Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(417,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.417");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.g (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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 417.31 | ||
Character | \(\chi\) | \(=\) | 1216.417 |
Dual form | 1216.3.g.e.417.30 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.73941 | 0.913138 | 0.456569 | − | 0.889688i | \(-0.349078\pi\) | ||||
0.456569 | + | 0.889688i | \(0.349078\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.26292i | 1.05258i | 0.850304 | + | 0.526292i | \(0.176418\pi\) | ||||
−0.850304 | + | 0.526292i | \(0.823582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.69464 | −0.670662 | −0.335331 | − | 0.942100i | \(-0.608848\pi\) | ||||
−0.335331 | + | 0.942100i | \(0.608848\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.49561 | −0.166179 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.2686i | 0.933507i | 0.884388 | + | 0.466753i | \(0.154576\pi\) | ||||
−0.884388 | + | 0.466753i | \(0.845424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.6737 | −1.35952 | −0.679758 | − | 0.733437i | \(-0.737915\pi\) | ||||
−0.679758 | + | 0.733437i | \(0.737915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.4173i | 0.961155i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.2750 | 1.48676 | 0.743382 | − | 0.668867i | \(-0.233220\pi\) | ||||
0.743382 | + | 0.668867i | \(0.233220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.7565 | − | 14.9259i | −0.618765 | − | 0.785576i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.8606 | −0.612407 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.4985 | −0.456455 | −0.228228 | − | 0.973608i | \(-0.573293\pi\) | ||||
−0.228228 | + | 0.973608i | \(0.573293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.69834 | −0.107934 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −28.7518 | −1.06488 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.2666 | 0.940226 | 0.470113 | − | 0.882606i | \(-0.344213\pi\) | ||||
0.470113 | + | 0.882606i | \(0.344213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 34.2018i | − | 1.10328i | −0.834081 | − | 0.551642i | \(-0.814002\pi\) | ||
0.834081 | − | 0.551642i | \(-0.185998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 28.1299i | 0.852420i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 24.7075i | − | 0.705929i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −69.6637 | −1.88280 | −0.941402 | − | 0.337287i | \(-0.890491\pi\) | ||||
−0.941402 | + | 0.337287i | \(0.890491\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −48.4156 | −1.24142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 45.1232i | − | 1.10057i | −0.834978 | − | 0.550283i | \(-0.814520\pi\) | ||
0.834978 | − | 0.550283i | \(-0.185480\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.45023i | − | 0.173261i | −0.996241 | − | 0.0866306i | \(-0.972390\pi\) | ||
0.996241 | − | 0.0866306i | \(-0.0276100\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 7.87130i | − | 0.174918i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.8506 | −0.975545 | −0.487772 | − | 0.872971i | \(-0.662190\pi\) | ||||
−0.487772 | + | 0.872971i | \(0.662190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.9604 | −0.550212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 69.2387 | 1.35762 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −18.3757 | −0.346711 | −0.173356 | − | 0.984859i | \(-0.555461\pi\) | ||||
−0.173356 | + | 0.984859i | \(0.555461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.0427 | −0.982594 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −32.2060 | − | 40.8883i | −0.565018 | − | 0.717339i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 71.0173 | 1.20368 | 0.601841 | − | 0.798616i | \(-0.294434\pi\) | ||||
0.601841 | + | 0.798616i | \(0.294434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 75.5544i | 1.23860i | 0.785156 | + | 0.619298i | \(0.212583\pi\) | ||||
−0.785156 | + | 0.619298i | \(0.787417\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.02137 | 0.111450 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 93.0153i | − | 1.43100i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −96.9126 | −1.44646 | −0.723228 | − | 0.690609i | \(-0.757343\pi\) | ||||
−0.723228 | + | 0.690609i | \(0.757343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −28.7597 | −0.416807 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 19.5780i | − | 0.275746i | −0.990450 | − | 0.137873i | \(-0.955973\pi\) | ||
0.990450 | − | 0.137873i | \(-0.0440265\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −62.7616 | −0.859748 | −0.429874 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429874 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.39187 | −0.0985583 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 48.2072i | − | 0.626068i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62.4377i | 0.790350i | 0.918606 | + | 0.395175i | \(0.129316\pi\) | ||||
−0.918606 | + | 0.395175i | \(0.870684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −65.3026 | −0.806205 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 101.658i | − | 1.22480i | −0.790549 | − | 0.612399i | \(-0.790205\pi\) | ||
0.790549 | − | 0.612399i | \(-0.209795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 133.020i | 1.56495i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 74.6944 | 0.858556 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 73.5179i | 0.826043i | 0.910721 | + | 0.413022i | \(0.135527\pi\) | ||||
−0.910721 | + | 0.413022i | \(0.864473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 82.9716 | 0.911776 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 93.6928i | − | 1.00745i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 78.5541 | − | 61.8737i | 0.826885 | − | 0.651303i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 107.607i | − | 1.10935i | −0.832068 | − | 0.554674i | \(-0.812843\pi\) | ||
0.832068 | − | 0.554674i | \(-0.187157\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 15.3578i | − | 0.155130i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 160.350i | 1.58763i | 0.608160 | + | 0.793814i | \(0.291908\pi\) | ||||
−0.608160 | + | 0.793814i | \(0.708092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 189.735i | − | 1.84209i | −0.389456 | − | 0.921045i | \(-0.627337\pi\) | ||
0.389456 | − | 0.921045i | \(-0.372663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 67.6841i | − | 0.644610i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 148.162 | 1.38469 | 0.692347 | − | 0.721565i | \(-0.256577\pi\) | ||||
0.692347 | + | 0.721565i | \(0.256577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −50.2608 | −0.461108 | −0.230554 | − | 0.973060i | \(-0.574054\pi\) | ||||
