Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, 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("2475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.48704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 4x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.28632\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28632 | −1.61667 | −0.808337 | − | 0.588720i | \(-0.799632\pi\) | ||||
−0.808337 | + | 0.588720i | \(0.799632\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.22727 | 1.61364 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51962 | −0.952328 | −0.476164 | − | 0.879356i | \(-0.657973\pi\) | ||||
−0.476164 | + | 0.879356i | \(0.657973\pi\) | |||||||
\(8\) | −2.80595 | −0.992052 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.05302 | −1.67881 | −0.839403 | − | 0.543509i | \(-0.817095\pi\) | ||||
−0.839403 | + | 0.543509i | \(0.817095\pi\) | |||||||
\(14\) | 5.76067 | 1.53960 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0392472 | −0.00981179 | ||||||||
\(17\) | 4.97417 | 1.20641 | 0.603207 | − | 0.797585i | \(-0.293889\pi\) | ||||
0.603207 | + | 0.797585i | \(0.293889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.02720 | −1.61215 | −0.806075 | − | 0.591814i | \(-0.798412\pi\) | ||||
−0.806075 | + | 0.591814i | \(0.798412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.28632 | −0.487446 | ||||||||
\(23\) | −4.45455 | −0.928838 | −0.464419 | − | 0.885616i | \(-0.653737\pi\) | ||||
−0.464419 | + | 0.885616i | \(0.653737\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.8392 | 2.71408 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.13152 | −1.53671 | ||||||||
\(29\) | 0.921150 | 0.171053 | 0.0855266 | − | 0.996336i | \(-0.472743\pi\) | ||||
0.0855266 | + | 0.996336i | \(0.472743\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.03925 | 0.545865 | 0.272932 | − | 0.962033i | \(-0.412006\pi\) | ||||
0.272932 | + | 0.962033i | \(0.412006\pi\) | |||||||
\(32\) | 5.70163 | 1.00791 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.3726 | −1.95038 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.49380 | 0.574377 | 0.287188 | − | 0.957874i | \(-0.407279\pi\) | ||||
0.287188 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(38\) | 16.0664 | 2.60632 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0664 | −1.57211 | −0.786057 | − | 0.618154i | \(-0.787881\pi\) | ||||
−0.786057 | + | 0.618154i | \(0.787881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.48038 | −0.225755 | −0.112878 | − | 0.993609i | \(-0.536007\pi\) | ||||
−0.112878 | + | 0.993609i | \(0.536007\pi\) | |||||||
\(44\) | 3.22727 | 0.486530 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.1845 | 1.50163 | ||||||||
\(47\) | 8.10605 | 1.18239 | 0.591194 | − | 0.806529i | \(-0.298657\pi\) | ||||
0.591194 | + | 0.806529i | \(0.298657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.651497 | −0.0930710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.5348 | −2.70899 | ||||||||
\(53\) | 1.54545 | 0.212284 | 0.106142 | − | 0.994351i | \(-0.466150\pi\) | ||||
0.106142 | + | 0.994351i | \(0.466150\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.06993 | 0.944759 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.10605 | −0.276537 | ||||||||
\(59\) | −7.59984 | −0.989415 | −0.494708 | − | 0.869059i | \(-0.664725\pi\) | ||||
−0.494708 | + | 0.869059i | \(0.664725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1060 | 1.29395 | 0.646973 | − | 0.762513i | \(-0.276034\pi\) | ||||
0.646973 | + | 0.762513i | \(0.276034\pi\) | |||||||
\(62\) | −6.94870 | −0.882486 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9573 | −1.61966 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.69074 | 1.06174 | 0.530872 | − | 0.847452i | \(-0.321865\pi\) | ||||
0.530872 | + | 0.847452i | \(0.321865\pi\) | |||||||
\(68\) | 16.0530 | 1.94672 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.54545 | 0.183411 | 0.0917056 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917056 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05302 | −0.708453 | −0.354226 | − | 0.935160i | \(-0.615256\pi\) | ||||
−0.354226 | + | 0.935160i | \(0.615256\pi\) | |||||||
\(74\) | −7.98795 | −0.928580 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.6787 | −2.60142 | ||||||||
\(77\) | −2.51962 | −0.287138 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0272 | 1.24066 | 0.620328 | − | 0.784342i | \(-0.286999\pi\) | ||||
0.620328 | + | 0.784342i | \(0.286999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 23.0151 | 2.54160 | ||||||||
\(83\) | 8.50757 | 0.933827 | 0.466914 | − | 0.884303i | \(-0.345366\pi\) | ||||
0.466914 | + | 0.884303i | \(0.345366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.38462 | 0.364973 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.80595 | −0.299115 | ||||||||
\(89\) | 15.1453 | 1.60540 | 0.802699 | − | 0.596384i | \(-0.203397\pi\) | ||||
0.802699 | + | 0.596384i | \(0.203397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2513 | 1.59877 | ||||||||
\(92\) | −14.3761 | −1.49881 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.5330 | −1.91154 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5998 | 1.17779 | 0.588893 | − | 0.808211i | \(-0.299564\pi\) | ||||
0.588893 | + | 0.808211i | \(0.299564\pi\) | |||||||
\(98\) | 1.48953 | 0.150466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.118097 | −0.0117511 | −0.00587556 | − | 0.999983i | \(-0.501870\pi\) | ||||
−0.00587556 | + | 0.999983i | \(0.501870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6391 | −1.04830 | −0.524150 | − | 0.851626i | \(-0.675617\pi\) | ||||
−0.524150 | + | 0.851626i | \(0.675617\pi\) | |||||||
\(104\) | 16.9845 | 1.66546 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.53340 | −0.343194 | ||||||||
\(107\) | −18.6921 | −1.80703 | −0.903517 | − | 0.428551i | \(-0.859024\pi\) | ||||
−0.903517 | + | 0.428551i | \(0.859024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.14529 | −0.684395 | −0.342198 | − | 0.939628i | \(-0.611171\pi\) | ||||
