Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.13 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.13 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.667815 | + | 0.667815i | 0.298656 | + | 0.298656i | 0.840487 | − | 0.541831i | \(-0.182269\pi\) |
−0.541831 | + | 0.840487i | \(0.682269\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.57551 | + | 1.57551i | −0.475033 | + | 0.475033i | −0.903539 | − | 0.428506i | \(-0.859040\pi\) |
0.428506 | + | 0.903539i | \(0.359040\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.83034 | − | 1.83034i | −0.507644 | − | 0.507644i | 0.406159 | − | 0.913803i | \(-0.366868\pi\) |
−0.913803 | + | 0.406159i | \(0.866868\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.40687i | − | 0.826287i | −0.910666 | − | 0.413143i | \(-0.864431\pi\) | ||
0.910666 | − | 0.413143i | \(-0.135569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.18485 | + | 3.18485i | −0.730656 | + | 0.730656i | −0.970750 | − | 0.240094i | \(-0.922822\pi\) |
0.240094 | + | 0.970750i | \(0.422822\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.793288i | − | 0.165412i | −0.996574 | − | 0.0827060i | \(-0.973644\pi\) | ||
0.996574 | − | 0.0827060i | \(-0.0263562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.10805i | − | 0.821609i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.73542 | + | 1.73542i | −0.322260 | + | 0.322260i | −0.849634 | − | 0.527373i | \(-0.823177\pi\) |
0.527373 | + | 0.849634i | \(0.323177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28367i | 0.589765i | 0.955534 | + | 0.294882i | \(0.0952805\pi\) | ||||
−0.955534 | + | 0.294882i | \(0.904720\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.667815 | − | 0.667815i | −0.112881 | − | 0.112881i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.72049 | − | 7.72049i | 1.26924 | − | 1.26924i | 0.322760 | − | 0.946481i | \(-0.395389\pi\) |
0.946481 | − | 0.322760i | \(-0.104611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.19799 | 1.12414 | 0.562069 | − | 0.827091i | \(-0.310006\pi\) | ||||
0.562069 | + | 0.827091i | \(0.310006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.84265 | + | 5.84265i | 0.890996 | + | 0.890996i | 0.994617 | − | 0.103621i | \(-0.0330430\pi\) |
−0.103621 | + | 0.994617i | \(0.533043\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.0051 | 1.89699 | 0.948497 | − | 0.316786i | \(-0.102604\pi\) | ||||
0.948497 | + | 0.316786i | \(0.102604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.34052 | + | 3.34052i | 0.458856 | + | 0.458856i | 0.898280 | − | 0.439424i | \(-0.144817\pi\) |
−0.439424 | + | 0.898280i | \(0.644817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.10430 | −0.283743 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.41533 | − | 7.41533i | 0.965394 | − | 0.965394i | −0.0340273 | − | 0.999421i | \(-0.510833\pi\) |
0.999421 | + | 0.0340273i | \(0.0108333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.93050 | + | 1.93050i | 0.247175 | + | 0.247175i | 0.819810 | − | 0.572635i | \(-0.194079\pi\) |
−0.572635 | + | 0.819810i | \(0.694079\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.44465i | − | 0.303222i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.38033 | + | 6.38033i | −0.779481 | + | 0.779481i | −0.979742 | − | 0.200262i | \(-0.935821\pi\) |
0.200262 | + | 0.979742i | \(0.435821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.41542i | − | 0.405336i | −0.979247 | − | 0.202668i | \(-0.935039\pi\) | ||
0.979247 | − | 0.202668i | \(-0.0649612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.13689i | 0.952351i | 0.879350 | + | 0.476176i | \(0.157977\pi\) | ||||
−0.879350 | + | 0.476176i | \(0.842023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.57551 | − | 1.57551i | 0.179546 | − | 0.179546i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.0502773i | − | 0.00565663i | −0.999996 | − | 0.00282832i | \(-0.999100\pi\) | ||
0.999996 | − | 0.00282832i | \(-0.000900282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.29129 | − | 2.29129i | −0.251502 | − | 0.251502i | 0.570084 | − | 0.821586i | \(-0.306911\pi\) |
−0.821586 | + | 0.570084i | \(0.806911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.27516 | − | 2.27516i | 0.246776 | − | 0.246776i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.18090 | −0.761174 | −0.380587 | − | 0.924745i | \(-0.624278\pi\) | ||||
−0.380587 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.83034 | + | 1.83034i | 0.191871 | + | 0.191871i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.25379 | −0.436429 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.49996 | 0.152298 | 0.0761490 | − | 0.997096i | \(-0.475738\pi\) | ||||
0.0761490 | + | 0.997096i | \(0.475738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.08005 | + | 6.08005i | 0.604988 | + | 0.604988i | 0.941632 | − | 0.336644i | \(-0.109292\pi\) |
−0.336644 | + | 0.941632i | \(0.609292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74912 | 0.763543 | 0.381772 | − | 0.924257i | \(-0.375314\pi\) | ||||
0.381772 | + | 0.924257i | \(0.375314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.05853 | − | 2.05853i | 0.199006 | − | 0.199006i | −0.600568 | − | 0.799574i | \(-0.705059\pi\) |
0.799574 | + | 0.600568i | \(0.205059\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.13047 | + | 7.13047i | 0.682975 | + | 0.682975i | 0.960670 | − | 0.277694i | \(-0.0895702\pi\) |
−0.277694 | + | 0.960670i | \(0.589570\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.17748i | − | 0.392984i | −0.980505 | − | 0.196492i | \(-0.937045\pi\) | ||
