Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.d.1471.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.41421 | −1.48284 | −0.741421 | − | 0.671040i | \(-0.765848\pi\) | ||||
−0.741421 | + | 0.671040i | \(0.765848\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 20.1903i | − 1.83548i | −0.397183 | − | 0.917739i | \(-0.630012\pi\) | ||||
0.397183 | − | 0.917739i | \(-0.369988\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.8995 | −1.68458 | −0.842288 | − | 0.539027i | \(-0.818792\pi\) | ||||
−0.842288 | + | 0.539027i | \(0.818792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 12.8418i | − 0.856120i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.0711 | −0.768886 | −0.384443 | − | 0.923149i | \(-0.625607\pi\) | ||||
−0.384443 | + | 0.923149i | \(0.625607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.6969i | 0.773523i | 0.922180 | + | 0.386762i | \(0.126406\pi\) | ||||
−0.922180 | + | 0.386762i | \(0.873594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 40.9749i | − 1.78152i | −0.454478 | − | 0.890758i | \(-0.650174\pi\) | ||||
0.454478 | − | 0.890758i | \(-0.349826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.9706 | 1.19882 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32.4853 | 1.12018 | 0.560091 | − | 0.828431i | \(-0.310766\pi\) | ||||
0.560091 | + | 0.828431i | \(0.310766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 51.0190i | − 1.64577i | −0.568204 | − | 0.822887i | \(-0.692362\pi\) | ||||
0.568204 | − | 0.822887i | \(-0.307638\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 34.9706 | 1.05971 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.9411 | −0.917328 | −0.458664 | − | 0.888610i | \(-0.651672\pi\) | ||||
−0.458664 | + | 0.888610i | \(0.651672\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 37.9310i | − 0.972591i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.10051 | 0.197573 | 0.0987866 | − | 0.995109i | \(-0.468504\pi\) | ||||
0.0987866 | + | 0.995109i | \(0.468504\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 69.7744i | 1.62266i | 0.584588 | + | 0.811330i | \(0.301256\pi\) | ||||
−0.584588 | + | 0.811330i | \(0.698744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 22.2426 | 0.494281 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 28.5533i | 0.607518i | 0.952749 | + | 0.303759i | \(0.0982418\pi\) | ||||
−0.952749 | + | 0.303759i | \(0.901758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 22.6398i | − 0.443917i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −72.9117 | −1.37569 | −0.687846 | − | 0.725857i | \(-0.741444\pi\) | ||||
−0.687846 | + | 0.725857i | \(0.741444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149.695i | 2.72173i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −25.4558 | −0.446594 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.40661i | 0.0746883i | 0.999302 | + | 0.0373441i | \(0.0118898\pi\) | ||||
−0.999302 | + | 0.0373441i | \(0.988110\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.9828 | 0.557094 | 0.278547 | − | 0.960423i | \(-0.410147\pi\) | ||||
0.278547 | + | 0.960423i | \(0.410147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 162.368 | 2.49796 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30.5826i | 0.456456i | 0.973608 | + | 0.228228i | \(0.0732932\pi\) | ||||
−0.973608 | + | 0.228228i | \(0.926707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 70.9706 | 1.02856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 27.6108i | 0.388885i | 0.980914 | + | 0.194443i | \(0.0622898\pi\) | ||||
−0.980914 | + | 0.194443i | \(0.937710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −61.4975 | −0.842431 | −0.421216 | − | 0.906961i | \(-0.638396\pi\) | ||||
−0.421216 | + | 0.906961i | \(0.638396\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 51.9105i | 0.692140i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 90.5590i | − 1.14632i | −0.819445 | − | 0.573158i | \(-0.805718\pi\) | ||||
0.819445 | − | 0.573158i | \(-0.194282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.24714i | 0.0632185i | 0.999500 | + | 0.0316093i | \(0.0100632\pi\) | ||||
−0.999500 | + | 0.0316093i | \(0.989937\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.9117 | 1.14014 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 56.2662i | 0.646737i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 56.8701 | 0.638989 | 0.319495 | − | 0.947588i | \(-0.396487\pi\) | ||||
0.319495 | + | 0.947588i | \(0.396487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 88.3675 | 0.950189 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 108.966i | − 1.14701i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −123.556 | −1.27378 | −0.636888 | − | 0.770956i | \(-0.719779\pi\) | ||||
−0.636888 | + | 0.770956i | \(0.719779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 60.5708i | 0.611826i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 70.3259 | 0.696296 | 0.348148 | − | 0.937440i | \(-0.386811\pi\) | ||||
0.348148 | + | 0.937440i | \(0.386811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 109.807i | − 1.06609i | −0.846088 | − | 0.533043i | \(-0.821049\pi\) | ||||
0.846088 | − | 0.533043i | \(-0.178951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1471i | 0.141561i | 0.997492 | + | 0.0707807i | \(0.0225491\pi\) | ||||
−0.997492 | + | 0.0707807i | \(0.977451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 72.8528 | 0.668374 | 0.334187 | − | 0.942507i | \(-0.391538\pi\) | ||||
0.334187 | + | 0.942507i | \(0.391538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 58.7878i | − 0.529619i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −87.8234 | −0.777198 | −0.388599 | − | 0.921407i | \(-0.627041\pi\) | ||||
