Newspace parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(28.9018654169\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
Defining polynomial: | \(x^{3} - 3876249523 x - 18467420411022\) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4792.65\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 264126. | 0.356226 | 0.178113 | − | 0.984010i | \(-0.443001\pi\) | ||||
0.178113 | + | 0.984010i | \(0.443001\pi\) | |||||||
\(3\) | −1.16226e9 | −0.577350 | ||||||||
\(4\) | −4.79993e11 | −0.873103 | ||||||||
\(5\) | −6.30487e13 | −1.47829 | −0.739147 | − | 0.673544i | \(-0.764771\pi\) | ||||
−0.739147 | + | 0.673544i | \(0.764771\pi\) | |||||||
\(6\) | −3.06983e14 | −0.205667 | ||||||||
\(7\) | −4.59086e16 | −1.52224 | −0.761119 | − | 0.648613i | \(-0.775350\pi\) | ||||
−0.761119 | + | 0.648613i | \(0.775350\pi\) | |||||||
\(8\) | −2.71983e17 | −0.667248 | ||||||||
\(9\) | 1.35085e18 | 0.333333 | ||||||||
\(10\) | −1.66528e19 | −0.526607 | ||||||||
\(11\) | −1.42816e20 | −0.704075 | −0.352037 | − | 0.935986i | \(-0.614511\pi\) | ||||
−0.352037 | + | 0.935986i | \(0.614511\pi\) | |||||||
\(12\) | 5.57878e20 | 0.504086 | ||||||||
\(13\) | 2.23742e20 | 0.0424474 | 0.0212237 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212237 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(14\) | −1.21256e22 | −0.542261 | ||||||||
\(15\) | 7.32790e22 | 0.853493 | ||||||||
\(16\) | 1.92041e23 | 0.635412 | ||||||||
\(17\) | 3.05051e23 | 0.309470 | 0.154735 | − | 0.987956i | \(-0.450548\pi\) | ||||
0.154735 | + | 0.987956i | \(0.450548\pi\) | |||||||
\(18\) | 3.56795e23 | 0.118742 | ||||||||
\(19\) | −1.47192e25 | −1.70683 | −0.853413 | − | 0.521235i | \(-0.825472\pi\) | ||||
−0.853413 | + | 0.521235i | \(0.825472\pi\) | |||||||
\(20\) | 3.02629e25 | 1.29070 | ||||||||
\(21\) | 5.33578e25 | 0.878864 | ||||||||
\(22\) | −3.77213e25 | −0.250810 | ||||||||
\(23\) | −5.75448e26 | −1.60810 | −0.804050 | − | 0.594562i | \(-0.797325\pi\) | ||||
−0.804050 | + | 0.594562i | \(0.797325\pi\) | |||||||
\(24\) | 3.16116e26 | 0.385236 | ||||||||
\(25\) | 2.15614e27 | 1.18535 | ||||||||
\(26\) | 5.90959e25 | 0.0151209 | ||||||||
\(27\) | −1.57004e27 | −0.192450 | ||||||||
\(28\) | 2.20358e28 | 1.32907 | ||||||||
\(29\) | 1.59256e28 | 0.484546 | 0.242273 | − | 0.970208i | \(-0.422107\pi\) | ||||
0.242273 | + | 0.970208i | \(0.422107\pi\) | |||||||
\(30\) | 1.93549e28 | 0.304037 | ||||||||
\(31\) | 2.90720e28 | 0.240947 | 0.120474 | − | 0.992717i | \(-0.461559\pi\) | ||||
0.120474 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(32\) | 2.00247e29 | 0.893598 | ||||||||
\(33\) | 1.65989e29 | 0.406498 | ||||||||
\(34\) | 8.05717e28 | 0.110241 | ||||||||
\(35\) | 2.89448e30 | 2.25031 | ||||||||
\(36\) | −6.48400e29 | −0.291034 | ||||||||
\(37\) | 4.49195e30 | 1.18168 | 0.590842 | − | 0.806787i | \(-0.298796\pi\) | ||||
0.590842 | + | 0.806787i | \(0.298796\pi\) | |||||||
\(38\) | −3.88772e30 | −0.608016 | ||||||||
\(39\) | −2.60046e29 | −0.0245070 | ||||||||
\(40\) | 1.71482e31 | 0.986389 | ||||||||
\(41\) | −3.98145e31 | −1.41500 | −0.707499 | − | 0.706715i | \(-0.750176\pi\) | ||||
−0.707499 | + | 0.706715i | \(0.750176\pi\) | |||||||
\(42\) | 1.40932e31 | 0.313074 | ||||||||
\(43\) | −1.13795e32 | −1.59768 | −0.798840 | − | 0.601544i | \(-0.794552\pi\) | ||||
−0.798840 | + | 0.601544i | \(0.794552\pi\) | |||||||
\(44\) | 6.85506e31 | 0.614730 | ||||||||
\(45\) | −8.51694e31 | −0.492765 | ||||||||
\(46\) | −1.51990e32 | −0.572847 | ||||||||
\(47\) | −4.87913e32 | −1.20902 | −0.604511 | − | 0.796597i | \(-0.706631\pi\) | ||||
−0.604511 | + | 0.796597i | \(0.706631\pi\) | |||||||
\(48\) | −2.23202e32 | −0.366855 | ||||||||
\(49\) | 1.19806e33 | 1.31721 | ||||||||
\(50\) | 5.69493e32 | 0.422253 | ||||||||
\(51\) | −3.54549e32 | −0.178672 | ||||||||
\(52\) | −1.07395e32 | −0.0370610 | ||||||||
\(53\) | −5.94518e32 | −0.141509 | −0.0707547 | − | 0.997494i | \(-0.522541\pi\) | ||||
−0.0707547 | + | 0.997494i | \(0.522541\pi\) | |||||||
\(54\) | −4.14689e32 | −0.0685557 | ||||||||
\(55\) | 9.00434e33 | 1.04083 | ||||||||
\(56\) | 1.24864e34 | 1.01571 | ||||||||
\(57\) | 1.71076e34 | 0.985437 | ||||||||
\(58\) | 4.20636e33 | 0.172608 | ||||||||
\(59\) | −2.61158e34 | −0.767872 | −0.383936 | − | 0.923360i | \(-0.625432\pi\) | ||||
−0.383936 | + | 0.923360i | \(0.625432\pi\) | |||||||
\(60\) | −3.51734e34 | −0.745188 | ||||||||
\(61\) | −4.20907e34 | −0.646032 | −0.323016 | − | 0.946393i | \(-0.604697\pi\) | ||||
−0.323016 | + | 0.946393i | \(0.604697\pi\) | |||||||
\(62\) | 7.67866e33 | 0.0858317 | ||||||||
\(63\) | −6.20157e34 | −0.507413 | ||||||||
\(64\) | −5.26854e34 | −0.317089 | ||||||||
\(65\) | −1.41066e34 | −0.0627498 | ||||||||
\(66\) | 4.38420e34 | 0.144805 | ||||||||
\(67\) | −4.97358e35 | −1.22521 | −0.612605 | − | 0.790389i | \(-0.709878\pi\) | ||||
−0.612605 | + | 0.790389i | \(0.709878\pi\) | |||||||
\(68\) | −1.46422e35 | −0.270199 | ||||||||
\(69\) | 6.68820e35 | 0.928437 | ||||||||
\(70\) | 7.64506e35 | 0.801621 | ||||||||
\(71\) | 8.30261e35 | 0.660202 | 0.330101 | − | 0.943946i | \(-0.392917\pi\) | ||||
0.330101 | + | 0.943946i | \(0.392917\pi\) | |||||||
\(72\) | −3.67409e35 | −0.222416 | ||||||||
\(73\) | −5.71462e35 | −0.264358 | −0.132179 | − | 0.991226i | \(-0.542197\pi\) | ||||
−0.132179 | + | 0.991226i | \(0.542197\pi\) | |||||||
\(74\) | 1.18644e36 | 0.420947 | ||||||||
\(75\) | −2.50600e36 | −0.684364 | ||||||||
\(76\) | 7.06513e36 | 1.49024 | ||||||||
\(77\) | 6.55647e36 | 1.07177 | ||||||||
\(78\) | −6.86849e34 | −0.00873005 | ||||||||
\(79\) | −1.34537e37 | −1.33387 | −0.666935 | − | 0.745116i | \(-0.732394\pi\) | ||||
−0.666935 | + | 0.745116i | \(0.732394\pi\) | |||||||
\(80\) | −1.21080e37 | −0.939325 | ||||||||
\(81\) | 1.82480e36 | 0.111111 | ||||||||
\(82\) | −1.05160e37 | −0.504059 | ||||||||
\(83\) | 2.31025e37 | 0.874252 | 0.437126 | − | 0.899400i | \(-0.355996\pi\) | ||||
0.437126 | + | 0.899400i | \(0.355996\pi\) | |||||||
\(84\) | −2.56114e37 | −0.767339 | ||||||||
\(85\) | −1.92330e37 | −0.457487 | ||||||||
\(86\) | −3.00563e37 | −0.569135 | ||||||||
\(87\) | −1.85097e37 | −0.279753 | ||||||||
\(88\) | 3.88435e37 | 0.469793 | ||||||||
\(89\) | 5.53932e37 | 0.537466 | 0.268733 | − | 0.963215i | \(-0.413395\pi\) | ||||
0.268733 | + | 0.963215i | \(0.413395\pi\) | |||||||
\(90\) | −2.24954e37 | −0.175536 | ||||||||
\(91\) | −1.02717e37 | −0.0646151 | ||||||||
\(92\) | 2.76211e38 | 1.40404 | ||||||||
\(93\) | −3.37893e37 | −0.139111 | ||||||||
\(94\) | −1.28870e38 | −0.430685 | ||||||||
\(95\) | 9.28027e38 | 2.52319 | ||||||||
\(96\) | −2.32740e38 | −0.515919 | ||||||||
\(97\) | −5.58017e38 | −1.01065 | −0.505323 | − | 0.862930i | \(-0.668627\pi\) | ||||
−0.505323 | + | 0.862930i | \(0.668627\pi\) | |||||||
\(98\) | 3.16438e38 | 0.469224 | ||||||||
\(99\) | −1.92923e38 | −0.234692 | ||||||||
\(100\) | −1.03493e39 | −1.03493 | ||||||||
\(101\) | −8.58640e38 | −0.707203 | −0.353602 | − | 0.935396i | \(-0.615043\pi\) | ||||
−0.353602 | + | 0.935396i | \(0.615043\pi\) | |||||||
\(102\) | −9.36454e37 | −0.0636478 | ||||||||
\(103\) | 7.23179e38 | 0.406368 | 0.203184 | − | 0.979141i | \(-0.434871\pi\) | ||||
0.203184 | + | 0.979141i | \(0.434871\pi\) | |||||||
\(104\) | −6.08540e37 | −0.0283230 | ||||||||
\(105\) | −3.36414e39 | −1.29922 | ||||||||
\(106\) | −1.57027e38 | −0.0504094 | ||||||||
\(107\) | 6.55460e39 | 1.75211 | 0.876057 | − | 0.482208i | \(-0.160165\pi\) | ||||
0.876057 | + | 0.482208i | \(0.160165\pi\) | |||||||
\(108\) | 7.53610e38 | 0.168029 | ||||||||
\(109\) | −5.87754e39 | −1.09491 | −0.547456 | − | 0.836835i | \(-0.684403\pi\) | ||||
