Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | −0.654654 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205 | 0.522233 | 0.261116 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.46410 | 0.597632 | 0.298816 | − | 0.954311i | \(-0.403408\pi\) | ||||
0.298816 | + | 0.954311i | \(0.403408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46410 | −0.794719 | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.92820 | 0.729449 | 0.364725 | − | 0.931115i | \(-0.381163\pi\) | ||||
0.364725 | + | 0.931115i | \(0.381163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.19615 | −1.65168 | −0.825839 | − | 0.563906i | \(-0.809298\pi\) | ||||
−0.825839 | + | 0.563906i | \(0.809298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73205 | 0.301511 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.535898 | 0.0881012 | 0.0440506 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440506 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.53590 | −0.396041 | −0.198020 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198020 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.92820 | −1.36154 | −0.680769 | − | 0.732498i | \(-0.738354\pi\) | ||||
−0.680769 | + | 0.732498i | \(0.738354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.66025 | 0.971498 | 0.485749 | − | 0.874098i | \(-0.338547\pi\) | ||||
0.485749 | + | 0.874098i | \(0.338547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.00000 | −0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.46410 | 0.345043 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9282 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.73205 | 0.225494 | 0.112747 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112747 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4641 | −1.59586 | −0.797932 | − | 0.602747i | \(-0.794073\pi\) | ||||
−0.797932 | + | 0.602747i | \(0.794073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | −0.218218 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.26795 | −0.521413 | −0.260706 | − | 0.965418i | \(-0.583955\pi\) | ||||
−0.260706 | + | 0.965418i | \(0.583955\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3923 | −1.70805 | −0.854026 | − | 0.520230i | \(-0.825846\pi\) | ||||
−0.854026 | + | 0.520230i | \(0.825846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.46410 | 0.405442 | 0.202721 | − | 0.979236i | \(-0.435021\pi\) | ||||
0.202721 | + | 0.979236i | \(0.435021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7321 | −1.50729 | −0.753644 | − | 0.657283i | \(-0.771706\pi\) | ||||
−0.753644 | + | 0.657283i | \(0.771706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.92820 | 0.421148 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.92820 | −0.310389 | −0.155194 | − | 0.987884i | \(-0.549600\pi\) | ||||
−0.155194 | + | 0.987884i | \(0.549600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.73205 | 0.181568 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.19615 | −0.953597 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.92820 | −0.500383 | −0.250192 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250192 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.73205 | 0.174078 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | 0.298511 | 0.149256 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149256 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3205 | 1.50957 | 0.754787 | − | 0.655970i | \(-0.227740\pi\) | ||||
0.754787 | + | 0.655970i | \(0.227740\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.46410 | 0.721582 | 0.360791 | − | 0.932647i | \(-0.382507\pi\) | ||||
0.360791 | + | 0.932647i | \(0.382507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.53590 | −0.242895 | −0.121448 | − | 0.992598i | \(-0.538754\pi\) | ||||
−0.121448 | + | 0.992598i | \(0.538754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.535898 | 0.0508652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.26795 | −0.391242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.53590 | −0.228654 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.928203 | −0.0823647 | −0.0411824 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411824 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.92820 | −0.786084 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.4641 | −1.87533 | −0.937664 | − | 0.347544i | \(-0.887016\pi\) | ||||
−0.937664 | + | 0.347544i | \(0.887016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.92820 | −0.250173 | −0.125087 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125087 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3923 | −1.22074 | −0.610370 | − | 0.792117i | \(-0.708979\pi\) | ||||
−0.610370 | + | 0.792117i | \(0.708979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.66025 | 0.560895 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.73205 | −0.144841 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.00000 | −0.329914 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.8564 | 0.971315 | 0.485657 | − | 0.874149i | \(-0.338580\pi\) | ||||
0.485657 | + | 0.874149i | \(0.338580\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.12436 | 0.661151 | 0.330575 | − | 0.943780i | \(-0.392757\pi\) | ||||
0.330575 | + | 0.943780i | \(0.392757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.46410 | 0.199211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.39230 | 0.749588 | 0.374794 | − | 0.927108i | \(-0.377714\pi\) | ||||
0.374794 | + | 0.927108i | \(0.377714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.9282 | 0.945968 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.39230 | 0.500684 | 0.250342 | − | 0.968157i | \(-0.419457\pi\) | ||||
