Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,4,Mod(31,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.31");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bl (of order \(6\), degree \(2\), 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: | \(39.6492835239\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.9 | ||
Character | \(\chi\) | \(=\) | 672.607 |
Dual form | 672.4.bl.b.31.9 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.30657 | − | 2.48640i | −0.385191 | − | 0.222390i | 0.294883 | − | 0.955533i | \(-0.404719\pi\) |
−0.680074 | + | 0.733143i | \(0.738053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.80887 | + | 15.7094i | −0.529629 | + | 0.848229i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.9632 | − | 16.7219i | 0.793884 | − | 0.458349i | −0.0474439 | − | 0.998874i | \(-0.515108\pi\) |
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 19.9184i | − | 0.424951i | −0.977166 | − | 0.212475i | \(-0.931847\pi\) | ||
0.977166 | − | 0.212475i | \(-0.0681526\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 14.9184i | − | 0.256794i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 105.462 | − | 60.8886i | 1.50461 | − | 0.868685i | 0.504621 | − | 0.863341i | \(-0.331632\pi\) |
0.999986 | − | 0.00534432i | \(-0.00170116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.472943 | − | 0.819161i | 0.00571056 | − | 0.00989097i | −0.863156 | − | 0.504937i | \(-0.831516\pi\) |
0.868867 | + | 0.495046i | \(0.164849\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −55.5276 | − | 1.92007i | −0.577005 | − | 0.0199521i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 66.3780 | + | 38.3234i | 0.601773 | + | 0.347434i | 0.769739 | − | 0.638359i | \(-0.220387\pi\) |
−0.167966 | + | 0.985793i | \(0.553720\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −50.1357 | − | 86.8375i | −0.401085 | − | 0.694700i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −41.8752 | −0.268139 | −0.134070 | − | 0.990972i | \(-0.542805\pi\) | ||||
−0.134070 | + | 0.990972i | \(0.542805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 94.8284 | + | 164.248i | 0.549409 | + | 0.951604i | 0.998315 | + | 0.0580255i | \(0.0184805\pi\) |
−0.448906 | + | 0.893579i | \(0.648186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 86.8895 | + | 50.1657i | 0.458349 | + | 0.264628i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 81.3025 | − | 43.2649i | 0.392646 | − | 0.208946i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −85.6165 | + | 148.292i | −0.380413 | + | 0.658894i | −0.991121 | − | 0.132961i | \(-0.957551\pi\) |
0.610709 | + | 0.791855i | \(0.290885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 51.7494 | − | 29.8776i | 0.212475 | − | 0.122673i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 496.810i | 1.89241i | 0.323572 | + | 0.946204i | \(0.395116\pi\) | ||||
−0.323572 | + | 0.946204i | \(0.604884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 165.386i | 0.586538i | 0.956030 | + | 0.293269i | \(0.0947431\pi\) | ||||
−0.956030 | + | 0.293269i | \(0.905257\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 38.7591 | − | 22.3776i | 0.128397 | − | 0.0741301i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −94.3560 | + | 163.429i | −0.292835 | + | 0.507205i | −0.974479 | − | 0.224479i | \(-0.927932\pi\) |
0.681644 | + | 0.731684i | \(0.261265\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −150.572 | − | 308.184i | −0.438985 | − | 0.898494i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 316.386 | + | 182.666i | 0.868685 | + | 0.501536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 209.370 | + | 362.640i | 0.542627 | + | 0.939857i | 0.998752 | + | 0.0499414i | \(0.0159035\pi\) |
−0.456126 | + | 0.889915i | \(0.650763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −166.309 | −0.407730 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.83766 | 0.00659398 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.1623 | − | 104.204i | −0.132754 | − | 0.229936i | 0.791983 | − | 0.610543i | \(-0.209049\pi\) |
−0.924737 | + | 0.380606i | \(0.875715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 319.617 | + | 184.531i | 0.670864 | + | 0.387324i | 0.796404 | − | 0.604765i | \(-0.206733\pi\) |
−0.125540 | + | 0.992089i | \(0.540066\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −78.3029 | − | 147.145i | −0.156591 | − | 0.294262i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −49.5250 | + | 85.7798i | −0.0945049 | + | 0.163687i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 822.793 | − | 475.040i | 1.50030 | − | 0.866199i | 0.500301 | − | 0.865852i | \(-0.333223\pi\) |
1.00000 | 0.000347228i | \(-0.000110526\pi\) | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 229.940i | 0.401182i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 467.087i | 0.780747i | 0.920657 | + | 0.390374i | \(0.127654\pi\) | ||||
−0.920657 | + | 0.390374i | \(0.872346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −388.860 | + | 224.508i | −0.623460 | + | 0.359955i | −0.778215 | − | 0.627998i | \(-0.783875\pi\) |
0.154755 | + | 0.987953i | \(0.450541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 150.407 | − | 260.512i | 0.231567 | − | 0.401085i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.4048 | + | 619.018i | −0.0316793 | + | 0.916151i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 788.392 | + | 455.178i | 1.12280 | + | 0.648248i | 0.942114 | − | 0.335294i | \(-0.108835\pi\) |
0.180684 | + | 0.983541i | \(0.442169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1052.65 | 1.39209 | 0.696043 | − | 0.718000i | \(-0.254942\pi\) | ||||
0.696043 | + | 0.718000i | \(0.254942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −605.573 | −0.772748 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −62.8128 | − | 108.795i | −0.0774051 | − | 0.134070i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1126.90 | − | 650.614i | −1.34214 | − | 0.774887i | −0.355022 | − | 0.934858i | \(-0.615527\pi\) |
−0.987122 | + | 0.159971i | \(0.948860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 312.906 | + | 195.377i | 0.360456 | + | 0.225067i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −284.485 | + | 492.743i | −0.317201 | + | 0.549409i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.07352 | + | 2.35185i | −0.00439931 | + | 0.00253994i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 950.793i | 0.995242i | 0.867395 | + | 0.497621i | \(0.165793\pi\) | ||||
−0.867395 | + | 0.497621i | \(0.834207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 300.994i | 0.305566i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −310.107 | + | 179.040i | −0.305513 | + | 0.176388i | −0.644917 | − | 0.764253i | \(-0.723108\pi\) |
0.339404 | + | 0.940641i | \(0.389775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 537.408 | − | 930.818i | 0.514101 | − | 0.890449i | −0.485765 | − | 0.874089i | \(-0.661459\pi\) |
0.999866 | − | 0.0163595i | \(-0.00520763\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 234.359 | + | 146.333i | 0.217820 | + | 0.136006i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −381.168 | − | 220.068i | −0.344383 | − | 0.198829i | 0.317826 | − | 0.948149i | \(-0.397047\pi\) |
−0.662208 | + | 0.749320i | \(0.730381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.06875 | + | 7.04727i | 0.00357537 | + | 0.00619272i | 0.867808 | − | 0.496900i | \(-0.165529\pi\) |
−0.864232 | + | 0.503093i | \(0.832195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −513.699 | −0.439263 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 206.244 | 0.171697 | 0.0858486 | − | 0.996308i | \(-0.472640\pi\) | ||||