−0.388599 | + | 0.921407i | \(0.627041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 303.796i | 2.64171i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 65.6985 | 0.561526 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −286.647 | −2.36898 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.0305i | 0.114069i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −36.8528 | −0.294823 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.211i | 0.820563i | 0.911959 | + | 0.410281i | \(0.134570\pi\) | ||||
−0.911959 | + | 0.410281i | \(0.865430\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −120.853 | −0.936844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.7477i | 0.700364i | 0.936682 | + | 0.350182i | \(0.113880\pi\) | ||||
−0.936682 | + | 0.350182i | \(0.886120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 38.5254i | 0.285373i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 186.426 | 1.36078 | 0.680388 | − | 0.732852i | \(-0.261811\pi\) | ||||
0.680388 | + | 0.732852i | \(0.261811\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 141.722i | − 1.01958i | −0.860298 | − | 0.509792i | \(-0.829722\pi\) | ||||
0.860298 | − | 0.509792i | \(-0.170278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −49.4558 | −0.350751 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 442.157i | 3.09200i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −240.853 | −1.66105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −48.9117 | −0.328266 | −0.164133 | − | 0.986438i | \(-0.552483\pi\) | ||||
−0.164133 | + | 0.986438i | \(0.552483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 214.366i | − 1.41965i | −0.704381 | − | 0.709823i | \(-0.748775\pi\) | ||||
0.704381 | − | 0.709823i | \(-0.251225\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 39.2132 | 0.256295 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 378.266i | 2.44043i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −55.0711 | −0.350771 | −0.175386 | − | 0.984500i | \(-0.556117\pi\) | ||||
−0.175386 | + | 0.984500i | \(0.556117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 126.287i | − 0.794256i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128.274i | 0.786955i | 0.919334 | + | 0.393478i | \(0.128728\pi\) | ||||
−0.919334 | + | 0.393478i | \(0.871272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −259.279 | −1.57139 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 239.762i | 1.43570i | 0.696199 | + | 0.717849i | \(0.254873\pi\) | ||||
−0.696199 | + | 0.717849i | \(0.745127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 310.588 | 1.83780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 44.0908i | − 0.257841i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.7330 | 0.0909420 | 0.0454710 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454710 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.63247 | −0.0431213 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 95.9081i | 0.535800i | 0.963447 | + | 0.267900i | \(0.0863296\pi\) | ||||
−0.963447 | + | 0.267900i | \(0.913670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −221.012 | −1.22106 | −0.610531 | − | 0.791992i | \(-0.709044\pi\) | ||||
−0.610531 | + | 0.791992i | \(0.709044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 58.8599i | 0.321639i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 251.647 | 1.36025 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 263.908i | 1.41127i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 51.9615i | 0.272050i | 0.990705 | + | 0.136025i | \(0.0434327\pi\) | ||||
−0.990705 | + | 0.136025i | \(0.956567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −187.823 | −0.973178 | −0.486589 | − | 0.873631i | \(-0.661759\pi\) | ||||
−0.486589 | + | 0.873631i | \(0.661759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 281.229i | 1.44220i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −47.0883 | −0.239027 | −0.119513 | − | 0.992833i | \(-0.538133\pi\) | ||||
−0.119513 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252.777i | 1.27024i | 0.772414 | + | 0.635119i | \(0.219049\pi\) | ||||
−0.772414 | + | 0.635119i | \(0.780951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −52.9706 | −0.263535 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −60.0589 | −0.292970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 122.925i | 0.593839i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 296.735 | 1.41978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 350.061i | 1.65906i | 0.558465 | + | 0.829528i | \(0.311390\pi\) | ||||
−0.558465 | + | 0.829528i | \(0.688610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −47.8234 | −0.224523 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 517.322i | − 2.40615i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 106.517i | − 0.486378i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 286.250 | 1.29525 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 17.2185i | − 0.0772132i | −0.999254 | − | 0.0386066i | \(-0.987708\pi\) | ||||
0.999254 | − | 0.0386066i | \(-0.0122919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −89.9117 | −0.399608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 61.1054i | − 0.269187i | −0.990901 | − | 0.134593i | \(-0.957027\pi\) | ||||
0.990901 | − | 0.134593i | \(-0.0429728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.10051 | −0.00917251 | −0.00458626 | − | 0.999989i | \(-0.501460\pi\) | ||||
−0.00458626 | + | 0.999989i | \(0.501460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 425.220 | 1.82498 | 0.912490 | − | 0.409099i | \(-0.134157\pi\) | ||||
0.912490 | + | 0.409099i | \(0.134157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 211.701i | − 0.900854i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 156.853 | 0.661826 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 230.991i | 0.966488i | 0.875486 | + | 0.483244i | \(0.160542\pi\) | ||||
