Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.13183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.13183 | 1.50743 | 0.753714 | − | 0.657203i | \(-0.228260\pi\) | ||||
0.753714 | + | 0.657203i | \(0.228260\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.54468 | 1.27234 | ||||||||
\(5\) | −2.36072 | −1.05575 | −0.527873 | − | 0.849324i | \(-0.677010\pi\) | ||||
−0.527873 | + | 0.849324i | \(0.677010\pi\) | |||||||
\(6\) | −2.13183 | −0.870314 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.16116 | 0.410532 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.03264 | −1.59146 | ||||||||
\(11\) | 4.44436 | 1.34002 | 0.670012 | − | 0.742350i | \(-0.266289\pi\) | ||||
0.670012 | + | 0.742350i | \(0.266289\pi\) | |||||||
\(12\) | −2.54468 | −0.734586 | ||||||||
\(13\) | 0.290057 | 0.0804475 | 0.0402237 | − | 0.999191i | \(-0.487193\pi\) | ||||
0.0402237 | + | 0.999191i | \(0.487193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36072 | 0.609535 | ||||||||
\(16\) | −2.61397 | −0.653492 | ||||||||
\(17\) | −1.80941 | −0.438847 | −0.219423 | − | 0.975630i | \(-0.570418\pi\) | ||||
−0.219423 | + | 0.975630i | \(0.570418\pi\) | |||||||
\(18\) | 2.13183 | 0.502476 | ||||||||
\(19\) | −4.99859 | −1.14675 | −0.573377 | − | 0.819291i | \(-0.694367\pi\) | ||||
−0.573377 | + | 0.819291i | \(0.694367\pi\) | |||||||
\(20\) | −6.00727 | −1.34327 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.47459 | 2.01999 | ||||||||
\(23\) | −1.55849 | −0.324968 | −0.162484 | − | 0.986711i | \(-0.551951\pi\) | ||||
−0.162484 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(24\) | −1.16116 | −0.237021 | ||||||||
\(25\) | 0.572989 | 0.114598 | ||||||||
\(26\) | 0.618352 | 0.121269 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.05686 | 1.49612 | 0.748060 | − | 0.663631i | \(-0.230985\pi\) | ||||
0.748060 | + | 0.663631i | \(0.230985\pi\) | |||||||
\(30\) | 5.03264 | 0.918830 | ||||||||
\(31\) | 9.92711 | 1.78296 | 0.891481 | − | 0.453058i | \(-0.149667\pi\) | ||||
0.891481 | + | 0.453058i | \(0.149667\pi\) | |||||||
\(32\) | −7.89484 | −1.39562 | ||||||||
\(33\) | −4.44436 | −0.773663 | ||||||||
\(34\) | −3.85735 | −0.661530 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.54468 | 0.424113 | ||||||||
\(37\) | 6.77139 | 1.11321 | 0.556605 | − | 0.830777i | \(-0.312104\pi\) | ||||
0.556605 | + | 0.830777i | \(0.312104\pi\) | |||||||
\(38\) | −10.6561 | −1.72865 | ||||||||
\(39\) | −0.290057 | −0.0464464 | ||||||||
\(40\) | −2.74117 | −0.433417 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.70057 | −1.02183 | −0.510914 | − | 0.859632i | \(-0.670693\pi\) | ||||
−0.510914 | + | 0.859632i | \(0.670693\pi\) | |||||||
\(44\) | 11.3095 | 1.70497 | ||||||||
\(45\) | −2.36072 | −0.351915 | ||||||||
\(46\) | −3.32244 | −0.489866 | ||||||||
\(47\) | −0.0265330 | −0.00387024 | −0.00193512 | − | 0.999998i | \(-0.500616\pi\) | ||||
−0.00193512 | + | 0.999998i | \(0.500616\pi\) | |||||||
\(48\) | 2.61397 | 0.377294 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.22151 | 0.172748 | ||||||||
\(51\) | 1.80941 | 0.253368 | ||||||||
\(52\) | 0.738103 | 0.102356 | ||||||||
\(53\) | −2.59306 | −0.356185 | −0.178092 | − | 0.984014i | \(-0.556993\pi\) | ||||
−0.178092 | + | 0.984014i | \(0.556993\pi\) | |||||||
\(54\) | −2.13183 | −0.290105 | ||||||||
\(55\) | −10.4919 | −1.41472 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.99859 | 0.662079 | ||||||||
\(58\) | 17.1758 | 2.25529 | ||||||||
\(59\) | 12.0597 | 1.57004 | 0.785020 | − | 0.619470i | \(-0.212653\pi\) | ||||
0.785020 | + | 0.619470i | \(0.212653\pi\) | |||||||
\(60\) | 6.00727 | 0.775535 | ||||||||
\(61\) | −1.73842 | −0.222582 | −0.111291 | − | 0.993788i | \(-0.535499\pi\) | ||||
−0.111291 | + | 0.993788i | \(0.535499\pi\) | |||||||
\(62\) | 21.1629 | 2.68769 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.6025 | −1.45031 | ||||||||
\(65\) | −0.684744 | −0.0849320 | ||||||||
\(66\) | −9.47459 | −1.16624 | ||||||||
\(67\) | 13.8400 | 1.69082 | 0.845412 | − | 0.534115i | \(-0.179355\pi\) | ||||
0.845412 | + | 0.534115i | \(0.179355\pi\) | |||||||
\(68\) | −4.60437 | −0.558362 | ||||||||
\(69\) | 1.55849 | 0.187621 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2484 | −1.21626 | −0.608131 | − | 0.793837i | \(-0.708080\pi\) | ||||
−0.608131 | + | 0.793837i | \(0.708080\pi\) | |||||||
\(72\) | 1.16116 | 0.136844 | ||||||||
\(73\) | 7.01139 | 0.820621 | 0.410310 | − | 0.911946i | \(-0.365420\pi\) | ||||
0.410310 | + | 0.911946i | \(0.365420\pi\) | |||||||
\(74\) | 14.4354 | 1.67808 | ||||||||
\(75\) | −0.572989 | −0.0661631 | ||||||||
\(76\) | −12.7198 | −1.45906 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.618352 | −0.0700146 | ||||||||
\(79\) | 14.8949 | 1.67580 | 0.837901 | − | 0.545822i | \(-0.183783\pi\) | ||||
0.837901 | + | 0.545822i | \(0.183783\pi\) | |||||||
\(80\) | 6.17084 | 0.689921 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.13183 | −0.235421 | ||||||||
\(83\) | −6.61380 | −0.725959 | −0.362979 | − | 0.931797i | \(-0.618240\pi\) | ||||
−0.362979 | + | 0.931797i | \(0.618240\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.27151 | 0.463310 | ||||||||
\(86\) | −14.2844 | −1.54033 | ||||||||
\(87\) | −8.05686 | −0.863786 | ||||||||
\(88\) | 5.16061 | 0.550123 | ||||||||
\(89\) | 13.1333 | 1.39213 | 0.696066 | − | 0.717978i | \(-0.254932\pi\) | ||||
0.696066 | + | 0.717978i | \(0.254932\pi\) | |||||||
\(90\) | −5.03264 | −0.530487 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.96587 | −0.413470 | ||||||||
\(93\) | −9.92711 | −1.02939 | ||||||||
\(94\) | −0.0565637 | −0.00583410 | ||||||||
\(95\) | 11.8003 | 1.21068 | ||||||||
\(96\) | 7.89484 | 0.805764 | ||||||||
\(97\) | 4.50954 | 0.457874 | 0.228937 | − | 0.973441i | \(-0.426475\pi\) | ||||
0.228937 | + | 0.973441i | \(0.426475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.44436 | 0.446675 | ||||||||
\(100\) | 1.45807 | 0.145807 | ||||||||
\(101\) | −14.8611 | −1.47873 | −0.739366 | − | 0.673304i | \(-0.764875\pi\) | ||||
−0.739366 | + | 0.673304i | \(0.764875\pi\) | |||||||
\(102\) | 3.85735 | 0.381934 | ||||||||
\(103\) | 2.74435 | 0.270409 | 0.135205 | − | 0.990818i | \(-0.456831\pi\) | ||||
0.135205 | + | 0.990818i | \(0.456831\pi\) | |||||||
\(104\) | 0.336803 | 0.0330263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.52796 | −0.536923 | ||||||||
\(107\) | 3.07941 | 0.297698 | 0.148849 | − | 0.988860i | \(-0.452443\pi\) | ||||
0.148849 | + | 0.988860i | \(0.452443\pi\) | |||||||
\(108\) | −2.54468 | −0.244862 | ||||||||
\(109\) | −10.8608 | −1.04027 | −0.520137 | − | 0.854083i | \(-0.674119\pi\) | ||||
−0.520137 | + | 0.854083i | \(0.674119\pi\) | |||||||
\(110\) | −22.3668 | −2.13259 | ||||||||
\(111\) | −6.77139 | −0.642712 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.65327 | 0.531815 | 0.265907 | − | 0.963999i | \(-0.414328\pi\) | ||||
0.265907 | + | 0.963999i | \(0.414328\pi\) | |||||||
