Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 23 x^{10} + 142 x^{9} + 104 x^{8} - 1302 x^{7} + 607 x^{6} + 4323 x^{5} - 4461 x^{4} + \cdots - 553 \) |
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 | 1.3 | ||
Root | \(2.74383\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.74383 | −1.22708 | −0.613539 | − | 0.789664i | \(-0.710255\pi\) | ||||
−0.613539 | + | 0.789664i | \(0.710255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.881706 | 0.333253 | 0.166627 | − | 0.986020i | \(-0.446713\pi\) | ||||
0.166627 | + | 0.986020i | \(0.446713\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.74383 | 0.867675 | ||||||||
\(11\) | −0.654634 | −0.197380 | −0.0986898 | − | 0.995118i | \(-0.531465\pi\) | ||||
−0.0986898 | + | 0.995118i | \(0.531465\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.06791 | 0.573534 | 0.286767 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286767 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(14\) | −0.881706 | −0.235646 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.11554 | 1.24070 | 0.620351 | − | 0.784325i | \(-0.286990\pi\) | ||||
0.620351 | + | 0.784325i | \(0.286990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.28170 | −1.21170 | −0.605852 | − | 0.795577i | \(-0.707168\pi\) | ||||
−0.605852 | + | 0.795577i | \(0.707168\pi\) | |||||||
\(20\) | −2.74383 | −0.613539 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.654634 | 0.139568 | ||||||||
\(23\) | −3.61517 | −0.753815 | −0.376908 | − | 0.926251i | \(-0.623013\pi\) | ||||
−0.376908 | + | 0.926251i | \(0.623013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.52860 | 0.505720 | ||||||||
\(26\) | −2.06791 | −0.405550 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.881706 | 0.166627 | ||||||||
\(29\) | −1.25966 | −0.233912 | −0.116956 | − | 0.993137i | \(-0.537314\pi\) | ||||
−0.116956 | + | 0.993137i | \(0.537314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.23726 | 0.581428 | 0.290714 | − | 0.956810i | \(-0.406107\pi\) | ||||
0.290714 | + | 0.956810i | \(0.406107\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.11554 | −0.877308 | ||||||||
\(35\) | −2.41925 | −0.408928 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.59094 | 0.754746 | 0.377373 | − | 0.926061i | \(-0.376827\pi\) | ||||
0.377373 | + | 0.926061i | \(0.376827\pi\) | |||||||
\(38\) | 5.28170 | 0.856805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.74383 | 0.433838 | ||||||||
\(41\) | 0.963823 | 0.150524 | 0.0752619 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752619 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50227 | 0.839088 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(44\) | −0.654634 | −0.0986898 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.61517 | 0.533028 | ||||||||
\(47\) | −12.4487 | −1.81583 | −0.907917 | − | 0.419149i | \(-0.862328\pi\) | ||||
−0.907917 | + | 0.419149i | \(0.862328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.22260 | −0.888942 | ||||||||
\(50\) | −2.52860 | −0.357598 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.06791 | 0.286767 | ||||||||
\(53\) | −6.64771 | −0.913134 | −0.456567 | − | 0.889689i | \(-0.650921\pi\) | ||||
−0.456567 | + | 0.889689i | \(0.650921\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79620 | 0.242200 | ||||||||
\(56\) | −0.881706 | −0.117823 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.25966 | 0.165401 | ||||||||
\(59\) | 9.13256 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23226 | 0.925996 | 0.462998 | − | 0.886359i | \(-0.346774\pi\) | ||||
0.462998 | + | 0.886359i | \(0.346774\pi\) | |||||||
\(62\) | −3.23726 | −0.411132 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.67399 | −0.703771 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.54516 | 0.310940 | 0.155470 | − | 0.987841i | \(-0.450311\pi\) | ||||
0.155470 | + | 0.987841i | \(0.450311\pi\) | |||||||
\(68\) | 5.11554 | 0.620351 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.41925 | 0.289156 | ||||||||
\(71\) | 8.61358 | 1.02224 | 0.511122 | − | 0.859508i | \(-0.329230\pi\) | ||||
0.511122 | + | 0.859508i | \(0.329230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.32891 | 0.623702 | 0.311851 | − | 0.950131i | \(-0.399051\pi\) | ||||
0.311851 | + | 0.950131i | \(0.399051\pi\) | |||||||
\(74\) | −4.59094 | −0.533686 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.28170 | −0.605852 | ||||||||
\(77\) | −0.577195 | −0.0657774 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.75447 | 0.197394 | 0.0986969 | − | 0.995118i | \(-0.468533\pi\) | ||||
0.0986969 | + | 0.995118i | \(0.468533\pi\) | |||||||
\(80\) | −2.74383 | −0.306770 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.963823 | −0.106436 | ||||||||
\(83\) | −16.3610 | −1.79586 | −0.897928 | − | 0.440142i | \(-0.854928\pi\) | ||||
−0.897928 | + | 0.440142i | \(0.854928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.0362 | −1.52244 | ||||||||
\(86\) | −5.50227 | −0.593325 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.654634 | 0.0697842 | ||||||||
\(89\) | −10.7640 | −1.14099 | −0.570493 | − | 0.821302i | \(-0.693248\pi\) | ||||
−0.570493 | + | 0.821302i | \(0.693248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.82329 | 0.191132 | ||||||||
\(92\) | −3.61517 | −0.376908 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.4487 | 1.28399 | ||||||||
\(95\) | 14.4921 | 1.48686 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.52733 | 0.155077 | 0.0775384 | − | 0.996989i | \(-0.475294\pi\) | ||||
0.0775384 | + | 0.996989i | \(0.475294\pi\) | |||||||
\(98\) | 6.22260 | 0.628577 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.52860 | 0.252860 | ||||||||
\(101\) | −6.41245 | −0.638063 | −0.319031 | − | 0.947744i | \(-0.603358\pi\) | ||||
−0.319031 | + | 0.947744i | \(0.603358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.90008 | 0.975484 | 0.487742 | − | 0.872988i | \(-0.337821\pi\) | ||||
0.487742 | + | 0.872988i | \(0.337821\pi\) | |||||||
\(104\) | −2.06791 | −0.202775 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.64771 | 0.645683 | ||||||||
\(107\) | −6.14489 | −0.594049 | −0.297025 | − | 0.954870i | \(-0.595994\pi\) | ||||
−0.297025 | + | 0.954870i | \(0.595994\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.91047 | 0.757686 | 0.378843 | − | 0.925461i | \(-0.376322\pi\) | ||||
0.378843 | + | 0.925461i | \(0.376322\pi\) | |||||||
\(110\) | −1.79620 | −0.171261 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.881706 | 0.0833134 | ||||||||
\(113\) | −14.6098 | −1.37438 | −0.687188 | − | 0.726480i | \(-0.741155\pi\) | ||||
