Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), 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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.4 | ||
Root | \(-1.72458 + 2.24184i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.g.895.9 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 6.58775i | − | 0.589226i | −0.955617 | − | 0.294613i | \(-0.904809\pi\) | ||
0.955617 | − | 0.294613i | \(-0.0951908\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.1925 | + | 10.5918i | −0.820321 | + | 0.571904i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 54.2380i | − | 1.48667i | −0.668919 | − | 0.743335i | \(-0.733243\pi\) | ||
0.668919 | − | 0.743335i | \(-0.266757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 40.9722i | − | 0.874125i | −0.899431 | − | 0.437063i | \(-0.856019\pi\) | ||
0.899431 | − | 0.437063i | \(-0.143981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.7632i | 0.340190i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 69.4988i | − | 0.991526i | −0.868458 | − | 0.495763i | \(-0.834889\pi\) | ||
0.868458 | − | 0.495763i | \(-0.165111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 160.189 | 1.93420 | 0.967102 | − | 0.254389i | \(-0.0818744\pi\) | ||||
0.967102 | + | 0.254389i | \(0.0818744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 45.5776 | − | 31.7754i | 0.473612 | − | 0.330189i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 87.8244i | 0.796202i | 0.917342 | + | 0.398101i | \(0.130331\pi\) | ||||
−0.917342 | + | 0.398101i | \(0.869669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 81.6016 | 0.652812 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −236.369 | −1.51354 | −0.756771 | − | 0.653680i | \(-0.773224\pi\) | ||||
−0.756771 | + | 0.653680i | \(0.773224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 131.598 | 0.762443 | 0.381222 | − | 0.924484i | \(-0.375503\pi\) | ||||
0.381222 | + | 0.924484i | \(0.375503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 162.714i | 0.858330i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 69.7762 | + | 100.085i | 0.336981 | + | 0.483354i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.6257 | 0.104974 | 0.0524871 | − | 0.998622i | \(-0.483285\pi\) | ||||
0.0524871 | + | 0.998622i | \(0.483285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 122.916i | 0.504677i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 112.106i | 0.427024i | 0.976940 | + | 0.213512i | \(0.0684903\pi\) | ||||
−0.976940 | + | 0.213512i | \(0.931510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 194.017i | 0.688076i | 0.938956 | + | 0.344038i | \(0.111795\pi\) | ||||
−0.938956 | + | 0.344038i | \(0.888205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 59.2897i | − | 0.196409i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 269.914 | 0.837682 | 0.418841 | − | 0.908060i | \(-0.362436\pi\) | ||||
0.418841 | + | 0.908060i | \(0.362436\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 118.627 | − | 321.833i | 0.345852 | − | 0.938289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 208.496i | 0.572458i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 120.407 | 0.312059 | 0.156030 | − | 0.987752i | \(-0.450130\pi\) | ||||
0.156030 | + | 0.987752i | \(0.450130\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −357.307 | −0.875985 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −480.567 | −1.11671 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −338.109 | −0.746069 | −0.373035 | − | 0.927817i | \(-0.621683\pi\) | ||||
−0.373035 | + | 0.927817i | \(0.621683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 267.146i | − | 0.560729i | −0.959894 | − | 0.280365i | \(-0.909545\pi\) | ||
0.959894 | − | 0.280365i | \(-0.0904554\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −136.733 | + | 95.3263i | −0.273440 | + | 0.190635i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −269.914 | −0.515058 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 275.691i | − | 0.502702i | −0.967896 | − | 0.251351i | \(-0.919125\pi\) | ||
0.967896 | − | 0.251351i | \(-0.0808749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 263.473i | − | 0.459687i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 270.482i | 0.452117i | 0.974114 | + | 0.226058i | \(0.0725840\pi\) | ||||
−0.974114 | + | 0.226058i | \(0.927416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1237.57i | − | 1.98420i | −0.125469 | − | 0.992098i | \(-0.540044\pi\) | ||
0.125469 | − | 0.992098i | \(-0.459956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −244.805 | −0.376901 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 574.479 | + | 824.014i | 0.850233 | + | 1.21955i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 691.966i | − | 0.985472i | −0.870179 | − | 0.492736i | \(-0.835997\pi\) | ||
0.870179 | − | 0.492736i | \(-0.164003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 430.482 | 0.569296 | 0.284648 | − | 0.958632i | \(-0.408123\pi\) | ||||
0.284648 | + | 0.958632i | \(0.408123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −457.841 | −0.584233 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 709.108 | 0.873844 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1220.75i | 1.45392i | 0.686680 | + | 0.726960i | \(0.259067\pi\) | ||||
−0.686680 | + | 0.726960i | \(0.740933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 433.969 | + | 622.472i | 0.499916 | + | 0.717063i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −394.795 | −0.440197 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1055.28i | − | 1.13968i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 381.884i | − | 0.399736i | −0.979823 | − | 0.199868i | \(-0.935949\pi\) | ||
0.979823 | − | 0.199868i | \(-0.0640513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 488.142i | − | 0.495557i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 696.862i | − | 0.686538i | −0.939237 | − | 0.343269i | \(-0.888466\pi\) | ||
0.939237 | − | 0.343269i | \(-0.111534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 621.333 | 0.594386 | 0.297193 | − | 0.954817i | \(-0.403950\pi\) | ||||
0.297193 | + | 0.954817i | \(0.403950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −209.329 | − | 300.254i | −0.194556 | − | 0.279065i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 295.518i | − | 0.266999i | −0.991049 | − | 0.133499i | \(-0.957379\pi\) | ||
0.991049 | − | 0.133499i | \(-0.0426214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −669.548 | −0.588358 | −0.294179 | − | 0.955750i | \(-0.595046\pi\) | ||||
−0.294179 | + | 0.955750i | \(0.595046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −70.8772 | −0.0606069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1093.94 | −0.910703 | −0.455352 | − | 0.890312i | \(-0.650486\pi\) | ||||