−0.230554 | + | 0.973060i | \(0.574054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −190.838 | −1.71926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186.687i | 1.65210i | 0.563600 | + | 0.826048i | \(0.309416\pi\) | ||||
−0.563600 | + | 0.826048i | \(0.690584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 55.2526i | − | 0.480458i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.4330 | 0.225923 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −118.657 | −0.997117 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.5564 | 0.128566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 123.611i | − | 1.00497i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 117.372i | 0.938975i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 24.5981i | − | 0.193686i | −0.995300 | − | 0.0968430i | \(-0.969126\pi\) | ||
0.995300 | − | 0.0968430i | \(-0.0308745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 20.4093i | − | 0.158211i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 65.8406i | − | 0.502600i | −0.967909 | − | 0.251300i | \(-0.919142\pi\) | ||
0.967909 | − | 0.251300i | \(-0.0808581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 55.1927 | + | 70.0719i | 0.414983 | + | 0.526856i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 151.319i | − | 1.12088i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −201.126 | −1.46807 | −0.734037 | − | 0.679109i | \(-0.762366\pi\) | ||||
−0.734037 | + | 0.679109i | \(0.762366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 102.084i | 0.734417i | 0.930139 | + | 0.367209i | \(0.119686\pi\) | ||||
−0.930139 | + | 0.367209i | \(0.880314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −125.604 | −0.890807 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 181.484i | − | 1.26912i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 143.502i | 0.989667i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −73.8556 | −0.502419 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 85.2086i | 0.571870i | 0.958249 | + | 0.285935i | \(0.0923041\pi\) | ||||
−0.958249 | + | 0.285935i | \(0.907696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 30.9703i | − | 0.205101i | −0.994728 | − | 0.102551i | \(-0.967300\pi\) | ||
0.994728 | − | 0.102551i | \(-0.0327003\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.8016 | −0.247070 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 180.001 | 1.16130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 127.135i | 0.809777i | 0.914366 | + | 0.404888i | \(0.132690\pi\) | ||||
−0.914366 | + | 0.404888i | \(0.867310\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −50.3386 | −0.316595 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 49.2865 | 0.306127 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 295.514i | 1.81297i | 0.422240 | + | 0.906484i | \(0.361244\pi\) | ||||
−0.422240 | + | 0.906484i | \(0.638756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −148.045 | −0.897244 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 89.2035i | 0.534153i | 0.963675 | + | 0.267076i | \(0.0860576\pi\) | ||||
−0.963675 | + | 0.267076i | \(0.913942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 143.360 | 0.848281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.5832 | + | 22.3235i | 0.102826 | + | 0.130547i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 29.8953 | 0.172805 | 0.0864027 | − | 0.996260i | \(-0.472463\pi\) | ||||
0.0864027 | + | 0.996260i | \(0.472463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.6677 | 0.0723871 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 194.546 | 1.09913 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.6560 | 0.104224 | 0.0521119 | − | 0.998641i | \(-0.483405\pi\) | ||||
0.0521119 | + | 0.998641i | \(0.483405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.73288 | −0.0537728 | −0.0268864 | − | 0.999638i | \(-0.508559\pi\) | ||||
−0.0268864 | + | 0.999638i | \(0.508559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 206.975i | 1.13101i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 366.635i | − | 1.98181i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 259.538i | 1.38790i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 134.979 | 0.714177 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −50.1333 | −0.262478 | −0.131239 | − | 0.991351i | \(-0.541896\pi\) | ||||
−0.131239 | + | 0.991351i | \(0.541896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 128.499i | 0.665797i | 0.942963 | + | 0.332899i | \(0.108027\pi\) | ||||
−0.942963 | + | 0.332899i | \(0.891973\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 254.807i | − | 1.30670i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 147.060i | 0.746496i | 0.927732 | + | 0.373248i | \(0.121756\pi\) | ||||
−0.927732 | + | 0.373248i | \(0.878244\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −105.724 | −0.531276 | −0.265638 | − | 0.964073i | \(-0.585583\pi\) | ||||
−0.265638 | + | 0.964073i | \(0.585583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −265.484 | −1.32081 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −128.007 | −0.630574 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 237.480 | 1.15844 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.7017 | 0.0758535 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 153.268 | − | 120.723i | 0.733340 | − | 0.577621i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −301.385 | −1.42836 | −0.714181 | − | 0.699961i | \(-0.753201\pi\) | ||||
−0.714181 | + | 0.699961i | \(0.753201\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 53.6321i | − | 0.251794i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.2100 | 0.182372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 160.565i | 0.739931i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −171.930 | −0.785069 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −446.703 | −2.02128 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 399.952i | − | 1.79351i | −0.442531 | − | 0.896753i | \(-0.645919\pi\) | ||
0.442531 | − | 0.896753i | \(-0.354081\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.03568 | 0.0179364 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.58217 | 0.0245910 | 0.0122955 | − | 0.999924i | \(-0.496086\pi\) | ||||
0.0122955 | + | 0.999924i | \(0.496086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 378.433i | − | 1.65254i | −0.563272 | − | 0.826272i | \(-0.690457\pi\) | ||
0.563272 | − | 0.826272i | \(-0.309543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 132.060i | − | 0.571686i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −375.953 | −1.61353 | −0.806766 | − | 0.590871i | \(-0.798784\pi\) | ||||
