Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 18 x^{10} + 16 x^{9} + 118 x^{8} - 90 x^{7} - 339 x^{6} + 212 x^{5} + 388 x^{4} + \cdots + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.67318\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67318 | 1.18312 | 0.591559 | − | 0.806262i | \(-0.298513\pi\) | ||||
0.591559 | + | 0.806262i | \(0.298513\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.799537 | 0.399768 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.20111 | 0.831941 | 0.415970 | − | 0.909378i | \(-0.363442\pi\) | ||||
0.415970 | + | 0.909378i | \(0.363442\pi\) | |||||||
\(8\) | −2.00859 | −0.710145 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.67318 | −0.529106 | ||||||||
\(11\) | 5.87787 | 1.77225 | 0.886123 | − | 0.463451i | \(-0.153389\pi\) | ||||
0.886123 | + | 0.463451i | \(0.153389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.68285 | 0.984284 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.95981 | −1.23995 | ||||||||
\(17\) | −2.98518 | −0.724014 | −0.362007 | − | 0.932175i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932175i | \(0.617908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00315 | 0.688969 | 0.344485 | − | 0.938792i | \(-0.388054\pi\) | ||||
0.344485 | + | 0.938792i | \(0.388054\pi\) | |||||||
\(20\) | −0.799537 | −0.178782 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.83475 | 2.09678 | ||||||||
\(23\) | 3.33124 | 0.694612 | 0.347306 | − | 0.937752i | \(-0.387097\pi\) | ||||
0.347306 | + | 0.937752i | \(0.387097\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.75987 | 0.332584 | ||||||||
\(29\) | 3.00604 | 0.558207 | 0.279103 | − | 0.960261i | \(-0.409963\pi\) | ||||
0.279103 | + | 0.960261i | \(0.409963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.61735 | −1.36812 | −0.684058 | − | 0.729427i | \(-0.739787\pi\) | ||||
−0.684058 | + | 0.729427i | \(0.739787\pi\) | |||||||
\(32\) | −4.28148 | −0.756867 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.99476 | −0.856594 | ||||||||
\(35\) | −2.20111 | −0.372055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5340 | 1.73178 | 0.865889 | − | 0.500236i | \(-0.166754\pi\) | ||||
0.865889 | + | 0.500236i | \(0.166754\pi\) | |||||||
\(38\) | 5.02481 | 0.815132 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00859 | 0.317586 | ||||||||
\(41\) | 0.0937812 | 0.0146462 | 0.00732308 | − | 0.999973i | \(-0.497669\pi\) | ||||
0.00732308 | + | 0.999973i | \(0.497669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.55346 | 0.846895 | 0.423447 | − | 0.905921i | \(-0.360820\pi\) | ||||
0.423447 | + | 0.905921i | \(0.360820\pi\) | |||||||
\(44\) | 4.69958 | 0.708488 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.57377 | 0.821808 | ||||||||
\(47\) | 8.31052 | 1.21221 | 0.606107 | − | 0.795383i | \(-0.292730\pi\) | ||||
0.606107 | + | 0.795383i | \(0.292730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.15512 | −0.307875 | ||||||||
\(50\) | 1.67318 | 0.236624 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.39923 | −1.15372 | −0.576862 | − | 0.816842i | \(-0.695723\pi\) | ||||
−0.576862 | + | 0.816842i | \(0.695723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.87787 | −0.792572 | ||||||||
\(56\) | −4.42113 | −0.590798 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.02964 | 0.660425 | ||||||||
\(59\) | −7.52009 | −0.979032 | −0.489516 | − | 0.871994i | \(-0.662826\pi\) | ||||
−0.489516 | + | 0.871994i | \(0.662826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5698 | −1.73743 | −0.868716 | − | 0.495310i | \(-0.835054\pi\) | ||||
−0.868716 | + | 0.495310i | \(0.835054\pi\) | |||||||
\(62\) | −12.7452 | −1.61864 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.75593 | 0.344491 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7165 | 1.30923 | 0.654615 | − | 0.755963i | \(-0.272831\pi\) | ||||
0.654615 | + | 0.755963i | \(0.272831\pi\) | |||||||
\(68\) | −2.38676 | −0.289438 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.68285 | −0.440185 | ||||||||
\(71\) | 8.88350 | 1.05428 | 0.527139 | − | 0.849779i | \(-0.323265\pi\) | ||||
0.527139 | + | 0.849779i | \(0.323265\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.62382 | −0.541177 | −0.270589 | − | 0.962695i | \(-0.587218\pi\) | ||||
−0.270589 | + | 0.962695i | \(0.587218\pi\) | |||||||
\(74\) | 17.6253 | 2.04890 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.40113 | 0.275428 | ||||||||
\(77\) | 12.9378 | 1.47440 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.51410 | −1.07042 | −0.535210 | − | 0.844719i | \(-0.679768\pi\) | ||||
−0.535210 | + | 0.844719i | \(0.679768\pi\) | |||||||
\(80\) | 4.95981 | 0.554524 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.156913 | 0.0173281 | ||||||||
\(83\) | −3.47128 | −0.381023 | −0.190511 | − | 0.981685i | \(-0.561015\pi\) | ||||
−0.190511 | + | 0.981685i | \(0.561015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98518 | 0.323789 | ||||||||
\(86\) | 9.29195 | 1.00198 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.8063 | −1.25855 | ||||||||
\(89\) | −4.95616 | −0.525352 | −0.262676 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262676 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.66345 | 0.277684 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.9050 | 1.43419 | ||||||||
\(95\) | −3.00315 | −0.308117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8578 | 1.20397 | 0.601987 | − | 0.798506i | \(-0.294376\pi\) | ||||
0.601987 | + | 0.798506i | \(0.294376\pi\) | |||||||
\(98\) | −3.60591 | −0.364252 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.799537 | 0.0799537 | ||||||||
\(101\) | 8.12602 | 0.808569 | 0.404285 | − | 0.914633i | \(-0.367520\pi\) | ||||
0.404285 | + | 0.914633i | \(0.367520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.31734 | 0.918064 | 0.459032 | − | 0.888420i | \(-0.348196\pi\) | ||||
0.459032 | + | 0.888420i | \(0.348196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.0534 | −1.36499 | ||||||||
\(107\) | 10.0810 | 0.974569 | 0.487285 | − | 0.873243i | \(-0.337987\pi\) | ||||
0.487285 | + | 0.873243i | \(0.337987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0112 | 0.958896 | 0.479448 | − | 0.877570i | \(-0.340837\pi\) | ||||
0.479448 | + | 0.877570i | \(0.340837\pi\) | |||||||