−0.875486 | + | 0.483244i | \(0.839458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −53.1787 | −0.220659 | −0.110329 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110329 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 321.856i | − 1.30306i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.08831 | −0.0364992 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 269.359i | 1.07314i | 0.843854 | + | 0.536572i | \(0.180281\pi\) | ||||
−0.843854 | + | 0.536572i | \(0.819719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −827.294 | −3.26993 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 167.856i | 0.658259i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −116.517 | −0.453373 | −0.226686 | − | 0.973968i | \(-0.572789\pi\) | ||||
−0.226686 | + | 0.973968i | \(0.572789\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −97.4558 | −0.373394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 164.782i | − 0.626549i | −0.949663 | − | 0.313274i | \(-0.898574\pi\) | ||||
0.949663 | − | 0.313274i | \(-0.101426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 540.583 | 2.03994 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 98.5018i | 0.368921i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 482.590 | 1.79401 | 0.897007 | − | 0.442016i | \(-0.145736\pi\) | ||||
0.897007 | + | 0.442016i | \(0.145736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 225.701i | 0.832846i | 0.909171 | + | 0.416423i | \(0.136716\pi\) | ||||
−0.909171 | + | 0.416423i | \(0.863284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 605.114i | − 2.20041i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −76.1766 | −0.275006 | −0.137503 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137503 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 153.057i | 0.548592i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −86.3087 | −0.307148 | −0.153574 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153574 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 285.101i | 1.00742i | 0.863872 | + | 0.503712i | \(0.168033\pi\) | ||||
−0.863872 | + | 0.503712i | \(0.831967\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 188.735 | 0.662228 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −118.147 | −0.408814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 214.006i | − 0.735415i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −454.056 | −1.54968 | −0.774839 | − | 0.632158i | \(-0.782169\pi\) | ||||
−0.774839 | + | 0.632158i | \(0.782169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 32.6715i | − 0.110751i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −104.912 | −0.353238 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 897.329i | 3.00110i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 121.808i | 0.402007i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −251.955 | −0.826083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 300.230i | 0.977949i | 0.872298 | + | 0.488975i | \(0.162629\pi\) | ||||
−0.872298 | + | 0.488975i | \(0.837371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 190.191 | 0.615505 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 253.210i | − 0.814180i | −0.913388 | − | 0.407090i | \(-0.866543\pi\) | ||||
0.913388 | − | 0.407090i | \(-0.133457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 333.296 | 1.06484 | 0.532422 | − | 0.846479i | \(-0.321282\pi\) | ||||
0.532422 | + | 0.846479i | \(0.321282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 109.265 | 0.344684 | 0.172342 | − | 0.985037i | \(-0.444867\pi\) | ||||
0.172342 | + | 0.985037i | \(0.444867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 655.886i | − 2.05607i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.2355 | −0.0817305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 192.105i | − 0.594751i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −656.340 | −2.01951 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 126.185i | 0.385886i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 345.018i | − 1.04235i | −0.853450 | − | 0.521175i | \(-0.825494\pi\) | ||||
0.853450 | − | 0.521175i | \(-0.174506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 101.823 | 0.305776 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 226.746i | − 0.676853i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 374.558 | 1.11145 | 0.555725 | − | 0.831366i | \(-0.312441\pi\) | ||||
0.555725 | + | 0.831366i | \(0.312441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 152.115i | − 0.448715i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1030.09 | −3.02078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −526.191 | −1.52519 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 333.148i | − 0.960081i | −0.877246 | − | 0.480040i | \(-0.840622\pi\) | ||||
0.877246 | − | 0.480040i | \(-0.159378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 119.958 | 0.343720 | 0.171860 | − | 0.985121i | \(-0.445022\pi\) | ||||
0.171860 | + | 0.985121i | \(0.445022\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 113.793i | 0.324197i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 82.6589 | 0.234161 | 0.117081 | − | 0.993122i | \(-0.462646\pi\) | ||||
0.117081 | + | 0.993122i | \(0.462646\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 204.713i | − 0.576655i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 22.5676i | − 0.0628625i | −0.999506 | − | 0.0314313i | \(-0.989993\pi\) | ||||
0.999506 | − | 0.0314313i | \(-0.0100065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 145.000 | 0.401662 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 496.487i | − 1.36773i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 455.955 | 1.24919 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 583.242i | − 1.58922i | −0.607123 | − | 0.794608i | \(-0.707676\pi\) | ||||