−0.342198 | + | 0.939628i | \(0.611171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0988881 | 0.00934405 | ||||||||
\(113\) | 2.58470 | 0.243148 | 0.121574 | − | 0.992582i | \(-0.461206\pi\) | ||||
0.121574 | + | 0.992582i | \(0.461206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.97280 | 0.276018 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.3757 | 1.59956 | ||||||||
\(119\) | −12.5330 | −1.14890 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −23.1057 | −2.09189 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.80849 | 0.880828 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4287 | −1.01414 | −0.507068 | − | 0.861906i | \(-0.669271\pi\) | ||||
−0.507068 | + | 0.861906i | \(0.669271\pi\) | |||||||
\(128\) | 18.2212 | 1.61055 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.10605 | 0.708229 | 0.354114 | − | 0.935202i | \(-0.384782\pi\) | ||||
0.354114 | + | 0.935202i | \(0.384782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.7059 | 1.53530 | ||||||||
\(134\) | −19.8699 | −1.71649 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.9573 | −1.19683 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0664 | −1.70201 | −0.851007 | − | 0.525155i | \(-0.824007\pi\) | ||||
−0.851007 | + | 0.525155i | \(0.824007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.53340 | −0.296516 | ||||||||
\(143\) | −6.05302 | −0.506179 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.8392 | 1.14534 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2754 | 0.926836 | ||||||||
\(149\) | 21.2634 | 1.74196 | 0.870982 | − | 0.491314i | \(-0.163483\pi\) | ||||
0.870982 | + | 0.491314i | \(0.163483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.02720 | −0.571865 | −0.285933 | − | 0.958250i | \(-0.592303\pi\) | ||||
−0.285933 | + | 0.958250i | \(0.592303\pi\) | |||||||
\(152\) | 19.7179 | 1.59934 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.76067 | 0.464208 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.0936 | −1.68346 | −0.841728 | − | 0.539902i | \(-0.818461\pi\) | ||||
−0.841728 | + | 0.539902i | \(0.818461\pi\) | |||||||
\(158\) | −25.2117 | −2.00574 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2238 | 0.884558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.65150 | 0.599311 | 0.299656 | − | 0.954047i | \(-0.403128\pi\) | ||||
0.299656 | + | 0.954047i | \(0.403128\pi\) | |||||||
\(164\) | −32.4872 | −2.53682 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.4511 | −1.50970 | ||||||||
\(167\) | 3.49243 | 0.270252 | 0.135126 | − | 0.990828i | \(-0.456856\pi\) | ||||
0.135126 | + | 0.990828i | \(0.456856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.6391 | 1.81839 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.77758 | −0.364287 | ||||||||
\(173\) | 16.9742 | 1.29052 | 0.645261 | − | 0.763962i | \(-0.276749\pi\) | ||||
0.645261 | + | 0.763962i | \(0.276749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.0392472 | −0.00295837 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −34.6270 | −2.59541 | ||||||||
\(179\) | 9.14529 | 0.683551 | 0.341776 | − | 0.939782i | \(-0.388972\pi\) | ||||
0.341776 | + | 0.939782i | \(0.388972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6391 | 1.68275 | 0.841375 | − | 0.540452i | \(-0.181747\pi\) | ||||
0.841375 | + | 0.540452i | \(0.181747\pi\) | |||||||
\(182\) | −34.8695 | −2.58470 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.4992 | 0.921455 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.97417 | 0.363748 | ||||||||
\(188\) | 26.1604 | 1.90795 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2362 | 0.885380 | 0.442690 | − | 0.896675i | \(-0.354024\pi\) | ||||
0.442690 | + | 0.896675i | \(0.354024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.03788 | −0.0747081 | −0.0373540 | − | 0.999302i | \(-0.511893\pi\) | ||||
−0.0373540 | + | 0.999302i | \(0.511893\pi\) | |||||||
\(194\) | −26.5210 | −1.90410 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.10256 | −0.150183 | ||||||||
\(197\) | 8.06507 | 0.574613 | 0.287306 | − | 0.957839i | \(-0.407240\pi\) | ||||
0.287306 | + | 0.957839i | \(0.407240\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1453 | −0.931845 | −0.465923 | − | 0.884825i | \(-0.654277\pi\) | ||||
−0.465923 | + | 0.884825i | \(0.654277\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.270009 | 0.0189977 | ||||||||
\(203\) | −2.32095 | −0.162899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 24.3244 | 1.69476 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.237564 | 0.0164721 | ||||||||
\(209\) | −7.02720 | −0.486081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.05130 | −0.210060 | −0.105030 | − | 0.994469i | \(-0.533494\pi\) | ||||
−0.105030 | + | 0.994469i | \(0.533494\pi\) | |||||||
\(212\) | 4.98759 | 0.342549 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 42.7362 | 2.92139 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.65776 | −0.519843 | ||||||||
\(218\) | 16.3365 | 1.10644 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.1088 | −2.02534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9483 | 0.934050 | 0.467025 | − | 0.884244i | \(-0.345326\pi\) | ||||
0.467025 | + | 0.884244i | \(0.345326\pi\) | |||||||
\(224\) | −14.3660 | −0.959865 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.90945 | −0.393091 | ||||||||
\(227\) | 29.6529 | 1.96813 | 0.984065 | − | 0.177809i | \(-0.0569011\pi\) | ||||
0.984065 | + | 0.177809i | \(0.0569011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2121 | 1.20349 | 0.601744 | − | 0.798689i | \(-0.294473\pi\) | ||||
0.601744 | + | 0.798689i | \(0.294473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.58470 | −0.169694 | ||||||||
\(233\) | −13.0802 | −0.856914 | −0.428457 | − | 0.903562i | \(-0.640943\pi\) | ||||
−0.428457 | + | 0.903562i | \(0.640943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −24.5268 | −1.59656 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.6546 | 1.85740 | ||||||||
