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 | 1.15 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16187 | −0.0477711 | −0.0238855 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238855 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −2043.33 | −0.997718 | ||||||||
\(5\) | 654.400 | 0.0936502 | 0.0468251 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468251 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(6\) | −525.335 | −0.0275806 | ||||||||
\(7\) | 79533.7 | 1.78859 | 0.894297 | − | 0.447473i | \(-0.147676\pi\) | ||||
0.894297 | + | 0.447473i | \(0.147676\pi\) | |||||||
\(8\) | 8844.92 | 0.0954331 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −1414.73 | −0.00447377 | ||||||||
\(11\) | −361945. | −0.677615 | −0.338808 | − | 0.940856i | \(-0.610024\pi\) | ||||
−0.338808 | + | 0.940856i | \(0.610024\pi\) | |||||||
\(12\) | −496528. | −0.576033 | ||||||||
\(13\) | −608677. | −0.454672 | −0.227336 | − | 0.973816i | \(-0.573002\pi\) | ||||
−0.227336 | + | 0.973816i | \(0.573002\pi\) | |||||||
\(14\) | −171942. | −0.0854431 | ||||||||
\(15\) | 159019. | 0.0540689 | ||||||||
\(16\) | 4.16561e6 | 0.993159 | ||||||||
\(17\) | 1.14080e6 | 0.194867 | 0.0974336 | − | 0.995242i | \(-0.468937\pi\) | ||||
0.0974336 | + | 0.995242i | \(0.468937\pi\) | |||||||
\(18\) | −127656. | −0.0159237 | ||||||||
\(19\) | −6.87969e6 | −0.637418 | −0.318709 | − | 0.947853i | \(-0.603249\pi\) | ||||
−0.318709 | + | 0.947853i | \(0.603249\pi\) | |||||||
\(20\) | −1.33715e6 | −0.0934364 | ||||||||
\(21\) | 1.93267e7 | 1.03265 | ||||||||
\(22\) | 782479. | 0.0323704 | ||||||||
\(23\) | −2.10594e7 | −0.682248 | −0.341124 | − | 0.940018i | \(-0.610808\pi\) | ||||
−0.341124 | + | 0.940018i | \(0.610808\pi\) | |||||||
\(24\) | 2.14932e6 | 0.0550983 | ||||||||
\(25\) | −4.83999e7 | −0.991230 | ||||||||
\(26\) | 1.31588e6 | 0.0217202 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −1.62513e8 | −1.78451 | ||||||||
\(29\) | −1.41194e8 | −1.27829 | −0.639143 | − | 0.769088i | \(-0.720711\pi\) | ||||
−0.639143 | + | 0.769088i | \(0.720711\pi\) | |||||||
\(30\) | −343779. | −0.00258293 | ||||||||
\(31\) | 8.71043e7 | 0.546450 | 0.273225 | − | 0.961950i | \(-0.411910\pi\) | ||||
0.273225 | + | 0.961950i | \(0.411910\pi\) | |||||||
\(32\) | −2.71199e7 | −0.142877 | ||||||||
\(33\) | −8.79527e7 | −0.391221 | ||||||||
\(34\) | −2.46625e6 | −0.00930901 | ||||||||
\(35\) | 5.20469e7 | 0.167502 | ||||||||
\(36\) | −1.20656e8 | −0.332573 | ||||||||
\(37\) | 5.08594e8 | 1.20576 | 0.602881 | − | 0.797831i | \(-0.294019\pi\) | ||||
0.602881 | + | 0.797831i | \(0.294019\pi\) | |||||||
\(38\) | 1.48730e7 | 0.0304501 | ||||||||
\(39\) | −1.47909e8 | −0.262505 | ||||||||
\(40\) | 5.78812e6 | 0.00893733 | ||||||||
\(41\) | −2.45057e8 | −0.330336 | −0.165168 | − | 0.986265i | \(-0.552817\pi\) | ||||
−0.165168 | + | 0.986265i | \(0.552817\pi\) | |||||||
\(42\) | −4.17818e7 | −0.0493306 | ||||||||
\(43\) | 1.63401e8 | 0.169503 | 0.0847514 | − | 0.996402i | \(-0.472990\pi\) | ||||
0.0847514 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(44\) | 7.39572e8 | 0.676069 | ||||||||
\(45\) | 3.86417e7 | 0.0312167 | ||||||||
\(46\) | 4.55276e7 | 0.0325917 | ||||||||
\(47\) | 1.77966e9 | 1.13188 | 0.565938 | − | 0.824448i | \(-0.308514\pi\) | ||||
0.565938 | + | 0.824448i | \(0.308514\pi\) | |||||||
\(48\) | 1.01224e9 | 0.573401 | ||||||||
\(49\) | 4.34828e9 | 2.19907 | ||||||||
\(50\) | 1.04634e8 | 0.0473521 | ||||||||
\(51\) | 2.77213e8 | 0.112507 | ||||||||
\(52\) | 1.24373e9 | 0.453635 | ||||||||
\(53\) | −4.11758e9 | −1.35246 | −0.676231 | − | 0.736690i | \(-0.736388\pi\) | ||||
−0.676231 | + | 0.736690i | \(0.736388\pi\) | |||||||
\(54\) | −3.10205e7 | −0.00919355 | ||||||||
\(55\) | −2.36857e8 | −0.0634588 | ||||||||
\(56\) | 7.03469e8 | 0.170691 | ||||||||
\(57\) | −1.67176e9 | −0.368013 | ||||||||
\(58\) | 3.05244e8 | 0.0610651 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −3.24928e8 | −0.0539456 | ||||||||
\(61\) | −2.50892e9 | −0.380340 | −0.190170 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190170 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(62\) | −1.88308e8 | −0.0261045 | ||||||||
\(63\) | 4.69639e9 | 0.596198 | ||||||||
\(64\) | −8.47254e9 | −0.986334 | ||||||||
\(65\) | −3.98318e8 | −0.0425801 | ||||||||
\(66\) | 1.90142e8 | 0.0186891 | ||||||||
\(67\) | −3.37618e9 | −0.305502 | −0.152751 | − | 0.988265i | \(-0.548813\pi\) | ||||
−0.152751 | + | 0.988265i | \(0.548813\pi\) | |||||||
\(68\) | −2.33102e9 | −0.194423 | ||||||||
\(69\) | −5.11743e9 | −0.393896 | ||||||||
\(70\) | −1.12519e8 | −0.00800176 | ||||||||
\(71\) | −6.16327e9 | −0.405406 | −0.202703 | − | 0.979240i | \(-0.564973\pi\) | ||||
−0.202703 | + | 0.979240i | \(0.564973\pi\) | |||||||
\(72\) | 5.22284e8 | 0.0318110 | ||||||||
\(73\) | 2.20149e9 | 0.124292 | 0.0621458 | − | 0.998067i | \(-0.480206\pi\) | ||||
0.0621458 | + | 0.998067i | \(0.480206\pi\) | |||||||
\(74\) | −1.09951e9 | −0.0576005 | ||||||||
\(75\) | −1.17612e10 | −0.572287 | ||||||||
\(76\) | 1.40574e10 | 0.635963 | ||||||||
\(77\) | −2.87868e10 | −1.21198 | ||||||||
\(78\) | 3.19759e8 | 0.0125402 | ||||||||
\(79\) | 2.69116e10 | 0.983991 | 0.491995 | − | 0.870598i | \(-0.336268\pi\) | ||||
0.491995 | + | 0.870598i | \(0.336268\pi\) | |||||||
\(80\) | 2.72598e9 | 0.0930095 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 5.29781e8 | 0.0157805 | ||||||||
\(83\) | −1.69513e10 | −0.472361 | −0.236180 | − | 0.971709i | \(-0.575896\pi\) | ||||
−0.236180 | + | 0.971709i | \(0.575896\pi\) | |||||||
\(84\) | −3.94907e10 | −1.03029 | ||||||||
\(85\) | 7.46537e8 | 0.0182493 | ||||||||
\(86\) | −3.53251e8 | −0.00809733 | ||||||||
\(87\) | −3.43102e10 | −0.738019 | ||||||||
\(88\) | −3.20138e9 | −0.0646669 | ||||||||
\(89\) | −5.65822e10 | −1.07408 | −0.537038 | − | 0.843558i | \(-0.680457\pi\) | ||||
−0.537038 | + | 0.843558i | \(0.680457\pi\) | |||||||
\(90\) | −8.35384e7 | −0.00149126 | ||||||||
\(91\) | −4.84103e10 | −0.813224 | ||||||||
\(92\) | 4.30312e10 | 0.680691 | ||||||||
\(93\) | 2.11663e10 | 0.315493 | ||||||||
\(94\) | −3.84740e9 | −0.0540710 | ||||||||
\(95\) | −4.50207e9 | −0.0596942 | ||||||||
\(96\) | −6.59014e9 | −0.0824903 | ||||||||
\(97\) | −2.14261e9 | −0.0253336 | −0.0126668 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126668 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(98\) | −9.40043e9 | −0.105052 | ||||||||
\(99\) | −2.13725e10 | −0.225872 | ||||||||
\(100\) | 9.88968e10 | 0.988968 | ||||||||
\(101\) | 9.24270e10 | 0.875047 | 0.437524 | − | 0.899207i | \(-0.355856\pi\) | ||||
0.437524 | + | 0.899207i | \(0.355856\pi\) | |||||||
\(102\) | −5.99300e8 | −0.00537456 | ||||||||
\(103\) | −1.07966e11 | −0.917665 | −0.458832 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458832 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(104\) | −5.38370e9 | −0.0433908 | ||||||||
\(105\) | 1.26474e10 | 0.0967074 | ||||||||
\(106\) | 8.90168e9 | 0.0646085 | ||||||||
\(107\) | 5.38904e10 | 0.371450 | 0.185725 | − | 0.982602i | \(-0.440537\pi\) | ||||
0.185725 | + | 0.982602i | \(0.440537\pi\) | |||||||
\(108\) | −2.93195e10 | −0.192011 | ||||||||
\(109\) | −8.67119e10 | −0.539800 | −0.269900 | − | 0.962888i | \(-0.586991\pi\) | ||||
−0.269900 | + | 0.962888i | \(0.586991\pi\) | |||||||
\(110\) | 5.12055e8 | 0.00303149 | ||||||||
\(111\) | 1.23588e11 | 0.696147 | ||||||||
\(112\) | 3.31306e11 | 1.77636 | ||||||||
\(113\) | −2.77274e11 | −1.41572 | −0.707861 | − | 0.706352i | \(-0.750340\pi\) | ||||
−0.707861 | + | 0.706352i | \(0.750340\pi\) | |||||||
