Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46840000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.13324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13324 | −1.50843 | −0.754216 | − | 0.656627i | \(-0.771983\pi\) | ||||
−0.754216 | + | 0.656627i | \(0.771983\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.55073 | 1.27536 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.13324 | −0.870893 | ||||||||
\(7\) | 2.16876 | 0.819716 | 0.409858 | − | 0.912149i | \(-0.365578\pi\) | ||||
0.409858 | + | 0.912149i | \(0.365578\pi\) | |||||||
\(8\) | −1.17484 | −0.415369 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50913 | −0.756532 | −0.378266 | − | 0.925697i | \(-0.623480\pi\) | ||||
−0.378266 | + | 0.925697i | \(0.623480\pi\) | |||||||
\(12\) | 2.55073 | 0.736332 | ||||||||
\(13\) | −4.33379 | −1.20198 | −0.600989 | − | 0.799257i | \(-0.705226\pi\) | ||||
−0.600989 | + | 0.799257i | \(0.705226\pi\) | |||||||
\(14\) | −4.62650 | −1.23648 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.59524 | −0.648810 | ||||||||
\(17\) | −6.77562 | −1.64333 | −0.821665 | − | 0.569971i | \(-0.806954\pi\) | ||||
−0.821665 | + | 0.569971i | \(0.806954\pi\) | |||||||
\(18\) | −2.13324 | −0.502810 | ||||||||
\(19\) | 6.83602 | 1.56829 | 0.784145 | − | 0.620578i | \(-0.213102\pi\) | ||||
0.784145 | + | 0.620578i | \(0.213102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.16876 | 0.473263 | ||||||||
\(22\) | 5.35259 | 1.14118 | ||||||||
\(23\) | −1.67843 | −0.349977 | −0.174989 | − | 0.984570i | \(-0.555989\pi\) | ||||
−0.174989 | + | 0.984570i | \(0.555989\pi\) | |||||||
\(24\) | −1.17484 | −0.239813 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.24504 | 1.81310 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.53193 | 1.04544 | ||||||||
\(29\) | 4.44927 | 0.826209 | 0.413104 | − | 0.910684i | \(-0.364444\pi\) | ||||
0.413104 | + | 0.910684i | \(0.364444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56295 | 1.17874 | 0.589371 | − | 0.807863i | \(-0.299376\pi\) | ||||
0.589371 | + | 0.807863i | \(0.299376\pi\) | |||||||
\(32\) | 7.88596 | 1.39405 | ||||||||
\(33\) | −2.50913 | −0.436784 | ||||||||
\(34\) | 14.4541 | 2.47885 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.55073 | 0.425122 | ||||||||
\(37\) | 7.97720 | 1.31144 | 0.655722 | − | 0.755002i | \(-0.272364\pi\) | ||||
0.655722 | + | 0.755002i | \(0.272364\pi\) | |||||||
\(38\) | −14.5829 | −2.36566 | ||||||||
\(39\) | −4.33379 | −0.693962 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2249 | 1.75303 | 0.876517 | − | 0.481371i | \(-0.159861\pi\) | ||||
0.876517 | + | 0.481371i | \(0.159861\pi\) | |||||||
\(42\) | −4.62650 | −0.713885 | ||||||||
\(43\) | −4.25487 | −0.648861 | −0.324431 | − | 0.945909i | \(-0.605173\pi\) | ||||
−0.324431 | + | 0.945909i | \(0.605173\pi\) | |||||||
\(44\) | −6.40012 | −0.964854 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.58050 | 0.527916 | ||||||||
\(47\) | 4.98652 | 0.727358 | 0.363679 | − | 0.931524i | \(-0.381521\pi\) | ||||
0.363679 | + | 0.931524i | \(0.381521\pi\) | |||||||
\(48\) | −2.59524 | −0.374590 | ||||||||
\(49\) | −2.29646 | −0.328066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.77562 | −0.948777 | ||||||||
\(52\) | −11.0543 | −1.53296 | ||||||||
\(53\) | −8.21338 | −1.12820 | −0.564098 | − | 0.825708i | \(-0.690776\pi\) | ||||
−0.564098 | + | 0.825708i | \(0.690776\pi\) | |||||||
\(54\) | −2.13324 | −0.290298 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.54795 | −0.340484 | ||||||||
\(57\) | 6.83602 | 0.905453 | ||||||||
\(58\) | −9.49138 | −1.24628 | ||||||||
\(59\) | 3.67416 | 0.478335 | 0.239168 | − | 0.970978i | \(-0.423125\pi\) | ||||
0.239168 | + | 0.970978i | \(0.423125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.93960 | 0.632451 | 0.316226 | − | 0.948684i | \(-0.397584\pi\) | ||||
0.316226 | + | 0.948684i | \(0.397584\pi\) | |||||||
\(62\) | −14.0004 | −1.77805 | ||||||||
\(63\) | 2.16876 | 0.273239 | ||||||||
\(64\) | −11.6322 | −1.45402 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.35259 | 0.658859 | ||||||||
\(67\) | 11.5812 | 1.41487 | 0.707436 | − | 0.706778i | \(-0.249852\pi\) | ||||
0.707436 | + | 0.706778i | \(0.249852\pi\) | |||||||
\(68\) | −17.2828 | −2.09584 | ||||||||
\(69\) | −1.67843 | −0.202059 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.30251 | −0.273257 | −0.136629 | − | 0.990622i | \(-0.543627\pi\) | ||||
−0.136629 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(72\) | −1.17484 | −0.138456 | ||||||||
\(73\) | −1.11599 | −0.130617 | −0.0653084 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653084 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(74\) | −17.0173 | −1.97822 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.4368 | 2.00014 | ||||||||
\(77\) | −5.44172 | −0.620141 | ||||||||
\(78\) | 9.24504 | 1.04679 | ||||||||
\(79\) | 7.78306 | 0.875663 | 0.437831 | − | 0.899057i | \(-0.355747\pi\) | ||||
0.437831 | + | 0.899057i | \(0.355747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −23.9454 | −2.64433 | ||||||||
\(83\) | 9.87708 | 1.08415 | 0.542075 | − | 0.840330i | \(-0.317639\pi\) | ||||
0.542075 | + | 0.840330i | \(0.317639\pi\) | |||||||
\(84\) | 5.53193 | 0.603583 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.07667 | 0.978763 | ||||||||
\(87\) | 4.44927 | 0.477012 | ||||||||
\(88\) | 2.94783 | 0.314240 | ||||||||
\(89\) | −1.24025 | −0.131466 | −0.0657329 | − | 0.997837i | \(-0.520939\pi\) | ||||
−0.0657329 | + | 0.997837i | \(0.520939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.39897 | −0.985280 | ||||||||
\(92\) | −4.28122 | −0.446348 | ||||||||
\(93\) | 6.56295 | 0.680546 | ||||||||
\(94\) | −10.6375 | −1.09717 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.88596 | 0.804857 | ||||||||
\(97\) | 15.0488 | 1.52797 | 0.763985 | − | 0.645234i | \(-0.223240\pi\) | ||||
0.763985 | + | 0.645234i | \(0.223240\pi\) | |||||||
\(98\) | 4.89892 | 0.494866 | ||||||||
\(99\) | −2.50913 | −0.252177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.0211 | −1.69366 | −0.846830 | − | 0.531864i | \(-0.821492\pi\) | ||||
−0.846830 | + | 0.531864i | \(0.821492\pi\) | |||||||
\(102\) | 14.4541 | 1.43116 | ||||||||
\(103\) | 10.0859 | 0.993793 | 0.496897 | − | 0.867810i | \(-0.334473\pi\) | ||||
0.496897 | + | 0.867810i | \(0.334473\pi\) | |||||||
\(104\) | 5.09151 | 0.499264 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.5212 | 1.70180 | ||||||||
\(107\) | 5.67218 | 0.548351 | 0.274175 | − | 0.961680i | \(-0.411595\pi\) | ||||
0.274175 | + | 0.961680i | \(0.411595\pi\) | |||||||
\(108\) | 2.55073 | 0.245444 | ||||||||
\(109\) | 8.34557 | 0.799361 | 0.399680 | − | 0.916655i | \(-0.369121\pi\) | ||||
0.399680 | + | 0.916655i | \(0.369121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.97720 | 0.757163 | ||||||||
\(112\) | −5.62846 | −0.531839 | ||||||||