\(239\) | 0.803053 | 0.0519452 | 0.0259726 | − | 0.999663i | \(-0.491732\pi\) | ||||
0.0259726 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.03925 | 0.195775 | 0.0978876 | − | 0.995197i | \(-0.468791\pi\) | ||||
0.0978876 | + | 0.995197i | \(0.468791\pi\) | |||||||
\(242\) | −2.28632 | −0.146970 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.6150 | 2.08796 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.5358 | 2.70649 | ||||||||
\(248\) | −8.52797 | −0.541526 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.36365 | 0.464789 | 0.232395 | − | 0.972622i | \(-0.425344\pi\) | ||||
0.232395 | + | 0.972622i | \(0.425344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.45455 | −0.280055 | ||||||||
\(254\) | 26.1298 | 1.63953 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7451 | −0.984071 | ||||||||
\(257\) | 3.94835 | 0.246291 | 0.123146 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123146 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.80305 | −0.546995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.5330 | −1.14498 | ||||||||
\(263\) | −28.6405 | −1.76605 | −0.883023 | − | 0.469329i | \(-0.844496\pi\) | ||||
−0.883023 | + | 0.469329i | \(0.844496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −40.4814 | −2.48207 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 28.0474 | 1.71327 | ||||||||
\(269\) | 28.2121 | 1.72012 | 0.860061 | − | 0.510191i | \(-0.170425\pi\) | ||||
0.860061 | + | 0.510191i | \(0.170425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2634 | 0.684202 | 0.342101 | − | 0.939663i | \(-0.388861\pi\) | ||||
0.342101 | + | 0.939663i | \(0.388861\pi\) | |||||||
\(272\) | −0.195222 | −0.0118371 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.7179 | 0.828731 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.0165 | 1.74343 | 0.871717 | − | 0.490010i | \(-0.163007\pi\) | ||||
0.871717 | + | 0.490010i | \(0.163007\pi\) | |||||||
\(278\) | 45.8784 | 2.75160 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.9755 | 1.84785 | 0.923923 | − | 0.382579i | \(-0.124964\pi\) | ||||
0.923923 | + | 0.382579i | \(0.124964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7951 | 1.41447 | 0.707235 | − | 0.706979i | \(-0.249942\pi\) | ||||
0.707235 | + | 0.706979i | \(0.249942\pi\) | |||||||
\(284\) | 4.98759 | 0.295959 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.8392 | 0.818327 | ||||||||
\(287\) | 25.3636 | 1.49717 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.74240 | 0.455435 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.5348 | −1.14319 | ||||||||
\(293\) | 0.998275 | 0.0583198 | 0.0291599 | − | 0.999575i | \(-0.490717\pi\) | ||||
0.0291599 | + | 0.999575i | \(0.490717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.80341 | −0.569812 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −48.6150 | −2.81619 | ||||||||
\(299\) | 26.9635 | 1.55934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.72999 | 0.214993 | ||||||||
\(302\) | 16.0664 | 0.924520 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.275798 | 0.0158181 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7710 | 1.58497 | 0.792486 | − | 0.609890i | \(-0.208786\pi\) | ||||
0.792486 | + | 0.609890i | \(0.208786\pi\) | |||||||
\(308\) | −8.13152 | −0.463336 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5213 | −0.993545 | −0.496772 | − | 0.867881i | \(-0.665482\pi\) | ||||
−0.496772 | + | 0.867881i | \(0.665482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.41530 | −0.306091 | −0.153045 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153045 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(314\) | 48.2269 | 2.72160 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 35.5878 | 2.00197 | ||||||||
\(317\) | −6.79679 | −0.381746 | −0.190873 | − | 0.981615i | \(-0.561132\pi\) | ||||
−0.190873 | + | 0.981615i | \(0.561132\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.921150 | 0.0515745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25.6612 | −1.43004 | ||||||||
\(323\) | −34.9545 | −1.94492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.4938 | −0.968892 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.2459 | 1.55962 | ||||||||
\(329\) | −20.4242 | −1.12602 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.11845 | −0.391266 | −0.195633 | − | 0.980677i | \(-0.562676\pi\) | ||||
−0.195633 | + | 0.980677i | \(0.562676\pi\) | |||||||
\(332\) | 27.4563 | 1.50686 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.98482 | −0.436910 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.9105 | −1.35696 | −0.678480 | − | 0.734619i | \(-0.737361\pi\) | ||||
−0.678480 | + | 0.734619i | \(0.737361\pi\) | |||||||
\(338\) | −54.0466 | −2.93975 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.03925 | 0.164584 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2789 | 1.04096 | ||||||||
\(344\) | 4.15386 | 0.223961 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.8084 | −2.08636 | ||||||||
\(347\) | 23.6253 | 1.26827 | 0.634137 | − | 0.773221i | \(-0.281356\pi\) | ||||
0.634137 | + | 0.773221i | \(0.281356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1721 | −1.66861 | −0.834303 | − | 0.551306i | \(-0.814130\pi\) | ||||
−0.834303 | + | 0.551306i | \(0.814130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.70163 | 0.303898 | ||||||||
\(353\) | 0.533044 | 0.0283711 | 0.0141855 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141855 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.8780 | 2.59053 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.9091 | −1.10508 | ||||||||
\(359\) | −12.0268 | −0.634752 | −0.317376 | − | 0.948300i | \(-0.602802\pi\) | ||||
−0.317376 | + | 0.948300i | \(0.602802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.3815 | 1.59903 | ||||||||
\(362\) | −51.7603 | −2.72046 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 49.2203 | 2.57984 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9608 | 0.780945 | 0.390472 | − | 0.920615i | \(-0.372312\pi\) | ||||