−0.547456 | + | 0.836835i | \(0.684403\pi\) | |||||||
\(110\) | 2.37828e39 | 0.370771 | ||||||||
\(111\) | −5.22082e39 | −0.682246 | ||||||||
\(112\) | −8.81636e39 | −0.967248 | ||||||||
\(113\) | 1.66536e40 | 1.53631 | 0.768154 | − | 0.640265i | \(-0.221175\pi\) | ||||
0.768154 | + | 0.640265i | \(0.221175\pi\) | |||||||
\(114\) | 4.51855e39 | 0.351038 | ||||||||
\(115\) | 3.62812e40 | 2.37724 | ||||||||
\(116\) | −7.64418e39 | −0.423058 | ||||||||
\(117\) | 3.02242e38 | 0.0141491 | ||||||||
\(118\) | −6.89785e39 | −0.273536 | ||||||||
\(119\) | −1.40045e40 | −0.471086 | ||||||||
\(120\) | −1.99307e40 | −0.569492 | ||||||||
\(121\) | −2.07484e40 | −0.504279 | ||||||||
\(122\) | −1.11172e40 | −0.230133 | ||||||||
\(123\) | 4.62748e40 | 0.816949 | ||||||||
\(124\) | −1.39544e40 | −0.210372 | ||||||||
\(125\) | −2.12571e40 | −0.274005 | ||||||||
\(126\) | −1.63799e40 | −0.180754 | ||||||||
\(127\) | −1.17179e41 | −1.10835 | −0.554177 | − | 0.832399i | \(-0.686967\pi\) | ||||
−0.554177 | + | 0.832399i | \(0.686967\pi\) | |||||||
\(128\) | −1.24003e41 | −1.00655 | ||||||||
\(129\) | 1.32260e41 | 0.922420 | ||||||||
\(130\) | −3.72592e39 | −0.0223531 | ||||||||
\(131\) | −2.69471e40 | −0.139227 | −0.0696133 | − | 0.997574i | \(-0.522177\pi\) | ||||
−0.0696133 | + | 0.997574i | \(0.522177\pi\) | |||||||
\(132\) | −7.96737e40 | −0.354914 | ||||||||
\(133\) | 6.75739e41 | 2.59820 | ||||||||
\(134\) | −1.31365e41 | −0.436452 | ||||||||
\(135\) | 9.89891e40 | 0.284498 | ||||||||
\(136\) | −8.29687e40 | −0.206493 | ||||||||
\(137\) | 1.62934e41 | 0.351528 | 0.175764 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175764 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(138\) | 1.76653e41 | 0.330733 | ||||||||
\(139\) | 5.71049e41 | 0.928720 | 0.464360 | − | 0.885647i | \(-0.346284\pi\) | ||||
0.464360 | + | 0.885647i | \(0.346284\pi\) | |||||||
\(140\) | −1.38933e42 | −1.96476 | ||||||||
\(141\) | 5.67083e41 | 0.698029 | ||||||||
\(142\) | 2.19293e41 | 0.235181 | ||||||||
\(143\) | −3.19538e40 | −0.0298862 | ||||||||
\(144\) | 2.59419e41 | 0.211804 | ||||||||
\(145\) | −1.00409e42 | −0.716301 | ||||||||
\(146\) | −1.50938e41 | −0.0941711 | ||||||||
\(147\) | −1.39246e42 | −0.760490 | ||||||||
\(148\) | −2.15611e42 | −1.03173 | ||||||||
\(149\) | −4.00637e41 | −0.168120 | −0.0840598 | − | 0.996461i | \(-0.526789\pi\) | ||||
−0.0840598 | + | 0.996461i | \(0.526789\pi\) | |||||||
\(150\) | −6.61900e41 | −0.243788 | ||||||||
\(151\) | 8.19755e41 | 0.265237 | 0.132618 | − | 0.991167i | \(-0.457662\pi\) | ||||
0.132618 | + | 0.991167i | \(0.457662\pi\) | |||||||
\(152\) | 4.00338e42 | 1.13888 | ||||||||
\(153\) | 4.12078e41 | 0.103157 | ||||||||
\(154\) | 1.73173e42 | 0.381792 | ||||||||
\(155\) | −1.83295e42 | −0.356191 | ||||||||
\(156\) | 1.24820e41 | 0.0213972 | ||||||||
\(157\) | 2.75060e42 | 0.416279 | 0.208139 | − | 0.978099i | \(-0.433259\pi\) | ||||
0.208139 | + | 0.978099i | \(0.433259\pi\) | |||||||
\(158\) | −3.55347e42 | −0.475159 | ||||||||
\(159\) | 6.90985e41 | 0.0817005 | ||||||||
\(160\) | −1.26253e43 | −1.32100 | ||||||||
\(161\) | 2.64180e43 | 2.44791 | ||||||||
\(162\) | 4.81977e41 | 0.0395807 | ||||||||
\(163\) | −3.05226e41 | −0.0222313 | −0.0111156 | − | 0.999938i | \(-0.503538\pi\) | ||||
−0.0111156 | + | 0.999938i | \(0.503538\pi\) | |||||||
\(164\) | 1.91107e43 | 1.23544 | ||||||||
\(165\) | −1.04654e43 | −0.600923 | ||||||||
\(166\) | 6.10197e42 | 0.311431 | ||||||||
\(167\) | −8.60063e42 | −0.390444 | −0.195222 | − | 0.980759i | \(-0.562543\pi\) | ||||
−0.195222 | + | 0.980759i | \(0.562543\pi\) | |||||||
\(168\) | −1.45124e43 | −0.586421 | ||||||||
\(169\) | −2.77337e43 | −0.998198 | ||||||||
\(170\) | −5.07994e42 | −0.162969 | ||||||||
\(171\) | −1.98835e43 | −0.568942 | ||||||||
\(172\) | 5.46210e43 | 1.39494 | ||||||||
\(173\) | −3.58571e43 | −0.817856 | −0.408928 | − | 0.912567i | \(-0.634097\pi\) | ||||
−0.408928 | + | 0.912567i | \(0.634097\pi\) | |||||||
\(174\) | −4.88889e42 | −0.0996551 | ||||||||
\(175\) | −9.89856e43 | −1.80439 | ||||||||
\(176\) | −2.74265e43 | −0.447377 | ||||||||
\(177\) | 3.03534e43 | 0.443331 | ||||||||
\(178\) | 1.46308e43 | 0.191459 | ||||||||
\(179\) | 1.32734e44 | 1.55721 | 0.778606 | − | 0.627514i | \(-0.215927\pi\) | ||||
0.778606 | + | 0.627514i | \(0.215927\pi\) | |||||||
\(180\) | 4.08807e43 | 0.430234 | ||||||||
\(181\) | 4.48145e43 | 0.423337 | 0.211668 | − | 0.977342i | \(-0.432110\pi\) | ||||
0.211668 | + | 0.977342i | \(0.432110\pi\) | |||||||
\(182\) | −2.71301e42 | −0.0230176 | ||||||||
\(183\) | 4.89204e43 | 0.372987 | ||||||||
\(184\) | 1.56512e44 | 1.07300 | ||||||||
\(185\) | −2.83211e44 | −1.74688 | ||||||||
\(186\) | −8.92462e42 | −0.0495550 | ||||||||
\(187\) | −4.35661e43 | −0.217890 | ||||||||
\(188\) | 2.34195e44 | 1.05560 | ||||||||
\(189\) | 7.20785e43 | 0.292955 | ||||||||
\(190\) | 2.45116e44 | 0.898826 | ||||||||
\(191\) | −3.37653e44 | −1.11769 | −0.558843 | − | 0.829274i | \(-0.688755\pi\) | ||||
−0.558843 | + | 0.829274i | \(0.688755\pi\) | |||||||
\(192\) | 6.12342e43 | 0.183071 | ||||||||
\(193\) | −3.65762e43 | −0.0988168 | −0.0494084 | − | 0.998779i | \(-0.515734\pi\) | ||||
−0.0494084 | + | 0.998779i | \(0.515734\pi\) | |||||||
\(194\) | −1.47387e44 | −0.360018 | ||||||||
\(195\) | 1.63956e43 | 0.0362286 | ||||||||
\(196\) | −5.75060e44 | −1.15006 | ||||||||
\(197\) | −2.25016e44 | −0.407494 | −0.203747 | − | 0.979024i | \(-0.565312\pi\) | ||||
−0.203747 | + | 0.979024i | \(0.565312\pi\) | |||||||
\(198\) | −5.09559e43 | −0.0836033 | ||||||||
\(199\) | 4.01172e43 | 0.0596617 | 0.0298308 | − | 0.999555i | \(-0.490503\pi\) | ||||
0.0298308 | + | 0.999555i | \(0.490503\pi\) | |||||||
\(200\) | −5.86435e44 | −0.790924 | ||||||||
\(201\) | 5.78060e44 | 0.707375 | ||||||||
\(202\) | −2.26789e44 | −0.251924 | ||||||||
\(203\) | −7.31122e44 | −0.737593 | ||||||||
\(204\) | 1.70181e44 | 0.155999 | ||||||||
\(205\) | 2.51025e45 | 2.09178 | ||||||||
\(206\) | 1.91010e44 | 0.144759 | ||||||||
\(207\) | −7.77344e44 | −0.536033 | ||||||||
\(208\) | 4.29677e43 | 0.0269716 | ||||||||
\(209\) | 2.10214e45 | 1.20173 | ||||||||
\(210\) | −8.88555e44 | −0.462816 | ||||||||
\(211\) | −2.64355e45 | −1.25510 | −0.627552 | − | 0.778575i | \(-0.715943\pi\) | ||||
−0.627552 | + | 0.778575i | \(0.715943\pi\) | |||||||
\(212\) | 2.85365e44 | 0.123552 | ||||||||
\(213\) | −9.64981e44 | −0.381168 | ||||||||
\(214\) | 1.73124e45 | 0.624149 | ||||||||
\(215\) | 7.17464e45 | 2.36184 | ||||||||
\(216\) | 4.27025e44 | 0.128412 | ||||||||
\(217\) | −1.33466e45 | −0.366779 | ||||||||
\(218\) | −1.55241e45 | −0.390036 | ||||||||
\(219\) | 6.64189e44 | 0.152627 | ||||||||
\(220\) | −4.32202e45 | −0.908751 | ||||||||
\(221\) | 6.82526e43 | 0.0131362 | ||||||||
\(222\) | −1.37895e45 | −0.243034 | ||||||||
\(223\) | −6.61885e45 | −1.06866 | −0.534328 | − | 0.845277i | \(-0.679435\pi\) | ||||
−0.534328 | + | 0.845277i | \(0.679435\pi\) | |||||||
\(224\) | −9.19308e45 | −1.36027 | ||||||||
\(225\) | 2.91263e45 | 0.395117 | ||||||||
\(226\) | 4.39864e45 | 0.547273 | ||||||||
\(227\) | 1.14636e46 | 1.30863 | 0.654317 | − | 0.756220i | \(-0.272956\pi\) | ||||
0.654317 | + | 0.756220i | \(0.272956\pi\) | |||||||
\(228\) | −8.21152e45 | −0.860388 | ||||||||
\(229\) | −5.43505e45 | −0.522892 | −0.261446 | − | 0.965218i | \(-0.584199\pi\) | ||||
−0.261446 | + | 0.965218i | \(0.584199\pi\) | |||||||
\(230\) | 9.58279e45 | 0.846836 | ||||||||
\(231\) | −7.62034e45 | −0.618786 | ||||||||
\(232\) | −4.33149e45 | −0.323312 | ||||||||