\(110\) | −9.83475 | −0.937706 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.9171 | −1.03157 | ||||||||
\(113\) | 19.6705 | 1.85045 | 0.925224 | − | 0.379422i | \(-0.123877\pi\) | ||||
0.925224 | + | 0.379422i | \(0.123877\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.33124 | −0.310640 | ||||||||
\(116\) | 2.40344 | 0.223153 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5825 | −1.15831 | ||||||||
\(119\) | −6.57071 | −0.602336 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5494 | 2.14085 | ||||||||
\(122\) | −22.7047 | −2.05559 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.09035 | −0.546930 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.688946 | 0.0611341 | 0.0305670 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305670 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(128\) | 13.1741 | 1.16444 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9409 | 1.48013 | 0.740067 | − | 0.672533i | \(-0.234794\pi\) | ||||
0.740067 | + | 0.672533i | \(0.234794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.61025 | 0.573182 | ||||||||
\(134\) | 17.9307 | 1.54897 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.99602 | 0.514155 | ||||||||
\(137\) | 13.3796 | 1.14310 | 0.571548 | − | 0.820569i | \(-0.306343\pi\) | ||||
0.571548 | + | 0.820569i | \(0.306343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4455 | −1.47971 | −0.739854 | − | 0.672768i | \(-0.765105\pi\) | ||||
−0.739854 | + | 0.672768i | \(0.765105\pi\) | |||||||
\(140\) | −1.75987 | −0.148736 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.8637 | 1.24734 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00604 | −0.249638 | ||||||||
\(146\) | −7.73649 | −0.640277 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.42232 | 0.692310 | ||||||||
\(149\) | 5.78235 | 0.473709 | 0.236854 | − | 0.971545i | \(-0.423884\pi\) | ||||
0.236854 | + | 0.971545i | \(0.423884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.801937 | −0.0652607 | −0.0326304 | − | 0.999467i | \(-0.510388\pi\) | ||||
−0.0326304 | + | 0.999467i | \(0.510388\pi\) | |||||||
\(152\) | −6.03210 | −0.489268 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.6473 | 1.74439 | ||||||||
\(155\) | 7.61735 | 0.611840 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.63125 | −0.609040 | −0.304520 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(158\) | −15.9188 | −1.26643 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.28148 | 0.338481 | ||||||||
\(161\) | 7.33243 | 0.577876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.90400 | −0.149133 | −0.0745664 | − | 0.997216i | \(-0.523757\pi\) | ||||
−0.0745664 | + | 0.997216i | \(0.523757\pi\) | |||||||
\(164\) | 0.0749815 | 0.00585507 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.80809 | −0.450795 | ||||||||
\(167\) | 5.90128 | 0.456655 | 0.228328 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228328 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.99476 | 0.383080 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.44020 | 0.338562 | ||||||||
\(173\) | 4.84337 | 0.368235 | 0.184117 | − | 0.982904i | \(-0.441057\pi\) | ||||
0.184117 | + | 0.982904i | \(0.441057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.20111 | 0.166388 | ||||||||
\(176\) | −29.1532 | −2.19750 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.29256 | −0.621554 | ||||||||
\(179\) | 19.8739 | 1.48544 | 0.742722 | − | 0.669600i | \(-0.233534\pi\) | ||||
0.742722 | + | 0.669600i | \(0.233534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.40011 | −0.178399 | −0.0891993 | − | 0.996014i | \(-0.528431\pi\) | ||||
−0.0891993 | + | 0.996014i | \(0.528431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.69111 | −0.493275 | ||||||||
\(185\) | −10.5340 | −0.774475 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5465 | −1.28313 | ||||||||
\(188\) | 6.64457 | 0.484605 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.02481 | −0.364538 | ||||||||
\(191\) | −5.83817 | −0.422435 | −0.211218 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211218 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.99325 | 0.359422 | 0.179711 | − | 0.983719i | \(-0.442484\pi\) | ||||
0.179711 | + | 0.983719i | \(0.442484\pi\) | |||||||
\(194\) | 19.8402 | 1.42444 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.72310 | −0.123079 | ||||||||
\(197\) | −10.5751 | −0.753447 | −0.376724 | − | 0.926326i | \(-0.622949\pi\) | ||||
−0.376724 | + | 0.926326i | \(0.622949\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7003 | 1.04208 | 0.521040 | − | 0.853532i | \(-0.325544\pi\) | ||||
0.521040 | + | 0.853532i | \(0.325544\pi\) | |||||||
\(200\) | −2.00859 | −0.142029 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.5963 | 0.956633 | ||||||||
\(203\) | 6.61661 | 0.464395 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0937812 | −0.00654996 | ||||||||
\(206\) | 15.5896 | 1.08618 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.6521 | 1.22102 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0465 | −1.10468 | −0.552342 | − | 0.833617i | \(-0.686266\pi\) | ||||
−0.552342 | + | 0.833617i | \(0.686266\pi\) | |||||||
\(212\) | −6.71550 | −0.461222 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.8674 | 1.15303 | ||||||||
\(215\) | −5.55346 | −0.378743 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.7666 | −1.13819 | ||||||||
\(218\) | 16.7505 | 1.13449 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.69958 | −0.316845 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.1697 | −1.95335 | −0.976675 | − | 0.214723i | \(-0.931115\pi\) | ||||
−0.976675 | + | 0.214723i | \(0.931115\pi\) | |||||||
\(224\) | −9.42401 | −0.629668 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.9124 | 2.18930 | ||||||||
\(227\) | −18.4618 | −1.22535 | −0.612675 | − | 0.790335i | \(-0.709907\pi\) | ||||
−0.612675 | + | 0.790335i | \(0.709907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.4947 | 1.55258 | 0.776288 | − | 0.630378i | \(-0.217100\pi\) | ||||
0.776288 | + | 0.630378i | \(0.217100\pi\) | |||||||
\(230\) | −5.57377 | −0.367524 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.03790 | −0.396408 | ||||||||
\(233\) | 3.70678 | 0.242839 | 0.121419 | − | 0.992601i | \(-0.461255\pi\) | ||||
0.121419 | + | 0.992601i | \(0.461255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.31052 | −0.542119 | ||||||||
