Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.13 | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.i.2591.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.680677i | − 0.304408i | −0.988349 | − | 0.152204i | \(-0.951363\pi\) | ||||
0.988349 | − | 0.152204i | \(-0.0486371\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70297 | −0.513464 | −0.256732 | − | 0.966483i | \(-0.582646\pi\) | ||||
−0.256732 | + | 0.966483i | \(0.582646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.59108 | 1.55069 | 0.775343 | − | 0.631540i | \(-0.217577\pi\) | ||||
0.775343 | + | 0.631540i | \(0.217577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.68812i | 0.894500i | 0.894409 | + | 0.447250i | \(0.147596\pi\) | ||||
−0.894409 | + | 0.447250i | \(0.852404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.46651i | − 1.02469i | −0.858780 | − | 0.512344i | \(-0.828777\pi\) | ||||
0.858780 | − | 0.512344i | \(-0.171223\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16396 | −0.242703 | −0.121352 | − | 0.992610i | \(-0.538723\pi\) | ||||
−0.121352 | + | 0.992610i | \(0.538723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.53668 | 0.907336 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.77705i | − 0.329990i | −0.986294 | − | 0.164995i | \(-0.947239\pi\) | ||||
0.986294 | − | 0.164995i | \(-0.0527609\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.58733i | 0.464698i | 0.972633 | + | 0.232349i | \(0.0746411\pi\) | ||||
−0.972633 | + | 0.232349i | \(0.925359\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.680677 | −0.115055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36230 | 0.223961 | 0.111980 | − | 0.993710i | \(-0.464281\pi\) | ||||
0.111980 | + | 0.993710i | \(0.464281\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.31635i | − 0.205580i | −0.994703 | − | 0.102790i | \(-0.967223\pi\) | ||||
0.994703 | − | 0.102790i | \(-0.0327769\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.71189i | − 0.718557i | −0.933230 | − | 0.359279i | \(-0.883023\pi\) | ||||
0.933230 | − | 0.359279i | \(-0.116977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.87479 | 0.565196 | 0.282598 | − | 0.959238i | \(-0.408804\pi\) | ||||
0.282598 | + | 0.959238i | \(0.408804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.39069i | 0.877828i | 0.898529 | + | 0.438914i | \(0.144637\pi\) | ||||
−0.898529 | + | 0.438914i | \(0.855363\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.15917i | 0.156303i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.948207 | 0.123446 | 0.0617230 | − | 0.998093i | \(-0.480340\pi\) | ||||
0.0617230 | + | 0.998093i | \(0.480340\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.40831 | −0.180315 | −0.0901575 | − | 0.995928i | \(-0.528737\pi\) | ||||
−0.0901575 | + | 0.995928i | \(0.528737\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.80572i | − 0.472041i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.28379i | 0.156840i | 0.996920 | + | 0.0784202i | \(0.0249876\pi\) | ||||
−0.996920 | + | 0.0784202i | \(0.975012\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.09744 | 0.367599 | 0.183799 | − | 0.982964i | \(-0.441160\pi\) | ||||
0.183799 | + | 0.982964i | \(0.441160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.79256 | −0.677968 | −0.338984 | − | 0.940792i | \(-0.610083\pi\) | ||||
−0.338984 | + | 0.940792i | \(0.610083\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.70297i | 0.194071i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 1.72001i | − 0.193517i | −0.995308 | − | 0.0967583i | \(-0.969153\pi\) | ||||
0.995308 | − | 0.0967583i | \(-0.0308474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.69122 | 0.844221 | 0.422111 | − | 0.906544i | \(-0.361289\pi\) | ||||
0.422111 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.51041 | 0.272293 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.962856i | 0.102063i | 0.998697 | + | 0.0510313i | \(0.0162508\pi\) | ||||
−0.998697 | + | 0.0510313i | \(0.983749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.59108i | − 0.586104i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.04025 | −0.311923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3918 | 1.25819 | 0.629096 | − | 0.777328i | \(-0.283425\pi\) | ||||
0.629096 | + | 0.777328i | \(0.283425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.74056i | 0.670711i | 0.942092 | + | 0.335355i | \(0.108856\pi\) | ||||
−0.942092 | + | 0.335355i | \(0.891144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.66964i | − 0.952778i | −0.879235 | − | 0.476389i | \(-0.841945\pi\) | ||||
0.879235 | − | 0.476389i | \(-0.158055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.78531 | −0.172592 | −0.0862962 | − | 0.996270i | \(-0.527503\pi\) | ||||
−0.0862962 | + | 0.996270i | \(0.527503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.61143 | 0.537478 | 0.268739 | − | 0.963213i | \(-0.413393\pi\) | ||||