0.250342 | + | 0.968157i | \(0.419457\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.46410 | −0.264906 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.92820 | −0.298656 | −0.149328 | − | 0.988788i | \(-0.547711\pi\) | ||||
−0.149328 | + | 0.988788i | \(0.547711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73205 | 0.130189 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.392305 | −0.0293222 | −0.0146611 | − | 0.999893i | \(-0.504667\pi\) | ||||
−0.0146611 | + | 0.999893i | \(0.504667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.53590 | −0.262821 | −0.131411 | − | 0.991328i | \(-0.541951\pi\) | ||||
−0.131411 | + | 0.991328i | \(0.541951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4641 | −0.921373 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.26795 | 0.312103 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.73205 | −0.125988 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3923 | 1.04139 | 0.520695 | − | 0.853743i | \(-0.325673\pi\) | ||||
0.520695 | + | 0.853743i | \(0.325673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.46410 | −0.105388 | −0.0526942 | − | 0.998611i | \(-0.516781\pi\) | ||||
−0.0526942 | + | 0.998611i | \(0.516781\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.39230 | −0.312939 | −0.156469 | − | 0.987683i | \(-0.550011\pi\) | ||||
−0.156469 | + | 0.987683i | \(0.550011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.3205 | 1.51137 | 0.755685 | − | 0.654935i | \(-0.227304\pi\) | ||||
0.755685 | + | 0.654935i | \(0.227304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.26795 | −0.301038 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.80385 | −0.477536 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | −0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0000 | −1.78991 | −0.894957 | − | 0.446153i | \(-0.852794\pi\) | ||||
−0.894957 | + | 0.446153i | \(0.852794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.3923 | −0.986144 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.9282 | 1.08128 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.46410 | 0.234082 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.46410 | −0.165753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.2487 | −1.89167 | −0.945837 | − | 0.324642i | \(-0.894756\pi\) | ||||
−0.945837 | + | 0.324642i | \(0.894756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.26795 | 0.150529 | 0.0752645 | − | 0.997164i | \(-0.476020\pi\) | ||||
0.0752645 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7846 | −1.24132 | −0.620661 | − | 0.784079i | \(-0.713136\pi\) | ||||
−0.620661 | + | 0.784079i | \(0.713136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | −0.197386 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8564 | −1.30084 | −0.650418 | − | 0.759576i | \(-0.725406\pi\) | ||||
−0.650418 | + | 0.759576i | \(0.725406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.19615 | 0.206742 | 0.103371 | − | 0.994643i | \(-0.467037\pi\) | ||||
0.103371 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3923 | −1.31358 | −0.656792 | − | 0.754072i | \(-0.728087\pi\) | ||||
−0.656792 | + | 0.754072i | \(0.728087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.46410 | 0.220416 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.7321 | −0.870233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.39230 | 0.277240 | 0.138620 | − | 0.990346i | \(-0.455733\pi\) | ||||
0.138620 | + | 0.990346i | \(0.455733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.46410 | −0.217786 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.2487 | 1.20070 | 0.600351 | − | 0.799737i | \(-0.295028\pi\) | ||||
0.600351 | + | 0.799737i | \(0.295028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.928203 | −0.0576757 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92820 | 0.243150 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3205 | −1.43800 | −0.719002 | − | 0.695008i | \(-0.755401\pi\) | ||||
−0.719002 | + | 0.695008i | \(0.755401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.92820 | −0.179203 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.0000 | −1.15845 | −0.579225 | − | 0.815168i | \(-0.696645\pi\) | ||||
−0.579225 | + | 0.815168i | \(0.696645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.7321 | −1.32013 | −0.660064 | − | 0.751209i | \(-0.729471\pi\) | ||||
−0.660064 | + | 0.751209i | \(0.729471\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73205 | 0.104828 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9282 | 1.25745 | 0.628727 | − | 0.777626i | \(-0.283576\pi\) | ||||
0.628727 | + | 0.777626i | \(0.283576\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.19615 | −0.550559 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.32051 | −0.554047 | −0.277023 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277023 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.39230 | 0.259270 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9282 | −0.642835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.92820 | −0.288896 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8564 | 0.926341 | 0.463171 | − | 0.886269i | \(-0.346712\pi\) | ||||
0.463171 | + | 0.886269i | \(0.346712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | 0.100504 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4641 | 0.891336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.00000 | 0.172345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.53590 | −0.258877 | −0.129439 | − | 0.991587i | \(-0.541318\pi\) | ||||
