Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8025,2,Mod(1,8025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8025, 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("8025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8025 = 3 \cdot 5^{2} \cdot 107 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8025.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: | \(64.0799476221\) |
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: | \( x^{12} - 3 x^{11} - 15 x^{10} + 49 x^{9} + 71 x^{8} - 278 x^{7} - 92 x^{6} + 649 x^{5} - 127 x^{4} + \cdots - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1605) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.37578\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37578 | 0.972825 | 0.486412 | − | 0.873729i | \(-0.338305\pi\) | ||||
0.486412 | + | 0.873729i | \(0.338305\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.107224 | −0.0536121 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.37578 | −0.561661 | ||||||||
\(7\) | 1.29286 | 0.488655 | 0.244327 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244327 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(8\) | −2.89908 | −1.02498 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.18674 | −1.56386 | −0.781931 | − | 0.623365i | \(-0.785765\pi\) | ||||
−0.781931 | + | 0.623365i | \(0.785765\pi\) | |||||||
\(12\) | 0.107224 | 0.0309530 | ||||||||
\(13\) | 1.56082 | 0.432894 | 0.216447 | − | 0.976294i | \(-0.430553\pi\) | ||||
0.216447 | + | 0.976294i | \(0.430553\pi\) | |||||||
\(14\) | 1.77869 | 0.475375 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.77405 | −0.943514 | ||||||||
\(17\) | 5.67618 | 1.37668 | 0.688338 | − | 0.725390i | \(-0.258341\pi\) | ||||
0.688338 | + | 0.725390i | \(0.258341\pi\) | |||||||
\(18\) | 1.37578 | 0.324275 | ||||||||
\(19\) | 0.785965 | 0.180313 | 0.0901564 | − | 0.995928i | \(-0.471263\pi\) | ||||
0.0901564 | + | 0.995928i | \(0.471263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.29286 | −0.282125 | ||||||||
\(22\) | −7.13582 | −1.52136 | ||||||||
\(23\) | −9.21903 | −1.92230 | −0.961150 | − | 0.276025i | \(-0.910983\pi\) | ||||
−0.961150 | + | 0.276025i | \(0.910983\pi\) | |||||||
\(24\) | 2.89908 | 0.591772 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.14735 | 0.421130 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.138626 | −0.0261978 | ||||||||
\(29\) | 9.36714 | 1.73944 | 0.869718 | − | 0.493550i | \(-0.164301\pi\) | ||||
0.869718 | + | 0.493550i | \(0.164301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.91330 | 1.78048 | 0.890241 | − | 0.455490i | \(-0.150536\pi\) | ||||
0.890241 | + | 0.455490i | \(0.150536\pi\) | |||||||
\(32\) | 0.605886 | 0.107107 | ||||||||
\(33\) | 5.18674 | 0.902896 | ||||||||
\(34\) | 7.80919 | 1.33926 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.107224 | −0.0178707 | ||||||||
\(37\) | −4.37397 | −0.719075 | −0.359538 | − | 0.933131i | \(-0.617066\pi\) | ||||
−0.359538 | + | 0.933131i | \(0.617066\pi\) | |||||||
\(38\) | 1.08132 | 0.175413 | ||||||||
\(39\) | −1.56082 | −0.249932 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.756558 | −0.118154 | −0.0590772 | − | 0.998253i | \(-0.518816\pi\) | ||||
−0.0590772 | + | 0.998253i | \(0.518816\pi\) | |||||||
\(42\) | −1.77869 | −0.274458 | ||||||||
\(43\) | 3.28845 | 0.501484 | 0.250742 | − | 0.968054i | \(-0.419325\pi\) | ||||
0.250742 | + | 0.968054i | \(0.419325\pi\) | |||||||
\(44\) | 0.556144 | 0.0838419 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.6834 | −1.87006 | ||||||||
\(47\) | 4.30876 | 0.628498 | 0.314249 | − | 0.949341i | \(-0.398247\pi\) | ||||
0.314249 | + | 0.949341i | \(0.398247\pi\) | |||||||
\(48\) | 3.77405 | 0.544738 | ||||||||
\(49\) | −5.32852 | −0.761217 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.67618 | −0.794824 | ||||||||
\(52\) | −0.167358 | −0.0232084 | ||||||||
\(53\) | −6.56151 | −0.901293 | −0.450646 | − | 0.892703i | \(-0.648806\pi\) | ||||
−0.450646 | + | 0.892703i | \(0.648806\pi\) | |||||||
\(54\) | −1.37578 | −0.187220 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.74810 | −0.500861 | ||||||||
\(57\) | −0.785965 | −0.104104 | ||||||||
\(58\) | 12.8871 | 1.69217 | ||||||||
\(59\) | 3.51171 | 0.457186 | 0.228593 | − | 0.973522i | \(-0.426587\pi\) | ||||
0.228593 | + | 0.973522i | \(0.426587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.507656 | −0.0649987 | −0.0324994 | − | 0.999472i | \(-0.510347\pi\) | ||||
−0.0324994 | + | 0.999472i | \(0.510347\pi\) | |||||||
\(62\) | 13.6385 | 1.73210 | ||||||||
\(63\) | 1.29286 | 0.162885 | ||||||||
\(64\) | 8.38168 | 1.04771 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.13582 | 0.878359 | ||||||||
\(67\) | −11.1427 | −1.36130 | −0.680651 | − | 0.732607i | \(-0.738303\pi\) | ||||
−0.680651 | + | 0.732607i | \(0.738303\pi\) | |||||||
\(68\) | −0.608624 | −0.0738065 | ||||||||
\(69\) | 9.21903 | 1.10984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.08780 | −0.485133 | −0.242567 | − | 0.970135i | \(-0.577989\pi\) | ||||
−0.242567 | + | 0.970135i | \(0.577989\pi\) | |||||||
\(72\) | −2.89908 | −0.341660 | ||||||||
\(73\) | −14.7644 | −1.72805 | −0.864024 | − | 0.503451i | \(-0.832064\pi\) | ||||
−0.864024 | + | 0.503451i | \(0.832064\pi\) | |||||||
\(74\) | −6.01762 | −0.699534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0842745 | −0.00966695 | ||||||||
\(77\) | −6.70572 | −0.764188 | ||||||||
\(78\) | −2.14735 | −0.243140 | ||||||||
\(79\) | 7.34598 | 0.826488 | 0.413244 | − | 0.910620i | \(-0.364396\pi\) | ||||
0.413244 | + | 0.910620i | \(0.364396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.04086 | −0.114944 | ||||||||
\(83\) | 12.1115 | 1.32941 | 0.664703 | − | 0.747108i | \(-0.268558\pi\) | ||||
0.664703 | + | 0.747108i | \(0.268558\pi\) | |||||||
\(84\) | 0.138626 | 0.0151253 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.52419 | 0.487856 | ||||||||
\(87\) | −9.36714 | −1.00426 | ||||||||
\(88\) | 15.0368 | 1.60293 | ||||||||
\(89\) | −11.1117 | −1.17783 | −0.588917 | − | 0.808194i | \(-0.700445\pi\) | ||||
−0.588917 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.01792 | 0.211536 | ||||||||
\(92\) | 0.988504 | 0.103059 | ||||||||
\(93\) | −9.91330 | −1.02796 | ||||||||
\(94\) | 5.92792 | 0.611418 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.605886 | −0.0618380 | ||||||||
\(97\) | −11.6889 | −1.18683 | −0.593416 | − | 0.804896i | \(-0.702221\pi\) | ||||
−0.593416 | + | 0.804896i | \(0.702221\pi\) | |||||||
\(98\) | −7.33088 | −0.740530 | ||||||||
\(99\) | −5.18674 | −0.521287 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.11771 | −0.210720 | −0.105360 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105360 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(102\) | −7.80919 | −0.773225 | ||||||||
\(103\) | −19.3063 | −1.90231 | −0.951154 | − | 0.308717i | \(-0.900100\pi\) | ||||
