Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("384.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.1 | ||
Root | \(2.29679i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.d.383.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.00172 | − | 1.40813i | −0.962581 | − | 0.270995i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.86626i | 0.524694i | 0.964974 | + | 0.262347i | \(0.0844966\pi\) | ||||
−0.964974 | + | 0.262347i | \(0.915503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.92149i | − | 0.319730i | −0.987139 | − | 0.159865i | \(-0.948894\pi\) | ||
0.987139 | − | 0.159865i | \(-0.0511060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.0343 | + | 14.0861i | 0.853124 | + | 0.521709i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.9652 | −0.766531 | −0.383265 | − | 0.923638i | \(-0.625201\pi\) | ||||
−0.383265 | + | 0.923638i | \(0.625201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0653967 | 0.00139521 | 0.000697607 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000697607 | 1.00000i | \(0.499778\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.26046 | − | 29.3414i | 0.142189 | − | 0.505061i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.9675i | 0.527408i | 0.964604 | + | 0.263704i | \(0.0849443\pi\) | ||||
−0.964604 | + | 0.263704i | \(0.915056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.7691i | 0.371522i | 0.982595 | + | 0.185761i | \(0.0594751\pi\) | ||||
−0.982595 | + | 0.185761i | \(0.940525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.33823 | + | 29.6176i | −0.0866452 | + | 0.307766i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 61.2864 | 0.555613 | 0.277806 | − | 0.960637i | \(-0.410393\pi\) | ||||
0.277806 | + | 0.960637i | \(0.410393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 90.5870 | 0.724696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −95.3761 | − | 102.890i | −0.679820 | − | 0.733379i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 143.566i | 0.919294i | 0.888102 | + | 0.459647i | \(0.152024\pi\) | ||||
−0.888102 | + | 0.459647i | \(0.847976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 299.568i | − | 1.73562i | −0.496900 | − | 0.867808i | \(-0.665529\pi\) | ||
0.496900 | − | 0.867808i | \(-0.334471\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 139.874 | + | 39.3787i | 0.737848 | + | 0.207726i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34.7370 | 0.167761 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −340.559 | −1.51318 | −0.756589 | − | 0.653891i | \(-0.773135\pi\) | ||||
−0.756589 | + | 0.653891i | \(0.773135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.327096 | − | 0.0920870i | −0.00134301 | − | 0.000378095i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 379.315i | − | 1.44486i | −0.691447 | − | 0.722428i | \(-0.743026\pi\) | ||
0.691447 | − | 0.722428i | \(-0.256974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 470.926i | − | 1.67013i | −0.550152 | − | 0.835065i | \(-0.685430\pi\) | ||
0.550152 | − | 0.835065i | \(-0.314570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −82.6330 | + | 135.125i | −0.273738 | + | 0.447629i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −428.593 | −1.33014 | −0.665072 | − | 0.746779i | \(-0.731599\pi\) | ||||
−0.665072 | + | 0.746779i | \(0.731599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 307.936 | 0.897772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.0551 | − | 184.901i | 0.142925 | − | 0.507673i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 505.868i | − | 1.31106i | −0.755168 | − | 0.655531i | \(-0.772445\pi\) | ||
0.755168 | − | 0.655531i | \(-0.227555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 164.051i | − | 0.402194i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 43.3269 | − | 153.898i | 0.100681 | − | 0.357620i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 207.827 | 0.458589 | 0.229295 | − | 0.973357i | \(-0.426358\pi\) | ||||
0.229295 | + | 0.973357i | \(0.426358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −578.221 | −1.21367 | −0.606833 | − | 0.794830i | \(-0.707560\pi\) | ||||
−0.606833 | + | 0.794830i | \(0.707560\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 83.4109 | − | 136.398i | 0.166806 | − | 0.272770i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.383634i | 0.000732061i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 415.350i | − | 0.757359i | −0.925528 | − | 0.378679i | \(-0.876378\pi\) | ||
0.925528 | − | 0.378679i | \(-0.123622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −306.537 | − | 86.2992i | −0.534822 | − | 0.150568i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −547.669 | −0.915441 | −0.457721 | − | 0.889096i | \(-0.651334\pi\) | ||||
−0.457721 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 194.572 | 0.311957 | 0.155979 | − | 0.987760i | \(-0.450147\pi\) | ||||
0.155979 | + | 0.987760i | \(0.450147\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −453.090 | − | 127.558i | −0.697578 | − | 0.196389i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 165.596i | 0.245083i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 308.374i | − | 0.439175i | −0.975593 | − | 0.219587i | \(-0.929529\pi\) | ||
0.975593 | − | 0.219587i | \(-0.0704711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 332.162 | + | 648.930i | 0.455640 | + | 0.890164i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −62.3019 | −0.0823918 | −0.0411959 | − | 0.999151i | \(-0.513117\pi\) | ||||
−0.0411959 | + | 0.999151i | \(0.513117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −216.861 | −0.276728 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 202.159 | − | 718.076i | 0.249124 | − | 0.884895i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1065.01i | − | 1.26844i | −0.773153 | − | 0.634220i | \(-0.781321\pi\) | ||
0.773153 | − | 0.634220i | \(-0.218679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.387246i | − | 0.000446092i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −421.831 | + | 1498.36i | −0.470343 | + | 1.67067i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −180.500 | −0.194936 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 703.293 | 0.736171 | 0.368085 | − | 0.929792i | \(-0.380013\pi\) | ||||
0.368085 | + | 0.929792i | \(0.380013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −644.161 | − | 393.922i | −0.653946 | − | 0.399906i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 942.553i | − | 0.928589i | −0.885681 | − | 0.464295i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464295i | \(-0.153692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 86.0316i | − | 0.0823005i | −0.999153 | − | 0.0411502i | \(-0.986898\pi\) | ||
0.999153 | − | 0.0411502i | \(-0.0131022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −173.745 | − | 48.9142i | −0.161483 | − | 0.0454623i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 688.082 | 0.621676 | 0.310838 | − | 0.950463i | \(-0.399390\pi\) | ||||
0.310838 | + | 0.950463i | \(0.399390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1849.94 | 1.62561 | 0.812807 | − | 0.582534i | \(-0.197939\pi\) | ||||
0.812807 | + | 0.582534i | \(0.197939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1703.38 | + | 479.551i | 1.45656 | + | 0.410063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1054.54i | 0.877902i | 0.898511 | + | 0.438951i | \(0.144650\pi\) | ||||