−0.129439 | + | 0.991587i | \(0.541318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.3205 | 0.871553 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.46410 | −0.423250 | −0.211625 | − | 0.977351i | \(-0.567876\pi\) | ||||
−0.211625 | + | 0.977351i | \(0.567876\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.92820 | 0.108988 | 0.0544942 | − | 0.998514i | \(-0.482645\pi\) | ||||
0.0544942 | + | 0.998514i | \(0.482645\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5359 | 0.704086 | 0.352043 | − | 0.935984i | \(-0.385487\pi\) | ||||
0.352043 | + | 0.935984i | \(0.385487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.80385 | 0.380942 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.46410 | 0.416606 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.53590 | −0.474950 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.53590 | −0.140236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.5359 | −0.635995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.53590 | −0.249316 | −0.124658 | − | 0.992200i | \(-0.539783\pi\) | ||||
−0.124658 | + | 0.992200i | \(0.539783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.535898 | 0.0293671 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.14359 | 0.171242 | 0.0856212 | − | 0.996328i | \(-0.472713\pi\) | ||||
0.0856212 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.9282 | −0.862561 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.2487 | −0.872277 | −0.436138 | − | 0.899880i | \(-0.643654\pi\) | ||||
−0.436138 | + | 0.899880i | \(0.643654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3923 | −0.770402 | −0.385201 | − | 0.922833i | \(-0.625868\pi\) | ||||
−0.385201 | + | 0.922833i | \(0.625868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.32051 | 0.389631 | 0.194816 | − | 0.980840i | \(-0.437589\pi\) | ||||
0.194816 | + | 0.980840i | \(0.437589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.26795 | −0.225884 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.73205 | 0.196970 | 0.0984851 | − | 0.995139i | \(-0.468600\pi\) | ||||
0.0984851 | + | 0.995139i | \(0.468600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.00000 | −0.419891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.92820 | −0.361649 | −0.180825 | − | 0.983515i | \(-0.557877\pi\) | ||||
−0.180825 | + | 0.983515i | \(0.557877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.53590 | −0.132014 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.6603 | −1.07263 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.3923 | 1.10765 | 0.553826 | − | 0.832633i | \(-0.313167\pi\) | ||||
0.553826 | + | 0.832633i | \(0.313167\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.92820 | −0.202313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.80385 | 0.246757 | 0.123379 | − | 0.992360i | \(-0.460627\pi\) | ||||
0.123379 | + | 0.992360i | \(0.460627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.928203 | −0.0475533 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.53590 | −0.436164 | −0.218082 | − | 0.975930i | \(-0.569980\pi\) | ||||
−0.218082 | + | 0.975930i | \(0.569980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.92820 | −0.453846 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.85641 | −0.398336 | −0.199168 | − | 0.979965i | \(-0.563824\pi\) | ||||
−0.199168 | + | 0.979965i | \(0.563824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.92820 | −0.249230 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.4641 | −1.08272 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.00000 | 0.300376 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.1051 | −1.90288 | −0.951439 | − | 0.307836i | \(-0.900395\pi\) | ||||
−0.951439 | + | 0.307836i | \(0.900395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.19615 | 0.458093 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.928203 | 0.0460093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3205 | 0.559763 | 0.279882 | − | 0.960035i | \(-0.409705\pi\) | ||||
0.279882 | + | 0.960035i | \(0.409705\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.92820 | −0.144438 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.00000 | −0.147620 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.3923 | −0.704794 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.3205 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.07180 | −0.247184 | −0.123592 | − | 0.992333i | \(-0.539441\pi\) | ||||
−0.123592 | + | 0.992333i | \(0.539441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.66025 | 0.323833 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5885 | 1.04474 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.73205 | −0.0836242 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.39230 | 0.115233 | 0.0576166 | − | 0.998339i | \(-0.481650\pi\) | ||||
0.0576166 | + | 0.998339i | \(0.481650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.928203 | −0.0446066 | −0.0223033 | − | 0.999751i | \(-0.507100\pi\) | ||||
−0.0223033 | + | 0.999751i | \(0.507100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.92820 | 0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.7846 | 0.514721 | 0.257361 | − | 0.966315i | \(-0.417147\pi\) | ||||
0.257361 | + | 0.966315i | \(0.417147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.00000 | −0.190476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.92820 | −0.424192 | −0.212096 | − | 0.977249i | \(-0.568029\pi\) | ||||