0.390472 | + | 0.920615i | \(0.372312\pi\) | |||||||
\(368\) | 0.174828 | 0.00911357 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.89395 | −0.202164 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1315 | −1.04237 | −0.521185 | − | 0.853444i | \(-0.674510\pi\) | ||||
−0.521185 | + | 0.853444i | \(0.674510\pi\) | |||||||
\(374\) | −11.3726 | −0.588062 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.7451 | −1.17299 | ||||||||
\(377\) | −5.57574 | −0.287165 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.8967 | 0.816558 | 0.408279 | − | 0.912857i | \(-0.366129\pi\) | ||||
0.408279 | + | 0.912857i | \(0.366129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.9759 | −1.43137 | ||||||||
\(383\) | 2.63909 | 0.134851 | 0.0674256 | − | 0.997724i | \(-0.478521\pi\) | ||||
0.0674256 | + | 0.997724i | \(0.478521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.37292 | 0.120779 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 37.4359 | 1.90052 | ||||||||
\(389\) | 13.8423 | 0.701832 | 0.350916 | − | 0.936407i | \(-0.385870\pi\) | ||||
0.350916 | + | 0.936407i | \(0.385870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.1577 | −1.12056 | ||||||||
\(392\) | 1.82807 | 0.0923313 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.4394 | −0.928962 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.6783 | 1.28876 | 0.644379 | − | 0.764706i | \(-0.277116\pi\) | ||||
0.644379 | + | 0.764706i | \(0.277116\pi\) | |||||||
\(398\) | 30.0544 | 1.50649 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.1212 | 1.55412 | 0.777059 | − | 0.629428i | \(-0.216711\pi\) | ||||
0.777059 | + | 0.629428i | \(0.216711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.3966 | −0.916402 | ||||||||
\(404\) | −0.381133 | −0.0189621 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.30644 | 0.263354 | ||||||||
\(407\) | 3.49380 | 0.173181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7514 | 0.630516 | 0.315258 | − | 0.949006i | \(-0.397909\pi\) | ||||
0.315258 | + | 0.949006i | \(0.397909\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −34.3353 | −1.69158 | ||||||||
\(413\) | 19.1487 | 0.942248 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −34.5121 | −1.69209 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.0664 | 0.785835 | ||||||||
\(419\) | 0.236195 | 0.0115389 | 0.00576943 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576943 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7300 | −1.05905 | −0.529527 | − | 0.848293i | \(-0.677631\pi\) | ||||
−0.529527 | + | 0.848293i | \(0.677631\pi\) | |||||||
\(422\) | 6.97625 | 0.339599 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.33645 | −0.210597 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.4634 | −1.23226 | ||||||||
\(428\) | −60.3246 | −2.91590 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2121 | −0.780909 | −0.390455 | − | 0.920622i | \(-0.627682\pi\) | ||||
−0.390455 | + | 0.920622i | \(0.627682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5213 | −0.649795 | −0.324897 | − | 0.945749i | \(-0.605330\pi\) | ||||
−0.324897 | + | 0.945749i | \(0.605330\pi\) | |||||||
\(434\) | 17.5081 | 0.840416 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.0598 | −1.10437 | ||||||||
\(437\) | 31.3030 | 1.49743 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0664435 | 0.00317118 | 0.00158559 | − | 0.999999i | \(-0.499495\pi\) | ||||
0.00158559 | + | 0.999999i | \(0.499495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 68.8384 | 3.27431 | ||||||||
\(443\) | 0.560596 | 0.0266347 | 0.0133174 | − | 0.999911i | \(-0.495761\pi\) | ||||
0.0133174 | + | 0.999911i | \(0.495761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −31.8904 | −1.51006 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.6474 | 1.54245 | ||||||||
\(449\) | 9.92079 | 0.468191 | 0.234096 | − | 0.972214i | \(-0.424787\pi\) | ||||
0.234096 | + | 0.972214i | \(0.424787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0664 | −0.474010 | ||||||||
\(452\) | 8.34153 | 0.392353 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −67.7960 | −3.18183 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.93457 | −0.417942 | −0.208971 | − | 0.977922i | \(-0.567011\pi\) | ||||
−0.208971 | + | 0.977922i | \(0.567011\pi\) | |||||||
\(458\) | −41.6387 | −1.94565 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.1484 | 1.59045 | 0.795225 | − | 0.606315i | \(-0.207353\pi\) | ||||
0.795225 | + | 0.606315i | \(0.207353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9359 | 1.15887 | 0.579436 | − | 0.815018i | \(-0.303273\pi\) | ||||
0.579436 | + | 0.815018i | \(0.303273\pi\) | |||||||
\(464\) | −0.0361525 | −0.00167834 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.9056 | 1.38535 | ||||||||
\(467\) | 2.84844 | 0.131810 | 0.0659051 | − | 0.997826i | \(-0.479007\pi\) | ||||
0.0659051 | + | 0.997826i | \(0.479007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8974 | −1.01113 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.3248 | 0.981552 | ||||||||
\(473\) | −1.48038 | −0.0680678 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −40.4476 | −1.85391 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.83604 | −0.0839784 | ||||||||
\(479\) | −15.1177 | −0.690747 | −0.345374 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345374 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.1480 | −0.964267 | ||||||||
\(482\) | −6.94870 | −0.316505 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.22727 | 0.146694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.53376 | 0.205444 | 0.102722 | − | 0.994710i | \(-0.467245\pi\) | ||||
0.102722 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(488\) | −28.3570 | −1.28366 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0909 | −0.681043 | −0.340521 | − | 0.940237i | \(-0.610604\pi\) | ||||
−0.340521 | + | 0.940237i | \(0.610604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.58196 | 0.206361 | ||||||||
