Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(305,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.305");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 156x^{10} + 8721x^{8} + 208784x^{6} + 2024760x^{4} + 7117056x^{2} + 6533136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.12 | ||
Root | \(7.53519i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.305 |
Dual form | 684.3.e.a.305.1 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.53519i | 1.50704i | 0.657426 | + | 0.753519i | \(0.271645\pi\) | ||||
−0.657426 | + | 0.753519i | \(0.728355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.18161 | 0.740230 | 0.370115 | − | 0.928986i | \(-0.379318\pi\) | ||||
0.370115 | + | 0.928986i | \(0.379318\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.8851i | 1.89865i | 0.314301 | + | 0.949323i | \(0.398230\pi\) | ||||
−0.314301 | + | 0.949323i | \(0.601770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.35632 | 0.412024 | 0.206012 | − | 0.978549i | \(-0.433951\pi\) | ||||
0.206012 | + | 0.978549i | \(0.433951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 8.47306i | − 0.498415i | −0.968450 | − | 0.249208i | \(-0.919830\pi\) | ||||
0.968450 | − | 0.249208i | \(-0.0801701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35890 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 22.0052i | − 0.956746i | −0.878157 | − | 0.478373i | \(-0.841227\pi\) | ||||
0.878157 | − | 0.478373i | \(-0.158773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −31.7791 | −1.27116 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.4800i | 1.18897i | 0.804108 | + | 0.594483i | \(0.202643\pi\) | ||||
−0.804108 | + | 0.594483i | \(0.797357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.1551 | −1.13404 | −0.567018 | − | 0.823705i | \(-0.691903\pi\) | ||||
−0.567018 | + | 0.823705i | \(0.691903\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39.0444i | 1.11555i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.3168 | 0.413967 | 0.206984 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206984 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 19.8541i | − 0.484247i | −0.970245 | − | 0.242123i | \(-0.922156\pi\) | ||||
0.970245 | − | 0.242123i | \(-0.0778439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.9768 | 0.580855 | 0.290427 | − | 0.956897i | \(-0.406203\pi\) | ||||
0.290427 | + | 0.956897i | \(0.406203\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0976i | 0.236119i | 0.993007 | + | 0.118060i | \(0.0376674\pi\) | ||||
−0.993007 | + | 0.118060i | \(0.962333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −22.1509 | −0.452060 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 90.7505i | 1.71227i | 0.516749 | + | 0.856137i | \(0.327142\pi\) | ||||
−0.516749 | + | 0.856137i | \(0.672858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −157.373 | −2.86133 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 51.2576i | − 0.868773i | −0.900727 | − | 0.434387i | \(-0.856965\pi\) | ||||
0.900727 | − | 0.434387i | \(-0.143035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47.6464 | −0.781088 | −0.390544 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390544 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 40.3609i | 0.620936i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.34056 | 0.0647844 | 0.0323922 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323922 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 30.5108i | 0.429730i | 0.976644 | + | 0.214865i | \(0.0689311\pi\) | ||||
−0.976644 | + | 0.214865i | \(0.931069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 79.8288 | 1.09354 | 0.546772 | − | 0.837281i | \(-0.315856\pi\) | ||||
0.546772 | + | 0.837281i | \(0.315856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 108.219i | 1.40544i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −152.066 | −1.92488 | −0.962442 | − | 0.271486i | \(-0.912485\pi\) | ||||
−0.962442 | + | 0.271486i | \(0.912485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 22.6822i | − 0.273279i | −0.990621 | − | 0.136639i | \(-0.956370\pi\) | ||||
0.990621 | − | 0.136639i | \(-0.0436302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63.8461 | 0.751130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 134.723i | 1.51375i | 0.653562 | + | 0.756873i | \(0.273274\pi\) | ||||
−0.653562 | + | 0.756873i | \(0.726726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7543 | 0.304993 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 32.8451i | − 0.345738i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −32.4684 | −0.334726 | −0.167363 | − | 0.985895i | \(-0.553525\pi\) | ||||
−0.167363 | + | 0.985895i | \(0.553525\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 20.3927i | − 0.201908i | −0.994891 | − | 0.100954i | \(-0.967811\pi\) | ||||
0.994891 | − | 0.100954i | \(-0.0321895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 146.777 | 1.42502 | 0.712510 | − | 0.701662i | \(-0.247558\pi\) | ||||