0.607123 | − | 0.794608i | \(-0.292324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.3015 | −0.0658578 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 87.4701 | 0.234504 | 0.117252 | − | 0.993102i | \(-0.462591\pi\) | ||||
0.117252 | + | 0.993102i | \(0.462591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 63.8309i | − 0.170216i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −711.411 | −1.88703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 122.330i | − 0.322771i | −0.986891 | − | 0.161386i | \(-0.948404\pi\) | ||||
0.986891 | − | 0.161386i | \(-0.0515963\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −180.500 | −0.473752 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.4485i | 0.0351136i | 0.999846 | + | 0.0175568i | \(0.00558879\pi\) | ||||
−0.999846 | + | 0.0175568i | \(0.994411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 209.323i | − 0.540887i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −79.2792 | −0.203803 | −0.101901 | − | 0.994795i | \(-0.532493\pi\) | ||||
−0.101901 | + | 0.994795i | \(0.532493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 535.585i | 1.36978i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −158.912 | −0.404355 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 671.424i | 1.69981i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 374.600 | 0.943577 | 0.471789 | − | 0.881712i | \(-0.343609\pi\) | ||||
0.471789 | + | 0.881712i | \(0.343609\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 60.1035 | 0.149884 | 0.0749420 | − | 0.997188i | \(-0.476123\pi\) | ||||
0.0749420 | + | 0.997188i | \(0.476123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1117.29i | 2.77243i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −66.7279 | −0.164760 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 685.280i | 1.68374i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 801.296 | 1.95916 | 0.979580 | − | 0.201055i | \(-0.0644369\pi\) | ||||
0.979580 | + | 0.201055i | \(0.0644369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 322.900i | 0.785645i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 38.9034i | − 0.0937432i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 245.470 | 0.588657 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 171.957i | 0.410398i | 0.978720 | + | 0.205199i | \(0.0657841\pi\) | ||||
−0.978720 | + | 0.205199i | \(0.934216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −369.294 | −0.877182 | −0.438591 | − | 0.898687i | \(-0.644522\pi\) | ||||
−0.438591 | + | 0.898687i | \(0.644522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 85.6600i | − 0.202506i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −391.747 | −0.921758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −765.838 | −1.78517 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 415.675i | − 0.964442i | −0.876049 | − | 0.482221i | \(-0.839830\pi\) | ||||
0.876049 | − | 0.482221i | \(-0.160170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 484.409 | 1.11873 | 0.559364 | − | 0.828922i | \(-0.311045\pi\) | ||||
0.559364 | + | 0.828922i | \(0.311045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 417.169i | − 0.959010i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 602.205 | 1.37804 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 543.762i | − 1.23864i | −0.785140 | − | 0.619319i | \(-0.787409\pi\) | ||||
0.785140 | − | 0.619319i | \(-0.212591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 418.952i | 0.945716i | 0.881139 | + | 0.472858i | \(0.156778\pi\) | ||||
−0.881139 | + | 0.472858i | \(0.843222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −421.647 | −0.947521 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 84.7175i | − 0.189525i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 697.647 | 1.55378 | 0.776889 | − | 0.629637i | \(-0.216796\pi\) | ||||
0.776889 | + | 0.629637i | \(0.216796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 163.551i | − 0.362642i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 371.294 | 0.819632 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 129.647 | 0.283691 | 0.141845 | − | 0.989889i | \(-0.454696\pi\) | ||||
0.141845 | + | 0.989889i | \(0.454696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 67.9193i | 0.147972i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −185.002 | −0.401306 | −0.200653 | − | 0.979662i | \(-0.564306\pi\) | ||||
−0.200653 | + | 0.979662i | \(0.564306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 632.436i | 1.36595i | 0.730441 | + | 0.682976i | \(0.239315\pi\) | ||||
−0.730441 | + | 0.682976i | \(0.760685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −655.176 | −1.40898 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 716.992i | − 1.53531i | −0.640861 | − | 0.767657i | \(-0.721422\pi\) | ||||
0.640861 | − | 0.767657i | \(-0.278578\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 95.3859i | − 0.202518i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1408.76 | 2.97836 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 440.476i | 0.927317i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 218.735 | 0.458564 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 466.915i | − 0.974771i | −0.873187 | − | 0.487385i | \(-0.837951\pi\) | ||||
0.873187 | − | 0.487385i | \(-0.162049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 743.294 | 1.54531 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 916.073 | 1.88881 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 358.093i | 0.735304i | 0.929963 | + | 0.367652i | \(0.119838\pi\) | ||||
−0.929963 | + | 0.367652i | \(0.880162\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −222.177 | −0.454349 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 908.850i | − 1.85102i | −0.378724 | − | 0.925509i | \(-0.623637\pi\) | ||||