−0.806766 | + | 0.590871i | \(0.798784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 241.308i | − | 1.02684i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 171.043i | 0.721699i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 54.6197 | 0.228534 | 0.114267 | − | 0.993450i | \(-0.463548\pi\) | ||||
0.114267 | + | 0.993450i | \(0.463548\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 138.818i | 0.576008i | 0.957629 | + | 0.288004i | \(0.0929916\pi\) | ||||
−0.957629 | + | 0.288004i | \(0.907008\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 79.8756 | 0.328706 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 141.890i | − | 0.579144i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 207.781 | + | 263.797i | 0.841221 | + | 1.06800i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 278.484i | − | 1.11841i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 222.994i | − | 0.888424i | −0.895922 | − | 0.444212i | \(-0.853484\pi\) | ||
0.895922 | − | 0.444212i | \(-0.146516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 107.804i | − | 0.426104i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 364.398i | 1.42901i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 173.190i | 0.673891i | 0.941524 | + | 0.336945i | \(0.109394\pi\) | ||||
−0.941524 | + | 0.336945i | \(0.890606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 327.046 | 1.26273 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.7802 | −0.156246 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −209.372 | −0.796090 | −0.398045 | − | 0.917366i | \(-0.630311\pi\) | ||||
−0.398045 | + | 0.917366i | \(0.630311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 96.7098i | − | 0.364943i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 201.396i | 0.754292i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −78.6403 | −0.292343 | −0.146172 | − | 0.989259i | \(-0.546695\pi\) | ||||
−0.146172 | + | 0.989259i | \(0.546695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −110.916 | −0.409285 | −0.204642 | − | 0.978837i | \(-0.565603\pi\) | ||||
−0.204642 | + | 0.978837i | \(0.565603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 227.293 | 0.832577 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 27.7081i | − | 0.100757i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 357.833i | − | 1.29181i | −0.763416 | − | 0.645907i | \(-0.776479\pi\) | ||
0.763416 | − | 0.645907i | \(-0.223521\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 51.1527i | 0.183343i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 183.167i | 0.651839i | 0.945398 | + | 0.325919i | \(0.105674\pi\) | ||||
−0.945398 | + | 0.325919i | \(0.894326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 158.895i | 0.561465i | 0.959786 | + | 0.280732i | \(0.0905773\pi\) | ||||
−0.959786 | + | 0.280732i | \(0.909423\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 215.192 | − | 169.498i | 0.755060 | − | 0.594729i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 211.837i | 0.738109i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 349.826 | 1.21047 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 294.779i | − | 1.01299i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 128.281 | 0.437817 | 0.218909 | − | 0.975745i | \(-0.429750\pi\) | ||||
0.218909 | + | 0.975745i | \(0.429750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 373.758i | 1.26698i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 295.240i | − | 0.994075i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 185.547 | 0.620558 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.9761i | 0.116200i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 439.266i | 1.44972i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −397.637 | −1.30373 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −259.621 | −0.845670 | −0.422835 | − | 0.906207i | \(-0.638965\pi\) | ||||
−0.422835 | + | 0.906207i | \(0.638965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 519.763i | − | 1.68208i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 556.165 | 1.78831 | 0.894157 | − | 0.447754i | \(-0.147776\pi\) | ||||
0.894157 | + | 0.447754i | \(0.147776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 197.344 | 0.630492 | 0.315246 | − | 0.949010i | \(-0.397913\pi\) | ||||
0.315246 | + | 0.949010i | \(0.397913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 36.9529i | 0.117311i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 46.0689 | 0.145328 | 0.0726639 | − | 0.997356i | \(-0.476850\pi\) | ||||
0.0726639 | + | 0.997356i | \(0.476850\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 279.989i | 0.877707i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 405.877 | 1.26442 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −297.147 | − | 377.253i | −0.919958 | − | 1.16797i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 47.6897 | 0.146737 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −137.685 | −0.421055 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 215.252 | 0.654261 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 202.375 | 0.611405 | 0.305703 | − | 0.952127i | \(-0.401109\pi\) | ||||
0.305703 | + | 0.952127i | \(0.401109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 104.190 | 0.312883 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 510.043i | − | 1.52252i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.5252i | − | 0.0609056i | −0.999536 | − | 0.0304528i | \(-0.990305\pi\) | ||
0.999536 | − | 0.0304528i | \(-0.00969493\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 511.412i | 1.50859i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 351.203 | 1.02992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 356.606 | 1.03967 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 151.360i | − | 0.438724i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 197.014i | 0.567763i | 0.958859 | + | 0.283881i | \(0.0916222\pi\) | ||||
−0.958859 | + | 0.283881i | \(0.908378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 219.206i | 0.628098i | 0.949407 | + | 0.314049i | \(0.101686\pi\) | ||||
−0.949407 | + | 0.314049i | \(0.898314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 508.151 | 1.44772 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 218.242 | 0.618249 | 0.309124 | − | 0.951022i | \(-0.399964\pi\) | ||||
0.309124 | + | 0.951022i | \(0.399964\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 103.037 | 0.290246 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −325.050 | −0.910506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 67.2437 | 0.187308 | 0.0936541 | − | 0.995605i | \(-0.470145\pi\) | ||||
