Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46162368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 17x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 819) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.734503\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.734503 | 0.519372 | 0.259686 | − | 0.965693i | \(-0.416381\pi\) | ||||
0.259686 | + | 0.965693i | \(0.416381\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.46050 | −0.730252 | ||||||||
\(5\) | −2.54175 | −1.13671 | −0.568353 | − | 0.822785i | \(-0.692419\pi\) | ||||
−0.568353 | + | 0.822785i | \(0.692419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.54175 | −0.898645 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.86693 | −0.590374 | ||||||||
\(11\) | −3.71224 | −1.11928 | −0.559641 | − | 0.828735i | \(-0.689061\pi\) | ||||
−0.559641 | + | 0.828735i | \(0.689061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.05408 | 0.263521 | ||||||||
\(17\) | 2.10577 | 0.510723 | 0.255362 | − | 0.966846i | \(-0.417805\pi\) | ||||
0.255362 | + | 0.966846i | \(0.417805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.92101 | 1.35837 | 0.679186 | − | 0.733966i | \(-0.262333\pi\) | ||||
0.679186 | + | 0.733966i | \(0.262333\pi\) | |||||||
\(20\) | 3.71224 | 0.830082 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.72665 | −0.581325 | ||||||||
\(23\) | 6.25399 | 1.30405 | 0.652024 | − | 0.758198i | \(-0.273920\pi\) | ||||
0.652024 | + | 0.758198i | \(0.273920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.46050 | 0.292101 | ||||||||
\(26\) | −0.734503 | −0.144048 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.83547 | 1.64071 | 0.820353 | − | 0.571858i | \(-0.193777\pi\) | ||||
0.820353 | + | 0.571858i | \(0.193777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.70175 | −1.02406 | −0.512032 | − | 0.858966i | \(-0.671107\pi\) | ||||
−0.512032 | + | 0.858966i | \(0.671107\pi\) | |||||||
\(32\) | 5.85773 | 1.03551 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.54669 | 0.265256 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.56867 | 1.07988 | 0.539942 | − | 0.841702i | \(-0.318446\pi\) | ||||
0.539942 | + | 0.841702i | \(0.318446\pi\) | |||||||
\(38\) | 4.34900 | 0.705501 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.46050 | 1.02150 | ||||||||
\(41\) | 10.3045 | 1.60929 | 0.804645 | − | 0.593757i | \(-0.202356\pi\) | ||||
0.804645 | + | 0.593757i | \(0.202356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6477 | −1.62375 | −0.811877 | − | 0.583829i | \(-0.801554\pi\) | ||||
−0.811877 | + | 0.583829i | \(0.801554\pi\) | |||||||
\(44\) | 5.42175 | 0.817359 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.59358 | 0.677286 | ||||||||
\(47\) | −1.46901 | −0.214277 | −0.107138 | − | 0.994244i | \(-0.534169\pi\) | ||||
−0.107138 | + | 0.994244i | \(0.534169\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.07275 | 0.151709 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.46050 | 0.202536 | ||||||||
\(53\) | −6.45477 | −0.886631 | −0.443315 | − | 0.896366i | \(-0.646198\pi\) | ||||
−0.443315 | + | 0.896366i | \(0.646198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.43560 | 1.27230 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.48968 | 0.852137 | ||||||||
\(59\) | 11.4352 | 1.48874 | 0.744371 | − | 0.667766i | \(-0.232750\pi\) | ||||
0.744371 | + | 0.667766i | \(0.232750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.11537 | −1.16710 | −0.583551 | − | 0.812076i | \(-0.698337\pi\) | ||||
−0.583551 | + | 0.812076i | \(0.698337\pi\) | |||||||
\(62\) | −4.18795 | −0.531871 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.19436 | 0.274294 | ||||||||
\(65\) | 2.54175 | 0.315266 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0541 | −1.71698 | −0.858490 | − | 0.512831i | \(-0.828597\pi\) | ||||
−0.858490 | + | 0.512831i | \(0.828597\pi\) | |||||||
\(68\) | −3.07548 | −0.372957 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4527 | −1.71522 | −0.857610 | − | 0.514300i | \(-0.828052\pi\) | ||||
−0.857610 | + | 0.514300i | \(0.828052\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.14027 | −0.718664 | −0.359332 | − | 0.933210i | \(-0.616996\pi\) | ||||
−0.359332 | + | 0.933210i | \(0.616996\pi\) | |||||||
\(74\) | 4.82471 | 0.560861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.64766 | −0.991955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96790 | −0.896458 | −0.448229 | − | 0.893919i | \(-0.647945\pi\) | ||||
−0.448229 | + | 0.893919i | \(0.647945\pi\) | |||||||
\(80\) | −2.67922 | −0.299546 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.56867 | 0.835820 | ||||||||
\(83\) | −12.1515 | −1.33380 | −0.666898 | − | 0.745149i | \(-0.732378\pi\) | ||||
−0.666898 | + | 0.745149i | \(0.732378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35234 | −0.580542 | ||||||||
\(86\) | −7.82074 | −0.843333 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.43560 | 1.00584 | ||||||||
\(89\) | 11.8132 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.13399 | −0.952284 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.07899 | −0.111289 | ||||||||
\(95\) | −15.0497 | −1.54407 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.10097 | 0.720994 | 0.360497 | − | 0.932760i | \(-0.382607\pi\) | ||||
0.360497 | + | 0.932760i | \(0.382607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.13307 | −0.213307 | ||||||||
\(101\) | 8.49723 | 0.845506 | 0.422753 | − | 0.906245i | \(-0.361064\pi\) | ||||
0.422753 | + | 0.906245i | \(0.361064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.18716 | 0.215507 | 0.107754 | − | 0.994178i | \(-0.465634\pi\) | ||||
0.107754 | + | 0.994178i | \(0.465634\pi\) | |||||||
\(104\) | 2.54175 | 0.249239 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.74105 | −0.460491 | ||||||||
\(107\) | −7.52751 | −0.727712 | −0.363856 | − | 0.931455i | \(-0.618540\pi\) | ||||
−0.363856 | + | 0.931455i | \(0.618540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0540842 | 0.00518033 | 0.00259016 | − | 0.999997i | \(-0.499176\pi\) | ||||
0.00259016 | + | 0.999997i | \(0.499176\pi\) | |||||||
