Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{10} + 202x^{8} + 362x^{6} + 245x^{4} + 63x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.2 | ||
Root | \(-0.687758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.j.2431.11 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.95229i | − | 1.49383i | −0.664922 | − | 0.746913i | \(-0.731535\pi\) | ||
0.664922 | − | 0.746913i | \(-0.268465\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16866i | 0.653875i | 0.945046 | + | 0.326937i | \(0.106017\pi\) | ||||
−0.945046 | + | 0.326937i | \(0.893983\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.98743i | − | 1.93796i | −0.247130 | − | 0.968982i | \(-0.579487\pi\) | ||
0.247130 | − | 0.968982i | \(-0.420513\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.03991 | −0.494750 | −0.247375 | − | 0.968920i | \(-0.579568\pi\) | ||||
−0.247375 | + | 0.968920i | \(0.579568\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.20175 | − | 3.76196i | −0.505115 | − | 0.863052i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.95229i | 0.862461i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.87858i | − | 1.85131i | −0.378366 | − | 0.925656i | \(-0.623514\pi\) | ||
0.378366 | − | 0.925656i | \(-0.376486\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.63276i | 1.04598i | 0.852340 | + | 0.522989i | \(0.175183\pi\) | ||||
−0.852340 | + | 0.522989i | \(0.824817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.31415 | −0.236028 | −0.118014 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118014 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.16866i | − | 0.377515i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.95229i | − | 0.668059i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.77374i | − | 0.291601i | −0.989314 | − | 0.145801i | \(-0.953424\pi\) | ||
0.989314 | − | 0.145801i | \(-0.0465758\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.98743i | 1.11888i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.92629i | 0.769357i | 0.923051 | + | 0.384679i | \(0.125688\pi\) | ||||
−0.923051 | + | 0.384679i | \(0.874312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.57516i | − | 1.46020i | −0.683341 | − | 0.730099i | \(-0.739474\pi\) | ||
0.683341 | − | 0.730099i | \(-0.260526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.15609i | 1.33555i | 0.744362 | + | 0.667776i | \(0.232754\pi\) | ||||
−0.744362 | + | 0.667776i | \(0.767246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.62061 | −1.23152 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.03991 | 0.285644 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.41448i | 0.743736i | 0.928286 | + | 0.371868i | \(0.121283\pi\) | ||||
−0.928286 | + | 0.371868i | \(0.878717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.16866i | 0.292422i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.20175 | + | 3.76196i | 0.291629 | + | 0.498283i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.9348 | −1.68396 | −0.841981 | − | 0.539507i | \(-0.818611\pi\) | ||||
−0.841981 | + | 0.539507i | \(0.818611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.62061 | 0.207497 | 0.103749 | − | 0.994604i | \(-0.466916\pi\) | ||||
0.103749 | + | 0.994604i | \(0.466916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.95229i | − | 0.497942i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.98743i | − | 0.866684i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.56189 | −0.801662 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.87858i | 1.06886i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.35406 | −0.635410 | −0.317705 | − | 0.948190i | \(-0.602912\pi\) | ||||
−0.317705 | + | 0.948190i | \(0.602912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.95056 | 0.345337 | 0.172669 | − | 0.984980i | \(-0.444761\pi\) | ||||
0.172669 | + | 0.984980i | \(0.444761\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.57117 | 0.976775 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1906 | 1.25904 | 0.629521 | − | 0.776984i | \(-0.283251\pi\) | ||||
0.629521 | + | 0.776984i | \(0.283251\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.37136i | 0.479819i | 0.970795 | + | 0.239910i | \(0.0771178\pi\) | ||||
−0.970795 | + | 0.239910i | \(0.922882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.03991 | −0.221259 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.63276i | − | 0.603895i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.91831i | 0.733340i | 0.930351 | + | 0.366670i | \(0.119502\pi\) | ||||
−0.930351 | + | 0.366670i | \(0.880498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.6164 | −2.89498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.31415 | 0.136271 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.20175 | − | 3.76196i | −0.225894 | − | 0.385968i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.0393i | − | 1.32394i | −0.749532 | − | 0.661968i | \(-0.769721\pi\) | ||
0.749532 | − | 0.661968i | \(-0.230279\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.16866i | 0.217958i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.88415 | 0.684998 | 0.342499 | − | 0.939518i | \(-0.388727\pi\) | ||||
0.342499 | + | 0.939518i | \(0.388727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.56189 | 0.646562 | 0.323281 | − | 0.946303i | \(-0.395214\pi\) | ||||
0.323281 | + | 0.946303i | \(0.395214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.95229i | 0.385704i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.20783 | −0.890155 | −0.445077 | − | 0.895492i | \(-0.646824\pi\) | ||||
−0.445077 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5873i | 1.68455i | 0.539045 | + | 0.842277i | \(0.318785\pi\) | ||||
−0.539045 | + | 0.842277i | \(0.681215\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.77374i | 0.168356i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.870836i | − | 0.0819213i | −0.999161 | − | 0.0409607i | \(-0.986958\pi\) | ||
0.999161 | − | 0.0409607i | \(-0.0130418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.87858i | − | 0.827932i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 6.98743i | − | 0.645988i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.06230i | 0.739070i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.29692 | 0.572447 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.92629i | − | 0.444189i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.61133 | 0.497925 | 0.248962 | − | 0.968513i | \(-0.419910\pi\) | ||||
