Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,3,Mod(91,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2070.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.c (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: | \(56.4034147226\) |
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: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.9 | ||
Root | \(-2.98291i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.91 |
Dual form | 2070.3.c.a.91.16 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8.51262i | − | 1.21609i | −0.793903 | − | 0.608044i | \(-0.791954\pi\) | ||
0.793903 | − | 0.608044i | \(-0.208046\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | − | 7.57553i | − | 0.688684i | −0.938844 | − | 0.344342i | \(-0.888102\pi\) | ||
0.938844 | − | 0.344342i | \(-0.111898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64076 | −0.203135 | −0.101568 | − | 0.994829i | \(-0.532386\pi\) | ||||
−0.101568 | + | 0.994829i | \(0.532386\pi\) | |||||||
\(14\) | − | 12.0387i | − | 0.859904i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 7.56057i | 0.444739i | 0.974962 | + | 0.222370i | \(0.0713792\pi\) | ||||
−0.974962 | + | 0.222370i | \(0.928621\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24.2676i | − | 1.27724i | −0.769522 | − | 0.638620i | \(-0.779505\pi\) | ||
0.769522 | − | 0.638620i | \(-0.220495\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 10.7134i | − | 0.486973i | ||||||
\(23\) | 15.7366 | + | 16.7738i | 0.684199 | + | 0.729295i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −3.73460 | −0.143638 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 17.0252i | − | 0.608044i | ||||||
\(29\) | 31.8513 | 1.09832 | 0.549161 | − | 0.835717i | \(-0.314947\pi\) | ||||
0.549161 | + | 0.835717i | \(0.314947\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.6923i | 0.314478i | ||||||||
\(35\) | −19.0348 | −0.543851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 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 | 0 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | 42.5710 | 1.03832 | 0.519159 | − | 0.854678i | \(-0.326245\pi\) | ||||
0.519159 | + | 0.854678i | \(0.326245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 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 | \(0.854158\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −23.4647 | −0.478871 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.28152 | −0.101568 | ||||||||
\(53\) | 11.9189i | 0.224885i | 0.993658 | + | 0.112443i | \(0.0358674\pi\) | ||||
−0.993658 | + | 0.112443i | \(0.964133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.9394 | −0.307989 | ||||||||
\(56\) | − | 24.0773i | − | 0.429952i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 45.0446 | 0.776631 | ||||||||
\(59\) | −67.6561 | −1.14671 | −0.573357 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573357 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.1621i | 0.576428i | 0.957566 | + | 0.288214i | \(0.0930614\pi\) | ||||
−0.957566 | + | 0.288214i | \(0.906939\pi\) | |||||||
\(62\) | −79.9131 | −1.28892 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 5.90492i | 0.0908449i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 44.0660i | − | 0.657701i | −0.944382 | − | 0.328850i | \(-0.893339\pi\) | ||
0.944382 | − | 0.328850i | \(-0.106661\pi\) | |||||||
\(68\) | 15.1211i | 0.222370i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −26.9193 | −0.384561 | ||||||||
\(71\) | −8.86597 | −0.124873 | −0.0624364 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624364 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −87.4150 | −1.19747 | −0.598733 | − | 0.800949i | \(-0.704329\pi\) | ||||
−0.598733 | + | 0.800949i | \(0.704329\pi\) | |||||||
\(74\) | − | 56.4805i | − | 0.763250i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 48.5352i | − | 0.638620i | ||||||
\(77\) | −64.4876 | −0.837501 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 154.217i | 1.95211i | 0.217517 | + | 0.976057i | \(0.430204\pi\) | ||||
−0.217517 | + | 0.976057i | \(0.569796\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 60.2046 | 0.734202 | ||||||||
\(83\) | − | 141.642i | − | 1.70653i | −0.521476 | − | 0.853266i | \(-0.674618\pi\) | ||
0.521476 | − | 0.853266i | \(-0.325382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9059 | 0.198893 | ||||||||
\(86\) | − | 29.0933i | − | 0.338294i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 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 | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −119.225 | −1.26835 | ||||||||
\(95\) | −54.2639 | −0.571199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 143.322i | − | 1.47755i | −0.673952 | − | 0.738775i | \(-0.735404\pi\) | ||
0.673952 | − | 0.738775i | \(-0.264596\pi\) | |||||||
\(98\) | −33.1841 | −0.338613 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −27.7102 | −0.274359 | −0.137179 | − | 0.990546i | \(-0.543804\pi\) | ||||
−0.137179 | + | 0.990546i | \(0.543804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | \(0.0755383\pi\) | ||||
−0.971974 | + | 0.235089i | \(0.924462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 128.819i | − | 1.18182i | −0.806737 | − | 0.590911i | \(-0.798768\pi\) | ||
0.806737 | − | 0.590911i | \(-0.201232\pi\) | |||||||
\(110\) | −23.9559 | −0.217781 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 34.0505i | − | 0.304022i | ||||||
\(113\) | 86.3028i | 0.763742i | 0.924216 | + | 0.381871i | \(0.124720\pi\) | ||||