\(110\) | 6.93048 | 0.660795 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.25399 | −0.588326 | −0.294163 | − | 0.955755i | \(-0.595041\pi\) | ||||
−0.294163 | + | 0.955755i | \(0.595041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8961 | −1.48232 | ||||||||
\(116\) | −12.9042 | −1.19813 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.39922 | 0.773211 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.78074 | 0.252794 | ||||||||
\(122\) | −6.69527 | −0.606161 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.32743 | 0.747825 | ||||||||
\(125\) | 8.99652 | 0.804673 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.49261 | −0.221183 | −0.110592 | − | 0.993866i | \(-0.535275\pi\) | ||||
−0.110592 | + | 0.993866i | \(0.535275\pi\) | |||||||
\(128\) | −10.1037 | −0.893050 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.86693 | 0.163740 | ||||||||
\(131\) | −8.85376 | −0.773557 | −0.386779 | − | 0.922173i | \(-0.626412\pi\) | ||||
−0.386779 | + | 0.922173i | \(0.626412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.3228 | −0.891752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.35234 | −0.458959 | ||||||||
\(137\) | 2.71895 | 0.232295 | 0.116148 | − | 0.993232i | \(-0.462945\pi\) | ||||
0.116148 | + | 0.993232i | \(0.462945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1694 | 1.11702 | 0.558509 | − | 0.829498i | \(-0.311374\pi\) | ||||
0.558509 | + | 0.829498i | \(0.311374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.6156 | −0.890838 | ||||||||
\(143\) | 3.71224 | 0.310433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.4576 | −1.86500 | ||||||||
\(146\) | −4.51005 | −0.373254 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.59358 | −0.788587 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.29533 | −0.593685 | −0.296843 | − | 0.954926i | \(-0.595934\pi\) | ||||
−0.296843 | + | 0.954926i | \(0.595934\pi\) | |||||||
\(152\) | −15.0497 | −1.22070 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4924 | 1.16406 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.67257 | −0.452720 | −0.226360 | − | 0.974044i | \(-0.572683\pi\) | ||||
−0.226360 | + | 0.974044i | \(0.572683\pi\) | |||||||
\(158\) | −5.85245 | −0.465596 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.8889 | −1.17707 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.7161 | −1.62261 | −0.811307 | − | 0.584621i | \(-0.801243\pi\) | ||||
−0.811307 | + | 0.584621i | \(0.801243\pi\) | |||||||
\(164\) | −15.0497 | −1.17519 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.92528 | −0.692736 | ||||||||
\(167\) | 14.3152 | 1.10775 | 0.553873 | − | 0.832601i | \(-0.313149\pi\) | ||||
0.553873 | + | 0.832601i | \(0.313149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.93131 | −0.301518 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.5510 | 1.18575 | ||||||||
\(173\) | −22.4162 | −1.70427 | −0.852136 | − | 0.523320i | \(-0.824693\pi\) | ||||
−0.852136 | + | 0.523320i | \(0.824693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.91302 | −0.294955 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.67684 | 0.650357 | ||||||||
\(179\) | 8.26202 | 0.617532 | 0.308766 | − | 0.951138i | \(-0.400084\pi\) | ||||
0.308766 | + | 0.951138i | \(0.400084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.787935 | −0.0585668 | −0.0292834 | − | 0.999571i | \(-0.509323\pi\) | ||||
−0.0292834 | + | 0.999571i | \(0.509323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.8961 | −1.17188 | ||||||||
\(185\) | −16.6959 | −1.22751 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.81711 | −0.571644 | ||||||||
\(188\) | 2.14549 | 0.156476 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.0541 | −0.801948 | ||||||||
\(191\) | 0.396261 | 0.0286724 | 0.0143362 | − | 0.999897i | \(-0.495436\pi\) | ||||
0.0143362 | + | 0.999897i | \(0.495436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.78794 | 0.272662 | 0.136331 | − | 0.990663i | \(-0.456469\pi\) | ||||
0.136331 | + | 0.990663i | \(0.456469\pi\) | |||||||
\(194\) | 5.21569 | 0.374464 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0484 | 0.858415 | 0.429207 | − | 0.903206i | \(-0.358793\pi\) | ||||
0.429207 | + | 0.903206i | \(0.358793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.16225 | −0.365942 | −0.182971 | − | 0.983118i | \(-0.558572\pi\) | ||||
−0.182971 | + | 0.983118i | \(0.558572\pi\) | |||||||
\(200\) | −3.71224 | −0.262495 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.24124 | 0.439132 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.1914 | −1.82929 | ||||||||
\(206\) | 1.60648 | 0.111928 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.05408 | −0.0730876 | ||||||||
\(209\) | −21.9802 | −1.52040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9794 | 1.23775 | 0.618875 | − | 0.785489i | \(-0.287589\pi\) | ||||
0.618875 | + | 0.785489i | \(0.287589\pi\) | |||||||
\(212\) | 9.42722 | 0.647464 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.52898 | −0.377954 | ||||||||
\(215\) | 27.0637 | 1.84573 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0397250 | 0.00269052 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.7807 | −0.929097 | ||||||||
\(221\) | −2.10577 | −0.141649 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.96790 | 0.131780 | 0.0658901 | − | 0.997827i | \(-0.479011\pi\) | ||||
0.0658901 | + | 0.997827i | \(0.479011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.59358 | −0.305560 | ||||||||
\(227\) | −12.4285 | −0.824911 | −0.412456 | − | 0.910978i | \(-0.635329\pi\) | ||||
−0.412456 | + | 0.910978i | \(0.635329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0584 | 1.39158 | 0.695788 | − | 0.718248i | \(-0.255055\pi\) | ||||
0.695788 | + | 0.718248i | \(0.255055\pi\) | |||||||
\(230\) | −11.6757 | −0.769876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22.4576 | −1.47441 | ||||||||
\(233\) | −7.26872 | −0.476190 | −0.238095 | − | 0.971242i | \(-0.576523\pi\) | ||||
−0.238095 | + | 0.971242i | \(0.576523\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.73385 | 0.243570 | ||||||||
