Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-4.06168\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | 4.06168 | 1.81644 | 0.908219 | − | 0.418496i | \(-0.137442\pi\) | ||||
0.908219 | + | 0.418496i | \(0.137442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52198 | −0.575253 | −0.287627 | − | 0.957743i | \(-0.592866\pi\) | ||||
−0.287627 | + | 0.957743i | \(0.592866\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.75016 | 1.13071 | 0.565357 | − | 0.824846i | \(-0.308738\pi\) | ||||
0.565357 | + | 0.824846i | \(0.308738\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.808587 | −0.224262 | −0.112131 | − | 0.993693i | \(-0.535768\pi\) | ||||
−0.112131 | + | 0.993693i | \(0.535768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.48425 | 0.359984 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.96105 | −1.36756 | −0.683779 | − | 0.729689i | \(-0.739665\pi\) | ||||
−0.683779 | + | 0.729689i | \(0.739665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.26017 | 1.72236 | 0.861182 | − | 0.508297i | \(-0.169725\pi\) | ||||
0.861182 | + | 0.508297i | \(0.169725\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.4972 | 2.29945 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.45397 | 1.01278 | 0.506388 | − | 0.862306i | \(-0.330980\pi\) | ||||
0.506388 | + | 0.862306i | \(0.330980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.18417 | 1.46992 | 0.734960 | − | 0.678110i | \(-0.237201\pi\) | ||||
0.734960 | + | 0.678110i | \(0.237201\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.18178 | −1.04491 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.32365 | −0.875203 | −0.437602 | − | 0.899169i | \(-0.644172\pi\) | ||||
−0.437602 | + | 0.899169i | \(0.644172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.14543 | −0.803581 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00707 | −0.763572 | −0.381786 | − | 0.924251i | \(-0.624691\pi\) | ||||
−0.381786 | + | 0.924251i | \(0.624691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.25196 | −0.474347 | −0.237173 | − | 0.971467i | \(-0.576221\pi\) | ||||
−0.237173 | + | 0.971467i | \(0.576221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.68358 | −0.669084 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.56769 | −1.03950 | −0.519751 | − | 0.854318i | \(-0.673975\pi\) | ||||
−0.519751 | + | 0.854318i | \(0.673975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.2319 | 2.05387 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2066 | 1.84954 | 0.924770 | − | 0.380527i | \(-0.124258\pi\) | ||||
0.924770 | + | 0.380527i | \(0.124258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.91923 | 0.373769 | 0.186885 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186885 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.28422 | −0.407357 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6127 | 1.90739 | 0.953695 | − | 0.300775i | \(-0.0972454\pi\) | ||||
0.953695 | + | 0.300775i | \(0.0972454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.362319 | −0.0429994 | −0.0214997 | − | 0.999769i | \(-0.506844\pi\) | ||||
−0.0214997 | + | 0.999769i | \(0.506844\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1669 | −1.42403 | −0.712014 | − | 0.702165i | \(-0.752217\pi\) | ||||
−0.712014 | + | 0.702165i | \(0.752217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.70765 | −0.650448 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8747 | 1.33601 | 0.668006 | − | 0.744156i | \(-0.267148\pi\) | ||||
0.668006 | + | 0.744156i | \(0.267148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.55930 | 0.280919 | 0.140460 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140460 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.02855 | 0.653888 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6827 | −1.23836 | −0.619179 | − | 0.785250i | \(-0.712535\pi\) | ||||
−0.619179 | + | 0.785250i | \(0.712535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23065 | 0.129007 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.2119 | −2.48409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.54466 | 0.664510 | 0.332255 | − | 0.943190i | \(-0.392191\pi\) | ||||
0.332255 | + | 0.943190i | \(0.392191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5654 | −1.74782 | −0.873912 | − | 0.486085i | \(-0.838425\pi\) | ||||
−0.873912 | + | 0.486085i | \(0.838425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8844 | 1.76220 | 0.881100 | − | 0.472930i | \(-0.156804\pi\) | ||||
0.881100 | + | 0.472930i | \(0.156804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.38542 | 0.810649 | 0.405325 | − | 0.914173i | \(-0.367159\pi\) | ||||
0.405325 | + | 0.914173i | \(0.367159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.932415 | 0.0893092 | 0.0446546 | − | 0.999002i | \(-0.485781\pi\) | ||||