0.712510 | + | 0.701662i | \(0.247558\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 103.067i | 0.963242i | 0.876380 | + | 0.481621i | \(0.159952\pi\) | ||||
−0.876380 | + | 0.481621i | \(0.840048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 141.461 | 1.29781 | 0.648906 | − | 0.760869i | \(-0.275227\pi\) | ||||
0.648906 | + | 0.760869i | \(0.275227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 148.052i | 1.31020i | 0.755544 | + | 0.655098i | \(0.227373\pi\) | ||||
−0.755544 | + | 0.655098i | \(0.772627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 165.813 | 1.44185 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 43.9041i | − 0.368942i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −315.188 | −2.60486 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 51.0814i | − 0.408652i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 222.419 | 1.75133 | 0.875666 | − | 0.482918i | \(-0.160423\pi\) | ||||
0.875666 | + | 0.482918i | \(0.160423\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 171.157i | − 1.30654i | −0.757124 | − | 0.653271i | \(-0.773396\pi\) | ||||
0.757124 | − | 0.653271i | \(-0.226604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.5861 | −0.169820 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 222.459i | − 1.62379i | −0.583805 | − | 0.811894i | \(-0.698437\pi\) | ||||
0.583805 | − | 0.811894i | \(-0.301563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.22356 | −0.0303853 | −0.0151927 | − | 0.999885i | \(-0.504836\pi\) | ||||
−0.0151927 | + | 0.999885i | \(0.504836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 111.867i | 0.782289i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −259.814 | −1.79182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 38.3311i | 0.257255i | 0.991693 | + | 0.128628i | \(0.0410572\pi\) | ||||
−0.991693 | + | 0.128628i | \(0.958943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 52.5136 | 0.347772 | 0.173886 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173886 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 264.901i | − 1.70904i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −308.922 | −1.96765 | −0.983827 | − | 0.179120i | \(-0.942675\pi\) | ||||
−0.983827 | + | 0.179120i | \(0.942675\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 114.022i | − 0.708212i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 67.5587 | 0.414471 | 0.207235 | − | 0.978291i | \(-0.433553\pi\) | ||||
0.207235 | + | 0.978291i | \(0.433553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 279.364i | − 1.67284i | −0.548092 | − | 0.836418i | \(-0.684646\pi\) | ||||
0.548092 | − | 0.836418i | \(-0.315354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −140.310 | −0.830236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 75.4624i | 0.436199i | 0.975927 | + | 0.218100i | \(0.0699857\pi\) | ||||
−0.975927 | + | 0.218100i | \(0.930014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −164.667 | −0.940952 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66.5626i | 0.371858i | 0.982563 | + | 0.185929i | \(0.0595294\pi\) | ||||
−0.982563 | + | 0.185929i | \(0.940471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 107.560 | 0.594253 | 0.297127 | − | 0.954838i | \(-0.403972\pi\) | ||||
0.297127 | + | 0.954838i | \(0.403972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 115.415i | 0.623864i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 176.961 | 0.946314 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 81.2713i | − 0.425504i | −0.977106 | − | 0.212752i | \(-0.931757\pi\) | ||||
0.977106 | − | 0.212752i | \(-0.0682427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 181.379 | 0.939787 | 0.469893 | − | 0.882723i | \(-0.344292\pi\) | ||||
0.469893 | + | 0.882723i | \(0.344292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 170.455i | − 0.865254i | −0.901573 | − | 0.432627i | \(-0.857587\pi\) | ||||
0.901573 | − | 0.432627i | \(-0.142413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 174.952 | 0.879158 | 0.439579 | − | 0.898204i | \(-0.355128\pi\) | ||||
0.439579 | + | 0.898204i | \(0.355128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 178.662i | 0.880109i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 149.605 | 0.729778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 91.0361i | − 0.435579i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 365.354 | 1.73154 | 0.865768 | − | 0.500445i | \(-0.166830\pi\) | ||||
0.865768 | + | 0.500445i | \(0.166830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 188.205i | 0.875370i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −182.160 | −0.839448 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 45.3844i | − 0.205359i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 303.853 | 1.36257 | 0.681284 | − | 0.732019i | \(-0.261422\pi\) | ||||
0.681284 | + | 0.732019i | \(0.261422\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 243.551i | − 1.07291i | −0.843928 | − | 0.536457i | \(-0.819762\pi\) | ||||