0.248962 | + | 0.968513i | \(0.419910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.57516i | 0.843046i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1751i | 1.15112i | 0.817761 | + | 0.575558i | \(0.195215\pi\) | ||||
−0.817761 | + | 0.575558i | \(0.804785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.8683 | + | 8.70195i | −1.28925 | + | 0.754554i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9976 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.0062i | − | 1.78173i | −0.454273 | − | 0.890863i | \(-0.650101\pi\) | ||
0.454273 | − | 0.890863i | \(-0.349899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.15609i | − | 0.771082i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.1533 | 1.26719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.63276i | 0.467775i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.62061 | 0.711016 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.98236 | 0.490094 | 0.245047 | − | 0.969511i | \(-0.421197\pi\) | ||||
0.245047 | + | 0.969511i | \(0.421197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2317 | 0.995400 | 0.497700 | − | 0.867349i | \(-0.334178\pi\) | ||||
0.497700 | + | 0.867349i | \(0.334178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.03991 | −0.164917 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.31415 | −0.105555 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.13042 | −0.489261 | −0.244630 | − | 0.969616i | \(-0.578667\pi\) | ||||
−0.244630 | + | 0.969616i | \(0.578667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.41448i | − | 0.429396i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −35.0907 | −2.76554 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.47515i | 0.742151i | 0.928603 | + | 0.371076i | \(0.121011\pi\) | ||||
−0.928603 | + | 0.371076i | \(0.878989\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2.16866i | − | 0.168830i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.7817 | −1.68551 | −0.842757 | − | 0.538294i | \(-0.819069\pi\) | ||||
−0.842757 | + | 0.538294i | \(0.819069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.8242 | −2.75571 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.20175 | − | 3.76196i | −0.168372 | − | 0.287684i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4728i | 1.70857i | 0.519802 | + | 0.854287i | \(0.326006\pi\) | ||||
−0.519802 | + | 0.854287i | \(0.673994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.95229i | − | 0.298765i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9348 | 0.972236 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.11079 | 0.232512 | 0.116256 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116256 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.28171i | − | 0.169598i | −0.996398 | − | 0.0847992i | \(-0.972975\pi\) | ||
0.996398 | − | 0.0847992i | \(-0.0270249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.62061 | −0.119799 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.77374i | − | 0.130408i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.42386i | − | 0.323505i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.95229i | 0.287487i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 25.4170i | − | 1.83911i | −0.392960 | − | 0.919555i | \(-0.628549\pi\) | ||
0.392960 | − | 0.919555i | \(-0.371451\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2011i | 0.878256i | 0.898425 | + | 0.439128i | \(0.144713\pi\) | ||||
−0.898425 | + | 0.439128i | \(0.855287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.98743i | 0.500380i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.2941 | −1.65964 | −0.829818 | − | 0.558034i | \(-0.811556\pi\) | ||||
−0.829818 | + | 0.558034i | \(0.811556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.68961i | 0.403326i | 0.979455 | + | 0.201663i | \(0.0646345\pi\) | ||||
−0.979455 | + | 0.201663i | \(0.935365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.56189 | 0.462840 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.2623 | 1.56251 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.92629i | 0.344067i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 8.87858i | − | 0.617104i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.15839 | − | 4.77484i | 0.564328 | − | 0.330282i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4764 | 1.40965 | 0.704827 | − | 0.709379i | \(-0.251025\pi\) | ||||
0.704827 | + | 0.709379i | \(0.251025\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.35406 | 0.366854 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.57516i | − | 0.653021i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19391i | 0.352585i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.95056 | −0.199381 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2537i | 0.958808i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.2530 | −1.62410 | −0.812051 | − | 0.583586i | \(-0.801649\pi\) | ||||
−0.812051 | + | 0.583586i | \(0.801649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0735 | −0.734976 | −0.367488 | − | 0.930028i | \(-0.619782\pi\) | ||||
−0.367488 | + | 0.930028i | \(0.619782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.6524 | −1.36475 | −0.682375 | − | 0.731003i | \(-0.739053\pi\) | ||||
−0.682375 | + | 0.731003i | \(0.739053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.57117 | −0.563941 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.98277 | −0.260920 | −0.130460 | − | 0.991454i | \(-0.541645\pi\) | ||||
−0.130460 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.15609i | 0.597277i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.1906 | −0.726908 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.8555i | − | 0.896241i | −0.893973 | − | 0.448120i | \(-0.852094\pi\) | ||
0.893973 | − | 0.448120i | \(-0.147906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.1943i | − | 0.721091i | −0.932742 | − | 0.360545i | \(-0.882591\pi\) | ||
0.932742 | − | 0.360545i | \(-0.117409\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.62061 | −0.550750 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.2864 | + | 15.3846i | −1.67256 | + | 0.978896i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.37136i | − | 0.277024i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.3655i | − | 1.09610i | −0.836446 | − | 0.548050i | \(-0.815370\pi\) | ||
