Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 106x^{12} - 384x^{10} + 1005x^{8} - 1200x^{6} + 1030x^{4} - 252x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.13 | ||
Root | \(-1.47769 + 0.853147i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.e.1322.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70629i | 1.20653i | 0.797540 | + | 0.603266i | \(0.206134\pi\) | ||||
−0.797540 | + | 0.603266i | \(0.793866\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.911441 | −0.455720 | ||||||||
\(5\) | −0.829297 | −0.370873 | −0.185437 | − | 0.982656i | \(-0.559370\pi\) | ||||
−0.185437 | + | 0.982656i | \(0.559370\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.85740i | 0.656691i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.41503i | − 0.447470i | ||||||||
\(11\) | 0.190855i | 0.0575449i | 0.999586 | + | 0.0287724i | \(0.00915981\pi\) | ||||
−0.999586 | + | 0.0287724i | \(0.990840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53188i | 0.979568i | 0.871844 | + | 0.489784i | \(0.162924\pi\) | ||||
−0.871844 | + | 0.489784i | \(0.837076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99216 | −1.24804 | ||||||||
\(17\) | 4.60484 | 1.11684 | 0.558418 | − | 0.829559i | \(-0.311408\pi\) | ||||
0.558418 | + | 0.829559i | \(0.311408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.09593i | − 0.939671i | −0.882754 | − | 0.469836i | \(-0.844313\pi\) | ||||
0.882754 | − | 0.469836i | \(-0.155687\pi\) | |||||||
\(20\) | 0.755855 | 0.169014 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.325654 | −0.0694297 | ||||||||
\(23\) | 8.79438i | 1.83376i | 0.399169 | + | 0.916878i | \(0.369299\pi\) | ||||
−0.399169 | + | 0.916878i | \(0.630701\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.31227 | −0.862453 | ||||||||
\(26\) | −6.02643 | −1.18188 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.99271i | 1.48421i | 0.670284 | + | 0.742105i | \(0.266172\pi\) | ||||
−0.670284 | + | 0.742105i | \(0.733828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.56325i | − 1.17879i | −0.807843 | − | 0.589397i | \(-0.799365\pi\) | ||||
0.807843 | − | 0.589397i | \(-0.200635\pi\) | |||||||
\(32\) | − 4.80328i | − 0.849109i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.85721i | 1.34750i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.45644 | 0.239438 | 0.119719 | − | 0.992808i | \(-0.461801\pi\) | ||||
0.119719 | + | 0.992808i | \(0.461801\pi\) | |||||||
\(38\) | 6.98887 | 1.13374 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 1.54034i | − 0.243549i | ||||||||
\(41\) | −12.1217 | −1.89309 | −0.946546 | − | 0.322569i | \(-0.895454\pi\) | ||||
−0.946546 | + | 0.322569i | \(0.895454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.83253 | 0.431957 | 0.215978 | − | 0.976398i | \(-0.430706\pi\) | ||||
0.215978 | + | 0.976398i | \(0.430706\pi\) | |||||||
\(44\) | − 0.173953i | − 0.0262244i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.0058 | −2.21248 | ||||||||
\(47\) | −1.49423 | −0.217955 | −0.108978 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108978 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 7.35800i | − 1.04058i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 3.21910i | − 0.446409i | ||||||||
\(53\) | 4.55622i | 0.625845i | 0.949779 | + | 0.312922i | \(0.101308\pi\) | ||||
−0.949779 | + | 0.312922i | \(0.898692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.158275i | − 0.0213418i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.6379 | −1.79075 | ||||||||
\(59\) | −5.67378 | −0.738663 | −0.369331 | − | 0.929298i | \(-0.620413\pi\) | ||||
−0.369331 | + | 0.929298i | \(0.620413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9229i | 1.39854i | 0.714859 | + | 0.699268i | \(0.246491\pi\) | ||||
−0.714859 | + | 0.699268i | \(0.753509\pi\) | |||||||
\(62\) | 11.1988 | 1.42225 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.78850 | −0.223562 | ||||||||
\(65\) | − 2.92898i | − 0.363295i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.64347 | −0.567290 | −0.283645 | − | 0.958929i | \(-0.591544\pi\) | ||||
−0.283645 | + | 0.958929i | \(0.591544\pi\) | |||||||
\(68\) | −4.19704 | −0.508965 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0568i | 1.19352i | 0.802418 | + | 0.596762i | \(0.203546\pi\) | ||||
−0.802418 | + | 0.596762i | \(0.796454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.95020i | − 0.930501i | −0.885179 | − | 0.465250i | \(-0.845964\pi\) | ||||
0.885179 | − | 0.465250i | \(-0.154036\pi\) | |||||||
\(74\) | 2.48512i | 0.288889i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.73320i | 0.428227i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.96332 | −0.670926 | −0.335463 | − | 0.942053i | \(-0.608893\pi\) | ||||
−0.335463 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(80\) | 4.13998 | 0.462864 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 20.6832i | − 2.28408i | ||||||||
\(83\) | 2.05346 | 0.225396 | 0.112698 | − | 0.993629i | \(-0.464051\pi\) | ||||
0.112698 | + | 0.993629i | \(0.464051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.81878 | −0.414205 | ||||||||
\(86\) | 4.83313i | 0.521170i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.354494 | −0.0377892 | ||||||||
\(89\) | 8.83575 | 0.936587 | 0.468294 | − | 0.883573i | \(-0.344869\pi\) | ||||
0.468294 | + | 0.883573i | \(0.344869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 8.01556i | − 0.835680i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 2.54959i | − 0.262970i | ||||||||
\(95\) | 3.39675i | 0.348499i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.15962i | 0.726949i | 0.931604 | + | 0.363475i | \(0.118410\pi\) | ||||
−0.931604 | + | 0.363475i | \(0.881590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.93037 | 0.393037 | ||||||||
\(101\) | −9.87162 | −0.982263 | −0.491132 | − | 0.871085i | \(-0.663417\pi\) | ||||
−0.491132 | + | 0.871085i | \(0.663417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.10848i | 0.798952i | 0.916744 | + | 0.399476i | \(0.130808\pi\) | ||||
−0.916744 | + | 0.399476i | \(0.869192\pi\) | |||||||
\(104\) | −6.56013 | −0.643273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.77425 | −0.755102 | ||||||||
\(107\) | − 15.1370i | − 1.46335i | −0.681654 | − | 0.731675i | \(-0.738739\pi\) | ||||