0.843928 | − | 0.536457i | \(-0.180238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 226.668 | 0.989816 | 0.494908 | − | 0.868945i | \(-0.335202\pi\) | ||||
0.494908 | + | 0.868945i | \(0.335202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 382.360i | − 1.64103i | −0.571626 | − | 0.820514i | \(-0.693687\pi\) | ||||
0.571626 | − | 0.820514i | \(-0.306313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −83.6225 | −0.355841 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 77.8251i | − 0.325628i | −0.986657 | − | 0.162814i | \(-0.947943\pi\) | ||||
0.986657 | − | 0.162814i | \(-0.0520570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 248.887 | 1.03273 | 0.516363 | − | 0.856370i | \(-0.327286\pi\) | ||||
0.516363 | + | 0.856370i | \(0.327286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 166.911i | − 0.681271i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.3476 | −0.0945249 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 30.9963i | − 0.123491i | −0.998092 | − | 0.0617456i | \(-0.980333\pi\) | ||||
0.998092 | − | 0.0617456i | \(-0.0196667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 459.580 | 1.81652 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 297.917i | 1.15921i | 0.814897 | + | 0.579606i | \(0.196793\pi\) | ||||
−0.814897 | + | 0.579606i | \(0.803207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 79.3657 | 0.306431 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 204.533i | − 0.777693i | −0.921303 | − | 0.388846i | \(-0.872874\pi\) | ||||
0.921303 | − | 0.388846i | \(-0.127126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −683.822 | −2.58046 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 379.300i | 1.41004i | 0.709189 | + | 0.705018i | \(0.249061\pi\) | ||||
−0.709189 | + | 0.705018i | \(0.750939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 349.060 | 1.28804 | 0.644022 | − | 0.765007i | \(-0.277264\pi\) | ||||
0.644022 | + | 0.765007i | \(0.277264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 663.709i | − 2.41349i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −95.1319 | −0.343436 | −0.171718 | − | 0.985146i | \(-0.554932\pi\) | ||||
−0.171718 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 458.688i | 1.63234i | 0.577811 | + | 0.816170i | \(0.303907\pi\) | ||||
−0.577811 | + | 0.816170i | \(0.696093\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −397.496 | −1.40458 | −0.702291 | − | 0.711890i | \(-0.747839\pi\) | ||||
−0.702291 | + | 0.711890i | \(0.747839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 102.876i | − 0.358454i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 217.207 | 0.751582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.12469i | 0.0243163i | 0.999926 | + | 0.0121582i | \(0.00387016\pi\) | ||||
−0.999926 | + | 0.0121582i | \(0.996130\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 386.236 | 1.30927 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 117.867i | − 0.394203i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 129.420 | 0.429966 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 359.024i | − 1.17713i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 41.5633 | 0.135385 | 0.0676927 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676927 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 91.9061i | − 0.295518i | −0.989023 | − | 0.147759i | \(-0.952794\pi\) | ||||
0.989023 | − | 0.147759i | \(-0.0472060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −259.708 | −0.829739 | −0.414869 | − | 0.909881i | \(-0.636173\pi\) | ||||
−0.414869 | + | 0.909881i | \(0.636173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 344.258i | 1.08599i | 0.839737 | + | 0.542994i | \(0.182709\pi\) | ||||
−0.839737 | + | 0.542994i | \(0.817291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −720.119 | −2.25743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.9332i | 0.114344i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −170.219 | −0.523750 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 57.5035i | 0.174783i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −433.674 | −1.31019 | −0.655097 | − | 0.755545i | \(-0.727372\pi\) | ||||
−0.655097 | + | 0.755545i | \(0.727372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.7069i | 0.0976326i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 502.810 | 1.49202 | 0.746009 | − | 0.665936i | \(-0.231968\pi\) | ||||
0.746009 | + | 0.665936i | \(0.231968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 734.219i | − 2.15313i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −368.676 | −1.07486 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 129.071i | 0.371963i | 0.982553 | + | 0.185981i | \(0.0595464\pi\) | ||||
−0.982553 | + | 0.185981i | \(0.940454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 464.174 | 1.33001 | 0.665006 | − | 0.746838i | \(-0.268429\pi\) | ||||
0.665006 | + | 0.746838i | \(0.268429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 669.313i | 1.89607i | 0.318167 | + | 0.948035i | \(0.396933\pi\) | ||||
