Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 32 x^{14} + 356 x^{13} + 1348 x^{12} - 8992 x^{11} + 22064 x^{10} + \cdots + 21479188203 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.14 | ||
Root | \(-3.05642 - 3.40211i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.5.e.c.257.13 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 7.95805 | + | 4.20350i | 0.884228 | + | 0.467056i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 19.3338i | − | 0.773353i | −0.922216 | − | 0.386676i | \(-0.873623\pi\) | ||
0.922216 | − | 0.386676i | \(-0.126377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −67.6413 | −1.38044 | −0.690218 | − | 0.723602i | \(-0.742485\pi\) | ||||
−0.690218 | + | 0.723602i | \(0.742485\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 45.6611 | + | 66.9034i | 0.563718 | + | 0.825968i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 77.9559i | − | 0.644264i | −0.946695 | − | 0.322132i | \(-0.895601\pi\) | ||
0.946695 | − | 0.322132i | \(-0.104399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −79.2239 | −0.468781 | −0.234390 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234390 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 81.2697 | − | 153.859i | 0.361199 | − | 0.683820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 309.300i | 1.07024i | 0.844775 | + | 0.535121i | \(0.179734\pi\) | ||||
−0.844775 | + | 0.535121i | \(0.820266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 468.110 | 1.29670 | 0.648352 | − | 0.761340i | \(-0.275458\pi\) | ||||
0.648352 | + | 0.761340i | \(0.275458\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −538.293 | − | 284.331i | −1.22062 | − | 0.644741i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 617.359i | 1.16703i | 0.812102 | + | 0.583515i | \(0.198323\pi\) | ||||
−0.812102 | + | 0.583515i | \(0.801677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 251.204 | 0.401926 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 82.1450 | + | 724.357i | 0.112682 | + | 0.993631i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 939.786i | 1.11746i | 0.829349 | + | 0.558731i | \(0.188712\pi\) | ||||
−0.829349 | + | 0.558731i | \(0.811288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1103.99 | 1.14880 | 0.574398 | − | 0.818576i | \(-0.305236\pi\) | ||||
0.574398 | + | 0.818576i | \(0.305236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 327.688 | − | 620.377i | 0.300907 | − | 0.569676i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1307.77i | 1.06756i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 720.359 | 0.526193 | 0.263097 | − | 0.964769i | \(-0.415256\pi\) | ||||
0.263097 | + | 0.964769i | \(0.415256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −630.468 | − | 333.018i | −0.414509 | − | 0.218947i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2300.12i | 1.36830i | 0.729340 | + | 0.684151i | \(0.239827\pi\) | ||||
−0.729340 | + | 0.684151i | \(0.760173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2032.68 | 1.09934 | 0.549669 | − | 0.835382i | \(-0.314754\pi\) | ||||
0.549669 | + | 0.835382i | \(0.314754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1293.50 | − | 882.804i | 0.638764 | − | 0.435952i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2151.47i | − | 0.973958i | −0.873414 | − | 0.486979i | \(-0.838099\pi\) | ||
0.873414 | − | 0.486979i | \(-0.161901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2174.35 | 0.905602 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1300.14 | + | 2461.42i | −0.499863 | + | 0.946338i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2378.30i | 0.846671i | 0.905973 | + | 0.423335i | \(0.139141\pi\) | ||||
−0.905973 | + | 0.423335i | \(0.860859\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1507.19 | −0.498243 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3725.25 | + | 1967.70i | 1.14658 | + | 0.605634i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2586.95i | − | 0.743162i | −0.928401 | − | 0.371581i | \(-0.878816\pi\) | ||
0.928401 | − | 0.371581i | \(-0.121184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3135.05 | 0.842529 | 0.421265 | − | 0.906938i | \(-0.361586\pi\) | ||||
0.421265 | + | 0.906938i | \(0.361586\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3088.58 | − | 4525.43i | −0.778176 | − | 1.14019i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1531.70i | 0.362533i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2472.03 | −0.550687 | −0.275343 | − | 0.961346i | \(-0.588792\pi\) | ||||
−0.275343 | + | 0.961346i | \(0.588792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2595.07 | + | 4912.97i | −0.545068 | + | 1.03192i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7746.80i | − | 1.53676i | −0.639994 | − | 0.768380i | \(-0.721063\pi\) | ||
0.639994 | − | 0.768380i | \(-0.278937\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10238.3 | −1.92123 | −0.960617 | − | 0.277877i | \(-0.910369\pi\) | ||||
−0.960617 | + | 0.277877i | \(0.910369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1999.09 | + | 1055.94i | 0.355394 | + | 0.187722i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5273.04i | 0.889365i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5314.05 | −0.851474 | −0.425737 | − | 0.904847i | \(-0.639985\pi\) | ||||
−0.425737 | + | 0.904847i | \(0.639985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2391.12 | + | 6109.77i | −0.364445 | + | 0.931225i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10678.6i | 1.55010i | 0.631903 | + | 0.775048i | \(0.282274\pi\) | ||||
−0.631903 | + | 0.775048i | \(0.717726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5979.95 | 0.827675 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3950.39 | + | 7478.86i | −0.521917 | + | 0.988091i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2024.39i | − | 0.255572i | −0.991802 | − | 0.127786i | \(-0.959213\pi\) | ||
0.991802 | − | 0.127786i | \(-0.0407871\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5358.81 | 0.647121 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8785.63 | + | 4640.64i | 1.01580 | + | 0.536552i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 9050.36i | − | 1.00281i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16858.0 | 1.79169 | 0.895846 | − | 0.444365i | \(-0.146571\pi\) | ||||
0.895846 | + | 0.444365i | \(0.146571\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5215.51 | − | 3559.55i | 0.532141 | − | 0.363183i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19505.3i | 1.91210i | 0.293209 | + | 0.956048i | \(0.405277\pi\) | ||||
−0.293209 | + | 0.956048i | \(0.594723\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8458.43 | −0.797288 | −0.398644 | − | 0.917106i | \(-0.630519\pi\) | ||||
−0.398644 | + | 0.917106i | \(0.630519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5497.19 | + | 10407.3i | −0.498612 | + | 0.943969i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11493.8i | 1.00392i | 0.864892 | + | 0.501958i | \(0.167387\pi\) | ||||
−0.864892 | + | 0.501958i | \(0.832613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5163.95 | 0.434639 | 0.217319 | − | 0.976101i | \(-0.430269\pi\) | ||||