0.836446 | − | 0.548050i | \(-0.184630\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2546 | 1.21053 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.03991 | 0.127744 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.35467i | − | 0.0845021i | −0.999107 | − | 0.0422510i | \(-0.986547\pi\) | ||
0.999107 | − | 0.0422510i | \(-0.0134529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.01035 | −0.435602 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.63276i | 0.348659i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.19286i | − | 0.320205i | −0.987100 | − | 0.160103i | \(-0.948817\pi\) | ||
0.987100 | − | 0.160103i | \(-0.0511826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.41448i | 0.332609i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.91831i | − | 0.423394i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.931395i | 0.0567882i | 0.999597 | + | 0.0283941i | \(0.00903933\pi\) | ||||
−0.999597 | + | 0.0283941i | \(0.990961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4790i | 1.60848i | 0.594302 | + | 0.804242i | \(0.297428\pi\) | ||||
−0.594302 | + | 0.804242i | \(0.702572\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 27.6164 | 1.67142 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.16866i | 0.130775i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.62871 | 0.398281 | 0.199140 | − | 0.979971i | \(-0.436185\pi\) | ||||
0.199140 | + | 0.979971i | \(0.436185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.31415 | −0.0786762 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.67106i | − | 0.517272i | −0.965975 | − | 0.258636i | \(-0.916727\pi\) | ||
0.965975 | − | 0.258636i | \(-0.0832730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2409i | 1.55986i | 0.625866 | + | 0.779930i | \(0.284746\pi\) | ||||
−0.625866 | + | 0.779930i | \(0.715254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.20175 | + | 3.76196i | 0.130420 | + | 0.222839i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.4701 | 1.14929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8388 | −0.755223 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.0393i | 0.764375i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.0239i | − | 1.40349i | −0.712426 | − | 0.701747i | \(-0.752404\pi\) | ||
0.712426 | − | 0.701747i | \(-0.247596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9348 | −0.753091 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.16866i | − | 0.125838i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −62.0385 | −3.58778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −37.8438 | −2.18128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.88415 | −0.395484 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.62061 | 0.0927956 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6908 | −0.895523 | −0.447761 | − | 0.894153i | \(-0.647779\pi\) | ||||
−0.447761 | + | 0.894153i | \(0.647779\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.56189 | −0.373293 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.71614i | − | 0.324133i | −0.986780 | − | 0.162066i | \(-0.948184\pi\) | ||
0.986780 | − | 0.162066i | \(-0.0518159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.66076 | 0.150395 | 0.0751976 | − | 0.997169i | \(-0.476041\pi\) | ||||
0.0751976 | + | 0.997169i | \(0.476041\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.95229i | − | 0.222686i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 21.7787i | − | 1.22321i | −0.791163 | − | 0.611606i | \(-0.790524\pi\) | ||
0.791163 | − | 0.611606i | \(-0.209476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2155 | −0.683938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.20783 | 0.513931 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.49136 | + | 7.67403i | 0.249906 | + | 0.426995i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.98743i | − | 0.387593i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 17.5873i | − | 0.972578i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.1875 | 1.99508 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6834 | −1.02693 | −0.513467 | − | 0.858109i | \(-0.671639\pi\) | ||||
−0.513467 | + | 0.858109i | \(0.671639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.77374i | − | 0.0972005i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.56189 | −0.358514 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 21.2652i | − | 1.15839i | −0.815189 | − | 0.579195i | \(-0.803367\pi\) | ||
0.815189 | − | 0.579195i | \(-0.196633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.870836i | 0.0472973i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.84994i | − | 0.154333i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.40510i | 0.345843i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.87858i | 0.478007i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.6435i | − | 1.00084i | −0.865784 | − | 0.500418i | \(-0.833180\pi\) | ||
0.865784 | − | 0.500418i | \(-0.166820\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.9270 | 1.81607 | 0.908036 | − | 0.418891i | \(-0.137581\pi\) | ||||
0.908036 | + | 0.418891i | \(0.137581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.98743i | 0.372961i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.05835 | −0.0563303 | −0.0281652 | − | 0.999603i | \(-0.508966\pi\) | ||||
−0.0281652 | + | 0.999603i | \(0.508966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.35406 | −0.284164 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8.06230i | − | 0.426702i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.4331i | − | 1.44786i | −0.689871 | − | 0.723932i | \(-0.742333\pi\) | ||
0.689871 | − | 0.723932i | \(-0.257667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30462 | + | 16.5657i | −0.489717 | + | 0.871882i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.29692 | −0.330503 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.95056 | 0.154439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.09954i | 0.109595i | 0.998497 | + | 0.0547975i | \(0.0174513\pi\) | ||||
−0.998497 | + | 0.0547975i | \(0.982549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.92629i | 0.256452i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.3996 | 1.11101 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.00721i | 0.362820i | 0.983408 | + | 0.181410i | \(0.0580661\pi\) | ||||
