Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.a (trivial) |
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: | yes |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | 2.41421 | 1.07967 | 0.539835 | − | 0.841771i | \(-0.318487\pi\) | ||||
0.539835 | + | 0.841771i | \(0.318487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41421 | −0.727913 | −0.363956 | − | 0.931416i | \(-0.618574\pi\) | ||||
−0.363956 | + | 0.931416i | \(0.618574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.82843 | −0.878301 | −0.439151 | − | 0.898413i | \(-0.644721\pi\) | ||||
−0.439151 | + | 0.898413i | \(0.644721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.24264 | −1.09317 | −0.546583 | − | 0.837405i | \(-0.684072\pi\) | ||||
−0.546583 | + | 0.837405i | \(0.684072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.828427 | 0.165685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.65685 | −0.836396 | −0.418198 | − | 0.908356i | \(-0.637338\pi\) | ||||
−0.418198 | + | 0.908356i | \(0.637338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.41421 | −0.408077 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.171573 | 0.0282064 | 0.0141032 | − | 0.999901i | \(-0.495511\pi\) | ||||
0.0141032 | + | 0.999901i | \(0.495511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.07107 | −0.323446 | −0.161723 | − | 0.986836i | \(-0.551705\pi\) | ||||
−0.161723 | + | 0.986836i | \(0.551705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.82843 | −0.736328 | −0.368164 | − | 0.929761i | \(-0.620014\pi\) | ||||
−0.368164 | + | 0.929761i | \(0.620014\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.343146 | −0.0500530 | −0.0250265 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250265 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.82843 | −0.785905 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.65685 | 0.476082 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3137 | −1.44857 | −0.724286 | − | 0.689500i | \(-0.757830\pi\) | ||||
−0.724286 | + | 0.689500i | \(0.757830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.48528 | 0.547964 | 0.273982 | − | 0.961735i | \(-0.411659\pi\) | ||||
0.273982 | + | 0.961735i | \(0.411659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.58579 | −0.662911 | −0.331455 | − | 0.943471i | \(-0.607540\pi\) | ||||
−0.331455 | + | 0.943471i | \(0.607540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.17157 | −0.371205 | −0.185602 | − | 0.982625i | \(-0.559424\pi\) | ||||
−0.185602 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.41421 | 0.275125 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82843 | 0.543240 | 0.271620 | − | 0.962405i | \(-0.412441\pi\) | ||||
0.271620 | + | 0.962405i | \(0.412441\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8284 | −1.18857 | −0.594287 | − | 0.804253i | \(-0.702566\pi\) | ||||
−0.594287 | + | 0.804253i | \(0.702566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82843 | 0.740647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.24264 | 0.131720 | 0.0658598 | − | 0.997829i | \(-0.479021\pi\) | ||||
0.0658598 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.24264 | −0.948275 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.65685 | −0.980505 | −0.490252 | − | 0.871580i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871580i | \(0.663095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4853 | −1.24233 | −0.621166 | − | 0.783679i | \(-0.713341\pi\) | ||||
−0.621166 | + | 0.783679i | \(0.713341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.65685 | 0.655919 | 0.327960 | − | 0.944692i | \(-0.393639\pi\) | ||||
0.327960 | + | 0.944692i | \(0.393639\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.31371 | 0.513696 | 0.256848 | − | 0.966452i | \(-0.417316\pi\) | ||||
0.256848 | + | 0.966452i | \(0.417316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.3137 | 1.75414 | 0.877068 | − | 0.480367i | \(-0.159497\pi\) | ||||
0.877068 | + | 0.480367i | \(0.159497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1421 | 1.14224 | 0.571118 | − | 0.820868i | \(-0.306510\pi\) | ||||
0.571118 | + | 0.820868i | \(0.306510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6569 | −1.18026 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82843 | −0.259281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17157 | −0.470143 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0711 | −0.900784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | −0.174741 | −0.0873704 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873704 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.82843 | 0.331967 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.82843 | −0.241649 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.65685 | −0.140533 | −0.0702663 | − | 0.997528i | \(-0.522385\pi\) | ||||
−0.0702663 | + | 0.997528i | \(0.522385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.82843 | −0.571022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.82843 | −0.567070 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.17157 | 0.259825 | 0.129913 | − | 0.991525i | \(-0.458530\pi\) | ||||
