Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + 5778 x^{8} - 5124 x^{7} - 9405 x^{6} + 8288 x^{5} + 6405 x^{4} - 6032 x^{3} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.40306\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40306 | −0.992112 | −0.496056 | − | 0.868291i | \(-0.665219\pi\) | ||||
−0.496056 | + | 0.868291i | \(0.665219\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.0314276 | −0.0157138 | ||||||||
\(5\) | 1.13298 | 0.506683 | 0.253341 | − | 0.967377i | \(-0.418470\pi\) | ||||
0.253341 | + | 0.967377i | \(0.418470\pi\) | |||||||
\(6\) | −1.40306 | −0.572796 | ||||||||
\(7\) | −1.90949 | −0.721718 | −0.360859 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360859 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(8\) | 2.85021 | 1.00770 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.58963 | −0.502686 | ||||||||
\(11\) | 5.04448 | 1.52097 | 0.760484 | − | 0.649356i | \(-0.224962\pi\) | ||||
0.760484 | + | 0.649356i | \(0.224962\pi\) | |||||||
\(12\) | −0.0314276 | −0.00907236 | ||||||||
\(13\) | 3.78403 | 1.04950 | 0.524751 | − | 0.851256i | \(-0.324159\pi\) | ||||
0.524751 | + | 0.851256i | \(0.324159\pi\) | |||||||
\(14\) | 2.67912 | 0.716025 | ||||||||
\(15\) | 1.13298 | 0.292533 | ||||||||
\(16\) | −3.93616 | −0.984039 | ||||||||
\(17\) | 7.36033 | 1.78514 | 0.892571 | − | 0.450907i | \(-0.148899\pi\) | ||||
0.892571 | + | 0.450907i | \(0.148899\pi\) | |||||||
\(18\) | −1.40306 | −0.330704 | ||||||||
\(19\) | −0.713891 | −0.163778 | −0.0818889 | − | 0.996641i | \(-0.526095\pi\) | ||||
−0.0818889 | + | 0.996641i | \(0.526095\pi\) | |||||||
\(20\) | −0.0356067 | −0.00796190 | ||||||||
\(21\) | −1.90949 | −0.416684 | ||||||||
\(22\) | −7.07770 | −1.50897 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.85021 | 0.581797 | ||||||||
\(25\) | −3.71636 | −0.743273 | ||||||||
\(26\) | −5.30922 | −1.04122 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.0600106 | 0.0113409 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.58963 | −0.290226 | ||||||||
\(31\) | 4.34024 | 0.779529 | 0.389765 | − | 0.920914i | \(-0.372556\pi\) | ||||
0.389765 | + | 0.920914i | \(0.372556\pi\) | |||||||
\(32\) | −0.177765 | −0.0314247 | ||||||||
\(33\) | 5.04448 | 0.878132 | ||||||||
\(34\) | −10.3270 | −1.77106 | ||||||||
\(35\) | −2.16340 | −0.365682 | ||||||||
\(36\) | −0.0314276 | −0.00523793 | ||||||||
\(37\) | 7.55271 | 1.24166 | 0.620829 | − | 0.783946i | \(-0.286796\pi\) | ||||
0.620829 | + | 0.783946i | \(0.286796\pi\) | |||||||
\(38\) | 1.00163 | 0.162486 | ||||||||
\(39\) | 3.78403 | 0.605930 | ||||||||
\(40\) | 3.22922 | 0.510585 | ||||||||
\(41\) | −10.0365 | −1.56743 | −0.783717 | − | 0.621118i | \(-0.786679\pi\) | ||||
−0.783717 | + | 0.621118i | \(0.786679\pi\) | |||||||
\(42\) | 2.67912 | 0.413397 | ||||||||
\(43\) | −12.7870 | −1.95000 | −0.974998 | − | 0.222215i | \(-0.928671\pi\) | ||||
−0.974998 | + | 0.222215i | \(0.928671\pi\) | |||||||
\(44\) | −0.158536 | −0.0239002 | ||||||||
\(45\) | 1.13298 | 0.168894 | ||||||||
\(46\) | 1.40306 | 0.206870 | ||||||||
\(47\) | −1.16858 | −0.170455 | −0.0852277 | − | 0.996362i | \(-0.527162\pi\) | ||||
−0.0852277 | + | 0.996362i | \(0.527162\pi\) | |||||||
\(48\) | −3.93616 | −0.568135 | ||||||||
\(49\) | −3.35386 | −0.479123 | ||||||||
\(50\) | 5.21428 | 0.737410 | ||||||||
\(51\) | 7.36033 | 1.03065 | ||||||||
\(52\) | −0.118923 | −0.0164916 | ||||||||
\(53\) | −4.59897 | −0.631717 | −0.315859 | − | 0.948806i | \(-0.602292\pi\) | ||||
−0.315859 | + | 0.948806i | \(0.602292\pi\) | |||||||
\(54\) | −1.40306 | −0.190932 | ||||||||
\(55\) | 5.71528 | 0.770648 | ||||||||
\(56\) | −5.44244 | −0.727277 | ||||||||
\(57\) | −0.713891 | −0.0945572 | ||||||||
\(58\) | 1.40306 | 0.184231 | ||||||||
\(59\) | 4.46982 | 0.581921 | 0.290960 | − | 0.956735i | \(-0.406025\pi\) | ||||
0.290960 | + | 0.956735i | \(0.406025\pi\) | |||||||
\(60\) | −0.0356067 | −0.00459681 | ||||||||
\(61\) | −1.01012 | −0.129332 | −0.0646662 | − | 0.997907i | \(-0.520598\pi\) | ||||
−0.0646662 | + | 0.997907i | \(0.520598\pi\) | |||||||
\(62\) | −6.08960 | −0.773380 | ||||||||
\(63\) | −1.90949 | −0.240573 | ||||||||
\(64\) | 8.12173 | 1.01522 | ||||||||
\(65\) | 4.28722 | 0.531764 | ||||||||
\(66\) | −7.07770 | −0.871205 | ||||||||
\(67\) | 16.2568 | 1.98608 | 0.993041 | − | 0.117771i | \(-0.0375749\pi\) | ||||
0.993041 | + | 0.117771i | \(0.0375749\pi\) | |||||||
\(68\) | −0.231317 | −0.0280513 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 3.03538 | 0.362798 | ||||||||
\(71\) | 13.7025 | 1.62619 | 0.813096 | − | 0.582129i | \(-0.197780\pi\) | ||||
0.813096 | + | 0.582129i | \(0.197780\pi\) | |||||||
\(72\) | 2.85021 | 0.335901 | ||||||||
\(73\) | 14.2596 | 1.66896 | 0.834481 | − | 0.551037i | \(-0.185768\pi\) | ||||
0.834481 | + | 0.551037i | \(0.185768\pi\) | |||||||
\(74\) | −10.5969 | −1.23186 | ||||||||
\(75\) | −3.71636 | −0.429129 | ||||||||
\(76\) | 0.0224359 | 0.00257357 | ||||||||
\(77\) | −9.63238 | −1.09771 | ||||||||
\(78\) | −5.30922 | −0.601150 | ||||||||
\(79\) | −0.947565 | −0.106609 | −0.0533047 | − | 0.998578i | \(-0.516975\pi\) | ||||
−0.0533047 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(80\) | −4.45957 | −0.498596 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.0818 | 1.55507 | ||||||||
\(83\) | 11.2596 | 1.23591 | 0.617953 | − | 0.786215i | \(-0.287962\pi\) | ||||
0.617953 | + | 0.786215i | \(0.287962\pi\) | |||||||
\(84\) | 0.0600106 | 0.00654769 | ||||||||
\(85\) | 8.33908 | 0.904500 | ||||||||
\(86\) | 17.9409 | 1.93461 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 14.3778 | 1.53268 | ||||||||
\(89\) | −9.66768 | −1.02477 | −0.512386 | − | 0.858755i | \(-0.671238\pi\) | ||||
−0.512386 | + | 0.858755i | \(0.671238\pi\) | |||||||
\(90\) | −1.58963 | −0.167562 | ||||||||
\(91\) | −7.22556 | −0.757444 | ||||||||
\(92\) | 0.0314276 | 0.00327655 | ||||||||
\(93\) | 4.34024 | 0.450062 | ||||||||
\(94\) | 1.63959 | 0.169111 | ||||||||
\(95\) | −0.808822 | −0.0829834 | ||||||||
\(96\) | −0.177765 | −0.0181430 | ||||||||
\(97\) | −3.19378 | −0.324279 | −0.162139 | − | 0.986768i | \(-0.551839\pi\) | ||||
−0.162139 | + | 0.986768i | \(0.551839\pi\) | |||||||
\(98\) | 4.70566 | 0.475343 | ||||||||
\(99\) | 5.04448 | 0.506990 | ||||||||
\(100\) | 0.116796 | 0.0116796 | ||||||||
\(101\) | −1.42381 | −0.141674 | −0.0708372 | − | 0.997488i | \(-0.522567\pi\) | ||||
−0.0708372 | + | 0.997488i | \(0.522567\pi\) | |||||||
\(102\) | −10.3270 | −1.02252 | ||||||||
\(103\) | −4.14252 | −0.408175 | −0.204087 | − | 0.978953i | \(-0.565423\pi\) | ||||
−0.204087 | + | 0.978953i | \(0.565423\pi\) | |||||||
\(104\) | 10.7853 | 1.05758 | ||||||||
\(105\) | −2.16340 | −0.211127 | ||||||||
\(106\) | 6.45262 | 0.626734 | ||||||||
\(107\) | 0.700112 | 0.0676823 | 0.0338412 | − | 0.999427i | \(-0.489226\pi\) | ||||
0.0338412 | + | 0.999427i | \(0.489226\pi\) | |||||||
\(108\) | −0.0314276 | −0.00302412 | ||||||||
\(109\) | 9.22855 | 0.883935 | 0.441968 | − | 0.897031i | \(-0.354281\pi\) | ||||
0.441968 | + | 0.897031i | \(0.354281\pi\) | |||||||
\(110\) | −8.01887 | −0.764569 | ||||||||
\(111\) | 7.55271 | 0.716872 | ||||||||
\(112\) | 7.51604 | 0.710199 | ||||||||
