Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(1711,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, 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("2736.1711");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 50 x^{10} - 136 x^{9} + 2215 x^{8} - 5020 x^{7} + 18282 x^{6} - 12094 x^{5} + 48457 x^{4} - 30372 x^{3} + 89392 x^{2} + 9344 x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1711.11 | ||
Root | \(-3.37682 + 5.84883i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1711 |
Dual form | 2736.3.m.f.1711.12 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.26675 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 9.51333i | − 1.35905i | −0.733654 | − | 0.679523i | \(-0.762187\pi\) | ||||
0.733654 | − | 0.679523i | \(-0.237813\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.9729i | 1.81572i | 0.419272 | + | 0.907861i | \(0.362286\pi\) | ||||
−0.419272 | + | 0.907861i | \(0.637714\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.11018 | 0.546937 | 0.273468 | − | 0.961881i | \(-0.411829\pi\) | ||||
0.273468 | + | 0.961881i | \(0.411829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.2396 | 1.13174 | 0.565870 | − | 0.824495i | \(-0.308540\pi\) | ||||
0.565870 | + | 0.824495i | \(0.308540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.6988i | 1.24778i | 0.781514 | + | 0.623888i | \(0.214448\pi\) | ||||
−0.781514 | + | 0.623888i | \(0.785552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 43.3391 | 1.73356 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.08981 | 0.209993 | 0.104997 | − | 0.994473i | \(-0.466517\pi\) | ||||
0.104997 | + | 0.994473i | \(0.466517\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.434440i | 0.0140142i | 0.999975 | + | 0.00700709i | \(0.00223044\pi\) | ||||
−0.999975 | + | 0.00700709i | \(0.997770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 78.6443i | − 2.24698i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56772 | 0.0964248 | 0.0482124 | − | 0.998837i | \(-0.484648\pi\) | ||||
0.0482124 | + | 0.998837i | \(0.484648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −52.7023 | −1.28542 | −0.642711 | − | 0.766108i | \(-0.722191\pi\) | ||||
−0.642711 | + | 0.766108i | \(0.722191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 67.7920i | 1.57656i | 0.615318 | + | 0.788279i | \(0.289028\pi\) | ||||
−0.615318 | + | 0.788279i | \(0.710972\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.7325i | 0.356011i | 0.984029 | + | 0.178006i | \(0.0569645\pi\) | ||||
−0.984029 | + | 0.178006i | \(0.943035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.5034 | −0.847008 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.2965 | 1.76031 | 0.880156 | − | 0.474685i | \(-0.157438\pi\) | ||||
0.880156 | + | 0.474685i | \(0.157438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 165.111i | 3.00202i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.1130i | 1.56124i | 0.625007 | + | 0.780619i | \(0.285096\pi\) | ||||
−0.625007 | + | 0.780619i | \(0.714904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −91.4439 | −1.49908 | −0.749540 | − | 0.661959i | \(-0.769725\pi\) | ||||
−0.749540 | + | 0.661959i | \(0.769725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.7780 | 0.904278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.1041i | 1.03140i | 0.856768 | + | 0.515702i | \(0.172469\pi\) | ||||
−0.856768 | + | 0.515702i | \(0.827531\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 111.081i | − 1.56452i | −0.622950 | − | 0.782262i | \(-0.714066\pi\) | ||||
0.622950 | − | 0.782262i | \(-0.285934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0069 | −0.150780 | −0.0753898 | − | 0.997154i | \(-0.524020\pi\) | ||||
−0.0753898 | + | 0.997154i | \(0.524020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 190.009 | 2.46765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.2810i | 0.509886i | 0.966956 | + | 0.254943i | \(0.0820566\pi\) | ||||
−0.966956 | + | 0.254943i | \(0.917943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 25.1933i | − 0.303534i | −0.988416 | − | 0.151767i | \(-0.951504\pi\) | ||||
0.988416 | − | 0.151767i | \(-0.0484963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 159.049 | 1.87116 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −156.317 | −1.75637 | −0.878183 | − | 0.478325i | \(-0.841244\pi\) | ||||
−0.878183 | + | 0.478325i | \(0.841244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 67.6414i | − 0.743313i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 36.0339i | 0.379304i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 177.845 | 1.83346 | 0.916729 | − | 0.399509i | \(-0.130819\pi\) | ||||
0.916729 | + | 0.399509i | \(0.130819\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 139.570 | 1.38188 | 0.690942 | − | 0.722910i | \(-0.257196\pi\) | ||||
0.690942 | + | 0.722910i | \(0.257196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 93.8246i | − 0.910918i | −0.890257 | − | 0.455459i | \(-0.849475\pi\) | ||||