0.129913 | + | 0.991525i | \(0.458530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.31371 | −0.432423 | −0.216212 | − | 0.976346i | \(-0.569370\pi\) | ||||
−0.216212 | + | 0.976346i | \(0.569370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2426 | −0.903031 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1421 | −1.12867 | −0.564333 | − | 0.825547i | \(-0.690866\pi\) | ||||
−0.564333 | + | 0.825547i | \(0.690866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.24264 | 0.413178 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4853 | 1.29123 | 0.645613 | − | 0.763664i | \(-0.276602\pi\) | ||||
0.645613 | + | 0.763664i | \(0.276602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.51472 | −0.117212 | −0.0586062 | − | 0.998281i | \(-0.518666\pi\) | ||||
−0.0586062 | + | 0.998281i | \(0.518666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.24264 | 0.702705 | 0.351352 | − | 0.936243i | \(-0.385722\pi\) | ||||
0.351352 | + | 0.936243i | \(0.385722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.828427 | −0.0626232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.6569 | −1.46922 | −0.734611 | − | 0.678488i | \(-0.762635\pi\) | ||||
−0.734611 | + | 0.678488i | \(0.762635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6569 | 1.46108 | 0.730541 | − | 0.682869i | \(-0.239268\pi\) | ||||
0.730541 | + | 0.682869i | \(0.239268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.414214 | 0.0304536 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82843 | −0.499344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4142 | −0.898261 | −0.449130 | − | 0.893466i | \(-0.648266\pi\) | ||||
−0.449130 | + | 0.893466i | \(0.648266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.65685 | −0.263226 | −0.131613 | − | 0.991301i | \(-0.542016\pi\) | ||||
−0.131613 | + | 0.991301i | \(0.542016\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.8284 | −1.76895 | −0.884476 | − | 0.466586i | \(-0.845484\pi\) | ||||
−0.884476 | + | 0.466586i | \(0.845484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.48528 | 0.247065 | 0.123533 | − | 0.992341i | \(-0.460578\pi\) | ||||
0.123533 | + | 0.992341i | \(0.460578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | 0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | −0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.24264 | 0.639327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6569 | −0.794991 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.65685 | 0.316128 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7990 | 1.66066 | 0.830332 | − | 0.557270i | \(-0.188151\pi\) | ||||
0.830332 | + | 0.557270i | \(0.188151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.8284 | −1.38243 | −0.691216 | − | 0.722649i | \(-0.742925\pi\) | ||||
−0.691216 | + | 0.722649i | \(0.742925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3137 | 1.27629 | 0.638143 | − | 0.769918i | \(-0.279703\pi\) | ||||
0.638143 | + | 0.769918i | \(0.279703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8284 | −0.840418 | −0.420209 | − | 0.907427i | \(-0.638043\pi\) | ||||
−0.420209 | + | 0.907427i | \(0.638043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.828427 | −0.0540406 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6569 | −1.01276 | −0.506379 | − | 0.862311i | \(-0.669016\pi\) | ||||
−0.506379 | + | 0.862311i | \(0.669016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.1421 | −1.55513 | −0.777566 | − | 0.628802i | \(-0.783546\pi\) | ||||
−0.777566 | + | 0.628802i | \(0.783546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.41421 | 0.154238 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8284 | −0.688996 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9706 | −1.57613 | −0.788064 | − | 0.615593i | \(-0.788916\pi\) | ||||
−0.788064 | + | 0.615593i | \(0.788916\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.6569 | 0.795730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.27208 | 0.391241 | 0.195621 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195621 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.171573 | −0.0106610 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3848 | 0.825341 | 0.412670 | − | 0.910880i | \(-0.364596\pi\) | ||||
0.412670 | + | 0.910880i | \(0.364596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.65685 | −0.593216 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.5858 | −0.950282 | −0.475141 | − | 0.879910i | \(-0.657603\pi\) | ||||
−0.475141 | + | 0.879910i | \(0.657603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.8284 | 0.830870 | 0.415435 | − | 0.909623i | \(-0.363629\pi\) | ||||
0.415435 | + | 0.909623i | \(0.363629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3137 | 0.910305 | 0.455153 | − | 0.890413i | \(-0.349585\pi\) | ||||
0.455153 | + | 0.890413i | \(0.349585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.07107 | 0.122251 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.17157 | 0.535809 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.82843 | 0.514011 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.8284 | −0.857550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.82843 | 0.278306 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.3137 | −1.56398 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.8284 | 0.789230 | 0.394615 | − | 0.918847i | \(-0.370878\pi\) | ||||