\(114\) | 10.6561 | 0.998036 | ||||||||
\(115\) | 3.67916 | 0.343084 | ||||||||
\(116\) | 20.5021 | 1.90357 | ||||||||
\(117\) | 0.290057 | 0.0268158 | ||||||||
\(118\) | 25.7092 | 2.36672 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.74117 | 0.250234 | ||||||||
\(121\) | 8.75230 | 0.795664 | ||||||||
\(122\) | −3.70601 | −0.335527 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 25.2613 | 2.26853 | ||||||||
\(125\) | 10.4509 | 0.934759 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.66494 | 0.147739 | 0.0738697 | − | 0.997268i | \(-0.476465\pi\) | ||||
0.0738697 | + | 0.997268i | \(0.476465\pi\) | |||||||
\(128\) | −8.94479 | −0.790616 | ||||||||
\(129\) | 6.70057 | 0.589952 | ||||||||
\(130\) | −1.45975 | −0.128029 | ||||||||
\(131\) | 20.1673 | 1.76202 | 0.881012 | − | 0.473094i | \(-0.156863\pi\) | ||||
0.881012 | + | 0.473094i | \(0.156863\pi\) | |||||||
\(132\) | −11.3095 | −0.984362 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 29.5044 | 2.54879 | ||||||||
\(135\) | 2.36072 | 0.203178 | ||||||||
\(136\) | −2.10102 | −0.180161 | ||||||||
\(137\) | 14.2458 | 1.21710 | 0.608551 | − | 0.793515i | \(-0.291751\pi\) | ||||
0.608551 | + | 0.793515i | \(0.291751\pi\) | |||||||
\(138\) | 3.32244 | 0.282825 | ||||||||
\(139\) | −11.5913 | −0.983159 | −0.491580 | − | 0.870833i | \(-0.663580\pi\) | ||||
−0.491580 | + | 0.870833i | \(0.663580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0265330 | 0.00223448 | ||||||||
\(142\) | −21.8478 | −1.83343 | ||||||||
\(143\) | 1.28912 | 0.107802 | ||||||||
\(144\) | −2.61397 | −0.217831 | ||||||||
\(145\) | −19.0200 | −1.57952 | ||||||||
\(146\) | 14.9471 | 1.23703 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.2310 | 1.41638 | ||||||||
\(149\) | 17.0799 | 1.39924 | 0.699619 | − | 0.714516i | \(-0.253353\pi\) | ||||
0.699619 | + | 0.714516i | \(0.253353\pi\) | |||||||
\(150\) | −1.22151 | −0.0997361 | ||||||||
\(151\) | 4.28647 | 0.348828 | 0.174414 | − | 0.984672i | \(-0.444197\pi\) | ||||
0.174414 | + | 0.984672i | \(0.444197\pi\) | |||||||
\(152\) | −5.80416 | −0.470780 | ||||||||
\(153\) | −1.80941 | −0.146282 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.4351 | −1.88235 | ||||||||
\(156\) | −0.738103 | −0.0590955 | ||||||||
\(157\) | 5.53484 | 0.441728 | 0.220864 | − | 0.975305i | \(-0.429112\pi\) | ||||
0.220864 | + | 0.975305i | \(0.429112\pi\) | |||||||
\(158\) | 31.7532 | 2.52615 | ||||||||
\(159\) | 2.59306 | 0.205643 | ||||||||
\(160\) | 18.6375 | 1.47342 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.13183 | 0.167492 | ||||||||
\(163\) | 4.92782 | 0.385977 | 0.192988 | − | 0.981201i | \(-0.438182\pi\) | ||||
0.192988 | + | 0.981201i | \(0.438182\pi\) | |||||||
\(164\) | −2.54468 | −0.198706 | ||||||||
\(165\) | 10.4919 | 0.816791 | ||||||||
\(166\) | −14.0995 | −1.09433 | ||||||||
\(167\) | 11.0874 | 0.857966 | 0.428983 | − | 0.903313i | \(-0.358872\pi\) | ||||
0.428983 | + | 0.903313i | \(0.358872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9159 | −0.993528 | ||||||||
\(170\) | 9.10611 | 0.698407 | ||||||||
\(171\) | −4.99859 | −0.382251 | ||||||||
\(172\) | −17.0508 | −1.30011 | ||||||||
\(173\) | 15.4355 | 1.17354 | 0.586768 | − | 0.809755i | \(-0.300400\pi\) | ||||
0.586768 | + | 0.809755i | \(0.300400\pi\) | |||||||
\(174\) | −17.1758 | −1.30209 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.6174 | −0.875695 | ||||||||
\(177\) | −12.0597 | −0.906463 | ||||||||
\(178\) | 27.9980 | 2.09854 | ||||||||
\(179\) | 3.64551 | 0.272478 | 0.136239 | − | 0.990676i | \(-0.456498\pi\) | ||||
0.136239 | + | 0.990676i | \(0.456498\pi\) | |||||||
\(180\) | −6.00727 | −0.447755 | ||||||||
\(181\) | −3.63738 | −0.270364 | −0.135182 | − | 0.990821i | \(-0.543162\pi\) | ||||
−0.135182 | + | 0.990821i | \(0.543162\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.73842 | 0.128508 | ||||||||
\(184\) | −1.80966 | −0.133410 | ||||||||
\(185\) | −15.9853 | −1.17527 | ||||||||
\(186\) | −21.1629 | −1.55174 | ||||||||
\(187\) | −8.04167 | −0.588065 | ||||||||
\(188\) | −0.0675180 | −0.00492426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.1561 | 1.82501 | ||||||||
\(191\) | −10.3820 | −0.751212 | −0.375606 | − | 0.926779i | \(-0.622565\pi\) | ||||
−0.375606 | + | 0.926779i | \(0.622565\pi\) | |||||||
\(192\) | 11.6025 | 0.837337 | ||||||||
\(193\) | 19.0283 | 1.36969 | 0.684844 | − | 0.728690i | \(-0.259870\pi\) | ||||
0.684844 | + | 0.728690i | \(0.259870\pi\) | |||||||
\(194\) | 9.61354 | 0.690212 | ||||||||
\(195\) | 0.684744 | 0.0490355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.16377 | 0.510398 | 0.255199 | − | 0.966889i | \(-0.417859\pi\) | ||||
0.255199 | + | 0.966889i | \(0.417859\pi\) | |||||||
\(198\) | 9.47459 | 0.673330 | ||||||||
\(199\) | 4.63169 | 0.328332 | 0.164166 | − | 0.986433i | \(-0.447507\pi\) | ||||
0.164166 | + | 0.986433i | \(0.447507\pi\) | |||||||
\(200\) | 0.665332 | 0.0470461 | ||||||||
\(201\) | −13.8400 | −0.976197 | ||||||||
\(202\) | −31.6812 | −2.22908 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.60437 | 0.322370 | ||||||||
\(205\) | 2.36072 | 0.164880 | ||||||||
\(206\) | 5.85048 | 0.407622 | ||||||||
\(207\) | −1.55849 | −0.108323 | ||||||||
\(208\) | −0.758201 | −0.0525718 | ||||||||
\(209\) | −22.2155 | −1.53668 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.15161 | −0.0792801 | −0.0396401 | − | 0.999214i | \(-0.512621\pi\) | ||||
−0.0396401 | + | 0.999214i | \(0.512621\pi\) | |||||||
\(212\) | −6.59852 | −0.453188 | ||||||||
\(213\) | 10.2484 | 0.702209 | ||||||||
\(214\) | 6.56477 | 0.448759 | ||||||||
\(215\) | 15.8182 | 1.07879 | ||||||||
\(216\) | −1.16116 | −0.0790069 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −23.1533 | −1.56814 | ||||||||
\(219\) | −7.01139 | −0.473786 | ||||||||
\(220\) | −26.6984 | −1.80001 | ||||||||
\(221\) | −0.524833 | −0.0353041 | ||||||||
\(222\) | −14.4354 | −0.968842 | ||||||||
\(223\) | 21.3568 | 1.43016 | 0.715080 | − | 0.699043i | \(-0.246390\pi\) | ||||
0.715080 | + | 0.699043i | \(0.246390\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.572989 | 0.0381993 | ||||||||
\(226\) | 12.0518 | 0.801672 | ||||||||
\(227\) | 0.453953 | 0.0301299 | 0.0150650 | − | 0.999887i | \(-0.495204\pi\) | ||||
0.0150650 | + | 0.999887i | \(0.495204\pi\) | |||||||
\(228\) | 12.7198 | 0.842389 | ||||||||
\(229\) | −18.5024 | −1.22268 | −0.611338 | − | 0.791370i | \(-0.709368\pi\) | ||||
−0.611338 | + | 0.791370i | \(0.709368\pi\) | |||||||
\(230\) | 7.84333 | 0.517174 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.35530 | 0.614206 | ||||||||
\(233\) | −0.886114 | −0.0580513 | −0.0290256 | − | 0.999579i | \(-0.509240\pi\) | ||||
−0.0290256 | + | 0.999579i | \(0.509240\pi\) | |||||||
\(234\) | 0.618352 | 0.0404229 | ||||||||
\(235\) | 0.0626370 | 0.00408598 | ||||||||
\(236\) | 30.6881 | 1.99762 | ||||||||