0.980505 | − | 0.196492i | \(-0.0629550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.529770 | − | 0.529770i | 0.0494013 | − | 0.0494013i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.40687i | 0.312307i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.03555i | 0.548686i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.08249 | − | 6.08249i | 0.544035 | − | 0.544035i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.16063i | 0.457932i | 0.973434 | + | 0.228966i | \(0.0735345\pi\) | ||||
−0.973434 | + | 0.228966i | \(0.926466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.53587 | − | 1.53587i | −0.134189 | − | 0.134189i | 0.636822 | − | 0.771011i | \(-0.280249\pi\) |
−0.771011 | + | 0.636822i | \(0.780249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.18485 | − | 3.18485i | 0.276162 | − | 0.276162i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0645 | 1.71423 | 0.857113 | − | 0.515128i | \(-0.172256\pi\) | ||||
0.857113 | + | 0.515128i | \(0.172256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.01947 | + | 3.01947i | 0.256108 | + | 0.256108i | 0.823469 | − | 0.567361i | \(-0.192036\pi\) |
−0.567361 | + | 0.823469i | \(0.692036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.76742 | 0.482296 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.31789 | −0.192490 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.11391 | + | 2.11391i | 0.173178 | + | 0.173178i | 0.788374 | − | 0.615196i | \(-0.210923\pi\) |
−0.615196 | + | 0.788374i | \(0.710923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.08056 | −0.576208 | −0.288104 | − | 0.957599i | \(-0.593025\pi\) | ||||
−0.288104 | + | 0.957599i | \(0.593025\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.19289 | + | 2.19289i | −0.176137 | + | 0.176137i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0565 | + | 16.0565i | 1.28144 | + | 1.28144i | 0.939846 | + | 0.341598i | \(0.110968\pi\) |
0.341598 | + | 0.939846i | \(0.389032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.793288i | 0.0625199i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9257 | + | 10.9257i | −0.855764 | + | 0.855764i | −0.990836 | − | 0.135072i | \(-0.956873\pi\) |
0.135072 | + | 0.990836i | \(0.456873\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.8556i | − | 1.14956i | −0.818307 | − | 0.574782i | \(-0.805087\pi\) | ||
0.818307 | − | 0.574782i | \(-0.194913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.29974i | − | 0.484595i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.49652 | − | 2.49652i | 0.189807 | − | 0.189807i | −0.605806 | − | 0.795613i | \(-0.707149\pi\) |
0.795613 | + | 0.605806i | \(0.207149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.10805i | 0.310539i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5658 | − | 13.5658i | −1.01396 | − | 1.01396i | −0.999901 | − | 0.0140578i | \(-0.995525\pi\) |
−0.0140578 | − | 0.999901i | \(-0.504475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.13837 | + | 4.13837i | −0.307602 | + | 0.307602i | −0.843979 | − | 0.536376i | \(-0.819793\pi\) |
0.536376 | + | 0.843979i | \(0.319793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.3117 | 0.758133 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.36755 | + | 5.36755i | 0.392514 | + | 0.392514i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9065 | 1.58510 | 0.792549 | − | 0.609808i | \(-0.208754\pi\) | ||||
0.792549 | + | 0.609808i | \(0.208754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1429 | −1.52190 | −0.760950 | − | 0.648811i | \(-0.775267\pi\) | ||||
−0.760950 | + | 0.648811i | \(0.775267\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.95026 | + | 4.95026i | 0.352692 | + | 0.352692i | 0.861110 | − | 0.508418i | \(-0.169770\pi\) |
−0.508418 | + | 0.861110i | \(0.669770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.6455 | −0.754639 | −0.377319 | − | 0.926083i | \(-0.623154\pi\) | ||||
−0.377319 | + | 0.926083i | \(0.623154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.73542 | − | 1.73542i | 0.121803 | − | 0.121803i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.80693 | + | 4.80693i | 0.335730 | + | 0.335730i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.0355i | − | 0.694172i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.563683 | + | 0.563683i | −0.0388056 | + | 0.0388056i | −0.726243 | − | 0.687438i | \(-0.758735\pi\) |
0.687438 | + | 0.726243i | \(0.258735\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.80362i | 0.532202i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.28367i | − | 0.222910i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.23571 | + | 6.23571i | −0.419459 | + | 0.419459i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.6604i | − | 1.45049i | −0.688493 | − | 0.725243i | \(-0.741727\pi\) | ||
0.688493 | − | 0.725243i | \(-0.258273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.98117 | − | 2.98117i | −0.197867 | − | 0.197867i | 0.601218 | − | 0.799085i | \(-0.294682\pi\) |
−0.799085 | + | 0.601218i | \(0.794682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1998 | + | 10.1998i | −0.674019 | + | 0.674019i | −0.958640 | − | 0.284621i | \(-0.908132\pi\) |
0.284621 | + | 0.958640i | \(0.408132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9408 | 1.10983 | 0.554914 | − | 0.831907i | \(-0.312751\pi\) | ||||