\(233\) | −2.44861e46 | −1.68066 | −0.840328 | − | 0.542079i | \(-0.817638\pi\) | ||||
−0.840328 | + | 0.542079i | \(0.817638\pi\) | |||||||
\(234\) | 7.98298e43 | 0.00504029 | ||||||||
\(235\) | 3.07623e46 | 1.78729 | ||||||||
\(236\) | 1.25354e46 | 0.670432 | ||||||||
\(237\) | 1.56367e46 | 0.770110 | ||||||||
\(238\) | −3.69894e45 | −0.167813 | ||||||||
\(239\) | 3.20935e46 | 1.34171 | 0.670855 | − | 0.741589i | \(-0.265927\pi\) | ||||
0.670855 | + | 0.741589i | \(0.265927\pi\) | |||||||
\(240\) | 1.40726e46 | 0.542320 | ||||||||
\(241\) | −4.03396e45 | −0.143351 | −0.0716753 | − | 0.997428i | \(-0.522835\pi\) | ||||
−0.0716753 | + | 0.997428i | \(0.522835\pi\) | |||||||
\(242\) | −5.48020e45 | −0.179637 | ||||||||
\(243\) | −2.12090e45 | −0.0641500 | ||||||||
\(244\) | 2.02032e46 | 0.564053 | ||||||||
\(245\) | −7.55359e46 | −1.94722 | ||||||||
\(246\) | 1.22224e46 | 0.291019 | ||||||||
\(247\) | −3.29330e45 | −0.0724504 | ||||||||
\(248\) | −7.90710e45 | −0.160772 | ||||||||
\(249\) | −2.68512e46 | −0.504750 | ||||||||
\(250\) | −5.61455e45 | −0.0976079 | ||||||||
\(251\) | −9.02920e46 | −1.45215 | −0.726076 | − | 0.687615i | \(-0.758658\pi\) | ||||
−0.726076 | + | 0.687615i | \(0.758658\pi\) | |||||||
\(252\) | 2.97671e46 | 0.443023 | ||||||||
\(253\) | 8.21830e46 | 1.13222 | ||||||||
\(254\) | −3.09501e46 | −0.394824 | ||||||||
\(255\) | 2.23538e46 | 0.264130 | ||||||||
\(256\) | −3.78821e45 | −0.0414720 | ||||||||
\(257\) | 4.29725e45 | 0.0436008 | 0.0218004 | − | 0.999762i | \(-0.493060\pi\) | ||||
0.0218004 | + | 0.999762i | \(0.493060\pi\) | |||||||
\(258\) | 3.49332e46 | 0.328590 | ||||||||
\(259\) | −2.06219e47 | −1.79880 | ||||||||
\(260\) | 6.77108e45 | 0.0547870 | ||||||||
\(261\) | 2.15131e46 | 0.161515 | ||||||||
\(262\) | −7.11742e45 | −0.0495961 | ||||||||
\(263\) | 1.26887e47 | 0.820879 | 0.410439 | − | 0.911888i | \(-0.365375\pi\) | ||||
0.410439 | + | 0.911888i | \(0.365375\pi\) | |||||||
\(264\) | −4.51463e46 | −0.271235 | ||||||||
\(265\) | 3.74835e46 | 0.209193 | ||||||||
\(266\) | 1.78480e47 | 0.925545 | ||||||||
\(267\) | −6.43813e46 | −0.310306 | ||||||||
\(268\) | 2.38729e47 | 1.06973 | ||||||||
\(269\) | 5.74667e46 | 0.239468 | 0.119734 | − | 0.992806i | \(-0.461796\pi\) | ||||
0.119734 | + | 0.992806i | \(0.461796\pi\) | |||||||
\(270\) | 2.61456e46 | 0.101346 | ||||||||
\(271\) | −3.95688e46 | −0.142709 | −0.0713546 | − | 0.997451i | \(-0.522732\pi\) | ||||
−0.0713546 | + | 0.997451i | \(0.522732\pi\) | |||||||
\(272\) | 5.85824e46 | 0.196641 | ||||||||
\(273\) | 1.19384e46 | 0.0373055 | ||||||||
\(274\) | 4.30349e46 | 0.125223 | ||||||||
\(275\) | −3.07931e47 | −0.834577 | ||||||||
\(276\) | −3.21029e47 | −0.810621 | ||||||||
\(277\) | 4.47297e47 | 1.05254 | 0.526272 | − | 0.850316i | \(-0.323589\pi\) | ||||
0.526272 | + | 0.850316i | \(0.323589\pi\) | |||||||
\(278\) | 1.50829e47 | 0.330834 | ||||||||
\(279\) | 3.92720e46 | 0.0803158 | ||||||||
\(280\) | −7.87249e47 | −1.50152 | ||||||||
\(281\) | 3.99175e47 | 0.710215 | 0.355108 | − | 0.934825i | \(-0.384444\pi\) | ||||
0.355108 | + | 0.934825i | \(0.384444\pi\) | |||||||
\(282\) | 1.49781e47 | 0.248656 | ||||||||
\(283\) | −8.24030e47 | −1.27675 | −0.638377 | − | 0.769724i | \(-0.720394\pi\) | ||||
−0.638377 | + | 0.769724i | \(0.720394\pi\) | |||||||
\(284\) | −3.98520e47 | −0.576424 | ||||||||
\(285\) | −1.07861e48 | −1.45676 | ||||||||
\(286\) | −8.43983e45 | −0.0106462 | ||||||||
\(287\) | 1.82783e48 | 2.15396 | ||||||||
\(288\) | 2.70505e47 | 0.297866 | ||||||||
\(289\) | −8.78590e47 | −0.904228 | ||||||||
\(290\) | −2.65205e47 | −0.255165 | ||||||||
\(291\) | 6.48562e47 | 0.583497 | ||||||||
\(292\) | 2.74298e47 | 0.230811 | ||||||||
\(293\) | −6.28416e47 | −0.494685 | −0.247343 | − | 0.968928i | \(-0.579557\pi\) | ||||
−0.247343 | + | 0.968928i | \(0.579557\pi\) | |||||||
\(294\) | −3.67783e47 | −0.270906 | ||||||||
\(295\) | 1.64657e48 | 1.13514 | ||||||||
\(296\) | −1.22174e48 | −0.788476 | ||||||||
\(297\) | 2.24227e47 | 0.135499 | ||||||||
\(298\) | −1.05818e47 | −0.0598886 | ||||||||
\(299\) | −1.28752e47 | −0.0682597 | ||||||||
\(300\) | 1.20286e48 | 0.597520 | ||||||||
\(301\) | 5.22419e48 | 2.43205 | ||||||||
\(302\) | 2.16518e47 | 0.0944842 | ||||||||
\(303\) | 9.97964e47 | 0.408304 | ||||||||
\(304\) | −2.82670e48 | −1.08454 | ||||||||
\(305\) | 2.65376e48 | 0.955025 | ||||||||
\(306\) | 1.08840e47 | 0.0367471 | ||||||||
\(307\) | −2.43683e48 | −0.772018 | −0.386009 | − | 0.922495i | \(-0.626147\pi\) | ||||
−0.386009 | + | 0.922495i | \(0.626147\pi\) | |||||||
\(308\) | −3.14706e48 | −0.935765 | ||||||||
\(309\) | −8.40523e47 | −0.234617 | ||||||||
\(310\) | −4.84129e47 | −0.126884 | ||||||||
\(311\) | −6.81462e48 | −1.67731 | −0.838657 | − | 0.544660i | \(-0.816659\pi\) | ||||
−0.838657 | + | 0.544660i | \(0.816659\pi\) | |||||||
\(312\) | 7.07282e46 | 0.0163523 | ||||||||
\(313\) | −2.62388e48 | −0.569941 | −0.284970 | − | 0.958536i | \(-0.591984\pi\) | ||||
−0.284970 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(314\) | 7.26504e47 | 0.148289 | ||||||||
\(315\) | 3.91001e48 | 0.750105 | ||||||||
\(316\) | 6.45769e48 | 1.16461 | ||||||||
\(317\) | −6.51955e48 | −1.10551 | −0.552754 | − | 0.833344i | \(-0.686423\pi\) | ||||
−0.552754 | + | 0.833344i | \(0.686423\pi\) | |||||||
\(318\) | 1.82507e47 | 0.0291039 | ||||||||
\(319\) | −2.27443e48 | −0.341156 | ||||||||
\(320\) | 3.32174e48 | 0.468750 | ||||||||
\(321\) | −7.61816e48 | −1.01158 | ||||||||
\(322\) | 6.97767e48 | 0.872009 | ||||||||
\(323\) | −4.49011e48 | −0.528211 | ||||||||
\(324\) | −8.75892e47 | −0.0970114 | ||||||||
\(325\) | 4.82419e47 | 0.0503152 | ||||||||
\(326\) | −8.06181e46 | −0.00791935 | ||||||||
\(327\) | 6.83124e48 | 0.632147 | ||||||||
\(328\) | 1.08289e49 | 0.944154 | ||||||||
\(329\) | 2.23994e49 | 1.84042 | ||||||||
\(330\) | −2.76418e48 | −0.214064 | ||||||||
\(331\) | −2.04347e49 | −1.49184 | −0.745919 | − | 0.666036i | \(-0.767990\pi\) | ||||
−0.745919 | + | 0.666036i | \(0.767990\pi\) | |||||||
\(332\) | −1.10891e49 | −0.763312 | ||||||||
\(333\) | 6.06796e48 | 0.393895 | ||||||||
\(334\) | −2.27165e48 | −0.139087 | ||||||||
\(335\) | 3.13577e49 | 1.81122 | ||||||||
\(336\) | 1.02469e49 | 0.558441 | ||||||||
\(337\) | −1.34582e49 | −0.692154 | −0.346077 | − | 0.938206i | \(-0.612486\pi\) | ||||
−0.346077 | + | 0.938206i | \(0.612486\pi\) | |||||||
\(338\) | −7.32518e48 | −0.355584 | ||||||||
\(339\) | −1.93558e49 | −0.886988 | ||||||||
\(340\) | 9.23173e48 | 0.399433 | ||||||||
\(341\) | −4.15194e48 | −0.169645 | ||||||||
\(342\) | −5.25174e48 | −0.202672 | ||||||||
\(343\) | −1.32453e49 | −0.482865 | ||||||||
\(344\) | 3.09504e49 | 1.06605 | ||||||||
\(345\) | −4.21682e49 | −1.37250 | ||||||||
\(346\) | −9.47079e48 | −0.291342 | ||||||||
\(347\) | 3.60982e49 | 1.04969 | 0.524844 | − | 0.851198i | \(-0.324124\pi\) | ||||
0.524844 | + | 0.851198i | \(0.324124\pi\) | |||||||
\(348\) | 8.88454e48 | 0.244253 | ||||||||
\(349\) | 1.29981e49 | 0.337896 | 0.168948 | − | 0.985625i | \(-0.445963\pi\) | ||||
0.168948 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(350\) | −2.61446e49 | −0.642770 | ||||||||
\(351\) | −3.51284e47 | −0.00816901 | ||||||||
\(352\) | −2.85985e49 | −0.629160 | ||||||||
\(353\) | −7.99353e49 | −1.66392 | −0.831959 | − | 0.554837i | \(-0.812781\pi\) | ||||
−0.831959 | + | 0.554837i | \(0.812781\pi\) | |||||||
\(354\) | 8.01711e48 | 0.157926 | ||||||||
\(355\) | −5.23469e49 | −0.975973 | ||||||||
\(356\) | −2.65884e49 | −0.469263 | ||||||||
\(357\) | 1.62768e49 | 0.271982 | ||||||||
\(358\) | 3.50584e49 | 0.554719 | ||||||||