0.394615 | + | 0.918847i | \(0.370878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.485281 | 0.0275178 | 0.0137589 | − | 0.999905i | \(-0.495620\pi\) | ||||
0.0137589 | + | 0.999905i | \(0.495620\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8284 | −1.06425 | −0.532123 | − | 0.846667i | \(-0.678606\pi\) | ||||
−0.532123 | + | 0.846667i | \(0.678606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.2843 | 1.92560 | 0.962798 | − | 0.270221i | \(-0.0870968\pi\) | ||||
0.962798 | + | 0.270221i | \(0.0870968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.82843 | 0.382319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.8284 | −0.602510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.34315 | 0.129974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.343146 | 0.0189182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.6274 | 1.90329 | 0.951647 | − | 0.307192i | \(-0.0993895\pi\) | ||||
0.951647 | + | 0.307192i | \(0.0993895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8284 | 0.591620 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.6274 | 1.39601 | 0.698007 | − | 0.716091i | \(-0.254070\pi\) | ||||
0.698007 | + | 0.716091i | \(0.254070\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.2426 | 0.608823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0711 | −0.970106 | −0.485053 | − | 0.874485i | \(-0.661200\pi\) | ||||
−0.485053 | + | 0.874485i | \(0.661200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6569 | 1.05221 | 0.526104 | − | 0.850420i | \(-0.323652\pi\) | ||||
0.526104 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.414214 | 0.0220464 | 0.0110232 | − | 0.999939i | \(-0.496491\pi\) | ||||
0.0110232 | + | 0.999939i | \(0.496491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4853 | −0.715724 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.3137 | −1.12489 | −0.562447 | − | 0.826833i | \(-0.690140\pi\) | ||||
−0.562447 | + | 0.826833i | \(0.690140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.34315 | −0.228587 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.65685 | −0.400778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.51472 | 0.131267 | 0.0656336 | − | 0.997844i | \(-0.479093\pi\) | ||||
0.0656336 | + | 0.997844i | \(0.479093\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.68629 | 0.190869 | 0.0954345 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954345 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4853 | 0.744059 | 0.372029 | − | 0.928221i | \(-0.378662\pi\) | ||||
0.372029 | + | 0.928221i | \(0.378662\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.4558 | −1.81171 | −0.905855 | − | 0.423589i | \(-0.860770\pi\) | ||||
−0.905855 | + | 0.423589i | \(0.860770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.82843 | 0.297044 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.3137 | −0.573628 | −0.286814 | − | 0.957986i | \(-0.592596\pi\) | ||||
−0.286814 | + | 0.957986i | \(0.592596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8284 | −0.749906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.6569 | 0.586520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.65685 | −0.183532 | −0.0917661 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917661 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.8284 | 1.14000 | 0.569999 | − | 0.821646i | \(-0.306944\pi\) | ||||
0.569999 | + | 0.821646i | \(0.306944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1716 | −0.656123 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.414214 | −0.0205318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4853 | −1.70519 | −0.852594 | − | 0.522574i | \(-0.824972\pi\) | ||||
−0.852594 | + | 0.522574i | \(0.824972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.65685 | −0.179942 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.1421 | −1.28327 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.142136 | 0.00694378 | 0.00347189 | − | 0.999994i | \(-0.498895\pi\) | ||||
0.00347189 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5147 | 0.512456 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.34315 | 0.113659 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3137 | 0.547509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2132 | 1.06997 | 0.534986 | − | 0.844861i | \(-0.320317\pi\) | ||||
0.534986 | + | 0.844861i | \(0.320317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4558 | 1.03110 | 0.515551 | − | 0.856859i | \(-0.327587\pi\) | ||||
0.515551 | + | 0.856859i | \(0.327587\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0711 | 0.960129 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0710678 | 0.00337653 | 0.00168827 | − | 0.999999i | \(-0.499463\pi\) | ||||
0.00168827 | + | 0.999999i | \(0.499463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | 0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.8284 | −1.36050 | −0.680249 | − | 0.732981i | \(-0.738128\pi\) | ||||