0.268739 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.46274i | 0.231675i | 0.993268 | + | 0.115838i | \(0.0369552\pi\) | ||||
−0.993268 | + | 0.115838i | \(0.963045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.792283i | 0.0738808i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.68812 | 0.338089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.09990 | −0.736354 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.49139i | − 0.580608i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.85480i | − 0.342058i | −0.985266 | − | 0.171029i | \(-0.945291\pi\) | ||||
0.985266 | − | 0.171029i | \(-0.0547092\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0680 | 0.967013 | 0.483507 | − | 0.875341i | \(-0.339363\pi\) | ||||
0.483507 | + | 0.875341i | \(0.339363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.46651 | −0.387296 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 14.9424i | − 1.27661i | −0.769782 | − | 0.638307i | \(-0.779635\pi\) | ||||
0.769782 | − | 0.638307i | \(-0.220365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.25129i | 0.445409i | 0.974886 | + | 0.222704i | \(0.0714885\pi\) | ||||
−0.974886 | + | 0.222704i | \(0.928512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.52143 | −0.796222 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.20960 | −0.100452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.2480i | 1.33109i | 0.746357 | + | 0.665545i | \(0.231801\pi\) | ||||
−0.746357 | + | 0.665545i | \(0.768199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 9.61927i | − 0.782805i | −0.920220 | − | 0.391402i | \(-0.871990\pi\) | ||||
0.920220 | − | 0.391402i | \(-0.128010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.76113 | 0.141458 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5745 | 1.16317 | 0.581587 | − | 0.813484i | \(-0.302432\pi\) | ||||
0.581587 | + | 0.813484i | \(0.302432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16396i | 0.0917332i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.6184i | − 0.910021i | −0.890486 | − | 0.455011i | \(-0.849635\pi\) | ||||
0.890486 | − | 0.455011i | \(-0.150365\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.6376 | −1.67437 | −0.837185 | − | 0.546920i | \(-0.815800\pi\) | ||||
−0.837185 | + | 0.546920i | \(0.815800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.2602 | 1.40463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 21.3069i | − 1.61994i | −0.586474 | − | 0.809968i | \(-0.699485\pi\) | ||||
0.586474 | − | 0.809968i | \(-0.300515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.53668i | − 0.342941i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7701 | 1.10397 | 0.551986 | − | 0.833853i | \(-0.313870\pi\) | ||||
0.551986 | + | 0.833853i | \(0.313870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7394 | 1.09557 | 0.547786 | − | 0.836619i | \(-0.315471\pi\) | ||||
0.547786 | + | 0.836619i | \(0.315471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 0.927286i | − 0.0681754i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.28074i | − 0.459294i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1122 | −1.59998 | −0.799991 | − | 0.600012i | \(-0.795162\pi\) | ||||
−0.799991 | + | 0.600012i | \(0.795162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6487 | 1.41435 | 0.707173 | − | 0.707041i | \(-0.249970\pi\) | ||||
0.707173 | + | 0.707041i | \(0.249970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.6467i | − 1.25728i | −0.777698 | − | 0.628638i | \(-0.783613\pi\) | ||||
0.777698 | − | 0.628638i | \(-0.216387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.47875i | 0.317490i | 0.987320 | + | 0.158745i | \(0.0507448\pi\) | ||||
−0.987320 | + | 0.158745i | \(0.949255\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.77705 | −0.124725 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.896009 | −0.0625800 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.60633i | 0.526141i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 18.6143i | − 1.28146i | −0.767765 | − | 0.640732i | \(-0.778631\pi\) | ||||
0.767765 | − | 0.640732i | \(-0.221369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.20728 | −0.218734 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.58733 | 0.175639 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.6205i | 1.38709i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.333825i | 0.0223546i | 0.999938 | + | 0.0111773i | \(0.00355792\pi\) | ||||
−0.999938 | + | 0.0111773i | \(0.996442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.2768 | 1.08033 | 0.540164 | − | 0.841559i | \(-0.318362\pi\) | ||||
0.540164 | + | 0.841559i | \(0.318362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.30762 | −0.548983 | −0.274491 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274491 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 26.9212i | − 1.76367i | −0.471560 | − | 0.881834i | \(-0.656309\pi\) | ||||
