Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1444,3,Mod(721,1444)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1444.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1444 = 2^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1444.c (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: | \(39.3461501736\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.6 | ||
Character | \(\chi\) | \(=\) | 1444.721 |
Dual form | 1444.3.c.d.721.19 |
$q$-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 \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).
\(n\) | \(723\) | \(1085\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.56718i | − 1.18906i | −0.804074 | − | 0.594529i | \(-0.797338\pi\) | ||||
0.804074 | − | 0.594529i | \(-0.202662\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.91277 | −0.582553 | −0.291277 | − | 0.956639i | \(-0.594080\pi\) | ||||
−0.291277 | + | 0.956639i | \(0.594080\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.95359 | −0.421941 | −0.210971 | − | 0.977492i | \(-0.567662\pi\) | ||||
−0.210971 | + | 0.977492i | \(0.567662\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.72474 | −0.413860 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.8845 | −1.98950 | −0.994751 | − | 0.102323i | \(-0.967373\pi\) | ||||
−0.994751 | + | 0.102323i | \(0.967373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0774i | 0.775182i | 0.921831 | + | 0.387591i | \(0.126693\pi\) | ||||
−0.921831 | + | 0.387591i | \(0.873307\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.3903i | 0.692690i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.21959 | 0.483505 | 0.241753 | − | 0.970338i | \(-0.422278\pi\) | ||||
0.241753 | + | 0.970338i | \(0.422278\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.5360i | 0.501713i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.5196 | 0.544330 | 0.272165 | − | 0.962251i | \(-0.412260\pi\) | ||||
0.272165 | + | 0.962251i | \(0.412260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.5158 | −0.660632 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 18.8178i | − 0.696955i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 21.5020i | − 0.741449i | −0.928743 | − | 0.370725i | \(-0.879109\pi\) | ||||
0.928743 | − | 0.370725i | \(-0.120891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.3632i | 1.33430i | 0.744926 | + | 0.667148i | \(0.232485\pi\) | ||||
−0.744926 | + | 0.667148i | \(0.767515\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0660i | 2.36563i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.60312 | 0.245803 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 32.6932i | − 0.883601i | −0.897113 | − | 0.441800i | \(-0.854340\pi\) | ||||
0.897113 | − | 0.441800i | \(-0.145660\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 35.9477 | 0.921737 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.4085i | 1.18070i | 0.807149 | + | 0.590348i | \(0.201009\pi\) | ||||
−0.807149 | + | 0.590348i | \(0.798991\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.2505 | 1.14536 | 0.572680 | − | 0.819779i | \(-0.305904\pi\) | ||||
0.572680 | + | 0.819779i | \(0.305904\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.8493 | 0.241096 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 74.2654 | 1.58012 | 0.790058 | − | 0.613033i | \(-0.210051\pi\) | ||||
0.790058 | + | 0.613033i | \(0.210051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40.2763 | −0.821965 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 29.3207i | − 0.574916i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 31.2444i | 0.589517i | 0.955572 | + | 0.294759i | \(0.0952393\pi\) | ||||
−0.955572 | + | 0.294759i | \(0.904761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.7445 | 1.15899 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.0781i | 0.916578i | 0.888803 | + | 0.458289i | \(0.151537\pi\) | ||||
−0.888803 | + | 0.458289i | \(0.848463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 105.977 | 1.73733 | 0.868666 | − | 0.495398i | \(-0.164978\pi\) | ||||
0.868666 | + | 0.495398i | \(0.164978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.0014 | 0.174625 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 29.3530i | − 0.451585i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 101.564i | − 1.51589i | −0.652320 | − | 0.757944i | \(-0.726204\pi\) | ||||
0.652320 | − | 0.757944i | \(-0.273796\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 44.6596i | − 0.647241i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61.8458i | 0.871067i | 0.900172 | + | 0.435534i | \(0.143440\pi\) | ||||
−0.900172 | + | 0.435534i | \(0.856560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26.3088 | 0.360395 | 0.180198 | − | 0.983630i | \(-0.442326\pi\) | ||||
0.180198 | + | 0.983630i | \(0.442326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 58.9147i | 0.785530i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 64.6379 | 0.839453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 144.433i | − 1.82827i | −0.405413 | − | 0.914134i | \(-0.632872\pi\) | ||||
0.405413 | − | 0.914134i | \(-0.367128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.649 | −1.24258 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.17164 | 0.0261643 | 0.0130821 | − | 0.999914i | \(-0.495836\pi\) | ||||
0.0130821 | + | 0.999914i | \(0.495836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.9417 | −0.281668 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −76.7015 | −0.881626 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19.7114i | 0.221477i | 0.993850 | + | 0.110738i | \(0.0353216\pi\) | ||||
−0.993850 | + | 0.110738i | \(0.964678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 29.7644i | − 0.327081i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 147.550 | 1.58656 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110.583i | 1.14003i | 0.821635 | + | 0.570014i | \(0.193062\pi\) | ||||
−0.821635 | + | 0.570014i | \(0.806938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 81.5142 | 0.823376 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −93.9678 | −0.930374 | −0.465187 | − | 0.885212i | \(-0.654013\pi\) | ||||
−0.465187 | + | 0.885212i | \(0.654013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 103.900i | 1.00874i | 0.863487 | + | 0.504371i | \(0.168276\pi\) | ||||