\(237\) | −14.8949 | −0.967525 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.3105 | −0.666930 | −0.333465 | − | 0.942763i | \(-0.608218\pi\) | ||||
−0.333465 | + | 0.942763i | \(0.608218\pi\) | |||||||
\(240\) | −6.17084 | −0.398326 | ||||||||
\(241\) | 10.7928 | 0.695227 | 0.347614 | − | 0.937638i | \(-0.386992\pi\) | ||||
0.347614 | + | 0.937638i | \(0.386992\pi\) | |||||||
\(242\) | 18.6584 | 1.19941 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.42373 | −0.283200 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.13183 | 0.135920 | ||||||||
\(247\) | −1.44988 | −0.0922535 | ||||||||
\(248\) | 11.5270 | 0.731963 | ||||||||
\(249\) | 6.61380 | 0.419133 | ||||||||
\(250\) | 22.2795 | 1.40908 | ||||||||
\(251\) | 13.9975 | 0.883513 | 0.441756 | − | 0.897135i | \(-0.354356\pi\) | ||||
0.441756 | + | 0.897135i | \(0.354356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.92650 | −0.435465 | ||||||||
\(254\) | 3.54936 | 0.222707 | ||||||||
\(255\) | −4.27151 | −0.267492 | ||||||||
\(256\) | 4.13624 | 0.258515 | ||||||||
\(257\) | −8.45313 | −0.527292 | −0.263646 | − | 0.964620i | \(-0.584925\pi\) | ||||
−0.263646 | + | 0.964620i | \(0.584925\pi\) | |||||||
\(258\) | 14.2844 | 0.889311 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.74245 | −0.108062 | ||||||||
\(261\) | 8.05686 | 0.498707 | ||||||||
\(262\) | 42.9931 | 2.65612 | ||||||||
\(263\) | −29.3309 | −1.80862 | −0.904310 | − | 0.426875i | \(-0.859614\pi\) | ||||
−0.904310 | + | 0.426875i | \(0.859614\pi\) | |||||||
\(264\) | −5.16061 | −0.317614 | ||||||||
\(265\) | 6.12149 | 0.376040 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.1333 | −0.803748 | ||||||||
\(268\) | 35.2183 | 2.15130 | ||||||||
\(269\) | −1.45573 | −0.0887573 | −0.0443787 | − | 0.999015i | \(-0.514131\pi\) | ||||
−0.0443787 | + | 0.999015i | \(0.514131\pi\) | |||||||
\(270\) | 5.03264 | 0.306277 | ||||||||
\(271\) | −30.5158 | −1.85370 | −0.926850 | − | 0.375432i | \(-0.877494\pi\) | ||||
−0.926850 | + | 0.375432i | \(0.877494\pi\) | |||||||
\(272\) | 4.72974 | 0.286783 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 30.3696 | 1.83469 | ||||||||
\(275\) | 2.54657 | 0.153564 | ||||||||
\(276\) | 3.96587 | 0.238717 | ||||||||
\(277\) | 29.2660 | 1.75842 | 0.879211 | − | 0.476433i | \(-0.158071\pi\) | ||||
0.879211 | + | 0.476433i | \(0.158071\pi\) | |||||||
\(278\) | −24.7106 | −1.48204 | ||||||||
\(279\) | 9.92711 | 0.594321 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6815 | −0.756512 | −0.378256 | − | 0.925701i | \(-0.623476\pi\) | ||||
−0.378256 | + | 0.925701i | \(0.623476\pi\) | |||||||
\(282\) | 0.0565637 | 0.00336832 | ||||||||
\(283\) | 26.4622 | 1.57301 | 0.786506 | − | 0.617583i | \(-0.211888\pi\) | ||||
0.786506 | + | 0.617583i | \(0.211888\pi\) | |||||||
\(284\) | −26.0789 | −1.54750 | ||||||||
\(285\) | −11.8003 | −0.698987 | ||||||||
\(286\) | 2.74818 | 0.162503 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.89484 | −0.465208 | ||||||||
\(289\) | −13.7260 | −0.807414 | ||||||||
\(290\) | −40.5472 | −2.38102 | ||||||||
\(291\) | −4.50954 | −0.264354 | ||||||||
\(292\) | 17.8417 | 1.04411 | ||||||||
\(293\) | −2.35974 | −0.137857 | −0.0689287 | − | 0.997622i | \(-0.521958\pi\) | ||||
−0.0689287 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4696 | −1.65756 | ||||||||
\(296\) | 7.86267 | 0.457008 | ||||||||
\(297\) | −4.44436 | −0.257888 | ||||||||
\(298\) | 36.4113 | 2.10925 | ||||||||
\(299\) | −0.452053 | −0.0261429 | ||||||||
\(300\) | −1.45807 | −0.0841819 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.13800 | 0.525833 | ||||||||
\(303\) | 14.8611 | 0.853747 | ||||||||
\(304\) | 13.0661 | 0.749395 | ||||||||
\(305\) | 4.10393 | 0.234990 | ||||||||
\(306\) | −3.85735 | −0.220510 | ||||||||
\(307\) | 10.3588 | 0.591205 | 0.295603 | − | 0.955311i | \(-0.404480\pi\) | ||||
0.295603 | + | 0.955311i | \(0.404480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.74435 | −0.156121 | ||||||||
\(310\) | −49.9596 | −2.83751 | ||||||||
\(311\) | 4.07018 | 0.230799 | 0.115399 | − | 0.993319i | \(-0.463185\pi\) | ||||
0.115399 | + | 0.993319i | \(0.463185\pi\) | |||||||
\(312\) | −0.336803 | −0.0190677 | ||||||||
\(313\) | 17.4202 | 0.984649 | 0.492324 | − | 0.870412i | \(-0.336147\pi\) | ||||
0.492324 | + | 0.870412i | \(0.336147\pi\) | |||||||
\(314\) | 11.7993 | 0.665874 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 37.9026 | 2.13219 | ||||||||
\(317\) | −28.1622 | −1.58175 | −0.790873 | − | 0.611980i | \(-0.790373\pi\) | ||||
−0.790873 | + | 0.611980i | \(0.790373\pi\) | |||||||
\(318\) | 5.52796 | 0.309993 | ||||||||
\(319\) | 35.8075 | 2.00484 | ||||||||
\(320\) | 27.3902 | 1.53116 | ||||||||
\(321\) | −3.07941 | −0.171876 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.04450 | 0.503249 | ||||||||
\(324\) | 2.54468 | 0.141371 | ||||||||
\(325\) | 0.166200 | 0.00921911 | ||||||||
\(326\) | 10.5052 | 0.581832 | ||||||||
\(327\) | 10.8608 | 0.600602 | ||||||||
\(328\) | −1.16116 | −0.0641143 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 22.3668 | 1.23125 | ||||||||
\(331\) | −9.65052 | −0.530441 | −0.265220 | − | 0.964188i | \(-0.585445\pi\) | ||||
−0.265220 | + | 0.964188i | \(0.585445\pi\) | |||||||
\(332\) | −16.8300 | −0.923666 | ||||||||
\(333\) | 6.77139 | 0.371070 | ||||||||
\(334\) | 23.6363 | 1.29332 | ||||||||
\(335\) | −32.6723 | −1.78508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.72939 | 0.475520 | 0.237760 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237760 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(338\) | −27.5344 | −1.49767 | ||||||||
\(339\) | −5.65327 | −0.307043 | ||||||||
\(340\) | 10.8696 | 0.589488 | ||||||||
\(341\) | 44.1196 | 2.38921 | ||||||||
\(342\) | −10.6561 | −0.576217 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.78044 | −0.419493 | ||||||||
\(345\) | −3.67916 | −0.198080 | ||||||||
\(346\) | 32.9057 | 1.76902 | ||||||||
\(347\) | 31.1565 | 1.67257 | 0.836284 | − | 0.548296i | \(-0.184723\pi\) | ||||
0.836284 | + | 0.548296i | \(0.184723\pi\) | |||||||
\(348\) | −20.5021 | −1.09903 | ||||||||
\(349\) | −5.77148 | −0.308940 | −0.154470 | − | 0.987997i | \(-0.549367\pi\) | ||||
−0.154470 | + | 0.987997i | \(0.549367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.290057 | −0.0154821 | ||||||||
\(352\) | −35.0875 | −1.87017 | ||||||||
\(353\) | 5.70652 | 0.303727 | 0.151864 | − | 0.988401i | \(-0.451473\pi\) | ||||
0.151864 | + | 0.988401i | \(0.451473\pi\) | |||||||
\(354\) | −25.7092 | −1.36643 | ||||||||
\(355\) | 24.1936 | 1.28406 | ||||||||
\(356\) | 33.4201 | 1.77126 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.77159 | 0.410741 | ||||||||
\(359\) | 14.2254 | 0.750789 | 0.375394 | − | 0.926865i | \(-0.377507\pi\) | ||||
0.375394 | + | 0.926865i | \(0.377507\pi\) | |||||||
\(360\) | −2.74117 | −0.144472 | ||||||||
\(361\) | 5.98587 | 0.315046 | ||||||||
\(362\) | −7.75426 | −0.407555 | ||||||||