0.217319 | + | 0.976101i | \(0.430269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5732.65 | + | 3028.03i | 0.465275 | + | 0.245762i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4118.50i | − | 0.322539i | −0.986910 | − | 0.161269i | \(-0.948441\pi\) | ||
0.986910 | − | 0.161269i | \(-0.0515588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11935.9 | 0.902526 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3617.45 | − | 5300.35i | −0.264260 | − | 0.387198i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 20921.5i | − | 1.47740i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8563.88 | 0.584924 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9668.55 | + | 18304.4i | −0.639074 | + | 1.20989i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 16940.4i | − | 1.08418i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6955.17 | 0.431221 | 0.215611 | − | 0.976479i | \(-0.430826\pi\) | ||||
0.215611 | + | 0.976479i | \(0.430826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16176.1 | + | 8544.36i | 0.972066 | + | 0.513453i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12734.3i | − | 0.742048i | −0.928623 | − | 0.371024i | \(-0.879007\pi\) | ||
0.928623 | − | 0.371024i | \(-0.120993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31663.6 | −1.79002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14004.6 | − | 1588.18i | 0.768427 | − | 0.0871427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 23048.5i | 1.22801i | 0.789302 | + | 0.614006i | \(0.210443\pi\) | ||||
−0.789302 | + | 0.614006i | \(0.789557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13779.7 | −0.713199 | −0.356600 | − | 0.934257i | \(-0.616064\pi\) | ||||
−0.356600 | + | 0.934257i | \(0.616064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9043.72 | − | 17121.5i | 0.454893 | − | 0.861200i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6175.97i | 0.302018i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18169.6 | 0.864192 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17303.6 | + | 9139.89i | 0.800759 | + | 0.422967i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 861.178i | 0.0387901i | 0.999812 | + | 0.0193950i | \(0.00617402\pi\) | ||||
−0.999812 | + | 0.0193950i | \(0.993826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11857.7 | 0.520052 | 0.260026 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260026 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20693.2 | + | 14123.0i | −0.883985 | + | 0.603314i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 21344.4i | − | 0.888424i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24128.3 | 0.978874 | 0.489437 | − | 0.872039i | \(-0.337202\pi\) | ||||
0.489437 | + | 0.872039i | \(0.337202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9997.18 | + | 18926.6i | −0.395443 | + | 0.748650i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 41759.0i | − | 1.61101i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18099.6 | −0.681230 | −0.340615 | − | 0.940203i | \(-0.610635\pi\) | ||||
−0.340615 | + | 0.940203i | \(0.610635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11994.3 | − | 6335.46i | −0.440560 | − | 0.232707i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13135.2i | 0.470981i | 0.971877 | + | 0.235490i | \(0.0756696\pi\) | ||||
−0.971877 | + | 0.235490i | \(0.924330\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22284.6 | −0.780245 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21374.5 | + | 31318.2i | 0.730975 | + | 1.07104i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 37599.9i | 1.25630i | 0.778092 | + | 0.628151i | \(0.216188\pi\) | ||||
−0.778092 | + | 0.628151i | \(0.783812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16991.8 | −0.554833 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10874.2 | − | 20587.1i | 0.347098 | − | 0.657125i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 30293.4i | − | 0.945456i | −0.881208 | − | 0.472728i | \(-0.843269\pi\) | ||
0.881208 | − | 0.472728i | \(-0.156731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −41419.0 | −1.26428 | −0.632138 | − | 0.774855i | \(-0.717823\pi\) | ||||
−0.632138 | + | 0.774855i | \(0.717823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24948.9 | + | 13178.2i | 0.744988 | + | 0.393508i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 13927.3i | − | 0.406933i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24111.8 | 0.689518 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5556.40 | − | 48996.5i | −0.155550 | − | 1.37164i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26217.3i | 0.718655i | 0.933211 | + | 0.359328i | \(0.116994\pi\) | ||||
−0.933211 | + | 0.359328i | \(0.883006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24871.7 | −0.667716 | −0.333858 | − | 0.942623i | \(-0.608351\pi\) | ||||
−0.333858 | + | 0.942623i | \(0.608351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6438.51 | + | 12189.4i | −0.169323 | + | 0.320561i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 44861.5i | 1.15595i | 0.816053 | + | 0.577977i | \(0.196158\pi\) | ||||
−0.816053 | + | 0.577977i | \(0.803842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1782.37 | −0.0450081 | −0.0225041 | − | 0.999747i | \(-0.507164\pi\) | ||||
−0.0225041 | + | 0.999747i | \(0.507164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19672.6 | − | 10391.2i | −0.486932 | − | 0.257201i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 63568.4i | − | 1.54258i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 44470.0 | 1.05818 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −41303.4 | + | 28189.3i | −0.963929 | + | 0.657876i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 36492.0i | − | 0.835420i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27516.8 | −0.618064 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32563.7 | − | 61649.5i | 0.717753 | − | 1.35885i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 39299.4i | − | 0.850176i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −74675.5 | −1.58584 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −81476.5 | − | 43036.5i | −1.69881 | − | 0.897323i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 24504.0i | − | 0.501709i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 58322.1 | 1.17280 | 0.586399 | − | 0.810023i | \(-0.300545\pi\) | ||||
0.586399 | + | 0.810023i | \(0.300545\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11470.2 | + | 16806.4i | 0.226573 | + | 0.331978i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 96363.0i | − | 1.87007i | −0.354552 | − | 0.935036i | \(-0.615367\pi\) | ||
0.354552 | − | 0.935036i | \(-0.384633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −63619.0 | −1.21315 | −0.606577 | − | 0.795025i | \(-0.707458\pi\) | ||||
−0.606577 | + | 0.795025i | \(0.707458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22165.2 | + | 41963.1i | −0.415383 | + | 0.786401i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 104862.i | − | 1.93155i | −0.259380 | − | 0.965775i | \(-0.583518\pi\) | ||
0.259380 | − | 0.965775i | \(-0.416482\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41596.2 | −0.753213 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42289.4 | − | 22337.6i | −0.752897 | − | 0.397686i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 54132.9i | − | 0.947688i | −0.880609 | − | 0.473844i | \(-0.842866\pi\) | ||
