Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 225) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54077 | −1.08949 | −0.544745 | − | 0.838602i | \(-0.683374\pi\) | ||||
−0.544745 | + | 0.838602i | \(0.683374\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.373979 | 0.186989 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.37636 | −1.27615 | −0.638073 | − | 0.769976i | \(-0.720268\pi\) | ||||
−0.638073 | + | 0.769976i | \(0.720268\pi\) | |||||||
\(8\) | 2.50533 | 0.885767 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.275476 | 0.0830591 | 0.0415296 | − | 0.999137i | \(-0.486777\pi\) | ||||
0.0415296 | + | 0.999137i | \(0.486777\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.74270 | −1.59274 | −0.796369 | − | 0.604811i | \(-0.793248\pi\) | ||||
−0.796369 | + | 0.604811i | \(0.793248\pi\) | |||||||
\(14\) | 5.20221 | 1.39035 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.60810 | −1.15202 | ||||||||
\(17\) | −6.11846 | −1.48395 | −0.741973 | − | 0.670430i | \(-0.766110\pi\) | ||||
−0.741973 | + | 0.670430i | \(0.766110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.04824 | −1.15815 | −0.579073 | − | 0.815275i | \(-0.696586\pi\) | ||||
−0.579073 | + | 0.815275i | \(0.696586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.424446 | −0.0904921 | ||||||||
\(23\) | −2.66559 | −0.555813 | −0.277907 | − | 0.960608i | \(-0.589641\pi\) | ||||
−0.277907 | + | 0.960608i | \(0.589641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.84819 | 1.73527 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.26269 | −0.238626 | ||||||||
\(29\) | −6.27782 | −1.16576 | −0.582881 | − | 0.812558i | \(-0.698075\pi\) | ||||
−0.582881 | + | 0.812558i | \(0.698075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.987076 | 0.177284 | 0.0886421 | − | 0.996064i | \(-0.471747\pi\) | ||||
0.0886421 | + | 0.996064i | \(0.471747\pi\) | |||||||
\(32\) | 2.08937 | 0.369352 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.42716 | 1.61674 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.20480 | −1.02006 | −0.510032 | − | 0.860156i | \(-0.670366\pi\) | ||||
−0.510032 | + | 0.860156i | \(0.670366\pi\) | |||||||
\(38\) | 7.77820 | 1.26179 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.876571 | −0.136897 | −0.0684487 | − | 0.997655i | \(-0.521805\pi\) | ||||
−0.0684487 | + | 0.997655i | \(0.521805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0269678 | −0.00411255 | −0.00205628 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205628 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(44\) | 0.103022 | 0.0155312 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.10706 | 0.605553 | ||||||||
\(47\) | −11.2757 | −1.64473 | −0.822365 | − | 0.568961i | \(-0.807346\pi\) | ||||
−0.822365 | + | 0.568961i | \(0.807346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.39983 | 0.628547 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.14765 | −0.297825 | ||||||||
\(53\) | 2.16918 | 0.297960 | 0.148980 | − | 0.988840i | \(-0.452401\pi\) | ||||
0.148980 | + | 0.988840i | \(0.452401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.45890 | −1.13037 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.67269 | 1.27009 | ||||||||
\(59\) | −13.3441 | −1.73725 | −0.868625 | − | 0.495470i | \(-0.834996\pi\) | ||||
−0.868625 | + | 0.495470i | \(0.834996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.33819 | 0.683486 | 0.341743 | − | 0.939793i | \(-0.388983\pi\) | ||||
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(62\) | −1.52086 | −0.193149 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.99695 | 0.749619 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.95192 | −0.360634 | −0.180317 | − | 0.983609i | \(-0.557712\pi\) | ||||
−0.180317 | + | 0.983609i | \(0.557712\pi\) | |||||||
\(68\) | −2.28818 | −0.277482 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.03195 | −0.597183 | −0.298591 | − | 0.954381i | \(-0.596517\pi\) | ||||
−0.298591 | + | 0.954381i | \(0.596517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.45304 | 0.521189 | 0.260594 | − | 0.965448i | \(-0.416081\pi\) | ||||
0.260594 | + | 0.965448i | \(0.416081\pi\) | |||||||
\(74\) | 9.56019 | 1.11135 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.88794 | −0.216561 | ||||||||
\(77\) | −0.930107 | −0.105996 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6841 | 1.53959 | 0.769793 | − | 0.638294i | \(-0.220359\pi\) | ||||
0.769793 | + | 0.638294i | \(0.220359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.35060 | 0.149148 | ||||||||
\(83\) | 8.71814 | 0.956940 | 0.478470 | − | 0.878104i | \(-0.341192\pi\) | ||||
0.478470 | + | 0.878104i | \(0.341192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0415513 | 0.00448059 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.690158 | 0.0735711 | ||||||||
\(89\) | 14.2494 | 1.51044 | 0.755219 | − | 0.655473i | \(-0.227531\pi\) | ||||
0.755219 | + | 0.655473i | \(0.227531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.3894 | 2.03256 | ||||||||
\(92\) | −0.996873 | −0.103931 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.3733 | 1.79192 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.72170 | −0.580951 | −0.290475 | − | 0.956882i | \(-0.593813\pi\) | ||||
−0.290475 | + | 0.956882i | \(0.593813\pi\) | |||||||
\(98\) | −6.77913 | −0.684795 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.34839 | −0.930199 | −0.465100 | − | 0.885258i | \(-0.653981\pi\) | ||||
−0.465100 | + | 0.885258i | \(0.653981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5178 | −1.23342 | −0.616708 | − | 0.787192i | \(-0.711534\pi\) | ||||
−0.616708 | + | 0.787192i | \(0.711534\pi\) | |||||||
\(104\) | −14.3873 | −1.41079 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.34221 | −0.324624 | ||||||||
\(107\) | −3.10152 | −0.299835 | −0.149918 | − | 0.988699i | \(-0.547901\pi\) | ||||
−0.149918 | + | 0.988699i | \(0.547901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.88328 | −0.180386 | −0.0901929 | − | 0.995924i | \(-0.528748\pi\) | ||||