0.0858486 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −190.574 | − | 330.084i | −0.154532 | − | 0.267657i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 155.248 | + | 89.6327i | 0.122673 | + | 0.0708252i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −77.9401 | + | 2254.00i | −0.0600400 | + | 1.73633i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −106.256 | + | 184.041i | −0.0798318 | + | 0.138273i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1290.75 | + | 745.215i | −0.946204 | + | 0.546291i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1120.23i | 0.801570i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 139.196i | − | 0.0972568i | −0.998817 | − | 0.0486284i | \(-0.984515\pi\) | ||
0.998817 | − | 0.0486284i | \(-0.0154850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −429.685 | + | 248.079i | −0.293269 | + | 0.169319i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 358.948 | − | 621.717i | 0.239400 | − | 0.414654i | −0.721142 | − | 0.692787i | \(-0.756382\pi\) |
0.960542 | + | 0.278134i | \(0.0897158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.22951 | + | 15.4647i | 0.00536533 | + | 0.0100824i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 116.277 | + | 67.1327i | 0.0741301 | + | 0.0427990i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 961.682 | + | 1665.68i | 0.599723 | + | 1.03875i | 0.992862 | + | 0.119271i | \(0.0380557\pi\) |
−0.393139 | + | 0.919479i | \(0.628611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2775.81 | 1.69382 | 0.846912 | − | 0.531733i | \(-0.178459\pi\) | ||||
0.846912 | + | 0.531733i | \(0.178459\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −566.136 | −0.338136 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −333.073 | − | 576.899i | −0.194776 | − | 0.337362i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 180.338 | + | 104.118i | 0.103285 | + | 0.0596315i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 574.826 | − | 853.473i | 0.322523 | − | 0.478866i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −425.524 | + | 737.029i | −0.233961 | + | 0.405233i | −0.958970 | − | 0.283506i | \(-0.908502\pi\) |
0.725009 | + | 0.688740i | \(0.241836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2030.26 | + | 1172.17i | −1.09417 | + | 0.631721i | −0.934684 | − | 0.355479i | \(-0.884318\pi\) |
−0.159488 | + | 0.987200i | \(0.550984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1095.99i | 0.579123i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 943.124i | − | 0.488733i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 134.779 | − | 77.8149i | 0.0685131 | − | 0.0395561i | −0.465352 | − | 0.885126i | \(-0.654072\pi\) |
0.533865 | + | 0.845570i | \(0.320739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −628.111 | + | 1087.92i | −0.313286 | + | 0.542627i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1253.13 | + | 666.851i | −0.613420 | + | 0.326430i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3054.30 | + | 1763.40i | 1.46768 | + | 0.847364i | 0.999345 | − | 0.0361888i | \(-0.0115218\pi\) |
0.468332 | + | 0.883553i | \(0.344855\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −249.464 | − | 432.084i | −0.117701 | − | 0.203865i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1186.63 | −0.549845 | −0.274923 | − | 0.961466i | \(-0.588652\pi\) | ||||
−0.274923 | + | 0.961466i | \(0.588652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1800.26 | 0.819417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.25649 | + | 7.37245i | 0.00190352 | + | 0.00329699i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1357.56 | − | 783.790i | −0.596611 | − | 0.344453i | 0.171096 | − | 0.985254i | \(-0.445269\pi\) |
−0.767707 | + | 0.640801i | \(0.778602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1855.94 | + | 64.1759i | 0.801691 | + | 0.0277214i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 180.487 | − | 312.613i | 0.0766454 | − | 0.132754i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1015.61 | − | 586.365i | 0.424082 | − | 0.244844i | −0.272741 | − | 0.962088i | \(-0.587930\pi\) |
0.696822 | + | 0.717244i | \(0.254597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2290.66i | − | 0.940682i | −0.882485 | − | 0.470341i | \(-0.844131\pi\) | ||
0.882485 | − | 0.470341i | \(-0.155869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1107.18i | 0.447243i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 737.427 | − | 425.753i | 0.293063 | − | 0.169200i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2036.35 | − | 3527.05i | 0.796323 | − | 1.37927i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 264.840 | − | 424.154i | 0.101927 | − | 0.163242i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1341.10 | − | 774.287i | −0.508057 | − | 0.293327i | 0.223978 | − | 0.974594i | \(-0.428096\pi\) |
−0.732035 | + | 0.681267i | \(0.761429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1641.86 | − | 2843.79i | −0.612352 | − | 1.06063i | −0.990843 | − | 0.135020i | \(-0.956890\pi\) |
0.378491 | − | 0.925605i | \(-0.376443\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −297.150 | −0.109125 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4435.77 | 1.60424 | 0.802121 | − | 0.597161i | \(-0.203705\pi\) | ||||
0.802121 | + | 0.597161i | \(0.203705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1389.85 | + | 2407.29i | 0.495096 | + | 0.857531i | 0.999984 | − | 0.00565397i | \(-0.00179972\pi\) |
−0.504888 | + | 0.863185i | \(0.668466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2468.38 | + | 1425.12i | 0.866199 | + | 0.500100i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 410.749 | − | 657.836i | 0.142014 | − | 0.227443i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1235.27 | − | 2139.55i | 0.420853 | − | 0.728938i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −597.402 | + | 344.910i | −0.200591 | + | 0.115811i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 31.6340i | − | 0.0104697i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 69.9294i | − | 0.0228158i | −0.999935 | − | 0.0114079i | \(-0.996369\pi\) | ||
0.999935 | − | 0.0114079i | \(-0.00363133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1213.53 | + | 700.631i | −0.390374 | + | 0.225382i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 411.215 | − | 712.246i | 0.130440 | − | 0.225929i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3510.39 | − | 121.385i | −1.09816 | − | 0.0379729i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1166.58 | − | 673.524i | −0.359955 | − | 0.207820i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1212.80 | − | 2100.63i | −0.369149 | − | 0.639384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3043.66 | −0.913985 | −0.456992 | − | 0.889471i | \(-0.651073\pi\) | ||||
−0.456992 | + | 0.889471i | \(0.651073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 902.442 | 0.267390 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1175.84 | + | 2036.61i | 0.343802 | + | 0.595483i | 0.985135 | − | 0.171780i | \(-0.0549518\pi\) |
−0.641333 | + | 0.767262i | \(0.721618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3674.13 | − | 2121.26i | −1.06023 | − | 0.612125i | −0.134736 | − | 0.990882i | \(-0.543019\pi\) |
−0.925496 | + | 0.378756i | \(0.876352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1640.36 | + | 872.916i | −0.467221 | + | 0.248630i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −183.707 | + | 318.190i | −0.0516525 | + | 0.0894648i | −0.890696 | − | 0.454600i | \(-0.849782\pi\) |
0.839043 | + | 0.544065i | \(0.183115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 812.701 | − | 469.213i | 0.225595 | − | 0.130247i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2731.07i | 0.748532i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4210.06i | 1.13944i | 0.821839 | + | 0.569720i | \(0.192948\pi\) | ||||