−0.951154 | + | 0.308717i | \(0.900100\pi\) | |||||||
\(104\) | −4.52495 | −0.443708 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.02721 | −0.876800 | ||||||||
\(107\) | −1.00000 | −0.0966736 | ||||||||
\(108\) | 0.107224 | 0.0103177 | ||||||||
\(109\) | 3.75798 | 0.359950 | 0.179975 | − | 0.983671i | \(-0.442398\pi\) | ||||
0.179975 | + | 0.983671i | \(0.442398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.37397 | 0.415158 | ||||||||
\(112\) | −4.87932 | −0.461052 | ||||||||
\(113\) | 13.7716 | 1.29553 | 0.647763 | − | 0.761842i | \(-0.275705\pi\) | ||||
0.647763 | + | 0.761842i | \(0.275705\pi\) | |||||||
\(114\) | −1.08132 | −0.101275 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00438 | −0.0932548 | ||||||||
\(117\) | 1.56082 | 0.144298 | ||||||||
\(118\) | 4.83135 | 0.444762 | ||||||||
\(119\) | 7.33850 | 0.672719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.9023 | 1.44566 | ||||||||
\(122\) | −0.698424 | −0.0632324 | ||||||||
\(123\) | 0.756558 | 0.0682165 | ||||||||
\(124\) | −1.06295 | −0.0954554 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.77869 | 0.158458 | ||||||||
\(127\) | −9.71645 | −0.862196 | −0.431098 | − | 0.902305i | \(-0.641874\pi\) | ||||
−0.431098 | + | 0.902305i | \(0.641874\pi\) | |||||||
\(128\) | 10.3196 | 0.912131 | ||||||||
\(129\) | −3.28845 | −0.289532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.43178 | 0.649317 | 0.324659 | − | 0.945831i | \(-0.394751\pi\) | ||||
0.324659 | + | 0.945831i | \(0.394751\pi\) | |||||||
\(132\) | −0.556144 | −0.0484062 | ||||||||
\(133\) | 1.01614 | 0.0881107 | ||||||||
\(134\) | −15.3300 | −1.32431 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.4557 | −1.41107 | ||||||||
\(137\) | −13.9411 | −1.19107 | −0.595533 | − | 0.803330i | \(-0.703059\pi\) | ||||
−0.595533 | + | 0.803330i | \(0.703059\pi\) | |||||||
\(138\) | 12.6834 | 1.07968 | ||||||||
\(139\) | −17.8433 | −1.51345 | −0.756725 | − | 0.653734i | \(-0.773202\pi\) | ||||
−0.756725 | + | 0.653734i | \(0.773202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.30876 | −0.362863 | ||||||||
\(142\) | −5.62393 | −0.471949 | ||||||||
\(143\) | −8.09558 | −0.676986 | ||||||||
\(144\) | −3.77405 | −0.314505 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −20.3127 | −1.68109 | ||||||||
\(147\) | 5.32852 | 0.439489 | ||||||||
\(148\) | 0.468995 | 0.0385512 | ||||||||
\(149\) | 14.3146 | 1.17270 | 0.586348 | − | 0.810059i | \(-0.300565\pi\) | ||||
0.586348 | + | 0.810059i | \(0.300565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.452621 | −0.0368338 | −0.0184169 | − | 0.999830i | \(-0.505863\pi\) | ||||
−0.0184169 | + | 0.999830i | \(0.505863\pi\) | |||||||
\(152\) | −2.27858 | −0.184817 | ||||||||
\(153\) | 5.67618 | 0.458892 | ||||||||
\(154\) | −9.22561 | −0.743421 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.167358 | 0.0133994 | ||||||||
\(157\) | −17.6813 | −1.41112 | −0.705562 | − | 0.708648i | \(-0.749305\pi\) | ||||
−0.705562 | + | 0.708648i | \(0.749305\pi\) | |||||||
\(158\) | 10.1065 | 0.804028 | ||||||||
\(159\) | 6.56151 | 0.520362 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.9189 | −0.939341 | ||||||||
\(162\) | 1.37578 | 0.108092 | ||||||||
\(163\) | −12.2108 | −0.956424 | −0.478212 | − | 0.878244i | \(-0.658715\pi\) | ||||
−0.478212 | + | 0.878244i | \(0.658715\pi\) | |||||||
\(164\) | 0.0811213 | 0.00633451 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6627 | 1.29328 | ||||||||
\(167\) | 0.255788 | 0.0197935 | 0.00989674 | − | 0.999951i | \(-0.496850\pi\) | ||||
0.00989674 | + | 0.999951i | \(0.496850\pi\) | |||||||
\(168\) | 3.74810 | 0.289172 | ||||||||
\(169\) | −10.5638 | −0.812603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.785965 | 0.0601043 | ||||||||
\(172\) | −0.352601 | −0.0268856 | ||||||||
\(173\) | 1.67384 | 0.127259 | 0.0636297 | − | 0.997974i | \(-0.479732\pi\) | ||||
0.0636297 | + | 0.997974i | \(0.479732\pi\) | |||||||
\(174\) | −12.8871 | −0.976972 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.5750 | 1.47552 | ||||||||
\(177\) | −3.51171 | −0.263957 | ||||||||
\(178\) | −15.2872 | −1.14583 | ||||||||
\(179\) | −14.4146 | −1.07740 | −0.538698 | − | 0.842499i | \(-0.681084\pi\) | ||||
−0.538698 | + | 0.842499i | \(0.681084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.82843 | −0.581883 | −0.290941 | − | 0.956741i | \(-0.593968\pi\) | ||||
−0.290941 | + | 0.956741i | \(0.593968\pi\) | |||||||
\(182\) | 2.77622 | 0.205787 | ||||||||
\(183\) | 0.507656 | 0.0375270 | ||||||||
\(184\) | 26.7267 | 1.97032 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.6385 | −1.00003 | ||||||||
\(187\) | −29.4409 | −2.15293 | ||||||||
\(188\) | −0.462004 | −0.0336951 | ||||||||
\(189\) | −1.29286 | −0.0940416 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7680 | −0.923859 | −0.461929 | − | 0.886917i | \(-0.652843\pi\) | ||||
−0.461929 | + | 0.886917i | \(0.652843\pi\) | |||||||
\(192\) | −8.38168 | −0.604895 | ||||||||
\(193\) | 7.36412 | 0.530081 | 0.265040 | − | 0.964237i | \(-0.414615\pi\) | ||||
0.265040 | + | 0.964237i | \(0.414615\pi\) | |||||||
\(194\) | −16.0814 | −1.15458 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.571346 | 0.0408104 | ||||||||
\(197\) | 10.0463 | 0.715768 | 0.357884 | − | 0.933766i | \(-0.383498\pi\) | ||||
0.357884 | + | 0.933766i | \(0.383498\pi\) | |||||||
\(198\) | −7.13582 | −0.507121 | ||||||||
\(199\) | 15.0806 | 1.06904 | 0.534518 | − | 0.845157i | \(-0.320493\pi\) | ||||
0.534518 | + | 0.845157i | \(0.320493\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1427 | 0.785949 | ||||||||
\(202\) | −2.91351 | −0.204994 | ||||||||
\(203\) | 12.1104 | 0.849983 | ||||||||
\(204\) | 0.608624 | 0.0426122 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −26.5613 | −1.85061 | ||||||||
\(207\) | −9.21903 | −0.640767 | ||||||||
\(208\) | −5.89063 | −0.408441 | ||||||||
\(209\) | −4.07660 | −0.281984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.03224 | −0.621805 | −0.310902 | − | 0.950442i | \(-0.600631\pi\) | ||||
−0.310902 | + | 0.950442i | \(0.600631\pi\) | |||||||
\(212\) | 0.703553 | 0.0483202 | ||||||||
\(213\) | 4.08780 | 0.280092 | ||||||||
\(214\) | −1.37578 | −0.0940465 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.89908 | 0.197257 | ||||||||
\(217\) | 12.8165 | 0.870041 | ||||||||
\(218\) | 5.17017 | 0.350168 | ||||||||
\(219\) | 14.7644 | 0.997689 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.85951 | 0.595955 | ||||||||
\(222\) | 6.01762 | 0.403876 | ||||||||
\(223\) | −21.9892 | −1.47250 | −0.736252 | − | 0.676708i | \(-0.763406\pi\) | ||||
−0.736252 | + | 0.676708i | \(0.763406\pi\) | |||||||
\(224\) | 0.783325 | 0.0523381 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.9468 | 1.26032 | ||||||||
\(227\) | −25.9768 | −1.72414 | −0.862070 | − | 0.506790i | \(-0.830832\pi\) | ||||
−0.862070 | + | 0.506790i | \(0.830832\pi\) | |||||||
\(228\) | 0.0842745 | 0.00558122 | ||||||||
