Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.2441 | −0.381044 | −0.190522 | − | 0.981683i | \(-0.561018\pi\) | ||||
−0.190522 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1750.64 | −0.854805 | ||||||||
\(5\) | 7994.91 | 1.14414 | 0.572069 | − | 0.820205i | \(-0.306141\pi\) | ||||
0.572069 | + | 0.820205i | \(0.306141\pi\) | |||||||
\(6\) | −4190.32 | −0.219996 | ||||||||
\(7\) | 1325.62 | 0.0298112 | 0.0149056 | − | 0.999889i | \(-0.495255\pi\) | ||||
0.0149056 | + | 0.999889i | \(0.495255\pi\) | |||||||
\(8\) | 65504.2 | 0.706763 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −137865. | −0.435968 | ||||||||
\(11\) | 134920. | 0.252590 | 0.126295 | − | 0.991993i | \(-0.459691\pi\) | ||||
0.126295 | + | 0.991993i | \(0.459691\pi\) | |||||||
\(12\) | −425406. | −0.493522 | ||||||||
\(13\) | −29851.6 | −0.0222987 | −0.0111493 | − | 0.999938i | \(-0.503549\pi\) | ||||
−0.0111493 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(14\) | −22859.1 | −0.0113594 | ||||||||
\(15\) | 1.94276e6 | 0.660569 | ||||||||
\(16\) | 2.45575e6 | 0.585497 | ||||||||
\(17\) | −3.25895e6 | −0.556684 | −0.278342 | − | 0.960482i | \(-0.589785\pi\) | ||||
−0.278342 | + | 0.960482i | \(0.589785\pi\) | |||||||
\(18\) | −1.01825e6 | −0.127015 | ||||||||
\(19\) | −1.09243e7 | −1.01216 | −0.506079 | − | 0.862487i | \(-0.668905\pi\) | ||||
−0.506079 | + | 0.862487i | \(0.668905\pi\) | |||||||
\(20\) | −1.39962e7 | −0.978016 | ||||||||
\(21\) | 322125. | 0.0172115 | ||||||||
\(22\) | −2.32657e6 | −0.0962479 | ||||||||
\(23\) | 185019. | 0.00599396 | 0.00299698 | − | 0.999996i | \(-0.499046\pi\) | ||||
0.00299698 | + | 0.999996i | \(0.499046\pi\) | |||||||
\(24\) | 1.59175e7 | 0.408050 | ||||||||
\(25\) | 1.50905e7 | 0.309054 | ||||||||
\(26\) | 514764. | 0.00849678 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −2.32068e6 | −0.0254828 | ||||||||
\(29\) | 1.68886e7 | 0.152899 | 0.0764495 | − | 0.997073i | \(-0.475642\pi\) | ||||
0.0764495 | + | 0.997073i | \(0.475642\pi\) | |||||||
\(30\) | −3.35012e7 | −0.251706 | ||||||||
\(31\) | −5.53827e7 | −0.347444 | −0.173722 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173722 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(32\) | −1.76500e8 | −0.929864 | ||||||||
\(33\) | 3.27855e7 | 0.145833 | ||||||||
\(34\) | 5.61977e7 | 0.212121 | ||||||||
\(35\) | 1.05982e7 | 0.0341081 | ||||||||
\(36\) | −1.03374e8 | −0.284935 | ||||||||
\(37\) | −7.21695e8 | −1.71098 | −0.855489 | − | 0.517821i | \(-0.826743\pi\) | ||||
−0.855489 | + | 0.517821i | \(0.826743\pi\) | |||||||
\(38\) | 1.88379e8 | 0.385677 | ||||||||
\(39\) | −7.25393e6 | −0.0128741 | ||||||||
\(40\) | 5.23700e8 | 0.808635 | ||||||||
\(41\) | −8.63631e8 | −1.16417 | −0.582086 | − | 0.813128i | \(-0.697763\pi\) | ||||
−0.582086 | + | 0.813128i | \(0.697763\pi\) | |||||||
\(42\) | −5.55476e6 | −0.00655834 | ||||||||
\(43\) | 1.00149e9 | 1.03889 | 0.519444 | − | 0.854505i | \(-0.326139\pi\) | ||||
0.519444 | + | 0.854505i | \(0.326139\pi\) | |||||||
\(44\) | −2.36196e8 | −0.215915 | ||||||||
\(45\) | 4.72092e8 | 0.381380 | ||||||||
\(46\) | −3.19049e6 | −0.00228397 | ||||||||
\(47\) | 3.01812e9 | 1.91954 | 0.959772 | − | 0.280779i | \(-0.0905929\pi\) | ||||
0.959772 | + | 0.280779i | \(0.0905929\pi\) | |||||||
\(48\) | 5.96748e8 | 0.338037 | ||||||||
\(49\) | −1.97557e9 | −0.999111 | ||||||||
\(50\) | −2.60222e8 | −0.117763 | ||||||||
\(51\) | −7.91925e8 | −0.321402 | ||||||||
\(52\) | 5.22594e7 | 0.0190610 | ||||||||
\(53\) | 2.68649e9 | 0.882405 | 0.441203 | − | 0.897407i | \(-0.354552\pi\) | ||||
0.441203 | + | 0.897407i | \(0.354552\pi\) | |||||||
\(54\) | −2.47434e8 | −0.0733320 | ||||||||
\(55\) | 1.07867e9 | 0.288998 | ||||||||
\(56\) | 8.68335e7 | 0.0210694 | ||||||||
\(57\) | −2.65460e9 | −0.584369 | ||||||||
\(58\) | −2.91229e8 | −0.0582613 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −3.40108e9 | −0.564658 | ||||||||
\(61\) | −1.08583e10 | −1.64607 | −0.823035 | − | 0.567990i | \(-0.807721\pi\) | ||||
−0.823035 | + | 0.567990i | \(0.807721\pi\) | |||||||
\(62\) | 9.55025e8 | 0.132392 | ||||||||
\(63\) | 7.82764e7 | 0.00993706 | ||||||||
\(64\) | −1.98580e9 | −0.231178 | ||||||||
\(65\) | −2.38661e8 | −0.0255128 | ||||||||
\(66\) | −5.65356e8 | −0.0555687 | ||||||||
\(67\) | 1.61605e10 | 1.46233 | 0.731163 | − | 0.682203i | \(-0.238978\pi\) | ||||
0.731163 | + | 0.682203i | \(0.238978\pi\) | |||||||
\(68\) | 5.70525e9 | 0.475856 | ||||||||
\(69\) | 4.49597e7 | 0.00346062 | ||||||||
\(70\) | −1.82756e8 | −0.0129967 | ||||||||
\(71\) | 3.75065e9 | 0.246710 | 0.123355 | − | 0.992363i | \(-0.460635\pi\) | ||||
0.123355 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(72\) | 3.86795e9 | 0.235588 | ||||||||
\(73\) | −2.36110e10 | −1.33302 | −0.666512 | − | 0.745495i | \(-0.732213\pi\) | ||||
−0.666512 | + | 0.745495i | \(0.732213\pi\) | |||||||
\(74\) | 1.24450e10 | 0.651959 | ||||||||
\(75\) | 3.66699e9 | 0.178432 | ||||||||
\(76\) | 1.91245e10 | 0.865197 | ||||||||
\(77\) | 1.78852e8 | 0.00752999 | ||||||||
\(78\) | 1.25088e8 | 0.00490562 | ||||||||
\(79\) | −4.18117e10 | −1.52879 | −0.764397 | − | 0.644746i | \(-0.776963\pi\) | ||||
−0.764397 | + | 0.644746i | \(0.776963\pi\) | |||||||
\(80\) | 1.96335e10 | 0.669890 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 1.48925e10 | 0.443601 | ||||||||
\(83\) | 2.14444e10 | 0.597564 | 0.298782 | − | 0.954321i | \(-0.403420\pi\) | ||||
0.298782 | + | 0.954321i | \(0.403420\pi\) | |||||||
\(84\) | −5.63926e8 | −0.0147125 | ||||||||
\(85\) | −2.60550e10 | −0.636924 | ||||||||
\(86\) | −1.72697e10 | −0.395862 | ||||||||
\(87\) | 4.10393e9 | 0.0882762 | ||||||||
\(88\) | 8.83780e9 | 0.178521 | ||||||||
\(89\) | 2.25760e10 | 0.428550 | 0.214275 | − | 0.976773i | \(-0.431261\pi\) | ||||
0.214275 | + | 0.976773i | \(0.431261\pi\) | |||||||
\(90\) | −8.14080e9 | −0.145323 | ||||||||
\(91\) | −3.95718e7 | −0.000664749 0 | ||||||||
\(92\) | −3.23902e8 | −0.00512367 | ||||||||
\(93\) | −1.34580e10 | −0.200597 | ||||||||
\(94\) | −5.20448e10 | −0.731432 | ||||||||
\(95\) | −8.73387e10 | −1.15805 | ||||||||
\(96\) | −4.28894e10 | −0.536857 | ||||||||
\(97\) | −3.27724e10 | −0.387493 | −0.193747 | − | 0.981052i | \(-0.562064\pi\) | ||||
−0.193747 | + | 0.981052i | \(0.562064\pi\) | |||||||
\(98\) | 3.40669e10 | 0.380706 | ||||||||
\(99\) | 7.96687e9 | 0.0841965 | ||||||||
\(100\) | −2.64181e10 | −0.264181 | ||||||||
\(101\) | 8.33085e10 | 0.788718 | 0.394359 | − | 0.918957i | \(-0.370967\pi\) | ||||
0.394359 | + | 0.918957i | \(0.370967\pi\) | |||||||
\(102\) | 1.36560e10 | 0.122468 | ||||||||
\(103\) | 2.29703e11 | 1.95237 | 0.976187 | − | 0.216932i | \(-0.0696051\pi\) | ||||
0.976187 | + | 0.216932i | \(0.0696051\pi\) | |||||||
\(104\) | −1.95540e9 | −0.0157599 | ||||||||
\(105\) | 2.57536e9 | 0.0196923 | ||||||||
\(106\) | −4.63261e10 | −0.336236 | ||||||||
\(107\) | −1.56240e11 | −1.07692 | −0.538459 | − | 0.842652i | \(-0.680993\pi\) | ||||
−0.538459 | + | 0.842652i | \(0.680993\pi\) | |||||||
\(108\) | −2.51198e10 | −0.164507 | ||||||||
\(109\) | −2.21150e11 | −1.37670 | −0.688352 | − | 0.725377i | \(-0.741666\pi\) | ||||
−0.688352 | + | 0.725377i | \(0.741666\pi\) | |||||||
\(110\) | −1.86007e10 | −0.110121 | ||||||||
\(111\) | −1.75372e11 | −0.987833 | ||||||||
\(112\) | 3.25539e9 | 0.0174544 | ||||||||
\(113\) | 3.63850e11 | 1.85777 | 0.928883 | − | 0.370373i | \(-0.120770\pi\) | ||||
0.928883 | + | 0.370373i | \(0.120770\pi\) | |||||||
\(114\) | 4.57762e10 | 0.222671 | ||||||||
\(115\) | 1.47921e9 | 0.00685793 | ||||||||