−0.924216 | + | 0.381871i | \(0.875280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37.5073 | − | 35.1881i | 0.326151 | − | 0.305983i | ||||
\(116\) | 63.7027 | 0.549161 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −95.6802 | −0.810849 | ||||||||
\(119\) | 64.3602 | 0.540842 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 63.6114 | 0.525714 | ||||||||
\(122\) | 49.7267i | 0.407596i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −113.014 | −0.911405 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0135 | −0.0867206 | −0.0433603 | − | 0.999059i | \(-0.513806\pi\) | ||||
−0.0433603 | + | 0.999059i | \(0.513806\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.35081i | 0.0642370i | ||||||||
\(131\) | −3.63941 | −0.0277818 | −0.0138909 | − | 0.999904i | \(-0.504422\pi\) | ||||
−0.0138909 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | \(-0.988732\pi\) | ||
0.999373 | − | 0.0353936i | \(-0.0112685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.05485 | 0.0579486 | 0.0289743 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289743 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(140\) | −38.0696 | −0.271926 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.5384 | −0.0882984 | ||||||||
\(143\) | 20.0051i | 0.139896i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 71.2217i | − | 0.491184i | ||||||
\(146\) | −123.624 | −0.846737 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 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 | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −91.1992 | −0.592202 | ||||||||
\(155\) | 126.354i | 0.815185i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 24.8208i | − | 0.158094i | −0.996871 | − | 0.0790471i | \(-0.974812\pi\) | ||
0.996871 | − | 0.0790471i | \(-0.0251877\pi\) | |||||||
\(158\) | 218.096i | 1.38035i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | 142.789 | − | 133.960i | 0.886887 | − | 0.832047i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 108.964 | 0.668489 | 0.334244 | − | 0.942486i | \(-0.391519\pi\) | ||||
0.334244 | + | 0.942486i | \(0.391519\pi\) | |||||||
\(164\) | 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 | \(0.569296\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −162.026 | −0.958736 | ||||||||
\(170\) | 23.9086 | 0.140639 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 41.1441i | − | 0.239210i | ||||||
\(173\) | 150.077 | 0.867497 | 0.433748 | − | 0.901034i | \(-0.357191\pi\) | ||||
0.433748 | + | 0.901034i | \(0.357191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.5631i | 0.243218i | ||||||||
\(176\) | − | 30.3021i | − | 0.172171i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 90.1210i | − | 0.506298i | ||||||
\(179\) | −207.058 | −1.15675 | −0.578375 | − | 0.815771i | \(-0.696313\pi\) | ||||
−0.578375 | + | 0.815771i | \(0.696313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 331.138i | − | 1.82949i | −0.404031 | − | 0.914746i | \(-0.632391\pi\) | ||
0.404031 | − | 0.914746i | \(-0.367609\pi\) | |||||||
\(182\) | 31.7912i | 0.174677i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 44.5098 | + | 47.4434i | 0.241901 | + | 0.257845i | ||||
\(185\) | −89.3036 | −0.482722 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 57.2753 | 0.306285 | ||||||||
\(188\) | −168.610 | −0.896860 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −76.7408 | −0.403899 | ||||||||
\(191\) | 172.749i | 0.904447i | 0.891905 | + | 0.452223i | \(0.149369\pi\) | ||||
−0.891905 | + | 0.452223i | \(0.850631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 136.450 | 0.706996 | 0.353498 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353498 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(194\) | − | 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 | \(0.258469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 257.292i | − | 1.29292i | −0.762946 | − | 0.646462i | \(-0.776248\pi\) | ||
0.762946 | − | 0.646462i | \(-0.223752\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −39.1882 | −0.194001 | ||||||||
\(203\) | − | 271.138i | − | 1.33566i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 95.1918i | − | 0.464350i | ||||||
\(206\) | 188.857i | 0.916780i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 71.1478i | 0.332467i | ||||||||
\(215\) | −46.0005 | −0.213956 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 481.023i | 2.21670i | ||||||||
\(218\) | − | 182.177i | − | 0.835674i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −33.8788 | −0.153994 | ||||||||
\(221\) | − | 19.9656i | − | 0.0903423i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 104.611 | 0.469105 | 0.234553 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234553 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(224\) | − | 48.1546i | − | 0.214976i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 122.051i | 0.540047i | ||||||||
\(227\) | 200.484i | 0.883190i | 0.897215 | + | 0.441595i | \(0.145587\pi\) | ||||
−0.897215 | + | 0.441595i | \(0.854413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.0718i | − | 0.0963834i | −0.998838 | − | 0.0481917i | \(-0.984654\pi\) | ||
0.998838 | − | 0.0481917i | \(-0.0153458\pi\) | |||||||
\(230\) | 53.0434 | − | 49.7634i | 0.230623 | − | 0.216363i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 90.0892 | 0.388315 | ||||||||
\(233\) | 338.632 | 1.45335 | 0.726677 | − | 0.686979i | \(-0.241064\pi\) | ||||
0.726677 | + | 0.686979i | \(0.241064\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 188.511i | 0.802176i | ||||||||
