Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 306x^{10} + 30777x^{8} + 1381040x^{6} + 28918584x^{4} + 243888288x^{2} + 366645904 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.6 | ||
Root | \(7.39017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.541 |
Dual form | 1620.4.i.w.1081.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.6578 | − | 20.1920i | 0.629465 | − | 1.09026i | −0.358195 | − | 0.933647i | \(-0.616608\pi\) |
0.987659 | − | 0.156618i | \(-0.0500591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.8745 | + | 29.2275i | −0.462532 | + | 0.801128i | −0.999086 | − | 0.0427371i | \(-0.986392\pi\) |
0.536555 | + | 0.843866i | \(0.319726\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.4469 | + | 76.9843i | 0.948258 | + | 1.64243i | 0.749092 | + | 0.662466i | \(0.230490\pi\) |
0.199166 | + | 0.979966i | \(0.436177\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 108.661 | 1.55025 | 0.775124 | − | 0.631809i | \(-0.217687\pi\) | ||||
0.775124 | + | 0.631809i | \(0.217687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.4799 | 0.259359 | 0.129679 | − | 0.991556i | \(-0.458605\pi\) | ||||
0.129679 | + | 0.991556i | \(0.458605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −42.9612 | − | 74.4110i | −0.389480 | − | 0.674599i | 0.602900 | − | 0.797817i | \(-0.294012\pi\) |
−0.992380 | + | 0.123218i | \(0.960679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.48907 | − | 16.4355i | 0.0607612 | − | 0.105242i | −0.834045 | − | 0.551697i | \(-0.813981\pi\) |
0.894806 | + | 0.446455i | \(0.147314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 83.1724 | + | 144.059i | 0.481877 | + | 0.834636i | 0.999784 | − | 0.0208014i | \(-0.00662176\pi\) |
−0.517906 | + | 0.855437i | \(0.673288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −116.578 | −0.563010 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −167.664 | −0.744966 | −0.372483 | − | 0.928039i | \(-0.621493\pi\) | ||||
−0.372483 | + | 0.928039i | \(0.621493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −189.143 | − | 327.605i | −0.720466 | − | 1.24788i | −0.960813 | − | 0.277197i | \(-0.910595\pi\) |
0.240347 | − | 0.970687i | \(-0.422739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −190.222 | + | 329.474i | −0.674618 | + | 1.16847i | 0.301962 | + | 0.953320i | \(0.402358\pi\) |
−0.976580 | + | 0.215153i | \(0.930975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −123.414 | + | 213.760i | −0.383018 | + | 0.663406i | −0.991492 | − | 0.130167i | \(-0.958449\pi\) |
0.608474 | + | 0.793574i | \(0.291782\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −100.311 | − | 173.744i | −0.292452 | − | 0.506541i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −284.344 | −0.736937 | −0.368469 | − | 0.929640i | \(-0.620118\pi\) | ||||
−0.368469 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 168.745 | 0.413701 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 363.699 | + | 629.945i | 0.802534 | + | 1.39003i | 0.917943 | + | 0.396712i | \(0.129849\pi\) |
−0.115409 | + | 0.993318i | \(0.536818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −235.434 | + | 407.783i | −0.494168 | + | 0.855923i | −0.999977 | − | 0.00672169i | \(-0.997860\pi\) |
0.505810 | + | 0.862645i | \(0.331194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 222.235 | − | 384.922i | 0.424074 | − | 0.734518i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 375.978 | + | 651.213i | 0.685567 | + | 1.18744i | 0.973258 | + | 0.229714i | \(0.0737791\pi\) |
−0.287691 | + | 0.957723i | \(0.592888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −864.963 | −1.44581 | −0.722903 | − | 0.690949i | \(-0.757193\pi\) | ||||
−0.722903 | + | 0.690949i | \(0.757193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1003.53 | −1.60896 | −0.804479 | − | 0.593982i | \(-0.797555\pi\) | ||||
−0.804479 | + | 0.593982i | \(0.797555\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 393.440 | + | 681.459i | 0.582295 | + | 1.00856i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 419.251 | − | 726.163i | 0.597081 | − | 1.03417i | −0.396169 | − | 0.918178i | \(-0.629661\pi\) |
0.993250 | − | 0.115996i | \(-0.0370061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −238.057 | + | 412.327i | −0.314821 | + | 0.545287i | −0.979399 | − | 0.201932i | \(-0.935278\pi\) |
0.664578 | + | 0.747219i | \(0.268611\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −271.653 | − | 470.517i | −0.346646 | − | 0.600408i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 554.055 | 0.659884 | 0.329942 | − | 0.944001i | \(-0.392971\pi\) | ||||
0.329942 | + | 0.944001i | \(0.392971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2072.62 | 2.38758 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −53.6996 | − | 93.0105i | −0.0579944 | − | 0.100449i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 523.994 | − | 907.584i | 0.548490 | − | 0.950012i | −0.449888 | − | 0.893085i | \(-0.648536\pi\) |
0.998378 | − | 0.0569275i | \(-0.0181304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 209.199 | − | 362.343i | 0.206100 | − | 0.356975i | −0.744383 | − | 0.667753i | \(-0.767256\pi\) |
0.950483 | + | 0.310778i | \(0.100590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 640.394 | + | 1109.19i | 0.612620 | + | 1.06109i | 0.990797 | + | 0.135356i | \(0.0432178\pi\) |
−0.378177 | + | 0.925733i | \(0.623449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 351.116 | 0.317231 | 0.158615 | − | 0.987340i | \(-0.449297\pi\) | ||||
0.158615 | + | 0.987340i | \(0.449297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1762.43 | 1.54872 | 0.774360 | − | 0.632746i | \(-0.218072\pi\) | ||||