\(113\) | −20.1001 | −1.89086 | −0.945429 | − | 0.325829i | \(-0.894357\pi\) | ||||
−0.945429 | + | 0.325829i | \(0.894357\pi\) | |||||||
\(114\) | 1.00163 | 0.0938113 | ||||||||
\(115\) | −1.13298 | −0.105651 | ||||||||
\(116\) | 0.0314276 | 0.00291798 | ||||||||
\(117\) | 3.78403 | 0.349834 | ||||||||
\(118\) | −6.27141 | −0.577330 | ||||||||
\(119\) | −14.0545 | −1.28837 | ||||||||
\(120\) | 3.22922 | 0.294786 | ||||||||
\(121\) | 14.4468 | 1.31335 | ||||||||
\(122\) | 1.41725 | 0.128312 | ||||||||
\(123\) | −10.0365 | −0.904958 | ||||||||
\(124\) | −0.136403 | −0.0122494 | ||||||||
\(125\) | −9.87544 | −0.883286 | ||||||||
\(126\) | 2.67912 | 0.238675 | ||||||||
\(127\) | 2.50338 | 0.222139 | 0.111069 | − | 0.993813i | \(-0.464572\pi\) | ||||
0.111069 | + | 0.993813i | \(0.464572\pi\) | |||||||
\(128\) | −11.0397 | −0.975783 | ||||||||
\(129\) | −12.7870 | −1.12583 | ||||||||
\(130\) | −6.01522 | −0.527569 | ||||||||
\(131\) | −5.46381 | −0.477375 | −0.238688 | − | 0.971096i | \(-0.576717\pi\) | ||||
−0.238688 | + | 0.971096i | \(0.576717\pi\) | |||||||
\(132\) | −0.158536 | −0.0137988 | ||||||||
\(133\) | 1.36317 | 0.118202 | ||||||||
\(134\) | −22.8092 | −1.97042 | ||||||||
\(135\) | 1.13298 | 0.0975111 | ||||||||
\(136\) | 20.9785 | 1.79889 | ||||||||
\(137\) | 11.6644 | 0.996560 | 0.498280 | − | 0.867016i | \(-0.333965\pi\) | ||||
0.498280 | + | 0.867016i | \(0.333965\pi\) | |||||||
\(138\) | 1.40306 | 0.119436 | ||||||||
\(139\) | 10.1861 | 0.863970 | 0.431985 | − | 0.901881i | \(-0.357813\pi\) | ||||
0.431985 | + | 0.901881i | \(0.357813\pi\) | |||||||
\(140\) | 0.0679906 | 0.00574625 | ||||||||
\(141\) | −1.16858 | −0.0984125 | ||||||||
\(142\) | −19.2255 | −1.61337 | ||||||||
\(143\) | 19.0885 | 1.59626 | ||||||||
\(144\) | −3.93616 | −0.328013 | ||||||||
\(145\) | −1.13298 | −0.0940886 | ||||||||
\(146\) | −20.0071 | −1.65580 | ||||||||
\(147\) | −3.35386 | −0.276622 | ||||||||
\(148\) | −0.237363 | −0.0195112 | ||||||||
\(149\) | −3.54639 | −0.290532 | −0.145266 | − | 0.989393i | \(-0.546404\pi\) | ||||
−0.145266 | + | 0.989393i | \(0.546404\pi\) | |||||||
\(150\) | 5.21428 | 0.425744 | ||||||||
\(151\) | 9.02885 | 0.734758 | 0.367379 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367379 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(152\) | −2.03474 | −0.165039 | ||||||||
\(153\) | 7.36033 | 0.595047 | ||||||||
\(154\) | 13.5148 | 1.08905 | ||||||||
\(155\) | 4.91739 | 0.394974 | ||||||||
\(156\) | −0.118923 | −0.00952146 | ||||||||
\(157\) | −16.9807 | −1.35521 | −0.677605 | − | 0.735426i | \(-0.736982\pi\) | ||||
−0.677605 | + | 0.735426i | \(0.736982\pi\) | |||||||
\(158\) | 1.32949 | 0.105768 | ||||||||
\(159\) | −4.59897 | −0.364722 | ||||||||
\(160\) | −0.201403 | −0.0159223 | ||||||||
\(161\) | 1.90949 | 0.150489 | ||||||||
\(162\) | −1.40306 | −0.110235 | ||||||||
\(163\) | 7.63708 | 0.598182 | 0.299091 | − | 0.954225i | \(-0.403317\pi\) | ||||
0.299091 | + | 0.954225i | \(0.403317\pi\) | |||||||
\(164\) | 0.315422 | 0.0246303 | ||||||||
\(165\) | 5.71528 | 0.444934 | ||||||||
\(166\) | −15.7979 | −1.22616 | ||||||||
\(167\) | 9.37125 | 0.725169 | 0.362585 | − | 0.931951i | \(-0.381894\pi\) | ||||
0.362585 | + | 0.931951i | \(0.381894\pi\) | |||||||
\(168\) | −5.44244 | −0.419894 | ||||||||
\(169\) | 1.31889 | 0.101453 | ||||||||
\(170\) | −11.7002 | −0.897366 | ||||||||
\(171\) | −0.713891 | −0.0545926 | ||||||||
\(172\) | 0.401864 | 0.0306418 | ||||||||
\(173\) | 14.5789 | 1.10841 | 0.554205 | − | 0.832380i | \(-0.313022\pi\) | ||||
0.554205 | + | 0.832380i | \(0.313022\pi\) | |||||||
\(174\) | 1.40306 | 0.106366 | ||||||||
\(175\) | 7.09635 | 0.536434 | ||||||||
\(176\) | −19.8559 | −1.49669 | ||||||||
\(177\) | 4.46982 | 0.335972 | ||||||||
\(178\) | 13.5643 | 1.01669 | ||||||||
\(179\) | 1.72578 | 0.128991 | 0.0644954 | − | 0.997918i | \(-0.479456\pi\) | ||||
0.0644954 | + | 0.997918i | \(0.479456\pi\) | |||||||
\(180\) | −0.0356067 | −0.00265397 | ||||||||
\(181\) | −12.1091 | −0.900066 | −0.450033 | − | 0.893012i | \(-0.648588\pi\) | ||||
−0.450033 | + | 0.893012i | \(0.648588\pi\) | |||||||
\(182\) | 10.1379 | 0.751470 | ||||||||
\(183\) | −1.01012 | −0.0746701 | ||||||||
\(184\) | −2.85021 | −0.210120 | ||||||||
\(185\) | 8.55704 | 0.629126 | ||||||||
\(186\) | −6.08960 | −0.446511 | ||||||||
\(187\) | 37.1291 | 2.71515 | ||||||||
\(188\) | 0.0367257 | 0.00267850 | ||||||||
\(189\) | −1.90949 | −0.138895 | ||||||||
\(190\) | 1.13482 | 0.0823288 | ||||||||
\(191\) | 18.1357 | 1.31225 | 0.656126 | − | 0.754651i | \(-0.272194\pi\) | ||||
0.656126 | + | 0.754651i | \(0.272194\pi\) | |||||||
\(192\) | 8.12173 | 0.586135 | ||||||||
\(193\) | −4.56459 | −0.328566 | −0.164283 | − | 0.986413i | \(-0.552531\pi\) | ||||
−0.164283 | + | 0.986413i | \(0.552531\pi\) | |||||||
\(194\) | 4.48106 | 0.321721 | ||||||||
\(195\) | 4.28722 | 0.307014 | ||||||||
\(196\) | 0.105404 | 0.00752883 | ||||||||
\(197\) | −2.63724 | −0.187896 | −0.0939479 | − | 0.995577i | \(-0.529949\pi\) | ||||
−0.0939479 | + | 0.995577i | \(0.529949\pi\) | |||||||
\(198\) | −7.07770 | −0.502991 | ||||||||
\(199\) | −21.7181 | −1.53955 | −0.769777 | − | 0.638313i | \(-0.779633\pi\) | ||||
−0.769777 | + | 0.638313i | \(0.779633\pi\) | |||||||
\(200\) | −10.5924 | −0.748997 | ||||||||
\(201\) | 16.2568 | 1.14666 | ||||||||
\(202\) | 1.99769 | 0.140557 | ||||||||
\(203\) | 1.90949 | 0.134020 | ||||||||
\(204\) | −0.231317 | −0.0161955 | ||||||||
\(205\) | −11.3711 | −0.794191 | ||||||||
\(206\) | 5.81220 | 0.404955 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −14.8945 | −1.03275 | ||||||||
\(209\) | −3.60121 | −0.249101 | ||||||||
\(210\) | 3.03538 | 0.209461 | ||||||||
\(211\) | 13.5636 | 0.933758 | 0.466879 | − | 0.884321i | \(-0.345378\pi\) | ||||
0.466879 | + | 0.884321i | \(0.345378\pi\) | |||||||
\(212\) | 0.144534 | 0.00992667 | ||||||||
\(213\) | 13.7025 | 0.938883 | ||||||||
\(214\) | −0.982297 | −0.0671485 | ||||||||
\(215\) | −14.4873 | −0.988029 | ||||||||
\(216\) | 2.85021 | 0.193932 | ||||||||
\(217\) | −8.28763 | −0.562601 | ||||||||
\(218\) | −12.9482 | −0.876963 | ||||||||
\(219\) | 14.2596 | 0.963576 | ||||||||
\(220\) | −0.179617 | −0.0121098 | ||||||||
\(221\) | 27.8517 | 1.87351 | ||||||||
\(222\) | −10.5969 | −0.711217 | ||||||||
\(223\) | 9.70226 | 0.649711 | 0.324856 | − | 0.945764i | \(-0.394684\pi\) | ||||
0.324856 | + | 0.945764i | \(0.394684\pi\) | |||||||
\(224\) | 0.339439 | 0.0226798 | ||||||||
\(225\) | −3.71636 | −0.247758 | ||||||||
\(226\) | 28.2016 | 1.87594 | ||||||||
\(227\) | −20.8423 | −1.38335 | −0.691676 | − | 0.722208i | \(-0.743127\pi\) | ||||
−0.691676 | + | 0.722208i | \(0.743127\pi\) | |||||||
\(228\) | 0.0224359 | 0.00148585 | ||||||||
\(229\) | 11.7579 | 0.776984 | 0.388492 | − | 0.921452i | \(-0.372996\pi\) | ||||
0.388492 | + | 0.921452i | \(0.372996\pi\) | |||||||
\(230\) | 1.58963 | 0.104817 | ||||||||
\(231\) | −9.63238 | −0.633764 | ||||||||
\(232\) | −2.85021 | −0.187126 | ||||||||
\(233\) | −0.963016 | −0.0630893 | −0.0315446 | − | 0.999502i | \(-0.510043\pi\) | ||||
−0.0315446 | + | 0.999502i | \(0.510043\pi\) | |||||||
\(234\) | −5.30922 | −0.347074 | ||||||||
\(235\) | −1.32398 | −0.0863668 | ||||||||