−0.0901929 | + | 0.995924i | \(0.528748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.5586 | 1.47015 | ||||||||
\(113\) | −9.54846 | −0.898244 | −0.449122 | − | 0.893470i | \(-0.648263\pi\) | ||||
−0.449122 | + | 0.893470i | \(0.648263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.34777 | −0.217985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.5602 | 1.89272 | ||||||||
\(119\) | 20.6582 | 1.89373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9241 | −0.993101 | ||||||||
\(122\) | −8.22494 | −0.744651 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.369146 | 0.0331503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.32755 | 0.384008 | 0.192004 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192004 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(128\) | −13.4187 | −1.18605 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.62288 | 0.316532 | 0.158266 | − | 0.987396i | \(-0.449410\pi\) | ||||
0.158266 | + | 0.987396i | \(0.449410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.0447 | 1.47796 | ||||||||
\(134\) | 4.54823 | 0.392907 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.3288 | −1.31443 | ||||||||
\(137\) | −16.2787 | −1.39079 | −0.695394 | − | 0.718629i | \(-0.744770\pi\) | ||||
−0.695394 | + | 0.718629i | \(0.744770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.02585 | 0.680743 | 0.340372 | − | 0.940291i | \(-0.389447\pi\) | ||||
0.340372 | + | 0.940291i | \(0.389447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.75309 | 0.650625 | ||||||||
\(143\) | −1.58198 | −0.132291 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.86112 | −0.567830 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.32047 | −0.190741 | ||||||||
\(149\) | −20.6766 | −1.69389 | −0.846947 | − | 0.531678i | \(-0.821562\pi\) | ||||
−0.846947 | + | 0.531678i | \(0.821562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.42836 | −0.278996 | −0.139498 | − | 0.990222i | \(-0.544549\pi\) | ||||
−0.139498 | + | 0.990222i | \(0.544549\pi\) | |||||||
\(152\) | −12.6475 | −1.02585 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.43308 | 0.115481 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8901 | 1.18836 | 0.594180 | − | 0.804332i | \(-0.297477\pi\) | ||||
0.594180 | + | 0.804332i | \(0.297477\pi\) | |||||||
\(158\) | −21.0841 | −1.67736 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.99999 | 0.709299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.7139 | −1.85742 | −0.928708 | − | 0.370812i | \(-0.879080\pi\) | ||||
−0.928708 | + | 0.370812i | \(0.879080\pi\) | |||||||
\(164\) | −0.327819 | −0.0255983 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.4327 | −1.04258 | ||||||||
\(167\) | −17.3913 | −1.34578 | −0.672888 | − | 0.739744i | \(-0.734946\pi\) | ||||
−0.672888 | + | 0.739744i | \(0.734946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.9786 | 1.53681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0100854 | −0.000769004 0 | ||||||||
\(173\) | 12.2246 | 0.929421 | 0.464710 | − | 0.885463i | \(-0.346158\pi\) | ||||
0.464710 | + | 0.885463i | \(0.346158\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.26942 | −0.0956862 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.9551 | −1.64561 | ||||||||
\(179\) | −11.2504 | −0.840896 | −0.420448 | − | 0.907317i | \(-0.638127\pi\) | ||||
−0.420448 | + | 0.907317i | \(0.638127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.69070 | 0.348657 | 0.174329 | − | 0.984688i | \(-0.444225\pi\) | ||||
0.174329 | + | 0.984688i | \(0.444225\pi\) | |||||||
\(182\) | −29.8747 | −2.21446 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.67817 | −0.492321 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.68549 | −0.123255 | ||||||||
\(188\) | −4.21687 | −0.307547 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7614 | 1.57460 | 0.787301 | − | 0.616569i | \(-0.211478\pi\) | ||||
0.787301 | + | 0.616569i | \(0.211478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.450776 | −0.0324476 | −0.0162238 | − | 0.999868i | \(-0.505164\pi\) | ||||
−0.0162238 | + | 0.999868i | \(0.505164\pi\) | |||||||
\(194\) | 8.81584 | 0.632940 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.64544 | 0.117532 | ||||||||
\(197\) | 9.45165 | 0.673402 | 0.336701 | − | 0.941612i | \(-0.390689\pi\) | ||||
0.336701 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8515 | 1.40724 | 0.703618 | − | 0.710578i | \(-0.251567\pi\) | ||||
0.703618 | + | 0.710578i | \(0.251567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.4037 | 1.01344 | ||||||||
\(203\) | 21.1962 | 1.48768 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.2871 | 1.34379 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.4629 | 1.83487 | ||||||||
\(209\) | −1.39067 | −0.0961947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1175 | 0.696515 | 0.348257 | − | 0.937399i | \(-0.386773\pi\) | ||||
0.348257 | + | 0.937399i | \(0.386773\pi\) | |||||||
\(212\) | 0.811227 | 0.0557153 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.77873 | 0.326667 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.33273 | −0.226240 | ||||||||
\(218\) | 2.90171 | 0.196529 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.1365 | 2.36354 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0964 | −0.876998 | −0.438499 | − | 0.898732i | \(-0.644490\pi\) | ||||
−0.438499 | + | 0.898732i | \(0.644490\pi\) | |||||||
\(224\) | −7.05448 | −0.471347 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.7120 | 0.978628 | ||||||||
\(227\) | −12.6754 | −0.841299 | −0.420649 | − | 0.907223i | \(-0.638198\pi\) | ||||
−0.420649 | + | 0.907223i | \(0.638198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3525 | −0.750197 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.7280 | −1.03259 | ||||||||
\(233\) | −3.02165 | −0.197955 | −0.0989774 | − | 0.995090i | \(-0.531557\pi\) | ||||
