Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.54764.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.655762\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.46569 | −1.68787 | −0.843937 | − | 0.536443i | \(-0.819768\pi\) | ||||
−0.843937 | + | 0.536443i | \(0.819768\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.39413 | −1.02337 | −0.511684 | − | 0.859174i | \(-0.670978\pi\) | ||||
−0.511684 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.70565 | −1.30511 | −0.652556 | − | 0.757740i | \(-0.726303\pi\) | ||||
−0.652556 | + | 0.757740i | \(0.726303\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.54830 | −1.58819 | −0.794097 | − | 0.607790i | \(-0.792056\pi\) | ||||
−0.794097 | + | 0.607790i | \(0.792056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.22574 | 1.42828 | 0.714141 | − | 0.700002i | \(-0.246817\pi\) | ||||
0.714141 | + | 0.700002i | \(0.246817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.46569 | −0.974494 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.448521 | 0.0832882 | 0.0416441 | − | 0.999133i | \(-0.486740\pi\) | ||||
0.0416441 | + | 0.999133i | \(0.486740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.15417 | 0.925716 | 0.462858 | − | 0.886432i | \(-0.346824\pi\) | ||||
0.462858 | + | 0.886432i | \(0.346824\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.39413 | −0.590841 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.46569 | 0.754840 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.98578 | −0.984057 | −0.492028 | − | 0.870579i | \(-0.663744\pi\) | ||||
−0.492028 | + | 0.870579i | \(0.663744\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.70565 | −0.753507 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.07157 | 0.479698 | 0.239849 | − | 0.970810i | \(-0.422902\pi\) | ||||
0.239849 | + | 0.970810i | \(0.422902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.47991 | 0.683180 | 0.341590 | − | 0.939849i | \(-0.389035\pi\) | ||||
0.341590 | + | 0.939849i | \(0.389035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.22574 | −0.908117 | −0.454059 | − | 0.890972i | \(-0.650024\pi\) | ||||
−0.454059 | + | 0.890972i | \(0.650024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9424 | 1.84892 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.54830 | −0.916945 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.59166 | −0.355991 | −0.177996 | − | 0.984031i | \(-0.556961\pi\) | ||||
−0.177996 | + | 0.984031i | \(0.556961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.39413 | 0.457664 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.22574 | 0.824619 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.55148 | 0.201985 | 0.100993 | − | 0.994887i | \(-0.467798\pi\) | ||||
0.100993 | + | 0.994887i | \(0.467798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.91421 | −0.629201 | −0.314600 | − | 0.949224i | \(-0.601870\pi\) | ||||
−0.314600 | + | 0.949224i | \(0.601870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.46569 | −0.562625 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.70565 | 0.583664 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.08556 | −0.743469 | −0.371735 | − | 0.928339i | \(-0.621237\pi\) | ||||
−0.371735 | + | 0.928339i | \(0.621237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.07157 | −0.127172 | −0.0635859 | − | 0.997976i | \(-0.520254\pi\) | ||||
−0.0635859 | + | 0.997976i | \(0.520254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.70565 | −1.01892 | −0.509460 | − | 0.860495i | \(-0.670155\pi\) | ||||
−0.509460 | + | 0.860495i | \(0.670155\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.1571 | 1.72731 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1400 | 1.47836 | 0.739180 | − | 0.673508i | \(-0.235213\pi\) | ||||
0.739180 | + | 0.673508i | \(0.235213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0282 | 1.43003 | 0.715016 | − | 0.699108i | \(-0.246420\pi\) | ||||
0.715016 | + | 0.699108i | \(0.246420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.54830 | 0.710262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.448521 | 0.0480865 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6199 | 1.23170 | 0.615852 | − | 0.787862i | \(-0.288812\pi\) | ||||
0.615852 | + | 0.787862i | \(0.288812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.0140 | 2.20286 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.15417 | 0.534463 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.22574 | −0.638747 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.30834 | 0.437446 | 0.218723 | − | 0.975787i | \(-0.429811\pi\) | ||||
0.218723 | + | 0.975787i | \(0.429811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.39413 | −0.341122 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3397 | 1.02884 | 0.514421 | − | 0.857538i | \(-0.328007\pi\) | ||||
0.514421 | + | 0.857538i | \(0.328007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8316 | 1.06727 | 0.533635 | − | 0.845715i | \(-0.320826\pi\) | ||||
0.533635 | + | 0.845715i | \(0.320826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.46569 | 0.435807 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.76004 | 0.170150 | 0.0850750 | − | 0.996375i | \(-0.472887\pi\) | ||||
0.0850750 | + | 0.996375i | \(0.472887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.39413 | −0.133533 | −0.0667665 | − | 0.997769i | \(-0.521268\pi\) | ||||
−0.0667665 | + | 0.997769i | \(0.521268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.98578 | −0.568145 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17134 | 0.110191 | 0.0550954 | − | 0.998481i | \(-0.482454\pi\) | ||||
0.0550954 | + | 0.998481i | \(0.482454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.70565 | −0.435037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.2427 | 2.68067 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.520089 | 0.0472808 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.07157 | 0.276954 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9454 | −1.23745 | −0.618726 | − | 0.785607i | \(-0.712351\pi\) | ||||