−0.898511 | + | 0.438951i | \(0.855350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 359.522i | 0.291527i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.50637 | + | 0.921186i | 0.00119029 | + | 0.000727895i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 218.903 | 0.168628 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −548.945 | −0.412431 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −534.125 | + | 1897.23i | −0.391548 | + | 1.39079i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1264.69i | 0.904938i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 957.493i | 0.669006i | 0.942395 | + | 0.334503i | \(0.108568\pi\) | ||||
−0.942395 | + | 0.334503i | \(0.891432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −663.125 | + | 2355.44i | −0.452596 | + | 1.60763i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 550.306 | 0.367026 | 0.183513 | − | 0.983017i | \(-0.441253\pi\) | ||||
0.183513 | + | 0.983017i | \(0.441253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 182.199 | 0.118787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 603.581 | − | 559.501i | 0.384800 | − | 0.356698i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1991.37i | − | 1.24185i | −0.783869 | − | 0.620926i | \(-0.786757\pi\) | ||
0.783869 | − | 0.620926i | \(-0.213243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 746.850i | 0.455733i | 0.973692 | + | 0.227867i | \(0.0731751\pi\) | ||||
−0.973692 | + | 0.227867i | \(0.926825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2143.70 | + | 603.515i | 1.28037 | + | 0.360462i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.82883 | −0.00106947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −842.195 | −0.482348 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1540.21 | − | 433.614i | −0.864179 | − | 0.243292i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3198.80i | − | 1.75877i | −0.476114 | − | 0.879383i | \(-0.657955\pi\) | ||
0.476114 | − | 0.879383i | \(-0.342045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1475.50i | 0.795195i | 0.917560 | + | 0.397598i | \(0.130156\pi\) | ||||
−0.917560 | + | 0.397598i | \(0.869844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −520.730 | + | 851.523i | −0.275154 | + | 0.449945i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1757.35 | 0.910668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −713.140 | −0.362514 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −712.328 | + | 2530.21i | −0.355291 | + | 1.26200i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 362.907i | − | 0.177646i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1986.44i | 0.954538i | 0.878757 | + | 0.477269i | \(0.158373\pi\) | ||||
−0.878757 | + | 0.477269i | \(0.841627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −231.006 | + | 820.539i | −0.108993 | + | 0.387145i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3376.74 | −1.56467 | −0.782336 | − | 0.622857i | \(-0.785972\pi\) | ||||
−0.782336 | + | 0.622857i | \(0.785972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2197.00 | −0.999998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −433.418 | + | 708.747i | −0.193826 | + | 0.316954i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2696.12i | − | 1.18487i | −0.805619 | − | 0.592435i | \(-0.798167\pi\) | ||
0.805619 | − | 0.592435i | \(-0.201833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 536.410i | − | 0.231707i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1039.49 | − | 292.647i | −0.441429 | − | 0.124275i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3347.25 | 1.39768 | 0.698842 | − | 0.715276i | \(-0.253699\pi\) | ||||
0.698842 | + | 0.715276i | \(0.253699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1843.89 | 0.757210 | 0.378605 | − | 0.925558i | \(-0.376404\pi\) | ||||
0.378605 | + | 0.925558i | \(0.376404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2892.10 | + | 814.210i | 1.16825 | + | 0.328897i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1997.81i | − | 0.793956i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1033.81i | − | 0.404275i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −609.263 | + | 564.769i | −0.234483 | + | 0.217359i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2382.31 | −0.902501 | −0.451251 | − | 0.892397i | \(-0.649022\pi\) | ||||
−0.451251 | + | 0.892397i | \(0.649022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2546.25 | −0.949654 | −0.474827 | − | 0.880079i | \(-0.657489\pi\) | ||||
−0.474827 | + | 0.880079i | \(0.657489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.540207 | − | 1.91883i | 0.000198385 | − | 0.000704668i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2189.58i | − | 0.791885i | −0.918275 | − | 0.395943i | \(-0.870418\pi\) | ||
0.918275 | − | 0.395943i | \(-0.129582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5379.16i | 1.91617i | 0.286476 | + | 0.958087i | \(0.407516\pi\) | ||||
−0.286476 | + | 0.958087i | \(0.592484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −584.866 | + | 2077.46i | −0.205240 | + | 0.729019i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 850.124 | 0.293926 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2225.16 | 0.758107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1411.69 | + | 863.288i | 0.474006 | + | 0.289868i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 860.466i | − | 0.284783i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5320.28i | 1.73584i | 0.496701 | + | 0.867922i | \(0.334544\pi\) | ||||
−0.496701 | + | 0.867922i | \(0.665456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2739.28 | + | 771.189i | 0.881186 | + | 0.248080i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2762.58 | 0.876307 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1773.89 | −0.554929 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −973.192 | − | 273.982i | −0.300284 | − | 0.0845388i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.41755i | 0.000735847i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2708.41i | − | 0.813310i | −0.913582 | − | 0.406655i | \(-0.866695\pi\) | ||
0.913582 | − | 0.406655i | \(-0.133305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2086.61 | + | 1276.02i | 0.618255 | + | 0.378080i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2335.26 | 0.682806 | 0.341403 | − | 0.939917i | \(-0.389098\pi\) | ||||
0.341403 | + | 0.939917i | \(0.389098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −139.302 | −0.0401980 | −0.0200990 | − | 0.999798i | \(-0.506398\pi\) | ||||
−0.0200990 | + | 0.999798i | \(0.506398\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 233.181 | − | 828.264i | 0.0664162 | − | 0.235912i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.07987i | − | 0.00199064i | −1.00000 | 0.000995318i | \(-0.999683\pi\) | |||
1.00000 | 0.000995318i | \(-0.000316819\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2514.24i | − | 0.697919i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −434.231 | + | 1542.40i | −0.119014 | + | 0.422741i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 890.272 | 0.240949 | 0.120475 | − | 0.992716i | \(-0.461558\pi\) | ||||