−0.680249 | + | 0.732981i | \(0.738128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00000 | 0.235441 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.82843 | −0.320122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.65685 | −0.404951 | −0.202475 | − | 0.979287i | \(-0.564899\pi\) | ||||
−0.202475 | + | 0.979287i | \(0.564899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.2426 | 1.17567 | 0.587833 | − | 0.808982i | \(-0.299981\pi\) | ||||
0.587833 | + | 0.808982i | \(0.299981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.3431 | −0.573635 | −0.286817 | − | 0.957985i | \(-0.592597\pi\) | ||||
−0.286817 | + | 0.957985i | \(0.592597\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.6274 | 0.769425 | 0.384713 | − | 0.923036i | \(-0.374301\pi\) | ||||
0.384713 | + | 0.923036i | \(0.374301\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.48528 | −0.207111 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6569 | 0.535983 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.17157 | −0.145522 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.9706 | −1.68923 | −0.844614 | − | 0.535376i | \(-0.820170\pi\) | ||||
−0.844614 | + | 0.535376i | \(0.820170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.485281 | 0.0221269 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.3137 | −1.05862 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4853 | −1.01891 | −0.509453 | − | 0.860499i | \(-0.670152\pi\) | ||||
−0.509453 | + | 0.860499i | \(0.670152\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8701 | 1.25776 | 0.628879 | − | 0.777503i | \(-0.283514\pi\) | ||||
0.628879 | + | 0.777503i | \(0.283514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | −0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.58579 | 0.250557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.7696 | −1.55650 | −0.778249 | − | 0.627955i | \(-0.783892\pi\) | ||||
−0.778249 | + | 0.627955i | \(0.783892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.1421 | 0.452215 | 0.226108 | − | 0.974102i | \(-0.427400\pi\) | ||||
0.226108 | + | 0.974102i | \(0.427400\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.1421 | −1.34131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.4853 | 1.43988 | 0.719942 | − | 0.694034i | \(-0.244168\pi\) | ||||
0.719942 | + | 0.694034i | \(0.244168\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.17157 | 0.140302 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0711 | 0.708176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.828427 | 0.0364342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.2426 | −1.19352 | −0.596761 | − | 0.802419i | \(-0.703546\pi\) | ||||
−0.596761 | + | 0.802419i | \(0.703546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9706 | −0.523436 | −0.261718 | − | 0.965144i | \(-0.584289\pi\) | ||||
−0.261718 | + | 0.965144i | \(0.584289\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.1716 | −0.573763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.48528 | 0.195012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.85786 | −0.253732 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.8284 | 0.554621 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.41421 | −0.103988 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7990 | −1.06619 | −0.533096 | − | 0.846055i | \(-0.678972\pi\) | ||||
−0.533096 | + | 0.846055i | \(0.678972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.2132 | 1.89389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9706 | −0.725609 | −0.362804 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362804 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8284 | 0.461307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.82843 | −0.205326 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.7696 | 1.30375 | 0.651874 | − | 0.758327i | \(-0.273983\pi\) | ||||
0.651874 | + | 0.758327i | \(0.273983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6569 | −0.577623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.7990 | −1.00301 | −0.501504 | − | 0.865155i | \(-0.667220\pi\) | ||||
−0.501504 | + | 0.865155i | \(0.667220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.3137 | 1.23324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.79899 | −0.410795 | −0.205398 | − | 0.978679i | \(-0.565849\pi\) | ||||
−0.205398 | + | 0.978679i | \(0.565849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.6274 | −0.528441 | −0.264220 | − | 0.964462i | \(-0.585115\pi\) | ||||
−0.264220 | + | 0.964462i | \(0.585115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.34315 | −0.181122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.9411 | −1.66277 | −0.831385 | − | 0.555696i | \(-0.812452\pi\) | ||||
−0.831385 | + | 0.555696i | \(0.812452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8284 | 0.449239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.65685 | 0.399946 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.4558 | −1.29832 | −0.649161 | − | 0.760651i | \(-0.724880\pi\) | ||||