−0.863487 | + | 0.504371i | \(0.831724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − 30.6888i | − 0.292275i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 183.795i | − 1.71771i | −0.512216 | − | 0.858856i | \(-0.671175\pi\) | ||||
0.512216 | − | 0.858856i | \(-0.328825\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.6611i | 0.428083i | 0.976825 | + | 0.214042i | \(0.0686628\pi\) | ||||
−0.976825 | + | 0.214042i | \(0.931337\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −116.623 | −1.05065 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186.762i | 1.65276i | 0.563110 | + | 0.826382i | \(0.309605\pi\) | ||||
−0.563110 | + | 0.826382i | \(0.690395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.4667 | −0.317101 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 37.5356i | − 0.320817i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.2773 | −0.204011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 357.933 | 2.95812 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 172.682 | 1.40392 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 120.926 | 0.967406 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 84.8853i | − 0.668388i | −0.942504 | − | 0.334194i | \(-0.891536\pi\) | ||||
0.942504 | − | 0.334194i | \(-0.108464\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 175.685i | − 1.36190i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 34.2072 | 0.261124 | 0.130562 | − | 0.991440i | \(-0.458322\pi\) | ||||
0.130562 | + | 0.991440i | \(0.458322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 54.8118i | 0.406013i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −42.7457 | −0.312012 | −0.156006 | − | 0.987756i | \(-0.549862\pi\) | ||||
−0.156006 | + | 0.987756i | \(0.549862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 69.4802 | 0.499858 | 0.249929 | − | 0.968264i | \(-0.419593\pi\) | ||||
0.249929 | + | 0.968264i | \(0.419593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 264.918i | − 1.87885i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 220.538i | − 1.54223i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 62.6304i | 0.431934i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 143.673i | 0.977365i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −244.901 | −1.64363 | −0.821814 | − | 0.569755i | \(-0.807038\pi\) | ||||
−0.821814 | + | 0.569755i | \(0.807038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 41.9634i | − 0.277904i | −0.990299 | − | 0.138952i | \(-0.955627\pi\) | ||||
0.990299 | − | 0.138952i | \(-0.0443733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −30.6158 | −0.200104 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 120.481i | − 0.777298i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 179.430 | 1.14286 | 0.571432 | − | 0.820649i | \(-0.306388\pi\) | ||||
0.571432 | + | 0.820649i | \(0.306388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 111.454 | 0.700971 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −36.9778 | −0.229676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 242.887 | 1.49011 | 0.745053 | − | 0.667005i | \(-0.232424\pi\) | ||||
0.745053 | + | 0.667005i | \(0.232424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 227.388i | − 1.37811i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 80.3087i | − 0.480891i | −0.970663 | − | 0.240445i | \(-0.922707\pi\) | ||||
0.970663 | − | 0.240445i | \(-0.0772935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 67.4467 | 0.399093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 138.007i | 0.797730i | 0.917010 | + | 0.398865i | \(0.130596\pi\) | ||||
−0.917010 | + | 0.398865i | \(0.869404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 48.7809 | 0.278748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 192.906 | 1.08986 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66.7312i | 0.372800i | 0.982474 | + | 0.186400i | \(0.0596821\pi\) | ||||
−0.982474 | + | 0.186400i | \(0.940318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 189.905i | 1.04920i | 0.851349 | + | 0.524600i | \(0.175785\pi\) | ||||
−0.851349 | + | 0.524600i | \(0.824215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 378.040i | − 2.06579i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 95.2277i | 0.514745i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −179.882 | −0.961935 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 55.5800i | 0.294074i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −96.8587 | −0.507113 | −0.253557 | − | 0.967321i | \(-0.581600\pi\) | ||||
−0.253557 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 41.6748i | − 0.215931i | −0.994155 | − | 0.107966i | \(-0.965566\pi\) | ||||
0.994155 | − | 0.107966i | \(-0.0344337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −104.707 | −0.536961 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 269.420 | 1.36761 | 0.683807 | − | 0.729663i | \(-0.260323\pi\) | ||||
0.683807 | + | 0.729663i | \(0.260323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 95.7815 | 0.481314 | 0.240657 | − | 0.970610i | \(-0.422637\pi\) | ||||
0.240657 | + | 0.970610i | \(0.422637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −362.298 | −1.80248 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 63.5082i | 0.312848i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 141.003i | − 0.687818i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −46.6323 | −0.225277 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 229.049i | 1.08554i | 0.839881 | + | 0.542770i | \(0.182624\pi\) | ||||
−0.839881 | + | 0.542770i | \(0.817376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 220.615 | 1.03575 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −143.455 | −0.667233 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 122.170i | − 0.562994i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 93.8482i | − 0.428531i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 82.8318i | 0.374805i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 217.766i | − 0.976529i | −0.872696 | − | 0.488264i | \(-0.837630\pi\) | ||||
0.872696 | − | 0.488264i | \(-0.162370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 61.5171 | 0.273409 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 48.9342i | − 0.215569i | −0.994174 | − | 0.107785i | \(-0.965624\pi\) | ||||
