Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4840) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-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 | ||||||||
\(3\) | 0.414214 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.414214 | −0.156558 | −0.0782790 | − | 0.996931i | \(-0.524942\pi\) | ||||
−0.0782790 | + | 0.996931i | \(0.524942\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.65685 | 1.37199 | 0.685994 | − | 0.727607i | \(-0.259367\pi\) | ||||
0.685994 | + | 0.727607i | \(0.259367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.828427 | −0.190054 | −0.0950271 | − | 0.995475i | \(-0.530294\pi\) | ||||
−0.0950271 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.171573 | −0.0374403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.65685 | 1.59656 | 0.798282 | − | 0.602284i | \(-0.205742\pi\) | ||||
0.798282 | + | 0.602284i | \(0.205742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65685 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.414214 | −0.0700149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.48528 | −1.16900 | −0.584502 | − | 0.811392i | \(-0.698710\pi\) | ||||
−0.584502 | + | 0.811392i | \(0.698710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.41421 | 0.978158 | 0.489079 | − | 0.872239i | \(-0.337333\pi\) | ||||
0.489079 | + | 0.872239i | \(0.337333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4142 | −1.51907 | −0.759535 | − | 0.650467i | \(-0.774573\pi\) | ||||
−0.759535 | + | 0.650467i | \(0.774573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82843 | −0.975490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.34315 | 0.328106 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65685 | 0.502308 | 0.251154 | − | 0.967947i | \(-0.419190\pi\) | ||||
0.251154 | + | 0.967947i | \(0.419190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.343146 | −0.0454508 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3137 | −1.47292 | −0.736460 | − | 0.676481i | \(-0.763504\pi\) | ||||
−0.736460 | + | 0.676481i | \(0.763504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.17157 | 0.147604 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.58579 | 0.438074 | 0.219037 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219037 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.17157 | 0.381813 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.414214 | 0.0478293 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.48528 | 0.279616 | 0.139808 | − | 0.990179i | \(-0.455351\pi\) | ||||
0.139808 | + | 0.990179i | \(0.455351\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.31371 | 1.02231 | 0.511156 | − | 0.859488i | \(-0.329217\pi\) | ||||
0.511156 | + | 0.859488i | \(0.329217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.65685 | 0.613572 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.828427 | −0.0888167 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.65685 | −0.917625 | −0.458812 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.828427 | 0.0868428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.34315 | −0.242973 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.828427 | −0.0849948 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.31371 | 0.539525 | 0.269763 | − | 0.962927i | \(-0.413055\pi\) | ||||
0.269763 | + | 0.962927i | \(0.413055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.8284 | −1.57499 | −0.787494 | − | 0.616323i | \(-0.788622\pi\) | ||||
−0.787494 | + | 0.616323i | \(0.788622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.31371 | 0.917707 | 0.458853 | − | 0.888512i | \(-0.348260\pi\) | ||||
0.458853 | + | 0.888512i | \(0.348260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.171573 | −0.0167438 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.75736 | 0.653259 | 0.326629 | − | 0.945153i | \(-0.394087\pi\) | ||||
0.326629 | + | 0.945153i | \(0.394087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.34315 | −0.511781 | −0.255890 | − | 0.966706i | \(-0.582369\pi\) | ||||
−0.255890 | + | 0.966706i | \(0.582369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65685 | −0.157262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.31371 | −0.499872 | −0.249936 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249936 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.65685 | 0.714005 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.34315 | −0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.10051 | −0.279563 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.58579 | −0.140716 | −0.0703579 | − | 0.997522i | \(-0.522414\pi\) | ||||
−0.0703579 | + | 0.997522i | \(0.522414\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.65685 | 0.233923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.4853 | 1.26558 | 0.632792 | − | 0.774321i | \(-0.281909\pi\) | ||||
0.632792 | + | 0.774321i | \(0.281909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.343146 | 0.0297545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.41421 | −0.207782 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.31371 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.31371 | −0.363280 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.82843 | −0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0000 | 1.39269 | 0.696347 | − | 0.717705i | \(-0.254807\pi\) | ||||