\(229\) | 8.53416 | 0.563953 | 0.281976 | − | 0.959421i | \(-0.409010\pi\) | ||||
0.281976 | + | 0.959421i | \(0.409010\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.70572 | 0.441204 | ||||||||
\(232\) | −27.1561 | −1.78289 | ||||||||
\(233\) | 27.1213 | 1.77678 | 0.888389 | − | 0.459091i | \(-0.151825\pi\) | ||||
0.888389 | + | 0.459091i | \(0.151825\pi\) | |||||||
\(234\) | 2.14735 | 0.140377 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.376541 | −0.0245107 | ||||||||
\(237\) | −7.34598 | −0.477173 | ||||||||
\(238\) | 10.0962 | 0.654438 | ||||||||
\(239\) | 25.6285 | 1.65777 | 0.828886 | − | 0.559417i | \(-0.188975\pi\) | ||||
0.828886 | + | 0.559417i | \(0.188975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6681 | −1.33135 | −0.665676 | − | 0.746241i | \(-0.731857\pi\) | ||||
−0.665676 | + | 0.746241i | \(0.731857\pi\) | |||||||
\(242\) | 21.8781 | 1.40638 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.0544331 | 0.00348472 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.04086 | 0.0663627 | ||||||||
\(247\) | 1.22675 | 0.0780563 | ||||||||
\(248\) | −28.7395 | −1.82496 | ||||||||
\(249\) | −12.1115 | −0.767533 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3902 | 0.971419 | 0.485710 | − | 0.874120i | \(-0.338561\pi\) | ||||
0.485710 | + | 0.874120i | \(0.338561\pi\) | |||||||
\(252\) | −0.138626 | −0.00873260 | ||||||||
\(253\) | 47.8167 | 3.00621 | ||||||||
\(254\) | −13.3677 | −0.838765 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.56585 | −0.160366 | ||||||||
\(257\) | 19.0856 | 1.19053 | 0.595264 | − | 0.803530i | \(-0.297047\pi\) | ||||
0.595264 | + | 0.803530i | \(0.297047\pi\) | |||||||
\(258\) | −4.52419 | −0.281664 | ||||||||
\(259\) | −5.65492 | −0.351380 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.36714 | 0.579812 | ||||||||
\(262\) | 10.2245 | 0.631672 | ||||||||
\(263\) | −1.71026 | −0.105459 | −0.0527296 | − | 0.998609i | \(-0.516792\pi\) | ||||
−0.0527296 | + | 0.998609i | \(0.516792\pi\) | |||||||
\(264\) | −15.0368 | −0.925450 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.39799 | 0.0857163 | ||||||||
\(267\) | 11.1117 | 0.680022 | ||||||||
\(268\) | 1.19477 | 0.0729823 | ||||||||
\(269\) | −8.42120 | −0.513450 | −0.256725 | − | 0.966485i | \(-0.582643\pi\) | ||||
−0.256725 | + | 0.966485i | \(0.582643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.5279 | −1.24698 | −0.623491 | − | 0.781830i | \(-0.714286\pi\) | ||||
−0.623491 | + | 0.781830i | \(0.714286\pi\) | |||||||
\(272\) | −21.4222 | −1.29891 | ||||||||
\(273\) | −2.01792 | −0.122130 | ||||||||
\(274\) | −19.1799 | −1.15870 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.988504 | −0.0595009 | ||||||||
\(277\) | 12.4087 | 0.745568 | 0.372784 | − | 0.927918i | \(-0.378403\pi\) | ||||
0.372784 | + | 0.927918i | \(0.378403\pi\) | |||||||
\(278\) | −24.5485 | −1.47232 | ||||||||
\(279\) | 9.91330 | 0.593494 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.56318 | 0.0932516 | 0.0466258 | − | 0.998912i | \(-0.485153\pi\) | ||||
0.0466258 | + | 0.998912i | \(0.485153\pi\) | |||||||
\(282\) | −5.92792 | −0.353003 | ||||||||
\(283\) | −8.97776 | −0.533672 | −0.266836 | − | 0.963742i | \(-0.585978\pi\) | ||||
−0.266836 | + | 0.963742i | \(0.585978\pi\) | |||||||
\(284\) | 0.438312 | 0.0260090 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.1378 | −0.658589 | ||||||||
\(287\) | −0.978122 | −0.0577367 | ||||||||
\(288\) | 0.605886 | 0.0357022 | ||||||||
\(289\) | 15.2190 | 0.895237 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6889 | 0.685217 | ||||||||
\(292\) | 1.58311 | 0.0926443 | ||||||||
\(293\) | 3.15706 | 0.184437 | 0.0922187 | − | 0.995739i | \(-0.470604\pi\) | ||||
0.0922187 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(294\) | 7.33088 | 0.427545 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.6805 | 0.737038 | ||||||||
\(297\) | 5.18674 | 0.300965 | ||||||||
\(298\) | 19.6937 | 1.14083 | ||||||||
\(299\) | −14.3893 | −0.832153 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.25150 | 0.245052 | ||||||||
\(302\) | −0.622708 | −0.0358328 | ||||||||
\(303\) | 2.11771 | 0.121659 | ||||||||
\(304\) | −2.96628 | −0.170128 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.80919 | 0.446421 | ||||||||
\(307\) | −14.9338 | −0.852318 | −0.426159 | − | 0.904648i | \(-0.640134\pi\) | ||||
−0.426159 | + | 0.904648i | \(0.640134\pi\) | |||||||
\(308\) | 0.719016 | 0.0409697 | ||||||||
\(309\) | 19.3063 | 1.09830 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1905 | 0.747964 | 0.373982 | − | 0.927436i | \(-0.377992\pi\) | ||||
0.373982 | + | 0.927436i | \(0.377992\pi\) | |||||||
\(312\) | 4.52495 | 0.256175 | ||||||||
\(313\) | −34.8029 | −1.96718 | −0.983588 | − | 0.180429i | \(-0.942251\pi\) | ||||
−0.983588 | + | 0.180429i | \(0.942251\pi\) | |||||||
\(314\) | −24.3257 | −1.37278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.787668 | −0.0443098 | ||||||||
\(317\) | −24.5194 | −1.37715 | −0.688574 | − | 0.725166i | \(-0.741763\pi\) | ||||
−0.688574 | + | 0.725166i | \(0.741763\pi\) | |||||||
\(318\) | 9.02721 | 0.506221 | ||||||||
\(319\) | −48.5850 | −2.72024 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00000 | 0.0558146 | ||||||||
\(322\) | −16.3978 | −0.913814 | ||||||||
\(323\) | 4.46128 | 0.248232 | ||||||||
\(324\) | −0.107224 | −0.00595690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.7994 | −0.930433 | ||||||||
\(327\) | −3.75798 | −0.207817 | ||||||||
\(328\) | 2.19332 | 0.121106 | ||||||||
\(329\) | 5.57062 | 0.307118 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.92043 | −0.160521 | −0.0802607 | − | 0.996774i | \(-0.525575\pi\) | ||||
−0.0802607 | + | 0.996774i | \(0.525575\pi\) | |||||||
\(332\) | −1.29864 | −0.0712723 | ||||||||
\(333\) | −4.37397 | −0.239692 | ||||||||
\(334\) | 0.351909 | 0.0192556 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.87932 | 0.266189 | ||||||||
\(337\) | 20.2923 | 1.10539 | 0.552697 | − | 0.833383i | \(-0.313599\pi\) | ||||
0.552697 | + | 0.833383i | \(0.313599\pi\) | |||||||
\(338\) | −14.5335 | −0.790520 | ||||||||
\(339\) | −13.7716 | −0.747972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.4177 | −2.78443 | ||||||||
\(342\) | 1.08132 | 0.0584709 | ||||||||
\(343\) | −15.9390 | −0.860627 | ||||||||
\(344\) | −9.53348 | −0.514011 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.30283 | 0.123801 | ||||||||
\(347\) | −16.9121 | −0.907892 | −0.453946 | − | 0.891029i | \(-0.649984\pi\) | ||||
−0.453946 | + | 0.891029i | \(0.649984\pi\) | |||||||
\(348\) | 1.00438 | 0.0538407 | ||||||||
\(349\) | 11.0357 | 0.590729 | 0.295365 | − | 0.955385i | \(-0.404559\pi\) | ||||
0.295365 | + | 0.955385i | \(0.404559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.56082 | −0.0833105 | ||||||||
\(352\) | −3.14257 | −0.167500 | ||||||||
\(353\) | 16.3137 | 0.868291 | 0.434146 | − | 0.900843i | \(-0.357050\pi\) | ||||