−0.318167 | + | 0.948035i | \(0.603067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −229.905 | −0.647619 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.1893i | 0.100806i | 0.998729 | + | 0.0504029i | \(0.0160505\pi\) | ||||
−0.998729 | + | 0.0504029i | \(0.983949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 601.525i | 1.64801i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 666.378 | 1.81574 | 0.907871 | − | 0.419249i | \(-0.137706\pi\) | ||||
0.907871 | + | 0.419249i | \(0.137706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 470.234i | 1.26748i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −452.256 | −1.21248 | −0.606241 | − | 0.795281i | \(-0.707323\pi\) | ||||
−0.606241 | + | 0.795281i | \(0.707323\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 184.686i | 0.489883i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −186.492 | −0.492062 | −0.246031 | − | 0.969262i | \(-0.579127\pi\) | ||||
−0.246031 | + | 0.969262i | \(0.579127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 344.258i | − 0.898846i | −0.893319 | − | 0.449423i | \(-0.851630\pi\) | ||||
0.893319 | − | 0.449423i | \(-0.148370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −815.447 | −2.11804 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 236.543i | 0.608079i | 0.952659 | + | 0.304039i | \(0.0983355\pi\) | ||||
−0.952659 | + | 0.304039i | \(0.901665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −186.451 | −0.476857 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1145.84i | − 2.90087i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 334.506 | 0.842585 | 0.421292 | − | 0.906925i | \(-0.361577\pi\) | ||||
0.421292 | + | 0.906925i | \(0.361577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 224.617i | − 0.560143i | −0.959979 | − | 0.280071i | \(-0.909642\pi\) | ||||
0.959979 | − | 0.280071i | \(-0.0903581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −188.302 | −0.467251 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 319.893i | 0.785978i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −277.610 | −0.678753 | −0.339377 | − | 0.940651i | \(-0.610216\pi\) | ||||
−0.339377 | + | 0.940651i | \(0.610216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 265.597i | − 0.643092i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.914 | 0.411842 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.3658i | 0.0867919i | 0.999058 | + | 0.0433960i | \(0.0138177\pi\) | ||||
−0.999058 | + | 0.0433960i | \(0.986182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 349.661 | 0.830548 | 0.415274 | − | 0.909696i | \(-0.363686\pi\) | ||||
0.415274 | + | 0.909696i | \(0.363686\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 269.266i | 0.633566i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −246.885 | −0.578185 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 259.539i | 0.602179i | 0.953596 | + | 0.301090i | \(0.0973503\pi\) | ||||
−0.953596 | + | 0.301090i | \(0.902650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 50.2963 | 0.116158 | 0.0580788 | − | 0.998312i | \(-0.481503\pi\) | ||||
0.0580788 | + | 0.998312i | \(0.481503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 95.9183i | 0.219493i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 277.042 | 0.631075 | 0.315538 | − | 0.948913i | \(-0.397815\pi\) | ||||
0.315538 | + | 0.948913i | \(0.397815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 217.214i | 0.490326i | 0.969482 | + | 0.245163i | \(0.0788415\pi\) | ||||
−0.969482 | + | 0.245163i | \(0.921159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1015.17 | −2.28127 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 776.946i | 1.73039i | 0.501434 | + | 0.865196i | \(0.332806\pi\) | ||||
−0.501434 | + | 0.865196i | \(0.667194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 414.656 | 0.919414 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 209.134i | 0.459636i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −71.9468 | −0.157433 | −0.0787164 | − | 0.996897i | \(-0.525082\pi\) | ||||
−0.0787164 | + | 0.996897i | \(0.525082\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 221.825i | 0.481183i | 0.970626 | + | 0.240592i | \(0.0773414\pi\) | ||||
−0.970626 | + | 0.240592i | \(0.922659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.3588 | 0.0850081 | 0.0425041 | − | 0.999096i | \(-0.486466\pi\) | ||||
0.0425041 | + | 0.999096i | \(0.486466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 639.280i | 1.36891i | 0.729056 | + | 0.684454i | \(0.239959\pi\) | ||||
−0.729056 | + | 0.684454i | \(0.760041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.4911 | 0.0479554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 521.642i | 1.10284i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 138.522 | 0.291625 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 338.214i | 0.706084i | 0.935607 | + | 0.353042i | \(0.114853\pi\) | ||||