0.696347 | + | 0.717705i | \(0.254807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.65685 | −0.460348 | −0.230174 | − | 0.973149i | \(-0.573930\pi\) | ||||
−0.230174 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0000 | −1.29352 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.65685 | −0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.34315 | 0.506238 | 0.253119 | − | 0.967435i | \(-0.418544\pi\) | ||||
0.253119 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.51472 | 0.120125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.17157 | −0.249955 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4142 | −0.815704 | −0.407852 | − | 0.913048i | \(-0.633722\pi\) | ||||
−0.407852 | + | 0.913048i | \(0.633722\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.58579 | 0.277476 | 0.138738 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138738 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34315 | 0.179185 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.65685 | −0.582140 | −0.291070 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291070 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.414214 | −0.0313116 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.68629 | −0.352243 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7990 | −1.62933 | −0.814667 | − | 0.579930i | \(-0.803080\pi\) | ||||
−0.814667 | + | 0.579930i | \(0.803080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.1716 | −1.49934 | −0.749671 | − | 0.661811i | \(-0.769788\pi\) | ||||
−0.749671 | + | 0.661811i | \(0.769788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.414214 | −0.0306195 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1716 | −0.808347 | −0.404173 | − | 0.914682i | \(-0.632441\pi\) | ||||
−0.404173 | + | 0.914682i | \(0.632441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3137 | 1.53419 | 0.767097 | − | 0.641531i | \(-0.221700\pi\) | ||||
0.767097 | + | 0.641531i | \(0.221700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.828427 | −0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.9706 | −1.92157 | −0.960787 | − | 0.277289i | \(-0.910564\pi\) | ||||
−0.960787 | + | 0.277289i | \(0.910564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8284 | 0.909383 | 0.454692 | − | 0.890649i | \(-0.349750\pi\) | ||||
0.454692 | + | 0.890649i | \(0.349750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.48528 | 0.104764 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.828427 | 0.0581442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.48528 | −0.522795 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.6569 | −1.50526 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.65685 | 0.113526 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.41421 | 0.437446 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.34315 | 0.159063 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.65685 | −0.111960 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.3137 | −0.761042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0711 | −1.47799 | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
−0.738994 | + | 0.673712i | \(0.764699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9289 | 0.791751 | 0.395876 | − | 0.918304i | \(-0.370441\pi\) | ||||
0.395876 | + | 0.918304i | \(0.370441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.48528 | −0.362478 | −0.181239 | − | 0.983439i | \(-0.558011\pi\) | ||||
−0.181239 | + | 0.983439i | \(0.558011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.6569 | −1.02571 | −0.512857 | − | 0.858474i | \(-0.671413\pi\) | ||||
−0.512857 | + | 0.858474i | \(0.671413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4142 | −0.679348 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.02944 | 0.0668691 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.14214 | 0.267932 | 0.133966 | − | 0.990986i | \(-0.457229\pi\) | ||||
0.133966 | + | 0.990986i | \(0.457229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8284 | −1.40609 | −0.703046 | − | 0.711144i | \(-0.748177\pi\) | ||||
−0.703046 | + | 0.711144i | \(0.748177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3431 | 0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.82843 | −0.436252 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.65685 | 0.105423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.85786 | 0.244482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.3137 | −1.47155 | −0.735774 | − | 0.677227i | \(-0.763181\pi\) | ||||
−0.735774 | + | 0.677227i | \(0.763181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.34315 | 0.146733 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.9706 | −1.30811 | −0.654054 | − | 0.756448i | \(-0.726933\pi\) | ||||
−0.654054 | + | 0.756448i | \(0.726933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.65685 | 0.102952 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65685 | 0.350150 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.6274 | −1.27194 | −0.635971 | − | 0.771713i | \(-0.719400\pi\) | ||||