0.890257 | − | 0.455459i | \(-0.150525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 62.9124i | − 0.587966i | −0.955811 | − | 0.293983i | \(-0.905019\pi\) | ||||
0.955811 | − | 0.293983i | \(-0.0949809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.14412 | −0.0747167 | −0.0373583 | − | 0.999302i | \(-0.511894\pi\) | ||||
−0.0373583 | + | 0.999302i | \(0.511894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −23.6334 | −0.209145 | −0.104573 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104573 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 237.246i | 2.06301i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 183.032i | − 1.53809i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −277.918 | −2.29685 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 151.605 | 1.21284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 38.4328i | 0.302620i | 0.988486 | + | 0.151310i | \(0.0483492\pi\) | ||||
−0.988486 | + | 0.151310i | \(0.951651\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 78.6785i | 0.600599i | 0.953845 | + | 0.300299i | \(0.0970866\pi\) | ||||
−0.953845 | + | 0.300299i | \(0.902913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.4676 | 0.311787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −147.488 | −1.07656 | −0.538278 | − | 0.842767i | \(-0.680925\pi\) | ||||
−0.538278 | + | 0.842767i | \(0.680925\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 7.30345i | − 0.0525428i | −0.999655 | − | 0.0262714i | \(-0.991637\pi\) | ||||
0.999655 | − | 0.0262714i | \(-0.00836341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 142.011i | 0.993085i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 50.3429 | 0.347192 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.67149 | 0.0112181 | 0.00560903 | − | 0.999984i | \(-0.498215\pi\) | ||||
0.00560903 | + | 0.999984i | \(0.498215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 286.836i | − 1.89957i | −0.312899 | − | 0.949786i | \(-0.601300\pi\) | ||||
0.312899 | − | 0.949786i | \(-0.398700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.59140i | 0.0231703i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 30.5840 | 0.194803 | 0.0974013 | − | 0.995245i | \(-0.468947\pi\) | ||||
0.0974013 | + | 0.995245i | \(0.468947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 273.021 | 1.69579 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 87.0132i | − 0.533823i | −0.963721 | − | 0.266912i | \(-0.913997\pi\) | ||||
0.963721 | − | 0.266912i | \(-0.0860032\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.3317i | 0.151687i | 0.997120 | + | 0.0758433i | \(0.0241649\pi\) | ||||
−0.997120 | + | 0.0758433i | \(0.975835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −118.445 | −0.700860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 47.0106 | 0.271738 | 0.135869 | − | 0.990727i | \(-0.456617\pi\) | ||||
0.135869 | + | 0.990727i | \(0.456617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 412.299i | − 2.35599i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5579i | 0.0869159i | 0.999055 | + | 0.0434579i | \(0.0138375\pi\) | ||||
−0.999055 | + | 0.0434579i | \(0.986163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 298.993 | 1.65189 | 0.825947 | − | 0.563748i | \(-0.190641\pi\) | ||||
0.825947 | + | 0.563748i | \(0.190641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.4934 | 0.159424 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 384.271i | 2.05492i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 317.098i | − 1.66020i | −0.557614 | − | 0.830100i | \(-0.688283\pi\) | ||||
0.557614 | − | 0.830100i | \(-0.311717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 176.434 | 0.914168 | 0.457084 | − | 0.889424i | \(-0.348894\pi\) | ||||
0.457084 | + | 0.889424i | \(0.348894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 173.653 | 0.881487 | 0.440743 | − | 0.897633i | \(-0.354715\pi\) | ||||
0.440743 | + | 0.897633i | \(0.354715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 167.157i | − 0.839984i | −0.907528 | − | 0.419992i | \(-0.862033\pi\) | ||||
0.907528 | − | 0.419992i | \(-0.137967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 57.9343i | − 0.285391i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −435.677 | −2.12525 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −87.0600 | −0.416555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 86.0298i | 0.407724i | 0.979000 | + | 0.203862i | \(0.0653494\pi\) | ||||
−0.979000 | + | 0.203862i | \(0.934651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 560.419i | 2.60660i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.13297 | 0.0190459 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 136.797 | 0.618990 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 321.231i | − 1.44050i | −0.693717 | − | 0.720248i | \(-0.744028\pi\) | ||||
0.693717 | − | 0.720248i | \(-0.255972\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 204.788i | − 0.902152i | −0.892486 | − | 0.451076i | \(-0.851040\pi\) | ||||