0.471560 | − | 0.881834i | \(-0.343691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.63748i | − 0.172050i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.40591 | −0.414364 | −0.207182 | − | 0.978302i | \(-0.566429\pi\) | ||||
−0.207182 | + | 0.978302i | \(0.566429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1800 | 0.784583 | 0.392291 | − | 0.919841i | \(-0.371682\pi\) | ||||
0.392291 | + | 0.919841i | \(0.371682\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.680677i | 0.0434868i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 24.9726i | − 1.58897i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.3399 | 1.59944 | 0.799720 | − | 0.600373i | \(-0.204981\pi\) | ||||
0.799720 | + | 0.600373i | \(0.204981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.98219 | 0.124619 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.8079i | 1.85937i | 0.368359 | + | 0.929684i | \(0.379920\pi\) | ||||
−0.368359 | + | 0.929684i | \(0.620080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.36230i | − 0.0846492i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0318 | −1.11189 | −0.555943 | − | 0.831221i | \(-0.687643\pi\) | ||||
−0.555943 | + | 0.831221i | \(0.687643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.34999 | 0.267218 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.18664i | − 0.255264i | −0.991822 | − | 0.127632i | \(-0.959262\pi\) | ||||
0.991822 | − | 0.127632i | \(-0.0407376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 22.4083i | − 1.36121i | −0.732653 | − | 0.680603i | \(-0.761718\pi\) | ||||
0.732653 | − | 0.680603i | \(-0.238282\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.72582 | −0.465885 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9099 | 0.775680 | 0.387840 | − | 0.921727i | \(-0.373221\pi\) | ||||
0.387840 | + | 0.921727i | \(0.373221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.98114i | 0.535770i | 0.963451 | + | 0.267885i | \(0.0863247\pi\) | ||||
−0.963451 | + | 0.267885i | \(0.913675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.4072i | − 0.678087i | −0.940771 | − | 0.339043i | \(-0.889897\pi\) | ||||
0.940771 | − | 0.339043i | \(-0.110103\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.31635 | −0.0777018 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.39780 | 0.199871 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9.19308i | − 0.537066i | −0.963271 | − | 0.268533i | \(-0.913461\pi\) | ||||
0.963271 | − | 0.268533i | \(-0.0865388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 0.645422i | − 0.0375779i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.50781 | −0.376357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.71189 | −0.271589 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.958601i | 0.0548893i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 26.3888i | − 1.50609i | −0.657972 | − | 0.753043i | \(-0.728585\pi\) | ||||
0.657972 | − | 0.753043i | \(-0.271415\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.0780 | −1.42204 | −0.711021 | − | 0.703171i | \(-0.751767\pi\) | ||||
−0.711021 | + | 0.703171i | \(0.751767\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.86592 | −0.275038 | −0.137519 | − | 0.990499i | \(-0.543913\pi\) | ||||
−0.137519 | + | 0.990499i | \(0.543913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.8835i | 0.667441i | 0.942672 | + | 0.333721i | \(0.108304\pi\) | ||||
−0.942672 | + | 0.333721i | \(0.891696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.02626i | 0.169438i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4730 | 0.916583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.3649 | 1.40699 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.87479i | − 0.213624i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 19.0454i | − 1.04683i | −0.852079 | − | 0.523414i | \(-0.824658\pi\) | ||||
0.852079 | − | 0.523414i | \(-0.175342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.873848 | 0.0477434 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2381 | 0.721128 | 0.360564 | − | 0.932734i | \(-0.382584\pi\) | ||||
0.360564 | + | 0.932734i | \(0.382584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.40614i | − 0.238606i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.4049 | 0.988027 | 0.494014 | − | 0.869454i | \(-0.335529\pi\) | ||||
0.494014 | + | 0.869454i | \(0.335529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3574 | −1.03618 | −0.518090 | − | 0.855326i | \(-0.673357\pi\) | ||||
−0.518090 | + | 0.855326i | \(0.673357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.4485i | 0.875464i | 0.899106 | + | 0.437732i | \(0.144218\pi\) | ||||
−0.899106 | + | 0.437732i | \(0.855782\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.10836i | − 0.111900i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.6461 | 1.08966 | 0.544830 | − | 0.838547i | \(-0.316594\pi\) | ||||