\(236\) | −6.01258 | −0.391386 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.9940 | −0.712635 | ||||||||
\(239\) | 14.1927 | 0.918051 | 0.459025 | − | 0.888423i | \(-0.348199\pi\) | ||||
0.459025 | + | 0.888423i | \(0.348199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.71915 | 0.239572 | 0.119786 | − | 0.992800i | \(-0.461779\pi\) | ||||
0.119786 | + | 0.992800i | \(0.461779\pi\) | |||||||
\(242\) | 39.4024 | 2.53288 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.8495 | −0.694571 | ||||||||
\(245\) | 2.15512 | 0.137686 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.3002 | 0.971561 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.67318 | −0.105821 | ||||||||
\(251\) | −17.8109 | −1.12421 | −0.562106 | − | 0.827065i | \(-0.690009\pi\) | ||||
−0.562106 | + | 0.827065i | \(0.690009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5806 | 1.23102 | ||||||||
\(254\) | 1.15273 | 0.0723288 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.5309 | 1.03318 | ||||||||
\(257\) | −4.06775 | −0.253739 | −0.126870 | − | 0.991919i | \(-0.540493\pi\) | ||||
−0.126870 | + | 0.991919i | \(0.540493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.1865 | 1.44074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28.3452 | 1.75117 | ||||||||
\(263\) | −21.2603 | −1.31097 | −0.655483 | − | 0.755210i | \(-0.727535\pi\) | ||||
−0.655483 | + | 0.755210i | \(0.727535\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.39923 | 0.515961 | ||||||||
\(266\) | 11.0602 | 0.678142 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.56824 | 0.523389 | ||||||||
\(269\) | 23.1780 | 1.41319 | 0.706595 | − | 0.707618i | \(-0.250230\pi\) | ||||
0.706595 | + | 0.707618i | \(0.250230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.3674 | 1.90543 | 0.952716 | − | 0.303862i | \(-0.0982761\pi\) | ||||
0.952716 | + | 0.303862i | \(0.0982761\pi\) | |||||||
\(272\) | 14.8060 | 0.897743 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.3865 | 1.35242 | ||||||||
\(275\) | 5.87787 | 0.354449 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.82232 | 0.590166 | 0.295083 | − | 0.955472i | \(-0.404653\pi\) | ||||
0.295083 | + | 0.955472i | \(0.404653\pi\) | |||||||
\(278\) | −29.1895 | −1.75067 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.42113 | 0.264213 | ||||||||
\(281\) | −14.9335 | −0.890860 | −0.445430 | − | 0.895317i | \(-0.646949\pi\) | ||||
−0.445430 | + | 0.895317i | \(0.646949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.76373 | −0.461506 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(284\) | 7.10269 | 0.421467 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.206423 | 0.0121847 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.08867 | −0.475804 | ||||||||
\(290\) | −5.02964 | −0.295351 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.69692 | −0.216346 | ||||||||
\(293\) | −13.4541 | −0.785997 | −0.392998 | − | 0.919539i | \(-0.628562\pi\) | ||||
−0.392998 | + | 0.919539i | \(0.628562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.52009 | 0.437836 | ||||||||
\(296\) | −21.1585 | −1.22981 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.67492 | 0.560453 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2238 | 0.704566 | ||||||||
\(302\) | −1.34179 | −0.0772111 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.8951 | −0.854290 | ||||||||
\(305\) | 13.5698 | 0.777003 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8497 | −0.790442 | −0.395221 | − | 0.918586i | \(-0.629332\pi\) | ||||
−0.395221 | + | 0.918586i | \(0.629332\pi\) | |||||||
\(308\) | 10.3443 | 0.589420 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.7452 | 0.723879 | ||||||||
\(311\) | 10.7515 | 0.609662 | 0.304831 | − | 0.952406i | \(-0.401400\pi\) | ||||
0.304831 | + | 0.952406i | \(0.401400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.0893 | 1.64422 | 0.822112 | − | 0.569326i | \(-0.192796\pi\) | ||||
0.822112 | + | 0.569326i | \(0.192796\pi\) | |||||||
\(314\) | −12.7685 | −0.720567 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.60687 | −0.427920 | ||||||||
\(317\) | −14.8613 | −0.834692 | −0.417346 | − | 0.908748i | \(-0.637040\pi\) | ||||
−0.417346 | + | 0.908748i | \(0.637040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6691 | 0.989279 | ||||||||
\(320\) | −2.75593 | −0.154061 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.2685 | 0.683696 | ||||||||
\(323\) | −8.96495 | −0.498823 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.18574 | −0.176442 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.188368 | −0.0104009 | ||||||||
\(329\) | 18.2924 | 1.00849 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.24530 | −0.0684478 | −0.0342239 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342239 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(332\) | −2.77542 | −0.152321 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.87392 | 0.540277 | ||||||||
\(335\) | −10.7165 | −0.585505 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1736 | 0.772086 | 0.386043 | − | 0.922481i | \(-0.373842\pi\) | ||||
0.386043 | + | 0.922481i | \(0.373842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.38676 | 0.129441 | ||||||||
\(341\) | −44.7738 | −2.42464 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1514 | −1.08807 | ||||||||
\(344\) | −11.1546 | −0.601418 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.10384 | 0.435665 | ||||||||
\(347\) | 25.4917 | 1.36846 | 0.684232 | − | 0.729264i | \(-0.260137\pi\) | ||||
0.684232 | + | 0.729264i | \(0.260137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.1516 | −1.88162 | −0.940810 | − | 0.338935i | \(-0.889933\pi\) | ||||
−0.940810 | + | 0.338935i | \(0.889933\pi\) | |||||||
\(350\) | 3.68285 | 0.196857 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.1660 | −1.34135 | ||||||||
\(353\) | −7.86270 | −0.418489 | −0.209245 | − | 0.977863i | \(-0.567100\pi\) | ||||
−0.209245 | + | 0.977863i | \(0.567100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.88350 | −0.471487 | ||||||||
\(356\) | −3.96263 | −0.210019 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33.2526 | 1.75746 | ||||||||
\(359\) | 27.0340 | 1.42680 | 0.713401 | − | 0.700756i | \(-0.247154\pi\) | ||||
0.713401 | + | 0.700756i | \(0.247154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.98110 | −0.525321 | ||||||||
