Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(145,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("684.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.y (of order \(6\), degree \(2\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 34x^{6} + 921x^{4} - 7990x^{2} + 55225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.4 | ||
Root | \(4.27333 + 2.46721i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.3.y.g.217.4 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 3.48916 | + | 6.04340i | 0.697832 | + | 1.20868i | 0.969217 | + | 0.246209i | \(0.0791851\pi\) |
−0.271385 | + | 0.962471i | \(0.587482\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44949 | −0.492784 | −0.246392 | − | 0.969170i | \(-0.579245\pi\) | ||||
−0.246392 | + | 0.969170i | \(0.579245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.1150 | 0.919546 | 0.459773 | − | 0.888037i | \(-0.347931\pi\) | ||||
0.459773 | + | 0.888037i | \(0.347931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.151531 | − | 0.0874863i | −0.0116562 | − | 0.00672972i | 0.494161 | − | 0.869371i | \(-0.335475\pi\) |
−0.505817 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.56834 | + | 2.71645i | 0.0922554 | + | 0.159791i | 0.908460 | − | 0.417972i | \(-0.137259\pi\) |
−0.816204 | + | 0.577763i | \(0.803926\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.3485 | + | 15.2385i | 0.597288 | + | 0.802027i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.48916 | − | 6.04340i | 0.151703 | − | 0.262757i | −0.780151 | − | 0.625591i | \(-0.784858\pi\) |
0.931853 | + | 0.362835i | \(0.118191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.8485 | + | 20.5222i | −0.473939 | + | 0.820886i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.70502 | − | 2.71645i | −0.162242 | − | 0.0936706i | 0.416681 | − | 0.909053i | \(-0.363193\pi\) |
−0.578923 | + | 0.815382i | \(0.696527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.8017i | 1.18715i | 0.804779 | + | 0.593575i | \(0.202284\pi\) | ||||
−0.804779 | + | 0.593575i | \(0.797716\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0358 | − | 20.8467i | −0.343881 | − | 0.595619i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.1879i | 0.734808i | 0.930061 | + | 0.367404i | \(0.119753\pi\) | ||||
−0.930061 | + | 0.367404i | \(0.880247\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −51.2800 | + | 29.6065i | −1.25073 | + | 0.722110i | −0.971255 | − | 0.238043i | \(-0.923494\pi\) |
−0.279476 | + | 0.960153i | \(0.590161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9722 | + | 19.0044i | 0.255167 | + | 0.441963i | 0.964941 | − | 0.262467i | \(-0.0845361\pi\) |
−0.709774 | + | 0.704430i | \(0.751203\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27337 | − | 10.8658i | 0.133476 | − | 0.231187i | −0.791538 | − | 0.611120i | \(-0.790719\pi\) |
0.925014 | + | 0.379933i | \(0.124053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −37.1010 | −0.757164 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36.1075 | − | 20.8467i | −0.681273 | − | 0.393333i | 0.119062 | − | 0.992887i | \(-0.462011\pi\) |
−0.800334 | + | 0.599554i | \(0.795345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.2929 | + | 61.1290i | 0.641688 | + | 1.11144i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21.9924 | − | 12.6973i | 0.372752 | − | 0.215209i | −0.301908 | − | 0.953337i | \(-0.597624\pi\) |
0.674660 | + | 0.738128i | \(0.264290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.1413 | + | 45.2781i | −0.428546 | + | 0.742264i | −0.996744 | − | 0.0806279i | \(-0.974307\pi\) |
0.568198 | + | 0.822892i | \(0.307641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.22102i | − | 0.0187848i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41.3105 | + | 23.8506i | 0.616574 | + | 0.355979i | 0.775534 | − | 0.631306i | \(-0.217481\pi\) |
−0.158960 | + | 0.987285i | \(0.550814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1151 | − | 8.14934i | 0.198804 | − | 0.114779i | −0.397294 | − | 0.917692i | \(-0.630051\pi\) |
0.596097 | + | 0.802912i | \(0.296717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9495 | + | 25.8933i | 0.204788 | + | 0.354702i | 0.950065 | − | 0.312052i | \(-0.101016\pi\) |
−0.745277 | + | 0.666754i | \(0.767683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −34.8916 | −0.453138 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −53.1742 | + | 30.7002i | −0.673092 | + | 0.388610i | −0.797247 | − | 0.603653i | \(-0.793711\pi\) |
0.124155 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 148.976 | 1.79490 | 0.897448 | − | 0.441119i | \(-0.145419\pi\) | ||||
0.897448 | + | 0.441119i | \(0.145419\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9444 | + | 18.9562i | −0.128757 | + | 0.223015i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 54.9276 | + | 31.7124i | 0.617164 | + | 0.356320i | 0.775764 | − | 0.631023i | \(-0.217365\pi\) |
−0.158600 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.522704 | + | 0.301783i | 0.00574400 | + | 0.00331630i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −52.4958 | + | 121.753i | −0.552588 | + | 1.28161i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 27.0000 | − | 15.5885i | 0.278351 | − | 0.160706i | −0.354326 | − | 0.935122i | \(-0.615290\pi\) |
0.632676 | + | 0.774416i | \(0.281956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49.0067 | − | 84.8820i | 0.485215 | − | 0.840416i | −0.514641 | − | 0.857406i | \(-0.672075\pi\) |
0.999856 | + | 0.0169894i | \(0.00540817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 100.713i | 0.977792i | 0.872342 | + | 0.488896i | \(0.162600\pi\) | ||||
−0.872342 | + | 0.488896i | \(0.837400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.43289i | − | 0.0507747i | −0.999678 | − | 0.0253874i | \(-0.991918\pi\) | ||
