Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.f (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: | \(45.3134668844\) |
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: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.3 | ||
Root | \(-1.08600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.4.f.e.383.4 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.21320 | − | 3.04120i | −0.810831 | − | 0.585280i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.33303 | −0.834771 | −0.417386 | − | 0.908729i | \(-0.637054\pi\) | ||||
−0.417386 | + | 0.908729i | \(0.637054\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 36.3792i | 1.96429i | 0.188120 | + | 0.982146i | \(0.439760\pi\) | ||||
−0.188120 | + | 0.982146i | \(0.560240\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.50216 | + | 25.6264i | 0.314895 | + | 0.949127i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.4408i | 1.32777i | 0.747836 | + | 0.663884i | \(0.231093\pi\) | ||||
−0.747836 | + | 0.663884i | \(0.768907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.8988i | 0.552541i | 0.961080 | + | 0.276270i | \(0.0890985\pi\) | ||||
−0.961080 | + | 0.276270i | \(0.910901\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 39.3219 | + | 28.3836i | 0.676859 | + | 0.488575i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 74.2219i | 1.05891i | 0.848338 | + | 0.529455i | \(0.177603\pi\) | ||||
−0.848338 | + | 0.529455i | \(0.822397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −82.9826 | −1.00197 | −0.500987 | − | 0.865455i | \(-0.667030\pi\) | ||||
−0.500987 | + | 0.865455i | \(0.667030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 110.637 | − | 153.273i | 1.14966 | − | 1.59271i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 179.084 | 1.62355 | 0.811775 | − | 0.583971i | \(-0.198502\pi\) | ||||
0.811775 | + | 0.583971i | \(0.198502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −37.8946 | −0.303157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 42.1138 | − | 133.826i | 0.300178 | − | 0.953883i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122.309 | −0.783180 | −0.391590 | − | 0.920140i | \(-0.628075\pi\) | ||||
−0.391590 | + | 0.920140i | \(0.628075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.1893i | 0.371895i | 0.982560 | + | 0.185947i | \(0.0595354\pi\) | ||||
−0.982560 | + | 0.185947i | \(0.940465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 147.318 | − | 204.091i | 0.777116 | − | 1.07660i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 339.528i | − | 1.63973i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.01487i | − | 0.0222822i | −0.999938 | − | 0.0111411i | \(-0.996454\pi\) | ||
0.999938 | − | 0.0111411i | \(-0.00354639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 78.7635 | − | 109.117i | 0.323391 | − | 0.448017i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 325.933i | 1.24152i | 0.784003 | + | 0.620758i | \(0.213175\pi\) | ||||
−0.784003 | + | 0.620758i | \(0.786825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 321.853 | 1.14144 | 0.570722 | − | 0.821143i | \(-0.306663\pi\) | ||||
0.570722 | + | 0.821143i | \(0.306663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −79.3509 | − | 239.172i | −0.262865 | − | 0.792304i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 95.9780 | 0.297869 | 0.148934 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148934 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −980.446 | −2.85844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 225.724 | − | 312.712i | 0.619758 | − | 0.858597i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 185.069 | 0.479645 | 0.239822 | − | 0.970817i | \(-0.422911\pi\) | ||||
0.239822 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 452.099i | − | 1.10838i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 349.623 | + | 252.367i | 0.812432 | + | 0.586436i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 226.316i | 0.499386i | 0.968325 | + | 0.249693i | \(0.0803297\pi\) | ||||
−0.968325 | + | 0.249693i | \(0.919670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 198.851i | 0.417382i | 0.977982 | + | 0.208691i | \(0.0669203\pi\) | ||||
−0.977982 | + | 0.208691i | \(0.933080\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −932.268 | + | 309.302i | −1.86436 | + | 0.618545i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 241.714i | − | 0.461245i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.9524 | 0.0436753 | 0.0218377 | − | 0.999762i | \(-0.493048\pi\) | ||||
0.0218377 | + | 0.999762i | \(0.493048\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −754.518 | − | 544.632i | −1.31642 | − | 0.950231i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 399.741 | 0.668176 | 0.334088 | − | 0.942542i | \(-0.391572\pi\) | ||||
0.334088 | + | 0.942542i | \(0.391572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −669.631 | −1.07362 | −0.536811 | − | 0.843703i | \(-0.680371\pi\) | ||||
−0.536811 | + | 0.843703i | \(0.680371\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 159.658 | + | 115.245i | 0.245809 | + | 0.177432i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1762.24 | −2.60812 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 229.453i | 0.326778i | 0.986562 | + | 0.163389i | \(0.0522426\pi\) | ||||
−0.986562 | + | 0.163389i | \(0.947757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −584.427 | + | 435.760i | −0.801683 | + | 0.597750i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 321.150i | 0.424709i | 0.977193 | + | 0.212354i | \(0.0681131\pi\) | ||||
−0.977193 | + | 0.212354i | \(0.931887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 692.715i | − | 0.883947i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 515.313 | + | 371.967i | 0.635027 | + | 0.458380i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 131.446i | 0.156554i | 0.996932 | + | 0.0782768i | \(0.0249418\pi\) | ||||
−0.996932 | + | 0.0782768i | \(0.975058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −942.177 | −1.08535 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 195.213 | − | 270.443i | 0.217663 | − | 0.301544i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 774.479 | 0.836420 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 136.371 | 0.142746 | 0.0713732 | − | 0.997450i | \(-0.477262\pi\) | ||||
0.0713732 | + | 0.997450i | \(0.477262\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1241.36 | + | 411.851i | −1.26022 | + | 0.418107i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 411.095 | 0.405005 | 0.202502 | − | 0.979282i | \(-0.435093\pi\) | ||||
0.202502 | + | 0.979282i | \(0.435093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 137.507i | 0.131543i | 0.997835 | + | 0.0657716i | \(0.0209509\pi\) | ||||
−0.997835 | + | 0.0657716i | \(0.979049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1032.57 | + | 1430.50i | −0.959704 | + | 1.32955i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2113.08i | 1.90915i | 0.297964 | + | 0.954577i | \(0.403692\pi\) | ||||
−0.297964 | + | 0.954577i | \(0.596308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1310.07i | − | 1.15121i | −0.817727 | − | 0.575606i | \(-0.804766\pi\) | ||
