Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.145 |
Dual form | 1008.3.cg.h.577.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.24264 | + | 0.717439i | 0.248528 | + | 0.143488i | 0.619090 | − | 0.785320i | \(-0.287502\pi\) |
−0.370562 | + | 0.928808i | \(0.620835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | 0.696832 | − | 0.717234i | \(-0.254592\pi\) |
−0.969559 | + | 0.244857i | \(0.921259\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.3280i | 1.64061i | 0.571924 | + | 0.820306i | \(0.306197\pi\) | ||||
−0.571924 | + | 0.820306i | \(0.693803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.75736 | − | 4.47871i | 0.456315 | − | 0.263454i | −0.254178 | − | 0.967157i | \(-0.581805\pi\) |
0.710494 | + | 0.703704i | \(0.248472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.25736 | + | 3.61269i | 0.329335 | + | 0.190141i | 0.655546 | − | 0.755156i | \(-0.272439\pi\) |
−0.326211 | + | 0.945297i | \(0.605772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.7279 | − | 32.4377i | 0.814257 | − | 1.41034i | −0.0956024 | − | 0.995420i | \(-0.530478\pi\) |
0.909860 | − | 0.414916i | \(-0.136189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4706 | − | 19.8676i | −0.458823 | − | 0.794704i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.9411 | 1.17038 | 0.585192 | − | 0.810895i | \(-0.301019\pi\) | ||||
0.585192 | + | 0.810895i | \(0.301019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.2279 | + | 22.0709i | −1.23316 | + | 0.711965i | −0.967687 | − | 0.252154i | \(-0.918861\pi\) |
−0.265472 | + | 0.964119i | \(0.585528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.69848 | − | 9.67487i | 0.0770996 | − | 0.276425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.9853 | − | 24.2232i | 0.377981 | − | 0.654682i | −0.612788 | − | 0.790248i | \(-0.709952\pi\) |
0.990768 | + | 0.135566i | \(0.0432853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 54.8313i | − | 1.33735i | −0.743556 | − | 0.668674i | \(-0.766862\pi\) | ||
0.743556 | − | 0.668674i | \(-0.233138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48528 | 0.0345414 | 0.0172707 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172707 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −37.2426 | − | 21.5020i | −0.792397 | − | 0.457490i | 0.0484090 | − | 0.998828i | \(-0.484585\pi\) |
−0.840806 | + | 0.541337i | \(0.817918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.9264 | + | 23.6289i | −0.876049 | + | 0.482222i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.7279 | − | 74.0069i | −0.806187 | − | 1.39636i | −0.915487 | − | 0.402348i | \(-0.868194\pi\) |
0.109299 | − | 0.994009i | \(-0.465139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.60927i | − | 0.156532i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35.6985 | + | 20.6105i | −0.605059 | + | 0.349331i | −0.771029 | − | 0.636800i | \(-0.780258\pi\) |
0.165970 | + | 0.986131i | \(0.446924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.02944 | − | 0.594346i | −0.0168760 | − | 0.00974337i | 0.491538 | − | 0.870856i | \(-0.336435\pi\) |
−0.508414 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.3015 | + | 26.5030i | −0.235408 | + | 0.407738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.19848 | + | 3.80789i | 0.0328132 | + | 0.0568341i | 0.881966 | − | 0.471314i | \(-0.156220\pi\) |
−0.849152 | + | 0.528148i | \(0.822887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 137.397 | 1.93517 | 0.967584 | − | 0.252548i | \(-0.0812687\pi\) | ||||
0.967584 | + | 0.252548i | \(0.0812687\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.3528 | − | 39.4635i | 0.936340 | − | 0.540596i | 0.0475288 | − | 0.998870i | \(-0.484865\pi\) |
0.888811 | + | 0.458274i | \(0.151532\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.0000 | + | 29.3939i | −0.389610 | + | 0.381739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 49.1690 | − | 85.1633i | 0.622393 | − | 1.07802i | −0.366646 | − | 0.930361i | \(-0.619494\pi\) |
0.989039 | − | 0.147656i | \(-0.0471728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 110.401i | − | 1.33013i | −0.746784 | − | 0.665067i | \(-0.768403\pi\) | ||
0.746784 | − | 0.665067i | \(-0.231597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8528 | 0.151210 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.0000 | + | 10.3923i | 0.202247 | + | 0.116767i | 0.597703 | − | 0.801717i | \(-0.296080\pi\) |
−0.395456 | + | 0.918485i | \(0.629413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 144.595 | − | 37.1670i | 1.58896 | − | 0.408428i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.18377 | + | 8.97855i | 0.0545660 | + | 0.0945110i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9867i | 0.113264i | 0.998395 | + | 0.0566322i | \(0.0180362\pi\) | ||||
−0.998395 | + | 0.0566322i | \(0.981964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.8234 | − | 53.5916i | 0.919043 | − | 0.530610i | 0.0357136 | − | 0.999362i | \(-0.488630\pi\) |
0.883330 | + | 0.468752i | \(0.155296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −91.1102 | − | 52.6025i | −0.884565 | − | 0.510704i | −0.0124040 | − | 0.999923i | \(-0.503948\pi\) |
−0.872161 | + | 0.489219i | \(0.837282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −59.2721 | + | 102.662i | −0.553945 | + | 0.959460i | 0.444040 | + | 0.896007i | \(0.353545\pi\) |
−0.997985 | + | 0.0634534i | \(0.979789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −55.5294 | − | 96.1798i | −0.509444 | − | 0.882384i | −0.999940 | − | 0.0109400i | \(-0.996518\pi\) |
0.490496 | − | 0.871444i | \(-0.336816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −101.397 | −0.897318 | −0.448659 | − | 0.893703i | \(-0.648098\pi\) | ||||