−0.618726 | + | 0.785607i | \(0.712351\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.47991 | 0.394434 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8628 | −1.21120 | −0.605598 | − | 0.795771i | \(-0.707066\pi\) | ||||
−0.605598 | + | 0.795771i | \(0.707066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.8022 | −2.41076 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4081 | −1.23097 | −0.615484 | − | 0.788149i | \(-0.711039\pi\) | ||||
−0.615484 | + | 0.788149i | \(0.711039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1140 | 0.857858 | 0.428929 | − | 0.903338i | \(-0.358891\pi\) | ||||
0.428929 | + | 0.903338i | \(0.358891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.22574 | −0.524302 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.9716 | 1.33561 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.448521 | −0.0372476 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.9424 | 1.06747 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.32870 | 0.272697 | 0.136349 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136349 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.3427 | 1.81822 | 0.909111 | − | 0.416554i | \(-0.136762\pi\) | ||||
0.909111 | + | 0.416554i | \(0.136762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.54830 | −0.529398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.15417 | −0.413993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.63090 | 0.529203 | 0.264602 | − | 0.964358i | \(-0.414760\pi\) | ||||
0.264602 | + | 0.964358i | \(0.414760\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.59166 | −0.205532 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.46569 | 0.351946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.3083 | 1.74732 | 0.873662 | − | 0.486533i | \(-0.161739\pi\) | ||||
0.873662 | + | 0.486533i | \(0.161739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.39413 | 0.264232 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0885 | 1.86403 | 0.932013 | − | 0.362426i | \(-0.118051\pi\) | ||||
0.932013 | + | 0.362426i | \(0.118051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.14314 | 0.703318 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.22574 | 0.476094 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9314 | −1.43933 | −0.719663 | − | 0.694323i | \(-0.755704\pi\) | ||||
−0.719663 | + | 0.694323i | \(0.755704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.46569 | −0.337575 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.55148 | 0.116616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7598 | 1.40217 | 0.701087 | − | 0.713075i | \(-0.252698\pi\) | ||||
0.701087 | + | 0.713075i | \(0.252698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.1964 | −1.57551 | −0.787757 | − | 0.615986i | \(-0.788758\pi\) | ||||
−0.787757 | + | 0.615986i | \(0.788758\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.91421 | −0.363269 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.98578 | 0.440083 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.2257 | 1.62531 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.46569 | −0.324831 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3909 | −1.04129 | −0.520646 | − | 0.853773i | \(-0.674309\pi\) | ||||
−0.520646 | + | 0.853773i | \(0.674309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0966 | 0.798750 | 0.399375 | − | 0.916788i | \(-0.369227\pi\) | ||||
0.399375 | + | 0.916788i | \(0.369227\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.70565 | 0.336979 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1652 | 1.00923 | 0.504614 | − | 0.863345i | \(-0.331635\pi\) | ||||
0.504614 | + | 0.863345i | \(0.331635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.66004 | −0.613894 | −0.306947 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306947 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.08556 | −0.429242 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00296 | −0.140580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.07157 | −0.214528 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1309 | −1.46166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1321 | 0.766366 | 0.383183 | − | 0.923673i | \(-0.374828\pi\) | ||||
0.383183 | + | 0.923673i | \(0.374828\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.07157 | −0.0734226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.47991 | −0.305527 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.0169 | −1.56249 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.70565 | −0.588273 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.8140 | 2.07277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1711 | −1.35076 | −0.675379 | − | 0.737471i | \(-0.736020\pi\) | ||||
−0.675379 | + | 0.737471i | \(0.736020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.523273 | 0.0347308 | 0.0173654 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173654 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.33359 | −0.220290 | −0.110145 | − | 0.993916i | \(-0.535132\pi\) | ||||
−0.110145 | + | 0.993916i | \(0.535132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.1571 | 0.997266 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5481 | 1.01859 | 0.509294 | − | 0.860593i | \(-0.329907\pi\) | ||||
0.509294 | + | 0.860593i | \(0.329907\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.22574 | 0.406122 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.1400 | 0.853532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.5451 | −1.78175 | −0.890873 | − | 0.454253i | \(-0.849906\pi\) | ||||
−0.890873 | + | 0.454253i | \(0.849906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.74000 | 0.562993 | 0.281496 | − | 0.959562i | \(-0.409169\pi\) | ||||
0.281496 | + | 0.959562i | \(0.409169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.9424 | −0.826861 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.2961 | −1.86407 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.0282 | 0.825629 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0312 | −0.948759 | −0.474379 | − | 0.880321i | \(-0.657327\pi\) | ||||