−0.455352 | + | 0.890312i | \(0.650486\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 578.565 | 0.469143 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 368.749i | − | 0.291375i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 736.118 | + | 1055.86i | 0.567058 | + | 0.813369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1610.76 | −1.21019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 336.318i | − | 0.246543i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1361.04i | − | 0.973880i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 837.266i | − | 0.585003i | −0.956265 | − | 0.292501i | \(-0.905512\pi\) | ||
0.956265 | − | 0.292501i | \(-0.0944876\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 582.050i | − | 0.397261i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1821.00 | −1.21452 | −0.607258 | − | 0.794504i | \(-0.707731\pi\) | ||||
−0.607258 | + | 0.794504i | \(0.707731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2433.68 | + | 1696.69i | −1.58667 | + | 1.10618i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 177.869i | 0.113397i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 321.471 | 0.200475 | 0.100238 | − | 0.994964i | \(-0.468040\pi\) | ||||
0.100238 | + | 0.994964i | \(0.468040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1339.35 | 0.817284 | 0.408642 | − | 0.912695i | \(-0.366002\pi\) | ||||
0.408642 | + | 0.912695i | \(0.366002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −809.743 | −0.483636 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2222.25 | −1.29954 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1557.14i | 0.891818i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −355.881 | + | 965.500i | −0.199678 | + | 0.541722i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2748.96 | −1.51144 | −0.755718 | − | 0.654898i | \(-0.772712\pi\) | ||||
−0.755718 | + | 0.654898i | \(0.772712\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1950.99i | 1.05145i | 0.850655 | + | 0.525725i | \(0.176206\pi\) | ||||
−0.850655 | + | 0.525725i | \(0.823794\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 625.489i | − | 0.330509i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 866.936i | − | 0.449252i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3019.82i | − | 1.53508i | −0.641000 | − | 0.767540i | \(-0.721480\pi\) | ||
0.641000 | − | 0.767540i | \(-0.278520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −361.220 | −0.180168 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −930.219 | − | 1334.28i | −0.455351 | − | 0.653141i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2882.36i | − | 1.38506i | −0.721391 | − | 0.692528i | \(-0.756497\pi\) | ||
0.721391 | − | 0.692528i | \(-0.243503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1071.92 | 0.505750 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2512.97 | −1.16443 | −0.582213 | − | 0.813036i | \(-0.697813\pi\) | ||||
−0.582213 | + | 0.813036i | \(0.697813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 518.282 | 0.235905 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1441.70 | 0.644735 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1307.12i | − | 0.574442i | −0.957864 | − | 0.287221i | \(-0.907269\pi\) | ||
0.957864 | − | 0.287221i | \(-0.0927314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1239.74 | + | 864.308i | −0.535515 | + | 0.373346i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1014.33 | 0.430743 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3555.19i | 1.48451i | 0.670117 | + | 0.742256i | \(0.266244\pi\) | ||||
−0.670117 | + | 0.742256i | \(0.733756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1746.96i | 0.717406i | 0.933452 | + | 0.358703i | \(0.116781\pi\) | ||||
−0.933452 | + | 0.358703i | \(0.883219\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 801.437i | 0.323737i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 155.640i | − | 0.0618536i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3769.48 | −1.47407 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 410.199 | − | 285.979i | 0.157871 | − | 0.110063i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1935.70i | 0.733310i | 0.930357 | + | 0.366655i | \(0.119497\pi\) | ||||
−0.930357 | + | 0.366655i | \(0.880503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3842.27 | −1.43302 | −0.716509 | − | 0.697578i | \(-0.754261\pi\) | ||||
−0.716509 | + | 0.697578i | \(0.754261\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 809.743 | 0.297369 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −490.616 | −0.177436 | −0.0887181 | − | 0.996057i | \(-0.528277\pi\) | ||||
−0.0887181 | + | 0.996057i | \(0.528277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3630.14 | 1.29314 | 0.646568 | − | 0.762857i | \(-0.276204\pi\) | ||||
0.646568 | + | 0.762857i | \(0.276204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 827.074i | 0.290235i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3591.05 | − | 2503.58i | 1.24159 | − | 0.865600i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 738.525 | 0.251614 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 790.419i | 0.265401i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8688.33i | − | 2.87552i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2486.62i | 0.811308i | 0.914027 | + | 0.405654i | \(0.132956\pi\) | ||||
−0.914027 | + | 0.405654i | \(0.867044\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 811.446i | − | 0.261030i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1278.13 | 0.405432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1999.31 | + | 1393.86i | −0.625448 | + | 0.436044i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3712.70i | 1.14558i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2847.52 | −0.866718 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 992.723 | 0.298106 | 0.149053 | − | 0.988829i | \(-0.452377\pi\) | ||||
0.149053 | + | 0.988829i | \(0.452377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 734.414 | 0.217604 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5666.03 | −1.65668 | −0.828342 | − | 0.560223i | \(-0.810716\pi\) | ||||
−0.828342 | + | 0.560223i | \(0.810716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6488.31i | − | 1.87231i | −0.351583 | − | 0.936157i | \(-0.614357\pi\) | ||
0.351583 | − | 0.936157i | \(-0.385643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1723.44 | − | 2472.04i | −0.490882 | − | 0.704106i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3657.30 | −1.02832 | −0.514158 | − | 0.857696i | \(-0.671895\pi\) | ||||
−0.514158 | + | 0.857696i | \(0.671895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1778.13i | − | 0.493584i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2075.90i | 0.568962i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5806.11i | − | 1.57141i | −0.618604 | − | 0.785703i | \(-0.712302\pi\) | ||
