Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48119 | 1.04736 | 0.523681 | − | 0.851914i | \(-0.324558\pi\) | ||||
0.523681 | + | 0.851914i | \(0.324558\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.193937 | 0.0969683 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.48119 | 0.604695 | ||||||||
\(7\) | −1.19394 | −0.451266 | −0.225633 | − | 0.974212i | \(-0.572445\pi\) | ||||
−0.225633 | + | 0.974212i | \(0.572445\pi\) | |||||||
\(8\) | −2.67513 | −0.945802 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.193937 | 0.0559847 | ||||||||
\(13\) | −0.806063 | −0.223562 | −0.111781 | − | 0.993733i | \(-0.535655\pi\) | ||||
−0.111781 | + | 0.993733i | \(0.535655\pi\) | |||||||
\(14\) | −1.76845 | −0.472639 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.35026 | −1.08757 | ||||||||
\(17\) | −3.76845 | −0.913984 | −0.456992 | − | 0.889471i | \(-0.651073\pi\) | ||||
−0.456992 | + | 0.889471i | \(0.651073\pi\) | |||||||
\(18\) | 1.48119 | 0.349121 | ||||||||
\(19\) | 5.35026 | 1.22743 | 0.613717 | − | 0.789526i | \(-0.289674\pi\) | ||||
0.613717 | + | 0.789526i | \(0.289674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.19394 | −0.260538 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −2.67513 | −0.546059 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.19394 | −0.234150 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.231548 | −0.0437585 | ||||||||
\(29\) | 4.31265 | 0.800839 | 0.400420 | − | 0.916332i | \(-0.368864\pi\) | ||||
0.400420 | + | 0.916332i | \(0.368864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.962389 | 0.172850 | 0.0864250 | − | 0.996258i | \(-0.472456\pi\) | ||||
0.0864250 | + | 0.996258i | \(0.472456\pi\) | |||||||
\(32\) | −1.09332 | −0.193274 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.58181 | −0.957272 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.193937 | 0.0323228 | ||||||||
\(37\) | 1.61213 | 0.265032 | 0.132516 | − | 0.991181i | \(-0.457694\pi\) | ||||
0.132516 | + | 0.991181i | \(0.457694\pi\) | |||||||
\(38\) | 7.92478 | 1.28557 | ||||||||
\(39\) | −0.806063 | −0.129073 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.08840 | −1.41937 | −0.709685 | − | 0.704520i | \(-0.751163\pi\) | ||||
−0.709685 | + | 0.704520i | \(0.751163\pi\) | |||||||
\(42\) | −1.76845 | −0.272878 | ||||||||
\(43\) | −4.41819 | −0.673768 | −0.336884 | − | 0.941546i | \(-0.609373\pi\) | ||||
−0.336884 | + | 0.941546i | \(0.609373\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.92478 | 0.873561 | ||||||||
\(47\) | 12.3127 | 1.79598 | 0.897992 | − | 0.440011i | \(-0.145026\pi\) | ||||
0.897992 | + | 0.440011i | \(0.145026\pi\) | |||||||
\(48\) | −4.35026 | −0.627906 | ||||||||
\(49\) | −5.57452 | −0.796359 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.76845 | −0.527689 | ||||||||
\(52\) | −0.156325 | −0.0216784 | ||||||||
\(53\) | 1.42548 | 0.195805 | 0.0979027 | − | 0.995196i | \(-0.468787\pi\) | ||||
0.0979027 | + | 0.995196i | \(0.468787\pi\) | |||||||
\(54\) | 1.48119 | 0.201565 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.19394 | 0.426808 | ||||||||
\(57\) | 5.35026 | 0.708659 | ||||||||
\(58\) | 6.38787 | 0.838769 | ||||||||
\(59\) | 13.2750 | 1.72826 | 0.864131 | − | 0.503266i | \(-0.167868\pi\) | ||||
0.864131 | + | 0.503266i | \(0.167868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0752228 | 0.00963129 | 0.00481565 | − | 0.999988i | \(-0.498467\pi\) | ||||
0.00481565 | + | 0.999988i | \(0.498467\pi\) | |||||||
\(62\) | 1.42548 | 0.181037 | ||||||||
\(63\) | −1.19394 | −0.150422 | ||||||||
\(64\) | 7.08110 | 0.885138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.70052 | −0.329921 | −0.164961 | − | 0.986300i | \(-0.552750\pi\) | ||||
−0.164961 | + | 0.986300i | \(0.552750\pi\) | |||||||
\(68\) | −0.730841 | −0.0886274 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0508 | −1.66752 | −0.833761 | − | 0.552126i | \(-0.813817\pi\) | ||||
−0.833761 | + | 0.552126i | \(0.813817\pi\) | |||||||
\(72\) | −2.67513 | −0.315267 | ||||||||
\(73\) | 10.7308 | 1.25595 | 0.627975 | − | 0.778234i | \(-0.283884\pi\) | ||||
0.627975 | + | 0.778234i | \(0.283884\pi\) | |||||||
\(74\) | 2.38787 | 0.277585 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.03761 | 0.119022 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.19394 | −0.135187 | ||||||||
\(79\) | −13.9756 | −1.57237 | −0.786187 | − | 0.617989i | \(-0.787948\pi\) | ||||
−0.786187 | + | 0.617989i | \(0.787948\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.4617 | −1.48659 | ||||||||
\(83\) | 9.89446 | 1.08606 | 0.543029 | − | 0.839714i | \(-0.317277\pi\) | ||||
0.543029 | + | 0.839714i | \(0.317277\pi\) | |||||||
\(84\) | −0.231548 | −0.0252640 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.54420 | −0.705679 | ||||||||
\(87\) | 4.31265 | 0.462365 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.8872 | 1.79004 | 0.895018 | − | 0.446030i | \(-0.147163\pi\) | ||||
0.895018 | + | 0.446030i | \(0.147163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.962389 | 0.100886 | ||||||||
\(92\) | 0.775746 | 0.0808771 | ||||||||
\(93\) | 0.962389 | 0.0997950 | ||||||||
\(94\) | 18.2374 | 1.88105 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.09332 | −0.111587 | ||||||||
\(97\) | 11.4763 | 1.16524 | 0.582619 | − | 0.812745i | \(-0.302028\pi\) | ||||
0.582619 | + | 0.812745i | \(0.302028\pi\) | |||||||
\(98\) | −8.25694 | −0.834077 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7612 | −1.07078 | −0.535388 | − | 0.844606i | \(-0.679834\pi\) | ||||
−0.535388 | + | 0.844606i | \(0.679834\pi\) | |||||||
\(102\) | −5.58181 | −0.552682 | ||||||||
\(103\) | 16.9380 | 1.66895 | 0.834473 | − | 0.551049i | \(-0.185772\pi\) | ||||
0.834473 | + | 0.551049i | \(0.185772\pi\) | |||||||
\(104\) | 2.15633 | 0.211445 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.11142 | 0.205079 | ||||||||
\(107\) | −8.28233 | −0.800683 | −0.400342 | − | 0.916366i | \(-0.631109\pi\) | ||||
−0.400342 | + | 0.916366i | \(0.631109\pi\) | |||||||
\(108\) | 0.193937 | 0.0186616 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.61213 | 0.153016 | ||||||||
\(112\) | 5.19394 | 0.490781 | ||||||||
\(113\) | 2.26187 | 0.212778 | 0.106389 | − | 0.994325i | \(-0.466071\pi\) | ||||
0.106389 | + | 0.994325i | \(0.466071\pi\) | |||||||
\(114\) | 7.92478 | 0.742223 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.836381 | 0.0776560 | ||||||||
\(117\) | −0.806063 | −0.0745206 | ||||||||
\(118\) | 19.6629 | 1.81012 | ||||||||
\(119\) | 4.49929 | 0.412449 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.111420 | 0.0100875 | ||||||||
