Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.15 | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.b.239.16 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.99829 | − | 4.79655i | 0.384570 | − | 0.923096i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 16.7287i | − | 1.49626i | −0.663554 | − | 0.748128i | \(-0.730953\pi\) | ||
0.663554 | − | 0.748128i | \(-0.269047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.0137 | − | 19.1697i | −0.704211 | − | 0.709990i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.9218 | 1.66987 | 0.834937 | − | 0.550345i | \(-0.185504\pi\) | ||||
0.834937 | + | 0.550345i | \(0.185504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 73.9074 | 1.57679 | 0.788393 | − | 0.615171i | \(-0.210913\pi\) | ||||
0.788393 | + | 0.615171i | \(0.210913\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −80.2398 | − | 33.4286i | −1.38119 | − | 0.575416i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.3004i | 0.232555i | 0.993217 | + | 0.116277i | \(0.0370961\pi\) | ||||
−0.993217 | + | 0.116277i | \(0.962904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 153.871i | − | 1.85792i | −0.370182 | − | 0.928959i | \(-0.620705\pi\) | ||
0.370182 | − | 0.928959i | \(-0.379295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.5758 | − | 13.9880i | −0.348897 | − | 0.145354i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −111.882 | −1.01430 | −0.507152 | − | 0.861856i | \(-0.669302\pi\) | ||||
−0.507152 | + | 0.861856i | \(0.669302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −154.848 | −1.23878 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −129.943 | + | 52.8935i | −0.926208 | + | 0.377013i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 155.121i | 0.993284i | 0.867955 | + | 0.496642i | \(0.165434\pi\) | ||||
−0.867955 | + | 0.496642i | \(0.834566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.7611i | 0.311477i | 0.987798 | + | 0.155738i | \(0.0497756\pi\) | ||||
−0.987798 | + | 0.155738i | \(0.950224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 121.739 | − | 292.214i | 0.642184 | − | 1.54145i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −117.101 | −0.565532 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −63.0884 | −0.280315 | −0.140158 | − | 0.990129i | \(-0.544761\pi\) | ||||
−0.140158 | + | 0.990129i | \(0.544761\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 147.688 | − | 354.500i | 0.606385 | − | 1.45553i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 458.858i | 1.74784i | 0.486067 | + | 0.873921i | \(0.338431\pi\) | ||||
−0.486067 | + | 0.873921i | \(0.661569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 95.5852i | − | 0.338991i | −0.985531 | − | 0.169495i | \(-0.945786\pi\) | ||
0.985531 | − | 0.169495i | \(-0.0542138\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −320.684 | + | 318.074i | −1.06233 | + | 1.05368i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −70.5132 | −0.218839 | −0.109419 | − | 0.993996i | \(-0.534899\pi\) | ||||
−0.109419 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 78.1857 | + | 32.5729i | 0.214670 | + | 0.0894336i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 417.021i | 1.08080i | 0.841410 | + | 0.540398i | \(0.181726\pi\) | ||||
−0.841410 | + | 0.540398i | \(0.818274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1019.14i | − | 2.49856i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −738.050 | − | 307.478i | −1.71504 | − | 0.714500i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 328.024 | 0.723815 | 0.361907 | − | 0.932214i | \(-0.382126\pi\) | ||||
0.361907 | + | 0.932214i | \(0.382126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −637.654 | −1.33841 | −0.669207 | − | 0.743076i | \(-0.733366\pi\) | ||||
−0.669207 | + | 0.743076i | \(0.733366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −134.188 | + | 133.096i | −0.268351 | + | 0.266167i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1236.37i | − | 2.35928i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 201.474i | − | 0.367372i | −0.982985 | − | 0.183686i | \(-0.941197\pi\) | ||
0.982985 | − | 0.183686i | \(-0.0588030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −223.572 | + | 536.647i | −0.390071 | + | 0.936300i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −394.426 | −0.659293 | −0.329646 | − | 0.944105i | \(-0.606929\pi\) | ||||
−0.329646 | + | 0.944105i | \(0.606929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 977.889 | 1.56785 | 0.783926 | − | 0.620854i | \(-0.213214\pi\) | ||||
0.783926 | + | 0.620854i | \(0.213214\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −309.430 | + | 742.735i | −0.476399 | + | 1.14352i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 426.453i | − | 0.631153i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 514.984i | − | 0.733420i | −0.930335 | − | 0.366710i | \(-0.880484\pi\) | ||
0.930335 | − | 0.366710i | \(-0.119516\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.95806 | + | 728.976i | −0.00817293 | + | 0.999967i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1133.84 | 1.49946 | 0.749728 | − | 0.661746i | \(-0.230184\pi\) | ||||
0.749728 | + | 0.661746i | \(0.230184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 272.684 | 0.347961 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 744.045 | + | 309.976i | 0.916897 | + | 0.381988i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1035.66i | 1.23348i | 0.787167 | + | 0.616740i | \(0.211547\pi\) | ||||
−0.787167 | + | 0.616740i | \(0.788453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 517.352i | − | 0.595969i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 257.867 | + | 107.430i | 0.287523 | + | 0.119785i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2574.06 | −2.77992 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 995.638 | 1.04218 | 0.521092 | − | 0.853501i | \(-0.325525\pi\) | ||||
0.521092 | + | 0.853501i | \(0.325525\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1158.35 | − | 1167.86i | −1.17594 | − | 1.18560i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1457.31i | − | 1.43572i | −0.696190 | − | 0.717858i | \(-0.745123\pi\) | ||
0.696190 | − | 0.717858i | \(-0.254877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 359.018i | 0.343448i | 0.985145 | + | 0.171724i | \(0.0549337\pi\) | ||||
−0.985145 | + | 0.171724i | \(0.945066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −234.000 | + | 561.678i | −0.217487 | + | 0.522040i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −765.314 | −0.691455 | −0.345728 | − | 0.938335i | \(-0.612368\pi\) | ||||
−0.345728 | + | 0.938335i | \(0.612368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 736.101 | 0.646842 | 0.323421 | − | 0.946255i | \(-0.395167\pi\) | ||||
0.323421 | + | 0.946255i | \(0.395167\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −126.069 | + | 302.606i | −0.107801 | + | 0.258758i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1228.45i | − | 1.02268i | −0.859380 | − | 0.511338i | \(-0.829150\pi\) | ||
