Newspace parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(30.1683633611\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
Defining polynomial: |
\( x^{4} - 29258x^{2} + 97377280 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{10}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(159.463\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4783.90 | 1.65172 | 0.825861 | − | 0.563873i | \(-0.190689\pi\) | ||||
0.825861 | + | 0.563873i | \(0.190689\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.44971e7 | 1.72819 | ||||||||
\(5\) | 1.42520e8 | 1.30533 | 0.652663 | − | 0.757648i | \(-0.273652\pi\) | ||||
0.652663 | + | 0.757648i | \(0.273652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.49474e9 | 1.24146 | 0.620732 | − | 0.784023i | \(-0.286835\pi\) | ||||
0.620732 | + | 0.784023i | \(0.286835\pi\) | |||||||
\(8\) | 2.92224e10 | 1.20276 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.81799e11 | 2.15604 | ||||||||
\(11\) | −6.56843e11 | −0.694138 | −0.347069 | − | 0.937840i | \(-0.612823\pi\) | ||||
−0.347069 | + | 0.937840i | \(0.612823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03084e13 | −1.59529 | −0.797647 | − | 0.603125i | \(-0.793922\pi\) | ||||
−0.797647 | + | 0.603125i | \(0.793922\pi\) | |||||||
\(14\) | 3.10702e13 | 2.05056 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.81865e13 | 0.258445 | ||||||||
\(17\) | 2.36156e14 | 1.67123 | 0.835617 | − | 0.549313i | \(-0.185110\pi\) | ||||
0.835617 | + | 0.549313i | \(0.185110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.53329e14 | 1.08973 | 0.544863 | − | 0.838525i | \(-0.316582\pi\) | ||||
0.544863 | + | 0.838525i | \(0.316582\pi\) | |||||||
\(20\) | 2.06612e15 | 2.25585 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.14227e15 | −1.14652 | ||||||||
\(23\) | 3.36472e15 | 0.736341 | 0.368171 | − | 0.929758i | \(-0.379984\pi\) | ||||
0.368171 | + | 0.929758i | \(0.379984\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.39088e15 | 0.703878 | ||||||||
\(26\) | −4.93141e16 | −2.63498 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.41548e16 | 2.14548 | ||||||||
\(29\) | −8.75953e15 | −0.133323 | −0.0666613 | − | 0.997776i | \(-0.521235\pi\) | ||||
−0.0666613 | + | 0.997776i | \(0.521235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.61750e17 | −1.14336 | −0.571681 | − | 0.820476i | \(-0.693709\pi\) | ||||
−0.571681 | + | 0.820476i | \(0.693709\pi\) | |||||||
\(32\) | −1.58133e17 | −0.775884 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.12975e18 | 2.76041 | ||||||||
\(35\) | 9.25627e17 | 1.62052 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42652e18 | 1.31813 | 0.659063 | − | 0.752088i | \(-0.270953\pi\) | ||||
0.659063 | + | 0.752088i | \(0.270953\pi\) | |||||||
\(38\) | 2.64707e18 | 1.79992 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.16476e18 | 1.57000 | ||||||||
\(41\) | −4.86336e18 | −1.38014 | −0.690069 | − | 0.723744i | \(-0.742420\pi\) | ||||
−0.690069 | + | 0.723744i | \(0.742420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.63780e18 | −0.596969 | −0.298485 | − | 0.954414i | \(-0.596481\pi\) | ||||
−0.298485 | + | 0.954414i | \(0.596481\pi\) | |||||||
\(44\) | −9.52231e18 | −1.19960 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.60965e19 | 1.21623 | ||||||||
\(47\) | −1.28817e19 | −0.760062 | −0.380031 | − | 0.924974i | \(-0.624087\pi\) | ||||
−0.380031 | + | 0.924974i | \(0.624087\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.48129e19 | 0.541234 | ||||||||
\(50\) | 4.01411e19 | 1.16261 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.49441e20 | −2.75697 | ||||||||
\(53\) | 1.00229e19 | 0.148533 | 0.0742664 | − | 0.997238i | \(-0.476338\pi\) | ||||
0.0742664 | + | 0.997238i | \(0.476338\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.36129e19 | −0.906077 | ||||||||
\(56\) | 1.89792e20 | 1.49319 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.19047e19 | −0.220212 | ||||||||
\(59\) | 1.29320e19 | 0.0558301 | 0.0279150 | − | 0.999610i | \(-0.491113\pi\) | ||||
0.0279150 | + | 0.999610i | \(0.491113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.60482e20 | 0.472207 | 0.236104 | − | 0.971728i | \(-0.424130\pi\) | ||||
0.236104 | + | 0.971728i | \(0.424130\pi\) | |||||||
\(62\) | −7.73794e20 | −1.88852 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.09050e20 | −1.53999 | ||||||||
\(65\) | −1.46914e21 | −2.08238 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50743e20 | 0.350856 | 0.175428 | − | 0.984492i | \(-0.443869\pi\) | ||||
0.175428 | + | 0.984492i | \(0.443869\pi\) | |||||||
\(68\) | 3.42358e21 | 2.88821 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.42811e21 | 2.67664 | ||||||||
\(71\) | −2.05647e21 | −1.05597 | −0.527985 | − | 0.849254i | \(-0.677052\pi\) | ||||
−0.527985 | + | 0.849254i | \(0.677052\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.56238e20 | −0.356741 | −0.178370 | − | 0.983963i | \(-0.557083\pi\) | ||||
−0.178370 | + | 0.983963i | \(0.557083\pi\) | |||||||
\(74\) | 6.82431e21 | 2.17718 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.02166e21 | 1.88325 | ||||||||
\(77\) | −4.26602e21 | −0.861747 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.09106e21 | −0.615353 | −0.307677 | − | 0.951491i | \(-0.599551\pi\) | ||||
−0.307677 | + | 0.951491i | \(0.599551\pi\) | |||||||
\(80\) | 2.59193e21 | 0.337356 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.32658e22 | −2.27960 | ||||||||
\(83\) | −1.62083e22 | −1.38146 | −0.690730 | − | 0.723113i | \(-0.742711\pi\) | ||||
−0.690730 | + | 0.723113i | \(0.742711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.36569e22 | 2.18151 | ||||||||
\(86\) | −1.74029e22 | −0.986028 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.91945e22 | −0.834884 | ||||||||
\(89\) | −2.59976e21 | −0.0992997 | −0.0496499 | − | 0.998767i | \(-0.515811\pi\) | ||||
−0.0496499 | + | 0.998767i | \(0.515811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.69501e22 | −1.98050 | ||||||||
\(92\) | 4.87787e22 | 1.27254 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.16249e22 | −1.25541 | ||||||||
\(95\) | 7.88602e22 | 1.42245 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.98925e22 | 0.424314 | 0.212157 | − | 0.977236i | \(-0.431951\pi\) | ||||
0.212157 | + | 0.977236i | \(0.431951\pi\) | |||||||
\(98\) | 7.08634e22 | 0.893968 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.21643e23 | 1.21643 | ||||||||
\(101\) | −1.72257e23 | −1.53632 | −0.768159 | − | 0.640259i | \(-0.778827\pi\) | ||||
−0.768159 | + | 0.640259i | \(0.778827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.51134e23 | 1.07580 | 0.537902 | − | 0.843007i | \(-0.319217\pi\) | ||||
0.537902 | + | 0.843007i | \(0.319217\pi\) | |||||||
\(104\) | −3.01234e23 | −1.91876 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.79487e22 | 0.245335 | ||||||||
\(107\) | 3.38525e23 | 1.55481 | 0.777405 | − | 0.629000i | \(-0.216536\pi\) | ||||