0.994174 | − | 0.107785i | \(-0.0343757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 314.156 | 1.37186 | 0.685930 | − | 0.727667i | \(-0.259395\pi\) | ||||
0.685930 | + | 0.727667i | \(0.259395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 230.575i | − 0.998159i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −279.711 | −1.20048 | −0.600238 | − | 0.799822i | \(-0.704927\pi\) | ||||
−0.600238 | + | 0.799822i | \(0.704927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −216.318 | −0.920501 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −515.218 | −2.17392 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.573252 | −0.00239854 | −0.00119927 | − | 0.999999i | \(-0.500382\pi\) | ||||
−0.00119927 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 288.744i | 1.19811i | 0.800709 | + | 0.599054i | \(0.204457\pi\) | ||||
−0.800709 | + | 0.599054i | \(0.795543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 189.673i | 0.780546i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 117.315 | 0.478839 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 7.74661i | − 0.0311109i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −58.3244 | −0.232368 | −0.116184 | − | 0.993228i | \(-0.537066\pi\) | ||||
−0.116184 | + | 0.993228i | \(0.537066\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −273.986 | −1.08295 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 85.4044i | 0.334919i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 6.31597i | − 0.0245757i | −0.999925 | − | 0.0122879i | \(-0.996089\pi\) | ||||
0.999925 | − | 0.0122879i | \(-0.00391145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96.5624i | 0.372828i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 80.0895i | 0.306856i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 375.469 | 1.42764 | 0.713820 | − | 0.700329i | \(-0.246963\pi\) | ||||
0.713820 | + | 0.700329i | \(0.246963\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 91.0077i | − 0.343425i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 70.3141 | 0.263349 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 288.521i | 1.07257i | 0.844038 | + | 0.536284i | \(0.180172\pi\) | ||||
−0.844038 | + | 0.536284i | \(0.819828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 63.0550 | 0.232675 | 0.116338 | − | 0.993210i | \(-0.462885\pi\) | ||||
0.116338 | + | 0.993210i | \(0.462885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −106.175 | −0.388919 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 361.440 | 1.31433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −117.696 | −0.424896 | −0.212448 | − | 0.977172i | \(-0.568144\pi\) | ||||
−0.212448 | + | 0.977172i | \(0.568144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 154.067i | − 0.552212i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 34.4275i | − 0.122518i | −0.998122 | − | 0.0612589i | \(-0.980488\pi\) | ||||
0.998122 | − | 0.0612589i | \(-0.0195115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 281.782 | 0.995696 | 0.497848 | − | 0.867264i | \(-0.334124\pi\) | ||||
0.497848 | + | 0.867264i | \(0.334124\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 142.979i | − 0.498184i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −221.438 | −0.766223 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 394.468 | 1.35556 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 309.955i | 1.05787i | 0.848663 | + | 0.528934i | \(0.177408\pi\) | ||||
−0.848663 | + | 0.528934i | \(0.822592\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 157.517i | − 0.533955i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 411.818i | 1.38659i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 126.165i | 0.421955i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −145.466 | −0.483275 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 335.200i | 1.10627i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −308.687 | −1.01209 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 414.620i | 1.35055i | 0.737564 | + | 0.675277i | \(0.235976\pi\) | ||||
−0.737564 | + | 0.675277i | \(0.764024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 370.631 | 1.19945 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −387.400 | −1.24566 | −0.622830 | − | 0.782357i | \(-0.714017\pi\) | ||||
−0.622830 | + | 0.782357i | \(0.714017\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 368.585 | 1.17759 | 0.588794 | − | 0.808283i | \(-0.299603\pi\) | ||||
0.588794 | + | 0.808283i | \(0.299603\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −32.0444 | −0.101728 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 213.580i | 0.673755i | 0.941549 | + | 0.336877i | \(0.109371\pi\) | ||||
−0.941549 | + | 0.336877i | \(0.890629\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 470.562i | 1.47511i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −655.630 | −2.04246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 166.436i | − 0.512110i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 166.448 | 0.509016 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −219.350 | −0.666716 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 231.565i | − 0.699592i | −0.936826 | − | 0.349796i | \(-0.886251\pi\) | ||||
0.936826 | − | 0.349796i | \(-0.113749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 121.774i | 0.365687i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 295.833i | 0.883085i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 308.471i | 0.915344i | 0.889121 | + | 0.457672i | \(0.151317\pi\) | ||||
−0.889121 | + | 0.457672i | \(0.848683\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 666.214 | 1.96523 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 905.213i | − 2.65458i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 263.686 | 0.768763 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 130.083i | 0.377052i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 270.251 | 0.778821 | 0.389411 | − | 0.921064i | \(-0.372679\pi\) | ||||
0.389411 | + | 0.921064i | \(0.372679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −515.867 | −1.47813 | −0.739065 | − | 0.673634i | \(-0.764732\pi\) | ||||
−0.739065 | + | 0.673634i | \(0.764732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 189.634 | 0.540267 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 196.162 | 0.555699 | 0.277850 | − | 0.960625i | \(-0.410378\pi\) | ||||