0.859380 | − | 0.511338i | \(-0.170850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1871.63i | 1.51766i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1405.25 | − | 1416.79i | −1.11039 | − | 1.11950i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 114.103 | 0.0878974 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2380.47 | 1.78848 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2200.93 | + | 916.929i | 1.61343 | + | 0.672168i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 499.315i | 0.357281i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 127.914i | − | 0.0893745i | −0.999001 | − | 0.0446872i | \(-0.985771\pi\) | ||
0.999001 | − | 0.0446872i | \(-0.0142291\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −458.479 | − | 191.007i | −0.312921 | − | 0.130366i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1142.47 | 0.761968 | 0.380984 | − | 0.924582i | \(-0.375585\pi\) | ||||
0.380984 | + | 0.924582i | \(0.375585\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1077.10 | −0.702227 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 884.837 | + | 2173.78i | 0.564108 | + | 1.38584i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 660.795i | 0.412084i | 0.978543 | + | 0.206042i | \(0.0660583\pi\) | ||||
−0.978543 | + | 0.206042i | \(0.933942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 502.841i | 0.306837i | 0.988161 | + | 0.153419i | \(0.0490283\pi\) | ||||
−0.988161 | + | 0.153419i | \(0.950972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −140.906 | + | 338.220i | −0.0841588 | + | 0.202009i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4502.57 | 2.63304 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2594.97 | 1.48621 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −97.9160 | + | 235.031i | −0.0549386 | + | 0.131871i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 470.137i | 0.258491i | 0.991613 | + | 0.129245i | \(0.0412555\pi\) | ||||
−0.991613 | + | 0.129245i | \(0.958745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 833.149i | − | 0.449011i | −0.974473 | − | 0.224506i | \(-0.927923\pi\) | ||
0.974473 | − | 0.224506i | \(-0.0720767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 312.475 | − | 309.931i | 0.165112 | − | 0.163768i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 899.350 | 0.466049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1091.24 | −0.554715 | −0.277358 | − | 0.960767i | \(-0.589459\pi\) | ||||
−0.277358 | + | 0.960767i | \(0.589459\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2000.26 | + | 833.326i | 0.997678 | + | 0.415642i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 783.174i | 0.383371i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 26.3933i | 0.0126827i | 0.999980 | + | 0.00634135i | \(0.00201853\pi\) | ||||
−0.999980 | + | 0.00634135i | \(0.997981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4888.35 | − | 2036.53i | −2.30641 | − | 0.960872i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2067.92 | −0.958206 | −0.479103 | − | 0.877759i | \(-0.659038\pi\) | ||||
−0.479103 | + | 0.877759i | \(0.659038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3265.31 | 1.48626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2949.67 | + | 2925.66i | −1.31910 | + | 1.30837i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2289.25i | 1.00606i | 0.864269 | + | 0.503030i | \(0.167781\pi\) | ||||
−0.864269 | + | 0.503030i | \(0.832219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1083.94i | 0.468216i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 655.485 | − | 1573.38i | 0.278358 | − | 0.668150i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 108.183 | 0.0451731 | 0.0225865 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225865 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 752.631 | 0.309075 | 0.154538 | − | 0.987987i | \(-0.450611\pi\) | ||||
0.154538 | + | 0.987987i | \(0.450611\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1274.22 | + | 3058.54i | −0.514714 | + | 1.23548i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1055.38i | 0.419423i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 993.051i | 0.388337i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 370.254 | + | 909.604i | 0.142498 | + | 0.350074i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2279.55 | 0.863572 | 0.431786 | − | 0.901976i | \(-0.357884\pi\) | ||||
0.431786 | + | 0.901976i | \(0.357884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −766.149 | −0.285744 | −0.142872 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142872 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5930.31 | − | 2470.62i | −2.17784 | − | 0.907308i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3890.03i | 1.40687i | 0.710760 | + | 0.703435i | \(0.248351\pi\) | ||||
−0.710760 | + | 0.703435i | \(0.751649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2577.77i | 0.918257i | 0.888370 | + | 0.459129i | \(0.151838\pi\) | ||||
−0.888370 | + | 0.459129i | \(0.848162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −966.378 | − | 402.602i | −0.339119 | − | 0.141280i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1085.85 | 0.375426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7676.07 | 2.61522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2127.29 | + | 2144.75i | 0.714285 | + | 0.720147i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9374.11i | − | 3.10249i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4839.87i | − | 1.57910i | −0.613685 | − | 0.789551i | \(-0.710313\pi\) | ||
0.613685 | − | 0.789551i | \(-0.289687\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −788.176 | + | 1891.88i | −0.253544 | + | 0.608590i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1599.01 | −0.507217 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 376.327 | 0.117727 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1954.10 | − | 4690.49i | 0.602950 | − | 1.44728i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1204.72i | 0.366689i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1258.94i | 0.378049i | 0.981972 | + | 0.189024i | \(0.0605325\pi\) | ||||
−0.981972 | + | 0.189024i | \(0.939467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2944.23 | + | 2968.39i | 0.872365 | + | 0.879524i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3028.13 | −0.885393 | −0.442696 | − | 0.896672i | \(-0.645978\pi\) | ||||
−0.442696 | + | 0.896672i | \(0.645978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4162.54 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705066\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2045.50 | − | 852.175i | −0.582615 | − | 0.242723i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 631.397i | 0.177529i | 0.996053 | + | 0.0887644i | \(0.0282918\pi\) | ||||
−0.996053 | + | 0.0887644i | \(0.971708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1179.59i | 0.327439i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2470.14 | − | 1029.08i | −0.677017 | − | 0.282052i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1634.45 | 0.442358 | 0.221179 | − | 0.975233i | \(-0.429010\pi\) | ||||