\(123\) | −9.08840 | −0.819473 | ||||||||
\(124\) | 0.186642 | 0.0167610 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.76845 | −0.157546 | ||||||||
\(127\) | 13.8192 | 1.22626 | 0.613130 | − | 0.789982i | \(-0.289910\pi\) | ||||
0.613130 | + | 0.789982i | \(0.289910\pi\) | |||||||
\(128\) | 12.6751 | 1.12033 | ||||||||
\(129\) | −4.41819 | −0.389000 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.92478 | 0.517650 | 0.258825 | − | 0.965924i | \(-0.416665\pi\) | ||||
0.258825 | + | 0.965924i | \(0.416665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.38787 | −0.553899 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.0811 | 0.864447 | ||||||||
\(137\) | 3.35026 | 0.286232 | 0.143116 | − | 0.989706i | \(-0.454288\pi\) | ||||
0.143116 | + | 0.989706i | \(0.454288\pi\) | |||||||
\(138\) | 5.92478 | 0.504351 | ||||||||
\(139\) | 21.1998 | 1.79814 | 0.899072 | − | 0.437800i | \(-0.144242\pi\) | ||||
0.899072 | + | 0.437800i | \(0.144242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.3127 | 1.03691 | ||||||||
\(142\) | −20.8119 | −1.74650 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.35026 | −0.362522 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.8945 | 1.31543 | ||||||||
\(147\) | −5.57452 | −0.459778 | ||||||||
\(148\) | 0.312650 | 0.0256997 | ||||||||
\(149\) | −6.38787 | −0.523315 | −0.261657 | − | 0.965161i | \(-0.584269\pi\) | ||||
−0.261657 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.64974 | 0.215633 | 0.107816 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107816 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(152\) | −14.3127 | −1.16091 | ||||||||
\(153\) | −3.76845 | −0.304661 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.156325 | −0.0125160 | ||||||||
\(157\) | 1.61213 | 0.128662 | 0.0643309 | − | 0.997929i | \(-0.479509\pi\) | ||||
0.0643309 | + | 0.997929i | \(0.479509\pi\) | |||||||
\(158\) | −20.7005 | −1.64685 | ||||||||
\(159\) | 1.42548 | 0.113048 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.77575 | −0.376382 | ||||||||
\(162\) | 1.48119 | 0.116374 | ||||||||
\(163\) | −0.312650 | −0.0244887 | −0.0122443 | − | 0.999925i | \(-0.503898\pi\) | ||||
−0.0122443 | + | 0.999925i | \(0.503898\pi\) | |||||||
\(164\) | −1.76257 | −0.137634 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.6556 | 1.13750 | ||||||||
\(167\) | −0.493413 | −0.0381815 | −0.0190907 | − | 0.999818i | \(-0.506077\pi\) | ||||
−0.0190907 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(168\) | 3.19394 | 0.246418 | ||||||||
\(169\) | −12.3503 | −0.950020 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.35026 | 0.409145 | ||||||||
\(172\) | −0.856849 | −0.0653341 | ||||||||
\(173\) | 23.3054 | 1.77187 | 0.885937 | − | 0.463806i | \(-0.153517\pi\) | ||||
0.885937 | + | 0.463806i | \(0.153517\pi\) | |||||||
\(174\) | 6.38787 | 0.484263 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2750 | 0.997813 | ||||||||
\(178\) | 25.0132 | 1.87482 | ||||||||
\(179\) | −10.7005 | −0.799795 | −0.399897 | − | 0.916560i | \(-0.630954\pi\) | ||||
−0.399897 | + | 0.916560i | \(0.630954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.79877 | −0.579678 | −0.289839 | − | 0.957075i | \(-0.593602\pi\) | ||||
−0.289839 | + | 0.957075i | \(0.593602\pi\) | |||||||
\(182\) | 1.42548 | 0.105664 | ||||||||
\(183\) | 0.0752228 | 0.00556063 | ||||||||
\(184\) | −10.7005 | −0.788853 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.42548 | 0.104522 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.38787 | 0.174154 | ||||||||
\(189\) | −1.19394 | −0.0868461 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.29948 | 0.0940268 | 0.0470134 | − | 0.998894i | \(-0.485030\pi\) | ||||
0.0470134 | + | 0.998894i | \(0.485030\pi\) | |||||||
\(192\) | 7.08110 | 0.511035 | ||||||||
\(193\) | −8.59498 | −0.618680 | −0.309340 | − | 0.950951i | \(-0.600108\pi\) | ||||
−0.309340 | + | 0.950951i | \(0.600108\pi\) | |||||||
\(194\) | 16.9986 | 1.22043 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.08110 | −0.0772216 | ||||||||
\(197\) | 20.7064 | 1.47527 | 0.737635 | − | 0.675200i | \(-0.235943\pi\) | ||||
0.737635 | + | 0.675200i | \(0.235943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.55149 | 0.393535 | 0.196767 | − | 0.980450i | \(-0.436956\pi\) | ||||
0.196767 | + | 0.980450i | \(0.436956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.70052 | −0.190480 | ||||||||
\(202\) | −15.9394 | −1.12149 | ||||||||
\(203\) | −5.14903 | −0.361391 | ||||||||
\(204\) | −0.730841 | −0.0511691 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 25.0884 | 1.74799 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 3.50659 | 0.243138 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4993 | 1.27354 | 0.636772 | − | 0.771052i | \(-0.280269\pi\) | ||||
0.636772 | + | 0.771052i | \(0.280269\pi\) | |||||||
\(212\) | 0.276454 | 0.0189869 | ||||||||
\(213\) | −14.0508 | −0.962744 | ||||||||
\(214\) | −12.2677 | −0.838606 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.67513 | −0.182020 | ||||||||
\(217\) | −1.14903 | −0.0780013 | ||||||||
\(218\) | 14.8119 | 1.00319 | ||||||||
\(219\) | 10.7308 | 0.725123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.03761 | 0.204332 | ||||||||
\(222\) | 2.38787 | 0.160264 | ||||||||
\(223\) | 17.6121 | 1.17940 | 0.589698 | − | 0.807624i | \(-0.299247\pi\) | ||||
0.589698 | + | 0.807624i | \(0.299247\pi\) | |||||||
\(224\) | 1.30536 | 0.0872178 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.35026 | 0.222856 | ||||||||
\(227\) | 17.4314 | 1.15696 | 0.578480 | − | 0.815696i | \(-0.303646\pi\) | ||||
0.578480 | + | 0.815696i | \(0.303646\pi\) | |||||||
\(228\) | 1.03761 | 0.0687175 | ||||||||
\(229\) | 13.0738 | 0.863942 | 0.431971 | − | 0.901888i | \(-0.357818\pi\) | ||||
0.431971 | + | 0.901888i | \(0.357818\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.5369 | −0.757435 | ||||||||
\(233\) | 13.8437 | 0.906929 | 0.453465 | − | 0.891274i | \(-0.350188\pi\) | ||||
0.453465 | + | 0.891274i | \(0.350188\pi\) | |||||||
\(234\) | −1.19394 | −0.0780501 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.57452 | 0.167587 | ||||||||
\(237\) | −13.9756 | −0.907810 | ||||||||
\(238\) | 6.66433 | 0.431984 | ||||||||
\(239\) | 12.3733 | 0.800361 | 0.400181 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400181 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5501 | 1.58141 | 0.790705 | − | 0.612198i | \(-0.209714\pi\) | ||||
0.790705 | + | 0.612198i | \(0.209714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.0145884 | 0.000933930 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.4617 | −0.858285 | ||||||||