\(113\) | −14.8224 | −1.39438 | −0.697188 | − | 0.716888i | \(-0.745566\pi\) | ||||
−0.697188 | + | 0.716888i | \(0.745566\pi\) | |||||||
\(114\) | −14.5829 | −1.36581 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.3489 | 1.05372 | ||||||||
\(117\) | −4.33379 | −0.400659 | ||||||||
\(118\) | −7.83788 | −0.721536 | ||||||||
\(119\) | −14.6947 | −1.34706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.70425 | −0.427659 | ||||||||
\(122\) | −10.5374 | −0.954009 | ||||||||
\(123\) | 11.2249 | 1.01211 | ||||||||
\(124\) | 16.7403 | 1.50332 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.62650 | −0.412162 | ||||||||
\(127\) | −0.502113 | −0.0445553 | −0.0222777 | − | 0.999752i | \(-0.507092\pi\) | ||||
−0.0222777 | + | 0.999752i | \(0.507092\pi\) | |||||||
\(128\) | 9.04239 | 0.799242 | ||||||||
\(129\) | −4.25487 | −0.374620 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.05788 | 0.529280 | 0.264640 | − | 0.964347i | \(-0.414747\pi\) | ||||
0.264640 | + | 0.964347i | \(0.414747\pi\) | |||||||
\(132\) | −6.40012 | −0.557059 | ||||||||
\(133\) | 14.8257 | 1.28555 | ||||||||
\(134\) | −24.7056 | −2.13424 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.96027 | 0.682588 | ||||||||
\(137\) | −1.94014 | −0.165757 | −0.0828786 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828786 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(138\) | 3.58050 | 0.304793 | ||||||||
\(139\) | 19.2023 | 1.62872 | 0.814358 | − | 0.580363i | \(-0.197089\pi\) | ||||
0.814358 | + | 0.580363i | \(0.197089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.98652 | 0.419940 | ||||||||
\(142\) | 4.91181 | 0.412190 | ||||||||
\(143\) | 10.8741 | 0.909335 | ||||||||
\(144\) | −2.59524 | −0.216270 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.38068 | 0.197026 | ||||||||
\(147\) | −2.29646 | −0.189409 | ||||||||
\(148\) | 20.3477 | 1.67257 | ||||||||
\(149\) | 9.49138 | 0.777564 | 0.388782 | − | 0.921330i | \(-0.372896\pi\) | ||||
0.388782 | + | 0.921330i | \(0.372896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5747 | −1.02332 | −0.511659 | − | 0.859189i | \(-0.670969\pi\) | ||||
−0.511659 | + | 0.859189i | \(0.670969\pi\) | |||||||
\(152\) | −8.03123 | −0.651419 | ||||||||
\(153\) | −6.77562 | −0.547776 | ||||||||
\(154\) | 11.6085 | 0.935440 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.0543 | −0.885055 | ||||||||
\(157\) | −18.7991 | −1.50033 | −0.750165 | − | 0.661250i | \(-0.770026\pi\) | ||||
−0.750165 | + | 0.661250i | \(0.770026\pi\) | |||||||
\(158\) | −16.6032 | −1.32088 | ||||||||
\(159\) | −8.21338 | −0.651364 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.64012 | −0.286882 | ||||||||
\(162\) | −2.13324 | −0.167603 | ||||||||
\(163\) | −7.29949 | −0.571740 | −0.285870 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285870 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(164\) | 28.6317 | 2.23576 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.0702 | −1.63537 | ||||||||
\(167\) | 14.7991 | 1.14519 | 0.572594 | − | 0.819839i | \(-0.305937\pi\) | ||||
0.572594 | + | 0.819839i | \(0.305937\pi\) | |||||||
\(168\) | −2.54795 | −0.196579 | ||||||||
\(169\) | 5.78176 | 0.444750 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.83602 | 0.522763 | ||||||||
\(172\) | −10.8530 | −0.827535 | ||||||||
\(173\) | 2.29460 | 0.174455 | 0.0872276 | − | 0.996188i | \(-0.472199\pi\) | ||||
0.0872276 | + | 0.996188i | \(0.472199\pi\) | |||||||
\(174\) | −9.49138 | −0.719540 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.51180 | 0.490845 | ||||||||
\(177\) | 3.67416 | 0.276167 | ||||||||
\(178\) | 2.64575 | 0.198307 | ||||||||
\(179\) | 13.6637 | 1.02127 | 0.510636 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510636 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.71878 | 0.648062 | 0.324031 | − | 0.946046i | \(-0.394962\pi\) | ||||
0.324031 | + | 0.946046i | \(0.394962\pi\) | |||||||
\(182\) | 20.0503 | 1.48623 | ||||||||
\(183\) | 4.93960 | 0.365146 | ||||||||
\(184\) | 1.97189 | 0.145370 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.0004 | −1.02656 | ||||||||
\(187\) | 17.0009 | 1.24323 | ||||||||
\(188\) | 12.7193 | 0.927647 | ||||||||
\(189\) | 2.16876 | 0.157754 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6080 | 0.839925 | 0.419963 | − | 0.907541i | \(-0.362043\pi\) | ||||
0.419963 | + | 0.907541i | \(0.362043\pi\) | |||||||
\(192\) | −11.6322 | −0.839481 | ||||||||
\(193\) | 14.8653 | 1.07002 | 0.535012 | − | 0.844844i | \(-0.320307\pi\) | ||||
0.535012 | + | 0.844844i | \(0.320307\pi\) | |||||||
\(194\) | −32.1027 | −2.30484 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.85766 | −0.418404 | ||||||||
\(197\) | −22.8292 | −1.62651 | −0.813256 | − | 0.581906i | \(-0.802307\pi\) | ||||
−0.813256 | + | 0.581906i | \(0.802307\pi\) | |||||||
\(198\) | 5.35259 | 0.380392 | ||||||||
\(199\) | 5.87697 | 0.416607 | 0.208304 | − | 0.978064i | \(-0.433206\pi\) | ||||
0.208304 | + | 0.978064i | \(0.433206\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.5812 | 0.816876 | ||||||||
\(202\) | 36.3101 | 2.55477 | ||||||||
\(203\) | 9.64942 | 0.677256 | ||||||||
\(204\) | −17.2828 | −1.21004 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.5157 | −1.49907 | ||||||||
\(207\) | −1.67843 | −0.116659 | ||||||||
\(208\) | 11.2472 | 0.779855 | ||||||||
\(209\) | −17.1525 | −1.18646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.6884 | −1.69962 | −0.849810 | − | 0.527090i | \(-0.823283\pi\) | ||||
−0.849810 | + | 0.527090i | \(0.823283\pi\) | |||||||
\(212\) | −20.9501 | −1.43886 | ||||||||
\(213\) | −2.30251 | −0.157765 | ||||||||
\(214\) | −12.1002 | −0.827149 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.17484 | −0.0799378 | ||||||||
\(217\) | 14.2335 | 0.966232 | ||||||||
\(218\) | −17.8031 | −1.20578 | ||||||||
\(219\) | −1.11599 | −0.0754116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.3641 | 1.97525 | ||||||||
\(222\) | −17.0173 | −1.14213 | ||||||||
\(223\) | 3.31060 | 0.221694 | 0.110847 | − | 0.993837i | \(-0.464644\pi\) | ||||
0.110847 | + | 0.993837i | \(0.464644\pi\) | |||||||
\(224\) | 17.1028 | 1.14273 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.6198 | 2.10332 | ||||||||
\(227\) | 2.70185 | 0.179328 | 0.0896641 | − | 0.995972i | \(-0.471421\pi\) | ||||
0.0896641 | + | 0.995972i | \(0.471421\pi\) | |||||||
\(228\) | 17.4368 | 1.15478 | ||||||||
\(229\) | −9.33473 | −0.616856 | −0.308428 | − | 0.951248i | \(-0.599803\pi\) | ||||
−0.308428 | + | 0.951248i | \(0.599803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.44172 | −0.358039 | ||||||||
\(232\) | −5.22718 | −0.343181 | ||||||||
\(233\) | −9.52491 | −0.623998 | −0.311999 | − | 0.950083i | \(-0.600998\pi\) | ||||
−0.311999 | + | 0.950083i | \(0.600998\pi\) | |||||||
\(234\) | 9.24504 | 0.604367 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.37179 | 0.610052 | ||||||||