0.0446546 | + | 0.999002i | \(0.485781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4832 | 1.26839 | 0.634196 | − | 0.773172i | \(-0.281331\pi\) | ||||
0.634196 | + | 0.773172i | \(0.281331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.5501 | 3.12857 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.25900 | −0.207082 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.06368 | 0.278516 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 26.3897 | 2.36036 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.8720 | −1.76335 | −0.881675 | − | 0.471857i | \(-0.843584\pi\) | ||||
−0.881675 | + | 0.471857i | \(0.843584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4780 | 1.78918 | 0.894588 | − | 0.446893i | \(-0.147469\pi\) | ||||
0.894588 | + | 0.446893i | \(0.147469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.07259 | 0.786693 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.96583 | 0.167952 | 0.0839761 | − | 0.996468i | \(-0.473238\pi\) | ||||
0.0839761 | + | 0.996468i | \(0.473238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.35402 | 0.284485 | 0.142242 | − | 0.989832i | \(-0.454569\pi\) | ||||
0.142242 | + | 0.989832i | \(0.454569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.03233 | −0.253576 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.1523 | 1.83965 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8386 | −0.887932 | −0.443966 | − | 0.896044i | \(-0.646429\pi\) | ||||
−0.443966 | + | 0.896044i | \(0.646429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.05641 | −0.737001 | −0.368500 | − | 0.929628i | \(-0.620129\pi\) | ||||
−0.368500 | + | 0.929628i | \(0.620129\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.2415 | 2.67002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1306 | 1.28736 | 0.643682 | − | 0.765293i | \(-0.277406\pi\) | ||||
0.643682 | + | 0.765293i | \(0.277406\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5718 | −0.990796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.30832 | 0.415780 | 0.207890 | − | 0.978152i | \(-0.433340\pi\) | ||||
0.207890 | + | 0.978152i | \(0.433340\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3462 | −0.949707 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.04182 | −0.611408 | −0.305704 | − | 0.952127i | \(-0.598892\pi\) | ||||
−0.305704 | + | 0.952127i | \(0.598892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.4985 | −1.32276 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8439 | −1.03474 | −0.517371 | − | 0.855761i | \(-0.673089\pi\) | ||||
−0.517371 | + | 0.855761i | \(0.673089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.189929 | −0.0141173 | −0.00705864 | − | 0.999975i | \(-0.502247\pi\) | ||||
−0.00705864 | + | 0.999975i | \(0.502247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.6230 | −1.58975 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.56618 | 0.407039 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.16497 | −0.373724 | −0.186862 | − | 0.982386i | \(-0.559832\pi\) | ||||
−0.186862 | + | 0.982386i | \(0.559832\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4877 | 1.04284 | 0.521422 | − | 0.853299i | \(-0.325402\pi\) | ||||
0.521422 | + | 0.853299i | \(0.325402\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.95294 | 0.566624 | 0.283312 | − | 0.959028i | \(-0.408567\pi\) | ||||
0.283312 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0286 | −0.923575 | −0.461788 | − | 0.886991i | \(-0.652792\pi\) | ||||
−0.461788 | + | 0.886991i | \(0.652792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.30082 | −0.582603 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.8991 | −1.45965 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.3549 | −1.54632 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3340 | −1.12448 | −0.562239 | − | 0.826975i | \(-0.690060\pi\) | ||||
−0.562239 | + | 0.826975i | \(0.690060\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.3371 | −1.38698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4561 | −0.845577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.20015 | −0.0807306 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.4549 | −1.97245 | −0.986224 | − | 0.165414i | \(-0.947104\pi\) | ||||
−0.986224 | + | 0.165414i | \(0.947104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2229 | 0.744889 | 0.372445 | − | 0.928054i | \(-0.378520\pi\) | ||||
0.372445 | + | 0.928054i | \(0.378520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.35856 | −0.155858 | −0.0779291 | − | 0.996959i | \(-0.524831\pi\) | ||||
−0.0779291 | + | 0.996959i | \(0.524831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.6121 | 1.28483 | 0.642415 | − | 0.766357i | \(-0.277933\pi\) | ||||