\(114\) | 3.61414e9 | 0.0175804 | ||||||||
\(115\) | −1.37813e10 | −0.0638926 | ||||||||
\(116\) | 2.88506e11 | 1.27537 | ||||||||
\(117\) | −3.59418e10 | −0.151557 | ||||||||
\(118\) | 1.54557e9 | 0.00621926 | ||||||||
\(119\) | 9.07317e10 | 0.348538 | ||||||||
\(120\) | 1.40651e9 | 0.00515997 | ||||||||
\(121\) | −1.54307e11 | −0.540838 | ||||||||
\(122\) | 5.42396e9 | 0.0181693 | ||||||||
\(123\) | −5.95488e10 | −0.190719 | ||||||||
\(124\) | −1.77982e11 | −0.545203 | ||||||||
\(125\) | −6.36260e10 | −0.186479 | ||||||||
\(126\) | −1.01530e10 | −0.0284810 | ||||||||
\(127\) | −2.23170e11 | −0.599399 | −0.299700 | − | 0.954034i | \(-0.596886\pi\) | ||||
−0.299700 | + | 0.954034i | \(0.596886\pi\) | |||||||
\(128\) | 7.38581e10 | 0.189996 | ||||||||
\(129\) | 3.97063e10 | 0.0978625 | ||||||||
\(130\) | 8.61113e8 | 0.00203410 | ||||||||
\(131\) | −8.35848e10 | −0.189293 | −0.0946467 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946467 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(132\) | 1.79716e11 | 0.390329 | ||||||||
\(133\) | −5.47167e11 | −1.14008 | ||||||||
\(134\) | 7.29887e9 | 0.0145942 | ||||||||
\(135\) | 9.38993e9 | 0.0180230 | ||||||||
\(136\) | 1.00902e10 | 0.0185968 | ||||||||
\(137\) | 4.52915e10 | 0.0801777 | 0.0400889 | − | 0.999196i | \(-0.487236\pi\) | ||||
0.0400889 | + | 0.999196i | \(0.487236\pi\) | |||||||
\(138\) | 1.10632e10 | 0.0188168 | ||||||||
\(139\) | −4.20037e11 | −0.686604 | −0.343302 | − | 0.939225i | \(-0.611545\pi\) | ||||
−0.343302 | + | 0.939225i | \(0.611545\pi\) | |||||||
\(140\) | −1.06349e11 | −0.167120 | ||||||||
\(141\) | 4.32458e11 | 0.653489 | ||||||||
\(142\) | 1.33242e10 | 0.0193667 | ||||||||
\(143\) | 2.20308e11 | 0.308093 | ||||||||
\(144\) | 2.45975e11 | 0.331053 | ||||||||
\(145\) | −9.23976e10 | −0.119712 | ||||||||
\(146\) | −4.75934e9 | −0.00593754 | ||||||||
\(147\) | 1.05663e12 | 1.26963 | ||||||||
\(148\) | −1.03922e12 | −1.20301 | ||||||||
\(149\) | 3.64336e11 | 0.406422 | 0.203211 | − | 0.979135i | \(-0.434862\pi\) | ||||
0.203211 | + | 0.979135i | \(0.434862\pi\) | |||||||
\(150\) | 2.54261e10 | 0.0273387 | ||||||||
\(151\) | −1.39489e12 | −1.44599 | −0.722996 | − | 0.690852i | \(-0.757236\pi\) | ||||
−0.722996 | + | 0.690852i | \(0.757236\pi\) | |||||||
\(152\) | −6.08503e10 | −0.0608307 | ||||||||
\(153\) | 6.73628e10 | 0.0649557 | ||||||||
\(154\) | 6.22335e10 | 0.0578975 | ||||||||
\(155\) | 5.70011e10 | 0.0511751 | ||||||||
\(156\) | 3.02225e11 | 0.261906 | ||||||||
\(157\) | 4.10340e11 | 0.343317 | 0.171659 | − | 0.985156i | \(-0.445087\pi\) | ||||
0.171659 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(158\) | −5.81795e10 | −0.0470063 | ||||||||
\(159\) | −1.00057e12 | −0.780844 | ||||||||
\(160\) | −1.77473e10 | −0.0133805 | ||||||||
\(161\) | −1.67493e12 | −1.22027 | ||||||||
\(162\) | −7.53798e9 | −0.00530790 | ||||||||
\(163\) | −2.54325e12 | −1.73124 | −0.865620 | − | 0.500701i | \(-0.833076\pi\) | ||||
−0.865620 | + | 0.500701i | \(0.833076\pi\) | |||||||
\(164\) | 5.00731e11 | 0.329582 | ||||||||
\(165\) | −5.75563e10 | −0.0366379 | ||||||||
\(166\) | 3.66465e10 | 0.0225652 | ||||||||
\(167\) | −1.38079e11 | −0.0822598 | −0.0411299 | − | 0.999154i | \(-0.513096\pi\) | ||||
−0.0411299 | + | 0.999154i | \(0.513096\pi\) | |||||||
\(168\) | 1.70943e11 | 0.0985486 | ||||||||
\(169\) | −1.42167e12 | −0.793273 | ||||||||
\(170\) | −1.61392e9 | −0.000871791 0 | ||||||||
\(171\) | −4.06239e11 | −0.212473 | ||||||||
\(172\) | −3.33881e11 | −0.169116 | ||||||||
\(173\) | 1.91015e11 | 0.0937159 | 0.0468580 | − | 0.998902i | \(-0.485079\pi\) | ||||
0.0468580 | + | 0.998902i | \(0.485079\pi\) | |||||||
\(174\) | 7.41743e10 | 0.0352559 | ||||||||
\(175\) | −3.84942e12 | −1.77291 | ||||||||
\(176\) | −1.50772e12 | −0.672980 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 1.22323e11 | 0.0513097 | ||||||||
\(179\) | 3.55183e12 | 1.44464 | 0.722321 | − | 0.691558i | \(-0.243075\pi\) | ||||
0.722321 | + | 0.691558i | \(0.243075\pi\) | |||||||
\(180\) | −7.89576e10 | −0.0311455 | ||||||||
\(181\) | 3.50928e12 | 1.34272 | 0.671360 | − | 0.741132i | \(-0.265711\pi\) | ||||
0.671360 | + | 0.741132i | \(0.265711\pi\) | |||||||
\(182\) | 1.04657e11 | 0.0388486 | ||||||||
\(183\) | −6.09667e11 | −0.219589 | ||||||||
\(184\) | −1.86268e11 | −0.0651090 | ||||||||
\(185\) | 3.32824e11 | 0.112920 | ||||||||
\(186\) | −4.57589e10 | −0.0150714 | ||||||||
\(187\) | −4.12906e11 | −0.132045 | ||||||||
\(188\) | −3.63643e12 | −1.12929 | ||||||||
\(189\) | 1.14122e12 | 0.344215 | ||||||||
\(190\) | 9.73290e9 | 0.00285166 | ||||||||
\(191\) | −4.78607e12 | −1.36237 | −0.681186 | − | 0.732111i | \(-0.738535\pi\) | ||||
−0.681186 | + | 0.732111i | \(0.738535\pi\) | |||||||
\(192\) | −2.05883e12 | −0.569460 | ||||||||
\(193\) | −2.49448e12 | −0.670524 | −0.335262 | − | 0.942125i | \(-0.608825\pi\) | ||||
−0.335262 | + | 0.942125i | \(0.608825\pi\) | |||||||
\(194\) | 4.63204e9 | 0.00121022 | ||||||||
\(195\) | −9.67914e10 | −0.0245836 | ||||||||
\(196\) | −8.88496e12 | −2.19405 | ||||||||
\(197\) | −7.83320e12 | −1.88094 | −0.940470 | − | 0.339877i | \(-0.889615\pi\) | ||||
−0.940470 | + | 0.339877i | \(0.889615\pi\) | |||||||
\(198\) | 4.62046e10 | 0.0107901 | ||||||||
\(199\) | 1.97236e12 | 0.448016 | 0.224008 | − | 0.974587i | \(-0.428086\pi\) | ||||
0.224008 | + | 0.974587i | \(0.428086\pi\) | |||||||
\(200\) | −4.28093e11 | −0.0945961 | ||||||||
\(201\) | −8.20412e11 | −0.176382 | ||||||||
\(202\) | −1.99815e11 | −0.0418019 | ||||||||
\(203\) | −1.12297e13 | −2.28634 | ||||||||
\(204\) | −5.66437e11 | −0.112250 | ||||||||
\(205\) | −1.60365e11 | −0.0309360 | ||||||||
\(206\) | 2.33410e11 | 0.0438378 | ||||||||
\(207\) | −1.24353e12 | −0.227416 | ||||||||
\(208\) | −2.53551e12 | −0.451562 | ||||||||
\(209\) | 2.49007e12 | 0.431924 | ||||||||
\(210\) | −2.73420e10 | −0.00461982 | ||||||||
\(211\) | −1.10288e12 | −0.181540 | −0.0907702 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907702 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(212\) | 8.41356e12 | 1.34937 | ||||||||
\(213\) | −1.49768e12 | −0.234061 | ||||||||
\(214\) | −1.16504e11 | −0.0177446 | ||||||||
\(215\) | 1.06929e11 | 0.0158740 | ||||||||
\(216\) | 1.26915e11 | 0.0183661 | ||||||||
\(217\) | 6.92773e12 | 0.977377 | ||||||||
\(218\) | 1.87460e11 | 0.0257868 | ||||||||
\(219\) | 5.34963e11 | 0.0717597 | ||||||||
\(220\) | 4.83976e11 | 0.0633139 | ||||||||
\(221\) | −6.94376e11 | −0.0886007 | ||||||||
\(222\) | −2.67182e11 | −0.0332557 | ||||||||
\(223\) | −6.53558e12 | −0.793610 | −0.396805 | − | 0.917903i | \(-0.629881\pi\) | ||||
−0.396805 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(224\) | −2.15695e12 | −0.255550 | ||||||||
\(225\) | −2.85796e12 | −0.330410 | ||||||||
\(226\) | 5.99431e11 | 0.0676305 | ||||||||
\(227\) | 1.24917e13 | 1.37556 | 0.687778 | − | 0.725921i | \(-0.258586\pi\) | ||||
0.687778 | + | 0.725921i | \(0.258586\pi\) | |||||||
\(228\) | 3.41596e12 | 0.367173 | ||||||||
\(229\) | 6.05763e12 | 0.635635 | 0.317817 | − | 0.948152i | \(-0.397050\pi\) | ||||
0.317817 | + | 0.948152i | \(0.397050\pi\) | |||||||
\(230\) | 2.97933e10 | 0.00305222 | ||||||||
\(231\) | −6.99520e12 | −0.699736 | ||||||||
\(232\) | −1.24885e12 | −0.121991 | ||||||||
\(233\) | −8.58130e12 | −0.818644 | −0.409322 | − | 0.912390i | \(-0.634235\pi\) | ||||
−0.409322 | + | 0.912390i | \(0.634235\pi\) | |||||||
\(234\) | 7.77015e10 | 0.00724006 | ||||||||
\(235\) | 1.16461e12 | 0.106000 | ||||||||
\(236\) | 1.46082e12 | 0.129892 | ||||||||
\(237\) | 6.53953e12 | 0.568107 | ||||||||