0.999678 | − | 0.0253874i | \(-0.00808191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −59.6969 | + | 34.4660i | −0.547678 | + | 0.316202i | −0.748185 | − | 0.663490i | \(-0.769074\pi\) |
0.200507 | + | 0.979692i | \(0.435741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 200.043i | 1.77029i | 0.465315 | + | 0.885145i | \(0.345941\pi\) | ||||
−0.465315 | + | 0.885145i | \(0.654059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48.6969 | 0.423452 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.40998 | − | 9.37036i | −0.0454620 | − | 0.0787425i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.6867 | −0.154436 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.09318 | 0.0727454 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.5755 | + | 57.4899i | 0.784059 | + | 0.452677i | 0.837867 | − | 0.545875i | \(-0.183802\pi\) |
−0.0538078 | + | 0.998551i | \(0.517136\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −51.8265 | − | 89.7661i | −0.395622 | − | 0.685237i | 0.597558 | − | 0.801825i | \(-0.296138\pi\) |
−0.993180 | + | 0.116588i | \(0.962804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.1464 | − | 52.5651i | −0.294334 | − | 0.395226i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 64.3732 | − | 111.498i | 0.469877 | − | 0.813852i | −0.529529 | − | 0.848292i | \(-0.677631\pi\) |
0.999407 | + | 0.0344400i | \(0.0109648\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.17423 | + | 15.8902i | −0.0660017 | + | 0.114318i | −0.897138 | − | 0.441751i | \(-0.854358\pi\) |
0.831136 | + | 0.556069i | \(0.187691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.53273 | − | 0.884924i | −0.0107184 | − | 0.00618828i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 37.9125i | − | 0.261465i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −114.437 | − | 198.211i | −0.768036 | − | 1.33028i | −0.938627 | − | 0.344935i | \(-0.887901\pi\) |
0.170591 | − | 0.985342i | \(-0.445432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 161.063i | − | 1.06664i | −0.845913 | − | 0.533321i | \(-0.820944\pi\) | ||
0.845913 | − | 0.533321i | \(-0.179056\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −222.407 | + | 128.407i | −1.43489 | + | 0.828431i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −131.030 | − | 226.951i | −0.834587 | − | 1.44555i | −0.894367 | − | 0.447335i | \(-0.852373\pi\) |
0.0597799 | − | 0.998212i | \(-0.480960\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0358 | + | 20.8467i | −0.0747566 | + | 0.129482i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 109.833 | 0.673823 | 0.336912 | − | 0.941536i | \(-0.390618\pi\) | ||||
0.336912 | + | 0.941536i | \(0.390618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −198.882 | − | 114.825i | −1.19091 | − | 0.687573i | −0.232398 | − | 0.972621i | \(-0.574657\pi\) |
−0.958513 | + | 0.285048i | \(0.907990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −84.4847 | − | 146.332i | −0.499909 | − | 0.865869i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 244.400 | − | 141.104i | 1.41271 | − | 0.815631i | 0.417071 | − | 0.908874i | \(-0.363057\pi\) |
0.995643 | + | 0.0932428i | \(0.0297233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.8712 | − | 70.7909i | 0.233550 | − | 0.404520i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 22.9526i | − | 0.128227i | −0.997943 | − | 0.0641134i | \(-0.979578\pi\) | ||
0.997943 | − | 0.0641134i | \(-0.0204219\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27.4699 | + | 15.8598i | 0.151767 | + | 0.0876230i | 0.573961 | − | 0.818883i | \(-0.305406\pi\) |
−0.422193 | + | 0.906506i | \(0.638740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −164.307 | + | 94.8629i | −0.888148 | + | 0.512772i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8638 | + | 27.4769i | 0.0848330 | + | 0.146935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −96.6746 | −0.506150 | −0.253075 | − | 0.967447i | \(-0.581442\pi\) | ||||
−0.253075 | + | 0.967447i | \(0.581442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 92.5454 | − | 53.4311i | 0.479510 | − | 0.276845i | −0.240702 | − | 0.970599i | \(-0.577378\pi\) |
0.720212 | + | 0.693754i | \(0.244044\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 253.651 | 1.28757 | 0.643785 | − | 0.765207i | \(-0.277363\pi\) | ||||
0.643785 | + | 0.765207i | \(0.277363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 89.4115 | − | 154.865i | 0.449304 | − | 0.778217i | −0.549037 | − | 0.835798i | \(-0.685005\pi\) |
0.998341 | + | 0.0575809i | \(0.0183387\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.2299 | + | 9.37036i | 0.0799504 | + | 0.0461594i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −357.848 | − | 206.604i | −1.74560 | − | 1.00782i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 114.790 | + | 154.138i | 0.549233 | + | 0.737500i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 211.098 | − | 121.878i | 1.00047 | − | 0.577619i | 0.0920795 | − | 0.995752i | \(-0.470649\pi\) |
0.908386 | + | 0.418133i | \(0.137315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −76.5675 | + | 132.619i | −0.356128 | + | 0.616831i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 126.947i | − | 0.585009i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.548834i | − | 0.00248341i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3559 | − | 7.13366i | 0.0554075 | − | 0.0319895i | −0.472040 | − | 0.881577i | \(-0.656482\pi\) |
0.527448 | + | 0.849587i | \(0.323149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 259.256i | 1.14210i | 0.820917 | + | 0.571048i | \(0.193463\pi\) | ||||
−0.820917 | + | 0.571048i | \(0.806537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 56.4143 | 0.246351 | 0.123175 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123175 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 54.5751 | + | 94.5268i | 0.234228 | + | 0.405694i | 0.959048 | − | 0.283244i | \(-0.0914105\pi\) |