−0.0989774 | + | 0.995090i | \(0.531557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.99040 | −0.324847 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −31.8295 | −2.06320 | ||||||||
\(239\) | −2.81485 | −0.182078 | −0.0910389 | − | 0.995847i | \(-0.529019\pi\) | ||||
−0.0910389 | + | 0.995847i | \(0.529019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0303 | −1.22585 | −0.612923 | − | 0.790142i | \(-0.710007\pi\) | ||||
−0.612923 | + | 0.790142i | \(0.710007\pi\) | |||||||
\(242\) | 16.8316 | 1.08197 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.99637 | 0.127805 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9905 | 1.84462 | ||||||||
\(248\) | 2.47295 | 0.157032 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.5606 | −1.86585 | −0.932924 | − | 0.360074i | \(-0.882751\pi\) | ||||
−0.932924 | + | 0.360074i | \(0.882751\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.734306 | −0.0461654 | ||||||||
\(254\) | −6.66776 | −0.418373 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.68122 | 0.542576 | ||||||||
\(257\) | 6.05640 | 0.377788 | 0.188894 | − | 0.981998i | \(-0.439510\pi\) | ||||
0.188894 | + | 0.981998i | \(0.439510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.9497 | 1.30175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.58203 | −0.344859 | ||||||||
\(263\) | 2.79610 | 0.172415 | 0.0862074 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862074 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.2620 | −1.61023 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.10395 | −0.0674347 | ||||||||
\(269\) | 16.4711 | 1.00426 | 0.502130 | − | 0.864792i | \(-0.332550\pi\) | ||||
0.502130 | + | 0.864792i | \(0.332550\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1663 | 1.28576 | 0.642880 | − | 0.765967i | \(-0.277739\pi\) | ||||
0.642880 | + | 0.765967i | \(0.277739\pi\) | |||||||
\(272\) | 28.1945 | 1.70954 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.0818 | 1.51525 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4330 | −1.46803 | −0.734017 | − | 0.679131i | \(-0.762357\pi\) | ||||
−0.734017 | + | 0.679131i | \(0.762357\pi\) | |||||||
\(278\) | −12.3660 | −0.741664 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.89064 | −0.112786 | −0.0563931 | − | 0.998409i | \(-0.517960\pi\) | ||||
−0.0563931 | + | 0.998409i | \(0.517960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.75517 | −0.401553 | −0.200777 | − | 0.979637i | \(-0.564347\pi\) | ||||
−0.200777 | + | 0.979637i | \(0.564347\pi\) | |||||||
\(284\) | −1.88184 | −0.111667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.43746 | 0.144130 | ||||||||
\(287\) | 2.95962 | 0.174701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.4356 | 1.20209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.66534 | 0.0974568 | ||||||||
\(293\) | 9.98977 | 0.583609 | 0.291804 | − | 0.956478i | \(-0.405744\pi\) | ||||
0.291804 | + | 0.956478i | \(0.405744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.5451 | −0.903539 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 31.8579 | 1.84548 | ||||||||
\(299\) | 15.3077 | 0.885265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0910531 | 0.00524822 | ||||||||
\(302\) | 5.28233 | 0.303964 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.2628 | 1.33421 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4510 | 0.881832 | 0.440916 | − | 0.897548i | \(-0.354654\pi\) | ||||
0.440916 | + | 0.897548i | \(0.354654\pi\) | |||||||
\(308\) | −0.347840 | −0.0198200 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5330 | −1.39114 | −0.695570 | − | 0.718458i | \(-0.744848\pi\) | ||||
−0.695570 | + | 0.718458i | \(0.744848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.90435 | −0.559827 | −0.279914 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279914 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(314\) | −22.9423 | −1.29471 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.11758 | 0.287886 | ||||||||
\(317\) | 11.0669 | 0.621576 | 0.310788 | − | 0.950479i | \(-0.399407\pi\) | ||||
0.310788 | + | 0.950479i | \(0.399407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.72939 | −0.0968272 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.8669 | −0.772774 | ||||||||
\(323\) | 30.8875 | 1.71863 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 36.5377 | 2.02364 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.19610 | −0.121259 | ||||||||
\(329\) | 38.0708 | 2.09891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0271 | −0.716034 | −0.358017 | − | 0.933715i | \(-0.616547\pi\) | ||||
−0.358017 | + | 0.933715i | \(0.616547\pi\) | |||||||
\(332\) | 3.26040 | 0.178938 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.7960 | 1.46621 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4458 | −0.895858 | −0.447929 | − | 0.894069i | \(-0.647838\pi\) | ||||
−0.447929 | + | 0.894069i | \(0.647838\pi\) | |||||||
\(338\) | −30.7824 | −1.67434 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.271916 | 0.0147251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.77913 | 0.474029 | ||||||||
\(344\) | −0.0675632 | −0.00364277 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.8354 | −1.01260 | ||||||||
\(347\) | −18.4439 | −0.990119 | −0.495059 | − | 0.868859i | \(-0.664854\pi\) | ||||
−0.495059 | + | 0.868859i | \(0.664854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3683 | −0.555005 | −0.277502 | − | 0.960725i | \(-0.589507\pi\) | ||||
−0.277502 | + | 0.960725i | \(0.589507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.575572 | 0.0306781 | ||||||||
\(353\) | 6.65119 | 0.354007 | 0.177003 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177003 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.32899 | 0.282436 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.3343 | 0.916149 | ||||||||
\(359\) | 13.4702 | 0.710932 | 0.355466 | − | 0.934689i | \(-0.384322\pi\) | ||||
0.355466 | + | 0.934689i | \(0.384322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.48478 | 0.341304 | ||||||||