\(236\) | −16.7012 | −1.08716 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8698 | 0.832479 | 0.416239 | − | 0.909255i | \(-0.363348\pi\) | ||||
0.416239 | + | 0.909255i | \(0.363348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1986 | 0.850198 | 0.425099 | − | 0.905147i | \(-0.360239\pi\) | ||||
0.425099 | + | 0.905147i | \(0.360239\pi\) | |||||||
\(242\) | 2.04246 | 0.131294 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.3130 | 0.852280 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.92101 | −0.376745 | ||||||||
\(248\) | 14.4924 | 0.920270 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.60797 | 0.417925 | ||||||||
\(251\) | 10.1617 | 0.641402 | 0.320701 | − | 0.947180i | \(-0.396081\pi\) | ||||
0.320701 | + | 0.947180i | \(0.396081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.2163 | −1.45960 | ||||||||
\(254\) | −1.83083 | −0.114876 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8099 | −0.738120 | ||||||||
\(257\) | 0.240499 | 0.0150019 | 0.00750095 | − | 0.999972i | \(-0.497612\pi\) | ||||
0.00750095 | + | 0.999972i | \(0.497612\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.71224 | −0.230223 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50312 | −0.401764 | ||||||||
\(263\) | 16.7592 | 1.03342 | 0.516710 | − | 0.856161i | \(-0.327157\pi\) | ||||
0.516710 | + | 0.856161i | \(0.327157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4064 | 1.00784 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.5261 | 1.25383 | ||||||||
\(269\) | −14.8307 | −0.904242 | −0.452121 | − | 0.891957i | \(-0.649332\pi\) | ||||
−0.452121 | + | 0.891957i | \(0.649332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2704 | 1.65656 | 0.828280 | − | 0.560314i | \(-0.189320\pi\) | ||||
0.828280 | + | 0.560314i | \(0.189320\pi\) | |||||||
\(272\) | 2.21966 | 0.134586 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.99707 | 0.120648 | ||||||||
\(275\) | −5.42175 | −0.326944 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.6912 | −1.66381 | −0.831903 | − | 0.554922i | \(-0.812748\pi\) | ||||
−0.831903 | + | 0.554922i | \(0.812748\pi\) | |||||||
\(278\) | 9.67300 | 0.580148 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6959 | −0.995996 | −0.497998 | − | 0.867178i | \(-0.665931\pi\) | ||||
−0.497998 | + | 0.867178i | \(0.665931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.320233 | −0.0190359 | −0.00951794 | − | 0.999955i | \(-0.503030\pi\) | ||||
−0.00951794 | + | 0.999955i | \(0.503030\pi\) | |||||||
\(284\) | 21.1082 | 1.25254 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72665 | 0.161230 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.5657 | −0.739162 | ||||||||
\(290\) | −16.4952 | −0.968630 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.96790 | 0.524806 | ||||||||
\(293\) | 8.07954 | 0.472012 | 0.236006 | − | 0.971752i | \(-0.424162\pi\) | ||||
0.236006 | + | 0.971752i | \(0.424162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.0656 | −1.69226 | ||||||||
\(296\) | −16.6959 | −0.970432 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.25399 | −0.361678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.35844 | −0.308344 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.24124 | 0.357960 | ||||||||
\(305\) | 23.1690 | 1.32665 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.94299 | −0.282111 | −0.141056 | − | 0.990002i | \(-0.545050\pi\) | ||||
−0.141056 | + | 0.990002i | \(0.545050\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.6447 | 0.604581 | ||||||||
\(311\) | −4.05048 | −0.229682 | −0.114841 | − | 0.993384i | \(-0.536636\pi\) | ||||
−0.114841 | + | 0.993384i | \(0.536636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3671 | −0.585984 | −0.292992 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292992 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(314\) | −4.16652 | −0.235130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6372 | 0.654641 | ||||||||
\(317\) | 12.0773 | 0.678328 | 0.339164 | − | 0.940727i | \(-0.389856\pi\) | ||||
0.339164 | + | 0.940727i | \(0.389856\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.7994 | −1.83641 | ||||||||
\(320\) | −5.57751 | −0.311792 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4683 | 0.693753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.46050 | −0.0810142 | ||||||||
\(326\) | −15.2161 | −0.842740 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.1914 | −1.44618 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1766 | −1.21894 | −0.609469 | − | 0.792810i | \(-0.708617\pi\) | ||||
−0.609469 | + | 0.792810i | \(0.708617\pi\) | |||||||
\(332\) | 17.7473 | 0.974007 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5146 | 0.575333 | ||||||||
\(335\) | 35.7220 | 1.95170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.95311 | −0.324287 | −0.162143 | − | 0.986767i | \(-0.551841\pi\) | ||||
−0.162143 | + | 0.986767i | \(0.551841\pi\) | |||||||
\(338\) | 0.734503 | 0.0399517 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.81711 | 0.423942 | ||||||||
\(341\) | 21.1663 | 1.14622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 27.0637 | 1.45918 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4648 | −0.885152 | ||||||||
\(347\) | −19.0422 | −1.02224 | −0.511120 | − | 0.859510i | \(-0.670769\pi\) | ||||
−0.511120 | + | 0.859510i | \(0.670769\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.61556 | −0.193537 | −0.0967683 | − | 0.995307i | \(-0.530851\pi\) | ||||
−0.0967683 | + | 0.995307i | \(0.530851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.7453 | −1.15903 | ||||||||
\(353\) | 5.97691 | 0.318119 | 0.159059 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159059 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.7352 | 1.94970 | ||||||||
\(356\) | −17.2533 | −0.914420 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.06848 | 0.320729 | ||||||||
\(359\) | −15.1528 | −0.799733 | −0.399866 | − | 0.916573i | \(-0.630943\pi\) | ||||
−0.399866 | + | 0.916573i | \(0.630943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0584 | 0.845177 | ||||||||