0.378724 | − | 0.925509i | \(-0.376363\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −424.617 | −0.861293 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 449.085i | − 0.907242i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 678.760i | 1.36024i | 0.733101 | + | 0.680120i | \(0.238072\pi\) | ||||
−0.733101 | + | 0.680120i | \(0.761928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −415.279 | −0.828901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 154.102i | − 0.306365i | −0.988198 | − | 0.153182i | \(-0.951048\pi\) | ||||
0.988198 | − | 0.153182i | \(-0.0489522\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −521.411 | −1.03250 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 537.954i | 1.06105i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 474.561 | 0.932341 | 0.466170 | − | 0.884695i | \(-0.345633\pi\) | ||||
0.466170 | + | 0.884695i | \(0.345633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 76.3675 | 0.148865 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 814.131i | 1.58084i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 576.500 | 1.11509 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.2503i | 0.0525054i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −527.282 | −1.01206 | −0.506029 | − | 0.862516i | \(-0.668887\pi\) | ||||
−0.506029 | + | 0.862516i | \(0.668887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 77.4834i | − 0.148152i | −0.997253 | − | 0.0740759i | \(-0.976399\pi\) | ||||
0.997253 | − | 0.0740759i | \(-0.0236007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 666.873i | 1.26541i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1149.94 | −2.17380 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 13.2198i | − 0.0248961i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −177.397 | −0.332827 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 112.304i | − 0.209913i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −166.118 | −0.309344 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 986.764 | 1.82396 | 0.911981 | − | 0.410232i | \(-0.134552\pi\) | ||||
0.911981 | + | 0.410232i | \(0.134552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 382.804i | − 0.704980i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −540.146 | −0.991094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 152.301i | − 0.278430i | −0.990262 | − | 0.139215i | \(-0.955542\pi\) | ||||
0.990262 | − | 0.139215i | \(-0.0444579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −101.948 | −0.185698 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 477.434i | 0.866487i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 435.865i | 0.785342i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.20519 | −0.00754972 | −0.00377486 | − | 0.999993i | \(-0.501202\pi\) | ||||
−0.00377486 | + | 0.999993i | \(0.501202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1528.02i | − 2.73350i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −457.103 | −0.814800 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 564.571i | 1.00279i | 0.865218 | + | 0.501395i | \(0.167180\pi\) | ||||
−0.865218 | + | 0.501395i | \(0.832820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 651.141 | 1.15246 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 818.662 | 1.43877 | 0.719387 | − | 0.694610i | \(-0.244423\pi\) | ||||
0.719387 | + | 0.694610i | \(0.244423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 472.968i | 0.828315i | 0.910205 | + | 0.414157i | \(0.135924\pi\) | ||||
−0.910205 | + | 0.414157i | \(0.864076\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −90.0000 | −0.157068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1228.04i | − 2.13572i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −950.060 | −1.64655 | −0.823276 | − | 0.567642i | \(-0.807856\pi\) | ||||
−0.823276 | + | 0.567642i | \(0.807856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 325.320i | − 0.561865i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1472.11i | 2.52505i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −487.103 | −0.832654 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1123.87i | − 1.91460i | −0.289095 | − | 0.957300i | \(-0.593354\pi\) | ||||
0.289095 | − | 0.957300i | \(-0.406646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 749.823 | 1.27304 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 81.5593i | − 0.138002i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −562.159 | −0.947992 | −0.473996 | − | 0.880527i | \(-0.657189\pi\) | ||||
−0.473996 | + | 0.880527i | \(0.657189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −437.823 | −0.733372 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 394.025i | 0.657804i | 0.944364 | + | 0.328902i | \(0.106679\pi\) | ||||
−0.944364 | + | 0.328902i | \(0.893321\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 824.943 | 1.37262 | 0.686309 | − | 0.727310i | \(-0.259230\pi\) | ||||
0.686309 | + | 0.727310i | \(0.259230\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 91.7477i | − 0.152152i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2125.26 | 3.51283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 380.031i | 0.626081i | 0.949740 | + | 0.313041i | \(0.101348\pi\) | ||||
−0.949740 | + | 0.313041i | \(0.898652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 625.304i | − 1.02341i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 53.4701 | 0.0872270 | 0.0436135 | − | 0.999048i | \(-0.486113\pi\) | ||||
0.0436135 | + | 0.999048i | \(0.486113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 104.025i | − 0.169146i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −304.514 | −0.493539 | −0.246770 | − | 0.969074i | \(-0.579369\pi\) | ||||