\(236\) | −0.140476 | −0.00914418 | ||||||||
\(237\) | −0.947565 | −0.0615510 | ||||||||
\(238\) | 19.7192 | 1.27821 | ||||||||
\(239\) | −28.8074 | −1.86339 | −0.931697 | − | 0.363237i | \(-0.881672\pi\) | ||||
−0.931697 | + | 0.363237i | \(0.881672\pi\) | |||||||
\(240\) | −4.45957 | −0.287864 | ||||||||
\(241\) | 11.7498 | 0.756869 | 0.378435 | − | 0.925628i | \(-0.376462\pi\) | ||||
0.378435 | + | 0.925628i | \(0.376462\pi\) | |||||||
\(242\) | −20.2697 | −1.30299 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.0317456 | 0.00203230 | ||||||||
\(245\) | −3.79984 | −0.242763 | ||||||||
\(246\) | 14.0818 | 0.897820 | ||||||||
\(247\) | −2.70139 | −0.171885 | ||||||||
\(248\) | 12.3706 | 0.785533 | ||||||||
\(249\) | 11.2596 | 0.713551 | ||||||||
\(250\) | 13.8558 | 0.876319 | ||||||||
\(251\) | 15.1439 | 0.955872 | 0.477936 | − | 0.878395i | \(-0.341385\pi\) | ||||
0.477936 | + | 0.878395i | \(0.341385\pi\) | |||||||
\(252\) | 0.0600106 | 0.00378031 | ||||||||
\(253\) | −5.04448 | −0.317144 | ||||||||
\(254\) | −3.51238 | −0.220387 | ||||||||
\(255\) | 8.33908 | 0.522213 | ||||||||
\(256\) | −0.754075 | −0.0471297 | ||||||||
\(257\) | −7.48604 | −0.466966 | −0.233483 | − | 0.972361i | \(-0.575012\pi\) | ||||
−0.233483 | + | 0.972361i | \(0.575012\pi\) | |||||||
\(258\) | 17.9409 | 1.11695 | ||||||||
\(259\) | −14.4218 | −0.896127 | ||||||||
\(260\) | −0.134737 | −0.00835603 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 7.66604 | 0.473609 | ||||||||
\(263\) | −0.748198 | −0.0461359 | −0.0230679 | − | 0.999734i | \(-0.507343\pi\) | ||||
−0.0230679 | + | 0.999734i | \(0.507343\pi\) | |||||||
\(264\) | 14.3778 | 0.884895 | ||||||||
\(265\) | −5.21052 | −0.320080 | ||||||||
\(266\) | −1.91260 | −0.117269 | ||||||||
\(267\) | −9.66768 | −0.591653 | ||||||||
\(268\) | −0.510911 | −0.0312089 | ||||||||
\(269\) | 5.29003 | 0.322539 | 0.161269 | − | 0.986910i | \(-0.448441\pi\) | ||||
0.161269 | + | 0.986910i | \(0.448441\pi\) | |||||||
\(270\) | −1.58963 | −0.0967419 | ||||||||
\(271\) | 25.5087 | 1.54954 | 0.774771 | − | 0.632242i | \(-0.217865\pi\) | ||||
0.774771 | + | 0.632242i | \(0.217865\pi\) | |||||||
\(272\) | −28.9714 | −1.75665 | ||||||||
\(273\) | −7.22556 | −0.437311 | ||||||||
\(274\) | −16.3659 | −0.988699 | ||||||||
\(275\) | −18.7471 | −1.13049 | ||||||||
\(276\) | 0.0314276 | 0.00189172 | ||||||||
\(277\) | −11.7482 | −0.705884 | −0.352942 | − | 0.935645i | \(-0.614819\pi\) | ||||
−0.352942 | + | 0.935645i | \(0.614819\pi\) | |||||||
\(278\) | −14.2916 | −0.857155 | ||||||||
\(279\) | 4.34024 | 0.259843 | ||||||||
\(280\) | −6.16616 | −0.368498 | ||||||||
\(281\) | −12.3525 | −0.736890 | −0.368445 | − | 0.929650i | \(-0.620110\pi\) | ||||
−0.368445 | + | 0.929650i | \(0.620110\pi\) | |||||||
\(282\) | 1.63959 | 0.0976362 | ||||||||
\(283\) | 7.72479 | 0.459191 | 0.229596 | − | 0.973286i | \(-0.426260\pi\) | ||||
0.229596 | + | 0.973286i | \(0.426260\pi\) | |||||||
\(284\) | −0.430638 | −0.0255537 | ||||||||
\(285\) | −0.808822 | −0.0479105 | ||||||||
\(286\) | −26.7822 | −1.58367 | ||||||||
\(287\) | 19.1645 | 1.13125 | ||||||||
\(288\) | −0.177765 | −0.0104749 | ||||||||
\(289\) | 37.1744 | 2.18673 | ||||||||
\(290\) | 1.58963 | 0.0933464 | ||||||||
\(291\) | −3.19378 | −0.187223 | ||||||||
\(292\) | −0.448145 | −0.0262257 | ||||||||
\(293\) | 19.8822 | 1.16153 | 0.580765 | − | 0.814071i | \(-0.302754\pi\) | ||||
0.580765 | + | 0.814071i | \(0.302754\pi\) | |||||||
\(294\) | 4.70566 | 0.274440 | ||||||||
\(295\) | 5.06420 | 0.294849 | ||||||||
\(296\) | 21.5268 | 1.25122 | ||||||||
\(297\) | 5.04448 | 0.292711 | ||||||||
\(298\) | 4.97579 | 0.288240 | ||||||||
\(299\) | −3.78403 | −0.218836 | ||||||||
\(300\) | 0.116796 | 0.00674324 | ||||||||
\(301\) | 24.4166 | 1.40735 | ||||||||
\(302\) | −12.6680 | −0.728962 | ||||||||
\(303\) | −1.42381 | −0.0817957 | ||||||||
\(304\) | 2.80999 | 0.161164 | ||||||||
\(305\) | −1.14444 | −0.0655304 | ||||||||
\(306\) | −10.3270 | −0.590354 | ||||||||
\(307\) | −23.7258 | −1.35410 | −0.677050 | − | 0.735937i | \(-0.736742\pi\) | ||||
−0.677050 | + | 0.735937i | \(0.736742\pi\) | |||||||
\(308\) | 0.302722 | 0.0172492 | ||||||||
\(309\) | −4.14252 | −0.235660 | ||||||||
\(310\) | −6.89938 | −0.391858 | ||||||||
\(311\) | 18.1409 | 1.02868 | 0.514338 | − | 0.857587i | \(-0.328038\pi\) | ||||
0.514338 | + | 0.857587i | \(0.328038\pi\) | |||||||
\(312\) | 10.7853 | 0.610597 | ||||||||
\(313\) | 9.20479 | 0.520285 | 0.260143 | − | 0.965570i | \(-0.416230\pi\) | ||||
0.260143 | + | 0.965570i | \(0.416230\pi\) | |||||||
\(314\) | 23.8249 | 1.34452 | ||||||||
\(315\) | −2.16340 | −0.121894 | ||||||||
\(316\) | 0.0297797 | 0.00167524 | ||||||||
\(317\) | −17.6458 | −0.991087 | −0.495544 | − | 0.868583i | \(-0.665031\pi\) | ||||
−0.495544 | + | 0.868583i | \(0.665031\pi\) | |||||||
\(318\) | 6.45262 | 0.361845 | ||||||||
\(319\) | −5.04448 | −0.282437 | ||||||||
\(320\) | 9.20173 | 0.514392 | ||||||||
\(321\) | 0.700112 | 0.0390764 | ||||||||
\(322\) | −2.67912 | −0.149302 | ||||||||
\(323\) | −5.25447 | −0.292367 | ||||||||
\(324\) | −0.0314276 | −0.00174598 | ||||||||
\(325\) | −14.0628 | −0.780066 | ||||||||
\(326\) | −10.7153 | −0.593464 | ||||||||
\(327\) | 9.22855 | 0.510340 | ||||||||
\(328\) | −28.6061 | −1.57951 | ||||||||
\(329\) | 2.23139 | 0.123021 | ||||||||
\(330\) | −8.01887 | −0.441424 | ||||||||
\(331\) | 9.43619 | 0.518660 | 0.259330 | − | 0.965789i | \(-0.416498\pi\) | ||||
0.259330 | + | 0.965789i | \(0.416498\pi\) | |||||||
\(332\) | −0.353863 | −0.0194208 | ||||||||
\(333\) | 7.55271 | 0.413886 | ||||||||
\(334\) | −13.1484 | −0.719449 | ||||||||
\(335\) | 18.4185 | 1.00631 | ||||||||
\(336\) | 7.51604 | 0.410034 | ||||||||
\(337\) | 2.46272 | 0.134153 | 0.0670765 | − | 0.997748i | \(-0.478633\pi\) | ||||
0.0670765 | + | 0.997748i | \(0.478633\pi\) | |||||||
\(338\) | −1.85048 | −0.100653 | ||||||||
\(339\) | −20.1001 | −1.09169 | ||||||||
\(340\) | −0.262077 | −0.0142131 | ||||||||
\(341\) | 21.8942 | 1.18564 | ||||||||
\(342\) | 1.00163 | 0.0541620 | ||||||||
\(343\) | 19.7706 | 1.06751 | ||||||||
\(344\) | −36.4456 | −1.96501 | ||||||||
\(345\) | −1.13298 | −0.0609974 | ||||||||
\(346\) | −20.4550 | −1.09967 | ||||||||
\(347\) | −13.6465 | −0.732581 | −0.366291 | − | 0.930501i | \(-0.619372\pi\) | ||||
−0.366291 | + | 0.930501i | \(0.619372\pi\) | |||||||
\(348\) | 0.0314276 | 0.00168470 | ||||||||
\(349\) | 35.4897 | 1.89972 | 0.949860 | − | 0.312677i | \(-0.101226\pi\) | ||||
0.949860 | + | 0.312677i | \(0.101226\pi\) | |||||||
\(350\) | −9.95659 | −0.532202 | ||||||||
\(351\) | 3.78403 | 0.201977 | ||||||||
\(352\) | −0.896731 | −0.0477959 | ||||||||
\(353\) | −24.3193 | −1.29439 | −0.647194 | − | 0.762326i | \(-0.724057\pi\) | ||||
−0.647194 | + | 0.762326i | \(0.724057\pi\) | |||||||
\(354\) | −6.27141 | −0.333322 | ||||||||
\(355\) | 15.5247 | 0.823964 | ||||||||
\(356\) | 0.303832 | 0.0161031 | ||||||||
\(357\) | −14.0545 | −0.743841 | ||||||||
\(358\) | −2.42137 | −0.127973 | ||||||||
\(359\) | −25.0671 | −1.32299 | −0.661496 | − | 0.749948i | \(-0.730078\pi\) | ||||
−0.661496 | + | 0.749948i | \(0.730078\pi\) | |||||||
\(360\) | 3.22922 | 0.170195 | ||||||||
