\) | 2.76603e8 | 0.0347975 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.31661e9 | −0.412934 | ||||||||
\(677\) | 7.29031e9 | 0.902995 | 0.451498 | − | 0.892272i | \(-0.350890\pi\) | ||||
0.451498 | + | 0.892272i | \(0.350890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.02767e9 | 0.738933 | ||||||||
\(680\) | 3.15716e8 | 0.0385048 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.66167e6 | 0.000924865 0 | ||||||||
\(683\) | −7.10884e9 | −0.853742 | −0.426871 | − | 0.904313i | \(-0.640384\pi\) | ||||
−0.426871 | + | 0.904313i | \(0.640384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.39227e9 | 0.640996 | ||||||||
\(686\) | −3.16324e8 | −0.0374108 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.46319e10 | −1.71294 | ||||||||
\(689\) | −8.57847e9 | −0.999177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.26683e10 | −1.46065 | −0.730324 | − | 0.683100i | \(-0.760631\pi\) | ||||
−0.730324 | + | 0.683100i | \(0.760631\pi\) | |||||||
\(692\) | 9.68924e9 | 1.11152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.24391e8 | −0.0141264 | ||||||||
\(695\) | −1.38258e10 | −1.56223 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.76284e8 | 0.0197196 | ||||||||
\(698\) | −2.65863e8 | −0.0295913 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.41910e9 | −0.156376 | ||||||||
\(701\) | 1.78862e10 | 1.96113 | 0.980564 | − | 0.196201i | \(-0.0628606\pi\) | ||||
0.980564 | + | 0.196201i | \(0.0628606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.85155e10 | 2.00998 | ||||||||
\(704\) | −5.15657e9 | −0.557002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.63022e8 | −0.0495205 | ||||||||
\(707\) | 3.17033e9 | 0.337393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.24346e10 | −1.31030 | −0.655150 | − | 0.755499i | \(-0.727395\pi\) | ||||
−0.655150 | + | 0.755499i | \(0.727395\pi\) | |||||||
\(710\) | 3.29349e8 | 0.0345344 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.34119e8 | 0.0554572 | ||||||||
\(713\) | −4.65920e8 | −0.0481392 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.76757e9 | −0.590095 | ||||||||
\(716\) | −1.46043e8 | −0.0148691 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.75854e8 | 0.0681424 | ||||||||
\(719\) | −2.69952e9 | −0.270854 | −0.135427 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135427 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.83656e9 | 0.281850 | ||||||||
\(722\) | −3.25128e8 | −0.0321495 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.73029e10 | −1.69447 | ||||||||
\(725\) | 3.61368e9 | 0.352182 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.43778e9 | −0.428346 | −0.214173 | − | 0.976796i | \(-0.568706\pi\) | ||||
−0.214173 | + | 0.976796i | \(0.568706\pi\) | |||||||
\(728\) | −6.24327e8 | −0.0599725 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.52845e7 | 0.00430844 | ||||||||
\(731\) | 1.12738e10 | 1.06748 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.21884e9 | 0.770808 | 0.385404 | − | 0.922748i | \(-0.374062\pi\) | ||||
0.385404 | + | 0.922748i | \(0.374062\pi\) | |||||||
\(734\) | −3.78809e8 | −0.0353577 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.16420e9 | −0.107635 | ||||||||
\(737\) | −9.49146e9 | −0.873367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.71653e9 | −0.794490 | −0.397245 | − | 0.917713i | \(-0.630034\pi\) | ||||
−0.397245 | + | 0.917713i | \(0.630034\pi\) | |||||||
\(740\) | −1.41391e10 | −1.28266 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.36030e8 | −0.0212106 | ||||||||
\(743\) | 1.01228e9 | 0.0905396 | 0.0452698 | − | 0.998975i | \(-0.485585\pi\) | ||||
0.0452698 | + | 0.998975i | \(0.485585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.05098e10 | 0.931207 | ||||||||
\(746\) | −5.64087e8 | −0.0497462 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.98296e9 | 0.347977 | ||||||||
\(749\) | −4.31266e9 | −0.375024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.76039e10 | 1.51659 | 0.758295 | − | 0.651911i | \(-0.226032\pi\) | ||||
0.758295 | + | 0.651911i | \(0.226032\pi\) | |||||||
\(752\) | −3.48123e8 | −0.0298518 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.94422e8 | 0.0674919 | ||||||||
\(755\) | 6.65393e9 | 0.562684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.48620e10 | 1.24520 | 0.622602 | − | 0.782539i | \(-0.286076\pi\) | ||||