0.817727 | − | 0.575606i | \(-0.195234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.2512 | + | 21.1287i | −0.0130413 | + | 0.0180671i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1403.62i | 1.16851i | 0.811571 | + | 0.584254i | \(0.198613\pi\) | ||||
−0.811571 | + | 0.584254i | \(0.801387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1671.40 | −1.35529 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −663.693 | + | 220.196i | −0.524431 | + | 0.173992i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2700.13 | −2.08001 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1015.51 | −0.762967 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 991.227 | − | 1373.22i | 0.726634 | − | 1.00666i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1520.30 | 1.08784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1583.69i | − | 1.10653i | −0.833004 | − | 0.553267i | \(-0.813381\pi\) | ||
0.833004 | − | 0.553267i | \(-0.186619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1356.03 | − | 978.820i | −0.925519 | − | 0.668065i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 160.326i | − | 0.106929i | −0.998570 | − | 0.0534646i | \(-0.982974\pi\) | ||
0.998570 | − | 0.0534646i | \(-0.0170264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3018.84i | − | 1.96817i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −393.050 | + | 1249.00i | −0.250580 | + | 0.796274i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1487.47i | − | 0.927614i | −0.885936 | − | 0.463807i | \(-0.846483\pi\) | ||
0.885936 | − | 0.463807i | \(-0.153517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −58.7660 | −0.0358595 | −0.0179298 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179298 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −404.375 | − | 291.889i | −0.241521 | − | 0.174337i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1254.56 | −0.733646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1141.51 | 0.653776 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4130.82 | + | 2981.74i | 2.31771 | + | 1.67299i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −940.146 | −0.516911 | −0.258456 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258456 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1800.43i | − | 0.970308i | −0.874429 | − | 0.485154i | \(-0.838763\pi\) | ||
0.874429 | − | 0.485154i | \(-0.161237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1902.04 | + | 631.046i | −1.00504 | + | 0.333445i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 599.081i | − | 0.310447i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3024.10i | − | 1.53726i | −0.639695 | − | 0.768629i | \(-0.720939\pi\) | ||
0.639695 | − | 0.768629i | \(-0.279061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −779.733 | − | 562.832i | −0.388911 | − | 0.280726i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6514.94i | 3.18913i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3124.46 | 1.50139 | 0.750694 | − | 0.660650i | \(-0.229719\pi\) | ||||
0.750694 | + | 0.660650i | \(0.229719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1374.93 | + | 1904.79i | −0.648714 | + | 0.898711i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −371.384 | −0.172087 | −0.0860435 | − | 0.996291i | \(-0.527422\pi\) | ||||
−0.0860435 | + | 0.996291i | \(0.527422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1526.25 | 0.694699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −705.531 | − | 2126.55i | −0.315517 | − | 0.951001i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2931.24 | −1.28820 | −0.644099 | − | 0.764943i | \(-0.722767\pi\) | ||||
−0.644099 | + | 0.764943i | \(0.722767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1378.58i | − | 0.595489i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 688.272 | − | 953.513i | 0.292281 | − | 0.404918i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2834.46i | − | 1.18356i | −0.806098 | − | 0.591781i | \(-0.798425\pi\) | ||
0.806098 | − | 0.591781i | \(-0.201575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1819.98i | 0.747392i | 0.927551 | + | 0.373696i | \(0.121910\pi\) | ||||
−0.927551 | + | 0.373696i | \(0.878090\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 604.747 | − | 837.800i | 0.244285 | − | 0.338426i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 46.8039i | 0.0186005i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3595.37 | −1.40599 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4868.49 | + | 1532.07i | 1.87370 | + | 0.589638i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4627.06 | 1.75289 | 0.876446 | − | 0.481500i | \(-0.159908\pi\) | ||||
0.876446 | + | 0.481500i | \(0.159908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2770.29 | −1.03321 | −0.516606 | − | 0.856223i | \(-0.672805\pi\) | ||||
−0.516606 | + | 0.856223i | \(0.672805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −735.102 | + | 1018.39i | −0.269958 | + | 0.373992i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3880.01 | −1.40324 | −0.701622 | − | 0.712550i | \(-0.747540\pi\) | ||||
−0.701622 | + | 0.712550i | \(0.747540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2015.00i | 0.717785i | 0.933379 | + | 0.358893i | \(0.116846\pi\) | ||||
−0.933379 | + | 0.358893i | \(0.883154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −100.916 | − | 72.8440i | −0.0354133 | − | 0.0255623i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4449.51i | − | 1.53839i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3041.94i | − | 1.03638i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1522.60 | + | 4589.29i | 0.511247 | + | 1.54095i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4019.74i | − | 1.33039i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5611.42 | −1.83084 | −0.915418 | − | 0.402505i | \(-0.868140\pi\) | ||||
−0.915418 | + | 0.402505i | \(0.868140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1684.19 | − | 1215.69i | −0.541778 | − | 0.391070i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3003.86 | −0.952845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2335.16 | −0.730510 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2821.29 | + | 2036.48i | 0.870526 | + | 0.628369i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1922.26 | −0.585091 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2025.65i | − | 0.608285i | −0.952627 | − | 0.304142i | \(-0.901630\pi\) | ||
0.952627 | − | 0.304142i | \(-0.0983699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −322.186 | − | 971.103i | −0.0954625 | − | 0.287734i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 404.049i | 0.118140i | 0.998254 | + | 0.0590698i | \(0.0188135\pi\) | ||||
−0.998254 | + | 0.0590698i | \(0.981187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4735.42i | 1.36649i | 0.730191 | + | 0.683243i | \(0.239431\pi\) | ||||
−0.730191 | + | 0.683243i | \(0.760569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7424.66 | + | 5359.32i | 2.11475 | + | 1.52648i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3703.79i | − | 1.04139i | −0.853744 | − | 0.520694i | \(-0.825673\pi\) | ||
0.853744 | − | 0.520694i | \(-0.174327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −895.765 | −0.248652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 697.814 | − | 966.733i | 0.191257 | − | 0.264962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6398.83 | 1.73182 | 0.865912 | − | 0.500197i | \(-0.166739\pi\) | ||||