0.221179 | + | 0.975233i | \(0.429010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3537.63 | −0.945555 | −0.472777 | − | 0.881182i | \(-0.656748\pi\) | ||||
−0.472777 | + | 0.881182i | \(0.656748\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3484.66 | + | 1485.28i | 0.919922 | + | 0.392102i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 819.704i | 0.213751i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11372.2i | − | 2.92954i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2265.73 | − | 5438.50i | 0.576646 | − | 1.38414i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3866.21 | 0.972244 | 0.486122 | − | 0.873891i | \(-0.338411\pi\) | ||||
0.486122 | + | 0.873891i | \(0.338411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6816.05 | −1.69376 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 544.901 | − | 1307.94i | 0.133816 | − | 0.321202i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2615.37i | − | 0.634794i | −0.948293 | − | 0.317397i | \(-0.897191\pi\) | ||
0.948293 | − | 0.317397i | \(-0.102809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 441.619i | 0.105949i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2973.63 | − | 2949.43i | 0.705223 | − | 0.699482i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7004.30 | −1.64222 | −0.821110 | − | 0.570770i | \(-0.806645\pi\) | ||||
−0.821110 | + | 0.570770i | \(0.806645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6976.19 | 1.61715 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4967.59 | + | 2069.54i | 1.13862 | + | 0.474360i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 404.298i | − | 0.0916374i | −0.998950 | − | 0.0458187i | \(-0.985410\pi\) | ||
0.998950 | − | 0.0458187i | \(-0.0145897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 758.555i | − | 0.170033i | −0.996380 | − | 0.0850165i | \(-0.972906\pi\) | ||
0.996380 | − | 0.0850165i | \(-0.0270943\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2481.50 | − | 1033.82i | −0.550137 | − | 0.229192i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9433.62 | −2.06861 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1084.77 | −0.235298 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1030.59 | − | 1022.20i | 0.221145 | − | 0.219345i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4094.10i | − | 0.869159i | −0.900633 | − | 0.434580i | \(-0.856897\pi\) | ||
0.900633 | − | 0.434580i | \(-0.143103\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5030.95i | − | 1.05675i | −0.849013 | − | 0.528373i | \(-0.822802\pi\) | ||
0.849013 | − | 0.528373i | \(-0.177198\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5143.70 | + | 12346.6i | −1.06908 | + | 2.56613i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3212.00 | 0.660622 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4647.30 | 0.945918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1989.57 | − | 4775.62i | 0.400793 | − | 0.962035i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2585.51i | − | 0.515519i | −0.966209 | − | 0.257759i | \(-0.917016\pi\) | ||
0.966209 | − | 0.257759i | \(-0.0829842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5487.40i | − | 1.08301i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7916.39 | + | 3222.37i | −1.54665 | + | 0.629565i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8268.91 | −1.59934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −669.097 | −0.128127 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6990.03 | − | 2912.11i | −1.32530 | − | 0.552134i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10667.1i | 2.00261i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 766.680i | − | 0.142530i | −0.997457 | − | 0.0712651i | \(-0.977296\pi\) | ||
0.997457 | − | 0.0712651i | \(-0.0227036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1722.05 | + | 717.421i | 0.317035 | + | 0.132080i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5681.41 | 1.03589 | 0.517947 | − | 0.855412i | \(-0.326696\pi\) | ||||
0.517947 | + | 0.855412i | \(0.326696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9636.05 | −1.74013 | −0.870067 | − | 0.492934i | \(-0.835924\pi\) | ||||
−0.870067 | + | 0.492934i | \(0.835924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2226.52 | + | 2244.79i | 0.398254 | + | 0.401522i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1585.82i | − | 0.280972i | −0.990083 | − | 0.140486i | \(-0.955133\pi\) | ||
0.990083 | − | 0.140486i | \(-0.0448666\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9450.26i | 1.65866i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1529.32 | + | 3670.86i | −0.265913 | + | 0.638279i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2508.16 | 0.432068 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11444.4 | −1.95330 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1470.94 | − | 3530.74i | 0.248756 | − | 0.597097i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 493.593i | 0.0827132i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3330.99i | 0.553135i | 0.960995 | + | 0.276567i | \(0.0891969\pi\) | ||||
−0.960995 | + | 0.276567i | \(0.910803\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1199.54 | + | 1209.39i | 0.197401 | + | 0.199021i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3370.38 | −0.549683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10234.2 | 1.65428 | 0.827140 | − | 0.561996i | \(-0.189967\pi\) | ||||
0.827140 | + | 0.561996i | \(0.189967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5892.30 | − | 2454.79i | −0.944028 | − | 0.393291i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3275.22i | 0.520127i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8977.38 | + | 3740.06i | 1.40095 | + | 0.583647i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4657.40 | 0.720525 | 0.360263 | − | 0.932851i | \(-0.382687\pi\) | ||||
0.360263 | + | 0.932851i | \(0.382687\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3280.13 | 0.503098 | 0.251549 | − | 0.967845i | \(-0.419060\pi\) | ||||
0.251549 | + | 0.967845i | \(0.419060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9603.78 | + | 3909.22i | −1.46043 | + | 0.594469i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6977.11i | 1.05200i | 0.850486 | + | 0.525998i | \(0.176308\pi\) | ||||
−0.850486 | + | 0.525998i | \(0.823692\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6598.22i | 0.986471i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 228.010 | − | 547.300i | 0.0338027 | − | 0.0811377i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 457.102 | 0.0672004 | 0.0336002 | − | 0.999435i | \(-0.489303\pi\) | ||||
0.0336002 | + | 0.999435i | \(0.489303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16817.3 | −2.45186 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4756.86 | − | 11418.0i | 0.687797 | − | 1.65094i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 16358.8i | − | 2.34591i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6117.95i | − | 0.870175i | −0.900388 | − | 0.435088i | \(-0.856717\pi\) | ||