0.880609 | − | 0.473844i | \(-0.157134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18650.0 | 0.321103 | 0.160552 | − | 0.987027i | \(-0.448673\pi\) | ||||
0.160552 | + | 0.987027i | \(0.448673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −44711.1 | + | 38570.7i | −0.757186 | + | 0.653199i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 42038.5i | − | 0.700350i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37085.6 | −0.607870 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44887.6 | + | 84980.9i | −0.723981 | + | 1.37064i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1998.43i | 0.0317206i | 0.999874 | + | 0.0158603i | \(0.00504871\pi\) | ||||
−0.999874 | + | 0.0158603i | \(0.994951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48126.8 | 0.751875 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 47588.7 | + | 25136.7i | 0.731853 | + | 0.386570i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 68298.2i | − | 1.03405i | −0.855969 | − | 0.517027i | \(-0.827039\pi\) | ||
0.855969 | − | 0.517027i | \(-0.172961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48726.0 | −0.726376 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −62874.8 | + | 42911.7i | −0.922987 | + | 0.629933i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 84260.2i | 1.21818i | 0.793102 | + | 0.609089i | \(0.208465\pi\) | ||||
−0.793102 | + | 0.609089i | \(0.791535\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45981.6 | 0.654775 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8509.52 | − | 16110.2i | 0.119367 | − | 0.225984i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 84312.3i | − | 1.16516i | −0.812773 | − | 0.582581i | \(-0.802043\pi\) | ||
0.812773 | − | 0.582581i | \(-0.197957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 97886.0 | 1.33285 | 0.666426 | − | 0.745571i | \(-0.267823\pi\) | ||||
0.666426 | + | 0.745571i | \(0.267823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 42645.7 | + | 22525.8i | 0.572203 | + | 0.302242i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 19582.8i | − | 0.258946i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 104604. | 1.36329 | 0.681646 | − | 0.731682i | \(-0.261264\pi\) | ||||
0.681646 | + | 0.731682i | \(0.261264\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 50409.6 | + | 73860.8i | 0.647596 | + | 0.948868i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 76354.4i | − | 0.966988i | −0.875348 | − | 0.483494i | \(-0.839367\pi\) | ||
0.875348 | − | 0.483494i | \(-0.160633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 129472. | 1.61660 | 0.808300 | − | 0.588771i | \(-0.200388\pi\) | ||||
0.808300 | + | 0.588771i | \(0.200388\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38043.2 | − | 72023.2i | 0.468368 | − | 0.886713i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 155583.i | − | 1.88885i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12145.5 | −0.145418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 134157. | + | 70862.8i | 1.58426 | + | 0.836820i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 100946.i | 1.17585i | 0.808915 | + | 0.587926i | \(0.200055\pi\) | ||||
−0.808915 | + | 0.587926i | \(0.799945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −50015.6 | −0.574726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 56467.9 | − | 6403.69i | 0.640161 | − | 0.0725968i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 48909.6i | − | 0.547081i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −137493. | −1.51757 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −81990.6 | + | 155224.i | −0.893056 | + | 1.69073i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 60612.5i | − | 0.651572i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11808.0 | 0.125285 | 0.0626426 | − | 0.998036i | \(-0.480047\pi\) | ||||
0.0626426 | + | 0.998036i | \(0.480047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −67312.6 | − | 35555.0i | −0.704985 | − | 0.372378i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 36362.0i | 0.375947i | 0.982174 | + | 0.187974i | \(0.0601920\pi\) | ||||
−0.982174 | + | 0.187974i | \(0.939808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −66566.3 | −0.679463 | −0.339731 | − | 0.940522i | \(-0.610336\pi\) | ||||
−0.339731 | + | 0.940522i | \(0.610336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −87493.9 | + | 59714.0i | −0.881773 | + | 0.601804i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 105833.i | 1.05318i | 0.850119 | + | 0.526591i | \(0.176530\pi\) | ||||
−0.850119 | + | 0.526591i | \(0.823470\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 73261.8 | 0.719940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −48314.4 | + | 91468.5i | −0.468885 | + | 0.887691i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144787.i | 1.38779i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19901.3 | −0.188415 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41094.9 | + | 21706.7i | 0.384320 | + | 0.203001i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 145528.i | 1.34449i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58819.5 | 0.536865 | 0.268432 | − | 0.963298i | \(-0.413494\pi\) | ||||
0.268432 | + | 0.963298i | \(0.413494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32892.4 | + | 48194.4i | 0.296624 | + | 0.434619i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 47793.8i | 0.425875i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19308.9 | 0.170020 | 0.0850098 | − | 0.996380i | \(-0.472908\pi\) | ||||
0.0850098 | + | 0.996380i | \(0.472908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17312.1 | − | 32775.2i | 0.150644 | − | 0.285198i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 86062.8i | − | 0.740127i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15330.9 | 0.130310 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 94986.5 | + | 50172.6i | 0.798039 | + | 0.421530i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 49750.9i | − | 0.413182i | −0.978427 | − | 0.206591i | \(-0.933763\pi\) | ||
0.978427 | − | 0.206591i | \(-0.0662370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −149030. | −1.22355 | −0.611777 | − | 0.791030i | \(-0.709545\pi\) | ||||
−0.611777 | + | 0.791030i | \(0.709545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6507.85 | − | 57386.4i | −0.0528230 | − | 0.465795i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 98810.0i | 0.792960i | 0.918043 | + | 0.396480i | \(0.129768\pi\) | ||||
−0.918043 | + | 0.396480i | \(0.870232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −149775. | −1.18846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 87943.4 | − | 166494.i | 0.690028 | − | 1.30636i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 233349.i | − | 1.81058i | −0.424798 | − | 0.905288i | \(-0.639655\pi\) | ||
0.424798 | − | 0.905288i | \(-0.360345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 88806.4 | 0.681444 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 68151.7 | + | 35998.3i | 0.517206 | + | 0.273192i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 197944.i | 1.48579i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −187106. | −1.38917 | −0.694587 | − | 0.719409i | \(-0.744413\pi\) | ||||