0.277850 | + | 0.960625i | \(0.410378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 180.142i | − 0.507443i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 86.6014i | 0.242581i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.8616 | −0.0720378 | −0.0360189 | − | 0.999351i | \(-0.511468\pi\) | ||||
−0.0360189 | + | 0.999351i | \(0.511468\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1276.81i | − 3.51738i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −76.6315 | −0.209949 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −198.474 | −0.540801 | −0.270401 | − | 0.962748i | \(-0.587156\pi\) | ||||
−0.270401 | + | 0.962748i | \(0.587156\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 180.309i | − 0.488643i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 92.2832i | − 0.248742i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 41.2092i | − 0.110480i | −0.998473 | − | 0.0552402i | \(-0.982408\pi\) | ||||
0.998473 | − | 0.0552402i | \(-0.0175925\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 431.364i | − 1.15030i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 216.684 | 0.574758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 419.992i | 1.10816i | 0.832464 | + | 0.554079i | \(0.186929\pi\) | ||||
−0.832464 | + | 0.554079i | \(0.813071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −302.801 | −0.794753 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 7.84945i | − 0.0204947i | −0.999947 | − | 0.0102473i | \(-0.996738\pi\) | ||||
0.999947 | − | 0.0102473i | \(-0.00326188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −188.275 | −0.489026 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −183.445 | −0.474019 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −645.273 | −1.65880 | −0.829400 | − | 0.558656i | \(-0.811317\pi\) | ||||
−0.829400 | + | 0.558656i | \(0.811317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 102.906 | 0.263187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 122.023i | − 0.310492i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 420.700i | 1.06506i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −149.939 | −0.377681 | −0.188840 | − | 0.982008i | \(-0.560473\pi\) | ||||
−0.188840 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 472.855i | 1.17919i | 0.807699 | + | 0.589595i | \(0.200713\pi\) | ||||
−0.807699 | + | 0.589595i | \(0.799287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −416.832 | −1.03432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 293.167 | 0.723869 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 715.476i | 1.75793i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 700.328i | 1.71229i | 0.516734 | + | 0.856146i | \(0.327148\pi\) | ||||
−0.516734 | + | 0.856146i | \(0.672852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 152.481i | 0.371001i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 159.724i | − 0.386742i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.32547 | −0.0152421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 247.848i | − 0.594360i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −161.641 | −0.385779 | −0.192889 | − | 0.981220i | \(-0.561786\pi\) | ||||
−0.192889 | + | 0.981220i | \(0.561786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 179.229i | 0.425723i | 0.977082 | + | 0.212861i | \(0.0682782\pi\) | ||||
−0.977082 | + | 0.212861i | \(0.931722\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −276.620 | −0.653947 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −135.753 | −0.319419 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −313.013 | −0.733053 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −786.699 | −1.83380 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 749.177i | 1.73823i | 0.494610 | + | 0.869115i | \(0.335311\pi\) | ||||
−0.494610 | + | 0.869115i | \(0.664689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 327.825i | 0.757101i | 0.925581 | + | 0.378550i | \(0.123577\pi\) | ||||
−0.925581 | + | 0.378550i | \(0.876423\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 223.414 | 0.513594 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 40.8286i | − 0.0930036i | −0.998918 | − | 0.0465018i | \(-0.985193\pi\) | ||||
0.998918 | − | 0.0465018i | \(-0.0148073\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 150.019 | 0.340179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −560.481 | −1.26519 | −0.632597 | − | 0.774481i | \(-0.718011\pi\) | ||||
−0.632597 | + | 0.774481i | \(0.718011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 57.4148i | − 0.129022i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 873.604i | 1.95437i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 138.943i | 0.309450i | 0.987958 | + | 0.154725i | \(0.0494492\pi\) | ||||
−0.987958 | + | 0.154725i | \(0.950551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1059.40i | − 2.34900i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −149.691 | −0.330444 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 86.6968i | 0.190542i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 357.592 | 0.782477 | 0.391239 | − | 0.920289i | \(-0.372047\pi\) | ||||
0.391239 | + | 0.920289i | \(0.372047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 154.674i | − 0.336981i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.35160 | 0.0159471 | 0.00797354 | − | 0.999968i | \(-0.497462\pi\) | ||||
0.00797354 | + | 0.999968i | \(0.497462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −485.832 | −1.04931 | −0.524656 | − | 0.851314i | \(-0.675806\pi\) | ||||
−0.524656 | + | 0.851314i | \(0.675806\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −429.778 | −0.924253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 790.719 | 1.69319 | 0.846594 | − | 0.532239i | \(-0.178649\pi\) | ||||
0.846594 | + | 0.532239i | \(0.178649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 299.980i | 0.639615i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 640.057i | − 1.35893i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1077.82 | −2.27870 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 116.377i | − 0.243978i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −343.994 | −0.718150 | −0.359075 | − | 0.933309i | \(-0.616908\pi\) | ||||