−0.687188 | + | 0.726480i | \(0.741155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.91941 | 0.924990 | ||||||||
\(116\) | −1.25966 | −0.116956 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.13256 | −0.840721 | ||||||||
\(119\) | 4.51040 | 0.413468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5715 | −0.961041 | ||||||||
\(122\) | −7.23226 | −0.654778 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.23726 | 0.290714 | ||||||||
\(125\) | 6.78109 | 0.606520 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1994 | 1.52620 | 0.763101 | − | 0.646279i | \(-0.223676\pi\) | ||||
0.763101 | + | 0.646279i | \(0.223676\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.67399 | 0.497642 | ||||||||
\(131\) | 6.90241 | 0.603067 | 0.301533 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301533 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.65690 | −0.403805 | ||||||||
\(134\) | −2.54516 | −0.219868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.11554 | −0.438654 | ||||||||
\(137\) | 11.6555 | 0.995799 | 0.497900 | − | 0.867235i | \(-0.334105\pi\) | ||||
0.497900 | + | 0.867235i | \(0.334105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.96954 | 0.845605 | 0.422803 | − | 0.906222i | \(-0.361046\pi\) | ||||
0.422803 | + | 0.906222i | \(0.361046\pi\) | |||||||
\(140\) | −2.41925 | −0.204464 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.61358 | −0.722836 | ||||||||
\(143\) | −1.35372 | −0.113204 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.45628 | 0.287029 | ||||||||
\(146\) | −5.32891 | −0.441024 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.59094 | 0.377373 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8287 | −1.20674 | −0.603370 | − | 0.797461i | \(-0.706176\pi\) | ||||
−0.603370 | + | 0.797461i | \(0.706176\pi\) | |||||||
\(152\) | 5.28170 | 0.428402 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.577195 | 0.0465117 | ||||||||
\(155\) | −8.88248 | −0.713458 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.11784 | −0.568066 | −0.284033 | − | 0.958815i | \(-0.591673\pi\) | ||||
−0.284033 | + | 0.958815i | \(0.591673\pi\) | |||||||
\(158\) | −1.75447 | −0.139578 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.74383 | 0.216919 | ||||||||
\(161\) | −3.18752 | −0.251212 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.33495 | 0.182888 | 0.0914439 | − | 0.995810i | \(-0.470852\pi\) | ||||
0.0914439 | + | 0.995810i | \(0.470852\pi\) | |||||||
\(164\) | 0.963823 | 0.0752619 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.3610 | 1.26986 | ||||||||
\(167\) | 9.14665 | 0.707789 | 0.353894 | − | 0.935285i | \(-0.384857\pi\) | ||||
0.353894 | + | 0.935285i | \(0.384857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.72376 | −0.671058 | ||||||||
\(170\) | 14.0362 | 1.07653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.50227 | 0.419544 | ||||||||
\(173\) | −5.85264 | −0.444968 | −0.222484 | − | 0.974936i | \(-0.571417\pi\) | ||||
−0.222484 | + | 0.974936i | \(0.571417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.22948 | 0.168533 | ||||||||
\(176\) | −0.654634 | −0.0493449 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.7640 | 0.806799 | ||||||||
\(179\) | 21.7372 | 1.62471 | 0.812356 | − | 0.583162i | \(-0.198185\pi\) | ||||
0.812356 | + | 0.583162i | \(0.198185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7960 | −0.876790 | −0.438395 | − | 0.898782i | \(-0.644453\pi\) | ||||
−0.438395 | + | 0.898782i | \(0.644453\pi\) | |||||||
\(182\) | −1.82329 | −0.135151 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.61517 | 0.266514 | ||||||||
\(185\) | −12.5968 | −0.926133 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.34881 | −0.244889 | ||||||||
\(188\) | −12.4487 | −0.907917 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.4921 | −1.05137 | ||||||||
\(191\) | 4.40425 | 0.318680 | 0.159340 | − | 0.987224i | \(-0.449063\pi\) | ||||
0.159340 | + | 0.987224i | \(0.449063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.02221 | 0.433488 | 0.216744 | − | 0.976228i | \(-0.430456\pi\) | ||||
0.216744 | + | 0.976228i | \(0.430456\pi\) | |||||||
\(194\) | −1.52733 | −0.109656 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.22260 | −0.444471 | ||||||||
\(197\) | 6.13256 | 0.436927 | 0.218464 | − | 0.975845i | \(-0.429896\pi\) | ||||
0.218464 | + | 0.975845i | \(0.429896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.361191 | 0.0256041 | 0.0128021 | − | 0.999918i | \(-0.495925\pi\) | ||||
0.0128021 | + | 0.999918i | \(0.495925\pi\) | |||||||
\(200\) | −2.52860 | −0.178799 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.41245 | 0.451178 | ||||||||
\(203\) | −1.11065 | −0.0779521 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.64457 | −0.184704 | ||||||||
\(206\) | −9.90008 | −0.689772 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.06791 | 0.143384 | ||||||||
\(209\) | 3.45758 | 0.239166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9869 | −0.962897 | −0.481449 | − | 0.876474i | \(-0.659889\pi\) | ||||
−0.481449 | + | 0.876474i | \(0.659889\pi\) | |||||||
\(212\) | −6.64771 | −0.456567 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.14489 | 0.420056 | ||||||||
\(215\) | −15.0973 | −1.02963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.85431 | 0.193763 | ||||||||
\(218\) | −7.91047 | −0.535765 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.79620 | 0.121100 | ||||||||
\(221\) | 10.5785 | 0.711585 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0975 | −1.14493 | −0.572467 | − | 0.819928i | \(-0.694013\pi\) | ||||
−0.572467 | + | 0.819928i | \(0.694013\pi\) | |||||||
\(224\) | −0.881706 | −0.0589114 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6098 | 0.971830 | ||||||||
\(227\) | 14.5376 | 0.964893 | 0.482446 | − | 0.875926i | \(-0.339748\pi\) | ||||
0.482446 | + | 0.875926i | \(0.339748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2720 | −1.40569 | −0.702847 | − | 0.711341i | \(-0.748088\pi\) | ||||
−0.702847 | + | 0.711341i | \(0.748088\pi\) | |||||||
\(230\) | −9.91941 | −0.654067 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.25966 | 0.0827005 | ||||||||
\(233\) | −10.7432 | −0.703807 | −0.351904 | − | 0.936036i | \(-0.614466\pi\) | ||||
−0.351904 | + | 0.936036i | \(0.614466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.1572 | 2.22817 | ||||||||
\(236\) | 9.13256 | 0.594479 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.51040 | −0.292366 | ||||||||
\(239\) | −24.5694 | −1.58926 | −0.794632 | − | 0.607091i | \(-0.792336\pi\) | ||||