−0.635971 | + | 0.771713i | \(0.719400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.65685 | 0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.58579 | −0.219447 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.31371 | 0.384954 | 0.192477 | − | 0.981302i | \(-0.438348\pi\) | ||||
0.192477 | + | 0.981302i | \(0.438348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.3137 | 0.687259 | 0.343629 | − | 0.939105i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939105i | \(0.388344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.343146 | 0.0207681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.6274 | 0.999045 | 0.499522 | − | 0.866301i | \(-0.333509\pi\) | ||||
0.499522 | + | 0.866301i | \(0.333509\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3137 | −1.03285 | −0.516425 | − | 0.856333i | \(-0.672737\pi\) | ||||
−0.516425 | + | 0.856333i | \(0.672737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2132 | 1.32044 | 0.660219 | − | 0.751073i | \(-0.270463\pi\) | ||||
0.660219 | + | 0.751073i | \(0.270463\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.343146 | −0.0203262 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.10051 | 0.183017 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.20101 | 0.129025 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.31371 | −0.193589 | −0.0967945 | − | 0.995304i | \(-0.530859\pi\) | ||||
−0.0967945 | + | 0.995304i | \(0.530859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3137 | −0.658710 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.3137 | −0.885615 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.65685 | −0.153139 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.55635 | −0.376652 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | −0.0572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.68629 | −0.153315 | −0.0766574 | − | 0.997057i | \(-0.524425\pi\) | ||||
−0.0766574 | + | 0.997057i | \(0.524425\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.85786 | 0.219466 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.17157 | −0.406663 | −0.203331 | − | 0.979110i | \(-0.565177\pi\) | ||||
−0.203331 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31371 | 0.0742552 | 0.0371276 | − | 0.999311i | \(-0.488179\pi\) | ||||
0.0371276 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.17157 | 0.0660107 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.3137 | −1.42176 | −0.710880 | − | 0.703314i | \(-0.751703\pi\) | ||||
−0.710880 | + | 0.703314i | \(0.751703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.79899 | 0.156224 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.68629 | −0.260752 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.21320 | −0.122390 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.31371 | 0.237822 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.828427 | 0.0455345 | 0.0227672 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227672 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3137 | 0.619987 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.58579 | 0.195912 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.20101 | −0.119542 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.72792 | 0.309279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.17157 | 0.170752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.3848 | −1.89955 | −0.949777 | − | 0.312927i | \(-0.898690\pi\) | ||||
−0.949777 | + | 0.312927i | \(0.898690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3137 | −0.926782 | −0.463391 | − | 0.886154i | \(-0.653367\pi\) | ||||
−0.463391 | + | 0.886154i | \(0.653367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.82843 | 0.257722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6274 | 0.565640 | 0.282820 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282820 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | 0.212298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.970563 | −0.0513676 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.82843 | −0.465947 | −0.232973 | − | 0.972483i | \(-0.574845\pi\) | ||||
−0.232973 | + | 0.972483i | \(0.574845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.24264 | 0.169264 | 0.0846322 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846322 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.1716 | 1.10215 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.51472 | −0.0786403 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.9706 | −0.671590 | −0.335795 | − | 0.941935i | \(-0.609005\pi\) | ||||
−0.335795 | + | 0.941935i | \(0.609005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.414214 | 0.0213899 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.14214 | −0.418233 | −0.209117 | − | 0.977891i | \(-0.567059\pi\) | ||||
−0.209117 | + | 0.977891i | \(0.567059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.656854 | −0.0336517 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.97056 | 0.151789 | 0.0758943 | − | 0.997116i | \(-0.475819\pi\) | ||||
0.0758943 | + | 0.997116i | \(0.475819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.1421 | −0.922217 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.68629 | 0.186902 | 0.0934512 | − | 0.995624i | \(-0.470210\pi\) | ||||