\(237\) | 7.78306 | 0.505564 | ||||||||
\(238\) | 31.3474 | 2.03195 | ||||||||
\(239\) | 7.84648 | 0.507546 | 0.253773 | − | 0.967264i | \(-0.418328\pi\) | ||||
0.253773 | + | 0.967264i | \(0.418328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.42783 | 0.0919747 | 0.0459874 | − | 0.998942i | \(-0.485357\pi\) | ||||
0.0459874 | + | 0.998942i | \(0.485357\pi\) | |||||||
\(242\) | 10.0353 | 0.645095 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.5996 | 0.806606 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −23.9454 | −1.52670 | ||||||||
\(247\) | −29.6259 | −1.88505 | ||||||||
\(248\) | −7.71042 | −0.489612 | ||||||||
\(249\) | 9.87708 | 0.625935 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.5762 | −1.10940 | −0.554701 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554701 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(252\) | 5.53193 | 0.348479 | ||||||||
\(253\) | 4.21141 | 0.264769 | ||||||||
\(254\) | 1.07113 | 0.0672087 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97476 | 0.248423 | ||||||||
\(257\) | 19.2890 | 1.20322 | 0.601608 | − | 0.798791i | \(-0.294527\pi\) | ||||
0.601608 | + | 0.798791i | \(0.294527\pi\) | |||||||
\(258\) | 9.07667 | 0.565089 | ||||||||
\(259\) | 17.3007 | 1.07501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.44927 | 0.275403 | ||||||||
\(262\) | −12.9229 | −0.798382 | ||||||||
\(263\) | 22.2432 | 1.37157 | 0.685786 | − | 0.727803i | \(-0.259459\pi\) | ||||
0.685786 | + | 0.727803i | \(0.259459\pi\) | |||||||
\(264\) | 2.94783 | 0.181426 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −31.6268 | −1.93917 | ||||||||
\(267\) | −1.24025 | −0.0759018 | ||||||||
\(268\) | 29.5406 | 1.80448 | ||||||||
\(269\) | 25.1785 | 1.53516 | 0.767581 | − | 0.640951i | \(-0.221460\pi\) | ||||
0.767581 | + | 0.640951i | \(0.221460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.70091 | −0.346306 | −0.173153 | − | 0.984895i | \(-0.555395\pi\) | ||||
−0.173153 | + | 0.984895i | \(0.555395\pi\) | |||||||
\(272\) | 17.5843 | 1.06621 | ||||||||
\(273\) | −9.39897 | −0.568852 | ||||||||
\(274\) | 4.13879 | 0.250033 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.28122 | −0.257699 | ||||||||
\(277\) | −19.1611 | −1.15128 | −0.575638 | − | 0.817704i | \(-0.695246\pi\) | ||||
−0.575638 | + | 0.817704i | \(0.695246\pi\) | |||||||
\(278\) | −40.9631 | −2.45681 | ||||||||
\(279\) | 6.56295 | 0.392914 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.36015 | 0.260105 | 0.130052 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130052 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(282\) | −10.6375 | −0.633451 | ||||||||
\(283\) | 24.9081 | 1.48063 | 0.740317 | − | 0.672258i | \(-0.234676\pi\) | ||||
0.740317 | + | 0.672258i | \(0.234676\pi\) | |||||||
\(284\) | −5.87307 | −0.348503 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.1970 | −1.37167 | ||||||||
\(287\) | 24.3441 | 1.43699 | ||||||||
\(288\) | 7.88596 | 0.464684 | ||||||||
\(289\) | 28.9090 | 1.70053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.0488 | 0.882174 | ||||||||
\(292\) | −2.84659 | −0.166584 | ||||||||
\(293\) | 13.5651 | 0.792484 | 0.396242 | − | 0.918146i | \(-0.370314\pi\) | ||||
0.396242 | + | 0.918146i | \(0.370314\pi\) | |||||||
\(294\) | 4.89892 | 0.285711 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.37194 | −0.544733 | ||||||||
\(297\) | −2.50913 | −0.145595 | ||||||||
\(298\) | −20.2474 | −1.17290 | ||||||||
\(299\) | 7.27397 | 0.420665 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.22780 | −0.531882 | ||||||||
\(302\) | 26.8250 | 1.54360 | ||||||||
\(303\) | −17.0211 | −0.977835 | ||||||||
\(304\) | −17.7411 | −1.01752 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.4541 | 0.826283 | ||||||||
\(307\) | 11.9672 | 0.683007 | 0.341504 | − | 0.939880i | \(-0.389064\pi\) | ||||
0.341504 | + | 0.939880i | \(0.389064\pi\) | |||||||
\(308\) | −13.8803 | −0.790906 | ||||||||
\(309\) | 10.0859 | 0.573767 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.66452 | 0.434615 | 0.217308 | − | 0.976103i | \(-0.430273\pi\) | ||||
0.217308 | + | 0.976103i | \(0.430273\pi\) | |||||||
\(312\) | 5.09151 | 0.288250 | ||||||||
\(313\) | −26.3840 | −1.49131 | −0.745655 | − | 0.666332i | \(-0.767863\pi\) | ||||
−0.745655 | + | 0.666332i | \(0.767863\pi\) | |||||||
\(314\) | 40.1030 | 2.26315 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.8525 | 1.11679 | ||||||||
\(317\) | 10.8880 | 0.611529 | 0.305765 | − | 0.952107i | \(-0.401088\pi\) | ||||
0.305765 | + | 0.952107i | \(0.401088\pi\) | |||||||
\(318\) | 17.5212 | 0.982537 | ||||||||
\(319\) | −11.1638 | −0.625053 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.67218 | 0.316590 | ||||||||
\(322\) | 7.76526 | 0.432741 | ||||||||
\(323\) | −46.3183 | −2.57722 | ||||||||
\(324\) | 2.55073 | 0.141707 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5716 | 0.862431 | ||||||||
\(327\) | 8.34557 | 0.461511 | ||||||||
\(328\) | −13.1875 | −0.728155 | ||||||||
\(329\) | 10.8146 | 0.596227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.2137 | −1.77062 | −0.885312 | − | 0.464998i | \(-0.846055\pi\) | ||||
−0.885312 | + | 0.464998i | \(0.846055\pi\) | |||||||
\(332\) | 25.1938 | 1.38269 | ||||||||
\(333\) | 7.97720 | 0.437148 | ||||||||
\(334\) | −31.5701 | −1.72744 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.62846 | −0.307058 | ||||||||
\(337\) | 3.47169 | 0.189115 | 0.0945576 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945576 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(338\) | −12.3339 | −0.670875 | ||||||||
\(339\) | −14.8224 | −0.805043 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4673 | −0.891755 | ||||||||
\(342\) | −14.5829 | −0.788553 | ||||||||
\(343\) | −20.1618 | −1.08864 | ||||||||
\(344\) | 4.99879 | 0.269517 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.89494 | −0.263154 | ||||||||
\(347\) | 10.9805 | 0.589465 | 0.294733 | − | 0.955580i | \(-0.404769\pi\) | ||||
0.294733 | + | 0.955580i | \(0.404769\pi\) | |||||||
\(348\) | 11.3489 | 0.608364 | ||||||||
\(349\) | −26.3158 | −1.40865 | −0.704325 | − | 0.709878i | \(-0.748750\pi\) | ||||
−0.704325 | + | 0.709878i | \(0.748750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.33379 | −0.231321 | ||||||||
\(352\) | −19.7869 | −1.05465 | ||||||||
\(353\) | 16.3668 | 0.871119 | 0.435559 | − | 0.900160i | \(-0.356551\pi\) | ||||
0.435559 | + | 0.900160i | \(0.356551\pi\) | |||||||
\(354\) | −7.83788 | −0.416579 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.16353 | −0.167667 | ||||||||
\(357\) | −14.6947 | −0.777727 | ||||||||
\(358\) | −29.1480 | −1.54052 | ||||||||
\(359\) | −17.4871 | −0.922934 | −0.461467 | − | 0.887157i | \(-0.652677\pi\) | ||||
−0.461467 | + | 0.887157i | \(0.652677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.7311 | 1.45953 | ||||||||