0.618604 | − | 0.785703i | \(-0.287698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 584.133i | 0.156130i | 0.996948 | + | 0.0780649i | \(0.0248741\pi\) | ||||
−0.996948 | + | 0.0780649i | \(0.975126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2120.16 | − | 781.486i | −0.552865 | − | 0.203785i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6563.29i | − | 1.69074i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1291.45 | −0.328683 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3459.63 | −0.870000 | −0.435000 | − | 0.900430i | \(-0.643252\pi\) | ||||
−0.435000 | + | 0.900430i | \(0.643252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4763.42 | 1.18369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1373.52 | 0.337307 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1501.55i | − | 0.364453i | −0.983257 | − | 0.182226i | \(-0.941670\pi\) | ||
0.983257 | − | 0.182226i | \(-0.0583304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −358.935 | + | 250.239i | −0.0861125 | + | 0.0600352i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2127.33 | −0.504514 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5235.13i | − | 1.22742i | −0.789531 | − | 0.613711i | \(-0.789676\pi\) | ||
0.789531 | − | 0.613711i | \(-0.210324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 793.210i | − | 0.183874i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3662.24i | − | 0.839421i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 34.2010i | 0.00775193i | 0.999992 | + | 0.00387597i | \(0.00123376\pi\) | ||||
−0.999992 | + | 0.00387597i | \(0.998766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −653.935 | −0.146582 | −0.0732910 | − | 0.997311i | \(-0.523350\pi\) | ||||
−0.0732910 | + | 0.997311i | \(0.523350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1301.91 | − | 1867.41i | −0.288627 | − | 0.413997i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4425.91i | − | 0.970517i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2250.58 | −0.488174 | −0.244087 | − | 0.969753i | \(-0.578488\pi\) | ||||
−0.244087 | + | 0.969753i | \(0.578488\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1184.38 | 0.254148 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4213.47 | 0.894500 | 0.447250 | − | 0.894409i | \(-0.352403\pi\) | ||||
0.447250 | + | 0.894409i | \(0.352403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2069.17 | 0.434627 | 0.217313 | − | 0.976102i | \(-0.430271\pi\) | ||||
0.217313 | + | 0.976102i | \(0.430271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3165.85i | 0.657997i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1187.40 | − | 1703.17i | −0.244217 | − | 0.350297i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 82.9156 | 0.0168768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1145.65i | 0.230788i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2027.49i | 0.404257i | 0.979359 | + | 0.202128i | \(0.0647859\pi\) | ||||
−0.979359 | + | 0.202128i | \(0.935214\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2227.38i | 0.439604i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1464.43i | 0.286110i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3598.35 | 0.695981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2054.99 | − | 2947.61i | −0.393513 | − | 0.564443i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2090.59i | 0.396373i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1759.89 | −0.330396 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 167.377 | 0.0311162 | 0.0155581 | − | 0.999879i | \(-0.495047\pi\) | ||||
0.0155581 | + | 0.999879i | \(0.495047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1864.00 | −0.343169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4720.36 | −0.860666 | −0.430333 | − | 0.902670i | \(-0.641604\pi\) | ||||
−0.430333 | + | 0.902670i | \(0.641604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6008.08i | − | 1.08497i | −0.840064 | − | 0.542487i | \(-0.817483\pi\) | ||
0.840064 | − | 0.542487i | \(-0.182517\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 627.986 | + | 900.762i | 0.112327 | + | 0.161118i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1790.11 | 0.317170 | 0.158585 | − | 0.987345i | \(-0.449307\pi\) | ||||
0.158585 | + | 0.987345i | \(0.449307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12820.2i | 2.25014i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 886.555i | 0.154152i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11132.9i | − | 1.91781i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3343.39i | − | 0.570640i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2008.64 | 0.339689 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4100.69 | + | 2858.88i | −0.687168 | + | 0.479074i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5059.04i | 0.840090i | 0.907503 | + | 0.420045i | \(0.137986\pi\) | ||||
−0.907503 | + | 0.420045i | \(0.862014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 212.632 | 0.0349914 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1816.19 | −0.296205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12120.3 | −1.95915 | −0.979574 | − | 0.201084i | \(-0.935554\pi\) | ||||
−0.979574 | + | 0.201084i | \(0.935554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3281.83 | 0.525795 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7137.63i | − | 1.13350i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1606.55 | + | 6145.94i | 0.252902 | + | 0.967492i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1735.69 | −0.270860 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6366.23i | 0.984892i | 0.870343 | + | 0.492446i | \(0.163897\pi\) | ||||
−0.870343 | + | 0.492446i | \(0.836103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4912.76i | 0.753508i | 0.926313 | + | 0.376754i | \(0.122960\pi\) | ||||
−0.926313 | + | 0.376754i | \(0.877040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1106.25i | 0.168226i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5847.50i | 0.881674i | 0.897587 | + | 0.440837i | \(0.145318\pi\) | ||||
−0.897587 | + | 0.440837i | \(0.854682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1781.87 | 0.266399 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2208.35 | − | 3167.59i | −0.327391 | − | 0.469599i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7074.15i | 1.04000i | 0.854167 | + | 0.519999i | \(0.174068\pi\) | ||||
−0.854167 | + | 0.519999i | \(0.825932\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18801.5 | 2.74114 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4832.29 | 0.698704 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8152.78 | −1.16914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3730.67 | −0.530625 | −0.265312 | − | 0.964163i | \(-0.585475\pi\) | ||||