\(361\) | −18.4904 | −0.973177 | ||||||||
\(362\) | 16.9898 | 0.892966 | ||||||||
\(363\) | 14.4468 | 0.758261 | ||||||||
\(364\) | 0.227082 | 0.0119023 | ||||||||
\(365\) | 16.1558 | 0.845634 | ||||||||
\(366\) | 1.41725 | 0.0740811 | ||||||||
\(367\) | 4.93174 | 0.257435 | 0.128717 | − | 0.991681i | \(-0.458914\pi\) | ||||
0.128717 | + | 0.991681i | \(0.458914\pi\) | |||||||
\(368\) | 3.93616 | 0.205186 | ||||||||
\(369\) | −10.0365 | −0.522478 | ||||||||
\(370\) | −12.0060 | −0.624164 | ||||||||
\(371\) | 8.78167 | 0.455922 | ||||||||
\(372\) | −0.136403 | −0.00707217 | ||||||||
\(373\) | −11.4296 | −0.591801 | −0.295901 | − | 0.955219i | \(-0.595620\pi\) | ||||
−0.295901 | + | 0.955219i | \(0.595620\pi\) | |||||||
\(374\) | −52.0942 | −2.69373 | ||||||||
\(375\) | −9.87544 | −0.509965 | ||||||||
\(376\) | −3.33071 | −0.171768 | ||||||||
\(377\) | −3.78403 | −0.194888 | ||||||||
\(378\) | 2.67912 | 0.137799 | ||||||||
\(379\) | 11.1586 | 0.573181 | 0.286590 | − | 0.958053i | \(-0.407478\pi\) | ||||
0.286590 | + | 0.958053i | \(0.407478\pi\) | |||||||
\(380\) | 0.0254193 | 0.00130398 | ||||||||
\(381\) | 2.50338 | 0.128252 | ||||||||
\(382\) | −25.4454 | −1.30190 | ||||||||
\(383\) | −1.36723 | −0.0698624 | −0.0349312 | − | 0.999390i | \(-0.511121\pi\) | ||||
−0.0349312 | + | 0.999390i | \(0.511121\pi\) | |||||||
\(384\) | −11.0397 | −0.563369 | ||||||||
\(385\) | −10.9133 | −0.556191 | ||||||||
\(386\) | 6.40439 | 0.325975 | ||||||||
\(387\) | −12.7870 | −0.649999 | ||||||||
\(388\) | 0.100373 | 0.00509565 | ||||||||
\(389\) | 11.2965 | 0.572755 | 0.286378 | − | 0.958117i | \(-0.407549\pi\) | ||||
0.286378 | + | 0.958117i | \(0.407549\pi\) | |||||||
\(390\) | −6.01522 | −0.304592 | ||||||||
\(391\) | −7.36033 | −0.372228 | ||||||||
\(392\) | −9.55920 | −0.482813 | ||||||||
\(393\) | −5.46381 | −0.275613 | ||||||||
\(394\) | 3.70021 | 0.186414 | ||||||||
\(395\) | −1.07357 | −0.0540171 | ||||||||
\(396\) | −0.158536 | −0.00796673 | ||||||||
\(397\) | 22.7967 | 1.14413 | 0.572067 | − | 0.820207i | \(-0.306142\pi\) | ||||
0.572067 | + | 0.820207i | \(0.306142\pi\) | |||||||
\(398\) | 30.4717 | 1.52741 | ||||||||
\(399\) | 1.36317 | 0.0682437 | ||||||||
\(400\) | 14.6282 | 0.731410 | ||||||||
\(401\) | 14.6666 | 0.732415 | 0.366207 | − | 0.930533i | \(-0.380656\pi\) | ||||
0.366207 | + | 0.930533i | \(0.380656\pi\) | |||||||
\(402\) | −22.8092 | −1.13762 | ||||||||
\(403\) | 16.4236 | 0.818117 | ||||||||
\(404\) | 0.0447469 | 0.00222624 | ||||||||
\(405\) | 1.13298 | 0.0562981 | ||||||||
\(406\) | −2.67912 | −0.132963 | ||||||||
\(407\) | 38.0995 | 1.88852 | ||||||||
\(408\) | 20.9785 | 1.03859 | ||||||||
\(409\) | −28.2408 | −1.39642 | −0.698210 | − | 0.715893i | \(-0.746020\pi\) | ||||
−0.698210 | + | 0.715893i | \(0.746020\pi\) | |||||||
\(410\) | 15.9543 | 0.787927 | ||||||||
\(411\) | 11.6644 | 0.575364 | ||||||||
\(412\) | 0.130189 | 0.00641397 | ||||||||
\(413\) | −8.53506 | −0.419983 | ||||||||
\(414\) | 1.40306 | 0.0689566 | ||||||||
\(415\) | 12.7569 | 0.626212 | ||||||||
\(416\) | −0.672667 | −0.0329802 | ||||||||
\(417\) | 10.1861 | 0.498813 | ||||||||
\(418\) | 5.05271 | 0.247136 | ||||||||
\(419\) | 4.68128 | 0.228696 | 0.114348 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114348 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(420\) | 0.0679906 | 0.00331760 | ||||||||
\(421\) | −22.7427 | −1.10841 | −0.554205 | − | 0.832380i | \(-0.686978\pi\) | ||||
−0.554205 | + | 0.832380i | \(0.686978\pi\) | |||||||
\(422\) | −19.0305 | −0.926392 | ||||||||
\(423\) | −1.16858 | −0.0568185 | ||||||||
\(424\) | −13.1080 | −0.636582 | ||||||||
\(425\) | −27.3537 | −1.32685 | ||||||||
\(426\) | −19.2255 | −0.931477 | ||||||||
\(427\) | 1.92881 | 0.0933415 | ||||||||
\(428\) | −0.0220028 | −0.00106355 | ||||||||
\(429\) | 19.0885 | 0.921600 | ||||||||
\(430\) | 20.3266 | 0.980235 | ||||||||
\(431\) | 1.39056 | 0.0669808 | 0.0334904 | − | 0.999439i | \(-0.489338\pi\) | ||||
0.0334904 | + | 0.999439i | \(0.489338\pi\) | |||||||
\(432\) | −3.93616 | −0.189378 | ||||||||
\(433\) | −22.3475 | −1.07395 | −0.536976 | − | 0.843598i | \(-0.680433\pi\) | ||||
−0.536976 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(434\) | 11.6280 | 0.558163 | ||||||||
\(435\) | −1.13298 | −0.0543221 | ||||||||
\(436\) | −0.290031 | −0.0138900 | ||||||||
\(437\) | 0.713891 | 0.0341500 | ||||||||
\(438\) | −20.0071 | −0.955975 | ||||||||
\(439\) | −30.6009 | −1.46050 | −0.730251 | − | 0.683179i | \(-0.760597\pi\) | ||||
−0.730251 | + | 0.683179i | \(0.760597\pi\) | |||||||
\(440\) | 16.2898 | 0.776584 | ||||||||
\(441\) | −3.35386 | −0.159708 | ||||||||
\(442\) | −39.0776 | −1.85873 | ||||||||
\(443\) | −10.0083 | −0.475506 | −0.237753 | − | 0.971326i | \(-0.576411\pi\) | ||||
−0.237753 | + | 0.971326i | \(0.576411\pi\) | |||||||
\(444\) | −0.237363 | −0.0112648 | ||||||||
\(445\) | −10.9533 | −0.519234 | ||||||||
\(446\) | −13.6128 | −0.644586 | ||||||||
\(447\) | −3.54639 | −0.167739 | ||||||||
\(448\) | −15.5083 | −0.732700 | ||||||||
\(449\) | −26.4391 | −1.24774 | −0.623869 | − | 0.781529i | \(-0.714440\pi\) | ||||
−0.623869 | + | 0.781529i | \(0.714440\pi\) | |||||||
\(450\) | 5.21428 | 0.245803 | ||||||||
\(451\) | −50.6288 | −2.38402 | ||||||||
\(452\) | 0.631697 | 0.0297125 | ||||||||
\(453\) | 9.02885 | 0.424213 | ||||||||
\(454\) | 29.2430 | 1.37244 | ||||||||
\(455\) | −8.18639 | −0.383784 | ||||||||
\(456\) | −2.03474 | −0.0952855 | ||||||||
\(457\) | −13.9533 | −0.652709 | −0.326354 | − | 0.945248i | \(-0.605820\pi\) | ||||
−0.326354 | + | 0.945248i | \(0.605820\pi\) | |||||||
\(458\) | −16.4970 | −0.770855 | ||||||||
\(459\) | 7.36033 | 0.343551 | ||||||||
\(460\) | 0.0356067 | 0.00166017 | ||||||||
\(461\) | −11.7230 | −0.545996 | −0.272998 | − | 0.962015i | \(-0.588015\pi\) | ||||
−0.272998 | + | 0.962015i | \(0.588015\pi\) | |||||||
\(462\) | 13.5148 | 0.628765 | ||||||||
\(463\) | −14.6877 | −0.682595 | −0.341298 | − | 0.939955i | \(-0.610866\pi\) | ||||
−0.341298 | + | 0.939955i | \(0.610866\pi\) | |||||||
\(464\) | 3.93616 | 0.182732 | ||||||||
\(465\) | 4.91739 | 0.228038 | ||||||||
\(466\) | 1.35117 | 0.0625916 | ||||||||
\(467\) | 25.1197 | 1.16240 | 0.581200 | − | 0.813761i | \(-0.302583\pi\) | ||||
0.581200 | + | 0.813761i | \(0.302583\pi\) | |||||||
\(468\) | −0.118923 | −0.00549722 | ||||||||
\(469\) | −31.0421 | −1.43339 | ||||||||
\(470\) | 1.85762 | 0.0856855 | ||||||||
\(471\) | −16.9807 | −0.782431 | ||||||||
\(472\) | 12.7399 | 0.586402 | ||||||||
\(473\) | −64.5037 | −2.96588 | ||||||||
\(474\) | 1.32949 | 0.0610654 | ||||||||
\(475\) | 2.65308 | 0.121732 | ||||||||
\(476\) | 0.441698 | 0.0202452 | ||||||||
\(477\) | −4.59897 | −0.210572 | ||||||||
\(478\) | 40.4184 | 1.84870 | ||||||||
\(479\) | −11.1186 | −0.508022 | −0.254011 | − | 0.967201i | \(-0.581750\pi\) | ||||
−0.254011 | + | 0.967201i | \(0.581750\pi\) | |||||||
\(480\) | −0.201403 | −0.00919276 | ||||||||
\(481\) | 28.5797 | 1.30312 | ||||||||
\(482\) | −16.4856 | −0.750899 | ||||||||
\(483\) | 1.90949 | 0.0868847 | ||||||||
\(484\) | −0.454028 | −0.0206377 | ||||||||
\(485\) | −3.61847 | −0.164306 | ||||||||
\(486\) | −1.40306 | −0.0636440 | ||||||||