0.681654 | − | 0.731675i | \(-0.261261\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5779 | −1.30053 | −0.650266 | − | 0.759707i | \(-0.725342\pi\) | ||||
−0.650266 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(110\) | 0.270064 | 0.0257496 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.9456i | − 1.31189i | −0.754809 | − | 0.655944i | \(-0.772271\pi\) | ||||
0.754809 | − | 0.655944i | \(-0.227729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.29316i | − 0.680090i | ||||||||
\(116\) | − 7.28488i | − 0.676384i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 9.68113i | − 0.891221i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9636 | 0.996689 | ||||||||
\(122\) | −18.6377 | −1.68738 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.98201i | 0.537201i | ||||||||
\(125\) | 7.72264 | 0.690734 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6627 | 1.56731 | 0.783654 | − | 0.621198i | \(-0.213354\pi\) | ||||
0.783654 | + | 0.621198i | \(0.213354\pi\) | |||||||
\(128\) | − 12.6583i | − 1.11884i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.99770 | 0.438328 | ||||||||
\(131\) | 21.0008 | 1.83485 | 0.917424 | − | 0.397910i | \(-0.130264\pi\) | ||||
0.917424 | + | 0.397910i | \(0.130264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 7.92312i | − 0.684453i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.55303i | 0.733417i | ||||||||
\(137\) | 4.08661i | 0.349143i | 0.984645 | + | 0.174571i | \(0.0558540\pi\) | ||||
−0.984645 | + | 0.174571i | \(0.944146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0668i | 1.27795i | 0.769229 | + | 0.638974i | \(0.220641\pi\) | ||||
−0.769229 | + | 0.638974i | \(0.779359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.1599 | −1.44003 | ||||||||
\(143\) | −0.674076 | −0.0563691 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 6.62833i | − 0.550453i | ||||||||
\(146\) | 13.5654 | 1.12268 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.32746 | −0.109117 | ||||||||
\(149\) | − 3.91310i | − 0.320574i | −0.987070 | − | 0.160287i | \(-0.948758\pi\) | ||||
0.987070 | − | 0.160287i | \(-0.0512419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.3370 | 1.32949 | 0.664743 | − | 0.747072i | \(-0.268541\pi\) | ||||
0.664743 | + | 0.747072i | \(0.268541\pi\) | |||||||
\(152\) | 7.60779 | 0.617074 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.44289i | 0.437183i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.39104i | 0.589869i | 0.955517 | + | 0.294934i | \(0.0952978\pi\) | ||||
−0.955517 | + | 0.294934i | \(0.904702\pi\) | |||||||
\(158\) | − 10.1752i | − 0.809494i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.98335i | 0.314912i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.6571 | 1.46134 | 0.730669 | − | 0.682732i | \(-0.239208\pi\) | ||||
0.730669 | + | 0.682732i | \(0.239208\pi\) | |||||||
\(164\) | 11.0482 | 0.862721 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50381i | 0.271948i | ||||||||
\(167\) | −12.7703 | −0.988195 | −0.494098 | − | 0.869406i | \(-0.664501\pi\) | ||||
−0.494098 | + | 0.869406i | \(0.664501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.525810 | 0.0404469 | ||||||||
\(170\) | − 6.51596i | − 0.499751i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.58168 | −0.196852 | ||||||||
\(173\) | 5.20168 | 0.395477 | 0.197738 | − | 0.980255i | \(-0.436640\pi\) | ||||
0.197738 | + | 0.980255i | \(0.436640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 0.952777i | − 0.0718182i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.0764i | 1.13002i | ||||||||
\(179\) | 4.97724i | 0.372016i | 0.982548 | + | 0.186008i | \(0.0595551\pi\) | ||||
−0.982548 | + | 0.186008i | \(0.940445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 20.9730i | − 1.55891i | −0.626458 | − | 0.779455i | \(-0.715496\pi\) | ||||
0.626458 | − | 0.779455i | \(-0.284504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.3347 | −1.20421 | ||||||||
\(185\) | −1.20782 | −0.0888009 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.878855i | 0.0642682i | ||||||||
\(188\) | 1.36190 | 0.0993267 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.79585 | −0.420475 | ||||||||
\(191\) | − 11.1280i | − 0.805190i | −0.915378 | − | 0.402595i | \(-0.868108\pi\) | ||||
0.915378 | − | 0.402595i | \(-0.131892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.60498 | 0.691381 | 0.345691 | − | 0.938349i | \(-0.387645\pi\) | ||||
0.345691 | + | 0.938349i | \(0.387645\pi\) | |||||||
\(194\) | −12.2164 | −0.877088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.94588i | 0.209885i | 0.994478 | + | 0.104943i | \(0.0334659\pi\) | ||||
−0.994478 | + | 0.104943i | \(0.966534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.571631i | 0.0405219i | 0.999795 | + | 0.0202609i | \(0.00644970\pi\) | ||||
−0.999795 | + | 0.0202609i | \(0.993550\pi\) | |||||||
\(200\) | − 8.00961i | − 0.566365i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 16.8439i | − 1.18513i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0525 | 0.702097 | ||||||||
\(206\) | −13.8354 | −0.963961 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 17.6317i | − 1.22254i | ||||||||
\(209\) | 0.781728 | 0.0540732 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9965 | 1.03240 | 0.516201 | − | 0.856467i | \(-0.327346\pi\) | ||||
0.516201 | + | 0.856467i | \(0.327346\pi\) | |||||||
\(212\) | − 4.15272i | − 0.285210i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.8282 | 1.76558 | ||||||||
\(215\) | −2.34901 | −0.160201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 23.1680i | − 1.56913i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.144259i | 0.00972591i | ||||||||
\(221\) | 16.2637i | 1.09402i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.78315i | 0.253339i | 0.991945 | + | 0.126669i | \(0.0404287\pi\) | ||||
−0.991945 | + | 0.126669i | \(0.959571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.7953 | 1.58284 | ||||||||
\(227\) | −13.8016 | −0.916043 | −0.458021 | − | 0.888941i | \(-0.651442\pi\) | ||||
−0.458021 | + | 0.888941i | \(0.651442\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9876i | 0.990412i | 0.868776 | + | 0.495206i | \(0.164907\pi\) | ||||
−0.868776 | + | 0.495206i | \(0.835093\pi\) | |||||||
\(230\) | 12.4443 | 0.820551 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.8457 | −0.974667 | ||||||||
