Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (of order \(2\), degree \(1\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.2 | ||
Root | \(1.20036 + 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.k.703.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.64469 | −1.92894 | −0.964469 | − | 0.264195i | \(-0.914894\pi\) | ||||
−0.964469 | + | 0.264195i | \(0.914894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12019i | 0.160027i | 0.996794 | + | 0.0800133i | \(0.0254963\pi\) | ||||
−0.996794 | + | 0.0800133i | \(0.974504\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.8529i | 1.25935i | 0.776858 | + | 0.629675i | \(0.216812\pi\) | ||||
−0.776858 | + | 0.629675i | \(0.783188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.65671 | 0.665901 | 0.332950 | − | 0.942944i | \(-0.391956\pi\) | ||||
0.332950 | + | 0.942944i | \(0.391956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.6567 | 0.744512 | 0.372256 | − | 0.928130i | \(-0.378584\pi\) | ||||
0.372256 | + | 0.928130i | \(0.378584\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.6817i | 1.45693i | 0.685082 | + | 0.728466i | \(0.259766\pi\) | ||||
−0.685082 | + | 0.728466i | \(0.740234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 27.5298i | − 1.19695i | −0.801143 | − | 0.598473i | \(-0.795774\pi\) | ||||
0.801143 | − | 0.598473i | \(-0.204226\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 68.0201 | 2.72080 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.15193 | −0.212136 | −0.106068 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106068 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 13.2481i | − 0.427358i | −0.976904 | − | 0.213679i | \(-0.931455\pi\) | ||||
0.976904 | − | 0.213679i | \(-0.0685446\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 10.8038i | − 0.308681i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.9316 | 0.890044 | 0.445022 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445022 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −60.2500 | −1.46951 | −0.734756 | − | 0.678332i | \(-0.762703\pi\) | ||||
−0.734756 | + | 0.678332i | \(0.762703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 25.3479i | − 0.589487i | −0.955576 | − | 0.294744i | \(-0.904766\pi\) | ||||
0.955576 | − | 0.294744i | \(-0.0952342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.7652i | 1.42054i | 0.703931 | + | 0.710268i | \(0.251426\pi\) | ||||
−0.703931 | + | 0.710268i | \(0.748574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.7452 | 0.974392 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1698 | −0.248487 | −0.124243 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124243 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 133.607i | − 2.42921i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 83.2556i | − 1.41111i | −0.708655 | − | 0.705556i | \(-0.750698\pi\) | ||||
0.708655 | − | 0.705556i | \(-0.249302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −101.413 | −1.66251 | −0.831257 | − | 0.555888i | \(-0.812378\pi\) | ||||
−0.831257 | + | 0.555888i | \(0.812378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −83.4913 | −1.28448 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 112.006i | 1.67173i | 0.548938 | + | 0.835863i | \(0.315032\pi\) | ||||
−0.548938 | + | 0.835863i | \(0.684968\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 85.9221i | 1.21017i | 0.796161 | + | 0.605085i | \(0.206861\pi\) | ||||
−0.796161 | + | 0.605085i | \(0.793139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 25.0798 | 0.343559 | 0.171780 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171780 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.5178 | −0.201530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.4604i | 0.803296i | 0.915794 | + | 0.401648i | \(0.131563\pi\) | ||||
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 111.443i | 1.34269i | 0.741146 | + | 0.671344i | \(0.234283\pi\) | ||||
−0.741146 | + | 0.671344i | \(0.765717\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −122.070 | −1.43612 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −22.4278 | −0.251998 | −0.125999 | − | 0.992030i | \(-0.540214\pi\) | ||||
−0.125999 | + | 0.992030i | \(0.540214\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.69712i | 0.106562i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 266.981i | − 2.81033i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −71.2151 | −0.734177 | −0.367088 | − | 0.930186i | \(-0.619645\pi\) | ||||
−0.367088 | + | 0.930186i | \(0.619645\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −138.475 | −1.37104 | −0.685521 | − | 0.728052i | \(-0.740426\pi\) | ||||
−0.685521 | + | 0.728052i | \(0.740426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 117.157i | − 1.13744i | −0.822530 | − | 0.568721i | \(-0.807438\pi\) | ||||
0.822530 | − | 0.568721i | \(-0.192562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 39.2155i | − 0.366500i | −0.983066 | − | 0.183250i | \(-0.941338\pi\) | ||||