\(362\) | −18.5993 | −0.977557 | ||||||||
\(363\) | −4.70425 | −0.246909 | ||||||||
\(364\) | −23.9742 | −1.25659 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5374 | −0.550798 | ||||||||
\(367\) | −8.29594 | −0.433044 | −0.216522 | − | 0.976278i | \(-0.569471\pi\) | ||||
−0.216522 | + | 0.976278i | \(0.569471\pi\) | |||||||
\(368\) | 4.35593 | 0.227068 | ||||||||
\(369\) | 11.2249 | 0.584345 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.8129 | −0.924799 | ||||||||
\(372\) | 16.7403 | 0.867945 | ||||||||
\(373\) | 19.1295 | 0.990486 | 0.495243 | − | 0.868755i | \(-0.335079\pi\) | ||||
0.495243 | + | 0.868755i | \(0.335079\pi\) | |||||||
\(374\) | −36.2671 | −1.87533 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.85836 | −0.302122 | ||||||||
\(377\) | −19.2822 | −0.993085 | ||||||||
\(378\) | −4.62650 | −0.237962 | ||||||||
\(379\) | −27.0952 | −1.39179 | −0.695894 | − | 0.718145i | \(-0.744992\pi\) | ||||
−0.695894 | + | 0.718145i | \(0.744992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.502113 | −0.0257240 | ||||||||
\(382\) | −24.7627 | −1.26697 | ||||||||
\(383\) | −19.8026 | −1.01187 | −0.505933 | − | 0.862573i | \(-0.668852\pi\) | ||||
−0.505933 | + | 0.862573i | \(0.668852\pi\) | |||||||
\(384\) | 9.04239 | 0.461443 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −31.7112 | −1.61406 | ||||||||
\(387\) | −4.25487 | −0.216287 | ||||||||
\(388\) | 38.3853 | 1.94872 | ||||||||
\(389\) | −23.0130 | −1.16680 | −0.583402 | − | 0.812183i | \(-0.698279\pi\) | ||||
−0.583402 | + | 0.812183i | \(0.698279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3724 | 0.575128 | ||||||||
\(392\) | 2.69798 | 0.136269 | ||||||||
\(393\) | 6.05788 | 0.305580 | ||||||||
\(394\) | 48.7002 | 2.45348 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.40012 | −0.321618 | ||||||||
\(397\) | 20.5745 | 1.03260 | 0.516301 | − | 0.856407i | \(-0.327309\pi\) | ||||
0.516301 | + | 0.856407i | \(0.327309\pi\) | |||||||
\(398\) | −12.5370 | −0.628423 | ||||||||
\(399\) | 14.8257 | 0.742214 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1542 | −0.656889 | −0.328444 | − | 0.944523i | \(-0.606524\pi\) | ||||
−0.328444 | + | 0.944523i | \(0.606524\pi\) | |||||||
\(402\) | −24.7056 | −1.23220 | ||||||||
\(403\) | −28.4425 | −1.41682 | ||||||||
\(404\) | −43.4161 | −2.16003 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.5846 | −1.02159 | ||||||||
\(407\) | −20.0159 | −0.992150 | ||||||||
\(408\) | 7.96027 | 0.394092 | ||||||||
\(409\) | 2.76531 | 0.136736 | 0.0683679 | − | 0.997660i | \(-0.478221\pi\) | ||||
0.0683679 | + | 0.997660i | \(0.478221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.94014 | −0.0956999 | ||||||||
\(412\) | 25.7264 | 1.26745 | ||||||||
\(413\) | 7.96839 | 0.392099 | ||||||||
\(414\) | 3.58050 | 0.175972 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −34.1761 | −1.67562 | ||||||||
\(417\) | 19.2023 | 0.940340 | ||||||||
\(418\) | 36.5904 | 1.78970 | ||||||||
\(419\) | −9.70852 | −0.474292 | −0.237146 | − | 0.971474i | \(-0.576212\pi\) | ||||
−0.237146 | + | 0.971474i | \(0.576212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.21745 | −0.205546 | −0.102773 | − | 0.994705i | \(-0.532772\pi\) | ||||
−0.102773 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(422\) | 52.6664 | 2.56376 | ||||||||
\(423\) | 4.98652 | 0.242453 | ||||||||
\(424\) | 9.64942 | 0.468617 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.91181 | 0.237978 | ||||||||
\(427\) | 10.7128 | 0.518430 | ||||||||
\(428\) | 14.4682 | 0.699347 | ||||||||
\(429\) | 10.8741 | 0.525005 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.9785 | 0.914164 | 0.457082 | − | 0.889425i | \(-0.348895\pi\) | ||||
0.457082 | + | 0.889425i | \(0.348895\pi\) | |||||||
\(432\) | −2.59524 | −0.124863 | ||||||||
\(433\) | −13.7054 | −0.658640 | −0.329320 | − | 0.944218i | \(-0.606819\pi\) | ||||
−0.329320 | + | 0.944218i | \(0.606819\pi\) | |||||||
\(434\) | −30.3635 | −1.45750 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.2873 | 1.01948 | ||||||||
\(437\) | −11.4738 | −0.548866 | ||||||||
\(438\) | 2.38068 | 0.113753 | ||||||||
\(439\) | −33.3843 | −1.59335 | −0.796673 | − | 0.604410i | \(-0.793409\pi\) | ||||
−0.796673 | + | 0.604410i | \(0.793409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.29646 | −0.109355 | ||||||||
\(442\) | −62.6409 | −2.97952 | ||||||||
\(443\) | −11.6290 | −0.552512 | −0.276256 | − | 0.961084i | \(-0.589094\pi\) | ||||
−0.276256 | + | 0.961084i | \(0.589094\pi\) | |||||||
\(444\) | 20.3477 | 0.965659 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.06231 | −0.334410 | ||||||||
\(447\) | 9.49138 | 0.448927 | ||||||||
\(448\) | −25.2275 | −1.19189 | ||||||||
\(449\) | −13.3509 | −0.630069 | −0.315034 | − | 0.949080i | \(-0.602016\pi\) | ||||
−0.315034 | + | 0.949080i | \(0.602016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.1647 | −1.32623 | ||||||||
\(452\) | −37.8080 | −1.77834 | ||||||||
\(453\) | −12.5747 | −0.590813 | ||||||||
\(454\) | −5.76371 | −0.270504 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.03123 | −0.376097 | ||||||||
\(457\) | 23.3042 | 1.09013 | 0.545063 | − | 0.838395i | \(-0.316506\pi\) | ||||
0.545063 | + | 0.838395i | \(0.316506\pi\) | |||||||
\(458\) | 19.9132 | 0.930485 | ||||||||
\(459\) | −6.77562 | −0.316259 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.03269 | 0.234396 | 0.117198 | − | 0.993109i | \(-0.462609\pi\) | ||||
0.117198 | + | 0.993109i | \(0.462609\pi\) | |||||||
\(462\) | 11.6085 | 0.540077 | ||||||||
\(463\) | 12.7759 | 0.593746 | 0.296873 | − | 0.954917i | \(-0.404056\pi\) | ||||
0.296873 | + | 0.954917i | \(0.404056\pi\) | |||||||
\(464\) | −11.5469 | −0.536052 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3190 | 0.941257 | ||||||||
\(467\) | −4.86284 | −0.225025 | −0.112513 | − | 0.993650i | \(-0.535890\pi\) | ||||
−0.112513 | + | 0.993650i | \(0.535890\pi\) | |||||||
\(468\) | −11.0543 | −0.510987 | ||||||||
\(469\) | 25.1169 | 1.15979 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7991 | −0.866216 | ||||||||
\(472\) | −4.31655 | −0.198685 | ||||||||
\(473\) | 10.6760 | 0.490884 | ||||||||
\(474\) | −16.6032 | −0.762609 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −37.4823 | −1.71800 | ||||||||
\(477\) | −8.21338 | −0.376065 | ||||||||
\(478\) | −16.7385 | −0.765599 | ||||||||
\(479\) | 4.79202 | 0.218953 | 0.109476 | − | 0.993989i | \(-0.465083\pi\) | ||||
0.109476 | + | 0.993989i | \(0.465083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.5715 | −1.57633 | ||||||||
\(482\) | −3.04591 | −0.138738 | ||||||||
\(483\) | −3.64012 | −0.165631 | ||||||||
\(484\) | −11.9993 | −0.545421 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.13324 | −0.0967659 | ||||||||
\(487\) | −9.16949 | −0.415509 | −0.207755 | − | 0.978181i | \(-0.566616\pi\) | ||||
−0.207755 | + | 0.978181i | \(0.566616\pi\) | |||||||
