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 | 1.3 | ||
Root | \(61.8825\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1856.48 | 0.640980 | 0.320490 | − | 0.947252i | \(-0.396152\pi\) | ||||
0.320490 | + | 0.947252i | \(0.396152\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.94211e6 | −0.589145 | ||||||||
\(5\) | −1.25135e8 | −1.14610 | −0.573051 | − | 0.819520i | \(-0.694240\pi\) | ||||
−0.573051 | + | 0.819520i | \(0.694240\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21402e9 | −0.423208 | −0.211604 | − | 0.977355i | \(-0.567869\pi\) | ||||
−0.211604 | + | 0.977355i | \(0.567869\pi\) | |||||||
\(8\) | −2.47481e10 | −1.01861 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.32310e11 | −0.734628 | ||||||||
\(11\) | 9.54062e11 | 1.00823 | 0.504116 | − | 0.863636i | \(-0.331818\pi\) | ||||
0.504116 | + | 0.863636i | \(0.331818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54107e12 | 0.548006 | 0.274003 | − | 0.961729i | \(-0.411652\pi\) | ||||
0.274003 | + | 0.961729i | \(0.411652\pi\) | |||||||
\(14\) | −4.11027e12 | −0.271268 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.48694e12 | −0.0637632 | ||||||||
\(17\) | 1.97591e14 | 1.39831 | 0.699157 | − | 0.714968i | \(-0.253559\pi\) | ||||
0.699157 | + | 0.714968i | \(0.253559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41772e14 | −0.279205 | −0.139603 | − | 0.990208i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990208i | \(0.544583\pi\) | |||||||
\(20\) | 6.18429e14 | 0.675220 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.77119e15 | 0.646257 | ||||||||
\(23\) | −1.35827e15 | −0.297246 | −0.148623 | − | 0.988894i | \(-0.547484\pi\) | ||||
−0.148623 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.73779e15 | 0.313548 | ||||||||
\(26\) | 6.57390e15 | 0.351261 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.09419e16 | 0.249331 | ||||||||
\(29\) | −1.17210e17 | −1.78397 | −0.891986 | − | 0.452063i | \(-0.850688\pi\) | ||||
−0.891986 | + | 0.452063i | \(0.850688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.61332e17 | 1.84728 | 0.923642 | − | 0.383255i | \(-0.125197\pi\) | ||||
0.923642 | + | 0.383255i | \(0.125197\pi\) | |||||||
\(32\) | 1.99273e17 | 0.977739 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.66823e17 | 0.896291 | ||||||||
\(35\) | 2.77051e17 | 0.485040 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.63064e18 | 1.50674 | 0.753370 | − | 0.657597i | \(-0.228427\pi\) | ||||
0.753370 | + | 0.657597i | \(0.228427\pi\) | |||||||
\(38\) | −2.63196e17 | −0.178965 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.09685e18 | 1.16743 | ||||||||
\(41\) | 1.39986e18 | 0.397255 | 0.198628 | − | 0.980075i | \(-0.436352\pi\) | ||||
0.198628 | + | 0.980075i | \(0.436352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.83002e18 | 1.28492 | 0.642459 | − | 0.766320i | \(-0.277914\pi\) | ||||
0.642459 | + | 0.766320i | \(0.277914\pi\) | |||||||
\(44\) | −4.71508e18 | −0.593995 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.52160e18 | −0.190529 | ||||||||
\(47\) | −1.10807e19 | −0.653796 | −0.326898 | − | 0.945060i | \(-0.606003\pi\) | ||||
−0.326898 | + | 0.945060i | \(0.606003\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.24669e19 | −0.820895 | ||||||||
\(50\) | 6.93911e18 | 0.200978 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.75003e19 | −0.322855 | ||||||||
\(53\) | 6.84789e19 | 1.01481 | 0.507404 | − | 0.861708i | \(-0.330605\pi\) | ||||
0.507404 | + | 0.861708i | \(0.330605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.19386e20 | −1.15554 | ||||||||
\(56\) | 5.47929e19 | 0.431084 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.17598e20 | −1.14349 | ||||||||
\(59\) | −3.80399e20 | −1.64226 | −0.821128 | − | 0.570744i | \(-0.806655\pi\) | ||||
−0.821128 | + | 0.570744i | \(0.806655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.54300e20 | −0.748260 | −0.374130 | − | 0.927376i | \(-0.622059\pi\) | ||||
−0.374130 | + | 0.927376i | \(0.622059\pi\) | |||||||
\(62\) | 4.85157e20 | 1.18407 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.07584e20 | 0.690474 | ||||||||
\(65\) | −4.43111e20 | −0.628071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.58191e20 | 0.758435 | 0.379218 | − | 0.925308i | \(-0.376193\pi\) | ||||
0.379218 | + | 0.925308i | \(0.376193\pi\) | |||||||
\(68\) | −9.76516e20 | −0.823810 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.14338e20 | 0.310901 | ||||||||
\(71\) | 1.65470e21 | 0.849668 | 0.424834 | − | 0.905271i | \(-0.360333\pi\) | ||||
0.424834 | + | 0.905271i | \(0.360333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.73535e21 | 1.39354 | 0.696768 | − | 0.717297i | \(-0.254621\pi\) | ||||
0.696768 | + | 0.717297i | \(0.254621\pi\) | |||||||
\(74\) | 3.02724e21 | 0.965790 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00652e20 | 0.164493 | ||||||||
\(77\) | −2.11231e21 | −0.426692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.30977e21 | 0.497836 | 0.248918 | − | 0.968525i | \(-0.419925\pi\) | ||||
0.248918 | + | 0.968525i | \(0.419925\pi\) | |||||||
\(80\) | 5.61472e20 | 0.0730791 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.59880e21 | 0.254632 | ||||||||
\(83\) | −1.73160e22 | −1.47588 | −0.737939 | − | 0.674868i | \(-0.764201\pi\) | ||||
−0.737939 | + | 0.674868i | \(0.764201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47255e22 | −1.60261 | ||||||||
\(86\) | 1.45362e22 | 0.823607 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.36113e22 | −1.02700 | ||||||||
\(89\) | −7.98037e20 | −0.0304816 | −0.0152408 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152408 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.83999e21 | −0.231921 | ||||||||
\(92\) | 6.71272e21 | 0.175121 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.05711e22 | −0.419070 | ||||||||
\(95\) | 1.77406e22 | 0.319998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.51761e20 | 0.0135099 | 0.00675496 | − | 0.999977i | \(-0.497850\pi\) | ||||
0.00675496 | + | 0.999977i | \(0.497850\pi\) | |||||||
\(98\) | −4.17092e22 | −0.526177 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.84725e22 | −0.184725 | ||||||||
\(101\) | 1.42407e23 | 1.27009 | 0.635045 | − | 0.772476i | \(-0.280982\pi\) | ||||
0.635045 | + | 0.772476i | \(0.280982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.25632e23 | 0.894275 | 0.447137 | − | 0.894465i | \(-0.352444\pi\) | ||||
0.447137 | + | 0.894465i | \(0.352444\pi\) | |||||||
\(104\) | −8.76348e22 | −0.558204 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.27129e23 | 0.650472 | ||||||||
\(107\) | −2.55948e23 | −1.17554 | −0.587772 | − | 0.809027i | \(-0.699995\pi\) | ||||
−0.587772 | + | 0.809027i | \(0.699995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.89375e23 | 1.44532 | 0.722658 | − | 0.691205i | \(-0.242920\pi\) | ||||
0.722658 | + | 0.691205i | \(0.242920\pi\) | |||||||