\(236\) | −135.312 | −0.573357 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 91.0191 | 0.382433 | ||||||||
\(239\) | −149.374 | −0.624997 | −0.312499 | − | 0.949918i | \(-0.601166\pi\) | ||||
−0.312499 | + | 0.949918i | \(0.601166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 133.030i | − | 0.551991i | −0.961159 | − | 0.275995i | \(-0.910993\pi\) | ||
0.961159 | − | 0.275995i | \(-0.0890074\pi\) | |||||||
\(242\) | 89.9601 | 0.371736 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 70.3242i | 0.288214i | ||||||||
\(245\) | 52.4686i | 0.214158i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 64.0848i | 0.259453i | ||||||||
\(248\) | −159.826 | −0.644461 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | − | 376.920i | − | 1.50167i | −0.660489 | − | 0.750836i | \(-0.729651\pi\) | ||
0.660489 | − | 0.750836i | \(-0.270349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(0.644970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −339.975 | −1.31264 | ||||||||
\(260\) | 11.8098i | 0.0454224i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.14690 | −0.0196447 | ||||||||
\(263\) | − | 2.43654i | − | 0.00926441i | −0.999989 | − | 0.00463221i | \(-0.998526\pi\) | ||
0.999989 | − | 0.00463221i | \(-0.00147448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.6515 | 0.100572 | ||||||||
\(266\) | −292.149 | −1.09830 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 88.1319i | − | 0.328850i | ||||||
\(269\) | 311.337 | 1.15739 | 0.578694 | − | 0.815545i | \(-0.303563\pi\) | ||||
0.578694 | + | 0.815545i | \(0.303563\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 13.7148i | − | 0.0500541i | ||||||
\(275\) | 37.8776i | 0.137737i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −182.267 | −0.658004 | −0.329002 | − | 0.944329i | \(-0.606712\pi\) | ||||
−0.329002 | + | 0.944329i | \(0.606712\pi\) | |||||||
\(278\) | 11.3913 | 0.0409758 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −53.8385 | −0.192280 | ||||||||
\(281\) | 4.60502i | 0.0163880i | 0.999966 | + | 0.00819398i | \(0.00260825\pi\) | ||||
−0.999966 | + | 0.00819398i | \(0.997392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 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 | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 231.838 | 0.802207 | ||||||||
\(290\) | − | 100.723i | − | 0.347320i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −174.830 | −0.598733 | ||||||||
\(293\) | 336.114i | 1.14715i | 0.819154 | + | 0.573574i | \(0.194443\pi\) | ||||
−0.819154 | + | 0.573574i | \(0.805557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 151.284i | 0.512826i | ||||||||
\(296\) | − | 112.961i | − | 0.381625i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 97.0703i | − | 0.319310i | ||||||
\(305\) | 78.6248 | 0.257786 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −457.934 | −1.49164 | −0.745821 | − | 0.666147i | \(-0.767943\pi\) | ||||
−0.745821 | + | 0.666147i | \(0.767943\pi\) | |||||||
\(308\) | −128.975 | −0.418750 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 178.691i | 0.576423i | ||||||||
\(311\) | 455.620 | 1.46502 | 0.732508 | − | 0.680758i | \(-0.238350\pi\) | ||||
0.732508 | + | 0.680758i | \(0.238350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | \(0.291479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 241.291i | − | 0.756397i | ||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 201.934 | − | 189.447i | 0.627124 | − | 0.588346i | ||||
\(323\) | 183.477 | 0.568039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.2038 | 0.0406271 | ||||||||
\(326\) | 154.098 | 0.472693 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −102.019 | −0.305446 | ||||||||
\(335\) | −98.5345 | −0.294133 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 193.563i | − | 0.574371i | −0.957875 | − | 0.287185i | \(-0.907280\pi\) | ||
0.957875 | − | 0.287185i | \(-0.0927196\pi\) | |||||||
\(338\) | −229.140 | −0.677929 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.8119 | 0.0994467 | ||||||||
\(341\) | 428.071i | 1.25534i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 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 | \(0.376564\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 229.831 | 0.658543 | 0.329271 | − | 0.944235i | \(-0.393197\pi\) | ||||
0.329271 | + | 0.944235i | \(0.393197\pi\) | |||||||
\(350\) | 60.1933i | 0.171981i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 42.8536i | − | 0.121743i | ||||||
\(353\) | −367.482 | −1.04103 | −0.520513 | − | 0.853854i | \(-0.674259\pi\) | ||||
−0.520513 | + | 0.853854i | \(0.674259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.8249i | 0.0558448i | ||||||||
\(356\) | − | 127.450i | − | 0.358007i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −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 | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 44.9595i | 0.123515i | ||||||||
\(365\) | 195.466i | 0.535523i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −126.294 | −0.341336 | ||||||||
\(371\) | 101.461 | 0.273480 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 295.837i | 0.780573i | 0.920693 | + | 0.390287i | \(0.127624\pi\) | ||||
−0.920693 | + | 0.390287i | \(0.872376\pi\) | |||||||
\(380\) | −108.528 | −0.285600 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 244.304i | 0.639541i | ||||||||
\(383\) | 566.033i | 1.47789i | 0.673765 | + | 0.738946i | \(0.264676\pi\) | ||||
−0.673765 | + | 0.738946i | \(0.735324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 144.199i | 0.374542i | ||||||||