\(238\) | −1.96150e11 | −0.0166501 | ||||||||
\(239\) | −1.96699e12 | −0.163160 | −0.0815799 | − | 0.996667i | \(-0.525997\pi\) | ||||
−0.0815799 | + | 0.996667i | \(0.525997\pi\) | |||||||
\(240\) | 6.62412e11 | 0.0536991 | ||||||||
\(241\) | 1.96077e13 | 1.55358 | 0.776789 | − | 0.629761i | \(-0.216847\pi\) | ||||
0.776789 | + | 0.629761i | \(0.216847\pi\) | |||||||
\(242\) | 3.33593e11 | 0.0258364 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 5.12654e12 | 0.379472 | ||||||||
\(245\) | 2.84552e12 | 0.205943 | ||||||||
\(246\) | 1.28737e11 | 0.00911087 | ||||||||
\(247\) | 4.18751e12 | 0.289816 | ||||||||
\(248\) | 7.70431e11 | 0.0521494 | ||||||||
\(249\) | −4.11917e12 | −0.272718 | ||||||||
\(250\) | 1.37551e11 | 0.00890830 | ||||||||
\(251\) | −4.19882e12 | −0.266025 | −0.133012 | − | 0.991114i | \(-0.542465\pi\) | ||||
−0.133012 | + | 0.991114i | \(0.542465\pi\) | |||||||
\(252\) | −9.59625e12 | −0.594838 | ||||||||
\(253\) | 7.62234e12 | 0.462302 | ||||||||
\(254\) | 4.82466e11 | 0.0286339 | ||||||||
\(255\) | 1.81409e11 | 0.0105363 | ||||||||
\(256\) | 1.71921e13 | 0.977257 | ||||||||
\(257\) | −2.94651e13 | −1.63937 | −0.819684 | − | 0.572816i | \(-0.805851\pi\) | ||||
−0.819684 | + | 0.572816i | \(0.805851\pi\) | |||||||
\(258\) | −8.58400e10 | −0.00467500 | ||||||||
\(259\) | 4.04503e13 | 2.15662 | ||||||||
\(260\) | 8.13895e11 | 0.0424830 | ||||||||
\(261\) | −8.33738e12 | −0.426095 | ||||||||
\(262\) | 1.80700e11 | 0.00904274 | ||||||||
\(263\) | −1.13059e13 | −0.554049 | −0.277024 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277024 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(264\) | −7.77935e11 | −0.0373355 | ||||||||
\(265\) | −2.69455e12 | −0.126658 | ||||||||
\(266\) | 1.18290e12 | 0.0544629 | ||||||||
\(267\) | −1.37495e13 | −0.620118 | ||||||||
\(268\) | 6.89864e12 | 0.304805 | ||||||||
\(269\) | −3.82578e13 | −1.65608 | −0.828042 | − | 0.560665i | \(-0.810545\pi\) | ||||
−0.828042 | + | 0.560665i | \(0.810545\pi\) | |||||||
\(270\) | −2.02998e10 | −0.000860977 0 | ||||||||
\(271\) | −9.60782e12 | −0.399295 | −0.199647 | − | 0.979868i | \(-0.563980\pi\) | ||||
−0.199647 | + | 0.979868i | \(0.563980\pi\) | |||||||
\(272\) | 4.75211e12 | 0.193534 | ||||||||
\(273\) | −1.17637e13 | −0.469515 | ||||||||
\(274\) | −9.79144e10 | −0.00383017 | ||||||||
\(275\) | 1.75181e13 | 0.671672 | ||||||||
\(276\) | 1.04566e13 | 0.392997 | ||||||||
\(277\) | −2.31076e13 | −0.851366 | −0.425683 | − | 0.904872i | \(-0.639966\pi\) | ||||
−0.425683 | + | 0.904872i | \(0.639966\pi\) | |||||||
\(278\) | 9.08066e11 | 0.0327998 | ||||||||
\(279\) | 5.14342e12 | 0.182150 | ||||||||
\(280\) | 4.60351e11 | 0.0159853 | ||||||||
\(281\) | −3.08669e13 | −1.05101 | −0.525506 | − | 0.850790i | \(-0.676124\pi\) | ||||
−0.525506 | + | 0.850790i | \(0.676124\pi\) | |||||||
\(282\) | −9.34918e11 | −0.0312179 | ||||||||
\(283\) | −2.49874e13 | −0.818268 | −0.409134 | − | 0.912474i | \(-0.634169\pi\) | ||||
−0.409134 | + | 0.912474i | \(0.634169\pi\) | |||||||
\(284\) | 1.25936e13 | 0.404481 | ||||||||
\(285\) | −1.09400e12 | −0.0344645 | ||||||||
\(286\) | −4.76277e11 | −0.0147179 | ||||||||
\(287\) | −1.94903e13 | −0.590837 | ||||||||
\(288\) | −1.60140e12 | −0.0476258 | ||||||||
\(289\) | −3.29705e13 | −0.962027 | ||||||||
\(290\) | 1.99752e11 | 0.00571875 | ||||||||
\(291\) | −5.20653e11 | −0.0146264 | ||||||||
\(292\) | −4.49837e12 | −0.124008 | ||||||||
\(293\) | −2.28908e13 | −0.619283 | −0.309642 | − | 0.950853i | \(-0.600209\pi\) | ||||
−0.309642 | + | 0.950853i | \(0.600209\pi\) | |||||||
\(294\) | −2.28430e12 | −0.0606518 | ||||||||
\(295\) | −4.67847e11 | −0.0121922 | ||||||||
\(296\) | 4.49847e12 | 0.115070 | ||||||||
\(297\) | −5.19352e12 | −0.130407 | ||||||||
\(298\) | −7.87647e11 | −0.0194152 | ||||||||
\(299\) | 1.28184e13 | 0.310199 | ||||||||
\(300\) | 2.40319e13 | 0.570981 | ||||||||
\(301\) | 1.29958e13 | 0.303172 | ||||||||
\(302\) | 3.01557e12 | 0.0690766 | ||||||||
\(303\) | 2.24598e13 | 0.505209 | ||||||||
\(304\) | −2.86581e13 | −0.633057 | ||||||||
\(305\) | −1.64184e12 | −0.0356189 | ||||||||
\(306\) | −1.45630e11 | −0.00310300 | ||||||||
\(307\) | 9.03824e12 | 0.189157 | 0.0945786 | − | 0.995517i | \(-0.469850\pi\) | ||||
0.0945786 | + | 0.995517i | \(0.469850\pi\) | |||||||
\(308\) | 5.88209e13 | 1.20921 | ||||||||
\(309\) | −2.62358e13 | −0.529814 | ||||||||
\(310\) | −1.23229e11 | −0.00244469 | ||||||||
\(311\) | 2.75466e13 | 0.536891 | 0.268445 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268445 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(312\) | −1.30824e12 | −0.0250517 | ||||||||
\(313\) | −5.33653e13 | −1.00407 | −0.502036 | − | 0.864847i | \(-0.667415\pi\) | ||||
−0.502036 | + | 0.864847i | \(0.667415\pi\) | |||||||
\(314\) | −8.87103e11 | −0.0164006 | ||||||||
\(315\) | 3.07332e12 | 0.0558341 | ||||||||
\(316\) | −5.49892e13 | −0.981745 | ||||||||
\(317\) | 2.18062e13 | 0.382607 | 0.191304 | − | 0.981531i | \(-0.438728\pi\) | ||||
0.191304 | + | 0.981531i | \(0.438728\pi\) | |||||||
\(318\) | 2.16311e12 | 0.0373017 | ||||||||
\(319\) | 5.11046e13 | 0.866186 | ||||||||
\(320\) | −5.54443e12 | −0.0923703 | ||||||||
\(321\) | 1.30954e13 | 0.214457 | ||||||||
\(322\) | 3.62098e12 | 0.0582934 | ||||||||
\(323\) | −7.84832e12 | −0.124212 | ||||||||
\(324\) | −7.12464e12 | −0.110858 | ||||||||
\(325\) | 2.94599e13 | 0.450685 | ||||||||
\(326\) | 5.49818e12 | 0.0827032 | ||||||||
\(327\) | −2.10710e13 | −0.311654 | ||||||||
\(328\) | −2.16751e12 | −0.0315250 | ||||||||
\(329\) | 1.41543e14 | 2.02447 | ||||||||
\(330\) | 1.24429e11 | 0.00175023 | ||||||||
\(331\) | 5.38836e13 | 0.745423 | 0.372712 | − | 0.927947i | \(-0.378428\pi\) | ||||
0.372712 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(332\) | 3.46371e13 | 0.471283 | ||||||||
\(333\) | 3.00320e13 | 0.401921 | ||||||||
\(334\) | 2.98509e11 | 0.00392964 | ||||||||
\(335\) | −2.20937e12 | −0.0286103 | ||||||||
\(336\) | 8.05075e13 | 1.02558 | ||||||||
\(337\) | 6.64623e13 | 0.832935 | 0.416467 | − | 0.909151i | \(-0.363268\pi\) | ||||
0.416467 | + | 0.909151i | \(0.363268\pi\) | |||||||
\(338\) | 3.07347e12 | 0.0378955 | ||||||||
\(339\) | −6.73776e13 | −0.817367 | ||||||||
\(340\) | −1.52542e12 | −0.0182077 | ||||||||
\(341\) | −3.15270e13 | −0.370283 | ||||||||
\(342\) | 8.78236e11 | 0.0101500 | ||||||||
\(343\) | 1.88571e14 | 2.14465 | ||||||||
\(344\) | 1.44527e12 | 0.0161762 | ||||||||
\(345\) | −3.34885e12 | −0.0368884 | ||||||||
\(346\) | −4.12949e11 | −0.00447691 | ||||||||
\(347\) | −7.03218e12 | −0.0750374 | −0.0375187 | − | 0.999296i | \(-0.511945\pi\) | ||||
−0.0375187 | + | 0.999296i | \(0.511945\pi\) | |||||||
\(348\) | 7.01069e13 | 0.736335 | ||||||||
\(349\) | −8.02464e13 | −0.829632 | −0.414816 | − | 0.909905i | \(-0.636154\pi\) | ||||
−0.414816 | + | 0.909905i | \(0.636154\pi\) | |||||||
\(350\) | 8.32195e12 | 0.0846937 | ||||||||
\(351\) | −8.73385e12 | −0.0875017 | ||||||||
\(352\) | 9.81592e12 | 0.0968159 | ||||||||
\(353\) | 4.65152e13 | 0.451683 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(354\) | 3.75575e11 | 0.00359069 | ||||||||
\(355\) | −4.03325e12 | −0.0379664 | ||||||||
\(356\) | 1.15616e14 | 1.07162 | ||||||||
\(357\) | 2.20478e13 | 0.201229 | ||||||||
\(358\) | −7.67860e12 | −0.0690121 | ||||||||
\(359\) | 3.18415e13 | 0.281822 | 0.140911 | − | 0.990022i | \(-0.454997\pi\) | ||||
0.140911 | + | 0.990022i | \(0.454997\pi\) | |||||||
\(360\) | 3.41783e11 | 0.00297911 | ||||||||
\(361\) | −6.91601e13 | −0.593699 | ||||||||
\(362\) | −7.58660e12 | −0.0641431 | ||||||||