−0.212096 | + | 0.977249i | \(0.568029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.8564 | 0.560789 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.9282 | −1.64836 | −0.824182 | − | 0.566325i | \(-0.808365\pi\) | ||||
−0.824182 | + | 0.566325i | \(0.808365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.39230 | −0.206826 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.12436 | 0.381716 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3205 | −0.529551 | −0.264776 | − | 0.964310i | \(-0.585298\pi\) | ||||
−0.264776 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.46410 | 0.115014 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.07180 | −0.329366 | −0.164683 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164683 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.26795 | 0.291296 | 0.145648 | − | 0.989336i | \(-0.453473\pi\) | ||||
0.145648 | + | 0.989336i | \(0.453473\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.8564 | 1.19649 | 0.598246 | − | 0.801313i | \(-0.295865\pi\) | ||||
0.598246 | + | 0.801313i | \(0.295865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.39230 | 0.341345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.39230 | 0.432775 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.4641 | −0.711040 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.9282 | 0.546155 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.0526 | −1.14468 | −0.572340 | − | 0.820016i | \(-0.693964\pi\) | ||||
−0.572340 | + | 0.820016i | \(0.693964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.535898 | −0.0244349 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46410 | 0.157622 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.80385 | 0.308312 | 0.154156 | − | 0.988047i | \(-0.450734\pi\) | ||||
0.154156 | + | 0.988047i | \(0.450734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.39230 | 0.289070 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.67949 | −0.120924 | −0.0604619 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604619 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.67949 | 0.435942 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.9282 | 1.11818 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.58846 | 0.429238 | 0.214619 | − | 0.976698i | \(-0.431149\pi\) | ||||
0.214619 | + | 0.976698i | \(0.431149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3205 | −0.773823 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5359 | −0.648124 | −0.324062 | − | 0.946036i | \(-0.605049\pi\) | ||||
−0.324062 | + | 0.946036i | \(0.605049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.2487 | −0.631563 | −0.315782 | − | 0.948832i | \(-0.602267\pi\) | ||||
−0.315782 | + | 0.948832i | \(0.602267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.46410 | −0.152944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.5359 | 0.507348 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.92820 | −0.172429 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3205 | 0.932281 | 0.466140 | − | 0.884711i | \(-0.345644\pi\) | ||||
0.466140 | + | 0.884711i | \(0.345644\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.6603 | −0.987096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.73205 | 0.0751646 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.53590 | 0.109842 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.392305 | −0.0169292 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.92820 | −0.298419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3923 | −0.790747 | −0.395373 | − | 0.918520i | \(-0.629385\pi\) | ||||
−0.395373 | + | 0.918520i | \(0.629385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.53590 | −0.151740 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.46410 | 0.404656 | 0.202328 | − | 0.979318i | \(-0.435149\pi\) | ||||
0.202328 | + | 0.979318i | \(0.435149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4641 | −0.531955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6077 | −0.579707 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.2487 | −1.03116 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.3923 | 1.37251 | 0.686253 | − | 0.727363i | \(-0.259254\pi\) | ||||
0.686253 | + | 0.727363i | \(0.259254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.92820 | 0.377623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.26795 | 0.180193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.2487 | 0.806948 | 0.403474 | − | 0.914991i | \(-0.367803\pi\) | ||||
0.403474 | + | 0.914991i | \(0.367803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.8564 | −1.16575 | −0.582877 | − | 0.812560i | \(-0.698073\pi\) | ||||
−0.582877 | + | 0.812560i | \(0.698073\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.3923 | 0.601247 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.6410 | 1.35886 | 0.679432 | − | 0.733739i | \(-0.262226\pi\) | ||||
0.679432 | + | 0.733739i | \(0.262226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.46410 | −0.0608460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.7846 | 0.986752 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.6603 | 0.855660 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5885 | −0.973600 | −0.486800 | − | 0.873514i | \(-0.661836\pi\) | ||||
−0.486800 | + | 0.873514i | \(0.661836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.8564 | 1.31262 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.39230 | −0.180675 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9282 | 0.530898 | 0.265449 | − | 0.964125i | \(-0.414480\pi\) | ||||