−0.821839 | + | 0.569720i | \(0.807052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3898.76 | − | 2250.95i | 1.04208 | − | 0.601645i | 0.121658 | − | 0.992572i | \(-0.461179\pi\) |
0.920422 | + | 0.390927i | \(0.127846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −117.819 | + | 1701.59i | −0.0307231 | + | 0.443718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.3164 | − | 9.42025i | −0.00420318 | − | 0.00242671i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1578.97 | + | 2734.86i | 0.401860 | + | 0.696043i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 154.212 | 0.0387801 | 0.0193900 | − | 0.999812i | \(-0.493828\pi\) | ||||
0.0193900 | + | 0.999812i | \(0.493828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2563.36 | 0.636984 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −908.359 | − | 1573.32i | −0.223073 | − | 0.386374i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 327.313 | + | 188.974i | 0.0794445 | + | 0.0458673i | 0.539196 | − | 0.842180i | \(-0.318728\pi\) |
−0.459752 | + | 0.888048i | \(0.652062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1489.78 | − | 2799.56i | −0.357415 | − | 0.671647i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 188.439 | − | 326.385i | 0.0446899 | − | 0.0774051i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5621.20 | + | 3245.40i | −1.31794 | + | 0.760913i | −0.983397 | − | 0.181468i | \(-0.941915\pi\) |
−0.334542 | + | 0.942381i | \(0.608582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2082.31i | − | 0.482699i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3903.69i | − | 0.894763i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7386.37 | − | 4264.52i | 1.67418 | − | 0.966590i | 0.708927 | − | 0.705282i | \(-0.249180\pi\) |
0.965256 | − | 0.261308i | \(-0.0841538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −669.102 | + | 1158.92i | −0.149982 | + | 0.259776i | −0.931220 | − | 0.364456i | \(-0.881255\pi\) |
0.781239 | + | 0.624232i | \(0.214588\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.2446 | + | 1106.02i | −0.00847865 | + | 0.245199i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2904.18 | − | 1676.73i | −0.636830 | − | 0.367674i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2892.57 | − | 5010.08i | −0.627428 | − | 1.08674i | −0.988066 | − | 0.154031i | \(-0.950774\pi\) |
0.360638 | − | 0.932706i | \(-0.382559\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1706.91 | −0.366273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6452.76 | −1.36989 | −0.684945 | − | 0.728595i | \(-0.740174\pi\) | ||||
−0.684945 | + | 0.728595i | \(0.740174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3360.26 | − | 5820.14i | −0.705818 | − | 1.22251i | −0.966395 | − | 0.257060i | \(-0.917246\pi\) |
0.260577 | − | 0.965453i | \(-0.416087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.2206 | − | 7.05555i | −0.00253994 | − | 0.00146644i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7804.60 | − | 4873.15i | −1.60520 | − | 1.00227i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4958.34 | − | 8588.09i | 1.00923 | − | 1.74803i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2470.23 | + | 1426.19i | −0.497621 | + | 0.287301i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5406.60i | 1.07801i | 0.842303 | + | 0.539005i | \(0.181199\pi\) | ||||
−0.842303 | + | 0.539005i | \(0.818801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 598.350i | 0.118092i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −782.006 | + | 451.491i | −0.152783 | + | 0.0882094i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 763.339 | − | 1322.14i | 0.147642 | − | 0.255724i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2598.12 | − | 1622.25i | −0.497518 | − | 0.310648i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −930.320 | − | 537.121i | −0.176388 | − | 0.101838i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −917.634 | − | 1589.39i | −0.172274 | − | 0.298387i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 767.110 | 0.142610 | 0.0713050 | − | 0.997455i | \(-0.477284\pi\) | ||||
0.0713050 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3224.45 | 0.593633 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3962.67 | − | 6863.54i | −0.722515 | − | 1.25143i | −0.959989 | − | 0.280039i | \(-0.909653\pi\) |
0.237473 | − | 0.971394i | \(-0.423681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1659.12 | − | 957.891i | −0.299613 | − | 0.172982i | 0.342656 | − | 0.939461i | \(-0.388673\pi\) |
−0.642269 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.6443 | + | 828.382i | −0.00512357 | + | 0.148172i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −399.219 | + | 691.468i | −0.0707331 | + | 0.122513i | −0.899223 | − | 0.437491i | \(-0.855867\pi\) |
0.828490 | + | 0.560004i | \(0.189201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1212.84 | + | 700.233i | −0.212871 | + | 0.122901i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1320.41i | − | 0.229588i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 115.187i | − | 0.0198427i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1729.66 | + | 998.620i | −0.295213 | + | 0.170442i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.2062 | + | 21.1418i | −0.00206424 | + | 0.00357537i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1641.85 | − | 3085.34i | −0.275132 | − | 0.517021i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7373.90 | + | 4257.33i | 1.22449 | + | 0.706960i | 0.965872 | − | 0.259020i | \(-0.0833994\pi\) |
0.258619 | + | 0.965980i | \(0.416733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −770.549 | − | 1334.63i | −0.126804 | − | 0.219631i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4724.55 | −0.770537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1742.77 | −0.281706 | −0.140853 | − | 0.990031i | \(-0.544984\pi\) | ||||
−0.140853 | + | 0.990031i | \(0.544984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 309.366 | + | 535.837i | 0.0495647 | + | 0.0858486i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5493.06 | + | 3171.42i | 0.872334 | + | 0.503643i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6318.33 | + | 657.535i | 0.994629 | + | 0.103509i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 571.723 | − | 990.253i | 0.0892189 | − | 0.154532i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8128.44 | + | 4692.95i | −1.25751 | + | 0.726026i | −0.972591 | − | 0.232524i | \(-0.925301\pi\) |
−0.284923 | + | 0.958550i | \(0.591968\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9429.62i | − | 1.44629i | −0.690695 | − | 0.723146i | \(-0.742695\pi\) | ||
0.690695 | − | 0.723146i | \(-0.257305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 537.796i | 0.0817818i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −971.440 | + | 560.861i | −0.146472 | + | 0.0845655i | −0.571445 | − | 0.820640i | \(-0.693617\pi\) |
0.424973 | + | 0.905206i | \(0.360284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1161.36 | − | 2011.54i | 0.173631 | − | 0.300737i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5972.97 | + | 3178.50i | −0.885498 | + | 0.471216i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5933.52 | + | 3425.72i | 0.872309 | + | 0.503628i | 0.868115 | − | 0.496363i | \(-0.165332\pi\) |
0.00419433 | + | 0.999991i | \(0.498665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3429.05 | + | 5939.29i | 0.499935 | + | 0.865912i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −637.537 | −0.0921818 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2232.87 | 0.320202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1531.09 | − | 2651.93i | −0.217772 | − | 0.377192i | 0.736354 | − | 0.676596i | \(-0.236546\pi\) |