0.642415 | + | 0.766357i | \(0.277933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.2084 | −0.861622 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.61893 | 0.363458 | 0.181729 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181729 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5680 | 1.45373 | 0.726867 | − | 0.686778i | \(-0.240976\pi\) | ||||
0.726867 | + | 0.686778i | \(0.240976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.0232 | −1.21535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.82003 | 0.306691 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.49552 | −0.157516 | −0.0787578 | − | 0.996894i | \(-0.525095\pi\) | ||||
−0.0787578 | + | 0.996894i | \(0.525095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.9769 | 1.94750 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.7511 | 1.60631 | 0.803153 | − | 0.595772i | \(-0.203154\pi\) | ||||
0.803153 | + | 0.595772i | \(0.203154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.10248 | 0.503464 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.8069 | 1.22135 | 0.610673 | − | 0.791883i | \(-0.290899\pi\) | ||||
0.610673 | + | 0.791883i | \(0.290899\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.7375 | −1.88819 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.54672 | −0.216247 | −0.108124 | − | 0.994137i | \(-0.534484\pi\) | ||||
−0.108124 | + | 0.994137i | \(0.534484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6862 | 0.831380 | 0.415690 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415690 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 43.1164 | 2.60002 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.28135 | −0.137073 | −0.0685366 | − | 0.997649i | \(-0.521833\pi\) | ||||
−0.0685366 | + | 0.997649i | \(0.521833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.9176 | −1.48646 | −0.743230 | − | 0.669036i | \(-0.766707\pi\) | ||||
−0.743230 | + | 0.669036i | \(0.766707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7901 | −0.760295 | −0.380147 | − | 0.924926i | \(-0.624127\pi\) | ||||
−0.380147 | + | 0.924926i | \(0.624127\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.83122 | 0.462263 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7970 | −0.870412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7252 | −0.626571 | −0.313285 | − | 0.949659i | \(-0.601430\pi\) | ||||
−0.313285 | + | 0.949659i | \(0.601430\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 57.7026 | 3.35957 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.67906 | −0.386260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.62065 | 0.439247 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.8570 | 0.678929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8870 | −0.906720 | −0.453360 | − | 0.891328i | \(-0.649775\pi\) | ||||
−0.453360 | + | 0.891328i | \(0.649775\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4982 | 0.595297 | 0.297649 | − | 0.954675i | \(-0.403798\pi\) | ||||
0.297649 | + | 0.954675i | \(0.403798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699154 | − | 0.714971i | \(-0.253560\pi\) | ||||
0.699154 | + | 0.714971i | \(0.253560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.85429 | −0.216478 | −0.108239 | − | 0.994125i | \(-0.534521\pi\) | ||||
−0.108239 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.4532 | 1.14516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.84770 | −0.492299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.29651 | −0.515678 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.94941 | 0.272870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4529 | 0.794405 | 0.397203 | − | 0.917731i | \(-0.369981\pi\) | ||||
0.397203 | + | 0.917731i | \(0.369981\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 63.4136 | 3.46466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1456 | −1.09740 | −0.548702 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548702 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.6919 | 1.66206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7822 | 0.960146 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.01744 | 0.108302 | 0.0541510 | − | 0.998533i | \(-0.482755\pi\) | ||||
0.0541510 | + | 0.998533i | \(0.482755\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.37224 | −0.448156 | −0.224078 | − | 0.974571i | \(-0.571937\pi\) | ||||
−0.224078 | + | 0.974571i | \(0.571937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.4168 | −0.980227 | −0.490113 | − | 0.871659i | \(-0.663045\pi\) | ||||
−0.490113 | + | 0.871659i | \(0.663045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.47162 | −0.0781057 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.18725 | −0.168217 | −0.0841083 | − | 0.996457i | \(-0.526804\pi\) | ||||