0.983066 | − | 0.183250i | \(-0.0586618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −153.735 | −1.41042 | −0.705208 | − | 0.709000i | \(-0.749146\pi\) | ||||
−0.705208 | + | 0.709000i | \(0.749146\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −113.527 | −1.00466 | −0.502332 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502332 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 265.516i | 2.30883i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1779i | 0.119142i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −70.9017 | −0.585965 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −414.915 | −3.31932 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 120.302i | 0.947263i | 0.880723 | + | 0.473632i | \(0.157057\pi\) | ||||
−0.880723 | + | 0.473632i | \(0.842943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 60.2137i | 0.459646i | 0.973232 | + | 0.229823i | \(0.0738148\pi\) | ||||
−0.973232 | + | 0.229823i | \(0.926185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.0086 | −0.233148 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0339 | −0.102437 | −0.0512186 | − | 0.998687i | \(-0.516311\pi\) | ||||
−0.0512186 | + | 0.998687i | \(0.516311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 234.127i | − 1.68436i | −0.539194 | − | 0.842182i | \(-0.681271\pi\) | ||||
0.539194 | − | 0.842182i | \(-0.318729\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 119.920i | 0.838603i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 59.3335 | 0.409197 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 50.9812 | 0.342155 | 0.171078 | − | 0.985258i | \(-0.445275\pi\) | ||||
0.171078 | + | 0.985258i | \(0.445275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 158.996i | − 1.05295i | −0.850190 | − | 0.526475i | \(-0.823513\pi\) | ||||
0.850190 | − | 0.526475i | \(-0.176487\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 127.774i | 0.824347i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.68658 | 0.0171120 | 0.00855600 | − | 0.999963i | \(-0.497277\pi\) | ||||
0.00855600 | + | 0.999963i | \(0.497277\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.8384 | 0.191543 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 146.659i | − 0.899746i | −0.893093 | − | 0.449873i | \(-0.851469\pi\) | ||||
0.893093 | − | 0.449873i | \(-0.148531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7844i | 0.112481i | 0.998417 | + | 0.0562407i | \(0.0179114\pi\) | ||||
−0.998417 | + | 0.0562407i | \(0.982089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −94.0614 | −0.556576 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 170.434 | 0.985166 | 0.492583 | − | 0.870266i | \(-0.336053\pi\) | ||||
0.492583 | + | 0.870266i | \(0.336053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 76.1951i | 0.435401i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 186.431i | − 1.04151i | −0.853706 | − | 0.520756i | \(-0.825650\pi\) | ||||
0.853706 | − | 0.520756i | \(-0.174350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −115.886 | −0.640255 | −0.320127 | − | 0.947375i | \(-0.603726\pi\) | ||||
−0.320127 | + | 0.947375i | \(0.603726\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −317.615 | −1.71684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 175.332i | 0.937602i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 46.4872i | 0.243389i | 0.992568 | + | 0.121694i | \(0.0388328\pi\) | ||||
−0.992568 | + | 0.121694i | \(0.961167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62.0795 | 0.321656 | 0.160828 | − | 0.986982i | \(-0.448584\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −98.1691 | −0.498320 | −0.249160 | − | 0.968462i | \(-0.580155\pi\) | ||||
−0.249160 | + | 0.968462i | \(0.580155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 104.609i | − 0.525671i | −0.964841 | − | 0.262836i | \(-0.915342\pi\) | ||||
0.964841 | − | 0.262836i | \(-0.0846577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 6.89131i | − 0.0339473i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 581.092 | 2.83460 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −383.471 | −1.83479 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 44.1261i | − 0.209128i | −0.994518 | − | 0.104564i | \(-0.966655\pi\) | ||||
0.994518 | − | 0.104564i | \(-0.0333447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 244.473i | 1.13708i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.8403 | 0.0683886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 109.565 | 0.495771 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 353.445i | 1.58496i | 0.609901 | + | 0.792478i | \(0.291209\pi\) | ||||
−0.609901 | + | 0.792478i | \(0.708791\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 192.295i | − 0.847116i | −0.905869 | − | 0.423558i | \(-0.860781\pi\) | ||||
0.905869 | − | 0.423558i | \(-0.139219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 356.455 | 1.55657 | 0.778286 | − | 0.627909i | \(-0.216089\pi\) | ||||
0.778286 | + | 0.627909i | \(0.216089\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −190.754 | −0.818687 | −0.409344 | − | 0.912380i | \(-0.634242\pi\) | ||||