\(362\) | −7.22730 | −0.379859 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.25123 | 0.380068 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2948 | 1.00718 | 0.503591 | − | 0.863942i | \(-0.332012\pi\) | ||||
0.503591 | + | 0.863942i | \(0.332012\pi\) | |||||||
\(368\) | 12.2833 | 0.640311 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.32394 | −0.380240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0180 | 0.622270 | 0.311135 | − | 0.950366i | \(-0.399291\pi\) | ||||
0.311135 | + | 0.950366i | \(0.399291\pi\) | |||||||
\(374\) | 2.59696 | 0.134285 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −28.2493 | −1.45685 | ||||||||
\(377\) | 36.0516 | 1.85675 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3248 | 0.941282 | 0.470641 | − | 0.882325i | \(-0.344023\pi\) | ||||
0.470641 | + | 0.882325i | \(0.344023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −33.5294 | −1.71551 | ||||||||
\(383\) | 4.47653 | 0.228740 | 0.114370 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114370 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.694543 | 0.0353513 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.13979 | −0.108632 | ||||||||
\(389\) | −14.3455 | −0.727344 | −0.363672 | − | 0.931527i | \(-0.618477\pi\) | ||||
−0.363672 | + | 0.931527i | \(0.618477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3093 | 0.824797 | ||||||||
\(392\) | 11.0230 | 0.556746 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.5628 | −0.733665 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.06703 | 0.204119 | 0.102059 | − | 0.994778i | \(-0.467457\pi\) | ||||
0.102059 | + | 0.994778i | \(0.467457\pi\) | |||||||
\(398\) | −30.5867 | −1.53317 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8735 | −0.792685 | −0.396342 | − | 0.918103i | \(-0.629721\pi\) | ||||
−0.396342 | + | 0.918103i | \(0.629721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.66848 | −0.282367 | ||||||||
\(404\) | −3.49610 | −0.173937 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −32.6585 | −1.62081 | ||||||||
\(407\) | −1.70928 | −0.0847256 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.2178 | 0.554682 | 0.277341 | − | 0.960772i | \(-0.410547\pi\) | ||||
0.277341 | + | 0.960772i | \(0.410547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.68139 | −0.230636 | ||||||||
\(413\) | 45.0544 | 2.21698 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.9986 | −0.588281 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.14271 | 0.104803 | ||||||||
\(419\) | −34.0818 | −1.66500 | −0.832502 | − | 0.554022i | \(-0.813092\pi\) | ||||
−0.832502 | + | 0.554022i | \(0.813092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.20959 | 0.0589518 | 0.0294759 | − | 0.999565i | \(-0.490616\pi\) | ||||
0.0294759 | + | 0.999565i | \(0.490616\pi\) | |||||||
\(422\) | −15.5887 | −0.758846 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.43451 | 0.263923 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.0237 | −0.872227 | ||||||||
\(428\) | −1.15990 | −0.0560660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8571 | −0.860144 | −0.430072 | − | 0.902795i | \(-0.641512\pi\) | ||||
−0.430072 | + | 0.902795i | \(0.641512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.8056 | 1.52848 | 0.764240 | − | 0.644931i | \(-0.223114\pi\) | ||||
0.764240 | + | 0.644931i | \(0.223114\pi\) | |||||||
\(434\) | 5.13497 | 0.246487 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.704308 | −0.0337302 | ||||||||
\(437\) | 13.4565 | 0.643714 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.65773 | −0.413211 | −0.206605 | − | 0.978424i | \(-0.566242\pi\) | ||||
−0.206605 | + | 0.978424i | \(0.566242\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −54.1373 | −2.57505 | ||||||||
\(443\) | −14.2382 | −0.676477 | −0.338238 | − | 0.941061i | \(-0.609831\pi\) | ||||
−0.338238 | + | 0.941061i | \(0.609831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.1785 | 0.955481 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.2479 | −0.956622 | ||||||||
\(449\) | −13.4056 | −0.632650 | −0.316325 | − | 0.948651i | \(-0.602449\pi\) | ||||
−0.316325 | + | 0.948651i | \(0.602449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.241474 | −0.0113706 | ||||||||
\(452\) | −3.57092 | −0.167962 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.5300 | 0.916587 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.05447 | 0.236438 | 0.118219 | − | 0.992988i | \(-0.462281\pi\) | ||||
0.118219 | + | 0.992988i | \(0.462281\pi\) | |||||||
\(458\) | 17.4917 | 0.817333 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.48890 | 0.395368 | 0.197684 | − | 0.980266i | \(-0.436658\pi\) | ||||
0.197684 | + | 0.980266i | \(0.436658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.1118 | 0.981148 | 0.490574 | − | 0.871399i | \(-0.336787\pi\) | ||||
0.490574 | + | 0.871399i | \(0.336787\pi\) | |||||||
\(464\) | 28.9288 | 1.34299 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.65567 | 0.215670 | ||||||||
\(467\) | 10.0250 | 0.463901 | 0.231951 | − | 0.972728i | \(-0.425489\pi\) | ||||
0.231951 | + | 0.972728i | \(0.425489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.96674 | 0.460221 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.4313 | −1.53880 | ||||||||
\(473\) | −0.00742899 | −0.000341585 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.72571 | 0.354107 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.33705 | 0.198372 | ||||||||
\(479\) | −6.34922 | −0.290103 | −0.145052 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145052 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.6323 | 1.62469 | ||||||||
\(482\) | 29.3213 | 1.33555 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.08539 | −0.185699 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9418 | 1.17554 | 0.587768 | − | 0.809030i | \(-0.300007\pi\) | ||||
0.587768 | + | 0.809030i | \(0.300007\pi\) | |||||||