\(363\) | −8.75230 | −0.459377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.5519 | −0.866367 | ||||||||
\(366\) | 3.70601 | 0.193716 | ||||||||
\(367\) | 13.5717 | 0.708438 | 0.354219 | − | 0.935163i | \(-0.384747\pi\) | ||||
0.354219 | + | 0.935163i | \(0.384747\pi\) | |||||||
\(368\) | 4.07385 | 0.212364 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −34.0779 | −1.77163 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −25.2613 | −1.30974 | ||||||||
\(373\) | −5.56422 | −0.288104 | −0.144052 | − | 0.989570i | \(-0.546013\pi\) | ||||
−0.144052 | + | 0.989570i | \(0.546013\pi\) | |||||||
\(374\) | −17.1434 | −0.886466 | ||||||||
\(375\) | −10.4509 | −0.539683 | ||||||||
\(376\) | −0.0308091 | −0.00158886 | ||||||||
\(377\) | 2.33695 | 0.120359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0210 | −1.23388 | −0.616939 | − | 0.787011i | \(-0.711627\pi\) | ||||
−0.616939 | + | 0.787011i | \(0.711627\pi\) | |||||||
\(380\) | 30.0279 | 1.54040 | ||||||||
\(381\) | −1.66494 | −0.0852974 | ||||||||
\(382\) | −22.1325 | −1.13240 | ||||||||
\(383\) | −22.6618 | −1.15797 | −0.578983 | − | 0.815340i | \(-0.696550\pi\) | ||||
−0.578983 | + | 0.815340i | \(0.696550\pi\) | |||||||
\(384\) | 8.94479 | 0.456462 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.5650 | 2.06471 | ||||||||
\(387\) | −6.70057 | −0.340609 | ||||||||
\(388\) | 11.4753 | 0.582571 | ||||||||
\(389\) | 14.8536 | 0.753106 | 0.376553 | − | 0.926395i | \(-0.377109\pi\) | ||||
0.376553 | + | 0.926395i | \(0.377109\pi\) | |||||||
\(390\) | 1.45975 | 0.0739175 | ||||||||
\(391\) | 2.81996 | 0.142611 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.1673 | −1.01731 | ||||||||
\(394\) | 15.2719 | 0.769388 | ||||||||
\(395\) | −35.1625 | −1.76922 | ||||||||
\(396\) | 11.3095 | 0.568322 | ||||||||
\(397\) | 31.7430 | 1.59313 | 0.796567 | − | 0.604551i | \(-0.206647\pi\) | ||||
0.796567 | + | 0.604551i | \(0.206647\pi\) | |||||||
\(398\) | 9.87395 | 0.494936 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.49778 | −0.0748888 | ||||||||
\(401\) | −14.5053 | −0.724360 | −0.362180 | − | 0.932108i | \(-0.617968\pi\) | ||||
−0.362180 | + | 0.932108i | \(0.617968\pi\) | |||||||
\(402\) | −29.5044 | −1.47155 | ||||||||
\(403\) | 2.87943 | 0.143435 | ||||||||
\(404\) | −37.8167 | −1.88145 | ||||||||
\(405\) | −2.36072 | −0.117305 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.0945 | 1.49173 | ||||||||
\(408\) | 2.10102 | 0.104016 | ||||||||
\(409\) | −14.3986 | −0.711965 | −0.355982 | − | 0.934493i | \(-0.615854\pi\) | ||||
−0.355982 | + | 0.934493i | \(0.615854\pi\) | |||||||
\(410\) | 5.03264 | 0.248544 | ||||||||
\(411\) | −14.2458 | −0.702694 | ||||||||
\(412\) | 6.98350 | 0.344052 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.32244 | −0.163289 | ||||||||
\(415\) | 15.6133 | 0.766428 | ||||||||
\(416\) | −2.28996 | −0.112274 | ||||||||
\(417\) | 11.5913 | 0.567627 | ||||||||
\(418\) | −47.3596 | −2.31643 | ||||||||
\(419\) | −30.8227 | −1.50579 | −0.752893 | − | 0.658143i | \(-0.771342\pi\) | ||||
−0.752893 | + | 0.658143i | \(0.771342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.694209 | −0.0338337 | −0.0169168 | − | 0.999857i | \(-0.505385\pi\) | ||||
−0.0169168 | + | 0.999857i | \(0.505385\pi\) | |||||||
\(422\) | −2.45503 | −0.119509 | ||||||||
\(423\) | −0.0265330 | −0.00129008 | ||||||||
\(424\) | −3.01096 | −0.146225 | ||||||||
\(425\) | −1.03677 | −0.0502909 | ||||||||
\(426\) | 21.8478 | 1.05853 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.83612 | 0.378773 | ||||||||
\(429\) | −1.28912 | −0.0622392 | ||||||||
\(430\) | 33.7215 | 1.62620 | ||||||||
\(431\) | −19.6946 | −0.948657 | −0.474328 | − | 0.880348i | \(-0.657309\pi\) | ||||
−0.474328 | + | 0.880348i | \(0.657309\pi\) | |||||||
\(432\) | 2.61397 | 0.125765 | ||||||||
\(433\) | −21.8904 | −1.05199 | −0.525993 | − | 0.850489i | \(-0.676306\pi\) | ||||
−0.525993 | + | 0.850489i | \(0.676306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.0200 | 0.911938 | ||||||||
\(436\) | −27.6372 | −1.32358 | ||||||||
\(437\) | 7.79027 | 0.372659 | ||||||||
\(438\) | −14.9471 | −0.714198 | ||||||||
\(439\) | −3.09324 | −0.147632 | −0.0738161 | − | 0.997272i | \(-0.523518\pi\) | ||||
−0.0738161 | + | 0.997272i | \(0.523518\pi\) | |||||||
\(440\) | −12.1827 | −0.580790 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.11885 | −0.0532184 | ||||||||
\(443\) | −28.9415 | −1.37505 | −0.687526 | − | 0.726159i | \(-0.741303\pi\) | ||||
−0.687526 | + | 0.726159i | \(0.741303\pi\) | |||||||
\(444\) | −17.2310 | −0.817748 | ||||||||
\(445\) | −31.0041 | −1.46974 | ||||||||
\(446\) | 45.5290 | 2.15586 | ||||||||
\(447\) | −17.0799 | −0.807851 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2696 | −1.19255 | −0.596274 | − | 0.802781i | \(-0.703353\pi\) | ||||
−0.596274 | + | 0.802781i | \(0.703353\pi\) | |||||||
\(450\) | 1.22151 | 0.0575827 | ||||||||
\(451\) | −4.44436 | −0.209277 | ||||||||
\(452\) | 14.3857 | 0.676649 | ||||||||
\(453\) | −4.28647 | −0.201396 | ||||||||
\(454\) | 0.967749 | 0.0454187 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.80416 | 0.271805 | ||||||||
\(457\) | −10.0789 | −0.471473 | −0.235736 | − | 0.971817i | \(-0.575750\pi\) | ||||
−0.235736 | + | 0.971817i | \(0.575750\pi\) | |||||||
\(458\) | −39.4440 | −1.84310 | ||||||||
\(459\) | 1.80941 | 0.0844561 | ||||||||
\(460\) | 9.36229 | 0.436519 | ||||||||
\(461\) | −0.973232 | −0.0453279 | −0.0226640 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226640 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9337 | 0.647553 | 0.323776 | − | 0.946134i | \(-0.395047\pi\) | ||||
0.323776 | + | 0.946134i | \(0.395047\pi\) | |||||||
\(464\) | −21.0604 | −0.977702 | ||||||||
\(465\) | 23.4351 | 1.08678 | ||||||||
\(466\) | −1.88904 | −0.0875081 | ||||||||
\(467\) | −2.67442 | −0.123758 | −0.0618788 | − | 0.998084i | \(-0.519709\pi\) | ||||
−0.0618788 | + | 0.998084i | \(0.519709\pi\) | |||||||
\(468\) | 0.738103 | 0.0341188 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.133531 | 0.00615933 | ||||||||
\(471\) | −5.53484 | −0.255032 | ||||||||
\(472\) | 14.0033 | 0.644552 | ||||||||
\(473\) | −29.7797 | −1.36927 | ||||||||
\(474\) | −31.7532 | −1.45847 | ||||||||
\(475\) | −2.86414 | −0.131416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.59306 | −0.118728 | ||||||||
\(478\) | −21.9801 | −1.00535 | ||||||||
\(479\) | −7.15536 | −0.326937 | −0.163468 | − | 0.986549i | \(-0.552268\pi\) | ||||
−0.163468 | + | 0.986549i | \(0.552268\pi\) | |||||||
\(480\) | −18.6375 | −0.850681 | ||||||||
\(481\) | 1.96409 | 0.0895549 | ||||||||
\(482\) | 23.0084 | 1.04801 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.2718 | 1.01235 | ||||||||
\(485\) | −10.6457 | −0.483398 | ||||||||
\(486\) | −2.13183 | −0.0967016 | ||||||||
\(487\) | 38.5585 | 1.74725 | 0.873625 | − | 0.486599i | \(-0.161763\pi\) | ||||
0.873625 | + | 0.486599i | \(0.161763\pi\) | |||||||