−0.794632 | + | 0.607091i | \(0.792336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.91923 | 0.123628 | 0.0618142 | − | 0.998088i | \(-0.480311\pi\) | ||||
0.0618142 | + | 0.998088i | \(0.480311\pi\) | |||||||
\(242\) | 10.5715 | 0.679559 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.23226 | 0.462998 | ||||||||
\(245\) | 17.0737 | 1.09080 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9221 | −0.694954 | ||||||||
\(248\) | −3.23726 | −0.205566 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.78109 | −0.428874 | ||||||||
\(251\) | 25.4734 | 1.60787 | 0.803934 | − | 0.594719i | \(-0.202737\pi\) | ||||
0.803934 | + | 0.594719i | \(0.202737\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.36661 | 0.148788 | ||||||||
\(254\) | −17.1994 | −1.07919 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.41342 | −0.150545 | −0.0752725 | − | 0.997163i | \(-0.523983\pi\) | ||||
−0.0752725 | + | 0.997163i | \(0.523983\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.04786 | 0.251522 | ||||||||
\(260\) | −5.67399 | −0.351886 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.90241 | −0.426433 | ||||||||
\(263\) | −23.8545 | −1.47093 | −0.735464 | − | 0.677563i | \(-0.763036\pi\) | ||||
−0.735464 | + | 0.677563i | \(0.763036\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.2402 | 1.12049 | ||||||||
\(266\) | 4.65690 | 0.285533 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.54516 | 0.155470 | ||||||||
\(269\) | −12.8156 | −0.781382 | −0.390691 | − | 0.920522i | \(-0.627764\pi\) | ||||
−0.390691 | + | 0.920522i | \(0.627764\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.2316 | −1.53271 | −0.766355 | − | 0.642417i | \(-0.777932\pi\) | ||||
−0.766355 | + | 0.642417i | \(0.777932\pi\) | |||||||
\(272\) | 5.11554 | 0.310175 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.6555 | −0.704136 | ||||||||
\(275\) | −1.65531 | −0.0998189 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4492 | −0.808082 | −0.404041 | − | 0.914741i | \(-0.632395\pi\) | ||||
−0.404041 | + | 0.914741i | \(0.632395\pi\) | |||||||
\(278\) | −9.96954 | −0.597933 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.41925 | 0.144578 | ||||||||
\(281\) | 13.8105 | 0.823865 | 0.411933 | − | 0.911214i | \(-0.364854\pi\) | ||||
0.411933 | + | 0.911214i | \(0.364854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.49024 | 0.445249 | 0.222624 | − | 0.974904i | \(-0.428538\pi\) | ||||
0.222624 | + | 0.974904i | \(0.428538\pi\) | |||||||
\(284\) | 8.61358 | 0.511122 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.35372 | 0.0800473 | ||||||||
\(287\) | 0.849808 | 0.0501626 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.16877 | 0.539339 | ||||||||
\(290\) | −3.45628 | −0.202960 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.32891 | 0.311851 | ||||||||
\(293\) | 32.1572 | 1.87865 | 0.939323 | − | 0.343034i | \(-0.111455\pi\) | ||||
0.939323 | + | 0.343034i | \(0.111455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.0582 | −1.45894 | ||||||||
\(296\) | −4.59094 | −0.266843 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −7.47584 | −0.432339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.85138 | 0.279629 | ||||||||
\(302\) | 14.8287 | 0.853294 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.28170 | −0.302926 | ||||||||
\(305\) | −19.8441 | −1.13627 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.50165 | 0.542288 | 0.271144 | − | 0.962539i | \(-0.412598\pi\) | ||||
0.271144 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(308\) | −0.577195 | −0.0328887 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.88248 | 0.504491 | ||||||||
\(311\) | 6.21901 | 0.352647 | 0.176324 | − | 0.984332i | \(-0.443579\pi\) | ||||
0.176324 | + | 0.984332i | \(0.443579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3247 | −1.54448 | −0.772240 | − | 0.635331i | \(-0.780864\pi\) | ||||
−0.772240 | + | 0.635331i | \(0.780864\pi\) | |||||||
\(314\) | 7.11784 | 0.401683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.75447 | 0.0986969 | ||||||||
\(317\) | 4.08185 | 0.229260 | 0.114630 | − | 0.993408i | \(-0.463432\pi\) | ||||
0.114630 | + | 0.993408i | \(0.463432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.824615 | 0.0461696 | ||||||||
\(320\) | −2.74383 | −0.153385 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.18752 | 0.177633 | ||||||||
\(323\) | −27.0187 | −1.50336 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.22892 | 0.290048 | ||||||||
\(326\) | −2.33495 | −0.129321 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.963823 | −0.0532182 | ||||||||
\(329\) | −10.9761 | −0.605133 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.523601 | 0.0287797 | 0.0143898 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143898 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(332\) | −16.3610 | −0.897928 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.14665 | −0.500482 | ||||||||
\(335\) | −6.98347 | −0.381548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.2794 | −1.37706 | −0.688528 | − | 0.725210i | \(-0.741743\pi\) | ||||
−0.688528 | + | 0.725210i | \(0.741743\pi\) | |||||||
\(338\) | 8.72376 | 0.474510 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.0362 | −0.761219 | ||||||||
\(341\) | −2.11922 | −0.114762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.6584 | −0.629496 | ||||||||
\(344\) | −5.50227 | −0.296662 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.85264 | 0.314640 | ||||||||
\(347\) | −14.9548 | −0.802814 | −0.401407 | − | 0.915900i | \(-0.631479\pi\) | ||||
−0.401407 | + | 0.915900i | \(0.631479\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7902 | −0.684643 | −0.342322 | − | 0.939583i | \(-0.611213\pi\) | ||||
−0.342322 | + | 0.939583i | \(0.611213\pi\) | |||||||
\(350\) | −2.22948 | −0.119171 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.654634 | 0.0348921 | ||||||||
\(353\) | −28.3355 | −1.50815 | −0.754073 | − | 0.656790i | \(-0.771914\pi\) | ||||
−0.754073 | + | 0.656790i | \(0.771914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.6342 | −1.25437 | ||||||||
\(356\) | −10.7640 | −0.570493 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.7372 | −1.14885 | ||||||||
\(359\) | 0.307421 | 0.0162251 | 0.00811254 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811254 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.89634 | 0.468228 | ||||||||
\(362\) | 11.7960 | 0.619984 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.82329 | 0.0955662 | ||||||||