\(487\) | −31.6400 | −1.43374 | −0.716872 | − | 0.697204i | \(-0.754427\pi\) | ||||
−0.716872 | + | 0.697204i | \(0.754427\pi\) | |||||||
\(488\) | −2.87905 | −0.130328 | ||||||||
\(489\) | 7.63708 | 0.345361 | ||||||||
\(490\) | 5.33140 | 0.240848 | ||||||||
\(491\) | 4.47521 | 0.201963 | 0.100982 | − | 0.994888i | \(-0.467802\pi\) | ||||
0.100982 | + | 0.994888i | \(0.467802\pi\) | |||||||
\(492\) | 0.315422 | 0.0142203 | ||||||||
\(493\) | −7.36033 | −0.331493 | ||||||||
\(494\) | 3.79020 | 0.170529 | ||||||||
\(495\) | 5.71528 | 0.256883 | ||||||||
\(496\) | −17.0839 | −0.767088 | ||||||||
\(497\) | −26.1648 | −1.17365 | ||||||||
\(498\) | −15.7979 | −0.707922 | ||||||||
\(499\) | −24.9535 | −1.11707 | −0.558537 | − | 0.829480i | \(-0.688637\pi\) | ||||
−0.558537 | + | 0.829480i | \(0.688637\pi\) | |||||||
\(500\) | 0.310361 | 0.0138798 | ||||||||
\(501\) | 9.37125 | 0.418677 | ||||||||
\(502\) | −21.2477 | −0.948332 | ||||||||
\(503\) | 27.4289 | 1.22299 | 0.611496 | − | 0.791247i | \(-0.290568\pi\) | ||||
0.611496 | + | 0.791247i | \(0.290568\pi\) | |||||||
\(504\) | −5.44244 | −0.242426 | ||||||||
\(505\) | −1.61314 | −0.0717839 | ||||||||
\(506\) | 7.07770 | 0.314642 | ||||||||
\(507\) | 1.31889 | 0.0585739 | ||||||||
\(508\) | −0.0786751 | −0.00349064 | ||||||||
\(509\) | 7.90743 | 0.350491 | 0.175245 | − | 0.984525i | \(-0.443928\pi\) | ||||
0.175245 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(510\) | −11.7002 | −0.518094 | ||||||||
\(511\) | −27.2286 | −1.20452 | ||||||||
\(512\) | 23.1375 | 1.02254 | ||||||||
\(513\) | −0.713891 | −0.0315191 | ||||||||
\(514\) | 10.5034 | 0.463283 | ||||||||
\(515\) | −4.69338 | −0.206815 | ||||||||
\(516\) | 0.401864 | 0.0176911 | ||||||||
\(517\) | −5.89490 | −0.259257 | ||||||||
\(518\) | 20.2346 | 0.889059 | ||||||||
\(519\) | 14.5789 | 0.639941 | ||||||||
\(520\) | 12.2195 | 0.535860 | ||||||||
\(521\) | 24.6282 | 1.07898 | 0.539491 | − | 0.841992i | \(-0.318617\pi\) | ||||
0.539491 | + | 0.841992i | \(0.318617\pi\) | |||||||
\(522\) | 1.40306 | 0.0614102 | ||||||||
\(523\) | 13.5197 | 0.591174 | 0.295587 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295587 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(524\) | 0.171714 | 0.00750137 | ||||||||
\(525\) | 7.09635 | 0.309710 | ||||||||
\(526\) | 1.04977 | 0.0457720 | ||||||||
\(527\) | 31.9456 | 1.39157 | ||||||||
\(528\) | −19.8559 | −0.864116 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 7.31067 | 0.317555 | ||||||||
\(531\) | 4.46982 | 0.193974 | ||||||||
\(532\) | −0.0428410 | −0.00185739 | ||||||||
\(533\) | −37.9783 | −1.64502 | ||||||||
\(534\) | 13.5643 | 0.586986 | ||||||||
\(535\) | 0.793210 | 0.0342935 | ||||||||
\(536\) | 46.3353 | 2.00138 | ||||||||
\(537\) | 1.72578 | 0.0744728 | ||||||||
\(538\) | −7.42222 | −0.319995 | ||||||||
\(539\) | −16.9185 | −0.728731 | ||||||||
\(540\) | −0.0356067 | −0.00153227 | ||||||||
\(541\) | 9.32195 | 0.400782 | 0.200391 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200391 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(542\) | −35.7901 | −1.53732 | ||||||||
\(543\) | −12.1091 | −0.519653 | ||||||||
\(544\) | −1.30841 | −0.0560975 | ||||||||
\(545\) | 10.4557 | 0.447875 | ||||||||
\(546\) | 10.1379 | 0.433861 | ||||||||
\(547\) | −19.8523 | −0.848825 | −0.424413 | − | 0.905469i | \(-0.639519\pi\) | ||||
−0.424413 | + | 0.905469i | \(0.639519\pi\) | |||||||
\(548\) | −0.366585 | −0.0156597 | ||||||||
\(549\) | −1.01012 | −0.0431108 | ||||||||
\(550\) | 26.3033 | 1.12158 | ||||||||
\(551\) | 0.713891 | 0.0304128 | ||||||||
\(552\) | −2.85021 | −0.121313 | ||||||||
\(553\) | 1.80936 | 0.0769420 | ||||||||
\(554\) | 16.4835 | 0.700316 | ||||||||
\(555\) | 8.55704 | 0.363226 | ||||||||
\(556\) | −0.320123 | −0.0135762 | ||||||||
\(557\) | −41.2989 | −1.74989 | −0.874946 | − | 0.484221i | \(-0.839103\pi\) | ||||
−0.874946 | + | 0.484221i | \(0.839103\pi\) | |||||||
\(558\) | −6.08960 | −0.257793 | ||||||||
\(559\) | −48.3863 | −2.04652 | ||||||||
\(560\) | 8.51550 | 0.359846 | ||||||||
\(561\) | 37.1291 | 1.56759 | ||||||||
\(562\) | 17.3313 | 0.731078 | ||||||||
\(563\) | −37.1011 | −1.56363 | −0.781813 | − | 0.623513i | \(-0.785705\pi\) | ||||
−0.781813 | + | 0.623513i | \(0.785705\pi\) | |||||||
\(564\) | 0.0367257 | 0.00154643 | ||||||||
\(565\) | −22.7729 | −0.958064 | ||||||||
\(566\) | −10.8383 | −0.455569 | ||||||||
\(567\) | −1.90949 | −0.0801909 | ||||||||
\(568\) | 39.0551 | 1.63872 | ||||||||
\(569\) | −20.3186 | −0.851800 | −0.425900 | − | 0.904770i | \(-0.640043\pi\) | ||||
−0.425900 | + | 0.904770i | \(0.640043\pi\) | |||||||
\(570\) | 1.13482 | 0.0475326 | ||||||||
\(571\) | 18.4758 | 0.773190 | 0.386595 | − | 0.922250i | \(-0.373651\pi\) | ||||
0.386595 | + | 0.922250i | \(0.373651\pi\) | |||||||
\(572\) | −0.599905 | −0.0250833 | ||||||||
\(573\) | 18.1357 | 0.757629 | ||||||||
\(574\) | −26.8889 | −1.12232 | ||||||||
\(575\) | 3.71636 | 0.154983 | ||||||||
\(576\) | 8.12173 | 0.338405 | ||||||||
\(577\) | 34.6426 | 1.44219 | 0.721095 | − | 0.692837i | \(-0.243639\pi\) | ||||
0.721095 | + | 0.692837i | \(0.243639\pi\) | |||||||
\(578\) | −52.1579 | −2.16948 | ||||||||
\(579\) | −4.56459 | −0.189698 | ||||||||
\(580\) | 0.0356067 | 0.00147849 | ||||||||
\(581\) | −21.5001 | −0.891976 | ||||||||
\(582\) | 4.48106 | 0.185746 | ||||||||
\(583\) | −23.1994 | −0.960822 | ||||||||
\(584\) | 40.6429 | 1.68182 | ||||||||
\(585\) | 4.28722 | 0.177255 | ||||||||
\(586\) | −27.8959 | −1.15237 | ||||||||
\(587\) | 20.5344 | 0.847544 | 0.423772 | − | 0.905769i | \(-0.360706\pi\) | ||||
0.423772 | + | 0.905769i | \(0.360706\pi\) | |||||||
\(588\) | 0.105404 | 0.00434677 | ||||||||
\(589\) | −3.09846 | −0.127670 | ||||||||
\(590\) | −7.10536 | −0.292523 | ||||||||
\(591\) | −2.63724 | −0.108482 | ||||||||
\(592\) | −29.7287 | −1.22184 | ||||||||
\(593\) | −33.0577 | −1.35752 | −0.678759 | − | 0.734361i | \(-0.737482\pi\) | ||||
−0.678759 | + | 0.734361i | \(0.737482\pi\) | |||||||
\(594\) | −7.07770 | −0.290402 | ||||||||
\(595\) | −15.9234 | −0.652794 | ||||||||
\(596\) | 0.111454 | 0.00456535 | ||||||||
\(597\) | −21.7181 | −0.888862 | ||||||||
\(598\) | 5.30922 | 0.217110 | ||||||||
\(599\) | 16.6667 | 0.680984 | 0.340492 | − | 0.940247i | \(-0.389406\pi\) | ||||
0.340492 | + | 0.940247i | \(0.389406\pi\) | |||||||
\(600\) | −10.5924 | −0.432434 | ||||||||
\(601\) | −29.9855 | −1.22313 | −0.611566 | − | 0.791193i | \(-0.709460\pi\) | ||||
−0.611566 | + | 0.791193i | \(0.709460\pi\) | |||||||
\(602\) | −34.2579 | −1.39625 | ||||||||
\(603\) | 16.2568 | 0.662027 | ||||||||
\(604\) | −0.283755 | −0.0115458 | ||||||||
\(605\) | 16.3679 | 0.665450 | ||||||||
\(606\) | 1.99769 | 0.0811505 | ||||||||
\(607\) | −7.14403 | −0.289967 | −0.144984 | − | 0.989434i | \(-0.546313\pi\) | ||||
−0.144984 | + | 0.989434i | \(0.546313\pi\) | |||||||
\(608\) | 0.126905 | 0.00514666 | ||||||||
\(609\) | 1.90949 | 0.0773763 | ||||||||
\(610\) | 1.60572 | 0.0650135 | ||||||||
\(611\) | −4.42196 | −0.178893 | ||||||||
\(612\) | −0.231317 | −0.00935045 | ||||||||
\(613\) | 30.1935 | 1.21951 | 0.609753 | − | 0.792592i | \(-0.291269\pi\) | ||||
0.609753 | + | 0.792592i | \(0.291269\pi\) | |||||||