\(359\) | 7.75277e49 | 1.16176 | 0.580878 | − | 0.813990i | \(-0.302709\pi\) | ||||
0.580878 | + | 0.813990i | \(0.302709\pi\) | |||||||
\(360\) | 2.31646e49 | 0.328796 | ||||||||
\(361\) | 1.42286e50 | 1.91326 | ||||||||
\(362\) | 1.18367e49 | 0.150804 | ||||||||
\(363\) | 2.41151e49 | 0.291146 | ||||||||
\(364\) | 4.93033e48 | 0.0564156 | ||||||||
\(365\) | 3.60299e49 | 0.390798 | ||||||||
\(366\) | 1.29211e49 | 0.132868 | ||||||||
\(367\) | 1.56697e49 | 0.152782 | 0.0763909 | − | 0.997078i | \(-0.475660\pi\) | ||||
0.0763909 | + | 0.997078i | \(0.475660\pi\) | |||||||
\(368\) | −1.10510e50 | −1.02181 | ||||||||
\(369\) | −5.37834e49 | −0.471666 | ||||||||
\(370\) | −7.48034e49 | −0.622283 | ||||||||
\(371\) | 2.72935e49 | 0.215411 | ||||||||
\(372\) | 1.62186e49 | 0.121458 | ||||||||
\(373\) | 5.67952e49 | 0.403636 | 0.201818 | − | 0.979423i | \(-0.435315\pi\) | ||||
0.201818 | + | 0.979423i | \(0.435315\pi\) | |||||||
\(374\) | −1.15069e49 | −0.0776180 | ||||||||
\(375\) | 2.47063e49 | 0.158197 | ||||||||
\(376\) | 1.32704e50 | 0.806718 | ||||||||
\(377\) | 3.56322e48 | 0.0205677 | ||||||||
\(378\) | 1.90378e49 | 0.104358 | ||||||||
\(379\) | −3.40282e49 | −0.177163 | −0.0885817 | − | 0.996069i | \(-0.528233\pi\) | ||||
−0.0885817 | + | 0.996069i | \(0.528233\pi\) | |||||||
\(380\) | −4.45447e50 | −2.20301 | ||||||||
\(381\) | 1.36193e50 | 0.639908 | ||||||||
\(382\) | −8.91828e49 | −0.398149 | ||||||||
\(383\) | −1.51395e50 | −0.642295 | −0.321147 | − | 0.947029i | \(-0.604068\pi\) | ||||
−0.321147 | + | 0.947029i | \(0.604068\pi\) | |||||||
\(384\) | 1.44124e50 | 0.581134 | ||||||||
\(385\) | −4.13377e50 | −1.58439 | ||||||||
\(386\) | −9.66071e48 | −0.0352011 | ||||||||
\(387\) | −1.53721e50 | −0.532560 | ||||||||
\(388\) | 2.67845e50 | 0.882398 | ||||||||
\(389\) | 3.64065e50 | 1.14068 | 0.570338 | − | 0.821410i | \(-0.306812\pi\) | ||||
0.570338 | + | 0.821410i | \(0.306812\pi\) | |||||||
\(390\) | 4.33049e48 | 0.0129056 | ||||||||
\(391\) | −1.75541e50 | −0.497658 | ||||||||
\(392\) | −3.25852e50 | −0.878904 | ||||||||
\(393\) | 3.13196e49 | 0.0803825 | ||||||||
\(394\) | −5.94324e49 | −0.145160 | ||||||||
\(395\) | 8.48238e50 | 1.97185 | ||||||||
\(396\) | 9.26017e49 | 0.204910 | ||||||||
\(397\) | 6.19440e50 | 1.30492 | 0.652461 | − | 0.757823i | \(-0.273737\pi\) | ||||
0.652461 | + | 0.757823i | \(0.273737\pi\) | |||||||
\(398\) | 1.05960e49 | 0.0212530 | ||||||||
\(399\) | −7.85385e50 | −1.50007 | ||||||||
\(400\) | 4.14069e50 | 0.753187 | ||||||||
\(401\) | 1.98149e50 | 0.343302 | 0.171651 | − | 0.985158i | \(-0.445090\pi\) | ||||
0.171651 | + | 0.985158i | \(0.445090\pi\) | |||||||
\(402\) | 1.52680e50 | 0.251985 | ||||||||
\(403\) | 6.50462e48 | 0.0102276 | ||||||||
\(404\) | 4.12141e50 | 0.617461 | ||||||||
\(405\) | −1.15051e50 | −0.164255 | ||||||||
\(406\) | −1.93108e50 | −0.262750 | ||||||||
\(407\) | −6.41521e50 | −0.831994 | ||||||||
\(408\) | 9.64313e49 | 0.119219 | ||||||||
\(409\) | −8.18635e50 | −0.964908 | −0.482454 | − | 0.875921i | \(-0.660254\pi\) | ||||
−0.482454 | + | 0.875921i | \(0.660254\pi\) | |||||||
\(410\) | 6.63021e50 | 0.745147 | ||||||||
\(411\) | −1.89371e50 | −0.202955 | ||||||||
\(412\) | −3.47121e50 | −0.354802 | ||||||||
\(413\) | 1.19894e51 | 1.16888 | ||||||||
\(414\) | −2.05317e50 | −0.190949 | ||||||||
\(415\) | −1.45658e51 | −1.29240 | ||||||||
\(416\) | 4.48037e49 | 0.0379310 | ||||||||
\(417\) | −6.63708e50 | −0.536197 | ||||||||
\(418\) | 5.55228e50 | 0.428089 | ||||||||
\(419\) | −9.92910e50 | −0.730696 | −0.365348 | − | 0.930871i | \(-0.619050\pi\) | ||||
−0.365348 | + | 0.930871i | \(0.619050\pi\) | |||||||
\(420\) | 1.61476e51 | 1.13435 | ||||||||
\(421\) | −6.39132e50 | −0.428637 | −0.214319 | − | 0.976764i | \(-0.568753\pi\) | ||||
−0.214319 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(422\) | −6.98230e50 | −0.447101 | ||||||||
\(423\) | −6.59098e50 | −0.403007 | ||||||||
\(424\) | 1.61699e50 | 0.0944219 | ||||||||
\(425\) | 6.57733e50 | 0.366831 | ||||||||
\(426\) | −2.54876e50 | −0.135782 | ||||||||
\(427\) | 1.93232e51 | 0.983414 | ||||||||
\(428\) | −3.14616e51 | −1.52978 | ||||||||
\(429\) | 3.71387e49 | 0.0172548 | ||||||||
\(430\) | 1.89501e51 | 0.841349 | ||||||||
\(431\) | 3.21896e50 | 0.136587 | 0.0682935 | − | 0.997665i | \(-0.478245\pi\) | ||||
0.0682935 | + | 0.997665i | \(0.478245\pi\) | |||||||
\(432\) | −3.01513e50 | −0.122285 | ||||||||
\(433\) | −4.43633e51 | −1.71993 | −0.859963 | − | 0.510356i | \(-0.829514\pi\) | ||||
−0.859963 | + | 0.510356i | \(0.829514\pi\) | |||||||
\(434\) | −3.52517e50 | −0.130656 | ||||||||
\(435\) | 1.16701e51 | 0.413556 | ||||||||
\(436\) | 2.82118e51 | 0.955970 | ||||||||
\(437\) | 8.47013e51 | 2.74475 | ||||||||
\(438\) | 1.75429e50 | 0.0543697 | ||||||||
\(439\) | 3.25569e51 | 0.965128 | 0.482564 | − | 0.875861i | \(-0.339706\pi\) | ||||
0.482564 | + | 0.875861i | \(0.339706\pi\) | |||||||
\(440\) | −2.44903e51 | −0.694491 | ||||||||
\(441\) | 1.61840e51 | 0.439069 | ||||||||
\(442\) | 1.80273e49 | 0.00467946 | ||||||||
\(443\) | −4.09722e51 | −1.01769 | −0.508846 | − | 0.860858i | \(-0.669928\pi\) | ||||
−0.508846 | + | 0.860858i | \(0.669928\pi\) | |||||||
\(444\) | 2.50596e51 | 0.595671 | ||||||||
\(445\) | −3.49246e51 | −0.794533 | ||||||||
\(446\) | −1.74821e51 | −0.380683 | ||||||||
\(447\) | 4.65644e50 | 0.0970639 | ||||||||
\(448\) | 2.41871e51 | 0.482684 | ||||||||
\(449\) | −8.07315e51 | −1.54255 | −0.771275 | − | 0.636502i | \(-0.780381\pi\) | ||||
−0.771275 | + | 0.636502i | \(0.780381\pi\) | |||||||
\(450\) | 7.69300e50 | 0.140751 | ||||||||
\(451\) | 5.68613e51 | 0.996264 | ||||||||
\(452\) | −7.99362e51 | −1.34136 | ||||||||
\(453\) | −9.52770e50 | −0.153134 | ||||||||
\(454\) | 3.02784e51 | 0.466170 | ||||||||
\(455\) | 6.47615e50 | 0.0955201 | ||||||||
\(456\) | −4.65297e51 | −0.657531 | ||||||||
\(457\) | 3.57503e51 | 0.484076 | 0.242038 | − | 0.970267i | \(-0.422184\pi\) | ||||
0.242038 | + | 0.970267i | \(0.422184\pi\) | |||||||
\(458\) | −1.43554e51 | −0.186268 | ||||||||
\(459\) | −4.78943e50 | −0.0595575 | ||||||||
\(460\) | −1.74147e52 | −2.07558 | ||||||||
\(461\) | 8.00610e51 | 0.914645 | 0.457323 | − | 0.889301i | \(-0.348808\pi\) | ||||
0.457323 | + | 0.889301i | \(0.348808\pi\) | |||||||
\(462\) | −2.01273e51 | −0.220428 | ||||||||
\(463\) | −8.57929e51 | −0.900787 | −0.450393 | − | 0.892830i | \(-0.648716\pi\) | ||||
−0.450393 | + | 0.892830i | \(0.648716\pi\) | |||||||
\(464\) | 3.05837e51 | 0.307886 | ||||||||
\(465\) | 2.13037e51 | 0.205647 | ||||||||
\(466\) | −6.46740e51 | −0.598693 | ||||||||
\(467\) | 1.12846e52 | 1.00186 | 0.500932 | − | 0.865487i | \(-0.332991\pi\) | ||||
0.500932 | + | 0.865487i | \(0.332991\pi\) | |||||||
\(468\) | −1.45074e50 | −0.0123537 | ||||||||
\(469\) | 2.28330e52 | 1.86506 | ||||||||
\(470\) | 8.12510e51 | 0.636679 | ||||||||
\(471\) | −3.19692e51 | −0.240339 | ||||||||
\(472\) | 7.10306e51 | 0.512361 | ||||||||
\(473\) | 1.62518e52 | 1.12489 | ||||||||
\(474\) | 4.13006e51 | 0.274333 | ||||||||
\(475\) | −3.17367e52 | −2.02319 | ||||||||
\(476\) | 6.72205e51 | 0.411307 | ||||||||
\(477\) | −8.03105e50 | −0.0471698 | ||||||||
\(478\) | 8.47673e51 | 0.477952 | ||||||||
\(479\) | −2.24291e52 | −1.21414 | −0.607071 | − | 0.794648i | \(-0.707656\pi\) | ||||
−0.607071 | + | 0.794648i | \(0.707656\pi\) | |||||||
\(480\) | 1.46739e52 | 0.762680 | ||||||||
\(481\) | 1.00504e51 | 0.0501594 | ||||||||
\(482\) | −1.06547e51 | −0.0510652 | ||||||||
\(483\) | −3.07046e52 | −1.41330 | ||||||||
\(484\) | 9.95912e51 | 0.440287 | ||||||||
\(485\) | 3.51822e52 | 1.49403 | ||||||||