−0.474379 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.39413 | 0.213387 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.54830 | 0.410070 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.1571 | −0.820719 | −0.410359 | − | 0.911924i | \(-0.634597\pi\) | ||||
−0.410359 | + | 0.911924i | \(0.634597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.7307 | 1.66096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.448521 | 0.0277627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.5795 | 1.45397 | 0.726986 | − | 0.686652i | \(-0.240921\pi\) | ||||
0.726986 | + | 0.686652i | \(0.240921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.59166 | 0.159204 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6199 | 0.711124 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.52304 | −0.458688 | −0.229344 | − | 0.973345i | \(-0.573658\pi\) | ||||
−0.229344 | + | 0.973345i | \(0.573658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5370 | −1.12604 | −0.563022 | − | 0.826442i | \(-0.690361\pi\) | ||||
−0.563022 | + | 0.826442i | \(0.690361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.0140 | 1.27182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.39413 | −0.204673 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.8628 | 1.43378 | 0.716888 | − | 0.697189i | \(-0.245566\pi\) | ||||
0.716888 | + | 0.697189i | \(0.245566\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.15417 | 0.308572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.6118 | −1.34891 | −0.674453 | − | 0.738318i | \(-0.735620\pi\) | ||||
−0.674453 | + | 0.738318i | \(0.735620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6684 | −0.812504 | −0.406252 | − | 0.913761i | \(-0.633164\pi\) | ||||
−0.406252 | + | 0.913761i | \(0.633164\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.22574 | −0.368781 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.7167 | −0.809670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.8802 | 1.52236 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.30834 | 0.252559 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.0431 | −0.878829 | −0.439415 | − | 0.898284i | \(-0.644814\pi\) | ||||
−0.439415 | + | 0.898284i | \(0.644814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.55148 | −0.0903306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.39413 | −0.196947 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.70565 | 0.272135 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0059 | −1.15312 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.3397 | 0.594002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.91421 | 0.281387 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.9674 | 1.82448 | 0.912239 | − | 0.409658i | \(-0.134352\pi\) | ||||
0.912239 | + | 0.409658i | \(0.134352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8316 | 0.616189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.1932 | 1.93892 | 0.969459 | − | 0.245254i | \(-0.0788715\pi\) | ||||
0.969459 | + | 0.245254i | \(0.0788715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5713 | −0.654049 | −0.327024 | − | 0.945016i | \(-0.606046\pi\) | ||||
−0.327024 | + | 0.945016i | \(0.606046\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.46569 | 0.251613 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.12915 | 0.175750 | 0.0878752 | − | 0.996131i | \(-0.471992\pi\) | ||||
0.0878752 | + | 0.996131i | \(0.471992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.52234 | −0.0852344 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.76004 | 0.0982361 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −40.7680 | −2.26839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.70565 | −0.261022 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.39413 | −0.0770953 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.8022 | 1.53279 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.988966 | 0.0543585 | 0.0271793 | − | 0.999631i | \(-0.491348\pi\) | ||||
0.0271793 | + | 0.999631i | \(0.491348\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.98578 | −0.328019 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.08556 | 0.332490 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.2397 | 1.15700 | 0.578501 | − | 0.815682i | \(-0.303638\pi\) | ||||
0.578501 | + | 0.815682i | \(0.303638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.17134 | 0.0636186 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.4939 | −0.947348 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.5370 | −1.43287 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.78825 | 0.149681 | 0.0748406 | − | 0.997196i | \(-0.476155\pi\) | ||||
0.0748406 | + | 0.997196i | \(0.476155\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3939 | 1.62695 | 0.813474 | − | 0.581601i | \(-0.197574\pi\) | ||||
0.813474 | + | 0.581601i | \(0.197574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.70565 | −0.251169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6993 | 0.569465 | 0.284733 | − | 0.958607i | \(-0.408095\pi\) | ||||
0.284733 | + | 0.958607i | \(0.408095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.07157 | 0.0568729 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.2427 | 1.54769 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.5120 | −0.977027 | −0.488513 | − | 0.872556i | \(-0.662461\pi\) | ||||
−0.488513 | + | 0.872556i | \(0.662461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.7598 | 1.03999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.520089 | 0.0272976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.70565 | 0.455675 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.6937 | 1.28900 | 0.644500 | − | 0.764605i | \(-0.277066\pi\) | ||||
0.644500 | + | 0.764605i | \(0.277066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.07157 | 0.159899 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5735 | 0.600869 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.9968 | −1.29429 | −0.647143 | − | 0.762369i | \(-0.724036\pi\) | ||||