0.777405 | + | 0.629000i | \(0.216536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.51292e22 | −0.0561579 | −0.0280789 | − | 0.999606i | \(-0.508939\pi\) | ||||
−0.0280789 | + | 0.999606i | \(0.508939\pi\) | |||||||
\(110\) | −4.47835e23 | −1.49659 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.18116e23 | 0.320851 | ||||||||
\(113\) | 2.35991e23 | 0.578753 | 0.289377 | − | 0.957215i | \(-0.406552\pi\) | ||||
0.289377 | + | 0.957215i | \(0.406552\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.79539e23 | 0.961166 | ||||||||
\(116\) | −1.26988e23 | −0.230406 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.18655e22 | 0.0922158 | ||||||||
\(119\) | 1.53377e24 | 2.07478 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.63987e23 | −0.518173 | ||||||||
\(122\) | 7.67728e23 | 0.779955 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.34490e24 | −1.97595 | ||||||||
\(125\) | −5.03100e23 | −0.386536 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.15026e24 | 0.736295 | 0.368147 | − | 0.929767i | \(-0.379992\pi\) | ||||
0.368147 | + | 0.929767i | \(0.379992\pi\) | |||||||
\(128\) | −3.02229e24 | −1.76775 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.02822e24 | −3.43951 | ||||||||
\(131\) | −2.28724e24 | −1.02493 | −0.512463 | − | 0.858709i | \(-0.671267\pi\) | ||||
−0.512463 | + | 0.858709i | \(0.671267\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.59373e24 | 1.35285 | ||||||||
\(134\) | 1.67792e24 | 0.579517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.90105e24 | 2.01010 | ||||||||
\(137\) | −6.77439e24 | −1.81378 | −0.906888 | − | 0.421372i | \(-0.861549\pi\) | ||||
−0.906888 | + | 0.421372i | \(0.861549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.54141e24 | 0.575976 | 0.287988 | − | 0.957634i | \(-0.407014\pi\) | ||||
0.287988 | + | 0.957634i | \(0.407014\pi\) | |||||||
\(140\) | 1.34189e25 | 2.80056 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.83795e24 | −1.74417 | ||||||||
\(143\) | 6.77097e24 | 1.10735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.24840e24 | −0.174030 | ||||||||
\(146\) | −4.57455e24 | −0.589237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.06803e25 | 2.27797 | ||||||||
\(149\) | −5.05631e24 | −0.515456 | −0.257728 | − | 0.966217i | \(-0.582974\pi\) | ||||
−0.257728 | + | 0.966217i | \(0.582974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.95057e25 | 1.70579 | 0.852897 | − | 0.522079i | \(-0.174843\pi\) | ||||
0.852897 | + | 0.522079i | \(0.174843\pi\) | |||||||
\(152\) | 1.61696e25 | 1.31068 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.04082e25 | −1.42337 | ||||||||
\(155\) | −2.30525e25 | −1.49246 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.88837e25 | 1.05497 | 0.527487 | − | 0.849563i | \(-0.323134\pi\) | ||||
0.527487 | + | 0.849563i | \(0.323134\pi\) | |||||||
\(158\) | −1.95712e25 | −1.01639 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.25370e25 | −1.01278 | ||||||||
\(161\) | 2.18530e25 | 0.914141 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.04668e25 | −1.10578 | −0.552891 | − | 0.833253i | \(-0.686475\pi\) | ||||
−0.552891 | + | 0.833253i | \(0.686475\pi\) | |||||||
\(164\) | −7.05046e25 | −2.38514 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.75387e25 | −2.28179 | ||||||||
\(167\) | −1.11101e24 | −0.0305127 | −0.0152563 | − | 0.999884i | \(-0.504856\pi\) | ||||
−0.0152563 | + | 0.999884i | \(0.504856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.45082e25 | 1.54496 | ||||||||
\(170\) | 1.61011e26 | 3.60324 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.27376e25 | −1.03168 | ||||||||
\(173\) | 2.97282e25 | 0.544049 | 0.272025 | − | 0.962290i | \(-0.412307\pi\) | ||||
0.272025 | + | 0.962290i | \(0.412307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.44966e25 | 0.873840 | ||||||||
\(176\) | −1.19457e25 | −0.179397 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.24370e25 | −0.164016 | ||||||||
\(179\) | 3.56213e25 | 0.440453 | 0.220227 | − | 0.975449i | \(-0.429320\pi\) | ||||
0.220227 | + | 0.975449i | \(0.429320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.89955e25 | −0.315520 | −0.157760 | − | 0.987478i | \(-0.550427\pi\) | ||||
−0.157760 | + | 0.987478i | \(0.550427\pi\) | |||||||
\(182\) | −3.20282e26 | −3.27124 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.83252e25 | 0.885645 | ||||||||
\(185\) | 2.03306e26 | 1.72059 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.55118e26 | −1.16007 | ||||||||
\(188\) | −1.86748e26 | −1.31353 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.77259e26 | 2.34949 | ||||||||
\(191\) | −1.36977e26 | −0.803090 | −0.401545 | − | 0.915839i | \(-0.631527\pi\) | ||||
−0.401545 | + | 0.915839i | \(0.631527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.06538e25 | 0.471495 | 0.235747 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235747 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(194\) | 1.43003e26 | 0.700848 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14744e26 | 0.935354 | ||||||||
\(197\) | 8.23482e25 | 0.338292 | 0.169146 | − | 0.985591i | \(-0.445899\pi\) | ||||
0.169146 | + | 0.985591i | \(0.445899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.07308e26 | 1.48975 | 0.744874 | − | 0.667205i | \(-0.232510\pi\) | ||||
0.744874 | + | 0.667205i | \(0.232510\pi\) | |||||||
\(200\) | 2.45201e26 | 0.846600 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.24061e26 | −2.53757 | ||||||||
\(203\) | −5.68908e25 | −0.165515 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.93124e26 | −1.80153 | ||||||||
\(206\) | 7.23008e26 | 1.77693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.87473e26 | −0.412296 | ||||||||
\(209\) | −3.63450e26 | −0.756419 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.71522e26 | −0.506474 | −0.253237 | − | 0.967404i | \(-0.581495\pi\) | ||||
−0.253237 | + | 0.967404i | \(0.581495\pi\) | |||||||
\(212\) | 1.45303e26 | 0.256693 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.61947e27 | 2.56812 | ||||||||
\(215\) | −5.18458e26 | −0.779240 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.05052e27 | −1.41944 | ||||||||
\(218\) | −7.23765e25 | −0.0927572 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.35712e27 | −1.56587 | ||||||||
\(221\) | −2.43438e27 | −2.66611 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.26296e26 | −0.322185 | −0.161093 | − | 0.986939i | \(-0.551502\pi\) | ||||
−0.161093 | + | 0.986939i | \(0.551502\pi\) | |||||||
\(224\) | −1.02703e27 | −0.963233 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.12896e27 | 0.955940 | ||||||||
\(227\) | 2.34616e27 | 1.88826 | 0.944128 | − | 0.329580i | \(-0.106907\pi\) | ||||
0.944128 | + | 0.329580i | \(0.106907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.12251e27 | 0.816739 | 0.408370 | − | 0.912817i | \(-0.366097\pi\) | ||||