0.892486 | − | 0.451076i | \(-0.148960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 31.7066 | 0.138457 | 0.0692283 | − | 0.997601i | \(-0.477946\pi\) | ||||
0.0692283 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 351.865 | 1.51015 | 0.755074 | − | 0.655640i | \(-0.227601\pi\) | ||||
0.755074 | + | 0.655640i | \(0.227601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 138.324i | 0.588611i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 287.952i | 1.20482i | 0.798188 | + | 0.602409i | \(0.205792\pi\) | ||||
−0.798188 | + | 0.602409i | \(0.794208\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −341.159 | −1.41560 | −0.707799 | − | 0.706414i | \(-0.750312\pi\) | ||||
−0.707799 | + | 0.706414i | \(0.750312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −343.098 | −1.40040 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.9925i | 0.125476i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 83.6498i | 0.333266i | 0.986019 | + | 0.166633i | \(0.0532896\pi\) | ||||
−0.986019 | + | 0.166633i | \(0.946710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −573.200 | −2.26561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −256.627 | −0.998547 | −0.499274 | − | 0.866444i | \(-0.666400\pi\) | ||||
−0.499274 | + | 0.866444i | \(0.666400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 33.9408i | − 0.131046i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 35.0162i | − 0.133141i | −0.997782 | − | 0.0665707i | \(-0.978794\pi\) | ||||
0.997782 | − | 0.0665707i | \(-0.0212058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 771.259 | 2.91041 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 242.681 | 0.902161 | 0.451081 | − | 0.892483i | \(-0.351039\pi\) | ||||
0.451081 | + | 0.892483i | \(0.351039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 319.878i | 1.18036i | 0.807270 | + | 0.590182i | \(0.200944\pi\) | ||||
−0.807270 | + | 0.590182i | \(0.799056\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 865.609i | 3.14767i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −185.014 | −0.667921 | −0.333960 | − | 0.942587i | \(-0.608385\pi\) | ||||
−0.333960 | + | 0.942587i | \(0.608385\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 258.307 | 0.919243 | 0.459621 | − | 0.888115i | \(-0.347985\pi\) | ||||
0.459621 | + | 0.888115i | \(0.347985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 210.101i | − 0.742408i | −0.928551 | − | 0.371204i | \(-0.878945\pi\) | ||||
0.928551 | − | 0.371204i | \(-0.121055\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 501.375i | 1.74695i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 81.1612 | 0.280835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 327.177 | 1.11665 | 0.558323 | − | 0.829624i | \(-0.311445\pi\) | ||||
0.558323 | + | 0.829624i | \(0.311445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 761.475i | 2.58127i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 204.054i | 0.682454i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 644.927 | 2.14262 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −755.943 | −2.47850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 65.9862i | 0.214939i | 0.994208 | + | 0.107469i | \(0.0342748\pi\) | ||||
−0.994208 | + | 0.107469i | \(0.965725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 241.984i | 0.778084i | 0.921220 | + | 0.389042i | \(0.127194\pi\) | ||||
−0.921220 | + | 0.389042i | \(0.872806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 384.453 | 1.22828 | 0.614142 | − | 0.789195i | \(-0.289502\pi\) | ||||
0.614142 | + | 0.789195i | \(0.289502\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −524.546 | −1.65472 | −0.827359 | − | 0.561673i | \(-0.810158\pi\) | ||||
−0.827359 | + | 0.561673i | \(0.810158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 121.631i | 0.381289i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 83.8634i | 0.259639i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 308.149 | 0.948150 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 159.182 | 0.483836 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 286.540i | − 0.865681i | −0.901471 | − | 0.432840i | \(-0.857511\pi\) | ||||
0.901471 | − | 0.432840i | \(-0.142489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 571.266i | 1.70527i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 418.094 | 1.24063 | 0.620317 | − | 0.784351i | \(-0.287004\pi\) | ||||
0.620317 | + | 0.784351i | \(0.287004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.67703 | −0.0254458 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 71.3179i | − 0.207924i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 296.826i | 0.855407i | 0.903919 | + | 0.427703i | \(0.140677\pi\) | ||||
−0.903919 | + | 0.427703i | \(0.859323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 65.1648 | 0.186719 | 0.0933593 | − | 0.995632i | \(-0.470239\pi\) | ||||
0.0933593 | + | 0.995632i | \(0.470239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 334.322 | 0.947087 | 0.473544 | − | 0.880770i | \(-0.342975\pi\) | ||||