0.622602 | + | 0.782539i | \(0.286076\pi\) | |||||||
\(758\) | −1.18624e8 | −0.00989304 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.03898e9 | 0.0858537 | ||||||||
\(761\) | −1.01144e10 | −0.831939 | −0.415970 | − | 0.909378i | \(-0.636558\pi\) | ||||
−0.415970 | + | 0.909378i | \(0.636558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.79414e9 | 0.146225 | ||||||||
\(764\) | 1.42472e10 | 1.15585 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.04760e8 | −0.00842157 | ||||||||
\(767\) | 1.93418e9 | 0.154779 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.01233e10 | −0.802748 | −0.401374 | − | 0.915914i | \(-0.631467\pi\) | ||||
−0.401374 | + | 0.915914i | \(0.631467\pi\) | |||||||
\(770\) | −1.58690e8 | −0.0125266 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.86568e9 | 0.458836 | ||||||||
\(773\) | −1.87926e10 | −1.46339 | −0.731693 | − | 0.681635i | \(-0.761269\pi\) | ||||
−0.731693 | + | 0.681635i | \(0.761269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.32500e8 | 0.0102250 | ||||||||
\(776\) | −9.37320e8 | −0.0720066 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.81081e8 | −0.0518525 | ||||||||
\(779\) | 5.80127e8 | 0.0439685 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.31503e9 | 0.624576 | ||||||||
\(782\) | 2.98389e8 | 0.0223131 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.48415e9 | −0.480559 | ||||||||
\(785\) | 1.50677e10 | 1.11174 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.04611e10 | 0.765009 | 0.382505 | − | 0.923954i | \(-0.375062\pi\) | ||||
0.382505 | + | 0.923954i | \(0.375062\pi\) | |||||||
\(788\) | 1.56804e10 | 1.14160 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.34477e8 | −0.00970405 | ||||||||
\(791\) | −2.01557e9 | −0.144804 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.63092e9 | 0.543402 | ||||||||
\(794\) | −2.28122e8 | −0.0161732 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.31047e9 | 0.0920937 | ||||||||
\(797\) | −2.15776e10 | −1.50973 | −0.754865 | − | 0.655880i | \(-0.772298\pi\) | ||||
−0.754865 | + | 0.655880i | \(0.772298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.68228e8 | 0.0186033 | ||||||||
\(800\) | 3.31079e8 | 0.0228622 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.55529e8 | −0.0311821 | ||||||||
\(803\) | 1.14329e9 | 0.0779206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.65025e9 | 0.652008 | ||||||||
\(806\) | 2.91285e7 | 0.00195950 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.92995e8 | −0.0328778 | ||||||||
\(809\) | −1.89775e10 | −1.26014 | −0.630070 | − | 0.776538i | \(-0.716974\pi\) | ||||
−0.630070 | + | 0.776538i | \(0.716974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.70722e9 | −0.309879 | −0.154939 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154939 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(812\) | −1.77427e10 | −1.16298 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.39763e8 | 0.0285781 | ||||||||
\(815\) | −6.01252e9 | −0.389049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.71007e10 | 2.38015 | ||||||||
\(818\) | 1.76961e6 | 0.000113042 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.43005e8 | −0.0280582 | ||||||||
\(821\) | 2.74939e10 | 1.73395 | 0.866973 | − | 0.498355i | \(-0.166062\pi\) | ||||
0.866973 | + | 0.498355i | \(0.166062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.47691e9 | −0.0923540 | −0.0461770 | − | 0.998933i | \(-0.514704\pi\) | ||||
−0.0461770 | + | 0.998933i | \(0.514704\pi\) | |||||||
\(824\) | −4.41093e8 | −0.0274654 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.32175e7 | 0.00328567 | ||||||||
\(827\) | 3.11067e10 | 1.91243 | 0.956213 | − | 0.292671i | \(-0.0945439\pi\) | ||||
0.956213 | + | 0.292671i | \(0.0945439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06946e9 | 0.126158 | 0.0630792 | − | 0.998009i | \(-0.479908\pi\) | ||||
0.0630792 | + | 0.998009i | \(0.479908\pi\) | |||||||
\(830\) | 7.49037e8 | 0.0454705 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.96045e10 | −1.18012 | ||||||||
\(833\) | 4.99601e9 | 0.299479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.39214e9 | 0.320522 | ||||||||
\(836\) | 1.31074e10 | 0.775880 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.08145e9 | 0.0634825 | ||||||||