0.408370 | + | 0.912817i | \(0.366097\pi\) | |||||||
\(230\) | 2.29406e27 | 1.58758 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.55974e26 | −0.160356 | ||||||||
\(233\) | 1.38324e27 | 0.824719 | 0.412359 | − | 0.911021i | \(-0.364705\pi\) | ||||
0.412359 | + | 0.911021i | \(0.364705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.83590e27 | −0.992129 | ||||||||
\(236\) | 1.87477e26 | 0.0964849 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.33742e27 | 3.42696 | ||||||||
\(239\) | 3.66637e26 | 0.163178 | 0.0815888 | − | 0.996666i | \(-0.474001\pi\) | ||||
0.0815888 | + | 0.996666i | \(0.474001\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.56991e27 | 0.634862 | 0.317431 | − | 0.948281i | \(-0.397180\pi\) | ||||
0.317431 | + | 0.948281i | \(0.397180\pi\) | |||||||
\(242\) | −2.21967e27 | −0.855878 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.32652e27 | 0.816062 | ||||||||
\(245\) | 2.11113e27 | 0.706487 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.70391e27 | −1.73843 | ||||||||
\(248\) | −4.72671e27 | −1.37520 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.40678e27 | −0.638450 | ||||||||
\(251\) | −3.08385e27 | −0.781349 | −0.390674 | − | 0.920529i | \(-0.627758\pi\) | ||||
−0.390674 | + | 0.920529i | \(0.627758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.21009e27 | −0.511122 | ||||||||
\(254\) | 5.50271e27 | 1.21615 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.83268e27 | −1.37985 | ||||||||
\(257\) | −1.78781e27 | −0.345216 | −0.172608 | − | 0.984991i | \(-0.555219\pi\) | ||||
−0.172608 | + | 0.984991i | \(0.555219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.26485e27 | 1.63641 | ||||||||
\(260\) | −2.12983e28 | −3.59874 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.09419e28 | −1.69289 | ||||||||
\(263\) | 1.23162e28 | 1.82384 | 0.911921 | − | 0.410367i | \(-0.134599\pi\) | ||||
0.911921 | + | 0.410367i | \(0.134599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.42846e27 | 0.193884 | ||||||||
\(266\) | 1.71920e28 | 2.23454 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.08476e27 | 0.606345 | ||||||||
\(269\) | 5.19149e27 | 0.593118 | 0.296559 | − | 0.955015i | \(-0.404161\pi\) | ||||
0.296559 | + | 0.955015i | \(0.404161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.52253e27 | 0.474498 | 0.237249 | − | 0.971449i | \(-0.423754\pi\) | ||||
0.237249 | + | 0.971449i | \(0.423754\pi\) | |||||||
\(272\) | 4.29485e27 | 0.431923 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.24080e28 | −2.99585 | ||||||||
\(275\) | −5.51149e27 | −0.488589 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.44055e27 | −0.606859 | −0.303429 | − | 0.952854i | \(-0.598132\pi\) | ||||
−0.303429 | + | 0.952854i | \(0.598132\pi\) | |||||||
\(278\) | 1.21578e28 | 0.951353 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.70490e28 | 1.94910 | ||||||||
\(281\) | 2.32245e27 | 0.160629 | 0.0803145 | − | 0.996770i | \(-0.474408\pi\) | ||||
0.0803145 | + | 0.996770i | \(0.474408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.10788e27 | 0.453102 | 0.226551 | − | 0.973999i | \(-0.427255\pi\) | ||||
0.226551 | + | 0.973999i | \(0.427255\pi\) | |||||||
\(284\) | −2.98128e28 | −1.82491 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.23916e28 | 1.82904 | ||||||||
\(287\) | −3.15863e28 | −1.71339 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.58023e28 | 1.79302 | ||||||||
\(290\) | −5.97224e27 | −0.287449 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.38627e28 | −0.616515 | ||||||||
\(293\) | −1.07564e28 | −0.459928 | −0.229964 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229964 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.84307e27 | 0.0728765 | ||||||||
\(296\) | 4.16862e28 | 1.58540 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.41889e28 | −0.851391 | ||||||||
\(299\) | −3.46847e28 | −1.17468 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.36266e28 | −0.741116 | ||||||||
\(302\) | 9.33133e28 | 2.81750 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00631e28 | 0.281634 | ||||||||
\(305\) | 2.28718e28 | 0.616384 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.66353e28 | 1.16580 | 0.582899 | − | 0.812545i | \(-0.301918\pi\) | ||||
0.582899 | + | 0.812545i | \(0.301918\pi\) | |||||||
\(308\) | −6.18449e28 | −1.48926 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.10281e29 | −2.46513 | ||||||||
\(311\) | −1.35856e28 | −0.292639 | −0.146320 | − | 0.989237i | \(-0.546743\pi\) | ||||
−0.146320 | + | 0.989237i | \(0.546743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.25524e28 | 0.451267 | 0.225633 | − | 0.974212i | \(-0.427555\pi\) | ||||
0.225633 | + | 0.974212i | \(0.427555\pi\) | |||||||
\(314\) | 9.03379e28 | 1.74252 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.93085e28 | −1.06345 | ||||||||
\(317\) | 2.03254e28 | 0.351445 | 0.175723 | − | 0.984440i | \(-0.443774\pi\) | ||||
0.175723 | + | 0.984440i | \(0.443774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.75363e27 | 0.0925442 | ||||||||
\(320\) | −1.29557e29 | −2.01019 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.04543e29 | 1.50991 | ||||||||
\(323\) | 1.30672e29 | 1.82119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.64962e28 | −1.12289 | ||||||||
\(326\) | −1.45750e29 | −1.82645 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.42119e29 | −1.65998 | ||||||||
\(329\) | −8.36635e28 | −0.943590 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.51986e28 | −0.791020 | −0.395510 | − | 0.918462i | \(-0.629432\pi\) | ||||
−0.395510 | + | 0.918462i | \(0.629432\pi\) | |||||||
\(332\) | −2.34973e29 | −2.38742 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.31498e27 | −0.0503984 | ||||||||
\(335\) | 4.99878e28 | 0.457982 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.54497e29 | 1.32183 | 0.660916 | − | 0.750460i | \(-0.270168\pi\) | ||||
0.660916 | + | 0.750460i | \(0.270168\pi\) | |||||||
\(338\) | 3.08601e29 | 2.55185 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.87927e29 | 3.77005 | ||||||||
\(341\) | 1.06244e29 | 0.793651 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.15470e28 | −0.569542 | ||||||||
\(344\) | −1.06305e29 | −0.718013 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.42217e29 | 0.898618 | ||||||||
\(347\) | 2.64051e29 | 1.61398 | 0.806991 | − | 0.590564i | \(-0.201095\pi\) | ||||
0.806991 | + | 0.590564i | \(0.201095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.13409e29 | −0.648864 | −0.324432 | − | 0.945909i | \(-0.605173\pi\) | ||||
−0.324432 | + | 0.945909i | \(0.605173\pi\) | |||||||
\(350\) | 2.60706e29 | 1.44334 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.03868e29 | 0.538571 | ||||||||
\(353\) | −2.02443e29 | −1.01600 | −0.508000 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508000 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.93087e29 | −1.37839 | ||||||||