0.120475 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1273.98 | 0.340515 | 0.170258 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170258 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −747.601 | − | 3713.49i | −0.197361 | − | 0.980331i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1806.43i | 0.471056i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.01220i | 0.000518353i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 311.616 | + | 87.7291i | 0.0793088 | + | 0.0223277i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3032.85 | −0.762678 | −0.381339 | − | 0.924435i | \(-0.624537\pi\) | ||||
−0.381339 | + | 0.924435i | \(0.624537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1713.89 | −0.425894 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1084.68 | + | 305.369i | 0.266373 | + | 0.0749919i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2585.22i | − | 0.627478i | −0.949509 | − | 0.313739i | \(-0.898418\pi\) | ||
0.949509 | − | 0.313739i | \(-0.101582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2016.62i | 0.483809i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2022.29 | + | 3306.95i | −0.479604 | + | 0.784271i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5444.20 | −1.27644 | −0.638220 | − | 0.769854i | \(-0.720329\pi\) | ||||
−0.638220 | + | 0.769854i | \(0.720329\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2967.55 | 0.687907 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1499.68 | + | 5326.89i | −0.343740 | + | 1.22098i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2061.38i | − | 0.467229i | −0.972329 | − | 0.233614i | \(-0.924945\pi\) | ||
0.972329 | − | 0.233614i | \(-0.0750553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5846.72i | − | 1.31056i | −0.755384 | − | 0.655282i | \(-0.772550\pi\) | ||
0.755384 | − | 0.655282i | \(-0.227450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.545292 | + | 1.93689i | −0.000120889 | + | 0.000429400i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2533.29 | −0.555502 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1488.28 | −0.322823 | −0.161412 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161412 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4219.76 | − | 6900.36i | 0.905485 | − | 1.48069i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6456.97i | 1.37079i | 0.728174 | + | 0.685393i | \(0.240369\pi\) | ||||
−0.728174 | + | 0.685393i | \(0.759631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5390.67i | − | 1.13231i | −0.824301 | − | 0.566153i | \(-0.808431\pi\) | ||
0.824301 | − | 0.566153i | \(-0.191569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 902.809 | + | 254.167i | 0.187641 | + | 0.0528265i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2246.11 | −0.461964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3546.40 | 0.721840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3517.67 | − | 990.328i | −0.708624 | − | 0.199498i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5400.85i | 1.07686i | 0.842669 | + | 0.538432i | \(0.180983\pi\) | ||||
−0.842669 | + | 0.538432i | \(0.819017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1219.17i | 0.240619i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2667.22 | + | 2877.35i | 0.521103 | + | 0.562157i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00793 | 0.000775198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2788.58 | −0.533991 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1327.24 | + | 4714.38i | −0.251643 | + | 0.893842i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3391.99i | − | 0.636803i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3598.12i | − | 0.668910i | −0.942412 | − | 0.334455i | \(-0.891448\pi\) | ||
0.942412 | − | 0.334455i | \(-0.108552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −121.144 | + | 430.306i | −0.0223030 | + | 0.0792209i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7894.55 | 1.43942 | 0.719709 | − | 0.694276i | \(-0.244275\pi\) | ||||
0.719709 | + | 0.694276i | \(0.244275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8500.57 | 1.53508 | 0.767541 | − | 0.641000i | \(-0.221480\pi\) | ||||
0.767541 | + | 0.641000i | \(0.221480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 800.144 | + | 489.310i | 0.143121 | + | 0.0875222i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7352.01i | − | 1.30262i | −0.758813 | − | 0.651309i | \(-0.774220\pi\) | ||
0.758813 | − | 0.651309i | \(-0.225780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4014.86i | − | 0.704667i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3441.59 | − | 968.908i | −0.598414 | − | 0.168471i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1137.46 | −0.195944 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.92409 | 0.00101111 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9252.86 | − | 2604.95i | −1.56478 | − | 0.440533i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2537.91i | 0.425287i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4348.48i | − | 0.722097i | −0.932547 | − | 0.361048i | \(-0.882419\pi\) | ||
0.932547 | − | 0.361048i | \(-0.117581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7844.55 | − | 4797.16i | −1.29093 | − | 0.789438i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2436.55 | 0.397382 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2451.75 | −0.396307 | −0.198153 | − | 0.980171i | \(-0.563494\pi\) | ||||
−0.198153 | + | 0.980171i | \(0.563494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1484.93 | − | 5274.52i | 0.237907 | − | 0.845051i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8377.50i | 1.33040i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3854.51i | − | 0.606776i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 506.254 | − | 1798.23i | 0.0790023 | − | 0.280618i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3671.15 | 0.567947 | 0.283974 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283974 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2543.31 | −0.390086 | −0.195043 | − | 0.980795i | \(-0.562485\pi\) | ||||
−0.195043 | + | 0.980795i | \(0.562485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.23728 | − | 6.72868i | −0.000948494 | − | 0.00102322i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12015.9i | − | 1.81173i | −0.423562 | − | 0.905867i | \(-0.639221\pi\) | ||
0.423562 | − | 0.905867i | \(-0.360779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3212.77i | − | 0.480327i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1094.89 | − | 308.244i | −0.162319 | − | 0.0456974i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11569.3 | −1.70085 | −0.850424 | − | 0.526097i | \(-0.823655\pi\) | ||||
−0.850424 | + | 0.526097i | \(0.823655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5912.26 | 0.861971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2745.67 | + | 772.986i | 0.396998 | + | 0.111767i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1141.41i | 0.163682i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 675.208i | 0.0960370i | 0.998846 | + | 0.0480185i | \(0.0152906\pi\) | ||||