0.774360 | + | 0.632746i | \(0.218072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 500.931 | + | 867.638i | 0.417023 | + | 0.722306i | 0.995639 | − | 0.0932949i | \(-0.0297399\pi\) |
−0.578615 | + | 0.815601i | \(0.696407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −214.806 | + | 372.055i | −0.174181 | + | 0.301690i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1266.76 | − | 2194.09i | 0.975826 | − | 1.69018i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 96.0034 | + | 166.283i | 0.0721288 | + | 0.124931i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 852.753 | 0.595824 | 0.297912 | − | 0.954593i | \(-0.403710\pi\) | ||||
0.297912 | + | 0.954593i | \(0.403710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1339.12 | − | 2319.42i | −0.893123 | − | 1.54693i | −0.836110 | − | 0.548562i | \(-0.815176\pi\) |
−0.0570131 | − | 0.998373i | \(-0.518158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 250.409 | − | 433.721i | 0.163257 | − | 0.282770i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 211.997 | − | 367.189i | 0.132205 | − | 0.228986i | −0.792321 | − | 0.610104i | \(-0.791128\pi\) |
0.924526 | + | 0.381118i | \(0.124461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 335.757 | + | 581.549i | 0.204882 | + | 0.354866i | 0.950095 | − | 0.311960i | \(-0.100986\pi\) |
−0.745213 | + | 0.666826i | \(0.767652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3000.08 | −1.75440 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −94.8907 | −0.0543465 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1198.72 | + | 2076.24i | 0.659080 | + | 1.14156i | 0.980854 | + | 0.194743i | \(0.0623874\pi\) |
−0.321774 | + | 0.946816i | \(0.604279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 151.005 | − | 261.547i | 0.0813813 | − | 0.140957i | −0.822462 | − | 0.568820i | \(-0.807400\pi\) |
0.903843 | + | 0.427863i | \(0.140734\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 415.862 | − | 720.294i | 0.215502 | − | 0.373261i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1117.50 | + | 1935.56i | 0.568063 | + | 0.983914i | 0.996757 | + | 0.0804642i | \(0.0256403\pi\) |
−0.428695 | + | 0.903449i | \(0.641026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2003.34 | −0.980655 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −45.7276 | −0.0219734 | −0.0109867 | − | 0.999940i | \(-0.503497\pi\) | ||||
−0.0109867 | + | 0.999940i | \(0.503497\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1238.07 | + | 2144.40i | 0.573681 | + | 0.993645i | 0.996184 | + | 0.0872833i | \(0.0278185\pi\) |
−0.422502 | + | 0.906362i | \(0.638848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2852.56 | + | 4940.77i | −1.29839 | + | 2.24887i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1574.72 | − | 2727.49i | 0.692044 | − | 1.19866i | −0.279123 | − | 0.960255i | \(-0.590044\pi\) |
0.971167 | − | 0.238400i | \(-0.0766228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 291.446 | + | 504.800i | 0.125893 | + | 0.218053i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4111.57 | 1.71683 | 0.858417 | − | 0.512953i | \(-0.171448\pi\) | ||||
0.858417 | + | 0.512953i | \(0.171448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1344.52 | −0.552138 | −0.276069 | − | 0.961138i | \(-0.589032\pi\) | ||||
−0.276069 | + | 0.961138i | \(0.589032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 419.159 | + | 726.005i | 0.166579 | + | 0.288524i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1833.60 | + | 3175.89i | −0.717039 | + | 1.24195i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1264.78 | + | 2190.67i | −0.479144 | + | 0.829901i | −0.999714 | − | 0.0239175i | \(-0.992386\pi\) |
0.520570 | + | 0.853819i | \(0.325719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2004.82 | + | 3472.45i | 0.747722 | + | 1.29509i | 0.948912 | + | 0.315540i | \(0.102186\pi\) |
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2489.65 | −0.900408 | −0.450204 | − | 0.892926i | \(-0.648649\pi\) | ||||
−0.450204 | + | 0.892926i | \(0.648649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1358.91 | 0.484073 | 0.242037 | − | 0.970267i | \(-0.422185\pi\) | ||||
0.242037 | + | 0.970267i | \(0.422185\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −221.244 | − | 383.206i | −0.0764941 | − | 0.132492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −945.713 | + | 1638.02i | −0.322202 | + | 0.558071i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −362.462 | + | 627.802i | −0.119962 | + | 0.207780i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1897.31 | + | 3286.24i | 0.619034 | + | 1.07220i | 0.989662 | + | 0.143417i | \(0.0458090\pi\) |
−0.370628 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1902.22 | 0.603397 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3878.44 | 1.21330 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4829.66 | + | 8365.21i | 1.47004 | + | 2.54618i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 664.359 | − | 1150.70i | 0.199501 | − | 0.345546i | −0.748866 | − | 0.662722i | \(-0.769401\pi\) |
0.948367 | + | 0.317176i | \(0.102734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 495.789 | − | 858.731i | 0.144963 | − | 0.251084i | −0.784396 | − | 0.620260i | \(-0.787027\pi\) |
0.929359 | + | 0.369177i | \(0.120360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1987.89 | + | 3443.13i | 0.573640 | + | 0.993574i | 0.996188 | + | 0.0872336i | \(0.0278026\pi\) |
−0.422547 | + | 0.906341i | \(0.638864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4850.18 | −1.36372 | −0.681858 | − | 0.731484i | \(-0.738828\pi\) | ||||