−0.409344 | + | 0.912380i | \(0.634242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 643.930i | − 2.74013i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 230.647i | − 0.965051i | −0.875882 | − | 0.482526i | \(-0.839720\pi\) | ||||
0.875882 | − | 0.482526i | \(-0.160280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 120.413 | 0.499639 | 0.249820 | − | 0.968292i | \(-0.419629\pi\) | ||||
0.249820 | + | 0.968292i | \(0.419629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −460.488 | −1.87954 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 239.632i | 0.970171i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 453.709i | − 1.80761i | −0.427948 | − | 0.903803i | \(-0.640763\pi\) | ||||
0.427948 | − | 0.903803i | \(-0.359237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 381.366 | 1.50737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −109.467 | −0.425940 | −0.212970 | − | 0.977059i | \(-0.568314\pi\) | ||||
−0.212970 | + | 0.977059i | \(0.568314\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.8895i | 0.142431i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 99.7622i | − 0.379324i | −0.981849 | − | 0.189662i | \(-0.939261\pi\) | ||||
0.981849 | − | 0.189662i | \(-0.0607392\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 127.019 | 0.479316 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −320.980 | −1.19324 | −0.596618 | − | 0.802525i | \(-0.703489\pi\) | ||||
−0.596618 | + | 0.802525i | \(0.703489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 297.292i | − 1.09702i | −0.836145 | − | 0.548509i | \(-0.815196\pi\) | ||||
0.836145 | − | 0.548509i | \(-0.184804\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 942.273i | 3.42645i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −90.4130 | −0.326401 | −0.163200 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163200 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 318.187 | 1.13234 | 0.566169 | − | 0.824289i | \(-0.308425\pi\) | ||||
0.566169 | + | 0.824289i | \(0.308425\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 365.829i | 1.29268i | 0.763049 | + | 0.646340i | \(0.223701\pi\) | ||||
−0.763049 | + | 0.646340i | \(0.776299\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 67.4912i | − 0.235161i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −128.808 | −0.445702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 54.6252 | 0.186434 | 0.0932171 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932171 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 802.974i | 2.72195i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 238.317i | − 0.797047i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.3944 | 0.0943336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 978.100 | 3.20689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 25.2901i | − 0.0823781i | −0.999151 | − | 0.0411891i | \(-0.986885\pi\) | ||||
0.999151 | − | 0.0411891i | \(-0.0131146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 449.554i | 1.44551i | 0.691103 | + | 0.722756i | \(0.257125\pi\) | ||||
−0.691103 | + | 0.722756i | \(0.742875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −278.962 | −0.891253 | −0.445627 | − | 0.895219i | \(-0.647019\pi\) | ||||
−0.445627 | + | 0.895219i | \(0.647019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 363.560 | 1.14688 | 0.573439 | − | 0.819248i | \(-0.305609\pi\) | ||||
0.573439 | + | 0.819248i | \(0.305609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 85.2219i | − 0.267153i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 350.359i | 1.08470i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 588.830 | 1.81178 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −74.7895 | −0.227324 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 209.510i | − 0.632962i | −0.948599 | − | 0.316481i | \(-0.897499\pi\) | ||||
0.948599 | − | 0.316481i | \(-0.102501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1080.26i | − 3.22466i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −446.770 | −1.32573 | −0.662864 | − | 0.748740i | \(-0.730659\pi\) | ||||
−0.662864 | + | 0.748740i | \(0.730659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 183.524 | 0.538193 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 108.373i | 0.315955i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 109.320i | 0.315043i | 0.987516 | + | 0.157522i | \(0.0503504\pi\) | ||||
−0.987516 | + | 0.157522i | \(0.949650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −669.523 | −1.91840 | −0.959201 | − | 0.282724i | \(-0.908762\pi\) | ||||
−0.959201 | + | 0.282724i | \(0.908762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −472.139 | −1.33751 | −0.668753 | − | 0.743485i | \(-0.733171\pi\) | ||||
−0.668753 | + | 0.743485i | \(0.733171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 828.692i | − 2.33434i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 148.271i | 0.413012i | 0.978445 | + | 0.206506i | \(0.0662094\pi\) | ||||