\(116\) | −2.95659e10 | −0.130699 | ||||||||
\(117\) | −1.76271e9 | −0.00743289 | ||||||||
\(118\) | 1.23282e10 | 0.0496078 | ||||||||
\(119\) | −4.32012e9 | −0.0165954 | ||||||||
\(120\) | 1.27259e11 | 0.466866 | ||||||||
\(121\) | −2.67108e11 | −0.936198 | ||||||||
\(122\) | 1.87242e11 | 0.627226 | ||||||||
\(123\) | −2.09862e11 | −0.672135 | ||||||||
\(124\) | 9.69552e10 | 0.296997 | ||||||||
\(125\) | −2.69729e11 | −0.790539 | ||||||||
\(126\) | −1.34981e9 | −0.00378646 | ||||||||
\(127\) | −3.83293e11 | −1.02946 | −0.514732 | − | 0.857351i | \(-0.672108\pi\) | ||||
−0.514732 | + | 0.857351i | \(0.672108\pi\) | |||||||
\(128\) | 3.95715e11 | 1.01795 | ||||||||
\(129\) | 2.43361e11 | 0.599802 | ||||||||
\(130\) | 4.11549e9 | 0.00972149 | ||||||||
\(131\) | 4.10464e11 | 0.929571 | 0.464785 | − | 0.885423i | \(-0.346131\pi\) | ||||
0.464785 | + | 0.885423i | \(0.346131\pi\) | |||||||
\(132\) | −5.73956e10 | −0.124659 | ||||||||
\(133\) | −1.44814e10 | −0.0301736 | ||||||||
\(134\) | −2.78674e11 | −0.557211 | ||||||||
\(135\) | 1.14718e11 | 0.220190 | ||||||||
\(136\) | −2.13475e11 | −0.393444 | ||||||||
\(137\) | 2.08833e11 | 0.369689 | 0.184845 | − | 0.982768i | \(-0.440822\pi\) | ||||
0.184845 | + | 0.982768i | \(0.440822\pi\) | |||||||
\(138\) | −7.75290e8 | −0.00131865 | ||||||||
\(139\) | 4.49732e11 | 0.735145 | 0.367572 | − | 0.929995i | \(-0.380189\pi\) | ||||
0.367572 | + | 0.929995i | \(0.380189\pi\) | |||||||
\(140\) | −1.85536e10 | −0.0291558 | ||||||||
\(141\) | 7.33403e11 | 1.10825 | ||||||||
\(142\) | −6.46767e10 | −0.0940073 | ||||||||
\(143\) | −4.02756e9 | −0.00563241 | ||||||||
\(144\) | 1.45010e11 | 0.195166 | ||||||||
\(145\) | 1.35023e11 | 0.174938 | ||||||||
\(146\) | 4.07150e11 | 0.507941 | ||||||||
\(147\) | −4.80063e11 | −0.576837 | ||||||||
\(148\) | 1.26343e12 | 1.46255 | ||||||||
\(149\) | 1.77907e10 | 0.0198458 | 0.00992288 | − | 0.999951i | \(-0.496841\pi\) | ||||
0.00992288 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(150\) | −6.32340e10 | −0.0679906 | ||||||||
\(151\) | −1.59845e12 | −1.65701 | −0.828506 | − | 0.559980i | \(-0.810809\pi\) | ||||
−0.828506 | + | 0.559980i | \(0.810809\pi\) | |||||||
\(152\) | −7.15586e11 | −0.715356 | ||||||||
\(153\) | −1.92438e11 | −0.185561 | ||||||||
\(154\) | −3.08414e9 | −0.00286926 | ||||||||
\(155\) | −4.42780e11 | −0.397524 | ||||||||
\(156\) | 1.26990e10 | 0.0110049 | ||||||||
\(157\) | −1.19670e12 | −1.00124 | −0.500619 | − | 0.865668i | \(-0.666894\pi\) | ||||
−0.500619 | + | 0.865668i | \(0.666894\pi\) | |||||||
\(158\) | 7.21005e11 | 0.582538 | ||||||||
\(159\) | 6.52817e11 | 0.509457 | ||||||||
\(160\) | −1.41110e12 | −1.06389 | ||||||||
\(161\) | 2.45265e8 | 0.000178687 0 | ||||||||
\(162\) | −6.01265e10 | −0.0423383 | ||||||||
\(163\) | −1.67271e12 | −1.13865 | −0.569324 | − | 0.822113i | \(-0.692795\pi\) | ||||
−0.569324 | + | 0.822113i | \(0.692795\pi\) | |||||||
\(164\) | 1.51191e12 | 0.995140 | ||||||||
\(165\) | 2.62117e11 | 0.166853 | ||||||||
\(166\) | −3.69790e11 | −0.227699 | ||||||||
\(167\) | −1.38696e12 | −0.826274 | −0.413137 | − | 0.910669i | \(-0.635567\pi\) | ||||
−0.413137 | + | 0.910669i | \(0.635567\pi\) | |||||||
\(168\) | 2.11005e10 | 0.0121644 | ||||||||
\(169\) | −1.79127e12 | −0.999503 | ||||||||
\(170\) | 4.49295e11 | 0.242696 | ||||||||
\(171\) | −6.45068e11 | −0.337386 | ||||||||
\(172\) | −1.75324e12 | −0.888047 | ||||||||
\(173\) | −3.50693e12 | −1.72058 | −0.860288 | − | 0.509808i | \(-0.829717\pi\) | ||||
−0.860288 | + | 0.509808i | \(0.829717\pi\) | |||||||
\(174\) | −7.07685e10 | −0.0336372 | ||||||||
\(175\) | 2.00042e10 | 0.00921325 | ||||||||
\(176\) | 3.31329e11 | 0.147890 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −3.89302e11 | −0.163297 | ||||||||
\(179\) | −4.28803e12 | −1.74408 | −0.872039 | − | 0.489436i | \(-0.837203\pi\) | ||||
−0.872039 | + | 0.489436i | \(0.837203\pi\) | |||||||
\(180\) | −8.26463e11 | −0.326005 | ||||||||
\(181\) | −1.32012e12 | −0.505105 | −0.252553 | − | 0.967583i | \(-0.581270\pi\) | ||||
−0.252553 | + | 0.967583i | \(0.581270\pi\) | |||||||
\(182\) | 6.82380e8 | 0.000253299 0 | ||||||||
\(183\) | −2.63857e12 | −0.950359 | ||||||||
\(184\) | 1.21195e10 | 0.00423631 | ||||||||
\(185\) | −5.76989e12 | −1.95760 | ||||||||
\(186\) | 2.32071e11 | 0.0764363 | ||||||||
\(187\) | −4.39696e11 | −0.140613 | ||||||||
\(188\) | −5.28364e12 | −1.64084 | ||||||||
\(189\) | 1.90212e10 | 0.00573716 | ||||||||
\(190\) | 1.50608e12 | 0.441268 | ||||||||
\(191\) | 4.44766e11 | 0.126604 | 0.0633021 | − | 0.997994i | \(-0.479837\pi\) | ||||
0.0633021 | + | 0.997994i | \(0.479837\pi\) | |||||||
\(192\) | −4.82550e11 | −0.133471 | ||||||||
\(193\) | −4.40420e12 | −1.18386 | −0.591932 | − | 0.805988i | \(-0.701635\pi\) | ||||
−0.591932 | + | 0.805988i | \(0.701635\pi\) | |||||||
\(194\) | 5.65131e11 | 0.147652 | ||||||||
\(195\) | −5.79946e10 | −0.0147298 | ||||||||
\(196\) | 3.45851e12 | 0.854045 | ||||||||
\(197\) | −1.08074e12 | −0.259511 | −0.129756 | − | 0.991546i | \(-0.541419\pi\) | ||||
−0.129756 | + | 0.991546i | \(0.541419\pi\) | |||||||
\(198\) | −1.37382e11 | −0.0320826 | ||||||||
\(199\) | 1.76499e12 | 0.400914 | 0.200457 | − | 0.979703i | \(-0.435757\pi\) | ||||
0.200457 | + | 0.979703i | \(0.435757\pi\) | |||||||
\(200\) | 9.88491e11 | 0.218428 | ||||||||
\(201\) | 3.92701e12 | 0.844274 | ||||||||
\(202\) | −1.43658e12 | −0.300536 | ||||||||
\(203\) | 2.23878e10 | 0.00455810 | ||||||||
\(204\) | 1.38638e12 | 0.274736 | ||||||||
\(205\) | −6.90465e12 | −1.33197 | ||||||||
\(206\) | −3.96103e12 | −0.743941 | ||||||||
\(207\) | 1.09252e10 | 0.00199799 | ||||||||
\(208\) | −7.33081e10 | −0.0130558 | ||||||||
\(209\) | −1.47390e12 | −0.255660 | ||||||||
\(210\) | −4.44098e10 | −0.00750366 | ||||||||
\(211\) | −9.48437e12 | −1.56119 | −0.780593 | − | 0.625039i | \(-0.785083\pi\) | ||||
−0.780593 | + | 0.625039i | \(0.785083\pi\) | |||||||
\(212\) | −4.70308e12 | −0.754285 | ||||||||
\(213\) | 9.11409e11 | 0.142438 | ||||||||
\(214\) | 2.69422e12 | 0.410353 | ||||||||
\(215\) | 8.00680e12 | 1.18863 | ||||||||
\(216\) | 9.39913e11 | 0.136017 | ||||||||
\(217\) | −7.34163e10 | −0.0103577 | ||||||||
\(218\) | 3.81353e12 | 0.524585 | ||||||||
\(219\) | −5.73746e12 | −0.769621 | ||||||||
\(220\) | −1.88837e12 | −0.247037 | ||||||||
\(221\) | 9.72848e10 | 0.0124133 | ||||||||
\(222\) | 3.02413e12 | 0.376408 | ||||||||
\(223\) | 1.52602e13 | 1.85303 | 0.926514 | − | 0.376260i | \(-0.122790\pi\) | ||||
0.926514 | + | 0.376260i | \(0.122790\pi\) | |||||||
\(224\) | −2.33971e11 | −0.0277203 | ||||||||
\(225\) | 8.91079e11 | 0.103018 | ||||||||
\(226\) | −6.27427e12 | −0.707892 | ||||||||
\(227\) | 1.23239e12 | 0.135709 | 0.0678543 | − | 0.997695i | \(-0.478385\pi\) | ||||
0.0678543 | + | 0.997695i | \(0.478385\pi\) | |||||||
\(228\) | 4.64725e12 | 0.499522 | ||||||||
\(229\) | 9.34468e11 | 0.0980549 | 0.0490275 | − | 0.998797i | \(-0.484388\pi\) | ||||
0.0490275 | + | 0.998797i | \(0.484388\pi\) | |||||||
\(230\) | −2.55077e10 | −0.00261317 | ||||||||
\(231\) | 4.34610e10 | 0.00434744 | ||||||||
\(232\) | 1.10627e12 | 0.108063 | ||||||||
\(233\) | −1.10618e13 | −1.05528 | −0.527641 | − | 0.849468i | \(-0.676923\pi\) | ||||
−0.527641 | + | 0.849468i | \(0.676923\pi\) | |||||||
\(234\) | 3.03963e10 | 0.00283226 | ||||||||
\(235\) | 2.41296e13 | 2.19623 | ||||||||
\(236\) | 1.25158e12 | 0.111286 | ||||||||
\(237\) | −1.01602e13 | −0.882649 | ||||||||
\(238\) | 7.44966e10 | 0.00632359 | ||||||||
\(239\) | −1.79204e13 | −1.48648 | −0.743240 | − | 0.669024i | \(-0.766712\pi\) | ||||