−0.265312 | + | 0.964163i | \(0.585475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1008.95i | 0.142341i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1829.29 | + | 1275.33i | −0.255989 | + | 0.178468i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9966.13 | −1.38345 | −0.691725 | − | 0.722161i | \(-0.743149\pi\) | ||||
−0.691725 | + | 0.722161i | \(0.743149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4083.12i | 0.562270i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9684.57i | 1.32303i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11391.4i | 1.54390i | 0.635686 | + | 0.771948i | \(0.280717\pi\) | ||||
−0.635686 | + | 0.771948i | \(0.719283\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2511.80i | 0.337752i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3889.70 | −0.518941 | −0.259471 | − | 0.965751i | \(-0.583548\pi\) | ||||
−0.259471 | + | 0.965751i | \(0.583548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5428.40 | − | 3784.52i | 0.718589 | − | 0.500980i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1746.15i | 0.229359i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9689.51 | 1.26292 | 0.631462 | − | 0.775407i | \(-0.282455\pi\) | ||||
0.631462 | + | 0.775407i | \(0.282455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6103.69 | 0.789455 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5463.01 | 0.701201 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4558.50 | −0.580666 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10767.0i | 1.36116i | 0.732672 | + | 0.680582i | \(0.238273\pi\) | ||||
−0.732672 | + | 0.680582i | \(0.761727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7301.04 | − | 5090.07i | 0.916063 | − | 0.638653i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4053.14 | −0.504749 | −0.252374 | − | 0.967630i | \(-0.581211\pi\) | ||||
−0.252374 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5391.86i | − | 0.666471i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 533.608i | − | 0.0654696i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1281.41i | − | 0.156062i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1517.85i | − | 0.183503i | −0.995782 | − | 0.0917517i | \(-0.970753\pi\) | ||
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −964.413 | −0.115744 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5136.74 | − | 3581.19i | 0.612016 | − | 0.426680i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2835.91i | − | 0.335444i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4018.06 | −0.471859 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1429.41 | 0.166662 | 0.0833310 | − | 0.996522i | \(-0.473444\pi\) | ||||
0.0833310 | + | 0.996522i | \(0.473444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 924.052 | 0.106973 | 0.0534864 | − | 0.998569i | \(-0.482967\pi\) | ||||
0.0534864 | + | 0.998569i | \(0.482967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2429.23 | 0.279227 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5671.21i | − | 0.647280i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2829.56 | + | 4058.62i | 0.320683 | + | 0.459978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6666.75 | 0.750288 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4099.49i | − | 0.458157i | −0.973408 | − | 0.229078i | \(-0.926429\pi\) | ||
0.973408 | − | 0.229078i | \(-0.0735712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6350.16i | 0.704779i | 0.935853 | + | 0.352390i | \(0.114631\pi\) | ||||
−0.935853 | + | 0.352390i | \(0.885369\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4671.43i | − | 0.514892i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14068.5i | 1.54002i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5385.88 | −0.585545 | −0.292772 | − | 0.956182i | \(-0.594578\pi\) | ||||
−0.292772 | + | 0.956182i | \(0.594578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1067.64 | − | 2896.50i | 0.115284 | − | 0.312763i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1259.12i | 0.135040i | 0.997718 | + | 0.0675200i | \(0.0215087\pi\) | ||||
−0.997718 | + | 0.0675200i | \(0.978491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8041.97 | 0.856688 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8246.89 | 0.872627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 434.975 | 0.0457187 | 0.0228594 | − | 0.999739i | \(-0.492723\pi\) | ||||
0.0228594 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6080.40 | 0.634845 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5852.96i | − | 0.607055i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4100.69 | − | 2858.88i | 0.422512 | − | 0.294564i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3172.32 | −0.324715 | −0.162357 | − | 0.986732i | \(-0.551910\pi\) | ||||
−0.162357 | + | 0.986732i | \(0.551910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1876.47i | 0.190819i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12644.2i | − | 1.27744i | −0.769441 | − | 0.638718i | \(-0.779465\pi\) | ||
0.769441 | − | 0.638718i | \(-0.220535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13829.8i | − | 1.38818i | −0.719890 | − | 0.694089i | \(-0.755808\pi\) | ||
0.719890 | − | 0.694089i | \(-0.244192\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2600.81i | 0.259376i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17043.7 | −1.68884 | −0.844419 | − | 0.535684i | \(-0.820054\pi\) | ||||
−0.844419 | + | 0.535684i | \(0.820054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2920.07 | + | 4188.45i | 0.287497 | + | 0.412377i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9059.45i | 0.886279i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10523.1 | 1.02294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13071.7 | 1.26267 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1083.66 | 0.104020 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4131.98 | −0.394144 | −0.197072 | − | 0.980389i | \(-0.563143\pi\) | ||||
−0.197072 | + | 0.980389i | \(0.563143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 967.997i | − | 0.0917607i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2790.66 | + | 4002.83i | 0.262897 | + | 0.377091i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2515.75 | −0.235535 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11356.0i | − | 1.05665i | −0.849042 | − | 0.528325i | \(-0.822820\pi\) | ||
0.849042 | − | 0.528325i | \(-0.177180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8647.09i | 0.799663i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7964.89i | − | 0.732079i | −0.930599 | − | 0.366039i | \(-0.880714\pi\) | ||