\(365\) | −14.6216 | −0.765331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0168 | 1.35807 | 0.679034 | − | 0.734107i | \(-0.262399\pi\) | ||||
0.679034 | + | 0.734107i | \(0.262399\pi\) | |||||||
\(368\) | −3.61517 | −0.188454 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.5968 | 0.654875 | ||||||||
\(371\) | −5.86133 | −0.304305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1658 | −0.629924 | −0.314962 | − | 0.949104i | \(-0.601992\pi\) | ||||
−0.314962 | + | 0.949104i | \(0.601992\pi\) | |||||||
\(374\) | 3.34881 | 0.173163 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.4487 | 0.641994 | ||||||||
\(377\) | −2.60485 | −0.134157 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.40259 | −0.482979 | −0.241489 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241489 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(380\) | 14.4921 | 0.743428 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.40425 | −0.225341 | ||||||||
\(383\) | −29.2440 | −1.49430 | −0.747150 | − | 0.664655i | \(-0.768579\pi\) | ||||
−0.747150 | + | 0.664655i | \(0.768579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.58372 | 0.0807141 | ||||||||
\(386\) | −6.02221 | −0.306522 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.52733 | 0.0775384 | ||||||||
\(389\) | −10.0683 | −0.510483 | −0.255242 | − | 0.966877i | \(-0.582155\pi\) | ||||
−0.255242 | + | 0.966877i | \(0.582155\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.4936 | −0.935259 | ||||||||
\(392\) | 6.22260 | 0.314289 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.13256 | −0.308954 | ||||||||
\(395\) | −4.81398 | −0.242218 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.1277 | −1.16075 | −0.580373 | − | 0.814351i | \(-0.697093\pi\) | ||||
−0.580373 | + | 0.814351i | \(0.697093\pi\) | |||||||
\(398\) | −0.361191 | −0.0181049 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.52860 | 0.126430 | ||||||||
\(401\) | −16.4894 | −0.823439 | −0.411719 | − | 0.911311i | \(-0.635072\pi\) | ||||
−0.411719 | + | 0.911311i | \(0.635072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.69435 | 0.333469 | ||||||||
\(404\) | −6.41245 | −0.319031 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.11065 | 0.0551205 | ||||||||
\(407\) | −3.00539 | −0.148972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.10611 | −0.351375 | −0.175687 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175687 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(410\) | 2.64457 | 0.130606 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.90008 | 0.487742 | ||||||||
\(413\) | 8.05223 | 0.396224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.8919 | 2.20366 | ||||||||
\(416\) | −2.06791 | −0.101388 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.45758 | −0.169116 | ||||||||
\(419\) | −34.4695 | −1.68395 | −0.841973 | − | 0.539519i | \(-0.818606\pi\) | ||||
−0.841973 | + | 0.539519i | \(0.818606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.87761 | −0.140246 | −0.0701230 | − | 0.997538i | \(-0.522339\pi\) | ||||
−0.0701230 | + | 0.997538i | \(0.522339\pi\) | |||||||
\(422\) | 13.9869 | 0.680871 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.64771 | 0.322842 | ||||||||
\(425\) | 12.9352 | 0.627448 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.37672 | 0.308591 | ||||||||
\(428\) | −6.14489 | −0.297025 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.0973 | 0.728056 | ||||||||
\(431\) | 23.7630 | 1.14462 | 0.572311 | − | 0.820036i | \(-0.306047\pi\) | ||||
0.572311 | + | 0.820036i | \(0.306047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.6626 | −0.656585 | −0.328292 | − | 0.944576i | \(-0.606473\pi\) | ||||
−0.328292 | + | 0.944576i | \(0.606473\pi\) | |||||||
\(434\) | −2.85431 | −0.137011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.91047 | 0.378843 | ||||||||
\(437\) | 19.0942 | 0.913401 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.28894 | −0.252428 | −0.126214 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126214 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(440\) | −1.79620 | −0.0856307 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.5785 | −0.503166 | ||||||||
\(443\) | −38.3895 | −1.82394 | −0.911969 | − | 0.410258i | \(-0.865439\pi\) | ||||
−0.911969 | + | 0.410258i | \(0.865439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.5347 | 1.40008 | ||||||||
\(446\) | 17.0975 | 0.809590 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.881706 | 0.0416567 | ||||||||
\(449\) | 22.5010 | 1.06189 | 0.530943 | − | 0.847407i | \(-0.321838\pi\) | ||||
0.530943 | + | 0.847407i | \(0.321838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.630951 | −0.0297103 | ||||||||
\(452\) | −14.6098 | −0.687188 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.5376 | −0.682282 | ||||||||
\(455\) | −5.00279 | −0.234534 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8987 | 1.21149 | 0.605745 | − | 0.795659i | \(-0.292875\pi\) | ||||
0.605745 | + | 0.795659i | \(0.292875\pi\) | |||||||
\(458\) | 21.2720 | 0.993975 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.91941 | 0.462495 | ||||||||
\(461\) | 6.58463 | 0.306677 | 0.153338 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153338 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.12487 | −0.238173 | −0.119087 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119087 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(464\) | −1.25966 | −0.0584781 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7432 | 0.497667 | ||||||||
\(467\) | −42.0808 | −1.94727 | −0.973634 | − | 0.228114i | \(-0.926744\pi\) | ||||
−0.973634 | + | 0.228114i | \(0.926744\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.24408 | 0.103622 | ||||||||
\(470\) | −34.1572 | −1.57555 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.13256 | −0.420360 | ||||||||
\(473\) | −3.60197 | −0.165619 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.3553 | −0.612784 | ||||||||
\(476\) | 4.51040 | 0.206734 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.5694 | 1.12378 | ||||||||
\(479\) | 35.8024 | 1.63585 | 0.817926 | − | 0.575323i | \(-0.195124\pi\) | ||||
0.817926 | + | 0.575323i | \(0.195124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.49365 | 0.432873 | ||||||||
\(482\) | −1.91923 | −0.0874185 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5715 | −0.480521 | ||||||||
\(485\) | −4.19073 | −0.190291 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.56477 | 0.342793 | 0.171396 | − | 0.985202i | \(-0.445172\pi\) | ||||
0.171396 | + | 0.985202i | \(0.445172\pi\) | |||||||