−0.448659 | + | 0.893703i | \(0.648098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 46.5442 | − | 26.8723i | 0.404732 | − | 0.233672i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −43.8823 | − | 44.7871i | −0.368758 | − | 0.376362i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42.5000 | − | 73.6122i | 0.351240 | − | 0.608365i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 68.7897i | − | 0.550317i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −82.5736 | −0.650186 | −0.325093 | − | 0.945682i | \(-0.605396\pi\) | ||||
−0.325093 | + | 0.945682i | \(0.605396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −52.4558 | − | 30.2854i | −0.400426 | − | 0.231186i | 0.286242 | − | 0.958157i | \(-0.407594\pi\) |
−0.686668 | + | 0.726971i | \(0.740927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5883 | − | 48.7181i | 0.102168 | − | 0.366302i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 33.5147 | + | 58.0492i | 0.244633 | + | 0.423717i | 0.962028 | − | 0.272949i | \(-0.0879992\pi\) |
−0.717395 | + | 0.696666i | \(0.754666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 91.5525i | 0.658651i | 0.944216 | + | 0.329326i | \(0.106821\pi\) | ||||
−0.944216 | + | 0.329326i | \(0.893179\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 110.823 | − | 63.9839i | 0.774989 | − | 0.447440i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42.1766 | + | 24.3507i | 0.290873 | + | 0.167936i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 40.5442 | − | 70.2245i | 0.272108 | − | 0.471306i | −0.697293 | − | 0.716786i | \(-0.745612\pi\) |
0.969402 | + | 0.245480i | \(0.0789457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −25.6030 | − | 44.3457i | −0.169556 | − | 0.293680i | 0.768708 | − | 0.639600i | \(-0.220900\pi\) |
−0.938264 | + | 0.345920i | \(0.887567\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −63.3381 | −0.408633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.000 | − | 93.5307i | 1.03185 | − | 0.595737i | 0.114334 | − | 0.993442i | \(-0.463527\pi\) |
0.917513 | + | 0.397705i | \(0.130193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −252.551 | − | 70.4409i | −1.56864 | − | 0.437521i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 41.9706 | − | 72.6951i | 0.257488 | − | 0.445982i | −0.708080 | − | 0.706132i | \(-0.750439\pi\) |
0.965568 | + | 0.260149i | \(0.0837718\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 127.620i | 0.764190i | 0.924123 | + | 0.382095i | \(0.124797\pi\) | ||||
−0.924123 | + | 0.382095i | \(0.875203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −285.882 | −1.69161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 123.816 | + | 71.4853i | 0.715701 | + | 0.413210i | 0.813168 | − | 0.582029i | \(-0.197741\pi\) |
−0.0974675 | + | 0.995239i | \(0.531074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −114.706 | + | 112.388i | −0.655461 | + | 0.642218i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −84.6396 | − | 146.600i | −0.472847 | − | 0.818995i | 0.526670 | − | 0.850070i | \(-0.323440\pi\) |
−0.999517 | + | 0.0310748i | \(0.990107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 209.969i | 1.16005i | 0.814600 | + | 0.580024i | \(0.196957\pi\) | ||||
−0.814600 | + | 0.580024i | \(0.803043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 34.7574 | − | 20.0672i | 0.187878 | − | 0.108471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −46.5442 | − | 26.8723i | −0.248899 | − | 0.143702i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −33.3015 | + | 57.6799i | −0.174353 | + | 0.301989i | −0.939937 | − | 0.341347i | \(-0.889117\pi\) |
0.765584 | + | 0.643336i | \(0.222450\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.89697 | + | 8.48180i | 0.0253729 | + | 0.0439472i | 0.878433 | − | 0.477865i | \(-0.158589\pi\) |
−0.853060 | + | 0.521813i | \(0.825256\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 267.161 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 113.397 | − | 65.4698i | 0.569834 | − | 0.328994i | −0.187249 | − | 0.982312i | \(-0.559957\pi\) |
0.757083 | + | 0.653319i | \(0.226624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −59.1472 | − | 230.108i | −0.291365 | − | 1.13354i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.3381 | − | 68.1356i | 0.191893 | − | 0.332369i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 43.3523i | − | 0.207427i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0883 | 0.109423 | 0.0547116 | − | 0.998502i | \(-0.482576\pi\) | ||||
0.0547116 | + | 0.998502i | \(0.482576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.84567 | + | 1.06560i | 0.00858452 | + | 0.00495627i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 216.250 | + | 220.709i | 0.996543 | + | 1.01709i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 95.5219 | + | 165.449i | 0.432226 | + | 0.748637i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 228.631i | 1.02525i | 0.858613 | + | 0.512625i | \(0.171327\pi\) | ||||
−0.858613 | + | 0.512625i | \(0.828673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 56.8234 | − | 32.8070i | 0.250323 | − | 0.144524i | −0.369589 | − | 0.929195i | \(-0.620502\pi\) |
0.619912 | + | 0.784671i | \(0.287168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 80.9558 | + | 46.7399i | 0.353519 | + | 0.204104i | 0.666234 | − | 0.745743i | \(-0.267905\pi\) |
−0.312715 | + | 0.949847i | \(0.601239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −118.757 | + | 205.694i | −0.509688 | + | 0.882806i | 0.490249 | + | 0.871583i | \(0.336906\pi\) |
−0.999937 | + | 0.0112234i | \(0.996427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.8528 | − | 53.4386i | −0.131289 | − | 0.227398i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 366.853 | 1.53495 | 0.767475 | − | 0.641079i | \(-0.221513\pi\) | ||||
0.767475 | + | 0.641079i | \(0.221513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −364.617 | + | 210.512i | −1.51293 | + | 0.873493i | −0.513049 | + | 0.858359i | \(0.671484\pi\) |
−0.999885 | + | 0.0151343i | \(0.995182\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −70.2944 | − | 1.43488i | −0.286916 | − | 0.00585664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −77.0513 | + | 133.457i | −0.311949 | + | 0.540311i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 146.621i | 0.584148i | 0.956396 | + | 0.292074i | \(0.0943454\pi\) | ||||