0.554914 | + | 0.831907i | \(0.312751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.68503 | + | 8.68503i | 0.566549 | + | 0.566549i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7743 | 0.761618 | 0.380809 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380809 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.77496 | −0.114335 | −0.0571677 | − | 0.998365i | \(-0.518207\pi\) | ||||
−0.0571677 | + | 0.998365i | \(0.518207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.667815 | + | 0.667815i | 0.0426652 | + | 0.0426652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.6587 | 0.741826 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.7495 | + | 10.7495i | −0.678503 | + | 0.678503i | −0.959661 | − | 0.281158i | \(-0.909281\pi\) |
0.281158 | + | 0.959661i | \(0.409281\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.24983 | + | 1.24983i | 0.0785762 | + | 0.0785762i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 23.2878i | − | 1.45265i | −0.687351 | − | 0.726325i | \(-0.741227\pi\) | ||
0.687351 | − | 0.726325i | \(-0.258773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.72049 | + | 7.72049i | −0.479728 | + | 0.479728i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.00910i | − | 0.308874i | −0.988003 | − | 0.154437i | \(-0.950644\pi\) | ||
0.988003 | − | 0.154437i | \(-0.0493564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.46170i | 0.274080i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1632 | − | 11.1632i | 0.680633 | − | 0.680633i | −0.279510 | − | 0.960143i | \(-0.590172\pi\) |
0.960143 | + | 0.279510i | \(0.0901718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.1939i | − | 0.983706i | −0.870678 | − | 0.491853i | \(-0.836320\pi\) | ||
0.870678 | − | 0.491853i | \(-0.163680\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.47226 | + | 6.47226i | 0.390292 | + | 0.390292i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0299 | − | 19.0299i | 1.14339 | − | 1.14339i | 0.155568 | − | 0.987825i | \(-0.450279\pi\) |
0.987825 | − | 0.155568i | \(-0.0497207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3974 | −0.858875 | −0.429438 | − | 0.903097i | \(-0.641288\pi\) | ||||
−0.429438 | + | 0.903097i | \(0.641288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.2690 | + | 21.2690i | 1.26431 | + | 1.26431i | 0.948982 | + | 0.315331i | \(0.102116\pi\) |
0.315331 | + | 0.948982i | \(0.397884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.19799 | −0.424884 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.39325 | 0.317250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9536 | + | 18.9536i | 1.10728 | + | 1.10728i | 0.993507 | + | 0.113775i | \(0.0362942\pi\) |
0.113775 | + | 0.993507i | \(0.463706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.90414 | 0.576641 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.45198 | + | 1.45198i | −0.0839704 | + | 0.0839704i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.84265 | − | 5.84265i | −0.336765 | − | 0.336765i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.57843i | 0.147641i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.90363 | − | 7.90363i | 0.451084 | − | 0.451084i | −0.444630 | − | 0.895714i | \(-0.646665\pi\) |
0.895714 | + | 0.444630i | \(0.146665\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.8764i | − | 1.41061i | −0.708904 | − | 0.705305i | \(-0.750810\pi\) | ||
0.708904 | − | 0.705305i | \(-0.249190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.7289i | 1.62385i | 0.583759 | + | 0.811927i | \(0.301581\pi\) | ||||
−0.583759 | + | 0.811927i | \(0.698419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.354075 | − | 0.354075i | 0.0198869 | − | 0.0198869i | −0.697093 | − | 0.716980i | \(-0.745524\pi\) |
0.716980 | + | 0.697093i | \(0.245524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.46835i | − | 0.306169i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8504 | + | 10.8504i | 0.603731 | + | 0.603731i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.51910 | + | 7.51910i | −0.417085 | + | 0.417085i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.0051 | −0.716996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1492 | + | 11.1492i | 0.612818 | + | 0.612818i | 0.943679 | − | 0.330862i | \(-0.107339\pi\) |
−0.330862 | + | 0.943679i | \(0.607339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.52176 | −0.465593 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.8646 | −1.79025 | −0.895124 | − | 0.445817i | \(-0.852913\pi\) | ||||
−0.895124 | + | 0.445817i | \(0.852913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.17345 | − | 5.17345i | −0.280158 | − | 0.280158i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.4329 | + | 11.4329i | −0.613751 | + | 0.613751i | −0.943921 | − | 0.330170i | \(-0.892894\pi\) |
0.330170 | + | 0.943921i | \(0.392894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4418 | + | 19.4418i | 1.04070 | + | 1.04070i | 0.999136 | + | 0.0415602i | \(0.0132328\pi\) |
0.0415602 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.70827i | − | 0.516719i | −0.966049 | − | 0.258360i | \(-0.916818\pi\) | ||
0.966049 | − | 0.258360i | \(-0.0831819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.28087 | − | 2.28087i | 0.121056 | − | 0.121056i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.535153i | 0.0282443i | 0.999900 | + | 0.0141222i | \(0.00449537\pi\) | ||||
−0.999900 | + | 0.0141222i | \(0.995505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.28659i | − | 0.0677152i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.43394 | + | 5.43394i | −0.284426 | + | 0.284426i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.3854i | − | 0.750913i | −0.926840 | − | 0.375456i | \(-0.877486\pi\) | ||