\(363\) | −3.74967e13 | −0.312253 | ||||||||
\(364\) | 9.89181e13 | 0.811369 | ||||||||
\(365\) | 1.44066e12 | 0.0116399 | ||||||||
\(366\) | 1.31802e12 | 0.0104900 | ||||||||
\(367\) | 1.63532e14 | 1.28215 | 0.641074 | − | 0.767479i | \(-0.278489\pi\) | ||||
0.641074 | + | 0.767479i | \(0.278489\pi\) | |||||||
\(368\) | −8.77251e13 | −0.677581 | ||||||||
\(369\) | −1.44704e13 | −0.110112 | ||||||||
\(370\) | −7.19523e11 | −0.00539430 | ||||||||
\(371\) | −3.27486e14 | −2.41900 | ||||||||
\(372\) | −4.32497e13 | −0.314773 | ||||||||
\(373\) | 1.16018e14 | 0.832010 | 0.416005 | − | 0.909362i | \(-0.363430\pi\) | ||||
0.416005 | + | 0.909362i | \(0.363430\pi\) | |||||||
\(374\) | 8.92649e11 | 0.00630793 | ||||||||
\(375\) | −1.54611e13 | −0.107664 | ||||||||
\(376\) | 1.57410e13 | 0.108019 | ||||||||
\(377\) | 8.59417e13 | 0.581201 | ||||||||
\(378\) | −2.46717e12 | −0.0164435 | ||||||||
\(379\) | 2.33930e14 | 1.53664 | 0.768318 | − | 0.640069i | \(-0.221094\pi\) | ||||
0.768318 | + | 0.640069i | \(0.221094\pi\) | |||||||
\(380\) | 9.19920e12 | 0.0595580 | ||||||||
\(381\) | −5.42304e13 | −0.346063 | ||||||||
\(382\) | 1.03469e13 | 0.0650819 | ||||||||
\(383\) | 3.07371e14 | 1.90577 | 0.952884 | − | 0.303336i | \(-0.0981005\pi\) | ||||
0.952884 | + | 0.303336i | \(0.0981005\pi\) | |||||||
\(384\) | 1.79475e13 | 0.109694 | ||||||||
\(385\) | −1.88381e13 | −0.113502 | ||||||||
\(386\) | 5.39274e12 | 0.0320316 | ||||||||
\(387\) | 9.64864e12 | 0.0565010 | ||||||||
\(388\) | 4.37804e12 | 0.0252758 | ||||||||
\(389\) | −1.43081e14 | −0.814442 | −0.407221 | − | 0.913330i | \(-0.633502\pi\) | ||||
−0.407221 | + | 0.913330i | \(0.633502\pi\) | |||||||
\(390\) | 2.09251e11 | 0.00117439 | ||||||||
\(391\) | −2.40244e13 | −0.132948 | ||||||||
\(392\) | 3.84602e13 | 0.209864 | ||||||||
\(393\) | −2.03111e13 | −0.109289 | ||||||||
\(394\) | 1.69344e13 | 0.0898545 | ||||||||
\(395\) | 1.76110e13 | 0.0921509 | ||||||||
\(396\) | 4.36710e13 | 0.225356 | ||||||||
\(397\) | 1.73602e14 | 0.883502 | 0.441751 | − | 0.897138i | \(-0.354358\pi\) | ||||
0.441751 | + | 0.897138i | \(0.354358\pi\) | |||||||
\(398\) | −4.26398e12 | −0.0214022 | ||||||||
\(399\) | −1.32962e14 | −0.658226 | ||||||||
\(400\) | −2.01615e14 | −0.984449 | ||||||||
\(401\) | 2.06844e14 | 0.996206 | 0.498103 | − | 0.867118i | \(-0.334030\pi\) | ||||
0.498103 | + | 0.867118i | \(0.334030\pi\) | |||||||
\(402\) | 1.77362e12 | 0.00842594 | ||||||||
\(403\) | −5.30184e13 | −0.248456 | ||||||||
\(404\) | −1.88859e14 | −0.873050 | ||||||||
\(405\) | 2.28175e12 | 0.0104056 | ||||||||
\(406\) | 2.42772e13 | 0.109221 | ||||||||
\(407\) | −1.84083e14 | −0.817043 | ||||||||
\(408\) | 2.45193e12 | 0.0107369 | ||||||||
\(409\) | 4.82766e13 | 0.208573 | 0.104287 | − | 0.994547i | \(-0.466744\pi\) | ||||
0.104287 | + | 0.994547i | \(0.466744\pi\) | |||||||
\(410\) | 3.46689e11 | 0.00147784 | ||||||||
\(411\) | 1.10058e13 | 0.0462906 | ||||||||
\(412\) | 2.20611e14 | 0.915570 | ||||||||
\(413\) | −5.68606e13 | −0.232855 | ||||||||
\(414\) | 2.68836e12 | 0.0108639 | ||||||||
\(415\) | −1.10929e13 | −0.0442366 | ||||||||
\(416\) | 1.65073e13 | 0.0649624 | ||||||||
\(417\) | −1.02069e14 | −0.396411 | ||||||||
\(418\) | −5.38321e12 | −0.0206335 | ||||||||
\(419\) | 9.62691e13 | 0.364175 | 0.182087 | − | 0.983282i | \(-0.441715\pi\) | ||||
0.182087 | + | 0.983282i | \(0.441715\pi\) | |||||||
\(420\) | −2.58427e13 | −0.0964867 | ||||||||
\(421\) | 3.57648e14 | 1.31797 | 0.658984 | − | 0.752157i | \(-0.270987\pi\) | ||||
0.658984 | + | 0.752157i | \(0.270987\pi\) | |||||||
\(422\) | 2.38428e12 | 0.00867238 | ||||||||
\(423\) | 1.05087e14 | 0.377292 | ||||||||
\(424\) | −3.64197e13 | −0.129070 | ||||||||
\(425\) | −5.52144e13 | −0.193158 | ||||||||
\(426\) | 3.23778e12 | 0.0111814 | ||||||||
\(427\) | −1.99543e14 | −0.680274 | ||||||||
\(428\) | −1.10116e14 | −0.370603 | ||||||||
\(429\) | 5.35348e13 | 0.177877 | ||||||||
\(430\) | −2.31168e11 | −0.000758316 0 | ||||||||
\(431\) | −1.62300e14 | −0.525648 | −0.262824 | − | 0.964844i | \(-0.584654\pi\) | ||||
−0.262824 | + | 0.964844i | \(0.584654\pi\) | |||||||
\(432\) | 5.97720e13 | 0.191134 | ||||||||
\(433\) | 1.89586e14 | 0.598581 | 0.299290 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299290 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(434\) | −1.49769e13 | −0.0466903 | ||||||||
\(435\) | −2.24526e13 | −0.0691156 | ||||||||
\(436\) | 1.77181e14 | 0.538569 | ||||||||
\(437\) | 1.44882e14 | 0.434877 | ||||||||
\(438\) | −1.15652e12 | −0.00342804 | ||||||||
\(439\) | 5.87391e14 | 1.71938 | 0.859691 | − | 0.510815i | \(-0.170656\pi\) | ||||
0.859691 | + | 0.510815i | \(0.170656\pi\) | |||||||
\(440\) | −2.09498e12 | −0.00605607 | ||||||||
\(441\) | 2.56762e14 | 0.733024 | ||||||||
\(442\) | 1.50115e12 | 0.00423255 | ||||||||
\(443\) | 9.54123e13 | 0.265695 | 0.132848 | − | 0.991136i | \(-0.457588\pi\) | ||||
0.132848 | + | 0.991136i | \(0.457588\pi\) | |||||||
\(444\) | −2.52531e14 | −0.694558 | ||||||||
\(445\) | −3.70274e13 | −0.100587 | ||||||||
\(446\) | 1.41291e13 | 0.0379116 | ||||||||
\(447\) | 8.85335e13 | 0.234648 | ||||||||
\(448\) | −6.73852e14 | −1.76415 | ||||||||
\(449\) | −2.82045e14 | −0.729396 | −0.364698 | − | 0.931126i | \(-0.618828\pi\) | ||||
−0.364698 | + | 0.931126i | \(0.618828\pi\) | |||||||
\(450\) | 6.17855e12 | 0.0157840 | ||||||||
\(451\) | 8.86971e13 | 0.223840 | ||||||||
\(452\) | 5.66562e14 | 1.41249 | ||||||||
\(453\) | −3.38958e14 | −0.834844 | ||||||||
\(454\) | −2.70054e13 | −0.0657117 | ||||||||
\(455\) | −3.16797e13 | −0.0761586 | ||||||||
\(456\) | −1.47866e13 | −0.0351206 | ||||||||
\(457\) | −5.40931e14 | −1.26941 | −0.634706 | − | 0.772754i | \(-0.718879\pi\) | ||||
−0.634706 | + | 0.772754i | \(0.718879\pi\) | |||||||
\(458\) | −1.30958e13 | −0.0303649 | ||||||||
\(459\) | 1.63692e13 | 0.0375022 | ||||||||
\(460\) | 2.81596e13 | 0.0637468 | ||||||||
\(461\) | 3.87690e14 | 0.867221 | 0.433610 | − | 0.901100i | \(-0.357239\pi\) | ||||
0.433610 | + | 0.901100i | \(0.357239\pi\) | |||||||
\(462\) | 1.51227e13 | 0.0334271 | ||||||||
\(463\) | −6.36506e14 | −1.39029 | −0.695147 | − | 0.718867i | \(-0.744661\pi\) | ||||
−0.695147 | + | 0.718867i | \(0.744661\pi\) | |||||||
\(464\) | −5.88160e14 | −1.26954 | ||||||||
\(465\) | 1.38513e13 | 0.0295460 | ||||||||
\(466\) | 1.85517e13 | 0.0391075 | ||||||||
\(467\) | −5.78961e14 | −1.20616 | −0.603082 | − | 0.797679i | \(-0.706061\pi\) | ||||
−0.603082 | + | 0.797679i | \(0.706061\pi\) | |||||||
\(468\) | 7.34408e13 | 0.151212 | ||||||||
\(469\) | −2.68520e14 | −0.546419 | ||||||||
\(470\) | −2.51774e12 | −0.00506375 | ||||||||
\(471\) | 9.97126e13 | 0.198214 | ||||||||
\(472\) | −6.32345e12 | −0.0124243 | ||||||||
\(473\) | −5.91421e13 | −0.114858 | ||||||||
\(474\) | −1.41376e13 | −0.0271391 | ||||||||
\(475\) | 3.32976e14 | 0.631827 | ||||||||
\(476\) | −1.85394e14 | −0.347743 | ||||||||
\(477\) | −2.43139e14 | −0.450820 | ||||||||
\(478\) | 4.25237e12 | 0.00779432 | ||||||||
\(479\) | −3.77517e14 | −0.684055 | −0.342027 | − | 0.939690i | \(-0.611114\pi\) | ||||
−0.342027 | + | 0.939690i | \(0.611114\pi\) | |||||||
\(480\) | −4.31259e12 | −0.00772523 | ||||||||
\(481\) | −3.09569e14 | −0.548227 | ||||||||
\(482\) | −4.23894e13 | −0.0742161 | ||||||||
\(483\) | −4.07008e14 | −0.704520 | ||||||||
\(484\) | 3.15300e14 | 0.539603 | ||||||||
\(485\) | −1.40212e12 | −0.00237250 | ||||||||
\(486\) | −1.83173e12 | −0.00306452 | ||||||||
\(487\) | 5.88866e14 | 0.974109 | 0.487054 | − | 0.873372i | \(-0.338071\pi\) | ||||