0.900388 | − | 0.435088i | \(-0.143283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8796.19 | − | 8724.59i | 1.24095 | − | 1.23085i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2919.14 | 0.408502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2466.70 | −0.342415 | −0.171208 | − | 0.985235i | \(-0.554767\pi\) | ||||
−0.171208 | + | 0.985235i | \(0.554767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2394.99 | + | 997.775i | 0.329804 | + | 0.137400i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11464.6i | 1.56620i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6021.87i | 0.816155i | 0.912947 | + | 0.408078i | \(0.133801\pi\) | ||||
−0.912947 | + | 0.408078i | \(0.866199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −613.547 | − | 255.609i | −0.0825012 | − | 0.0343708i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4212.17 | 0.561963 | 0.280982 | − | 0.959713i | \(-0.409340\pi\) | ||||
0.280982 | + | 0.959713i | \(0.409340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7133.98 | −0.944367 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1832.34 | + | 1817.43i | −0.240680 | + | 0.238721i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2689.11i | − | 0.350497i | −0.984524 | − | 0.175248i | \(-0.943927\pi\) | ||
0.984524 | − | 0.175248i | \(-0.0560729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1823.72i | − | 0.235881i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2282.98 | − | 5479.90i | 0.293030 | − | 0.703369i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8614.98 | −1.09738 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8370.78 | −1.05823 | −0.529115 | − | 0.848550i | \(-0.677476\pi\) | ||||
−0.529115 | + | 0.848550i | \(0.677476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2152.35 | + | 5166.35i | −0.270056 | + | 0.648223i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4771.81i | − | 0.594247i | −0.954839 | − | 0.297123i | \(-0.903973\pi\) | ||
0.954839 | − | 0.297123i | \(-0.0960272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3973.34i | 0.491132i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12194.8 | + | 99.6704i | 1.49621 | + | 0.0122288i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3843.46 | −0.468091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3505.84 | −0.423846 | −0.211923 | − | 0.977286i | \(-0.567973\pi\) | ||||
−0.211923 | + | 0.977286i | \(0.567973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3169.53 | + | 1320.46i | 0.380393 | + | 0.158475i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2296.17i | − | 0.273576i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 18967.6i | − | 2.24357i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2411.90 | + | 1004.82i | 0.283240 | + | 0.118001i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13302.4 | 1.55099 | 0.775496 | − | 0.631352i | \(-0.217500\pi\) | ||||
0.775496 | + | 0.631352i | \(0.217500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5120.87 | 0.592816 | 0.296408 | − | 0.955061i | \(-0.404211\pi\) | ||||
0.296408 | + | 0.955061i | \(0.404211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1340.72 | + | 1351.72i | 0.154109 | + | 0.155373i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2524.08i | − | 0.288085i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4463.58i | 0.505873i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8997.43 | − | 21596.8i | 1.01259 | − | 2.43054i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17758.5 | 1.98468 | 0.992339 | − | 0.123544i | \(-0.0394259\pi\) | ||||
0.992339 | + | 0.123544i | \(0.0394259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17278.3 | 1.91765 | 0.958826 | − | 0.283994i | \(-0.0916595\pi\) | ||||
0.958826 | + | 0.283994i | \(0.0916595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5185.48 | − | 12446.9i | 0.571552 | − | 1.37191i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17215.4i | 1.88449i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4721.22i | − | 0.513284i | −0.966507 | − | 0.256642i | \(-0.917384\pi\) | ||
0.966507 | − | 0.256642i | \(-0.0826162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 931.672 | + | 939.317i | 0.100602 | + | 0.101427i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2733.59 | −0.293176 | −0.146588 | − | 0.989198i | \(-0.546829\pi\) | ||||
−0.146588 | + | 0.989198i | \(0.546829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17325.2 | 1.84560 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2255.03 | + | 939.467i | 0.238611 | + | 0.0994078i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2204.08i | − | 0.231663i | −0.993269 | − | 0.115832i | \(-0.963047\pi\) | ||
0.993269 | − | 0.115832i | \(-0.0369533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27954.5i | 2.91868i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3996.24 | − | 1664.87i | −0.414480 | − | 0.172676i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8654.60 | −0.891723 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1401.18 | −0.143423 | −0.0717116 | − | 0.997425i | \(-0.522846\pi\) | ||||
−0.0717116 | + | 0.997425i | \(0.522846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −862.185 | − | 2118.13i | −0.0876762 | − | 0.215394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5775.00i | 0.583446i | 0.956503 | + | 0.291723i | \(0.0942285\pi\) | ||||
−0.956503 | + | 0.291723i | \(0.905772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15866.2i | 1.59258i | 0.604916 | + | 0.796289i | \(0.293207\pi\) | ||||
−0.604916 | + | 0.796289i | \(0.706793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1797.16 | − | 4313.77i | 0.179229 | − | 0.430208i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4802.77 | 0.475900 | 0.237950 | − | 0.971277i | \(-0.423524\pi\) | ||||
0.237950 | + | 0.971277i | \(0.423524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1410.32 | −0.138854 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2180.61 | + | 5234.17i | −0.213327 | + | 0.512055i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5823.23i | − | 0.566072i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23826.6i | 2.30156i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7994.18 | − | 7929.11i | 0.767355 | − | 0.761109i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5778.37 | −0.551191 | −0.275595 | − | 0.961274i | \(-0.588875\pi\) | ||||
−0.275595 | + | 0.961274i | \(0.588875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4662.70 | −0.441997 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3756.53 | + | 1565.01i | 0.353888 | + | 0.147433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16655.7i | − | 1.55937i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8916.11i | 0.829625i | 0.909907 | + | 0.414813i | \(0.136153\pi\) | ||||
−0.909907 | + | 0.414813i | \(0.863847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 126.597 | + | 52.7413i | 0.0117074 | + | 0.00487739i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9826.22 | −0.903159 | −0.451579 | − | 0.892231i | \(-0.649139\pi\) | ||||