\(488\) | −2.01859 | −0.0913772 | ||||||||
\(489\) | −4.92782 | −0.222844 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.3676 | −1.82176 | −0.910882 | − | 0.412667i | \(-0.864597\pi\) | ||||
−0.910882 | + | 0.412667i | \(0.864597\pi\) | |||||||
\(492\) | 2.54468 | 0.114723 | ||||||||
\(493\) | −14.5782 | −0.656568 | ||||||||
\(494\) | −3.09089 | −0.139066 | ||||||||
\(495\) | −10.4919 | −0.471575 | ||||||||
\(496\) | −25.9491 | −1.16515 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.0995 | 0.631812 | ||||||||
\(499\) | 12.9878 | 0.581414 | 0.290707 | − | 0.956812i | \(-0.406110\pi\) | ||||
0.290707 | + | 0.956812i | \(0.406110\pi\) | |||||||
\(500\) | 26.5942 | 1.18933 | ||||||||
\(501\) | −11.0874 | −0.495347 | ||||||||
\(502\) | 29.8402 | 1.33183 | ||||||||
\(503\) | 28.4964 | 1.27059 | 0.635296 | − | 0.772269i | \(-0.280878\pi\) | ||||
0.635296 | + | 0.772269i | \(0.280878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.0828 | 1.56116 | ||||||||
\(506\) | −14.7661 | −0.656433 | ||||||||
\(507\) | 12.9159 | 0.573614 | ||||||||
\(508\) | 4.23674 | 0.187975 | ||||||||
\(509\) | 3.91314 | 0.173447 | 0.0867235 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867235 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(510\) | −9.10611 | −0.403225 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 26.7073 | 1.18031 | ||||||||
\(513\) | 4.99859 | 0.220693 | ||||||||
\(514\) | −18.0206 | −0.794854 | ||||||||
\(515\) | −6.47864 | −0.285483 | ||||||||
\(516\) | 17.0508 | 0.750620 | ||||||||
\(517\) | −0.117922 | −0.00518621 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.4355 | −0.677542 | ||||||||
\(520\) | −0.795097 | −0.0348673 | ||||||||
\(521\) | −29.5289 | −1.29369 | −0.646843 | − | 0.762624i | \(-0.723911\pi\) | ||||
−0.646843 | + | 0.762624i | \(0.723911\pi\) | |||||||
\(522\) | 17.1758 | 0.751765 | ||||||||
\(523\) | 38.8288 | 1.69786 | 0.848932 | − | 0.528502i | \(-0.177246\pi\) | ||||
0.848932 | + | 0.528502i | \(0.177246\pi\) | |||||||
\(524\) | 51.3193 | 2.24189 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −62.5284 | −2.72637 | ||||||||
\(527\) | −17.9622 | −0.782447 | ||||||||
\(528\) | 11.6174 | 0.505582 | ||||||||
\(529\) | −20.5711 | −0.894396 | ||||||||
\(530\) | 13.0500 | 0.566854 | ||||||||
\(531\) | 12.0597 | 0.523347 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.290057 | −0.0125638 | ||||||||
\(534\) | −27.9980 | −1.21159 | ||||||||
\(535\) | −7.26963 | −0.314293 | ||||||||
\(536\) | 16.0704 | 0.694137 | ||||||||
\(537\) | −3.64551 | −0.157315 | ||||||||
\(538\) | −3.10336 | −0.133795 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.00727 | 0.258512 | ||||||||
\(541\) | −23.2651 | −1.00025 | −0.500123 | − | 0.865954i | \(-0.666712\pi\) | ||||
−0.500123 | + | 0.865954i | \(0.666712\pi\) | |||||||
\(542\) | −65.0543 | −2.79432 | ||||||||
\(543\) | 3.63738 | 0.156095 | ||||||||
\(544\) | 14.2850 | 0.612465 | ||||||||
\(545\) | 25.6392 | 1.09826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.34737 | −0.356908 | −0.178454 | − | 0.983948i | \(-0.557110\pi\) | ||||
−0.178454 | + | 0.983948i | \(0.557110\pi\) | |||||||
\(548\) | 36.2510 | 1.54857 | ||||||||
\(549\) | −1.73842 | −0.0741941 | ||||||||
\(550\) | 5.42884 | 0.231486 | ||||||||
\(551\) | −40.2729 | −1.71568 | ||||||||
\(552\) | 1.80966 | 0.0770243 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 62.3899 | 2.65069 | ||||||||
\(555\) | 15.9853 | 0.678540 | ||||||||
\(556\) | −29.4961 | −1.25091 | ||||||||
\(557\) | −8.69009 | −0.368211 | −0.184106 | − | 0.982906i | \(-0.558939\pi\) | ||||
−0.184106 | + | 0.982906i | \(0.558939\pi\) | |||||||
\(558\) | 21.1629 | 0.895896 | ||||||||
\(559\) | −1.94355 | −0.0822034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.04167 | 0.339519 | ||||||||
\(562\) | −27.0347 | −1.14039 | ||||||||
\(563\) | −35.6405 | −1.50207 | −0.751034 | − | 0.660263i | \(-0.770445\pi\) | ||||
−0.751034 | + | 0.660263i | \(0.770445\pi\) | |||||||
\(564\) | 0.0675180 | 0.00284302 | ||||||||
\(565\) | −13.3458 | −0.561461 | ||||||||
\(566\) | 56.4127 | 2.37120 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.9000 | −0.499315 | ||||||||
\(569\) | −2.01831 | −0.0846120 | −0.0423060 | − | 0.999105i | \(-0.513470\pi\) | ||||
−0.0423060 | + | 0.999105i | \(0.513470\pi\) | |||||||
\(570\) | −25.1561 | −1.05367 | ||||||||
\(571\) | 45.5386 | 1.90573 | 0.952866 | − | 0.303392i | \(-0.0981193\pi\) | ||||
0.952866 | + | 0.303392i | \(0.0981193\pi\) | |||||||
\(572\) | 3.28039 | 0.137160 | ||||||||
\(573\) | 10.3820 | 0.433713 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.893000 | −0.0372407 | ||||||||
\(576\) | −11.6025 | −0.483437 | ||||||||
\(577\) | −12.2375 | −0.509454 | −0.254727 | − | 0.967013i | \(-0.581986\pi\) | ||||
−0.254727 | + | 0.967013i | \(0.581986\pi\) | |||||||
\(578\) | −29.2615 | −1.21712 | ||||||||
\(579\) | −19.0283 | −0.790789 | ||||||||
\(580\) | −48.3997 | −2.00969 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.61354 | −0.398494 | ||||||||
\(583\) | −11.5245 | −0.477296 | ||||||||
\(584\) | 8.14134 | 0.336891 | ||||||||
\(585\) | −0.684744 | −0.0283107 | ||||||||
\(586\) | −5.03055 | −0.207810 | ||||||||
\(587\) | 19.8859 | 0.820777 | 0.410389 | − | 0.911911i | \(-0.365393\pi\) | ||||
0.410389 | + | 0.911911i | \(0.365393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.6215 | −2.04462 | ||||||||
\(590\) | −60.6921 | −2.49866 | ||||||||
\(591\) | −7.16377 | −0.294678 | ||||||||
\(592\) | −17.7002 | −0.727473 | ||||||||
\(593\) | 9.29758 | 0.381806 | 0.190903 | − | 0.981609i | \(-0.438858\pi\) | ||||
0.190903 | + | 0.981609i | \(0.438858\pi\) | |||||||
\(594\) | −9.47459 | −0.388747 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43.4628 | 1.78031 | ||||||||
\(597\) | −4.63169 | −0.189562 | ||||||||
\(598\) | −0.963698 | −0.0394085 | ||||||||
\(599\) | −14.3452 | −0.586127 | −0.293063 | − | 0.956093i | \(-0.594675\pi\) | ||||
−0.293063 | + | 0.956093i | \(0.594675\pi\) | |||||||
\(600\) | −0.665332 | −0.0271621 | ||||||||
\(601\) | −24.4136 | −0.995851 | −0.497925 | − | 0.867220i | \(-0.665905\pi\) | ||||
−0.497925 | + | 0.867220i | \(0.665905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.8400 | 0.563608 | ||||||||
\(604\) | 10.9077 | 0.443827 | ||||||||
\(605\) | −20.6617 | −0.840018 | ||||||||
\(606\) | 31.6812 | 1.28696 | ||||||||
\(607\) | 6.54301 | 0.265573 | 0.132786 | − | 0.991145i | \(-0.457608\pi\) | ||||
0.132786 | + | 0.991145i | \(0.457608\pi\) | |||||||
\(608\) | 39.4631 | 1.60044 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.74886 | 0.354231 | ||||||||
\(611\) | −0.00769610 | −0.000311351 0 | ||||||||
\(612\) | −4.60437 | −0.186121 | ||||||||
\(613\) | −4.74967 | −0.191837 | −0.0959186 | − | 0.995389i | \(-0.530579\pi\) | ||||
−0.0959186 | + | 0.995389i | \(0.530579\pi\) | |||||||
\(614\) | 22.0830 | 0.891199 | ||||||||