0.487054 | + | 0.873372i | \(0.338071\pi\) | |||||||
\(488\) | −2.21912e13 | −0.0362970 | ||||||||
\(489\) | −6.18010e14 | −0.999532 | ||||||||
\(490\) | −6.15164e12 | −0.00983813 | ||||||||
\(491\) | 7.81722e14 | 1.23624 | 0.618122 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618122 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(492\) | 1.21678e14 | 0.190284 | ||||||||
\(493\) | −1.61074e14 | −0.249096 | ||||||||
\(494\) | −9.05286e12 | −0.0138448 | ||||||||
\(495\) | −1.39862e13 | −0.0211529 | ||||||||
\(496\) | 3.62843e14 | 0.542711 | ||||||||
\(497\) | −4.90188e14 | −0.725108 | ||||||||
\(498\) | 8.90511e12 | 0.0130280 | ||||||||
\(499\) | 3.04135e14 | 0.440062 | 0.220031 | − | 0.975493i | \(-0.429384\pi\) | ||||
0.220031 | + | 0.975493i | \(0.429384\pi\) | |||||||
\(500\) | 1.30009e14 | 0.186053 | ||||||||
\(501\) | −3.35532e13 | −0.0474927 | ||||||||
\(502\) | 9.07731e12 | 0.0127083 | ||||||||
\(503\) | 5.32879e14 | 0.737912 | 0.368956 | − | 0.929447i | \(-0.379715\pi\) | ||||
0.368956 | + | 0.929447i | \(0.379715\pi\) | |||||||
\(504\) | 4.15392e13 | 0.0568970 | ||||||||
\(505\) | 6.04843e13 | 0.0819483 | ||||||||
\(506\) | −1.64785e13 | −0.0220846 | ||||||||
\(507\) | −3.45466e14 | −0.457996 | ||||||||
\(508\) | 4.56010e14 | 0.598031 | ||||||||
\(509\) | −1.28977e15 | −1.67326 | −0.836631 | − | 0.547767i | \(-0.815478\pi\) | ||||
−0.836631 | + | 0.547767i | \(0.815478\pi\) | |||||||
\(510\) | −3.92182e11 | −0.000503329 0 | ||||||||
\(511\) | 1.75093e14 | 0.222307 | ||||||||
\(512\) | −1.88429e14 | −0.236680 | ||||||||
\(513\) | −9.87160e13 | −0.122671 | ||||||||
\(514\) | 6.36998e13 | 0.0783143 | ||||||||
\(515\) | −7.06533e13 | −0.0859394 | ||||||||
\(516\) | −8.11330e13 | −0.0976392 | ||||||||
\(517\) | −6.44140e14 | −0.766977 | ||||||||
\(518\) | −8.74485e13 | −0.103024 | ||||||||
\(519\) | 4.64166e13 | 0.0541069 | ||||||||
\(520\) | −3.52310e12 | −0.00406355 | ||||||||
\(521\) | −1.32247e15 | −1.50930 | −0.754652 | − | 0.656125i | \(-0.772194\pi\) | ||||
−0.754652 | + | 0.656125i | \(0.772194\pi\) | |||||||
\(522\) | 1.80243e13 | 0.0203550 | ||||||||
\(523\) | 4.00732e14 | 0.447811 | 0.223906 | − | 0.974611i | \(-0.428119\pi\) | ||||
0.223906 | + | 0.974611i | \(0.428119\pi\) | |||||||
\(524\) | 1.70791e14 | 0.188861 | ||||||||
\(525\) | −9.35409e14 | −1.02359 | ||||||||
\(526\) | 2.44419e13 | 0.0264675 | ||||||||
\(527\) | 9.93682e13 | 0.106485 | ||||||||
\(528\) | −3.66377e14 | −0.388545 | ||||||||
\(529\) | −5.09313e14 | −0.534538 | ||||||||
\(530\) | 5.82526e12 | 0.00605060 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 1.11804e15 | 1.13748 | ||||||||
\(533\) | 1.49160e14 | 0.150194 | ||||||||
\(534\) | 2.97246e13 | 0.0296237 | ||||||||
\(535\) | 3.52659e13 | 0.0347864 | ||||||||
\(536\) | −2.98621e13 | −0.0291550 | ||||||||
\(537\) | 8.63094e14 | 0.834065 | ||||||||
\(538\) | 8.27085e13 | 0.0791129 | ||||||||
\(539\) | −1.57384e15 | −1.49012 | ||||||||
\(540\) | −1.91867e13 | −0.0179819 | ||||||||
\(541\) | −7.68108e14 | −0.712586 | −0.356293 | − | 0.934374i | \(-0.615959\pi\) | ||||
−0.356293 | + | 0.934374i | \(0.615959\pi\) | |||||||
\(542\) | 2.07709e13 | 0.0190747 | ||||||||
\(543\) | 8.52754e14 | 0.775219 | ||||||||
\(544\) | −3.09383e13 | −0.0278421 | ||||||||
\(545\) | −5.67443e13 | −0.0505524 | ||||||||
\(546\) | 2.54316e13 | 0.0224292 | ||||||||
\(547\) | 1.79943e14 | 0.157111 | 0.0785553 | − | 0.996910i | \(-0.474969\pi\) | ||||
0.0785553 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(548\) | −9.25453e13 | −0.0799947 | ||||||||
\(549\) | −1.48149e14 | −0.126780 | ||||||||
\(550\) | −3.78719e13 | −0.0320865 | ||||||||
\(551\) | 9.71373e14 | 0.814802 | ||||||||
\(552\) | −4.52632e13 | −0.0375907 | ||||||||
\(553\) | 2.14038e15 | 1.75996 | ||||||||
\(554\) | 4.99557e13 | 0.0406707 | ||||||||
\(555\) | 8.08762e13 | 0.0651943 | ||||||||
\(556\) | 8.58273e14 | 0.685037 | ||||||||
\(557\) | −2.08144e14 | −0.164498 | −0.0822491 | − | 0.996612i | \(-0.526210\pi\) | ||||
−0.0822491 | + | 0.996612i | \(0.526210\pi\) | |||||||
\(558\) | −1.11194e13 | −0.00870150 | ||||||||
\(559\) | −9.94582e13 | −0.0770682 | ||||||||
\(560\) | 2.16807e14 | 0.166356 | ||||||||
\(561\) | −1.00336e14 | −0.0762362 | ||||||||
\(562\) | 6.67302e13 | 0.0502080 | ||||||||
\(563\) | −1.07254e14 | −0.0799131 | −0.0399566 | − | 0.999201i | \(-0.512722\pi\) | ||||
−0.0399566 | + | 0.999201i | \(0.512722\pi\) | |||||||
\(564\) | −8.83652e14 | −0.651998 | ||||||||
\(565\) | −1.81448e14 | −0.132583 | ||||||||
\(566\) | 5.40196e13 | 0.0390895 | ||||||||
\(567\) | 2.77317e14 | 0.198733 | ||||||||
\(568\) | −5.45137e13 | −0.0386892 | ||||||||
\(569\) | −2.74553e15 | −1.92978 | −0.964892 | − | 0.262648i | \(-0.915404\pi\) | ||||
−0.964892 | + | 0.262648i | \(0.915404\pi\) | |||||||
\(570\) | 2.36509e12 | 0.00164641 | ||||||||
\(571\) | 2.88426e14 | 0.198855 | 0.0994275 | − | 0.995045i | \(-0.468299\pi\) | ||||
0.0994275 | + | 0.995045i | \(0.468299\pi\) | |||||||
\(572\) | −4.50161e14 | −0.307390 | ||||||||
\(573\) | −1.16301e15 | −0.786565 | ||||||||
\(574\) | 4.21355e13 | 0.0282249 | ||||||||
\(575\) | 1.01927e15 | 0.676264 | ||||||||
\(576\) | −5.00295e14 | −0.328778 | ||||||||
\(577\) | −7.87983e13 | −0.0512920 | −0.0256460 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256460 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(578\) | 7.12779e13 | 0.0459570 | ||||||||
\(579\) | −6.06158e14 | −0.387127 | ||||||||
\(580\) | 1.88798e14 | 0.119438 | ||||||||
\(581\) | −1.34820e15 | −0.844862 | ||||||||
\(582\) | 1.12559e12 | 0.000698718 0 | ||||||||
\(583\) | 1.49034e15 | 0.916448 | ||||||||
\(584\) | 1.94720e13 | 0.0118615 | ||||||||
\(585\) | −2.35203e13 | −0.0141934 | ||||||||
\(586\) | 4.94870e13 | 0.0295838 | ||||||||
\(587\) | 4.26298e14 | 0.252466 | 0.126233 | − | 0.992001i | \(-0.459711\pi\) | ||||
0.126233 | + | 0.992001i | \(0.459711\pi\) | |||||||
\(588\) | −2.15904e15 | −1.26674 | ||||||||
\(589\) | −5.99250e14 | −0.348317 | ||||||||
\(590\) | 1.01142e12 | 0.000582435 0 | ||||||||
\(591\) | −1.90347e15 | −1.08596 | ||||||||
\(592\) | 2.11860e15 | 1.19751 | ||||||||
\(593\) | −2.68295e15 | −1.50249 | −0.751245 | − | 0.660023i | \(-0.770546\pi\) | ||||
−0.751245 | + | 0.660023i | \(0.770546\pi\) | |||||||
\(594\) | 1.12277e13 | 0.00622969 | ||||||||
\(595\) | 5.93748e13 | 0.0326407 | ||||||||
\(596\) | −7.44456e14 | −0.405494 | ||||||||
\(597\) | 4.79283e14 | 0.258662 | ||||||||
\(598\) | −2.77116e13 | −0.0148185 | ||||||||
\(599\) | −1.34478e15 | −0.712533 | −0.356266 | − | 0.934384i | \(-0.615950\pi\) | ||||
−0.356266 | + | 0.934384i | \(0.615950\pi\) | |||||||
\(600\) | −1.04027e14 | −0.0546151 | ||||||||
\(601\) | −1.99759e15 | −1.03919 | −0.519597 | − | 0.854412i | \(-0.673918\pi\) | ||||
−0.519597 | + | 0.854412i | \(0.673918\pi\) | |||||||
\(602\) | −2.80954e13 | −0.0144828 | ||||||||
\(603\) | −1.99360e14 | −0.101834 | ||||||||
\(604\) | 2.85021e15 | 1.44269 | ||||||||
\(605\) | −1.00979e14 | −0.0506495 | ||||||||
\(606\) | −4.85551e13 | −0.0241344 | ||||||||
\(607\) | −1.08277e15 | −0.533331 | −0.266666 | − | 0.963789i | \(-0.585922\pi\) | ||||
−0.266666 | + | 0.963789i | \(0.585922\pi\) | |||||||
\(608\) | 1.86577e14 | 0.0910725 | ||||||||
\(609\) | −2.72882e15 | −1.32002 | ||||||||
\(610\) | 3.54944e12 | 0.00170155 | ||||||||
\(611\) | −1.08324e15 | −0.514633 | ||||||||
\(612\) | −1.37644e14 | −0.0648075 | ||||||||
\(613\) | 2.68608e15 | 1.25339 | 0.626694 | − | 0.779265i | \(-0.284407\pi\) | ||||
0.626694 | + | 0.779265i | \(0.284407\pi\) | |||||||
\(614\) | −1.95395e13 | −0.00903624 | ||||||||