−0.724820 | + | 0.688938i | \(0.758077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 87.5551 | 0.372575 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 405.764 | 1.69776 | 0.848879 | − | 0.528587i | \(-0.177278\pi\) | ||||
0.848879 | + | 0.528587i | \(0.177278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −245.787 | − | 141.905i | −1.01986 | − | 0.588819i | −0.105799 | − | 0.994387i | \(-0.533740\pi\) |
−0.914065 | + | 0.405569i | \(0.867074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −129.451 | − | 224.216i | −0.528373 | − | 0.915169i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.386481 | − | 3.30194i | −0.00156470 | − | 0.0133682i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 139.566 | − | 241.736i | 0.556041 | − | 0.963092i | −0.441780 | − | 0.897123i | \(-0.645653\pi\) |
0.997822 | − | 0.0659686i | \(-0.0210137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.2929 | − | 61.1290i | 0.139497 | − | 0.241617i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 278.868 | + | 161.004i | 1.08509 | + | 0.626476i | 0.932264 | − | 0.361778i | \(-0.117830\pi\) |
0.152823 | + | 0.988254i | \(0.451163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 93.7844i | − | 0.362102i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −44.1432 | − | 76.4583i | −0.167845 | − | 0.290716i | 0.769817 | − | 0.638265i | \(-0.220347\pi\) |
−0.937662 | + | 0.347549i | \(0.887014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 290.949i | − | 1.09792i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −198.407 | + | 114.550i | −0.737572 | + | 0.425837i | −0.821186 | − | 0.570661i | \(-0.806687\pi\) |
0.0836140 | + | 0.996498i | \(0.473354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.0908 | + | 43.4586i | 0.0925860 | + | 0.160364i | 0.908599 | − | 0.417670i | \(-0.137153\pi\) |
−0.816013 | + | 0.578034i | \(0.803820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −119.847 | + | 207.582i | −0.435808 | + | 0.754842i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −323.918 | −1.16938 | −0.584690 | − | 0.811257i | \(-0.698784\pi\) | ||||
−0.584690 | + | 0.811257i | \(0.698784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05743 | − | 0.610508i | −0.00376310 | − | 0.00217262i | 0.498117 | − | 0.867110i | \(-0.334025\pi\) |
−0.501880 | + | 0.864937i | \(0.667358\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 203.247 | + | 352.035i | 0.718189 | + | 1.24394i | 0.961717 | + | 0.274046i | \(0.0883620\pi\) |
−0.243528 | + | 0.969894i | \(0.578305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 176.890 | − | 102.127i | 0.616340 | − | 0.355844i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 139.581 | − | 241.761i | 0.482978 | − | 0.836542i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 362.604i | − | 1.23756i | −0.785566 | − | 0.618778i | \(-0.787628\pi\) | ||
0.785566 | − | 0.618778i | \(-0.212372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 153.470 | + | 88.6059i | 0.520237 | + | 0.300359i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.05743 | + | 0.610508i | −0.00353656 | + | 0.00204183i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −37.8485 | − | 65.5555i | −0.125742 | − | 0.217792i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −364.845 | −1.19621 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −54.3031 | + | 31.3519i | −0.176883 | + | 0.102123i | −0.585827 | − | 0.810436i | \(-0.699230\pi\) |
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 248.471 | 0.798942 | 0.399471 | − | 0.916746i | \(-0.369194\pi\) | ||||
0.399471 | + | 0.916746i | \(0.369194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 164.000 | − | 284.056i | 0.523962 | − | 0.907528i | −0.475649 | − | 0.879635i | \(-0.657787\pi\) |
0.999611 | − | 0.0278932i | \(-0.00887983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −292.983 | − | 169.154i | −0.924235 | − | 0.533607i | −0.0392515 | − | 0.999229i | \(-0.512497\pi\) |
−0.884984 | + | 0.465622i | \(0.845831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.5913 | − | 27.4769i | −0.149189 | − | 0.0861344i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5963 | + | 54.7267i | −0.0730537 | + | 0.169433i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.59082 | − | 2.07316i | 0.0110487 | − | 0.00637895i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.6399 | + | 37.4814i | −0.0657748 | + | 0.113925i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 197.707i | − | 0.597303i | −0.954362 | − | 0.298652i | \(-0.903463\pi\) | ||
0.954362 | − | 0.298652i | \(-0.0965369\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 332.874i | 0.993654i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −288.591 | + | 166.618i | −0.856353 | + | 0.494415i | −0.862789 | − | 0.505564i | \(-0.831284\pi\) |
0.00643660 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 372.249i | 1.09164i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 297.005 | 0.865903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −204.221 | − | 353.721i | −0.588533 | − | 1.01937i | −0.994425 | − | 0.105448i | \(-0.966372\pi\) |
0.405892 | − | 0.913921i | \(-0.366961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −378.444 | −1.08437 | −0.542183 | − | 0.840260i | \(-0.682402\pi\) | ||||
−0.542183 | + | 0.840260i | \(0.682402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −356.528 | −1.00999 | −0.504997 | − | 0.863121i | \(-0.668506\pi\) | ||||
−0.504997 | + | 0.863121i | \(0.668506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 98.4995 | + | 56.8687i | 0.277463 | + | 0.160194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −305.248 | − | 528.705i | −0.850273 | − | 1.47272i | −0.880962 | − | 0.473187i | \(-0.843103\pi\) |