\(247\) | −4.31265 | −0.274407 | ||||||||
\(248\) | −2.57452 | −0.163482 | ||||||||
\(249\) | 9.89446 | 0.627036 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9003 | 0.877382 | 0.438691 | − | 0.898638i | \(-0.355442\pi\) | ||||
0.438691 | + | 0.898638i | \(0.355442\pi\) | |||||||
\(252\) | −0.231548 | −0.0145862 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 20.4690 | 1.28434 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.61213 | 0.288258 | ||||||||
\(257\) | −18.8872 | −1.17815 | −0.589075 | − | 0.808079i | \(-0.700508\pi\) | ||||
−0.589075 | + | 0.808079i | \(0.700508\pi\) | |||||||
\(258\) | −6.54420 | −0.407424 | ||||||||
\(259\) | −1.92478 | −0.119600 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.31265 | 0.266946 | ||||||||
\(262\) | 8.77575 | 0.542167 | ||||||||
\(263\) | −20.8061 | −1.28296 | −0.641478 | − | 0.767141i | \(-0.721679\pi\) | ||||
−0.641478 | + | 0.767141i | \(0.721679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.46168 | −0.580133 | ||||||||
\(267\) | 16.8872 | 1.03348 | ||||||||
\(268\) | −0.523730 | −0.0319919 | ||||||||
\(269\) | −32.3996 | −1.97544 | −0.987720 | − | 0.156233i | \(-0.950065\pi\) | ||||
−0.987720 | + | 0.156233i | \(0.950065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8265 | 1.02214 | 0.511069 | − | 0.859539i | \(-0.329249\pi\) | ||||
0.511069 | + | 0.859539i | \(0.329249\pi\) | |||||||
\(272\) | 16.3938 | 0.994017 | ||||||||
\(273\) | 0.962389 | 0.0582464 | ||||||||
\(274\) | 4.96239 | 0.299789 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.775746 | 0.0466944 | ||||||||
\(277\) | −16.9076 | −1.01588 | −0.507941 | − | 0.861392i | \(-0.669593\pi\) | ||||
−0.507941 | + | 0.861392i | \(0.669593\pi\) | |||||||
\(278\) | 31.4010 | 1.88331 | ||||||||
\(279\) | 0.962389 | 0.0576167 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.61213 | −0.334791 | −0.167396 | − | 0.985890i | \(-0.553536\pi\) | ||||
−0.167396 | + | 0.985890i | \(0.553536\pi\) | |||||||
\(282\) | 18.2374 | 1.08602 | ||||||||
\(283\) | −5.81924 | −0.345918 | −0.172959 | − | 0.984929i | \(-0.555333\pi\) | ||||
−0.172959 | + | 0.984929i | \(0.555333\pi\) | |||||||
\(284\) | −2.72496 | −0.161697 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.8510 | 0.640512 | ||||||||
\(288\) | −1.09332 | −0.0644246 | ||||||||
\(289\) | −2.79877 | −0.164633 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4763 | 0.672751 | ||||||||
\(292\) | 2.08110 | 0.121787 | ||||||||
\(293\) | 8.29218 | 0.484434 | 0.242217 | − | 0.970222i | \(-0.422125\pi\) | ||||
0.242217 | + | 0.970222i | \(0.422125\pi\) | |||||||
\(294\) | −8.25694 | −0.481555 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.31265 | −0.250668 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.46168 | −0.548100 | ||||||||
\(299\) | −3.22425 | −0.186463 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.27504 | 0.304048 | ||||||||
\(302\) | 3.92478 | 0.225846 | ||||||||
\(303\) | −10.7612 | −0.618212 | ||||||||
\(304\) | −23.2750 | −1.33492 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.58181 | −0.319091 | ||||||||
\(307\) | −25.6688 | −1.46500 | −0.732498 | − | 0.680770i | \(-0.761646\pi\) | ||||
−0.732498 | + | 0.680770i | \(0.761646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.9380 | 0.963566 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7235 | −0.891601 | −0.445800 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445800 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(312\) | 2.15633 | 0.122078 | ||||||||
\(313\) | −26.8627 | −1.51837 | −0.759186 | − | 0.650874i | \(-0.774403\pi\) | ||||
−0.759186 | + | 0.650874i | \(0.774403\pi\) | |||||||
\(314\) | 2.38787 | 0.134755 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.71037 | −0.152470 | ||||||||
\(317\) | 0.710373 | 0.0398985 | 0.0199492 | − | 0.999801i | \(-0.493650\pi\) | ||||
0.0199492 | + | 0.999801i | \(0.493650\pi\) | |||||||
\(318\) | 2.11142 | 0.118403 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.28233 | −0.462275 | ||||||||
\(322\) | −7.07381 | −0.394208 | ||||||||
\(323\) | −20.1622 | −1.12186 | ||||||||
\(324\) | 0.193937 | 0.0107743 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.463096 | −0.0256485 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | 24.3127 | 1.34244 | ||||||||
\(329\) | −14.7005 | −0.810466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.962389 | 0.0528977 | 0.0264488 | − | 0.999650i | \(-0.491580\pi\) | ||||
0.0264488 | + | 0.999650i | \(0.491580\pi\) | |||||||
\(332\) | 1.91890 | 0.105313 | ||||||||
\(333\) | 1.61213 | 0.0883440 | ||||||||
\(334\) | −0.730841 | −0.0399898 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.19394 | 0.283352 | ||||||||
\(337\) | −19.8192 | −1.07962 | −0.539811 | − | 0.841786i | \(-0.681504\pi\) | ||||
−0.539811 | + | 0.841786i | \(0.681504\pi\) | |||||||
\(338\) | −18.2931 | −0.995015 | ||||||||
\(339\) | 2.26187 | 0.122848 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.92478 | 0.428523 | ||||||||
\(343\) | 15.0132 | 0.810635 | ||||||||
\(344\) | 11.8192 | 0.637251 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.5198 | 1.85579 | ||||||||
\(347\) | −6.20711 | −0.333215 | −0.166608 | − | 0.986023i | \(-0.553281\pi\) | ||||
−0.166608 | + | 0.986023i | \(0.553281\pi\) | |||||||
\(348\) | 0.836381 | 0.0448347 | ||||||||
\(349\) | −4.44851 | −0.238123 | −0.119062 | − | 0.992887i | \(-0.537989\pi\) | ||||
−0.119062 | + | 0.992887i | \(0.537989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.806063 | −0.0430245 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.57452 | 0.349926 | 0.174963 | − | 0.984575i | \(-0.444019\pi\) | ||||
0.174963 | + | 0.984575i | \(0.444019\pi\) | |||||||
\(354\) | 19.6629 | 1.04507 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.27504 | 0.173577 | ||||||||
\(357\) | 4.49929 | 0.238128 | ||||||||
\(358\) | −15.8496 | −0.837675 | ||||||||
\(359\) | −8.62530 | −0.455226 | −0.227613 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227613 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.62530 | 0.506595 | ||||||||
\(362\) | −11.5515 | −0.607133 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.186642 | 0.00978272 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.111420 | 0.00582399 | ||||||||
\(367\) | 23.0132 | 1.20128 | 0.600639 | − | 0.799520i | \(-0.294913\pi\) | ||||
0.600639 | + | 0.799520i | \(0.294913\pi\) | |||||||
\(368\) | −17.4010 | −0.907092 | ||||||||
\(369\) | −9.08840 | −0.473123 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.70194 | −0.0883602 | ||||||||
\(372\) | 0.186642 | 0.00967695 | ||||||||