−0.451579 | + | 0.892231i | \(0.649139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2528.54 | −0.230993 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19536.7 | + | 19377.6i | −1.77395 | + | 1.75951i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2760.98i | 0.249189i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14608.3i | − | 1.31053i | −0.755398 | − | 0.655266i | \(-0.772557\pi\) | ||
0.755398 | − | 0.655266i | \(-0.227443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4132.29 | + | 9918.87i | −0.368497 | + | 0.884515i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10453.8 | −0.926662 | −0.463331 | − | 0.886185i | \(-0.653346\pi\) | ||||
−0.463331 | + | 0.886185i | \(0.653346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24378.8 | −2.14820 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6525.02 | − | 15662.2i | 0.571570 | − | 1.37196i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9286.13i | 0.808645i | 0.914616 | + | 0.404323i | \(0.132493\pi\) | ||||
−0.914616 | + | 0.404323i | \(0.867507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6845.22i | − | 0.592593i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8138.78 | + | 19994.5i | 0.700460 | + | 1.72082i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6005.89 | 0.513886 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4295.80 | −0.365433 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10980.5 | + | 4574.57i | 0.928689 | + | 0.386901i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2764.21i | − | 0.232442i | −0.993223 | − | 0.116221i | \(-0.962922\pi\) | ||
0.993223 | − | 0.116221i | \(-0.0370781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11042.1i | 0.923209i | 0.887086 | + | 0.461605i | \(0.152726\pi\) | ||||
−0.887086 | + | 0.461605i | \(0.847274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5199.15 | + | 2166.01i | 0.432208 | + | 0.180062i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −876.327 | −0.0724353 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 350.576 | 0.0288137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6236.95 | − | 6288.13i | −0.509718 | − | 0.513902i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33913.0i | 2.75598i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12802.7i | 1.03459i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 216.181 | − | 518.905i | 0.0173722 | − | 0.0416991i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2985.17 | −0.238554 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23666.7 | 1.88080 | 0.940398 | − | 0.340075i | \(-0.110452\pi\) | ||||
0.940398 | + | 0.340075i | \(0.110452\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1503.97 | − | 3610.03i | 0.118861 | − | 0.285306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12314.0i | − | 0.967841i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6867.33i | − | 0.536793i | −0.963309 | − | 0.268397i | \(-0.913506\pi\) | ||
0.963309 | − | 0.268397i | \(-0.0864938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12124.2 | + | 12223.7i | 0.942526 | + | 0.950261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23868.6 | 1.84544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3604.88 | −0.277207 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5062.19 | + | 2108.96i | 0.387168 | + | 0.161298i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17973.1i | − | 1.36722i | −0.729845 | − | 0.683612i | \(-0.760408\pi\) | ||
0.729845 | − | 0.683612i | \(-0.239592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7064.46i | − | 0.534516i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4763.21 | + | 1984.40i | 0.358472 | + | 0.149343i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19148.6 | 1.43342 | 0.716711 | − | 0.697370i | \(-0.245647\pi\) | ||||
0.716711 | + | 0.697370i | \(0.245647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20550.2 | −1.53019 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5102.83 | + | 41.7064i | 0.377952 | + | 0.00308908i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 13679.2i | − | 1.00784i | −0.863750 | − | 0.503921i | \(-0.831890\pi\) | ||
0.863750 | − | 0.503921i | \(-0.168110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10288.3i | 0.754033i | 0.926207 | + | 0.377017i | \(0.123050\pi\) | ||||
−0.926207 | + | 0.377017i | \(0.876950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4555.19 | − | 10934.0i | 0.332104 | − | 0.797160i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17324.7 | 1.25650 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13939.4 | −1.00573 | −0.502864 | − | 0.864365i | \(-0.667720\pi\) | ||||
−0.502864 | + | 0.864365i | \(0.667720\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1530.99 | + | 3674.87i | −0.109889 | + | 0.263769i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 7936.86i | − | 0.566741i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25405.7i | 1.80479i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23700.9 | + | 23508.0i | −1.67506 | + | 1.66143i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8490.79 | −0.597023 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8272.27 | 0.578698 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18658.7 | + | 7773.40i | 1.29868 | + | 0.541040i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3335.30i | 0.230968i | 0.993309 | + | 0.115484i | \(0.0368420\pi\) | ||||
−0.993309 | + | 0.115484i | \(0.963158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1908.79i | − | 0.131517i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12364.4 | + | 5151.12i | 0.847639 | + | 0.353134i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14950.3 | −1.01978 | −0.509892 | − | 0.860238i | \(-0.670315\pi\) | ||||
−0.509892 | + | 0.860238i | \(0.670315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15554.3 | −1.05570 | −0.527849 | − | 0.849338i | \(-0.677001\pi\) | ||||
−0.527849 | + | 0.849338i | \(0.677001\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3862.20 | + | 3830.76i | −0.260831 | + | 0.258707i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 39822.0i | − | 2.67603i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 23162.9i | − | 1.54885i | −0.632663 | − | 0.774427i | \(-0.718038\pi\) | ||
0.632663 | − | 0.774427i | \(-0.281962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2169.83 | − | 5208.32i | 0.144378 | − | 0.346554i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5211.45 | −0.345062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −517.112 | −0.0340717 | −0.0170359 | − | 0.999855i | \(-0.505423\pi\) | ||||
−0.0170359 | + | 0.999855i | \(0.505423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15339.0 | − | 36818.6i | 1.00574 | − | 2.41410i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3318.03i | − | 0.216497i | −0.994124 | − | 0.108249i | \(-0.965476\pi\) | ||
0.994124 | − | 0.108249i | \(-0.0345242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6295.88i | − | 0.408809i | −0.978886 | − | 0.204405i | \(-0.934474\pi\) | ||