−0.743240 | + | 0.669024i | \(0.766712\pi\) | |||||||
\(240\) | 4.77095e12 | 0.386761 | ||||||||
\(241\) | −9.45537e11 | −0.0749177 | −0.0374589 | − | 0.999298i | \(-0.511926\pi\) | ||||
−0.0374589 | + | 0.999298i | \(0.511926\pi\) | |||||||
\(242\) | 4.60604e12 | 0.356733 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.90090e13 | 1.40707 | ||||||||
\(245\) | −1.57945e13 | −1.14312 | ||||||||
\(246\) | 3.61889e12 | 0.256113 | ||||||||
\(247\) | 3.26107e11 | 0.0225698 | ||||||||
\(248\) | −3.62780e12 | −0.245561 | ||||||||
\(249\) | 5.21099e12 | 0.345004 | ||||||||
\(250\) | 4.65124e12 | 0.301230 | ||||||||
\(251\) | −1.19285e13 | −0.755752 | −0.377876 | − | 0.925856i | \(-0.623345\pi\) | ||||
−0.377876 | + | 0.925856i | \(0.623345\pi\) | |||||||
\(252\) | −1.37034e11 | −0.00849425 | ||||||||
\(253\) | 2.49627e10 | 0.00151401 | ||||||||
\(254\) | 6.60955e12 | 0.392271 | ||||||||
\(255\) | −6.33137e12 | −0.367728 | ||||||||
\(256\) | −2.75683e12 | −0.156707 | ||||||||
\(257\) | 1.72401e13 | 0.959196 | 0.479598 | − | 0.877488i | \(-0.340783\pi\) | ||||
0.479598 | + | 0.877488i | \(0.340783\pi\) | |||||||
\(258\) | −4.19655e12 | −0.228551 | ||||||||
\(259\) | −9.56692e11 | −0.0510063 | ||||||||
\(260\) | 4.17809e11 | 0.0218084 | ||||||||
\(261\) | 9.97254e11 | 0.0509663 | ||||||||
\(262\) | −7.07807e12 | −0.354208 | ||||||||
\(263\) | −1.30175e13 | −0.637928 | −0.318964 | − | 0.947767i | \(-0.603335\pi\) | ||||
−0.318964 | + | 0.947767i | \(0.603335\pi\) | |||||||
\(264\) | 2.14758e12 | 0.103069 | ||||||||
\(265\) | 2.14783e13 | 1.00959 | ||||||||
\(266\) | 2.49719e11 | 0.0114975 | ||||||||
\(267\) | 5.48596e12 | 0.247423 | ||||||||
\(268\) | −2.82913e13 | −1.25000 | ||||||||
\(269\) | 2.39837e13 | 1.03819 | 0.519096 | − | 0.854716i | \(-0.326269\pi\) | ||||
0.519096 | + | 0.854716i | \(0.326269\pi\) | |||||||
\(270\) | −1.97821e12 | −0.0839020 | ||||||||
\(271\) | 8.58896e12 | 0.356952 | 0.178476 | − | 0.983944i | \(-0.442883\pi\) | ||||
0.178476 | + | 0.983944i | \(0.442883\pi\) | |||||||
\(272\) | −8.00318e12 | −0.325937 | ||||||||
\(273\) | −9.61594e9 | −0.000383793 0 | ||||||||
\(274\) | −3.60114e12 | −0.140868 | ||||||||
\(275\) | 2.03601e12 | 0.0780637 | ||||||||
\(276\) | −7.87083e10 | −0.00295815 | ||||||||
\(277\) | 3.88767e13 | 1.43235 | 0.716177 | − | 0.697919i | \(-0.245890\pi\) | ||||
0.716177 | + | 0.697919i | \(0.245890\pi\) | |||||||
\(278\) | −7.75523e12 | −0.280123 | ||||||||
\(279\) | −3.27029e12 | −0.115815 | ||||||||
\(280\) | 6.94226e11 | 0.0241064 | ||||||||
\(281\) | −5.40461e13 | −1.84026 | −0.920130 | − | 0.391612i | \(-0.871917\pi\) | ||||
−0.920130 | + | 0.391612i | \(0.871917\pi\) | |||||||
\(282\) | −1.26469e13 | −0.422292 | ||||||||
\(283\) | −3.02124e13 | −0.989371 | −0.494686 | − | 0.869072i | \(-0.664717\pi\) | ||||
−0.494686 | + | 0.869072i | \(0.664717\pi\) | |||||||
\(284\) | −6.56605e12 | −0.210889 | ||||||||
\(285\) | −2.12233e13 | −0.668600 | ||||||||
\(286\) | 6.94517e10 | 0.00214620 | ||||||||
\(287\) | −1.14484e12 | −0.0347053 | ||||||||
\(288\) | −1.04221e13 | −0.309955 | ||||||||
\(289\) | −2.36511e13 | −0.690103 | ||||||||
\(290\) | −2.32835e12 | −0.0666590 | ||||||||
\(291\) | −7.96370e12 | −0.223719 | ||||||||
\(292\) | 4.13343e13 | 1.13948 | ||||||||
\(293\) | 5.03877e13 | 1.36318 | 0.681589 | − | 0.731735i | \(-0.261289\pi\) | ||||
0.681589 | + | 0.731735i | \(0.261289\pi\) | |||||||
\(294\) | 8.27826e12 | 0.219801 | ||||||||
\(295\) | −5.71576e12 | −0.148954 | ||||||||
\(296\) | −4.72740e13 | −1.20926 | ||||||||
\(297\) | 1.93595e12 | 0.0486109 | ||||||||
\(298\) | −3.06784e11 | −0.00756211 | ||||||||
\(299\) | −5.52312e9 | −0.000133657 0 | ||||||||
\(300\) | −6.41959e12 | −0.152525 | ||||||||
\(301\) | 1.32759e12 | 0.0309705 | ||||||||
\(302\) | 2.75638e13 | 0.631395 | ||||||||
\(303\) | 2.02440e13 | 0.455366 | ||||||||
\(304\) | −2.68273e13 | −0.592615 | ||||||||
\(305\) | −8.68113e13 | −1.88333 | ||||||||
\(306\) | 3.31842e12 | 0.0707071 | ||||||||
\(307\) | −4.20907e13 | −0.880897 | −0.440448 | − | 0.897778i | \(-0.645181\pi\) | ||||
−0.440448 | + | 0.897778i | \(0.645181\pi\) | |||||||
\(308\) | −3.13106e11 | −0.00643668 | ||||||||
\(309\) | 5.58179e13 | 1.12720 | ||||||||
\(310\) | 7.63534e12 | 0.151474 | ||||||||
\(311\) | 9.40628e12 | 0.183331 | 0.0916655 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916655 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(312\) | −4.75163e11 | −0.00909897 | ||||||||
\(313\) | 7.43970e13 | 1.39979 | 0.699893 | − | 0.714248i | \(-0.253231\pi\) | ||||
0.699893 | + | 0.714248i | \(0.253231\pi\) | |||||||
\(314\) | 2.06360e13 | 0.381516 | ||||||||
\(315\) | 6.25813e11 | 0.0113694 | ||||||||
\(316\) | 7.31973e13 | 1.30682 | ||||||||
\(317\) | 2.30400e13 | 0.404257 | 0.202128 | − | 0.979359i | \(-0.435214\pi\) | ||||
0.202128 | + | 0.979359i | \(0.435214\pi\) | |||||||
\(318\) | −1.12573e13 | −0.194126 | ||||||||
\(319\) | 2.27860e12 | 0.0386207 | ||||||||
\(320\) | −1.58763e13 | −0.264499 | ||||||||
\(321\) | −3.79664e13 | −0.621758 | ||||||||
\(322\) | −4.22937e9 | −6.80877e−5 0 | ||||||||
\(323\) | 3.56017e13 | 0.563452 | ||||||||
\(324\) | −6.10411e12 | −0.0949784 | ||||||||
\(325\) | −4.50475e11 | −0.00689148 | ||||||||
\(326\) | 2.88444e13 | 0.433875 | ||||||||
\(327\) | −5.37394e13 | −0.794840 | ||||||||
\(328\) | −5.65714e13 | −0.822793 | ||||||||
\(329\) | 4.00087e12 | 0.0572239 | ||||||||
\(330\) | −4.51997e12 | −0.0635783 | ||||||||
\(331\) | −1.02273e13 | −0.141483 | −0.0707417 | − | 0.997495i | \(-0.522537\pi\) | ||||
−0.0707417 | + | 0.997495i | \(0.522537\pi\) | |||||||
\(332\) | −3.75415e13 | −0.510801 | ||||||||
\(333\) | −4.26154e13 | −0.570326 | ||||||||
\(334\) | 2.39169e13 | 0.314847 | ||||||||
\(335\) | 1.29202e14 | 1.67310 | ||||||||
\(336\) | 7.91060e11 | 0.0100773 | ||||||||
\(337\) | −2.55314e13 | −0.319971 | −0.159986 | − | 0.987119i | \(-0.551145\pi\) | ||||
−0.159986 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(338\) | 3.08888e13 | 0.380855 | ||||||||
\(339\) | 8.84156e13 | 1.07258 | ||||||||
\(340\) | 4.56130e13 | 0.544446 | ||||||||
\(341\) | −7.47222e12 | −0.0877608 | ||||||||
\(342\) | 1.11236e13 | 0.128559 | ||||||||
\(343\) | −5.24003e12 | −0.0595959 | ||||||||
\(344\) | 6.56015e13 | 0.734248 | ||||||||
\(345\) | 3.59449e11 | 0.00395943 | ||||||||
\(346\) | 6.04739e13 | 0.655616 | ||||||||
\(347\) | 9.22758e13 | 0.984636 | 0.492318 | − | 0.870415i | \(-0.336150\pi\) | ||||
0.492318 | + | 0.870415i | \(0.336150\pi\) | |||||||
\(348\) | −7.18450e12 | −0.0754590 | ||||||||
\(349\) | 8.18322e13 | 0.846027 | 0.423013 | − | 0.906123i | \(-0.360972\pi\) | ||||
0.423013 | + | 0.906123i | \(0.360972\pi\) | |||||||
\(350\) | −3.44955e11 | −0.00351066 | ||||||||
\(351\) | −4.28337e11 | −0.00429138 | ||||||||
\(352\) | −2.38133e13 | −0.234874 | ||||||||
\(353\) | 1.64332e14 | 1.59573 | 0.797867 | − | 0.602833i | \(-0.205961\pi\) | ||||
0.797867 | + | 0.602833i | \(0.205961\pi\) | |||||||
\(354\) | 2.99576e12 | 0.0286411 | ||||||||
\(355\) | 2.99862e13 | 0.282270 | ||||||||
\(356\) | −3.95224e13 | −0.366327 | ||||||||
\(357\) | −1.04979e12 | −0.00958136 | ||||||||
\(358\) | 7.39432e13 | 0.664571 | ||||||||
\(359\) | 4.41523e13 | 0.390781 | 0.195391 | − | 0.980725i | \(-0.437403\pi\) | ||||
0.195391 | + | 0.980725i | \(0.437403\pi\) | |||||||
\(360\) | 3.09240e13 | 0.269545 | ||||||||
\(361\) | 2.84965e12 | 0.0244625 | ||||||||
\(362\) | 2.27643e13 | 0.192468 | ||||||||
\(363\) | −6.49073e13 | −0.540514 | ||||||||
\(364\) | 6.92760e10 | 0.000568231 0 | ||||||||