0.473544 | + | 0.880770i | \(0.342975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 918.280i | − 2.58670i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 100.554i | − 0.280094i | −0.990145 | − | 0.140047i | \(-0.955275\pi\) | ||||
0.990145 | − | 0.140047i | \(-0.0447253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −90.9914 | −0.249291 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 247.124i | 0.673362i | 0.941619 | + | 0.336681i | \(0.109304\pi\) | ||||
−0.941619 | + | 0.336681i | \(0.890696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 887.560i | − 2.39235i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 301.594 | 0.808563 | 0.404282 | − | 0.914635i | \(-0.367522\pi\) | ||||
0.404282 | + | 0.914635i | \(0.367522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.2996 | 0.114853 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0620i | 0.0450186i | 0.999747 | + | 0.0225093i | \(0.00716553\pi\) | ||||
−0.999747 | + | 0.0225093i | \(0.992834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 505.600i | − 1.32010i | −0.751220 | − | 0.660052i | \(-0.770534\pi\) | ||||
0.751220 | − | 0.660052i | \(-0.229466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1570.76 | 4.07989 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −62.8932 | −0.161679 | −0.0808396 | − | 0.996727i | \(-0.525760\pi\) | ||||
−0.0808396 | + | 0.996727i | \(0.525760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 552.153i | 1.41216i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 332.993i | 0.843019i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −179.718 | −0.452690 | −0.226345 | − | 0.974047i | \(-0.572678\pi\) | ||||
−0.226345 | + | 0.974047i | \(0.572678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 545.788 | 1.36107 | 0.680534 | − | 0.732716i | \(-0.261748\pi\) | ||||
0.680534 | + | 0.732716i | \(0.261748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.08894i | 0.00766487i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 71.2578i | 0.175081i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 437.863 | 1.07057 | 0.535285 | − | 0.844671i | \(-0.320204\pi\) | ||||
0.535285 | + | 0.844671i | \(0.320204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 876.301 | 2.12179 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 208.267i | − 0.501848i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 291.925i | 0.696719i | 0.937361 | + | 0.348359i | \(0.113261\pi\) | ||||
−0.937361 | + | 0.348359i | \(0.886739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −372.544 | −0.884902 | −0.442451 | − | 0.896793i | \(-0.645891\pi\) | ||||
−0.442451 | + | 0.896793i | \(0.645891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 833.826 | 1.96194 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 869.935i | 2.03732i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 13.6862i | − 0.0317546i | −0.999874 | − | 0.0158773i | \(-0.994946\pi\) | ||||
0.999874 | − | 0.0158773i | \(-0.00505411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −830.034 | −1.91694 | −0.958469 | − | 0.285197i | \(-0.907941\pi\) | ||||
−0.958469 | + | 0.285197i | \(0.907941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −125.095 | −0.286259 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 753.055i | − 1.71539i | −0.514161 | − | 0.857694i | \(-0.671897\pi\) | ||||
0.514161 | − | 0.857694i | \(-0.328103\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 320.555i | − 0.723600i | −0.932256 | − | 0.361800i | \(-0.882162\pi\) | ||||
0.932256 | − | 0.361800i | \(-0.117838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1292.23 | −2.90389 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 602.223 | 1.34125 | 0.670627 | − | 0.741795i | \(-0.266025\pi\) | ||||
0.670627 | + | 0.741795i | \(0.266025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1052.62i | − 2.33397i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 559.175i | − 1.22896i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −450.930 | −0.986719 | −0.493359 | − | 0.869826i | \(-0.664231\pi\) | ||||
−0.493359 | + | 0.869826i | \(0.664231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −83.5485 | −0.181233 | −0.0906166 | − | 0.995886i | \(-0.528884\pi\) | ||||
−0.0906166 | + | 0.995886i | \(0.528884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 167.556i | 0.361893i | 0.983493 | + | 0.180946i | \(0.0579161\pi\) | ||||
−0.983493 | + | 0.180946i | \(0.942084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 448.878i | 0.961196i | 0.876941 | + | 0.480598i | \(0.159580\pi\) | ||||
−0.876941 | + | 0.480598i | \(0.840420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 657.410 | 1.40173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1354.01 | −2.86259 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 188.911i | 0.397707i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 269.049i | − 0.561690i | −0.959753 | − | 0.280845i | \(-0.909385\pi\) | ||||