\(488\) | −7.23226 | −0.327389 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.0737 | −0.771313 | ||||||||
\(491\) | −13.9200 | −0.628200 | −0.314100 | − | 0.949390i | \(-0.601703\pi\) | ||||
−0.314100 | + | 0.949390i | \(0.601703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.44383 | −0.290215 | ||||||||
\(494\) | 10.9221 | 0.491407 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.23726 | 0.145357 | ||||||||
\(497\) | 7.59464 | 0.340666 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8560 | 1.15747 | 0.578737 | − | 0.815514i | \(-0.303546\pi\) | ||||
0.578737 | + | 0.815514i | \(0.303546\pi\) | |||||||
\(500\) | 6.78109 | 0.303260 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.4734 | −1.13693 | ||||||||
\(503\) | 5.88329 | 0.262323 | 0.131162 | − | 0.991361i | \(-0.458129\pi\) | ||||
0.131162 | + | 0.991361i | \(0.458129\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.5947 | 0.782953 | ||||||||
\(506\) | −2.36661 | −0.105209 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.1994 | 0.763101 | ||||||||
\(509\) | 20.3791 | 0.903288 | 0.451644 | − | 0.892198i | \(-0.350838\pi\) | ||||
0.451644 | + | 0.892198i | \(0.350838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.69853 | 0.207851 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.41342 | 0.106451 | ||||||||
\(515\) | −27.1641 | −1.19700 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.14937 | 0.358409 | ||||||||
\(518\) | −4.04786 | −0.177853 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.67399 | 0.248821 | ||||||||
\(521\) | 10.2325 | 0.448295 | 0.224148 | − | 0.974555i | \(-0.428040\pi\) | ||||
0.224148 | + | 0.974555i | \(0.428040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4969 | 0.721361 | 0.360680 | − | 0.932689i | \(-0.382545\pi\) | ||||
0.360680 | + | 0.932689i | \(0.382545\pi\) | |||||||
\(524\) | 6.90241 | 0.301533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.8545 | 1.04010 | ||||||||
\(527\) | 16.5603 | 0.721379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.93054 | −0.431763 | ||||||||
\(530\) | −18.2402 | −0.792303 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.65690 | −0.201902 | ||||||||
\(533\) | 1.99310 | 0.0863306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8605 | 0.728944 | ||||||||
\(536\) | −2.54516 | −0.109934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.8156 | 0.552520 | ||||||||
\(539\) | 4.07352 | 0.175459 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4996 | 0.494405 | 0.247203 | − | 0.968964i | \(-0.420489\pi\) | ||||
0.247203 | + | 0.968964i | \(0.420489\pi\) | |||||||
\(542\) | 25.2316 | 1.08379 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.11554 | −0.219327 | ||||||||
\(545\) | −21.7050 | −0.929739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.1095 | −1.92874 | −0.964371 | − | 0.264554i | \(-0.914775\pi\) | ||||
−0.964371 | + | 0.264554i | \(0.914775\pi\) | |||||||
\(548\) | 11.6555 | 0.497900 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.65531 | 0.0705826 | ||||||||
\(551\) | 6.65313 | 0.283433 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54693 | 0.0657822 | ||||||||
\(554\) | 13.4492 | 0.571400 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.96954 | 0.422803 | ||||||||
\(557\) | 6.85321 | 0.290380 | 0.145190 | − | 0.989404i | \(-0.453621\pi\) | ||||
0.145190 | + | 0.989404i | \(0.453621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3782 | 0.481246 | ||||||||
\(560\) | −2.41925 | −0.102232 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.8105 | −0.582561 | ||||||||
\(563\) | −28.6899 | −1.20914 | −0.604568 | − | 0.796554i | \(-0.706654\pi\) | ||||
−0.604568 | + | 0.796554i | \(0.706654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.0868 | 1.68647 | ||||||||
\(566\) | −7.49024 | −0.314838 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.61358 | −0.361418 | ||||||||
\(569\) | −25.0202 | −1.04890 | −0.524452 | − | 0.851440i | \(-0.675730\pi\) | ||||
−0.524452 | + | 0.851440i | \(0.675730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.30805 | −0.263984 | −0.131992 | − | 0.991251i | \(-0.542137\pi\) | ||||
−0.131992 | + | 0.991251i | \(0.542137\pi\) | |||||||
\(572\) | −1.35372 | −0.0566020 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.849808 | −0.0354703 | ||||||||
\(575\) | −9.14133 | −0.381220 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.1971 | −1.00734 | −0.503668 | − | 0.863897i | \(-0.668017\pi\) | ||||
−0.503668 | + | 0.863897i | \(0.668017\pi\) | |||||||
\(578\) | −9.16877 | −0.381370 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.45628 | 0.143514 | ||||||||
\(581\) | −14.4256 | −0.598475 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.35182 | 0.180234 | ||||||||
\(584\) | −5.32891 | −0.220512 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.1572 | −1.32840 | ||||||||
\(587\) | −9.40596 | −0.388225 | −0.194113 | − | 0.980979i | \(-0.562183\pi\) | ||||
−0.194113 | + | 0.980979i | \(0.562183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0982 | −0.704520 | ||||||||
\(590\) | 25.0582 | 1.03163 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.59094 | 0.188687 | ||||||||
\(593\) | 22.5935 | 0.927802 | 0.463901 | − | 0.885887i | \(-0.346449\pi\) | ||||
0.463901 | + | 0.885887i | \(0.346449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.3758 | −0.507357 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.47584 | 0.305710 | ||||||||
\(599\) | −27.0858 | −1.10670 | −0.553349 | − | 0.832950i | \(-0.686650\pi\) | ||||
−0.553349 | + | 0.832950i | \(0.686650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9213 | −1.46526 | −0.732631 | − | 0.680626i | \(-0.761708\pi\) | ||||
−0.732631 | + | 0.680626i | \(0.761708\pi\) | |||||||
\(602\) | −4.85138 | −0.197728 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.8287 | −0.603370 | ||||||||
\(605\) | 29.0063 | 1.17927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.7764 | −1.28976 | −0.644882 | − | 0.764282i | \(-0.723094\pi\) | ||||
−0.644882 | + | 0.764282i | \(0.723094\pi\) | |||||||
\(608\) | 5.28170 | 0.214201 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.8441 | 0.803463 | ||||||||
\(611\) | −25.7428 | −1.04144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.8926 | −1.81319 | −0.906597 | − | 0.421998i | \(-0.861329\pi\) | ||||
−0.906597 | + | 0.421998i | \(0.861329\pi\) | |||||||
\(614\) | −9.50165 | −0.383455 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.577195 | 0.0232558 | ||||||||
\(617\) | −16.7955 | −0.676161 | −0.338080 | − | 0.941117i | \(-0.609778\pi\) | ||||