\(365\) | −1.88767e14 | −1.52516 | ||||||||
\(366\) | 4.54998e13 | 0.362129 | ||||||||
\(367\) | −8.52900e13 | −0.668705 | −0.334353 | − | 0.942448i | \(-0.608518\pi\) | ||||
−0.334353 | + | 0.942448i | \(0.608518\pi\) | |||||||
\(368\) | 4.54362e11 | 0.00350945 | ||||||||
\(369\) | −5.09965e13 | −0.388057 | ||||||||
\(370\) | 9.94966e13 | 0.745931 | ||||||||
\(371\) | 3.56126e12 | 0.0263055 | ||||||||
\(372\) | 2.35601e13 | 0.171471 | ||||||||
\(373\) | 2.26293e14 | 1.62283 | 0.811414 | − | 0.584471i | \(-0.198698\pi\) | ||||
0.811414 | + | 0.584471i | \(0.198698\pi\) | |||||||
\(374\) | 7.58217e12 | 0.0535796 | ||||||||
\(375\) | −6.55442e13 | −0.456418 | ||||||||
\(376\) | 1.97699e14 | 1.35666 | ||||||||
\(377\) | −5.04151e11 | −0.00340944 | ||||||||
\(378\) | −3.28003e11 | −0.00218611 | ||||||||
\(379\) | 2.21395e13 | 0.145429 | 0.0727147 | − | 0.997353i | \(-0.476834\pi\) | ||||
0.0727147 | + | 0.997353i | \(0.476834\pi\) | |||||||
\(380\) | 1.52899e14 | 0.989906 | ||||||||
\(381\) | −9.31403e13 | −0.594361 | ||||||||
\(382\) | −7.66960e12 | −0.0482419 | ||||||||
\(383\) | −2.57233e14 | −1.59490 | −0.797451 | − | 0.603384i | \(-0.793819\pi\) | ||||
−0.797451 | + | 0.603384i | \(0.793819\pi\) | |||||||
\(384\) | 9.61587e13 | 0.587715 | ||||||||
\(385\) | 1.42991e12 | 0.00861536 | ||||||||
\(386\) | 7.59465e13 | 0.451105 | ||||||||
\(387\) | 5.91368e13 | 0.346296 | ||||||||
\(388\) | 5.73728e13 | 0.331231 | ||||||||
\(389\) | 1.48946e14 | 0.847825 | 0.423913 | − | 0.905703i | \(-0.360656\pi\) | ||||
0.423913 | + | 0.905703i | \(0.360656\pi\) | |||||||
\(390\) | 1.00006e12 | 0.00561271 | ||||||||
\(391\) | −6.02969e11 | −0.00333674 | ||||||||
\(392\) | −1.29408e14 | −0.706135 | ||||||||
\(393\) | 9.97426e13 | 0.536688 | ||||||||
\(394\) | 1.86364e13 | 0.0988854 | ||||||||
\(395\) | −3.34281e14 | −1.74915 | ||||||||
\(396\) | −1.39471e13 | −0.0719716 | ||||||||
\(397\) | −3.16206e14 | −1.60925 | −0.804623 | − | 0.593786i | \(-0.797632\pi\) | ||||
−0.804623 | + | 0.593786i | \(0.797632\pi\) | |||||||
\(398\) | −3.04357e13 | −0.152766 | ||||||||
\(399\) | −3.51899e12 | −0.0174207 | ||||||||
\(400\) | 3.70585e13 | 0.180950 | ||||||||
\(401\) | 1.69636e14 | 0.817004 | 0.408502 | − | 0.912757i | \(-0.366051\pi\) | ||||
0.408502 | + | 0.912757i | \(0.366051\pi\) | |||||||
\(402\) | −6.77177e13 | −0.321706 | ||||||||
\(403\) | 1.65326e12 | 0.00774754 | ||||||||
\(404\) | −1.45843e14 | −0.674200 | ||||||||
\(405\) | 2.78765e13 | 0.127127 | ||||||||
\(406\) | −3.86058e11 | −0.00173684 | ||||||||
\(407\) | −9.73709e13 | −0.432175 | ||||||||
\(408\) | −5.18744e13 | −0.227155 | ||||||||
\(409\) | −1.55395e14 | −0.671366 | −0.335683 | − | 0.941975i | \(-0.608967\pi\) | ||||
−0.335683 | + | 0.941975i | \(0.608967\pi\) | |||||||
\(410\) | 1.19065e14 | 0.507541 | ||||||||
\(411\) | 5.07465e13 | 0.213440 | ||||||||
\(412\) | −4.02128e14 | −1.66890 | ||||||||
\(413\) | −9.47717e11 | −0.00388109 | ||||||||
\(414\) | −1.88395e11 | −0.000761322 0 | ||||||||
\(415\) | 1.71446e14 | 0.683696 | ||||||||
\(416\) | 5.26879e12 | 0.0207347 | ||||||||
\(417\) | 1.09285e14 | 0.424436 | ||||||||
\(418\) | 2.54161e13 | 0.0974180 | ||||||||
\(419\) | 5.61588e13 | 0.212442 | 0.106221 | − | 0.994343i | \(-0.466125\pi\) | ||||
0.106221 | + | 0.994343i | \(0.466125\pi\) | |||||||
\(420\) | −4.50854e12 | −0.0168331 | ||||||||
\(421\) | 4.27803e13 | 0.157649 | 0.0788247 | − | 0.996888i | \(-0.474883\pi\) | ||||
0.0788247 | + | 0.996888i | \(0.474883\pi\) | |||||||
\(422\) | 1.63549e14 | 0.594882 | ||||||||
\(423\) | 1.78217e14 | 0.639848 | ||||||||
\(424\) | 1.75976e14 | 0.623652 | ||||||||
\(425\) | −4.91792e13 | −0.172045 | ||||||||
\(426\) | −1.57164e13 | −0.0542752 | ||||||||
\(427\) | −1.43940e13 | −0.0490713 | ||||||||
\(428\) | 2.73521e14 | 0.920554 | ||||||||
\(429\) | −9.78698e11 | −0.00325187 | ||||||||
\(430\) | −1.38070e14 | −0.452922 | ||||||||
\(431\) | −2.22098e14 | −0.719317 | −0.359658 | − | 0.933084i | \(-0.617107\pi\) | ||||
−0.359658 | + | 0.933084i | \(0.617107\pi\) | |||||||
\(432\) | 3.52374e13 | 0.112679 | ||||||||
\(433\) | 4.37273e14 | 1.38061 | 0.690303 | − | 0.723521i | \(-0.257477\pi\) | ||||
0.690303 | + | 0.723521i | \(0.257477\pi\) | |||||||
\(434\) | 1.26600e12 | 0.00394675 | ||||||||
\(435\) | 3.28105e13 | 0.101000 | ||||||||
\(436\) | 3.87154e14 | 1.17681 | ||||||||
\(437\) | −2.02120e12 | −0.00606683 | ||||||||
\(438\) | 9.89374e13 | 0.293260 | ||||||||
\(439\) | −1.67284e14 | −0.489667 | −0.244833 | − | 0.969565i | \(-0.578733\pi\) | ||||
−0.244833 | + | 0.969565i | \(0.578733\pi\) | |||||||
\(440\) | 7.06574e13 | 0.204253 | ||||||||
\(441\) | −1.16655e14 | −0.333037 | ||||||||
\(442\) | −1.67759e12 | −0.00473002 | ||||||||
\(443\) | −5.50257e14 | −1.53231 | −0.766153 | − | 0.642659i | \(-0.777831\pi\) | ||||
−0.766153 | + | 0.642659i | \(0.777831\pi\) | |||||||
\(444\) | 3.07013e14 | 0.844405 | ||||||||
\(445\) | 1.80493e14 | 0.490321 | ||||||||
\(446\) | −2.63148e14 | −0.706086 | ||||||||
\(447\) | 4.32313e12 | 0.0114579 | ||||||||
\(448\) | −2.63241e12 | −0.00689168 | ||||||||
\(449\) | 1.21006e14 | 0.312933 | 0.156467 | − | 0.987683i | \(-0.449990\pi\) | ||||
0.156467 | + | 0.987683i | \(0.449990\pi\) | |||||||
\(450\) | −1.53659e13 | −0.0392544 | ||||||||
\(451\) | −1.16521e14 | −0.294058 | ||||||||
\(452\) | −6.36971e14 | −1.58803 | ||||||||
\(453\) | −3.88423e14 | −0.956677 | ||||||||
\(454\) | −2.12515e13 | −0.0517110 | ||||||||
\(455\) | −3.16373e11 | −0.000760566 0 | ||||||||
\(456\) | −1.73887e14 | −0.413011 | ||||||||
\(457\) | 6.51012e14 | 1.52774 | 0.763871 | − | 0.645369i | \(-0.223296\pi\) | ||||
0.763871 | + | 0.645369i | \(0.223296\pi\) | |||||||
\(458\) | −1.61141e13 | −0.0373633 | ||||||||
\(459\) | −4.67624e13 | −0.107134 | ||||||||
\(460\) | −2.58957e12 | −0.00586219 | ||||||||
\(461\) | 1.38009e14 | 0.308710 | 0.154355 | − | 0.988015i | \(-0.450670\pi\) | ||||
0.154355 | + | 0.988015i | \(0.450670\pi\) | |||||||
\(462\) | −7.49446e11 | −0.00165657 | ||||||||
\(463\) | −1.78732e14 | −0.390396 | −0.195198 | − | 0.980764i | \(-0.562535\pi\) | ||||
−0.195198 | + | 0.980764i | \(0.562535\pi\) | |||||||
\(464\) | 4.14742e13 | 0.0895219 | ||||||||
\(465\) | −1.07596e14 | −0.229511 | ||||||||
\(466\) | 1.90751e14 | 0.402109 | ||||||||
\(467\) | 6.46209e14 | 1.34626 | 0.673132 | − | 0.739523i | \(-0.264949\pi\) | ||||
0.673132 | + | 0.739523i | \(0.264949\pi\) | |||||||
\(468\) | 3.08586e12 | 0.00635367 | ||||||||
\(469\) | 2.14227e13 | 0.0435937 | ||||||||
\(470\) | −4.16093e14 | −0.836859 | ||||||||
\(471\) | −2.90798e14 | −0.578065 | ||||||||
\(472\) | −4.68305e13 | −0.0920127 | ||||||||
\(473\) | 1.35120e14 | 0.262412 | ||||||||
\(474\) | 1.75204e14 | 0.336328 | ||||||||
\(475\) | −1.64853e14 | −0.312811 | ||||||||
\(476\) | 7.56299e12 | 0.0141858 | ||||||||
\(477\) | 1.58635e14 | 0.294135 | ||||||||
\(478\) | 3.09021e14 | 0.566415 | ||||||||
\(479\) | −2.06190e14 | −0.373613 | −0.186806 | − | 0.982397i | \(-0.559814\pi\) | ||||
−0.186806 | + | 0.982397i | \(0.559814\pi\) | |||||||
\(480\) | −3.42897e14 | −0.614239 | ||||||||
\(481\) | 2.15437e13 | 0.0381525 | ||||||||
\(482\) | 1.63049e13 | 0.0285470 | ||||||||
\(483\) | 5.95994e10 | 0.000103165 0 | ||||||||
\(484\) | 4.67611e14 | 0.800267 | ||||||||
\(485\) | −2.62013e14 | −0.443346 | ||||||||
\(486\) | −1.46107e13 | −0.0244440 | ||||||||
\(487\) | −1.41182e14 | −0.233545 | −0.116772 | − | 0.993159i | \(-0.537255\pi\) | ||||
−0.116772 | + | 0.993159i | \(0.537255\pi\) | |||||||
\(488\) | −7.11265e14 | −1.16338 | ||||||||