−0.647143 | + | 0.762369i | \(0.724036\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.11058 | −0.108700 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6167 | −1.05901 | −0.529504 | − | 0.848308i | \(-0.677622\pi\) | ||||
−0.529504 | + | 0.848308i | \(0.677622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.9454 | −0.714443 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.42645 | −0.226181 | −0.113091 | − | 0.993585i | \(-0.536075\pi\) | ||||
−0.113091 | + | 0.993585i | \(0.536075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.1571 | −0.772479 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.47991 | 0.227727 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.7417 | −1.00094 | −0.500472 | − | 0.865753i | \(-0.666840\pi\) | ||||
−0.500472 | + | 0.865753i | \(0.666840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.54830 | 0.331162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8628 | −0.699285 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1400 | −0.661143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.68529 | −0.285337 | −0.142668 | − | 0.989771i | \(-0.545568\pi\) | ||||
−0.142668 | + | 0.989771i | \(0.545568\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.8022 | −1.39185 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1341 | 0.605949 | 0.302975 | − | 0.952999i | \(-0.402020\pi\) | ||||
0.302975 | + | 0.952999i | \(0.402020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.2537 | −1.20816 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.3165 | 1.00705 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0454 | 1.23841 | 0.619207 | − | 0.785228i | \(-0.287454\pi\) | ||||
0.619207 | + | 0.785228i | \(0.287454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4081 | −0.710700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.92843 | −0.340926 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.0282 | −0.639530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1140 | 0.495284 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.3314 | −1.57949 | −0.789747 | − | 0.613433i | \(-0.789788\pi\) | ||||
−0.789747 | + | 0.613433i | \(0.789788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8858 | 1.21286 | 0.606429 | − | 0.795137i | \(-0.292601\pi\) | ||||
0.606429 | + | 0.795137i | \(0.292601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.22574 | −0.302706 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.54830 | −0.317639 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.9454 | 1.06201 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.9716 | 0.771114 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0343 | −1.35037 | −0.675183 | − | 0.737650i | \(-0.735936\pi\) | ||||
−0.675183 | + | 0.737650i | \(0.735936\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7370 | −0.900445 | −0.450222 | − | 0.892916i | \(-0.648655\pi\) | ||||
−0.450222 | + | 0.892916i | \(0.648655\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.448521 | −0.0215049 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.22574 | −0.297817 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.01811 | 0.0485918 | 0.0242959 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242959 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9424 | 0.616306 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.4311 | −0.828177 | −0.414089 | − | 0.910237i | \(-0.635900\pi\) | ||||
−0.414089 | + | 0.910237i | \(0.635900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6199 | −0.550834 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.32870 | 0.157442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.6138 | −1.58633 | −0.793167 | − | 0.609005i | \(-0.791569\pi\) | ||||
−0.793167 | + | 0.609005i | \(0.791569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4253 | −0.490908 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.3427 | 1.04975 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.0140 | −0.985151 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.01695 | −0.234683 | −0.117341 | − | 0.993092i | \(-0.537437\pi\) | ||||
−0.117341 | + | 0.993092i | \(0.537437\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.54830 | −0.305648 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.49165 | −0.255772 | −0.127886 | − | 0.991789i | \(-0.540819\pi\) | ||||
−0.127886 | + | 0.991789i | \(0.540819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.3684 | 1.96903 | 0.984514 | − | 0.175308i | \(-0.0560920\pi\) | ||||
0.984514 | + | 0.175308i | \(0.0560920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.15417 | −0.239019 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.95959 | 0.275777 | 0.137889 | − | 0.990448i | \(-0.455968\pi\) | ||||
0.137889 | + | 0.990448i | \(0.455968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.1762 | 1.25488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.63090 | 0.305536 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.2054 | −0.699144 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.22574 | 0.285656 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.59166 | −0.118664 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.2135 | −1.51757 | −0.758783 | − | 0.651344i | \(-0.774206\pi\) | ||||
−0.758783 | + | 0.651344i | \(0.774206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.1670 | 1.28430 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.46569 | 0.203196 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.30834 | −0.195632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7336 | 1.30204 | 0.651022 | − | 0.759058i | \(-0.274340\pi\) | ||||
0.651022 | + | 0.759058i | \(0.274340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3083 | 1.00882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4427 | −0.877436 | −0.438718 | − | 0.898625i | \(-0.644567\pi\) | ||||
−0.438718 | + | 0.898625i | \(0.644567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93705 | −0.132278 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.39413 | 0.152555 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.78530 | 0.214650 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.21695 | 0.233543 | 0.116771 | − | 0.993159i | \(-0.462746\pi\) | ||||