\(356\) | −3.76889e28 | −0.171609 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.70409e29 | 0.727506 | ||||||||
\(359\) | −3.35901e29 | −1.38875 | −0.694377 | − | 0.719612i | \(-0.744320\pi\) | ||||
−0.694377 | + | 0.719612i | \(0.744320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.83433e28 | 0.187501 | ||||||||
\(362\) | −1.38711e29 | −0.521151 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.70581e29 | −3.42268 | ||||||||
\(365\) | −1.36283e29 | −0.465664 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.32640e29 | 1.38825 | 0.694125 | − | 0.719855i | \(-0.255792\pi\) | ||||
0.694125 | + | 0.719855i | \(0.255792\pi\) | |||||||
\(368\) | 6.11924e28 | 0.190304 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.72598e29 | 2.84193 | ||||||||
\(371\) | 6.50964e28 | 0.184398 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.52581e29 | −1.73773 | −0.868866 | − | 0.495048i | \(-0.835151\pi\) | ||||
−0.868866 | + | 0.495048i | \(0.835151\pi\) | |||||||
\(374\) | −7.42068e29 | −1.91611 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.76435e29 | −0.914175 | ||||||||
\(377\) | 9.02963e28 | 0.212689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.54426e29 | −0.785551 | −0.392775 | − | 0.919634i | \(-0.628485\pi\) | ||||
−0.392775 | + | 0.919634i | \(0.628485\pi\) | |||||||
\(380\) | 1.14324e30 | 2.45826 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.55285e29 | −1.32648 | ||||||||
\(383\) | −2.02823e29 | −0.398411 | −0.199206 | − | 0.979958i | \(-0.563836\pi\) | ||||
−0.199206 | + | 0.979958i | \(0.563836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.07992e29 | −1.12486 | ||||||||
\(386\) | 4.33679e29 | 0.778779 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.33354e29 | 0.733293 | ||||||||
\(389\) | −2.72682e29 | −0.447957 | −0.223979 | − | 0.974594i | \(-0.571905\pi\) | ||||
−0.223979 | + | 0.974594i | \(0.571905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.94601e29 | 1.23060 | ||||||||
\(392\) | 4.32868e29 | 0.650977 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.93945e29 | 0.558765 | ||||||||
\(395\) | −5.83056e29 | −0.803237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.06349e29 | 0.138243 | 0.0691213 | − | 0.997608i | \(-0.477980\pi\) | ||||
0.0691213 | + | 0.997608i | \(0.477980\pi\) | |||||||
\(398\) | 1.94852e30 | 2.46065 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.52601e29 | 0.181914 | ||||||||
\(401\) | 9.48539e29 | 1.09874 | 0.549370 | − | 0.835579i | \(-0.314868\pi\) | ||||
0.549370 | + | 0.835579i | \(0.314868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.66737e30 | 1.82400 | ||||||||
\(404\) | −2.49723e30 | −2.65505 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.72160e29 | −0.273385 | ||||||||
\(407\) | −9.36997e29 | −0.914961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.99433e29 | 0.830139 | 0.415069 | − | 0.909790i | \(-0.363757\pi\) | ||||
0.415069 | + | 0.909790i | \(0.363757\pi\) | |||||||
\(410\) | −3.31584e30 | −2.97563 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.19100e30 | 1.85919 | ||||||||
\(413\) | 8.39901e28 | 0.0693111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.30999e30 | −1.80326 | ||||||||
\(416\) | 1.63009e30 | 1.23776 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.73871e30 | −1.24940 | ||||||||
\(419\) | 5.82139e29 | 0.406973 | 0.203487 | − | 0.979078i | \(-0.434773\pi\) | ||||
0.203487 | + | 0.979078i | \(0.434773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.99599e29 | −0.595394 | −0.297697 | − | 0.954660i | \(-0.596219\pi\) | ||||
−0.297697 | + | 0.954660i | \(0.596219\pi\) | |||||||
\(422\) | −1.29894e30 | −0.836555 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.92894e29 | 0.178650 | ||||||||
\(425\) | 1.98156e30 | 1.17635 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04229e30 | 0.586228 | ||||||||
\(428\) | 4.90763e30 | 2.68700 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.48025e30 | −1.28709 | ||||||||
\(431\) | 1.72002e30 | 0.869051 | 0.434525 | − | 0.900660i | \(-0.356916\pi\) | ||||
0.434525 | + | 0.900660i | \(0.356916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.04694e30 | 1.93872 | 0.969362 | − | 0.245635i | \(-0.0789965\pi\) | ||||
0.969362 | + | 0.245635i | \(0.0789965\pi\) | |||||||
\(434\) | −5.02559e30 | −2.34453 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19329e29 | −0.0970513 | ||||||||
\(437\) | 1.86180e30 | 0.802410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.61226e30 | 0.659317 | 0.329659 | − | 0.944100i | \(-0.393066\pi\) | ||||
0.329659 | + | 0.944100i | \(0.393066\pi\) | |||||||
\(440\) | −2.73559e30 | −1.08980 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.16458e31 | −4.40367 | ||||||||
\(443\) | 4.83888e30 | 1.78280 | 0.891398 | − | 0.453221i | \(-0.149725\pi\) | ||||
0.891398 | + | 0.453221i | \(0.149725\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.70516e29 | −0.129619 | ||||||||
\(446\) | −1.56097e30 | −0.532161 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.90404e30 | −1.91184 | ||||||||
\(449\) | −4.75344e30 | −1.50029 | −0.750145 | − | 0.661273i | \(-0.770016\pi\) | ||||
−0.750145 | + | 0.661273i | \(0.770016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.19447e30 | 0.958005 | ||||||||
\(452\) | 3.42118e30 | 1.00019 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.12238e31 | 3.11887 | ||||||||
\(455\) | −9.54169e30 | −2.58520 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.88472e30 | −1.77358 | −0.886788 | − | 0.462176i | \(-0.847069\pi\) | ||||
−0.886788 | + | 0.462176i | \(0.847069\pi\) | |||||||
\(458\) | 5.36999e30 | 1.34903 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.95191e30 | 1.66108 | ||||||||
\(461\) | −7.02180e30 | −1.63639 | −0.818197 | − | 0.574938i | \(-0.805026\pi\) | ||||
−0.818197 | + | 0.574938i | \(0.805026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.31929e29 | 0.0957703 | 0.0478852 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478852 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(464\) | −1.59305e29 | −0.0344566 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.61730e30 | 1.36221 | ||||||||
\(467\) | 8.75520e30 | 1.75842 | 0.879208 | − | 0.476437i | \(-0.158072\pi\) | ||||
0.879208 | + | 0.476437i | \(0.158072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.27799e30 | 0.435576 | ||||||||
\(470\) | −8.78275e30 | −1.63872 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.77904e29 | 0.0671504 | ||||||||
\(473\) | 2.38947e30 | 0.414379 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.64292e30 | 0.767034 | ||||||||
\(476\) | 2.22353e31 | 3.58560 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.75395e30 | 0.269524 | ||||||||
\(479\) | −1.07807e31 | −1.61729 | −0.808647 | − | 0.588294i | \(-0.799800\pi\) | ||||
−0.808647 | + | 0.588294i | \(0.799800\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.47050e31 | −2.10280 | ||||||||