\(615\) | −3.89687e13 | −0.0178609 | ||||||||
\(616\) | −2.54617e14 | −0.115663 | ||||||||
\(617\) | 1.09022e15 | 0.490847 | 0.245423 | − | 0.969416i | \(-0.421073\pi\) | ||||
0.245423 | + | 0.969416i | \(0.421073\pi\) | |||||||
\(618\) | 5.67185e13 | 0.0253098 | ||||||||
\(619\) | 1.99913e15 | 0.884182 | 0.442091 | − | 0.896970i | \(-0.354237\pi\) | ||||
0.442091 | + | 0.896970i | \(0.354237\pi\) | |||||||
\(620\) | −1.16472e14 | −0.0510583 | ||||||||
\(621\) | −3.02179e14 | −0.131299 | ||||||||
\(622\) | −5.95522e13 | −0.0256479 | ||||||||
\(623\) | −4.50019e15 | −1.92109 | ||||||||
\(624\) | −6.16129e14 | −0.260709 | ||||||||
\(625\) | 2.32164e15 | 0.973766 | ||||||||
\(626\) | 1.15369e14 | 0.0479656 | ||||||||
\(627\) | 6.05087e14 | 0.249371 | ||||||||
\(628\) | −8.38459e14 | −0.342534 | ||||||||
\(629\) | 5.80202e14 | 0.234964 | ||||||||
\(630\) | −6.64411e12 | −0.00266725 | ||||||||
\(631\) | −1.60230e14 | −0.0637650 | −0.0318825 | − | 0.999492i | \(-0.510150\pi\) | ||||
−0.0318825 | + | 0.999492i | \(0.510150\pi\) | |||||||
\(632\) | 2.38031e14 | 0.0939053 | ||||||||
\(633\) | −2.67999e14 | −0.104812 | ||||||||
\(634\) | −4.71421e13 | −0.0182776 | ||||||||
\(635\) | −1.46043e14 | −0.0561338 | ||||||||
\(636\) | 2.04450e15 | 0.779062 | ||||||||
\(637\) | −2.64670e15 | −0.999857 | ||||||||
\(638\) | −1.10482e14 | −0.0413786 | ||||||||
\(639\) | −3.63935e14 | −0.135135 | ||||||||
\(640\) | 4.83328e13 | 0.0177931 | ||||||||
\(641\) | 3.08509e15 | 1.12603 | 0.563013 | − | 0.826448i | \(-0.309642\pi\) | ||||
0.563013 | + | 0.826448i | \(0.309642\pi\) | |||||||
\(642\) | −2.83105e13 | −0.0102448 | ||||||||
\(643\) | 1.17294e15 | 0.420837 | 0.210419 | − | 0.977611i | \(-0.432517\pi\) | ||||
0.210419 | + | 0.977611i | \(0.432517\pi\) | |||||||
\(644\) | 3.42243e15 | 1.21748 | ||||||||
\(645\) | 2.59838e13 | 0.00916484 | ||||||||
\(646\) | 1.69671e13 | 0.00593373 | ||||||||
\(647\) | 1.06206e15 | 0.368277 | 0.184139 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184139 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(648\) | 3.08403e13 | 0.0106037 | ||||||||
\(649\) | 2.58763e14 | 0.0882180 | ||||||||
\(650\) | −6.36885e13 | −0.0215297 | ||||||||
\(651\) | 1.68344e15 | 0.564289 | ||||||||
\(652\) | 5.19669e15 | 1.72729 | ||||||||
\(653\) | 5.17742e15 | 1.70644 | 0.853219 | − | 0.521552i | \(-0.174647\pi\) | ||||
0.853219 | + | 0.521552i | \(0.174647\pi\) | |||||||
\(654\) | 4.55528e13 | 0.0148880 | ||||||||
\(655\) | −5.46979e13 | −0.0177273 | ||||||||
\(656\) | −1.02081e15 | −0.328076 | ||||||||
\(657\) | 1.29996e14 | 0.0414305 | ||||||||
\(658\) | −3.05998e14 | −0.0967110 | ||||||||
\(659\) | −5.76292e15 | −1.80623 | −0.903114 | − | 0.429400i | \(-0.858725\pi\) | ||||
−0.903114 | + | 0.429400i | \(0.858725\pi\) | |||||||
\(660\) | 1.17606e14 | 0.0365543 | ||||||||
\(661\) | 1.35104e15 | 0.416447 | 0.208224 | − | 0.978081i | \(-0.433232\pi\) | ||||
0.208224 | + | 0.978081i | \(0.433232\pi\) | |||||||
\(662\) | −1.16489e14 | −0.0356097 | ||||||||
\(663\) | −1.68733e14 | −0.0511537 | ||||||||
\(664\) | −1.49933e14 | −0.0450788 | ||||||||
\(665\) | −3.58066e14 | −0.106769 | ||||||||
\(666\) | −6.49252e13 | −0.0192002 | ||||||||
\(667\) | 2.97346e15 | 0.872108 | ||||||||
\(668\) | 2.82141e14 | 0.0820720 | ||||||||
\(669\) | −1.58815e15 | −0.458191 | ||||||||
\(670\) | 4.77638e12 | 0.00136675 | ||||||||
\(671\) | 9.08091e14 | 0.257724 | ||||||||
\(672\) | −5.24138e14 | −0.147542 | ||||||||
\(673\) | −3.33582e14 | −0.0931364 | −0.0465682 | − | 0.998915i | \(-0.514828\pi\) | ||||
−0.0465682 | + | 0.998915i | \(0.514828\pi\) | |||||||
\(674\) | −1.43683e14 | −0.0397902 | ||||||||
\(675\) | −6.94485e14 | −0.190762 | ||||||||
\(676\) | 2.90494e15 | 0.791463 | ||||||||
\(677\) | 1.21173e15 | 0.327469 | 0.163734 | − | 0.986504i | \(-0.447646\pi\) | ||||
0.163734 | + | 0.986504i | \(0.447646\pi\) | |||||||
\(678\) | 1.45662e14 | 0.0390465 | ||||||||
\(679\) | −1.70409e14 | −0.0453116 | ||||||||
\(680\) | 6.60306e12 | 0.00174159 | ||||||||
\(681\) | 3.03547e15 | 0.794177 | ||||||||
\(682\) | 6.81573e13 | 0.0176888 | ||||||||
\(683\) | 3.59538e15 | 0.925617 | 0.462808 | − | 0.886458i | \(-0.346842\pi\) | ||||
0.462808 | + | 0.886458i | \(0.346842\pi\) | |||||||
\(684\) | 8.30078e14 | 0.211988 | ||||||||
\(685\) | 2.96388e13 | 0.00750866 | ||||||||
\(686\) | −4.07666e14 | −0.102452 | ||||||||
\(687\) | 1.47200e15 | 0.366984 | ||||||||
\(688\) | 6.80663e14 | 0.168343 | ||||||||
\(689\) | 2.50628e15 | 0.614927 | ||||||||
\(690\) | 7.23977e12 | 0.00176220 | ||||||||
\(691\) | −1.63600e15 | −0.395051 | −0.197525 | − | 0.980298i | \(-0.563290\pi\) | ||||
−0.197525 | + | 0.980298i | \(0.563290\pi\) | |||||||
\(692\) | −3.90305e14 | −0.0935020 | ||||||||
\(693\) | −1.69983e15 | −0.403993 | ||||||||
\(694\) | 1.52027e13 | 0.00358462 | ||||||||
\(695\) | −2.74872e14 | −0.0643005 | ||||||||
\(696\) | −3.03471e14 | −0.0704314 | ||||||||
\(697\) | −2.79560e14 | −0.0643716 | ||||||||
\(698\) | 1.73482e14 | 0.0396324 | ||||||||
\(699\) | −2.08525e15 | −0.472645 | ||||||||
\(700\) | 7.86562e15 | 1.76886 | ||||||||
\(701\) | −3.60539e15 | −0.804458 | −0.402229 | − | 0.915539i | \(-0.631764\pi\) | ||||
−0.402229 | + | 0.915539i | \(0.631764\pi\) | |||||||
\(702\) | 1.88815e13 | 0.00418005 | ||||||||
\(703\) | −3.49897e15 | −0.768574 | ||||||||
\(704\) | 3.06660e15 | 0.668355 | ||||||||
\(705\) | 2.83000e14 | 0.0611994 | ||||||||
\(706\) | −1.00560e14 | −0.0215774 | ||||||||
\(707\) | 7.35106e15 | 1.56510 | ||||||||
\(708\) | 3.54980e14 | 0.0749931 | ||||||||
\(709\) | 3.80021e15 | 0.796624 | 0.398312 | − | 0.917250i | \(-0.369596\pi\) | ||||
0.398312 | + | 0.917250i | \(0.369596\pi\) | |||||||
\(710\) | 8.71937e12 | 0.00181369 | ||||||||
\(711\) | 1.58910e15 | 0.327997 | ||||||||
\(712\) | −5.00465e14 | −0.102502 | ||||||||
\(713\) | −1.83436e15 | −0.372814 | ||||||||
\(714\) | −4.76645e13 | −0.00961291 | ||||||||
\(715\) | 1.44169e14 | 0.0288529 | ||||||||
\(716\) | −7.25755e15 | −1.44135 | ||||||||
\(717\) | −4.77978e14 | −0.0942003 | ||||||||
\(718\) | −6.88373e13 | −0.0134629 | ||||||||
\(719\) | −3.94798e15 | −0.766243 | −0.383121 | − | 0.923698i | \(-0.625151\pi\) | ||||
−0.383121 | + | 0.923698i | \(0.625151\pi\) | |||||||
\(720\) | 1.60966e14 | 0.0310032 | ||||||||
\(721\) | −8.58697e15 | −1.64133 | ||||||||
\(722\) | 1.49515e14 | 0.0283616 | ||||||||
\(723\) | 4.76467e15 | 0.896959 | ||||||||
\(724\) | −7.17059e15 | −1.33966 | ||||||||
\(725\) | 6.83379e15 | 1.26708 | ||||||||
\(726\) | 8.10630e13 | 0.0149166 | ||||||||
\(727\) | 3.22833e15 | 0.589574 | 0.294787 | − | 0.955563i | \(-0.404751\pi\) | ||||
0.294787 | + | 0.955563i | \(0.404751\pi\) | |||||||
\(728\) | −4.28186e14 | −0.0776085 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.11452e12 | −0.000556051 0 | ||||||||
\(731\) | 1.86407e14 | 0.0330306 | ||||||||
\(732\) | 1.24575e15 | 0.219088 | ||||||||
\(733\) | −3.11347e14 | −0.0543466 | −0.0271733 | − | 0.999631i | \(-0.508651\pi\) | ||||
−0.0271733 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(734\) | −3.53534e14 | −0.0612496 | ||||||||
\(735\) | 6.91461e14 | 0.118901 | ||||||||
\(736\) | 5.71128e14 | 0.0974778 | ||||||||
\(737\) | 1.22199e15 | 0.207013 | ||||||||
\(738\) | 3.12830e13 | 0.00526016 | ||||||||
\(739\) | −8.06786e15 | −1.34652 | −0.673262 | − | 0.739404i | \(-0.735107\pi\) | ||||
−0.673262 | + | 0.739404i | \(0.735107\pi\) | |||||||
\(740\) | −6.80068e14 | −0.112662 | ||||||||
\(741\) | 1.01756e15 | 0.167325 | ||||||||
\(742\) | 7.07983e14 | 0.115558 | ||||||||