0.0936541 | + | 0.995605i | \(0.470145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −84.5676 | + | 350.955i | −0.234259 | + | 0.972174i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 42.6155 | 0.117398 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 330.310i | − | 0.904958i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −234.617 | −0.639283 | −0.319642 | − | 0.947538i | \(-0.603563\pi\) | ||||
−0.319642 | + | 0.947538i | \(0.603563\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.4869i | 0.182891i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 86.2672 | 0.232526 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 393.307 | 1.05444 | 0.527221 | − | 0.849728i | \(-0.323234\pi\) | ||||
0.527221 | + | 0.849728i | \(0.323234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 321.530i | 0.857414i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −481.901 | −1.27825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −459.442 | −1.21225 | −0.606124 | − | 0.795370i | \(-0.707277\pi\) | ||||
−0.606124 | + | 0.795370i | \(0.707277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 67.3844i | − | 0.176862i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 87.1105i | 0.227442i | 0.993513 | + | 0.113721i | \(0.0362771\pi\) | ||||
−0.993513 | + | 0.113721i | \(0.963723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 253.711 | 0.658989 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.1427i | 0.0287924i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 317.883i | 0.817179i | 0.912718 | + | 0.408589i | \(0.133979\pi\) | ||||
−0.912718 | + | 0.408589i | \(0.866021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −265.349 | −0.678642 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 180.365i | − | 0.458943i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −328.605 | −0.831910 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 338.098i | 0.851632i | 0.904810 | + | 0.425816i | \(0.140013\pi\) | ||||
−0.904810 | + | 0.425816i | \(0.859987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 151.196 | + | 191.956i | 0.378936 | + | 0.481092i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 798.720i | 1.99182i | 0.0903539 | + | 0.995910i | \(0.471200\pi\) | ||||
−0.0903539 | + | 0.995910i | \(0.528800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 604.472i | 1.49993i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 343.683i | − | 0.848599i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 715.347i | − | 1.75761i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 237.012i | − | 0.579492i | −0.957104 | − | 0.289746i | \(-0.906429\pi\) | ||
0.957104 | − | 0.289746i | \(-0.0935708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −550.968 | −1.34055 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −333.400 | −0.807265 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 535.019 | 1.28920 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 279.650i | 0.670624i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 124.585i | 0.297338i | 0.988887 | + | 0.148669i | \(0.0474988\pi\) | ||||
−0.988887 | + | 0.148669i | \(0.952501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 448.383 | 1.06504 | 0.532522 | − | 0.846416i | \(-0.321244\pi\) | ||||
0.532522 | + | 0.846416i | \(0.321244\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 68.5748 | 0.162115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −68.2006 | −0.160472 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 354.700i | − | 0.830680i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 497.159i | − | 1.15888i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 174.115i | 0.403979i | 0.979388 | + | 0.201989i | \(0.0647406\pi\) | ||||
−0.979388 | + | 0.201989i | \(0.935259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 461.148i | 1.06501i | 0.846428 | + | 0.532503i | \(0.178749\pi\) | ||||
−0.846428 | + | 0.532503i | \(0.821251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 393.111i | 0.903703i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 123.426 | + | 156.700i | 0.282439 | + | 0.358580i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 435.302i | − | 0.991577i | −0.868443 | − | 0.495788i | \(-0.834879\pi\) | ||
0.868443 | − | 0.495788i | \(-0.165121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 40.3223 | 0.0914338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 160.935i | 0.363283i | 0.983365 | + | 0.181642i | \(0.0581411\pi\) | ||||
−0.983365 | + | 0.181642i | \(0.941859\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −386.919 | −0.869480 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 233.421i | 0.522196i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 171.555i | − | 0.382082i | −0.981582 | − | 0.191041i | \(-0.938814\pi\) | ||
0.981582 | − | 0.191041i | \(-0.0611864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 463.351 | 1.02739 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 84.8403i | − | 0.187285i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 436.673i | 0.959721i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −361.665 | −0.791390 | −0.395695 | − | 0.918382i | \(-0.629496\pi\) | ||||
−0.395695 | + | 0.918382i | \(0.629496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −726.702 | −1.58323 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 406.221i | − | 0.881174i | −0.897710 | − | 0.440587i | \(-0.854770\pi\) | ||
0.897710 | − | 0.440587i | \(-0.145230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 815.644 | 1.76165 | 0.880825 | − | 0.473441i | \(-0.156988\pi\) | ||||
0.880825 | + | 0.473441i | \(0.156988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 493.098 | 1.06043 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 711.741i | 1.52407i | 0.647536 | + | 0.762035i | \(0.275800\pi\) | ||||
−0.647536 | + | 0.762035i | \(0.724200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 454.969 | 0.970084 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 348.275i | 0.739438i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 76.5032 | 0.161740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7232 | + | 40.2753i | 0.0667856 | + | 0.0847901i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.4829 | 0.0576162 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −752.130 | −1.57021 | −0.785104 | − | 0.619364i | \(-0.787390\pi\) | ||||
−0.785104 | + | 0.619364i | \(0.787390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1231.22 | 2.55970 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 135.016 | 0.279537 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 566.326 | 1.16768 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 725.897i | − | 1.49055i | −0.666758 | − | 0.745274i | \(-0.732319\pi\) | ||