−0.694587 | + | 0.719409i | \(0.744413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −153886. | + | 105026.i | −1.13017 | + | 0.771336i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 160871.i | − | 1.16877i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33982.5 | 0.244252 | 0.122126 | − | 0.992515i | \(-0.461029\pi\) | ||||
0.122126 | + | 0.992515i | \(0.461029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 71208.8 | − | 134812.i | 0.506374 | − | 0.958665i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 74453.5i | − | 0.523845i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 150006. | 1.04431 | 0.522156 | − | 0.852850i | \(-0.325128\pi\) | ||||
0.522156 | + | 0.852850i | \(0.325128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 55349.6 | + | 29236.1i | 0.381298 | + | 0.201405i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 71272.7i | − | 0.485876i | −0.970042 | − | 0.242938i | \(-0.921889\pi\) | ||
0.970042 | − | 0.242938i | \(-0.0781112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 101948. | 0.687792 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 92814.3 | + | 135993.i | 0.619717 | + | 0.908018i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 90246.1i | 0.596388i | 0.954505 | + | 0.298194i | \(0.0963843\pi\) | ||||
−0.954505 | + | 0.298194i | \(0.903616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −190949. | −1.24901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 53528.6 | − | 101340.i | 0.346578 | − | 0.656139i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 102741.i | 0.658489i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 145813. | 0.925158 | 0.462579 | − | 0.886578i | \(-0.346924\pi\) | ||||
0.462579 | + | 0.886578i | \(0.346924\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −251981. | − | 133098.i | −1.58278 | − | 0.836038i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 108331.i | 0.673695i | 0.941559 | + | 0.336848i | \(0.109361\pi\) | ||||
−0.941559 | + | 0.336848i | \(0.890639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −87462.6 | −0.538533 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 118125. | + | 46229.5i | 0.720165 | + | 0.281844i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 56156.2i | − | 0.339007i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 294079. | 1.75800 | 0.878998 | − | 0.476825i | \(-0.158213\pi\) | ||||
0.878998 | + | 0.476825i | \(0.158213\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −96884.6 | + | 183421.i | −0.573550 | + | 1.08584i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 174985.i | 1.02589i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 206458. | 1.19877 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −109660. | − | 57923.1i | −0.630631 | − | 0.333104i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 17811.7i | − | 0.101456i | −0.998713 | − | 0.0507281i | \(-0.983846\pi\) | ||
0.998713 | − | 0.0507281i | \(-0.0161542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 349782. | 1.97348 | 0.986741 | − | 0.162304i | \(-0.0518924\pi\) | ||||
0.986741 | + | 0.162304i | \(0.0518924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 143941. | − | 98238.6i | 0.804457 | − | 0.549037i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 77697.3i | 0.430158i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −212059. | −1.16306 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25960.7 | + | 49148.7i | −0.141059 | + | 0.267053i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 149894.i | 0.806920i | 0.914997 | + | 0.403460i | \(0.132193\pi\) | ||||
−0.914997 | + | 0.403460i | \(0.867807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −248766. | −1.32683 | −0.663415 | − | 0.748252i | \(-0.730893\pi\) | ||||
−0.663415 | + | 0.748252i | \(0.730893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 144595. | + | 76376.1i | 0.764143 | + | 0.403626i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 288992.i | 1.51329i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −120416. | −0.624822 | −0.312411 | − | 0.949947i | \(-0.601137\pi\) | ||||
−0.312411 | + | 0.949947i | \(0.601137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 99283.3 | + | 145471.i | 0.510504 | + | 0.747998i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 168777.i | 0.860014i | 0.902826 | + | 0.430007i | \(0.141489\pi\) | ||||
−0.902826 | + | 0.430007i | \(0.858511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39139.1 | −0.197647 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3619.97 | + | 6853.30i | −0.0181171 | + | 0.0342993i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1278.50i | 0.00634173i | 0.999995 | + | 0.00317087i | \(0.00100932\pi\) | ||||
−0.999995 | + | 0.00317087i | \(0.998991\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 179308. | 0.881548 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 94364.2 | + | 49843.9i | 0.459844 | + | 0.242893i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 103606.i | − | 0.500453i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −202856. | −0.971306 | −0.485653 | − | 0.874152i | \(-0.661418\pi\) | ||||
−0.485653 | + | 0.874152i | \(0.661418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −224044. | + | 25407.5i | −1.06343 | + | 0.120597i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 65727.6i | 0.309276i | 0.987971 | + | 0.154638i | \(0.0494211\pi\) | ||||
−0.987971 | + | 0.154638i | \(0.950579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −266165. | −1.24162 | −0.620812 | − | 0.783960i | \(-0.713197\pi\) | ||||
−0.620812 | + | 0.783960i | \(0.713197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 89721.2 | − | 169860.i | 0.414944 | − | 0.785569i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 83490.5i | 0.382828i | 0.981509 | + | 0.191414i | \(0.0613072\pi\) | ||||
−0.981509 | + | 0.191414i | \(0.938693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 167212. | 0.760187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 192014. | + | 101423.i | 0.865547 | + | 0.457189i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 158459.i | − | 0.708264i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 117591. | 0.521179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −159116. | + | 108596.i | −0.699323 | + | 0.477283i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 203102.i | − | 0.885205i | −0.896718 | − | 0.442603i | \(-0.854055\pi\) | ||
0.896718 | − | 0.442603i | \(-0.145945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −57069.6 | −0.246669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 175534. | − | 332320.i | 0.752432 | − | 1.42450i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 325930.i | − | 1.38561i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −360891. | −1.52166 | −0.760831 | − | 0.648950i | \(-0.775208\pi\) | ||||
−0.760831 | + | 0.648950i | \(0.775208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −144038. | − | 76081.7i | −0.602362 | − | 0.318172i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 102193.i | 0.423895i | 0.977281 | + | 0.211947i | \(0.0679805\pi\) | ||||