\(743\) | −5.25372e15 | −0.851194 | −0.425597 | − | 0.904913i | \(-0.639936\pi\) | ||||
−0.425597 | + | 0.904913i | \(0.639936\pi\) | |||||||
\(744\) | 1.87215e14 | 0.0301085 | ||||||||
\(745\) | 2.38421e14 | 0.0380615 | ||||||||
\(746\) | −2.50817e14 | −0.0397460 | ||||||||
\(747\) | −1.00096e15 | −0.157454 | ||||||||
\(748\) | 8.43701e14 | 0.131744 | ||||||||
\(749\) | 4.28610e15 | 0.664374 | ||||||||
\(750\) | 3.34250e13 | 0.00514321 | ||||||||
\(751\) | 9.17937e15 | 1.40215 | 0.701073 | − | 0.713090i | \(-0.252705\pi\) | ||||
0.701073 | + | 0.713090i | \(0.252705\pi\) | |||||||
\(752\) | 7.41338e15 | 1.12413 | ||||||||
\(753\) | −1.02031e15 | −0.153589 | ||||||||
\(754\) | −1.85795e14 | −0.0277646 | ||||||||
\(755\) | −9.12815e14 | −0.135417 | ||||||||
\(756\) | −2.33189e15 | −0.343430 | ||||||||
\(757\) | 4.74779e15 | 0.694168 | 0.347084 | − | 0.937834i | \(-0.387172\pi\) | ||||
0.347084 | + | 0.937834i | \(0.387172\pi\) | |||||||
\(758\) | −5.05727e14 | −0.0734067 | ||||||||
\(759\) | 1.85223e15 | 0.266910 | ||||||||
\(760\) | −3.98205e13 | −0.00569681 | ||||||||
\(761\) | −1.64969e14 | −0.0234307 | −0.0117154 | − | 0.999931i | \(-0.503729\pi\) | ||||
−0.0117154 | + | 0.999931i | \(0.503729\pi\) | |||||||
\(762\) | 1.17239e14 | 0.0165318 | ||||||||
\(763\) | −6.89652e15 | −0.965484 | ||||||||
\(764\) | 9.77950e15 | 1.35926 | ||||||||
\(765\) | 4.40823e13 | 0.00608311 | ||||||||
\(766\) | −6.64497e14 | −0.0910405 | ||||||||
\(767\) | 4.35158e14 | 0.0591933 | ||||||||
\(768\) | 4.17768e15 | 0.564220 | ||||||||
\(769\) | −7.50627e15 | −1.00654 | −0.503268 | − | 0.864130i | \(-0.667869\pi\) | ||||
−0.503268 | + | 0.864130i | \(0.667869\pi\) | |||||||
\(770\) | 4.07256e13 | 0.00542211 | ||||||||
\(771\) | −7.16003e15 | −0.946489 | ||||||||
\(772\) | 5.09703e15 | 0.668993 | ||||||||
\(773\) | −9.39637e15 | −1.22454 | −0.612270 | − | 0.790649i | \(-0.709743\pi\) | ||||
−0.612270 | + | 0.790649i | \(0.709743\pi\) | |||||||
\(774\) | −2.08591e13 | −0.00269911 | ||||||||
\(775\) | −4.21584e15 | −0.541657 | ||||||||
\(776\) | −1.89512e13 | −0.00241767 | ||||||||
\(777\) | 9.82943e15 | 1.24512 | ||||||||
\(778\) | 3.09324e14 | 0.0389068 | ||||||||
\(779\) | 1.68591e15 | 0.210562 | ||||||||
\(780\) | 1.97776e14 | 0.0245275 | ||||||||
\(781\) | 2.23077e15 | 0.274710 | ||||||||
\(782\) | 5.19377e13 | 0.00635106 | ||||||||
\(783\) | −2.02598e15 | −0.246006 | ||||||||
\(784\) | 1.81132e16 | 2.18403 | ||||||||
\(785\) | 2.68527e14 | 0.0321517 | ||||||||
\(786\) | 4.39100e13 | 0.00522083 | ||||||||
\(787\) | 9.95129e15 | 1.17495 | 0.587474 | − | 0.809243i | \(-0.300123\pi\) | ||||
0.587474 | + | 0.809243i | \(0.300123\pi\) | |||||||
\(788\) | 1.60058e16 | 1.87665 | ||||||||
\(789\) | −2.74733e15 | −0.319880 | ||||||||
\(790\) | −3.80727e13 | −0.00440214 | ||||||||
\(791\) | −2.20526e16 | −2.53215 | ||||||||
\(792\) | −1.89038e14 | −0.0215556 | ||||||||
\(793\) | 1.52712e15 | 0.172930 | ||||||||
\(794\) | −3.75306e14 | −0.0422058 | ||||||||
\(795\) | −6.54775e14 | −0.0731261 | ||||||||
\(796\) | −4.03017e15 | −0.446994 | ||||||||
\(797\) | 1.29552e15 | 0.142700 | 0.0713498 | − | 0.997451i | \(-0.477269\pi\) | ||||
0.0713498 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(798\) | 2.87446e14 | 0.0314442 | ||||||||
\(799\) | 2.03023e15 | 0.220566 | ||||||||
\(800\) | 1.31260e15 | 0.141624 | ||||||||
\(801\) | −3.34112e15 | −0.358025 | ||||||||
\(802\) | −4.47171e14 | −0.0475898 | ||||||||
\(803\) | −7.96820e14 | −0.0842218 | ||||||||
\(804\) | 1.67637e15 | 0.175979 | ||||||||
\(805\) | −1.09607e15 | −0.114278 | ||||||||
\(806\) | 1.14619e14 | 0.0118690 | ||||||||
\(807\) | −9.29665e15 | −0.956141 | ||||||||
\(808\) | 8.17510e14 | 0.0835085 | ||||||||
\(809\) | −1.76699e16 | −1.79274 | −0.896372 | − | 0.443303i | \(-0.853807\pi\) | ||||
−0.896372 | + | 0.443303i | \(0.853807\pi\) | |||||||
\(810\) | −4.93286e12 | −0.000497085 0 | ||||||||
\(811\) | 5.13792e15 | 0.514248 | 0.257124 | − | 0.966378i | \(-0.417225\pi\) | ||||
0.257124 | + | 0.966378i | \(0.417225\pi\) | |||||||
\(812\) | 2.29459e16 | 2.28112 | ||||||||
\(813\) | −2.33470e15 | −0.230533 | ||||||||
\(814\) | 3.97964e14 | 0.0390310 | ||||||||
\(815\) | −1.66430e15 | −0.162131 | ||||||||
\(816\) | 1.15476e15 | 0.111737 | ||||||||
\(817\) | −1.12415e15 | −0.108044 | ||||||||
\(818\) | −1.04368e14 | −0.00996377 | ||||||||
\(819\) | −2.85858e15 | −0.271075 | ||||||||
\(820\) | 3.27678e14 | 0.0308654 | ||||||||
\(821\) | 1.65798e16 | 1.55128 | 0.775641 | − | 0.631174i | \(-0.217427\pi\) | ||||
0.775641 | + | 0.631174i | \(0.217427\pi\) | |||||||
\(822\) | −2.37932e13 | −0.00221135 | ||||||||
\(823\) | 8.54594e15 | 0.788970 | 0.394485 | − | 0.918902i | \(-0.370923\pi\) | ||||
0.394485 | + | 0.918902i | \(0.370923\pi\) | |||||||
\(824\) | −9.54955e14 | −0.0875756 | ||||||||
\(825\) | 4.25690e15 | 0.387790 | ||||||||
\(826\) | 1.22925e14 | 0.0111237 | ||||||||
\(827\) | −9.25100e15 | −0.831588 | −0.415794 | − | 0.909459i | \(-0.636496\pi\) | ||||
−0.415794 | + | 0.909459i | \(0.636496\pi\) | |||||||
\(828\) | 2.54095e15 | 0.226897 | ||||||||
\(829\) | 1.22466e16 | 1.08634 | 0.543168 | − | 0.839624i | \(-0.317225\pi\) | ||||
0.543168 | + | 0.839624i | \(0.317225\pi\) | |||||||
\(830\) | 2.39815e13 | 0.00211323 | ||||||||
\(831\) | −5.61515e15 | −0.491536 | ||||||||
\(832\) | 5.15704e15 | 0.448459 | ||||||||
\(833\) | 4.96050e15 | 0.428527 | ||||||||
\(834\) | 2.20660e14 | 0.0189370 | ||||||||
\(835\) | −9.03590e13 | −0.00770364 | ||||||||
\(836\) | −5.08803e15 | −0.430938 | ||||||||
\(837\) | 1.24985e15 | 0.105164 | ||||||||
\(838\) | −2.08121e14 | −0.0173970 | ||||||||
\(839\) | 1.38137e16 | 1.14715 | 0.573575 | − | 0.819153i | \(-0.305556\pi\) | ||||
0.573575 | + | 0.819153i | \(0.305556\pi\) | |||||||
\(840\) | 1.11865e14 | 0.00922909 | ||||||||
\(841\) | 7.73531e15 | 0.634015 | ||||||||
\(842\) | −7.73190e14 | −0.0629607 | ||||||||
\(843\) | −7.50065e15 | −0.606802 | ||||||||
\(844\) | 2.25354e15 | 0.181126 | ||||||||
\(845\) | −9.30343e14 | −0.0742901 | ||||||||
\(846\) | −2.27185e14 | −0.0180237 | ||||||||
\(847\) | −1.22726e16 | −0.967339 | ||||||||
\(848\) | −1.71522e16 | −1.34321 | ||||||||
\(849\) | −6.07194e15 | −0.472427 | ||||||||
\(850\) | 1.19366e14 | 0.00922737 | ||||||||
\(851\) | −1.07107e16 | −0.822629 | ||||||||
\(852\) | 3.06024e15 | 0.233527 | ||||||||
\(853\) | 1.29744e16 | 0.983712 | 0.491856 | − | 0.870677i | \(-0.336319\pi\) | ||||
0.491856 | + | 0.870677i | \(0.336319\pi\) | |||||||
\(854\) | 4.31387e14 | 0.0324974 | ||||||||
\(855\) | −2.65843e14 | −0.0198981 | ||||||||
\(856\) | 4.76657e14 | 0.0354487 | ||||||||
\(857\) | 6.64958e15 | 0.491360 | 0.245680 | − | 0.969351i | \(-0.420989\pi\) | ||||
0.245680 | + | 0.969351i | \(0.420989\pi\) | |||||||
\(858\) | −1.15735e14 | −0.00849740 | ||||||||
\(859\) | 1.88846e15 | 0.137767 | 0.0688836 | − | 0.997625i | \(-0.478056\pi\) | ||||
0.0688836 | + | 0.997625i | \(0.478056\pi\) | |||||||
\(860\) | −2.18492e14 | −0.0158377 | ||||||||
\(861\) | −4.73613e15 | −0.341120 | ||||||||
\(862\) | 3.50873e14 | 0.0251108 | ||||||||
\(863\) | −1.84854e16 | −1.31453 | −0.657264 | − | 0.753661i | \(-0.728286\pi\) | ||||
−0.657264 | + | 0.753661i | \(0.728286\pi\) | |||||||
\(864\) | −3.89141e14 | −0.0274968 | ||||||||
\(865\) | 1.25000e14 | 0.00877651 | ||||||||
\(866\) | −4.09860e14 | −0.0285948 | ||||||||
\(867\) | −8.01183e15 | −0.555426 | ||||||||
\(868\) | −1.41556e16 | −0.975147 | ||||||||
\(869\) | −9.74054e15 | −0.666767 | ||||||||
\(870\) | 4.85397e13 | 0.00330172 | ||||||||
\(871\) | 2.05500e15 | 0.138903 | ||||||||
\(872\) | −7.66960e14 | −0.0515148 | ||||||||