−0.246770 | + | 0.969074i | \(0.579369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 523.843i | 0.846272i | 0.906066 | + | 0.423136i | \(0.139071\pi\) | ||||
−0.906066 | + | 0.423136i | \(0.860929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −212.912 | −0.342853 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −476.029 | −0.761647 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 513.960i | 0.819713i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 443.647 | 0.705321 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 214.943i | − 0.340639i | −0.985389 | − | 0.170320i | \(-0.945520\pi\) | ||||
0.985389 | − | 0.170320i | \(-0.0544800\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −606.323 | −0.957856 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 772.646i | − 1.21677i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 82.8325i | − 0.129628i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1216.51 | 1.89784 | 0.948919 | − | 0.315520i | \(-0.102179\pi\) | ||||
0.948919 | + | 0.315520i | \(0.102179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 522.341i | − 0.812350i | −0.913795 | − | 0.406175i | \(-0.866862\pi\) | ||||
0.913795 | − | 0.406175i | \(-0.133138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 896.029 | 1.38919 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1072.42i | − 1.65753i | −0.559600 | − | 0.828763i | \(-0.689045\pi\) | ||||
0.559600 | − | 0.828763i | \(-0.310955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 88.9706 | 0.137089 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −672.043 | −1.02916 | −0.514581 | − | 0.857442i | \(-0.672053\pi\) | ||||
−0.514581 | + | 0.857442i | \(0.672053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 680.237i | − 1.03853i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 184.492 | 0.280810 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 329.005i | 0.499249i | 0.968343 | + | 0.249625i | \(0.0803072\pi\) | ||||
−0.968343 | + | 0.249625i | \(0.919693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −845.658 | −1.27936 | −0.639681 | − | 0.768641i | \(-0.720933\pi\) | ||||
−0.639681 | + | 0.768641i | \(0.720933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 495.799i | 0.747812i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1331.08i | − 1.99562i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.8234 | 0.0445790 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 686.121i | − 1.02253i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −214.648 | −0.318941 | −0.159471 | − | 0.987203i | \(-0.550979\pi\) | ||||
−0.159471 | + | 0.987203i | \(0.550979\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 155.732i | − 0.230713i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 234.145 | 0.345857 | 0.172928 | − | 0.984934i | \(-0.444677\pi\) | ||||
0.172928 | + | 0.984934i | \(0.444677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 105.838 | 0.155415 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 738.396i | 1.08111i | 0.841310 | + | 0.540553i | \(0.181785\pi\) | ||||
−0.841310 | + | 0.540553i | \(0.818215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1382.21 | −2.01782 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.63818i | − 0.00529575i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1596.73 | 2.31746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 732.505i | 1.06006i | 0.847978 | + | 0.530032i | \(0.177820\pi\) | ||||
−0.847978 | + | 0.530032i | \(0.822180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1050.76i | 1.51188i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −105.882 | −0.151911 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 736.503i | 1.05365i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 538.690 | 0.768460 | 0.384230 | − | 0.923237i | \(-0.374467\pi\) | ||||
0.384230 | + | 0.923237i | \(0.374467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 498.831i | − 0.709574i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 366.676 | 0.520108 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1277.97 | −1.80250 | −0.901248 | − | 0.433304i | \(-0.857348\pi\) | ||||
−0.901248 | + | 0.433304i | \(0.857348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 271.677i | 0.382106i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2090.50 | −2.93197 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3278.24i | − 4.58496i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −400.087 | −0.558002 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 615.541i | − 0.856107i | −0.903753 | − | 0.428053i | \(-0.859199\pi\) | ||||
0.903753 | − | 0.428053i | \(-0.140801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 92.1082i | − 0.127397i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 973.602 | 1.34290 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 273.129i | − 0.375694i | −0.982198 | − | 0.187847i | \(-0.939849\pi\) | ||||
0.982198 | − | 0.187847i | \(-0.0601509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 912.026i | − 1.24764i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1013.51 | −1.38269 | −0.691345 | − | 0.722525i | \(-0.742982\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 617.470 | 0.837816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 152.048i | − 0.205748i | −0.994694 | − | 0.102874i | \(-0.967196\pi\) | ||||
0.994694 | − | 0.102874i | \(-0.0328038\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 557.470 | 0.752321 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 601.582i | 0.809667i | 0.914390 | + | 0.404833i | \(0.132670\pi\) | ||||
−0.914390 | + | 0.404833i | \(0.867330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 362.642 | 0.486767 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 15.7414i | − 0.0210728i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 739.602i | 0.984822i | 0.870363 | + | 0.492411i | \(0.163884\pi\) | ||||