0.926840 | − | 0.375456i | \(-0.122514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.34052 | − | 3.34052i | −0.173431 | − | 0.173431i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7345 | − | 12.7345i | 0.659368 | − | 0.659368i | −0.295862 | − | 0.955231i | \(-0.595607\pi\) |
0.955231 | + | 0.295862i | \(0.0956070\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.35282 | 0.327187 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4758 | − | 18.4758i | −0.949037 | − | 0.949037i | 0.0497262 | − | 0.998763i | \(-0.484165\pi\) |
−0.998763 | + | 0.0497262i | \(0.984165\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.0133 | 1.48251 | 0.741256 | − | 0.671222i | \(-0.234230\pi\) | ||||
0.741256 | + | 0.671222i | \(0.234230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.10430 | 0.107245 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.75723 | − | 7.75723i | −0.393307 | − | 0.393307i | 0.482557 | − | 0.875864i | \(-0.339708\pi\) |
−0.875864 | + | 0.482557i | \(0.839708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.70263 | −0.136678 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0335759 | − | 0.0335759i | 0.00168939 | − | 0.00168939i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0436 | + | 13.0436i | 0.654638 | + | 0.654638i | 0.954106 | − | 0.299468i | \(-0.0968093\pi\) |
−0.299468 | + | 0.954106i | \(0.596809\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.31443i | 0.115577i | 0.998329 | + | 0.0577887i | \(0.0184050\pi\) | ||||
−0.998329 | + | 0.0577887i | \(0.981595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.01022 | − | 6.01022i | 0.299390 | − | 0.299390i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.3274i | 1.20586i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.87844i | − | 0.191777i | −0.995392 | − | 0.0958883i | \(-0.969431\pi\) | ||
0.995392 | − | 0.0958883i | \(-0.0305692\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.41533 | + | 7.41533i | −0.364884 | + | 0.364884i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.06032i | − | 0.150225i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.40127 | − | 1.40127i | −0.0684563 | − | 0.0684563i | 0.672050 | − | 0.740506i | \(-0.265414\pi\) |
−0.740506 | + | 0.672050i | \(0.765414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.61424 | − | 7.61424i | 0.371095 | − | 0.371095i | −0.496781 | − | 0.867876i | \(-0.665485\pi\) |
0.867876 | + | 0.496781i | \(0.165485\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.9956 | −0.678885 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.93050 | − | 1.93050i | −0.0934234 | − | 0.0934234i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.496260 | −0.0239040 | −0.0119520 | − | 0.999929i | \(-0.503805\pi\) | ||||
−0.0119520 | + | 0.999929i | \(0.503805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.9889 | −1.58535 | −0.792673 | − | 0.609647i | \(-0.791311\pi\) | ||||
−0.792673 | + | 0.609647i | \(0.791311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.52651 | + | 2.52651i | 0.120859 | + | 0.120859i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.1034 | 1.34130 | 0.670651 | − | 0.741773i | \(-0.266015\pi\) | ||||
0.670651 | + | 0.741773i | \(0.266015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.8047 | − | 23.8047i | 1.13099 | − | 1.13099i | 0.140981 | − | 0.990012i | \(-0.454974\pi\) |
0.990012 | − | 0.140981i | \(-0.0450257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.79552 | − | 4.79552i | −0.227329 | − | 0.227329i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.3175i | − | 1.28919i | −0.764523 | − | 0.644597i | \(-0.777025\pi\) | ||
0.764523 | − | 0.644597i | \(-0.222975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3405 | + | 11.3405i | −0.534003 | + | 0.534003i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.44465i | 0.114607i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.28370i | − | 0.153605i | −0.997046 | − | 0.0768026i | \(-0.975529\pi\) | ||
0.997046 | − | 0.0768026i | \(-0.0244711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3723 | + | 21.3723i | −0.995407 | + | 0.995407i | −0.999989 | − | 0.00458260i | \(-0.998541\pi\) |
0.00458260 | + | 0.999989i | \(0.498541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.4190i | − | 1.69254i | −0.532758 | − | 0.846268i | \(-0.678844\pi\) | ||
0.532758 | − | 0.846268i | \(-0.321156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.4979 | + | 22.4979i | 1.04108 | + | 1.04108i | 0.999119 | + | 0.0419609i | \(0.0133605\pi\) |
0.0419609 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.38033 | − | 6.38033i | 0.294616 | − | 0.294616i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.4103 | −0.846505 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0835 | + | 13.0835i | 0.600313 | + | 0.600313i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.8888 | 1.13720 | 0.568598 | − | 0.822616i | \(-0.307486\pi\) | ||||
0.568598 | + | 0.822616i | \(0.307486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.2622 | −1.28864 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00170 | + | 1.00170i | 0.0454847 | + | 0.0454847i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.96454 | −0.0890217 | −0.0445108 | − | 0.999009i | \(-0.514173\pi\) | ||||
−0.0445108 | + | 0.999009i | \(0.514173\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.24360 | − | 2.24360i | 0.101252 | − | 0.101252i | −0.654666 | − | 0.755918i | \(-0.727191\pi\) |