0.0306887 | − | 0.999529i | \(-0.490230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −103.424 | + | 345.868i | −0.286494 | + | 0.958082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −104.322 | + | 180.692i | −0.285815 | + | 0.495045i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7497 | + | 22.0832i | −0.0347404 | + | 0.0601722i | −0.882873 | − | 0.469612i | \(-0.844394\pi\) |
0.848132 | + | 0.529784i | \(0.177727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 124.552 | + | 71.9103i | 0.335721 | + | 0.193828i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 443.527i | 1.18908i | 0.804066 | + | 0.594540i | \(0.202666\pi\) | ||||
−0.804066 | + | 0.594540i | \(0.797334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.475304 | + | 0.823251i | 0.00126075 | + | 0.00218369i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146.375i | 0.386214i | 0.981178 | + | 0.193107i | \(0.0618564\pi\) | ||||
−0.981178 | + | 0.193107i | \(0.938144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 434.822 | − | 251.045i | 1.13531 | − | 0.655469i | 0.190042 | − | 0.981776i | \(-0.439138\pi\) |
0.945264 | + | 0.326307i | \(0.105804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −121.742 | − | 210.864i | −0.316214 | − | 0.547699i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −38.8561 | + | 67.3007i | −0.0998870 | + | 0.173009i | −0.911638 | − | 0.410995i | \(-0.865181\pi\) |
0.811751 | + | 0.584004i | \(0.198515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8888 | 0.0559815 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −371.067 | − | 214.236i | −0.939410 | − | 0.542368i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 99.3332 | + | 172.050i | 0.250209 | + | 0.433376i | 0.963583 | − | 0.267408i | \(-0.0861672\pi\) |
−0.713374 | + | 0.700784i | \(0.752834\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 329.197 | − | 190.062i | 0.820940 | − | 0.473970i | −0.0298006 | − | 0.999556i | \(-0.509487\pi\) |
0.850740 | + | 0.525586i | \(0.176154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.21964 | − | 5.57658i | 0.00798919 | − | 0.0138377i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 275.006i | 0.675689i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 384.909 | + | 222.227i | 0.941098 | + | 0.543343i | 0.890304 | − | 0.455366i | \(-0.150492\pi\) |
0.0507938 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −75.8625 | + | 43.7992i | −0.183686 | + | 0.106051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 519.803 | + | 900.324i | 1.25254 | + | 2.16946i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 492.182 | 1.17466 | 0.587329 | − | 0.809348i | \(-0.300180\pi\) | ||||
0.587329 | + | 0.809348i | \(0.300180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −435.681 | + | 251.541i | −1.03487 | + | 0.597484i | −0.918377 | − | 0.395708i | \(-0.870499\pi\) |
−0.116495 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −74.3298 | −0.174894 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 90.1742 | − | 156.186i | 0.211181 | − | 0.365776i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 79.5101 | + | 45.9052i | 0.184478 | + | 0.106509i | 0.589395 | − | 0.807845i | \(-0.299366\pi\) |
−0.404917 | + | 0.914354i | \(0.632700\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 268.847 | + | 155.219i | 0.620895 | + | 0.358474i | 0.777217 | − | 0.629232i | \(-0.216631\pi\) |
−0.156323 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 131.689 | − | 15.4138i | 0.301348 | − | 0.0352718i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −195.901 | + | 113.103i | −0.446243 | + | 0.257639i | −0.706242 | − | 0.707970i | \(-0.749611\pi\) |
0.259999 | + | 0.965609i | \(0.416278\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −49.3235 | + | 85.4309i | −0.111340 | + | 0.192846i | −0.916311 | − | 0.400468i | \(-0.868848\pi\) |
0.804971 | + | 0.593314i | \(0.202181\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 442.599i | 0.994605i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 258.035i | 0.574688i | 0.957828 | + | 0.287344i | \(0.0927722\pi\) | ||||
−0.957828 | + | 0.287344i | \(0.907228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −518.697 | + | 299.470i | −1.15010 | + | 0.664013i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.21188i | 0.00925688i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 102.212 | 0.223659 | 0.111830 | − | 0.993727i | \(-0.464329\pi\) | ||||
0.111830 | + | 0.993727i | \(0.464329\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 53.9057 | + | 93.3675i | 0.116932 | + | 0.202532i | 0.918550 | − | 0.395304i | \(-0.129361\pi\) |
−0.801618 | + | 0.597836i | \(0.796027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −271.692 | −0.586809 | −0.293404 | − | 0.955988i | \(-0.594788\pi\) | ||||
−0.293404 | + | 0.955988i | \(0.594788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 617.403 | 1.32206 | 0.661031 | − | 0.750358i | \(-0.270119\pi\) | ||||
0.661031 | + | 0.750358i | \(0.270119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −142.500 | − | 82.2724i | −0.303838 | − | 0.175421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 110.984 | + | 192.230i | 0.234638 | + | 0.406405i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −447.189 | + | 52.3420i | −0.941451 | + | 0.110194i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 53.2364 | − | 92.2081i | 0.111141 | − | 0.192501i | −0.805090 | − | 0.593153i | \(-0.797883\pi\) |
0.916230 | + | 0.400652i | \(0.131216\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.37857 | − | 4.11980i | 0.00494505 | − | 0.00856508i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 188.415 | + | 108.781i | 0.388484 | + | 0.224291i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 719.920i | 1.47827i | 0.673555 | + | 0.739137i | \(0.264767\pi\) | ||||