−0.977281 | + | 0.211947i | \(0.932019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −290676. | −1.19596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −68819.8 | − | 100836.i | −0.280868 | − | 0.411533i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 524004.i | 2.12140i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −76271.0 | −0.306308 | −0.153154 | − | 0.988202i | \(-0.548943\pi\) | ||||
−0.153154 | + | 0.988202i | \(0.548943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55213.8 | + | 104530.i | −0.219974 | + | 0.416454i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 285141.i | − | 1.12700i | −0.826116 | − | 0.563500i | \(-0.809454\pi\) | ||
0.826116 | − | 0.563500i | \(-0.190546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 377112. | 1.47873 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −177342. | − | 93673.3i | −0.689914 | − | 0.364418i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 169808.i | − | 0.655425i | −0.944777 | − | 0.327713i | \(-0.893722\pi\) | ||
0.944777 | − | 0.327713i | \(-0.106278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 692529. | 2.65214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 38452.9 | + | 339079.i | 0.146115 | + | 1.28845i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 163534.i | 0.616585i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −167720. | −0.627486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −158051. | + | 299222.i | −0.586763 | + | 1.11086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 169037.i | 0.622738i | 0.950289 | + | 0.311369i | \(0.100787\pi\) | ||||
−0.950289 | + | 0.311369i | \(0.899213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 467508. | 1.70917 | 0.854586 | − | 0.519309i | \(-0.173811\pi\) | ||||
0.854586 | + | 0.519309i | \(0.173811\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −135221. | − | 71424.9i | −0.490598 | − | 0.259138i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 341465.i | 1.22949i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −101291. | −0.361960 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 173076. | − | 118123.i | 0.613828 | − | 0.418934i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 182224.i | − | 0.641434i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 222220. | 0.776381 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 127338. | − | 241076.i | 0.441581 | − | 0.835999i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 169504.i | − | 0.583447i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −228195. | −0.779673 | −0.389837 | − | 0.920884i | \(-0.627468\pi\) | ||||
−0.389837 | + | 0.920884i | \(0.627468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −329614. | − | 174105.i | −1.11791 | − | 0.590488i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 99838.8i | − | 0.336129i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −190129. | −0.635440 | −0.317720 | − | 0.948185i | \(-0.602917\pi\) | ||||
−0.317720 | + | 0.948185i | \(0.602917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 143150. | + | 209745.i | 0.474948 | + | 0.695902i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 439923.i | 1.44902i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 359449. | 1.17540 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 58543.4 | − | 110834.i | 0.190060 | − | 0.359821i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 183226.i | − | 0.590579i | −0.955408 | − | 0.295289i | \(-0.904584\pi\) | ||
0.955408 | − | 0.295289i | \(-0.0954160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −161037. | −0.515349 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 191883. | + | 101354.i | 0.609691 | + | 0.322044i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 339876.i | 1.07227i | 0.844133 | + | 0.536134i | \(0.180116\pi\) | ||||
−0.844133 | + | 0.536134i | \(0.819884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −79626.3 | −0.249436 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 161739. | − | 413273.i | 0.503093 | − | 1.28550i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 263919.i | − | 0.815165i | −0.913168 | − | 0.407582i | \(-0.866372\pi\) | ||
0.913168 | − | 0.407582i | \(-0.133628\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 168475. | 0.516730 | 0.258365 | − | 0.966047i | \(-0.416816\pi\) | ||||
0.258365 | + | 0.966047i | \(0.416816\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −110204. | + | 208638.i | −0.335652 | + | 0.635455i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 155083.i | 0.469060i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −452005. | −1.35766 | −0.678831 | − | 0.734295i | \(-0.737513\pi\) | ||||
−0.678831 | + | 0.734295i | \(0.737513\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −197931. | − | 104548.i | −0.590413 | − | 0.311860i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 722315.i | − | 2.13981i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 185402. | 0.545479 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −102476. | + | 69939.2i | −0.299440 | + | 0.204366i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4585.69i | − | 0.0133085i | −0.999978 | − | 0.00665424i | \(-0.997882\pi\) | ||
0.999978 | − | 0.00665424i | \(-0.00211813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 516791. | 1.48965 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −188575. | + | 357010.i | −0.539895 | + | 1.02213i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 277349.i | − | 0.788710i | −0.918958 | − | 0.394355i | \(-0.870968\pi\) | ||
0.918958 | − | 0.394355i | \(-0.129032\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −404492. | −1.14255 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14184.2 | − | 7492.18i | −0.0397974 | − | 0.0210213i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 354316.i | 0.987501i | 0.869604 | + | 0.493751i | \(0.164374\pi\) | ||||
−0.869604 | + | 0.493751i | \(0.835626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −286642. | −0.793582 | −0.396791 | − | 0.917909i | \(-0.629876\pi\) | ||||
−0.396791 | + | 0.917909i | \(0.629876\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −112876. | − | 165387.i | −0.310432 | − | 0.454849i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 165572.i | − | 0.452353i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 690944. | 1.87528 | 0.937639 | − | 0.347611i | \(-0.113007\pi\) | ||||
0.937639 | + | 0.347611i | \(0.113007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 267210. | − | 505880.i | 0.720473 | − | 1.36400i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 170448.i | 0.456572i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 139902. | 0.372309 | 0.186154 | − | 0.982520i | \(-0.440398\pi\) | ||||
0.186154 | + | 0.982520i | \(0.440398\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 353895. | + | 186930.i | 0.935672 | + | 0.494229i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 280737.i | − | 0.737444i | −0.929540 | − | 0.368722i | \(-0.879795\pi\) | ||
0.929540 | − | 0.368722i | \(-0.120205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 403456. | 1.05297 | 0.526483 | − | 0.850185i | \(-0.323510\pi\) | ||||