0.544830 | + | 0.838547i | \(0.316594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.949721 | −0.0499853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.94286i | 0.206379i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.24477i | − 0.221575i | −0.993844 | − | 0.110788i | \(-0.964663\pi\) | ||||
0.993844 | − | 0.110788i | \(-0.0353373\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.39069 | 0.331788 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.74622 | −0.0904160 | −0.0452080 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452080 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 9.93564i | − 0.511712i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.6903i | 1.88465i | 0.334695 | + | 0.942326i | \(0.391367\pi\) | ||||
−0.334695 | + | 0.942326i | \(0.608633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.2853 | −1.08763 | −0.543814 | − | 0.839206i | \(-0.683020\pi\) | ||||
−0.543814 | + | 0.839206i | \(0.683020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15917 | 0.0590768 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 30.2083i | − 1.53162i | −0.643066 | − | 0.765811i | \(-0.722338\pi\) | ||||
0.643066 | − | 0.765811i | \(-0.277662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.29283i | − 0.217098i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.17077 | −0.0589080 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5830 | 0.882466 | 0.441233 | − | 0.897393i | \(-0.354541\pi\) | ||||
0.441233 | + | 0.897393i | \(0.354541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.83123i | 0.391073i | 0.980696 | + | 0.195536i | \(0.0626448\pi\) | ||||
−0.980696 | + | 0.195536i | \(0.937355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4660i | 0.720600i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.31995 | −0.114996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.8638 | 1.03165 | 0.515825 | − | 0.856694i | \(-0.327486\pi\) | ||||
0.515825 | + | 0.856694i | \(0.327486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 0.948207i | − 0.0466582i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 5.23524i | − 0.256988i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.2529 | −1.47795 | −0.738976 | − | 0.673732i | \(-0.764690\pi\) | ||||
−0.738976 | + | 0.673732i | \(0.764690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4874 | 0.706072 | 0.353036 | − | 0.935610i | \(-0.385149\pi\) | ||||
0.353036 | + | 0.935610i | \(0.385149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.7318i | 0.811611i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.40831i | 0.0681527i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.2713 | 0.639254 | 0.319627 | − | 0.947543i | \(-0.396442\pi\) | ||||
0.319627 | + | 0.947543i | \(0.396442\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.9913 | −1.10489 | −0.552446 | − | 0.833549i | \(-0.686306\pi\) | ||||
−0.552446 | + | 0.833549i | \(0.686306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.19886i | 0.248695i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9306i | 0.664871i | 0.943126 | + | 0.332435i | \(0.107870\pi\) | ||||
−0.943126 | + | 0.332435i | \(0.892130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8147 | 0.798892 | 0.399446 | − | 0.916757i | \(-0.369203\pi\) | ||||
0.399446 | + | 0.916757i | \(0.369203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.655394 | 0.0310686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 13.6213i | − 0.642829i | −0.946939 | − | 0.321415i | \(-0.895842\pi\) | ||||
0.946939 | − | 0.321415i | \(-0.104158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24170i | 0.105558i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.80572 | −0.178415 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.94687 | 0.278183 | 0.139091 | − | 0.990280i | \(-0.455582\pi\) | ||||
0.139091 | + | 0.990280i | \(0.455582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9987i | 0.605410i | 0.953084 | + | 0.302705i | \(0.0978896\pi\) | ||||
−0.953084 | + | 0.302705i | \(0.902110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.3487i | 1.64280i | 0.570356 | + | 0.821398i | \(0.306805\pi\) | ||||
−0.570356 | + | 0.821398i | \(0.693195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9651 | 0.553679 | 0.276839 | − | 0.960916i | \(-0.410713\pi\) | ||||
0.276839 | + | 0.960916i | \(0.410713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28379 | 0.0592801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.02421i | 0.368953i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 20.2631i | − 0.929736i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4802 | 1.25560 | 0.627801 | − | 0.778374i | \(-0.283955\pi\) | ||||
0.627801 | + | 0.778374i | \(0.283955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.61673 | 0.347293 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.43478i | − 0.383004i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.03432i | − 0.228127i | −0.993473 | − | 0.114063i | \(-0.963613\pi\) | ||||