0.116771 | + | 0.993159i | \(0.462746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0885 | 1.07620 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.06574 | 0.270458 | 0.135229 | − | 0.990814i | \(-0.456823\pi\) | ||||
0.135229 | + | 0.990814i | \(0.456823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3397 | −0.460112 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.14314 | 0.406061 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5079 | 0.554402 | 0.277201 | − | 0.960812i | \(-0.410593\pi\) | ||||
0.277201 | + | 0.960812i | \(0.410593\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.8768 | 1.71981 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.22574 | 0.274873 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.8316 | −0.477298 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1309 | 0.929338 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.9314 | −0.830996 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.1539 | −1.05820 | −0.529102 | − | 0.848558i | \(-0.677471\pi\) | ||||
−0.529102 | + | 0.848558i | \(0.677471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.1427 | 1.23059 | 0.615297 | − | 0.788296i | \(-0.289036\pi\) | ||||
0.615297 | + | 0.788296i | \(0.289036\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.46569 | −0.194899 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.7510 | −1.47022 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.55148 | 0.0673285 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4537 | −0.626060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.76004 | −0.0760934 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.7598 | 0.809546 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −43.9282 | −1.89212 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0117 | −0.731392 | −0.365696 | − | 0.930734i | \(-0.619169\pi\) | ||||
−0.365696 | + | 0.930734i | \(0.619169\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.1964 | −0.909623 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.39413 | 0.0597178 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0402 | 0.814099 | 0.407050 | − | 0.913406i | \(-0.366558\pi\) | ||||
0.407050 | + | 0.913406i | \(0.366558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.91421 | −0.209734 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.79237 | 0.118959 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −58.6790 | −2.49529 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.98578 | 0.254082 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6882 | 1.00370 | 0.501852 | − | 0.864954i | \(-0.332652\pi\) | ||||
0.501852 | + | 0.864954i | \(0.332652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.0809 | −0.891627 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.2257 | 0.938371 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.8630 | 0.542111 | 0.271055 | − | 0.962564i | \(-0.412627\pi\) | ||||
0.271055 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.17134 | −0.0492788 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.46569 | −0.187542 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.4709 | −0.438963 | −0.219481 | − | 0.975617i | \(-0.570437\pi\) | ||||
−0.219481 | + | 0.975617i | \(0.570437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0361 | 0.461845 | 0.230922 | − | 0.972972i | \(-0.425826\pi\) | ||||
0.230922 | + | 0.972972i | \(0.425826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.3909 | −0.601190 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.9535 | −1.91307 | −0.956535 | − | 0.291616i | \(-0.905807\pi\) | ||||
−0.956535 | + | 0.291616i | \(0.905807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0966 | 0.461159 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −58.1800 | −2.41371 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.79641 | 0.364310 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.70565 | 0.194555 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2578 | 1.00123 | 0.500614 | − | 0.865671i | \(-0.333108\pi\) | ||||
0.500614 | + | 0.865671i | \(0.333108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0885 | 1.32218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1652 | 0.582679 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.5282 | −1.13045 | −0.565225 | − | 0.824937i | \(-0.691211\pi\) | ||||
−0.565225 | + | 0.824937i | \(0.691211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.2427 | −1.19883 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.66004 | −0.354432 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.2741 | −1.27782 | −0.638912 | − | 0.769280i | \(-0.720615\pi\) | ||||
−0.638912 | + | 0.769280i | \(0.720615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3253 | 1.76728 | 0.883638 | − | 0.468171i | \(-0.155087\pi\) | ||||
0.883638 | + | 0.468171i | \(0.155087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.08556 | −0.247823 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.520089 | −0.0211446 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7802 | −1.20874 | −0.604370 | − | 0.796704i | \(-0.706575\pi\) | ||||
−0.604370 | + | 0.796704i | \(0.706575\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00296 | −0.0811639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.2961 | 1.18520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6763 | 0.552380 | 0.276190 | − | 0.961103i | \(-0.410928\pi\) | ||||
0.276190 | + | 0.961103i | \(0.410928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.07157 | −0.123858 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9130 | 0.600377 | 0.300188 | − | 0.953880i | \(-0.402950\pi\) | ||||
0.300188 | + | 0.953880i | \(0.402950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.3021 | 1.66007 | 0.830035 | − | 0.557712i | \(-0.188320\pi\) | ||||