0.0934512 | + | 0.995624i | \(0.470210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.3137 | 2.19047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.48528 | 0.125048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0000 | −1.20453 | −0.602263 | − | 0.798298i | \(-0.705734\pi\) | ||||
−0.602263 | + | 0.798298i | \(0.705734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.142136 | 0.00711568 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.3137 | −0.814668 | −0.407334 | − | 0.913279i | \(-0.633541\pi\) | ||||
−0.407334 | + | 0.913279i | \(0.633541\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3137 | 0.563576 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.7696 | −1.66980 | −0.834898 | − | 0.550404i | \(-0.814474\pi\) | ||||
−0.834898 | + | 0.550404i | \(0.814474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.85786 | −0.190294 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.68629 | 0.230597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.31371 | 0.457192 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.97056 | 0.243410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.4853 | 1.68472 | 0.842358 | − | 0.538918i | \(-0.181167\pi\) | ||||
0.842358 | + | 0.538918i | \(0.181167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3137 | −1.47740 | −0.738700 | − | 0.674034i | \(-0.764560\pi\) | ||||
−0.738700 | + | 0.674034i | \(0.764560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.4558 | 1.43219 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.65685 | 0.274398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.414214 | 0.0200452 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.4853 | 1.66110 | 0.830549 | − | 0.556946i | \(-0.188027\pi\) | ||||
0.830549 | + | 0.556946i | \(0.188027\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.97056 | 0.238870 | 0.119435 | − | 0.992842i | \(-0.461892\pi\) | ||||
0.119435 | + | 0.992842i | \(0.461892\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.828427 | −0.0397200 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.34315 | −0.303434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.2843 | 1.54084 | 0.770422 | − | 0.637534i | \(-0.220046\pi\) | ||||
0.770422 | + | 0.637534i | \(0.220046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3137 | 0.919700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.757359 | −0.0359832 | −0.0179916 | − | 0.999838i | \(-0.505727\pi\) | ||||
−0.0179916 | + | 0.999838i | \(0.505727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.65685 | −0.410374 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.04163 | 0.333058 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4558 | 0.493442 | 0.246721 | − | 0.969087i | \(-0.420647\pi\) | ||||
0.246721 | + | 0.969087i | \(0.420647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.34315 | −0.110091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.828427 | 0.0388373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3137 | 0.903457 | 0.451729 | − | 0.892155i | \(-0.350808\pi\) | ||||
0.451729 | + | 0.892155i | \(0.350808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.6569 | −0.637447 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1421 | −0.891538 | −0.445769 | − | 0.895148i | \(-0.647070\pi\) | ||||
−0.445769 | + | 0.895148i | \(0.647070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.75736 | −0.314041 | −0.157021 | − | 0.987595i | \(-0.550189\pi\) | ||||
−0.157021 | + | 0.987595i | \(0.550189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.34315 | −0.108661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4437 | −0.529549 | −0.264775 | − | 0.964310i | \(-0.585298\pi\) | ||||
−0.264775 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.48528 | −0.0685839 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.62742 | 0.121065 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.828427 | −0.0380108 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3431 | −0.473580 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.7990 | 1.72708 | 0.863540 | − | 0.504280i | \(-0.168242\pi\) | ||||
0.863540 | + | 0.504280i | \(0.168242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.31371 | −0.0597758 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.31371 | 0.241283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.3137 | −1.87210 | −0.936051 | − | 0.351863i | \(-0.885548\pi\) | ||||
−0.936051 | + | 0.351863i | \(0.885548\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.31371 | −0.195073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.4853 | 1.55630 | 0.778149 | − | 0.628079i | \(-0.216159\pi\) | ||||
0.778149 | + | 0.628079i | \(0.216159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3137 | −0.509544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.65685 | −0.0743201 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.79899 | −0.0805338 | −0.0402669 | − | 0.999189i | \(-0.512821\pi\) | ||||
−0.0402669 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.48528 | 0.0663575 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.3848 | −1.22103 | −0.610513 | − | 0.792006i | \(-0.709037\pi\) | ||||
−0.610513 | + | 0.792006i | \(0.709037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8284 | −0.704356 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.72792 | −0.165563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.48528 | −0.243131 | −0.121565 | − | 0.992583i | \(-0.538791\pi\) | ||||