\(362\) | −4.01582 | −0.211067 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.62382 | 0.242022 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.4607 | −1.48564 | −0.742818 | − | 0.669493i | \(-0.766511\pi\) | ||||
−0.742818 | + | 0.669493i | \(0.766511\pi\) | |||||||
\(368\) | −16.5223 | −0.861287 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.6253 | −0.916295 | ||||||||
\(371\) | −18.4876 | −0.959830 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5026 | 0.595585 | 0.297792 | − | 0.954631i | \(-0.403750\pi\) | ||||
0.297792 | + | 0.954631i | \(0.403750\pi\) | |||||||
\(374\) | −29.3585 | −1.51809 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.6925 | −0.860848 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.74009 | 0.294848 | 0.147424 | − | 0.989073i | \(-0.452902\pi\) | ||||
0.147424 | + | 0.989073i | \(0.452902\pi\) | |||||||
\(380\) | −2.40113 | −0.123175 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.76833 | −0.499791 | ||||||||
\(383\) | −10.0615 | −0.514121 | −0.257060 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257060 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9378 | −0.659373 | ||||||||
\(386\) | 8.35462 | 0.425239 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.48072 | 0.481311 | ||||||||
\(389\) | 11.3900 | 0.577495 | 0.288748 | − | 0.957405i | \(-0.406761\pi\) | ||||
0.288748 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.94437 | −0.502909 | ||||||||
\(392\) | 4.32876 | 0.218636 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.6941 | −0.891417 | ||||||||
\(395\) | 9.51410 | 0.478706 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5495 | −0.830596 | −0.415298 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415298 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(398\) | 24.5963 | 1.23290 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.95981 | −0.247991 | ||||||||
\(401\) | 30.9846 | 1.54730 | 0.773648 | − | 0.633616i | \(-0.218430\pi\) | ||||
0.773648 | + | 0.633616i | \(0.218430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.49705 | 0.323241 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.0708 | 0.549434 | ||||||||
\(407\) | 61.9175 | 3.06913 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.2934 | 1.79459 | 0.897297 | − | 0.441426i | \(-0.145527\pi\) | ||||
0.897297 | + | 0.441426i | \(0.145527\pi\) | |||||||
\(410\) | −0.156913 | −0.00774938 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.44955 | 0.367013 | ||||||||
\(413\) | −16.5525 | −0.814496 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.47128 | 0.170399 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.5352 | 1.44461 | ||||||||
\(419\) | 20.4467 | 0.998889 | 0.499444 | − | 0.866346i | \(-0.333537\pi\) | ||||
0.499444 | + | 0.866346i | \(0.333537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.03925 | 0.245598 | 0.122799 | − | 0.992432i | \(-0.460813\pi\) | ||||
0.122799 | + | 0.992432i | \(0.460813\pi\) | |||||||
\(422\) | −26.8487 | −1.30697 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.8706 | 0.819311 | ||||||||
\(425\) | −2.98518 | −0.144803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.8686 | −1.44544 | ||||||||
\(428\) | 8.06015 | 0.389602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.29195 | −0.448097 | ||||||||
\(431\) | −33.0261 | −1.59081 | −0.795406 | − | 0.606077i | \(-0.792743\pi\) | ||||
−0.795406 | + | 0.606077i | \(0.792743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.17568 | −0.104556 | −0.0522782 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522782 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(434\) | −28.0536 | −1.34662 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00430 | 0.383336 | ||||||||
\(437\) | 10.0042 | 0.478567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0779 | 0.576449 | 0.288224 | − | 0.957563i | \(-0.406935\pi\) | ||||
0.288224 | + | 0.957563i | \(0.406935\pi\) | |||||||
\(440\) | 11.8063 | 0.562841 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.75110 | −0.368266 | −0.184133 | − | 0.982901i | \(-0.558948\pi\) | ||||
−0.184133 | + | 0.982901i | \(0.558948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.95616 | 0.234945 | ||||||||
\(446\) | −48.8063 | −2.31104 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.06609 | 0.286596 | ||||||||
\(449\) | 6.71779 | 0.317032 | 0.158516 | − | 0.987356i | \(-0.449329\pi\) | ||||
0.158516 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.551234 | 0.0259566 | ||||||||
\(452\) | 15.7273 | 0.739750 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.8899 | −1.44973 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.1739 | −1.64536 | −0.822682 | − | 0.568502i | \(-0.807523\pi\) | ||||
−0.822682 | + | 0.568502i | \(0.807523\pi\) | |||||||
\(458\) | 39.3110 | 1.83688 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.66345 | −0.124184 | ||||||||
\(461\) | −17.0505 | −0.794120 | −0.397060 | − | 0.917793i | \(-0.629969\pi\) | ||||
−0.397060 | + | 0.917793i | \(0.629969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1017 | −1.16657 | −0.583287 | − | 0.812266i | \(-0.698234\pi\) | ||||
−0.583287 | + | 0.812266i | \(0.698234\pi\) | |||||||
\(464\) | −14.9094 | −0.692151 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.20211 | 0.287307 | ||||||||
\(467\) | −0.113343 | −0.00524488 | −0.00262244 | − | 0.999997i | \(-0.500835\pi\) | ||||
−0.00262244 | + | 0.999997i | \(0.500835\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5882 | 1.08920 | ||||||||
\(470\) | −13.9050 | −0.641391 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.1048 | 0.695254 | ||||||||
\(473\) | 32.6425 | 1.50090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.00315 | 0.137794 | ||||||||
\(476\) | −5.25353 | −0.240795 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.7470 | 1.08616 | ||||||||
\(479\) | 10.2305 | 0.467442 | 0.233721 | − | 0.972304i | \(-0.424910\pi\) | ||||
0.233721 | + | 0.972304i | \(0.424910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.22281 | 0.283441 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.8286 | 0.855845 | ||||||||
\(485\) | −11.8578 | −0.538434 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9235 | −0.902819 | −0.451409 | − | 0.892317i | \(-0.649079\pi\) | ||||
−0.451409 | + | 0.892317i | \(0.649079\pi\) | |||||||