\(386\) | 192.970 | 0.499921 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 383.380 | 0.973045 | ||||||||
\(395\) | 344.840 | 0.873012 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −298.788 | −0.752616 | −0.376308 | − | 0.926495i | \(-0.622806\pi\) | ||||
−0.376308 | + | 0.926495i | \(0.622806\pi\) | |||||||
\(398\) | − | 363.866i | − | 0.914236i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 785.114i | − | 1.95789i | −0.204121 | − | 0.978946i | \(-0.565433\pi\) | ||
0.204121 | − | 0.978946i | \(-0.434567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 149.222 | 0.370277 | ||||||||
\(404\) | −55.4204 | −0.137179 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 383.447i | − | 0.944452i | ||||||
\(407\) | −302.550 | −0.743365 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 358.186 | 0.875761 | 0.437881 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437881 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(410\) | − | 134.621i | − | 0.328345i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 267.084i | 0.648261i | ||||||||
\(413\) | 575.930i | 1.39450i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −316.722 | −0.763184 | ||||||||
\(416\) | −14.9384 | −0.0359096 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −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 | \(-0.634410\pi\) | ||
0.409826 | − | 0.912164i | \(-0.365590\pi\) | |||||||
\(422\) | 76.6425 | 0.181617 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 33.7118i | 0.0795089i | ||||||||
\(425\) | − | 37.8028i | − | 0.0889479i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 299.321 | 0.700987 | ||||||||
\(428\) | 100.618i | 0.235089i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −65.0546 | −0.151290 | ||||||||
\(431\) | − | 333.122i | − | 0.772905i | −0.922309 | − | 0.386453i | \(-0.873700\pi\) | ||
0.922309 | − | 0.386453i | \(-0.126300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −303.939 | −0.692344 | −0.346172 | − | 0.938171i | \(-0.612519\pi\) | ||||
−0.346172 | + | 0.938171i | \(0.612519\pi\) | |||||||
\(440\) | −47.9118 | −0.108891 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 28.2357i | − | 0.0638816i | ||||||
\(443\) | −637.145 | −1.43825 | −0.719125 | − | 0.694881i | \(-0.755457\pi\) | ||||
−0.719125 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −142.494 | −0.320211 | ||||||||
\(446\) | 147.942 | 0.331708 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 68.1009i | − | 0.152011i | ||||||
\(449\) | −88.9331 | −0.198069 | −0.0990346 | − | 0.995084i | \(-0.531575\pi\) | ||||
−0.0990346 | + | 0.995084i | \(0.531575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 322.498i | − | 0.715073i | ||||||
\(452\) | 172.606i | 0.381871i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 283.527i | 0.624509i | ||||||||
\(455\) | 50.2663 | 0.110475 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 377.669i | 0.826410i | 0.910638 | + | 0.413205i | \(0.135591\pi\) | ||||
−0.910638 | + | 0.413205i | \(0.864409\pi\) | |||||||
\(458\) | − | 31.2142i | − | 0.0681534i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 75.0147 | − | 70.3761i | 0.163075 | − | 0.152992i | ||||
\(461\) | 585.070 | 1.26913 | 0.634566 | − | 0.772869i | \(-0.281179\pi\) | ||||
0.634566 | + | 0.772869i | \(0.281179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −225.877 | −0.487854 | −0.243927 | − | 0.969794i | \(-0.578436\pi\) | ||||
−0.243927 | + | 0.969794i | \(0.578436\pi\) | |||||||
\(464\) | 127.405 | 0.274580 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 478.897 | 1.02768 | ||||||||
\(467\) | 702.984i | 1.50532i | 0.658410 | + | 0.752659i | \(0.271229\pi\) | ||||
−0.658410 | + | 0.752659i | \(0.728771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −375.117 | −0.799822 | ||||||||
\(470\) | 266.595i | 0.567224i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −191.360 | −0.405424 | ||||||||
\(473\) | −155.844 | −0.329480 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 121.338i | 0.255448i | ||||||||
\(476\) | 128.720 | 0.270421 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −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 | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 127.223 | 0.262857 | ||||||||
\(485\) | −320.479 | −0.660781 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 205.957 | 0.422909 | 0.211454 | − | 0.977388i | \(-0.432180\pi\) | ||||
0.211454 | + | 0.977388i | \(0.432180\pi\) | |||||||
\(488\) | 99.4534i | 0.203798i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 74.2018i | 0.151432i | ||||||||
\(491\) | 192.478 | 0.392012 | 0.196006 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196006 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 240.814i | 0.488467i | ||||||||
\(494\) | 90.6296i | 0.183461i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −226.028 | −0.455703 | ||||||||
\(497\) | 75.4726i | 0.151856i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 887.386 | 1.77833 | 0.889164 | − | 0.457589i | \(-0.151287\pi\) | ||||
0.889164 | + | 0.457589i | \(0.151287\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 533.045i | − | 1.06184i | ||||||
\(503\) | 330.810i | 0.657673i | 0.944387 | + | 0.328837i | \(0.106657\pi\) | ||||
−0.944387 | + | 0.328837i | \(0.893343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 61.9619i | 0.122697i | ||||||||
\(506\) | 179.704 | − | 168.592i | 0.355147 | − | 0.333187i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.0270 | −0.0433603 | ||||||||