\(110\) | −2.21638e23 | −0.740675 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.93417e21 | 0.0269851 | ||||||||
\(113\) | 5.25664e23 | 1.28916 | 0.644579 | − | 0.764538i | \(-0.277033\pi\) | ||||
0.644579 | + | 0.764538i | \(0.277033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.69967e23 | 0.340674 | ||||||||
\(116\) | 5.79265e23 | 1.05102 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.06201e23 | −1.05265 | ||||||||
\(119\) | −4.37471e23 | −0.591778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.48038e22 | 0.0165326 | ||||||||
\(122\) | −4.72101e23 | −0.479620 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.29153e24 | −1.08832 | ||||||||
\(125\) | 1.02400e24 | 0.786743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.27123e23 | −0.465441 | −0.232721 | − | 0.972544i | \(-0.574763\pi\) | ||||
−0.232721 | + | 0.972544i | \(0.574763\pi\) | |||||||
\(128\) | −9.14950e23 | −0.535159 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.22624e23 | −0.402581 | ||||||||
\(131\) | −1.29816e24 | −0.581711 | −0.290856 | − | 0.956767i | \(-0.593940\pi\) | ||||
−0.290856 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.13886e23 | 0.118162 | ||||||||
\(134\) | 1.40756e24 | 0.486142 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.89001e24 | −1.42434 | ||||||||
\(137\) | −1.56938e24 | −0.420187 | −0.210093 | − | 0.977681i | \(-0.567377\pi\) | ||||
−0.210093 | + | 0.977681i | \(0.567377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.97766e24 | 1.35476 | 0.677378 | − | 0.735635i | \(-0.263116\pi\) | ||||
0.677378 | + | 0.735635i | \(0.263116\pi\) | |||||||
\(140\) | −1.36922e24 | −0.285759 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.07192e24 | 0.544620 | ||||||||
\(143\) | 3.37840e24 | 0.552518 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.46671e25 | 2.04461 | ||||||||
\(146\) | 6.93458e24 | 0.893228 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.05880e24 | −0.887688 | ||||||||
\(149\) | 1.50771e24 | 0.153700 | 0.0768502 | − | 0.997043i | \(-0.475514\pi\) | ||||
0.0768502 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.13154e25 | 0.989548 | 0.494774 | − | 0.869022i | \(-0.335251\pi\) | ||||
0.494774 | + | 0.869022i | \(0.335251\pi\) | |||||||
\(152\) | 3.50859e24 | 0.284401 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.92146e24 | −0.273501 | ||||||||
\(155\) | −3.27018e25 | −2.11718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.43402e24 | 0.247715 | 0.123857 | − | 0.992300i | \(-0.460473\pi\) | ||||
0.123857 | + | 0.992300i | \(0.460473\pi\) | |||||||
\(158\) | 6.14450e24 | 0.319103 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.49359e25 | −1.12059 | ||||||||
\(161\) | 3.00724e24 | 0.125797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.82788e24 | 0.284110 | 0.142055 | − | 0.989859i | \(-0.454629\pi\) | ||||
0.142055 | + | 0.989859i | \(0.454629\pi\) | |||||||
\(164\) | −6.91824e24 | −0.234041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.21468e25 | −0.946008 | ||||||||
\(167\) | 6.36666e25 | 1.74853 | 0.874264 | − | 0.485452i | \(-0.161345\pi\) | ||||
0.874264 | + | 0.485452i | \(0.161345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.92148e25 | −0.699689 | ||||||||
\(170\) | −4.59023e25 | −1.02724 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.86968e25 | −0.757004 | ||||||||
\(173\) | −1.87367e25 | −0.342896 | −0.171448 | − | 0.985193i | \(-0.554844\pi\) | ||||
−0.171448 | + | 0.985193i | \(0.554844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.27554e24 | −0.132696 | ||||||||
\(176\) | −4.28081e24 | −0.0642881 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.48154e24 | −0.0195381 | ||||||||
\(179\) | 1.38944e26 | 1.71802 | 0.859012 | − | 0.511955i | \(-0.171079\pi\) | ||||
0.859012 | + | 0.511955i | \(0.171079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.32272e25 | 0.905652 | 0.452826 | − | 0.891599i | \(-0.350416\pi\) | ||||
0.452826 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(182\) | −1.45548e25 | −0.148657 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.36147e25 | 0.302778 | ||||||||
\(185\) | −2.04050e26 | −1.72688 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88514e26 | 1.40983 | ||||||||
\(188\) | 5.47621e25 | 0.385181 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.29350e25 | 0.205112 | ||||||||
\(191\) | −1.26673e26 | −0.742679 | −0.371340 | − | 0.928497i | \(-0.621101\pi\) | ||||
−0.371340 | + | 0.928497i | \(0.621101\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.03237e25 | 0.157715 | 0.0788577 | − | 0.996886i | \(-0.474873\pi\) | ||||
0.0788577 | + | 0.996886i | \(0.474873\pi\) | |||||||
\(194\) | 1.76692e24 | 0.00865958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.11034e26 | 0.483626 | ||||||||
\(197\) | 2.46843e26 | 1.01405 | 0.507025 | − | 0.861932i | \(-0.330745\pi\) | ||||
0.507025 | + | 0.861932i | \(0.330745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.44174e26 | −0.893078 | −0.446539 | − | 0.894764i | \(-0.647344\pi\) | ||||
−0.446539 | + | 0.894764i | \(0.647344\pi\) | |||||||
\(200\) | −9.25033e25 | −0.319383 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.64374e26 | 0.814101 | ||||||||
\(203\) | 2.59506e26 | 0.754992 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.75171e26 | −0.455295 | ||||||||
\(206\) | 2.33232e26 | 0.573212 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.58885e25 | −0.0349426 | ||||||||
\(209\) | −1.35259e26 | −0.281504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.76884e26 | −1.63566 | −0.817832 | − | 0.575457i | \(-0.804824\pi\) | ||||
−0.817832 | + | 0.575457i | \(0.804824\pi\) | |||||||
\(212\) | −3.38430e26 | −0.597869 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.75162e26 | −0.753500 | ||||||||
\(215\) | −9.79808e26 | −1.47265 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.78595e26 | −0.781786 | ||||||||
\(218\) | 7.22865e26 | 0.926419 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.90020e26 | 0.680779 | ||||||||
\(221\) | 6.99683e26 | 0.766285 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83665e26 | −0.280091 | −0.140046 | − | 0.990145i | \(-0.544725\pi\) | ||||
−0.140046 | + | 0.990145i | \(0.544725\pi\) | |||||||
\(224\) | −4.41194e26 | −0.413787 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.75882e26 | 0.826324 | ||||||||
\(227\) | −7.65440e26 | −0.616047 | −0.308024 | − | 0.951379i | \(-0.599668\pi\) | ||||
−0.308024 | + | 0.951379i | \(0.599668\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.18669e26 | −0.668422 | −0.334211 | − | 0.942498i | \(-0.608470\pi\) | ||||
−0.334211 | + | 0.942498i | \(0.608470\pi\) | |||||||
\(230\) | 3.15539e26 | 0.218365 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.90073e27 | 1.81717 | ||||||||
\(233\) | −6.69203e26 | −0.398993 | −0.199496 | − | 0.979899i | \(-0.563931\pi\) | ||||