−0.338080 | + | 0.941117i | \(0.609778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.8667 | −0.758317 | −0.379158 | − | 0.925332i | \(-0.623786\pi\) | ||||
−0.379158 | + | 0.925332i | \(0.623786\pi\) | |||||||
\(620\) | −8.88248 | −0.356729 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.21901 | −0.249359 | ||||||||
\(623\) | −9.49072 | −0.380238 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2492 | −1.24997 | ||||||||
\(626\) | 27.3247 | 1.09211 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.11784 | −0.284033 | ||||||||
\(629\) | 23.4852 | 0.936415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.81880 | −0.390880 | −0.195440 | − | 0.980716i | \(-0.562614\pi\) | ||||
−0.195440 | + | 0.980716i | \(0.562614\pi\) | |||||||
\(632\) | −1.75447 | −0.0697892 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.08185 | −0.162111 | ||||||||
\(635\) | −47.1923 | −1.87277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.8678 | −0.509839 | ||||||||
\(638\) | −0.824615 | −0.0326468 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.74383 | 0.108459 | ||||||||
\(641\) | −17.7828 | −0.702379 | −0.351190 | − | 0.936304i | \(-0.614223\pi\) | ||||
−0.351190 | + | 0.936304i | \(0.614223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.35039 | 0.250435 | 0.125218 | − | 0.992129i | \(-0.460037\pi\) | ||||
0.125218 | + | 0.992129i | \(0.460037\pi\) | |||||||
\(644\) | −3.18752 | −0.125606 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.0187 | 1.06304 | ||||||||
\(647\) | 32.9331 | 1.29473 | 0.647366 | − | 0.762179i | \(-0.275870\pi\) | ||||
0.647366 | + | 0.762179i | \(0.275870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.97849 | −0.234676 | ||||||||
\(650\) | −5.22892 | −0.205095 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.33495 | 0.0914439 | ||||||||
\(653\) | 22.1156 | 0.865449 | 0.432725 | − | 0.901526i | \(-0.357552\pi\) | ||||
0.432725 | + | 0.901526i | \(0.357552\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9390 | −0.740010 | ||||||||
\(656\) | 0.963823 | 0.0376310 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.9761 | 0.427894 | ||||||||
\(659\) | 17.3171 | 0.674578 | 0.337289 | − | 0.941401i | \(-0.390490\pi\) | ||||
0.337289 | + | 0.941401i | \(0.390490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.42379 | −0.172066 | −0.0860328 | − | 0.996292i | \(-0.527419\pi\) | ||||
−0.0860328 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(662\) | −0.523601 | −0.0203503 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.3610 | 0.634931 | ||||||||
\(665\) | 12.7778 | 0.495500 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.55388 | 0.176327 | ||||||||
\(668\) | 9.14665 | 0.353894 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.98347 | 0.269795 | ||||||||
\(671\) | −4.73448 | −0.182773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3839 | 1.01702 | 0.508512 | − | 0.861055i | \(-0.330196\pi\) | ||||
0.508512 | + | 0.861055i | \(0.330196\pi\) | |||||||
\(674\) | 25.2794 | 0.973725 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.72376 | −0.335529 | ||||||||
\(677\) | −3.14491 | −0.120869 | −0.0604343 | − | 0.998172i | \(-0.519249\pi\) | ||||
−0.0604343 | + | 0.998172i | \(0.519249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34666 | 0.0516799 | ||||||||
\(680\) | 14.0362 | 0.538263 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.11922 | 0.0811491 | ||||||||
\(683\) | 27.6076 | 1.05638 | 0.528189 | − | 0.849127i | \(-0.322871\pi\) | ||||
0.528189 | + | 0.849127i | \(0.322871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.9808 | −1.22192 | ||||||||
\(686\) | 11.6584 | 0.445121 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.50227 | 0.209772 | ||||||||
\(689\) | −13.7469 | −0.523714 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8817 | −0.984588 | −0.492294 | − | 0.870429i | \(-0.663841\pi\) | ||||
−0.492294 | + | 0.870429i | \(0.663841\pi\) | |||||||
\(692\) | −5.85264 | −0.222484 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9548 | 0.567675 | ||||||||
\(695\) | −27.3547 | −1.03762 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.93048 | 0.186755 | ||||||||
\(698\) | 12.7902 | 0.484116 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.22948 | 0.0842665 | ||||||||
\(701\) | −7.63957 | −0.288543 | −0.144271 | − | 0.989538i | \(-0.546084\pi\) | ||||
−0.144271 | + | 0.989538i | \(0.546084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.2480 | −0.914530 | ||||||||
\(704\) | −0.654634 | −0.0246725 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.3355 | 1.06642 | ||||||||
\(707\) | −5.65389 | −0.212637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8901 | 0.784544 | 0.392272 | − | 0.919849i | \(-0.371689\pi\) | ||||
0.392272 | + | 0.919849i | \(0.371689\pi\) | |||||||
\(710\) | 23.6342 | 0.886976 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.7640 | 0.403400 | ||||||||
\(713\) | −11.7032 | −0.438290 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.71439 | 0.138910 | ||||||||
\(716\) | 21.7372 | 0.812356 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.307421 | −0.0114729 | ||||||||
\(719\) | 38.9438 | 1.45236 | 0.726179 | − | 0.687506i | \(-0.241294\pi\) | ||||
0.726179 | + | 0.687506i | \(0.241294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.72896 | 0.325083 | ||||||||
\(722\) | −8.89634 | −0.331087 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.7960 | −0.438395 | ||||||||
\(725\) | −3.18517 | −0.118294 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.2983 | −1.49458 | −0.747290 | − | 0.664498i | \(-0.768645\pi\) | ||||
−0.747290 | + | 0.664498i | \(0.768645\pi\) | |||||||
\(728\) | −1.82329 | −0.0675755 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.6216 | 0.541170 | ||||||||
\(731\) | 28.1471 | 1.04106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8806 | 0.512693 | 0.256346 | − | 0.966585i | \(-0.417481\pi\) | ||||
0.256346 | + | 0.966585i | \(0.417481\pi\) | |||||||
\(734\) | −26.0168 | −0.960299 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.61517 | 0.133257 | ||||||||
\(737\) | −1.66615 | −0.0613733 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1572 | 0.483995 | 0.241998 | − | 0.970277i | \(-0.422197\pi\) | ||||
0.241998 | + | 0.970277i | \(0.422197\pi\) | |||||||
\(740\) | −12.5968 | −0.463066 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.86133 | 0.215176 | ||||||||
\(743\) | 2.41022 | 0.0884223 | 0.0442111 | − | 0.999022i | \(-0.485923\pi\) | ||||
0.0442111 | + | 0.999022i | \(0.485923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.74383 | −0.100526 | ||||||||