0.959753 | − | 0.280845i | \(-0.0906146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.3671 | 0.0527383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1470.20 | 3.03135 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 398.113i | 0.817481i | 0.912651 | + | 0.408741i | \(0.134032\pi\) | ||||
−0.912651 | + | 0.408741i | \(0.865968\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 638.967i | − 1.30136i | −0.759353 | − | 0.650679i | \(-0.774484\pi\) | ||||
0.759353 | − | 0.650679i | \(-0.225516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 117.165 | 0.237658 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1056.75 | −2.12626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 289.639i | − 0.580439i | −0.956960 | − | 0.290220i | \(-0.906272\pi\) | ||||
0.956960 | − | 0.290220i | \(-0.0937283\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 635.303i | − 1.26303i | −0.775365 | − | 0.631514i | \(-0.782434\pi\) | ||||
0.775365 | − | 0.631514i | \(-0.217566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1153.79 | 2.28474 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 547.921 | 1.07647 | 0.538233 | − | 0.842796i | \(-0.319092\pi\) | ||||
0.538233 | + | 0.842796i | \(0.319092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 104.712i | 0.204917i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 775.624i | − 1.50607i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −334.198 | −0.646417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −127.108 | −0.243969 | −0.121985 | − | 0.992532i | \(-0.538926\pi\) | ||||
−0.121985 | + | 0.992532i | \(0.538926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 431.535i | 0.825115i | 0.910932 | + | 0.412557i | \(0.135364\pi\) | ||||
−0.910932 | + | 0.412557i | \(0.864636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.35843i | 0.0158604i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −294.623 | −0.556944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −374.723 | −0.703045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 520.081i | − 0.972113i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 828.944i | − 1.53793i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −999.802 | −1.84806 | −0.924032 | − | 0.382316i | \(-0.875127\pi\) | ||||
−0.924032 | + | 0.382316i | \(0.875127\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −67.3254 | −0.123533 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 236.004i | 0.431451i | 0.976454 | + | 0.215726i | \(0.0692117\pi\) | ||||
−0.976454 | + | 0.215726i | \(0.930788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.5449i | 0.0481758i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 383.206 | 0.692958 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 866.326 | 1.55534 | 0.777671 | − | 0.628671i | \(-0.216401\pi\) | ||||
0.777671 | + | 0.628671i | \(0.216401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 482.013i | 0.862278i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 587.885i | − 1.04420i | −0.852884 | − | 0.522101i | \(-0.825149\pi\) | ||||
0.852884 | − | 0.522101i | \(-0.174851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −195.371 | −0.345790 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −191.363 | −0.336314 | −0.168157 | − | 0.985760i | \(-0.553782\pi\) | ||||
−0.168157 | + | 0.985760i | \(0.553782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 287.222i | − 0.503016i | −0.967855 | − | 0.251508i | \(-0.919073\pi\) | ||||
0.967855 | − | 0.251508i | \(-0.0809266\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1243.78i | 2.16310i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −443.562 | −0.768738 | −0.384369 | − | 0.923180i | \(-0.625581\pi\) | ||||
−0.384369 | + | 0.923180i | \(0.625581\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −239.672 | −0.412517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1863.41i | 3.19624i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 514.692i | − 0.876817i | −0.898776 | − | 0.438408i | \(-0.855542\pi\) | ||||
0.898776 | − | 0.438408i | \(-0.144458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.89368 | −0.00321507 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −227.211 | −0.383156 | −0.191578 | − | 0.981477i | \(-0.561360\pi\) | ||||
−0.191578 | + | 0.981477i | \(0.561360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1513.08i | − 2.54300i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 805.147i | 1.34415i | 0.740482 | + | 0.672076i | \(0.234597\pi\) | ||||
−0.740482 | + | 0.672076i | \(0.765403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1110.23 | −1.84730 | −0.923649 | − | 0.383238i | \(-0.874809\pi\) | ||||
−0.923649 | + | 0.383238i | \(0.874809\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2297.48 | −3.79749 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 293.733i | 0.483909i | 0.970288 | + | 0.241955i | \(0.0777886\pi\) | ||||
−0.970288 | + | 0.241955i | \(0.922211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 118.971i | 0.194716i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 702.779 | 1.14646 | 0.573230 | − | 0.819395i | \(-0.305690\pi\) | ||||