\(615\) | −2.36072 | −0.0951933 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.3997 | −1.62643 | −0.813216 | − | 0.581962i | \(-0.802285\pi\) | ||||
−0.813216 | + | 0.581962i | \(0.802285\pi\) | |||||||
\(618\) | −5.85048 | −0.235341 | ||||||||
\(619\) | −26.1618 | −1.05153 | −0.525766 | − | 0.850629i | \(-0.676221\pi\) | ||||
−0.525766 | + | 0.850629i | \(0.676221\pi\) | |||||||
\(620\) | −59.6348 | −2.39499 | ||||||||
\(621\) | 1.55849 | 0.0625402 | ||||||||
\(622\) | 8.67691 | 0.347913 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.758201 | 0.0303523 | ||||||||
\(625\) | −27.5366 | −1.10147 | ||||||||
\(626\) | 37.1369 | 1.48429 | ||||||||
\(627\) | 22.2155 | 0.887202 | ||||||||
\(628\) | 14.0844 | 0.562028 | ||||||||
\(629\) | −12.2522 | −0.488528 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0225 | −1.11556 | −0.557778 | − | 0.829990i | \(-0.688346\pi\) | ||||
−0.557778 | + | 0.829990i | \(0.688346\pi\) | |||||||
\(632\) | 17.2953 | 0.687970 | ||||||||
\(633\) | 1.15161 | 0.0457724 | ||||||||
\(634\) | −60.0369 | −2.38437 | ||||||||
\(635\) | −3.93045 | −0.155975 | ||||||||
\(636\) | 6.59852 | 0.261648 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 76.3354 | 3.02215 | ||||||||
\(639\) | −10.2484 | −0.405421 | ||||||||
\(640\) | 21.1161 | 0.834689 | ||||||||
\(641\) | 0.737870 | 0.0291441 | 0.0145721 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145721 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(642\) | −6.56477 | −0.259091 | ||||||||
\(643\) | 34.8978 | 1.37624 | 0.688118 | − | 0.725599i | \(-0.258437\pi\) | ||||
0.688118 | + | 0.725599i | \(0.258437\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.8182 | −0.622839 | ||||||||
\(646\) | 19.2813 | 0.758612 | ||||||||
\(647\) | −11.0952 | −0.436197 | −0.218098 | − | 0.975927i | \(-0.569985\pi\) | ||||
−0.218098 | + | 0.975927i | \(0.569985\pi\) | |||||||
\(648\) | 1.16116 | 0.0456147 | ||||||||
\(649\) | 53.5976 | 2.10389 | ||||||||
\(650\) | 0.354309 | 0.0138971 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5397 | 0.491093 | ||||||||
\(653\) | −5.40616 | −0.211559 | −0.105780 | − | 0.994390i | \(-0.533734\pi\) | ||||
−0.105780 | + | 0.994390i | \(0.533734\pi\) | |||||||
\(654\) | 23.1533 | 0.905365 | ||||||||
\(655\) | −47.6093 | −1.86025 | ||||||||
\(656\) | 2.61397 | 0.102058 | ||||||||
\(657\) | 7.01139 | 0.273540 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.2471 | −1.06140 | −0.530698 | − | 0.847561i | \(-0.678070\pi\) | ||||
−0.530698 | + | 0.847561i | \(0.678070\pi\) | |||||||
\(660\) | 26.6984 | 1.03924 | ||||||||
\(661\) | 37.0310 | 1.44034 | 0.720169 | − | 0.693799i | \(-0.244064\pi\) | ||||
0.720169 | + | 0.693799i | \(0.244064\pi\) | |||||||
\(662\) | −20.5732 | −0.799601 | ||||||||
\(663\) | 0.524833 | 0.0203828 | ||||||||
\(664\) | −7.67968 | −0.298029 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.4354 | 0.559361 | ||||||||
\(667\) | −12.5566 | −0.486192 | ||||||||
\(668\) | 28.2138 | 1.09162 | ||||||||
\(669\) | −21.3568 | −0.825703 | ||||||||
\(670\) | −69.6516 | −2.69088 | ||||||||
\(671\) | −7.72617 | −0.298266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1780 | 1.43311 | 0.716554 | − | 0.697532i | \(-0.245719\pi\) | ||||
0.716554 | + | 0.697532i | \(0.245719\pi\) | |||||||
\(674\) | 18.6095 | 0.716813 | ||||||||
\(675\) | −0.572989 | −0.0220544 | ||||||||
\(676\) | −32.8667 | −1.26411 | ||||||||
\(677\) | 13.6605 | 0.525017 | 0.262508 | − | 0.964930i | \(-0.415450\pi\) | ||||
0.262508 | + | 0.964930i | \(0.415450\pi\) | |||||||
\(678\) | −12.0518 | −0.462846 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.95991 | 0.190204 | ||||||||
\(681\) | −0.453953 | −0.0173955 | ||||||||
\(682\) | 94.0553 | 3.60156 | ||||||||
\(683\) | −24.8142 | −0.949489 | −0.474744 | − | 0.880124i | \(-0.657459\pi\) | ||||
−0.474744 | + | 0.880124i | \(0.657459\pi\) | |||||||
\(684\) | −12.7198 | −0.486354 | ||||||||
\(685\) | −33.6303 | −1.28495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.5024 | 0.705912 | ||||||||
\(688\) | 17.5151 | 0.667756 | ||||||||
\(689\) | −0.752138 | −0.0286542 | ||||||||
\(690\) | −7.84333 | −0.298591 | ||||||||
\(691\) | 4.35305 | 0.165598 | 0.0827989 | − | 0.996566i | \(-0.473614\pi\) | ||||
0.0827989 | + | 0.996566i | \(0.473614\pi\) | |||||||
\(692\) | 39.2783 | 1.49314 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 66.4202 | 2.52128 | ||||||||
\(695\) | 27.3637 | 1.03797 | ||||||||
\(696\) | −9.35530 | −0.354612 | ||||||||
\(697\) | 1.80941 | 0.0685363 | ||||||||
\(698\) | −12.3038 | −0.465705 | ||||||||
\(699\) | 0.886114 | 0.0335159 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.411635 | 0.0155472 | 0.00777361 | − | 0.999970i | \(-0.497526\pi\) | ||||
0.00777361 | + | 0.999970i | \(0.497526\pi\) | |||||||
\(702\) | −0.618352 | −0.0233382 | ||||||||
\(703\) | −33.8474 | −1.27658 | ||||||||
\(704\) | −51.5656 | −1.94345 | ||||||||
\(705\) | −0.0626370 | −0.00235904 | ||||||||
\(706\) | 12.1653 | 0.457847 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −30.6881 | −1.15333 | ||||||||
\(709\) | −15.0664 | −0.565831 | −0.282915 | − | 0.959145i | \(-0.591302\pi\) | ||||
−0.282915 | + | 0.959145i | \(0.591302\pi\) | |||||||
\(710\) | 51.5765 | 1.93563 | ||||||||
\(711\) | 14.8949 | 0.558601 | ||||||||
\(712\) | 15.2499 | 0.571515 | ||||||||
\(713\) | −15.4713 | −0.579406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.04325 | −0.113811 | ||||||||
\(716\) | 9.27665 | 0.346685 | ||||||||
\(717\) | 10.3105 | 0.385052 | ||||||||
\(718\) | 30.3261 | 1.13176 | ||||||||
\(719\) | −35.8607 | −1.33738 | −0.668688 | − | 0.743543i | \(-0.733144\pi\) | ||||
−0.668688 | + | 0.743543i | \(0.733144\pi\) | |||||||
\(720\) | 6.17084 | 0.229974 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.7608 | 0.474909 | ||||||||
\(723\) | −10.7928 | −0.401390 | ||||||||
\(724\) | −9.25596 | −0.343995 | ||||||||
\(725\) | 4.61649 | 0.171452 | ||||||||
\(726\) | −18.6584 | −0.692477 | ||||||||
\(727\) | 27.2538 | 1.01079 | 0.505394 | − | 0.862889i | \(-0.331347\pi\) | ||||
0.505394 | + | 0.862889i | \(0.331347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.2858 | −1.30599 | ||||||||
\(731\) | 12.1241 | 0.448426 | ||||||||
\(732\) | 4.42373 | 0.163506 | ||||||||
\(733\) | −50.8127 | −1.87681 | −0.938405 | − | 0.345538i | \(-0.887697\pi\) | ||||
−0.938405 | + | 0.345538i | \(0.887697\pi\) | |||||||
\(734\) | 28.9325 | 1.06792 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.3041 | 0.453534 | ||||||||
\(737\) | 61.5098 | 2.26574 | ||||||||
\(738\) | −2.13183 | −0.0784736 | ||||||||
\(739\) | 6.60828 | 0.243090 | 0.121545 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121545 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(740\) | −40.6776 | −1.49534 | ||||||||
\(741\) | 1.44988 | 0.0532626 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.8065 | 0.983434 | 0.491717 | − | 0.870755i | \(-0.336369\pi\) | ||||