−0.956396 | + | 0.292074i | \(0.905655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224.735 | −0.888281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.7279 | − | 12.5446i | −0.0845444 | − | 0.0488118i | 0.457132 | − | 0.889399i | \(-0.348877\pi\) |
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −188.595 | − | 52.6025i | −0.728168 | − | 0.203098i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 45.3381 | + | 78.5279i | 0.172388 | + | 0.298585i | 0.939254 | − | 0.343222i | \(-0.111518\pi\) |
−0.766866 | + | 0.641807i | \(0.778185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 122.619i | − | 0.462712i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 59.2355 | − | 34.1996i | 0.220206 | − | 0.127136i | −0.385839 | − | 0.922566i | \(-0.626088\pi\) |
0.606046 | + | 0.795430i | \(0.292755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 106.971 | + | 61.7595i | 0.394725 | + | 0.227895i | 0.684206 | − | 0.729289i | \(-0.260149\pi\) |
−0.289480 | + | 0.957184i | \(0.593482\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68.8234 | + | 119.206i | −0.250267 | + | 0.433475i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 136.441 | + | 236.323i | 0.492567 | + | 0.853151i | 0.999963 | − | 0.00856145i | \(-0.00272523\pi\) |
−0.507396 | + | 0.861713i | \(0.669392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −133.103 | −0.473675 | −0.236837 | − | 0.971549i | \(-0.576111\pi\) | ||||
−0.236837 | + | 0.971549i | \(0.576111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 111.507 | − | 64.3787i | 0.394018 | − | 0.227486i | −0.289882 | − | 0.957063i | \(-0.593616\pi\) |
0.683900 | + | 0.729576i | \(0.260283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −371.735 | + | 95.5512i | −1.29524 | + | 0.332931i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −104.382 | + | 180.795i | −0.361184 | + | 0.625589i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 308.984i | − | 1.05455i | −0.849694 | − | 0.527276i | \(-0.823213\pi\) | ||
0.849694 | − | 0.527276i | \(-0.176787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −59.1472 | −0.200499 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 691.831 | + | 399.429i | 2.31381 | + | 1.33588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.58831 | − | 10.0696i | −0.00859904 | − | 0.0334539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.852814 | − | 1.47712i | −0.00279611 | − | 0.00484301i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 606.090i | 1.97423i | 0.160003 | + | 0.987117i | \(0.448850\pi\) | ||||
−0.160003 | + | 0.987117i | \(0.551150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −176.044 | + | 101.639i | −0.566057 | + | 0.326813i | −0.755573 | − | 0.655064i | \(-0.772641\pi\) |
0.189516 | + | 0.981878i | \(0.439308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −351.294 | − | 202.820i | −1.12234 | − | 0.647986i | −0.180346 | − | 0.983603i | \(-0.557722\pi\) |
−0.941999 | + | 0.335617i | \(0.891055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0294 | + | 22.5676i | −0.0411023 | + | 0.0711913i | −0.885845 | − | 0.463982i | \(-0.846420\pi\) |
0.844742 | + | 0.535173i | \(0.179754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −101.823 | − | 176.363i | −0.319196 | − | 0.552863i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 64.7208 | 0.200374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 423.735 | − | 244.644i | 1.30380 | − | 0.752750i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −80.8751 | + | 289.961i | −0.245821 | + | 0.881341i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −54.3162 | + | 94.0785i | −0.164097 | + | 0.284225i | −0.936334 | − | 0.351110i | \(-0.885804\pi\) |
0.772237 | + | 0.635335i | \(0.219138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.30911i | 0.0188332i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 441.735 | 1.31079 | 0.655393 | − | 0.755288i | \(-0.272503\pi\) | ||||
0.655393 | + | 0.755288i | \(0.272503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 229.368 | + | 132.425i | 0.672632 | + | 0.388344i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 235.000 | + | 249.848i | 0.685131 | + | 0.728420i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0955 | − | 29.6102i | −0.0492664 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 221.787i | − | 0.635493i | −0.948176 | − | 0.317746i | \(-0.897074\pi\) | ||
0.948176 | − | 0.317746i | \(-0.102926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −387.448 | + | 223.693i | −1.09759 | + | 0.633692i | −0.935586 | − | 0.353099i | \(-0.885128\pi\) |
−0.162000 | + | 0.986791i | \(0.551794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 170.735 | + | 98.5739i | 0.480944 | + | 0.277673i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −145.882 | + | 252.675i | −0.406357 | + | 0.703831i | −0.994478 | − | 0.104941i | \(-0.966534\pi\) |
0.588121 | + | 0.808773i | \(0.299868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −154.397 | − | 267.423i | −0.427692 | − | 0.740785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 113.251 | 0.310276 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 363.169 | − | 209.676i | 0.989561 | − | 0.571324i | 0.0844183 | − | 0.996430i | \(-0.473097\pi\) |
0.905143 | + | 0.425107i | \(0.139763\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −427.279 | + | 418.646i | −1.15170 | + | 1.12843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6909 | + | 27.1775i | −0.0420668 | + | 0.0728618i | −0.886292 | − | 0.463127i | \(-0.846728\pi\) |
0.844225 | + | 0.535988i | \(0.180061\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 723.895i | 1.92015i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −206.779 | −0.545590 | −0.272795 | − | 0.962072i | \(-0.587948\pi\) | ||||