\(489\) | −4.06469e14 | −0.657398 | ||||||||
\(490\) | 2.72362e14 | 0.435580 | ||||||||
\(491\) | −2.31067e14 | −0.365417 | −0.182709 | − | 0.983167i | \(-0.558487\pi\) | ||||
−0.182709 | + | 0.983167i | \(0.558487\pi\) | |||||||
\(492\) | 3.67393e14 | 0.574544 | ||||||||
\(493\) | −5.50391e13 | −0.0851164 | ||||||||
\(494\) | −5.62342e12 | −0.00860008 | ||||||||
\(495\) | 6.36944e13 | 0.0963325 | ||||||||
\(496\) | −1.36006e14 | −0.203427 | ||||||||
\(497\) | 4.97193e12 | 0.00735471 | ||||||||
\(498\) | −8.98589e13 | −0.131462 | ||||||||
\(499\) | 5.09795e14 | 0.737637 | 0.368818 | − | 0.929501i | \(-0.379762\pi\) | ||||
0.368818 | + | 0.929501i | \(0.379762\pi\) | |||||||
\(500\) | 4.72199e14 | 0.675757 | ||||||||
\(501\) | −3.37032e14 | −0.477050 | ||||||||
\(502\) | 2.05696e14 | 0.287975 | ||||||||
\(503\) | −2.71402e14 | −0.375828 | −0.187914 | − | 0.982185i | \(-0.560173\pi\) | ||||
−0.187914 | + | 0.982185i | \(0.560173\pi\) | |||||||
\(504\) | 5.12743e12 | 0.00702315 | ||||||||
\(505\) | 6.66044e14 | 0.902402 | ||||||||
\(506\) | −4.30460e11 | −0.000576906 0 | ||||||||
\(507\) | −4.35278e14 | −0.577063 | ||||||||
\(508\) | 6.71009e14 | 0.879990 | ||||||||
\(509\) | −1.29361e15 | −1.67825 | −0.839123 | − | 0.543941i | \(-0.816931\pi\) | ||||
−0.839123 | + | 0.543941i | \(0.816931\pi\) | |||||||
\(510\) | 1.09179e14 | 0.140121 | ||||||||
\(511\) | −3.12991e13 | −0.0397390 | ||||||||
\(512\) | −7.62885e14 | −0.958240 | ||||||||
\(513\) | −1.56751e14 | −0.194790 | ||||||||
\(514\) | −2.97290e14 | −0.365496 | ||||||||
\(515\) | 1.83646e15 | 2.23379 | ||||||||
\(516\) | −4.26038e14 | −0.512714 | ||||||||
\(517\) | 4.07204e14 | 0.484857 | ||||||||
\(518\) | 1.64973e13 | 0.0194357 | ||||||||
\(519\) | −8.52185e14 | −0.993376 | ||||||||
\(520\) | −1.56333e13 | −0.0180315 | ||||||||
\(521\) | 6.01854e14 | 0.686884 | 0.343442 | − | 0.939174i | \(-0.388407\pi\) | ||||
0.343442 | + | 0.939174i | \(0.388407\pi\) | |||||||
\(522\) | −1.71968e13 | −0.0194204 | ||||||||
\(523\) | −1.06743e15 | −1.19284 | −0.596418 | − | 0.802674i | \(-0.703410\pi\) | ||||
−0.596418 | + | 0.802674i | \(0.703410\pi\) | |||||||
\(524\) | −7.18574e14 | −0.794602 | ||||||||
\(525\) | 4.86103e12 | 0.00531927 | ||||||||
\(526\) | 2.24475e14 | 0.243079 | ||||||||
\(527\) | 1.80490e14 | 0.193417 | ||||||||
\(528\) | 8.05130e13 | 0.0853846 | ||||||||
\(529\) | −9.52776e14 | −0.999964 | ||||||||
\(530\) | −3.70373e14 | −0.384700 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 2.53518e13 | 0.0257926 | ||||||||
\(533\) | 2.57807e13 | 0.0259595 | ||||||||
\(534\) | −9.46005e13 | −0.0942793 | ||||||||
\(535\) | −1.24913e15 | −1.23214 | ||||||||
\(536\) | 1.05858e15 | 1.03352 | ||||||||
\(537\) | −1.04199e15 | −1.00694 | ||||||||
\(538\) | −4.13577e14 | −0.395598 | ||||||||
\(539\) | −2.66543e14 | −0.252365 | ||||||||
\(540\) | −2.00830e14 | −0.188219 | ||||||||
\(541\) | 2.76164e14 | 0.256202 | 0.128101 | − | 0.991761i | \(-0.459112\pi\) | ||||
0.128101 | + | 0.991761i | \(0.459112\pi\) | |||||||
\(542\) | −1.48109e14 | −0.136014 | ||||||||
\(543\) | −3.20790e14 | −0.291623 | ||||||||
\(544\) | 5.75204e14 | 0.517640 | ||||||||
\(545\) | −1.76807e15 | −1.57514 | ||||||||
\(546\) | 1.65818e11 | 0.000146242 0 | ||||||||
\(547\) | −3.59061e14 | −0.313500 | −0.156750 | − | 0.987638i | \(-0.550102\pi\) | ||||
−0.156750 | + | 0.987638i | \(0.550102\pi\) | |||||||
\(548\) | −3.65592e14 | −0.316012 | ||||||||
\(549\) | −6.41173e14 | −0.548690 | ||||||||
\(550\) | −3.51091e13 | −0.0297457 | ||||||||
\(551\) | −1.84496e14 | −0.154758 | ||||||||
\(552\) | 2.94505e12 | 0.00244584 | ||||||||
\(553\) | −5.54263e13 | −0.0455751 | ||||||||
\(554\) | −6.70393e14 | −0.545790 | ||||||||
\(555\) | −1.40208e15 | −1.13022 | ||||||||
\(556\) | −7.87320e14 | −0.628405 | ||||||||
\(557\) | 3.36952e14 | 0.266296 | 0.133148 | − | 0.991096i | \(-0.457491\pi\) | ||||
0.133148 | + | 0.991096i | \(0.457491\pi\) | |||||||
\(558\) | 5.63933e13 | 0.0441305 | ||||||||
\(559\) | −2.98960e13 | −0.0231658 | ||||||||
\(560\) | 2.60266e13 | 0.0199702 | ||||||||
\(561\) | −1.06846e14 | −0.0811827 | ||||||||
\(562\) | 9.31976e14 | 0.701221 | ||||||||
\(563\) | 2.16086e15 | 1.61001 | 0.805007 | − | 0.593265i | \(-0.202162\pi\) | ||||
0.805007 | + | 0.593265i | \(0.202162\pi\) | |||||||
\(564\) | −1.28393e15 | −0.947338 | ||||||||
\(565\) | 2.90895e15 | 2.12554 | ||||||||
\(566\) | 5.20985e14 | 0.376994 | ||||||||
\(567\) | 4.62214e12 | 0.00331235 | ||||||||
\(568\) | 2.45683e14 | 0.174365 | ||||||||
\(569\) | −8.33757e14 | −0.586033 | −0.293016 | − | 0.956107i | \(-0.594659\pi\) | ||||
−0.293016 | + | 0.956107i | \(0.594659\pi\) | |||||||
\(570\) | 3.65977e14 | 0.254766 | ||||||||
\(571\) | −1.16917e15 | −0.806080 | −0.403040 | − | 0.915182i | \(-0.632046\pi\) | ||||
−0.403040 | + | 0.915182i | \(0.632046\pi\) | |||||||
\(572\) | 7.05082e12 | 0.00481461 | ||||||||
\(573\) | 1.08078e14 | 0.0730950 | ||||||||
\(574\) | 1.97418e13 | 0.0132243 | ||||||||
\(575\) | 2.79204e12 | 0.00185246 | ||||||||
\(576\) | −1.17260e14 | −0.0770592 | ||||||||
\(577\) | −8.63090e14 | −0.561810 | −0.280905 | − | 0.959736i | \(-0.590635\pi\) | ||||
−0.280905 | + | 0.959736i | \(0.590635\pi\) | |||||||
\(578\) | 4.07843e14 | 0.262960 | ||||||||
\(579\) | −1.07022e15 | −0.683504 | ||||||||
\(580\) | −2.36376e14 | −0.149538 | ||||||||
\(581\) | 2.84271e13 | 0.0178141 | ||||||||
\(582\) | 1.37327e14 | 0.0852470 | ||||||||
\(583\) | 3.62461e14 | 0.222886 | ||||||||
\(584\) | −1.54662e15 | −0.942132 | ||||||||
\(585\) | −1.40927e13 | −0.00850425 | ||||||||
\(586\) | −8.68890e14 | −0.519431 | ||||||||
\(587\) | −1.15770e15 | −0.685627 | −0.342813 | − | 0.939404i | \(-0.611380\pi\) | ||||
−0.342813 | + | 0.939404i | \(0.611380\pi\) | |||||||
\(588\) | 8.40419e14 | 0.493083 | ||||||||
\(589\) | 6.05016e14 | 0.351668 | ||||||||
\(590\) | 9.85631e13 | 0.0567582 | ||||||||
\(591\) | −2.62620e14 | −0.149829 | ||||||||
\(592\) | −1.77230e15 | −1.00177 | ||||||||
\(593\) | 3.40899e14 | 0.190908 | 0.0954542 | − | 0.995434i | \(-0.469570\pi\) | ||||
0.0954542 | + | 0.995434i | \(0.469570\pi\) | |||||||
\(594\) | −3.33837e13 | −0.0185229 | ||||||||
\(595\) | −3.45390e13 | −0.0189874 | ||||||||
\(596\) | −3.11451e13 | −0.0169643 | ||||||||
\(597\) | 4.28893e14 | 0.231468 | ||||||||
\(598\) | 9.52412e10 | 5.09294e−5 0 | ||||||||
\(599\) | 6.59440e14 | 0.349404 | 0.174702 | − | 0.984621i | \(-0.444104\pi\) | ||||
0.174702 | + | 0.984621i | \(0.444104\pi\) | |||||||
\(600\) | 2.40203e14 | 0.126109 | ||||||||
\(601\) | −7.80789e14 | −0.406185 | −0.203093 | − | 0.979160i | \(-0.565099\pi\) | ||||
−0.203093 | + | 0.979160i | \(0.565099\pi\) | |||||||
\(602\) | −2.28931e13 | −0.0118011 | ||||||||
\(603\) | 9.54263e14 | 0.487442 | ||||||||
\(604\) | 2.79831e15 | 1.41642 | ||||||||
\(605\) | −2.13551e15 | −1.07114 | ||||||||
\(606\) | −3.49089e14 | −0.173515 | ||||||||
\(607\) | 3.21551e15 | 1.58384 | 0.791921 | − | 0.610623i | \(-0.209081\pi\) | ||||
0.791921 | + | 0.610623i | \(0.209081\pi\) | |||||||
\(608\) | 1.92813e15 | 0.941168 | ||||||||
\(609\) | 5.44024e12 | 0.00263162 | ||||||||
\(610\) | 1.49698e15 | 0.717633 | ||||||||
\(611\) | −9.00956e13 | −0.0428033 | ||||||||
\(612\) | 3.36889e14 | 0.158619 | ||||||||
\(613\) | 3.43995e15 | 1.60517 | 0.802583 | − | 0.596541i | \(-0.203459\pi\) | ||||
0.802583 | + | 0.596541i | \(0.203459\pi\) | |||||||
\(614\) | 7.25816e14 | 0.335661 | ||||||||
\(615\) | −1.67783e15 | −0.769015 | ||||||||
\(616\) | 1.17155e13 | 0.00532192 | ||||||||