0.573230 | + | 0.819395i | \(0.305690\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 823.243 | 1.33427 | 0.667134 | − | 0.744938i | \(-0.267521\pi\) | ||||
0.667134 | + | 0.744938i | \(0.267521\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 400.632i | 0.647225i | 0.946190 | + | 0.323612i | \(0.104897\pi\) | ||||
−0.946190 | + | 0.323612i | \(0.895103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1487.09i | 2.38698i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 169.800 | 0.271680 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 68.6413 | 0.109128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 354.013i | − 0.561034i | −0.959849 | − | 0.280517i | \(-0.909494\pi\) | ||||
0.959849 | − | 0.280517i | \(-0.0905059\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 317.714i | 0.500337i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −295.096 | −0.463260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −577.597 | −0.901088 | −0.450544 | − | 0.892754i | \(-0.648770\pi\) | ||||
−0.450544 | + | 0.892754i | \(0.648770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 791.746i | 1.23133i | 0.788007 | + | 0.615666i | \(0.211113\pi\) | ||||
−0.788007 | + | 0.615666i | \(0.788887\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1047.43i | 1.61890i | 0.587192 | + | 0.809448i | \(0.300234\pi\) | ||||
−0.587192 | + | 0.809448i | \(0.699766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1839.77 | −2.83477 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −815.274 | −1.24851 | −0.624253 | − | 0.781222i | \(-0.714596\pi\) | ||||
−0.624253 | + | 0.781222i | \(0.714596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 650.415i | 0.993000i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 238.992i | − 0.362659i | −0.983422 | − | 0.181330i | \(-0.941960\pi\) | ||||
0.983422 | − | 0.181330i | \(-0.0580401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −542.358 | −0.820511 | −0.410256 | − | 0.911971i | \(-0.634561\pi\) | ||||
−0.410256 | + | 0.911971i | \(0.634561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 342.802 | 0.515492 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 174.770i | 0.262025i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1826.40i | − 2.72191i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 468.193 | 0.695681 | 0.347840 | − | 0.937554i | \(-0.386915\pi\) | ||||
0.347840 | + | 0.937554i | \(0.386915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −771.400 | −1.13944 | −0.569719 | − | 0.821839i | \(-0.692948\pi\) | ||||
−0.569719 | + | 0.821839i | \(0.692948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1691.90i | − 2.49176i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 821.359i | − 1.20258i | −0.799033 | − | 0.601288i | \(-0.794655\pi\) | ||||
0.799033 | − | 0.601288i | \(-0.205345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1219.25 | −1.77992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 663.355 | 0.962779 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 971.147i | − 1.40542i | −0.711475 | − | 0.702711i | \(-0.751972\pi\) | ||||
0.711475 | − | 0.702711i | \(-0.248028\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 60.3758i | − 0.0868716i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1013.97 | −1.45476 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 128.066 | 0.182691 | 0.0913453 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913453 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5513i | 0.0221214i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1327.78i | − 1.87804i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.7470 | −0.0631128 | −0.0315564 | − | 0.999502i | \(-0.510046\pi\) | ||||
−0.0315564 | + | 0.999502i | \(0.510046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.4679 | −0.0174866 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1173.97i | 1.64192i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 298.311i | − 0.414897i | −0.978246 | − | 0.207448i | \(-0.933484\pi\) | ||||
0.978246 | − | 0.207448i | \(-0.0665159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −892.584 | −1.23798 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 263.927 | 0.364037 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1306.36i | − 1.79692i | −0.439052 | − | 0.898461i | \(-0.644686\pi\) | ||||
0.439052 | − | 0.898461i | \(-0.355314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1304.29i | 1.78425i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −480.550 | −0.655593 | −0.327796 | − | 0.944748i | \(-0.606306\pi\) | ||||
−0.327796 | + | 0.944748i | \(0.606306\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1380.21 | −1.87274 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 748.985i | 1.01351i | 0.862090 | + | 0.506756i | \(0.169155\pi\) | ||||
−0.862090 | + | 0.506756i | \(0.830845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 397.466i | − 0.534948i | −0.963565 | − | 0.267474i | \(-0.913811\pi\) | ||||