−0.983408 | + | 0.181410i | \(0.941934\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.3585 | 2.02707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9907 | −0.718655 | −0.359328 | − | 0.933212i | \(-0.616994\pi\) | ||||
−0.359328 | + | 0.933212i | \(0.616994\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.61133 | −0.287477 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.72187 | −0.394569 | −0.197284 | − | 0.980346i | \(-0.563212\pi\) | ||||
−0.197284 | + | 0.980346i | \(0.563212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.57117 | 0.436827 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 9.57516i | − | 0.486733i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8868 | −0.551983 | −0.275991 | − | 0.961160i | \(-0.589006\pi\) | ||||
−0.275991 | + | 0.961160i | \(0.589006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.1115i | 0.915936i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 13.1751i | − | 0.664597i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.1906 | 0.563060 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7551 | −1.19224 | −0.596118 | − | 0.802897i | \(-0.703291\pi\) | ||||
−0.596118 | + | 0.802897i | \(0.703291\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.8683 | − | 8.70195i | 0.744348 | − | 0.435642i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 26.6810i | − | 1.33238i | −0.745780 | − | 0.666192i | \(-0.767923\pi\) | ||
0.745780 | − | 0.666192i | \(-0.232077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.18254i | 0.457415i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.84664 | 0.190671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 24.1730i | − | 1.19528i | −0.801765 | − | 0.597640i | \(-0.796105\pi\) | ||
0.801765 | − | 0.597640i | \(-0.203895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.9976 | −0.690450 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 51.1219i | 2.51555i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.37136i | 0.214582i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.0062i | 1.02868i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.72367i | 0.133060i | 0.997784 | + | 0.0665300i | \(0.0211928\pi\) | ||||
−0.997784 | + | 0.0665300i | \(0.978807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 31.1453i | − | 1.51793i | −0.651131 | − | 0.758966i | \(-0.725705\pi\) | ||
0.651131 | − | 0.758966i | \(-0.274295\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.15609i | 0.445184i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.03991 | −0.0989500 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.40510i | − | 0.309965i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.1533 | −0.731611 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.7900 | 0.760578 | 0.380289 | − | 0.924868i | \(-0.375824\pi\) | ||||
0.380289 | + | 0.924868i | \(0.375824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.1696i | − | 1.78626i | −0.449801 | − | 0.893129i | \(-0.648505\pi\) | ||
0.449801 | − | 0.893129i | \(-0.351495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.63276i | − | 0.270070i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −33.4008 | + | 19.5484i | −1.59778 | + | 0.935127i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.94673 | 0.331549 | 0.165775 | − | 0.986164i | \(-0.446988\pi\) | ||||
0.165775 | + | 0.986164i | \(0.446988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.62061 | −0.410505 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3896i | 0.826206i | 0.910684 | + | 0.413103i | \(0.135555\pi\) | ||||
−0.910684 | + | 0.413103i | \(0.864445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.91831i | 0.327959i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.98236 | −0.282956 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.9370i | 0.988079i | 0.869439 | + | 0.494040i | \(0.164480\pi\) | ||||
−0.869439 | + | 0.494040i | \(0.835520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6834 | −0.503064 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.2317 | −0.574694 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.6164 | −1.29468 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.09321 | 0.0979162 | 0.0489581 | − | 0.998801i | \(-0.484410\pi\) | ||||
0.0489581 | + | 0.998801i | \(0.484410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.03991 | 0.0952146 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2212 | −0.708923 | −0.354462 | − | 0.935071i | \(-0.615336\pi\) | ||||
−0.354462 | + | 0.935071i | \(0.615336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.1211i | − | 1.07453i | −0.843415 | − | 0.537263i | \(-0.819458\pi\) | ||
0.843415 | − | 0.537263i | \(-0.180542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.31415 | 0.0609423 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.8388i | 1.10313i | 0.834133 | + | 0.551563i | \(0.185968\pi\) | ||||
−0.834133 | + | 0.551563i | \(0.814032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.9345i | 1.19754i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.13042 | 0.282475 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.7652 | 0.954787 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.20175 | − | 3.76196i | −0.101023 | − | 0.172610i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.41448i | 0.247912i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 3.04636i | − | 0.139192i | −0.997575 | − | 0.0695959i | \(-0.977829\pi\) | ||
0.997575 | − | 0.0695959i | \(-0.0221710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.3939 | −0.565113 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.0907 | 1.59668 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.0393i | − | 0.592082i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7706 | 1.43967 | 0.719833 | − | 0.694148i | \(-0.244219\pi\) | ||||
0.719833 | + | 0.694148i | \(0.244219\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.47515i | − | 0.428481i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.9060i | − | 0.898347i | −0.893445 | − | 0.449174i | \(-0.851718\pi\) | ||
0.893445 | − | 0.449174i | \(-0.148282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.4903i | − | 0.517497i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.16866i | 0.0974739i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.1608i | 0.949191i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.90847i | 0.443564i | 0.975096 | + | 0.221782i | \(0.0711873\pi\) | ||||