−0.199496 | + | 0.979899i | \(0.563931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.38658e27 | 0.749317 | ||||||||
\(236\) | 1.87997e27 | 0.967527 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.12154e26 | −0.379318 | ||||||||
\(239\) | 1.32134e27 | 0.588081 | 0.294041 | − | 0.955793i | \(-0.405000\pi\) | ||||
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.67571e26 | 0.391279 | 0.195640 | − | 0.980676i | \(-0.437322\pi\) | ||||
0.195640 | + | 0.980676i | \(0.437322\pi\) | |||||||
\(242\) | 2.74828e25 | 0.0105970 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.25678e27 | 0.440834 | ||||||||
\(245\) | 2.81139e27 | 0.940829 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.02024e26 | −0.153006 | ||||||||
\(248\) | −6.46749e27 | −1.88166 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.90102e27 | 0.504286 | ||||||||
\(251\) | −2.70487e27 | −0.685328 | −0.342664 | − | 0.939458i | \(-0.611329\pi\) | ||||
−0.342664 | + | 0.939458i | \(0.611329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.29587e27 | −0.299693 | ||||||||
\(254\) | −1.34989e27 | −0.298339 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.11764e27 | −1.03350 | ||||||||
\(257\) | 1.75032e27 | 0.337977 | 0.168988 | − | 0.985618i | \(-0.445950\pi\) | ||||
0.168988 | + | 0.985618i | \(0.445950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.61027e27 | −0.637665 | ||||||||
\(260\) | 2.18990e27 | 0.370025 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.41000e27 | −0.372865 | ||||||||
\(263\) | 5.05191e27 | 0.748108 | 0.374054 | − | 0.927407i | \(-0.377967\pi\) | ||||
0.374054 | + | 0.927407i | \(0.377967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.56909e27 | −1.16307 | ||||||||
\(266\) | 5.82722e26 | 0.0757395 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.74706e27 | −0.446828 | ||||||||
\(269\) | −2.79663e27 | −0.319509 | −0.159754 | − | 0.987157i | \(-0.551070\pi\) | ||||
−0.159754 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.12408e27 | 0.327775 | 0.163887 | − | 0.986479i | \(-0.447597\pi\) | ||||
0.163887 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(272\) | −8.86579e26 | −0.0891610 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.91352e27 | −0.269331 | ||||||||
\(275\) | 3.56608e27 | 0.316130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.33237e28 | 1.90230 | 0.951152 | − | 0.308723i | \(-0.0999016\pi\) | ||||
0.951152 | + | 0.308723i | \(0.0999016\pi\) | |||||||
\(278\) | 1.10974e28 | 0.868371 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.85650e27 | −0.494066 | ||||||||
\(281\) | −1.54956e28 | −1.07173 | −0.535866 | − | 0.844303i | \(-0.680015\pi\) | ||||
−0.535866 | + | 0.844303i | \(0.680015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.17195e27 | 0.329694 | 0.164847 | − | 0.986319i | \(-0.447287\pi\) | ||||
0.164847 | + | 0.986319i | \(0.447287\pi\) | |||||||
\(284\) | −8.17772e27 | −0.500578 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.27191e27 | 0.354153 | ||||||||
\(287\) | −3.09931e27 | −0.168122 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.90747e28 | 0.955283 | ||||||||
\(290\) | 2.72290e28 | 1.31056 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.84605e28 | −0.820995 | ||||||||
\(293\) | −9.81588e27 | −0.419712 | −0.209856 | − | 0.977732i | \(-0.567300\pi\) | ||||
−0.209856 | + | 0.977732i | \(0.567300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.76011e28 | 1.88219 | ||||||||
\(296\) | −4.03553e28 | −1.53478 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.79902e27 | 0.0985189 | ||||||||
\(299\) | −4.80972e27 | −0.162893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.73358e28 | −0.543788 | ||||||||
\(302\) | 2.10069e28 | 0.634280 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.36122e26 | 0.0178030 | ||||||||
\(305\) | 3.18217e28 | 0.857582 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.51274e28 | −0.378158 | −0.189079 | − | 0.981962i | \(-0.560550\pi\) | ||||
−0.189079 | + | 0.981962i | \(0.560550\pi\) | |||||||
\(308\) | 1.04393e28 | 0.251384 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.07101e28 | −1.35707 | ||||||||
\(311\) | 5.90519e28 | 1.27201 | 0.636003 | − | 0.771686i | \(-0.280586\pi\) | ||||
0.636003 | + | 0.771686i | \(0.280586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.74763e27 | 0.155028 | 0.0775138 | − | 0.996991i | \(-0.475302\pi\) | ||||
0.0775138 | + | 0.996991i | \(0.475302\pi\) | |||||||
\(314\) | 8.23165e27 | 0.158780 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.63572e28 | −0.293297 | ||||||||
\(317\) | −8.76539e28 | −1.51562 | −0.757809 | − | 0.652476i | \(-0.773730\pi\) | ||||
−0.757809 | + | 0.652476i | \(0.773730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.11826e29 | −1.79866 | ||||||||
\(320\) | −5.10029e28 | −0.791353 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.58286e27 | 0.0806333 | ||||||||
\(323\) | −2.80129e28 | −0.390417 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32358e28 | 0.171826 | ||||||||
\(326\) | 1.45323e28 | 0.182109 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.46439e28 | −0.404648 | ||||||||
\(329\) | 2.45329e28 | 0.276692 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.28558e29 | 1.35231 | 0.676155 | − | 0.736759i | \(-0.263645\pi\) | ||||
0.676155 | + | 0.736759i | \(0.263645\pi\) | |||||||
\(332\) | 8.55777e28 | 0.869506 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.18196e29 | 1.12077 | ||||||||
\(335\) | −9.48761e28 | −0.869244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.77046e29 | −1.51475 | −0.757377 | − | 0.652978i | \(-0.773520\pi\) | ||||
−0.757377 | + | 0.652978i | \(0.773520\pi\) | |||||||
\(338\) | −5.42365e28 | −0.448487 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.22196e29 | 0.944170 | ||||||||
\(341\) | 2.49327e29 | 1.86249 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.10337e29 | 0.770618 | ||||||||
\(344\) | −1.93779e29 | −1.30883 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.47841e28 | −0.219789 | ||||||||
\(347\) | −1.60648e27 | −0.00981942 | −0.00490971 | − | 0.999988i | \(-0.501563\pi\) | ||||
−0.00490971 | + | 0.999988i | \(0.501563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80178e29 | 1.03088 | 0.515442 | − | 0.856925i | \(-0.327628\pi\) | ||||
0.515442 | + | 0.856925i | \(0.327628\pi\) | |||||||
\(350\) | −1.53633e28 | −0.0850556 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.90118e29 | 0.985788 | ||||||||
\(353\) | 3.12751e29 | 1.56960 | 0.784801 | − | 0.619748i | \(-0.212765\pi\) | ||||
0.784801 | + | 0.619748i | \(0.212765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.07061e29 | −0.973805 | ||||||||
\(356\) | 3.94398e27 | 0.0179581 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.57946e29 | 1.10122 | ||||||||
\(359\) | −1.81842e29 | −0.751811 | −0.375906 | − | 0.926658i | \(-0.622668\pi\) | ||||
−0.375906 | + | 0.926658i | \(0.622668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.37730e29 | −0.922044 | ||||||||