\(233\) | 10.5808i | 0.693170i | 0.938018 | + | 0.346585i | \(0.112659\pi\) | ||||
−0.938018 | + | 0.346585i | \(0.887341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.23916 | 0.0808338 | ||||||||
\(236\) | 5.17131 | 0.336624 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.98571i | 0.516553i | 0.966071 | + | 0.258276i | \(0.0831545\pi\) | ||||
−0.966071 | + | 0.258276i | \(0.916845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 21.5364i | − 1.38728i | −0.720321 | − | 0.693640i | \(-0.756006\pi\) | ||||
0.720321 | − | 0.693640i | \(-0.243994\pi\) | |||||||
\(242\) | 18.7071i | 1.20254i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 9.95559i | − 0.637342i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4663 | 0.920472 | ||||||||
\(248\) | 12.1906 | 0.774104 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.1771i | 0.833393i | ||||||||
\(251\) | −14.2569 | −0.899890 | −0.449945 | − | 0.893056i | \(-0.648556\pi\) | ||||
−0.449945 | + | 0.893056i | \(0.648556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.67845 | −0.105523 | ||||||||
\(254\) | 30.1377i | 1.89101i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.0217 | 1.12636 | ||||||||
\(257\) | 1.44368 | 0.0900542 | 0.0450271 | − | 0.998986i | \(-0.485663\pi\) | ||||
0.0450271 | + | 0.998986i | \(0.485663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.66959i | 0.165561i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 35.8336i | 2.21380i | ||||||||
\(263\) | − 15.5401i | − 0.958241i | −0.877749 | − | 0.479121i | \(-0.840956\pi\) | ||||
0.877749 | − | 0.479121i | \(-0.159044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 3.77846i | − 0.232109i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.23224 | 0.258525 | ||||||||
\(269\) | 13.6464 | 0.832033 | 0.416016 | − | 0.909357i | \(-0.363426\pi\) | ||||
0.416016 | + | 0.909357i | \(0.363426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.27251i | 0.259537i | 0.991544 | + | 0.129768i | \(0.0414233\pi\) | ||||
−0.991544 | + | 0.129768i | \(0.958577\pi\) | |||||||
\(272\) | −22.9881 | −1.39386 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.97297 | −0.421252 | ||||||||
\(275\) | − 0.823016i | − 0.0496297i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.91170 | 0.355199 | 0.177600 | − | 0.984103i | \(-0.443167\pi\) | ||||
0.177600 | + | 0.984103i | \(0.443167\pi\) | |||||||
\(278\) | −25.7084 | −1.54188 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7012i | 1.41390i | 0.707265 | + | 0.706948i | \(0.249929\pi\) | ||||
−0.707265 | + | 0.706948i | \(0.750071\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0056i | 1.24865i | 0.781164 | + | 0.624326i | \(0.214626\pi\) | ||||
−0.781164 | + | 0.624326i | \(0.785374\pi\) | |||||||
\(284\) | − 9.16619i | − 0.543913i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 1.15017i | − 0.0680111i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.20452 | 0.247324 | ||||||||
\(290\) | 11.3099 | 0.664140 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.24614i | 0.424048i | ||||||||
\(293\) | 29.4325 | 1.71947 | 0.859734 | − | 0.510743i | \(-0.170629\pi\) | ||||
0.859734 | + | 0.510743i | \(0.170629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.70525 | 0.273950 | ||||||||
\(296\) | 2.70520i | 0.157236i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.67690 | 0.386782 | ||||||||
\(299\) | −31.0607 | −1.79629 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.8757i | 1.60407i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.4475i | 1.17275i | ||||||||
\(305\) | − 9.05835i | − 0.518679i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.6735i | − 0.951608i | −0.879551 | − | 0.475804i | \(-0.842157\pi\) | ||||
0.879551 | − | 0.475804i | \(-0.157843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.28717 | −0.527476 | ||||||||
\(311\) | 29.7981 | 1.68970 | 0.844848 | − | 0.535006i | \(-0.179691\pi\) | ||||
0.844848 | + | 0.535006i | \(0.179691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5935i | 1.33358i | 0.745244 | + | 0.666792i | \(0.232333\pi\) | ||||
−0.745244 | + | 0.666792i | \(0.767667\pi\) | |||||||
\(314\) | −12.6113 | −0.711696 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.43521 | 0.305754 | ||||||||
\(317\) | 12.6339i | 0.709592i | 0.934944 | + | 0.354796i | \(0.115450\pi\) | ||||
−0.934944 | + | 0.354796i | \(0.884550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.52545 | −0.0854086 | ||||||||
\(320\) | 1.48320 | 0.0829131 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 18.8611i | − 1.04946i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 15.2304i | − 0.844831i | ||||||||
\(326\) | 31.8345i | 1.76315i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 22.5149i | − 1.24318i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0909 | 0.829470 | 0.414735 | − | 0.909942i | \(-0.363874\pi\) | ||||
0.414735 | + | 0.909942i | \(0.363874\pi\) | |||||||
\(332\) | −1.87161 | −0.102718 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 21.7899i | − 1.19229i | ||||||||
\(335\) | 3.85081 | 0.210392 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.8864 | −1.79143 | −0.895717 | − | 0.444624i | \(-0.853337\pi\) | ||||
−0.895717 | + | 0.444624i | \(0.853337\pi\) | |||||||
\(338\) | 0.897187i | 0.0488005i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.48059 | 0.188762 | ||||||||
\(341\) | 1.25263 | 0.0678336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.26115i | 0.283662i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.87560i | 0.477155i | ||||||||
\(347\) | 0.127644i | 0.00685227i | 0.999994 | + | 0.00342613i | \(0.00109057\pi\) | ||||
−0.999994 | + | 0.00342613i | \(0.998909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 22.3227i | − 1.19491i | −0.801903 | − | 0.597454i | \(-0.796179\pi\) | ||||
0.801903 | − | 0.597454i | \(-0.203821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.916729 | 0.0488618 | ||||||||
\(353\) | −4.12738 | −0.219678 | −0.109839 | − | 0.993949i | \(-0.535034\pi\) | ||||
−0.109839 | + | 0.993949i | \(0.535034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.34009i | − 0.442646i | ||||||||
\(356\) | −8.05326 | −0.426822 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.49263 | −0.448850 | ||||||||