0.930599 | − | 0.366039i | \(-0.119286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16427.4i | 1.50072i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3215.76 | −0.291995 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2864.89 | − | 4109.31i | −0.258567 | − | 0.370881i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2086.90i | 0.187219i | 0.995609 | + | 0.0936096i | \(0.0298406\pi\) | ||||
−0.995609 | + | 0.0936096i | \(0.970159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7538.90 | 0.672282 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10945.8 | 0.970277 | 0.485138 | − | 0.874437i | \(-0.338769\pi\) | ||||
0.485138 | + | 0.874437i | \(0.338769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4590.75 | −0.404526 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1554.85 | −0.136200 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21490.9i | 1.87145i | 0.352732 | + | 0.935724i | \(0.385253\pi\) | ||||
−0.352732 | + | 0.935724i | \(0.614747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13108.1 | + | 18801.8i | 1.13477 | + | 1.62768i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4325.10 | −0.372238 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4093.18i | − | 0.350228i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 14639.6i | − | 1.24536i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3921.36i | 0.331654i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6155.93i | 0.517651i | 0.965924 | + | 0.258826i | \(0.0833355\pi\) | ||||
−0.965924 | + | 0.258826i | \(0.916665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5018.12 | 0.419555 | 0.209777 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209777 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3719.21 | − | 2592.92i | 0.309180 | − | 0.215551i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9145.92i | − | 0.755982i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4453.88 | 0.366062 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3042.98 | −0.248690 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4593.22 | 0.373273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1946.80 | −0.157323 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10665.6i | − | 0.857083i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17455.6 | − | 6434.10i | −1.39493 | − | 0.514168i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1260.99 | 0.100211 | 0.0501055 | − | 0.998744i | \(-0.484044\pi\) | ||||
0.0501055 | + | 0.998744i | \(0.484044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5240.88i | − | 0.414194i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4410.81i | 0.346676i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16180.1i | 1.26474i | 0.774666 | + | 0.632370i | \(0.217918\pi\) | ||||
−0.774666 | + | 0.632370i | \(0.782082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2404.31i | − | 0.186910i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −37863.8 | −2.92750 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7329.17 | + | 10512.7i | 0.563595 | + | 0.808403i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 466.921i | 0.0357112i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21384.1 | 1.62670 | 0.813351 | − | 0.581774i | \(-0.197641\pi\) | ||||
0.813351 | + | 0.581774i | \(0.197641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7949.28 | 0.601464 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11308.4 | 0.851056 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2029.82 | 0.151948 | 0.0759739 | − | 0.997110i | \(-0.475793\pi\) | ||||
0.0759739 | + | 0.997110i | \(0.475793\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7206.62i | 0.536610i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1230.60 | + | 857.937i | −0.0911467 | + | 0.0635449i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21597.4 | 1.59123 | 0.795616 | − | 0.605801i | \(-0.207147\pi\) | ||||
0.795616 | + | 0.605801i | \(0.207147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 13250.6i | − | 0.971137i | −0.874199 | − | 0.485568i | \(-0.838613\pi\) | ||
0.874199 | − | 0.485568i | \(-0.161387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5807.10i | − | 0.423377i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7166.61i | 0.519771i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17602.4i | − | 1.27001i | −0.772507 | − | 0.635006i | \(-0.780998\pi\) | ||
0.772507 | − | 0.635006i | \(-0.219002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11526.8 | 0.827353 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6540.12 | + | 4559.59i | −0.467005 | + | 0.325583i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6530.63i | − | 0.463930i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2429.23 | −0.171686 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10190.1 | −0.716510 | −0.358255 | − | 0.933624i | \(-0.616628\pi\) | ||||
−0.358255 | + | 0.933624i | \(0.616628\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21080.6 | 1.47472 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1471.85 | 0.102443 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1211.86i | 0.0839213i | 0.999119 | + | 0.0419606i | \(0.0133604\pi\) | ||||
−0.999119 | + | 0.0419606i | \(0.986640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6955.77 | − | 4849.36i | 0.479258 | − | 0.334125i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10890.4 | −0.746592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9213.72i | − | 0.628485i | −0.949343 | − | 0.314243i | \(-0.898249\pi\) | ||
0.949343 | − | 0.314243i | \(-0.101751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17051.3i | 1.15730i | 0.815575 | + | 0.578651i | \(0.196421\pi\) | ||||
−0.815575 | + | 0.578651i | \(0.803579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2481.22i | − | 0.167567i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10611.3i | 0.713076i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9836.13 | −0.657721 | −0.328860 | − | 0.944379i | \(-0.606665\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10773.2 | + | 7510.74i | −0.716832 | + | 0.499755i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11059.0i | − | 0.732239i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10697.4 | −0.704837 | −0.352418 | − | 0.935843i | \(-0.614641\pi\) | ||||
−0.352418 | + | 0.935843i | \(0.614641\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2215.58 | −0.145269 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18439.5 | 1.20316 | 0.601578 | − | 0.798814i | \(-0.294539\pi\) | ||||
0.601578 | + | 0.798814i | \(0.294539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26672.5 | −1.73192 | −0.865960 | − | 0.500113i | \(-0.833292\pi\) | ||||
−0.865960 | + | 0.500113i | \(0.833292\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2371.26i | − | 0.153229i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12929.9 | − | 18546.3i | −0.831503 | − | 1.19268i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1234.01 | 0.0789766 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26065.0i | 1.66018i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1641.96i | − | 0.104085i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10491.0i | 0.661870i | 0.943653 | + | 0.330935i | \(0.107364\pi\) | ||||