\(614\) | 33.2886 | 1.34342 | ||||||||
\(615\) | −11.3711 | −0.458527 | ||||||||
\(616\) | −27.4543 | −1.10617 | ||||||||
\(617\) | −18.0943 | −0.728449 | −0.364225 | − | 0.931311i | \(-0.618666\pi\) | ||||
−0.364225 | + | 0.931311i | \(0.618666\pi\) | |||||||
\(618\) | 5.81220 | 0.233801 | ||||||||
\(619\) | −19.8935 | −0.799588 | −0.399794 | − | 0.916605i | \(-0.630918\pi\) | ||||
−0.399794 | + | 0.916605i | \(0.630918\pi\) | |||||||
\(620\) | −0.154542 | −0.00620654 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −25.4527 | −1.02056 | ||||||||
\(623\) | 18.4603 | 0.739597 | ||||||||
\(624\) | −14.8945 | −0.596259 | ||||||||
\(625\) | 7.39318 | 0.295727 | ||||||||
\(626\) | −12.9149 | −0.516181 | ||||||||
\(627\) | −3.60121 | −0.143819 | ||||||||
\(628\) | 0.533663 | 0.0212955 | ||||||||
\(629\) | 55.5904 | 2.21654 | ||||||||
\(630\) | 3.03538 | 0.120933 | ||||||||
\(631\) | 24.6952 | 0.983100 | 0.491550 | − | 0.870849i | \(-0.336430\pi\) | ||||
0.491550 | + | 0.870849i | \(0.336430\pi\) | |||||||
\(632\) | −2.70076 | −0.107430 | ||||||||
\(633\) | 13.5636 | 0.539105 | ||||||||
\(634\) | 24.7581 | 0.983270 | ||||||||
\(635\) | 2.83627 | 0.112554 | ||||||||
\(636\) | 0.144534 | 0.00573117 | ||||||||
\(637\) | −12.6911 | −0.502840 | ||||||||
\(638\) | 7.07770 | 0.280209 | ||||||||
\(639\) | 13.7025 | 0.542064 | ||||||||
\(640\) | −12.5078 | −0.494412 | ||||||||
\(641\) | −7.28526 | −0.287750 | −0.143875 | − | 0.989596i | \(-0.545956\pi\) | ||||
−0.143875 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(642\) | −0.982297 | −0.0387682 | ||||||||
\(643\) | 9.67614 | 0.381590 | 0.190795 | − | 0.981630i | \(-0.438893\pi\) | ||||
0.190795 | + | 0.981630i | \(0.438893\pi\) | |||||||
\(644\) | −0.0600106 | −0.00236475 | ||||||||
\(645\) | −14.4873 | −0.570439 | ||||||||
\(646\) | 7.37233 | 0.290061 | ||||||||
\(647\) | −48.4492 | −1.90474 | −0.952368 | − | 0.304951i | \(-0.901360\pi\) | ||||
−0.952368 | + | 0.304951i | \(0.901360\pi\) | |||||||
\(648\) | 2.85021 | 0.111967 | ||||||||
\(649\) | 22.5479 | 0.885083 | ||||||||
\(650\) | 19.7310 | 0.773913 | ||||||||
\(651\) | −8.28763 | −0.324818 | ||||||||
\(652\) | −0.240015 | −0.00939971 | ||||||||
\(653\) | 2.44513 | 0.0956854 | 0.0478427 | − | 0.998855i | \(-0.484765\pi\) | ||||
0.0478427 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(654\) | −12.9482 | −0.506315 | ||||||||
\(655\) | −6.19037 | −0.241878 | ||||||||
\(656\) | 39.5051 | 1.54242 | ||||||||
\(657\) | 14.2596 | 0.556321 | ||||||||
\(658\) | −3.13078 | −0.122050 | ||||||||
\(659\) | −0.362884 | −0.0141360 | −0.00706798 | − | 0.999975i | \(-0.502250\pi\) | ||||
−0.00706798 | + | 0.999975i | \(0.502250\pi\) | |||||||
\(660\) | −0.179617 | −0.00699160 | ||||||||
\(661\) | 9.07466 | 0.352963 | 0.176482 | − | 0.984304i | \(-0.443528\pi\) | ||||
0.176482 | + | 0.984304i | \(0.443528\pi\) | |||||||
\(662\) | −13.2395 | −0.514569 | ||||||||
\(663\) | 27.8517 | 1.08167 | ||||||||
\(664\) | 32.0924 | 1.24542 | ||||||||
\(665\) | 1.54444 | 0.0598906 | ||||||||
\(666\) | −10.5969 | −0.410621 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −0.294516 | −0.0113952 | ||||||||
\(669\) | 9.70226 | 0.375111 | ||||||||
\(670\) | −25.8423 | −0.998375 | ||||||||
\(671\) | −5.09552 | −0.196710 | ||||||||
\(672\) | 0.339439 | 0.0130942 | ||||||||
\(673\) | −25.6908 | −0.990308 | −0.495154 | − | 0.868805i | \(-0.664888\pi\) | ||||
−0.495154 | + | 0.868805i | \(0.664888\pi\) | |||||||
\(674\) | −3.45534 | −0.133095 | ||||||||
\(675\) | −3.71636 | −0.143043 | ||||||||
\(676\) | −0.0414495 | −0.00159421 | ||||||||
\(677\) | −2.75399 | −0.105844 | −0.0529222 | − | 0.998599i | \(-0.516854\pi\) | ||||
−0.0529222 | + | 0.998599i | \(0.516854\pi\) | |||||||
\(678\) | 28.2016 | 1.08308 | ||||||||
\(679\) | 6.09848 | 0.234038 | ||||||||
\(680\) | 23.7681 | 0.911467 | ||||||||
\(681\) | −20.8423 | −0.798679 | ||||||||
\(682\) | −30.7189 | −1.17629 | ||||||||
\(683\) | −7.37036 | −0.282019 | −0.141009 | − | 0.990008i | \(-0.545035\pi\) | ||||
−0.141009 | + | 0.990008i | \(0.545035\pi\) | |||||||
\(684\) | 0.0224359 | 0.000857857 0 | ||||||||
\(685\) | 13.2155 | 0.504939 | ||||||||
\(686\) | −27.7392 | −1.05909 | ||||||||
\(687\) | 11.7579 | 0.448592 | ||||||||
\(688\) | 50.3315 | 1.91887 | ||||||||
\(689\) | −17.4026 | −0.662988 | ||||||||
\(690\) | 1.58963 | 0.0605163 | ||||||||
\(691\) | −0.879847 | −0.0334710 | −0.0167355 | − | 0.999860i | \(-0.505327\pi\) | ||||
−0.0167355 | + | 0.999860i | \(0.505327\pi\) | |||||||
\(692\) | −0.458179 | −0.0174173 | ||||||||
\(693\) | −9.63238 | −0.365904 | ||||||||
\(694\) | 19.1468 | 0.726803 | ||||||||
\(695\) | 11.5406 | 0.437758 | ||||||||
\(696\) | −2.85021 | −0.108037 | ||||||||
\(697\) | −73.8718 | −2.79809 | ||||||||
\(698\) | −49.7941 | −1.88473 | ||||||||
\(699\) | −0.963016 | −0.0364246 | ||||||||
\(700\) | −0.223021 | −0.00842941 | ||||||||
\(701\) | 37.0825 | 1.40059 | 0.700293 | − | 0.713855i | \(-0.253053\pi\) | ||||
0.700293 | + | 0.713855i | \(0.253053\pi\) | |||||||
\(702\) | −5.30922 | −0.200383 | ||||||||
\(703\) | −5.39181 | −0.203356 | ||||||||
\(704\) | 40.9699 | 1.54411 | ||||||||
\(705\) | −1.32398 | −0.0498639 | ||||||||
\(706\) | 34.1214 | 1.28418 | ||||||||
\(707\) | 2.71875 | 0.102249 | ||||||||
\(708\) | −0.140476 | −0.00527939 | ||||||||
\(709\) | −19.9284 | −0.748426 | −0.374213 | − | 0.927343i | \(-0.622087\pi\) | ||||
−0.374213 | + | 0.927343i | \(0.622087\pi\) | |||||||
\(710\) | −21.7820 | −0.817464 | ||||||||
\(711\) | −0.947565 | −0.0355365 | ||||||||
\(712\) | −27.5549 | −1.03266 | ||||||||
\(713\) | −4.34024 | −0.162543 | ||||||||
\(714\) | 19.7192 | 0.737973 | ||||||||
\(715\) | 21.6268 | 0.808796 | ||||||||
\(716\) | −0.0542370 | −0.00202693 | ||||||||
\(717\) | −28.8074 | −1.07583 | ||||||||
\(718\) | 35.1706 | 1.31256 | ||||||||
\(719\) | −7.28652 | −0.271741 | −0.135871 | − | 0.990727i | \(-0.543383\pi\) | ||||
−0.135871 | + | 0.990727i | \(0.543383\pi\) | |||||||
\(720\) | −4.45957 | −0.166199 | ||||||||
\(721\) | 7.91009 | 0.294587 | ||||||||
\(722\) | 25.9431 | 0.965500 | ||||||||
\(723\) | 11.7498 | 0.436979 | ||||||||
\(724\) | 0.380561 | 0.0141435 | ||||||||
\(725\) | 3.71636 | 0.138022 | ||||||||
\(726\) | −20.2697 | −0.752280 | ||||||||
\(727\) | 41.8878 | 1.55353 | 0.776766 | − | 0.629790i | \(-0.216859\pi\) | ||||
0.776766 | + | 0.629790i | \(0.216859\pi\) | |||||||
\(728\) | −20.5944 | −0.763278 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −22.6675 | −0.838964 | ||||||||
\(731\) | −94.1163 | −3.48102 | ||||||||
\(732\) | 0.0317456 | 0.00117335 | ||||||||
\(733\) | 6.92995 | 0.255964 | 0.127982 | − | 0.991777i | \(-0.459150\pi\) | ||||
0.127982 | + | 0.991777i | \(0.459150\pi\) | |||||||
\(734\) | −6.91952 | −0.255404 | ||||||||
\(735\) | −3.79984 | −0.140159 | ||||||||
\(736\) | 0.177765 | 0.00655249 | ||||||||
\(737\) | 82.0070 | 3.02077 | ||||||||
\(738\) | 14.0818 | 0.518357 | ||||||||
\(739\) | 41.3802 | 1.52220 | 0.761098 | − | 0.648637i | \(-0.224661\pi\) | ||||
0.761098 | + | 0.648637i | \(0.224661\pi\) | |||||||
\(740\) | −0.268927 | −0.00988596 | ||||||||
\(741\) | −2.70139 | −0.0992379 | ||||||||
\(742\) | −12.3212 | −0.452325 | ||||||||