−0.954127 | + | 0.299404i | \(0.903212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3872.25 | − | 2235.65i | −0.546291 | − | 0.315401i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7750.55 | − | 268.003i | −1.08460 | − | 0.0375042i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2872.17 | − | 4974.75i | 0.398701 | − | 0.690570i | −0.594865 | − | 0.803826i | \(-0.702794\pi\) |
0.993566 | + | 0.113255i | \(0.0361278\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2910.44 | + | 1680.34i | −0.400785 | + | 0.231393i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 834.086i | 0.113946i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7365.74i | − | 0.998291i | −0.866518 | − | 0.499146i | \(-0.833647\pi\) | ||
0.866518 | − | 0.499146i | \(-0.166353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 361.641 | − | 208.793i | 0.0486284 | − | 0.0280756i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3386.37 | − | 5865.36i | 0.451789 | − | 0.782522i | −0.546708 | − | 0.837323i | \(-0.684119\pi\) |
0.998497 | + | 0.0548014i | \(0.0174526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1631.31 | − | 2612.62i | 0.215946 | − | 0.345848i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1289.06 | − | 744.237i | −0.169319 | − | 0.0977563i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6645.07 | + | 11509.6i | 0.866114 | + | 1.50015i | 0.865937 | + | 0.500153i | \(0.166723\pi\) |
0.000176464 | 1.00000i | \(0.499944\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9333.82 | 1.20724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2153.69 | 0.276436 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2263.51 | − | 3920.51i | −0.288328 | − | 0.499398i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9128.38 | − | 5270.27i | −1.15401 | − | 0.666266i | −0.204146 | − | 0.978940i | \(-0.565442\pi\) |
−0.949860 | + | 0.312675i | \(0.898775\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.8342 | + | 44.5780i | −0.00349237 | + | 0.00559321i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1861.92 | − | 3224.93i | 0.231869 | − | 0.401610i | −0.726489 | − | 0.687178i | \(-0.758849\pi\) |
0.958358 | + | 0.285569i | \(0.0921824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3271.54 | − | 1888.83i | 0.404385 | − | 0.233472i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 402.796i | 0.0494200i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5726.68i | 0.697447i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10451.8 | − | 6034.35i | 1.26359 | − | 0.729534i | 0.289823 | − | 0.957080i | \(-0.406403\pi\) |
0.973767 | + | 0.227546i | \(0.0730701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2885.04 | + | 4997.04i | −0.346250 | + | 0.599723i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2227.11 | + | 77.0105i | 0.265349 | + | 0.00917540i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4533.30 | − | 2617.30i | −0.536219 | − | 0.309586i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4163.72 | + | 7211.78i | 0.488965 | + | 0.846912i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1298.82 | −0.151435 | −0.0757177 | − | 0.997129i | \(-0.524125\pi\) | ||||
−0.0757177 | + | 0.997129i | \(0.524125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6628.23 | −0.767316 | −0.383658 | − | 0.923475i | \(-0.625336\pi\) | ||||
−0.383658 | + | 0.923475i | \(0.625336\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −849.204 | − | 1470.86i | −0.0976116 | − | 0.169068i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10574.8 | − | 6105.38i | −1.20695 | − | 0.696834i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6033.95 | + | 3210.95i | −0.683849 | + | 0.363909i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 999.219 | − | 1730.70i | 0.112454 | − | 0.194776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −786.502 | + | 454.087i | −0.0878990 | + | 0.0507485i | −0.543305 | − | 0.839535i | \(-0.682827\pi\) |
0.455406 | + | 0.890284i | \(0.349494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 466.437i | − | 0.0517680i | −0.999665 | − | 0.0258840i | \(-0.991760\pi\) | ||
0.999665 | − | 0.0258840i | \(-0.00824005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 624.711i | 0.0688565i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 62.7860 | − | 36.2495i | 0.00687291 | − | 0.00396808i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9047.30 | − | 15670.4i | 0.983608 | − | 1.70366i | 0.335643 | − | 0.941989i | \(-0.391047\pi\) |
0.647965 | − | 0.761670i | \(-0.275620\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3079.63 | + | 213.234i | 0.332537 | + | 0.0230249i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13326.1 | + | 7693.81i | 1.42921 | + | 0.825156i | 0.997058 | − | 0.0766446i | \(-0.0244207\pi\) |
0.432153 | + | 0.901800i | \(0.357754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3235.37 | + | 5603.83i | 0.344655 | + | 0.596959i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2553.14 | −0.270155 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2326.87 | 0.244570 | 0.122285 | − | 0.992495i | \(-0.460978\pi\) | ||||
0.122285 | + | 0.992495i | \(0.460978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8307.61 | + | 14389.2i | 0.867384 | + | 1.50235i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6090.77 | − | 3516.51i | −0.631721 | − | 0.364724i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −861.767 | − | 1619.41i | −0.0887918 | − | 0.166855i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 171.175 | − | 296.483i | 0.0175213 | − | 0.0303477i | −0.857132 | − | 0.515097i | \(-0.827756\pi\) |
0.874653 | + | 0.484749i | \(0.161089\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2847.48 | + | 1643.99i | −0.289562 | + | 0.167179i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3365.88i | − | 0.340053i | −0.985439 | − | 0.170027i | \(-0.945615\pi\) | ||
0.985439 | − | 0.170027i | \(-0.0543854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8521.95i | 0.855397i | 0.903921 | + | 0.427698i | \(0.140675\pi\) | ||||
−0.903921 | + | 0.427698i | \(0.859325\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2450.31 | − | 1414.69i | 0.244366 | − | 0.141085i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −631.959 | + | 1094.58i | −0.0626201 | + | 0.108461i | −0.895636 | − | 0.444788i | \(-0.853279\pi\) |
0.833016 | + | 0.553249i | \(0.186612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −608.072 | + | 17585.2i | −0.0598682 | + | 1.73136i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 404.338 | + | 233.445i | 0.0395561 | + | 0.0228377i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2765.57 | + | 4790.10i | 0.268839 | + | 0.465643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −94.8452 | −0.00916168 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3768.66 | −0.361751 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5647.64 | + | 9782.00i | 0.538721 | + | 0.933092i | 0.998973 | + | 0.0453039i | \(0.0144256\pi\) |
−0.460252 | + | 0.887788i | \(0.652241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2953.74 | + | 1705.34i | 0.279998 | + | 0.161657i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3612.23 | − | 2255.45i | −0.340294 | − | 0.212478i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2364.05 | − | 4094.66i | 0.221332 | − | 0.383358i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2589.66 | − | 1495.14i | 0.240963 | − | 0.139120i | −0.374656 | − | 0.927164i | \(-0.622239\pi\) |
0.615619 | + | 0.788044i | \(0.288906\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10580.4i | 0.978451i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3839.89i | − | 0.352936i | −0.984306 | − | 0.176468i | \(-0.943533\pi\) | ||