\(362\) | 1.54509e29 | 0.580505 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.87461e28 | 0.136635 | ||||||||
\(365\) | −4.67422e29 | −1.59713 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.10392e29 | −0.675103 | −0.337552 | − | 0.941307i | \(-0.609599\pi\) | ||||
−0.337552 | + | 0.941307i | \(0.609599\pi\) | |||||||
\(368\) | 6.09447e27 | 0.0189534 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.78813e29 | −1.10689 | ||||||||
\(371\) | −1.51614e29 | −0.429475 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.19125e29 | −1.64864 | −0.824322 | − | 0.566122i | \(-0.808443\pi\) | ||||
−0.824322 | + | 0.566122i | \(0.808443\pi\) | |||||||
\(374\) | 3.49972e29 | 0.903670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.74227e29 | 0.665963 | ||||||||
\(377\) | −4.15049e29 | −0.977628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.16748e28 | −0.181024 | −0.0905122 | − | 0.995895i | \(-0.528850\pi\) | ||||
−0.0905122 | + | 0.995895i | \(0.528850\pi\) | |||||||
\(380\) | −8.76760e28 | −0.188525 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.35166e29 | −0.476042 | ||||||||
\(383\) | 7.92901e29 | 1.55752 | 0.778759 | − | 0.627323i | \(-0.215849\pi\) | ||||
0.778759 | + | 0.627323i | \(0.215849\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.64324e29 | 0.489033 | ||||||||
\(386\) | 5.62953e28 | 0.101092 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.70370e27 | −0.00795930 | ||||||||
\(389\) | 2.41701e29 | 0.397062 | 0.198531 | − | 0.980095i | \(-0.436383\pi\) | ||||
0.198531 | + | 0.980095i | \(0.436383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.68382e29 | −0.415643 | ||||||||
\(392\) | 5.56013e29 | 0.836171 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.58258e29 | 0.649985 | ||||||||
\(395\) | −4.14167e29 | −0.570570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.74027e29 | 0.616187 | 0.308094 | − | 0.951356i | \(-0.400309\pi\) | ||||
0.308094 | + | 0.951356i | \(0.400309\pi\) | |||||||
\(398\) | −4.53303e29 | −0.572445 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.67712e28 | −0.0199928 | ||||||||
\(401\) | −9.97411e29 | −1.15535 | −0.577676 | − | 0.816266i | \(-0.696040\pi\) | ||||
−0.577676 | + | 0.816266i | \(0.696040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.25395e29 | 1.01232 | ||||||||
\(404\) | −7.03788e29 | −0.748267 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.81766e29 | 0.483934 | ||||||||
\(407\) | 1.55573e30 | 1.51914 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.82542e29 | 0.168478 | 0.0842391 | − | 0.996446i | \(-0.473154\pi\) | ||||
0.0842391 | + | 0.996446i | \(0.473154\pi\) | |||||||
\(410\) | −3.25200e29 | −0.291835 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.20885e29 | −0.526857 | ||||||||
\(413\) | 8.42211e29 | 0.695016 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.16684e30 | 1.69151 | ||||||||
\(416\) | 7.05637e29 | 0.535807 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.51105e29 | −0.180438 | ||||||||
\(419\) | −2.31769e30 | −1.62029 | −0.810146 | − | 0.586228i | \(-0.800612\pi\) | ||||
−0.810146 | + | 0.586228i | \(0.800612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.84805e29 | 0.188497 | 0.0942483 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942483 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(422\) | −1.62791e30 | −1.04843 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.69473e30 | −1.03369 | ||||||||
\(425\) | 7.38554e29 | 0.438439 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.63025e29 | 0.316670 | ||||||||
\(428\) | 1.26492e30 | 0.692566 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.81899e30 | −0.943937 | ||||||||
\(431\) | 2.68991e30 | 1.35910 | 0.679548 | − | 0.733632i | \(-0.262176\pi\) | ||||
0.679548 | + | 0.733632i | \(0.262176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.83636e30 | −1.35879 | −0.679393 | − | 0.733774i | \(-0.737757\pi\) | ||||
−0.679393 | + | 0.733774i | \(0.737757\pi\) | |||||||
\(434\) | −1.07415e30 | −0.501109 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.92433e30 | −0.851501 | ||||||||
\(437\) | 1.92565e29 | 0.0829927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.34373e29 | −0.259419 | −0.129710 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129710 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(440\) | 2.95459e30 | 1.17704 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.29894e30 | 0.491173 | ||||||||
\(443\) | −1.41158e30 | −0.520072 | −0.260036 | − | 0.965599i | \(-0.583734\pi\) | ||||
−0.260036 | + | 0.965599i | \(0.583734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.98622e28 | 0.0349350 | ||||||||
\(446\) | −5.26617e29 | −0.179533 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.02399e29 | −0.292214 | ||||||||
\(449\) | −3.28307e30 | −1.03621 | −0.518104 | − | 0.855318i | \(-0.673362\pi\) | ||||
−0.518104 | + | 0.855318i | \(0.673362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.33555e30 | 0.400525 | ||||||||
\(452\) | −2.59789e30 | −0.759501 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.42102e30 | −0.394874 | ||||||||
\(455\) | 9.81056e29 | 0.265805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.77120e29 | 0.0971501 | 0.0485750 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485750 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(458\) | −1.70549e30 | −0.428445 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.39994e29 | −0.200706 | ||||||||
\(461\) | 1.82043e30 | 0.424243 | 0.212121 | − | 0.977243i | \(-0.431963\pi\) | ||||
0.212121 | + | 0.977243i | \(0.431963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.46419e30 | 1.87674 | 0.938370 | − | 0.345633i | \(-0.112336\pi\) | ||||
0.938370 | + | 0.345633i | \(0.112336\pi\) | |||||||
\(464\) | 5.25914e29 | 0.113752 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.24236e30 | −0.255746 | ||||||||
\(467\) | −1.55072e30 | −0.311451 | −0.155725 | − | 0.987800i | \(-0.549771\pi\) | ||||
−0.155725 | + | 0.987800i | \(0.549771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.67865e30 | −0.320976 | ||||||||
\(470\) | 2.57416e30 | 0.480297 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.41416e30 | 1.67282 | ||||||||
\(473\) | 7.47033e30 | 1.29550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.29914e29 | −0.0875444 | ||||||||
\(476\) | 2.16203e30 | 0.348643 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.45303e30 | 0.376948 | ||||||||
\(479\) | −9.58203e30 | −1.43747 | −0.718736 | − | 0.695284i | \(-0.755279\pi\) | ||||
−0.718736 | + | 0.695284i | \(0.755279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.77420e30 | 0.825703 | ||||||||
\(482\) | 1.79627e30 | 0.250802 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.31618e28 | −0.00974008 | ||||||||