\(486\) | −5.60183e50 | −0.0228519 | ||||||||
\(487\) | 6.05465e51 | 0.237287 | 0.118644 | − | 0.992937i | \(-0.462145\pi\) | ||||
0.118644 | + | 0.992937i | \(0.462145\pi\) | |||||||
\(488\) | 1.14480e52 | 0.431064 | ||||||||
\(489\) | 3.54753e50 | 0.0128352 | ||||||||
\(490\) | −1.99510e52 | −0.693650 | ||||||||
\(491\) | −3.63912e52 | −1.21593 | −0.607963 | − | 0.793965i | \(-0.708013\pi\) | ||||
−0.607963 | + | 0.793965i | \(0.708013\pi\) | |||||||
\(492\) | −2.22116e52 | −0.713281 | ||||||||
\(493\) | 4.85811e51 | 0.149952 | ||||||||
\(494\) | −8.69845e50 | −0.0258087 | ||||||||
\(495\) | 1.21635e52 | 0.346943 | ||||||||
\(496\) | 5.58303e51 | 0.153101 | ||||||||
\(497\) | −3.81161e52 | −1.00498 | ||||||||
\(498\) | −7.09209e51 | −0.179805 | ||||||||
\(499\) | −5.72391e52 | −1.39551 | −0.697754 | − | 0.716337i | \(-0.745817\pi\) | ||||
−0.697754 | + | 0.716337i | \(0.745817\pi\) | |||||||
\(500\) | 1.02033e52 | 0.239235 | ||||||||
\(501\) | 9.99619e51 | 0.225423 | ||||||||
\(502\) | −2.38484e52 | −0.517294 | ||||||||
\(503\) | 1.75324e52 | 0.365818 | 0.182909 | − | 0.983130i | \(-0.441449\pi\) | ||||
0.182909 | + | 0.983130i | \(0.441449\pi\) | |||||||
\(504\) | 1.68672e52 | 0.338570 | ||||||||
\(505\) | 5.41361e52 | 1.04545 | ||||||||
\(506\) | 2.17066e52 | 0.403327 | ||||||||
\(507\) | 3.22338e52 | 0.576310 | ||||||||
\(508\) | 5.62453e52 | 0.967707 | ||||||||
\(509\) | −9.36160e52 | −1.55008 | −0.775039 | − | 0.631913i | \(-0.782270\pi\) | ||||
−0.775039 | + | 0.631913i | \(0.782270\pi\) | |||||||
\(510\) | 5.90422e51 | 0.0940901 | ||||||||
\(511\) | 2.62351e52 | 0.402415 | ||||||||
\(512\) | 6.71707e52 | 0.991780 | ||||||||
\(513\) | 2.31098e52 | 0.328479 | ||||||||
\(514\) | 1.13501e51 | 0.0155317 | ||||||||
\(515\) | −4.55955e52 | −0.600732 | ||||||||
\(516\) | −6.34839e52 | −0.805368 | ||||||||
\(517\) | 6.96817e52 | 0.851242 | ||||||||
\(518\) | −5.44678e52 | −0.640781 | ||||||||
\(519\) | 4.16754e52 | 0.472189 | ||||||||
\(520\) | 3.83676e51 | 0.0418697 | ||||||||
\(521\) | −6.14605e52 | −0.646042 | −0.323021 | − | 0.946392i | \(-0.604698\pi\) | ||||
−0.323021 | + | 0.946392i | \(0.604698\pi\) | |||||||
\(522\) | 5.68217e51 | 0.0575359 | ||||||||
\(523\) | −2.50871e52 | −0.244719 | −0.122359 | − | 0.992486i | \(-0.539046\pi\) | ||||
−0.122359 | + | 0.992486i | \(0.539046\pi\) | |||||||
\(524\) | 1.29344e52 | 0.121559 | ||||||||
\(525\) | 1.15047e53 | 1.04176 | ||||||||
\(526\) | 3.35140e52 | 0.292418 | ||||||||
\(527\) | 8.86844e51 | 0.0745659 | ||||||||
\(528\) | 3.18768e52 | 0.258293 | ||||||||
\(529\) | 2.03088e53 | 1.58598 | ||||||||
\(530\) | 9.90037e51 | 0.0745198 | ||||||||
\(531\) | −3.52786e52 | −0.255957 | ||||||||
\(532\) | −3.24350e53 | −2.26849 | ||||||||
\(533\) | −8.90815e51 | −0.0600630 | ||||||||
\(534\) | −1.70048e52 | −0.110539 | ||||||||
\(535\) | −4.13259e53 | −2.59014 | ||||||||
\(536\) | 1.35273e53 | 0.817519 | ||||||||
\(537\) | −1.54271e53 | −0.899056 | ||||||||
\(538\) | 1.51784e52 | 0.0853046 | ||||||||
\(539\) | −1.71101e53 | −0.927412 | ||||||||
\(540\) | −4.75141e52 | −0.248396 | ||||||||
\(541\) | 2.37622e53 | 1.19823 | 0.599114 | − | 0.800664i | \(-0.295520\pi\) | ||||
0.599114 | + | 0.800664i | \(0.295520\pi\) | |||||||
\(542\) | −1.04511e52 | −0.0508368 | ||||||||
\(543\) | −5.20861e52 | −0.244414 | ||||||||
\(544\) | 6.10856e52 | 0.276542 | ||||||||
\(545\) | 3.70571e53 | 1.61860 | ||||||||
\(546\) | 3.15323e51 | 0.0132892 | ||||||||
\(547\) | 1.01438e53 | 0.412524 | 0.206262 | − | 0.978497i | \(-0.433870\pi\) | ||||
0.206262 | + | 0.978497i | \(0.433870\pi\) | |||||||
\(548\) | −7.82071e52 | −0.306920 | ||||||||
\(549\) | −5.68583e52 | −0.215344 | ||||||||
\(550\) | −8.13325e52 | −0.297298 | ||||||||
\(551\) | −2.34412e53 | −0.827035 | ||||||||
\(552\) | −1.81908e53 | −0.619498 | ||||||||
\(553\) | 6.17641e53 | 2.03047 | ||||||||
\(554\) | 1.18143e53 | 0.374944 | ||||||||
\(555\) | 3.29166e53 | 1.00856 | ||||||||
\(556\) | −2.74100e53 | −0.810868 | ||||||||
\(557\) | 3.06102e53 | 0.874358 | 0.437179 | − | 0.899374i | \(-0.355978\pi\) | ||||
0.437179 | + | 0.899374i | \(0.355978\pi\) | |||||||
\(558\) | 1.03727e52 | 0.0286106 | ||||||||
\(559\) | −2.54608e52 | −0.0678174 | ||||||||
\(560\) | 5.55859e53 | 1.42988 | ||||||||
\(561\) | 5.06351e52 | 0.125799 | ||||||||
\(562\) | 1.05432e53 | 0.252997 | ||||||||
\(563\) | 1.09661e53 | 0.254179 | 0.127090 | − | 0.991891i | \(-0.459436\pi\) | ||||
0.127090 | + | 0.991891i | \(0.459436\pi\) | |||||||
\(564\) | −2.72196e53 | −0.609451 | ||||||||
\(565\) | −1.04999e54 | −2.27111 | ||||||||
\(566\) | −2.17647e53 | −0.454813 | ||||||||
\(567\) | −8.37741e52 | −0.169138 | ||||||||
\(568\) | −2.25817e53 | −0.440519 | ||||||||
\(569\) | 6.98263e53 | 1.31622 | 0.658112 | − | 0.752920i | \(-0.271355\pi\) | ||||
0.658112 | + | 0.752920i | \(0.271355\pi\) | |||||||
\(570\) | −2.84888e53 | −0.518938 | ||||||||
\(571\) | −2.15970e53 | −0.380180 | −0.190090 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190090 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(572\) | 1.53376e52 | 0.0260937 | ||||||||
\(573\) | 3.92441e53 | 0.645296 | ||||||||
\(574\) | 4.82776e53 | 0.767298 | ||||||||
\(575\) | −1.24075e54 | −1.90616 | ||||||||
\(576\) | −7.11702e52 | −0.105696 | ||||||||
\(577\) | 2.02592e53 | 0.290867 | 0.145433 | − | 0.989368i | \(-0.453542\pi\) | ||||
0.145433 | + | 0.989368i | \(0.453542\pi\) | |||||||
\(578\) | −2.32058e53 | −0.322110 | ||||||||
\(579\) | 4.25111e52 | 0.0570519 | ||||||||
\(580\) | 4.81955e53 | 0.625404 | ||||||||
\(581\) | −1.06061e54 | −1.33082 | ||||||||
\(582\) | 1.71302e53 | 0.207857 | ||||||||
\(583\) | 8.49065e52 | 0.0996332 | ||||||||
\(584\) | 1.55428e53 | 0.176392 | ||||||||
\(585\) | −1.90559e52 | −0.0209166 | ||||||||
\(586\) | −1.65981e53 | −0.176220 | ||||||||
\(587\) | −7.06852e53 | −0.725914 | −0.362957 | − | 0.931806i | \(-0.618233\pi\) | ||||
−0.362957 | + | 0.931806i | \(0.618233\pi\) | |||||||
\(588\) | 6.68370e53 | 0.663986 | ||||||||
\(589\) | −4.27917e53 | −0.411255 | ||||||||
\(590\) | 4.34900e53 | 0.404367 | ||||||||
\(591\) | 2.61527e53 | 0.235267 | ||||||||
\(592\) | 8.62641e53 | 0.750856 | ||||||||
\(593\) | −1.68827e53 | −0.142192 | −0.0710959 | − | 0.997469i | \(-0.522650\pi\) | ||||
−0.0710959 | + | 0.997469i | \(0.522650\pi\) | |||||||
\(594\) | 5.92241e52 | 0.0482684 | ||||||||
\(595\) | 8.82962e53 | 0.696404 | ||||||||
\(596\) | 1.92303e53 | 0.146786 | ||||||||
\(597\) | −4.66267e52 | −0.0344457 | ||||||||
\(598\) | −3.40066e52 | −0.0243159 | ||||||||
\(599\) | −8.66168e53 | −0.599486 | −0.299743 | − | 0.954020i | \(-0.596901\pi\) | ||||
−0.299743 | + | 0.954020i | \(0.596901\pi\) | |||||||
\(600\) | 6.81591e53 | 0.456640 | ||||||||
\(601\) | 1.01881e54 | 0.660758 | 0.330379 | − | 0.943848i | \(-0.392823\pi\) | ||||
0.330379 | + | 0.943848i | \(0.392823\pi\) | |||||||
\(602\) | 1.37984e54 | 0.866359 | ||||||||
\(603\) | −6.71857e53 | −0.408403 | ||||||||
\(604\) | −3.93477e53 | −0.231579 | ||||||||
\(605\) | 1.30816e54 | 0.745472 | ||||||||
\(606\) | 2.63588e53 | 0.145449 | ||||||||
\(607\) | −3.59220e53 | −0.191947 | −0.0959734 | − | 0.995384i | \(-0.530596\pi\) | ||||
−0.0959734 | + | 0.995384i | \(0.530596\pi\) | |||||||
\(608\) | −2.94748e54 | −1.52522 | ||||||||
\(609\) | 8.49755e53 | 0.425850 | ||||||||
\(610\) | 7.00926e53 | 0.340205 | ||||||||
\(611\) | −1.09166e53 | −0.0513199 | ||||||||
\(612\) | −1.97795e53 | −0.0900663 | ||||||||
\(613\) | 9.11862e53 | 0.402207 | 0.201104 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201104 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(614\) | −6.43631e53 | −0.275013 | ||||||||