−0.998846 | + | 0.0480185i | \(0.984709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5343.08 | − | 8737.27i | 0.753793 | − | 1.23264i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2995.49 | −0.419186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9000.61 | −1.24942 | −0.624710 | − | 0.780857i | \(-0.714783\pi\) | ||||
−0.624710 | + | 0.780857i | \(0.714783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1780.85 | − | 6325.62i | 0.245234 | − | 0.871076i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.38873i | 0.00128261i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6453.84i | − | 0.874700i | −0.899291 | − | 0.437350i | \(-0.855917\pi\) | ||
0.899291 | − | 0.437350i | \(-0.144083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1348.28 | − | 4789.11i | 0.181297 | − | 0.643973i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5211.10 | −0.695234 | −0.347617 | − | 0.937637i | \(-0.613009\pi\) | ||||
−0.347617 | + | 0.937637i | \(0.613009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −971.429 | −0.128594 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6633.53 | − | 10847.5i | 0.871321 | − | 1.42483i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1399.05i | 0.182351i | 0.995835 | + | 0.0911756i | \(0.0290625\pi\) | ||||
−0.995835 | + | 0.0911756i | \(0.970938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2265.61i | 0.293035i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2752.47 | − | 774.902i | −0.353292 | − | 0.0994622i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1809.00 | 0.230433 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6624.77 | −0.837500 | −0.418750 | − | 0.908101i | \(-0.637532\pi\) | ||||
−0.418750 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −911.308 | − | 256.560i | −0.114342 | − | 0.0321906i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5283.09i | 0.657918i | 0.944344 | + | 0.328959i | \(0.106698\pi\) | ||||
−0.944344 | + | 0.328959i | \(0.893302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 19.5908i | − | 0.00242155i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3806.79 | + | 1948.55i | −0.467064 | + | 0.239072i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9523.81 | 1.15990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7555.96 | −0.913492 | −0.456746 | − | 0.889597i | \(-0.650985\pi\) | ||||
−0.456746 | + | 0.889597i | \(0.650985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2804.10 | + | 9960.25i | −0.336536 | + | 1.19538i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1230.65i | − | 0.146625i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 365.479i | − | 0.0432305i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1051.66 | − | 3735.53i | 0.123501 | − | 0.438680i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6784.17 | −0.790999 | −0.395500 | − | 0.918466i | \(-0.629429\pi\) | ||||
−0.395500 | + | 0.918466i | \(0.629429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12740.9 | 1.47495 | 0.737476 | − | 0.675374i | \(-0.236018\pi\) | ||||
0.737476 | + | 0.675374i | \(0.236018\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9872.36 | − | 6037.22i | −1.13478 | − | 0.693947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3348.78i | 0.382211i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3423.93i | 0.388046i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.14731 | + | 2.57524i | 0.00102946 | + | 0.000289822i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16239.7 | 1.81493 | 0.907467 | − | 0.420123i | \(-0.138013\pi\) | ||||
0.907467 | + | 0.420123i | \(0.138013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4832.73 | 0.536365 | 0.268183 | − | 0.963368i | \(-0.413577\pi\) | ||||
0.268183 | + | 0.963368i | \(0.413577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4212.42 | + | 1185.92i | 0.464299 | + | 0.130714i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1885.73i | 0.206422i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4286.58i | 0.466031i | 0.972473 | + | 0.233015i | \(0.0748592\pi\) | ||||
−0.972473 | + | 0.233015i | \(0.925141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7093.10 | + | 4337.63i | 0.765911 | + | 0.468376i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2140.54 | −0.229572 | −0.114786 | − | 0.993390i | \(-0.536618\pi\) | ||||
−0.114786 | + | 0.993390i | \(0.536618\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6247.64 | 0.665543 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4504.33 | + | 15999.5i | −0.476617 | + | 1.69296i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9598.09i | 1.00882i | 0.863463 | + | 0.504412i | \(0.168291\pi\) | ||||
−0.863463 | + | 0.504412i | \(0.831709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10607.6i | 1.10753i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2077.70 | − | 7380.03i | 0.215494 | − | 0.765440i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.27168 | 0.000234062 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9542.53 | −0.976763 | −0.488382 | − | 0.872630i | \(-0.662413\pi\) | ||||
−0.488382 | + | 0.872630i | \(0.662413\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3803.60 | − | 3525.82i | 0.386790 | − | 0.358543i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8017.02i | 0.809956i | 0.914326 | + | 0.404978i | \(0.132721\pi\) | ||||
−0.914326 | + | 0.404978i | \(0.867279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10933.1i | − | 1.09742i | −0.836014 | − | 0.548709i | \(-0.815120\pi\) | ||
0.836014 | − | 0.548709i | \(-0.184880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8789.75 | − | 2474.57i | −0.876591 | − | 0.246786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3991.55 | −0.395518 | −0.197759 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197759 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2459.49 | −0.242151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3566.92 | + | 1004.19i | 0.348949 | + | 0.0982394i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13169.6i | 1.28021i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2787.28i | 0.269241i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7125.72 | − | 11652.3i | 0.683993 | − | 1.11850i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10524.5 | −1.00392 | −0.501958 | − | 0.864892i | \(-0.667387\pi\) | ||||
−0.501958 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2714 | −0.00211120 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −511.020 | + | 1815.16i | −0.0481412 | + | 0.170999i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4125.70i | 0.386265i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10750.1i | 1.00028i | 0.865946 | + | 0.500138i | \(0.166717\pi\) | ||||
−0.865946 | + | 0.500138i | \(0.833283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2797.16 | − | 9935.60i | 0.258675 | − | 0.918820i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18059.8 | −1.65994 | −0.829968 | − | 0.557811i | \(-0.811641\pi\) | ||||
−0.829968 | + | 0.557811i | \(0.811641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5307.28 | −0.484843 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2310.85 | − | 3778.82i | 0.209828 | − | 0.343122i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3243.02i | 0.292694i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15164.6i | 1.36044i | 0.733007 | + | 0.680221i | \(0.238116\pi\) | ||||
