Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(551,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.551");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.d (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: | \(31.3352304014\) |
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: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.13 | ||
Root | \(-2.98291i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.551 |
Dual form | 1150.3.d.b.551.14 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0.278523 | 0.0928408 | 0.0464204 | − | 0.998922i | \(-0.485219\pi\) | ||||
0.0464204 | + | 0.998922i | \(0.485219\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.393890 | 0.0656484 | ||||||||
\(7\) | − | 8.51262i | − | 1.21609i | −0.793903 | − | 0.608044i | \(-0.791954\pi\) | ||
0.793903 | − | 0.608044i | \(-0.208046\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −8.92243 | −0.991381 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.57553i | − | 0.688684i | −0.938844 | − | 0.344342i | \(-0.888102\pi\) | ||
0.938844 | − | 0.344342i | \(-0.111898\pi\) | |||||||
\(12\) | 0.557045 | 0.0464204 | ||||||||
\(13\) | 2.64076 | 0.203135 | 0.101568 | − | 0.994829i | \(-0.467614\pi\) | ||||
0.101568 | + | 0.994829i | \(0.467614\pi\) | |||||||
\(14\) | − | 12.0387i | − | 0.859904i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 7.56057i | − | 0.444739i | −0.974962 | − | 0.222370i | \(-0.928621\pi\) | ||
0.974962 | − | 0.222370i | \(-0.0713792\pi\) | |||||||
\(18\) | −12.6182 | −0.701012 | ||||||||
\(19\) | 24.2676i | 1.27724i | 0.769522 | + | 0.638620i | \(0.220495\pi\) | ||||
−0.769522 | + | 0.638620i | \(0.779505\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.37096i | − | 0.112903i | ||||||
\(22\) | − | 10.7134i | − | 0.486973i | ||||||
\(23\) | 15.7366 | − | 16.7738i | 0.684199 | − | 0.729295i | ||||
\(24\) | 0.787781 | 0.0328242 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.73460 | 0.143638 | ||||||||
\(27\) | −4.99180 | −0.184881 | ||||||||
\(28\) | − | 17.0252i | − | 0.608044i | ||||||
\(29\) | −31.8513 | −1.09832 | −0.549161 | − | 0.835717i | \(-0.685053\pi\) | ||||
−0.549161 | + | 0.835717i | \(0.685053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.5071 | −1.82281 | −0.911405 | − | 0.411511i | \(-0.865001\pi\) | ||||
−0.911405 | + | 0.411511i | \(0.865001\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 2.10995i | − | 0.0639380i | ||||||
\(34\) | − | 10.6923i | − | 0.314478i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.8449 | −0.495690 | ||||||||
\(37\) | − | 39.9378i | − | 1.07940i | −0.841858 | − | 0.539700i | \(-0.818538\pi\) | ||
0.841858 | − | 0.539700i | \(-0.181462\pi\) | |||||||
\(38\) | 34.3195i | 0.903146i | ||||||||
\(39\) | 0.735511 | 0.0188593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.5710 | −1.03832 | −0.519159 | − | 0.854678i | \(-0.673755\pi\) | ||||
−0.519159 | + | 0.854678i | \(0.673755\pi\) | |||||||
\(42\) | − | 3.35304i | − | 0.0798342i | ||||||
\(43\) | − | 20.5721i | − | 0.478420i | −0.970968 | − | 0.239210i | \(-0.923112\pi\) | ||
0.970968 | − | 0.239210i | \(-0.0768884\pi\) | |||||||
\(44\) | − | 15.1511i | − | 0.344342i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 22.2549 | − | 23.7217i | 0.483802 | − | 0.515690i | ||||
\(47\) | −84.3049 | −1.79372 | −0.896860 | − | 0.442314i | \(-0.854158\pi\) | ||||
−0.896860 | + | 0.442314i | \(0.854158\pi\) | |||||||
\(48\) | 1.11409 | 0.0232102 | ||||||||
\(49\) | −23.4647 | −0.478871 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.10579i | − | 0.0412900i | ||||||
\(52\) | 5.28152 | 0.101568 | ||||||||
\(53\) | − | 11.9189i | − | 0.224885i | −0.993658 | − | 0.112443i | \(-0.964133\pi\) | ||
0.993658 | − | 0.112443i | \(-0.0358674\pi\) | |||||||
\(54\) | −7.05947 | −0.130731 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 24.0773i | − | 0.429952i | ||||||
\(57\) | 6.75907i | 0.118580i | ||||||||
\(58\) | −45.0446 | −0.776631 | ||||||||
\(59\) | 67.6561 | 1.14671 | 0.573357 | − | 0.819306i | \(-0.305641\pi\) | ||||
0.573357 | + | 0.819306i | \(0.305641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 35.1621i | − | 0.576428i | −0.957566 | − | 0.288214i | \(-0.906939\pi\) | ||
0.957566 | − | 0.288214i | \(-0.0930614\pi\) | |||||||
\(62\) | −79.9131 | −1.28892 | ||||||||
\(63\) | 75.9532i | 1.20561i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 2.98393i | − | 0.0452110i | ||||||
\(67\) | − | 44.0660i | − | 0.657701i | −0.944382 | − | 0.328850i | \(-0.893339\pi\) | ||
0.944382 | − | 0.328850i | \(-0.106661\pi\) | |||||||
\(68\) | − | 15.1211i | − | 0.222370i | ||||||
\(69\) | 4.38299 | − | 4.67188i | 0.0635216 | − | 0.0677084i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.86597 | 0.124873 | 0.0624364 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624364 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(72\) | −25.2364 | −0.350506 | ||||||||
\(73\) | 87.4150 | 1.19747 | 0.598733 | − | 0.800949i | \(-0.295671\pi\) | ||||
0.598733 | + | 0.800949i | \(0.295671\pi\) | |||||||
\(74\) | − | 56.4805i | − | 0.763250i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.5352i | 0.638620i | ||||||||
\(77\) | −64.4876 | −0.837501 | ||||||||
\(78\) | 1.04017 | 0.0133355 | ||||||||
\(79\) | − | 154.217i | − | 1.95211i | −0.217517 | − | 0.976057i | \(-0.569796\pi\) | ||
0.217517 | − | 0.976057i | \(-0.430204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.9115 | 0.974216 | ||||||||
\(82\) | −60.2046 | −0.734202 | ||||||||
\(83\) | 141.642i | 1.70653i | 0.521476 | + | 0.853266i | \(0.325382\pi\) | ||||
−0.521476 | + | 0.853266i | \(0.674618\pi\) | |||||||
\(84\) | − | 4.74191i | − | 0.0564513i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 29.0933i | − | 0.338294i | ||||||
\(87\) | −8.87131 | −0.101969 | ||||||||
\(88\) | − | 21.4268i | − | 0.243487i | ||||||
\(89\) | − | 63.7252i | − | 0.716013i | −0.933719 | − | 0.358007i | \(-0.883457\pi\) | ||
0.933719 | − | 0.358007i | \(-0.116543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 22.4798i | − | 0.247030i | ||||||
\(92\) | 31.4732 | − | 33.5476i | 0.342100 | − | 0.364648i | ||||
\(93\) | −15.7385 | −0.169231 | ||||||||
\(94\) | −119.225 | −1.26835 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.57556 | 0.0164121 | ||||||||
\(97\) | − | 143.322i | − | 1.47755i | −0.673952 | − | 0.738775i | \(-0.735404\pi\) | ||
0.673952 | − | 0.738775i | \(-0.264596\pi\) | |||||||
\(98\) | −33.1841 | −0.338613 | ||||||||
\(99\) | 67.5921i | 0.682748i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 27.7102 | 0.274359 | 0.137179 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137179 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(102\) | − | 2.97803i | − | 0.0291964i | ||||||
\(103\) | 133.542i | 1.29652i | 0.761418 | + | 0.648261i | \(0.224503\pi\) | ||||
−0.761418 | + | 0.648261i | \(0.775497\pi\) | |||||||
\(104\) | 7.46919 | 0.0718192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 16.8559i | − | 0.159018i | ||||||
\(107\) | − | 50.3091i | − | 0.470179i | −0.971974 | − | 0.235089i | \(-0.924462\pi\) | ||
0.971974 | − | 0.235089i | \(-0.0755383\pi\) | |||||||
\(108\) | −9.98360 | −0.0924407 | ||||||||
\(109\) | 128.819i | 1.18182i | 0.806737 | + | 0.590911i | \(0.201232\pi\) | ||||
−0.806737 | + | 0.590911i | \(0.798768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.1236i | − | 0.100212i | ||||||