0.666758 | − | 0.745274i | \(-0.267681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 809.534i | 1.65549i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 732.543i | 1.49194i | 0.665979 | + | 0.745971i | \(0.268014\pi\) | ||||
−0.665979 | + | 0.745971i | \(0.731986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 689.162 | 1.39790 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 80.8270 | 0.163287 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 91.9114i | 0.184932i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 110.238i | − | 0.220919i | −0.993881 | − | 0.110459i | \(-0.964768\pi\) | ||
0.993881 | − | 0.110459i | \(-0.0352322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 244.365i | 0.487755i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 259.861 | 0.516622 | 0.258311 | − | 0.966062i | \(-0.416834\pi\) | ||||
0.258311 | + | 0.966062i | \(0.416834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −843.912 | −1.67111 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 392.721 | 0.774598 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 914.579 | 1.79681 | 0.898407 | − | 0.439163i | \(-0.144725\pi\) | ||||
0.898407 | + | 0.439163i | \(0.144725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 294.643 | 0.576601 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 338.022 | + | 429.148i | 0.658912 | + | 0.836546i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 998.562 | 1.93896 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 470.820i | − | 0.910677i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 81.8956 | 0.157795 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1019.80i | − | 1.95739i | −0.205318 | − | 0.978695i | \(-0.565823\pi\) | ||
0.205318 | − | 0.978695i | \(-0.434177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 448.157 | 0.856897 | 0.428449 | − | 0.903566i | \(-0.359060\pi\) | ||||
0.428449 | + | 0.903566i | \(0.359060\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 34.7022 | 0.0660994 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 864.450i | − | 1.64032i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −418.782 | −0.791648 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −106.214 | −0.200027 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 797.494i | 1.49624i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 779.766i | 1.45751i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.1066 | 0.0951706 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 276.845i | − | 0.513626i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 500.797i | − | 0.925687i | −0.886440 | − | 0.462843i | \(-0.846829\pi\) | ||
0.886440 | − | 0.462843i | \(-0.153171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.6624 | −0.0491020 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 264.519i | − | 0.485355i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −886.809 | −1.62122 | −0.810612 | − | 0.585584i | \(-0.800865\pi\) | ||||
−0.810612 | + | 0.585584i | \(0.800865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 113.000i | − | 0.205829i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −320.560 | − | 406.979i | −0.581779 | − | 0.738619i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 293.122i | − | 0.530058i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1004.36i | − | 1.80967i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 403.210i | 0.723896i | 0.932198 | + | 0.361948i | \(0.117888\pi\) | ||||
−0.932198 | + | 0.361948i | \(0.882112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 131.673i | 0.235551i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 710.982i | 1.26735i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −494.180 | −0.877762 | −0.438881 | − | 0.898545i | \(-0.644625\pi\) | ||||
−0.438881 | + | 0.898545i | \(0.644625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −982.518 | −1.73897 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 306.572 | 0.540691 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 588.191i | − | 1.03373i | −0.856068 | − | 0.516864i | \(-0.827099\pi\) | ||
0.856068 | − | 0.516864i | \(-0.172901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 185.627i | 0.325092i | 0.986701 | + | 0.162546i | \(0.0519706\pi\) | ||||
−0.986701 | + | 0.162546i | \(0.948029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −137.336 | −0.239679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.3285 | 0.0492669 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −128.772 | −0.223174 | −0.111587 | − | 0.993755i | \(-0.535593\pi\) | ||||
−0.111587 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 352.011i | 0.607965i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 477.248i | 0.821426i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 188.692i | − | 0.323657i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 139.115i | 0.237803i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 867.915i | − | 1.47856i | −0.673397 | − | 0.739281i | \(-0.735166\pi\) | ||
0.673397 | − | 0.739281i | \(-0.264834\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −510.494 | + | 402.095i | −0.866713 | + | 0.682673i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 402.857i | 0.681654i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 452.273 | 0.762687 | 0.381344 | − | 0.924433i | \(-0.375462\pi\) | ||||
0.381344 | + | 0.924433i | \(0.375462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 624.482i | − | 1.04955i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −289.622 | −0.485128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 733.094i | 1.22386i | 0.790910 | + | 0.611932i | \(0.209607\pi\) | ||||
−0.790910 | + | 0.611932i | \(0.790393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 488.835i | − | 0.813370i | −0.913568 | − | 0.406685i | \(-0.866685\pi\) | ||
0.913568 | − | 0.406685i | \(-0.133315\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 144.944 | 0.240371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 81.8723i | 0.135326i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 303.240i | 0.499572i | 0.968301 | + | 0.249786i | \(0.0803603\pi\) | ||||
−0.968301 | + | 0.249786i | \(0.919640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −350.663 | −0.575801 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 810.350 | 1.32627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 570.220i | − | 0.930212i | −0.885255 | − | 0.465106i | \(-0.846016\pi\) | ||
0.885255 | − | 0.465106i | \(-0.153984\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 650.556 | 1.05781 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −67.8845 | −0.110024 | −0.0550118 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550118 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 584.121i | − | 0.943652i | −0.881692 | − | 0.471826i | \(-0.843595\pi\) | ||