0.978886 | − | 0.204405i | \(-0.0655258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14538.3 | − | 5917.83i | 0.939457 | − | 0.382406i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7249.61 | 0.466211 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11003.1 | −0.704199 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −44963.3 | − | 18732.1i | −2.86390 | − | 1.19313i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1028.37i | − | 0.0651886i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16754.4i | − | 1.05702i | −0.848926 | − | 0.528511i | \(-0.822750\pi\) | ||
0.848926 | − | 0.528511i | \(-0.177250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23214.7 | − | 9671.45i | −1.45766 | − | 0.607276i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2139.83 | −0.133727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3621.46 | −0.225255 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7499.50 | + | 7561.05i | 0.464281 | + | 0.468091i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5871.80i | 0.361813i | 0.983500 | + | 0.180907i | \(0.0579032\pi\) | ||||
−0.983500 | + | 0.180907i | \(0.942097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12954.8i | 0.794539i | 0.917702 | + | 0.397269i | \(0.130042\pi\) | ||||
−0.917702 | + | 0.397269i | \(0.869958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3195.28 | + | 7669.74i | −0.195061 | + | 0.468210i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20113.4 | −1.22216 | −0.611080 | − | 0.791569i | \(-0.709265\pi\) | ||||
−0.611080 | + | 0.791569i | \(0.709265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19983.8 | 1.20868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 752.010 | − | 1805.07i | 0.0452743 | − | 0.108673i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31517.3i | 1.88877i | 0.328844 | + | 0.944384i | \(0.393341\pi\) | ||||
−0.328844 | + | 0.944384i | \(0.606659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19111.9i | − | 1.14010i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18593.3 | − | 18745.9i | −1.10410 | − | 1.11316i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19556.1 | −1.15599 | −0.577994 | − | 0.816041i | \(-0.696164\pi\) | ||||
−0.577994 | + | 0.816041i | \(0.696164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26582.3 | 1.56419 | 0.782097 | − | 0.623157i | \(-0.214150\pi\) | ||||
0.782097 | + | 0.623157i | \(0.214150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5778.50 | + | 2407.38i | 0.338489 | + | 0.141018i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18018.4i | 1.05071i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 17355.2i | − | 1.00749i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6038.57 | + | 2515.72i | 0.348975 | + | 0.145386i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38847.1 | −2.23498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 201.721 | 0.0115539 | 0.00577695 | − | 0.999983i | \(-0.498161\pi\) | ||||
0.00577695 | + | 0.999983i | \(0.498161\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20121.5 | − | 8190.44i | 1.14737 | − | 0.467038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4804.24i | − | 0.272736i | −0.990658 | − | 0.136368i | \(-0.956457\pi\) | ||
0.990658 | − | 0.136368i | \(-0.0435429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6969.47i | − | 0.393908i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6051.07 | + | 14524.6i | −0.340496 | + | 0.817302i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3043.76 | −0.170521 | −0.0852607 | − | 0.996359i | \(-0.527172\pi\) | ||||
−0.0852607 | + | 0.996359i | \(0.527172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11054.2 | 0.616583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8317.94 | + | 19965.8i | −0.461935 | + | 1.10880i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30820.9i | 1.70418i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8025.16i | − | 0.441811i | −0.975295 | − | 0.220906i | \(-0.929099\pi\) | ||
0.975295 | − | 0.220906i | \(-0.0709013\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8174.99 | + | 8108.45i | −0.448113 | + | 0.444465i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8411.85 | 0.459108 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7479.57 | −0.406469 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3028.52 | + | 1261.71i | 0.163876 | + | 0.0682723i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9256.11i | 0.498714i | 0.968412 | + | 0.249357i | \(0.0802192\pi\) | ||||
−0.968412 | + | 0.249357i | \(0.919781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9707.47i | 0.520803i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5657.97 | + | 2357.16i | 0.302257 | + | 0.125923i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10201.1 | −0.542650 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10786.1 | −0.571342 | −0.285671 | − | 0.958328i | \(-0.592217\pi\) | ||||
−0.285671 | + | 0.958328i | \(0.592217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9872.10 | + | 9791.74i | −0.520721 | + | 0.516483i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6014.89i | − | 0.315932i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 75322.0i | − | 3.93970i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3266.09 | − | 7839.69i | 0.170118 | − | 0.408338i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16903.4 | −0.876759 | −0.438379 | − | 0.898790i | \(-0.644447\pi\) | ||||
−0.438379 | + | 0.898790i | \(0.644447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2513.13 | 0.129811 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7069.19 | + | 16968.4i | −0.363632 | + | 0.872837i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 24020.2i | − | 1.23046i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17968.4i | 0.916661i | 0.888782 | + | 0.458330i | \(0.151552\pi\) | ||||
−0.888782 | + | 0.458330i | \(0.848448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14087.6 | − | 13746.3i | 0.715722 | − | 0.698385i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1558.08 | 0.0788339 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26141.6 | 1.31728 | 0.658638 | − | 0.752460i | \(-0.271133\pi\) | ||||
0.658638 | + | 0.752460i | \(0.271133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3931.75 | + | 1638.00i | 0.197313 | + | 0.0822023i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12274.1i | − | 0.613465i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20364.7i | 1.01370i | 0.862033 | + | 0.506851i | \(0.169191\pi\) | ||||
−0.862033 | + | 0.506851i | \(0.830809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54547.4 | − | 22724.9i | −2.70425 | − | 1.12661i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5300.06 | 0.261696 | 0.130848 | − | 0.991402i | \(-0.458230\pi\) | ||||
0.130848 | + | 0.991402i | \(0.458230\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7864.75 | 0.386768 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21558.5 | − | 21735.4i | −1.05593 | − | 1.06460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5357.20i | 0.261346i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38359.6i | − | 1.86386i | −0.362634 | − | 0.931932i | \(-0.618123\pi\) | ||