−0.681858 | + | 0.731484i | \(0.738828\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1234.14 | 0.342582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1835.50 | − | 3179.18i | −0.496773 | − | 0.860437i | 0.503220 | − | 0.864159i | \(-0.332149\pi\) |
−0.999993 | + | 0.00372178i | \(0.998815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1137.89 | − | 1970.88i | 0.304140 | − | 0.526786i | −0.672929 | − | 0.739707i | \(-0.734964\pi\) |
0.977069 | + | 0.212921i | \(0.0682976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −501.555 | + | 868.718i | −0.130788 | + | 0.226532i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 954.713 | + | 1653.61i | 0.245939 | + | 0.425979i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 816.764 | 0.205393 | 0.102697 | − | 0.994713i | \(-0.467253\pi\) | ||||
0.102697 | + | 0.994713i | \(0.467253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2899.80 | 0.720587 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3147.07 | − | 5450.88i | −0.763847 | − | 1.32302i | −0.940854 | − | 0.338812i | \(-0.889975\pi\) |
0.177008 | − | 0.984209i | \(-0.443358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1954.60 | + | 3385.46i | −0.468930 | + | 0.812210i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −927.493 | + | 1606.47i | −0.217459 | + | 0.376650i | −0.954030 | − | 0.299710i | \(-0.903110\pi\) |
0.736572 | + | 0.676360i | \(0.236443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 710.861 | + | 1231.25i | 0.164784 | + | 0.285415i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3602.16 | −0.816460 | −0.408230 | − | 0.912879i | \(-0.633854\pi\) | ||||
−0.408230 | + | 0.912879i | \(0.633854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2920.88 | 0.654727 | 0.327363 | − | 0.944898i | \(-0.393840\pi\) | ||||
0.327363 | + | 0.944898i | \(0.393840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −421.862 | − | 730.687i | −0.0925063 | − | 0.160226i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 268.940 | − | 465.817i | 0.0583358 | − | 0.101041i | −0.835383 | − | 0.549669i | \(-0.814754\pi\) |
0.893718 | + | 0.448628i | \(0.148087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2035.26 | − | 3525.18i | 0.432077 | − | 0.748379i | −0.564975 | − | 0.825108i | \(-0.691114\pi\) |
0.997052 | + | 0.0767289i | \(0.0244476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 805.835 | + | 1395.75i | 0.169265 | + | 0.293175i | 0.938162 | − | 0.346198i | \(-0.112527\pi\) |
−0.768897 | + | 0.639373i | \(0.779194\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8819.98 | −1.81403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6894.26 | 1.40327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2228.29 | − | 3859.51i | −0.444293 | − | 0.769539i | 0.553709 | − | 0.832710i | \(-0.313212\pi\) |
−0.998003 | + | 0.0631712i | \(0.979879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1818.49 | − | 3149.72i | 0.358904 | − | 0.621640i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3818.99 | − | 6614.68i | 0.738655 | − | 1.27939i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4435.16 | + | 7681.92i | 0.849297 | + | 1.47102i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2354.34 | 0.441997 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9533 | −0.00222219 | −0.00111109 | − | 0.999999i | \(-0.500354\pi\) | ||||
−0.00111109 | + | 0.999999i | \(0.500354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4672.56 | + | 8093.12i | 0.851951 | + | 1.47562i | 0.879445 | + | 0.476000i | \(0.157914\pi\) |
−0.0274941 | + | 0.999622i | \(0.508753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4384.12 | − | 7593.51i | 0.791709 | − | 1.37128i | −0.133199 | − | 0.991089i | \(-0.542525\pi\) |
0.924908 | − | 0.380191i | \(-0.124142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 988.087 | − | 1711.42i | 0.175068 | − | 0.303226i | −0.765117 | − | 0.643891i | \(-0.777319\pi\) |
0.940185 | + | 0.340665i | \(0.110652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 320.246 | + | 554.683i | 0.0562080 | + | 0.0973551i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2334.03 | 0.402070 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2222.35 | −0.379303 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2877.49 | + | 4983.96i | 0.482192 | + | 0.835182i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3644.28 | + | 6312.08i | −0.605159 | + | 1.04817i | 0.386867 | + | 0.922135i | \(0.373557\pi\) |
−0.992026 | + | 0.126031i | \(0.959776\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1879.89 | − | 3256.06i | 0.306595 | − | 0.531038i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3649.89 | − | 6321.80i | −0.589977 | − | 1.02187i | −0.994235 | − | 0.107225i | \(-0.965803\pi\) |
0.404258 | − | 0.914645i | \(-0.367530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5613.96 | −0.891534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3319.65 | 0.522577 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3381.18 | + | 5856.37i | 0.523087 | + | 0.906013i | 0.999639 | + | 0.0268668i | \(0.00855299\pi\) |
−0.476552 | + | 0.879146i | \(0.658114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3436.48 | − | 5952.16i | 0.527079 | − | 0.912928i | −0.472423 | − | 0.881372i | \(-0.656621\pi\) |
0.999502 | − | 0.0315556i | \(-0.0100461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4805.59 | − | 8323.53i | 0.724578 | − | 1.25501i | −0.234570 | − | 0.972099i | \(-0.575368\pi\) |
0.959148 | − | 0.282906i | \(-0.0912984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2162.41 | + | 3745.40i | 0.323292 | + | 0.559958i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7951.69 | −1.16901 | −0.584504 | − | 0.811391i | \(-0.698711\pi\) | ||||