0.881692 | − | 0.471826i | \(-0.156405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 301.850 | 0.486071 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 345.140i | − | 0.553996i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −685.178 | −1.09628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 419.865 | − | 330.710i | 0.669641 | − | 0.527448i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1760.75 | −2.79929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 566.835 | 0.898311 | 0.449156 | − | 0.893453i | \(-0.351725\pi\) | ||||
0.449156 | + | 0.893453i | \(0.351725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −825.617 | −1.30429 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 129.458 | 0.203871 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 476.490 | 0.748021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.2811i | 0.0458233i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 714.270i | − | 1.11431i | −0.830410 | − | 0.557153i | \(-0.811894\pi\) | ||
0.830410 | − | 0.557153i | \(-0.188106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 483.851i | 0.752490i | 0.926520 | + | 0.376245i | \(0.122785\pi\) | ||||
−0.926520 | + | 0.376245i | \(0.877215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 107.412 | 0.166531 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −680.997 | −1.05255 | −0.526273 | − | 0.850316i | \(-0.676411\pi\) | ||||
−0.526273 | + | 0.850316i | \(0.676411\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 729.246i | 1.12365i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 439.854i | 0.675659i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 932.232i | 1.42761i | 0.700342 | + | 0.713807i | \(0.253031\pi\) | ||||
−0.700342 | + | 0.713807i | \(0.746969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 346.514 | 0.529029 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 93.8672 | 0.142872 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −465.128 | −0.705808 | −0.352904 | − | 0.935659i | \(-0.614806\pi\) | ||||
−0.352904 | + | 0.935659i | \(0.614806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 961.648 | 1.45484 | 0.727419 | − | 0.686193i | \(-0.240720\pi\) | ||||
0.727419 | + | 0.686193i | \(0.240720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1223.70 | −1.84571 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −368.783 | + | 290.475i | −0.554561 | + | 0.436804i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −286.257 | −0.429171 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1095.63i | − | 1.63772i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −775.835 | −1.15624 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 310.790i | 0.461798i | 0.972978 | + | 0.230899i | \(0.0741667\pi\) | ||||
−0.972978 | + | 0.230899i | \(0.925833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 77.5823 | 0.114937 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −999.473 | −1.47633 | −0.738163 | − | 0.674623i | \(-0.764306\pi\) | ||||
−0.738163 | + | 0.674623i | \(0.764306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 505.175i | 0.743998i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.2919 | 0.0224550 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 225.474 | 0.330123 | 0.165061 | − | 0.986283i | \(-0.447218\pi\) | ||||
0.165061 | + | 0.986283i | \(0.447218\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1058.51i | − | 1.54527i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1036.68i | − | 1.50900i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 324.766 | 0.471359 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 257.168i | 0.372168i | 0.982534 | + | 0.186084i | \(0.0595796\pi\) | ||||
−0.982534 | + | 0.186084i | \(0.940420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 72.0994i | 0.104040i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −537.260 | −0.773036 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1140.49i | − | 1.63628i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1029.89 | −1.47338 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 75.7758i | − | 0.108097i | −0.998538 | − | 0.0540484i | \(-0.982787\pi\) | ||
0.998538 | − | 0.0540484i | \(-0.0172125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 819.004 | + | 1039.80i | 1.16501 | + | 1.47909i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 661.043i | − | 0.937649i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 752.787i | − | 1.06476i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 396.211i | − | 0.558831i | −0.960170 | − | 0.279415i | \(-0.909859\pi\) | ||
0.960170 | − | 0.279415i | \(-0.0901407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 93.3827i | − | 0.131340i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 359.066i | 0.503600i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 955.134 | 1.33585 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 149.626 | 0.208683 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −238.120 | −0.331182 | −0.165591 | − | 0.986194i | \(-0.552953\pi\) | ||||
−0.165591 | + | 0.986194i | \(0.552953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 890.738i | 1.23542i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 380.280i | 0.525974i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −73.5745 | −0.101482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −987.494 | −1.35831 | −0.679157 | − | 0.733993i | \(-0.737654\pi\) | ||||
−0.679157 | + | 0.733993i | \(0.737654\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 806.536 | 1.10636 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 188.305i | − | 0.257599i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 892.138i | 1.21711i | 0.793514 | + | 0.608553i | \(0.208250\pi\) | ||||
−0.793514 | + | 0.608553i | \(0.791750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 388.696i | − | 0.528839i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 995.154i | − | 1.35028i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1196.05i | − | 1.61847i | −0.587486 | − | 0.809235i | \(-0.699882\pi\) | ||
0.587486 | − | 0.809235i | \(-0.300118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 569.199 | + | 722.648i | 0.768150 | + | 0.975233i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 991.010i | − | 1.33380i | −0.745149 | − | 0.666898i | \(-0.767622\pi\) | ||
0.745149 | − | 0.666898i | \(-0.232378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −448.446 | −0.601941 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 152.041i | 0.203536i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −695.568 | −0.928662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 287.993i | 0.383480i | 0.981446 | + | 0.191740i | \(0.0614130\pi\) | ||||