−0.359075 | + | 0.933309i | \(0.616908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 329.462 | 0.684952 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 131.906i | 0.273098i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 322.101i | − 0.664126i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 150.026i | 0.308062i | 0.988066 | + | 0.154031i | \(0.0492255\pi\) | ||||
−0.988066 | + | 0.154031i | \(0.950774\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 866.422i | − 1.77182i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 99.6980 | 0.203051 | 0.101525 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101525 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 176.738i | − 0.358495i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −237.432 | −0.479660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 182.667i | − 0.367539i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −104.779 | −0.209978 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −286.475 | −0.571807 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −337.201 | −0.670379 | −0.335190 | − | 0.942151i | \(-0.608800\pi\) | ||||
−0.335190 | + | 0.942151i | \(0.608800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 273.706 | 0.541992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 240.594i | − 0.474545i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 596.834i | − 1.17256i | −0.810108 | − | 0.586281i | \(-0.800591\pi\) | ||||
0.810108 | − | 0.586281i | \(-0.199409\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −77.7055 | −0.152066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 302.637i | − 0.587646i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1625.26 | −3.14364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 492.296 | 0.948548 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 407.775i | − 0.782677i | −0.920247 | − | 0.391339i | \(-0.872012\pi\) | ||||
0.920247 | − | 0.391339i | \(-0.127988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.72800i | 0.00521606i | 0.999997 | + | 0.00260803i | \(0.000830163\pi\) | ||||
−0.999997 | + | 0.00260803i | \(0.999170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 174.010i | − 0.331448i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 339.988i | 0.645139i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −372.260 | −0.703704 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 201.427i | − 0.379335i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −487.831 | −0.915254 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 535.353i | 1.00066i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 238.042 | 0.443281 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 881.428 | 1.63530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 199.085 | 0.367994 | 0.183997 | − | 0.982927i | \(-0.441096\pi\) | ||||
0.183997 | + | 0.982927i | \(0.441096\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 677.425 | 1.24756 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 135.913i | − 0.249381i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 181.698i | − 0.332172i | −0.986111 | − | 0.166086i | \(-0.946887\pi\) | ||||
0.986111 | − | 0.166086i | \(-0.0531129\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −394.738 | −0.719013 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 426.596i | 0.771422i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 339.694 | 0.612061 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 665.560 | 1.19490 | 0.597451 | − | 0.801906i | \(-0.296180\pi\) | ||||
0.597451 | + | 0.801906i | \(0.296180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 496.315i | 0.887863i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 641.670i | 1.14380i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 813.921i | − 1.44569i | −0.691012 | − | 0.722843i | \(-0.742835\pi\) | ||||
0.691012 | − | 0.722843i | \(-0.257165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 543.995i | − 0.962823i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 297.276 | 0.524296 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 787.495i | − 1.38400i | −0.721898 | − | 0.691999i | \(-0.756730\pi\) | ||||
0.721898 | − | 0.691999i | \(-0.243270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −750.796 | −1.31488 | −0.657439 | − | 0.753508i | \(-0.728360\pi\) | ||||
−0.657439 | + | 0.753508i | \(0.728360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 345.512i | 0.602988i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −206.771 | −0.359602 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 433.999 | 0.752165 | 0.376082 | − | 0.926586i | \(-0.377271\pi\) | ||||
0.376082 | + | 0.926586i | \(0.377271\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −148.661 | −0.256755 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.41412 | −0.0110398 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 683.770i | − 1.17285i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 109.332i | 0.186893i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −984.663 | −1.67745 | −0.838724 | − | 0.544556i | \(-0.816698\pi\) | ||||
−0.838724 | + | 0.544556i | \(0.816698\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 961.068i | − 1.62617i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −327.699 | −0.552613 | −0.276306 | − | 0.961070i | \(-0.589110\pi\) | ||||
−0.276306 | + | 0.961070i | \(0.589110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 70.7141 | 0.118847 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 341.669i | − 0.572310i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 366.105i | 0.611193i | 0.952161 | + | 0.305597i | \(0.0988559\pi\) | ||||
−0.952161 | + | 0.305597i | \(0.901144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 827.746i | 1.37728i | 0.725103 | + | 0.688641i | \(0.241792\pi\) | ||||
−0.725103 | + | 0.688641i | \(0.758208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 378.301i | 0.627365i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1042.57 | −1.72326 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 863.473i | 1.42253i | 0.702926 | + | 0.711263i | \(0.251876\pi\) | ||||
−0.702926 | + | 0.711263i | \(0.748124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 226.545 | 0.371995 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 748.400i | 1.22488i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 512.515 | 0.836076 | 0.418038 | − | 0.908430i | \(-0.362718\pi\) | ||||