\(359\) | 30.0512i | 1.58604i | 0.609195 | + | 0.793021i | \(0.291493\pi\) | ||||
−0.609195 | + | 0.793021i | \(0.708507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.22334 | 0.117018 | ||||||||
\(362\) | 35.7861 | 1.88087 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.59308i | 0.345098i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.65946i | 0.295421i | 0.989031 | + | 0.147711i | \(0.0471905\pi\) | ||||
−0.989031 | + | 0.147711i | \(0.952810\pi\) | |||||||
\(368\) | − 43.9029i | − 2.28860i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 2.06090i | − 0.107141i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.4449 | 1.00682 | 0.503408 | − | 0.864049i | \(-0.332079\pi\) | ||||
0.503408 | + | 0.864049i | \(0.332079\pi\) | |||||||
\(374\) | −1.49958 | −0.0775417 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 2.77538i | − 0.143129i | ||||||||
\(377\) | −28.2293 | −1.45388 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4544 | 0.742473 | 0.371236 | − | 0.928538i | \(-0.378934\pi\) | ||||
0.371236 | + | 0.928538i | \(0.378934\pi\) | |||||||
\(380\) | − 3.09593i | − 0.158818i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.9876 | 0.971488 | ||||||||
\(383\) | −32.2952 | −1.65021 | −0.825103 | − | 0.564982i | \(-0.808883\pi\) | ||||
−0.825103 | + | 0.564982i | \(0.808883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.3889i | 0.834174i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6.52557i | − 0.331286i | ||||||||
\(389\) | − 24.5805i | − 1.24628i | −0.782111 | − | 0.623139i | \(-0.785857\pi\) | ||||
0.782111 | − | 0.623139i | \(-0.214143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.4967i | 2.04801i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.02654 | −0.253234 | ||||||||
\(395\) | 4.94536 | 0.248828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.7615i | 1.24274i | 0.783516 | + | 0.621372i | \(0.213424\pi\) | ||||
−0.783516 | + | 0.621372i | \(0.786576\pi\) | |||||||
\(398\) | −0.975371 | −0.0488909 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5275 | 1.07638 | ||||||||
\(401\) | 5.67595i | 0.283443i | 0.989907 | + | 0.141722i | \(0.0452638\pi\) | ||||
−0.989907 | + | 0.141722i | \(0.954736\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.1806 | 1.15471 | ||||||||
\(404\) | 8.99740 | 0.447637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.277969i | 0.0137784i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 15.7394i | − 0.778265i | −0.921182 | − | 0.389132i | \(-0.872775\pi\) | ||||
0.921182 | − | 0.389132i | \(-0.127225\pi\) | |||||||
\(410\) | 17.1525i | 0.847103i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 7.39039i | − 0.364099i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.70293 | −0.0835935 | ||||||||
\(416\) | 16.9646 | 0.831760 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.33386i | 0.0652411i | ||||||||
\(419\) | 26.4182 | 1.29061 | 0.645307 | − | 0.763923i | \(-0.276729\pi\) | ||||
0.645307 | + | 0.763923i | \(0.276729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3312 | 0.942145 | 0.471073 | − | 0.882094i | \(-0.343867\pi\) | ||||
0.471073 | + | 0.882094i | \(0.343867\pi\) | |||||||
\(422\) | 25.5885i | 1.24563i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.46274 | −0.410987 | ||||||||
\(425\) | −19.8573 | −0.963219 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.7965i | 0.666878i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 4.00810i | − 0.193288i | ||||||||
\(431\) | 11.5013i | 0.553996i | 0.960870 | + | 0.276998i | \(0.0893396\pi\) | ||||
−0.960870 | + | 0.276998i | \(0.910660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.87564i | − 0.0901374i | −0.998984 | − | 0.0450687i | \(-0.985649\pi\) | ||||
0.998984 | − | 0.0450687i | \(-0.0143507\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3755 | 0.592679 | ||||||||
\(437\) | 36.0212 | 1.72313 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 15.8957i | − 0.758659i | −0.925262 | − | 0.379330i | \(-0.876155\pi\) | ||||
0.925262 | − | 0.379330i | \(-0.123845\pi\) | |||||||
\(440\) | 0.293981 | 0.0140150 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.7507 | −1.31997 | ||||||||
\(443\) | 15.2772i | 0.725840i | 0.931820 | + | 0.362920i | \(0.118220\pi\) | ||||
−0.931820 | + | 0.362920i | \(0.881780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.32746 | −0.347355 | ||||||||
\(446\) | −6.45517 | −0.305661 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 22.7142i | − 1.07195i | −0.844234 | − | 0.535975i | \(-0.819944\pi\) | ||||
0.844234 | − | 0.535975i | \(-0.180056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.31348i | − 0.108938i | ||||||||
\(452\) | 12.7106i | 0.597855i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 23.5495i | − 1.10523i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.8978 | −1.07111 | −0.535557 | − | 0.844499i | \(-0.679898\pi\) | ||||
−0.535557 | + | 0.844499i | \(0.679898\pi\) | |||||||
\(458\) | −25.5733 | −1.19496 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.64728i | 0.309931i | ||||||||
\(461\) | −25.9796 | −1.20999 | −0.604995 | − | 0.796230i | \(-0.706825\pi\) | ||||
−0.604995 | + | 0.796230i | \(0.706825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.42642 | 0.205713 | 0.102857 | − | 0.994696i | \(-0.467202\pi\) | ||||
0.102857 | + | 0.994696i | \(0.467202\pi\) | |||||||
\(464\) | − 39.9009i | − 1.85235i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.0539 | −0.836333 | ||||||||
\(467\) | 19.1657 | 0.886884 | 0.443442 | − | 0.896303i | \(-0.353757\pi\) | ||||
0.443442 | + | 0.896303i | \(0.353757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.11437i | 0.0975285i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 10.5385i | − 0.485073i | ||||||||
\(473\) | 0.540602i | 0.0248569i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.6627i | 0.810422i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.6260 | −0.623238 | ||||||||
\(479\) | −33.5569 | −1.53326 | −0.766628 | − | 0.642092i | \(-0.778067\pi\) | ||||
−0.766628 | + | 0.642092i | \(0.778067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.14398i | 0.234545i | ||||||||
\(482\) | 36.7474 | 1.67380 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.99265 | −0.454211 | ||||||||