−0.975096 | + | 0.221782i | \(0.928813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.7817 | 0.973132 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.97119i | − | 0.0878911i | −0.999034 | − | 0.0439456i | \(-0.986007\pi\) | ||
0.999034 | − | 0.0439456i | \(-0.0139928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.88415 | 0.306341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.8242 | 1.59101 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 23.7299i | − | 1.05181i | −0.850544 | − | 0.525905i | \(-0.823727\pi\) | ||
0.850544 | − | 0.525905i | \(-0.176273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 11.6615i | − | 0.515874i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.20175 | + | 3.76196i | 0.0972095 | + | 0.166094i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.56189 | 0.289151 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.8564 | −0.873285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.4728i | − | 0.986445i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.2733i | 1.45773i | 0.684657 | + | 0.728865i | \(0.259952\pi\) | ||||
−0.684657 | + | 0.728865i | \(0.740048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.3328 | 1.76363 | 0.881816 | − | 0.471594i | \(-0.156321\pi\) | ||||
0.881816 | + | 0.471594i | \(0.156321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.95229i | 0.172492i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.68074 | 0.116775 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.8292 | −2.42736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.9348 | −0.561321 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.4221 | 1.49099 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.20783 | −0.398089 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.11079 | −0.134241 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 18.6951i | − | 0.805257i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3966 | 0.790932 | 0.395466 | − | 0.918481i | \(-0.370583\pi\) | ||||
0.395466 | + | 0.918481i | \(0.370583\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.28171i | 0.0979177i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.5873i | 0.753355i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.64717 | −0.369726 | −0.184863 | − | 0.982764i | \(-0.559184\pi\) | ||||
−0.184863 | + | 0.982764i | \(0.559184\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.62061 | 0.0691658 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.1902 | − | 12.4019i | 0.902732 | − | 0.528339i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 44.2285i | − | 1.88079i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.77374i | 0.0752912i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.6277 | −1.21300 | −0.606498 | − | 0.795085i | \(-0.707426\pi\) | ||||
−0.606498 | + | 0.795085i | \(0.707426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −66.9058 | −2.82981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.42386i | 0.186775i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.69899 | −0.408764 | −0.204382 | − | 0.978891i | \(-0.565518\pi\) | ||||
−0.204382 | + | 0.978891i | \(0.565518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.870836i | − | 0.0366363i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.95229i | − | 0.165981i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.1831i | 0.678431i | 0.940709 | + | 0.339215i | \(0.110162\pi\) | ||||
−0.940709 | + | 0.339215i | \(0.889838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.53056i | 0.231447i | 0.993281 | + | 0.115723i | \(0.0369186\pi\) | ||||
−0.993281 | + | 0.115723i | \(0.963081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.4170i | 1.06181i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.87858i | − | 0.370262i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.8363 | −0.451121 | −0.225560 | − | 0.974229i | \(-0.572421\pi\) | ||||
−0.225560 | + | 0.974229i | \(0.572421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 12.2011i | − | 0.507061i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2769 | 0.716766 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7422 | −0.486310 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6.98743i | − | 0.288895i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.2720i | 1.82730i | 0.406500 | + | 0.913651i | \(0.366749\pi\) | ||||
−0.406500 | + | 0.913651i | \(0.633251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.89343 | + | 4.94378i | 0.119222 | + | 0.203705i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2941 | 0.958191 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.1477 | 0.539912 | 0.269956 | − | 0.962873i | \(-0.412991\pi\) | ||||
0.269956 | + | 0.962873i | \(0.412991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.06230i | 0.330522i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 5.68961i | − | 0.232860i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0279 | −0.654883 | −0.327441 | − | 0.944872i | \(-0.606186\pi\) | ||||
−0.327441 | + | 0.944872i | \(0.606186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.74553i | − | 0.315947i | −0.987443 | − | 0.157973i | \(-0.949504\pi\) | ||
0.987443 | − | 0.157973i | \(-0.0504960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.56189 | −0.267221 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.29692 | 0.256006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.88150 | 0.198134 | 0.0990670 | − | 0.995081i | \(-0.468414\pi\) | ||||
0.0990670 | + | 0.995081i | \(0.468414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.2623 | −0.902114 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.9775 | 2.58825 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.2515 | −0.777563 | −0.388781 | − | 0.921330i | \(-0.627104\pi\) | ||||
−0.388781 | + | 0.921330i | \(0.627104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.92629i | − | 0.198647i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.1822 | −0.772248 | −0.386124 | − | 0.922447i | \(-0.626186\pi\) | ||||
−0.386124 | + | 0.922447i | \(0.626186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0144i | 0.442705i | 0.975194 | + | 0.221353i | \(0.0710472\pi\) | ||||