−0.673555 | + | 0.739137i | \(0.735233\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.8263 | + | 75.9094i | 0.0892593 | + | 0.154602i | 0.907198 | − | 0.420703i | \(-0.138217\pi\) |
−0.817939 | + | 0.575305i | \(0.804883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17.0413i | − | 0.0345665i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −48.6898 | + | 28.1111i | −0.0979674 | + | 0.0565615i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 78.7293 | + | 136.363i | 0.157774 | + | 0.273273i | 0.934066 | − | 0.357101i | \(-0.116235\pi\) |
−0.776292 | + | 0.630374i | \(0.782902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −141.523 | + | 245.125i | −0.281357 | + | 0.487325i | −0.971719 | − | 0.236139i | \(-0.924118\pi\) |
0.690362 | + | 0.723464i | \(0.257451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 683.968 | 1.35439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 747.314 | + | 431.462i | 1.46820 | + | 0.847666i | 0.999365 | − | 0.0356201i | \(-0.0113406\pi\) |
0.468835 | + | 0.883286i | \(0.344674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.5681 | − | 89.3186i | −0.100916 | − | 0.174792i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −608.647 | + | 351.402i | −1.18184 | + | 0.682334i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.4551 | − | 109.907i | 0.122737 | − | 0.212587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 426.578i | − | 0.818767i | −0.912362 | − | 0.409384i | \(-0.865744\pi\) | ||
0.912362 | − | 0.409384i | \(-0.134256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 703.309 | + | 406.056i | 1.34476 | + | 0.776397i | 0.987502 | − | 0.157608i | \(-0.0503783\pi\) |
0.357258 | + | 0.934006i | \(0.383712\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −99.9698 | + | 57.7176i | −0.189696 | + | 0.109521i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 240.152 | + | 415.955i | 0.453973 | + | 0.786304i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3607 | 0.0194384 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.8332 | − | 18.9562i | 0.0613704 | − | 0.0354322i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −375.277 | −0.696247 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 49.7429 | − | 86.1572i | 0.0919461 | − | 0.159255i | −0.816384 | − | 0.577510i | \(-0.804025\pi\) |
0.908330 | + | 0.418254i | \(0.137358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −416.584 | − | 240.515i | −0.764375 | − | 0.441312i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −552.901 | − | 319.217i | −1.01079 | − | 0.583578i | −0.0993654 | − | 0.995051i | \(-0.531681\pi\) |
−0.911422 | + | 0.411473i | \(0.865015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0002 | − | 102.525i | −0.0217790 | − | 0.186071i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 183.424 | − | 105.900i | 0.331689 | − | 0.191501i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.18040 | + | 15.9009i | −0.0164819 | + | 0.0285474i | −0.874149 | − | 0.485658i | \(-0.838580\pi\) |
0.857667 | + | 0.514206i | \(0.171913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.83967i | − | 0.00686882i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 579.618i | − | 1.02952i | −0.857335 | − | 0.514758i | \(-0.827882\pi\) | ||
0.857335 | − | 0.514758i | \(-0.172118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1208.94 | + | 697.981i | −2.13971 | + | 1.23536i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 785.519i | − | 1.38053i | −0.723559 | − | 0.690263i | \(-0.757495\pi\) | ||
0.723559 | − | 0.690263i | \(-0.242505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.6219 | 0.0658878 | 0.0329439 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329439 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 82.6824 | + | 143.210i | 0.143795 | + | 0.249061i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 720.504 | 1.24871 | 0.624354 | − | 0.781142i | \(-0.285362\pi\) | ||||
0.624354 | + | 0.781142i | \(0.285362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −513.893 | −0.884497 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −365.227 | − | 210.864i | −0.626461 | − | 0.361688i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 100.869 | + | 174.710i | 0.171838 | + | 0.297632i | 0.939062 | − | 0.343747i | \(-0.111696\pi\) |
−0.767225 | + | 0.641378i | \(0.778363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −560.803 | + | 417.643i | −0.952127 | + | 0.709070i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −70.3653 | + | 121.876i | −0.118660 | + | 0.205525i | −0.919237 | − | 0.393705i | \(-0.871193\pi\) |
0.800577 | + | 0.599230i | \(0.204526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.7526 | − | 65.3893i | 0.0634497 | − | 0.109898i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −841.997 | − | 486.127i | −1.40567 | − | 0.811564i | −0.410703 | − | 0.911769i | \(-0.634717\pi\) |
−0.994967 | + | 0.100205i | \(0.968050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 486.915i | − | 0.810174i | −0.914278 | − | 0.405087i | \(-0.867241\pi\) | ||
0.914278 | − | 0.405087i | \(-0.132759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −65.2010 | − | 112.931i | −0.107770 | − | 0.186664i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 819.811i | − | 1.35059i | −0.737546 | − | 0.675297i | \(-0.764015\pi\) | ||
0.737546 | − | 0.675297i | \(-0.235985\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.90122 | + | 1.09767i | −0.00311165 | + | 0.00179651i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 262.388 | + | 454.470i | 0.428040 | + | 0.741386i | 0.996699 | − | 0.0811869i | \(-0.0258711\pi\) |