0.984306 | − | 0.176468i | \(-0.0564672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4416.25 | + | 2549.72i | −0.403444 | + | 0.232928i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 748.391 | − | 1296.25i | 0.0679549 | − | 0.117701i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7337.67 | − | 4581.60i | −0.662252 | − | 0.413507i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1495.79 | + | 863.597i | 0.134190 | + | 0.0774748i | 0.565592 | − | 0.824685i | \(-0.308648\pi\) |
−0.431402 | + | 0.902160i | \(0.641981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1779.94 | − | 3082.95i | −0.158727 | − | 0.274923i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5651.51 | −0.500971 | −0.250485 | − | 0.968120i | \(-0.580590\pi\) | ||||
−0.250485 | + | 0.968120i | \(0.580590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1780.66 | 0.156908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2700.39 | + | 4677.21i | 0.236545 | + | 0.409708i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3547.89 | + | 2048.38i | 0.308954 | + | 0.178375i | 0.646458 | − | 0.762949i | \(-0.276249\pi\) |
−0.337504 | + | 0.941324i | \(0.609583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 287.381 | − | 8310.93i | 0.0248786 | − | 0.719479i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.7695 | + | 22.1174i | −0.00109900 | + | 0.00190352i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4628.77 | + | 2672.42i | −0.396054 | + | 0.228662i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6311.24i | 0.536882i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4702.74i | − | 0.397741i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11501.5 | + | 6640.40i | −0.967159 | + | 0.558390i | −0.898369 | − | 0.439241i | \(-0.855247\pi\) |
−0.0687902 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1676.16 | + | 2903.20i | −0.140141 | + | 0.242731i | −0.927549 | − | 0.373700i | \(-0.878089\pi\) |
0.787409 | + | 0.616431i | \(0.211422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2617.18 | + | 4918.14i | 0.217568 | + | 0.408848i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20001.6 | + | 11547.9i | 1.65329 | + | 0.954527i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3146.14 | − | 5449.27i | −0.258580 | − | 0.447873i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1082.92 | 0.0885024 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9895.65 | 0.804180 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1094.35 | + | 1895.47i | 0.0884354 | + | 0.153175i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3046.84 | + | 1759.10i | 0.244844 | + | 0.141361i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9514.46 | − | 6408.13i | −0.760328 | − | 0.512092i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11412.4 | − | 19766.8i | 0.906943 | − | 1.57087i | 0.0886555 | − | 0.996062i | \(-0.471743\pi\) |
0.818288 | − | 0.574809i | \(-0.194924\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5951.31 | − | 3435.99i | 0.470341 | − | 0.271552i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 40.4661i | − | 0.00318051i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14723.1i | 1.15085i | 0.817856 | + | 0.575423i | \(0.195163\pi\) | ||||
−0.817856 | + | 0.575423i | \(0.804837\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2876.55 | + | 1660.78i | −0.223621 | + | 0.129108i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.8046 | + | 34.3026i | −0.00153122 | + | 0.00265216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14883.8 | + | 7920.40i | −1.14453 | + | 0.609059i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2212.28 | + | 1277.26i | 0.169200 | + | 0.0976877i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3803.43 | + | 6587.74i | 0.289330 | + | 0.501134i | 0.973650 | − | 0.228048i | \(-0.0732343\pi\) |
−0.684320 | + | 0.729182i | \(0.739901\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3294.22 | 0.249250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12218.1 | 0.919514 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −753.915 | − | 1305.82i | −0.0564365 | − | 0.0977509i | 0.836427 | − | 0.548079i | \(-0.184641\pi\) |
−0.892863 | + | 0.450328i | \(0.851307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −888.202 | − | 512.804i | −0.0661362 | − | 0.0381838i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1499.24 | + | 51.8418i | 0.111045 | + | 0.00383978i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4836.05 | + | 8376.29i | −0.356306 | + | 0.617140i | −0.987341 | − | 0.158615i | \(-0.949297\pi\) |
0.631035 | + | 0.775755i | \(0.282630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10863.1 | + | 6271.82i | −0.796159 | + | 0.459663i | −0.842126 | − | 0.539280i | \(-0.818696\pi\) |
0.0459671 | + | 0.998943i | \(0.485363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4645.72i | − | 0.338705i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7685.47i | − | 0.557402i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4457.96 | − | 2573.81i | 0.321642 | − | 0.185700i | −0.330482 | − | 0.943812i | \(-0.607211\pi\) |
0.652124 | + | 0.758112i | \(0.273878\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4925.59 | − | 8531.38i | 0.353542 | − | 0.612352i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10325.3 | + | 16536.5i | −0.737289 | + | 1.18081i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12128.1 | + | 7002.14i | 0.861565 | + | 0.497425i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −445.725 | − | 772.018i | −0.0315016 | − | 0.0545624i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4377.91 | 0.307829 | 0.153915 | − | 0.988084i | \(-0.450812\pi\) | ||||
0.153915 | + | 0.988084i | \(0.450812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 179.394 | 0.0125497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6653.66 | + | 11524.5i | 0.463105 | + | 0.802121i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18761.9 | − | 10832.2i | −1.29925 | − | 0.750124i | −0.318978 | − | 0.947762i | \(-0.603340\pi\) |
−0.980275 | + | 0.197638i | \(0.936673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5939.99 | − | 9513.20i | 0.409270 | − | 0.655468i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4169.56 | + | 7221.88i | −0.285844 | + | 0.495096i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14592.1 | − | 8424.76i | 0.995355 | − | 0.574668i | 0.0884841 | − | 0.996078i | \(-0.471798\pi\) |
0.906871 | + | 0.421409i | \(0.138464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19969.1i | 1.35534i | 0.735368 | + | 0.677668i | \(0.237009\pi\) | ||||
−0.735368 | + | 0.677668i | \(0.762991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8550.71i | 0.577466i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 915.199 | − | 528.390i | 0.0615010 | − | 0.0355076i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9588.04 | − | 16607.0i | 0.641131 | − | 1.11047i | −0.344050 | − | 0.938951i | \(-0.611799\pi\) |
0.985181 | − | 0.171520i | \(-0.0548678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2325.23 | + | 80.4033i | 0.154718 | + | 0.00534993i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3255.25 | + | 1879.42i | 0.215537 | + | 0.124440i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3370.29 | − | 5837.52i | −0.222063 | − | 0.384625i | 0.733371 | − | 0.679829i | \(-0.237946\pi\) |
−0.955434 | + | 0.295204i | \(0.904613\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7411.61 | 0.485959 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22084.1 | −1.44096 | −0.720481 | − | 0.693474i | \(-0.756079\pi\) | ||||
−0.720481 | + | 0.693474i | \(0.756079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9128.06 | + | 15810.3i | 0.592711 | + | 1.02660i | 0.993866 | + | 0.110595i | \(0.0352755\pi\) |