−0.978445 | + | 0.206506i | \(0.933791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −405.276 | −1.12265 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −241.887 | −0.662705 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 248.314i | 0.676604i | 0.941038 | + | 0.338302i | \(0.109853\pi\) | ||||
−0.941038 | + | 0.338302i | \(0.890147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 14.7526i | − 0.0397645i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −168.343 | −0.451322 | −0.225661 | − | 0.974206i | \(-0.572454\pi\) | ||||
−0.225661 | + | 0.974206i | \(0.572454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.2555 | −0.141261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 517.108i | 1.36440i | 0.731165 | + | 0.682201i | \(0.238977\pi\) | ||||
−0.731165 | + | 0.682201i | \(0.761023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 303.786i | 0.793175i | 0.917997 | + | 0.396588i | \(0.129806\pi\) | ||||
−0.917997 | + | 0.396588i | \(0.870194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 149.664 | 0.388738 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 114.745 | 0.294974 | 0.147487 | − | 0.989064i | \(-0.452881\pi\) | ||||
0.147487 | + | 0.989064i | \(0.452881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 348.436i | − 0.891141i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 612.056i | − 1.54951i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −602.700 | −1.51814 | −0.759068 | − | 0.651011i | \(-0.774345\pi\) | ||||
−0.759068 | + | 0.651011i | \(0.774345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −336.618 | −0.839447 | −0.419724 | − | 0.907652i | \(-0.637873\pi\) | ||||
−0.419724 | + | 0.907652i | \(0.637873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 114.685i | − 0.284578i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 456.197i | 1.12088i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −312.211 | −0.763353 | −0.381676 | − | 0.924296i | \(-0.624653\pi\) | ||||
−0.381676 | + | 0.924296i | \(0.624653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 93.2617 | 0.225815 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1074.83i | − 2.58996i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.3367i | 0.0962690i | 0.998841 | + | 0.0481345i | \(0.0153276\pi\) | ||||
−0.998841 | + | 0.0481345i | \(0.984672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −170.177 | −0.404221 | −0.202110 | − | 0.979363i | \(-0.564780\pi\) | ||||
−0.202110 | + | 0.979363i | \(0.564780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 860.910 | 2.02567 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 113.602i | − 0.266046i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 172.213i | 0.399565i | 0.979840 | + | 0.199783i | \(0.0640236\pi\) | ||||
−0.979840 | + | 0.199783i | \(0.935976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −759.997 | −1.75519 | −0.877595 | − | 0.479403i | \(-0.840853\pi\) | ||||
−0.877595 | + | 0.479403i | \(0.840853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 762.070 | 1.74387 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 558.574i | 1.27238i | 0.771534 | + | 0.636189i | \(0.219490\pi\) | ||||
−0.771534 | + | 0.636189i | \(0.780510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 857.477i | − 1.93562i | −0.251691 | − | 0.967808i | \(-0.580987\pi\) | ||||
0.251691 | − | 0.967808i | \(-0.419013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 216.309 | 0.486089 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 64.5889 | 0.143851 | 0.0719253 | − | 0.997410i | \(-0.477086\pi\) | ||||
0.0719253 | + | 0.997410i | \(0.477086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 834.634i | − 1.85063i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 93.5258i | − 0.205551i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 446.676 | 0.977410 | 0.488705 | − | 0.872449i | \(-0.337469\pi\) | ||||
0.488705 | + | 0.872449i | \(0.337469\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 591.058 | 1.28212 | 0.641060 | − | 0.767491i | \(-0.278495\pi\) | ||||
0.641060 | + | 0.767491i | \(0.278495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 117.571i | − 0.253933i | −0.991907 | − | 0.126967i | \(-0.959476\pi\) | ||||
0.991907 | − | 0.126967i | \(-0.0405241\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 26.1484i | − 0.0559923i | −0.999608 | − | 0.0279962i | \(-0.991087\pi\) | ||||
0.999608 | − | 0.0279962i | \(-0.00891262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −125.467 | −0.267521 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 351.142 | 0.742371 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1882.91i | 3.96402i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 342.053i | 0.714098i | 0.934086 | + | 0.357049i | \(0.116217\pi\) | ||||
−0.934086 | + | 0.357049i | \(0.883783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 285.079 | 0.592680 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 686.848 | 1.41618 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 58.9556i | − 0.121059i | −0.998166 | − | 0.0605293i | \(-0.980721\pi\) | ||||