0.830035 | + | 0.557712i | \(0.188320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.8908 | −2.07896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.1309 | −0.843888 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.1967 | 1.56287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.2104 | −1.75999 | −0.879993 | − | 0.474986i | \(-0.842453\pi\) | ||||
−0.879993 | + | 0.474986i | \(0.842453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1321 | 0.442461 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.9454 | 0.553405 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −60.9025 | −2.41304 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.07157 | −0.0423906 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.2750 | 1.27479 | 0.637393 | − | 0.770539i | \(-0.280013\pi\) | ||||
0.637393 | + | 0.770539i | \(0.280013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2689 | 0.917635 | 0.458817 | − | 0.888531i | \(-0.348273\pi\) | ||||
0.458817 | + | 0.888531i | \(0.348273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.47991 | −0.176396 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.49390 | 0.0587313 | 0.0293656 | − | 0.999569i | \(-0.490651\pi\) | ||||
0.0293656 | + | 0.999569i | \(0.490651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.26592 | −0.206705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.0169 | −0.902105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.30663 | 0.364197 | 0.182098 | − | 0.983280i | \(-0.441711\pi\) | ||||
0.182098 | + | 0.983280i | \(0.441711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8628 | 0.541663 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.70565 | −0.339640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.8903 | −1.35913 | −0.679566 | − | 0.733614i | \(-0.737832\pi\) | ||||
−0.679566 | + | 0.733614i | \(0.737832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.14578 | 0.0834613 | 0.0417307 | − | 0.999129i | \(-0.486713\pi\) | ||||
0.0417307 | + | 0.999129i | \(0.486713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.8140 | 1.19672 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.8022 | 1.07812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.448521 | −0.0173668 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.1711 | −0.779860 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.6795 | 0.643903 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.0483 | 1.04264 | 0.521318 | − | 0.853362i | \(-0.325440\pi\) | ||||
0.521318 | + | 0.853362i | \(0.325440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.9442 | 1.76578 | 0.882890 | − | 0.469580i | \(-0.155595\pi\) | ||||
0.882890 | + | 0.469580i | \(0.155595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.2397 | −0.738353 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.523273 | 0.0200518 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.9571 | 0.954958 | 0.477479 | − | 0.878643i | \(-0.341551\pi\) | ||||
0.477479 | + | 0.878643i | \(0.341551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4081 | 0.550506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.33359 | −0.127184 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.1954 | 0.464609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8167 | 0.715820 | 0.357910 | − | 0.933756i | \(-0.383489\pi\) | ||||
0.357910 | + | 0.933756i | \(0.383489\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.1571 | 0.575772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1140 | −0.383646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1135 | −0.761855 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.5481 | 0.588082 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0601 | 1.58859 | 0.794294 | − | 0.607534i | \(-0.207841\pi\) | ||||
0.794294 | + | 0.607534i | \(0.207841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.2659 | −1.40551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.22574 | 0.234475 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.1741 | −1.73655 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3133 | −1.10088 | −0.550442 | − | 0.834873i | \(-0.685541\pi\) | ||||
−0.550442 | + | 0.834873i | \(0.685541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.1400 | 0.492787 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.15417 | −0.193025 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.9716 | −0.597303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.5451 | −1.02869 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.95641 | 0.334018 | 0.167009 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167009 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.3707 | −1.80142 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.74000 | 0.325044 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.448521 | 0.0166576 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4313 | 0.609405 | 0.304702 | − | 0.952448i | \(-0.401443\pi\) | ||||
0.304702 | + | 0.952448i | \(0.401443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.3358 | −1.08502 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.41519 | 0.310822 | 0.155411 | − | 0.987850i | \(-0.450330\pi\) | ||||
0.155411 | + | 0.987850i | \(0.450330\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.9424 | −0.477388 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.6551 | 0.760842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3375 | −0.380270 | −0.190135 | − | 0.981758i | \(-0.560893\pi\) | ||||
−0.190135 | + | 0.981758i | \(0.560893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.2961 | −1.07622 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6388 | 1.30746 | 0.653731 | − | 0.756727i | \(-0.273203\pi\) | ||||
0.653731 | + | 0.756727i | \(0.273203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.32870 | −0.121954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.0282 | 0.476677 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.85982 | −0.287192 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.4402 | −1.11078 | −0.555390 | − | 0.831590i | \(-0.687431\pi\) | ||||