\(362\) | −0.578741 | −0.0304180 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.6070 | 0.816910 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.75156 | −0.352429 | −0.176214 | − | 0.984352i | \(-0.556385\pi\) | ||||
−0.176214 | + | 0.984352i | \(0.556385\pi\) | |||||||
\(368\) | 6.59224 | 0.343644 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.2632 | −0.637535 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.30972 | 0.326705 | 0.163352 | − | 0.986568i | \(-0.447769\pi\) | ||||
0.163352 | + | 0.986568i | \(0.447769\pi\) | |||||||
\(374\) | −5.74170 | −0.296896 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.73385 | 0.192559 | ||||||||
\(377\) | −8.83547 | −0.455050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0861875 | 0.00442715 | 0.00221358 | − | 0.999998i | \(-0.499295\pi\) | ||||
0.00221358 | + | 0.999998i | \(0.499295\pi\) | |||||||
\(380\) | 21.9802 | 1.12756 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.291055 | 0.0148917 | ||||||||
\(383\) | −21.3779 | −1.09236 | −0.546180 | − | 0.837668i | \(-0.683918\pi\) | ||||
−0.546180 | + | 0.837668i | \(0.683918\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.78225 | 0.141613 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.3710 | −0.526508 | ||||||||
\(389\) | −32.0839 | −1.62672 | −0.813360 | − | 0.581761i | \(-0.802364\pi\) | ||||
−0.813360 | + | 0.581761i | \(0.802364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.1694 | 0.666008 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.84961 | 0.445837 | ||||||||
\(395\) | 20.2524 | 1.01901 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1196 | 0.608267 | 0.304134 | − | 0.952629i | \(-0.401633\pi\) | ||||
0.304134 | + | 0.952629i | \(0.401633\pi\) | |||||||
\(398\) | −3.79169 | −0.190060 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.53950 | 0.0769748 | ||||||||
\(401\) | 26.6277 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.70175 | 0.284024 | ||||||||
\(404\) | −12.4102 | −0.617433 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.3845 | −1.20869 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.48968 | −0.320894 | −0.160447 | − | 0.987044i | \(-0.551294\pi\) | ||||
−0.160447 | + | 0.987044i | \(0.551294\pi\) | |||||||
\(410\) | −19.2377 | −0.950082 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.19436 | −0.157375 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.8860 | 1.51613 | ||||||||
\(416\) | −5.85773 | −0.287199 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.1445 | −0.789655 | ||||||||
\(419\) | −31.3097 | −1.52958 | −0.764789 | − | 0.644280i | \(-0.777157\pi\) | ||||
−0.764789 | + | 0.644280i | \(0.777157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3097 | −1.18478 | −0.592392 | − | 0.805650i | \(-0.701816\pi\) | ||||
−0.592392 | + | 0.805650i | \(0.701816\pi\) | |||||||
\(422\) | 13.2059 | 0.642853 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.4064 | 0.796766 | ||||||||
\(425\) | 3.07548 | 0.149183 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.9940 | 0.531414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.8784 | 0.958621 | ||||||||
\(431\) | 19.7950 | 0.953492 | 0.476746 | − | 0.879041i | \(-0.341816\pi\) | ||||
0.476746 | + | 0.879041i | \(0.341816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.8932 | −1.53269 | −0.766344 | − | 0.642430i | \(-0.777926\pi\) | ||||
−0.766344 | + | 0.642430i | \(0.777926\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0789903 | −0.00378295 | ||||||||
\(437\) | 37.0300 | 1.77138 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.8463 | −1.37676 | −0.688379 | − | 0.725351i | \(-0.741677\pi\) | ||||
−0.688379 | + | 0.725351i | \(0.741677\pi\) | |||||||
\(440\) | −23.9830 | −1.14334 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.54669 | −0.0735687 | ||||||||
\(443\) | 3.25796 | 0.154790 | 0.0773952 | − | 0.997000i | \(-0.475340\pi\) | ||||
0.0773952 | + | 0.997000i | \(0.475340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.0263 | −1.42338 | ||||||||
\(446\) | 1.44543 | 0.0684429 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.03302 | 0.0487513 | 0.0243756 | − | 0.999703i | \(-0.492240\pi\) | ||||
0.0243756 | + | 0.999703i | \(0.492240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.2527 | −1.80125 | ||||||||
\(452\) | 9.13399 | 0.429627 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.12880 | −0.428436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.4648 | −0.816968 | −0.408484 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408484 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(458\) | 15.4674 | 0.722746 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.2163 | 1.08247 | ||||||||
\(461\) | −32.4060 | −1.50930 | −0.754649 | − | 0.656128i | \(-0.772193\pi\) | ||||
−0.754649 | + | 0.656128i | \(0.772193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8788 | −1.62095 | −0.810477 | − | 0.585770i | \(-0.800792\pi\) | ||||
−0.810477 | + | 0.585770i | \(0.800792\pi\) | |||||||
\(464\) | 9.31333 | 0.432361 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.33890 | −0.247320 | ||||||||
\(467\) | −32.5252 | −1.50509 | −0.752543 | − | 0.658543i | \(-0.771173\pi\) | ||||
−0.752543 | + | 0.658543i | \(0.771173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.74253 | 0.126503 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −29.0656 | −1.33785 | ||||||||
\(473\) | 39.5267 | 1.81744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.64766 | 0.396782 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.45292 | 0.432366 | ||||||||
\(479\) | −5.04378 | −0.230456 | −0.115228 | − | 0.993339i | \(-0.536760\pi\) | ||||
−0.115228 | + | 0.993339i | \(0.536760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.56867 | −0.299506 | ||||||||
\(482\) | 9.69444 | 0.441569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.06128 | −0.184604 | ||||||||
\(485\) | −18.0489 | −0.819559 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2019 | −0.507608 | −0.253804 | − | 0.967256i | \(-0.581682\pi\) | ||||
−0.253804 | + | 0.967256i | \(0.581682\pi\) | |||||||
\(488\) | 23.1690 | 1.04881 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.6420 | −0.976689 | −0.488344 | − | 0.872651i | \(-0.662399\pi\) | ||||