−0.272795 | + | 0.962072i | \(0.587948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −431.772 | − | 249.283i | −1.12734 | − | 0.650871i | −0.184076 | − | 0.982912i | \(-0.558929\pi\) |
−0.943265 | + | 0.332041i | \(0.892263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58.3675 | + | 15.0029i | −0.151604 | + | 0.0389685i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −324.213 | − | 561.554i | −0.833453 | − | 1.44358i | −0.895284 | − | 0.445496i | \(-0.853027\pi\) |
0.0618308 | − | 0.998087i | \(-0.480306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 335.508i | − | 0.858077i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 122.199 | − | 70.5516i | 0.309364 | − | 0.178612i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 65.6026 | + | 37.8757i | 0.165246 | + | 0.0954047i | 0.580342 | − | 0.814373i | \(-0.302919\pi\) |
−0.415096 | + | 0.909777i | \(0.636252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −282.125 | + | 488.655i | −0.703553 | + | 1.21859i | 0.263658 | + | 0.964616i | \(0.415071\pi\) |
−0.967211 | + | 0.253974i | \(0.918262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −470.727 | − | 815.324i | −1.16806 | − | 2.02314i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −167.823 | −0.412342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −309.559 | + | 178.724i | −0.756868 | + | 0.436978i | −0.828170 | − | 0.560477i | \(-0.810618\pi\) |
0.0713023 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 201.941 | + | 206.105i | 0.488962 | + | 0.499044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 79.2061 | − | 137.189i | 0.190858 | − | 0.330576i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 502.175i | 1.19851i | 0.800559 | + | 0.599254i | \(0.204536\pi\) | ||||
−0.800559 | + | 0.599254i | \(0.795464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7939 | 0.0802706 | 0.0401353 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401353 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −177.963 | − | 102.747i | −0.418735 | − | 0.241757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.23550 | + | 8.01492i | −0.00523536 | + | 0.0187703i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −251.860 | − | 436.234i | −0.584362 | − | 1.01214i | −0.994955 | − | 0.100326i | \(-0.968012\pi\) |
0.410593 | − | 0.911819i | \(-0.365322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 837.548i | 1.93429i | 0.254224 | + | 0.967145i | \(0.418180\pi\) | ||||
−0.254224 | + | 0.967145i | \(0.581820\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 234.375 | − | 135.316i | 0.536326 | − | 0.309648i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 164.558 | + | 95.0079i | 0.374848 | + | 0.216419i | 0.675575 | − | 0.737292i | \(-0.263896\pi\) |
−0.300726 | + | 0.953711i | \(0.597229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 84.7279 | − | 146.753i | 0.191259 | − | 0.331271i | −0.754408 | − | 0.656405i | \(-0.772076\pi\) |
0.945668 | + | 0.325134i | \(0.105409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9117 | + | 25.8278i | 0.0335094 | + | 0.0580400i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1035 | −0.0403195 | −0.0201598 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201598 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −284.912 | + | 164.494i | −0.631733 | + | 0.364731i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 206.345 | + | 57.5532i | 0.453506 | + | 0.126491i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 164.412 | − | 284.769i | 0.359763 | − | 0.623128i | −0.628158 | − | 0.778086i | \(-0.716191\pi\) |
0.987921 | + | 0.154958i | \(0.0495242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 794.331i | 1.72306i | 0.507706 | + | 0.861530i | \(0.330494\pi\) | ||||
−0.507706 | + | 0.861530i | \(0.669506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 403.396 | 0.871266 | 0.435633 | − | 0.900124i | \(-0.356525\pi\) | ||||
0.435633 | + | 0.900124i | \(0.356525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.44870 | − | 1.41376i | −0.00524347 | − | 0.00302732i | 0.497376 | − | 0.867535i | \(-0.334297\pi\) |
−0.502619 | + | 0.864508i | \(0.667630\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.9848 | − | 21.5407i | 0.0468760 | − | 0.0459289i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.45584 | − | 7.71775i | −0.00942039 | − | 0.0163166i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 165.758i | − | 0.348965i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 328.669 | − | 189.757i | 0.686157 | − | 0.396153i | −0.116014 | − | 0.993248i | \(-0.537012\pi\) |
0.802171 | + | 0.597095i | \(0.203678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 516.632 | + | 298.278i | 1.07408 | + | 0.620120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.88225 | + | 13.6525i | −0.0162521 | + | 0.0281494i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 287.757 | + | 498.410i | 0.590877 | + | 1.02343i | 0.994115 | + | 0.108333i | \(0.0345513\pi\) |
−0.403238 | + | 0.915095i | \(0.632115\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 238.441 | 0.485623 | 0.242811 | − | 0.970074i | \(-0.421930\pi\) | ||||
0.242811 | + | 0.970074i | \(0.421930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 263.294 | − | 152.013i | 0.534064 | − | 0.308342i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −239.434 | − | 931.499i | −0.481758 | − | 1.87424i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −143.287 | + | 248.180i | −0.287148 | + | 0.497355i | −0.973128 | − | 0.230266i | \(-0.926040\pi\) |
0.685980 | + | 0.727620i | \(0.259374\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4374i | 0.0505714i | 0.999680 | + | 0.0252857i | \(0.00804954\pi\) | ||||
−0.999680 | + | 0.0252857i | \(0.991950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 153.795 | 0.304544 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 697.889 | + | 402.926i | 1.37110 | + | 0.791603i | 0.991066 | − | 0.133370i | \(-0.0425800\pi\) |