\(509\) | 407.928 | 0.801430 | 0.400715 | − | 0.916203i | \(-0.368762\pi\) | ||||
0.400715 | + | 0.916203i | \(0.368762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 744.131i | 1.45622i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −319.733 | −0.622048 | ||||||||
\(515\) | 298.609 | 0.579822 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 638.654i | 1.23531i | ||||||||
\(518\) | −480.797 | −0.928180 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.7016i | 0.0321185i | ||||||||
\(521\) | 458.780i | 0.880576i | 0.897857 | + | 0.440288i | \(0.145124\pi\) | ||||
−0.897857 | + | 0.440288i | \(0.854876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 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 | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33.7199 | + | 527.924i | −0.0637427 | + | 0.997966i | ||||
\(530\) | 37.6909 | 0.0711149 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −413.161 | −0.776619 | ||||||||
\(533\) | −112.420 | −0.210919 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 112.495 | 0.210270 | ||||||||
\(536\) | − | 124.637i | − | 0.232532i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 42.7690i | 0.0786195i | ||||||||
\(545\) | −288.047 | −0.528527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 123.784 | 0.226296 | 0.113148 | − | 0.993578i | \(-0.463907\pi\) | ||||
0.113148 | + | 0.993578i | \(0.463907\pi\) | |||||||
\(548\) | − | 19.3957i | − | 0.0353936i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 53.5671i | 0.0973946i | ||||||||
\(551\) | − | 772.955i | − | 1.40282i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(-0.929039\pi\) | ||
0.975254 | − | 0.221088i | \(-0.0709608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.3259i | 0.0971840i | ||||||||
\(560\) | −76.1392 | −0.135963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.51248i | 0.0115880i | ||||||||
\(563\) | − | 574.776i | − | 1.02092i | −0.859902 | − | 0.510458i | \(-0.829476\pi\) | ||
0.859902 | − | 0.510458i | \(-0.170524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 192.979 | 0.341556 | ||||||||
\(566\) | − | 470.787i | − | 0.831780i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −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 | \(-0.881111\pi\) | ||
0.931056 | − | 0.364876i | \(-0.118889\pi\) | |||||||
\(572\) | 40.0103i | 0.0699480i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 512.498i | − | 0.892854i | ||||||
\(575\) | −78.6829 | − | 83.8689i | −0.136840 | − | 0.145859i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −282.647 | −0.489856 | −0.244928 | − | 0.969541i | \(-0.578764\pi\) | ||||
−0.244928 | + | 0.969541i | \(0.578764\pi\) | |||||||
\(578\) | 327.868 | 0.567246 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 142.443i | − | 0.245592i | ||||||
\(581\) | −1205.75 | −2.07529 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.454259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1371.29i | 2.32817i | ||||||||
\(590\) | 213.947i | 0.362623i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 159.751i | − | 0.269850i | ||||||
\(593\) | 419.364 | 0.707191 | 0.353595 | − | 0.935398i | \(-0.384959\pi\) | ||||
0.353595 | + | 0.935398i | \(0.384959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 143.914i | − | 0.241872i | ||||||
\(596\) | − | 288.124i | − | 0.483430i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −58.7698 | − | 62.6433i | −0.0982773 | − | 0.104755i | ||||
\(599\) | 519.774 | 0.867736 | 0.433868 | − | 0.900977i | \(-0.357148\pi\) | ||||
0.433868 | + | 0.900977i | \(0.357148\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −219.913 | −0.364094 | ||||||||
\(605\) | − | 142.239i | − | 0.235107i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 890.673 | 1.46734 | 0.733668 | − | 0.679508i | \(-0.237807\pi\) | ||||
0.733668 | + | 0.679508i | \(0.237807\pi\) | |||||||
\(608\) | − | 137.278i | − | 0.225786i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 111.192 | 0.182282 | ||||||||
\(611\) | 222.629 | 0.364368 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 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 | \(-0.959343\pi\) | ||
0.991854 | − | 0.127380i | \(-0.0406568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 462.293i | 0.746838i | 0.927663 | + | 0.373419i | \(0.121815\pi\) | ||||
−0.927663 | + | 0.373419i | \(0.878185\pi\) | |||||||
\(620\) | 252.707i | 0.407593i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 644.344 | 1.03592 | ||||||||
\(623\) | −542.468 | −0.870735 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 833.471i | 1.33142i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 49.6416i | − | 0.0790471i | ||||||
\(629\) | 301.952 | 0.480051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 411.630i | 0.652345i | 0.945310 | + | 0.326173i | \(0.105759\pi\) | ||||
−0.945310 | + | 0.326173i | \(0.894241\pi\) | |||||||
\(632\) | 436.191i | 0.690176i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 546.242 | 0.861581 | ||||||||
\(635\) | 24.6270i | 0.0387827i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 61.9645 | 0.0972756 | ||||||||
\(638\) | − | 341.236i | − | 0.534853i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | 251.089i | 0.391715i | 0.980632 | + | 0.195857i | \(0.0627490\pi\) | ||||
−0.980632 | + | 0.195857i | \(0.937251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | \(0.390251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 512.530i | 0.789723i | ||||||||