\(488\) | −5.80325 | −0.262701 | ||||||||
\(489\) | −7.29949 | −0.330094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.9054 | 1.43987 | 0.719935 | − | 0.694042i | \(-0.244172\pi\) | ||||
0.719935 | + | 0.694042i | \(0.244172\pi\) | |||||||
\(492\) | 28.6317 | 1.29081 | ||||||||
\(493\) | −30.1466 | −1.35773 | ||||||||
\(494\) | 63.1992 | 2.84347 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.0324 | −0.764778 | ||||||||
\(497\) | −4.99359 | −0.223993 | ||||||||
\(498\) | −21.0702 | −0.944179 | ||||||||
\(499\) | 9.07297 | 0.406162 | 0.203081 | − | 0.979162i | \(-0.434905\pi\) | ||||
0.203081 | + | 0.979162i | \(0.434905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7991 | 0.661175 | ||||||||
\(502\) | 37.4944 | 1.67346 | ||||||||
\(503\) | −38.7485 | −1.72771 | −0.863856 | − | 0.503739i | \(-0.831957\pi\) | ||||
−0.863856 | + | 0.503739i | \(0.831957\pi\) | |||||||
\(504\) | −2.54795 | −0.113495 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.98396 | −0.399386 | ||||||||
\(507\) | 5.78176 | 0.256777 | ||||||||
\(508\) | −1.28075 | −0.0568243 | ||||||||
\(509\) | 32.9367 | 1.45989 | 0.729947 | − | 0.683503i | \(-0.239545\pi\) | ||||
0.729947 | + | 0.683503i | \(0.239545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.42032 | −0.107069 | ||||||||
\(512\) | −26.5639 | −1.17397 | ||||||||
\(513\) | 6.83602 | 0.301818 | ||||||||
\(514\) | −41.1482 | −1.81497 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.8530 | −0.477777 | ||||||||
\(517\) | −12.5118 | −0.550270 | ||||||||
\(518\) | −36.9065 | −1.62158 | ||||||||
\(519\) | 2.29460 | 0.100722 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.7521 | −0.777735 | −0.388867 | − | 0.921294i | \(-0.627134\pi\) | ||||
−0.388867 | + | 0.921294i | \(0.627134\pi\) | |||||||
\(522\) | −9.49138 | −0.415426 | ||||||||
\(523\) | 4.98678 | 0.218056 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(524\) | 15.4520 | 0.675025 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.4501 | −2.06892 | ||||||||
\(527\) | −44.4681 | −1.93706 | ||||||||
\(528\) | 6.51180 | 0.283390 | ||||||||
\(529\) | −20.1829 | −0.877516 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.67416 | 0.159445 | ||||||||
\(532\) | 37.8164 | 1.63955 | ||||||||
\(533\) | −48.6463 | −2.10711 | ||||||||
\(534\) | 2.64575 | 0.114493 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.6061 | −0.587693 | ||||||||
\(537\) | 13.6637 | 0.589632 | ||||||||
\(538\) | −53.7120 | −2.31569 | ||||||||
\(539\) | 5.76214 | 0.248193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.49960 | −0.150460 | −0.0752298 | − | 0.997166i | \(-0.523969\pi\) | ||||
−0.0752298 | + | 0.997166i | \(0.523969\pi\) | |||||||
\(542\) | 12.1614 | 0.522378 | ||||||||
\(543\) | 8.71878 | 0.374159 | ||||||||
\(544\) | −53.4322 | −2.29089 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.0503 | 0.858073 | ||||||||
\(547\) | 17.4640 | 0.746709 | 0.373354 | − | 0.927689i | \(-0.378208\pi\) | ||||
0.373354 | + | 0.927689i | \(0.378208\pi\) | |||||||
\(548\) | −4.94877 | −0.211401 | ||||||||
\(549\) | 4.93960 | 0.210817 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.4153 | 1.29574 | ||||||||
\(552\) | 1.97189 | 0.0839291 | ||||||||
\(553\) | 16.8796 | 0.717795 | ||||||||
\(554\) | 40.8752 | 1.73662 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 48.9798 | 2.07721 | ||||||||
\(557\) | −6.02774 | −0.255403 | −0.127702 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127702 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(558\) | −14.0004 | −0.592683 | ||||||||
\(559\) | 18.4397 | 0.779917 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.0009 | 0.717780 | ||||||||
\(562\) | −9.30126 | −0.392350 | ||||||||
\(563\) | −9.19823 | −0.387659 | −0.193830 | − | 0.981035i | \(-0.562091\pi\) | ||||
−0.193830 | + | 0.981035i | \(0.562091\pi\) | |||||||
\(564\) | 12.7193 | 0.535577 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −53.1351 | −2.23343 | ||||||||
\(567\) | 2.16876 | 0.0910795 | ||||||||
\(568\) | 2.70508 | 0.113503 | ||||||||
\(569\) | 9.06517 | 0.380032 | 0.190016 | − | 0.981781i | \(-0.439146\pi\) | ||||
0.190016 | + | 0.981781i | \(0.439146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.34688 | −0.265609 | −0.132804 | − | 0.991142i | \(-0.542398\pi\) | ||||
−0.132804 | + | 0.991142i | \(0.542398\pi\) | |||||||
\(572\) | 27.7368 | 1.15973 | ||||||||
\(573\) | 11.6080 | 0.484931 | ||||||||
\(574\) | −51.9320 | −2.16760 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.6322 | −0.484675 | ||||||||
\(577\) | −2.41418 | −0.100504 | −0.0502519 | − | 0.998737i | \(-0.516002\pi\) | ||||
−0.0502519 | + | 0.998737i | \(0.516002\pi\) | |||||||
\(578\) | −61.6700 | −2.56513 | ||||||||
\(579\) | 14.8653 | 0.617779 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.4211 | 0.888695 | ||||||||
\(582\) | −32.1027 | −1.33070 | ||||||||
\(583\) | 20.6085 | 0.853516 | ||||||||
\(584\) | 1.31111 | 0.0542541 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.9378 | −1.19541 | ||||||||
\(587\) | −4.50976 | −0.186138 | −0.0930689 | − | 0.995660i | \(-0.529668\pi\) | ||||
−0.0930689 | + | 0.995660i | \(0.529668\pi\) | |||||||
\(588\) | −5.85766 | −0.241566 | ||||||||
\(589\) | 44.8645 | 1.84861 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.8292 | −0.939067 | ||||||||
\(592\) | −20.7027 | −0.850877 | ||||||||
\(593\) | 33.2824 | 1.36674 | 0.683371 | − | 0.730071i | \(-0.260513\pi\) | ||||
0.683371 | + | 0.730071i | \(0.260513\pi\) | |||||||
\(594\) | 5.35259 | 0.219620 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.2099 | 0.991678 | ||||||||
\(597\) | 5.87697 | 0.240528 | ||||||||
\(598\) | −15.5172 | −0.634544 | ||||||||
\(599\) | 39.1061 | 1.59783 | 0.798915 | − | 0.601444i | \(-0.205408\pi\) | ||||
0.798915 | + | 0.601444i | \(0.205408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.8076 | −1.17509 | −0.587543 | − | 0.809193i | \(-0.699905\pi\) | ||||
−0.587543 | + | 0.809193i | \(0.699905\pi\) | |||||||
\(602\) | 19.6852 | 0.802307 | ||||||||
\(603\) | 11.5812 | 0.471624 | ||||||||
\(604\) | −32.0747 | −1.30510 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 36.3101 | 1.47500 | ||||||||
\(607\) | 23.0933 | 0.937327 | 0.468663 | − | 0.883377i | \(-0.344736\pi\) | ||||
0.468663 | + | 0.883377i | \(0.344736\pi\) | |||||||
\(608\) | 53.9085 | 2.18628 | ||||||||
\(609\) | 9.64942 | 0.391014 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.6105 | −0.874268 | ||||||||
\(612\) | −17.2828 | −0.698615 | ||||||||
\(613\) | 18.2228 | 0.736013 | 0.368007 | − | 0.929823i | \(-0.380040\pi\) | ||||
0.368007 | + | 0.929823i | \(0.380040\pi\) | |||||||
\(614\) | −25.5291 | −1.03027 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.39315 | 0.257587 | ||||||||
\(617\) | −15.4484 | −0.621930 | −0.310965 | − | 0.950421i | \(-0.600652\pi\) | ||||
−0.310965 | + | 0.950421i | \(0.600652\pi\) | |||||||