−0.401155 | + | 0.916010i | \(0.631391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1792.21 | − | 1034.73i | −0.115811 | − | 0.0668636i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21274.4 | − | 11321.1i | 1.36812 | − | 0.728043i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3481.62 | + | 6030.35i | −0.222824 | + | 0.385942i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 82.1876 | − | 47.4510i | 0.00523486 | − | 0.00302235i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20852.3i | 1.32184i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15516.1i | 0.978898i | 0.872032 | + | 0.489449i | \(0.162802\pi\) | ||||
−0.872032 | + | 0.489449i | \(0.837198\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 181.682 | − | 104.894i | 0.0114079 | − | 0.00658636i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −346.096 | + | 599.455i | −0.0216289 | + | 0.0374624i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6138.51 | + | 2999.15i | −0.381816 | + | 0.186547i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3640.58 | − | 2101.89i | −0.225382 | − | 0.130125i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8848.14 | + | 15325.4i | 0.545211 | + | 0.944334i | 0.998594 | + | 0.0530177i | \(0.0168840\pi\) |
−0.453382 | + | 0.891316i | \(0.649783\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22939.0 | −1.40688 | −0.703440 | − | 0.710754i | \(-0.748354\pi\) | ||||
−0.703440 | + | 0.710754i | \(0.748354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2467.29 | 0.150619 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1665.72 | + | 2885.11i | 0.101215 | + | 0.175309i | 0.912185 | − | 0.409778i | \(-0.134394\pi\) |
−0.810971 | + | 0.585087i | \(0.801060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3484.98 | − | 2012.06i | −0.210782 | − | 0.121695i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4950.23 | − | 9302.35i | −0.298026 | − | 0.560043i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12177.9 | − | 21092.8i | 0.729800 | − | 1.26405i | −0.227167 | − | 0.973856i | \(-0.572946\pi\) |
0.956967 | − | 0.290195i | \(-0.0937203\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3091.67 | + | 1784.98i | −0.184430 | + | 0.106481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4041.15i | − | 0.239970i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12209.3i | 0.721707i | 0.932622 | + | 0.360854i | \(0.117515\pi\) | ||||
−0.932622 | + | 0.360854i | \(0.882485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21962.3 | + | 12680.0i | −1.29234 | + | 0.746132i | −0.979068 | − | 0.203532i | \(-0.934758\pi\) |
−0.313270 | + | 0.949664i | \(0.601425\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3638.40 | − | 6301.90i | 0.213128 | − | 0.369149i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.01047 | − | 87.0617i | 0.000175551 | − | 0.00507685i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2779.59 | − | 1604.80i | −0.161359 | − | 0.0931605i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4565.49 | − | 7907.66i | −0.263845 | − | 0.456992i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12342.8 | 0.710118 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −747.690 | −0.0428252 | −0.0214126 | − | 0.999771i | \(-0.506816\pi\) | ||||
−0.0214126 | + | 0.999771i | \(0.506816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1353.66 | + | 2344.61i | 0.0771889 | + | 0.133695i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2391.40 | − | 1380.67i | −0.135759 | − | 0.0783805i | 0.430582 | − | 0.902551i | \(-0.358308\pi\) |
−0.566341 | + | 0.824171i | \(0.691642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14936.4 | − | 9326.21i | −0.844193 | − | 0.527109i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3527.51 | + | 6109.83i | −0.198494 | + | 0.343802i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 337.194 | − | 194.679i | 0.0188907 | − | 0.0109066i | −0.490525 | − | 0.871427i | \(-0.663195\pi\) |
0.509416 | + | 0.860521i | \(0.329862\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9564.49i | − | 0.533490i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12727.6i | − | 0.706821i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7223.19 | − | 4170.31i | 0.399393 | − | 0.230590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6572.13 | − | 11383.3i | 0.361817 | − | 0.626686i | −0.626443 | − | 0.779468i | \(-0.715490\pi\) |
0.988260 | + | 0.152781i | \(0.0488231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4728.45 | − | 2952.41i | −0.259190 | − | 0.161837i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11954.2 | − | 6901.78i | −0.652446 | − | 0.376690i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30250.1 | + | 52394.6i | 1.64391 | + | 2.84733i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1102.24 | −0.0596432 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27202.0 | 1.46563 | 0.732813 | − | 0.680430i | \(-0.238207\pi\) | ||||
0.732813 | + | 0.680430i | \(0.238207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.9835 | + | 140.267i | 0.00434474 | + | 0.00752530i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2438.10 | + | 1407.64i | 0.130247 | + | 0.0751982i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 229.180 | − | 6627.78i | 0.0121912 | − | 0.352565i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13296.5 | + | 23030.1i | −0.704314 | + | 1.21991i | 0.262624 | + | 0.964898i | \(0.415412\pi\) |
−0.966938 | + | 0.255010i | \(0.917921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7095.53 | + | 4096.60i | −0.374266 | + | 0.216083i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14536.6i | 0.763533i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3312.61i | 0.173265i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10938.0 | + | 6315.09i | −0.569720 | + | 0.328928i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6224.10 | − | 10780.5i | 0.322837 | − | 0.559170i | −0.658235 | − | 0.752812i | \(-0.728697\pi\) |
0.981072 | + | 0.193642i | \(0.0620302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9351.25 | + | 17572.6i | 0.483022 | + | 0.907683i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11696.3 | + | 6752.85i | 0.601645 | + | 0.347360i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2099.44 | + | 3636.34i | 0.107547 | + | 0.186276i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36106.8 | −1.84199 | −0.920995 | − | 0.389575i | \(-0.872622\pi\) | ||||
−0.920995 | + | 0.389575i | \(0.872622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10070.1 | + | 17441.9i | 0.509517 | + | 0.882509i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20109.9 | − | 11610.5i | −1.01334 | − | 0.585051i | −0.101170 | − | 0.994869i | \(-0.532259\pi\) |
−0.912167 | + | 0.409819i | \(0.865592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4597.60 | + | 2246.29i | −0.230728 | + | 0.112729i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15887.1 | − | 27517.3i | 0.794043 | − | 1.37532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33233.8 | + | 19187.6i | −1.65430 | + | 0.955109i | −0.679023 | + | 0.734117i | \(0.737596\pi\) |
−0.975276 | + | 0.220992i | \(0.929070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 56.5215i | − | 0.00280212i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10558.8i | − | 0.521352i | −0.965426 | − | 0.260676i | \(-0.916055\pi\) | ||
0.965426 | − | 0.260676i | \(-0.0839454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3665.09 | − | 2116.04i | 0.180240 | − | 0.104061i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4736.91 | + | 8204.58i | −0.232014 | + | 0.401860i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7195.97 | − | 3829.32i | 0.351048 | − | 0.186809i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26802.6 | + | 15474.5i | 1.30232 | + | 0.751893i | 0.980801 | − | 0.195012i | \(-0.0624745\pi\) |