−0.943653 | + | 0.330935i | \(0.892636\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 7459.86i | − | 0.468409i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5515.70 | −0.344699 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13186.2 | − | 4860.41i | −0.820183 | − | 0.302318i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2434.34i | 0.150706i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2839.23 | 0.174950 | 0.0874749 | − | 0.996167i | \(-0.472120\pi\) | ||||
0.0874749 | + | 0.996167i | \(0.472120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6153.86 | −0.377426 | −0.188713 | − | 0.982032i | \(-0.560432\pi\) | ||||
−0.188713 | + | 0.982032i | \(0.560432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3834.40 | −0.234076 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3054.45 | 0.185599 | 0.0927996 | − | 0.995685i | \(-0.470418\pi\) | ||||
0.0927996 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18338.4i | 1.10916i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5997.94 | − | 4181.59i | 0.361103 | − | 0.251750i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17522.7 | 1.05010 | 0.525052 | − | 0.851070i | \(-0.324046\pi\) | ||||
0.525052 | + | 0.851070i | \(0.324046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11996.3i | 0.715625i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 11138.1i | − | 0.661398i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 131.768i | − | 0.00778899i | −0.999992 | − | 0.00389450i | \(-0.998760\pi\) | ||
0.999992 | − | 0.00389450i | \(-0.00123966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 21150.0i | − | 1.24454i | −0.782803 | − | 0.622270i | \(-0.786211\pi\) | ||
0.782803 | − | 0.622270i | \(-0.213789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8542.55 | 0.500400 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11177.4 | + | 16032.5i | 0.651790 | + | 0.934906i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20759.0i | − | 1.20508i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2978.17 | −0.172112 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14489.5 | −0.833620 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11238.3 | 0.643693 | 0.321846 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321846 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2203.24 | −0.125634 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4728.28i | − | 0.268423i | −0.990953 | − | 0.134212i | \(-0.957150\pi\) | ||
0.990953 | − | 0.134212i | \(-0.0428502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4044.84 | + | 5801.78i | 0.228611 | + | 0.327912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16998.1 | 0.956487 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26608.6i | − | 1.49070i | −0.666673 | − | 0.745350i | \(-0.732282\pi\) | ||
0.666673 | − | 0.745350i | \(-0.267718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2117.77i | − | 0.118125i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19464.9i | 1.08098i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4933.33i | − | 0.272779i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9292.47 | 0.511580 | 0.255790 | − | 0.966732i | \(-0.417664\pi\) | ||||
0.255790 | + | 0.966732i | \(0.417664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5170.31 | + | 7416.12i | 0.283411 | + | 0.406516i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8823.33i | − | 0.481565i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7791.22 | 0.423406 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10971.9 | 0.593698 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13950.7 | 0.751657 | 0.375829 | − | 0.926689i | \(-0.377358\pi\) | ||||
0.375829 | + | 0.926689i | \(0.377358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3784.58 | 0.203042 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5334.38i | 0.284971i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7381.03 | + | 10587.1i | 0.392634 | + | 0.563181i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29363.4 | 1.55538 | 0.777691 | − | 0.628646i | \(-0.216391\pi\) | ||||
0.777691 | + | 0.628646i | \(0.216391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6227.69i | − | 0.328491i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11557.5i | 0.607059i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14639.6i | 0.765721i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17418.3i | 0.907251i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8612.18 | −0.446704 | −0.223352 | − | 0.974738i | \(-0.571700\pi\) | ||||
−0.223352 | + | 0.974738i | \(0.571700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9439.63 | + | 6581.04i | −0.487587 | + | 0.339932i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1752.40i | − | 0.0901416i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19288.1 | −0.988059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19226.6 | 0.980846 | 0.490423 | − | 0.871484i | \(-0.336842\pi\) | ||||
0.490423 | + | 0.871484i | \(0.336842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13483.9 | 0.682245 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33053.9i | 1.66559i | 0.553584 | + | 0.832793i | \(0.313260\pi\) | ||||
−0.553584 | + | 0.832793i | \(0.686740\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6360.47 | + | 2344.46i | 0.319197 | + | 0.117655i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14953.0 | −0.747353 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4071.71i | 0.202679i | 0.994852 | + | 0.101340i | \(0.0323129\pi\) | ||||
−0.994852 | + | 0.101340i | \(0.967687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19689.9i | 0.976147i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 807.693i | 0.0398807i | 0.999801 | + | 0.0199404i | \(0.00634763\pi\) | ||||
−0.999801 | + | 0.0199404i | \(0.993652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18109.5i | 0.890577i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3874.34 | 0.189765 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3130.07 | + | 4489.68i | 0.152698 | + | 0.219024i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12604.7i | 0.612454i | 0.951959 | + | 0.306227i | \(0.0990666\pi\) | ||||
−0.951959 | + | 0.306227i | \(0.900933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10378.9 | 0.502295 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12852.6 | 0.619542 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18825.2 | 0.903848 | 0.451924 | − | 0.892056i | \(-0.350738\pi\) | ||||