0.865912 | + | 0.500197i | \(0.166739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3766.48 | 1.00672 | 0.503362 | − | 0.864076i | \(-0.332096\pi\) | ||||
0.503362 | + | 0.864076i | \(0.332096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3787.54 | − | 58.5842i | 0.999880 | − | 0.0154658i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9150.53 | 2.38615 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2149.15i | − | 0.553632i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 976.683 | − | 1353.07i | 0.248573 | − | 0.344367i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1979.71i | 0.497841i | 0.968524 | + | 0.248921i | \(0.0800758\pi\) | ||||
−0.968524 | + | 0.248921i | \(0.919924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8674.98i | 2.15570i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2106.69 | + | 2918.55i | −0.517356 | + | 0.716732i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1081.54i | − | 0.262508i | −0.991349 | − | 0.131254i | \(-0.958100\pi\) | ||
0.991349 | − | 0.131254i | \(-0.0419004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 182.437 | 0.0437687 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1039.89 | − | 3134.34i | −0.246619 | − | 0.743337i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1121.20 | 0.262875 | 0.131438 | − | 0.991324i | \(-0.458041\pi\) | ||||
0.131438 | + | 0.991324i | \(0.458041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1727.25 | −0.400394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 399.755 | − | 553.810i | 0.0916277 | − | 0.126939i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1844.86 | 0.418153 | 0.209076 | − | 0.977899i | \(-0.432954\pi\) | ||||
0.209076 | + | 0.977899i | \(0.432954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 938.970i | − | 0.210474i | −0.994447 | − | 0.105237i | \(-0.966440\pi\) | ||
0.994447 | − | 0.105237i | \(-0.0335601\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3969.58 | + | 2865.35i | 0.880037 | + | 0.635234i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1835.64i | − | 0.402522i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1100.93i | − | 0.238803i | −0.992846 | − | 0.119401i | \(-0.961902\pi\) | ||
0.992846 | − | 0.119401i | \(-0.0380975\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1644.94 | + | 545.748i | −0.352975 | + | 0.117108i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 748.208i | − | 0.158841i | −0.996841 | − | 0.0794205i | \(-0.974693\pi\) | ||
0.996841 | − | 0.0794205i | \(-0.0253070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2150.15 | 0.451636 | 0.225818 | − | 0.974170i | \(-0.427495\pi\) | ||||
0.225818 | + | 0.974170i | \(0.427495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3263.04 | − | 2355.35i | −0.678195 | − | 0.489540i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11857.2 | −2.43870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −595.891 | −0.121289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −574.559 | − | 414.733i | −0.115743 | − | 0.0835466i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5252.83 | 1.04735 | 0.523675 | − | 0.851918i | \(-0.324561\pi\) | ||||
0.523675 | + | 0.851918i | \(0.324561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2112.21i | − | 0.416873i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6482.64 | + | 2040.03i | 1.26654 | + | 0.398567i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4638.06i | 0.897077i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11708.8i | 2.24213i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1732.03 | − | 1250.22i | −0.328390 | − | 0.237041i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1855.88i | − | 0.348418i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5337.06 | −0.992190 | −0.496095 | − | 0.868268i | \(-0.665233\pi\) | ||||
−0.496095 | + | 0.868268i | \(0.665233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 418.186 | − | 579.344i | 0.0769896 | − | 0.106659i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1034.85 | −0.188685 | −0.0943424 | − | 0.995540i | \(-0.530075\pi\) | ||||
−0.0943424 | + | 0.995540i | \(0.530075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9570.33 | 1.72826 | 0.864132 | − | 0.503265i | \(-0.167868\pi\) | ||||
0.864132 | + | 0.503265i | \(0.167868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8700.89 | − | 2886.72i | 1.55632 | − | 0.516344i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3593.05 | 0.636612 | 0.318306 | − | 0.947988i | \(-0.396886\pi\) | ||||
0.318306 | + | 0.947988i | \(0.396886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5924.75i | − | 1.03988i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6426.32 | − | 8902.85i | 1.11739 | − | 1.54800i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6159.13i | − | 1.06100i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 981.425i | − | 0.167507i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3984.19 | + | 5519.60i | −0.673781 | + | 0.933438i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3491.60i | 0.585101i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4119.28 | −0.684037 | −0.342018 | − | 0.939693i | \(-0.611110\pi\) | ||||
−0.342018 | + | 0.939693i | \(0.611110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 128.513 | − | 42.6372i | 0.0211486 | − | 0.00701654i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −223.548 | −0.0364589 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6488.93 | −1.04889 | −0.524443 | − | 0.851446i | \(-0.675726\pi\) | ||||
−0.524443 | + | 0.851446i | \(0.675726\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4268.69 | − | 5913.73i | 0.683904 | − | 0.947462i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3109.38 | −0.493790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 23189.8i | − | 3.65052i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7041.94 | + | 5083.06i | 1.09891 | + | 0.793225i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7085.97i | 1.09624i | 0.836400 | + | 0.548119i | \(0.184656\pi\) | ||||
−0.836400 | + | 0.548119i | \(0.815344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6075.79i | − | 0.931891i | −0.884814 | − | 0.465945i | \(-0.845714\pi\) | ||
0.884814 | − | 0.465945i | \(-0.154286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3465.93 | + | 1090.70i | 0.527059 | + | 0.165861i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4451.86i | − | 0.671242i | −0.941997 | − | 0.335621i | \(-0.891054\pi\) | ||
0.941997 | − | 0.335621i | \(-0.108946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3730.79 | −0.557774 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11376.2 | + | 8211.66i | 1.68653 | + | 1.21739i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10771.6 | 1.58357 | 0.791785 | − | 0.610800i | \(-0.209152\pi\) | ||||
0.791785 | + | 0.610800i | \(0.209152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.1131 | 0.00395293 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4278.54 | + | 3088.37i | 0.618637 | + | 0.446549i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6249.68 | 0.896228 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6671.95i | 0.948973i | 0.880263 | + | 0.474486i | \(0.157366\pi\) | ||||