0.434146 | + | 0.900843i | \(0.357050\pi\) | |||||||
\(354\) | −4.83135 | −0.256783 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.19144 | 0.0631461 | ||||||||
\(357\) | −7.33850 | −0.388395 | ||||||||
\(358\) | −19.8313 | −1.04812 | ||||||||
\(359\) | −15.4892 | −0.817488 | −0.408744 | − | 0.912649i | \(-0.634033\pi\) | ||||
−0.408744 | + | 0.912649i | \(0.634033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3823 | −0.967487 | ||||||||
\(362\) | −10.7702 | −0.566070 | ||||||||
\(363\) | −15.9023 | −0.834654 | ||||||||
\(364\) | −0.216370 | −0.0113409 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.698424 | 0.0365072 | ||||||||
\(367\) | −5.49447 | −0.286809 | −0.143404 | − | 0.989664i | \(-0.545805\pi\) | ||||
−0.143404 | + | 0.989664i | \(0.545805\pi\) | |||||||
\(368\) | 34.7931 | 1.81372 | ||||||||
\(369\) | −0.756558 | −0.0393848 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48311 | −0.440421 | ||||||||
\(372\) | 1.06295 | 0.0551112 | ||||||||
\(373\) | 6.38304 | 0.330501 | 0.165251 | − | 0.986252i | \(-0.447157\pi\) | ||||
0.165251 | + | 0.986252i | \(0.447157\pi\) | |||||||
\(374\) | −40.5042 | −2.09442 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.4915 | −0.644198 | ||||||||
\(377\) | 14.6204 | 0.752991 | ||||||||
\(378\) | −1.77869 | −0.0914860 | ||||||||
\(379\) | −25.3489 | −1.30209 | −0.651043 | − | 0.759041i | \(-0.725668\pi\) | ||||
−0.651043 | + | 0.759041i | \(0.725668\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.71645 | 0.497789 | ||||||||
\(382\) | −17.5660 | −0.898753 | ||||||||
\(383\) | −27.6697 | −1.41386 | −0.706929 | − | 0.707284i | \(-0.749920\pi\) | ||||
−0.706929 | + | 0.707284i | \(0.749920\pi\) | |||||||
\(384\) | −10.3196 | −0.526619 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1314 | 0.515676 | ||||||||
\(387\) | 3.28845 | 0.167161 | ||||||||
\(388\) | 1.25334 | 0.0636285 | ||||||||
\(389\) | 27.3305 | 1.38571 | 0.692855 | − | 0.721077i | \(-0.256353\pi\) | ||||
0.692855 | + | 0.721077i | \(0.256353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.3289 | −2.64639 | ||||||||
\(392\) | 15.4478 | 0.780232 | ||||||||
\(393\) | −7.43178 | −0.374884 | ||||||||
\(394\) | 13.8215 | 0.696317 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.556144 | 0.0279473 | ||||||||
\(397\) | 1.93421 | 0.0970754 | 0.0485377 | − | 0.998821i | \(-0.484544\pi\) | ||||
0.0485377 | + | 0.998821i | \(0.484544\pi\) | |||||||
\(398\) | 20.7476 | 1.03998 | ||||||||
\(399\) | −1.01614 | −0.0508707 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4305 | −1.12013 | −0.560063 | − | 0.828450i | \(-0.689223\pi\) | ||||
−0.560063 | + | 0.828450i | \(0.689223\pi\) | |||||||
\(402\) | 15.3300 | 0.764590 | ||||||||
\(403\) | 15.4729 | 0.770760 | ||||||||
\(404\) | 0.227070 | 0.0112972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.6613 | 0.826885 | ||||||||
\(407\) | 22.6866 | 1.12453 | ||||||||
\(408\) | 16.4557 | 0.814679 | ||||||||
\(409\) | −9.89267 | −0.489161 | −0.244581 | − | 0.969629i | \(-0.578650\pi\) | ||||
−0.244581 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9411 | 0.687663 | ||||||||
\(412\) | 2.07010 | 0.101987 | ||||||||
\(413\) | 4.54015 | 0.223406 | ||||||||
\(414\) | −12.6834 | −0.623354 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.945680 | 0.0463658 | ||||||||
\(417\) | 17.8433 | 0.873791 | ||||||||
\(418\) | −5.60851 | −0.274321 | ||||||||
\(419\) | 2.10990 | 0.103075 | 0.0515376 | − | 0.998671i | \(-0.483588\pi\) | ||||
0.0515376 | + | 0.998671i | \(0.483588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1115 | −1.02891 | −0.514456 | − | 0.857517i | \(-0.672006\pi\) | ||||
−0.514456 | + | 0.857517i | \(0.672006\pi\) | |||||||
\(422\) | −12.4264 | −0.604907 | ||||||||
\(423\) | 4.30876 | 0.209499 | ||||||||
\(424\) | 19.0223 | 0.923807 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.62393 | 0.272480 | ||||||||
\(427\) | −0.656328 | −0.0317619 | ||||||||
\(428\) | 0.107224 | 0.00518288 | ||||||||
\(429\) | 8.09558 | 0.390858 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.81994 | −0.280337 | −0.140168 | − | 0.990128i | \(-0.544764\pi\) | ||||
−0.140168 | + | 0.990128i | \(0.544764\pi\) | |||||||
\(432\) | 3.77405 | 0.181579 | ||||||||
\(433\) | 12.5241 | 0.601868 | 0.300934 | − | 0.953645i | \(-0.402702\pi\) | ||||
0.300934 | + | 0.953645i | \(0.402702\pi\) | |||||||
\(434\) | 17.6327 | 0.846397 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.402947 | −0.0192977 | ||||||||
\(437\) | −7.24584 | −0.346615 | ||||||||
\(438\) | 20.3127 | 0.970576 | ||||||||
\(439\) | −23.8382 | −1.13774 | −0.568868 | − | 0.822429i | \(-0.692619\pi\) | ||||
−0.568868 | + | 0.822429i | \(0.692619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.32852 | −0.253739 | ||||||||
\(442\) | 12.1887 | 0.579760 | ||||||||
\(443\) | −8.63521 | −0.410271 | −0.205136 | − | 0.978734i | \(-0.565764\pi\) | ||||
−0.205136 | + | 0.978734i | \(0.565764\pi\) | |||||||
\(444\) | −0.468995 | −0.0222575 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.2523 | −1.43249 | ||||||||
\(447\) | −14.3146 | −0.677056 | ||||||||
\(448\) | 10.8363 | 0.511968 | ||||||||
\(449\) | −25.7021 | −1.21296 | −0.606479 | − | 0.795099i | \(-0.707419\pi\) | ||||
−0.606479 | + | 0.795099i | \(0.707419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.92407 | 0.184777 | ||||||||
\(452\) | −1.47665 | −0.0694559 | ||||||||
\(453\) | 0.452621 | 0.0212660 | ||||||||
\(454\) | −35.7384 | −1.67729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.27858 | 0.106704 | ||||||||
\(457\) | 24.2914 | 1.13630 | 0.568152 | − | 0.822924i | \(-0.307659\pi\) | ||||
0.568152 | + | 0.822924i | \(0.307659\pi\) | |||||||
\(458\) | 11.7411 | 0.548627 | ||||||||
\(459\) | −5.67618 | −0.264941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.8142 | 0.689965 | 0.344982 | − | 0.938609i | \(-0.387885\pi\) | ||||
0.344982 | + | 0.938609i | \(0.387885\pi\) | |||||||
\(462\) | 9.22561 | 0.429214 | ||||||||
\(463\) | 23.0000 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | −35.3521 | −1.64118 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.3130 | 1.72849 | ||||||||
\(467\) | 34.0153 | 1.57404 | 0.787020 | − | 0.616928i | \(-0.211623\pi\) | ||||
0.787020 | + | 0.616928i | \(0.211623\pi\) | |||||||
\(468\) | −0.167358 | −0.00773612 | ||||||||
\(469\) | −14.4060 | −0.665207 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.6813 | 0.814713 | ||||||||
\(472\) | −10.1807 | −0.468607 | ||||||||
\(473\) | −17.0563 | −0.784251 | ||||||||
\(474\) | −10.1065 | −0.464206 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.786865 | −0.0360659 | ||||||||
\(477\) | −6.56151 | −0.300431 | ||||||||
\(478\) | 35.2593 | 1.61272 | ||||||||
\(479\) | 0.220254 | 0.0100637 | 0.00503184 | − | 0.999987i | \(-0.498398\pi\) | ||||
0.00503184 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.82698 | −0.311284 | ||||||||
\(482\) | −28.4348 | −1.29517 | ||||||||