\(485\) | −1.19098e29 | −0.0154837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.05601e30 | −0.502940 | −0.251470 | − | 0.967865i | \(-0.580914\pi\) | ||||
−0.251470 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(488\) | 6.29344e30 | 0.762185 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.21927e30 | 0.603052 | ||||||||
\(491\) | −5.18224e30 | −0.584898 | −0.292449 | − | 0.956281i | \(-0.594470\pi\) | ||||
−0.292449 | + | 0.956281i | \(0.594470\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.31597e31 | −2.49455 | ||||||||
\(494\) | −9.31995e29 | −0.0980740 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.17258e30 | −0.117789 | ||||||||
\(497\) | −3.66355e30 | −0.359586 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.83971e30 | 0.453590 | 0.226795 | − | 0.973943i | \(-0.427175\pi\) | ||||
0.226795 | + | 0.973943i | \(0.427175\pi\) | |||||||
\(500\) | −5.06070e30 | −0.463506 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.02152e30 | −0.439281 | ||||||||
\(503\) | 1.61218e31 | 1.37842 | 0.689211 | − | 0.724561i | \(-0.257957\pi\) | ||||
0.689211 | + | 0.724561i | \(0.257957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.78200e31 | −1.45565 | ||||||||
\(506\) | −2.40576e30 | −0.192097 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.59352e30 | 0.274212 | ||||||||
\(509\) | −1.33185e31 | −0.993577 | −0.496789 | − | 0.867872i | \(-0.665488\pi\) | ||||
−0.496789 | + | 0.867872i | \(0.665488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.27014e30 | −0.589756 | ||||||||
\(512\) | −1.82562e30 | −0.127294 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.24943e30 | 0.216636 | ||||||||
\(515\) | −1.57209e31 | −1.02493 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.05717e31 | −0.659179 | ||||||||
\(518\) | −6.70238e30 | −0.408730 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.09662e31 | 0.639759 | ||||||||
\(521\) | 2.34032e31 | 1.33549 | 0.667745 | − | 0.744390i | \(-0.267260\pi\) | ||||
0.667745 | + | 0.744390i | \(0.267260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.49020e31 | 0.813722 | 0.406861 | − | 0.913490i | \(-0.366623\pi\) | ||||
0.406861 | + | 0.913490i | \(0.366623\pi\) | |||||||
\(524\) | 6.41563e30 | 0.342712 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.37874e30 | 0.479522 | ||||||||
\(527\) | 5.16370e31 | 2.58308 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.90356e31 | −0.911645 | ||||||||
\(530\) | −1.59083e31 | −0.745507 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.55126e30 | −0.0696146 | ||||||||
\(533\) | 4.95699e30 | 0.217698 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.20281e31 | 1.34729 | ||||||||
\(536\) | −1.87638e31 | −0.772549 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.19187e30 | −0.204799 | ||||||||
\(539\) | −2.14348e31 | −0.827653 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.98916e30 | 0.332622 | 0.166311 | − | 0.986073i | \(-0.446814\pi\) | ||||
0.166311 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(542\) | 5.79978e30 | 0.210097 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.93745e31 | 1.36719 | ||||||||
\(545\) | −4.87243e31 | −1.65648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.92608e31 | 0.953743 | 0.476871 | − | 0.878973i | \(-0.341771\pi\) | ||||
0.476871 | + | 0.878973i | \(0.341771\pi\) | |||||||
\(548\) | 7.75605e30 | 0.247551 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.62034e30 | 0.202633 | ||||||||
\(551\) | 1.66171e31 | 0.498095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.32790e30 | −0.210688 | ||||||||
\(554\) | 4.32999e31 | 1.21934 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.95422e31 | −0.798148 | ||||||||
\(557\) | −3.88195e31 | −1.02734 | −0.513671 | − | 0.857987i | \(-0.671715\pi\) | ||||
−0.513671 | + | 0.857987i | \(0.671715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.77266e31 | 0.704144 | ||||||||
\(560\) | −1.24311e30 | −0.0309277 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.87673e31 | −0.686959 | ||||||||
\(563\) | −1.23043e31 | −0.287878 | −0.143939 | − | 0.989587i | \(-0.545977\pi\) | ||||
−0.143939 | + | 0.989587i | \(0.545977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.57788e31 | −1.47751 | ||||||||
\(566\) | 9.60160e30 | 0.211327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.09508e31 | −0.865480 | ||||||||
\(569\) | 3.60714e31 | 0.747088 | 0.373544 | − | 0.927612i | \(-0.378142\pi\) | ||||
0.373544 | + | 0.927612i | \(0.378142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.10890e31 | 0.817354 | 0.408677 | − | 0.912679i | \(-0.365990\pi\) | ||||
0.408677 | + | 0.912679i | \(0.365990\pi\) | |||||||
\(572\) | −1.66964e31 | −0.325513 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.75380e30 | −0.107763 | ||||||||
\(575\) | −5.07693e30 | −0.0932010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.71556e31 | −1.00818 | −0.504089 | − | 0.863652i | \(-0.668172\pi\) | ||||
−0.504089 | + | 0.863652i | \(0.668172\pi\) | |||||||
\(578\) | 3.54117e31 | 0.612317 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.24862e31 | −1.20457 | ||||||||
\(581\) | 3.83381e31 | 0.624604 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.53331e31 | 1.02316 | ||||||||
\(584\) | −9.24429e31 | −1.41947 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.82229e31 | −0.269027 | ||||||||
\(587\) | 2.06703e30 | 0.0299233 | 0.0149616 | − | 0.999888i | \(-0.495237\pi\) | ||||
0.0149616 | + | 0.999888i | \(0.495237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.70496e31 | −0.515772 | ||||||||
\(590\) | 8.83703e31 | 1.20645 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.31658e30 | −0.0960745 | ||||||||
\(593\) | 3.79598e31 | 0.488872 | 0.244436 | − | 0.969665i | \(-0.421397\pi\) | ||||
0.244436 | + | 0.969665i | \(0.421397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.47428e31 | 0.678238 | ||||||||
\(596\) | −7.45125e30 | −0.0905519 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.92914e30 | −0.104411 | ||||||||
\(599\) | −1.17051e32 | −1.34266 | −0.671331 | − | 0.741158i | \(-0.734277\pi\) | ||||
−0.671331 | + | 0.741158i | \(0.734277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.55159e31 | 0.723254 | 0.361627 | − | 0.932323i | \(-0.382221\pi\) | ||||
0.361627 | + | 0.932323i | \(0.382221\pi\) | |||||||
\(602\) | −3.21835e31 | −0.348557 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.59222e31 | −0.582987 | ||||||||
\(605\) | −1.85247e30 | −0.0189480 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.95239e31 | 0.783119 | 0.391560 | − | 0.920153i | \(-0.371936\pi\) | ||||
0.391560 | + | 0.920153i | \(0.371936\pi\) | |||||||
\(608\) | −2.82513e31 | −0.272990 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.90763e31 | 0.549693 | ||||||||
\(611\) | −3.92375e31 | −0.358284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.67217e30 | 0.0322944 | 0.0161472 | − | 0.999870i | \(-0.494860\pi\) | ||||
0.0161472 | + | 0.999870i | \(0.494860\pi\) | |||||||