\(488\) | 13.3739 | 0.605409 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4375 | 0.651554 | 0.325777 | − | 0.945447i | \(-0.394374\pi\) | ||||
0.325777 | + | 0.945447i | \(0.394374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.4106 | 1.72993 | ||||||||
\(494\) | −44.6678 | −2.00970 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.54854 | −0.204236 | ||||||||
\(497\) | 16.9897 | 0.762092 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.4648 | −1.22949 | −0.614746 | − | 0.788725i | \(-0.710741\pi\) | ||||
−0.614746 | + | 0.788725i | \(0.710741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 45.5461 | 2.03282 | ||||||||
\(503\) | 24.3612 | 1.08621 | 0.543106 | − | 0.839664i | \(-0.317248\pi\) | ||||
0.543106 | + | 0.839664i | \(0.317248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.13140 | 0.0502968 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.61841 | 0.0718054 | ||||||||
\(509\) | −5.86899 | −0.260138 | −0.130069 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130069 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0351 | −0.665113 | ||||||||
\(512\) | 13.4616 | 0.594923 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.33153 | −0.411596 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.10618 | −0.136610 | ||||||||
\(518\) | −32.2787 | −1.41824 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3976 | −1.28793 | −0.643965 | − | 0.765055i | \(-0.722712\pi\) | ||||
−0.643965 | + | 0.765055i | \(0.722712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9982 | −0.568373 | −0.284187 | − | 0.958769i | \(-0.591724\pi\) | ||||
−0.284187 | + | 0.958769i | \(0.591724\pi\) | |||||||
\(524\) | 1.35488 | 0.0591882 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.30815 | −0.187844 | ||||||||
\(527\) | −6.03939 | −0.263080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8946 | −0.691071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.37436 | 0.276363 | ||||||||
\(533\) | 5.03388 | 0.218041 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.39552 | −0.319438 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.3782 | −1.09413 | ||||||||
\(539\) | 1.21205 | 0.0522065 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.83813 | 0.422974 | 0.211487 | − | 0.977381i | \(-0.432169\pi\) | ||||
0.211487 | + | 0.977381i | \(0.432169\pi\) | |||||||
\(542\) | −32.6124 | −1.40082 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.7837 | −0.548099 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9058 | −0.893868 | −0.446934 | − | 0.894567i | \(-0.647484\pi\) | ||||
−0.446934 | + | 0.894567i | \(0.647484\pi\) | |||||||
\(548\) | −6.08791 | −0.260062 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.6920 | 1.35012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46.2026 | −1.96474 | ||||||||
\(554\) | 37.6456 | 1.59941 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.00150 | 0.127292 | ||||||||
\(557\) | 20.8969 | 0.885431 | 0.442716 | − | 0.896662i | \(-0.354015\pi\) | ||||
0.442716 | + | 0.896662i | \(0.354015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.154868 | 0.00655022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.91304 | 0.122879 | ||||||||
\(563\) | −18.5889 | −0.783428 | −0.391714 | − | 0.920087i | \(-0.628118\pi\) | ||||
−0.391714 | + | 0.920087i | \(0.628118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.4082 | 0.437488 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.6067 | −0.528965 | ||||||||
\(569\) | −30.6786 | −1.28611 | −0.643057 | − | 0.765819i | \(-0.722334\pi\) | ||||
−0.643057 | + | 0.765819i | \(0.722334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2650 | 0.596970 | 0.298485 | − | 0.954414i | \(-0.403519\pi\) | ||||
0.298485 | + | 0.954414i | \(0.403519\pi\) | |||||||
\(572\) | −0.591625 | −0.0247371 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.56010 | −0.190335 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1484 | −1.54651 | −0.773254 | − | 0.634096i | \(-0.781372\pi\) | ||||
−0.773254 | + | 0.634096i | \(0.781372\pi\) | |||||||
\(578\) | −31.4866 | −1.30967 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.4356 | −1.22119 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.597557 | 0.0247483 | ||||||||
\(584\) | 11.1563 | 0.461652 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.3920 | −0.635836 | ||||||||
\(587\) | 30.7079 | 1.26745 | 0.633726 | − | 0.773558i | \(-0.281525\pi\) | ||||
0.633726 | + | 0.773558i | \(0.281525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.98300 | −0.205321 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.5923 | 1.17514 | ||||||||
\(593\) | 30.6705 | 1.25949 | 0.629744 | − | 0.776803i | \(-0.283160\pi\) | ||||
0.629744 | + | 0.776803i | \(0.283160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.73261 | −0.316740 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.5856 | −0.964488 | ||||||||
\(599\) | 32.8329 | 1.34152 | 0.670759 | − | 0.741676i | \(-0.265969\pi\) | ||||
0.670759 | + | 0.741676i | \(0.265969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.8051 | 1.74606 | 0.873029 | − | 0.487669i | \(-0.162153\pi\) | ||||
0.873029 | + | 0.487669i | \(0.162153\pi\) | |||||||
\(602\) | −0.140292 | −0.00571788 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.28214 | −0.0521694 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.5366 | 1.68592 | 0.842959 | − | 0.537977i | \(-0.180811\pi\) | ||||
0.842959 | + | 0.537977i | \(0.180811\pi\) | |||||||
\(608\) | −10.5477 | −0.427764 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.7529 | 2.61962 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1045 | 0.610067 | 0.305033 | − | 0.952342i | \(-0.401332\pi\) | ||||
0.305033 | + | 0.952342i | \(0.401332\pi\) | |||||||
\(614\) | −23.8064 | −0.960748 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.33022 | −0.0938874 | ||||||||
\(617\) | −16.5874 | −0.667782 | −0.333891 | − | 0.942612i | \(-0.608362\pi\) | ||||
−0.333891 | + | 0.942612i | \(0.608362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.3284 | 0.817068 | 0.408534 | − | 0.912743i | \(-0.366040\pi\) | ||||