0.380031 | + | 0.924974i | \(0.375913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −386.662 | − | 394.635i | −0.756677 | − | 0.772280i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −75.4781 | − | 130.732i | −0.146559 | − | 0.253848i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 258.025i | 0.499080i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 661.706 | − | 382.036i | 1.27007 | − | 0.733274i | 0.295068 | − | 0.955476i | \(-0.404658\pi\) |
0.975001 | + | 0.222202i | \(0.0713244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 153.096 | + | 88.3900i | 0.292726 | + | 0.169006i | 0.639171 | − | 0.769065i | \(-0.279278\pi\) |
−0.346444 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −197.698 | + | 342.424i | −0.375139 | + | 0.649761i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −436.970 | − | 756.854i | −0.826030 | − | 1.43073i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1169.44 | 2.19407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −147.308 | + | 85.0482i | −0.275342 | + | 0.158969i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 251.558 | + | 152.166i | 0.466713 | + | 0.282311i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.58831 | + | 14.8754i | −0.0158749 | + | 0.0274961i | −0.873854 | − | 0.486189i | \(-0.838387\pi\) |
0.857979 | + | 0.513685i | \(0.171720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 159.356i | − | 0.292396i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −212.676 | −0.388805 | −0.194402 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194402 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 212.382 | + | 122.619i | 0.385448 | + | 0.222538i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −663.058 | − | 184.938i | −1.19902 | − | 0.334427i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −440.823 | − | 763.528i | −0.791424 | − | 1.37079i | −0.925085 | − | 0.379760i | \(-0.876007\pi\) |
0.133661 | − | 0.991027i | \(-0.457327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.6780i | 0.0566691i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 664.301 | − | 383.534i | 1.17993 | − | 0.681233i | 0.223932 | − | 0.974605i | \(-0.428111\pi\) |
0.955998 | + | 0.293372i | \(0.0947774\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −126.000 | − | 72.7461i | −0.223009 | − | 0.128754i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.6468 | + | 25.3689i | −0.0257412 | + | 0.0445851i | −0.878609 | − | 0.477542i | \(-0.841528\pi\) |
0.852868 | + | 0.522127i | \(0.174861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 482.521 | + | 835.752i | 0.845046 | + | 1.46366i | 0.885581 | + | 0.464485i | \(0.153761\pi\) |
−0.0405347 | + | 0.999178i | \(0.512906\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −859.279 | −1.49440 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 227.883 | − | 131.568i | 0.394944 | − | 0.228021i | −0.289356 | − | 0.957222i | \(-0.593441\pi\) |
0.684300 | + | 0.729201i | \(0.260108\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −748.477 | + | 192.389i | −1.28826 | + | 0.331135i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −256.368 | + | 444.042i | −0.439738 | + | 0.761649i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 436.477i | − | 0.743572i | −0.928318 | − | 0.371786i | \(-0.878746\pi\) | ||
0.928318 | − | 0.371786i | \(-0.121254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −318.941 | −0.541496 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −603.603 | − | 348.490i | −1.01788 | − | 0.587673i | −0.104391 | − | 0.994536i | \(-0.533289\pi\) |
−0.913489 | + | 0.406863i | \(0.866623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.3978 | − | 87.1372i | −0.0376434 | − | 0.146449i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −199.206 | − | 345.035i | −0.332564 | − | 0.576018i | 0.650450 | − | 0.759549i | \(-0.274581\pi\) |
−0.983014 | + | 0.183531i | \(0.941247\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.1691i | − | 0.0601816i | −0.999547 | − | 0.0300908i | \(-0.990420\pi\) | ||
0.999547 | − | 0.0300908i | \(-0.00957964\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 105.624 | − | 60.9823i | 0.174586 | − | 0.100797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.3457 | − | 15.7880i | −0.0450505 | − | 0.0260099i | 0.477306 | − | 0.878737i | \(-0.341613\pi\) |
−0.522356 | + | 0.852727i | \(0.674947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 458.595 | − | 794.310i | 0.750565 | − | 1.30002i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 204.632 | + | 354.434i | 0.333821 | + | 0.578195i | 0.983258 | − | 0.182220i | \(-0.0583285\pi\) |
−0.649436 | + | 0.760416i | \(0.724995\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1227.38 | −1.98927 | −0.994636 | − | 0.103436i | \(-0.967016\pi\) | ||||
−0.994636 | + | 0.103436i | \(0.967016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −412.022 | + | 237.881i | −0.665625 | + | 0.384299i | −0.794417 | − | 0.607373i | \(-0.792223\pi\) |
0.128792 | + | 0.991672i | \(0.458890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0883 | − | 140.143i | 0.0627421 | − | 0.224949i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −237.412 | + | 411.209i | −0.379859 | + | 0.657935i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 250.544i | − | 0.398322i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 54.9420 | 0.0870713 | 0.0435357 | − | 0.999052i | \(-0.486138\pi\) | ||||
0.0435357 | + | 0.999052i | \(0.486138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −102.609 | − | 59.2415i | −0.161589 | − | 0.0932937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −503.956 | − | 915.533i | −0.791139 | − | 1.43726i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −114.551 | − | 198.409i | −0.178707 | − | 0.309530i | 0.762731 | − | 0.646716i | \(-0.223858\pi\) |
−0.941438 | + | 0.337186i | \(0.890525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 854.640i | − | 1.32914i | −0.747224 | − | 0.664572i | \(-0.768614\pi\) | ||