−0.935607 | + | 0.353042i | \(0.885147\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 82.0416 | 0.170565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 244.656i | − 0.504445i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0212 | 0.0493248 | 0.0246624 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246624 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 141.161i | 0.287497i | 0.989614 | + | 0.143748i | \(0.0459156\pi\) | ||||
−0.989614 | + | 0.143748i | \(0.954084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 292.151 | 0.592599 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 158.095i | 0.318099i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 403.559 | 0.808736 | 0.404368 | − | 0.914596i | \(-0.367492\pi\) | ||||
0.404368 | + | 0.914596i | \(0.367492\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 535.176i | − 1.06397i | −0.846754 | − | 0.531985i | \(-0.821446\pi\) | ||||
0.846754 | − | 0.531985i | \(-0.178554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 153.663 | 0.304283 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 91.6004i | − 0.179962i | −0.995944 | − | 0.0899808i | \(-0.971319\pi\) | ||||
0.995944 | − | 0.0899808i | \(-0.0286806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 413.641 | 0.809475 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1105.99i | 2.14756i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −231.775 | −0.448307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 160.806i | 0.308649i | 0.988020 | + | 0.154324i | \(0.0493201\pi\) | ||||
−0.988020 | + | 0.154324i | \(0.950680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 52.2686 | 0.0999399 | 0.0499700 | − | 0.998751i | \(-0.484087\pi\) | ||||
0.0499700 | + | 0.998751i | \(0.484087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 297.871i | 0.565221i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.7728 | 0.0846367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 106.345i | − 0.199522i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −776.628 | −1.45164 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 462.624i | − 0.858301i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 551.075 | 1.01862 | 0.509311 | − | 0.860582i | \(-0.329900\pi\) | ||||
0.509311 | + | 0.860582i | \(0.329900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1065.94i | 1.95585i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −135.636 | −0.247963 | −0.123981 | − | 0.992285i | \(-0.539566\pi\) | ||||
−0.123981 | + | 0.992285i | \(0.539566\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 150.295i | − 0.272768i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −787.946 | −1.42486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 652.252i | − 1.17101i | −0.810669 | − | 0.585504i | \(-0.800896\pi\) | ||||
0.810669 | − | 0.585504i | \(-0.199104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 133.783 | 0.239326 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 322.081i | 0.572080i | 0.958218 | + | 0.286040i | \(0.0923390\pi\) | ||||
−0.958218 | + | 0.286040i | \(0.907661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1115.60 | −1.97451 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 528.919i | − 0.929559i | −0.885426 | − | 0.464780i | \(-0.846134\pi\) | ||||
0.885426 | − | 0.464780i | \(-0.153866\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −536.810 | −0.940123 | −0.470062 | − | 0.882634i | \(-0.655768\pi\) | ||||
−0.470062 | + | 0.882634i | \(0.655768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 699.303i | 1.21618i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −560.381 | −0.971197 | −0.485599 | − | 0.874182i | \(-0.661398\pi\) | ||||
−0.485599 | + | 0.874182i | \(0.661398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 117.530i | − 0.202289i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1895.34 | −3.25100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 479.579i | − 0.817000i | −0.912758 | − | 0.408500i | \(-0.866052\pi\) | ||||
0.912758 | − | 0.408500i | \(-0.133948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 153.238 | 0.260166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 966.804i | 1.63036i | 0.579207 | + | 0.815181i | \(0.303362\pi\) | ||||
−0.579207 | + | 0.815181i | \(0.696638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 330.825 | 0.556009 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1144.37i | − 1.91047i | −0.295855 | − | 0.955233i | \(-0.595605\pi\) | ||||
0.295855 | − | 0.955233i | \(-0.404395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 824.038 | 1.37111 | 0.685556 | − | 0.728020i | \(-0.259559\pi\) | ||||
0.685556 | + | 0.728020i | \(0.259559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2375.00i | − 3.92562i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 833.071 | 1.37244 | 0.686220 | − | 0.727394i | \(-0.259269\pi\) | ||||
0.686220 | + | 0.727394i | \(0.259269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.4423i | 0.0972869i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −527.455 | −0.860449 | −0.430225 | − | 0.902722i | \(-0.641566\pi\) | ||||