−0.649161 | + | 0.760651i | \(0.724880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8284 | 0.734608 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.2426 | −0.790201 | −0.395100 | − | 0.918638i | \(-0.629290\pi\) | ||||
−0.395100 | + | 0.918638i | \(0.629290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.82843 | −0.279938 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.0416 | −1.10489 | −0.552446 | − | 0.833549i | \(-0.686305\pi\) | ||||
−0.552446 | + | 0.833549i | \(0.686305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.85786 | −0.402111 | −0.201055 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201055 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4853 | −0.507599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.6569 | 1.04138 | 0.520690 | − | 0.853746i | \(-0.325675\pi\) | ||||
0.520690 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.970563 | −0.0392648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.02944 | 0.324306 | 0.162153 | − | 0.986766i | \(-0.448156\pi\) | ||||
0.162153 | + | 0.986766i | \(0.448156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.2843 | −1.86333 | −0.931667 | − | 0.363313i | \(-0.881646\pi\) | ||||
−0.931667 | + | 0.363313i | \(0.881646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.3137 | −1.62034 | −0.810172 | − | 0.586192i | \(-0.800627\pi\) | ||||
−0.810172 | + | 0.586192i | \(0.800627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.24264 | −0.0497853 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.4558 | −1.13823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.485281 | 0.0193494 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.85786 | −0.153579 | −0.0767896 | − | 0.997047i | \(-0.524467\pi\) | ||||
−0.0767896 | + | 0.997047i | \(0.524467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.82843 | 0.270978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.82843 | 0.112066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.51472 | −0.217818 | −0.108909 | − | 0.994052i | \(-0.534736\pi\) | ||||
−0.108909 | + | 0.994052i | \(0.534736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.48528 | 0.137446 | 0.0687230 | − | 0.997636i | \(-0.478108\pi\) | ||||
0.0687230 | + | 0.997636i | \(0.478108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.6863 | 0.420121 | 0.210061 | − | 0.977688i | \(-0.432634\pi\) | ||||
0.210061 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.82843 | −0.346546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.02944 | 0.196817 | 0.0984085 | − | 0.995146i | \(-0.468625\pi\) | ||||
0.0984085 | + | 0.995146i | \(0.468625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.82843 | −0.188662 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8995 | 1.43740 | 0.718700 | − | 0.695320i | \(-0.244737\pi\) | ||||
0.718700 | + | 0.695320i | \(0.244737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.8284 | 0.421177 | 0.210589 | − | 0.977575i | \(-0.432462\pi\) | ||||
0.210589 | + | 0.977575i | \(0.432462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.24264 | 0.358414 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8284 | 0.574159 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.3137 | 1.05443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2843 | 1.32156 | 0.660781 | − | 0.750579i | \(-0.270225\pi\) | ||||
0.660781 | + | 0.750579i | \(0.270225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.04163 | −0.193766 | −0.0968828 | − | 0.995296i | \(-0.530887\pi\) | ||||
−0.0968828 | + | 0.995296i | \(0.530887\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.65685 | 0.370596 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8995 | −0.493585 | −0.246793 | − | 0.969068i | \(-0.579377\pi\) | ||||
−0.246793 | + | 0.969068i | \(0.579377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.82843 | −0.260901 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3137 | −0.431018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.6863 | −0.939111 | −0.469555 | − | 0.882903i | \(-0.655586\pi\) | ||||
−0.469555 | + | 0.882903i | \(0.655586\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00000 | −0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.85786 | −0.221882 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.5147 | −1.19029 | −0.595147 | − | 0.803617i | \(-0.702906\pi\) | ||||
−0.595147 | + | 0.803617i | \(0.702906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.656854 | −0.0247737 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.4853 | 0.469557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.3137 | 0.988232 | 0.494116 | − | 0.869396i | \(-0.335492\pi\) | ||||
0.494116 | + | 0.869396i | \(0.335492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.4142 | 0.914319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4853 | −0.616515 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.65685 | −0.285552 | −0.142776 | − | 0.989755i | \(-0.545603\pi\) | ||||