0.755918 | + | 0.654666i | \(0.227191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.91236 | + | 5.91236i | 0.266279 | + | 0.266279i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.41542i | 0.153203i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8623 | + | 25.8623i | −1.15776 | + | 1.15776i | −0.172800 | + | 0.984957i | \(0.555282\pi\) |
−0.984957 | + | 0.172800i | \(0.944718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.7702i | 1.46115i | 0.682833 | + | 0.730575i | \(0.260748\pi\) | ||||
−0.682833 | + | 0.730575i | \(0.739252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.12070i | 0.361366i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.28132 | + | 1.28132i | −0.0567935 | + | 0.0567935i | −0.734933 | − | 0.678140i | \(-0.762786\pi\) |
0.678140 | + | 0.734933i | \(0.262786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.13689i | − | 0.359955i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.17498 | + | 5.17498i | 0.228037 | + | 0.228037i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4897 | + | 20.4897i | −0.901136 | + | 0.901136i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.9473 | 1.13677 | 0.568386 | − | 0.822762i | \(-0.307568\pi\) | ||||
0.568386 | + | 0.822762i | \(0.307568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.8853 | − | 10.8853i | −0.475981 | − | 0.475981i | 0.427862 | − | 0.903844i | \(-0.359267\pi\) |
−0.903844 | + | 0.427862i | \(0.859267\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.1870 | 0.487315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3707 | 0.972639 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.1747 | − | 13.1747i | −0.570661 | − | 0.570661i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.74943 | 0.118868 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.57551 | + | 1.57551i | −0.0678619 | + | 0.0678619i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4352 | − | 11.4352i | −0.491637 | − | 0.491637i | 0.417185 | − | 0.908822i | \(-0.363017\pi\) |
−0.908822 | + | 0.417185i | \(0.863017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.52368i | 0.407949i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.00768172 | + | 0.00768172i | −0.000328447 | + | 0.000328447i | −0.707271 | − | 0.706943i | \(-0.750074\pi\) |
0.706943 | + | 0.707271i | \(0.250074\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.0541i | − | 0.470922i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0502773i | 0.00213801i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.247153 | − | 0.247153i | 0.0104722 | − | 0.0104722i | −0.701851 | − | 0.712324i | \(-0.747643\pi\) |
0.712324 | + | 0.701851i | \(0.247643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.3880i | − | 0.904617i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.42038 | + | 4.42038i | 0.186297 | + | 0.186297i | 0.794093 | − | 0.607796i | \(-0.207946\pi\) |
−0.607796 | + | 0.794093i | \(0.707946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.78978 | − | 2.78978i | 0.117367 | − | 0.117367i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.4012 | −1.02295 | −0.511476 | − | 0.859297i | \(-0.670901\pi\) | ||||
−0.511476 | + | 0.859297i | \(0.670901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.33750 | − | 8.33750i | −0.348914 | − | 0.348914i | 0.510791 | − | 0.859705i | \(-0.329353\pi\) |
−0.859705 | + | 0.510791i | \(0.829353\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.25886 | −0.135904 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.92478 | 0.121760 | 0.0608800 | − | 0.998145i | \(-0.480609\pi\) | ||||
0.0608800 | + | 0.998145i | \(0.480609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.29129 | + | 2.29129i | 0.0950589 | + | 0.0950589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.5260 | −0.435944 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.6434 | + | 16.6434i | −0.686945 | + | 0.686945i | −0.961556 | − | 0.274611i | \(-0.911451\pi\) |
0.274611 | + | 0.961556i | \(0.411451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4580 | − | 10.4580i | −0.430915 | − | 0.430915i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16.7065i | − | 0.686054i | −0.939326 | − | 0.343027i | \(-0.888548\pi\) | ||
0.939326 | − | 0.343027i | \(-0.111452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.27516 | + | 2.27516i | −0.0932724 | + | 0.0932724i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 33.1559i | − | 1.35471i | −0.735655 | − | 0.677356i | \(-0.763126\pi\) | ||
0.735655 | − | 0.677356i | \(-0.236874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.5909i | − | 1.53336i | −0.642027 | − | 0.766682i | \(-0.721906\pi\) | ||
0.642027 | − | 0.766682i | \(-0.278094\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.03063 | + | 4.03063i | −0.163869 | + | 0.163869i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.720055i | 0.0292261i | 0.999893 | + | 0.0146131i | \(0.00465165\pi\) | ||||
−0.999893 | + | 0.0146131i | \(0.995348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.8038 | − | 23.8038i | −0.962998 | − | 0.962998i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6327 | + | 11.6327i | −0.469839 | + | 0.469839i | −0.901862 | − | 0.432024i | \(-0.857800\pi\) |
0.432024 | + | 0.901862i | \(0.357800\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.3378 | −1.90575 | −0.952873 | − | 0.303369i | \(-0.901889\pi\) | ||||
−0.952873 | + | 0.303369i | \(0.901889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9927 | + | 10.9927i | 0.441832 | + | 0.441832i | 0.892628 | − | 0.450795i | \(-0.148859\pi\) |