\(483\) | 11.9189 | 0.542329 | ||||||||
\(484\) | −1.70511 | −0.0775050 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.37578 | −0.0624067 | ||||||||
\(487\) | −13.3357 | −0.604298 | −0.302149 | − | 0.953261i | \(-0.597704\pi\) | ||||
−0.302149 | + | 0.953261i | \(0.597704\pi\) | |||||||
\(488\) | 1.47174 | 0.0666224 | ||||||||
\(489\) | 12.2108 | 0.552192 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.1922 | −1.81385 | −0.906924 | − | 0.421295i | \(-0.861576\pi\) | ||||
−0.906924 | + | 0.421295i | \(0.861576\pi\) | |||||||
\(492\) | −0.0811213 | −0.00365723 | ||||||||
\(493\) | 53.1696 | 2.39464 | ||||||||
\(494\) | 1.68774 | 0.0759351 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.4133 | −1.67991 | ||||||||
\(497\) | −5.28495 | −0.237063 | ||||||||
\(498\) | −16.6627 | −0.746675 | ||||||||
\(499\) | 9.90868 | 0.443573 | 0.221787 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.255788 | −0.0114278 | ||||||||
\(502\) | 21.1735 | 0.945020 | ||||||||
\(503\) | −5.90437 | −0.263263 | −0.131631 | − | 0.991299i | \(-0.542022\pi\) | ||||
−0.131631 | + | 0.991299i | \(0.542022\pi\) | |||||||
\(504\) | −3.74810 | −0.166954 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 65.7854 | 2.92452 | ||||||||
\(507\) | 10.5638 | 0.469156 | ||||||||
\(508\) | 1.04184 | 0.0462241 | ||||||||
\(509\) | 8.73646 | 0.387237 | 0.193618 | − | 0.981077i | \(-0.437978\pi\) | ||||
0.193618 | + | 0.981077i | \(0.437978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.0883 | −0.844419 | ||||||||
\(512\) | −24.1692 | −1.06814 | ||||||||
\(513\) | −0.785965 | −0.0347012 | ||||||||
\(514\) | 26.2577 | 1.15818 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.352601 | 0.0155224 | ||||||||
\(517\) | −22.3485 | −0.982884 | ||||||||
\(518\) | −7.77994 | −0.341831 | ||||||||
\(519\) | −1.67384 | −0.0734733 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.189571 | 0.00830524 | 0.00415262 | − | 0.999991i | \(-0.498678\pi\) | ||||
0.00415262 | + | 0.999991i | \(0.498678\pi\) | |||||||
\(522\) | 12.8871 | 0.564055 | ||||||||
\(523\) | −30.8578 | −1.34932 | −0.674659 | − | 0.738129i | \(-0.735709\pi\) | ||||
−0.674659 | + | 0.738129i | \(0.735709\pi\) | |||||||
\(524\) | −0.796867 | −0.0348113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.35295 | −0.102593 | ||||||||
\(527\) | 56.2697 | 2.45115 | ||||||||
\(528\) | −19.5750 | −0.851894 | ||||||||
\(529\) | 61.9905 | 2.69524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.51171 | 0.152395 | ||||||||
\(532\) | −0.108955 | −0.00472380 | ||||||||
\(533\) | −1.18085 | −0.0511484 | ||||||||
\(534\) | 15.2872 | 0.661543 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 32.3037 | 1.39531 | ||||||||
\(537\) | 14.4146 | 0.622035 | ||||||||
\(538\) | −11.5857 | −0.499497 | ||||||||
\(539\) | 27.6376 | 1.19044 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.4654 | 1.39580 | 0.697899 | − | 0.716197i | \(-0.254119\pi\) | ||||
0.697899 | + | 0.716197i | \(0.254119\pi\) | |||||||
\(542\) | −28.2420 | −1.21310 | ||||||||
\(543\) | 7.82843 | 0.335950 | ||||||||
\(544\) | 3.43912 | 0.147451 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.77622 | −0.118811 | ||||||||
\(547\) | −26.7396 | −1.14330 | −0.571651 | − | 0.820497i | \(-0.693697\pi\) | ||||
−0.571651 | + | 0.820497i | \(0.693697\pi\) | |||||||
\(548\) | 1.49482 | 0.0638556 | ||||||||
\(549\) | −0.507656 | −0.0216662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.36225 | 0.313642 | ||||||||
\(552\) | −26.7267 | −1.13756 | ||||||||
\(553\) | 9.49732 | 0.403867 | ||||||||
\(554\) | 17.0717 | 0.725307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.91324 | 0.0811392 | ||||||||
\(557\) | 6.95257 | 0.294590 | 0.147295 | − | 0.989093i | \(-0.452943\pi\) | ||||
0.147295 | + | 0.989093i | \(0.452943\pi\) | |||||||
\(558\) | 13.6385 | 0.577366 | ||||||||
\(559\) | 5.13268 | 0.217089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.4409 | 1.24300 | ||||||||
\(562\) | 2.15060 | 0.0907175 | ||||||||
\(563\) | −32.8101 | −1.38278 | −0.691390 | − | 0.722482i | \(-0.743001\pi\) | ||||
−0.691390 | + | 0.722482i | \(0.743001\pi\) | |||||||
\(564\) | 0.462004 | 0.0194539 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.3514 | −0.519170 | ||||||||
\(567\) | 1.29286 | 0.0542950 | ||||||||
\(568\) | 11.8509 | 0.497252 | ||||||||
\(569\) | 32.7831 | 1.37434 | 0.687168 | − | 0.726498i | \(-0.258853\pi\) | ||||
0.687168 | + | 0.726498i | \(0.258853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.61675 | 0.402448 | 0.201224 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201224 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(572\) | 0.868042 | 0.0362947 | ||||||||
\(573\) | 12.7680 | 0.533390 | ||||||||
\(574\) | −1.34568 | −0.0561677 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.38168 | 0.349237 | ||||||||
\(577\) | −3.14542 | −0.130945 | −0.0654727 | − | 0.997854i | \(-0.520856\pi\) | ||||
−0.0654727 | + | 0.997854i | \(0.520856\pi\) | |||||||
\(578\) | 20.9381 | 0.870909 | ||||||||
\(579\) | −7.36412 | −0.306042 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6584 | 0.649621 | ||||||||
\(582\) | 16.0814 | 0.666596 | ||||||||
\(583\) | 34.0329 | 1.40950 | ||||||||
\(584\) | 42.8033 | 1.77121 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.34343 | 0.179425 | ||||||||
\(587\) | 8.31983 | 0.343396 | 0.171698 | − | 0.985150i | \(-0.445075\pi\) | ||||
0.171698 | + | 0.985150i | \(0.445075\pi\) | |||||||
\(588\) | −0.571346 | −0.0235619 | ||||||||
\(589\) | 7.79151 | 0.321044 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0463 | −0.413249 | ||||||||
\(592\) | 16.5076 | 0.678457 | ||||||||
\(593\) | −23.2391 | −0.954315 | −0.477157 | − | 0.878818i | \(-0.658333\pi\) | ||||
−0.477157 | + | 0.878818i | \(0.658333\pi\) | |||||||
\(594\) | 7.13582 | 0.292786 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.53487 | −0.0628707 | ||||||||
\(597\) | −15.0806 | −0.617208 | ||||||||
\(598\) | −19.7965 | −0.809539 | ||||||||
\(599\) | −36.4894 | −1.49092 | −0.745459 | − | 0.666551i | \(-0.767770\pi\) | ||||
−0.745459 | + | 0.666551i | \(0.767770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.67854 | 0.150051 | 0.0750254 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750254 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(602\) | 5.84914 | 0.238393 | ||||||||
\(603\) | −11.1427 | −0.453768 | ||||||||
\(604\) | 0.0485320 | 0.00197474 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.91351 | 0.118353 | ||||||||
\(607\) | 12.5719 | 0.510279 | 0.255140 | − | 0.966904i | \(-0.417879\pi\) | ||||
0.255140 | + | 0.966904i | \(0.417879\pi\) | |||||||
\(608\) | 0.476205 | 0.0193127 | ||||||||
\(609\) | −12.1104 | −0.490738 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.72521 | 0.272073 | ||||||||
\(612\) | −0.608624 | −0.0246022 | ||||||||
\(613\) | 24.5055 | 0.989767 | 0.494883 | − | 0.868959i | \(-0.335211\pi\) | ||||