0.747224 | − | 0.664572i | \(-0.231386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 868.632 | − | 501.505i | 1.34255 | − | 0.775124i | 0.355372 | − | 0.934725i | \(-0.384354\pi\) |
0.987182 | + | 0.159601i | \(0.0510207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 214.191 | + | 123.663i | 0.330032 | + | 0.190544i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 635.382 | − | 1100.51i | 0.973020 | − | 1.68532i | 0.286698 | − | 0.958021i | \(-0.407442\pi\) |
0.686321 | − | 0.727299i | \(-0.259224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.4558 | − | 75.2677i | −0.0663448 | − | 0.114913i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −783.308 | −1.18863 | −0.594315 | − | 0.804232i | \(-0.702577\pi\) | ||||
−0.594315 | + | 0.804232i | \(0.702577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 72.5589 | − | 41.8919i | 0.109771 | − | 0.0633765i | −0.444109 | − | 0.895973i | \(-0.646480\pi\) |
0.553881 | + | 0.832596i | \(0.313146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51.8377 | − | 50.7903i | 0.0779514 | − | 0.0763764i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 635.647 | − | 1100.97i | 0.952994 | − | 1.65063i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.13215i | 0.0106291i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 415.676 | 0.617647 | 0.308823 | − | 0.951119i | \(-0.400065\pi\) | ||||
0.308823 | + | 0.951119i | \(0.400065\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −685.279 | − | 395.646i | −1.01223 | − | 0.584411i | −0.100386 | − | 0.994949i | \(-0.532008\pi\) |
−0.911844 | + | 0.410538i | \(0.865341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 74.4853 | − | 19.1458i | 0.109698 | − | 0.0281970i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 164.080 | + | 284.195i | 0.240235 | + | 0.416099i | 0.960781 | − | 0.277308i | \(-0.0894423\pi\) |
−0.720546 | + | 0.693407i | \(0.756109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 96.1791i | 0.140407i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1578.42 | − | 911.300i | 2.29088 | − | 1.32264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −875.182 | − | 505.287i | −1.26654 | − | 0.731240i | −0.292212 | − | 0.956353i | \(-0.594391\pi\) |
−0.974333 | + | 0.225113i | \(0.927725\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −65.6833 | + | 113.767i | −0.0945084 | + | 0.163693i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −245.574 | − | 425.346i | −0.352329 | − | 0.610252i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.103464 | 0.000147594 | 7.37972e−5 | − | 1.00000i | \(-0.499977\pi\) | ||||
7.37972e−5 | 1.00000i | \(0.499977\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 175.022 | − | 101.049i | 0.248964 | − | 0.143740i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −525.088 | − | 535.916i | −0.742699 | − | 0.758014i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −602.588 | + | 1043.71i | −0.849912 | + | 1.47209i | 0.0313734 | + | 0.999508i | \(0.490012\pi\) |
−0.881286 | + | 0.472584i | \(0.843321\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1653.37i | 2.31889i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 183.618 | 0.256809 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 850.925 | + | 491.282i | 1.18348 | + | 0.683285i | 0.956818 | − | 0.290688i | \(-0.0938840\pi\) |
0.226666 | + | 0.973973i | \(0.427217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −197.852 | + | 709.359i | −0.274414 | + | 0.983855i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −389.324 | − | 674.329i | −0.536998 | − | 0.930108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 630.440i | − | 0.867181i | −0.901110 | − | 0.433590i | \(-0.857247\pi\) | ||
0.901110 | − | 0.433590i | \(-0.142753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.5219 | − | 6.65215i | 0.0157618 | − | 0.00910007i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 258.486 | + | 149.237i | 0.352641 | + | 0.203597i | 0.665848 | − | 0.746088i | \(-0.268070\pi\) |
−0.313207 | + | 0.949685i | \(0.601403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.1909 | − | 22.8473i | 0.0178981 | − | 0.0310004i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 172.684 | + | 299.097i | 0.233672 | + | 0.404732i | 0.958886 | − | 0.283792i | \(-0.0915924\pi\) |
−0.725214 | + | 0.688524i | \(0.758259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 683.616 | 0.920076 | 0.460038 | − | 0.887899i | \(-0.347836\pi\) | ||||
0.460038 | + | 0.887899i | \(0.347836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 100.764 | − | 58.1759i | 0.135253 | − | 0.0780885i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 799.301 | + | 222.939i | 1.06716 | + | 0.297648i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −289.169 | + | 500.855i | −0.385045 | + | 0.666918i | −0.991775 | − | 0.127990i | \(-0.959148\pi\) |
0.606730 | + | 0.794908i | \(0.292481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 73.4744i | − | 0.0973171i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1204.82 | 1.59158 | 0.795788 | − | 0.605576i | \(-0.207057\pi\) | ||||
0.795788 | + | 0.605576i | \(0.207057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 202.669 | + | 117.011i | 0.266319 | + | 0.153760i | 0.627214 | − | 0.778847i | \(-0.284195\pi\) |
−0.360894 | + | 0.932607i | \(0.617529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −555.294 | + | 544.075i | −0.727778 | + | 0.713074i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −439.581 | − | 761.376i | −0.573117 | − | 0.992668i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1290.16i | − | 1.67771i | −0.544358 | − | 0.838853i | \(-0.683226\pi\) | ||
0.544358 | − | 0.838853i | \(-0.316774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −345.646 | + | 199.559i | −0.447149 | + | 0.258161i | −0.706625 | − | 0.707588i | \(-0.749783\pi\) |