−0.584504 | + | 0.811391i | \(0.698711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6397.62 | −0.932733 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2508.82 | + | 4345.40i | 0.359774 | + | 0.623146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3194.49 | + | 5533.02i | −0.454362 | + | 0.786978i | −0.998651 | − | 0.0519193i | \(-0.983466\pi\) |
0.544289 | + | 0.838898i | \(0.316799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3314.84 | + | 5741.48i | −0.463876 | + | 0.803457i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4581.58 | + | 7935.52i | 0.635992 | + | 1.10157i | 0.986304 | + | 0.164938i | \(0.0527423\pi\) |
−0.350312 | + | 0.936633i | \(0.613924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1687.04 | 0.230469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10303.5 | −1.39646 | −0.698228 | − | 0.715875i | \(-0.746028\pi\) | ||||
−0.698228 | + | 0.715875i | \(0.746028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1859.95 | + | 3221.53i | 0.248144 | + | 0.429798i | 0.963011 | − | 0.269463i | \(-0.0868461\pi\) |
−0.714867 | + | 0.699260i | \(0.753513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1967.20 | − | 3407.29i | 0.260410 | − | 0.451044i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2235.23 | + | 3871.54i | −0.291339 | + | 0.504614i | −0.974127 | − | 0.226003i | \(-0.927434\pi\) |
0.682788 | + | 0.730617i | \(0.260767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4668.22 | − | 8085.59i | −0.603790 | − | 1.04580i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4192.51 | −0.534045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4848.35 | 0.612927 | 0.306463 | − | 0.951882i | \(-0.400854\pi\) | ||||
0.306463 | + | 0.951882i | \(0.400854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −74.7667 | − | 129.500i | −0.00931090 | − | 0.0161269i | 0.861332 | − | 0.508042i | \(-0.169630\pi\) |
−0.870643 | + | 0.491915i | \(0.836297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7393.51 | + | 12805.9i | −0.913888 | + | 1.58290i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2829.24 | − | 4900.38i | 0.344570 | − | 0.596813i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5324.84 | − | 9222.89i | −0.643756 | − | 1.11502i | −0.984587 | − | 0.174894i | \(-0.944042\pi\) |
0.340831 | − | 0.940125i | \(-0.389292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16959.8 | 2.02067 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2380.57 | 0.281585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −169.897 | − | 294.269i | −0.0198090 | − | 0.0343103i | 0.855951 | − | 0.517057i | \(-0.172972\pi\) |
−0.875760 | + | 0.482747i | \(0.839639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1066.02 | + | 1846.40i | −0.123408 | + | 0.213748i | −0.921109 | − | 0.389304i | \(-0.872716\pi\) |
0.797702 | + | 0.603052i | \(0.206049\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1358.27 | + | 2352.58i | −0.155025 | + | 0.268511i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5489.31 | + | 9507.76i | 0.622122 | + | 1.07755i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2509.67 | −0.280480 | −0.140240 | − | 0.990118i | \(-0.544787\pi\) | ||||
−0.140240 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2792.17 | 0.309891 | 0.154946 | − | 0.987923i | \(-0.450480\pi\) | ||||
0.154946 | + | 0.987923i | \(0.450480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −922.801 | − | 1598.34i | −0.101015 | − | 0.174963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3278.50 | − | 5678.53i | 0.356433 | − | 0.617361i | −0.630929 | − | 0.775841i | \(-0.717326\pi\) |
0.987362 | + | 0.158480i | \(0.0506594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −949.888 | + | 1645.25i | −0.101875 | + | 0.176452i | −0.912457 | − | 0.409172i | \(-0.865817\pi\) |
0.810582 | + | 0.585625i | \(0.199151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1385.14 | − | 2399.13i | −0.147555 | − | 0.255572i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9468.83 | −0.995238 | −0.497619 | − | 0.867396i | \(-0.665792\pi\) | ||||
−0.497619 | + | 0.867396i | \(0.665792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12766.7 | 1.33295 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5181.55 | − | 8974.72i | −0.533879 | − | 0.924706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1449.85 | + | 2511.21i | −0.148405 | + | 0.257045i | −0.930638 | − | 0.365941i | \(-0.880747\pi\) |
0.782233 | + | 0.622986i | \(0.214081\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2758.81 | + | 4778.39i | −0.278721 | + | 0.482759i | −0.971067 | − | 0.238806i | \(-0.923244\pi\) |
0.692346 | + | 0.721566i | \(0.256577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4485.15 | + | 7768.50i | 0.450200 | + | 0.779769i | 0.998398 | − | 0.0565795i | \(-0.0180194\pi\) |
−0.548198 | + | 0.836348i | \(0.684686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12314.8 | 1.22026 | 0.610130 | − | 0.792302i | \(-0.291117\pi\) | ||||
0.610130 | + | 0.792302i | \(0.291117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17532.4 | 1.72616 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6419.80 | − | 11119.4i | −0.624065 | − | 1.08091i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −268.498 | + | 465.053i | −0.0259359 | + | 0.0449223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6364.47 | + | 11023.6i | −0.607098 | + | 1.05153i | 0.384618 | + | 0.923076i | \(0.374333\pi\) |
−0.991716 | + | 0.128449i | \(0.959000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7452.13 | − | 12907.5i | −0.706420 | − | 1.22356i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5239.94 | −0.490584 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7230.67 | −0.672798 | −0.336399 | − | 0.941719i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941719i | \(0.609209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8803.45 | − | 15248.0i | −0.809153 | − | 1.40149i | −0.913451 | − | 0.406949i | \(-0.866593\pi\) |