0.408534 | + | 0.912743i | \(0.366040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 37.7998 | 1.51563 | ||||||||
\(623\) | −48.1113 | −1.92754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.2603 | 0.609926 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.56858 | 0.222211 | ||||||||
\(629\) | 37.9639 | 1.51372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.0922 | 0.839668 | 0.419834 | − | 0.907601i | \(-0.362088\pi\) | ||||
0.419834 | + | 0.907601i | \(0.362088\pi\) | |||||||
\(632\) | 34.2833 | 1.36371 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.0515 | −0.677202 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.2669 | −1.00111 | ||||||||
\(638\) | 2.66459 | 0.105492 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6154 | 0.498279 | 0.249140 | − | 0.968468i | \(-0.419852\pi\) | ||||
0.249140 | + | 0.968468i | \(0.419852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.3450 | −0.723457 | −0.361728 | − | 0.932284i | \(-0.617813\pi\) | ||||
−0.361728 | + | 0.932284i | \(0.617813\pi\) | |||||||
\(644\) | 3.36581 | 0.132631 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −47.5906 | −1.87243 | ||||||||
\(647\) | 32.1546 | 1.26413 | 0.632064 | − | 0.774916i | \(-0.282208\pi\) | ||||
0.632064 | + | 0.774916i | \(0.282208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.67597 | −0.144295 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.86850 | −0.347317 | ||||||||
\(653\) | −49.5727 | −1.93993 | −0.969964 | − | 0.243249i | \(-0.921787\pi\) | ||||
−0.969964 | + | 0.243249i | \(0.921787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.03932 | 0.157709 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −58.6585 | −2.28675 | ||||||||
\(659\) | 26.8273 | 1.04504 | 0.522521 | − | 0.852626i | \(-0.324992\pi\) | ||||
0.522521 | + | 0.852626i | \(0.324992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.66845 | 0.259373 | 0.129686 | − | 0.991555i | \(-0.458603\pi\) | ||||
0.129686 | + | 0.991555i | \(0.458603\pi\) | |||||||
\(662\) | 20.0718 | 0.780112 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.8418 | 0.847626 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.7341 | 0.647946 | ||||||||
\(668\) | −6.50396 | −0.251646 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.47054 | 0.0567697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.4981 | 1.05997 | 0.529987 | − | 0.848006i | \(-0.322197\pi\) | ||||
0.529987 | + | 0.848006i | \(0.322197\pi\) | |||||||
\(674\) | 25.3392 | 0.976029 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.47156 | 0.287368 | ||||||||
\(677\) | 20.1952 | 0.776163 | 0.388082 | − | 0.921625i | \(-0.373138\pi\) | ||||
0.388082 | + | 0.921625i | \(0.373138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.3185 | 0.741377 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.418960 | −0.0160428 | ||||||||
\(683\) | 44.3125 | 1.69557 | 0.847786 | − | 0.530339i | \(-0.177935\pi\) | ||||
0.847786 | + | 0.530339i | \(0.177935\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.5266 | −0.516450 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.124270 | 0.00473776 | ||||||||
\(689\) | −12.4569 | −0.474572 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.7685 | −1.05636 | −0.528182 | − | 0.849131i | \(-0.677126\pi\) | ||||
−0.528182 | + | 0.849131i | \(0.677126\pi\) | |||||||
\(692\) | 4.57175 | 0.173792 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.4178 | 1.07872 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.36327 | 0.203148 | ||||||||
\(698\) | 15.9753 | 0.604672 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.8116 | −1.31481 | −0.657407 | − | 0.753535i | \(-0.728347\pi\) | ||||
−0.657407 | + | 0.753535i | \(0.728347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3234 | 1.18138 | ||||||||
\(704\) | 1.65202 | 0.0622627 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2480 | −0.385687 | ||||||||
\(707\) | 31.5635 | 1.18707 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.0887 | −1.65579 | −0.827893 | − | 0.560886i | \(-0.810461\pi\) | ||||
−0.827893 | + | 0.560886i | \(0.810461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35.6995 | 1.33790 | ||||||||
\(713\) | −2.63114 | −0.0985369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.20742 | −0.157239 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.7546 | −0.774554 | ||||||||
\(719\) | −38.4272 | −1.43309 | −0.716547 | − | 0.697539i | \(-0.754278\pi\) | ||||
−0.716547 | + | 0.697539i | \(0.754278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.2646 | 1.57402 | ||||||||
\(722\) | −9.99156 | −0.371848 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.75422 | 0.0651952 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3236 | 1.05046 | 0.525232 | − | 0.850959i | \(-0.323979\pi\) | ||||
0.525232 | + | 0.850959i | \(0.323979\pi\) | |||||||
\(728\) | 48.5769 | 1.80038 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.165002 | 0.00610281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.46695 | −0.0911190 | −0.0455595 | − | 0.998962i | \(-0.514507\pi\) | ||||
−0.0455595 | + | 0.998962i | \(0.514507\pi\) | |||||||
\(734\) | −29.7289 | −1.09732 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.56940 | −0.205291 | ||||||||
\(737\) | −0.813182 | −0.0299540 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6368 | −0.759136 | −0.379568 | − | 0.925164i | \(-0.623927\pi\) | ||||
−0.379568 | + | 0.925164i | \(0.623927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.2845 | 0.414268 | ||||||||
\(743\) | −29.8469 | −1.09498 | −0.547488 | − | 0.836814i | \(-0.684416\pi\) | ||||
−0.547488 | + | 0.836814i | \(0.684416\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.5170 | −0.677957 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.630338 | −0.0230474 | ||||||||
\(749\) | 10.4718 | 0.382633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.8172 | 1.01506 | 0.507532 | − | 0.861633i | \(-0.330558\pi\) | ||||