0.998166 | − | 0.0605293i | \(-0.0192789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 253.074i | 0.515426i | 0.966222 | + | 0.257713i | \(0.0829688\pi\) | ||||
−0.966222 | + | 0.257713i | \(0.917031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −77.8632 | −0.157938 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −96.2487 | −0.193659 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 440.150i | 0.882063i | 0.897492 | + | 0.441032i | \(0.145387\pi\) | ||||
−0.897492 | + | 0.441032i | \(0.854613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 299.245i | 0.594921i | 0.954734 | + | 0.297461i | \(0.0961397\pi\) | ||||
−0.954734 | + | 0.297461i | \(0.903860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1335.55 | 2.64466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 380.415 | 0.747378 | 0.373689 | − | 0.927554i | \(-0.378093\pi\) | ||||
0.373689 | + | 0.927554i | \(0.378093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0941i | 0.0549786i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1129.94i | 2.19406i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −924.889 | −1.78895 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −523.369 | −1.00455 | −0.502273 | − | 0.864709i | \(-0.667503\pi\) | ||||
−0.502273 | + | 0.864709i | \(0.667503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 641.527i | − 1.22663i | −0.789839 | − | 0.613315i | \(-0.789836\pi\) | ||||
0.789839 | − | 0.613315i | \(-0.210164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 167.677i | − 0.318173i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −228.887 | −0.432680 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −521.566 | −0.978548 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 378.222i | 0.706956i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 661.407i | 1.22710i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −366.964 | −0.678307 | −0.339154 | − | 0.940731i | \(-0.610141\pi\) | ||||
−0.339154 | + | 0.940731i | \(0.610141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1482.73 | 2.72061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 550.755i | 1.00686i | 0.864035 | + | 0.503432i | \(0.167930\pi\) | ||||
−0.864035 | + | 0.503432i | \(0.832070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 170.296i | − 0.309067i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −71.0875 | −0.128549 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −498.904 | −0.895698 | −0.447849 | − | 0.894109i | \(-0.647810\pi\) | ||||
−0.447849 | + | 0.894109i | \(0.647810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 219.430i | − 0.392540i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 823.441i | − 1.46260i | −0.682058 | − | 0.731298i | \(-0.738915\pi\) | ||||
0.682058 | − | 0.731298i | \(-0.261085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1094.93 | 1.93793 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 372.094 | 0.653944 | 0.326972 | − | 0.945034i | \(-0.393972\pi\) | ||||
0.326972 | + | 0.945034i | \(0.393972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 800.325i | 1.40162i | 0.713348 | + | 0.700810i | \(0.247178\pi\) | ||||
−0.713348 | + | 0.700810i | \(0.752822\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1872.58i | − 3.25665i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 404.343 | 0.700768 | 0.350384 | − | 0.936606i | \(-0.386051\pi\) | ||||
0.350384 | + | 0.936606i | \(0.386051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −124.837 | −0.214866 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 182.439i | − 0.312932i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 23.7837i | − 0.0405173i | −0.999795 | − | 0.0202586i | \(-0.993551\pi\) | ||||
0.999795 | − | 0.0202586i | \(-0.00644897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 366.729 | 0.622631 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 568.416 | 0.958544 | 0.479272 | − | 0.877667i | \(-0.340901\pi\) | ||||
0.479272 | + | 0.877667i | \(0.340901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 136.741i | − 0.229817i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 244.953i | 0.408936i | 0.978873 | + | 0.204468i | \(0.0655465\pi\) | ||||
−0.978873 | + | 0.204468i | \(0.934454\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.682820 | −0.00113614 | −0.000568070 | − | 1.00000i | \(-0.500181\pi\) | ||||
−0.000568070 | 1.00000i | \(0.500181\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 683.825 | 1.13029 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1075.29i | − 1.77149i | −0.464173 | − | 0.885744i | \(-0.653649\pi\) | ||||
0.464173 | − | 0.885744i | \(-0.346351\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 577.967i | 0.945936i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −284.127 | −0.463503 | −0.231752 | − | 0.972775i | \(-0.574446\pi\) | ||||
−0.231752 | + | 0.972775i | \(0.574446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 740.574 | 1.20028 | 0.600141 | − | 0.799894i | \(-0.295111\pi\) | ||||
0.600141 | + | 0.799894i | \(0.295111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2690i | 0.0262827i | 0.999914 | + | 0.0131413i | \(0.00418314\pi\) | ||||