−0.568659 | + | 0.822573i | \(0.692538\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 420.462 | − | 728.261i | 0.681461 | − | 1.18033i | −0.293074 | − | 0.956090i | \(-0.594678\pi\) |
0.974535 | − | 0.224236i | \(-0.0719885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −420.196 | −0.678831 | −0.339416 | − | 0.940637i | \(-0.610229\pi\) | ||||
−0.339416 | + | 0.940637i | \(0.610229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −189.472 | − | 109.392i | −0.304128 | − | 0.175589i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 327.939 | + | 568.008i | 0.524703 | + | 0.908812i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −73.8545 | + | 42.6399i | −0.117416 | + | 0.0677900i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 472.805 | − | 818.923i | 0.749295 | − | 1.29782i | −0.198866 | − | 0.980027i | \(-0.563726\pi\) |
0.948161 | − | 0.317791i | \(-0.102941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 802.366i | 1.26357i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.62195 | + | 3.24583i | 0.00882566 | + | 0.00509550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 244.875 | − | 141.379i | 0.382020 | − | 0.220559i | −0.296677 | − | 0.954978i | \(-0.595878\pi\) |
0.678697 | + | 0.734419i | \(0.262545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 575.275 | + | 996.406i | 0.894674 | + | 1.54962i | 0.834208 | + | 0.551450i | \(0.185925\pi\) |
0.0604660 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −366.501 | −0.566461 | −0.283231 | − | 0.959052i | \(-0.591406\pi\) | ||||
−0.283231 | + | 0.959052i | \(0.591406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 222.453 | − | 128.433i | 0.342763 | − | 0.197894i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −712.248 | −1.09073 | −0.545366 | − | 0.838198i | \(-0.683609\pi\) | ||||
−0.545366 | + | 0.838198i | \(0.683609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 361.662 | − | 626.417i | 0.552155 | − | 0.956361i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 804.356 | + | 464.395i | 1.22057 | + | 0.704697i | 0.965040 | − | 0.262104i | \(-0.0844163\pi\) |
0.255531 | + | 0.966801i | \(0.417750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −788.697 | − | 455.354i | −1.19319 | − | 0.688887i | −0.234159 | − | 0.972198i | \(-0.575234\pi\) |
−0.959028 | + | 0.283311i | \(0.908567\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 181.084 | − | 419.986i | 0.272306 | − | 0.631557i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.8332 | + | 18.9562i | −0.0492251 | + | 0.0284201i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −264.420 | + | 457.988i | −0.394068 | + | 0.682546i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 197.173i | − | 0.292976i | −0.989212 | − | 0.146488i | \(-0.953203\pi\) | ||
0.989212 | − | 0.146488i | \(-0.0467970\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 38.5791i | − | 0.0569854i | −0.999594 | − | 0.0284927i | \(-0.990929\pi\) | ||
0.999594 | − | 0.0284927i | \(-0.00907073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −93.1362 | + | 53.7722i | −0.137167 | + | 0.0791933i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1073.83i | − | 1.57223i | −0.618081 | − | 0.786114i | \(-0.712090\pi\) | ||
0.618081 | − | 0.786114i | \(-0.287910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 898.434 | 1.31158 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.64759 | + | 6.31782i | 0.00529404 | + | 0.00916955i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −966.786 | −1.39911 | −0.699555 | − | 0.714578i | \(-0.746619\pi\) | ||||
−0.699555 | + | 0.714578i | \(0.746619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −128.041 | −0.184232 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −160.849 | − | 92.8662i | −0.230773 | − | 0.133237i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 691.064 | + | 1196.96i | 0.985825 | + | 1.70750i | 0.638209 | + | 0.769863i | \(0.279675\pi\) |
0.347616 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −414.303 | + | 308.541i | −0.589336 | + | 0.438892i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −169.048 | + | 292.800i | −0.239106 | + | 0.414144i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 183.197 | − | 317.306i | 0.258388 | − | 0.447541i | −0.707422 | − | 0.706791i | \(-0.750142\pi\) |
0.965810 | + | 0.259250i | \(0.0834754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 222.407 | + | 128.407i | 0.311932 | + | 0.180094i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 12.3506i | − | 0.0172735i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 674.358 | + | 1168.02i | 0.937912 | + | 1.62451i | 0.769358 | + | 0.638818i | \(0.220576\pi\) |
0.168554 | + | 0.985692i | \(0.446090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 347.407i | − | 0.481840i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 111.495 | − | 64.3715i | 0.153786 | − | 0.0887882i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −594.082 | − | 1028.98i | −0.817170 | − | 1.41538i | −0.907759 | − | 0.419491i | \(-0.862209\pi\) |
0.0905897 | − | 0.995888i | \(-0.471125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.4163 | + | 59.6108i | −0.0470811 | + | 0.0815469i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.5143 | 0.0648217 | 0.0324108 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324108 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 417.855 | + | 241.249i | 0.566968 | + | 0.327339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3717 | + | 43.9451i | 0.0343325 | + | 0.0594656i | 0.882681 | − | 0.469972i | \(-0.155736\pi\) |
−0.848349 | + | 0.529438i | \(0.822403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −712.157 | + | 411.164i | −0.958489 | + | 0.553384i | −0.895708 | − | 0.444644i | \(-0.853330\pi\) |