0.507532 | + | 0.861633i | \(0.330558\pi\) | |||||||
\(752\) | 51.9595 | 1.89477 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −55.5473 | −2.02291 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.1959 | −1.13383 | −0.566916 | − | 0.823775i | \(-0.691864\pi\) | ||||
−0.566916 | + | 0.823775i | \(0.691864\pi\) | |||||||
\(758\) | −28.2344 | −1.02552 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.40270 | 0.340848 | 0.170424 | − | 0.985371i | \(-0.445486\pi\) | ||||
0.170424 | + | 0.985371i | \(0.445486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.35864 | 0.230198 | ||||||||
\(764\) | 8.13831 | 0.294434 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.89732 | −0.249210 | ||||||||
\(767\) | 76.6310 | 2.76698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0633 | −0.687439 | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.168581 | −0.00606735 | ||||||||
\(773\) | 0.364033 | 0.0130934 | 0.00654668 | − | 0.999979i | \(-0.497916\pi\) | ||||
0.00654668 | + | 0.999979i | \(0.497916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.3347 | −0.514587 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.1031 | 0.792434 | ||||||||
\(779\) | 4.42514 | 0.158547 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.38618 | −0.0496015 | ||||||||
\(782\) | −25.1289 | −0.898608 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.2748 | −0.724101 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0565 | −0.821876 | −0.410938 | − | 0.911663i | \(-0.634799\pi\) | ||||
−0.410938 | + | 0.911663i | \(0.634799\pi\) | |||||||
\(788\) | 3.53472 | 0.125919 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.2391 | 1.14629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6556 | −1.08861 | ||||||||
\(794\) | −6.26637 | −0.222385 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.42405 | 0.263138 | ||||||||
\(797\) | −4.33846 | −0.153676 | −0.0768380 | − | 0.997044i | \(-0.524482\pi\) | ||||
−0.0768380 | + | 0.997044i | \(0.524482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.9899 | 2.44069 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.4574 | 0.863623 | ||||||||
\(803\) | 1.22671 | 0.0432895 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.73384 | 0.307636 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.4208 | −0.823940 | ||||||||
\(809\) | −11.0758 | −0.389406 | −0.194703 | − | 0.980862i | \(-0.562374\pi\) | ||||
−0.194703 | + | 0.980862i | \(0.562374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0100 | 1.54540 | 0.772701 | − | 0.634771i | \(-0.218905\pi\) | ||||
0.772701 | + | 0.634771i | \(0.218905\pi\) | |||||||
\(812\) | 7.92693 | 0.278181 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.63360 | 0.0923077 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.136140 | 0.00476294 | ||||||||
\(818\) | −17.2840 | −0.604321 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.81681 | −0.0634072 | −0.0317036 | − | 0.999497i | \(-0.510093\pi\) | ||||
−0.0317036 | + | 0.999497i | \(0.510093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1162 | 0.352627 | 0.176314 | − | 0.984334i | \(-0.443583\pi\) | ||||
0.176314 | + | 0.984334i | \(0.443583\pi\) | |||||||
\(824\) | −31.3612 | −1.09252 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.4186 | −2.41538 | ||||||||
\(827\) | −24.7123 | −0.859332 | −0.429666 | − | 0.902988i | \(-0.641369\pi\) | ||||
−0.429666 | + | 0.902988i | \(0.641369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2271 | −1.57080 | −0.785400 | − | 0.618988i | \(-0.787543\pi\) | ||||
−0.785400 | + | 0.618988i | \(0.787543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −34.4387 | −1.19395 | ||||||||
\(833\) | −26.9202 | −0.932729 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.520081 | −0.0179874 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 52.5122 | 1.81401 | ||||||||
\(839\) | −38.1856 | −1.31831 | −0.659157 | − | 0.752005i | \(-0.729087\pi\) | ||||
−0.659157 | + | 0.752005i | \(0.729087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.4110 | 0.359001 | ||||||||
\(842\) | −1.86370 | −0.0642274 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.78372 | 0.130241 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.8838 | 1.26734 | ||||||||
\(848\) | −9.99579 | −0.343257 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5395 | 0.566965 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.8622 | 1.57029 | 0.785145 | − | 0.619312i | \(-0.212588\pi\) | ||||
0.785145 | + | 0.619312i | \(0.212588\pi\) | |||||||
\(854\) | 27.7704 | 0.950283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.77032 | −0.265584 | ||||||||
\(857\) | −33.5199 | −1.14502 | −0.572508 | − | 0.819899i | \(-0.694030\pi\) | ||||
−0.572508 | + | 0.819899i | \(0.694030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.9508 | 1.56782 | 0.783911 | − | 0.620873i | \(-0.213222\pi\) | ||||
0.783911 | + | 0.620873i | \(0.213222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.5137 | 0.937119 | ||||||||
\(863\) | 11.3593 | 0.386675 | 0.193337 | − | 0.981132i | \(-0.438069\pi\) | ||||
0.193337 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −49.0052 | −1.66527 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.24637 | −0.0423045 | ||||||||
\(869\) | 3.76965 | 0.127877 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9520 | 0.574395 | ||||||||
\(872\) | −4.71824 | −0.159780 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.7335 | −0.701320 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.38169 | 0.316797 | 0.158399 | − | 0.987375i | \(-0.449367\pi\) | ||||
0.158399 | + | 0.987375i | \(0.449367\pi\) | |||||||
\(878\) | 13.3396 | 0.450189 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.77079 | 0.228114 | 0.114057 | − | 0.993474i | \(-0.463615\pi\) | ||||
0.114057 | + | 0.993474i | \(0.463615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7878 | −0.531301 | −0.265651 | − | 0.964069i | \(-0.585587\pi\) | ||||
−0.265651 | + | 0.964069i | \(0.585587\pi\) | |||||||