−0.0841083 | + | 0.996457i | \(0.526804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5341 | 0.870217 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −49.4180 | −2.58666 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.27091 | 0.222940 | 0.111470 | − | 0.993768i | \(-0.464444\pi\) | ||||
0.111470 | + | 0.993768i | \(0.464444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5178 | 0.597977 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1400 | 0.680361 | 0.340181 | − | 0.940360i | \(-0.389512\pi\) | ||||
0.340181 | + | 0.940360i | \(0.389512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.41001 | −0.227127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8851 | −1.07280 | −0.536398 | − | 0.843965i | \(-0.680215\pi\) | ||||
−0.536398 | + | 0.843965i | \(0.680215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8312 | −1.52430 | −0.762152 | − | 0.647398i | \(-0.775857\pi\) | ||||
−0.762152 | + | 0.647398i | \(0.775857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.1827 | −1.18150 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.6104 | 1.55201 | 0.776004 | − | 0.630728i | \(-0.217244\pi\) | ||||
0.776004 | + | 0.630728i | \(0.217244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2602 | 0.620023 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.2313 | 2.42678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7310 | 1.14083 | 0.570417 | − | 0.821355i | \(-0.306782\pi\) | ||||
0.570417 | + | 0.821355i | \(0.306782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1345 | −0.705841 | −0.352920 | − | 0.935653i | \(-0.614811\pi\) | ||||
−0.352920 | + | 0.935653i | \(0.614811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.61762 | −0.329647 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.9645 | −0.989605 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.7975 | 1.07782 | 0.538908 | − | 0.842365i | \(-0.318837\pi\) | ||||
0.538908 | + | 0.842365i | \(0.318837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.6221 | −1.06395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3950 | 0.510272 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.5721 | −1.93322 | −0.966612 | − | 0.256245i | \(-0.917515\pi\) | ||||
−0.966612 | + | 0.256245i | \(0.917515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4056 | 0.994510 | 0.497255 | − | 0.867604i | \(-0.334341\pi\) | ||||
0.497255 | + | 0.867604i | \(0.334341\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.0648 | 0.827764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.44301 | −0.215012 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.2385 | 1.79371 | 0.896857 | − | 0.442321i | \(-0.145845\pi\) | ||||
0.896857 | + | 0.442321i | \(0.145845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6179 | −0.558322 | −0.279161 | − | 0.960244i | \(-0.590056\pi\) | ||||
−0.279161 | + | 0.960244i | \(0.590056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −49.2393 | −2.35543 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.9288 | −1.42843 | −0.714213 | − | 0.699929i | \(-0.753215\pi\) | ||||
−0.714213 | + | 0.699929i | \(0.753215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.7037 | 1.26873 | 0.634366 | − | 0.773033i | \(-0.281261\pi\) | ||||
0.634366 | + | 0.773033i | \(0.281261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.4512 | −2.24940 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.31122 | 0.439423 | 0.219712 | − | 0.975565i | \(-0.429488\pi\) | ||||
0.219712 | + | 0.975565i | \(0.429488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.2962 | −0.908621 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.99851 | 0.234334 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.552255 | −0.0258334 | −0.0129167 | − | 0.999917i | \(-0.504112\pi\) | ||||
−0.0129167 | + | 0.999917i | \(0.504112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1939 | −0.940525 | −0.470263 | − | 0.882527i | \(-0.655841\pi\) | ||||
−0.470263 | + | 0.882527i | \(0.655841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7307 | 1.19581 | 0.597903 | − | 0.801568i | \(-0.296001\pi\) | ||||
0.597903 | + | 0.801568i | \(0.296001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.08232 | 0.420280 | 0.210140 | − | 0.977671i | \(-0.432608\pi\) | ||||
0.210140 | + | 0.977671i | \(0.432608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.7621 | −1.09723 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.7773 | −0.863382 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −68.5356 | −3.14463 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2393 | −0.879064 | −0.439532 | − | 0.898227i | \(-0.644856\pi\) | ||||
−0.439532 | + | 0.898227i | \(0.644856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.30464 | 0.196275 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.5823 | 1.20704 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.48245 | −0.157805 | −0.0789024 | − | 0.996882i | \(-0.525142\pi\) | ||||