\(618\) | −21.5157 | −0.865488 | ||||||||
\(619\) | 16.5042 | 0.663359 | 0.331680 | − | 0.943392i | \(-0.392385\pi\) | ||||
0.331680 | + | 0.943392i | \(0.392385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.67843 | −0.0673531 | ||||||||
\(622\) | −16.3503 | −0.655587 | ||||||||
\(623\) | −2.68980 | −0.107765 | ||||||||
\(624\) | 11.2472 | 0.450249 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 56.2835 | 2.24954 | ||||||||
\(627\) | −17.1525 | −0.685004 | ||||||||
\(628\) | −47.9514 | −1.91347 | ||||||||
\(629\) | −54.0505 | −2.15513 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1237 | −1.51768 | −0.758841 | − | 0.651276i | \(-0.774234\pi\) | ||||
−0.758841 | + | 0.651276i | \(0.774234\pi\) | |||||||
\(632\) | −9.14386 | −0.363723 | ||||||||
\(633\) | −24.6884 | −0.981276 | ||||||||
\(634\) | −23.2267 | −0.922450 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −20.9501 | −0.830726 | ||||||||
\(637\) | 9.95240 | 0.394329 | ||||||||
\(638\) | 23.8151 | 0.942850 | ||||||||
\(639\) | −2.30251 | −0.0910858 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.9299 | 1.53764 | 0.768819 | − | 0.639466i | \(-0.220845\pi\) | ||||
0.768819 | + | 0.639466i | \(0.220845\pi\) | |||||||
\(642\) | −12.1002 | −0.477555 | ||||||||
\(643\) | −40.5346 | −1.59853 | −0.799265 | − | 0.600979i | \(-0.794778\pi\) | ||||
−0.799265 | + | 0.600979i | \(0.794778\pi\) | |||||||
\(644\) | −9.28496 | −0.365879 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 98.8082 | 3.88755 | ||||||||
\(647\) | −31.8752 | −1.25315 | −0.626573 | − | 0.779363i | \(-0.715543\pi\) | ||||
−0.626573 | + | 0.779363i | \(0.715543\pi\) | |||||||
\(648\) | −1.17484 | −0.0461521 | ||||||||
\(649\) | −9.21896 | −0.361876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2335 | 0.557855 | ||||||||
\(652\) | −18.6190 | −0.729177 | ||||||||
\(653\) | 19.5285 | 0.764210 | 0.382105 | − | 0.924119i | \(-0.375199\pi\) | ||||
0.382105 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(654\) | −17.8031 | −0.696158 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.1313 | −1.13738 | ||||||||
\(657\) | −1.11599 | −0.0435389 | ||||||||
\(658\) | −23.0701 | −0.899367 | ||||||||
\(659\) | 47.6562 | 1.85642 | 0.928211 | − | 0.372055i | \(-0.121347\pi\) | ||||
0.928211 | + | 0.372055i | \(0.121347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.91738 | 0.152368 | 0.0761842 | − | 0.997094i | \(-0.475726\pi\) | ||||
0.0761842 | + | 0.997094i | \(0.475726\pi\) | |||||||
\(662\) | 68.7196 | 2.67086 | ||||||||
\(663\) | 29.3641 | 1.14041 | ||||||||
\(664\) | −11.6040 | −0.450322 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.0173 | −0.659408 | ||||||||
\(667\) | −7.46779 | −0.289154 | ||||||||
\(668\) | 37.7485 | 1.46053 | ||||||||
\(669\) | 3.31060 | 0.127995 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.3941 | −0.478470 | ||||||||
\(672\) | 17.1028 | 0.659754 | ||||||||
\(673\) | −28.1866 | −1.08651 | −0.543257 | − | 0.839566i | \(-0.682809\pi\) | ||||
−0.543257 | + | 0.839566i | \(0.682809\pi\) | |||||||
\(674\) | −7.40597 | −0.285267 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.7477 | 0.567219 | ||||||||
\(677\) | 9.50611 | 0.365350 | 0.182675 | − | 0.983173i | \(-0.441524\pi\) | ||||
0.182675 | + | 0.983173i | \(0.441524\pi\) | |||||||
\(678\) | 31.6198 | 1.21435 | ||||||||
\(679\) | 32.6372 | 1.25250 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.70185 | 0.103535 | ||||||||
\(682\) | 35.1288 | 1.34515 | ||||||||
\(683\) | −7.49565 | −0.286813 | −0.143407 | − | 0.989664i | \(-0.545806\pi\) | ||||
−0.143407 | + | 0.989664i | \(0.545806\pi\) | |||||||
\(684\) | 17.4368 | 0.666714 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 43.0101 | 1.64213 | ||||||||
\(687\) | −9.33473 | −0.356142 | ||||||||
\(688\) | 11.0424 | 0.420987 | ||||||||
\(689\) | 35.5951 | 1.35607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.745188 | −0.0283483 | −0.0141741 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141741 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(692\) | 5.85290 | 0.222494 | ||||||||
\(693\) | −5.44172 | −0.206714 | ||||||||
\(694\) | −23.4241 | −0.889167 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.22718 | −0.198136 | ||||||||
\(697\) | −76.0556 | −2.88081 | ||||||||
\(698\) | 56.1379 | 2.12485 | ||||||||
\(699\) | −9.52491 | −0.360265 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.6488 | 1.19536 | 0.597679 | − | 0.801735i | \(-0.296090\pi\) | ||||
0.597679 | + | 0.801735i | \(0.296090\pi\) | |||||||
\(702\) | 9.24504 | 0.348931 | ||||||||
\(703\) | 54.5323 | 2.05672 | ||||||||
\(704\) | 29.1867 | 1.10002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.9145 | −1.31402 | ||||||||
\(707\) | −36.9147 | −1.38832 | ||||||||
\(708\) | 9.37179 | 0.352214 | ||||||||
\(709\) | −16.0181 | −0.601571 | −0.300785 | − | 0.953692i | \(-0.597249\pi\) | ||||
−0.300785 | + | 0.953692i | \(0.597249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.78306 | 0.291888 | ||||||||
\(712\) | 1.45709 | 0.0546068 | ||||||||
\(713\) | −11.0155 | −0.412532 | ||||||||
\(714\) | 31.3474 | 1.17315 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34.8524 | 1.30250 | ||||||||
\(717\) | 7.84648 | 0.293032 | ||||||||
\(718\) | 37.3043 | 1.39218 | ||||||||
\(719\) | 14.3316 | 0.534478 | 0.267239 | − | 0.963630i | \(-0.413889\pi\) | ||||
0.267239 | + | 0.963630i | \(0.413889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.8739 | 0.814628 | ||||||||
\(722\) | −59.1573 | −2.20161 | ||||||||
\(723\) | 1.42783 | 0.0531016 | ||||||||
\(724\) | 22.2393 | 0.826515 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.0353 | 0.372445 | ||||||||
\(727\) | 18.3551 | 0.680755 | 0.340377 | − | 0.940289i | \(-0.389445\pi\) | ||||
0.340377 | + | 0.940289i | \(0.389445\pi\) | |||||||
\(728\) | 11.0423 | 0.409254 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.8294 | 1.06629 | ||||||||
\(732\) | 12.5996 | 0.465694 | ||||||||
\(733\) | 0.665145 | 0.0245677 | 0.0122838 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122838 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(734\) | 17.6973 | 0.653218 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.2360 | −0.487887 | ||||||||
\(737\) | −29.0588 | −1.07040 | ||||||||
\(738\) | −23.9454 | −0.881443 | ||||||||
\(739\) | −32.8332 | −1.20779 | −0.603895 | − | 0.797064i | \(-0.706385\pi\) | ||||
−0.603895 | + | 0.797064i | \(0.706385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.6259 | −1.08833 | ||||||||
\(742\) | 37.9992 | 1.39500 | ||||||||
\(743\) | −29.6004 | −1.08593 | −0.542967 | − | 0.839754i | \(-0.682699\pi\) | ||||
−0.542967 | + | 0.839754i | \(0.682699\pi\) | |||||||
\(744\) | −7.71042 | −0.282678 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −40.8078 | −1.49408 | ||||||||
\(747\) | 9.87708 | 0.361383 | ||||||||
\(748\) | 43.3648 | 1.58557 | ||||||||