\(617\) | −2.37363e15 | −1.06867 | −0.534337 | − | 0.845272i | \(-0.679439\pi\) | ||||
−0.534337 | + | 0.845272i | \(0.679439\pi\) | |||||||
\(618\) | −9.62530e14 | −0.429515 | ||||||||
\(619\) | −5.35918e14 | −0.237028 | −0.118514 | − | 0.992952i | \(-0.537813\pi\) | ||||
−0.118514 | + | 0.992952i | \(0.537813\pi\) | |||||||
\(620\) | 7.75149e14 | 0.339806 | ||||||||
\(621\) | 2.65483e12 | 0.00115354 | ||||||||
\(622\) | −1.62203e14 | −0.0698573 | ||||||||
\(623\) | 2.99271e13 | 0.0127756 | ||||||||
\(624\) | −1.78139e13 | −0.00753777 | ||||||||
\(625\) | −2.89330e15 | −1.21354 | ||||||||
\(626\) | −1.28291e15 | −0.533381 | ||||||||
\(627\) | −3.58158e14 | −0.147606 | ||||||||
\(628\) | 2.09499e15 | 0.855863 | ||||||||
\(629\) | 2.35197e15 | 0.952474 | ||||||||
\(630\) | −1.07916e13 | −0.00433224 | ||||||||
\(631\) | 1.90985e15 | 0.760044 | 0.380022 | − | 0.924978i | \(-0.375916\pi\) | ||||
0.380022 | + | 0.924978i | \(0.375916\pi\) | |||||||
\(632\) | −2.73884e15 | −1.08049 | ||||||||
\(633\) | −2.30470e15 | −0.901352 | ||||||||
\(634\) | −3.97305e14 | −0.154040 | ||||||||
\(635\) | −3.06440e15 | −1.17785 | ||||||||
\(636\) | −1.14285e15 | −0.435487 | ||||||||
\(637\) | 5.89739e13 | 0.0222788 | ||||||||
\(638\) | −3.92925e13 | −0.0147162 | ||||||||
\(639\) | 2.21472e14 | 0.0822365 | ||||||||
\(640\) | 3.16371e15 | 1.16468 | ||||||||
\(641\) | 4.57415e15 | 1.66952 | 0.834760 | − | 0.550614i | \(-0.185606\pi\) | ||||
0.834760 | + | 0.550614i | \(0.185606\pi\) | |||||||
\(642\) | 6.54696e14 | 0.236918 | ||||||||
\(643\) | −6.28032e14 | −0.225331 | −0.112666 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112666 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(644\) | −4.29371e11 | −0.000152743 0 | ||||||||
\(645\) | 1.94565e15 | 0.686257 | ||||||||
\(646\) | −6.13919e14 | −0.214700 | ||||||||
\(647\) | −4.79908e15 | −1.66412 | −0.832060 | − | 0.554686i | \(-0.812838\pi\) | ||||
−0.832060 | + | 0.554686i | \(0.812838\pi\) | |||||||
\(648\) | 2.28399e14 | 0.0785292 | ||||||||
\(649\) | −9.64573e13 | −0.0328844 | ||||||||
\(650\) | 7.76804e12 | 0.00262596 | ||||||||
\(651\) | −1.78402e13 | −0.00598003 | ||||||||
\(652\) | 2.92832e15 | 0.973322 | ||||||||
\(653\) | −3.50364e15 | −1.15478 | −0.577388 | − | 0.816470i | \(-0.695928\pi\) | ||||
−0.577388 | + | 0.816470i | \(0.695928\pi\) | |||||||
\(654\) | 9.26687e14 | 0.302869 | ||||||||
\(655\) | 3.28162e15 | 1.06356 | ||||||||
\(656\) | −2.12086e15 | −0.681619 | ||||||||
\(657\) | −1.39420e15 | −0.444341 | ||||||||
\(658\) | −6.89915e13 | −0.0218048 | ||||||||
\(659\) | 3.69398e15 | 1.15778 | 0.578889 | − | 0.815407i | \(-0.303487\pi\) | ||||
0.578889 | + | 0.815407i | \(0.303487\pi\) | |||||||
\(660\) | −4.58873e14 | −0.142627 | ||||||||
\(661\) | −3.57572e15 | −1.10219 | −0.551093 | − | 0.834444i | \(-0.685789\pi\) | ||||
−0.551093 | + | 0.834444i | \(0.685789\pi\) | |||||||
\(662\) | 1.76360e14 | 0.0539114 | ||||||||
\(663\) | 2.36402e13 | 0.00716683 | ||||||||
\(664\) | 1.40470e15 | 0.422336 | ||||||||
\(665\) | −1.15778e14 | −0.0345228 | ||||||||
\(666\) | 7.34864e14 | 0.217320 | ||||||||
\(667\) | 3.12472e12 | 0.000916471 0 | ||||||||
\(668\) | 2.42807e15 | 0.706303 | ||||||||
\(669\) | 3.70822e15 | 1.06985 | ||||||||
\(670\) | −2.22797e15 | −0.637527 | ||||||||
\(671\) | −1.46500e15 | −0.415780 | ||||||||
\(672\) | −5.68550e13 | −0.0160043 | ||||||||
\(673\) | −1.82280e15 | −0.508927 | −0.254464 | − | 0.967082i | \(-0.581899\pi\) | ||||
−0.254464 | + | 0.967082i | \(0.581899\pi\) | |||||||
\(674\) | 4.40267e14 | 0.121923 | ||||||||
\(675\) | 2.16532e14 | 0.0594774 | ||||||||
\(676\) | 3.13587e15 | 0.854380 | ||||||||
\(677\) | −3.90103e15 | −1.05424 | −0.527122 | − | 0.849789i | \(-0.676729\pi\) | ||||
−0.527122 | + | 0.849789i | \(0.676729\pi\) | |||||||
\(678\) | −1.52465e15 | −0.408701 | ||||||||
\(679\) | −4.34437e13 | −0.0115516 | ||||||||
\(680\) | −1.70671e15 | −0.450154 | ||||||||
\(681\) | 2.99472e14 | 0.0783514 | ||||||||
\(682\) | 1.28852e14 | 0.0334407 | ||||||||
\(683\) | −1.94562e15 | −0.500891 | −0.250446 | − | 0.968131i | \(-0.580577\pi\) | ||||
−0.250446 | + | 0.968131i | \(0.580577\pi\) | |||||||
\(684\) | 1.12928e15 | 0.288399 | ||||||||
\(685\) | 1.66960e15 | 0.422976 | ||||||||
\(686\) | 9.03596e13 | 0.0227087 | ||||||||
\(687\) | 2.27076e14 | 0.0566120 | ||||||||
\(688\) | 2.45940e15 | 0.608266 | ||||||||
\(689\) | −8.01960e13 | −0.0196765 | ||||||||
\(690\) | −6.19837e12 | −0.00150872 | ||||||||
\(691\) | −6.12024e15 | −1.47788 | −0.738941 | − | 0.673771i | \(-0.764674\pi\) | ||||
−0.738941 | + | 0.673771i | \(0.764674\pi\) | |||||||
\(692\) | 6.13938e15 | 1.47076 | ||||||||
\(693\) | 1.05610e13 | 0.00251000 | ||||||||
\(694\) | −1.59121e15 | −0.375190 | ||||||||
\(695\) | 3.59557e15 | 0.841107 | ||||||||
\(696\) | 2.68824e14 | 0.0623904 | ||||||||
\(697\) | 2.81453e15 | 0.648075 | ||||||||
\(698\) | −1.41112e15 | −0.322374 | ||||||||
\(699\) | −2.68802e15 | −0.609267 | ||||||||
\(700\) | −3.50203e13 | −0.00787553 | ||||||||
\(701\) | 6.24454e15 | 1.39332 | 0.696661 | − | 0.717401i | \(-0.254668\pi\) | ||||
0.696661 | + | 0.717401i | \(0.254668\pi\) | |||||||
\(702\) | 7.38629e12 | 0.00163521 | ||||||||
\(703\) | 7.88400e15 | 1.73178 | ||||||||
\(704\) | −2.67924e14 | −0.0583931 | ||||||||
\(705\) | 5.86349e15 | 1.26799 | ||||||||
\(706\) | −2.83375e15 | −0.608046 | ||||||||
\(707\) | 1.10435e14 | 0.0235126 | ||||||||
\(708\) | 3.04133e14 | 0.0642511 | ||||||||
\(709\) | 1.48232e15 | 0.310734 | 0.155367 | − | 0.987857i | \(-0.450344\pi\) | ||||
0.155367 | + | 0.987857i | \(0.450344\pi\) | |||||||
\(710\) | −5.17084e14 | −0.107557 | ||||||||
\(711\) | −2.46894e15 | −0.509598 | ||||||||
\(712\) | 1.47882e15 | 0.302883 | ||||||||
\(713\) | −1.02469e13 | −0.00208257 | ||||||||
\(714\) | 1.81027e13 | 0.00365092 | ||||||||
\(715\) | −3.22000e13 | −0.00644426 | ||||||||
\(716\) | 7.50680e15 | 1.49085 | ||||||||
\(717\) | −4.35466e15 | −0.858220 | ||||||||
\(718\) | −7.61366e14 | −0.148905 | ||||||||
\(719\) | −8.47515e15 | −1.64490 | −0.822448 | − | 0.568840i | \(-0.807393\pi\) | ||||
−0.822448 | + | 0.568840i | \(0.807393\pi\) | |||||||
\(720\) | 1.15934e15 | 0.223297 | ||||||||
\(721\) | 3.04499e14 | 0.0582026 | ||||||||
\(722\) | −4.91396e13 | −0.00932131 | ||||||||
\(723\) | −2.29765e14 | −0.0432538 | ||||||||
\(724\) | 2.31106e15 | 0.431767 | ||||||||
\(725\) | 2.54857e14 | 0.0472540 | ||||||||
\(726\) | 1.11927e15 | 0.205960 | ||||||||
\(727\) | 1.05823e16 | 1.93260 | 0.966301 | − | 0.257415i | \(-0.0828706\pi\) | ||||
0.966301 | + | 0.257415i | \(0.0828706\pi\) | |||||||
\(728\) | −2.59212e12 | −0.000469820 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 3.25513e15 | 0.581155 | ||||||||
\(731\) | −3.26380e15 | −0.578332 | ||||||||
\(732\) | 4.61919e15 | 0.812372 | ||||||||
\(733\) | 6.21466e15 | 1.08479 | 0.542395 | − | 0.840124i | \(-0.317518\pi\) | ||||
0.542395 | + | 0.840124i | \(0.317518\pi\) | |||||||
\(734\) | 1.47075e15 | 0.254806 | ||||||||
\(735\) | −3.83806e15 | −0.659982 | ||||||||
\(736\) | −3.26559e13 | −0.00557357 | ||||||||
\(737\) | 2.18037e15 | 0.369368 | ||||||||
\(738\) | 8.79389e14 | 0.147867 | ||||||||
\(739\) | −9.46484e14 | −0.157968 | −0.0789840 | − | 0.996876i | \(-0.525168\pi\) | ||||
−0.0789840 | + | 0.996876i | \(0.525168\pi\) | |||||||
\(740\) | 1.01010e16 | 1.67336 | ||||||||
\(741\) | 7.92440e13 | 0.0130307 | ||||||||
\(742\) | −6.14108e13 | −0.0100236 | ||||||||
\(743\) | 2.09825e15 | 0.339953 | 0.169977 | − | 0.985448i | \(-0.445631\pi\) | ||||