\(494\) | −97.2506 | −4.37551 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.119282 | −0.00535591 | ||||||||
\(497\) | −3.89395 | −0.174668 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.93320 | −0.399905 | −0.199952 | − | 0.979806i | \(-0.564079\pi\) | ||||
−0.199952 | + | 0.979806i | \(0.564079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.8357 | −0.751413 | ||||||||
\(503\) | −26.7162 | −1.19122 | −0.595609 | − | 0.803275i | \(-0.703089\pi\) | ||||
−0.595609 | + | 0.803275i | \(0.703089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1845 | 0.452758 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −36.8836 | −1.63645 | ||||||||
\(509\) | −10.9876 | −0.487017 | −0.243508 | − | 0.969899i | \(-0.578298\pi\) | ||||
−0.243508 | + | 0.969899i | \(0.578298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.2513 | 0.674680 | ||||||||
\(512\) | −0.444024 | −0.0196233 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.02720 | −0.398173 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.10605 | 0.356504 | ||||||||
\(518\) | 20.1266 | 0.884313 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2782 | −1.01984 | −0.509918 | − | 0.860223i | \(-0.670324\pi\) | ||||
−0.509918 | + | 0.860223i | \(0.670324\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.4163 | 0.805289 | 0.402645 | − | 0.915356i | \(-0.368091\pi\) | ||||
0.402645 | + | 0.915356i | \(0.368091\pi\) | |||||||
\(524\) | 26.1604 | 1.14282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 65.4814 | 2.85512 | ||||||||
\(527\) | 15.1177 | 0.658539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.15699 | −0.137260 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 57.1418 | 2.47741 | ||||||||
\(533\) | 60.9324 | 2.63928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.3858 | −1.05330 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −64.5020 | −2.78088 | ||||||||
\(539\) | −0.651497 | −0.0280620 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.3815 | −1.34920 | −0.674598 | − | 0.738186i | \(-0.735683\pi\) | ||||
−0.674598 | + | 0.738186i | \(0.735683\pi\) | |||||||
\(542\) | −25.7518 | −1.10613 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.3609 | 1.21596 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.74412 | 0.160087 | 0.0800436 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800436 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(548\) | −19.3636 | −0.827174 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.47310 | −0.275763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.7844 | −1.18151 | ||||||||
\(554\) | −66.3411 | −2.81856 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −64.7599 | −2.74643 | ||||||||
\(557\) | 25.3164 | 1.07269 | 0.536345 | − | 0.843999i | \(-0.319804\pi\) | ||||
0.536345 | + | 0.843999i | \(0.319804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.96075 | 0.378999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −70.8201 | −2.98737 | ||||||||
\(563\) | 24.7465 | 1.04294 | 0.521470 | − | 0.853269i | \(-0.325384\pi\) | ||||
0.521470 | + | 0.853269i | \(0.325384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −54.4032 | −2.28674 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.33645 | −0.181953 | ||||||||
\(569\) | −44.0148 | −1.84520 | −0.922598 | − | 0.385763i | \(-0.873938\pi\) | ||||
−0.922598 | + | 0.385763i | \(0.873938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.01205 | −0.0842017 | −0.0421009 | − | 0.999113i | \(-0.513405\pi\) | ||||
−0.0421009 | + | 0.999113i | \(0.513405\pi\) | |||||||
\(572\) | −19.5348 | −0.816790 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −57.9895 | −2.42044 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.3181 | −1.09564 | −0.547819 | − | 0.836597i | \(-0.684542\pi\) | ||||
−0.547819 | + | 0.836597i | \(0.684542\pi\) | |||||||
\(578\) | −17.7016 | −0.736291 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.4359 | −0.889310 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.54545 | 0.0640060 | ||||||||
\(584\) | 16.9845 | 0.702822 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.28238 | −0.0942842 | ||||||||
\(587\) | −35.8112 | −1.47809 | −0.739044 | − | 0.673657i | \(-0.764722\pi\) | ||||
−0.739044 | + | 0.673657i | \(0.764722\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.3574 | −0.880016 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.137122 | −0.00563567 | ||||||||
\(593\) | 7.61953 | 0.312896 | 0.156448 | − | 0.987686i | \(-0.449996\pi\) | ||||
0.156448 | + | 0.987686i | \(0.449996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 68.6228 | 2.81090 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −61.6473 | −2.52094 | ||||||||
\(599\) | 40.2121 | 1.64302 | 0.821511 | − | 0.570193i | \(-0.193132\pi\) | ||||
0.821511 | + | 0.570193i | \(0.193132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.3181 | 1.07354 | 0.536770 | − | 0.843729i | \(-0.319644\pi\) | ||||
0.536770 | + | 0.843729i | \(0.319644\pi\) | |||||||
\(602\) | −8.52797 | −0.347574 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.6787 | −0.922783 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.4287 | −0.463878 | −0.231939 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231939 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(608\) | −40.0664 | −1.62491 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.0661 | −1.98500 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1198 | 0.853022 | 0.426511 | − | 0.904482i | \(-0.359743\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359743\pi\) | |||||||
\(614\) | −63.4934 | −2.56239 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.06993 | 0.284856 | ||||||||
\(617\) | −31.3905 | −1.26373 | −0.631867 | − | 0.775077i | \(-0.717711\pi\) | ||||
−0.631867 | + | 0.775077i | \(0.717711\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.11845 | −0.286115 | −0.143057 | − | 0.989714i | \(-0.545693\pi\) | ||||
−0.143057 | + | 0.989714i | \(0.545693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.0595 | 1.60624 | ||||||||