\(749\) | 12.3016 | 0.449492 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9709 | 0.911199 | 0.455600 | − | 0.890185i | \(-0.349425\pi\) | ||||
0.455600 | + | 0.890185i | \(0.349425\pi\) | |||||||
\(752\) | −12.9412 | −0.471917 | ||||||||
\(753\) | −17.5762 | −0.640514 | ||||||||
\(754\) | 41.1337 | 1.49800 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.53193 | 0.201194 | ||||||||
\(757\) | −11.2173 | −0.407700 | −0.203850 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203850 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(758\) | 57.8007 | 2.09942 | ||||||||
\(759\) | 4.21141 | 0.152864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3105 | 0.700004 | 0.350002 | − | 0.936749i | \(-0.386181\pi\) | ||||
0.350002 | + | 0.936749i | \(0.386181\pi\) | |||||||
\(762\) | 1.07113 | 0.0388029 | ||||||||
\(763\) | 18.0996 | 0.655249 | ||||||||
\(764\) | 29.6089 | 1.07121 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.2438 | 1.52633 | ||||||||
\(767\) | −15.9231 | −0.574948 | ||||||||
\(768\) | 3.97476 | 0.143427 | ||||||||
\(769\) | −19.3372 | −0.697318 | −0.348659 | − | 0.937250i | \(-0.613363\pi\) | ||||
−0.348659 | + | 0.937250i | \(0.613363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.2890 | 0.694677 | ||||||||
\(772\) | 37.9172 | 1.36467 | ||||||||
\(773\) | 7.79217 | 0.280265 | 0.140132 | − | 0.990133i | \(-0.455247\pi\) | ||||
0.140132 | + | 0.990133i | \(0.455247\pi\) | |||||||
\(774\) | 9.07667 | 0.326254 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.6799 | −0.634671 | ||||||||
\(777\) | 17.3007 | 0.620658 | ||||||||
\(778\) | 49.0923 | 1.76004 | ||||||||
\(779\) | 76.7336 | 2.74926 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.77730 | 0.206728 | ||||||||
\(782\) | −24.2601 | −0.867540 | ||||||||
\(783\) | 4.44927 | 0.159004 | ||||||||
\(784\) | 5.95987 | 0.212853 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.9229 | −0.460946 | ||||||||
\(787\) | −9.07666 | −0.323548 | −0.161774 | − | 0.986828i | \(-0.551722\pi\) | ||||
−0.161774 | + | 0.986828i | \(0.551722\pi\) | |||||||
\(788\) | −58.2311 | −2.07440 | ||||||||
\(789\) | 22.2432 | 0.791877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.1463 | −1.14299 | ||||||||
\(792\) | 2.94783 | 0.104747 | ||||||||
\(793\) | −21.4072 | −0.760192 | ||||||||
\(794\) | −43.8903 | −1.55761 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9906 | 0.531326 | ||||||||
\(797\) | −22.9954 | −0.814541 | −0.407270 | − | 0.913308i | \(-0.633519\pi\) | ||||
−0.407270 | + | 0.913308i | \(0.633519\pi\) | |||||||
\(798\) | −31.6268 | −1.11958 | ||||||||
\(799\) | −33.7867 | −1.19529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.24025 | −0.0438219 | ||||||||
\(802\) | 28.0611 | 0.990872 | ||||||||
\(803\) | 2.80017 | 0.0988158 | ||||||||
\(804\) | 29.5406 | 1.04182 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60.6747 | 2.13718 | ||||||||
\(807\) | 25.1785 | 0.886327 | ||||||||
\(808\) | 19.9970 | 0.703493 | ||||||||
\(809\) | −50.6773 | −1.78172 | −0.890860 | − | 0.454278i | \(-0.849897\pi\) | ||||
−0.890860 | + | 0.454278i | \(0.849897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7614 | 0.939720 | 0.469860 | − | 0.882741i | \(-0.344304\pi\) | ||||
0.469860 | + | 0.882741i | \(0.344304\pi\) | |||||||
\(812\) | 24.6130 | 0.863749 | ||||||||
\(813\) | −5.70091 | −0.199940 | ||||||||
\(814\) | 42.6987 | 1.49659 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.5843 | 0.615575 | ||||||||
\(817\) | −29.0864 | −1.01760 | ||||||||
\(818\) | −5.89908 | −0.206256 | ||||||||
\(819\) | −9.39897 | −0.328427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.832947 | −0.0290700 | −0.0145350 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145350 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(822\) | 4.13879 | 0.144357 | ||||||||
\(823\) | −6.67034 | −0.232514 | −0.116257 | − | 0.993219i | \(-0.537090\pi\) | ||||
−0.116257 | + | 0.993219i | \(0.537090\pi\) | |||||||
\(824\) | −11.8493 | −0.412791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.9985 | −0.591454 | ||||||||
\(827\) | 1.34470 | 0.0467599 | 0.0233799 | − | 0.999727i | \(-0.492557\pi\) | ||||
0.0233799 | + | 0.999727i | \(0.492557\pi\) | |||||||
\(828\) | −4.28122 | −0.148783 | ||||||||
\(829\) | −24.7770 | −0.860541 | −0.430270 | − | 0.902700i | \(-0.641582\pi\) | ||||
−0.430270 | + | 0.902700i | \(0.641582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.1611 | −0.664690 | ||||||||
\(832\) | 50.4115 | 1.74770 | ||||||||
\(833\) | 15.5600 | 0.539121 | ||||||||
\(834\) | −40.9631 | −1.41844 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −43.7513 | −1.51317 | ||||||||
\(837\) | 6.56295 | 0.226849 | ||||||||
\(838\) | 20.7106 | 0.715437 | ||||||||
\(839\) | −6.72534 | −0.232184 | −0.116092 | − | 0.993238i | \(-0.537037\pi\) | ||||
−0.116092 | + | 0.993238i | \(0.537037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.20399 | −0.317379 | ||||||||
\(842\) | 8.99685 | 0.310052 | ||||||||
\(843\) | 4.36015 | 0.150171 | ||||||||
\(844\) | −62.9734 | −2.16763 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.6375 | −0.365723 | ||||||||
\(847\) | −10.2024 | −0.350559 | ||||||||
\(848\) | 21.3157 | 0.731984 | ||||||||
\(849\) | 24.9081 | 0.854844 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.3892 | −0.458975 | ||||||||
\(852\) | −5.87307 | −0.201208 | ||||||||
\(853\) | 16.7244 | 0.572632 | 0.286316 | − | 0.958135i | \(-0.407569\pi\) | ||||
0.286316 | + | 0.958135i | \(0.407569\pi\) | |||||||
\(854\) | −22.8531 | −0.782016 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.66391 | −0.227768 | ||||||||
\(857\) | −12.9930 | −0.443831 | −0.221915 | − | 0.975066i | \(-0.571231\pi\) | ||||
−0.221915 | + | 0.975066i | \(0.571231\pi\) | |||||||
\(858\) | −23.1970 | −0.791933 | ||||||||
\(859\) | −36.5682 | −1.24769 | −0.623845 | − | 0.781548i | \(-0.714430\pi\) | ||||
−0.623845 | + | 0.781548i | \(0.714430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.3441 | 0.829646 | ||||||||
\(862\) | −40.4859 | −1.37895 | ||||||||
\(863\) | 46.3384 | 1.57738 | 0.788688 | − | 0.614794i | \(-0.210761\pi\) | ||||
0.788688 | + | 0.614794i | \(0.210761\pi\) | |||||||
\(864\) | 7.88596 | 0.268286 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.2370 | 0.993513 | ||||||||
\(867\) | 28.9090 | 0.981802 | ||||||||
\(868\) | 36.3058 | 1.23230 | ||||||||
\(869\) | −19.5287 | −0.662467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50.1906 | −1.70064 | ||||||||
\(872\) | −9.80472 | −0.332030 | ||||||||
\(873\) | 15.0488 | 0.509323 | ||||||||
\(874\) | 24.4764 | 0.827926 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.84659 | −0.0961773 | ||||||||
\(877\) | 44.2548 | 1.49438 | 0.747190 | − | 0.664611i | \(-0.231403\pi\) | ||||
0.747190 | + | 0.664611i | \(0.231403\pi\) | |||||||
\(878\) | 71.2169 | 2.40345 | ||||||||