0.451924 | + | 0.892056i | \(0.350738\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14290.3 | −0.683404 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7341.96i | − | 0.349732i | −0.984592 | − | 0.174866i | \(-0.944051\pi\) | ||
0.984592 | − | 0.174866i | \(-0.0559492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10172.1 | − | 7091.72i | 0.482642 | − | 0.336484i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4120.57 | −0.194744 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13853.1i | 0.652158i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37425.8i | − | 1.75502i | −0.479560 | − | 0.877509i | \(-0.659204\pi\) | ||
0.479560 | − | 0.877509i | \(-0.340796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4504.66i | 0.210417i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36961.6i | − | 1.71982i | −0.510449 | − | 0.859908i | \(-0.670521\pi\) | ||
0.510449 | − | 0.859908i | \(-0.329479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10738.6 | 0.497733 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1076.81 | − | 750.718i | 0.0497171 | − | 0.0346613i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17958.1i | 0.825952i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14670.4 | 0.672149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6381.98 | 0.291281 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19893.8 | −0.904510 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22096.0 | 1.00081 | 0.500406 | − | 0.865791i | \(-0.333184\pi\) | ||||
0.500406 | + | 0.865791i | \(0.333184\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15705.4i | 0.708652i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16619.8 | − | 11586.8i | 0.747068 | − | 0.520835i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10945.5 | −0.490148 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2379.63i | 0.106159i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40538.6i | 1.80170i | 0.434134 | + | 0.900848i | \(0.357054\pi\) | ||||
−0.434134 | + | 0.900848i | \(0.642946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18758.7i | − | 0.830583i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10986.7i | 0.484640i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67123.2 | −2.94985 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8789.88 | + | 6128.05i | −0.384848 | + | 0.268305i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 102.603i | − | 0.00447558i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15624.5 | −0.679022 | −0.339511 | − | 0.940602i | \(-0.610262\pi\) | ||||
−0.339511 | + | 0.940602i | \(0.610262\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4997.93 | 0.216401 | 0.108200 | − | 0.994129i | \(-0.465491\pi\) | ||||
0.108200 | + | 0.994129i | \(0.465491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1961.80 | 0.0846292 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18988.3 | −0.816111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31079.3i | 1.33088i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3905.72 | + | 5602.24i | 0.166639 | + | 0.239021i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45367.1 | −1.92853 | −0.964266 | − | 0.264937i | \(-0.914649\pi\) | ||||
−0.964266 | + | 0.264937i | \(0.914649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3913.77i | − | 0.165766i | −0.996559 | − | 0.0828829i | \(-0.973587\pi\) | ||
0.996559 | − | 0.0828829i | \(-0.0264128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13277.7i | 0.560328i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7368.11i | − | 0.309812i | −0.987929 | − | 0.154906i | \(-0.950493\pi\) | ||
0.987929 | − | 0.154906i | \(-0.0495074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25074.8i | − | 1.05052i | −0.850941 | − | 0.525261i | \(-0.823968\pi\) | ||
0.850941 | − | 0.525261i | \(-0.176032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6751.74 | 0.281848 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22367.0 | − | 8244.44i | −0.930338 | − | 0.342921i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16554.8i | 0.686110i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3553.15 | −0.146732 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11380.1 | 0.468279 | 0.234139 | − | 0.972203i | \(-0.424773\pi\) | ||||
0.234139 | + | 0.972203i | \(0.424773\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31481.5 | 1.29081 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12640.4 | −0.516440 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3414.31i | − | 0.139001i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24471.6 | − | 17060.9i | 0.992744 | − | 0.692113i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6207.51 | −0.250932 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2074.92i | 0.0835807i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2040.57i | − | 0.0819082i | −0.999161 | − | 0.0409541i | \(-0.986960\pi\) | ||
0.999161 | − | 0.0409541i | \(-0.0130397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 9497.56i | − | 0.379895i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 14755.7i | − | 0.588152i | −0.955782 | − | 0.294076i | \(-0.904988\pi\) | ||
0.955782 | − | 0.294076i | \(-0.0950120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44194.2 | −1.75540 | −0.877698 | − | 0.479213i | \(-0.840922\pi\) | ||||
−0.877698 | + | 0.479213i | \(0.840922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3562.21 | + | 5109.52i | 0.140999 | + | 0.202244i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 47866.0i | − | 1.88804i | −0.329888 | − | 0.944020i | \(-0.607011\pi\) | ||
0.329888 | − | 0.944020i | \(-0.392989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8610.97 | −0.338476 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −248.747 | −0.00974381 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37530.9 | −1.46507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11295.7 | −0.439425 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3436.95i | − | 0.133245i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14415.9 | + | 20677.7i | 0.556966 | + | 0.798894i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25430.0 | 0.979146 | 0.489573 | − | 0.871962i | \(-0.337153\pi\) | ||||
0.489573 | + | 0.871962i | \(0.337153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 6082.47i | − | 0.233398i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13602.8i | − | 0.520192i | −0.965583 | − | 0.260096i | \(-0.916246\pi\) | ||
0.965583 | − | 0.260096i | \(-0.0837541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16042.8i | 0.611419i | 0.952125 | + | 0.305710i | \(0.0988937\pi\) | ||||
−0.952125 | + | 0.305710i | \(0.901106\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 6682.14i | − | 0.253805i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45834.8 | −1.73504 | −0.867520 | − | 0.497402i | \(-0.834287\pi\) | ||||