−0.450795 | + | 0.892628i | \(0.648859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.18090 | 0.287697 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4163 | −0.496651 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.3027 | − | 26.3027i | −1.04876 | − | 1.04876i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.33698 | 0.0532242 | 0.0266121 | − | 0.999646i | \(-0.491528\pi\) | ||||
0.0266121 | + | 0.999646i | \(0.491528\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.44635 | + | 3.44635i | −0.136764 | + | 0.136764i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.83034 | − | 1.83034i | −0.0725206 | − | 0.0725206i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.9298i | 1.06367i | 0.846850 | + | 0.531833i | \(0.178496\pi\) | ||||
−0.846850 | + | 0.531833i | \(0.821504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.8299 | − | 29.8299i | 1.17638 | − | 1.17638i | 0.195716 | − | 0.980661i | \(-0.437297\pi\) |
0.980661 | − | 0.195716i | \(-0.0627030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.0946i | 1.14383i | 0.820314 | + | 0.571914i | \(0.193799\pi\) | ||||
−0.820314 | + | 0.571914i | \(0.806201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.3658i | 0.917189i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.8462 | − | 24.8462i | 0.972308 | − | 0.972308i | −0.0273185 | − | 0.999627i | \(-0.508697\pi\) |
0.999627 | + | 0.0273185i | \(0.00869683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.05135i | − | 0.0801530i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.2096 | − | 22.2096i | −0.865164 | − | 0.865164i | 0.126769 | − | 0.991932i | \(-0.459539\pi\) |
−0.991932 | + | 0.126769i | \(0.959539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.7200 | − | 18.7200i | 0.728122 | − | 0.728122i | −0.242124 | − | 0.970245i | \(-0.577844\pi\) |
0.970245 | + | 0.242124i | \(0.0778440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.25379 | 0.164955 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.37669 | + | 1.37669i | 0.0533057 | + | 0.0533057i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.08303 | −0.234833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1228 | 0.621488 | 0.310744 | − | 0.950494i | \(-0.399422\pi\) | ||||
0.310744 | + | 0.950494i | \(0.399422\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0537 | − | 12.0537i | −0.463261 | − | 0.463261i | 0.436462 | − | 0.899723i | \(-0.356231\pi\) |
−0.899723 | + | 0.436462i | \(0.856231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.49996 | −0.0575632 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7416 | + | 32.7416i | −1.25282 | + | 1.25282i | −0.298372 | + | 0.954450i | \(0.596444\pi\) |
−0.954450 | + | 0.298372i | \(0.903556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3994 | + | 13.3994i | 0.511964 | + | 0.511964i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.2285i | − | 0.465871i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3170 | − | 21.3170i | 0.810936 | − | 0.810936i | −0.173838 | − | 0.984774i | \(-0.555617\pi\) |
0.984774 | + | 0.173838i | \(0.0556169\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.03290i | 0.152977i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 24.5226i | − | 0.928860i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.9475 | + | 23.9475i | −0.904483 | + | 0.904483i | −0.995820 | − | 0.0913369i | \(-0.970886\pi\) |
0.0913369 | + | 0.995820i | \(0.470886\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.1773i | 1.85476i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.08005 | − | 6.08005i | −0.228664 | − | 0.228664i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.3189 | − | 20.3189i | 0.763092 | − | 0.763092i | −0.213788 | − | 0.976880i | \(-0.568580\pi\) |
0.976880 | + | 0.213788i | \(0.0685801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.60490 | 0.0975542 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85157 | + | 3.85157i | 0.144041 | + | 0.144041i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.54623 | −0.206839 | −0.103420 | − | 0.994638i | \(-0.532978\pi\) | ||||
−0.103420 | + | 0.994638i | \(0.532978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.74912 | −0.288592 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.12920 | + | 7.12920i | 0.264772 | + | 0.264772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.2516 | −1.30741 | −0.653704 | − | 0.756750i | \(-0.726786\pi\) | ||||
−0.653704 | + | 0.756750i | \(0.726786\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.9051 | − | 19.9051i | 0.736218 | − | 0.736218i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7407 | − | 25.7407i | −0.950753 | − | 0.950753i | 0.0480899 | − | 0.998843i | \(-0.484687\pi\) |
−0.998843 | + | 0.0480899i | \(0.984687\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 20.1045i | − | 0.740559i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.42027 | + | 8.42027i | −0.309745 | + | 0.309745i | −0.844810 | − | 0.535066i | \(-0.820287\pi\) |
0.535066 | + | 0.844810i | \(0.320287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6054i | 1.37961i | 0.723996 | + | 0.689805i | \(0.242304\pi\) | ||||
−0.723996 | + | 0.689805i | \(0.757696\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.82341i | 0.103442i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.05853 | + | 2.05853i | −0.0752170 | + | 0.0752170i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.8331i | 1.23459i | 0.786732 | + | 0.617294i | \(0.211771\pi\) | ||||