−0.733007 | + | 0.680221i | \(0.761884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16889.5 | + | 4754.89i | 1.50612 | + | 0.424018i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21362.1 | 1.89362 | 0.946808 | − | 0.321799i | \(-0.104288\pi\) | ||||
0.946808 | + | 0.321799i | \(0.104288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5529.26 | 0.487226 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10988.8 | + | 3093.66i | 0.962579 | + | 0.270994i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4921.82i | 0.428597i | 0.976768 | + | 0.214299i | \(0.0687466\pi\) | ||||
−0.976768 | + | 0.214299i | \(0.931253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1152.15i | − | 0.0997422i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3165.84 | − | 2934.64i | 0.272467 | − | 0.252568i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 504.684 | 0.0431826 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11985.7 | 1.01960 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3796.49 | + | 13485.2i | −0.321093 | + | 1.14053i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9816.25i | 0.825446i | 0.910857 | + | 0.412723i | \(0.135422\pi\) | ||||
−0.910857 | + | 0.412723i | \(0.864578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11120.7i | − | 0.929783i | −0.885368 | − | 0.464891i | \(-0.846093\pi\) | ||
0.885368 | − | 0.464891i | \(-0.153907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −755.335 | + | 2682.97i | −0.0627914 | + | 0.223037i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11074.3 | 0.915378 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8410.98 | −0.691295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4787.16 | + | 2927.48i | 0.391233 | + | 0.239250i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.8059i | − | 0.00201588i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4036.47i | 0.326190i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16742.0 | − | 4713.37i | −1.34538 | − | 0.378765i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8611.50 | −0.688170 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15949.1 | 1.26748 | 0.633740 | − | 0.773546i | \(-0.281519\pi\) | ||||
0.633740 | + | 0.773546i | \(0.281519\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9222.60 | − | 2596.43i | −0.728876 | − | 0.205200i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10852.2i | 0.852950i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12775.8i | 0.998637i | 0.866419 | + | 0.499318i | \(0.166416\pi\) | ||||
−0.866419 | + | 0.499318i | \(0.833584\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13318.9 | − | 8144.89i | −1.03541 | − | 0.633180i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4417.40 | −0.341538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1826.04 | −0.140418 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2813.17 | + | 9992.47i | −0.215158 | + | 0.764246i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9120.09i | 0.693772i | 0.937907 | + | 0.346886i | \(0.112761\pi\) | ||||
−0.937907 | + | 0.346886i | \(0.887239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30.7970i | − | 0.00233019i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1455.73 | + | 5170.80i | −0.109556 | + | 0.389147i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4530.65 | 0.339155 | 0.169577 | − | 0.985517i | \(-0.445760\pi\) | ||||
0.169577 | + | 0.985517i | \(0.445760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6186.21 | −0.460630 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3842.63 | − | 1966.89i | 0.284612 | − | 0.145682i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17896.0i | − | 1.31853i | −0.751913 | − | 0.659263i | \(-0.770868\pi\) | ||
0.751913 | − | 0.659263i | \(-0.229132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11840.1i | 0.867760i | 0.900971 | + | 0.433880i | \(0.142856\pi\) | ||||
−0.900971 | + | 0.433880i | \(0.857144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11915.6 | + | 3354.60i | 0.868731 | + | 0.244573i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5551.75 | 0.402650 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18102.9 | −1.30612 | −0.653060 | − | 0.757306i | \(-0.726515\pi\) | ||||
−0.653060 | + | 0.757306i | \(0.726515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12735.6 | + | 3585.45i | 0.914119 | + | 0.257351i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 368.920i | 0.0263432i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14146.7i | 1.00497i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.40392 | + | 8.83676i | −0.000381922 | + | 0.000624538i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21946.7 | 1.54317 | 0.771583 | − | 0.636129i | \(-0.219465\pi\) | ||||
0.771583 | + | 0.636129i | \(0.219465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9217.46 | 0.644820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3083.22 | + | 10951.7i | −0.214597 | + | 0.762253i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8554.64i | 0.592406i | 0.955125 | + | 0.296203i | \(0.0957206\pi\) | ||||
−0.955125 | + | 0.296203i | \(0.904279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1284.14i | 0.0884784i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7574.56 | − | 26905.0i | 0.519273 | − | 1.84447i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19321.4 | 1.31795 | 0.658973 | − | 0.752167i | \(-0.270991\pi\) | ||||
0.658973 | + | 0.752167i | \(0.270991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18248.6 | −1.23856 | −0.619281 | − | 0.785170i | \(-0.712576\pi\) | ||||
−0.619281 | + | 0.785170i | \(0.712576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5850.67 | − | 9567.30i | 0.395121 | − | 0.646121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3220.26i | − | 0.216400i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18473.4i | 1.23528i | 0.786462 | + | 0.617639i | \(0.211911\pi\) | ||||
−0.786462 | + | 0.617639i | \(0.788089\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4252.08 | − | 1197.08i | −0.282928 | − | 0.0796524i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.0286 | −0.00185583 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1007.68 | 0.0663946 | 0.0331973 | − | 0.999449i | \(-0.489431\pi\) | ||||
0.0331973 | + | 0.999449i | \(0.489431\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11129.6 | − | 3133.32i | −0.729740 | − | 0.205443i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8342.82i | − | 0.544359i | −0.962247 | − | 0.272179i | \(-0.912256\pi\) | ||
0.962247 | − | 0.272179i | \(-0.0877444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5153.14i | − | 0.334608i | −0.985905 | − | 0.167304i | \(-0.946494\pi\) | ||
0.985905 | − | 0.167304i | \(-0.0535061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5845.26 | − | 6305.77i | −0.377717 | − | 0.407475i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6306.46 | −0.405559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3904.37 | 0.249880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1211.65 | + | 4303.81i | −0.0771748 | + | 0.274127i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12589.6i | − | 0.798062i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3224.67i | 0.203442i | 0.994813 | + | 0.101721i | \(0.0324350\pi\) | ||||