0.259477 | + | 0.965749i | \(0.416450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 876.992 | + | 506.331i | 1.13160 | + | 0.653331i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 198.088 | − | 343.099i | 0.254285 | − | 0.440435i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −412.191 | − | 713.936i | −0.527773 | − | 0.914130i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 268.410 | 0.341924 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1348.16 | − | 778.361i | 1.71304 | − | 0.989023i | 0.782637 | − | 0.622478i | \(-0.213874\pi\) |
0.930401 | − | 0.366544i | \(-0.119459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 176.698 | + | 687.433i | 0.223386 | + | 0.869068i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6762 | − | 21.9558i | 0.0159851 | − | 0.0276870i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 600.232i | 0.753114i | 0.926393 | + | 0.376557i | \(0.122892\pi\) | ||||
−0.926393 | + | 0.376557i | \(0.877108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −385.206 | −0.482110 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −410.117 | − | 236.781i | −0.510731 | − | 0.294871i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −263.294 | − | 268.723i | −0.327073 | − | 0.333817i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −114.640 | − | 198.562i | −0.141705 | − | 0.245441i | 0.786434 | − | 0.617675i | \(-0.211925\pi\) |
−0.928139 | + | 0.372234i | \(0.878592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 529.955i | 0.653459i | 0.945118 | + | 0.326729i | \(0.105947\pi\) | ||||
−0.945118 | + | 0.326729i | \(0.894053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 104.309 | − | 60.2226i | 0.127986 | − | 0.0738928i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.29394 | + | 5.36586i | 0.0113757 | + | 0.00656776i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −151.669 | + | 262.698i | −0.184737 | + | 0.319974i | −0.943488 | − | 0.331407i | \(-0.892477\pi\) |
0.758751 | + | 0.651381i | \(0.225810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −564.955 | − | 978.531i | −0.686459 | − | 1.18898i | −0.972976 | − | 0.230906i | \(-0.925831\pi\) |
0.286517 | − | 0.958075i | \(-0.407502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −161.604 | −0.195410 | −0.0977049 | − | 0.995215i | \(-0.531150\pi\) | ||||
−0.0977049 | + | 0.995215i | \(0.531150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1325.32 | − | 765.175i | 1.59870 | − | 0.923010i | 0.606962 | − | 0.794731i | \(-0.292388\pi\) |
0.991738 | − | 0.128279i | \(-0.0409454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −227.169 | + | 375.553i | −0.272711 | + | 0.450844i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −91.5593 | + | 158.585i | −0.109652 | + | 0.189923i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 218.629i | 0.260583i | 0.991476 | + | 0.130291i | \(0.0415913\pi\) | ||||
−0.991476 | + | 0.130291i | \(0.958409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −355.249 | − | 205.103i | −0.420413 | − | 0.242726i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −573.124 | − | 159.854i | −0.676652 | − | 0.188730i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −523.831 | − | 907.301i | −0.615547 | − | 1.06616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 762.730i | − | 0.894174i | −0.894491 | − | 0.447087i | \(-0.852461\pi\) | ||
0.894491 | − | 0.447087i | \(-0.147539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 795.015 | − | 459.002i | 0.927672 | − | 0.535592i | 0.0415977 | − | 0.999134i | \(-0.486755\pi\) |
0.886075 | + | 0.463543i | \(0.153422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 761.367 | + | 439.575i | 0.886341 | + | 0.511729i | 0.872744 | − | 0.488179i | \(-0.162339\pi\) |
0.0135969 | + | 0.999908i | \(0.495672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −175.294 | + | 303.619i | −0.203122 | + | 0.351818i | −0.949533 | − | 0.313668i | \(-0.898442\pi\) |
0.746411 | + | 0.665486i | \(0.231776\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 102.573 | + | 177.661i | 0.118581 | + | 0.205389i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −590.029 | −0.678974 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −81.2145 | + | 46.8892i | −0.0932428 | + | 0.0538338i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −466.368 | + | 119.876i | −0.532991 | + | 0.137001i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.77965 | + | 3.08245i | −0.00202925 | + | 0.00351477i | −0.867038 | − | 0.498242i | \(-0.833979\pi\) |
0.865009 | + | 0.501756i | \(0.167313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 488.565i | − | 0.554557i | −0.960790 | − | 0.277279i | \(-0.910567\pi\) | ||
0.960790 | − | 0.277279i | \(-0.0894325\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1162.16 | 1.31615 | 0.658075 | − | 0.752953i | \(-0.271371\pi\) | ||||
0.658075 | + | 0.752953i | \(0.271371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 75.2801 | + | 43.4630i | 0.0848704 | + | 0.0490000i | 0.541835 | − | 0.840485i | \(-0.317730\pi\) |
−0.456964 | + | 0.889485i | \(0.651063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 143.896 | + | 559.817i | 0.161863 | + | 0.629716i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −155.360 | − | 269.092i | −0.173976 | − | 0.301335i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 242.895i | − | 0.271391i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1297.50 | + | 749.111i | −1.44327 | + | 0.833272i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −662.912 | − | 382.732i | −0.735751 | − | 0.424786i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −150.640 | + | 260.915i | −0.166453 | + | 0.288304i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −230.448 | − | 399.148i | −0.254077 | − | 0.440075i | 0.710567 | − | 0.703629i | \(-0.248438\pi\) |
−0.964645 | + | 0.263554i | \(0.915105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1184.28 | −1.29998 | −0.649988 | − | 0.759944i | \(-0.725226\pi\) | ||||