\(650\) | 18.6730 | 0.0287277 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 217.927 | 0.334244 | ||||||||
\(653\) | 94.4001 | 0.144564 | 0.0722819 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722819 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.13797i | 0.0124244i | ||||||||
\(656\) | 170.284 | 0.259580 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(-0.854959\pi\) | ||
0.897970 | − | 0.440056i | \(-0.145041\pi\) | |||||||
\(662\) | 312.134 | 0.471501 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 400.625i | − | 0.603350i | ||||||
\(665\) | 461.928i | 0.694629i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 501.231 | + | 534.267i | 0.751471 | + | 0.801001i | ||||
\(668\) | −144.277 | −0.215983 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −139.349 | −0.207983 | ||||||||
\(671\) | 266.371 | 0.396977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −831.173 | −1.23503 | −0.617513 | − | 0.786560i | \(-0.711860\pi\) | ||||
−0.617513 | + | 0.786560i | \(0.711860\pi\) | |||||||
\(674\) | − | 273.739i | − | 0.406142i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −324.053 | −0.479368 | ||||||||
\(677\) | 106.706i | 0.157616i | 0.996890 | + | 0.0788079i | \(0.0251114\pi\) | ||||
−0.996890 | + | 0.0788079i | \(0.974889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1220.05 | −1.79683 | ||||||||
\(680\) | 47.8172 | 0.0703195 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 605.384i | 0.887660i | ||||||||
\(683\) | −380.675 | −0.557357 | −0.278678 | − | 0.960385i | \(-0.589896\pi\) | ||||
−0.278678 | + | 0.960385i | \(0.589896\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6851 | −0.0316570 | ||||||||
\(686\) | − | 307.411i | − | 0.448121i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 371.130 | 0.534769 | ||||||||
\(695\) | − | 18.0112i | − | 0.0259154i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 321.861i | 0.461781i | ||||||||
\(698\) | 325.031 | 0.465660 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 85.1262i | 0.121609i | ||||||||
\(701\) | 112.754i | 0.160848i | 0.996761 | + | 0.0804239i | \(0.0256274\pi\) | ||||
−0.996761 | + | 0.0804239i | \(0.974373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −969.193 | −1.37865 | ||||||||
\(704\) | − | 60.6042i | − | 0.0860855i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −519.698 | −0.736116 | ||||||||
\(707\) | 235.887i | 0.333644i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 465.481i | 0.656531i | 0.944585 | + | 0.328266i | \(0.106464\pi\) | ||||
−0.944585 | + | 0.328266i | \(0.893536\pi\) | |||||||
\(710\) | 28.0367i | 0.0394883i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 180.242i | − | 0.253149i | ||||||
\(713\) | −889.229 | − | 947.838i | −1.24717 | − | 1.32937i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.7328 | 0.0625634 | ||||||||
\(716\) | −414.116 | −0.578375 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 339.370i | 0.472660i | ||||||||
\(719\) | 347.913 | 0.483885 | 0.241943 | − | 0.970291i | \(-0.422215\pi\) | ||||
0.241943 | + | 0.970291i | \(0.422215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1136.79 | 1.57669 | ||||||||
\(722\) | −322.321 | −0.446428 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 662.276i | − | 0.914746i | ||||||
\(725\) | −159.257 | −0.219664 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 88.3077i | − | 0.121469i | −0.998154 | − | 0.0607343i | \(-0.980656\pi\) | ||
0.998154 | − | 0.0607343i | \(-0.0193442\pi\) | |||||||
\(728\) | 63.5824i | 0.0873385i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 276.431i | 0.378672i | ||||||||
\(731\) | 155.536 | 0.212772 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −416.763 | −0.563955 | −0.281978 | − | 0.959421i | \(-0.590990\pi\) | ||||
−0.281978 | + | 0.959421i | \(0.590990\pi\) | |||||||
\(740\) | −178.607 | −0.241361 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 143.488 | 0.193380 | ||||||||
\(743\) | 633.469i | 0.852583i | 0.904586 | + | 0.426291i | \(0.140180\pi\) | ||||
−0.904586 | + | 0.426291i | \(0.859820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −322.132 | −0.432393 | ||||||||
\(746\) | 772.597i | 1.03565i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 114.551 | 0.153142 | ||||||||
\(749\) | 428.262 | 0.571779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1282.52i | − | 1.70775i | −0.520475 | − | 0.853877i | \(-0.674245\pi\) | ||
0.520475 | − | 0.853877i | \(-0.325755\pi\) | |||||||
\(752\) | −337.219 | −0.448430 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −118.952 | −0.157761 | ||||||||
\(755\) | 245.870i | 0.325655i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1233.64i | − | 1.62964i | −0.579716 | − | 0.814819i | \(-0.696836\pi\) | ||
0.579716 | − | 0.814819i | \(-0.303164\pi\) | |||||||
\(758\) | 418.377i | 0.551949i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −153.482 | −0.201950 | ||||||||
\(761\) | 262.559 | 0.345018 | 0.172509 | − | 0.985008i | \(-0.444813\pi\) | ||||
0.172509 | + | 0.985008i | \(0.444813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1096.58 | −1.43720 | ||||||||
\(764\) | 345.499i | 0.452223i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 800.491i | 1.04503i | ||||||||
\(767\) | 178.663 | 0.232938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 801.510i | 1.04228i | 0.853473 | + | 0.521138i | \(0.174492\pi\) | ||||
−0.853473 | + | 0.521138i | \(0.825508\pi\) | |||||||
\(770\) | 203.928i | 0.264841i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 272.900 | 0.353498 | ||||||||