−0.994813 | + | 0.101721i | \(0.967565\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7491.64 | − | 26610.5i | 0.470404 | − | 1.67089i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5616.91 | −0.351024 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.1380 | 0.00125258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12615.2 | − | 7714.54i | −0.780985 | − | 0.477594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13243.1i | 0.816025i | 0.912976 | + | 0.408013i | \(0.133778\pi\) | ||||
−0.912976 | + | 0.408013i | \(0.866222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17030.3i | − | 1.04449i | −0.852795 | − | 0.522246i | \(-0.825094\pi\) | ||
0.852795 | − | 0.522246i | \(-0.174906\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13817.6 | − | 3890.07i | −0.843517 | − | 0.237475i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29077.9 | −1.76688 | −0.883438 | − | 0.468548i | \(-0.844777\pi\) | ||||
−0.883438 | + | 0.468548i | \(0.844777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5811.93 | −0.351523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8872.50 | + | 2497.87i | 0.534164 | + | 0.150383i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14617.7i | 0.876008i | 0.898973 | + | 0.438004i | \(0.144315\pi\) | ||||
−0.898973 | + | 0.438004i | \(0.855685\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3228.24i | 0.192577i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4481.83 | + | 2740.76i | 0.266138 | + | 0.162751i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3426.04 | 0.202518 | 0.101259 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101259 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9256.76 | −0.544699 | −0.272350 | − | 0.962198i | \(-0.587801\pi\) | ||||
−0.272350 | + | 0.962198i | \(0.587801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.40423 | − | 12.0919i | 0.000199411 | − | 0.000708312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1068.83i | 0.0623269i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8798.63i | 0.510771i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3813.79 | + | 13546.7i | −0.220403 | + | 0.782877i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16170.1 | 0.930312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26622.1 | 1.52482 | 0.762412 | − | 0.647092i | \(-0.224015\pi\) | ||||
0.762412 | + | 0.647092i | \(0.224015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8639.84 | − | 9320.51i | −0.492663 | − | 0.531476i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 23048.4i | − | 1.30845i | −0.756300 | − | 0.654225i | \(-0.772995\pi\) | ||
0.756300 | − | 0.654225i | \(-0.227005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4164.54i | − | 0.235376i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11680.3 | − | 3288.36i | −0.657256 | − | 0.185037i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27884.8 | −1.56220 | −0.781100 | − | 0.624406i | \(-0.785341\pi\) | ||||
−0.781100 | + | 0.624406i | \(0.785341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11681.9 | 0.651593 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 696.749 | + | 196.155i | 0.0386938 | + | 0.0108934i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 33.0821i | − | 0.00182921i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8029.81i | − | 0.442067i | −0.975266 | − | 0.221034i | \(-0.929057\pi\) | ||
0.975266 | − | 0.221034i | \(-0.0709431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2332.61 | + | 3814.39i | −0.127862 | + | 0.209086i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4381.22 | −0.239121 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14022.3 | 0.762029 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.96938 | + | 35.4115i | −0.000539452 | + | 0.00191615i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19827.7i | 1.06830i | 0.845388 | + | 0.534152i | \(0.179369\pi\) | ||||
−0.845388 | + | 0.534152i | \(0.820631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10478.7i | − | 0.562179i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3540.38 | + | 12575.5i | −0.189132 | + | 0.671803i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5581.32 | −0.296898 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5444.68 | 0.288405 | 0.144202 | − | 0.989548i | \(-0.453938\pi\) | ||||
0.144202 | + | 0.989548i | \(0.453938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4343.80 | − | 7103.20i | 0.229121 | − | 0.374671i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18359.5i | − | 0.964330i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10.7284i | − | 0.000561147i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4452.89 | − | 1253.62i | −0.231933 | − | 0.0652960i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4118.06 | 0.213599 | 0.106799 | − | 0.994281i | \(-0.465940\pi\) | ||||
0.106799 | + | 0.994281i | \(0.465940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −509.435 | −0.0263140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6372.08 | − | 1793.93i | −0.327774 | − | 0.0922779i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13005.2i | 0.666208i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26169.4i | − | 1.33504i | −0.744594 | − | 0.667518i | \(-0.767357\pi\) | ||
0.744594 | − | 0.667518i | \(-0.232643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1489.78 | + | 19626.5i | −0.0756889 | + | 0.997131i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17409.0 | 0.880840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28634.0 | −1.44286 | −0.721432 | − | 0.692485i | \(-0.756516\pi\) | ||||
−0.721432 | + | 0.692485i | \(0.756516\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2543.69 | − | 9035.27i | 0.127654 | − | 0.453430i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11615.4i | 0.580539i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1607.43i | − | 0.0800139i | −0.999199 | − | 0.0400070i | \(-0.987262\pi\) | ||
0.999199 | − | 0.0400070i | \(-0.0127380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.83344 | − | 10.0644i | 0.000140471 | − | 0.000498957i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 600.872 | 0.0296687 | 0.0148344 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148344 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18765.0 | 0.922815 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1435.08 | − | 877.593i | −0.0702904 | − | 0.0429845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4074.47i | − | 0.198769i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16005.7i | 0.777707i | 0.921300 | + | 0.388854i | \(0.127129\pi\) | ||||
−0.921300 | + | 0.388854i | \(0.872871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15169.5 | + | 4270.65i | 0.734139 | + | 0.206682i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8655.67 | −0.417235 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16731.0 | −0.803300 | −0.401650 | − | 0.915793i | \(-0.631563\pi\) | ||||
−0.401650 | + | 0.915793i | \(0.631563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8572.38 | + | 2413.38i | 0.409958 | + | 0.115415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2885.92i | 0.137470i | 0.997635 | + | 0.0687349i | \(0.0218963\pi\) | ||||