0.362634 | − | 0.931932i | \(-0.381877\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7725.80 | − | 18544.5i | 0.373896 | − | 0.897474i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13937.5 | −0.671836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29775.4 | −1.42960 | −0.714799 | − | 0.699330i | \(-0.753482\pi\) | ||||
−0.714799 | + | 0.699330i | \(0.753482\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13620.4 | + | 32693.5i | −0.651370 | + | 1.56350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24451.7i | 1.16475i | 0.812921 | + | 0.582373i | \(0.197876\pi\) | ||||
−0.812921 | + | 0.582373i | \(0.802124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5152.71i | − | 0.244483i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5184.73 | − | 5227.28i | −0.245038 | − | 0.247049i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24243.4 | 1.14130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20070.8 | 0.941187 | 0.470593 | − | 0.882350i | \(-0.344040\pi\) | ||||
0.470593 | + | 0.882350i | \(0.344040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12544.7 | − | 5226.25i | −0.585976 | − | 0.244123i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39134.5i | − | 1.82092i | −0.413597 | − | 0.910460i | \(-0.635728\pi\) | ||
0.413597 | − | 0.910460i | \(-0.364272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8324.79i | − | 0.385852i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2118.24 | + | 882.480i | 0.0978012 | + | 0.0407449i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 70605.0 | 3.24735 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24029.2 | −1.10094 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8204.89 | − | 20156.9i | −0.374481 | − | 0.919988i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18254.9i | 0.829996i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9041.56i | − | 0.409526i | −0.978812 | − | 0.204763i | \(-0.934358\pi\) | ||
0.978812 | − | 0.204763i | \(-0.0656423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13996.6 | + | 33596.5i | −0.631549 | + | 1.51593i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8599.12 | −0.386535 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47127.4 | −2.11039 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13940.4 | − | 33461.6i | 0.621907 | − | 1.49278i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36193.9i | 1.60860i | 0.594222 | + | 0.804301i | \(0.297460\pi\) | ||||
−0.594222 | + | 0.804301i | \(0.702540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1149.39i | − | 0.0508919i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19853.3 | − | 19691.7i | 0.875758 | − | 0.868630i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59574.8 | 2.61812 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13101.4 | 0.573621 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1939.23 | − | 807.902i | −0.0845901 | − | 0.0352410i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13745.8i | 0.597377i | 0.954351 | + | 0.298689i | \(0.0965492\pi\) | ||||
−0.954351 | + | 0.298689i | \(0.903451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38555.3i | 1.66937i | 0.550728 | + | 0.834685i | \(0.314350\pi\) | ||||
−0.550728 | + | 0.834685i | \(0.685650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3638.44 | − | 1515.81i | −0.156957 | − | 0.0653896i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 441.524 | 0.0189766 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14707.8 | −0.629817 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9917.50 | + | 9836.78i | −0.423133 | + | 0.419688i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36235.3i | 1.54034i | 0.637838 | + | 0.770171i | \(0.279829\pi\) | ||||
−0.637838 | + | 0.770171i | \(0.720171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23707.3i | − | 1.00411i | −0.864835 | − | 0.502056i | \(-0.832577\pi\) | ||
0.864835 | − | 0.502056i | \(-0.167423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18851.1 | + | 45248.8i | −0.795527 | + | 1.90953i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35174.4 | −1.47900 | −0.739500 | − | 0.673156i | \(-0.764938\pi\) | ||||
−0.739500 | + | 0.673156i | \(0.764938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24029.0 | 1.00671 | 0.503355 | − | 0.864080i | \(-0.332099\pi\) | ||||
0.503355 | + | 0.864080i | \(0.332099\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2167.68 | + | 5203.15i | −0.0904887 | + | 0.217203i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 798.720i | − | 0.0332221i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34593.5i | 1.43372i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2843.61 | − | 6985.89i | −0.117431 | − | 0.288492i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46306.1 | 1.90544 | 0.952720 | − | 0.303850i | \(-0.0982722\pi\) | ||||
0.952720 | + | 0.303850i | \(0.0982722\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 326.470 | 0.0133860 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19637.6 | − | 8181.19i | −0.802317 | − | 0.334253i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 54624.2i | − | 2.22382i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 16663.3i | − | 0.675982i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24131.2 | − | 10053.3i | −0.975477 | − | 0.406393i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7058.45 | 0.284325 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44352.0 | 1.78028 | 0.890142 | − | 0.455684i | \(-0.150605\pi\) | ||||
0.890142 | + | 0.455684i | \(0.150605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48942.3 | + | 49344.0i | 1.95765 | + | 1.97372i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42349.5i | 1.68802i | 0.536328 | + | 0.844009i | \(0.319811\pi\) | ||||
−0.536328 | + | 0.844009i | \(0.680189\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41927.4i | 1.66536i | 0.553755 | + | 0.832680i | \(0.313194\pi\) | ||||
−0.553755 | + | 0.832680i | \(0.686806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6418.50 | − | 15406.5i | 0.254056 | − | 0.609818i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28670.6 | −1.13089 | −0.565445 | − | 0.824786i | \(-0.691296\pi\) | ||||
−0.565445 | + | 0.824786i | \(0.691296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38296.0 | 1.50532 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9286.63 | − | 22291.0i | 0.363772 | − | 0.873173i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 31373.7i | − | 1.22472i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14890.4i | − | 0.579267i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18930.8 | − | 19086.1i | −0.733917 | − | 0.739940i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3495.21 | 0.135039 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1035.04 | −0.0398529 | −0.0199264 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199264 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12401.5 | − | 5166.58i | −0.475873 | − | 0.198253i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7978.04i | − | 0.305093i | −0.988296 | − | 0.152547i | \(-0.951253\pi\) | ||