\(373\) | −28.1925 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760423\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760423\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.9380 | −1.69865 | ||||||||
\(377\) | −3.47627 | −0.179037 | ||||||||
\(378\) | −1.76845 | −0.0909594 | ||||||||
\(379\) | 3.74798 | 0.192521 | 0.0962605 | − | 0.995356i | \(-0.469312\pi\) | ||||
0.0962605 | + | 0.995356i | \(0.469312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.8192 | 0.707981 | ||||||||
\(382\) | 1.92478 | 0.0984802 | ||||||||
\(383\) | 1.76257 | 0.0900632 | 0.0450316 | − | 0.998986i | \(-0.485661\pi\) | ||||
0.0450316 | + | 0.998986i | \(0.485661\pi\) | |||||||
\(384\) | 12.6751 | 0.646825 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.7308 | −0.647983 | ||||||||
\(387\) | −4.41819 | −0.224589 | ||||||||
\(388\) | 2.22567 | 0.112991 | ||||||||
\(389\) | 6.52373 | 0.330766 | 0.165383 | − | 0.986229i | \(-0.447114\pi\) | ||||
0.165383 | + | 0.986229i | \(0.447114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.0738 | −0.762315 | ||||||||
\(392\) | 14.9126 | 0.753198 | ||||||||
\(393\) | 5.92478 | 0.298865 | ||||||||
\(394\) | 30.6702 | 1.54514 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6991 | −1.18942 | −0.594712 | − | 0.803939i | \(-0.702734\pi\) | ||||
−0.594712 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(398\) | 8.22284 | 0.412174 | ||||||||
\(399\) | −6.38787 | −0.319794 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.88717 | 0.443804 | 0.221902 | − | 0.975069i | \(-0.428774\pi\) | ||||
0.221902 | + | 0.975069i | \(0.428774\pi\) | |||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | −0.775746 | −0.0386427 | ||||||||
\(404\) | −2.08698 | −0.103831 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.62672 | −0.378508 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 10.0811 | 0.499089 | ||||||||
\(409\) | 4.85097 | 0.239865 | 0.119932 | − | 0.992782i | \(-0.461732\pi\) | ||||
0.119932 | + | 0.992782i | \(0.461732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.35026 | 0.165256 | ||||||||
\(412\) | 3.28489 | 0.161835 | ||||||||
\(413\) | −15.8496 | −0.779906 | ||||||||
\(414\) | 5.92478 | 0.291187 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.881286 | 0.0432086 | ||||||||
\(417\) | 21.1998 | 1.03816 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7005 | −0.522755 | −0.261377 | − | 0.965237i | \(-0.584177\pi\) | ||||
−0.261377 | + | 0.965237i | \(0.584177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.6009 | −1.49139 | −0.745697 | − | 0.666285i | \(-0.767884\pi\) | ||||
−0.745697 | + | 0.666285i | \(0.767884\pi\) | |||||||
\(422\) | 27.4010 | 1.33386 | ||||||||
\(423\) | 12.3127 | 0.598662 | ||||||||
\(424\) | −3.81336 | −0.185193 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.8119 | −1.00834 | ||||||||
\(427\) | −0.0898112 | −0.00434627 | ||||||||
\(428\) | −1.60625 | −0.0776409 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.92478 | 0.285386 | 0.142693 | − | 0.989767i | \(-0.454424\pi\) | ||||
0.142693 | + | 0.989767i | \(0.454424\pi\) | |||||||
\(432\) | −4.35026 | −0.209302 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | −1.70194 | −0.0816956 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.93937 | 0.0928788 | ||||||||
\(437\) | 21.4010 | 1.02375 | ||||||||
\(438\) | 15.8945 | 0.759467 | ||||||||
\(439\) | −5.35026 | −0.255354 | −0.127677 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127677 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.57452 | −0.265453 | ||||||||
\(442\) | 4.49929 | 0.214010 | ||||||||
\(443\) | 19.6873 | 0.935374 | 0.467687 | − | 0.883894i | \(-0.345087\pi\) | ||||
0.467687 | + | 0.883894i | \(0.345087\pi\) | |||||||
\(444\) | 0.312650 | 0.0148377 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.0870 | 1.23525 | ||||||||
\(447\) | −6.38787 | −0.302136 | ||||||||
\(448\) | −8.45439 | −0.399432 | ||||||||
\(449\) | −31.3357 | −1.47882 | −0.739411 | − | 0.673254i | \(-0.764896\pi\) | ||||
−0.739411 | + | 0.673254i | \(0.764896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.438658 | 0.0206328 | ||||||||
\(453\) | 2.64974 | 0.124496 | ||||||||
\(454\) | 25.8192 | 1.21176 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.3127 | −0.670251 | ||||||||
\(457\) | 37.5936 | 1.75855 | 0.879276 | − | 0.476312i | \(-0.158027\pi\) | ||||
0.879276 | + | 0.476312i | \(0.158027\pi\) | |||||||
\(458\) | 19.3649 | 0.904860 | ||||||||
\(459\) | −3.76845 | −0.175896 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.9854 | −0.837664 | −0.418832 | − | 0.908064i | \(-0.637560\pi\) | ||||
−0.418832 | + | 0.908064i | \(0.637560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.0132 | 1.81310 | 0.906548 | − | 0.422103i | \(-0.138708\pi\) | ||||
0.906548 | + | 0.422103i | \(0.138708\pi\) | |||||||
\(464\) | −18.7612 | −0.870965 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.5052 | 0.949884 | ||||||||
\(467\) | 14.5501 | 0.673297 | 0.336649 | − | 0.941630i | \(-0.390707\pi\) | ||||
0.336649 | + | 0.941630i | \(0.390707\pi\) | |||||||
\(468\) | −0.156325 | −0.00722613 | ||||||||
\(469\) | 3.22425 | 0.148882 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.61213 | 0.0742829 | ||||||||
\(472\) | −35.5125 | −1.63459 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −20.7005 | −0.950807 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.872577 | 0.0399945 | ||||||||
\(477\) | 1.42548 | 0.0652685 | ||||||||
\(478\) | 18.3272 | 0.838268 | ||||||||
\(479\) | −28.6253 | −1.30792 | −0.653962 | − | 0.756528i | \(-0.726894\pi\) | ||||
−0.653962 | + | 0.756528i | \(0.726894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.29948 | −0.0592510 | ||||||||
\(482\) | 36.3634 | 1.65631 | ||||||||
\(483\) | −4.77575 | −0.217304 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.48119 | 0.0671883 | ||||||||
\(487\) | 1.44992 | 0.0657022 | 0.0328511 | − | 0.999460i | \(-0.489541\pi\) | ||||
0.0328511 | + | 0.999460i | \(0.489541\pi\) | |||||||
\(488\) | −0.201231 | −0.00910929 | ||||||||
\(489\) | −0.312650 | −0.0141385 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | −1.76257 | −0.0794629 | ||||||||
\(493\) | −16.2520 | −0.731954 | ||||||||
\(494\) | −6.38787 | −0.287404 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.18664 | −0.187986 | ||||||||
\(497\) | 16.7757 | 0.752495 | ||||||||
\(498\) | 14.6556 | 0.656734 | ||||||||
\(499\) | 30.7005 | 1.37434 | 0.687172 | − | 0.726495i | \(-0.258852\pi\) | ||||
0.687172 | + | 0.726495i | \(0.258852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.493413 | −0.0220441 | ||||||||
\(502\) | 20.5891 | 0.918937 | ||||||||