\(482\) | 7.51030e30 | 1.04862 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.72647e30 | −0.895500 | ||||||||
\(485\) | 4.26026e30 | 0.553868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.49272e30 | 1.17708 | 0.588542 | − | 0.808466i | \(-0.299702\pi\) | ||||
0.588542 | + | 0.808466i | \(0.299702\pi\) | |||||||
\(488\) | 4.68966e30 | 0.567954 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00994e31 | 1.16692 | ||||||||
\(491\) | 5.62204e30 | 0.634537 | 0.317269 | − | 0.948336i | \(-0.397234\pi\) | ||||
0.317269 | + | 0.948336i | \(0.397234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.06862e30 | −0.222813 | ||||||||
\(494\) | −2.72869e31 | −2.87141 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.94166e30 | −0.295497 | ||||||||
\(497\) | −1.33562e31 | −1.31095 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.40826e29 | −0.0131986 | −0.00659928 | − | 0.999978i | \(-0.502101\pi\) | ||||
−0.00659928 | + | 0.999978i | \(0.502101\pi\) | |||||||
\(500\) | −7.29349e30 | −0.668006 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.47528e31 | −1.29057 | ||||||||
\(503\) | 7.85202e30 | 0.671351 | 0.335675 | − | 0.941978i | \(-0.391035\pi\) | ||||
0.335675 | + | 0.941978i | \(0.391035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.45500e31 | −2.00540 | ||||||||
\(506\) | −1.05729e31 | −0.844232 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.66754e31 | 1.27246 | ||||||||
\(509\) | −6.86794e30 | −0.512356 | −0.256178 | − | 0.966630i | \(-0.582463\pi\) | ||||
−0.256178 | + | 0.966630i | \(0.582463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.21052e30 | −0.442881 | ||||||||
\(512\) | −7.33402e30 | −0.511373 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.55272e30 | −0.570202 | ||||||||
\(515\) | 2.15395e31 | 1.40428 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.46127e30 | 0.527588 | ||||||||
\(518\) | 4.43221e31 | 2.70289 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.29318e31 | −2.50461 | ||||||||
\(521\) | 2.37730e31 | 1.35660 | 0.678299 | − | 0.734786i | \(-0.262718\pi\) | ||||
0.678299 | + | 0.734786i | \(0.262718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.46642e31 | −0.800733 | −0.400366 | − | 0.916355i | \(-0.631117\pi\) | ||||
−0.400366 | + | 0.916355i | \(0.631117\pi\) | |||||||
\(524\) | −3.31584e31 | −1.77127 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.89197e31 | 3.01248 | ||||||||
\(527\) | −3.81982e31 | −1.91083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.55911e30 | −0.457802 | ||||||||
\(530\) | 6.83363e30 | 0.320243 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.20986e31 | 2.33799 | ||||||||
\(533\) | 5.01332e31 | 2.20172 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.82464e31 | 2.02954 | ||||||||
\(536\) | 1.02496e31 | 0.421997 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.48356e31 | 0.979666 | ||||||||
\(539\) | −9.72975e30 | −0.375691 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.35565e31 | −1.61170 | −0.805851 | − | 0.592119i | \(-0.798292\pi\) | ||||
−0.805851 | + | 0.592119i | \(0.798292\pi\) | |||||||
\(542\) | 2.16353e31 | 0.783740 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.73441e31 | −1.29668 | ||||||||
\(545\) | −2.15620e30 | −0.0733044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.29429e31 | 0.747816 | 0.373908 | − | 0.927466i | \(-0.378018\pi\) | ||||
0.373908 | + | 0.927466i | \(0.378018\pi\) | |||||||
\(548\) | −9.82089e31 | −3.13455 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.63664e31 | −0.807013 | ||||||||
\(551\) | −4.84690e30 | −0.145285 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.65704e31 | −0.763939 | ||||||||
\(554\) | −3.55948e31 | −1.00236 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.68430e31 | 0.995395 | ||||||||
\(557\) | 3.17560e29 | 0.00840410 | 0.00420205 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420205 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.74998e31 | 0.952341 | ||||||||
\(560\) | 1.68339e31 | 0.418815 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.11104e31 | 0.265315 | ||||||||
\(563\) | −2.42453e31 | −0.567260 | −0.283630 | − | 0.958934i | \(-0.591539\pi\) | ||||
−0.283630 | + | 0.958934i | \(0.591539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.36333e31 | 0.755462 | ||||||||
\(566\) | 3.40034e31 | 0.748399 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00949e31 | −1.27008 | ||||||||
\(569\) | −1.73034e31 | −0.358376 | −0.179188 | − | 0.983815i | \(-0.557347\pi\) | ||||
−0.179188 | + | 0.983815i | \(0.557347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.56501e31 | 0.311317 | 0.155658 | − | 0.987811i | \(-0.450250\pi\) | ||||
0.155658 | + | 0.987811i | \(0.450250\pi\) | |||||||
\(572\) | 9.81593e31 | 1.91372 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.51106e32 | −2.83005 | ||||||||
\(575\) | 2.82330e31 | 0.518295 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.29233e30 | 0.0404348 | 0.0202174 | − | 0.999796i | \(-0.493564\pi\) | ||||
0.0202174 | + | 0.999796i | \(0.493564\pi\) | |||||||
\(578\) | 1.71275e32 | 2.96158 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.80982e31 | −0.300756 | ||||||||
\(581\) | −1.05268e32 | −1.71503 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.58350e30 | −0.103102 | ||||||||
\(584\) | −2.79435e31 | −0.429075 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.14576e31 | −0.759674 | ||||||||
\(587\) | 7.82714e30 | 0.113309 | 0.0566545 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566545 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.95008e31 | −1.24595 | ||||||||
\(590\) | 8.81704e30 | 0.120372 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.59433e31 | 0.340664 | ||||||||
\(593\) | −5.20855e31 | −0.670792 | −0.335396 | − | 0.942077i | \(-0.608870\pi\) | ||||
−0.335396 | + | 0.942077i | \(0.608870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.18593e32 | 2.70826 | ||||||||
\(596\) | −7.33018e31 | −0.890805 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.65928e32 | −1.94025 | ||||||||
\(599\) | −2.46078e31 | −0.282270 | −0.141135 | − | 0.989990i | \(-0.545075\pi\) | ||||
−0.141135 | + | 0.989990i | \(0.545075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.01876e31 | −0.664432 | −0.332216 | − | 0.943203i | \(-0.607796\pi\) | ||||
−0.332216 | + | 0.943203i | \(0.607796\pi\) | |||||||
\(602\) | −1.13027e32 | −1.22412 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.82776e32 | 2.94793 | ||||||||
\(605\) | −6.61273e31 | −0.676385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.78920e32 | 1.76193 | 0.880964 | − | 0.473183i | \(-0.156895\pi\) | ||||
0.880964 | + | 0.473183i | \(0.156895\pi\) | |||||||
\(608\) | −8.74994e31 | −0.845501 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.09416e32 | 1.01810 | ||||||||