\(488\) | 27.2562 | 1.23383 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.60591 | 0.162898 | ||||||||
\(491\) | 38.1677 | 1.72249 | 0.861243 | − | 0.508193i | \(-0.169686\pi\) | ||||
0.861243 | + | 0.508193i | \(0.169686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.97357 | −0.404149 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 37.7806 | 1.69640 | ||||||||
\(497\) | 19.5536 | 0.877097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8474 | 0.619893 | 0.309947 | − | 0.950754i | \(-0.399689\pi\) | ||||
0.309947 | + | 0.950754i | \(0.399689\pi\) | |||||||
\(500\) | −0.799537 | −0.0357564 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −29.8008 | −1.33008 | ||||||||
\(503\) | 11.5990 | 0.517172 | 0.258586 | − | 0.965988i | \(-0.416744\pi\) | ||||
0.258586 | + | 0.965988i | \(0.416744\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.12602 | −0.361603 | ||||||||
\(506\) | 32.7619 | 1.45645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.550838 | 0.0244395 | ||||||||
\(509\) | 15.3222 | 0.679143 | 0.339572 | − | 0.940580i | \(-0.389718\pi\) | ||||
0.339572 | + | 0.940580i | \(0.389718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1775 | −0.450228 | ||||||||
\(512\) | 1.31087 | 0.0579330 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.80608 | −0.300203 | ||||||||
\(515\) | −9.31734 | −0.410571 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.8482 | 2.14834 | ||||||||
\(518\) | 38.7952 | 1.70456 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.2960 | 1.28348 | 0.641740 | − | 0.766922i | \(-0.278213\pi\) | ||||
0.641740 | + | 0.766922i | \(0.278213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.91749 | 0.389934 | 0.194967 | − | 0.980810i | \(-0.437540\pi\) | ||||
0.194967 | + | 0.980810i | \(0.437540\pi\) | |||||||
\(524\) | 13.5449 | 0.591711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.5723 | −1.55103 | ||||||||
\(527\) | 22.7392 | 0.990535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.9028 | −0.517514 | ||||||||
\(530\) | 14.0534 | 0.610443 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.28514 | 0.229140 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0810 | −0.435841 | ||||||||
\(536\) | −21.5251 | −0.929743 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 38.7811 | 1.67197 | ||||||||
\(539\) | −12.6675 | −0.545629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9141 | 1.54407 | 0.772034 | − | 0.635582i | \(-0.219240\pi\) | ||||
0.772034 | + | 0.635582i | \(0.219240\pi\) | |||||||
\(542\) | 52.4833 | 2.25435 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.7810 | 0.547982 | ||||||||
\(545\) | −10.0112 | −0.428831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1490 | −0.733238 | −0.366619 | − | 0.930371i | \(-0.619485\pi\) | ||||
−0.366619 | + | 0.930371i | \(0.619485\pi\) | |||||||
\(548\) | 10.6975 | 0.456973 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.83475 | 0.419355 | ||||||||
\(551\) | 9.02757 | 0.384587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.9416 | −0.890526 | ||||||||
\(554\) | 16.4345 | 0.698236 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.9483 | −0.591540 | ||||||||
\(557\) | 10.6737 | 0.452257 | 0.226129 | − | 0.974097i | \(-0.427393\pi\) | ||||
0.226129 | + | 0.974097i | \(0.427393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.9171 | 0.461331 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.9865 | −1.05399 | ||||||||
\(563\) | 8.69238 | 0.366340 | 0.183170 | − | 0.983081i | \(-0.441364\pi\) | ||||
0.183170 | + | 0.983081i | \(0.441364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.6705 | −0.827545 | ||||||||
\(566\) | −12.9901 | −0.546016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.8433 | −0.748690 | ||||||||
\(569\) | −8.20176 | −0.343835 | −0.171918 | − | 0.985111i | \(-0.554996\pi\) | ||||
−0.171918 | + | 0.985111i | \(0.554996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.86423 | −0.287259 | −0.143630 | − | 0.989632i | \(-0.545877\pi\) | ||||
−0.143630 | + | 0.989632i | \(0.545877\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.345382 | 0.0144160 | ||||||||
\(575\) | 3.33124 | 0.138922 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.6348 | −1.02556 | −0.512780 | − | 0.858520i | \(-0.671384\pi\) | ||||
−0.512780 | + | 0.858520i | \(0.671384\pi\) | |||||||
\(578\) | −13.5338 | −0.562933 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.40344 | −0.0997973 | ||||||||
\(581\) | −7.64067 | −0.316989 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.3696 | −2.04468 | ||||||||
\(584\) | 9.28738 | 0.384314 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.5111 | −0.929927 | ||||||||
\(587\) | −22.1699 | −0.915048 | −0.457524 | − | 0.889197i | \(-0.651264\pi\) | ||||
−0.457524 | + | 0.889197i | \(0.651264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8760 | −0.942590 | ||||||||
\(590\) | 12.5825 | 0.518012 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −52.2467 | −2.14732 | ||||||||
\(593\) | 40.4785 | 1.66225 | 0.831127 | − | 0.556083i | \(-0.187696\pi\) | ||||
0.831127 | + | 0.556083i | \(0.187696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.57071 | 0.269373 | ||||||||
\(596\) | 4.62320 | 0.189374 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.9642 | −0.979153 | −0.489576 | − | 0.871960i | \(-0.662849\pi\) | ||||
−0.489576 | + | 0.871960i | \(0.662849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.15250 | −0.0878024 | −0.0439012 | − | 0.999036i | \(-0.513979\pi\) | ||||
−0.0439012 | + | 0.999036i | \(0.513979\pi\) | |||||||
\(602\) | 20.4526 | 0.833585 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.641178 | −0.0260892 | ||||||||
\(605\) | −23.5494 | −0.957418 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0772 | 0.571375 | 0.285687 | − | 0.958323i | \(-0.407778\pi\) | ||||
0.285687 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(608\) | −12.8579 | −0.521458 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.7047 | 0.919287 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.4908 | −1.27190 | −0.635950 | − | 0.771730i | \(-0.719392\pi\) | ||||
−0.635950 | + | 0.771730i | \(0.719392\pi\) | |||||||
\(614\) | −23.1730 | −0.935187 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.9868 | −1.04704 | ||||||||
\(617\) | 48.4698 | 1.95132 | 0.975660 | − | 0.219289i | \(-0.0703738\pi\) | ||||