\(503\) | 19.7586 | 0.880993 | 0.440496 | − | 0.897754i | \(-0.354802\pi\) | ||||
0.440496 | + | 0.897754i | \(0.354802\pi\) | |||||||
\(504\) | 3.19394 | 0.142269 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3503 | −0.548494 | ||||||||
\(508\) | 2.68006 | 0.118908 | ||||||||
\(509\) | 22.1016 | 0.979635 | 0.489817 | − | 0.871825i | \(-0.337063\pi\) | ||||
0.489817 | + | 0.871825i | \(0.337063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8119 | −0.566767 | ||||||||
\(512\) | −18.5188 | −0.818423 | ||||||||
\(513\) | 5.35026 | 0.236220 | ||||||||
\(514\) | −27.9756 | −1.23395 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.856849 | −0.0377207 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.85097 | −0.125264 | ||||||||
\(519\) | 23.3054 | 1.02299 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8119 | −0.999409 | −0.499705 | − | 0.866196i | \(-0.666558\pi\) | ||||
−0.499705 | + | 0.866196i | \(0.666558\pi\) | |||||||
\(522\) | 6.38787 | 0.279590 | ||||||||
\(523\) | 12.2677 | 0.536431 | 0.268216 | − | 0.963359i | \(-0.413566\pi\) | ||||
0.268216 | + | 0.963359i | \(0.413566\pi\) | |||||||
\(524\) | 1.14903 | 0.0501957 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.8178 | −1.34372 | ||||||||
\(527\) | −3.62672 | −0.157982 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.2750 | 0.576088 | ||||||||
\(532\) | −1.23884 | −0.0537106 | ||||||||
\(533\) | 7.32582 | 0.317317 | ||||||||
\(534\) | 25.0132 | 1.08243 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.22425 | 0.312040 | ||||||||
\(537\) | −10.7005 | −0.461762 | ||||||||
\(538\) | −47.9902 | −2.06900 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.22425 | 0.224608 | 0.112304 | − | 0.993674i | \(-0.464177\pi\) | ||||
0.112304 | + | 0.993674i | \(0.464177\pi\) | |||||||
\(542\) | 24.9234 | 1.07055 | ||||||||
\(543\) | −7.79877 | −0.334677 | ||||||||
\(544\) | 4.12013 | 0.176649 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.42548 | 0.0610051 | ||||||||
\(547\) | 17.9697 | 0.768328 | 0.384164 | − | 0.923265i | \(-0.374490\pi\) | ||||
0.384164 | + | 0.923265i | \(0.374490\pi\) | |||||||
\(548\) | 0.649738 | 0.0277554 | ||||||||
\(549\) | 0.0752228 | 0.00321043 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.0738 | 0.982977 | ||||||||
\(552\) | −10.7005 | −0.455445 | ||||||||
\(553\) | 16.6859 | 0.709558 | ||||||||
\(554\) | −25.0435 | −1.06400 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.11142 | 0.174363 | ||||||||
\(557\) | −15.8700 | −0.672434 | −0.336217 | − | 0.941784i | \(-0.609148\pi\) | ||||
−0.336217 | + | 0.941784i | \(0.609148\pi\) | |||||||
\(558\) | 1.42548 | 0.0603456 | ||||||||
\(559\) | 3.56134 | 0.150629 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.31265 | −0.350648 | ||||||||
\(563\) | −31.6688 | −1.33468 | −0.667340 | − | 0.744753i | \(-0.732567\pi\) | ||||
−0.667340 | + | 0.744753i | \(0.732567\pi\) | |||||||
\(564\) | 2.38787 | 0.100548 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.61942 | −0.362301 | ||||||||
\(567\) | −1.19394 | −0.0501406 | ||||||||
\(568\) | 37.5877 | 1.57714 | ||||||||
\(569\) | 24.3127 | 1.01924 | 0.509620 | − | 0.860400i | \(-0.329786\pi\) | ||||
0.509620 | + | 0.860400i | \(0.329786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.05079 | −0.336915 | −0.168457 | − | 0.985709i | \(-0.553879\pi\) | ||||
−0.168457 | + | 0.985709i | \(0.553879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.29948 | 0.0542864 | ||||||||
\(574\) | 16.0724 | 0.670849 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.08110 | 0.295046 | ||||||||
\(577\) | −44.5355 | −1.85404 | −0.927018 | − | 0.375016i | \(-0.877637\pi\) | ||||
−0.927018 | + | 0.375016i | \(0.877637\pi\) | |||||||
\(578\) | −4.14552 | −0.172431 | ||||||||
\(579\) | −8.59498 | −0.357195 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8134 | −0.490101 | ||||||||
\(582\) | 16.9986 | 0.704614 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −28.7064 | −1.18788 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.2823 | 0.507379 | ||||||||
\(587\) | −15.4763 | −0.638774 | −0.319387 | − | 0.947624i | \(-0.603477\pi\) | ||||
−0.319387 | + | 0.947624i | \(0.603477\pi\) | |||||||
\(588\) | −1.08110 | −0.0445839 | ||||||||
\(589\) | 5.14903 | 0.212162 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.7064 | 0.851748 | ||||||||
\(592\) | −7.01317 | −0.288240 | ||||||||
\(593\) | 9.53102 | 0.391392 | 0.195696 | − | 0.980665i | \(-0.437303\pi\) | ||||
0.195696 | + | 0.980665i | \(0.437303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.23884 | −0.0507450 | ||||||||
\(597\) | 5.55149 | 0.227207 | ||||||||
\(598\) | −4.77575 | −0.195295 | ||||||||
\(599\) | −25.5515 | −1.04401 | −0.522003 | − | 0.852944i | \(-0.674815\pi\) | ||||
−0.522003 | + | 0.852944i | \(0.674815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0263 | −0.490565 | −0.245282 | − | 0.969452i | \(-0.578881\pi\) | ||||
−0.245282 | + | 0.969452i | \(0.578881\pi\) | |||||||
\(602\) | 7.81336 | 0.318449 | ||||||||
\(603\) | −2.70052 | −0.109974 | ||||||||
\(604\) | 0.513881 | 0.0209095 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.9394 | −0.647492 | ||||||||
\(607\) | 6.86670 | 0.278711 | 0.139355 | − | 0.990242i | \(-0.455497\pi\) | ||||
0.139355 | + | 0.990242i | \(0.455497\pi\) | |||||||
\(608\) | −5.84955 | −0.237231 | ||||||||
\(609\) | −5.14903 | −0.208649 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.92478 | −0.401514 | ||||||||
\(612\) | −0.730841 | −0.0295425 | ||||||||
\(613\) | 7.25457 | 0.293009 | 0.146505 | − | 0.989210i | \(-0.453198\pi\) | ||||
0.146505 | + | 0.989210i | \(0.453198\pi\) | |||||||
\(614\) | −38.0205 | −1.53438 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.3634 | 1.54445 | 0.772227 | − | 0.635347i | \(-0.219143\pi\) | ||||
0.772227 | + | 0.635347i | \(0.219143\pi\) | |||||||
\(618\) | 25.0884 | 1.00920 | ||||||||
\(619\) | −29.6893 | −1.19331 | −0.596656 | − | 0.802497i | \(-0.703504\pi\) | ||||
−0.596656 | + | 0.802497i | \(0.703504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | −23.2896 | −0.933829 | ||||||||
\(623\) | −20.1622 | −0.807782 | ||||||||
\(624\) | 3.50659 | 0.140376 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −39.7889 | −1.59029 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.312650 | 0.0124761 | ||||||||
\(629\) | −6.07522 | −0.242235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6991 | −0.784209 | −0.392105 | − | 0.919921i | \(-0.628253\pi\) | ||||
−0.392105 | + | 0.919921i | \(0.628253\pi\) | |||||||
\(632\) | 37.3865 | 1.48715 | ||||||||
\(633\) | 18.4993 | 0.735281 | ||||||||