−0.870363 | + | 0.492411i | \(0.836116\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −466.544 | −0.619581 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1589.36i | 2.10511i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.9117 | −0.0196984 | −0.00984920 | − | 0.999951i | \(-0.503135\pi\) | ||||
−0.00984920 | + | 0.999951i | \(0.503135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1432.91i | − 1.88790i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 361.341 | 0.474824 | 0.237412 | − | 0.971409i | \(-0.423701\pi\) | ||||
0.237412 | + | 0.971409i | \(0.423701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −290.735 | −0.380046 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 96.5025i | − 0.125818i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 137.762 | 0.179144 | 0.0895719 | − | 0.995980i | \(-0.471450\pi\) | ||||
0.0895719 | + | 0.995980i | \(0.471450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 201.813i | − 0.261755i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −512.974 | −0.663614 | −0.331807 | − | 0.943347i | \(-0.607658\pi\) | ||||
−0.331807 | + | 0.943347i | \(0.607658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1529.07i | − 1.97299i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 119.053i | 0.152828i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 557.470 | 0.713790 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 168.798i | − 0.215579i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 408.309 | 0.520138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1531.59i | − 1.94611i | −0.230569 | − | 0.973056i | \(-0.574059\pi\) | ||||
0.230569 | − | 0.973056i | \(-0.425941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 285.411 | 0.361738 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −744.205 | −0.938468 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 936.317i | 1.17776i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1319.33 | 1.65536 | 0.827682 | − | 0.561197i | \(-0.189659\pi\) | ||||
0.827682 | + | 0.561197i | \(0.189659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 373.223i | − 0.467112i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −170.610 | −0.212996 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1241.65i | 1.54626i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 835.870i | 1.03577i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1487.53 | −1.83872 | −0.919362 | − | 0.393413i | \(-0.871294\pi\) | ||||
−0.919362 | + | 0.393413i | \(0.871294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 50.1785i | − 0.0618724i | −0.999521 | − | 0.0309362i | \(-0.990151\pi\) | ||||
0.999521 | − | 0.0309362i | \(-0.00984886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −390.926 | −0.480844 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 951.049i | − 1.16693i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1025.47 | −1.25517 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 798.029 | 0.972020 | 0.486010 | − | 0.873953i | \(-0.338452\pi\) | ||||
0.486010 | + | 0.873953i | \(0.338452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 351.861i | 0.427535i | 0.976885 | + | 0.213767i | \(0.0685735\pi\) | ||||
−0.976885 | + | 0.213767i | \(0.931427\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1048.09 | 1.27041 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1240.79i | − 1.50035i | −0.661237 | − | 0.750177i | \(-0.729968\pi\) | ||||
0.661237 | − | 0.750177i | \(-0.270032\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −978.281 | −1.18007 | −0.590037 | − | 0.807376i | \(-0.700887\pi\) | ||||
−0.590037 | + | 0.807376i | \(0.700887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 131.942i | − 0.158775i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1777.64i | − 2.12891i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −265.103 | −0.316730 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 263.296i | 0.313822i | 0.987613 | + | 0.156911i | \(0.0501535\pi\) | ||||
−0.987613 | + | 0.156911i | \(0.949846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 214.294 | 0.254808 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 149.491i | − 0.177332i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2302.76 | −2.72517 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −493.809 | −0.581636 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1390.73i | 1.63423i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −591.806 | −0.693794 | −0.346897 | − | 0.937903i | \(-0.612765\pi\) | ||||
−0.346897 | + | 0.937903i | \(0.612765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 326.899i | 0.382338i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 201.869 | 0.235553 | 0.117777 | − | 0.993040i | \(-0.462423\pi\) | ||||
0.117777 | + | 0.993040i | \(0.462423\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 822.596i | 0.957620i | 0.877918 | + | 0.478810i | \(0.158932\pi\) | ||||
−0.877918 | + | 0.478810i | \(0.841068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1464.70i | − 1.69722i | −0.529017 | − | 0.848611i | \(-0.677439\pi\) | ||||
0.529017 | − | 0.848611i | \(-0.322561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −116.648 | −0.134853 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 204.637i | − 0.236029i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1828.41 | −2.10404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 669.743i | − 0.768935i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 370.669 | 0.424592 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −217.352 | −0.247836 | −0.123918 | − | 0.992292i | \(-0.539546\pi\) | ||||
−0.123918 | + | 0.992292i | \(0.539546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 786.448i | − 0.894708i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 99.8995 | 0.113393 | 0.0566966 | − | 0.998391i | \(-0.481943\pi\) | ||||