0.975660 | + | 0.219289i | \(0.0703738\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5608 | −0.987181 | −0.493590 | − | 0.869695i | \(-0.664316\pi\) | ||||
−0.493590 | + | 0.869695i | \(0.664316\pi\) | |||||||
\(620\) | 6.09035 | 0.244594 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.9892 | 0.721303 | ||||||||
\(623\) | −10.9090 | −0.437062 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 48.6717 | 1.94531 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.10147 | −0.243475 | ||||||||
\(629\) | −31.4459 | −1.25383 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4290 | −0.972503 | −0.486251 | − | 0.873819i | \(-0.661636\pi\) | ||||
−0.486251 | + | 0.873819i | \(0.661636\pi\) | |||||||
\(632\) | 19.1100 | 0.760153 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.8656 | −0.987539 | ||||||||
\(635\) | −0.688946 | −0.0273400 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.5636 | 1.17043 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.1741 | −0.520753 | ||||||||
\(641\) | −42.4077 | −1.67500 | −0.837501 | − | 0.546436i | \(-0.815984\pi\) | ||||
−0.837501 | + | 0.546436i | \(0.815984\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.7911 | −1.76639 | −0.883195 | − | 0.469006i | \(-0.844612\pi\) | ||||
−0.883195 | + | 0.469006i | \(0.844612\pi\) | |||||||
\(644\) | 5.86254 | 0.231017 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.0000 | −0.590167 | ||||||||
\(647\) | 24.9327 | 0.980204 | 0.490102 | − | 0.871665i | \(-0.336959\pi\) | ||||
0.490102 | + | 0.871665i | \(0.336959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.2021 | −1.73508 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.52232 | −0.0596186 | ||||||||
\(653\) | −28.6239 | −1.12014 | −0.560069 | − | 0.828446i | \(-0.689225\pi\) | ||||
−0.560069 | + | 0.828446i | \(0.689225\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.9409 | −0.661936 | ||||||||
\(656\) | −0.465137 | −0.0181606 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.6064 | 1.19316 | ||||||||
\(659\) | 28.5647 | 1.11272 | 0.556361 | − | 0.830941i | \(-0.312197\pi\) | ||||
0.556361 | + | 0.830941i | \(0.312197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.4211 | −1.53330 | −0.766652 | − | 0.642063i | \(-0.778079\pi\) | ||||
−0.766652 | + | 0.642063i | \(0.778079\pi\) | |||||||
\(662\) | −2.08361 | −0.0809819 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.97240 | 0.270582 | ||||||||
\(665\) | −6.61025 | −0.256335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0138 | 0.387737 | ||||||||
\(668\) | 4.71829 | 0.182556 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.9307 | −0.692722 | ||||||||
\(671\) | −79.7614 | −3.07916 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.5953 | −1.44919 | −0.724596 | − | 0.689174i | \(-0.757974\pi\) | ||||
−0.724596 | + | 0.689174i | \(0.757974\pi\) | |||||||
\(674\) | 23.7150 | 0.913469 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.1459 | −1.77353 | −0.886765 | − | 0.462221i | \(-0.847053\pi\) | ||||
−0.886765 | + | 0.462221i | \(0.847053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.1002 | 1.00163 | ||||||||
\(680\) | −5.99602 | −0.229937 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −74.9147 | −2.86863 | ||||||||
\(683\) | −35.5813 | −1.36148 | −0.680740 | − | 0.732525i | \(-0.738342\pi\) | ||||
−0.680740 | + | 0.732525i | \(0.738342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3796 | −0.511208 | ||||||||
\(686\) | −33.7170 | −1.28732 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.5441 | −1.05011 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.0144 | −1.56026 | −0.780131 | − | 0.625617i | \(-0.784847\pi\) | ||||
−0.780131 | + | 0.625617i | \(0.784847\pi\) | |||||||
\(692\) | 3.87245 | 0.147209 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.6522 | 1.61906 | ||||||||
\(695\) | 17.4455 | 0.661745 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.279954 | −0.0106040 | ||||||||
\(698\) | −58.8149 | −2.22618 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.75987 | 0.0665167 | ||||||||
\(701\) | −27.7156 | −1.04680 | −0.523402 | − | 0.852086i | \(-0.675337\pi\) | ||||
−0.523402 | + | 0.852086i | \(0.675337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.6351 | 1.19314 | ||||||||
\(704\) | 16.1990 | 0.610522 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.1557 | −0.495122 | ||||||||
\(707\) | 17.8863 | 0.672682 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.63088 | 0.211472 | 0.105736 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105736 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(710\) | −14.8637 | −0.557825 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.95491 | 0.373076 | ||||||||
\(713\) | −25.3752 | −0.950310 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.8899 | 0.593834 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 45.2329 | 1.68808 | ||||||||
\(719\) | −27.6971 | −1.03293 | −0.516464 | − | 0.856309i | \(-0.672752\pi\) | ||||
−0.516464 | + | 0.856309i | \(0.672752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5085 | 0.763775 | ||||||||
\(722\) | −16.7002 | −0.621517 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.91897 | −0.0713181 | ||||||||
\(725\) | 3.00604 | 0.111641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.1083 | 0.634510 | 0.317255 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317255 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.73649 | 0.286340 | ||||||||
\(731\) | −16.5781 | −0.613163 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.64370 | −0.134583 | −0.0672915 | − | 0.997733i | \(-0.521436\pi\) | ||||
−0.0672915 | + | 0.997733i | \(0.521436\pi\) | |||||||
\(734\) | −47.6199 | −1.75768 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.2627 | −0.525729 | ||||||||
\(737\) | 62.9903 | 2.32028 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5246 | −0.387155 | −0.193577 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193577 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(740\) | −8.42232 | −0.309610 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.9332 | −1.13559 | ||||||||
\(743\) | −29.4629 | −1.08089 | −0.540445 | − | 0.841379i | \(-0.681744\pi\) | ||||
−0.540445 | + | 0.841379i | \(0.681744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.78235 | −0.211849 | ||||||||