−0.999914 | + | 0.0131413i | \(0.995817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 25.1233i | − 0.0403264i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2301.23 | 3.68197 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 416.806 | 0.662648 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 600.999i | − 0.952455i | −0.879322 | − | 0.476227i | \(-0.842004\pi\) | ||||
0.879322 | − | 0.476227i | \(-0.157996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1160.28i | − 1.82721i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 413.316 | 0.648848 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 733.908 | 1.14494 | 0.572471 | − | 0.819925i | \(-0.305985\pi\) | ||||
0.572471 | + | 0.819925i | \(0.305985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 269.442i | − 0.419039i | −0.977804 | − | 0.209520i | \(-0.932810\pi\) | ||||
0.977804 | − | 0.209520i | \(-0.0671900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 685.853i | 1.06005i | 0.847982 | + | 0.530026i | \(0.177818\pi\) | ||||
−0.847982 | + | 0.530026i | \(0.822182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1153.33 | 1.77708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 264.611 | 0.405223 | 0.202612 | − | 0.979259i | \(-0.435057\pi\) | ||||
0.202612 | + | 0.979259i | \(0.435057\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 580.742i | − 0.886629i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 798.019i | 1.21095i | 0.795863 | + | 0.605477i | \(0.207018\pi\) | ||||
−0.795863 | + | 0.605477i | \(0.792982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −395.442 | −0.598248 | −0.299124 | − | 0.954214i | \(-0.596694\pi\) | ||||
−0.299124 | + | 0.954214i | \(0.596694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 299.069 | 0.449727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 169.361i | 0.253915i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1404.86i | − 2.09369i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0196 | −0.0535209 | −0.0267604 | − | 0.999642i | \(-0.508519\pi\) | ||||
−0.0267604 | + | 0.999642i | \(0.508519\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 107.190 | 0.158331 | 0.0791654 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791654 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 79.7742i | − 0.117488i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 529.124i | − 0.774705i | −0.921932 | − | 0.387353i | \(-0.873390\pi\) | ||||
0.921932 | − | 0.387353i | \(-0.126610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 135.353 | 0.197595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −114.007 | −0.165467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1134.76i | 1.64220i | 0.570788 | + | 0.821098i | \(0.306638\pi\) | ||||
−0.570788 | + | 0.821098i | \(0.693362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2258.08i | 3.24903i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −762.566 | −1.09407 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1092.79 | 1.55890 | 0.779451 | − | 0.626463i | \(-0.215498\pi\) | ||||
0.779451 | + | 0.626463i | \(0.215498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 911.603i | 1.29673i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 155.118i | − 0.219403i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −494.678 | −0.697713 | −0.348856 | − | 0.937176i | \(-0.613430\pi\) | ||||
−0.348856 | + | 0.937176i | \(0.613430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −364.717 | −0.511524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1156.59i | − 1.61761i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 431.893i | 0.600686i | 0.953831 | + | 0.300343i | \(0.0971011\pi\) | ||||
−0.953831 | + | 0.300343i | \(0.902899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 131.237 | 0.182021 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −418.455 | −0.577179 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 273.895i | − 0.376747i | −0.982097 | − | 0.188374i | \(-0.939678\pi\) | ||||
0.982097 | − | 0.188374i | \(-0.0603216\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 320.822i | − 0.438880i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 667.160 | 0.910177 | 0.455089 | − | 0.890446i | \(-0.349608\pi\) | ||||
0.455089 | + | 0.890446i | \(0.349608\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1551.60 | −2.10529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 202.851i | − 0.274494i | −0.990537 | − | 0.137247i | \(-0.956175\pi\) | ||||
0.990537 | − | 0.137247i | \(-0.0438254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.4215i | 0.0315229i | 0.999876 | + | 0.0157614i | \(0.00501723\pi\) | ||||
−0.999876 | + | 0.0157614i | \(0.994983\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −491.698 | −0.659997 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.9287 | 0.0586498 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 131.874i | 0.175598i | 0.996138 | + | 0.0877988i | \(0.0279833\pi\) | ||||