0.321515 | + | 0.946904i | \(0.395808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 231.319 | + | 400.655i | 0.0111948 | + | 0.0193900i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11657.9 | 0.561954 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16987.8 | 0.815633 | 0.407816 | − | 0.913064i | \(-0.366290\pi\) | ||||
0.407816 | + | 0.913064i | \(0.366290\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3845.04 | + | 6659.80i | 0.183881 | + | 0.318492i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25984.3 | − | 15002.0i | −1.23775 | − | 0.714617i | −0.269118 | − | 0.963107i | \(-0.586732\pi\) |
−0.968634 | + | 0.248491i | \(0.920065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −150.618 | − | 5.20818i | −0.00714647 | − | 0.000247115i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2725.08 | − | 4719.97i | 0.128791 | − | 0.223073i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2075.58 | + | 1198.34i | −0.0977116 | + | 0.0564138i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26163.2i | − | 1.22688i | −0.789743 | − | 0.613438i | \(-0.789786\pi\) | ||
0.789743 | − | 0.613438i | \(-0.210214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1133.85i | 0.0529630i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32953.0 | + | 19025.4i | −1.53330 | + | 0.885249i | −0.534089 | + | 0.845428i | \(0.679345\pi\) |
−0.999207 | + | 0.0398204i | \(0.987321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9508.57 | − | 16469.3i | 0.440720 | − | 0.763349i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5038.81 | − | 8069.92i | 0.232646 | − | 0.372595i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 406.968 | + | 234.963i | 0.0187178 | + | 0.0108067i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7810.58 | + | 13528.3i | 0.357855 | + | 0.619823i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1130.63 | 0.0516034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −773.915 | −0.0351875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13392.5 | − | 23196.6i | −0.606598 | − | 1.05066i | −0.991797 | − | 0.127825i | \(-0.959200\pi\) |
0.385198 | − | 0.922834i | \(-0.374133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16863.6 | − | 9736.20i | −0.760913 | − | 0.439313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2023.02 | + | 3239.97i | −0.0909358 | + | 0.145638i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3675.55 | − | 6366.24i | 0.164594 | − | 0.285084i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5410.00 | − | 3123.47i | 0.241350 | − | 0.139343i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 11406.4i | − | 0.506947i | −0.967342 | − | 0.253473i | \(-0.918427\pi\) | ||
0.967342 | − | 0.253473i | \(-0.0815731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22980.8i | 1.01752i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10142.1 | − | 5855.53i | 0.447381 | − | 0.258296i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7508.41 | + | 13004.9i | −0.329970 | + | 0.571525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7054.75 | + | 243.944i | 0.308879 | + | 0.0106806i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22159.1 | + | 12793.6i | 0.966590 | + | 0.558061i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7836.06 | + | 13572.5i | 0.340545 | + | 0.589842i | 0.984534 | − | 0.175193i | \(-0.0560550\pi\) |
−0.643989 | + | 0.765035i | \(0.722722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23645.9 | −1.02382 | −0.511912 | − | 0.859038i | \(-0.671062\pi\) | ||||
−0.511912 | + | 0.859038i | \(0.671062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4014.61 | −0.173184 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8769.04 | − | 15188.4i | −0.376891 | − | 0.652794i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 135.478 | + | 78.2181i | 0.00580143 | + | 0.00334946i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2930.89 | + | 1559.67i | −0.125047 | + | 0.0665435i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23149.8 | − | 40096.7i | 0.984086 | − | 1.70449i | 0.338155 | − | 0.941090i | \(-0.390197\pi\) |
0.645930 | − | 0.763396i | \(-0.276470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21582.4 | − | 12460.6i | 0.914112 | − | 0.527763i | 0.0323599 | − | 0.999476i | \(-0.489698\pi\) |
0.881752 | + | 0.471714i | \(0.156364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 10060.4i | − | 0.424554i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30279.0i | 1.27316i | 0.771210 | + | 0.636581i | \(0.219652\pi\) | ||||
−0.771210 | + | 0.636581i | \(0.780348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3100.58 | + | 1790.12i | −0.129901 | + | 0.0749981i | −0.563542 | − | 0.826087i | \(-0.690562\pi\) |
0.433642 | + | 0.901085i | \(0.357228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8677.70 | − | 15030.2i | 0.362246 | − | 0.627428i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34644.5 | − | 23333.6i | −1.44101 | − | 0.970541i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5110.30 | + | 2950.43i | 0.211795 | + | 0.122280i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2560.37 | − | 4434.68i | −0.105734 | − | 0.183136i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24560.9 | −1.01065 | −0.505325 | − | 0.862929i | \(-0.668627\pi\) | ||||
−0.505325 | + | 0.862929i | \(0.668627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22635.5 | −0.928101 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9679.14 | − | 16764.8i | −0.395453 | − | 0.684945i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7752.93 | − | 4476.16i | −0.315632 | − | 0.182230i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1848.93 | − | 3474.46i | −0.0750057 | − | 0.140949i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10080.8 | − | 17460.4i | 0.407504 | − | 0.705818i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11366.1 | + | 6562.22i | −0.457844 | + | 0.264336i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5489.29i | 0.220339i | 0.993913 | + | 0.110170i | \(0.0351394\pi\) | ||||
−0.993913 | + | 0.110170i | \(0.964861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 42.3333i | − | 0.00169330i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28019.1 | − | 16176.9i | 1.11682 | − | 0.644797i | 0.176233 | − | 0.984348i | \(-0.443609\pi\) |
0.940587 | + | 0.339552i | \(0.110275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6643.25 | − | 11506.4i | 0.263870 | − | 0.457037i | −0.703397 | − | 0.710798i | \(-0.748334\pi\) |
0.967267 | + | 0.253761i | \(0.0816675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 953.909 | − | 27586.7i | 0.0377574 | − | 1.09193i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20491.8 | + | 11830.9i | 0.808283 | + | 0.466662i | 0.846359 | − | 0.532612i | \(-0.178790\pi\) |
−0.0380762 | + | 0.999275i | \(0.512123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3897.63 | + | 6750.89i | 0.153206 | + | 0.265361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29750.0 | 1.16536 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30445.8 | 1.18850 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9462.02 | − | 16388.7i | −0.368092 | − | 0.637554i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7410.70 | − | 4278.57i | −0.287301 | − | 0.165874i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17598.1 | − | 10988.2i | −0.679915 | − | 0.424535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16008.4 | − | 27727.4i | 0.616380 | − | 1.06760i | −0.373761 | − | 0.927525i | \(-0.621932\pi\) |