\(746\) | 19.2460 | 0.704647 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.0291 | −0.512955 | ||||||||
\(749\) | 22.1894 | 0.810784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.5122 | 1.58778 | 0.793892 | − | 0.608058i | \(-0.208051\pi\) | ||||
0.793892 | + | 0.608058i | \(0.208051\pi\) | |||||||
\(752\) | −41.2187 | −1.50309 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.801937 | 0.0291855 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.869490 | −0.0316022 | −0.0158011 | − | 0.999875i | \(-0.505030\pi\) | ||||
−0.0158011 | + | 0.999875i | \(0.505030\pi\) | |||||||
\(758\) | 9.60421 | 0.348841 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.03210 | 0.218807 | ||||||||
\(761\) | −45.0860 | −1.63437 | −0.817184 | − | 0.576377i | \(-0.804466\pi\) | ||||
−0.817184 | + | 0.576377i | \(0.804466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0357 | 0.797745 | ||||||||
\(764\) | −4.66784 | −0.168876 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.8348 | −0.608265 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9400 | −0.610873 | −0.305437 | − | 0.952212i | \(-0.598802\pi\) | ||||
−0.305437 | + | 0.952212i | \(0.598802\pi\) | |||||||
\(770\) | −21.6473 | −0.780116 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.99229 | 0.143686 | ||||||||
\(773\) | 39.7998 | 1.43150 | 0.715750 | − | 0.698356i | \(-0.246085\pi\) | ||||
0.715750 | + | 0.698356i | \(0.246085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.61735 | −0.273623 | ||||||||
\(776\) | −23.8174 | −0.854996 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.0575 | 0.683245 | ||||||||
\(779\) | 0.281639 | 0.0100908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.2161 | 1.86844 | ||||||||
\(782\) | −16.6387 | −0.595000 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.6890 | 0.381750 | ||||||||
\(785\) | 7.63125 | 0.272371 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.30295 | −0.153384 | −0.0766918 | − | 0.997055i | \(-0.524436\pi\) | ||||
−0.0766918 | + | 0.997055i | \(0.524436\pi\) | |||||||
\(788\) | −8.45521 | −0.301205 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.9188 | 0.566366 | ||||||||
\(791\) | 43.2970 | 1.53946 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −27.6903 | −0.982694 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.7535 | 0.416590 | ||||||||
\(797\) | 38.9711 | 1.38043 | 0.690214 | − | 0.723605i | \(-0.257516\pi\) | ||||
0.690214 | + | 0.723605i | \(0.257516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.8084 | −0.877660 | ||||||||
\(800\) | −4.28148 | −0.151373 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 51.8428 | 1.83063 | ||||||||
\(803\) | −27.1782 | −0.959099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.33243 | −0.258434 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.3219 | −0.574201 | ||||||||
\(809\) | 48.3036 | 1.69826 | 0.849132 | − | 0.528180i | \(-0.177125\pi\) | ||||
0.849132 | + | 0.528180i | \(0.177125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0369 | −0.984508 | −0.492254 | − | 0.870452i | \(-0.663827\pi\) | ||||
−0.492254 | + | 0.870452i | \(0.663827\pi\) | |||||||
\(812\) | 5.29022 | 0.185650 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 103.599 | 3.63115 | ||||||||
\(815\) | 1.90400 | 0.0666942 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.6779 | 0.583485 | ||||||||
\(818\) | 60.7255 | 2.12322 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0749815 | −0.00261847 | ||||||||
\(821\) | 18.1825 | 0.634574 | 0.317287 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317287 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.6571 | −1.52179 | −0.760896 | − | 0.648874i | \(-0.775240\pi\) | ||||
−0.760896 | + | 0.648874i | \(0.775240\pi\) | |||||||
\(824\) | −18.7147 | −0.651959 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.6954 | −0.963645 | ||||||||
\(827\) | −5.89278 | −0.204912 | −0.102456 | − | 0.994738i | \(-0.532670\pi\) | ||||
−0.102456 | + | 0.994738i | \(0.532670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.42371 | 0.153642 | 0.0768209 | − | 0.997045i | \(-0.475523\pi\) | ||||
0.0768209 | + | 0.997045i | \(0.475523\pi\) | |||||||
\(830\) | 5.80809 | 0.201602 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.43344 | 0.222905 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.90128 | −0.204222 | ||||||||
\(836\) | 14.1135 | 0.488126 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.2111 | 1.18180 | ||||||||
\(839\) | 13.7390 | 0.474324 | 0.237162 | − | 0.971470i | \(-0.423783\pi\) | ||||
0.237162 | + | 0.971470i | \(0.423783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.9637 | −0.688405 | ||||||||
\(842\) | 8.43158 | 0.290571 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.8297 | −0.441618 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.8347 | 1.78106 | ||||||||
\(848\) | 41.6586 | 1.43056 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.99476 | −0.171319 | ||||||||
\(851\) | 35.0913 | 1.20291 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.4971 | 1.42083 | 0.710417 | − | 0.703781i | \(-0.248506\pi\) | ||||
0.710417 | + | 0.703781i | \(0.248506\pi\) | |||||||
\(854\) | −49.9755 | −1.71013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.2487 | −0.692085 | ||||||||
\(857\) | −21.1626 | −0.722901 | −0.361450 | − | 0.932391i | \(-0.617718\pi\) | ||||
−0.361450 | + | 0.932391i | \(0.617718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.5958 | 1.58983 | 0.794914 | − | 0.606722i | \(-0.207516\pi\) | ||||
0.794914 | + | 0.606722i | \(0.207516\pi\) | |||||||
\(860\) | −4.44020 | −0.151409 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.2587 | −1.88212 | ||||||||
\(863\) | −29.3444 | −0.998895 | −0.499448 | − | 0.866344i | \(-0.666464\pi\) | ||||
−0.499448 | + | 0.866344i | \(0.666464\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.84337 | −0.164680 | ||||||||
\(866\) | −3.64030 | −0.123702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.4055 | −0.455013 | ||||||||
\(869\) | −55.9227 | −1.89705 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.1084 | −0.680955 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.7389 | 0.566201 | ||||||||
\(875\) | −2.20111 | −0.0744110 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.1148 | −1.72602 | −0.863012 | − | 0.505184i | \(-0.831425\pi\) | ||||