−0.0627811 | + | 0.998027i | \(0.519997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 798.580 | − | 1383.18i | 1.07192 | − | 1.85662i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.7407i | 0.0250210i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.3115 | + | 19.2324i | 0.0443562 | + | 0.0256091i | 0.522014 | − | 0.852937i | \(-0.325181\pi\) |
−0.477658 | + | 0.878546i | \(0.658514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 973.369 | − | 561.975i | 1.28923 | − | 0.744337i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 155.046 | + | 268.547i | 0.204816 | + | 0.354752i | 0.950074 | − | 0.312024i | \(-0.101007\pi\) |
−0.745258 | + | 0.666776i | \(0.767674\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 923.570 | 1.21363 | 0.606813 | − | 0.794844i | \(-0.292448\pi\) | ||||
0.606813 | + | 0.794844i | \(0.292448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 205.924 | − | 118.890i | 0.269887 | − | 0.155819i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.44336 | −0.00579317 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 749.307 | − | 1297.84i | 0.974392 | − | 1.68770i | 0.292463 | − | 0.956277i | \(-0.405525\pi\) |
0.681928 | − | 0.731419i | \(-0.261142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 588.080 | + | 339.528i | 0.760776 | + | 0.439234i | 0.829574 | − | 0.558396i | \(-0.188583\pi\) |
−0.0687981 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −755.249 | − | 436.043i | −0.974515 | − | 0.562637i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1033.11 | − | 445.442i | −1.32620 | − | 0.571812i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 142.774 | − | 82.4306i | 0.182809 | − | 0.105545i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 914.370 | − | 1583.74i | 1.16480 | − | 2.01750i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1166.31i | − | 1.48197i | −0.671524 | − | 0.740983i | \(-0.734360\pi\) | ||
0.671524 | − | 0.740983i | \(-0.265640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 690.045i | − | 0.872371i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.92243 | − | 4.57402i | 0.00999045 | − | 0.00576799i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 771.416i | 0.967899i | 0.875096 | + | 0.483950i | \(0.160798\pi\) | ||||
−0.875096 | + | 0.483950i | \(0.839202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.3551 | 0.0492555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 151.214 | + | 261.911i | 0.188311 | + | 0.326165i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −167.980 | −0.208670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1399.05 | −1.72935 | −0.864676 | − | 0.502330i | \(-0.832476\pi\) | ||||
−0.864676 | + | 0.502330i | \(0.832476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −886.665 | − | 511.916i | −1.09330 | − | 0.631216i | −0.158846 | − | 0.987303i | \(-0.550777\pi\) |
−0.934453 | + | 0.356087i | \(0.884111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 383.225 | + | 663.766i | 0.470215 | + | 0.814437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −165.081 | + | 382.871i | −0.202058 | + | 0.468630i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −351.435 | + | 608.703i | −0.428057 | + | 0.741417i | −0.996700 | − | 0.0811675i | \(-0.974135\pi\) |
0.568643 | + | 0.822584i | \(0.307468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.2418 | − | 76.6291i | 0.0537568 | − | 0.0931095i | −0.837895 | − | 0.545832i | \(-0.816214\pi\) |
0.891652 | + | 0.452722i | \(0.149547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −616.049 | − | 355.676i | −0.744920 | − | 0.430080i | 0.0789357 | − | 0.996880i | \(-0.474848\pi\) |
−0.823855 | + | 0.566800i | \(0.808181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 763.135i | 0.920548i | 0.887777 | + | 0.460274i | \(0.152249\pi\) | ||||
−0.887777 | + | 0.460274i | \(0.847751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −58.1871 | − | 100.783i | −0.0698524 | − | 0.120988i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1602.57i | − | 1.91924i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1136.25 | − | 656.014i | 1.35429 | − | 0.781900i | 0.365444 | − | 0.930833i | \(-0.380917\pi\) |
0.988847 | + | 0.148933i | \(0.0475839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −405.742 | − | 702.765i | −0.482452 | − | 0.835631i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 589.561 | − | 1021.15i | 0.697706 | − | 1.20846i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 64.4597 | 0.0761035 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 164.307 | + | 94.8629i | 0.193076 | + | 0.111472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 231.166 | + | 400.392i | 0.271004 | + | 0.469393i | 0.969119 | − | 0.246593i | \(-0.0793110\pi\) |
−0.698115 | + | 0.715985i | \(0.745978\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −881.383 | + | 508.867i | −1.02845 | + | 0.593777i | −0.916541 | − | 0.399941i | \(-0.869030\pi\) |
−0.111911 | + | 0.993718i | \(0.535697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 315.957 | − | 547.254i | 0.367820 | − | 0.637083i | −0.621404 | − | 0.783490i | \(-0.713438\pi\) |
0.989224 | + | 0.146407i | \(0.0467709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 436.469i | 0.505758i | 0.967498 | + | 0.252879i | \(0.0813775\pi\) | ||||
−0.967498 | + | 0.252879i | \(0.918623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1705.50 | + | 984.670i | 1.97167 | + | 1.13835i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −537.857 | + | 310.532i | −0.618938 | + | 0.357344i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.17320 | − | 7.22820i | −0.00479128 | − | 0.00829874i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.3668 | −0.0358478 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −515.348 | + | 297.536i | −0.587626 | + | 0.339266i | −0.764158 | − | 0.645029i | \(-0.776845\pi\) |