0.988296 | − | 0.152547i | \(-0.0487474\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22682.9i | 0.864484i | 0.901758 | + | 0.432242i | \(0.142277\pi\) | ||||
−0.901758 | + | 0.432242i | \(0.857723\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26320.6 | − | 10965.4i | −0.999724 | − | 0.416494i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41695.5 | −1.57835 | −0.789175 | − | 0.614168i | \(-0.789492\pi\) | ||||
−0.789175 | + | 0.614168i | \(0.789492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −895.400 | −0.0337804 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −362.976 | + | 44410.5i | −0.0136478 | + | 1.66982i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10849.9i | 0.406584i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1809.76i | − | 0.0675905i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16523.6 | + | 39662.2i | −0.615060 | + | 1.47635i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8339.47 | −0.309385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6797.61 | −0.251344 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1337.05 | + | 3209.35i | −0.0492737 | + | 0.118273i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12590.5i | − | 0.462456i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5918.76i | − | 0.216680i | −0.994114 | − | 0.108340i | \(-0.965446\pi\) | ||
0.994114 | − | 0.108340i | \(-0.0345536\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27936.2 | + | 27708.8i | −1.01934 | + | 1.01105i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16275.8 | −0.591921 | −0.295961 | − | 0.955200i | \(-0.595640\pi\) | ||||
−0.295961 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69075.5 | 2.50390 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 51165.2 | + | 21315.9i | 1.84860 | + | 0.770145i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7997.27i | − | 0.287997i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10367.7i | 0.372141i | 0.982536 | + | 0.186070i | \(0.0595752\pi\) | ||||
−0.982536 | + | 0.186070i | \(0.940425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3677.42 | − | 1532.05i | −0.131569 | − | 0.0548129i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29151.0 | −1.03956 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9769.10 | 0.347250 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6882.29 | − | 6826.27i | 0.243845 | − | 0.241860i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 38112.2i | − | 1.34598i | −0.739649 | − | 0.672992i | \(-0.765009\pi\) | ||
0.739649 | − | 0.672992i | \(-0.234991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7539.68i | 0.265417i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11353.1 | − | 27251.2i | 0.398375 | − | 0.956230i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16612.4 | 0.581052 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36739.1 | −1.28091 | −0.640456 | − | 0.767995i | \(-0.721255\pi\) | ||||
−0.640456 | + | 0.767995i | \(0.721255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19255.6 | + | 46219.8i | −0.669204 | + | 1.60631i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31135.3i | 1.07862i | 0.842107 | + | 0.539310i | \(0.181315\pi\) | ||||
−0.842107 | + | 0.539310i | \(0.818685\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 51337.9i | − | 1.77284i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15216.4 | − | 6193.86i | 0.523800 | − | 0.213213i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16651.0 | −0.571368 | −0.285684 | − | 0.958324i | \(-0.592221\pi\) | ||||
−0.285684 | + | 0.958324i | \(0.592221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72273.2 | 2.47217 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7606.44 | − | 3168.91i | −0.259364 | − | 0.108054i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21802.6i | − | 0.741086i | −0.928815 | − | 0.370543i | \(-0.879172\pi\) | ||
0.928815 | − | 0.370543i | \(-0.120828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38133.8i | − | 1.29213i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45328.6 | + | 18884.3i | 1.53110 | + | 0.637872i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4625.56 | 0.155753 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26900.7 | 0.902982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14551.5 | + | 14670.9i | 0.486931 | + | 0.490927i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12816.6i | 0.427546i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2820.93i | 0.0938106i | 0.998899 | + | 0.0469053i | \(0.0149359\pi\) | ||||
−0.998899 | + | 0.0469053i | \(0.985064\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5012.02 | − | 12030.5i | 0.166160 | − | 0.398840i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40165.3 | −1.32746 | −0.663730 | − | 0.747972i | \(-0.731028\pi\) | ||||
−0.663730 | + | 0.747972i | \(0.731028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3519.89 | 0.115974 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22869.2 | + | 54893.6i | −0.751180 | + | 1.80308i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18264.9i | − | 0.598102i | −0.954237 | − | 0.299051i | \(-0.903330\pi\) | ||
0.954237 | − | 0.299051i | \(-0.0966701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63094.2i | 2.05976i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13996.0 | − | 14110.9i | −0.455513 | − | 0.459251i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1405.50 | 0.0456038 | 0.0228019 | − | 0.999740i | \(-0.492741\pi\) | ||||
0.0228019 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65075.0 | 2.10504 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2367.54 | + | 986.339i | 0.0763522 | + | 0.0318090i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10694.3i | 0.343840i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32951.8i | 1.05625i | 0.849165 | + | 0.528127i | \(0.177105\pi\) | ||||
−0.849165 | + | 0.528127i | \(0.822895\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15977.2 | + | 6656.26i | 0.510596 | + | 0.212719i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43122.6 | 1.37395 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19008.7 | −0.603822 | −0.301911 | − | 0.953336i | \(-0.597625\pi\) | ||||
−0.301911 | + | 0.953336i | \(0.597625\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8197.91 | − | 3336.96i | 0.259630 | − | 0.105683i |
(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 | 336.4.h.b.239.15 | yes | 24 | |
3.2 | odd | 2 | inner | 336.4.h.b.239.9 | ✓ | 24 | |
4.3 | odd | 2 | inner | 336.4.h.b.239.10 | yes | 24 | |
12.11 | even | 2 | inner | 336.4.h.b.239.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.b.239.9 | ✓ | 24 | 3.2 | odd | 2 | inner | |
336.4.h.b.239.10 | yes | 24 | 4.3 | odd | 2 | inner | |
336.4.h.b.239.15 | yes | 24 | 1.1 | even | 1 | trivial | |
336.4.h.b.239.16 | yes | 24 | 12.11 | even | 2 | inner |