\(485\) | − 5.93745i | − 0.269606i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.9091 | 0.856855 | 0.428428 | − | 0.903576i | \(-0.359068\pi\) | ||||
0.428428 | + | 0.903576i | \(0.359068\pi\) | |||||||
\(488\) | −20.2883 | −0.918406 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.27292i | 0.102575i | 0.998684 | + | 0.0512876i | \(0.0163325\pi\) | ||||
−0.998684 | + | 0.0512876i | \(0.983667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.8051i | 1.65762i | ||||||||
\(494\) | 24.6838i | 1.11058i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.7648i | 1.47118i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.35630 | −0.195015 | −0.0975074 | − | 0.995235i | \(-0.531087\pi\) | ||||
−0.0975074 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(500\) | −7.03873 | −0.314781 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 24.3265i | − 1.08575i | ||||||||
\(503\) | 31.8828 | 1.42158 | 0.710792 | − | 0.703402i | \(-0.248337\pi\) | ||||
0.710792 | + | 0.703402i | \(0.248337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.18651 | 0.364295 | ||||||||
\(506\) | − 2.86393i | − 0.127317i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.0985 | −0.714254 | ||||||||
\(509\) | 31.0185 | 1.37487 | 0.687435 | − | 0.726245i | \(-0.258736\pi\) | ||||
0.687435 | + | 0.726245i | \(0.258736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.43386i | 0.240145i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.46334i | 0.108653i | ||||||||
\(515\) | − 6.72434i | − 0.296310i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.285180i | − 0.0125422i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.44030 | 0.238573 | ||||||||
\(521\) | −27.1816 | −1.19085 | −0.595425 | − | 0.803411i | \(-0.703016\pi\) | ||||
−0.595425 | + | 0.803411i | \(0.703016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 20.8034i | − 0.909667i | −0.890576 | − | 0.454834i | \(-0.849699\pi\) | ||||
0.890576 | − | 0.454834i | \(-0.150301\pi\) | |||||||
\(524\) | −19.1410 | −0.836178 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.5159 | 1.15615 | ||||||||
\(527\) | − 30.2227i | − 1.31652i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −54.3411 | −2.36266 | ||||||||
\(530\) | 6.44717 | 0.280047 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 42.8124i | − 1.85441i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5531i | 0.542717i | ||||||||
\(536\) | − 8.62479i | − 0.372534i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.2847i | 1.00387i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.11946 | 0.134116 | 0.0670581 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670581 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(542\) | −7.29016 | −0.313139 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 22.1183i | − 0.948316i | ||||||||
\(545\) | 11.2602 | 0.482332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5589 | 0.836278 | 0.418139 | − | 0.908383i | \(-0.362682\pi\) | ||||
0.418139 | + | 0.908383i | \(0.362682\pi\) | |||||||
\(548\) | − 3.72471i | − 0.159112i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.40431 | 0.0598799 | ||||||||
\(551\) | 32.7376 | 1.39467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0871i | 0.428560i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 13.7325i | − 0.582387i | ||||||||
\(557\) | − 9.72325i | − 0.411988i | −0.978553 | − | 0.205994i | \(-0.933957\pi\) | ||||
0.978553 | − | 0.205994i | \(-0.0660427\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0042i | 0.423131i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.4413 | −1.70591 | ||||||||
\(563\) | 13.3090 | 0.560908 | 0.280454 | − | 0.959867i | \(-0.409515\pi\) | ||||
0.280454 | + | 0.959867i | \(0.409515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.5650i | 0.486544i | ||||||||
\(566\) | −35.8417 | −1.50654 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.6796 | −0.783777 | ||||||||
\(569\) | − 30.3767i | − 1.27346i | −0.771088 | − | 0.636729i | \(-0.780287\pi\) | ||||
0.771088 | − | 0.636729i | \(-0.219713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.23540 | 0.0516997 | 0.0258498 | − | 0.999666i | \(-0.491771\pi\) | ||||
0.0258498 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(572\) | 0.614381 | 0.0256885 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 37.9237i | − 1.58153i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 24.3910i | − 1.01541i | −0.861531 | − | 0.507705i | \(-0.830494\pi\) | ||||
0.861531 | − | 0.507705i | \(-0.169506\pi\) | |||||||
\(578\) | 7.17414i | 0.298405i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.04133i | 0.250853i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.869576 | −0.0360142 | ||||||||
\(584\) | 14.7667 | 0.611051 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 50.2206i | 2.07459i | ||||||||
\(587\) | 2.65150 | 0.109439 | 0.0547196 | − | 0.998502i | \(-0.482574\pi\) | ||||
0.0547196 | + | 0.998502i | \(0.482574\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.8826 | −1.10768 | ||||||||
\(590\) | 8.02854i | 0.330530i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.27079 | −0.298827 | ||||||||
\(593\) | −44.8945 | −1.84360 | −0.921799 | − | 0.387668i | \(-0.873281\pi\) | ||||
−0.921799 | + | 0.387668i | \(0.873281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.56656i | 0.146092i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 52.9987i | − 2.16728i | ||||||||
\(599\) | 10.8714i | 0.444194i | 0.975025 | + | 0.222097i | \(0.0712902\pi\) | ||||
−0.975025 | + | 0.222097i | \(0.928710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 28.7100i | − 1.17111i | −0.810634 | − | 0.585553i | \(-0.800877\pi\) | ||||
0.810634 | − | 0.585553i | \(-0.199123\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.8902 | −0.605874 | ||||||||
\(605\) | −9.09206 | −0.369645 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 33.1928i | − 1.34726i | −0.739071 | − | 0.673628i | \(-0.764735\pi\) | ||||
0.739071 | − | 0.673628i | \(-0.235265\pi\) | |||||||
\(608\) | −19.6739 | −0.797883 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.4562 | 0.625804 | ||||||||
\(611\) | − 5.27743i | − 0.213502i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.08420 | 0.0841800 | 0.0420900 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420900 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(614\) | 28.4499 | 1.14815 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.4764i | − 0.502283i | −0.967950 | − | 0.251141i | \(-0.919194\pi\) | ||||