−0.996138 | + | 0.0877988i | \(0.972017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1533.46i | 2.03108i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 771.905 | 1.01969 | 0.509845 | − | 0.860266i | \(-0.329703\pi\) | ||||
0.509845 | + | 0.860266i | \(0.329703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −727.077 | −0.955423 | −0.477711 | − | 0.878517i | \(-0.658534\pi\) | ||||
−0.477711 | + | 0.878517i | \(0.658534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 172.212i | − 0.225704i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 720.719i | − 0.939660i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −609.801 | −0.792979 | −0.396490 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396490 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1108.68 | 1.43426 | 0.717130 | − | 0.696939i | \(-0.245455\pi\) | ||||
0.717130 | + | 0.696939i | \(0.245455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 901.136i | − 1.16276i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1667.82i | − 2.14098i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1190.27 | −1.52403 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.9113 | −0.0330080 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 822.206i | 1.04473i | 0.852721 | + | 0.522367i | \(0.174951\pi\) | ||||
−0.852721 | + | 0.522367i | \(0.825049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 127.171i | − 0.160773i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −877.906 | −1.10707 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1310.57 | −1.64438 | −0.822189 | − | 0.569215i | \(-0.807247\pi\) | ||||
−0.822189 | + | 0.569215i | \(0.807247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 845.028i | 1.05761i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 347.428i | 0.432662i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −297.427 | −0.369475 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −645.853 | −0.798335 | −0.399168 | − | 0.916878i | \(-0.630701\pi\) | ||||
−0.399168 | + | 0.916878i | \(0.630701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.06590i | − 0.00131430i | −1.00000 | 0.000657151i | \(-0.999791\pi\) | |||||
1.00000 | 0.000657151i | \(-0.000209178\pi\) | ||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1414.48i | 1.73555i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 701.674 | 0.858842 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 727.892 | 0.886592 | 0.443296 | − | 0.896375i | \(-0.353809\pi\) | ||||
0.443296 | + | 0.896375i | \(0.353809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 197.736i | 0.240262i | 0.992758 | + | 0.120131i | \(0.0383315\pi\) | ||||
−0.992758 | + | 0.120131i | \(0.961669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 287.442i | 0.347571i | 0.984783 | + | 0.173786i | \(0.0556000\pi\) | ||||
−0.984783 | + | 0.173786i | \(0.944400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1080.80 | −1.30374 | −0.651871 | − | 0.758330i | \(-0.726016\pi\) | ||||
−0.651871 | + | 0.758330i | \(0.726016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 604.297 | 0.725446 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 181.170i | − 0.216970i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 120.216i | 0.143284i | 0.997430 | + | 0.0716422i | \(0.0228240\pi\) | ||||
−0.997430 | + | 0.0716422i | \(0.977176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −803.154 | −0.954998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 907.193 | 1.07360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 79.4231i | − 0.0937699i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 906.599i | − 1.06533i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1270.01 | −1.48888 | −0.744438 | − | 0.667691i | \(-0.767283\pi\) | ||||
−0.744438 | + | 0.667691i | \(0.767283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 76.0067 | 0.0886892 | 0.0443446 | − | 0.999016i | \(-0.485880\pi\) | ||||
0.0443446 | + | 0.999016i | \(0.485880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 424.136i | − 0.493756i | −0.969047 | − | 0.246878i | \(-0.920595\pi\) | ||||
0.969047 | − | 0.246878i | \(-0.0794047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1036.76i | − 1.20134i | −0.799495 | − | 0.600672i | \(-0.794900\pi\) | ||||
0.799495 | − | 0.600672i | \(-0.205100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1643.78 | −1.90032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −879.108 | −1.01163 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 969.600i | 1.11320i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 464.782i | − 0.531180i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.6471 | 0.0474881 | 0.0237441 | − | 0.999718i | \(-0.492441\pi\) | ||||
0.0237441 | + | 0.999718i | \(0.492441\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1196.29 | 1.35788 | 0.678940 | − | 0.734194i | \(-0.262440\pi\) | ||||
0.678940 | + | 0.734194i | \(0.262440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 106.778i | 0.120926i | 0.998170 | + | 0.0604629i | \(0.0192577\pi\) | ||||