\(634\) | 1.05220 | 0.0417882 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.276454 | 0.0109621 | ||||||||
\(637\) | 4.49341 | 0.178036 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.0508 | −0.555840 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4372 | −1.24170 | −0.620848 | − | 0.783931i | \(-0.713212\pi\) | ||||
−0.620848 | + | 0.783931i | \(0.713212\pi\) | |||||||
\(642\) | −12.2677 | −0.484169 | ||||||||
\(643\) | −34.4894 | −1.36013 | −0.680065 | − | 0.733151i | \(-0.738049\pi\) | ||||
−0.680065 | + | 0.733151i | \(0.738049\pi\) | |||||||
\(644\) | −0.926192 | −0.0364971 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.8641 | −1.17499 | ||||||||
\(647\) | −5.61213 | −0.220635 | −0.110318 | − | 0.993896i | \(-0.535187\pi\) | ||||
−0.110318 | + | 0.993896i | \(0.535187\pi\) | |||||||
\(648\) | −2.67513 | −0.105089 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.14903 | −0.0450341 | ||||||||
\(652\) | −0.0606343 | −0.00237462 | ||||||||
\(653\) | 4.06537 | 0.159090 | 0.0795452 | − | 0.996831i | \(-0.474653\pi\) | ||||
0.0795452 | + | 0.996831i | \(0.474653\pi\) | |||||||
\(654\) | 14.8119 | 0.579193 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 39.5369 | 1.54366 | ||||||||
\(657\) | 10.7308 | 0.418650 | ||||||||
\(658\) | −21.7743 | −0.848852 | ||||||||
\(659\) | −11.3747 | −0.443095 | −0.221548 | − | 0.975150i | \(-0.571111\pi\) | ||||
−0.221548 | + | 0.975150i | \(0.571111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.4749 | −1.65208 | −0.826040 | − | 0.563611i | \(-0.809412\pi\) | ||||
−0.826040 | + | 0.563611i | \(0.809412\pi\) | |||||||
\(662\) | 1.42548 | 0.0554030 | ||||||||
\(663\) | 3.03761 | 0.117971 | ||||||||
\(664\) | −26.4690 | −1.02720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.38787 | 0.0925282 | ||||||||
\(667\) | 17.2506 | 0.667946 | ||||||||
\(668\) | −0.0956908 | −0.00370239 | ||||||||
\(669\) | 17.6121 | 0.680924 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.30536 | 0.0503552 | ||||||||
\(673\) | 14.8813 | 0.573631 | 0.286816 | − | 0.957986i | \(-0.407403\pi\) | ||||
0.286816 | + | 0.957986i | \(0.407403\pi\) | |||||||
\(674\) | −29.3561 | −1.13076 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39517 | −0.0921218 | ||||||||
\(677\) | 27.7685 | 1.06723 | 0.533614 | − | 0.845728i | \(-0.320833\pi\) | ||||
0.533614 | + | 0.845728i | \(0.320833\pi\) | |||||||
\(678\) | 3.35026 | 0.128666 | ||||||||
\(679\) | −13.7019 | −0.525832 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4314 | 0.667971 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4617 | −0.974264 | −0.487132 | − | 0.873328i | \(-0.661957\pi\) | ||||
−0.487132 | + | 0.873328i | \(0.661957\pi\) | |||||||
\(684\) | 1.03761 | 0.0396741 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 22.2374 | 0.849029 | ||||||||
\(687\) | 13.0738 | 0.498797 | ||||||||
\(688\) | 19.2203 | 0.732766 | ||||||||
\(689\) | −1.14903 | −0.0437746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.6991 | 1.66239 | 0.831196 | − | 0.555979i | \(-0.187657\pi\) | ||||
0.831196 | + | 0.555979i | \(0.187657\pi\) | |||||||
\(692\) | 4.51976 | 0.171816 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.19394 | −0.348997 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11.5369 | −0.437305 | ||||||||
\(697\) | 34.2492 | 1.29728 | ||||||||
\(698\) | −6.58910 | −0.249401 | ||||||||
\(699\) | 13.8437 | 0.523616 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.01317 | −0.264884 | −0.132442 | − | 0.991191i | \(-0.542282\pi\) | ||||
−0.132442 | + | 0.991191i | \(0.542282\pi\) | |||||||
\(702\) | −1.19394 | −0.0450622 | ||||||||
\(703\) | 8.62530 | 0.325309 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.73813 | 0.366500 | ||||||||
\(707\) | 12.8481 | 0.483204 | ||||||||
\(708\) | 2.57452 | 0.0967562 | ||||||||
\(709\) | 45.6747 | 1.71535 | 0.857674 | − | 0.514194i | \(-0.171909\pi\) | ||||
0.857674 | + | 0.514194i | \(0.171909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.9756 | −0.524125 | ||||||||
\(712\) | −45.1754 | −1.69302 | ||||||||
\(713\) | 3.84955 | 0.144167 | ||||||||
\(714\) | 6.66433 | 0.249406 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.07522 | −0.0775547 | ||||||||
\(717\) | 12.3733 | 0.462089 | ||||||||
\(718\) | −12.7757 | −0.476787 | ||||||||
\(719\) | 16.2520 | 0.606098 | 0.303049 | − | 0.952975i | \(-0.401995\pi\) | ||||
0.303049 | + | 0.952975i | \(0.401995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.2228 | −0.753138 | ||||||||
\(722\) | 14.2569 | 0.530588 | ||||||||
\(723\) | 24.5501 | 0.913027 | ||||||||
\(724\) | −1.51247 | −0.0562104 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2243 | 0.564636 | 0.282318 | − | 0.959321i | \(-0.408897\pi\) | ||||
0.282318 | + | 0.959321i | \(0.408897\pi\) | |||||||
\(728\) | −2.57452 | −0.0954179 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.6497 | 0.615813 | ||||||||
\(732\) | 0.0145884 | 0.000539205 0 | ||||||||
\(733\) | 43.5066 | 1.60695 | 0.803476 | − | 0.595337i | \(-0.202981\pi\) | ||||
0.803476 | + | 0.595337i | \(0.202981\pi\) | |||||||
\(734\) | 34.0870 | 1.25817 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.37328 | −0.161201 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −13.4617 | −0.495531 | ||||||||
\(739\) | 7.02302 | 0.258346 | 0.129173 | − | 0.991622i | \(-0.458768\pi\) | ||||
0.129173 | + | 0.991622i | \(0.458768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.31265 | −0.158429 | ||||||||
\(742\) | −2.52090 | −0.0925452 | ||||||||
\(743\) | 2.94192 | 0.107929 | 0.0539643 | − | 0.998543i | \(-0.482814\pi\) | ||||
0.0539643 | + | 0.998543i | \(0.482814\pi\) | |||||||
\(744\) | −2.57452 | −0.0943863 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −41.7586 | −1.52889 | ||||||||
\(747\) | 9.89446 | 0.362019 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.88858 | 0.361321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1016 | 0.879479 | 0.439739 | − | 0.898125i | \(-0.355071\pi\) | ||||
0.439739 | + | 0.898125i | \(0.355071\pi\) | |||||||
\(752\) | −53.5633 | −1.95325 | ||||||||
\(753\) | 13.9003 | 0.506557 | ||||||||
\(754\) | −5.14903 | −0.187517 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.231548 | −0.00842132 | ||||||||
\(757\) | −16.3127 | −0.592893 | −0.296447 | − | 0.955049i | \(-0.595802\pi\) | ||||
−0.296447 | + | 0.955049i | \(0.595802\pi\) | |||||||
\(758\) | 5.55149 | 0.201639 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.08840 | 0.184454 | 0.0922271 | − | 0.995738i | \(-0.470601\pi\) | ||||
0.0922271 | + | 0.995738i | \(0.470601\pi\) | |||||||
\(762\) | 20.4690 | 0.741513 | ||||||||