\(623\) | −38.1604 | −1.52887 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.3811 | 0.494850 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −68.0750 | −2.71649 | ||||||||
\(629\) | 17.3787 | 0.692936 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3574 | 0.850224 | 0.425112 | − | 0.905141i | \(-0.360235\pi\) | ||||
0.425112 | + | 0.905141i | \(0.360235\pi\) | |||||||
\(632\) | −30.9417 | −1.23080 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.5397 | 0.617159 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.94353 | 0.156248 | ||||||||
\(638\) | −2.10605 | −0.0833792 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.1329 | −1.03219 | −0.516093 | − | 0.856532i | \(-0.672614\pi\) | ||||
−0.516093 | + | 0.856532i | \(0.672614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.5358 | −1.20421 | −0.602107 | − | 0.798416i | \(-0.705672\pi\) | ||||
−0.602107 | + | 0.798416i | \(0.705672\pi\) | |||||||
\(644\) | 36.2222 | 1.42736 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 79.9173 | 3.14430 | ||||||||
\(647\) | −11.5482 | −0.454006 | −0.227003 | − | 0.973894i | \(-0.572893\pi\) | ||||
−0.227003 | + | 0.973894i | \(0.572893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59984 | −0.298320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.6935 | 0.967071 | ||||||||
\(653\) | −22.2389 | −0.870277 | −0.435138 | − | 0.900364i | \(-0.643301\pi\) | ||||
−0.435138 | + | 0.900364i | \(0.643301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.395079 | 0.0154253 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 46.6963 | 1.82041 | ||||||||
\(659\) | −39.4359 | −1.53620 | −0.768102 | − | 0.640328i | \(-0.778799\pi\) | ||||
−0.768102 | + | 0.640328i | \(0.778799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.8967 | 0.851683 | 0.425841 | − | 0.904798i | \(-0.359978\pi\) | ||||
0.425841 | + | 0.904798i | \(0.359978\pi\) | |||||||
\(662\) | 16.2751 | 0.632549 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.8718 | −0.926405 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.10331 | −0.158881 | ||||||||
\(668\) | 11.2710 | 0.436089 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1060 | 0.390140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2920 | 0.705103 | 0.352552 | − | 0.935792i | \(-0.385314\pi\) | ||||
0.352552 | + | 0.935792i | \(0.385314\pi\) | |||||||
\(674\) | 56.9534 | 2.19376 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 76.2898 | 2.93422 | ||||||||
\(677\) | 0.817184 | 0.0314069 | 0.0157035 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157035 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.2272 | −1.12164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.94870 | −0.266080 | ||||||||
\(683\) | −12.8031 | −0.489895 | −0.244948 | − | 0.969536i | \(-0.578771\pi\) | ||||
−0.244948 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −44.0778 | −1.68290 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0581006 | 0.00221506 | ||||||||
\(689\) | −9.35465 | −0.356384 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.9394 | −0.872656 | −0.436328 | − | 0.899788i | \(-0.643721\pi\) | ||||
−0.436328 | + | 0.899788i | \(0.643721\pi\) | |||||||
\(692\) | 54.7803 | 2.08244 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54.0151 | −2.05039 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.0722 | −1.89662 | ||||||||
\(698\) | 71.2696 | 2.69759 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.3329 | 1.22120 | 0.610599 | − | 0.791940i | \(-0.290929\pi\) | ||||
0.610599 | + | 0.791940i | \(0.290929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.5516 | −0.925981 | ||||||||
\(704\) | −12.9573 | −0.488345 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.21871 | −0.0458668 | ||||||||
\(707\) | 0.297561 | 0.0111909 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.25760 | −0.347677 | −0.173838 | − | 0.984774i | \(-0.555617\pi\) | ||||
−0.173838 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −42.4969 | −1.59264 | ||||||||
\(713\) | −13.5385 | −0.507020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.5144 | 1.10300 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.4972 | 1.02619 | ||||||||
\(719\) | 7.01170 | 0.261492 | 0.130746 | − | 0.991416i | \(-0.458263\pi\) | ||||
0.130746 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8065 | 0.998326 | ||||||||
\(722\) | −69.4619 | −2.58510 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 73.0626 | 2.71535 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0303 | −0.668706 | −0.334353 | − | 0.942448i | \(-0.608518\pi\) | ||||
−0.334353 | + | 0.942448i | \(0.608518\pi\) | |||||||
\(728\) | −42.7945 | −1.58607 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.36365 | −0.272354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.9890 | 0.849117 | 0.424558 | − | 0.905401i | \(-0.360429\pi\) | ||||
0.424558 | + | 0.905401i | \(0.360429\pi\) | |||||||
\(734\) | −34.2051 | −1.26253 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.3982 | −0.936189 | ||||||||
\(737\) | 8.69074 | 0.320128 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0967 | −1.10713 | −0.553563 | − | 0.832807i | \(-0.686732\pi\) | ||||
−0.553563 | + | 0.832807i | \(0.686732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.90284 | 0.326833 | ||||||||
\(743\) | 32.7706 | 1.20224 | 0.601119 | − | 0.799160i | \(-0.294722\pi\) | ||||
0.601119 | + | 0.799160i | \(0.294722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 46.0272 | 1.68517 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0530 | 0.586957 | ||||||||
\(749\) | 47.0971 | 1.72089 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.132887 | −0.00484912 | −0.00242456 | − | 0.999997i | \(-0.500772\pi\) | ||||
−0.00242456 | + | 0.999997i | \(0.500772\pi\) | |||||||
\(752\) | −0.318139 | −0.0116014 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.7479 | 0.464253 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.1363 | 1.45878 | 0.729390 | − | 0.684098i | \(-0.239804\pi\) | ||||