0.967950 | − | 0.251141i | \(-0.0808059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 48.2241i | − 1.93829i | −0.246489 | − | 0.969146i | \(-0.579277\pi\) | ||||
0.246489 | − | 0.969146i | \(-0.420723\pi\) | |||||||
\(620\) | − 4.96087i | − 0.199233i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 50.8444i | 2.03867i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1570 | 0.606279 | ||||||||
\(626\) | −40.2574 | −1.60901 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 6.73649i | − 0.268815i | ||||||||
\(629\) | 6.70668 | 0.267413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7024 | 0.903767 | 0.451883 | − | 0.892077i | \(-0.350752\pi\) | ||||
0.451883 | + | 0.892077i | \(0.350752\pi\) | |||||||
\(632\) | − 11.0763i | − 0.440591i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.5572 | −0.856146 | ||||||||
\(635\) | −14.6476 | −0.581272 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 2.60286i | − 0.103048i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.4975i | 0.414949i | ||||||||
\(641\) | − 0.622832i | − 0.0246004i | −0.999924 | − | 0.0123002i | \(-0.996085\pi\) | ||||
0.999924 | − | 0.0123002i | \(-0.00391537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8900i | 0.508332i | 0.967161 | + | 0.254166i | \(0.0818010\pi\) | ||||
−0.967161 | + | 0.254166i | \(0.918199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.1826 | 1.26621 | ||||||||
\(647\) | −18.1592 | −0.713913 | −0.356957 | − | 0.934121i | \(-0.616186\pi\) | ||||
−0.356957 | + | 0.934121i | \(0.616186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 1.08287i | − 0.0425062i | ||||||||
\(650\) | 25.9876 | 1.01932 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0049 | −0.665961 | ||||||||
\(653\) | − 22.5352i | − 0.881870i | −0.897539 | − | 0.440935i | \(-0.854647\pi\) | ||||
0.897539 | − | 0.440935i | \(-0.145353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.4159 | −0.680496 | ||||||||
\(656\) | 60.5135 | 2.36265 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.39800i | 0.0934130i | 0.998909 | + | 0.0467065i | \(0.0148725\pi\) | ||||
−0.998909 | + | 0.0467065i | \(0.985127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.08466i | − 0.314457i | −0.987562 | − | 0.157228i | \(-0.949744\pi\) | ||||
0.987562 | − | 0.157228i | \(-0.0502559\pi\) | |||||||
\(662\) | 25.7495i | 1.00078i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.81410i | 0.148016i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −70.2910 | −2.72168 | ||||||||
\(668\) | 11.6394 | 0.450341 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.57062i | 0.253845i | ||||||||
\(671\) | −2.08469 | −0.0804786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3603 | −1.05466 | −0.527331 | − | 0.849660i | \(-0.676807\pi\) | ||||
−0.527331 | + | 0.849660i | \(0.676807\pi\) | |||||||
\(674\) | − 56.1138i | − 2.16142i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.479245 | −0.0184325 | ||||||||
\(677\) | −25.4870 | −0.979545 | −0.489773 | − | 0.871850i | \(-0.662920\pi\) | ||||
−0.489773 | + | 0.871850i | \(0.662920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 7.09301i | − 0.272004i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.13735i | 0.0818434i | ||||||||
\(683\) | − 31.6527i | − 1.21116i | −0.795786 | − | 0.605578i | \(-0.792942\pi\) | ||||
0.795786 | − | 0.605578i | \(-0.207058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.38902i | − 0.129488i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.1404 | −0.539099 | ||||||||
\(689\) | −16.0920 | −0.613058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 9.59867i | − 0.365150i | −0.983192 | − | 0.182575i | \(-0.941557\pi\) | ||||
0.983192 | − | 0.182575i | \(-0.0584433\pi\) | |||||||
\(692\) | −4.74102 | −0.180227 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.217798 | −0.00826748 | ||||||||
\(695\) | − 12.4948i | − 0.473956i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.8185 | −2.11427 | ||||||||
\(698\) | 38.0891 | 1.44170 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.57884i | 0.324018i | 0.986789 | + | 0.162009i | \(0.0517974\pi\) | ||||
−0.986789 | + | 0.162009i | \(0.948203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.96549i | − 0.224993i | ||||||||
\(704\) | − 0.341343i | − 0.0128648i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 7.04253i | − 0.265049i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9079 | −0.559876 | −0.279938 | − | 0.960018i | \(-0.590314\pi\) | ||||
−0.279938 | + | 0.960018i | \(0.590314\pi\) | |||||||
\(710\) | 14.2306 | 0.534067 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.4115i | 0.615048i | ||||||||
\(713\) | 57.7197 | 2.16162 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.559010 | 0.0209058 | ||||||||
\(716\) | − 4.53646i | − 0.169535i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −51.2762 | −1.91361 | ||||||||
\(719\) | 24.8323 | 0.926087 | 0.463043 | − | 0.886336i | \(-0.346757\pi\) | ||||
0.463043 | + | 0.886336i | \(0.346757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.79368i | 0.141186i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.1156i | 0.710427i | ||||||||
\(725\) | − 34.4667i | − 1.28006i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 4.55497i | − 0.168934i | −0.996426 | − | 0.0844672i | \(-0.973081\pi\) | ||||
0.996426 | − | 0.0844672i | \(-0.0269188\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.2497 | −0.416371 | ||||||||
\(731\) | 13.0433 | 0.482425 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 11.4165i | − 0.421678i | −0.977521 | − | 0.210839i | \(-0.932380\pi\) | ||||
0.977521 | − | 0.210839i | \(-0.0676195\pi\) | |||||||
\(734\) | −9.65671 | −0.356436 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42.2419 | 1.55706 | ||||||||
\(737\) | − 0.886227i | − 0.0326446i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3965 | 0.566368 | 0.283184 | − | 0.959066i | \(-0.408609\pi\) | ||||
0.283184 | + | 0.959066i | \(0.408609\pi\) | |||||||
\(740\) | 1.10086 | 0.0404684 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 45.6525i | − 1.67483i | −0.546571 | − | 0.837413i | \(-0.684067\pi\) | ||||