−0.880263 | + | 0.474486i | \(0.842634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8352.48 | + | 2771.13i | −1.17835 | + | 0.390947i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6732.66i | 0.942162i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12618.5i | 1.75164i | 0.482641 | + | 0.875819i | \(0.339678\pi\) | ||||
−0.482641 | + | 0.875819i | \(0.660322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6405.33 | − | 4623.54i | −0.882053 | − | 0.636690i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3167.66i | − | 0.432739i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7915.38 | −1.07279 | −0.536393 | − | 0.843968i | \(-0.680213\pi\) | ||||
−0.536393 | + | 0.843968i | \(0.680213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4816.32 | + | 6672.40i | −0.647632 | + | 0.897212i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10820.5 | −1.44360 | −0.721802 | − | 0.692099i | \(-0.756686\pi\) | ||||
−0.721802 | + | 0.692099i | \(0.756686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16447.0 | 2.17719 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2736.45 | + | 8247.94i | 0.359435 | + | 1.08338i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7990.57 | 1.04149 | 0.520743 | − | 0.853714i | \(-0.325655\pi\) | ||||
0.520743 | + | 0.853714i | \(0.325655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13292.0i | 1.71919i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −487.583 | + | 675.485i | −0.0625835 | + | 0.0867016i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2141.49i | − | 0.272785i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5526.21i | 0.698620i | 0.937007 | + | 0.349310i | \(0.113584\pi\) | ||||
−0.937007 | + | 0.349310i | \(0.886416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9180.91 | + | 12719.0i | −1.15193 | + | 1.59585i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7844.55i | − | 0.976903i | −0.872591 | − | 0.488451i | \(-0.837562\pi\) | ||
0.872591 | − | 0.488451i | \(-0.162438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1662.43 | −0.205487 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5454.47 | − | 4066.96i | 0.669222 | − | 0.498985i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 242.924 | 0.0295855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4407.65 | 0.532871 | 0.266435 | − | 0.963853i | \(-0.414154\pi\) | ||||
0.266435 | + | 0.963853i | \(0.414154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4523.70 | + | 6267.01i | −0.542914 | + | 0.752138i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8233.18 | −0.980940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2997.30i | − | 0.354534i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 247.593 | + | 178.720i | 0.0290760 | + | 0.0209878i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12032.8i | 1.40296i | 0.712688 | + | 0.701481i | \(0.247477\pi\) | ||||
−0.712688 | + | 0.701481i | \(0.752523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10320.3i | − | 1.19473i | −0.801969 | − | 0.597365i | \(-0.796214\pi\) | ||
0.801969 | − | 0.597365i | \(-0.203786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 816.021 | + | 2459.57i | 0.0937973 | + | 0.282715i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2812.61i | − | 0.321016i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7234.05 | −0.819860 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5285.70 | + | 3815.36i | 0.594863 | + | 0.429388i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8068.52 | 0.901733 | 0.450866 | − | 0.892591i | \(-0.351115\pi\) | ||||
0.450866 | + | 0.892591i | \(0.351115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3236.75 | −0.359234 | −0.179617 | − | 0.983737i | \(-0.557486\pi\) | ||||
−0.179617 | + | 0.983737i | \(0.557486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4809.43 | − | 3471.58i | −0.530102 | − | 0.382642i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14860.9 | −1.62676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2207.71i | − | 0.240019i | −0.992773 | − | 0.120009i | \(-0.961708\pi\) | ||
0.992773 | − | 0.120009i | \(-0.0382924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8335.91 | − | 25125.3i | −0.900109 | − | 2.71302i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1058.18i | 0.113489i | 0.998389 | + | 0.0567447i | \(0.0180721\pi\) | ||||
−0.998389 | + | 0.0567447i | \(0.981928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1226.79i | − | 0.130686i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3961.03 | + | 2859.18i | 0.419128 | + | 0.302538i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10836.4i | − | 1.13898i | −0.822000 | − | 0.569488i | \(-0.807142\pi\) | ||
0.822000 | − | 0.569488i | \(-0.192858\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15788.4 | −1.64844 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5475.46 | + | 7585.56i | −0.567902 | + | 0.786756i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8793.36 | 0.906020 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9827.12 | 1.00589 | 0.502947 | − | 0.864317i | \(-0.332249\pi\) | ||||
0.502947 | + | 0.864317i | \(0.332249\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9932.83 | + | 3125.77i | 1.01008 | + | 0.317861i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9311.74 | 0.940761 | 0.470381 | − | 0.882464i | \(-0.344117\pi\) | ||||
0.470381 | + | 0.882464i | \(0.344117\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7601.37i | − | 0.762993i | −0.924370 | − | 0.381497i | \(-0.875409\pi\) | ||
0.924370 | − | 0.381497i | \(-0.124591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1821.93 | + | 2524.05i | −0.181699 | + | 0.251720i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4446.20i | 0.440569i | 0.975436 | + | 0.220284i | \(0.0706985\pi\) | ||||
−0.975436 | + | 0.220284i | \(0.929301\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 871.368i | 0.0857911i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9196.90 | + | 12741.1i | −0.899726 | + | 1.24646i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15590.8i | 1.51557i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3144.59 | 0.303756 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1573.49 | + | 4742.65i | 0.151038 | + | 0.455244i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12285.9 | 1.17194 | 0.585970 | − | 0.810333i | \(-0.300714\pi\) | ||||
0.585970 | + | 0.810333i | \(0.300714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 129.879 | 0.0123118 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19813.3 | − | 27448.8i | 1.86653 | − | 2.58584i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1272.76 | −0.119161 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8464.78i | 0.787630i | 0.919190 | + | 0.393815i | \(0.128845\pi\) | ||||
−0.919190 | + | 0.393815i | \(0.871155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13164.0 | − | 9502.11i | −1.21737 | − | 0.878732i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6356.37i | − | 0.584234i | −0.956383 | − | 0.292117i | \(-0.905640\pi\) | ||