0.265449 | + | 0.964125i | \(0.414480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.3205 | 0.872590 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1769 | 1.19214 | 0.596068 | − | 0.802934i | \(-0.296729\pi\) | ||||
0.596068 | + | 0.802934i | \(0.296729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7128 | 0.926475 | 0.463237 | − | 0.886234i | \(-0.346688\pi\) | ||||
0.463237 | + | 0.886234i | \(0.346688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.26795 | −0.173804 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.6795 | −0.433467 | −0.216734 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216734 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.80385 | −0.275706 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.66025 | −0.269445 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0718 | −0.447186 | −0.223593 | − | 0.974683i | \(-0.571779\pi\) | ||||
−0.223593 | + | 0.974683i | \(0.571779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.85641 | 0.316287 | 0.158144 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158144 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.3205 | 1.01772 | 0.508859 | − | 0.860850i | \(-0.330068\pi\) | ||||
0.508859 | + | 0.860850i | \(0.330068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.07180 | 0.203197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | −0.239617 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.32051 | 0.0526521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.2487 | 1.60228 | 0.801138 | − | 0.598480i | \(-0.204228\pi\) | ||||
0.801138 | + | 0.598480i | \(0.204228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.0000 | −1.03341 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | 0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.3923 | −0.569351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.3923 | 1.95088 | 0.975439 | − | 0.220268i | \(-0.0706932\pi\) | ||||
0.975439 | + | 0.220268i | \(0.0706932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.3205 | 0.840799 | 0.420399 | − | 0.907339i | \(-0.361890\pi\) | ||||
0.420399 | + | 0.907339i | \(0.361890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.7128 | 1.87578 | 0.937892 | − | 0.346927i | \(-0.112775\pi\) | ||||
0.937892 | + | 0.346927i | \(0.112775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | 0.117760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.9282 | 0.624276 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.9282 | 1.40598 | 0.702990 | − | 0.711200i | \(-0.251848\pi\) | ||||
0.702990 | + | 0.711200i | \(0.251848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.46410 | 0.135147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.7128 | 1.15745 | 0.578723 | − | 0.815524i | \(-0.303551\pi\) | ||||
0.578723 | + | 0.815524i | \(0.303551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.3923 | −1.41550 | −0.707748 | − | 0.706465i | \(-0.750289\pi\) | ||||
−0.707748 | + | 0.706465i | \(0.750289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.46410 | −0.0956978 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.85641 | −0.304201 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.2487 | −1.09216 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.5885 | −0.833413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.8564 | 1.49780 | 0.748902 | − | 0.662681i | \(-0.230581\pi\) | ||||
0.748902 | + | 0.662681i | \(0.230581\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.6410 | −1.56196 | −0.780981 | − | 0.624555i | \(-0.785280\pi\) | ||||
−0.780981 | + | 0.624555i | \(0.785280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.53590 | 0.327578 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.26795 | 0.0869080 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0526 | −1.64736 | −0.823680 | − | 0.567055i | \(-0.808083\pi\) | ||||
−0.823680 | + | 0.567055i | \(0.808083\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7846 | −0.716678 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.9282 | −0.454428 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.1244 | −1.45032 | −0.725159 | − | 0.688581i | \(-0.758234\pi\) | ||||
−0.725159 | + | 0.688581i | \(0.758234\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.00000 | −0.113961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.24871 | −0.236687 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.8564 | −0.751038 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.14359 | 0.0431929 | 0.0215965 | − | 0.999767i | \(-0.493125\pi\) | ||||
0.0215965 | + | 0.999767i | \(0.493125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.85641 | −0.0700157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.19615 | −0.195421 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.4641 | −0.655878 | −0.327939 | − | 0.944699i | \(-0.606354\pi\) | ||||
−0.327939 | + | 0.944699i | \(0.606354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.3923 | 0.688797 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.19615 | 0.119362 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.4641 | −0.502126 | −0.251063 | − | 0.967971i | \(-0.580780\pi\) | ||||
−0.251063 | + | 0.967971i | \(0.580780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.5359 | −0.988248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.3923 | −0.758398 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2487 | −0.825159 | −0.412580 | − | 0.910922i | \(-0.635372\pi\) | ||||
−0.412580 | + | 0.910922i | \(0.635372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.0000 | −0.813699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.7846 | −0.619954 | −0.309977 | − | 0.950744i | \(-0.600321\pi\) | ||||