−0.488344 | + | 0.872651i | \(0.662399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.6054 | 0.837947 | ||||||||
\(494\) | −4.34900 | −0.195671 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.01012 | −0.269862 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8128 | −0.573582 | −0.286791 | − | 0.957993i | \(-0.592588\pi\) | ||||
−0.286791 | + | 0.957993i | \(0.592588\pi\) | |||||||
\(500\) | −13.1395 | −0.587615 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.46382 | 0.333127 | ||||||||
\(503\) | 24.9763 | 1.11364 | 0.556818 | − | 0.830635i | \(-0.312022\pi\) | ||||
0.556818 | + | 0.830635i | \(0.312022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.5979 | −0.961092 | ||||||||
\(506\) | −17.0525 | −0.758075 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.64047 | 0.161520 | ||||||||
\(509\) | 35.6007 | 1.57797 | 0.788986 | − | 0.614411i | \(-0.210606\pi\) | ||||
0.788986 | + | 0.614411i | \(0.210606\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.5330 | 0.509691 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.176647 | 0.00779157 | ||||||||
\(515\) | −5.55922 | −0.244968 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.45331 | 0.239836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.46050 | −0.283312 | ||||||||
\(521\) | −36.8078 | −1.61258 | −0.806288 | − | 0.591523i | \(-0.798527\pi\) | ||||
−0.806288 | + | 0.591523i | \(0.798527\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5175 | −0.678534 | −0.339267 | − | 0.940690i | \(-0.610179\pi\) | ||||
−0.339267 | + | 0.940690i | \(0.610179\pi\) | |||||||
\(524\) | 12.9310 | 0.564892 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.3097 | 0.536729 | ||||||||
\(527\) | −12.0065 | −0.523013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1124 | 0.700541 | ||||||||
\(530\) | 12.0506 | 0.523443 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.3045 | −0.446336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.1331 | 0.827195 | ||||||||
\(536\) | 35.7220 | 1.54296 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.8932 | −0.469638 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5261 | 0.968471 | 0.484235 | − | 0.874938i | \(-0.339098\pi\) | ||||
0.484235 | + | 0.874938i | \(0.339098\pi\) | |||||||
\(542\) | 20.0302 | 0.860371 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.3350 | 0.528859 | ||||||||
\(545\) | −0.137469 | −0.00588851 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.73812 | 0.0743168 | 0.0371584 | − | 0.999309i | \(-0.488169\pi\) | ||||
0.0371584 | + | 0.999309i | \(0.488169\pi\) | |||||||
\(548\) | −3.97103 | −0.169634 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.98229 | −0.169805 | ||||||||
\(551\) | 52.3149 | 2.22869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.3393 | −0.864134 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.2340 | −0.815705 | ||||||||
\(557\) | −26.3056 | −1.11461 | −0.557303 | − | 0.830309i | \(-0.688164\pi\) | ||||
−0.557303 | + | 0.830309i | \(0.688164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6477 | 0.450348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.2632 | −0.517293 | ||||||||
\(563\) | 13.7365 | 0.578924 | 0.289462 | − | 0.957189i | \(-0.406524\pi\) | ||||
0.289462 | + | 0.957189i | \(0.406524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.8961 | 0.668754 | ||||||||
\(566\) | −0.235212 | −0.00988671 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.7352 | 1.54137 | ||||||||
\(569\) | 19.6522 | 0.823865 | 0.411933 | − | 0.911214i | \(-0.364854\pi\) | ||||
0.411933 | + | 0.911214i | \(0.364854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.7516 | −0.701031 | −0.350515 | − | 0.936557i | \(-0.613994\pi\) | ||||
−0.350515 | + | 0.936557i | \(0.613994\pi\) | |||||||
\(572\) | −5.42175 | −0.226695 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.13399 | 0.380914 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3930 | −0.973863 | −0.486931 | − | 0.873440i | \(-0.661884\pi\) | ||||
−0.486931 | + | 0.873440i | \(0.661884\pi\) | |||||||
\(578\) | −9.22958 | −0.383900 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.7994 | 1.36192 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.9617 | 0.992390 | ||||||||
\(584\) | 15.6070 | 0.645824 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.93445 | 0.245150 | ||||||||
\(587\) | 6.05322 | 0.249843 | 0.124922 | − | 0.992167i | \(-0.460132\pi\) | ||||
0.124922 | + | 0.992167i | \(0.460132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.7601 | −1.39106 | ||||||||
\(590\) | −21.3487 | −0.878914 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.92393 | 0.284572 | ||||||||
\(593\) | 6.54722 | 0.268862 | 0.134431 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134431 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.59358 | −0.187845 | ||||||||
\(599\) | −2.36241 | −0.0965255 | −0.0482627 | − | 0.998835i | \(-0.515368\pi\) | ||||
−0.0482627 | + | 0.998835i | \(0.515368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.5408 | 1.65370 | 0.826848 | − | 0.562426i | \(-0.190132\pi\) | ||||
0.826848 | + | 0.562426i | \(0.190132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.6549 | 0.433540 | ||||||||
\(605\) | −7.06795 | −0.287353 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.4461 | −0.464583 | −0.232292 | − | 0.972646i | \(-0.574622\pi\) | ||||
−0.232292 | + | 0.972646i | \(0.574622\pi\) | |||||||
\(608\) | 34.6837 | 1.40661 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.0177 | 0.689027 | ||||||||
\(611\) | 1.46901 | 0.0594296 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7060 | 0.513191 | 0.256596 | − | 0.966519i | \(-0.417399\pi\) | ||||
0.256596 | + | 0.966519i | \(0.417399\pi\) | |||||||
\(614\) | −3.63064 | −0.146521 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.9500 | 1.24600 | 0.623000 | − | 0.782221i | \(-0.285913\pi\) | ||||
0.623000 | + | 0.782221i | \(0.285913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.56440 | 0.183459 | 0.0917294 | − | 0.995784i | \(-0.470761\pi\) | ||||
0.0917294 | + | 0.995784i | \(0.470761\pi\) | |||||||