−0.121565 | + | 0.992583i | \(0.538791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65685 | 0.0732949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.31371 | 0.410411 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.17157 | −0.139217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.9706 | 1.75114 | 0.875571 | − | 0.483089i | \(-0.160485\pi\) | ||||
0.875571 | + | 0.483089i | \(0.160485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.31371 | 0.407260 | 0.203630 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203630 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.171573 | −0.00748805 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0000 | −1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.0000 | 1.38868 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.9706 | 0.648447 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.75736 | 0.292146 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.02944 | −0.389649 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1421 | −0.994958 | −0.497479 | − | 0.867476i | \(-0.665741\pi\) | ||||
−0.497479 | + | 0.867476i | \(0.665741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.35534 | −0.358562 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.34315 | −0.228875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0000 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.82843 | 0.120714 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.65685 | 0.0705844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.02944 | −0.0437761 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.65685 | −0.0703295 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.6274 | 0.958754 | 0.479377 | − | 0.877609i | \(-0.340863\pi\) | ||||
0.479377 | + | 0.877609i | \(0.340863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.8284 | −0.542585 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8995 | −0.712229 | −0.356114 | − | 0.934442i | \(-0.615899\pi\) | ||||
−0.356114 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.31371 | −0.223549 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.10051 | −0.130209 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.4558 | −1.44446 | −0.722232 | − | 0.691651i | \(-0.756884\pi\) | ||||
−0.722232 | + | 0.691651i | \(0.756884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4558 | −1.14899 | −0.574496 | − | 0.818508i | \(-0.694802\pi\) | ||||
−0.574496 | + | 0.818508i | \(0.694802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.62742 | −0.193313 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.65685 | 0.319313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9411 | 1.41299 | 0.706494 | − | 0.707719i | \(-0.250276\pi\) | ||||
0.706494 | + | 0.707719i | \(0.250276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.82843 | 0.366897 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.85786 | −0.160051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.65685 | 0.233882 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6985 | 0.936867 | 0.468433 | − | 0.883499i | \(-0.344819\pi\) | ||||
0.468433 | + | 0.883499i | \(0.344819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.68629 | 0.193095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1716 | −0.459537 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3431 | 0.506872 | 0.253436 | − | 0.967352i | \(-0.418439\pi\) | ||||
0.253436 | + | 0.967352i | \(0.418439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34315 | −0.0960596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.31371 | 0.217476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.1421 | −1.80360 | −0.901799 | − | 0.432155i | \(-0.857753\pi\) | ||||
−0.901799 | + | 0.432155i | \(0.857753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.9411 | 1.13974 | 0.569871 | − | 0.821734i | \(-0.306993\pi\) | ||||
0.569871 | + | 0.821734i | \(0.306993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.1421 | −0.413020 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.5980 | −1.85076 | −0.925382 | − | 0.379035i | \(-0.876256\pi\) | ||||
−0.925382 | + | 0.379035i | \(0.876256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.343146 | 0.0139050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.8284 | 0.842628 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9706 | 0.766214 | 0.383107 | − | 0.923704i | \(-0.374854\pi\) | ||||
0.383107 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.10051 | −0.125024 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.0000 | −1.61034 | −0.805170 | − | 0.593045i | \(-0.797926\pi\) | ||||
−0.805170 | + | 0.593045i | \(0.797926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3137 | 0.615510 | 0.307755 | − | 0.951466i | \(-0.400422\pi\) | ||||
0.307755 | + | 0.951466i | \(0.400422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4853 | −0.741789 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.58579 | 0.143662 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.6274 | −0.902214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.6569 | −1.81757 | −0.908785 | − | 0.417264i | \(-0.862989\pi\) | ||||