\(611\) | 1.32789e32 | 1.21252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.26160e32 | −1.10950 | −0.554748 | − | 0.832018i | \(-0.687185\pi\) | ||||
−0.554748 | + | 0.832018i | \(0.687185\pi\) | |||||||
\(614\) | 2.23099e32 | 1.92558 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.24663e32 | −1.03648 | ||||||||
\(617\) | 1.03069e32 | 0.841101 | 0.420550 | − | 0.907269i | \(-0.361837\pi\) | ||||
0.420550 | + | 0.907269i | \(0.361837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.21348e32 | 0.954096 | 0.477048 | − | 0.878877i | \(-0.341707\pi\) | ||||
0.477048 | + | 0.878877i | \(0.341707\pi\) | |||||||
\(620\) | −3.34194e32 | −2.57925 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.49919e31 | −0.483359 | ||||||||
\(623\) | −1.68848e31 | −0.123277 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.71729e32 | −1.20843 | ||||||||
\(626\) | 1.07889e32 | 0.745368 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.73759e32 | 1.82319 | ||||||||
\(629\) | 3.36881e32 | 2.20290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50812e31 | 0.221175 | 0.110588 | − | 0.993866i | \(-0.464727\pi\) | ||||
0.110588 | + | 0.993866i | \(0.464727\pi\) | |||||||
\(632\) | −1.19550e32 | −0.740125 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.72346e31 | 0.580490 | ||||||||
\(635\) | 1.63934e32 | 0.961105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52697e32 | −0.863427 | ||||||||
\(638\) | 2.75248e31 | 0.152857 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.30736e32 | −2.30750 | ||||||||
\(641\) | −1.36428e32 | −0.717855 | −0.358927 | − | 0.933366i | \(-0.616857\pi\) | ||||
−0.358927 | + | 0.933366i | \(0.616857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.01130e31 | 0.406702 | 0.203351 | − | 0.979106i | \(-0.434817\pi\) | ||||
0.203351 | + | 0.979106i | \(0.434817\pi\) | |||||||
\(644\) | 3.16805e32 | 1.57981 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.25123e32 | 3.00809 | ||||||||
\(647\) | 1.62553e32 | 0.768416 | 0.384208 | − | 0.923246i | \(-0.374474\pi\) | ||||
0.384208 | + | 0.923246i | \(0.374474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.49431e30 | −0.0387538 | ||||||||
\(650\) | −4.13789e32 | −1.85471 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.41680e32 | −1.91100 | ||||||||
\(653\) | −4.57884e32 | −1.94650 | −0.973249 | − | 0.229751i | \(-0.926209\pi\) | ||||
−0.973249 | + | 0.229751i | \(0.926209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.25977e32 | −1.33786 | ||||||||
\(656\) | −8.84474e31 | −0.356690 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.00238e32 | −1.55855 | ||||||||
\(659\) | −4.46949e32 | −1.71031 | −0.855157 | − | 0.518369i | \(-0.826539\pi\) | ||||
−0.855157 | + | 0.518369i | \(0.826539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.68932e32 | −0.624301 | −0.312151 | − | 0.950033i | \(-0.601049\pi\) | ||||
−0.312151 | + | 0.950033i | \(0.601049\pi\) | |||||||
\(662\) | −3.59742e32 | −1.30655 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.73644e32 | −1.66157 | ||||||||
\(665\) | 5.12176e32 | 1.76592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.94734e31 | −0.0981709 | ||||||||
\(668\) | −1.61065e31 | −0.0527316 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.39136e32 | 0.756459 | ||||||||
\(671\) | −1.05411e32 | −0.327777 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.31206e32 | 1.59621 | 0.798104 | − | 0.602519i | \(-0.205836\pi\) | ||||
0.798104 | + | 0.602519i | \(0.205836\pi\) | |||||||
\(674\) | 7.39098e32 | 2.18330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.35181e32 | 2.66998 | ||||||||
\(677\) | 1.10916e32 | 0.311333 | 0.155666 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155666 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94144e32 | 0.526770 | ||||||||
\(680\) | 9.83534e32 | 2.62384 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.08261e32 | 1.31089 | ||||||||
\(683\) | −4.30126e32 | −1.09083 | −0.545415 | − | 0.838166i | \(-0.683628\pi\) | ||||
−0.545415 | + | 0.838166i | \(0.683628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.65483e32 | −2.36757 | ||||||||
\(686\) | −3.90113e32 | −0.940725 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.61588e31 | −0.154284 | ||||||||
\(689\) | −1.03320e32 | −0.236954 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.48977e32 | −0.330461 | −0.165231 | − | 0.986255i | \(-0.552837\pi\) | ||||
−0.165231 | + | 0.986255i | \(0.552837\pi\) | |||||||
\(692\) | 4.30972e32 | 0.940219 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.26319e33 | 2.66585 | ||||||||
\(695\) | 3.62200e32 | 0.751837 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14851e33 | −2.30653 | ||||||||
\(698\) | −5.42535e32 | −1.07174 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.90042e32 | 1.51016 | ||||||||
\(701\) | 1.71421e32 | 0.322334 | 0.161167 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161167 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.89333e32 | 1.43640 | ||||||||
\(704\) | 5.97103e32 | 1.06897 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.68467e32 | −1.67815 | ||||||||
\(707\) | −1.11876e33 | −1.90728 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.24223e32 | 0.205008 | 0.102504 | − | 0.994733i | \(-0.467315\pi\) | ||||
0.102504 | + | 0.994733i | \(0.467315\pi\) | |||||||
\(710\) | −1.40210e33 | −2.27671 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.59711e31 | −0.119434 | ||||||||
\(713\) | −5.44243e32 | −0.841905 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.64995e32 | 1.44546 | ||||||||
\(716\) | 5.16405e32 | 0.761186 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.60692e33 | −2.29384 | ||||||||
\(719\) | 1.12436e33 | 1.57951 | 0.789753 | − | 0.613425i | \(-0.210209\pi\) | ||||
0.789753 | + | 0.613425i | \(0.210209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.81574e32 | 1.33557 | ||||||||
\(722\) | 2.31269e32 | 0.309699 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.20350e32 | −0.545277 | ||||||||
\(725\) | −7.35002e31 | −0.0938429 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.20007e32 | 0.643225 | 0.321613 | − | 0.946871i | \(-0.395775\pi\) | ||||
0.321613 | + | 0.946871i | \(0.395775\pi\) | |||||||
\(728\) | −1.95644e33 | −2.38208 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.51962e32 | −0.769147 | ||||||||
\(731\) | −8.59091e32 | −0.997675 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.16237e33 | −1.30812 | −0.654060 | − | 0.756443i | \(-0.726935\pi\) | ||||
−0.654060 | + | 0.756443i | \(0.726935\pi\) | |||||||
\(734\) | 2.06971e33 | 2.29300 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.32073e32 | −0.571316 | ||||||||
\(737\) | −2.30383e32 | −0.243543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.47548e33 | −1.51190 | −0.755950 | − | 0.654629i | \(-0.772825\pi\) | ||||
−0.755950 | + | 0.654629i | \(0.772825\pi\) | |||||||
\(740\) | 2.94735e33 | 2.97349 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.11415e32 | 0.304575 | ||||||||