0.956383 | − | 0.292117i | \(-0.0943596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9078.02i | − | 0.829317i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11585.7 | − | 3843.82i | 1.05200 | − | 0.349024i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14542.2i | 1.31249i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11856.6 | 1.06368 | 0.531840 | − | 0.846845i | \(-0.321501\pi\) | ||||
0.531840 | + | 0.846845i | \(0.321501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1564.72 | + | 1129.45i | 0.139534 | + | 0.100719i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17032.5 | −1.50982 | −0.754912 | − | 0.655826i | \(-0.772321\pi\) | ||||
−0.754912 | + | 0.655826i | \(0.772321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3836.76 | −0.338086 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6430.41 | − | 4641.65i | −0.563283 | − | 0.406593i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1563.18 | −0.136123 | −0.0680617 | − | 0.997681i | \(-0.521681\pi\) | ||||
−0.0680617 | + | 0.997681i | \(0.521681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 24360.6i | − | 2.10891i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3494.72 | + | 11105.2i | −0.300771 | + | 0.955767i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1283.36i | − | 0.109809i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4649.25i | 0.395501i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12349.9 | + | 8914.50i | 1.04451 | + | 0.753956i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9096.23i | 0.764900i | 0.923976 | + | 0.382450i | \(0.124920\pi\) | ||||
−0.923976 | + | 0.382450i | \(0.875080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10108.4 | 0.845143 | 0.422572 | − | 0.906330i | \(-0.361127\pi\) | ||||
0.422572 | + | 0.906330i | \(0.361127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4192.53 | + | 5808.22i | −0.348528 | + | 0.482841i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4764.25 | −0.393803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19904.2 | 1.63591 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5799.66 | + | 1924.17i | −0.473980 | + | 0.157254i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8441.26 | −0.685988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 19721.5i | − | 1.59371i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8620.18 | + | 11942.2i | −0.692716 | + | 0.959670i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 47493.6i | − | 3.79535i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10097.6i | − | 0.802462i | −0.915977 | − | 0.401231i | \(-0.868583\pi\) | ||
0.915977 | − | 0.401231i | \(-0.131417\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5534.93 | − | 7667.94i | 0.437434 | − | 0.606009i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12226.9i | 0.960998i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2064.83 | −0.161400 | −0.0806998 | − | 0.996738i | \(-0.525716\pi\) | ||||
−0.0806998 | + | 0.996738i | \(0.525716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5095.84 | + | 1690.66i | −0.396148 | + | 0.131431i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10149.5 | 0.784727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8347.32 | −0.641888 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 142.340 | − | 197.194i | 0.0108865 | − | 0.0150819i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12125.7 | 0.922409 | 0.461204 | − | 0.887294i | \(-0.347417\pi\) | ||||
0.461204 | + | 0.887294i | \(0.347417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8335.60i | 0.630695i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15148.0 | + | 10934.2i | 1.14002 | + | 0.822895i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7278.58i | 0.544859i | 0.962176 | + | 0.272429i | \(0.0878271\pi\) | ||||
−0.962176 | + | 0.272429i | \(0.912173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 13100.0i | − | 0.975436i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15852.6 | − | 21261.0i | −1.17416 | − | 1.57474i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17428.1i | − | 1.28405i | −0.766685 | − | 0.642024i | \(-0.778095\pi\) | ||
0.766685 | − | 0.642024i | \(-0.221905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2423.73 | 0.177635 | 0.0888177 | − | 0.996048i | \(-0.471691\pi\) | ||||
0.0888177 | + | 0.996048i | \(0.471691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19494.7 | − | 14071.8i | −1.42130 | − | 1.02593i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6786.33 | −0.492190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17471.1 | −1.26054 | −0.630268 | − | 0.776377i | \(-0.717055\pi\) | ||||
−0.630268 | + | 0.776377i | \(0.717055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11671.8 | + | 8425.03i | 0.837761 | + | 0.604719i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11683.2 | −0.834252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8964.88i | 0.636857i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6194.27 | − | 2055.09i | 0.437780 | − | 0.145244i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7273.06i | 0.511399i | 0.966756 | + | 0.255700i | \(0.0823058\pi\) | ||||
−0.966756 | + | 0.255700i | \(0.917694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5326.60i | − | 0.372629i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16347.3 | + | 11799.9i | 1.13779 | + | 0.821290i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19957.9i | − | 1.38208i | −0.722818 | − | 0.691038i | \(-0.757154\pi\) | ||
0.722818 | − | 0.691038i | \(-0.242846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25200.4 | 1.73633 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6128.01 | − | 8489.59i | 0.420105 | − | 0.582003i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6101.48 | 0.416193 | 0.208097 | − | 0.978108i | \(-0.433273\pi\) | ||||
0.208097 | + | 0.978108i | \(0.433273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16659.6 | −1.13071 | −0.565357 | − | 0.824846i | \(-0.691262\pi\) | ||||
−0.565357 | + | 0.824846i | \(0.691262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 203.647 | + | 613.813i | 0.0137531 | + | 0.0414534i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9477.77 | 0.636903 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13728.6i | 0.917999i | 0.888437 | + | 0.458999i | \(0.151792\pi\) | ||||
−0.888437 | + | 0.458999i | \(0.848208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13531.9 | + | 18746.7i | −0.900392 | + | 1.24738i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2485.71i | 0.164585i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 7514.10i | − | 0.495093i | −0.968876 | − | 0.247546i | \(-0.920376\pi\) | ||
0.968876 | − | 0.247546i | \(-0.0796242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9251.15 | + | 12816.3i | −0.606573 | + | 0.840330i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8052.78i | − | 0.525434i | −0.964873 | − | 0.262717i | \(-0.915381\pi\) | ||
0.964873 | − | 0.262717i | \(-0.0846186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25194.4 | −1.63594 | −0.817970 | − | 0.575261i | \(-0.804900\pi\) | ||||