\(746\) | 12.1658 | 0.445423 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.34881 | −0.122445 | ||||||||
\(749\) | −5.41799 | −0.197969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4198 | 1.00056 | 0.500281 | − | 0.865863i | \(-0.333230\pi\) | ||||
0.500281 | + | 0.865863i | \(0.333230\pi\) | |||||||
\(752\) | −12.4487 | −0.453959 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.60485 | 0.0948632 | ||||||||
\(755\) | 40.6874 | 1.48076 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.82894 | 0.211856 | 0.105928 | − | 0.994374i | \(-0.466219\pi\) | ||||
0.105928 | + | 0.994374i | \(0.466219\pi\) | |||||||
\(758\) | 9.40259 | 0.341518 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.4921 | −0.525683 | ||||||||
\(761\) | 2.46204 | 0.0892488 | 0.0446244 | − | 0.999004i | \(-0.485791\pi\) | ||||
0.0446244 | + | 0.999004i | \(0.485791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.97471 | 0.252501 | ||||||||
\(764\) | 4.40425 | 0.159340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.2440 | 1.05663 | ||||||||
\(767\) | 18.8853 | 0.681909 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.5369 | −0.776639 | −0.388319 | − | 0.921525i | \(-0.626944\pi\) | ||||
−0.388319 | + | 0.921525i | \(0.626944\pi\) | |||||||
\(770\) | −1.58372 | −0.0570735 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.02221 | 0.216744 | ||||||||
\(773\) | 3.60779 | 0.129763 | 0.0648816 | − | 0.997893i | \(-0.479333\pi\) | ||||
0.0648816 | + | 0.997893i | \(0.479333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.18573 | 0.294040 | ||||||||
\(776\) | −1.52733 | −0.0548280 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0683 | 0.360966 | ||||||||
\(779\) | −5.09062 | −0.182390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.63875 | −0.201770 | ||||||||
\(782\) | 18.4936 | 0.661328 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.22260 | −0.222236 | ||||||||
\(785\) | 19.5302 | 0.697061 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5637 | 0.626079 | 0.313039 | − | 0.949740i | \(-0.398653\pi\) | ||||
0.313039 | + | 0.949740i | \(0.398653\pi\) | |||||||
\(788\) | 6.13256 | 0.218464 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.81398 | 0.171274 | ||||||||
\(791\) | −12.8816 | −0.458015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9556 | 0.531090 | ||||||||
\(794\) | 23.1277 | 0.820771 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.361191 | 0.0128021 | ||||||||
\(797\) | −24.2790 | −0.860006 | −0.430003 | − | 0.902827i | \(-0.641488\pi\) | ||||
−0.430003 | + | 0.902827i | \(0.641488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.6820 | −2.25291 | ||||||||
\(800\) | −2.52860 | −0.0893996 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.4894 | 0.582259 | ||||||||
\(803\) | −3.48849 | −0.123106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.74600 | 0.308256 | ||||||||
\(806\) | −6.69435 | −0.235798 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.41245 | 0.225589 | ||||||||
\(809\) | −39.1163 | −1.37525 | −0.687627 | − | 0.726064i | \(-0.741348\pi\) | ||||
−0.687627 | + | 0.726064i | \(0.741348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9556 | 1.05188 | 0.525942 | − | 0.850520i | \(-0.323713\pi\) | ||||
0.525942 | + | 0.850520i | \(0.323713\pi\) | |||||||
\(812\) | −1.11065 | −0.0389761 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.00539 | 0.105339 | ||||||||
\(815\) | −6.40672 | −0.224417 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0613 | −1.01673 | ||||||||
\(818\) | 7.10611 | 0.248459 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.64457 | −0.0923522 | ||||||||
\(821\) | 29.4060 | 1.02628 | 0.513139 | − | 0.858306i | \(-0.328483\pi\) | ||||
0.513139 | + | 0.858306i | \(0.328483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.6993 | −1.55812 | −0.779061 | − | 0.626949i | \(-0.784304\pi\) | ||||
−0.779061 | + | 0.626949i | \(0.784304\pi\) | |||||||
\(824\) | −9.90008 | −0.344886 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.05223 | −0.280173 | ||||||||
\(827\) | −20.0409 | −0.696891 | −0.348446 | − | 0.937329i | \(-0.613290\pi\) | ||||
−0.348446 | + | 0.937329i | \(0.613290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3328 | 0.949306 | 0.474653 | − | 0.880173i | \(-0.342574\pi\) | ||||
0.474653 | + | 0.880173i | \(0.342574\pi\) | |||||||
\(830\) | −44.8919 | −1.55822 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.06791 | 0.0716918 | ||||||||
\(833\) | −31.8319 | −1.10291 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.0968 | −0.868512 | ||||||||
\(836\) | 3.45758 | 0.119583 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.4695 | 1.19073 | ||||||||
\(839\) | −42.2357 | −1.45814 | −0.729068 | − | 0.684441i | \(-0.760046\pi\) | ||||
−0.729068 | + | 0.684441i | \(0.760046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4133 | −0.945285 | ||||||||
\(842\) | 2.87761 | 0.0991689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.9869 | −0.481449 | ||||||||
\(845\) | 23.9365 | 0.823441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.32091 | −0.320270 | ||||||||
\(848\) | −6.64771 | −0.228283 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.9352 | −0.443673 | ||||||||
\(851\) | −16.5970 | −0.568939 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.18645 | 0.280299 | 0.140149 | − | 0.990130i | \(-0.455242\pi\) | ||||
0.140149 | + | 0.990130i | \(0.455242\pi\) | |||||||
\(854\) | −6.37672 | −0.218207 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.14489 | 0.210028 | ||||||||
\(857\) | 7.39028 | 0.252447 | 0.126224 | − | 0.992002i | \(-0.459714\pi\) | ||||
0.126224 | + | 0.992002i | \(0.459714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.94257 | 0.270997 | 0.135498 | − | 0.990778i | \(-0.456736\pi\) | ||||
0.135498 | + | 0.990778i | \(0.456736\pi\) | |||||||
\(860\) | −15.0973 | −0.514813 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.7630 | −0.809370 | ||||||||
\(863\) | −23.4692 | −0.798900 | −0.399450 | − | 0.916755i | \(-0.630799\pi\) | ||||
−0.399450 | + | 0.916755i | \(0.630799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0587 | 0.546011 | ||||||||
\(866\) | 13.6626 | 0.464276 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.85431 | 0.0968815 | ||||||||
\(869\) | −1.14854 | −0.0389615 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.26315 | 0.178335 | ||||||||
\(872\) | −7.91047 | −0.267882 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19.0942 | −0.645872 | ||||||||