−0.786732 | + | 0.617294i | \(0.788229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.72850 | − | 4.72850i | −0.172088 | − | 0.172088i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.38072 | + | 3.38072i | −0.122874 | + | 0.122874i | −0.765870 | − | 0.642996i | \(-0.777691\pi\) |
0.642996 | + | 0.765870i | \(0.277691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7200 | −0.606100 | −0.303050 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303050 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.13047 | − | 7.13047i | −0.258140 | − | 0.258140i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1451 | −0.980152 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.6721 | 0.493030 | 0.246515 | − | 0.969139i | \(-0.420715\pi\) | ||||
0.246515 | + | 0.969139i | \(0.420715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.3858 | + | 29.3858i | 1.05694 | + | 1.05694i | 0.998278 | + | 0.0586568i | \(0.0186818\pi\) |
0.0586568 | + | 0.998278i | \(0.481318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4895 | 0.484556 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.9245 | + | 22.9245i | −0.821357 | + | 0.821357i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.38103 | + | 5.38103i | 0.192548 | + | 0.192548i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.4455i | 0.765422i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.3525 | + | 31.3525i | −1.11760 | + | 1.11760i | −0.125504 | + | 0.992093i | \(0.540055\pi\) |
−0.992093 | + | 0.125504i | \(0.959945\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.17748i | 0.148534i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.06693i | − | 0.250954i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0542 | + | 33.0542i | −1.17084 | + | 1.17084i | −0.188830 | + | 0.982010i | \(0.560470\pi\) |
−0.982010 | + | 0.188830i | \(0.939530\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 44.3068i | − | 1.56746i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.8197 | − | 12.8197i | −0.452399 | − | 0.452399i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.529770 | + | 0.529770i | −0.0186719 | + | 0.0186719i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.3611 | 0.751016 | 0.375508 | − | 0.926819i | \(-0.377468\pi\) | ||||
0.375508 | + | 0.926819i | \(0.377468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.81041 | − | 5.81041i | −0.204031 | − | 0.204031i | 0.597694 | − | 0.801725i | \(-0.296084\pi\) |
−0.801725 | + | 0.597694i | \(0.796084\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.5926 | −0.511158 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.2160 | −1.30202 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5077 | + | 38.5077i | 1.34393 | + | 1.34393i | 0.892111 | + | 0.451816i | \(0.149224\pi\) |
0.451816 | + | 0.892111i | \(0.350776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.6315 | −1.76490 | −0.882451 | − | 0.470404i | \(-0.844108\pi\) | ||||
−0.882451 | + | 0.470404i | \(0.844108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.9992 | + | 25.9992i | −0.904081 | + | 0.904081i | −0.995786 | − | 0.0917052i | \(-0.970768\pi\) |
0.0917052 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.45810 | + | 5.45810i | 0.189568 | + | 0.189568i | 0.795509 | − | 0.605941i | \(-0.207203\pi\) |
−0.605941 | + | 0.795509i | \(0.707203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.40687i | − | 0.118041i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.92082 | − | 9.92082i | 0.343324 | − | 0.343324i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 33.0422i | − | 1.14074i | −0.821387 | − | 0.570372i | \(-0.806799\pi\) | ||
0.821387 | − | 0.570372i | \(-0.193201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9766i | 0.792297i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.20706 | − | 4.20706i | 0.144727 | − | 0.144727i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.03555i | − | 0.207384i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.12457 | − | 6.12457i | −0.209948 | − | 0.209948i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.05330 | + | 8.05330i | −0.275740 | + | 0.275740i | −0.831406 | − | 0.555666i | \(-0.812463\pi\) |
0.555666 | + | 0.831406i | \(0.312463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.6143 | 1.52400 | 0.761998 | − | 0.647579i | \(-0.224218\pi\) | ||||
0.761998 | + | 0.647579i | \(0.224218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.721531 | + | 0.721531i | 0.0246183 | + | 0.0246183i | 0.719309 | − | 0.694690i | \(-0.244459\pi\) |
−0.694690 | + | 0.719309i | \(0.744459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.1045 | −0.888609 | −0.444304 | − | 0.895876i | \(-0.646549\pi\) | ||||
−0.444304 | + | 0.895876i | \(0.646549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.33443 | 0.113374 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0792122 | + | 0.0792122i | 0.00268709 | + | 0.00268709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.3563 | 0.791397 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.08249 | + | 6.08249i | −0.205626 | + | 0.205626i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.63163 | − | 2.63163i | −0.0888637 | − | 0.0888637i | 0.661278 | − | 0.750141i | \(-0.270015\pi\) |
−0.750141 | + | 0.661278i | \(0.770015\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.58849i | 0.221972i | 0.993822 | + | 0.110986i | \(0.0354009\pi\) | ||||
−0.993822 | + | 0.110986i | \(0.964599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8297 | + | 10.8297i | −0.364449 | + | 0.364449i | −0.865448 | − | 0.500999i | \(-0.832966\pi\) |
0.500999 | + | 0.865448i | \(0.332966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.7156i | 0.729138i | 0.931176 | + | 0.364569i | \(0.118784\pi\) | ||||