\(112\) | − | 34.0505i | − | 0.304022i | ||||||
\(113\) | − | 86.3028i | − | 0.763742i | −0.924216 | − | 0.381871i | \(-0.875280\pi\) | ||
0.924216 | − | 0.381871i | \(-0.124720\pi\) | |||||||
\(114\) | 9.55876i | 0.0838488i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −63.7027 | −0.549161 | ||||||||
\(117\) | −23.5620 | −0.201384 | ||||||||
\(118\) | 95.6802 | 0.810849 | ||||||||
\(119\) | −64.3602 | −0.540842 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 63.6114 | 0.525714 | ||||||||
\(122\) | − | 49.7267i | − | 0.407596i | ||||||
\(123\) | −11.8570 | −0.0963983 | ||||||||
\(124\) | −113.014 | −0.911405 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 107.414i | 0.852492i | ||||||||
\(127\) | 11.0135 | 0.0867206 | 0.0433603 | − | 0.999059i | \(-0.486194\pi\) | ||||
0.0433603 | + | 0.999059i | \(0.486194\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 5.72978i | − | 0.0444169i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.63941 | 0.0277818 | 0.0138909 | − | 0.999904i | \(-0.495578\pi\) | ||||
0.0138909 | + | 0.999904i | \(0.495578\pi\) | |||||||
\(132\) | − | 4.21991i | − | 0.0319690i | ||||||
\(133\) | 206.581 | 1.55324 | ||||||||
\(134\) | − | 62.3187i | − | 0.465065i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 21.3845i | − | 0.157239i | ||||||
\(137\) | 9.69785i | 0.0707873i | 0.999373 | + | 0.0353936i | \(0.0112685\pi\) | ||||
−0.999373 | + | 0.0353936i | \(0.988732\pi\) | |||||||
\(138\) | 6.19849 | − | 6.60703i | 0.0449166 | − | 0.0478771i | ||||
\(139\) | 8.05485 | 0.0579486 | 0.0289743 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289743 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.4808 | −0.166531 | ||||||||
\(142\) | 12.5384 | 0.0882984 | ||||||||
\(143\) | − | 20.0051i | − | 0.139896i | ||||||
\(144\) | −35.6897 | −0.247845 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 123.624 | 0.846737 | ||||||||
\(147\) | −6.53544 | −0.0444588 | ||||||||
\(148\) | − | 79.8755i | − | 0.539700i | ||||||
\(149\) | − | 144.062i | − | 0.966859i | −0.875383 | − | 0.483430i | \(-0.839391\pi\) | ||
0.875383 | − | 0.483430i | \(-0.160609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −109.956 | −0.728188 | −0.364094 | − | 0.931362i | \(-0.618621\pi\) | ||||
−0.364094 | + | 0.931362i | \(0.618621\pi\) | |||||||
\(152\) | 68.6391i | 0.451573i | ||||||||
\(153\) | 67.4586i | 0.440906i | ||||||||
\(154\) | −91.1992 | −0.592202 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.47102 | 0.00942963 | ||||||||
\(157\) | − | 24.8208i | − | 0.158094i | −0.996871 | − | 0.0790471i | \(-0.974812\pi\) | ||
0.996871 | − | 0.0790471i | \(-0.0251877\pi\) | |||||||
\(158\) | − | 218.096i | − | 1.38035i | ||||||
\(159\) | − | 3.31969i | − | 0.0208785i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −142.789 | − | 133.960i | −0.886887 | − | 0.832047i | ||||
\(162\) | 111.598 | 0.688875 | ||||||||
\(163\) | −108.964 | −0.668489 | −0.334244 | − | 0.942486i | \(-0.608481\pi\) | ||||
−0.334244 | + | 0.942486i | \(0.608481\pi\) | |||||||
\(164\) | −85.1421 | −0.519159 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 200.312i | 1.20670i | ||||||||
\(167\) | −72.1383 | −0.431966 | −0.215983 | − | 0.976397i | \(-0.569296\pi\) | ||||
−0.215983 | + | 0.976397i | \(0.569296\pi\) | |||||||
\(168\) | − | 6.70608i | − | 0.0399171i | ||||||
\(169\) | −162.026 | −0.958736 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 216.526i | − | 1.26623i | ||||||
\(172\) | − | 41.1441i | − | 0.239210i | ||||||
\(173\) | 150.077 | 0.867497 | 0.433748 | − | 0.901034i | \(-0.357191\pi\) | ||||
0.433748 | + | 0.901034i | \(0.357191\pi\) | |||||||
\(174\) | −12.5459 | −0.0721031 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 30.3021i | − | 0.172171i | ||||||
\(177\) | 18.8437 | 0.106462 | ||||||||
\(178\) | − | 90.1210i | − | 0.506298i | ||||||
\(179\) | 207.058 | 1.15675 | 0.578375 | − | 0.815771i | \(-0.303687\pi\) | ||||
0.578375 | + | 0.815771i | \(0.303687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 331.138i | 1.82949i | 0.404031 | + | 0.914746i | \(0.367609\pi\) | ||||
−0.404031 | + | 0.914746i | \(0.632391\pi\) | |||||||
\(182\) | − | 31.7912i | − | 0.174677i | ||||||
\(183\) | − | 9.79343i | − | 0.0535160i | ||||||
\(184\) | 44.5098 | − | 47.4434i | 0.241901 | − | 0.257845i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −22.2576 | −0.119665 | ||||||||
\(187\) | −57.2753 | −0.306285 | ||||||||
\(188\) | −168.610 | −0.896860 | ||||||||
\(189\) | 42.4933i | 0.224832i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 172.749i | 0.904447i | 0.891905 | + | 0.452223i | \(0.149369\pi\) | ||||
−0.891905 | + | 0.452223i | \(0.850631\pi\) | |||||||
\(192\) | 2.22818 | 0.0116051 | ||||||||
\(193\) | −136.450 | −0.706996 | −0.353498 | − | 0.935435i | \(-0.615008\pi\) | ||||
−0.353498 | + | 0.935435i | \(0.615008\pi\) | |||||||
\(194\) | − | 202.689i | − | 1.04479i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −46.9293 | −0.239435 | ||||||||
\(197\) | 271.090 | 1.37609 | 0.688046 | − | 0.725667i | \(-0.258469\pi\) | ||||
0.688046 | + | 0.725667i | \(0.258469\pi\) | |||||||
\(198\) | 95.5896i | 0.482776i | ||||||||
\(199\) | 257.292i | 1.29292i | 0.762946 | + | 0.646462i | \(0.223752\pi\) | ||||
−0.762946 | + | 0.646462i | \(0.776248\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 12.2734i | − | 0.0610615i | ||||||
\(202\) | 39.1882 | 0.194001 | ||||||||
\(203\) | 271.138i | 1.33566i | ||||||||
\(204\) | − | 4.21158i | − | 0.0206450i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 188.857i | 0.916780i | ||||||||
\(207\) | −140.408 | + | 149.663i | −0.678302 | + | 0.723009i | ||||
\(208\) | 10.5630 | 0.0507838 | ||||||||
\(209\) | 183.840 | 0.879615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 54.1944 | 0.256846 | 0.128423 | − | 0.991720i | \(-0.459009\pi\) | ||||
0.128423 | + | 0.991720i | \(0.459009\pi\) | |||||||
\(212\) | − | 23.8378i | − | 0.112443i | ||||||
\(213\) | 2.46937 | 0.0115933 | ||||||||
\(214\) | − | 71.1478i | − | 0.332467i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.1189 | −0.0653655 | ||||||||
\(217\) | 481.023i | 2.21670i | ||||||||
\(218\) | 182.177i | 0.835674i | ||||||||
\(219\) | 24.3471 | 0.111174 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.9656i | − | 0.0903423i | ||||||
\(222\) | − | 15.7311i | − | 0.0708608i | ||||||
\(223\) | −104.611 | −0.469105 | −0.234553 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234553 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(224\) | − | 48.1546i | − | 0.214976i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 122.051i | − | 0.540047i | ||||||
\(227\) | − | 200.484i | − | 0.883190i | −0.897215 | − | 0.441595i | \(-0.854413\pi\) | ||
0.897215 | − | 0.441595i | \(-0.145587\pi\) | |||||||
\(228\) | 13.5181i | 0.0592901i | ||||||||
\(229\) | 22.0718i | 0.0963834i | 0.998838 | + | 0.0481917i | \(0.0153458\pi\) | ||||
−0.998838 | + | 0.0481917i | \(0.984654\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.9612 | −0.0777543 | ||||||||
\(232\) | −90.0892 | −0.388315 | ||||||||
\(233\) | 338.632 | 1.45335 | 0.726677 | − | 0.686979i | \(-0.241064\pi\) | ||||
0.726677 | + | 0.686979i | \(0.241064\pi\) | |||||||
\(234\) | −33.3217 | −0.142400 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 135.312 | 0.573357 | ||||||||
\(237\) | − | 42.9529i | − | 0.181236i | ||||||