0.494883 | + | 0.868959i | \(0.335211\pi\) | |||||||
\(614\) | −20.5457 | −0.829156 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.4404 | 0.783278 | ||||||||
\(617\) | −4.56364 | −0.183725 | −0.0918626 | − | 0.995772i | \(-0.529282\pi\) | ||||
−0.0918626 | + | 0.995772i | \(0.529282\pi\) | |||||||
\(618\) | 26.5613 | 1.06845 | ||||||||
\(619\) | 12.2757 | 0.493401 | 0.246700 | − | 0.969092i | \(-0.420654\pi\) | ||||
0.246700 | + | 0.969092i | \(0.420654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.21903 | 0.369947 | ||||||||
\(622\) | 18.1472 | 0.727638 | ||||||||
\(623\) | −14.3658 | −0.575554 | ||||||||
\(624\) | 5.89063 | 0.235814 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −47.8812 | −1.91372 | ||||||||
\(627\) | 4.07660 | 0.162804 | ||||||||
\(628\) | 1.89587 | 0.0756534 | ||||||||
\(629\) | −24.8274 | −0.989934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.2099 | 1.20264 | 0.601319 | − | 0.799009i | \(-0.294642\pi\) | ||||
0.601319 | + | 0.799009i | \(0.294642\pi\) | |||||||
\(632\) | −21.2966 | −0.847133 | ||||||||
\(633\) | 9.03224 | 0.358999 | ||||||||
\(634\) | −33.7334 | −1.33972 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.703553 | −0.0278977 | ||||||||
\(637\) | −8.31686 | −0.329526 | ||||||||
\(638\) | −66.8423 | −2.64631 | ||||||||
\(639\) | −4.08780 | −0.161711 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.3717 | −1.47609 | −0.738047 | − | 0.674749i | \(-0.764252\pi\) | ||||
−0.738047 | + | 0.674749i | \(0.764252\pi\) | |||||||
\(642\) | 1.37578 | 0.0542978 | ||||||||
\(643\) | 25.5582 | 1.00792 | 0.503958 | − | 0.863728i | \(-0.331876\pi\) | ||||
0.503958 | + | 0.863728i | \(0.331876\pi\) | |||||||
\(644\) | 1.27800 | 0.0503601 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.13775 | 0.241487 | ||||||||
\(647\) | −17.8098 | −0.700176 | −0.350088 | − | 0.936717i | \(-0.613848\pi\) | ||||
−0.350088 | + | 0.936717i | \(0.613848\pi\) | |||||||
\(648\) | −2.89908 | −0.113887 | ||||||||
\(649\) | −18.2144 | −0.714976 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8165 | −0.502318 | ||||||||
\(652\) | 1.30929 | 0.0512759 | ||||||||
\(653\) | −2.36879 | −0.0926979 | −0.0463489 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463489 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(654\) | −5.17017 | −0.202170 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.85529 | 0.111480 | ||||||||
\(657\) | −14.7644 | −0.576016 | ||||||||
\(658\) | 7.66396 | 0.298772 | ||||||||
\(659\) | −5.22016 | −0.203349 | −0.101674 | − | 0.994818i | \(-0.532420\pi\) | ||||
−0.101674 | + | 0.994818i | \(0.532420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3940 | 1.64893 | 0.824467 | − | 0.565910i | \(-0.191475\pi\) | ||||
0.824467 | + | 0.565910i | \(0.191475\pi\) | |||||||
\(662\) | −4.01787 | −0.156159 | ||||||||
\(663\) | −8.85951 | −0.344075 | ||||||||
\(664\) | −35.1121 | −1.36261 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.01762 | −0.233178 | ||||||||
\(667\) | −86.3560 | −3.34372 | ||||||||
\(668\) | −0.0274267 | −0.00106117 | ||||||||
\(669\) | 21.9892 | 0.850150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.63308 | 0.101649 | ||||||||
\(672\) | −0.783325 | −0.0302174 | ||||||||
\(673\) | −11.2210 | −0.432536 | −0.216268 | − | 0.976334i | \(-0.569389\pi\) | ||||
−0.216268 | + | 0.976334i | \(0.569389\pi\) | |||||||
\(674\) | 27.9178 | 1.07535 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.13270 | 0.0435654 | ||||||||
\(677\) | 33.8810 | 1.30215 | 0.651075 | − | 0.759013i | \(-0.274318\pi\) | ||||
0.651075 | + | 0.759013i | \(0.274318\pi\) | |||||||
\(678\) | −18.9468 | −0.727646 | ||||||||
\(679\) | −15.1121 | −0.579951 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9768 | 0.995432 | ||||||||
\(682\) | −70.7396 | −2.70876 | ||||||||
\(683\) | 51.9618 | 1.98826 | 0.994132 | − | 0.108171i | \(-0.0344994\pi\) | ||||
0.994132 | + | 0.108171i | \(0.0344994\pi\) | |||||||
\(684\) | −0.0842745 | −0.00322232 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.9286 | −0.837239 | ||||||||
\(687\) | −8.53416 | −0.325598 | ||||||||
\(688\) | −12.4108 | −0.473157 | ||||||||
\(689\) | −10.2413 | −0.390164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4024 | −0.700060 | −0.350030 | − | 0.936739i | \(-0.613829\pi\) | ||||
−0.350030 | + | 0.936739i | \(0.613829\pi\) | |||||||
\(692\) | −0.179476 | −0.00682265 | ||||||||
\(693\) | −6.70572 | −0.254729 | ||||||||
\(694\) | −23.2674 | −0.883219 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 27.1561 | 1.02935 | ||||||||
\(697\) | −4.29436 | −0.162660 | ||||||||
\(698\) | 15.1828 | 0.574676 | ||||||||
\(699\) | −27.1213 | −1.02582 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.2148 | −1.85882 | −0.929408 | − | 0.369054i | \(-0.879682\pi\) | ||||
−0.929408 | + | 0.369054i | \(0.879682\pi\) | |||||||
\(702\) | −2.14735 | −0.0810465 | ||||||||
\(703\) | −3.43778 | −0.129659 | ||||||||
\(704\) | −43.4736 | −1.63847 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.4441 | 0.844695 | ||||||||
\(707\) | −2.73790 | −0.102969 | ||||||||
\(708\) | 0.376541 | 0.0141513 | ||||||||
\(709\) | −18.6015 | −0.698595 | −0.349297 | − | 0.937012i | \(-0.613580\pi\) | ||||
−0.349297 | + | 0.937012i | \(0.613580\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.34598 | 0.275496 | ||||||||
\(712\) | 32.2136 | 1.20726 | ||||||||
\(713\) | −91.3910 | −3.42262 | ||||||||
\(714\) | −10.0962 | −0.377840 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.54559 | 0.0577615 | ||||||||
\(717\) | −25.6285 | −0.957115 | ||||||||
\(718\) | −21.3098 | −0.795273 | ||||||||
\(719\) | −34.5054 | −1.28683 | −0.643417 | − | 0.765516i | \(-0.722484\pi\) | ||||
−0.643417 | + | 0.765516i | \(0.722484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.9603 | −0.929571 | ||||||||
\(722\) | −25.2900 | −0.941196 | ||||||||
\(723\) | 20.6681 | 0.768656 | ||||||||
\(724\) | 0.839398 | 0.0311960 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.8781 | −0.811972 | ||||||||
\(727\) | 9.29638 | 0.344784 | 0.172392 | − | 0.985028i | \(-0.444850\pi\) | ||||
0.172392 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(728\) | −5.85012 | −0.216820 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.6658 | 0.690381 | ||||||||
\(732\) | −0.0544331 | −0.00201190 | ||||||||
\(733\) | −37.2005 | −1.37403 | −0.687017 | − | 0.726642i | \(-0.741080\pi\) | ||||
−0.687017 | + | 0.726642i | \(0.741080\pi\) | |||||||
\(734\) | −7.55919 | −0.279015 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.58568 | −0.205891 | ||||||||
\(737\) | 57.7945 | 2.12889 | ||||||||
\(738\) | −1.04086 | −0.0383145 | ||||||||
\(739\) | 6.41527 | 0.235990 | 0.117995 | − | 0.993014i | \(-0.462353\pi\) | ||||
0.117995 | + | 0.993014i | \(0.462353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.22675 | −0.0450659 | ||||||||
\(742\) | −11.6709 | −0.428452 | ||||||||