0.993473 | − | 0.114063i | \(-0.0363867\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1007 | −0.771745 | −0.385873 | − | 0.922552i | \(-0.626100\pi\) | ||||
−0.385873 | + | 0.922552i | \(0.626100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.55398 | 0.295176 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 3.09744i | − 0.138939i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.4214i | 0.600826i | 0.953809 | + | 0.300413i | \(0.0971245\pi\) | ||||
−0.953809 | + | 0.300413i | \(0.902876\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.44363 | −0.287307 | −0.143654 | − | 0.989628i | \(-0.545885\pi\) | ||||
−0.143654 | + | 0.989628i | \(0.545885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.58814 | 0.204170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.37393i | 0.149547i | 0.997201 | + | 0.0747734i | \(0.0238233\pi\) | ||||
−0.997201 | + | 0.0747734i | \(0.976177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.79256i | 0.256248i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.58190 | −0.290033 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.59865 | −0.290208 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 25.7512i | − 1.12818i | −0.825714 | − | 0.564090i | \(-0.809227\pi\) | ||||
0.825714 | − | 0.564090i | \(-0.190773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.41398i | − 0.193010i | −0.995333 | − | 0.0965050i | \(-0.969234\pi\) | ||||
0.995333 | − | 0.0965050i | \(-0.0307664\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.54236 | −0.415672 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6452 | −0.941095 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.35982i | − 0.318789i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21522i | 0.0525385i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.70297 | 0.0733520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.91406 | 0.125285 | 0.0626425 | − | 0.998036i | \(-0.480047\pi\) | ||||
0.0626425 | + | 0.998036i | \(0.480047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 3.81957i | − 0.163613i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7674i | 0.887949i | 0.896039 | + | 0.443975i | \(0.146432\pi\) | ||||
−0.896039 | + | 0.443975i | \(0.853568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.93723 | −0.338137 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.72001 | −0.0731424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.79984i | 0.118633i | 0.998239 | + | 0.0593166i | \(0.0188921\pi\) | ||||
−0.998239 | + | 0.0593166i | \(0.981108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 26.3446i | − 1.11426i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.81944 | −0.371695 | −0.185847 | − | 0.982579i | \(-0.559503\pi\) | ||||
−0.185847 | + | 0.982579i | \(0.559503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.67633 | 0.0705237 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 22.7894i | − 0.955382i | −0.878528 | − | 0.477691i | \(-0.841474\pi\) | ||||
0.878528 | − | 0.477691i | \(-0.158526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 0.247117i | − 0.0103415i | −0.999987 | − | 0.00517075i | \(-0.998354\pi\) | ||||
0.999987 | − | 0.00517075i | \(-0.00164591\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.28053 | −0.220213 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.45713 | −0.352075 | −0.176037 | − | 0.984383i | \(-0.556328\pi\) | ||||
−0.176037 | + | 0.984383i | \(0.556328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.69122i | − 0.319086i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10.8831i | − 0.450733i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.8861 | 1.56373 | 0.781864 | − | 0.623449i | \(-0.214269\pi\) | ||||
0.781864 | + | 0.623449i | \(0.214269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5563 | 0.476170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3736i | 0.508124i | 0.967188 | + | 0.254062i | \(0.0817667\pi\) | ||||
−0.967188 | + | 0.254062i | \(0.918233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.51041i | − 0.102917i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.5376 | −0.675706 | −0.337853 | − | 0.941199i | \(-0.609701\pi\) | ||||
−0.337853 | + | 0.941199i | \(0.609701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0968 | −0.942138 | −0.471069 | − | 0.882096i | \(-0.656132\pi\) | ||||
−0.471069 | + | 0.882096i | \(0.656132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.51341i | 0.224152i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 35.9691i | − 1.45994i | −0.683478 | − | 0.729971i | \(-0.739534\pi\) | ||||
0.683478 | − | 0.729971i | \(-0.260466\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.6643 | 0.876442 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.18328 | 0.128571 | 0.0642857 | − | 0.997932i | \(-0.479523\pi\) | ||||