−0.998170 | + | 0.0604629i | \(0.980742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 216.134i | − 0.243668i | −0.992550 | − | 0.121834i | \(-0.961122\pi\) | ||||
0.992550 | − | 0.121834i | \(-0.0388776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −134.761 | −0.151587 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1848.17 | −2.06962 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1798.07i | 2.00901i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 81.5014i | 0.0906578i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −166.686 | −0.185001 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1117.69 | 1.23501 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1672.90i | − 1.84444i | −0.386670 | − | 0.922218i | \(-0.626375\pi\) | ||||
0.386670 | − | 0.922218i | \(-0.373625\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 238.389i | 0.261678i | 0.991404 | + | 0.130839i | \(0.0417672\pi\) | ||||
−0.991404 | + | 0.130839i | \(0.958233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1543.81 | −1.69091 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −67.4505 | −0.0735556 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 771.672i | − 0.839687i | −0.907596 | − | 0.419844i | \(-0.862085\pi\) | ||||
0.907596 | − | 0.419844i | \(-0.137915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 743.802i | 0.805853i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2240.01 | 2.42163 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 97.4649 | 0.104914 | 0.0524569 | − | 0.998623i | \(-0.483295\pi\) | ||||
0.0524569 | + | 0.998623i | \(0.483295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1321.67i | 1.41962i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1691.02i | − 1.80858i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1399.93 | −1.49406 | −0.747028 | − | 0.664793i | \(-0.768520\pi\) | ||||
−0.747028 | + | 0.664793i | \(0.768520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 253.338 | 0.269222 | 0.134611 | − | 0.990898i | \(-0.457021\pi\) | ||||
0.134611 | + | 0.990898i | \(0.457021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1658.67i | 1.75893i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 223.848i | 0.236376i | 0.992991 | + | 0.118188i | \(0.0377085\pi\) | ||||
−0.992991 | + | 0.118188i | \(0.962292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 217.109 | 0.228776 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 968.543 | 1.01631 | 0.508155 | − | 0.861266i | \(-0.330328\pi\) | ||||
0.508155 | + | 0.861266i | \(0.330328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 448.355i | − 0.469482i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 15.7206i | − 0.0163927i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 785.488 | 0.817365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −598.738 | −0.620454 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1198.55i | − 1.23945i | −0.784818 | − | 0.619726i | \(-0.787244\pi\) | ||||
0.784818 | − | 0.619726i | \(-0.212756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1759.74i | 1.81230i | 0.422961 | + | 0.906148i | \(0.360991\pi\) | ||||
−0.422961 | + | 0.906148i | \(0.639009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 262.265 | 0.269543 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1502.13 | −1.53749 | −0.768746 | − | 0.639554i | \(-0.779119\pi\) | ||||
−0.768746 | + | 0.639554i | \(0.779119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 310.689i | − 0.317354i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 410.455i | − 0.417554i | −0.977963 | − | 0.208777i | \(-0.933052\pi\) | ||||
0.977963 | − | 0.208777i | \(-0.0669483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 946.811 | 0.961229 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −697.823 | −0.705584 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 210.418i | − 0.212329i | −0.994349 | − | 0.106164i | \(-0.966143\pi\) | ||||
0.994349 | − | 0.106164i | \(-0.0338570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1008.92i | 1.01399i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −450.591 | −0.451947 | −0.225973 | − | 0.974134i | \(-0.572556\pi\) | ||||
−0.225973 | + | 0.974134i | \(0.572556\pi\) | |||||||
\(998\) | 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 | 1728.3.g.k.703.2 | 8 | ||
3.2 | odd | 2 | 1728.3.g.n.703.8 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.k.703.1 | 8 | ||
8.3 | odd | 2 | 864.3.g.c.703.7 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.c.703.8 | yes | 8 | ||
12.11 | even | 2 | 1728.3.g.n.703.7 | 8 | |||
24.5 | odd | 2 | 864.3.g.a.703.2 | yes | 8 | ||
24.11 | even | 2 | 864.3.g.a.703.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.a.703.1 | ✓ | 8 | 24.11 | even | 2 | ||
864.3.g.a.703.2 | yes | 8 | 24.5 | odd | 2 | ||
864.3.g.c.703.7 | yes | 8 | 8.3 | odd | 2 | ||
864.3.g.c.703.8 | yes | 8 | 8.5 | even | 2 | ||
1728.3.g.k.703.1 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.g.k.703.2 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.n.703.7 | 8 | 12.11 | even | 2 | |||
1728.3.g.n.703.8 | 8 | 3.2 | odd | 2 |