−0.430225 | + | 0.902722i | \(0.641566\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 421.181i | − 0.682628i | −0.939949 | − | 0.341314i | \(-0.889128\pi\) | ||||
0.939949 | − | 0.341314i | \(-0.110872\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −855.134 | −1.38148 | −0.690738 | − | 0.723105i | \(-0.742714\pi\) | ||||
−0.690738 | + | 0.723105i | \(0.742714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 698.084i | 1.12052i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −409.568 | −0.655309 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 129.780i | − 0.206328i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −828.566 | −1.31310 | −0.656550 | − | 0.754283i | \(-0.727985\pi\) | ||||
−0.656550 | + | 0.754283i | \(0.727985\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1675.97i | 2.63932i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −118.647 | −0.186260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1279.90i | − 1.99672i | −0.0572528 | − | 0.998360i | \(-0.518234\pi\) | ||||
0.0572528 | − | 0.998360i | \(-0.481766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −302.928 | −0.471116 | −0.235558 | − | 0.971860i | \(-0.575692\pi\) | ||||
−0.235558 | + | 0.971860i | \(0.575692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 330.443i | − 0.510731i | −0.966845 | − | 0.255366i | \(-0.917804\pi\) | ||||
0.966845 | − | 0.255366i | \(-0.0821959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1070.52 | 1.64949 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 150.460i | − 0.230413i | −0.993342 | − | 0.115207i | \(-0.963247\pi\) | ||||
0.993342 | − | 0.115207i | \(-0.0367530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1289.70 | 1.96901 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 476.960i | − 0.723764i | −0.932224 | − | 0.361882i | \(-0.882134\pi\) | ||||
0.932224 | − | 0.361882i | \(-0.117866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1077.26 | 1.62975 | 0.814873 | − | 0.579639i | \(-0.196806\pi\) | ||||
0.814873 | + | 0.579639i | \(0.196806\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 170.191i | − 0.255926i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 758.739 | 1.13754 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 995.100i | − 1.48301i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 258.876 | 0.384660 | 0.192330 | − | 0.981330i | \(-0.438396\pi\) | ||||
0.192330 | + | 0.981330i | \(0.438396\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 428.473i | − 0.632899i | −0.948609 | − | 0.316450i | \(-0.897509\pi\) | ||||
0.948609 | − | 0.316450i | \(-0.102491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −168.239 | −0.247774 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 980.386i | 1.43541i | 0.696347 | + | 0.717706i | \(0.254808\pi\) | ||||
−0.696347 | + | 0.717706i | \(0.745192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1676.27 | 2.44711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 486.089i | 0.705499i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1193.72 | 1.72753 | 0.863766 | − | 0.503894i | \(-0.168100\pi\) | ||||
0.863766 | + | 0.503894i | \(0.168100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 31.8253i | − 0.0457918i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −168.225 | −0.241356 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 885.039i | 1.26254i | 0.775564 | + | 0.631269i | \(0.217466\pi\) | ||||
−0.775564 | + | 0.631269i | \(0.782534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −66.7644 | −0.0949706 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 105.667i | − 0.149458i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1128.51 | −1.59170 | −0.795850 | − | 0.605494i | \(-0.792975\pi\) | ||||
−0.795850 | + | 0.605494i | \(0.792975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 773.594i | 1.08499i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −842.941 | −1.17894 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 383.648i | 0.533586i | 0.963754 | + | 0.266793i | \(0.0859640\pi\) | ||||
−0.963754 | + | 0.266793i | \(0.914036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 760.541 | 1.05484 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1095.74i | − 1.51137i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 827.848 | 1.13872 | 0.569359 | − | 0.822089i | \(-0.307191\pi\) | ||||
0.569359 | + | 0.822089i | \(0.307191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 211.629i | − 0.289507i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −339.718 | −0.463462 | −0.231731 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231731 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 90.6530i | 0.123003i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 508.257 | 0.687763 | 0.343881 | − | 0.939013i | \(-0.388258\pi\) | ||||
0.343881 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1102.51i | − 1.48386i | −0.670479 | − | 0.741929i | \(-0.733911\pi\) | ||||