−0.975194 | + | 0.221353i | \(0.928953\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.87858i | 0.356285i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.3432 | 1.09548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.15839 | + | 4.77484i | −0.325815 | + | 0.190689i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.61827i | 0.144270i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9494i | 0.595127i | 0.954702 | + | 0.297563i | \(0.0961740\pi\) | ||||
−0.954702 | + | 0.297563i | \(0.903826\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4764 | −0.813864 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.61133 | 0.222679 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 60.2359i | 2.38663i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.35406 | −0.211803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42.1693i | − | 1.66559i | −0.553584 | − | 0.832794i | \(-0.686740\pi\) | ||
0.553584 | − | 0.832794i | \(-0.313260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.9247i | 0.667446i | 0.942671 | + | 0.333723i | \(0.108305\pi\) | ||||
−0.942671 | + | 0.333723i | \(0.891695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.57516i | 0.377022i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.87195i | 0.230850i | 0.993316 | + | 0.115425i | \(0.0368230\pi\) | ||||
−0.993316 | + | 0.115425i | \(0.963177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.0511i | − | 1.10110i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 5.19391i | − | 0.203565i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.4871 | 1.34959 | 0.674793 | − | 0.738007i | \(-0.264233\pi\) | ||||
0.674793 | + | 0.738007i | \(0.264233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.1751i | 0.514795i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.95056 | 0.115112 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.72034 | 0.222833 | 0.111416 | − | 0.993774i | \(-0.464461\pi\) | ||||
0.111416 | + | 0.993774i | \(0.464461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5610i | 0.916415i | 0.888845 | + | 0.458208i | \(0.151508\pi\) | ||||
−0.888845 | + | 0.458208i | \(0.848492\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 14.2537i | − | 0.553568i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.8683 | + | 8.70195i | −0.576570 | + | 0.337447i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.0109 | 1.93643 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.2530 | 0.937676 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.51454i | 0.135677i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.9200i | − | 1.34607i | −0.739611 | − | 0.673034i | \(-0.764991\pi\) | ||
0.739611 | − | 0.673034i | \(-0.235009\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.6191i | 1.52269i | 0.648349 | + | 0.761343i | \(0.275460\pi\) | ||||
−0.648349 | + | 0.761343i | \(0.724540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.5350 | −1.97773 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0735 | 0.424339 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.9690 | 0.457980 | 0.228990 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228990 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.9976 | 0.534821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.6524 | 0.787938 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.8333 | 1.44133 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6282i | 0.480399i | 0.970724 | + | 0.240200i | \(0.0772129\pi\) | ||||
−0.970724 | + | 0.240200i | \(0.922787\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.57117 | 0.325592 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21.0062i | − | 0.796812i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.0492i | − | 0.380639i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.98277 | 0.150642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.33677 | −0.314875 | −0.157438 | − | 0.987529i | \(-0.550323\pi\) | ||||
−0.157438 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.67274 | + | 3.90533i | −0.251667 | + | 0.147292i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 9.15609i | − | 0.344838i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 27.2082i | − | 1.02327i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.89450 | −0.371596 | −0.185798 | − | 0.982588i | \(-0.559487\pi\) | ||||
−0.185798 | + | 0.982588i | \(0.559487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.1906 | 0.419680 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6678i | 0.436962i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.1533 | 0.566703 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.8555i | 0.517445i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.30971i | − | 0.123431i | −0.998094 | − | 0.0617157i | \(-0.980343\pi\) | ||
0.998094 | − | 0.0617157i | \(-0.0196572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 25.9345i | − | 0.965851i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1943i | 0.416322i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.63276i | 0.209195i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.2801i | 1.45682i | 0.685143 | + | 0.728409i | \(0.259740\pi\) | ||||
−0.685143 | + | 0.728409i | \(0.740260\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.5324i | 0.722433i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.89079 | −0.0698379 | −0.0349189 | − | 0.999390i | \(-0.511117\pi\) | ||||
−0.0349189 | + | 0.999390i | \(0.511117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.62061 | 0.317976 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 14.2305i | − | 0.524187i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.4982i | 1.04832i | 0.851619 | + | 0.524161i | \(0.175621\pi\) | ||||
−0.851619 | + | 0.524161i | \(0.824379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.2864 | − | 15.3846i | 0.965655 | − | 0.565166i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.36639 | −0.160187 | −0.0800936 | − | 0.996787i | \(-0.525522\pi\) | ||||
−0.0800936 | + | 0.996787i | \(0.525522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.98236 | 0.219177 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.37136i | 0.159940i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.3920i | 1.32974i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.16726 | 0.0790845 | 0.0395422 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395422 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3655i | 0.632834i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2317 | 0.445156 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.5274 | 1.54568 | 0.772842 | − | 0.634599i | \(-0.218835\pi\) | ||||