0.0642857 | + | 0.997932i | \(0.479523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.65916i | 0.107054i | 0.998566 | + | 0.0535268i | \(0.0170463\pi\) | ||||
−0.998566 | + | 0.0535268i | \(0.982954\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00728i | 0.161066i | 0.996752 | + | 0.0805331i | \(0.0256623\pi\) | ||||
−0.996752 | + | 0.0805331i | \(0.974338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.962856 | 0.0385760 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.2649 | 0.730594 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.02432i | 0.200333i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9712i | 0.635804i | 0.948124 | + | 0.317902i | \(0.102978\pi\) | ||||
−0.948124 | + | 0.317902i | \(0.897022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.62387 | −0.104125 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.59108 | −0.221527 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 21.9427i | − 0.866685i | −0.901229 | − | 0.433342i | \(-0.857334\pi\) | ||||
0.901229 | − | 0.433342i | \(-0.142666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.00112i | − 0.236661i | −0.992974 | − | 0.118331i | \(-0.962246\pi\) | ||||
0.992974 | − | 0.118331i | \(-0.0377542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.2522 | −1.26796 | −0.633982 | − | 0.773348i | \(-0.718581\pi\) | ||||
−0.633982 | + | 0.773348i | \(0.718581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.61477 | −0.0633851 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.3807i | 1.50195i | 0.660328 | + | 0.750977i | \(0.270417\pi\) | ||||
−0.660328 | + | 0.750977i | \(0.729583\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7.53371i | − 0.294366i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.7292 | 1.43076 | 0.715382 | − | 0.698733i | \(-0.246252\pi\) | ||||
0.715382 | + | 0.698733i | \(0.246252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.95296 | −0.114857 | −0.0574284 | − | 0.998350i | \(-0.518290\pi\) | ||||
−0.0574284 | + | 0.998350i | \(0.518290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04025i | 0.117896i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.06843i | 0.0800898i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.39830 | 0.0925853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.6334 | 1.64340 | 0.821698 | − | 0.569923i | \(-0.193027\pi\) | ||||
0.821698 | + | 0.569923i | \(0.193027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 29.1217i | − 1.11924i | −0.828750 | − | 0.559619i | \(-0.810947\pi\) | ||||
0.828750 | − | 0.559619i | \(-0.189053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 12.3918i | − 0.475552i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0935 | 1.15150 | 0.575749 | − | 0.817627i | \(-0.304711\pi\) | ||||
0.575749 | + | 0.817627i | \(0.304711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1709 | −0.388611 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.7308i | 1.36124i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 29.8979i | − 1.13737i | −0.822555 | − | 0.568685i | \(-0.807452\pi\) | ||||
0.822555 | − | 0.568685i | \(-0.192548\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.57443 | 0.135586 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.85486 | 0.183891 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7692i | 1.76645i | 0.468950 | + | 0.883225i | \(0.344633\pi\) | ||||
−0.468950 | + | 0.883225i | \(0.655367\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.08473i | − 0.229490i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.74056 | 0.253505 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.29936 | 0.199022 | 0.0995108 | − | 0.995036i | \(-0.468272\pi\) | ||||
0.0995108 | + | 0.995036i | \(0.468272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.01156i | − 0.112784i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.48101i | 0.242376i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9460 | −0.482805 | −0.241402 | − | 0.970425i | \(-0.577607\pi\) | ||||
−0.241402 | + | 0.970425i | \(0.577607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.66964 | −0.360116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 8.06192i | − 0.299412i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 33.7044i | − 1.25003i | −0.780613 | − | 0.625014i | \(-0.785093\pi\) | ||||
0.780613 | − | 0.625014i | \(-0.214907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.3780 | 0.642749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7469 | −0.914048 | −0.457024 | − | 0.889454i | \(-0.651085\pi\) | ||||
−0.457024 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.18626i | − 0.0805319i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.35804i | 0.233884i | 0.993139 | + | 0.116942i | \(0.0373092\pi\) | ||||
−0.993139 | + | 0.116942i | \(0.962691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.8301 | −1.27779 | −0.638896 | − | 0.769293i | \(-0.720608\pi\) | ||||