−0.981446 | + | 0.191740i | \(0.938587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 610.874i | − | 0.811254i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 162.994 | 0.215886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 844.099i | 1.11506i | 0.830157 | + | 0.557529i | \(0.188251\pi\) | ||||
−0.830157 | + | 0.557529i | \(0.811749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 295.321i | − | 0.389092i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 448.650 | 0.589553 | 0.294777 | − | 0.955566i | \(-0.404755\pi\) | ||||
0.294777 | + | 0.955566i | \(0.404755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 235.956 | 0.309248 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 198.947i | − | 0.260062i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1255.14 | −1.63642 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 701.512 | 0.912239 | 0.456120 | − | 0.889919i | \(-0.349239\pi\) | ||||
0.456120 | + | 0.889919i | \(0.349239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 474.439i | 0.615355i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1099.51 | −1.42240 | −0.711198 | − | 0.702992i | \(-0.751847\pi\) | ||||
−0.711198 | + | 0.702992i | \(0.751847\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 92.2881i | 0.119081i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 895.914 | 1.15304 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −673.507 | + | 530.493i | −0.864579 | + | 0.680992i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 201.038 | 0.257410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −783.963 | −1.00123 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −669.101 | −0.852358 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 420.402 | 0.534183 | 0.267092 | − | 0.963671i | \(-0.413937\pi\) | ||||
0.267092 | + | 0.963671i | \(0.413937\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −573.556 | −0.726940 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 876.427i | − | 1.10800i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1335.32i | − | 1.68389i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 264.928i | − | 0.333243i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5902 | 0.0408911 | 0.0204455 | − | 0.999791i | \(-0.493492\pi\) | ||||
0.0204455 | + | 0.999791i | \(0.493492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1158.87 | −1.45041 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 109.954i | − | 0.137271i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 644.472i | − | 0.802581i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 259.391i | 0.322225i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −215.428 | −0.266950 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −972.332 | −1.20189 | −0.600947 | − | 0.799289i | \(-0.705210\pi\) | ||||
−0.600947 | + | 0.799289i | \(0.705210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −992.060 | −1.22325 | −0.611627 | − | 0.791146i | \(-0.709485\pi\) | ||||
−0.611627 | + | 0.791146i | \(0.709485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −303.845 | −0.373733 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1555.27 | −1.90830 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −111.202 | + | 87.5889i | −0.136110 | + | 0.107208i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −124.093 | −0.151518 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 386.695i | 0.471005i | 0.971874 | + | 0.235502i | \(0.0756736\pi\) | ||||
−0.971874 | + | 0.235502i | \(0.924326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 624.294 | 0.758559 | 0.379279 | − | 0.925282i | \(-0.376172\pi\) | ||||
0.379279 | + | 0.925282i | \(0.376172\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 75.9040i | − | 0.0920048i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −184.998 | −0.223698 | −0.111849 | − | 0.993725i | \(-0.535677\pi\) | ||||
−0.111849 | + | 0.993725i | \(0.535677\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1489.30 | −1.79651 | −0.898253 | − | 0.439478i | \(-0.855163\pi\) | ||||
−0.898253 | + | 0.439478i | \(0.855163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 980.251i | − | 1.17960i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −681.424 | −0.818036 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −469.471 | −0.562241 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 983.364i | 1.17487i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1103.27i | 1.31498i | 0.753465 | + | 0.657489i | \(0.228381\pi\) | ||||
−0.753465 | + | 0.657489i | \(0.771619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −97.5349 | −0.115975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 501.769i | 0.595219i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 754.490i | 0.892887i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −73.0318 | −0.0862241 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 435.278i | 0.512695i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 731.363 | 0.859416 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1005.86i | − | 1.17920i | −0.807696 | − | 0.589599i | \(-0.799286\pi\) | ||
0.807696 | − | 0.589599i | \(-0.200714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −117.487 | + | 92.5392i | −0.137411 | + | 0.108233i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1160.47i | 1.35411i | 0.735935 | + | 0.677053i | \(0.236743\pi\) | ||||
−0.735935 | + | 0.677053i | \(0.763257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 944.049i | 1.09901i | 0.835491 | + | 0.549505i | \(0.185184\pi\) | ||||
−0.835491 | + | 0.549505i | \(0.814816\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 580.310i | 0.673995i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1345.70i | − | 1.55932i | −0.626201 | − | 0.779662i | \(-0.715391\pi\) | ||
0.626201 | − | 0.779662i | \(-0.284609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 157.337i | 0.181892i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 958.317 | 1.10533 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −641.146 | −0.737797 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1712.80 | 1.96648 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 160.938i | 0.184351i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 551.018i | − | 0.629735i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −371.035 | −0.423073 | −0.211536 | − | 0.977370i | \(-0.567847\pi\) | ||||
−0.211536 | + | 0.977370i | \(0.567847\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 351.413 | 0.399788 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −862.919 | −0.979476 | −0.489738 | − | 0.871870i | \(-0.662908\pi\) | ||||
−0.489738 | + | 0.871870i | \(0.662908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 445.613i | 0.504658i | 0.967641 | + | 0.252329i | \(0.0811965\pi\) | ||||