\(615\) | −2.91757e54 | −1.20769 | ||||||||
\(616\) | −1.78325e54 | −0.715136 | ||||||||
\(617\) | 2.52497e54 | 0.981061 | 0.490530 | − | 0.871424i | \(-0.336803\pi\) | ||||
0.490530 | + | 0.871424i | \(0.336803\pi\) | |||||||
\(618\) | −2.22004e53 | −0.0835767 | ||||||||
\(619\) | 3.13318e53 | 0.114292 | 0.0571462 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571462 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(620\) | 8.79804e53 | 0.310991 | ||||||||
\(621\) | 9.03477e53 | 0.309479 | ||||||||
\(622\) | −1.79992e54 | −0.597503 | ||||||||
\(623\) | −2.54302e54 | −0.818151 | ||||||||
\(624\) | −4.99397e52 | −0.0155721 | ||||||||
\(625\) | −2.58177e54 | −0.780292 | ||||||||
\(626\) | −6.93035e53 | −0.203028 | ||||||||
\(627\) | −2.44323e54 | −0.693821 | ||||||||
\(628\) | −1.32027e54 | −0.363454 | ||||||||
\(629\) | 1.37027e54 | 0.365695 | ||||||||
\(630\) | 1.03273e54 | 0.267207 | ||||||||
\(631\) | −3.45716e54 | −0.867256 | −0.433628 | − | 0.901092i | \(-0.642767\pi\) | ||||
−0.433628 | + | 0.901092i | \(0.642767\pi\) | |||||||
\(632\) | 3.65918e54 | 0.890022 | ||||||||
\(633\) | 3.07250e54 | 0.724635 | ||||||||
\(634\) | −1.72198e54 | −0.393811 | ||||||||
\(635\) | 7.38800e54 | 1.63847 | ||||||||
\(636\) | −3.31668e53 | −0.0713330 | ||||||||
\(637\) | 2.68055e53 | 0.0559121 | ||||||||
\(638\) | −6.00734e53 | −0.121529 | ||||||||
\(639\) | 1.12156e54 | 0.220067 | ||||||||
\(640\) | 7.81821e54 | 1.48798 | ||||||||
\(641\) | 3.85151e54 | 0.711050 | 0.355525 | − | 0.934667i | \(-0.384302\pi\) | ||||
0.355525 | + | 0.934667i | \(0.384302\pi\) | |||||||
\(642\) | −2.01215e54 | −0.360352 | ||||||||
\(643\) | 1.53024e54 | 0.265855 | 0.132928 | − | 0.991126i | \(-0.457562\pi\) | ||||
0.132928 | + | 0.991126i | \(0.457562\pi\) | |||||||
\(644\) | −1.26805e55 | −2.13728 | ||||||||
\(645\) | −8.33881e54 | −1.36361 | ||||||||
\(646\) | −1.18595e54 | −0.188163 | ||||||||
\(647\) | 1.27086e55 | 1.95644 | 0.978219 | − | 0.207577i | \(-0.0665578\pi\) | ||||
0.978219 | + | 0.207577i | \(0.0665578\pi\) | |||||||
\(648\) | −4.96315e53 | −0.0741387 | ||||||||
\(649\) | 3.72975e54 | 0.540639 | ||||||||
\(650\) | 1.27419e53 | 0.0179236 | ||||||||
\(651\) | 1.55122e54 | 0.211760 | ||||||||
\(652\) | 1.46507e53 | 0.0194102 | ||||||||
\(653\) | 9.19237e54 | 1.18201 | 0.591004 | − | 0.806669i | \(-0.298732\pi\) | ||||
0.591004 | + | 0.806669i | \(0.298732\pi\) | |||||||
\(654\) | 1.80431e54 | 0.225187 | ||||||||
\(655\) | 1.69898e54 | 0.205818 | ||||||||
\(656\) | −7.64603e54 | −0.899106 | ||||||||
\(657\) | −7.71961e53 | −0.0881192 | ||||||||
\(658\) | 5.91626e54 | 0.655605 | ||||||||
\(659\) | −2.57996e54 | −0.277554 | −0.138777 | − | 0.990324i | \(-0.544317\pi\) | ||||
−0.138777 | + | 0.990324i | \(0.544317\pi\) | |||||||
\(660\) | 5.02332e54 | 0.524668 | ||||||||
\(661\) | −1.12332e55 | −1.13914 | −0.569568 | − | 0.821944i | \(-0.692890\pi\) | ||||
−0.569568 | + | 0.821944i | \(0.692890\pi\) | |||||||
\(662\) | −5.39732e54 | −0.531432 | ||||||||
\(663\) | −7.93273e52 | −0.00758419 | ||||||||
\(664\) | −6.28350e54 | −0.583343 | ||||||||
\(665\) | −4.26044e55 | −3.84090 | ||||||||
\(666\) | 1.60270e54 | 0.140316 | ||||||||
\(667\) | −9.16434e54 | −0.779197 | ||||||||
\(668\) | 4.12825e54 | 0.340898 | ||||||||
\(669\) | 7.69283e54 | 0.616989 | ||||||||
\(670\) | 8.28239e54 | 0.645204 | ||||||||
\(671\) | 6.01121e54 | 0.454855 | ||||||||
\(672\) | 1.06848e55 | 0.785352 | ||||||||
\(673\) | −1.50888e54 | −0.107736 | −0.0538681 | − | 0.998548i | \(-0.517155\pi\) | ||||
−0.0538681 | + | 0.998548i | \(0.517155\pi\) | |||||||
\(674\) | −3.55464e54 | −0.246563 | ||||||||
\(675\) | −3.38524e54 | −0.228121 | ||||||||
\(676\) | 1.33120e55 | 0.871530 | ||||||||
\(677\) | 5.88105e54 | 0.374090 | 0.187045 | − | 0.982351i | \(-0.440109\pi\) | ||||
0.187045 | + | 0.982351i | \(0.440109\pi\) | |||||||
\(678\) | −5.11237e54 | −0.315968 | ||||||||
\(679\) | 2.56178e55 | 1.53844 | ||||||||
\(680\) | 5.23106e54 | 0.305257 | ||||||||
\(681\) | −1.33237e55 | −0.755540 | ||||||||
\(682\) | −1.09663e54 | −0.0604319 | ||||||||
\(683\) | 1.21018e55 | 0.648109 | 0.324054 | − | 0.946038i | \(-0.394954\pi\) | ||||
0.324054 | + | 0.946038i | \(0.394954\pi\) | |||||||
\(684\) | 9.54394e54 | 0.496745 | ||||||||
\(685\) | −1.02727e55 | −0.519661 | ||||||||
\(686\) | −3.49842e54 | −0.172009 | ||||||||
\(687\) | 6.31695e54 | 0.301892 | ||||||||
\(688\) | −2.18534e55 | −1.01518 | ||||||||
\(689\) | −1.33018e53 | −0.00600671 | ||||||||
\(690\) | −1.11377e55 | −0.488921 | ||||||||
\(691\) | 1.62764e55 | 0.694601 | 0.347300 | − | 0.937754i | \(-0.387098\pi\) | ||||
0.347300 | + | 0.937754i | \(0.387098\pi\) | |||||||
\(692\) | 1.72112e55 | 0.714072 | ||||||||
\(693\) | 8.85682e54 | 0.357256 | ||||||||
\(694\) | 9.53445e54 | 0.373926 | ||||||||
\(695\) | −3.60039e55 | −1.37292 | ||||||||
\(696\) | 5.03433e54 | 0.186664 | ||||||||
\(697\) | −1.21454e55 | −0.437899 | ||||||||
\(698\) | 3.43312e54 | 0.120367 | ||||||||
\(699\) | 2.84592e55 | 0.970327 | ||||||||
\(700\) | 4.75124e55 | 1.57542 | ||||||||
\(701\) | 1.79427e55 | 0.578610 | 0.289305 | − | 0.957237i | \(-0.406576\pi\) | ||||
0.289305 | + | 0.957237i | \(0.406576\pi\) | |||||||
\(702\) | −9.27831e52 | −0.00291002 | ||||||||
\(703\) | −6.61180e55 | −2.01693 | ||||||||
\(704\) | 7.52430e54 | 0.223254 | ||||||||
\(705\) | −3.57538e55 | −1.03189 | ||||||||
\(706\) | −2.11130e55 | −0.592731 | ||||||||
\(707\) | 3.94190e55 | 1.07653 | ||||||||
\(708\) | −1.45694e55 | −0.387074 | ||||||||
\(709\) | 1.14395e55 | 0.295669 | 0.147834 | − | 0.989012i | \(-0.452770\pi\) | ||||
0.147834 | + | 0.989012i | \(0.452770\pi\) | |||||||
\(710\) | −1.38261e55 | −0.347667 | ||||||||
\(711\) | −1.81740e55 | −0.444623 | ||||||||
\(712\) | −1.50660e55 | −0.358623 | ||||||||
\(713\) | −1.67294e55 | −0.387467 | ||||||||
\(714\) | 4.29913e54 | 0.0968870 | ||||||||
\(715\) | 2.01465e54 | 0.0441805 | ||||||||
\(716\) | −6.37114e55 | −1.35961 | ||||||||
\(717\) | −3.73011e55 | −0.774636 | ||||||||
\(718\) | 2.04771e55 | 0.413848 | ||||||||
\(719\) | 6.82369e55 | 1.34216 | 0.671082 | − | 0.741383i | \(-0.265830\pi\) | ||||
0.671082 | + | 0.741383i | \(0.265830\pi\) | |||||||
\(720\) | −1.63560e55 | −0.313108 | ||||||||
\(721\) | −3.32002e55 | −0.618589 | ||||||||
\(722\) | 3.75815e55 | 0.681552 | ||||||||
\(723\) | 4.68852e54 | 0.0827635 | ||||||||
\(724\) | −2.15107e55 | −0.369617 | ||||||||
\(725\) | 3.43379e55 | 0.574357 | ||||||||
\(726\) | 6.36942e54 | 0.103714 | ||||||||
\(727\) | 4.73186e55 | 0.750085 | 0.375043 | − | 0.927008i | \(-0.377628\pi\) | ||||
0.375043 | + | 0.927008i | \(0.377628\pi\) | |||||||
\(728\) | 2.79372e54 | 0.0431143 | ||||||||
\(729\) | 2.46503e54 | 0.0370370 | ||||||||
\(730\) | 9.51643e54 | 0.139213 | ||||||||
\(731\) | −3.47134e55 | −0.494433 | ||||||||
\(732\) | −2.34815e55 | −0.325656 | ||||||||
\(733\) | 7.44240e54 | 0.100505 | 0.0502523 | − | 0.998737i | \(-0.483997\pi\) | ||||
0.0502523 | + | 0.998737i | \(0.483997\pi\) | |||||||
\(734\) | 4.13876e54 | 0.0544248 | ||||||||
\(735\) | 8.77925e55 | 1.12423 | ||||||||
\(736\) | −1.15232e56 | −1.43700 | ||||||||
\(737\) | 7.10305e55 | 0.862639 | ||||||||
\(738\) | −1.42056e55 | −0.168020 | ||||||||
\(739\) | 9.48337e55 | 1.09244 | 0.546218 | − | 0.837643i | \(-0.316067\pi\) | ||||
0.546218 | + | 0.837643i | \(0.316067\pi\) | |||||||
\(740\) | 1.35940e56 | 1.52520 | ||||||||
\(741\) | 3.82768e54 | 0.0418293 | ||||||||
\(742\) | 7.20891e54 | 0.0767350 | ||||||||
\(743\) | −2.79365e55 | −0.289661 | −0.144830 | − | 0.989456i | \(-0.546264\pi\) | ||||