\(743\) | −31.2008 | −1.14465 | −0.572323 | − | 0.820028i | \(-0.693958\pi\) | ||||
−0.572323 | + | 0.820028i | \(0.693958\pi\) | |||||||
\(744\) | 28.7395 | 1.05364 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.78168 | 0.321520 | ||||||||
\(747\) | 12.1115 | 0.443135 | ||||||||
\(748\) | 3.15678 | 0.115423 | ||||||||
\(749\) | −1.29286 | −0.0472400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.5714 | 0.677679 | 0.338840 | − | 0.940844i | \(-0.389966\pi\) | ||||
0.338840 | + | 0.940844i | \(0.389966\pi\) | |||||||
\(752\) | −16.2615 | −0.592996 | ||||||||
\(753\) | −15.3902 | −0.560849 | ||||||||
\(754\) | 20.1145 | 0.732528 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.138626 | 0.00504177 | ||||||||
\(757\) | 33.9894 | 1.23536 | 0.617682 | − | 0.786428i | \(-0.288072\pi\) | ||||
0.617682 | + | 0.786428i | \(0.288072\pi\) | |||||||
\(758\) | −34.8745 | −1.26670 | ||||||||
\(759\) | −47.8167 | −1.73564 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2251 | 0.769410 | 0.384705 | − | 0.923040i | \(-0.374303\pi\) | ||||
0.384705 | + | 0.923040i | \(0.374303\pi\) | |||||||
\(762\) | 13.3677 | 0.484261 | ||||||||
\(763\) | 4.85854 | 0.175891 | ||||||||
\(764\) | 1.36904 | 0.0495300 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.0675 | −1.37544 | ||||||||
\(767\) | 5.48116 | 0.197913 | ||||||||
\(768\) | 2.56585 | 0.0925872 | ||||||||
\(769\) | 53.1763 | 1.91759 | 0.958793 | − | 0.284107i | \(-0.0916971\pi\) | ||||
0.958793 | + | 0.284107i | \(0.0916971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.0856 | −0.687352 | ||||||||
\(772\) | −0.789612 | −0.0284188 | ||||||||
\(773\) | −21.3776 | −0.768899 | −0.384449 | − | 0.923146i | \(-0.625609\pi\) | ||||
−0.384449 | + | 0.923146i | \(0.625609\pi\) | |||||||
\(774\) | 4.52419 | 0.162619 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 33.8872 | 1.21648 | ||||||||
\(777\) | 5.65492 | 0.202869 | ||||||||
\(778\) | 37.6007 | 1.34805 | ||||||||
\(779\) | −0.594628 | −0.0213048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.2024 | 0.758681 | ||||||||
\(782\) | −71.9931 | −2.57447 | ||||||||
\(783\) | −9.36714 | −0.334754 | ||||||||
\(784\) | 20.1101 | 0.718218 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.2245 | −0.364696 | ||||||||
\(787\) | 6.24888 | 0.222748 | 0.111374 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111374 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(788\) | −1.07721 | −0.0383739 | ||||||||
\(789\) | 1.71026 | 0.0608869 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.8048 | 0.633065 | ||||||||
\(792\) | 15.0368 | 0.534309 | ||||||||
\(793\) | −0.792361 | −0.0281376 | ||||||||
\(794\) | 2.66106 | 0.0944373 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.61701 | −0.0573133 | ||||||||
\(797\) | 37.8159 | 1.33951 | 0.669753 | − | 0.742584i | \(-0.266400\pi\) | ||||
0.669753 | + | 0.742584i | \(0.266400\pi\) | |||||||
\(798\) | −1.39799 | −0.0494883 | ||||||||
\(799\) | 24.4573 | 0.865238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1117 | −0.392611 | ||||||||
\(802\) | −30.8595 | −1.08969 | ||||||||
\(803\) | 76.5794 | 2.70243 | ||||||||
\(804\) | −1.19477 | −0.0421364 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.2873 | 0.749814 | ||||||||
\(807\) | 8.42120 | 0.296440 | ||||||||
\(808\) | 6.13942 | 0.215984 | ||||||||
\(809\) | 12.0344 | 0.423108 | 0.211554 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211554 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3896 | 0.610633 | 0.305316 | − | 0.952251i | \(-0.401238\pi\) | ||||
0.305316 | + | 0.952251i | \(0.401238\pi\) | |||||||
\(812\) | −1.29853 | −0.0455694 | ||||||||
\(813\) | 20.5279 | 0.719946 | ||||||||
\(814\) | 31.2119 | 1.09397 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21.4222 | 0.749928 | ||||||||
\(817\) | 2.58461 | 0.0904240 | ||||||||
\(818\) | −13.6102 | −0.475868 | ||||||||
\(819\) | 2.01792 | 0.0705119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3564 | −1.05945 | −0.529723 | − | 0.848171i | \(-0.677704\pi\) | ||||
−0.529723 | + | 0.848171i | \(0.677704\pi\) | |||||||
\(822\) | 19.1799 | 0.668975 | ||||||||
\(823\) | −20.2579 | −0.706147 | −0.353074 | − | 0.935596i | \(-0.614864\pi\) | ||||
−0.353074 | + | 0.935596i | \(0.614864\pi\) | |||||||
\(824\) | 55.9706 | 1.94983 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.24626 | 0.217335 | ||||||||
\(827\) | −28.2739 | −0.983179 | −0.491589 | − | 0.870827i | \(-0.663584\pi\) | ||||
−0.491589 | + | 0.870827i | \(0.663584\pi\) | |||||||
\(828\) | 0.988504 | 0.0343529 | ||||||||
\(829\) | −17.3221 | −0.601623 | −0.300811 | − | 0.953684i | \(-0.597257\pi\) | ||||
−0.300811 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4087 | −0.430454 | ||||||||
\(832\) | 13.0823 | 0.453547 | ||||||||
\(833\) | −30.2456 | −1.04795 | ||||||||
\(834\) | 24.5485 | 0.850045 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.437110 | 0.0151178 | ||||||||
\(837\) | −9.91330 | −0.342654 | ||||||||
\(838\) | 2.90276 | 0.100274 | ||||||||
\(839\) | 12.1522 | 0.419539 | 0.209769 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209769 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.7434 | 2.02563 | ||||||||
\(842\) | −29.0448 | −1.00095 | ||||||||
\(843\) | −1.56318 | −0.0538388 | ||||||||
\(844\) | 0.968475 | 0.0333363 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.92792 | 0.203806 | ||||||||
\(847\) | 20.5594 | 0.706430 | ||||||||
\(848\) | 24.7635 | 0.850382 | ||||||||
\(849\) | 8.97776 | 0.308116 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.3237 | 1.38228 | ||||||||
\(852\) | −0.438312 | −0.0150163 | ||||||||
\(853\) | 42.6561 | 1.46052 | 0.730258 | − | 0.683172i | \(-0.239400\pi\) | ||||
0.730258 | + | 0.683172i | \(0.239400\pi\) | |||||||
\(854\) | −0.902964 | −0.0308988 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.89908 | 0.0990885 | ||||||||
\(857\) | 11.7238 | 0.400478 | 0.200239 | − | 0.979747i | \(-0.435828\pi\) | ||||
0.200239 | + | 0.979747i | \(0.435828\pi\) | |||||||
\(858\) | 11.1378 | 0.380237 | ||||||||
\(859\) | −39.2770 | −1.34011 | −0.670057 | − | 0.742310i | \(-0.733730\pi\) | ||||
−0.670057 | + | 0.742310i | \(0.733730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.978122 | 0.0333343 | ||||||||
\(862\) | −8.00696 | −0.272718 | ||||||||
\(863\) | 17.9138 | 0.609793 | 0.304896 | − | 0.952386i | \(-0.401378\pi\) | ||||
0.304896 | + | 0.952386i | \(0.401378\pi\) | |||||||
\(864\) | −0.605886 | −0.0206127 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.2304 | 0.585512 | ||||||||
\(867\) | −15.2190 | −0.516865 | ||||||||
\(868\) | −1.37424 | −0.0466447 | ||||||||
\(869\) | −38.1017 | −1.29251 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.3918 | −0.589300 | ||||||||
\(872\) | −10.8947 | −0.368941 | ||||||||
\(873\) | −11.6889 | −0.395610 | ||||||||
\(874\) | −9.96869 | −0.337196 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.58311 | −0.0534882 | ||||||||