\(884\) | 13.1403 | 0.441956 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.9378 | 0.737015 | ||||||||
\(887\) | −9.65613 | −0.324221 | −0.162111 | − | 0.986773i | \(-0.551830\pi\) | ||||
−0.162111 | + | 0.986773i | \(0.551830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6114 | −0.490050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.89777 | −0.163989 | ||||||||
\(893\) | 56.9225 | 1.90484 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 45.3063 | 1.51358 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.6550 | 0.689266 | ||||||||
\(899\) | −6.19669 | −0.206671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2721 | −0.442156 | ||||||||
\(902\) | 0.372057 | 0.0123881 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.9220 | −0.795635 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.2743 | 1.20447 | 0.602233 | − | 0.798320i | \(-0.294278\pi\) | ||||
0.602233 | + | 0.798320i | \(0.294278\pi\) | |||||||
\(908\) | −4.74035 | −0.157314 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.7978 | −1.88179 | −0.940897 | − | 0.338692i | \(-0.890016\pi\) | ||||
−0.940897 | + | 0.338692i | \(0.890016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.40164 | 0.0794826 | ||||||||
\(914\) | −7.78779 | −0.257597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.24561 | −0.140279 | ||||||||
\(917\) | −12.2322 | −0.403941 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.8300 | −1.34686 | −0.673429 | − | 0.739252i | \(-0.735179\pi\) | ||||
−0.673429 | + | 0.739252i | \(0.735179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.0795 | −0.430749 | ||||||||
\(923\) | 28.8970 | 0.951155 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32.5285 | −1.06895 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.1167 | −0.430577 | ||||||||
\(929\) | −33.5585 | −1.10102 | −0.550509 | − | 0.834829i | \(-0.685566\pi\) | ||||
−0.550509 | + | 0.834829i | \(0.685566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.2114 | −0.727949 | ||||||||
\(932\) | −1.13003 | −0.0370154 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.4462 | −0.505416 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0417 | −0.426053 | −0.213026 | − | 0.977046i | \(-0.568332\pi\) | ||||
−0.213026 | + | 0.977046i | \(0.568332\pi\) | |||||||
\(938\) | −15.3565 | −0.501407 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.2301 | −1.11587 | −0.557935 | − | 0.829884i | \(-0.688406\pi\) | ||||
−0.557935 | + | 0.829884i | \(0.688406\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.33658 | 0.0760894 | ||||||||
\(944\) | 61.4908 | 2.00136 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0114464 | 0.000372154 0 | ||||||||
\(947\) | −3.22739 | −0.104876 | −0.0524381 | − | 0.998624i | \(-0.516699\pi\) | ||||
−0.0524381 | + | 0.998624i | \(0.516699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.5725 | −0.830117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 51.7555 | 1.67740 | ||||||||
\(953\) | −6.33220 | −0.205120 | −0.102560 | − | 0.994727i | \(-0.532703\pi\) | ||||
−0.102560 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.05270 | −0.0340466 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.78270 | 0.316065 | ||||||||
\(959\) | 54.9630 | 1.77485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0257 | −0.968570 | ||||||||
\(962\) | −54.9013 | −1.77009 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.11691 | −0.229220 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1469 | −0.358460 | −0.179230 | − | 0.983807i | \(-0.557361\pi\) | ||||
−0.179230 | + | 0.983807i | \(0.557361\pi\) | |||||||
\(968\) | −27.3685 | −0.879657 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.8854 | −0.991159 | −0.495580 | − | 0.868563i | \(-0.665044\pi\) | ||||
−0.495580 | + | 0.868563i | \(0.665044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.0982 | −0.868728 | ||||||||
\(974\) | −39.9704 | −1.28073 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.5989 | −0.787392 | ||||||||
\(977\) | −24.5207 | −0.784486 | −0.392243 | − | 0.919862i | \(-0.628301\pi\) | ||||
−0.392243 | + | 0.919862i | \(0.628301\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.92538 | 0.125456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.2449 | −0.709862 | ||||||||
\(983\) | −9.12390 | −0.291007 | −0.145504 | − | 0.989358i | \(-0.546480\pi\) | ||||
−0.145504 | + | 0.989358i | \(0.546480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −59.1820 | −1.88474 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.8418 | 0.344925 | ||||||||
\(989\) | 0.0718851 | 0.00228581 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.78580 | 0.247324 | 0.123662 | − | 0.992324i | \(-0.460536\pi\) | ||||
0.123662 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(992\) | 2.06237 | 0.0654803 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −26.1773 | −0.830292 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7566 | −0.562357 | −0.281178 | − | 0.959656i | \(-0.590725\pi\) | ||||
−0.281178 | + | 0.959656i | \(0.590725\pi\) | |||||||
\(998\) | 42.3169 | 1.33952 | ||||||||
\(999\) | 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 | 5625.2.a.bf.1.7 | 24 | ||
3.2 | odd | 2 | inner | 5625.2.a.bf.1.17 | 24 | ||
5.4 | even | 2 | inner | 5625.2.a.bf.1.18 | 24 | ||
15.14 | odd | 2 | inner | 5625.2.a.bf.1.8 | 24 | ||
25.12 | odd | 20 | 225.2.m.c.19.5 | yes | 24 | ||
25.23 | odd | 20 | 225.2.m.c.154.5 | yes | 24 | ||
75.23 | even | 20 | 225.2.m.c.154.2 | yes | 24 | ||
75.62 | even | 20 | 225.2.m.c.19.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.m.c.19.2 | ✓ | 24 | 75.62 | even | 20 | ||
225.2.m.c.19.5 | yes | 24 | 25.12 | odd | 20 | ||
225.2.m.c.154.2 | yes | 24 | 75.23 | even | 20 | ||
225.2.m.c.154.5 | yes | 24 | 25.23 | odd | 20 | ||
5625.2.a.bf.1.7 | 24 | 1.1 | even | 1 | trivial | ||
5625.2.a.bf.1.8 | 24 | 15.14 | odd | 2 | inner | ||
5625.2.a.bf.1.17 | 24 | 3.2 | odd | 2 | inner | ||
5625.2.a.bf.1.18 | 24 | 5.4 | even | 2 | inner |