\(238\) | −91.0191 | −0.382433 | ||||||||
\(239\) | 149.374 | 0.624997 | 0.312499 | − | 0.949918i | \(-0.398834\pi\) | ||||
0.312499 | + | 0.949918i | \(0.398834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 133.030i | 0.551991i | 0.961159 | + | 0.275995i | \(0.0890074\pi\) | ||||
−0.961159 | + | 0.275995i | \(0.910993\pi\) | |||||||
\(242\) | 89.9601 | 0.371736 | ||||||||
\(243\) | 66.9048 | 0.275328 | ||||||||
\(244\) | − | 70.3242i | − | 0.288214i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.7683 | −0.0681639 | ||||||||
\(247\) | 64.0848i | 0.259453i | ||||||||
\(248\) | −159.826 | −0.644461 | ||||||||
\(249\) | 39.4505i | 0.158436i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 376.920i | − | 1.50167i | −0.660489 | − | 0.750836i | \(-0.729651\pi\) | ||
0.660489 | − | 0.750836i | \(-0.270349\pi\) | |||||||
\(252\) | 151.906i | 0.602803i | ||||||||
\(253\) | −127.070 | − | 119.213i | −0.502254 | − | 0.471197i | ||||
\(254\) | 15.5755 | 0.0613208 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −226.085 | −0.879708 | −0.439854 | − | 0.898069i | \(-0.644970\pi\) | ||||
−0.439854 | + | 0.898069i | \(0.644970\pi\) | |||||||
\(258\) | − | 8.10314i | − | 0.0314075i | ||||||
\(259\) | −339.975 | −1.31264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 284.191 | 1.08885 | ||||||||
\(262\) | 5.14690 | 0.0196447 | ||||||||
\(263\) | 2.43654i | 0.00926441i | 0.999989 | + | 0.00463221i | \(0.00147448\pi\) | ||||
−0.999989 | + | 0.00463221i | \(0.998526\pi\) | |||||||
\(264\) | − | 5.96785i | − | 0.0226055i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 292.149 | 1.09830 | ||||||||
\(267\) | − | 17.7489i | − | 0.0664753i | ||||||
\(268\) | − | 88.1319i | − | 0.328850i | ||||||
\(269\) | −311.337 | −1.15739 | −0.578694 | − | 0.815545i | \(-0.696437\pi\) | ||||
−0.578694 | + | 0.815545i | \(0.696437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 260.751 | 0.962182 | 0.481091 | − | 0.876671i | \(-0.340241\pi\) | ||||
0.481091 | + | 0.876671i | \(0.340241\pi\) | |||||||
\(272\) | − | 30.2423i | − | 0.111185i | ||||||
\(273\) | − | 6.26112i | − | 0.0229345i | ||||||
\(274\) | 13.7148i | 0.0500541i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.76599 | − | 9.34376i | 0.0317608 | − | 0.0338542i | ||||
\(277\) | 182.267 | 0.658004 | 0.329002 | − | 0.944329i | \(-0.393288\pi\) | ||||
0.329002 | + | 0.944329i | \(0.393288\pi\) | |||||||
\(278\) | 11.3913 | 0.0409758 | ||||||||
\(279\) | 504.180 | 1.80710 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.60502i | 0.0163880i | 0.999966 | + | 0.00819398i | \(0.00260825\pi\) | ||||
−0.999966 | + | 0.00819398i | \(0.997392\pi\) | |||||||
\(282\) | −33.2069 | −0.117755 | ||||||||
\(283\) | − | 332.897i | − | 1.17631i | −0.808747 | − | 0.588157i | \(-0.799854\pi\) | ||
0.808747 | − | 0.588157i | \(-0.200146\pi\) | |||||||
\(284\) | 17.7319 | 0.0624364 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 28.2915i | − | 0.0989215i | ||||||
\(287\) | 362.391i | 1.26269i | ||||||||
\(288\) | −50.4729 | −0.175253 | ||||||||
\(289\) | 231.838 | 0.802207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 39.9185i | − | 0.137177i | ||||||
\(292\) | 174.830 | 0.598733 | ||||||||
\(293\) | − | 336.114i | − | 1.14715i | −0.819154 | − | 0.573574i | \(-0.805557\pi\) | ||
0.819154 | − | 0.573574i | \(-0.194443\pi\) | |||||||
\(294\) | −9.24251 | −0.0314371 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 112.961i | − | 0.381625i | ||||||
\(297\) | 37.8155i | 0.127325i | ||||||||
\(298\) | − | 203.734i | − | 0.683673i | ||||||
\(299\) | 41.5565 | − | 44.2955i | 0.138985 | − | 0.148146i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −175.122 | −0.581801 | ||||||||
\(302\) | −155.502 | −0.514907 | ||||||||
\(303\) | 7.71792 | 0.0254717 | ||||||||
\(304\) | 97.0703i | 0.319310i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 95.4009i | 0.311768i | ||||||||
\(307\) | 457.934 | 1.49164 | 0.745821 | − | 0.666147i | \(-0.232057\pi\) | ||||
0.745821 | + | 0.666147i | \(0.232057\pi\) | |||||||
\(308\) | −128.975 | −0.418750 | ||||||||
\(309\) | 37.1944i | 0.120370i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −455.620 | −1.46502 | −0.732508 | − | 0.680758i | \(-0.761650\pi\) | ||||
−0.732508 | + | 0.680758i | \(0.761650\pi\) | |||||||
\(312\) | 2.08034 | 0.00666775 | ||||||||
\(313\) | 589.353i | 1.88292i | 0.337130 | + | 0.941458i | \(0.390544\pi\) | ||||
−0.337130 | + | 0.941458i | \(0.609456\pi\) | |||||||
\(314\) | − | 35.1019i | − | 0.111789i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 308.434i | − | 0.976057i | ||||||
\(317\) | 386.251 | 1.21846 | 0.609229 | − | 0.792994i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792994i | \(0.291479\pi\) | |||||||
\(318\) | − | 4.69475i | − | 0.0147634i | ||||||
\(319\) | 241.291i | 0.756397i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 14.0122i | − | 0.0436518i | ||||||
\(322\) | −201.934 | − | 189.447i | −0.627124 | − | 0.588346i | ||||
\(323\) | 183.477 | 0.568039 | ||||||||
\(324\) | 157.823 | 0.487108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −154.098 | −0.472693 | ||||||||
\(327\) | 35.8789i | 0.109721i | ||||||||
\(328\) | −120.409 | −0.367101 | ||||||||
\(329\) | 717.655i | 2.18132i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 220.712 | 0.666803 | 0.333402 | − | 0.942785i | \(-0.391804\pi\) | ||||
0.333402 | + | 0.942785i | \(0.391804\pi\) | |||||||
\(332\) | 283.284i | 0.853266i | ||||||||
\(333\) | 356.342i | 1.07010i | ||||||||
\(334\) | −102.019 | −0.305446 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 9.48382i | − | 0.0282257i | ||||||
\(337\) | − | 193.563i | − | 0.574371i | −0.957875 | − | 0.287185i | \(-0.907280\pi\) | ||
0.957875 | − | 0.287185i | \(-0.0927196\pi\) | |||||||
\(338\) | −229.140 | −0.677929 | ||||||||
\(339\) | − | 24.0373i | − | 0.0709064i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 428.071i | 1.25534i | ||||||||
\(342\) | − | 306.213i | − | 0.895361i | ||||||
\(343\) | − | 217.373i | − | 0.633739i | ||||||
\(344\) | − | 58.1866i | − | 0.169147i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 212.241 | 0.613413 | ||||||||
\(347\) | 262.429 | 0.756278 | 0.378139 | − | 0.925749i | \(-0.376564\pi\) | ||||
0.378139 | + | 0.925749i | \(0.376564\pi\) | |||||||
\(348\) | −17.7426 | −0.0509846 | ||||||||
\(349\) | 229.831 | 0.658543 | 0.329271 | − | 0.944235i | \(-0.393197\pi\) | ||||
0.329271 | + | 0.944235i | \(0.393197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.1821 | −0.0375560 | ||||||||
\(352\) | − | 42.8536i | − | 0.121743i | ||||||
\(353\) | −367.482 | −1.04103 | −0.520513 | − | 0.853854i | \(-0.674259\pi\) | ||||
−0.520513 | + | 0.853854i | \(0.674259\pi\) | |||||||
\(354\) | 26.6491 | 0.0752799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 127.450i | − | 0.358007i | ||||||
\(357\) | −17.9258 | −0.0502123 | ||||||||
\(358\) | 292.824 | 0.817945 | ||||||||
\(359\) | 239.971i | 0.668442i | 0.942495 | + | 0.334221i | \(0.108473\pi\) | ||||
−0.942495 | + | 0.334221i | \(0.891527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −227.915 | −0.631344 | ||||||||
\(362\) | 468.300i | 1.29365i | ||||||||
\(363\) | 17.7172 | 0.0488077 | ||||||||
\(364\) | − | 44.9595i | − | 0.123515i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 13.8500i | − | 0.0378416i | ||||||