−0.967641 | + | 0.252329i | \(0.918803\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1023.88i | 1.15692i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 833.493i | − | 0.939676i | −0.882753 | − | 0.469838i | \(-0.844312\pi\) | ||
0.882753 | − | 0.469838i | \(-0.155688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 115.479i | 0.129898i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 670.565i | − | 0.752598i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 539.044 | + | 684.363i | 0.603633 | + | 0.766364i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 98.1853i | 0.109704i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 508.289 | 0.566655 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 932.565i | − | 1.03734i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −464.446 | −0.515478 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 95.8140i | 0.106106i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 51.2234i | − | 0.0566004i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 440.320 | 0.485469 | 0.242734 | − | 0.970093i | \(-0.421956\pi\) | ||||
0.242734 | + | 0.970093i | \(0.421956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 239.822i | − | 0.263831i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 525.421i | 0.576752i | 0.957517 | + | 0.288376i | \(0.0931153\pi\) | ||||
−0.957517 | + | 0.288376i | \(0.906885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1043.88 | 1.14336 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1089.29 | −1.19048 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 309.098i | 0.337075i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 285.119 | 0.310249 | 0.155124 | − | 0.987895i | \(-0.450422\pi\) | ||||
0.155124 | + | 0.987895i | \(0.450422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −711.208 | −0.772213 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 346.015i | 0.374881i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 187.977 | 0.203218 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 283.771i | 0.306117i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −97.2881 | −0.104724 | −0.0523618 | − | 0.998628i | \(-0.516675\pi\) | ||||
−0.0523618 | + | 0.998628i | \(0.516675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 316.961 | + | 402.409i | 0.340452 | + | 0.432233i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1523.57 | 1.63298 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1365.93 | −1.46089 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.8602 | −0.0436075 | −0.0218037 | − | 0.999762i | \(-0.506941\pi\) | ||||
−0.0218037 | + | 0.999762i | \(0.506941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 540.607 | 0.575726 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1426.18 | −1.51560 | −0.757800 | − | 0.652487i | \(-0.773726\pi\) | ||||
−0.757800 | + | 0.652487i | \(0.773726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 473.725i | 0.502360i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 710.386i | 0.751731i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 328.560i | − | 0.346948i | −0.984838 | − | 0.173474i | \(-0.944501\pi\) | ||
0.984838 | − | 0.173474i | \(-0.0554992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1109.23 | 1.16884 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 126.202 | 0.132704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 133.225i | 0.139796i | 0.997554 | + | 0.0698979i | \(0.0222674\pi\) | ||||
−0.997554 | + | 0.0698979i | \(0.977733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 263.848i | − | 0.276280i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 767.005i | 0.801468i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 944.214 | 0.984582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −208.762 | −0.217234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −221.593 | −0.230107 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −676.279 | −0.700808 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1580.53 | −1.63447 | −0.817236 | − | 0.576303i | \(-0.804495\pi\) | ||||
−0.817236 | + | 0.576303i | \(0.804495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −814.007 | − | 1033.45i | −0.840049 | − | 1.06651i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 691.676 | 0.712333 | 0.356167 | − | 0.934422i | \(-0.384084\pi\) | ||||
0.356167 | + | 0.934422i | \(0.384084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 479.247i | − | 0.492546i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 130.642 | 0.133992 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 287.830i | 0.294606i | 0.989091 | + | 0.147303i | \(0.0470592\pi\) | ||||
−0.989091 | + | 0.147303i | \(0.952941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −754.923 | −0.771117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 75.1708 | 0.0766267 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1925.56i | − | 1.95886i | −0.201794 | − | 0.979428i | \(-0.564677\pi\) | ||
0.201794 | − | 0.979428i | \(-0.435323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −773.964 | −0.785750 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 589.664 | 0.597431 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.2160i | 0.0790860i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1310.31i | − | 1.32221i | −0.750292 | − | 0.661107i | \(-0.770087\pi\) | ||
0.750292 | − | 0.661107i | \(-0.229913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 554.389 | 0.558297 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 556.417i | − | 0.559213i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 911.840i | − | 0.914583i | −0.889317 | − | 0.457292i | \(-0.848820\pi\) | ||
0.889317 | − | 0.457292i | \(-0.151180\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2002.96 | 2.00496 |
(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 | 1216.3.g.e.417.31 | yes | 48 | |
4.3 | odd | 2 | inner | 1216.3.g.e.417.19 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.g.e.417.32 | yes | 48 | |
8.5 | even | 2 | inner | 1216.3.g.e.417.20 | yes | 48 | |
19.18 | odd | 2 | inner | 1216.3.g.e.417.17 | ✓ | 48 | |
76.75 | even | 2 | inner | 1216.3.g.e.417.29 | yes | 48 | |
152.37 | odd | 2 | inner | 1216.3.g.e.417.30 | yes | 48 | |
152.75 | even | 2 | inner | 1216.3.g.e.417.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.g.e.417.17 | ✓ | 48 | 19.18 | odd | 2 | inner | |
1216.3.g.e.417.18 | yes | 48 | 152.75 | even | 2 | inner | |
1216.3.g.e.417.19 | yes | 48 | 4.3 | odd | 2 | inner | |
1216.3.g.e.417.20 | yes | 48 | 8.5 | even | 2 | inner | |
1216.3.g.e.417.29 | yes | 48 | 76.75 | even | 2 | inner | |
1216.3.g.e.417.30 | yes | 48 | 152.37 | odd | 2 | inner | |
1216.3.g.e.417.31 | yes | 48 | 1.1 | even | 1 | trivial | |
1216.3.g.e.417.32 | yes | 48 | 8.3 | odd | 2 | inner |