−0.309977 | + | 0.950744i | \(0.600321\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.39230 | −0.272299 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.2679 | 1.33414 | 0.667069 | − | 0.744996i | \(-0.267549\pi\) | ||||
0.667069 | + | 0.744996i | \(0.267549\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.46410 | 0.127257 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.8038 | −1.20346 | −0.601728 | − | 0.798701i | \(-0.705521\pi\) | ||||
−0.601728 | + | 0.798701i | \(0.705521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.7321 | −0.502429 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9282 | −0.472386 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8564 | −0.578608 | −0.289304 | − | 0.957237i | \(-0.593424\pi\) | ||||
−0.289304 | + | 0.957237i | \(0.593424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.39230 | 0.160064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4641 | 1.25262 | 0.626310 | − | 0.779574i | \(-0.284565\pi\) | ||||
0.626310 | + | 0.779574i | \(0.284565\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.46410 | −0.125739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.3923 | 1.39172 | 0.695860 | − | 0.718177i | \(-0.255023\pi\) | ||||
0.695860 | + | 0.718177i | \(0.255023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.39230 | 0.159012 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.73205 | −0.0625407 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7846 | 0.749512 | 0.374756 | − | 0.927123i | \(-0.377726\pi\) | ||||
0.374756 | + | 0.927123i | \(0.377726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.2487 | 0.693225 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8564 | −0.426445 | −0.213223 | − | 0.977004i | \(-0.568396\pi\) | ||||
−0.213223 | + | 0.977004i | \(0.568396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.928203 | −0.0332991 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.78461 | 0.314741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9282 | −0.892001 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.92820 | 0.140383 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8038 | −0.456408 | −0.228204 | − | 0.973613i | \(-0.573285\pi\) | ||||
−0.228204 | + | 0.973613i | \(0.573285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.3205 | −0.830232 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.3205 | 0.615846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.4641 | 0.442613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.8564 | −0.809615 | −0.404808 | − | 0.914402i | \(-0.632662\pi\) | ||||
−0.404808 | + | 0.914402i | \(0.632662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4115 | 0.580599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.92820 | −0.103463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00000 | 0.211735 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.0000 | −0.668832 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0718 | 0.389264 | 0.194632 | − | 0.980876i | \(-0.437649\pi\) | ||||
0.194632 | + | 0.980876i | \(0.437649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.58846 | 0.0557783 | 0.0278891 | − | 0.999611i | \(-0.491121\pi\) | ||||
0.0278891 | + | 0.999611i | \(0.491121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.7321 | −0.762176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.9282 | 1.08204 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.73205 | 0.0605228 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4641 | 0.958504 | 0.479252 | − | 0.877677i | \(-0.340908\pi\) | ||||
0.479252 | + | 0.877677i | \(0.340908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1436 | 0.353583 | 0.176792 | − | 0.984248i | \(-0.443428\pi\) | ||||
0.176792 | + | 0.984248i | \(0.443428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.1244 | −0.699792 | −0.349896 | − | 0.936788i | \(-0.613783\pi\) | ||||
−0.349896 | + | 0.936788i | \(0.613783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6077 | 0.507346 | 0.253673 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253673 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.9282 | 0.725991 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.85641 | −0.341504 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.19615 | −0.317866 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.3205 | −1.01226 | −0.506128 | − | 0.862458i | \(-0.668924\pi\) | ||||
−0.506128 | + | 0.862458i | \(0.668924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5692 | −0.467904 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.9282 | 0.445271 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8564 | 0.476112 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.32051 | −0.319879 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.07180 | −0.0367407 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.7846 | 1.67035 | 0.835177 | − | 0.549982i | \(-0.185365\pi\) | ||||
0.835177 | + | 0.549982i | \(0.185365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.7128 | −0.741696 | −0.370848 | − | 0.928694i | \(-0.620933\pi\) | ||||
−0.370848 | + | 0.928694i | \(0.620933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.71281 | −0.331397 | −0.165698 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165698 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.39230 | 0.149689 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.9474 | −0.372655 | −0.186328 | − | 0.982488i | \(-0.559659\pi\) | ||||