\(367\) | − | 389.113i | − | 1.06025i | −0.847918 | − | 0.530127i | \(-0.822144\pi\) | ||
0.847918 | − | 0.530127i | \(-0.177856\pi\) | |||||||
\(368\) | 62.9463 | − | 67.0952i | 0.171050 | − | 0.182324i | ||||
\(369\) | 379.837 | 1.02937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −101.461 | −0.273480 | ||||||||
\(372\) | −31.4770 | −0.0846156 | ||||||||
\(373\) | 546.309i | 1.46463i | 0.680964 | + | 0.732317i | \(0.261561\pi\) | ||||
−0.680964 | + | 0.732317i | \(0.738439\pi\) | |||||||
\(374\) | −80.9995 | −0.216576 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −238.450 | −0.634176 | ||||||||
\(377\) | −84.1117 | −0.223108 | ||||||||
\(378\) | 60.0946i | 0.158980i | ||||||||
\(379\) | − | 295.837i | − | 0.780573i | −0.920693 | − | 0.390287i | \(-0.872376\pi\) | ||
0.920693 | − | 0.390287i | \(-0.127624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.06751 | 0.00805122 | ||||||||
\(382\) | 244.304i | 0.639541i | ||||||||
\(383\) | − | 566.033i | − | 1.47789i | −0.673765 | − | 0.738946i | \(-0.735324\pi\) | ||
0.673765 | − | 0.738946i | \(-0.264676\pi\) | |||||||
\(384\) | 3.15112 | 0.00820605 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −192.970 | −0.499921 | ||||||||
\(387\) | 183.553i | 0.474296i | ||||||||
\(388\) | − | 286.645i | − | 0.738775i | ||||||
\(389\) | 196.043i | 0.503966i | 0.967732 | + | 0.251983i | \(0.0810826\pi\) | ||||
−0.967732 | + | 0.251983i | \(0.918917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −126.819 | − | 118.978i | −0.324346 | − | 0.304290i | ||||
\(392\) | −66.3681 | −0.169306 | ||||||||
\(393\) | 1.01366 | 0.00257928 | ||||||||
\(394\) | 383.380 | 0.973045 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 135.184i | 0.341374i | ||||||||
\(397\) | 298.788 | 0.752616 | 0.376308 | − | 0.926495i | \(-0.377194\pi\) | ||||
0.376308 | + | 0.926495i | \(0.377194\pi\) | |||||||
\(398\) | 363.866i | 0.914236i | ||||||||
\(399\) | 57.5374 | 0.144204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 785.114i | − | 1.95789i | −0.204121 | − | 0.978946i | \(-0.565433\pi\) | ||
0.204121 | − | 0.978946i | \(-0.434567\pi\) | |||||||
\(402\) | − | 17.3572i | − | 0.0431770i | ||||||
\(403\) | −149.222 | −0.370277 | ||||||||
\(404\) | 55.4204 | 0.137179 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 383.447i | 0.944452i | ||||||||
\(407\) | −302.550 | −0.743365 | ||||||||
\(408\) | − | 5.95607i | − | 0.0145982i | ||||||
\(409\) | 358.186 | 0.875761 | 0.437881 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437881 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.70107i | 0.00657195i | ||||||||
\(412\) | 267.084i | 0.648261i | ||||||||
\(413\) | − | 575.930i | − | 1.39450i | ||||||
\(414\) | −198.568 | + | 211.655i | −0.479632 | + | 0.511245i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.9384 | 0.0359096 | ||||||||
\(417\) | 2.24346 | 0.00537999 | ||||||||
\(418\) | 259.988 | 0.621982 | ||||||||
\(419\) | 195.271i | 0.466042i | 0.972472 | + | 0.233021i | \(0.0748610\pi\) | ||||
−0.972472 | + | 0.233021i | \(0.925139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 768.042i | 1.82433i | 0.409826 | + | 0.912164i | \(0.365590\pi\) | ||||
−0.409826 | + | 0.912164i | \(0.634410\pi\) | |||||||
\(422\) | 76.6425 | 0.181617 | ||||||||
\(423\) | 752.204 | 1.77826 | ||||||||
\(424\) | − | 33.7118i | − | 0.0795089i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.49222 | 0.00819770 | ||||||||
\(427\) | −299.321 | −0.700987 | ||||||||
\(428\) | − | 100.618i | − | 0.235089i | ||||||
\(429\) | − | 5.57188i | − | 0.0129881i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 333.122i | − | 0.772905i | −0.922309 | − | 0.386453i | \(-0.873700\pi\) | ||
0.922309 | − | 0.386453i | \(-0.126300\pi\) | |||||||
\(432\) | −19.9672 | −0.0462204 | ||||||||
\(433\) | − | 7.49741i | − | 0.0173150i | −0.999963 | − | 0.00865752i | \(-0.997244\pi\) | ||
0.999963 | − | 0.00865752i | \(-0.00275581\pi\) | |||||||
\(434\) | 680.270i | 1.56744i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 257.637i | 0.590911i | ||||||||
\(437\) | 407.059 | + | 381.889i | 0.931485 | + | 0.873887i | ||||
\(438\) | 34.4319 | 0.0786117 | ||||||||
\(439\) | −303.939 | −0.692344 | −0.346172 | − | 0.938171i | \(-0.612519\pi\) | ||||
−0.346172 | + | 0.938171i | \(0.612519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 209.362 | 0.474743 | ||||||||
\(442\) | − | 28.2357i | − | 0.0638816i | ||||||
\(443\) | −637.145 | −1.43825 | −0.719125 | − | 0.694881i | \(-0.755457\pi\) | ||||
−0.719125 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(444\) | − | 22.2471i | − | 0.0501062i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −147.942 | −0.331708 | ||||||||
\(447\) | − | 40.1245i | − | 0.0897640i | ||||||
\(448\) | − | 68.1009i | − | 0.152011i | ||||||
\(449\) | 88.9331 | 0.198069 | 0.0990346 | − | 0.995084i | \(-0.468425\pi\) | ||||
0.0990346 | + | 0.995084i | \(0.468425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 322.498i | 0.715073i | ||||||||
\(452\) | − | 172.606i | − | 0.381871i | ||||||
\(453\) | −30.6253 | −0.0676056 | ||||||||
\(454\) | − | 283.527i | − | 0.624509i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.1175i | 0.0419244i | ||||||||
\(457\) | 377.669i | 0.826410i | 0.910638 | + | 0.413205i | \(0.135591\pi\) | ||||
−0.910638 | + | 0.413205i | \(0.864409\pi\) | |||||||
\(458\) | 31.2142i | 0.0681534i | ||||||||
\(459\) | 37.7408i | 0.0822240i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −585.070 | −1.26913 | −0.634566 | − | 0.772869i | \(-0.718821\pi\) | ||||
−0.634566 | + | 0.772869i | \(0.718821\pi\) | |||||||
\(462\) | −25.4010 | −0.0549806 | ||||||||
\(463\) | 225.877 | 0.487854 | 0.243927 | − | 0.969794i | \(-0.421564\pi\) | ||||
0.243927 | + | 0.969794i | \(0.421564\pi\) | |||||||
\(464\) | −127.405 | −0.274580 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 478.897 | 1.02768 | ||||||||
\(467\) | − | 702.984i | − | 1.50532i | −0.658410 | − | 0.752659i | \(-0.728771\pi\) | ||
0.658410 | − | 0.752659i | \(-0.271229\pi\) | |||||||
\(468\) | −47.1240 | −0.100692 | ||||||||
\(469\) | −375.117 | −0.799822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.91315i | − | 0.0146776i | ||||||
\(472\) | 191.360 | 0.405424 | ||||||||
\(473\) | −155.844 | −0.329480 | ||||||||
\(474\) | − | 60.7446i | − | 0.128153i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −128.720 | −0.270421 | ||||||||
\(477\) | 106.346i | 0.222947i | ||||||||
\(478\) | 211.247 | 0.441940 | ||||||||
\(479\) | 291.706i | 0.608989i | 0.952514 | + | 0.304494i | \(0.0984875\pi\) | ||||
−0.952514 | + | 0.304494i | \(0.901512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 105.466i | − | 0.219264i | ||||||
\(482\) | 188.132i | 0.390316i | ||||||||
\(483\) | −39.7699 | − | 37.3107i | −0.0823394 | − | 0.0772479i | ||||
\(484\) | 127.223 | 0.262857 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 94.6177 | 0.194687 | ||||||||
\(487\) | −205.957 | −0.422909 | −0.211454 | − | 0.977388i | \(-0.567820\pi\) | ||||
−0.211454 | + | 0.977388i | \(0.567820\pi\) | |||||||
\(488\) | − | 99.4534i | − | 0.203798i | ||||||
\(489\) | −30.3488 | −0.0620630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −192.478 | −0.392012 | −0.196006 | − | 0.980603i | \(-0.562797\pi\) | ||||
−0.196006 | + | 0.980603i | \(0.562797\pi\) | |||||||
\(492\) | −23.7140 | −0.0481992 | ||||||||
\(493\) | 240.814i | 0.488467i | ||||||||