0.104298 | − | 0.994546i | \(-0.466741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1031.09 | − | 1785.91i | 0.0941950 | − | 0.163150i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10083.6 | + | 17465.3i | −0.910084 | + | 1.57631i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10175.8 | + | 17625.0i | 0.912886 | + | 1.58116i | 0.809967 | + | 0.586475i | \(0.199485\pi\) |
0.102918 | + | 0.994690i | \(0.467182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14477.1 | 1.28331 | 0.641654 | − | 0.766995i | \(-0.278249\pi\) | ||||
0.641654 | + | 0.766995i | \(0.278249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2091.99 | −0.184341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1841.81 | + | 3190.11i | 0.160387 | + | 0.277798i | 0.935007 | − | 0.354628i | \(-0.115393\pi\) |
−0.774621 | + | 0.632426i | \(0.782059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11699.0 | + | 20263.2i | −1.01278 | + | 1.75419i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3201.97 | − | 5545.97i | 0.273972 | − | 0.474534i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4165.11 | − | 7214.18i | −0.354316 | − | 0.613693i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20684.0 | 1.73931 | 0.869655 | − | 0.493660i | \(-0.164341\pi\) | ||||
0.869655 | + | 0.493660i | \(0.164341\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18781.8 | −1.57031 | −0.785153 | − | 0.619302i | \(-0.787416\pi\) | ||||
−0.785153 | + | 0.619302i | \(0.787416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9037.61 | + | 15653.6i | 0.747029 | + | 1.29389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2392.16 | − | 4143.35i | 0.196611 | − | 0.340540i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16813.6 | − | 29122.0i | 1.36638 | − | 2.36663i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −877.791 | − | 1520.38i | −0.0709349 | − | 0.122863i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6770.78 | 0.541073 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9322.54 | 0.740864 | 0.370432 | − | 0.928860i | \(-0.379210\pi\) | ||||
0.370432 | + | 0.928860i | \(0.379210\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4406.08 | − | 7631.56i | −0.346304 | − | 0.599816i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4072.48 | − | 7053.74i | 0.318330 | − | 0.551364i | −0.661809 | − | 0.749672i | \(-0.730211\pi\) |
0.980140 | + | 0.198308i | \(0.0635446\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 203.824 | − | 353.033i | 0.0157590 | − | 0.0272953i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9775.12 | − | 16931.0i | −0.751682 | − | 1.30195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1025.83 | −0.0780355 | −0.0390177 | − | 0.999239i | \(-0.512423\pi\) | ||||
−0.0390177 | + | 0.999239i | \(0.512423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33819.1 | −2.55885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4406.31 | − | 7631.95i | −0.329847 | − | 0.571311i | 0.652634 | − | 0.757673i | \(-0.273664\pi\) |
−0.982481 | + | 0.186362i | \(0.940330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2504.66 | − | 4338.19i | 0.186499 | − | 0.323025i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3186.43 | + | 5519.07i | −0.234767 | + | 0.406628i | −0.959205 | − | 0.282712i | \(-0.908766\pi\) |
0.724438 | + | 0.689340i | \(0.242099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5420.99 | − | 9389.44i | −0.397306 | − | 0.688154i | 0.596087 | − | 0.802920i | \(-0.296721\pi\) |
−0.993393 | + | 0.114766i | \(0.963388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2148.06 | 0.155792 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1494.00 | −0.107792 | −0.0538959 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538959 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5550.47 | + | 9613.70i | 0.396338 | + | 0.686477i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4798.16 | − | 8310.66i | 0.340857 | − | 0.590382i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7829.53 | + | 13561.1i | −0.550527 | + | 0.953541i | 0.447710 | + | 0.894179i | \(0.352240\pi\) |
−0.998237 | + | 0.0593617i | \(0.981093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1786.53 | + | 3094.36i | 0.124979 | + | 0.216470i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1722.59 | −0.119289 | −0.0596444 | − | 0.998220i | \(-0.518997\pi\) | ||||
−0.0596444 | + | 0.998220i | \(0.518997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12667.6 | −0.872806 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3301.86 | − | 5718.98i | −0.225226 | − | 0.390102i | 0.731161 | − | 0.682205i | \(-0.238979\pi\) |
−0.956387 | + | 0.292102i | \(0.905645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3237.98 | − | 5608.35i | 0.219767 | − | 0.380648i | −0.734970 | − | 0.678100i | \(-0.762804\pi\) |
0.954737 | + | 0.297452i | \(0.0961369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 480.017 | − | 831.414i | 0.0322570 | − | 0.0558707i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3965.93 | + | 6869.20i | 0.265193 | + | 0.459328i | 0.967614 | − | 0.252434i | \(-0.0812309\pi\) |
−0.702421 | + | 0.711762i | \(0.747898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21941.6 | −1.45280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16332.6 | −1.07613 | −0.538065 | − | 0.842903i | \(-0.680845\pi\) | ||||
−0.538065 | + | 0.842903i | \(0.680845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5835.76 | + | 10107.8i | 0.380776 | + | 0.659524i | 0.991173 | − | 0.132572i | \(-0.0423235\pi\) |