−0.142776 | + | 0.989755i | \(0.545603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.65685 | −0.247914 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.34315 | −0.0870222 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.62742 | −0.245797 | −0.122899 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122899 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6569 | −0.505117 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.828427 | −0.0305987 | −0.0152993 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0152993 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8284 | −0.398870 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.9706 | 1.13927 | 0.569635 | − | 0.821898i | \(-0.307084\pi\) | ||||
0.569635 | + | 0.821898i | \(0.307084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8995 | −0.619982 | −0.309991 | − | 0.950739i | \(-0.600326\pi\) | ||||
−0.309991 | + | 0.950739i | \(0.600326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.65685 | 0.280525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.31371 | −0.194159 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.4853 | −1.84223 | −0.921117 | − | 0.389286i | \(-0.872722\pi\) | ||||
−0.921117 | + | 0.389286i | \(0.872722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.8284 | −0.466874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.2843 | 1.10070 | 0.550350 | − | 0.834934i | \(-0.314494\pi\) | ||||
0.550350 | + | 0.834934i | \(0.314494\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.7990 | 1.73271 | 0.866356 | − | 0.499427i | \(-0.166456\pi\) | ||||
0.866356 | + | 0.499427i | \(0.166456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3137 | −0.663001 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3431 | 0.373469 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.85786 | 0.0669963 | 0.0334982 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334982 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.4142 | −1.38166 | −0.690832 | − | 0.723016i | \(-0.742755\pi\) | ||||
−0.690832 | + | 0.723016i | \(0.742755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.85786 | −0.138579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.92893 | 0.284083 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4853 | 0.482541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.1421 | −1.21859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.9411 | 0.924701 | 0.462351 | − | 0.886697i | \(-0.347006\pi\) | ||||
0.462351 | + | 0.886697i | \(0.347006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1421 | −0.431725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.8995 | 1.44873 | 0.724367 | − | 0.689414i | \(-0.242132\pi\) | ||||
0.724367 | + | 0.689414i | \(0.242132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.970563 | −0.0343360 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.65685 | 0.270205 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6569 | 0.446095 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.4853 | −1.70465 | −0.852326 | − | 0.523011i | \(-0.824809\pi\) | ||||
−0.852326 | + | 0.523011i | \(0.824809\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.34315 | 0.328082 | 0.164041 | − | 0.986454i | \(-0.447547\pi\) | ||||
0.164041 | + | 0.986454i | \(0.447547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.7990 | 1.39410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4853 | 0.646718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.28427 | −0.219323 | −0.109661 | − | 0.993969i | \(-0.534977\pi\) | ||||
−0.109661 | + | 0.993969i | \(0.534977\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.6274 | 1.69505 | 0.847523 | − | 0.530759i | \(-0.178093\pi\) | ||||
0.847523 | + | 0.530759i | \(0.178093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.58579 | −0.263784 | −0.131892 | − | 0.991264i | \(-0.542105\pi\) | ||||
−0.131892 | + | 0.991264i | \(0.542105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.14214 | 0.282788 | 0.141394 | − | 0.989953i | \(-0.454842\pi\) | ||||
0.141394 | + | 0.989953i | \(0.454842\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.82843 | 0.0979992 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.65685 | −0.126551 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.1421 | 1.17872 | 0.589359 | − | 0.807871i | \(-0.299380\pi\) | ||||
0.589359 | + | 0.807871i | \(0.299380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.0711 | −0.415257 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.17157 | 0.177697 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.899495 | −0.0308343 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0294 | 0.377641 | 0.188820 | − | 0.982012i | \(-0.439534\pi\) | ||||
0.188820 | + | 0.982012i | \(0.439534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.44365 | −0.254270 | −0.127135 | − | 0.991885i | \(-0.540578\pi\) | ||||
−0.127135 | + | 0.991885i | \(0.540578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.1127 | 1.57334 | 0.786672 | − | 0.617371i | \(-0.211802\pi\) | ||||
0.786672 | + | 0.617371i | \(0.211802\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.6569 | 1.21377 | 0.606887 | − | 0.794788i | \(-0.292418\pi\) | ||||