\(494\) | 90.6296i | 0.183461i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −226.028 | −0.455703 | ||||||||
\(497\) | − | 75.4726i | − | 0.151856i | ||||||
\(498\) | 55.7915i | 0.112031i | ||||||||
\(499\) | 887.386 | 1.77833 | 0.889164 | − | 0.457589i | \(-0.151287\pi\) | ||||
0.889164 | + | 0.457589i | \(0.151287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0921 | −0.0401041 | ||||||||
\(502\) | − | 533.045i | − | 1.06184i | ||||||
\(503\) | − | 330.810i | − | 0.657673i | −0.944387 | − | 0.328837i | \(-0.893343\pi\) | ||
0.944387 | − | 0.328837i | \(-0.106657\pi\) | |||||||
\(504\) | 214.828i | 0.426246i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −179.704 | − | 168.592i | −0.355147 | − | 0.333187i | ||||
\(507\) | −45.1280 | −0.0890099 | ||||||||
\(508\) | 22.0270 | 0.0433603 | ||||||||
\(509\) | −407.928 | −0.801430 | −0.400715 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400715 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 744.131i | − | 1.45622i | ||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 121.139i | − | 0.236138i | ||||||
\(514\) | −319.733 | −0.622048 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 11.4596i | − | 0.0222085i | ||||||
\(517\) | 638.654i | 1.23531i | ||||||||
\(518\) | −480.797 | −0.928180 | ||||||||
\(519\) | 41.7998 | 0.0805391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 458.780i | 0.880576i | 0.897857 | + | 0.440288i | \(0.145124\pi\) | ||||
−0.897857 | + | 0.440288i | \(0.854876\pi\) | |||||||
\(522\) | 401.907 | 0.769937 | ||||||||
\(523\) | − | 404.987i | − | 0.774354i | −0.922005 | − | 0.387177i | \(-0.873450\pi\) | ||
0.922005 | − | 0.387177i | \(-0.126550\pi\) | |||||||
\(524\) | 7.27882 | 0.0138909 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.44579i | 0.00655093i | ||||||||
\(527\) | 427.226i | 0.810675i | ||||||||
\(528\) | − | 8.43982i | − | 0.0159845i | ||||||
\(529\) | −33.7199 | − | 527.924i | −0.0637427 | − | 0.997966i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −603.656 | −1.13683 | ||||||||
\(532\) | 413.161 | 0.776619 | ||||||||
\(533\) | −112.420 | −0.210919 | ||||||||
\(534\) | − | 25.1007i | − | 0.0470051i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 124.637i | − | 0.232532i | ||||||
\(537\) | 57.6703 | 0.107394 | ||||||||
\(538\) | −440.298 | −0.818397 | ||||||||
\(539\) | 177.757i | 0.329791i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1047.51 | 1.93625 | 0.968123 | − | 0.250477i | \(-0.0805875\pi\) | ||||
0.968123 | + | 0.250477i | \(0.0805875\pi\) | |||||||
\(542\) | 368.758 | 0.680366 | ||||||||
\(543\) | 92.2294i | 0.169851i | ||||||||
\(544\) | − | 42.7690i | − | 0.0786195i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 8.85457i | − | 0.0162172i | ||||||
\(547\) | −123.784 | −0.226296 | −0.113148 | − | 0.993578i | \(-0.536093\pi\) | ||||
−0.113148 | + | 0.993578i | \(0.536093\pi\) | |||||||
\(548\) | 19.3957i | 0.0353936i | ||||||||
\(549\) | 313.731i | 0.571459i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 772.955i | − | 1.40282i | ||||||
\(552\) | 12.3970 | − | 13.2141i | 0.0224583 | − | 0.0239385i | ||||
\(553\) | −1312.79 | −2.37394 | ||||||||
\(554\) | 257.765 | 0.465279 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1097 | 0.0289743 | ||||||||
\(557\) | 246.292i | 0.442176i | 0.975254 | + | 0.221088i | \(0.0709608\pi\) | ||||
−0.975254 | + | 0.221088i | \(0.929039\pi\) | |||||||
\(558\) | 713.019 | 1.27781 | ||||||||
\(559\) | − | 54.3259i | − | 0.0971840i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.9525 | −0.0284357 | ||||||||
\(562\) | 6.51248i | 0.0115880i | ||||||||
\(563\) | 574.776i | 1.02092i | 0.859902 | + | 0.510458i | \(0.170524\pi\) | ||||
−0.859902 | + | 0.510458i | \(0.829476\pi\) | |||||||
\(564\) | −46.9616 | −0.0832653 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 470.787i | − | 0.831780i | ||||||
\(567\) | − | 671.743i | − | 1.18473i | ||||||
\(568\) | 25.0768 | 0.0441492 | ||||||||
\(569\) | − | 794.332i | − | 1.39601i | −0.716091 | − | 0.698007i | \(-0.754070\pi\) | ||
0.716091 | − | 0.698007i | \(-0.245930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 416.688i | 0.729751i | 0.931056 | + | 0.364876i | \(0.118889\pi\) | ||||
−0.931056 | + | 0.364876i | \(0.881111\pi\) | |||||||
\(572\) | − | 40.0103i | − | 0.0699480i | ||||||
\(573\) | 48.1146i | 0.0839696i | ||||||||
\(574\) | 512.498i | 0.892854i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −71.3794 | −0.123923 | ||||||||
\(577\) | 282.647 | 0.489856 | 0.244928 | − | 0.969541i | \(-0.421236\pi\) | ||||
0.244928 | + | 0.969541i | \(0.421236\pi\) | |||||||
\(578\) | 327.868 | 0.567246 | ||||||||
\(579\) | −38.0044 | −0.0656381 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1205.75 | 2.07529 | ||||||||
\(582\) | − | 56.4533i | − | 0.0969988i | ||||||
\(583\) | −90.2920 | −0.154875 | ||||||||
\(584\) | 247.247 | 0.423368 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 475.337i | − | 0.811156i | ||||||
\(587\) | 168.123 | 0.286410 | 0.143205 | − | 0.989693i | \(-0.454259\pi\) | ||||
0.143205 | + | 0.989693i | \(0.454259\pi\) | |||||||
\(588\) | −13.0709 | −0.0222294 | ||||||||
\(589\) | − | 1371.29i | − | 2.32817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 75.5048 | 0.127758 | ||||||||
\(592\) | − | 159.751i | − | 0.269850i | ||||||
\(593\) | 419.364 | 0.707191 | 0.353595 | − | 0.935398i | \(-0.384959\pi\) | ||||
0.353595 | + | 0.935398i | \(0.384959\pi\) | |||||||
\(594\) | 53.4792i | 0.0900323i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 288.124i | − | 0.483430i | ||||||
\(597\) | 71.6616i | 0.120036i | ||||||||
\(598\) | 58.7698 | − | 62.6433i | 0.0982773 | − | 0.104755i | ||||
\(599\) | −519.774 | −0.867736 | −0.433868 | − | 0.900977i | \(-0.642852\pi\) | ||||
−0.433868 | + | 0.900977i | \(0.642852\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1089.19 | 1.81230 | 0.906151 | − | 0.422955i | \(-0.139007\pi\) | ||||
0.906151 | + | 0.422955i | \(0.139007\pi\) | |||||||
\(602\) | −247.660 | −0.411395 | ||||||||
\(603\) | 393.175i | 0.652032i | ||||||||
\(604\) | −219.913 | −0.364094 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.9148 | 0.0180112 | ||||||||
\(607\) | −890.673 | −1.46734 | −0.733668 | − | 0.679508i | \(-0.762193\pi\) | ||||
−0.733668 | + | 0.679508i | \(0.762193\pi\) | |||||||
\(608\) | 137.278i | 0.225786i | ||||||||
\(609\) | 75.5181i | 0.124003i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −222.629 | −0.364368 | ||||||||
\(612\) | 134.917i | 0.220453i | ||||||||
\(613\) | − | 629.354i | − | 1.02668i | −0.858186 | − | 0.513339i | \(-0.828408\pi\) | ||
0.858186 | − | 0.513339i | \(-0.171592\pi\) | |||||||
\(614\) | 647.616 | 1.05475 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −182.398 | −0.296101 | ||||||||
\(617\) | 157.187i | 0.254760i | 0.991854 | + | 0.127380i | \(0.0406568\pi\) | ||||
−0.991854 | + | 0.127380i | \(0.959343\pi\) | |||||||
\(618\) | 52.6008i | 0.0851146i | ||||||||
\(619\) | − | 462.293i | − | 0.746838i | −0.927663 | − | 0.373419i | \(-0.878185\pi\) | ||
0.927663 | − | 0.373419i | \(-0.121815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −78.5539 | + | 83.7314i | −0.126496 | + | 0.134833i | ||||
\(622\) | −644.344 | −1.03592 | ||||||||
\(623\) | −542.468 | −0.870735 | ||||||||
\(624\) | 2.94204 | 0.00471481 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 833.471i | 1.33142i | ||||||||