\(743\) | 21.4539 | 0.787068 | 0.393534 | − | 0.919310i | \(-0.371252\pi\) | ||||
0.393534 | + | 0.919310i | \(0.371252\pi\) | |||||||
\(744\) | 12.3706 | 0.453528 | ||||||||
\(745\) | −4.01798 | −0.147207 | ||||||||
\(746\) | 16.0364 | 0.587133 | ||||||||
\(747\) | 11.2596 | 0.411969 | ||||||||
\(748\) | −1.16688 | −0.0426652 | ||||||||
\(749\) | −1.33685 | −0.0488476 | ||||||||
\(750\) | 13.8558 | 0.505943 | ||||||||
\(751\) | 48.2066 | 1.75908 | 0.879542 | − | 0.475821i | \(-0.157849\pi\) | ||||
0.879542 | + | 0.475821i | \(0.157849\pi\) | |||||||
\(752\) | 4.59973 | 0.167735 | ||||||||
\(753\) | 15.1439 | 0.551873 | ||||||||
\(754\) | 5.30922 | 0.193350 | ||||||||
\(755\) | 10.2295 | 0.372289 | ||||||||
\(756\) | 0.0600106 | 0.00218256 | ||||||||
\(757\) | 21.8131 | 0.792811 | 0.396406 | − | 0.918075i | \(-0.370257\pi\) | ||||
0.396406 | + | 0.918075i | \(0.370257\pi\) | |||||||
\(758\) | −15.6562 | −0.568659 | ||||||||
\(759\) | −5.04448 | −0.183103 | ||||||||
\(760\) | −2.30531 | −0.0836225 | ||||||||
\(761\) | −1.72952 | −0.0626949 | −0.0313475 | − | 0.999509i | \(-0.509980\pi\) | ||||
−0.0313475 | + | 0.999509i | \(0.509980\pi\) | |||||||
\(762\) | −3.51238 | −0.127240 | ||||||||
\(763\) | −17.6218 | −0.637952 | ||||||||
\(764\) | −0.569961 | −0.0206205 | ||||||||
\(765\) | 8.33908 | 0.301500 | ||||||||
\(766\) | 1.91831 | 0.0693113 | ||||||||
\(767\) | 16.9139 | 0.610726 | ||||||||
\(768\) | −0.754075 | −0.0272103 | ||||||||
\(769\) | −1.19902 | −0.0432377 | −0.0216188 | − | 0.999766i | \(-0.506882\pi\) | ||||
−0.0216188 | + | 0.999766i | \(0.506882\pi\) | |||||||
\(770\) | 15.3119 | 0.551804 | ||||||||
\(771\) | −7.48604 | −0.269603 | ||||||||
\(772\) | 0.143454 | 0.00516302 | ||||||||
\(773\) | 14.0133 | 0.504023 | 0.252011 | − | 0.967724i | \(-0.418908\pi\) | ||||
0.252011 | + | 0.967724i | \(0.418908\pi\) | |||||||
\(774\) | 17.9409 | 0.644871 | ||||||||
\(775\) | −16.1299 | −0.579403 | ||||||||
\(776\) | −9.10294 | −0.326776 | ||||||||
\(777\) | −14.4218 | −0.517379 | ||||||||
\(778\) | −15.8497 | −0.568238 | ||||||||
\(779\) | 7.16495 | 0.256711 | ||||||||
\(780\) | −0.134737 | −0.00482436 | ||||||||
\(781\) | 69.1223 | 2.47339 | ||||||||
\(782\) | 10.3270 | 0.369292 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 13.2013 | 0.471475 | ||||||||
\(785\) | −19.2388 | −0.686661 | ||||||||
\(786\) | 7.66604 | 0.273439 | ||||||||
\(787\) | 11.0327 | 0.393273 | 0.196637 | − | 0.980476i | \(-0.436998\pi\) | ||||
0.196637 | + | 0.980476i | \(0.436998\pi\) | |||||||
\(788\) | 0.0828822 | 0.00295256 | ||||||||
\(789\) | −0.748198 | −0.0266366 | ||||||||
\(790\) | 1.50628 | 0.0535910 | ||||||||
\(791\) | 38.3809 | 1.36467 | ||||||||
\(792\) | 14.3778 | 0.510894 | ||||||||
\(793\) | −3.82232 | −0.135734 | ||||||||
\(794\) | −31.9851 | −1.13511 | ||||||||
\(795\) | −5.21052 | −0.184798 | ||||||||
\(796\) | 0.682547 | 0.0241922 | ||||||||
\(797\) | 26.2929 | 0.931341 | 0.465670 | − | 0.884958i | \(-0.345813\pi\) | ||||
0.465670 | + | 0.884958i | \(0.345813\pi\) | |||||||
\(798\) | −1.91260 | −0.0677054 | ||||||||
\(799\) | −8.60116 | −0.304287 | ||||||||
\(800\) | 0.660638 | 0.0233571 | ||||||||
\(801\) | −9.66768 | −0.341591 | ||||||||
\(802\) | −20.5781 | −0.726637 | ||||||||
\(803\) | 71.9324 | 2.53844 | ||||||||
\(804\) | −0.510911 | −0.0180185 | ||||||||
\(805\) | 2.16340 | 0.0762500 | ||||||||
\(806\) | −23.0432 | −0.811664 | ||||||||
\(807\) | 5.29003 | 0.186218 | ||||||||
\(808\) | −4.05816 | −0.142766 | ||||||||
\(809\) | −29.4769 | −1.03635 | −0.518176 | − | 0.855274i | \(-0.673389\pi\) | ||||
−0.518176 | + | 0.855274i | \(0.673389\pi\) | |||||||
\(810\) | −1.58963 | −0.0558540 | ||||||||
\(811\) | −1.87348 | −0.0657866 | −0.0328933 | − | 0.999459i | \(-0.510472\pi\) | ||||
−0.0328933 | + | 0.999459i | \(0.510472\pi\) | |||||||
\(812\) | −0.0600106 | −0.00210596 | ||||||||
\(813\) | 25.5087 | 0.894628 | ||||||||
\(814\) | −53.4558 | −1.87363 | ||||||||
\(815\) | 8.65263 | 0.303088 | ||||||||
\(816\) | −28.9714 | −1.01420 | ||||||||
\(817\) | 9.12851 | 0.319366 | ||||||||
\(818\) | 39.6236 | 1.38541 | ||||||||
\(819\) | −7.22556 | −0.252481 | ||||||||
\(820\) | 0.357366 | 0.0124798 | ||||||||
\(821\) | 30.2249 | 1.05486 | 0.527429 | − | 0.849599i | \(-0.323156\pi\) | ||||
0.527429 | + | 0.849599i | \(0.323156\pi\) | |||||||
\(822\) | −16.3659 | −0.570826 | ||||||||
\(823\) | −52.7186 | −1.83765 | −0.918827 | − | 0.394661i | \(-0.870862\pi\) | ||||
−0.918827 | + | 0.394661i | \(0.870862\pi\) | |||||||
\(824\) | −11.8071 | −0.411318 | ||||||||
\(825\) | −18.7471 | −0.652692 | ||||||||
\(826\) | 11.9752 | 0.416670 | ||||||||
\(827\) | −22.5735 | −0.784957 | −0.392479 | − | 0.919761i | \(-0.628382\pi\) | ||||
−0.392479 | + | 0.919761i | \(0.628382\pi\) | |||||||
\(828\) | 0.0314276 | 0.00109218 | ||||||||
\(829\) | 21.7513 | 0.755453 | 0.377727 | − | 0.925917i | \(-0.376706\pi\) | ||||
0.377727 | + | 0.925917i | \(0.376706\pi\) | |||||||
\(830\) | −17.8987 | −0.621272 | ||||||||
\(831\) | −11.7482 | −0.407542 | ||||||||
\(832\) | 30.7329 | 1.06547 | ||||||||
\(833\) | −24.6855 | −0.855302 | ||||||||
\(834\) | −14.2916 | −0.494879 | ||||||||
\(835\) | 10.6174 | 0.367431 | ||||||||
\(836\) | 0.113177 | 0.00391432 | ||||||||
\(837\) | 4.34024 | 0.150021 | ||||||||
\(838\) | −6.56811 | −0.226892 | ||||||||
\(839\) | −2.97271 | −0.102629 | −0.0513146 | − | 0.998683i | \(-0.516341\pi\) | ||||
−0.0513146 | + | 0.998683i | \(0.516341\pi\) | |||||||
\(840\) | −6.16616 | −0.212753 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 31.9093 | 1.09967 | ||||||||
\(843\) | −12.3525 | −0.425444 | ||||||||
\(844\) | −0.426272 | −0.0146729 | ||||||||
\(845\) | 1.49427 | 0.0514045 | ||||||||
\(846\) | 1.63959 | 0.0563703 | ||||||||
\(847\) | −27.5860 | −0.947866 | ||||||||
\(848\) | 18.1023 | 0.621634 | ||||||||
\(849\) | 7.72479 | 0.265114 | ||||||||
\(850\) | 38.3788 | 1.31638 | ||||||||
\(851\) | −7.55271 | −0.258904 | ||||||||
\(852\) | −0.430638 | −0.0147534 | ||||||||
\(853\) | −30.9077 | −1.05826 | −0.529130 | − | 0.848540i | \(-0.677482\pi\) | ||||
−0.529130 | + | 0.848540i | \(0.677482\pi\) | |||||||
\(854\) | −2.70623 | −0.0926053 | ||||||||
\(855\) | −0.808822 | −0.0276611 | ||||||||
\(856\) | 1.99547 | 0.0682036 | ||||||||
\(857\) | −34.0716 | −1.16387 | −0.581933 | − | 0.813237i | \(-0.697703\pi\) | ||||
−0.581933 | + | 0.813237i | \(0.697703\pi\) | |||||||
\(858\) | −26.7822 | −0.914331 | ||||||||
\(859\) | −46.6389 | −1.59130 | −0.795650 | − | 0.605757i | \(-0.792871\pi\) | ||||
−0.795650 | + | 0.605757i | \(0.792871\pi\) | |||||||
\(860\) | 0.455302 | 0.0155257 | ||||||||
\(861\) | 19.1645 | 0.653125 | ||||||||
\(862\) | −1.95103 | −0.0664525 | ||||||||
\(863\) | −6.08275 | −0.207059 | −0.103530 | − | 0.994626i | \(-0.533014\pi\) | ||||
−0.103530 | + | 0.994626i | \(0.533014\pi\) | |||||||
\(864\) | −0.177765 | −0.00604768 | ||||||||
\(865\) | 16.5175 | 0.561612 | ||||||||
\(866\) | 31.3548 | 1.06548 | ||||||||
\(867\) | 37.1744 | 1.26251 | ||||||||
\(868\) | 0.260460 | 0.00884059 | ||||||||
\(869\) | −4.77998 | −0.162150 | ||||||||
\(870\) | 1.58963 | 0.0538936 | ||||||||
\(871\) | 61.5161 | 2.08440 | ||||||||
\(872\) | 26.3033 | 0.890743 | ||||||||