\(620\) | −21.1663 | −0.850058 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.97509 | −0.119290 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1694 | −1.20678 | ||||||||
\(626\) | −7.61468 | −0.304344 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.28482 | 0.330600 | ||||||||
\(629\) | 13.8321 | 0.551522 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0803 | 0.600339 | 0.300169 | − | 0.953886i | \(-0.402957\pi\) | ||||
0.300169 | + | 0.953886i | \(0.402957\pi\) | |||||||
\(632\) | 20.2524 | 0.805598 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.87081 | 0.352305 | ||||||||
\(635\) | 6.33559 | 0.251420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.0913 | −0.953783 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.6811 | 1.01514 | ||||||||
\(641\) | −6.04236 | −0.238659 | −0.119329 | − | 0.992855i | \(-0.538074\pi\) | ||||
−0.119329 | + | 0.992855i | \(0.538074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.2881 | −0.642341 | −0.321171 | − | 0.947021i | \(-0.604076\pi\) | ||||
−0.321171 | + | 0.947021i | \(0.604076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.15798 | 0.360316 | ||||||||
\(647\) | −7.16040 | −0.281505 | −0.140752 | − | 0.990045i | \(-0.544952\pi\) | ||||
−0.140752 | + | 0.990045i | \(0.544952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.4504 | −1.66632 | ||||||||
\(650\) | −1.07275 | −0.0420765 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.2560 | 1.18492 | ||||||||
\(653\) | 23.5255 | 0.920625 | 0.460313 | − | 0.887757i | \(-0.347737\pi\) | ||||
0.460313 | + | 0.887757i | \(0.347737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5041 | 0.879307 | ||||||||
\(656\) | 10.8618 | 0.424082 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.73459 | −0.340251 | −0.170126 | − | 0.985422i | \(-0.554417\pi\) | ||||
−0.170126 | + | 0.985422i | \(0.554417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2016 | 0.435690 | 0.217845 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217845 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(662\) | −16.2888 | −0.633083 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30.8860 | 1.19861 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.2570 | 2.13956 | ||||||||
\(668\) | −20.9075 | −0.808934 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.2379 | 1.01366 | ||||||||
\(671\) | 33.8384 | 1.30632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0728 | −0.426823 | −0.213412 | − | 0.976962i | \(-0.568458\pi\) | ||||
−0.213412 | + | 0.976962i | \(0.568458\pi\) | |||||||
\(674\) | −4.37258 | −0.168426 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.46050 | −0.0561733 | ||||||||
\(677\) | −36.0838 | −1.38681 | −0.693407 | − | 0.720546i | \(-0.743891\pi\) | ||||
−0.693407 | + | 0.720546i | \(0.743891\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.6043 | 0.521702 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.5467 | 0.595314 | ||||||||
\(683\) | 48.9248 | 1.87205 | 0.936027 | − | 0.351928i | \(-0.114474\pi\) | ||||
0.936027 | + | 0.351928i | \(0.114474\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.91089 | −0.264051 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.2235 | −0.427893 | ||||||||
\(689\) | 6.45477 | 0.245907 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.6706 | −1.43306 | −0.716529 | − | 0.697558i | \(-0.754270\pi\) | ||||
−0.716529 | + | 0.697558i | \(0.754270\pi\) | |||||||
\(692\) | 32.7390 | 1.24455 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.9866 | −0.530923 | ||||||||
\(695\) | −33.4735 | −1.26972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.6988 | 0.821902 | ||||||||
\(698\) | −2.65564 | −0.100517 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9325 | −0.752839 | −0.376420 | − | 0.926449i | \(-0.622845\pi\) | ||||
−0.376420 | + | 0.926449i | \(0.622845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.8932 | 1.46688 | ||||||||
\(704\) | −8.14598 | −0.307013 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.39006 | 0.165222 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.07607 | −0.153080 | −0.0765399 | − | 0.997067i | \(-0.524387\pi\) | ||||
−0.0765399 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(710\) | 26.9821 | 1.01262 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.0263 | −1.12528 | ||||||||
\(713\) | −35.6587 | −1.33543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.43560 | −0.352871 | ||||||||
\(716\) | −12.0667 | −0.450954 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.1298 | −0.415359 | ||||||||
\(719\) | −4.12465 | −0.153823 | −0.0769117 | − | 0.997038i | \(-0.524506\pi\) | ||||
−0.0769117 | + | 0.997038i | \(0.524506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.7949 | 0.438961 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.15078 | 0.0427685 | ||||||||
\(725\) | 12.9042 | 0.479252 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.39203 | −0.274155 | −0.137078 | − | 0.990560i | \(-0.543771\pi\) | ||||
−0.137078 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.4634 | 0.424281 | ||||||||
\(731\) | −22.4215 | −0.829289 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.05836 | −0.260706 | −0.130353 | − | 0.991468i | \(-0.541611\pi\) | ||||
−0.130353 | + | 0.991468i | \(0.541611\pi\) | |||||||
\(734\) | −4.95904 | −0.183042 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.6342 | 1.35036 | ||||||||
\(737\) | 52.1722 | 1.92179 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.9033 | −1.24715 | −0.623577 | − | 0.781762i | \(-0.714321\pi\) | ||||
−0.623577 | + | 0.781762i | \(0.714321\pi\) | |||||||
\(740\) | 24.3845 | 0.896392 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3211 | −0.598763 | −0.299382 | − | 0.954133i | \(-0.596780\pi\) | ||||
−0.299382 | + | 0.954133i | \(0.596780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.63451 | 0.169682 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.4169 | 0.417444 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5467 | −0.859231 | −0.429616 | − | 0.903012i | \(-0.641351\pi\) | ||||
−0.429616 | + | 0.903012i | \(0.641351\pi\) | |||||||