−0.610397 | + | 0.792095i | \(0.708990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5361.24 | − | 9285.93i | 0.348120 | − | 0.602961i | −0.637796 | − | 0.770206i | \(-0.720154\pi\) |
0.985915 | + | 0.167244i | \(0.0534869\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6459.09 | − | 11187.5i | 0.415374 | − | 0.719448i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18218.5 | −1.15488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9754.15 | 0.615383 | 0.307691 | − | 0.951486i | \(-0.400444\pi\) | ||||
0.307691 | + | 0.951486i | \(0.400444\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2131.88 | − | 3692.53i | −0.133230 | − | 0.230761i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8917.02 | − | 15444.7i | 0.554639 | − | 0.960664i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9682.73 | + | 16771.0i | −0.596638 | + | 1.03341i | 0.396676 | + | 0.917959i | \(0.370164\pi\) |
−0.993313 | + | 0.115448i | \(0.963170\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14537.7 | − | 25180.0i | −0.891616 | − | 1.54432i | −0.837938 | − | 0.545766i | \(-0.816239\pi\) |
−0.0536786 | − | 0.998558i | \(-0.517095\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17400.3 | 1.05730 | 0.528651 | − | 0.848839i | \(-0.322698\pi\) | ||||
0.528651 | + | 0.848839i | \(0.322698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24548.9 | −1.48479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4233.84 | + | 7333.23i | 0.253726 | + | 0.439466i | 0.964549 | − | 0.263905i | \(-0.0850105\pi\) |
−0.710823 | + | 0.703371i | \(0.751677\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6695.58 | + | 11597.1i | −0.399417 | + | 0.691810i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11991.3 | + | 20769.5i | −0.708822 | + | 1.22772i | 0.256472 | + | 0.966552i | \(0.417440\pi\) |
−0.965294 | + | 0.261164i | \(0.915894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13361.5 | − | 23142.9i | −0.786238 | − | 1.36180i | −0.928256 | − | 0.371941i | \(-0.878692\pi\) |
0.142018 | − | 0.989864i | \(-0.454641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2504.09 | −0.146022 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1630.65 | −0.0946611 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7945.65 | − | 13762.3i | −0.457136 | − | 0.791783i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7560.71 | − | 13095.5i | 0.433052 | − | 0.750068i | −0.564082 | − | 0.825719i | \(-0.690770\pi\) |
0.997134 | + | 0.0756503i | \(0.0241033\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7468.82 | − | 12936.4i | 0.424003 | − | 0.734395i | −0.572324 | − | 0.820028i | \(-0.693958\pi\) |
0.996327 | + | 0.0856328i | \(0.0272912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12217.3 | − | 21161.0i | −0.690510 | − | 1.19600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11141.0 | 0.624158 | 0.312079 | − | 0.950056i | \(-0.398975\pi\) | ||||
0.312079 | + | 0.950056i | \(0.398975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2119.97 | −0.118248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12638.2 | − | 21890.0i | −0.698807 | − | 1.21037i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5981.42 | − | 10360.1i | 0.329297 | − | 0.570359i | −0.653076 | − | 0.757293i | \(-0.726522\pi\) |
0.982373 | + | 0.186934i | \(0.0598550\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1678.79 | − | 2907.74i | 0.0916259 | − | 0.158701i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20552.5 | − | 35597.9i | −1.11690 | − | 1.93453i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17436.0 | −0.939442 | −0.469721 | − | 0.882815i | \(-0.655646\pi\) | ||||
−0.469721 | + | 0.882815i | \(0.655646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3601.39 | −0.193213 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4877.62 | − | 8448.28i | −0.259465 | − | 0.449406i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5664.21 | + | 9810.70i | −0.300034 | + | 0.519673i | −0.976143 | − | 0.217128i | \(-0.930331\pi\) |
0.676110 | + | 0.736801i | \(0.263665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7146.37 | − | 12377.9i | 0.375363 | − | 0.650148i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7500.19 | + | 12990.7i | 0.392295 | + | 0.679475i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36889.9 | 1.91344 | 0.956718 | − | 0.291015i | \(-0.0939931\pi\) | ||||
0.956718 | + | 0.291015i | \(0.0939931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29862.5 | 1.54249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 237.227 | + | 410.889i | 0.0121522 | + | 0.0210483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5477.89 | + | 9487.99i | −0.279455 | + | 0.484030i | −0.971249 | − | 0.238064i | \(-0.923487\pi\) |
0.691794 | + | 0.722095i | \(0.256820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20669.7 | + | 35801.1i | −1.04583 | + | 1.81142i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11191.0 | + | 19383.4i | 0.563915 | + | 0.976730i | 0.997150 | + | 0.0754488i | \(0.0240390\pi\) |
−0.433234 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25377.7 | −1.26839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27800.0 | 1.38382 | 0.691908 | − | 0.721985i | \(-0.256770\pi\) | ||||
0.691908 | + | 0.721985i | \(0.256770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8963.13 | − | 15524.6i | −0.442564 | − | 0.766544i | 0.555315 | − | 0.831640i | \(-0.312598\pi\) |
−0.997879 | + | 0.0650965i | \(0.979264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5993.59 | − | 10381.2i | 0.294749 | − | 0.510521i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4093.26 | − | 7089.74i | 0.199686 | − | 0.345866i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12059.9 | − | 20888.4i | −0.585982 | − | 1.01495i | −0.994752 | − | 0.102313i | \(-0.967376\pi\) |