−0.867520 | + | 0.497402i | \(0.834287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8868.17 | + | 12720.2i | 0.334565 | + | 0.479890i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4393.28i | − | 0.165186i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43237.3 | 1.62025 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23420.7 | 0.874713 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10795.1 | −0.401825 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31105.8 | −1.15399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8368.13i | − | 0.309415i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6164.96 | + | 8842.82i | 0.227195 | + | 0.325881i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11508.5 | 0.422714 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11789.5i | 0.431603i | 0.976437 | + | 0.215801i | \(0.0692363\pi\) | ||||
−0.976437 | + | 0.215801i | \(0.930764\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6271.76i | − | 0.228846i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34980.3i | 1.27217i | 0.771618 | + | 0.636087i | \(0.219448\pi\) | ||||
−0.771618 | + | 0.636087i | \(0.780552\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23348.5i | − | 0.846356i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5279.67 | 0.190754 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27665.7 | − | 19287.7i | 0.996293 | − | 0.694587i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34836.9i | 1.25045i | 0.780444 | + | 0.625225i | \(0.214993\pi\) | ||||
−0.780444 | + | 0.625225i | \(0.785007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −502.130 | −0.0179650 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11082.2 | 0.395207 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1927.90 | 0.0685285 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5591.99 | 0.198129 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8027.80i | − | 0.283513i | −0.989902 | − | 0.141757i | \(-0.954725\pi\) | ||
0.989902 | − | 0.141757i | \(-0.0452750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19002.8 | − | 51554.1i | 0.668948 | − | 1.81484i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14161.1 | 0.496906 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24832.4i | 0.868562i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 31147.0i | − | 1.08594i | −0.839751 | − | 0.542972i | \(-0.817299\pi\) | ||
0.839751 | − | 0.542972i | \(-0.182701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18024.3i | 0.626410i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14386.4i | − | 0.498389i | −0.968453 | − | 0.249195i | \(-0.919834\pi\) | ||
0.968453 | − | 0.249195i | \(-0.0801659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9845.63 | −0.339998 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1883.96 | − | 2702.29i | −0.0648520 | − | 0.0930216i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1481.87i | 0.0508494i | 0.999677 | + | 0.0254247i | \(0.00809380\pi\) | ||||
−0.999677 | + | 0.0254247i | \(0.991906\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50705.8 | −1.73444 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5370.34 | −0.183118 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4125.04 | −0.140213 | −0.0701065 | − | 0.997540i | \(-0.522334\pi\) | ||||
−0.0701065 | + | 0.997540i | \(0.522334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12751.9 | 0.432086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 38460.6i | − | 1.29912i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4883.96 | + | 3404.96i | −0.164454 | + | 0.114653i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12472.9 | −0.418680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2659.67i | − | 0.0889995i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25311.9i | 0.844372i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17872.4i | − | 0.594351i | −0.954823 | − | 0.297175i | \(-0.903955\pi\) | ||
0.954823 | − | 0.297175i | \(-0.0960446\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33398.8i | 1.10725i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6473.23 | −0.213940 | −0.106970 | − | 0.994262i | \(-0.534115\pi\) | ||||
−0.106970 | + | 0.994262i | \(0.534115\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20348.2 | + | 14186.2i | −0.670435 | + | 0.467408i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10030.2i | 0.329459i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32958.4 | 1.07926 | 0.539628 | − | 0.841904i | \(-0.318565\pi\) | ||||
0.539628 | + | 0.841904i | \(0.318565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66210.9 | 2.16150 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6025.93 | −0.196119 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11342.0 | 0.368010 | 0.184005 | − | 0.982925i | \(-0.441094\pi\) | ||||
0.184005 | + | 0.982925i | \(0.441094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3232.06i | 0.104550i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12302.1 | − | 8576.64i | 0.396736 | − | 0.276593i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17039.4 | −0.547847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15910.0i | 0.509987i | 0.966943 | + | 0.254994i | \(0.0820733\pi\) | ||||
−0.966943 | + | 0.254994i | \(0.917927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15177.1i | − | 0.485026i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 23914.5i | − | 0.761949i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3756.74i | 0.119335i | 0.998218 | + | 0.0596676i | \(0.0190041\pi\) | ||||
−0.998218 | + | 0.0596676i | \(0.980996\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −637.895 | −0.0202023 |
(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 | 1344.4.b.g.895.4 | 12 | ||
4.3 | odd | 2 | 1344.4.b.h.895.4 | 12 | |||
7.6 | odd | 2 | 1344.4.b.h.895.9 | 12 | |||
8.3 | odd | 2 | 84.4.b.a.55.3 | ✓ | 12 | ||
8.5 | even | 2 | 84.4.b.b.55.4 | yes | 12 | ||
24.5 | odd | 2 | 252.4.b.e.55.9 | 12 | |||
24.11 | even | 2 | 252.4.b.f.55.10 | 12 | |||
28.27 | even | 2 | inner | 1344.4.b.g.895.9 | 12 | ||
56.13 | odd | 2 | 84.4.b.a.55.4 | yes | 12 | ||
56.27 | even | 2 | 84.4.b.b.55.3 | yes | 12 | ||
168.83 | odd | 2 | 252.4.b.e.55.10 | 12 | |||
168.125 | even | 2 | 252.4.b.f.55.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.3 | ✓ | 12 | 8.3 | odd | 2 | ||
84.4.b.a.55.4 | yes | 12 | 56.13 | odd | 2 | ||
84.4.b.b.55.3 | yes | 12 | 56.27 | even | 2 | ||
84.4.b.b.55.4 | yes | 12 | 8.5 | even | 2 | ||
252.4.b.e.55.9 | 12 | 24.5 | odd | 2 | |||
252.4.b.e.55.10 | 12 | 168.83 | odd | 2 | |||
252.4.b.f.55.9 | 12 | 168.125 | even | 2 | |||
252.4.b.f.55.10 | 12 | 24.11 | even | 2 | |||
1344.4.b.g.895.4 | 12 | 1.1 | even | 1 | trivial | ||
1344.4.b.g.895.9 | 12 | 28.27 | even | 2 | inner | ||
1344.4.b.h.895.4 | 12 | 4.3 | odd | 2 | |||
1344.4.b.h.895.9 | 12 | 7.6 | odd | 2 |