−0.817970 | + | 0.575261i | \(0.804900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7541.92 | − | 23966.1i | 0.487354 | − | 1.54868i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4781.91 | −0.307517 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9452.17 | −0.604939 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12224.9 | + | 16936.0i | −0.778650 | + | 1.07872i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 372.213 | 0.0235948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14945.1i | 0.942876i | 0.881899 | + | 0.471438i | \(0.156265\pi\) | ||||
−0.881899 | + | 0.471438i | \(0.843735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23642.1 | + | 17065.5i | 1.48450 | + | 1.07155i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14780.6i | 0.923702i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 25392.4i | − | 1.57941i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3398.66 | + | 10243.9i | 0.210405 | + | 0.634184i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13909.9i | 0.857109i | 0.903516 | + | 0.428555i | \(0.140977\pi\) | ||||
−0.903516 | + | 0.428555i | \(0.859023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13338.7 | −0.818084 | −0.409042 | − | 0.912516i | \(-0.634137\pi\) | ||||
−0.409042 | + | 0.912516i | \(0.634137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12655.9 | + | 9135.36i | 0.772597 | + | 0.557681i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 719.190 | 0.0437006 | 0.0218503 | − | 0.999761i | \(-0.493044\pi\) | ||||
0.0218503 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10962.9 | −0.663069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9838.49 | + | 7101.69i | 0.592321 | + | 0.427553i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19019.4 | 1.13980 | 0.569899 | − | 0.821714i | \(-0.306982\pi\) | ||||
0.569899 | + | 0.821714i | \(0.306982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1496.32i | 0.0892615i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5693.31 | − | 17160.2i | −0.338078 | − | 1.01900i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22748.7i | − | 1.34471i | −0.740230 | − | 0.672354i | \(-0.765283\pi\) | ||
0.740230 | − | 0.672354i | \(-0.234717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23275.3i | 1.36960i | 0.728733 | + | 0.684798i | \(0.240110\pi\) | ||||
−0.728733 | + | 0.684798i | \(0.759890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8098.86 | + | 5845.98i | 0.474410 | + | 0.342442i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28174.9i | 1.64297i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21903.6 | −1.27153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6160.41 | + | 8534.47i | −0.356017 | + | 0.493216i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9632.51 | −0.554186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28195.5 | −1.61495 | −0.807473 | − | 0.589905i | \(-0.799165\pi\) | ||||
−0.807473 | + | 0.589905i | \(0.799165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1595.89 | + | 5071.29i | −0.0910011 | + | 0.289176i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32369.7 | −1.83762 | −0.918809 | − | 0.394701i | \(-0.870848\pi\) | ||||
−0.918809 | + | 0.394701i | \(0.870848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4961.07i | 0.280396i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1228.80 | − | 1702.34i | 0.0691447 | − | 0.0957913i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1227.33i | − | 0.0687592i | −0.999409 | − | 0.0343796i | \(-0.989054\pi\) | ||
0.999409 | − | 0.0343796i | \(-0.0109455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13882.6i | 0.774345i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14401.4 | − | 19951.3i | 0.799776 | − | 1.10799i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4793.06i | 0.265023i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3563.29 | −0.196170 | −0.0980852 | − | 0.995178i | \(-0.531272\pi\) | ||||
−0.0980852 | + | 0.995178i | \(0.531272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14982.8 | − | 45159.8i | −0.821284 | − | 2.47544i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 548.465 | 0.0299345 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24191.3 | −1.31465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11264.0 | + | 15604.8i | −0.609503 | + | 0.844389i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11942.4 | −0.643448 | −0.321724 | − | 0.946834i | \(-0.604262\pi\) | ||||
−0.321724 | + | 0.946834i | \(0.604262\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 416.147i | 0.0223262i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3774.04 | + | 2724.21i | 0.201615 | + | 0.145531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14955.3i | 0.795547i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 22547.9i | − | 1.19436i | −0.802105 | − | 0.597182i | \(-0.796287\pi\) | ||
0.802105 | − | 0.597182i | \(-0.203713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5880.06 | + | 1950.85i | −0.310154 | + | 0.102901i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11495.3i | 0.603790i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11708.8 | 0.612426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26959.6 | − | 19460.1i | −1.40422 | − | 1.01360i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2034.54 | −0.105529 | −0.0527647 | − | 0.998607i | \(-0.516803\pi\) | ||||
−0.0527647 | + | 0.998607i | \(0.516803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5002.39 | −0.258389 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15869.0 | − | 11454.6i | −0.816283 | − | 0.589215i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4634.86 | 0.237427 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26487.5i | − | 1.35126i | −0.737240 | − | 0.675631i | \(-0.763871\pi\) | ||
0.737240 | − | 0.675631i | \(-0.236129\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16135.9 | − | 11271.9i | −0.819786 | − | 0.572670i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23888.5i | 1.20869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38967.7i | 1.96358i | 0.189964 | + | 0.981791i | \(0.439163\pi\) | ||||
−0.189964 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38553.0 | − | 27828.6i | −1.93476 | − | 1.39656i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1160.27i | 0.0579907i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14312.2 | −0.712425 | −0.356212 | − | 0.934405i | \(-0.615932\pi\) | ||||
−0.356212 | + | 0.934405i | \(0.615932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6536.00 | + | 9054.80i | −0.324030 | + | 0.448902i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12790.0 | 0.631520 | 0.315760 | − | 0.948839i | \(-0.397741\pi\) | ||||
0.315760 | + | 0.948839i | \(0.397741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8774.41 | 0.431503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8229.93 | + | 2730.47i | −0.403102 | + | 0.133739i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −76872.3 | −3.75014 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19441.6i | 0.944653i | 0.881424 | + | 0.472327i | \(0.156586\pi\) | ||||
−0.881424 | + | 0.472327i | \(0.843414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6020.70 | − | 8340.92i | 0.291376 | − | 0.403665i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16803.4i | 0.809985i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13901.0i | 0.667424i | 0.942675 | + | 0.333712i | \(0.108301\pi\) | ||||