0.546571 | − | 0.837413i | \(-0.315933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.24512i | 0.118892i | ||||||||
\(746\) | 33.1787i | 1.21476i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 0.801024i | − 0.0292883i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.7591 | 0.793999 | 0.397000 | − | 0.917819i | \(-0.370051\pi\) | ||||
0.397000 | + | 0.917819i | \(0.370051\pi\) | |||||||
\(752\) | 7.45941 | 0.272017 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 48.1675i | − 1.75416i | ||||||||
\(755\) | −13.5482 | −0.493071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.5031 | −1.83556 | −0.917782 | − | 0.397084i | \(-0.870022\pi\) | ||||
−0.917782 | + | 0.397084i | \(0.870022\pi\) | |||||||
\(758\) | 24.6635i | 0.895817i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.30912 | −0.228856 | ||||||||
\(761\) | 7.75425 | 0.281092 | 0.140546 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140546 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1425i | 0.366942i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 55.1051i | − 1.99103i | ||||||||
\(767\) | − 20.0391i | − 0.723570i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.4354i | 0.917226i | 0.888636 | + | 0.458613i | \(0.151654\pi\) | ||||
−0.888636 | + | 0.458613i | \(0.848346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.75437 | −0.315077 | ||||||||
\(773\) | 1.43074 | 0.0514602 | 0.0257301 | − | 0.999669i | \(-0.491809\pi\) | ||||
0.0257301 | + | 0.999669i | \(0.491809\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.3025i | 1.01666i | ||||||||
\(776\) | −13.2983 | −0.477381 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.9415 | 1.50368 | ||||||||
\(779\) | 49.6497i | 1.77888i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.91939 | −0.0686812 | ||||||||
\(782\) | −69.0993 | −2.47098 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.12937i | − 0.218766i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.5756i | 1.62459i | 0.583244 | + | 0.812297i | \(0.301783\pi\) | ||||
−0.583244 | + | 0.812297i | \(0.698217\pi\) | |||||||
\(788\) | − 2.68500i | − 0.0956491i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.43825i | 0.300219i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.5785 | −1.36996 | ||||||||
\(794\) | −42.2504 | −1.49941 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 0.521008i | − 0.0184666i | ||||||||
\(797\) | −20.8400 | −0.738189 | −0.369095 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369095 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.88067 | −0.243421 | ||||||||
\(800\) | 20.7130i | 0.732317i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.68484 | −0.341984 | ||||||||
\(803\) | 1.51733 | 0.0535455 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 39.5530i | 1.39319i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 18.3356i | − 0.645043i | ||||||||
\(809\) | 51.6009i | 1.81419i | 0.420926 | + | 0.907095i | \(0.361705\pi\) | ||||
−0.420926 | + | 0.907095i | \(0.638295\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4591i | 0.823759i | 0.911238 | + | 0.411879i | \(0.135127\pi\) | ||||
−0.911238 | + | 0.411879i | \(0.864873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.474296 | −0.0166241 | ||||||||
\(815\) | −15.4723 | −0.541971 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 11.6019i | − 0.405897i | ||||||||
\(818\) | 26.8561 | 0.939002 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.16226 | −0.319960 | ||||||||
\(821\) | 22.1858i | 0.774289i | 0.922019 | + | 0.387145i | \(0.126539\pi\) | ||||
−0.922019 | + | 0.387145i | \(0.873461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.09677 | 0.212520 | 0.106260 | − | 0.994338i | \(-0.466112\pi\) | ||||
0.106260 | + | 0.994338i | \(0.466112\pi\) | |||||||
\(824\) | −15.0607 | −0.524664 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.2806i | 1.36592i | 0.730456 | + | 0.682960i | \(0.239308\pi\) | ||||
−0.730456 | + | 0.682960i | \(0.760692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2813i | 0.426548i | 0.976992 | + | 0.213274i | \(0.0684127\pi\) | ||||
−0.976992 | + | 0.213274i | \(0.931587\pi\) | |||||||
\(830\) | − 2.90570i | − 0.100858i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 6.31676i | − 0.218994i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5904 | 0.366495 | ||||||||
\(836\) | −0.712499 | −0.0246423 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 45.0773i | 1.55717i | ||||||||
\(839\) | −23.9901 | −0.828229 | −0.414115 | − | 0.910225i | \(-0.635909\pi\) | ||||
−0.414115 | + | 0.910225i | \(0.635909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.8834 | −1.20288 | ||||||||
\(842\) | 32.9847i | 1.13673i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.6684 | −0.470487 | ||||||||
\(845\) | −0.436053 | −0.0150007 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 22.7454i | − 0.781079i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 33.8824i | − 1.16216i | ||||||||
\(851\) | 12.8085i | 0.439070i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 19.7464i | − 0.676103i | −0.941128 | − | 0.338051i | \(-0.890232\pi\) | ||||
0.941128 | − | 0.338051i | \(-0.109768\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.1155 | 0.960969 | ||||||||
\(857\) | 33.6350 | 1.14895 | 0.574475 | − | 0.818522i | \(-0.305206\pi\) | ||||
0.574475 | + | 0.818522i | \(0.305206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9836i | 0.511233i | 0.966778 | + | 0.255617i | \(0.0822785\pi\) | ||||
−0.966778 | + | 0.255617i | \(0.917722\pi\) | |||||||
\(860\) | 2.14098 | 0.0730069 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.6245 | −0.668414 | ||||||||
\(863\) | − 17.7153i | − 0.603037i | −0.953460 | − | 0.301519i | \(-0.902506\pi\) | ||||
0.953460 | − | 0.301519i | \(-0.0974936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.31374 | −0.146672 | ||||||||
\(866\) | 3.20039 | 0.108754 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.13813i | − 0.0386083i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 16.4002i | − 0.555699i | ||||||||
\(872\) | − 25.2197i | − 0.854047i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 61.4627i | 2.07901i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.93977 | 0.335642 | 0.167821 | − | 0.985817i | \(-0.446327\pi\) | ||||