0.670479 | − | 0.741929i | \(-0.266089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −288.832 | −0.387694 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 534.052i | 0.713020i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −661.082 | −0.880269 | −0.440134 | − | 0.897932i | \(-0.645069\pi\) | ||||
−0.440134 | + | 0.897932i | \(0.645069\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 395.700i | 0.524106i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 882.880 | 1.16629 | 0.583144 | − | 0.812369i | \(-0.301822\pi\) | ||||
0.583144 | + | 0.812369i | \(0.301822\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0466i | 0.0237143i | 0.999930 | + | 0.0118571i | \(0.00377433\pi\) | ||||
−0.999930 | + | 0.0118571i | \(0.996226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 732.998 | 0.960679 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 274.552i | − 0.357956i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1302.05 | 1.69317 | 0.846584 | − | 0.532255i | \(-0.178655\pi\) | ||||
0.846584 | + | 0.532255i | \(0.178655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 924.196i | − 1.19560i | −0.801647 | − | 0.597798i | \(-0.796042\pi\) | ||||
0.801647 | − | 0.597798i | \(-0.203958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1117.20 | 1.44154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 86.5421i | 0.111094i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −637.222 | −0.815905 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 2327.78i | − 2.96533i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −281.015 | −0.357071 | −0.178535 | − | 0.983933i | \(-0.557136\pi\) | ||||
−0.178535 | + | 0.983933i | \(0.557136\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 767.148i | 0.969846i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −255.209 | −0.321827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 614.820i | − 0.771418i | −0.922620 | − | 0.385709i | \(-0.873957\pi\) | ||||
0.922620 | − | 0.385709i | \(-0.126043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 94.0306 | 0.117685 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1667.23i | 2.07626i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 859.178 | 1.06730 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1378.73i | 1.70424i | 0.523348 | + | 0.852119i | \(0.324683\pi\) | ||||
−0.523348 | + | 0.852119i | \(0.675317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1161.09 | −1.43167 | −0.715837 | − | 0.698268i | \(-0.753954\pi\) | ||||
−0.715837 | + | 0.698268i | \(0.753954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 509.067i | 0.624623i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −108.871 | −0.133257 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 548.846i | − 0.668510i | −0.942483 | − | 0.334255i | \(-0.891515\pi\) | ||||
0.942483 | − | 0.334255i | \(-0.108485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1250.98 | −1.52002 | −0.760012 | − | 0.649909i | \(-0.774807\pi\) | ||||
−0.760012 | + | 0.649909i | \(0.774807\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1327.93i | − 1.60572i | −0.596165 | − | 0.802862i | \(-0.703309\pi\) | ||||
0.596165 | − | 0.802862i | \(-0.296691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1015.57 | −1.22506 | −0.612528 | − | 0.790449i | \(-0.709847\pi\) | ||||
−0.612528 | + | 0.790449i | \(0.709847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 187.686i | 0.225313i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2105.06 | 2.52103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 950.704i | − 1.13314i | −0.824014 | − | 0.566570i | \(-0.808270\pi\) | ||||
0.824014 | − | 0.566570i | \(-0.191730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −347.873 | −0.413642 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1057.26i | − 1.25120i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1633.18 | −1.92819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 337.049i | − 0.396062i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1487.29 | 1.74359 | 0.871797 | − | 0.489868i | \(-0.162955\pi\) | ||||
0.871797 | + | 0.489868i | \(0.162955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 9.01645i | − 0.0105209i | −0.999986 | − | 0.00526047i | \(-0.998326\pi\) | ||||
0.999986 | − | 0.00526047i | \(-0.00167447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 433.625 | 0.504802 | 0.252401 | − | 0.967623i | \(-0.418780\pi\) | ||||
0.252401 | + | 0.967623i | \(0.418780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1301.22i | 1.50778i | 0.656998 | + | 0.753892i | \(0.271826\pi\) | ||||
−0.656998 | + | 0.753892i | \(0.728174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −568.624 | −0.657368 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3175.91i | − 3.65468i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2494 | 0.0266928 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 264.684i | − 0.302496i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −969.321 | −1.10527 | −0.552634 | − | 0.833424i | \(-0.686377\pi\) | ||||