\(839\) | −2.02258e9 | −0.118233 | −0.0591166 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591166 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.79312e10 | 1.61921 | ||||||||
\(842\) | 7.87963e8 | 0.0454898 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.08546e10 | 1.19400 | ||||||||
\(845\) | −6.41395e9 | −0.365702 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.71731e9 | 0.492936 | ||||||||
\(848\) | −1.48691e10 | −0.837332 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.48572e7 | −0.00473939 | ||||||||
\(851\) | −2.67428e10 | −1.48749 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.22240e10 | −1.77770 | −0.888849 | − | 0.458201i | \(-0.848494\pi\) | ||||
−0.888849 | + | 0.458201i | \(0.848494\pi\) | |||||||
\(854\) | 2.09959e8 | 0.0115354 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.70632e8 | 0.0365448 | ||||||||
\(857\) | −6.94237e9 | −0.376769 | −0.188384 | − | 0.982095i | \(-0.560325\pi\) | ||||
−0.188384 | + | 0.982095i | \(0.560325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.91744e9 | −0.372365 | −0.186183 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186183 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(860\) | −2.83314e10 | −1.51888 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.54922e8 | −0.0188737 | ||||||||
\(863\) | 2.83705e10 | 1.50255 | 0.751275 | − | 0.659990i | \(-0.229439\pi\) | ||||
0.751275 | + | 0.659990i | \(0.229439\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.87379e10 | 0.984384 | ||||||||
\(866\) | 1.11878e9 | 0.0585375 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.50559e8 | −0.0337651 | ||||||||
\(869\) | −3.39512e9 | −0.175504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.60851e10 | −1.85040 | ||||||||
\(872\) | −2.78995e8 | −0.0142491 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.81960e8 | 0.0497512 | ||||||||
\(875\) | −1.53557e10 | −0.774895 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.27420e9 | −0.163910 | −0.0819552 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819552 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(878\) | −5.98083e8 | −0.0298216 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.99693e9 | −0.494512 | ||||||||
\(881\) | −1.44579e10 | −0.712346 | −0.356173 | − | 0.934420i | \(-0.615919\pi\) | ||||
−0.356173 | + | 0.934420i | \(0.615919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.75453e9 | 0.427928 | 0.213964 | − | 0.976842i | \(-0.431363\pi\) | ||||
0.213964 | + | 0.976842i | \(0.431363\pi\) | |||||||
\(884\) | 1.51426e10 | 0.737256 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.18835e8 | 0.0250618 | ||||||||
\(887\) | −1.54047e10 | −0.741175 | −0.370588 | − | 0.928798i | \(-0.620844\pi\) | ||||
−0.370588 | + | 0.928798i | \(0.620844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.70311e9 | −0.319978 | ||||||||
\(890\) | 5.16144e8 | 0.0245418 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.76211e10 | −1.30306 | ||||||||
\(893\) | 8.82702e8 | 0.0414796 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.82431e8 | −0.0131684 | ||||||||
\(896\) | −2.16696e9 | −0.100641 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.02795e9 | −0.0473701 | ||||||||
\(899\) | 1.65662e9 | 0.0760441 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14566e10 | 0.521816 | ||||||||
\(902\) | 1.37786e7 | 0.000625147 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.13427e8 | 0.0141107 | ||||||||
\(905\) | −3.34619e10 | −1.50065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.05126e10 | 1.80287 | 0.901435 | − | 0.432915i | \(-0.142515\pi\) | ||||
0.901435 | + | 0.432915i | \(0.142515\pi\) | |||||||
\(908\) | −1.21008e10 | −0.536430 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.03317e8 | −0.0265400 | ||||||||
\(911\) | −9.95690e9 | −0.436325 | −0.218162 | − | 0.975912i | \(-0.570006\pi\) | ||||
−0.218162 | + | 0.975912i | \(0.570006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.89108e10 | 0.822361 | ||||||||
\(914\) | 1.19387e9 | 0.0517186 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.18590e9 | −0.308921 | ||||||||
\(917\) | −1.99140e10 | −0.852838 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.67638e10 | 0.712472 | 0.356236 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356236 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(920\) | −1.50064e9 | −0.0635360 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.14179e8 | 0.0216051 | ||||||||