\(873\) | −1.26519e14 | −0.00844455 | ||||||||
\(874\) | −3.13216e14 | −0.0207745 | ||||||||
\(875\) | −5.06041e15 | −0.333535 | ||||||||
\(876\) | −1.09310e15 | −0.0715960 | ||||||||
\(877\) | −1.83116e16 | −1.19187 | −0.595934 | − | 0.803033i | \(-0.703218\pi\) | ||||
−0.595934 | + | 0.803033i | \(0.703218\pi\) | |||||||
\(878\) | −1.26986e15 | −0.0821367 | ||||||||
\(879\) | −5.56247e15 | −0.357543 | ||||||||
\(880\) | −9.86654e14 | −0.0630246 | ||||||||
\(881\) | −2.42101e16 | −1.53684 | −0.768419 | − | 0.639947i | \(-0.778956\pi\) | ||||
−0.768419 | + | 0.639947i | \(0.778956\pi\) | |||||||
\(882\) | −5.55086e14 | −0.0350173 | ||||||||
\(883\) | −8.16078e14 | −0.0511620 | −0.0255810 | − | 0.999673i | \(-0.508144\pi\) | ||||
−0.0255810 | + | 0.999673i | \(0.508144\pi\) | |||||||
\(884\) | 1.41884e15 | 0.0883985 | ||||||||
\(885\) | −1.13687e14 | −0.00703918 | ||||||||
\(886\) | −2.06269e14 | −0.0126925 | ||||||||
\(887\) | 3.04467e16 | 1.86192 | 0.930959 | − | 0.365124i | \(-0.118974\pi\) | ||||
0.930959 | + | 0.365124i | \(0.118974\pi\) | |||||||
\(888\) | 1.09313e15 | 0.0664355 | ||||||||
\(889\) | −1.77496e16 | −1.07208 | ||||||||
\(890\) | 8.00485e13 | 0.00480516 | ||||||||
\(891\) | −1.26203e15 | −0.0752906 | ||||||||
\(892\) | 1.33543e16 | 0.791799 | ||||||||
\(893\) | −1.22435e16 | −0.721478 | ||||||||
\(894\) | −1.91398e14 | −0.0112094 | ||||||||
\(895\) | 2.32432e15 | 0.135291 | ||||||||
\(896\) | 5.87421e15 | 0.339825 | ||||||||
\(897\) | 3.11486e15 | 0.179094 | ||||||||
\(898\) | 6.09745e14 | 0.0348440 | ||||||||
\(899\) | −1.22986e16 | −0.698519 | ||||||||
\(900\) | 5.83975e15 | 0.329656 | ||||||||
\(901\) | −4.69732e15 | −0.263550 | ||||||||
\(902\) | −1.91752e14 | −0.0106931 | ||||||||
\(903\) | 3.15799e15 | 0.175036 | ||||||||
\(904\) | −2.45247e15 | −0.135107 | ||||||||
\(905\) | 2.29647e15 | 0.125746 | ||||||||
\(906\) | 7.32783e14 | 0.0398814 | ||||||||
\(907\) | −6.06387e15 | −0.328027 | −0.164013 | − | 0.986458i | \(-0.552444\pi\) | ||||
−0.164013 | + | 0.986458i | \(0.552444\pi\) | |||||||
\(908\) | −2.55245e16 | −1.37242 | ||||||||
\(909\) | 5.45772e15 | 0.291682 | ||||||||
\(910\) | 6.84875e13 | 0.00363818 | ||||||||
\(911\) | −2.44461e16 | −1.29080 | −0.645400 | − | 0.763845i | \(-0.723309\pi\) | ||||
−0.645400 | + | 0.763845i | \(0.723309\pi\) | |||||||
\(912\) | −6.96392e15 | −0.365496 | ||||||||
\(913\) | 6.13545e15 | 0.320079 | ||||||||
\(914\) | 1.16942e15 | 0.0606412 | ||||||||
\(915\) | −3.98966e14 | −0.0205646 | ||||||||
\(916\) | −1.23777e16 | −0.634184 | ||||||||
\(917\) | −6.64781e15 | −0.338569 | ||||||||
\(918\) | −3.53880e13 | −0.00179152 | ||||||||
\(919\) | −4.61347e15 | −0.232162 | −0.116081 | − | 0.993240i | \(-0.537033\pi\) | ||||
−0.116081 | + | 0.993240i | \(0.537033\pi\) | |||||||
\(920\) | −1.21894e14 | −0.00609747 | ||||||||
\(921\) | 2.19629e15 | 0.109210 | ||||||||
\(922\) | −8.38136e14 | −0.0414281 | ||||||||
\(923\) | 3.75144e15 | 0.184327 | ||||||||
\(924\) | 1.42935e16 | 0.698139 | ||||||||
\(925\) | −2.46159e16 | −1.19519 | ||||||||
\(926\) | 1.37604e15 | 0.0664159 | ||||||||
\(927\) | −6.37531e15 | −0.305888 | ||||||||
\(928\) | 3.82918e15 | 0.182638 | ||||||||
\(929\) | −1.59191e16 | −0.754802 | −0.377401 | − | 0.926050i | \(-0.623182\pi\) | ||||
−0.377401 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(930\) | −2.99446e13 | −0.00141144 | ||||||||
\(931\) | −2.99148e16 | −1.40173 | ||||||||
\(932\) | 1.75344e16 | 0.816776 | ||||||||
\(933\) | 6.69383e15 | 0.309974 | ||||||||
\(934\) | 1.25164e15 | 0.0576197 | ||||||||
\(935\) | −2.70206e14 | −0.0123660 | ||||||||
\(936\) | −3.17902e14 | −0.0144636 | ||||||||
\(937\) | 9.86284e15 | 0.446102 | 0.223051 | − | 0.974807i | \(-0.428398\pi\) | ||||
0.223051 | + | 0.974807i | \(0.428398\pi\) | |||||||
\(938\) | 5.80506e14 | 0.0261030 | ||||||||
\(939\) | −1.29678e16 | −0.579701 | ||||||||
\(940\) | −2.37968e15 | −0.105759 | ||||||||
\(941\) | 4.42260e16 | 1.95404 | 0.977022 | − | 0.213138i | \(-0.0683685\pi\) | ||||
0.977022 | + | 0.213138i | \(0.0683685\pi\) | |||||||
\(942\) | −2.15566e14 | −0.00946891 | ||||||||
\(943\) | 5.16074e15 | 0.225371 | ||||||||
\(944\) | −2.97810e15 | −0.129298 | ||||||||
\(945\) | 7.46816e14 | 0.0322358 | ||||||||
\(946\) | 1.27858e14 | 0.00548687 | ||||||||
\(947\) | −1.88298e16 | −0.803381 | −0.401690 | − | 0.915776i | \(-0.631577\pi\) | ||||
−0.401690 | + | 0.915776i | \(0.631577\pi\) | |||||||
\(948\) | −1.33624e16 | −0.566811 | ||||||||
\(949\) | −1.34000e15 | −0.0565119 | ||||||||
\(950\) | −7.19852e14 | −0.0301831 | ||||||||
\(951\) | 5.29890e15 | 0.220898 | ||||||||
\(952\) | 8.02515e14 | 0.0332621 | ||||||||
\(953\) | −1.95109e15 | −0.0804018 | −0.0402009 | − | 0.999192i | \(-0.512800\pi\) | ||||
−0.0402009 | + | 0.999192i | \(0.512800\pi\) | |||||||
\(954\) | 5.25635e14 | 0.0215362 | ||||||||
\(955\) | −3.13200e15 | −0.127586 | ||||||||
\(956\) | 4.01920e15 | 0.162787 | ||||||||
\(957\) | 1.24184e16 | 0.500093 | ||||||||
\(958\) | 8.16142e14 | 0.0326780 | ||||||||
\(959\) | 3.60220e15 | 0.143405 | ||||||||
\(960\) | −1.34730e15 | −0.0533300 | ||||||||
\(961\) | −1.78213e16 | −0.701393 | ||||||||
\(962\) | 6.69249e14 | 0.0261894 | ||||||||
\(963\) | 3.18218e15 | 0.123817 | ||||||||
\(964\) | −4.00650e16 | −1.55003 | ||||||||
\(965\) | −1.63239e15 | −0.0627946 | ||||||||
\(966\) | 8.79899e14 | 0.0336557 | ||||||||
\(967\) | 3.19445e16 | 1.21493 | 0.607464 | − | 0.794347i | \(-0.292187\pi\) | ||||
0.607464 | + | 0.794347i | \(0.292187\pi\) | |||||||
\(968\) | −1.36484e15 | −0.0516138 | ||||||||
\(969\) | −1.90714e15 | −0.0717137 | ||||||||
\(970\) | 3.03121e12 | 0.000113337 0 | ||||||||
\(971\) | 1.80781e16 | 0.672120 | 0.336060 | − | 0.941841i | \(-0.390905\pi\) | ||||
0.336060 | + | 0.941841i | \(0.390905\pi\) | |||||||
\(972\) | −1.73129e15 | −0.0640036 | ||||||||
\(973\) | −3.34071e16 | −1.22806 | ||||||||
\(974\) | −1.27305e15 | −0.0465342 | ||||||||
\(975\) | 7.15876e15 | 0.260203 | ||||||||
\(976\) | −1.04512e16 | −0.377738 | ||||||||
\(977\) | 1.30976e16 | 0.470731 | 0.235366 | − | 0.971907i | \(-0.424371\pi\) | ||||
0.235366 | + | 0.971907i | \(0.424371\pi\) | |||||||
\(978\) | 1.33606e15 | 0.0477487 | ||||||||
\(979\) | 2.04797e16 | 0.727810 | ||||||||
\(980\) | −5.81432e15 | −0.205473 | ||||||||
\(981\) | −5.12025e15 | −0.179933 | ||||||||
\(982\) | −1.68998e15 | −0.0590567 | ||||||||
\(983\) | −4.30264e16 | −1.49517 | −0.747586 | − | 0.664165i | \(-0.768787\pi\) | ||||
−0.747586 | + | 0.664165i | \(0.768787\pi\) | |||||||
\(984\) | −5.26704e14 | −0.0182009 | ||||||||
\(985\) | −5.12605e15 | −0.176150 | ||||||||
\(986\) | 3.48221e14 | 0.0118996 | ||||||||
\(987\) | 3.43950e16 | 1.16883 | ||||||||
\(988\) | −8.55645e15 | −0.289155 | ||||||||
\(989\) | −3.44111e15 | −0.115643 | ||||||||
\(990\) | 3.02363e13 | 0.00101050 | ||||||||
\(991\) | −1.77981e16 | −0.591520 | −0.295760 | − | 0.955262i | \(-0.595573\pi\) | ||||
−0.295760 | + | 0.955262i | \(0.595573\pi\) | |||||||
\(992\) | −2.36226e15 | −0.0780753 | ||||||||
\(993\) | 1.30937e16 | 0.430370 | ||||||||
\(994\) | 1.05972e15 | 0.0346392 | ||||||||
\(995\) | 1.29071e15 | 0.0419568 | ||||||||
\(996\) | 8.41680e15 | 0.272095 | ||||||||
\(997\) | −2.02344e16 | −0.650529 | −0.325264 | − | 0.945623i | \(-0.605453\pi\) | ||||
−0.325264 | + | 0.945623i | \(0.605453\pi\) | |||||||
\(998\) | −6.57501e14 | −0.0210222 | ||||||||
\(999\) | 7.29777e15 | 0.232049 |
(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.1.15 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.15 | ✓ | 27 | 1.1 | even | 1 | trivial |