\(614\) | −2.80837e31 | −0.242391 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.22758e31 | 0.434633 | ||||||||
\(617\) | −3.41957e31 | −0.279057 | −0.139528 | − | 0.990218i | \(-0.544559\pi\) | ||||
−0.139528 | + | 0.990218i | \(0.544559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.21499e32 | 1.74152 | 0.870762 | − | 0.491704i | \(-0.163626\pi\) | ||||
0.870762 | + | 0.491704i | \(0.163626\pi\) | |||||||
\(620\) | 1.61616e32 | 1.24732 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.09628e32 | 0.815330 | ||||||||
\(623\) | 1.76687e30 | 0.0129001 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.72695e32 | −1.21524 | ||||||||
\(626\) | 1.43833e31 | 0.0993695 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.19134e31 | −0.145940 | ||||||||
\(629\) | 3.22200e32 | 2.10690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.58296e32 | 0.998002 | 0.499001 | − | 0.866601i | \(-0.333700\pi\) | ||||
0.499001 | + | 0.866601i | \(0.333700\pi\) | |||||||
\(632\) | −8.19106e31 | −0.507100 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.62727e32 | −0.971481 | ||||||||
\(635\) | 9.09884e31 | 0.533443 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.95566e31 | −0.449855 | ||||||||
\(638\) | −2.07602e32 | −1.15290 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.14492e32 | 0.613346 | ||||||||
\(641\) | −1.97318e32 | −1.03824 | −0.519121 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519121 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.91777e32 | −1.48124 | −0.740618 | − | 0.671926i | \(-0.765467\pi\) | ||||
−0.740618 | + | 0.671926i | \(0.765467\pi\) | |||||||
\(644\) | −1.48621e31 | −0.0741127 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.20052e31 | −0.250249 | ||||||||
\(647\) | 6.05387e31 | 0.286176 | 0.143088 | − | 0.989710i | \(-0.454297\pi\) | ||||
0.143088 | + | 0.989710i | \(0.454297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.62924e32 | −1.65578 | ||||||||
\(650\) | 2.45719e31 | 0.110137 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.86862e31 | −0.167382 | ||||||||
\(653\) | −2.70051e32 | −1.14801 | −0.574003 | − | 0.818853i | \(-0.694610\pi\) | ||||
−0.574003 | + | 0.818853i | \(0.694610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.62445e32 | 0.666700 | ||||||||
\(656\) | −6.28107e30 | −0.0253302 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.55448e31 | 0.177354 | ||||||||
\(659\) | 3.41256e32 | 1.30587 | 0.652933 | − | 0.757416i | \(-0.273538\pi\) | ||||
0.652933 | + | 0.757416i | \(0.273538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.65199e32 | −1.71918 | −0.859592 | − | 0.510982i | \(-0.829282\pi\) | ||||
−0.859592 | + | 0.510982i | \(0.829282\pi\) | |||||||
\(662\) | 2.38664e32 | 0.866804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.28540e32 | 1.50334 | ||||||||
\(665\) | −3.92781e31 | −0.135426 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.59203e32 | 0.530279 | ||||||||
\(668\) | −3.14647e32 | −1.03014 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.76135e32 | −0.557168 | ||||||||
\(671\) | −2.42618e32 | −0.754420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.76445e32 | −1.43166 | −0.715829 | − | 0.698276i | \(-0.753951\pi\) | ||||
−0.715829 | + | 0.698276i | \(0.753951\pi\) | |||||||
\(674\) | −3.28682e32 | −0.970927 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.44382e32 | 0.412218 | ||||||||
\(677\) | −4.41103e31 | −0.123814 | −0.0619071 | − | 0.998082i | \(-0.519718\pi\) | ||||
−0.0619071 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.10722e30 | −0.00571751 | ||||||||
\(680\) | 6.11911e32 | 1.63243 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.62870e32 | 1.19382 | ||||||||
\(683\) | 2.77520e32 | 0.703812 | 0.351906 | − | 0.936035i | \(-0.385534\pi\) | ||||
0.351906 | + | 0.936035i | \(0.385534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.96384e32 | 0.481576 | ||||||||
\(686\) | 2.04838e32 | 0.493950 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.51328e31 | −0.0819305 | ||||||||
\(689\) | 2.42488e32 | 0.556121 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.25247e32 | 1.83057 | 0.915286 | − | 0.402806i | \(-0.131965\pi\) | ||||
0.915286 | + | 0.402806i | \(0.131965\pi\) | |||||||
\(692\) | 9.25986e31 | 0.202015 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.98239e30 | −0.00629405 | ||||||||
\(695\) | −7.48014e32 | −1.55269 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.76599e32 | 0.555487 | ||||||||
\(698\) | 3.34496e32 | 0.660775 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.08986e31 | 0.0781773 | ||||||||
\(701\) | −1.99680e32 | −0.375472 | −0.187736 | − | 0.982220i | \(-0.560115\pi\) | ||||
−0.187736 | + | 0.982220i | \(0.560115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.31179e32 | −0.420690 | ||||||||
\(704\) | 3.88860e32 | 0.696158 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.80614e32 | 1.00608 | ||||||||
\(707\) | −3.15291e32 | −0.537512 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.31374e32 | −0.216809 | −0.108404 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108404 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(710\) | −3.84404e32 | −0.624190 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.97499e31 | 0.0310489 | ||||||||
\(713\) | −3.54960e32 | −0.549098 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.22755e32 | −0.633241 | ||||||||
\(716\) | −6.86675e32 | −1.01217 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.37586e32 | −0.481896 | ||||||||
\(719\) | 8.81786e32 | 1.23874 | 0.619371 | − | 0.785098i | \(-0.287388\pi\) | ||||
0.619371 | + | 0.785098i | \(0.287388\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.78151e32 | −0.378464 | ||||||||
\(722\) | −4.41341e32 | −0.591012 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.11317e32 | −0.533560 | ||||||||
\(725\) | −4.38106e32 | −0.559362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.53127e32 | −0.189412 | −0.0947059 | − | 0.995505i | \(-0.530191\pi\) | ||||
−0.0947059 | + | 0.995505i | \(0.530191\pi\) | |||||||
\(728\) | 1.94025e32 | 0.236237 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.67757e32 | −1.02373 | ||||||||
\(731\) | 1.54714e33 | 1.79672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.26963e32 | −0.480502 | −0.240251 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240251 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(734\) | −3.90588e32 | −0.432728 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.70666e32 | −0.290629 | ||||||||
\(737\) | 7.23361e32 | 0.764679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.20770e32 | 0.636091 | 0.318046 | − | 0.948075i | \(-0.396973\pi\) | ||||
0.318046 | + | 0.948075i | \(0.396973\pi\) | |||||||
\(740\) | 1.00844e33 | 1.01738 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.81467e32 | −0.275285 | ||||||||