−0.0789024 | + | 0.996882i | \(0.525142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.3570 | 1.14435 | 0.572173 | − | 0.820133i | \(-0.306101\pi\) | ||||
0.572173 | + | 0.820133i | \(0.306101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.09506 | 0.364583 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.551441 | 0.0247355 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6852 | −0.523102 | −0.261551 | − | 0.965190i | \(-0.584234\pi\) | ||||
−0.261551 | + | 0.965190i | \(0.584234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.88462 | 0.440734 | 0.220367 | − | 0.975417i | \(-0.429275\pi\) | ||||
0.220367 | + | 0.975417i | \(0.429275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −71.3450 | −3.17481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.67964 | −0.340394 | −0.170197 | − | 0.985410i | \(-0.554440\pi\) | ||||
−0.170197 | + | 0.985410i | \(0.554440\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.5177 | 0.819177 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 72.6406 | 3.20093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.1954 | −0.536351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.9007 | 0.784242 | 0.392121 | − | 0.919914i | \(-0.371741\pi\) | ||||
0.392121 | + | 0.919914i | \(0.371741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.7100 | −1.91131 | −0.955653 | − | 0.294495i | \(-0.904848\pi\) | ||||
−0.955653 | + | 0.294495i | \(0.904848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.1474 | 0.529148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.2303 | 1.96654 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.16053 | 0.180212 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.0589 | 1.47249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.5642 | −0.756543 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.15894 | 0.264794 | 0.132397 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132397 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.78717 | 0.162225 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9938 | 1.53898 | 0.769492 | − | 0.638656i | \(-0.220509\pi\) | ||||
0.769492 | + | 0.638656i | \(0.220509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.5114 | −1.38503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.0731 | −0.768545 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1340 | 0.683620 | 0.341810 | − | 0.939769i | \(-0.388960\pi\) | ||||
0.341810 | + | 0.939769i | \(0.388960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.04866 | 0.171240 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.71176 | 0.0721421 | 0.0360711 | − | 0.999349i | \(-0.488516\pi\) | ||||
0.0360711 | + | 0.999349i | \(0.488516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.7644 | 2.30396 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0289 | −0.965422 | −0.482711 | − | 0.875780i | \(-0.660348\pi\) | ||||
−0.482711 | + | 0.875780i | \(0.660348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.81798 | 0.285324 | 0.142662 | − | 0.989771i | \(-0.454434\pi\) | ||||
0.142662 | + | 0.989771i | \(0.454434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 94.9690 | 3.96048 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5267 | 0.563124 | 0.281562 | − | 0.959543i | \(-0.409147\pi\) | ||||
0.281562 | + | 0.959543i | \(0.409147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.89519 | −0.161600 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.3800 | −1.17538 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.89395 | 0.243269 | 0.121635 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121635 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.7863 | −2.01020 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5539 | 0.967244 | 0.483622 | − | 0.875277i | \(-0.339321\pi\) | ||||
0.483622 | + | 0.875277i | \(0.339321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.17532 | −0.376152 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0084 | −0.408931 | −0.204466 | − | 0.978874i | \(-0.565546\pi\) | ||||
−0.204466 | + | 0.978874i | \(0.565546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.20219 | −0.252993 | −0.126496 | − | 0.991967i | \(-0.540373\pi\) | ||||
−0.126496 | + | 0.991967i | \(0.540373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4437 | 0.505907 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.7183 | −0.840931 | −0.420466 | − | 0.907308i | \(-0.638133\pi\) | ||||
−0.420466 | + | 0.907308i | \(0.638133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.62949 | 0.106378 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.1939 | −1.54264 | −0.771319 | − | 0.636449i | \(-0.780403\pi\) | ||||