−0.555390 | + | 0.831590i | \(0.687431\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.0312 | −0.547766 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.3427 | −0.813134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.4941 | −0.381416 | −0.190708 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190708 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.39413 | 0.123199 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.99704 | −0.144893 | −0.0724464 | − | 0.997372i | \(-0.523081\pi\) | ||||
−0.0724464 | + | 0.997372i | \(0.523081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.22574 | 0.225387 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.54830 | 0.236754 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.30072 | −0.263614 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.6307 | −0.563656 | −0.281828 | − | 0.959465i | \(-0.590941\pi\) | ||||
−0.281828 | + | 0.959465i | \(0.590941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.1571 | −0.473842 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.6912 | 1.21179 | 0.605894 | − | 0.795545i | \(-0.292815\pi\) | ||||
0.605894 | + | 0.795545i | \(0.292815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.15417 | 0.185143 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.7307 | 0.958958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.1228 | 0.685145 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.63704 | 0.130143 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.448521 | 0.0160288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.63090 | −0.236667 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.57721 | −0.0562215 | −0.0281108 | − | 0.999605i | \(-0.508949\pi\) | ||||
−0.0281108 | + | 0.999605i | \(0.508949\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.5795 | 0.839451 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.23086 | −0.185988 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1246 | 0.821178 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.59166 | 0.0919166 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5677 | −0.516015 | −0.258007 | − | 0.966143i | \(-0.583066\pi\) | ||||
−0.258007 | + | 0.966143i | \(0.583066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.7680 | 1.44227 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6199 | 0.410568 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.5481 | 1.04273 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.46569 | −0.157395 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.52304 | −0.264824 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.1280 | 1.02409 | 0.512043 | − | 0.858960i | \(-0.328889\pi\) | ||||
0.512043 | + | 0.858960i | \(0.328889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0351 | 0.984444 | 0.492222 | − | 0.870470i | \(-0.336185\pi\) | ||||
0.492222 | + | 0.870470i | \(0.336185\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.5370 | −0.650122 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3083 | −0.781427 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.8908 | 0.975774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.0140 | 0.734288 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.5015 | 1.48331 | 0.741657 | − | 0.670780i | \(-0.234040\pi\) | ||||
0.741657 | + | 0.670780i | \(0.234040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5662 | 0.507745 | 0.253873 | − | 0.967238i | \(-0.418296\pi\) | ||||
0.253873 | + | 0.967238i | \(0.418296\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.39413 | −0.118168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.7880 | −0.409910 | −0.204955 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204955 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34385 | −0.0814053 | −0.0407027 | − | 0.999171i | \(-0.512960\pi\) | ||||
−0.0407027 | + | 0.999171i | \(0.512960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.8628 | 0.827791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84.7508 | −2.93644 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0885 | −0.833617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.15417 | 0.178154 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.97157 | −0.275209 | −0.137604 | − | 0.990487i | \(-0.543940\pi\) | ||||
−0.137604 | + | 0.990487i | \(0.543940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7988 | −0.993063 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.6118 | −0.778791 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.14314 | −0.314533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.32256 | −0.0798040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.6684 | −0.469099 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.98578 | 0.205190 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.4736 | 1.69394 | 0.846972 | − | 0.531637i | \(-0.178423\pi\) | ||||
0.846972 | + | 0.531637i | \(0.178423\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.22574 | −0.212916 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.7359 | 1.25487 | 0.627437 | − | 0.778667i | \(-0.284104\pi\) | ||||
0.627437 | + | 0.778667i | \(0.284104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8277 | −0.471796 | −0.235898 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235898 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.7167 | −0.467463 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.43337 | −0.116873 | −0.0584366 | − | 0.998291i | \(-0.518612\pi\) | ||||
−0.0584366 | + | 0.998291i | \(0.518612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9314 | 0.643686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.8802 | 0.878937 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.5987 | −1.51291 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6365 | 0.970311 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.30834 | 0.145815 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.46569 | 0.150968 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9838 | 0.944947 | 0.472474 | − | 0.881345i | \(-0.343361\pi\) | ||||