\(743\) | −8.09984e32 | −0.780019 | −0.390010 | − | 0.920811i | \(-0.627528\pi\) | ||||
−0.390010 | + | 0.920811i | \(0.627528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.88667e32 | −0.176156 | ||||||||
\(746\) | −1.14939e33 | −1.05675 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.31657e32 | −0.830592 | ||||||||
\(749\) | 5.66675e32 | 0.497500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.33627e33 | 1.13772 | 0.568859 | − | 0.822435i | \(-0.307385\pi\) | ||||
0.568859 | + | 0.822435i | \(0.307385\pi\) | |||||||
\(752\) | 4.97185e31 | 0.0416881 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.70528e32 | −0.626640 | ||||||||
\(755\) | −1.41596e33 | −1.13412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.60404e32 | 0.513106 | 0.256553 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256553 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(758\) | −1.51627e32 | −0.116033 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.39047e32 | −0.325953 | ||||||||
\(761\) | 1.77866e33 | 1.30068 | 0.650338 | − | 0.759645i | \(-0.274627\pi\) | ||||
0.650338 | + | 0.759645i | \(0.274627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.62084e32 | −0.611670 | ||||||||
\(764\) | 6.26033e32 | 0.437546 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.47200e33 | 0.998338 | ||||||||
\(767\) | −1.34702e33 | −0.899967 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.31911e33 | 1.50372 | 0.751861 | − | 0.659322i | \(-0.229156\pi\) | ||||
0.751861 | + | 0.659322i | \(0.229156\pi\) | |||||||
\(770\) | 4.90711e32 | 0.313460 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.49863e32 | −0.0929172 | ||||||||
\(773\) | −7.88012e32 | −0.481359 | −0.240679 | − | 0.970605i | \(-0.577370\pi\) | ||||
−0.240679 | + | 0.970605i | \(0.577370\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.76805e32 | 0.579213 | ||||||||
\(776\) | −2.35543e31 | −0.0137613 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.48712e32 | 0.254508 | ||||||||
\(779\) | −1.98461e32 | −0.110916 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.57869e33 | 0.856663 | ||||||||
\(782\) | −4.98245e32 | −0.266419 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00807e32 | 0.0523429 | ||||||||
\(785\) | −5.54850e32 | −0.283906 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.06876e33 | 1.02802 | 0.514010 | − | 0.857784i | \(-0.328160\pi\) | ||||
0.514010 | + | 0.857784i | \(0.328160\pi\) | |||||||
\(788\) | −1.21992e33 | −0.597422 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.68891e32 | −0.365724 | ||||||||
\(791\) | −1.16383e33 | −0.545582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.00492e32 | −0.410051 | ||||||||
\(794\) | 8.80020e32 | 0.394964 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.20673e33 | 0.526152 | ||||||||
\(797\) | 3.07381e33 | 1.32101 | 0.660506 | − | 0.750821i | \(-0.270342\pi\) | ||||
0.660506 | + | 0.750821i | \(0.270342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.18945e33 | −0.914213 | ||||||||
\(800\) | 7.44839e32 | 0.306568 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.85167e33 | −0.740557 | ||||||||
\(803\) | 3.56375e33 | 1.40501 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.76310e32 | −0.144176 | ||||||||
\(806\) | 1.71797e33 | 0.648879 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.52430e33 | −1.29373 | ||||||||
\(809\) | −1.24720e33 | −0.451367 | −0.225683 | − | 0.974201i | \(-0.572461\pi\) | ||||
−0.225683 | + | 0.974201i | \(0.572461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.90918e33 | −0.671593 | −0.335797 | − | 0.941934i | \(-0.609006\pi\) | ||||
−0.335797 | + | 0.941934i | \(0.609006\pi\) | |||||||
\(812\) | −1.28250e33 | −0.444800 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.88818e33 | 0.973740 | ||||||||
\(815\) | −9.79540e32 | −0.325619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.11008e33 | −0.358756 | ||||||||
\(818\) | 3.38884e32 | 0.107991 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.65713e32 | 0.268234 | ||||||||
\(821\) | −5.44054e33 | −1.66225 | −0.831123 | − | 0.556088i | \(-0.812302\pi\) | ||||
−0.831123 | + | 0.556088i | \(0.812302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.68984e33 | −1.39335 | −0.696675 | − | 0.717387i | \(-0.745338\pi\) | ||||
−0.696675 | + | 0.717387i | \(0.745338\pi\) | |||||||
\(824\) | −3.10915e33 | −0.910917 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.56354e33 | 0.445491 | ||||||||
\(827\) | 2.85324e33 | 0.801723 | 0.400861 | − | 0.916139i | \(-0.368711\pi\) | ||||
0.400861 | + | 0.916139i | \(0.368711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.68450e32 | −0.182680 | −0.0913402 | − | 0.995820i | \(-0.529115\pi\) | ||||
−0.0913402 | + | 0.995820i | \(0.529115\pi\) | |||||||
\(830\) | 4.02268e33 | 1.08422 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.44328e33 | 0.378384 | ||||||||
\(833\) | −4.43925e33 | −1.14787 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.96691e33 | −2.00399 | ||||||||
\(836\) | 6.68465e32 | 0.165847 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.30273e33 | −1.03857 | ||||||||
\(839\) | −9.91584e32 | −0.236084 | −0.118042 | − | 0.993009i | \(-0.537662\pi\) | ||||
−0.118042 | + | 0.993009i | \(0.537662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.42149e33 | 2.18256 | ||||||||
\(842\) | 5.28734e32 | 0.120823 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.33365e33 | 0.963643 | ||||||||
\(845\) | 3.65578e33 | 0.801915 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.27758e31 | −0.00699672 | ||||||||
\(848\) | −3.07260e32 | −0.0647074 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.37111e33 | 0.281031 | ||||||||
\(851\) | −2.21485e33 | −0.447872 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.46591e33 | −1.07584 | −0.537921 | − | 0.842995i | \(-0.680790\pi\) | ||||
−0.537921 | + | 0.842995i | \(0.680790\pi\) | |||||||
\(854\) | 1.04524e33 | 0.202979 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.33425e33 | 1.19742 | ||||||||
\(857\) | −4.01521e33 | −0.748909 | −0.374454 | − | 0.927245i | \(-0.622170\pi\) | ||||
−0.374454 | + | 0.927245i | \(0.622170\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.42976e33 | 0.259622 | 0.129811 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129811 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(860\) | 4.84232e33 | 0.867603 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.99376e33 | 0.871152 | ||||||||
\(863\) | 1.03231e34 | 1.77699 | 0.888493 | − | 0.458890i | \(-0.151753\pi\) | ||||
0.888493 | + | 0.458890i | \(0.151753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.34461e33 | 0.392993 | ||||||||
\(866\) | −5.26564e33 | −0.870955 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.85948e33 | 0.460585 | ||||||||
\(869\) | 3.15772e33 | 0.501934 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.68480e33 | 0.415627 | ||||||||