−0.908785 | + | 0.417264i | \(0.862989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.31371 | −0.131708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.58579 | −0.0629300 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6569 | 0.541104 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3137 | −0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.37258 | −0.133209 | −0.0666045 | − | 0.997779i | \(-0.521217\pi\) | ||||
−0.0666045 | + | 0.997779i | \(0.521217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.7279 | −1.01461 | −0.507305 | − | 0.861767i | \(-0.669358\pi\) | ||||
−0.507305 | + | 0.861767i | \(0.669358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.65685 | 0.104614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.8701 | −0.938429 | −0.469214 | − | 0.883084i | \(-0.655463\pi\) | ||||
−0.469214 | + | 0.883084i | \(0.655463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.970563 | 0.0380394 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.65685 | 0.143104 | 0.0715519 | − | 0.997437i | \(-0.477205\pi\) | ||||
0.0715519 | + | 0.997437i | \(0.477205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4853 | 0.565987 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3137 | 0.441390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.8284 | −1.12300 | −0.561498 | − | 0.827478i | \(-0.689775\pi\) | ||||
−0.561498 | + | 0.827478i | \(0.689775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.6569 | 1.81474 | 0.907371 | − | 0.420331i | \(-0.138086\pi\) | ||||
0.907371 | + | 0.420331i | \(0.138086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.68629 | −0.182000 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.343146 | 0.0133066 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3137 | −0.592949 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.14214 | −0.353455 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.9706 | 0.654167 | 0.327084 | − | 0.944995i | \(-0.393934\pi\) | ||||
0.327084 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.41421 | −0.0929231 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.3137 | 1.20348 | 0.601742 | − | 0.798691i | \(-0.294474\pi\) | ||||
0.601742 | + | 0.798691i | \(0.294474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.20101 | −0.0844670 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.94113 | 0.189344 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.8701 | 1.29600 | 0.648001 | − | 0.761640i | \(-0.275605\pi\) | ||||
0.648001 | + | 0.761640i | \(0.275605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.31371 | −0.355859 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.27208 | −0.0866852 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.31371 | −0.278630 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.48528 | −0.0945446 | −0.0472723 | − | 0.998882i | \(-0.515053\pi\) | ||||
−0.0472723 | + | 0.998882i | \(0.515053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000 | 0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.3431 | −1.60386 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.48528 | −0.245296 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.9411 | 1.05532 | 0.527661 | − | 0.849455i | \(-0.323069\pi\) | ||||
0.527661 | + | 0.849455i | \(0.323069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.31371 | 0.124979 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.31371 | −0.162464 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.55635 | 0.246577 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.85786 | −0.257553 | −0.128776 | − | 0.991674i | \(-0.541105\pi\) | ||||
−0.128776 | + | 0.991674i | \(0.541105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.02944 | −0.263624 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.3137 | −1.62211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.71573 | 0.0640751 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.8284 | 1.37347 | 0.686734 | − | 0.726909i | \(-0.259044\pi\) | ||||
0.686734 | + | 0.726909i | \(0.259044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.85786 | −0.143674 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.04163 | −0.336262 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9289 | −1.40671 | −0.703353 | − | 0.710841i | \(-0.748315\pi\) | ||||
−0.703353 | + | 0.710841i | \(0.748315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.2843 | 1.34202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2843 | 0.601473 | 0.300737 | − | 0.953707i | \(-0.402767\pi\) | ||||
0.300737 | + | 0.953707i | \(0.402767\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.82843 | −0.104328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.4853 | −1.85713 | −0.928566 | − | 0.371168i | \(-0.878957\pi\) | ||||
−0.928566 | + | 0.371168i | \(0.878957\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.686292 | 0.0252115 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.5858 | 1.08540 | 0.542699 | − | 0.839928i | \(-0.317403\pi\) | ||||
0.542699 | + | 0.839928i | \(0.317403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0000 | 0.622832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.3431 | −0.963845 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.79899 | −0.102273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.828427 | 0.0302297 | 0.0151149 | − | 0.999886i | \(-0.495189\pi\) | ||||