−0.638896 | + | 0.769293i | \(0.720608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.0597 | 0.405195 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.78531i | 0.0652338i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9033i | 0.397867i | 0.980013 | + | 0.198933i | \(0.0637478\pi\) | ||||
−0.980013 | + | 0.198933i | \(0.936252\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.54761 | −0.238292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2117 | 1.49786 | 0.748932 | − | 0.662647i | \(-0.230567\pi\) | ||||
0.748932 | + | 0.662647i | \(0.230567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.7395i | 0.534306i | 0.963654 | + | 0.267153i | \(0.0860830\pi\) | ||||
−0.963654 | + | 0.267153i | \(0.913917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.61143i | − 0.203148i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.30150 | 0.191426 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.0357 | −1.40766 | −0.703832 | − | 0.710367i | \(-0.748529\pi\) | ||||
−0.703832 | + | 0.710367i | \(0.748529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 44.0345i | − 1.58381i | −0.610643 | − | 0.791906i | \(-0.709089\pi\) | ||||
0.610643 | − | 0.791906i | \(-0.290911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7379i | 0.421637i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.87950 | −0.210655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.27485 | −0.188749 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 9.92054i | − 0.354079i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.77184i | 0.0988055i | 0.998779 | + | 0.0494028i | \(0.0157318\pi\) | ||||
−0.998779 | + | 0.0494028i | \(0.984268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.46274 | 0.0875650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.87395 | −0.279612 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.0469i | 1.77275i | 0.462967 | + | 0.886375i | \(0.346785\pi\) | ||||
−0.462967 | + | 0.886375i | \(0.653215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.2907i | 0.505568i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.86454 | 0.348112 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.792283 | 0.0279243 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8463i | 0.908707i | 0.890821 | + | 0.454354i | \(0.150130\pi\) | ||||
−0.890821 | + | 0.454354i | \(0.849870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 23.4798i | − 0.824489i | −0.911073 | − | 0.412244i | \(-0.864745\pi\) | ||||
0.911073 | − | 0.412244i | \(-0.135255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.90836 | −0.277018 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0457 | −0.736297 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.1359i | 0.702747i | 0.936235 | + | 0.351373i | \(0.114285\pi\) | ||||
−0.936235 | + | 0.351373i | \(0.885715\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.51467i | − 0.0527982i | −0.999651 | − | 0.0263991i | \(-0.991596\pi\) | ||||
0.999651 | − | 0.0263991i | \(-0.00840407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8499 | 0.620702 | 0.310351 | − | 0.950622i | \(-0.399553\pi\) | ||||
0.310351 | + | 0.950622i | \(0.399553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1908 | 0.353942 | 0.176971 | − | 0.984216i | \(-0.443370\pi\) | ||||
0.176971 | + | 0.984216i | \(0.443370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.68812i | − 0.127786i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7282i | 0.509691i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.6943 | −0.438256 | −0.219128 | − | 0.975696i | \(-0.570321\pi\) | ||||
−0.219128 | + | 0.975696i | \(0.570321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.8421 | 0.891106 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 12.4293i | − 0.427580i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.09990i | 0.278316i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.58567 | −0.0543560 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.6149 | −0.842797 | −0.421399 | − | 0.906876i | \(-0.638461\pi\) | ||||
−0.421399 | + | 0.906876i | \(0.638461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 5.98500i | − 0.204444i | −0.994762 | − | 0.102222i | \(-0.967405\pi\) | ||||
0.994762 | − | 0.102222i | \(-0.0325952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.9197i | 0.474934i | 0.971396 | + | 0.237467i | \(0.0763171\pi\) | ||||
−0.971396 | + | 0.237467i | \(0.923683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.3075 | −1.37208 | −0.686042 | − | 0.727562i | \(-0.740653\pi\) | ||||
−0.686042 | + | 0.727562i | \(0.740653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5031 | −0.493121 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.92913i | 0.0993638i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.17779i | 0.243210i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.49139 | −0.219449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.5498 | −1.50434 | −0.752170 | − | 0.658969i | \(-0.770993\pi\) | ||||