\(627\) | 51.2035 | 0.0816642 | ||||||||
\(628\) | − | 49.6416i | − | 0.0790471i | ||||||
\(629\) | −301.952 | −0.480051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 411.630i | − | 0.652345i | −0.945310 | − | 0.326173i | \(-0.894241\pi\) | ||
0.945310 | − | 0.326173i | \(-0.105759\pi\) | |||||||
\(632\) | − | 436.191i | − | 0.690176i | ||||||
\(633\) | 15.0944 | 0.0238458 | ||||||||
\(634\) | 546.242 | 0.861581 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 6.63937i | − | 0.0104393i | ||||||
\(637\) | −61.9645 | −0.0972756 | ||||||||
\(638\) | 341.236i | 0.534853i | ||||||||
\(639\) | −79.1060 | −0.123797 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 251.089i | 0.391715i | 0.980632 | + | 0.195857i | \(0.0627490\pi\) | ||||
−0.980632 | + | 0.195857i | \(0.937251\pi\) | |||||||
\(642\) | − | 19.8163i | − | 0.0308665i | ||||||
\(643\) | 102.907i | 0.160042i | 0.996793 | + | 0.0800211i | \(0.0254988\pi\) | ||||
−0.996793 | + | 0.0800211i | \(0.974501\pi\) | |||||||
\(644\) | −285.578 | − | 267.919i | −0.443444 | − | 0.416023i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 259.475 | 0.401664 | ||||||||
\(647\) | 437.368 | 0.675993 | 0.337997 | − | 0.941147i | \(-0.390251\pi\) | ||||
0.337997 | + | 0.941147i | \(0.390251\pi\) | |||||||
\(648\) | 223.195 | 0.344437 | ||||||||
\(649\) | − | 512.530i | − | 0.789723i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 133.976i | 0.205800i | ||||||||
\(652\) | −217.927 | −0.334244 | ||||||||
\(653\) | 94.4001 | 0.144564 | 0.0722819 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722819 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(654\) | 50.7404i | 0.0775847i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −170.284 | −0.259580 | ||||||||
\(657\) | −779.954 | −1.18714 | ||||||||
\(658\) | 1014.92i | 1.54243i | ||||||||
\(659\) | 759.727i | 1.15285i | 0.817151 | + | 0.576424i | \(0.195552\pi\) | ||||
−0.817151 | + | 0.576424i | \(0.804448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 581.754i | 0.880112i | 0.897970 | + | 0.440056i | \(0.145041\pi\) | ||||
−0.897970 | + | 0.440056i | \(0.854959\pi\) | |||||||
\(662\) | 312.134 | 0.471501 | ||||||||
\(663\) | − | 5.56088i | − | 0.00838745i | ||||||
\(664\) | 400.625i | 0.603350i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 503.943i | 0.756672i | ||||||||
\(667\) | −501.231 | + | 534.267i | −0.751471 | + | 0.801001i | ||||
\(668\) | −144.277 | −0.215983 | ||||||||
\(669\) | −29.1364 | −0.0435521 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −266.371 | −0.396977 | ||||||||
\(672\) | − | 13.4122i | − | 0.0199586i | ||||||
\(673\) | 831.173 | 1.23503 | 0.617513 | − | 0.786560i | \(-0.288140\pi\) | ||||
0.617513 | + | 0.786560i | \(0.288140\pi\) | |||||||
\(674\) | − | 273.739i | − | 0.406142i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −324.053 | −0.479368 | ||||||||
\(677\) | − | 106.706i | − | 0.157616i | −0.996890 | − | 0.0788079i | \(-0.974889\pi\) | ||
0.996890 | − | 0.0788079i | \(-0.0251114\pi\) | |||||||
\(678\) | − | 33.9938i | − | 0.0501384i | ||||||
\(679\) | −1220.05 | −1.79683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 55.8393i | − | 0.0819961i | ||||||
\(682\) | 605.384i | 0.887660i | ||||||||
\(683\) | −380.675 | −0.557357 | −0.278678 | − | 0.960385i | \(-0.589896\pi\) | ||||
−0.278678 | + | 0.960385i | \(0.589896\pi\) | |||||||
\(684\) | − | 433.051i | − | 0.633116i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 307.411i | − | 0.448121i | ||||||
\(687\) | 6.14749i | 0.00894832i | ||||||||
\(688\) | − | 82.2883i | − | 0.119605i | ||||||
\(689\) | − | 31.4750i | − | 0.0456821i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −318.845 | −0.461425 | −0.230713 | − | 0.973022i | \(-0.574106\pi\) | ||||
−0.230713 | + | 0.973022i | \(0.574106\pi\) | |||||||
\(692\) | 300.154 | 0.433748 | ||||||||
\(693\) | 575.385 | 0.830282 | ||||||||
\(694\) | 371.130 | 0.534769 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.0919 | −0.0360515 | ||||||||
\(697\) | 321.861i | 0.461781i | ||||||||
\(698\) | 325.031 | 0.465660 | ||||||||
\(699\) | 94.3165 | 0.134931 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 112.754i | 0.160848i | 0.996761 | + | 0.0804239i | \(0.0256274\pi\) | ||||
−0.996761 | + | 0.0804239i | \(0.974373\pi\) | |||||||
\(702\) | −18.6424 | −0.0265561 | ||||||||
\(703\) | 969.193 | 1.37865 | ||||||||
\(704\) | − | 60.6042i | − | 0.0860855i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −519.698 | −0.736116 | ||||||||
\(707\) | − | 235.887i | − | 0.333644i | ||||||
\(708\) | 37.6875 | 0.0532309 | ||||||||
\(709\) | − | 465.481i | − | 0.656531i | −0.944585 | − | 0.328266i | \(-0.893536\pi\) | ||
0.944585 | − | 0.328266i | \(-0.106464\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1375.99i | 1.93529i | ||||||||
\(712\) | − | 180.242i | − | 0.253149i | ||||||
\(713\) | −889.229 | + | 947.838i | −1.24717 | + | 1.32937i | ||||
\(714\) | −25.3509 | −0.0355054 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 414.116 | 0.578375 | ||||||||
\(717\) | 41.6041 | 0.0580253 | ||||||||
\(718\) | 339.370i | 0.472660i | ||||||||
\(719\) | −347.913 | −0.483885 | −0.241943 | − | 0.970291i | \(-0.577785\pi\) | ||||
−0.241943 | + | 0.970291i | \(0.577785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1136.79 | 1.57669 | ||||||||
\(722\) | −322.321 | −0.446428 | ||||||||
\(723\) | 37.0518i | 0.0512473i | ||||||||
\(724\) | 662.276i | 0.914746i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.0559 | 0.0345123 | ||||||||
\(727\) | − | 88.3077i | − | 0.121469i | −0.998154 | − | 0.0607343i | \(-0.980656\pi\) | ||
0.998154 | − | 0.0607343i | \(-0.0193442\pi\) | |||||||
\(728\) | − | 63.5824i | − | 0.0873385i | ||||||
\(729\) | −691.569 | −0.948654 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −155.536 | −0.212772 | ||||||||
\(732\) | − | 19.5869i | − | 0.0267580i | ||||||
\(733\) | 510.848i | 0.696928i | 0.937322 | + | 0.348464i | \(0.113297\pi\) | ||||
−0.937322 | + | 0.348464i | \(0.886703\pi\) | |||||||
\(734\) | − | 550.289i | − | 0.749712i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 89.0196 | − | 94.8869i | 0.120950 | − | 0.128922i | ||||
\(737\) | −333.823 | −0.452948 | ||||||||
\(738\) | 537.171 | 0.727873 | ||||||||
\(739\) | −416.763 | −0.563955 | −0.281978 | − | 0.959421i | \(-0.590990\pi\) | ||||
−0.281978 | + | 0.959421i | \(0.590990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.8491i | 0.0240878i | ||||||||
\(742\) | −143.488 | −0.193380 | ||||||||
\(743\) | − | 633.469i | − | 0.852583i | −0.904586 | − | 0.426291i | \(-0.859820\pi\) | ||
0.904586 | − | 0.426291i | \(-0.140180\pi\) | |||||||
\(744\) | −44.5152 | −0.0598323 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 772.597i | 1.03565i | ||||||||
\(747\) | − | 1263.79i | − | 1.69182i | ||||||
\(748\) | −114.551 | −0.153142 | ||||||||
\(749\) | −428.262 | −0.571779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1282.52i | 1.70775i | 0.520475 | + | 0.853877i | \(0.325755\pi\) | ||||
−0.520475 | + | 0.853877i | \(0.674245\pi\) | |||||||
\(752\) | −337.219 | −0.448430 | ||||||||
\(753\) | − | 104.981i | − | 0.139416i | ||||||
\(754\) | −118.952 | −0.157761 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 84.9866i | 0.112416i | ||||||||
\(757\) | − | 1233.64i | − | 1.62964i | −0.579716 | − | 0.814819i | \(-0.696836\pi\) | ||