−0.771319 | + | 0.636449i | \(0.780403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1762 | −0.892781 | −0.446391 | − | 0.894838i | \(-0.647291\pi\) | ||||
−0.446391 | + | 0.894838i | \(0.647291\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0203 | −0.804684 | −0.402342 | − | 0.915489i | \(-0.631804\pi\) | ||||
−0.402342 | + | 0.915489i | \(0.631804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.7807 | 0.712370 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49.7001 | 1.98801 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.90164 | −0.315059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.74136 | 0.268369 | 0.134185 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134185 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −80.7135 | −3.20302 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.78709 | 0.150050 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5423 | 0.574386 | 0.287193 | − | 0.957873i | \(-0.407278\pi\) | ||||
0.287193 | + | 0.957873i | \(0.407278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.1380 | −0.596985 | −0.298493 | − | 0.954412i | \(-0.596484\pi\) | ||||
−0.298493 | + | 0.954412i | \(0.596484\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.0389 | −1.41683 | −0.708417 | − | 0.705794i | \(-0.750591\pi\) | ||||
−0.708417 | + | 0.705794i | \(0.750591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.2769 | 2.09130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.9667 | −0.507428 | −0.253714 | − | 0.967279i | \(-0.581652\pi\) | ||||
−0.253714 | + | 0.967279i | \(0.581652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 83.1752 | 3.24993 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.8284 | −1.86313 | −0.931564 | − | 0.363577i | \(-0.881556\pi\) | ||||
−0.931564 | + | 0.363577i | \(0.881556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8577 | 0.694582 | 0.347291 | − | 0.937757i | \(-0.387102\pi\) | ||||
0.347291 | + | 0.937757i | \(0.387102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.8499 | 1.42898 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.0507 | 1.74437 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9476 | 0.422627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.6031 | −1.64223 | −0.821115 | − | 0.570763i | \(-0.806647\pi\) | ||||
−0.821115 | + | 0.570763i | \(0.806647\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.8028 | −0.492053 | −0.246027 | − | 0.969263i | \(-0.579125\pi\) | ||||
−0.246027 | + | 0.969263i | \(0.579125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.96083 | −0.382261 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.7459 | 1.13819 | 0.569097 | − | 0.822270i | \(-0.307293\pi\) | ||||
0.569097 | + | 0.822270i | \(0.307293\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.98457 | 0.305075 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.11913 | 0.233120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7414 | 1.58792 | 0.793959 | − | 0.607972i | \(-0.208017\pi\) | ||||
0.793959 | + | 0.607972i | \(0.208017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6230 | 0.516748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.63711 | −0.289276 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4690 | 1.15080 | 0.575399 | − | 0.817873i | \(-0.304847\pi\) | ||||
0.575399 | + | 0.817873i | \(0.304847\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.7346 | 1.19689 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.7342 | 1.00544 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.5858 | 1.37401 | 0.687005 | − | 0.726653i | \(-0.258925\pi\) | ||||
0.687005 | + | 0.726653i | \(0.258925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 67.6026 | 2.53174 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.3163 | −0.460605 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.8911 | −1.63686 | −0.818430 | − | 0.574606i | \(-0.805155\pi\) | ||||
−0.818430 | + | 0.574606i | \(0.805155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.2196 | −1.01371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.7055 | 2.32882 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9724 | 0.740737 | 0.370368 | − | 0.928885i | \(-0.379231\pi\) | ||||
0.370368 | + | 0.928885i | \(0.379231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.43176 | −0.274874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.84512 | −0.252830 | −0.126415 | − | 0.991977i | \(-0.540347\pi\) | ||||
−0.126415 | + | 0.991977i | \(0.540347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.5499 | 2.15671 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.6138 | −0.905434 | −0.452717 | − | 0.891654i | \(-0.649545\pi\) | ||||
−0.452717 | + | 0.891654i | \(0.649545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.20444 | 0.190932 | 0.0954661 | − | 0.995433i | \(-0.469566\pi\) | ||||