\(763\) | −11.9394 | −0.432234 | ||||||||
\(764\) | 0.252016 | 0.00911762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.61071 | 0.0943289 | ||||||||
\(767\) | −10.7005 | −0.386374 | ||||||||
\(768\) | 4.61213 | 0.166426 | ||||||||
\(769\) | −2.10157 | −0.0757846 | −0.0378923 | − | 0.999282i | \(-0.512064\pi\) | ||||
−0.0378923 | + | 0.999282i | \(0.512064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8872 | −0.680205 | ||||||||
\(772\) | −1.66688 | −0.0599924 | ||||||||
\(773\) | 46.0625 | 1.65675 | 0.828377 | − | 0.560171i | \(-0.189264\pi\) | ||||
0.828377 | + | 0.560171i | \(0.189264\pi\) | |||||||
\(774\) | −6.54420 | −0.235226 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.7005 | −1.10208 | ||||||||
\(777\) | −1.92478 | −0.0690510 | ||||||||
\(778\) | 9.66291 | 0.346432 | ||||||||
\(779\) | −48.6253 | −1.74218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −22.3272 | −0.798420 | ||||||||
\(783\) | 4.31265 | 0.154122 | ||||||||
\(784\) | 24.2506 | 0.866093 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.77575 | 0.313021 | ||||||||
\(787\) | 26.0303 | 0.927881 | 0.463940 | − | 0.885866i | \(-0.346435\pi\) | ||||
0.463940 | + | 0.885866i | \(0.346435\pi\) | |||||||
\(788\) | 4.01573 | 0.143054 | ||||||||
\(789\) | −20.8061 | −0.740715 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.70052 | −0.0960196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0606343 | −0.00215319 | ||||||||
\(794\) | −35.1030 | −1.24576 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.07664 | 0.0381604 | ||||||||
\(797\) | −29.9902 | −1.06231 | −0.531153 | − | 0.847276i | \(-0.678241\pi\) | ||||
−0.531153 | + | 0.847276i | \(0.678241\pi\) | |||||||
\(798\) | −9.46168 | −0.334940 | ||||||||
\(799\) | −46.3996 | −1.64150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.8872 | 0.596679 | ||||||||
\(802\) | 13.1636 | 0.464824 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.523730 | −0.0184705 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.14903 | −0.0404729 | ||||||||
\(807\) | −32.3996 | −1.14052 | ||||||||
\(808\) | 28.7875 | 1.01274 | ||||||||
\(809\) | −39.7597 | −1.39788 | −0.698939 | − | 0.715181i | \(-0.746344\pi\) | ||||
−0.698939 | + | 0.715181i | \(0.746344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2765 | 0.360855 | 0.180428 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180428 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(812\) | −0.998585 | −0.0350435 | ||||||||
\(813\) | 16.8265 | 0.590132 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16.3938 | 0.573896 | ||||||||
\(817\) | −23.6385 | −0.827006 | ||||||||
\(818\) | 7.18523 | 0.251226 | ||||||||
\(819\) | 0.962389 | 0.0336286 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.0870 | −1.74805 | −0.874024 | − | 0.485883i | \(-0.838498\pi\) | ||||
−0.874024 | + | 0.485883i | \(0.838498\pi\) | |||||||
\(822\) | 4.96239 | 0.173083 | ||||||||
\(823\) | 29.7137 | 1.03575 | 0.517877 | − | 0.855455i | \(-0.326722\pi\) | ||||
0.517877 | + | 0.855455i | \(0.326722\pi\) | |||||||
\(824\) | −45.3112 | −1.57849 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.4763 | −0.816844 | ||||||||
\(827\) | 2.41819 | 0.0840887 | 0.0420444 | − | 0.999116i | \(-0.486613\pi\) | ||||
0.0420444 | + | 0.999116i | \(0.486613\pi\) | |||||||
\(828\) | 0.775746 | 0.0269590 | ||||||||
\(829\) | −23.2750 | −0.808376 | −0.404188 | − | 0.914676i | \(-0.632446\pi\) | ||||
−0.404188 | + | 0.914676i | \(0.632446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9076 | −0.586519 | ||||||||
\(832\) | −5.70782 | −0.197883 | ||||||||
\(833\) | 21.0073 | 0.727860 | ||||||||
\(834\) | 31.4010 | 1.08733 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.962389 | 0.0332650 | ||||||||
\(838\) | −15.8496 | −0.547514 | ||||||||
\(839\) | −18.8265 | −0.649964 | −0.324982 | − | 0.945720i | \(-0.605358\pi\) | ||||
−0.324982 | + | 0.945720i | \(0.605358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.4010 | −0.358657 | ||||||||
\(842\) | −45.3258 | −1.56203 | ||||||||
\(843\) | −5.61213 | −0.193292 | ||||||||
\(844\) | 3.58769 | 0.123493 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.2374 | 0.627016 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.20123 | −0.212951 | ||||||||
\(849\) | −5.81924 | −0.199716 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.44851 | 0.221052 | ||||||||
\(852\) | −2.72496 | −0.0933556 | ||||||||
\(853\) | 24.9076 | 0.852821 | 0.426411 | − | 0.904530i | \(-0.359778\pi\) | ||||
0.426411 | + | 0.904530i | \(0.359778\pi\) | |||||||
\(854\) | −0.133028 | −0.00455212 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.1563 | 0.757288 | ||||||||
\(857\) | 7.60625 | 0.259824 | 0.129912 | − | 0.991525i | \(-0.458530\pi\) | ||||
0.129912 | + | 0.991525i | \(0.458530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.14060 | −0.0730362 | −0.0365181 | − | 0.999333i | \(-0.511627\pi\) | ||||
−0.0365181 | + | 0.999333i | \(0.511627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8510 | 0.369800 | ||||||||
\(862\) | 8.77575 | 0.298903 | ||||||||
\(863\) | 29.3112 | 0.997766 | 0.498883 | − | 0.866669i | \(-0.333744\pi\) | ||||
0.498883 | + | 0.866669i | \(0.333744\pi\) | |||||||
\(864\) | −1.09332 | −0.0371955 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.6991 | −0.805329 | ||||||||
\(867\) | −2.79877 | −0.0950512 | ||||||||
\(868\) | −0.222839 | −0.00756365 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.17679 | 0.0737578 | ||||||||
\(872\) | −26.7513 | −0.905914 | ||||||||
\(873\) | 11.4763 | 0.388413 | ||||||||
\(874\) | 31.6991 | 1.07224 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.08110 | 0.0703139 | ||||||||
\(877\) | −31.5183 | −1.06430 | −0.532149 | − | 0.846650i | \(-0.678616\pi\) | ||||
−0.532149 | + | 0.846650i | \(0.678616\pi\) | |||||||
\(878\) | −7.92478 | −0.267448 | ||||||||
\(879\) | 8.29218 | 0.279688 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.6253 | 0.357975 | 0.178988 | − | 0.983851i | \(-0.442718\pi\) | ||||
0.178988 | + | 0.983851i | \(0.442718\pi\) | |||||||
\(882\) | −8.25694 | −0.278026 | ||||||||
\(883\) | −6.29806 | −0.211947 | −0.105973 | − | 0.994369i | \(-0.533796\pi\) | ||||
−0.105973 | + | 0.994369i | \(0.533796\pi\) | |||||||
\(884\) | 0.589104 | 0.0198137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.1608 | 0.979676 | ||||||||
\(887\) | −29.1187 | −0.977711 | −0.488855 | − | 0.872365i | \(-0.662585\pi\) | ||||
−0.488855 | + | 0.872365i | \(0.662585\pi\) | |||||||
\(888\) | −4.31265 | −0.144723 | ||||||||
\(889\) | −16.4993 | −0.553369 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.41564 | 0.114364 | ||||||||