0.579716 | − | 0.814819i | \(-0.303164\pi\) | |||||||
\(758\) | − | 418.377i | − | 0.551949i | ||||||
\(759\) | −35.3919 | − | 33.2035i | −0.0466297 | − | 0.0437463i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −262.559 | −0.345018 | −0.172509 | − | 0.985008i | \(-0.555187\pi\) | ||||
−0.172509 | + | 0.985008i | \(0.555187\pi\) | |||||||
\(762\) | 4.33812 | 0.00569307 | ||||||||
\(763\) | 1096.58 | 1.43720 | ||||||||
\(764\) | 345.499i | 0.452223i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 800.491i | − | 1.04503i | ||||||
\(767\) | 178.663 | 0.232938 | ||||||||
\(768\) | 4.45636 | 0.00580255 | ||||||||
\(769\) | − | 801.510i | − | 1.04228i | −0.853473 | − | 0.521138i | \(-0.825508\pi\) | ||
0.853473 | − | 0.521138i | \(-0.174492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62.9698 | −0.0816729 | ||||||||
\(772\) | −272.900 | −0.353498 | ||||||||
\(773\) | − | 1143.79i | − | 1.47967i | −0.672786 | − | 0.739837i | \(-0.734903\pi\) | ||
0.672786 | − | 0.739837i | \(-0.265097\pi\) | |||||||
\(774\) | 259.583i | 0.335378i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 405.377i | − | 0.522393i | ||||||
\(777\) | −94.6907 | −0.121867 | ||||||||
\(778\) | 277.246i | 0.356357i | ||||||||
\(779\) | − | 1033.10i | − | 1.32618i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 67.1644i | − | 0.0859979i | ||||||
\(782\) | −179.350 | − | 168.260i | −0.229347 | − | 0.215166i | ||||
\(783\) | 158.995 | 0.203059 | ||||||||
\(784\) | −93.8587 | −0.119718 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.43353 | 0.00182383 | ||||||||
\(787\) | − | 111.467i | − | 0.141635i | −0.997489 | − | 0.0708175i | \(-0.977439\pi\) | ||
0.997489 | − | 0.0708175i | \(-0.0225608\pi\) | |||||||
\(788\) | 542.181 | 0.688046 | ||||||||
\(789\) | 0.678632i | 0.000860116i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −734.663 | −0.928777 | ||||||||
\(792\) | 191.179i | 0.241388i | ||||||||
\(793\) | − | 92.8546i | − | 0.117093i | ||||||
\(794\) | 422.551 | 0.532180 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 514.584i | 0.646462i | ||||||||
\(797\) | − | 231.014i | − | 0.289855i | −0.989442 | − | 0.144927i | \(-0.953705\pi\) | ||
0.989442 | − | 0.144927i | \(-0.0462949\pi\) | |||||||
\(798\) | 81.3701 | 0.101968 | ||||||||
\(799\) | 637.393i | 0.797738i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 568.583i | 0.709842i | ||||||||
\(802\) | − | 1110.32i | − | 1.38444i | ||||||
\(803\) | − | 662.215i | − | 0.824676i | ||||||
\(804\) | − | 24.5467i | − | 0.0305307i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −211.031 | −0.261825 | ||||||||
\(807\) | −86.7145 | −0.107453 | ||||||||
\(808\) | 78.3763 | 0.0970004 | ||||||||
\(809\) | −165.201 | −0.204204 | −0.102102 | − | 0.994774i | \(-0.532557\pi\) | ||||
−0.102102 | + | 0.994774i | \(0.532557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 317.322 | 0.391273 | 0.195636 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195636 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(812\) | 542.276i | 0.667828i | ||||||||
\(813\) | 72.6251 | 0.0893298 | ||||||||
\(814\) | −427.870 | −0.525638 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 8.42315i | − | 0.0103225i | ||||||
\(817\) | 499.234 | 0.611058 | ||||||||
\(818\) | 506.552 | 0.619257 | ||||||||
\(819\) | 200.574i | 0.244901i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1389.82 | −1.69284 | −0.846421 | − | 0.532514i | \(-0.821247\pi\) | ||||
−0.846421 | + | 0.532514i | \(0.821247\pi\) | |||||||
\(822\) | 3.81989i | 0.00464707i | ||||||||
\(823\) | −948.001 | −1.15188 | −0.575942 | − | 0.817490i | \(-0.695365\pi\) | ||||
−0.575942 | + | 0.817490i | \(0.695365\pi\) | |||||||
\(824\) | 377.713i | 0.458390i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 814.489i | − | 0.986064i | ||||||
\(827\) | − | 1177.54i | − | 1.42387i | −0.702245 | − | 0.711935i | \(-0.747819\pi\) | ||
0.702245 | − | 0.711935i | \(-0.252181\pi\) | |||||||
\(828\) | −280.817 | + | 299.326i | −0.339151 | + | 0.361505i | ||||
\(829\) | −1278.78 | −1.54256 | −0.771279 | − | 0.636497i | \(-0.780383\pi\) | ||||
−0.771279 | + | 0.636497i | \(0.780383\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.7655 | 0.0610897 | ||||||||
\(832\) | 21.1261 | 0.0253919 | ||||||||
\(833\) | 177.406i | 0.212973i | ||||||||
\(834\) | 3.17273 | 0.00380423 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 367.679 | 0.439808 | ||||||||
\(837\) | 282.072 | 0.337004 | ||||||||
\(838\) | 276.156i | 0.329541i | ||||||||
\(839\) | − | 1435.77i | − | 1.71128i | −0.517570 | − | 0.855641i | \(-0.673163\pi\) | ||
0.517570 | − | 0.855641i | \(-0.326837\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 173.507 | 0.206311 | ||||||||
\(842\) | 1086.18i | 1.28999i | ||||||||
\(843\) | 1.28260i | 0.00152147i | ||||||||
\(844\) | 108.389 | 0.128423 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1063.78 | 1.25742 | ||||||||
\(847\) | − | 541.500i | − | 0.639315i | ||||||
\(848\) | − | 47.6757i | − | 0.0562213i | ||||||
\(849\) | − | 92.7193i | − | 0.109210i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −669.908 | − | 628.484i | −0.787201 | − | 0.738524i | ||||
\(852\) | 4.93875 | 0.00579665 | ||||||||
\(853\) | −812.996 | −0.953102 | −0.476551 | − | 0.879147i | \(-0.658113\pi\) | ||||
−0.476551 | + | 0.879147i | \(0.658113\pi\) | |||||||
\(854\) | −423.304 | −0.495673 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 142.296i | − | 0.166233i | ||||||
\(857\) | 958.841 | 1.11883 | 0.559417 | − | 0.828886i | \(-0.311025\pi\) | ||||
0.559417 | + | 0.828886i | \(0.311025\pi\) | |||||||
\(858\) | − | 7.87983i | − | 0.00918395i | ||||||
\(859\) | −383.654 | −0.446628 | −0.223314 | − | 0.974747i | \(-0.571688\pi\) | ||||
−0.223314 | + | 0.974747i | \(0.571688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 100.934i | 0.117229i | ||||||||
\(862\) | − | 471.106i | − | 0.546526i | ||||||
\(863\) | −1017.48 | −1.17900 | −0.589502 | − | 0.807767i | \(-0.700676\pi\) | ||||
−0.589502 | + | 0.807767i | \(0.700676\pi\) | |||||||
\(864\) | −28.2379 | −0.0326827 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10.6029i | − | 0.0122436i | ||||||
\(867\) | 64.5721 | 0.0744776 | ||||||||
\(868\) | 962.047i | 1.10835i | ||||||||
\(869\) | −1168.27 | −1.34439 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 116.368i | − | 0.133602i | ||||||
\(872\) | 364.354i | 0.417837i | ||||||||
\(873\) | 1278.78i | 1.46482i | ||||||||
\(874\) | 575.669 | + | 540.072i | 0.658660 | + | 0.617932i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 48.6941 | 0.0555869 | ||||||||
\(877\) | −1443.83 | −1.64633 | −0.823163 | − | 0.567806i | \(-0.807793\pi\) | ||||
−0.823163 | + | 0.567806i | \(0.807793\pi\) | |||||||
\(878\) | −429.835 | −0.489561 | ||||||||
\(879\) | − | 93.6154i | − | 0.106502i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 894.988i | − | 1.01588i | −0.861393 | − | 0.507939i | \(-0.830408\pi\) | ||
0.861393 | − | 0.507939i | \(-0.169592\pi\) | |||||||
\(882\) | 296.082 | 0.335694 | ||||||||
\(883\) | 870.115 | 0.985407 | 0.492704 | − | 0.870197i | \(-0.336009\pi\) | ||||
0.492704 | + | 0.870197i | \(0.336009\pi\) | |||||||
\(884\) | − | 39.9313i | − | 0.0451711i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −901.058 | −1.01700 | ||||||||
\(887\) | 529.330 | 0.596764 | 0.298382 | − | 0.954446i | \(-0.403553\pi\) | ||||