\(743\) | 1.35734e33 | 1.30712 | 0.653561 | − | 0.756874i | \(-0.273274\pi\) | ||||
0.653561 | + | 0.756874i | \(0.273274\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.20623e32 | −0.672839 | ||||||||
\(746\) | −3.12188e33 | −2.87025 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.24876e33 | −2.00481 | ||||||||
\(749\) | 2.19863e33 | 1.93024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.72188e33 | 1.46603 | 0.733016 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733016 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(752\) | −2.34273e32 | −0.196434 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.31968e32 | 0.351303 | ||||||||
\(755\) | 2.77994e33 | 2.22662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.32468e33 | 1.80618 | 0.903091 | − | 0.429450i | \(-0.141293\pi\) | ||||
0.903091 | + | 0.429450i | \(0.141293\pi\) | |||||||
\(758\) | −1.69554e33 | −1.29751 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.30448e33 | 1.71087 | ||||||||
\(761\) | −1.60288e33 | −1.17214 | −0.586068 | − | 0.810262i | \(-0.699325\pi\) | ||||
−0.586068 | + | 0.810262i | \(0.699325\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.82601e31 | −0.0697180 | ||||||||
\(764\) | −1.98577e33 | −1.38789 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.70285e32 | −0.658065 | ||||||||
\(767\) | −1.33308e32 | −0.0890654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94080e33 | 1.25842 | 0.629212 | − | 0.777234i | \(-0.283378\pi\) | ||||
0.629212 | + | 0.777234i | \(0.283378\pi\) | |||||||
\(770\) | −2.90857e33 | −1.85796 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.31422e33 | 0.814831 | ||||||||
\(773\) | −1.83275e33 | −1.11954 | −0.559768 | − | 0.828649i | \(-0.689110\pi\) | ||||
−0.559768 | + | 0.828649i | \(0.689110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.35722e33 | −0.804788 | ||||||||
\(776\) | 8.73529e32 | 0.510349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.30448e33 | −0.739901 | ||||||||
\(779\) | −2.69104e33 | −1.50397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.35078e33 | 0.732989 | ||||||||
\(782\) | 3.80129e33 | 2.03261 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.69394e32 | 0.139879 | ||||||||
\(785\) | 2.69130e33 | 1.37709 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.71269e32 | 0.432955 | 0.216477 | − | 0.976288i | \(-0.430543\pi\) | ||||
0.216477 | + | 0.976288i | \(0.430543\pi\) | |||||||
\(788\) | 1.19381e33 | 0.584633 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.78928e33 | −1.32672 | ||||||||
\(791\) | 1.53270e33 | 0.718502 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65430e33 | −0.753309 | ||||||||
\(794\) | 5.08762e32 | 0.228338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.90478e33 | 2.57456 | ||||||||
\(797\) | −2.50263e33 | −1.07554 | −0.537769 | − | 0.843092i | \(-0.680733\pi\) | ||||
−0.537769 | + | 0.843092i | \(0.680733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.04210e33 | −1.27024 | ||||||||
\(800\) | −1.32687e33 | −0.546128 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.53772e33 | 1.81481 | ||||||||
\(803\) | 6.28098e32 | 0.247627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.11448e33 | 1.19325 | ||||||||
\(806\) | 7.97654e33 | 3.01274 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.03376e33 | −1.84783 | ||||||||
\(809\) | −1.81340e33 | −0.656273 | −0.328136 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328136 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.10505e33 | 0.388726 | 0.194363 | − | 0.980930i | \(-0.437736\pi\) | ||||
0.194363 | + | 0.980930i | \(0.437736\pi\) | |||||||
\(812\) | −8.24752e32 | −0.286041 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.48250e33 | −1.51126 | ||||||||
\(815\) | −4.34212e33 | −1.44341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.01290e33 | −0.650532 | ||||||||
\(818\) | 4.30280e33 | 1.37116 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.00483e34 | −3.11338 | ||||||||
\(821\) | −2.80900e33 | −0.858234 | −0.429117 | − | 0.903249i | \(-0.641175\pi\) | ||||
−0.429117 | + | 0.903249i | \(0.641175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.09759e33 | −1.51449 | −0.757245 | − | 0.653131i | \(-0.773455\pi\) | ||||
−0.757245 | + | 0.653131i | \(0.773455\pi\) | |||||||
\(824\) | 4.41648e33 | 1.29394 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.01800e32 | 0.114483 | ||||||||
\(827\) | −7.25325e32 | −0.203807 | −0.101904 | − | 0.994794i | \(-0.532493\pi\) | ||||
−0.101904 | + | 0.994794i | \(0.532493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.48272e33 | 0.678500 | 0.339250 | − | 0.940696i | \(-0.389827\pi\) | ||||
0.339250 | + | 0.940696i | \(0.389827\pi\) | |||||||
\(830\) | −1.10508e34 | −2.97848 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.37081e33 | 2.45674 | ||||||||
\(833\) | 3.49816e33 | 0.904528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.58341e32 | −0.0398290 | ||||||||
\(836\) | −5.26897e33 | −1.30723 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.78490e33 | 0.672207 | ||||||||
\(839\) | −6.12814e33 | −1.45904 | −0.729519 | − | 0.683961i | \(-0.760256\pi\) | ||||
−0.729519 | + | 0.683961i | \(0.760256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.23999e33 | −0.982225 | ||||||||
\(842\) | −4.30359e33 | −0.983427 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.93628e33 | −0.875283 | ||||||||
\(845\) | 9.19368e33 | 2.01668 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.01348e33 | −0.643293 | ||||||||
\(848\) | 1.82282e32 | 0.0383876 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.47959e33 | 1.94300 | ||||||||
\(851\) | 4.79983e33 | 0.970591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.01234e33 | 0.986567 | 0.493283 | − | 0.869869i | \(-0.335797\pi\) | ||||
0.493283 | + | 0.869869i | \(0.335797\pi\) | |||||||
\(854\) | 4.98620e33 | 0.968286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.89250e33 | 1.87007 | ||||||||
\(857\) | 3.25628e33 | 0.607355 | 0.303678 | − | 0.952775i | \(-0.401785\pi\) | ||||
0.303678 | + | 0.952775i | \(0.401785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.33067e33 | −0.967968 | −0.483984 | − | 0.875077i | \(-0.660811\pi\) | ||||
−0.483984 | + | 0.875077i | \(0.660811\pi\) | |||||||
\(860\) | −7.51613e33 | −1.34667 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.22841e33 | 1.43543 | ||||||||
\(863\) | −1.52320e32 | −0.0262199 | −0.0131100 | − | 0.999914i | \(-0.504173\pi\) | ||||
−0.0131100 | + | 0.999914i | \(0.504173\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.23685e33 | 0.710162 | ||||||||
\(866\) | 1.93602e34 | 3.20224 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.52295e34 | −2.45307 | ||||||||
\(869\) | 2.68718e33 | 0.427140 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.61559e33 | −0.559719 | ||||||||