0.0954661 | + | 0.995433i | \(0.469566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.0229 | −1.61287 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.7624 | −0.466329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.2658 | 1.06792 | 0.533962 | − | 0.845508i | \(-0.320702\pi\) | ||||
0.533962 | + | 0.845508i | \(0.320702\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.7842 | −1.33872 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.9464 | −1.23380 | −0.616901 | − | 0.787041i | \(-0.711612\pi\) | ||||
−0.616901 | + | 0.787041i | \(0.711612\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.6786 | −0.858348 | −0.429174 | − | 0.903222i | \(-0.641195\pi\) | ||||
−0.429174 | + | 0.903222i | \(0.641195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.41911 | −0.0513754 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.4873 | −0.414781 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8397 | 0.679378 | 0.339689 | − | 0.940538i | \(-0.389678\pi\) | ||||
0.339689 | + | 0.940538i | \(0.389678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0546 | −0.397605 | −0.198803 | − | 0.980040i | \(-0.563705\pi\) | ||||
−0.198803 | + | 0.980040i | \(0.563705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 94.0953 | 3.38000 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.6722 | 1.09894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.35875 | −0.0486200 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.5174 | 2.33841 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9181 | 0.745651 | 0.372825 | − | 0.927902i | \(-0.378389\pi\) | ||||
0.372825 | + | 0.927902i | \(0.378389\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.5211 | −0.729647 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.36045 | −0.0838222 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.6335 | −1.51016 | −0.755078 | − | 0.655635i | \(-0.772401\pi\) | ||||
−0.755078 | + | 0.655635i | \(0.772401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.82673 | −0.170757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.6278 | −1.61017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51.0626 | −1.79972 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.21586 | −0.183380 | −0.0916899 | − | 0.995788i | \(-0.529227\pi\) | ||||
−0.0916899 | + | 0.995788i | \(0.529227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.3972 | 0.891817 | 0.445908 | − | 0.895079i | \(-0.352881\pi\) | ||||
0.445908 | + | 0.895079i | \(0.352881\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.5607 | 0.755238 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.8474 | 1.04423 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.54482 | 0.298216 | 0.149108 | − | 0.988821i | \(-0.452360\pi\) | ||||
0.149108 | + | 0.988821i | \(0.452360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5315 | 0.541393 | 0.270697 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270697 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.4424 | −1.09336 | −0.546680 | − | 0.837341i | \(-0.684109\pi\) | ||||
−0.546680 | + | 0.837341i | \(0.684109\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.1091 | −1.01100 | −0.505501 | − | 0.862826i | \(-0.668692\pi\) | ||||
−0.505501 | + | 0.862826i | \(0.668692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.95162 | −0.240859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.06168 | 0.140560 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.39747 | −0.0482461 | −0.0241231 | − | 0.999709i | \(-0.507679\pi\) | ||||
−0.0241231 | + | 0.999709i | \(0.507679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.745762 | 0.0257159 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.1462 | −1.72508 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.66285 | −0.160217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.9743 | −1.50742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.5987 | −1.08192 | −0.540959 | − | 0.841049i | \(-0.681938\pi\) | ||||
−0.540959 | + | 0.841049i | \(0.681938\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.76282 | −0.265173 | −0.132586 | − | 0.991171i | \(-0.542328\pi\) | ||||
−0.132586 | + | 0.991171i | \(0.542328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9777 | 0.715750 | 0.357875 | − | 0.933769i | \(-0.383501\pi\) | ||||
0.357875 | + | 0.933769i | \(0.383501\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.46954 | −0.152145 | −0.0760725 | − | 0.997102i | \(-0.524238\pi\) | ||||
−0.0760725 | + | 0.997102i | \(0.524238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.6633 | −1.11059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.5321 | 1.51065 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6242 | −0.427755 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.1645 | −1.35781 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.68629 | −0.225780 | −0.112890 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112890 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.7196 | −1.20342 | −0.601711 | − | 0.798714i | \(-0.705514\pi\) | ||||