0.990141 | − | 0.140076i | \(-0.0447347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14046.7 | + | 8109.89i | −0.539005 | + | 0.311194i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20954.6i | − | 0.801336i | −0.916223 | − | 0.400668i | \(-0.868778\pi\) | ||
0.916223 | − | 0.400668i | \(-0.131222\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14392.3i | − | 0.548518i | −0.961656 | − | 0.274259i | \(-0.911568\pi\) | ||
0.961656 | − | 0.274259i | \(-0.0884325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1554.56 | + | 897.525i | −0.0590462 | + | 0.0340904i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4578.13 | − | 7929.55i | 0.173301 | − | 0.300167i | −0.766271 | − | 0.642518i | \(-0.777890\pi\) |
0.939572 | + | 0.342351i | \(0.111223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2186.68 | + | 1365.35i | 0.0824960 | + | 0.0515100i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2346.02 | − | 1354.47i | −0.0882094 | − | 0.0509277i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 89.2500 | + | 154.586i | 0.00334450 | + | 0.00579284i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5831.75 | −0.217803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4580.03 | 0.170483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3970.96 | − | 6877.91i | −0.147318 | − | 0.255162i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44161.2 | + | 25496.5i | 1.63288 | + | 0.942743i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 317.552 | − | 9183.48i | 0.0117026 | − | 0.338435i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5695.50 | + | 9864.89i | −0.209199 | + | 0.362342i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −420.151 | + | 242.574i | −0.0153813 | + | 0.00888042i | −0.507671 | − | 0.861551i | \(-0.669493\pi\) |
0.492290 | + | 0.870431i | \(0.336160\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 3222.72i | − | 0.117592i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1645.90i | − | 0.0598585i | −0.999552 | − | 0.0299292i | \(-0.990472\pi\) | ||
0.999552 | − | 0.0299292i | \(-0.00952819\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30488.0 | − | 17602.3i | 1.10515 | − | 0.638061i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2752.90 | − | 4768.17i | 0.0994624 | − | 0.172274i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6245.93 | + | 11737.2i | 0.224928 | + | 0.422679i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39639.0 | − | 22885.6i | −1.42282 | − | 0.821465i | −0.426280 | − | 0.904591i | \(-0.640176\pi\) |
−0.996539 | + | 0.0831261i | \(0.973510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1150.66 | + | 1993.01i | 0.0411679 | + | 0.0713050i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9303.62 | 0.331779 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17169.8 | 0.610311 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4836.67 | + | 8377.36i | 0.171367 | + | 0.296816i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35669.7 | − | 20593.9i | −1.25973 | − | 0.727303i | −0.286705 | − | 0.958019i | \(-0.592560\pi\) |
−0.973021 | + | 0.230716i | \(0.925893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −323.664 | − | 22.4105i | −0.0113938 | − | 0.000788910i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11888.0 | − | 20590.6i | 0.417144 | − | 0.722515i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17539.3 | + | 10126.3i | −0.613473 | + | 0.354189i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2545.59i | 0.0887523i | 0.999015 | + | 0.0443761i | \(0.0141300\pi\) | ||||
−0.999015 | + | 0.0443761i | \(0.985870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 5747.35i | − | 0.199742i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4507.93 | − | 2602.65i | 0.156168 | − | 0.0901637i | −0.419879 | − | 0.907580i | \(-0.637928\pi\) |
0.576048 | + | 0.817416i | \(0.304594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19039.4 | + | 32977.3i | −0.657486 | + | 1.13880i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2195.17 | + | 1168.15i | −0.0755648 | + | 0.0402117i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9404.38 | − | 5429.62i | −0.322705 | − | 0.186314i | 0.329893 | − | 0.944018i | \(-0.392987\pi\) |
−0.652597 | + | 0.757705i | \(0.726321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4471.84 | + | 7745.45i | 0.152963 | + | 0.264940i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2395.32 | −0.0816755 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3621.29 | −0.123090 | −0.0615452 | − | 0.998104i | \(-0.519603\pi\) | ||||
−0.0615452 | + | 0.998104i | \(0.519603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3850.37 | + | 6669.04i | 0.130466 | + | 0.225974i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3638.52 | − | 2100.70i | −0.122901 | − | 0.0709571i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35599.9 | − | 1231.00i | −1.19873 | − | 0.0414504i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3089.35 | + | 5350.91i | −0.103701 | + | 0.179615i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3430.52 | − | 1980.61i | 0.114794 | − | 0.0662765i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16329.3i | 0.544725i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39475.5i | 1.31277i | 0.754427 | + | 0.656384i | \(0.227915\pi\) | ||||
−0.754427 | + | 0.656384i | \(0.772085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 299.265 | − | 172.781i | 0.00992135 | − | 0.00572809i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12949.3 | − | 22428.9i | 0.427975 | − | 0.741275i | −0.568718 | − | 0.822533i | \(-0.692560\pi\) |
0.996693 | + | 0.0812578i | \(0.0258937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27227.6 | + | 43606.4i | −0.897099 | + | 1.43675i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5188.98 | − | 2995.86i | −0.170442 | − | 0.0984045i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14445.1 | − | 25019.6i | −0.473018 | − | 0.819290i | 0.526506 | − | 0.850172i | \(-0.323502\pi\) |
−0.999523 | + | 0.0308813i | \(0.990169\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43518.0 | −1.42068 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −73.2374 | −0.00238358 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9662.90 | + | 16736.6i | 0.313529 | + | 0.543048i | 0.979124 | − | 0.203266i | \(-0.0651555\pi\) |
−0.665595 | + | 0.746313i | \(0.731822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19103.0 | − | 11029.1i | −0.617940 | − | 0.356768i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5553.16 | − | 8893.67i | 0.179087 | − | 0.286817i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6338.14 | + | 10978.0i | −0.203783 | + | 0.352962i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50483.8 | + | 29146.9i | −1.61824 | + | 0.934289i | −0.630860 | + | 0.775897i | \(0.717298\pi\) |
−0.987376 | + | 0.158392i | \(0.949369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25544.0i | 0.816327i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13822.9i | − | 0.440418i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7827.39 | − | 4519.15i | 0.248642 | − | 0.143554i | −0.370500 | − | 0.928832i | \(-0.620814\pi\) |
0.619142 | + | 0.785279i | \(0.287480\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2311.65 | − | 4003.89i | 0.0732104 | − | 0.126804i |
(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 | 672.4.bl.b.607.9 | yes | 48 | |
4.3 | odd | 2 | 672.4.bl.a.607.9 | yes | 48 | ||
7.3 | odd | 6 | 672.4.bl.a.31.9 | ✓ | 48 | ||
28.3 | even | 6 | inner | 672.4.bl.b.31.9 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.bl.a.31.9 | ✓ | 48 | 7.3 | odd | 6 | ||
672.4.bl.a.607.9 | yes | 48 | 4.3 | odd | 2 | ||
672.4.bl.b.31.9 | yes | 48 | 28.3 | even | 6 | inner | |
672.4.bl.b.607.9 | yes | 48 | 1.1 | even | 1 | trivial |