0.408770 | − | 0.912637i | \(-0.365958\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1510.05 | −0.0727896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10582.4 | 0.508088 | 0.254044 | − | 0.967193i | \(-0.418239\pi\) | ||||
0.254044 | + | 0.967193i | \(0.418239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18291.5 | + | 31681.9i | 0.871312 | + | 1.50916i | 0.860641 | + | 0.509213i | \(0.170063\pi\) |
0.0106710 | + | 0.999943i | \(0.496603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20546.2 | − | 35587.0i | 0.974864 | − | 1.68851i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32330.6 | + | 55998.2i | −1.52202 | + | 2.63622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7388.24 | − | 12796.8i | −0.346459 | − | 0.600084i | 0.639159 | − | 0.769075i | \(-0.279283\pi\) |
−0.985618 | + | 0.168991i | \(0.945949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3195.12 | 0.148668 | 0.0743340 | − | 0.997233i | \(-0.476317\pi\) | ||||
0.0743340 | + | 0.997233i | \(0.476317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4158.62 | −0.192751 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4062.76 | − | 7036.90i | −0.186859 | − | 0.323650i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14595.8 | − | 25280.7i | 0.668731 | − | 1.15828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5587.48 | − | 9677.80i | 0.254045 | − | 0.440020i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15493.6 | − | 26835.6i | −0.701761 | − | 1.21549i | −0.967848 | − | 0.251537i | \(-0.919064\pi\) |
0.266087 | − | 0.963949i | \(-0.414269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23359.1 | 1.05001 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41857.2 | −1.87439 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18541.5 | − | 32114.9i | −0.824059 | − | 1.42731i | −0.902636 | − | 0.430405i | \(-0.858371\pi\) |
0.0785767 | − | 0.996908i | \(-0.474962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13410.4 | + | 23227.4i | −0.593772 | + | 1.02844i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16934.0 | − | 29330.5i | 0.744194 | − | 1.28898i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5008.36 | + | 8674.73i | 0.219281 | + | 0.379806i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −648.034 | −0.0281627 | −0.0140814 | − | 0.999901i | \(-0.504482\pi\) | ||||
−0.0140814 | + | 0.999901i | \(0.504482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36017.4 | −1.55948 | −0.779742 | − | 0.626101i | \(-0.784650\pi\) | ||||
−0.779742 | + | 0.626101i | \(0.784650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 114.319 | + | 198.006i | 0.00491340 | + | 0.00851025i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4085.94 | + | 7077.06i | −0.174968 | + | 0.303054i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14404.5 | + | 24949.3i | −0.612326 | + | 1.06058i | 0.378522 | + | 0.925592i | \(0.376433\pi\) |
−0.990847 | + | 0.134987i | \(0.956901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13777.3 | + | 23863.0i | 0.583533 | + | 1.01071i | 0.995057 | + | 0.0993094i | \(0.0316634\pi\) |
−0.411524 | + | 0.911399i | \(0.635003\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34914.4 | 1.46807 | 0.734035 | − | 0.679111i | \(-0.237635\pi\) | ||||
0.734035 | + | 0.679111i | \(0.237635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 749.124 | 0.0313850 | 0.0156925 | − | 0.999877i | \(-0.495005\pi\) | ||||
0.0156925 | + | 0.999877i | \(0.495005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10899.9 | − | 18879.2i | −0.453373 | − | 0.785264i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6190.35 | − | 10722.0i | 0.256558 | − | 0.444372i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18727.9 | + | 32437.6i | −0.770629 | + | 1.33477i | 0.166590 | + | 0.986026i | \(0.446724\pi\) |
−0.937219 | + | 0.348742i | \(0.886609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12014.4 | + | 20809.6i | 0.492616 | + | 0.853236i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28525.6 | 1.16131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4476.77 | 0.181610 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7203.04 | + | 12476.0i | 0.290149 | + | 0.502553i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5903.02 | − | 10224.3i | 0.236947 | − | 0.410404i | −0.722890 | − | 0.690963i | \(-0.757187\pi\) |
0.959837 | + | 0.280559i | \(0.0905199\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12034.6 | − | 20844.5i | 0.479688 | − | 0.830844i | −0.520041 | − | 0.854141i | \(-0.674083\pi\) |
0.999729 | + | 0.0232978i | \(0.00741659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5683.98 | + | 9844.94i | 0.225768 | + | 0.391042i | 0.956550 | − | 0.291570i | \(-0.0941775\pi\) |
−0.730782 | + | 0.682611i | \(0.760844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10733.7 | 0.423382 | 0.211691 | − | 0.977337i | \(-0.432103\pi\) | ||||
0.211691 | + | 0.977337i | \(0.432103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15747.2 | −0.618983 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14149.3 | + | 24507.3i | 0.552338 | + | 0.956677i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33422.1 | + | 57888.8i | −1.30019 | + | 2.25199i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1457.23 | − | 2524.00i | 0.0563010 | − | 0.0975163i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9775.48 | − | 16931.6i | −0.376391 | − | 0.651928i | 0.614143 | − | 0.789194i | \(-0.289502\pi\) |
−0.990534 | + | 0.137267i | \(0.956168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35047.7 | 1.34028 | 0.670140 | − | 0.742235i | \(-0.266234\pi\) | ||||