0.0151149 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.65685 | −0.351915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.97056 | 0.107967 | 0.0539835 | − | 0.998542i | \(-0.482808\pi\) | ||||
0.0539835 | + | 0.998542i | \(0.482808\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.21320 | 0.0801233 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0000 | −0.578481 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6274 | 0.817029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.68629 | −0.312829 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.97056 | 0.178779 | 0.0893894 | − | 0.995997i | \(-0.471508\pi\) | ||||
0.0893894 | + | 0.995997i | \(0.471508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.65685 | −0.203200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.686292 | 0.0246206 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.20101 | 0.222174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.82843 | 0.172554 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.34315 | 0.226397 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.2132 | −1.50474 | −0.752369 | − | 0.658742i | \(-0.771089\pi\) | ||||
−0.752369 | + | 0.658742i | \(0.771089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.54416 | −0.304180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.20101 | 0.0782589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.51472 | 0.0537215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.6569 | 1.61725 | 0.808624 | − | 0.588325i | \(-0.200213\pi\) | ||||
0.808624 | + | 0.588325i | \(0.200213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.9117 | −2.08415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.4853 | 0.865145 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.17157 | −0.111783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.61522 | 0.0920602 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.6274 | 0.725221 | 0.362611 | − | 0.931941i | \(-0.381885\pi\) | ||||
0.362611 | + | 0.931941i | \(0.381885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.65685 | 0.198639 | 0.0993195 | − | 0.995056i | \(-0.468333\pi\) | ||||
0.0993195 | + | 0.995056i | \(0.468333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.68629 | 0.164355 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4142 | −0.364794 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.31371 | −0.185903 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.34315 | −0.0818761 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.9706 | −1.04598 | −0.522990 | − | 0.852339i | \(-0.675183\pi\) | ||||
−0.522990 | + | 0.852339i | \(0.675183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0711 | 0.560202 | 0.280101 | − | 0.959971i | \(-0.409632\pi\) | ||||
0.280101 | + | 0.959971i | \(0.409632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.3553 | 1.33375 | 0.666873 | − | 0.745171i | \(-0.267632\pi\) | ||||
0.666873 | + | 0.745171i | \(0.267632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.9411 | −1.21356 | −0.606778 | − | 0.794872i | \(-0.707538\pi\) | ||||
−0.606778 | + | 0.794872i | \(0.707538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.88730 | 0.238918 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.6274 | −1.33836 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.58579 | 0.124091 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.6569 | 0.472050 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.20101 | −0.0759873 | −0.0379937 | − | 0.999278i | \(-0.512097\pi\) | ||||
−0.0379937 | + | 0.999278i | \(0.512097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.17157 | −0.247002 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.20101 | 0.315778 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.6274 | −1.04989 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3431 | 0.628057 | 0.314029 | − | 0.949413i | \(-0.398321\pi\) | ||||
0.314029 | + | 0.949413i | \(0.398321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.34315 | 0.0801339 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9706 | −0.784659 | −0.392330 | − | 0.919825i | \(-0.628331\pi\) | ||||
−0.392330 | + | 0.919825i | \(0.628331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.1421 | 1.23315 | 0.616577 | − | 0.787295i | \(-0.288519\pi\) | ||||
0.616577 | + | 0.787295i | \(0.288519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.28427 | 0.0437678 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.8701 | −1.56143 | −0.780717 | − | 0.624884i | \(-0.785146\pi\) | ||||
−0.780717 | + | 0.624884i | \(0.785146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.65685 | −0.260341 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.21320 | 0.211011 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.17157 | −0.242999 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.0294 | −0.508669 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.414214 | −0.0140030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6863 | 0.833597 | 0.416798 | − | 0.908999i | \(-0.363152\pi\) | ||||
0.416798 | + | 0.908999i | \(0.363152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.37258 | −0.0462961 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.4853 | 0.656476 | 0.328238 | − | 0.944595i | \(-0.393545\pi\) | ||||