−0.931176 | + | 0.364569i | \(0.881216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.16063i | − | 0.173082i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.4195 | + | 41.4195i | −1.38605 | + | 1.38605i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.1190i | − | 0.605650i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.69856 | − | 5.69856i | −0.190058 | − | 0.190058i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3807 | − | 11.3807i | 0.379146 | − | 0.379146i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.52733 | −0.183735 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7390 | − | 22.7390i | −0.755035 | − | 0.755035i | 0.220379 | − | 0.975414i | \(-0.429271\pi\) |
−0.975414 | + | 0.220379i | \(0.929271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.1521 | −0.899589 | −0.449794 | − | 0.893132i | \(-0.648503\pi\) | ||||
−0.449794 | + | 0.893132i | \(0.648503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.21991 | 0.238944 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.53587 | + | 1.53587i | 0.0507189 | + | 0.0507189i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.2903 | 0.801262 | 0.400631 | − | 0.916239i | \(-0.368791\pi\) | ||||
0.400631 | + | 0.916239i | \(0.368791\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.25137 | + | 6.25137i | −0.205766 | + | 0.205766i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.7161 | − | 31.7161i | −1.04282 | − | 1.04282i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.4028i | 1.29276i | 0.763014 | + | 0.646382i | \(0.223719\pi\) | ||||
−0.763014 | + | 0.646382i | \(0.776281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.18485 | + | 3.18485i | −0.104379 | + | 0.104379i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.16906i | 0.234453i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.2135i | − | 1.67307i | −0.547913 | − | 0.836536i | \(-0.684577\pi\) | ||
0.547913 | − | 0.836536i | \(-0.315423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4201 | − | 28.4201i | 0.926470 | − | 0.926470i | −0.0710057 | − | 0.997476i | \(-0.522621\pi\) |
0.997476 | + | 0.0710057i | \(0.0226209\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.71008i | − | 0.185946i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5107 | − | 25.5107i | −0.828985 | − | 0.828985i | 0.158391 | − | 0.987376i | \(-0.449369\pi\) |
−0.987376 | + | 0.158391i | \(0.949369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.8933 | − | 14.8933i | 0.483455 | − | 0.483455i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.5373 | −1.44270 | −0.721352 | − | 0.692569i | \(-0.756479\pi\) | ||||
−0.721352 | + | 0.692569i | \(0.756479\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6295 | + | 14.6295i | 0.473399 | + | 0.473399i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.0645 | −0.647917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2175 | 0.652178 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.1196 | − | 14.1196i | −0.454525 | − | 0.454525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.17126 | 0.0698231 | 0.0349116 | − | 0.999390i | \(-0.488885\pi\) | ||||
0.0349116 | + | 0.999390i | \(0.488885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.9194 | − | 31.9194i | 1.02434 | − | 1.02434i | 0.0246475 | − | 0.999696i | \(-0.492154\pi\) |
0.999696 | − | 0.0246475i | \(-0.00784632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.01947 | − | 3.01947i | −0.0967998 | − | 0.0967998i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.5480i | 0.689381i | 0.938716 | + | 0.344691i | \(0.112016\pi\) | ||||
−0.938716 | + | 0.344691i | \(0.887984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3136 | − | 11.3136i | 0.361583 | − | 0.361583i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 45.1484i | − | 1.44001i | −0.693968 | − | 0.720006i | \(-0.744139\pi\) | ||
0.693968 | − | 0.720006i | \(-0.255861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.61172i | 0.210667i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.63490 | − | 4.63490i | 0.147381 | − | 0.147381i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.3053i | − | 0.390892i | −0.980714 | − | 0.195446i | \(-0.937385\pi\) | ||
0.980714 | − | 0.195446i | \(-0.0626154\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.10922 | − | 7.10922i | −0.225377 | − | 0.225377i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.19520 | + | 2.19520i | −0.0695227 | + | 0.0695227i | −0.741013 | − | 0.671491i | \(-0.765654\pi\) |
0.671491 | + | 0.741013i | \(0.265654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.e.1583.13 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.8 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.13 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.8 | ✓ | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.8 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.8 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.13 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.13 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.8 | ✓ | 40 | 12.11 | even | 2 | ||
1008.2.v.e.323.13 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.8 | yes | 40 | 16.5 | even | 4 | ||
1008.2.v.e.827.13 | yes | 40 | 48.5 | odd | 4 | ||
4032.2.v.e.1583.8 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.1583.13 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.3599.8 | 40 | 16.11 | odd | 4 | inner | ||
4032.2.v.e.3599.13 | 40 | 48.11 | even | 4 | inner |