−0.942675 | + | 0.333712i | \(0.891699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26382.4 | − | 36549.4i | 1.26169 | − | 1.74791i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8818.58i | − | 0.420070i | −0.977694 | − | 0.210035i | \(-0.932642\pi\) | ||
0.977694 | − | 0.210035i | \(-0.0673578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47659.3 | 2.26132 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17751.8 | − | 5889.57i | 0.838978 | − | 0.278350i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5861.30 | −0.275931 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1323.39 | 0.0620582 | 0.0310291 | − | 0.999518i | \(-0.490122\pi\) | ||||
0.0310291 | + | 0.999518i | \(0.490122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3289.18 | + | 4556.75i | −0.153641 | + | 0.212850i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34327.1 | 1.59723 | 0.798617 | − | 0.601840i | \(-0.205565\pi\) | ||||
0.798617 | + | 0.601840i | \(0.205565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2432.43i | − | 0.112743i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −768.644 | − | 554.828i | −0.0354890 | − | 0.0256169i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 27046.7i | − | 1.24397i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19363.8i | 0.887183i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5150.91 | + | 16368.2i | −0.235094 | + | 0.747063i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28224.0i | 1.28326i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15375.3 | 0.696405 | 0.348203 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348203 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4723.84 | − | 3409.80i | −0.213147 | − | 0.153856i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51062.5 | −2.29529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5150.00 | −0.230620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7277.27 | + | 5252.93i | 0.324652 | + | 0.234342i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3347.25 | 0.148765 | 0.0743826 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743826 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7123.67i | 0.315416i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3368.50 | + | 1117.58i | −0.148589 | + | 0.0492979i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 32437.4i | − | 1.42552i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 60804.1i | − | 2.66219i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7772.76 | − | 5610.59i | −0.339051 | − | 0.244736i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39577.3i | 1.71998i | 0.510309 | + | 0.859991i | \(0.329531\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12614.4 | 0.546180 | 0.273090 | − | 0.961989i | \(-0.411954\pi\) | ||||
0.273090 | + | 0.961989i | \(0.411954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2855.60 | + | 3956.07i | −0.123186 | + | 0.170659i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29160.6 | −1.25332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26708.2 | −1.14370 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8010.54 | − | 24144.6i | −0.341772 | − | 1.03014i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18243.6 | 0.775526 | 0.387763 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387763 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18350.6i | 0.777230i | 0.921400 | + | 0.388615i | \(0.127046\pi\) | ||||
−0.921400 | + | 0.388615i | \(0.872954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5582.57 | + | 7733.94i | −0.235588 | + | 0.326377i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15785.4i | 0.663739i | 0.943325 | + | 0.331869i | \(0.107679\pi\) | ||||
−0.943325 | + | 0.331869i | \(0.892321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36102.8i | − | 1.51255i | −0.654255 | − | 0.756274i | \(-0.727018\pi\) | ||
0.654255 | − | 0.756274i | \(-0.272982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3348.15 | + | 4638.43i | −0.139766 | + | 0.193629i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 72770.6i | − | 3.02683i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3466.13 | 0.143653 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8590.21 | + | 2703.26i | 0.354744 | + | 0.111635i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18961.8 | −0.780255 | −0.390127 | − | 0.920761i | \(-0.627569\pi\) | ||||
−0.390127 | + | 0.920761i | \(0.627569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9429.48 | −0.386628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2275.45 | + | 3152.35i | −0.0929665 | + | 0.128793i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14244.6 | −0.579914 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 36943.4i | − | 1.49869i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9059.00 | − | 6539.03i | −0.366201 | − | 0.264333i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 898.084i | − | 0.0361762i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27761.8i | 1.11435i | 0.830394 | + | 0.557177i | \(0.188116\pi\) | ||||
−0.830394 | + | 0.557177i | \(0.811884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6584.74 | + | 19847.1i | 0.263384 | + | 0.793868i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2082.01i | − | 0.0829874i | −0.999139 | − | 0.0414937i | \(-0.986788\pi\) | ||
0.999139 | − | 0.0414937i | \(-0.0132117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34995.2 | 1.39001 | 0.695005 | − | 0.719004i | \(-0.255402\pi\) | ||||
0.695005 | + | 0.719004i | \(0.255402\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49956.6 | + | 36060.1i | 1.97737 | + | 1.42732i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6045.46 | 0.238459 | 0.119229 | − | 0.992867i | \(-0.461958\pi\) | ||||
0.119229 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27357.3 | 1.07535 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2510.61 | + | 1812.23i | 0.0983446 | + | 0.0709878i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11114.9 | −0.433886 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 620.337i | 0.0241324i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1159.45 | + | 3494.70i | 0.0449501 | + | 0.135484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 55307.3i | 2.13683i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30101.8i | − | 1.15903i | −0.814963 | − | 0.579514i | \(-0.803243\pi\) | ||
0.814963 | − | 0.579514i | \(-0.196757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22131.2 | − | 15974.9i | −0.849224 | − | 0.612993i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16655.3i | 0.636926i | 0.947935 | + | 0.318463i | \(0.103167\pi\) | ||||
−0.947935 | + | 0.318463i | \(0.896833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24940.5 | −0.950528 | −0.475264 | − | 0.879843i | \(-0.657647\pi\) | ||||
−0.475264 | + | 0.879843i | \(0.657647\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6423.66 | + | 8899.16i | −0.243987 | + | 0.338014i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32143.9 | 1.21678 | 0.608391 | − | 0.793637i | \(-0.291815\pi\) | ||||