0.670140 | + | 0.742235i | \(0.266234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35769.3 | −1.36323 | −0.681615 | − | 0.731711i | \(-0.738722\pi\) | ||||
−0.681615 | + | 0.731711i | \(0.738722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9019.69 | − | 15622.6i | −0.341434 | − | 0.591380i | 0.643266 | − | 0.765643i | \(-0.277579\pi\) |
−0.984699 | + | 0.174263i | \(0.944246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9941.27 | − | 17218.8i | 0.375050 | − | 0.649606i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2650.92 | + | 4591.53i | −0.0993390 | + | 0.172060i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10278.9 | − | 17803.6i | −0.383896 | − | 0.664927i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3156.91 | 0.117118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30897.2 | −1.14244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3361.29 | + | 5821.92i | 0.123462 | + | 0.213842i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14525.1 | + | 25158.2i | −0.531750 | + | 0.921019i | 0.467563 | + | 0.883960i | \(0.345132\pi\) |
−0.999313 | + | 0.0370589i | \(0.988201\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5273.31 | + | 9133.64i | −0.191781 | + | 0.332174i | −0.945841 | − | 0.324632i | \(-0.894760\pi\) |
0.754060 | + | 0.656806i | \(0.228093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8034.19 | − | 13915.6i | −0.291230 | − | 0.504425i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −62444.9 | −2.24876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2975.12 | 0.106790 | 0.0533951 | − | 0.998573i | \(-0.482996\pi\) | ||||
0.0533951 | + | 0.998573i | \(0.482996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38444.9 | − | 66588.6i | −1.37100 | − | 2.37464i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2095.80 | − | 3630.02i | 0.0744966 | − | 0.129032i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25152.3 | − | 43565.1i | 0.888290 | − | 1.53856i | 0.0463940 | − | 0.998923i | \(-0.485227\pi\) |
0.841896 | − | 0.539640i | \(-0.181440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2154.66 | − | 3731.99i | −0.0758499 | − | 0.131376i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18336.0 | 0.641339 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44253.7 | −1.54291 | −0.771454 | − | 0.636285i | \(-0.780470\pi\) | ||||
−0.771454 | + | 0.636285i | \(0.780470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23676.1 | + | 41008.1i | 0.820210 | + | 1.42064i | 0.905526 | + | 0.424291i | \(0.139477\pi\) |
−0.0853163 | + | 0.996354i | \(0.527190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16251.6 | + | 28148.6i | −0.561214 | + | 0.972051i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11982.1 | − | 20753.5i | 0.411156 | − | 0.712143i | −0.583861 | − | 0.811854i | \(-0.698459\pi\) |
0.995016 | + | 0.0997113i | \(0.0317919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44603.7 | − | 77255.8i | −1.52571 | − | 2.64260i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6697.41 | −0.227650 | −0.113825 | − | 0.993501i | \(-0.536310\pi\) | ||||
−0.113825 | + | 0.993501i | \(0.536310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12647.8 | 0.428559 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4942.85 | − | 8561.26i | −0.166437 | − | 0.288277i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1060.22 | − | 1836.35i | 0.0355885 | − | 0.0616411i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10024.1 | − | 17362.3i | 0.334391 | − | 0.579183i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18497.8 | + | 32039.2i | 0.615150 | + | 1.06547i | 0.990358 | + | 0.138530i | \(0.0442379\pi\) |
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32987.1 | −1.09022 | −0.545111 | − | 0.838364i | \(-0.683513\pi\) | ||||
−0.545111 | + | 0.838364i | \(0.683513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15656.8 | 0.515864 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9924.79 | + | 17190.2i | 0.324997 | + | 0.562911i | 0.981512 | − | 0.191402i | \(-0.0613034\pi\) |
−0.656515 | + | 0.754313i | \(0.727970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9349.39 | + | 16193.6i | −0.305217 | + | 0.528652i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6503.35 | − | 11264.1i | 0.211012 | − | 0.365483i | −0.741020 | − | 0.671483i | \(-0.765657\pi\) |
0.952031 | + | 0.306000i | \(0.0989908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6224.13 | + | 10780.5i | 0.201337 | + | 0.348727i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32688.7 | 1.05100 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14119.3 | 0.452588 | 0.226294 | − | 0.974059i | \(-0.427339\pi\) | ||||
0.226294 | + | 0.974059i | \(0.427339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3397.28 | − | 5884.25i | −0.108242 | − | 0.187481i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9958.43 | + | 17248.5i | −0.316336 | + | 0.547910i | −0.979721 | − | 0.200369i | \(-0.935786\pi\) |
0.663385 | + | 0.748278i | \(0.269119\pi\) | |||||||
\(998\) | 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 | 1620.4.i.w.541.6 | 12 | ||
3.2 | odd | 2 | 1620.4.i.x.541.6 | 12 | |||
9.2 | odd | 6 | 1620.4.a.i.1.1 | ✓ | 6 | ||
9.4 | even | 3 | inner | 1620.4.i.w.1081.6 | 12 | ||
9.5 | odd | 6 | 1620.4.i.x.1081.6 | 12 | |||
9.7 | even | 3 | 1620.4.a.j.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.i.1.1 | ✓ | 6 | 9.2 | odd | 6 | ||
1620.4.a.j.1.1 | yes | 6 | 9.7 | even | 3 | ||
1620.4.i.w.541.6 | 12 | 1.1 | even | 1 | trivial | ||
1620.4.i.w.1081.6 | 12 | 9.4 | even | 3 | inner | ||
1620.4.i.x.541.6 | 12 | 3.2 | odd | 2 | |||
1620.4.i.x.1081.6 | 12 | 9.5 | odd | 6 |