\(893\) | 65.8759 | 2.20445 | ||||||||
\(894\) | −9.46168 | −0.316446 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15.1333 | −0.505568 | ||||||||
\(897\) | −3.22425 | −0.107655 | ||||||||
\(898\) | −46.4142 | −1.54886 | ||||||||
\(899\) | 4.15045 | 0.138425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.37187 | −0.178963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.27504 | 0.175542 | ||||||||
\(904\) | −6.05079 | −0.201246 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.92478 | 0.130392 | ||||||||
\(907\) | −57.3112 | −1.90299 | −0.951494 | − | 0.307667i | \(-0.900452\pi\) | ||||
−0.951494 | + | 0.307667i | \(0.900452\pi\) | |||||||
\(908\) | 3.38058 | 0.112188 | ||||||||
\(909\) | −10.7612 | −0.356925 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.52232 | −0.182962 | −0.0914812 | − | 0.995807i | \(-0.529160\pi\) | ||||
−0.0914812 | + | 0.995807i | \(0.529160\pi\) | |||||||
\(912\) | −23.2750 | −0.770714 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 55.6834 | 1.84184 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.53549 | 0.0837749 | ||||||||
\(917\) | −7.07381 | −0.233598 | ||||||||
\(918\) | −5.58181 | −0.184227 | ||||||||
\(919\) | 5.75272 | 0.189765 | 0.0948824 | − | 0.995488i | \(-0.469752\pi\) | ||||
0.0948824 | + | 0.995488i | \(0.469752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.6688 | −0.845815 | ||||||||
\(922\) | −26.6399 | −0.877338 | ||||||||
\(923\) | 11.3258 | 0.372794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 57.7861 | 1.89897 | ||||||||
\(927\) | 16.9380 | 0.556315 | ||||||||
\(928\) | −4.71511 | −0.154781 | ||||||||
\(929\) | 41.4274 | 1.35919 | 0.679594 | − | 0.733588i | \(-0.262156\pi\) | ||||
0.679594 | + | 0.733588i | \(0.262156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.8251 | −0.977479 | ||||||||
\(932\) | 2.68479 | 0.0879434 | ||||||||
\(933\) | −15.7235 | −0.514766 | ||||||||
\(934\) | 21.5515 | 0.705186 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.15633 | 0.0704817 | ||||||||
\(937\) | 14.9222 | 0.487488 | 0.243744 | − | 0.969840i | \(-0.421624\pi\) | ||||
0.243744 | + | 0.969840i | \(0.421624\pi\) | |||||||
\(938\) | 4.77575 | 0.155934 | ||||||||
\(939\) | −26.8627 | −0.876632 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.0395 | −1.85944 | −0.929718 | − | 0.368273i | \(-0.879949\pi\) | ||||
−0.929718 | + | 0.368273i | \(0.879949\pi\) | |||||||
\(942\) | 2.38787 | 0.0778011 | ||||||||
\(943\) | −36.3536 | −1.18384 | ||||||||
\(944\) | −57.7499 | −1.87960 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2374 | 0.982584 | 0.491292 | − | 0.870995i | \(-0.336525\pi\) | ||||
0.491292 | + | 0.870995i | \(0.336525\pi\) | |||||||
\(948\) | −2.71037 | −0.0880288 | ||||||||
\(949\) | −8.64974 | −0.280782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.710373 | 0.0230354 | ||||||||
\(952\) | −12.0362 | −0.390095 | ||||||||
\(953\) | 46.2697 | 1.49882 | 0.749411 | − | 0.662106i | \(-0.230337\pi\) | ||||
0.749411 | + | 0.662106i | \(0.230337\pi\) | |||||||
\(954\) | 2.11142 | 0.0683597 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.39963 | 0.0776097 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −42.3996 | −1.36987 | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0738 | −0.970123 | ||||||||
\(962\) | −1.92478 | −0.0620573 | ||||||||
\(963\) | −8.28233 | −0.266894 | ||||||||
\(964\) | 4.76116 | 0.153347 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.07381 | −0.227596 | ||||||||
\(967\) | −49.5790 | −1.59435 | −0.797176 | − | 0.603747i | \(-0.793674\pi\) | ||||
−0.797176 | + | 0.603747i | \(0.793674\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.1622 | −0.647703 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.12268 | −0.100212 | −0.0501058 | − | 0.998744i | \(-0.515956\pi\) | ||||
−0.0501058 | + | 0.998744i | \(0.515956\pi\) | |||||||
\(972\) | 0.193937 | 0.00622052 | ||||||||
\(973\) | −25.3112 | −0.811441 | ||||||||
\(974\) | 2.14762 | 0.0688141 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.327239 | −0.0104747 | ||||||||
\(977\) | 5.15377 | 0.164884 | 0.0824419 | − | 0.996596i | \(-0.473728\pi\) | ||||
0.0824419 | + | 0.996596i | \(0.473728\pi\) | |||||||
\(978\) | −0.463096 | −0.0148082 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 11.8496 | 0.378134 | ||||||||
\(983\) | 14.8627 | 0.474047 | 0.237024 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237024 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(984\) | 24.3127 | 0.775059 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.0724 | −0.766621 | ||||||||
\(987\) | −14.7005 | −0.467923 | ||||||||
\(988\) | −0.836381 | −0.0266088 | ||||||||
\(989\) | −17.6728 | −0.561961 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.43866 | 0.140999 | 0.0704993 | − | 0.997512i | \(-0.477541\pi\) | ||||
0.0704993 | + | 0.997512i | \(0.477541\pi\) | |||||||
\(992\) | −1.05220 | −0.0334074 | ||||||||
\(993\) | 0.962389 | 0.0305405 | ||||||||
\(994\) | 24.8481 | 0.788135 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.91890 | 0.0608026 | ||||||||
\(997\) | 38.8324 | 1.22983 | 0.614917 | − | 0.788592i | \(-0.289189\pi\) | ||||
0.614917 | + | 0.788592i | \(0.289189\pi\) | |||||||
\(998\) | 45.4734 | 1.43944 | ||||||||
\(999\) | 1.61213 | 0.0510054 |
(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 | 9075.2.a.cg.1.3 | 3 | ||
5.2 | odd | 4 | 1815.2.c.e.364.5 | 6 | |||
5.3 | odd | 4 | 1815.2.c.e.364.2 | 6 | |||
5.4 | even | 2 | 9075.2.a.ch.1.1 | 3 | |||
11.10 | odd | 2 | 825.2.a.l.1.1 | 3 | |||
33.32 | even | 2 | 2475.2.a.ba.1.3 | 3 | |||
55.32 | even | 4 | 165.2.c.b.34.2 | ✓ | 6 | ||
55.43 | even | 4 | 165.2.c.b.34.5 | yes | 6 | ||
55.54 | odd | 2 | 825.2.a.j.1.3 | 3 | |||
165.32 | odd | 4 | 495.2.c.e.199.5 | 6 | |||
165.98 | odd | 4 | 495.2.c.e.199.2 | 6 | |||
165.164 | even | 2 | 2475.2.a.bc.1.1 | 3 | |||
220.43 | odd | 4 | 2640.2.d.h.529.1 | 6 | |||
220.87 | odd | 4 | 2640.2.d.h.529.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.b.34.2 | ✓ | 6 | 55.32 | even | 4 | ||
165.2.c.b.34.5 | yes | 6 | 55.43 | even | 4 | ||
495.2.c.e.199.2 | 6 | 165.98 | odd | 4 | |||
495.2.c.e.199.5 | 6 | 165.32 | odd | 4 | |||
825.2.a.j.1.3 | 3 | 55.54 | odd | 2 | |||
825.2.a.l.1.1 | 3 | 11.10 | odd | 2 | |||
1815.2.c.e.364.2 | 6 | 5.3 | odd | 4 | |||
1815.2.c.e.364.5 | 6 | 5.2 | odd | 4 | |||
2475.2.a.ba.1.3 | 3 | 33.32 | even | 2 | |||
2475.2.a.bc.1.1 | 3 | 165.164 | even | 2 | |||
2640.2.d.h.529.1 | 6 | 220.43 | odd | 4 | |||
2640.2.d.h.529.4 | 6 | 220.87 | odd | 4 | |||
9075.2.a.cg.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9075.2.a.ch.1.1 | 3 | 5.4 | even | 2 |