\(773\) | 1143.79i | 1.47967i | 0.672786 | + | 0.739837i | \(0.265097\pi\) | ||||
−0.672786 | + | 0.739837i | \(0.734903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 282.536 | 0.364562 | ||||||||
\(776\) | − | 405.377i | − | 0.522393i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −93.8587 | −0.119718 | ||||||||
\(785\) | −55.5010 | −0.0707019 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 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 | 0 | ||||||||
\(790\) | 487.677 | 0.617312 | ||||||||
\(791\) | 734.663 | 0.928777 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 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 | \(0.0462949\pi\) | ||||
−0.989442 | + | 0.144927i | \(0.953705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 637.393i | − | 0.797738i | ||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1110.32i | − | 1.38444i | ||||||
\(803\) | 662.215i | 0.824676i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −299.543 | − | 319.286i | −0.372103 | − | 0.396628i | ||||
\(806\) | 211.031 | 0.261825 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −78.3763 | −0.0970004 | ||||||||
\(809\) | 165.201 | 0.204204 | 0.102102 | − | 0.994774i | \(-0.467443\pi\) | ||||
0.102102 | + | 0.994774i | \(0.467443\pi\) | |||||||
\(810\) | 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 | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −427.870 | −0.525638 | ||||||||
\(815\) | − | 243.650i | − | 0.298957i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −499.234 | −0.611058 | ||||||||
\(818\) | 506.552 | 0.619257 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 190.384i | − | 0.232175i | ||||||
\(821\) | 1389.82 | 1.69284 | 0.846421 | − | 0.532514i | \(-0.178753\pi\) | ||||
0.846421 | + | 0.532514i | \(0.178753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 948.001 | 1.15188 | 0.575942 | − | 0.817490i | \(-0.304635\pi\) | ||||
0.575942 | + | 0.817490i | \(0.304635\pi\) | |||||||
\(824\) | 377.713i | 0.458390i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 814.489i | 0.986064i | ||||||||
\(827\) | 1177.54i | 1.42387i | 0.702245 | + | 0.711935i | \(0.252181\pi\) | ||||
−0.702245 | + | 0.711935i | \(0.747819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1278.78 | −1.54256 | −0.771279 | − | 0.636497i | \(-0.780383\pi\) | ||||
−0.771279 | + | 0.636497i | \(0.780383\pi\) | |||||||
\(830\) | −447.912 | −0.539653 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.1261 | −0.0253919 | ||||||||
\(833\) | − | 177.406i | − | 0.212973i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 161.306i | 0.193181i | ||||||||
\(836\) | −367.679 | −0.439808 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 108.389 | 0.128423 | ||||||||
\(845\) | 362.302i | 0.428760i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 541.500i | − | 0.639315i | ||||||
\(848\) | 47.6757i | 0.0562213i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 53.4613i | − | 0.0628956i | ||||||
\(851\) | 669.908 | − | 628.484i | 0.787201 | − | 0.738524i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 812.996 | 0.953102 | 0.476551 | − | 0.879147i | \(-0.341887\pi\) | ||||
0.476551 | + | 0.879147i | \(0.341887\pi\) | |||||||
\(854\) | 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 | \(0.311025\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −383.654 | −0.446628 | −0.223314 | − | 0.974747i | \(-0.571688\pi\) | ||||
−0.223314 | + | 0.974747i | \(0.571688\pi\) | |||||||
\(860\) | −92.0011 | −0.106978 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 471.106i | − | 0.546526i | ||||||
\(863\) | −1017.48 | −1.17900 | −0.589502 | − | 0.807767i | \(-0.700676\pi\) | ||||
−0.589502 | + | 0.807767i | \(0.700676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 335.582i | − | 0.387956i | ||||||
\(866\) | − | 10.6029i | − | 0.0122436i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 962.047i | 1.10835i | ||||||||
\(869\) | 1168.27 | 1.34439 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 116.368i | 0.133602i | ||||||||
\(872\) | − | 364.354i | − | 0.417837i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 575.669 | − | 540.072i | 0.658660 | − | 0.617932i | ||||
\(875\) | 95.1740 | 0.108770 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1443.83 | 1.64633 | 0.823163 | − | 0.567806i | \(-0.192207\pi\) | ||||
0.823163 | + | 0.567806i | \(0.192207\pi\) | |||||||
\(878\) | −429.835 | −0.489561 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −67.7576 | −0.0769972 | ||||||||
\(881\) | − | 894.988i | − | 1.01588i | −0.861393 | − | 0.507939i | \(-0.830408\pi\) | ||
0.861393 | − | 0.507939i | \(-0.169592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −870.115 | −0.985407 | −0.492704 | − | 0.870197i | \(-0.663991\pi\) | ||||
−0.492704 | + | 0.870197i | \(0.663991\pi\) | |||||||
\(884\) | − | 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 | \(0.403553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 93.7539i | 0.105460i | ||||||||
\(890\) | −201.517 | −0.226423 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 209.221 | 0.234553 | ||||||||
\(893\) | 2045.87i | 2.29101i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 462.996i | 0.517314i | ||||||||
\(896\) | − | 96.3093i | − | 0.107488i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −125.770 | −0.140056 | ||||||||
\(899\) | −1799.83 | −2.00203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.1138 | −0.100015 | ||||||||