\(752\) | −1.54846 | −0.0564664 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.48968 | −0.236340 | ||||||||
\(755\) | 18.5429 | 0.674846 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.1019 | 1.27580 | 0.637901 | − | 0.770119i | \(-0.279803\pi\) | ||||
0.637901 | + | 0.770119i | \(0.279803\pi\) | |||||||
\(758\) | 0.0633050 | 0.00229934 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.2527 | 1.38757 | ||||||||
\(761\) | −45.4692 | −1.64826 | −0.824128 | − | 0.566404i | \(-0.808334\pi\) | ||||
−0.824128 | + | 0.566404i | \(0.808334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.578741 | −0.0209381 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.7021 | −0.567341 | ||||||||
\(767\) | −11.4352 | −0.412903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4543 | −1.53094 | −0.765470 | − | 0.643472i | \(-0.777493\pi\) | ||||
−0.765470 | + | 0.643472i | \(0.777493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.53230 | −0.199112 | ||||||||
\(773\) | −46.6021 | −1.67616 | −0.838080 | − | 0.545547i | \(-0.816322\pi\) | ||||
−0.838080 | + | 0.545547i | \(0.816322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.32743 | −0.299130 | ||||||||
\(776\) | −18.0489 | −0.647918 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.5657 | −0.844873 | ||||||||
\(779\) | 61.0129 | 2.18601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.6519 | 1.91982 | ||||||||
\(782\) | 9.67300 | 0.345906 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4183 | 0.514610 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3815 | 0.940399 | 0.470200 | − | 0.882560i | \(-0.344182\pi\) | ||||
0.470200 | + | 0.882560i | \(0.344182\pi\) | |||||||
\(788\) | −17.5968 | −0.626859 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.8755 | 0.529245 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.11537 | 0.323696 | ||||||||
\(794\) | 8.90191 | 0.315917 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.53950 | 0.267230 | ||||||||
\(797\) | −17.6474 | −0.625102 | −0.312551 | − | 0.949901i | \(-0.601183\pi\) | ||||
−0.312551 | + | 0.949901i | \(0.601183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.09338 | −0.109436 | ||||||||
\(800\) | 8.55525 | 0.302474 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.5582 | 0.690623 | ||||||||
\(803\) | 22.7942 | 0.804389 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.18795 | 0.147514 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.5979 | −0.759810 | ||||||||
\(809\) | 17.9716 | 0.631848 | 0.315924 | − | 0.948784i | \(-0.397686\pi\) | ||||
0.315924 | + | 0.948784i | \(0.397686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5159 | 1.52805 | 0.764026 | − | 0.645186i | \(-0.223220\pi\) | ||||
0.764026 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.9105 | −0.627763 | ||||||||
\(815\) | 52.6553 | 1.84443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −63.0449 | −2.20566 | ||||||||
\(818\) | −4.76669 | −0.166664 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.2527 | 1.33584 | ||||||||
\(821\) | −36.7283 | −1.28183 | −0.640913 | − | 0.767613i | \(-0.721444\pi\) | ||||
−0.640913 | + | 0.767613i | \(0.721444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.2235 | −1.43696 | −0.718481 | − | 0.695547i | \(-0.755162\pi\) | ||||
−0.718481 | + | 0.695547i | \(0.755162\pi\) | |||||||
\(824\) | −5.55922 | −0.193664 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0060 | 0.347941 | 0.173971 | − | 0.984751i | \(-0.444340\pi\) | ||||
0.173971 | + | 0.984751i | \(0.444340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.9607 | 0.519607 | 0.259803 | − | 0.965662i | \(-0.416342\pi\) | ||||
0.259803 | + | 0.965662i | \(0.416342\pi\) | |||||||
\(830\) | 22.6859 | 0.787438 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.19436 | −0.0760756 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.3858 | −1.25918 | ||||||||
\(836\) | 32.1022 | 1.11028 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.9971 | −0.794421 | ||||||||
\(839\) | 27.0026 | 0.932232 | 0.466116 | − | 0.884724i | \(-0.345653\pi\) | ||||
0.466116 | + | 0.884724i | \(0.345653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.0656 | 1.69192 | ||||||||
\(842\) | −17.8556 | −0.615344 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.2590 | −0.903870 | ||||||||
\(845\) | −2.54175 | −0.0874389 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.80387 | −0.233646 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.25895 | 0.0774814 | ||||||||
\(851\) | 41.0804 | 1.40822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5438 | −0.361012 | −0.180506 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180506 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1331 | 0.653955 | ||||||||
\(857\) | 7.48035 | 0.255524 | 0.127762 | − | 0.991805i | \(-0.459221\pi\) | ||||
0.127762 | + | 0.991805i | \(0.459221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.3724 | 1.47985 | 0.739923 | − | 0.672692i | \(-0.234862\pi\) | ||||
0.739923 | + | 0.672692i | \(0.234862\pi\) | |||||||
\(860\) | −39.5267 | −1.34785 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.5395 | 0.495217 | ||||||||
\(863\) | 32.0228 | 1.09007 | 0.545034 | − | 0.838414i | \(-0.316517\pi\) | ||||
0.545034 | + | 0.838414i | \(0.316517\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.9764 | 1.93726 | ||||||||
\(866\) | −23.4256 | −0.796036 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.5788 | 1.00339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0541 | 0.476204 | ||||||||
\(872\) | −0.137469 | −0.00465528 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.1986 | 0.920007 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.6156 | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314371\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314371\pi\) | |||||||
\(878\) | −21.1877 | −0.715050 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.94592 | 0.335277 | ||||||||
\(881\) | −34.6890 | −1.16870 | −0.584351 | − | 0.811501i | \(-0.698651\pi\) | ||||
−0.584351 | + | 0.811501i | \(0.698651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.36381 | 0.247812 | 0.123906 | − | 0.992294i | \(-0.460458\pi\) | ||||