0.418038 | + | 0.908430i | \(0.362718\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −502.981 | −0.817856 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −167.197 | −0.270984 | −0.135492 | − | 0.990778i | \(-0.543261\pi\) | ||||
−0.135492 | + | 0.990778i | \(0.543261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 948.222 | 1.53186 | 0.765930 | − | 0.642923i | \(-0.222279\pi\) | ||||
0.765930 | + | 0.642923i | \(0.222279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 235.591i | − 0.379374i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 58.2195i | − 0.0934502i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 60.6663 | 0.0970661 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 268.725i | − 0.427226i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 856.658 | 1.35762 | 0.678810 | − | 0.734314i | \(-0.262496\pi\) | ||||
0.678810 | + | 0.734314i | \(0.262496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 817.058 | 1.29077 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 247.251i | 0.389372i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 405.879i | − 0.637173i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 230.360i | − 0.360500i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 521.034i | − 0.812845i | −0.913685 | − | 0.406423i | \(-0.866776\pi\) | ||||
0.913685 | − | 0.406423i | \(-0.133224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 654.879 | 1.01847 | 0.509237 | − | 0.860626i | \(-0.329928\pi\) | ||||
0.509237 | + | 0.860626i | \(0.329928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 511.730i | 0.793380i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −262.226 | −0.405295 | −0.202648 | − | 0.979252i | \(-0.564955\pi\) | ||||
−0.202648 | + | 0.979252i | \(0.564955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 1183.47i | − 1.82353i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −435.801 | −0.669433 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −371.470 | −0.568866 | −0.284433 | − | 0.958696i | \(-0.591805\pi\) | ||||
−0.284433 | + | 0.958696i | \(0.591805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −99.6377 | −0.152119 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −97.9936 | −0.149153 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 515.532i | 0.782294i | 0.920328 | + | 0.391147i | \(0.127922\pi\) | ||||
−0.920328 | + | 0.391147i | \(0.872078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1265.78i | − 1.91495i | −0.288518 | − | 0.957474i | \(-0.593163\pi\) | ||||
0.288518 | − | 0.957474i | \(-0.406837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 295.476 | 0.445665 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 269.197i | − 0.403593i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −776.809 | −1.16115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2319.26 | −3.45643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 516.203i | − 0.767019i | −0.923537 | − | 0.383509i | \(-0.874715\pi\) | ||||
0.923537 | − | 0.383509i | \(-0.125285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 310.790i | 0.460430i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 985.790i | − 1.45611i | −0.685516 | − | 0.728057i | \(-0.740423\pi\) | ||||
0.685516 | − | 0.728057i | \(-0.259577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 326.616i | − 0.481025i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −174.557 | −0.256324 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 74.0653i | 0.108441i | 0.998529 | + | 0.0542206i | \(0.0172674\pi\) | ||||
−0.998529 | + | 0.0542206i | \(0.982733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 124.508 | 0.181764 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1120.65i | − 1.63122i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −314.862 | −0.456983 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 691.086 | 1.00013 | 0.500063 | − | 0.865989i | \(-0.333310\pi\) | ||||
0.500063 | + | 0.865989i | \(0.333310\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −240.760 | −0.347416 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −202.380 | −0.291194 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 397.898i | 0.570873i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 997.777i | 1.42744i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 875.548 | 1.24900 | 0.624499 | − | 0.781025i | \(-0.285303\pi\) | ||||
0.624499 | + | 0.781025i | \(0.285303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 771.643i | 1.09453i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 277.542 | 0.392563 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 481.812 | 0.679565 | 0.339783 | − | 0.940504i | \(-0.389647\pi\) | ||||
0.339783 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 537.976i | 0.756647i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 517.850i | 0.726298i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 642.377i | 0.898429i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.04489i | 0.00285201i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 357.773 | 0.497598 | 0.248799 | − | 0.968555i | \(-0.419964\pi\) | ||||
0.248799 | + | 0.968555i | \(0.419964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 306.879i | − 0.425630i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1030.00 | 1.42462 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 355.123i | 0.489825i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 249.823 | 0.343635 | 0.171818 | − | 0.985129i | \(-0.445036\pi\) | ||||
0.171818 | + | 0.985129i | \(0.445036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −229.245 | −0.314465 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 404.819 | 0.553788 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1409.10 | −1.92238 | −0.961189 | − | 0.275890i | \(-0.911028\pi\) | ||||
−0.961189 | + | 0.275890i | \(0.911028\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 418.485i | − 0.569367i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2222.69i | 3.01586i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 975.430 | 1.31993 | 0.659966 | − | 0.751295i | \(-0.270571\pi\) | ||||