−0.752170 | + | 0.658969i | \(0.770993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 21.4243i | − 0.721801i | −0.932604 | − | 0.360901i | \(-0.882469\pi\) | ||||
0.932604 | − | 0.360901i | \(-0.117531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.9222i | 1.81463i | 0.420455 | + | 0.907314i | \(0.361871\pi\) | ||||
−0.420455 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8932 | −0.533640 | −0.266820 | − | 0.963746i | \(-0.585973\pi\) | ||||
−0.266820 | + | 0.963746i | \(0.585973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.85480 | −0.129286 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 17.3068i | − 0.579150i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 10.0537i | − 0.336058i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.59782 | 0.153346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.5696 | −0.785217 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 10.0328i | − 0.333501i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.8494i | 0.393452i | 0.980459 | + | 0.196726i | \(0.0630309\pi\) | ||||
−0.980459 | + | 0.196726i | \(0.936969\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.1245 | −0.799280 | −0.399640 | − | 0.916672i | \(-0.630865\pi\) | ||||
−0.399640 | + | 0.916672i | \(0.630865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.0979 | −0.433477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 11.0680i | − 0.365497i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.1085i | 1.45501i | 0.686105 | + | 0.727503i | \(0.259319\pi\) | ||||
−0.686105 | + | 0.727503i | \(0.740681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.3181 | 0.570031 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.18032 | 0.203208 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 6.83370i | − 0.224207i | −0.993697 | − | 0.112103i | \(-0.964241\pi\) | ||||
0.993697 | − | 0.112103i | \(-0.0357587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.46651i | 0.146384i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.27516 | −0.139813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.2524 | −1.70701 | −0.853505 | − | 0.521084i | \(-0.825528\pi\) | ||||
−0.853505 | + | 0.521084i | \(0.825528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.35658i | 0.239818i | 0.992785 | + | 0.119909i | \(0.0382602\pi\) | ||||
−0.992785 | + | 0.119909i | \(0.961740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.53219i | 0.0498948i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7826 | 1.52023 | 0.760115 | − | 0.649789i | \(-0.225143\pi\) | ||||
0.760115 | + | 0.649789i | \(0.225143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.3867 | −1.05132 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.44950i | 0.0469538i | 0.999724 | + | 0.0234769i | \(0.00747361\pi\) | ||||
−0.999724 | + | 0.0234769i | \(0.992526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0512i | 0.487047i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.9424 | −0.482515 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.3057 | 0.784056 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 13.3744i | − 0.430538i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.6909i | 1.53364i | 0.641864 | + | 0.766819i | \(0.278161\pi\) | ||||
−0.641864 | + | 0.766819i | \(0.721839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.5871 | 0.371848 | 0.185924 | − | 0.982564i | \(-0.440472\pi\) | ||||
0.185924 | + | 0.982564i | \(0.440472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.25129 | 0.168349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.6994i | 1.49405i | 0.664799 | + | 0.747023i | \(0.268517\pi\) | ||||
−0.664799 | + | 0.747023i | \(0.731483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.63971i | − 0.0524055i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.31157 | 0.296993 | 0.148497 | − | 0.988913i | \(-0.452557\pi\) | ||||
0.148497 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0117 | −0.382725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.48448i | 0.174396i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8616i | 0.630925i | 0.948938 | + | 0.315463i | \(0.102160\pi\) | ||||
−0.948938 | + | 0.315463i | \(0.897840\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.04858 | 0.0966465 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.9244 | −1.51778 | −0.758890 | − | 0.651218i | \(-0.774258\pi\) | ||||
−0.758890 | + | 0.651218i | \(0.774258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 6048.2.h.i.2591.13 | yes | 24 | |
3.2 | odd | 2 | inner | 6048.2.h.i.2591.12 | yes | 24 | |
4.3 | odd | 2 | inner | 6048.2.h.i.2591.11 | ✓ | 24 | |
12.11 | even | 2 | inner | 6048.2.h.i.2591.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.i.2591.11 | ✓ | 24 | 4.3 | odd | 2 | inner | |
6048.2.h.i.2591.12 | yes | 24 | 3.2 | odd | 2 | inner | |
6048.2.h.i.2591.13 | yes | 24 | 1.1 | even | 1 | trivial | |
6048.2.h.i.2591.14 | yes | 24 | 12.11 | even | 2 | inner |