0.472474 | + | 0.881345i | \(0.343361\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.0431 | −0.507392 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.77108 | −0.0933600 | −0.0466800 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466800 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.9052 | −1.44387 | −0.721937 | − | 0.691958i | \(-0.756748\pi\) | ||||
−0.721937 | + | 0.691958i | \(0.756748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.55148 | −0.0521524 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.1991 | −1.81983 | −0.909914 | − | 0.414798i | \(-0.863852\pi\) | ||||
−0.909914 | + | 0.414798i | \(0.863852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62.2758 | 2.08866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.39413 | −0.113707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.7598 | −1.29705 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.7598 | −0.627072 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.70565 | 0.157117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.31175 | 0.0771012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.9709 | 0.565384 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0059 | −0.665755 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.1964 | 0.704591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.4003 | 0.876606 | 0.438303 | − | 0.898827i | \(-0.355580\pi\) | ||||
0.438303 | + | 0.898827i | \(0.355580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3397 | 0.342947 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5662 | 1.27775 | 0.638877 | − | 0.769309i | \(-0.279399\pi\) | ||||
0.638877 | + | 0.769309i | \(0.279399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.2194 | −1.46345 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.91421 | 0.162459 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.9069 | 2.04435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.56345 | 0.249495 | 0.124748 | − | 0.992189i | \(-0.460188\pi\) | ||||
0.124748 | + | 0.992189i | \(0.460188\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.9674 | 1.05336 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.04242 | 0.165973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.98578 | −0.196811 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8316 | 0.355757 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.5329 | −0.936135 | −0.468067 | − | 0.883693i | \(-0.655050\pi\) | ||||
−0.468067 | + | 0.883693i | \(0.655050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 80.5761 | 2.64078 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.1932 | 1.11943 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.2257 | −0.726859 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.9535 | −1.23989 | −0.619944 | − | 0.784646i | \(-0.712845\pi\) | ||||
−0.619944 | + | 0.784646i | \(0.712845\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.5713 | −0.377615 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.79633 | −0.188955 | −0.0944775 | − | 0.995527i | \(-0.530118\pi\) | ||||
−0.0944775 | + | 0.995527i | \(0.530118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.07157 | −0.100024 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.46569 | 0.145269 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.1588 | 1.11001 | 0.555007 | − | 0.831846i | \(-0.312716\pi\) | ||||
0.555007 | + | 0.831846i | \(0.312716\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.9657 | 1.32980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.12915 | 0.101470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.3110 | −0.722724 | −0.361362 | − | 0.932426i | \(-0.617688\pi\) | ||||
−0.361362 | + | 0.932426i | \(0.617688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3909 | 0.465680 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.52234 | −0.0492101 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 64.3422 | 2.07772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.43453 | −0.143049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.76004 | 0.0567166 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.0966 | −0.357212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5282 | −0.692302 | −0.346151 | − | 0.938179i | \(-0.612511\pi\) | ||||
−0.346151 | + | 0.938179i | \(0.612511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.7680 | −1.30966 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.0939 | 0.869486 | 0.434743 | − | 0.900555i | \(-0.356839\pi\) | ||||
0.434743 | + | 0.900555i | \(0.356839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.1660 | −1.44796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.70565 | −0.150701 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.9880 | −0.895416 | −0.447708 | − | 0.894180i | \(-0.647760\pi\) | ||||
−0.447708 | + | 0.894180i | \(0.647760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.4393 | −1.26048 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.39413 | −0.0445110 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2711 | −0.678443 | −0.339222 | − | 0.940706i | \(-0.610164\pi\) | ||||
−0.339222 | + | 0.940706i | \(0.610164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.1652 | −0.451341 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.8022 | 0.884955 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.47991 | −0.142453 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.7023 | −1.64238 | −0.821189 | − | 0.570656i | \(-0.806689\pi\) | ||||
−0.821189 | + | 0.570656i | \(0.806689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.988966 | 0.0313839 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.66004 | 0.274542 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8687 | 0.882610 | 0.441305 | − | 0.897357i | \(-0.354516\pi\) | ||||
0.441305 | + | 0.897357i | \(0.354516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.98578 | −0.189382 |
(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 | 5520.2.a.cb.1.1 | 4 | ||
4.3 | odd | 2 | 2760.2.a.v.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 8280.2.a.bq.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.v.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
5520.2.a.cb.1.1 | 4 | 1.1 | even | 1 | trivial | ||
8280.2.a.bq.1.4 | 4 | 12.11 | even | 2 |