\(923\) | 3.16125e10 | 1.32328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.60523e9 | 0.315948 | ||||||||
\(926\) | −3.13130e7 | −0.00129594 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.13941e9 | 0.170028 | ||||||||
\(929\) | 2.97001e10 | 1.21536 | 0.607678 | − | 0.794184i | \(-0.292101\pi\) | ||||
0.607678 | + | 0.794184i | \(0.292101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.64412e10 | 0.667744 | ||||||||
\(932\) | 3.99639e10 | 1.61701 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.82847e8 | −0.0314386 | ||||||||
\(935\) | 7.70260e9 | 0.308174 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.54569e10 | 1.40803 | 0.704015 | − | 0.710185i | \(-0.251389\pi\) | ||||
0.704015 | + | 0.710185i | \(0.251389\pi\) | |||||||
\(938\) | −9.92854e8 | −0.0392804 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.74063e8 | −0.0264699 | ||||||||
\(941\) | −1.78640e10 | −0.698900 | −0.349450 | − | 0.936955i | \(-0.613631\pi\) | ||||
−0.349450 | + | 0.936955i | \(0.613631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.37902e8 | −0.0325389 | ||||||||
\(944\) | 3.35251e9 | 0.129709 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.81180e8 | 0.0338412 | ||||||||
\(947\) | 4.19426e10 | 1.60483 | 0.802417 | − | 0.596764i | \(-0.203547\pi\) | ||||
0.802417 | + | 0.596764i | \(0.203547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.34662e9 | 0.165090 | ||||||||
\(950\) | −2.79254e8 | −0.0105674 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.33789e8 | 0.0313204 | ||||||||
\(953\) | 2.78513e10 | 1.04236 | 0.521182 | − | 0.853445i | \(-0.325491\pi\) | ||||
0.521182 | + | 0.853445i | \(0.325491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.75524e10 | 1.02364 | ||||||||
\(956\) | 4.15431e10 | 1.53779 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.25642e7 | 0.00119663 | ||||||||
\(959\) | 1.42407e10 | 0.521395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.74519e10 | −0.997792 | ||||||||
\(962\) | 1.67191e9 | 0.0605482 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.27074e10 | −1.17592 | ||||||||
\(965\) | 1.13436e10 | 0.406353 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00043e10 | −0.355789 | −0.177895 | − | 0.984050i | \(-0.556929\pi\) | ||||
−0.177895 | + | 0.984050i | \(0.556929\pi\) | |||||||
\(968\) | −1.35557e9 | −0.0480350 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.05778e8 | −0.0318655 | ||||||||
\(971\) | 2.19879e10 | 0.770755 | 0.385377 | − | 0.922759i | \(-0.374071\pi\) | ||||
0.385377 | + | 0.922759i | \(0.374071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.65132e10 | −1.27074 | ||||||||
\(974\) | −1.11807e9 | −0.0387714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.32267e10 | 0.455383 | ||||||||
\(977\) | 4.29793e10 | 1.47444 | 0.737222 | − | 0.675651i | \(-0.236137\pi\) | ||||
0.737222 | + | 0.675651i | \(0.236137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.30310e10 | 0.443853 | ||||||||
\(980\) | −1.25551e10 | −0.426117 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.72335e9 | −0.0580741 | ||||||||
\(983\) | 2.32107e10 | 0.779383 | 0.389691 | − | 0.920946i | \(-0.372582\pi\) | ||||
0.389691 | + | 0.920946i | \(0.372582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.03240e10 | 1.01102 | ||||||||
\(986\) | −1.06095e9 | −0.0352474 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.98324e10 | 1.64385 | ||||||||
\(989\) | −5.35862e10 | −1.76143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.22560e10 | −0.400030 | −0.200015 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200015 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(992\) | 1.51777e8 | 0.00493646 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.69793e8 | 0.0280908 | ||||||||
\(995\) | 2.53429e9 | 0.0815598 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.51059e10 | −0.482740 | −0.241370 | − | 0.970433i | \(-0.577597\pi\) | ||||
−0.241370 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(998\) | 1.11866e9 | 0.0356238 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.8.a.d.1.9 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.9 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.9 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.9 | 17 | 1.1 | even | 1 | trivial |