0.772842 | + | 0.634599i | \(0.218835\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.2546 | −0.698898 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7893 | 0.681113 | 0.340557 | − | 0.940224i | \(-0.389384\pi\) | ||||
0.340557 | + | 0.940224i | \(0.389384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 69.5100 | 2.51643 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.03991 | −0.0737529 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 90.3807i | 3.26346i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0559 | 1.58870 | 0.794349 | − | 0.607462i | \(-0.207812\pi\) | ||||
0.794349 | + | 0.607462i | \(0.207812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.35467i | 0.0487873i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.9855i | − | 1.15044i | −0.817999 | − | 0.575220i | \(-0.804916\pi\) | ||
0.817999 | − | 0.575220i | \(-0.195084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.31415 | −0.0472057 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.01035 | 0.251495 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.5325 | − | 10.8464i | 0.663995 | − | 0.388614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.6111i | − | 0.415478i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.63276i | − | 0.201298i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.13042 | −0.218804 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.82963 | 0.136512 | 0.0682558 | − | 0.997668i | \(-0.478257\pi\) | ||||
0.0682558 | + | 0.997668i | \(0.478257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.19286i | 0.184871i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.44180 | −0.122376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.3239i | − | 0.402122i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 5.41448i | − | 0.192032i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2446i | 0.858788i | 0.903117 | + | 0.429394i | \(0.141273\pi\) | ||||
−0.903117 | + | 0.429394i | \(0.858727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.6776i | − | 0.660765i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.91831i | 0.244447i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.39876i | 0.225807i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.0907 | −1.23679 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 0.931395i | − | 0.0327867i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.6643 | 0.691361 | 0.345681 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345681 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.14796 | 0.145655 | 0.0728273 | − | 0.997345i | \(-0.476798\pi\) | ||||
0.0728273 | + | 0.997345i | \(0.476798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 26.4790i | − | 0.928658i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.47515i | 0.331900i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0213 | + | 21.0821i | −1.26023 | + | 0.737569i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.6164 | −0.964994 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.77273 | 0.236370 | 0.118185 | − | 0.992992i | \(-0.462292\pi\) | ||||
0.118185 | + | 0.992992i | \(0.462292\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.4578i | − | 0.364536i | −0.983249 | − | 0.182268i | \(-0.941656\pi\) | ||
0.983249 | − | 0.182268i | \(-0.0583438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.16866i | − | 0.0755030i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.0931 | −1.95055 | −0.975274 | − | 0.220997i | \(-0.929069\pi\) | ||||
−0.975274 | + | 0.220997i | \(0.929069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.6745i | 0.856981i | 0.903546 | + | 0.428491i | \(0.140955\pi\) | ||||
−0.903546 | + | 0.428491i | \(0.859045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.62871 | −0.229948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.5852 | 0.609292 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.7817 | −0.753785 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.31415 | 0.0454237 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.9966 | 0.483217 | 0.241608 | − | 0.970374i | \(-0.422325\pi\) | ||||
0.241608 | + | 0.970374i | \(0.422325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.72798 | −0.0940683 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.67106i | 0.298647i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.8242 | −1.23239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24.8873i | − | 0.855137i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 26.2409i | − | 0.900586i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.7483 | −0.539845 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.62871 | 0.226963 | 0.113481 | − | 0.993540i | \(-0.463800\pi\) | ||||
0.113481 | + | 0.993540i | \(0.463800\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.20175 | − | 3.76196i | −0.0752982 | − | 0.128656i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 52.9338i | − | 1.80818i | −0.427338 | − | 0.904092i | \(-0.640548\pi\) | ||
0.427338 | − | 0.904092i | \(-0.359452\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.9080i | − | 0.849851i | −0.905228 | − | 0.424925i | \(-0.860300\pi\) | ||
0.905228 | − | 0.424925i | \(-0.139700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.4701 | −0.663541 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.7187 | 1.52224 | 0.761121 | − | 0.648610i | \(-0.224649\pi\) | ||||
0.761121 | + | 0.648610i | \(0.224649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.4728i | 0.764097i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.8388 | 0.436028 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.2686i | 0.823256i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.8507i | 1.55359i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.0393i | − | 0.441312i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.95229i | − | 0.133612i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20.8670i | − | 0.704630i | −0.935881 | − | 0.352315i | \(-0.885395\pi\) | ||
0.935881 | − | 0.352315i | \(-0.114605\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.0239i | 0.810308i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.2852 | 1.28986 | 0.644930 | − | 0.764241i | \(-0.276886\pi\) | ||||