\(875\) | 5.97893 | 0.202125 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.53521 | 0.0518404 | 0.0259202 | − | 0.999664i | \(-0.491748\pi\) | ||||
0.0259202 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(878\) | 5.28894 | 0.178493 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.79620 | 0.0605501 | ||||||||
\(881\) | −35.6573 | −1.20133 | −0.600663 | − | 0.799503i | \(-0.705096\pi\) | ||||
−0.600663 | + | 0.799503i | \(0.705096\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.45880 | −0.183703 | −0.0918517 | − | 0.995773i | \(-0.529279\pi\) | ||||
−0.0918517 | + | 0.995773i | \(0.529279\pi\) | |||||||
\(884\) | 10.5785 | 0.355792 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.3895 | 1.28972 | ||||||||
\(887\) | −37.2684 | −1.25135 | −0.625675 | − | 0.780084i | \(-0.715176\pi\) | ||||
−0.625675 | + | 0.780084i | \(0.715176\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.1648 | 0.508612 | ||||||||
\(890\) | −29.5347 | −0.990006 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.0975 | −0.572467 | ||||||||
\(893\) | 65.7505 | 2.20026 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.6431 | −1.99365 | ||||||||
\(896\) | −0.881706 | −0.0294557 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.5010 | −0.750867 | ||||||||
\(899\) | −4.07783 | −0.136003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0067 | −1.13293 | ||||||||
\(902\) | 0.630951 | 0.0210084 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.6098 | 0.485915 | ||||||||
\(905\) | 32.3662 | 1.07589 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.828857 | −0.0275217 | −0.0137609 | − | 0.999905i | \(-0.504380\pi\) | ||||
−0.0137609 | + | 0.999905i | \(0.504380\pi\) | |||||||
\(908\) | 14.5376 | 0.482446 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.00279 | 0.165841 | ||||||||
\(911\) | −43.4321 | −1.43897 | −0.719484 | − | 0.694509i | \(-0.755622\pi\) | ||||
−0.719484 | + | 0.694509i | \(0.755622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7105 | 0.354465 | ||||||||
\(914\) | −25.8987 | −0.856652 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.2720 | −0.702847 | ||||||||
\(917\) | 6.08590 | 0.200974 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3603 | 0.638636 | 0.319318 | − | 0.947648i | \(-0.396546\pi\) | ||||
0.319318 | + | 0.947648i | \(0.396546\pi\) | |||||||
\(920\) | −9.91941 | −0.327033 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.58463 | −0.216853 | ||||||||
\(923\) | 17.8121 | 0.586292 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6087 | 0.381691 | ||||||||
\(926\) | 5.12487 | 0.168414 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.25966 | 0.0413503 | ||||||||
\(929\) | −21.2919 | −0.698566 | −0.349283 | − | 0.937017i | \(-0.613575\pi\) | ||||
−0.349283 | + | 0.937017i | \(0.613575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.8659 | 1.07714 | ||||||||
\(932\) | −10.7432 | −0.351904 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42.0808 | 1.37693 | ||||||||
\(935\) | 9.18856 | 0.300498 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.3462 | 0.599343 | 0.299671 | − | 0.954043i | \(-0.403123\pi\) | ||||
0.299671 | + | 0.954043i | \(0.403123\pi\) | |||||||
\(938\) | −2.24408 | −0.0732717 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34.1572 | 1.11409 | ||||||||
\(941\) | −17.6325 | −0.574802 | −0.287401 | − | 0.957810i | \(-0.592791\pi\) | ||||
−0.287401 | + | 0.957810i | \(0.592791\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.48438 | −0.113467 | ||||||||
\(944\) | 9.13256 | 0.297240 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.60197 | 0.117110 | ||||||||
\(947\) | 14.4320 | 0.468977 | 0.234488 | − | 0.972119i | \(-0.424658\pi\) | ||||
0.234488 | + | 0.972119i | \(0.424658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0197 | 0.357714 | ||||||||
\(950\) | 13.3553 | 0.433304 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.51040 | −0.146183 | ||||||||
\(953\) | 51.4239 | 1.66578 | 0.832892 | − | 0.553436i | \(-0.186684\pi\) | ||||
0.832892 | + | 0.553436i | \(0.186684\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0845 | −0.391045 | ||||||||
\(956\) | −24.5694 | −0.794632 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.8024 | −1.15672 | ||||||||
\(959\) | 10.2767 | 0.331853 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5202 | −0.661941 | ||||||||
\(962\) | −9.49365 | −0.306087 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.91923 | 0.0618142 | ||||||||
\(965\) | −16.5239 | −0.531924 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.8182 | 0.605152 | 0.302576 | − | 0.953125i | \(-0.402153\pi\) | ||||
0.302576 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(968\) | 10.5715 | 0.339779 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.19073 | 0.134556 | ||||||||
\(971\) | 24.8210 | 0.796543 | 0.398271 | − | 0.917268i | \(-0.369610\pi\) | ||||
0.398271 | + | 0.917268i | \(0.369610\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.79020 | 0.281801 | ||||||||
\(974\) | −7.56477 | −0.242391 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23226 | 0.231499 | ||||||||
\(977\) | −31.2465 | −0.999664 | −0.499832 | − | 0.866122i | \(-0.666605\pi\) | ||||
−0.499832 | + | 0.866122i | \(0.666605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.04651 | 0.225208 | ||||||||
\(980\) | 17.0737 | 0.545401 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.9200 | 0.444204 | ||||||||
\(983\) | −37.6007 | −1.19928 | −0.599638 | − | 0.800271i | \(-0.704689\pi\) | ||||
−0.599638 | + | 0.800271i | \(0.704689\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8267 | −0.536144 | ||||||||
\(986\) | 6.44383 | 0.205213 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.9221 | −0.347477 | ||||||||
\(989\) | −19.8916 | −0.632517 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.6189 | 1.73503 | 0.867514 | − | 0.497413i | \(-0.165717\pi\) | ||||
0.867514 | + | 0.497413i | \(0.165717\pi\) | |||||||
\(992\) | −3.23726 | −0.102783 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.59464 | −0.240887 | ||||||||
\(995\) | −0.991046 | −0.0314183 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.14087 | −0.0678019 | −0.0339009 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0339009 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(998\) | −25.8560 | −0.818458 | ||||||||
\(999\) | 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 | 8046.2.a.i.1.3 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.p.1.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.i.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.p.1.10 | yes | 12 | 3.2 | odd | 2 |