0.526483 | + | 0.850185i | \(0.323510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −447188. | + | 50713.0i | −1.15960 | + | 0.131503i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 136932.i | 0.352801i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −170519. | −0.436530 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 153394. | − | 290405.i | 0.390188 | − | 0.738702i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 222807.i | 0.563154i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 124703. | 0.313198 | 0.156599 | − | 0.987662i | \(-0.449947\pi\) | ||||
0.156599 | + | 0.987662i | \(0.449947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −218980. | − | 115667.i | −0.546509 | − | 0.288670i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 134470.i | − | 0.333486i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −172261. | −0.424529 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 518287. | − | 353728.i | 1.26931 | − | 0.866298i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25834.8i | 0.0628766i | 0.999506 | + | 0.0314383i | \(0.0100088\pi\) | ||||
−0.999506 | + | 0.0314383i | \(0.989991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −621594. | −1.50343 | −0.751717 | − | 0.659485i | \(-0.770774\pi\) | ||||
−0.751717 | + | 0.659485i | \(0.770774\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 165195. | − | 312747.i | 0.397080 | − | 0.751750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 667951.i | 1.59564i | 0.602893 | + | 0.797822i | \(0.294015\pi\) | ||||
−0.602893 | + | 0.797822i | \(0.705985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −201668. | −0.478792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −594272. | − | 313899.i | −1.40224 | − | 0.740675i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 330534.i | − | 0.775157i | −0.921837 | − | 0.387579i | \(-0.873312\pi\) | ||
0.921837 | − | 0.387579i | \(-0.126688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −246202. | −0.573865 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −467490. | − | 684974.i | −1.08303 | − | 1.58688i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 273975.i | 0.630869i | 0.948947 | + | 0.315435i | \(0.102150\pi\) | ||||
−0.948947 | + | 0.315435i | \(0.897850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −841184. | −1.92525 | −0.962627 | − | 0.270831i | \(-0.912702\pi\) | ||||
−0.962627 | + | 0.270831i | \(0.912702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 103002. | − | 195004.i | 0.234326 | − | 0.443625i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 612179.i | 1.38431i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −580185. | −1.30411 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 464130. | + | 245157.i | 1.03702 | + | 0.547762i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 244396.i | − | 0.542811i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 365221. | 0.806354 | 0.403177 | − | 0.915122i | \(-0.367906\pi\) | ||||
0.403177 | + | 0.915122i | \(0.367906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20635.1 | + | 181961.i | 0.0452897 | + | 0.399366i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 204902.i | − | 0.447062i | −0.974697 | − | 0.223531i | \(-0.928242\pi\) | ||
0.974697 | − | 0.223531i | \(-0.0717585\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.14030e6 | −2.47332 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 405062. | − | 766861.i | 0.873429 | − | 1.65357i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 651055.i | − | 1.39565i | −0.716268 | − | 0.697825i | \(-0.754151\pi\) | ||
0.716268 | − | 0.697825i | \(-0.245849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 445616. | 0.949686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −506283. | − | 267423.i | −1.07270 | − | 0.566610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 188418.i | − | 0.396903i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 81069.8 | 0.169786 | 0.0848932 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848932 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −352784. | + | 240773.i | −0.734586 | + | 0.501350i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 266415.i | 0.551554i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −711426. | −1.46442 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 440788. | − | 834497.i | 0.902142 | − | 1.70793i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 202875.i | − | 0.412851i | −0.978462 | − | 0.206425i | \(-0.933817\pi\) | ||
0.978462 | − | 0.206425i | \(-0.0661831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 337207. | 0.682317 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −331024. | − | 174850.i | −0.666011 | − | 0.351792i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.31936e6i | − | 2.63953i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 309617. | 0.615932 | 0.307966 | − | 0.951397i | \(-0.400352\pi\) | ||||
0.307966 | + | 0.951397i | \(0.400352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −242645. | − | 355528.i | −0.479991 | − | 0.703290i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 681560.i | 1.34068i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 119405. | 0.233567 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 227548. | − | 430792.i | 0.442623 | − | 0.837972i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 722490.i | 1.39757i | 0.715331 | + | 0.698785i | \(0.246276\pi\) | ||||
−0.715331 | + | 0.698785i | \(0.753724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 572140. | 1.10061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 148418. | + | 78395.3i | 0.283928 | + | 0.149973i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 236078.i | 0.449137i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −187688. | −0.355113 | −0.177557 | − | 0.984111i | \(-0.556819\pi\) | ||||
−0.177557 | + | 0.984111i | \(0.556819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −517945. | + | 119005.i | −0.974606 | + | 0.223928i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 628707.i | 1.17656i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35683.0 | −0.0664130 | −0.0332065 | − | 0.999449i | \(-0.510572\pi\) | ||||
−0.0332065 | + | 0.999449i | \(0.510572\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 176709. | − | 334544.i | 0.327102 | − | 0.619269i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 192710.i | 0.354787i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 136210. | 0.249413 | 0.124707 | − | 0.992194i | \(-0.460201\pi\) | ||||
0.124707 | + | 0.992194i | \(0.460201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −295129. | − | 155889.i | −0.537496 | − | 0.283909i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 73802.1i | − | 0.133688i | −0.997763 | − | 0.0668438i | \(-0.978707\pi\) | ||
0.997763 | − | 0.0668438i | \(-0.0212929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16649.9 | 0.0299984 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −714435. | + | 487597.i | −1.28033 | + | 0.873816i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 777459.i | − | 1.38584i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −231199. | −0.409926 | −0.204963 | − | 0.978770i | \(-0.565707\pi\) | ||||