−0.649988 | + | 0.759944i | \(0.725226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −573.661 | + | 331.203i | −0.628325 | + | 0.362764i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −113.912 | + | 408.407i | −0.124222 | + | 0.445373i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −270.919 | + | 469.246i | −0.294798 | + | 0.510605i | −0.974938 | − | 0.222477i | \(-0.928586\pi\) |
0.680140 | + | 0.733082i | \(0.261919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2930.40i | 3.17486i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −641.676 | −0.693704 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 779.610 | + | 450.108i | 0.839193 | + | 0.484508i | 0.856990 | − | 0.515333i | \(-0.172332\pi\) |
−0.0177969 | + | 0.999842i | \(0.505665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −353.970 | − | 7.22538i | −0.380204 | − | 0.00776088i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −38.5584 | − | 66.7852i | −0.0412390 | − | 0.0714280i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 233.964i | − | 0.249695i | −0.992176 | − | 0.124847i | \(-0.960156\pi\) | ||
0.992176 | − | 0.124847i | \(-0.0398441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1132.49 | + | 653.845i | −1.20350 | + | 0.694840i | −0.961331 | − | 0.275394i | \(-0.911192\pi\) |
−0.242167 | + | 0.970234i | \(0.577858\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1778.60 | − | 1026.88i | −1.88611 | − | 1.08895i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 563.881 | − | 976.671i | 0.595440 | − | 1.03133i | −0.398045 | − | 0.917366i | \(-0.630311\pi\) |
0.993485 | − | 0.113966i | \(-0.0363555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 841.677 | + | 1457.83i | 0.886909 | + | 1.53617i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 91.4255 | 0.0959345 | 0.0479672 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479672 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −82.7636 | + | 47.7836i | −0.0866635 | + | 0.0500352i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 335.147 | − | 328.376i | 0.349476 | − | 0.342415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 493.749 | − | 855.199i | 0.513787 | − | 0.889905i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0531i | 0.0145628i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1098.19 | 1.13567 | 0.567834 | − | 0.823143i | \(-0.307782\pi\) | ||||
0.567834 | + | 0.823143i | \(0.307782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 114.405 | + | 66.0517i | 0.117822 | + | 0.0680245i | 0.557753 | − | 0.830007i | \(-0.311664\pi\) |
−0.439931 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 620.691 | − | 159.543i | 0.637915 | − | 0.163970i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 224.117 | + | 388.182i | 0.229393 | + | 0.397320i | 0.957628 | − | 0.288007i | \(-0.0929926\pi\) |
−0.728235 | + | 0.685327i | \(0.759659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 124.708i | − | 0.127383i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1426.14 | − | 823.382i | 1.45080 | − | 0.837621i | 0.452276 | − | 0.891878i | \(-0.350612\pi\) |
0.998527 | + | 0.0542567i | \(0.0172789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 331.986 | + | 191.672i | 0.337041 | + | 0.194591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.8162 | − | 48.1791i | 0.0281256 | − | 0.0487150i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −314.448 | − | 544.640i | −0.317304 | − | 0.549587i | 0.662621 | − | 0.748955i | \(-0.269444\pi\) |
−0.979925 | + | 0.199369i | \(0.936111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 187.882 | 0.188826 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −869.645 | + | 502.090i | −0.872262 | + | 0.503601i | −0.868099 | − | 0.496390i | \(-0.834658\pi\) |
−0.00416289 | + | 0.999991i | \(0.501325\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.3.cg.h.145.2 | 4 | ||
3.2 | odd | 2 | 336.3.bh.e.145.1 | 4 | |||
4.3 | odd | 2 | 126.3.n.a.19.1 | 4 | |||
7.3 | odd | 6 | inner | 1008.3.cg.h.577.2 | 4 | ||
12.11 | even | 2 | 42.3.g.a.19.2 | ✓ | 4 | ||
21.2 | odd | 6 | 2352.3.f.e.97.2 | 4 | |||
21.5 | even | 6 | 2352.3.f.e.97.3 | 4 | |||
21.17 | even | 6 | 336.3.bh.e.241.1 | 4 | |||
28.3 | even | 6 | 126.3.n.a.73.1 | 4 | |||
28.11 | odd | 6 | 882.3.n.e.325.1 | 4 | |||
28.19 | even | 6 | 882.3.c.b.685.4 | 4 | |||
28.23 | odd | 6 | 882.3.c.b.685.3 | 4 | |||
28.27 | even | 2 | 882.3.n.e.19.1 | 4 | |||
60.23 | odd | 4 | 1050.3.q.a.649.2 | 8 | |||
60.47 | odd | 4 | 1050.3.q.a.649.3 | 8 | |||
60.59 | even | 2 | 1050.3.p.a.901.1 | 4 | |||
84.11 | even | 6 | 294.3.g.a.31.2 | 4 | |||
84.23 | even | 6 | 294.3.c.a.97.2 | 4 | |||
84.47 | odd | 6 | 294.3.c.a.97.1 | 4 | |||
84.59 | odd | 6 | 42.3.g.a.31.2 | yes | 4 | ||
84.83 | odd | 2 | 294.3.g.a.19.2 | 4 | |||
420.59 | odd | 6 | 1050.3.p.a.451.1 | 4 | |||
420.143 | even | 12 | 1050.3.q.a.199.3 | 8 | |||
420.227 | even | 12 | 1050.3.q.a.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.2 | ✓ | 4 | 12.11 | even | 2 | ||
42.3.g.a.31.2 | yes | 4 | 84.59 | odd | 6 | ||
126.3.n.a.19.1 | 4 | 4.3 | odd | 2 | |||
126.3.n.a.73.1 | 4 | 28.3 | even | 6 | |||
294.3.c.a.97.1 | 4 | 84.47 | odd | 6 | |||
294.3.c.a.97.2 | 4 | 84.23 | even | 6 | |||
294.3.g.a.19.2 | 4 | 84.83 | odd | 2 | |||
294.3.g.a.31.2 | 4 | 84.11 | even | 6 | |||
336.3.bh.e.145.1 | 4 | 3.2 | odd | 2 | |||
336.3.bh.e.241.1 | 4 | 21.17 | even | 6 | |||
882.3.c.b.685.3 | 4 | 28.23 | odd | 6 | |||
882.3.c.b.685.4 | 4 | 28.19 | even | 6 | |||
882.3.n.e.19.1 | 4 | 28.27 | even | 2 | |||
882.3.n.e.325.1 | 4 | 28.11 | odd | 6 | |||
1008.3.cg.h.145.2 | 4 | 1.1 | even | 1 | trivial | ||
1008.3.cg.h.577.2 | 4 | 7.3 | odd | 6 | inner | ||
1050.3.p.a.451.1 | 4 | 420.59 | odd | 6 | |||
1050.3.p.a.901.1 | 4 | 60.59 | even | 2 | |||
1050.3.q.a.199.2 | 8 | 420.227 | even | 12 | |||
1050.3.q.a.199.3 | 8 | 420.143 | even | 12 | |||
1050.3.q.a.649.2 | 8 | 60.23 | odd | 4 | |||
1050.3.q.a.649.3 | 8 | 60.47 | odd | 4 | |||
2352.3.f.e.97.2 | 4 | 21.2 | odd | 6 | |||
2352.3.f.e.97.3 | 4 | 21.5 | even | 6 |