0.176532 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1532.34 | −1.73932 | −0.869659 | − | 0.493653i | \(-0.835661\pi\) | ||||
−0.869659 | + | 0.493653i | \(0.835661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 623.164 | − | 1079.35i | 0.705735 | − | 1.22237i | −0.260691 | − | 0.965422i | \(-0.583950\pi\) |
0.966426 | − | 0.256947i | \(-0.0827164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −532.677 | − | 307.541i | −0.600538 | − | 0.346721i | 0.168715 | − | 0.985665i | \(-0.446038\pi\) |
−0.769253 | + | 0.638944i | \(0.779372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −343.485 | − | 198.311i | −0.386372 | − | 0.223072i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 236.772 | − | 27.7133i | 0.265142 | − | 0.0310339i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 138.712 | − | 80.0853i | 0.154985 | − | 0.0894807i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 99.9698 | − | 173.153i | 0.111201 | − | 0.192606i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 130.779i | − | 0.145148i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 221.349i | 0.244584i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1373.26 | + | 792.851i | −1.51407 | + | 0.874146i | −0.514202 | + | 0.857669i | \(0.671912\pi\) |
−0.999864 | + | 0.0164769i | \(0.994755\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1608.77i | − | 1.76593i | −0.469435 | − | 0.882967i | \(-0.655542\pi\) | ||
0.469435 | − | 0.882967i | \(-0.344458\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1506.90 | 1.65049 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 178.775 | + | 309.647i | 0.194956 | + | 0.337674i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1057.74 | −1.15097 | −0.575485 | − | 0.817812i | \(-0.695187\pi\) | ||||
−0.575485 | + | 0.817812i | \(0.695187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.85182 | −0.00308973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −557.954 | − | 322.135i | −0.603194 | − | 0.348254i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 362.449 | + | 627.780i | 0.390150 | + | 0.675759i | 0.992469 | − | 0.122496i | \(-0.0390900\pi\) |
−0.602319 | + | 0.798255i | \(0.705757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −421.040 | − | 565.364i | −0.452245 | − | 0.607266i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −110.702 | + | 191.742i | −0.118398 | + | 0.205072i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 376.045 | − | 651.329i | 0.401329 | − | 0.695122i | −0.592558 | − | 0.805528i | \(-0.701882\pi\) |
0.993887 | + | 0.110406i | \(0.0352152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1593.91 | − | 920.244i | −1.69385 | − | 0.977942i | −0.951361 | − | 0.308079i | \(-0.900314\pi\) |
−0.742485 | − | 0.669863i | \(-0.766353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 413.207i | 0.438184i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.6460 | + | 66.9369i | 0.0408089 | + | 0.0706831i | 0.885708 | − | 0.464242i | \(-0.153673\pi\) |
−0.844900 | + | 0.534925i | \(0.820340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.23150i | − | 0.00551265i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −465.643 | + | 268.839i | −0.488607 | + | 0.282097i | −0.723996 | − | 0.689804i | \(-0.757697\pi\) |
0.235389 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −337.313 | − | 584.244i | −0.353208 | − | 0.611774i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −222.055 | + | 384.610i | −0.231548 | + | 0.401053i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −393.362 | −0.409326 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 645.811 | + | 372.859i | 0.669235 | + | 0.386383i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 195.326 | + | 338.315i | 0.201992 | + | 0.349860i | 0.949170 | − | 0.314763i | \(-0.101925\pi\) |
−0.747178 | + | 0.664624i | \(0.768592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −614.623 | + | 354.853i | −0.632979 | + | 0.365451i | −0.781905 | − | 0.623398i | \(-0.785752\pi\) |
0.148926 | + | 0.988848i | \(0.452418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.6464 | − | 54.8132i | 0.0325246 | − | 0.0563342i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.13076i | − | 0.00525154i | −0.999997 | − | 0.00262577i | \(-0.999164\pi\) | ||
0.999997 | − | 0.00262577i | \(-0.000835810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 555.592 | + | 320.771i | 0.567510 | + | 0.327652i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 209.932 | − | 121.204i | 0.213562 | − | 0.123300i | −0.389404 | − | 0.921067i | \(-0.627319\pi\) |
0.602966 | + | 0.797767i | \(0.293986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 885.030 | + | 1532.92i | 0.898507 | + | 1.55626i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 153.135 | 0.154838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1052.70 | + | 607.778i | −1.06226 | + | 0.613298i | −0.926057 | − | 0.377383i | \(-0.876824\pi\) |
−0.136205 | + | 0.990681i | \(0.543491\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1247.88 | 1.25415 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 134.788 | − | 233.460i | 0.135194 | − | 0.234163i | −0.790478 | − | 0.612491i | \(-0.790168\pi\) |
0.925671 | + | 0.378328i | \(0.123501\pi\) | |||||||
\(998\) | 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 | 684.3.y.g.145.4 | yes | 8 | |
3.2 | odd | 2 | inner | 684.3.y.g.145.1 | ✓ | 8 | |
19.8 | odd | 6 | inner | 684.3.y.g.217.4 | yes | 8 | |
57.8 | even | 6 | inner | 684.3.y.g.217.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.y.g.145.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
684.3.y.g.145.4 | yes | 8 | 1.1 | even | 1 | trivial | |
684.3.y.g.217.1 | yes | 8 | 57.8 | even | 6 | inner | |
684.3.y.g.217.4 | yes | 8 | 19.8 | odd | 6 | inner |