\(877\) | 21.9915 | 0.742602 | 0.371301 | − | 0.928513i | \(-0.378912\pi\) | ||||
0.371301 | + | 0.928513i | \(0.378912\pi\) | |||||||
\(878\) | −32.7962 | −1.10682 | ||||||||
\(879\) | −3.15706 | −0.106485 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4690 | 0.554855 | 0.277427 | − | 0.960747i | \(-0.410518\pi\) | ||||
0.277427 | + | 0.960747i | \(0.410518\pi\) | |||||||
\(882\) | −7.33088 | −0.246843 | ||||||||
\(883\) | −52.1294 | −1.75430 | −0.877148 | − | 0.480221i | \(-0.840556\pi\) | ||||
−0.877148 | + | 0.480221i | \(0.840556\pi\) | |||||||
\(884\) | −0.949954 | −0.0319504 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8802 | −0.399122 | ||||||||
\(887\) | −46.6500 | −1.56635 | −0.783177 | − | 0.621798i | \(-0.786402\pi\) | ||||
−0.783177 | + | 0.621798i | \(0.786402\pi\) | |||||||
\(888\) | −12.6805 | −0.425529 | ||||||||
\(889\) | −12.5620 | −0.421316 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.18674 | −0.173762 | ||||||||
\(892\) | 2.35777 | 0.0789440 | ||||||||
\(893\) | 3.38654 | 0.113326 | ||||||||
\(894\) | −19.6937 | −0.658657 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.3418 | 0.445717 | ||||||||
\(897\) | 14.3893 | 0.480444 | ||||||||
\(898\) | −35.3605 | −1.18000 | ||||||||
\(899\) | 92.8593 | 3.09703 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.2443 | −1.24079 | ||||||||
\(902\) | 5.39866 | 0.179756 | ||||||||
\(903\) | −4.25150 | −0.141481 | ||||||||
\(904\) | −39.9251 | −1.32789 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.622708 | 0.0206881 | ||||||||
\(907\) | −31.3316 | −1.04035 | −0.520174 | − | 0.854060i | \(-0.674133\pi\) | ||||
−0.520174 | + | 0.854060i | \(0.674133\pi\) | |||||||
\(908\) | 2.78534 | 0.0924348 | ||||||||
\(909\) | −2.11771 | −0.0702401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59385 | 0.119069 | 0.0595347 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595347 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(912\) | 2.96628 | 0.0982232 | ||||||||
\(913\) | −62.8191 | −2.07901 | ||||||||
\(914\) | 33.4196 | 1.10542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.915068 | −0.0302347 | ||||||||
\(917\) | 9.60824 | 0.317292 | ||||||||
\(918\) | −7.80919 | −0.257742 | ||||||||
\(919\) | −22.3591 | −0.737559 | −0.368780 | − | 0.929517i | \(-0.620224\pi\) | ||||
−0.368780 | + | 0.929517i | \(0.620224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.9338 | 0.492086 | ||||||||
\(922\) | 20.3811 | 0.671215 | ||||||||
\(923\) | −6.38033 | −0.210011 | ||||||||
\(924\) | −0.719016 | −0.0236539 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.6430 | 1.03985 | ||||||||
\(927\) | −19.3063 | −0.634103 | ||||||||
\(928\) | 5.67542 | 0.186305 | ||||||||
\(929\) | −38.1453 | −1.25151 | −0.625754 | − | 0.780021i | \(-0.715208\pi\) | ||||
−0.625754 | + | 0.780021i | \(0.715208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.18803 | −0.137257 | ||||||||
\(932\) | −2.90806 | −0.0952568 | ||||||||
\(933\) | −13.1905 | −0.431837 | ||||||||
\(934\) | 46.7976 | 1.53126 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.52495 | −0.147903 | ||||||||
\(937\) | 45.9282 | 1.50041 | 0.750205 | − | 0.661206i | \(-0.229955\pi\) | ||||
0.750205 | + | 0.661206i | \(0.229955\pi\) | |||||||
\(938\) | −19.8195 | −0.647130 | ||||||||
\(939\) | 34.8029 | 1.13575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.90156 | −0.127187 | −0.0635936 | − | 0.997976i | \(-0.520256\pi\) | ||||
−0.0635936 | + | 0.997976i | \(0.520256\pi\) | |||||||
\(942\) | 24.3257 | 0.792573 | ||||||||
\(943\) | 6.97473 | 0.227128 | ||||||||
\(944\) | −13.2534 | −0.431361 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.4658 | −0.762939 | ||||||||
\(947\) | 28.3789 | 0.922189 | 0.461095 | − | 0.887351i | \(-0.347457\pi\) | ||||
0.461095 | + | 0.887351i | \(0.347457\pi\) | |||||||
\(948\) | 0.787668 | 0.0255823 | ||||||||
\(949\) | −23.0447 | −0.748062 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5194 | 0.795097 | ||||||||
\(952\) | −21.2749 | −0.689524 | ||||||||
\(953\) | −28.2289 | −0.914425 | −0.457212 | − | 0.889358i | \(-0.651152\pi\) | ||||
−0.457212 | + | 0.889358i | \(0.651152\pi\) | |||||||
\(954\) | −9.02721 | −0.292267 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.74800 | −0.0888767 | ||||||||
\(957\) | 48.5850 | 1.57053 | ||||||||
\(958\) | 0.303022 | 0.00979020 | ||||||||
\(959\) | −18.0238 | −0.582020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.2736 | 2.17012 | ||||||||
\(962\) | −9.39244 | −0.302824 | ||||||||
\(963\) | −1.00000 | −0.0322245 | ||||||||
\(964\) | 2.21612 | 0.0713765 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.3978 | 0.527591 | ||||||||
\(967\) | 13.2130 | 0.424902 | 0.212451 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212451 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(968\) | −46.1020 | −1.48178 | ||||||||
\(969\) | −4.46128 | −0.143317 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.4953 | 1.68465 | 0.842327 | − | 0.538967i | \(-0.181185\pi\) | ||||
0.842327 | + | 0.538967i | \(0.181185\pi\) | |||||||
\(972\) | 0.107224 | 0.00343922 | ||||||||
\(973\) | −23.0689 | −0.739554 | ||||||||
\(974\) | −18.3470 | −0.587876 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.91592 | 0.0613272 | ||||||||
\(977\) | 30.6472 | 0.980491 | 0.490245 | − | 0.871584i | \(-0.336907\pi\) | ||||
0.490245 | + | 0.871584i | \(0.336907\pi\) | |||||||
\(978\) | 16.7994 | 0.537186 | ||||||||
\(979\) | 57.6333 | 1.84197 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.75798 | 0.119983 | ||||||||
\(982\) | −55.2957 | −1.76456 | ||||||||
\(983\) | 34.4922 | 1.10013 | 0.550066 | − | 0.835121i | \(-0.314603\pi\) | ||||
0.550066 | + | 0.835121i | \(0.314603\pi\) | |||||||
\(984\) | −2.19332 | −0.0699206 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 73.1498 | 2.32956 | ||||||||
\(987\) | −5.57062 | −0.177315 | ||||||||
\(988\) | −0.131538 | −0.00418477 | ||||||||
\(989\) | −30.3163 | −0.964003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9433 | 0.379393 | 0.189696 | − | 0.981843i | \(-0.439250\pi\) | ||||
0.189696 | + | 0.981843i | \(0.439250\pi\) | |||||||
\(992\) | 6.00633 | 0.190701 | ||||||||
\(993\) | 2.92043 | 0.0926770 | ||||||||
\(994\) | −7.27094 | −0.230620 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.29864 | 0.0411491 | ||||||||
\(997\) | 29.1180 | 0.922176 | 0.461088 | − | 0.887354i | \(-0.347459\pi\) | ||||
0.461088 | + | 0.887354i | \(0.347459\pi\) | |||||||
\(998\) | 13.6322 | 0.431519 | ||||||||
\(999\) | 4.37397 | 0.138386 |
(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 | 8025.2.a.bf.1.9 | 12 | ||
5.4 | even | 2 | 1605.2.a.n.1.4 | ✓ | 12 | ||
15.14 | odd | 2 | 4815.2.a.u.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1605.2.a.n.1.4 | ✓ | 12 | 5.4 | even | 2 | ||
4815.2.a.u.1.9 | 12 | 15.14 | odd | 2 | |||
8025.2.a.bf.1.9 | 12 | 1.1 | even | 1 | trivial |