0.729390 | + | 0.684098i | \(0.239804\pi\) | |||||||
\(758\) | −36.3450 | −1.32011 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.9487 | 1.12189 | 0.560945 | − | 0.827853i | \(-0.310438\pi\) | ||||
0.560945 | + | 0.827853i | \(0.310438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0035 | 0.651769 | ||||||||
\(764\) | 39.4896 | 1.42868 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.03381 | −0.218011 | ||||||||
\(767\) | 46.0020 | 1.66104 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.17213 | −0.258634 | −0.129317 | − | 0.991603i | \(-0.541278\pi\) | ||||
−0.129317 | + | 0.991603i | \(0.541278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.34952 | −0.120552 | ||||||||
\(773\) | 15.3546 | 0.552268 | 0.276134 | − | 0.961119i | \(-0.410947\pi\) | ||||
0.276134 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −32.5485 | −1.16842 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.6480 | −1.13463 | ||||||||
\(779\) | 70.7389 | 2.53448 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.54545 | 0.0553006 | ||||||||
\(782\) | 50.6597 | 1.81159 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0255694 | 0.000913193 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.8619 | −0.387184 | −0.193592 | − | 0.981082i | \(-0.562014\pi\) | ||||
−0.193592 | + | 0.981082i | \(0.562014\pi\) | |||||||
\(788\) | 26.0282 | 0.927217 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.51247 | −0.231557 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.1721 | −2.17229 | ||||||||
\(794\) | −58.7090 | −2.08350 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42.4235 | −1.50366 | ||||||||
\(797\) | 40.7720 | 1.44422 | 0.722109 | − | 0.691780i | \(-0.243173\pi\) | ||||
0.722109 | + | 0.691780i | \(0.243173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.3209 | 1.42645 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −71.1531 | −2.51250 | ||||||||
\(803\) | −6.05302 | −0.213607 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 42.0607 | 1.48152 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.331375 | 0.0116577 | ||||||||
\(809\) | −14.7634 | −0.519055 | −0.259528 | − | 0.965736i | \(-0.583567\pi\) | ||||
−0.259528 | + | 0.965736i | \(0.583567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.93356 | 0.138126 | 0.0690629 | − | 0.997612i | \(-0.477999\pi\) | ||||
0.0690629 | + | 0.997612i | \(0.477999\pi\) | |||||||
\(812\) | −7.49035 | −0.262860 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.98795 | −0.279977 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4029 | 0.363951 | ||||||||
\(818\) | −29.1538 | −1.01934 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4603 | 0.714071 | 0.357035 | − | 0.934091i | \(-0.383788\pi\) | ||||
0.357035 | + | 0.934091i | \(0.383788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.7603 | −0.828231 | −0.414116 | − | 0.910224i | \(-0.635909\pi\) | ||||
−0.414116 | + | 0.910224i | \(0.635909\pi\) | |||||||
\(824\) | 29.8527 | 1.03997 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.7802 | −1.52331 | ||||||||
\(827\) | −30.1253 | −1.04756 | −0.523779 | − | 0.851854i | \(-0.675478\pi\) | ||||
−0.523779 | + | 0.851854i | \(0.675478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8388 | 1.31420 | 0.657098 | − | 0.753806i | \(-0.271784\pi\) | ||||
0.657098 | + | 0.753806i | \(0.271784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 78.4306 | 2.71909 | ||||||||
\(833\) | −3.24066 | −0.112282 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.6787 | −0.784359 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.540017 | −0.0186546 | ||||||||
\(839\) | 45.7871 | 1.58075 | 0.790374 | − | 0.612625i | \(-0.209886\pi\) | ||||
0.790374 | + | 0.612625i | \(0.209886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1515 | −0.970741 | ||||||||
\(842\) | 49.6818 | 1.71215 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.84738 | −0.338961 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.51962 | −0.0865753 | ||||||||
\(848\) | −0.0606546 | −0.00208289 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5633 | −0.533503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.3312 | −0.798845 | −0.399423 | − | 0.916767i | \(-0.630789\pi\) | ||||
−0.399423 | + | 0.916767i | \(0.630789\pi\) | |||||||
\(854\) | 58.2176 | 1.99217 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 52.4491 | 1.79267 | ||||||||
\(857\) | −16.0892 | −0.549596 | −0.274798 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274798 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1969 | 0.450274 | 0.225137 | − | 0.974327i | \(-0.427717\pi\) | ||||
0.225137 | + | 0.974327i | \(0.427717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.0661 | 1.26248 | ||||||||
\(863\) | −48.5606 | −1.65302 | −0.826511 | − | 0.562921i | \(-0.809678\pi\) | ||||
−0.826511 | + | 0.562921i | \(0.809678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.9142 | 1.05051 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.7137 | −0.838837 | ||||||||
\(869\) | 11.0272 | 0.374072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.6053 | −1.78246 | ||||||||
\(872\) | 20.0493 | 0.678955 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −71.5688 | −2.42085 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.4862 | −0.590466 | −0.295233 | − | 0.955425i | \(-0.595397\pi\) | ||||
−0.295233 | + | 0.955425i | \(0.595397\pi\) | |||||||
\(878\) | −0.151911 | −0.00512676 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2238 | 0.782429 | 0.391215 | − | 0.920299i | \(-0.372055\pi\) | ||||
0.391215 | + | 0.920299i | \(0.372055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8967 | −1.34263 | −0.671315 | − | 0.741172i | \(-0.734270\pi\) | ||||
−0.671315 | + | 0.741172i | \(0.734270\pi\) | |||||||
\(884\) | −97.1693 | −3.26816 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.28170 | −0.0430597 | ||||||||