0.491717 | + | 0.870755i | \(0.336369\pi\) | |||||||
\(744\) | −11.5270 | −0.422599 | ||||||||
\(745\) | −40.3208 | −1.47724 | ||||||||
\(746\) | −11.8619 | −0.434297 | ||||||||
\(747\) | −6.61380 | −0.241986 | ||||||||
\(748\) | −20.4635 | −0.748218 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.2795 | −0.813534 | ||||||||
\(751\) | 20.8690 | 0.761522 | 0.380761 | − | 0.924674i | \(-0.375662\pi\) | ||||
0.380761 | + | 0.924674i | \(0.375662\pi\) | |||||||
\(752\) | 0.0693564 | 0.00252917 | ||||||||
\(753\) | −13.9975 | −0.510096 | ||||||||
\(754\) | 4.98197 | 0.181433 | ||||||||
\(755\) | −10.1191 | −0.368273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8198 | −0.465942 | −0.232971 | − | 0.972484i | \(-0.574845\pi\) | ||||
−0.232971 | + | 0.972484i | \(0.574845\pi\) | |||||||
\(758\) | −51.2086 | −1.85998 | ||||||||
\(759\) | 6.92650 | 0.251416 | ||||||||
\(760\) | 13.7020 | 0.497023 | ||||||||
\(761\) | −36.2182 | −1.31291 | −0.656454 | − | 0.754366i | \(-0.727944\pi\) | ||||
−0.656454 | + | 0.754366i | \(0.727944\pi\) | |||||||
\(762\) | −3.54936 | −0.128580 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26.4188 | −0.955797 | ||||||||
\(765\) | 4.27151 | 0.154437 | ||||||||
\(766\) | −48.3111 | −1.74555 | ||||||||
\(767\) | 3.49801 | 0.126306 | ||||||||
\(768\) | −4.13624 | −0.149254 | ||||||||
\(769\) | 14.7160 | 0.530671 | 0.265336 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265336 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.45313 | 0.304432 | ||||||||
\(772\) | 48.4209 | 1.74271 | ||||||||
\(773\) | −33.6972 | −1.21200 | −0.606002 | − | 0.795463i | \(-0.707228\pi\) | ||||
−0.606002 | + | 0.795463i | \(0.707228\pi\) | |||||||
\(774\) | −14.2844 | −0.513444 | ||||||||
\(775\) | 5.68813 | 0.204324 | ||||||||
\(776\) | 5.23629 | 0.187972 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.6652 | 1.13525 | ||||||||
\(779\) | 4.99859 | 0.179093 | ||||||||
\(780\) | 1.74245 | 0.0623898 | ||||||||
\(781\) | −45.5476 | −1.62982 | ||||||||
\(782\) | 6.01165 | 0.214976 | ||||||||
\(783\) | −8.05686 | −0.287929 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.0662 | −0.466353 | ||||||||
\(786\) | −42.9931 | −1.53351 | ||||||||
\(787\) | −44.9121 | −1.60094 | −0.800472 | − | 0.599370i | \(-0.795418\pi\) | ||||
−0.800472 | + | 0.599370i | \(0.795418\pi\) | |||||||
\(788\) | 18.2295 | 0.649399 | ||||||||
\(789\) | 29.3309 | 1.04421 | ||||||||
\(790\) | −74.9604 | −2.66697 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.16061 | 0.183374 | ||||||||
\(793\) | −0.504243 | −0.0179062 | ||||||||
\(794\) | 67.6704 | 2.40153 | ||||||||
\(795\) | −6.12149 | −0.217107 | ||||||||
\(796\) | 11.7862 | 0.417749 | ||||||||
\(797\) | −22.6417 | −0.802009 | −0.401004 | − | 0.916076i | \(-0.631339\pi\) | ||||
−0.401004 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0480091 | 0.00169844 | ||||||||
\(800\) | −4.52366 | −0.159936 | ||||||||
\(801\) | 13.1333 | 0.464044 | ||||||||
\(802\) | −30.9228 | −1.09192 | ||||||||
\(803\) | 31.1611 | 1.09965 | ||||||||
\(804\) | −35.2183 | −1.24205 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.13845 | 0.216218 | ||||||||
\(807\) | 1.45573 | 0.0512441 | ||||||||
\(808\) | −17.2561 | −0.607067 | ||||||||
\(809\) | 21.5559 | 0.757864 | 0.378932 | − | 0.925425i | \(-0.376291\pi\) | ||||
0.378932 | + | 0.925425i | \(0.376291\pi\) | |||||||
\(810\) | −5.03264 | −0.176829 | ||||||||
\(811\) | −21.0625 | −0.739603 | −0.369801 | − | 0.929111i | \(-0.620574\pi\) | ||||
−0.369801 | + | 0.929111i | \(0.620574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.5158 | 1.07023 | ||||||||
\(814\) | 64.1561 | 2.24867 | ||||||||
\(815\) | −11.6332 | −0.407493 | ||||||||
\(816\) | −4.72974 | −0.165574 | ||||||||
\(817\) | 33.4934 | 1.17179 | ||||||||
\(818\) | −30.6953 | −1.07324 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00727 | 0.209783 | ||||||||
\(821\) | 31.9922 | 1.11653 | 0.558267 | − | 0.829661i | \(-0.311467\pi\) | ||||
0.558267 | + | 0.829661i | \(0.311467\pi\) | |||||||
\(822\) | −30.3696 | −1.05926 | ||||||||
\(823\) | 30.9541 | 1.07899 | 0.539495 | − | 0.841989i | \(-0.318615\pi\) | ||||
0.539495 | + | 0.841989i | \(0.318615\pi\) | |||||||
\(824\) | 3.18663 | 0.111012 | ||||||||
\(825\) | −2.54657 | −0.0886601 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.33182 | −0.185405 | −0.0927027 | − | 0.995694i | \(-0.529551\pi\) | ||||
−0.0927027 | + | 0.995694i | \(0.529551\pi\) | |||||||
\(828\) | −3.96587 | −0.137823 | ||||||||
\(829\) | 25.4635 | 0.884383 | 0.442191 | − | 0.896921i | \(-0.354201\pi\) | ||||
0.442191 | + | 0.896921i | \(0.354201\pi\) | |||||||
\(830\) | 33.2849 | 1.15533 | ||||||||
\(831\) | −29.2660 | −1.01523 | ||||||||
\(832\) | −3.36539 | −0.116674 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 24.7106 | 0.855657 | ||||||||
\(835\) | −26.1741 | −0.905793 | ||||||||
\(836\) | −56.5313 | −1.95518 | ||||||||
\(837\) | −9.92711 | −0.343131 | ||||||||
\(838\) | −65.7086 | −2.26987 | ||||||||
\(839\) | −20.2282 | −0.698356 | −0.349178 | − | 0.937056i | \(-0.613539\pi\) | ||||
−0.349178 | + | 0.937056i | \(0.613539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.9129 | 1.23838 | ||||||||
\(842\) | −1.47993 | −0.0510018 | ||||||||
\(843\) | 12.6815 | 0.436773 | ||||||||
\(844\) | −2.93048 | −0.100871 | ||||||||
\(845\) | 30.4907 | 1.04891 | ||||||||
\(846\) | −0.0565637 | −0.00194470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.77819 | 0.232764 | ||||||||
\(849\) | −26.4622 | −0.908179 | ||||||||
\(850\) | −2.21022 | −0.0758099 | ||||||||
\(851\) | −10.5532 | −0.361758 | ||||||||
\(852\) | 26.0789 | 0.893448 | ||||||||
\(853\) | 4.47575 | 0.153247 | 0.0766233 | − | 0.997060i | \(-0.475586\pi\) | ||||
0.0766233 | + | 0.997060i | \(0.475586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.8003 | 0.403560 | ||||||||
\(856\) | 3.57569 | 0.122215 | ||||||||
\(857\) | 6.14745 | 0.209993 | 0.104997 | − | 0.994473i | \(-0.466517\pi\) | ||||
0.104997 | + | 0.994473i | \(0.466517\pi\) | |||||||
\(858\) | −2.74818 | −0.0938212 | ||||||||
\(859\) | −8.71423 | −0.297326 | −0.148663 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148663 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(860\) | 40.2521 | 1.37259 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.9855 | −1.43003 | ||||||||
\(863\) | 43.6551 | 1.48604 | 0.743019 | − | 0.669270i | \(-0.233393\pi\) | ||||
0.743019 | + | 0.669270i | \(0.233393\pi\) | |||||||
\(864\) | 7.89484 | 0.268588 | ||||||||
\(865\) | −36.4388 | −1.23896 | ||||||||
\(866\) | −46.6665 | −1.58579 | ||||||||
\(867\) | 13.7260 | 0.466160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.1980 | 2.24561 | ||||||||
\(870\) | 40.5472 | 1.37468 | ||||||||
\(871\) | 4.01439 | 0.136022 | ||||||||
\(872\) | −12.6111 | −0.427066 | ||||||||
\(873\) | 4.50954 | 0.152625 | ||||||||
\(874\) | 16.6075 | 0.561757 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.8417 | −0.602816 | ||||||||