0.0566966 | + | 0.998391i | \(0.481943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 86.1277i | 0.0975398i | 0.998810 | + | 0.0487699i | \(0.0155301\pi\) | ||||
−0.998810 | + | 0.0487699i | \(0.984470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.5887 | 0.0639421 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 81.0247i | − 0.0913469i | −0.998956 | − | 0.0456735i | \(-0.985457\pi\) | ||||
0.998956 | − | 0.0456735i | \(-0.0145434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 181.712i | − 0.203942i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −419.647 | −0.469929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 711.083i | − 0.794507i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1554.22 | −1.73269 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1657.37i | − 1.84357i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 953.034 | 1.05775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1638.63 | 1.81064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1289.83i | − 1.42209i | −0.703147 | − | 0.711044i | \(-0.748222\pi\) | ||||
0.703147 | − | 0.711044i | \(-0.251778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −210.978 | −0.232099 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 495.859i | − 0.544302i | −0.962255 | − | 0.272151i | \(-0.912265\pi\) | ||||
0.962255 | − | 0.272151i | \(-0.0877350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 105.941 | 0.116036 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 436.400i | − 0.476939i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1323.91i | 1.44060i | 0.693662 | + | 0.720301i | \(0.255996\pi\) | ||||
−0.693662 | + | 0.720301i | \(0.744004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −520.014 | −0.564619 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 604.663i | − 0.655107i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1017.23 | −1.09971 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 329.420i | 0.355362i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 439.664 | 0.473266 | 0.236633 | − | 0.971599i | \(-0.423956\pi\) | ||||
0.236633 | + | 0.971599i | \(0.423956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 438.573 | 0.470067 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1956.67i | − 2.09270i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0315 | 0.0320507 | 0.0160254 | − | 0.999872i | \(-0.494899\pi\) | ||||
0.0160254 | + | 0.999872i | \(0.494899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 577.286i | 0.614789i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 981.266 | 1.04279 | 0.521395 | − | 0.853315i | \(-0.325412\pi\) | ||||
0.521395 | + | 0.853315i | \(0.325412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 331.917i | − 0.351980i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 633.642i | 0.669105i | 0.942377 | + | 0.334552i | \(0.108585\pi\) | ||||
−0.942377 | + | 0.334552i | \(0.891415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1346.76 | 1.41914 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 189.252i | 0.199004i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1058.76 | 1.11098 | 0.555490 | − | 0.831523i | \(-0.312531\pi\) | ||||
0.555490 | + | 0.831523i | \(0.312531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 385.254i | − 0.403407i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1136.03 | 1.18707 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1641.94 | −1.70857 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 45.4412i | − 0.0471871i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1392.56 | 1.44307 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 309.103i | 0.319652i | 0.987145 | + | 0.159826i | \(0.0510933\pi\) | ||||
−0.987145 | + | 0.159826i | \(0.948907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 332.735 | 0.343380 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1197.76i | 1.23354i | 0.787145 | + | 0.616768i | \(0.211558\pi\) | ||||
−0.787145 | + | 0.616768i | \(0.788442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1136.81i | − 1.16596i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 837.131 | 0.856838 | 0.428419 | − | 0.903580i | \(-0.359071\pi\) | ||||
0.428419 | + | 0.903580i | \(0.359071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1148.22i | − 1.17285i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −218.558 | −0.222791 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 512.687i | − 0.521553i | −0.965399 | − | 0.260777i | \(-0.916021\pi\) | ||||
0.965399 | − | 0.260777i | \(-0.0839786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 349.123 | 0.354439 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2859.00 | 2.89080 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 984.874i | 0.993818i | 0.867803 | + | 0.496909i | \(0.165532\pi\) | ||||
−0.867803 | + | 0.496909i | \(0.834468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 597.588 | 0.601800 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1874.15i | − 1.88356i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 880.929 | 0.883580 | 0.441790 | − | 0.897119i | \(-0.354344\pi\) | ||||
0.441790 | + | 0.897119i | \(0.354344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 176.363i | 0.176540i |
(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 | 2352.3.m.d.1471.3 | yes | 4 | |
4.3 | odd | 2 | inner | 2352.3.m.d.1471.1 | ✓ | 4 | |
7.6 | odd | 2 | 2352.3.m.l.1471.2 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.l.1471.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.3.m.d.1471.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
2352.3.m.d.1471.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.3.m.l.1471.2 | yes | 4 | 7.6 | odd | 2 | ||
2352.3.m.l.1471.4 | yes | 4 | 28.27 | even | 2 |