0.298382 | + | 0.954446i | \(0.403553\pi\) | |||||||
\(888\) | − | 31.4622i | − | 0.0354304i | ||||||
\(889\) | − | 93.7539i | − | 0.105460i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 597.796i | − | 0.670927i | ||||||
\(892\) | −209.221 | −0.234553 | ||||||||
\(893\) | − | 2045.87i | − | 2.29101i | ||||||
\(894\) | − | 56.7446i | − | 0.0634728i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 96.3093i | − | 0.107488i | ||||||
\(897\) | 11.5744 | − | 12.3373i | 0.0129035 | − | 0.0137540i | ||||
\(898\) | 125.770 | 0.140056 | ||||||||
\(899\) | 1799.83 | 2.00203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.1138 | −0.100015 | ||||||||
\(902\) | 456.081i | 0.505633i | ||||||||
\(903\) | −48.7755 | −0.0540149 | ||||||||
\(904\) | − | 244.101i | − | 0.270023i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −43.3107 | −0.0478044 | ||||||||
\(907\) | − | 691.482i | − | 0.762384i | −0.924496 | − | 0.381192i | \(-0.875514\pi\) | ||
0.924496 | − | 0.381192i | \(-0.124486\pi\) | |||||||
\(908\) | − | 400.968i | − | 0.441595i | ||||||
\(909\) | −247.242 | −0.271994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1794.49i | − | 1.96980i | −0.173115 | − | 0.984902i | \(-0.555383\pi\) | ||
0.173115 | − | 0.984902i | \(-0.444617\pi\) | |||||||
\(912\) | 27.0363i | 0.0296450i | ||||||||
\(913\) | 1073.01 | 1.17526 | ||||||||
\(914\) | 534.105i | 0.584360i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.1436i | 0.0481917i | ||||||||
\(917\) | − | 30.9809i | − | 0.0337851i | ||||||
\(918\) | 53.3736i | 0.0581412i | ||||||||
\(919\) | 428.705i | 0.466491i | 0.972418 | + | 0.233245i | \(0.0749345\pi\) | ||||
−0.972418 | + | 0.233245i | \(0.925065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 127.545 | 0.138485 | ||||||||
\(922\) | −827.413 | −0.897411 | ||||||||
\(923\) | 23.4129 | 0.0253661 | ||||||||
\(924\) | −35.9225 | −0.0388771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 319.438 | 0.344965 | ||||||||
\(927\) | − | 1191.52i | − | 1.28535i | ||||||
\(928\) | −180.178 | −0.194158 | ||||||||
\(929\) | 1577.01 | 1.69754 | 0.848768 | − | 0.528766i | \(-0.177345\pi\) | ||||
0.848768 | + | 0.528766i | \(0.177345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 569.431i | − | 0.611633i | ||||||
\(932\) | 677.263 | 0.726677 | ||||||||
\(933\) | −126.900 | −0.136013 | ||||||||
\(934\) | − | 994.169i | − | 1.06442i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −66.6433 | −0.0712001 | ||||||||
\(937\) | − | 141.317i | − | 0.150818i | −0.997153 | − | 0.0754091i | \(-0.975974\pi\) | ||
0.997153 | − | 0.0754091i | \(-0.0240263\pi\) | |||||||
\(938\) | −530.495 | −0.565560 | ||||||||
\(939\) | 164.148i | 0.174812i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1506.21i | 1.60065i | 0.599566 | + | 0.800325i | \(0.295340\pi\) | ||||
−0.599566 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(942\) | − | 9.77667i | − | 0.0103786i | ||||||
\(943\) | −669.923 | + | 714.078i | −0.710417 | + | 0.757240i | ||||
\(944\) | 270.624 | 0.286678 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −220.397 | −0.232978 | ||||||||
\(947\) | −1689.84 | −1.78441 | −0.892205 | − | 0.451632i | \(-0.850842\pi\) | ||||
−0.892205 | + | 0.451632i | \(0.850842\pi\) | |||||||
\(948\) | − | 85.9058i | − | 0.0906179i | ||||||
\(949\) | 230.842 | 0.243248 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 107.580 | 0.113123 | ||||||||
\(952\) | −182.038 | −0.191217 | ||||||||
\(953\) | − | 990.482i | − | 1.03933i | −0.854370 | − | 0.519665i | \(-0.826057\pi\) | ||
0.854370 | − | 0.519665i | \(-0.173943\pi\) | |||||||
\(954\) | 150.395i | 0.157647i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 298.749 | 0.312499 | ||||||||
\(957\) | 67.2049i | 0.0702245i | ||||||||
\(958\) | 412.534i | 0.430620i | ||||||||
\(959\) | 82.5541 | 0.0860836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2232.05 | 2.32264 | ||||||||
\(962\) | − | 149.151i | − | 0.155043i | ||||||
\(963\) | 448.879i | 0.466126i | ||||||||
\(964\) | 266.059i | 0.275995i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −56.2432 | − | 52.7654i | −0.0582227 | − | 0.0546225i | ||||
\(967\) | −1528.09 | −1.58024 | −0.790118 | − | 0.612954i | \(-0.789981\pi\) | ||||
−0.790118 | + | 0.612954i | \(0.789981\pi\) | |||||||
\(968\) | 179.920 | 0.185868 | ||||||||
\(969\) | 51.1024 | 0.0527372 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 616.239i | − | 0.634643i | −0.948318 | − | 0.317322i | \(-0.897217\pi\) | ||
0.948318 | − | 0.317322i | \(-0.102783\pi\) | |||||||
\(972\) | 133.810 | 0.137664 | ||||||||
\(973\) | − | 68.5679i | − | 0.0704706i | ||||||
\(974\) | −291.267 | −0.299042 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 140.648i | − | 0.144107i | ||||||
\(977\) | 1393.79i | 1.42660i | 0.700859 | + | 0.713299i | \(0.252800\pi\) | ||||
−0.700859 | + | 0.713299i | \(0.747200\pi\) | |||||||
\(978\) | −42.9197 | −0.0438852 | ||||||||
\(979\) | −482.752 | −0.493107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1149.37i | − | 1.17164i | ||||||
\(982\) | −272.205 | −0.277195 | ||||||||
\(983\) | 1033.22i | 1.05109i | 0.850767 | + | 0.525543i | \(0.176138\pi\) | ||||
−0.850767 | + | 0.525543i | \(0.823862\pi\) | |||||||
\(984\) | −33.5367 | −0.0340820 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 340.563i | 0.345398i | ||||||||
\(987\) | 199.883i | 0.202516i | ||||||||
\(988\) | 128.170i | 0.129726i | ||||||||
\(989\) | −345.071 | − | 323.734i | −0.348909 | − | 0.327335i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1122.80 | −1.13300 | −0.566501 | − | 0.824061i | \(-0.691703\pi\) | ||||
−0.566501 | + | 0.824061i | \(0.691703\pi\) | |||||||
\(992\) | −319.652 | −0.322230 | ||||||||
\(993\) | 61.4732 | 0.0619066 | ||||||||
\(994\) | − | 106.734i | − | 0.107379i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 78.9011i | 0.0792179i | ||||||||
\(997\) | 718.650 | 0.720812 | 0.360406 | − | 0.932795i | \(-0.382638\pi\) | ||||
0.360406 | + | 0.932795i | \(0.382638\pi\) | |||||||
\(998\) | 1254.95 | 1.25747 | ||||||||
\(999\) | 199.361i | 0.199561i |
(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 | 1150.3.d.b.551.13 | 16 | ||
5.2 | odd | 4 | 1150.3.c.c.1149.8 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.25 | 32 | |||
5.4 | even | 2 | 230.3.d.a.91.3 | ✓ | 16 | ||
15.14 | odd | 2 | 2070.3.c.a.91.16 | 16 | |||
20.19 | odd | 2 | 1840.3.k.d.321.9 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.d.b.551.14 | 16 | ||
115.22 | even | 4 | 1150.3.c.c.1149.26 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.7 | 32 | |||
115.114 | odd | 2 | 230.3.d.a.91.4 | yes | 16 | ||
345.344 | even | 2 | 2070.3.c.a.91.9 | 16 | |||
460.459 | even | 2 | 1840.3.k.d.321.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.3 | ✓ | 16 | 5.4 | even | 2 | ||
230.3.d.a.91.4 | yes | 16 | 115.114 | odd | 2 | ||
1150.3.c.c.1149.7 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.8 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.25 | 32 | 5.3 | odd | 4 | |||
1150.3.c.c.1149.26 | 32 | 115.22 | even | 4 | |||
1150.3.d.b.551.13 | 16 | 1.1 | even | 1 | trivial | ||
1150.3.d.b.551.14 | 16 | 23.22 | odd | 2 | inner | ||
1840.3.k.d.321.9 | 16 | 20.19 | odd | 2 | |||
1840.3.k.d.321.10 | 16 | 460.459 | even | 2 | |||
2070.3.c.a.91.9 | 16 | 345.344 | even | 2 | |||
2070.3.c.a.91.16 | 16 | 15.14 | odd | 2 |