−0.204963 | + | 0.978770i | \(0.565707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8400.41 | + | 15903.6i | −0.0148153 | + | 0.0280483i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 229255.i | − | 0.402183i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26453.5 | 0.0461627 | 0.0230813 | − | 0.999734i | \(-0.492652\pi\) | ||||
0.0230813 | + | 0.999734i | \(0.492652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 382995. | + | 202301.i | 0.664829 | + | 0.351168i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 254385.i | 0.439260i | 0.975583 | + | 0.219630i | \(0.0704851\pi\) | ||||
−0.975583 | + | 0.219630i | \(0.929515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −349296. | −0.599991 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 273051. | + | 400079.i | 0.466575 | + | 0.683632i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 204948.i | 0.348380i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −87292.0 | −0.147612 | −0.0738060 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738060 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 287092. | − | 543521.i | 0.482961 | − | 0.914339i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 318085.i | 0.532334i | 0.963927 | + | 0.266167i | \(0.0857573\pi\) | ||||
−0.963927 | + | 0.266167i | \(0.914243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 277327. | 0.461731 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −387764. | − | 204820.i | −0.642282 | − | 0.339258i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.07671e6i | 1.77428i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −603909. | −0.990078 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −680740. | + | 77198.7i | −1.11035 | + | 0.125918i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 466491.i | − | 0.757014i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11698.3 | −0.0188874 | −0.00944372 | − | 0.999955i | \(-0.503006\pi\) | ||||
−0.00944372 | + | 0.999955i | \(0.503006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −354188. | + | 670547.i | −0.568958 | + | 1.07715i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 278581.i | 0.445244i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −248371. | −0.394961 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 365924. | + | 193284.i | 0.578970 | + | 0.305817i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 210654.i | 0.331629i | 0.986157 | + | 0.165814i | \(0.0530253\pi\) | ||||
−0.986157 | + | 0.165814i | \(0.946975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 665450. | 1.04237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 135438. | − | 92435.8i | 0.211094 | − | 0.144071i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 798132.i | 1.23778i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −807361. | −1.24588 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 354407. | − | 670961.i | 0.544196 | − | 1.03027i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 732334.i | − | 1.11895i | −0.828846 | − | 0.559477i | \(-0.811002\pi\) | ||
0.828846 | − | 0.559477i | \(-0.188998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 440995. | 0.670490 | 0.335245 | − | 0.942131i | \(-0.391181\pi\) | ||||
0.335245 | + | 0.942131i | \(0.391181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 778982. | + | 411464.i | 1.17855 | + | 0.622517i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 349934.i | 0.526831i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 951518. | 1.42552 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 244689. | + | 358523.i | 0.364794 | + | 0.534501i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 813364.i | − | 1.20670i | −0.797477 | − | 0.603349i | \(-0.793833\pi\) | ||
0.797477 | − | 0.603349i | \(-0.206167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 350711. | 0.517785 | 0.258892 | − | 0.965906i | \(-0.416642\pi\) | ||||
0.258892 | + | 0.965906i | \(0.416642\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 82316.4 | − | 155841.i | 0.120942 | − | 0.228967i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 95232.7i | − | 0.139244i | −0.997573 | − | 0.0696218i | \(-0.977821\pi\) | ||
0.997573 | − | 0.0696218i | \(-0.0221793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −160042. | −0.232876 | −0.116438 | − | 0.993198i | \(-0.537148\pi\) | ||||
−0.116438 | + | 0.993198i | \(0.537148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 832444. | + | 439703.i | 1.20546 | + | 0.636733i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 672527.i | 0.969214i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 253953. | 0.364234 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 90687.5 | + | 799685.i | 0.129448 | + | 1.14148i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35266.1i | 0.0500995i | 0.999686 | + | 0.0250498i | \(0.00797442\pi\) | ||||
−0.999686 | + | 0.0250498i | \(0.992026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −175916. | −0.248721 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 320956. | − | 607632.i | 0.451638 | − | 0.855038i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 430846.i | 0.603404i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −579272. | −0.807450 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.03034e6 | + | 544235.i | 1.42944 | + | 0.755043i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 444720.i | 0.614084i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 668061. | 0.918159 | 0.459080 | − | 0.888395i | \(-0.348179\pi\) | ||||
0.459080 | + | 0.888395i | \(0.348179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 605500. | − | 413250.i | 0.828289 | − | 0.565302i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 409636.i | 0.557746i | 0.960328 | + | 0.278873i | \(0.0899608\pi\) | ||||
−0.960328 | + | 0.278873i | \(0.910039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −96808.2 | −0.131198 | −0.0655988 | − | 0.997846i | \(-0.520896\pi\) | ||||
−0.0655988 | + | 0.997846i | \(0.520896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 653993. | − | 1.23814e6i | 0.882200 | − | 1.67018i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 627704.i | − | 0.842817i | −0.906871 | − | 0.421408i | \(-0.861536\pi\) | ||
0.906871 | − | 0.421408i | \(-0.138464\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 726949. | 0.971564 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −96654.4 | − | 51053.6i | −0.128583 | − | 0.0679185i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 414261.i | 0.548574i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 195844. | 0.258151 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 769757. | + | 1.12786e6i | 1.01001 | + | 1.47988i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14587e6i | 1.49664i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.29296e6 | 1.68107 | 0.840533 | − | 0.541761i | \(-0.182242\pi\) | ||||
0.840533 | + | 0.541761i | \(0.182242\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −424326. | + | 803331.i | −0.549189 | + | 1.03972i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.13499e6i | 1.46231i | 0.682213 | + | 0.731153i | \(0.261018\pi\) | ||||
−0.682213 | + | 0.731153i | \(0.738982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −216522. | −0.277703 | −0.138851 | − | 0.990313i | \(-0.544341\pi\) | ||||