0.169977 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(744\) | −8.81555e14 | −0.141775 | ||||||||
\(745\) | 1.42235e14 | 0.0227063 | ||||||||
\(746\) | −3.90222e15 | −0.618370 | ||||||||
\(747\) | 1.26627e15 | 0.199188 | ||||||||
\(748\) | 7.69751e14 | 0.120196 | ||||||||
\(749\) | −2.07115e14 | −0.0321042 | ||||||||
\(750\) | 1.13025e15 | 0.173915 | ||||||||
\(751\) | 5.77633e14 | 0.0882332 | 0.0441166 | − | 0.999026i | \(-0.485953\pi\) | ||||
0.0441166 | + | 0.999026i | \(0.485953\pi\) | |||||||
\(752\) | 7.41175e15 | 1.12389 | ||||||||
\(753\) | −2.89862e15 | −0.436333 | ||||||||
\(754\) | 8.69363e12 | 0.00129915 | ||||||||
\(755\) | −1.27795e16 | −1.89585 | ||||||||
\(756\) | −3.32992e13 | −0.00490416 | ||||||||
\(757\) | 5.59338e15 | 0.817800 | 0.408900 | − | 0.912579i | \(-0.365913\pi\) | ||||
0.408900 | + | 0.912579i | \(0.365913\pi\) | |||||||
\(758\) | −3.81776e14 | −0.0554150 | ||||||||
\(759\) | 6.06595e12 | 0.000874116 0 | ||||||||
\(760\) | −5.72105e15 | −0.818466 | ||||||||
\(761\) | −1.23287e16 | −1.75107 | −0.875533 | − | 0.483158i | \(-0.839490\pi\) | ||||
−0.875533 | + | 0.483158i | \(0.839490\pi\) | |||||||
\(762\) | 1.60612e15 | 0.226478 | ||||||||
\(763\) | −2.93160e14 | −0.0410412 | ||||||||
\(764\) | −7.78626e14 | −0.108222 | ||||||||
\(765\) | −1.53852e15 | −0.212308 | ||||||||
\(766\) | 4.43576e15 | 0.607728 | ||||||||
\(767\) | 2.13416e13 | 0.00290304 | ||||||||
\(768\) | −6.69909e14 | −0.0904751 | ||||||||
\(769\) | 7.07708e15 | 0.948985 | 0.474492 | − | 0.880260i | \(-0.342632\pi\) | ||||
0.474492 | + | 0.880260i | \(0.342632\pi\) | |||||||
\(770\) | −2.46574e13 | −0.00328283 | ||||||||
\(771\) | 4.18934e15 | 0.553792 | ||||||||
\(772\) | 7.71017e15 | 1.01197 | ||||||||
\(773\) | 7.41041e15 | 0.965728 | 0.482864 | − | 0.875695i | \(-0.339597\pi\) | ||||
0.482864 | + | 0.875695i | \(0.339597\pi\) | |||||||
\(774\) | −1.01976e15 | −0.131954 | ||||||||
\(775\) | −8.35753e14 | −0.107379 | ||||||||
\(776\) | −2.14673e15 | −0.273866 | ||||||||
\(777\) | −2.32476e14 | −0.0294485 | ||||||||
\(778\) | −2.56844e15 | −0.323059 | ||||||||
\(779\) | 9.43454e15 | 1.17832 | ||||||||
\(780\) | 1.01528e14 | 0.0125911 | ||||||||
\(781\) | 5.06037e14 | 0.0623163 | ||||||||
\(782\) | 1.03977e13 | 0.00127145 | ||||||||
\(783\) | 2.42333e14 | 0.0294254 | ||||||||
\(784\) | −4.85151e15 | −0.584977 | ||||||||
\(785\) | −9.56751e15 | −1.14555 | ||||||||
\(786\) | −1.71997e15 | −0.204502 | ||||||||
\(787\) | −1.46049e16 | −1.72440 | −0.862200 | − | 0.506568i | \(-0.830914\pi\) | ||||
−0.862200 | + | 0.506568i | \(0.830914\pi\) | |||||||
\(788\) | 1.89199e15 | 0.221832 | ||||||||
\(789\) | −3.16326e15 | −0.368308 | ||||||||
\(790\) | 5.76437e15 | 0.666504 | ||||||||
\(791\) | 4.82326e14 | 0.0553822 | ||||||||
\(792\) | 5.21863e14 | 0.0595070 | ||||||||
\(793\) | 3.24138e14 | 0.0367052 | ||||||||
\(794\) | 5.45269e15 | 0.613194 | ||||||||
\(795\) | 5.21922e15 | 0.582890 | ||||||||
\(796\) | −3.08987e15 | −0.342703 | ||||||||
\(797\) | 1.41948e16 | 1.56353 | 0.781767 | − | 0.623571i | \(-0.214319\pi\) | ||||
0.781767 | + | 0.623571i | \(0.214319\pi\) | |||||||
\(798\) | 6.06817e13 | 0.00663808 | ||||||||
\(799\) | −9.83590e15 | −1.06858 | ||||||||
\(800\) | −2.66347e15 | −0.287378 | ||||||||
\(801\) | 1.33309e15 | 0.142850 | ||||||||
\(802\) | −2.92522e15 | −0.311315 | ||||||||
\(803\) | −3.18558e15 | −0.336708 | ||||||||
\(804\) | −6.87478e15 | −0.721690 | ||||||||
\(805\) | 1.96087e12 | 0.000204443 0 | ||||||||
\(806\) | −2.85090e13 | −0.00295216 | ||||||||
\(807\) | 5.82803e15 | 0.599401 | ||||||||
\(808\) | 5.45705e15 | 0.557436 | ||||||||
\(809\) | −1.91599e15 | −0.194391 | −0.0971956 | − | 0.995265i | \(-0.530987\pi\) | ||||
−0.0971956 | + | 0.995265i | \(0.530987\pi\) | |||||||
\(810\) | −4.80706e14 | −0.0484409 | ||||||||
\(811\) | 1.00041e16 | 1.00130 | 0.500648 | − | 0.865651i | \(-0.333095\pi\) | ||||
0.500648 | + | 0.865651i | \(0.333095\pi\) | |||||||
\(812\) | −3.91930e13 | −0.00389629 | ||||||||
\(813\) | 2.08712e15 | 0.206086 | ||||||||
\(814\) | 1.67907e15 | 0.164678 | ||||||||
\(815\) | −1.33732e16 | −1.30277 | ||||||||
\(816\) | −1.94477e15 | −0.188180 | ||||||||
\(817\) | −1.09405e16 | −1.05152 | ||||||||
\(818\) | 2.67965e15 | 0.255820 | ||||||||
\(819\) | −2.33667e12 | −0.000221583 0 | ||||||||
\(820\) | 1.20876e16 | 1.13858 | ||||||||
\(821\) | −1.46063e16 | −1.36663 | −0.683317 | − | 0.730122i | \(-0.739463\pi\) | ||||
−0.683317 | + | 0.730122i | \(0.739463\pi\) | |||||||
\(822\) | −8.75078e14 | −0.0813302 | ||||||||
\(823\) | 5.76089e15 | 0.531852 | 0.265926 | − | 0.963993i | \(-0.414322\pi\) | ||||
0.265926 | + | 0.963993i | \(0.414322\pi\) | |||||||
\(824\) | 1.50465e16 | 1.37987 | ||||||||
\(825\) | 4.94749e14 | 0.0450701 | ||||||||
\(826\) | 1.63425e13 | 0.00147887 | ||||||||
\(827\) | 1.07854e16 | 0.969519 | 0.484760 | − | 0.874647i | \(-0.338907\pi\) | ||||
0.484760 | + | 0.874647i | \(0.338907\pi\) | |||||||
\(828\) | −1.91261e13 | −0.00170789 | ||||||||
\(829\) | −1.84718e15 | −0.163854 | −0.0819272 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819272 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(830\) | −2.95644e15 | −0.260519 | ||||||||
\(831\) | 9.44703e15 | 0.826970 | ||||||||
\(832\) | 5.92793e13 | 0.00515495 | ||||||||
\(833\) | 6.43828e15 | 0.556189 | ||||||||
\(834\) | −1.88452e15 | −0.161729 | ||||||||
\(835\) | −1.10886e16 | −0.945372 | ||||||||
\(836\) | 2.58027e15 | 0.218540 | ||||||||
\(837\) | −7.94681e14 | −0.0668656 | ||||||||
\(838\) | −9.68408e14 | −0.0809499 | ||||||||
\(839\) | −1.40672e16 | −1.16820 | −0.584100 | − | 0.811682i | \(-0.698552\pi\) | ||||
−0.584100 | + | 0.811682i | \(0.698552\pi\) | |||||||
\(840\) | 1.68697e14 | 0.0139178 | ||||||||
\(841\) | −1.19153e16 | −0.976622 | ||||||||
\(842\) | −7.37708e14 | −0.0600714 | ||||||||
\(843\) | −1.31332e16 | −1.06247 | ||||||||
\(844\) | 1.66037e16 | 1.33451 | ||||||||
\(845\) | −1.43210e16 | −1.14357 | ||||||||
\(846\) | −3.07319e15 | −0.243811 | ||||||||
\(847\) | −3.54084e14 | −0.0279092 | ||||||||
\(848\) | 6.59736e15 | 0.516646 | ||||||||
\(849\) | −7.34161e15 | −0.571214 | ||||||||
\(850\) | 8.48051e14 | 0.0655568 | ||||||||
\(851\) | −1.33528e14 | −0.0102555 | ||||||||
\(852\) | −1.59555e15 | −0.121757 | ||||||||
\(853\) | 2.39241e16 | 1.81391 | 0.906954 | − | 0.421230i | \(-0.138401\pi\) | ||||
0.906954 | + | 0.421230i | \(0.138401\pi\) | |||||||
\(854\) | 2.48211e14 | 0.0186983 | ||||||||
\(855\) | −5.15726e15 | −0.386016 | ||||||||
\(856\) | −1.02344e16 | −0.761125 | ||||||||
\(857\) | 2.19672e16 | 1.62323 | 0.811614 | − | 0.584194i | \(-0.198589\pi\) | ||||
0.811614 | + | 0.584194i | \(0.198589\pi\) | |||||||
\(858\) | 1.68768e13 | 0.00123911 | ||||||||
\(859\) | −2.63625e14 | −0.0192320 | −0.00961601 | − | 0.999954i | \(-0.503061\pi\) | ||||
−0.00961601 | + | 0.999954i | \(0.503061\pi\) | |||||||
\(860\) | −1.40170e16 | −1.01605 | ||||||||
\(861\) | −2.78197e14 | −0.0200371 | ||||||||
\(862\) | 3.82988e15 | 0.274092 | ||||||||
\(863\) | −5.79310e14 | −0.0411957 | −0.0205978 | − | 0.999788i | \(-0.506557\pi\) | ||||
−0.0205978 | + | 0.999788i | \(0.506557\pi\) | |||||||
\(864\) | −2.53258e15 | −0.178952 | ||||||||
\(865\) | −2.80376e16 | −1.96858 | ||||||||
\(866\) | −7.54039e15 | −0.526072 | ||||||||
\(867\) | −5.74723e15 | −0.398431 | ||||||||
\(868\) | 1.28526e14 | 0.00885383 | ||||||||
\(869\) | −5.64122e15 | −0.386157 | ||||||||
\(870\) | −5.65788e14 | −0.0384856 | ||||||||
\(871\) | −4.82417e14 | −0.0326079 | ||||||||
\(872\) | −1.44862e16 | −0.973004 | ||||||||
\(873\) | −1.93518e15 | −0.129164 | ||||||||