0.328238 | + | 0.944595i | \(0.393545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.6569 | 1.46917 | 0.734585 | − | 0.678517i | \(-0.237377\pi\) | ||||
0.734585 | + | 0.678517i | \(0.237377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.68629 | −0.157528 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.3848 | −1.25526 | −0.627629 | − | 0.778513i | \(-0.715974\pi\) | ||||
−0.627629 | + | 0.778513i | \(0.715974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.656854 | 0.0220302 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.62742 | 0.288706 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.7990 | −0.728660 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.34315 | −0.211791 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3137 | 0.377333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6863 | 0.689160 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.10051 | −0.0366225 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.1716 | −0.670526 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.6985 | 0.620873 | 0.310436 | − | 0.950594i | \(-0.399525\pi\) | ||||
0.310436 | + | 0.950594i | \(0.399525\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.7696 | 1.48491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8284 | 1.08765 | 0.543827 | − | 0.839197i | \(-0.316975\pi\) | ||||
0.543827 | + | 0.839197i | \(0.316975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.414214 | −0.0136935 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | −0.198137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.4264 | −1.72939 | −0.864694 | − | 0.502299i | \(-0.832488\pi\) | ||||
−0.864694 | + | 0.502299i | \(0.832488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.11270 | −0.0366647 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.00000 | −0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.3431 | −0.865222 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.65685 | 0.185396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.97056 | −0.0972519 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.544156 | 0.0177579 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.1716 | −1.50515 | −0.752575 | − | 0.658506i | \(-0.771189\pi\) | ||||
−0.752575 | + | 0.658506i | \(0.771189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57.3137 | −1.86639 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.0000 | −0.324956 | −0.162478 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162478 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.4853 | −0.340009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.2843 | 1.04579 | 0.522895 | − | 0.852397i | \(-0.324852\pi\) | ||||
0.522895 | + | 0.852397i | \(0.324852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.1716 | −0.361504 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.85786 | 0.124577 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1127 | −0.615898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.3137 | 0.686113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.5980 | −1.20907 | −0.604535 | − | 0.796579i | \(-0.706641\pi\) | ||||
−0.604535 | + | 0.796579i | \(0.706641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.94113 | −0.0623579 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.2843 | 1.93461 | 0.967307 | − | 0.253608i | \(-0.0816172\pi\) | ||||
0.967307 | + | 0.253608i | \(0.0816172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.97056 | −0.159349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.828427 | −0.0265309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.6274 | −1.36377 | −0.681886 | − | 0.731459i | \(-0.738840\pi\) | ||||
−0.681886 | + | 0.731459i | \(0.738840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1127 | 0.482511 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0711 | 0.640168 | 0.320084 | − | 0.947389i | \(-0.396289\pi\) | ||||
0.320084 | + | 0.947389i | \(0.396289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.9706 | −0.859354 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.78680 | 0.0568744 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.1127 | 1.56169 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5147 | −1.31876 | −0.659379 | − | 0.751810i | \(-0.729181\pi\) | ||||
−0.659379 | + | 0.751810i | \(0.729181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.343146 | 0.0108894 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8284 | 0.406688 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.68629 | 0.211757 | 0.105878 | − | 0.994379i | \(-0.466235\pi\) | ||||
0.105878 | + | 0.994379i | \(0.466235\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.65685 | 0.305529 |
(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 | 9680.2.a.bk.1.2 | 2 | ||
4.3 | odd | 2 | 4840.2.a.o.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | 9680.2.a.bj.1.2 | 2 | |||
44.43 | even | 2 | 4840.2.a.p.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4840.2.a.o.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
4840.2.a.p.1.1 | yes | 2 | 44.43 | even | 2 | ||
9680.2.a.bj.1.2 | 2 | 11.10 | odd | 2 | |||
9680.2.a.bk.1.2 | 2 | 1.1 | even | 1 | trivial |