\(877\) | −8.85811 | −0.299117 | −0.149559 | − | 0.988753i | \(-0.547785\pi\) | ||||
−0.149559 | + | 0.988753i | \(0.547785\pi\) | |||||||
\(878\) | −6.59425 | −0.222545 | ||||||||
\(879\) | 2.35974 | 0.0795920 | ||||||||
\(880\) | 27.4254 | 0.924510 | ||||||||
\(881\) | 17.2141 | 0.579957 | 0.289978 | − | 0.957033i | \(-0.406352\pi\) | ||||
0.289978 | + | 0.957033i | \(0.406352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.4313 | 0.990441 | 0.495221 | − | 0.868767i | \(-0.335087\pi\) | ||||
0.495221 | + | 0.868767i | \(0.335087\pi\) | |||||||
\(884\) | −1.33553 | −0.0449188 | ||||||||
\(885\) | 28.4696 | 0.956994 | ||||||||
\(886\) | −61.6983 | −2.07279 | ||||||||
\(887\) | −48.1948 | −1.61822 | −0.809111 | − | 0.587656i | \(-0.800051\pi\) | ||||
−0.809111 | + | 0.587656i | \(0.800051\pi\) | |||||||
\(888\) | −7.86267 | −0.263854 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −66.0954 | −2.21552 | ||||||||
\(891\) | 4.44436 | 0.148892 | ||||||||
\(892\) | 54.3463 | 1.81965 | ||||||||
\(893\) | 0.132628 | 0.00443821 | ||||||||
\(894\) | −36.4113 | −1.21778 | ||||||||
\(895\) | −8.60602 | −0.287667 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.452053 | 0.0150936 | ||||||||
\(898\) | −53.8704 | −1.79768 | ||||||||
\(899\) | 79.9813 | 2.66753 | ||||||||
\(900\) | 1.45807 | 0.0486025 | ||||||||
\(901\) | 4.69192 | 0.156311 | ||||||||
\(902\) | −9.47459 | −0.315469 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.56435 | 0.218327 | ||||||||
\(905\) | 8.58683 | 0.285436 | ||||||||
\(906\) | −9.13800 | −0.303590 | ||||||||
\(907\) | 4.87399 | 0.161838 | 0.0809190 | − | 0.996721i | \(-0.474214\pi\) | ||||
0.0809190 | + | 0.996721i | \(0.474214\pi\) | |||||||
\(908\) | 1.15517 | 0.0383355 | ||||||||
\(909\) | −14.8611 | −0.492911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.16921 | 0.105001 | 0.0525003 | − | 0.998621i | \(-0.483281\pi\) | ||||
0.0525003 | + | 0.998621i | \(0.483281\pi\) | |||||||
\(912\) | −13.0661 | −0.432663 | ||||||||
\(913\) | −29.3941 | −0.972802 | ||||||||
\(914\) | −21.4865 | −0.710711 | ||||||||
\(915\) | −4.10393 | −0.135672 | ||||||||
\(916\) | −47.0828 | −1.55566 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.85735 | 0.127311 | ||||||||
\(919\) | 5.06669 | 0.167135 | 0.0835673 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835673 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(920\) | 4.27210 | 0.140847 | ||||||||
\(921\) | −10.3588 | −0.341332 | ||||||||
\(922\) | −2.07476 | −0.0683286 | ||||||||
\(923\) | −2.97263 | −0.0978452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.87993 | 0.127571 | ||||||||
\(926\) | 29.7042 | 0.976139 | ||||||||
\(927\) | 2.74435 | 0.0901364 | ||||||||
\(928\) | −63.6076 | −2.08802 | ||||||||
\(929\) | 28.7365 | 0.942814 | 0.471407 | − | 0.881916i | \(-0.343746\pi\) | ||||
0.471407 | + | 0.881916i | \(0.343746\pi\) | |||||||
\(930\) | 49.9596 | 1.63824 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.25488 | −0.0738609 | ||||||||
\(933\) | −4.07018 | −0.133252 | ||||||||
\(934\) | −5.70140 | −0.186556 | ||||||||
\(935\) | 18.9841 | 0.620847 | ||||||||
\(936\) | 0.336803 | 0.0110088 | ||||||||
\(937\) | 8.98878 | 0.293651 | 0.146825 | − | 0.989162i | \(-0.453094\pi\) | ||||
0.146825 | + | 0.989162i | \(0.453094\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.4202 | −0.568487 | ||||||||
\(940\) | 0.159391 | 0.00519876 | ||||||||
\(941\) | −41.6826 | −1.35881 | −0.679406 | − | 0.733762i | \(-0.737763\pi\) | ||||
−0.679406 | + | 0.733762i | \(0.737763\pi\) | |||||||
\(942\) | −11.7993 | −0.384442 | ||||||||
\(943\) | 1.55849 | 0.0507515 | ||||||||
\(944\) | −31.5237 | −1.02601 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.4852 | −2.06408 | ||||||||
\(947\) | −49.3593 | −1.60396 | −0.801981 | − | 0.597349i | \(-0.796221\pi\) | ||||
−0.801981 | + | 0.597349i | \(0.796221\pi\) | |||||||
\(948\) | −37.9026 | −1.23102 | ||||||||
\(949\) | 2.03371 | 0.0660169 | ||||||||
\(950\) | −6.10584 | −0.198100 | ||||||||
\(951\) | 28.1622 | 0.913222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.39228 | 0.239460 | 0.119730 | − | 0.992807i | \(-0.461797\pi\) | ||||
0.119730 | + | 0.992807i | \(0.461797\pi\) | |||||||
\(954\) | −5.52796 | −0.178974 | ||||||||
\(955\) | 24.5089 | 0.793089 | ||||||||
\(956\) | −26.2369 | −0.848561 | ||||||||
\(957\) | −35.8075 | −1.15749 | ||||||||
\(958\) | −15.2540 | −0.492834 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27.3902 | −0.884015 | ||||||||
\(961\) | 67.5475 | 2.17895 | ||||||||
\(962\) | 4.18710 | 0.134998 | ||||||||
\(963\) | 3.07941 | 0.0992327 | ||||||||
\(964\) | 27.4643 | 0.884565 | ||||||||
\(965\) | −44.9205 | −1.44604 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.9143 | −1.38003 | −0.690016 | − | 0.723795i | \(-0.742396\pi\) | ||||
−0.690016 | + | 0.723795i | \(0.742396\pi\) | |||||||
\(968\) | 10.1628 | 0.326646 | ||||||||
\(969\) | −9.04450 | −0.290551 | ||||||||
\(970\) | −22.6949 | −0.728688 | ||||||||
\(971\) | 28.9224 | 0.928165 | 0.464083 | − | 0.885792i | \(-0.346384\pi\) | ||||
0.464083 | + | 0.885792i | \(0.346384\pi\) | |||||||
\(972\) | −2.54468 | −0.0816206 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 82.1999 | 2.63385 | ||||||||
\(975\) | −0.166200 | −0.00532265 | ||||||||
\(976\) | 4.54418 | 0.145456 | ||||||||
\(977\) | 22.2031 | 0.710339 | 0.355169 | − | 0.934802i | \(-0.384423\pi\) | ||||
0.355169 | + | 0.934802i | \(0.384423\pi\) | |||||||
\(978\) | −10.5052 | −0.335921 | ||||||||
\(979\) | 58.3693 | 1.86549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8608 | −0.346758 | ||||||||
\(982\) | −86.0566 | −2.74618 | ||||||||
\(983\) | 32.9506 | 1.05096 | 0.525480 | − | 0.850806i | \(-0.323886\pi\) | ||||
0.525480 | + | 0.850806i | \(0.323886\pi\) | |||||||
\(984\) | 1.16116 | 0.0370164 | ||||||||
\(985\) | −16.9117 | −0.538850 | ||||||||
\(986\) | −31.0781 | −0.989728 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.68947 | −0.117378 | ||||||||
\(989\) | 10.4428 | 0.332062 | ||||||||
\(990\) | −22.3668 | −0.710865 | ||||||||
\(991\) | −24.4004 | −0.775104 | −0.387552 | − | 0.921848i | \(-0.626679\pi\) | ||||
−0.387552 | + | 0.921848i | \(0.626679\pi\) | |||||||
\(992\) | −78.3730 | −2.48834 | ||||||||
\(993\) | 9.65052 | 0.306250 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.9341 | −0.346635 | ||||||||
\(996\) | 16.8300 | 0.533279 | ||||||||
\(997\) | −4.47325 | −0.141669 | −0.0708346 | − | 0.997488i | \(-0.522566\pi\) | ||||
−0.0708346 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(998\) | 27.6877 | 0.876440 | ||||||||
\(999\) | −6.77139 | −0.214237 |
(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 | 6027.2.a.bd.1.8 | ✓ | 10 | |
7.6 | odd | 2 | 6027.2.a.be.1.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bd.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6027.2.a.be.1.8 | yes | 10 | 7.6 | odd | 2 |