−0.997635 | + | 0.0687349i | \(0.978104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10954.4i | − | 0.519758i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4995.26 | − | 3054.74i | −0.236083 | − | 0.144372i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.5912 | 0.000639830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5456.60 | 0.255878 | 0.127939 | − | 0.991782i | \(-0.459164\pi\) | ||||
0.127939 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3640.33 | + | 12930.6i | −0.170043 | + | 0.603998i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1995.30i | 0.0928407i | 0.998922 | + | 0.0464204i | \(0.0147814\pi\) | ||||
−0.998922 | + | 0.0464204i | \(0.985219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 27137.0i | − | 1.25779i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2839.66 | − | 10086.5i | 0.131110 | − | 0.465705i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11671.2 | 0.536796 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15315.7 | 0.701714 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14771.5 | − | 13692.8i | 0.674191 | − | 0.624954i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4183.46i | − | 0.190209i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38385.1i | − | 1.73860i | −0.494282 | − | 0.869302i | \(-0.664569\pi\) | ||
0.494282 | − | 0.869302i | \(-0.335431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27230.4 | + | 7666.14i | 1.22868 | + | 0.345909i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6244.45 | 0.280692 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.8137 | −0.00169332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14842.9 | − | 4178.70i | −0.662166 | − | 0.186419i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27449.4i | 1.21996i | 0.792417 | + | 0.609980i | \(0.208822\pi\) | ||||
−0.792417 | + | 0.609980i | \(0.791178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15844.0i | − | 0.701529i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15001.9 | − | 24531.9i | 0.661756 | − | 1.08214i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5441.24 | −0.239125 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2128.91 | 0.0932100 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2902.69 | + | 10310.4i | −0.126617 | + | 0.449745i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 430.948i | − | 0.0187285i | −0.999956 | − | 0.00936424i | \(-0.997019\pi\) | ||
0.999956 | − | 0.00936424i | \(-0.00298077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30047.5i | 1.30100i | 0.759506 | + | 0.650500i | \(0.225441\pi\) | ||||
−0.759506 | + | 0.650500i | \(0.774559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8232.94 | + | 29243.6i | −0.355156 | + | 1.26152i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11653.0 | −0.500841 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14490.0 | 0.620490 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.45480 | − | 8.91995i | 0.000232730 | − | 0.000380572i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 27225.8i | − | 1.15736i | −0.815556 | − | 0.578678i | \(-0.803569\pi\) | ||
0.815556 | − | 0.578678i | \(-0.196431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 41196.3i | − | 1.74485i | −0.488748 | − | 0.872425i | \(-0.662546\pi\) | ||
0.488748 | − | 0.872425i | \(-0.337454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12670.8 | + | 3567.20i | 0.534715 | + | 0.150538i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9322.06 | −0.391971 | −0.195985 | − | 0.980607i | \(-0.562791\pi\) | ||||
−0.195985 | + | 0.980607i | \(0.562791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39860.8 | −1.66999 | −0.834996 | − | 0.550256i | \(-0.814530\pi\) | ||||
−0.834996 | + | 0.550256i | \(0.814530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7443.95 | + | 2095.69i | 0.310743 | + | 0.0874833i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11383.6i | 0.473493i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 19808.9i | − | 0.820975i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30822.6 | + | 28571.7i | −1.27286 | + | 1.17991i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8509.74 | −0.350165 | −0.175083 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175083 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3777.83 | 0.154899 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9092.26 | − | 32295.9i | 0.371476 | − | 1.31949i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12888.2i | − | 0.524693i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3250.57i | 0.131867i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7590.77 | + | 26962.6i | −0.306849 | + | 1.08994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20871.6 | −0.840740 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37505.9 | −1.50548 | −0.752741 | − | 0.658317i | \(-0.771269\pi\) | ||||
−0.752741 | + | 0.658317i | \(0.771269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4157.69 | − | 2542.54i | −0.166304 | − | 0.101700i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40647.9i | − | 1.62019i | −0.586296 | − | 0.810097i | \(-0.699415\pi\) | ||
0.586296 | − | 0.810097i | \(-0.300585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14040.1i | − | 0.557673i | −0.960339 | − | 0.278836i | \(-0.910051\pi\) | ||
0.960339 | − | 0.278836i | \(-0.0899487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11234.4 | + | 3162.81i | 0.444678 | + | 0.125190i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12519.6 | −0.493826 | −0.246913 | − | 0.969038i | \(-0.579416\pi\) | ||||
−0.246913 | + | 0.969038i | \(0.579416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15816.2 | 0.621694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17738.1 | − | 4993.79i | −0.694830 | − | 0.195615i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8623.76i | 0.336641i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.1625i | − | 0.00105668i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16199.9 | + | 9906.68i | 0.628045 | + | 0.384067i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7488.85 | 0.289336 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27995.4 | 1.07792 | 0.538962 | − | 0.842330i | \(-0.318817\pi\) | ||||
0.538962 | + | 0.842330i | \(0.318817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7605.11 | − | 27013.5i | 0.291825 | − | 1.03657i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16934.0i | − | 0.647583i | −0.946128 | − | 0.323792i | \(-0.895042\pi\) | ||
0.946128 | − | 0.323792i | \(-0.104958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5835.41i | − | 0.222398i | −0.993798 | − | 0.111199i | \(-0.964531\pi\) | ||
0.993798 | − | 0.111199i | \(-0.0354691\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1716.75 | − | 6097.93i | 0.0652066 | − | 0.231615i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12966.0 | −0.490818 | −0.245409 | − | 0.969420i | \(-0.578922\pi\) | ||||