0.123906 | + | 0.992294i | \(0.460458\pi\) | |||||||
\(884\) | 3.07548 | 0.103440 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.39298 | 0.0803939 | ||||||||
\(887\) | 31.2517 | 1.04933 | 0.524664 | − | 0.851309i | \(-0.324191\pi\) | ||||
0.524664 | + | 0.851309i | \(0.324191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −22.0544 | −0.739265 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.87412 | −0.0962327 | ||||||||
\(893\) | −8.69800 | −0.291068 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0000 | −0.701953 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.758757 | 0.0253201 | ||||||||
\(899\) | −50.3776 | −1.68019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5922 | −0.452823 | ||||||||
\(902\) | −28.0967 | −0.935519 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.8961 | 0.528697 | ||||||||
\(905\) | 2.00274 | 0.0665732 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.7204 | −1.88337 | −0.941685 | − | 0.336495i | \(-0.890758\pi\) | ||||
−0.941685 | + | 0.336495i | \(0.890758\pi\) | |||||||
\(908\) | 18.1519 | 0.602393 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.4742 | −0.744604 | −0.372302 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372302 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.1091 | 1.49289 | ||||||||
\(914\) | −12.8279 | −0.424310 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.7558 | −1.01620 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.48541 | 0.0819861 | 0.0409931 | − | 0.999159i | \(-0.486948\pi\) | ||||
0.0409931 | + | 0.999159i | \(0.486948\pi\) | |||||||
\(920\) | 40.4040 | 1.33208 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.8023 | −0.783888 | ||||||||
\(923\) | 14.4527 | 0.475717 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.59358 | 0.315435 | ||||||||
\(926\) | −25.6186 | −0.841879 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 51.7558 | 1.69897 | ||||||||
\(929\) | 35.1991 | 1.15485 | 0.577423 | − | 0.816445i | \(-0.304058\pi\) | ||||
0.577423 | + | 0.816445i | \(0.304058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.6160 | 0.347739 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.8899 | −0.781700 | ||||||||
\(935\) | 19.8692 | 0.649791 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.0613 | 1.30875 | 0.654373 | − | 0.756172i | \(-0.272933\pi\) | ||||
0.654373 | + | 0.756172i | \(0.272933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.45331 | −0.177867 | ||||||||
\(941\) | −32.0076 | −1.04342 | −0.521709 | − | 0.853123i | \(-0.674705\pi\) | ||||
−0.521709 | + | 0.853123i | \(0.674705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.4441 | 2.09859 | ||||||||
\(944\) | 12.0537 | 0.392315 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.0325 | 0.943928 | ||||||||
\(947\) | −22.7383 | −0.738896 | −0.369448 | − | 0.929251i | \(-0.620453\pi\) | ||||
−0.369448 | + | 0.929251i | \(0.620453\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.14027 | 0.199322 | ||||||||
\(950\) | 6.35174 | 0.206078 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.7884 | 0.543830 | 0.271915 | − | 0.962321i | \(-0.412343\pi\) | ||||
0.271915 | + | 0.962321i | \(0.412343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00720 | −0.0325921 | ||||||||
\(956\) | −18.7964 | −0.607920 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.70467 | −0.119693 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.50993 | 0.0487073 | ||||||||
\(962\) | −4.82471 | −0.155555 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.2767 | −0.620859 | ||||||||
\(965\) | −9.62799 | −0.309936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3533 | 1.42631 | 0.713153 | − | 0.701009i | \(-0.247267\pi\) | ||||
0.713153 | + | 0.701009i | \(0.247267\pi\) | |||||||
\(968\) | −7.06795 | −0.227172 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.2570 | −0.425656 | ||||||||
\(971\) | −4.07935 | −0.130913 | −0.0654563 | − | 0.997855i | \(-0.520850\pi\) | ||||
−0.0654563 | + | 0.997855i | \(0.520850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.22786 | −0.263638 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.60836 | −0.307556 | ||||||||
\(977\) | 9.76018 | 0.312256 | 0.156128 | − | 0.987737i | \(-0.450099\pi\) | ||||
0.156128 | + | 0.987737i | \(0.450099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.8535 | −1.40156 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.8961 | −0.507265 | ||||||||
\(983\) | −51.3163 | −1.63674 | −0.818368 | − | 0.574694i | \(-0.805121\pi\) | ||||
−0.818368 | + | 0.574694i | \(0.805121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.6241 | −0.975765 | ||||||||
\(986\) | 13.6658 | 0.435206 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.64766 | 0.275119 | ||||||||
\(989\) | −66.5904 | −2.11745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.704673 | −0.0223847 | −0.0111923 | − | 0.999937i | \(-0.503563\pi\) | ||||
−0.0111923 | + | 0.999937i | \(0.503563\pi\) | |||||||
\(992\) | −33.3993 | −1.06043 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1212 | 0.415969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.0259 | 1.07761 | 0.538805 | − | 0.842431i | \(-0.318876\pi\) | ||||
0.538805 | + | 0.842431i | \(0.318876\pi\) | |||||||
\(998\) | −9.41107 | −0.297902 | ||||||||
\(999\) | 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 | 5733.2.a.bs.1.4 | 6 | ||
3.2 | odd | 2 | inner | 5733.2.a.bs.1.3 | 6 | ||
7.2 | even | 3 | 819.2.j.i.235.3 | ✓ | 12 | ||
7.4 | even | 3 | 819.2.j.i.352.3 | yes | 12 | ||
7.6 | odd | 2 | 5733.2.a.bt.1.4 | 6 | |||
21.2 | odd | 6 | 819.2.j.i.235.4 | yes | 12 | ||
21.11 | odd | 6 | 819.2.j.i.352.4 | yes | 12 | ||
21.20 | even | 2 | 5733.2.a.bt.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
819.2.j.i.235.3 | ✓ | 12 | 7.2 | even | 3 | ||
819.2.j.i.235.4 | yes | 12 | 21.2 | odd | 6 | ||
819.2.j.i.352.3 | yes | 12 | 7.4 | even | 3 | ||
819.2.j.i.352.4 | yes | 12 | 21.11 | odd | 6 | ||
5733.2.a.bs.1.3 | 6 | 3.2 | odd | 2 | inner | ||
5733.2.a.bs.1.4 | 6 | 1.1 | even | 1 | trivial | ||
5733.2.a.bt.1.3 | 6 | 21.20 | even | 2 | |||
5733.2.a.bt.1.4 | 6 | 7.6 | odd | 2 |