\(874\) | 3.48538e13 | 0.00231173 | ||||||||
\(875\) | −3.57558e14 | −0.0235669 | ||||||||
\(876\) | 1.00442e16 | 0.657876 | ||||||||
\(877\) | −1.32387e16 | −0.861680 | −0.430840 | − | 0.902428i | \(-0.641783\pi\) | ||||
−0.430840 | + | 0.902428i | \(0.641783\pi\) | |||||||
\(878\) | 2.88467e15 | 0.186585 | ||||||||
\(879\) | 1.22442e16 | 0.787031 | ||||||||
\(880\) | 2.64895e15 | 0.169207 | ||||||||
\(881\) | 2.12452e16 | 1.34863 | 0.674317 | − | 0.738442i | \(-0.264438\pi\) | ||||
0.674317 | + | 0.738442i | \(0.264438\pi\) | |||||||
\(882\) | 2.01162e15 | 0.126902 | ||||||||
\(883\) | 6.50488e15 | 0.407807 | 0.203904 | − | 0.978991i | \(-0.434637\pi\) | ||||
0.203904 | + | 0.978991i | \(0.434637\pi\) | |||||||
\(884\) | −1.70311e14 | −0.0106110 | ||||||||
\(885\) | −1.38893e15 | −0.0859987 | ||||||||
\(886\) | 9.48869e15 | 0.583876 | ||||||||
\(887\) | −1.40683e15 | −0.0860326 | −0.0430163 | − | 0.999074i | \(-0.513697\pi\) | ||||
−0.0430163 | + | 0.999074i | \(0.513697\pi\) | |||||||
\(888\) | −1.14876e16 | −0.698164 | ||||||||
\(889\) | −5.08101e14 | −0.0306895 | ||||||||
\(890\) | −3.11244e15 | −0.186834 | ||||||||
\(891\) | 4.70436e14 | 0.0280655 | ||||||||
\(892\) | −2.67150e16 | −1.58398 | ||||||||
\(893\) | −3.29708e16 | −1.94288 | ||||||||
\(894\) | −7.45485e13 | −0.00436599 | ||||||||
\(895\) | −3.42824e16 | −1.99547 | ||||||||
\(896\) | 5.24567e14 | 0.0303464 | ||||||||
\(897\) | −1.34212e12 | −7.71671e−5 0 | ||||||||
\(898\) | −2.08664e15 | −0.119242 | ||||||||
\(899\) | −9.35336e14 | −0.0531238 | ||||||||
\(900\) | −1.55996e15 | −0.0880602 | ||||||||
\(901\) | −8.75514e15 | −0.491221 | ||||||||
\(902\) | 2.00930e15 | 0.112049 | ||||||||
\(903\) | 3.22604e14 | 0.0178808 | ||||||||
\(904\) | 2.38337e16 | 1.31300 | ||||||||
\(905\) | −1.05543e16 | −0.577911 | ||||||||
\(906\) | 6.69801e15 | 0.364536 | ||||||||
\(907\) | 4.31251e15 | 0.233287 | 0.116643 | − | 0.993174i | \(-0.462787\pi\) | ||||
0.116643 | + | 0.993174i | \(0.462787\pi\) | |||||||
\(908\) | −2.15748e15 | −0.116004 | ||||||||
\(909\) | 4.91928e15 | 0.262906 | ||||||||
\(910\) | 5.45557e12 | 0.000289809 0 | ||||||||
\(911\) | −7.59414e14 | −0.0400984 | −0.0200492 | − | 0.999799i | \(-0.506382\pi\) | ||||
−0.0200492 | + | 0.999799i | \(0.506382\pi\) | |||||||
\(912\) | −6.51904e15 | −0.342146 | ||||||||
\(913\) | 2.89327e15 | 0.150939 | ||||||||
\(914\) | −1.12261e16 | −0.582138 | ||||||||
\(915\) | −2.10951e16 | −1.08734 | ||||||||
\(916\) | −1.63592e15 | −0.0838179 | ||||||||
\(917\) | 5.44118e14 | 0.0277116 | ||||||||
\(918\) | 8.06375e14 | 0.0408228 | ||||||||
\(919\) | 2.69528e16 | 1.35634 | 0.678170 | − | 0.734905i | \(-0.262773\pi\) | ||||
0.678170 | + | 0.734905i | \(0.262773\pi\) | |||||||
\(920\) | 9.68946e13 | 0.00484693 | ||||||||
\(921\) | −1.02280e16 | −0.508586 | ||||||||
\(922\) | −2.37983e15 | −0.117632 | ||||||||
\(923\) | −1.11963e14 | −0.00550129 | ||||||||
\(924\) | −7.60846e13 | −0.00371622 | ||||||||
\(925\) | −1.08907e16 | −0.528784 | ||||||||
\(926\) | 3.08207e15 | 0.148758 | ||||||||
\(927\) | 1.35638e16 | 0.650791 | ||||||||
\(928\) | −2.98083e15 | −0.142175 | ||||||||
\(929\) | −2.52655e16 | −1.19796 | −0.598980 | − | 0.800764i | \(-0.704427\pi\) | ||||
−0.598980 | + | 0.800764i | \(0.704427\pi\) | |||||||
\(930\) | 1.85539e15 | 0.0874538 | ||||||||
\(931\) | 2.15817e16 | 1.01126 | ||||||||
\(932\) | 1.93652e16 | 0.902060 | ||||||||
\(933\) | 2.28573e15 | 0.105846 | ||||||||
\(934\) | −1.11433e16 | −0.512986 | ||||||||
\(935\) | −3.51533e15 | −0.160880 | ||||||||
\(936\) | −1.15465e14 | −0.00525329 | ||||||||
\(937\) | 7.21858e15 | 0.326500 | 0.163250 | − | 0.986585i | \(-0.447802\pi\) | ||||
0.163250 | + | 0.986585i | \(0.447802\pi\) | |||||||
\(938\) | −3.69415e14 | −0.0166111 | ||||||||
\(939\) | 1.80785e16 | 0.808167 | ||||||||
\(940\) | −4.22423e16 | −1.87734 | ||||||||
\(941\) | −1.23022e16 | −0.543551 | −0.271775 | − | 0.962361i | \(-0.587611\pi\) | ||||
−0.271775 | + | 0.962361i | \(0.587611\pi\) | |||||||
\(942\) | 5.01455e15 | 0.220268 | ||||||||
\(943\) | −1.59788e14 | −0.00697800 | ||||||||
\(944\) | −1.75568e15 | −0.0762252 | ||||||||
\(945\) | 1.52073e14 | 0.00656411 | ||||||||
\(946\) | −2.33003e15 | −0.0999907 | ||||||||
\(947\) | −1.82694e16 | −0.779470 | −0.389735 | − | 0.920927i | \(-0.627433\pi\) | ||||
−0.389735 | + | 0.920927i | \(0.627433\pi\) | |||||||
\(948\) | 1.77869e16 | 0.754493 | ||||||||
\(949\) | 7.04824e14 | 0.0297246 | ||||||||
\(950\) | 2.84274e15 | 0.119195 | ||||||||
\(951\) | 5.59873e15 | 0.233398 | ||||||||
\(952\) | −2.82986e14 | −0.0117290 | ||||||||
\(953\) | −4.67260e15 | −0.192552 | −0.0962759 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962759 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(954\) | −2.73551e15 | −0.112079 | ||||||||
\(955\) | 3.55587e15 | 0.144853 | ||||||||
\(956\) | 3.13722e16 | 1.27065 | ||||||||
\(957\) | 5.53701e14 | 0.0222977 | ||||||||
\(958\) | 3.55556e15 | 0.142363 | ||||||||
\(959\) | 2.76833e14 | 0.0110209 | ||||||||
\(960\) | −3.85794e15 | −0.152709 | ||||||||
\(961\) | −2.23412e16 | −0.879283 | ||||||||
\(962\) | −3.71502e14 | −0.0145378 | ||||||||
\(963\) | −9.22583e15 | −0.358972 | ||||||||
\(964\) | 1.65530e15 | 0.0640401 | ||||||||
\(965\) | −3.52112e16 | −1.35450 | ||||||||
\(966\) | −1.02774e12 | −3.93105e−5 0 | ||||||||
\(967\) | −3.47991e16 | −1.32349 | −0.661747 | − | 0.749727i | \(-0.730185\pi\) | ||||
−0.661747 | + | 0.749727i | \(0.730185\pi\) | |||||||
\(968\) | −1.74967e16 | −0.661671 | ||||||||
\(969\) | 8.65121e15 | 0.325309 | ||||||||
\(970\) | 4.51818e15 | 0.168935 | ||||||||
\(971\) | 1.97264e16 | 0.733402 | 0.366701 | − | 0.930339i | \(-0.380487\pi\) | ||||
0.366701 | + | 0.930339i | \(0.380487\pi\) | |||||||
\(972\) | −1.48330e15 | −0.0548358 | ||||||||
\(973\) | 5.96173e14 | 0.0219155 | ||||||||
\(974\) | 2.43456e15 | 0.0889909 | ||||||||
\(975\) | −1.09465e14 | −0.00397880 | ||||||||
\(976\) | −2.66653e16 | −0.963769 | ||||||||
\(977\) | 3.00929e16 | 1.08154 | 0.540771 | − | 0.841170i | \(-0.318133\pi\) | ||||
0.540771 | + | 0.841170i | \(0.318133\pi\) | |||||||
\(978\) | 7.00919e15 | 0.250498 | ||||||||
\(979\) | 3.04594e15 | 0.108247 | ||||||||
\(980\) | 2.76505e16 | 0.977147 | ||||||||
\(981\) | −1.30587e16 | −0.458901 | ||||||||
\(982\) | 3.98454e15 | 0.139240 | ||||||||
\(983\) | 4.40527e16 | 1.53084 | 0.765418 | − | 0.643533i | \(-0.222532\pi\) | ||||
0.765418 | + | 0.643533i | \(0.222532\pi\) | |||||||
\(984\) | −1.37468e16 | −0.475040 | ||||||||
\(985\) | −8.64041e15 | −0.296917 | ||||||||
\(986\) | 9.49100e14 | 0.0324331 | ||||||||
\(987\) | 9.72212e14 | 0.0330382 | ||||||||
\(988\) | −5.70896e14 | −0.0192927 | ||||||||
\(989\) | 1.85294e14 | 0.00622706 | ||||||||
\(990\) | −1.09835e15 | −0.0367070 | ||||||||
\(991\) | 3.88270e14 | 0.0129041 | 0.00645206 | − | 0.999979i | \(-0.497946\pi\) | ||||
0.00645206 | + | 0.999979i | \(0.497946\pi\) | |||||||
\(992\) | 9.77503e15 | 0.323076 | ||||||||
\(993\) | −2.48522e15 | −0.0816855 | ||||||||
\(994\) | −8.57365e13 | −0.00280247 | ||||||||
\(995\) | 1.41110e16 | 0.458701 | ||||||||
\(996\) | −9.12258e15 | −0.294911 | ||||||||
\(997\) | 5.91431e15 | 0.190143 | 0.0950715 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950715 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(998\) | −8.79096e15 | −0.281072 | ||||||||
\(999\) | −1.03555e16 | −0.329278 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.12.a.b.1.13 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.13 | ✓ | 27 | 1.1 | even | 1 | trivial |