−0.144830 | + | 0.989456i | \(0.546264\pi\) | |||||||
\(744\) | 9.19012e54 | 0.0928215 | ||||||||
\(745\) | 2.52596e55 | 0.248530 | ||||||||
\(746\) | 1.50011e55 | 0.143786 | ||||||||
\(747\) | 3.12081e55 | 0.291417 | ||||||||
\(748\) | 2.09114e55 | 0.190240 | ||||||||
\(749\) | −3.00912e56 | −2.66713 | ||||||||
\(750\) | 6.52557e54 | 0.0563539 | ||||||||
\(751\) | −8.12653e55 | −0.683796 | −0.341898 | − | 0.939737i | \(-0.611070\pi\) | ||||
−0.341898 | + | 0.939737i | \(0.611070\pi\) | |||||||
\(752\) | −9.36995e55 | −0.768227 | ||||||||
\(753\) | 1.04943e56 | 0.838400 | ||||||||
\(754\) | 9.41137e53 | 0.00732676 | ||||||||
\(755\) | −5.16845e55 | −0.392098 | ||||||||
\(756\) | −3.45972e55 | −0.255780 | ||||||||
\(757\) | 2.71381e56 | 1.95528 | 0.977642 | − | 0.210277i | \(-0.0674367\pi\) | ||||
0.977642 | + | 0.210277i | \(0.0674367\pi\) | |||||||
\(758\) | −8.98771e54 | −0.0631102 | ||||||||
\(759\) | −9.55181e55 | −0.653689 | ||||||||
\(760\) | −2.52408e56 | −1.68359 | ||||||||
\(761\) | −2.53928e56 | −1.65086 | −0.825428 | − | 0.564507i | \(-0.809066\pi\) | ||||
−0.825428 | + | 0.564507i | \(0.809066\pi\) | |||||||
\(762\) | 3.59721e55 | 0.227952 | ||||||||
\(763\) | 2.69830e56 | 1.66671 | ||||||||
\(764\) | 1.62071e56 | 0.975855 | ||||||||
\(765\) | −2.59810e55 | −0.152496 | ||||||||
\(766\) | −3.99872e55 | −0.228802 | ||||||||
\(767\) | −5.84319e54 | −0.0325942 | ||||||||
\(768\) | 4.40289e54 | 0.0239439 | ||||||||
\(769\) | −3.16540e56 | −1.67828 | −0.839140 | − | 0.543915i | \(-0.816941\pi\) | ||||
−0.839140 | + | 0.543915i | \(0.816941\pi\) | |||||||
\(770\) | −1.09183e56 | −0.564401 | ||||||||
\(771\) | −4.99452e54 | −0.0251729 | ||||||||
\(772\) | 1.75563e55 | 0.0862773 | ||||||||
\(773\) | −8.83478e55 | −0.423346 | −0.211673 | − | 0.977341i | \(-0.567891\pi\) | ||||
−0.211673 | + | 0.977341i | \(0.567891\pi\) | |||||||
\(774\) | −4.06016e55 | −0.189712 | ||||||||
\(775\) | 6.26834e55 | 0.285607 | ||||||||
\(776\) | 1.51771e56 | 0.674352 | ||||||||
\(777\) | 2.39681e56 | 1.03854 | ||||||||
\(778\) | 9.61590e55 | 0.406338 | ||||||||
\(779\) | 5.86038e56 | 2.41516 | ||||||||
\(780\) | −7.86976e54 | −0.0316313 | ||||||||
\(781\) | −1.18574e56 | −0.464832 | ||||||||
\(782\) | −4.63648e55 | −0.177279 | ||||||||
\(783\) | −2.50039e55 | −0.0932508 | ||||||||
\(784\) | 2.30077e56 | 0.836969 | ||||||||
\(785\) | −1.73422e56 | −0.615382 | ||||||||
\(786\) | 8.27231e54 | 0.0286343 | ||||||||
\(787\) | 2.01468e56 | 0.680299 | 0.340149 | − | 0.940371i | \(-0.389522\pi\) | ||||
0.340149 | + | 0.940371i | \(0.389522\pi\) | |||||||
\(788\) | 1.08006e56 | 0.355784 | ||||||||
\(789\) | −1.47475e56 | −0.473934 | ||||||||
\(790\) | 2.24041e56 | 0.702425 | ||||||||
\(791\) | −7.64544e56 | −2.33863 | ||||||||
\(792\) | 5.24718e55 | 0.156598 | ||||||||
\(793\) | −9.41744e54 | −0.0274224 | ||||||||
\(794\) | 1.63610e56 | 0.464847 | ||||||||
\(795\) | −4.35657e55 | −0.120777 | ||||||||
\(796\) | −1.92560e55 | −0.0520908 | ||||||||
\(797\) | 4.87383e56 | 1.28657 | 0.643285 | − | 0.765627i | \(-0.277571\pi\) | ||||
0.643285 | + | 0.765627i | \(0.277571\pi\) | |||||||
\(798\) | −2.07440e56 | −0.534364 | ||||||||
\(799\) | −1.48838e56 | −0.374156 | ||||||||
\(800\) | 4.31762e56 | 1.05923 | ||||||||
\(801\) | 7.48279e55 | 0.179155 | ||||||||
\(802\) | 5.23362e55 | 0.122293 | ||||||||
\(803\) | 8.16138e55 | 0.186128 | ||||||||
\(804\) | −2.77465e56 | −0.617611 | ||||||||
\(805\) | −1.66562e57 | −3.61873 | ||||||||
\(806\) | 1.71804e54 | 0.00364333 | ||||||||
\(807\) | −6.67913e55 | −0.138257 | ||||||||
\(808\) | 2.33536e56 | 0.471880 | ||||||||
\(809\) | 2.97630e56 | 0.587057 | 0.293529 | − | 0.955950i | \(-0.405170\pi\) | ||||
0.293529 | + | 0.955950i | \(0.405170\pi\) | |||||||
\(810\) | −3.03880e55 | −0.0585119 | ||||||||
\(811\) | −7.70370e56 | −1.44808 | −0.724041 | − | 0.689757i | \(-0.757717\pi\) | ||||
−0.724041 | + | 0.689757i | \(0.757717\pi\) | |||||||
\(812\) | 3.50934e56 | 0.643995 | ||||||||
\(813\) | 4.59893e55 | 0.0823932 | ||||||||
\(814\) | −1.69442e56 | −0.296378 | ||||||||
\(815\) | 1.92441e55 | 0.0328643 | ||||||||
\(816\) | −6.80880e55 | −0.113531 | ||||||||
\(817\) | 1.67498e57 | 2.72696 | ||||||||
\(818\) | −2.16223e56 | −0.343725 | ||||||||
\(819\) | −1.38755e55 | −0.0215384 | ||||||||
\(820\) | −1.20490e57 | −1.82634 | ||||||||
\(821\) | 4.31761e55 | 0.0639075 | 0.0319537 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319537 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(822\) | −5.00179e55 | −0.0722977 | ||||||||
\(823\) | 4.12553e56 | 0.582348 | 0.291174 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291174 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(824\) | −1.96693e56 | −0.271149 | ||||||||
\(825\) | 3.57897e56 | 0.481843 | ||||||||
\(826\) | 3.16671e56 | 0.416387 | ||||||||
\(827\) | −6.96480e56 | −0.894440 | −0.447220 | − | 0.894424i | \(-0.647586\pi\) | ||||
−0.447220 | + | 0.894424i | \(0.647586\pi\) | |||||||
\(828\) | 3.73120e56 | 0.468012 | ||||||||
\(829\) | 1.42775e57 | 1.74920 | 0.874600 | − | 0.484845i | \(-0.161124\pi\) | ||||
0.874600 | + | 0.484845i | \(0.161124\pi\) | |||||||
\(830\) | −3.84721e56 | −0.460387 | ||||||||
\(831\) | −5.19876e56 | −0.607686 | ||||||||
\(832\) | −1.17879e55 | −0.0134596 | ||||||||
\(833\) | 3.65468e56 | 0.407636 | ||||||||
\(834\) | −1.75302e56 | −0.191007 | ||||||||
\(835\) | 5.42258e56 | 0.577192 | ||||||||
\(836\) | −1.00901e57 | −1.04924 | ||||||||
\(837\) | −4.56443e55 | −0.0463703 | ||||||||
\(838\) | −2.62253e56 | −0.260293 | ||||||||
\(839\) | 6.94535e56 | 0.673497 | 0.336749 | − | 0.941595i | \(-0.390673\pi\) | ||||
0.336749 | + | 0.941595i | \(0.390673\pi\) | |||||||
\(840\) | 9.14989e56 | 0.866902 | ||||||||
\(841\) | −8.26620e56 | −0.765216 | ||||||||
\(842\) | −1.68811e56 | −0.152692 | ||||||||
\(843\) | −4.63946e56 | −0.410043 | ||||||||
\(844\) | 1.26889e57 | 1.09584 | ||||||||
\(845\) | 1.74857e57 | 1.47563 | ||||||||
\(846\) | −1.74085e56 | −0.143562 | ||||||||
\(847\) | 9.52532e56 | 0.767632 | ||||||||
\(848\) | −1.14172e56 | −0.0899168 | ||||||||
\(849\) | 9.57738e56 | 0.737135 | ||||||||
\(850\) | 1.73724e56 | 0.130675 | ||||||||
\(851\) | −2.58488e57 | −1.90027 | ||||||||
\(852\) | 4.63184e56 | 0.332799 | ||||||||
\(853\) | −4.76945e56 | −0.334936 | −0.167468 | − | 0.985878i | \(-0.553559\pi\) | ||||
−0.167468 | + | 0.985878i | \(0.553559\pi\) | |||||||
\(854\) | 5.10377e56 | 0.350318 | ||||||||
\(855\) | 1.25363e57 | 0.841064 | ||||||||
\(856\) | −1.78274e57 | −1.16909 | ||||||||
\(857\) | −7.15190e56 | −0.458454 | −0.229227 | − | 0.973373i | \(-0.573620\pi\) | ||||
−0.229227 | + | 0.973373i | \(0.573620\pi\) | |||||||
\(858\) | 9.80928e54 | 0.00614660 | ||||||||
\(859\) | −3.14874e57 | −1.92872 | −0.964362 | − | 0.264586i | \(-0.914765\pi\) | ||||
−0.964362 | + | 0.264586i | \(0.914765\pi\) | |||||||
\(860\) | −3.44378e57 | −2.06213 | ||||||||
\(861\) | −2.12441e57 | −1.24359 | ||||||||
\(862\) | 8.50211e55 | 0.0486558 | ||||||||
\(863\) | 6.33719e56 | 0.354557 | 0.177279 | − | 0.984161i | \(-0.443271\pi\) | ||||
0.177279 | + | 0.984161i | \(0.443271\pi\) | |||||||
\(864\) | −3.14397e56 | −0.171973 | ||||||||
\(865\) | 2.26074e57 | 1.20903 | ||||||||
\(866\) | −1.17175e57 | −0.612683 | ||||||||
\(867\) | 1.02115e57 | 0.522057 | ||||||||
\(868\) | 6.40626e56 | 0.320236 | ||||||||
\(869\) | 1.92140e57 | 0.939144 | ||||||||
\(870\) | 3.08238e56 | 0.147320 | ||||||||
\(871\) | −1.11280e56 | −0.0520070 | ||||||||
\(872\) | 1.59859e57 | 0.730577 | ||||||||
\(873\) | −7.53799e56 | −0.336882 | ||||||||