\(872\) | −4.42110e32 | −0.0675447 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.90666e33 | 1.32536 | ||||||||
\(875\) | −3.26751e33 | −0.479870 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.21094e33 | −0.745454 | −0.372727 | − | 0.927941i | \(-0.621577\pi\) | ||||
−0.372727 | + | 0.927941i | \(0.621577\pi\) | |||||||
\(878\) | 7.71291e33 | 1.08901 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.70249e33 | −0.234171 | ||||||||
\(881\) | −3.11935e33 | −0.423488 | −0.211744 | − | 0.977325i | \(-0.567914\pi\) | ||||
−0.211744 | + | 0.977325i | \(0.567914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.95233e33 | −0.787298 | −0.393649 | − | 0.919261i | \(-0.628787\pi\) | ||||
−0.393649 | + | 0.919261i | \(0.628787\pi\) | |||||||
\(884\) | −3.52915e34 | −4.60754 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.31487e34 | 2.94469 | ||||||||
\(887\) | 1.22417e34 | 1.53716 | 0.768582 | − | 0.639751i | \(-0.220963\pi\) | ||||
0.768582 | + | 0.639751i | \(0.220963\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.47061e33 | 0.914084 | ||||||||
\(890\) | −1.77251e33 | −0.214094 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.73034e33 | −0.556796 | ||||||||
\(893\) | −7.12783e33 | −0.828258 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.07673e33 | 0.574935 | ||||||||
\(896\) | −1.96290e34 | −2.19460 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.27400e34 | −2.47806 | ||||||||
\(899\) | 1.41685e33 | 0.152436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.36698e33 | 0.248233 | ||||||||
\(902\) | 1.52820e34 | 1.58236 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.89622e33 | 0.696104 | ||||||||
\(905\) | −4.13242e33 | −0.411856 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.82802e34 | −1.77622 | −0.888109 | − | 0.459632i | \(-0.847981\pi\) | ||||
−0.888109 | + | 0.459632i | \(0.847981\pi\) | |||||||
\(908\) | 3.40125e34 | 3.26326 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.56465e34 | −4.27003 | ||||||||
\(911\) | 2.70847e33 | 0.250185 | 0.125093 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125093 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.06463e34 | 0.958924 | ||||||||
\(914\) | −3.29358e34 | −2.92946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.62732e34 | 1.41148 | ||||||||
\(917\) | −1.48551e34 | −1.27241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.04477e32 | 0.0254346 | 0.0127173 | − | 0.999919i | \(-0.495952\pi\) | ||||
0.0127173 | + | 0.999919i | \(0.495952\pi\) | |||||||
\(920\) | 1.40133e34 | 1.15606 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.35916e34 | −2.70287 | ||||||||
\(923\) | 2.11988e34 | 1.68458 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.19697e34 | 0.927800 | ||||||||
\(926\) | 2.06630e33 | 0.158186 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.38517e33 | 0.103443 | ||||||||
\(929\) | 8.26259e33 | 0.609446 | 0.304723 | − | 0.952441i | \(-0.401436\pi\) | ||||
0.304723 | + | 0.952441i | \(0.401436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.19640e33 | 0.589796 | ||||||||
\(932\) | 2.00530e34 | 1.42527 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.18840e34 | 2.90442 | ||||||||
\(935\) | −2.21073e34 | −1.51427 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.63092e34 | 1.75834 | 0.879169 | − | 0.476510i | \(-0.158098\pi\) | ||||
0.879169 | + | 0.476510i | \(0.158098\pi\) | |||||||
\(938\) | 1.08977e34 | 0.719450 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.66152e34 | −1.71459 | ||||||||
\(941\) | 5.07997e33 | 0.323281 | 0.161641 | − | 0.986850i | \(-0.448321\pi\) | ||||
0.161641 | + | 0.986850i | \(0.448321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63639e34 | −1.01625 | ||||||||
\(944\) | 2.35188e32 | 0.0144290 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.14310e34 | 0.684439 | ||||||||
\(947\) | −3.02144e33 | −0.178727 | −0.0893634 | − | 0.995999i | \(-0.528483\pi\) | ||||
−0.0893634 | + | 0.995999i | \(0.528483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.85723e33 | 0.569107 | ||||||||
\(950\) | 2.22113e34 | 1.26693 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.48205e34 | 2.49547 | ||||||||
\(953\) | −2.84405e34 | −1.56448 | −0.782239 | − | 0.622979i | \(-0.785922\pi\) | ||||
−0.782239 | + | 0.622979i | \(0.785922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.95219e34 | −1.04830 | ||||||||
\(956\) | 5.31517e33 | 0.282001 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.15738e34 | −2.67132 | ||||||||
\(959\) | −4.39979e34 | −2.25174 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.14965e33 | 0.307278 | ||||||||
\(962\) | −7.03474e34 | −3.47324 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.27592e34 | 1.09716 | ||||||||
\(965\) | 1.29199e34 | 0.615455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.35564e33 | 0.0630581 | 0.0315291 | − | 0.999503i | \(-0.489962\pi\) | ||||
0.0315291 | + | 0.999503i | \(0.489962\pi\) | |||||||
\(968\) | −1.35588e34 | −0.623240 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.03807e34 | 0.914836 | ||||||||
\(971\) | 1.58853e34 | 0.704651 | 0.352326 | − | 0.935877i | \(-0.385391\pi\) | ||||
0.352326 | + | 0.935877i | \(0.385391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.65058e34 | 0.715054 | ||||||||
\(974\) | 4.54122e34 | 1.94422 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.91860e33 | 0.122040 | ||||||||
\(977\) | 1.73918e33 | 0.0718714 | 0.0359357 | − | 0.999354i | \(-0.488559\pi\) | ||||
0.0359357 | + | 0.999354i | \(0.488559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.70763e33 | 0.0689277 | ||||||||
\(980\) | 3.06052e34 | 1.22094 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.68953e34 | 1.04808 | ||||||||
\(983\) | 7.60342e33 | 0.292849 | 0.146424 | − | 0.989222i | \(-0.453223\pi\) | ||||
0.146424 | + | 0.989222i | \(0.453223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.17362e34 | 0.441582 | ||||||||
\(986\) | −9.89606e33 | −0.368026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.26901e34 | −3.00434 | ||||||||
\(989\) | −1.22402e34 | −0.439573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.03285e34 | 1.06415 | 0.532076 | − | 0.846697i | \(-0.321412\pi\) | ||||
0.532076 | + | 0.846697i | \(0.321412\pi\) | |||||||
\(992\) | 2.55779e34 | 0.887117 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.38949e34 | −2.16532 | ||||||||
\(995\) | 5.80494e34 | 1.94461 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.74476e34 | −0.571137 | −0.285568 | − | 0.958358i | \(-0.592182\pi\) | ||||
−0.285568 | + | 0.958358i | \(0.592182\pi\) | |||||||
\(998\) | −6.73697e32 | −0.0218004 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.24.a.d.1.4 | yes | 4 | |
3.2 | odd | 2 | inner | 9.24.a.d.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.24.a.d.1.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
9.24.a.d.1.4 | yes | 4 | 1.1 | even | 1 | trivial |