0.659966 | + | 0.751295i | \(0.270571\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1289.68i | 1.73577i | 0.496763 | + | 0.867886i | \(0.334522\pi\) | ||||
−0.496763 | + | 0.867886i | \(0.665478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 713.338 | 0.957501 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.08878 | −0.0108284 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 542.856i | 0.724774i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 639.407i | − 0.851408i | −0.904863 | − | 0.425704i | \(-0.860027\pi\) | ||||
0.904863 | − | 0.425704i | \(-0.139973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 208.053i | 0.276299i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 122.230i | 0.161894i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 300.388 | 0.396813 | 0.198407 | − | 0.980120i | \(-0.436423\pi\) | ||||
0.198407 | + | 0.980120i | \(0.436423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 977.355i | 1.28769i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −560.059 | −0.735952 | −0.367976 | − | 0.929835i | \(-0.619949\pi\) | ||||
−0.367976 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 137.818i | − 0.180626i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 89.1768 | 0.116571 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −544.965 | −0.710515 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 596.650 | 0.775878 | 0.387939 | − | 0.921685i | \(-0.373187\pi\) | ||||
0.387939 | + | 0.921685i | \(0.373187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.5302 | −0.0292220 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1008.16i | 1.30421i | 0.758128 | + | 0.652106i | \(0.226114\pi\) | ||||
−0.758128 | + | 0.652106i | \(0.773886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 683.145i | − 0.881478i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 344.455 | 0.443314 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1353.47i | − 1.73299i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −404.620 | −0.516756 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −522.637 | −0.665779 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 738.630i | 0.938539i | 0.883055 | + | 0.469270i | \(0.155483\pi\) | ||||
−0.883055 | + | 0.469270i | \(0.844517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1339.37i | − 1.69755i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 551.619i | − 0.697370i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1067.97i | 1.34675i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −324.640 | −0.408353 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1039.69i | − 1.30451i | −0.758001 | − | 0.652254i | \(-0.773824\pi\) | ||||
0.758001 | − | 0.652254i | \(-0.226176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 610.431 | 0.763994 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 73.4200i | − 0.0916604i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −575.756 | −0.717007 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 107.708 | 0.133798 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1029.20 | 1.27535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 567.506 | 0.701491 | 0.350745 | − | 0.936471i | \(-0.385928\pi\) | ||||
0.350745 | + | 0.936471i | \(0.385928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 233.648i | 0.288099i | 0.989571 | + | 0.144049i | \(0.0460124\pi\) | ||||
−0.989571 | + | 0.144049i | \(0.953988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 224.928i | − 0.276664i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −707.474 | −0.868066 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 110.865i | 0.135366i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1515.76 | 1.84624 | 0.923120 | − | 0.384513i | \(-0.125631\pi\) | ||||
0.923120 | + | 0.384513i | \(0.125631\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 132.814 | 0.161378 | 0.0806892 | − | 0.996739i | \(-0.474288\pi\) | ||||
0.0806892 | + | 0.996739i | \(0.474288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 1289.32i | − 1.56281i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1130.49i | − 1.36698i | −0.729959 | − | 0.683491i | \(-0.760461\pi\) | ||||
0.729959 | − | 0.683491i | \(-0.239539\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 681.015i | 0.821490i | 0.911750 | + | 0.410745i | \(0.134731\pi\) | ||||
−0.911750 | + | 0.410745i | \(0.865269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 419.843i | 0.505226i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −331.055 | −0.397425 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 233.920i | 0.280144i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 778.362 | 0.929943 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 803.332i | 0.957487i | 0.877955 | + | 0.478744i | \(0.158908\pi\) | ||||
−0.877955 | + | 0.478744i | \(0.841092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 378.663 | 0.450253 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −122.809 | −0.145681 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −196.456 | −0.232493 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1057.19 | −1.24815 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − 1005.17i | − 1.18394i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 409.306i | − 0.480971i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0736 | 0.0504966 | 0.0252483 | − | 0.999681i | \(-0.491962\pi\) | ||||
0.0252483 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1302.82i | 1.52021i | 0.649799 | + | 0.760106i | \(0.274853\pi\) | ||||
−0.649799 | + | 0.760106i | \(0.725147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 588.536 | 0.685140 | 0.342570 | − | 0.939492i | \(-0.388703\pi\) | ||||
0.342570 | + | 0.939492i | \(0.388703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −510.031 | −0.592370 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1149.51i | − 1.33199i | −0.745955 | − | 0.665996i | \(-0.768007\pi\) | ||||
0.745955 | − | 0.665996i | \(-0.231993\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 401.983i | − 0.464720i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 789.909i | 0.911084i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3160.85i | 3.63734i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1023.50 | 1.17509 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 411.892i | − 0.471812i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −357.165 | −0.408189 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8876i | 0.0124146i | 0.999981 | + | 0.00620731i | \(0.00197586\pi\) | ||||