0.167821 | + | 0.985817i | \(0.446327\pi\) | |||||||
\(878\) | 27.1227 | 0.915347 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.790135i | 0.0266354i | ||||||||
\(881\) | 31.8591 | 1.07336 | 0.536680 | − | 0.843786i | \(-0.319678\pi\) | ||||
0.536680 | + | 0.843786i | \(0.319678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3061 | 1.49102 | 0.745510 | − | 0.666495i | \(-0.232206\pi\) | ||||
0.745510 | + | 0.666495i | \(0.232206\pi\) | |||||||
\(884\) | − 14.8234i | − 0.498566i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.0673 | −0.875749 | ||||||||
\(887\) | 14.9375 | 0.501551 | 0.250775 | − | 0.968045i | \(-0.419314\pi\) | ||||
0.250775 | + | 0.968045i | \(0.419314\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 12.5028i | − 0.419095i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 3.44812i | − 0.115452i | ||||||||
\(893\) | 6.12025i | 0.204806i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4.12761i | − 0.137971i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.7571 | 1.29334 | ||||||||
\(899\) | 52.4582 | 1.74958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9806i | 0.698967i | ||||||||
\(902\) | 3.94748 | 0.131437 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.9025 | 0.861506 | ||||||||
\(905\) | 17.3928i | 0.578158i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.4257 | 1.44193 | 0.720963 | − | 0.692973i | \(-0.243700\pi\) | ||||
0.720963 | + | 0.692973i | \(0.243700\pi\) | |||||||
\(908\) | 12.5793 | 0.417459 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2646i | 1.16837i | 0.811621 | + | 0.584185i | \(0.198586\pi\) | ||||
−0.811621 | + | 0.584185i | \(0.801414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.391912i | 0.0129704i | ||||||||
\(914\) | − 39.0704i | − 1.29233i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 13.6604i | − 0.451351i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8975 | −1.25012 | −0.625061 | − | 0.780576i | \(-0.714926\pi\) | ||||
−0.625061 | + | 0.780576i | \(0.714926\pi\) | |||||||
\(920\) | 13.5463 | 0.446609 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 44.3288i | − 1.45989i | ||||||||
\(923\) | −35.5195 | −1.16914 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.28056 | −0.206504 | ||||||||
\(926\) | 7.55277i | 0.248199i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38.3913 | 1.26026 | ||||||||
\(929\) | −11.6636 | −0.382671 | −0.191335 | − | 0.981525i | \(-0.561282\pi\) | ||||
−0.191335 | + | 0.981525i | \(0.561282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 9.64376i | − 0.315892i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.7024i | 1.07005i | ||||||||
\(935\) | − 0.728832i | − 0.0238353i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.46450i | − 0.145849i | −0.997337 | − | 0.0729244i | \(-0.976767\pi\) | ||||
0.997337 | − | 0.0729244i | \(-0.0232332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.12942 | −0.0368376 | ||||||||
\(941\) | −52.6172 | −1.71527 | −0.857636 | − | 0.514257i | \(-0.828068\pi\) | ||||
−0.857636 | + | 0.514257i | \(0.828068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 106.603i | − 3.47147i | ||||||||
\(944\) | 28.3244 | 0.921880 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.922426 | −0.0299906 | ||||||||
\(947\) | − 7.88685i | − 0.256288i | −0.991756 | − | 0.128144i | \(-0.959098\pi\) | ||||
0.991756 | − | 0.128144i | \(-0.0409020\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0792 | 0.911488 | ||||||||
\(950\) | −30.1378 | −0.977801 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.5322i | 0.924250i | 0.886815 | + | 0.462125i | \(0.152913\pi\) | ||||
−0.886815 | + | 0.462125i | \(0.847087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.22838i | 0.298623i | ||||||||
\(956\) | − 7.27850i | − 0.235404i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 57.2580i | − 1.84992i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0763 | −0.389556 | ||||||||
\(962\) | −8.77714 | −0.282986 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.6291i | 0.632212i | ||||||||
\(965\) | −7.96538 | −0.256415 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0897 | 1.32135 | 0.660677 | − | 0.750670i | \(-0.270269\pi\) | ||||
0.660677 | + | 0.750670i | \(0.270269\pi\) | |||||||
\(968\) | 20.3638i | 0.654516i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.1310 | 0.325288 | ||||||||
\(971\) | −43.4767 | −1.39523 | −0.697617 | − | 0.716470i | \(-0.745756\pi\) | ||||
−0.697617 | + | 0.716470i | \(0.745756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32.2646i | 1.03382i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 54.5289i | − 1.74543i | ||||||||
\(977\) | 8.99914i | 0.287908i | 0.989584 | + | 0.143954i | \(0.0459818\pi\) | ||||
−0.989584 | + | 0.143954i | \(0.954018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.68634i | 0.0538958i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.87826 | −0.123760 | ||||||||
\(983\) | 54.7852 | 1.74738 | 0.873689 | − | 0.486486i | \(-0.161721\pi\) | ||||
0.873689 | + | 0.486486i | \(0.161721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 2.44301i | − 0.0778408i | ||||||||
\(986\) | −62.8004 | −1.99997 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.1852 | −0.419478 | ||||||||
\(989\) | 24.9103i | 0.792103i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.33301 | 0.0423443 | 0.0211722 | − | 0.999776i | \(-0.493260\pi\) | ||||
0.0211722 | + | 0.999776i | \(0.493260\pi\) | |||||||
\(992\) | −31.5252 | −1.00092 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 0.474052i | − 0.0150285i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4835i | 0.775399i | 0.921786 | + | 0.387700i | \(0.126730\pi\) | ||||
−0.921786 | + | 0.387700i | \(0.873270\pi\) | |||||||
\(998\) | − 7.43313i | − 0.235292i | ||||||||
\(999\) | 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 | 1323.2.c.e.1322.13 | yes | 16 | |
3.2 | odd | 2 | inner | 1323.2.c.e.1322.4 | yes | 16 | |
7.6 | odd | 2 | inner | 1323.2.c.e.1322.14 | yes | 16 | |
21.20 | even | 2 | inner | 1323.2.c.e.1322.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.c.e.1322.3 | ✓ | 16 | 21.20 | even | 2 | inner | |
1323.2.c.e.1322.4 | yes | 16 | 3.2 | odd | 2 | inner | |
1323.2.c.e.1322.13 | yes | 16 | 1.1 | even | 1 | trivial | |
1323.2.c.e.1322.14 | yes | 16 | 7.6 | odd | 2 | inner |