−0.138851 | + | 0.990313i | \(0.544341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −398026. | − | 210241.i | −0.508189 | − | 0.268429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.24588e6i | − | 1.58354i | −0.610821 | − | 0.791769i | \(-0.709160\pi\) | ||
0.610821 | − | 0.791769i | \(-0.290840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −470457. | −0.595273 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 476292. | + | 186402.i | 0.599954 | + | 0.234799i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.00713e6i | − | 1.26294i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −585686. | −0.731171 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 205592. | − | 389225.i | 0.255518 | − | 0.483744i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.03752e6i | 1.28374i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −735608. | −0.906143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.09418e6 | − | 577952.i | −1.34187 | − | 0.708788i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 800787.i | 0.977732i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 71744.4 | 0.0872115 | 0.0436057 | − | 0.999049i | \(-0.486115\pi\) | ||||
0.0436057 | + | 0.999049i | \(0.486115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.30497e6 | + | 890634.i | −1.57933 | + | 1.07788i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 463492.i | − | 0.558477i | −0.960222 | − | 0.279239i | \(-0.909918\pi\) | ||
0.960222 | − | 0.279239i | \(-0.0900821\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 832461. | 0.998670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 254785. | − | 482357.i | 0.304321 | − | 0.576138i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 861364.i | 1.02435i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 540851. | 0.640393 | 0.320196 | − | 0.947351i | \(-0.396251\pi\) | ||||
0.320196 | + | 0.947351i | \(0.396251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 93968.7 | + | 49635.0i | 0.110781 | + | 0.0585152i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 613732.i | 0.720403i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 180957. | 0.211491 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −386222. | − | 565898.i | −0.449446 | − | 0.658534i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 818980.i | − | 0.948947i | −0.880270 | − | 0.474474i | \(-0.842638\pi\) | ||
0.880270 | − | 0.474474i | \(-0.157362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.01784e6 | 1.17430 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −152848. | + | 289371.i | −0.175588 | + | 0.332423i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 466172.i | − | 0.533241i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −388827. | −0.442871 | −0.221435 | − | 0.975175i | \(-0.571074\pi\) | ||||
−0.221435 | + | 0.975175i | \(0.571074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −529738. | − | 279812.i | −0.600800 | − | 0.317347i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 165913.i | − | 0.187371i | −0.995602 | − | 0.0936855i | \(-0.970135\pi\) | ||
0.995602 | − | 0.0936855i | \(-0.0298648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.42000e6 | −1.59685 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −947289. | + | 107426.i | −1.06076 | + | 0.120295i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 764662.i | − | 0.852647i | −0.904571 | − | 0.426324i | \(-0.859809\pi\) | ||
0.904571 | − | 0.426324i | \(-0.140191\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 811115. | 0.900637 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −444870. | + | 842225.i | −0.491894 | + | 0.931252i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05066e6i | 1.15685i | 0.815737 | + | 0.578424i | \(0.196332\pi\) | ||||
−0.815737 | + | 0.578424i | \(0.803668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 506880. | 0.555774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 583021. | + | 307956.i | 0.636591 | + | 0.336252i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.55903e6i | − | 1.69519i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 295279. | 0.319732 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −768977. | + | 524822.i | −0.829202 | + | 0.565925i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 480865.i | 0.516379i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 201023. | 0.214977 | 0.107488 | − | 0.994206i | \(-0.465719\pi\) | ||||
0.107488 | + | 0.994206i | \(0.465719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −608611. | + | 1.15222e6i | −0.648175 | + | 1.22712i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.06992e6i | − | 1.13478i | −0.823448 | − | 0.567392i | \(-0.807952\pi\) | ||
0.823448 | − | 0.567392i | \(-0.192048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 932079. | 0.984525 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −158376. | − | 83655.3i | −0.166602 | − | 0.0880004i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.04258e6i | − | 1.09224i | −0.837706 | − | 0.546121i | \(-0.816104\pi\) | ||
0.837706 | − | 0.546121i | \(-0.183896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −157813. | −0.164656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 235792. | + | 345485.i | 0.245014 | + | 0.358998i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 201986.i | − | 0.209033i | −0.994523 | − | 0.104516i | \(-0.966671\pi\) | ||
0.994523 | − | 0.104516i | \(-0.0333294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 867343. | 0.893961 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −611729. | + | 1.15812e6i | −0.627950 | + | 1.18883i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.25489e6i | 1.28296i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 905070. | 0.921584 | 0.460792 | − | 0.887508i | \(-0.347565\pi\) | ||||
0.460792 | + | 0.887508i | \(0.347565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 468088. | + | 247248.i | 0.474711 | + | 0.250746i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34459.9i | 0.0348071i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −772571. | −0.777227 | −0.388614 | − | 0.921401i | \(-0.627046\pi\) | ||||
−0.388614 | + | 0.921401i | \(0.627046\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 59173.9 | + | 521797.i | 0.0592924 | + | 0.522842i |
(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 | 384.5.e.c.257.14 | yes | 16 | |
3.2 | odd | 2 | inner | 384.5.e.c.257.13 | yes | 16 | |
4.3 | odd | 2 | 384.5.e.b.257.3 | yes | 16 | ||
8.3 | odd | 2 | 384.5.e.d.257.14 | yes | 16 | ||
8.5 | even | 2 | 384.5.e.a.257.3 | ✓ | 16 | ||
12.11 | even | 2 | 384.5.e.b.257.4 | yes | 16 | ||
24.5 | odd | 2 | 384.5.e.a.257.4 | yes | 16 | ||
24.11 | even | 2 | 384.5.e.d.257.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.e.a.257.3 | ✓ | 16 | 8.5 | even | 2 | ||
384.5.e.a.257.4 | yes | 16 | 24.5 | odd | 2 | ||
384.5.e.b.257.3 | yes | 16 | 4.3 | odd | 2 | ||
384.5.e.b.257.4 | yes | 16 | 12.11 | even | 2 | ||
384.5.e.c.257.13 | yes | 16 | 3.2 | odd | 2 | inner | |
384.5.e.c.257.14 | yes | 16 | 1.1 | even | 1 | trivial | |
384.5.e.d.257.13 | yes | 16 | 24.11 | even | 2 | ||
384.5.e.d.257.14 | yes | 16 | 8.3 | odd | 2 |