−0.999981 | + | 0.00620731i | \(0.998024\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1105.67 | 1.25787 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 458.646 | 0.520597 | 0.260298 | − | 0.965528i | \(-0.416179\pi\) | ||||
0.260298 | + | 0.965528i | \(0.416179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 204.491 | 0.231586 | 0.115793 | − | 0.993273i | \(-0.463059\pi\) | ||||
0.115793 | + | 0.993273i | \(0.463059\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −561.890 | −0.634904 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1727.40i | − 1.94746i | −0.227706 | − | 0.973730i | \(-0.573122\pi\) | ||||
0.227706 | − | 0.973730i | \(-0.426878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 250.716i | 0.282021i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2202.66 | 2.47212 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 194.373i | − 0.217176i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 450.051 | 0.501729 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 889.392 | 0.989312 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 256.816i | 0.285035i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 518.902i | 0.574642i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 553.149i | − 0.611214i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 855.204i | 0.942893i | 0.881895 | + | 0.471447i | \(0.156268\pi\) | ||||
−0.881895 | + | 0.471447i | \(0.843732\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 350.006 | 0.385045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 22.7639i | − 0.0249878i | −0.999922 | − | 0.0124939i | \(-0.996023\pi\) | ||||
0.999922 | − | 0.0124939i | \(-0.00397703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.5252 | −0.0520539 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1101.14i | 1.20343i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −101.034 | −0.110179 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 369.613 | 0.402191 | 0.201095 | − | 0.979572i | \(-0.435550\pi\) | ||||
0.201095 | + | 0.979572i | \(0.435550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1479.02 | 1.60589 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −623.243 | −0.675236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 539.955i | 0.583735i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 387.002i | − 0.417478i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −762.812 | −0.821111 | −0.410555 | − | 0.911836i | \(-0.634665\pi\) | ||||
−0.410555 | + | 0.911836i | \(0.634665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1381.93i | 1.48116i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 523.954 | 0.560378 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 978.242 | 1.04402 | 0.522008 | − | 0.852941i | \(-0.325183\pi\) | ||||
0.522008 | + | 0.852941i | \(0.325183\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1314.81i | − 1.40022i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 702.289i | − 0.746322i | −0.927767 | − | 0.373161i | \(-0.878274\pi\) | ||||
0.927767 | − | 0.373161i | \(-0.121726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 606.055i | 0.642689i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − 161.891i | − 0.171314i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 660.149 | 0.697095 | 0.348547 | − | 0.937291i | \(-0.386675\pi\) | ||||
0.348547 | + | 0.937291i | \(0.386675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 265.124i | 0.279372i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 761.878 | 0.801134 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 615.697i | 0.646062i | 0.946388 | + | 0.323031i | \(0.104702\pi\) | ||||
−0.946388 | + | 0.323031i | \(0.895298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 282.127 | 0.295421 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1678.58 | 1.75400 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 126.253 | 0.131651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −749.911 | −0.780344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 684.590i | 0.710893i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 121.389i | 0.125792i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 214.810 | 0.222141 | 0.111070 | − | 0.993813i | \(-0.464572\pi\) | ||||
0.111070 | + | 0.993813i | \(0.464572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 679.022i | − 0.699301i | −0.936880 | − | 0.349651i | \(-0.886300\pi\) | ||||
0.936880 | − | 0.349651i | \(-0.113700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −205.216 | −0.210911 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −593.705 | −0.608929 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1088.94i | 1.11457i | 0.830320 | + | 0.557287i | \(0.188158\pi\) | ||||
−0.830320 | + | 0.557287i | \(0.811842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 431.375i | − 0.440629i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 173.801i | − 0.177167i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1330.59i | 1.35360i | 0.736166 | + | 0.676800i | \(0.236634\pi\) | ||||
−0.736166 | + | 0.676800i | \(0.763366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −784.757 | −0.796708 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 782.458i | 0.792764i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 616.597 | 0.623455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1579.98i | − 1.59433i | −0.603761 | − | 0.797166i | \(-0.706332\pi\) | ||||
0.603761 | − | 0.797166i | \(-0.293668\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −826.033 | −0.831856 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −278.989 | −0.280391 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1456.40 | −1.46078 | −0.730391 | − | 0.683029i | \(-0.760662\pi\) | ||||
−0.730391 | + | 0.683029i | \(0.760662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −615.214 | −0.615830 |
(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 | 1444.3.c.d.721.6 | ✓ | 24 | |
19.18 | odd | 2 | inner | 1444.3.c.d.721.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1444.3.c.d.721.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1444.3.c.d.721.19 | yes | 24 | 19.18 | odd | 2 | inner |