−0.863012 | + | 0.505184i | \(0.831425\pi\) | |||||||
\(878\) | 20.2086 | 0.682007 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 29.1532 | 0.982753 | ||||||||
\(881\) | 1.51537 | 0.0510540 | 0.0255270 | − | 0.999674i | \(-0.491874\pi\) | ||||
0.0255270 | + | 0.999674i | \(0.491874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.8608 | −0.533760 | −0.266880 | − | 0.963730i | \(-0.585993\pi\) | ||||
−0.266880 | + | 0.963730i | \(0.585993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9690 | −0.435702 | ||||||||
\(887\) | 29.0167 | 0.974285 | 0.487142 | − | 0.873323i | \(-0.338039\pi\) | ||||
0.487142 | + | 0.873323i | \(0.338039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51644 | 0.0508599 | ||||||||
\(890\) | 8.29256 | 0.277967 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.3223 | −0.780888 | ||||||||
\(893\) | 24.9577 | 0.835179 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8739 | −0.664311 | ||||||||
\(896\) | 28.9977 | 0.968745 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.2401 | 0.375087 | ||||||||
\(899\) | −22.8980 | −0.763692 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.0733 | 0.835311 | ||||||||
\(902\) | 0.922314 | 0.0307097 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −39.5101 | −1.31409 | ||||||||
\(905\) | 2.40011 | 0.0797823 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.3710 | −1.17448 | −0.587238 | − | 0.809414i | \(-0.699785\pi\) | ||||
−0.587238 | + | 0.809414i | \(0.699785\pi\) | |||||||
\(908\) | −14.7609 | −0.489856 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.4023 | 0.642827 | 0.321413 | − | 0.946939i | \(-0.395842\pi\) | ||||
0.321413 | + | 0.946939i | \(0.395842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.4038 | −0.675266 | ||||||||
\(914\) | −58.8523 | −1.94666 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.7849 | 0.620671 | ||||||||
\(917\) | 37.2888 | 1.23138 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.2070 | −1.12838 | −0.564192 | − | 0.825644i | \(-0.690812\pi\) | ||||
−0.564192 | + | 0.825644i | \(0.690812\pi\) | |||||||
\(920\) | 6.69111 | 0.220599 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.5285 | −0.939537 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5340 | 0.346356 | ||||||||
\(926\) | −41.9997 | −1.38019 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.8703 | −0.422488 | ||||||||
\(929\) | 22.2676 | 0.730576 | 0.365288 | − | 0.930895i | \(-0.380971\pi\) | ||||
0.365288 | + | 0.930895i | \(0.380971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.47215 | −0.212116 | ||||||||
\(932\) | 2.96370 | 0.0970793 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.189643 | −0.00620532 | ||||||||
\(935\) | 17.5465 | 0.573833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.7527 | −0.481950 | −0.240975 | − | 0.970531i | \(-0.577467\pi\) | ||||
−0.240975 | + | 0.970531i | \(0.577467\pi\) | |||||||
\(938\) | 39.4673 | 1.28865 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.64457 | −0.216722 | ||||||||
\(941\) | 38.4869 | 1.25464 | 0.627318 | − | 0.778763i | \(-0.284153\pi\) | ||||
0.627318 | + | 0.778763i | \(0.284153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.312408 | 0.0101734 | ||||||||
\(944\) | 37.2982 | 1.21395 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.6169 | 1.77575 | ||||||||
\(947\) | −43.5707 | −1.41586 | −0.707929 | − | 0.706284i | \(-0.750370\pi\) | ||||
−0.707929 | + | 0.706284i | \(0.750370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.02481 | 0.163026 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.1979 | 0.427746 | ||||||||
\(953\) | 17.9696 | 0.582093 | 0.291047 | − | 0.956709i | \(-0.405997\pi\) | ||||
0.291047 | + | 0.956709i | \(0.405997\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.83817 | 0.188919 | ||||||||
\(956\) | 11.3476 | 0.367008 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.1174 | 0.553039 | ||||||||
\(959\) | 29.4499 | 0.950987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0240 | 0.871742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.97360 | 0.0957731 | ||||||||
\(965\) | −4.99325 | −0.160738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0395 | −0.387163 | −0.193581 | − | 0.981084i | \(-0.562010\pi\) | ||||
−0.193581 | + | 0.981084i | \(0.562010\pi\) | |||||||
\(968\) | −47.3011 | −1.52032 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.8402 | −0.637030 | ||||||||
\(971\) | −40.1570 | −1.28870 | −0.644350 | − | 0.764730i | \(-0.722872\pi\) | ||||
−0.644350 | + | 0.764730i | \(0.722872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.3994 | −1.23103 | ||||||||
\(974\) | −33.3356 | −1.06814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.3036 | 2.15434 | ||||||||
\(977\) | −5.99845 | −0.191907 | −0.0959537 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959537 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.1317 | −0.931053 | ||||||||
\(980\) | 1.72310 | 0.0550424 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 63.8616 | 2.03790 | ||||||||
\(983\) | −26.6303 | −0.849374 | −0.424687 | − | 0.905340i | \(-0.639616\pi\) | ||||
−0.424687 | + | 0.905340i | \(0.639616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5751 | 0.336952 | ||||||||
\(986\) | −15.0144 | −0.478156 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.4999 | 0.588263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0648 | −0.415017 | −0.207508 | − | 0.978233i | \(-0.566535\pi\) | ||||
−0.207508 | + | 0.978233i | \(0.566535\pi\) | |||||||
\(992\) | 32.6136 | 1.03548 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.7166 | 1.03771 | ||||||||
\(995\) | −14.7003 | −0.466032 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.5777 | 1.60181 | 0.800907 | − | 0.598789i | \(-0.204351\pi\) | ||||
0.800907 | + | 0.598789i | \(0.204351\pi\) | |||||||
\(998\) | 23.1692 | 0.733407 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7605.2.a.cx.1.9 | yes | 12 | |
3.2 | odd | 2 | 7605.2.a.cv.1.4 | ✓ | 12 | ||
13.12 | even | 2 | 7605.2.a.cw.1.4 | yes | 12 | ||
39.38 | odd | 2 | 7605.2.a.cy.1.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7605.2.a.cv.1.4 | ✓ | 12 | 3.2 | odd | 2 | ||
7605.2.a.cw.1.4 | yes | 12 | 13.12 | even | 2 | ||
7605.2.a.cx.1.9 | yes | 12 | 1.1 | even | 1 | trivial | |
7605.2.a.cy.1.9 | yes | 12 | 39.38 | odd | 2 |