−0.601711 | + | 0.798714i | \(0.705514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00066 | −0.0336747 | −0.0168374 | − | 0.999858i | \(-0.505360\pi\) | ||||
−0.0168374 | + | 0.999858i | \(0.505360\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.70835 | 0.0909374 | 0.0454687 | − | 0.998966i | \(-0.485522\pi\) | ||||
0.0454687 | + | 0.998966i | \(0.485522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.2447 | 1.01437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.3851 | 0.648697 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.2295 | −1.87955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.6362 | 1.48870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2324 | −0.374204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.771429 | −0.0256432 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.5715 | −0.716268 | −0.358134 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358134 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.3148 | −1.96519 | −0.982594 | − | 0.185767i | \(-0.940523\pi\) | ||||
−0.982594 | + | 0.185767i | \(0.940523\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.59776 | 0.317640 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.1671 | −1.02923 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6875 | −0.550471 | −0.275236 | − | 0.961377i | \(-0.588756\pi\) | ||||
−0.275236 | + | 0.961377i | \(0.588756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.292967 | 0.00964311 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −61.2073 | −2.01248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.5294 | −0.837592 | −0.418796 | − | 0.908080i | \(-0.637548\pi\) | ||||
−0.418796 | + | 0.908080i | \(0.637548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9191 | 0.915011 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.6080 | 0.739361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.94170 | 0.194107 | 0.0970535 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970535 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.9869 | −1.89032 | −0.945159 | − | 0.326609i | \(-0.894094\pi\) | ||||
−0.945159 | + | 0.326609i | \(0.894094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.5021 | −1.38406 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.4862 | −1.02316 | −0.511582 | − | 0.859235i | \(-0.670940\pi\) | ||||
−0.511582 | + | 0.859235i | \(0.670940\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.83800 | 0.319355 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.63227 | 0.117661 | 0.0588304 | − | 0.998268i | \(-0.481263\pi\) | ||||
0.0588304 | + | 0.998268i | \(0.481263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.9785 | −0.678847 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.99195 | −0.0966151 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.9807 | 1.16067 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 58.8442 | 1.89426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.2944 | −1.32794 | −0.663970 | − | 0.747760i | \(-0.731130\pi\) | ||||
−0.663970 | + | 0.747760i | \(0.731130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5508 | −0.370684 | −0.185342 | − | 0.982674i | \(-0.559339\pi\) | ||||
−0.185342 | + | 0.982674i | \(0.559339\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.10475 | −0.163651 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.65595 | 0.116964 | 0.0584821 | − | 0.998288i | \(-0.481374\pi\) | ||||
0.0584821 | + | 0.998288i | \(0.481374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.8118 | −1.40023 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.3408 | 0.393610 | 0.196805 | − | 0.980443i | \(-0.436943\pi\) | ||||
0.196805 | + | 0.980443i | \(0.436943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.3023 | 1.02924 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.3593 | −1.31515 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7724 | 1.10458 | 0.552291 | − | 0.833651i | \(-0.313754\pi\) | ||||
0.552291 | + | 0.833651i | \(0.313754\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.9181 | −1.67762 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.6009 | 1.50754 | 0.753768 | − | 0.657141i | \(-0.228234\pi\) | ||||
0.753768 | + | 0.657141i | \(0.228234\pi\) | |||||||
\(998\) | 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 | 6012.2.a.i.1.9 | 9 | ||
3.2 | odd | 2 | 2004.2.a.c.1.1 | ✓ | 9 | ||
12.11 | even | 2 | 8016.2.a.bc.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.1 | ✓ | 9 | 3.2 | odd | 2 | ||
6012.2.a.i.1.9 | 9 | 1.1 | even | 1 | trivial | ||
8016.2.a.bc.1.1 | 9 | 12.11 | even | 2 |