−0.186328 | + | 0.982488i | \(0.559659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.9282 | −0.371141 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.2487 | 0.822581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.26795 | 0.144614 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.92820 | −0.166794 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9282 | 1.58465 | 0.792326 | − | 0.610097i | \(-0.208870\pi\) | ||||
0.792326 | + | 0.610097i | \(0.208870\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.8564 | 0.534823 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.464102 | −0.0156360 | −0.00781799 | − | 0.999969i | \(-0.502489\pi\) | ||||
−0.00781799 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0718 | 0.709122 | 0.354561 | − | 0.935033i | \(-0.384630\pi\) | ||||
0.354561 | + | 0.935033i | \(0.384630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.78461 | 0.0934980 | 0.0467490 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467490 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.60770 | 0.0539204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73205 | 0.0580259 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.0718 | −0.772068 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.00000 | 0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.1244 | −1.20481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.3923 | 0.979200 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.4641 | 0.514613 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.00000 | 0.0995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.928203 | −0.0307527 | −0.0153764 | − | 0.999882i | \(-0.504895\pi\) | ||||
−0.0153764 | + | 0.999882i | \(0.504895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.7846 | −0.787156 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.1769 | 1.22769 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −57.0333 | −1.88136 | −0.940678 | − | 0.339301i | \(-0.889809\pi\) | ||||
−0.940678 | + | 0.339301i | \(0.889809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.53590 | −0.149463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.3923 | 0.473728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3205 | 0.503192 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.6410 | −1.72710 | −0.863548 | − | 0.504267i | \(-0.831763\pi\) | ||||
−0.863548 | + | 0.504267i | \(0.831763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8564 | 0.454125 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.46410 | −0.244364 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.6410 | 1.49103 | 0.745514 | − | 0.666491i | \(-0.232204\pi\) | ||||
0.745514 | + | 0.666491i | \(0.232204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.92820 | 0.0629245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.75129 | 0.122289 | 0.0611443 | − | 0.998129i | \(-0.480525\pi\) | ||||
0.0611443 | + | 0.998129i | \(0.480525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.07180 | 0.165160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.33975 | −0.238510 | −0.119255 | − | 0.992864i | \(-0.538051\pi\) | ||||
−0.119255 | + | 0.992864i | \(0.538051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.46410 | −0.112449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5359 | 0.406504 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.2487 | −0.947459 | −0.473729 | − | 0.880670i | \(-0.657093\pi\) | ||||
−0.473729 | + | 0.880670i | \(0.657093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.80385 | 0.219937 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.07180 | 0.163777 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.5692 | 1.72804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.46410 | 0.240527 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.4449 | 1.07551 | 0.537757 | − | 0.843100i | \(-0.319272\pi\) | ||||
0.537757 | + | 0.843100i | \(0.319272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.53590 | −0.274213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.1769 | −0.872149 | −0.436074 | − | 0.899911i | \(-0.643632\pi\) | ||||
−0.436074 | + | 0.899911i | \(0.643632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.9282 | 0.799162 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.5692 | 1.32992 | 0.664959 | − | 0.746880i | \(-0.268449\pi\) | ||||
0.664959 | + | 0.746880i | \(0.268449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.07180 | −0.162095 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.53590 | −0.0809650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.7321 | 0.501774 | 0.250887 | − | 0.968016i | \(-0.419278\pi\) | ||||
0.250887 | + | 0.968016i | \(0.419278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.5359 | −0.367192 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.8564 | 0.567801 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7128 | −1.57918 | −0.789590 | − | 0.613635i | \(-0.789707\pi\) | ||||
−0.789590 | + | 0.613635i | \(0.789707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.53590 | −0.143942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.0333 | −1.45789 | −0.728945 | − | 0.684572i | \(-0.759989\pi\) | ||||
−0.728945 | + | 0.684572i | \(0.759989\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.535898 | 0.0169551 |
(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 | 7800.2.a.bc.1.1 | yes | 2 | |
5.4 | even | 2 | 7800.2.a.y.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.y.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
7800.2.a.bc.1.1 | yes | 2 | 1.1 | even | 1 | trivial |