\(872\) | −9.63630e33 | −1.47221 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.57492e32 | 0.0531967 | ||||||||
\(875\) | −2.26715e33 | −0.332956 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.03125e34 | 1.47526 | 0.737629 | − | 0.675207i | \(-0.235946\pi\) | ||||
0.737629 | + | 0.675207i | \(0.235946\pi\) | |||||||
\(878\) | −1.17770e33 | −0.166283 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.35679e32 | 0.0736807 | ||||||||
\(881\) | 1.04287e34 | 1.41582 | 0.707908 | − | 0.706305i | \(-0.249639\pi\) | ||||
0.707908 | + | 0.706305i | \(0.249639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.35131e34 | −1.78734 | −0.893669 | − | 0.448727i | \(-0.851878\pi\) | ||||
−0.893669 | + | 0.448727i | \(0.851878\pi\) | |||||||
\(884\) | −3.45791e33 | −0.451453 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.62057e33 | −0.333356 | ||||||||
\(887\) | 6.46528e33 | 0.811831 | 0.405916 | − | 0.913911i | \(-0.366953\pi\) | ||||
0.405916 | + | 0.913911i | \(0.366953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.60986e33 | 0.196979 | ||||||||
\(890\) | 1.85392e32 | 0.0223926 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.40190e33 | 0.165014 | ||||||||
\(893\) | 1.57093e33 | 0.182543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.73867e34 | −1.96903 | ||||||||
\(896\) | 2.02572e33 | 0.226484 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.09493e33 | −0.664188 | ||||||||
\(899\) | −3.06308e34 | −3.29550 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.35308e34 | 1.41902 | ||||||||
\(902\) | 2.47942e33 | 0.256729 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.30092e34 | −1.31315 | ||||||||
\(905\) | −1.04146e34 | −1.03797 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.63933e33 | 0.159288 | 0.0796439 | − | 0.996823i | \(-0.474622\pi\) | ||||
0.0796439 | + | 0.996823i | \(0.474622\pi\) | |||||||
\(908\) | 3.78289e33 | 0.362941 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.82131e33 | 0.170375 | ||||||||
\(911\) | 1.72363e34 | 1.59214 | 0.796072 | − | 0.605202i | \(-0.206908\pi\) | ||||
0.796072 | + | 0.605202i | \(0.206908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.65206e34 | −1.48803 | ||||||||
\(914\) | 7.00114e32 | 0.0622712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.54016e33 | 0.393798 | ||||||||
\(917\) | 2.87415e33 | 0.246185 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.99436e33 | −0.166600 | −0.0833000 | − | 0.996525i | \(-0.526546\pi\) | ||||
−0.0833000 | + | 0.996525i | \(0.526546\pi\) | |||||||
\(920\) | −4.20636e33 | −0.347014 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.37959e33 | 0.271931 | ||||||||
\(923\) | 5.85941e33 | 0.465623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.09499e33 | 0.472436 | ||||||||
\(926\) | 1.57136e34 | 1.20295 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.33568e34 | −1.74426 | ||||||||
\(929\) | 1.66371e34 | 1.22715 | 0.613573 | − | 0.789638i | \(-0.289732\pi\) | ||||
0.613573 | + | 0.789638i | \(0.289732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.18517e33 | 0.229198 | ||||||||
\(932\) | 3.30727e33 | 0.235064 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.87887e33 | −0.199634 | ||||||||
\(935\) | −2.35897e34 | −1.61580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.29325e34 | 1.53266 | 0.766331 | − | 0.642446i | \(-0.222080\pi\) | ||||
0.766331 | + | 0.642446i | \(0.222080\pi\) | |||||||
\(938\) | −3.11637e33 | −0.205739 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.85264e33 | −0.441456 | ||||||||
\(941\) | −9.97814e33 | −0.634993 | −0.317496 | − | 0.948259i | \(-0.602842\pi\) | ||||
−0.317496 | + | 0.948259i | \(0.602842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90138e33 | −0.118082 | ||||||||
\(944\) | 1.70682e33 | 0.104715 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.38685e34 | 0.830387 | ||||||||
\(947\) | −9.45460e33 | −0.559266 | −0.279633 | − | 0.960107i | \(-0.590213\pi\) | ||||
−0.279633 | + | 0.960107i | \(0.590213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.32271e34 | 0.763666 | ||||||||
\(950\) | −9.83772e32 | −0.0561142 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.08266e34 | 0.602791 | ||||||||
\(953\) | 2.62732e33 | 0.144525 | 0.0722627 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722627 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.58512e34 | 0.851186 | ||||||||
\(956\) | −6.53018e33 | −0.346465 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.77888e34 | −0.921390 | ||||||||
\(959\) | 3.47464e33 | 0.177826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.82813e34 | 2.41246 | ||||||||
\(962\) | 1.07197e34 | 0.529259 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.78184e33 | −0.230520 | ||||||||
\(965\) | −3.79456e33 | −0.180758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.74056e33 | −0.0809625 | −0.0404813 | − | 0.999180i | \(-0.512889\pi\) | ||||
−0.0404813 | + | 0.999180i | \(0.512889\pi\) | |||||||
\(968\) | −3.66366e32 | −0.0168402 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.21103e32 | −0.00992476 | ||||||||
\(971\) | 7.22515e33 | 0.320498 | 0.160249 | − | 0.987077i | \(-0.448770\pi\) | ||||
0.160249 | + | 0.987077i | \(0.448770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.32347e34 | −0.573344 | ||||||||
\(974\) | −7.52989e33 | −0.322374 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.14103e33 | 0.0477115 | ||||||||
\(977\) | −4.44312e33 | −0.183612 | −0.0918059 | − | 0.995777i | \(-0.529264\pi\) | ||||
−0.0918059 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.61377e32 | −0.0307326 | ||||||||
\(980\) | −1.38942e34 | −0.554284 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.62070e33 | −0.374908 | ||||||||
\(983\) | 2.62175e34 | 1.00978 | 0.504890 | − | 0.863184i | \(-0.331533\pi\) | ||||
0.504890 | + | 0.863184i | \(0.331533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.08886e34 | −1.16220 | ||||||||
\(986\) | −4.29954e34 | −1.59896 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.48106e33 | 0.0901429 | ||||||||
\(989\) | −1.06353e34 | −0.381937 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84277e33 | 0.0997458 | 0.0498729 | − | 0.998756i | \(-0.484118\pi\) | ||||
0.0498729 | + | 0.998756i | \(0.484118\pi\) | |||||||
\(992\) | 5.20764e34 | 1.80616 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.80129e33 | −0.230488 | ||||||||
\(995\) | 3.05547e34 | 1.02356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.04071e33 | 0.263209 | 0.131604 | − | 0.991302i | \(-0.457987\pi\) | ||||
0.131604 | + | 0.991302i | \(0.457987\pi\) | |||||||
\(998\) | 8.98481e33 | 0.290742 | ||||||||
\(999\) | 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.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 9.24.a.d.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.24.a.d.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
9.24.a.d.1.3 | yes | 4 | 1.1 | even | 1 | trivial |