0.963565 | − | 0.267474i | \(-0.0861890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8178 | 0.0185474 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −598.506 | −0.799073 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1287.95i | 1.71498i | 0.514504 | + | 0.857488i | \(0.327976\pi\) | ||||
−0.514504 | + | 0.857488i | \(0.672024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2371.20i | − 3.14066i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −812.408 | −1.07319 | −0.536597 | − | 0.843838i | \(-0.680291\pi\) | ||||
−0.536597 | + | 0.843838i | \(0.680291\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 680.285 | 0.893935 | 0.446968 | − | 0.894550i | \(-0.352504\pi\) | ||||
0.446968 | + | 0.894550i | \(0.352504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.4776i | 0.101543i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 654.940i | 0.853898i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −61.3875 | −0.0798277 | −0.0399139 | − | 0.999203i | \(-0.512708\pi\) | ||||
−0.0399139 | + | 0.999203i | \(0.512708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −597.488 | −0.772947 | −0.386473 | − | 0.922301i | \(-0.626307\pi\) | ||||
−0.386473 | + | 0.922301i | \(0.626307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.8282i | 0.0242945i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 229.724i | − 0.294896i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2218.62 | 2.84074 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 252.830 | 0.322077 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1493.71i | − 1.89798i | −0.315313 | − | 0.948988i | \(-0.602109\pi\) | ||||
0.315313 | − | 0.948988i | \(-0.397891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.832i | 0.284238i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −650.182 | −0.819902 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 95.1729 | 0.119414 | 0.0597070 | − | 0.998216i | \(-0.480983\pi\) | ||||
0.0597070 | + | 0.998216i | \(0.480983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 321.927i | 0.402912i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 219.840i | − 0.273774i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2257.00 | 2.80373 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −916.775 | −1.13322 | −0.566610 | − | 0.823986i | \(-0.691745\pi\) | ||||
−0.566610 | + | 0.823986i | \(0.691745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 577.775i | − 0.712423i | −0.934405 | − | 0.356211i | \(-0.884068\pi\) | ||||
0.934405 | − | 0.356211i | \(-0.115932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 719.316i | − 0.882596i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −295.498 | −0.361687 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 854.788 | 1.04115 | 0.520577 | − | 0.853815i | \(-0.325717\pi\) | ||||
0.520577 | + | 0.853815i | \(0.325717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 963.867i | 1.17116i | 0.810614 | + | 0.585581i | \(0.199134\pi\) | ||||
−0.810614 | + | 0.585581i | \(0.800866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 476.984i | 0.576764i | 0.957515 | + | 0.288382i | \(0.0931172\pi\) | ||||
−0.957515 | + | 0.288382i | \(0.906883\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.7605 | −0.0371055 | −0.0185528 | − | 0.999828i | \(-0.505906\pi\) | ||||
−0.0185528 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −798.507 | −0.958592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 209.411i | 0.250791i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 811.970i | 0.967783i | 0.875128 | + | 0.483892i | \(0.160777\pi\) | ||||
−0.875128 | + | 0.483892i | \(0.839223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −803.914 | −0.955903 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −979.158 | −1.15877 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2643.93i | 3.12152i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 102.389i | 0.120316i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 122.095 | 0.143136 | 0.0715682 | − | 0.997436i | \(-0.477200\pi\) | ||||
0.0715682 | + | 0.997436i | \(0.477200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −577.474 | −0.673832 | −0.336916 | − | 0.941535i | \(-0.609384\pi\) | ||||
−0.336916 | + | 0.941535i | \(0.609384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1651.98i | − 1.92314i | −0.274556 | − | 0.961571i | \(-0.588531\pi\) | ||||
0.274556 | − | 0.961571i | \(-0.411469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 479.262i | − 0.555344i | −0.960676 | − | 0.277672i | \(-0.910437\pi\) | ||||
0.960676 | − | 0.277672i | \(-0.0895629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 388.625 | 0.449277 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −804.529 | −0.925810 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 491.342i | 0.564113i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1442.27i | − 1.64830i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 634.569 | 0.723568 | 0.361784 | − | 0.932262i | \(-0.382168\pi\) | ||||