\(874\) | 2.23718e57 | 0.977750 | ||||||||
\(875\) | 9.75885e56 | 0.417101 | ||||||||
\(876\) | −3.18806e56 | −0.133259 | ||||||||
\(877\) | −2.07724e57 | −0.849171 | −0.424585 | − | 0.905388i | \(-0.639580\pi\) | ||||
−0.424585 | + | 0.905388i | \(0.639580\pi\) | |||||||
\(878\) | 8.59911e56 | 0.343804 | ||||||||
\(879\) | 7.30384e56 | 0.285607 | ||||||||
\(880\) | 1.72921e57 | 0.661355 | ||||||||
\(881\) | −1.44068e57 | −0.538937 | −0.269468 | − | 0.963009i | \(-0.586848\pi\) | ||||
−0.269468 | + | 0.963009i | \(0.586848\pi\) | |||||||
\(882\) | 4.27460e56 | 0.156408 | ||||||||
\(883\) | −2.21527e57 | −0.792852 | −0.396426 | − | 0.918067i | \(-0.629750\pi\) | ||||
−0.396426 | + | 0.918067i | \(0.629750\pi\) | |||||||
\(884\) | −3.27608e55 | −0.0114693 | ||||||||
\(885\) | −1.91374e57 | −0.655374 | ||||||||
\(886\) | −1.08218e57 | −0.362528 | ||||||||
\(887\) | 4.62524e56 | 0.151574 | 0.0757868 | − | 0.997124i | \(-0.475853\pi\) | ||||
0.0757868 | + | 0.997124i | \(0.475853\pi\) | |||||||
\(888\) | 1.41998e57 | 0.455227 | ||||||||
\(889\) | 5.37954e57 | 1.68718 | ||||||||
\(890\) | −9.22450e56 | −0.283033 | ||||||||
\(891\) | −2.60610e56 | −0.0782305 | ||||||||
\(892\) | 3.17700e57 | 0.933046 | ||||||||
\(893\) | 7.18170e57 | 2.06359 | ||||||||
\(894\) | 1.22989e56 | 0.0345767 | ||||||||
\(895\) | −8.36869e57 | −2.30202 | ||||||||
\(896\) | 5.69280e57 | 1.53221 | ||||||||
\(897\) | 1.49643e56 | 0.0394097 | ||||||||
\(898\) | −2.13233e57 | −0.549497 | ||||||||
\(899\) | 4.62989e56 | 0.116750 | ||||||||
\(900\) | −1.39804e57 | −0.344978 | ||||||||
\(901\) | −1.81358e56 | −0.0437929 | ||||||||
\(902\) | 1.50185e57 | 0.354895 | ||||||||
\(903\) | −6.07187e57 | −1.40414 | ||||||||
\(904\) | −4.52950e57 | −1.02510 | ||||||||
\(905\) | −2.82549e57 | −0.625816 | ||||||||
\(906\) | −2.51651e56 | −0.0545505 | ||||||||
\(907\) | 5.47083e57 | 1.16068 | 0.580339 | − | 0.814375i | \(-0.302920\pi\) | ||||
0.580339 | + | 0.814375i | \(0.302920\pi\) | |||||||
\(908\) | −5.50247e57 | −1.14257 | ||||||||
\(909\) | −1.15989e57 | −0.235734 | ||||||||
\(910\) | 1.71052e56 | 0.0340267 | ||||||||
\(911\) | −5.88844e56 | −0.114655 | −0.0573274 | − | 0.998355i | \(-0.518258\pi\) | ||||
−0.0573274 | + | 0.998355i | \(0.518258\pi\) | |||||||
\(912\) | 3.28536e57 | 0.626158 | ||||||||
\(913\) | −3.29940e57 | −0.615539 | ||||||||
\(914\) | 9.44258e56 | 0.172441 | ||||||||
\(915\) | −3.08436e57 | −0.551384 | ||||||||
\(916\) | 2.60879e57 | 0.456538 | ||||||||
\(917\) | 1.23710e57 | 0.211936 | ||||||||
\(918\) | −1.26501e56 | −0.0212159 | ||||||||
\(919\) | −3.41668e57 | −0.560986 | −0.280493 | − | 0.959856i | \(-0.590498\pi\) | ||||
−0.280493 | + | 0.959856i | \(0.590498\pi\) | |||||||
\(920\) | −9.86788e57 | −1.58621 | ||||||||
\(921\) | 2.83224e57 | 0.445725 | ||||||||
\(922\) | 2.11462e57 | 0.325821 | ||||||||
\(923\) | 1.85764e56 | 0.0280239 | ||||||||
\(924\) | 3.65771e57 | 0.540264 | ||||||||
\(925\) | 9.68529e57 | 1.40071 | ||||||||
\(926\) | −2.26601e57 | −0.320884 | ||||||||
\(927\) | 9.76908e56 | 0.135456 | ||||||||
\(928\) | 3.18906e57 | 0.432989 | ||||||||
\(929\) | −5.60274e57 | −0.744893 | −0.372447 | − | 0.928054i | \(-0.621481\pi\) | ||||
−0.372447 | + | 0.928054i | \(0.621481\pi\) | |||||||
\(930\) | 5.62685e56 | 0.0732568 | ||||||||
\(931\) | −1.76345e58 | −2.24824 | ||||||||
\(932\) | 1.17532e58 | 1.46739 | ||||||||
\(933\) | 7.92037e57 | 0.968397 | ||||||||
\(934\) | 2.98056e57 | 0.356890 | ||||||||
\(935\) | 2.74678e57 | 0.322105 | ||||||||
\(936\) | −8.22047e55 | −0.00944099 | ||||||||
\(937\) | 2.84316e57 | 0.319800 | 0.159900 | − | 0.987133i | \(-0.448883\pi\) | ||||
0.159900 | + | 0.987133i | \(0.448883\pi\) | |||||||
\(938\) | 6.03079e57 | 0.664383 | ||||||||
\(939\) | 3.04964e57 | 0.329055 | ||||||||
\(940\) | −1.47657e58 | −1.56049 | ||||||||
\(941\) | −3.10342e57 | −0.321250 | −0.160625 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160625 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(942\) | −8.44388e56 | −0.0856149 | ||||||||
\(943\) | 2.29111e58 | 2.27546 | ||||||||
\(944\) | −5.01531e57 | −0.487915 | ||||||||
\(945\) | −4.54445e57 | −0.433073 | ||||||||
\(946\) | 4.29251e57 | 0.400714 | ||||||||
\(947\) | 1.09739e58 | 1.00354 | 0.501771 | − | 0.865000i | \(-0.332682\pi\) | ||||
0.501771 | + | 0.865000i | \(0.332682\pi\) | |||||||
\(948\) | −7.50552e57 | −0.672386 | ||||||||
\(949\) | −1.27860e56 | −0.0112213 | ||||||||
\(950\) | −8.38249e57 | −0.720713 | ||||||||
\(951\) | 7.57742e57 | 0.638265 | ||||||||
\(952\) | 3.80898e57 | 0.314332 | ||||||||
\(953\) | −1.56833e58 | −1.26802 | −0.634009 | − | 0.773326i | \(-0.718592\pi\) | ||||
−0.634009 | + | 0.773326i | \(0.718592\pi\) | |||||||
\(954\) | −2.12121e56 | −0.0168031 | ||||||||
\(955\) | 2.12886e58 | 1.65227 | ||||||||
\(956\) | −1.54047e58 | −1.17145 | ||||||||
\(957\) | 2.64348e57 | 0.196967 | ||||||||
\(958\) | −5.92410e57 | −0.432509 | ||||||||
\(959\) | −7.48006e57 | −0.535109 | ||||||||
\(960\) | −3.86073e57 | −0.270633 | ||||||||
\(961\) | −1.37130e58 | −0.941944 | ||||||||
\(962\) | 2.65456e56 | 0.0178681 | ||||||||
\(963\) | 8.85429e57 | 0.584038 | ||||||||
\(964\) | 1.93627e57 | 0.125160 | ||||||||
\(965\) | 2.30608e57 | 0.146080 | ||||||||
\(966\) | −8.10988e57 | −0.503455 | ||||||||
\(967\) | −6.70320e57 | −0.407817 | −0.203909 | − | 0.978990i | \(-0.565365\pi\) | ||||
−0.203909 | + | 0.978990i | \(0.565365\pi\) | |||||||
\(968\) | 5.64323e57 | 0.336479 | ||||||||
\(969\) | 5.21868e57 | 0.304963 | ||||||||
\(970\) | 9.29254e57 | 0.532213 | ||||||||
\(971\) | −1.00902e57 | −0.0566405 | −0.0283202 | − | 0.999599i | \(-0.509016\pi\) | ||||
−0.0283202 | + | 0.999599i | \(0.509016\pi\) | |||||||
\(972\) | 1.01802e57 | 0.0560096 | ||||||||
\(973\) | −2.62161e58 | −1.41373 | ||||||||
\(974\) | 1.59919e57 | 0.0845279 | ||||||||
\(975\) | −5.60697e56 | −0.0290495 | ||||||||
\(976\) | −8.08315e57 | −0.410496 | ||||||||
\(977\) | −1.41653e58 | −0.705150 | −0.352575 | − | 0.935784i | \(-0.614694\pi\) | ||||
−0.352575 | + | 0.935784i | \(0.614694\pi\) | |||||||
\(978\) | 9.36994e55 | 0.00457224 | ||||||||
\(979\) | −7.91101e57 | −0.378416 | ||||||||
\(980\) | 3.62567e58 | 1.70012 | ||||||||
\(981\) | −7.93968e57 | −0.364970 | ||||||||
\(982\) | −9.61185e57 | −0.433145 | ||||||||
\(983\) | −8.83216e57 | −0.390187 | −0.195094 | − | 0.980785i | \(-0.562501\pi\) | ||||
−0.195094 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(984\) | −1.25860e58 | −0.545108 | ||||||||
\(985\) | 1.41869e58 | 0.602396 | ||||||||
\(986\) | 1.28315e57 | 0.0534169 | ||||||||
\(987\) | −2.60340e58 | −1.06257 | ||||||||
\(988\) | 1.58076e57 | 0.0632567 | ||||||||
\(989\) | 6.54832e58 | 2.56923 | ||||||||
\(990\) | 3.21270e57 | 0.123590 | ||||||||
\(991\) | 2.39176e58 | 0.902156 | 0.451078 | − | 0.892484i | \(-0.351040\pi\) | ||||
0.451078 | + | 0.892484i | \(0.351040\pi\) | |||||||
\(992\) | 5.82159e57 | 0.215310 | ||||||||
\(993\) | 2.37504e58 | 0.861313 | ||||||||
\(994\) | −1.00675e58 | −0.358002 | ||||||||
\(995\) | −2.52933e57 | −0.0881975 | ||||||||
\(996\) | 1.28884e58 | 0.440698 | ||||||||
\(997\) | 1.65650e58 | 0.555439 | 0.277719 | − | 0.960662i | \(-0.410421\pi\) | ||||
0.277719 | + | 0.960662i | \(0.410421\pi\) | |||||||
\(998\) | −1.51183e58 | −0.497116 | ||||||||
\(999\) | −7.05255e57 | −0.227415 |
(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 | 3.40.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 9.40.a.c.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.40.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.40.a.c.1.2 | 3 | 3.2 | odd | 2 |