−0.552634 | + | 0.833424i | \(0.686377\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 958.937i | − 1.08846i | −0.838935 | − | 0.544232i | \(-0.816821\pi\) | ||||
0.838935 | − | 0.544232i | \(-0.183179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −124.679 | −0.141200 | −0.0705999 | − | 0.997505i | \(-0.522491\pi\) | ||||
−0.0705999 | + | 0.997505i | \(0.522491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1699.20i | 1.91568i | 0.287309 | + | 0.957838i | \(0.407239\pi\) | ||||
−0.287309 | + | 0.957838i | \(0.592761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1152.49 | 1.29639 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 48.3733i | − 0.0541695i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −501.561 | −0.560404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1212.15i | − 1.34833i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 768.935 | 0.853423 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 810.484i | 0.895562i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 682.473 | 0.752450 | 0.376225 | − | 0.926528i | \(-0.377222\pi\) | ||||
0.376225 | + | 0.926528i | \(0.377222\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 162.119i | 0.177957i | 0.996034 | + | 0.0889785i | \(0.0283602\pi\) | ||||
−0.996034 | + | 0.0889785i | \(0.971640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 473.719 | 0.518860 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 886.868i | − 0.967141i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1172.42 | 1.27576 | 0.637880 | − | 0.770135i | \(-0.279811\pi\) | ||||
0.637880 | + | 0.770135i | \(0.279811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 163.426i | 0.177059i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −486.753 | −0.526220 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 129.000i | − 0.138858i | −0.997587 | − | 0.0694292i | \(-0.977882\pi\) | ||||
0.997587 | − | 0.0694292i | \(-0.0221178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 96.5536 | 0.103710 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1333.43i | 1.42613i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.2758 | −0.0579251 | −0.0289625 | − | 0.999580i | \(-0.509220\pi\) | ||||
−0.0289625 | + | 0.999580i | \(0.509220\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 726.918i | − 0.772495i | −0.922395 | − | 0.386247i | \(-0.873771\pi\) | ||||
0.922395 | − | 0.386247i | \(-0.126229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −436.893 | −0.463301 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1859.88i | − 1.96397i | −0.188969 | − | 0.981983i | \(-0.560515\pi\) | ||||
0.188969 | − | 0.981983i | \(-0.439485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 427.588 | 0.450567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1412.84i | 1.48252i | 0.671217 | + | 0.741261i | \(0.265772\pi\) | ||||
−0.671217 | + | 0.741261i | \(0.734228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 612.395 | 0.641251 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1152.70i | − 1.20198i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 274.883 | 0.286039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1366.72i | 1.41629i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1127.14 | −1.16561 | −0.582804 | − | 0.812613i | \(-0.698045\pi\) | ||||
−0.582804 | + | 0.812613i | \(0.698045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1224.06i | − 1.26062i | −0.776342 | − | 0.630311i | \(-0.782927\pi\) | ||||
0.776342 | − | 0.630311i | \(-0.217073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.8848 | −0.0224921 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 873.223i | 0.893780i | 0.894589 | + | 0.446890i | \(0.147468\pi\) | ||||
−0.894589 | + | 0.446890i | \(0.852532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2813.71 | −2.87407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1330.86i | − 1.35388i | −0.736038 | − | 0.676940i | \(-0.763305\pi\) | ||||
0.736038 | − | 0.676940i | \(-0.236695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1284.41 | 1.30397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 549.618i | − 0.555731i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −265.348 | −0.267758 | −0.133879 | − | 0.990998i | \(-0.542743\pi\) | ||||
−0.133879 | + | 0.990998i | \(0.542743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1318.30i | 1.32492i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1179.05 | 1.18260 | 0.591298 | − | 0.806453i | \(-0.298616\pi\) | ||||
0.591298 | + | 0.806453i | \(0.298616\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 684.3.e.a.305.12 | yes | 12 | |
3.2 | odd | 2 | inner | 684.3.e.a.305.1 | ✓ | 12 | |
4.3 | odd | 2 | 2736.3.h.c.305.12 | 12 | |||
12.11 | even | 2 | 2736.3.h.c.305.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.e.a.305.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
684.3.e.a.305.12 | yes | 12 | 1.1 | even | 1 | trivial | |
2736.3.h.c.305.1 | 12 | 12.11 | even | 2 | |||
2736.3.h.c.305.12 | 12 | 4.3 | odd | 2 |