0.361784 | + | 0.932262i | \(0.382168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1027.14 | −1.16588 | −0.582939 | − | 0.812516i | \(-0.698097\pi\) | ||||
−0.582939 | + | 0.812516i | \(0.698097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 539.788i | − 0.611312i | −0.952142 | − | 0.305656i | \(-0.901124\pi\) | ||||
0.952142 | − | 0.305656i | \(-0.0988757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 707.980i | − 0.798174i | −0.916913 | − | 0.399087i | \(-0.869327\pi\) | ||||
0.916913 | − | 0.399087i | \(-0.130673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 365.624 | 0.411275 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −72.9354 | −0.0816746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 128.614i | 0.143702i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.64565i | 0.00294288i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1794.99 | 1.99221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2471.70 | 2.73116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 683.854i | 0.753974i | 0.926219 | + | 0.376987i | \(0.123040\pi\) | ||||
−0.926219 | + | 0.376987i | \(0.876960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 912.906i | − 1.00209i | −0.865421 | − | 0.501046i | \(-0.832949\pi\) | ||||
0.865421 | − | 0.501046i | \(-0.167051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 503.185 | 0.551133 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 748.494 | 0.816242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1549.13i | − 1.68567i | −0.538175 | − | 0.842833i | \(-0.680886\pi\) | ||||
0.538175 | − | 0.842833i | \(-0.319114\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 789.807i | − 0.855695i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 154.622 | 0.167159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1359.01 | −1.46287 | −0.731436 | − | 0.681910i | \(-0.761150\pi\) | ||||
−0.731436 | + | 0.681910i | \(0.761150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 180.909i | − 0.194317i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3176.67i | 3.39751i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1426.90 | −1.52284 | −0.761420 | − | 0.648259i | \(-0.775497\pi\) | ||||
−0.761420 | + | 0.648259i | \(0.775497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 922.895 | 0.980759 | 0.490380 | − | 0.871509i | \(-0.336858\pi\) | ||||
0.490380 | + | 0.871509i | \(0.336858\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1512.50i | − 1.60392i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 416.165i | 0.439456i | 0.975561 | + | 0.219728i | \(0.0705170\pi\) | ||||
−0.975561 | + | 0.219728i | \(0.929483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −78.2611 | −0.0824669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1181.47 | 1.23974 | 0.619870 | − | 0.784705i | \(-0.287185\pi\) | ||||
0.619870 | + | 0.784705i | \(0.287185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2621.37i | − 2.74489i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1403.10i | 1.46309i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.811 | 0.999804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1458.54 | 1.51144 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 913.101i | 0.944262i | 0.881528 | + | 0.472131i | \(0.156515\pi\) | ||||
−0.881528 | + | 0.472131i | \(0.843485\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 877.256i | − 0.903456i | −0.892156 | − | 0.451728i | \(-0.850808\pi\) | ||||
0.892156 | − | 0.451728i | \(-0.149192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.4801 | −0.0714081 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 745.908 | 0.763467 | 0.381734 | − | 0.924272i | \(-0.375327\pi\) | ||||
0.381734 | + | 0.924272i | \(0.375327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3122.10i | − 3.18907i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 51.0071i | − 0.0518893i | −0.999663 | − | 0.0259446i | \(-0.991741\pi\) | ||||
0.999663 | − | 0.0259446i | \(-0.00825936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1435.54 | 1.45741 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1945.55 | −1.96719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 87.7408i | − 0.0885376i | −0.999020 | − | 0.0442688i | \(-0.985904\pi\) | ||||
0.999020 | − | 0.0442688i | \(-0.0140958\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1381.84i | − 1.38879i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 562.992 | 0.564686 | 0.282343 | − | 0.959314i | \(-0.408888\pi\) | ||||
0.282343 | + | 0.959314i | \(0.408888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.3.m.f.1711.11 | 12 | ||
3.2 | odd | 2 | 912.3.m.a.799.1 | ✓ | 12 | ||
4.3 | odd | 2 | inner | 2736.3.m.f.1711.12 | 12 | ||
12.11 | even | 2 | 912.3.m.a.799.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.3.m.a.799.1 | ✓ | 12 | 3.2 | odd | 2 | ||
912.3.m.a.799.7 | yes | 12 | 12.11 | even | 2 | ||
2736.3.m.f.1711.11 | 12 | 1.1 | even | 1 | trivial | ||
2736.3.m.f.1711.12 | 12 | 4.3 | odd | 2 | inner |