\(873\) | −3.19378 | −0.108093 | ||||||||
\(874\) | −1.00163 | −0.0338807 | ||||||||
\(875\) | 18.8570 | 0.637484 | ||||||||
\(876\) | −0.448145 | −0.0151414 | ||||||||
\(877\) | 32.2078 | 1.08758 | 0.543791 | − | 0.839221i | \(-0.316988\pi\) | ||||
0.543791 | + | 0.839221i | \(0.316988\pi\) | |||||||
\(878\) | 42.9349 | 1.44898 | ||||||||
\(879\) | 19.8822 | 0.670610 | ||||||||
\(880\) | −22.4962 | −0.758348 | ||||||||
\(881\) | −15.9775 | −0.538296 | −0.269148 | − | 0.963099i | \(-0.586742\pi\) | ||||
−0.269148 | + | 0.963099i | \(0.586742\pi\) | |||||||
\(882\) | 4.70566 | 0.158448 | ||||||||
\(883\) | −52.3366 | −1.76127 | −0.880633 | − | 0.473798i | \(-0.842883\pi\) | ||||
−0.880633 | + | 0.473798i | \(0.842883\pi\) | |||||||
\(884\) | −0.875312 | −0.0294399 | ||||||||
\(885\) | 5.06420 | 0.170231 | ||||||||
\(886\) | 14.0422 | 0.471756 | ||||||||
\(887\) | −34.9470 | −1.17340 | −0.586702 | − | 0.809803i | \(-0.699574\pi\) | ||||
−0.586702 | + | 0.809803i | \(0.699574\pi\) | |||||||
\(888\) | 21.5268 | 0.722393 | ||||||||
\(889\) | −4.78017 | −0.160322 | ||||||||
\(890\) | 15.3681 | 0.515138 | ||||||||
\(891\) | 5.04448 | 0.168997 | ||||||||
\(892\) | −0.304918 | −0.0102094 | ||||||||
\(893\) | 0.834241 | 0.0279168 | ||||||||
\(894\) | 4.97579 | 0.166415 | ||||||||
\(895\) | 1.95527 | 0.0653573 | ||||||||
\(896\) | 21.0802 | 0.704241 | ||||||||
\(897\) | −3.78403 | −0.126345 | ||||||||
\(898\) | 37.0956 | 1.23790 | ||||||||
\(899\) | −4.34024 | −0.144755 | ||||||||
\(900\) | 0.116796 | 0.00389321 | ||||||||
\(901\) | −33.8499 | −1.12770 | ||||||||
\(902\) | 71.0352 | 2.36521 | ||||||||
\(903\) | 24.4166 | 0.812532 | ||||||||
\(904\) | −57.2895 | −1.90542 | ||||||||
\(905\) | −13.7194 | −0.456048 | ||||||||
\(906\) | −12.6680 | −0.420866 | ||||||||
\(907\) | 34.1605 | 1.13428 | 0.567140 | − | 0.823622i | \(-0.308050\pi\) | ||||
0.567140 | + | 0.823622i | \(0.308050\pi\) | |||||||
\(908\) | 0.655023 | 0.0217377 | ||||||||
\(909\) | −1.42381 | −0.0472248 | ||||||||
\(910\) | 11.4860 | 0.380757 | ||||||||
\(911\) | −47.2422 | −1.56520 | −0.782601 | − | 0.622523i | \(-0.786108\pi\) | ||||
−0.782601 | + | 0.622523i | \(0.786108\pi\) | |||||||
\(912\) | 2.80999 | 0.0930480 | ||||||||
\(913\) | 56.7991 | 1.87977 | ||||||||
\(914\) | 19.5773 | 0.647560 | ||||||||
\(915\) | −1.14444 | −0.0378340 | ||||||||
\(916\) | −0.369523 | −0.0122094 | ||||||||
\(917\) | 10.4331 | 0.344530 | ||||||||
\(918\) | −10.3270 | −0.340841 | ||||||||
\(919\) | −57.8655 | −1.90881 | −0.954403 | − | 0.298522i | \(-0.903506\pi\) | ||||
−0.954403 | + | 0.298522i | \(0.903506\pi\) | |||||||
\(920\) | −3.22922 | −0.106464 | ||||||||
\(921\) | −23.7258 | −0.781790 | ||||||||
\(922\) | 16.4481 | 0.541690 | ||||||||
\(923\) | 51.8509 | 1.70669 | ||||||||
\(924\) | 0.302722 | 0.00995883 | ||||||||
\(925\) | −28.0686 | −0.922891 | ||||||||
\(926\) | 20.6077 | 0.677211 | ||||||||
\(927\) | −4.14252 | −0.136058 | ||||||||
\(928\) | 0.177765 | 0.00583541 | ||||||||
\(929\) | −4.71461 | −0.154681 | −0.0773406 | − | 0.997005i | \(-0.524643\pi\) | ||||
−0.0773406 | + | 0.997005i | \(0.524643\pi\) | |||||||
\(930\) | −6.89938 | −0.226240 | ||||||||
\(931\) | 2.39429 | 0.0784697 | ||||||||
\(932\) | 0.0302653 | 0.000991372 0 | ||||||||
\(933\) | 18.1409 | 0.593907 | ||||||||
\(934\) | −35.2444 | −1.15323 | ||||||||
\(935\) | 42.0663 | 1.37572 | ||||||||
\(936\) | 10.7853 | 0.352528 | ||||||||
\(937\) | −43.2695 | −1.41355 | −0.706776 | − | 0.707437i | \(-0.749851\pi\) | ||||
−0.706776 | + | 0.707437i | \(0.749851\pi\) | |||||||
\(938\) | 43.5539 | 1.42208 | ||||||||
\(939\) | 9.20479 | 0.300387 | ||||||||
\(940\) | 0.0416094 | 0.00135715 | ||||||||
\(941\) | 26.7756 | 0.872858 | 0.436429 | − | 0.899739i | \(-0.356243\pi\) | ||||
0.436429 | + | 0.899739i | \(0.356243\pi\) | |||||||
\(942\) | 23.8249 | 0.776259 | ||||||||
\(943\) | 10.0365 | 0.326833 | ||||||||
\(944\) | −17.5939 | −0.572633 | ||||||||
\(945\) | −2.16340 | −0.0703755 | ||||||||
\(946\) | 90.5024 | 2.94249 | ||||||||
\(947\) | 28.1314 | 0.914148 | 0.457074 | − | 0.889429i | \(-0.348898\pi\) | ||||
0.457074 | + | 0.889429i | \(0.348898\pi\) | |||||||
\(948\) | 0.0297797 | 0.000967199 0 | ||||||||
\(949\) | 53.9588 | 1.75158 | ||||||||
\(950\) | −3.72243 | −0.120771 | ||||||||
\(951\) | −17.6458 | −0.572205 | ||||||||
\(952\) | −40.0582 | −1.29829 | ||||||||
\(953\) | −20.0115 | −0.648238 | −0.324119 | − | 0.946016i | \(-0.605068\pi\) | ||||
−0.324119 | + | 0.946016i | \(0.605068\pi\) | |||||||
\(954\) | 6.45262 | 0.208911 | ||||||||
\(955\) | 20.5473 | 0.664895 | ||||||||
\(956\) | 0.905346 | 0.0292810 | ||||||||
\(957\) | −5.04448 | −0.163065 | ||||||||
\(958\) | 15.6001 | 0.504015 | ||||||||
\(959\) | −22.2731 | −0.719235 | ||||||||
\(960\) | 9.20173 | 0.296984 | ||||||||
\(961\) | −12.1624 | −0.392334 | ||||||||
\(962\) | −40.0990 | −1.29284 | ||||||||
\(963\) | 0.700112 | 0.0225608 | ||||||||
\(964\) | −0.369267 | −0.0118933 | ||||||||
\(965\) | −5.17157 | −0.166479 | ||||||||
\(966\) | −2.67912 | −0.0861993 | ||||||||
\(967\) | −40.3456 | −1.29743 | −0.648714 | − | 0.761032i | \(-0.724693\pi\) | ||||
−0.648714 | + | 0.761032i | \(0.724693\pi\) | |||||||
\(968\) | 41.1765 | 1.32346 | ||||||||
\(969\) | −5.25447 | −0.168798 | ||||||||
\(970\) | 5.07693 | 0.163010 | ||||||||
\(971\) | −14.3640 | −0.460961 | −0.230481 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230481 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(972\) | −0.0314276 | −0.00100804 | ||||||||
\(973\) | −19.4501 | −0.623543 | ||||||||
\(974\) | 44.3927 | 1.42244 | ||||||||
\(975\) | −14.0628 | −0.450371 | ||||||||
\(976\) | 3.97598 | 0.127268 | ||||||||
\(977\) | −26.5524 | −0.849487 | −0.424744 | − | 0.905314i | \(-0.639636\pi\) | ||||
−0.424744 | + | 0.905314i | \(0.639636\pi\) | |||||||
\(978\) | −10.7153 | −0.342636 | ||||||||
\(979\) | −48.7685 | −1.55865 | ||||||||
\(980\) | 0.119420 | 0.00381473 | ||||||||
\(981\) | 9.22855 | 0.294645 | ||||||||
\(982\) | −6.27898 | −0.200370 | ||||||||
\(983\) | 21.8041 | 0.695441 | 0.347721 | − | 0.937598i | \(-0.386956\pi\) | ||||
0.347721 | + | 0.937598i | \(0.386956\pi\) | |||||||
\(984\) | −28.6061 | −0.911928 | ||||||||
\(985\) | −2.98794 | −0.0952036 | ||||||||
\(986\) | 10.3270 | 0.328878 | ||||||||
\(987\) | 2.23139 | 0.0710261 | ||||||||
\(988\) | 0.0848980 | 0.00270097 | ||||||||
\(989\) | 12.7870 | 0.406602 | ||||||||
\(990\) | −8.01887 | −0.254856 | ||||||||
\(991\) | 30.5663 | 0.970969 | 0.485485 | − | 0.874245i | \(-0.338643\pi\) | ||||
0.485485 | + | 0.874245i | \(0.338643\pi\) | |||||||
\(992\) | −0.771541 | −0.0244964 | ||||||||
\(993\) | 9.43619 | 0.299448 | ||||||||
\(994\) | 36.7108 | 1.16440 | ||||||||
\(995\) | −24.6061 | −0.780065 | ||||||||
\(996\) | −0.353863 | −0.0112126 | ||||||||
\(997\) | −37.1186 | −1.17556 | −0.587779 | − | 0.809021i | \(-0.699998\pi\) | ||||
−0.587779 | + | 0.809021i | \(0.699998\pi\) | |||||||
\(998\) | 35.0113 | 1.10826 | ||||||||
\(999\) | 7.55271 | 0.238957 |
(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 | 2001.2.a.n.1.6 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.r.1.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.r.1.11 | 16 | 3.2 | odd | 2 |