\(887\) | 13.6770 | 0.459228 | 0.229614 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229614 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.7961 | 0.965789 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.0151 | 1.50722 | ||||||||
\(893\) | −56.9628 | −1.90619 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −45.9107 | −1.53377 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.6821 | −0.756913 | ||||||||
\(899\) | 2.79960 | 0.0933720 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.68734 | 0.256102 | ||||||||
\(902\) | 23.0151 | 0.766321 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.25252 | −0.241215 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.73625 | −0.0576513 | −0.0288257 | − | 0.999584i | \(-0.509177\pi\) | ||||
−0.0288257 | + | 0.999584i | \(0.509177\pi\) | |||||||
\(908\) | 95.6979 | 3.17585 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.4662 | −1.63889 | −0.819444 | − | 0.573160i | \(-0.805717\pi\) | ||||
−0.819444 | + | 0.573160i | \(0.805717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.50757 | 0.281560 | ||||||||
\(914\) | 20.4273 | 0.675676 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 58.7754 | 1.94199 | ||||||||
\(917\) | −20.4242 | −0.674466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0423 | 1.32087 | 0.660437 | − | 0.750881i | \(-0.270371\pi\) | ||||
0.660437 | + | 0.750881i | \(0.270371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −78.0743 | −2.57124 | ||||||||
\(923\) | −9.35465 | −0.307912 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −57.0116 | −1.87352 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.25205 | 0.172407 | ||||||||
\(929\) | 29.0420 | 0.952837 | 0.476418 | − | 0.879219i | \(-0.341935\pi\) | ||||
0.476418 | + | 0.879219i | \(0.341935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.57820 | 0.150044 | ||||||||
\(932\) | −42.2135 | −1.38275 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.51247 | −0.213094 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.0282 | −1.30766 | −0.653832 | − | 0.756639i | \(-0.726840\pi\) | ||||
−0.653832 | + | 0.756639i | \(0.726840\pi\) | |||||||
\(938\) | 50.0645 | 1.63467 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.9604 | 0.455096 | 0.227548 | − | 0.973767i | \(-0.426929\pi\) | ||||
0.227548 | + | 0.973767i | \(0.426929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.8415 | 1.46024 | ||||||||
\(944\) | 0.298272 | 0.00970794 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.38462 | 0.110043 | ||||||||
\(947\) | −17.4875 | −0.568269 | −0.284134 | − | 0.958785i | \(-0.591706\pi\) | ||||
−0.284134 | + | 0.958785i | \(0.591706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.6391 | 1.18936 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35.1671 | 1.13977 | ||||||||
\(953\) | 49.1890 | 1.59339 | 0.796694 | − | 0.604383i | \(-0.206580\pi\) | ||||
0.796694 | + | 0.604383i | \(0.206580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.59167 | 0.0838206 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.5640 | 1.11671 | ||||||||
\(959\) | 15.1177 | 0.488177 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7630 | −0.702032 | ||||||||
\(962\) | 48.3512 | 1.55891 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.80849 | 0.315910 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.5589 | 0.757602 | 0.378801 | − | 0.925478i | \(-0.376336\pi\) | ||||
0.378801 | + | 0.925478i | \(0.376336\pi\) | |||||||
\(968\) | −2.80595 | −0.0901866 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.16940 | −0.165894 | −0.0829469 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829469 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.5599 | 1.62088 | ||||||||
\(974\) | −10.3656 | −0.332136 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396634 | −0.0126959 | ||||||||
\(977\) | 9.73970 | 0.311601 | 0.155800 | − | 0.987789i | \(-0.450204\pi\) | ||||
0.155800 | + | 0.987789i | \(0.450204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.1453 | 0.484046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.5027 | 1.10102 | ||||||||
\(983\) | −2.16670 | −0.0691070 | −0.0345535 | − | 0.999403i | \(-0.511001\pi\) | ||||
−0.0345535 | + | 0.999403i | \(0.511001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.4758 | −0.333619 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 137.275 | 4.36729 | ||||||||
\(989\) | 6.59441 | 0.209690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2265 | −0.801347 | −0.400674 | − | 0.916221i | \(-0.631224\pi\) | ||||
−0.400674 | + | 0.916221i | \(0.631224\pi\) | |||||||
\(992\) | 17.3286 | 0.550185 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.90284 | 0.282381 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.5950 | −0.937281 | −0.468641 | − | 0.883389i | \(-0.655256\pi\) | ||||
−0.468641 | + | 0.883389i | \(0.655256\pi\) | |||||||
\(998\) | 20.4242 | 0.646516 | ||||||||
\(999\) | 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 | 2475.2.a.bj.1.1 | 4 | ||
3.2 | odd | 2 | 2475.2.a.bf.1.4 | 4 | |||
5.2 | odd | 4 | 2475.2.c.t.199.2 | 8 | |||
5.3 | odd | 4 | 2475.2.c.t.199.7 | 8 | |||
5.4 | even | 2 | 495.2.a.f.1.4 | ✓ | 4 | ||
15.2 | even | 4 | 2475.2.c.s.199.7 | 8 | |||
15.8 | even | 4 | 2475.2.c.s.199.2 | 8 | |||
15.14 | odd | 2 | 495.2.a.g.1.1 | yes | 4 | ||
20.19 | odd | 2 | 7920.2.a.cm.1.2 | 4 | |||
55.54 | odd | 2 | 5445.2.a.bs.1.1 | 4 | |||
60.59 | even | 2 | 7920.2.a.cn.1.2 | 4 | |||
165.164 | even | 2 | 5445.2.a.bh.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.a.f.1.4 | ✓ | 4 | 5.4 | even | 2 | ||
495.2.a.g.1.1 | yes | 4 | 15.14 | odd | 2 | ||
2475.2.a.bf.1.4 | 4 | 3.2 | odd | 2 | |||
2475.2.a.bj.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.c.s.199.2 | 8 | 15.8 | even | 4 | |||
2475.2.c.s.199.7 | 8 | 15.2 | even | 4 | |||
2475.2.c.t.199.2 | 8 | 5.2 | odd | 4 | |||
2475.2.c.t.199.7 | 8 | 5.3 | odd | 4 | |||
5445.2.a.bh.1.4 | 4 | 165.164 | even | 2 | |||
5445.2.a.bs.1.1 | 4 | 55.54 | odd | 2 | |||
7920.2.a.cm.1.2 | 4 | 20.19 | odd | 2 | |||
7920.2.a.cn.1.2 | 4 | 60.59 | even | 2 |