0.608391 | + | 0.793637i | \(0.291815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57613.3 | 2.17355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21108.5 | − | 28310.1i | −0.793673 | − | 1.06445i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7964.51 | −0.298457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26454.1i | 0.988004i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14105.3 | − | 19541.1i | 0.525041 | − | 0.727378i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7850.94i | − | 0.291261i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13736.2i | 0.507900i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35608.7 | − | 49331.3i | 1.31227 | − | 1.81799i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16985.9i | − | 0.623902i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3376.58 | 0.123613 | 0.0618067 | − | 0.998088i | \(-0.480314\pi\) | ||||
0.0618067 | + | 0.998088i | \(0.480314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3495.19 | + | 10534.9i | 0.127534 | + | 0.384401i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45248.4 | 1.64561 | 0.822803 | − | 0.568326i | \(-0.192409\pi\) | ||||
0.822803 | + | 0.568326i | \(0.192409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15556.8 | −0.563914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5644.12 | + | 7819.21i | −0.203922 | + | 0.282508i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5832.52 | 0.210040 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18545.2i | 0.665668i | 0.942985 | + | 0.332834i | \(0.108005\pi\) | ||||
−0.942985 | + | 0.332834i | \(0.891995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22486.1 | + | 16231.1i | 0.804498 | + | 0.580709i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10352.8i | 0.369195i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 190.037i | 0.00675499i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3523.81 | + | 1169.11i | −0.124851 | + | 0.0414223i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33976.7i | 1.19993i | 0.800024 | + | 0.599967i | \(0.204820\pi\) | ||||
−0.800024 | + | 0.599967i | \(0.795180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 81360.0 | 2.86409 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4360.03 | + | 3147.19i | 0.152992 | + | 0.110433i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33555.7 | 1.17368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22803.1 | 0.795031 | 0.397516 | − | 0.917595i | \(-0.369872\pi\) | ||||
0.397516 | + | 0.917595i | \(0.369872\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40321.7 | − | 29105.3i | −1.40133 | − | 1.01152i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24174.7 | 0.837484 | 0.418742 | − | 0.908105i | \(-0.362471\pi\) | ||||
0.418742 | + | 0.908105i | \(0.362471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58369.4i | 2.01566i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45437.7 | − | 14298.8i | −1.56412 | − | 0.492213i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 8044.99i | − | 0.276058i | −0.990428 | − | 0.138029i | \(-0.955923\pi\) | ||
0.990428 | − | 0.138029i | \(-0.0440767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 17342.6i | − | 0.593220i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15138.3 | − | 10927.2i | −0.516185 | − | 0.372596i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39730.8i | − | 1.35048i | −0.737598 | − | 0.675240i | \(-0.764040\pi\) | ||
0.737598 | − | 0.675240i | \(-0.235960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43184.5 | −1.46326 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18018.4 | + | 24962.2i | −0.608622 | + | 0.843169i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 54112.9 | 1.82210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25670.7 | 0.861694 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54150.8 | + | 17965.8i | −1.81203 | + | 0.601183i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25855.2 | 0.862496 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17685.2i | 0.588126i | 0.955786 | + | 0.294063i | \(0.0950076\pi\) | ||||
−0.955786 | + | 0.294063i | \(0.904992\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18731.2 | + | 25949.7i | −0.620982 | + | 0.860292i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 44010.1i | − | 1.45453i | −0.686355 | − | 0.727267i | \(-0.740790\pi\) | ||
0.686355 | − | 0.727267i | \(-0.259210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2137.86i | − | 0.0704385i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2984.71 | + | 4134.94i | −0.0980382 | + | 0.135820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33518.4i | 1.09759i | 0.835956 | + | 0.548796i | \(0.184914\pi\) | ||||
−0.835956 | + | 0.548796i | \(0.815086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6367.36 | −0.207867 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33572.4 | − | 11138.4i | 1.09265 | − | 0.362511i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43740.3 | 1.41923 | 0.709613 | − | 0.704592i | \(-0.248870\pi\) | ||||
0.709613 | + | 0.704592i | \(0.248870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36212.2 | 1.17139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10618.7 | − | 14710.8i | 0.342448 | − | 0.474418i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57638.8 | 1.85319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10468.7i | 0.335568i | 0.985824 | + | 0.167784i | \(0.0536611\pi\) | ||||
−0.985824 | + | 0.167784i | \(0.946339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17355.4 | + | 12527.6i | 0.554638 | + | 0.400353i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18806.0i | − | 0.599186i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9561.56i | 0.303729i | 0.988401 | + | 0.151864i | \(0.0485277\pi\) | ||||
−0.988401 | + | 0.151864i | \(0.951472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −671.121 | − | 211.195i | −0.0212546 | − | 0.00668862i |
(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 | 768.4.f.e.383.3 | 12 | ||
3.2 | odd | 2 | 768.4.f.f.383.4 | 12 | |||
4.3 | odd | 2 | 768.4.f.g.383.10 | 12 | |||
8.3 | odd | 2 | 768.4.f.f.383.3 | 12 | |||
8.5 | even | 2 | 768.4.f.h.383.10 | 12 | |||
12.11 | even | 2 | 768.4.f.h.383.9 | 12 | |||
16.3 | odd | 4 | 384.4.c.b.383.6 | yes | 12 | ||
16.5 | even | 4 | 384.4.c.a.383.6 | yes | 12 | ||
16.11 | odd | 4 | 384.4.c.d.383.7 | yes | 12 | ||
16.13 | even | 4 | 384.4.c.c.383.7 | yes | 12 | ||
24.5 | odd | 2 | 768.4.f.g.383.9 | 12 | |||
24.11 | even | 2 | inner | 768.4.f.e.383.4 | 12 | ||
48.5 | odd | 4 | 384.4.c.d.383.8 | yes | 12 | ||
48.11 | even | 4 | 384.4.c.a.383.5 | ✓ | 12 | ||
48.29 | odd | 4 | 384.4.c.b.383.5 | yes | 12 | ||
48.35 | even | 4 | 384.4.c.c.383.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.5 | ✓ | 12 | 48.11 | even | 4 | ||
384.4.c.a.383.6 | yes | 12 | 16.5 | even | 4 | ||
384.4.c.b.383.5 | yes | 12 | 48.29 | odd | 4 | ||
384.4.c.b.383.6 | yes | 12 | 16.3 | odd | 4 | ||
384.4.c.c.383.7 | yes | 12 | 16.13 | even | 4 | ||
384.4.c.c.383.8 | yes | 12 | 48.35 | even | 4 | ||
384.4.c.d.383.7 | yes | 12 | 16.11 | odd | 4 | ||
384.4.c.d.383.8 | yes | 12 | 48.5 | odd | 4 | ||
768.4.f.e.383.3 | 12 | 1.1 | even | 1 | trivial | ||
768.4.f.e.383.4 | 12 | 24.11 | even | 2 | inner | ||
768.4.f.f.383.3 | 12 | 8.3 | odd | 2 | |||
768.4.f.f.383.4 | 12 | 3.2 | odd | 2 | |||
768.4.f.g.383.9 | 12 | 24.5 | odd | 2 | |||
768.4.f.g.383.10 | 12 | 4.3 | odd | 2 | |||
768.4.f.h.383.9 | 12 | 12.11 | even | 2 | |||
768.4.f.h.383.10 | 12 | 8.5 | even | 2 |