−0.245409 | + | 0.969420i | \(0.578922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5669.79 | 0.213902 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9288.98 | − | 18147.5i | −0.349262 | − | 0.682338i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13187.4i | − | 0.494178i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19635.9i | 0.733357i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.0465 | − | 5.64368i | −0.000746191 | − | 0.000210075i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43007.8 | 1.59554 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18700.7 | 0.691465 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13947.7 | + | 3926.69i | 0.514009 | + | 0.144709i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10816.7i | 0.397304i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14718.0i | 0.538812i | 0.963027 | + | 0.269406i | \(0.0868273\pi\) | ||||
−0.963027 | + | 0.269406i | \(0.913173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13276.9 | − | 21711.1i | 0.484453 | − | 0.792202i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38859.8 | −1.41326 | −0.706632 | − | 0.707581i | \(-0.749786\pi\) | ||||
−0.706632 | + | 0.707581i | \(0.749786\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1742.29 | 0.0631559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4776.37 | + | 16965.8i | −0.172570 | + | 0.612975i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3258.63i | − | 0.117349i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38295.3i | 1.37459i | 0.726380 | + | 0.687294i | \(0.241201\pi\) | ||||
−0.726380 | + | 0.687294i | \(0.758799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5066.61 | + | 17996.8i | −0.181271 | + | 0.643880i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.8157 | −0.00127724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30850.2 | −1.09659 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1211.85 | − | 1981.68i | 0.0429369 | − | 0.0702125i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43777.6i | − | 1.54607i | −0.634364 | − | 0.773034i | \(-0.718738\pi\) | ||
0.634364 | − | 0.773034i | \(-0.281262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9474.92i | 0.333542i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39486.3 | − | 11116.6i | −1.38556 | − | 0.390075i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6064.58 | 0.212121 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28384.6 | −0.989631 | −0.494816 | − | 0.868998i | \(-0.664764\pi\) | ||||
−0.494816 | + | 0.868998i | \(0.664764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42517.4 | − | 11969.9i | −1.47764 | − | 0.415999i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 54057.6i | − | 1.87272i | −0.351044 | − | 0.936359i | \(-0.614173\pi\) | ||
0.351044 | − | 0.936359i | \(-0.385827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 23246.8i | − | 0.802780i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3313.08 | − | 3574.10i | −0.114047 | − | 0.123032i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54179.3 | 1.85912 | 0.929562 | − | 0.368665i | \(-0.120185\pi\) | ||||
0.929562 | + | 0.368665i | \(0.120185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7243 | 0.000435247 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10352.6 | + | 36772.7i | −0.353003 | + | 1.25388i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2964.61i | 0.100769i | 0.998730 | + | 0.0503846i | \(0.0160447\pi\) | ||||
−0.998730 | + | 0.0503846i | \(0.983955\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13975.2i | − | 0.473537i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5653.44 | + | 20081.2i | −0.190961 | + | 0.678299i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11791.8 | −0.397058 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −59950.2 | −2.01236 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15849.5 | + | 9692.41i | 0.530367 | + | 0.324334i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 14937.0i | − | 0.498278i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12087.0i | − | 0.401956i | −0.979596 | − | 0.200978i | \(-0.935588\pi\) | ||
0.979596 | − | 0.200978i | \(-0.0644119\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5689.25 | + | 1601.69i | 0.188612 | + | 0.0530998i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34336.2 | 1.13481 | 0.567405 | − | 0.823439i | \(-0.307947\pi\) | ||||
0.567405 | + | 0.823439i | \(0.307947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4422.46 | 0.145712 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.6306 | − | 8.34188i | −0.000973271 | − | 0.000274004i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12445.9i | − | 0.407555i | −0.979017 | − | 0.203777i | \(-0.934678\pi\) | ||
0.979017 | − | 0.203777i | \(-0.0653218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29783.3i | 0.972298i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42612.1 | + | 26058.5i | 1.38685 | + | 0.848097i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50850.7 | −1.64994 | −0.824968 | − | 0.565180i | \(-0.808807\pi\) | ||||
−0.824968 | + | 0.565180i | \(0.808807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12844.7 | 0.415498 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3573.71 | − | 12693.9i | 0.115251 | − | 0.409373i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 28861.3i | − | 0.927945i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16973.3i | 0.544071i | 0.962287 | + | 0.272035i | \(0.0876968\pi\) | ||||
−0.962287 | + | 0.272035i | \(0.912303\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6123.23 | + | 21749.9i | −0.195684 | + | 0.695077i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31555.6 | −1.00541 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20434.2 | 0.649104 | 0.324552 | − | 0.945868i | \(-0.394787\pi\) | ||||
0.324552 | + | 0.945868i | \(0.394787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32481.2 | + | 35040.2i | 1.02869 | + | 1.10973i |
(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 | 384.4.c.d.383.1 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.a.383.11 | ✓ | 12 | ||
4.3 | odd | 2 | 384.4.c.a.383.12 | yes | 12 | ||
8.3 | odd | 2 | 384.4.c.c.383.1 | yes | 12 | ||
8.5 | even | 2 | 384.4.c.b.383.12 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.d.383.2 | yes | 12 | |
16.3 | odd | 4 | 768.4.f.h.383.6 | 12 | |||
16.5 | even | 4 | 768.4.f.g.383.6 | 12 | |||
16.11 | odd | 4 | 768.4.f.e.383.7 | 12 | |||
16.13 | even | 4 | 768.4.f.f.383.7 | 12 | |||
24.5 | odd | 2 | 384.4.c.c.383.2 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.b.383.11 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.h.383.5 | 12 | |||
48.11 | even | 4 | 768.4.f.f.383.8 | 12 | |||
48.29 | odd | 4 | 768.4.f.e.383.8 | 12 | |||
48.35 | even | 4 | 768.4.f.g.383.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.11 | ✓ | 12 | 3.2 | odd | 2 | ||
384.4.c.a.383.12 | yes | 12 | 4.3 | odd | 2 | ||
384.4.c.b.383.11 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.b.383.12 | yes | 12 | 8.5 | even | 2 | ||
384.4.c.c.383.1 | yes | 12 | 8.3 | odd | 2 | ||
384.4.c.c.383.2 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.d.383.1 | yes | 12 | 1.1 | even | 1 | trivial | |
384.4.c.d.383.2 | yes | 12 | 12.11 | even | 2 | inner | |
768.4.f.e.383.7 | 12 | 16.11 | odd | 4 | |||
768.4.f.e.383.8 | 12 | 48.29 | odd | 4 | |||
768.4.f.f.383.7 | 12 | 16.13 | even | 4 | |||
768.4.f.f.383.8 | 12 | 48.11 | even | 4 | |||
768.4.f.g.383.5 | 12 | 48.35 | even | 4 | |||
768.4.f.g.383.6 | 12 | 16.5 | even | 4 | |||
768.4.f.h.383.5 | 12 | 48.5 | odd | 4 | |||
768.4.f.h.383.6 | 12 | 16.3 | odd | 4 |