\(902\) | − | 456.081i | − | 0.505633i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 244.101i | 0.270023i | ||||||||
\(905\) | −740.447 | −0.818173 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 691.482i | − | 0.762384i | −0.924496 | − | 0.381192i | \(-0.875514\pi\) | ||
0.924496 | − | 0.381192i | \(-0.124486\pi\) | |||||||
\(908\) | 400.968i | 0.441595i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 71.0873 | 0.0781179 | ||||||||
\(911\) | − | 1794.49i | − | 1.96980i | −0.173115 | − | 0.984902i | \(-0.555383\pi\) | ||
0.173115 | − | 0.984902i | \(-0.444617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1073.01 | −1.17526 | ||||||||
\(914\) | 534.105i | 0.584360i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 44.1436i | − | 0.0481917i | ||||||
\(917\) | 30.9809i | 0.0337851i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 428.705i | − | 0.466491i | −0.972418 | − | 0.233245i | \(-0.925065\pi\) | ||
0.972418 | − | 0.233245i | \(-0.0749345\pi\) | |||||||
\(920\) | 106.087 | − | 99.5269i | 0.115312 | − | 0.108181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 827.413 | 0.897411 | ||||||||
\(923\) | 23.4129 | 0.0253661 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 199.689i | 0.215880i | ||||||||
\(926\) | −319.438 | −0.344965 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 180.178 | 0.194158 | ||||||||
\(929\) | −1577.01 | −1.69754 | −0.848768 | − | 0.528766i | \(-0.822655\pi\) | ||||
−0.848768 | + | 0.528766i | \(0.822655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 569.431i | 0.611633i | ||||||||
\(932\) | 677.263 | 0.726677 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 994.169i | 1.06442i | ||||||||
\(935\) | − | 128.071i | − | 0.136975i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 141.317i | − | 0.150818i | −0.997153 | − | 0.0754091i | \(-0.975974\pi\) | ||
0.997153 | − | 0.0754091i | \(-0.0240263\pi\) | |||||||
\(938\) | −530.495 | −0.565560 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 377.023i | 0.401088i | ||||||||
\(941\) | 1506.21i | 1.60065i | 0.599566 | + | 0.800325i | \(0.295340\pi\) | ||||
−0.599566 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(0.850842\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 230.842 | 0.243248 | ||||||||
\(950\) | 171.598i | 0.180629i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 182.038 | 0.191217 | ||||||||
\(953\) | 990.482i | 1.03933i | 0.854370 | + | 0.519665i | \(0.173943\pi\) | ||||
−0.854370 | + | 0.519665i | \(0.826057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 386.279 | 0.404481 | ||||||||
\(956\) | −298.749 | −0.312499 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 412.534i | 0.430620i | ||||||||
\(959\) | −82.5541 | −0.0860836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2232.05 | 2.32264 | ||||||||
\(962\) | 149.151i | 0.155043i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 266.059i | − | 0.275995i | ||||||
\(965\) | − | 305.112i | − | 0.316178i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1528.09 | 1.58024 | 0.790118 | − | 0.612954i | \(-0.210019\pi\) | ||||
0.790118 | + | 0.612954i | \(0.210019\pi\) | |||||||
\(968\) | 179.920 | 0.185868 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −453.225 | −0.467243 | ||||||||
\(971\) | − | 616.239i | − | 0.634643i | −0.948318 | − | 0.317322i | \(-0.897217\pi\) | ||
0.948318 | − | 0.317322i | \(-0.102783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 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 | \(-0.747200\pi\) | ||
0.700859 | − | 0.713299i | \(-0.252800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −482.752 | −0.493107 | ||||||||
\(980\) | 104.937i | 0.107079i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 272.205 | 0.277195 | ||||||||
\(983\) | − | 1033.22i | − | 1.05109i | −0.850767 | − | 0.525543i | \(-0.823862\pi\) | ||
0.850767 | − | 0.525543i | \(-0.176138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 606.176i | − | 0.615407i | ||||||
\(986\) | 340.563i | 0.345398i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 106.734i | 0.107379i | ||||||||
\(995\) | −575.323 | −0.578214 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −718.650 | −0.720812 | −0.360406 | − | 0.932795i | \(-0.617362\pi\) | ||||
−0.360406 | + | 0.932795i | \(0.617362\pi\) | |||||||
\(998\) | 1254.95 | 1.25747 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.3.c.a.91.9 | 16 | ||
3.2 | odd | 2 | 230.3.d.a.91.4 | yes | 16 | ||
12.11 | even | 2 | 1840.3.k.d.321.10 | 16 | |||
15.2 | even | 4 | 1150.3.c.c.1149.7 | 32 | |||
15.8 | even | 4 | 1150.3.c.c.1149.26 | 32 | |||
15.14 | odd | 2 | 1150.3.d.b.551.14 | 16 | |||
23.22 | odd | 2 | inner | 2070.3.c.a.91.16 | 16 | ||
69.68 | even | 2 | 230.3.d.a.91.3 | ✓ | 16 | ||
276.275 | odd | 2 | 1840.3.k.d.321.9 | 16 | |||
345.68 | odd | 4 | 1150.3.c.c.1149.8 | 32 | |||
345.137 | odd | 4 | 1150.3.c.c.1149.25 | 32 | |||
345.344 | even | 2 | 1150.3.d.b.551.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.3 | ✓ | 16 | 69.68 | even | 2 | ||
230.3.d.a.91.4 | yes | 16 | 3.2 | odd | 2 | ||
1150.3.c.c.1149.7 | 32 | 15.2 | even | 4 | |||
1150.3.c.c.1149.8 | 32 | 345.68 | odd | 4 | |||
1150.3.c.c.1149.25 | 32 | 345.137 | odd | 4 | |||
1150.3.c.c.1149.26 | 32 | 15.8 | even | 4 | |||
1150.3.d.b.551.13 | 16 | 345.344 | even | 2 | |||
1150.3.d.b.551.14 | 16 | 15.14 | odd | 2 | |||
1840.3.k.d.321.9 | 16 | 276.275 | odd | 2 | |||
1840.3.k.d.321.10 | 16 | 12.11 | even | 2 | |||
2070.3.c.a.91.9 | 16 | 1.1 | even | 1 | trivial | ||
2070.3.c.a.91.16 | 16 | 23.22 | odd | 2 | inner |