0.606887 | + | 0.794788i | \(0.292418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.3137 | 0.758689 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.6569 | −0.395432 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6863 | 0.429859 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.0711 | 0.340464 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.9411 | 1.34872 | 0.674358 | − | 0.738405i | \(-0.264420\pi\) | ||||
0.674358 | + | 0.738405i | \(0.264420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7279 | 1.06894 | 0.534470 | − | 0.845187i | \(-0.320511\pi\) | ||||
0.534470 | + | 0.845187i | \(0.320511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.6863 | 0.561538 | 0.280769 | − | 0.959775i | \(-0.409410\pi\) | ||||
0.280769 | + | 0.959775i | \(0.409410\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.7696 | 1.10029 | 0.550147 | − | 0.835068i | \(-0.314572\pi\) | ||||
0.550147 | + | 0.835068i | \(0.314572\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.82843 | −0.0948624 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.31371 | 0.0439616 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.4558 | −1.58627 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.1716 | 0.439297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3137 | −0.376914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.4558 | 1.57749 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.6863 | −0.354832 | −0.177416 | − | 0.984136i | \(-0.556774\pi\) | ||||
−0.177416 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.02944 | 0.299159 | 0.149579 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149579 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.1421 | 0.865178 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.00000 | 0.0660458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.3431 | −1.00093 | −0.500464 | − | 0.865757i | \(-0.666837\pi\) | ||||
−0.500464 | + | 0.865757i | \(0.666837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.7990 | −0.520030 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.142136 | 0.00467339 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.1421 | 1.51387 | 0.756937 | − | 0.653488i | \(-0.226695\pi\) | ||||
0.756937 | + | 0.653488i | \(0.226695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.82843 | −0.125472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.4853 | −0.539126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.3137 | −0.369603 | −0.184801 | − | 0.982776i | \(-0.559164\pi\) | ||||
−0.184801 | + | 0.982776i | \(0.559164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.38478 | 0.240737 | 0.120368 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120368 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8579 | 0.353581 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.72792 | 0.121141 | 0.0605706 | − | 0.998164i | \(-0.480708\pi\) | ||||
0.0605706 | + | 0.998164i | \(0.480708\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.97056 | −0.291197 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.1716 | −1.72240 | −0.861198 | − | 0.508269i | \(-0.830285\pi\) | ||||
−0.861198 | + | 0.508269i | \(0.830285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.9706 | −0.969825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.82843 | 0.0913347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.31371 | −0.300442 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.82843 | −0.284197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.2843 | −0.330720 | −0.165360 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165360 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.1716 | 1.32126 | 0.660629 | − | 0.750712i | \(-0.270290\pi\) | ||||
0.660629 | + | 0.750712i | \(0.270290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.65685 | 0.0531163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0294 | 0.480834 | 0.240417 | − | 0.970670i | \(-0.422716\pi\) | ||||
0.240417 | + | 0.970670i | \(0.422716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | −0.0958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.5980 | 0.816449 | 0.408224 | − | 0.912882i | \(-0.366148\pi\) | ||||
0.408224 | + | 0.912882i | \(0.366148\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.9411 | −1.90988 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.3137 | 0.804929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.4558 | 1.18982 | 0.594912 | − | 0.803791i | \(-0.297187\pi\) | ||||
0.594912 | + | 0.803791i | \(0.297187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.41421 | 0.266749 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6863 | 0.718482 | 0.359241 | − | 0.933245i | \(-0.383036\pi\) | ||||
0.359241 | + | 0.933245i | \(0.383036\pi\) | |||||||
\(998\) | 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 | 6048.2.a.bg.1.2 | yes | 2 | |
3.2 | odd | 2 | 6048.2.a.z.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 6048.2.a.bj.1.2 | yes | 2 | ||
12.11 | even | 2 | 6048.2.a.ba.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.z.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
6048.2.a.ba.1.1 | yes | 2 | 12.11 | even | 2 | ||
6048.2.a.bg.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
6048.2.a.bj.1.2 | yes | 2 | 4.3 | odd | 2 |