0.644930 | + | 0.764241i | \(0.276886\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.0029i | − | 1.54812i | −0.633111 | − | 0.774061i | \(-0.718222\pi\) | ||
0.633111 | − | 0.774061i | \(-0.281778\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.9348 | 0.434797 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.4722 | 1.62754 | 0.813768 | − | 0.581190i | \(-0.197413\pi\) | ||||
0.813768 | + | 0.581190i | \(0.197413\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 22.1776i | − | 0.743813i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.16866i | 0.0726528i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.4448 | − | 20.1594i | 1.15265 | − | 0.674608i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.11079 | 0.103982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 62.0385 | 2.07140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.40230i | − | 0.246880i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.0450i | − | 0.367963i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.8438 | 1.25936 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.28171i | − | 0.0758467i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5139 | 1.07961 | 0.539803 | − | 0.841792i | \(-0.318499\pi\) | ||||
0.539803 | + | 0.841792i | \(0.318499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.88415 | 0.228333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.4971 | −0.447177 | −0.223589 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223589 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.47999 | −0.313742 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.62061 | −0.0535756 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.0719 | 1.71957 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.05976i | − | 0.0349583i | −0.999847 | − | 0.0174792i | \(-0.994436\pi\) | ||
0.999847 | − | 0.0174792i | \(-0.00556408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.6908 | 0.517030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.4111i | 1.23140i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.77374i | − | 0.0583203i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.56189 | 0.215521 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.3492 | 1.29101 | 0.645503 | − | 0.763757i | \(-0.276648\pi\) | ||||
0.645503 | + | 0.763757i | \(0.276648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9804 | + | 32.4303i | 0.622057 | + | 1.06286i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.71614i | 0.187138i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.42386i | − | 0.144676i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.6710 | −0.413944 | −0.206972 | − | 0.978347i | \(-0.566361\pi\) | ||||
−0.206972 | + | 0.978347i | \(0.566361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.66076 | −0.0868308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.5980i | − | 0.932268i | −0.884714 | − | 0.466134i | \(-0.845646\pi\) | ||
0.884714 | − | 0.466134i | \(-0.154354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.7385 | 1.42432 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.95229i | 0.128568i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 31.7407i | − | 1.03143i | −0.856759 | − | 0.515717i | \(-0.827526\pi\) | ||
0.856759 | − | 0.515717i | \(-0.172474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 20.6169i | − | 0.669251i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7787i | 0.706221i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 59.1874i | − | 1.91727i | −0.284642 | − | 0.958634i | \(-0.591875\pi\) | ||
0.284642 | − | 0.958634i | \(-0.408125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 25.4170i | − | 0.822475i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.2155 | 0.394872 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 55.3226i | − | 1.78646i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2730 | −0.944291 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.20783 | −0.296718 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.2011i | 0.392768i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4451i | 0.753943i | 0.926225 | + | 0.376972i | \(0.123035\pi\) | ||||
−0.926225 | + | 0.376972i | \(0.876965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.49136 | − | 7.67403i | −0.144283 | − | 0.246526i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.0763 | −0.740555 | −0.370277 | − | 0.928921i | \(-0.620737\pi\) | ||||
−0.370277 | + | 0.928921i | \(0.620737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −83.0227 | −2.66159 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.98743i | 0.223777i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 52.1745i | − | 1.66921i | −0.550848 | − | 0.834606i | \(-0.685695\pi\) | ||
0.550848 | − | 0.834606i | \(-0.314305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.0035 | −0.479512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.5873i | 0.561518i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.6841 | −0.436455 | −0.218228 | − | 0.975898i | \(-0.570028\pi\) | ||||
−0.218228 | + | 0.975898i | \(0.570028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2941 | −0.742212 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.1875 | −1.15186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −85.0139 | −2.70328 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0734 | 1.52710 | 0.763550 | − | 0.645748i | \(-0.223455\pi\) | ||||
0.763550 | + | 0.645748i | \(0.223455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6834 | 0.592901 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.68961i | 0.180373i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.43801 | 0.108883 | 0.0544414 | − | 0.998517i | \(-0.482662\pi\) | ||||
0.0544414 | + | 0.998517i | \(0.482662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77374i | 0.0561187i |
(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 | 4560.2.d.j.2431.2 | ✓ | 12 | |
4.3 | odd | 2 | 4560.2.d.l.2431.11 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.l.2431.2 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.j.2431.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.j.2431.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.j.2431.11 | yes | 12 | 76.75 | even | 2 | inner | |
4560.2.d.l.2431.2 | yes | 12 | 19.18 | odd | 2 | ||
4560.2.d.l.2431.11 | yes | 12 | 4.3 | odd | 2 |