\(879\) | 13.5651 | 0.457541 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.2495 | −1.42342 | −0.711712 | − | 0.702472i | \(-0.752080\pi\) | ||||
−0.711712 | + | 0.702472i | \(0.752080\pi\) | |||||||
\(882\) | 4.89892 | 0.164955 | ||||||||
\(883\) | −3.49289 | −0.117545 | −0.0587726 | − | 0.998271i | \(-0.518719\pi\) | ||||
−0.0587726 | + | 0.998271i | \(0.518719\pi\) | |||||||
\(884\) | 74.9000 | 2.51916 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.8076 | 0.833427 | ||||||||
\(887\) | −14.7275 | −0.494501 | −0.247250 | − | 0.968952i | \(-0.579527\pi\) | ||||
−0.247250 | + | 0.968952i | \(0.579527\pi\) | |||||||
\(888\) | −9.37194 | −0.314502 | ||||||||
\(889\) | −1.08896 | −0.0365227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.50913 | −0.0840591 | ||||||||
\(892\) | 8.44444 | 0.282741 | ||||||||
\(893\) | 34.0879 | 1.14071 | ||||||||
\(894\) | −20.2474 | −0.677175 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.6108 | 0.655151 | ||||||||
\(897\) | 7.27397 | 0.242871 | ||||||||
\(898\) | 28.4808 | 0.950416 | ||||||||
\(899\) | 29.2004 | 0.973886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.6508 | 1.85400 | ||||||||
\(902\) | 60.0823 | 2.00052 | ||||||||
\(903\) | −9.22780 | −0.307082 | ||||||||
\(904\) | 17.4140 | 0.579180 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 26.8250 | 0.891200 | ||||||||
\(907\) | −7.33785 | −0.243649 | −0.121825 | − | 0.992552i | \(-0.538875\pi\) | ||||
−0.121825 | + | 0.992552i | \(0.538875\pi\) | |||||||
\(908\) | 6.89169 | 0.228709 | ||||||||
\(909\) | −17.0211 | −0.564553 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.5731 | −1.77496 | −0.887479 | − | 0.460849i | \(-0.847545\pi\) | ||||
−0.887479 | + | 0.460849i | \(0.847545\pi\) | |||||||
\(912\) | −17.7411 | −0.587466 | ||||||||
\(913\) | −24.7829 | −0.820195 | ||||||||
\(914\) | −49.7136 | −1.64438 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.8104 | −0.786717 | ||||||||
\(917\) | 13.1381 | 0.433859 | ||||||||
\(918\) | 14.4541 | 0.477055 | ||||||||
\(919\) | −43.2016 | −1.42509 | −0.712545 | − | 0.701627i | \(-0.752458\pi\) | ||||
−0.712545 | + | 0.701627i | \(0.752458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.9672 | 0.394334 | ||||||||
\(922\) | −10.7359 | −0.353570 | ||||||||
\(923\) | 9.97859 | 0.328449 | ||||||||
\(924\) | −13.8803 | −0.456630 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.2541 | −0.895625 | ||||||||
\(927\) | 10.0859 | 0.331264 | ||||||||
\(928\) | 35.0868 | 1.15178 | ||||||||
\(929\) | −14.8420 | −0.486951 | −0.243476 | − | 0.969907i | \(-0.578288\pi\) | ||||
−0.243476 | + | 0.969907i | \(0.578288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.6987 | −0.514503 | ||||||||
\(932\) | −24.2955 | −0.795824 | ||||||||
\(933\) | 7.66452 | 0.250925 | ||||||||
\(934\) | 10.3736 | 0.339435 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.09151 | 0.166421 | ||||||||
\(937\) | 3.75611 | 0.122707 | 0.0613534 | − | 0.998116i | \(-0.480458\pi\) | ||||
0.0613534 | + | 0.998116i | \(0.480458\pi\) | |||||||
\(938\) | −53.5805 | −1.74947 | ||||||||
\(939\) | −26.3840 | −0.861008 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.9208 | 1.95336 | 0.976682 | − | 0.214692i | \(-0.0688747\pi\) | ||||
0.976682 | + | 0.214692i | \(0.0688747\pi\) | |||||||
\(942\) | 40.1030 | 1.30663 | ||||||||
\(943\) | −18.8402 | −0.613521 | ||||||||
\(944\) | −9.53532 | −0.310348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7746 | −0.740465 | ||||||||
\(947\) | 24.4212 | 0.793581 | 0.396791 | − | 0.917909i | \(-0.370124\pi\) | ||||
0.396791 | + | 0.917909i | \(0.370124\pi\) | |||||||
\(948\) | 19.8525 | 0.644779 | ||||||||
\(949\) | 4.83647 | 0.156998 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.8880 | 0.353067 | ||||||||
\(952\) | 17.2639 | 0.559528 | ||||||||
\(953\) | 36.6466 | 1.18710 | 0.593550 | − | 0.804797i | \(-0.297726\pi\) | ||||
0.593550 | + | 0.804797i | \(0.297726\pi\) | |||||||
\(954\) | 17.5212 | 0.567268 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.0142 | 0.647307 | ||||||||
\(957\) | −11.1638 | −0.360875 | ||||||||
\(958\) | −10.2225 | −0.330275 | ||||||||
\(959\) | −4.20770 | −0.135874 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0723 | 0.389431 | ||||||||
\(962\) | 73.7495 | 2.37778 | ||||||||
\(963\) | 5.67218 | 0.182784 | ||||||||
\(964\) | 3.64201 | 0.117301 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.76526 | 0.249843 | ||||||||
\(967\) | 47.4395 | 1.52555 | 0.762776 | − | 0.646663i | \(-0.223836\pi\) | ||||
0.762776 | + | 0.646663i | \(0.223836\pi\) | |||||||
\(968\) | 5.52674 | 0.177636 | ||||||||
\(969\) | −46.3183 | −1.48796 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.68782 | −0.182531 | −0.0912655 | − | 0.995827i | \(-0.529091\pi\) | ||||
−0.0912655 | + | 0.995827i | \(0.529091\pi\) | |||||||
\(972\) | 2.55073 | 0.0818147 | ||||||||
\(973\) | 41.6452 | 1.33508 | ||||||||
\(974\) | 19.5608 | 0.626767 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.8194 | −0.410340 | ||||||||
\(977\) | −2.29901 | −0.0735518 | −0.0367759 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367759 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(978\) | 15.5716 | 0.497925 | ||||||||
\(979\) | 3.11194 | 0.0994581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.34557 | 0.266454 | ||||||||
\(982\) | −68.0620 | −2.17194 | ||||||||
\(983\) | −2.35879 | −0.0752336 | −0.0376168 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376168 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(984\) | −13.1875 | −0.420401 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 64.3100 | 2.04805 | ||||||||
\(987\) | 10.8146 | 0.344232 | ||||||||
\(988\) | −75.5676 | −2.40413 | ||||||||
\(989\) | 7.14150 | 0.227087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.76677 | −0.246720 | −0.123360 | − | 0.992362i | \(-0.539367\pi\) | ||||
−0.123360 | + | 0.992362i | \(0.539367\pi\) | |||||||
\(992\) | 51.7552 | 1.64323 | ||||||||
\(993\) | −32.2137 | −1.02227 | ||||||||
\(994\) | 10.6526 | 0.337879 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 25.1938 | 0.798295 | ||||||||
\(997\) | 8.35947 | 0.264747 | 0.132374 | − | 0.991200i | \(-0.457740\pi\) | ||||
0.132374 | + | 0.991200i | \(0.457740\pi\) | |||||||
\(998\) | −19.3549 | −0.612668 | ||||||||
\(999\) | 7.97720 | 0.252388 |
(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 | 1875.2.a.i.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 5625.2.a.r.1.5 | 6 | |||
5.2 | odd | 4 | 1875.2.b.e.1249.3 | 12 | |||
5.3 | odd | 4 | 1875.2.b.e.1249.10 | 12 | |||
5.4 | even | 2 | 1875.2.a.l.1.5 | yes | 6 | ||
15.14 | odd | 2 | 5625.2.a.o.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1875.2.a.l.1.5 | yes | 6 | 5.4 | even | 2 | ||
1875.2.b.e.1249.3 | 12 | 5.2 | odd | 4 | |||
1875.2.b.e.1249.10 | 12 | 5.3 | odd | 4 | |||
5625.2.a.o.1.2 | 6 | 15.14 | odd | 2 | |||
5625.2.a.r.1.5 | 6 | 3.2 | odd | 2 |